%------------------------------------------------------------------------------ % File : Zenon---0.7.1 % Problem : ALG149+1 : TPTP v8.1.0. Released v2.7.0. % Transfm : none % Format : tptp:raw % Command : run_zenon %s %d % Computer : n027.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 18:30:32 EDT 2022 % Result : Unsatisfiable 18.45s 18.67s % Output : Proof 19.13s % Verified : % SZS Type : - % Comments : %------------------------------------------------------------------------------ %----WARNING: Could not form TPTP format derivation %------------------------------------------------------------------------------ %----ORIGINAL SYSTEM OUTPUT % 0.07/0.12 % Problem : ALG149+1 : TPTP v8.1.0. Released v2.7.0. % 0.07/0.13 % Command : run_zenon %s %d % 0.12/0.34 % Computer : n027.cluster.edu % 0.12/0.34 % Model : x86_64 x86_64 % 0.12/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz % 0.12/0.34 % Memory : 8042.1875MB % 0.12/0.34 % OS : Linux 3.10.0-693.el7.x86_64 % 0.12/0.35 % CPULimit : 300 % 0.12/0.35 % WCLimit : 600 % 0.12/0.35 % DateTime : Wed Jun 8 17:44:41 EDT 2022 % 0.12/0.35 % CPUTime : % 18.45/18.67 (* PROOF-FOUND *) % 18.45/18.67 % SZS status Unsatisfiable % 18.45/18.67 (* BEGIN-PROOF *) % 18.45/18.67 % SZS output start Proof % 18.45/18.67 Theorem zenon_thm : False. % 18.45/18.67 Proof. % 18.45/18.67 assert (zenon_L1_ : (~((op (e0) (e3)) = (op (e1) (e3)))) -> ((op (e0) (e3)) = (e0)) -> ((op (e1) (e3)) = (e0)) -> False). % 18.45/18.67 do 0 intro. intros zenon_H1d zenon_H1e zenon_H1f. % 18.45/18.67 cut (((op (e0) (e3)) = (e0)) = ((op (e0) (e3)) = (op (e1) (e3)))). % 18.45/18.67 intro zenon_D_pnotp. % 18.45/18.67 apply zenon_H1d. % 18.45/18.67 rewrite <- zenon_D_pnotp. % 18.45/18.67 exact zenon_H1e. % 18.45/18.67 cut (((e0) = (op (e1) (e3)))); [idtac | apply NNPP; zenon_intro zenon_H20]. % 18.45/18.67 cut (((op (e0) (e3)) = (op (e0) (e3)))); [idtac | apply NNPP; zenon_intro zenon_H21]. % 18.45/18.67 congruence. % 18.45/18.67 apply zenon_H21. apply refl_equal. % 18.45/18.67 apply zenon_H20. apply sym_equal. exact zenon_H1f. % 18.45/18.67 (* end of lemma zenon_L1_ *) % 18.45/18.67 assert (zenon_L2_ : (((op (e1) (e0)) = (e0))\/(((op (e1) (e1)) = (e0))\/(((op (e1) (e2)) = (e0))\/((op (e1) (e3)) = (e0))))) -> (~((op (e1) (e0)) = (e0))) -> (~((op (e1) (e1)) = (e0))) -> (~((op (e1) (e2)) = (e0))) -> (~((op (e0) (e3)) = (op (e1) (e3)))) -> ((op (e0) (e3)) = (e0)) -> False). % 18.45/18.67 do 0 intro. intros zenon_H22 zenon_H23 zenon_H24 zenon_H25 zenon_H1d zenon_H1e. % 18.45/18.67 apply (zenon_or_s _ _ zenon_H22); [ zenon_intro zenon_H27 | zenon_intro zenon_H26 ]. % 18.45/18.67 exact (zenon_H23 zenon_H27). % 18.45/18.67 apply (zenon_or_s _ _ zenon_H26); [ zenon_intro zenon_H29 | zenon_intro zenon_H28 ]. % 18.45/18.67 exact (zenon_H24 zenon_H29). % 18.45/18.67 apply (zenon_or_s _ _ zenon_H28); [ zenon_intro zenon_H2a | zenon_intro zenon_H1f ]. % 18.45/18.67 exact (zenon_H25 zenon_H2a). % 18.45/18.67 apply (zenon_L1_); trivial. % 18.45/18.67 (* end of lemma zenon_L2_ *) % 18.45/18.67 assert (zenon_L3_ : (~((op (e1) (e2)) = (op (e2) (e2)))) -> ((op (e1) (e2)) = (e0)) -> ((op (e2) (e2)) = (e0)) -> False). % 18.45/18.67 do 0 intro. intros zenon_H2b zenon_H2a zenon_H2c. % 18.45/18.67 cut (((op (e1) (e2)) = (e0)) = ((op (e1) (e2)) = (op (e2) (e2)))). % 18.45/18.67 intro zenon_D_pnotp. % 18.45/18.67 apply zenon_H2b. % 18.45/18.67 rewrite <- zenon_D_pnotp. % 18.45/18.67 exact zenon_H2a. % 18.45/18.67 cut (((e0) = (op (e2) (e2)))); [idtac | apply NNPP; zenon_intro zenon_H2d]. % 18.45/18.67 cut (((op (e1) (e2)) = (op (e1) (e2)))); [idtac | apply NNPP; zenon_intro zenon_H2e]. % 18.45/18.67 congruence. % 18.45/18.67 apply zenon_H2e. apply refl_equal. % 18.45/18.67 apply zenon_H2d. apply sym_equal. exact zenon_H2c. % 18.45/18.67 (* end of lemma zenon_L3_ *) % 18.45/18.67 assert (zenon_L4_ : (((op (e2) (e0)) = (e0))\/(((op (e2) (e1)) = (e0))\/(((op (e2) (e2)) = (e0))\/((op (e2) (e3)) = (e0))))) -> (~((op (e2) (e0)) = (e0))) -> (~((op (e2) (e1)) = (e0))) -> ((op (e1) (e2)) = (e0)) -> (~((op (e1) (e2)) = (op (e2) (e2)))) -> (~((op (e2) (e3)) = (e0))) -> False). % 18.45/18.67 do 0 intro. intros zenon_H2f zenon_H30 zenon_H31 zenon_H2a zenon_H2b zenon_H32. % 18.45/18.67 apply (zenon_or_s _ _ zenon_H2f); [ zenon_intro zenon_H34 | zenon_intro zenon_H33 ]. % 18.45/18.67 exact (zenon_H30 zenon_H34). % 18.45/18.67 apply (zenon_or_s _ _ zenon_H33); [ zenon_intro zenon_H36 | zenon_intro zenon_H35 ]. % 18.45/18.67 exact (zenon_H31 zenon_H36). % 18.45/18.67 apply (zenon_or_s _ _ zenon_H35); [ zenon_intro zenon_H2c | zenon_intro zenon_H37 ]. % 18.45/18.67 apply (zenon_L3_); trivial. % 18.45/18.67 exact (zenon_H32 zenon_H37). % 18.45/18.67 (* end of lemma zenon_L4_ *) % 18.45/18.67 assert (zenon_L5_ : (((op (e1) (e0)) = (e0))\/(((op (e1) (e1)) = (e0))\/(((op (e1) (e2)) = (e0))\/((op (e1) (e3)) = (e0))))) -> (~((op (e1) (e0)) = (e0))) -> (~((op (e1) (e1)) = (e0))) -> (~((op (e2) (e3)) = (e0))) -> (~((op (e1) (e2)) = (op (e2) (e2)))) -> (~((op (e2) (e1)) = (e0))) -> (~((op (e2) (e0)) = (e0))) -> (((op (e2) (e0)) = (e0))\/(((op (e2) (e1)) = (e0))\/(((op (e2) (e2)) = (e0))\/((op (e2) (e3)) = (e0))))) -> (~((op (e1) (e3)) = (e0))) -> False). % 18.45/18.67 do 0 intro. intros zenon_H22 zenon_H23 zenon_H24 zenon_H32 zenon_H2b zenon_H31 zenon_H30 zenon_H2f zenon_H38. % 18.45/18.67 apply (zenon_or_s _ _ zenon_H22); [ zenon_intro zenon_H27 | zenon_intro zenon_H26 ]. % 18.45/18.67 exact (zenon_H23 zenon_H27). % 18.45/18.67 apply (zenon_or_s _ _ zenon_H26); [ zenon_intro zenon_H29 | zenon_intro zenon_H28 ]. % 18.45/18.67 exact (zenon_H24 zenon_H29). % 18.45/18.67 apply (zenon_or_s _ _ zenon_H28); [ zenon_intro zenon_H2a | zenon_intro zenon_H1f ]. % 18.45/18.67 apply (zenon_L4_); trivial. % 18.45/18.67 exact (zenon_H38 zenon_H1f). % 18.45/18.67 (* end of lemma zenon_L5_ *) % 18.45/18.67 assert (zenon_L6_ : (~((op (e0) (e0)) = (op (e2) (e0)))) -> ((op (e0) (e0)) = (e3)) -> ((op (e2) (e0)) = (e3)) -> False). % 18.45/18.67 do 0 intro. intros zenon_H39 zenon_H3a zenon_H3b. % 18.45/18.67 cut (((op (e0) (e0)) = (e3)) = ((op (e0) (e0)) = (op (e2) (e0)))). % 18.45/18.67 intro zenon_D_pnotp. % 18.45/18.67 apply zenon_H39. % 18.45/18.67 rewrite <- zenon_D_pnotp. % 18.45/18.67 exact zenon_H3a. % 18.45/18.67 cut (((e3) = (op (e2) (e0)))); [idtac | apply NNPP; zenon_intro zenon_H3c]. % 18.45/18.67 cut (((op (e0) (e0)) = (op (e0) (e0)))); [idtac | apply NNPP; zenon_intro zenon_H3d]. % 18.45/18.67 congruence. % 18.45/18.67 apply zenon_H3d. apply refl_equal. % 18.45/18.67 apply zenon_H3c. apply sym_equal. exact zenon_H3b. % 18.45/18.67 (* end of lemma zenon_L6_ *) % 18.45/18.67 assert (zenon_L7_ : (((op (e0) (e0)) = (e0))\/(((op (e1) (e0)) = (e0))\/(((op (e2) (e0)) = (e0))\/((op (e3) (e0)) = (e0))))) -> (~((op (e0) (e0)) = (e0))) -> (~((op (e1) (e0)) = (e0))) -> (~((op (e2) (e0)) = (e0))) -> (~((op (e3) (e0)) = (e0))) -> False). % 18.45/18.67 do 0 intro. intros zenon_H3e zenon_H3f zenon_H23 zenon_H30 zenon_H40. % 18.45/18.67 apply (zenon_or_s _ _ zenon_H3e); [ zenon_intro zenon_H42 | zenon_intro zenon_H41 ]. % 18.45/18.67 exact (zenon_H3f zenon_H42). % 18.45/18.67 apply (zenon_or_s _ _ zenon_H41); [ zenon_intro zenon_H27 | zenon_intro zenon_H43 ]. % 18.45/18.67 exact (zenon_H23 zenon_H27). % 18.45/18.67 apply (zenon_or_s _ _ zenon_H43); [ zenon_intro zenon_H34 | zenon_intro zenon_H44 ]. % 18.45/18.67 exact (zenon_H30 zenon_H34). % 18.45/18.67 exact (zenon_H40 zenon_H44). % 18.45/18.67 (* end of lemma zenon_L7_ *) % 18.45/18.67 assert (zenon_L8_ : (~((op (e1) (e0)) = (op (e1) (e1)))) -> ((op (e1) (e0)) = (e0)) -> ((op (e1) (e1)) = (e0)) -> False). % 18.45/18.67 do 0 intro. intros zenon_H45 zenon_H27 zenon_H29. % 18.45/18.67 cut (((op (e1) (e0)) = (e0)) = ((op (e1) (e0)) = (op (e1) (e1)))). % 18.45/18.67 intro zenon_D_pnotp. % 18.45/18.67 apply zenon_H45. % 18.45/18.67 rewrite <- zenon_D_pnotp. % 18.45/18.67 exact zenon_H27. % 18.45/18.67 cut (((e0) = (op (e1) (e1)))); [idtac | apply NNPP; zenon_intro zenon_H46]. % 18.45/18.67 cut (((op (e1) (e0)) = (op (e1) (e0)))); [idtac | apply NNPP; zenon_intro zenon_H47]. % 18.45/18.67 congruence. % 18.45/18.67 apply zenon_H47. apply refl_equal. % 18.45/18.67 apply zenon_H46. apply sym_equal. exact zenon_H29. % 18.45/18.67 (* end of lemma zenon_L8_ *) % 18.45/18.67 assert (zenon_L9_ : ((op (e0) (e2)) = (e0)) -> ((op (e0) (e1)) = (e0)) -> (~((op (e0) (e1)) = (op (e0) (e2)))) -> False). % 18.45/18.67 do 0 intro. intros zenon_H48 zenon_H49 zenon_H4a. % 18.45/18.67 elim (classic ((op (e0) (e2)) = (op (e0) (e2)))); [ zenon_intro zenon_H4b | zenon_intro zenon_H4c ]. % 18.45/18.67 cut (((op (e0) (e2)) = (op (e0) (e2))) = ((op (e0) (e1)) = (op (e0) (e2)))). % 18.45/18.67 intro zenon_D_pnotp. % 18.45/18.67 apply zenon_H4a. % 18.45/18.67 rewrite <- zenon_D_pnotp. % 18.45/18.67 exact zenon_H4b. % 18.45/18.67 cut (((op (e0) (e2)) = (op (e0) (e2)))); [idtac | apply NNPP; zenon_intro zenon_H4c]. % 18.45/18.67 cut (((op (e0) (e2)) = (op (e0) (e1)))); [idtac | apply NNPP; zenon_intro zenon_H4d]. % 18.45/18.67 congruence. % 18.45/18.67 cut (((op (e0) (e2)) = (e0)) = ((op (e0) (e2)) = (op (e0) (e1)))). % 18.45/18.67 intro zenon_D_pnotp. % 18.45/18.67 apply zenon_H4d. % 18.45/18.67 rewrite <- zenon_D_pnotp. % 18.45/18.67 exact zenon_H48. % 18.45/18.67 cut (((e0) = (op (e0) (e1)))); [idtac | apply NNPP; zenon_intro zenon_H4e]. % 18.45/18.67 cut (((op (e0) (e2)) = (op (e0) (e2)))); [idtac | apply NNPP; zenon_intro zenon_H4c]. % 18.45/18.67 congruence. % 18.45/18.67 apply zenon_H4c. apply refl_equal. % 18.45/18.67 apply zenon_H4e. apply sym_equal. exact zenon_H49. % 18.45/18.67 apply zenon_H4c. apply refl_equal. % 18.45/18.67 apply zenon_H4c. apply refl_equal. % 18.45/18.67 (* end of lemma zenon_L9_ *) % 18.45/18.67 assert (zenon_L10_ : ((op (e1) (e2)) = (e0)) -> ((op (e1) (e1)) = (e0)) -> (~((op (e1) (e1)) = (op (e1) (e2)))) -> False). % 18.45/18.67 do 0 intro. intros zenon_H2a zenon_H29 zenon_H4f. % 18.45/18.67 elim (classic ((op (e1) (e2)) = (op (e1) (e2)))); [ zenon_intro zenon_H50 | zenon_intro zenon_H2e ]. % 18.45/18.67 cut (((op (e1) (e2)) = (op (e1) (e2))) = ((op (e1) (e1)) = (op (e1) (e2)))). % 18.45/18.67 intro zenon_D_pnotp. % 18.45/18.67 apply zenon_H4f. % 18.45/18.67 rewrite <- zenon_D_pnotp. % 18.45/18.67 exact zenon_H50. % 18.45/18.67 cut (((op (e1) (e2)) = (op (e1) (e2)))); [idtac | apply NNPP; zenon_intro zenon_H2e]. % 18.45/18.67 cut (((op (e1) (e2)) = (op (e1) (e1)))); [idtac | apply NNPP; zenon_intro zenon_H51]. % 18.45/18.67 congruence. % 18.45/18.67 cut (((op (e1) (e2)) = (e0)) = ((op (e1) (e2)) = (op (e1) (e1)))). % 18.45/18.67 intro zenon_D_pnotp. % 18.45/18.67 apply zenon_H51. % 18.45/18.67 rewrite <- zenon_D_pnotp. % 18.45/18.67 exact zenon_H2a. % 18.45/18.67 cut (((e0) = (op (e1) (e1)))); [idtac | apply NNPP; zenon_intro zenon_H46]. % 18.45/18.67 cut (((op (e1) (e2)) = (op (e1) (e2)))); [idtac | apply NNPP; zenon_intro zenon_H2e]. % 18.45/18.67 congruence. % 18.45/18.67 apply zenon_H2e. apply refl_equal. % 18.45/18.67 apply zenon_H46. apply sym_equal. exact zenon_H29. % 18.45/18.67 apply zenon_H2e. apply refl_equal. % 18.45/18.67 apply zenon_H2e. apply refl_equal. % 18.45/18.67 (* end of lemma zenon_L10_ *) % 18.45/18.67 assert (zenon_L11_ : (~((op (e2) (e0)) = (op (e2) (e2)))) -> ((op (e2) (e0)) = (e0)) -> ((op (e2) (e2)) = (e0)) -> False). % 18.45/18.67 do 0 intro. intros zenon_H52 zenon_H34 zenon_H2c. % 18.45/18.67 cut (((op (e2) (e0)) = (e0)) = ((op (e2) (e0)) = (op (e2) (e2)))). % 18.45/18.67 intro zenon_D_pnotp. % 18.45/18.67 apply zenon_H52. % 18.45/18.67 rewrite <- zenon_D_pnotp. % 18.45/18.67 exact zenon_H34. % 18.45/18.67 cut (((e0) = (op (e2) (e2)))); [idtac | apply NNPP; zenon_intro zenon_H2d]. % 18.45/18.67 cut (((op (e2) (e0)) = (op (e2) (e0)))); [idtac | apply NNPP; zenon_intro zenon_H53]. % 18.45/18.67 congruence. % 18.45/18.67 apply zenon_H53. apply refl_equal. % 18.45/18.67 apply zenon_H2d. apply sym_equal. exact zenon_H2c. % 18.45/18.67 (* end of lemma zenon_L11_ *) % 18.45/18.67 assert (zenon_L12_ : ((op (e0) (e3)) = (e0)) -> ((op (e0) (e1)) = (e0)) -> (~((op (e0) (e1)) = (op (e0) (e3)))) -> False). % 18.45/18.67 do 0 intro. intros zenon_H1e zenon_H49 zenon_H54. % 18.45/18.67 elim (classic ((op (e0) (e3)) = (op (e0) (e3)))); [ zenon_intro zenon_H55 | zenon_intro zenon_H21 ]. % 18.45/18.67 cut (((op (e0) (e3)) = (op (e0) (e3))) = ((op (e0) (e1)) = (op (e0) (e3)))). % 18.45/18.67 intro zenon_D_pnotp. % 18.45/18.67 apply zenon_H54. % 18.45/18.67 rewrite <- zenon_D_pnotp. % 18.45/18.67 exact zenon_H55. % 18.45/18.67 cut (((op (e0) (e3)) = (op (e0) (e3)))); [idtac | apply NNPP; zenon_intro zenon_H21]. % 18.45/18.67 cut (((op (e0) (e3)) = (op (e0) (e1)))); [idtac | apply NNPP; zenon_intro zenon_H56]. % 18.45/18.67 congruence. % 18.45/18.67 cut (((op (e0) (e3)) = (e0)) = ((op (e0) (e3)) = (op (e0) (e1)))). % 18.45/18.67 intro zenon_D_pnotp. % 18.45/18.67 apply zenon_H56. % 18.45/18.67 rewrite <- zenon_D_pnotp. % 18.45/18.67 exact zenon_H1e. % 18.45/18.67 cut (((e0) = (op (e0) (e1)))); [idtac | apply NNPP; zenon_intro zenon_H4e]. % 18.45/18.67 cut (((op (e0) (e3)) = (op (e0) (e3)))); [idtac | apply NNPP; zenon_intro zenon_H21]. % 18.45/18.67 congruence. % 18.45/18.67 apply zenon_H21. apply refl_equal. % 18.45/18.67 apply zenon_H4e. apply sym_equal. exact zenon_H49. % 18.45/18.67 apply zenon_H21. apply refl_equal. % 18.45/18.67 apply zenon_H21. apply refl_equal. % 18.45/18.67 (* end of lemma zenon_L12_ *) % 18.45/18.67 assert (zenon_L13_ : ((op (e1) (e3)) = (e0)) -> ((op (e1) (e1)) = (e0)) -> (~((op (e1) (e1)) = (op (e1) (e3)))) -> False). % 18.45/18.67 do 0 intro. intros zenon_H1f zenon_H29 zenon_H57. % 18.45/18.67 elim (classic ((op (e1) (e3)) = (op (e1) (e3)))); [ zenon_intro zenon_H58 | zenon_intro zenon_H59 ]. % 18.45/18.67 cut (((op (e1) (e3)) = (op (e1) (e3))) = ((op (e1) (e1)) = (op (e1) (e3)))). % 18.45/18.67 intro zenon_D_pnotp. % 18.45/18.67 apply zenon_H57. % 18.45/18.67 rewrite <- zenon_D_pnotp. % 18.45/18.67 exact zenon_H58. % 18.45/18.67 cut (((op (e1) (e3)) = (op (e1) (e3)))); [idtac | apply NNPP; zenon_intro zenon_H59]. % 18.45/18.67 cut (((op (e1) (e3)) = (op (e1) (e1)))); [idtac | apply NNPP; zenon_intro zenon_H5a]. % 18.45/18.67 congruence. % 18.45/18.67 cut (((op (e1) (e3)) = (e0)) = ((op (e1) (e3)) = (op (e1) (e1)))). % 18.45/18.67 intro zenon_D_pnotp. % 18.45/18.67 apply zenon_H5a. % 18.45/18.67 rewrite <- zenon_D_pnotp. % 18.45/18.67 exact zenon_H1f. % 18.45/18.67 cut (((e0) = (op (e1) (e1)))); [idtac | apply NNPP; zenon_intro zenon_H46]. % 18.45/18.67 cut (((op (e1) (e3)) = (op (e1) (e3)))); [idtac | apply NNPP; zenon_intro zenon_H59]. % 18.45/18.67 congruence. % 18.45/18.67 apply zenon_H59. apply refl_equal. % 18.45/18.67 apply zenon_H46. apply sym_equal. exact zenon_H29. % 18.45/18.67 apply zenon_H59. apply refl_equal. % 18.45/18.67 apply zenon_H59. apply refl_equal. % 18.45/18.67 (* end of lemma zenon_L13_ *) % 18.45/18.67 assert (zenon_L14_ : ((op (e2) (e3)) = (e0)) -> ((op (e2) (e0)) = (e0)) -> (~((op (e2) (e0)) = (op (e2) (e3)))) -> False). % 18.45/18.67 do 0 intro. intros zenon_H37 zenon_H34 zenon_H5b. % 18.45/18.67 elim (classic ((op (e2) (e3)) = (op (e2) (e3)))); [ zenon_intro zenon_H5c | zenon_intro zenon_H5d ]. % 18.45/18.67 cut (((op (e2) (e3)) = (op (e2) (e3))) = ((op (e2) (e0)) = (op (e2) (e3)))). % 18.45/18.67 intro zenon_D_pnotp. % 18.45/18.67 apply zenon_H5b. % 18.45/18.67 rewrite <- zenon_D_pnotp. % 18.45/18.67 exact zenon_H5c. % 18.45/18.67 cut (((op (e2) (e3)) = (op (e2) (e3)))); [idtac | apply NNPP; zenon_intro zenon_H5d]. % 18.45/18.67 cut (((op (e2) (e3)) = (op (e2) (e0)))); [idtac | apply NNPP; zenon_intro zenon_H5e]. % 18.45/18.67 congruence. % 18.45/18.67 cut (((op (e2) (e3)) = (e0)) = ((op (e2) (e3)) = (op (e2) (e0)))). % 18.45/18.67 intro zenon_D_pnotp. % 18.45/18.67 apply zenon_H5e. % 18.45/18.67 rewrite <- zenon_D_pnotp. % 18.45/18.67 exact zenon_H37. % 18.45/18.67 cut (((e0) = (op (e2) (e0)))); [idtac | apply NNPP; zenon_intro zenon_H5f]. % 18.45/18.67 cut (((op (e2) (e3)) = (op (e2) (e3)))); [idtac | apply NNPP; zenon_intro zenon_H5d]. % 18.45/18.67 congruence. % 18.45/18.67 apply zenon_H5d. apply refl_equal. % 18.45/18.67 apply zenon_H5f. apply sym_equal. exact zenon_H34. % 18.45/18.67 apply zenon_H5d. apply refl_equal. % 18.45/18.67 apply zenon_H5d. apply refl_equal. % 18.45/18.67 (* end of lemma zenon_L14_ *) % 18.45/18.67 assert (zenon_L15_ : ((op (e3) (e3)) = (e0)) -> ((op (e3) (e2)) = (e0)) -> (~((op (e3) (e2)) = (op (e3) (e3)))) -> False). % 18.45/18.67 do 0 intro. intros zenon_H60 zenon_H61 zenon_H62. % 18.45/18.67 elim (classic ((op (e3) (e3)) = (op (e3) (e3)))); [ zenon_intro zenon_H63 | zenon_intro zenon_H64 ]. % 18.45/18.67 cut (((op (e3) (e3)) = (op (e3) (e3))) = ((op (e3) (e2)) = (op (e3) (e3)))). % 18.45/18.67 intro zenon_D_pnotp. % 18.45/18.67 apply zenon_H62. % 18.45/18.67 rewrite <- zenon_D_pnotp. % 18.45/18.67 exact zenon_H63. % 18.45/18.67 cut (((op (e3) (e3)) = (op (e3) (e3)))); [idtac | apply NNPP; zenon_intro zenon_H64]. % 18.45/18.67 cut (((op (e3) (e3)) = (op (e3) (e2)))); [idtac | apply NNPP; zenon_intro zenon_H65]. % 18.45/18.67 congruence. % 18.45/18.67 cut (((op (e3) (e3)) = (e0)) = ((op (e3) (e3)) = (op (e3) (e2)))). % 18.45/18.67 intro zenon_D_pnotp. % 18.45/18.67 apply zenon_H65. % 18.45/18.67 rewrite <- zenon_D_pnotp. % 18.45/18.67 exact zenon_H60. % 18.45/18.67 cut (((e0) = (op (e3) (e2)))); [idtac | apply NNPP; zenon_intro zenon_H66]. % 18.45/18.67 cut (((op (e3) (e3)) = (op (e3) (e3)))); [idtac | apply NNPP; zenon_intro zenon_H64]. % 18.45/18.67 congruence. % 18.45/18.67 apply zenon_H64. apply refl_equal. % 18.45/18.67 apply zenon_H66. apply sym_equal. exact zenon_H61. % 18.45/18.67 apply zenon_H64. apply refl_equal. % 18.45/18.67 apply zenon_H64. apply refl_equal. % 18.45/18.67 (* end of lemma zenon_L15_ *) % 18.45/18.67 assert (zenon_L16_ : (((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) (e1)) = (op (e1) (e3)))) -> ((op (e1) (e1)) = (e0)) -> (~((op (e2) (e0)) = (op (e2) (e3)))) -> ((op (e2) (e0)) = (e0)) -> ((op (e3) (e2)) = (e0)) -> (~((op (e3) (e2)) = (op (e3) (e3)))) -> False). % 18.45/18.67 do 0 intro. intros zenon_H67 zenon_H54 zenon_H49 zenon_H57 zenon_H29 zenon_H5b zenon_H34 zenon_H61 zenon_H62. % 18.45/18.67 apply (zenon_or_s _ _ zenon_H67); [ zenon_intro zenon_H1e | zenon_intro zenon_H68 ]. % 18.45/18.67 apply (zenon_L12_); trivial. % 18.45/18.67 apply (zenon_or_s _ _ zenon_H68); [ zenon_intro zenon_H1f | zenon_intro zenon_H69 ]. % 18.45/18.67 apply (zenon_L13_); trivial. % 18.45/18.67 apply (zenon_or_s _ _ zenon_H69); [ zenon_intro zenon_H37 | zenon_intro zenon_H60 ]. % 18.45/18.67 apply (zenon_L14_); trivial. % 18.45/18.67 apply (zenon_L15_); trivial. % 18.45/18.67 (* end of lemma zenon_L16_ *) % 18.45/18.67 assert (zenon_L17_ : (((op (e0) (e2)) = (e0))\/(((op (e1) (e2)) = (e0))\/(((op (e2) (e2)) = (e0))\/((op (e3) (e2)) = (e0))))) -> (~((op (e0) (e1)) = (op (e0) (e2)))) -> (~((op (e1) (e1)) = (op (e1) (e2)))) -> (~((op (e2) (e0)) = (op (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) (e1)) = (e0)) -> (~((op (e1) (e1)) = (op (e1) (e3)))) -> ((op (e1) (e1)) = (e0)) -> (~((op (e2) (e0)) = (op (e2) (e3)))) -> ((op (e2) (e0)) = (e0)) -> (~((op (e3) (e2)) = (op (e3) (e3)))) -> False). % 18.45/18.68 do 0 intro. intros zenon_H6a zenon_H4a zenon_H4f zenon_H52 zenon_H67 zenon_H54 zenon_H49 zenon_H57 zenon_H29 zenon_H5b zenon_H34 zenon_H62. % 18.45/18.68 apply (zenon_or_s _ _ zenon_H6a); [ zenon_intro zenon_H48 | zenon_intro zenon_H6b ]. % 18.45/18.68 apply (zenon_L9_); trivial. % 18.45/18.68 apply (zenon_or_s _ _ zenon_H6b); [ zenon_intro zenon_H2a | zenon_intro zenon_H6c ]. % 18.45/18.68 apply (zenon_L10_); trivial. % 18.45/18.68 apply (zenon_or_s _ _ zenon_H6c); [ zenon_intro zenon_H2c | zenon_intro zenon_H61 ]. % 18.45/18.68 apply (zenon_L11_); trivial. % 18.45/18.68 apply (zenon_L16_); trivial. % 18.45/18.68 (* end of lemma zenon_L17_ *) % 18.45/18.68 assert (zenon_L18_ : ((op (e2) (e3)) = (e0)) -> ((op (e2) (e2)) = (e0)) -> (~((op (e2) (e2)) = (op (e2) (e3)))) -> False). % 18.45/18.68 do 0 intro. intros zenon_H37 zenon_H2c zenon_H6d. % 18.45/18.68 elim (classic ((op (e2) (e3)) = (op (e2) (e3)))); [ zenon_intro zenon_H5c | zenon_intro zenon_H5d ]. % 18.45/18.68 cut (((op (e2) (e3)) = (op (e2) (e3))) = ((op (e2) (e2)) = (op (e2) (e3)))). % 18.45/18.68 intro zenon_D_pnotp. % 18.45/18.68 apply zenon_H6d. % 18.45/18.68 rewrite <- zenon_D_pnotp. % 18.45/18.68 exact zenon_H5c. % 18.45/18.68 cut (((op (e2) (e3)) = (op (e2) (e3)))); [idtac | apply NNPP; zenon_intro zenon_H5d]. % 18.45/18.68 cut (((op (e2) (e3)) = (op (e2) (e2)))); [idtac | apply NNPP; zenon_intro zenon_H6e]. % 18.45/18.68 congruence. % 18.45/18.68 cut (((op (e2) (e3)) = (e0)) = ((op (e2) (e3)) = (op (e2) (e2)))). % 18.45/18.68 intro zenon_D_pnotp. % 18.45/18.68 apply zenon_H6e. % 18.45/18.68 rewrite <- zenon_D_pnotp. % 18.45/18.68 exact zenon_H37. % 18.45/18.68 cut (((e0) = (op (e2) (e2)))); [idtac | apply NNPP; zenon_intro zenon_H2d]. % 18.45/18.68 cut (((op (e2) (e3)) = (op (e2) (e3)))); [idtac | apply NNPP; zenon_intro zenon_H5d]. % 18.45/18.68 congruence. % 18.45/18.68 apply zenon_H5d. apply refl_equal. % 18.45/18.68 apply zenon_H2d. apply sym_equal. exact zenon_H2c. % 18.45/18.68 apply zenon_H5d. apply refl_equal. % 18.45/18.68 apply zenon_H5d. apply refl_equal. % 18.45/18.68 (* end of lemma zenon_L18_ *) % 18.45/18.68 assert (zenon_L19_ : (~((op (e3) (e0)) = (op (e3) (e2)))) -> ((op (e3) (e0)) = (e0)) -> ((op (e3) (e2)) = (e0)) -> False). % 18.45/18.68 do 0 intro. intros zenon_H6f zenon_H44 zenon_H61. % 18.45/18.68 cut (((op (e3) (e0)) = (e0)) = ((op (e3) (e0)) = (op (e3) (e2)))). % 18.45/18.68 intro zenon_D_pnotp. % 18.45/18.68 apply zenon_H6f. % 18.45/18.68 rewrite <- zenon_D_pnotp. % 18.45/18.68 exact zenon_H44. % 18.45/18.68 cut (((e0) = (op (e3) (e2)))); [idtac | apply NNPP; zenon_intro zenon_H66]. % 18.45/18.68 cut (((op (e3) (e0)) = (op (e3) (e0)))); [idtac | apply NNPP; zenon_intro zenon_H70]. % 18.45/18.68 congruence. % 18.45/18.68 apply zenon_H70. apply refl_equal. % 18.45/18.68 apply zenon_H66. apply sym_equal. exact zenon_H61. % 18.45/18.68 (* end of lemma zenon_L19_ *) % 18.45/18.68 assert (zenon_L20_ : (((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) (e1)) = (op (e1) (e2)))) -> ((op (e1) (e1)) = (e0)) -> (~((op (e2) (e2)) = (op (e2) (e3)))) -> ((op (e2) (e3)) = (e0)) -> (~((op (e3) (e0)) = (op (e3) (e2)))) -> ((op (e3) (e0)) = (e0)) -> False). % 18.45/18.68 do 0 intro. intros zenon_H6a zenon_H4a zenon_H49 zenon_H4f zenon_H29 zenon_H6d zenon_H37 zenon_H6f zenon_H44. % 18.45/18.68 apply (zenon_or_s _ _ zenon_H6a); [ zenon_intro zenon_H48 | zenon_intro zenon_H6b ]. % 18.45/18.68 apply (zenon_L9_); trivial. % 18.45/18.68 apply (zenon_or_s _ _ zenon_H6b); [ zenon_intro zenon_H2a | zenon_intro zenon_H6c ]. % 18.45/18.68 apply (zenon_L10_); trivial. % 18.45/18.68 apply (zenon_or_s _ _ zenon_H6c); [ zenon_intro zenon_H2c | zenon_intro zenon_H61 ]. % 18.45/18.68 apply (zenon_L18_); trivial. % 18.45/18.68 apply (zenon_L19_); trivial. % 18.45/18.68 (* end of lemma zenon_L20_ *) % 18.45/18.68 assert (zenon_L21_ : ((op (e3) (e3)) = (e0)) -> ((op (e3) (e0)) = (e0)) -> (~((op (e3) (e0)) = (op (e3) (e3)))) -> False). % 18.45/18.68 do 0 intro. intros zenon_H60 zenon_H44 zenon_H71. % 18.45/18.68 elim (classic ((op (e3) (e3)) = (op (e3) (e3)))); [ zenon_intro zenon_H63 | zenon_intro zenon_H64 ]. % 18.45/18.68 cut (((op (e3) (e3)) = (op (e3) (e3))) = ((op (e3) (e0)) = (op (e3) (e3)))). % 18.45/18.68 intro zenon_D_pnotp. % 18.45/18.68 apply zenon_H71. % 18.45/18.68 rewrite <- zenon_D_pnotp. % 18.45/18.68 exact zenon_H63. % 18.45/18.68 cut (((op (e3) (e3)) = (op (e3) (e3)))); [idtac | apply NNPP; zenon_intro zenon_H64]. % 18.45/18.68 cut (((op (e3) (e3)) = (op (e3) (e0)))); [idtac | apply NNPP; zenon_intro zenon_H72]. % 18.45/18.68 congruence. % 18.45/18.68 cut (((op (e3) (e3)) = (e0)) = ((op (e3) (e3)) = (op (e3) (e0)))). % 18.45/18.68 intro zenon_D_pnotp. % 18.45/18.68 apply zenon_H72. % 18.45/18.68 rewrite <- zenon_D_pnotp. % 18.45/18.68 exact zenon_H60. % 18.45/18.68 cut (((e0) = (op (e3) (e0)))); [idtac | apply NNPP; zenon_intro zenon_H73]. % 18.45/18.68 cut (((op (e3) (e3)) = (op (e3) (e3)))); [idtac | apply NNPP; zenon_intro zenon_H64]. % 18.45/18.68 congruence. % 18.45/18.68 apply zenon_H64. apply refl_equal. % 18.45/18.68 apply zenon_H73. apply sym_equal. exact zenon_H44. % 18.45/18.68 apply zenon_H64. apply refl_equal. % 18.45/18.68 apply zenon_H64. apply refl_equal. % 18.45/18.68 (* end of lemma zenon_L21_ *) % 18.45/18.68 assert (zenon_L22_ : (((op (e0) (e3)) = (e0))\/(((op (e1) (e3)) = (e0))\/(((op (e2) (e3)) = (e0))\/((op (e3) (e3)) = (e0))))) -> (~((op (e0) (e1)) = (op (e0) (e3)))) -> (~((op (e1) (e1)) = (op (e1) (e3)))) -> (~((op (e3) (e0)) = (op (e3) (e2)))) -> (~((op (e2) (e2)) = (op (e2) (e3)))) -> ((op (e1) (e1)) = (e0)) -> (~((op (e1) (e1)) = (op (e1) (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 (e3) (e0)) = (e0)) -> (~((op (e3) (e0)) = (op (e3) (e3)))) -> False). % 18.45/18.68 do 0 intro. intros zenon_H67 zenon_H54 zenon_H57 zenon_H6f zenon_H6d zenon_H29 zenon_H4f zenon_H49 zenon_H4a zenon_H6a zenon_H44 zenon_H71. % 18.45/18.68 apply (zenon_or_s _ _ zenon_H67); [ zenon_intro zenon_H1e | zenon_intro zenon_H68 ]. % 18.45/18.68 apply (zenon_L12_); trivial. % 18.45/18.68 apply (zenon_or_s _ _ zenon_H68); [ zenon_intro zenon_H1f | zenon_intro zenon_H69 ]. % 18.45/18.68 apply (zenon_L13_); trivial. % 18.45/18.68 apply (zenon_or_s _ _ zenon_H69); [ zenon_intro zenon_H37 | zenon_intro zenon_H60 ]. % 18.45/18.68 apply (zenon_L20_); trivial. % 18.45/18.68 apply (zenon_L21_); trivial. % 18.45/18.68 (* end of lemma zenon_L22_ *) % 18.45/18.68 assert (zenon_L23_ : (((op (e0) (e0)) = (e0))\/(((op (e1) (e0)) = (e0))\/(((op (e2) (e0)) = (e0))\/((op (e3) (e0)) = (e0))))) -> (~((op (e0) (e0)) = (e0))) -> (~((op (e1) (e0)) = (op (e1) (e1)))) -> (~((op (e3) (e2)) = (op (e3) (e3)))) -> (~((op (e2) (e0)) = (op (e2) (e3)))) -> (~((op (e2) (e0)) = (op (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 (e1) (e1)) = (op (e1) (e3)))) -> (~((op (e3) (e0)) = (op (e3) (e2)))) -> (~((op (e2) (e2)) = (op (e2) (e3)))) -> ((op (e1) (e1)) = (e0)) -> (~((op (e1) (e1)) = (op (e1) (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 (e3) (e0)) = (op (e3) (e3)))) -> False). % 18.45/18.68 do 0 intro. intros zenon_H3e zenon_H3f zenon_H45 zenon_H62 zenon_H5b zenon_H52 zenon_H67 zenon_H54 zenon_H57 zenon_H6f zenon_H6d zenon_H29 zenon_H4f zenon_H49 zenon_H4a zenon_H6a zenon_H71. % 18.45/18.68 apply (zenon_or_s _ _ zenon_H3e); [ zenon_intro zenon_H42 | zenon_intro zenon_H41 ]. % 18.45/18.68 exact (zenon_H3f zenon_H42). % 18.45/18.68 apply (zenon_or_s _ _ zenon_H41); [ zenon_intro zenon_H27 | zenon_intro zenon_H43 ]. % 18.45/18.68 apply (zenon_L8_); trivial. % 18.45/18.68 apply (zenon_or_s _ _ zenon_H43); [ zenon_intro zenon_H34 | zenon_intro zenon_H44 ]. % 18.45/18.68 apply (zenon_L17_); trivial. % 18.45/18.68 apply (zenon_L22_); trivial. % 18.45/18.68 (* end of lemma zenon_L23_ *) % 18.45/18.68 assert (zenon_L24_ : (((op (e0) (e0)) = (e0))\/(((op (e0) (e1)) = (e0))\/(((op (e0) (e2)) = (e0))\/((op (e0) (e3)) = (e0))))) -> (~((op (e1) (e3)) = (e0))) -> (~((op (e1) (e2)) = (e0))) -> (((op (e0) (e0)) = (e0))\/(((op (e1) (e0)) = (e0))\/(((op (e2) (e0)) = (e0))\/((op (e3) (e0)) = (e0))))) -> (~((op (e0) (e0)) = (e0))) -> (~((op (e1) (e0)) = (op (e1) (e1)))) -> (~((op (e3) (e2)) = (op (e3) (e3)))) -> (~((op (e2) (e0)) = (op (e2) (e3)))) -> (~((op (e2) (e0)) = (op (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 (e1) (e1)) = (op (e1) (e3)))) -> (~((op (e3) (e0)) = (op (e3) (e2)))) -> (~((op (e2) (e2)) = (op (e2) (e3)))) -> (~((op (e1) (e1)) = (op (e1) (e2)))) -> (~((op (e0) (e1)) = (op (e0) (e2)))) -> (((op (e0) (e2)) = (e0))\/(((op (e1) (e2)) = (e0))\/(((op (e2) (e2)) = (e0))\/((op (e3) (e2)) = (e0))))) -> (~((op (e3) (e0)) = (op (e3) (e3)))) -> (~((op (e1) (e0)) = (e0))) -> (((op (e1) (e0)) = (e0))\/(((op (e1) (e1)) = (e0))\/(((op (e1) (e2)) = (e0))\/((op (e1) (e3)) = (e0))))) -> (~((op (e0) (e2)) = (e0))) -> (~((op (e0) (e3)) = (e0))) -> False). % 18.45/18.68 do 0 intro. intros zenon_H74 zenon_H38 zenon_H25 zenon_H3e zenon_H3f zenon_H45 zenon_H62 zenon_H5b zenon_H52 zenon_H67 zenon_H54 zenon_H57 zenon_H6f zenon_H6d zenon_H4f zenon_H4a zenon_H6a zenon_H71 zenon_H23 zenon_H22 zenon_H75 zenon_H76. % 18.45/18.68 apply (zenon_or_s _ _ zenon_H74); [ zenon_intro zenon_H42 | zenon_intro zenon_H77 ]. % 18.45/18.68 exact (zenon_H3f zenon_H42). % 18.45/18.68 apply (zenon_or_s _ _ zenon_H77); [ zenon_intro zenon_H49 | zenon_intro zenon_H78 ]. % 18.45/18.68 apply (zenon_or_s _ _ zenon_H22); [ zenon_intro zenon_H27 | zenon_intro zenon_H26 ]. % 18.45/18.68 exact (zenon_H23 zenon_H27). % 18.45/18.68 apply (zenon_or_s _ _ zenon_H26); [ zenon_intro zenon_H29 | zenon_intro zenon_H28 ]. % 18.45/18.68 apply (zenon_L23_); trivial. % 18.45/18.68 apply (zenon_or_s _ _ zenon_H28); [ zenon_intro zenon_H2a | zenon_intro zenon_H1f ]. % 18.45/18.68 exact (zenon_H25 zenon_H2a). % 18.45/18.68 exact (zenon_H38 zenon_H1f). % 18.45/18.68 apply (zenon_or_s _ _ zenon_H78); [ zenon_intro zenon_H48 | zenon_intro zenon_H1e ]. % 18.45/18.68 exact (zenon_H75 zenon_H48). % 18.45/18.68 exact (zenon_H76 zenon_H1e). % 18.45/18.68 (* end of lemma zenon_L24_ *) % 18.45/18.68 assert (zenon_L25_ : (~((e1) = (e1))) -> False). % 18.45/18.68 do 0 intro. intros zenon_H79. % 18.45/18.68 apply zenon_H79. apply refl_equal. % 18.45/18.68 (* end of lemma zenon_L25_ *) % 18.45/18.68 assert (zenon_L26_ : ((op (e0) (e0)) = (e1)) -> ((op (e0) (e0)) = (e2)) -> (~((e1) = (e2))) -> False). % 18.45/18.68 do 0 intro. intros zenon_H7a zenon_H7b zenon_H7c. % 18.45/18.68 elim (classic ((e2) = (e2))); [ zenon_intro zenon_H7d | zenon_intro zenon_H7e ]. % 18.45/18.68 cut (((e2) = (e2)) = ((e1) = (e2))). % 18.45/18.68 intro zenon_D_pnotp. % 18.45/18.68 apply zenon_H7c. % 18.45/18.68 rewrite <- zenon_D_pnotp. % 18.45/18.68 exact zenon_H7d. % 18.45/18.68 cut (((e2) = (e2))); [idtac | apply NNPP; zenon_intro zenon_H7e]. % 18.45/18.68 cut (((e2) = (e1))); [idtac | apply NNPP; zenon_intro zenon_H7f]. % 18.45/18.68 congruence. % 18.45/18.68 cut (((op (e0) (e0)) = (e1)) = ((e2) = (e1))). % 18.45/18.68 intro zenon_D_pnotp. % 18.45/18.68 apply zenon_H7f. % 18.45/18.68 rewrite <- zenon_D_pnotp. % 18.45/18.68 exact zenon_H7a. % 18.45/18.68 cut (((e1) = (e1))); [idtac | apply NNPP; zenon_intro zenon_H79]. % 18.45/18.68 cut (((op (e0) (e0)) = (e2))); [idtac | apply NNPP; zenon_intro zenon_H80]. % 18.45/18.68 congruence. % 18.45/18.68 exact (zenon_H80 zenon_H7b). % 18.45/18.68 apply zenon_H79. apply refl_equal. % 18.45/18.68 apply zenon_H7e. apply refl_equal. % 18.45/18.68 apply zenon_H7e. apply refl_equal. % 18.45/18.68 (* end of lemma zenon_L26_ *) % 18.45/18.68 assert (zenon_L27_ : (((op (e2) (e0)) = (e0))\/(((op (e2) (e1)) = (e0))\/(((op (e2) (e2)) = (e0))\/((op (e2) (e3)) = (e0))))) -> (~((op (e2) (e0)) = (e0))) -> (~((op (e2) (e1)) = (e0))) -> (~((op (e2) (e2)) = (e0))) -> (~((op (e2) (e3)) = (e0))) -> False). % 18.45/18.68 do 0 intro. intros zenon_H2f zenon_H30 zenon_H31 zenon_H81 zenon_H32. % 18.45/18.68 apply (zenon_or_s _ _ zenon_H2f); [ zenon_intro zenon_H34 | zenon_intro zenon_H33 ]. % 18.45/18.68 exact (zenon_H30 zenon_H34). % 18.45/18.68 apply (zenon_or_s _ _ zenon_H33); [ zenon_intro zenon_H36 | zenon_intro zenon_H35 ]. % 18.45/18.68 exact (zenon_H31 zenon_H36). % 18.45/18.68 apply (zenon_or_s _ _ zenon_H35); [ zenon_intro zenon_H2c | zenon_intro zenon_H37 ]. % 18.45/18.68 exact (zenon_H81 zenon_H2c). % 18.45/18.68 exact (zenon_H32 zenon_H37). % 18.45/18.68 (* end of lemma zenon_L27_ *) % 18.45/18.68 assert (zenon_L28_ : (~((e0) = (e0))) -> False). % 18.45/18.68 do 0 intro. intros zenon_H82. % 18.45/18.68 apply zenon_H82. apply refl_equal. % 18.45/18.68 (* end of lemma zenon_L28_ *) % 18.45/18.68 assert (zenon_L29_ : (~((op (op (e0) (e0)) (e0)) = (op (e1) (e0)))) -> ((op (e0) (e0)) = (e1)) -> False). % 18.45/18.68 do 0 intro. intros zenon_H83 zenon_H7a. % 18.45/18.68 cut (((e0) = (e0))); [idtac | apply NNPP; zenon_intro zenon_H82]. % 18.45/18.68 cut (((op (e0) (e0)) = (e1))); [idtac | apply NNPP; zenon_intro zenon_H84]. % 18.45/18.68 congruence. % 18.45/18.68 exact (zenon_H84 zenon_H7a). % 18.45/18.68 apply zenon_H82. apply refl_equal. % 18.45/18.68 (* end of lemma zenon_L29_ *) % 18.45/18.68 assert (zenon_L30_ : (~((e2) = (e2))) -> False). % 18.45/18.68 do 0 intro. intros zenon_H7e. % 18.45/18.68 apply zenon_H7e. apply refl_equal. % 18.45/18.68 (* end of lemma zenon_L30_ *) % 18.45/18.68 assert (zenon_L31_ : (~((e3) = (e3))) -> False). % 18.45/18.68 do 0 intro. intros zenon_H85. % 18.45/18.68 apply zenon_H85. apply refl_equal. % 18.45/18.68 (* end of lemma zenon_L31_ *) % 18.45/18.68 assert (zenon_L32_ : ((op (e1) (e0)) = (e2)) -> ((op (e0) (e0)) = (e1)) -> (~((e2) = (op (op (e0) (e0)) (e0)))) -> False). % 18.45/18.68 do 0 intro. intros zenon_H86 zenon_H7a zenon_H87. % 18.45/18.68 elim (classic ((op (op (e0) (e0)) (e0)) = (op (op (e0) (e0)) (e0)))); [ zenon_intro zenon_H88 | zenon_intro zenon_H89 ]. % 18.45/18.68 cut (((op (op (e0) (e0)) (e0)) = (op (op (e0) (e0)) (e0))) = ((e2) = (op (op (e0) (e0)) (e0)))). % 18.45/18.68 intro zenon_D_pnotp. % 18.45/18.68 apply zenon_H87. % 18.45/18.68 rewrite <- zenon_D_pnotp. % 18.45/18.68 exact zenon_H88. % 18.45/18.68 cut (((op (op (e0) (e0)) (e0)) = (op (op (e0) (e0)) (e0)))); [idtac | apply NNPP; zenon_intro zenon_H89]. % 18.45/18.68 cut (((op (op (e0) (e0)) (e0)) = (e2))); [idtac | apply NNPP; zenon_intro zenon_H8a]. % 18.45/18.68 congruence. % 18.45/18.68 cut (((op (e1) (e0)) = (e2)) = ((op (op (e0) (e0)) (e0)) = (e2))). % 18.45/18.68 intro zenon_D_pnotp. % 18.45/18.68 apply zenon_H8a. % 18.45/18.68 rewrite <- zenon_D_pnotp. % 18.45/18.68 exact zenon_H86. % 18.45/18.68 cut (((e2) = (e2))); [idtac | apply NNPP; zenon_intro zenon_H7e]. % 18.45/18.68 cut (((op (e1) (e0)) = (op (op (e0) (e0)) (e0)))); [idtac | apply NNPP; zenon_intro zenon_H8b]. % 18.45/18.68 congruence. % 18.45/18.68 elim (classic ((op (op (e0) (e0)) (e0)) = (op (op (e0) (e0)) (e0)))); [ zenon_intro zenon_H88 | zenon_intro zenon_H89 ]. % 18.45/18.68 cut (((op (op (e0) (e0)) (e0)) = (op (op (e0) (e0)) (e0))) = ((op (e1) (e0)) = (op (op (e0) (e0)) (e0)))). % 18.45/18.68 intro zenon_D_pnotp. % 18.45/18.68 apply zenon_H8b. % 18.45/18.68 rewrite <- zenon_D_pnotp. % 18.45/18.68 exact zenon_H88. % 18.45/18.68 cut (((op (op (e0) (e0)) (e0)) = (op (op (e0) (e0)) (e0)))); [idtac | apply NNPP; zenon_intro zenon_H89]. % 18.45/18.68 cut (((op (op (e0) (e0)) (e0)) = (op (e1) (e0)))); [idtac | apply NNPP; zenon_intro zenon_H83]. % 18.45/18.68 congruence. % 18.45/18.68 apply (zenon_L29_); trivial. % 18.45/18.68 apply zenon_H89. apply refl_equal. % 18.45/18.68 apply zenon_H89. apply refl_equal. % 18.45/18.68 apply zenon_H7e. apply refl_equal. % 18.45/18.68 apply zenon_H89. apply refl_equal. % 18.45/18.68 apply zenon_H89. apply refl_equal. % 18.45/18.68 (* end of lemma zenon_L32_ *) % 18.45/18.68 assert (zenon_L33_ : ((op (e2) (e0)) = (e3)) -> ((op (e1) (e0)) = (e2)) -> ((op (e0) (e0)) = (e1)) -> False). % 18.45/18.68 do 0 intro. intros zenon_H3b zenon_H86 zenon_H7a. % 18.45/18.68 apply (zenon_notand_s _ _ ax11); [ zenon_intro zenon_H8d | zenon_intro zenon_H8c ]. % 18.45/18.68 elim (classic ((op (op (op (e0) (e0)) (e0)) (e0)) = (op (op (op (e0) (e0)) (e0)) (e0)))); [ zenon_intro zenon_H8e | zenon_intro zenon_H8f ]. % 18.45/18.68 cut (((op (op (op (e0) (e0)) (e0)) (e0)) = (op (op (op (e0) (e0)) (e0)) (e0))) = ((e3) = (op (op (op (e0) (e0)) (e0)) (e0)))). % 18.45/18.68 intro zenon_D_pnotp. % 18.45/18.68 apply zenon_H8d. % 18.45/18.68 rewrite <- zenon_D_pnotp. % 18.45/18.68 exact zenon_H8e. % 18.45/18.68 cut (((op (op (op (e0) (e0)) (e0)) (e0)) = (op (op (op (e0) (e0)) (e0)) (e0)))); [idtac | apply NNPP; zenon_intro zenon_H8f]. % 18.45/18.68 cut (((op (op (op (e0) (e0)) (e0)) (e0)) = (e3))); [idtac | apply NNPP; zenon_intro zenon_H90]. % 18.45/18.68 congruence. % 18.45/18.68 cut (((op (e2) (e0)) = (e3)) = ((op (op (op (e0) (e0)) (e0)) (e0)) = (e3))). % 18.45/18.68 intro zenon_D_pnotp. % 18.45/18.68 apply zenon_H90. % 18.45/18.68 rewrite <- zenon_D_pnotp. % 18.45/18.68 exact zenon_H3b. % 18.45/18.68 cut (((e3) = (e3))); [idtac | apply NNPP; zenon_intro zenon_H85]. % 18.45/18.68 cut (((op (e2) (e0)) = (op (op (op (e0) (e0)) (e0)) (e0)))); [idtac | apply NNPP; zenon_intro zenon_H91]. % 18.45/18.68 congruence. % 18.45/18.68 elim (classic ((op (op (op (e0) (e0)) (e0)) (e0)) = (op (op (op (e0) (e0)) (e0)) (e0)))); [ zenon_intro zenon_H8e | zenon_intro zenon_H8f ]. % 18.45/18.68 cut (((op (op (op (e0) (e0)) (e0)) (e0)) = (op (op (op (e0) (e0)) (e0)) (e0))) = ((op (e2) (e0)) = (op (op (op (e0) (e0)) (e0)) (e0)))). % 18.45/18.68 intro zenon_D_pnotp. % 18.45/18.68 apply zenon_H91. % 18.45/18.68 rewrite <- zenon_D_pnotp. % 18.45/18.68 exact zenon_H8e. % 18.45/18.68 cut (((op (op (op (e0) (e0)) (e0)) (e0)) = (op (op (op (e0) (e0)) (e0)) (e0)))); [idtac | apply NNPP; zenon_intro zenon_H8f]. % 18.45/18.68 cut (((op (op (op (e0) (e0)) (e0)) (e0)) = (op (e2) (e0)))); [idtac | apply NNPP; zenon_intro zenon_H92]. % 18.45/18.68 congruence. % 18.45/18.68 cut (((e0) = (e0))); [idtac | apply NNPP; zenon_intro zenon_H82]. % 18.45/18.68 cut (((op (op (e0) (e0)) (e0)) = (e2))); [idtac | apply NNPP; zenon_intro zenon_H8a]. % 18.45/18.68 congruence. % 18.45/18.68 cut (((op (e1) (e0)) = (e2)) = ((op (op (e0) (e0)) (e0)) = (e2))). % 18.45/18.68 intro zenon_D_pnotp. % 18.45/18.68 apply zenon_H8a. % 18.45/18.68 rewrite <- zenon_D_pnotp. % 18.45/18.68 exact zenon_H86. % 18.45/18.68 cut (((e2) = (e2))); [idtac | apply NNPP; zenon_intro zenon_H7e]. % 18.45/18.68 cut (((op (e1) (e0)) = (op (op (e0) (e0)) (e0)))); [idtac | apply NNPP; zenon_intro zenon_H8b]. % 18.45/18.68 congruence. % 18.45/18.68 elim (classic ((op (op (e0) (e0)) (e0)) = (op (op (e0) (e0)) (e0)))); [ zenon_intro zenon_H88 | zenon_intro zenon_H89 ]. % 18.45/18.68 cut (((op (op (e0) (e0)) (e0)) = (op (op (e0) (e0)) (e0))) = ((op (e1) (e0)) = (op (op (e0) (e0)) (e0)))). % 18.45/18.68 intro zenon_D_pnotp. % 18.45/18.68 apply zenon_H8b. % 18.45/18.68 rewrite <- zenon_D_pnotp. % 18.45/18.68 exact zenon_H88. % 18.45/18.68 cut (((op (op (e0) (e0)) (e0)) = (op (op (e0) (e0)) (e0)))); [idtac | apply NNPP; zenon_intro zenon_H89]. % 18.45/18.68 cut (((op (op (e0) (e0)) (e0)) = (op (e1) (e0)))); [idtac | apply NNPP; zenon_intro zenon_H83]. % 18.45/18.68 congruence. % 18.45/18.68 apply (zenon_L29_); trivial. % 18.45/18.68 apply zenon_H89. apply refl_equal. % 18.45/18.68 apply zenon_H89. apply refl_equal. % 18.45/18.68 apply zenon_H7e. apply refl_equal. % 18.45/18.68 apply zenon_H82. apply refl_equal. % 18.45/18.68 apply zenon_H8f. apply refl_equal. % 18.45/18.68 apply zenon_H8f. apply refl_equal. % 18.45/18.68 apply zenon_H85. apply refl_equal. % 18.45/18.68 apply zenon_H8f. apply refl_equal. % 18.45/18.68 apply zenon_H8f. apply refl_equal. % 18.45/18.68 apply (zenon_notand_s _ _ zenon_H8c); [ zenon_intro zenon_H87 | zenon_intro zenon_H93 ]. % 18.45/18.68 apply (zenon_L32_); trivial. % 18.45/18.68 apply zenon_H93. apply sym_equal. exact zenon_H7a. % 18.45/18.68 (* end of lemma zenon_L33_ *) % 18.45/18.68 assert (zenon_L34_ : ((~((op (e2) (e3)) = (e0)))\/((op (e2) (e0)) = (e3))) -> ((op (e1) (e0)) = (e2)) -> ((op (e0) (e0)) = (e1)) -> (~((op (e2) (e0)) = (e0))) -> (~((op (e2) (e1)) = (e0))) -> (~((op (e2) (e2)) = (e0))) -> (((op (e2) (e0)) = (e0))\/(((op (e2) (e1)) = (e0))\/(((op (e2) (e2)) = (e0))\/((op (e2) (e3)) = (e0))))) -> False). % 18.45/18.68 do 0 intro. intros zenon_H94 zenon_H86 zenon_H7a zenon_H30 zenon_H31 zenon_H81 zenon_H2f. % 18.45/18.68 apply (zenon_or_s _ _ zenon_H94); [ zenon_intro zenon_H32 | zenon_intro zenon_H3b ]. % 18.45/18.68 apply (zenon_L27_); trivial. % 18.45/18.68 apply (zenon_L33_); trivial. % 18.45/18.68 (* end of lemma zenon_L34_ *) % 18.45/18.68 assert (zenon_L35_ : ((op (e0) (e0)) = (e1)) -> ((op (e0) (e0)) = (e3)) -> (~((e1) = (e3))) -> False). % 18.45/18.68 do 0 intro. intros zenon_H7a zenon_H3a zenon_H95. % 18.45/18.68 elim (classic ((e3) = (e3))); [ zenon_intro zenon_H96 | zenon_intro zenon_H85 ]. % 18.45/18.68 cut (((e3) = (e3)) = ((e1) = (e3))). % 18.45/18.68 intro zenon_D_pnotp. % 18.45/18.68 apply zenon_H95. % 18.45/18.68 rewrite <- zenon_D_pnotp. % 18.45/18.68 exact zenon_H96. % 18.45/18.68 cut (((e3) = (e3))); [idtac | apply NNPP; zenon_intro zenon_H85]. % 18.45/18.68 cut (((e3) = (e1))); [idtac | apply NNPP; zenon_intro zenon_H97]. % 18.45/18.68 congruence. % 18.45/18.68 cut (((op (e0) (e0)) = (e1)) = ((e3) = (e1))). % 18.45/18.68 intro zenon_D_pnotp. % 18.45/18.68 apply zenon_H97. % 18.45/18.68 rewrite <- zenon_D_pnotp. % 18.45/18.68 exact zenon_H7a. % 18.45/18.68 cut (((e1) = (e1))); [idtac | apply NNPP; zenon_intro zenon_H79]. % 18.45/18.68 cut (((op (e0) (e0)) = (e3))); [idtac | apply NNPP; zenon_intro zenon_H98]. % 18.45/18.68 congruence. % 18.45/18.68 exact (zenon_H98 zenon_H3a). % 18.45/18.68 apply zenon_H79. apply refl_equal. % 18.45/18.68 apply zenon_H85. apply refl_equal. % 18.45/18.68 apply zenon_H85. apply refl_equal. % 18.45/18.68 (* end of lemma zenon_L35_ *) % 18.45/18.68 assert (zenon_L36_ : ((op (e0) (e1)) = (e0)) -> ((op (e0) (e1)) = (e3)) -> (~((e0) = (e3))) -> False). % 18.45/18.68 do 0 intro. intros zenon_H49 zenon_H99 zenon_H9a. % 18.45/18.68 elim (classic ((e3) = (e3))); [ zenon_intro zenon_H96 | zenon_intro zenon_H85 ]. % 18.45/18.68 cut (((e3) = (e3)) = ((e0) = (e3))). % 18.45/18.68 intro zenon_D_pnotp. % 18.45/18.68 apply zenon_H9a. % 18.45/18.68 rewrite <- zenon_D_pnotp. % 18.45/18.68 exact zenon_H96. % 18.45/18.68 cut (((e3) = (e3))); [idtac | apply NNPP; zenon_intro zenon_H85]. % 18.45/18.68 cut (((e3) = (e0))); [idtac | apply NNPP; zenon_intro zenon_H9b]. % 18.45/18.68 congruence. % 18.45/18.68 cut (((op (e0) (e1)) = (e0)) = ((e3) = (e0))). % 18.45/18.68 intro zenon_D_pnotp. % 18.45/18.68 apply zenon_H9b. % 18.45/18.68 rewrite <- zenon_D_pnotp. % 18.45/18.68 exact zenon_H49. % 18.45/18.68 cut (((e0) = (e0))); [idtac | apply NNPP; zenon_intro zenon_H82]. % 18.45/18.68 cut (((op (e0) (e1)) = (e3))); [idtac | apply NNPP; zenon_intro zenon_H9c]. % 18.45/18.68 congruence. % 18.45/18.68 exact (zenon_H9c zenon_H99). % 18.45/18.68 apply zenon_H82. apply refl_equal. % 18.45/18.68 apply zenon_H85. apply refl_equal. % 18.45/18.68 apply zenon_H85. apply refl_equal. % 18.45/18.68 (* end of lemma zenon_L36_ *) % 18.45/18.68 assert (zenon_L37_ : ((op (e1) (e0)) = (e1)) -> ((op (e1) (e0)) = (e3)) -> (~((e1) = (e3))) -> False). % 18.45/18.68 do 0 intro. intros zenon_H9d zenon_H9e zenon_H95. % 18.45/18.68 elim (classic ((e3) = (e3))); [ zenon_intro zenon_H96 | zenon_intro zenon_H85 ]. % 18.45/18.68 cut (((e3) = (e3)) = ((e1) = (e3))). % 18.45/18.68 intro zenon_D_pnotp. % 18.45/18.68 apply zenon_H95. % 18.45/18.68 rewrite <- zenon_D_pnotp. % 18.45/18.68 exact zenon_H96. % 18.45/18.68 cut (((e3) = (e3))); [idtac | apply NNPP; zenon_intro zenon_H85]. % 18.45/18.68 cut (((e3) = (e1))); [idtac | apply NNPP; zenon_intro zenon_H97]. % 18.45/18.68 congruence. % 18.45/18.68 cut (((op (e1) (e0)) = (e1)) = ((e3) = (e1))). % 18.45/18.68 intro zenon_D_pnotp. % 18.45/18.68 apply zenon_H97. % 18.45/18.68 rewrite <- zenon_D_pnotp. % 18.45/18.68 exact zenon_H9d. % 18.45/18.68 cut (((e1) = (e1))); [idtac | apply NNPP; zenon_intro zenon_H79]. % 18.45/18.68 cut (((op (e1) (e0)) = (e3))); [idtac | apply NNPP; zenon_intro zenon_H9f]. % 18.45/18.68 congruence. % 18.45/18.68 exact (zenon_H9f zenon_H9e). % 18.45/18.68 apply zenon_H79. apply refl_equal. % 18.45/18.68 apply zenon_H85. apply refl_equal. % 18.45/18.68 apply zenon_H85. apply refl_equal. % 18.45/18.68 (* end of lemma zenon_L37_ *) % 18.45/18.68 assert (zenon_L38_ : ((op (e0) (e1)) = (e0)) -> ((op (e0) (e1)) = (e1)) -> (~((e0) = (e1))) -> False). % 18.45/18.68 do 0 intro. intros zenon_H49 zenon_Ha0 zenon_Ha1. % 18.45/18.68 elim (classic ((e1) = (e1))); [ zenon_intro zenon_Ha2 | zenon_intro zenon_H79 ]. % 18.45/18.68 cut (((e1) = (e1)) = ((e0) = (e1))). % 18.45/18.68 intro zenon_D_pnotp. % 18.45/18.68 apply zenon_Ha1. % 18.45/18.68 rewrite <- zenon_D_pnotp. % 18.45/18.68 exact zenon_Ha2. % 18.45/18.68 cut (((e1) = (e1))); [idtac | apply NNPP; zenon_intro zenon_H79]. % 18.45/18.68 cut (((e1) = (e0))); [idtac | apply NNPP; zenon_intro zenon_Ha3]. % 18.45/18.68 congruence. % 18.45/18.68 cut (((op (e0) (e1)) = (e0)) = ((e1) = (e0))). % 18.45/18.68 intro zenon_D_pnotp. % 18.45/18.68 apply zenon_Ha3. % 18.45/18.68 rewrite <- zenon_D_pnotp. % 18.45/18.68 exact zenon_H49. % 18.45/18.68 cut (((e0) = (e0))); [idtac | apply NNPP; zenon_intro zenon_H82]. % 18.45/18.68 cut (((op (e0) (e1)) = (e1))); [idtac | apply NNPP; zenon_intro zenon_Ha4]. % 18.45/18.68 congruence. % 18.45/18.68 exact (zenon_Ha4 zenon_Ha0). % 18.45/18.68 apply zenon_H82. apply refl_equal. % 18.45/18.68 apply zenon_H79. apply refl_equal. % 18.45/18.68 apply zenon_H79. apply refl_equal. % 18.45/18.68 (* end of lemma zenon_L38_ *) % 18.45/18.68 assert (zenon_L39_ : ((op (e2) (e1)) = (e1)) -> ((op (e2) (e1)) = (e3)) -> (~((e1) = (e3))) -> False). % 18.45/18.68 do 0 intro. intros zenon_Ha5 zenon_Ha6 zenon_H95. % 18.45/18.68 elim (classic ((e3) = (e3))); [ zenon_intro zenon_H96 | zenon_intro zenon_H85 ]. % 18.45/18.68 cut (((e3) = (e3)) = ((e1) = (e3))). % 18.45/18.68 intro zenon_D_pnotp. % 18.45/18.68 apply zenon_H95. % 18.45/18.68 rewrite <- zenon_D_pnotp. % 18.45/18.68 exact zenon_H96. % 18.45/18.68 cut (((e3) = (e3))); [idtac | apply NNPP; zenon_intro zenon_H85]. % 18.45/18.68 cut (((e3) = (e1))); [idtac | apply NNPP; zenon_intro zenon_H97]. % 18.45/18.68 congruence. % 18.45/18.68 cut (((op (e2) (e1)) = (e1)) = ((e3) = (e1))). % 18.45/18.68 intro zenon_D_pnotp. % 18.45/18.68 apply zenon_H97. % 18.45/18.68 rewrite <- zenon_D_pnotp. % 18.45/18.68 exact zenon_Ha5. % 18.45/18.68 cut (((e1) = (e1))); [idtac | apply NNPP; zenon_intro zenon_H79]. % 18.45/18.68 cut (((op (e2) (e1)) = (e3))); [idtac | apply NNPP; zenon_intro zenon_Ha7]. % 18.45/18.68 congruence. % 18.45/18.68 exact (zenon_Ha7 zenon_Ha6). % 18.45/18.68 apply zenon_H79. apply refl_equal. % 18.45/18.68 apply zenon_H85. apply refl_equal. % 18.45/18.68 apply zenon_H85. apply refl_equal. % 18.45/18.68 (* end of lemma zenon_L39_ *) % 18.45/18.68 assert (zenon_L40_ : (~((op (e0) (e2)) = (op (e2) (e2)))) -> ((op (e0) (e2)) = (e3)) -> ((op (e2) (e2)) = (e3)) -> False). % 18.45/18.68 do 0 intro. intros zenon_Ha8 zenon_Ha9 zenon_Haa. % 18.45/18.68 cut (((op (e0) (e2)) = (e3)) = ((op (e0) (e2)) = (op (e2) (e2)))). % 18.45/18.68 intro zenon_D_pnotp. % 18.45/18.68 apply zenon_Ha8. % 18.45/18.68 rewrite <- zenon_D_pnotp. % 18.45/18.68 exact zenon_Ha9. % 18.45/18.68 cut (((e3) = (op (e2) (e2)))); [idtac | apply NNPP; zenon_intro zenon_Hab]. % 18.45/18.68 cut (((op (e0) (e2)) = (op (e0) (e2)))); [idtac | apply NNPP; zenon_intro zenon_H4c]. % 18.45/18.68 congruence. % 18.45/18.68 apply zenon_H4c. apply refl_equal. % 18.45/18.68 apply zenon_Hab. apply sym_equal. exact zenon_Haa. % 18.45/18.68 (* end of lemma zenon_L40_ *) % 18.45/18.68 assert (zenon_L41_ : ((op (e3) (e0)) = (e0)) -> ((op (e3) (e0)) = (e1)) -> (~((e0) = (e1))) -> False). % 18.45/18.68 do 0 intro. intros zenon_H44 zenon_Hac zenon_Ha1. % 18.45/18.68 elim (classic ((e1) = (e1))); [ zenon_intro zenon_Ha2 | zenon_intro zenon_H79 ]. % 18.45/18.68 cut (((e1) = (e1)) = ((e0) = (e1))). % 18.45/18.68 intro zenon_D_pnotp. % 18.45/18.68 apply zenon_Ha1. % 18.45/18.68 rewrite <- zenon_D_pnotp. % 18.45/18.68 exact zenon_Ha2. % 18.45/18.68 cut (((e1) = (e1))); [idtac | apply NNPP; zenon_intro zenon_H79]. % 18.45/18.68 cut (((e1) = (e0))); [idtac | apply NNPP; zenon_intro zenon_Ha3]. % 18.45/18.68 congruence. % 18.45/18.68 cut (((op (e3) (e0)) = (e0)) = ((e1) = (e0))). % 18.45/18.68 intro zenon_D_pnotp. % 18.45/18.68 apply zenon_Ha3. % 18.45/18.68 rewrite <- zenon_D_pnotp. % 18.45/18.68 exact zenon_H44. % 18.45/18.68 cut (((e0) = (e0))); [idtac | apply NNPP; zenon_intro zenon_H82]. % 18.45/18.68 cut (((op (e3) (e0)) = (e1))); [idtac | apply NNPP; zenon_intro zenon_Had]. % 18.45/18.68 congruence. % 18.45/18.68 exact (zenon_Had zenon_Hac). % 18.45/18.68 apply zenon_H82. apply refl_equal. % 18.45/18.68 apply zenon_H79. apply refl_equal. % 18.45/18.68 apply zenon_H79. apply refl_equal. % 18.45/18.68 (* end of lemma zenon_L41_ *) % 18.45/18.68 assert (zenon_L42_ : ((op (e3) (e1)) = (e1)) -> ((op (e2) (e1)) = (e1)) -> (~((op (e2) (e1)) = (op (e3) (e1)))) -> False). % 18.45/18.68 do 0 intro. intros zenon_Hae zenon_Ha5 zenon_Haf. % 18.45/18.68 elim (classic ((op (e3) (e1)) = (op (e3) (e1)))); [ zenon_intro zenon_Hb0 | zenon_intro zenon_Hb1 ]. % 18.45/18.68 cut (((op (e3) (e1)) = (op (e3) (e1))) = ((op (e2) (e1)) = (op (e3) (e1)))). % 18.45/18.68 intro zenon_D_pnotp. % 18.45/18.68 apply zenon_Haf. % 18.45/18.68 rewrite <- zenon_D_pnotp. % 18.45/18.68 exact zenon_Hb0. % 18.45/18.68 cut (((op (e3) (e1)) = (op (e3) (e1)))); [idtac | apply NNPP; zenon_intro zenon_Hb1]. % 18.45/18.68 cut (((op (e3) (e1)) = (op (e2) (e1)))); [idtac | apply NNPP; zenon_intro zenon_Hb2]. % 18.45/18.68 congruence. % 18.45/18.68 cut (((op (e3) (e1)) = (e1)) = ((op (e3) (e1)) = (op (e2) (e1)))). % 18.45/18.68 intro zenon_D_pnotp. % 18.45/18.68 apply zenon_Hb2. % 18.45/18.68 rewrite <- zenon_D_pnotp. % 18.45/18.68 exact zenon_Hae. % 18.45/18.68 cut (((e1) = (op (e2) (e1)))); [idtac | apply NNPP; zenon_intro zenon_Hb3]. % 18.45/18.68 cut (((op (e3) (e1)) = (op (e3) (e1)))); [idtac | apply NNPP; zenon_intro zenon_Hb1]. % 18.45/18.68 congruence. % 18.45/18.68 apply zenon_Hb1. apply refl_equal. % 18.45/18.68 apply zenon_Hb3. apply sym_equal. exact zenon_Ha5. % 18.45/18.68 apply zenon_Hb1. apply refl_equal. % 18.45/18.68 apply zenon_Hb1. apply refl_equal. % 18.45/18.68 (* end of lemma zenon_L42_ *) % 18.45/18.68 assert (zenon_L43_ : (~((op (op (e2) (e2)) (e2)) = (op (e0) (e2)))) -> ((op (e2) (e2)) = (e0)) -> False). % 18.45/18.68 do 0 intro. intros zenon_Hb4 zenon_H2c. % 18.45/18.68 cut (((e2) = (e2))); [idtac | apply NNPP; zenon_intro zenon_H7e]. % 18.45/18.68 cut (((op (e2) (e2)) = (e0))); [idtac | apply NNPP; zenon_intro zenon_H81]. % 18.45/18.68 congruence. % 18.45/18.68 exact (zenon_H81 zenon_H2c). % 18.45/18.68 apply zenon_H7e. apply refl_equal. % 18.45/18.68 (* end of lemma zenon_L43_ *) % 18.45/18.68 assert (zenon_L44_ : ((op (e0) (e2)) = (e3)) -> ((op (e2) (e2)) = (e0)) -> (~((e3) = (op (op (e2) (e2)) (e2)))) -> False). % 18.45/18.68 do 0 intro. intros zenon_Ha9 zenon_H2c zenon_Hb5. % 18.45/18.68 elim (classic ((op (op (e2) (e2)) (e2)) = (op (op (e2) (e2)) (e2)))); [ zenon_intro zenon_Hb6 | zenon_intro zenon_Hb7 ]. % 18.45/18.68 cut (((op (op (e2) (e2)) (e2)) = (op (op (e2) (e2)) (e2))) = ((e3) = (op (op (e2) (e2)) (e2)))). % 18.45/18.68 intro zenon_D_pnotp. % 18.45/18.68 apply zenon_Hb5. % 18.45/18.68 rewrite <- zenon_D_pnotp. % 18.45/18.68 exact zenon_Hb6. % 18.45/18.68 cut (((op (op (e2) (e2)) (e2)) = (op (op (e2) (e2)) (e2)))); [idtac | apply NNPP; zenon_intro zenon_Hb7]. % 18.45/18.68 cut (((op (op (e2) (e2)) (e2)) = (e3))); [idtac | apply NNPP; zenon_intro zenon_Hb8]. % 18.45/18.68 congruence. % 18.45/18.68 cut (((op (e0) (e2)) = (e3)) = ((op (op (e2) (e2)) (e2)) = (e3))). % 18.45/18.68 intro zenon_D_pnotp. % 18.45/18.68 apply zenon_Hb8. % 18.45/18.68 rewrite <- zenon_D_pnotp. % 18.45/18.68 exact zenon_Ha9. % 18.45/18.68 cut (((e3) = (e3))); [idtac | apply NNPP; zenon_intro zenon_H85]. % 18.45/18.68 cut (((op (e0) (e2)) = (op (op (e2) (e2)) (e2)))); [idtac | apply NNPP; zenon_intro zenon_Hb9]. % 18.45/18.68 congruence. % 18.45/18.68 elim (classic ((op (op (e2) (e2)) (e2)) = (op (op (e2) (e2)) (e2)))); [ zenon_intro zenon_Hb6 | zenon_intro zenon_Hb7 ]. % 18.45/18.68 cut (((op (op (e2) (e2)) (e2)) = (op (op (e2) (e2)) (e2))) = ((op (e0) (e2)) = (op (op (e2) (e2)) (e2)))). % 18.45/18.68 intro zenon_D_pnotp. % 18.45/18.68 apply zenon_Hb9. % 18.45/18.68 rewrite <- zenon_D_pnotp. % 18.45/18.68 exact zenon_Hb6. % 18.45/18.68 cut (((op (op (e2) (e2)) (e2)) = (op (op (e2) (e2)) (e2)))); [idtac | apply NNPP; zenon_intro zenon_Hb7]. % 18.45/18.68 cut (((op (op (e2) (e2)) (e2)) = (op (e0) (e2)))); [idtac | apply NNPP; zenon_intro zenon_Hb4]. % 18.45/18.68 congruence. % 18.45/18.68 apply (zenon_L43_); trivial. % 18.45/18.68 apply zenon_Hb7. apply refl_equal. % 18.45/18.68 apply zenon_Hb7. apply refl_equal. % 18.45/18.68 apply zenon_H85. apply refl_equal. % 18.45/18.68 apply zenon_Hb7. apply refl_equal. % 18.45/18.68 apply zenon_Hb7. apply refl_equal. % 18.45/18.68 (* end of lemma zenon_L44_ *) % 18.45/18.68 assert (zenon_L45_ : ((op (e3) (e2)) = (e1)) -> ((op (e0) (e2)) = (e3)) -> ((op (e2) (e2)) = (e0)) -> False). % 18.45/18.68 do 0 intro. intros zenon_Hba zenon_Ha9 zenon_H2c. % 18.45/18.68 apply (zenon_notand_s _ _ ax21); [ zenon_intro zenon_Hbc | zenon_intro zenon_Hbb ]. % 18.45/18.68 elim (classic ((op (op (op (e2) (e2)) (e2)) (e2)) = (op (op (op (e2) (e2)) (e2)) (e2)))); [ zenon_intro zenon_Hbd | zenon_intro zenon_Hbe ]. % 18.45/18.68 cut (((op (op (op (e2) (e2)) (e2)) (e2)) = (op (op (op (e2) (e2)) (e2)) (e2))) = ((e1) = (op (op (op (e2) (e2)) (e2)) (e2)))). % 18.45/18.68 intro zenon_D_pnotp. % 18.45/18.68 apply zenon_Hbc. % 18.45/18.68 rewrite <- zenon_D_pnotp. % 18.45/18.68 exact zenon_Hbd. % 18.45/18.68 cut (((op (op (op (e2) (e2)) (e2)) (e2)) = (op (op (op (e2) (e2)) (e2)) (e2)))); [idtac | apply NNPP; zenon_intro zenon_Hbe]. % 18.45/18.68 cut (((op (op (op (e2) (e2)) (e2)) (e2)) = (e1))); [idtac | apply NNPP; zenon_intro zenon_Hbf]. % 18.45/18.68 congruence. % 18.45/18.68 cut (((op (e3) (e2)) = (e1)) = ((op (op (op (e2) (e2)) (e2)) (e2)) = (e1))). % 18.45/18.68 intro zenon_D_pnotp. % 18.45/18.68 apply zenon_Hbf. % 18.45/18.68 rewrite <- zenon_D_pnotp. % 18.45/18.68 exact zenon_Hba. % 18.45/18.68 cut (((e1) = (e1))); [idtac | apply NNPP; zenon_intro zenon_H79]. % 18.45/18.68 cut (((op (e3) (e2)) = (op (op (op (e2) (e2)) (e2)) (e2)))); [idtac | apply NNPP; zenon_intro zenon_Hc0]. % 18.45/18.68 congruence. % 18.45/18.68 elim (classic ((op (op (op (e2) (e2)) (e2)) (e2)) = (op (op (op (e2) (e2)) (e2)) (e2)))); [ zenon_intro zenon_Hbd | zenon_intro zenon_Hbe ]. % 18.45/18.68 cut (((op (op (op (e2) (e2)) (e2)) (e2)) = (op (op (op (e2) (e2)) (e2)) (e2))) = ((op (e3) (e2)) = (op (op (op (e2) (e2)) (e2)) (e2)))). % 18.45/18.68 intro zenon_D_pnotp. % 18.45/18.68 apply zenon_Hc0. % 18.45/18.68 rewrite <- zenon_D_pnotp. % 18.45/18.68 exact zenon_Hbd. % 18.45/18.68 cut (((op (op (op (e2) (e2)) (e2)) (e2)) = (op (op (op (e2) (e2)) (e2)) (e2)))); [idtac | apply NNPP; zenon_intro zenon_Hbe]. % 18.45/18.68 cut (((op (op (op (e2) (e2)) (e2)) (e2)) = (op (e3) (e2)))); [idtac | apply NNPP; zenon_intro zenon_Hc1]. % 18.45/18.68 congruence. % 18.45/18.68 cut (((e2) = (e2))); [idtac | apply NNPP; zenon_intro zenon_H7e]. % 18.45/18.68 cut (((op (op (e2) (e2)) (e2)) = (e3))); [idtac | apply NNPP; zenon_intro zenon_Hb8]. % 18.45/18.68 congruence. % 18.45/18.68 cut (((op (e0) (e2)) = (e3)) = ((op (op (e2) (e2)) (e2)) = (e3))). % 18.45/18.68 intro zenon_D_pnotp. % 18.45/18.68 apply zenon_Hb8. % 18.45/18.68 rewrite <- zenon_D_pnotp. % 18.45/18.68 exact zenon_Ha9. % 18.45/18.68 cut (((e3) = (e3))); [idtac | apply NNPP; zenon_intro zenon_H85]. % 18.45/18.68 cut (((op (e0) (e2)) = (op (op (e2) (e2)) (e2)))); [idtac | apply NNPP; zenon_intro zenon_Hb9]. % 18.45/18.68 congruence. % 18.45/18.68 elim (classic ((op (op (e2) (e2)) (e2)) = (op (op (e2) (e2)) (e2)))); [ zenon_intro zenon_Hb6 | zenon_intro zenon_Hb7 ]. % 18.45/18.68 cut (((op (op (e2) (e2)) (e2)) = (op (op (e2) (e2)) (e2))) = ((op (e0) (e2)) = (op (op (e2) (e2)) (e2)))). % 18.45/18.68 intro zenon_D_pnotp. % 18.45/18.68 apply zenon_Hb9. % 18.45/18.68 rewrite <- zenon_D_pnotp. % 18.45/18.68 exact zenon_Hb6. % 18.45/18.68 cut (((op (op (e2) (e2)) (e2)) = (op (op (e2) (e2)) (e2)))); [idtac | apply NNPP; zenon_intro zenon_Hb7]. % 18.45/18.68 cut (((op (op (e2) (e2)) (e2)) = (op (e0) (e2)))); [idtac | apply NNPP; zenon_intro zenon_Hb4]. % 18.45/18.68 congruence. % 18.45/18.68 apply (zenon_L43_); trivial. % 18.45/18.68 apply zenon_Hb7. apply refl_equal. % 18.45/18.68 apply zenon_Hb7. apply refl_equal. % 18.45/18.68 apply zenon_H85. apply refl_equal. % 18.45/18.68 apply zenon_H7e. apply refl_equal. % 18.45/18.68 apply zenon_Hbe. apply refl_equal. % 18.45/18.68 apply zenon_Hbe. apply refl_equal. % 18.45/18.68 apply zenon_H79. apply refl_equal. % 18.45/18.68 apply zenon_Hbe. apply refl_equal. % 18.45/18.68 apply zenon_Hbe. apply refl_equal. % 18.45/18.68 apply (zenon_notand_s _ _ zenon_Hbb); [ zenon_intro zenon_Hb5 | zenon_intro zenon_H2d ]. % 18.45/18.68 apply (zenon_L44_); trivial. % 18.45/18.68 apply zenon_H2d. apply sym_equal. exact zenon_H2c. % 18.45/18.68 (* end of lemma zenon_L45_ *) % 18.45/18.68 assert (zenon_L46_ : (~((op (e0) (e3)) = (op (e3) (e3)))) -> ((op (e0) (e3)) = (e1)) -> ((op (e3) (e3)) = (e1)) -> False). % 18.45/18.68 do 0 intro. intros zenon_Hc2 zenon_Hc3 zenon_Hc4. % 18.45/18.68 cut (((op (e0) (e3)) = (e1)) = ((op (e0) (e3)) = (op (e3) (e3)))). % 18.45/18.68 intro zenon_D_pnotp. % 18.45/18.68 apply zenon_Hc2. % 18.45/18.68 rewrite <- zenon_D_pnotp. % 18.45/18.68 exact zenon_Hc3. % 18.45/18.68 cut (((e1) = (op (e3) (e3)))); [idtac | apply NNPP; zenon_intro zenon_Hc5]. % 18.45/18.68 cut (((op (e0) (e3)) = (op (e0) (e3)))); [idtac | apply NNPP; zenon_intro zenon_H21]. % 18.45/18.68 congruence. % 18.45/18.68 apply zenon_H21. apply refl_equal. % 18.45/18.68 apply zenon_Hc5. apply sym_equal. exact zenon_Hc4. % 18.45/18.68 (* end of lemma zenon_L46_ *) % 18.45/18.68 assert (zenon_L47_ : (~((op (op (e3) (e3)) (e3)) = (op (e1) (e3)))) -> ((op (e3) (e3)) = (e1)) -> False). % 18.45/18.68 do 0 intro. intros zenon_Hc6 zenon_Hc4. % 18.45/18.68 cut (((e3) = (e3))); [idtac | apply NNPP; zenon_intro zenon_H85]. % 18.45/18.68 cut (((op (e3) (e3)) = (e1))); [idtac | apply NNPP; zenon_intro zenon_Hc7]. % 18.45/18.68 congruence. % 18.45/18.68 exact (zenon_Hc7 zenon_Hc4). % 18.45/18.68 apply zenon_H85. apply refl_equal. % 18.45/18.68 (* end of lemma zenon_L47_ *) % 18.45/18.68 assert (zenon_L48_ : ((op (e1) (e3)) = (e0)) -> ((op (e3) (e3)) = (e1)) -> (~((e0) = (op (op (e3) (e3)) (e3)))) -> False). % 18.45/18.68 do 0 intro. intros zenon_H1f zenon_Hc4 zenon_Hc8. % 18.45/18.68 elim (classic ((op (op (e3) (e3)) (e3)) = (op (op (e3) (e3)) (e3)))); [ zenon_intro zenon_Hc9 | zenon_intro zenon_Hca ]. % 18.45/18.68 cut (((op (op (e3) (e3)) (e3)) = (op (op (e3) (e3)) (e3))) = ((e0) = (op (op (e3) (e3)) (e3)))). % 18.45/18.68 intro zenon_D_pnotp. % 18.45/18.68 apply zenon_Hc8. % 18.45/18.68 rewrite <- zenon_D_pnotp. % 18.45/18.68 exact zenon_Hc9. % 18.45/18.68 cut (((op (op (e3) (e3)) (e3)) = (op (op (e3) (e3)) (e3)))); [idtac | apply NNPP; zenon_intro zenon_Hca]. % 18.45/18.68 cut (((op (op (e3) (e3)) (e3)) = (e0))); [idtac | apply NNPP; zenon_intro zenon_Hcb]. % 18.45/18.68 congruence. % 18.45/18.68 cut (((op (e1) (e3)) = (e0)) = ((op (op (e3) (e3)) (e3)) = (e0))). % 18.45/18.68 intro zenon_D_pnotp. % 18.45/18.68 apply zenon_Hcb. % 18.45/18.68 rewrite <- zenon_D_pnotp. % 18.45/18.68 exact zenon_H1f. % 18.45/18.68 cut (((e0) = (e0))); [idtac | apply NNPP; zenon_intro zenon_H82]. % 18.45/18.68 cut (((op (e1) (e3)) = (op (op (e3) (e3)) (e3)))); [idtac | apply NNPP; zenon_intro zenon_Hcc]. % 18.45/18.68 congruence. % 18.45/18.68 elim (classic ((op (op (e3) (e3)) (e3)) = (op (op (e3) (e3)) (e3)))); [ zenon_intro zenon_Hc9 | zenon_intro zenon_Hca ]. % 18.45/18.68 cut (((op (op (e3) (e3)) (e3)) = (op (op (e3) (e3)) (e3))) = ((op (e1) (e3)) = (op (op (e3) (e3)) (e3)))). % 18.45/18.68 intro zenon_D_pnotp. % 18.45/18.68 apply zenon_Hcc. % 18.45/18.68 rewrite <- zenon_D_pnotp. % 18.45/18.68 exact zenon_Hc9. % 18.45/18.68 cut (((op (op (e3) (e3)) (e3)) = (op (op (e3) (e3)) (e3)))); [idtac | apply NNPP; zenon_intro zenon_Hca]. % 18.45/18.68 cut (((op (op (e3) (e3)) (e3)) = (op (e1) (e3)))); [idtac | apply NNPP; zenon_intro zenon_Hc6]. % 18.45/18.68 congruence. % 18.45/18.68 apply (zenon_L47_); trivial. % 18.45/18.68 apply zenon_Hca. apply refl_equal. % 18.45/18.68 apply zenon_Hca. apply refl_equal. % 18.45/18.68 apply zenon_H82. apply refl_equal. % 18.45/18.68 apply zenon_Hca. apply refl_equal. % 18.45/18.68 apply zenon_Hca. apply refl_equal. % 18.45/18.68 (* end of lemma zenon_L48_ *) % 18.45/18.68 assert (zenon_L49_ : ((op (e0) (e3)) = (e2)) -> ((op (e1) (e3)) = (e0)) -> ((op (e3) (e3)) = (e1)) -> False). % 18.45/18.68 do 0 intro. intros zenon_Hcd zenon_H1f zenon_Hc4. % 18.45/18.68 apply (zenon_notand_s _ _ ax28); [ zenon_intro zenon_Hcf | zenon_intro zenon_Hce ]. % 18.45/18.68 elim (classic ((op (op (op (e3) (e3)) (e3)) (e3)) = (op (op (op (e3) (e3)) (e3)) (e3)))); [ zenon_intro zenon_Hd0 | zenon_intro zenon_Hd1 ]. % 18.45/18.68 cut (((op (op (op (e3) (e3)) (e3)) (e3)) = (op (op (op (e3) (e3)) (e3)) (e3))) = ((e2) = (op (op (op (e3) (e3)) (e3)) (e3)))). % 18.45/18.68 intro zenon_D_pnotp. % 18.45/18.68 apply zenon_Hcf. % 18.45/18.68 rewrite <- zenon_D_pnotp. % 18.45/18.68 exact zenon_Hd0. % 18.45/18.68 cut (((op (op (op (e3) (e3)) (e3)) (e3)) = (op (op (op (e3) (e3)) (e3)) (e3)))); [idtac | apply NNPP; zenon_intro zenon_Hd1]. % 18.45/18.68 cut (((op (op (op (e3) (e3)) (e3)) (e3)) = (e2))); [idtac | apply NNPP; zenon_intro zenon_Hd2]. % 18.45/18.68 congruence. % 18.45/18.68 cut (((op (e0) (e3)) = (e2)) = ((op (op (op (e3) (e3)) (e3)) (e3)) = (e2))). % 18.45/18.68 intro zenon_D_pnotp. % 18.45/18.68 apply zenon_Hd2. % 18.45/18.68 rewrite <- zenon_D_pnotp. % 18.45/18.68 exact zenon_Hcd. % 18.45/18.68 cut (((e2) = (e2))); [idtac | apply NNPP; zenon_intro zenon_H7e]. % 18.45/18.68 cut (((op (e0) (e3)) = (op (op (op (e3) (e3)) (e3)) (e3)))); [idtac | apply NNPP; zenon_intro zenon_Hd3]. % 18.45/18.68 congruence. % 18.45/18.68 elim (classic ((op (op (op (e3) (e3)) (e3)) (e3)) = (op (op (op (e3) (e3)) (e3)) (e3)))); [ zenon_intro zenon_Hd0 | zenon_intro zenon_Hd1 ]. % 18.45/18.68 cut (((op (op (op (e3) (e3)) (e3)) (e3)) = (op (op (op (e3) (e3)) (e3)) (e3))) = ((op (e0) (e3)) = (op (op (op (e3) (e3)) (e3)) (e3)))). % 18.45/18.68 intro zenon_D_pnotp. % 18.45/18.68 apply zenon_Hd3. % 18.45/18.68 rewrite <- zenon_D_pnotp. % 18.45/18.68 exact zenon_Hd0. % 18.45/18.68 cut (((op (op (op (e3) (e3)) (e3)) (e3)) = (op (op (op (e3) (e3)) (e3)) (e3)))); [idtac | apply NNPP; zenon_intro zenon_Hd1]. % 18.45/18.68 cut (((op (op (op (e3) (e3)) (e3)) (e3)) = (op (e0) (e3)))); [idtac | apply NNPP; zenon_intro zenon_Hd4]. % 18.45/18.68 congruence. % 18.45/18.68 cut (((e3) = (e3))); [idtac | apply NNPP; zenon_intro zenon_H85]. % 18.45/18.68 cut (((op (op (e3) (e3)) (e3)) = (e0))); [idtac | apply NNPP; zenon_intro zenon_Hcb]. % 18.45/18.68 congruence. % 18.45/18.68 cut (((op (e1) (e3)) = (e0)) = ((op (op (e3) (e3)) (e3)) = (e0))). % 18.45/18.68 intro zenon_D_pnotp. % 18.45/18.68 apply zenon_Hcb. % 18.45/18.68 rewrite <- zenon_D_pnotp. % 18.45/18.68 exact zenon_H1f. % 18.45/18.68 cut (((e0) = (e0))); [idtac | apply NNPP; zenon_intro zenon_H82]. % 18.45/18.68 cut (((op (e1) (e3)) = (op (op (e3) (e3)) (e3)))); [idtac | apply NNPP; zenon_intro zenon_Hcc]. % 18.45/18.68 congruence. % 18.45/18.68 elim (classic ((op (op (e3) (e3)) (e3)) = (op (op (e3) (e3)) (e3)))); [ zenon_intro zenon_Hc9 | zenon_intro zenon_Hca ]. % 18.45/18.68 cut (((op (op (e3) (e3)) (e3)) = (op (op (e3) (e3)) (e3))) = ((op (e1) (e3)) = (op (op (e3) (e3)) (e3)))). % 18.45/18.68 intro zenon_D_pnotp. % 18.45/18.68 apply zenon_Hcc. % 18.45/18.68 rewrite <- zenon_D_pnotp. % 18.45/18.68 exact zenon_Hc9. % 18.45/18.68 cut (((op (op (e3) (e3)) (e3)) = (op (op (e3) (e3)) (e3)))); [idtac | apply NNPP; zenon_intro zenon_Hca]. % 18.45/18.68 cut (((op (op (e3) (e3)) (e3)) = (op (e1) (e3)))); [idtac | apply NNPP; zenon_intro zenon_Hc6]. % 18.45/18.68 congruence. % 18.45/18.68 apply (zenon_L47_); trivial. % 18.45/18.68 apply zenon_Hca. apply refl_equal. % 18.45/18.68 apply zenon_Hca. apply refl_equal. % 18.45/18.68 apply zenon_H82. apply refl_equal. % 18.45/18.68 apply zenon_H85. apply refl_equal. % 18.45/18.68 apply zenon_Hd1. apply refl_equal. % 18.45/18.68 apply zenon_Hd1. apply refl_equal. % 18.45/18.68 apply zenon_H7e. apply refl_equal. % 18.45/18.68 apply zenon_Hd1. apply refl_equal. % 18.45/18.68 apply zenon_Hd1. apply refl_equal. % 18.45/18.68 apply (zenon_notand_s _ _ zenon_Hce); [ zenon_intro zenon_Hc8 | zenon_intro zenon_Hc5 ]. % 18.45/18.68 apply (zenon_L48_); trivial. % 18.45/18.68 apply zenon_Hc5. apply sym_equal. exact zenon_Hc4. % 18.45/18.68 (* end of lemma zenon_L49_ *) % 18.45/18.68 assert (zenon_L50_ : (~((op (e1) (e3)) = (op (e3) (e3)))) -> ((op (e1) (e3)) = (e1)) -> ((op (e3) (e3)) = (e1)) -> False). % 18.45/18.68 do 0 intro. intros zenon_Hd5 zenon_Hd6 zenon_Hc4. % 18.45/18.68 cut (((op (e1) (e3)) = (e1)) = ((op (e1) (e3)) = (op (e3) (e3)))). % 18.45/18.68 intro zenon_D_pnotp. % 18.45/18.68 apply zenon_Hd5. % 18.45/18.68 rewrite <- zenon_D_pnotp. % 18.45/18.68 exact zenon_Hd6. % 18.45/18.68 cut (((e1) = (op (e3) (e3)))); [idtac | apply NNPP; zenon_intro zenon_Hc5]. % 18.45/18.68 cut (((op (e1) (e3)) = (op (e1) (e3)))); [idtac | apply NNPP; zenon_intro zenon_H59]. % 18.45/18.68 congruence. % 18.45/18.68 apply zenon_H59. apply refl_equal. % 18.45/18.68 apply zenon_Hc5. apply sym_equal. exact zenon_Hc4. % 18.45/18.68 (* end of lemma zenon_L50_ *) % 18.45/18.68 assert (zenon_L51_ : ((op (e1) (e3)) = (e2)) -> ((op (e1) (e0)) = (e2)) -> (~((op (e1) (e0)) = (op (e1) (e3)))) -> False). % 18.45/18.68 do 0 intro. intros zenon_Hd7 zenon_H86 zenon_Hd8. % 18.45/18.68 elim (classic ((op (e1) (e3)) = (op (e1) (e3)))); [ zenon_intro zenon_H58 | zenon_intro zenon_H59 ]. % 18.45/18.68 cut (((op (e1) (e3)) = (op (e1) (e3))) = ((op (e1) (e0)) = (op (e1) (e3)))). % 18.45/18.68 intro zenon_D_pnotp. % 18.45/18.68 apply zenon_Hd8. % 18.45/18.68 rewrite <- zenon_D_pnotp. % 18.45/18.68 exact zenon_H58. % 18.45/18.68 cut (((op (e1) (e3)) = (op (e1) (e3)))); [idtac | apply NNPP; zenon_intro zenon_H59]. % 18.45/18.68 cut (((op (e1) (e3)) = (op (e1) (e0)))); [idtac | apply NNPP; zenon_intro zenon_Hd9]. % 18.45/18.68 congruence. % 18.45/18.68 cut (((op (e1) (e3)) = (e2)) = ((op (e1) (e3)) = (op (e1) (e0)))). % 18.45/18.68 intro zenon_D_pnotp. % 18.45/18.68 apply zenon_Hd9. % 18.45/18.68 rewrite <- zenon_D_pnotp. % 18.45/18.68 exact zenon_Hd7. % 18.45/18.68 cut (((e2) = (op (e1) (e0)))); [idtac | apply NNPP; zenon_intro zenon_Hda]. % 18.45/18.68 cut (((op (e1) (e3)) = (op (e1) (e3)))); [idtac | apply NNPP; zenon_intro zenon_H59]. % 18.45/18.68 congruence. % 18.45/18.68 apply zenon_H59. apply refl_equal. % 18.45/18.68 apply zenon_Hda. apply sym_equal. exact zenon_H86. % 18.45/18.68 apply zenon_H59. apply refl_equal. % 18.45/18.68 apply zenon_H59. apply refl_equal. % 18.45/18.68 (* end of lemma zenon_L51_ *) % 18.45/18.68 assert (zenon_L52_ : (~((op (e1) (e3)) = (op (e2) (e3)))) -> ((op (e1) (e3)) = (e3)) -> ((op (e2) (e3)) = (e3)) -> False). % 18.45/18.68 do 0 intro. intros zenon_Hdb zenon_Hdc zenon_Hdd. % 18.45/18.68 cut (((op (e1) (e3)) = (e3)) = ((op (e1) (e3)) = (op (e2) (e3)))). % 18.45/18.68 intro zenon_D_pnotp. % 18.45/18.68 apply zenon_Hdb. % 18.45/18.68 rewrite <- zenon_D_pnotp. % 18.45/18.68 exact zenon_Hdc. % 18.45/18.68 cut (((e3) = (op (e2) (e3)))); [idtac | apply NNPP; zenon_intro zenon_Hde]. % 18.45/18.68 cut (((op (e1) (e3)) = (op (e1) (e3)))); [idtac | apply NNPP; zenon_intro zenon_H59]. % 18.45/18.68 congruence. % 18.45/18.68 apply zenon_H59. apply refl_equal. % 18.45/18.68 apply zenon_Hde. apply sym_equal. exact zenon_Hdd. % 18.45/18.68 (* end of lemma zenon_L52_ *) % 18.45/18.68 assert (zenon_L53_ : (((op (e1) (e3)) = (e0))\/(((op (e1) (e3)) = (e1))\/(((op (e1) (e3)) = (e2))\/((op (e1) (e3)) = (e3))))) -> ((op (e0) (e3)) = (e2)) -> ((op (e3) (e3)) = (e1)) -> (~((op (e1) (e3)) = (op (e3) (e3)))) -> (~((op (e1) (e0)) = (op (e1) (e3)))) -> ((op (e1) (e0)) = (e2)) -> (~((op (e1) (e3)) = (op (e2) (e3)))) -> ((op (e2) (e3)) = (e3)) -> False). % 18.45/18.68 do 0 intro. intros zenon_Hdf zenon_Hcd zenon_Hc4 zenon_Hd5 zenon_Hd8 zenon_H86 zenon_Hdb zenon_Hdd. % 18.45/18.68 apply (zenon_or_s _ _ zenon_Hdf); [ zenon_intro zenon_H1f | zenon_intro zenon_He0 ]. % 18.45/18.68 apply (zenon_L49_); trivial. % 18.45/18.68 apply (zenon_or_s _ _ zenon_He0); [ zenon_intro zenon_Hd6 | zenon_intro zenon_He1 ]. % 18.45/18.68 apply (zenon_L50_); trivial. % 18.45/18.68 apply (zenon_or_s _ _ zenon_He1); [ zenon_intro zenon_Hd7 | zenon_intro zenon_Hdc ]. % 18.45/18.68 apply (zenon_L51_); trivial. % 18.45/18.68 apply (zenon_L52_); trivial. % 18.45/18.68 (* end of lemma zenon_L53_ *) % 18.45/18.68 assert (zenon_L54_ : (~((op (e0) (e3)) = (op (e2) (e3)))) -> ((op (e0) (e3)) = (e3)) -> ((op (e2) (e3)) = (e3)) -> False). % 18.45/18.68 do 0 intro. intros zenon_He2 zenon_He3 zenon_Hdd. % 18.45/18.68 cut (((op (e0) (e3)) = (e3)) = ((op (e0) (e3)) = (op (e2) (e3)))). % 18.45/18.68 intro zenon_D_pnotp. % 18.45/18.68 apply zenon_He2. % 18.45/18.68 rewrite <- zenon_D_pnotp. % 18.45/18.68 exact zenon_He3. % 18.45/18.68 cut (((e3) = (op (e2) (e3)))); [idtac | apply NNPP; zenon_intro zenon_Hde]. % 18.45/18.68 cut (((op (e0) (e3)) = (op (e0) (e3)))); [idtac | apply NNPP; zenon_intro zenon_H21]. % 18.45/18.68 congruence. % 18.45/18.68 apply zenon_H21. apply refl_equal. % 18.45/18.68 apply zenon_Hde. apply sym_equal. exact zenon_Hdd. % 18.45/18.68 (* end of lemma zenon_L54_ *) % 18.45/18.68 assert (zenon_L55_ : (((op (e0) (e3)) = (e0))\/(((op (e0) (e3)) = (e1))\/(((op (e0) (e3)) = (e2))\/((op (e0) (e3)) = (e3))))) -> (~((op (e0) (e3)) = (e0))) -> (~((op (e0) (e3)) = (op (e3) (e3)))) -> (~((op (e1) (e3)) = (op (e2) (e3)))) -> ((op (e1) (e0)) = (e2)) -> (~((op (e1) (e0)) = (op (e1) (e3)))) -> (~((op (e1) (e3)) = (op (e3) (e3)))) -> ((op (e3) (e3)) = (e1)) -> (((op (e1) (e3)) = (e0))\/(((op (e1) (e3)) = (e1))\/(((op (e1) (e3)) = (e2))\/((op (e1) (e3)) = (e3))))) -> (~((op (e0) (e3)) = (op (e2) (e3)))) -> ((op (e2) (e3)) = (e3)) -> False). % 18.45/18.68 do 0 intro. intros zenon_He4 zenon_H76 zenon_Hc2 zenon_Hdb zenon_H86 zenon_Hd8 zenon_Hd5 zenon_Hc4 zenon_Hdf zenon_He2 zenon_Hdd. % 18.45/18.68 apply (zenon_or_s _ _ zenon_He4); [ zenon_intro zenon_H1e | zenon_intro zenon_He5 ]. % 18.45/18.68 exact (zenon_H76 zenon_H1e). % 18.45/18.68 apply (zenon_or_s _ _ zenon_He5); [ zenon_intro zenon_Hc3 | zenon_intro zenon_He6 ]. % 18.45/18.68 apply (zenon_L46_); trivial. % 18.45/18.68 apply (zenon_or_s _ _ zenon_He6); [ zenon_intro zenon_Hcd | zenon_intro zenon_He3 ]. % 18.45/18.68 apply (zenon_L53_); trivial. % 18.45/18.68 apply (zenon_L54_); trivial. % 18.45/18.68 (* end of lemma zenon_L55_ *) % 18.45/18.68 assert (zenon_L56_ : (((op (e2) (e0)) = (e3))\/(((op (e2) (e1)) = (e3))\/(((op (e2) (e2)) = (e3))\/((op (e2) (e3)) = (e3))))) -> ((op (e0) (e0)) = (e1)) -> (~((e1) = (e3))) -> (~((op (e0) (e2)) = (op (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 (e2) (e1)) = (op (e3) (e1)))) -> ((op (e2) (e1)) = (e1)) -> ((op (e2) (e2)) = (e0)) -> ((op (e0) (e2)) = (e3)) -> (((op (e0) (e3)) = (e0))\/(((op (e0) (e3)) = (e1))\/(((op (e0) (e3)) = (e2))\/((op (e0) (e3)) = (e3))))) -> (~((op (e0) (e3)) = (e0))) -> (~((op (e0) (e3)) = (op (e3) (e3)))) -> (~((op (e1) (e3)) = (op (e2) (e3)))) -> ((op (e1) (e0)) = (e2)) -> (~((op (e1) (e0)) = (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) (e3)) = (op (e2) (e3)))) -> False). % 18.45/18.68 do 0 intro. intros zenon_He7 zenon_H7a zenon_H95 zenon_Ha8 zenon_He8 zenon_Ha1 zenon_H44 zenon_Haf zenon_Ha5 zenon_H2c zenon_Ha9 zenon_He4 zenon_H76 zenon_Hc2 zenon_Hdb zenon_H86 zenon_Hd8 zenon_Hd5 zenon_Hdf zenon_He2. % 18.45/18.68 apply (zenon_or_s _ _ zenon_He7); [ zenon_intro zenon_H3b | zenon_intro zenon_He9 ]. % 18.45/18.68 apply (zenon_L33_); trivial. % 18.45/18.68 apply (zenon_or_s _ _ zenon_He9); [ zenon_intro zenon_Ha6 | zenon_intro zenon_Hea ]. % 18.45/18.68 apply (zenon_L39_); trivial. % 18.45/18.68 apply (zenon_or_s _ _ zenon_Hea); [ zenon_intro zenon_Haa | zenon_intro zenon_Hdd ]. % 18.45/18.68 apply (zenon_L40_); trivial. % 18.45/18.68 apply (zenon_or_s _ _ zenon_He8); [ zenon_intro zenon_Hac | zenon_intro zenon_Heb ]. % 18.45/18.68 apply (zenon_L41_); trivial. % 18.45/18.68 apply (zenon_or_s _ _ zenon_Heb); [ zenon_intro zenon_Hae | zenon_intro zenon_Hec ]. % 18.45/18.68 apply (zenon_L42_); trivial. % 18.45/18.68 apply (zenon_or_s _ _ zenon_Hec); [ zenon_intro zenon_Hba | zenon_intro zenon_Hc4 ]. % 18.45/18.68 apply (zenon_L45_); trivial. % 18.45/18.68 apply (zenon_L55_); trivial. % 18.45/18.68 (* end of lemma zenon_L56_ *) % 18.45/18.68 assert (zenon_L57_ : (((op (e2) (e0)) = (e0))\/(((op (e2) (e1)) = (e0))\/(((op (e2) (e2)) = (e0))\/((op (e2) (e3)) = (e0))))) -> (~((op (e2) (e0)) = (e0))) -> (~((op (e2) (e1)) = (e0))) -> (~((op (e0) (e3)) = (op (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 (e1) (e0)) = (op (e1) (e3)))) -> ((op (e1) (e0)) = (e2)) -> (~((op (e1) (e3)) = (op (e2) (e3)))) -> (~((op (e0) (e3)) = (op (e3) (e3)))) -> (~((op (e0) (e3)) = (e0))) -> (((op (e0) (e3)) = (e0))\/(((op (e0) (e3)) = (e1))\/(((op (e0) (e3)) = (e2))\/((op (e0) (e3)) = (e3))))) -> ((op (e0) (e2)) = (e3)) -> ((op (e2) (e1)) = (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) (e2)) = (op (e2) (e2)))) -> (~((e1) = (e3))) -> ((op (e0) (e0)) = (e1)) -> (((op (e2) (e0)) = (e3))\/(((op (e2) (e1)) = (e3))\/(((op (e2) (e2)) = (e3))\/((op (e2) (e3)) = (e3))))) -> (~((op (e2) (e3)) = (e0))) -> False). % 18.45/18.68 do 0 intro. intros zenon_H2f zenon_H30 zenon_H31 zenon_He2 zenon_Hdf zenon_Hd5 zenon_Hd8 zenon_H86 zenon_Hdb zenon_Hc2 zenon_H76 zenon_He4 zenon_Ha9 zenon_Ha5 zenon_Haf zenon_H44 zenon_Ha1 zenon_He8 zenon_Ha8 zenon_H95 zenon_H7a zenon_He7 zenon_H32. % 18.45/18.68 apply (zenon_or_s _ _ zenon_H2f); [ zenon_intro zenon_H34 | zenon_intro zenon_H33 ]. % 18.45/18.68 exact (zenon_H30 zenon_H34). % 18.45/18.68 apply (zenon_or_s _ _ zenon_H33); [ zenon_intro zenon_H36 | zenon_intro zenon_H35 ]. % 18.45/18.68 exact (zenon_H31 zenon_H36). % 18.45/18.68 apply (zenon_or_s _ _ zenon_H35); [ zenon_intro zenon_H2c | zenon_intro zenon_H37 ]. % 18.45/18.68 apply (zenon_L56_); trivial. % 18.45/18.68 exact (zenon_H32 zenon_H37). % 18.45/18.68 (* end of lemma zenon_L57_ *) % 18.45/18.68 assert (zenon_L58_ : ((op (e2) (e0)) = (e1)) -> ((op (e2) (e0)) = (e2)) -> (~((e1) = (e2))) -> False). % 18.45/18.68 do 0 intro. intros zenon_Hed zenon_Hee zenon_H7c. % 18.45/18.68 elim (classic ((e2) = (e2))); [ zenon_intro zenon_H7d | zenon_intro zenon_H7e ]. % 18.45/18.68 cut (((e2) = (e2)) = ((e1) = (e2))). % 18.45/18.68 intro zenon_D_pnotp. % 18.45/18.68 apply zenon_H7c. % 18.45/18.68 rewrite <- zenon_D_pnotp. % 18.45/18.68 exact zenon_H7d. % 18.45/18.68 cut (((e2) = (e2))); [idtac | apply NNPP; zenon_intro zenon_H7e]. % 18.45/18.68 cut (((e2) = (e1))); [idtac | apply NNPP; zenon_intro zenon_H7f]. % 18.45/18.68 congruence. % 18.45/18.68 cut (((op (e2) (e0)) = (e1)) = ((e2) = (e1))). % 18.45/18.68 intro zenon_D_pnotp. % 18.45/18.68 apply zenon_H7f. % 18.45/18.68 rewrite <- zenon_D_pnotp. % 18.45/18.68 exact zenon_Hed. % 18.45/18.68 cut (((e1) = (e1))); [idtac | apply NNPP; zenon_intro zenon_H79]. % 18.45/18.68 cut (((op (e2) (e0)) = (e2))); [idtac | apply NNPP; zenon_intro zenon_Hef]. % 18.45/18.68 congruence. % 18.45/18.68 exact (zenon_Hef zenon_Hee). % 18.45/18.68 apply zenon_H79. apply refl_equal. % 18.45/18.68 apply zenon_H7e. apply refl_equal. % 18.45/18.68 apply zenon_H7e. apply refl_equal. % 18.45/18.68 (* end of lemma zenon_L58_ *) % 18.45/18.68 assert (zenon_L59_ : (~((op (e1) (e2)) = (op (e2) (e2)))) -> ((op (e1) (e2)) = (e1)) -> ((op (e2) (e2)) = (e1)) -> False). % 18.45/18.68 do 0 intro. intros zenon_H2b zenon_Hf0 zenon_Hf1. % 18.45/18.68 cut (((op (e1) (e2)) = (e1)) = ((op (e1) (e2)) = (op (e2) (e2)))). % 18.45/18.68 intro zenon_D_pnotp. % 18.45/18.68 apply zenon_H2b. % 18.45/18.68 rewrite <- zenon_D_pnotp. % 18.45/18.68 exact zenon_Hf0. % 18.45/18.68 cut (((e1) = (op (e2) (e2)))); [idtac | apply NNPP; zenon_intro zenon_Hf2]. % 18.45/18.68 cut (((op (e1) (e2)) = (op (e1) (e2)))); [idtac | apply NNPP; zenon_intro zenon_H2e]. % 18.45/18.68 congruence. % 18.45/18.68 apply zenon_H2e. apply refl_equal. % 18.45/18.68 apply zenon_Hf2. apply sym_equal. exact zenon_Hf1. % 18.45/18.68 (* end of lemma zenon_L59_ *) % 18.45/18.68 assert (zenon_L60_ : (~((op (e2) (e3)) = (op (e3) (e3)))) -> ((op (e2) (e3)) = (e1)) -> ((op (e3) (e3)) = (e1)) -> False). % 18.45/18.68 do 0 intro. intros zenon_Hf3 zenon_Hf4 zenon_Hc4. % 18.45/18.68 cut (((op (e2) (e3)) = (e1)) = ((op (e2) (e3)) = (op (e3) (e3)))). % 18.45/18.68 intro zenon_D_pnotp. % 18.45/18.68 apply zenon_Hf3. % 18.45/18.68 rewrite <- zenon_D_pnotp. % 18.45/18.68 exact zenon_Hf4. % 18.45/18.68 cut (((e1) = (op (e3) (e3)))); [idtac | apply NNPP; zenon_intro zenon_Hc5]. % 18.45/18.68 cut (((op (e2) (e3)) = (op (e2) (e3)))); [idtac | apply NNPP; zenon_intro zenon_H5d]. % 18.45/18.68 congruence. % 18.45/18.68 apply zenon_H5d. apply refl_equal. % 18.45/18.68 apply zenon_Hc5. apply sym_equal. exact zenon_Hc4. % 18.45/18.68 (* end of lemma zenon_L60_ *) % 18.45/18.68 assert (zenon_L61_ : (~((op (op (e3) (e3)) (e3)) = (op (e2) (e3)))) -> ((op (e3) (e3)) = (e2)) -> False). % 18.45/18.68 do 0 intro. intros zenon_Hf5 zenon_Hf6. % 18.45/18.68 cut (((e3) = (e3))); [idtac | apply NNPP; zenon_intro zenon_H85]. % 18.45/18.68 cut (((op (e3) (e3)) = (e2))); [idtac | apply NNPP; zenon_intro zenon_Hf7]. % 18.45/18.68 congruence. % 18.45/18.68 exact (zenon_Hf7 zenon_Hf6). % 18.45/18.68 apply zenon_H85. apply refl_equal. % 18.45/18.68 (* end of lemma zenon_L61_ *) % 18.45/18.68 assert (zenon_L62_ : ((op (e2) (e3)) = (e1)) -> ((op (e3) (e3)) = (e2)) -> (~((e1) = (op (op (e3) (e3)) (e3)))) -> False). % 18.45/18.68 do 0 intro. intros zenon_Hf4 zenon_Hf6 zenon_Hf8. % 18.45/18.68 elim (classic ((op (op (e3) (e3)) (e3)) = (op (op (e3) (e3)) (e3)))); [ zenon_intro zenon_Hc9 | zenon_intro zenon_Hca ]. % 18.45/18.68 cut (((op (op (e3) (e3)) (e3)) = (op (op (e3) (e3)) (e3))) = ((e1) = (op (op (e3) (e3)) (e3)))). % 18.45/18.68 intro zenon_D_pnotp. % 18.45/18.68 apply zenon_Hf8. % 18.45/18.68 rewrite <- zenon_D_pnotp. % 18.45/18.68 exact zenon_Hc9. % 18.45/18.68 cut (((op (op (e3) (e3)) (e3)) = (op (op (e3) (e3)) (e3)))); [idtac | apply NNPP; zenon_intro zenon_Hca]. % 18.45/18.68 cut (((op (op (e3) (e3)) (e3)) = (e1))); [idtac | apply NNPP; zenon_intro zenon_Hf9]. % 18.45/18.68 congruence. % 18.45/18.68 cut (((op (e2) (e3)) = (e1)) = ((op (op (e3) (e3)) (e3)) = (e1))). % 18.45/18.68 intro zenon_D_pnotp. % 18.45/18.68 apply zenon_Hf9. % 18.45/18.68 rewrite <- zenon_D_pnotp. % 18.45/18.68 exact zenon_Hf4. % 18.45/18.68 cut (((e1) = (e1))); [idtac | apply NNPP; zenon_intro zenon_H79]. % 18.45/18.68 cut (((op (e2) (e3)) = (op (op (e3) (e3)) (e3)))); [idtac | apply NNPP; zenon_intro zenon_Hfa]. % 18.45/18.68 congruence. % 18.45/18.68 elim (classic ((op (op (e3) (e3)) (e3)) = (op (op (e3) (e3)) (e3)))); [ zenon_intro zenon_Hc9 | zenon_intro zenon_Hca ]. % 18.45/18.68 cut (((op (op (e3) (e3)) (e3)) = (op (op (e3) (e3)) (e3))) = ((op (e2) (e3)) = (op (op (e3) (e3)) (e3)))). % 18.45/18.68 intro zenon_D_pnotp. % 18.45/18.68 apply zenon_Hfa. % 18.45/18.68 rewrite <- zenon_D_pnotp. % 18.45/18.68 exact zenon_Hc9. % 18.45/18.68 cut (((op (op (e3) (e3)) (e3)) = (op (op (e3) (e3)) (e3)))); [idtac | apply NNPP; zenon_intro zenon_Hca]. % 18.45/18.68 cut (((op (op (e3) (e3)) (e3)) = (op (e2) (e3)))); [idtac | apply NNPP; zenon_intro zenon_Hf5]. % 18.45/18.68 congruence. % 18.45/18.68 apply (zenon_L61_); trivial. % 18.45/18.68 apply zenon_Hca. apply refl_equal. % 18.45/18.68 apply zenon_Hca. apply refl_equal. % 18.45/18.68 apply zenon_H79. apply refl_equal. % 18.45/18.68 apply zenon_Hca. apply refl_equal. % 18.45/18.68 apply zenon_Hca. apply refl_equal. % 18.45/18.68 (* end of lemma zenon_L62_ *) % 18.45/18.68 assert (zenon_L63_ : ((op (e1) (e3)) = (e0)) -> ((op (e2) (e3)) = (e1)) -> ((op (e3) (e3)) = (e2)) -> False). % 18.45/18.68 do 0 intro. intros zenon_H1f zenon_Hf4 zenon_Hf6. % 18.45/18.68 apply (zenon_notand_s _ _ ax24); [ zenon_intro zenon_Hfc | zenon_intro zenon_Hfb ]. % 18.45/18.68 elim (classic ((op (op (op (e3) (e3)) (e3)) (e3)) = (op (op (op (e3) (e3)) (e3)) (e3)))); [ zenon_intro zenon_Hd0 | zenon_intro zenon_Hd1 ]. % 18.45/18.68 cut (((op (op (op (e3) (e3)) (e3)) (e3)) = (op (op (op (e3) (e3)) (e3)) (e3))) = ((e0) = (op (op (op (e3) (e3)) (e3)) (e3)))). % 18.45/18.68 intro zenon_D_pnotp. % 18.45/18.68 apply zenon_Hfc. % 18.45/18.68 rewrite <- zenon_D_pnotp. % 18.45/18.68 exact zenon_Hd0. % 18.45/18.68 cut (((op (op (op (e3) (e3)) (e3)) (e3)) = (op (op (op (e3) (e3)) (e3)) (e3)))); [idtac | apply NNPP; zenon_intro zenon_Hd1]. % 18.45/18.68 cut (((op (op (op (e3) (e3)) (e3)) (e3)) = (e0))); [idtac | apply NNPP; zenon_intro zenon_Hfd]. % 18.45/18.68 congruence. % 18.45/18.68 cut (((op (e1) (e3)) = (e0)) = ((op (op (op (e3) (e3)) (e3)) (e3)) = (e0))). % 18.45/18.68 intro zenon_D_pnotp. % 18.45/18.68 apply zenon_Hfd. % 18.45/18.68 rewrite <- zenon_D_pnotp. % 18.45/18.68 exact zenon_H1f. % 18.45/18.68 cut (((e0) = (e0))); [idtac | apply NNPP; zenon_intro zenon_H82]. % 18.45/18.68 cut (((op (e1) (e3)) = (op (op (op (e3) (e3)) (e3)) (e3)))); [idtac | apply NNPP; zenon_intro zenon_Hfe]. % 18.45/18.68 congruence. % 18.45/18.68 elim (classic ((op (op (op (e3) (e3)) (e3)) (e3)) = (op (op (op (e3) (e3)) (e3)) (e3)))); [ zenon_intro zenon_Hd0 | zenon_intro zenon_Hd1 ]. % 18.45/18.68 cut (((op (op (op (e3) (e3)) (e3)) (e3)) = (op (op (op (e3) (e3)) (e3)) (e3))) = ((op (e1) (e3)) = (op (op (op (e3) (e3)) (e3)) (e3)))). % 18.45/18.68 intro zenon_D_pnotp. % 18.45/18.68 apply zenon_Hfe. % 18.45/18.68 rewrite <- zenon_D_pnotp. % 18.45/18.68 exact zenon_Hd0. % 18.45/18.68 cut (((op (op (op (e3) (e3)) (e3)) (e3)) = (op (op (op (e3) (e3)) (e3)) (e3)))); [idtac | apply NNPP; zenon_intro zenon_Hd1]. % 18.45/18.68 cut (((op (op (op (e3) (e3)) (e3)) (e3)) = (op (e1) (e3)))); [idtac | apply NNPP; zenon_intro zenon_Hff]. % 18.45/18.68 congruence. % 18.45/18.68 cut (((e3) = (e3))); [idtac | apply NNPP; zenon_intro zenon_H85]. % 18.45/18.68 cut (((op (op (e3) (e3)) (e3)) = (e1))); [idtac | apply NNPP; zenon_intro zenon_Hf9]. % 18.45/18.68 congruence. % 18.45/18.68 cut (((op (e2) (e3)) = (e1)) = ((op (op (e3) (e3)) (e3)) = (e1))). % 18.45/18.68 intro zenon_D_pnotp. % 18.45/18.68 apply zenon_Hf9. % 18.45/18.68 rewrite <- zenon_D_pnotp. % 18.45/18.68 exact zenon_Hf4. % 18.45/18.68 cut (((e1) = (e1))); [idtac | apply NNPP; zenon_intro zenon_H79]. % 18.45/18.68 cut (((op (e2) (e3)) = (op (op (e3) (e3)) (e3)))); [idtac | apply NNPP; zenon_intro zenon_Hfa]. % 18.45/18.68 congruence. % 18.45/18.68 elim (classic ((op (op (e3) (e3)) (e3)) = (op (op (e3) (e3)) (e3)))); [ zenon_intro zenon_Hc9 | zenon_intro zenon_Hca ]. % 18.45/18.68 cut (((op (op (e3) (e3)) (e3)) = (op (op (e3) (e3)) (e3))) = ((op (e2) (e3)) = (op (op (e3) (e3)) (e3)))). % 18.45/18.68 intro zenon_D_pnotp. % 18.45/18.68 apply zenon_Hfa. % 18.45/18.68 rewrite <- zenon_D_pnotp. % 18.45/18.68 exact zenon_Hc9. % 18.45/18.68 cut (((op (op (e3) (e3)) (e3)) = (op (op (e3) (e3)) (e3)))); [idtac | apply NNPP; zenon_intro zenon_Hca]. % 18.45/18.68 cut (((op (op (e3) (e3)) (e3)) = (op (e2) (e3)))); [idtac | apply NNPP; zenon_intro zenon_Hf5]. % 18.45/18.68 congruence. % 18.45/18.68 apply (zenon_L61_); trivial. % 18.45/18.68 apply zenon_Hca. apply refl_equal. % 18.45/18.68 apply zenon_Hca. apply refl_equal. % 18.45/18.68 apply zenon_H79. apply refl_equal. % 18.45/18.68 apply zenon_H85. apply refl_equal. % 18.45/18.68 apply zenon_Hd1. apply refl_equal. % 18.45/18.68 apply zenon_Hd1. apply refl_equal. % 18.45/18.68 apply zenon_H82. apply refl_equal. % 18.45/18.68 apply zenon_Hd1. apply refl_equal. % 18.45/18.68 apply zenon_Hd1. apply refl_equal. % 18.45/18.68 apply (zenon_notand_s _ _ zenon_Hfb); [ zenon_intro zenon_Hf8 | zenon_intro zenon_H100 ]. % 18.45/18.68 apply (zenon_L62_); trivial. % 18.45/18.68 apply zenon_H100. apply sym_equal. exact zenon_Hf6. % 18.45/18.68 (* end of lemma zenon_L63_ *) % 18.45/18.68 assert (zenon_L64_ : (((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 (e2) (e3)) = (op (e3) (e3)))) -> ((op (e2) (e3)) = (e1)) -> ((op (e1) (e3)) = (e0)) -> (~((op (e3) (e3)) = (e3))) -> False). % 18.45/18.68 do 0 intro. intros zenon_H101 zenon_H71 zenon_H44 zenon_Hf3 zenon_Hf4 zenon_H1f zenon_H102. % 18.45/18.68 apply (zenon_or_s _ _ zenon_H101); [ zenon_intro zenon_H60 | zenon_intro zenon_H103 ]. % 18.45/18.68 apply (zenon_L21_); trivial. % 18.45/18.68 apply (zenon_or_s _ _ zenon_H103); [ zenon_intro zenon_Hc4 | zenon_intro zenon_H104 ]. % 18.45/18.68 apply (zenon_L60_); trivial. % 18.45/18.68 apply (zenon_or_s _ _ zenon_H104); [ zenon_intro zenon_Hf6 | zenon_intro zenon_H105 ]. % 18.45/18.68 apply (zenon_L63_); trivial. % 18.45/18.68 exact (zenon_H102 zenon_H105). % 18.45/18.68 (* end of lemma zenon_L64_ *) % 18.45/18.68 assert (zenon_L65_ : (((op (e2) (e0)) = (e1))\/(((op (e2) (e1)) = (e1))\/(((op (e2) (e2)) = (e1))\/((op (e2) (e3)) = (e1))))) -> (~((e1) = (e2))) -> ((op (e2) (e0)) = (e2)) -> (~((op (e2) (e1)) = (op (e3) (e1)))) -> ((op (e3) (e1)) = (e1)) -> ((op (e1) (e2)) = (e1)) -> (~((op (e1) (e2)) = (op (e2) (e2)))) -> (((op (e3) (e3)) = (e0))\/(((op (e3) (e3)) = (e1))\/(((op (e3) (e3)) = (e2))\/((op (e3) (e3)) = (e3))))) -> (~((op (e3) (e0)) = (op (e3) (e3)))) -> ((op (e3) (e0)) = (e0)) -> (~((op (e2) (e3)) = (op (e3) (e3)))) -> ((op (e1) (e3)) = (e0)) -> (~((op (e3) (e3)) = (e3))) -> False). % 18.45/18.68 do 0 intro. intros zenon_H106 zenon_H7c zenon_Hee zenon_Haf zenon_Hae zenon_Hf0 zenon_H2b zenon_H101 zenon_H71 zenon_H44 zenon_Hf3 zenon_H1f zenon_H102. % 18.45/18.68 apply (zenon_or_s _ _ zenon_H106); [ zenon_intro zenon_Hed | zenon_intro zenon_H107 ]. % 18.45/18.68 apply (zenon_L58_); trivial. % 18.45/18.68 apply (zenon_or_s _ _ zenon_H107); [ zenon_intro zenon_Ha5 | zenon_intro zenon_H108 ]. % 18.45/18.68 apply (zenon_L42_); trivial. % 18.45/18.68 apply (zenon_or_s _ _ zenon_H108); [ zenon_intro zenon_Hf1 | zenon_intro zenon_Hf4 ]. % 18.45/18.68 apply (zenon_L59_); trivial. % 18.45/18.68 apply (zenon_L64_); trivial. % 18.45/18.68 (* end of lemma zenon_L65_ *) % 18.45/18.68 assert (zenon_L66_ : (((op (e0) (e1)) = (e1))\/(((op (e1) (e1)) = (e1))\/(((op (e2) (e1)) = (e1))\/((op (e3) (e1)) = (e1))))) -> ((op (e0) (e1)) = (e0)) -> (~((op (e1) (e1)) = (e1))) -> (~((op (e2) (e3)) = (e0))) -> (((op (e2) (e0)) = (e3))\/(((op (e2) (e1)) = (e3))\/(((op (e2) (e2)) = (e3))\/((op (e2) (e3)) = (e3))))) -> ((op (e0) (e0)) = (e1)) -> (~((e1) = (e3))) -> (~((op (e0) (e2)) = (op (e2) (e2)))) -> (((op (e3) (e0)) = (e1))\/(((op (e3) (e1)) = (e1))\/(((op (e3) (e2)) = (e1))\/((op (e3) (e3)) = (e1))))) -> (~((e0) = (e1))) -> ((op (e0) (e2)) = (e3)) -> (((op (e0) (e3)) = (e0))\/(((op (e0) (e3)) = (e1))\/(((op (e0) (e3)) = (e2))\/((op (e0) (e3)) = (e3))))) -> (~((op (e0) (e3)) = (e0))) -> (~((op (e0) (e3)) = (op (e3) (e3)))) -> (~((op (e1) (e3)) = (op (e2) (e3)))) -> ((op (e1) (e0)) = (e2)) -> (~((op (e1) (e0)) = (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) (e3)) = (op (e2) (e3)))) -> (~((op (e2) (e1)) = (e0))) -> (~((op (e2) (e0)) = (e0))) -> (((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) = (e2))) -> ((op (e2) (e0)) = (e2)) -> (~((op (e2) (e1)) = (op (e3) (e1)))) -> ((op (e1) (e2)) = (e1)) -> (~((op (e1) (e2)) = (op (e2) (e2)))) -> (((op (e3) (e3)) = (e0))\/(((op (e3) (e3)) = (e1))\/(((op (e3) (e3)) = (e2))\/((op (e3) (e3)) = (e3))))) -> (~((op (e3) (e0)) = (op (e3) (e3)))) -> ((op (e3) (e0)) = (e0)) -> (~((op (e2) (e3)) = (op (e3) (e3)))) -> ((op (e1) (e3)) = (e0)) -> (~((op (e3) (e3)) = (e3))) -> False). % 18.45/18.68 do 0 intro. intros zenon_H109 zenon_H49 zenon_H10a zenon_H32 zenon_He7 zenon_H7a zenon_H95 zenon_Ha8 zenon_He8 zenon_Ha1 zenon_Ha9 zenon_He4 zenon_H76 zenon_Hc2 zenon_Hdb zenon_H86 zenon_Hd8 zenon_Hd5 zenon_Hdf zenon_He2 zenon_H31 zenon_H30 zenon_H2f zenon_H106 zenon_H7c zenon_Hee zenon_Haf zenon_Hf0 zenon_H2b zenon_H101 zenon_H71 zenon_H44 zenon_Hf3 zenon_H1f zenon_H102. % 18.45/18.68 apply (zenon_or_s _ _ zenon_H109); [ zenon_intro zenon_Ha0 | zenon_intro zenon_H10b ]. % 18.45/18.68 apply (zenon_L38_); trivial. % 18.45/18.68 apply (zenon_or_s _ _ zenon_H10b); [ zenon_intro zenon_H10d | zenon_intro zenon_H10c ]. % 18.45/18.68 exact (zenon_H10a zenon_H10d). % 18.45/18.68 apply (zenon_or_s _ _ zenon_H10c); [ zenon_intro zenon_Ha5 | zenon_intro zenon_Hae ]. % 18.45/18.68 apply (zenon_L57_); trivial. % 18.45/18.68 apply (zenon_L65_); trivial. % 18.45/18.68 (* end of lemma zenon_L66_ *) % 18.45/18.68 assert (zenon_L67_ : (~((op (e0) (e1)) = (op (e1) (e1)))) -> ((op (e0) (e1)) = (e2)) -> ((op (e1) (e1)) = (e2)) -> False). % 18.45/18.68 do 0 intro. intros zenon_H10e zenon_H10f zenon_H110. % 18.45/18.68 cut (((op (e0) (e1)) = (e2)) = ((op (e0) (e1)) = (op (e1) (e1)))). % 18.45/18.68 intro zenon_D_pnotp. % 18.45/18.68 apply zenon_H10e. % 18.45/18.68 rewrite <- zenon_D_pnotp. % 18.45/18.68 exact zenon_H10f. % 18.45/18.68 cut (((e2) = (op (e1) (e1)))); [idtac | apply NNPP; zenon_intro zenon_H111]. % 18.45/18.68 cut (((op (e0) (e1)) = (op (e0) (e1)))); [idtac | apply NNPP; zenon_intro zenon_H112]. % 18.45/18.68 congruence. % 18.45/18.68 apply zenon_H112. apply refl_equal. % 18.45/18.68 apply zenon_H111. apply sym_equal. exact zenon_H110. % 18.45/18.68 (* end of lemma zenon_L67_ *) % 18.45/18.68 assert (zenon_L68_ : ((op (e1) (e2)) = (e1)) -> ((op (e1) (e2)) = (e2)) -> (~((e1) = (e2))) -> False). % 18.45/18.68 do 0 intro. intros zenon_Hf0 zenon_H113 zenon_H7c. % 18.45/18.68 elim (classic ((e2) = (e2))); [ zenon_intro zenon_H7d | zenon_intro zenon_H7e ]. % 18.45/18.68 cut (((e2) = (e2)) = ((e1) = (e2))). % 18.45/18.68 intro zenon_D_pnotp. % 18.45/18.68 apply zenon_H7c. % 18.45/18.68 rewrite <- zenon_D_pnotp. % 18.45/18.68 exact zenon_H7d. % 18.45/18.68 cut (((e2) = (e2))); [idtac | apply NNPP; zenon_intro zenon_H7e]. % 18.45/18.68 cut (((e2) = (e1))); [idtac | apply NNPP; zenon_intro zenon_H7f]. % 18.45/18.68 congruence. % 18.45/18.68 cut (((op (e1) (e2)) = (e1)) = ((e2) = (e1))). % 18.45/18.68 intro zenon_D_pnotp. % 18.45/18.68 apply zenon_H7f. % 18.45/18.68 rewrite <- zenon_D_pnotp. % 18.45/18.68 exact zenon_Hf0. % 18.45/18.68 cut (((e1) = (e1))); [idtac | apply NNPP; zenon_intro zenon_H79]. % 18.45/18.68 cut (((op (e1) (e2)) = (e2))); [idtac | apply NNPP; zenon_intro zenon_H114]. % 18.45/18.68 congruence. % 18.45/18.68 exact (zenon_H114 zenon_H113). % 18.45/18.68 apply zenon_H79. apply refl_equal. % 18.45/18.68 apply zenon_H7e. apply refl_equal. % 18.45/18.68 apply zenon_H7e. apply refl_equal. % 18.45/18.68 (* end of lemma zenon_L68_ *) % 18.45/18.68 assert (zenon_L69_ : (~((op (e1) (e2)) = (op (e3) (e2)))) -> ((op (e1) (e2)) = (e1)) -> ((op (e3) (e2)) = (e1)) -> False). % 18.45/18.68 do 0 intro. intros zenon_H115 zenon_Hf0 zenon_Hba. % 18.45/18.68 cut (((op (e1) (e2)) = (e1)) = ((op (e1) (e2)) = (op (e3) (e2)))). % 18.45/18.68 intro zenon_D_pnotp. % 18.45/18.68 apply zenon_H115. % 18.45/18.68 rewrite <- zenon_D_pnotp. % 18.45/18.68 exact zenon_Hf0. % 18.45/18.68 cut (((e1) = (op (e3) (e2)))); [idtac | apply NNPP; zenon_intro zenon_H116]. % 18.45/18.68 cut (((op (e1) (e2)) = (op (e1) (e2)))); [idtac | apply NNPP; zenon_intro zenon_H2e]. % 18.45/18.68 congruence. % 18.45/18.68 apply zenon_H2e. apply refl_equal. % 18.45/18.68 apply zenon_H116. apply sym_equal. exact zenon_Hba. % 18.45/18.68 (* end of lemma zenon_L69_ *) % 18.45/18.68 assert (zenon_L70_ : (~((op (e0) (e3)) = (op (e1) (e3)))) -> ((op (e0) (e3)) = (e2)) -> ((op (e1) (e3)) = (e2)) -> False). % 18.45/18.68 do 0 intro. intros zenon_H1d zenon_Hcd zenon_Hd7. % 18.45/18.68 cut (((op (e0) (e3)) = (e2)) = ((op (e0) (e3)) = (op (e1) (e3)))). % 18.45/18.68 intro zenon_D_pnotp. % 18.45/18.68 apply zenon_H1d. % 18.45/18.68 rewrite <- zenon_D_pnotp. % 18.45/18.68 exact zenon_Hcd. % 18.45/18.68 cut (((e2) = (op (e1) (e3)))); [idtac | apply NNPP; zenon_intro zenon_H117]. % 18.45/18.68 cut (((op (e0) (e3)) = (op (e0) (e3)))); [idtac | apply NNPP; zenon_intro zenon_H21]. % 18.45/18.68 congruence. % 18.45/18.68 apply zenon_H21. apply refl_equal. % 18.45/18.68 apply zenon_H117. apply sym_equal. exact zenon_Hd7. % 18.45/18.68 (* end of lemma zenon_L70_ *) % 18.45/18.68 assert (zenon_L71_ : ((op (e1) (e3)) = (e2)) -> ((op (e3) (e3)) = (e1)) -> (~((e2) = (op (op (e3) (e3)) (e3)))) -> False). % 18.45/18.68 do 0 intro. intros zenon_Hd7 zenon_Hc4 zenon_H118. % 18.52/18.68 elim (classic ((op (op (e3) (e3)) (e3)) = (op (op (e3) (e3)) (e3)))); [ zenon_intro zenon_Hc9 | zenon_intro zenon_Hca ]. % 18.52/18.68 cut (((op (op (e3) (e3)) (e3)) = (op (op (e3) (e3)) (e3))) = ((e2) = (op (op (e3) (e3)) (e3)))). % 18.52/18.68 intro zenon_D_pnotp. % 18.52/18.68 apply zenon_H118. % 18.52/18.68 rewrite <- zenon_D_pnotp. % 18.52/18.68 exact zenon_Hc9. % 18.52/18.68 cut (((op (op (e3) (e3)) (e3)) = (op (op (e3) (e3)) (e3)))); [idtac | apply NNPP; zenon_intro zenon_Hca]. % 18.52/18.68 cut (((op (op (e3) (e3)) (e3)) = (e2))); [idtac | apply NNPP; zenon_intro zenon_H119]. % 18.52/18.68 congruence. % 18.52/18.68 cut (((op (e1) (e3)) = (e2)) = ((op (op (e3) (e3)) (e3)) = (e2))). % 18.52/18.68 intro zenon_D_pnotp. % 18.52/18.68 apply zenon_H119. % 18.52/18.68 rewrite <- zenon_D_pnotp. % 18.52/18.68 exact zenon_Hd7. % 18.52/18.68 cut (((e2) = (e2))); [idtac | apply NNPP; zenon_intro zenon_H7e]. % 18.52/18.68 cut (((op (e1) (e3)) = (op (op (e3) (e3)) (e3)))); [idtac | apply NNPP; zenon_intro zenon_Hcc]. % 18.52/18.68 congruence. % 18.52/18.68 elim (classic ((op (op (e3) (e3)) (e3)) = (op (op (e3) (e3)) (e3)))); [ zenon_intro zenon_Hc9 | zenon_intro zenon_Hca ]. % 18.52/18.68 cut (((op (op (e3) (e3)) (e3)) = (op (op (e3) (e3)) (e3))) = ((op (e1) (e3)) = (op (op (e3) (e3)) (e3)))). % 18.52/18.68 intro zenon_D_pnotp. % 18.52/18.68 apply zenon_Hcc. % 18.52/18.68 rewrite <- zenon_D_pnotp. % 18.52/18.68 exact zenon_Hc9. % 18.52/18.68 cut (((op (op (e3) (e3)) (e3)) = (op (op (e3) (e3)) (e3)))); [idtac | apply NNPP; zenon_intro zenon_Hca]. % 18.52/18.68 cut (((op (op (e3) (e3)) (e3)) = (op (e1) (e3)))); [idtac | apply NNPP; zenon_intro zenon_Hc6]. % 18.52/18.68 congruence. % 18.52/18.68 apply (zenon_L47_); trivial. % 18.52/18.68 apply zenon_Hca. apply refl_equal. % 18.52/18.68 apply zenon_Hca. apply refl_equal. % 18.52/18.68 apply zenon_H7e. apply refl_equal. % 18.52/18.68 apply zenon_Hca. apply refl_equal. % 18.52/18.68 apply zenon_Hca. apply refl_equal. % 18.52/18.68 (* end of lemma zenon_L71_ *) % 18.52/18.68 assert (zenon_L72_ : ((op (e2) (e3)) = (e0)) -> ((op (e1) (e3)) = (e2)) -> ((op (e3) (e3)) = (e1)) -> False). % 18.52/18.68 do 0 intro. intros zenon_H37 zenon_Hd7 zenon_Hc4. % 18.52/18.68 apply (zenon_notand_s _ _ ax25); [ zenon_intro zenon_Hfc | zenon_intro zenon_H11a ]. % 18.52/18.68 elim (classic ((op (op (op (e3) (e3)) (e3)) (e3)) = (op (op (op (e3) (e3)) (e3)) (e3)))); [ zenon_intro zenon_Hd0 | zenon_intro zenon_Hd1 ]. % 18.52/18.68 cut (((op (op (op (e3) (e3)) (e3)) (e3)) = (op (op (op (e3) (e3)) (e3)) (e3))) = ((e0) = (op (op (op (e3) (e3)) (e3)) (e3)))). % 18.52/18.68 intro zenon_D_pnotp. % 18.52/18.68 apply zenon_Hfc. % 18.52/18.68 rewrite <- zenon_D_pnotp. % 18.52/18.68 exact zenon_Hd0. % 18.52/18.68 cut (((op (op (op (e3) (e3)) (e3)) (e3)) = (op (op (op (e3) (e3)) (e3)) (e3)))); [idtac | apply NNPP; zenon_intro zenon_Hd1]. % 18.52/18.68 cut (((op (op (op (e3) (e3)) (e3)) (e3)) = (e0))); [idtac | apply NNPP; zenon_intro zenon_Hfd]. % 18.52/18.68 congruence. % 18.52/18.68 cut (((op (e2) (e3)) = (e0)) = ((op (op (op (e3) (e3)) (e3)) (e3)) = (e0))). % 18.52/18.68 intro zenon_D_pnotp. % 18.52/18.68 apply zenon_Hfd. % 18.52/18.68 rewrite <- zenon_D_pnotp. % 18.52/18.68 exact zenon_H37. % 18.52/18.68 cut (((e0) = (e0))); [idtac | apply NNPP; zenon_intro zenon_H82]. % 18.52/18.68 cut (((op (e2) (e3)) = (op (op (op (e3) (e3)) (e3)) (e3)))); [idtac | apply NNPP; zenon_intro zenon_H11b]. % 18.52/18.68 congruence. % 18.52/18.68 elim (classic ((op (op (op (e3) (e3)) (e3)) (e3)) = (op (op (op (e3) (e3)) (e3)) (e3)))); [ zenon_intro zenon_Hd0 | zenon_intro zenon_Hd1 ]. % 18.52/18.68 cut (((op (op (op (e3) (e3)) (e3)) (e3)) = (op (op (op (e3) (e3)) (e3)) (e3))) = ((op (e2) (e3)) = (op (op (op (e3) (e3)) (e3)) (e3)))). % 18.52/18.68 intro zenon_D_pnotp. % 18.52/18.68 apply zenon_H11b. % 18.52/18.68 rewrite <- zenon_D_pnotp. % 18.52/18.68 exact zenon_Hd0. % 18.52/18.68 cut (((op (op (op (e3) (e3)) (e3)) (e3)) = (op (op (op (e3) (e3)) (e3)) (e3)))); [idtac | apply NNPP; zenon_intro zenon_Hd1]. % 18.52/18.68 cut (((op (op (op (e3) (e3)) (e3)) (e3)) = (op (e2) (e3)))); [idtac | apply NNPP; zenon_intro zenon_H11c]. % 18.52/18.68 congruence. % 18.52/18.68 cut (((e3) = (e3))); [idtac | apply NNPP; zenon_intro zenon_H85]. % 18.52/18.68 cut (((op (op (e3) (e3)) (e3)) = (e2))); [idtac | apply NNPP; zenon_intro zenon_H119]. % 18.52/18.68 congruence. % 18.52/18.68 cut (((op (e1) (e3)) = (e2)) = ((op (op (e3) (e3)) (e3)) = (e2))). % 18.52/18.68 intro zenon_D_pnotp. % 18.52/18.68 apply zenon_H119. % 18.52/18.68 rewrite <- zenon_D_pnotp. % 18.52/18.68 exact zenon_Hd7. % 18.52/18.68 cut (((e2) = (e2))); [idtac | apply NNPP; zenon_intro zenon_H7e]. % 18.52/18.68 cut (((op (e1) (e3)) = (op (op (e3) (e3)) (e3)))); [idtac | apply NNPP; zenon_intro zenon_Hcc]. % 18.52/18.68 congruence. % 18.52/18.68 elim (classic ((op (op (e3) (e3)) (e3)) = (op (op (e3) (e3)) (e3)))); [ zenon_intro zenon_Hc9 | zenon_intro zenon_Hca ]. % 18.52/18.68 cut (((op (op (e3) (e3)) (e3)) = (op (op (e3) (e3)) (e3))) = ((op (e1) (e3)) = (op (op (e3) (e3)) (e3)))). % 18.52/18.68 intro zenon_D_pnotp. % 18.52/18.68 apply zenon_Hcc. % 18.52/18.68 rewrite <- zenon_D_pnotp. % 18.52/18.68 exact zenon_Hc9. % 18.52/18.68 cut (((op (op (e3) (e3)) (e3)) = (op (op (e3) (e3)) (e3)))); [idtac | apply NNPP; zenon_intro zenon_Hca]. % 18.52/18.68 cut (((op (op (e3) (e3)) (e3)) = (op (e1) (e3)))); [idtac | apply NNPP; zenon_intro zenon_Hc6]. % 18.52/18.68 congruence. % 18.52/18.68 apply (zenon_L47_); trivial. % 18.52/18.68 apply zenon_Hca. apply refl_equal. % 18.52/18.68 apply zenon_Hca. apply refl_equal. % 18.52/18.68 apply zenon_H7e. apply refl_equal. % 18.52/18.68 apply zenon_H85. apply refl_equal. % 18.52/18.68 apply zenon_Hd1. apply refl_equal. % 18.52/18.68 apply zenon_Hd1. apply refl_equal. % 18.52/18.68 apply zenon_H82. apply refl_equal. % 18.52/18.68 apply zenon_Hd1. apply refl_equal. % 18.52/18.68 apply zenon_Hd1. apply refl_equal. % 18.52/18.68 apply (zenon_notand_s _ _ zenon_H11a); [ zenon_intro zenon_H118 | zenon_intro zenon_Hc5 ]. % 18.52/18.68 apply (zenon_L71_); trivial. % 18.52/18.68 apply zenon_Hc5. apply sym_equal. exact zenon_Hc4. % 18.52/18.68 (* end of lemma zenon_L72_ *) % 18.52/18.68 assert (zenon_L73_ : ((op (e2) (e3)) = (e2)) -> ((op (e2) (e0)) = (e2)) -> (~((op (e2) (e0)) = (op (e2) (e3)))) -> False). % 18.52/18.68 do 0 intro. intros zenon_H11d zenon_Hee zenon_H5b. % 18.52/18.68 elim (classic ((op (e2) (e3)) = (op (e2) (e3)))); [ zenon_intro zenon_H5c | zenon_intro zenon_H5d ]. % 18.52/18.68 cut (((op (e2) (e3)) = (op (e2) (e3))) = ((op (e2) (e0)) = (op (e2) (e3)))). % 18.52/18.68 intro zenon_D_pnotp. % 18.52/18.68 apply zenon_H5b. % 18.52/18.68 rewrite <- zenon_D_pnotp. % 18.52/18.68 exact zenon_H5c. % 18.52/18.68 cut (((op (e2) (e3)) = (op (e2) (e3)))); [idtac | apply NNPP; zenon_intro zenon_H5d]. % 18.52/18.68 cut (((op (e2) (e3)) = (op (e2) (e0)))); [idtac | apply NNPP; zenon_intro zenon_H5e]. % 18.52/18.68 congruence. % 18.52/18.68 cut (((op (e2) (e3)) = (e2)) = ((op (e2) (e3)) = (op (e2) (e0)))). % 18.52/18.68 intro zenon_D_pnotp. % 18.52/18.68 apply zenon_H5e. % 18.52/18.68 rewrite <- zenon_D_pnotp. % 18.52/18.68 exact zenon_H11d. % 18.52/18.68 cut (((e2) = (op (e2) (e0)))); [idtac | apply NNPP; zenon_intro zenon_H11e]. % 18.52/18.68 cut (((op (e2) (e3)) = (op (e2) (e3)))); [idtac | apply NNPP; zenon_intro zenon_H5d]. % 18.52/18.68 congruence. % 18.52/18.68 apply zenon_H5d. apply refl_equal. % 18.52/18.68 apply zenon_H11e. apply sym_equal. exact zenon_Hee. % 18.52/18.68 apply zenon_H5d. apply refl_equal. % 18.52/18.68 apply zenon_H5d. apply refl_equal. % 18.52/18.68 (* end of lemma zenon_L73_ *) % 18.52/18.68 assert (zenon_L74_ : (((op (e2) (e3)) = (e0))\/(((op (e2) (e3)) = (e1))\/(((op (e2) (e3)) = (e2))\/((op (e2) (e3)) = (e3))))) -> ((op (e1) (e3)) = (e2)) -> ((op (e3) (e3)) = (e1)) -> (~((op (e2) (e3)) = (op (e3) (e3)))) -> (~((op (e2) (e0)) = (op (e2) (e3)))) -> ((op (e2) (e0)) = (e2)) -> (~((op (e0) (e3)) = (op (e2) (e3)))) -> ((op (e0) (e3)) = (e3)) -> False). % 18.52/18.68 do 0 intro. intros zenon_H11f zenon_Hd7 zenon_Hc4 zenon_Hf3 zenon_H5b zenon_Hee zenon_He2 zenon_He3. % 18.52/18.68 apply (zenon_or_s _ _ zenon_H11f); [ zenon_intro zenon_H37 | zenon_intro zenon_H120 ]. % 18.52/18.68 apply (zenon_L72_); trivial. % 18.52/18.68 apply (zenon_or_s _ _ zenon_H120); [ zenon_intro zenon_Hf4 | zenon_intro zenon_H121 ]. % 18.52/18.68 apply (zenon_L60_); trivial. % 18.52/18.68 apply (zenon_or_s _ _ zenon_H121); [ zenon_intro zenon_H11d | zenon_intro zenon_Hdd ]. % 18.52/18.68 apply (zenon_L73_); trivial. % 18.52/18.68 apply (zenon_L54_); trivial. % 18.52/18.68 (* end of lemma zenon_L74_ *) % 18.52/18.68 assert (zenon_L75_ : (((op (e0) (e3)) = (e0))\/(((op (e0) (e3)) = (e1))\/(((op (e0) (e3)) = (e2))\/((op (e0) (e3)) = (e3))))) -> (~((op (e0) (e3)) = (e0))) -> (~((op (e0) (e3)) = (op (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)) = (e2)) -> ((op (e3) (e3)) = (e1)) -> (~((op (e2) (e3)) = (op (e3) (e3)))) -> (~((op (e2) (e0)) = (op (e2) (e3)))) -> ((op (e2) (e0)) = (e2)) -> (~((op (e0) (e3)) = (op (e2) (e3)))) -> False). % 18.52/18.68 do 0 intro. intros zenon_He4 zenon_H76 zenon_Hc2 zenon_H1d zenon_H11f zenon_Hd7 zenon_Hc4 zenon_Hf3 zenon_H5b zenon_Hee zenon_He2. % 18.52/18.68 apply (zenon_or_s _ _ zenon_He4); [ zenon_intro zenon_H1e | zenon_intro zenon_He5 ]. % 18.52/18.68 exact (zenon_H76 zenon_H1e). % 18.52/18.68 apply (zenon_or_s _ _ zenon_He5); [ zenon_intro zenon_Hc3 | zenon_intro zenon_He6 ]. % 18.52/18.68 apply (zenon_L46_); trivial. % 18.52/18.68 apply (zenon_or_s _ _ zenon_He6); [ zenon_intro zenon_Hcd | zenon_intro zenon_He3 ]. % 18.52/18.68 apply (zenon_L70_); trivial. % 18.52/18.68 apply (zenon_L74_); trivial. % 18.52/18.68 (* end of lemma zenon_L75_ *) % 18.52/18.68 assert (zenon_L76_ : (((op (e3) (e0)) = (e1))\/(((op (e3) (e1)) = (e1))\/(((op (e3) (e2)) = (e1))\/((op (e3) (e3)) = (e1))))) -> (~((e0) = (e1))) -> (~((op (e3) (e3)) = (e3))) -> ((op (e1) (e3)) = (e0)) -> ((op (e3) (e0)) = (e0)) -> (~((op (e3) (e0)) = (op (e3) (e3)))) -> (((op (e3) (e3)) = (e0))\/(((op (e3) (e3)) = (e1))\/(((op (e3) (e3)) = (e2))\/((op (e3) (e3)) = (e3))))) -> (~((op (e1) (e2)) = (op (e2) (e2)))) -> (~((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 (e1) (e2)) = (e1)) -> (~((op (e1) (e2)) = (op (e3) (e2)))) -> (((op (e0) (e3)) = (e0))\/(((op (e0) (e3)) = (e1))\/(((op (e0) (e3)) = (e2))\/((op (e0) (e3)) = (e3))))) -> (~((op (e0) (e3)) = (e0))) -> (~((op (e0) (e3)) = (op (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)) = (e2)) -> (~((op (e2) (e3)) = (op (e3) (e3)))) -> (~((op (e2) (e0)) = (op (e2) (e3)))) -> ((op (e2) (e0)) = (e2)) -> (~((op (e0) (e3)) = (op (e2) (e3)))) -> False). % 18.52/18.68 do 0 intro. intros zenon_He8 zenon_Ha1 zenon_H102 zenon_H1f zenon_H44 zenon_H71 zenon_H101 zenon_H2b zenon_Haf zenon_H7c zenon_H106 zenon_Hf0 zenon_H115 zenon_He4 zenon_H76 zenon_Hc2 zenon_H1d zenon_H11f zenon_Hd7 zenon_Hf3 zenon_H5b zenon_Hee zenon_He2. % 18.52/18.68 apply (zenon_or_s _ _ zenon_He8); [ zenon_intro zenon_Hac | zenon_intro zenon_Heb ]. % 18.52/18.68 apply (zenon_L41_); trivial. % 18.52/18.68 apply (zenon_or_s _ _ zenon_Heb); [ zenon_intro zenon_Hae | zenon_intro zenon_Hec ]. % 18.52/18.68 apply (zenon_L65_); trivial. % 18.52/18.68 apply (zenon_or_s _ _ zenon_Hec); [ zenon_intro zenon_Hba | zenon_intro zenon_Hc4 ]. % 18.52/18.68 apply (zenon_L69_); trivial. % 18.52/18.68 apply (zenon_L75_); trivial. % 18.52/18.68 (* end of lemma zenon_L76_ *) % 18.52/18.68 assert (zenon_L77_ : ((op (e0) (e2)) = (e1)) -> ((op (e0) (e2)) = (e3)) -> (~((e1) = (e3))) -> False). % 18.52/18.68 do 0 intro. intros zenon_H122 zenon_Ha9 zenon_H95. % 18.52/18.68 elim (classic ((e3) = (e3))); [ zenon_intro zenon_H96 | zenon_intro zenon_H85 ]. % 18.52/18.68 cut (((e3) = (e3)) = ((e1) = (e3))). % 18.52/18.68 intro zenon_D_pnotp. % 18.52/18.68 apply zenon_H95. % 18.52/18.68 rewrite <- zenon_D_pnotp. % 18.52/18.68 exact zenon_H96. % 18.52/18.68 cut (((e3) = (e3))); [idtac | apply NNPP; zenon_intro zenon_H85]. % 18.52/18.68 cut (((e3) = (e1))); [idtac | apply NNPP; zenon_intro zenon_H97]. % 18.52/18.68 congruence. % 18.52/18.68 cut (((op (e0) (e2)) = (e1)) = ((e3) = (e1))). % 18.52/18.68 intro zenon_D_pnotp. % 18.52/18.68 apply zenon_H97. % 18.52/18.68 rewrite <- zenon_D_pnotp. % 18.52/18.68 exact zenon_H122. % 18.52/18.68 cut (((e1) = (e1))); [idtac | apply NNPP; zenon_intro zenon_H79]. % 18.52/18.68 cut (((op (e0) (e2)) = (e3))); [idtac | apply NNPP; zenon_intro zenon_H123]. % 18.52/18.68 congruence. % 18.52/18.68 exact (zenon_H123 zenon_Ha9). % 18.52/18.68 apply zenon_H79. apply refl_equal. % 18.52/18.68 apply zenon_H85. apply refl_equal. % 18.52/18.68 apply zenon_H85. apply refl_equal. % 18.52/18.68 (* end of lemma zenon_L77_ *) % 18.52/18.68 assert (zenon_L78_ : ((op (e1) (e3)) = (e1)) -> ((op (e1) (e2)) = (e1)) -> (~((op (e1) (e2)) = (op (e1) (e3)))) -> False). % 18.52/18.68 do 0 intro. intros zenon_Hd6 zenon_Hf0 zenon_H124. % 18.52/18.68 elim (classic ((op (e1) (e3)) = (op (e1) (e3)))); [ zenon_intro zenon_H58 | zenon_intro zenon_H59 ]. % 18.52/18.68 cut (((op (e1) (e3)) = (op (e1) (e3))) = ((op (e1) (e2)) = (op (e1) (e3)))). % 18.52/18.68 intro zenon_D_pnotp. % 18.52/18.68 apply zenon_H124. % 18.52/18.68 rewrite <- zenon_D_pnotp. % 18.52/18.68 exact zenon_H58. % 18.52/18.68 cut (((op (e1) (e3)) = (op (e1) (e3)))); [idtac | apply NNPP; zenon_intro zenon_H59]. % 18.52/18.68 cut (((op (e1) (e3)) = (op (e1) (e2)))); [idtac | apply NNPP; zenon_intro zenon_H125]. % 18.52/18.68 congruence. % 18.52/18.68 cut (((op (e1) (e3)) = (e1)) = ((op (e1) (e3)) = (op (e1) (e2)))). % 18.52/18.68 intro zenon_D_pnotp. % 18.52/18.68 apply zenon_H125. % 18.52/18.68 rewrite <- zenon_D_pnotp. % 18.52/18.68 exact zenon_Hd6. % 18.52/18.68 cut (((e1) = (op (e1) (e2)))); [idtac | apply NNPP; zenon_intro zenon_H126]. % 18.52/18.68 cut (((op (e1) (e3)) = (op (e1) (e3)))); [idtac | apply NNPP; zenon_intro zenon_H59]. % 18.52/18.68 congruence. % 18.52/18.68 apply zenon_H59. apply refl_equal. % 18.52/18.68 apply zenon_H126. apply sym_equal. exact zenon_Hf0. % 18.52/18.68 apply zenon_H59. apply refl_equal. % 18.52/18.68 apply zenon_H59. apply refl_equal. % 18.52/18.68 (* end of lemma zenon_L78_ *) % 18.52/18.68 assert (zenon_L79_ : (~((op (e0) (e3)) = (op (e1) (e3)))) -> ((op (e0) (e3)) = (e1)) -> ((op (e1) (e3)) = (e1)) -> False). % 18.52/18.68 do 0 intro. intros zenon_H1d zenon_Hc3 zenon_Hd6. % 18.52/18.68 cut (((op (e0) (e3)) = (e1)) = ((op (e0) (e3)) = (op (e1) (e3)))). % 18.52/18.68 intro zenon_D_pnotp. % 18.52/18.68 apply zenon_H1d. % 18.52/18.68 rewrite <- zenon_D_pnotp. % 18.52/18.68 exact zenon_Hc3. % 18.52/18.68 cut (((e1) = (op (e1) (e3)))); [idtac | apply NNPP; zenon_intro zenon_H127]. % 18.52/18.68 cut (((op (e0) (e3)) = (op (e0) (e3)))); [idtac | apply NNPP; zenon_intro zenon_H21]. % 18.52/18.68 congruence. % 18.52/18.68 apply zenon_H21. apply refl_equal. % 18.52/18.68 apply zenon_H127. apply sym_equal. exact zenon_Hd6. % 18.52/18.68 (* end of lemma zenon_L79_ *) % 18.52/18.68 assert (zenon_L80_ : (((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))) -> ((op (e2) (e2)) = (e1)) -> (~((op (e1) (e2)) = (op (e2) (e2)))) -> (~((op (e0) (e3)) = (op (e1) (e3)))) -> ((op (e0) (e3)) = (e1)) -> False). % 18.52/18.68 do 0 intro. intros zenon_H128 zenon_H95 zenon_H9e zenon_H10a zenon_Hf1 zenon_H2b zenon_H1d zenon_Hc3. % 18.52/18.68 apply (zenon_or_s _ _ zenon_H128); [ zenon_intro zenon_H9d | zenon_intro zenon_H129 ]. % 18.52/18.68 apply (zenon_L37_); trivial. % 18.52/18.68 apply (zenon_or_s _ _ zenon_H129); [ zenon_intro zenon_H10d | zenon_intro zenon_H12a ]. % 18.52/18.68 exact (zenon_H10a zenon_H10d). % 18.52/18.68 apply (zenon_or_s _ _ zenon_H12a); [ zenon_intro zenon_Hf0 | zenon_intro zenon_Hd6 ]. % 18.52/18.68 apply (zenon_L59_); trivial. % 18.52/18.68 apply (zenon_L79_); trivial. % 18.52/18.68 (* end of lemma zenon_L80_ *) % 18.52/18.68 assert (zenon_L81_ : ((op (e0) (e3)) = (e2)) -> ((op (e0) (e3)) = (e3)) -> (~((e2) = (e3))) -> False). % 18.52/18.68 do 0 intro. intros zenon_Hcd zenon_He3 zenon_H12b. % 18.52/18.68 elim (classic ((e3) = (e3))); [ zenon_intro zenon_H96 | zenon_intro zenon_H85 ]. % 18.52/18.68 cut (((e3) = (e3)) = ((e2) = (e3))). % 18.52/18.68 intro zenon_D_pnotp. % 18.52/18.68 apply zenon_H12b. % 18.52/18.68 rewrite <- zenon_D_pnotp. % 18.52/18.68 exact zenon_H96. % 18.52/18.68 cut (((e3) = (e3))); [idtac | apply NNPP; zenon_intro zenon_H85]. % 18.52/18.68 cut (((e3) = (e2))); [idtac | apply NNPP; zenon_intro zenon_H12c]. % 18.52/18.68 congruence. % 18.52/18.68 cut (((op (e0) (e3)) = (e2)) = ((e3) = (e2))). % 18.52/18.68 intro zenon_D_pnotp. % 18.52/18.68 apply zenon_H12c. % 18.52/18.68 rewrite <- zenon_D_pnotp. % 18.52/18.68 exact zenon_Hcd. % 18.52/18.68 cut (((e2) = (e2))); [idtac | apply NNPP; zenon_intro zenon_H7e]. % 18.52/18.68 cut (((op (e0) (e3)) = (e3))); [idtac | apply NNPP; zenon_intro zenon_H12d]. % 18.52/18.68 congruence. % 18.52/18.68 exact (zenon_H12d zenon_He3). % 18.52/18.68 apply zenon_H7e. apply refl_equal. % 18.52/18.68 apply zenon_H85. apply refl_equal. % 18.52/18.68 apply zenon_H85. apply refl_equal. % 18.52/18.68 (* end of lemma zenon_L81_ *) % 18.52/18.68 assert (zenon_L82_ : ((op (e0) (e3)) = (e1)) -> ((op (e0) (e3)) = (e2)) -> (~((e1) = (e2))) -> False). % 18.52/18.68 do 0 intro. intros zenon_Hc3 zenon_Hcd zenon_H7c. % 18.52/18.68 elim (classic ((e2) = (e2))); [ zenon_intro zenon_H7d | zenon_intro zenon_H7e ]. % 18.52/18.68 cut (((e2) = (e2)) = ((e1) = (e2))). % 18.52/18.68 intro zenon_D_pnotp. % 18.52/18.68 apply zenon_H7c. % 18.52/18.68 rewrite <- zenon_D_pnotp. % 18.52/18.68 exact zenon_H7d. % 18.52/18.68 cut (((e2) = (e2))); [idtac | apply NNPP; zenon_intro zenon_H7e]. % 18.52/18.68 cut (((e2) = (e1))); [idtac | apply NNPP; zenon_intro zenon_H7f]. % 18.52/18.68 congruence. % 18.52/18.68 cut (((op (e0) (e3)) = (e1)) = ((e2) = (e1))). % 18.52/18.68 intro zenon_D_pnotp. % 18.52/18.68 apply zenon_H7f. % 18.52/18.68 rewrite <- zenon_D_pnotp. % 18.52/18.68 exact zenon_Hc3. % 18.52/18.68 cut (((e1) = (e1))); [idtac | apply NNPP; zenon_intro zenon_H79]. % 18.52/18.68 cut (((op (e0) (e3)) = (e2))); [idtac | apply NNPP; zenon_intro zenon_H12e]. % 18.52/18.68 congruence. % 18.52/18.68 exact (zenon_H12e zenon_Hcd). % 18.52/18.68 apply zenon_H79. apply refl_equal. % 18.52/18.68 apply zenon_H7e. apply refl_equal. % 18.52/18.68 apply zenon_H7e. apply refl_equal. % 18.52/18.68 (* end of lemma zenon_L82_ *) % 18.52/18.68 assert (zenon_L83_ : ((op (e1) (e3)) = (e1)) -> ((op (e1) (e3)) = (e3)) -> (~((e1) = (e3))) -> False). % 18.52/18.68 do 0 intro. intros zenon_Hd6 zenon_Hdc zenon_H95. % 18.52/18.68 elim (classic ((e3) = (e3))); [ zenon_intro zenon_H96 | zenon_intro zenon_H85 ]. % 18.52/18.68 cut (((e3) = (e3)) = ((e1) = (e3))). % 18.52/18.68 intro zenon_D_pnotp. % 18.52/18.68 apply zenon_H95. % 18.52/18.68 rewrite <- zenon_D_pnotp. % 18.52/18.68 exact zenon_H96. % 18.52/18.68 cut (((e3) = (e3))); [idtac | apply NNPP; zenon_intro zenon_H85]. % 18.52/18.68 cut (((e3) = (e1))); [idtac | apply NNPP; zenon_intro zenon_H97]. % 18.52/18.68 congruence. % 18.52/18.68 cut (((op (e1) (e3)) = (e1)) = ((e3) = (e1))). % 18.52/18.68 intro zenon_D_pnotp. % 18.52/18.68 apply zenon_H97. % 18.52/18.68 rewrite <- zenon_D_pnotp. % 18.52/18.68 exact zenon_Hd6. % 18.52/18.68 cut (((e1) = (e1))); [idtac | apply NNPP; zenon_intro zenon_H79]. % 18.52/18.68 cut (((op (e1) (e3)) = (e3))); [idtac | apply NNPP; zenon_intro zenon_H12f]. % 18.52/18.68 congruence. % 18.52/18.68 exact (zenon_H12f zenon_Hdc). % 18.52/18.68 apply zenon_H79. apply refl_equal. % 18.52/18.68 apply zenon_H85. apply refl_equal. % 18.52/18.68 apply zenon_H85. apply refl_equal. % 18.52/18.68 (* end of lemma zenon_L83_ *) % 18.52/18.68 assert (zenon_L84_ : ((op (e2) (e3)) = (e1)) -> ((op (e2) (e2)) = (e1)) -> (~((op (e2) (e2)) = (op (e2) (e3)))) -> False). % 18.52/18.68 do 0 intro. intros zenon_Hf4 zenon_Hf1 zenon_H6d. % 18.52/18.68 elim (classic ((op (e2) (e3)) = (op (e2) (e3)))); [ zenon_intro zenon_H5c | zenon_intro zenon_H5d ]. % 18.52/18.68 cut (((op (e2) (e3)) = (op (e2) (e3))) = ((op (e2) (e2)) = (op (e2) (e3)))). % 18.52/18.68 intro zenon_D_pnotp. % 18.52/18.68 apply zenon_H6d. % 18.52/18.68 rewrite <- zenon_D_pnotp. % 18.52/18.68 exact zenon_H5c. % 18.52/18.68 cut (((op (e2) (e3)) = (op (e2) (e3)))); [idtac | apply NNPP; zenon_intro zenon_H5d]. % 18.52/18.68 cut (((op (e2) (e3)) = (op (e2) (e2)))); [idtac | apply NNPP; zenon_intro zenon_H6e]. % 18.52/18.68 congruence. % 18.52/18.68 cut (((op (e2) (e3)) = (e1)) = ((op (e2) (e3)) = (op (e2) (e2)))). % 18.52/18.68 intro zenon_D_pnotp. % 18.52/18.68 apply zenon_H6e. % 18.52/18.68 rewrite <- zenon_D_pnotp. % 18.52/18.68 exact zenon_Hf4. % 18.52/18.68 cut (((e1) = (op (e2) (e2)))); [idtac | apply NNPP; zenon_intro zenon_Hf2]. % 18.52/18.68 cut (((op (e2) (e3)) = (op (e2) (e3)))); [idtac | apply NNPP; zenon_intro zenon_H5d]. % 18.52/18.68 congruence. % 18.52/18.68 apply zenon_H5d. apply refl_equal. % 18.52/18.68 apply zenon_Hf2. apply sym_equal. exact zenon_Hf1. % 18.52/18.68 apply zenon_H5d. apply refl_equal. % 18.52/18.68 apply zenon_H5d. apply refl_equal. % 18.52/18.68 (* end of lemma zenon_L84_ *) % 18.52/18.68 assert (zenon_L85_ : ((op (e3) (e3)) = (e1)) -> ((op (e3) (e1)) = (e1)) -> (~((op (e3) (e1)) = (op (e3) (e3)))) -> False). % 18.52/18.68 do 0 intro. intros zenon_Hc4 zenon_Hae zenon_H130. % 18.52/18.68 elim (classic ((op (e3) (e3)) = (op (e3) (e3)))); [ zenon_intro zenon_H63 | zenon_intro zenon_H64 ]. % 18.52/18.68 cut (((op (e3) (e3)) = (op (e3) (e3))) = ((op (e3) (e1)) = (op (e3) (e3)))). % 18.52/18.68 intro zenon_D_pnotp. % 18.52/18.68 apply zenon_H130. % 18.52/18.68 rewrite <- zenon_D_pnotp. % 18.52/18.68 exact zenon_H63. % 18.52/18.68 cut (((op (e3) (e3)) = (op (e3) (e3)))); [idtac | apply NNPP; zenon_intro zenon_H64]. % 18.52/18.68 cut (((op (e3) (e3)) = (op (e3) (e1)))); [idtac | apply NNPP; zenon_intro zenon_H131]. % 18.52/18.68 congruence. % 18.52/18.68 cut (((op (e3) (e3)) = (e1)) = ((op (e3) (e3)) = (op (e3) (e1)))). % 18.52/18.68 intro zenon_D_pnotp. % 18.52/18.68 apply zenon_H131. % 18.52/18.68 rewrite <- zenon_D_pnotp. % 18.52/18.68 exact zenon_Hc4. % 18.52/18.68 cut (((e1) = (op (e3) (e1)))); [idtac | apply NNPP; zenon_intro zenon_H132]. % 18.52/18.68 cut (((op (e3) (e3)) = (op (e3) (e3)))); [idtac | apply NNPP; zenon_intro zenon_H64]. % 18.52/18.68 congruence. % 18.52/18.68 apply zenon_H64. apply refl_equal. % 18.52/18.68 apply zenon_H132. apply sym_equal. exact zenon_Hae. % 18.52/18.68 apply zenon_H64. apply refl_equal. % 18.52/18.68 apply zenon_H64. apply refl_equal. % 18.52/18.68 (* end of lemma zenon_L85_ *) % 18.52/18.68 assert (zenon_L86_ : (((op (e0) (e3)) = (e1))\/(((op (e1) (e3)) = (e1))\/(((op (e2) (e3)) = (e1))\/((op (e3) (e3)) = (e1))))) -> (~((e1) = (e2))) -> ((op (e0) (e3)) = (e2)) -> (~((e1) = (e3))) -> ((op (e1) (e3)) = (e3)) -> (~((op (e2) (e2)) = (op (e2) (e3)))) -> ((op (e2) (e2)) = (e1)) -> ((op (e3) (e1)) = (e1)) -> (~((op (e3) (e1)) = (op (e3) (e3)))) -> False). % 18.52/18.68 do 0 intro. intros zenon_H133 zenon_H7c zenon_Hcd zenon_H95 zenon_Hdc zenon_H6d zenon_Hf1 zenon_Hae zenon_H130. % 18.52/18.68 apply (zenon_or_s _ _ zenon_H133); [ zenon_intro zenon_Hc3 | zenon_intro zenon_H134 ]. % 18.52/18.68 apply (zenon_L82_); trivial. % 18.52/18.68 apply (zenon_or_s _ _ zenon_H134); [ zenon_intro zenon_Hd6 | zenon_intro zenon_H135 ]. % 18.52/18.68 apply (zenon_L83_); trivial. % 18.52/18.68 apply (zenon_or_s _ _ zenon_H135); [ zenon_intro zenon_Hf4 | zenon_intro zenon_Hc4 ]. % 18.52/18.68 apply (zenon_L84_); trivial. % 18.52/18.68 apply (zenon_L85_); trivial. % 18.52/18.68 (* end of lemma zenon_L86_ *) % 18.52/18.68 assert (zenon_L87_ : (~((op (e0) (e3)) = (op (e3) (e3)))) -> ((op (e0) (e3)) = (e2)) -> ((op (e3) (e3)) = (e2)) -> False). % 18.52/18.68 do 0 intro. intros zenon_Hc2 zenon_Hcd zenon_Hf6. % 18.52/18.68 cut (((op (e0) (e3)) = (e2)) = ((op (e0) (e3)) = (op (e3) (e3)))). % 18.52/18.68 intro zenon_D_pnotp. % 18.52/18.68 apply zenon_Hc2. % 18.52/18.68 rewrite <- zenon_D_pnotp. % 18.52/18.68 exact zenon_Hcd. % 18.52/18.68 cut (((e2) = (op (e3) (e3)))); [idtac | apply NNPP; zenon_intro zenon_H100]. % 18.52/18.68 cut (((op (e0) (e3)) = (op (e0) (e3)))); [idtac | apply NNPP; zenon_intro zenon_H21]. % 18.52/18.68 congruence. % 18.52/18.68 apply zenon_H21. apply refl_equal. % 18.52/18.68 apply zenon_H100. apply sym_equal. exact zenon_Hf6. % 18.52/18.68 (* end of lemma zenon_L87_ *) % 18.52/18.68 assert (zenon_L88_ : (((op (e0) (e3)) = (e3))\/(((op (e1) (e3)) = (e3))\/(((op (e2) (e3)) = (e3))\/((op (e3) (e3)) = (e3))))) -> (~((e2) = (e3))) -> (~((op (e3) (e1)) = (op (e3) (e3)))) -> ((op (e3) (e1)) = (e1)) -> ((op (e2) (e2)) = (e1)) -> (~((op (e2) (e2)) = (op (e2) (e3)))) -> (~((e1) = (e3))) -> (~((e1) = (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)) = (e2)) -> (((op (e1) (e3)) = (e0))\/(((op (e1) (e3)) = (e1))\/(((op (e1) (e3)) = (e2))\/((op (e1) (e3)) = (e3))))) -> (~((op (e1) (e3)) = (op (e3) (e3)))) -> (~((op (e1) (e0)) = (op (e1) (e3)))) -> ((op (e1) (e0)) = (e2)) -> (~((op (e1) (e3)) = (op (e2) (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)) = (e3))) -> False). % 18.52/18.68 do 0 intro. intros zenon_H136 zenon_H12b zenon_H130 zenon_Hae zenon_Hf1 zenon_H6d zenon_H95 zenon_H7c zenon_H133 zenon_Hc2 zenon_Hcd zenon_Hdf zenon_Hd5 zenon_Hd8 zenon_H86 zenon_Hdb zenon_H44 zenon_H71 zenon_H101 zenon_H102. % 18.52/18.68 apply (zenon_or_s _ _ zenon_H136); [ zenon_intro zenon_He3 | zenon_intro zenon_H137 ]. % 18.52/18.68 apply (zenon_L81_); trivial. % 18.52/18.68 apply (zenon_or_s _ _ zenon_H137); [ zenon_intro zenon_Hdc | zenon_intro zenon_H138 ]. % 18.52/18.68 apply (zenon_L86_); trivial. % 18.52/18.68 apply (zenon_or_s _ _ zenon_H138); [ zenon_intro zenon_Hdd | zenon_intro zenon_H105 ]. % 18.52/18.68 apply (zenon_or_s _ _ zenon_H101); [ zenon_intro zenon_H60 | zenon_intro zenon_H103 ]. % 18.52/18.68 apply (zenon_L21_); trivial. % 18.52/18.68 apply (zenon_or_s _ _ zenon_H103); [ zenon_intro zenon_Hc4 | zenon_intro zenon_H104 ]. % 18.52/18.68 apply (zenon_L53_); trivial. % 18.52/18.68 apply (zenon_or_s _ _ zenon_H104); [ zenon_intro zenon_Hf6 | zenon_intro zenon_H105 ]. % 18.52/18.68 apply (zenon_L87_); trivial. % 18.52/18.68 exact (zenon_H102 zenon_H105). % 18.52/18.68 exact (zenon_H102 zenon_H105). % 18.52/18.68 (* end of lemma zenon_L88_ *) % 18.52/18.68 assert (zenon_L89_ : (((op (e0) (e3)) = (e0))\/(((op (e0) (e3)) = (e1))\/(((op (e0) (e3)) = (e2))\/((op (e0) (e3)) = (e3))))) -> (~((op (e0) (e3)) = (e0))) -> (~((op (e0) (e3)) = (op (e1) (e3)))) -> (~((op (e1) (e2)) = (op (e2) (e2)))) -> (~((op (e1) (e1)) = (e1))) -> ((op (e1) (e0)) = (e3)) -> (((op (e1) (e0)) = (e1))\/(((op (e1) (e1)) = (e1))\/(((op (e1) (e2)) = (e1))\/((op (e1) (e3)) = (e1))))) -> (~((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 (e3) (e0)) = (e0)) -> (~((op (e1) (e3)) = (op (e2) (e3)))) -> ((op (e1) (e0)) = (e2)) -> (~((op (e1) (e0)) = (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) (e3)) = (op (e3) (e3)))) -> (((op (e0) (e3)) = (e1))\/(((op (e1) (e3)) = (e1))\/(((op (e2) (e3)) = (e1))\/((op (e3) (e3)) = (e1))))) -> (~((e1) = (e2))) -> (~((e1) = (e3))) -> (~((op (e2) (e2)) = (op (e2) (e3)))) -> ((op (e2) (e2)) = (e1)) -> ((op (e3) (e1)) = (e1)) -> (~((op (e3) (e1)) = (op (e3) (e3)))) -> (~((e2) = (e3))) -> (((op (e0) (e3)) = (e3))\/(((op (e1) (e3)) = (e3))\/(((op (e2) (e3)) = (e3))\/((op (e3) (e3)) = (e3))))) -> (~((op (e0) (e3)) = (op (e2) (e3)))) -> ((op (e2) (e3)) = (e3)) -> False). % 18.52/18.68 do 0 intro. intros zenon_He4 zenon_H76 zenon_H1d zenon_H2b zenon_H10a zenon_H9e zenon_H128 zenon_H102 zenon_H101 zenon_H71 zenon_H44 zenon_Hdb zenon_H86 zenon_Hd8 zenon_Hd5 zenon_Hdf zenon_Hc2 zenon_H133 zenon_H7c zenon_H95 zenon_H6d zenon_Hf1 zenon_Hae zenon_H130 zenon_H12b zenon_H136 zenon_He2 zenon_Hdd. % 18.52/18.68 apply (zenon_or_s _ _ zenon_He4); [ zenon_intro zenon_H1e | zenon_intro zenon_He5 ]. % 18.52/18.68 exact (zenon_H76 zenon_H1e). % 18.52/18.68 apply (zenon_or_s _ _ zenon_He5); [ zenon_intro zenon_Hc3 | zenon_intro zenon_He6 ]. % 18.52/18.68 apply (zenon_L80_); trivial. % 18.52/18.68 apply (zenon_or_s _ _ zenon_He6); [ zenon_intro zenon_Hcd | zenon_intro zenon_He3 ]. % 18.52/18.68 apply (zenon_L88_); trivial. % 18.52/18.68 apply (zenon_L54_); trivial. % 18.52/18.68 (* end of lemma zenon_L89_ *) % 18.52/18.68 assert (zenon_L90_ : (((op (e3) (e0)) = (e1))\/(((op (e3) (e1)) = (e1))\/(((op (e3) (e2)) = (e1))\/((op (e3) (e3)) = (e1))))) -> (~((e0) = (e1))) -> (((op (e0) (e3)) = (e3))\/(((op (e1) (e3)) = (e3))\/(((op (e2) (e3)) = (e3))\/((op (e3) (e3)) = (e3))))) -> (~((e2) = (e3))) -> (~((op (e3) (e1)) = (op (e3) (e3)))) -> ((op (e2) (e2)) = (e1)) -> (~((op (e2) (e2)) = (op (e2) (e3)))) -> (~((e1) = (e3))) -> (~((e1) = (e2))) -> (((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 (e3) (e3)) = (e0))\/(((op (e3) (e3)) = (e1))\/(((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 (e1) (e0)) = (e3)) -> (~((op (e1) (e1)) = (e1))) -> (~((op (e1) (e2)) = (op (e2) (e2)))) -> (~((op (e0) (e3)) = (op (e1) (e3)))) -> ((op (e2) (e2)) = (e0)) -> ((op (e0) (e2)) = (e3)) -> (((op (e0) (e3)) = (e0))\/(((op (e0) (e3)) = (e1))\/(((op (e0) (e3)) = (e2))\/((op (e0) (e3)) = (e3))))) -> (~((op (e0) (e3)) = (e0))) -> (~((op (e0) (e3)) = (op (e3) (e3)))) -> (~((op (e1) (e3)) = (op (e2) (e3)))) -> ((op (e1) (e0)) = (e2)) -> (~((op (e1) (e0)) = (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) (e3)) = (op (e2) (e3)))) -> ((op (e2) (e3)) = (e3)) -> False). % 18.52/18.68 do 0 intro. intros zenon_He8 zenon_Ha1 zenon_H136 zenon_H12b zenon_H130 zenon_Hf1 zenon_H6d zenon_H95 zenon_H7c zenon_H133 zenon_H44 zenon_H71 zenon_H101 zenon_H102 zenon_H128 zenon_H9e zenon_H10a zenon_H2b zenon_H1d zenon_H2c zenon_Ha9 zenon_He4 zenon_H76 zenon_Hc2 zenon_Hdb zenon_H86 zenon_Hd8 zenon_Hd5 zenon_Hdf zenon_He2 zenon_Hdd. % 18.52/18.68 apply (zenon_or_s _ _ zenon_He8); [ zenon_intro zenon_Hac | zenon_intro zenon_Heb ]. % 18.52/18.68 apply (zenon_L41_); trivial. % 18.52/18.68 apply (zenon_or_s _ _ zenon_Heb); [ zenon_intro zenon_Hae | zenon_intro zenon_Hec ]. % 18.52/18.68 apply (zenon_L89_); trivial. % 18.52/18.68 apply (zenon_or_s _ _ zenon_Hec); [ zenon_intro zenon_Hba | zenon_intro zenon_Hc4 ]. % 18.52/18.68 apply (zenon_L45_); trivial. % 18.52/18.68 apply (zenon_L55_); trivial. % 18.52/18.68 (* end of lemma zenon_L90_ *) % 18.52/18.68 assert (zenon_L91_ : (((op (e2) (e0)) = (e0))\/(((op (e2) (e1)) = (e0))\/(((op (e2) (e2)) = (e0))\/((op (e2) (e3)) = (e0))))) -> (~((op (e2) (e0)) = (e0))) -> (~((op (e2) (e1)) = (e0))) -> ((op (e0) (e2)) = (e3)) -> (((op (e2) (e0)) = (e3))\/(((op (e2) (e1)) = (e3))\/(((op (e2) (e2)) = (e3))\/((op (e2) (e3)) = (e3))))) -> ((op (e0) (e0)) = (e1)) -> ((op (e2) (e1)) = (e1)) -> (~((op (e0) (e2)) = (op (e2) (e2)))) -> (((op (e3) (e0)) = (e1))\/(((op (e3) (e1)) = (e1))\/(((op (e3) (e2)) = (e1))\/((op (e3) (e3)) = (e1))))) -> (~((e0) = (e1))) -> (((op (e0) (e3)) = (e3))\/(((op (e1) (e3)) = (e3))\/(((op (e2) (e3)) = (e3))\/((op (e3) (e3)) = (e3))))) -> (~((e2) = (e3))) -> (~((op (e3) (e1)) = (op (e3) (e3)))) -> (~((op (e2) (e2)) = (op (e2) (e3)))) -> (~((e1) = (e3))) -> (~((e1) = (e2))) -> (((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 (e3) (e3)) = (e0))\/(((op (e3) (e3)) = (e1))\/(((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 (e1) (e0)) = (e3)) -> (~((op (e1) (e1)) = (e1))) -> (~((op (e1) (e2)) = (op (e2) (e2)))) -> (~((op (e0) (e3)) = (op (e1) (e3)))) -> (((op (e0) (e3)) = (e0))\/(((op (e0) (e3)) = (e1))\/(((op (e0) (e3)) = (e2))\/((op (e0) (e3)) = (e3))))) -> (~((op (e0) (e3)) = (e0))) -> (~((op (e0) (e3)) = (op (e3) (e3)))) -> (~((op (e1) (e3)) = (op (e2) (e3)))) -> ((op (e1) (e0)) = (e2)) -> (~((op (e1) (e0)) = (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) (e3)) = (op (e2) (e3)))) -> ((op (e1) (e3)) = (e1)) -> (~((op (e1) (e2)) = (op (e1) (e3)))) -> (((op (e0) (e2)) = (e1))\/(((op (e1) (e2)) = (e1))\/(((op (e2) (e2)) = (e1))\/((op (e3) (e2)) = (e1))))) -> (~((op (e2) (e3)) = (e0))) -> False). % 18.52/18.68 do 0 intro. intros zenon_H2f zenon_H30 zenon_H31 zenon_Ha9 zenon_He7 zenon_H7a zenon_Ha5 zenon_Ha8 zenon_He8 zenon_Ha1 zenon_H136 zenon_H12b zenon_H130 zenon_H6d zenon_H95 zenon_H7c zenon_H133 zenon_H44 zenon_H71 zenon_H101 zenon_H102 zenon_H128 zenon_H9e zenon_H10a zenon_H2b zenon_H1d zenon_He4 zenon_H76 zenon_Hc2 zenon_Hdb zenon_H86 zenon_Hd8 zenon_Hd5 zenon_Hdf zenon_He2 zenon_Hd6 zenon_H124 zenon_H139 zenon_H32. % 18.52/18.68 apply (zenon_or_s _ _ zenon_H2f); [ zenon_intro zenon_H34 | zenon_intro zenon_H33 ]. % 18.52/18.68 exact (zenon_H30 zenon_H34). % 18.52/18.68 apply (zenon_or_s _ _ zenon_H33); [ zenon_intro zenon_H36 | zenon_intro zenon_H35 ]. % 18.52/18.68 exact (zenon_H31 zenon_H36). % 18.52/18.68 apply (zenon_or_s _ _ zenon_H35); [ zenon_intro zenon_H2c | zenon_intro zenon_H37 ]. % 18.52/18.68 apply (zenon_or_s _ _ zenon_H139); [ zenon_intro zenon_H122 | zenon_intro zenon_H13a ]. % 18.52/18.68 apply (zenon_L77_); trivial. % 18.52/18.68 apply (zenon_or_s _ _ zenon_H13a); [ zenon_intro zenon_Hf0 | zenon_intro zenon_H13b ]. % 18.52/18.68 apply (zenon_L78_); trivial. % 18.52/18.68 apply (zenon_or_s _ _ zenon_H13b); [ zenon_intro zenon_Hf1 | zenon_intro zenon_Hba ]. % 18.52/18.68 apply (zenon_or_s _ _ zenon_He7); [ zenon_intro zenon_H3b | zenon_intro zenon_He9 ]. % 18.52/18.68 apply (zenon_L33_); trivial. % 18.52/18.68 apply (zenon_or_s _ _ zenon_He9); [ zenon_intro zenon_Ha6 | zenon_intro zenon_Hea ]. % 18.52/18.68 apply (zenon_L39_); trivial. % 18.52/18.68 apply (zenon_or_s _ _ zenon_Hea); [ zenon_intro zenon_Haa | zenon_intro zenon_Hdd ]. % 18.52/18.68 apply (zenon_L40_); trivial. % 18.52/18.68 apply (zenon_L90_); trivial. % 18.52/18.68 apply (zenon_L45_); trivial. % 18.52/18.68 exact (zenon_H32 zenon_H37). % 18.52/18.68 (* end of lemma zenon_L91_ *) % 18.52/18.68 assert (zenon_L92_ : ((op (e0) (e2)) = (e1)) -> ((op (e0) (e0)) = (e1)) -> (~((op (e0) (e0)) = (op (e0) (e2)))) -> False). % 18.52/18.68 do 0 intro. intros zenon_H122 zenon_H7a zenon_H13c. % 18.52/18.68 elim (classic ((op (e0) (e2)) = (op (e0) (e2)))); [ zenon_intro zenon_H4b | zenon_intro zenon_H4c ]. % 18.52/18.68 cut (((op (e0) (e2)) = (op (e0) (e2))) = ((op (e0) (e0)) = (op (e0) (e2)))). % 18.52/18.68 intro zenon_D_pnotp. % 18.52/18.68 apply zenon_H13c. % 18.52/18.68 rewrite <- zenon_D_pnotp. % 18.52/18.68 exact zenon_H4b. % 18.52/18.68 cut (((op (e0) (e2)) = (op (e0) (e2)))); [idtac | apply NNPP; zenon_intro zenon_H4c]. % 18.52/18.68 cut (((op (e0) (e2)) = (op (e0) (e0)))); [idtac | apply NNPP; zenon_intro zenon_H13d]. % 18.52/18.68 congruence. % 18.52/18.68 cut (((op (e0) (e2)) = (e1)) = ((op (e0) (e2)) = (op (e0) (e0)))). % 18.52/18.68 intro zenon_D_pnotp. % 18.52/18.68 apply zenon_H13d. % 18.52/18.68 rewrite <- zenon_D_pnotp. % 18.52/18.68 exact zenon_H122. % 18.52/18.68 cut (((e1) = (op (e0) (e0)))); [idtac | apply NNPP; zenon_intro zenon_H93]. % 18.52/18.68 cut (((op (e0) (e2)) = (op (e0) (e2)))); [idtac | apply NNPP; zenon_intro zenon_H4c]. % 18.52/18.68 congruence. % 18.52/18.68 apply zenon_H4c. apply refl_equal. % 18.52/18.68 apply zenon_H93. apply sym_equal. exact zenon_H7a. % 18.52/18.68 apply zenon_H4c. apply refl_equal. % 18.52/18.68 apply zenon_H4c. apply refl_equal. % 18.52/18.68 (* end of lemma zenon_L92_ *) % 18.52/18.68 assert (zenon_L93_ : (~((op (e2) (e0)) = (op (e2) (e2)))) -> ((op (e2) (e0)) = (e1)) -> ((op (e2) (e2)) = (e1)) -> False). % 18.52/18.68 do 0 intro. intros zenon_H52 zenon_Hed zenon_Hf1. % 18.52/18.68 cut (((op (e2) (e0)) = (e1)) = ((op (e2) (e0)) = (op (e2) (e2)))). % 18.52/18.68 intro zenon_D_pnotp. % 18.52/18.68 apply zenon_H52. % 18.52/18.68 rewrite <- zenon_D_pnotp. % 18.52/18.68 exact zenon_Hed. % 18.52/18.68 cut (((e1) = (op (e2) (e2)))); [idtac | apply NNPP; zenon_intro zenon_Hf2]. % 18.52/18.68 cut (((op (e2) (e0)) = (op (e2) (e0)))); [idtac | apply NNPP; zenon_intro zenon_H53]. % 18.52/18.68 congruence. % 18.52/18.68 apply zenon_H53. apply refl_equal. % 18.52/18.68 apply zenon_Hf2. apply sym_equal. exact zenon_Hf1. % 18.52/18.68 (* end of lemma zenon_L93_ *) % 18.52/18.68 assert (zenon_L94_ : (((op (e0) (e2)) = (e1))\/(((op (e1) (e2)) = (e1))\/(((op (e2) (e2)) = (e1))\/((op (e3) (e2)) = (e1))))) -> (~((op (e0) (e0)) = (op (e0) (e2)))) -> ((op (e0) (e0)) = (e1)) -> (~((op (e1) (e2)) = (op (e1) (e3)))) -> ((op (e1) (e3)) = (e1)) -> ((op (e2) (e0)) = (e1)) -> (~((op (e2) (e0)) = (op (e2) (e2)))) -> ((op (e0) (e2)) = (e3)) -> ((op (e2) (e2)) = (e0)) -> False). % 18.52/18.68 do 0 intro. intros zenon_H139 zenon_H13c zenon_H7a zenon_H124 zenon_Hd6 zenon_Hed zenon_H52 zenon_Ha9 zenon_H2c. % 18.52/18.68 apply (zenon_or_s _ _ zenon_H139); [ zenon_intro zenon_H122 | zenon_intro zenon_H13a ]. % 18.52/18.68 apply (zenon_L92_); trivial. % 18.52/18.68 apply (zenon_or_s _ _ zenon_H13a); [ zenon_intro zenon_Hf0 | zenon_intro zenon_H13b ]. % 18.52/18.68 apply (zenon_L78_); trivial. % 18.52/18.68 apply (zenon_or_s _ _ zenon_H13b); [ zenon_intro zenon_Hf1 | zenon_intro zenon_Hba ]. % 18.52/18.68 apply (zenon_L93_); trivial. % 18.52/18.68 apply (zenon_L45_); trivial. % 18.52/18.68 (* end of lemma zenon_L94_ *) % 18.52/18.68 assert (zenon_L95_ : (~((op (e1) (e1)) = (op (e2) (e1)))) -> ((op (e1) (e1)) = (e3)) -> ((op (e2) (e1)) = (e3)) -> False). % 18.52/18.68 do 0 intro. intros zenon_H13e zenon_H13f zenon_Ha6. % 18.52/18.68 cut (((op (e1) (e1)) = (e3)) = ((op (e1) (e1)) = (op (e2) (e1)))). % 18.52/18.68 intro zenon_D_pnotp. % 18.52/18.68 apply zenon_H13e. % 18.52/18.68 rewrite <- zenon_D_pnotp. % 18.52/18.68 exact zenon_H13f. % 18.52/18.68 cut (((e3) = (op (e2) (e1)))); [idtac | apply NNPP; zenon_intro zenon_H140]. % 18.52/18.68 cut (((op (e1) (e1)) = (op (e1) (e1)))); [idtac | apply NNPP; zenon_intro zenon_H141]. % 18.52/18.68 congruence. % 18.52/18.68 apply zenon_H141. apply refl_equal. % 18.52/18.68 apply zenon_H140. apply sym_equal. exact zenon_Ha6. % 18.52/18.68 (* end of lemma zenon_L95_ *) % 18.52/18.68 assert (zenon_L96_ : (((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)) = (op (e2) (e1)))) -> ((op (e2) (e1)) = (e3)) -> False). % 18.52/18.68 do 0 intro. intros zenon_H142 zenon_H24 zenon_H10a zenon_H10f zenon_H10e zenon_H13e zenon_Ha6. % 18.52/18.68 apply (zenon_or_s _ _ zenon_H142); [ zenon_intro zenon_H29 | zenon_intro zenon_H143 ]. % 18.52/18.68 exact (zenon_H24 zenon_H29). % 18.52/18.68 apply (zenon_or_s _ _ zenon_H143); [ zenon_intro zenon_H10d | zenon_intro zenon_H144 ]. % 18.52/18.68 exact (zenon_H10a zenon_H10d). % 18.52/18.68 apply (zenon_or_s _ _ zenon_H144); [ zenon_intro zenon_H110 | zenon_intro zenon_H13f ]. % 18.52/18.68 apply (zenon_L67_); trivial. % 18.52/18.68 apply (zenon_L95_); trivial. % 18.52/18.68 (* end of lemma zenon_L96_ *) % 18.52/18.68 assert (zenon_L97_ : (~((op (e2) (e3)) = (op (e3) (e3)))) -> ((op (e2) (e3)) = (e2)) -> ((op (e3) (e3)) = (e2)) -> False). % 18.52/18.68 do 0 intro. intros zenon_Hf3 zenon_H11d zenon_Hf6. % 18.52/18.68 cut (((op (e2) (e3)) = (e2)) = ((op (e2) (e3)) = (op (e3) (e3)))). % 18.52/18.68 intro zenon_D_pnotp. % 18.52/18.68 apply zenon_Hf3. % 18.52/18.68 rewrite <- zenon_D_pnotp. % 18.52/18.68 exact zenon_H11d. % 18.52/18.68 cut (((e2) = (op (e3) (e3)))); [idtac | apply NNPP; zenon_intro zenon_H100]. % 18.52/18.68 cut (((op (e2) (e3)) = (op (e2) (e3)))); [idtac | apply NNPP; zenon_intro zenon_H5d]. % 18.52/18.68 congruence. % 18.52/18.68 apply zenon_H5d. apply refl_equal. % 18.52/18.68 apply zenon_H100. apply sym_equal. exact zenon_Hf6. % 18.52/18.68 (* end of lemma zenon_L97_ *) % 18.52/18.68 assert (zenon_L98_ : (((op (e2) (e3)) = (e0))\/(((op (e2) (e3)) = (e1))\/(((op (e2) (e3)) = (e2))\/((op (e2) (e3)) = (e3))))) -> (~((op (e2) (e3)) = (e0))) -> ((op (e1) (e3)) = (e0)) -> ((op (e3) (e3)) = (e2)) -> (~((op (e2) (e3)) = (op (e3) (e3)))) -> (~((op (e0) (e3)) = (op (e2) (e3)))) -> ((op (e0) (e3)) = (e3)) -> False). % 18.52/18.68 do 0 intro. intros zenon_H11f zenon_H32 zenon_H1f zenon_Hf6 zenon_Hf3 zenon_He2 zenon_He3. % 18.52/18.68 apply (zenon_or_s _ _ zenon_H11f); [ zenon_intro zenon_H37 | zenon_intro zenon_H120 ]. % 18.52/18.68 exact (zenon_H32 zenon_H37). % 18.52/18.68 apply (zenon_or_s _ _ zenon_H120); [ zenon_intro zenon_Hf4 | zenon_intro zenon_H121 ]. % 18.52/18.68 apply (zenon_L63_); trivial. % 18.52/18.68 apply (zenon_or_s _ _ zenon_H121); [ zenon_intro zenon_H11d | zenon_intro zenon_Hdd ]. % 18.52/18.68 apply (zenon_L97_); trivial. % 18.52/18.68 apply (zenon_L54_); trivial. % 18.52/18.68 (* end of lemma zenon_L98_ *) % 18.52/18.68 assert (zenon_L99_ : (((op (e0) (e3)) = (e2))\/(((op (e1) (e3)) = (e2))\/(((op (e2) (e3)) = (e2))\/((op (e3) (e3)) = (e2))))) -> ((op (e3) (e3)) = (e1)) -> (~((op (e0) (e3)) = (op (e1) (e3)))) -> (~((op (e0) (e3)) = (op (e3) (e3)))) -> (~((op (e0) (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) (e0)) = (e2)) -> (((op (e2) (e3)) = (e0))\/(((op (e2) (e3)) = (e1))\/(((op (e2) (e3)) = (e2))\/((op (e2) (e3)) = (e3))))) -> (~((op (e2) (e3)) = (e0))) -> ((op (e1) (e3)) = (e0)) -> (~((op (e2) (e3)) = (op (e3) (e3)))) -> (~((op (e0) (e3)) = (op (e2) (e3)))) -> ((op (e0) (e3)) = (e3)) -> False). % 18.52/18.68 do 0 intro. intros zenon_H145 zenon_Hc4 zenon_H1d zenon_Hc2 zenon_H76 zenon_He4 zenon_H5b zenon_Hee zenon_H11f zenon_H32 zenon_H1f zenon_Hf3 zenon_He2 zenon_He3. % 18.52/18.68 apply (zenon_or_s _ _ zenon_H145); [ zenon_intro zenon_Hcd | zenon_intro zenon_H146 ]. % 18.52/18.68 apply (zenon_L49_); trivial. % 18.52/18.68 apply (zenon_or_s _ _ zenon_H146); [ zenon_intro zenon_Hd7 | zenon_intro zenon_H147 ]. % 18.52/18.68 apply (zenon_L75_); trivial. % 18.52/18.68 apply (zenon_or_s _ _ zenon_H147); [ zenon_intro zenon_H11d | zenon_intro zenon_Hf6 ]. % 18.52/18.68 apply (zenon_L73_); trivial. % 18.52/18.68 apply (zenon_L98_); trivial. % 18.52/18.68 (* end of lemma zenon_L99_ *) % 18.52/18.68 assert (zenon_L100_ : ((op (e3) (e0)) = (e0)) -> ((op (e3) (e0)) = (e2)) -> (~((e0) = (e2))) -> False). % 18.52/18.68 do 0 intro. intros zenon_H44 zenon_H148 zenon_H149. % 18.52/18.68 elim (classic ((e2) = (e2))); [ zenon_intro zenon_H7d | zenon_intro zenon_H7e ]. % 18.52/18.68 cut (((e2) = (e2)) = ((e0) = (e2))). % 18.52/18.68 intro zenon_D_pnotp. % 18.52/18.68 apply zenon_H149. % 18.52/18.68 rewrite <- zenon_D_pnotp. % 18.52/18.68 exact zenon_H7d. % 18.52/18.68 cut (((e2) = (e2))); [idtac | apply NNPP; zenon_intro zenon_H7e]. % 18.52/18.68 cut (((e2) = (e0))); [idtac | apply NNPP; zenon_intro zenon_H14a]. % 18.52/18.68 congruence. % 18.52/18.68 cut (((op (e3) (e0)) = (e0)) = ((e2) = (e0))). % 18.52/18.68 intro zenon_D_pnotp. % 18.52/18.68 apply zenon_H14a. % 18.52/18.68 rewrite <- zenon_D_pnotp. % 18.52/18.68 exact zenon_H44. % 18.52/18.68 cut (((e0) = (e0))); [idtac | apply NNPP; zenon_intro zenon_H82]. % 18.52/18.68 cut (((op (e3) (e0)) = (e2))); [idtac | apply NNPP; zenon_intro zenon_H14b]. % 18.52/18.68 congruence. % 18.52/18.68 exact (zenon_H14b zenon_H148). % 18.52/18.68 apply zenon_H82. apply refl_equal. % 18.52/18.68 apply zenon_H7e. apply refl_equal. % 18.52/18.68 apply zenon_H7e. apply refl_equal. % 18.52/18.68 (* end of lemma zenon_L100_ *) % 18.52/18.68 assert (zenon_L101_ : ((op (e1) (e3)) = (e1)) -> ((op (e1) (e3)) = (e2)) -> (~((e1) = (e2))) -> False). % 18.52/18.68 do 0 intro. intros zenon_Hd6 zenon_Hd7 zenon_H7c. % 18.52/18.68 elim (classic ((e2) = (e2))); [ zenon_intro zenon_H7d | zenon_intro zenon_H7e ]. % 18.52/18.68 cut (((e2) = (e2)) = ((e1) = (e2))). % 18.52/18.68 intro zenon_D_pnotp. % 18.52/18.68 apply zenon_H7c. % 18.52/18.68 rewrite <- zenon_D_pnotp. % 18.52/18.68 exact zenon_H7d. % 18.52/18.68 cut (((e2) = (e2))); [idtac | apply NNPP; zenon_intro zenon_H7e]. % 18.52/18.68 cut (((e2) = (e1))); [idtac | apply NNPP; zenon_intro zenon_H7f]. % 18.52/18.68 congruence. % 18.52/18.68 cut (((op (e1) (e3)) = (e1)) = ((e2) = (e1))). % 18.52/18.68 intro zenon_D_pnotp. % 18.52/18.68 apply zenon_H7f. % 18.52/18.68 rewrite <- zenon_D_pnotp. % 18.52/18.68 exact zenon_Hd6. % 18.52/18.68 cut (((e1) = (e1))); [idtac | apply NNPP; zenon_intro zenon_H79]. % 18.52/18.68 cut (((op (e1) (e3)) = (e2))); [idtac | apply NNPP; zenon_intro zenon_H14c]. % 18.52/18.68 congruence. % 18.52/18.68 exact (zenon_H14c zenon_Hd7). % 18.52/18.68 apply zenon_H79. apply refl_equal. % 18.52/18.68 apply zenon_H7e. apply refl_equal. % 18.52/18.68 apply zenon_H7e. apply refl_equal. % 18.52/18.68 (* end of lemma zenon_L101_ *) % 18.52/18.68 assert (zenon_L102_ : ((op (e3) (e3)) = (e2)) -> ((op (e3) (e1)) = (e2)) -> (~((op (e3) (e1)) = (op (e3) (e3)))) -> False). % 18.52/18.68 do 0 intro. intros zenon_Hf6 zenon_H14d zenon_H130. % 18.52/18.68 elim (classic ((op (e3) (e3)) = (op (e3) (e3)))); [ zenon_intro zenon_H63 | zenon_intro zenon_H64 ]. % 18.52/18.68 cut (((op (e3) (e3)) = (op (e3) (e3))) = ((op (e3) (e1)) = (op (e3) (e3)))). % 18.52/18.68 intro zenon_D_pnotp. % 18.52/18.68 apply zenon_H130. % 18.52/18.68 rewrite <- zenon_D_pnotp. % 18.52/18.68 exact zenon_H63. % 18.52/18.68 cut (((op (e3) (e3)) = (op (e3) (e3)))); [idtac | apply NNPP; zenon_intro zenon_H64]. % 18.52/18.68 cut (((op (e3) (e3)) = (op (e3) (e1)))); [idtac | apply NNPP; zenon_intro zenon_H131]. % 18.52/18.68 congruence. % 18.52/18.68 cut (((op (e3) (e3)) = (e2)) = ((op (e3) (e3)) = (op (e3) (e1)))). % 18.52/18.68 intro zenon_D_pnotp. % 18.52/18.68 apply zenon_H131. % 18.52/18.68 rewrite <- zenon_D_pnotp. % 18.52/18.68 exact zenon_Hf6. % 18.52/18.68 cut (((e2) = (op (e3) (e1)))); [idtac | apply NNPP; zenon_intro zenon_H14e]. % 18.52/18.68 cut (((op (e3) (e3)) = (op (e3) (e3)))); [idtac | apply NNPP; zenon_intro zenon_H64]. % 18.52/18.68 congruence. % 18.52/18.68 apply zenon_H64. apply refl_equal. % 18.52/18.68 apply zenon_H14e. apply sym_equal. exact zenon_H14d. % 18.52/18.68 apply zenon_H64. apply refl_equal. % 18.52/18.68 apply zenon_H64. apply refl_equal. % 18.52/18.68 (* end of lemma zenon_L102_ *) % 18.52/18.68 assert (zenon_L103_ : (((op (e0) (e3)) = (e2))\/(((op (e1) (e3)) = (e2))\/(((op (e2) (e3)) = (e2))\/((op (e3) (e3)) = (e2))))) -> (~((e2) = (e3))) -> ((op (e0) (e3)) = (e3)) -> (~((e1) = (e2))) -> ((op (e1) (e3)) = (e1)) -> (~((op (e2) (e0)) = (op (e2) (e3)))) -> ((op (e2) (e0)) = (e2)) -> ((op (e3) (e1)) = (e2)) -> (~((op (e3) (e1)) = (op (e3) (e3)))) -> False). % 18.52/18.68 do 0 intro. intros zenon_H145 zenon_H12b zenon_He3 zenon_H7c zenon_Hd6 zenon_H5b zenon_Hee zenon_H14d zenon_H130. % 18.52/18.68 apply (zenon_or_s _ _ zenon_H145); [ zenon_intro zenon_Hcd | zenon_intro zenon_H146 ]. % 18.52/18.68 apply (zenon_L81_); trivial. % 18.52/18.68 apply (zenon_or_s _ _ zenon_H146); [ zenon_intro zenon_Hd7 | zenon_intro zenon_H147 ]. % 18.52/18.68 apply (zenon_L101_); trivial. % 18.52/18.68 apply (zenon_or_s _ _ zenon_H147); [ zenon_intro zenon_H11d | zenon_intro zenon_Hf6 ]. % 18.52/18.68 apply (zenon_L73_); trivial. % 18.52/18.68 apply (zenon_L102_); trivial. % 18.52/18.68 (* end of lemma zenon_L103_ *) % 18.52/18.68 assert (zenon_L104_ : (~((op (e0) (e2)) = (op (e3) (e2)))) -> ((op (e0) (e2)) = (e2)) -> ((op (e3) (e2)) = (e2)) -> False). % 18.52/18.68 do 0 intro. intros zenon_H14f zenon_H150 zenon_H151. % 18.52/18.68 cut (((op (e0) (e2)) = (e2)) = ((op (e0) (e2)) = (op (e3) (e2)))). % 18.52/18.68 intro zenon_D_pnotp. % 18.52/18.68 apply zenon_H14f. % 18.52/18.68 rewrite <- zenon_D_pnotp. % 18.52/18.68 exact zenon_H150. % 18.52/18.68 cut (((e2) = (op (e3) (e2)))); [idtac | apply NNPP; zenon_intro zenon_H152]. % 18.52/18.68 cut (((op (e0) (e2)) = (op (e0) (e2)))); [idtac | apply NNPP; zenon_intro zenon_H4c]. % 18.52/18.68 congruence. % 18.52/18.68 apply zenon_H4c. apply refl_equal. % 18.52/18.68 apply zenon_H152. apply sym_equal. exact zenon_H151. % 18.52/18.68 (* end of lemma zenon_L104_ *) % 18.52/18.68 assert (zenon_L105_ : (((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)) = (op (e3) (e3)))) -> ((op (e2) (e0)) = (e2)) -> (~((op (e2) (e0)) = (op (e2) (e3)))) -> ((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 (e0) (e2)) = (e2)) -> (~((op (e0) (e2)) = (op (e3) (e2)))) -> (((op (e2) (e3)) = (e0))\/(((op (e2) (e3)) = (e1))\/(((op (e2) (e3)) = (e2))\/((op (e2) (e3)) = (e3))))) -> (~((op (e2) (e3)) = (e0))) -> ((op (e1) (e3)) = (e0)) -> (~((op (e2) (e3)) = (op (e3) (e3)))) -> (~((op (e0) (e3)) = (op (e2) (e3)))) -> ((op (e0) (e3)) = (e3)) -> False). % 18.52/18.68 do 0 intro. intros zenon_H153 zenon_H149 zenon_H44 zenon_H130 zenon_Hee zenon_H5b zenon_Hd6 zenon_H7c zenon_H12b zenon_H145 zenon_H150 zenon_H14f zenon_H11f zenon_H32 zenon_H1f zenon_Hf3 zenon_He2 zenon_He3. % 18.52/18.68 apply (zenon_or_s _ _ zenon_H153); [ zenon_intro zenon_H148 | zenon_intro zenon_H154 ]. % 18.52/18.68 apply (zenon_L100_); trivial. % 18.52/18.68 apply (zenon_or_s _ _ zenon_H154); [ zenon_intro zenon_H14d | zenon_intro zenon_H155 ]. % 18.52/18.68 apply (zenon_L103_); trivial. % 18.52/18.68 apply (zenon_or_s _ _ zenon_H155); [ zenon_intro zenon_H151 | zenon_intro zenon_Hf6 ]. % 18.52/18.68 apply (zenon_L104_); trivial. % 18.52/18.68 apply (zenon_L98_); trivial. % 18.52/18.68 (* end of lemma zenon_L105_ *) % 18.52/18.68 assert (zenon_L106_ : ((op (e1) (e0)) = (e3)) -> ((op (e0) (e0)) = (e1)) -> (~((e3) = (op (op (e0) (e0)) (e0)))) -> False). % 18.52/18.68 do 0 intro. intros zenon_H9e zenon_H7a zenon_H156. % 18.52/18.68 elim (classic ((op (op (e0) (e0)) (e0)) = (op (op (e0) (e0)) (e0)))); [ zenon_intro zenon_H88 | zenon_intro zenon_H89 ]. % 18.52/18.68 cut (((op (op (e0) (e0)) (e0)) = (op (op (e0) (e0)) (e0))) = ((e3) = (op (op (e0) (e0)) (e0)))). % 18.52/18.68 intro zenon_D_pnotp. % 18.52/18.68 apply zenon_H156. % 18.52/18.68 rewrite <- zenon_D_pnotp. % 18.52/18.68 exact zenon_H88. % 18.52/18.68 cut (((op (op (e0) (e0)) (e0)) = (op (op (e0) (e0)) (e0)))); [idtac | apply NNPP; zenon_intro zenon_H89]. % 18.52/18.68 cut (((op (op (e0) (e0)) (e0)) = (e3))); [idtac | apply NNPP; zenon_intro zenon_H157]. % 18.52/18.68 congruence. % 18.52/18.68 cut (((op (e1) (e0)) = (e3)) = ((op (op (e0) (e0)) (e0)) = (e3))). % 18.52/18.68 intro zenon_D_pnotp. % 18.52/18.68 apply zenon_H157. % 18.52/18.68 rewrite <- zenon_D_pnotp. % 18.52/18.68 exact zenon_H9e. % 18.52/18.68 cut (((e3) = (e3))); [idtac | apply NNPP; zenon_intro zenon_H85]. % 18.52/18.68 cut (((op (e1) (e0)) = (op (op (e0) (e0)) (e0)))); [idtac | apply NNPP; zenon_intro zenon_H8b]. % 18.52/18.68 congruence. % 18.52/18.68 elim (classic ((op (op (e0) (e0)) (e0)) = (op (op (e0) (e0)) (e0)))); [ zenon_intro zenon_H88 | zenon_intro zenon_H89 ]. % 18.52/18.68 cut (((op (op (e0) (e0)) (e0)) = (op (op (e0) (e0)) (e0))) = ((op (e1) (e0)) = (op (op (e0) (e0)) (e0)))). % 18.52/18.68 intro zenon_D_pnotp. % 18.52/18.68 apply zenon_H8b. % 18.52/18.68 rewrite <- zenon_D_pnotp. % 18.52/18.68 exact zenon_H88. % 18.52/18.68 cut (((op (op (e0) (e0)) (e0)) = (op (op (e0) (e0)) (e0)))); [idtac | apply NNPP; zenon_intro zenon_H89]. % 18.52/18.68 cut (((op (op (e0) (e0)) (e0)) = (op (e1) (e0)))); [idtac | apply NNPP; zenon_intro zenon_H83]. % 18.52/18.68 congruence. % 18.52/18.68 apply (zenon_L29_); trivial. % 18.52/18.68 apply zenon_H89. apply refl_equal. % 18.52/18.68 apply zenon_H89. apply refl_equal. % 18.52/18.68 apply zenon_H85. apply refl_equal. % 18.52/18.68 apply zenon_H89. apply refl_equal. % 18.52/18.68 apply zenon_H89. apply refl_equal. % 18.52/18.68 (* end of lemma zenon_L106_ *) % 18.52/18.68 assert (zenon_L107_ : ((op (e3) (e0)) = (e2)) -> ((op (e1) (e0)) = (e3)) -> ((op (e0) (e0)) = (e1)) -> False). % 18.52/18.68 do 0 intro. intros zenon_H148 zenon_H9e zenon_H7a. % 18.52/18.68 apply (zenon_notand_s _ _ ax9); [ zenon_intro zenon_H159 | zenon_intro zenon_H158 ]. % 18.52/18.68 elim (classic ((op (op (op (e0) (e0)) (e0)) (e0)) = (op (op (op (e0) (e0)) (e0)) (e0)))); [ zenon_intro zenon_H8e | zenon_intro zenon_H8f ]. % 18.52/18.68 cut (((op (op (op (e0) (e0)) (e0)) (e0)) = (op (op (op (e0) (e0)) (e0)) (e0))) = ((e2) = (op (op (op (e0) (e0)) (e0)) (e0)))). % 18.52/18.68 intro zenon_D_pnotp. % 18.52/18.68 apply zenon_H159. % 18.52/18.68 rewrite <- zenon_D_pnotp. % 18.52/18.68 exact zenon_H8e. % 18.52/18.68 cut (((op (op (op (e0) (e0)) (e0)) (e0)) = (op (op (op (e0) (e0)) (e0)) (e0)))); [idtac | apply NNPP; zenon_intro zenon_H8f]. % 18.52/18.68 cut (((op (op (op (e0) (e0)) (e0)) (e0)) = (e2))); [idtac | apply NNPP; zenon_intro zenon_H15a]. % 18.52/18.68 congruence. % 18.52/18.68 cut (((op (e3) (e0)) = (e2)) = ((op (op (op (e0) (e0)) (e0)) (e0)) = (e2))). % 18.52/18.68 intro zenon_D_pnotp. % 18.52/18.68 apply zenon_H15a. % 18.52/18.68 rewrite <- zenon_D_pnotp. % 18.52/18.68 exact zenon_H148. % 18.52/18.68 cut (((e2) = (e2))); [idtac | apply NNPP; zenon_intro zenon_H7e]. % 18.52/18.68 cut (((op (e3) (e0)) = (op (op (op (e0) (e0)) (e0)) (e0)))); [idtac | apply NNPP; zenon_intro zenon_H15b]. % 18.52/18.68 congruence. % 18.52/18.68 elim (classic ((op (op (op (e0) (e0)) (e0)) (e0)) = (op (op (op (e0) (e0)) (e0)) (e0)))); [ zenon_intro zenon_H8e | zenon_intro zenon_H8f ]. % 18.52/18.68 cut (((op (op (op (e0) (e0)) (e0)) (e0)) = (op (op (op (e0) (e0)) (e0)) (e0))) = ((op (e3) (e0)) = (op (op (op (e0) (e0)) (e0)) (e0)))). % 18.52/18.68 intro zenon_D_pnotp. % 18.52/18.68 apply zenon_H15b. % 18.52/18.68 rewrite <- zenon_D_pnotp. % 18.52/18.68 exact zenon_H8e. % 18.52/18.68 cut (((op (op (op (e0) (e0)) (e0)) (e0)) = (op (op (op (e0) (e0)) (e0)) (e0)))); [idtac | apply NNPP; zenon_intro zenon_H8f]. % 18.52/18.68 cut (((op (op (op (e0) (e0)) (e0)) (e0)) = (op (e3) (e0)))); [idtac | apply NNPP; zenon_intro zenon_H15c]. % 18.52/18.68 congruence. % 18.52/18.68 cut (((e0) = (e0))); [idtac | apply NNPP; zenon_intro zenon_H82]. % 18.52/18.68 cut (((op (op (e0) (e0)) (e0)) = (e3))); [idtac | apply NNPP; zenon_intro zenon_H157]. % 18.52/18.68 congruence. % 18.52/18.68 cut (((op (e1) (e0)) = (e3)) = ((op (op (e0) (e0)) (e0)) = (e3))). % 18.52/18.68 intro zenon_D_pnotp. % 18.52/18.68 apply zenon_H157. % 18.52/18.68 rewrite <- zenon_D_pnotp. % 18.52/18.68 exact zenon_H9e. % 18.52/18.68 cut (((e3) = (e3))); [idtac | apply NNPP; zenon_intro zenon_H85]. % 18.52/18.68 cut (((op (e1) (e0)) = (op (op (e0) (e0)) (e0)))); [idtac | apply NNPP; zenon_intro zenon_H8b]. % 18.52/18.68 congruence. % 18.52/18.68 elim (classic ((op (op (e0) (e0)) (e0)) = (op (op (e0) (e0)) (e0)))); [ zenon_intro zenon_H88 | zenon_intro zenon_H89 ]. % 18.52/18.68 cut (((op (op (e0) (e0)) (e0)) = (op (op (e0) (e0)) (e0))) = ((op (e1) (e0)) = (op (op (e0) (e0)) (e0)))). % 18.52/18.68 intro zenon_D_pnotp. % 18.52/18.68 apply zenon_H8b. % 18.52/18.68 rewrite <- zenon_D_pnotp. % 18.52/18.68 exact zenon_H88. % 18.52/18.68 cut (((op (op (e0) (e0)) (e0)) = (op (op (e0) (e0)) (e0)))); [idtac | apply NNPP; zenon_intro zenon_H89]. % 18.52/18.69 cut (((op (op (e0) (e0)) (e0)) = (op (e1) (e0)))); [idtac | apply NNPP; zenon_intro zenon_H83]. % 18.52/18.69 congruence. % 18.52/18.69 apply (zenon_L29_); trivial. % 18.52/18.69 apply zenon_H89. apply refl_equal. % 18.52/18.69 apply zenon_H89. apply refl_equal. % 18.52/18.69 apply zenon_H85. apply refl_equal. % 18.52/18.69 apply zenon_H82. apply refl_equal. % 18.52/18.69 apply zenon_H8f. apply refl_equal. % 18.52/18.69 apply zenon_H8f. apply refl_equal. % 18.52/18.69 apply zenon_H7e. apply refl_equal. % 18.52/18.69 apply zenon_H8f. apply refl_equal. % 18.52/18.69 apply zenon_H8f. apply refl_equal. % 18.52/18.69 apply (zenon_notand_s _ _ zenon_H158); [ zenon_intro zenon_H156 | zenon_intro zenon_H93 ]. % 18.52/18.69 apply (zenon_L106_); trivial. % 18.52/18.69 apply zenon_H93. apply sym_equal. exact zenon_H7a. % 18.52/18.69 (* end of lemma zenon_L107_ *) % 18.52/18.69 assert (zenon_L108_ : (~((op (e0) (e1)) = (op (e1) (e1)))) -> ((op (e0) (e1)) = (e3)) -> ((op (e1) (e1)) = (e3)) -> False). % 18.52/18.69 do 0 intro. intros zenon_H10e zenon_H99 zenon_H13f. % 18.52/18.69 cut (((op (e0) (e1)) = (e3)) = ((op (e0) (e1)) = (op (e1) (e1)))). % 18.52/18.69 intro zenon_D_pnotp. % 18.52/18.69 apply zenon_H10e. % 18.52/18.69 rewrite <- zenon_D_pnotp. % 18.52/18.69 exact zenon_H99. % 18.52/18.69 cut (((e3) = (op (e1) (e1)))); [idtac | apply NNPP; zenon_intro zenon_H15d]. % 18.52/18.69 cut (((op (e0) (e1)) = (op (e0) (e1)))); [idtac | apply NNPP; zenon_intro zenon_H112]. % 18.52/18.69 congruence. % 18.52/18.69 apply zenon_H112. apply refl_equal. % 18.52/18.69 apply zenon_H15d. apply sym_equal. exact zenon_H13f. % 18.52/18.69 (* end of lemma zenon_L108_ *) % 18.52/18.69 assert (zenon_L109_ : ((op (e3) (e0)) = (e2)) -> ((op (e3) (e0)) = (e3)) -> (~((e2) = (e3))) -> False). % 18.52/18.69 do 0 intro. intros zenon_H148 zenon_H15e zenon_H12b. % 18.52/18.69 elim (classic ((e3) = (e3))); [ zenon_intro zenon_H96 | zenon_intro zenon_H85 ]. % 18.52/18.69 cut (((e3) = (e3)) = ((e2) = (e3))). % 18.52/18.69 intro zenon_D_pnotp. % 18.52/18.69 apply zenon_H12b. % 18.52/18.69 rewrite <- zenon_D_pnotp. % 18.52/18.69 exact zenon_H96. % 18.52/18.69 cut (((e3) = (e3))); [idtac | apply NNPP; zenon_intro zenon_H85]. % 18.52/18.69 cut (((e3) = (e2))); [idtac | apply NNPP; zenon_intro zenon_H12c]. % 18.52/18.69 congruence. % 18.52/18.69 cut (((op (e3) (e0)) = (e2)) = ((e3) = (e2))). % 18.52/18.69 intro zenon_D_pnotp. % 18.52/18.69 apply zenon_H12c. % 18.52/18.69 rewrite <- zenon_D_pnotp. % 18.52/18.69 exact zenon_H148. % 18.52/18.69 cut (((e2) = (e2))); [idtac | apply NNPP; zenon_intro zenon_H7e]. % 18.52/18.69 cut (((op (e3) (e0)) = (e3))); [idtac | apply NNPP; zenon_intro zenon_H15f]. % 18.52/18.69 congruence. % 18.52/18.69 exact (zenon_H15f zenon_H15e). % 18.52/18.69 apply zenon_H7e. apply refl_equal. % 18.52/18.69 apply zenon_H85. apply refl_equal. % 18.52/18.69 apply zenon_H85. apply refl_equal. % 18.52/18.69 (* end of lemma zenon_L109_ *) % 18.52/18.69 assert (zenon_L110_ : (~((op (e1) (e1)) = (op (e3) (e1)))) -> ((op (e1) (e1)) = (e3)) -> ((op (e3) (e1)) = (e3)) -> False). % 18.52/18.69 do 0 intro. intros zenon_H160 zenon_H13f zenon_H161. % 18.52/18.69 cut (((op (e1) (e1)) = (e3)) = ((op (e1) (e1)) = (op (e3) (e1)))). % 18.52/18.69 intro zenon_D_pnotp. % 18.52/18.69 apply zenon_H160. % 18.52/18.69 rewrite <- zenon_D_pnotp. % 18.52/18.69 exact zenon_H13f. % 18.52/18.69 cut (((e3) = (op (e3) (e1)))); [idtac | apply NNPP; zenon_intro zenon_H162]. % 18.52/18.69 cut (((op (e1) (e1)) = (op (e1) (e1)))); [idtac | apply NNPP; zenon_intro zenon_H141]. % 18.52/18.69 congruence. % 18.52/18.69 apply zenon_H141. apply refl_equal. % 18.52/18.69 apply zenon_H162. apply sym_equal. exact zenon_H161. % 18.52/18.69 (* end of lemma zenon_L110_ *) % 18.52/18.69 assert (zenon_L111_ : (~((op (e0) (e2)) = (op (e3) (e2)))) -> ((op (e0) (e2)) = (e3)) -> ((op (e3) (e2)) = (e3)) -> False). % 18.52/18.69 do 0 intro. intros zenon_H14f zenon_Ha9 zenon_H163. % 18.52/18.69 cut (((op (e0) (e2)) = (e3)) = ((op (e0) (e2)) = (op (e3) (e2)))). % 18.52/18.69 intro zenon_D_pnotp. % 18.52/18.69 apply zenon_H14f. % 18.52/18.69 rewrite <- zenon_D_pnotp. % 18.52/18.69 exact zenon_Ha9. % 18.52/18.69 cut (((e3) = (op (e3) (e2)))); [idtac | apply NNPP; zenon_intro zenon_H164]. % 18.52/18.69 cut (((op (e0) (e2)) = (op (e0) (e2)))); [idtac | apply NNPP; zenon_intro zenon_H4c]. % 18.52/18.69 congruence. % 18.52/18.69 apply zenon_H4c. apply refl_equal. % 18.52/18.69 apply zenon_H164. apply sym_equal. exact zenon_H163. % 18.52/18.69 (* end of lemma zenon_L111_ *) % 18.52/18.69 assert (zenon_L112_ : (((op (e3) (e0)) = (e3))\/(((op (e3) (e1)) = (e3))\/(((op (e3) (e2)) = (e3))\/((op (e3) (e3)) = (e3))))) -> (~((e2) = (e3))) -> ((op (e3) (e0)) = (e2)) -> ((op (e1) (e1)) = (e3)) -> (~((op (e1) (e1)) = (op (e3) (e1)))) -> ((op (e0) (e2)) = (e3)) -> (~((op (e0) (e2)) = (op (e3) (e2)))) -> (~((op (e3) (e3)) = (e3))) -> False). % 18.52/18.69 do 0 intro. intros zenon_H165 zenon_H12b zenon_H148 zenon_H13f zenon_H160 zenon_Ha9 zenon_H14f zenon_H102. % 18.52/18.69 apply (zenon_or_s _ _ zenon_H165); [ zenon_intro zenon_H15e | zenon_intro zenon_H166 ]. % 18.52/18.69 apply (zenon_L109_); trivial. % 18.52/18.69 apply (zenon_or_s _ _ zenon_H166); [ zenon_intro zenon_H161 | zenon_intro zenon_H167 ]. % 18.52/18.69 apply (zenon_L110_); trivial. % 18.52/18.69 apply (zenon_or_s _ _ zenon_H167); [ zenon_intro zenon_H163 | zenon_intro zenon_H105 ]. % 18.52/18.69 apply (zenon_L111_); trivial. % 18.52/18.69 exact (zenon_H102 zenon_H105). % 18.52/18.69 (* end of lemma zenon_L112_ *) % 18.52/18.69 assert (zenon_L113_ : (((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 (e3) (e3)) = (e3))) -> (~((op (e0) (e2)) = (op (e3) (e2)))) -> (~((op (e1) (e1)) = (op (e3) (e1)))) -> ((op (e1) (e1)) = (e3)) -> ((op (e3) (e0)) = (e2)) -> (((op (e3) (e0)) = (e3))\/(((op (e3) (e1)) = (e3))\/(((op (e3) (e2)) = (e3))\/((op (e3) (e3)) = (e3))))) -> ((op (e0) (e3)) = (e2)) -> (~((e2) = (e3))) -> False). % 18.52/18.69 do 0 intro. intros zenon_H168 zenon_H95 zenon_H7a zenon_H10e zenon_H102 zenon_H14f zenon_H160 zenon_H13f zenon_H148 zenon_H165 zenon_Hcd zenon_H12b. % 18.52/18.69 apply (zenon_or_s _ _ zenon_H168); [ zenon_intro zenon_H3a | zenon_intro zenon_H169 ]. % 18.52/18.69 apply (zenon_L35_); trivial. % 18.52/18.69 apply (zenon_or_s _ _ zenon_H169); [ zenon_intro zenon_H99 | zenon_intro zenon_H16a ]. % 18.52/18.69 apply (zenon_L108_); trivial. % 18.52/18.69 apply (zenon_or_s _ _ zenon_H16a); [ zenon_intro zenon_Ha9 | zenon_intro zenon_He3 ]. % 18.52/18.69 apply (zenon_L112_); trivial. % 18.52/18.69 apply (zenon_L81_); trivial. % 18.52/18.69 (* end of lemma zenon_L113_ *) % 18.52/18.69 assert (zenon_L114_ : ((op (e3) (e3)) = (e2)) -> ((op (e3) (e0)) = (e2)) -> (~((op (e3) (e0)) = (op (e3) (e3)))) -> False). % 18.52/18.69 do 0 intro. intros zenon_Hf6 zenon_H148 zenon_H71. % 18.52/18.69 elim (classic ((op (e3) (e3)) = (op (e3) (e3)))); [ zenon_intro zenon_H63 | zenon_intro zenon_H64 ]. % 18.52/18.69 cut (((op (e3) (e3)) = (op (e3) (e3))) = ((op (e3) (e0)) = (op (e3) (e3)))). % 18.52/18.69 intro zenon_D_pnotp. % 18.52/18.69 apply zenon_H71. % 18.52/18.69 rewrite <- zenon_D_pnotp. % 18.52/18.69 exact zenon_H63. % 18.52/18.69 cut (((op (e3) (e3)) = (op (e3) (e3)))); [idtac | apply NNPP; zenon_intro zenon_H64]. % 18.52/18.69 cut (((op (e3) (e3)) = (op (e3) (e0)))); [idtac | apply NNPP; zenon_intro zenon_H72]. % 18.52/18.69 congruence. % 18.52/18.69 cut (((op (e3) (e3)) = (e2)) = ((op (e3) (e3)) = (op (e3) (e0)))). % 18.52/18.69 intro zenon_D_pnotp. % 18.52/18.69 apply zenon_H72. % 18.52/18.69 rewrite <- zenon_D_pnotp. % 18.52/18.69 exact zenon_Hf6. % 18.52/18.69 cut (((e2) = (op (e3) (e0)))); [idtac | apply NNPP; zenon_intro zenon_H16b]. % 18.52/18.69 cut (((op (e3) (e3)) = (op (e3) (e3)))); [idtac | apply NNPP; zenon_intro zenon_H64]. % 18.52/18.69 congruence. % 18.52/18.69 apply zenon_H64. apply refl_equal. % 18.52/18.69 apply zenon_H16b. apply sym_equal. exact zenon_H148. % 18.52/18.69 apply zenon_H64. apply refl_equal. % 18.52/18.69 apply zenon_H64. apply refl_equal. % 18.52/18.69 (* end of lemma zenon_L114_ *) % 18.52/18.69 assert (zenon_L115_ : (((op (e0) (e3)) = (e2))\/(((op (e1) (e3)) = (e2))\/(((op (e2) (e3)) = (e2))\/((op (e3) (e3)) = (e2))))) -> (~((e2) = (e3))) -> (((op (e3) (e0)) = (e3))\/(((op (e3) (e1)) = (e3))\/(((op (e3) (e2)) = (e3))\/((op (e3) (e3)) = (e3))))) -> ((op (e1) (e1)) = (e3)) -> (~((op (e1) (e1)) = (op (e3) (e1)))) -> (~((op (e0) (e2)) = (op (e3) (e2)))) -> (~((op (e3) (e3)) = (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))))) -> (~((e1) = (e2))) -> ((op (e1) (e3)) = (e1)) -> (~((op (e2) (e0)) = (op (e2) (e3)))) -> ((op (e2) (e0)) = (e2)) -> ((op (e3) (e0)) = (e2)) -> (~((op (e3) (e0)) = (op (e3) (e3)))) -> False). % 18.52/18.69 do 0 intro. intros zenon_H145 zenon_H12b zenon_H165 zenon_H13f zenon_H160 zenon_H14f zenon_H102 zenon_H10e zenon_H7a zenon_H95 zenon_H168 zenon_H7c zenon_Hd6 zenon_H5b zenon_Hee zenon_H148 zenon_H71. % 18.52/18.69 apply (zenon_or_s _ _ zenon_H145); [ zenon_intro zenon_Hcd | zenon_intro zenon_H146 ]. % 18.52/18.69 apply (zenon_L113_); trivial. % 18.52/18.69 apply (zenon_or_s _ _ zenon_H146); [ zenon_intro zenon_Hd7 | zenon_intro zenon_H147 ]. % 18.52/18.69 apply (zenon_L101_); trivial. % 18.52/18.69 apply (zenon_or_s _ _ zenon_H147); [ zenon_intro zenon_H11d | zenon_intro zenon_Hf6 ]. % 18.52/18.69 apply (zenon_L73_); trivial. % 18.52/18.69 apply (zenon_L114_); trivial. % 18.52/18.69 (* end of lemma zenon_L115_ *) % 18.52/18.69 assert (zenon_L116_ : ((op (e1) (e2)) = (e2)) -> ((op (e1) (e2)) = (e3)) -> (~((e2) = (e3))) -> False). % 18.52/18.69 do 0 intro. intros zenon_H113 zenon_H16c zenon_H12b. % 18.52/18.69 elim (classic ((e3) = (e3))); [ zenon_intro zenon_H96 | zenon_intro zenon_H85 ]. % 18.52/18.69 cut (((e3) = (e3)) = ((e2) = (e3))). % 18.52/18.69 intro zenon_D_pnotp. % 18.52/18.69 apply zenon_H12b. % 18.52/18.69 rewrite <- zenon_D_pnotp. % 18.52/18.69 exact zenon_H96. % 18.52/18.69 cut (((e3) = (e3))); [idtac | apply NNPP; zenon_intro zenon_H85]. % 18.52/18.69 cut (((e3) = (e2))); [idtac | apply NNPP; zenon_intro zenon_H12c]. % 18.52/18.69 congruence. % 18.52/18.69 cut (((op (e1) (e2)) = (e2)) = ((e3) = (e2))). % 18.52/18.69 intro zenon_D_pnotp. % 18.52/18.69 apply zenon_H12c. % 18.52/18.69 rewrite <- zenon_D_pnotp. % 18.52/18.69 exact zenon_H113. % 18.52/18.69 cut (((e2) = (e2))); [idtac | apply NNPP; zenon_intro zenon_H7e]. % 18.52/18.69 cut (((op (e1) (e2)) = (e3))); [idtac | apply NNPP; zenon_intro zenon_H16d]. % 18.52/18.69 congruence. % 18.52/18.69 exact (zenon_H16d zenon_H16c). % 18.52/18.69 apply zenon_H7e. apply refl_equal. % 18.52/18.69 apply zenon_H85. apply refl_equal. % 18.52/18.69 apply zenon_H85. apply refl_equal. % 18.52/18.69 (* end of lemma zenon_L116_ *) % 18.52/18.69 assert (zenon_L117_ : (~((op (e0) (e3)) = (op (e1) (e3)))) -> ((op (e0) (e3)) = (e3)) -> ((op (e1) (e3)) = (e3)) -> False). % 18.52/18.69 do 0 intro. intros zenon_H1d zenon_He3 zenon_Hdc. % 18.52/18.69 cut (((op (e0) (e3)) = (e3)) = ((op (e0) (e3)) = (op (e1) (e3)))). % 18.52/18.69 intro zenon_D_pnotp. % 18.52/18.69 apply zenon_H1d. % 18.52/18.69 rewrite <- zenon_D_pnotp. % 18.52/18.69 exact zenon_He3. % 18.52/18.69 cut (((e3) = (op (e1) (e3)))); [idtac | apply NNPP; zenon_intro zenon_H16e]. % 18.52/18.69 cut (((op (e0) (e3)) = (op (e0) (e3)))); [idtac | apply NNPP; zenon_intro zenon_H21]. % 18.52/18.69 congruence. % 18.52/18.69 apply zenon_H21. apply refl_equal. % 18.52/18.69 apply zenon_H16e. apply sym_equal. exact zenon_Hdc. % 18.52/18.69 (* end of lemma zenon_L117_ *) % 18.52/18.69 assert (zenon_L118_ : (((op (e1) (e0)) = (e3))\/(((op (e1) (e1)) = (e3))\/(((op (e1) (e2)) = (e3))\/((op (e1) (e3)) = (e3))))) -> (~((op (e3) (e0)) = (op (e3) (e3)))) -> ((op (e3) (e0)) = (e2)) -> ((op (e2) (e0)) = (e2)) -> (~((op (e2) (e0)) = (op (e2) (e3)))) -> ((op (e1) (e3)) = (e1)) -> (~((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 (e0) (e1)) = (op (e1) (e1)))) -> (~((op (e3) (e3)) = (e3))) -> (~((op (e0) (e2)) = (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 (e0) (e3)) = (e2))\/(((op (e1) (e3)) = (e2))\/(((op (e2) (e3)) = (e2))\/((op (e3) (e3)) = (e2))))) -> (~((e2) = (e3))) -> ((op (e1) (e2)) = (e2)) -> (~((op (e0) (e3)) = (op (e1) (e3)))) -> ((op (e0) (e3)) = (e3)) -> False). % 18.52/18.69 do 0 intro. intros zenon_H16f zenon_H71 zenon_H148 zenon_Hee zenon_H5b zenon_Hd6 zenon_H7c zenon_H168 zenon_H95 zenon_H7a zenon_H10e zenon_H102 zenon_H14f zenon_H160 zenon_H165 zenon_H145 zenon_H12b zenon_H113 zenon_H1d zenon_He3. % 18.52/18.69 apply (zenon_or_s _ _ zenon_H16f); [ zenon_intro zenon_H9e | zenon_intro zenon_H170 ]. % 18.52/18.69 apply (zenon_L107_); trivial. % 18.52/18.69 apply (zenon_or_s _ _ zenon_H170); [ zenon_intro zenon_H13f | zenon_intro zenon_H171 ]. % 18.52/18.69 apply (zenon_L115_); trivial. % 18.52/18.69 apply (zenon_or_s _ _ zenon_H171); [ zenon_intro zenon_H16c | zenon_intro zenon_Hdc ]. % 18.52/18.69 apply (zenon_L116_); trivial. % 18.52/18.69 apply (zenon_L117_); trivial. % 18.52/18.69 (* end of lemma zenon_L118_ *) % 18.52/18.69 assert (zenon_L119_ : ((op (e3) (e3)) = (e2)) -> ((op (e3) (e2)) = (e2)) -> (~((op (e3) (e2)) = (op (e3) (e3)))) -> False). % 18.52/18.69 do 0 intro. intros zenon_Hf6 zenon_H151 zenon_H62. % 18.52/18.69 elim (classic ((op (e3) (e3)) = (op (e3) (e3)))); [ zenon_intro zenon_H63 | zenon_intro zenon_H64 ]. % 18.52/18.69 cut (((op (e3) (e3)) = (op (e3) (e3))) = ((op (e3) (e2)) = (op (e3) (e3)))). % 18.52/18.69 intro zenon_D_pnotp. % 18.52/18.69 apply zenon_H62. % 18.52/18.69 rewrite <- zenon_D_pnotp. % 18.52/18.69 exact zenon_H63. % 18.52/18.69 cut (((op (e3) (e3)) = (op (e3) (e3)))); [idtac | apply NNPP; zenon_intro zenon_H64]. % 18.52/18.69 cut (((op (e3) (e3)) = (op (e3) (e2)))); [idtac | apply NNPP; zenon_intro zenon_H65]. % 18.52/18.69 congruence. % 18.52/18.69 cut (((op (e3) (e3)) = (e2)) = ((op (e3) (e3)) = (op (e3) (e2)))). % 18.52/18.69 intro zenon_D_pnotp. % 18.52/18.69 apply zenon_H65. % 18.52/18.69 rewrite <- zenon_D_pnotp. % 18.52/18.69 exact zenon_Hf6. % 18.52/18.69 cut (((e2) = (op (e3) (e2)))); [idtac | apply NNPP; zenon_intro zenon_H152]. % 18.52/18.69 cut (((op (e3) (e3)) = (op (e3) (e3)))); [idtac | apply NNPP; zenon_intro zenon_H64]. % 18.52/18.69 congruence. % 18.52/18.69 apply zenon_H64. apply refl_equal. % 18.52/18.69 apply zenon_H152. apply sym_equal. exact zenon_H151. % 18.52/18.69 apply zenon_H64. apply refl_equal. % 18.52/18.69 apply zenon_H64. apply refl_equal. % 18.52/18.69 (* end of lemma zenon_L119_ *) % 18.52/18.69 assert (zenon_L120_ : (((op (e0) (e3)) = (e2))\/(((op (e1) (e3)) = (e2))\/(((op (e2) (e3)) = (e2))\/((op (e3) (e3)) = (e2))))) -> (~((e2) = (e3))) -> ((op (e0) (e3)) = (e3)) -> (~((e1) = (e2))) -> ((op (e1) (e3)) = (e1)) -> (~((op (e2) (e0)) = (op (e2) (e3)))) -> ((op (e2) (e0)) = (e2)) -> ((op (e3) (e2)) = (e2)) -> (~((op (e3) (e2)) = (op (e3) (e3)))) -> False). % 18.52/18.69 do 0 intro. intros zenon_H145 zenon_H12b zenon_He3 zenon_H7c zenon_Hd6 zenon_H5b zenon_Hee zenon_H151 zenon_H62. % 18.52/18.69 apply (zenon_or_s _ _ zenon_H145); [ zenon_intro zenon_Hcd | zenon_intro zenon_H146 ]. % 18.52/18.69 apply (zenon_L81_); trivial. % 18.52/18.69 apply (zenon_or_s _ _ zenon_H146); [ zenon_intro zenon_Hd7 | zenon_intro zenon_H147 ]. % 18.52/18.69 apply (zenon_L101_); trivial. % 18.52/18.69 apply (zenon_or_s _ _ zenon_H147); [ zenon_intro zenon_H11d | zenon_intro zenon_Hf6 ]. % 18.52/18.69 apply (zenon_L73_); trivial. % 18.52/18.69 apply (zenon_L119_); trivial. % 18.52/18.69 (* end of lemma zenon_L120_ *) % 18.52/18.69 assert (zenon_L121_ : (((op (e0) (e2)) = (e2))\/(((op (e1) (e2)) = (e2))\/(((op (e2) (e2)) = (e2))\/((op (e3) (e2)) = (e2))))) -> ((op (e3) (e0)) = (e0)) -> (~((e0) = (e2))) -> (~((op (e0) (e3)) = (op (e2) (e3)))) -> (~((op (e2) (e3)) = (op (e3) (e3)))) -> ((op (e1) (e3)) = (e0)) -> (~((op (e2) (e3)) = (e0))) -> (((op (e2) (e3)) = (e0))\/(((op (e2) (e3)) = (e1))\/(((op (e2) (e3)) = (e2))\/((op (e2) (e3)) = (e3))))) -> (~((op (e3) (e1)) = (op (e3) (e3)))) -> (((op (e1) (e0)) = (e3))\/(((op (e1) (e1)) = (e3))\/(((op (e1) (e2)) = (e3))\/((op (e1) (e3)) = (e3))))) -> (~((op (e3) (e0)) = (op (e3) (e3)))) -> (((op (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 (e3) (e3)) = (e3))) -> (~((op (e0) (e2)) = (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 (e0) (e3)) = (op (e1) (e3)))) -> (((op (e3) (e0)) = (e2))\/(((op (e3) (e1)) = (e2))\/(((op (e3) (e2)) = (e2))\/((op (e3) (e3)) = (e2))))) -> (~((op (e2) (e2)) = (e2))) -> (((op (e0) (e3)) = (e2))\/(((op (e1) (e3)) = (e2))\/(((op (e2) (e3)) = (e2))\/((op (e3) (e3)) = (e2))))) -> (~((e2) = (e3))) -> ((op (e0) (e3)) = (e3)) -> (~((e1) = (e2))) -> ((op (e1) (e3)) = (e1)) -> (~((op (e2) (e0)) = (op (e2) (e3)))) -> ((op (e2) (e0)) = (e2)) -> (~((op (e3) (e2)) = (op (e3) (e3)))) -> False). % 18.52/18.69 do 0 intro. intros zenon_H172 zenon_H44 zenon_H149 zenon_He2 zenon_Hf3 zenon_H1f zenon_H32 zenon_H11f zenon_H130 zenon_H16f zenon_H71 zenon_H168 zenon_H95 zenon_H7a zenon_H10e zenon_H102 zenon_H14f zenon_H160 zenon_H165 zenon_H1d zenon_H153 zenon_H173 zenon_H145 zenon_H12b zenon_He3 zenon_H7c zenon_Hd6 zenon_H5b zenon_Hee zenon_H62. % 18.52/18.69 apply (zenon_or_s _ _ zenon_H172); [ zenon_intro zenon_H150 | zenon_intro zenon_H174 ]. % 18.52/18.69 apply (zenon_L105_); trivial. % 18.52/18.69 apply (zenon_or_s _ _ zenon_H174); [ zenon_intro zenon_H113 | zenon_intro zenon_H175 ]. % 18.52/18.69 apply (zenon_or_s _ _ zenon_H153); [ zenon_intro zenon_H148 | zenon_intro zenon_H154 ]. % 18.52/18.69 apply (zenon_L118_); trivial. % 18.52/18.69 apply (zenon_or_s _ _ zenon_H154); [ zenon_intro zenon_H14d | zenon_intro zenon_H155 ]. % 18.52/18.69 apply (zenon_L103_); trivial. % 18.52/18.69 apply (zenon_or_s _ _ zenon_H155); [ zenon_intro zenon_H151 | zenon_intro zenon_Hf6 ]. % 18.52/18.69 apply (zenon_L120_); trivial. % 18.52/18.69 apply (zenon_L98_); trivial. % 18.52/18.69 apply (zenon_or_s _ _ zenon_H175); [ zenon_intro zenon_H176 | zenon_intro zenon_H151 ]. % 18.52/18.69 exact (zenon_H173 zenon_H176). % 18.52/18.69 apply (zenon_L120_); trivial. % 18.52/18.69 (* end of lemma zenon_L121_ *) % 18.52/18.69 assert (zenon_L122_ : (((op (e1) (e0)) = (e0))\/(((op (e1) (e1)) = (e0))\/(((op (e1) (e2)) = (e0))\/((op (e1) (e3)) = (e0))))) -> (~((op (e1) (e0)) = (e0))) -> (~((op (e1) (e1)) = (e0))) -> (~((op (e2) (e1)) = (e0))) -> (~((op (e2) (e0)) = (e0))) -> (((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)) = (e3)) -> (((op (e3) (e3)) = (e0))\/(((op (e3) (e3)) = (e1))\/(((op (e3) (e3)) = (e2))\/((op (e3) (e3)) = (e3))))) -> (~((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 (e3) (e0)) = (e1))\/(((op (e3) (e1)) = (e1))\/(((op (e3) (e2)) = (e1))\/((op (e3) (e3)) = (e1))))) -> (~((e0) = (e1))) -> (~((op (e1) (e2)) = (op (e3) (e2)))) -> (~((op (e0) (e3)) = (op (e3) (e3)))) -> (~((op (e0) (e3)) = (e0))) -> (((op (e0) (e3)) = (e0))\/(((op (e0) (e3)) = (e1))\/(((op (e0) (e3)) = (e2))\/((op (e0) (e3)) = (e3))))) -> (~((op (e1) (e1)) = (e1))) -> ((op (e0) (e1)) = (e0)) -> (((op (e0) (e1)) = (e1))\/(((op (e1) (e1)) = (e1))\/(((op (e2) (e1)) = (e1))\/((op (e3) (e1)) = (e1))))) -> (((op (e0) (e2)) = (e2))\/(((op (e1) (e2)) = (e2))\/(((op (e2) (e2)) = (e2))\/((op (e3) (e2)) = (e2))))) -> ((op (e3) (e0)) = (e0)) -> (~((e0) = (e2))) -> (~((op (e0) (e3)) = (op (e2) (e3)))) -> (~((op (e2) (e3)) = (op (e3) (e3)))) -> (~((op (e2) (e3)) = (e0))) -> (((op (e2) (e3)) = (e0))\/(((op (e2) (e3)) = (e1))\/(((op (e2) (e3)) = (e2))\/((op (e2) (e3)) = (e3))))) -> (~((op (e3) (e1)) = (op (e3) (e3)))) -> (((op (e1) (e0)) = (e3))\/(((op (e1) (e1)) = (e3))\/(((op (e1) (e2)) = (e3))\/((op (e1) (e3)) = (e3))))) -> (~((op (e3) (e0)) = (op (e3) (e3)))) -> (((op (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 (e3) (e3)) = (e3))) -> (~((op (e0) (e2)) = (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 (e0) (e3)) = (op (e1) (e3)))) -> (((op (e3) (e0)) = (e2))\/(((op (e3) (e1)) = (e2))\/(((op (e3) (e2)) = (e2))\/((op (e3) (e3)) = (e2))))) -> (~((op (e2) (e2)) = (e2))) -> (((op (e0) (e3)) = (e2))\/(((op (e1) (e3)) = (e2))\/(((op (e2) (e3)) = (e2))\/((op (e3) (e3)) = (e2))))) -> (~((e2) = (e3))) -> ((op (e0) (e3)) = (e3)) -> (~((e1) = (e2))) -> (~((op (e2) (e0)) = (op (e2) (e3)))) -> ((op (e2) (e0)) = (e2)) -> (~((op (e3) (e2)) = (op (e3) (e3)))) -> False). % 18.52/18.69 do 0 intro. intros zenon_H22 zenon_H23 zenon_H24 zenon_H31 zenon_H30 zenon_H2f zenon_H128 zenon_H9e zenon_H101 zenon_H2b zenon_Haf zenon_H106 zenon_He8 zenon_Ha1 zenon_H115 zenon_Hc2 zenon_H76 zenon_He4 zenon_H10a zenon_H49 zenon_H109 zenon_H172 zenon_H44 zenon_H149 zenon_He2 zenon_Hf3 zenon_H32 zenon_H11f zenon_H130 zenon_H16f zenon_H71 zenon_H168 zenon_H95 zenon_H7a zenon_H10e zenon_H102 zenon_H14f zenon_H160 zenon_H165 zenon_H1d zenon_H153 zenon_H173 zenon_H145 zenon_H12b zenon_He3 zenon_H7c zenon_H5b zenon_Hee zenon_H62. % 18.52/18.69 apply (zenon_or_s _ _ zenon_H22); [ zenon_intro zenon_H27 | zenon_intro zenon_H26 ]. % 18.52/18.69 exact (zenon_H23 zenon_H27). % 18.52/18.69 apply (zenon_or_s _ _ zenon_H26); [ zenon_intro zenon_H29 | zenon_intro zenon_H28 ]. % 18.52/18.69 exact (zenon_H24 zenon_H29). % 18.52/18.69 apply (zenon_or_s _ _ zenon_H28); [ zenon_intro zenon_H2a | zenon_intro zenon_H1f ]. % 18.52/18.69 apply (zenon_L4_); trivial. % 18.52/18.69 apply (zenon_or_s _ _ zenon_H128); [ zenon_intro zenon_H9d | zenon_intro zenon_H129 ]. % 18.52/18.69 apply (zenon_L37_); trivial. % 18.52/18.69 apply (zenon_or_s _ _ zenon_H129); [ zenon_intro zenon_H10d | zenon_intro zenon_H12a ]. % 18.52/18.69 exact (zenon_H10a zenon_H10d). % 18.52/18.69 apply (zenon_or_s _ _ zenon_H12a); [ zenon_intro zenon_Hf0 | zenon_intro zenon_Hd6 ]. % 18.52/18.69 apply (zenon_or_s _ _ zenon_H109); [ zenon_intro zenon_Ha0 | zenon_intro zenon_H10b ]. % 18.52/18.69 apply (zenon_L38_); trivial. % 18.52/18.69 apply (zenon_or_s _ _ zenon_H10b); [ zenon_intro zenon_H10d | zenon_intro zenon_H10c ]. % 18.52/18.69 exact (zenon_H10a zenon_H10d). % 18.52/18.69 apply (zenon_or_s _ _ zenon_H10c); [ zenon_intro zenon_Ha5 | zenon_intro zenon_Hae ]. % 18.52/18.69 apply (zenon_or_s _ _ zenon_He8); [ zenon_intro zenon_Hac | zenon_intro zenon_Heb ]. % 18.52/18.69 apply (zenon_L41_); trivial. % 18.52/18.69 apply (zenon_or_s _ _ zenon_Heb); [ zenon_intro zenon_Hae | zenon_intro zenon_Hec ]. % 18.52/18.69 apply (zenon_L42_); trivial. % 18.52/18.69 apply (zenon_or_s _ _ zenon_Hec); [ zenon_intro zenon_Hba | zenon_intro zenon_Hc4 ]. % 18.52/18.69 apply (zenon_L69_); trivial. % 18.52/18.69 apply (zenon_L99_); trivial. % 18.52/18.69 apply (zenon_L65_); trivial. % 18.52/18.69 apply (zenon_L121_); trivial. % 18.52/18.69 (* end of lemma zenon_L122_ *) % 18.52/18.69 assert (zenon_L123_ : ((op (e1) (e0)) = (e1)) -> ((op (e1) (e0)) = (e2)) -> (~((e1) = (e2))) -> False). % 18.52/18.69 do 0 intro. intros zenon_H9d zenon_H86 zenon_H7c. % 18.52/18.69 elim (classic ((e2) = (e2))); [ zenon_intro zenon_H7d | zenon_intro zenon_H7e ]. % 18.52/18.69 cut (((e2) = (e2)) = ((e1) = (e2))). % 18.52/18.69 intro zenon_D_pnotp. % 18.52/18.69 apply zenon_H7c. % 18.52/18.69 rewrite <- zenon_D_pnotp. % 18.52/18.69 exact zenon_H7d. % 18.52/18.69 cut (((e2) = (e2))); [idtac | apply NNPP; zenon_intro zenon_H7e]. % 18.52/18.69 cut (((e2) = (e1))); [idtac | apply NNPP; zenon_intro zenon_H7f]. % 18.52/18.69 congruence. % 18.52/18.69 cut (((op (e1) (e0)) = (e1)) = ((e2) = (e1))). % 18.52/18.69 intro zenon_D_pnotp. % 18.52/18.69 apply zenon_H7f. % 18.52/18.69 rewrite <- zenon_D_pnotp. % 18.52/18.69 exact zenon_H9d. % 18.52/18.69 cut (((e1) = (e1))); [idtac | apply NNPP; zenon_intro zenon_H79]. % 18.52/18.69 cut (((op (e1) (e0)) = (e2))); [idtac | apply NNPP; zenon_intro zenon_H177]. % 18.52/18.69 congruence. % 18.52/18.69 exact (zenon_H177 zenon_H86). % 18.52/18.69 apply zenon_H79. apply refl_equal. % 18.52/18.69 apply zenon_H7e. apply refl_equal. % 18.52/18.69 apply zenon_H7e. apply refl_equal. % 18.52/18.69 (* end of lemma zenon_L123_ *) % 18.52/18.69 assert (zenon_L124_ : ((~((op (e1) (e2)) = (e0)))\/((op (e1) (e0)) = (e2))) -> (~((e1) = (e2))) -> (((op (e0) (e0)) = (e0))\/(((op (e0) (e1)) = (e0))\/(((op (e0) (e2)) = (e0))\/((op (e0) (e3)) = (e0))))) -> (~((op (e0) (e3)) = (e0))) -> (~((op (e0) (e2)) = (e0))) -> (~((op (e1) (e0)) = (e0))) -> (((op (e0) (e0)) = (e0))\/(((op (e1) (e0)) = (e0))\/(((op (e2) (e0)) = (e0))\/((op (e3) (e0)) = (e0))))) -> (~((op (e3) (e0)) = (op (e3) (e2)))) -> (~((op (e2) (e2)) = (op (e2) (e3)))) -> (~((op (e3) (e0)) = (op (e3) (e3)))) -> (~((op (e0) (e1)) = (op (e0) (e2)))) -> (~((op (e1) (e1)) = (op (e1) (e2)))) -> (~((op (e2) (e0)) = (op (e2) (e2)))) -> (((op (e0) (e3)) = (e0))\/(((op (e1) (e3)) = (e0))\/(((op (e2) (e3)) = (e0))\/((op (e3) (e3)) = (e0))))) -> (~((op (e3) (e2)) = (op (e3) (e3)))) -> (~((op (e2) (e0)) = (op (e2) (e3)))) -> (~((op (e1) (e1)) = (op (e1) (e3)))) -> (~((op (e0) (e1)) = (op (e0) (e3)))) -> (((op (e0) (e2)) = (e0))\/(((op (e1) (e2)) = (e0))\/(((op (e2) (e2)) = (e0))\/((op (e3) (e2)) = (e0))))) -> (~((op (e1) (e0)) = (op (e1) (e1)))) -> (((op (e1) (e0)) = (e0))\/(((op (e1) (e1)) = (e0))\/(((op (e1) (e2)) = (e0))\/((op (e1) (e3)) = (e0))))) -> (~((op (e0) (e0)) = (e0))) -> (~((e1) = (e3))) -> ((op (e1) (e0)) = (e1)) -> ((~((op (e1) (e3)) = (e0)))\/((op (e1) (e0)) = (e3))) -> False). % 18.52/18.69 do 0 intro. intros zenon_H178 zenon_H7c zenon_H74 zenon_H76 zenon_H75 zenon_H23 zenon_H3e zenon_H6f zenon_H6d zenon_H71 zenon_H4a zenon_H4f zenon_H52 zenon_H67 zenon_H62 zenon_H5b zenon_H57 zenon_H54 zenon_H6a zenon_H45 zenon_H22 zenon_H3f zenon_H95 zenon_H9d zenon_H179. % 18.52/18.69 apply (zenon_or_s _ _ zenon_H178); [ zenon_intro zenon_H25 | zenon_intro zenon_H86 ]. % 18.52/18.69 apply (zenon_or_s _ _ zenon_H179); [ zenon_intro zenon_H38 | zenon_intro zenon_H9e ]. % 18.52/18.69 apply (zenon_L24_); trivial. % 18.52/18.69 apply (zenon_L37_); trivial. % 18.52/18.69 apply (zenon_L123_); trivial. % 18.52/18.69 (* end of lemma zenon_L124_ *) % 18.52/18.69 assert (zenon_L125_ : (~((op (e2) (e3)) = (op (e3) (e3)))) -> ((op (e1) (e3)) = (e0)) -> (~((op (e2) (e3)) = (e0))) -> (((op (e2) (e3)) = (e0))\/(((op (e2) (e3)) = (e1))\/(((op (e2) (e3)) = (e2))\/((op (e2) (e3)) = (e3))))) -> (~((op (e0) (e2)) = (op (e3) (e2)))) -> ((op (e0) (e2)) = (e2)) -> (((op (e0) (e3)) = (e2))\/(((op (e1) (e3)) = (e2))\/(((op (e2) (e3)) = (e2))\/((op (e3) (e3)) = (e2))))) -> (~((op (e2) (e0)) = (op (e2) (e3)))) -> ((op (e2) (e0)) = (e2)) -> (~((e0) = (e2))) -> (((op (e3) (e0)) = (e2))\/(((op (e3) (e1)) = (e2))\/(((op (e3) (e2)) = (e2))\/((op (e3) (e3)) = (e2))))) -> ((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))))) -> (~((e2) = (e3))) -> (~((op (e3) (e1)) = (op (e3) (e3)))) -> ((op (e3) (e1)) = (e1)) -> ((op (e2) (e2)) = (e1)) -> (~((op (e2) (e2)) = (op (e2) (e3)))) -> (~((e1) = (e3))) -> (~((e1) = (e2))) -> (((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)) = (e0))\/(((op (e1) (e3)) = (e1))\/(((op (e1) (e3)) = (e2))\/((op (e1) (e3)) = (e3))))) -> (~((op (e1) (e3)) = (op (e3) (e3)))) -> (~((op (e1) (e0)) = (op (e1) (e3)))) -> ((op (e1) (e0)) = (e2)) -> (~((op (e1) (e3)) = (op (e2) (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) (e0)) = (e1))\/(((op (e1) (e1)) = (e1))\/(((op (e1) (e2)) = (e1))\/((op (e1) (e3)) = (e1))))) -> ((op (e1) (e0)) = (e3)) -> (~((op (e1) (e1)) = (e1))) -> (~((op (e1) (e2)) = (op (e2) (e2)))) -> (~((op (e0) (e3)) = (op (e1) (e3)))) -> (~((op (e0) (e3)) = (e0))) -> (((op (e0) (e3)) = (e0))\/(((op (e0) (e3)) = (e1))\/(((op (e0) (e3)) = (e2))\/((op (e0) (e3)) = (e3))))) -> (~((op (e3) (e3)) = (e3))) -> False). % 18.52/18.69 do 0 intro. intros zenon_Hf3 zenon_H1f zenon_H32 zenon_H11f zenon_H14f zenon_H150 zenon_H145 zenon_H5b zenon_Hee zenon_H149 zenon_H153 zenon_Hd6 zenon_He2 zenon_H136 zenon_H12b zenon_H130 zenon_Hae zenon_Hf1 zenon_H6d zenon_H95 zenon_H7c zenon_H133 zenon_Hc2 zenon_Hdf zenon_Hd5 zenon_Hd8 zenon_H86 zenon_Hdb zenon_H44 zenon_H71 zenon_H101 zenon_H128 zenon_H9e zenon_H10a zenon_H2b zenon_H1d zenon_H76 zenon_He4 zenon_H102. % 18.52/18.69 apply (zenon_or_s _ _ zenon_H136); [ zenon_intro zenon_He3 | zenon_intro zenon_H137 ]. % 18.52/18.69 apply (zenon_L105_); trivial. % 18.52/18.69 apply (zenon_or_s _ _ zenon_H137); [ zenon_intro zenon_Hdc | zenon_intro zenon_H138 ]. % 18.52/18.69 apply (zenon_L83_); trivial. % 18.52/18.69 apply (zenon_or_s _ _ zenon_H138); [ zenon_intro zenon_Hdd | zenon_intro zenon_H105 ]. % 18.52/18.69 apply (zenon_L89_); trivial. % 18.52/18.69 exact (zenon_H102 zenon_H105). % 18.52/18.69 (* end of lemma zenon_L125_ *) % 18.52/18.69 assert (zenon_L126_ : (~((op (e1) (e3)) = (op (e2) (e3)))) -> ((op (e1) (e3)) = (e1)) -> ((op (e2) (e3)) = (e1)) -> False). % 18.52/18.69 do 0 intro. intros zenon_Hdb zenon_Hd6 zenon_Hf4. % 18.52/18.69 cut (((op (e1) (e3)) = (e1)) = ((op (e1) (e3)) = (op (e2) (e3)))). % 18.52/18.69 intro zenon_D_pnotp. % 18.52/18.69 apply zenon_Hdb. % 18.52/18.69 rewrite <- zenon_D_pnotp. % 18.52/18.69 exact zenon_Hd6. % 18.52/18.69 cut (((e1) = (op (e2) (e3)))); [idtac | apply NNPP; zenon_intro zenon_H17a]. % 18.52/18.69 cut (((op (e1) (e3)) = (op (e1) (e3)))); [idtac | apply NNPP; zenon_intro zenon_H59]. % 18.52/18.69 congruence. % 18.52/18.69 apply zenon_H59. apply refl_equal. % 18.52/18.69 apply zenon_H17a. apply sym_equal. exact zenon_Hf4. % 18.52/18.69 (* end of lemma zenon_L126_ *) % 18.52/18.69 assert (zenon_L127_ : ((op (e3) (e0)) = (e0)) -> ((op (e2) (e0)) = (e0)) -> (~((op (e2) (e0)) = (op (e3) (e0)))) -> False). % 18.52/18.69 do 0 intro. intros zenon_H44 zenon_H34 zenon_H17b. % 18.52/18.69 elim (classic ((op (e3) (e0)) = (op (e3) (e0)))); [ zenon_intro zenon_H17c | zenon_intro zenon_H70 ]. % 18.52/18.69 cut (((op (e3) (e0)) = (op (e3) (e0))) = ((op (e2) (e0)) = (op (e3) (e0)))). % 18.52/18.69 intro zenon_D_pnotp. % 18.52/18.69 apply zenon_H17b. % 18.52/18.69 rewrite <- zenon_D_pnotp. % 18.52/18.69 exact zenon_H17c. % 18.52/18.69 cut (((op (e3) (e0)) = (op (e3) (e0)))); [idtac | apply NNPP; zenon_intro zenon_H70]. % 18.52/18.69 cut (((op (e3) (e0)) = (op (e2) (e0)))); [idtac | apply NNPP; zenon_intro zenon_H17d]. % 18.52/18.69 congruence. % 18.52/18.69 cut (((op (e3) (e0)) = (e0)) = ((op (e3) (e0)) = (op (e2) (e0)))). % 18.52/18.69 intro zenon_D_pnotp. % 18.52/18.69 apply zenon_H17d. % 18.52/18.69 rewrite <- zenon_D_pnotp. % 18.52/18.69 exact zenon_H44. % 18.52/18.69 cut (((e0) = (op (e2) (e0)))); [idtac | apply NNPP; zenon_intro zenon_H5f]. % 18.52/18.69 cut (((op (e3) (e0)) = (op (e3) (e0)))); [idtac | apply NNPP; zenon_intro zenon_H70]. % 18.52/18.69 congruence. % 18.52/18.69 apply zenon_H70. apply refl_equal. % 18.52/18.69 apply zenon_H5f. apply sym_equal. exact zenon_H34. % 18.52/18.69 apply zenon_H70. apply refl_equal. % 18.52/18.69 apply zenon_H70. apply refl_equal. % 18.52/18.69 (* end of lemma zenon_L127_ *) % 18.52/18.69 assert (zenon_L128_ : (~((op (e0) (e1)) = (op (e2) (e1)))) -> ((op (e0) (e1)) = (e0)) -> ((op (e2) (e1)) = (e0)) -> False). % 18.52/18.69 do 0 intro. intros zenon_H17e zenon_H49 zenon_H36. % 18.52/18.69 cut (((op (e0) (e1)) = (e0)) = ((op (e0) (e1)) = (op (e2) (e1)))). % 18.52/18.69 intro zenon_D_pnotp. % 18.52/18.69 apply zenon_H17e. % 18.52/18.69 rewrite <- zenon_D_pnotp. % 18.52/18.69 exact zenon_H49. % 18.52/18.69 cut (((e0) = (op (e2) (e1)))); [idtac | apply NNPP; zenon_intro zenon_H17f]. % 18.52/18.69 cut (((op (e0) (e1)) = (op (e0) (e1)))); [idtac | apply NNPP; zenon_intro zenon_H112]. % 18.52/18.69 congruence. % 18.52/18.69 apply zenon_H112. apply refl_equal. % 18.52/18.69 apply zenon_H17f. apply sym_equal. exact zenon_H36. % 18.52/18.69 (* end of lemma zenon_L128_ *) % 18.52/18.69 assert (zenon_L129_ : (((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)) = (op (e3) (e1)))) -> ((op (e2) (e1)) = (e1)) -> ((op (e2) (e2)) = (e0)) -> ((op (e0) (e2)) = (e3)) -> ((op (e0) (e3)) = (e2)) -> ((op (e1) (e3)) = (e0)) -> False). % 18.52/18.69 do 0 intro. intros zenon_He8 zenon_Ha1 zenon_H44 zenon_Haf zenon_Ha5 zenon_H2c zenon_Ha9 zenon_Hcd zenon_H1f. % 18.52/18.69 apply (zenon_or_s _ _ zenon_He8); [ zenon_intro zenon_Hac | zenon_intro zenon_Heb ]. % 18.52/18.69 apply (zenon_L41_); trivial. % 18.52/18.69 apply (zenon_or_s _ _ zenon_Heb); [ zenon_intro zenon_Hae | zenon_intro zenon_Hec ]. % 18.52/18.69 apply (zenon_L42_); trivial. % 18.52/18.69 apply (zenon_or_s _ _ zenon_Hec); [ zenon_intro zenon_Hba | zenon_intro zenon_Hc4 ]. % 18.52/18.69 apply (zenon_L45_); trivial. % 18.52/18.69 apply (zenon_L49_); trivial. % 18.52/18.69 (* end of lemma zenon_L129_ *) % 18.52/18.69 assert (zenon_L130_ : (~((op (e1) (e3)) = (op (e2) (e3)))) -> ((op (e1) (e3)) = (e0)) -> ((op (e2) (e3)) = (e0)) -> False). % 18.52/18.69 do 0 intro. intros zenon_Hdb zenon_H1f zenon_H37. % 18.52/18.69 cut (((op (e1) (e3)) = (e0)) = ((op (e1) (e3)) = (op (e2) (e3)))). % 18.52/18.69 intro zenon_D_pnotp. % 18.52/18.69 apply zenon_Hdb. % 18.52/18.69 rewrite <- zenon_D_pnotp. % 18.52/18.69 exact zenon_H1f. % 18.52/18.69 cut (((e0) = (op (e2) (e3)))); [idtac | apply NNPP; zenon_intro zenon_H180]. % 18.52/18.69 cut (((op (e1) (e3)) = (op (e1) (e3)))); [idtac | apply NNPP; zenon_intro zenon_H59]. % 18.52/18.69 congruence. % 18.52/18.69 apply zenon_H59. apply refl_equal. % 18.52/18.69 apply zenon_H180. apply sym_equal. exact zenon_H37. % 18.52/18.69 (* end of lemma zenon_L130_ *) % 18.52/18.69 assert (zenon_L131_ : (((op (e2) (e0)) = (e0))\/(((op (e2) (e1)) = (e0))\/(((op (e2) (e2)) = (e0))\/((op (e2) (e3)) = (e0))))) -> (~((op (e2) (e0)) = (op (e3) (e0)))) -> ((op (e0) (e1)) = (e0)) -> (~((op (e0) (e1)) = (op (e2) (e1)))) -> ((op (e0) (e3)) = (e2)) -> ((op (e0) (e2)) = (e3)) -> ((op (e2) (e1)) = (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 (e1) (e3)) = (op (e2) (e3)))) -> ((op (e1) (e3)) = (e0)) -> False). % 18.52/18.69 do 0 intro. intros zenon_H2f zenon_H17b zenon_H49 zenon_H17e zenon_Hcd zenon_Ha9 zenon_Ha5 zenon_Haf zenon_H44 zenon_Ha1 zenon_He8 zenon_Hdb zenon_H1f. % 18.52/18.69 apply (zenon_or_s _ _ zenon_H2f); [ zenon_intro zenon_H34 | zenon_intro zenon_H33 ]. % 18.52/18.69 apply (zenon_L127_); trivial. % 18.52/18.69 apply (zenon_or_s _ _ zenon_H33); [ zenon_intro zenon_H36 | zenon_intro zenon_H35 ]. % 18.52/18.69 apply (zenon_L128_); trivial. % 18.52/18.69 apply (zenon_or_s _ _ zenon_H35); [ zenon_intro zenon_H2c | zenon_intro zenon_H37 ]. % 18.52/18.69 apply (zenon_L129_); trivial. % 18.52/18.69 apply (zenon_L130_); trivial. % 18.52/18.69 (* end of lemma zenon_L131_ *) % 18.52/18.69 assert (zenon_L132_ : (((op (e0) (e1)) = (e1))\/(((op (e1) (e1)) = (e1))\/(((op (e2) (e1)) = (e1))\/((op (e3) (e1)) = (e1))))) -> (~((op (e1) (e1)) = (e1))) -> (~((op (e1) (e3)) = (op (e2) (e3)))) -> (((op (e3) (e0)) = (e1))\/(((op (e3) (e1)) = (e1))\/(((op (e3) (e2)) = (e1))\/((op (e3) (e3)) = (e1))))) -> (~((e0) = (e1))) -> ((op (e0) (e2)) = (e3)) -> ((op (e0) (e3)) = (e2)) -> (~((op (e0) (e1)) = (op (e2) (e1)))) -> ((op (e0) (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 (e2) (e0)) = (e1))\/(((op (e2) (e1)) = (e1))\/(((op (e2) (e2)) = (e1))\/((op (e2) (e3)) = (e1))))) -> (~((e1) = (e2))) -> ((op (e2) (e0)) = (e2)) -> (~((op (e2) (e1)) = (op (e3) (e1)))) -> ((op (e1) (e2)) = (e1)) -> (~((op (e1) (e2)) = (op (e2) (e2)))) -> (((op (e3) (e3)) = (e0))\/(((op (e3) (e3)) = (e1))\/(((op (e3) (e3)) = (e2))\/((op (e3) (e3)) = (e3))))) -> (~((op (e3) (e0)) = (op (e3) (e3)))) -> ((op (e3) (e0)) = (e0)) -> (~((op (e2) (e3)) = (op (e3) (e3)))) -> ((op (e1) (e3)) = (e0)) -> (~((op (e3) (e3)) = (e3))) -> False). % 18.52/18.69 do 0 intro. intros zenon_H109 zenon_H10a zenon_Hdb zenon_He8 zenon_Ha1 zenon_Ha9 zenon_Hcd zenon_H17e zenon_H49 zenon_H17b zenon_H2f zenon_H106 zenon_H7c zenon_Hee zenon_Haf zenon_Hf0 zenon_H2b zenon_H101 zenon_H71 zenon_H44 zenon_Hf3 zenon_H1f zenon_H102. % 18.52/18.69 apply (zenon_or_s _ _ zenon_H109); [ zenon_intro zenon_Ha0 | zenon_intro zenon_H10b ]. % 18.52/18.69 apply (zenon_L38_); trivial. % 18.52/18.69 apply (zenon_or_s _ _ zenon_H10b); [ zenon_intro zenon_H10d | zenon_intro zenon_H10c ]. % 18.52/18.69 exact (zenon_H10a zenon_H10d). % 18.52/18.69 apply (zenon_or_s _ _ zenon_H10c); [ zenon_intro zenon_Ha5 | zenon_intro zenon_Hae ]. % 18.52/18.69 apply (zenon_L131_); trivial. % 18.52/18.69 apply (zenon_L65_); trivial. % 18.52/18.69 (* end of lemma zenon_L132_ *) % 18.52/18.69 assert (zenon_L133_ : (((op (e0) (e1)) = (e1))\/(((op (e1) (e1)) = (e1))\/(((op (e2) (e1)) = (e1))\/((op (e3) (e1)) = (e1))))) -> (~((op (e1) (e1)) = (e1))) -> (~((op (e0) (e1)) = (op (e2) (e1)))) -> ((op (e0) (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 (e2) (e0)) = (e0))) -> (~((op (e2) (e1)) = (e0))) -> (~((op (e3) (e3)) = (e3))) -> ((op (e1) (e3)) = (e0)) -> (~((op (e2) (e3)) = (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 (e0) (e3)) = (e3))\/(((op (e1) (e3)) = (e3))\/(((op (e2) (e3)) = (e3))\/((op (e3) (e3)) = (e3))))) -> (~((e2) = (e3))) -> (~((op (e3) (e1)) = (op (e3) (e3)))) -> (~((op (e2) (e2)) = (op (e2) (e3)))) -> (~((e1) = (e3))) -> (~((e1) = (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)) = (e2)) -> (((op (e1) (e3)) = (e0))\/(((op (e1) (e3)) = (e1))\/(((op (e1) (e3)) = (e2))\/((op (e1) (e3)) = (e3))))) -> (~((op (e1) (e3)) = (op (e3) (e3)))) -> (~((op (e1) (e0)) = (op (e1) (e3)))) -> ((op (e1) (e0)) = (e2)) -> (~((op (e1) (e3)) = (op (e2) (e3)))) -> (((op (e3) (e0)) = (e1))\/(((op (e3) (e1)) = (e1))\/(((op (e3) (e2)) = (e1))\/((op (e3) (e3)) = (e1))))) -> (~((e0) = (e1))) -> (~((op (e2) (e1)) = (op (e3) (e1)))) -> ((op (e0) (e2)) = (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)) = (e1)) -> (~((op (e1) (e2)) = (op (e1) (e3)))) -> ((op (e1) (e3)) = (e1)) -> (~((op (e2) (e0)) = (op (e2) (e2)))) -> (((op (e2) (e0)) = (e1))\/(((op (e2) (e1)) = (e1))\/(((op (e2) (e2)) = (e1))\/((op (e2) (e3)) = (e1))))) -> (~((op (e2) (e3)) = (e0))) -> False). % 18.52/18.69 do 0 intro. intros zenon_H109 zenon_H10a zenon_H17e zenon_H49 zenon_H17b zenon_H2f zenon_H30 zenon_H31 zenon_H102 zenon_H1f zenon_Hf3 zenon_H44 zenon_H71 zenon_H101 zenon_H136 zenon_H12b zenon_H130 zenon_H6d zenon_H95 zenon_H7c zenon_H133 zenon_Hc2 zenon_Hcd zenon_Hdf zenon_Hd5 zenon_Hd8 zenon_H86 zenon_Hdb zenon_He8 zenon_Ha1 zenon_Haf zenon_Ha9 zenon_H139 zenon_H13c zenon_H7a zenon_H124 zenon_Hd6 zenon_H52 zenon_H106 zenon_H32. % 18.52/18.69 apply (zenon_or_s _ _ zenon_H109); [ zenon_intro zenon_Ha0 | zenon_intro zenon_H10b ]. % 18.52/18.69 apply (zenon_L38_); trivial. % 18.52/18.69 apply (zenon_or_s _ _ zenon_H10b); [ zenon_intro zenon_H10d | zenon_intro zenon_H10c ]. % 18.52/18.69 exact (zenon_H10a zenon_H10d). % 18.52/18.69 apply (zenon_or_s _ _ zenon_H10c); [ zenon_intro zenon_Ha5 | zenon_intro zenon_Hae ]. % 18.52/18.69 apply (zenon_L131_); trivial. % 18.52/18.69 apply (zenon_or_s _ _ zenon_H2f); [ zenon_intro zenon_H34 | zenon_intro zenon_H33 ]. % 18.52/18.69 exact (zenon_H30 zenon_H34). % 18.52/18.69 apply (zenon_or_s _ _ zenon_H33); [ zenon_intro zenon_H36 | zenon_intro zenon_H35 ]. % 18.52/18.69 exact (zenon_H31 zenon_H36). % 18.52/18.69 apply (zenon_or_s _ _ zenon_H35); [ zenon_intro zenon_H2c | zenon_intro zenon_H37 ]. % 18.52/18.69 apply (zenon_or_s _ _ zenon_H106); [ zenon_intro zenon_Hed | zenon_intro zenon_H107 ]. % 18.52/18.69 apply (zenon_L94_); trivial. % 18.52/18.69 apply (zenon_or_s _ _ zenon_H107); [ zenon_intro zenon_Ha5 | zenon_intro zenon_H108 ]. % 18.52/18.69 apply (zenon_L129_); trivial. % 18.52/18.69 apply (zenon_or_s _ _ zenon_H108); [ zenon_intro zenon_Hf1 | zenon_intro zenon_Hf4 ]. % 18.52/18.69 apply (zenon_L88_); trivial. % 18.52/18.69 apply (zenon_L64_); trivial. % 18.52/18.69 exact (zenon_H32 zenon_H37). % 18.52/18.69 (* end of lemma zenon_L133_ *) % 18.52/18.69 assert (zenon_L134_ : (~((op (e0) (e0)) = (op (e2) (e0)))) -> ((op (e0) (e0)) = (e1)) -> ((op (e2) (e0)) = (e1)) -> False). % 18.52/18.69 do 0 intro. intros zenon_H39 zenon_H7a zenon_Hed. % 18.52/18.69 cut (((op (e0) (e0)) = (e1)) = ((op (e0) (e0)) = (op (e2) (e0)))). % 18.52/18.69 intro zenon_D_pnotp. % 18.52/18.69 apply zenon_H39. % 18.52/18.69 rewrite <- zenon_D_pnotp. % 18.52/18.69 exact zenon_H7a. % 18.52/18.69 cut (((e1) = (op (e2) (e0)))); [idtac | apply NNPP; zenon_intro zenon_H181]. % 18.52/18.69 cut (((op (e0) (e0)) = (op (e0) (e0)))); [idtac | apply NNPP; zenon_intro zenon_H3d]. % 18.52/18.69 congruence. % 18.52/18.69 apply zenon_H3d. apply refl_equal. % 18.52/18.69 apply zenon_H181. apply sym_equal. exact zenon_Hed. % 18.52/18.69 (* end of lemma zenon_L134_ *) % 18.52/18.69 assert (zenon_L135_ : ((~((op (e2) (e1)) = (e0)))\/((op (e2) (e0)) = (e1))) -> (~((op (e0) (e0)) = (op (e2) (e0)))) -> ((~((op (e2) (e3)) = (e0)))\/((op (e2) (e0)) = (e3))) -> ((op (e1) (e0)) = (e2)) -> ((op (e0) (e0)) = (e1)) -> (~((op (e2) (e0)) = (e0))) -> (((op (e2) (e0)) = (e0))\/(((op (e2) (e1)) = (e0))\/(((op (e2) (e2)) = (e0))\/((op (e2) (e3)) = (e0))))) -> (((op (e0) (e0)) = (e0))\/(((op (e1) (e0)) = (e0))\/(((op (e2) (e0)) = (e0))\/((op (e3) (e0)) = (e0))))) -> (~((op (e1) (e0)) = (e0))) -> (~((op (e0) (e0)) = (e0))) -> (~((e1) = (e2))) -> (((op (e3) (e0)) = (e2))\/(((op (e3) (e1)) = (e2))\/(((op (e3) (e2)) = (e2))\/((op (e3) (e3)) = (e2))))) -> (~((op (e0) (e2)) = (op (e3) (e2)))) -> (~((e0) = (e2))) -> (~((op (e3) (e2)) = (op (e3) (e3)))) -> (((op (e3) (e0)) = (e3))\/(((op (e3) (e1)) = (e3))\/(((op (e3) (e2)) = (e3))\/((op (e3) (e3)) = (e3))))) -> (~((op (e1) (e1)) = (op (e3) (e1)))) -> (((op (e0) (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)) = (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)) = (e0))\/(((op (e2) (e3)) = (e1))\/(((op (e2) (e3)) = (e2))\/((op (e2) (e3)) = (e3))))) -> (((op (e0) (e3)) = (e2))\/(((op (e1) (e3)) = (e2))\/(((op (e2) (e3)) = (e2))\/((op (e3) (e3)) = (e2))))) -> (~((op (e1) (e2)) = (op (e3) (e2)))) -> (~((op (e1) (e1)) = (e0))) -> (~((op (e1) (e2)) = (op (e2) (e2)))) -> (~((op (e1) (e2)) = (op (e1) (e3)))) -> (~((e2) = (e3))) -> (((op (e0) (e3)) = (e1))\/(((op (e1) (e3)) = (e1))\/(((op (e2) (e3)) = (e1))\/((op (e3) (e3)) = (e1))))) -> (~((op (e3) (e1)) = (op (e3) (e3)))) -> (~((op (e2) (e2)) = (op (e2) (e3)))) -> (((op (e0) (e3)) = (e3))\/(((op (e1) (e3)) = (e3))\/(((op (e2) (e3)) = (e3))\/((op (e3) (e3)) = (e3))))) -> (~((op (e0) (e3)) = (op (e1) (e3)))) -> (((op (e1) (e0)) = (e1))\/(((op (e1) (e1)) = (e1))\/(((op (e1) (e2)) = (e1))\/((op (e1) (e3)) = (e1))))) -> (((op (e0) (e2)) = (e1))\/(((op (e1) (e2)) = (e1))\/(((op (e2) (e2)) = (e1))\/((op (e3) (e2)) = (e1))))) -> (~((op (e2) (e0)) = (op (e2) (e2)))) -> (~((op (e0) (e0)) = (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))))) -> (~((e0) = (e1))) -> (~((op (e0) (e2)) = (op (e2) (e2)))) -> (((op (e3) (e0)) = (e1))\/(((op (e3) (e1)) = (e1))\/(((op (e3) (e2)) = (e1))\/((op (e3) (e3)) = (e1))))) -> (~((op (e0) (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 (e1) (e3)) = (op (e2) (e3)))) -> (~((op (e1) (e0)) = (op (e1) (e3)))) -> (~((op (e1) (e3)) = (op (e3) (e3)))) -> (~((op (e0) (e3)) = (op (e2) (e3)))) -> (((op (e0) (e3)) = (e0))\/(((op (e0) (e3)) = (e1))\/(((op (e0) (e3)) = (e2))\/((op (e0) (e3)) = (e3))))) -> (~((op (e2) (e1)) = (op (e3) (e1)))) -> (((op (e2) (e0)) = (e3))\/(((op (e2) (e1)) = (e3))\/(((op (e2) (e2)) = (e3))\/((op (e2) (e3)) = (e3))))) -> (((op (e2) (e0)) = (e1))\/(((op (e2) (e1)) = (e1))\/(((op (e2) (e2)) = (e1))\/((op (e2) (e3)) = (e1))))) -> (~((op (e3) (e0)) = (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 (e0) (e1)) = (e1))\/(((op (e1) (e1)) = (e1))\/(((op (e2) (e1)) = (e1))\/((op (e3) (e1)) = (e1))))) -> (~((op (e1) (e1)) = (e1))) -> ((op (e1) (e0)) = (e3)) -> (((op (e1) (e0)) = (e0))\/(((op (e1) (e1)) = (e0))\/(((op (e1) (e2)) = (e0))\/((op (e1) (e3)) = (e0))))) -> (~((e0) = (e3))) -> (~((e1) = (e3))) -> ((~((op (e1) (e3)) = (e0)))\/((op (e1) (e0)) = (e3))) -> (~((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 (e0) (e3)))) -> (~((op (e1) (e1)) = (op (e1) (e3)))) -> (((op (e0) (e3)) = (e0))\/(((op (e1) (e3)) = (e0))\/(((op (e2) (e3)) = (e0))\/((op (e3) (e3)) = (e0))))) -> (~((op (e1) (e1)) = (op (e1) (e2)))) -> (~((op (e0) (e1)) = (op (e0) (e2)))) -> (~((op (e3) (e0)) = (op (e3) (e2)))) -> (~((op (e0) (e2)) = (e0))) -> (((op (e0) (e0)) = (e0))\/(((op (e0) (e1)) = (e0))\/(((op (e0) (e2)) = (e0))\/((op (e0) (e3)) = (e0))))) -> ((~((op (e1) (e2)) = (e0)))\/((op (e1) (e0)) = (e2))) -> (~((op (e0) (e1)) = (op (e2) (e1)))) -> (~((op (e2) (e0)) = (op (e3) (e0)))) -> (((op (e0) (e0)) = (e2))\/(((op (e0) (e1)) = (e2))\/(((op (e0) (e2)) = (e2))\/((op (e0) (e3)) = (e2))))) -> ((~((op (e3) (e0)) = (e0)))\/((op (e3) (e0)) = (e0))) -> ((~((op (e2) (e2)) = (e0)))\/((op (e2) (e0)) = (e2))) -> False). % 18.52/18.69 do 0 intro. intros zenon_H182 zenon_H39 zenon_H94 zenon_H86 zenon_H7a zenon_H30 zenon_H2f zenon_H3e zenon_H23 zenon_H3f zenon_H7c zenon_H153 zenon_H14f zenon_H149 zenon_H62 zenon_H165 zenon_H160 zenon_H168 zenon_H16f zenon_H173 zenon_H172 zenon_H5b zenon_H11f zenon_H145 zenon_H115 zenon_H24 zenon_H2b zenon_H124 zenon_H12b zenon_H133 zenon_H130 zenon_H6d zenon_H136 zenon_H1d zenon_H128 zenon_H139 zenon_H52 zenon_H13c zenon_H10e zenon_H13e zenon_H142 zenon_Ha1 zenon_Ha8 zenon_He8 zenon_H76 zenon_Hc2 zenon_Hdf zenon_Hdb zenon_Hd8 zenon_Hd5 zenon_He2 zenon_He4 zenon_Haf zenon_He7 zenon_H106 zenon_H71 zenon_Hf3 zenon_H102 zenon_H101 zenon_H109 zenon_H10a zenon_H9e zenon_H22 zenon_H9a zenon_H95 zenon_H179 zenon_H45 zenon_H6a zenon_H54 zenon_H57 zenon_H67 zenon_H4f zenon_H4a zenon_H6f zenon_H75 zenon_H74 zenon_H178 zenon_H17e zenon_H17b zenon_H183 zenon_H184 zenon_H185. % 18.52/18.69 apply (zenon_or_s _ _ zenon_H182); [ zenon_intro zenon_H31 | zenon_intro zenon_Hed ]. % 18.52/18.69 apply (zenon_or_s _ _ zenon_H185); [ zenon_intro zenon_H81 | zenon_intro zenon_Hee ]. % 18.52/18.69 apply (zenon_L34_); trivial. % 18.52/18.69 apply (zenon_or_s _ _ zenon_H94); [ zenon_intro zenon_H32 | zenon_intro zenon_H3b ]. % 18.52/18.69 apply (zenon_or_s _ _ zenon_H184); [ zenon_intro zenon_H40 | zenon_intro zenon_H44 ]. % 18.52/18.69 apply (zenon_L7_); trivial. % 18.52/18.69 apply (zenon_or_s _ _ zenon_H74); [ zenon_intro zenon_H42 | zenon_intro zenon_H77 ]. % 18.52/18.69 exact (zenon_H3f zenon_H42). % 18.52/18.69 apply (zenon_or_s _ _ zenon_H77); [ zenon_intro zenon_H49 | zenon_intro zenon_H78 ]. % 18.52/18.69 apply (zenon_or_s _ _ zenon_H183); [ zenon_intro zenon_H7b | zenon_intro zenon_H186 ]. % 18.52/18.69 apply (zenon_L26_); trivial. % 18.52/18.69 apply (zenon_or_s _ _ zenon_H186); [ zenon_intro zenon_H10f | zenon_intro zenon_H187 ]. % 18.52/18.69 apply (zenon_or_s _ _ zenon_H168); [ zenon_intro zenon_H3a | zenon_intro zenon_H169 ]. % 18.52/18.69 apply (zenon_L35_); trivial. % 18.52/18.69 apply (zenon_or_s _ _ zenon_H169); [ zenon_intro zenon_H99 | zenon_intro zenon_H16a ]. % 18.52/18.69 apply (zenon_L36_); trivial. % 18.52/18.69 apply (zenon_or_s _ _ zenon_H16a); [ zenon_intro zenon_Ha9 | zenon_intro zenon_He3 ]. % 18.52/18.69 apply (zenon_or_s _ _ zenon_H22); [ zenon_intro zenon_H27 | zenon_intro zenon_H26 ]. % 18.52/18.69 exact (zenon_H23 zenon_H27). % 18.52/18.69 apply (zenon_or_s _ _ zenon_H26); [ zenon_intro zenon_H29 | zenon_intro zenon_H28 ]. % 18.52/18.69 exact (zenon_H24 zenon_H29). % 18.52/18.69 apply (zenon_or_s _ _ zenon_H28); [ zenon_intro zenon_H2a | zenon_intro zenon_H1f ]. % 18.52/18.69 apply (zenon_L4_); trivial. % 18.52/18.69 apply (zenon_or_s _ _ zenon_H128); [ zenon_intro zenon_H9d | zenon_intro zenon_H129 ]. % 18.52/18.69 apply (zenon_L37_); trivial. % 18.52/18.69 apply (zenon_or_s _ _ zenon_H129); [ zenon_intro zenon_H10d | zenon_intro zenon_H12a ]. % 18.52/18.69 exact (zenon_H10a zenon_H10d). % 18.52/18.69 apply (zenon_or_s _ _ zenon_H12a); [ zenon_intro zenon_Hf0 | zenon_intro zenon_Hd6 ]. % 18.52/18.69 apply (zenon_L66_); trivial. % 18.52/18.69 apply (zenon_or_s _ _ zenon_H109); [ zenon_intro zenon_Ha0 | zenon_intro zenon_H10b ]. % 18.52/18.69 apply (zenon_L38_); trivial. % 18.52/18.69 apply (zenon_or_s _ _ zenon_H10b); [ zenon_intro zenon_H10d | zenon_intro zenon_H10c ]. % 18.52/18.69 exact (zenon_H10a zenon_H10d). % 18.52/18.69 apply (zenon_or_s _ _ zenon_H10c); [ zenon_intro zenon_Ha5 | zenon_intro zenon_Hae ]. % 18.52/18.69 apply (zenon_L91_); trivial. % 18.52/18.69 apply (zenon_or_s _ _ zenon_H2f); [ zenon_intro zenon_H34 | zenon_intro zenon_H33 ]. % 18.52/18.69 exact (zenon_H30 zenon_H34). % 18.52/18.69 apply (zenon_or_s _ _ zenon_H33); [ zenon_intro zenon_H36 | zenon_intro zenon_H35 ]. % 18.52/18.69 exact (zenon_H31 zenon_H36). % 18.52/18.69 apply (zenon_or_s _ _ zenon_H35); [ zenon_intro zenon_H2c | zenon_intro zenon_H37 ]. % 18.52/18.69 apply (zenon_or_s _ _ zenon_H106); [ zenon_intro zenon_Hed | zenon_intro zenon_H107 ]. % 18.52/18.69 apply (zenon_L94_); trivial. % 18.52/18.69 apply (zenon_or_s _ _ zenon_H107); [ zenon_intro zenon_Ha5 | zenon_intro zenon_H108 ]. % 18.52/18.69 apply (zenon_L56_); trivial. % 18.52/18.69 apply (zenon_or_s _ _ zenon_H108); [ zenon_intro zenon_Hf1 | zenon_intro zenon_Hf4 ]. % 18.52/18.69 apply (zenon_or_s _ _ zenon_He7); [ zenon_intro zenon_H3b | zenon_intro zenon_He9 ]. % 18.52/18.69 apply (zenon_L33_); trivial. % 18.52/18.69 apply (zenon_or_s _ _ zenon_He9); [ zenon_intro zenon_Ha6 | zenon_intro zenon_Hea ]. % 18.52/18.69 apply (zenon_L96_); trivial. % 18.52/18.69 apply (zenon_or_s _ _ zenon_Hea); [ zenon_intro zenon_Haa | zenon_intro zenon_Hdd ]. % 18.52/18.69 apply (zenon_L40_); trivial. % 18.52/18.69 apply (zenon_L89_); trivial. % 18.52/18.69 apply (zenon_L64_); trivial. % 18.52/18.69 exact (zenon_H32 zenon_H37). % 18.52/18.69 apply (zenon_L122_); trivial. % 18.52/18.69 apply (zenon_or_s _ _ zenon_H187); [ zenon_intro zenon_H150 | zenon_intro zenon_Hcd ]. % 18.52/18.69 apply (zenon_or_s _ _ zenon_H168); [ zenon_intro zenon_H3a | zenon_intro zenon_H169 ]. % 18.52/18.69 apply (zenon_L35_); trivial. % 18.52/18.69 apply (zenon_or_s _ _ zenon_H169); [ zenon_intro zenon_H99 | zenon_intro zenon_H16a ]. % 18.52/18.69 apply (zenon_L36_); trivial. % 18.52/18.69 apply (zenon_or_s _ _ zenon_H16a); [ zenon_intro zenon_Ha9 | zenon_intro zenon_He3 ]. % 18.52/18.69 apply (zenon_or_s _ _ zenon_H22); [ zenon_intro zenon_H27 | zenon_intro zenon_H26 ]. % 18.52/18.69 exact (zenon_H23 zenon_H27). % 18.52/18.69 apply (zenon_or_s _ _ zenon_H26); [ zenon_intro zenon_H29 | zenon_intro zenon_H28 ]. % 18.52/18.69 exact (zenon_H24 zenon_H29). % 18.52/18.69 apply (zenon_or_s _ _ zenon_H28); [ zenon_intro zenon_H2a | zenon_intro zenon_H1f ]. % 18.52/18.69 apply (zenon_L4_); trivial. % 18.52/18.69 apply (zenon_or_s _ _ zenon_H128); [ zenon_intro zenon_H9d | zenon_intro zenon_H129 ]. % 18.52/18.69 apply (zenon_L124_); trivial. % 18.52/18.69 apply (zenon_or_s _ _ zenon_H129); [ zenon_intro zenon_H10d | zenon_intro zenon_H12a ]. % 18.52/18.69 exact (zenon_H10a zenon_H10d). % 18.52/18.69 apply (zenon_or_s _ _ zenon_H12a); [ zenon_intro zenon_Hf0 | zenon_intro zenon_Hd6 ]. % 18.52/18.69 apply (zenon_L66_); trivial. % 18.52/18.69 apply (zenon_or_s _ _ zenon_H109); [ zenon_intro zenon_Ha0 | zenon_intro zenon_H10b ]. % 18.52/18.69 apply (zenon_L38_); trivial. % 18.52/18.69 apply (zenon_or_s _ _ zenon_H10b); [ zenon_intro zenon_H10d | zenon_intro zenon_H10c ]. % 18.52/18.69 exact (zenon_H10a zenon_H10d). % 18.52/18.69 apply (zenon_or_s _ _ zenon_H10c); [ zenon_intro zenon_Ha5 | zenon_intro zenon_Hae ]. % 18.52/18.69 apply (zenon_L91_); trivial. % 18.52/18.69 apply (zenon_or_s _ _ zenon_H2f); [ zenon_intro zenon_H34 | zenon_intro zenon_H33 ]. % 18.52/18.69 exact (zenon_H30 zenon_H34). % 18.52/18.69 apply (zenon_or_s _ _ zenon_H33); [ zenon_intro zenon_H36 | zenon_intro zenon_H35 ]. % 18.52/18.69 exact (zenon_H31 zenon_H36). % 18.52/18.69 apply (zenon_or_s _ _ zenon_H35); [ zenon_intro zenon_H2c | zenon_intro zenon_H37 ]. % 18.52/18.69 apply (zenon_or_s _ _ zenon_H106); [ zenon_intro zenon_Hed | zenon_intro zenon_H107 ]. % 18.52/18.69 apply (zenon_L94_); trivial. % 18.52/18.69 apply (zenon_or_s _ _ zenon_H107); [ zenon_intro zenon_Ha5 | zenon_intro zenon_H108 ]. % 18.52/18.69 apply (zenon_L42_); trivial. % 18.52/18.69 apply (zenon_or_s _ _ zenon_H108); [ zenon_intro zenon_Hf1 | zenon_intro zenon_Hf4 ]. % 18.52/18.69 apply (zenon_L125_); trivial. % 18.52/18.69 apply (zenon_L126_); trivial. % 18.52/18.69 exact (zenon_H32 zenon_H37). % 18.52/18.69 apply (zenon_L122_); trivial. % 18.52/18.69 apply (zenon_or_s _ _ zenon_H168); [ zenon_intro zenon_H3a | zenon_intro zenon_H169 ]. % 18.52/18.69 apply (zenon_L35_); trivial. % 18.52/18.69 apply (zenon_or_s _ _ zenon_H169); [ zenon_intro zenon_H99 | zenon_intro zenon_H16a ]. % 18.52/18.69 apply (zenon_L36_); trivial. % 18.52/18.69 apply (zenon_or_s _ _ zenon_H16a); [ zenon_intro zenon_Ha9 | zenon_intro zenon_He3 ]. % 18.52/18.69 apply (zenon_or_s _ _ zenon_H22); [ zenon_intro zenon_H27 | zenon_intro zenon_H26 ]. % 18.52/18.69 exact (zenon_H23 zenon_H27). % 18.52/18.69 apply (zenon_or_s _ _ zenon_H26); [ zenon_intro zenon_H29 | zenon_intro zenon_H28 ]. % 18.52/18.69 exact (zenon_H24 zenon_H29). % 18.52/18.69 apply (zenon_or_s _ _ zenon_H28); [ zenon_intro zenon_H2a | zenon_intro zenon_H1f ]. % 18.52/18.69 apply (zenon_L4_); trivial. % 18.52/18.69 apply (zenon_or_s _ _ zenon_H128); [ zenon_intro zenon_H9d | zenon_intro zenon_H129 ]. % 18.52/18.69 apply (zenon_L124_); trivial. % 18.52/18.69 apply (zenon_or_s _ _ zenon_H129); [ zenon_intro zenon_H10d | zenon_intro zenon_H12a ]. % 18.52/18.69 exact (zenon_H10a zenon_H10d). % 18.52/18.69 apply (zenon_or_s _ _ zenon_H12a); [ zenon_intro zenon_Hf0 | zenon_intro zenon_Hd6 ]. % 18.52/18.69 apply (zenon_L132_); trivial. % 18.52/18.69 apply (zenon_L133_); trivial. % 18.52/18.69 apply (zenon_L81_); trivial. % 18.52/18.69 apply (zenon_or_s _ _ zenon_H78); [ zenon_intro zenon_H48 | zenon_intro zenon_H1e ]. % 18.52/18.69 exact (zenon_H75 zenon_H48). % 18.52/18.69 exact (zenon_H76 zenon_H1e). % 18.52/18.69 apply (zenon_L33_); trivial. % 18.52/18.69 apply (zenon_L134_); trivial. % 18.52/18.69 (* end of lemma zenon_L135_ *) % 18.52/18.69 assert (zenon_L136_ : (~((op (e1) (e3)) = (op (e3) (e3)))) -> ((op (e1) (e3)) = (e0)) -> ((op (e3) (e3)) = (e0)) -> False). % 18.52/18.69 do 0 intro. intros zenon_Hd5 zenon_H1f zenon_H60. % 18.52/18.69 cut (((op (e1) (e3)) = (e0)) = ((op (e1) (e3)) = (op (e3) (e3)))). % 18.52/18.69 intro zenon_D_pnotp. % 18.52/18.69 apply zenon_Hd5. % 18.52/18.69 rewrite <- zenon_D_pnotp. % 18.52/18.69 exact zenon_H1f. % 18.52/18.69 cut (((e0) = (op (e3) (e3)))); [idtac | apply NNPP; zenon_intro zenon_H188]. % 18.52/18.69 cut (((op (e1) (e3)) = (op (e1) (e3)))); [idtac | apply NNPP; zenon_intro zenon_H59]. % 18.52/18.69 congruence. % 18.52/18.69 apply zenon_H59. apply refl_equal. % 18.52/18.69 apply zenon_H188. apply sym_equal. exact zenon_H60. % 18.52/18.69 (* end of lemma zenon_L136_ *) % 18.52/18.69 assert (zenon_L137_ : (((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 (e0) (e3)) = (e2)) -> (~((op (e0) (e3)) = (op (e3) (e3)))) -> (~((op (e3) (e3)) = (e3))) -> False). % 18.52/18.69 do 0 intro. intros zenon_H101 zenon_Hd5 zenon_H1f zenon_Hcd zenon_Hc2 zenon_H102. % 18.52/18.69 apply (zenon_or_s _ _ zenon_H101); [ zenon_intro zenon_H60 | zenon_intro zenon_H103 ]. % 18.52/18.69 apply (zenon_L136_); trivial. % 18.52/18.69 apply (zenon_or_s _ _ zenon_H103); [ zenon_intro zenon_Hc4 | zenon_intro zenon_H104 ]. % 18.52/18.69 apply (zenon_L49_); trivial. % 18.52/18.69 apply (zenon_or_s _ _ zenon_H104); [ zenon_intro zenon_Hf6 | zenon_intro zenon_H105 ]. % 18.52/18.69 apply (zenon_L87_); trivial. % 18.52/18.69 exact (zenon_H102 zenon_H105). % 18.52/18.69 (* end of lemma zenon_L137_ *) % 18.52/18.69 assert (zenon_L138_ : (((op (e2) (e3)) = (e0))\/(((op (e2) (e3)) = (e1))\/(((op (e2) (e3)) = (e2))\/((op (e2) (e3)) = (e3))))) -> (~((op (e2) (e2)) = (op (e2) (e3)))) -> ((op (e2) (e2)) = (e0)) -> ((op (e1) (e3)) = (e0)) -> ((op (e3) (e3)) = (e2)) -> (~((op (e2) (e3)) = (op (e3) (e3)))) -> (~((op (e0) (e3)) = (op (e2) (e3)))) -> ((op (e0) (e3)) = (e3)) -> False). % 18.52/18.69 do 0 intro. intros zenon_H11f zenon_H6d zenon_H2c zenon_H1f zenon_Hf6 zenon_Hf3 zenon_He2 zenon_He3. % 18.52/18.69 apply (zenon_or_s _ _ zenon_H11f); [ zenon_intro zenon_H37 | zenon_intro zenon_H120 ]. % 18.52/18.69 apply (zenon_L18_); trivial. % 18.52/18.69 apply (zenon_or_s _ _ zenon_H120); [ zenon_intro zenon_Hf4 | zenon_intro zenon_H121 ]. % 18.52/18.69 apply (zenon_L63_); trivial. % 18.52/18.69 apply (zenon_or_s _ _ zenon_H121); [ zenon_intro zenon_H11d | zenon_intro zenon_Hdd ]. % 18.52/18.69 apply (zenon_L97_); trivial. % 18.52/18.69 apply (zenon_L54_); trivial. % 18.52/18.69 (* end of lemma zenon_L138_ *) % 18.52/18.69 assert (zenon_L139_ : (((op (e3) (e0)) = (e2))\/(((op (e3) (e1)) = (e2))\/(((op (e3) (e2)) = (e2))\/((op (e3) (e3)) = (e2))))) -> (~((op (e0) (e3)) = (op (e1) (e3)))) -> ((op (e1) (e2)) = (e2)) -> (((op (e3) (e0)) = (e3))\/(((op (e3) (e1)) = (e3))\/(((op (e3) (e2)) = (e3))\/((op (e3) (e3)) = (e3))))) -> (~((op (e1) (e1)) = (op (e3) (e1)))) -> (~((op (e0) (e2)) = (op (e3) (e2)))) -> (~((op (e3) (e3)) = (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 (e3) (e0)) = (op (e3) (e3)))) -> (((op (e1) (e0)) = (e3))\/(((op (e1) (e1)) = (e3))\/(((op (e1) (e2)) = (e3))\/((op (e1) (e3)) = (e3))))) -> (~((op (e3) (e1)) = (op (e3) (e3)))) -> (~((op (e3) (e2)) = (op (e3) (e3)))) -> ((op (e2) (e0)) = (e2)) -> (~((op (e2) (e0)) = (op (e2) (e3)))) -> ((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 (e2) (e3)) = (e0))\/(((op (e2) (e3)) = (e1))\/(((op (e2) (e3)) = (e2))\/((op (e2) (e3)) = (e3))))) -> (~((op (e2) (e2)) = (op (e2) (e3)))) -> ((op (e2) (e2)) = (e0)) -> ((op (e1) (e3)) = (e0)) -> (~((op (e2) (e3)) = (op (e3) (e3)))) -> (~((op (e0) (e3)) = (op (e2) (e3)))) -> ((op (e0) (e3)) = (e3)) -> False). % 18.52/18.69 do 0 intro. intros zenon_H153 zenon_H1d zenon_H113 zenon_H165 zenon_H160 zenon_H14f zenon_H102 zenon_H10e zenon_H7a zenon_H95 zenon_H168 zenon_H71 zenon_H16f zenon_H130 zenon_H62 zenon_Hee zenon_H5b zenon_Hd6 zenon_H7c zenon_H12b zenon_H145 zenon_H11f zenon_H6d zenon_H2c zenon_H1f zenon_Hf3 zenon_He2 zenon_He3. % 18.52/18.69 apply (zenon_or_s _ _ zenon_H153); [ zenon_intro zenon_H148 | zenon_intro zenon_H154 ]. % 18.52/18.69 apply (zenon_L118_); trivial. % 18.52/18.69 apply (zenon_or_s _ _ zenon_H154); [ zenon_intro zenon_H14d | zenon_intro zenon_H155 ]. % 18.52/18.69 apply (zenon_L103_); trivial. % 18.52/18.69 apply (zenon_or_s _ _ zenon_H155); [ zenon_intro zenon_H151 | zenon_intro zenon_Hf6 ]. % 18.52/18.69 apply (zenon_L120_); trivial. % 18.52/18.69 apply (zenon_L138_); trivial. % 18.52/18.69 (* end of lemma zenon_L139_ *) % 18.52/18.69 assert (zenon_L140_ : ((op (e0) (e3)) = (e1)) -> ((op (e0) (e0)) = (e1)) -> (~((op (e0) (e0)) = (op (e0) (e3)))) -> False). % 18.52/18.69 do 0 intro. intros zenon_Hc3 zenon_H7a zenon_H189. % 18.52/18.69 elim (classic ((op (e0) (e3)) = (op (e0) (e3)))); [ zenon_intro zenon_H55 | zenon_intro zenon_H21 ]. % 18.52/18.69 cut (((op (e0) (e3)) = (op (e0) (e3))) = ((op (e0) (e0)) = (op (e0) (e3)))). % 18.52/18.69 intro zenon_D_pnotp. % 18.52/18.69 apply zenon_H189. % 18.52/18.69 rewrite <- zenon_D_pnotp. % 18.52/18.69 exact zenon_H55. % 18.52/18.69 cut (((op (e0) (e3)) = (op (e0) (e3)))); [idtac | apply NNPP; zenon_intro zenon_H21]. % 18.52/18.69 cut (((op (e0) (e3)) = (op (e0) (e0)))); [idtac | apply NNPP; zenon_intro zenon_H18a]. % 18.52/18.69 congruence. % 18.52/18.69 cut (((op (e0) (e3)) = (e1)) = ((op (e0) (e3)) = (op (e0) (e0)))). % 18.52/18.69 intro zenon_D_pnotp. % 18.52/18.69 apply zenon_H18a. % 18.52/18.69 rewrite <- zenon_D_pnotp. % 18.52/18.69 exact zenon_Hc3. % 18.52/18.69 cut (((e1) = (op (e0) (e0)))); [idtac | apply NNPP; zenon_intro zenon_H93]. % 18.52/18.69 cut (((op (e0) (e3)) = (op (e0) (e3)))); [idtac | apply NNPP; zenon_intro zenon_H21]. % 18.52/18.69 congruence. % 18.52/18.69 apply zenon_H21. apply refl_equal. % 18.52/18.69 apply zenon_H93. apply sym_equal. exact zenon_H7a. % 18.52/18.69 apply zenon_H21. apply refl_equal. % 18.52/18.69 apply zenon_H21. apply refl_equal. % 18.52/18.69 (* end of lemma zenon_L140_ *) % 18.52/18.69 assert (zenon_L141_ : (((op (e0) (e3)) = (e0))\/(((op (e0) (e3)) = (e1))\/(((op (e0) (e3)) = (e2))\/((op (e0) (e3)) = (e3))))) -> (~((op (e0) (e3)) = (e0))) -> (~((op (e0) (e0)) = (op (e0) (e3)))) -> ((op (e0) (e0)) = (e1)) -> ((op (e3) (e3)) = (e2)) -> (~((op (e0) (e3)) = (op (e3) (e3)))) -> (~((op (e0) (e3)) = (op (e2) (e3)))) -> ((op (e2) (e3)) = (e3)) -> False). % 18.52/18.69 do 0 intro. intros zenon_He4 zenon_H76 zenon_H189 zenon_H7a zenon_Hf6 zenon_Hc2 zenon_He2 zenon_Hdd. % 18.52/18.69 apply (zenon_or_s _ _ zenon_He4); [ zenon_intro zenon_H1e | zenon_intro zenon_He5 ]. % 18.52/18.69 exact (zenon_H76 zenon_H1e). % 18.52/18.69 apply (zenon_or_s _ _ zenon_He5); [ zenon_intro zenon_Hc3 | zenon_intro zenon_He6 ]. % 18.52/18.69 apply (zenon_L140_); trivial. % 18.52/18.69 apply (zenon_or_s _ _ zenon_He6); [ zenon_intro zenon_Hcd | zenon_intro zenon_He3 ]. % 18.52/18.69 apply (zenon_L87_); trivial. % 18.52/18.69 apply (zenon_L54_); trivial. % 18.52/18.69 (* end of lemma zenon_L141_ *) % 18.52/18.69 assert (zenon_L142_ : (((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)) = (e0)) -> ((op (e2) (e2)) = (e0)) -> (~((op (e2) (e2)) = (op (e2) (e3)))) -> (((op (e2) (e3)) = (e0))\/(((op (e2) (e3)) = (e1))\/(((op (e2) (e3)) = (e2))\/((op (e2) (e3)) = (e3))))) -> (((op (e0) (e3)) = (e2))\/(((op (e1) (e3)) = (e2))\/(((op (e2) (e3)) = (e2))\/((op (e3) (e3)) = (e2))))) -> (~((e2) = (e3))) -> (~((e1) = (e2))) -> (~((op (e2) (e0)) = (op (e2) (e3)))) -> ((op (e2) (e0)) = (e2)) -> (~((op (e3) (e2)) = (op (e3) (e3)))) -> (~((op (e3) (e1)) = (op (e3) (e3)))) -> (((op (e1) (e0)) = (e3))\/(((op (e1) (e1)) = (e3))\/(((op (e1) (e2)) = (e3))\/((op (e1) (e3)) = (e3))))) -> (~((op (e3) (e0)) = (op (e3) (e3)))) -> (((op (e0) (e0)) = (e3))\/(((op (e0) (e1)) = (e3))\/(((op (e0) (e2)) = (e3))\/((op (e0) (e3)) = (e3))))) -> (~((op (e0) (e1)) = (op (e1) (e1)))) -> (~((op (e0) (e2)) = (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 (e1) (e2)) = (e2)) -> (~((op (e0) (e3)) = (op (e1) (e3)))) -> (((op (e3) (e0)) = (e2))\/(((op (e3) (e1)) = (e2))\/(((op (e3) (e2)) = (e2))\/((op (e3) (e3)) = (e2))))) -> (~((e1) = (e3))) -> ((op (e1) (e3)) = (e1)) -> (~((op (e0) (e3)) = (op (e2) (e3)))) -> (~((op (e0) (e3)) = (op (e3) (e3)))) -> ((op (e3) (e3)) = (e2)) -> ((op (e0) (e0)) = (e1)) -> (~((op (e0) (e0)) = (op (e0) (e3)))) -> (~((op (e0) (e3)) = (e0))) -> (((op (e0) (e3)) = (e0))\/(((op (e0) (e3)) = (e1))\/(((op (e0) (e3)) = (e2))\/((op (e0) (e3)) = (e3))))) -> (~((op (e3) (e3)) = (e3))) -> False). % 18.52/18.69 do 0 intro. intros zenon_H136 zenon_Hf3 zenon_H1f zenon_H2c zenon_H6d zenon_H11f zenon_H145 zenon_H12b zenon_H7c zenon_H5b zenon_Hee zenon_H62 zenon_H130 zenon_H16f zenon_H71 zenon_H168 zenon_H10e zenon_H14f zenon_H160 zenon_H165 zenon_H113 zenon_H1d zenon_H153 zenon_H95 zenon_Hd6 zenon_He2 zenon_Hc2 zenon_Hf6 zenon_H7a zenon_H189 zenon_H76 zenon_He4 zenon_H102. % 18.52/18.69 apply (zenon_or_s _ _ zenon_H136); [ zenon_intro zenon_He3 | zenon_intro zenon_H137 ]. % 18.52/18.69 apply (zenon_L139_); trivial. % 18.52/18.69 apply (zenon_or_s _ _ zenon_H137); [ zenon_intro zenon_Hdc | zenon_intro zenon_H138 ]. % 18.52/18.69 apply (zenon_L83_); trivial. % 18.52/18.69 apply (zenon_or_s _ _ zenon_H138); [ zenon_intro zenon_Hdd | zenon_intro zenon_H105 ]. % 18.52/18.69 apply (zenon_L141_); trivial. % 18.52/18.69 exact (zenon_H102 zenon_H105). % 18.52/18.69 (* end of lemma zenon_L142_ *) % 18.52/18.69 assert (zenon_L143_ : (((op (e0) (e2)) = (e0))\/(((op (e1) (e2)) = (e0))\/(((op (e2) (e2)) = (e0))\/((op (e3) (e2)) = (e0))))) -> (~((op (e0) (e2)) = (e0))) -> (~((op (e1) (e2)) = (e0))) -> (~((op (e2) (e2)) = (op (e2) (e3)))) -> ((op (e2) (e3)) = (e0)) -> (~((op (e3) (e2)) = (e0))) -> False). % 18.52/18.69 do 0 intro. intros zenon_H6a zenon_H75 zenon_H25 zenon_H6d zenon_H37 zenon_H18b. % 18.52/18.69 apply (zenon_or_s _ _ zenon_H6a); [ zenon_intro zenon_H48 | zenon_intro zenon_H6b ]. % 18.52/18.69 exact (zenon_H75 zenon_H48). % 18.52/18.69 apply (zenon_or_s _ _ zenon_H6b); [ zenon_intro zenon_H2a | zenon_intro zenon_H6c ]. % 18.52/18.69 exact (zenon_H25 zenon_H2a). % 18.52/18.69 apply (zenon_or_s _ _ zenon_H6c); [ zenon_intro zenon_H2c | zenon_intro zenon_H61 ]. % 18.52/18.69 apply (zenon_L18_); trivial. % 18.52/18.69 exact (zenon_H18b zenon_H61). % 18.52/18.69 (* end of lemma zenon_L143_ *) % 18.52/18.69 assert (zenon_L144_ : (((op (e2) (e0)) = (e0))\/(((op (e2) (e1)) = (e0))\/(((op (e2) (e2)) = (e0))\/((op (e2) (e3)) = (e0))))) -> (~((op (e2) (e0)) = (e0))) -> (~((op (e2) (e1)) = (e0))) -> (~((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 (e0) (e0)) = (op (e0) (e3)))) -> ((op (e0) (e0)) = (e1)) -> (~((op (e0) (e3)) = (op (e3) (e3)))) -> (~((op (e0) (e3)) = (op (e2) (e3)))) -> ((op (e1) (e3)) = (e1)) -> (~((e1) = (e3))) -> (((op (e3) (e0)) = (e2))\/(((op (e3) (e1)) = (e2))\/(((op (e3) (e2)) = (e2))\/((op (e3) (e3)) = (e2))))) -> (~((op (e0) (e3)) = (op (e1) (e3)))) -> ((op (e1) (e2)) = (e2)) -> (((op (e3) (e0)) = (e3))\/(((op (e3) (e1)) = (e3))\/(((op (e3) (e2)) = (e3))\/((op (e3) (e3)) = (e3))))) -> (~((op (e1) (e1)) = (op (e3) (e1)))) -> (~((op (e0) (e2)) = (op (e3) (e2)))) -> (~((op (e0) (e1)) = (op (e1) (e1)))) -> (((op (e0) (e0)) = (e3))\/(((op (e0) (e1)) = (e3))\/(((op (e0) (e2)) = (e3))\/((op (e0) (e3)) = (e3))))) -> (~((op (e3) (e0)) = (op (e3) (e3)))) -> (((op (e1) (e0)) = (e3))\/(((op (e1) (e1)) = (e3))\/(((op (e1) (e2)) = (e3))\/((op (e1) (e3)) = (e3))))) -> (~((op (e3) (e1)) = (op (e3) (e3)))) -> (~((op (e3) (e2)) = (op (e3) (e3)))) -> ((op (e2) (e0)) = (e2)) -> (~((op (e2) (e0)) = (op (e2) (e3)))) -> (~((e1) = (e2))) -> (~((e2) = (e3))) -> (((op (e0) (e3)) = (e2))\/(((op (e1) (e3)) = (e2))\/(((op (e2) (e3)) = (e2))\/((op (e3) (e3)) = (e2))))) -> (((op (e2) (e3)) = (e0))\/(((op (e2) (e3)) = (e1))\/(((op (e2) (e3)) = (e2))\/((op (e2) (e3)) = (e3))))) -> ((op (e1) (e3)) = (e0)) -> (~((op (e2) (e3)) = (op (e3) (e3)))) -> (((op (e0) (e3)) = (e3))\/(((op (e1) (e3)) = (e3))\/(((op (e2) (e3)) = (e3))\/((op (e3) (e3)) = (e3))))) -> (((op (e3) (e3)) = (e0))\/(((op (e3) (e3)) = (e1))\/(((op (e3) (e3)) = (e2))\/((op (e3) (e3)) = (e3))))) -> (~((op (e1) (e3)) = (op (e3) (e3)))) -> (((op (e0) (e2)) = (e0))\/(((op (e1) (e2)) = (e0))\/(((op (e2) (e2)) = (e0))\/((op (e3) (e2)) = (e0))))) -> (~((op (e0) (e2)) = (e0))) -> (~((op (e1) (e2)) = (e0))) -> (~((op (e2) (e2)) = (op (e2) (e3)))) -> (~((op (e3) (e2)) = (e0))) -> False). % 18.52/18.69 do 0 intro. intros zenon_H2f zenon_H30 zenon_H31 zenon_H102 zenon_He4 zenon_H76 zenon_H189 zenon_H7a zenon_Hc2 zenon_He2 zenon_Hd6 zenon_H95 zenon_H153 zenon_H1d zenon_H113 zenon_H165 zenon_H160 zenon_H14f zenon_H10e zenon_H168 zenon_H71 zenon_H16f zenon_H130 zenon_H62 zenon_Hee zenon_H5b zenon_H7c zenon_H12b zenon_H145 zenon_H11f zenon_H1f zenon_Hf3 zenon_H136 zenon_H101 zenon_Hd5 zenon_H6a zenon_H75 zenon_H25 zenon_H6d zenon_H18b. % 18.52/18.69 apply (zenon_or_s _ _ zenon_H2f); [ zenon_intro zenon_H34 | zenon_intro zenon_H33 ]. % 18.52/18.69 exact (zenon_H30 zenon_H34). % 18.52/18.69 apply (zenon_or_s _ _ zenon_H33); [ zenon_intro zenon_H36 | zenon_intro zenon_H35 ]. % 18.52/18.69 exact (zenon_H31 zenon_H36). % 18.52/18.69 apply (zenon_or_s _ _ zenon_H35); [ zenon_intro zenon_H2c | zenon_intro zenon_H37 ]. % 18.52/18.69 apply (zenon_or_s _ _ zenon_H145); [ zenon_intro zenon_Hcd | zenon_intro zenon_H146 ]. % 18.52/18.69 apply (zenon_L137_); trivial. % 18.52/18.69 apply (zenon_or_s _ _ zenon_H146); [ zenon_intro zenon_Hd7 | zenon_intro zenon_H147 ]. % 18.52/18.69 apply (zenon_L101_); trivial. % 18.52/18.69 apply (zenon_or_s _ _ zenon_H147); [ zenon_intro zenon_H11d | zenon_intro zenon_Hf6 ]. % 18.52/18.69 apply (zenon_L73_); trivial. % 18.52/18.69 apply (zenon_L142_); trivial. % 18.52/18.69 apply (zenon_L143_); trivial. % 18.52/18.69 (* end of lemma zenon_L144_ *) % 18.52/18.69 assert (zenon_L145_ : (((op (e1) (e0)) = (e2))\/(((op (e1) (e1)) = (e2))\/(((op (e1) (e2)) = (e2))\/((op (e1) (e3)) = (e2))))) -> ((~((op (e2) (e2)) = (e0)))\/((op (e2) (e0)) = (e2))) -> ((~((op (e3) (e0)) = (e0)))\/((op (e3) (e0)) = (e0))) -> (((op (e0) (e0)) = (e2))\/(((op (e0) (e1)) = (e2))\/(((op (e0) (e2)) = (e2))\/((op (e0) (e3)) = (e2))))) -> (~((op (e2) (e0)) = (op (e3) (e0)))) -> (~((op (e0) (e1)) = (op (e2) (e1)))) -> ((~((op (e1) (e2)) = (e0)))\/((op (e1) (e0)) = (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) (e1)) = (op (e0) (e2)))) -> (~((op (e1) (e1)) = (op (e1) (e2)))) -> (((op (e0) (e3)) = (e0))\/(((op (e1) (e3)) = (e0))\/(((op (e2) (e3)) = (e0))\/((op (e3) (e3)) = (e0))))) -> (~((op (e1) (e1)) = (op (e1) (e3)))) -> (~((op (e0) (e1)) = (op (e0) (e3)))) -> (~((op (e1) (e0)) = (op (e1) (e1)))) -> ((~((op (e1) (e3)) = (e0)))\/((op (e1) (e0)) = (e3))) -> (~((e0) = (e3))) -> (((op (e1) (e0)) = (e0))\/(((op (e1) (e1)) = (e0))\/(((op (e1) (e2)) = (e0))\/((op (e1) (e3)) = (e0))))) -> ((op (e1) (e0)) = (e3)) -> (~((op (e1) (e1)) = (e1))) -> (((op (e0) (e1)) = (e1))\/(((op (e1) (e1)) = (e1))\/(((op (e2) (e1)) = (e1))\/((op (e3) (e1)) = (e1))))) -> (((op (e2) (e0)) = (e1))\/(((op (e2) (e1)) = (e1))\/(((op (e2) (e2)) = (e1))\/((op (e2) (e3)) = (e1))))) -> (((op (e2) (e0)) = (e3))\/(((op (e2) (e1)) = (e3))\/(((op (e2) (e2)) = (e3))\/((op (e2) (e3)) = (e3))))) -> (~((op (e2) (e1)) = (op (e3) (e1)))) -> (~((op (e1) (e0)) = (op (e1) (e3)))) -> (~((op (e1) (e3)) = (op (e2) (e3)))) -> (((op (e1) (e3)) = (e0))\/(((op (e1) (e3)) = (e1))\/(((op (e1) (e3)) = (e2))\/((op (e1) (e3)) = (e3))))) -> (((op (e3) (e0)) = (e1))\/(((op (e3) (e1)) = (e1))\/(((op (e3) (e2)) = (e1))\/((op (e3) (e3)) = (e1))))) -> (~((op (e0) (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) (e0)) = (op (e0) (e2)))) -> (~((op (e2) (e0)) = (op (e2) (e2)))) -> (((op (e0) (e2)) = (e1))\/(((op (e1) (e2)) = (e1))\/(((op (e2) (e2)) = (e1))\/((op (e3) (e2)) = (e1))))) -> (((op (e1) (e0)) = (e1))\/(((op (e1) (e1)) = (e1))\/(((op (e1) (e2)) = (e1))\/((op (e1) (e3)) = (e1))))) -> (((op (e0) (e3)) = (e1))\/(((op (e1) (e3)) = (e1))\/(((op (e2) (e3)) = (e1))\/((op (e3) (e3)) = (e1))))) -> (~((op (e1) (e2)) = (op (e1) (e3)))) -> (~((op (e1) (e2)) = (op (e2) (e2)))) -> (~((op (e1) (e1)) = (e0))) -> (~((op (e1) (e2)) = (op (e3) (e2)))) -> (((op (e0) (e2)) = (e2))\/(((op (e1) (e2)) = (e2))\/(((op (e2) (e2)) = (e2))\/((op (e3) (e2)) = (e2))))) -> (~((op (e2) (e2)) = (e2))) -> (~((e0) = (e2))) -> (~((op (e0) (e0)) = (e0))) -> (~((op (e1) (e0)) = (e0))) -> (((op (e0) (e0)) = (e0))\/(((op (e1) (e0)) = (e0))\/(((op (e2) (e0)) = (e0))\/((op (e3) (e0)) = (e0))))) -> ((~((op (e2) (e3)) = (e0)))\/((op (e2) (e0)) = (e3))) -> (~((op (e0) (e0)) = (op (e2) (e0)))) -> ((~((op (e2) (e1)) = (e0)))\/((op (e2) (e0)) = (e1))) -> ((op (e0) (e1)) = (e2)) -> (~((op (e3) (e2)) = (e0))) -> (~((op (e2) (e2)) = (op (e2) (e3)))) -> (~((op (e1) (e2)) = (e0))) -> (~((op (e0) (e2)) = (e0))) -> (((op (e0) (e2)) = (e0))\/(((op (e1) (e2)) = (e0))\/(((op (e2) (e2)) = (e0))\/((op (e3) (e2)) = (e0))))) -> (~((op (e1) (e3)) = (op (e3) (e3)))) -> (((op (e3) (e3)) = (e0))\/(((op (e3) (e3)) = (e1))\/(((op (e3) (e3)) = (e2))\/((op (e3) (e3)) = (e3))))) -> (((op (e0) (e3)) = (e3))\/(((op (e1) (e3)) = (e3))\/(((op (e2) (e3)) = (e3))\/((op (e3) (e3)) = (e3))))) -> (~((op (e2) (e3)) = (op (e3) (e3)))) -> ((op (e1) (e3)) = (e0)) -> (((op (e2) (e3)) = (e0))\/(((op (e2) (e3)) = (e1))\/(((op (e2) (e3)) = (e2))\/((op (e2) (e3)) = (e3))))) -> (((op (e0) (e3)) = (e2))\/(((op (e1) (e3)) = (e2))\/(((op (e2) (e3)) = (e2))\/((op (e3) (e3)) = (e2))))) -> (~((e2) = (e3))) -> (~((op (e2) (e0)) = (op (e2) (e3)))) -> ((op (e2) (e0)) = (e2)) -> (~((op (e3) (e2)) = (op (e3) (e3)))) -> (~((op (e3) (e1)) = (op (e3) (e3)))) -> (((op (e1) (e0)) = (e3))\/(((op (e1) (e1)) = (e3))\/(((op (e1) (e2)) = (e3))\/((op (e1) (e3)) = (e3))))) -> (~((op (e3) (e0)) = (op (e3) (e3)))) -> (((op (e0) (e0)) = (e3))\/(((op (e0) (e1)) = (e3))\/(((op (e0) (e2)) = (e3))\/((op (e0) (e3)) = (e3))))) -> (~((op (e0) (e1)) = (op (e1) (e1)))) -> (~((op (e0) (e2)) = (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 (e0) (e3)) = (op (e1) (e3)))) -> (((op (e3) (e0)) = (e2))\/(((op (e3) (e1)) = (e2))\/(((op (e3) (e2)) = (e2))\/((op (e3) (e3)) = (e2))))) -> (~((e1) = (e3))) -> (~((op (e0) (e3)) = (op (e2) (e3)))) -> (~((op (e0) (e3)) = (op (e3) (e3)))) -> ((op (e0) (e0)) = (e1)) -> (~((op (e0) (e0)) = (op (e0) (e3)))) -> (~((op (e0) (e3)) = (e0))) -> (((op (e0) (e3)) = (e0))\/(((op (e0) (e3)) = (e1))\/(((op (e0) (e3)) = (e2))\/((op (e0) (e3)) = (e3))))) -> (~((op (e3) (e3)) = (e3))) -> (~((op (e2) (e1)) = (e0))) -> (~((op (e2) (e0)) = (e0))) -> (((op (e2) (e0)) = (e0))\/(((op (e2) (e1)) = (e0))\/(((op (e2) (e2)) = (e0))\/((op (e2) (e3)) = (e0))))) -> ((op (e1) (e3)) = (e1)) -> (~((e1) = (e2))) -> False). % 18.52/18.69 do 0 intro. intros zenon_H18c zenon_H185 zenon_H184 zenon_H183 zenon_H17b zenon_H17e zenon_H178 zenon_H74 zenon_H6f zenon_H4a zenon_H4f zenon_H67 zenon_H57 zenon_H54 zenon_H45 zenon_H179 zenon_H9a zenon_H22 zenon_H9e zenon_H10a zenon_H109 zenon_H106 zenon_He7 zenon_Haf zenon_Hd8 zenon_Hdb zenon_Hdf zenon_He8 zenon_Ha8 zenon_Ha1 zenon_H142 zenon_H13e zenon_H13c zenon_H52 zenon_H139 zenon_H128 zenon_H133 zenon_H124 zenon_H2b zenon_H24 zenon_H115 zenon_H172 zenon_H173 zenon_H149 zenon_H3f zenon_H23 zenon_H3e zenon_H94 zenon_H39 zenon_H182 zenon_H10f zenon_H18b zenon_H6d zenon_H25 zenon_H75 zenon_H6a zenon_Hd5 zenon_H101 zenon_H136 zenon_Hf3 zenon_H1f zenon_H11f zenon_H145 zenon_H12b zenon_H5b zenon_Hee zenon_H62 zenon_H130 zenon_H16f zenon_H71 zenon_H168 zenon_H10e zenon_H14f zenon_H160 zenon_H165 zenon_H1d zenon_H153 zenon_H95 zenon_He2 zenon_Hc2 zenon_H7a zenon_H189 zenon_H76 zenon_He4 zenon_H102 zenon_H31 zenon_H30 zenon_H2f zenon_Hd6 zenon_H7c. % 18.52/18.69 apply (zenon_or_s _ _ zenon_H18c); [ zenon_intro zenon_H86 | zenon_intro zenon_H18d ]. % 18.52/18.69 apply (zenon_L135_); trivial. % 18.52/18.69 apply (zenon_or_s _ _ zenon_H18d); [ zenon_intro zenon_H110 | zenon_intro zenon_H18e ]. % 18.52/18.69 apply (zenon_L67_); trivial. % 18.52/18.69 apply (zenon_or_s _ _ zenon_H18e); [ zenon_intro zenon_H113 | zenon_intro zenon_Hd7 ]. % 18.52/18.69 apply (zenon_L144_); trivial. % 18.52/18.69 apply (zenon_L101_); trivial. % 18.52/18.69 (* end of lemma zenon_L145_ *) % 18.52/18.69 assert (zenon_L146_ : (~((op (e2) (e2)) = (op (e3) (e2)))) -> ((op (e2) (e2)) = (e0)) -> ((op (e3) (e2)) = (e0)) -> False). % 18.52/18.69 do 0 intro. intros zenon_H18f zenon_H2c zenon_H61. % 18.52/18.69 cut (((op (e2) (e2)) = (e0)) = ((op (e2) (e2)) = (op (e3) (e2)))). % 18.52/18.69 intro zenon_D_pnotp. % 18.52/18.69 apply zenon_H18f. % 18.52/18.69 rewrite <- zenon_D_pnotp. % 18.52/18.69 exact zenon_H2c. % 18.52/18.69 cut (((e0) = (op (e3) (e2)))); [idtac | apply NNPP; zenon_intro zenon_H66]. % 18.52/18.69 cut (((op (e2) (e2)) = (op (e2) (e2)))); [idtac | apply NNPP; zenon_intro zenon_H190]. % 18.52/18.69 congruence. % 18.52/18.69 apply zenon_H190. apply refl_equal. % 18.52/18.69 apply zenon_H66. apply sym_equal. exact zenon_H61. % 18.52/18.69 (* end of lemma zenon_L146_ *) % 18.52/18.69 assert (zenon_L147_ : ((op (e3) (e3)) = (e1)) -> ((op (e3) (e2)) = (e1)) -> (~((op (e3) (e2)) = (op (e3) (e3)))) -> False). % 18.52/18.69 do 0 intro. intros zenon_Hc4 zenon_Hba zenon_H62. % 18.52/18.69 elim (classic ((op (e3) (e3)) = (op (e3) (e3)))); [ zenon_intro zenon_H63 | zenon_intro zenon_H64 ]. % 18.52/18.69 cut (((op (e3) (e3)) = (op (e3) (e3))) = ((op (e3) (e2)) = (op (e3) (e3)))). % 18.52/18.69 intro zenon_D_pnotp. % 18.52/18.69 apply zenon_H62. % 18.52/18.69 rewrite <- zenon_D_pnotp. % 18.52/18.69 exact zenon_H63. % 18.52/18.69 cut (((op (e3) (e3)) = (op (e3) (e3)))); [idtac | apply NNPP; zenon_intro zenon_H64]. % 18.52/18.69 cut (((op (e3) (e3)) = (op (e3) (e2)))); [idtac | apply NNPP; zenon_intro zenon_H65]. % 18.52/18.69 congruence. % 18.52/18.69 cut (((op (e3) (e3)) = (e1)) = ((op (e3) (e3)) = (op (e3) (e2)))). % 18.52/18.70 intro zenon_D_pnotp. % 18.52/18.70 apply zenon_H65. % 18.52/18.70 rewrite <- zenon_D_pnotp. % 18.52/18.70 exact zenon_Hc4. % 18.52/18.70 cut (((e1) = (op (e3) (e2)))); [idtac | apply NNPP; zenon_intro zenon_H116]. % 18.52/18.70 cut (((op (e3) (e3)) = (op (e3) (e3)))); [idtac | apply NNPP; zenon_intro zenon_H64]. % 18.52/18.70 congruence. % 18.52/18.70 apply zenon_H64. apply refl_equal. % 18.52/18.70 apply zenon_H116. apply sym_equal. exact zenon_Hba. % 18.52/18.70 apply zenon_H64. apply refl_equal. % 18.52/18.70 apply zenon_H64. apply refl_equal. % 18.52/18.70 (* end of lemma zenon_L147_ *) % 18.52/18.70 assert (zenon_L148_ : (((op (e3) (e2)) = (e0))\/(((op (e3) (e2)) = (e1))\/(((op (e3) (e2)) = (e2))\/((op (e3) (e2)) = (e3))))) -> ((op (e2) (e2)) = (e0)) -> (~((op (e2) (e2)) = (op (e3) (e2)))) -> (~((op (e3) (e2)) = (op (e3) (e3)))) -> ((op (e3) (e3)) = (e1)) -> ((op (e0) (e2)) = (e2)) -> (~((op (e0) (e2)) = (op (e3) (e2)))) -> ((op (e0) (e2)) = (e3)) -> False). % 18.52/18.70 do 0 intro. intros zenon_H191 zenon_H2c zenon_H18f zenon_H62 zenon_Hc4 zenon_H150 zenon_H14f zenon_Ha9. % 18.52/18.70 apply (zenon_or_s _ _ zenon_H191); [ zenon_intro zenon_H61 | zenon_intro zenon_H192 ]. % 18.52/18.70 apply (zenon_L146_); trivial. % 18.52/18.70 apply (zenon_or_s _ _ zenon_H192); [ zenon_intro zenon_Hba | zenon_intro zenon_H193 ]. % 18.52/18.70 apply (zenon_L147_); trivial. % 18.52/18.70 apply (zenon_or_s _ _ zenon_H193); [ zenon_intro zenon_H151 | zenon_intro zenon_H163 ]. % 18.52/18.70 apply (zenon_L104_); trivial. % 18.52/18.70 apply (zenon_L111_); trivial. % 18.52/18.70 (* end of lemma zenon_L148_ *) % 18.52/18.70 assert (zenon_L149_ : (((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)) = (op (e3) (e1)))) -> ((op (e2) (e1)) = (e1)) -> (((op (e3) (e2)) = (e0))\/(((op (e3) (e2)) = (e1))\/(((op (e3) (e2)) = (e2))\/((op (e3) (e2)) = (e3))))) -> ((op (e2) (e2)) = (e0)) -> (~((op (e2) (e2)) = (op (e3) (e2)))) -> (~((op (e3) (e2)) = (op (e3) (e3)))) -> ((op (e0) (e2)) = (e2)) -> (~((op (e0) (e2)) = (op (e3) (e2)))) -> ((op (e0) (e2)) = (e3)) -> False). % 18.52/18.70 do 0 intro. intros zenon_He8 zenon_Ha1 zenon_H44 zenon_Haf zenon_Ha5 zenon_H191 zenon_H2c zenon_H18f zenon_H62 zenon_H150 zenon_H14f zenon_Ha9. % 18.52/18.70 apply (zenon_or_s _ _ zenon_He8); [ zenon_intro zenon_Hac | zenon_intro zenon_Heb ]. % 18.52/18.70 apply (zenon_L41_); trivial. % 18.52/18.70 apply (zenon_or_s _ _ zenon_Heb); [ zenon_intro zenon_Hae | zenon_intro zenon_Hec ]. % 18.52/18.70 apply (zenon_L42_); trivial. % 18.52/18.70 apply (zenon_or_s _ _ zenon_Hec); [ zenon_intro zenon_Hba | zenon_intro zenon_Hc4 ]. % 18.52/18.70 apply (zenon_L45_); trivial. % 18.52/18.70 apply (zenon_L148_); trivial. % 18.52/18.70 (* end of lemma zenon_L149_ *) % 18.52/18.70 assert (zenon_L150_ : (((op (e2) (e0)) = (e0))\/(((op (e2) (e1)) = (e0))\/(((op (e2) (e2)) = (e0))\/((op (e2) (e3)) = (e0))))) -> (~((op (e2) (e0)) = (e0))) -> (~((op (e2) (e1)) = (e0))) -> ((op (e0) (e2)) = (e3)) -> (~((op (e0) (e2)) = (op (e3) (e2)))) -> ((op (e0) (e2)) = (e2)) -> (~((op (e3) (e2)) = (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 (e2) (e1)) = (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) (e2)) = (e0))\/(((op (e1) (e2)) = (e0))\/(((op (e2) (e2)) = (e0))\/((op (e3) (e2)) = (e0))))) -> (~((op (e0) (e2)) = (e0))) -> (~((op (e1) (e2)) = (e0))) -> (~((op (e2) (e2)) = (op (e2) (e3)))) -> (~((op (e3) (e2)) = (e0))) -> False). % 18.52/18.70 do 0 intro. intros zenon_H2f zenon_H30 zenon_H31 zenon_Ha9 zenon_H14f zenon_H150 zenon_H62 zenon_H18f zenon_H191 zenon_Ha5 zenon_Haf zenon_H44 zenon_Ha1 zenon_He8 zenon_H6a zenon_H75 zenon_H25 zenon_H6d zenon_H18b. % 18.52/18.70 apply (zenon_or_s _ _ zenon_H2f); [ zenon_intro zenon_H34 | zenon_intro zenon_H33 ]. % 18.52/18.70 exact (zenon_H30 zenon_H34). % 18.52/18.70 apply (zenon_or_s _ _ zenon_H33); [ zenon_intro zenon_H36 | zenon_intro zenon_H35 ]. % 18.52/18.70 exact (zenon_H31 zenon_H36). % 18.52/18.70 apply (zenon_or_s _ _ zenon_H35); [ zenon_intro zenon_H2c | zenon_intro zenon_H37 ]. % 18.52/18.70 apply (zenon_L149_); trivial. % 18.52/18.70 apply (zenon_L143_); trivial. % 18.52/18.70 (* end of lemma zenon_L150_ *) % 18.52/18.70 assert (zenon_L151_ : (((op (e0) (e1)) = (e1))\/(((op (e1) (e1)) = (e1))\/(((op (e2) (e1)) = (e1))\/((op (e3) (e1)) = (e1))))) -> ((op (e0) (e1)) = (e0)) -> (~((op (e1) (e1)) = (e1))) -> (~((op (e3) (e2)) = (e0))) -> (~((op (e2) (e2)) = (op (e2) (e3)))) -> (~((op (e1) (e2)) = (e0))) -> (~((op (e0) (e2)) = (e0))) -> (((op (e0) (e2)) = (e0))\/(((op (e1) (e2)) = (e0))\/(((op (e2) (e2)) = (e0))\/((op (e3) (e2)) = (e0))))) -> (((op (e3) (e0)) = (e1))\/(((op (e3) (e1)) = (e1))\/(((op (e3) (e2)) = (e1))\/((op (e3) (e3)) = (e1))))) -> (~((e0) = (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) (e2)) = (op (e3) (e3)))) -> ((op (e0) (e2)) = (e2)) -> (~((op (e0) (e2)) = (op (e3) (e2)))) -> ((op (e0) (e2)) = (e3)) -> (~((op (e2) (e1)) = (e0))) -> (~((op (e2) (e0)) = (e0))) -> (((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) = (e2))) -> ((op (e2) (e0)) = (e2)) -> (~((op (e2) (e1)) = (op (e3) (e1)))) -> ((op (e1) (e2)) = (e1)) -> (~((op (e1) (e2)) = (op (e2) (e2)))) -> (((op (e3) (e3)) = (e0))\/(((op (e3) (e3)) = (e1))\/(((op (e3) (e3)) = (e2))\/((op (e3) (e3)) = (e3))))) -> (~((op (e3) (e0)) = (op (e3) (e3)))) -> ((op (e3) (e0)) = (e0)) -> (~((op (e2) (e3)) = (op (e3) (e3)))) -> ((op (e1) (e3)) = (e0)) -> (~((op (e3) (e3)) = (e3))) -> False). % 18.52/18.70 do 0 intro. intros zenon_H109 zenon_H49 zenon_H10a zenon_H18b zenon_H6d zenon_H25 zenon_H75 zenon_H6a zenon_He8 zenon_Ha1 zenon_H191 zenon_H18f zenon_H62 zenon_H150 zenon_H14f zenon_Ha9 zenon_H31 zenon_H30 zenon_H2f zenon_H106 zenon_H7c zenon_Hee zenon_Haf zenon_Hf0 zenon_H2b zenon_H101 zenon_H71 zenon_H44 zenon_Hf3 zenon_H1f zenon_H102. % 18.52/18.70 apply (zenon_or_s _ _ zenon_H109); [ zenon_intro zenon_Ha0 | zenon_intro zenon_H10b ]. % 18.52/18.70 apply (zenon_L38_); trivial. % 18.52/18.70 apply (zenon_or_s _ _ zenon_H10b); [ zenon_intro zenon_H10d | zenon_intro zenon_H10c ]. % 18.52/18.70 exact (zenon_H10a zenon_H10d). % 18.52/18.70 apply (zenon_or_s _ _ zenon_H10c); [ zenon_intro zenon_Ha5 | zenon_intro zenon_Hae ]. % 18.52/18.70 apply (zenon_L150_); trivial. % 18.52/18.70 apply (zenon_L65_); trivial. % 18.52/18.70 (* end of lemma zenon_L151_ *) % 18.52/18.70 assert (zenon_L152_ : ((op (e3) (e1)) = (e1)) -> ((op (e3) (e1)) = (e2)) -> (~((e1) = (e2))) -> False). % 18.52/18.70 do 0 intro. intros zenon_Hae zenon_H14d zenon_H7c. % 18.52/18.70 elim (classic ((e2) = (e2))); [ zenon_intro zenon_H7d | zenon_intro zenon_H7e ]. % 18.52/18.70 cut (((e2) = (e2)) = ((e1) = (e2))). % 18.52/18.70 intro zenon_D_pnotp. % 18.52/18.70 apply zenon_H7c. % 18.52/18.70 rewrite <- zenon_D_pnotp. % 18.52/18.70 exact zenon_H7d. % 18.52/18.70 cut (((e2) = (e2))); [idtac | apply NNPP; zenon_intro zenon_H7e]. % 18.52/18.70 cut (((e2) = (e1))); [idtac | apply NNPP; zenon_intro zenon_H7f]. % 18.52/18.70 congruence. % 18.52/18.70 cut (((op (e3) (e1)) = (e1)) = ((e2) = (e1))). % 18.52/18.70 intro zenon_D_pnotp. % 18.52/18.70 apply zenon_H7f. % 18.52/18.70 rewrite <- zenon_D_pnotp. % 18.52/18.70 exact zenon_Hae. % 18.52/18.70 cut (((e1) = (e1))); [idtac | apply NNPP; zenon_intro zenon_H79]. % 18.52/18.70 cut (((op (e3) (e1)) = (e2))); [idtac | apply NNPP; zenon_intro zenon_H194]. % 18.52/18.70 congruence. % 18.52/18.70 exact (zenon_H194 zenon_H14d). % 18.52/18.70 apply zenon_H79. apply refl_equal. % 18.52/18.70 apply zenon_H7e. apply refl_equal. % 18.52/18.70 apply zenon_H7e. apply refl_equal. % 18.52/18.70 (* end of lemma zenon_L152_ *) % 18.52/18.70 assert (zenon_L153_ : (~((op (e0) (e2)) = (op (e1) (e2)))) -> ((op (e0) (e2)) = (e2)) -> ((op (e1) (e2)) = (e2)) -> False). % 18.52/18.70 do 0 intro. intros zenon_H195 zenon_H150 zenon_H113. % 18.52/18.70 cut (((op (e0) (e2)) = (e2)) = ((op (e0) (e2)) = (op (e1) (e2)))). % 18.52/18.70 intro zenon_D_pnotp. % 18.52/18.70 apply zenon_H195. % 18.52/18.70 rewrite <- zenon_D_pnotp. % 18.52/18.70 exact zenon_H150. % 18.52/18.70 cut (((e2) = (op (e1) (e2)))); [idtac | apply NNPP; zenon_intro zenon_H196]. % 18.52/18.70 cut (((op (e0) (e2)) = (op (e0) (e2)))); [idtac | apply NNPP; zenon_intro zenon_H4c]. % 18.52/18.70 congruence. % 18.52/18.70 apply zenon_H4c. apply refl_equal. % 18.52/18.70 apply zenon_H196. apply sym_equal. exact zenon_H113. % 18.52/18.70 (* end of lemma zenon_L153_ *) % 18.52/18.70 assert (zenon_L154_ : (~((op (op (e2) (e2)) (e2)) = (op (e1) (e2)))) -> ((op (e2) (e2)) = (e1)) -> False). % 18.52/18.70 do 0 intro. intros zenon_H197 zenon_Hf1. % 18.52/18.70 cut (((e2) = (e2))); [idtac | apply NNPP; zenon_intro zenon_H7e]. % 18.52/18.70 cut (((op (e2) (e2)) = (e1))); [idtac | apply NNPP; zenon_intro zenon_H198]. % 18.52/18.70 congruence. % 18.52/18.70 exact (zenon_H198 zenon_Hf1). % 18.52/18.70 apply zenon_H7e. apply refl_equal. % 18.52/18.70 (* end of lemma zenon_L154_ *) % 18.52/18.70 assert (zenon_L155_ : ((op (e1) (e2)) = (e3)) -> ((op (e2) (e2)) = (e1)) -> (~((e3) = (op (op (e2) (e2)) (e2)))) -> False). % 18.52/18.70 do 0 intro. intros zenon_H16c zenon_Hf1 zenon_Hb5. % 18.52/18.70 elim (classic ((op (op (e2) (e2)) (e2)) = (op (op (e2) (e2)) (e2)))); [ zenon_intro zenon_Hb6 | zenon_intro zenon_Hb7 ]. % 18.52/18.70 cut (((op (op (e2) (e2)) (e2)) = (op (op (e2) (e2)) (e2))) = ((e3) = (op (op (e2) (e2)) (e2)))). % 18.52/18.70 intro zenon_D_pnotp. % 18.52/18.70 apply zenon_Hb5. % 18.52/18.70 rewrite <- zenon_D_pnotp. % 18.52/18.70 exact zenon_Hb6. % 18.52/18.70 cut (((op (op (e2) (e2)) (e2)) = (op (op (e2) (e2)) (e2)))); [idtac | apply NNPP; zenon_intro zenon_Hb7]. % 18.52/18.70 cut (((op (op (e2) (e2)) (e2)) = (e3))); [idtac | apply NNPP; zenon_intro zenon_Hb8]. % 18.52/18.70 congruence. % 18.52/18.70 cut (((op (e1) (e2)) = (e3)) = ((op (op (e2) (e2)) (e2)) = (e3))). % 18.52/18.70 intro zenon_D_pnotp. % 18.52/18.70 apply zenon_Hb8. % 18.52/18.70 rewrite <- zenon_D_pnotp. % 18.52/18.70 exact zenon_H16c. % 18.52/18.70 cut (((e3) = (e3))); [idtac | apply NNPP; zenon_intro zenon_H85]. % 18.52/18.70 cut (((op (e1) (e2)) = (op (op (e2) (e2)) (e2)))); [idtac | apply NNPP; zenon_intro zenon_H199]. % 18.52/18.70 congruence. % 18.52/18.70 elim (classic ((op (op (e2) (e2)) (e2)) = (op (op (e2) (e2)) (e2)))); [ zenon_intro zenon_Hb6 | zenon_intro zenon_Hb7 ]. % 18.52/18.70 cut (((op (op (e2) (e2)) (e2)) = (op (op (e2) (e2)) (e2))) = ((op (e1) (e2)) = (op (op (e2) (e2)) (e2)))). % 18.52/18.70 intro zenon_D_pnotp. % 18.52/18.70 apply zenon_H199. % 18.52/18.70 rewrite <- zenon_D_pnotp. % 18.52/18.70 exact zenon_Hb6. % 18.52/18.70 cut (((op (op (e2) (e2)) (e2)) = (op (op (e2) (e2)) (e2)))); [idtac | apply NNPP; zenon_intro zenon_Hb7]. % 18.52/18.70 cut (((op (op (e2) (e2)) (e2)) = (op (e1) (e2)))); [idtac | apply NNPP; zenon_intro zenon_H197]. % 18.52/18.70 congruence. % 18.52/18.70 apply (zenon_L154_); trivial. % 18.52/18.70 apply zenon_Hb7. apply refl_equal. % 18.52/18.70 apply zenon_Hb7. apply refl_equal. % 18.52/18.70 apply zenon_H85. apply refl_equal. % 18.52/18.70 apply zenon_Hb7. apply refl_equal. % 18.52/18.70 apply zenon_Hb7. apply refl_equal. % 18.52/18.70 (* end of lemma zenon_L155_ *) % 18.52/18.70 assert (zenon_L156_ : ((op (e3) (e2)) = (e0)) -> ((op (e1) (e2)) = (e3)) -> ((op (e2) (e2)) = (e1)) -> False). % 18.52/18.70 do 0 intro. intros zenon_H61 zenon_H16c zenon_Hf1. % 18.52/18.70 apply (zenon_notand_s _ _ ax19); [ zenon_intro zenon_H19b | zenon_intro zenon_H19a ]. % 18.52/18.70 elim (classic ((op (op (op (e2) (e2)) (e2)) (e2)) = (op (op (op (e2) (e2)) (e2)) (e2)))); [ zenon_intro zenon_Hbd | zenon_intro zenon_Hbe ]. % 18.52/18.70 cut (((op (op (op (e2) (e2)) (e2)) (e2)) = (op (op (op (e2) (e2)) (e2)) (e2))) = ((e0) = (op (op (op (e2) (e2)) (e2)) (e2)))). % 18.52/18.70 intro zenon_D_pnotp. % 18.52/18.70 apply zenon_H19b. % 18.52/18.70 rewrite <- zenon_D_pnotp. % 18.52/18.70 exact zenon_Hbd. % 18.52/18.70 cut (((op (op (op (e2) (e2)) (e2)) (e2)) = (op (op (op (e2) (e2)) (e2)) (e2)))); [idtac | apply NNPP; zenon_intro zenon_Hbe]. % 18.52/18.70 cut (((op (op (op (e2) (e2)) (e2)) (e2)) = (e0))); [idtac | apply NNPP; zenon_intro zenon_H19c]. % 18.52/18.70 congruence. % 18.52/18.70 cut (((op (e3) (e2)) = (e0)) = ((op (op (op (e2) (e2)) (e2)) (e2)) = (e0))). % 18.52/18.70 intro zenon_D_pnotp. % 18.52/18.70 apply zenon_H19c. % 18.52/18.70 rewrite <- zenon_D_pnotp. % 18.52/18.70 exact zenon_H61. % 18.52/18.70 cut (((e0) = (e0))); [idtac | apply NNPP; zenon_intro zenon_H82]. % 18.52/18.70 cut (((op (e3) (e2)) = (op (op (op (e2) (e2)) (e2)) (e2)))); [idtac | apply NNPP; zenon_intro zenon_Hc0]. % 18.52/18.70 congruence. % 18.52/18.70 elim (classic ((op (op (op (e2) (e2)) (e2)) (e2)) = (op (op (op (e2) (e2)) (e2)) (e2)))); [ zenon_intro zenon_Hbd | zenon_intro zenon_Hbe ]. % 18.52/18.70 cut (((op (op (op (e2) (e2)) (e2)) (e2)) = (op (op (op (e2) (e2)) (e2)) (e2))) = ((op (e3) (e2)) = (op (op (op (e2) (e2)) (e2)) (e2)))). % 18.52/18.70 intro zenon_D_pnotp. % 18.52/18.70 apply zenon_Hc0. % 18.52/18.70 rewrite <- zenon_D_pnotp. % 18.52/18.70 exact zenon_Hbd. % 18.52/18.70 cut (((op (op (op (e2) (e2)) (e2)) (e2)) = (op (op (op (e2) (e2)) (e2)) (e2)))); [idtac | apply NNPP; zenon_intro zenon_Hbe]. % 18.52/18.70 cut (((op (op (op (e2) (e2)) (e2)) (e2)) = (op (e3) (e2)))); [idtac | apply NNPP; zenon_intro zenon_Hc1]. % 18.52/18.70 congruence. % 18.52/18.70 cut (((e2) = (e2))); [idtac | apply NNPP; zenon_intro zenon_H7e]. % 18.52/18.70 cut (((op (op (e2) (e2)) (e2)) = (e3))); [idtac | apply NNPP; zenon_intro zenon_Hb8]. % 18.52/18.70 congruence. % 18.52/18.70 cut (((op (e1) (e2)) = (e3)) = ((op (op (e2) (e2)) (e2)) = (e3))). % 18.52/18.70 intro zenon_D_pnotp. % 18.52/18.70 apply zenon_Hb8. % 18.52/18.70 rewrite <- zenon_D_pnotp. % 18.52/18.70 exact zenon_H16c. % 18.52/18.70 cut (((e3) = (e3))); [idtac | apply NNPP; zenon_intro zenon_H85]. % 18.52/18.70 cut (((op (e1) (e2)) = (op (op (e2) (e2)) (e2)))); [idtac | apply NNPP; zenon_intro zenon_H199]. % 18.52/18.70 congruence. % 18.52/18.70 elim (classic ((op (op (e2) (e2)) (e2)) = (op (op (e2) (e2)) (e2)))); [ zenon_intro zenon_Hb6 | zenon_intro zenon_Hb7 ]. % 18.52/18.70 cut (((op (op (e2) (e2)) (e2)) = (op (op (e2) (e2)) (e2))) = ((op (e1) (e2)) = (op (op (e2) (e2)) (e2)))). % 18.52/18.70 intro zenon_D_pnotp. % 18.52/18.70 apply zenon_H199. % 18.52/18.70 rewrite <- zenon_D_pnotp. % 18.52/18.70 exact zenon_Hb6. % 18.52/18.70 cut (((op (op (e2) (e2)) (e2)) = (op (op (e2) (e2)) (e2)))); [idtac | apply NNPP; zenon_intro zenon_Hb7]. % 18.52/18.70 cut (((op (op (e2) (e2)) (e2)) = (op (e1) (e2)))); [idtac | apply NNPP; zenon_intro zenon_H197]. % 18.52/18.70 congruence. % 18.52/18.70 apply (zenon_L154_); trivial. % 18.52/18.70 apply zenon_Hb7. apply refl_equal. % 18.52/18.70 apply zenon_Hb7. apply refl_equal. % 18.52/18.70 apply zenon_H85. apply refl_equal. % 18.52/18.70 apply zenon_H7e. apply refl_equal. % 18.52/18.70 apply zenon_Hbe. apply refl_equal. % 18.52/18.70 apply zenon_Hbe. apply refl_equal. % 18.52/18.70 apply zenon_H82. apply refl_equal. % 18.52/18.70 apply zenon_Hbe. apply refl_equal. % 18.52/18.70 apply zenon_Hbe. apply refl_equal. % 18.52/18.70 apply (zenon_notand_s _ _ zenon_H19a); [ zenon_intro zenon_Hb5 | zenon_intro zenon_Hf2 ]. % 18.52/18.70 apply (zenon_L155_); trivial. % 18.52/18.70 apply zenon_Hf2. apply sym_equal. exact zenon_Hf1. % 18.52/18.70 (* end of lemma zenon_L156_ *) % 18.52/18.70 assert (zenon_L157_ : (((op (e0) (e2)) = (e0))\/(((op (e1) (e2)) = (e0))\/(((op (e2) (e2)) = (e0))\/((op (e3) (e2)) = (e0))))) -> (~((op (e0) (e2)) = (e0))) -> (~((op (e1) (e2)) = (e0))) -> (~((op (e2) (e2)) = (op (e2) (e3)))) -> ((op (e2) (e3)) = (e0)) -> (((op (e2) (e0)) = (e1))\/(((op (e2) (e1)) = (e1))\/(((op (e2) (e2)) = (e1))\/((op (e2) (e3)) = (e1))))) -> (~((e1) = (e2))) -> ((op (e2) (e0)) = (e2)) -> (~((op (e2) (e1)) = (op (e3) (e1)))) -> ((op (e3) (e1)) = (e1)) -> ((op (e1) (e2)) = (e3)) -> (~((op (e1) (e3)) = (op (e2) (e3)))) -> ((op (e1) (e3)) = (e1)) -> False). % 18.52/18.70 do 0 intro. intros zenon_H6a zenon_H75 zenon_H25 zenon_H6d zenon_H37 zenon_H106 zenon_H7c zenon_Hee zenon_Haf zenon_Hae zenon_H16c zenon_Hdb zenon_Hd6. % 18.52/18.70 apply (zenon_or_s _ _ zenon_H6a); [ zenon_intro zenon_H48 | zenon_intro zenon_H6b ]. % 18.52/18.70 exact (zenon_H75 zenon_H48). % 18.52/18.70 apply (zenon_or_s _ _ zenon_H6b); [ zenon_intro zenon_H2a | zenon_intro zenon_H6c ]. % 18.52/18.70 exact (zenon_H25 zenon_H2a). % 18.52/18.70 apply (zenon_or_s _ _ zenon_H6c); [ zenon_intro zenon_H2c | zenon_intro zenon_H61 ]. % 18.52/18.70 apply (zenon_L18_); trivial. % 18.52/18.70 apply (zenon_or_s _ _ zenon_H106); [ zenon_intro zenon_Hed | zenon_intro zenon_H107 ]. % 18.52/18.70 apply (zenon_L58_); trivial. % 18.52/18.70 apply (zenon_or_s _ _ zenon_H107); [ zenon_intro zenon_Ha5 | zenon_intro zenon_H108 ]. % 18.52/18.70 apply (zenon_L42_); trivial. % 18.52/18.70 apply (zenon_or_s _ _ zenon_H108); [ zenon_intro zenon_Hf1 | zenon_intro zenon_Hf4 ]. % 18.52/18.70 apply (zenon_L156_); trivial. % 18.52/18.70 apply (zenon_L126_); trivial. % 18.52/18.70 (* end of lemma zenon_L157_ *) % 18.52/18.70 assert (zenon_L158_ : (((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 (e1) (e2)) = (e3)) -> ((op (e3) (e1)) = (e1)) -> (~((op (e2) (e1)) = (op (e3) (e1)))) -> ((op (e2) (e0)) = (e2)) -> (~((e1) = (e2))) -> (((op (e2) (e0)) = (e1))\/(((op (e2) (e1)) = (e1))\/(((op (e2) (e2)) = (e1))\/((op (e2) (e3)) = (e1))))) -> (~((op (e2) (e2)) = (op (e2) (e3)))) -> (~((op (e1) (e2)) = (e0))) -> (~((op (e0) (e2)) = (e0))) -> (((op (e0) (e2)) = (e0))\/(((op (e1) (e2)) = (e0))\/(((op (e2) (e2)) = (e0))\/((op (e3) (e2)) = (e0))))) -> ((op (e1) (e3)) = (e0)) -> ((op (e3) (e3)) = (e2)) -> (~((op (e2) (e3)) = (op (e3) (e3)))) -> (~((op (e0) (e3)) = (op (e2) (e3)))) -> ((op (e0) (e3)) = (e3)) -> False). % 18.52/18.70 do 0 intro. intros zenon_H11f zenon_Hd6 zenon_Hdb zenon_H16c zenon_Hae zenon_Haf zenon_Hee zenon_H7c zenon_H106 zenon_H6d zenon_H25 zenon_H75 zenon_H6a zenon_H1f zenon_Hf6 zenon_Hf3 zenon_He2 zenon_He3. % 18.52/18.70 apply (zenon_or_s _ _ zenon_H11f); [ zenon_intro zenon_H37 | zenon_intro zenon_H120 ]. % 18.52/18.70 apply (zenon_L157_); trivial. % 18.52/18.70 apply (zenon_or_s _ _ zenon_H120); [ zenon_intro zenon_Hf4 | zenon_intro zenon_H121 ]. % 18.52/18.70 apply (zenon_L63_); trivial. % 18.52/18.70 apply (zenon_or_s _ _ zenon_H121); [ zenon_intro zenon_H11d | zenon_intro zenon_Hdd ]. % 18.52/18.70 apply (zenon_L97_); trivial. % 18.52/18.70 apply (zenon_L54_); trivial. % 18.52/18.70 (* end of lemma zenon_L158_ *) % 18.52/18.70 assert (zenon_L159_ : (((op (e1) (e2)) = (e0))\/(((op (e1) (e2)) = (e1))\/(((op (e1) (e2)) = (e2))\/((op (e1) (e2)) = (e3))))) -> ((op (e2) (e2)) = (e1)) -> (~((op (e1) (e2)) = (op (e2) (e2)))) -> ((op (e0) (e2)) = (e2)) -> (~((op (e0) (e2)) = (op (e1) (e2)))) -> (((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 (e3) (e1)) = (e1)) -> (~((op (e2) (e1)) = (op (e3) (e1)))) -> ((op (e2) (e0)) = (e2)) -> (~((e1) = (e2))) -> (((op (e2) (e0)) = (e1))\/(((op (e2) (e1)) = (e1))\/(((op (e2) (e2)) = (e1))\/((op (e2) (e3)) = (e1))))) -> (~((op (e2) (e2)) = (op (e2) (e3)))) -> (~((op (e1) (e2)) = (e0))) -> (~((op (e0) (e2)) = (e0))) -> (((op (e0) (e2)) = (e0))\/(((op (e1) (e2)) = (e0))\/(((op (e2) (e2)) = (e0))\/((op (e3) (e2)) = (e0))))) -> ((op (e1) (e3)) = (e0)) -> ((op (e3) (e3)) = (e2)) -> (~((op (e2) (e3)) = (op (e3) (e3)))) -> (~((op (e0) (e3)) = (op (e2) (e3)))) -> ((op (e0) (e3)) = (e3)) -> False). % 18.52/18.70 do 0 intro. intros zenon_H19d zenon_Hf1 zenon_H2b zenon_H150 zenon_H195 zenon_H11f zenon_Hd6 zenon_Hdb zenon_Hae zenon_Haf zenon_Hee zenon_H7c zenon_H106 zenon_H6d zenon_H25 zenon_H75 zenon_H6a zenon_H1f zenon_Hf6 zenon_Hf3 zenon_He2 zenon_He3. % 18.52/18.70 apply (zenon_or_s _ _ zenon_H19d); [ zenon_intro zenon_H2a | zenon_intro zenon_H19e ]. % 18.52/18.70 exact (zenon_H25 zenon_H2a). % 18.52/18.70 apply (zenon_or_s _ _ zenon_H19e); [ zenon_intro zenon_Hf0 | zenon_intro zenon_H19f ]. % 18.52/18.70 apply (zenon_L59_); trivial. % 18.52/18.70 apply (zenon_or_s _ _ zenon_H19f); [ zenon_intro zenon_H113 | zenon_intro zenon_H16c ]. % 18.52/18.70 apply (zenon_L153_); trivial. % 18.52/18.70 apply (zenon_L158_); trivial. % 18.52/18.70 (* end of lemma zenon_L159_ *) % 18.52/18.70 assert (zenon_L160_ : (((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)) = (e0)) -> (((op (e0) (e2)) = (e0))\/(((op (e1) (e2)) = (e0))\/(((op (e2) (e2)) = (e0))\/((op (e3) (e2)) = (e0))))) -> (~((op (e0) (e2)) = (e0))) -> (~((op (e1) (e2)) = (e0))) -> (~((op (e2) (e2)) = (op (e2) (e3)))) -> (((op (e2) (e0)) = (e1))\/(((op (e2) (e1)) = (e1))\/(((op (e2) (e2)) = (e1))\/((op (e2) (e3)) = (e1))))) -> (~((e1) = (e2))) -> ((op (e2) (e0)) = (e2)) -> (~((op (e2) (e1)) = (op (e3) (e1)))) -> ((op (e3) (e1)) = (e1)) -> (~((op (e1) (e3)) = (op (e2) (e3)))) -> (((op (e2) (e3)) = (e0))\/(((op (e2) (e3)) = (e1))\/(((op (e2) (e3)) = (e2))\/((op (e2) (e3)) = (e3))))) -> (~((op (e0) (e2)) = (op (e1) (e2)))) -> ((op (e0) (e2)) = (e2)) -> (~((op (e1) (e2)) = (op (e2) (e2)))) -> ((op (e2) (e2)) = (e1)) -> (((op (e1) (e2)) = (e0))\/(((op (e1) (e2)) = (e1))\/(((op (e1) (e2)) = (e2))\/((op (e1) (e2)) = (e3))))) -> (~((e1) = (e3))) -> ((op (e1) (e3)) = (e1)) -> (~((op (e0) (e3)) = (op (e2) (e3)))) -> (~((op (e0) (e3)) = (op (e3) (e3)))) -> ((op (e3) (e3)) = (e2)) -> ((op (e0) (e0)) = (e1)) -> (~((op (e0) (e0)) = (op (e0) (e3)))) -> (~((op (e0) (e3)) = (e0))) -> (((op (e0) (e3)) = (e0))\/(((op (e0) (e3)) = (e1))\/(((op (e0) (e3)) = (e2))\/((op (e0) (e3)) = (e3))))) -> (~((op (e3) (e3)) = (e3))) -> False). % 18.52/18.70 do 0 intro. intros zenon_H136 zenon_Hf3 zenon_H1f zenon_H6a zenon_H75 zenon_H25 zenon_H6d zenon_H106 zenon_H7c zenon_Hee zenon_Haf zenon_Hae zenon_Hdb zenon_H11f zenon_H195 zenon_H150 zenon_H2b zenon_Hf1 zenon_H19d zenon_H95 zenon_Hd6 zenon_He2 zenon_Hc2 zenon_Hf6 zenon_H7a zenon_H189 zenon_H76 zenon_He4 zenon_H102. % 18.52/18.70 apply (zenon_or_s _ _ zenon_H136); [ zenon_intro zenon_He3 | zenon_intro zenon_H137 ]. % 18.52/18.70 apply (zenon_L159_); trivial. % 18.52/18.70 apply (zenon_or_s _ _ zenon_H137); [ zenon_intro zenon_Hdc | zenon_intro zenon_H138 ]. % 18.52/18.70 apply (zenon_L83_); trivial. % 18.52/18.70 apply (zenon_or_s _ _ zenon_H138); [ zenon_intro zenon_Hdd | zenon_intro zenon_H105 ]. % 18.52/18.70 apply (zenon_L141_); trivial. % 18.52/18.70 exact (zenon_H102 zenon_H105). % 18.52/18.70 (* end of lemma zenon_L160_ *) % 18.52/18.70 assert (zenon_L161_ : (((op (e1) (e0)) = (e0))\/(((op (e1) (e1)) = (e0))\/(((op (e1) (e2)) = (e0))\/((op (e1) (e3)) = (e0))))) -> (~((op (e1) (e0)) = (e0))) -> (~((op (e1) (e1)) = (e0))) -> (~((op (e1) (e2)) = (e0))) -> (((op (e3) (e3)) = (e0))\/(((op (e3) (e3)) = (e1))\/(((op (e3) (e3)) = (e2))\/((op (e3) (e3)) = (e3))))) -> (~((op (e1) (e3)) = (op (e3) (e3)))) -> ((op (e0) (e3)) = (e2)) -> (~((op (e0) (e3)) = (op (e3) (e3)))) -> (~((op (e3) (e3)) = (e3))) -> False). % 18.52/18.70 do 0 intro. intros zenon_H22 zenon_H23 zenon_H24 zenon_H25 zenon_H101 zenon_Hd5 zenon_Hcd zenon_Hc2 zenon_H102. % 18.52/18.70 apply (zenon_or_s _ _ zenon_H22); [ zenon_intro zenon_H27 | zenon_intro zenon_H26 ]. % 18.52/18.70 exact (zenon_H23 zenon_H27). % 18.52/18.70 apply (zenon_or_s _ _ zenon_H26); [ zenon_intro zenon_H29 | zenon_intro zenon_H28 ]. % 18.52/18.70 exact (zenon_H24 zenon_H29). % 18.52/18.70 apply (zenon_or_s _ _ zenon_H28); [ zenon_intro zenon_H2a | zenon_intro zenon_H1f ]. % 18.52/18.70 exact (zenon_H25 zenon_H2a). % 18.52/18.70 apply (zenon_L137_); trivial. % 18.52/18.70 (* end of lemma zenon_L161_ *) % 18.52/18.70 assert (zenon_L162_ : (~((op (e0) (e2)) = (op (e1) (e2)))) -> ((op (e0) (e2)) = (e3)) -> ((op (e1) (e2)) = (e3)) -> False). % 18.52/18.70 do 0 intro. intros zenon_H195 zenon_Ha9 zenon_H16c. % 18.52/18.70 cut (((op (e0) (e2)) = (e3)) = ((op (e0) (e2)) = (op (e1) (e2)))). % 18.52/18.70 intro zenon_D_pnotp. % 18.52/18.70 apply zenon_H195. % 18.52/18.70 rewrite <- zenon_D_pnotp. % 18.52/18.70 exact zenon_Ha9. % 18.52/18.70 cut (((e3) = (op (e1) (e2)))); [idtac | apply NNPP; zenon_intro zenon_H1a0]. % 18.52/18.70 cut (((op (e0) (e2)) = (op (e0) (e2)))); [idtac | apply NNPP; zenon_intro zenon_H4c]. % 18.52/18.70 congruence. % 18.52/18.70 apply zenon_H4c. apply refl_equal. % 18.52/18.70 apply zenon_H1a0. apply sym_equal. exact zenon_H16c. % 18.52/18.70 (* end of lemma zenon_L162_ *) % 18.52/18.70 assert (zenon_L163_ : (((op (e1) (e0)) = (e3))\/(((op (e1) (e1)) = (e3))\/(((op (e1) (e2)) = (e3))\/((op (e1) (e3)) = (e3))))) -> ((op (e0) (e0)) = (e1)) -> (~((op (e3) (e3)) = (e3))) -> (~((op (e0) (e2)) = (op (e3) (e2)))) -> (~((op (e1) (e1)) = (op (e3) (e1)))) -> ((op (e3) (e0)) = (e2)) -> (~((e2) = (e3))) -> (((op (e3) (e0)) = (e3))\/(((op (e3) (e1)) = (e3))\/(((op (e3) (e2)) = (e3))\/((op (e3) (e3)) = (e3))))) -> ((op (e0) (e2)) = (e3)) -> (~((op (e0) (e2)) = (op (e1) (e2)))) -> ((op (e1) (e3)) = (e1)) -> (~((e1) = (e3))) -> False). % 18.52/18.70 do 0 intro. intros zenon_H16f zenon_H7a zenon_H102 zenon_H14f zenon_H160 zenon_H148 zenon_H12b zenon_H165 zenon_Ha9 zenon_H195 zenon_Hd6 zenon_H95. % 18.52/18.70 apply (zenon_or_s _ _ zenon_H16f); [ zenon_intro zenon_H9e | zenon_intro zenon_H170 ]. % 18.52/18.70 apply (zenon_L107_); trivial. % 18.52/18.70 apply (zenon_or_s _ _ zenon_H170); [ zenon_intro zenon_H13f | zenon_intro zenon_H171 ]. % 18.52/18.70 apply (zenon_L112_); trivial. % 18.52/18.70 apply (zenon_or_s _ _ zenon_H171); [ zenon_intro zenon_H16c | zenon_intro zenon_Hdc ]. % 18.52/18.70 apply (zenon_L162_); trivial. % 18.52/18.70 apply (zenon_L83_); trivial. % 18.52/18.70 (* end of lemma zenon_L163_ *) % 18.52/18.70 assert (zenon_L164_ : (~((op (e1) (e1)) = (op (e3) (e1)))) -> ((op (e1) (e1)) = (e2)) -> ((op (e3) (e1)) = (e2)) -> False). % 18.52/18.70 do 0 intro. intros zenon_H160 zenon_H110 zenon_H14d. % 18.52/18.70 cut (((op (e1) (e1)) = (e2)) = ((op (e1) (e1)) = (op (e3) (e1)))). % 18.52/18.70 intro zenon_D_pnotp. % 18.52/18.70 apply zenon_H160. % 18.52/18.70 rewrite <- zenon_D_pnotp. % 18.52/18.70 exact zenon_H110. % 18.52/18.70 cut (((e2) = (op (e3) (e1)))); [idtac | apply NNPP; zenon_intro zenon_H14e]. % 18.52/18.70 cut (((op (e1) (e1)) = (op (e1) (e1)))); [idtac | apply NNPP; zenon_intro zenon_H141]. % 18.52/18.70 congruence. % 18.52/18.70 apply zenon_H141. apply refl_equal. % 18.52/18.70 apply zenon_H14e. apply sym_equal. exact zenon_H14d. % 18.52/18.70 (* end of lemma zenon_L164_ *) % 18.52/18.70 assert (zenon_L165_ : (((op (e1) (e0)) = (e2))\/(((op (e1) (e1)) = (e2))\/(((op (e1) (e2)) = (e2))\/((op (e1) (e3)) = (e2))))) -> ((op (e0) (e0)) = (e1)) -> ((op (e2) (e0)) = (e3)) -> ((op (e3) (e1)) = (e2)) -> (~((op (e1) (e1)) = (op (e3) (e1)))) -> ((op (e0) (e2)) = (e2)) -> (~((op (e0) (e2)) = (op (e1) (e2)))) -> ((op (e1) (e3)) = (e1)) -> (~((e1) = (e2))) -> False). % 18.52/18.70 do 0 intro. intros zenon_H18c zenon_H7a zenon_H3b zenon_H14d zenon_H160 zenon_H150 zenon_H195 zenon_Hd6 zenon_H7c. % 18.52/18.70 apply (zenon_or_s _ _ zenon_H18c); [ zenon_intro zenon_H86 | zenon_intro zenon_H18d ]. % 18.52/18.70 apply (zenon_L33_); trivial. % 18.52/18.70 apply (zenon_or_s _ _ zenon_H18d); [ zenon_intro zenon_H110 | zenon_intro zenon_H18e ]. % 18.52/18.70 apply (zenon_L164_); trivial. % 18.52/18.70 apply (zenon_or_s _ _ zenon_H18e); [ zenon_intro zenon_H113 | zenon_intro zenon_Hd7 ]. % 18.52/18.70 apply (zenon_L153_); trivial. % 18.52/18.70 apply (zenon_L101_); trivial. % 18.52/18.70 (* end of lemma zenon_L165_ *) % 18.52/18.70 assert (zenon_L166_ : ((op (e1) (e1)) = (e2)) -> ((op (e1) (e1)) = (e3)) -> (~((e2) = (e3))) -> False). % 18.52/18.70 do 0 intro. intros zenon_H110 zenon_H13f zenon_H12b. % 18.52/18.70 elim (classic ((e3) = (e3))); [ zenon_intro zenon_H96 | zenon_intro zenon_H85 ]. % 18.52/18.70 cut (((e3) = (e3)) = ((e2) = (e3))). % 18.52/18.70 intro zenon_D_pnotp. % 18.52/18.70 apply zenon_H12b. % 18.52/18.70 rewrite <- zenon_D_pnotp. % 18.52/18.70 exact zenon_H96. % 18.52/18.70 cut (((e3) = (e3))); [idtac | apply NNPP; zenon_intro zenon_H85]. % 18.52/18.70 cut (((e3) = (e2))); [idtac | apply NNPP; zenon_intro zenon_H12c]. % 18.52/18.70 congruence. % 18.52/18.70 cut (((op (e1) (e1)) = (e2)) = ((e3) = (e2))). % 18.52/18.70 intro zenon_D_pnotp. % 18.52/18.70 apply zenon_H12c. % 18.52/18.70 rewrite <- zenon_D_pnotp. % 18.52/18.70 exact zenon_H110. % 18.52/18.70 cut (((e2) = (e2))); [idtac | apply NNPP; zenon_intro zenon_H7e]. % 18.52/18.70 cut (((op (e1) (e1)) = (e3))); [idtac | apply NNPP; zenon_intro zenon_H1a1]. % 18.52/18.70 congruence. % 18.52/18.70 exact (zenon_H1a1 zenon_H13f). % 18.52/18.70 apply zenon_H7e. apply refl_equal. % 18.52/18.70 apply zenon_H85. apply refl_equal. % 18.52/18.70 apply zenon_H85. apply refl_equal. % 18.52/18.70 (* end of lemma zenon_L166_ *) % 18.52/18.70 assert (zenon_L167_ : ((op (e1) (e2)) = (e1)) -> ((op (e1) (e2)) = (e3)) -> (~((e1) = (e3))) -> False). % 18.52/18.70 do 0 intro. intros zenon_Hf0 zenon_H16c zenon_H95. % 18.52/18.70 elim (classic ((e3) = (e3))); [ zenon_intro zenon_H96 | zenon_intro zenon_H85 ]. % 18.52/18.70 cut (((e3) = (e3)) = ((e1) = (e3))). % 18.52/18.70 intro zenon_D_pnotp. % 18.52/18.70 apply zenon_H95. % 18.52/18.70 rewrite <- zenon_D_pnotp. % 18.52/18.70 exact zenon_H96. % 18.52/18.70 cut (((e3) = (e3))); [idtac | apply NNPP; zenon_intro zenon_H85]. % 18.52/18.70 cut (((e3) = (e1))); [idtac | apply NNPP; zenon_intro zenon_H97]. % 18.52/18.70 congruence. % 18.52/18.70 cut (((op (e1) (e2)) = (e1)) = ((e3) = (e1))). % 18.52/18.70 intro zenon_D_pnotp. % 18.52/18.70 apply zenon_H97. % 18.52/18.70 rewrite <- zenon_D_pnotp. % 18.52/18.70 exact zenon_Hf0. % 18.52/18.70 cut (((e1) = (e1))); [idtac | apply NNPP; zenon_intro zenon_H79]. % 18.52/18.70 cut (((op (e1) (e2)) = (e3))); [idtac | apply NNPP; zenon_intro zenon_H16d]. % 18.52/18.70 congruence. % 18.52/18.70 exact (zenon_H16d zenon_H16c). % 18.52/18.70 apply zenon_H79. apply refl_equal. % 18.52/18.70 apply zenon_H85. apply refl_equal. % 18.52/18.70 apply zenon_H85. apply refl_equal. % 18.52/18.70 (* end of lemma zenon_L167_ *) % 18.52/18.70 assert (zenon_L168_ : ((op (e2) (e2)) = (e3)) -> ((op (e2) (e0)) = (e3)) -> (~((op (e2) (e0)) = (op (e2) (e2)))) -> False). % 18.52/18.70 do 0 intro. intros zenon_Haa zenon_H3b zenon_H52. % 18.52/18.70 elim (classic ((op (e2) (e2)) = (op (e2) (e2)))); [ zenon_intro zenon_H1a2 | zenon_intro zenon_H190 ]. % 18.52/18.70 cut (((op (e2) (e2)) = (op (e2) (e2))) = ((op (e2) (e0)) = (op (e2) (e2)))). % 18.52/18.70 intro zenon_D_pnotp. % 18.52/18.70 apply zenon_H52. % 18.52/18.70 rewrite <- zenon_D_pnotp. % 18.52/18.70 exact zenon_H1a2. % 18.52/18.70 cut (((op (e2) (e2)) = (op (e2) (e2)))); [idtac | apply NNPP; zenon_intro zenon_H190]. % 18.52/18.70 cut (((op (e2) (e2)) = (op (e2) (e0)))); [idtac | apply NNPP; zenon_intro zenon_H1a3]. % 18.52/18.70 congruence. % 18.52/18.70 cut (((op (e2) (e2)) = (e3)) = ((op (e2) (e2)) = (op (e2) (e0)))). % 18.52/18.70 intro zenon_D_pnotp. % 18.52/18.70 apply zenon_H1a3. % 18.52/18.70 rewrite <- zenon_D_pnotp. % 18.52/18.70 exact zenon_Haa. % 18.52/18.70 cut (((e3) = (op (e2) (e0)))); [idtac | apply NNPP; zenon_intro zenon_H3c]. % 18.52/18.70 cut (((op (e2) (e2)) = (op (e2) (e2)))); [idtac | apply NNPP; zenon_intro zenon_H190]. % 18.52/18.70 congruence. % 18.52/18.70 apply zenon_H190. apply refl_equal. % 18.52/18.70 apply zenon_H3c. apply sym_equal. exact zenon_H3b. % 18.52/18.70 apply zenon_H190. apply refl_equal. % 18.52/18.70 apply zenon_H190. apply refl_equal. % 18.52/18.70 (* end of lemma zenon_L168_ *) % 18.52/18.70 assert (zenon_L169_ : (~((op (e3) (e1)) = (op (e3) (e2)))) -> ((op (e3) (e1)) = (e3)) -> ((op (e3) (e2)) = (e3)) -> False). % 18.52/18.70 do 0 intro. intros zenon_H1a4 zenon_H161 zenon_H163. % 18.52/18.70 cut (((op (e3) (e1)) = (e3)) = ((op (e3) (e1)) = (op (e3) (e2)))). % 18.52/18.70 intro zenon_D_pnotp. % 18.52/18.70 apply zenon_H1a4. % 18.52/18.70 rewrite <- zenon_D_pnotp. % 18.52/18.70 exact zenon_H161. % 18.52/18.70 cut (((e3) = (op (e3) (e2)))); [idtac | apply NNPP; zenon_intro zenon_H164]. % 18.52/18.70 cut (((op (e3) (e1)) = (op (e3) (e1)))); [idtac | apply NNPP; zenon_intro zenon_Hb1]. % 18.52/18.70 congruence. % 18.52/18.70 apply zenon_Hb1. apply refl_equal. % 18.52/18.70 apply zenon_H164. apply sym_equal. exact zenon_H163. % 18.52/18.70 (* end of lemma zenon_L169_ *) % 18.52/18.70 assert (zenon_L170_ : (((op (e3) (e0)) = (e1))\/(((op (e3) (e1)) = (e1))\/(((op (e3) (e2)) = (e1))\/((op (e3) (e3)) = (e1))))) -> (~((e0) = (e1))) -> (~((op (e3) (e3)) = (e3))) -> ((op (e1) (e3)) = (e0)) -> ((op (e3) (e0)) = (e0)) -> (~((op (e3) (e0)) = (op (e3) (e3)))) -> (((op (e3) (e3)) = (e0))\/(((op (e3) (e3)) = (e1))\/(((op (e3) (e3)) = (e2))\/((op (e3) (e3)) = (e3))))) -> (~((op (e1) (e2)) = (op (e2) (e2)))) -> (~((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 (e1) (e2)) = (e1)) -> (~((op (e1) (e2)) = (op (e3) (e2)))) -> (((op (e2) (e3)) = (e0))\/(((op (e2) (e3)) = (e1))\/(((op (e2) (e3)) = (e2))\/((op (e2) (e3)) = (e3))))) -> ((op (e1) (e3)) = (e2)) -> (~((op (e2) (e3)) = (op (e3) (e3)))) -> (~((op (e2) (e0)) = (op (e2) (e3)))) -> ((op (e2) (e0)) = (e2)) -> (~((op (e0) (e3)) = (op (e2) (e3)))) -> ((op (e0) (e3)) = (e3)) -> False). % 18.52/18.70 do 0 intro. intros zenon_He8 zenon_Ha1 zenon_H102 zenon_H1f zenon_H44 zenon_H71 zenon_H101 zenon_H2b zenon_Haf zenon_H7c zenon_H106 zenon_Hf0 zenon_H115 zenon_H11f zenon_Hd7 zenon_Hf3 zenon_H5b zenon_Hee zenon_He2 zenon_He3. % 18.52/18.70 apply (zenon_or_s _ _ zenon_He8); [ zenon_intro zenon_Hac | zenon_intro zenon_Heb ]. % 18.52/18.70 apply (zenon_L41_); trivial. % 18.52/18.70 apply (zenon_or_s _ _ zenon_Heb); [ zenon_intro zenon_Hae | zenon_intro zenon_Hec ]. % 18.52/18.70 apply (zenon_L65_); trivial. % 18.52/18.70 apply (zenon_or_s _ _ zenon_Hec); [ zenon_intro zenon_Hba | zenon_intro zenon_Hc4 ]. % 18.52/18.70 apply (zenon_L69_); trivial. % 18.52/18.70 apply (zenon_L74_); trivial. % 18.52/18.70 (* end of lemma zenon_L170_ *) % 18.52/18.70 assert (zenon_L171_ : (((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) (e1)) = (op (e3) (e2)))) -> (((op (e0) (e0)) = (e0))\/(((op (e1) (e0)) = (e0))\/(((op (e2) (e0)) = (e0))\/((op (e3) (e0)) = (e0))))) -> (~((op (e2) (e0)) = (e0))) -> (~((op (e1) (e0)) = (e0))) -> (~((op (e0) (e0)) = (e0))) -> ((~((op (e3) (e2)) = (e0)))\/((op (e3) (e0)) = (e2))) -> (~((op (e2) (e2)) = (op (e3) (e2)))) -> (((op (e3) (e2)) = (e0))\/(((op (e3) (e2)) = (e1))\/(((op (e3) (e2)) = (e2))\/((op (e3) (e2)) = (e3))))) -> (~((op (e0) (e2)) = (op (e1) (e2)))) -> (((op (e1) (e2)) = (e0))\/(((op (e1) (e2)) = (e1))\/(((op (e1) (e2)) = (e2))\/((op (e1) (e2)) = (e3))))) -> (~((e1) = (e3))) -> (~((e0) = (e3))) -> ((op (e1) (e0)) = (e3)) -> (~((op (e1) (e1)) = (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) (e0)) = (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 (e0) (e1)) = (op (e1) (e1)))) -> (~((e0) = (e1))) -> (((op (e2) (e0)) = (e0))\/(((op (e2) (e1)) = (e0))\/(((op (e2) (e2)) = (e0))\/((op (e2) (e3)) = (e0))))) -> (~((op (e0) (e2)) = (op (e2) (e2)))) -> (((op (e3) (e0)) = (e1))\/(((op (e3) (e1)) = (e1))\/(((op (e3) (e2)) = (e1))\/((op (e3) (e3)) = (e1))))) -> (~((op (e0) (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 (e1) (e3)) = (op (e2) (e3)))) -> (~((op (e1) (e0)) = (op (e1) (e3)))) -> (~((op (e1) (e3)) = (op (e3) (e3)))) -> (~((op (e0) (e3)) = (op (e2) (e3)))) -> (((op (e0) (e3)) = (e0))\/(((op (e0) (e3)) = (e1))\/(((op (e0) (e3)) = (e2))\/((op (e0) (e3)) = (e3))))) -> (~((op (e2) (e1)) = (op (e3) (e1)))) -> (((op (e2) (e0)) = (e3))\/(((op (e2) (e1)) = (e3))\/(((op (e2) (e2)) = (e3))\/((op (e2) (e3)) = (e3))))) -> (~((op (e2) (e1)) = (e0))) -> (((op (e2) (e0)) = (e1))\/(((op (e2) (e1)) = (e1))\/(((op (e2) (e2)) = (e1))\/((op (e2) (e3)) = (e1))))) -> (~((op (e3) (e0)) = (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) (e2)) = (op (e2) (e2)))) -> ((op (e2) (e0)) = (e2)) -> (((op (e0) (e1)) = (e1))\/(((op (e1) (e1)) = (e1))\/(((op (e2) (e1)) = (e1))\/((op (e3) (e1)) = (e1))))) -> (~((op (e0) (e0)) = (op (e0) (e3)))) -> ((~((op (e2) (e2)) = (e0)))\/((op (e2) (e0)) = (e2))) -> ((~((op (e3) (e0)) = (e0)))\/((op (e3) (e0)) = (e0))) -> (((op (e0) (e0)) = (e2))\/(((op (e0) (e1)) = (e2))\/(((op (e0) (e2)) = (e2))\/((op (e0) (e3)) = (e2))))) -> (~((op (e2) (e0)) = (op (e3) (e0)))) -> (~((op (e0) (e1)) = (op (e2) (e1)))) -> ((~((op (e1) (e2)) = (e0)))\/((op (e1) (e0)) = (e2))) -> (((op (e0) (e0)) = (e0))\/(((op (e0) (e1)) = (e0))\/(((op (e0) (e2)) = (e0))\/((op (e0) (e3)) = (e0))))) -> (~((op (e0) (e2)) = (e0))) -> (~((op (e3) (e0)) = (op (e3) (e2)))) -> (~((op (e0) (e1)) = (op (e0) (e2)))) -> (~((op (e1) (e1)) = (op (e1) (e2)))) -> (((op (e0) (e3)) = (e0))\/(((op (e1) (e3)) = (e0))\/(((op (e2) (e3)) = (e0))\/((op (e3) (e3)) = (e0))))) -> (~((op (e1) (e1)) = (op (e1) (e3)))) -> (~((op (e0) (e1)) = (op (e0) (e3)))) -> (((op (e0) (e2)) = (e0))\/(((op (e1) (e2)) = (e0))\/(((op (e2) (e2)) = (e0))\/((op (e3) (e2)) = (e0))))) -> (~((op (e1) (e0)) = (op (e1) (e1)))) -> ((~((op (e1) (e3)) = (e0)))\/((op (e1) (e0)) = (e3))) -> (((op (e1) (e0)) = (e0))\/(((op (e1) (e1)) = (e0))\/(((op (e1) (e2)) = (e0))\/((op (e1) (e3)) = (e0))))) -> (((op (e1) (e1)) = (e0))\/(((op (e1) (e1)) = (e1))\/(((op (e1) (e1)) = (e2))\/((op (e1) (e1)) = (e3))))) -> (~((op (e1) (e1)) = (op (e2) (e1)))) -> (~((op (e0) (e0)) = (op (e0) (e2)))) -> (~((op (e2) (e0)) = (op (e2) (e2)))) -> (((op (e0) (e2)) = (e1))\/(((op (e1) (e2)) = (e1))\/(((op (e2) (e2)) = (e1))\/((op (e3) (e2)) = (e1))))) -> (((op (e1) (e0)) = (e1))\/(((op (e1) (e1)) = (e1))\/(((op (e1) (e2)) = (e1))\/((op (e1) (e3)) = (e1))))) -> (((op (e0) (e3)) = (e3))\/(((op (e1) (e3)) = (e3))\/(((op (e2) (e3)) = (e3))\/((op (e3) (e3)) = (e3))))) -> (~((op (e2) (e2)) = (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))))) -> (~((e2) = (e3))) -> (~((op (e1) (e2)) = (op (e1) (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 (e2) (e2)) = (e2))) -> (((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) (e1)) = (op (e3) (e1)))) -> (((op (e3) (e0)) = (e3))\/(((op (e3) (e1)) = (e3))\/(((op (e3) (e2)) = (e3))\/((op (e3) (e3)) = (e3))))) -> (~((op (e3) (e2)) = (op (e3) (e3)))) -> (~((e0) = (e2))) -> (~((op (e0) (e2)) = (op (e3) (e2)))) -> (((op (e3) (e0)) = (e2))\/(((op (e3) (e1)) = (e2))\/(((op (e3) (e2)) = (e2))\/((op (e3) (e3)) = (e2))))) -> ((~((op (e2) (e3)) = (e0)))\/((op (e2) (e0)) = (e3))) -> (~((op (e0) (e0)) = (op (e2) (e0)))) -> ((~((op (e2) (e1)) = (e0)))\/((op (e2) (e0)) = (e1))) -> (~((op (e1) (e2)) = (e0))) -> (~((op (e1) (e1)) = (e0))) -> ((op (e0) (e0)) = (e1)) -> (~((e1) = (e2))) -> False). % 18.52/18.70 do 0 intro. intros zenon_H1a5 zenon_H1a6 zenon_H1a4 zenon_H3e zenon_H30 zenon_H23 zenon_H3f zenon_H1a7 zenon_H18f zenon_H191 zenon_H195 zenon_H19d zenon_H95 zenon_H9a zenon_H9e zenon_H10a zenon_H18c zenon_H115 zenon_H5b zenon_H11f zenon_H1d zenon_H10e zenon_Ha1 zenon_H2f zenon_Ha8 zenon_He8 zenon_H76 zenon_Hc2 zenon_Hdf zenon_Hdb zenon_Hd8 zenon_Hd5 zenon_He2 zenon_He4 zenon_Haf zenon_He7 zenon_H31 zenon_H106 zenon_H71 zenon_Hf3 zenon_H102 zenon_H101 zenon_H2b zenon_Hee zenon_H109 zenon_H189 zenon_H185 zenon_H184 zenon_H183 zenon_H17b zenon_H17e zenon_H178 zenon_H74 zenon_H75 zenon_H6f zenon_H4a zenon_H4f zenon_H67 zenon_H57 zenon_H54 zenon_H6a zenon_H45 zenon_H179 zenon_H22 zenon_H142 zenon_H13e zenon_H13c zenon_H52 zenon_H139 zenon_H128 zenon_H136 zenon_H6d zenon_H130 zenon_H133 zenon_H12b zenon_H124 zenon_H145 zenon_H172 zenon_H173 zenon_H16f zenon_H168 zenon_H160 zenon_H165 zenon_H62 zenon_H149 zenon_H14f zenon_H153 zenon_H94 zenon_H39 zenon_H182 zenon_H25 zenon_H24 zenon_H7a zenon_H7c. % 18.52/18.70 apply (zenon_or_s _ _ zenon_H94); [ zenon_intro zenon_H32 | zenon_intro zenon_H3b ]. % 18.52/18.70 apply (zenon_or_s _ _ zenon_H184); [ zenon_intro zenon_H40 | zenon_intro zenon_H44 ]. % 18.52/18.70 apply (zenon_L7_); trivial. % 18.52/18.70 apply (zenon_or_s _ _ zenon_H1a7); [ zenon_intro zenon_H18b | zenon_intro zenon_H148 ]. % 18.52/18.70 apply (zenon_or_s _ _ zenon_H74); [ zenon_intro zenon_H42 | zenon_intro zenon_H77 ]. % 18.52/18.70 exact (zenon_H3f zenon_H42). % 18.52/18.70 apply (zenon_or_s _ _ zenon_H77); [ zenon_intro zenon_H49 | zenon_intro zenon_H78 ]. % 18.52/18.70 apply (zenon_or_s _ _ zenon_H183); [ zenon_intro zenon_H7b | zenon_intro zenon_H186 ]. % 18.52/18.70 apply (zenon_L26_); trivial. % 18.52/18.70 apply (zenon_or_s _ _ zenon_H186); [ zenon_intro zenon_H10f | zenon_intro zenon_H187 ]. % 18.52/18.70 apply (zenon_or_s _ _ zenon_H168); [ zenon_intro zenon_H3a | zenon_intro zenon_H169 ]. % 18.52/18.70 apply (zenon_L35_); trivial. % 18.52/18.70 apply (zenon_or_s _ _ zenon_H169); [ zenon_intro zenon_H99 | zenon_intro zenon_H16a ]. % 18.52/18.70 apply (zenon_L36_); trivial. % 18.52/18.70 apply (zenon_or_s _ _ zenon_H16a); [ zenon_intro zenon_Ha9 | zenon_intro zenon_He3 ]. % 18.52/18.70 apply (zenon_or_s _ _ zenon_H22); [ zenon_intro zenon_H27 | zenon_intro zenon_H26 ]. % 18.52/18.70 exact (zenon_H23 zenon_H27). % 18.52/18.70 apply (zenon_or_s _ _ zenon_H26); [ zenon_intro zenon_H29 | zenon_intro zenon_H28 ]. % 18.52/18.70 exact (zenon_H24 zenon_H29). % 18.52/18.70 apply (zenon_or_s _ _ zenon_H28); [ zenon_intro zenon_H2a | zenon_intro zenon_H1f ]. % 18.52/18.70 exact (zenon_H25 zenon_H2a). % 18.52/18.70 apply (zenon_or_s _ _ zenon_H128); [ zenon_intro zenon_H9d | zenon_intro zenon_H129 ]. % 18.52/18.70 apply (zenon_L37_); trivial. % 18.52/18.70 apply (zenon_or_s _ _ zenon_H129); [ zenon_intro zenon_H10d | zenon_intro zenon_H12a ]. % 18.52/18.70 exact (zenon_H10a zenon_H10d). % 18.52/18.70 apply (zenon_or_s _ _ zenon_H12a); [ zenon_intro zenon_Hf0 | zenon_intro zenon_Hd6 ]. % 18.52/18.70 apply (zenon_or_s _ _ zenon_H18c); [ zenon_intro zenon_H86 | zenon_intro zenon_H18d ]. % 18.52/18.70 apply (zenon_L66_); trivial. % 18.52/18.70 apply (zenon_or_s _ _ zenon_H18d); [ zenon_intro zenon_H110 | zenon_intro zenon_H18e ]. % 18.52/18.70 apply (zenon_L67_); trivial. % 18.52/18.70 apply (zenon_or_s _ _ zenon_H18e); [ zenon_intro zenon_H113 | zenon_intro zenon_Hd7 ]. % 18.52/18.70 apply (zenon_L68_); trivial. % 18.52/18.70 apply (zenon_L76_); trivial. % 18.52/18.70 apply (zenon_L145_); trivial. % 18.52/18.70 apply (zenon_L122_); trivial. % 18.52/18.70 apply (zenon_or_s _ _ zenon_H187); [ zenon_intro zenon_H150 | zenon_intro zenon_Hcd ]. % 18.52/18.70 apply (zenon_or_s _ _ zenon_H168); [ zenon_intro zenon_H3a | zenon_intro zenon_H169 ]. % 18.52/18.70 apply (zenon_L35_); trivial. % 18.52/18.70 apply (zenon_or_s _ _ zenon_H169); [ zenon_intro zenon_H99 | zenon_intro zenon_H16a ]. % 18.52/18.70 apply (zenon_L36_); trivial. % 18.52/18.70 apply (zenon_or_s _ _ zenon_H16a); [ zenon_intro zenon_Ha9 | zenon_intro zenon_He3 ]. % 18.52/18.70 apply (zenon_or_s _ _ zenon_H22); [ zenon_intro zenon_H27 | zenon_intro zenon_H26 ]. % 18.52/18.70 exact (zenon_H23 zenon_H27). % 18.52/18.70 apply (zenon_or_s _ _ zenon_H26); [ zenon_intro zenon_H29 | zenon_intro zenon_H28 ]. % 18.52/18.70 exact (zenon_H24 zenon_H29). % 18.52/18.70 apply (zenon_or_s _ _ zenon_H28); [ zenon_intro zenon_H2a | zenon_intro zenon_H1f ]. % 18.52/18.70 exact (zenon_H25 zenon_H2a). % 18.52/18.70 apply (zenon_or_s _ _ zenon_H128); [ zenon_intro zenon_H9d | zenon_intro zenon_H129 ]. % 18.52/18.70 apply (zenon_L124_); trivial. % 18.52/18.70 apply (zenon_or_s _ _ zenon_H129); [ zenon_intro zenon_H10d | zenon_intro zenon_H12a ]. % 18.52/18.70 exact (zenon_H10a zenon_H10d). % 18.52/18.70 apply (zenon_or_s _ _ zenon_H12a); [ zenon_intro zenon_Hf0 | zenon_intro zenon_Hd6 ]. % 18.52/18.70 apply (zenon_L151_); trivial. % 18.52/18.70 apply (zenon_or_s _ _ zenon_H109); [ zenon_intro zenon_Ha0 | zenon_intro zenon_H10b ]. % 18.52/18.70 apply (zenon_L38_); trivial. % 18.52/18.70 apply (zenon_or_s _ _ zenon_H10b); [ zenon_intro zenon_H10d | zenon_intro zenon_H10c ]. % 18.52/18.70 exact (zenon_H10a zenon_H10d). % 18.52/18.70 apply (zenon_or_s _ _ zenon_H10c); [ zenon_intro zenon_Ha5 | zenon_intro zenon_Hae ]. % 18.52/18.70 apply (zenon_L150_); trivial. % 18.52/18.70 apply (zenon_or_s _ _ zenon_H2f); [ zenon_intro zenon_H34 | zenon_intro zenon_H33 ]. % 18.52/18.70 exact (zenon_H30 zenon_H34). % 18.52/18.70 apply (zenon_or_s _ _ zenon_H33); [ zenon_intro zenon_H36 | zenon_intro zenon_H35 ]. % 18.52/18.70 exact (zenon_H31 zenon_H36). % 18.52/18.70 apply (zenon_or_s _ _ zenon_H35); [ zenon_intro zenon_H2c | zenon_intro zenon_H37 ]. % 18.52/18.70 apply (zenon_or_s _ _ zenon_H106); [ zenon_intro zenon_Hed | zenon_intro zenon_H107 ]. % 18.52/18.70 apply (zenon_L94_); trivial. % 18.52/18.70 apply (zenon_or_s _ _ zenon_H107); [ zenon_intro zenon_Ha5 | zenon_intro zenon_H108 ]. % 18.52/18.70 apply (zenon_L149_); trivial. % 18.52/18.70 apply (zenon_or_s _ _ zenon_H108); [ zenon_intro zenon_Hf1 | zenon_intro zenon_Hf4 ]. % 18.52/18.70 apply (zenon_or_s _ _ zenon_H153); [ zenon_intro zenon_H148 | zenon_intro zenon_H154 ]. % 18.52/18.70 apply (zenon_L107_); trivial. % 18.52/18.70 apply (zenon_or_s _ _ zenon_H154); [ zenon_intro zenon_H14d | zenon_intro zenon_H155 ]. % 18.52/18.70 apply (zenon_L152_); trivial. % 18.52/18.70 apply (zenon_or_s _ _ zenon_H155); [ zenon_intro zenon_H151 | zenon_intro zenon_Hf6 ]. % 18.52/18.70 apply (zenon_L104_); trivial. % 18.52/18.70 apply (zenon_L160_); trivial. % 18.52/18.70 apply (zenon_L64_); trivial. % 18.52/18.70 exact (zenon_H32 zenon_H37). % 18.52/18.70 apply (zenon_L122_); trivial. % 18.52/18.70 apply (zenon_L161_); trivial. % 18.52/18.70 apply (zenon_or_s _ _ zenon_H78); [ zenon_intro zenon_H48 | zenon_intro zenon_H1e ]. % 18.52/18.70 exact (zenon_H75 zenon_H48). % 18.52/18.70 exact (zenon_H76 zenon_H1e). % 18.52/18.70 apply (zenon_L107_); trivial. % 18.52/18.70 apply (zenon_or_s _ _ zenon_H184); [ zenon_intro zenon_H40 | zenon_intro zenon_H44 ]. % 18.52/18.70 apply (zenon_L7_); trivial. % 18.52/18.70 apply (zenon_or_s _ _ zenon_H1a7); [ zenon_intro zenon_H18b | zenon_intro zenon_H148 ]. % 18.52/18.70 apply (zenon_or_s _ _ zenon_H74); [ zenon_intro zenon_H42 | zenon_intro zenon_H77 ]. % 18.52/18.70 exact (zenon_H3f zenon_H42). % 18.52/18.70 apply (zenon_or_s _ _ zenon_H77); [ zenon_intro zenon_H49 | zenon_intro zenon_H78 ]. % 18.52/18.70 apply (zenon_or_s _ _ zenon_H183); [ zenon_intro zenon_H7b | zenon_intro zenon_H186 ]. % 18.52/18.70 apply (zenon_L26_); trivial. % 18.52/18.70 apply (zenon_or_s _ _ zenon_H186); [ zenon_intro zenon_H10f | zenon_intro zenon_H187 ]. % 18.52/18.70 apply (zenon_or_s _ _ zenon_H22); [ zenon_intro zenon_H27 | zenon_intro zenon_H26 ]. % 18.52/18.70 exact (zenon_H23 zenon_H27). % 18.52/18.70 apply (zenon_or_s _ _ zenon_H26); [ zenon_intro zenon_H29 | zenon_intro zenon_H28 ]. % 18.52/18.70 exact (zenon_H24 zenon_H29). % 18.52/18.70 apply (zenon_or_s _ _ zenon_H28); [ zenon_intro zenon_H2a | zenon_intro zenon_H1f ]. % 18.52/18.70 exact (zenon_H25 zenon_H2a). % 18.52/18.70 apply (zenon_or_s _ _ zenon_H128); [ zenon_intro zenon_H9d | zenon_intro zenon_H129 ]. % 18.52/18.70 apply (zenon_L37_); trivial. % 18.52/18.70 apply (zenon_or_s _ _ zenon_H129); [ zenon_intro zenon_H10d | zenon_intro zenon_H12a ]. % 18.52/18.70 exact (zenon_H10a zenon_H10d). % 18.52/18.70 apply (zenon_or_s _ _ zenon_H12a); [ zenon_intro zenon_Hf0 | zenon_intro zenon_Hd6 ]. % 18.52/18.70 apply (zenon_or_s _ _ zenon_H18c); [ zenon_intro zenon_H86 | zenon_intro zenon_H18d ]. % 18.52/18.70 apply (zenon_L33_); trivial. % 18.52/18.70 apply (zenon_or_s _ _ zenon_H18d); [ zenon_intro zenon_H110 | zenon_intro zenon_H18e ]. % 18.52/18.70 apply (zenon_L67_); trivial. % 18.52/18.70 apply (zenon_or_s _ _ zenon_H18e); [ zenon_intro zenon_H113 | zenon_intro zenon_Hd7 ]. % 18.52/18.70 apply (zenon_L68_); trivial. % 18.52/18.70 apply (zenon_L76_); trivial. % 18.52/18.70 apply (zenon_L145_); trivial. % 18.52/18.70 apply (zenon_or_s _ _ zenon_H187); [ zenon_intro zenon_H150 | zenon_intro zenon_Hcd ]. % 18.52/18.70 apply (zenon_or_s _ _ zenon_H168); [ zenon_intro zenon_H3a | zenon_intro zenon_H169 ]. % 18.52/18.70 apply (zenon_L35_); trivial. % 18.52/18.70 apply (zenon_or_s _ _ zenon_H169); [ zenon_intro zenon_H99 | zenon_intro zenon_H16a ]. % 18.52/18.70 apply (zenon_L36_); trivial. % 18.52/18.70 apply (zenon_or_s _ _ zenon_H16a); [ zenon_intro zenon_Ha9 | zenon_intro zenon_He3 ]. % 18.52/18.70 apply (zenon_or_s _ _ zenon_H22); [ zenon_intro zenon_H27 | zenon_intro zenon_H26 ]. % 18.52/18.70 exact (zenon_H23 zenon_H27). % 18.52/18.70 apply (zenon_or_s _ _ zenon_H26); [ zenon_intro zenon_H29 | zenon_intro zenon_H28 ]. % 18.52/18.70 exact (zenon_H24 zenon_H29). % 18.52/18.70 apply (zenon_or_s _ _ zenon_H28); [ zenon_intro zenon_H2a | zenon_intro zenon_H1f ]. % 18.52/18.70 exact (zenon_H25 zenon_H2a). % 18.52/18.70 apply (zenon_or_s _ _ zenon_H128); [ zenon_intro zenon_H9d | zenon_intro zenon_H129 ]. % 18.52/18.70 apply (zenon_L37_); trivial. % 18.52/18.70 apply (zenon_or_s _ _ zenon_H129); [ zenon_intro zenon_H10d | zenon_intro zenon_H12a ]. % 18.52/18.70 exact (zenon_H10a zenon_H10d). % 18.52/18.70 apply (zenon_or_s _ _ zenon_H12a); [ zenon_intro zenon_Hf0 | zenon_intro zenon_Hd6 ]. % 18.52/18.70 apply (zenon_L151_); trivial. % 18.52/18.70 apply (zenon_or_s _ _ zenon_H109); [ zenon_intro zenon_Ha0 | zenon_intro zenon_H10b ]. % 18.52/18.70 apply (zenon_L38_); trivial. % 18.52/18.70 apply (zenon_or_s _ _ zenon_H10b); [ zenon_intro zenon_H10d | zenon_intro zenon_H10c ]. % 18.52/18.70 exact (zenon_H10a zenon_H10d). % 18.52/18.70 apply (zenon_or_s _ _ zenon_H10c); [ zenon_intro zenon_Ha5 | zenon_intro zenon_Hae ]. % 18.52/18.70 apply (zenon_L150_); trivial. % 18.52/18.70 apply (zenon_or_s _ _ zenon_H2f); [ zenon_intro zenon_H34 | zenon_intro zenon_H33 ]. % 18.52/18.70 exact (zenon_H30 zenon_H34). % 18.52/18.70 apply (zenon_or_s _ _ zenon_H33); [ zenon_intro zenon_H36 | zenon_intro zenon_H35 ]. % 18.52/18.70 exact (zenon_H31 zenon_H36). % 18.52/18.70 apply (zenon_or_s _ _ zenon_H35); [ zenon_intro zenon_H2c | zenon_intro zenon_H37 ]. % 18.52/18.70 apply (zenon_or_s _ _ zenon_H106); [ zenon_intro zenon_Hed | zenon_intro zenon_H107 ]. % 18.52/18.70 apply (zenon_L94_); trivial. % 18.52/18.70 apply (zenon_or_s _ _ zenon_H107); [ zenon_intro zenon_Ha5 | zenon_intro zenon_H108 ]. % 18.52/18.70 apply (zenon_L149_); trivial. % 18.52/18.70 apply (zenon_or_s _ _ zenon_H108); [ zenon_intro zenon_Hf1 | zenon_intro zenon_Hf4 ]. % 18.52/18.70 apply (zenon_or_s _ _ zenon_H153); [ zenon_intro zenon_H148 | zenon_intro zenon_H154 ]. % 18.52/18.70 apply (zenon_L163_); trivial. % 18.52/18.70 apply (zenon_or_s _ _ zenon_H154); [ zenon_intro zenon_H14d | zenon_intro zenon_H155 ]. % 18.52/18.70 apply (zenon_L165_); trivial. % 18.52/18.70 apply (zenon_or_s _ _ zenon_H155); [ zenon_intro zenon_H151 | zenon_intro zenon_Hf6 ]. % 18.52/18.70 apply (zenon_L104_); trivial. % 18.52/18.70 apply (zenon_L160_); trivial. % 18.52/18.70 apply (zenon_L126_); trivial. % 18.52/18.70 apply (zenon_L130_); trivial. % 18.52/18.70 apply (zenon_or_s _ _ zenon_H22); [ zenon_intro zenon_H27 | zenon_intro zenon_H26 ]. % 18.52/18.70 exact (zenon_H23 zenon_H27). % 18.52/18.70 apply (zenon_or_s _ _ zenon_H26); [ zenon_intro zenon_H29 | zenon_intro zenon_H28 ]. % 18.52/18.70 exact (zenon_H24 zenon_H29). % 18.52/18.70 apply (zenon_or_s _ _ zenon_H28); [ zenon_intro zenon_H2a | zenon_intro zenon_H1f ]. % 18.52/18.70 exact (zenon_H25 zenon_H2a). % 18.52/18.70 apply (zenon_or_s _ _ zenon_H128); [ zenon_intro zenon_H9d | zenon_intro zenon_H129 ]. % 18.52/18.70 apply (zenon_L124_); trivial. % 18.52/18.70 apply (zenon_or_s _ _ zenon_H129); [ zenon_intro zenon_H10d | zenon_intro zenon_H12a ]. % 18.52/18.70 exact (zenon_H10a zenon_H10d). % 18.52/18.70 apply (zenon_or_s _ _ zenon_H12a); [ zenon_intro zenon_Hf0 | zenon_intro zenon_Hd6 ]. % 18.52/18.70 apply (zenon_or_s _ _ zenon_H109); [ zenon_intro zenon_Ha0 | zenon_intro zenon_H10b ]. % 18.52/18.70 apply (zenon_L38_); trivial. % 18.52/18.70 apply (zenon_or_s _ _ zenon_H10b); [ zenon_intro zenon_H10d | zenon_intro zenon_H10c ]. % 18.52/18.70 exact (zenon_H10a zenon_H10d). % 18.52/18.70 apply (zenon_or_s _ _ zenon_H10c); [ zenon_intro zenon_Ha5 | zenon_intro zenon_Hae ]. % 18.52/18.70 apply (zenon_or_s _ _ zenon_H18c); [ zenon_intro zenon_H86 | zenon_intro zenon_H18d ]. % 18.52/18.70 apply (zenon_L33_); trivial. % 18.52/18.70 apply (zenon_or_s _ _ zenon_H18d); [ zenon_intro zenon_H110 | zenon_intro zenon_H18e ]. % 18.52/18.70 apply (zenon_or_s _ _ zenon_H1a5); [ zenon_intro zenon_H99 | zenon_intro zenon_H1a8 ]. % 18.52/18.70 apply (zenon_L36_); trivial. % 18.52/18.70 apply (zenon_or_s _ _ zenon_H1a8); [ zenon_intro zenon_H13f | zenon_intro zenon_H1a9 ]. % 18.52/18.70 apply (zenon_L166_); trivial. % 18.52/18.70 apply (zenon_or_s _ _ zenon_H1a9); [ zenon_intro zenon_Ha6 | zenon_intro zenon_H161 ]. % 18.52/18.70 apply (zenon_L39_); trivial. % 18.52/18.70 apply (zenon_or_s _ _ zenon_H2f); [ zenon_intro zenon_H34 | zenon_intro zenon_H33 ]. % 18.52/18.70 exact (zenon_H30 zenon_H34). % 18.52/18.70 apply (zenon_or_s _ _ zenon_H33); [ zenon_intro zenon_H36 | zenon_intro zenon_H35 ]. % 18.52/18.70 exact (zenon_H31 zenon_H36). % 18.52/18.70 apply (zenon_or_s _ _ zenon_H35); [ zenon_intro zenon_H2c | zenon_intro zenon_H37 ]. % 18.52/18.70 apply (zenon_or_s _ _ zenon_H1a6); [ zenon_intro zenon_Ha9 | zenon_intro zenon_H1aa ]. % 18.52/18.70 apply (zenon_L149_); trivial. % 18.52/18.70 apply (zenon_or_s _ _ zenon_H1aa); [ zenon_intro zenon_H16c | zenon_intro zenon_H1ab ]. % 18.52/18.70 apply (zenon_L167_); trivial. % 18.52/18.70 apply (zenon_or_s _ _ zenon_H1ab); [ zenon_intro zenon_Haa | zenon_intro zenon_H163 ]. % 18.52/18.70 apply (zenon_L168_); trivial. % 18.52/18.70 apply (zenon_L169_); trivial. % 18.52/18.70 apply (zenon_L143_); trivial. % 18.52/18.70 apply (zenon_or_s _ _ zenon_H18e); [ zenon_intro zenon_H113 | zenon_intro zenon_Hd7 ]. % 18.52/18.70 apply (zenon_L68_); trivial. % 18.52/18.70 apply (zenon_L170_); trivial. % 18.52/18.70 apply (zenon_L65_); trivial. % 18.52/18.70 apply (zenon_or_s _ _ zenon_H2f); [ zenon_intro zenon_H34 | zenon_intro zenon_H33 ]. % 18.52/18.70 exact (zenon_H30 zenon_H34). % 18.52/18.70 apply (zenon_or_s _ _ zenon_H33); [ zenon_intro zenon_H36 | zenon_intro zenon_H35 ]. % 18.52/18.70 exact (zenon_H31 zenon_H36). % 18.52/18.70 apply (zenon_or_s _ _ zenon_H35); [ zenon_intro zenon_H2c | zenon_intro zenon_H37 ]. % 18.52/18.70 apply (zenon_or_s _ _ zenon_H153); [ zenon_intro zenon_H148 | zenon_intro zenon_H154 ]. % 18.52/18.70 apply (zenon_L100_); trivial. % 18.52/18.70 apply (zenon_or_s _ _ zenon_H154); [ zenon_intro zenon_H14d | zenon_intro zenon_H155 ]. % 18.52/18.70 apply (zenon_L165_); trivial. % 18.52/18.70 apply (zenon_or_s _ _ zenon_H155); [ zenon_intro zenon_H151 | zenon_intro zenon_Hf6 ]. % 18.52/18.70 apply (zenon_L120_); trivial. % 18.52/18.70 apply (zenon_L138_); trivial. % 18.52/18.70 apply (zenon_L143_); trivial. % 18.52/18.70 apply (zenon_L161_); trivial. % 18.52/18.70 apply (zenon_or_s _ _ zenon_H78); [ zenon_intro zenon_H48 | zenon_intro zenon_H1e ]. % 18.52/18.70 exact (zenon_H75 zenon_H48). % 18.52/18.70 exact (zenon_H76 zenon_H1e). % 18.52/18.70 apply (zenon_L100_); trivial. % 18.52/18.70 (* end of lemma zenon_L171_ *) % 18.52/18.70 assert (zenon_L172_ : ((~((op (e2) (e3)) = (e0)))\/((op (e2) (e0)) = (e3))) -> ((op (e1) (e0)) = (e2)) -> ((op (e0) (e0)) = (e1)) -> (~((op (e1) (e0)) = (e0))) -> (~((op (e1) (e1)) = (e0))) -> (((op (e2) (e0)) = (e0))\/(((op (e2) (e1)) = (e0))\/(((op (e2) (e2)) = (e0))\/((op (e2) (e3)) = (e0))))) -> (~((op (e1) (e2)) = (op (e2) (e2)))) -> (~((op (e2) (e1)) = (e0))) -> (~((op (e2) (e0)) = (e0))) -> (~((op (e1) (e3)) = (e0))) -> (((op (e1) (e0)) = (e0))\/(((op (e1) (e1)) = (e0))\/(((op (e1) (e2)) = (e0))\/((op (e1) (e3)) = (e0))))) -> False). % 18.52/18.70 do 0 intro. intros zenon_H94 zenon_H86 zenon_H7a zenon_H23 zenon_H24 zenon_H2f zenon_H2b zenon_H31 zenon_H30 zenon_H38 zenon_H22. % 18.52/18.70 apply (zenon_or_s _ _ zenon_H94); [ zenon_intro zenon_H32 | zenon_intro zenon_H3b ]. % 18.52/18.70 apply (zenon_L5_); trivial. % 18.52/18.70 apply (zenon_L33_); trivial. % 18.52/18.70 (* end of lemma zenon_L172_ *) % 18.52/18.70 assert (zenon_L173_ : ((~((op (e2) (e1)) = (e0)))\/((op (e2) (e0)) = (e1))) -> (~((op (e0) (e0)) = (op (e2) (e0)))) -> (((op (e1) (e0)) = (e0))\/(((op (e1) (e1)) = (e0))\/(((op (e1) (e2)) = (e0))\/((op (e1) (e3)) = (e0))))) -> (~((op (e1) (e3)) = (e0))) -> (~((op (e2) (e0)) = (e0))) -> (~((op (e1) (e2)) = (op (e2) (e2)))) -> (((op (e2) (e0)) = (e0))\/(((op (e2) (e1)) = (e0))\/(((op (e2) (e2)) = (e0))\/((op (e2) (e3)) = (e0))))) -> (~((op (e1) (e1)) = (e0))) -> (~((op (e1) (e0)) = (e0))) -> ((op (e0) (e0)) = (e1)) -> ((op (e1) (e0)) = (e2)) -> ((~((op (e2) (e3)) = (e0)))\/((op (e2) (e0)) = (e3))) -> False). % 18.52/18.70 do 0 intro. intros zenon_H182 zenon_H39 zenon_H22 zenon_H38 zenon_H30 zenon_H2b zenon_H2f zenon_H24 zenon_H23 zenon_H7a zenon_H86 zenon_H94. % 18.52/18.70 apply (zenon_or_s _ _ zenon_H182); [ zenon_intro zenon_H31 | zenon_intro zenon_Hed ]. % 18.52/18.70 apply (zenon_L172_); trivial. % 18.52/18.70 apply (zenon_L134_); trivial. % 18.52/18.70 (* end of lemma zenon_L173_ *) % 18.52/18.70 assert (zenon_L174_ : (((op (e3) (e0)) = (e0))\/(((op (e3) (e1)) = (e0))\/(((op (e3) (e2)) = (e0))\/((op (e3) (e3)) = (e0))))) -> (~((op (e3) (e0)) = (e0))) -> (~((op (e3) (e1)) = (e0))) -> (~((op (e3) (e2)) = (e0))) -> (~((op (e3) (e3)) = (e0))) -> False). % 18.52/18.70 do 0 intro. intros zenon_H1ac zenon_H40 zenon_H1ad zenon_H18b zenon_H1ae. % 18.52/18.70 apply (zenon_or_s _ _ zenon_H1ac); [ zenon_intro zenon_H44 | zenon_intro zenon_H1af ]. % 18.52/18.70 exact (zenon_H40 zenon_H44). % 18.52/18.70 apply (zenon_or_s _ _ zenon_H1af); [ zenon_intro zenon_H1b1 | zenon_intro zenon_H1b0 ]. % 18.52/18.70 exact (zenon_H1ad zenon_H1b1). % 18.52/18.70 apply (zenon_or_s _ _ zenon_H1b0); [ zenon_intro zenon_H61 | zenon_intro zenon_H60 ]. % 18.52/18.70 exact (zenon_H18b zenon_H61). % 18.52/18.70 exact (zenon_H1ae zenon_H60). % 18.52/18.70 (* end of lemma zenon_L174_ *) % 18.52/18.70 assert (zenon_L175_ : ((op (e0) (e1)) = (e2)) -> ((op (e0) (e1)) = (e3)) -> (~((e2) = (e3))) -> False). % 18.52/18.70 do 0 intro. intros zenon_H10f zenon_H99 zenon_H12b. % 18.52/18.70 elim (classic ((e3) = (e3))); [ zenon_intro zenon_H96 | zenon_intro zenon_H85 ]. % 18.52/18.70 cut (((e3) = (e3)) = ((e2) = (e3))). % 18.52/18.70 intro zenon_D_pnotp. % 18.52/18.70 apply zenon_H12b. % 18.52/18.70 rewrite <- zenon_D_pnotp. % 18.52/18.70 exact zenon_H96. % 18.52/18.70 cut (((e3) = (e3))); [idtac | apply NNPP; zenon_intro zenon_H85]. % 18.52/18.70 cut (((e3) = (e2))); [idtac | apply NNPP; zenon_intro zenon_H12c]. % 18.52/18.70 congruence. % 18.52/18.70 cut (((op (e0) (e1)) = (e2)) = ((e3) = (e2))). % 18.52/18.70 intro zenon_D_pnotp. % 18.52/18.70 apply zenon_H12c. % 18.52/18.70 rewrite <- zenon_D_pnotp. % 18.52/18.70 exact zenon_H10f. % 18.52/18.70 cut (((e2) = (e2))); [idtac | apply NNPP; zenon_intro zenon_H7e]. % 18.52/18.70 cut (((op (e0) (e1)) = (e3))); [idtac | apply NNPP; zenon_intro zenon_H9c]. % 18.52/18.70 congruence. % 18.52/18.70 exact (zenon_H9c zenon_H99). % 18.52/18.70 apply zenon_H7e. apply refl_equal. % 18.52/18.70 apply zenon_H85. apply refl_equal. % 18.52/18.70 apply zenon_H85. apply refl_equal. % 18.52/18.70 (* end of lemma zenon_L175_ *) % 18.52/18.70 assert (zenon_L176_ : (~((op (e1) (e2)) = (op (e3) (e2)))) -> ((op (e1) (e2)) = (e0)) -> ((op (e3) (e2)) = (e0)) -> False). % 18.52/18.70 do 0 intro. intros zenon_H115 zenon_H2a zenon_H61. % 18.52/18.70 cut (((op (e1) (e2)) = (e0)) = ((op (e1) (e2)) = (op (e3) (e2)))). % 18.52/18.70 intro zenon_D_pnotp. % 18.52/18.70 apply zenon_H115. % 18.52/18.70 rewrite <- zenon_D_pnotp. % 18.52/18.70 exact zenon_H2a. % 18.52/18.70 cut (((e0) = (op (e3) (e2)))); [idtac | apply NNPP; zenon_intro zenon_H66]. % 18.52/18.70 cut (((op (e1) (e2)) = (op (e1) (e2)))); [idtac | apply NNPP; zenon_intro zenon_H2e]. % 18.52/18.70 congruence. % 18.52/18.70 apply zenon_H2e. apply refl_equal. % 18.52/18.70 apply zenon_H66. apply sym_equal. exact zenon_H61. % 18.52/18.70 (* end of lemma zenon_L176_ *) % 18.52/18.70 assert (zenon_L177_ : (~((op (op (e2) (e2)) (e2)) = (op (e3) (e2)))) -> ((op (e2) (e2)) = (e3)) -> False). % 18.52/18.70 do 0 intro. intros zenon_H1b2 zenon_Haa. % 18.52/18.70 cut (((e2) = (e2))); [idtac | apply NNPP; zenon_intro zenon_H7e]. % 18.52/18.70 cut (((op (e2) (e2)) = (e3))); [idtac | apply NNPP; zenon_intro zenon_H1b3]. % 18.52/18.70 congruence. % 18.52/18.70 exact (zenon_H1b3 zenon_Haa). % 18.52/18.70 apply zenon_H7e. apply refl_equal. % 18.52/18.70 (* end of lemma zenon_L177_ *) % 18.52/18.70 assert (zenon_L178_ : ((op (e3) (e2)) = (e1)) -> ((op (e2) (e2)) = (e3)) -> (~((e1) = (op (op (e2) (e2)) (e2)))) -> False). % 18.52/18.70 do 0 intro. intros zenon_Hba zenon_Haa zenon_H1b4. % 18.52/18.70 elim (classic ((op (op (e2) (e2)) (e2)) = (op (op (e2) (e2)) (e2)))); [ zenon_intro zenon_Hb6 | zenon_intro zenon_Hb7 ]. % 18.52/18.70 cut (((op (op (e2) (e2)) (e2)) = (op (op (e2) (e2)) (e2))) = ((e1) = (op (op (e2) (e2)) (e2)))). % 18.52/18.70 intro zenon_D_pnotp. % 18.52/18.70 apply zenon_H1b4. % 18.52/18.70 rewrite <- zenon_D_pnotp. % 18.52/18.70 exact zenon_Hb6. % 18.52/18.70 cut (((op (op (e2) (e2)) (e2)) = (op (op (e2) (e2)) (e2)))); [idtac | apply NNPP; zenon_intro zenon_Hb7]. % 18.52/18.70 cut (((op (op (e2) (e2)) (e2)) = (e1))); [idtac | apply NNPP; zenon_intro zenon_H1b5]. % 18.52/18.70 congruence. % 18.52/18.70 cut (((op (e3) (e2)) = (e1)) = ((op (op (e2) (e2)) (e2)) = (e1))). % 18.52/18.70 intro zenon_D_pnotp. % 18.52/18.70 apply zenon_H1b5. % 18.52/18.70 rewrite <- zenon_D_pnotp. % 18.52/18.70 exact zenon_Hba. % 18.52/18.70 cut (((e1) = (e1))); [idtac | apply NNPP; zenon_intro zenon_H79]. % 18.52/18.70 cut (((op (e3) (e2)) = (op (op (e2) (e2)) (e2)))); [idtac | apply NNPP; zenon_intro zenon_H1b6]. % 18.52/18.70 congruence. % 18.52/18.70 elim (classic ((op (op (e2) (e2)) (e2)) = (op (op (e2) (e2)) (e2)))); [ zenon_intro zenon_Hb6 | zenon_intro zenon_Hb7 ]. % 18.52/18.70 cut (((op (op (e2) (e2)) (e2)) = (op (op (e2) (e2)) (e2))) = ((op (e3) (e2)) = (op (op (e2) (e2)) (e2)))). % 18.52/18.70 intro zenon_D_pnotp. % 18.52/18.70 apply zenon_H1b6. % 18.52/18.70 rewrite <- zenon_D_pnotp. % 18.52/18.70 exact zenon_Hb6. % 18.52/18.70 cut (((op (op (e2) (e2)) (e2)) = (op (op (e2) (e2)) (e2)))); [idtac | apply NNPP; zenon_intro zenon_Hb7]. % 18.52/18.70 cut (((op (op (e2) (e2)) (e2)) = (op (e3) (e2)))); [idtac | apply NNPP; zenon_intro zenon_H1b2]. % 18.52/18.70 congruence. % 18.52/18.70 apply (zenon_L177_); trivial. % 18.52/18.70 apply zenon_Hb7. apply refl_equal. % 18.52/18.70 apply zenon_Hb7. apply refl_equal. % 18.52/18.70 apply zenon_H79. apply refl_equal. % 18.52/18.70 apply zenon_Hb7. apply refl_equal. % 18.52/18.70 apply zenon_Hb7. apply refl_equal. % 18.52/18.70 (* end of lemma zenon_L178_ *) % 18.52/18.70 assert (zenon_L179_ : ((op (e1) (e2)) = (e0)) -> ((op (e3) (e2)) = (e1)) -> ((op (e2) (e2)) = (e3)) -> False). % 18.52/18.70 do 0 intro. intros zenon_H2a zenon_Hba zenon_Haa. % 18.52/18.70 apply (zenon_notand_s _ _ ax18); [ zenon_intro zenon_H19b | zenon_intro zenon_H1b7 ]. % 18.52/18.70 elim (classic ((op (op (op (e2) (e2)) (e2)) (e2)) = (op (op (op (e2) (e2)) (e2)) (e2)))); [ zenon_intro zenon_Hbd | zenon_intro zenon_Hbe ]. % 18.52/18.70 cut (((op (op (op (e2) (e2)) (e2)) (e2)) = (op (op (op (e2) (e2)) (e2)) (e2))) = ((e0) = (op (op (op (e2) (e2)) (e2)) (e2)))). % 18.52/18.70 intro zenon_D_pnotp. % 18.52/18.70 apply zenon_H19b. % 18.52/18.70 rewrite <- zenon_D_pnotp. % 18.52/18.70 exact zenon_Hbd. % 18.52/18.70 cut (((op (op (op (e2) (e2)) (e2)) (e2)) = (op (op (op (e2) (e2)) (e2)) (e2)))); [idtac | apply NNPP; zenon_intro zenon_Hbe]. % 18.52/18.70 cut (((op (op (op (e2) (e2)) (e2)) (e2)) = (e0))); [idtac | apply NNPP; zenon_intro zenon_H19c]. % 18.52/18.70 congruence. % 18.52/18.70 cut (((op (e1) (e2)) = (e0)) = ((op (op (op (e2) (e2)) (e2)) (e2)) = (e0))). % 18.52/18.70 intro zenon_D_pnotp. % 18.52/18.70 apply zenon_H19c. % 18.52/18.70 rewrite <- zenon_D_pnotp. % 18.52/18.70 exact zenon_H2a. % 18.52/18.70 cut (((e0) = (e0))); [idtac | apply NNPP; zenon_intro zenon_H82]. % 18.52/18.70 cut (((op (e1) (e2)) = (op (op (op (e2) (e2)) (e2)) (e2)))); [idtac | apply NNPP; zenon_intro zenon_H1b8]. % 18.52/18.70 congruence. % 18.52/18.70 elim (classic ((op (op (op (e2) (e2)) (e2)) (e2)) = (op (op (op (e2) (e2)) (e2)) (e2)))); [ zenon_intro zenon_Hbd | zenon_intro zenon_Hbe ]. % 18.52/18.70 cut (((op (op (op (e2) (e2)) (e2)) (e2)) = (op (op (op (e2) (e2)) (e2)) (e2))) = ((op (e1) (e2)) = (op (op (op (e2) (e2)) (e2)) (e2)))). % 18.52/18.70 intro zenon_D_pnotp. % 18.52/18.70 apply zenon_H1b8. % 18.52/18.70 rewrite <- zenon_D_pnotp. % 18.52/18.70 exact zenon_Hbd. % 18.52/18.70 cut (((op (op (op (e2) (e2)) (e2)) (e2)) = (op (op (op (e2) (e2)) (e2)) (e2)))); [idtac | apply NNPP; zenon_intro zenon_Hbe]. % 18.52/18.70 cut (((op (op (op (e2) (e2)) (e2)) (e2)) = (op (e1) (e2)))); [idtac | apply NNPP; zenon_intro zenon_H1b9]. % 18.52/18.70 congruence. % 18.52/18.70 cut (((e2) = (e2))); [idtac | apply NNPP; zenon_intro zenon_H7e]. % 18.52/18.70 cut (((op (op (e2) (e2)) (e2)) = (e1))); [idtac | apply NNPP; zenon_intro zenon_H1b5]. % 18.52/18.70 congruence. % 18.52/18.70 cut (((op (e3) (e2)) = (e1)) = ((op (op (e2) (e2)) (e2)) = (e1))). % 18.52/18.70 intro zenon_D_pnotp. % 18.52/18.70 apply zenon_H1b5. % 18.52/18.70 rewrite <- zenon_D_pnotp. % 18.52/18.70 exact zenon_Hba. % 18.52/18.70 cut (((e1) = (e1))); [idtac | apply NNPP; zenon_intro zenon_H79]. % 18.52/18.70 cut (((op (e3) (e2)) = (op (op (e2) (e2)) (e2)))); [idtac | apply NNPP; zenon_intro zenon_H1b6]. % 18.52/18.70 congruence. % 18.52/18.70 elim (classic ((op (op (e2) (e2)) (e2)) = (op (op (e2) (e2)) (e2)))); [ zenon_intro zenon_Hb6 | zenon_intro zenon_Hb7 ]. % 18.52/18.70 cut (((op (op (e2) (e2)) (e2)) = (op (op (e2) (e2)) (e2))) = ((op (e3) (e2)) = (op (op (e2) (e2)) (e2)))). % 18.52/18.70 intro zenon_D_pnotp. % 18.52/18.70 apply zenon_H1b6. % 18.52/18.70 rewrite <- zenon_D_pnotp. % 18.52/18.70 exact zenon_Hb6. % 18.52/18.70 cut (((op (op (e2) (e2)) (e2)) = (op (op (e2) (e2)) (e2)))); [idtac | apply NNPP; zenon_intro zenon_Hb7]. % 18.52/18.70 cut (((op (op (e2) (e2)) (e2)) = (op (e3) (e2)))); [idtac | apply NNPP; zenon_intro zenon_H1b2]. % 18.52/18.70 congruence. % 18.52/18.70 apply (zenon_L177_); trivial. % 18.52/18.70 apply zenon_Hb7. apply refl_equal. % 18.52/18.70 apply zenon_Hb7. apply refl_equal. % 18.52/18.70 apply zenon_H79. apply refl_equal. % 18.52/18.70 apply zenon_H7e. apply refl_equal. % 18.52/18.70 apply zenon_Hbe. apply refl_equal. % 18.52/18.70 apply zenon_Hbe. apply refl_equal. % 18.52/18.70 apply zenon_H82. apply refl_equal. % 18.52/18.70 apply zenon_Hbe. apply refl_equal. % 18.52/18.70 apply zenon_Hbe. apply refl_equal. % 18.52/18.70 apply (zenon_notand_s _ _ zenon_H1b7); [ zenon_intro zenon_H1b4 | zenon_intro zenon_Hab ]. % 18.52/18.70 apply (zenon_L178_); trivial. % 18.52/18.70 apply zenon_Hab. apply sym_equal. exact zenon_Haa. % 18.52/18.70 (* end of lemma zenon_L179_ *) % 18.52/18.70 assert (zenon_L180_ : (~((op (e2) (e2)) = (op (e3) (e2)))) -> ((op (e2) (e2)) = (e3)) -> ((op (e3) (e2)) = (e3)) -> False). % 18.52/18.70 do 0 intro. intros zenon_H18f zenon_Haa zenon_H163. % 18.52/18.70 cut (((op (e2) (e2)) = (e3)) = ((op (e2) (e2)) = (op (e3) (e2)))). % 18.52/18.70 intro zenon_D_pnotp. % 18.52/18.70 apply zenon_H18f. % 18.52/18.70 rewrite <- zenon_D_pnotp. % 18.52/18.70 exact zenon_Haa. % 18.52/18.70 cut (((e3) = (op (e3) (e2)))); [idtac | apply NNPP; zenon_intro zenon_H164]. % 18.52/18.70 cut (((op (e2) (e2)) = (op (e2) (e2)))); [idtac | apply NNPP; zenon_intro zenon_H190]. % 18.52/18.70 congruence. % 18.52/18.70 apply zenon_H190. apply refl_equal. % 18.52/18.70 apply zenon_H164. apply sym_equal. exact zenon_H163. % 18.52/18.70 (* end of lemma zenon_L180_ *) % 18.52/18.70 assert (zenon_L181_ : (((op (e3) (e2)) = (e0))\/(((op (e3) (e2)) = (e1))\/(((op (e3) (e2)) = (e2))\/((op (e3) (e2)) = (e3))))) -> (~((op (e1) (e2)) = (op (e3) (e2)))) -> ((op (e1) (e2)) = (e0)) -> ((op (e0) (e2)) = (e2)) -> (~((op (e0) (e2)) = (op (e3) (e2)))) -> (~((op (e2) (e2)) = (op (e3) (e2)))) -> ((op (e2) (e2)) = (e3)) -> False). % 18.52/18.70 do 0 intro. intros zenon_H191 zenon_H115 zenon_H2a zenon_H150 zenon_H14f zenon_H18f zenon_Haa. % 18.52/18.70 apply (zenon_or_s _ _ zenon_H191); [ zenon_intro zenon_H61 | zenon_intro zenon_H192 ]. % 18.52/18.70 apply (zenon_L176_); trivial. % 18.52/18.70 apply (zenon_or_s _ _ zenon_H192); [ zenon_intro zenon_Hba | zenon_intro zenon_H193 ]. % 18.52/18.70 apply (zenon_L179_); trivial. % 18.52/18.70 apply (zenon_or_s _ _ zenon_H193); [ zenon_intro zenon_H151 | zenon_intro zenon_H163 ]. % 18.52/18.70 apply (zenon_L104_); trivial. % 18.52/18.70 apply (zenon_L180_); trivial. % 18.52/18.70 (* end of lemma zenon_L181_ *) % 18.52/18.70 assert (zenon_L182_ : (((op (e0) (e2)) = (e0))\/(((op (e0) (e2)) = (e1))\/(((op (e0) (e2)) = (e2))\/((op (e0) (e2)) = (e3))))) -> (~((op (e0) (e2)) = (e0))) -> (~((op (e0) (e0)) = (op (e0) (e2)))) -> ((op (e0) (e0)) = (e1)) -> (~((op (e2) (e2)) = (op (e3) (e2)))) -> (~((op (e0) (e2)) = (op (e3) (e2)))) -> ((op (e1) (e2)) = (e0)) -> (~((op (e1) (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 (e2) (e2)) = (e3)) -> False). % 18.52/18.70 do 0 intro. intros zenon_H1ba zenon_H75 zenon_H13c zenon_H7a zenon_H18f zenon_H14f zenon_H2a zenon_H115 zenon_H191 zenon_Ha8 zenon_Haa. % 18.52/18.70 apply (zenon_or_s _ _ zenon_H1ba); [ zenon_intro zenon_H48 | zenon_intro zenon_H1bb ]. % 18.52/18.70 exact (zenon_H75 zenon_H48). % 18.52/18.70 apply (zenon_or_s _ _ zenon_H1bb); [ zenon_intro zenon_H122 | zenon_intro zenon_H1bc ]. % 18.52/18.70 apply (zenon_L92_); trivial. % 18.52/18.70 apply (zenon_or_s _ _ zenon_H1bc); [ zenon_intro zenon_H150 | zenon_intro zenon_Ha9 ]. % 18.52/18.70 apply (zenon_L181_); trivial. % 18.52/18.70 apply (zenon_L40_); trivial. % 18.52/18.70 (* end of lemma zenon_L182_ *) % 18.52/18.70 assert (zenon_L183_ : ((op (e1) (e2)) = (e0)) -> ((op (e2) (e2)) = (e1)) -> (~((e0) = (op (op (e2) (e2)) (e2)))) -> False). % 18.52/18.70 do 0 intro. intros zenon_H2a zenon_Hf1 zenon_H1bd. % 18.52/18.70 elim (classic ((op (op (e2) (e2)) (e2)) = (op (op (e2) (e2)) (e2)))); [ zenon_intro zenon_Hb6 | zenon_intro zenon_Hb7 ]. % 18.52/18.70 cut (((op (op (e2) (e2)) (e2)) = (op (op (e2) (e2)) (e2))) = ((e0) = (op (op (e2) (e2)) (e2)))). % 18.52/18.70 intro zenon_D_pnotp. % 18.52/18.70 apply zenon_H1bd. % 18.52/18.70 rewrite <- zenon_D_pnotp. % 18.52/18.70 exact zenon_Hb6. % 18.52/18.70 cut (((op (op (e2) (e2)) (e2)) = (op (op (e2) (e2)) (e2)))); [idtac | apply NNPP; zenon_intro zenon_Hb7]. % 18.52/18.70 cut (((op (op (e2) (e2)) (e2)) = (e0))); [idtac | apply NNPP; zenon_intro zenon_H1be]. % 18.52/18.70 congruence. % 18.52/18.70 cut (((op (e1) (e2)) = (e0)) = ((op (op (e2) (e2)) (e2)) = (e0))). % 18.52/18.70 intro zenon_D_pnotp. % 18.52/18.70 apply zenon_H1be. % 18.52/18.70 rewrite <- zenon_D_pnotp. % 18.52/18.70 exact zenon_H2a. % 18.52/18.70 cut (((e0) = (e0))); [idtac | apply NNPP; zenon_intro zenon_H82]. % 18.52/18.70 cut (((op (e1) (e2)) = (op (op (e2) (e2)) (e2)))); [idtac | apply NNPP; zenon_intro zenon_H199]. % 18.52/18.70 congruence. % 18.52/18.70 elim (classic ((op (op (e2) (e2)) (e2)) = (op (op (e2) (e2)) (e2)))); [ zenon_intro zenon_Hb6 | zenon_intro zenon_Hb7 ]. % 18.52/18.70 cut (((op (op (e2) (e2)) (e2)) = (op (op (e2) (e2)) (e2))) = ((op (e1) (e2)) = (op (op (e2) (e2)) (e2)))). % 18.52/18.70 intro zenon_D_pnotp. % 18.52/18.70 apply zenon_H199. % 18.52/18.70 rewrite <- zenon_D_pnotp. % 18.52/18.70 exact zenon_Hb6. % 18.52/18.70 cut (((op (op (e2) (e2)) (e2)) = (op (op (e2) (e2)) (e2)))); [idtac | apply NNPP; zenon_intro zenon_Hb7]. % 18.52/18.70 cut (((op (op (e2) (e2)) (e2)) = (op (e1) (e2)))); [idtac | apply NNPP; zenon_intro zenon_H197]. % 18.52/18.70 congruence. % 18.52/18.70 apply (zenon_L154_); trivial. % 18.52/18.70 apply zenon_Hb7. apply refl_equal. % 18.52/18.70 apply zenon_Hb7. apply refl_equal. % 18.52/18.70 apply zenon_H82. apply refl_equal. % 18.52/18.70 apply zenon_Hb7. apply refl_equal. % 18.52/18.70 apply zenon_Hb7. apply refl_equal. % 18.52/18.70 (* end of lemma zenon_L183_ *) % 18.52/18.70 assert (zenon_L184_ : ((op (e0) (e2)) = (e3)) -> ((op (e1) (e2)) = (e0)) -> ((op (e2) (e2)) = (e1)) -> False). % 18.52/18.70 do 0 intro. intros zenon_Ha9 zenon_H2a zenon_Hf1. % 18.52/18.70 apply (zenon_notand_s _ _ ax22); [ zenon_intro zenon_H1c0 | zenon_intro zenon_H1bf ]. % 18.52/18.70 elim (classic ((op (op (op (e2) (e2)) (e2)) (e2)) = (op (op (op (e2) (e2)) (e2)) (e2)))); [ zenon_intro zenon_Hbd | zenon_intro zenon_Hbe ]. % 18.52/18.70 cut (((op (op (op (e2) (e2)) (e2)) (e2)) = (op (op (op (e2) (e2)) (e2)) (e2))) = ((e3) = (op (op (op (e2) (e2)) (e2)) (e2)))). % 18.52/18.70 intro zenon_D_pnotp. % 18.52/18.70 apply zenon_H1c0. % 18.52/18.70 rewrite <- zenon_D_pnotp. % 18.52/18.70 exact zenon_Hbd. % 18.52/18.70 cut (((op (op (op (e2) (e2)) (e2)) (e2)) = (op (op (op (e2) (e2)) (e2)) (e2)))); [idtac | apply NNPP; zenon_intro zenon_Hbe]. % 18.52/18.70 cut (((op (op (op (e2) (e2)) (e2)) (e2)) = (e3))); [idtac | apply NNPP; zenon_intro zenon_H1c1]. % 18.52/18.70 congruence. % 18.52/18.70 cut (((op (e0) (e2)) = (e3)) = ((op (op (op (e2) (e2)) (e2)) (e2)) = (e3))). % 18.52/18.70 intro zenon_D_pnotp. % 18.52/18.70 apply zenon_H1c1. % 18.52/18.70 rewrite <- zenon_D_pnotp. % 18.52/18.70 exact zenon_Ha9. % 18.52/18.70 cut (((e3) = (e3))); [idtac | apply NNPP; zenon_intro zenon_H85]. % 18.52/18.70 cut (((op (e0) (e2)) = (op (op (op (e2) (e2)) (e2)) (e2)))); [idtac | apply NNPP; zenon_intro zenon_H1c2]. % 18.52/18.70 congruence. % 18.52/18.70 elim (classic ((op (op (op (e2) (e2)) (e2)) (e2)) = (op (op (op (e2) (e2)) (e2)) (e2)))); [ zenon_intro zenon_Hbd | zenon_intro zenon_Hbe ]. % 18.52/18.70 cut (((op (op (op (e2) (e2)) (e2)) (e2)) = (op (op (op (e2) (e2)) (e2)) (e2))) = ((op (e0) (e2)) = (op (op (op (e2) (e2)) (e2)) (e2)))). % 18.52/18.70 intro zenon_D_pnotp. % 18.52/18.70 apply zenon_H1c2. % 18.52/18.70 rewrite <- zenon_D_pnotp. % 18.52/18.70 exact zenon_Hbd. % 18.52/18.70 cut (((op (op (op (e2) (e2)) (e2)) (e2)) = (op (op (op (e2) (e2)) (e2)) (e2)))); [idtac | apply NNPP; zenon_intro zenon_Hbe]. % 18.52/18.70 cut (((op (op (op (e2) (e2)) (e2)) (e2)) = (op (e0) (e2)))); [idtac | apply NNPP; zenon_intro zenon_H1c3]. % 18.52/18.70 congruence. % 18.52/18.70 cut (((e2) = (e2))); [idtac | apply NNPP; zenon_intro zenon_H7e]. % 18.52/18.70 cut (((op (op (e2) (e2)) (e2)) = (e0))); [idtac | apply NNPP; zenon_intro zenon_H1be]. % 18.52/18.70 congruence. % 18.52/18.70 cut (((op (e1) (e2)) = (e0)) = ((op (op (e2) (e2)) (e2)) = (e0))). % 18.52/18.70 intro zenon_D_pnotp. % 18.52/18.70 apply zenon_H1be. % 18.52/18.70 rewrite <- zenon_D_pnotp. % 18.52/18.70 exact zenon_H2a. % 18.52/18.70 cut (((e0) = (e0))); [idtac | apply NNPP; zenon_intro zenon_H82]. % 18.52/18.70 cut (((op (e1) (e2)) = (op (op (e2) (e2)) (e2)))); [idtac | apply NNPP; zenon_intro zenon_H199]. % 18.52/18.70 congruence. % 18.52/18.70 elim (classic ((op (op (e2) (e2)) (e2)) = (op (op (e2) (e2)) (e2)))); [ zenon_intro zenon_Hb6 | zenon_intro zenon_Hb7 ]. % 18.52/18.70 cut (((op (op (e2) (e2)) (e2)) = (op (op (e2) (e2)) (e2))) = ((op (e1) (e2)) = (op (op (e2) (e2)) (e2)))). % 18.52/18.70 intro zenon_D_pnotp. % 18.52/18.70 apply zenon_H199. % 18.52/18.70 rewrite <- zenon_D_pnotp. % 18.52/18.70 exact zenon_Hb6. % 18.52/18.70 cut (((op (op (e2) (e2)) (e2)) = (op (op (e2) (e2)) (e2)))); [idtac | apply NNPP; zenon_intro zenon_Hb7]. % 18.52/18.70 cut (((op (op (e2) (e2)) (e2)) = (op (e1) (e2)))); [idtac | apply NNPP; zenon_intro zenon_H197]. % 18.52/18.71 congruence. % 18.52/18.71 apply (zenon_L154_); trivial. % 18.52/18.71 apply zenon_Hb7. apply refl_equal. % 18.52/18.71 apply zenon_Hb7. apply refl_equal. % 18.52/18.71 apply zenon_H82. apply refl_equal. % 18.52/18.71 apply zenon_H7e. apply refl_equal. % 18.52/18.71 apply zenon_Hbe. apply refl_equal. % 18.52/18.71 apply zenon_Hbe. apply refl_equal. % 18.52/18.71 apply zenon_H85. apply refl_equal. % 18.52/18.71 apply zenon_Hbe. apply refl_equal. % 18.52/18.71 apply zenon_Hbe. apply refl_equal. % 18.52/18.71 apply (zenon_notand_s _ _ zenon_H1bf); [ zenon_intro zenon_H1bd | zenon_intro zenon_Hf2 ]. % 18.52/18.71 apply (zenon_L183_); trivial. % 18.52/18.71 apply zenon_Hf2. apply sym_equal. exact zenon_Hf1. % 18.52/18.71 (* end of lemma zenon_L184_ *) % 18.52/18.71 assert (zenon_L185_ : (~((op (e2) (e2)) = (op (e3) (e2)))) -> ((op (e2) (e2)) = (e1)) -> ((op (e3) (e2)) = (e1)) -> False). % 18.52/18.71 do 0 intro. intros zenon_H18f zenon_Hf1 zenon_Hba. % 18.52/18.71 cut (((op (e2) (e2)) = (e1)) = ((op (e2) (e2)) = (op (e3) (e2)))). % 18.52/18.71 intro zenon_D_pnotp. % 18.52/18.71 apply zenon_H18f. % 18.52/18.71 rewrite <- zenon_D_pnotp. % 18.52/18.71 exact zenon_Hf1. % 18.52/18.71 cut (((e1) = (op (e3) (e2)))); [idtac | apply NNPP; zenon_intro zenon_H116]. % 18.52/18.71 cut (((op (e2) (e2)) = (op (e2) (e2)))); [idtac | apply NNPP; zenon_intro zenon_H190]. % 18.52/18.71 congruence. % 18.52/18.71 apply zenon_H190. apply refl_equal. % 18.52/18.71 apply zenon_H116. apply sym_equal. exact zenon_Hba. % 18.52/18.71 (* end of lemma zenon_L185_ *) % 18.52/18.71 assert (zenon_L186_ : (((op (e2) (e2)) = (e0))\/(((op (e2) (e2)) = (e1))\/(((op (e2) (e2)) = (e2))\/((op (e2) (e2)) = (e3))))) -> ((op (e0) (e2)) = (e3)) -> (~((op (e2) (e2)) = (op (e3) (e2)))) -> (~((op (e2) (e2)) = (e2))) -> ((op (e1) (e2)) = (e0)) -> ((op (e3) (e2)) = (e1)) -> False). % 18.52/18.71 do 0 intro. intros zenon_H1c4 zenon_Ha9 zenon_H18f zenon_H173 zenon_H2a zenon_Hba. % 18.52/18.71 apply (zenon_or_s _ _ zenon_H1c4); [ zenon_intro zenon_H2c | zenon_intro zenon_H1c5 ]. % 18.52/18.71 apply (zenon_L45_); trivial. % 18.52/18.71 apply (zenon_or_s _ _ zenon_H1c5); [ zenon_intro zenon_Hf1 | zenon_intro zenon_H1c6 ]. % 18.52/18.71 apply (zenon_L185_); trivial. % 18.52/18.71 apply (zenon_or_s _ _ zenon_H1c6); [ zenon_intro zenon_H176 | zenon_intro zenon_Haa ]. % 18.52/18.71 exact (zenon_H173 zenon_H176). % 18.52/18.71 apply (zenon_L179_); trivial. % 18.52/18.71 (* end of lemma zenon_L186_ *) % 18.52/18.71 assert (zenon_L187_ : (((op (e0) (e2)) = (e1))\/(((op (e1) (e2)) = (e1))\/(((op (e2) (e2)) = (e1))\/((op (e3) (e2)) = (e1))))) -> (~((e1) = (e3))) -> (~((op (e1) (e2)) = (op (e1) (e3)))) -> ((op (e1) (e3)) = (e1)) -> (((op (e2) (e2)) = (e0))\/(((op (e2) (e2)) = (e1))\/(((op (e2) (e2)) = (e2))\/((op (e2) (e2)) = (e3))))) -> ((op (e0) (e2)) = (e3)) -> (~((op (e2) (e2)) = (op (e3) (e2)))) -> (~((op (e2) (e2)) = (e2))) -> ((op (e1) (e2)) = (e0)) -> False). % 18.52/18.71 do 0 intro. intros zenon_H139 zenon_H95 zenon_H124 zenon_Hd6 zenon_H1c4 zenon_Ha9 zenon_H18f zenon_H173 zenon_H2a. % 18.52/18.71 apply (zenon_or_s _ _ zenon_H139); [ zenon_intro zenon_H122 | zenon_intro zenon_H13a ]. % 18.52/18.71 apply (zenon_L77_); trivial. % 18.52/18.71 apply (zenon_or_s _ _ zenon_H13a); [ zenon_intro zenon_Hf0 | zenon_intro zenon_H13b ]. % 18.52/18.71 apply (zenon_L78_); trivial. % 18.52/18.71 apply (zenon_or_s _ _ zenon_H13b); [ zenon_intro zenon_Hf1 | zenon_intro zenon_Hba ]. % 18.52/18.71 apply (zenon_L184_); trivial. % 18.52/18.71 apply (zenon_L186_); trivial. % 18.52/18.71 (* end of lemma zenon_L187_ *) % 18.52/18.71 assert (zenon_L188_ : ((op (e2) (e3)) = (e1)) -> ((op (e2) (e1)) = (e1)) -> (~((op (e2) (e1)) = (op (e2) (e3)))) -> False). % 18.52/18.71 do 0 intro. intros zenon_Hf4 zenon_Ha5 zenon_H1c7. % 18.52/18.71 elim (classic ((op (e2) (e3)) = (op (e2) (e3)))); [ zenon_intro zenon_H5c | zenon_intro zenon_H5d ]. % 18.52/18.71 cut (((op (e2) (e3)) = (op (e2) (e3))) = ((op (e2) (e1)) = (op (e2) (e3)))). % 18.52/18.71 intro zenon_D_pnotp. % 18.52/18.71 apply zenon_H1c7. % 18.52/18.71 rewrite <- zenon_D_pnotp. % 18.52/18.71 exact zenon_H5c. % 18.52/18.71 cut (((op (e2) (e3)) = (op (e2) (e3)))); [idtac | apply NNPP; zenon_intro zenon_H5d]. % 18.52/18.71 cut (((op (e2) (e3)) = (op (e2) (e1)))); [idtac | apply NNPP; zenon_intro zenon_H1c8]. % 18.52/18.71 congruence. % 18.52/18.71 cut (((op (e2) (e3)) = (e1)) = ((op (e2) (e3)) = (op (e2) (e1)))). % 18.52/18.71 intro zenon_D_pnotp. % 18.52/18.71 apply zenon_H1c8. % 18.52/18.71 rewrite <- zenon_D_pnotp. % 18.52/18.71 exact zenon_Hf4. % 18.52/18.71 cut (((e1) = (op (e2) (e1)))); [idtac | apply NNPP; zenon_intro zenon_Hb3]. % 18.52/18.71 cut (((op (e2) (e3)) = (op (e2) (e3)))); [idtac | apply NNPP; zenon_intro zenon_H5d]. % 18.52/18.71 congruence. % 18.52/18.71 apply zenon_H5d. apply refl_equal. % 18.52/18.71 apply zenon_Hb3. apply sym_equal. exact zenon_Ha5. % 18.52/18.71 apply zenon_H5d. apply refl_equal. % 18.52/18.71 apply zenon_H5d. apply refl_equal. % 18.52/18.71 (* end of lemma zenon_L188_ *) % 18.52/18.71 assert (zenon_L189_ : ((op (e3) (e3)) = (e1)) -> ((op (e3) (e0)) = (e1)) -> (~((op (e3) (e0)) = (op (e3) (e3)))) -> False). % 18.52/18.71 do 0 intro. intros zenon_Hc4 zenon_Hac zenon_H71. % 18.52/18.71 elim (classic ((op (e3) (e3)) = (op (e3) (e3)))); [ zenon_intro zenon_H63 | zenon_intro zenon_H64 ]. % 18.52/18.71 cut (((op (e3) (e3)) = (op (e3) (e3))) = ((op (e3) (e0)) = (op (e3) (e3)))). % 18.52/18.71 intro zenon_D_pnotp. % 18.52/18.71 apply zenon_H71. % 18.52/18.71 rewrite <- zenon_D_pnotp. % 18.52/18.71 exact zenon_H63. % 18.52/18.71 cut (((op (e3) (e3)) = (op (e3) (e3)))); [idtac | apply NNPP; zenon_intro zenon_H64]. % 18.52/18.71 cut (((op (e3) (e3)) = (op (e3) (e0)))); [idtac | apply NNPP; zenon_intro zenon_H72]. % 18.52/18.71 congruence. % 18.52/18.71 cut (((op (e3) (e3)) = (e1)) = ((op (e3) (e3)) = (op (e3) (e0)))). % 18.52/18.71 intro zenon_D_pnotp. % 18.52/18.71 apply zenon_H72. % 18.52/18.71 rewrite <- zenon_D_pnotp. % 18.52/18.71 exact zenon_Hc4. % 18.52/18.71 cut (((e1) = (op (e3) (e0)))); [idtac | apply NNPP; zenon_intro zenon_H1c9]. % 18.52/18.71 cut (((op (e3) (e3)) = (op (e3) (e3)))); [idtac | apply NNPP; zenon_intro zenon_H64]. % 18.52/18.71 congruence. % 18.52/18.71 apply zenon_H64. apply refl_equal. % 18.52/18.71 apply zenon_H1c9. apply sym_equal. exact zenon_Hac. % 18.52/18.71 apply zenon_H64. apply refl_equal. % 18.52/18.71 apply zenon_H64. apply refl_equal. % 18.52/18.71 (* end of lemma zenon_L189_ *) % 18.52/18.71 assert (zenon_L190_ : (((op (e0) (e3)) = (e1))\/(((op (e1) (e3)) = (e1))\/(((op (e2) (e3)) = (e1))\/((op (e3) (e3)) = (e1))))) -> (~((op (e0) (e0)) = (op (e0) (e3)))) -> ((op (e0) (e0)) = (e1)) -> ((op (e1) (e2)) = (e0)) -> (~((op (e2) (e2)) = (e2))) -> (~((op (e2) (e2)) = (op (e3) (e2)))) -> ((op (e0) (e2)) = (e3)) -> (((op (e2) (e2)) = (e0))\/(((op (e2) (e2)) = (e1))\/(((op (e2) (e2)) = (e2))\/((op (e2) (e2)) = (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))))) -> (~((op (e2) (e1)) = (op (e2) (e3)))) -> ((op (e2) (e1)) = (e1)) -> ((op (e3) (e0)) = (e1)) -> (~((op (e3) (e0)) = (op (e3) (e3)))) -> False). % 18.52/18.71 do 0 intro. intros zenon_H133 zenon_H189 zenon_H7a zenon_H2a zenon_H173 zenon_H18f zenon_Ha9 zenon_H1c4 zenon_H124 zenon_H95 zenon_H139 zenon_H1c7 zenon_Ha5 zenon_Hac zenon_H71. % 18.52/18.71 apply (zenon_or_s _ _ zenon_H133); [ zenon_intro zenon_Hc3 | zenon_intro zenon_H134 ]. % 18.52/18.71 apply (zenon_L140_); trivial. % 18.52/18.71 apply (zenon_or_s _ _ zenon_H134); [ zenon_intro zenon_Hd6 | zenon_intro zenon_H135 ]. % 18.52/18.71 apply (zenon_L187_); trivial. % 18.52/18.71 apply (zenon_or_s _ _ zenon_H135); [ zenon_intro zenon_Hf4 | zenon_intro zenon_Hc4 ]. % 18.52/18.71 apply (zenon_L188_); trivial. % 18.52/18.71 apply (zenon_L189_); trivial. % 18.52/18.71 (* end of lemma zenon_L190_ *) % 18.52/18.71 assert (zenon_L191_ : (~((op (e0) (e1)) = (op (e2) (e1)))) -> ((op (e0) (e1)) = (e2)) -> ((op (e2) (e1)) = (e2)) -> False). % 18.52/18.71 do 0 intro. intros zenon_H17e zenon_H10f zenon_H1ca. % 18.52/18.71 cut (((op (e0) (e1)) = (e2)) = ((op (e0) (e1)) = (op (e2) (e1)))). % 18.52/18.71 intro zenon_D_pnotp. % 18.52/18.71 apply zenon_H17e. % 18.52/18.71 rewrite <- zenon_D_pnotp. % 18.52/18.71 exact zenon_H10f. % 18.52/18.71 cut (((e2) = (op (e2) (e1)))); [idtac | apply NNPP; zenon_intro zenon_H1cb]. % 18.52/18.71 cut (((op (e0) (e1)) = (op (e0) (e1)))); [idtac | apply NNPP; zenon_intro zenon_H112]. % 18.52/18.71 congruence. % 18.52/18.71 apply zenon_H112. apply refl_equal. % 18.52/18.71 apply zenon_H1cb. apply sym_equal. exact zenon_H1ca. % 18.52/18.71 (* end of lemma zenon_L191_ *) % 18.52/18.71 assert (zenon_L192_ : (((op (e2) (e1)) = (e0))\/(((op (e2) (e1)) = (e1))\/(((op (e2) (e1)) = (e2))\/((op (e2) (e1)) = (e3))))) -> (~((op (e2) (e1)) = (e0))) -> (~((op (e2) (e1)) = (op (e3) (e1)))) -> ((op (e3) (e1)) = (e1)) -> ((op (e0) (e1)) = (e2)) -> (~((op (e0) (e1)) = (op (e2) (e1)))) -> (~((op (e1) (e1)) = (op (e2) (e1)))) -> ((op (e1) (e1)) = (e3)) -> False). % 18.52/18.71 do 0 intro. intros zenon_H1cc zenon_H31 zenon_Haf zenon_Hae zenon_H10f zenon_H17e zenon_H13e zenon_H13f. % 18.52/18.71 apply (zenon_or_s _ _ zenon_H1cc); [ zenon_intro zenon_H36 | zenon_intro zenon_H1cd ]. % 18.52/18.71 exact (zenon_H31 zenon_H36). % 18.52/18.71 apply (zenon_or_s _ _ zenon_H1cd); [ zenon_intro zenon_Ha5 | zenon_intro zenon_H1ce ]. % 18.52/18.71 apply (zenon_L42_); trivial. % 18.52/18.71 apply (zenon_or_s _ _ zenon_H1ce); [ zenon_intro zenon_H1ca | zenon_intro zenon_Ha6 ]. % 18.52/18.71 apply (zenon_L191_); trivial. % 18.52/18.71 apply (zenon_L95_); trivial. % 18.52/18.71 (* end of lemma zenon_L192_ *) % 18.52/18.71 assert (zenon_L193_ : ((op (e3) (e1)) = (e3)) -> ((op (e3) (e0)) = (e3)) -> (~((op (e3) (e0)) = (op (e3) (e1)))) -> False). % 18.52/18.71 do 0 intro. intros zenon_H161 zenon_H15e zenon_H1cf. % 18.52/18.71 elim (classic ((op (e3) (e1)) = (op (e3) (e1)))); [ zenon_intro zenon_Hb0 | zenon_intro zenon_Hb1 ]. % 18.52/18.71 cut (((op (e3) (e1)) = (op (e3) (e1))) = ((op (e3) (e0)) = (op (e3) (e1)))). % 18.52/18.71 intro zenon_D_pnotp. % 18.52/18.71 apply zenon_H1cf. % 18.52/18.71 rewrite <- zenon_D_pnotp. % 18.52/18.71 exact zenon_Hb0. % 18.52/18.71 cut (((op (e3) (e1)) = (op (e3) (e1)))); [idtac | apply NNPP; zenon_intro zenon_Hb1]. % 18.52/18.71 cut (((op (e3) (e1)) = (op (e3) (e0)))); [idtac | apply NNPP; zenon_intro zenon_H1d0]. % 18.52/18.71 congruence. % 18.52/18.71 cut (((op (e3) (e1)) = (e3)) = ((op (e3) (e1)) = (op (e3) (e0)))). % 18.52/18.71 intro zenon_D_pnotp. % 18.52/18.71 apply zenon_H1d0. % 18.52/18.71 rewrite <- zenon_D_pnotp. % 18.52/18.71 exact zenon_H161. % 18.52/18.71 cut (((e3) = (op (e3) (e0)))); [idtac | apply NNPP; zenon_intro zenon_H1d1]. % 18.52/18.71 cut (((op (e3) (e1)) = (op (e3) (e1)))); [idtac | apply NNPP; zenon_intro zenon_Hb1]. % 18.52/18.71 congruence. % 18.52/18.71 apply zenon_Hb1. apply refl_equal. % 18.52/18.71 apply zenon_H1d1. apply sym_equal. exact zenon_H15e. % 18.52/18.71 apply zenon_Hb1. apply refl_equal. % 18.52/18.71 apply zenon_Hb1. apply refl_equal. % 18.52/18.71 (* end of lemma zenon_L193_ *) % 18.52/18.71 assert (zenon_L194_ : (((op (e0) (e1)) = (e3))\/(((op (e1) (e1)) = (e3))\/(((op (e2) (e1)) = (e3))\/((op (e3) (e1)) = (e3))))) -> (~((e0) = (e3))) -> ((op (e0) (e1)) = (e0)) -> (~((op (e0) (e1)) = (op (e2) (e1)))) -> ((op (e3) (e1)) = (e1)) -> (~((op (e2) (e1)) = (op (e3) (e1)))) -> (~((op (e2) (e1)) = (e0))) -> (((op (e2) (e1)) = (e0))\/(((op (e2) (e1)) = (e1))\/(((op (e2) (e1)) = (e2))\/((op (e2) (e1)) = (e3))))) -> (~((op (e1) (e1)) = (op (e2) (e1)))) -> (~((op (e0) (e1)) = (op (e1) (e1)))) -> ((op (e0) (e1)) = (e2)) -> (~((op (e1) (e1)) = (e1))) -> (~((op (e1) (e1)) = (e0))) -> (((op (e1) (e1)) = (e0))\/(((op (e1) (e1)) = (e1))\/(((op (e1) (e1)) = (e2))\/((op (e1) (e1)) = (e3))))) -> ((op (e3) (e0)) = (e3)) -> (~((op (e3) (e0)) = (op (e3) (e1)))) -> False). % 18.52/18.71 do 0 intro. intros zenon_H1a5 zenon_H9a zenon_H49 zenon_H17e zenon_Hae zenon_Haf zenon_H31 zenon_H1cc zenon_H13e zenon_H10e zenon_H10f zenon_H10a zenon_H24 zenon_H142 zenon_H15e zenon_H1cf. % 18.52/18.71 apply (zenon_or_s _ _ zenon_H1a5); [ zenon_intro zenon_H99 | zenon_intro zenon_H1a8 ]. % 18.52/18.71 apply (zenon_L36_); trivial. % 18.52/18.71 apply (zenon_or_s _ _ zenon_H1a8); [ zenon_intro zenon_H13f | zenon_intro zenon_H1a9 ]. % 18.52/18.71 apply (zenon_L192_); trivial. % 18.52/18.71 apply (zenon_or_s _ _ zenon_H1a9); [ zenon_intro zenon_Ha6 | zenon_intro zenon_H161 ]. % 18.52/18.71 apply (zenon_L96_); trivial. % 18.52/18.71 apply (zenon_L193_); trivial. % 18.52/18.71 (* end of lemma zenon_L194_ *) % 18.52/18.71 assert (zenon_L195_ : (((op (e3) (e0)) = (e0))\/(((op (e3) (e1)) = (e0))\/(((op (e3) (e2)) = (e0))\/((op (e3) (e3)) = (e0))))) -> (~((op (e3) (e0)) = (e0))) -> (~((op (e3) (e1)) = (e0))) -> (~((op (e3) (e2)) = (e0))) -> (~((op (e1) (e3)) = (op (e3) (e3)))) -> ((op (e1) (e3)) = (e0)) -> False). % 18.52/18.71 do 0 intro. intros zenon_H1ac zenon_H40 zenon_H1ad zenon_H18b zenon_Hd5 zenon_H1f. % 18.52/18.71 apply (zenon_or_s _ _ zenon_H1ac); [ zenon_intro zenon_H44 | zenon_intro zenon_H1af ]. % 18.52/18.71 exact (zenon_H40 zenon_H44). % 18.52/18.71 apply (zenon_or_s _ _ zenon_H1af); [ zenon_intro zenon_H1b1 | zenon_intro zenon_H1b0 ]. % 18.52/18.71 exact (zenon_H1ad zenon_H1b1). % 18.52/18.71 apply (zenon_or_s _ _ zenon_H1b0); [ zenon_intro zenon_H61 | zenon_intro zenon_H60 ]. % 18.52/18.71 exact (zenon_H18b zenon_H61). % 18.52/18.71 apply (zenon_L136_); trivial. % 18.52/18.71 (* end of lemma zenon_L195_ *) % 18.52/18.71 assert (zenon_L196_ : (((op (e2) (e0)) = (e3))\/(((op (e2) (e1)) = (e3))\/(((op (e2) (e2)) = (e3))\/((op (e2) (e3)) = (e3))))) -> ((op (e1) (e0)) = (e2)) -> (~((op (e1) (e1)) = (op (e2) (e1)))) -> (~((op (e0) (e1)) = (op (e1) (e1)))) -> ((op (e0) (e1)) = (e2)) -> (~((op (e1) (e1)) = (e1))) -> (~((op (e1) (e1)) = (e0))) -> (((op (e1) (e1)) = (e0))\/(((op (e1) (e1)) = (e1))\/(((op (e1) (e1)) = (e2))\/((op (e1) (e1)) = (e3))))) -> (~((op (e0) (e2)) = (op (e2) (e2)))) -> (((op (e3) (e2)) = (e0))\/(((op (e3) (e2)) = (e1))\/(((op (e3) (e2)) = (e2))\/((op (e3) (e2)) = (e3))))) -> (~((op (e1) (e2)) = (op (e3) (e2)))) -> ((op (e1) (e2)) = (e0)) -> (~((op (e0) (e2)) = (op (e3) (e2)))) -> (~((op (e2) (e2)) = (op (e3) (e2)))) -> ((op (e0) (e0)) = (e1)) -> (~((op (e0) (e0)) = (op (e0) (e2)))) -> (~((op (e0) (e2)) = (e0))) -> (((op (e0) (e2)) = (e0))\/(((op (e0) (e2)) = (e1))\/(((op (e0) (e2)) = (e2))\/((op (e0) (e2)) = (e3))))) -> (~((op (e0) (e3)) = (op (e2) (e3)))) -> ((op (e0) (e3)) = (e3)) -> False). % 18.52/18.71 do 0 intro. intros zenon_He7 zenon_H86 zenon_H13e zenon_H10e zenon_H10f zenon_H10a zenon_H24 zenon_H142 zenon_Ha8 zenon_H191 zenon_H115 zenon_H2a zenon_H14f zenon_H18f zenon_H7a zenon_H13c zenon_H75 zenon_H1ba zenon_He2 zenon_He3. % 18.52/18.71 apply (zenon_or_s _ _ zenon_He7); [ zenon_intro zenon_H3b | zenon_intro zenon_He9 ]. % 18.52/18.71 apply (zenon_L33_); trivial. % 18.52/18.71 apply (zenon_or_s _ _ zenon_He9); [ zenon_intro zenon_Ha6 | zenon_intro zenon_Hea ]. % 18.52/18.71 apply (zenon_L96_); trivial. % 18.52/18.71 apply (zenon_or_s _ _ zenon_Hea); [ zenon_intro zenon_Haa | zenon_intro zenon_Hdd ]. % 18.52/18.71 apply (zenon_L182_); trivial. % 18.52/18.71 apply (zenon_L54_); trivial. % 18.52/18.71 (* end of lemma zenon_L196_ *) % 18.52/18.71 assert (zenon_L197_ : (((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))))) -> (~((e0) = (e1))) -> (~((e1) = (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) (e1)) = (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 (e0) (e0)) = (op (e0) (e3)))) -> (((op (e0) (e3)) = (e1))\/(((op (e1) (e3)) = (e1))\/(((op (e2) (e3)) = (e1))\/((op (e3) (e3)) = (e1))))) -> (~((op (e2) (e2)) = (e2))) -> (((op (e2) (e2)) = (e0))\/(((op (e2) (e2)) = (e1))\/(((op (e2) (e2)) = (e2))\/((op (e2) (e2)) = (e3))))) -> (((op (e0) (e3)) = (e0))\/(((op (e0) (e3)) = (e1))\/(((op (e0) (e3)) = (e2))\/((op (e0) (e3)) = (e3))))) -> (~((op (e0) (e3)) = (e0))) -> (~((op (e0) (e3)) = (op (e3) (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))))) -> (~((e2) = (e3))) -> (((op (e0) (e1)) = (e3))\/(((op (e1) (e1)) = (e3))\/(((op (e2) (e1)) = (e3))\/((op (e3) (e1)) = (e3))))) -> (~((e0) = (e3))) -> ((op (e0) (e1)) = (e0)) -> (~((op (e0) (e1)) = (op (e2) (e1)))) -> (~((op (e2) (e1)) = (op (e3) (e1)))) -> (~((op (e2) (e1)) = (e0))) -> (((op (e2) (e1)) = (e0))\/(((op (e2) (e1)) = (e1))\/(((op (e2) (e1)) = (e2))\/((op (e2) (e1)) = (e3))))) -> ((op (e3) (e0)) = (e3)) -> (~((op (e3) (e0)) = (op (e3) (e1)))) -> (((op (e1) (e0)) = (e0))\/(((op (e1) (e1)) = (e0))\/(((op (e1) (e2)) = (e0))\/((op (e1) (e3)) = (e0))))) -> (~((op (e1) (e0)) = (e0))) -> (~((op (e0) (e3)) = (op (e2) (e3)))) -> (((op (e0) (e2)) = (e0))\/(((op (e0) (e2)) = (e1))\/(((op (e0) (e2)) = (e2))\/((op (e0) (e2)) = (e3))))) -> (~((op (e0) (e2)) = (e0))) -> (~((op (e0) (e0)) = (op (e0) (e2)))) -> ((op (e0) (e0)) = (e1)) -> (~((op (e2) (e2)) = (op (e3) (e2)))) -> (~((op (e0) (e2)) = (op (e3) (e2)))) -> (~((op (e1) (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) (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)) = (op (e2) (e1)))) -> ((op (e1) (e0)) = (e2)) -> (((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) (e0)) = (e0))) -> (~((op (e3) (e1)) = (e0))) -> (~((op (e3) (e2)) = (e0))) -> (~((op (e1) (e3)) = (op (e3) (e3)))) -> False). % 18.52/18.71 do 0 intro. intros zenon_H168 zenon_H109 zenon_Ha1 zenon_H95 zenon_He8 zenon_H71 zenon_H1c7 zenon_H139 zenon_H124 zenon_H189 zenon_H133 zenon_H173 zenon_H1c4 zenon_He4 zenon_H76 zenon_Hc2 zenon_Hdb zenon_Hd8 zenon_Hdf zenon_H12b zenon_H1a5 zenon_H9a zenon_H49 zenon_H17e zenon_Haf zenon_H31 zenon_H1cc zenon_H15e zenon_H1cf zenon_H22 zenon_H23 zenon_He2 zenon_H1ba zenon_H75 zenon_H13c zenon_H7a zenon_H18f zenon_H14f zenon_H115 zenon_H191 zenon_Ha8 zenon_H142 zenon_H24 zenon_H10a zenon_H10f zenon_H10e zenon_H13e zenon_H86 zenon_He7 zenon_H1ac zenon_H40 zenon_H1ad zenon_H18b zenon_Hd5. % 18.52/18.71 apply (zenon_or_s _ _ zenon_H168); [ zenon_intro zenon_H3a | zenon_intro zenon_H169 ]. % 18.52/18.71 apply (zenon_L35_); trivial. % 18.52/18.71 apply (zenon_or_s _ _ zenon_H169); [ zenon_intro zenon_H99 | zenon_intro zenon_H16a ]. % 18.52/18.71 apply (zenon_L175_); trivial. % 18.52/18.71 apply (zenon_or_s _ _ zenon_H16a); [ zenon_intro zenon_Ha9 | zenon_intro zenon_He3 ]. % 18.52/18.71 apply (zenon_or_s _ _ zenon_H22); [ zenon_intro zenon_H27 | zenon_intro zenon_H26 ]. % 18.52/18.71 exact (zenon_H23 zenon_H27). % 18.52/18.71 apply (zenon_or_s _ _ zenon_H26); [ zenon_intro zenon_H29 | zenon_intro zenon_H28 ]. % 18.52/18.71 exact (zenon_H24 zenon_H29). % 18.52/18.71 apply (zenon_or_s _ _ zenon_H28); [ zenon_intro zenon_H2a | zenon_intro zenon_H1f ]. % 18.52/18.71 apply (zenon_or_s _ _ zenon_H109); [ zenon_intro zenon_Ha0 | zenon_intro zenon_H10b ]. % 18.52/18.71 apply (zenon_L38_); trivial. % 18.52/18.71 apply (zenon_or_s _ _ zenon_H10b); [ zenon_intro zenon_H10d | zenon_intro zenon_H10c ]. % 18.52/18.71 exact (zenon_H10a zenon_H10d). % 18.52/18.71 apply (zenon_or_s _ _ zenon_H10c); [ zenon_intro zenon_Ha5 | zenon_intro zenon_Hae ]. % 18.52/18.71 apply (zenon_or_s _ _ zenon_H1a5); [ zenon_intro zenon_H99 | zenon_intro zenon_H1a8 ]. % 18.52/18.71 apply (zenon_L175_); trivial. % 18.52/18.71 apply (zenon_or_s _ _ zenon_H1a8); [ zenon_intro zenon_H13f | zenon_intro zenon_H1a9 ]. % 18.52/18.71 apply (zenon_or_s _ _ zenon_He7); [ zenon_intro zenon_H3b | zenon_intro zenon_He9 ]. % 18.52/18.71 apply (zenon_L33_); trivial. % 18.52/18.71 apply (zenon_or_s _ _ zenon_He9); [ zenon_intro zenon_Ha6 | zenon_intro zenon_Hea ]. % 18.52/18.71 apply (zenon_L96_); trivial. % 18.52/18.71 apply (zenon_or_s _ _ zenon_Hea); [ zenon_intro zenon_Haa | zenon_intro zenon_Hdd ]. % 18.52/18.71 apply (zenon_L182_); trivial. % 18.52/18.71 apply (zenon_or_s _ _ zenon_He8); [ zenon_intro zenon_Hac | zenon_intro zenon_Heb ]. % 18.52/18.71 apply (zenon_L190_); trivial. % 18.52/18.71 apply (zenon_or_s _ _ zenon_Heb); [ zenon_intro zenon_Hae | zenon_intro zenon_Hec ]. % 18.52/18.71 apply (zenon_L192_); trivial. % 18.52/18.71 apply (zenon_or_s _ _ zenon_Hec); [ zenon_intro zenon_Hba | zenon_intro zenon_Hc4 ]. % 18.52/18.71 apply (zenon_L186_); trivial. % 18.52/18.71 apply (zenon_L55_); trivial. % 18.52/18.71 apply (zenon_or_s _ _ zenon_H1a9); [ zenon_intro zenon_Ha6 | zenon_intro zenon_H161 ]. % 18.52/18.71 apply (zenon_L39_); trivial. % 18.52/18.71 apply (zenon_L193_); trivial. % 18.52/18.71 apply (zenon_L194_); trivial. % 18.52/18.71 apply (zenon_L195_); trivial. % 18.52/18.71 apply (zenon_or_s _ _ zenon_H22); [ zenon_intro zenon_H27 | zenon_intro zenon_H26 ]. % 18.52/18.71 exact (zenon_H23 zenon_H27). % 18.52/18.71 apply (zenon_or_s _ _ zenon_H26); [ zenon_intro zenon_H29 | zenon_intro zenon_H28 ]. % 18.52/18.71 exact (zenon_H24 zenon_H29). % 18.52/18.71 apply (zenon_or_s _ _ zenon_H28); [ zenon_intro zenon_H2a | zenon_intro zenon_H1f ]. % 18.52/18.71 apply (zenon_L196_); trivial. % 18.52/18.71 apply (zenon_L195_); trivial. % 18.52/18.71 (* end of lemma zenon_L197_ *) % 18.52/18.71 assert (zenon_L198_ : (((op (e0) (e2)) = (e0))\/(((op (e1) (e2)) = (e0))\/(((op (e2) (e2)) = (e0))\/((op (e3) (e2)) = (e0))))) -> (~((op (e0) (e2)) = (e0))) -> (~((op (e3) (e0)) = (op (e3) (e3)))) -> ((op (e3) (e0)) = (e1)) -> ((op (e2) (e1)) = (e1)) -> (~((op (e2) (e1)) = (op (e2) (e3)))) -> (((op (e0) (e2)) = (e1))\/(((op (e1) (e2)) = (e1))\/(((op (e2) (e2)) = (e1))\/((op (e3) (e2)) = (e1))))) -> (~((e1) = (e3))) -> (~((op (e1) (e2)) = (op (e1) (e3)))) -> (((op (e2) (e2)) = (e0))\/(((op (e2) (e2)) = (e1))\/(((op (e2) (e2)) = (e2))\/((op (e2) (e2)) = (e3))))) -> ((op (e0) (e2)) = (e3)) -> (~((op (e2) (e2)) = (op (e3) (e2)))) -> (~((op (e2) (e2)) = (e2))) -> ((op (e0) (e0)) = (e1)) -> (~((op (e0) (e0)) = (op (e0) (e3)))) -> (((op (e0) (e3)) = (e1))\/(((op (e1) (e3)) = (e1))\/(((op (e2) (e3)) = (e1))\/((op (e3) (e3)) = (e1))))) -> (~((op (e2) (e2)) = (e0))) -> (~((op (e3) (e2)) = (e0))) -> False). % 18.52/18.71 do 0 intro. intros zenon_H6a zenon_H75 zenon_H71 zenon_Hac zenon_Ha5 zenon_H1c7 zenon_H139 zenon_H95 zenon_H124 zenon_H1c4 zenon_Ha9 zenon_H18f zenon_H173 zenon_H7a zenon_H189 zenon_H133 zenon_H81 zenon_H18b. % 18.52/18.71 apply (zenon_or_s _ _ zenon_H6a); [ zenon_intro zenon_H48 | zenon_intro zenon_H6b ]. % 18.52/18.71 exact (zenon_H75 zenon_H48). % 18.52/18.71 apply (zenon_or_s _ _ zenon_H6b); [ zenon_intro zenon_H2a | zenon_intro zenon_H6c ]. % 18.52/18.71 apply (zenon_L190_); trivial. % 18.52/18.71 apply (zenon_or_s _ _ zenon_H6c); [ zenon_intro zenon_H2c | zenon_intro zenon_H61 ]. % 18.52/18.71 exact (zenon_H81 zenon_H2c). % 18.52/18.71 exact (zenon_H18b zenon_H61). % 18.52/18.71 (* end of lemma zenon_L198_ *) % 18.52/18.71 assert (zenon_L199_ : (~((op (op (e3) (e3)) (e3)) = (op (e0) (e3)))) -> ((op (e3) (e3)) = (e0)) -> False). % 18.52/18.71 do 0 intro. intros zenon_H1d2 zenon_H60. % 18.52/18.71 cut (((e3) = (e3))); [idtac | apply NNPP; zenon_intro zenon_H85]. % 18.52/18.71 cut (((op (e3) (e3)) = (e0))); [idtac | apply NNPP; zenon_intro zenon_H1ae]. % 18.52/18.71 congruence. % 18.52/18.71 exact (zenon_H1ae zenon_H60). % 18.52/18.71 apply zenon_H85. apply refl_equal. % 18.52/18.71 (* end of lemma zenon_L199_ *) % 18.52/18.71 assert (zenon_L200_ : ((op (e0) (e3)) = (e1)) -> ((op (e3) (e3)) = (e0)) -> (~((e1) = (op (op (e3) (e3)) (e3)))) -> False). % 18.52/18.71 do 0 intro. intros zenon_Hc3 zenon_H60 zenon_Hf8. % 18.52/18.71 elim (classic ((op (op (e3) (e3)) (e3)) = (op (op (e3) (e3)) (e3)))); [ zenon_intro zenon_Hc9 | zenon_intro zenon_Hca ]. % 18.52/18.71 cut (((op (op (e3) (e3)) (e3)) = (op (op (e3) (e3)) (e3))) = ((e1) = (op (op (e3) (e3)) (e3)))). % 18.52/18.71 intro zenon_D_pnotp. % 18.52/18.71 apply zenon_Hf8. % 18.52/18.71 rewrite <- zenon_D_pnotp. % 18.52/18.71 exact zenon_Hc9. % 18.52/18.71 cut (((op (op (e3) (e3)) (e3)) = (op (op (e3) (e3)) (e3)))); [idtac | apply NNPP; zenon_intro zenon_Hca]. % 18.52/18.71 cut (((op (op (e3) (e3)) (e3)) = (e1))); [idtac | apply NNPP; zenon_intro zenon_Hf9]. % 18.52/18.71 congruence. % 18.52/18.71 cut (((op (e0) (e3)) = (e1)) = ((op (op (e3) (e3)) (e3)) = (e1))). % 18.52/18.71 intro zenon_D_pnotp. % 18.52/18.71 apply zenon_Hf9. % 18.52/18.71 rewrite <- zenon_D_pnotp. % 18.52/18.71 exact zenon_Hc3. % 18.52/18.71 cut (((e1) = (e1))); [idtac | apply NNPP; zenon_intro zenon_H79]. % 18.52/18.71 cut (((op (e0) (e3)) = (op (op (e3) (e3)) (e3)))); [idtac | apply NNPP; zenon_intro zenon_H1d3]. % 18.52/18.71 congruence. % 18.52/18.71 elim (classic ((op (op (e3) (e3)) (e3)) = (op (op (e3) (e3)) (e3)))); [ zenon_intro zenon_Hc9 | zenon_intro zenon_Hca ]. % 18.52/18.71 cut (((op (op (e3) (e3)) (e3)) = (op (op (e3) (e3)) (e3))) = ((op (e0) (e3)) = (op (op (e3) (e3)) (e3)))). % 18.52/18.71 intro zenon_D_pnotp. % 18.52/18.71 apply zenon_H1d3. % 18.52/18.71 rewrite <- zenon_D_pnotp. % 18.52/18.71 exact zenon_Hc9. % 18.52/18.71 cut (((op (op (e3) (e3)) (e3)) = (op (op (e3) (e3)) (e3)))); [idtac | apply NNPP; zenon_intro zenon_Hca]. % 18.52/18.71 cut (((op (op (e3) (e3)) (e3)) = (op (e0) (e3)))); [idtac | apply NNPP; zenon_intro zenon_H1d2]. % 18.52/18.71 congruence. % 18.52/18.71 apply (zenon_L199_); trivial. % 18.52/18.71 apply zenon_Hca. apply refl_equal. % 18.52/18.71 apply zenon_Hca. apply refl_equal. % 18.52/18.71 apply zenon_H79. apply refl_equal. % 18.52/18.71 apply zenon_Hca. apply refl_equal. % 18.52/18.71 apply zenon_Hca. apply refl_equal. % 18.52/18.71 (* end of lemma zenon_L200_ *) % 18.52/18.71 assert (zenon_L201_ : ((op (e1) (e3)) = (e2)) -> ((op (e0) (e3)) = (e1)) -> ((op (e3) (e3)) = (e0)) -> False). % 18.52/18.71 do 0 intro. intros zenon_Hd7 zenon_Hc3 zenon_H60. % 18.52/18.71 apply (zenon_notand_s _ _ ax29); [ zenon_intro zenon_Hcf | zenon_intro zenon_H1d4 ]. % 18.52/18.71 elim (classic ((op (op (op (e3) (e3)) (e3)) (e3)) = (op (op (op (e3) (e3)) (e3)) (e3)))); [ zenon_intro zenon_Hd0 | zenon_intro zenon_Hd1 ]. % 18.52/18.71 cut (((op (op (op (e3) (e3)) (e3)) (e3)) = (op (op (op (e3) (e3)) (e3)) (e3))) = ((e2) = (op (op (op (e3) (e3)) (e3)) (e3)))). % 18.52/18.71 intro zenon_D_pnotp. % 18.52/18.71 apply zenon_Hcf. % 18.52/18.71 rewrite <- zenon_D_pnotp. % 18.52/18.71 exact zenon_Hd0. % 18.52/18.71 cut (((op (op (op (e3) (e3)) (e3)) (e3)) = (op (op (op (e3) (e3)) (e3)) (e3)))); [idtac | apply NNPP; zenon_intro zenon_Hd1]. % 18.52/18.71 cut (((op (op (op (e3) (e3)) (e3)) (e3)) = (e2))); [idtac | apply NNPP; zenon_intro zenon_Hd2]. % 18.52/18.71 congruence. % 18.52/18.71 cut (((op (e1) (e3)) = (e2)) = ((op (op (op (e3) (e3)) (e3)) (e3)) = (e2))). % 18.52/18.71 intro zenon_D_pnotp. % 18.52/18.71 apply zenon_Hd2. % 18.52/18.71 rewrite <- zenon_D_pnotp. % 18.52/18.71 exact zenon_Hd7. % 18.52/18.71 cut (((e2) = (e2))); [idtac | apply NNPP; zenon_intro zenon_H7e]. % 18.52/18.71 cut (((op (e1) (e3)) = (op (op (op (e3) (e3)) (e3)) (e3)))); [idtac | apply NNPP; zenon_intro zenon_Hfe]. % 18.52/18.71 congruence. % 18.52/18.71 elim (classic ((op (op (op (e3) (e3)) (e3)) (e3)) = (op (op (op (e3) (e3)) (e3)) (e3)))); [ zenon_intro zenon_Hd0 | zenon_intro zenon_Hd1 ]. % 18.52/18.71 cut (((op (op (op (e3) (e3)) (e3)) (e3)) = (op (op (op (e3) (e3)) (e3)) (e3))) = ((op (e1) (e3)) = (op (op (op (e3) (e3)) (e3)) (e3)))). % 18.52/18.71 intro zenon_D_pnotp. % 18.52/18.71 apply zenon_Hfe. % 18.52/18.71 rewrite <- zenon_D_pnotp. % 18.52/18.71 exact zenon_Hd0. % 18.52/18.71 cut (((op (op (op (e3) (e3)) (e3)) (e3)) = (op (op (op (e3) (e3)) (e3)) (e3)))); [idtac | apply NNPP; zenon_intro zenon_Hd1]. % 18.52/18.71 cut (((op (op (op (e3) (e3)) (e3)) (e3)) = (op (e1) (e3)))); [idtac | apply NNPP; zenon_intro zenon_Hff]. % 18.52/18.71 congruence. % 18.52/18.71 cut (((e3) = (e3))); [idtac | apply NNPP; zenon_intro zenon_H85]. % 18.52/18.71 cut (((op (op (e3) (e3)) (e3)) = (e1))); [idtac | apply NNPP; zenon_intro zenon_Hf9]. % 18.52/18.71 congruence. % 18.52/18.71 cut (((op (e0) (e3)) = (e1)) = ((op (op (e3) (e3)) (e3)) = (e1))). % 18.52/18.71 intro zenon_D_pnotp. % 18.52/18.71 apply zenon_Hf9. % 18.52/18.71 rewrite <- zenon_D_pnotp. % 18.52/18.71 exact zenon_Hc3. % 18.52/18.71 cut (((e1) = (e1))); [idtac | apply NNPP; zenon_intro zenon_H79]. % 18.52/18.71 cut (((op (e0) (e3)) = (op (op (e3) (e3)) (e3)))); [idtac | apply NNPP; zenon_intro zenon_H1d3]. % 18.52/18.71 congruence. % 18.52/18.71 elim (classic ((op (op (e3) (e3)) (e3)) = (op (op (e3) (e3)) (e3)))); [ zenon_intro zenon_Hc9 | zenon_intro zenon_Hca ]. % 18.52/18.71 cut (((op (op (e3) (e3)) (e3)) = (op (op (e3) (e3)) (e3))) = ((op (e0) (e3)) = (op (op (e3) (e3)) (e3)))). % 18.52/18.71 intro zenon_D_pnotp. % 18.52/18.71 apply zenon_H1d3. % 18.52/18.71 rewrite <- zenon_D_pnotp. % 18.52/18.71 exact zenon_Hc9. % 18.52/18.71 cut (((op (op (e3) (e3)) (e3)) = (op (op (e3) (e3)) (e3)))); [idtac | apply NNPP; zenon_intro zenon_Hca]. % 18.52/18.71 cut (((op (op (e3) (e3)) (e3)) = (op (e0) (e3)))); [idtac | apply NNPP; zenon_intro zenon_H1d2]. % 18.52/18.71 congruence. % 18.52/18.71 apply (zenon_L199_); trivial. % 18.52/18.71 apply zenon_Hca. apply refl_equal. % 18.52/18.71 apply zenon_Hca. apply refl_equal. % 18.52/18.71 apply zenon_H79. apply refl_equal. % 18.52/18.71 apply zenon_H85. apply refl_equal. % 18.52/18.71 apply zenon_Hd1. apply refl_equal. % 18.52/18.71 apply zenon_Hd1. apply refl_equal. % 18.52/18.71 apply zenon_H7e. apply refl_equal. % 18.52/18.71 apply zenon_Hd1. apply refl_equal. % 18.52/18.71 apply zenon_Hd1. apply refl_equal. % 18.52/18.71 apply (zenon_notand_s _ _ zenon_H1d4); [ zenon_intro zenon_Hf8 | zenon_intro zenon_H188 ]. % 18.52/18.71 apply (zenon_L200_); trivial. % 18.52/18.71 apply zenon_H188. apply sym_equal. exact zenon_H60. % 18.52/18.71 (* end of lemma zenon_L201_ *) % 18.52/18.71 assert (zenon_L202_ : (((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 (e3) (e3)) = (e0)) -> ((op (e0) (e3)) = (e1)) -> (~((op (e1) (e3)) = (op (e2) (e3)))) -> ((op (e2) (e3)) = (e3)) -> False). % 18.52/18.71 do 0 intro. intros zenon_Hdf zenon_Hd5 zenon_H124 zenon_Hf0 zenon_H60 zenon_Hc3 zenon_Hdb zenon_Hdd. % 18.52/18.71 apply (zenon_or_s _ _ zenon_Hdf); [ zenon_intro zenon_H1f | zenon_intro zenon_He0 ]. % 18.52/18.71 apply (zenon_L136_); trivial. % 18.52/18.71 apply (zenon_or_s _ _ zenon_He0); [ zenon_intro zenon_Hd6 | zenon_intro zenon_He1 ]. % 18.52/18.71 apply (zenon_L78_); trivial. % 18.52/18.71 apply (zenon_or_s _ _ zenon_He1); [ zenon_intro zenon_Hd7 | zenon_intro zenon_Hdc ]. % 18.52/18.71 apply (zenon_L201_); trivial. % 18.52/18.71 apply (zenon_L52_); trivial. % 18.52/18.71 (* end of lemma zenon_L202_ *) % 18.52/18.71 assert (zenon_L203_ : (((op (e3) (e0)) = (e2))\/(((op (e3) (e1)) = (e2))\/(((op (e3) (e2)) = (e2))\/((op (e3) (e3)) = (e2))))) -> (~((op (e3) (e3)) = (e3))) -> ((op (e0) (e2)) = (e3)) -> (~((op (e1) (e1)) = (op (e3) (e1)))) -> ((op (e1) (e1)) = (e3)) -> (~((e2) = (e3))) -> (((op (e3) (e0)) = (e3))\/(((op (e3) (e1)) = (e3))\/(((op (e3) (e2)) = (e3))\/((op (e3) (e3)) = (e3))))) -> (~((e1) = (e2))) -> ((op (e3) (e1)) = (e1)) -> ((op (e0) (e2)) = (e2)) -> (~((op (e0) (e2)) = (op (e3) (e2)))) -> (((op (e0) (e3)) = (e0))\/(((op (e0) (e3)) = (e1))\/(((op (e0) (e3)) = (e2))\/((op (e0) (e3)) = (e3))))) -> (~((op (e0) (e3)) = (e0))) -> (~((op (e1) (e3)) = (op (e2) (e3)))) -> ((op (e3) (e3)) = (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))))) -> (~((op (e0) (e3)) = (op (e3) (e3)))) -> (~((op (e0) (e3)) = (op (e2) (e3)))) -> ((op (e2) (e3)) = (e3)) -> False). % 18.52/18.71 do 0 intro. intros zenon_H153 zenon_H102 zenon_Ha9 zenon_H160 zenon_H13f zenon_H12b zenon_H165 zenon_H7c zenon_Hae zenon_H150 zenon_H14f zenon_He4 zenon_H76 zenon_Hdb zenon_H60 zenon_Hf0 zenon_H124 zenon_Hd5 zenon_Hdf zenon_Hc2 zenon_He2 zenon_Hdd. % 18.52/18.71 apply (zenon_or_s _ _ zenon_H153); [ zenon_intro zenon_H148 | zenon_intro zenon_H154 ]. % 18.52/18.71 apply (zenon_L112_); trivial. % 18.52/18.71 apply (zenon_or_s _ _ zenon_H154); [ zenon_intro zenon_H14d | zenon_intro zenon_H155 ]. % 18.52/18.71 apply (zenon_L152_); trivial. % 18.52/18.71 apply (zenon_or_s _ _ zenon_H155); [ zenon_intro zenon_H151 | zenon_intro zenon_Hf6 ]. % 18.52/18.71 apply (zenon_L104_); trivial. % 18.52/18.71 apply (zenon_or_s _ _ zenon_He4); [ zenon_intro zenon_H1e | zenon_intro zenon_He5 ]. % 18.52/18.71 exact (zenon_H76 zenon_H1e). % 18.52/18.71 apply (zenon_or_s _ _ zenon_He5); [ zenon_intro zenon_Hc3 | zenon_intro zenon_He6 ]. % 18.52/18.71 apply (zenon_L202_); trivial. % 18.52/18.71 apply (zenon_or_s _ _ zenon_He6); [ zenon_intro zenon_Hcd | zenon_intro zenon_He3 ]. % 18.52/18.71 apply (zenon_L87_); trivial. % 18.52/18.71 apply (zenon_L54_); trivial. % 18.52/18.71 (* end of lemma zenon_L203_ *) % 18.52/18.71 assert (zenon_L204_ : ((op (e2) (e0)) = (e0)) -> ((op (e2) (e0)) = (e2)) -> (~((e0) = (e2))) -> False). % 18.52/18.71 do 0 intro. intros zenon_H34 zenon_Hee zenon_H149. % 18.52/18.71 elim (classic ((e2) = (e2))); [ zenon_intro zenon_H7d | zenon_intro zenon_H7e ]. % 18.52/18.71 cut (((e2) = (e2)) = ((e0) = (e2))). % 18.52/18.71 intro zenon_D_pnotp. % 18.52/18.71 apply zenon_H149. % 18.52/18.71 rewrite <- zenon_D_pnotp. % 18.52/18.71 exact zenon_H7d. % 18.52/18.71 cut (((e2) = (e2))); [idtac | apply NNPP; zenon_intro zenon_H7e]. % 18.52/18.71 cut (((e2) = (e0))); [idtac | apply NNPP; zenon_intro zenon_H14a]. % 18.52/18.71 congruence. % 18.52/18.71 cut (((op (e2) (e0)) = (e0)) = ((e2) = (e0))). % 18.52/18.71 intro zenon_D_pnotp. % 18.52/18.71 apply zenon_H14a. % 18.52/18.71 rewrite <- zenon_D_pnotp. % 18.52/18.71 exact zenon_H34. % 18.52/18.71 cut (((e0) = (e0))); [idtac | apply NNPP; zenon_intro zenon_H82]. % 18.52/18.71 cut (((op (e2) (e0)) = (e2))); [idtac | apply NNPP; zenon_intro zenon_Hef]. % 18.52/18.71 congruence. % 18.52/18.71 exact (zenon_Hef zenon_Hee). % 18.52/18.71 apply zenon_H82. apply refl_equal. % 18.52/18.71 apply zenon_H7e. apply refl_equal. % 18.52/18.71 apply zenon_H7e. apply refl_equal. % 18.52/18.71 (* end of lemma zenon_L204_ *) % 18.52/18.71 assert (zenon_L205_ : (((op (e3) (e0)) = (e2))\/(((op (e3) (e1)) = (e2))\/(((op (e3) (e2)) = (e2))\/((op (e3) (e3)) = (e2))))) -> (~((e2) = (e3))) -> ((op (e3) (e0)) = (e3)) -> (~((e1) = (e2))) -> ((op (e3) (e1)) = (e1)) -> ((op (e0) (e2)) = (e2)) -> (~((op (e0) (e2)) = (op (e3) (e2)))) -> (~((op (e2) (e3)) = (op (e3) (e3)))) -> ((op (e2) (e3)) = (e2)) -> False). % 18.52/18.71 do 0 intro. intros zenon_H153 zenon_H12b zenon_H15e zenon_H7c zenon_Hae zenon_H150 zenon_H14f zenon_Hf3 zenon_H11d. % 18.52/18.71 apply (zenon_or_s _ _ zenon_H153); [ zenon_intro zenon_H148 | zenon_intro zenon_H154 ]. % 18.52/18.71 apply (zenon_L109_); trivial. % 18.52/18.71 apply (zenon_or_s _ _ zenon_H154); [ zenon_intro zenon_H14d | zenon_intro zenon_H155 ]. % 18.52/18.71 apply (zenon_L152_); trivial. % 18.52/18.71 apply (zenon_or_s _ _ zenon_H155); [ zenon_intro zenon_H151 | zenon_intro zenon_Hf6 ]. % 18.52/18.71 apply (zenon_L104_); trivial. % 18.52/18.71 apply (zenon_L97_); trivial. % 18.52/18.71 (* end of lemma zenon_L205_ *) % 18.52/18.71 assert (zenon_L206_ : (((op (e2) (e0)) = (e2))\/(((op (e2) (e1)) = (e2))\/(((op (e2) (e2)) = (e2))\/((op (e2) (e3)) = (e2))))) -> (~((e0) = (e2))) -> ((op (e2) (e0)) = (e0)) -> ((op (e0) (e1)) = (e2)) -> (~((op (e0) (e1)) = (op (e2) (e1)))) -> (~((op (e2) (e2)) = (e2))) -> (((op (e3) (e0)) = (e2))\/(((op (e3) (e1)) = (e2))\/(((op (e3) (e2)) = (e2))\/((op (e3) (e3)) = (e2))))) -> (~((e2) = (e3))) -> ((op (e3) (e0)) = (e3)) -> (~((e1) = (e2))) -> ((op (e3) (e1)) = (e1)) -> ((op (e0) (e2)) = (e2)) -> (~((op (e0) (e2)) = (op (e3) (e2)))) -> (~((op (e2) (e3)) = (op (e3) (e3)))) -> False). % 18.52/18.71 do 0 intro. intros zenon_H1d5 zenon_H149 zenon_H34 zenon_H10f zenon_H17e zenon_H173 zenon_H153 zenon_H12b zenon_H15e zenon_H7c zenon_Hae zenon_H150 zenon_H14f zenon_Hf3. % 18.52/18.71 apply (zenon_or_s _ _ zenon_H1d5); [ zenon_intro zenon_Hee | zenon_intro zenon_H1d6 ]. % 18.52/18.71 apply (zenon_L204_); trivial. % 18.52/18.71 apply (zenon_or_s _ _ zenon_H1d6); [ zenon_intro zenon_H1ca | zenon_intro zenon_H1d7 ]. % 18.52/18.71 apply (zenon_L191_); trivial. % 18.52/18.71 apply (zenon_or_s _ _ zenon_H1d7); [ zenon_intro zenon_H176 | zenon_intro zenon_H11d ]. % 18.52/18.71 exact (zenon_H173 zenon_H176). % 18.52/18.71 apply (zenon_L205_); trivial. % 18.52/18.71 (* end of lemma zenon_L206_ *) % 18.52/18.71 assert (zenon_L207_ : ((op (e2) (e1)) = (e2)) -> ((op (e2) (e1)) = (e3)) -> (~((e2) = (e3))) -> False). % 18.52/18.71 do 0 intro. intros zenon_H1ca zenon_Ha6 zenon_H12b. % 18.52/18.71 elim (classic ((e3) = (e3))); [ zenon_intro zenon_H96 | zenon_intro zenon_H85 ]. % 18.52/18.71 cut (((e3) = (e3)) = ((e2) = (e3))). % 18.52/18.71 intro zenon_D_pnotp. % 18.52/18.71 apply zenon_H12b. % 18.52/18.71 rewrite <- zenon_D_pnotp. % 18.52/18.71 exact zenon_H96. % 18.52/18.71 cut (((e3) = (e3))); [idtac | apply NNPP; zenon_intro zenon_H85]. % 18.52/18.71 cut (((e3) = (e2))); [idtac | apply NNPP; zenon_intro zenon_H12c]. % 18.52/18.71 congruence. % 18.52/18.71 cut (((op (e2) (e1)) = (e2)) = ((e3) = (e2))). % 18.52/18.71 intro zenon_D_pnotp. % 18.52/18.71 apply zenon_H12c. % 18.52/18.71 rewrite <- zenon_D_pnotp. % 18.52/18.71 exact zenon_H1ca. % 18.52/18.71 cut (((e2) = (e2))); [idtac | apply NNPP; zenon_intro zenon_H7e]. % 18.52/18.71 cut (((op (e2) (e1)) = (e3))); [idtac | apply NNPP; zenon_intro zenon_Ha7]. % 18.52/18.71 congruence. % 18.52/18.71 exact (zenon_Ha7 zenon_Ha6). % 18.52/18.71 apply zenon_H7e. apply refl_equal. % 18.52/18.71 apply zenon_H85. apply refl_equal. % 18.52/18.71 apply zenon_H85. apply refl_equal. % 18.52/18.71 (* end of lemma zenon_L207_ *) % 18.52/18.71 assert (zenon_L208_ : (((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)) = (e3)) -> (~((op (e2) (e2)) = (e2))) -> (((op (e3) (e0)) = (e2))\/(((op (e3) (e1)) = (e2))\/(((op (e3) (e2)) = (e2))\/((op (e3) (e3)) = (e2))))) -> (~((e2) = (e3))) -> ((op (e3) (e0)) = (e3)) -> (~((e1) = (e2))) -> ((op (e3) (e1)) = (e1)) -> ((op (e0) (e2)) = (e2)) -> (~((op (e0) (e2)) = (op (e3) (e2)))) -> (~((op (e2) (e3)) = (op (e3) (e3)))) -> False). % 18.52/18.71 do 0 intro. intros zenon_H1d5 zenon_H149 zenon_H34 zenon_Ha6 zenon_H173 zenon_H153 zenon_H12b zenon_H15e zenon_H7c zenon_Hae zenon_H150 zenon_H14f zenon_Hf3. % 18.52/18.71 apply (zenon_or_s _ _ zenon_H1d5); [ zenon_intro zenon_Hee | zenon_intro zenon_H1d6 ]. % 18.52/18.71 apply (zenon_L204_); trivial. % 18.52/18.71 apply (zenon_or_s _ _ zenon_H1d6); [ zenon_intro zenon_H1ca | zenon_intro zenon_H1d7 ]. % 18.52/18.71 apply (zenon_L207_); trivial. % 18.52/18.71 apply (zenon_or_s _ _ zenon_H1d7); [ zenon_intro zenon_H176 | zenon_intro zenon_H11d ]. % 18.52/18.71 exact (zenon_H173 zenon_H176). % 18.52/18.71 apply (zenon_L205_); trivial. % 18.52/18.71 (* end of lemma zenon_L208_ *) % 18.52/18.71 assert (zenon_L209_ : (((op (e0) (e1)) = (e3))\/(((op (e1) (e1)) = (e3))\/(((op (e2) (e1)) = (e3))\/((op (e3) (e1)) = (e3))))) -> (~((e0) = (e3))) -> ((op (e0) (e1)) = (e0)) -> ((op (e1) (e1)) = (e2)) -> (~((op (e2) (e3)) = (op (e3) (e3)))) -> (~((op (e0) (e2)) = (op (e3) (e2)))) -> ((op (e0) (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 (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))))) -> ((op (e3) (e0)) = (e3)) -> (~((op (e3) (e0)) = (op (e3) (e1)))) -> False). % 18.52/18.71 do 0 intro. intros zenon_H1a5 zenon_H9a zenon_H49 zenon_H110 zenon_Hf3 zenon_H14f zenon_H150 zenon_Hae zenon_H7c zenon_H12b zenon_H153 zenon_H173 zenon_H34 zenon_H149 zenon_H1d5 zenon_H15e zenon_H1cf. % 18.52/18.71 apply (zenon_or_s _ _ zenon_H1a5); [ zenon_intro zenon_H99 | zenon_intro zenon_H1a8 ]. % 18.52/18.71 apply (zenon_L36_); trivial. % 18.52/18.71 apply (zenon_or_s _ _ zenon_H1a8); [ zenon_intro zenon_H13f | zenon_intro zenon_H1a9 ]. % 18.52/18.71 apply (zenon_L166_); trivial. % 18.52/18.71 apply (zenon_or_s _ _ zenon_H1a9); [ zenon_intro zenon_Ha6 | zenon_intro zenon_H161 ]. % 18.52/18.71 apply (zenon_L208_); trivial. % 18.52/18.71 apply (zenon_L193_); trivial. % 18.52/18.71 (* end of lemma zenon_L209_ *) % 18.52/18.71 assert (zenon_L210_ : (((op (e0) (e1)) = (e1))\/(((op (e1) (e1)) = (e1))\/(((op (e2) (e1)) = (e1))\/((op (e3) (e1)) = (e1))))) -> (~((e0) = (e1))) -> (~((op (e1) (e1)) = (e1))) -> (~((e1) = (e3))) -> (~((op (e1) (e2)) = (op (e3) (e2)))) -> (((op (e3) (e2)) = (e0))\/(((op (e3) (e2)) = (e1))\/(((op (e3) (e2)) = (e2))\/((op (e3) (e2)) = (e3))))) -> (((op (e3) (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))))) -> (~((op (e0) (e0)) = (op (e0) (e3)))) -> (((op (e0) (e2)) = (e1))\/(((op (e1) (e2)) = (e1))\/(((op (e2) (e2)) = (e1))\/((op (e3) (e2)) = (e1))))) -> (~((op (e2) (e1)) = (op (e2) (e3)))) -> (~((op (e3) (e0)) = (op (e3) (e3)))) -> (~((op (e0) (e2)) = (e0))) -> (((op (e0) (e2)) = (e0))\/(((op (e1) (e2)) = (e0))\/(((op (e2) (e2)) = (e0))\/((op (e3) (e2)) = (e0))))) -> ((op (e1) (e2)) = (e0)) -> (~((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) (e3)))) -> (((op (e0) (e1)) = (e2))\/(((op (e1) (e1)) = (e2))\/(((op (e2) (e1)) = (e2))\/((op (e3) (e1)) = (e2))))) -> (~((op (e0) (e1)) = (op (e2) (e1)))) -> (~((op (e3) (e0)) = (op (e3) (e1)))) -> ((op (e3) (e0)) = (e3)) -> (~((e2) = (e3))) -> (((op (e2) (e0)) = (e3))\/(((op (e2) (e1)) = (e3))\/(((op (e2) (e2)) = (e3))\/((op (e2) (e3)) = (e3))))) -> ((op (e0) (e0)) = (e1)) -> ((op (e1) (e0)) = (e2)) -> (~((op (e2) (e3)) = (op (e3) (e3)))) -> (~((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))))) -> (~((op (e0) (e2)) = (op (e2) (e2)))) -> (((op (e3) (e0)) = (e0))\/(((op (e3) (e1)) = (e0))\/(((op (e3) (e2)) = (e0))\/((op (e3) (e3)) = (e0))))) -> (~((op (e3) (e0)) = (e0))) -> (~((op (e3) (e1)) = (e0))) -> (~((op (e3) (e2)) = (e0))) -> (((op (e3) (e0)) = (e2))\/(((op (e3) (e1)) = (e2))\/(((op (e3) (e2)) = (e2))\/((op (e3) (e3)) = (e2))))) -> (~((op (e3) (e3)) = (e3))) -> ((op (e0) (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)) = (e2)) -> (~((op (e0) (e2)) = (op (e3) (e2)))) -> (((op (e0) (e3)) = (e0))\/(((op (e0) (e3)) = (e1))\/(((op (e0) (e3)) = (e2))\/((op (e0) (e3)) = (e3))))) -> (~((op (e0) (e3)) = (e0))) -> (~((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 (e0) (e3)) = (op (e3) (e3)))) -> (~((op (e0) (e3)) = (op (e2) (e3)))) -> ((op (e0) (e1)) = (e0)) -> (~((e0) = (e3))) -> (((op (e0) (e1)) = (e3))\/(((op (e1) (e1)) = (e3))\/(((op (e2) (e1)) = (e3))\/((op (e3) (e1)) = (e3))))) -> (~((e1) = (e2))) -> False). % 18.52/18.71 do 0 intro. intros zenon_H109 zenon_Ha1 zenon_H10a zenon_H95 zenon_H115 zenon_H191 zenon_He8 zenon_H81 zenon_H133 zenon_H189 zenon_H139 zenon_H1c7 zenon_H71 zenon_H75 zenon_H6a zenon_H2a zenon_H18f zenon_H1c4 zenon_Hd8 zenon_H1d8 zenon_H17e zenon_H1cf zenon_H15e zenon_H12b zenon_He7 zenon_H7a zenon_H86 zenon_Hf3 zenon_H173 zenon_H34 zenon_H149 zenon_H1d5 zenon_Ha8 zenon_H1ac zenon_H40 zenon_H1ad zenon_H18b zenon_H153 zenon_H102 zenon_Ha9 zenon_H160 zenon_H165 zenon_H150 zenon_H14f zenon_He4 zenon_H76 zenon_Hdb zenon_Hf0 zenon_H124 zenon_Hd5 zenon_Hdf zenon_Hc2 zenon_He2 zenon_H49 zenon_H9a zenon_H1a5 zenon_H7c. % 18.52/18.71 apply (zenon_or_s _ _ zenon_H109); [ zenon_intro zenon_Ha0 | zenon_intro zenon_H10b ]. % 18.52/18.71 apply (zenon_L38_); trivial. % 18.52/18.71 apply (zenon_or_s _ _ zenon_H10b); [ zenon_intro zenon_H10d | zenon_intro zenon_H10c ]. % 18.52/18.71 exact (zenon_H10a zenon_H10d). % 18.52/18.71 apply (zenon_or_s _ _ zenon_H10c); [ zenon_intro zenon_Ha5 | zenon_intro zenon_Hae ]. % 18.52/18.71 apply (zenon_or_s _ _ zenon_H1a5); [ zenon_intro zenon_H99 | zenon_intro zenon_H1a8 ]. % 18.52/18.71 apply (zenon_L36_); trivial. % 18.52/18.71 apply (zenon_or_s _ _ zenon_H1a8); [ zenon_intro zenon_H13f | zenon_intro zenon_H1a9 ]. % 18.52/18.71 apply (zenon_or_s _ _ zenon_He7); [ zenon_intro zenon_H3b | zenon_intro zenon_He9 ]. % 18.52/18.71 apply (zenon_L33_); trivial. % 18.52/18.71 apply (zenon_or_s _ _ zenon_He9); [ zenon_intro zenon_Ha6 | zenon_intro zenon_Hea ]. % 18.52/18.71 apply (zenon_L39_); trivial. % 18.52/18.71 apply (zenon_or_s _ _ zenon_Hea); [ zenon_intro zenon_Haa | zenon_intro zenon_Hdd ]. % 18.52/18.71 apply (zenon_L181_); trivial. % 18.52/18.71 apply (zenon_or_s _ _ zenon_H1ac); [ zenon_intro zenon_H44 | zenon_intro zenon_H1af ]. % 18.52/18.71 exact (zenon_H40 zenon_H44). % 18.52/18.71 apply (zenon_or_s _ _ zenon_H1af); [ zenon_intro zenon_H1b1 | zenon_intro zenon_H1b0 ]. % 18.52/18.71 exact (zenon_H1ad zenon_H1b1). % 18.52/18.71 apply (zenon_or_s _ _ zenon_H1b0); [ zenon_intro zenon_H61 | zenon_intro zenon_H60 ]. % 18.52/18.71 exact (zenon_H18b zenon_H61). % 18.52/18.71 apply (zenon_or_s _ _ zenon_He8); [ zenon_intro zenon_Hac | zenon_intro zenon_Heb ]. % 18.52/18.71 apply (zenon_L198_); trivial. % 18.52/18.71 apply (zenon_or_s _ _ zenon_Heb); [ zenon_intro zenon_Hae | zenon_intro zenon_Hec ]. % 18.52/18.71 apply (zenon_L203_); trivial. % 18.52/18.71 apply (zenon_or_s _ _ zenon_Hec); [ zenon_intro zenon_Hba | zenon_intro zenon_Hc4 ]. % 18.52/18.71 apply (zenon_L186_); trivial. % 18.52/18.71 apply (zenon_L55_); trivial. % 18.52/18.71 apply (zenon_or_s _ _ zenon_H1a9); [ zenon_intro zenon_Ha6 | zenon_intro zenon_H161 ]. % 18.52/18.71 apply (zenon_L39_); trivial. % 18.52/18.71 apply (zenon_L193_); trivial. % 18.52/18.71 apply (zenon_or_s _ _ zenon_H1d8); [ zenon_intro zenon_H10f | zenon_intro zenon_H1d9 ]. % 18.52/18.71 apply (zenon_L206_); trivial. % 18.52/18.71 apply (zenon_or_s _ _ zenon_H1d9); [ zenon_intro zenon_H110 | zenon_intro zenon_H1da ]. % 18.52/18.71 apply (zenon_L209_); trivial. % 18.52/18.71 apply (zenon_or_s _ _ zenon_H1da); [ zenon_intro zenon_H1ca | zenon_intro zenon_H14d ]. % 18.52/18.71 apply (zenon_or_s _ _ zenon_H1a5); [ zenon_intro zenon_H99 | zenon_intro zenon_H1a8 ]. % 18.52/18.71 apply (zenon_L36_); trivial. % 18.52/18.71 apply (zenon_or_s _ _ zenon_H1a8); [ zenon_intro zenon_H13f | zenon_intro zenon_H1a9 ]. % 18.52/18.71 apply (zenon_or_s _ _ zenon_He7); [ zenon_intro zenon_H3b | zenon_intro zenon_He9 ]. % 18.52/18.71 apply (zenon_L33_); trivial. % 18.52/18.71 apply (zenon_or_s _ _ zenon_He9); [ zenon_intro zenon_Ha6 | zenon_intro zenon_Hea ]. % 18.52/18.71 apply (zenon_L208_); trivial. % 18.52/18.71 apply (zenon_or_s _ _ zenon_Hea); [ zenon_intro zenon_Haa | zenon_intro zenon_Hdd ]. % 18.52/18.71 apply (zenon_L40_); trivial. % 18.52/18.71 apply (zenon_or_s _ _ zenon_H1ac); [ zenon_intro zenon_H44 | zenon_intro zenon_H1af ]. % 18.52/18.71 exact (zenon_H40 zenon_H44). % 18.52/18.71 apply (zenon_or_s _ _ zenon_H1af); [ zenon_intro zenon_H1b1 | zenon_intro zenon_H1b0 ]. % 18.52/18.71 exact (zenon_H1ad zenon_H1b1). % 18.52/18.71 apply (zenon_or_s _ _ zenon_H1b0); [ zenon_intro zenon_H61 | zenon_intro zenon_H60 ]. % 18.52/18.71 exact (zenon_H18b zenon_H61). % 18.52/18.71 apply (zenon_L203_); trivial. % 18.52/18.71 apply (zenon_or_s _ _ zenon_H1a9); [ zenon_intro zenon_Ha6 | zenon_intro zenon_H161 ]. % 18.52/18.71 apply (zenon_L207_); trivial. % 18.52/18.71 apply (zenon_L193_); trivial. % 18.52/18.71 apply (zenon_L152_); trivial. % 18.52/18.71 (* end of lemma zenon_L210_ *) % 18.52/18.71 assert (zenon_L211_ : (((op (e2) (e0)) = (e3))\/(((op (e2) (e1)) = (e3))\/(((op (e2) (e2)) = (e3))\/((op (e2) (e3)) = (e3))))) -> ((op (e0) (e0)) = (e1)) -> ((op (e1) (e0)) = (e2)) -> (~((e1) = (e3))) -> ((op (e2) (e1)) = (e1)) -> (~((op (e2) (e2)) = (op (e3) (e2)))) -> (~((op (e0) (e2)) = (op (e3) (e2)))) -> ((op (e0) (e2)) = (e2)) -> ((op (e1) (e2)) = (e0)) -> (~((op (e1) (e2)) = (op (e3) (e2)))) -> (((op (e3) (e2)) = (e0))\/(((op (e3) (e2)) = (e1))\/(((op (e3) (e2)) = (e2))\/((op (e3) (e2)) = (e3))))) -> (~((op (e0) (e3)) = (op (e2) (e3)))) -> ((op (e0) (e3)) = (e3)) -> False). % 18.52/18.71 do 0 intro. intros zenon_He7 zenon_H7a zenon_H86 zenon_H95 zenon_Ha5 zenon_H18f zenon_H14f zenon_H150 zenon_H2a zenon_H115 zenon_H191 zenon_He2 zenon_He3. % 18.52/18.71 apply (zenon_or_s _ _ zenon_He7); [ zenon_intro zenon_H3b | zenon_intro zenon_He9 ]. % 18.52/18.71 apply (zenon_L33_); trivial. % 18.52/18.71 apply (zenon_or_s _ _ zenon_He9); [ zenon_intro zenon_Ha6 | zenon_intro zenon_Hea ]. % 18.52/18.71 apply (zenon_L39_); trivial. % 18.52/18.71 apply (zenon_or_s _ _ zenon_Hea); [ zenon_intro zenon_Haa | zenon_intro zenon_Hdd ]. % 18.52/18.71 apply (zenon_L181_); trivial. % 18.52/18.71 apply (zenon_L54_); trivial. % 18.52/18.71 (* end of lemma zenon_L211_ *) % 18.52/18.71 assert (zenon_L212_ : (((op (e2) (e0)) = (e3))\/(((op (e2) (e1)) = (e3))\/(((op (e2) (e2)) = (e3))\/((op (e2) (e3)) = (e3))))) -> ((op (e0) (e0)) = (e1)) -> ((op (e1) (e0)) = (e2)) -> (~((e2) = (e3))) -> ((op (e2) (e1)) = (e2)) -> (~((op (e2) (e2)) = (op (e3) (e2)))) -> (~((op (e0) (e2)) = (op (e3) (e2)))) -> ((op (e0) (e2)) = (e2)) -> ((op (e1) (e2)) = (e0)) -> (~((op (e1) (e2)) = (op (e3) (e2)))) -> (((op (e3) (e2)) = (e0))\/(((op (e3) (e2)) = (e1))\/(((op (e3) (e2)) = (e2))\/((op (e3) (e2)) = (e3))))) -> (~((op (e0) (e3)) = (op (e2) (e3)))) -> ((op (e0) (e3)) = (e3)) -> False). % 18.52/18.71 do 0 intro. intros zenon_He7 zenon_H7a zenon_H86 zenon_H12b zenon_H1ca zenon_H18f zenon_H14f zenon_H150 zenon_H2a zenon_H115 zenon_H191 zenon_He2 zenon_He3. % 18.52/18.71 apply (zenon_or_s _ _ zenon_He7); [ zenon_intro zenon_H3b | zenon_intro zenon_He9 ]. % 18.52/18.71 apply (zenon_L33_); trivial. % 18.52/18.71 apply (zenon_or_s _ _ zenon_He9); [ zenon_intro zenon_Ha6 | zenon_intro zenon_Hea ]. % 18.52/18.71 apply (zenon_L207_); trivial. % 18.52/18.71 apply (zenon_or_s _ _ zenon_Hea); [ zenon_intro zenon_Haa | zenon_intro zenon_Hdd ]. % 18.52/18.71 apply (zenon_L181_); trivial. % 18.52/18.71 apply (zenon_L54_); trivial. % 18.52/18.71 (* end of lemma zenon_L212_ *) % 18.52/18.71 assert (zenon_L213_ : (((op (e0) (e2)) = (e0))\/(((op (e1) (e2)) = (e0))\/(((op (e2) (e2)) = (e0))\/((op (e3) (e2)) = (e0))))) -> (~((op (e0) (e2)) = (e0))) -> ((op (e0) (e3)) = (e3)) -> (~((op (e0) (e3)) = (op (e2) (e3)))) -> (((op (e3) (e2)) = (e0))\/(((op (e3) (e2)) = (e1))\/(((op (e3) (e2)) = (e2))\/((op (e3) (e2)) = (e3))))) -> (~((op (e1) (e2)) = (op (e3) (e2)))) -> ((op (e0) (e2)) = (e2)) -> (~((op (e0) (e2)) = (op (e3) (e2)))) -> (~((op (e2) (e2)) = (op (e3) (e2)))) -> ((op (e2) (e1)) = (e1)) -> (~((e1) = (e3))) -> ((op (e1) (e0)) = (e2)) -> ((op (e0) (e0)) = (e1)) -> (((op (e2) (e0)) = (e3))\/(((op (e2) (e1)) = (e3))\/(((op (e2) (e2)) = (e3))\/((op (e2) (e3)) = (e3))))) -> (~((op (e2) (e2)) = (e0))) -> (~((op (e3) (e2)) = (e0))) -> False). % 18.52/18.71 do 0 intro. intros zenon_H6a zenon_H75 zenon_He3 zenon_He2 zenon_H191 zenon_H115 zenon_H150 zenon_H14f zenon_H18f zenon_Ha5 zenon_H95 zenon_H86 zenon_H7a zenon_He7 zenon_H81 zenon_H18b. % 18.52/18.71 apply (zenon_or_s _ _ zenon_H6a); [ zenon_intro zenon_H48 | zenon_intro zenon_H6b ]. % 18.52/18.71 exact (zenon_H75 zenon_H48). % 18.52/18.71 apply (zenon_or_s _ _ zenon_H6b); [ zenon_intro zenon_H2a | zenon_intro zenon_H6c ]. % 18.52/18.71 apply (zenon_L211_); trivial. % 18.52/18.71 apply (zenon_or_s _ _ zenon_H6c); [ zenon_intro zenon_H2c | zenon_intro zenon_H61 ]. % 18.52/18.71 exact (zenon_H81 zenon_H2c). % 18.52/18.71 exact (zenon_H18b zenon_H61). % 18.52/18.71 (* end of lemma zenon_L213_ *) % 18.52/18.71 assert (zenon_L214_ : ((op (e2) (e0)) = (e0)) -> ((op (e2) (e0)) = (e1)) -> (~((e0) = (e1))) -> False). % 18.52/18.71 do 0 intro. intros zenon_H34 zenon_Hed zenon_Ha1. % 18.52/18.71 elim (classic ((e1) = (e1))); [ zenon_intro zenon_Ha2 | zenon_intro zenon_H79 ]. % 18.52/18.71 cut (((e1) = (e1)) = ((e0) = (e1))). % 18.52/18.71 intro zenon_D_pnotp. % 18.52/18.71 apply zenon_Ha1. % 18.52/18.71 rewrite <- zenon_D_pnotp. % 18.52/18.71 exact zenon_Ha2. % 18.52/18.71 cut (((e1) = (e1))); [idtac | apply NNPP; zenon_intro zenon_H79]. % 18.52/18.71 cut (((e1) = (e0))); [idtac | apply NNPP; zenon_intro zenon_Ha3]. % 18.52/18.71 congruence. % 18.52/18.71 cut (((op (e2) (e0)) = (e0)) = ((e1) = (e0))). % 18.52/18.71 intro zenon_D_pnotp. % 18.52/18.71 apply zenon_Ha3. % 18.52/18.71 rewrite <- zenon_D_pnotp. % 18.52/18.71 exact zenon_H34. % 18.52/18.71 cut (((e0) = (e0))); [idtac | apply NNPP; zenon_intro zenon_H82]. % 18.52/18.71 cut (((op (e2) (e0)) = (e1))); [idtac | apply NNPP; zenon_intro zenon_H1db]. % 18.52/18.71 congruence. % 18.52/18.71 exact (zenon_H1db zenon_Hed). % 18.52/18.71 apply zenon_H82. apply refl_equal. % 18.52/18.71 apply zenon_H79. apply refl_equal. % 18.52/18.71 apply zenon_H79. apply refl_equal. % 18.52/18.71 (* end of lemma zenon_L214_ *) % 18.52/18.71 assert (zenon_L215_ : (((op (e0) (e1)) = (e3))\/(((op (e1) (e1)) = (e3))\/(((op (e2) (e1)) = (e3))\/((op (e3) (e1)) = (e3))))) -> (~((e0) = (e3))) -> ((op (e0) (e1)) = (e0)) -> (~((e2) = (e3))) -> ((op (e1) (e1)) = (e2)) -> (~((e1) = (e3))) -> ((op (e2) (e1)) = (e1)) -> ((op (e3) (e0)) = (e3)) -> (~((op (e3) (e0)) = (op (e3) (e1)))) -> False). % 18.52/18.71 do 0 intro. intros zenon_H1a5 zenon_H9a zenon_H49 zenon_H12b zenon_H110 zenon_H95 zenon_Ha5 zenon_H15e zenon_H1cf. % 18.52/18.71 apply (zenon_or_s _ _ zenon_H1a5); [ zenon_intro zenon_H99 | zenon_intro zenon_H1a8 ]. % 18.52/18.71 apply (zenon_L36_); trivial. % 18.52/18.71 apply (zenon_or_s _ _ zenon_H1a8); [ zenon_intro zenon_H13f | zenon_intro zenon_H1a9 ]. % 18.52/18.71 apply (zenon_L166_); trivial. % 18.52/18.71 apply (zenon_or_s _ _ zenon_H1a9); [ zenon_intro zenon_Ha6 | zenon_intro zenon_H161 ]. % 18.52/18.71 apply (zenon_L39_); trivial. % 18.52/18.71 apply (zenon_L193_); trivial. % 18.52/18.71 (* end of lemma zenon_L215_ *) % 18.52/18.71 assert (zenon_L216_ : (((op (e1) (e0)) = (e3))\/(((op (e1) (e1)) = (e3))\/(((op (e1) (e2)) = (e3))\/((op (e1) (e3)) = (e3))))) -> ((op (e0) (e0)) = (e1)) -> ((op (e3) (e0)) = (e2)) -> (~((e2) = (e3))) -> ((op (e1) (e1)) = (e2)) -> (~((e1) = (e3))) -> ((op (e1) (e2)) = (e1)) -> (~((op (e0) (e3)) = (op (e1) (e3)))) -> ((op (e0) (e3)) = (e3)) -> False). % 18.52/18.71 do 0 intro. intros zenon_H16f zenon_H7a zenon_H148 zenon_H12b zenon_H110 zenon_H95 zenon_Hf0 zenon_H1d zenon_He3. % 18.52/18.71 apply (zenon_or_s _ _ zenon_H16f); [ zenon_intro zenon_H9e | zenon_intro zenon_H170 ]. % 18.52/18.71 apply (zenon_L107_); trivial. % 18.52/18.71 apply (zenon_or_s _ _ zenon_H170); [ zenon_intro zenon_H13f | zenon_intro zenon_H171 ]. % 18.52/18.71 apply (zenon_L166_); trivial. % 18.52/18.71 apply (zenon_or_s _ _ zenon_H171); [ zenon_intro zenon_H16c | zenon_intro zenon_Hdc ]. % 18.52/18.71 apply (zenon_L167_); trivial. % 18.52/18.71 apply (zenon_L117_); trivial. % 18.52/18.71 (* end of lemma zenon_L216_ *) % 18.52/18.71 assert (zenon_L217_ : (((op (e3) (e0)) = (e2))\/(((op (e3) (e1)) = (e2))\/(((op (e3) (e2)) = (e2))\/((op (e3) (e3)) = (e2))))) -> ((op (e0) (e3)) = (e3)) -> (~((op (e0) (e3)) = (op (e1) (e3)))) -> ((op (e1) (e2)) = (e1)) -> (~((e1) = (e3))) -> ((op (e1) (e1)) = (e2)) -> (~((e2) = (e3))) -> ((op (e0) (e0)) = (e1)) -> (((op (e1) (e0)) = (e3))\/(((op (e1) (e1)) = (e3))\/(((op (e1) (e2)) = (e3))\/((op (e1) (e3)) = (e3))))) -> (~((e1) = (e2))) -> ((op (e3) (e1)) = (e1)) -> ((op (e0) (e2)) = (e2)) -> (~((op (e0) (e2)) = (op (e3) (e2)))) -> ((op (e1) (e3)) = (e0)) -> ((op (e2) (e3)) = (e1)) -> False). % 18.52/18.71 do 0 intro. intros zenon_H153 zenon_He3 zenon_H1d zenon_Hf0 zenon_H95 zenon_H110 zenon_H12b zenon_H7a zenon_H16f zenon_H7c zenon_Hae zenon_H150 zenon_H14f zenon_H1f zenon_Hf4. % 18.52/18.71 apply (zenon_or_s _ _ zenon_H153); [ zenon_intro zenon_H148 | zenon_intro zenon_H154 ]. % 18.52/18.71 apply (zenon_L216_); trivial. % 18.52/18.71 apply (zenon_or_s _ _ zenon_H154); [ zenon_intro zenon_H14d | zenon_intro zenon_H155 ]. % 18.52/18.71 apply (zenon_L152_); trivial. % 18.52/18.71 apply (zenon_or_s _ _ zenon_H155); [ zenon_intro zenon_H151 | zenon_intro zenon_Hf6 ]. % 18.52/18.71 apply (zenon_L104_); trivial. % 18.52/18.71 apply (zenon_L63_); trivial. % 18.52/18.71 (* end of lemma zenon_L217_ *) % 18.52/18.71 assert (zenon_L218_ : (((op (e0) (e2)) = (e0))\/(((op (e1) (e2)) = (e0))\/(((op (e2) (e2)) = (e0))\/((op (e3) (e2)) = (e0))))) -> (~((op (e0) (e2)) = (e0))) -> ((op (e0) (e3)) = (e3)) -> (~((op (e0) (e3)) = (op (e2) (e3)))) -> (((op (e3) (e2)) = (e0))\/(((op (e3) (e2)) = (e1))\/(((op (e3) (e2)) = (e2))\/((op (e3) (e2)) = (e3))))) -> (~((op (e1) (e2)) = (op (e3) (e2)))) -> ((op (e0) (e2)) = (e2)) -> (~((op (e0) (e2)) = (op (e3) (e2)))) -> (~((op (e2) (e2)) = (op (e3) (e2)))) -> ((op (e2) (e1)) = (e2)) -> (~((e2) = (e3))) -> ((op (e1) (e0)) = (e2)) -> ((op (e0) (e0)) = (e1)) -> (((op (e2) (e0)) = (e3))\/(((op (e2) (e1)) = (e3))\/(((op (e2) (e2)) = (e3))\/((op (e2) (e3)) = (e3))))) -> (~((op (e2) (e2)) = (e0))) -> (~((op (e3) (e2)) = (e0))) -> False). % 18.52/18.71 do 0 intro. intros zenon_H6a zenon_H75 zenon_He3 zenon_He2 zenon_H191 zenon_H115 zenon_H150 zenon_H14f zenon_H18f zenon_H1ca zenon_H12b zenon_H86 zenon_H7a zenon_He7 zenon_H81 zenon_H18b. % 18.52/18.71 apply (zenon_or_s _ _ zenon_H6a); [ zenon_intro zenon_H48 | zenon_intro zenon_H6b ]. % 18.52/18.71 exact (zenon_H75 zenon_H48). % 18.52/18.71 apply (zenon_or_s _ _ zenon_H6b); [ zenon_intro zenon_H2a | zenon_intro zenon_H6c ]. % 18.52/18.71 apply (zenon_L212_); trivial. % 18.52/18.71 apply (zenon_or_s _ _ zenon_H6c); [ zenon_intro zenon_H2c | zenon_intro zenon_H61 ]. % 18.52/18.71 exact (zenon_H81 zenon_H2c). % 18.52/18.71 exact (zenon_H18b zenon_H61). % 18.52/18.71 (* end of lemma zenon_L218_ *) % 18.52/18.71 assert (zenon_L219_ : (~((op (e2) (e3)) = (op (e3) (e3)))) -> ((op (e2) (e3)) = (e0)) -> ((op (e3) (e3)) = (e0)) -> False). % 18.52/18.71 do 0 intro. intros zenon_Hf3 zenon_H37 zenon_H60. % 18.52/18.71 cut (((op (e2) (e3)) = (e0)) = ((op (e2) (e3)) = (op (e3) (e3)))). % 18.52/18.71 intro zenon_D_pnotp. % 18.52/18.71 apply zenon_Hf3. % 18.52/18.71 rewrite <- zenon_D_pnotp. % 18.52/18.71 exact zenon_H37. % 18.52/18.71 cut (((e0) = (op (e3) (e3)))); [idtac | apply NNPP; zenon_intro zenon_H188]. % 18.52/18.71 cut (((op (e2) (e3)) = (op (e2) (e3)))); [idtac | apply NNPP; zenon_intro zenon_H5d]. % 18.52/18.71 congruence. % 18.52/18.71 apply zenon_H5d. apply refl_equal. % 18.52/18.71 apply zenon_H188. apply sym_equal. exact zenon_H60. % 18.52/18.71 (* end of lemma zenon_L219_ *) % 18.52/18.71 assert (zenon_L220_ : (((op (e2) (e3)) = (e0))\/(((op (e2) (e3)) = (e1))\/(((op (e2) (e3)) = (e2))\/((op (e2) (e3)) = (e3))))) -> ((op (e3) (e3)) = (e0)) -> (~((op (e2) (e2)) = (op (e2) (e3)))) -> ((op (e2) (e2)) = (e1)) -> ((op (e3) (e3)) = (e2)) -> (~((op (e2) (e3)) = (op (e3) (e3)))) -> (~((op (e0) (e3)) = (op (e2) (e3)))) -> ((op (e0) (e3)) = (e3)) -> False). % 18.52/18.71 do 0 intro. intros zenon_H11f zenon_H60 zenon_H6d zenon_Hf1 zenon_Hf6 zenon_Hf3 zenon_He2 zenon_He3. % 18.52/18.71 apply (zenon_or_s _ _ zenon_H11f); [ zenon_intro zenon_H37 | zenon_intro zenon_H120 ]. % 18.52/18.71 apply (zenon_L219_); trivial. % 18.52/18.71 apply (zenon_or_s _ _ zenon_H120); [ zenon_intro zenon_Hf4 | zenon_intro zenon_H121 ]. % 18.52/18.71 apply (zenon_L84_); trivial. % 18.52/18.71 apply (zenon_or_s _ _ zenon_H121); [ zenon_intro zenon_H11d | zenon_intro zenon_Hdd ]. % 18.52/18.71 apply (zenon_L97_); trivial. % 18.52/18.71 apply (zenon_L54_); trivial. % 18.52/18.71 (* end of lemma zenon_L220_ *) % 18.52/18.71 assert (zenon_L221_ : (((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)) = (e1)) -> ((op (e0) (e3)) = (e3)) -> (~((op (e0) (e3)) = (op (e2) (e3)))) -> (~((op (e2) (e3)) = (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 (e0) (e2)) = (op (e3) (e2)))) -> ((op (e0) (e2)) = (e2)) -> (((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)) -> (~((op (e3) (e1)) = (op (e3) (e3)))) -> ((op (e3) (e0)) = (e3)) -> (((op (e3) (e0)) = (e2))\/(((op (e3) (e1)) = (e2))\/(((op (e3) (e2)) = (e2))\/((op (e3) (e3)) = (e2))))) -> (~((op (e3) (e2)) = (e0))) -> (~((op (e3) (e1)) = (e0))) -> (~((op (e3) (e0)) = (e0))) -> (((op (e3) (e0)) = (e0))\/(((op (e3) (e1)) = (e0))\/(((op (e3) (e2)) = (e0))\/((op (e3) (e3)) = (e0))))) -> (~((op (e1) (e3)) = (op (e2) (e3)))) -> ((op (e1) (e3)) = (e1)) -> False). % 18.52/18.71 do 0 intro. intros zenon_H106 zenon_Haf zenon_Hae zenon_He3 zenon_He2 zenon_Hf3 zenon_H6d zenon_H11f zenon_H14f zenon_H150 zenon_H145 zenon_H12b zenon_H7c zenon_H5b zenon_Hee zenon_H130 zenon_H15e zenon_H153 zenon_H18b zenon_H1ad zenon_H40 zenon_H1ac zenon_Hdb zenon_Hd6. % 18.52/18.71 apply (zenon_or_s _ _ zenon_H106); [ zenon_intro zenon_Hed | zenon_intro zenon_H107 ]. % 18.52/18.71 apply (zenon_L58_); trivial. % 18.52/18.71 apply (zenon_or_s _ _ zenon_H107); [ zenon_intro zenon_Ha5 | zenon_intro zenon_H108 ]. % 18.52/18.71 apply (zenon_L42_); trivial. % 18.52/18.71 apply (zenon_or_s _ _ zenon_H108); [ zenon_intro zenon_Hf1 | zenon_intro zenon_Hf4 ]. % 18.52/18.71 apply (zenon_or_s _ _ zenon_H1ac); [ zenon_intro zenon_H44 | zenon_intro zenon_H1af ]. % 18.52/18.71 exact (zenon_H40 zenon_H44). % 18.52/18.71 apply (zenon_or_s _ _ zenon_H1af); [ zenon_intro zenon_H1b1 | zenon_intro zenon_H1b0 ]. % 18.52/18.71 exact (zenon_H1ad zenon_H1b1). % 18.52/18.71 apply (zenon_or_s _ _ zenon_H1b0); [ zenon_intro zenon_H61 | zenon_intro zenon_H60 ]. % 18.52/18.71 exact (zenon_H18b zenon_H61). % 18.52/18.71 apply (zenon_or_s _ _ zenon_H153); [ zenon_intro zenon_H148 | zenon_intro zenon_H154 ]. % 18.52/18.71 apply (zenon_L109_); trivial. % 18.52/18.71 apply (zenon_or_s _ _ zenon_H154); [ zenon_intro zenon_H14d | zenon_intro zenon_H155 ]. % 18.52/18.71 apply (zenon_L103_); trivial. % 18.52/18.71 apply (zenon_or_s _ _ zenon_H155); [ zenon_intro zenon_H151 | zenon_intro zenon_Hf6 ]. % 18.52/18.71 apply (zenon_L104_); trivial. % 18.52/18.71 apply (zenon_L220_); trivial. % 18.52/18.71 apply (zenon_L126_); trivial. % 18.52/18.71 (* end of lemma zenon_L221_ *) % 18.52/18.71 assert (zenon_L222_ : (((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 (e3) (e0)) = (e0))\/(((op (e3) (e1)) = (e0))\/(((op (e3) (e2)) = (e0))\/((op (e3) (e3)) = (e0))))) -> (~((op (e3) (e0)) = (e0))) -> (~((op (e3) (e1)) = (e0))) -> (~((op (e3) (e2)) = (e0))) -> (~((op (e3) (e1)) = (op (e3) (e3)))) -> (~((op (e2) (e0)) = (op (e2) (e3)))) -> (((op (e0) (e3)) = (e2))\/(((op (e1) (e3)) = (e2))\/(((op (e2) (e3)) = (e2))\/((op (e3) (e3)) = (e2))))) -> (((op (e2) (e3)) = (e0))\/(((op (e2) (e3)) = (e1))\/(((op (e2) (e3)) = (e2))\/((op (e2) (e3)) = (e3))))) -> (~((op (e2) (e2)) = (op (e2) (e3)))) -> (~((op (e0) (e3)) = (op (e2) (e3)))) -> ((op (e0) (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) (e1)) = (e3)) -> (~((op (e2) (e2)) = (e2))) -> (((op (e3) (e0)) = (e2))\/(((op (e3) (e1)) = (e2))\/(((op (e3) (e2)) = (e2))\/((op (e3) (e3)) = (e2))))) -> (~((e2) = (e3))) -> ((op (e3) (e0)) = (e3)) -> (~((e1) = (e2))) -> ((op (e3) (e1)) = (e1)) -> ((op (e0) (e2)) = (e2)) -> (~((op (e0) (e2)) = (op (e3) (e2)))) -> (~((op (e2) (e3)) = (op (e3) (e3)))) -> False). % 18.52/18.71 do 0 intro. intros zenon_H1d5 zenon_Hd6 zenon_Hdb zenon_H1ac zenon_H40 zenon_H1ad zenon_H18b zenon_H130 zenon_H5b zenon_H145 zenon_H11f zenon_H6d zenon_He2 zenon_He3 zenon_Haf zenon_H106 zenon_Ha6 zenon_H173 zenon_H153 zenon_H12b zenon_H15e zenon_H7c zenon_Hae zenon_H150 zenon_H14f zenon_Hf3. % 18.52/18.71 apply (zenon_or_s _ _ zenon_H1d5); [ zenon_intro zenon_Hee | zenon_intro zenon_H1d6 ]. % 18.52/18.71 apply (zenon_L221_); trivial. % 18.52/18.71 apply (zenon_or_s _ _ zenon_H1d6); [ zenon_intro zenon_H1ca | zenon_intro zenon_H1d7 ]. % 18.52/18.71 apply (zenon_L207_); trivial. % 18.52/18.71 apply (zenon_or_s _ _ zenon_H1d7); [ zenon_intro zenon_H176 | zenon_intro zenon_H11d ]. % 18.52/18.71 exact (zenon_H173 zenon_H176). % 18.52/18.71 apply (zenon_L205_); trivial. % 18.52/18.71 (* end of lemma zenon_L222_ *) % 18.52/18.71 assert (zenon_L223_ : (((op (e0) (e1)) = (e3))\/(((op (e1) (e1)) = (e3))\/(((op (e2) (e1)) = (e3))\/((op (e3) (e1)) = (e3))))) -> (~((e0) = (e3))) -> ((op (e0) (e1)) = (e0)) -> ((op (e1) (e1)) = (e2)) -> (~((op (e2) (e3)) = (op (e3) (e3)))) -> (~((op (e0) (e2)) = (op (e3) (e2)))) -> ((op (e0) (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 (e2) (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 (e0) (e3)) = (e3)) -> (~((op (e0) (e3)) = (op (e2) (e3)))) -> (~((op (e2) (e2)) = (op (e2) (e3)))) -> (((op (e2) (e3)) = (e0))\/(((op (e2) (e3)) = (e1))\/(((op (e2) (e3)) = (e2))\/((op (e2) (e3)) = (e3))))) -> (((op (e0) (e3)) = (e2))\/(((op (e1) (e3)) = (e2))\/(((op (e2) (e3)) = (e2))\/((op (e3) (e3)) = (e2))))) -> (~((op (e2) (e0)) = (op (e2) (e3)))) -> (~((op (e3) (e1)) = (op (e3) (e3)))) -> (~((op (e3) (e2)) = (e0))) -> (~((op (e3) (e1)) = (e0))) -> (~((op (e3) (e0)) = (e0))) -> (((op (e3) (e0)) = (e0))\/(((op (e3) (e1)) = (e0))\/(((op (e3) (e2)) = (e0))\/((op (e3) (e3)) = (e0))))) -> (~((op (e1) (e3)) = (op (e2) (e3)))) -> ((op (e1) (e3)) = (e1)) -> (((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). % 18.52/18.71 do 0 intro. intros zenon_H1a5 zenon_H9a zenon_H49 zenon_H110 zenon_Hf3 zenon_H14f zenon_H150 zenon_Hae zenon_H7c zenon_H12b zenon_H153 zenon_H173 zenon_H106 zenon_Haf zenon_He3 zenon_He2 zenon_H6d zenon_H11f zenon_H145 zenon_H5b zenon_H130 zenon_H18b zenon_H1ad zenon_H40 zenon_H1ac zenon_Hdb zenon_Hd6 zenon_H1d5 zenon_H15e zenon_H1cf. % 18.52/18.71 apply (zenon_or_s _ _ zenon_H1a5); [ zenon_intro zenon_H99 | zenon_intro zenon_H1a8 ]. % 18.52/18.71 apply (zenon_L36_); trivial. % 18.52/18.71 apply (zenon_or_s _ _ zenon_H1a8); [ zenon_intro zenon_H13f | zenon_intro zenon_H1a9 ]. % 18.52/18.71 apply (zenon_L166_); trivial. % 18.52/18.71 apply (zenon_or_s _ _ zenon_H1a9); [ zenon_intro zenon_Ha6 | zenon_intro zenon_H161 ]. % 18.52/18.71 apply (zenon_L222_); trivial. % 18.52/18.71 apply (zenon_L193_); trivial. % 18.52/18.71 (* end of lemma zenon_L223_ *) % 18.52/18.71 assert (zenon_L224_ : ((op (e2) (e3)) = (e2)) -> ((op (e2) (e1)) = (e2)) -> (~((op (e2) (e1)) = (op (e2) (e3)))) -> False). % 18.52/18.71 do 0 intro. intros zenon_H11d zenon_H1ca zenon_H1c7. % 18.52/18.71 elim (classic ((op (e2) (e3)) = (op (e2) (e3)))); [ zenon_intro zenon_H5c | zenon_intro zenon_H5d ]. % 18.52/18.71 cut (((op (e2) (e3)) = (op (e2) (e3))) = ((op (e2) (e1)) = (op (e2) (e3)))). % 18.52/18.71 intro zenon_D_pnotp. % 18.52/18.71 apply zenon_H1c7. % 18.52/18.71 rewrite <- zenon_D_pnotp. % 18.52/18.71 exact zenon_H5c. % 18.52/18.71 cut (((op (e2) (e3)) = (op (e2) (e3)))); [idtac | apply NNPP; zenon_intro zenon_H5d]. % 18.52/18.71 cut (((op (e2) (e3)) = (op (e2) (e1)))); [idtac | apply NNPP; zenon_intro zenon_H1c8]. % 18.52/18.71 congruence. % 18.52/18.71 cut (((op (e2) (e3)) = (e2)) = ((op (e2) (e3)) = (op (e2) (e1)))). % 18.52/18.71 intro zenon_D_pnotp. % 18.52/18.71 apply zenon_H1c8. % 18.52/18.71 rewrite <- zenon_D_pnotp. % 18.52/18.71 exact zenon_H11d. % 18.52/18.71 cut (((e2) = (op (e2) (e1)))); [idtac | apply NNPP; zenon_intro zenon_H1cb]. % 18.52/18.71 cut (((op (e2) (e3)) = (op (e2) (e3)))); [idtac | apply NNPP; zenon_intro zenon_H5d]. % 18.52/18.71 congruence. % 18.52/18.71 apply zenon_H5d. apply refl_equal. % 18.52/18.71 apply zenon_H1cb. apply sym_equal. exact zenon_H1ca. % 18.52/18.71 apply zenon_H5d. apply refl_equal. % 18.52/18.71 apply zenon_H5d. apply refl_equal. % 18.52/18.71 (* end of lemma zenon_L224_ *) % 18.52/18.71 assert (zenon_L225_ : (((op (e2) (e3)) = (e0))\/(((op (e2) (e3)) = (e1))\/(((op (e2) (e3)) = (e2))\/((op (e2) (e3)) = (e3))))) -> (~((op (e2) (e0)) = (op (e2) (e3)))) -> ((op (e2) (e0)) = (e0)) -> ((op (e1) (e3)) = (e0)) -> ((op (e3) (e3)) = (e2)) -> (~((op (e2) (e3)) = (op (e3) (e3)))) -> (~((op (e0) (e3)) = (op (e2) (e3)))) -> ((op (e0) (e3)) = (e3)) -> False). % 18.52/18.71 do 0 intro. intros zenon_H11f zenon_H5b zenon_H34 zenon_H1f zenon_Hf6 zenon_Hf3 zenon_He2 zenon_He3. % 18.52/18.71 apply (zenon_or_s _ _ zenon_H11f); [ zenon_intro zenon_H37 | zenon_intro zenon_H120 ]. % 18.52/18.71 apply (zenon_L14_); trivial. % 18.52/18.71 apply (zenon_or_s _ _ zenon_H120); [ zenon_intro zenon_Hf4 | zenon_intro zenon_H121 ]. % 18.52/18.71 apply (zenon_L63_); trivial. % 18.52/18.71 apply (zenon_or_s _ _ zenon_H121); [ zenon_intro zenon_H11d | zenon_intro zenon_Hdd ]. % 18.52/18.71 apply (zenon_L97_); trivial. % 18.52/18.71 apply (zenon_L54_); trivial. % 18.52/18.71 (* end of lemma zenon_L225_ *) % 18.52/18.71 assert (zenon_L226_ : (((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) (e1)) = (op (e2) (e3)))) -> ((op (e2) (e1)) = (e2)) -> (((op (e2) (e3)) = (e0))\/(((op (e2) (e3)) = (e1))\/(((op (e2) (e3)) = (e2))\/((op (e2) (e3)) = (e3))))) -> (~((op (e2) (e0)) = (op (e2) (e3)))) -> ((op (e2) (e0)) = (e0)) -> ((op (e1) (e3)) = (e0)) -> (~((op (e2) (e3)) = (op (e3) (e3)))) -> (~((op (e0) (e3)) = (op (e2) (e3)))) -> ((op (e0) (e3)) = (e3)) -> False). % 18.52/18.71 do 0 intro. intros zenon_H145 zenon_H12b zenon_H7c zenon_Hd6 zenon_H1c7 zenon_H1ca zenon_H11f zenon_H5b zenon_H34 zenon_H1f zenon_Hf3 zenon_He2 zenon_He3. % 18.52/18.71 apply (zenon_or_s _ _ zenon_H145); [ zenon_intro zenon_Hcd | zenon_intro zenon_H146 ]. % 18.52/18.71 apply (zenon_L81_); trivial. % 18.52/18.71 apply (zenon_or_s _ _ zenon_H146); [ zenon_intro zenon_Hd7 | zenon_intro zenon_H147 ]. % 18.52/18.71 apply (zenon_L101_); trivial. % 18.52/18.71 apply (zenon_or_s _ _ zenon_H147); [ zenon_intro zenon_H11d | zenon_intro zenon_Hf6 ]. % 18.52/18.71 apply (zenon_L224_); trivial. % 18.52/18.71 apply (zenon_L225_); trivial. % 18.52/18.71 (* end of lemma zenon_L226_ *) % 18.52/18.71 assert (zenon_L227_ : (~((op (e1) (e1)) = (e0))) -> (((op (e1) (e0)) = (e1))\/(((op (e1) (e1)) = (e1))\/(((op (e1) (e2)) = (e1))\/((op (e1) (e3)) = (e1))))) -> ((~((op (e1) (e3)) = (e0)))\/((op (e1) (e0)) = (e3))) -> (~((op (e0) (e0)) = (e0))) -> (((op (e1) (e0)) = (e0))\/(((op (e1) (e1)) = (e0))\/(((op (e1) (e2)) = (e0))\/((op (e1) (e3)) = (e0))))) -> (~((op (e1) (e0)) = (op (e1) (e1)))) -> (~((op (e0) (e1)) = (op (e0) (e3)))) -> (~((op (e1) (e1)) = (op (e1) (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) (e0)) = (op (e2) (e2)))) -> (~((op (e1) (e1)) = (op (e1) (e2)))) -> (~((op (e0) (e1)) = (op (e0) (e2)))) -> (~((op (e3) (e0)) = (op (e3) (e3)))) -> (~((op (e3) (e0)) = (op (e3) (e2)))) -> (((op (e0) (e0)) = (e0))\/(((op (e1) (e0)) = (e0))\/(((op (e2) (e0)) = (e0))\/((op (e3) (e0)) = (e0))))) -> (~((op (e1) (e0)) = (e0))) -> (~((op (e0) (e3)) = (e0))) -> (((op (e0) (e0)) = (e0))\/(((op (e0) (e1)) = (e0))\/(((op (e0) (e2)) = (e0))\/((op (e0) (e3)) = (e0))))) -> ((~((op (e1) (e2)) = (e0)))\/((op (e1) (e0)) = (e2))) -> (~((op (e1) (e2)) = (op (e2) (e2)))) -> (~((op (e0) (e3)) = (op (e1) (e3)))) -> (((op (e1) (e0)) = (e3))\/(((op (e1) (e1)) = (e3))\/(((op (e1) (e2)) = (e3))\/((op (e1) (e3)) = (e3))))) -> (~((e0) = (e2))) -> (((op (e0) (e1)) = (e1))\/(((op (e1) (e1)) = (e1))\/(((op (e2) (e1)) = (e1))\/((op (e3) (e1)) = (e1))))) -> (~((e0) = (e1))) -> (~((op (e1) (e1)) = (e1))) -> (~((op (e2) (e2)) = (e0))) -> (((op (e2) (e0)) = (e3))\/(((op (e2) (e1)) = (e3))\/(((op (e2) (e2)) = (e3))\/((op (e2) (e3)) = (e3))))) -> ((op (e0) (e0)) = (e1)) -> ((op (e1) (e0)) = (e2)) -> (~((e1) = (e3))) -> (~((op (e2) (e2)) = (op (e3) (e2)))) -> (~((op (e1) (e2)) = (op (e3) (e2)))) -> (((op (e3) (e2)) = (e0))\/(((op (e3) (e2)) = (e1))\/(((op (e3) (e2)) = (e2))\/((op (e3) (e2)) = (e3))))) -> (~((op (e0) (e2)) = (e0))) -> (((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)) = (e0))\/(((op (e2) (e1)) = (e1))\/(((op (e2) (e1)) = (e2))\/((op (e2) (e1)) = (e3))))) -> (~((op (e2) (e1)) = (e0))) -> (~((op (e0) (e1)) = (op (e2) (e1)))) -> (~((op (e1) (e1)) = (op (e2) (e1)))) -> (~((op (e3) (e0)) = (op (e3) (e1)))) -> ((op (e3) (e0)) = (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) (e0)) = (e0))\/(((op (e3) (e1)) = (e0))\/(((op (e3) (e2)) = (e0))\/((op (e3) (e3)) = (e0))))) -> (~((op (e3) (e0)) = (e0))) -> (~((op (e3) (e1)) = (e0))) -> (~((op (e3) (e2)) = (e0))) -> (~((op (e3) (e1)) = (op (e3) (e3)))) -> (~((op (e2) (e2)) = (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 (e2) (e2)) = (e2))) -> (((op (e3) (e0)) = (e2))\/(((op (e3) (e1)) = (e2))\/(((op (e3) (e2)) = (e2))\/((op (e3) (e3)) = (e2))))) -> ((op (e0) (e2)) = (e2)) -> (~((op (e0) (e2)) = (op (e3) (e2)))) -> ((op (e0) (e1)) = (e0)) -> (~((e0) = (e3))) -> (((op (e0) (e1)) = (e3))\/(((op (e1) (e1)) = (e3))\/(((op (e2) (e1)) = (e3))\/((op (e3) (e1)) = (e3))))) -> ((op (e0) (e3)) = (e3)) -> (~((op (e0) (e3)) = (op (e2) (e3)))) -> (~((op (e2) (e3)) = (op (e3) (e3)))) -> ((op (e2) (e0)) = (e0)) -> (~((op (e2) (e0)) = (op (e2) (e3)))) -> (((op (e2) (e3)) = (e0))\/(((op (e2) (e3)) = (e1))\/(((op (e2) (e3)) = (e2))\/((op (e2) (e3)) = (e3))))) -> (~((op (e2) (e1)) = (op (e2) (e3)))) -> (~((e2) = (e3))) -> (((op (e0) (e3)) = (e2))\/(((op (e1) (e3)) = (e2))\/(((op (e2) (e3)) = (e2))\/((op (e3) (e3)) = (e2))))) -> (~((e1) = (e2))) -> False). % 18.52/18.71 do 0 intro. intros zenon_H24 zenon_H128 zenon_H179 zenon_H3f zenon_H22 zenon_H45 zenon_H54 zenon_H57 zenon_H62 zenon_H67 zenon_H52 zenon_H4f zenon_H4a zenon_H71 zenon_H6f zenon_H3e zenon_H23 zenon_H76 zenon_H74 zenon_H178 zenon_H2b zenon_H1d zenon_H16f zenon_H149 zenon_H109 zenon_Ha1 zenon_H10a zenon_H81 zenon_He7 zenon_H7a zenon_H86 zenon_H95 zenon_H18f zenon_H115 zenon_H191 zenon_H75 zenon_H6a zenon_H1d8 zenon_H1cc zenon_H31 zenon_H17e zenon_H13e zenon_H1cf zenon_H15e zenon_H1d5 zenon_Hdb zenon_H1ac zenon_H40 zenon_H1ad zenon_H18b zenon_H130 zenon_H6d zenon_Haf zenon_H106 zenon_H173 zenon_H153 zenon_H150 zenon_H14f zenon_H49 zenon_H9a zenon_H1a5 zenon_He3 zenon_He2 zenon_Hf3 zenon_H34 zenon_H5b zenon_H11f zenon_H1c7 zenon_H12b zenon_H145 zenon_H7c. % 18.52/18.71 apply (zenon_or_s _ _ zenon_H22); [ zenon_intro zenon_H27 | zenon_intro zenon_H26 ]. % 18.52/18.71 exact (zenon_H23 zenon_H27). % 18.52/18.71 apply (zenon_or_s _ _ zenon_H26); [ zenon_intro zenon_H29 | zenon_intro zenon_H28 ]. % 18.52/18.71 exact (zenon_H24 zenon_H29). % 18.52/18.71 apply (zenon_or_s _ _ zenon_H28); [ zenon_intro zenon_H2a | zenon_intro zenon_H1f ]. % 18.52/18.71 apply (zenon_or_s _ _ zenon_H109); [ zenon_intro zenon_Ha0 | zenon_intro zenon_H10b ]. % 18.52/18.71 apply (zenon_L38_); trivial. % 18.52/18.71 apply (zenon_or_s _ _ zenon_H10b); [ zenon_intro zenon_H10d | zenon_intro zenon_H10c ]. % 18.52/18.71 exact (zenon_H10a zenon_H10d). % 18.52/18.71 apply (zenon_or_s _ _ zenon_H10c); [ zenon_intro zenon_Ha5 | zenon_intro zenon_Hae ]. % 18.52/18.71 apply (zenon_L211_); trivial. % 18.52/18.71 apply (zenon_or_s _ _ zenon_H1d8); [ zenon_intro zenon_H10f | zenon_intro zenon_H1d9 ]. % 18.52/18.71 apply (zenon_L206_); trivial. % 18.52/18.71 apply (zenon_or_s _ _ zenon_H1d9); [ zenon_intro zenon_H110 | zenon_intro zenon_H1da ]. % 18.52/18.71 apply (zenon_L209_); trivial. % 18.52/18.71 apply (zenon_or_s _ _ zenon_H1da); [ zenon_intro zenon_H1ca | zenon_intro zenon_H14d ]. % 18.52/18.71 apply (zenon_L212_); trivial. % 18.52/18.71 apply (zenon_L152_); trivial. % 18.52/18.71 apply (zenon_or_s _ _ zenon_H128); [ zenon_intro zenon_H9d | zenon_intro zenon_H129 ]. % 18.52/18.71 apply (zenon_L124_); trivial. % 18.52/18.71 apply (zenon_or_s _ _ zenon_H129); [ zenon_intro zenon_H10d | zenon_intro zenon_H12a ]. % 18.52/18.71 exact (zenon_H10a zenon_H10d). % 18.52/18.71 apply (zenon_or_s _ _ zenon_H12a); [ zenon_intro zenon_Hf0 | zenon_intro zenon_Hd6 ]. % 18.52/18.71 apply (zenon_or_s _ _ zenon_H109); [ zenon_intro zenon_Ha0 | zenon_intro zenon_H10b ]. % 18.52/18.71 apply (zenon_L38_); trivial. % 18.52/18.71 apply (zenon_or_s _ _ zenon_H10b); [ zenon_intro zenon_H10d | zenon_intro zenon_H10c ]. % 18.52/18.71 exact (zenon_H10a zenon_H10d). % 18.52/18.71 apply (zenon_or_s _ _ zenon_H10c); [ zenon_intro zenon_Ha5 | zenon_intro zenon_Hae ]. % 18.52/18.71 apply (zenon_L213_); trivial. % 18.52/18.71 apply (zenon_or_s _ _ zenon_H1d8); [ zenon_intro zenon_H10f | zenon_intro zenon_H1d9 ]. % 18.52/18.71 apply (zenon_L206_); trivial. % 18.52/18.71 apply (zenon_or_s _ _ zenon_H1d9); [ zenon_intro zenon_H110 | zenon_intro zenon_H1da ]. % 18.52/18.71 apply (zenon_or_s _ _ zenon_H106); [ zenon_intro zenon_Hed | zenon_intro zenon_H107 ]. % 18.52/18.71 apply (zenon_L214_); trivial. % 18.52/18.71 apply (zenon_or_s _ _ zenon_H107); [ zenon_intro zenon_Ha5 | zenon_intro zenon_H108 ]. % 18.52/18.71 apply (zenon_L215_); trivial. % 18.52/18.71 apply (zenon_or_s _ _ zenon_H108); [ zenon_intro zenon_Hf1 | zenon_intro zenon_Hf4 ]. % 18.52/18.72 apply (zenon_L59_); trivial. % 18.52/18.72 apply (zenon_L217_); trivial. % 18.52/18.72 apply (zenon_or_s _ _ zenon_H1da); [ zenon_intro zenon_H1ca | zenon_intro zenon_H14d ]. % 18.52/18.72 apply (zenon_L218_); trivial. % 18.52/18.72 apply (zenon_L152_); trivial. % 18.52/18.72 apply (zenon_or_s _ _ zenon_H109); [ zenon_intro zenon_Ha0 | zenon_intro zenon_H10b ]. % 18.52/18.72 apply (zenon_L38_); trivial. % 18.52/18.72 apply (zenon_or_s _ _ zenon_H10b); [ zenon_intro zenon_H10d | zenon_intro zenon_H10c ]. % 18.52/18.72 exact (zenon_H10a zenon_H10d). % 18.52/18.72 apply (zenon_or_s _ _ zenon_H10c); [ zenon_intro zenon_Ha5 | zenon_intro zenon_Hae ]. % 18.52/18.72 apply (zenon_L213_); trivial. % 18.52/18.72 apply (zenon_or_s _ _ zenon_H1d8); [ zenon_intro zenon_H10f | zenon_intro zenon_H1d9 ]. % 18.52/18.72 apply (zenon_or_s _ _ zenon_H1a5); [ zenon_intro zenon_H99 | zenon_intro zenon_H1a8 ]. % 18.52/18.72 apply (zenon_L36_); trivial. % 18.52/18.72 apply (zenon_or_s _ _ zenon_H1a8); [ zenon_intro zenon_H13f | zenon_intro zenon_H1a9 ]. % 18.52/18.72 apply (zenon_L192_); trivial. % 18.52/18.72 apply (zenon_or_s _ _ zenon_H1a9); [ zenon_intro zenon_Ha6 | zenon_intro zenon_H161 ]. % 18.52/18.72 apply (zenon_L222_); trivial. % 18.52/18.72 apply (zenon_L193_); trivial. % 18.52/18.72 apply (zenon_or_s _ _ zenon_H1d9); [ zenon_intro zenon_H110 | zenon_intro zenon_H1da ]. % 18.52/18.72 apply (zenon_L223_); trivial. % 18.52/18.72 apply (zenon_or_s _ _ zenon_H1da); [ zenon_intro zenon_H1ca | zenon_intro zenon_H14d ]. % 18.52/18.72 apply (zenon_L226_); trivial. % 18.52/18.72 apply (zenon_L152_); trivial. % 18.52/18.72 (* end of lemma zenon_L227_ *) % 18.52/18.72 assert (zenon_L228_ : ((op (e0) (e3)) = (e2)) -> ((op (e3) (e3)) = (e0)) -> (~((e2) = (op (op (e3) (e3)) (e3)))) -> False). % 18.52/18.72 do 0 intro. intros zenon_Hcd zenon_H60 zenon_H118. % 18.52/18.72 elim (classic ((op (op (e3) (e3)) (e3)) = (op (op (e3) (e3)) (e3)))); [ zenon_intro zenon_Hc9 | zenon_intro zenon_Hca ]. % 18.52/18.72 cut (((op (op (e3) (e3)) (e3)) = (op (op (e3) (e3)) (e3))) = ((e2) = (op (op (e3) (e3)) (e3)))). % 18.52/18.72 intro zenon_D_pnotp. % 18.52/18.72 apply zenon_H118. % 18.52/18.72 rewrite <- zenon_D_pnotp. % 18.52/18.72 exact zenon_Hc9. % 18.52/18.72 cut (((op (op (e3) (e3)) (e3)) = (op (op (e3) (e3)) (e3)))); [idtac | apply NNPP; zenon_intro zenon_Hca]. % 18.52/18.72 cut (((op (op (e3) (e3)) (e3)) = (e2))); [idtac | apply NNPP; zenon_intro zenon_H119]. % 18.52/18.72 congruence. % 18.52/18.72 cut (((op (e0) (e3)) = (e2)) = ((op (op (e3) (e3)) (e3)) = (e2))). % 18.52/18.72 intro zenon_D_pnotp. % 18.52/18.72 apply zenon_H119. % 18.52/18.72 rewrite <- zenon_D_pnotp. % 18.52/18.72 exact zenon_Hcd. % 18.52/18.72 cut (((e2) = (e2))); [idtac | apply NNPP; zenon_intro zenon_H7e]. % 18.52/18.72 cut (((op (e0) (e3)) = (op (op (e3) (e3)) (e3)))); [idtac | apply NNPP; zenon_intro zenon_H1d3]. % 18.52/18.72 congruence. % 18.52/18.72 elim (classic ((op (op (e3) (e3)) (e3)) = (op (op (e3) (e3)) (e3)))); [ zenon_intro zenon_Hc9 | zenon_intro zenon_Hca ]. % 18.52/18.72 cut (((op (op (e3) (e3)) (e3)) = (op (op (e3) (e3)) (e3))) = ((op (e0) (e3)) = (op (op (e3) (e3)) (e3)))). % 18.52/18.72 intro zenon_D_pnotp. % 18.52/18.72 apply zenon_H1d3. % 18.52/18.72 rewrite <- zenon_D_pnotp. % 18.52/18.72 exact zenon_Hc9. % 18.52/18.72 cut (((op (op (e3) (e3)) (e3)) = (op (op (e3) (e3)) (e3)))); [idtac | apply NNPP; zenon_intro zenon_Hca]. % 18.52/18.72 cut (((op (op (e3) (e3)) (e3)) = (op (e0) (e3)))); [idtac | apply NNPP; zenon_intro zenon_H1d2]. % 18.52/18.72 congruence. % 18.52/18.72 apply (zenon_L199_); trivial. % 18.52/18.72 apply zenon_Hca. apply refl_equal. % 18.52/18.72 apply zenon_Hca. apply refl_equal. % 18.52/18.72 apply zenon_H7e. apply refl_equal. % 18.52/18.72 apply zenon_Hca. apply refl_equal. % 18.52/18.72 apply zenon_Hca. apply refl_equal. % 18.52/18.72 (* end of lemma zenon_L228_ *) % 18.52/18.72 assert (zenon_L229_ : ((op (e2) (e3)) = (e1)) -> ((op (e0) (e3)) = (e2)) -> ((op (e3) (e3)) = (e0)) -> False). % 18.52/18.72 do 0 intro. intros zenon_Hf4 zenon_Hcd zenon_H60. % 18.52/18.72 apply (zenon_notand_s _ _ ax27); [ zenon_intro zenon_H1dd | zenon_intro zenon_H1dc ]. % 18.52/18.72 elim (classic ((op (op (op (e3) (e3)) (e3)) (e3)) = (op (op (op (e3) (e3)) (e3)) (e3)))); [ zenon_intro zenon_Hd0 | zenon_intro zenon_Hd1 ]. % 18.52/18.72 cut (((op (op (op (e3) (e3)) (e3)) (e3)) = (op (op (op (e3) (e3)) (e3)) (e3))) = ((e1) = (op (op (op (e3) (e3)) (e3)) (e3)))). % 18.52/18.72 intro zenon_D_pnotp. % 18.52/18.72 apply zenon_H1dd. % 18.52/18.72 rewrite <- zenon_D_pnotp. % 18.52/18.72 exact zenon_Hd0. % 18.52/18.72 cut (((op (op (op (e3) (e3)) (e3)) (e3)) = (op (op (op (e3) (e3)) (e3)) (e3)))); [idtac | apply NNPP; zenon_intro zenon_Hd1]. % 18.52/18.72 cut (((op (op (op (e3) (e3)) (e3)) (e3)) = (e1))); [idtac | apply NNPP; zenon_intro zenon_H1de]. % 18.52/18.72 congruence. % 18.52/18.72 cut (((op (e2) (e3)) = (e1)) = ((op (op (op (e3) (e3)) (e3)) (e3)) = (e1))). % 18.52/18.72 intro zenon_D_pnotp. % 18.52/18.72 apply zenon_H1de. % 18.52/18.72 rewrite <- zenon_D_pnotp. % 18.52/18.72 exact zenon_Hf4. % 18.52/18.72 cut (((e1) = (e1))); [idtac | apply NNPP; zenon_intro zenon_H79]. % 18.52/18.72 cut (((op (e2) (e3)) = (op (op (op (e3) (e3)) (e3)) (e3)))); [idtac | apply NNPP; zenon_intro zenon_H11b]. % 18.52/18.72 congruence. % 18.52/18.72 elim (classic ((op (op (op (e3) (e3)) (e3)) (e3)) = (op (op (op (e3) (e3)) (e3)) (e3)))); [ zenon_intro zenon_Hd0 | zenon_intro zenon_Hd1 ]. % 18.52/18.72 cut (((op (op (op (e3) (e3)) (e3)) (e3)) = (op (op (op (e3) (e3)) (e3)) (e3))) = ((op (e2) (e3)) = (op (op (op (e3) (e3)) (e3)) (e3)))). % 18.52/18.72 intro zenon_D_pnotp. % 18.52/18.72 apply zenon_H11b. % 18.52/18.72 rewrite <- zenon_D_pnotp. % 18.52/18.72 exact zenon_Hd0. % 18.52/18.72 cut (((op (op (op (e3) (e3)) (e3)) (e3)) = (op (op (op (e3) (e3)) (e3)) (e3)))); [idtac | apply NNPP; zenon_intro zenon_Hd1]. % 18.52/18.72 cut (((op (op (op (e3) (e3)) (e3)) (e3)) = (op (e2) (e3)))); [idtac | apply NNPP; zenon_intro zenon_H11c]. % 18.52/18.72 congruence. % 18.52/18.72 cut (((e3) = (e3))); [idtac | apply NNPP; zenon_intro zenon_H85]. % 18.52/18.72 cut (((op (op (e3) (e3)) (e3)) = (e2))); [idtac | apply NNPP; zenon_intro zenon_H119]. % 18.52/18.72 congruence. % 18.52/18.72 cut (((op (e0) (e3)) = (e2)) = ((op (op (e3) (e3)) (e3)) = (e2))). % 18.52/18.72 intro zenon_D_pnotp. % 18.52/18.72 apply zenon_H119. % 18.52/18.72 rewrite <- zenon_D_pnotp. % 18.52/18.72 exact zenon_Hcd. % 18.52/18.72 cut (((e2) = (e2))); [idtac | apply NNPP; zenon_intro zenon_H7e]. % 18.52/18.72 cut (((op (e0) (e3)) = (op (op (e3) (e3)) (e3)))); [idtac | apply NNPP; zenon_intro zenon_H1d3]. % 18.52/18.72 congruence. % 18.52/18.72 elim (classic ((op (op (e3) (e3)) (e3)) = (op (op (e3) (e3)) (e3)))); [ zenon_intro zenon_Hc9 | zenon_intro zenon_Hca ]. % 18.52/18.72 cut (((op (op (e3) (e3)) (e3)) = (op (op (e3) (e3)) (e3))) = ((op (e0) (e3)) = (op (op (e3) (e3)) (e3)))). % 18.52/18.72 intro zenon_D_pnotp. % 18.52/18.72 apply zenon_H1d3. % 18.52/18.72 rewrite <- zenon_D_pnotp. % 18.52/18.72 exact zenon_Hc9. % 18.52/18.72 cut (((op (op (e3) (e3)) (e3)) = (op (op (e3) (e3)) (e3)))); [idtac | apply NNPP; zenon_intro zenon_Hca]. % 18.52/18.72 cut (((op (op (e3) (e3)) (e3)) = (op (e0) (e3)))); [idtac | apply NNPP; zenon_intro zenon_H1d2]. % 18.52/18.72 congruence. % 18.52/18.72 apply (zenon_L199_); trivial. % 18.52/18.72 apply zenon_Hca. apply refl_equal. % 18.52/18.72 apply zenon_Hca. apply refl_equal. % 18.52/18.72 apply zenon_H7e. apply refl_equal. % 18.52/18.72 apply zenon_H85. apply refl_equal. % 18.52/18.72 apply zenon_Hd1. apply refl_equal. % 18.52/18.72 apply zenon_Hd1. apply refl_equal. % 18.52/18.72 apply zenon_H79. apply refl_equal. % 18.52/18.72 apply zenon_Hd1. apply refl_equal. % 18.52/18.72 apply zenon_Hd1. apply refl_equal. % 18.52/18.72 apply (zenon_notand_s _ _ zenon_H1dc); [ zenon_intro zenon_H118 | zenon_intro zenon_H188 ]. % 18.52/18.72 apply (zenon_L228_); trivial. % 18.52/18.72 apply zenon_H188. apply sym_equal. exact zenon_H60. % 18.52/18.72 (* end of lemma zenon_L229_ *) % 18.52/18.72 assert (zenon_L230_ : (((op (e0) (e3)) = (e1))\/(((op (e1) (e3)) = (e1))\/(((op (e2) (e3)) = (e1))\/((op (e3) (e3)) = (e1))))) -> (~((e1) = (e2))) -> (~((op (e1) (e2)) = (op (e1) (e3)))) -> ((op (e1) (e2)) = (e1)) -> ((op (e3) (e3)) = (e0)) -> ((op (e0) (e3)) = (e2)) -> ((op (e3) (e0)) = (e1)) -> (~((op (e3) (e0)) = (op (e3) (e3)))) -> False). % 18.52/18.72 do 0 intro. intros zenon_H133 zenon_H7c zenon_H124 zenon_Hf0 zenon_H60 zenon_Hcd zenon_Hac zenon_H71. % 18.52/18.72 apply (zenon_or_s _ _ zenon_H133); [ zenon_intro zenon_Hc3 | zenon_intro zenon_H134 ]. % 18.52/18.72 apply (zenon_L82_); trivial. % 18.52/18.72 apply (zenon_or_s _ _ zenon_H134); [ zenon_intro zenon_Hd6 | zenon_intro zenon_H135 ]. % 18.52/18.72 apply (zenon_L78_); trivial. % 18.52/18.72 apply (zenon_or_s _ _ zenon_H135); [ zenon_intro zenon_Hf4 | zenon_intro zenon_Hc4 ]. % 18.52/18.72 apply (zenon_L229_); trivial. % 18.52/18.72 apply (zenon_L189_); trivial. % 18.52/18.72 (* end of lemma zenon_L230_ *) % 18.52/18.72 assert (zenon_L231_ : (((op (e3) (e0)) = (e0))\/(((op (e3) (e1)) = (e0))\/(((op (e3) (e2)) = (e0))\/((op (e3) (e3)) = (e0))))) -> (~((op (e3) (e0)) = (e0))) -> (~((op (e3) (e1)) = (e0))) -> (~((op (e3) (e2)) = (e0))) -> ((op (e2) (e3)) = (e1)) -> ((op (e0) (e3)) = (e2)) -> False). % 18.52/18.72 do 0 intro. intros zenon_H1ac zenon_H40 zenon_H1ad zenon_H18b zenon_Hf4 zenon_Hcd. % 18.52/18.72 apply (zenon_or_s _ _ zenon_H1ac); [ zenon_intro zenon_H44 | zenon_intro zenon_H1af ]. % 18.52/18.72 exact (zenon_H40 zenon_H44). % 18.52/18.72 apply (zenon_or_s _ _ zenon_H1af); [ zenon_intro zenon_H1b1 | zenon_intro zenon_H1b0 ]. % 18.52/18.72 exact (zenon_H1ad zenon_H1b1). % 18.52/18.72 apply (zenon_or_s _ _ zenon_H1b0); [ zenon_intro zenon_H61 | zenon_intro zenon_H60 ]. % 18.52/18.72 exact (zenon_H18b zenon_H61). % 18.52/18.72 apply (zenon_L229_); trivial. % 18.52/18.72 (* end of lemma zenon_L231_ *) % 18.52/18.72 assert (zenon_L232_ : (((op (e2) (e0)) = (e1))\/(((op (e2) (e1)) = (e1))\/(((op (e2) (e2)) = (e1))\/((op (e2) (e3)) = (e1))))) -> ((op (e0) (e0)) = (e1)) -> (~((op (e0) (e0)) = (op (e2) (e0)))) -> (~((op (e2) (e1)) = (op (e3) (e1)))) -> ((op (e3) (e1)) = (e1)) -> ((op (e1) (e2)) = (e0)) -> ((op (e0) (e2)) = (e3)) -> (((op (e3) (e0)) = (e0))\/(((op (e3) (e1)) = (e0))\/(((op (e3) (e2)) = (e0))\/((op (e3) (e3)) = (e0))))) -> (~((op (e3) (e0)) = (e0))) -> (~((op (e3) (e1)) = (e0))) -> (~((op (e3) (e2)) = (e0))) -> ((op (e0) (e3)) = (e2)) -> False). % 18.52/18.72 do 0 intro. intros zenon_H106 zenon_H7a zenon_H39 zenon_Haf zenon_Hae zenon_H2a zenon_Ha9 zenon_H1ac zenon_H40 zenon_H1ad zenon_H18b zenon_Hcd. % 18.52/18.72 apply (zenon_or_s _ _ zenon_H106); [ zenon_intro zenon_Hed | zenon_intro zenon_H107 ]. % 18.52/18.72 apply (zenon_L134_); trivial. % 18.52/18.72 apply (zenon_or_s _ _ zenon_H107); [ zenon_intro zenon_Ha5 | zenon_intro zenon_H108 ]. % 18.52/18.72 apply (zenon_L42_); trivial. % 18.52/18.72 apply (zenon_or_s _ _ zenon_H108); [ zenon_intro zenon_Hf1 | zenon_intro zenon_Hf4 ]. % 18.52/18.72 apply (zenon_L184_); trivial. % 18.52/18.72 apply (zenon_L231_); trivial. % 18.52/18.72 (* end of lemma zenon_L232_ *) % 18.52/18.72 assert (zenon_L233_ : (((op (e0) (e2)) = (e0))\/(((op (e1) (e2)) = (e0))\/(((op (e2) (e2)) = (e0))\/((op (e3) (e2)) = (e0))))) -> (~((op (e0) (e2)) = (e0))) -> ((op (e0) (e3)) = (e2)) -> (~((op (e3) (e1)) = (e0))) -> (~((op (e3) (e0)) = (e0))) -> (((op (e3) (e0)) = (e0))\/(((op (e3) (e1)) = (e0))\/(((op (e3) (e2)) = (e0))\/((op (e3) (e3)) = (e0))))) -> ((op (e0) (e2)) = (e3)) -> ((op (e3) (e1)) = (e1)) -> (~((op (e2) (e1)) = (op (e3) (e1)))) -> (~((op (e0) (e0)) = (op (e2) (e0)))) -> ((op (e0) (e0)) = (e1)) -> (((op (e2) (e0)) = (e1))\/(((op (e2) (e1)) = (e1))\/(((op (e2) (e2)) = (e1))\/((op (e2) (e3)) = (e1))))) -> (~((op (e2) (e2)) = (e0))) -> (~((op (e3) (e2)) = (e0))) -> False). % 18.52/18.72 do 0 intro. intros zenon_H6a zenon_H75 zenon_Hcd zenon_H1ad zenon_H40 zenon_H1ac zenon_Ha9 zenon_Hae zenon_Haf zenon_H39 zenon_H7a zenon_H106 zenon_H81 zenon_H18b. % 18.52/18.72 apply (zenon_or_s _ _ zenon_H6a); [ zenon_intro zenon_H48 | zenon_intro zenon_H6b ]. % 18.52/18.72 exact (zenon_H75 zenon_H48). % 18.52/18.72 apply (zenon_or_s _ _ zenon_H6b); [ zenon_intro zenon_H2a | zenon_intro zenon_H6c ]. % 18.52/18.72 apply (zenon_L232_); trivial. % 18.52/18.72 apply (zenon_or_s _ _ zenon_H6c); [ zenon_intro zenon_H2c | zenon_intro zenon_H61 ]. % 18.52/18.72 exact (zenon_H81 zenon_H2c). % 18.52/18.72 exact (zenon_H18b zenon_H61). % 18.52/18.72 (* end of lemma zenon_L233_ *) % 18.52/18.72 assert (zenon_L234_ : (~((op (e0) (e3)) = (op (e2) (e3)))) -> ((op (e0) (e3)) = (e2)) -> ((op (e2) (e3)) = (e2)) -> False). % 18.52/18.72 do 0 intro. intros zenon_He2 zenon_Hcd zenon_H11d. % 18.52/18.72 cut (((op (e0) (e3)) = (e2)) = ((op (e0) (e3)) = (op (e2) (e3)))). % 18.52/18.72 intro zenon_D_pnotp. % 18.52/18.72 apply zenon_He2. % 18.52/18.72 rewrite <- zenon_D_pnotp. % 18.52/18.72 exact zenon_Hcd. % 18.52/18.72 cut (((e2) = (op (e2) (e3)))); [idtac | apply NNPP; zenon_intro zenon_H1df]. % 18.52/18.72 cut (((op (e0) (e3)) = (op (e0) (e3)))); [idtac | apply NNPP; zenon_intro zenon_H21]. % 18.52/18.72 congruence. % 18.52/18.72 apply zenon_H21. apply refl_equal. % 18.52/18.72 apply zenon_H1df. apply sym_equal. exact zenon_H11d. % 18.52/18.72 (* end of lemma zenon_L234_ *) % 18.52/18.72 assert (zenon_L235_ : (((op (e2) (e3)) = (e0))\/(((op (e2) (e3)) = (e1))\/(((op (e2) (e3)) = (e2))\/((op (e2) (e3)) = (e3))))) -> ((op (e3) (e3)) = (e0)) -> (~((op (e2) (e3)) = (op (e3) (e3)))) -> (~((op (e2) (e1)) = (op (e2) (e3)))) -> ((op (e2) (e1)) = (e1)) -> ((op (e0) (e3)) = (e2)) -> (~((op (e0) (e3)) = (op (e2) (e3)))) -> (~((op (e1) (e3)) = (op (e2) (e3)))) -> ((op (e1) (e3)) = (e3)) -> False). % 18.52/18.72 do 0 intro. intros zenon_H11f zenon_H60 zenon_Hf3 zenon_H1c7 zenon_Ha5 zenon_Hcd zenon_He2 zenon_Hdb zenon_Hdc. % 18.52/18.72 apply (zenon_or_s _ _ zenon_H11f); [ zenon_intro zenon_H37 | zenon_intro zenon_H120 ]. % 18.52/18.72 apply (zenon_L219_); trivial. % 18.52/18.72 apply (zenon_or_s _ _ zenon_H120); [ zenon_intro zenon_Hf4 | zenon_intro zenon_H121 ]. % 18.52/18.72 apply (zenon_L188_); trivial. % 18.52/18.72 apply (zenon_or_s _ _ zenon_H121); [ zenon_intro zenon_H11d | zenon_intro zenon_Hdd ]. % 18.52/18.72 apply (zenon_L234_); trivial. % 18.52/18.72 apply (zenon_L52_); trivial. % 18.52/18.72 (* end of lemma zenon_L235_ *) % 18.52/18.72 assert (zenon_L236_ : (((op (e0) (e3)) = (e3))\/(((op (e1) (e3)) = (e3))\/(((op (e2) (e3)) = (e3))\/((op (e3) (e3)) = (e3))))) -> (~((e2) = (e3))) -> (~((op (e0) (e3)) = (op (e2) (e3)))) -> ((op (e2) (e1)) = (e1)) -> (~((op (e2) (e1)) = (op (e2) (e3)))) -> (~((op (e2) (e3)) = (op (e3) (e3)))) -> ((op (e3) (e3)) = (e0)) -> (((op (e2) (e3)) = (e0))\/(((op (e2) (e3)) = (e1))\/(((op (e2) (e3)) = (e2))\/((op (e2) (e3)) = (e3))))) -> (~((op (e1) (e3)) = (op (e2) (e3)))) -> ((op (e1) (e0)) = (e2)) -> (~((op (e1) (e0)) = (op (e1) (e3)))) -> (~((op (e1) (e3)) = (op (e3) (e3)))) -> ((op (e3) (e3)) = (e1)) -> ((op (e0) (e3)) = (e2)) -> (((op (e1) (e3)) = (e0))\/(((op (e1) (e3)) = (e1))\/(((op (e1) (e3)) = (e2))\/((op (e1) (e3)) = (e3))))) -> (~((op (e3) (e3)) = (e3))) -> False). % 18.52/18.72 do 0 intro. intros zenon_H136 zenon_H12b zenon_He2 zenon_Ha5 zenon_H1c7 zenon_Hf3 zenon_H60 zenon_H11f zenon_Hdb zenon_H86 zenon_Hd8 zenon_Hd5 zenon_Hc4 zenon_Hcd zenon_Hdf zenon_H102. % 18.52/18.72 apply (zenon_or_s _ _ zenon_H136); [ zenon_intro zenon_He3 | zenon_intro zenon_H137 ]. % 18.52/18.72 apply (zenon_L81_); trivial. % 18.52/18.72 apply (zenon_or_s _ _ zenon_H137); [ zenon_intro zenon_Hdc | zenon_intro zenon_H138 ]. % 18.52/18.72 apply (zenon_L235_); trivial. % 18.52/18.72 apply (zenon_or_s _ _ zenon_H138); [ zenon_intro zenon_Hdd | zenon_intro zenon_H105 ]. % 18.52/18.72 apply (zenon_L53_); trivial. % 18.52/18.72 exact (zenon_H102 zenon_H105). % 18.52/18.72 (* end of lemma zenon_L236_ *) % 18.52/18.72 assert (zenon_L237_ : (((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 (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 (e1) (e0)) = (op (e1) (e3)))) -> ((op (e1) (e0)) = (e2)) -> (~((op (e1) (e3)) = (op (e2) (e3)))) -> (((op (e2) (e3)) = (e0))\/(((op (e2) (e3)) = (e1))\/(((op (e2) (e3)) = (e2))\/((op (e2) (e3)) = (e3))))) -> (~((op (e2) (e3)) = (op (e3) (e3)))) -> (~((op (e2) (e1)) = (op (e2) (e3)))) -> (~((op (e0) (e3)) = (op (e2) (e3)))) -> (~((e2) = (e3))) -> (((op (e0) (e3)) = (e3))\/(((op (e1) (e3)) = (e3))\/(((op (e2) (e3)) = (e3))\/((op (e3) (e3)) = (e3))))) -> (((op (e2) (e2)) = (e0))\/(((op (e2) (e2)) = (e1))\/(((op (e2) (e2)) = (e2))\/((op (e2) (e2)) = (e3))))) -> (~((op (e2) (e2)) = (op (e3) (e2)))) -> (~((op (e2) (e2)) = (e2))) -> (((op (e0) (e2)) = (e0))\/(((op (e1) (e2)) = (e0))\/(((op (e2) (e2)) = (e0))\/((op (e3) (e2)) = (e0))))) -> (~((op (e0) (e2)) = (e0))) -> (~((op (e2) (e2)) = (e0))) -> (((op (e0) (e3)) = (e1))\/(((op (e1) (e3)) = (e1))\/(((op (e2) (e3)) = (e1))\/((op (e3) (e3)) = (e1))))) -> (~((e1) = (e2))) -> (~((op (e1) (e2)) = (op (e1) (e3)))) -> ((op (e1) (e2)) = (e1)) -> (~((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)) = (e1))\/(((op (e2) (e1)) = (e1))\/(((op (e2) (e2)) = (e1))\/((op (e2) (e3)) = (e1))))) -> ((op (e0) (e0)) = (e1)) -> (~((op (e0) (e0)) = (op (e2) (e0)))) -> (~((op (e2) (e1)) = (op (e3) (e1)))) -> ((op (e1) (e2)) = (e0)) -> ((op (e0) (e2)) = (e3)) -> (((op (e3) (e0)) = (e0))\/(((op (e3) (e1)) = (e0))\/(((op (e3) (e2)) = (e0))\/((op (e3) (e3)) = (e0))))) -> (~((op (e3) (e0)) = (e0))) -> (~((op (e3) (e1)) = (e0))) -> (~((op (e3) (e2)) = (e0))) -> ((op (e0) (e3)) = (e2)) -> False). % 18.52/18.72 do 0 intro. intros zenon_H109 zenon_Ha1 zenon_H49 zenon_H10a zenon_H102 zenon_Hdf zenon_Hd5 zenon_Hd8 zenon_H86 zenon_Hdb zenon_H11f zenon_Hf3 zenon_H1c7 zenon_He2 zenon_H12b zenon_H136 zenon_H1c4 zenon_H18f zenon_H173 zenon_H6a zenon_H75 zenon_H81 zenon_H133 zenon_H7c zenon_H124 zenon_Hf0 zenon_H71 zenon_He8 zenon_H106 zenon_H7a zenon_H39 zenon_Haf zenon_H2a zenon_Ha9 zenon_H1ac zenon_H40 zenon_H1ad zenon_H18b zenon_Hcd. % 18.52/18.72 apply (zenon_or_s _ _ zenon_H109); [ zenon_intro zenon_Ha0 | zenon_intro zenon_H10b ]. % 18.52/18.72 apply (zenon_L38_); trivial. % 18.52/18.72 apply (zenon_or_s _ _ zenon_H10b); [ zenon_intro zenon_H10d | zenon_intro zenon_H10c ]. % 18.52/18.72 exact (zenon_H10a zenon_H10d). % 18.52/18.72 apply (zenon_or_s _ _ zenon_H10c); [ zenon_intro zenon_Ha5 | zenon_intro zenon_Hae ]. % 18.52/18.72 apply (zenon_or_s _ _ zenon_H1ac); [ zenon_intro zenon_H44 | zenon_intro zenon_H1af ]. % 18.52/18.72 exact (zenon_H40 zenon_H44). % 18.52/18.72 apply (zenon_or_s _ _ zenon_H1af); [ zenon_intro zenon_H1b1 | zenon_intro zenon_H1b0 ]. % 18.52/18.72 exact (zenon_H1ad zenon_H1b1). % 18.52/18.72 apply (zenon_or_s _ _ zenon_H1b0); [ zenon_intro zenon_H61 | zenon_intro zenon_H60 ]. % 18.52/18.72 exact (zenon_H18b zenon_H61). % 18.52/18.72 apply (zenon_or_s _ _ zenon_He8); [ zenon_intro zenon_Hac | zenon_intro zenon_Heb ]. % 18.52/18.72 apply (zenon_L230_); trivial. % 18.52/18.72 apply (zenon_or_s _ _ zenon_Heb); [ zenon_intro zenon_Hae | zenon_intro zenon_Hec ]. % 18.52/18.72 apply (zenon_L233_); trivial. % 18.52/18.72 apply (zenon_or_s _ _ zenon_Hec); [ zenon_intro zenon_Hba | zenon_intro zenon_Hc4 ]. % 18.52/18.72 apply (zenon_L186_); trivial. % 18.52/18.72 apply (zenon_L236_); trivial. % 18.52/18.72 apply (zenon_L232_); trivial. % 18.52/18.72 (* end of lemma zenon_L237_ *) % 18.52/18.72 assert (zenon_L238_ : (((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)) = (e2)) -> ((op (e3) (e0)) = (e2)) -> (~((e2) = (e3))) -> False). % 18.52/18.72 do 0 intro. intros zenon_H1e0 zenon_H95 zenon_H7a zenon_H86 zenon_H148 zenon_H12b. % 18.52/18.72 apply (zenon_or_s _ _ zenon_H1e0); [ zenon_intro zenon_H3a | zenon_intro zenon_H1e1 ]. % 18.52/18.72 apply (zenon_L35_); trivial. % 18.52/18.72 apply (zenon_or_s _ _ zenon_H1e1); [ zenon_intro zenon_H9e | zenon_intro zenon_H1e2 ]. % 18.52/18.72 apply (zenon_L107_); trivial. % 18.52/18.72 apply (zenon_or_s _ _ zenon_H1e2); [ zenon_intro zenon_H3b | zenon_intro zenon_H15e ]. % 18.52/18.72 apply (zenon_L33_); trivial. % 18.52/18.72 apply (zenon_L109_); trivial. % 18.52/18.72 (* end of lemma zenon_L238_ *) % 18.52/18.72 assert (zenon_L239_ : (~((op (op (e0) (e0)) (e0)) = (op (e3) (e0)))) -> ((op (e0) (e0)) = (e3)) -> False). % 18.52/18.72 do 0 intro. intros zenon_H1e3 zenon_H3a. % 18.52/18.72 cut (((e0) = (e0))); [idtac | apply NNPP; zenon_intro zenon_H82]. % 18.52/18.72 cut (((op (e0) (e0)) = (e3))); [idtac | apply NNPP; zenon_intro zenon_H98]. % 18.52/18.72 congruence. % 18.52/18.72 exact (zenon_H98 zenon_H3a). % 18.52/18.72 apply zenon_H82. apply refl_equal. % 18.52/18.72 (* end of lemma zenon_L239_ *) % 18.52/18.72 assert (zenon_L240_ : ((op (e3) (e0)) = (e1)) -> ((op (e0) (e0)) = (e3)) -> (~((e1) = (op (op (e0) (e0)) (e0)))) -> False). % 18.52/18.72 do 0 intro. intros zenon_Hac zenon_H3a zenon_H1e4. % 18.52/18.72 elim (classic ((op (op (e0) (e0)) (e0)) = (op (op (e0) (e0)) (e0)))); [ zenon_intro zenon_H88 | zenon_intro zenon_H89 ]. % 18.52/18.72 cut (((op (op (e0) (e0)) (e0)) = (op (op (e0) (e0)) (e0))) = ((e1) = (op (op (e0) (e0)) (e0)))). % 18.52/18.72 intro zenon_D_pnotp. % 18.52/18.72 apply zenon_H1e4. % 18.52/18.72 rewrite <- zenon_D_pnotp. % 18.52/18.72 exact zenon_H88. % 18.52/18.72 cut (((op (op (e0) (e0)) (e0)) = (op (op (e0) (e0)) (e0)))); [idtac | apply NNPP; zenon_intro zenon_H89]. % 18.52/18.72 cut (((op (op (e0) (e0)) (e0)) = (e1))); [idtac | apply NNPP; zenon_intro zenon_H1e5]. % 18.52/18.72 congruence. % 18.52/18.72 cut (((op (e3) (e0)) = (e1)) = ((op (op (e0) (e0)) (e0)) = (e1))). % 18.52/18.72 intro zenon_D_pnotp. % 18.52/18.72 apply zenon_H1e5. % 18.52/18.72 rewrite <- zenon_D_pnotp. % 18.52/18.72 exact zenon_Hac. % 18.52/18.72 cut (((e1) = (e1))); [idtac | apply NNPP; zenon_intro zenon_H79]. % 18.52/18.72 cut (((op (e3) (e0)) = (op (op (e0) (e0)) (e0)))); [idtac | apply NNPP; zenon_intro zenon_H1e6]. % 18.52/18.72 congruence. % 18.52/18.72 elim (classic ((op (op (e0) (e0)) (e0)) = (op (op (e0) (e0)) (e0)))); [ zenon_intro zenon_H88 | zenon_intro zenon_H89 ]. % 18.52/18.72 cut (((op (op (e0) (e0)) (e0)) = (op (op (e0) (e0)) (e0))) = ((op (e3) (e0)) = (op (op (e0) (e0)) (e0)))). % 18.52/18.72 intro zenon_D_pnotp. % 18.52/18.72 apply zenon_H1e6. % 18.52/18.72 rewrite <- zenon_D_pnotp. % 18.52/18.72 exact zenon_H88. % 18.52/18.72 cut (((op (op (e0) (e0)) (e0)) = (op (op (e0) (e0)) (e0)))); [idtac | apply NNPP; zenon_intro zenon_H89]. % 18.52/18.72 cut (((op (op (e0) (e0)) (e0)) = (op (e3) (e0)))); [idtac | apply NNPP; zenon_intro zenon_H1e3]. % 18.52/18.72 congruence. % 18.52/18.72 apply (zenon_L239_); trivial. % 18.52/18.72 apply zenon_H89. apply refl_equal. % 18.52/18.72 apply zenon_H89. apply refl_equal. % 18.52/18.72 apply zenon_H79. apply refl_equal. % 18.52/18.72 apply zenon_H89. apply refl_equal. % 18.52/18.72 apply zenon_H89. apply refl_equal. % 18.52/18.72 (* end of lemma zenon_L240_ *) % 18.52/18.72 assert (zenon_L241_ : ((op (e1) (e0)) = (e2)) -> ((op (e3) (e0)) = (e1)) -> ((op (e0) (e0)) = (e3)) -> False). % 18.52/18.72 do 0 intro. intros zenon_H86 zenon_Hac zenon_H3a. % 18.52/18.72 apply (zenon_notand_s _ _ ax8); [ zenon_intro zenon_H159 | zenon_intro zenon_H1e7 ]. % 18.52/18.72 elim (classic ((op (op (op (e0) (e0)) (e0)) (e0)) = (op (op (op (e0) (e0)) (e0)) (e0)))); [ zenon_intro zenon_H8e | zenon_intro zenon_H8f ]. % 18.52/18.72 cut (((op (op (op (e0) (e0)) (e0)) (e0)) = (op (op (op (e0) (e0)) (e0)) (e0))) = ((e2) = (op (op (op (e0) (e0)) (e0)) (e0)))). % 18.52/18.72 intro zenon_D_pnotp. % 18.52/18.72 apply zenon_H159. % 18.52/18.72 rewrite <- zenon_D_pnotp. % 18.52/18.72 exact zenon_H8e. % 18.52/18.72 cut (((op (op (op (e0) (e0)) (e0)) (e0)) = (op (op (op (e0) (e0)) (e0)) (e0)))); [idtac | apply NNPP; zenon_intro zenon_H8f]. % 18.52/18.72 cut (((op (op (op (e0) (e0)) (e0)) (e0)) = (e2))); [idtac | apply NNPP; zenon_intro zenon_H15a]. % 18.52/18.72 congruence. % 18.52/18.72 cut (((op (e1) (e0)) = (e2)) = ((op (op (op (e0) (e0)) (e0)) (e0)) = (e2))). % 18.52/18.72 intro zenon_D_pnotp. % 18.52/18.72 apply zenon_H15a. % 18.52/18.72 rewrite <- zenon_D_pnotp. % 18.52/18.72 exact zenon_H86. % 18.52/18.72 cut (((e2) = (e2))); [idtac | apply NNPP; zenon_intro zenon_H7e]. % 18.52/18.72 cut (((op (e1) (e0)) = (op (op (op (e0) (e0)) (e0)) (e0)))); [idtac | apply NNPP; zenon_intro zenon_H1e8]. % 18.52/18.72 congruence. % 18.52/18.72 elim (classic ((op (op (op (e0) (e0)) (e0)) (e0)) = (op (op (op (e0) (e0)) (e0)) (e0)))); [ zenon_intro zenon_H8e | zenon_intro zenon_H8f ]. % 18.52/18.72 cut (((op (op (op (e0) (e0)) (e0)) (e0)) = (op (op (op (e0) (e0)) (e0)) (e0))) = ((op (e1) (e0)) = (op (op (op (e0) (e0)) (e0)) (e0)))). % 18.52/18.72 intro zenon_D_pnotp. % 18.52/18.72 apply zenon_H1e8. % 18.52/18.72 rewrite <- zenon_D_pnotp. % 18.52/18.72 exact zenon_H8e. % 18.52/18.72 cut (((op (op (op (e0) (e0)) (e0)) (e0)) = (op (op (op (e0) (e0)) (e0)) (e0)))); [idtac | apply NNPP; zenon_intro zenon_H8f]. % 18.52/18.72 cut (((op (op (op (e0) (e0)) (e0)) (e0)) = (op (e1) (e0)))); [idtac | apply NNPP; zenon_intro zenon_H1e9]. % 18.52/18.72 congruence. % 18.52/18.72 cut (((e0) = (e0))); [idtac | apply NNPP; zenon_intro zenon_H82]. % 18.52/18.72 cut (((op (op (e0) (e0)) (e0)) = (e1))); [idtac | apply NNPP; zenon_intro zenon_H1e5]. % 18.52/18.72 congruence. % 18.52/18.72 cut (((op (e3) (e0)) = (e1)) = ((op (op (e0) (e0)) (e0)) = (e1))). % 18.52/18.72 intro zenon_D_pnotp. % 18.52/18.72 apply zenon_H1e5. % 18.52/18.72 rewrite <- zenon_D_pnotp. % 18.52/18.72 exact zenon_Hac. % 18.52/18.72 cut (((e1) = (e1))); [idtac | apply NNPP; zenon_intro zenon_H79]. % 18.52/18.72 cut (((op (e3) (e0)) = (op (op (e0) (e0)) (e0)))); [idtac | apply NNPP; zenon_intro zenon_H1e6]. % 18.52/18.72 congruence. % 18.52/18.72 elim (classic ((op (op (e0) (e0)) (e0)) = (op (op (e0) (e0)) (e0)))); [ zenon_intro zenon_H88 | zenon_intro zenon_H89 ]. % 18.52/18.72 cut (((op (op (e0) (e0)) (e0)) = (op (op (e0) (e0)) (e0))) = ((op (e3) (e0)) = (op (op (e0) (e0)) (e0)))). % 18.52/18.72 intro zenon_D_pnotp. % 18.52/18.72 apply zenon_H1e6. % 18.52/18.72 rewrite <- zenon_D_pnotp. % 18.52/18.72 exact zenon_H88. % 18.52/18.72 cut (((op (op (e0) (e0)) (e0)) = (op (op (e0) (e0)) (e0)))); [idtac | apply NNPP; zenon_intro zenon_H89]. % 18.52/18.72 cut (((op (op (e0) (e0)) (e0)) = (op (e3) (e0)))); [idtac | apply NNPP; zenon_intro zenon_H1e3]. % 18.52/18.72 congruence. % 18.52/18.72 apply (zenon_L239_); trivial. % 18.52/18.72 apply zenon_H89. apply refl_equal. % 18.52/18.72 apply zenon_H89. apply refl_equal. % 18.52/18.72 apply zenon_H79. apply refl_equal. % 18.52/18.72 apply zenon_H82. apply refl_equal. % 18.52/18.72 apply zenon_H8f. apply refl_equal. % 18.52/18.72 apply zenon_H8f. apply refl_equal. % 18.52/18.72 apply zenon_H7e. apply refl_equal. % 18.52/18.72 apply zenon_H8f. apply refl_equal. % 18.52/18.72 apply zenon_H8f. apply refl_equal. % 18.52/18.72 apply (zenon_notand_s _ _ zenon_H1e7); [ zenon_intro zenon_H1e4 | zenon_intro zenon_H1ea ]. % 18.52/18.72 apply (zenon_L240_); trivial. % 18.52/18.72 apply zenon_H1ea. apply sym_equal. exact zenon_H3a. % 18.52/18.72 (* end of lemma zenon_L241_ *) % 18.52/18.72 assert (zenon_L242_ : (~((op (e3) (e0)) = (op (e3) (e1)))) -> ((op (e3) (e0)) = (e1)) -> ((op (e3) (e1)) = (e1)) -> False). % 18.52/18.72 do 0 intro. intros zenon_H1cf zenon_Hac zenon_Hae. % 18.52/18.72 cut (((op (e3) (e0)) = (e1)) = ((op (e3) (e0)) = (op (e3) (e1)))). % 18.52/18.72 intro zenon_D_pnotp. % 18.52/18.72 apply zenon_H1cf. % 18.52/18.72 rewrite <- zenon_D_pnotp. % 18.52/18.72 exact zenon_Hac. % 18.52/18.72 cut (((e1) = (op (e3) (e1)))); [idtac | apply NNPP; zenon_intro zenon_H132]. % 18.52/18.72 cut (((op (e3) (e0)) = (op (e3) (e0)))); [idtac | apply NNPP; zenon_intro zenon_H70]. % 18.52/18.72 congruence. % 18.52/18.72 apply zenon_H70. apply refl_equal. % 18.52/18.72 apply zenon_H132. apply sym_equal. exact zenon_Hae. % 18.52/18.72 (* end of lemma zenon_L242_ *) % 18.52/18.72 assert (zenon_L243_ : (((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 (e3) (e2)) = (e0))) -> (~((op (e2) (e2)) = (e0))) -> (((op (e0) (e3)) = (e1))\/(((op (e1) (e3)) = (e1))\/(((op (e2) (e3)) = (e1))\/((op (e3) (e3)) = (e1))))) -> (~((op (e0) (e0)) = (op (e0) (e3)))) -> ((op (e0) (e0)) = (e1)) -> (~((op (e2) (e2)) = (e2))) -> (~((op (e2) (e2)) = (op (e3) (e2)))) -> ((op (e0) (e2)) = (e3)) -> (((op (e2) (e2)) = (e0))\/(((op (e2) (e2)) = (e1))\/(((op (e2) (e2)) = (e2))\/((op (e2) (e2)) = (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))))) -> (~((op (e2) (e1)) = (op (e2) (e3)))) -> (~((op (e3) (e0)) = (op (e3) (e3)))) -> (~((op (e0) (e2)) = (e0))) -> (((op (e0) (e2)) = (e0))\/(((op (e1) (e2)) = (e0))\/(((op (e2) (e2)) = (e0))\/((op (e3) (e2)) = (e0))))) -> (~((op (e3) (e0)) = (op (e3) (e1)))) -> ((op (e3) (e0)) = (e1)) -> False). % 18.52/18.72 do 0 intro. intros zenon_H109 zenon_Ha1 zenon_H49 zenon_H10a zenon_H18b zenon_H81 zenon_H133 zenon_H189 zenon_H7a zenon_H173 zenon_H18f zenon_Ha9 zenon_H1c4 zenon_H124 zenon_H95 zenon_H139 zenon_H1c7 zenon_H71 zenon_H75 zenon_H6a zenon_H1cf zenon_Hac. % 18.52/18.72 apply (zenon_or_s _ _ zenon_H109); [ zenon_intro zenon_Ha0 | zenon_intro zenon_H10b ]. % 18.52/18.72 apply (zenon_L38_); trivial. % 18.52/18.72 apply (zenon_or_s _ _ zenon_H10b); [ zenon_intro zenon_H10d | zenon_intro zenon_H10c ]. % 18.52/18.72 exact (zenon_H10a zenon_H10d). % 18.52/18.72 apply (zenon_or_s _ _ zenon_H10c); [ zenon_intro zenon_Ha5 | zenon_intro zenon_Hae ]. % 18.52/18.72 apply (zenon_L198_); trivial. % 18.52/18.72 apply (zenon_L242_); trivial. % 18.52/18.72 (* end of lemma zenon_L243_ *) % 18.52/18.72 assert (zenon_L244_ : ((op (e3) (e3)) = (e0)) -> ((op (e3) (e1)) = (e0)) -> (~((op (e3) (e1)) = (op (e3) (e3)))) -> False). % 18.52/18.72 do 0 intro. intros zenon_H60 zenon_H1b1 zenon_H130. % 18.52/18.72 elim (classic ((op (e3) (e3)) = (op (e3) (e3)))); [ zenon_intro zenon_H63 | zenon_intro zenon_H64 ]. % 18.52/18.72 cut (((op (e3) (e3)) = (op (e3) (e3))) = ((op (e3) (e1)) = (op (e3) (e3)))). % 18.52/18.72 intro zenon_D_pnotp. % 18.52/18.72 apply zenon_H130. % 18.52/18.72 rewrite <- zenon_D_pnotp. % 18.52/18.72 exact zenon_H63. % 18.52/18.72 cut (((op (e3) (e3)) = (op (e3) (e3)))); [idtac | apply NNPP; zenon_intro zenon_H64]. % 18.52/18.72 cut (((op (e3) (e3)) = (op (e3) (e1)))); [idtac | apply NNPP; zenon_intro zenon_H131]. % 18.52/18.72 congruence. % 18.52/18.72 cut (((op (e3) (e3)) = (e0)) = ((op (e3) (e3)) = (op (e3) (e1)))). % 18.52/18.72 intro zenon_D_pnotp. % 18.52/18.72 apply zenon_H131. % 18.52/18.72 rewrite <- zenon_D_pnotp. % 18.52/18.72 exact zenon_H60. % 18.52/18.72 cut (((e0) = (op (e3) (e1)))); [idtac | apply NNPP; zenon_intro zenon_H1eb]. % 18.52/18.72 cut (((op (e3) (e3)) = (op (e3) (e3)))); [idtac | apply NNPP; zenon_intro zenon_H64]. % 18.52/18.72 congruence. % 18.52/18.72 apply zenon_H64. apply refl_equal. % 18.52/18.72 apply zenon_H1eb. apply sym_equal. exact zenon_H1b1. % 18.52/18.72 apply zenon_H64. apply refl_equal. % 18.52/18.72 apply zenon_H64. apply refl_equal. % 18.52/18.72 (* end of lemma zenon_L244_ *) % 18.52/18.72 assert (zenon_L245_ : (((op (e3) (e3)) = (e0))\/(((op (e3) (e3)) = (e1))\/(((op (e3) (e3)) = (e2))\/((op (e3) (e3)) = (e3))))) -> (~((op (e3) (e1)) = (op (e3) (e3)))) -> ((op (e3) (e1)) = (e0)) -> ((op (e0) (e3)) = (e1)) -> (~((op (e0) (e3)) = (op (e3) (e3)))) -> ((op (e2) (e3)) = (e2)) -> (~((op (e2) (e3)) = (op (e3) (e3)))) -> (~((op (e3) (e3)) = (e3))) -> False). % 18.52/18.72 do 0 intro. intros zenon_H101 zenon_H130 zenon_H1b1 zenon_Hc3 zenon_Hc2 zenon_H11d zenon_Hf3 zenon_H102. % 18.52/18.72 apply (zenon_or_s _ _ zenon_H101); [ zenon_intro zenon_H60 | zenon_intro zenon_H103 ]. % 18.52/18.72 apply (zenon_L244_); trivial. % 18.52/18.72 apply (zenon_or_s _ _ zenon_H103); [ zenon_intro zenon_Hc4 | zenon_intro zenon_H104 ]. % 18.52/18.72 apply (zenon_L46_); trivial. % 18.52/18.72 apply (zenon_or_s _ _ zenon_H104); [ zenon_intro zenon_Hf6 | zenon_intro zenon_H105 ]. % 18.52/18.72 apply (zenon_L97_); trivial. % 18.52/18.72 exact (zenon_H102 zenon_H105). % 18.52/18.72 (* end of lemma zenon_L245_ *) % 18.52/18.72 assert (zenon_L246_ : (~((op (e0) (e2)) = (op (e2) (e2)))) -> ((op (e0) (e2)) = (e1)) -> ((op (e2) (e2)) = (e1)) -> False). % 18.52/18.72 do 0 intro. intros zenon_Ha8 zenon_H122 zenon_Hf1. % 18.52/18.72 cut (((op (e0) (e2)) = (e1)) = ((op (e0) (e2)) = (op (e2) (e2)))). % 18.52/18.72 intro zenon_D_pnotp. % 18.52/18.72 apply zenon_Ha8. % 18.52/18.72 rewrite <- zenon_D_pnotp. % 18.52/18.72 exact zenon_H122. % 18.52/18.72 cut (((e1) = (op (e2) (e2)))); [idtac | apply NNPP; zenon_intro zenon_Hf2]. % 18.52/18.72 cut (((op (e0) (e2)) = (op (e0) (e2)))); [idtac | apply NNPP; zenon_intro zenon_H4c]. % 18.52/18.72 congruence. % 18.52/18.72 apply zenon_H4c. apply refl_equal. % 18.52/18.72 apply zenon_Hf2. apply sym_equal. exact zenon_Hf1. % 18.52/18.72 (* end of lemma zenon_L246_ *) % 18.52/18.72 assert (zenon_L247_ : (~((op (e3) (e1)) = (op (e3) (e2)))) -> ((op (e3) (e1)) = (e0)) -> ((op (e3) (e2)) = (e0)) -> False). % 18.52/18.72 do 0 intro. intros zenon_H1a4 zenon_H1b1 zenon_H61. % 18.52/18.72 cut (((op (e3) (e1)) = (e0)) = ((op (e3) (e1)) = (op (e3) (e2)))). % 18.52/18.72 intro zenon_D_pnotp. % 18.52/18.72 apply zenon_H1a4. % 18.52/18.72 rewrite <- zenon_D_pnotp. % 18.52/18.72 exact zenon_H1b1. % 18.52/18.72 cut (((e0) = (op (e3) (e2)))); [idtac | apply NNPP; zenon_intro zenon_H66]. % 18.52/18.72 cut (((op (e3) (e1)) = (op (e3) (e1)))); [idtac | apply NNPP; zenon_intro zenon_Hb1]. % 18.52/18.72 congruence. % 18.52/18.72 apply zenon_Hb1. apply refl_equal. % 18.52/18.72 apply zenon_H66. apply sym_equal. exact zenon_H61. % 18.52/18.72 (* end of lemma zenon_L247_ *) % 18.52/18.72 assert (zenon_L248_ : (((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 (e0) (e3)) = (e3)) -> (~((op (e0) (e3)) = (op (e2) (e3)))) -> (((op (e3) (e2)) = (e0))\/(((op (e3) (e2)) = (e1))\/(((op (e3) (e2)) = (e2))\/((op (e3) (e2)) = (e3))))) -> (~((op (e1) (e2)) = (op (e3) (e2)))) -> ((op (e0) (e2)) = (e2)) -> (~((op (e0) (e2)) = (op (e3) (e2)))) -> (~((op (e2) (e2)) = (op (e3) (e2)))) -> ((op (e2) (e1)) = (e1)) -> (~((e1) = (e3))) -> ((op (e1) (e0)) = (e2)) -> ((op (e0) (e0)) = (e1)) -> (((op (e2) (e0)) = (e3))\/(((op (e2) (e1)) = (e3))\/(((op (e2) (e2)) = (e3))\/((op (e2) (e3)) = (e3))))) -> ((op (e2) (e0)) = (e0)) -> (~((op (e2) (e0)) = (op (e2) (e2)))) -> (~((op (e3) (e1)) = (op (e3) (e2)))) -> ((op (e3) (e1)) = (e0)) -> False). % 18.52/18.72 do 0 intro. intros zenon_H6a zenon_H4a zenon_H49 zenon_He3 zenon_He2 zenon_H191 zenon_H115 zenon_H150 zenon_H14f zenon_H18f zenon_Ha5 zenon_H95 zenon_H86 zenon_H7a zenon_He7 zenon_H34 zenon_H52 zenon_H1a4 zenon_H1b1. % 18.52/18.72 apply (zenon_or_s _ _ zenon_H6a); [ zenon_intro zenon_H48 | zenon_intro zenon_H6b ]. % 18.52/18.72 apply (zenon_L9_); trivial. % 18.52/18.72 apply (zenon_or_s _ _ zenon_H6b); [ zenon_intro zenon_H2a | zenon_intro zenon_H6c ]. % 18.52/18.72 apply (zenon_L211_); trivial. % 18.52/18.72 apply (zenon_or_s _ _ zenon_H6c); [ zenon_intro zenon_H2c | zenon_intro zenon_H61 ]. % 18.52/18.72 apply (zenon_L11_); trivial. % 18.52/18.72 apply (zenon_L247_); trivial. % 18.52/18.72 (* end of lemma zenon_L248_ *) % 18.52/18.72 assert (zenon_L249_ : (~((op (e3) (e0)) = (op (e3) (e2)))) -> ((op (e3) (e0)) = (e1)) -> ((op (e3) (e2)) = (e1)) -> False). % 18.52/18.72 do 0 intro. intros zenon_H6f zenon_Hac zenon_Hba. % 18.52/18.72 cut (((op (e3) (e0)) = (e1)) = ((op (e3) (e0)) = (op (e3) (e2)))). % 18.52/18.72 intro zenon_D_pnotp. % 18.52/18.72 apply zenon_H6f. % 18.52/18.72 rewrite <- zenon_D_pnotp. % 18.52/18.72 exact zenon_Hac. % 18.52/18.72 cut (((e1) = (op (e3) (e2)))); [idtac | apply NNPP; zenon_intro zenon_H116]. % 18.52/18.72 cut (((op (e3) (e0)) = (op (e3) (e0)))); [idtac | apply NNPP; zenon_intro zenon_H70]. % 18.52/18.72 congruence. % 18.52/18.72 apply zenon_H70. apply refl_equal. % 18.52/18.72 apply zenon_H116. apply sym_equal. exact zenon_Hba. % 18.52/18.72 (* end of lemma zenon_L249_ *) % 18.52/18.72 assert (zenon_L250_ : (((op (e0) (e2)) = (e1))\/(((op (e1) (e2)) = (e1))\/(((op (e2) (e2)) = (e1))\/((op (e3) (e2)) = (e1))))) -> (~((op (e0) (e0)) = (op (e0) (e2)))) -> (~((op (e1) (e2)) = (op (e1) (e3)))) -> ((op (e1) (e3)) = (e1)) -> ((op (e0) (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 (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 (e0) (e1)) = (op (e0) (e2)))) -> ((op (e0) (e1)) = (e0)) -> (((op (e3) (e2)) = (e0))\/(((op (e3) (e2)) = (e1))\/(((op (e3) (e2)) = (e2))\/((op (e3) (e2)) = (e3))))) -> (~((op (e1) (e2)) = (op (e3) (e2)))) -> (~((op (e0) (e2)) = (op (e3) (e2)))) -> (~((op (e2) (e2)) = (op (e3) (e2)))) -> ((op (e2) (e1)) = (e1)) -> (~((e1) = (e3))) -> ((op (e1) (e0)) = (e2)) -> ((op (e0) (e0)) = (e1)) -> (((op (e2) (e0)) = (e3))\/(((op (e2) (e1)) = (e3))\/(((op (e2) (e2)) = (e3))\/((op (e2) (e3)) = (e3))))) -> ((op (e2) (e0)) = (e0)) -> (~((op (e2) (e0)) = (op (e2) (e2)))) -> (~((op (e3) (e1)) = (op (e3) (e2)))) -> (~((op (e0) (e2)) = (e0))) -> (((op (e0) (e2)) = (e0))\/(((op (e0) (e2)) = (e1))\/(((op (e0) (e2)) = (e2))\/((op (e0) (e2)) = (e3))))) -> (~((op (e3) (e2)) = (e0))) -> (~((op (e3) (e3)) = (e0))) -> (~((op (e3) (e0)) = (op (e3) (e2)))) -> ((op (e3) (e0)) = (e1)) -> False). % 18.52/18.72 do 0 intro. intros zenon_H139 zenon_H13c zenon_H124 zenon_Hd6 zenon_He3 zenon_He2 zenon_H1ac zenon_H40 zenon_Ha8 zenon_H6a zenon_H4a zenon_H49 zenon_H191 zenon_H115 zenon_H14f zenon_H18f zenon_Ha5 zenon_H95 zenon_H86 zenon_H7a zenon_He7 zenon_H34 zenon_H52 zenon_H1a4 zenon_H75 zenon_H1ba zenon_H18b zenon_H1ae zenon_H6f zenon_Hac. % 18.52/18.72 apply (zenon_or_s _ _ zenon_H139); [ zenon_intro zenon_H122 | zenon_intro zenon_H13a ]. % 18.52/18.72 apply (zenon_L92_); trivial. % 18.52/18.72 apply (zenon_or_s _ _ zenon_H13a); [ zenon_intro zenon_Hf0 | zenon_intro zenon_H13b ]. % 18.52/18.72 apply (zenon_L78_); trivial. % 18.52/18.72 apply (zenon_or_s _ _ zenon_H13b); [ zenon_intro zenon_Hf1 | zenon_intro zenon_Hba ]. % 18.52/18.72 apply (zenon_or_s _ _ zenon_He7); [ zenon_intro zenon_H3b | zenon_intro zenon_He9 ]. % 18.52/18.72 apply (zenon_L33_); trivial. % 18.52/18.72 apply (zenon_or_s _ _ zenon_He9); [ zenon_intro zenon_Ha6 | zenon_intro zenon_Hea ]. % 18.52/18.72 apply (zenon_L39_); trivial. % 18.52/18.72 apply (zenon_or_s _ _ zenon_Hea); [ zenon_intro zenon_Haa | zenon_intro zenon_Hdd ]. % 18.52/18.72 apply (zenon_or_s _ _ zenon_H1ac); [ zenon_intro zenon_H44 | zenon_intro zenon_H1af ]. % 18.52/18.72 exact (zenon_H40 zenon_H44). % 18.52/18.72 apply (zenon_or_s _ _ zenon_H1af); [ zenon_intro zenon_H1b1 | zenon_intro zenon_H1b0 ]. % 18.52/18.72 apply (zenon_or_s _ _ zenon_H1ba); [ zenon_intro zenon_H48 | zenon_intro zenon_H1bb ]. % 18.52/18.72 exact (zenon_H75 zenon_H48). % 18.52/18.72 apply (zenon_or_s _ _ zenon_H1bb); [ zenon_intro zenon_H122 | zenon_intro zenon_H1bc ]. % 18.52/18.72 apply (zenon_L246_); trivial. % 18.52/18.72 apply (zenon_or_s _ _ zenon_H1bc); [ zenon_intro zenon_H150 | zenon_intro zenon_Ha9 ]. % 18.52/18.72 apply (zenon_L248_); trivial. % 18.52/18.72 apply (zenon_L40_); trivial. % 18.52/18.72 apply (zenon_or_s _ _ zenon_H1b0); [ zenon_intro zenon_H61 | zenon_intro zenon_H60 ]. % 18.52/18.72 exact (zenon_H18b zenon_H61). % 18.52/18.72 exact (zenon_H1ae zenon_H60). % 18.52/18.72 apply (zenon_L54_); trivial. % 18.52/18.72 apply (zenon_L249_); trivial. % 18.52/18.72 (* end of lemma zenon_L250_ *) % 18.52/18.72 assert (zenon_L251_ : (((op (e0) (e2)) = (e0))\/(((op (e1) (e2)) = (e0))\/(((op (e2) (e2)) = (e0))\/((op (e3) (e2)) = (e0))))) -> (~((op (e0) (e2)) = (e0))) -> ((op (e1) (e3)) = (e0)) -> ((op (e0) (e3)) = (e2)) -> ((op (e2) (e1)) = (e1)) -> (~((op (e2) (e1)) = (op (e2) (e3)))) -> (((op (e0) (e2)) = (e1))\/(((op (e1) (e2)) = (e1))\/(((op (e2) (e2)) = (e1))\/((op (e3) (e2)) = (e1))))) -> (~((e1) = (e3))) -> (~((op (e1) (e2)) = (op (e1) (e3)))) -> (((op (e2) (e2)) = (e0))\/(((op (e2) (e2)) = (e1))\/(((op (e2) (e2)) = (e2))\/((op (e2) (e2)) = (e3))))) -> ((op (e0) (e2)) = (e3)) -> (~((op (e2) (e2)) = (op (e3) (e2)))) -> (~((op (e2) (e2)) = (e2))) -> (~((e1) = (e2))) -> (((op (e0) (e3)) = (e1))\/(((op (e1) (e3)) = (e1))\/(((op (e2) (e3)) = (e1))\/((op (e3) (e3)) = (e1))))) -> (~((op (e2) (e2)) = (e0))) -> (~((op (e3) (e2)) = (e0))) -> False). % 18.52/18.72 do 0 intro. intros zenon_H6a zenon_H75 zenon_H1f zenon_Hcd zenon_Ha5 zenon_H1c7 zenon_H139 zenon_H95 zenon_H124 zenon_H1c4 zenon_Ha9 zenon_H18f zenon_H173 zenon_H7c zenon_H133 zenon_H81 zenon_H18b. % 18.52/18.72 apply (zenon_or_s _ _ zenon_H6a); [ zenon_intro zenon_H48 | zenon_intro zenon_H6b ]. % 18.52/18.72 exact (zenon_H75 zenon_H48). % 18.52/18.72 apply (zenon_or_s _ _ zenon_H6b); [ zenon_intro zenon_H2a | zenon_intro zenon_H6c ]. % 18.52/18.72 apply (zenon_or_s _ _ zenon_H133); [ zenon_intro zenon_Hc3 | zenon_intro zenon_H134 ]. % 18.52/18.72 apply (zenon_L82_); trivial. % 18.52/18.72 apply (zenon_or_s _ _ zenon_H134); [ zenon_intro zenon_Hd6 | zenon_intro zenon_H135 ]. % 18.52/18.72 apply (zenon_L187_); trivial. % 18.52/18.72 apply (zenon_or_s _ _ zenon_H135); [ zenon_intro zenon_Hf4 | zenon_intro zenon_Hc4 ]. % 18.52/18.72 apply (zenon_L188_); trivial. % 18.52/18.72 apply (zenon_L49_); trivial. % 18.52/18.72 apply (zenon_or_s _ _ zenon_H6c); [ zenon_intro zenon_H2c | zenon_intro zenon_H61 ]. % 18.52/18.72 exact (zenon_H81 zenon_H2c). % 18.52/18.72 exact (zenon_H18b zenon_H61). % 18.52/18.72 (* end of lemma zenon_L251_ *) % 18.52/18.72 assert (zenon_L252_ : ((op (e3) (e0)) = (e1)) -> ((op (e3) (e0)) = (e3)) -> (~((e1) = (e3))) -> False). % 18.52/18.72 do 0 intro. intros zenon_Hac zenon_H15e zenon_H95. % 18.52/18.72 elim (classic ((e3) = (e3))); [ zenon_intro zenon_H96 | zenon_intro zenon_H85 ]. % 18.52/18.72 cut (((e3) = (e3)) = ((e1) = (e3))). % 18.52/18.72 intro zenon_D_pnotp. % 18.52/18.72 apply zenon_H95. % 18.52/18.72 rewrite <- zenon_D_pnotp. % 18.52/18.72 exact zenon_H96. % 18.52/18.72 cut (((e3) = (e3))); [idtac | apply NNPP; zenon_intro zenon_H85]. % 18.52/18.72 cut (((e3) = (e1))); [idtac | apply NNPP; zenon_intro zenon_H97]. % 18.52/18.72 congruence. % 18.52/18.72 cut (((op (e3) (e0)) = (e1)) = ((e3) = (e1))). % 18.52/18.72 intro zenon_D_pnotp. % 18.52/18.72 apply zenon_H97. % 18.52/18.72 rewrite <- zenon_D_pnotp. % 18.52/18.72 exact zenon_Hac. % 18.52/18.72 cut (((e1) = (e1))); [idtac | apply NNPP; zenon_intro zenon_H79]. % 18.52/18.72 cut (((op (e3) (e0)) = (e3))); [idtac | apply NNPP; zenon_intro zenon_H15f]. % 18.52/18.72 congruence. % 18.52/18.72 exact (zenon_H15f zenon_H15e). % 18.52/18.72 apply zenon_H79. apply refl_equal. % 18.52/18.72 apply zenon_H85. apply refl_equal. % 18.52/18.72 apply zenon_H85. apply refl_equal. % 18.52/18.72 (* end of lemma zenon_L252_ *) % 18.52/18.72 assert (zenon_L253_ : ((~((op (e3) (e3)) = (e0)))\/((op (e3) (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)) = (e0))) -> (~((op (e2) (e3)) = (e0))) -> (((op (e0) (e3)) = (e0))\/(((op (e1) (e3)) = (e0))\/(((op (e2) (e3)) = (e0))\/((op (e3) (e3)) = (e0))))) -> (~((e2) = (e3))) -> ((op (e3) (e0)) = (e1)) -> ((op (e1) (e0)) = (e2)) -> (~((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) (e2)) = (e0))) -> (((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)))) -> (~((e1) = (e3))) -> (~((op (e1) (e2)) = (op (e1) (e3)))) -> (((op (e2) (e2)) = (e0))\/(((op (e2) (e2)) = (e1))\/(((op (e2) (e2)) = (e2))\/((op (e2) (e2)) = (e3))))) -> (~((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 (e0) (e0)) = (op (e0) (e3)))) -> (~((op (e2) (e2)) = (e0))) -> (~((op (e3) (e2)) = (e0))) -> (((op (e0) (e2)) = (e0))\/(((op (e1) (e2)) = (e0))\/(((op (e2) (e2)) = (e0))\/((op (e3) (e2)) = (e0))))) -> (~((op (e1) (e1)) = (e1))) -> (~((e0) = (e1))) -> (~((e0) = (e2))) -> ((op (e2) (e0)) = (e0)) -> (~((op (e0) (e1)) = (op (e2) (e1)))) -> (((op (e3) (e3)) = (e0))\/(((op (e3) (e3)) = (e1))\/(((op (e3) (e3)) = (e2))\/((op (e3) (e3)) = (e3))))) -> (~((op (e3) (e3)) = (e3))) -> (~((op (e2) (e3)) = (op (e3) (e3)))) -> (~((op (e0) (e3)) = (op (e3) (e3)))) -> (~((op (e3) (e1)) = (op (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 (e0) (e2)) = (op (e2) (e2)))) -> (~((op (e3) (e1)) = (op (e3) (e2)))) -> (~((op (e2) (e0)) = (op (e2) (e2)))) -> (((op (e3) (e2)) = (e0))\/(((op (e3) (e2)) = (e1))\/(((op (e3) (e2)) = (e2))\/((op (e3) (e2)) = (e3))))) -> (~((op (e0) (e2)) = (op (e3) (e2)))) -> (~((op (e1) (e2)) = (op (e3) (e2)))) -> (~((op (e0) (e3)) = (op (e2) (e3)))) -> (((op (e2) (e0)) = (e3))\/(((op (e2) (e1)) = (e3))\/(((op (e2) (e2)) = (e3))\/((op (e2) (e3)) = (e3))))) -> (~((op (e0) (e1)) = (op (e0) (e2)))) -> (((op (e0) (e2)) = (e0))\/(((op (e0) (e2)) = (e1))\/(((op (e0) (e2)) = (e2))\/((op (e0) (e2)) = (e3))))) -> (~((op (e0) (e0)) = (op (e0) (e2)))) -> (~((op (e3) (e0)) = (e0))) -> (((op (e2) (e0)) = (e2))\/(((op (e2) (e1)) = (e2))\/(((op (e2) (e2)) = (e2))\/((op (e2) (e3)) = (e2))))) -> (((op (e0) (e0)) = (e3))\/(((op (e0) (e1)) = (e3))\/(((op (e0) (e2)) = (e3))\/((op (e0) (e3)) = (e3))))) -> ((op (e0) (e0)) = (e1)) -> (~((e1) = (e2))) -> (((op (e0) (e0)) = (e0))\/(((op (e0) (e1)) = (e0))\/(((op (e0) (e2)) = (e0))\/((op (e0) (e3)) = (e0))))) -> False). % 18.52/18.72 do 0 intro. intros zenon_H1ec zenon_H3f zenon_H183 zenon_H76 zenon_H32 zenon_H67 zenon_H12b zenon_Hac zenon_H86 zenon_H9a zenon_H109 zenon_H1cf zenon_H75 zenon_H133 zenon_H71 zenon_H1c7 zenon_H95 zenon_H124 zenon_H1c4 zenon_H173 zenon_H18f zenon_H139 zenon_H189 zenon_H81 zenon_H18b zenon_H6a zenon_H10a zenon_Ha1 zenon_H149 zenon_H34 zenon_H17e zenon_H101 zenon_H102 zenon_Hf3 zenon_Hc2 zenon_H130 zenon_H6f zenon_H1ac zenon_Ha8 zenon_H1a4 zenon_H52 zenon_H191 zenon_H14f zenon_H115 zenon_He2 zenon_He7 zenon_H4a zenon_H1ba zenon_H13c zenon_H40 zenon_H1d5 zenon_H168 zenon_H7a zenon_H7c zenon_H74. % 18.52/18.72 apply (zenon_or_s _ _ zenon_H1ec); [ zenon_intro zenon_H1ae | zenon_intro zenon_H15e ]. % 18.52/18.72 apply (zenon_or_s _ _ zenon_H74); [ zenon_intro zenon_H42 | zenon_intro zenon_H77 ]. % 18.52/18.72 exact (zenon_H3f zenon_H42). % 18.52/18.72 apply (zenon_or_s _ _ zenon_H77); [ zenon_intro zenon_H49 | zenon_intro zenon_H78 ]. % 18.52/18.72 apply (zenon_or_s _ _ zenon_H183); [ zenon_intro zenon_H7b | zenon_intro zenon_H186 ]. % 18.52/18.72 apply (zenon_L26_); trivial. % 18.52/18.72 apply (zenon_or_s _ _ zenon_H186); [ zenon_intro zenon_H10f | zenon_intro zenon_H187 ]. % 18.52/18.72 apply (zenon_or_s _ _ zenon_H168); [ zenon_intro zenon_H3a | zenon_intro zenon_H169 ]. % 18.52/18.72 apply (zenon_L241_); trivial. % 18.52/18.72 apply (zenon_or_s _ _ zenon_H169); [ zenon_intro zenon_H99 | zenon_intro zenon_H16a ]. % 18.52/18.72 apply (zenon_L36_); trivial. % 18.52/18.72 apply (zenon_or_s _ _ zenon_H16a); [ zenon_intro zenon_Ha9 | zenon_intro zenon_He3 ]. % 18.52/18.72 apply (zenon_L243_); trivial. % 18.52/18.72 apply (zenon_or_s _ _ zenon_H109); [ zenon_intro zenon_Ha0 | zenon_intro zenon_H10b ]. % 18.52/18.72 apply (zenon_L38_); trivial. % 18.52/18.72 apply (zenon_or_s _ _ zenon_H10b); [ zenon_intro zenon_H10d | zenon_intro zenon_H10c ]. % 18.52/18.72 exact (zenon_H10a zenon_H10d). % 18.52/18.72 apply (zenon_or_s _ _ zenon_H10c); [ zenon_intro zenon_Ha5 | zenon_intro zenon_Hae ]. % 18.52/18.72 apply (zenon_or_s _ _ zenon_H1d5); [ zenon_intro zenon_Hee | zenon_intro zenon_H1d6 ]. % 18.52/18.72 apply (zenon_L204_); trivial. % 18.52/18.72 apply (zenon_or_s _ _ zenon_H1d6); [ zenon_intro zenon_H1ca | zenon_intro zenon_H1d7 ]. % 18.52/18.72 apply (zenon_L191_); trivial. % 18.52/18.72 apply (zenon_or_s _ _ zenon_H1d7); [ zenon_intro zenon_H176 | zenon_intro zenon_H11d ]. % 18.52/18.72 exact (zenon_H173 zenon_H176). % 18.52/18.72 apply (zenon_or_s _ _ zenon_H1ac); [ zenon_intro zenon_H44 | zenon_intro zenon_H1af ]. % 18.52/18.72 exact (zenon_H40 zenon_H44). % 18.52/18.72 apply (zenon_or_s _ _ zenon_H1af); [ zenon_intro zenon_H1b1 | zenon_intro zenon_H1b0 ]. % 18.52/18.72 apply (zenon_or_s _ _ zenon_H133); [ zenon_intro zenon_Hc3 | zenon_intro zenon_H134 ]. % 18.52/18.72 apply (zenon_L245_); trivial. % 18.52/18.72 apply (zenon_or_s _ _ zenon_H134); [ zenon_intro zenon_Hd6 | zenon_intro zenon_H135 ]. % 18.52/18.72 apply (zenon_L250_); trivial. % 18.52/18.72 apply (zenon_or_s _ _ zenon_H135); [ zenon_intro zenon_Hf4 | zenon_intro zenon_Hc4 ]. % 18.52/18.72 apply (zenon_L188_); trivial. % 18.52/18.72 apply (zenon_L189_); trivial. % 18.52/18.72 apply (zenon_or_s _ _ zenon_H1b0); [ zenon_intro zenon_H61 | zenon_intro zenon_H60 ]. % 18.52/18.72 exact (zenon_H18b zenon_H61). % 18.52/18.72 exact (zenon_H1ae zenon_H60). % 18.52/18.72 apply (zenon_L242_); trivial. % 18.52/18.72 apply (zenon_or_s _ _ zenon_H187); [ zenon_intro zenon_H150 | zenon_intro zenon_Hcd ]. % 18.52/18.72 apply (zenon_or_s _ _ zenon_H168); [ zenon_intro zenon_H3a | zenon_intro zenon_H169 ]. % 18.52/18.72 apply (zenon_L35_); trivial. % 18.52/18.72 apply (zenon_or_s _ _ zenon_H169); [ zenon_intro zenon_H99 | zenon_intro zenon_H16a ]. % 18.52/18.72 apply (zenon_L36_); trivial. % 18.52/18.72 apply (zenon_or_s _ _ zenon_H16a); [ zenon_intro zenon_Ha9 | zenon_intro zenon_He3 ]. % 18.52/18.72 apply (zenon_L243_); trivial. % 18.52/18.72 apply (zenon_or_s _ _ zenon_H109); [ zenon_intro zenon_Ha0 | zenon_intro zenon_H10b ]. % 18.52/18.72 apply (zenon_L38_); trivial. % 18.52/18.72 apply (zenon_or_s _ _ zenon_H10b); [ zenon_intro zenon_H10d | zenon_intro zenon_H10c ]. % 18.52/18.72 exact (zenon_H10a zenon_H10d). % 18.52/18.72 apply (zenon_or_s _ _ zenon_H10c); [ zenon_intro zenon_Ha5 | zenon_intro zenon_Hae ]. % 18.52/18.72 apply (zenon_L213_); trivial. % 18.52/18.72 apply (zenon_L242_); trivial. % 18.52/18.72 apply (zenon_or_s _ _ zenon_H168); [ zenon_intro zenon_H3a | zenon_intro zenon_H169 ]. % 18.52/18.72 apply (zenon_L241_); trivial. % 18.52/18.72 apply (zenon_or_s _ _ zenon_H169); [ zenon_intro zenon_H99 | zenon_intro zenon_H16a ]. % 18.52/18.72 apply (zenon_L36_); trivial. % 18.52/18.72 apply (zenon_or_s _ _ zenon_H16a); [ zenon_intro zenon_Ha9 | zenon_intro zenon_He3 ]. % 18.52/18.72 apply (zenon_or_s _ _ zenon_H109); [ zenon_intro zenon_Ha0 | zenon_intro zenon_H10b ]. % 18.52/18.72 apply (zenon_L38_); trivial. % 18.52/18.72 apply (zenon_or_s _ _ zenon_H10b); [ zenon_intro zenon_H10d | zenon_intro zenon_H10c ]. % 18.52/18.72 exact (zenon_H10a zenon_H10d). % 18.52/18.72 apply (zenon_or_s _ _ zenon_H10c); [ zenon_intro zenon_Ha5 | zenon_intro zenon_Hae ]. % 18.52/18.72 apply (zenon_or_s _ _ zenon_H67); [ zenon_intro zenon_H1e | zenon_intro zenon_H68 ]. % 18.52/18.72 exact (zenon_H76 zenon_H1e). % 18.52/18.72 apply (zenon_or_s _ _ zenon_H68); [ zenon_intro zenon_H1f | zenon_intro zenon_H69 ]. % 18.52/18.72 apply (zenon_L251_); trivial. % 18.52/18.72 apply (zenon_or_s _ _ zenon_H69); [ zenon_intro zenon_H37 | zenon_intro zenon_H60 ]. % 18.52/18.72 exact (zenon_H32 zenon_H37). % 18.52/18.72 exact (zenon_H1ae zenon_H60). % 18.52/18.72 apply (zenon_L242_); trivial. % 18.52/18.72 apply (zenon_L81_); trivial. % 18.52/18.72 apply (zenon_or_s _ _ zenon_H78); [ zenon_intro zenon_H48 | zenon_intro zenon_H1e ]. % 18.52/18.72 exact (zenon_H75 zenon_H48). % 18.52/18.72 exact (zenon_H76 zenon_H1e). % 18.52/18.72 apply (zenon_L252_); trivial. % 18.52/18.72 (* end of lemma zenon_L253_ *) % 18.52/18.72 assert (zenon_L254_ : (((op (e0) (e0)) = (e3))\/(((op (e0) (e1)) = (e3))\/(((op (e0) (e2)) = (e3))\/((op (e0) (e3)) = (e3))))) -> (~((op (e1) (e3)) = (op (e3) (e3)))) -> ((op (e1) (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)) = (e0))\/(((op (e0) (e3)) = (e1))\/(((op (e0) (e3)) = (e2))\/((op (e0) (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 (e3) (e3)) = (e3))) -> (~((op (e0) (e2)) = (op (e2) (e2)))) -> (~((op (e1) (e0)) = (op (e1) (e3)))) -> (~((op (e0) (e0)) = (op (e0) (e3)))) -> (((op (e0) (e3)) = (e1))\/(((op (e1) (e3)) = (e1))\/(((op (e2) (e3)) = (e1))\/((op (e3) (e3)) = (e1))))) -> (((op (e3) (e0)) = (e1))\/(((op (e3) (e1)) = (e1))\/(((op (e3) (e2)) = (e1))\/((op (e3) (e3)) = (e1))))) -> (((op (e0) (e2)) = (e1))\/(((op (e1) (e2)) = (e1))\/(((op (e2) (e2)) = (e1))\/((op (e3) (e2)) = (e1))))) -> (~((op (e1) (e2)) = (op (e1) (e3)))) -> (((op (e2) (e2)) = (e0))\/(((op (e2) (e2)) = (e1))\/(((op (e2) (e2)) = (e2))\/((op (e2) (e2)) = (e3))))) -> (~((op (e1) (e1)) = (e0))) -> (((op (e1) (e0)) = (e1))\/(((op (e1) (e1)) = (e1))\/(((op (e1) (e2)) = (e1))\/((op (e1) (e3)) = (e1))))) -> ((~((op (e1) (e3)) = (e0)))\/((op (e1) (e0)) = (e3))) -> (~((op (e0) (e0)) = (e0))) -> (((op (e1) (e0)) = (e0))\/(((op (e1) (e1)) = (e0))\/(((op (e1) (e2)) = (e0))\/((op (e1) (e3)) = (e0))))) -> (~((op (e1) (e0)) = (op (e1) (e1)))) -> (~((op (e0) (e1)) = (op (e0) (e3)))) -> (~((op (e1) (e1)) = (op (e1) (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) (e0)) = (op (e2) (e2)))) -> (~((op (e1) (e1)) = (op (e1) (e2)))) -> (~((op (e0) (e1)) = (op (e0) (e2)))) -> (~((op (e3) (e0)) = (op (e3) (e3)))) -> (~((op (e3) (e0)) = (op (e3) (e2)))) -> (((op (e0) (e0)) = (e0))\/(((op (e1) (e0)) = (e0))\/(((op (e2) (e0)) = (e0))\/((op (e3) (e0)) = (e0))))) -> (~((op (e1) (e0)) = (e0))) -> (~((op (e0) (e3)) = (e0))) -> (((op (e0) (e0)) = (e0))\/(((op (e0) (e1)) = (e0))\/(((op (e0) (e2)) = (e0))\/((op (e0) (e3)) = (e0))))) -> ((~((op (e1) (e2)) = (e0)))\/((op (e1) (e0)) = (e2))) -> (~((op (e1) (e2)) = (op (e2) (e2)))) -> (~((op (e0) (e3)) = (op (e1) (e3)))) -> (((op (e1) (e0)) = (e3))\/(((op (e1) (e1)) = (e3))\/(((op (e1) (e2)) = (e3))\/((op (e1) (e3)) = (e3))))) -> (~((e0) = (e2))) -> (((op (e0) (e1)) = (e1))\/(((op (e1) (e1)) = (e1))\/(((op (e2) (e1)) = (e1))\/((op (e3) (e1)) = (e1))))) -> (~((e0) = (e1))) -> (~((op (e1) (e1)) = (e1))) -> (~((op (e2) (e2)) = (e0))) -> (((op (e2) (e0)) = (e3))\/(((op (e2) (e1)) = (e3))\/(((op (e2) (e2)) = (e3))\/((op (e2) (e3)) = (e3))))) -> ((op (e0) (e0)) = (e1)) -> ((op (e1) (e0)) = (e2)) -> (~((e1) = (e3))) -> (~((op (e2) (e2)) = (op (e3) (e2)))) -> (~((op (e1) (e2)) = (op (e3) (e2)))) -> (((op (e3) (e2)) = (e0))\/(((op (e3) (e2)) = (e1))\/(((op (e3) (e2)) = (e2))\/((op (e3) (e2)) = (e3))))) -> (~((op (e0) (e2)) = (e0))) -> (((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)) = (e0))\/(((op (e2) (e1)) = (e1))\/(((op (e2) (e1)) = (e2))\/((op (e2) (e1)) = (e3))))) -> (~((op (e2) (e1)) = (e0))) -> (~((op (e0) (e1)) = (op (e2) (e1)))) -> (~((op (e1) (e1)) = (op (e2) (e1)))) -> (~((op (e3) (e0)) = (op (e3) (e1)))) -> ((op (e3) (e0)) = (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) (e0)) = (e0))\/(((op (e3) (e1)) = (e0))\/(((op (e3) (e2)) = (e0))\/((op (e3) (e3)) = (e0))))) -> (~((op (e3) (e0)) = (e0))) -> (~((op (e3) (e1)) = (e0))) -> (~((op (e3) (e2)) = (e0))) -> (~((op (e3) (e1)) = (op (e3) (e3)))) -> (~((op (e2) (e2)) = (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 (e2) (e2)) = (e2))) -> (((op (e3) (e0)) = (e2))\/(((op (e3) (e1)) = (e2))\/(((op (e3) (e2)) = (e2))\/((op (e3) (e3)) = (e2))))) -> ((op (e0) (e2)) = (e2)) -> (~((op (e0) (e2)) = (op (e3) (e2)))) -> ((op (e0) (e1)) = (e0)) -> (~((e0) = (e3))) -> (((op (e0) (e1)) = (e3))\/(((op (e1) (e1)) = (e3))\/(((op (e2) (e1)) = (e3))\/((op (e3) (e1)) = (e3))))) -> (~((op (e0) (e3)) = (op (e2) (e3)))) -> (~((op (e2) (e3)) = (op (e3) (e3)))) -> ((op (e2) (e0)) = (e0)) -> (~((op (e2) (e0)) = (op (e2) (e3)))) -> (((op (e2) (e3)) = (e0))\/(((op (e2) (e3)) = (e1))\/(((op (e2) (e3)) = (e2))\/((op (e2) (e3)) = (e3))))) -> (~((op (e2) (e1)) = (op (e2) (e3)))) -> (~((e2) = (e3))) -> (((op (e0) (e3)) = (e2))\/(((op (e1) (e3)) = (e2))\/(((op (e2) (e3)) = (e2))\/((op (e3) (e3)) = (e2))))) -> (~((e1) = (e2))) -> False). % 18.52/18.72 do 0 intro. intros zenon_H168 zenon_Hd5 zenon_H9e zenon_Hc2 zenon_Hdf zenon_He4 zenon_H165 zenon_H160 zenon_H102 zenon_Ha8 zenon_Hd8 zenon_H189 zenon_H133 zenon_He8 zenon_H139 zenon_H124 zenon_H1c4 zenon_H24 zenon_H128 zenon_H179 zenon_H3f zenon_H22 zenon_H45 zenon_H54 zenon_H57 zenon_H62 zenon_H67 zenon_H52 zenon_H4f zenon_H4a zenon_H71 zenon_H6f zenon_H3e zenon_H23 zenon_H76 zenon_H74 zenon_H178 zenon_H2b zenon_H1d zenon_H16f zenon_H149 zenon_H109 zenon_Ha1 zenon_H10a zenon_H81 zenon_He7 zenon_H7a zenon_H86 zenon_H95 zenon_H18f zenon_H115 zenon_H191 zenon_H75 zenon_H6a zenon_H1d8 zenon_H1cc zenon_H31 zenon_H17e zenon_H13e zenon_H1cf zenon_H15e zenon_H1d5 zenon_Hdb zenon_H1ac zenon_H40 zenon_H1ad zenon_H18b zenon_H130 zenon_H6d zenon_Haf zenon_H106 zenon_H173 zenon_H153 zenon_H150 zenon_H14f zenon_H49 zenon_H9a zenon_H1a5 zenon_He2 zenon_Hf3 zenon_H34 zenon_H5b zenon_H11f zenon_H1c7 zenon_H12b zenon_H145 zenon_H7c. % 18.52/18.72 apply (zenon_or_s _ _ zenon_H168); [ zenon_intro zenon_H3a | zenon_intro zenon_H169 ]. % 18.52/18.72 apply (zenon_L35_); trivial. % 18.52/18.72 apply (zenon_or_s _ _ zenon_H169); [ zenon_intro zenon_H99 | zenon_intro zenon_H16a ]. % 18.52/18.72 apply (zenon_L36_); trivial. % 18.52/18.72 apply (zenon_or_s _ _ zenon_H16a); [ zenon_intro zenon_Ha9 | zenon_intro zenon_He3 ]. % 18.52/18.72 apply (zenon_or_s _ _ zenon_H22); [ zenon_intro zenon_H27 | zenon_intro zenon_H26 ]. % 18.52/18.72 exact (zenon_H23 zenon_H27). % 18.52/18.72 apply (zenon_or_s _ _ zenon_H26); [ zenon_intro zenon_H29 | zenon_intro zenon_H28 ]. % 18.52/18.72 exact (zenon_H24 zenon_H29). % 18.52/18.72 apply (zenon_or_s _ _ zenon_H28); [ zenon_intro zenon_H2a | zenon_intro zenon_H1f ]. % 18.52/18.72 apply (zenon_or_s _ _ zenon_H128); [ zenon_intro zenon_H9d | zenon_intro zenon_H129 ]. % 18.52/18.72 apply (zenon_L37_); trivial. % 18.52/18.72 apply (zenon_or_s _ _ zenon_H129); [ zenon_intro zenon_H10d | zenon_intro zenon_H12a ]. % 18.52/18.72 exact (zenon_H10a zenon_H10d). % 18.52/18.72 apply (zenon_or_s _ _ zenon_H12a); [ zenon_intro zenon_Hf0 | zenon_intro zenon_Hd6 ]. % 18.52/18.72 apply (zenon_L210_); trivial. % 18.52/18.72 apply (zenon_L187_); trivial. % 18.52/18.72 apply (zenon_L195_); trivial. % 18.52/18.72 apply (zenon_L227_); trivial. % 18.52/18.72 (* end of lemma zenon_L254_ *) % 18.52/18.72 assert (zenon_L255_ : (((op (e0) (e0)) = (e3))\/(((op (e0) (e1)) = (e3))\/(((op (e0) (e2)) = (e3))\/((op (e0) (e3)) = (e3))))) -> (~((e0) = (e3))) -> (~((op (e3) (e2)) = (e0))) -> (~((op (e2) (e2)) = (e0))) -> (((op (e2) (e0)) = (e1))\/(((op (e2) (e1)) = (e1))\/(((op (e2) (e2)) = (e1))\/((op (e2) (e3)) = (e1))))) -> ((op (e0) (e0)) = (e1)) -> (~((op (e0) (e0)) = (op (e2) (e0)))) -> (~((op (e2) (e1)) = (op (e3) (e1)))) -> (((op (e3) (e0)) = (e0))\/(((op (e3) (e1)) = (e0))\/(((op (e3) (e2)) = (e0))\/((op (e3) (e3)) = (e0))))) -> (~((op (e3) (e0)) = (e0))) -> (~((op (e3) (e1)) = (e0))) -> (~((op (e0) (e2)) = (e0))) -> (((op (e0) (e2)) = (e0))\/(((op (e1) (e2)) = (e0))\/(((op (e2) (e2)) = (e0))\/((op (e3) (e2)) = (e0))))) -> (~((op (e2) (e1)) = (op (e2) (e3)))) -> (((op (e0) (e2)) = (e1))\/(((op (e1) (e2)) = (e1))\/(((op (e2) (e2)) = (e1))\/((op (e3) (e2)) = (e1))))) -> (~((e1) = (e3))) -> (~((op (e1) (e2)) = (op (e1) (e3)))) -> (((op (e2) (e2)) = (e0))\/(((op (e2) (e2)) = (e1))\/(((op (e2) (e2)) = (e2))\/((op (e2) (e2)) = (e3))))) -> (~((op (e2) (e2)) = (op (e3) (e2)))) -> (~((op (e2) (e2)) = (e2))) -> (~((e1) = (e2))) -> (((op (e0) (e3)) = (e1))\/(((op (e1) (e3)) = (e1))\/(((op (e2) (e3)) = (e1))\/((op (e3) (e3)) = (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) (e0)) = (e1))\/(((op (e1) (e1)) = (e1))\/(((op (e1) (e2)) = (e1))\/((op (e1) (e3)) = (e1))))) -> ((op (e1) (e0)) = (e3)) -> (((op (e3) (e0)) = (e1))\/(((op (e3) (e1)) = (e1))\/(((op (e3) (e2)) = (e1))\/((op (e3) (e3)) = (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 (e2) (e3)))) -> (~((op (e2) (e3)) = (op (e3) (e3)))) -> (((op (e2) (e3)) = (e0))\/(((op (e2) (e3)) = (e1))\/(((op (e2) (e3)) = (e2))\/((op (e2) (e3)) = (e3))))) -> (~((op (e1) (e3)) = (op (e2) (e3)))) -> ((op (e1) (e0)) = (e2)) -> (~((op (e1) (e0)) = (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)) = (e3))) -> (~((op (e1) (e1)) = (e0))) -> (~((op (e1) (e0)) = (e0))) -> (((op (e1) (e0)) = (e0))\/(((op (e1) (e1)) = (e0))\/(((op (e1) (e2)) = (e0))\/((op (e1) (e3)) = (e0))))) -> ((op (e0) (e3)) = (e2)) -> (~((e2) = (e3))) -> False). % 18.52/18.72 do 0 intro. intros zenon_H168 zenon_H9a zenon_H18b zenon_H81 zenon_H106 zenon_H7a zenon_H39 zenon_Haf zenon_H1ac zenon_H40 zenon_H1ad zenon_H75 zenon_H6a zenon_H1c7 zenon_H139 zenon_H95 zenon_H124 zenon_H1c4 zenon_H18f zenon_H173 zenon_H7c zenon_H133 zenon_H10a zenon_H49 zenon_Ha1 zenon_H109 zenon_H128 zenon_H9e zenon_He8 zenon_H71 zenon_H136 zenon_He2 zenon_Hf3 zenon_H11f zenon_Hdb zenon_H86 zenon_Hd8 zenon_Hd5 zenon_Hdf zenon_H102 zenon_H24 zenon_H23 zenon_H22 zenon_Hcd zenon_H12b. % 18.52/18.72 apply (zenon_or_s _ _ zenon_H168); [ zenon_intro zenon_H3a | zenon_intro zenon_H169 ]. % 18.52/18.72 apply (zenon_L35_); trivial. % 18.52/18.72 apply (zenon_or_s _ _ zenon_H169); [ zenon_intro zenon_H99 | zenon_intro zenon_H16a ]. % 18.52/18.72 apply (zenon_L36_); trivial. % 18.52/18.72 apply (zenon_or_s _ _ zenon_H16a); [ zenon_intro zenon_Ha9 | zenon_intro zenon_He3 ]. % 18.52/18.72 apply (zenon_or_s _ _ zenon_H22); [ zenon_intro zenon_H27 | zenon_intro zenon_H26 ]. % 18.52/18.72 exact (zenon_H23 zenon_H27). % 18.52/18.72 apply (zenon_or_s _ _ zenon_H26); [ zenon_intro zenon_H29 | zenon_intro zenon_H28 ]. % 18.52/18.72 exact (zenon_H24 zenon_H29). % 18.52/18.72 apply (zenon_or_s _ _ zenon_H28); [ zenon_intro zenon_H2a | zenon_intro zenon_H1f ]. % 18.52/18.72 apply (zenon_or_s _ _ zenon_H128); [ zenon_intro zenon_H9d | zenon_intro zenon_H129 ]. % 18.52/18.72 apply (zenon_L37_); trivial. % 18.52/18.72 apply (zenon_or_s _ _ zenon_H129); [ zenon_intro zenon_H10d | zenon_intro zenon_H12a ]. % 18.52/18.72 exact (zenon_H10a zenon_H10d). % 18.52/18.72 apply (zenon_or_s _ _ zenon_H12a); [ zenon_intro zenon_Hf0 | zenon_intro zenon_Hd6 ]. % 18.52/18.72 apply (zenon_L237_); trivial. % 18.52/18.72 apply (zenon_L187_); trivial. % 18.52/18.72 apply (zenon_or_s _ _ zenon_H109); [ zenon_intro zenon_Ha0 | zenon_intro zenon_H10b ]. % 18.52/18.72 apply (zenon_L38_); trivial. % 18.52/18.72 apply (zenon_or_s _ _ zenon_H10b); [ zenon_intro zenon_H10d | zenon_intro zenon_H10c ]. % 18.52/18.72 exact (zenon_H10a zenon_H10d). % 18.52/18.72 apply (zenon_or_s _ _ zenon_H10c); [ zenon_intro zenon_Ha5 | zenon_intro zenon_Hae ]. % 18.52/18.72 apply (zenon_L251_); trivial. % 18.52/18.72 apply (zenon_L233_); trivial. % 18.52/18.72 apply (zenon_L81_); trivial. % 18.52/18.72 (* end of lemma zenon_L255_ *) % 18.52/18.72 assert (zenon_L256_ : (((op (e0) (e2)) = (e2))\/(((op (e1) (e2)) = (e2))\/(((op (e2) (e2)) = (e2))\/((op (e3) (e2)) = (e2))))) -> ((~((op (e2) (e1)) = (e0)))\/((op (e2) (e0)) = (e1))) -> (~((op (e0) (e0)) = (op (e2) (e0)))) -> (((op (e1) (e0)) = (e0))\/(((op (e1) (e1)) = (e0))\/(((op (e1) (e2)) = (e0))\/((op (e1) (e3)) = (e0))))) -> (~((op (e1) (e2)) = (op (e2) (e2)))) -> (((op (e2) (e0)) = (e0))\/(((op (e2) (e1)) = (e0))\/(((op (e2) (e2)) = (e0))\/((op (e2) (e3)) = (e0))))) -> (~((op (e1) (e1)) = (e0))) -> (~((op (e1) (e0)) = (e0))) -> ((op (e0) (e0)) = (e1)) -> ((op (e1) (e0)) = (e2)) -> ((~((op (e2) (e3)) = (e0)))\/((op (e2) (e0)) = (e3))) -> ((~((op (e3) (e1)) = (e0)))\/((op (e3) (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) (e3)) = (e0)))\/((op (e3) (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))\/(((op (e1) (e3)) = (e3))\/(((op (e2) (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)) = (op (e3) (e3)))) -> (~((e0) = (e2))) -> (((op (e0) (e1)) = (e2))\/(((op (e1) (e1)) = (e2))\/(((op (e2) (e1)) = (e2))\/((op (e3) (e1)) = (e2))))) -> (((op (e3) (e0)) = (e3))\/(((op (e3) (e1)) = (e3))\/(((op (e3) (e2)) = (e3))\/((op (e3) (e3)) = (e3))))) -> (~((op (e3) (e3)) = (e3))) -> (~((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)) = (e0))\/(((op (e1) (e2)) = (e0))\/(((op (e2) (e2)) = (e0))\/((op (e3) (e2)) = (e0))))) -> (((op (e1) (e0)) = (e1))\/(((op (e1) (e1)) = (e1))\/(((op (e1) (e2)) = (e1))\/((op (e1) (e3)) = (e1))))) -> ((~((op (e1) (e2)) = (e0)))\/((op (e1) (e0)) = (e2))) -> (((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)) = (op (e3) (e2)))) -> (~((op (e2) (e2)) = (op (e2) (e3)))) -> (~((op (e0) (e1)) = (op (e0) (e2)))) -> (~((op (e1) (e1)) = (op (e1) (e2)))) -> (~((op (e2) (e0)) = (op (e2) (e2)))) -> (((op (e0) (e3)) = (e0))\/(((op (e1) (e3)) = (e0))\/(((op (e2) (e3)) = (e0))\/((op (e3) (e3)) = (e0))))) -> (~((op (e3) (e2)) = (op (e3) (e3)))) -> (~((op (e2) (e0)) = (op (e2) (e3)))) -> (~((op (e1) (e1)) = (op (e1) (e3)))) -> (~((op (e0) (e1)) = (op (e0) (e3)))) -> (~((op (e1) (e0)) = (op (e1) (e1)))) -> ((~((op (e1) (e3)) = (e0)))\/((op (e1) (e0)) = (e3))) -> (((op (e2) (e0)) = (e1))\/(((op (e2) (e1)) = (e1))\/(((op (e2) (e2)) = (e1))\/((op (e2) (e3)) = (e1))))) -> (((op (e1) (e0)) = (e3))\/(((op (e1) (e1)) = (e3))\/(((op (e1) (e2)) = (e3))\/((op (e1) (e3)) = (e3))))) -> (~((op (e0) (e3)) = (op (e1) (e3)))) -> (((op (e2) (e3)) = (e0))\/(((op (e2) (e3)) = (e1))\/(((op (e2) (e3)) = (e2))\/((op (e2) (e3)) = (e3))))) -> (~((op (e3) (e1)) = (op (e3) (e3)))) -> (((op (e0) (e3)) = (e2))\/(((op (e1) (e3)) = (e2))\/(((op (e2) (e3)) = (e2))\/((op (e3) (e3)) = (e2))))) -> (~((e1) = (e3))) -> (~((e2) = (e3))) -> (~((e0) = (e1))) -> (~((op (e1) (e1)) = (e1))) -> (((op (e0) (e1)) = (e3))\/(((op (e1) (e1)) = (e3))\/(((op (e2) (e1)) = (e3))\/((op (e3) (e1)) = (e3))))) -> (~((op (e3) (e0)) = (op (e3) (e1)))) -> (((op (e1) (e1)) = (e0))\/(((op (e1) (e1)) = (e1))\/(((op (e1) (e1)) = (e2))\/((op (e1) (e1)) = (e3))))) -> (~((op (e1) (e1)) = (op (e2) (e1)))) -> (~((op (e0) (e1)) = (op (e1) (e1)))) -> (((op (e0) (e2)) = (e0))\/(((op (e0) (e2)) = (e1))\/(((op (e0) (e2)) = (e2))\/((op (e0) (e2)) = (e3))))) -> (~((op (e0) (e2)) = (op (e2) (e2)))) -> (~((op (e1) (e2)) = (op (e3) (e2)))) -> (~((op (e0) (e2)) = (op (e3) (e2)))) -> (~((op (e2) (e2)) = (op (e3) (e2)))) -> (((op (e3) (e2)) = (e0))\/(((op (e3) (e2)) = (e1))\/(((op (e3) (e2)) = (e2))\/((op (e3) (e2)) = (e3))))) -> (~((op (e0) (e0)) = (op (e0) (e2)))) -> (~((op (e0) (e2)) = (e0))) -> (((op (e3) (e0)) = (e1))\/(((op (e3) (e1)) = (e1))\/(((op (e3) (e2)) = (e1))\/((op (e3) (e3)) = (e1))))) -> (~((op (e0) (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 (e1) (e3)) = (op (e2) (e3)))) -> (~((op (e1) (e0)) = (op (e1) (e3)))) -> (~((op (e1) (e3)) = (op (e3) (e3)))) -> (~((op (e0) (e3)) = (op (e2) (e3)))) -> (((op (e0) (e3)) = (e0))\/(((op (e0) (e3)) = (e1))\/(((op (e0) (e3)) = (e2))\/((op (e0) (e3)) = (e3))))) -> (~((op (e2) (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 (e0) (e0)) = (op (e0) (e3)))) -> (((op (e0) (e2)) = (e1))\/(((op (e1) (e2)) = (e1))\/(((op (e2) (e2)) = (e1))\/((op (e3) (e2)) = (e1))))) -> (~((op (e2) (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 (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 (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 (e0) (e0)) = (e3))\/(((op (e0) (e1)) = (e3))\/(((op (e0) (e2)) = (e3))\/((op (e0) (e3)) = (e3))))) -> (~((e1) = (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 (e3) (e2)) = (e0)))\/((op (e3) (e0)) = (e2))) -> (~((op (e2) (e0)) = (op (e3) (e0)))) -> ((~((op (e3) (e0)) = (e0)))\/((op (e3) (e0)) = (e0))) -> ((~((op (e2) (e2)) = (e0)))\/((op (e2) (e0)) = (e2))) -> ((~((op (e2) (e0)) = (e0)))\/((op (e2) (e0)) = (e0))) -> False). % 18.52/18.72 do 0 intro. intros zenon_H172 zenon_H182 zenon_H39 zenon_H22 zenon_H2b zenon_H2f zenon_H24 zenon_H23 zenon_H7a zenon_H86 zenon_H94 zenon_H1ed zenon_H101 zenon_H1a4 zenon_H1ec zenon_H3f zenon_H183 zenon_H136 zenon_H1d5 zenon_Hf3 zenon_H149 zenon_H1d8 zenon_H165 zenon_H102 zenon_H160 zenon_H153 zenon_H6a zenon_H128 zenon_H178 zenon_H74 zenon_H3e zenon_H6f zenon_H6d zenon_H4a zenon_H4f zenon_H52 zenon_H67 zenon_H62 zenon_H5b zenon_H57 zenon_H54 zenon_H45 zenon_H179 zenon_H106 zenon_H16f zenon_H1d zenon_H11f zenon_H130 zenon_H145 zenon_H95 zenon_H12b zenon_Ha1 zenon_H10a zenon_H1a5 zenon_H1cf zenon_H142 zenon_H13e zenon_H10e zenon_H1ba zenon_Ha8 zenon_H115 zenon_H14f zenon_H18f zenon_H191 zenon_H13c zenon_H75 zenon_He8 zenon_H76 zenon_Hc2 zenon_Hdf zenon_Hdb zenon_Hd8 zenon_Hd5 zenon_He2 zenon_He4 zenon_Haf zenon_H17e zenon_H1cc zenon_H189 zenon_H139 zenon_H173 zenon_H1c4 zenon_H124 zenon_H1c7 zenon_H71 zenon_H133 zenon_He7 zenon_H9a zenon_H109 zenon_H168 zenon_H7c zenon_H1ac zenon_H1e0 zenon_H1a7 zenon_H17b zenon_H184 zenon_H185 zenon_H1ee. % 18.52/18.72 apply (zenon_or_s _ _ zenon_H179); [ zenon_intro zenon_H38 | zenon_intro zenon_H9e ]. % 18.52/18.72 apply (zenon_or_s _ _ zenon_H1ee); [ zenon_intro zenon_H30 | zenon_intro zenon_H34 ]. % 18.52/18.72 apply (zenon_L173_); trivial. % 18.52/18.72 apply (zenon_or_s _ _ zenon_H182); [ zenon_intro zenon_H31 | zenon_intro zenon_Hed ]. % 18.52/18.72 apply (zenon_or_s _ _ zenon_H185); [ zenon_intro zenon_H81 | zenon_intro zenon_Hee ]. % 18.52/18.72 apply (zenon_or_s _ _ zenon_H94); [ zenon_intro zenon_H32 | zenon_intro zenon_H3b ]. % 18.52/18.72 apply (zenon_or_s _ _ zenon_H184); [ zenon_intro zenon_H40 | zenon_intro zenon_H44 ]. % 18.52/18.72 apply (zenon_or_s _ _ zenon_H1ed); [ zenon_intro zenon_H1ad | zenon_intro zenon_Hac ]. % 18.52/18.72 apply (zenon_or_s _ _ zenon_H1a7); [ zenon_intro zenon_H18b | zenon_intro zenon_H148 ]. % 18.52/18.72 apply (zenon_or_s _ _ zenon_H1ec); [ zenon_intro zenon_H1ae | zenon_intro zenon_H15e ]. % 18.52/18.72 apply (zenon_L174_); trivial. % 18.52/18.72 apply (zenon_or_s _ _ zenon_H74); [ zenon_intro zenon_H42 | zenon_intro zenon_H77 ]. % 18.52/18.72 exact (zenon_H3f zenon_H42). % 18.52/18.72 apply (zenon_or_s _ _ zenon_H77); [ zenon_intro zenon_H49 | zenon_intro zenon_H78 ]. % 18.52/18.72 apply (zenon_or_s _ _ zenon_H183); [ zenon_intro zenon_H7b | zenon_intro zenon_H186 ]. % 18.52/18.72 apply (zenon_L26_); trivial. % 18.52/18.72 apply (zenon_or_s _ _ zenon_H186); [ zenon_intro zenon_H10f | zenon_intro zenon_H187 ]. % 18.52/18.72 apply (zenon_L197_); trivial. % 18.52/18.72 apply (zenon_or_s _ _ zenon_H187); [ zenon_intro zenon_H150 | zenon_intro zenon_Hcd ]. % 18.52/18.72 apply (zenon_or_s _ _ zenon_H168); [ zenon_intro zenon_H3a | zenon_intro zenon_H169 ]. % 18.52/18.72 apply (zenon_L35_); trivial. % 18.52/18.72 apply (zenon_or_s _ _ zenon_H169); [ zenon_intro zenon_H99 | zenon_intro zenon_H16a ]. % 18.52/18.72 apply (zenon_L36_); trivial. % 18.52/18.72 apply (zenon_or_s _ _ zenon_H16a); [ zenon_intro zenon_Ha9 | zenon_intro zenon_He3 ]. % 18.52/18.72 apply (zenon_or_s _ _ zenon_H22); [ zenon_intro zenon_H27 | zenon_intro zenon_H26 ]. % 18.52/18.72 exact (zenon_H23 zenon_H27). % 18.52/18.73 apply (zenon_or_s _ _ zenon_H26); [ zenon_intro zenon_H29 | zenon_intro zenon_H28 ]. % 18.52/18.73 exact (zenon_H24 zenon_H29). % 18.52/18.73 apply (zenon_or_s _ _ zenon_H28); [ zenon_intro zenon_H2a | zenon_intro zenon_H1f ]. % 18.52/18.73 apply (zenon_or_s _ _ zenon_H128); [ zenon_intro zenon_H9d | zenon_intro zenon_H129 ]. % 18.52/18.73 apply (zenon_L123_); trivial. % 18.52/18.73 apply (zenon_or_s _ _ zenon_H129); [ zenon_intro zenon_H10d | zenon_intro zenon_H12a ]. % 18.52/18.73 exact (zenon_H10a zenon_H10d). % 18.52/18.73 apply (zenon_or_s _ _ zenon_H12a); [ zenon_intro zenon_Hf0 | zenon_intro zenon_Hd6 ]. % 18.52/18.73 apply (zenon_L210_); trivial. % 18.52/18.73 apply (zenon_L187_); trivial. % 18.52/18.73 exact (zenon_H38 zenon_H1f). % 18.52/18.73 apply (zenon_L227_); trivial. % 18.52/18.73 apply (zenon_or_s _ _ zenon_H168); [ zenon_intro zenon_H3a | zenon_intro zenon_H169 ]. % 18.52/18.73 apply (zenon_L35_); trivial. % 18.52/18.73 apply (zenon_or_s _ _ zenon_H169); [ zenon_intro zenon_H99 | zenon_intro zenon_H16a ]. % 18.52/18.73 apply (zenon_L36_); trivial. % 18.52/18.73 apply (zenon_or_s _ _ zenon_H16a); [ zenon_intro zenon_Ha9 | zenon_intro zenon_He3 ]. % 18.52/18.73 apply (zenon_or_s _ _ zenon_H22); [ zenon_intro zenon_H27 | zenon_intro zenon_H26 ]. % 18.52/18.73 exact (zenon_H23 zenon_H27). % 18.52/18.73 apply (zenon_or_s _ _ zenon_H26); [ zenon_intro zenon_H29 | zenon_intro zenon_H28 ]. % 18.52/18.73 exact (zenon_H24 zenon_H29). % 18.52/18.73 apply (zenon_or_s _ _ zenon_H28); [ zenon_intro zenon_H2a | zenon_intro zenon_H1f ]. % 18.52/18.73 apply (zenon_or_s _ _ zenon_H128); [ zenon_intro zenon_H9d | zenon_intro zenon_H129 ]. % 18.52/18.73 apply (zenon_L124_); trivial. % 18.52/18.73 apply (zenon_or_s _ _ zenon_H129); [ zenon_intro zenon_H10d | zenon_intro zenon_H12a ]. % 18.52/18.73 exact (zenon_H10a zenon_H10d). % 18.52/18.73 apply (zenon_or_s _ _ zenon_H12a); [ zenon_intro zenon_Hf0 | zenon_intro zenon_Hd6 ]. % 18.52/18.73 apply (zenon_L237_); trivial. % 18.52/18.73 apply (zenon_L187_); trivial. % 18.52/18.73 exact (zenon_H38 zenon_H1f). % 18.52/18.73 apply (zenon_L81_); trivial. % 18.52/18.73 apply (zenon_or_s _ _ zenon_H78); [ zenon_intro zenon_H48 | zenon_intro zenon_H1e ]. % 18.52/18.73 exact (zenon_H75 zenon_H48). % 18.52/18.73 exact (zenon_H76 zenon_H1e). % 18.52/18.73 apply (zenon_L238_); trivial. % 18.52/18.73 apply (zenon_or_s _ _ zenon_H1a7); [ zenon_intro zenon_H18b | zenon_intro zenon_H148 ]. % 18.52/18.73 apply (zenon_L253_); trivial. % 18.52/18.73 apply (zenon_or_s _ _ zenon_H1e0); [ zenon_intro zenon_H3a | zenon_intro zenon_H1e1 ]. % 18.52/18.73 apply (zenon_L241_); trivial. % 18.52/18.73 apply (zenon_or_s _ _ zenon_H1e1); [ zenon_intro zenon_H9e | zenon_intro zenon_H1e2 ]. % 18.52/18.73 apply (zenon_L107_); trivial. % 18.52/18.73 apply (zenon_or_s _ _ zenon_H1e2); [ zenon_intro zenon_H3b | zenon_intro zenon_H15e ]. % 18.52/18.73 apply (zenon_L33_); trivial. % 18.52/18.73 apply (zenon_L252_); trivial. % 18.52/18.73 apply (zenon_L127_); trivial. % 18.52/18.73 apply (zenon_L33_); trivial. % 18.52/18.73 apply (zenon_L204_); trivial. % 18.52/18.73 apply (zenon_L214_); trivial. % 18.52/18.73 apply (zenon_or_s _ _ zenon_H1ee); [ zenon_intro zenon_H30 | zenon_intro zenon_H34 ]. % 18.52/18.73 apply (zenon_L135_); trivial. % 18.52/18.73 apply (zenon_or_s _ _ zenon_H182); [ zenon_intro zenon_H31 | zenon_intro zenon_Hed ]. % 18.52/18.73 apply (zenon_or_s _ _ zenon_H185); [ zenon_intro zenon_H81 | zenon_intro zenon_Hee ]. % 18.52/18.73 apply (zenon_or_s _ _ zenon_H94); [ zenon_intro zenon_H32 | zenon_intro zenon_H3b ]. % 18.52/18.73 apply (zenon_or_s _ _ zenon_H184); [ zenon_intro zenon_H40 | zenon_intro zenon_H44 ]. % 18.52/18.73 apply (zenon_or_s _ _ zenon_H1ed); [ zenon_intro zenon_H1ad | zenon_intro zenon_Hac ]. % 18.52/18.73 apply (zenon_or_s _ _ zenon_H1a7); [ zenon_intro zenon_H18b | zenon_intro zenon_H148 ]. % 18.52/18.73 apply (zenon_or_s _ _ zenon_H1ec); [ zenon_intro zenon_H1ae | zenon_intro zenon_H15e ]. % 18.52/18.73 apply (zenon_L174_); trivial. % 18.52/18.73 apply (zenon_or_s _ _ zenon_H74); [ zenon_intro zenon_H42 | zenon_intro zenon_H77 ]. % 18.52/18.73 exact (zenon_H3f zenon_H42). % 18.52/18.73 apply (zenon_or_s _ _ zenon_H77); [ zenon_intro zenon_H49 | zenon_intro zenon_H78 ]. % 18.52/18.73 apply (zenon_or_s _ _ zenon_H183); [ zenon_intro zenon_H7b | zenon_intro zenon_H186 ]. % 18.52/18.73 apply (zenon_L26_); trivial. % 18.52/18.73 apply (zenon_or_s _ _ zenon_H186); [ zenon_intro zenon_H10f | zenon_intro zenon_H187 ]. % 18.52/18.73 apply (zenon_L197_); trivial. % 18.52/18.73 apply (zenon_or_s _ _ zenon_H187); [ zenon_intro zenon_H150 | zenon_intro zenon_Hcd ]. % 18.52/18.73 apply (zenon_L254_); trivial. % 18.52/18.73 apply (zenon_L255_); trivial. % 18.52/18.73 apply (zenon_or_s _ _ zenon_H78); [ zenon_intro zenon_H48 | zenon_intro zenon_H1e ]. % 18.52/18.73 exact (zenon_H75 zenon_H48). % 18.52/18.73 exact (zenon_H76 zenon_H1e). % 18.52/18.73 apply (zenon_L107_); trivial. % 18.52/18.73 apply (zenon_or_s _ _ zenon_H1a7); [ zenon_intro zenon_H18b | zenon_intro zenon_H148 ]. % 18.52/18.73 apply (zenon_L253_); trivial. % 18.52/18.73 apply (zenon_L107_); trivial. % 18.52/18.73 apply (zenon_L127_); trivial. % 18.52/18.73 apply (zenon_L33_); trivial. % 18.52/18.73 apply (zenon_L204_); trivial. % 18.52/18.73 apply (zenon_L214_); trivial. % 18.52/18.73 (* end of lemma zenon_L256_ *) % 18.52/18.73 assert (zenon_L257_ : ((op (e1) (e0)) = (e0)) -> ((op (e1) (e0)) = (e2)) -> (~((e0) = (e2))) -> False). % 18.52/18.73 do 0 intro. intros zenon_H27 zenon_H86 zenon_H149. % 18.52/18.73 elim (classic ((e2) = (e2))); [ zenon_intro zenon_H7d | zenon_intro zenon_H7e ]. % 18.52/18.73 cut (((e2) = (e2)) = ((e0) = (e2))). % 18.52/18.73 intro zenon_D_pnotp. % 18.52/18.73 apply zenon_H149. % 18.52/18.73 rewrite <- zenon_D_pnotp. % 18.52/18.73 exact zenon_H7d. % 18.52/18.73 cut (((e2) = (e2))); [idtac | apply NNPP; zenon_intro zenon_H7e]. % 18.52/18.73 cut (((e2) = (e0))); [idtac | apply NNPP; zenon_intro zenon_H14a]. % 18.52/18.73 congruence. % 18.52/18.73 cut (((op (e1) (e0)) = (e0)) = ((e2) = (e0))). % 18.52/18.73 intro zenon_D_pnotp. % 18.52/18.73 apply zenon_H14a. % 18.52/18.73 rewrite <- zenon_D_pnotp. % 18.52/18.73 exact zenon_H27. % 18.52/18.73 cut (((e0) = (e0))); [idtac | apply NNPP; zenon_intro zenon_H82]. % 18.52/18.73 cut (((op (e1) (e0)) = (e2))); [idtac | apply NNPP; zenon_intro zenon_H177]. % 18.52/18.73 congruence. % 18.52/18.73 exact (zenon_H177 zenon_H86). % 18.52/18.73 apply zenon_H82. apply refl_equal. % 18.52/18.73 apply zenon_H7e. apply refl_equal. % 18.52/18.73 apply zenon_H7e. apply refl_equal. % 18.52/18.73 (* end of lemma zenon_L257_ *) % 18.52/18.73 assert (zenon_L258_ : (~((op (e1) (e0)) = (op (e1) (e3)))) -> ((op (e1) (e0)) = (e0)) -> ((op (e1) (e3)) = (e0)) -> False). % 18.52/18.73 do 0 intro. intros zenon_Hd8 zenon_H27 zenon_H1f. % 18.52/18.73 cut (((op (e1) (e0)) = (e0)) = ((op (e1) (e0)) = (op (e1) (e3)))). % 18.52/18.73 intro zenon_D_pnotp. % 18.52/18.73 apply zenon_Hd8. % 18.52/18.73 rewrite <- zenon_D_pnotp. % 18.52/18.73 exact zenon_H27. % 18.52/18.73 cut (((e0) = (op (e1) (e3)))); [idtac | apply NNPP; zenon_intro zenon_H20]. % 18.52/18.73 cut (((op (e1) (e0)) = (op (e1) (e0)))); [idtac | apply NNPP; zenon_intro zenon_H47]. % 18.52/18.73 congruence. % 18.52/18.73 apply zenon_H47. apply refl_equal. % 18.52/18.73 apply zenon_H20. apply sym_equal. exact zenon_H1f. % 18.52/18.73 (* end of lemma zenon_L258_ *) % 18.52/18.73 assert (zenon_L259_ : (((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) (e0)) = (e0)) -> (~((op (e1) (e0)) = (op (e1) (e3)))) -> (~((op (e2) (e2)) = (op (e2) (e3)))) -> ((op (e2) (e2)) = (e0)) -> ((op (e3) (e1)) = (e0)) -> (~((op (e3) (e1)) = (op (e3) (e3)))) -> False). % 18.52/18.73 do 0 intro. intros zenon_H67 zenon_H54 zenon_H49 zenon_H27 zenon_Hd8 zenon_H6d zenon_H2c zenon_H1b1 zenon_H130. % 18.52/18.73 apply (zenon_or_s _ _ zenon_H67); [ zenon_intro zenon_H1e | zenon_intro zenon_H68 ]. % 18.52/18.73 apply (zenon_L12_); trivial. % 18.52/18.73 apply (zenon_or_s _ _ zenon_H68); [ zenon_intro zenon_H1f | zenon_intro zenon_H69 ]. % 18.52/18.73 apply (zenon_L258_); trivial. % 18.52/18.73 apply (zenon_or_s _ _ zenon_H69); [ zenon_intro zenon_H37 | zenon_intro zenon_H60 ]. % 18.52/18.73 apply (zenon_L18_); trivial. % 18.52/18.73 apply (zenon_L244_); trivial. % 18.52/18.73 (* end of lemma zenon_L259_ *) % 18.52/18.73 assert (zenon_L260_ : (((op (e3) (e0)) = (e0))\/(((op (e3) (e1)) = (e0))\/(((op (e3) (e2)) = (e0))\/((op (e3) (e3)) = (e0))))) -> (~((op (e3) (e0)) = (e0))) -> (~((op (e3) (e1)) = (op (e3) (e3)))) -> ((op (e2) (e2)) = (e0)) -> (~((op (e2) (e2)) = (op (e2) (e3)))) -> (~((op (e1) (e0)) = (op (e1) (e3)))) -> ((op (e1) (e0)) = (e0)) -> ((op (e0) (e1)) = (e0)) -> (~((op (e0) (e1)) = (op (e0) (e3)))) -> (((op (e0) (e3)) = (e0))\/(((op (e1) (e3)) = (e0))\/(((op (e2) (e3)) = (e0))\/((op (e3) (e3)) = (e0))))) -> (~((op (e3) (e2)) = (e0))) -> (~((op (e3) (e3)) = (e0))) -> False). % 18.52/18.73 do 0 intro. intros zenon_H1ac zenon_H40 zenon_H130 zenon_H2c zenon_H6d zenon_Hd8 zenon_H27 zenon_H49 zenon_H54 zenon_H67 zenon_H18b zenon_H1ae. % 18.52/18.73 apply (zenon_or_s _ _ zenon_H1ac); [ zenon_intro zenon_H44 | zenon_intro zenon_H1af ]. % 18.52/18.73 exact (zenon_H40 zenon_H44). % 18.52/18.73 apply (zenon_or_s _ _ zenon_H1af); [ zenon_intro zenon_H1b1 | zenon_intro zenon_H1b0 ]. % 18.52/18.73 apply (zenon_L259_); trivial. % 18.52/18.73 apply (zenon_or_s _ _ zenon_H1b0); [ zenon_intro zenon_H61 | zenon_intro zenon_H60 ]. % 18.52/18.73 exact (zenon_H18b zenon_H61). % 18.52/18.73 exact (zenon_H1ae zenon_H60). % 18.52/18.73 (* end of lemma zenon_L260_ *) % 18.52/18.73 assert (zenon_L261_ : (((op (e0) (e0)) = (e0))\/(((op (e0) (e1)) = (e0))\/(((op (e0) (e2)) = (e0))\/((op (e0) (e3)) = (e0))))) -> (~((op (e0) (e0)) = (e0))) -> (~((op (e3) (e2)) = (e0))) -> (~((op (e2) (e2)) = (op (e2) (e3)))) -> (~((op (e1) (e2)) = (e0))) -> (((op (e0) (e2)) = (e0))\/(((op (e1) (e2)) = (e0))\/(((op (e2) (e2)) = (e0))\/((op (e3) (e2)) = (e0))))) -> (((op (e3) (e0)) = (e0))\/(((op (e3) (e1)) = (e0))\/(((op (e3) (e2)) = (e0))\/((op (e3) (e3)) = (e0))))) -> (~((op (e3) (e0)) = (e0))) -> (~((op (e3) (e1)) = (op (e3) (e3)))) -> (~((op (e1) (e0)) = (op (e1) (e3)))) -> ((op (e1) (e0)) = (e0)) -> (~((op (e0) (e1)) = (op (e0) (e3)))) -> (((op (e0) (e3)) = (e0))\/(((op (e1) (e3)) = (e0))\/(((op (e2) (e3)) = (e0))\/((op (e3) (e3)) = (e0))))) -> (~((op (e3) (e3)) = (e0))) -> (~((op (e2) (e1)) = (e0))) -> (~((op (e2) (e0)) = (e0))) -> (((op (e2) (e0)) = (e0))\/(((op (e2) (e1)) = (e0))\/(((op (e2) (e2)) = (e0))\/((op (e2) (e3)) = (e0))))) -> (~((op (e0) (e2)) = (e0))) -> (~((op (e0) (e3)) = (e0))) -> False). % 18.52/18.73 do 0 intro. intros zenon_H74 zenon_H3f zenon_H18b zenon_H6d zenon_H25 zenon_H6a zenon_H1ac zenon_H40 zenon_H130 zenon_Hd8 zenon_H27 zenon_H54 zenon_H67 zenon_H1ae zenon_H31 zenon_H30 zenon_H2f zenon_H75 zenon_H76. % 18.52/18.73 apply (zenon_or_s _ _ zenon_H74); [ zenon_intro zenon_H42 | zenon_intro zenon_H77 ]. % 18.52/18.73 exact (zenon_H3f zenon_H42). % 18.52/18.73 apply (zenon_or_s _ _ zenon_H77); [ zenon_intro zenon_H49 | zenon_intro zenon_H78 ]. % 18.52/18.73 apply (zenon_or_s _ _ zenon_H2f); [ zenon_intro zenon_H34 | zenon_intro zenon_H33 ]. % 18.52/18.73 exact (zenon_H30 zenon_H34). % 18.52/18.73 apply (zenon_or_s _ _ zenon_H33); [ zenon_intro zenon_H36 | zenon_intro zenon_H35 ]. % 18.52/18.73 exact (zenon_H31 zenon_H36). % 18.52/18.73 apply (zenon_or_s _ _ zenon_H35); [ zenon_intro zenon_H2c | zenon_intro zenon_H37 ]. % 18.52/18.73 apply (zenon_L260_); trivial. % 18.52/18.73 apply (zenon_L143_); trivial. % 18.52/18.73 apply (zenon_or_s _ _ zenon_H78); [ zenon_intro zenon_H48 | zenon_intro zenon_H1e ]. % 18.52/18.73 exact (zenon_H75 zenon_H48). % 18.52/18.73 exact (zenon_H76 zenon_H1e). % 18.52/18.73 (* end of lemma zenon_L261_ *) % 18.52/18.73 assert (zenon_L262_ : ((op (e1) (e0)) = (e0)) -> ((op (e1) (e0)) = (e1)) -> (~((e0) = (e1))) -> False). % 18.52/18.73 do 0 intro. intros zenon_H27 zenon_H9d zenon_Ha1. % 18.52/18.73 elim (classic ((e1) = (e1))); [ zenon_intro zenon_Ha2 | zenon_intro zenon_H79 ]. % 18.52/18.73 cut (((e1) = (e1)) = ((e0) = (e1))). % 18.52/18.73 intro zenon_D_pnotp. % 18.52/18.73 apply zenon_Ha1. % 18.52/18.73 rewrite <- zenon_D_pnotp. % 18.52/18.73 exact zenon_Ha2. % 18.52/18.73 cut (((e1) = (e1))); [idtac | apply NNPP; zenon_intro zenon_H79]. % 18.52/18.73 cut (((e1) = (e0))); [idtac | apply NNPP; zenon_intro zenon_Ha3]. % 18.52/18.73 congruence. % 18.52/18.73 cut (((op (e1) (e0)) = (e0)) = ((e1) = (e0))). % 18.52/18.73 intro zenon_D_pnotp. % 18.52/18.73 apply zenon_Ha3. % 18.52/18.73 rewrite <- zenon_D_pnotp. % 18.52/18.73 exact zenon_H27. % 18.52/18.73 cut (((e0) = (e0))); [idtac | apply NNPP; zenon_intro zenon_H82]. % 18.52/18.73 cut (((op (e1) (e0)) = (e1))); [idtac | apply NNPP; zenon_intro zenon_H1ef]. % 18.52/18.73 congruence. % 18.52/18.73 exact (zenon_H1ef zenon_H9d). % 18.52/18.73 apply zenon_H82. apply refl_equal. % 18.52/18.73 apply zenon_H79. apply refl_equal. % 18.52/18.73 apply zenon_H79. apply refl_equal. % 18.52/18.73 (* end of lemma zenon_L262_ *) % 18.52/18.73 assert (zenon_L263_ : ((op (e1) (e0)) = (e0)) -> ((op (e1) (e0)) = (e3)) -> (~((e0) = (e3))) -> False). % 18.52/18.73 do 0 intro. intros zenon_H27 zenon_H9e zenon_H9a. % 18.52/18.73 elim (classic ((e3) = (e3))); [ zenon_intro zenon_H96 | zenon_intro zenon_H85 ]. % 18.52/18.73 cut (((e3) = (e3)) = ((e0) = (e3))). % 18.52/18.73 intro zenon_D_pnotp. % 18.52/18.73 apply zenon_H9a. % 18.52/18.73 rewrite <- zenon_D_pnotp. % 18.52/18.73 exact zenon_H96. % 18.52/18.73 cut (((e3) = (e3))); [idtac | apply NNPP; zenon_intro zenon_H85]. % 18.52/18.73 cut (((e3) = (e0))); [idtac | apply NNPP; zenon_intro zenon_H9b]. % 18.52/18.73 congruence. % 18.52/18.73 cut (((op (e1) (e0)) = (e0)) = ((e3) = (e0))). % 18.52/18.73 intro zenon_D_pnotp. % 18.52/18.73 apply zenon_H9b. % 18.52/18.73 rewrite <- zenon_D_pnotp. % 18.52/18.73 exact zenon_H27. % 18.52/18.73 cut (((e0) = (e0))); [idtac | apply NNPP; zenon_intro zenon_H82]. % 18.52/18.73 cut (((op (e1) (e0)) = (e3))); [idtac | apply NNPP; zenon_intro zenon_H9f]. % 18.52/18.73 congruence. % 18.52/18.73 exact (zenon_H9f zenon_H9e). % 18.52/18.73 apply zenon_H82. apply refl_equal. % 18.52/18.73 apply zenon_H85. apply refl_equal. % 18.52/18.73 apply zenon_H85. apply refl_equal. % 18.52/18.73 (* end of lemma zenon_L263_ *) % 18.52/18.73 assert (zenon_L264_ : (((op (e3) (e0)) = (e3))\/(((op (e3) (e1)) = (e3))\/(((op (e3) (e2)) = (e3))\/((op (e3) (e3)) = (e3))))) -> (~((e1) = (e3))) -> ((op (e3) (e0)) = (e1)) -> ((op (e1) (e1)) = (e3)) -> (~((op (e1) (e1)) = (op (e3) (e1)))) -> ((op (e0) (e2)) = (e3)) -> (~((op (e0) (e2)) = (op (e3) (e2)))) -> (~((op (e3) (e3)) = (e3))) -> False). % 18.52/18.73 do 0 intro. intros zenon_H165 zenon_H95 zenon_Hac zenon_H13f zenon_H160 zenon_Ha9 zenon_H14f zenon_H102. % 18.52/18.73 apply (zenon_or_s _ _ zenon_H165); [ zenon_intro zenon_H15e | zenon_intro zenon_H166 ]. % 18.52/18.73 apply (zenon_L252_); trivial. % 18.52/18.73 apply (zenon_or_s _ _ zenon_H166); [ zenon_intro zenon_H161 | zenon_intro zenon_H167 ]. % 18.52/18.73 apply (zenon_L110_); trivial. % 18.52/18.73 apply (zenon_or_s _ _ zenon_H167); [ zenon_intro zenon_H163 | zenon_intro zenon_H105 ]. % 18.52/18.73 apply (zenon_L111_); trivial. % 18.52/18.73 exact (zenon_H102 zenon_H105). % 18.52/18.73 (* end of lemma zenon_L264_ *) % 18.52/18.73 assert (zenon_L265_ : (((op (e3) (e0)) = (e1))\/(((op (e3) (e1)) = (e1))\/(((op (e3) (e2)) = (e1))\/((op (e3) (e3)) = (e1))))) -> (~((op (e3) (e3)) = (e3))) -> (~((op (e0) (e2)) = (op (e3) (e2)))) -> (~((op (e1) (e1)) = (op (e3) (e1)))) -> (~((e1) = (e3))) -> (((op (e3) (e0)) = (e3))\/(((op (e3) (e1)) = (e3))\/(((op (e3) (e2)) = (e3))\/((op (e3) (e3)) = (e3))))) -> ((op (e1) (e1)) = (e3)) -> (~((op (e1) (e1)) = (op (e2) (e1)))) -> (~((op (e0) (e1)) = (op (e2) (e1)))) -> ((op (e0) (e1)) = (e2)) -> (~((op (e2) (e1)) = (op (e3) (e1)))) -> (~((op (e2) (e1)) = (e0))) -> (((op (e2) (e1)) = (e0))\/(((op (e2) (e1)) = (e1))\/(((op (e2) (e1)) = (e2))\/((op (e2) (e1)) = (e3))))) -> ((op (e2) (e2)) = (e0)) -> ((op (e0) (e2)) = (e3)) -> (((op (e0) (e3)) = (e0))\/(((op (e0) (e3)) = (e1))\/(((op (e0) (e3)) = (e2))\/((op (e0) (e3)) = (e3))))) -> (~((op (e0) (e3)) = (e0))) -> (~((op (e0) (e3)) = (op (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)) = (e2)) -> (~((op (e2) (e3)) = (op (e3) (e3)))) -> (~((op (e2) (e0)) = (op (e2) (e3)))) -> ((op (e2) (e0)) = (e2)) -> (~((op (e0) (e3)) = (op (e2) (e3)))) -> False). % 18.52/18.73 do 0 intro. intros zenon_He8 zenon_H102 zenon_H14f zenon_H160 zenon_H95 zenon_H165 zenon_H13f zenon_H13e zenon_H17e zenon_H10f zenon_Haf zenon_H31 zenon_H1cc zenon_H2c zenon_Ha9 zenon_He4 zenon_H76 zenon_Hc2 zenon_H1d zenon_H11f zenon_Hd7 zenon_Hf3 zenon_H5b zenon_Hee zenon_He2. % 18.52/18.73 apply (zenon_or_s _ _ zenon_He8); [ zenon_intro zenon_Hac | zenon_intro zenon_Heb ]. % 18.52/18.73 apply (zenon_L264_); trivial. % 18.52/18.73 apply (zenon_or_s _ _ zenon_Heb); [ zenon_intro zenon_Hae | zenon_intro zenon_Hec ]. % 18.52/18.73 apply (zenon_L192_); trivial. % 18.52/18.73 apply (zenon_or_s _ _ zenon_Hec); [ zenon_intro zenon_Hba | zenon_intro zenon_Hc4 ]. % 18.52/18.73 apply (zenon_L45_); trivial. % 18.52/18.73 apply (zenon_L75_); trivial. % 18.52/18.73 (* end of lemma zenon_L265_ *) % 18.52/18.73 assert (zenon_L266_ : ((op (e1) (e3)) = (e2)) -> ((op (e1) (e3)) = (e3)) -> (~((e2) = (e3))) -> False). % 18.52/18.73 do 0 intro. intros zenon_Hd7 zenon_Hdc zenon_H12b. % 18.52/18.73 elim (classic ((e3) = (e3))); [ zenon_intro zenon_H96 | zenon_intro zenon_H85 ]. % 18.52/18.73 cut (((e3) = (e3)) = ((e2) = (e3))). % 18.52/18.73 intro zenon_D_pnotp. % 18.52/18.73 apply zenon_H12b. % 18.52/18.73 rewrite <- zenon_D_pnotp. % 18.52/18.73 exact zenon_H96. % 18.52/18.73 cut (((e3) = (e3))); [idtac | apply NNPP; zenon_intro zenon_H85]. % 18.52/18.73 cut (((e3) = (e2))); [idtac | apply NNPP; zenon_intro zenon_H12c]. % 18.52/18.73 congruence. % 18.52/18.73 cut (((op (e1) (e3)) = (e2)) = ((e3) = (e2))). % 18.52/18.73 intro zenon_D_pnotp. % 18.52/18.73 apply zenon_H12c. % 18.52/18.73 rewrite <- zenon_D_pnotp. % 18.52/18.73 exact zenon_Hd7. % 18.52/18.73 cut (((e2) = (e2))); [idtac | apply NNPP; zenon_intro zenon_H7e]. % 18.52/18.73 cut (((op (e1) (e3)) = (e3))); [idtac | apply NNPP; zenon_intro zenon_H12f]. % 18.52/18.73 congruence. % 18.52/18.73 exact (zenon_H12f zenon_Hdc). % 18.52/18.73 apply zenon_H7e. apply refl_equal. % 18.52/18.73 apply zenon_H85. apply refl_equal. % 18.52/18.73 apply zenon_H85. apply refl_equal. % 18.52/18.73 (* end of lemma zenon_L266_ *) % 18.52/18.73 assert (zenon_L267_ : (((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)) = (op (e2) (e1)))) -> (~((op (e0) (e1)) = (op (e2) (e1)))) -> ((op (e0) (e1)) = (e2)) -> ((op (e3) (e1)) = (e1)) -> (~((op (e2) (e1)) = (op (e3) (e1)))) -> (~((op (e2) (e1)) = (e0))) -> (((op (e2) (e1)) = (e0))\/(((op (e2) (e1)) = (e1))\/(((op (e2) (e1)) = (e2))\/((op (e2) (e1)) = (e3))))) -> (~((e1) = (e3))) -> ((op (e1) (e2)) = (e1)) -> ((op (e1) (e3)) = (e2)) -> (~((e2) = (e3))) -> False). % 18.52/18.73 do 0 intro. intros zenon_H16f zenon_H9a zenon_H27 zenon_H13e zenon_H17e zenon_H10f zenon_Hae zenon_Haf zenon_H31 zenon_H1cc zenon_H95 zenon_Hf0 zenon_Hd7 zenon_H12b. % 18.52/18.73 apply (zenon_or_s _ _ zenon_H16f); [ zenon_intro zenon_H9e | zenon_intro zenon_H170 ]. % 18.52/18.73 apply (zenon_L263_); trivial. % 18.52/18.73 apply (zenon_or_s _ _ zenon_H170); [ zenon_intro zenon_H13f | zenon_intro zenon_H171 ]. % 18.52/18.73 apply (zenon_L192_); trivial. % 18.52/18.73 apply (zenon_or_s _ _ zenon_H171); [ zenon_intro zenon_H16c | zenon_intro zenon_Hdc ]. % 18.52/18.73 apply (zenon_L167_); trivial. % 18.52/18.73 apply (zenon_L266_); trivial. % 18.52/18.73 (* end of lemma zenon_L267_ *) % 18.52/18.73 assert (zenon_L268_ : (((op (e1) (e0)) = (e2))\/(((op (e1) (e1)) = (e2))\/(((op (e1) (e2)) = (e2))\/((op (e1) (e3)) = (e2))))) -> (~((e0) = (e2))) -> (~((op (e0) (e1)) = (op (e1) (e1)))) -> (~((e1) = (e2))) -> (((op (e1) (e0)) = (e3))\/(((op (e1) (e1)) = (e3))\/(((op (e1) (e2)) = (e3))\/((op (e1) (e3)) = (e3))))) -> (~((e0) = (e3))) -> ((op (e1) (e0)) = (e0)) -> (~((op (e1) (e1)) = (op (e2) (e1)))) -> (~((op (e0) (e1)) = (op (e2) (e1)))) -> ((op (e0) (e1)) = (e2)) -> ((op (e3) (e1)) = (e1)) -> (~((op (e2) (e1)) = (op (e3) (e1)))) -> (~((op (e2) (e1)) = (e0))) -> (((op (e2) (e1)) = (e0))\/(((op (e2) (e1)) = (e1))\/(((op (e2) (e1)) = (e2))\/((op (e2) (e1)) = (e3))))) -> (~((e1) = (e3))) -> ((op (e1) (e2)) = (e1)) -> (~((e2) = (e3))) -> False). % 18.52/18.73 do 0 intro. intros zenon_H18c zenon_H149 zenon_H10e zenon_H7c zenon_H16f zenon_H9a zenon_H27 zenon_H13e zenon_H17e zenon_H10f zenon_Hae zenon_Haf zenon_H31 zenon_H1cc zenon_H95 zenon_Hf0 zenon_H12b. % 18.52/18.73 apply (zenon_or_s _ _ zenon_H18c); [ zenon_intro zenon_H86 | zenon_intro zenon_H18d ]. % 18.52/18.73 apply (zenon_L257_); trivial. % 18.52/18.73 apply (zenon_or_s _ _ zenon_H18d); [ zenon_intro zenon_H110 | zenon_intro zenon_H18e ]. % 18.52/18.73 apply (zenon_L67_); trivial. % 18.52/18.73 apply (zenon_or_s _ _ zenon_H18e); [ zenon_intro zenon_H113 | zenon_intro zenon_Hd7 ]. % 18.52/18.73 apply (zenon_L68_); trivial. % 18.52/18.73 apply (zenon_L267_); trivial. % 18.52/18.73 (* end of lemma zenon_L268_ *) % 18.52/18.73 assert (zenon_L269_ : (((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)) = (op (e2) (e1)))) -> (~((op (e0) (e1)) = (op (e2) (e1)))) -> ((op (e0) (e1)) = (e2)) -> ((op (e3) (e1)) = (e1)) -> (~((op (e2) (e1)) = (op (e3) (e1)))) -> (~((op (e2) (e1)) = (e0))) -> (((op (e2) (e1)) = (e0))\/(((op (e2) (e1)) = (e1))\/(((op (e2) (e1)) = (e2))\/((op (e2) (e1)) = (e3))))) -> ((op (e0) (e2)) = (e3)) -> (~((op (e0) (e2)) = (op (e1) (e2)))) -> ((op (e1) (e3)) = (e1)) -> (~((e1) = (e3))) -> False). % 18.52/18.73 do 0 intro. intros zenon_H16f zenon_H9a zenon_H27 zenon_H13e zenon_H17e zenon_H10f zenon_Hae zenon_Haf zenon_H31 zenon_H1cc zenon_Ha9 zenon_H195 zenon_Hd6 zenon_H95. % 18.52/18.73 apply (zenon_or_s _ _ zenon_H16f); [ zenon_intro zenon_H9e | zenon_intro zenon_H170 ]. % 18.52/18.73 apply (zenon_L263_); trivial. % 18.52/18.73 apply (zenon_or_s _ _ zenon_H170); [ zenon_intro zenon_H13f | zenon_intro zenon_H171 ]. % 18.52/18.73 apply (zenon_L192_); trivial. % 18.52/18.73 apply (zenon_or_s _ _ zenon_H171); [ zenon_intro zenon_H16c | zenon_intro zenon_Hdc ]. % 18.52/18.73 apply (zenon_L162_); trivial. % 18.52/18.73 apply (zenon_L83_); trivial. % 18.52/18.73 (* end of lemma zenon_L269_ *) % 18.52/18.73 assert (zenon_L270_ : (((op (e3) (e0)) = (e1))\/(((op (e3) (e1)) = (e1))\/(((op (e3) (e2)) = (e1))\/((op (e3) (e3)) = (e1))))) -> ((op (e3) (e0)) = (e3)) -> (~((e1) = (e3))) -> (~((op (e0) (e2)) = (op (e1) (e2)))) -> (((op (e2) (e1)) = (e0))\/(((op (e2) (e1)) = (e1))\/(((op (e2) (e1)) = (e2))\/((op (e2) (e1)) = (e3))))) -> (~((op (e2) (e1)) = (e0))) -> (~((op (e2) (e1)) = (op (e3) (e1)))) -> ((op (e0) (e1)) = (e2)) -> (~((op (e0) (e1)) = (op (e2) (e1)))) -> (~((op (e1) (e1)) = (op (e2) (e1)))) -> ((op (e1) (e0)) = (e0)) -> (~((e0) = (e3))) -> (((op (e1) (e0)) = (e3))\/(((op (e1) (e1)) = (e3))\/(((op (e1) (e2)) = (e3))\/((op (e1) (e3)) = (e3))))) -> ((op (e2) (e2)) = (e0)) -> ((op (e0) (e2)) = (e3)) -> (~((op (e1) (e3)) = (op (e3) (e3)))) -> ((op (e1) (e3)) = (e1)) -> False). % 18.52/18.73 do 0 intro. intros zenon_He8 zenon_H15e zenon_H95 zenon_H195 zenon_H1cc zenon_H31 zenon_Haf zenon_H10f zenon_H17e zenon_H13e zenon_H27 zenon_H9a zenon_H16f zenon_H2c zenon_Ha9 zenon_Hd5 zenon_Hd6. % 18.52/18.73 apply (zenon_or_s _ _ zenon_He8); [ zenon_intro zenon_Hac | zenon_intro zenon_Heb ]. % 18.52/18.73 apply (zenon_L252_); trivial. % 18.52/18.73 apply (zenon_or_s _ _ zenon_Heb); [ zenon_intro zenon_Hae | zenon_intro zenon_Hec ]. % 18.52/18.73 apply (zenon_L269_); trivial. % 18.52/18.73 apply (zenon_or_s _ _ zenon_Hec); [ zenon_intro zenon_Hba | zenon_intro zenon_Hc4 ]. % 18.52/18.73 apply (zenon_L45_); trivial. % 18.52/18.73 apply (zenon_L50_); trivial. % 18.52/18.73 (* end of lemma zenon_L270_ *) % 18.52/18.73 assert (zenon_L271_ : ((~((op (e3) (e3)) = (e0)))\/((op (e3) (e0)) = (e3))) -> ((op (e3) (e0)) = (e1)) -> (~((e1) = (e3))) -> (~((op (e0) (e0)) = (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 (e0) (e2)) = (e0))\/(((op (e1) (e2)) = (e0))\/(((op (e2) (e2)) = (e0))\/((op (e3) (e2)) = (e0))))) -> (~((op (e3) (e0)) = (e0))) -> (((op (e0) (e3)) = (e0))\/(((op (e1) (e3)) = (e0))\/(((op (e2) (e3)) = (e0))\/((op (e3) (e3)) = (e0))))) -> (~((op (e3) (e1)) = (op (e3) (e3)))) -> (~((op (e2) (e2)) = (op (e2) (e3)))) -> ((op (e1) (e0)) = (e0)) -> (~((op (e1) (e0)) = (op (e1) (e3)))) -> (~((op (e0) (e1)) = (op (e0) (e3)))) -> (~((op (e3) (e2)) = (e0))) -> (((op (e3) (e0)) = (e0))\/(((op (e3) (e1)) = (e0))\/(((op (e3) (e2)) = (e0))\/((op (e3) (e3)) = (e0))))) -> (~((op (e2) (e1)) = (e0))) -> (~((op (e2) (e0)) = (e0))) -> (~((op (e0) (e3)) = (e0))) -> (((op (e0) (e0)) = (e0))\/(((op (e0) (e1)) = (e0))\/(((op (e0) (e2)) = (e0))\/((op (e0) (e3)) = (e0))))) -> False). % 18.52/18.73 do 0 intro. intros zenon_H1ec zenon_Hac zenon_H95 zenon_H3f zenon_H2f zenon_H75 zenon_H25 zenon_H6a zenon_H40 zenon_H67 zenon_H130 zenon_H6d zenon_H27 zenon_Hd8 zenon_H54 zenon_H18b zenon_H1ac zenon_H31 zenon_H30 zenon_H76 zenon_H74. % 18.52/18.73 apply (zenon_or_s _ _ zenon_H1ec); [ zenon_intro zenon_H1ae | zenon_intro zenon_H15e ]. % 18.52/18.73 apply (zenon_L261_); trivial. % 18.52/18.73 apply (zenon_L252_); trivial. % 18.52/18.73 (* end of lemma zenon_L271_ *) % 18.52/18.73 assert (zenon_L272_ : (~((op (e0) (e3)) = (op (e2) (e3)))) -> ((op (e0) (e3)) = (e1)) -> ((op (e2) (e3)) = (e1)) -> False). % 18.52/18.73 do 0 intro. intros zenon_He2 zenon_Hc3 zenon_Hf4. % 18.52/18.73 cut (((op (e0) (e3)) = (e1)) = ((op (e0) (e3)) = (op (e2) (e3)))). % 18.52/18.73 intro zenon_D_pnotp. % 18.52/18.73 apply zenon_He2. % 18.52/18.73 rewrite <- zenon_D_pnotp. % 18.52/18.73 exact zenon_Hc3. % 18.52/18.73 cut (((e1) = (op (e2) (e3)))); [idtac | apply NNPP; zenon_intro zenon_H17a]. % 18.52/18.73 cut (((op (e0) (e3)) = (op (e0) (e3)))); [idtac | apply NNPP; zenon_intro zenon_H21]. % 18.52/18.73 congruence. % 18.52/18.73 apply zenon_H21. apply refl_equal. % 18.52/18.73 apply zenon_H17a. apply sym_equal. exact zenon_Hf4. % 18.52/18.73 (* end of lemma zenon_L272_ *) % 18.52/18.73 assert (zenon_L273_ : (((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 (e3) (e0)) = (e3)) -> (((op (e2) (e0)) = (e1))\/(((op (e2) (e1)) = (e1))\/(((op (e2) (e2)) = (e1))\/((op (e2) (e3)) = (e1))))) -> ((op (e0) (e0)) = (e1)) -> (~((op (e0) (e0)) = (op (e2) (e0)))) -> (~((op (e3) (e1)) = (op (e3) (e3)))) -> ((op (e3) (e1)) = (e1)) -> (~((op (e2) (e2)) = (op (e2) (e3)))) -> (~((e1) = (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 (e3) (e0)) = (e0))) -> (~((op (e3) (e1)) = (e0))) -> (~((op (e3) (e2)) = (e0))) -> (~((e2) = (e3))) -> ((op (e0) (e1)) = (e0)) -> (~((e0) = (e3))) -> (((op (e0) (e1)) = (e3))\/(((op (e1) (e1)) = (e3))\/(((op (e2) (e1)) = (e3))\/((op (e3) (e1)) = (e3))))) -> ((op (e1) (e0)) = (e0)) -> (((op (e1) (e0)) = (e3))\/(((op (e1) (e1)) = (e3))\/(((op (e1) (e2)) = (e3))\/((op (e1) (e3)) = (e3))))) -> (~((e1) = (e2))) -> ((op (e1) (e2)) = (e1)) -> (~((op (e0) (e3)) = (op (e1) (e3)))) -> ((op (e0) (e3)) = (e2)) -> False). % 18.52/18.73 do 0 intro. intros zenon_H18c zenon_H149 zenon_H1cf zenon_H15e zenon_H106 zenon_H7a zenon_H39 zenon_H130 zenon_Hae zenon_H6d zenon_H95 zenon_H133 zenon_H1ac zenon_H40 zenon_H1ad zenon_H18b zenon_H12b zenon_H49 zenon_H9a zenon_H1a5 zenon_H27 zenon_H16f zenon_H7c zenon_Hf0 zenon_H1d zenon_Hcd. % 18.52/18.73 apply (zenon_or_s _ _ zenon_H18c); [ zenon_intro zenon_H86 | zenon_intro zenon_H18d ]. % 18.52/18.73 apply (zenon_L257_); trivial. % 18.52/18.73 apply (zenon_or_s _ _ zenon_H18d); [ zenon_intro zenon_H110 | zenon_intro zenon_H18e ]. % 18.52/18.73 apply (zenon_or_s _ _ zenon_H16f); [ zenon_intro zenon_H9e | zenon_intro zenon_H170 ]. % 18.52/18.73 apply (zenon_L263_); trivial. % 18.52/18.73 apply (zenon_or_s _ _ zenon_H170); [ zenon_intro zenon_H13f | zenon_intro zenon_H171 ]. % 18.52/18.73 apply (zenon_L166_); trivial. % 18.52/18.73 apply (zenon_or_s _ _ zenon_H171); [ zenon_intro zenon_H16c | zenon_intro zenon_Hdc ]. % 18.52/18.73 apply (zenon_L167_); trivial. % 18.52/18.73 apply (zenon_or_s _ _ zenon_H1a5); [ zenon_intro zenon_H99 | zenon_intro zenon_H1a8 ]. % 18.52/18.73 apply (zenon_L36_); trivial. % 18.52/18.73 apply (zenon_or_s _ _ zenon_H1a8); [ zenon_intro zenon_H13f | zenon_intro zenon_H1a9 ]. % 18.52/18.73 apply (zenon_L166_); trivial. % 18.52/18.73 apply (zenon_or_s _ _ zenon_H1a9); [ zenon_intro zenon_Ha6 | zenon_intro zenon_H161 ]. % 18.52/18.73 apply (zenon_or_s _ _ zenon_H106); [ zenon_intro zenon_Hed | zenon_intro zenon_H107 ]. % 18.52/18.73 apply (zenon_L134_); trivial. % 18.52/18.73 apply (zenon_or_s _ _ zenon_H107); [ zenon_intro zenon_Ha5 | zenon_intro zenon_H108 ]. % 18.52/18.73 apply (zenon_L39_); trivial. % 18.52/18.73 apply (zenon_or_s _ _ zenon_H108); [ zenon_intro zenon_Hf1 | zenon_intro zenon_Hf4 ]. % 18.52/18.73 apply (zenon_L86_); trivial. % 18.52/18.73 apply (zenon_L231_); trivial. % 18.52/18.73 apply (zenon_L193_); trivial. % 18.52/18.73 apply (zenon_or_s _ _ zenon_H18e); [ zenon_intro zenon_H113 | zenon_intro zenon_Hd7 ]. % 18.52/18.73 apply (zenon_L68_); trivial. % 18.52/18.73 apply (zenon_L70_); trivial. % 18.52/18.73 (* end of lemma zenon_L273_ *) % 18.52/18.73 assert (zenon_L274_ : (((op (e1) (e0)) = (e3))\/(((op (e1) (e1)) = (e3))\/(((op (e1) (e2)) = (e3))\/((op (e1) (e3)) = (e3))))) -> (~((e0) = (e3))) -> ((op (e1) (e0)) = (e0)) -> (~((e2) = (e3))) -> ((op (e1) (e1)) = (e2)) -> ((op (e0) (e2)) = (e3)) -> (~((op (e0) (e2)) = (op (e1) (e2)))) -> ((op (e1) (e3)) = (e1)) -> (~((e1) = (e3))) -> False). % 18.52/18.73 do 0 intro. intros zenon_H16f zenon_H9a zenon_H27 zenon_H12b zenon_H110 zenon_Ha9 zenon_H195 zenon_Hd6 zenon_H95. % 18.52/18.73 apply (zenon_or_s _ _ zenon_H16f); [ zenon_intro zenon_H9e | zenon_intro zenon_H170 ]. % 18.52/18.73 apply (zenon_L263_); trivial. % 18.52/18.73 apply (zenon_or_s _ _ zenon_H170); [ zenon_intro zenon_H13f | zenon_intro zenon_H171 ]. % 18.52/18.73 apply (zenon_L166_); trivial. % 18.52/18.73 apply (zenon_or_s _ _ zenon_H171); [ zenon_intro zenon_H16c | zenon_intro zenon_Hdc ]. % 18.52/18.73 apply (zenon_L162_); trivial. % 18.52/18.73 apply (zenon_L83_); trivial. % 18.52/18.73 (* end of lemma zenon_L274_ *) % 18.52/18.73 assert (zenon_L275_ : (((op (e3) (e3)) = (e0))\/(((op (e3) (e3)) = (e1))\/(((op (e3) (e3)) = (e2))\/((op (e3) (e3)) = (e3))))) -> ((op (e2) (e3)) = (e0)) -> (~((op (e2) (e3)) = (op (e3) (e3)))) -> ((op (e1) (e3)) = (e1)) -> (~((op (e1) (e3)) = (op (e3) (e3)))) -> ((op (e0) (e3)) = (e2)) -> (~((op (e0) (e3)) = (op (e3) (e3)))) -> (~((op (e3) (e3)) = (e3))) -> False). % 18.52/18.73 do 0 intro. intros zenon_H101 zenon_H37 zenon_Hf3 zenon_Hd6 zenon_Hd5 zenon_Hcd zenon_Hc2 zenon_H102. % 18.52/18.73 apply (zenon_or_s _ _ zenon_H101); [ zenon_intro zenon_H60 | zenon_intro zenon_H103 ]. % 18.52/18.73 apply (zenon_L219_); trivial. % 18.52/18.73 apply (zenon_or_s _ _ zenon_H103); [ zenon_intro zenon_Hc4 | zenon_intro zenon_H104 ]. % 18.52/18.73 apply (zenon_L50_); trivial. % 18.52/18.73 apply (zenon_or_s _ _ zenon_H104); [ zenon_intro zenon_Hf6 | zenon_intro zenon_H105 ]. % 18.52/18.73 apply (zenon_L87_); trivial. % 18.52/18.73 exact (zenon_H102 zenon_H105). % 18.52/18.73 (* end of lemma zenon_L275_ *) % 18.52/18.73 assert (zenon_L276_ : (((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)) = (e2)) -> (~((e2) = (e3))) -> ((op (e1) (e2)) = (e2)) -> ((op (e1) (e3)) = (e1)) -> (~((e1) = (e3))) -> False). % 18.52/18.73 do 0 intro. intros zenon_H16f zenon_H9a zenon_H27 zenon_H110 zenon_H12b zenon_H113 zenon_Hd6 zenon_H95. % 18.52/18.73 apply (zenon_or_s _ _ zenon_H16f); [ zenon_intro zenon_H9e | zenon_intro zenon_H170 ]. % 18.52/18.73 apply (zenon_L263_); trivial. % 18.52/18.73 apply (zenon_or_s _ _ zenon_H170); [ zenon_intro zenon_H13f | zenon_intro zenon_H171 ]. % 18.52/18.73 apply (zenon_L166_); trivial. % 18.52/18.73 apply (zenon_or_s _ _ zenon_H171); [ zenon_intro zenon_H16c | zenon_intro zenon_Hdc ]. % 18.52/18.73 apply (zenon_L116_); trivial. % 18.52/18.73 apply (zenon_L83_); trivial. % 18.52/18.73 (* end of lemma zenon_L276_ *) % 18.52/18.73 assert (zenon_L277_ : (~((op (e2) (e0)) = (op (e2) (e1)))) -> ((op (e2) (e0)) = (e2)) -> ((op (e2) (e1)) = (e2)) -> False). % 18.52/18.73 do 0 intro. intros zenon_H1f0 zenon_Hee zenon_H1ca. % 18.52/18.73 cut (((op (e2) (e0)) = (e2)) = ((op (e2) (e0)) = (op (e2) (e1)))). % 18.52/18.73 intro zenon_D_pnotp. % 18.52/18.73 apply zenon_H1f0. % 18.52/18.73 rewrite <- zenon_D_pnotp. % 18.52/18.73 exact zenon_Hee. % 18.52/18.73 cut (((e2) = (op (e2) (e1)))); [idtac | apply NNPP; zenon_intro zenon_H1cb]. % 18.52/18.73 cut (((op (e2) (e0)) = (op (e2) (e0)))); [idtac | apply NNPP; zenon_intro zenon_H53]. % 18.52/18.73 congruence. % 18.52/18.73 apply zenon_H53. apply refl_equal. % 18.52/18.73 apply zenon_H1cb. apply sym_equal. exact zenon_H1ca. % 18.52/18.73 (* end of lemma zenon_L277_ *) % 18.52/18.73 assert (zenon_L278_ : (((op (e3) (e0)) = (e1))\/(((op (e3) (e1)) = (e1))\/(((op (e3) (e2)) = (e1))\/((op (e3) (e3)) = (e1))))) -> (~((e1) = (e3))) -> ((op (e3) (e0)) = (e3)) -> (~((e1) = (e2))) -> ((op (e3) (e1)) = (e2)) -> ((op (e2) (e2)) = (e0)) -> ((op (e0) (e2)) = (e3)) -> (~((op (e1) (e3)) = (op (e3) (e3)))) -> ((op (e1) (e3)) = (e1)) -> False). % 18.52/18.73 do 0 intro. intros zenon_He8 zenon_H95 zenon_H15e zenon_H7c zenon_H14d zenon_H2c zenon_Ha9 zenon_Hd5 zenon_Hd6. % 18.52/18.73 apply (zenon_or_s _ _ zenon_He8); [ zenon_intro zenon_Hac | zenon_intro zenon_Heb ]. % 18.52/18.73 apply (zenon_L252_); trivial. % 18.52/18.73 apply (zenon_or_s _ _ zenon_Heb); [ zenon_intro zenon_Hae | zenon_intro zenon_Hec ]. % 18.52/18.73 apply (zenon_L152_); trivial. % 18.52/18.73 apply (zenon_or_s _ _ zenon_Hec); [ zenon_intro zenon_Hba | zenon_intro zenon_Hc4 ]. % 18.52/18.73 apply (zenon_L45_); trivial. % 18.52/18.73 apply (zenon_L50_); trivial. % 18.52/18.73 (* end of lemma zenon_L278_ *) % 18.52/18.73 assert (zenon_L279_ : (((op (e2) (e0)) = (e0))\/(((op (e2) (e1)) = (e0))\/(((op (e2) (e2)) = (e0))\/((op (e2) (e3)) = (e0))))) -> (~((op (e2) (e0)) = (e0))) -> (~((op (e2) (e1)) = (e0))) -> ((op (e1) (e3)) = (e1)) -> (~((op (e1) (e3)) = (op (e3) (e3)))) -> ((op (e0) (e2)) = (e3)) -> ((op (e3) (e1)) = (e2)) -> (~((e1) = (e2))) -> ((op (e3) (e0)) = (e3)) -> (~((e1) = (e3))) -> (((op (e3) (e0)) = (e1))\/(((op (e3) (e1)) = (e1))\/(((op (e3) (e2)) = (e1))\/((op (e3) (e3)) = (e1))))) -> (((op (e0) (e2)) = (e0))\/(((op (e1) (e2)) = (e0))\/(((op (e2) (e2)) = (e0))\/((op (e3) (e2)) = (e0))))) -> (~((op (e0) (e2)) = (e0))) -> (~((op (e1) (e2)) = (e0))) -> (~((op (e2) (e2)) = (op (e2) (e3)))) -> (~((op (e3) (e2)) = (e0))) -> False). % 18.52/18.73 do 0 intro. intros zenon_H2f zenon_H30 zenon_H31 zenon_Hd6 zenon_Hd5 zenon_Ha9 zenon_H14d zenon_H7c zenon_H15e zenon_H95 zenon_He8 zenon_H6a zenon_H75 zenon_H25 zenon_H6d zenon_H18b. % 18.52/18.73 apply (zenon_or_s _ _ zenon_H2f); [ zenon_intro zenon_H34 | zenon_intro zenon_H33 ]. % 18.52/18.73 exact (zenon_H30 zenon_H34). % 18.52/18.73 apply (zenon_or_s _ _ zenon_H33); [ zenon_intro zenon_H36 | zenon_intro zenon_H35 ]. % 18.52/18.73 exact (zenon_H31 zenon_H36). % 18.52/18.73 apply (zenon_or_s _ _ zenon_H35); [ zenon_intro zenon_H2c | zenon_intro zenon_H37 ]. % 18.52/18.73 apply (zenon_L278_); trivial. % 18.52/18.73 apply (zenon_L143_); trivial. % 18.52/18.73 (* end of lemma zenon_L279_ *) % 18.52/18.73 assert (zenon_L280_ : (((op (e0) (e1)) = (e2))\/(((op (e1) (e1)) = (e2))\/(((op (e2) (e1)) = (e2))\/((op (e3) (e1)) = (e2))))) -> (~((op (e3) (e3)) = (e3))) -> (~((op (e0) (e3)) = (op (e3) (e3)))) -> ((op (e0) (e3)) = (e2)) -> (~((op (e2) (e3)) = (op (e3) (e3)))) -> (((op (e3) (e3)) = (e0))\/(((op (e3) (e3)) = (e1))\/(((op (e3) (e3)) = (e2))\/((op (e3) (e3)) = (e3))))) -> (~((op (e0) (e2)) = (op (e1) (e2)))) -> (((op (e2) (e1)) = (e0))\/(((op (e2) (e1)) = (e1))\/(((op (e2) (e1)) = (e2))\/((op (e2) (e1)) = (e3))))) -> (~((op (e2) (e1)) = (op (e3) (e1)))) -> (~((op (e0) (e1)) = (op (e2) (e1)))) -> (~((op (e1) (e1)) = (op (e2) (e1)))) -> ((op (e1) (e2)) = (e2)) -> (~((e2) = (e3))) -> ((op (e1) (e0)) = (e0)) -> (~((e0) = (e3))) -> (((op (e1) (e0)) = (e3))\/(((op (e1) (e1)) = (e3))\/(((op (e1) (e2)) = (e3))\/((op (e1) (e3)) = (e3))))) -> ((op (e2) (e0)) = (e2)) -> (~((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) (e1)) = (e0))) -> ((op (e1) (e3)) = (e1)) -> (~((op (e1) (e3)) = (op (e3) (e3)))) -> ((op (e0) (e2)) = (e3)) -> (~((e1) = (e2))) -> ((op (e3) (e0)) = (e3)) -> (~((e1) = (e3))) -> (((op (e3) (e0)) = (e1))\/(((op (e3) (e1)) = (e1))\/(((op (e3) (e2)) = (e1))\/((op (e3) (e3)) = (e1))))) -> (((op (e0) (e2)) = (e0))\/(((op (e1) (e2)) = (e0))\/(((op (e2) (e2)) = (e0))\/((op (e3) (e2)) = (e0))))) -> (~((op (e0) (e2)) = (e0))) -> (~((op (e1) (e2)) = (e0))) -> (~((op (e2) (e2)) = (op (e2) (e3)))) -> (~((op (e3) (e2)) = (e0))) -> False). % 18.52/18.73 do 0 intro. intros zenon_H1d8 zenon_H102 zenon_Hc2 zenon_Hcd zenon_Hf3 zenon_H101 zenon_H195 zenon_H1cc zenon_Haf zenon_H17e zenon_H13e zenon_H113 zenon_H12b zenon_H27 zenon_H9a zenon_H16f zenon_Hee zenon_H1f0 zenon_H2f zenon_H30 zenon_H31 zenon_Hd6 zenon_Hd5 zenon_Ha9 zenon_H7c zenon_H15e zenon_H95 zenon_He8 zenon_H6a zenon_H75 zenon_H25 zenon_H6d zenon_H18b. % 18.52/18.73 apply (zenon_or_s _ _ zenon_H1d8); [ zenon_intro zenon_H10f | zenon_intro zenon_H1d9 ]. % 18.52/18.73 apply (zenon_or_s _ _ zenon_H2f); [ zenon_intro zenon_H34 | zenon_intro zenon_H33 ]. % 18.52/18.73 exact (zenon_H30 zenon_H34). % 18.52/18.73 apply (zenon_or_s _ _ zenon_H33); [ zenon_intro zenon_H36 | zenon_intro zenon_H35 ]. % 18.52/18.73 exact (zenon_H31 zenon_H36). % 18.52/18.73 apply (zenon_or_s _ _ zenon_H35); [ zenon_intro zenon_H2c | zenon_intro zenon_H37 ]. % 18.52/18.73 apply (zenon_L270_); trivial. % 18.52/18.73 apply (zenon_L275_); trivial. % 18.52/18.73 apply (zenon_or_s _ _ zenon_H1d9); [ zenon_intro zenon_H110 | zenon_intro zenon_H1da ]. % 18.52/18.73 apply (zenon_L276_); trivial. % 18.52/18.73 apply (zenon_or_s _ _ zenon_H1da); [ zenon_intro zenon_H1ca | zenon_intro zenon_H14d ]. % 18.52/18.73 apply (zenon_L277_); trivial. % 18.52/18.73 apply (zenon_L279_); trivial. % 18.52/18.73 (* end of lemma zenon_L280_ *) % 18.52/18.73 assert (zenon_L281_ : (((op (e1) (e0)) = (e1))\/(((op (e1) (e1)) = (e1))\/(((op (e1) (e2)) = (e1))\/((op (e1) (e3)) = (e1))))) -> (((op (e0) (e1)) = (e3))\/(((op (e1) (e1)) = (e3))\/(((op (e2) (e1)) = (e3))\/((op (e3) (e1)) = (e3))))) -> ((op (e0) (e1)) = (e0)) -> (~((op (e3) (e1)) = (e0))) -> (~((op (e3) (e0)) = (e0))) -> (((op (e3) (e0)) = (e0))\/(((op (e3) (e1)) = (e0))\/(((op (e3) (e2)) = (e0))\/((op (e3) (e3)) = (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) (e0)) = (op (e2) (e0)))) -> (((op (e2) (e0)) = (e1))\/(((op (e2) (e1)) = (e1))\/(((op (e2) (e2)) = (e1))\/((op (e2) (e3)) = (e1))))) -> (~((op (e3) (e0)) = (op (e3) (e1)))) -> (~((e0) = (e2))) -> (~((op (e1) (e1)) = (e1))) -> (~((e0) = (e1))) -> (((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) (e0)) = (e1)) -> ((op (e2) (e0)) = (e3)) -> (~((op (e3) (e2)) = (e0))) -> (~((op (e2) (e2)) = (op (e2) (e3)))) -> (~((op (e1) (e2)) = (e0))) -> (~((op (e0) (e2)) = (e0))) -> (((op (e0) (e2)) = (e0))\/(((op (e1) (e2)) = (e0))\/(((op (e2) (e2)) = (e0))\/((op (e3) (e2)) = (e0))))) -> (((op (e3) (e0)) = (e1))\/(((op (e3) (e1)) = (e1))\/(((op (e3) (e2)) = (e1))\/((op (e3) (e3)) = (e1))))) -> (~((e1) = (e3))) -> ((op (e3) (e0)) = (e3)) -> (~((e1) = (e2))) -> ((op (e0) (e2)) = (e3)) -> (~((op (e1) (e3)) = (op (e3) (e3)))) -> (~((op (e2) (e1)) = (e0))) -> (~((op (e2) (e0)) = (e0))) -> (((op (e2) (e0)) = (e0))\/(((op (e2) (e1)) = (e0))\/(((op (e2) (e2)) = (e0))\/((op (e2) (e3)) = (e0))))) -> (~((op (e2) (e0)) = (op (e2) (e1)))) -> ((op (e2) (e0)) = (e2)) -> (((op (e1) (e0)) = (e3))\/(((op (e1) (e1)) = (e3))\/(((op (e1) (e2)) = (e3))\/((op (e1) (e3)) = (e3))))) -> (~((e0) = (e3))) -> ((op (e1) (e0)) = (e0)) -> (~((e2) = (e3))) -> (~((op (e1) (e1)) = (op (e2) (e1)))) -> (~((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 (e0) (e2)) = (op (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 (e3) (e3)) = (e3))) -> (((op (e0) (e1)) = (e2))\/(((op (e1) (e1)) = (e2))\/(((op (e2) (e1)) = (e2))\/((op (e3) (e1)) = (e2))))) -> (~((op (e0) (e3)) = (op (e1) (e3)))) -> ((op (e0) (e3)) = (e2)) -> False). % 18.52/18.73 do 0 intro. intros zenon_H128 zenon_H1a5 zenon_H49 zenon_H1ad zenon_H40 zenon_H1ac zenon_H133 zenon_H130 zenon_H39 zenon_H106 zenon_H1cf zenon_H149 zenon_H10a zenon_Ha1 zenon_H109 zenon_H18c zenon_H7a zenon_H3b zenon_H18b zenon_H6d zenon_H25 zenon_H75 zenon_H6a zenon_He8 zenon_H95 zenon_H15e zenon_H7c zenon_Ha9 zenon_Hd5 zenon_H31 zenon_H30 zenon_H2f zenon_H1f0 zenon_Hee zenon_H16f zenon_H9a zenon_H27 zenon_H12b zenon_H13e zenon_H17e zenon_Haf zenon_H1cc zenon_H195 zenon_H101 zenon_Hf3 zenon_Hc2 zenon_H102 zenon_H1d8 zenon_H1d zenon_Hcd. % 18.52/18.73 apply (zenon_or_s _ _ zenon_H128); [ zenon_intro zenon_H9d | zenon_intro zenon_H129 ]. % 18.52/18.73 apply (zenon_L262_); trivial. % 18.52/18.73 apply (zenon_or_s _ _ zenon_H129); [ zenon_intro zenon_H10d | zenon_intro zenon_H12a ]. % 18.52/18.73 exact (zenon_H10a zenon_H10d). % 18.52/18.73 apply (zenon_or_s _ _ zenon_H12a); [ zenon_intro zenon_Hf0 | zenon_intro zenon_Hd6 ]. % 18.52/18.73 apply (zenon_or_s _ _ zenon_H109); [ zenon_intro zenon_Ha0 | zenon_intro zenon_H10b ]. % 18.52/18.73 apply (zenon_L38_); trivial. % 18.52/18.73 apply (zenon_or_s _ _ zenon_H10b); [ zenon_intro zenon_H10d | zenon_intro zenon_H10c ]. % 18.52/18.73 exact (zenon_H10a zenon_H10d). % 18.52/18.73 apply (zenon_or_s _ _ zenon_H10c); [ zenon_intro zenon_Ha5 | zenon_intro zenon_Hae ]. % 18.52/18.73 apply (zenon_or_s _ _ zenon_H18c); [ zenon_intro zenon_H86 | zenon_intro zenon_H18d ]. % 18.52/18.73 apply (zenon_L33_); trivial. % 18.52/18.73 apply (zenon_or_s _ _ zenon_H18d); [ zenon_intro zenon_H110 | zenon_intro zenon_H18e ]. % 18.52/18.73 apply (zenon_L215_); trivial. % 18.52/18.73 apply (zenon_or_s _ _ zenon_H18e); [ zenon_intro zenon_H113 | zenon_intro zenon_Hd7 ]. % 18.52/18.73 apply (zenon_L68_); trivial. % 18.52/18.73 apply (zenon_L70_); trivial. % 18.52/18.73 apply (zenon_L273_); trivial. % 18.52/18.73 apply (zenon_or_s _ _ zenon_H18c); [ zenon_intro zenon_H86 | zenon_intro zenon_H18d ]. % 18.52/18.73 apply (zenon_L33_); trivial. % 18.52/18.73 apply (zenon_or_s _ _ zenon_H18d); [ zenon_intro zenon_H110 | zenon_intro zenon_H18e ]. % 18.52/18.73 apply (zenon_L274_); trivial. % 18.52/18.73 apply (zenon_or_s _ _ zenon_H18e); [ zenon_intro zenon_H113 | zenon_intro zenon_Hd7 ]. % 18.52/18.73 apply (zenon_L280_); trivial. % 18.52/18.73 apply (zenon_L70_); trivial. % 18.52/18.73 (* end of lemma zenon_L281_ *) % 18.52/18.73 assert (zenon_L282_ : ((op (e1) (e1)) = (e2)) -> (~((op (e0) (e3)) = (op (e1) (e3)))) -> (((op (e1) (e0)) = (e1))\/(((op (e1) (e1)) = (e1))\/(((op (e1) (e2)) = (e1))\/((op (e1) (e3)) = (e1))))) -> (((op (e0) (e1)) = (e3))\/(((op (e1) (e1)) = (e3))\/(((op (e2) (e1)) = (e3))\/((op (e3) (e1)) = (e3))))) -> ((op (e0) (e1)) = (e0)) -> (~((op (e3) (e1)) = (e0))) -> (~((op (e3) (e0)) = (e0))) -> (((op (e3) (e0)) = (e0))\/(((op (e3) (e1)) = (e0))\/(((op (e3) (e2)) = (e0))\/((op (e3) (e3)) = (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) (e0)) = (op (e2) (e0)))) -> (((op (e2) (e0)) = (e1))\/(((op (e2) (e1)) = (e1))\/(((op (e2) (e2)) = (e1))\/((op (e2) (e3)) = (e1))))) -> (~((e0) = (e2))) -> (~((op (e1) (e1)) = (e1))) -> (~((e0) = (e1))) -> (((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) (e0)) = (e1)) -> ((op (e2) (e0)) = (e3)) -> (~((op (e3) (e2)) = (e0))) -> (~((op (e2) (e2)) = (op (e2) (e3)))) -> (~((op (e1) (e2)) = (e0))) -> (~((op (e0) (e2)) = (e0))) -> (((op (e0) (e2)) = (e0))\/(((op (e1) (e2)) = (e0))\/(((op (e2) (e2)) = (e0))\/((op (e3) (e2)) = (e0))))) -> (((op (e3) (e0)) = (e1))\/(((op (e3) (e1)) = (e1))\/(((op (e3) (e2)) = (e1))\/((op (e3) (e3)) = (e1))))) -> (~((e1) = (e3))) -> (~((e1) = (e2))) -> ((op (e0) (e2)) = (e3)) -> (~((op (e1) (e3)) = (op (e3) (e3)))) -> (~((op (e2) (e1)) = (e0))) -> (~((op (e2) (e0)) = (e0))) -> (((op (e2) (e0)) = (e0))\/(((op (e2) (e1)) = (e0))\/(((op (e2) (e2)) = (e0))\/((op (e2) (e3)) = (e0))))) -> (~((op (e2) (e0)) = (op (e2) (e1)))) -> ((op (e2) (e0)) = (e2)) -> (((op (e1) (e0)) = (e3))\/(((op (e1) (e1)) = (e3))\/(((op (e1) (e2)) = (e3))\/((op (e1) (e3)) = (e3))))) -> (~((e0) = (e3))) -> ((op (e1) (e0)) = (e0)) -> (~((e2) = (e3))) -> (~((op (e1) (e1)) = (op (e2) (e1)))) -> (~((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 (e0) (e2)) = (op (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 (e3) (e3)) = (e3))) -> (((op (e0) (e1)) = (e2))\/(((op (e1) (e1)) = (e2))\/(((op (e2) (e1)) = (e2))\/((op (e3) (e1)) = (e2))))) -> (~((op (e0) (e3)) = (op (e2) (e3)))) -> (~((op (e0) (e3)) = (e0))) -> (((op (e0) (e3)) = (e0))\/(((op (e0) (e3)) = (e1))\/(((op (e0) (e3)) = (e2))\/((op (e0) (e3)) = (e3))))) -> (~((op (e1) (e2)) = (op (e2) (e2)))) -> ((op (e1) (e2)) = (e1)) -> ((op (e3) (e0)) = (e3)) -> (~((op (e3) (e0)) = (op (e3) (e1)))) -> False). % 18.52/18.73 do 0 intro. intros zenon_H110 zenon_H1d zenon_H128 zenon_H1a5 zenon_H49 zenon_H1ad zenon_H40 zenon_H1ac zenon_H133 zenon_H130 zenon_H39 zenon_H106 zenon_H149 zenon_H10a zenon_Ha1 zenon_H109 zenon_H18c zenon_H7a zenon_H3b zenon_H18b zenon_H6d zenon_H25 zenon_H75 zenon_H6a zenon_He8 zenon_H95 zenon_H7c zenon_Ha9 zenon_Hd5 zenon_H31 zenon_H30 zenon_H2f zenon_H1f0 zenon_Hee zenon_H16f zenon_H9a zenon_H27 zenon_H12b zenon_H13e zenon_H17e zenon_Haf zenon_H1cc zenon_H195 zenon_H101 zenon_Hf3 zenon_Hc2 zenon_H102 zenon_H1d8 zenon_He2 zenon_H76 zenon_He4 zenon_H2b zenon_Hf0 zenon_H15e zenon_H1cf. % 18.52/18.73 apply (zenon_or_s _ _ zenon_H16f); [ zenon_intro zenon_H9e | zenon_intro zenon_H170 ]. % 18.52/18.73 apply (zenon_L263_); trivial. % 18.52/18.73 apply (zenon_or_s _ _ zenon_H170); [ zenon_intro zenon_H13f | zenon_intro zenon_H171 ]. % 18.52/18.73 apply (zenon_L166_); trivial. % 18.52/18.73 apply (zenon_or_s _ _ zenon_H171); [ zenon_intro zenon_H16c | zenon_intro zenon_Hdc ]. % 18.52/18.73 apply (zenon_L167_); trivial. % 18.52/18.73 apply (zenon_or_s _ _ zenon_H1a5); [ zenon_intro zenon_H99 | zenon_intro zenon_H1a8 ]. % 18.52/18.73 apply (zenon_L36_); trivial. % 18.52/18.73 apply (zenon_or_s _ _ zenon_H1a8); [ zenon_intro zenon_H13f | zenon_intro zenon_H1a9 ]. % 18.52/18.73 apply (zenon_L166_); trivial. % 18.52/18.73 apply (zenon_or_s _ _ zenon_H1a9); [ zenon_intro zenon_Ha6 | zenon_intro zenon_H161 ]. % 18.52/18.73 apply (zenon_or_s _ _ zenon_H106); [ zenon_intro zenon_Hed | zenon_intro zenon_H107 ]. % 18.52/18.73 apply (zenon_L134_); trivial. % 18.52/18.73 apply (zenon_or_s _ _ zenon_H107); [ zenon_intro zenon_Ha5 | zenon_intro zenon_H108 ]. % 18.52/18.73 apply (zenon_L39_); trivial. % 18.52/18.73 apply (zenon_or_s _ _ zenon_H108); [ zenon_intro zenon_Hf1 | zenon_intro zenon_Hf4 ]. % 18.52/18.73 apply (zenon_L59_); trivial. % 18.52/18.73 apply (zenon_or_s _ _ zenon_He4); [ zenon_intro zenon_H1e | zenon_intro zenon_He5 ]. % 18.52/18.73 exact (zenon_H76 zenon_H1e). % 18.52/18.73 apply (zenon_or_s _ _ zenon_He5); [ zenon_intro zenon_Hc3 | zenon_intro zenon_He6 ]. % 18.52/18.73 apply (zenon_L272_); trivial. % 18.52/18.73 apply (zenon_or_s _ _ zenon_He6); [ zenon_intro zenon_Hcd | zenon_intro zenon_He3 ]. % 18.52/18.73 apply (zenon_L281_); trivial. % 18.52/18.73 apply (zenon_L117_); trivial. % 18.52/18.73 apply (zenon_L193_); trivial. % 18.52/18.73 (* end of lemma zenon_L282_ *) % 18.52/18.73 assert (zenon_L283_ : ((op (e1) (e3)) = (e2)) -> ((op (e1) (e1)) = (e2)) -> (~((op (e1) (e1)) = (op (e1) (e3)))) -> False). % 18.52/18.73 do 0 intro. intros zenon_Hd7 zenon_H110 zenon_H57. % 18.52/18.73 elim (classic ((op (e1) (e3)) = (op (e1) (e3)))); [ zenon_intro zenon_H58 | zenon_intro zenon_H59 ]. % 18.52/18.73 cut (((op (e1) (e3)) = (op (e1) (e3))) = ((op (e1) (e1)) = (op (e1) (e3)))). % 18.52/18.73 intro zenon_D_pnotp. % 18.52/18.73 apply zenon_H57. % 18.52/18.73 rewrite <- zenon_D_pnotp. % 18.52/18.73 exact zenon_H58. % 18.52/18.73 cut (((op (e1) (e3)) = (op (e1) (e3)))); [idtac | apply NNPP; zenon_intro zenon_H59]. % 18.52/18.73 cut (((op (e1) (e3)) = (op (e1) (e1)))); [idtac | apply NNPP; zenon_intro zenon_H5a]. % 18.52/18.73 congruence. % 18.52/18.73 cut (((op (e1) (e3)) = (e2)) = ((op (e1) (e3)) = (op (e1) (e1)))). % 18.52/18.73 intro zenon_D_pnotp. % 18.52/18.73 apply zenon_H5a. % 18.52/18.73 rewrite <- zenon_D_pnotp. % 18.52/18.73 exact zenon_Hd7. % 18.52/18.73 cut (((e2) = (op (e1) (e1)))); [idtac | apply NNPP; zenon_intro zenon_H111]. % 18.52/18.73 cut (((op (e1) (e3)) = (op (e1) (e3)))); [idtac | apply NNPP; zenon_intro zenon_H59]. % 18.52/18.73 congruence. % 18.52/18.73 apply zenon_H59. apply refl_equal. % 18.52/18.73 apply zenon_H111. apply sym_equal. exact zenon_H110. % 18.52/18.73 apply zenon_H59. apply refl_equal. % 18.52/18.73 apply zenon_H59. apply refl_equal. % 18.52/18.73 (* end of lemma zenon_L283_ *) % 18.52/18.73 assert (zenon_L284_ : (((op (e0) (e1)) = (e2))\/(((op (e1) (e1)) = (e2))\/(((op (e2) (e1)) = (e2))\/((op (e3) (e1)) = (e2))))) -> (~((e2) = (e3))) -> ((op (e1) (e2)) = (e1)) -> (~((e1) = (e3))) -> (((op (e2) (e1)) = (e0))\/(((op (e2) (e1)) = (e1))\/(((op (e2) (e1)) = (e2))\/((op (e2) (e1)) = (e3))))) -> (~((op (e2) (e1)) = (e0))) -> (~((op (e2) (e1)) = (op (e3) (e1)))) -> (~((op (e0) (e1)) = (op (e2) (e1)))) -> (~((op (e1) (e1)) = (op (e2) (e1)))) -> ((op (e1) (e0)) = (e0)) -> (~((e0) = (e3))) -> (((op (e1) (e0)) = (e3))\/(((op (e1) (e1)) = (e3))\/(((op (e1) (e2)) = (e3))\/((op (e1) (e3)) = (e3))))) -> (~((op (e1) (e1)) = (op (e1) (e3)))) -> ((op (e1) (e3)) = (e2)) -> ((op (e2) (e0)) = (e2)) -> (~((op (e2) (e0)) = (op (e2) (e1)))) -> ((op (e3) (e1)) = (e1)) -> (~((e1) = (e2))) -> False). % 18.52/18.73 do 0 intro. intros zenon_H1d8 zenon_H12b zenon_Hf0 zenon_H95 zenon_H1cc zenon_H31 zenon_Haf zenon_H17e zenon_H13e zenon_H27 zenon_H9a zenon_H16f zenon_H57 zenon_Hd7 zenon_Hee zenon_H1f0 zenon_Hae zenon_H7c. % 18.52/18.73 apply (zenon_or_s _ _ zenon_H1d8); [ zenon_intro zenon_H10f | zenon_intro zenon_H1d9 ]. % 18.52/18.73 apply (zenon_L267_); trivial. % 18.52/18.73 apply (zenon_or_s _ _ zenon_H1d9); [ zenon_intro zenon_H110 | zenon_intro zenon_H1da ]. % 18.52/18.73 apply (zenon_L283_); trivial. % 18.52/18.73 apply (zenon_or_s _ _ zenon_H1da); [ zenon_intro zenon_H1ca | zenon_intro zenon_H14d ]. % 18.52/18.73 apply (zenon_L277_); trivial. % 18.52/18.73 apply (zenon_L152_); trivial. % 18.52/18.73 (* end of lemma zenon_L284_ *) % 18.52/18.73 assert (zenon_L285_ : (~((op (e3) (e0)) = (op (e3) (e1)))) -> ((op (e3) (e0)) = (e3)) -> (~((op (e1) (e2)) = (op (e2) (e2)))) -> (((op (e0) (e3)) = (e0))\/(((op (e0) (e3)) = (e1))\/(((op (e0) (e3)) = (e2))\/((op (e0) (e3)) = (e3))))) -> (~((op (e0) (e3)) = (e0))) -> (~((op (e0) (e3)) = (op (e2) (e3)))) -> (~((op (e3) (e3)) = (e3))) -> (~((op (e0) (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)) = (op (e1) (e2)))) -> (((op (e2) (e0)) = (e0))\/(((op (e2) (e1)) = (e0))\/(((op (e2) (e2)) = (e0))\/((op (e2) (e3)) = (e0))))) -> (~((op (e2) (e0)) = (e0))) -> (~((op (e1) (e3)) = (op (e3) (e3)))) -> ((op (e0) (e2)) = (e3)) -> (((op (e3) (e0)) = (e1))\/(((op (e3) (e1)) = (e1))\/(((op (e3) (e2)) = (e1))\/((op (e3) (e3)) = (e1))))) -> (((op (e0) (e2)) = (e0))\/(((op (e1) (e2)) = (e0))\/(((op (e2) (e2)) = (e0))\/((op (e3) (e2)) = (e0))))) -> (~((op (e0) (e2)) = (e0))) -> (~((op (e1) (e2)) = (e0))) -> (~((op (e2) (e2)) = (op (e2) (e3)))) -> (~((op (e3) (e2)) = (e0))) -> ((op (e2) (e0)) = (e3)) -> ((op (e0) (e0)) = (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))))) -> (~((e0) = (e1))) -> (~((op (e1) (e1)) = (e1))) -> (~((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 (e3) (e1)) = (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 (e3) (e0)) = (e0))) -> (~((op (e3) (e1)) = (e0))) -> ((op (e0) (e1)) = (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 (e0) (e3)) = (op (e1) (e3)))) -> (((op (e0) (e1)) = (e2))\/(((op (e1) (e1)) = (e2))\/(((op (e2) (e1)) = (e2))\/((op (e3) (e1)) = (e2))))) -> (~((e2) = (e3))) -> ((op (e1) (e2)) = (e1)) -> (~((e1) = (e3))) -> (((op (e2) (e1)) = (e0))\/(((op (e2) (e1)) = (e1))\/(((op (e2) (e1)) = (e2))\/((op (e2) (e1)) = (e3))))) -> (~((op (e2) (e1)) = (e0))) -> (~((op (e2) (e1)) = (op (e3) (e1)))) -> (~((op (e0) (e1)) = (op (e2) (e1)))) -> (~((op (e1) (e1)) = (op (e2) (e1)))) -> ((op (e1) (e0)) = (e0)) -> (~((e0) = (e3))) -> (((op (e1) (e0)) = (e3))\/(((op (e1) (e1)) = (e3))\/(((op (e1) (e2)) = (e3))\/((op (e1) (e3)) = (e3))))) -> (~((op (e1) (e1)) = (op (e1) (e3)))) -> ((op (e2) (e0)) = (e2)) -> (~((op (e2) (e0)) = (op (e2) (e1)))) -> ((op (e3) (e1)) = (e1)) -> (~((e1) = (e2))) -> False). % 18.52/18.73 do 0 intro. intros zenon_H1cf zenon_H15e zenon_H2b zenon_He4 zenon_H76 zenon_He2 zenon_H102 zenon_Hc2 zenon_Hf3 zenon_H101 zenon_H195 zenon_H2f zenon_H30 zenon_Hd5 zenon_Ha9 zenon_He8 zenon_H6a zenon_H75 zenon_H25 zenon_H6d zenon_H18b zenon_H3b zenon_H7a zenon_H18c zenon_H109 zenon_Ha1 zenon_H10a zenon_H149 zenon_H106 zenon_H39 zenon_H130 zenon_H133 zenon_H1ac zenon_H40 zenon_H1ad zenon_H49 zenon_H1a5 zenon_H128 zenon_H1d zenon_H1d8 zenon_H12b zenon_Hf0 zenon_H95 zenon_H1cc zenon_H31 zenon_Haf zenon_H17e zenon_H13e zenon_H27 zenon_H9a zenon_H16f zenon_H57 zenon_Hee zenon_H1f0 zenon_Hae zenon_H7c. % 18.52/18.73 apply (zenon_or_s _ _ zenon_H18c); [ zenon_intro zenon_H86 | zenon_intro zenon_H18d ]. % 18.52/18.73 apply (zenon_L257_); trivial. % 18.52/18.73 apply (zenon_or_s _ _ zenon_H18d); [ zenon_intro zenon_H110 | zenon_intro zenon_H18e ]. % 18.52/18.73 apply (zenon_L282_); trivial. % 18.52/18.73 apply (zenon_or_s _ _ zenon_H18e); [ zenon_intro zenon_H113 | zenon_intro zenon_Hd7 ]. % 18.52/18.73 apply (zenon_L68_); trivial. % 18.52/18.73 apply (zenon_L284_); trivial. % 18.52/18.73 (* end of lemma zenon_L285_ *) % 18.52/18.73 assert (zenon_L286_ : ((op (e3) (e2)) = (e3)) -> ((op (e3) (e0)) = (e3)) -> (~((op (e3) (e0)) = (op (e3) (e2)))) -> False). % 18.52/18.73 do 0 intro. intros zenon_H163 zenon_H15e zenon_H6f. % 18.52/18.73 elim (classic ((op (e3) (e2)) = (op (e3) (e2)))); [ zenon_intro zenon_H1f1 | zenon_intro zenon_H1f2 ]. % 18.52/18.73 cut (((op (e3) (e2)) = (op (e3) (e2))) = ((op (e3) (e0)) = (op (e3) (e2)))). % 18.52/18.73 intro zenon_D_pnotp. % 18.52/18.73 apply zenon_H6f. % 18.52/18.73 rewrite <- zenon_D_pnotp. % 18.52/18.73 exact zenon_H1f1. % 18.52/18.73 cut (((op (e3) (e2)) = (op (e3) (e2)))); [idtac | apply NNPP; zenon_intro zenon_H1f2]. % 18.52/18.73 cut (((op (e3) (e2)) = (op (e3) (e0)))); [idtac | apply NNPP; zenon_intro zenon_H1f3]. % 18.52/18.73 congruence. % 18.52/18.73 cut (((op (e3) (e2)) = (e3)) = ((op (e3) (e2)) = (op (e3) (e0)))). % 18.52/18.73 intro zenon_D_pnotp. % 18.52/18.73 apply zenon_H1f3. % 18.52/18.73 rewrite <- zenon_D_pnotp. % 18.52/18.73 exact zenon_H163. % 18.52/18.73 cut (((e3) = (op (e3) (e0)))); [idtac | apply NNPP; zenon_intro zenon_H1d1]. % 18.52/18.73 cut (((op (e3) (e2)) = (op (e3) (e2)))); [idtac | apply NNPP; zenon_intro zenon_H1f2]. % 18.52/18.73 congruence. % 18.52/18.73 apply zenon_H1f2. apply refl_equal. % 18.52/18.73 apply zenon_H1d1. apply sym_equal. exact zenon_H15e. % 18.52/18.73 apply zenon_H1f2. apply refl_equal. % 18.52/18.73 apply zenon_H1f2. apply refl_equal. % 18.52/18.73 (* end of lemma zenon_L286_ *) % 18.52/18.73 assert (zenon_L287_ : (((op (e0) (e2)) = (e3))\/(((op (e1) (e2)) = (e3))\/(((op (e2) (e2)) = (e3))\/((op (e3) (e2)) = (e3))))) -> ((op (e0) (e3)) = (e3)) -> (~((op (e0) (e3)) = (op (e2) (e3)))) -> ((op (e2) (e0)) = (e2)) -> (~((op (e2) (e0)) = (op (e2) (e3)))) -> (~((op (e2) (e3)) = (op (e3) (e3)))) -> ((op (e1) (e3)) = (e2)) -> (((op (e2) (e3)) = (e0))\/(((op (e2) (e3)) = (e1))\/(((op (e2) (e3)) = (e2))\/((op (e2) (e3)) = (e3))))) -> (~((op (e1) (e2)) = (op (e3) (e2)))) -> (~((op (e3) (e0)) = (op (e3) (e1)))) -> (~((op (e1) (e2)) = (op (e2) (e2)))) -> (((op (e0) (e3)) = (e0))\/(((op (e0) (e3)) = (e1))\/(((op (e0) (e3)) = (e2))\/((op (e0) (e3)) = (e3))))) -> (~((op (e0) (e3)) = (e0))) -> (~((op (e3) (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 (e2) (e0)) = (e0))\/(((op (e2) (e1)) = (e0))\/(((op (e2) (e2)) = (e0))\/((op (e2) (e3)) = (e0))))) -> (~((op (e2) (e0)) = (e0))) -> (~((op (e1) (e3)) = (op (e3) (e3)))) -> (((op (e3) (e0)) = (e1))\/(((op (e3) (e1)) = (e1))\/(((op (e3) (e2)) = (e1))\/((op (e3) (e3)) = (e1))))) -> (((op (e0) (e2)) = (e0))\/(((op (e1) (e2)) = (e0))\/(((op (e2) (e2)) = (e0))\/((op (e3) (e2)) = (e0))))) -> (~((op (e0) (e2)) = (e0))) -> (~((op (e1) (e2)) = (e0))) -> (~((op (e2) (e2)) = (op (e2) (e3)))) -> (~((op (e3) (e2)) = (e0))) -> ((op (e0) (e0)) = (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))))) -> (~((e0) = (e1))) -> (~((op (e1) (e1)) = (e1))) -> (~((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 (e3) (e1)) = (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 (e3) (e0)) = (e0))) -> (~((op (e3) (e1)) = (e0))) -> ((op (e0) (e1)) = (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 (e0) (e3)) = (op (e1) (e3)))) -> (((op (e0) (e1)) = (e2))\/(((op (e1) (e1)) = (e2))\/(((op (e2) (e1)) = (e2))\/((op (e3) (e1)) = (e2))))) -> (~((e2) = (e3))) -> (((op (e2) (e1)) = (e0))\/(((op (e2) (e1)) = (e1))\/(((op (e2) (e1)) = (e2))\/((op (e2) (e1)) = (e3))))) -> (~((op (e2) (e1)) = (e0))) -> (~((op (e2) (e1)) = (op (e3) (e1)))) -> (~((op (e0) (e1)) = (op (e2) (e1)))) -> (~((op (e1) (e1)) = (op (e2) (e1)))) -> ((op (e1) (e0)) = (e0)) -> (~((e0) = (e3))) -> (((op (e1) (e0)) = (e3))\/(((op (e1) (e1)) = (e3))\/(((op (e1) (e2)) = (e3))\/((op (e1) (e3)) = (e3))))) -> (~((op (e1) (e1)) = (op (e1) (e3)))) -> (~((op (e2) (e0)) = (op (e2) (e1)))) -> (~((e1) = (e2))) -> (((op (e3) (e0)) = (e3))\/(((op (e3) (e1)) = (e3))\/(((op (e3) (e2)) = (e3))\/((op (e3) (e3)) = (e3))))) -> ((op (e1) (e1)) = (e3)) -> (~((op (e1) (e1)) = (op (e3) (e1)))) -> (~((op (e0) (e2)) = (op (e3) (e2)))) -> (~((e1) = (e3))) -> ((op (e1) (e2)) = (e1)) -> (~((op (e2) (e0)) = (op (e2) (e2)))) -> ((op (e2) (e0)) = (e3)) -> ((op (e3) (e0)) = (e3)) -> (~((op (e3) (e0)) = (op (e3) (e2)))) -> False). % 18.52/18.73 do 0 intro. intros zenon_H1a6 zenon_He3 zenon_He2 zenon_Hee zenon_H5b zenon_Hf3 zenon_Hd7 zenon_H11f zenon_H115 zenon_H1cf zenon_H2b zenon_He4 zenon_H76 zenon_H102 zenon_Hc2 zenon_H101 zenon_H195 zenon_H2f zenon_H30 zenon_Hd5 zenon_He8 zenon_H6a zenon_H75 zenon_H25 zenon_H6d zenon_H18b zenon_H7a zenon_H18c zenon_H109 zenon_Ha1 zenon_H10a zenon_H149 zenon_H106 zenon_H39 zenon_H130 zenon_H133 zenon_H1ac zenon_H40 zenon_H1ad zenon_H49 zenon_H1a5 zenon_H128 zenon_H1d zenon_H1d8 zenon_H12b zenon_H1cc zenon_H31 zenon_Haf zenon_H17e zenon_H13e zenon_H27 zenon_H9a zenon_H16f zenon_H57 zenon_H1f0 zenon_H7c zenon_H165 zenon_H13f zenon_H160 zenon_H14f zenon_H95 zenon_Hf0 zenon_H52 zenon_H3b zenon_H15e zenon_H6f. % 18.52/18.73 apply (zenon_or_s _ _ zenon_H1a6); [ zenon_intro zenon_Ha9 | zenon_intro zenon_H1aa ]. % 18.52/18.73 apply (zenon_or_s _ _ zenon_He8); [ zenon_intro zenon_Hac | zenon_intro zenon_Heb ]. % 18.52/18.73 apply (zenon_L264_); trivial. % 18.52/18.73 apply (zenon_or_s _ _ zenon_Heb); [ zenon_intro zenon_Hae | zenon_intro zenon_Hec ]. % 18.52/18.73 apply (zenon_L285_); trivial. % 18.52/18.73 apply (zenon_or_s _ _ zenon_Hec); [ zenon_intro zenon_Hba | zenon_intro zenon_Hc4 ]. % 18.52/18.73 apply (zenon_L69_); trivial. % 18.52/18.73 apply (zenon_L74_); trivial. % 18.52/18.73 apply (zenon_or_s _ _ zenon_H1aa); [ zenon_intro zenon_H16c | zenon_intro zenon_H1ab ]. % 18.52/18.73 apply (zenon_L167_); trivial. % 18.52/18.73 apply (zenon_or_s _ _ zenon_H1ab); [ zenon_intro zenon_Haa | zenon_intro zenon_H163 ]. % 18.52/18.73 apply (zenon_L168_); trivial. % 18.52/18.73 apply (zenon_L286_); trivial. % 18.52/18.73 (* end of lemma zenon_L287_ *) % 18.52/18.73 assert (zenon_L288_ : (((op (e2) (e0)) = (e0))\/(((op (e2) (e1)) = (e0))\/(((op (e2) (e2)) = (e0))\/((op (e2) (e3)) = (e0))))) -> (~((op (e2) (e0)) = (e0))) -> (~((op (e3) (e0)) = (op (e3) (e2)))) -> ((op (e3) (e0)) = (e3)) -> ((op (e2) (e0)) = (e3)) -> (~((op (e2) (e0)) = (op (e2) (e2)))) -> ((op (e1) (e2)) = (e2)) -> (~((e2) = (e3))) -> (((op (e3) (e0)) = (e1))\/(((op (e3) (e1)) = (e1))\/(((op (e3) (e2)) = (e1))\/((op (e3) (e3)) = (e1))))) -> (~((e1) = (e3))) -> (~((op (e0) (e2)) = (op (e1) (e2)))) -> (((op (e2) (e1)) = (e0))\/(((op (e2) (e1)) = (e1))\/(((op (e2) (e1)) = (e2))\/((op (e2) (e1)) = (e3))))) -> (~((op (e2) (e1)) = (e0))) -> (~((op (e2) (e1)) = (op (e3) (e1)))) -> ((op (e0) (e1)) = (e2)) -> (~((op (e0) (e1)) = (op (e2) (e1)))) -> (~((op (e1) (e1)) = (op (e2) (e1)))) -> ((op (e1) (e0)) = (e0)) -> (~((e0) = (e3))) -> (((op (e1) (e0)) = (e3))\/(((op (e1) (e1)) = (e3))\/(((op (e1) (e2)) = (e3))\/((op (e1) (e3)) = (e3))))) -> (~((op (e1) (e3)) = (op (e3) (e3)))) -> ((op (e1) (e3)) = (e1)) -> (((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 (e0) (e2)) = (e0))) -> (~((op (e1) (e2)) = (e0))) -> (~((op (e2) (e2)) = (op (e2) (e3)))) -> (~((op (e3) (e2)) = (e0))) -> False). % 18.52/18.73 do 0 intro. intros zenon_H2f zenon_H30 zenon_H6f zenon_H15e zenon_H3b zenon_H52 zenon_H113 zenon_H12b zenon_He8 zenon_H95 zenon_H195 zenon_H1cc zenon_H31 zenon_Haf zenon_H10f zenon_H17e zenon_H13e zenon_H27 zenon_H9a zenon_H16f zenon_Hd5 zenon_Hd6 zenon_H1a6 zenon_H6a zenon_H75 zenon_H25 zenon_H6d zenon_H18b. % 18.52/18.73 apply (zenon_or_s _ _ zenon_H2f); [ zenon_intro zenon_H34 | zenon_intro zenon_H33 ]. % 18.52/18.73 exact (zenon_H30 zenon_H34). % 18.52/18.73 apply (zenon_or_s _ _ zenon_H33); [ zenon_intro zenon_H36 | zenon_intro zenon_H35 ]. % 18.52/18.73 exact (zenon_H31 zenon_H36). % 18.52/18.73 apply (zenon_or_s _ _ zenon_H35); [ zenon_intro zenon_H2c | zenon_intro zenon_H37 ]. % 18.52/18.73 apply (zenon_or_s _ _ zenon_H1a6); [ zenon_intro zenon_Ha9 | zenon_intro zenon_H1aa ]. % 18.52/18.73 apply (zenon_L270_); trivial. % 18.52/18.73 apply (zenon_or_s _ _ zenon_H1aa); [ zenon_intro zenon_H16c | zenon_intro zenon_H1ab ]. % 18.52/18.73 apply (zenon_L116_); trivial. % 18.52/18.73 apply (zenon_or_s _ _ zenon_H1ab); [ zenon_intro zenon_Haa | zenon_intro zenon_H163 ]. % 18.52/18.73 apply (zenon_L168_); trivial. % 18.52/18.73 apply (zenon_L286_); trivial. % 18.52/18.73 apply (zenon_L143_); trivial. % 18.52/18.73 (* end of lemma zenon_L288_ *) % 18.52/18.73 assert (zenon_L289_ : (((op (e1) (e0)) = (e2))\/(((op (e1) (e1)) = (e2))\/(((op (e1) (e2)) = (e2))\/((op (e1) (e3)) = (e2))))) -> ((op (e0) (e0)) = (e1)) -> (~((op (e0) (e1)) = (op (e1) (e1)))) -> (~((op (e3) (e2)) = (e0))) -> (~((op (e2) (e2)) = (op (e2) (e3)))) -> (~((op (e1) (e2)) = (e0))) -> (~((op (e0) (e2)) = (e0))) -> (((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 (e1) (e3)) = (op (e3) (e3)))) -> (((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)) = (op (e2) (e1)))) -> (~((op (e0) (e1)) = (op (e2) (e1)))) -> ((op (e0) (e1)) = (e2)) -> (~((op (e2) (e1)) = (op (e3) (e1)))) -> (~((op (e2) (e1)) = (e0))) -> (((op (e2) (e1)) = (e0))\/(((op (e2) (e1)) = (e1))\/(((op (e2) (e1)) = (e2))\/((op (e2) (e1)) = (e3))))) -> (~((op (e0) (e2)) = (op (e1) (e2)))) -> (~((e1) = (e3))) -> (((op (e3) (e0)) = (e1))\/(((op (e3) (e1)) = (e1))\/(((op (e3) (e2)) = (e1))\/((op (e3) (e3)) = (e1))))) -> (~((e2) = (e3))) -> (~((op (e2) (e0)) = (op (e2) (e2)))) -> ((op (e2) (e0)) = (e3)) -> ((op (e3) (e0)) = (e3)) -> (~((op (e3) (e0)) = (op (e3) (e2)))) -> (~((op (e2) (e0)) = (e0))) -> (((op (e2) (e0)) = (e0))\/(((op (e2) (e1)) = (e0))\/(((op (e2) (e2)) = (e0))\/((op (e2) (e3)) = (e0))))) -> ((op (e1) (e3)) = (e1)) -> (~((e1) = (e2))) -> False). % 18.52/18.73 do 0 intro. intros zenon_H18c zenon_H7a zenon_H10e zenon_H18b zenon_H6d zenon_H25 zenon_H75 zenon_H6a zenon_H1a6 zenon_Hd5 zenon_H16f zenon_H9a zenon_H27 zenon_H13e zenon_H17e zenon_H10f zenon_Haf zenon_H31 zenon_H1cc zenon_H195 zenon_H95 zenon_He8 zenon_H12b zenon_H52 zenon_H3b zenon_H15e zenon_H6f zenon_H30 zenon_H2f zenon_Hd6 zenon_H7c. % 18.52/18.73 apply (zenon_or_s _ _ zenon_H18c); [ zenon_intro zenon_H86 | zenon_intro zenon_H18d ]. % 18.52/18.73 apply (zenon_L33_); trivial. % 18.52/18.73 apply (zenon_or_s _ _ zenon_H18d); [ zenon_intro zenon_H110 | zenon_intro zenon_H18e ]. % 18.52/18.73 apply (zenon_L67_); trivial. % 18.52/18.73 apply (zenon_or_s _ _ zenon_H18e); [ zenon_intro zenon_H113 | zenon_intro zenon_Hd7 ]. % 18.52/18.73 apply (zenon_L288_); trivial. % 18.52/18.73 apply (zenon_L101_); trivial. % 18.52/18.73 (* end of lemma zenon_L289_ *) % 18.52/18.73 assert (zenon_L290_ : (((op (e1) (e0)) = (e3))\/(((op (e1) (e1)) = (e3))\/(((op (e1) (e2)) = (e3))\/((op (e1) (e3)) = (e3))))) -> (~((e0) = (e3))) -> ((op (e1) (e0)) = (e0)) -> (~((e2) = (e3))) -> ((op (e1) (e1)) = (e2)) -> (~((e1) = (e3))) -> ((op (e1) (e2)) = (e1)) -> (~((op (e0) (e3)) = (op (e1) (e3)))) -> ((op (e0) (e3)) = (e3)) -> False). % 18.52/18.73 do 0 intro. intros zenon_H16f zenon_H9a zenon_H27 zenon_H12b zenon_H110 zenon_H95 zenon_Hf0 zenon_H1d zenon_He3. % 18.52/18.73 apply (zenon_or_s _ _ zenon_H16f); [ zenon_intro zenon_H9e | zenon_intro zenon_H170 ]. % 18.52/18.74 apply (zenon_L263_); trivial. % 18.52/18.74 apply (zenon_or_s _ _ zenon_H170); [ zenon_intro zenon_H13f | zenon_intro zenon_H171 ]. % 18.52/18.74 apply (zenon_L166_); trivial. % 18.52/18.74 apply (zenon_or_s _ _ zenon_H171); [ zenon_intro zenon_H16c | zenon_intro zenon_Hdc ]. % 18.52/18.74 apply (zenon_L167_); trivial. % 18.52/18.74 apply (zenon_L117_); trivial. % 18.52/18.74 (* end of lemma zenon_L290_ *) % 18.52/18.74 assert (zenon_L291_ : (((op (e3) (e0)) = (e1))\/(((op (e3) (e1)) = (e1))\/(((op (e3) (e2)) = (e1))\/((op (e3) (e3)) = (e1))))) -> (~((op (e3) (e3)) = (e3))) -> (~((op (e1) (e1)) = (op (e3) (e1)))) -> ((op (e1) (e1)) = (e3)) -> (~((e1) = (e3))) -> (((op (e3) (e0)) = (e3))\/(((op (e3) (e1)) = (e3))\/(((op (e3) (e2)) = (e3))\/((op (e3) (e3)) = (e3))))) -> (~((op (e2) (e1)) = (op (e3) (e1)))) -> ((op (e2) (e1)) = (e1)) -> (((op (e3) (e2)) = (e0))\/(((op (e3) (e2)) = (e1))\/(((op (e3) (e2)) = (e2))\/((op (e3) (e2)) = (e3))))) -> ((op (e2) (e2)) = (e0)) -> (~((op (e2) (e2)) = (op (e3) (e2)))) -> (~((op (e3) (e2)) = (op (e3) (e3)))) -> ((op (e0) (e2)) = (e2)) -> (~((op (e0) (e2)) = (op (e3) (e2)))) -> ((op (e0) (e2)) = (e3)) -> False). % 18.52/18.74 do 0 intro. intros zenon_He8 zenon_H102 zenon_H160 zenon_H13f zenon_H95 zenon_H165 zenon_Haf zenon_Ha5 zenon_H191 zenon_H2c zenon_H18f zenon_H62 zenon_H150 zenon_H14f zenon_Ha9. % 18.52/18.74 apply (zenon_or_s _ _ zenon_He8); [ zenon_intro zenon_Hac | zenon_intro zenon_Heb ]. % 18.52/18.74 apply (zenon_L264_); trivial. % 18.52/18.74 apply (zenon_or_s _ _ zenon_Heb); [ zenon_intro zenon_Hae | zenon_intro zenon_Hec ]. % 18.52/18.74 apply (zenon_L42_); trivial. % 18.52/18.74 apply (zenon_or_s _ _ zenon_Hec); [ zenon_intro zenon_Hba | zenon_intro zenon_Hc4 ]. % 18.52/18.74 apply (zenon_L45_); trivial. % 18.52/18.74 apply (zenon_L148_); trivial. % 18.52/18.74 (* end of lemma zenon_L291_ *) % 18.52/18.74 assert (zenon_L292_ : (((op (e0) (e2)) = (e3))\/(((op (e1) (e2)) = (e3))\/(((op (e2) (e2)) = (e3))\/((op (e3) (e2)) = (e3))))) -> (~((op (e0) (e2)) = (op (e3) (e2)))) -> ((op (e0) (e2)) = (e2)) -> (~((op (e3) (e2)) = (op (e3) (e3)))) -> (~((op (e2) (e2)) = (op (e3) (e2)))) -> ((op (e2) (e2)) = (e0)) -> (((op (e3) (e2)) = (e0))\/(((op (e3) (e2)) = (e1))\/(((op (e3) (e2)) = (e2))\/((op (e3) (e2)) = (e3))))) -> ((op (e2) (e1)) = (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) (e1)) = (e3)) -> (~((op (e1) (e1)) = (op (e3) (e1)))) -> (~((op (e3) (e3)) = (e3))) -> (((op (e3) (e0)) = (e1))\/(((op (e3) (e1)) = (e1))\/(((op (e3) (e2)) = (e1))\/((op (e3) (e3)) = (e1))))) -> (~((e1) = (e3))) -> ((op (e1) (e2)) = (e1)) -> (~((op (e2) (e0)) = (op (e2) (e2)))) -> ((op (e2) (e0)) = (e3)) -> ((op (e3) (e0)) = (e3)) -> (~((op (e3) (e0)) = (op (e3) (e2)))) -> False). % 18.52/18.74 do 0 intro. intros zenon_H1a6 zenon_H14f zenon_H150 zenon_H62 zenon_H18f zenon_H2c zenon_H191 zenon_Ha5 zenon_Haf zenon_H165 zenon_H13f zenon_H160 zenon_H102 zenon_He8 zenon_H95 zenon_Hf0 zenon_H52 zenon_H3b zenon_H15e zenon_H6f. % 18.52/18.74 apply (zenon_or_s _ _ zenon_H1a6); [ zenon_intro zenon_Ha9 | zenon_intro zenon_H1aa ]. % 18.52/18.74 apply (zenon_L291_); trivial. % 18.52/18.74 apply (zenon_or_s _ _ zenon_H1aa); [ zenon_intro zenon_H16c | zenon_intro zenon_H1ab ]. % 18.52/18.74 apply (zenon_L167_); trivial. % 18.52/18.74 apply (zenon_or_s _ _ zenon_H1ab); [ zenon_intro zenon_Haa | zenon_intro zenon_H163 ]. % 18.52/18.74 apply (zenon_L168_); trivial. % 18.52/18.74 apply (zenon_L286_); trivial. % 18.52/18.74 (* end of lemma zenon_L292_ *) % 18.52/18.74 assert (zenon_L293_ : (((op (e2) (e0)) = (e0))\/(((op (e2) (e1)) = (e0))\/(((op (e2) (e2)) = (e0))\/((op (e2) (e3)) = (e0))))) -> (~((op (e2) (e0)) = (e0))) -> (~((op (e2) (e1)) = (e0))) -> (~((op (e3) (e0)) = (op (e3) (e2)))) -> ((op (e3) (e0)) = (e3)) -> ((op (e2) (e0)) = (e3)) -> (~((op (e2) (e0)) = (op (e2) (e2)))) -> ((op (e1) (e2)) = (e1)) -> (~((e1) = (e3))) -> (((op (e3) (e0)) = (e1))\/(((op (e3) (e1)) = (e1))\/(((op (e3) (e2)) = (e1))\/((op (e3) (e3)) = (e1))))) -> (~((op (e3) (e3)) = (e3))) -> (~((op (e1) (e1)) = (op (e3) (e1)))) -> ((op (e1) (e1)) = (e3)) -> (((op (e3) (e0)) = (e3))\/(((op (e3) (e1)) = (e3))\/(((op (e3) (e2)) = (e3))\/((op (e3) (e3)) = (e3))))) -> (~((op (e2) (e1)) = (op (e3) (e1)))) -> ((op (e2) (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) (e2)) = (op (e3) (e3)))) -> ((op (e0) (e2)) = (e2)) -> (~((op (e0) (e2)) = (op (e3) (e2)))) -> (((op (e0) (e2)) = (e3))\/(((op (e1) (e2)) = (e3))\/(((op (e2) (e2)) = (e3))\/((op (e3) (e2)) = (e3))))) -> (((op (e0) (e2)) = (e0))\/(((op (e1) (e2)) = (e0))\/(((op (e2) (e2)) = (e0))\/((op (e3) (e2)) = (e0))))) -> (~((op (e0) (e2)) = (e0))) -> (~((op (e1) (e2)) = (e0))) -> (~((op (e2) (e2)) = (op (e2) (e3)))) -> (~((op (e3) (e2)) = (e0))) -> False). % 18.52/18.74 do 0 intro. intros zenon_H2f zenon_H30 zenon_H31 zenon_H6f zenon_H15e zenon_H3b zenon_H52 zenon_Hf0 zenon_H95 zenon_He8 zenon_H102 zenon_H160 zenon_H13f zenon_H165 zenon_Haf zenon_Ha5 zenon_H191 zenon_H18f zenon_H62 zenon_H150 zenon_H14f zenon_H1a6 zenon_H6a zenon_H75 zenon_H25 zenon_H6d zenon_H18b. % 18.52/18.74 apply (zenon_or_s _ _ zenon_H2f); [ zenon_intro zenon_H34 | zenon_intro zenon_H33 ]. % 18.52/18.74 exact (zenon_H30 zenon_H34). % 18.52/18.74 apply (zenon_or_s _ _ zenon_H33); [ zenon_intro zenon_H36 | zenon_intro zenon_H35 ]. % 18.52/18.74 exact (zenon_H31 zenon_H36). % 18.52/18.74 apply (zenon_or_s _ _ zenon_H35); [ zenon_intro zenon_H2c | zenon_intro zenon_H37 ]. % 18.52/18.74 apply (zenon_L292_); trivial. % 18.52/18.74 apply (zenon_L143_); trivial. % 18.52/18.74 (* end of lemma zenon_L293_ *) % 18.52/18.74 assert (zenon_L294_ : (((op (e1) (e0)) = (e2))\/(((op (e1) (e1)) = (e2))\/(((op (e1) (e2)) = (e2))\/((op (e1) (e3)) = (e2))))) -> (~((e0) = (e2))) -> ((op (e1) (e0)) = (e0)) -> (~((op (e3) (e0)) = (op (e3) (e1)))) -> ((op (e3) (e0)) = (e3)) -> ((op (e2) (e1)) = (e1)) -> (~((e1) = (e3))) -> (~((e2) = (e3))) -> ((op (e0) (e1)) = (e0)) -> (~((e0) = (e3))) -> (((op (e0) (e1)) = (e3))\/(((op (e1) (e1)) = (e3))\/(((op (e2) (e1)) = (e3))\/((op (e3) (e1)) = (e3))))) -> ((op (e0) (e2)) = (e2)) -> (~((op (e0) (e2)) = (op (e1) (e2)))) -> ((op (e1) (e3)) = (e1)) -> (~((e1) = (e2))) -> False). % 18.52/18.74 do 0 intro. intros zenon_H18c zenon_H149 zenon_H27 zenon_H1cf zenon_H15e zenon_Ha5 zenon_H95 zenon_H12b zenon_H49 zenon_H9a zenon_H1a5 zenon_H150 zenon_H195 zenon_Hd6 zenon_H7c. % 18.52/18.74 apply (zenon_or_s _ _ zenon_H18c); [ zenon_intro zenon_H86 | zenon_intro zenon_H18d ]. % 18.52/18.74 apply (zenon_L257_); trivial. % 18.52/18.74 apply (zenon_or_s _ _ zenon_H18d); [ zenon_intro zenon_H110 | zenon_intro zenon_H18e ]. % 18.52/18.74 apply (zenon_L215_); trivial. % 18.52/18.74 apply (zenon_or_s _ _ zenon_H18e); [ zenon_intro zenon_H113 | zenon_intro zenon_Hd7 ]. % 18.52/18.74 apply (zenon_L153_); trivial. % 18.52/18.74 apply (zenon_L101_); trivial. % 18.52/18.74 (* end of lemma zenon_L294_ *) % 18.52/18.74 assert (zenon_L295_ : (((op (e1) (e0)) = (e2))\/(((op (e1) (e1)) = (e2))\/(((op (e1) (e2)) = (e2))\/((op (e1) (e3)) = (e2))))) -> (~((e0) = (e2))) -> ((op (e3) (e1)) = (e1)) -> (~((op (e2) (e0)) = (op (e2) (e1)))) -> ((op (e2) (e0)) = (e2)) -> (((op (e1) (e0)) = (e3))\/(((op (e1) (e1)) = (e3))\/(((op (e1) (e2)) = (e3))\/((op (e1) (e3)) = (e3))))) -> (~((e0) = (e3))) -> ((op (e1) (e0)) = (e0)) -> (~((e2) = (e3))) -> (~((e1) = (e3))) -> (~((op (e1) (e1)) = (op (e2) (e1)))) -> (~((op (e0) (e1)) = (op (e2) (e1)))) -> (~((op (e2) (e1)) = (op (e3) (e1)))) -> (~((op (e2) (e1)) = (e0))) -> (((op (e2) (e1)) = (e0))\/(((op (e2) (e1)) = (e1))\/(((op (e2) (e1)) = (e2))\/((op (e2) (e1)) = (e3))))) -> ((op (e0) (e2)) = (e3)) -> (~((op (e0) (e2)) = (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). % 18.52/18.74 do 0 intro. intros zenon_H18c zenon_H149 zenon_Hae zenon_H1f0 zenon_Hee zenon_H16f zenon_H9a zenon_H27 zenon_H12b zenon_H95 zenon_H13e zenon_H17e zenon_Haf zenon_H31 zenon_H1cc zenon_Ha9 zenon_H195 zenon_H1d8 zenon_Hd6 zenon_H7c. % 18.52/18.74 apply (zenon_or_s _ _ zenon_H18c); [ zenon_intro zenon_H86 | zenon_intro zenon_H18d ]. % 18.52/18.74 apply (zenon_L257_); trivial. % 18.52/18.74 apply (zenon_or_s _ _ zenon_H18d); [ zenon_intro zenon_H110 | zenon_intro zenon_H18e ]. % 18.52/18.74 apply (zenon_L274_); trivial. % 18.52/18.74 apply (zenon_or_s _ _ zenon_H18e); [ zenon_intro zenon_H113 | zenon_intro zenon_Hd7 ]. % 18.52/18.74 apply (zenon_or_s _ _ zenon_H1d8); [ zenon_intro zenon_H10f | zenon_intro zenon_H1d9 ]. % 18.52/18.74 apply (zenon_L269_); trivial. % 18.52/18.74 apply (zenon_or_s _ _ zenon_H1d9); [ zenon_intro zenon_H110 | zenon_intro zenon_H1da ]. % 18.52/18.74 apply (zenon_L276_); trivial. % 18.52/18.74 apply (zenon_or_s _ _ zenon_H1da); [ zenon_intro zenon_H1ca | zenon_intro zenon_H14d ]. % 18.52/18.74 apply (zenon_L277_); trivial. % 18.52/18.74 apply (zenon_L152_); trivial. % 18.52/18.74 apply (zenon_L101_); trivial. % 18.52/18.74 (* end of lemma zenon_L295_ *) % 18.52/18.74 assert (zenon_L296_ : (((op (e0) (e1)) = (e1))\/(((op (e1) (e1)) = (e1))\/(((op (e2) (e1)) = (e1))\/((op (e3) (e1)) = (e1))))) -> (~((e0) = (e1))) -> (~((op (e1) (e1)) = (e1))) -> ((op (e0) (e2)) = (e2)) -> (((op (e0) (e1)) = (e3))\/(((op (e1) (e1)) = (e3))\/(((op (e2) (e1)) = (e3))\/((op (e3) (e1)) = (e3))))) -> ((op (e0) (e1)) = (e0)) -> ((op (e3) (e0)) = (e3)) -> (~((op (e3) (e0)) = (op (e3) (e1)))) -> (((op (e1) (e0)) = (e2))\/(((op (e1) (e1)) = (e2))\/(((op (e1) (e2)) = (e2))\/((op (e1) (e3)) = (e2))))) -> (~((e0) = (e2))) -> (~((op (e2) (e0)) = (op (e2) (e1)))) -> ((op (e2) (e0)) = (e2)) -> (((op (e1) (e0)) = (e3))\/(((op (e1) (e1)) = (e3))\/(((op (e1) (e2)) = (e3))\/((op (e1) (e3)) = (e3))))) -> (~((e0) = (e3))) -> ((op (e1) (e0)) = (e0)) -> (~((e2) = (e3))) -> (~((e1) = (e3))) -> (~((op (e1) (e1)) = (op (e2) (e1)))) -> (~((op (e0) (e1)) = (op (e2) (e1)))) -> (~((op (e2) (e1)) = (op (e3) (e1)))) -> (~((op (e2) (e1)) = (e0))) -> (((op (e2) (e1)) = (e0))\/(((op (e2) (e1)) = (e1))\/(((op (e2) (e1)) = (e2))\/((op (e2) (e1)) = (e3))))) -> ((op (e0) (e2)) = (e3)) -> (~((op (e0) (e2)) = (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). % 18.52/18.74 do 0 intro. intros zenon_H109 zenon_Ha1 zenon_H10a zenon_H150 zenon_H1a5 zenon_H49 zenon_H15e zenon_H1cf zenon_H18c zenon_H149 zenon_H1f0 zenon_Hee zenon_H16f zenon_H9a zenon_H27 zenon_H12b zenon_H95 zenon_H13e zenon_H17e zenon_Haf zenon_H31 zenon_H1cc zenon_Ha9 zenon_H195 zenon_H1d8 zenon_Hd6 zenon_H7c. % 18.52/18.74 apply (zenon_or_s _ _ zenon_H109); [ zenon_intro zenon_Ha0 | zenon_intro zenon_H10b ]. % 18.52/18.74 apply (zenon_L38_); trivial. % 18.52/18.74 apply (zenon_or_s _ _ zenon_H10b); [ zenon_intro zenon_H10d | zenon_intro zenon_H10c ]. % 18.52/18.74 exact (zenon_H10a zenon_H10d). % 18.52/18.74 apply (zenon_or_s _ _ zenon_H10c); [ zenon_intro zenon_Ha5 | zenon_intro zenon_Hae ]. % 18.52/18.74 apply (zenon_L294_); trivial. % 18.52/18.74 apply (zenon_L295_); trivial. % 18.52/18.74 (* end of lemma zenon_L296_ *) % 18.52/18.74 assert (zenon_L297_ : (((op (e0) (e1)) = (e1))\/(((op (e1) (e1)) = (e1))\/(((op (e2) (e1)) = (e1))\/((op (e3) (e1)) = (e1))))) -> (~((e0) = (e1))) -> (~((op (e1) (e1)) = (e1))) -> (~((op (e0) (e2)) = (op (e1) (e2)))) -> (((op (e0) (e1)) = (e3))\/(((op (e1) (e1)) = (e3))\/(((op (e2) (e1)) = (e3))\/((op (e3) (e1)) = (e3))))) -> (~((e0) = (e3))) -> ((op (e0) (e1)) = (e0)) -> (~((e1) = (e3))) -> (~((op (e3) (e0)) = (op (e3) (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) (e0)) = (e1))\/(((op (e2) (e1)) = (e1))\/(((op (e2) (e2)) = (e1))\/((op (e2) (e3)) = (e1))))) -> (~((op (e2) (e1)) = (op (e3) (e1)))) -> ((op (e0) (e3)) = (e3)) -> (~((op (e0) (e3)) = (op (e2) (e3)))) -> (~((op (e2) (e3)) = (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 (e0) (e2)) = (op (e3) (e2)))) -> ((op (e0) (e2)) = (e2)) -> (((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)) -> (~((op (e3) (e1)) = (op (e3) (e3)))) -> ((op (e3) (e0)) = (e3)) -> (((op (e3) (e0)) = (e2))\/(((op (e3) (e1)) = (e2))\/(((op (e3) (e2)) = (e2))\/((op (e3) (e3)) = (e2))))) -> (~((op (e3) (e2)) = (e0))) -> (~((op (e3) (e1)) = (e0))) -> (~((op (e3) (e0)) = (e0))) -> (((op (e3) (e0)) = (e0))\/(((op (e3) (e1)) = (e0))\/(((op (e3) (e2)) = (e0))\/((op (e3) (e3)) = (e0))))) -> (~((op (e1) (e3)) = (op (e2) (e3)))) -> ((op (e1) (e3)) = (e1)) -> False). % 18.52/18.74 do 0 intro. intros zenon_H109 zenon_Ha1 zenon_H10a zenon_H195 zenon_H1a5 zenon_H9a zenon_H49 zenon_H95 zenon_H1cf zenon_H27 zenon_H149 zenon_H18c zenon_H106 zenon_Haf zenon_He3 zenon_He2 zenon_Hf3 zenon_H6d zenon_H11f zenon_H14f zenon_H150 zenon_H145 zenon_H12b zenon_H7c zenon_H5b zenon_Hee zenon_H130 zenon_H15e zenon_H153 zenon_H18b zenon_H1ad zenon_H40 zenon_H1ac zenon_Hdb zenon_Hd6. % 18.52/18.74 apply (zenon_or_s _ _ zenon_H109); [ zenon_intro zenon_Ha0 | zenon_intro zenon_H10b ]. % 18.52/18.74 apply (zenon_L38_); trivial. % 18.52/18.74 apply (zenon_or_s _ _ zenon_H10b); [ zenon_intro zenon_H10d | zenon_intro zenon_H10c ]. % 18.52/18.74 exact (zenon_H10a zenon_H10d). % 18.52/18.74 apply (zenon_or_s _ _ zenon_H10c); [ zenon_intro zenon_Ha5 | zenon_intro zenon_Hae ]. % 18.52/18.74 apply (zenon_L294_); trivial. % 18.52/18.74 apply (zenon_L221_); trivial. % 18.52/18.74 (* end of lemma zenon_L297_ *) % 18.52/18.74 assert (zenon_L298_ : (((op (e0) (e0)) = (e0))\/(((op (e0) (e1)) = (e0))\/(((op (e0) (e2)) = (e0))\/((op (e0) (e3)) = (e0))))) -> (~((op (e0) (e0)) = (e0))) -> (~((e2) = (e3))) -> (((op (e1) (e0)) = (e1))\/(((op (e1) (e1)) = (e1))\/(((op (e1) (e2)) = (e1))\/((op (e1) (e3)) = (e1))))) -> (((op (e0) (e1)) = (e3))\/(((op (e1) (e1)) = (e3))\/(((op (e2) (e1)) = (e3))\/((op (e3) (e1)) = (e3))))) -> (~((op (e3) (e1)) = (e0))) -> (~((op (e3) (e0)) = (e0))) -> (((op (e3) (e0)) = (e0))\/(((op (e3) (e1)) = (e0))\/(((op (e3) (e2)) = (e0))\/((op (e3) (e3)) = (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) (e0)) = (op (e2) (e0)))) -> (((op (e2) (e0)) = (e1))\/(((op (e2) (e1)) = (e1))\/(((op (e2) (e2)) = (e1))\/((op (e2) (e3)) = (e1))))) -> (~((op (e3) (e0)) = (op (e3) (e1)))) -> (~((e0) = (e2))) -> (~((op (e1) (e1)) = (e1))) -> (~((e0) = (e1))) -> (((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) (e0)) = (e1)) -> ((op (e2) (e0)) = (e3)) -> (~((op (e3) (e2)) = (e0))) -> (~((op (e2) (e2)) = (op (e2) (e3)))) -> (~((op (e1) (e2)) = (e0))) -> (((op (e0) (e2)) = (e0))\/(((op (e1) (e2)) = (e0))\/(((op (e2) (e2)) = (e0))\/((op (e3) (e2)) = (e0))))) -> (((op (e3) (e0)) = (e1))\/(((op (e3) (e1)) = (e1))\/(((op (e3) (e2)) = (e1))\/((op (e3) (e3)) = (e1))))) -> (~((e1) = (e3))) -> ((op (e3) (e0)) = (e3)) -> (~((e1) = (e2))) -> (~((op (e1) (e3)) = (op (e3) (e3)))) -> (~((op (e2) (e1)) = (e0))) -> (~((op (e2) (e0)) = (e0))) -> (((op (e2) (e0)) = (e0))\/(((op (e2) (e1)) = (e0))\/(((op (e2) (e2)) = (e0))\/((op (e2) (e3)) = (e0))))) -> (~((op (e2) (e0)) = (op (e2) (e1)))) -> ((op (e2) (e0)) = (e2)) -> (((op (e1) (e0)) = (e3))\/(((op (e1) (e1)) = (e3))\/(((op (e1) (e2)) = (e3))\/((op (e1) (e3)) = (e3))))) -> (~((e0) = (e3))) -> ((op (e1) (e0)) = (e0)) -> (~((op (e1) (e1)) = (op (e2) (e1)))) -> (~((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 (e0) (e2)) = (op (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 (e3) (e3)) = (e3))) -> (((op (e0) (e1)) = (e2))\/(((op (e1) (e1)) = (e2))\/(((op (e2) (e1)) = (e2))\/((op (e3) (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 (e1) (e2)) = (op (e2) (e2)))) -> (((op (e0) (e3)) = (e0))\/(((op (e0) (e3)) = (e1))\/(((op (e0) (e3)) = (e2))\/((op (e0) (e3)) = (e3))))) -> (~((op (e1) (e1)) = (op (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) (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 (e1) (e1)) = (op (e3) (e1)))) -> (~((op (e2) (e0)) = (op (e2) (e2)))) -> (~((op (e3) (e0)) = (op (e3) (e2)))) -> (~((op (e0) (e3)) = (op (e2) (e3)))) -> (((op (e2) (e3)) = (e0))\/(((op (e2) (e3)) = (e1))\/(((op (e2) (e3)) = (e2))\/((op (e2) (e3)) = (e3))))) -> (~((op (e0) (e2)) = (op (e3) (e2)))) -> (((op (e0) (e3)) = (e2))\/(((op (e1) (e3)) = (e2))\/(((op (e2) (e3)) = (e2))\/((op (e3) (e3)) = (e2))))) -> (~((op (e2) (e0)) = (op (e2) (e3)))) -> (((op (e3) (e0)) = (e2))\/(((op (e3) (e1)) = (e2))\/(((op (e3) (e2)) = (e2))\/((op (e3) (e3)) = (e2))))) -> (~((op (e1) (e3)) = (op (e2) (e3)))) -> (((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 (e1) (e2)) = (op (e1) (e3)))) -> (~((op (e1) (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) (e2)) = (e0))) -> (~((op (e0) (e3)) = (e0))) -> False). % 18.52/18.74 do 0 intro. intros zenon_H74 zenon_H3f zenon_H12b zenon_H128 zenon_H1a5 zenon_H1ad zenon_H40 zenon_H1ac zenon_H133 zenon_H130 zenon_H39 zenon_H106 zenon_H1cf zenon_H149 zenon_H10a zenon_Ha1 zenon_H109 zenon_H18c zenon_H7a zenon_H3b zenon_H18b zenon_H6d zenon_H25 zenon_H6a zenon_He8 zenon_H95 zenon_H15e zenon_H7c zenon_Hd5 zenon_H31 zenon_H30 zenon_H2f zenon_H1f0 zenon_Hee zenon_H16f zenon_H9a zenon_H27 zenon_H13e zenon_H17e zenon_Haf zenon_H1cc zenon_H195 zenon_H101 zenon_Hf3 zenon_Hc2 zenon_H102 zenon_H1d8 zenon_H1d zenon_H168 zenon_H2b zenon_He4 zenon_H57 zenon_H1a6 zenon_H62 zenon_H18f zenon_H191 zenon_H165 zenon_H160 zenon_H52 zenon_H6f zenon_He2 zenon_H11f zenon_H14f zenon_H145 zenon_H5b zenon_H153 zenon_Hdb zenon_H136 zenon_Hdf zenon_H124 zenon_H115 zenon_H10e zenon_H183 zenon_H75 zenon_H76. % 18.52/18.74 apply (zenon_or_s _ _ zenon_H74); [ zenon_intro zenon_H42 | zenon_intro zenon_H77 ]. % 18.52/18.74 exact (zenon_H3f zenon_H42). % 18.52/18.74 apply (zenon_or_s _ _ zenon_H77); [ zenon_intro zenon_H49 | zenon_intro zenon_H78 ]. % 18.52/18.74 apply (zenon_or_s _ _ zenon_H183); [ zenon_intro zenon_H7b | zenon_intro zenon_H186 ]. % 18.52/18.74 apply (zenon_L26_); trivial. % 18.52/18.74 apply (zenon_or_s _ _ zenon_H186); [ zenon_intro zenon_H10f | zenon_intro zenon_H187 ]. % 18.52/18.74 apply (zenon_or_s _ _ zenon_H168); [ zenon_intro zenon_H3a | zenon_intro zenon_H169 ]. % 18.52/18.74 apply (zenon_L35_); trivial. % 18.52/18.74 apply (zenon_or_s _ _ zenon_H169); [ zenon_intro zenon_H99 | zenon_intro zenon_H16a ]. % 18.52/18.74 apply (zenon_L36_); trivial. % 18.52/18.74 apply (zenon_or_s _ _ zenon_H16a); [ zenon_intro zenon_Ha9 | zenon_intro zenon_He3 ]. % 18.52/18.74 apply (zenon_or_s _ _ zenon_H128); [ zenon_intro zenon_H9d | zenon_intro zenon_H129 ]. % 18.52/18.74 apply (zenon_L262_); trivial. % 18.52/18.74 apply (zenon_or_s _ _ zenon_H129); [ zenon_intro zenon_H10d | zenon_intro zenon_H12a ]. % 18.52/18.74 exact (zenon_H10a zenon_H10d). % 18.52/18.74 apply (zenon_or_s _ _ zenon_H12a); [ zenon_intro zenon_Hf0 | zenon_intro zenon_Hd6 ]. % 18.52/18.74 apply (zenon_or_s _ _ zenon_H109); [ zenon_intro zenon_Ha0 | zenon_intro zenon_H10b ]. % 18.52/18.74 apply (zenon_L38_); trivial. % 18.52/18.74 apply (zenon_or_s _ _ zenon_H10b); [ zenon_intro zenon_H10d | zenon_intro zenon_H10c ]. % 18.52/18.74 exact (zenon_H10a zenon_H10d). % 18.52/18.74 apply (zenon_or_s _ _ zenon_H10c); [ zenon_intro zenon_Ha5 | zenon_intro zenon_Hae ]. % 18.52/18.74 apply (zenon_or_s _ _ zenon_H18c); [ zenon_intro zenon_H86 | zenon_intro zenon_H18d ]. % 18.52/18.74 apply (zenon_L257_); trivial. % 18.52/18.74 apply (zenon_or_s _ _ zenon_H18d); [ zenon_intro zenon_H110 | zenon_intro zenon_H18e ]. % 18.52/18.74 apply (zenon_L215_); trivial. % 18.52/18.74 apply (zenon_or_s _ _ zenon_H18e); [ zenon_intro zenon_H113 | zenon_intro zenon_Hd7 ]. % 18.52/18.74 apply (zenon_L68_); trivial. % 18.52/18.74 apply (zenon_or_s _ _ zenon_H16f); [ zenon_intro zenon_H9e | zenon_intro zenon_H170 ]. % 18.52/18.74 apply (zenon_L263_); trivial. % 18.52/18.74 apply (zenon_or_s _ _ zenon_H170); [ zenon_intro zenon_H13f | zenon_intro zenon_H171 ]. % 18.52/18.74 apply (zenon_or_s _ _ zenon_H1ac); [ zenon_intro zenon_H44 | zenon_intro zenon_H1af ]. % 18.52/18.74 exact (zenon_H40 zenon_H44). % 18.52/18.74 apply (zenon_or_s _ _ zenon_H1af); [ zenon_intro zenon_H1b1 | zenon_intro zenon_H1b0 ]. % 18.52/18.74 exact (zenon_H1ad zenon_H1b1). % 18.52/18.74 apply (zenon_or_s _ _ zenon_H1b0); [ zenon_intro zenon_H61 | zenon_intro zenon_H60 ]. % 18.52/18.74 exact (zenon_H18b zenon_H61). % 18.52/18.74 apply (zenon_or_s _ _ zenon_H136); [ zenon_intro zenon_He3 | zenon_intro zenon_H137 ]. % 18.52/18.74 apply (zenon_L287_); trivial. % 18.52/18.74 apply (zenon_or_s _ _ zenon_H137); [ zenon_intro zenon_Hdc | zenon_intro zenon_H138 ]. % 18.52/18.74 apply (zenon_L266_); trivial. % 18.52/18.74 apply (zenon_or_s _ _ zenon_H138); [ zenon_intro zenon_Hdd | zenon_intro zenon_H105 ]. % 18.52/18.74 apply (zenon_or_s _ _ zenon_He4); [ zenon_intro zenon_H1e | zenon_intro zenon_He5 ]. % 18.52/18.74 exact (zenon_H76 zenon_H1e). % 18.52/18.74 apply (zenon_or_s _ _ zenon_He5); [ zenon_intro zenon_Hc3 | zenon_intro zenon_He6 ]. % 18.52/18.74 apply (zenon_L202_); trivial. % 18.52/18.74 apply (zenon_or_s _ _ zenon_He6); [ zenon_intro zenon_Hcd | zenon_intro zenon_He3 ]. % 18.52/18.74 apply (zenon_L70_); trivial. % 18.52/18.74 apply (zenon_L287_); trivial. % 18.52/18.74 exact (zenon_H102 zenon_H105). % 18.52/18.74 apply (zenon_or_s _ _ zenon_H171); [ zenon_intro zenon_H16c | zenon_intro zenon_Hdc ]. % 18.52/18.74 apply (zenon_L167_); trivial. % 18.52/18.74 apply (zenon_L266_); trivial. % 18.52/18.74 apply (zenon_L285_); trivial. % 18.52/18.74 apply (zenon_L289_); trivial. % 18.52/18.74 apply (zenon_or_s _ _ zenon_H128); [ zenon_intro zenon_H9d | zenon_intro zenon_H129 ]. % 18.52/18.74 apply (zenon_L262_); trivial. % 18.52/18.74 apply (zenon_or_s _ _ zenon_H129); [ zenon_intro zenon_H10d | zenon_intro zenon_H12a ]. % 18.52/18.74 exact (zenon_H10a zenon_H10d). % 18.52/18.74 apply (zenon_or_s _ _ zenon_H12a); [ zenon_intro zenon_Hf0 | zenon_intro zenon_Hd6 ]. % 18.52/18.74 apply (zenon_or_s _ _ zenon_H18c); [ zenon_intro zenon_H86 | zenon_intro zenon_H18d ]. % 18.52/18.74 apply (zenon_L33_); trivial. % 18.52/18.74 apply (zenon_or_s _ _ zenon_H18d); [ zenon_intro zenon_H110 | zenon_intro zenon_H18e ]. % 18.52/18.74 apply (zenon_L290_); trivial. % 18.52/18.74 apply (zenon_or_s _ _ zenon_H18e); [ zenon_intro zenon_H113 | zenon_intro zenon_Hd7 ]. % 18.52/18.74 apply (zenon_L68_); trivial. % 18.52/18.74 apply (zenon_or_s _ _ zenon_H16f); [ zenon_intro zenon_H9e | zenon_intro zenon_H170 ]. % 18.52/18.74 apply (zenon_L263_); trivial. % 18.52/18.74 apply (zenon_or_s _ _ zenon_H170); [ zenon_intro zenon_H13f | zenon_intro zenon_H171 ]. % 18.52/18.74 apply (zenon_L287_); trivial. % 18.52/18.74 apply (zenon_or_s _ _ zenon_H171); [ zenon_intro zenon_H16c | zenon_intro zenon_Hdc ]. % 18.52/18.74 apply (zenon_L167_); trivial. % 18.52/18.74 apply (zenon_L266_); trivial. % 18.52/18.74 apply (zenon_L289_); trivial. % 18.52/18.74 apply (zenon_or_s _ _ zenon_H187); [ zenon_intro zenon_H150 | zenon_intro zenon_Hcd ]. % 18.52/18.74 apply (zenon_or_s _ _ zenon_H168); [ zenon_intro zenon_H3a | zenon_intro zenon_H169 ]. % 18.52/18.74 apply (zenon_L35_); trivial. % 18.52/18.74 apply (zenon_or_s _ _ zenon_H169); [ zenon_intro zenon_H99 | zenon_intro zenon_H16a ]. % 18.52/18.74 apply (zenon_L36_); trivial. % 18.52/18.74 apply (zenon_or_s _ _ zenon_H16a); [ zenon_intro zenon_Ha9 | zenon_intro zenon_He3 ]. % 18.52/18.74 apply (zenon_or_s _ _ zenon_H128); [ zenon_intro zenon_H9d | zenon_intro zenon_H129 ]. % 18.52/18.74 apply (zenon_L262_); trivial. % 18.52/18.74 apply (zenon_or_s _ _ zenon_H129); [ zenon_intro zenon_H10d | zenon_intro zenon_H12a ]. % 18.52/18.74 exact (zenon_H10a zenon_H10d). % 18.52/18.74 apply (zenon_or_s _ _ zenon_H12a); [ zenon_intro zenon_Hf0 | zenon_intro zenon_Hd6 ]. % 18.52/18.74 apply (zenon_or_s _ _ zenon_H109); [ zenon_intro zenon_Ha0 | zenon_intro zenon_H10b ]. % 18.52/18.74 apply (zenon_L38_); trivial. % 18.52/18.74 apply (zenon_or_s _ _ zenon_H10b); [ zenon_intro zenon_H10d | zenon_intro zenon_H10c ]. % 18.52/18.74 exact (zenon_H10a zenon_H10d). % 18.52/18.74 apply (zenon_or_s _ _ zenon_H10c); [ zenon_intro zenon_Ha5 | zenon_intro zenon_Hae ]. % 18.52/18.74 apply (zenon_or_s _ _ zenon_H18c); [ zenon_intro zenon_H86 | zenon_intro zenon_H18d ]. % 18.52/18.74 apply (zenon_L33_); trivial. % 18.52/18.74 apply (zenon_or_s _ _ zenon_H18d); [ zenon_intro zenon_H110 | zenon_intro zenon_H18e ]. % 18.52/18.74 apply (zenon_L282_); trivial. % 18.52/18.74 apply (zenon_or_s _ _ zenon_H18e); [ zenon_intro zenon_H113 | zenon_intro zenon_Hd7 ]. % 18.52/18.74 apply (zenon_L153_); trivial. % 18.52/18.74 apply (zenon_or_s _ _ zenon_H16f); [ zenon_intro zenon_H9e | zenon_intro zenon_H170 ]. % 18.52/18.74 apply (zenon_L263_); trivial. % 18.52/18.74 apply (zenon_or_s _ _ zenon_H170); [ zenon_intro zenon_H13f | zenon_intro zenon_H171 ]. % 18.52/18.74 apply (zenon_L293_); trivial. % 18.52/18.74 apply (zenon_or_s _ _ zenon_H171); [ zenon_intro zenon_H16c | zenon_intro zenon_Hdc ]. % 18.52/18.74 apply (zenon_L162_); trivial. % 18.52/18.74 apply (zenon_L266_); trivial. % 18.52/18.74 apply (zenon_L285_); trivial. % 18.52/18.74 apply (zenon_L296_); trivial. % 18.52/18.74 apply (zenon_or_s _ _ zenon_H128); [ zenon_intro zenon_H9d | zenon_intro zenon_H129 ]. % 18.52/18.74 apply (zenon_L262_); trivial. % 18.52/18.74 apply (zenon_or_s _ _ zenon_H129); [ zenon_intro zenon_H10d | zenon_intro zenon_H12a ]. % 18.52/18.74 exact (zenon_H10a zenon_H10d). % 18.52/18.74 apply (zenon_or_s _ _ zenon_H12a); [ zenon_intro zenon_Hf0 | zenon_intro zenon_Hd6 ]. % 18.52/18.74 apply (zenon_or_s _ _ zenon_H109); [ zenon_intro zenon_Ha0 | zenon_intro zenon_H10b ]. % 18.52/18.74 apply (zenon_L38_); trivial. % 18.52/18.74 apply (zenon_or_s _ _ zenon_H10b); [ zenon_intro zenon_H10d | zenon_intro zenon_H10c ]. % 18.52/18.74 exact (zenon_H10a zenon_H10d). % 18.52/18.74 apply (zenon_or_s _ _ zenon_H10c); [ zenon_intro zenon_Ha5 | zenon_intro zenon_Hae ]. % 18.52/18.74 apply (zenon_or_s _ _ zenon_H16f); [ zenon_intro zenon_H9e | zenon_intro zenon_H170 ]. % 18.52/18.74 apply (zenon_L263_); trivial. % 18.52/18.74 apply (zenon_or_s _ _ zenon_H170); [ zenon_intro zenon_H13f | zenon_intro zenon_H171 ]. % 18.52/18.74 apply (zenon_L293_); trivial. % 18.52/18.74 apply (zenon_or_s _ _ zenon_H171); [ zenon_intro zenon_H16c | zenon_intro zenon_Hdc ]. % 18.52/18.74 apply (zenon_L167_); trivial. % 18.52/18.74 apply (zenon_L117_); trivial. % 18.52/18.74 apply (zenon_or_s _ _ zenon_H18c); [ zenon_intro zenon_H86 | zenon_intro zenon_H18d ]. % 18.52/18.74 apply (zenon_L33_); trivial. % 18.52/18.74 apply (zenon_or_s _ _ zenon_H18d); [ zenon_intro zenon_H110 | zenon_intro zenon_H18e ]. % 18.52/18.74 apply (zenon_L290_); trivial. % 18.52/18.74 apply (zenon_or_s _ _ zenon_H18e); [ zenon_intro zenon_H113 | zenon_intro zenon_Hd7 ]. % 18.52/18.74 apply (zenon_L153_); trivial. % 18.52/18.74 apply (zenon_L284_); trivial. % 18.52/18.74 apply (zenon_L297_); trivial. % 18.52/18.74 apply (zenon_or_s _ _ zenon_H168); [ zenon_intro zenon_H3a | zenon_intro zenon_H169 ]. % 18.52/18.74 apply (zenon_L35_); trivial. % 18.52/18.74 apply (zenon_or_s _ _ zenon_H169); [ zenon_intro zenon_H99 | zenon_intro zenon_H16a ]. % 18.52/18.74 apply (zenon_L36_); trivial. % 18.52/18.74 apply (zenon_or_s _ _ zenon_H16a); [ zenon_intro zenon_Ha9 | zenon_intro zenon_He3 ]. % 18.52/18.74 apply (zenon_L281_); trivial. % 18.52/18.74 apply (zenon_L81_); trivial. % 18.52/18.74 apply (zenon_or_s _ _ zenon_H78); [ zenon_intro zenon_H48 | zenon_intro zenon_H1e ]. % 18.52/18.74 exact (zenon_H75 zenon_H48). % 18.52/18.74 exact (zenon_H76 zenon_H1e). % 18.52/18.74 (* end of lemma zenon_L298_ *) % 18.52/18.74 assert (zenon_L299_ : (((op (e3) (e0)) = (e0))\/(((op (e3) (e1)) = (e0))\/(((op (e3) (e2)) = (e0))\/((op (e3) (e3)) = (e0))))) -> (~((op (e3) (e0)) = (e0))) -> (~((op (e3) (e1)) = (op (e3) (e3)))) -> (~((op (e2) (e2)) = (op (e2) (e3)))) -> (~((op (e1) (e0)) = (op (e1) (e3)))) -> ((op (e1) (e0)) = (e0)) -> ((op (e0) (e1)) = (e0)) -> (~((op (e0) (e1)) = (op (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) (e3)) = (e0))) -> False). % 18.52/18.74 do 0 intro. intros zenon_H1ac zenon_H40 zenon_H130 zenon_H6d zenon_Hd8 zenon_H27 zenon_H49 zenon_H54 zenon_H67 zenon_H2c zenon_H18f zenon_H1ae. % 18.52/18.74 apply (zenon_or_s _ _ zenon_H1ac); [ zenon_intro zenon_H44 | zenon_intro zenon_H1af ]. % 18.52/18.74 exact (zenon_H40 zenon_H44). % 18.52/18.74 apply (zenon_or_s _ _ zenon_H1af); [ zenon_intro zenon_H1b1 | zenon_intro zenon_H1b0 ]. % 18.52/18.74 apply (zenon_L259_); trivial. % 18.52/18.74 apply (zenon_or_s _ _ zenon_H1b0); [ zenon_intro zenon_H61 | zenon_intro zenon_H60 ]. % 18.52/18.74 apply (zenon_L146_); trivial. % 18.52/18.74 exact (zenon_H1ae zenon_H60). % 18.52/18.74 (* end of lemma zenon_L299_ *) % 18.52/18.74 assert (zenon_L300_ : (((op (e2) (e2)) = (e0))\/(((op (e2) (e2)) = (e1))\/(((op (e2) (e2)) = (e2))\/((op (e2) (e2)) = (e3))))) -> (~((op (e2) (e2)) = (op (e2) (e3)))) -> ((op (e2) (e3)) = (e0)) -> ((op (e1) (e2)) = (e1)) -> (~((op (e1) (e2)) = (op (e2) (e2)))) -> (~((op (e2) (e2)) = (e2))) -> ((op (e2) (e0)) = (e3)) -> (~((op (e2) (e0)) = (op (e2) (e2)))) -> False). % 18.52/18.74 do 0 intro. intros zenon_H1c4 zenon_H6d zenon_H37 zenon_Hf0 zenon_H2b zenon_H173 zenon_H3b zenon_H52. % 18.52/18.74 apply (zenon_or_s _ _ zenon_H1c4); [ zenon_intro zenon_H2c | zenon_intro zenon_H1c5 ]. % 18.52/18.74 apply (zenon_L18_); trivial. % 18.52/18.74 apply (zenon_or_s _ _ zenon_H1c5); [ zenon_intro zenon_Hf1 | zenon_intro zenon_H1c6 ]. % 18.52/18.74 apply (zenon_L59_); trivial. % 18.52/18.74 apply (zenon_or_s _ _ zenon_H1c6); [ zenon_intro zenon_H176 | zenon_intro zenon_Haa ]. % 18.52/18.74 exact (zenon_H173 zenon_H176). % 18.52/18.74 apply (zenon_L168_); trivial. % 18.52/18.74 (* end of lemma zenon_L300_ *) % 18.52/18.74 assert (zenon_L301_ : (((op (e2) (e0)) = (e0))\/(((op (e2) (e1)) = (e0))\/(((op (e2) (e2)) = (e0))\/((op (e2) (e3)) = (e0))))) -> (~((op (e2) (e0)) = (e0))) -> (~((op (e2) (e1)) = (e0))) -> (~((op (e3) (e3)) = (e0))) -> (~((op (e2) (e2)) = (op (e3) (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) (e1)) = (e0)) -> ((op (e1) (e0)) = (e0)) -> (~((op (e1) (e0)) = (op (e1) (e3)))) -> (~((op (e3) (e1)) = (op (e3) (e3)))) -> (~((op (e3) (e0)) = (e0))) -> (((op (e3) (e0)) = (e0))\/(((op (e3) (e1)) = (e0))\/(((op (e3) (e2)) = (e0))\/((op (e3) (e3)) = (e0))))) -> (((op (e2) (e2)) = (e0))\/(((op (e2) (e2)) = (e1))\/(((op (e2) (e2)) = (e2))\/((op (e2) (e2)) = (e3))))) -> (~((op (e2) (e2)) = (op (e2) (e3)))) -> ((op (e1) (e2)) = (e1)) -> (~((op (e1) (e2)) = (op (e2) (e2)))) -> (~((op (e2) (e2)) = (e2))) -> ((op (e2) (e0)) = (e3)) -> (~((op (e2) (e0)) = (op (e2) (e2)))) -> False). % 18.52/18.74 do 0 intro. intros zenon_H2f zenon_H30 zenon_H31 zenon_H1ae zenon_H18f zenon_H67 zenon_H54 zenon_H49 zenon_H27 zenon_Hd8 zenon_H130 zenon_H40 zenon_H1ac zenon_H1c4 zenon_H6d zenon_Hf0 zenon_H2b zenon_H173 zenon_H3b zenon_H52. % 18.52/18.74 apply (zenon_or_s _ _ zenon_H2f); [ zenon_intro zenon_H34 | zenon_intro zenon_H33 ]. % 18.52/18.74 exact (zenon_H30 zenon_H34). % 18.52/18.74 apply (zenon_or_s _ _ zenon_H33); [ zenon_intro zenon_H36 | zenon_intro zenon_H35 ]. % 18.52/18.74 exact (zenon_H31 zenon_H36). % 18.52/18.74 apply (zenon_or_s _ _ zenon_H35); [ zenon_intro zenon_H2c | zenon_intro zenon_H37 ]. % 18.52/18.74 apply (zenon_L299_); trivial. % 18.52/18.74 apply (zenon_L300_); trivial. % 18.52/18.74 (* end of lemma zenon_L301_ *) % 18.52/18.74 assert (zenon_L302_ : (~((op (e0) (e2)) = (op (e1) (e2)))) -> (~((e0) = (e3))) -> (((op (e1) (e0)) = (e1))\/(((op (e1) (e1)) = (e1))\/(((op (e1) (e2)) = (e1))\/((op (e1) (e3)) = (e1))))) -> (~((e0) = (e1))) -> (~((op (e1) (e1)) = (e1))) -> (~((op (e2) (e0)) = (op (e2) (e2)))) -> (~((op (e2) (e2)) = (e2))) -> (~((op (e1) (e2)) = (op (e2) (e2)))) -> (~((op (e2) (e2)) = (op (e2) (e3)))) -> (((op (e2) (e2)) = (e0))\/(((op (e2) (e2)) = (e1))\/(((op (e2) (e2)) = (e2))\/((op (e2) (e2)) = (e3))))) -> (((op (e3) (e0)) = (e0))\/(((op (e3) (e1)) = (e0))\/(((op (e3) (e2)) = (e0))\/((op (e3) (e3)) = (e0))))) -> (~((op (e3) (e0)) = (e0))) -> (~((op (e3) (e1)) = (op (e3) (e3)))) -> (~((op (e1) (e0)) = (op (e1) (e3)))) -> ((op (e1) (e0)) = (e0)) -> ((op (e0) (e1)) = (e0)) -> (~((op (e0) (e1)) = (op (e0) (e3)))) -> (((op (e0) (e3)) = (e0))\/(((op (e1) (e3)) = (e0))\/(((op (e2) (e3)) = (e0))\/((op (e3) (e3)) = (e0))))) -> (~((op (e2) (e2)) = (op (e3) (e2)))) -> (~((op (e3) (e3)) = (e0))) -> (~((op (e2) (e1)) = (e0))) -> (~((op (e2) (e0)) = (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 (e2) (e0)) = (e3)) -> ((op (e0) (e1)) = (e2)) -> (~((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 (e3) (e0)) = (e3))\/(((op (e3) (e1)) = (e3))\/(((op (e3) (e2)) = (e3))\/((op (e3) (e3)) = (e3))))) -> (~((op (e1) (e1)) = (op (e3) (e1)))) -> (~((op (e0) (e2)) = (op (e3) (e2)))) -> (~((op (e3) (e3)) = (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 (e2) (e0)) = (op (e2) (e3)))) -> ((op (e2) (e0)) = (e2)) -> ((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))))) -> (~((e1) = (e2))) -> False). % 18.52/18.74 do 0 intro. intros zenon_H195 zenon_H9a zenon_H128 zenon_Ha1 zenon_H10a zenon_H52 zenon_H173 zenon_H2b zenon_H6d zenon_H1c4 zenon_H1ac zenon_H40 zenon_H130 zenon_Hd8 zenon_H27 zenon_H49 zenon_H54 zenon_H67 zenon_H18f zenon_H1ae zenon_H31 zenon_H30 zenon_H2f zenon_H18c zenon_H3b zenon_H10f zenon_H1d zenon_H12b zenon_H145 zenon_H165 zenon_H160 zenon_H14f zenon_H102 zenon_H10e zenon_H7a zenon_H95 zenon_H168 zenon_H5b zenon_Hee zenon_H148 zenon_H71 zenon_H16f zenon_H7c. % 18.52/18.74 apply (zenon_or_s _ _ zenon_H168); [ zenon_intro zenon_H3a | zenon_intro zenon_H169 ]. % 18.52/18.74 apply (zenon_L35_); trivial. % 18.52/18.74 apply (zenon_or_s _ _ zenon_H169); [ zenon_intro zenon_H99 | zenon_intro zenon_H16a ]. % 18.52/18.74 apply (zenon_L175_); trivial. % 18.52/18.74 apply (zenon_or_s _ _ zenon_H16a); [ zenon_intro zenon_Ha9 | zenon_intro zenon_He3 ]. % 18.52/18.74 apply (zenon_or_s _ _ zenon_H128); [ zenon_intro zenon_H9d | zenon_intro zenon_H129 ]. % 18.52/18.74 apply (zenon_L262_); trivial. % 18.52/18.74 apply (zenon_or_s _ _ zenon_H129); [ zenon_intro zenon_H10d | zenon_intro zenon_H12a ]. % 18.52/18.74 exact (zenon_H10a zenon_H10d). % 18.52/18.74 apply (zenon_or_s _ _ zenon_H12a); [ zenon_intro zenon_Hf0 | zenon_intro zenon_Hd6 ]. % 18.52/18.74 apply (zenon_L301_); trivial. % 18.52/18.74 apply (zenon_or_s _ _ zenon_H16f); [ zenon_intro zenon_H9e | zenon_intro zenon_H170 ]. % 18.52/18.74 apply (zenon_L263_); trivial. % 18.52/18.74 apply (zenon_or_s _ _ zenon_H170); [ zenon_intro zenon_H13f | zenon_intro zenon_H171 ]. % 18.52/18.74 apply (zenon_L115_); trivial. % 18.52/18.74 apply (zenon_or_s _ _ zenon_H171); [ zenon_intro zenon_H16c | zenon_intro zenon_Hdc ]. % 18.52/18.74 apply (zenon_L162_); trivial. % 18.52/18.74 apply (zenon_L83_); trivial. % 18.52/18.74 apply (zenon_or_s _ _ zenon_H128); [ zenon_intro zenon_H9d | zenon_intro zenon_H129 ]. % 18.52/18.74 apply (zenon_L262_); trivial. % 18.52/18.74 apply (zenon_or_s _ _ zenon_H129); [ zenon_intro zenon_H10d | zenon_intro zenon_H12a ]. % 18.52/18.74 exact (zenon_H10a zenon_H10d). % 18.52/18.74 apply (zenon_or_s _ _ zenon_H12a); [ zenon_intro zenon_Hf0 | zenon_intro zenon_Hd6 ]. % 18.52/18.74 apply (zenon_L301_); trivial. % 18.52/18.74 apply (zenon_or_s _ _ zenon_H18c); [ zenon_intro zenon_H86 | zenon_intro zenon_H18d ]. % 18.52/18.74 apply (zenon_L33_); trivial. % 18.52/18.74 apply (zenon_or_s _ _ zenon_H18d); [ zenon_intro zenon_H110 | zenon_intro zenon_H18e ]. % 18.52/18.74 apply (zenon_L67_); trivial. % 18.52/18.74 apply (zenon_or_s _ _ zenon_H18e); [ zenon_intro zenon_H113 | zenon_intro zenon_Hd7 ]. % 18.52/18.74 apply (zenon_L118_); trivial. % 18.52/18.74 apply (zenon_L101_); trivial. % 18.52/18.74 (* end of lemma zenon_L302_ *) % 18.52/18.74 assert (zenon_L303_ : (((op (e1) (e0)) = (e1))\/(((op (e1) (e1)) = (e1))\/(((op (e1) (e2)) = (e1))\/((op (e1) (e3)) = (e1))))) -> (~((e0) = (e1))) -> (~((op (e1) (e1)) = (e1))) -> (~((op (e2) (e0)) = (op (e2) (e2)))) -> ((op (e2) (e0)) = (e3)) -> (~((op (e2) (e2)) = (e2))) -> (~((op (e1) (e2)) = (op (e2) (e2)))) -> (~((op (e2) (e2)) = (op (e2) (e3)))) -> (((op (e2) (e2)) = (e0))\/(((op (e2) (e2)) = (e1))\/(((op (e2) (e2)) = (e2))\/((op (e2) (e2)) = (e3))))) -> (((op (e3) (e0)) = (e0))\/(((op (e3) (e1)) = (e0))\/(((op (e3) (e2)) = (e0))\/((op (e3) (e3)) = (e0))))) -> (~((op (e3) (e0)) = (e0))) -> (~((op (e3) (e1)) = (op (e3) (e3)))) -> (~((op (e1) (e0)) = (op (e1) (e3)))) -> ((op (e1) (e0)) = (e0)) -> ((op (e0) (e1)) = (e0)) -> (~((op (e0) (e1)) = (op (e0) (e3)))) -> (((op (e0) (e3)) = (e0))\/(((op (e1) (e3)) = (e0))\/(((op (e2) (e3)) = (e0))\/((op (e3) (e3)) = (e0))))) -> (~((op (e2) (e2)) = (op (e3) (e2)))) -> (~((op (e3) (e3)) = (e0))) -> (~((op (e2) (e1)) = (e0))) -> (~((op (e2) (e0)) = (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))))) -> (~((e2) = (e3))) -> ((op (e0) (e3)) = (e2)) -> (((op (e3) (e0)) = (e3))\/(((op (e3) (e1)) = (e3))\/(((op (e3) (e2)) = (e3))\/((op (e3) (e3)) = (e3))))) -> ((op (e3) (e0)) = (e2)) -> (~((op (e1) (e1)) = (op (e3) (e1)))) -> (~((op (e0) (e2)) = (op (e3) (e2)))) -> (~((op (e3) (e3)) = (e3))) -> (~((op (e0) (e1)) = (op (e1) (e1)))) -> ((op (e0) (e0)) = (e1)) -> (((op (e0) (e0)) = (e3))\/(((op (e0) (e1)) = (e3))\/(((op (e0) (e2)) = (e3))\/((op (e0) (e3)) = (e3))))) -> ((op (e0) (e2)) = (e3)) -> (~((op (e0) (e2)) = (op (e1) (e2)))) -> (~((e1) = (e3))) -> False). % 18.52/18.74 do 0 intro. intros zenon_H128 zenon_Ha1 zenon_H10a zenon_H52 zenon_H3b zenon_H173 zenon_H2b zenon_H6d zenon_H1c4 zenon_H1ac zenon_H40 zenon_H130 zenon_Hd8 zenon_H27 zenon_H49 zenon_H54 zenon_H67 zenon_H18f zenon_H1ae zenon_H31 zenon_H30 zenon_H2f zenon_H16f zenon_H12b zenon_Hcd zenon_H165 zenon_H148 zenon_H160 zenon_H14f zenon_H102 zenon_H10e zenon_H7a zenon_H168 zenon_Ha9 zenon_H195 zenon_H95. % 18.52/18.74 apply (zenon_or_s _ _ zenon_H128); [ zenon_intro zenon_H9d | zenon_intro zenon_H129 ]. % 18.52/18.74 apply (zenon_L262_); trivial. % 18.52/18.74 apply (zenon_or_s _ _ zenon_H129); [ zenon_intro zenon_H10d | zenon_intro zenon_H12a ]. % 18.52/18.74 exact (zenon_H10a zenon_H10d). % 18.52/18.74 apply (zenon_or_s _ _ zenon_H12a); [ zenon_intro zenon_Hf0 | zenon_intro zenon_Hd6 ]. % 18.52/18.74 apply (zenon_L301_); trivial. % 18.52/18.74 apply (zenon_or_s _ _ zenon_H16f); [ zenon_intro zenon_H9e | zenon_intro zenon_H170 ]. % 18.52/18.74 apply (zenon_L107_); trivial. % 18.52/18.74 apply (zenon_or_s _ _ zenon_H170); [ zenon_intro zenon_H13f | zenon_intro zenon_H171 ]. % 18.52/18.74 apply (zenon_L113_); trivial. % 18.52/18.74 apply (zenon_or_s _ _ zenon_H171); [ zenon_intro zenon_H16c | zenon_intro zenon_Hdc ]. % 18.52/18.74 apply (zenon_L162_); trivial. % 18.52/18.74 apply (zenon_L83_); trivial. % 18.52/18.74 (* end of lemma zenon_L303_ *) % 18.52/18.74 assert (zenon_L304_ : (~((e0) = (e3))) -> (~((e1) = (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) (e0)) = (e1)) -> (~((op (e0) (e1)) = (op (e1) (e1)))) -> (~((op (e3) (e3)) = (e3))) -> (~((op (e0) (e2)) = (op (e3) (e2)))) -> (~((op (e1) (e1)) = (op (e3) (e1)))) -> ((op (e3) (e0)) = (e2)) -> (((op (e3) (e0)) = (e3))\/(((op (e3) (e1)) = (e3))\/(((op (e3) (e2)) = (e3))\/((op (e3) (e3)) = (e3))))) -> (((op (e1) (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 (e2) (e0)) = (e0))) -> (~((op (e2) (e1)) = (e0))) -> (~((op (e3) (e3)) = (e0))) -> (~((op (e2) (e2)) = (op (e3) (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) (e1)) = (e0)) -> ((op (e1) (e0)) = (e0)) -> (~((op (e1) (e0)) = (op (e1) (e3)))) -> (~((op (e3) (e1)) = (op (e3) (e3)))) -> (~((op (e3) (e0)) = (e0))) -> (((op (e3) (e0)) = (e0))\/(((op (e3) (e1)) = (e0))\/(((op (e3) (e2)) = (e0))\/((op (e3) (e3)) = (e0))))) -> (((op (e2) (e2)) = (e0))\/(((op (e2) (e2)) = (e1))\/(((op (e2) (e2)) = (e2))\/((op (e2) (e2)) = (e3))))) -> (~((op (e2) (e2)) = (op (e2) (e3)))) -> (~((op (e1) (e2)) = (op (e2) (e2)))) -> (~((op (e2) (e2)) = (e2))) -> ((op (e2) (e0)) = (e3)) -> (~((op (e2) (e0)) = (op (e2) (e2)))) -> (~((op (e1) (e1)) = (e1))) -> (~((e0) = (e1))) -> (((op (e1) (e0)) = (e1))\/(((op (e1) (e1)) = (e1))\/(((op (e1) (e2)) = (e1))\/((op (e1) (e3)) = (e1))))) -> ((op (e0) (e3)) = (e2)) -> (~((e2) = (e3))) -> False). % 18.52/18.74 do 0 intro. intros zenon_H9a zenon_H95 zenon_H195 zenon_H168 zenon_H7a zenon_H10e zenon_H102 zenon_H14f zenon_H160 zenon_H148 zenon_H165 zenon_H16f zenon_H2f zenon_H30 zenon_H31 zenon_H1ae zenon_H18f zenon_H67 zenon_H54 zenon_H49 zenon_H27 zenon_Hd8 zenon_H130 zenon_H40 zenon_H1ac zenon_H1c4 zenon_H6d zenon_H2b zenon_H173 zenon_H3b zenon_H52 zenon_H10a zenon_Ha1 zenon_H128 zenon_Hcd zenon_H12b. % 18.52/18.74 apply (zenon_or_s _ _ zenon_H168); [ zenon_intro zenon_H3a | zenon_intro zenon_H169 ]. % 18.52/18.74 apply (zenon_L35_); trivial. % 18.52/18.74 apply (zenon_or_s _ _ zenon_H169); [ zenon_intro zenon_H99 | zenon_intro zenon_H16a ]. % 18.52/18.74 apply (zenon_L36_); trivial. % 18.52/18.74 apply (zenon_or_s _ _ zenon_H16a); [ zenon_intro zenon_Ha9 | zenon_intro zenon_He3 ]. % 18.52/18.74 apply (zenon_L303_); trivial. % 18.52/18.74 apply (zenon_L81_); trivial. % 18.52/18.74 (* end of lemma zenon_L304_ *) % 18.52/18.74 assert (zenon_L305_ : ((~((op (e3) (e2)) = (e0)))\/((op (e3) (e0)) = (e2))) -> (~((op (e2) (e2)) = (e2))) -> (((op (e2) (e2)) = (e0))\/(((op (e2) (e2)) = (e1))\/(((op (e2) (e2)) = (e2))\/((op (e2) (e2)) = (e3))))) -> (~((op (e3) (e0)) = (op (e3) (e3)))) -> (((op (e0) (e0)) = (e0))\/(((op (e0) (e1)) = (e0))\/(((op (e0) (e2)) = (e0))\/((op (e0) (e3)) = (e0))))) -> (~((op (e0) (e3)) = (e0))) -> (~((op (e2) (e0)) = (e0))) -> (~((op (e2) (e1)) = (e0))) -> (((op (e3) (e0)) = (e0))\/(((op (e3) (e1)) = (e0))\/(((op (e3) (e2)) = (e0))\/((op (e3) (e3)) = (e0))))) -> (~((op (e0) (e1)) = (op (e0) (e3)))) -> (~((op (e1) (e0)) = (op (e1) (e3)))) -> ((op (e1) (e0)) = (e0)) -> (~((op (e2) (e2)) = (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 (e3) (e0)) = (e0))) -> (((op (e0) (e2)) = (e0))\/(((op (e1) (e2)) = (e0))\/(((op (e2) (e2)) = (e0))\/((op (e3) (e2)) = (e0))))) -> (~((op (e1) (e2)) = (e0))) -> (~((op (e0) (e2)) = (e0))) -> (((op (e2) (e0)) = (e0))\/(((op (e2) (e1)) = (e0))\/(((op (e2) (e2)) = (e0))\/((op (e2) (e3)) = (e0))))) -> (~((op (e0) (e0)) = (e0))) -> (~((e1) = (e2))) -> ((op (e0) (e0)) = (e1)) -> (((op (e0) (e0)) = (e3))\/(((op (e0) (e1)) = (e3))\/(((op (e0) (e2)) = (e3))\/((op (e0) (e3)) = (e3))))) -> (~((e0) = (e1))) -> (~((op (e1) (e1)) = (e1))) -> (~((e0) = (e2))) -> (((op (e0) (e1)) = (e3))\/(((op (e1) (e1)) = (e3))\/(((op (e2) (e1)) = (e3))\/((op (e3) (e1)) = (e3))))) -> (~((op (e3) (e0)) = (op (e3) (e1)))) -> (~((e2) = (e3))) -> (~((op (e3) (e1)) = (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 (e1) (e3)) = (op (e2) (e3)))) -> (~((op (e1) (e2)) = (op (e1) (e3)))) -> (~((op (e2) (e0)) = (op (e2) (e3)))) -> (((op (e2) (e3)) = (e0))\/(((op (e2) (e3)) = (e1))\/(((op (e2) (e3)) = (e2))\/((op (e2) (e3)) = (e3))))) -> (~((op (e1) (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))))) -> (~((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)) = (e2)) -> (~((op (e2) (e0)) = (op (e2) (e1)))) -> (((op (e3) (e0)) = (e1))\/(((op (e3) (e1)) = (e1))\/(((op (e3) (e2)) = (e1))\/((op (e3) (e3)) = (e1))))) -> (~((op (e1) (e3)) = (op (e3) (e3)))) -> (((op (e2) (e1)) = (e0))\/(((op (e2) (e1)) = (e1))\/(((op (e2) (e1)) = (e2))\/((op (e2) (e1)) = (e3))))) -> (~((op (e1) (e1)) = (op (e2) (e1)))) -> (~((op (e0) (e1)) = (op (e2) (e1)))) -> (~((op (e2) (e1)) = (op (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 (e1) (e0)) = (e2))\/(((op (e1) (e1)) = (e2))\/(((op (e1) (e2)) = (e2))\/((op (e1) (e3)) = (e2))))) -> (~((op (e0) (e3)) = (op (e1) (e3)))) -> ((op (e2) (e0)) = (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 (e1) (e0)) = (e3))\/(((op (e1) (e1)) = (e3))\/(((op (e1) (e2)) = (e3))\/((op (e1) (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 (e1) (e2)) = (op (e2) (e2)))) -> (~((op (e0) (e0)) = (op (e2) (e0)))) -> (~((op (e1) (e1)) = (op (e1) (e3)))) -> (~((op (e1) (e1)) = (op (e3) (e1)))) -> (~((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))))) -> (~((op (e2) (e0)) = (op (e2) (e2)))) -> (~((op (e3) (e0)) = (op (e3) (e2)))) -> (((op (e0) (e2)) = (e3))\/(((op (e1) (e2)) = (e3))\/(((op (e2) (e2)) = (e3))\/((op (e3) (e2)) = (e3))))) -> (~((op (e0) (e1)) = (op (e1) (e1)))) -> (~((e0) = (e3))) -> (~((e1) = (e3))) -> (((op (e0) (e3)) = (e2))\/(((op (e1) (e3)) = (e2))\/(((op (e2) (e3)) = (e2))\/((op (e3) (e3)) = (e2))))) -> (((op (e3) (e0)) = (e2))\/(((op (e3) (e1)) = (e2))\/(((op (e3) (e2)) = (e2))\/((op (e3) (e3)) = (e2))))) -> (((op (e3) (e2)) = (e0))\/(((op (e3) (e2)) = (e1))\/(((op (e3) (e2)) = (e2))\/((op (e3) (e2)) = (e3))))) -> (~((op (e3) (e2)) = (op (e3) (e3)))) -> (~((op (e2) (e2)) = (op (e3) (e2)))) -> (((op (e0) (e0)) = (e2))\/(((op (e0) (e1)) = (e2))\/(((op (e0) (e2)) = (e2))\/((op (e0) (e3)) = (e2))))) -> ((~((op (e3) (e3)) = (e0)))\/((op (e3) (e0)) = (e3))) -> False). % 18.52/18.74 do 0 intro. intros zenon_H1a7 zenon_H173 zenon_H1c4 zenon_H71 zenon_H74 zenon_H76 zenon_H30 zenon_H31 zenon_H1ac zenon_H54 zenon_Hd8 zenon_H27 zenon_H6d zenon_H130 zenon_H67 zenon_H40 zenon_H6a zenon_H25 zenon_H75 zenon_H2f zenon_H3f zenon_H7c zenon_H7a zenon_H168 zenon_Ha1 zenon_H10a zenon_H149 zenon_H1a5 zenon_H1cf zenon_H12b zenon_H1ad zenon_H136 zenon_Hdf zenon_Hdb zenon_H124 zenon_H5b zenon_H11f zenon_H115 zenon_He2 zenon_H128 zenon_H195 zenon_H1d8 zenon_Hee zenon_H1f0 zenon_He8 zenon_Hd5 zenon_H1cc zenon_H13e zenon_H17e zenon_Haf zenon_H101 zenon_Hc2 zenon_Hf3 zenon_H18c zenon_H1d zenon_H3b zenon_H133 zenon_H106 zenon_H16f zenon_H109 zenon_He4 zenon_H2b zenon_H39 zenon_H57 zenon_H160 zenon_H14f zenon_H102 zenon_H165 zenon_H52 zenon_H6f zenon_H1a6 zenon_H10e zenon_H9a zenon_H95 zenon_H145 zenon_H153 zenon_H191 zenon_H62 zenon_H18f zenon_H183 zenon_H1ec. % 18.52/18.74 apply (zenon_or_s _ _ zenon_H1a7); [ zenon_intro zenon_H18b | zenon_intro zenon_H148 ]. % 18.52/18.74 apply (zenon_or_s _ _ zenon_H1ec); [ zenon_intro zenon_H1ae | zenon_intro zenon_H15e ]. % 18.52/18.74 apply (zenon_L261_); trivial. % 18.52/18.74 apply (zenon_L298_); trivial. % 18.52/18.74 apply (zenon_or_s _ _ zenon_H1ec); [ zenon_intro zenon_H1ae | zenon_intro zenon_H15e ]. % 18.52/18.74 apply (zenon_or_s _ _ zenon_H74); [ zenon_intro zenon_H42 | zenon_intro zenon_H77 ]. % 18.52/18.74 exact (zenon_H3f zenon_H42). % 18.52/18.74 apply (zenon_or_s _ _ zenon_H77); [ zenon_intro zenon_H49 | zenon_intro zenon_H78 ]. % 18.52/18.74 apply (zenon_or_s _ _ zenon_H183); [ zenon_intro zenon_H7b | zenon_intro zenon_H186 ]. % 18.52/18.74 apply (zenon_L26_); trivial. % 18.52/18.74 apply (zenon_or_s _ _ zenon_H186); [ zenon_intro zenon_H10f | zenon_intro zenon_H187 ]. % 18.52/18.74 apply (zenon_L302_); trivial. % 18.52/18.74 apply (zenon_or_s _ _ zenon_H187); [ zenon_intro zenon_H150 | zenon_intro zenon_Hcd ]. % 18.52/18.74 apply (zenon_or_s _ _ zenon_H128); [ zenon_intro zenon_H9d | zenon_intro zenon_H129 ]. % 18.52/18.74 apply (zenon_L262_); trivial. % 18.52/18.74 apply (zenon_or_s _ _ zenon_H129); [ zenon_intro zenon_H10d | zenon_intro zenon_H12a ]. % 18.52/18.74 exact (zenon_H10a zenon_H10d). % 18.52/18.74 apply (zenon_or_s _ _ zenon_H12a); [ zenon_intro zenon_Hf0 | zenon_intro zenon_Hd6 ]. % 18.52/18.74 apply (zenon_L301_); trivial. % 18.52/18.74 apply (zenon_or_s _ _ zenon_H18c); [ zenon_intro zenon_H86 | zenon_intro zenon_H18d ]. % 18.52/18.74 apply (zenon_L33_); trivial. % 18.52/18.74 apply (zenon_or_s _ _ zenon_H18d); [ zenon_intro zenon_H110 | zenon_intro zenon_H18e ]. % 18.52/18.74 apply (zenon_or_s _ _ zenon_H2f); [ zenon_intro zenon_H34 | zenon_intro zenon_H33 ]. % 18.52/18.74 exact (zenon_H30 zenon_H34). % 18.52/18.74 apply (zenon_or_s _ _ zenon_H33); [ zenon_intro zenon_H36 | zenon_intro zenon_H35 ]. % 18.52/18.74 exact (zenon_H31 zenon_H36). % 18.52/18.74 apply (zenon_or_s _ _ zenon_H35); [ zenon_intro zenon_H2c | zenon_intro zenon_H37 ]. % 18.52/18.74 apply (zenon_L299_); trivial. % 18.52/18.74 apply (zenon_or_s _ _ zenon_H145); [ zenon_intro zenon_Hcd | zenon_intro zenon_H146 ]. % 18.52/18.74 apply (zenon_L275_); trivial. % 18.52/18.74 apply (zenon_or_s _ _ zenon_H146); [ zenon_intro zenon_Hd7 | zenon_intro zenon_H147 ]. % 18.52/18.74 apply (zenon_L283_); trivial. % 18.52/18.74 apply (zenon_or_s _ _ zenon_H147); [ zenon_intro zenon_H11d | zenon_intro zenon_Hf6 ]. % 18.52/18.74 apply (zenon_L73_); trivial. % 18.52/18.74 apply (zenon_L114_); trivial. % 18.52/18.74 apply (zenon_or_s _ _ zenon_H18e); [ zenon_intro zenon_H113 | zenon_intro zenon_Hd7 ]. % 18.52/18.74 apply (zenon_L153_); trivial. % 18.52/18.74 apply (zenon_L101_); trivial. % 18.52/18.74 apply (zenon_L304_); trivial. % 18.52/18.74 apply (zenon_or_s _ _ zenon_H78); [ zenon_intro zenon_H48 | zenon_intro zenon_H1e ]. % 18.52/18.74 exact (zenon_H75 zenon_H48). % 18.52/18.74 exact (zenon_H76 zenon_H1e). % 18.52/18.74 apply (zenon_L109_); trivial. % 18.52/18.74 (* end of lemma zenon_L305_ *) % 18.52/18.74 assert (zenon_L306_ : (~((op (op (e0) (e0)) (e0)) = (op (e2) (e0)))) -> ((op (e0) (e0)) = (e2)) -> False). % 18.52/18.74 do 0 intro. intros zenon_H1f4 zenon_H7b. % 18.52/18.74 cut (((e0) = (e0))); [idtac | apply NNPP; zenon_intro zenon_H82]. % 18.52/18.74 cut (((op (e0) (e0)) = (e2))); [idtac | apply NNPP; zenon_intro zenon_H80]. % 18.52/18.74 congruence. % 18.52/18.74 exact (zenon_H80 zenon_H7b). % 18.52/18.74 apply zenon_H82. apply refl_equal. % 18.52/18.74 (* end of lemma zenon_L306_ *) % 18.52/18.74 assert (zenon_L307_ : ((op (e2) (e0)) = (e3)) -> ((op (e0) (e0)) = (e2)) -> (~((e3) = (op (op (e0) (e0)) (e0)))) -> False). % 18.52/18.74 do 0 intro. intros zenon_H3b zenon_H7b zenon_H156. % 18.52/18.74 elim (classic ((op (op (e0) (e0)) (e0)) = (op (op (e0) (e0)) (e0)))); [ zenon_intro zenon_H88 | zenon_intro zenon_H89 ]. % 18.52/18.74 cut (((op (op (e0) (e0)) (e0)) = (op (op (e0) (e0)) (e0))) = ((e3) = (op (op (e0) (e0)) (e0)))). % 18.52/18.74 intro zenon_D_pnotp. % 18.52/18.74 apply zenon_H156. % 18.52/18.74 rewrite <- zenon_D_pnotp. % 18.52/18.74 exact zenon_H88. % 18.52/18.74 cut (((op (op (e0) (e0)) (e0)) = (op (op (e0) (e0)) (e0)))); [idtac | apply NNPP; zenon_intro zenon_H89]. % 18.52/18.74 cut (((op (op (e0) (e0)) (e0)) = (e3))); [idtac | apply NNPP; zenon_intro zenon_H157]. % 18.52/18.74 congruence. % 18.52/18.74 cut (((op (e2) (e0)) = (e3)) = ((op (op (e0) (e0)) (e0)) = (e3))). % 18.52/18.74 intro zenon_D_pnotp. % 18.52/18.74 apply zenon_H157. % 18.52/18.74 rewrite <- zenon_D_pnotp. % 18.52/18.74 exact zenon_H3b. % 18.52/18.74 cut (((e3) = (e3))); [idtac | apply NNPP; zenon_intro zenon_H85]. % 18.52/18.74 cut (((op (e2) (e0)) = (op (op (e0) (e0)) (e0)))); [idtac | apply NNPP; zenon_intro zenon_H1f5]. % 18.52/18.74 congruence. % 18.52/18.74 elim (classic ((op (op (e0) (e0)) (e0)) = (op (op (e0) (e0)) (e0)))); [ zenon_intro zenon_H88 | zenon_intro zenon_H89 ]. % 18.52/18.74 cut (((op (op (e0) (e0)) (e0)) = (op (op (e0) (e0)) (e0))) = ((op (e2) (e0)) = (op (op (e0) (e0)) (e0)))). % 18.52/18.74 intro zenon_D_pnotp. % 18.52/18.74 apply zenon_H1f5. % 18.52/18.74 rewrite <- zenon_D_pnotp. % 18.52/18.74 exact zenon_H88. % 18.52/18.74 cut (((op (op (e0) (e0)) (e0)) = (op (op (e0) (e0)) (e0)))); [idtac | apply NNPP; zenon_intro zenon_H89]. % 18.52/18.74 cut (((op (op (e0) (e0)) (e0)) = (op (e2) (e0)))); [idtac | apply NNPP; zenon_intro zenon_H1f4]. % 18.52/18.74 congruence. % 18.52/18.74 apply (zenon_L306_); trivial. % 18.52/18.74 apply zenon_H89. apply refl_equal. % 18.52/18.74 apply zenon_H89. apply refl_equal. % 18.52/18.74 apply zenon_H85. apply refl_equal. % 18.52/18.74 apply zenon_H89. apply refl_equal. % 18.52/18.74 apply zenon_H89. apply refl_equal. % 18.52/18.74 (* end of lemma zenon_L307_ *) % 18.52/18.74 assert (zenon_L308_ : ((op (e3) (e0)) = (e1)) -> ((op (e2) (e0)) = (e3)) -> ((op (e0) (e0)) = (e2)) -> False). % 18.52/18.74 do 0 intro. intros zenon_Hac zenon_H3b zenon_H7b. % 18.52/18.74 apply (zenon_notand_s _ _ ax7); [ zenon_intro zenon_H1f7 | zenon_intro zenon_H1f6 ]. % 18.52/18.74 elim (classic ((op (op (op (e0) (e0)) (e0)) (e0)) = (op (op (op (e0) (e0)) (e0)) (e0)))); [ zenon_intro zenon_H8e | zenon_intro zenon_H8f ]. % 18.52/18.74 cut (((op (op (op (e0) (e0)) (e0)) (e0)) = (op (op (op (e0) (e0)) (e0)) (e0))) = ((e1) = (op (op (op (e0) (e0)) (e0)) (e0)))). % 18.52/18.74 intro zenon_D_pnotp. % 18.52/18.74 apply zenon_H1f7. % 18.52/18.74 rewrite <- zenon_D_pnotp. % 18.52/18.74 exact zenon_H8e. % 18.52/18.74 cut (((op (op (op (e0) (e0)) (e0)) (e0)) = (op (op (op (e0) (e0)) (e0)) (e0)))); [idtac | apply NNPP; zenon_intro zenon_H8f]. % 18.52/18.74 cut (((op (op (op (e0) (e0)) (e0)) (e0)) = (e1))); [idtac | apply NNPP; zenon_intro zenon_H1f8]. % 18.52/18.74 congruence. % 18.52/18.74 cut (((op (e3) (e0)) = (e1)) = ((op (op (op (e0) (e0)) (e0)) (e0)) = (e1))). % 18.52/18.74 intro zenon_D_pnotp. % 18.52/18.74 apply zenon_H1f8. % 18.52/18.74 rewrite <- zenon_D_pnotp. % 18.52/18.74 exact zenon_Hac. % 18.52/18.74 cut (((e1) = (e1))); [idtac | apply NNPP; zenon_intro zenon_H79]. % 18.52/18.74 cut (((op (e3) (e0)) = (op (op (op (e0) (e0)) (e0)) (e0)))); [idtac | apply NNPP; zenon_intro zenon_H15b]. % 18.52/18.74 congruence. % 18.52/18.74 elim (classic ((op (op (op (e0) (e0)) (e0)) (e0)) = (op (op (op (e0) (e0)) (e0)) (e0)))); [ zenon_intro zenon_H8e | zenon_intro zenon_H8f ]. % 18.52/18.74 cut (((op (op (op (e0) (e0)) (e0)) (e0)) = (op (op (op (e0) (e0)) (e0)) (e0))) = ((op (e3) (e0)) = (op (op (op (e0) (e0)) (e0)) (e0)))). % 18.52/18.74 intro zenon_D_pnotp. % 18.52/18.74 apply zenon_H15b. % 18.52/18.74 rewrite <- zenon_D_pnotp. % 18.52/18.74 exact zenon_H8e. % 18.52/18.74 cut (((op (op (op (e0) (e0)) (e0)) (e0)) = (op (op (op (e0) (e0)) (e0)) (e0)))); [idtac | apply NNPP; zenon_intro zenon_H8f]. % 18.52/18.74 cut (((op (op (op (e0) (e0)) (e0)) (e0)) = (op (e3) (e0)))); [idtac | apply NNPP; zenon_intro zenon_H15c]. % 18.52/18.74 congruence. % 18.52/18.74 cut (((e0) = (e0))); [idtac | apply NNPP; zenon_intro zenon_H82]. % 18.52/18.74 cut (((op (op (e0) (e0)) (e0)) = (e3))); [idtac | apply NNPP; zenon_intro zenon_H157]. % 18.52/18.74 congruence. % 18.52/18.74 cut (((op (e2) (e0)) = (e3)) = ((op (op (e0) (e0)) (e0)) = (e3))). % 18.52/18.74 intro zenon_D_pnotp. % 18.52/18.74 apply zenon_H157. % 18.52/18.74 rewrite <- zenon_D_pnotp. % 18.52/18.74 exact zenon_H3b. % 18.52/18.74 cut (((e3) = (e3))); [idtac | apply NNPP; zenon_intro zenon_H85]. % 18.52/18.74 cut (((op (e2) (e0)) = (op (op (e0) (e0)) (e0)))); [idtac | apply NNPP; zenon_intro zenon_H1f5]. % 18.52/18.74 congruence. % 18.52/18.74 elim (classic ((op (op (e0) (e0)) (e0)) = (op (op (e0) (e0)) (e0)))); [ zenon_intro zenon_H88 | zenon_intro zenon_H89 ]. % 18.52/18.74 cut (((op (op (e0) (e0)) (e0)) = (op (op (e0) (e0)) (e0))) = ((op (e2) (e0)) = (op (op (e0) (e0)) (e0)))). % 18.52/18.74 intro zenon_D_pnotp. % 18.52/18.74 apply zenon_H1f5. % 18.52/18.74 rewrite <- zenon_D_pnotp. % 18.52/18.74 exact zenon_H88. % 18.52/18.74 cut (((op (op (e0) (e0)) (e0)) = (op (op (e0) (e0)) (e0)))); [idtac | apply NNPP; zenon_intro zenon_H89]. % 18.52/18.74 cut (((op (op (e0) (e0)) (e0)) = (op (e2) (e0)))); [idtac | apply NNPP; zenon_intro zenon_H1f4]. % 18.52/18.74 congruence. % 18.52/18.74 apply (zenon_L306_); trivial. % 18.52/18.74 apply zenon_H89. apply refl_equal. % 18.52/18.74 apply zenon_H89. apply refl_equal. % 18.52/18.74 apply zenon_H85. apply refl_equal. % 18.52/18.74 apply zenon_H82. apply refl_equal. % 18.52/18.74 apply zenon_H8f. apply refl_equal. % 18.52/18.74 apply zenon_H8f. apply refl_equal. % 18.52/18.74 apply zenon_H79. apply refl_equal. % 18.52/18.74 apply zenon_H8f. apply refl_equal. % 18.52/18.74 apply zenon_H8f. apply refl_equal. % 18.52/18.74 apply (zenon_notand_s _ _ zenon_H1f6); [ zenon_intro zenon_H156 | zenon_intro zenon_H1f9 ]. % 18.52/18.74 apply (zenon_L307_); trivial. % 18.52/18.74 apply zenon_H1f9. apply sym_equal. exact zenon_H7b. % 18.52/18.74 (* end of lemma zenon_L308_ *) % 18.52/18.74 assert (zenon_L309_ : (((op (e1) (e0)) = (e2))\/(((op (e1) (e1)) = (e2))\/(((op (e1) (e2)) = (e2))\/((op (e1) (e3)) = (e2))))) -> (~((e0) = (e2))) -> ((op (e1) (e0)) = (e0)) -> (~((e2) = (e3))) -> ((op (e1) (e1)) = (e3)) -> ((op (e0) (e2)) = (e2)) -> (~((op (e0) (e2)) = (op (e1) (e2)))) -> ((op (e1) (e3)) = (e1)) -> (~((e1) = (e2))) -> False). % 18.52/18.74 do 0 intro. intros zenon_H18c zenon_H149 zenon_H27 zenon_H12b zenon_H13f zenon_H150 zenon_H195 zenon_Hd6 zenon_H7c. % 18.52/18.74 apply (zenon_or_s _ _ zenon_H18c); [ zenon_intro zenon_H86 | zenon_intro zenon_H18d ]. % 18.52/18.74 apply (zenon_L257_); trivial. % 18.52/18.74 apply (zenon_or_s _ _ zenon_H18d); [ zenon_intro zenon_H110 | zenon_intro zenon_H18e ]. % 18.52/18.74 apply (zenon_L166_); trivial. % 18.52/18.74 apply (zenon_or_s _ _ zenon_H18e); [ zenon_intro zenon_H113 | zenon_intro zenon_Hd7 ]. % 18.52/18.74 apply (zenon_L153_); trivial. % 18.52/18.74 apply (zenon_L101_); trivial. % 18.52/18.74 (* end of lemma zenon_L309_ *) % 18.52/18.74 assert (zenon_L310_ : (((op (e2) (e0)) = (e0))\/(((op (e2) (e1)) = (e0))\/(((op (e2) (e2)) = (e0))\/((op (e2) (e3)) = (e0))))) -> (~((op (e2) (e0)) = (e0))) -> (~((op (e2) (e1)) = (e0))) -> (~((op (e3) (e3)) = (e0))) -> (~((op (e2) (e2)) = (op (e3) (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) (e1)) = (e0)) -> ((op (e1) (e0)) = (e0)) -> (~((op (e1) (e0)) = (op (e1) (e3)))) -> (~((op (e3) (e1)) = (op (e3) (e3)))) -> (~((op (e3) (e0)) = (e0))) -> (((op (e3) (e0)) = (e0))\/(((op (e3) (e1)) = (e0))\/(((op (e3) (e2)) = (e0))\/((op (e3) (e3)) = (e0))))) -> (((op (e0) (e2)) = (e0))\/(((op (e1) (e2)) = (e0))\/(((op (e2) (e2)) = (e0))\/((op (e3) (e2)) = (e0))))) -> (~((op (e0) (e2)) = (e0))) -> (~((op (e1) (e2)) = (e0))) -> (((op (e0) (e2)) = (e1))\/(((op (e1) (e2)) = (e1))\/(((op (e2) (e2)) = (e1))\/((op (e3) (e2)) = (e1))))) -> (~((op (e0) (e0)) = (op (e0) (e2)))) -> ((op (e0) (e0)) = (e1)) -> (~((op (e2) (e0)) = (op (e2) (e2)))) -> ((op (e2) (e0)) = (e3)) -> (~((op (e2) (e2)) = (e2))) -> (~((op (e1) (e2)) = (op (e2) (e2)))) -> (~((op (e2) (e2)) = (op (e2) (e3)))) -> (((op (e2) (e2)) = (e0))\/(((op (e2) (e2)) = (e1))\/(((op (e2) (e2)) = (e2))\/((op (e2) (e2)) = (e3))))) -> ((op (e1) (e2)) = (e3)) -> (~((op (e3) (e0)) = (op (e3) (e2)))) -> ((op (e3) (e0)) = (e1)) -> False). % 18.52/18.74 do 0 intro. intros zenon_H2f zenon_H30 zenon_H31 zenon_H1ae zenon_H18f zenon_H67 zenon_H54 zenon_H49 zenon_H27 zenon_Hd8 zenon_H130 zenon_H40 zenon_H1ac zenon_H6a zenon_H75 zenon_H25 zenon_H139 zenon_H13c zenon_H7a zenon_H52 zenon_H3b zenon_H173 zenon_H2b zenon_H6d zenon_H1c4 zenon_H16c zenon_H6f zenon_Hac. % 18.52/18.74 apply (zenon_or_s _ _ zenon_H2f); [ zenon_intro zenon_H34 | zenon_intro zenon_H33 ]. % 18.52/18.74 exact (zenon_H30 zenon_H34). % 18.52/18.74 apply (zenon_or_s _ _ zenon_H33); [ zenon_intro zenon_H36 | zenon_intro zenon_H35 ]. % 18.52/18.74 exact (zenon_H31 zenon_H36). % 18.52/18.74 apply (zenon_or_s _ _ zenon_H35); [ zenon_intro zenon_H2c | zenon_intro zenon_H37 ]. % 18.52/18.74 apply (zenon_L299_); trivial. % 18.52/18.74 apply (zenon_or_s _ _ zenon_H6a); [ zenon_intro zenon_H48 | zenon_intro zenon_H6b ]. % 18.52/18.74 exact (zenon_H75 zenon_H48). % 18.52/18.74 apply (zenon_or_s _ _ zenon_H6b); [ zenon_intro zenon_H2a | zenon_intro zenon_H6c ]. % 18.52/18.74 exact (zenon_H25 zenon_H2a). % 18.52/18.74 apply (zenon_or_s _ _ zenon_H6c); [ zenon_intro zenon_H2c | zenon_intro zenon_H61 ]. % 18.52/18.74 apply (zenon_L18_); trivial. % 18.52/18.74 apply (zenon_or_s _ _ zenon_H139); [ zenon_intro zenon_H122 | zenon_intro zenon_H13a ]. % 18.52/18.74 apply (zenon_L92_); trivial. % 18.52/18.74 apply (zenon_or_s _ _ zenon_H13a); [ zenon_intro zenon_Hf0 | zenon_intro zenon_H13b ]. % 18.52/18.74 apply (zenon_L300_); trivial. % 18.52/18.74 apply (zenon_or_s _ _ zenon_H13b); [ zenon_intro zenon_Hf1 | zenon_intro zenon_Hba ]. % 18.52/18.74 apply (zenon_L156_); trivial. % 18.52/18.74 apply (zenon_L249_); trivial. % 18.52/18.74 (* end of lemma zenon_L310_ *) % 18.52/18.74 assert (zenon_L311_ : (((op (e1) (e0)) = (e1))\/(((op (e1) (e1)) = (e1))\/(((op (e1) (e2)) = (e1))\/((op (e1) (e3)) = (e1))))) -> (~((e0) = (e1))) -> (~((op (e1) (e1)) = (e1))) -> (((op (e1) (e0)) = (e3))\/(((op (e1) (e1)) = (e3))\/(((op (e1) (e2)) = (e3))\/((op (e1) (e3)) = (e3))))) -> (~((e0) = (e3))) -> (~((e1) = (e2))) -> (~((op (e0) (e2)) = (op (e1) (e2)))) -> ((op (e0) (e2)) = (e2)) -> (~((e2) = (e3))) -> (~((e0) = (e2))) -> (((op (e1) (e0)) = (e2))\/(((op (e1) (e1)) = (e2))\/(((op (e1) (e2)) = (e2))\/((op (e1) (e3)) = (e2))))) -> ((op (e3) (e0)) = (e1)) -> (~((op (e3) (e0)) = (op (e3) (e2)))) -> (((op (e2) (e2)) = (e0))\/(((op (e2) (e2)) = (e1))\/(((op (e2) (e2)) = (e2))\/((op (e2) (e2)) = (e3))))) -> (~((op (e2) (e2)) = (op (e2) (e3)))) -> (~((op (e1) (e2)) = (op (e2) (e2)))) -> (~((op (e2) (e2)) = (e2))) -> ((op (e2) (e0)) = (e3)) -> (~((op (e2) (e0)) = (op (e2) (e2)))) -> ((op (e0) (e0)) = (e1)) -> (~((op (e0) (e0)) = (op (e0) (e2)))) -> (((op (e0) (e2)) = (e1))\/(((op (e1) (e2)) = (e1))\/(((op (e2) (e2)) = (e1))\/((op (e3) (e2)) = (e1))))) -> (~((op (e1) (e2)) = (e0))) -> (~((op (e0) (e2)) = (e0))) -> (((op (e0) (e2)) = (e0))\/(((op (e1) (e2)) = (e0))\/(((op (e2) (e2)) = (e0))\/((op (e3) (e2)) = (e0))))) -> (((op (e3) (e0)) = (e0))\/(((op (e3) (e1)) = (e0))\/(((op (e3) (e2)) = (e0))\/((op (e3) (e3)) = (e0))))) -> (~((op (e3) (e0)) = (e0))) -> (~((op (e3) (e1)) = (op (e3) (e3)))) -> (~((op (e1) (e0)) = (op (e1) (e3)))) -> ((op (e1) (e0)) = (e0)) -> ((op (e0) (e1)) = (e0)) -> (~((op (e0) (e1)) = (op (e0) (e3)))) -> (((op (e0) (e3)) = (e0))\/(((op (e1) (e3)) = (e0))\/(((op (e2) (e3)) = (e0))\/((op (e3) (e3)) = (e0))))) -> (~((op (e2) (e2)) = (op (e3) (e2)))) -> (~((op (e3) (e3)) = (e0))) -> (~((op (e2) (e1)) = (e0))) -> (~((op (e2) (e0)) = (e0))) -> (((op (e2) (e0)) = (e0))\/(((op (e2) (e1)) = (e0))\/(((op (e2) (e2)) = (e0))\/((op (e2) (e3)) = (e0))))) -> (~((e1) = (e3))) -> False). % 18.52/18.74 do 0 intro. intros zenon_H128 zenon_Ha1 zenon_H10a zenon_H16f zenon_H9a zenon_H7c zenon_H195 zenon_H150 zenon_H12b zenon_H149 zenon_H18c zenon_Hac zenon_H6f zenon_H1c4 zenon_H6d zenon_H2b zenon_H173 zenon_H3b zenon_H52 zenon_H7a zenon_H13c zenon_H139 zenon_H25 zenon_H75 zenon_H6a zenon_H1ac zenon_H40 zenon_H130 zenon_Hd8 zenon_H27 zenon_H49 zenon_H54 zenon_H67 zenon_H18f zenon_H1ae zenon_H31 zenon_H30 zenon_H2f zenon_H95. % 18.52/18.74 apply (zenon_or_s _ _ zenon_H128); [ zenon_intro zenon_H9d | zenon_intro zenon_H129 ]. % 18.52/18.74 apply (zenon_L262_); trivial. % 18.52/18.74 apply (zenon_or_s _ _ zenon_H129); [ zenon_intro zenon_H10d | zenon_intro zenon_H12a ]. % 18.52/18.74 exact (zenon_H10a zenon_H10d). % 18.52/18.74 apply (zenon_or_s _ _ zenon_H12a); [ zenon_intro zenon_Hf0 | zenon_intro zenon_Hd6 ]. % 18.52/18.74 apply (zenon_L301_); trivial. % 18.52/18.74 apply (zenon_or_s _ _ zenon_H16f); [ zenon_intro zenon_H9e | zenon_intro zenon_H170 ]. % 18.52/18.74 apply (zenon_L263_); trivial. % 18.52/18.74 apply (zenon_or_s _ _ zenon_H170); [ zenon_intro zenon_H13f | zenon_intro zenon_H171 ]. % 18.52/18.74 apply (zenon_L309_); trivial. % 18.52/18.74 apply (zenon_or_s _ _ zenon_H171); [ zenon_intro zenon_H16c | zenon_intro zenon_Hdc ]. % 18.52/18.74 apply (zenon_L310_); trivial. % 18.52/18.74 apply (zenon_L83_); trivial. % 18.52/18.74 (* end of lemma zenon_L311_ *) % 18.52/18.74 assert (zenon_L312_ : ((op (e3) (e0)) = (e0)) -> ((op (e1) (e0)) = (e0)) -> (~((op (e1) (e0)) = (op (e3) (e0)))) -> False). % 18.52/18.74 do 0 intro. intros zenon_H44 zenon_H27 zenon_H1fa. % 18.52/18.74 elim (classic ((op (e3) (e0)) = (op (e3) (e0)))); [ zenon_intro zenon_H17c | zenon_intro zenon_H70 ]. % 18.52/18.74 cut (((op (e3) (e0)) = (op (e3) (e0))) = ((op (e1) (e0)) = (op (e3) (e0)))). % 18.52/18.74 intro zenon_D_pnotp. % 18.52/18.74 apply zenon_H1fa. % 18.52/18.74 rewrite <- zenon_D_pnotp. % 18.52/18.74 exact zenon_H17c. % 18.52/18.74 cut (((op (e3) (e0)) = (op (e3) (e0)))); [idtac | apply NNPP; zenon_intro zenon_H70]. % 18.52/18.74 cut (((op (e3) (e0)) = (op (e1) (e0)))); [idtac | apply NNPP; zenon_intro zenon_H1fb]. % 18.52/18.74 congruence. % 18.52/18.74 cut (((op (e3) (e0)) = (e0)) = ((op (e3) (e0)) = (op (e1) (e0)))). % 18.52/18.74 intro zenon_D_pnotp. % 18.52/18.74 apply zenon_H1fb. % 18.52/18.74 rewrite <- zenon_D_pnotp. % 18.52/18.74 exact zenon_H44. % 18.52/18.74 cut (((e0) = (op (e1) (e0)))); [idtac | apply NNPP; zenon_intro zenon_H1fc]. % 18.52/18.74 cut (((op (e3) (e0)) = (op (e3) (e0)))); [idtac | apply NNPP; zenon_intro zenon_H70]. % 18.52/18.74 congruence. % 18.52/18.74 apply zenon_H70. apply refl_equal. % 18.52/18.74 apply zenon_H1fc. apply sym_equal. exact zenon_H27. % 18.52/18.74 apply zenon_H70. apply refl_equal. % 18.52/18.74 apply zenon_H70. apply refl_equal. % 18.52/18.74 (* end of lemma zenon_L312_ *) % 18.52/18.74 assert (zenon_L313_ : ((~((op (e3) (e0)) = (e0)))\/((op (e3) (e0)) = (e0))) -> (~((op (e1) (e0)) = (op (e3) (e0)))) -> ((~((op (e3) (e2)) = (e0)))\/((op (e3) (e0)) = (e2))) -> (~((op (e2) (e2)) = (e2))) -> (((op (e2) (e2)) = (e0))\/(((op (e2) (e2)) = (e1))\/(((op (e2) (e2)) = (e2))\/((op (e2) (e2)) = (e3))))) -> (~((op (e3) (e0)) = (op (e3) (e3)))) -> (((op (e0) (e0)) = (e0))\/(((op (e0) (e1)) = (e0))\/(((op (e0) (e2)) = (e0))\/((op (e0) (e3)) = (e0))))) -> (~((op (e0) (e3)) = (e0))) -> (~((op (e2) (e0)) = (e0))) -> (~((op (e2) (e1)) = (e0))) -> (((op (e3) (e0)) = (e0))\/(((op (e3) (e1)) = (e0))\/(((op (e3) (e2)) = (e0))\/((op (e3) (e3)) = (e0))))) -> (~((op (e0) (e1)) = (op (e0) (e3)))) -> (~((op (e1) (e0)) = (op (e1) (e3)))) -> ((op (e1) (e0)) = (e0)) -> (~((op (e2) (e2)) = (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 (e0) (e2)) = (e0))\/(((op (e1) (e2)) = (e0))\/(((op (e2) (e2)) = (e0))\/((op (e3) (e2)) = (e0))))) -> (~((op (e1) (e2)) = (e0))) -> (~((op (e0) (e2)) = (e0))) -> (((op (e2) (e0)) = (e0))\/(((op (e2) (e1)) = (e0))\/(((op (e2) (e2)) = (e0))\/((op (e2) (e3)) = (e0))))) -> (~((op (e0) (e0)) = (e0))) -> (~((e1) = (e2))) -> ((op (e0) (e0)) = (e1)) -> (((op (e0) (e0)) = (e3))\/(((op (e0) (e1)) = (e3))\/(((op (e0) (e2)) = (e3))\/((op (e0) (e3)) = (e3))))) -> (~((e0) = (e1))) -> (~((op (e1) (e1)) = (e1))) -> (~((e0) = (e2))) -> (((op (e0) (e1)) = (e3))\/(((op (e1) (e1)) = (e3))\/(((op (e2) (e1)) = (e3))\/((op (e3) (e1)) = (e3))))) -> (~((op (e3) (e0)) = (op (e3) (e1)))) -> (~((e2) = (e3))) -> (((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 (e1) (e3)) = (op (e2) (e3)))) -> (~((op (e1) (e2)) = (op (e1) (e3)))) -> (~((op (e2) (e0)) = (op (e2) (e3)))) -> (((op (e2) (e3)) = (e0))\/(((op (e2) (e3)) = (e1))\/(((op (e2) (e3)) = (e2))\/((op (e2) (e3)) = (e3))))) -> (~((op (e1) (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))))) -> (~((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)) = (e2)) -> (~((op (e2) (e0)) = (op (e2) (e1)))) -> (((op (e3) (e0)) = (e1))\/(((op (e3) (e1)) = (e1))\/(((op (e3) (e2)) = (e1))\/((op (e3) (e3)) = (e1))))) -> (~((op (e1) (e3)) = (op (e3) (e3)))) -> (((op (e2) (e1)) = (e0))\/(((op (e2) (e1)) = (e1))\/(((op (e2) (e1)) = (e2))\/((op (e2) (e1)) = (e3))))) -> (~((op (e1) (e1)) = (op (e2) (e1)))) -> (~((op (e0) (e1)) = (op (e2) (e1)))) -> (~((op (e2) (e1)) = (op (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 (e1) (e0)) = (e2))\/(((op (e1) (e1)) = (e2))\/(((op (e1) (e2)) = (e2))\/((op (e1) (e3)) = (e2))))) -> (~((op (e0) (e3)) = (op (e1) (e3)))) -> ((op (e2) (e0)) = (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 (e1) (e0)) = (e3))\/(((op (e1) (e1)) = (e3))\/(((op (e1) (e2)) = (e3))\/((op (e1) (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 (e1) (e2)) = (op (e2) (e2)))) -> (~((op (e0) (e0)) = (op (e2) (e0)))) -> (~((op (e1) (e1)) = (op (e1) (e3)))) -> (~((op (e1) (e1)) = (op (e3) (e1)))) -> (~((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))))) -> (~((op (e2) (e0)) = (op (e2) (e2)))) -> (~((op (e3) (e0)) = (op (e3) (e2)))) -> (((op (e0) (e2)) = (e3))\/(((op (e1) (e2)) = (e3))\/(((op (e2) (e2)) = (e3))\/((op (e3) (e2)) = (e3))))) -> (~((op (e0) (e1)) = (op (e1) (e1)))) -> (~((e0) = (e3))) -> (~((e1) = (e3))) -> (((op (e0) (e3)) = (e2))\/(((op (e1) (e3)) = (e2))\/(((op (e2) (e3)) = (e2))\/((op (e3) (e3)) = (e2))))) -> (((op (e3) (e0)) = (e2))\/(((op (e3) (e1)) = (e2))\/(((op (e3) (e2)) = (e2))\/((op (e3) (e3)) = (e2))))) -> (((op (e3) (e2)) = (e0))\/(((op (e3) (e2)) = (e1))\/(((op (e3) (e2)) = (e2))\/((op (e3) (e2)) = (e3))))) -> (~((op (e3) (e2)) = (op (e3) (e3)))) -> (~((op (e2) (e2)) = (op (e3) (e2)))) -> (((op (e0) (e0)) = (e2))\/(((op (e0) (e1)) = (e2))\/(((op (e0) (e2)) = (e2))\/((op (e0) (e3)) = (e2))))) -> ((~((op (e3) (e3)) = (e0)))\/((op (e3) (e0)) = (e3))) -> (((op (e0) (e2)) = (e1))\/(((op (e1) (e2)) = (e1))\/(((op (e2) (e2)) = (e1))\/((op (e3) (e2)) = (e1))))) -> (~((op (e0) (e0)) = (op (e0) (e2)))) -> ((~((op (e3) (e1)) = (e0)))\/((op (e3) (e0)) = (e1))) -> False). % 18.52/18.75 do 0 intro. intros zenon_H184 zenon_H1fa zenon_H1a7 zenon_H173 zenon_H1c4 zenon_H71 zenon_H74 zenon_H76 zenon_H30 zenon_H31 zenon_H1ac zenon_H54 zenon_Hd8 zenon_H27 zenon_H6d zenon_H130 zenon_H67 zenon_H6a zenon_H25 zenon_H75 zenon_H2f zenon_H3f zenon_H7c zenon_H7a zenon_H168 zenon_Ha1 zenon_H10a zenon_H149 zenon_H1a5 zenon_H1cf zenon_H12b zenon_H136 zenon_Hdf zenon_Hdb zenon_H124 zenon_H5b zenon_H11f zenon_H115 zenon_He2 zenon_H128 zenon_H195 zenon_H1d8 zenon_Hee zenon_H1f0 zenon_He8 zenon_Hd5 zenon_H1cc zenon_H13e zenon_H17e zenon_Haf zenon_H101 zenon_Hc2 zenon_Hf3 zenon_H18c zenon_H1d zenon_H3b zenon_H133 zenon_H106 zenon_H16f zenon_H109 zenon_He4 zenon_H2b zenon_H39 zenon_H57 zenon_H160 zenon_H14f zenon_H102 zenon_H165 zenon_H52 zenon_H6f zenon_H1a6 zenon_H10e zenon_H9a zenon_H95 zenon_H145 zenon_H153 zenon_H191 zenon_H62 zenon_H18f zenon_H183 zenon_H1ec zenon_H139 zenon_H13c zenon_H1ed. % 18.52/18.75 apply (zenon_or_s _ _ zenon_H184); [ zenon_intro zenon_H40 | zenon_intro zenon_H44 ]. % 18.52/18.75 apply (zenon_or_s _ _ zenon_H1ed); [ zenon_intro zenon_H1ad | zenon_intro zenon_Hac ]. % 18.52/18.75 apply (zenon_L305_); trivial. % 18.52/18.75 apply (zenon_or_s _ _ zenon_H1a7); [ zenon_intro zenon_H18b | zenon_intro zenon_H148 ]. % 18.52/18.75 apply (zenon_L271_); trivial. % 18.52/18.75 apply (zenon_or_s _ _ zenon_H1ec); [ zenon_intro zenon_H1ae | zenon_intro zenon_H15e ]. % 18.52/18.75 apply (zenon_or_s _ _ zenon_H74); [ zenon_intro zenon_H42 | zenon_intro zenon_H77 ]. % 18.52/18.75 exact (zenon_H3f zenon_H42). % 18.52/18.75 apply (zenon_or_s _ _ zenon_H77); [ zenon_intro zenon_H49 | zenon_intro zenon_H78 ]. % 18.52/18.75 apply (zenon_or_s _ _ zenon_H183); [ zenon_intro zenon_H7b | zenon_intro zenon_H186 ]. % 18.52/18.75 apply (zenon_L308_); trivial. % 18.52/18.75 apply (zenon_or_s _ _ zenon_H186); [ zenon_intro zenon_H10f | zenon_intro zenon_H187 ]. % 18.52/18.75 apply (zenon_L302_); trivial. % 18.52/18.75 apply (zenon_or_s _ _ zenon_H187); [ zenon_intro zenon_H150 | zenon_intro zenon_Hcd ]. % 18.52/18.75 apply (zenon_L311_); trivial. % 18.52/18.75 apply (zenon_L304_); trivial. % 18.52/18.75 apply (zenon_or_s _ _ zenon_H78); [ zenon_intro zenon_H48 | zenon_intro zenon_H1e ]. % 18.52/18.75 exact (zenon_H75 zenon_H48). % 18.52/18.75 exact (zenon_H76 zenon_H1e). % 18.52/18.75 apply (zenon_L109_); trivial. % 18.52/18.75 apply (zenon_L312_); trivial. % 18.52/18.75 (* end of lemma zenon_L313_ *) % 18.52/18.75 assert (zenon_L314_ : (((op (e0) (e0)) = (e3))\/(((op (e1) (e0)) = (e3))\/(((op (e2) (e0)) = (e3))\/((op (e3) (e0)) = (e3))))) -> ((~((op (e3) (e1)) = (e0)))\/((op (e3) (e0)) = (e1))) -> (~((op (e0) (e0)) = (op (e0) (e2)))) -> (((op (e0) (e2)) = (e1))\/(((op (e1) (e2)) = (e1))\/(((op (e2) (e2)) = (e1))\/((op (e3) (e2)) = (e1))))) -> ((~((op (e3) (e3)) = (e0)))\/((op (e3) (e0)) = (e3))) -> (((op (e0) (e0)) = (e2))\/(((op (e0) (e1)) = (e2))\/(((op (e0) (e2)) = (e2))\/((op (e0) (e3)) = (e2))))) -> (~((op (e2) (e2)) = (op (e3) (e2)))) -> (~((op (e3) (e2)) = (op (e3) (e3)))) -> (((op (e3) (e2)) = (e0))\/(((op (e3) (e2)) = (e1))\/(((op (e3) (e2)) = (e2))\/((op (e3) (e2)) = (e3))))) -> (((op (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))))) -> (~((e1) = (e3))) -> (~((e0) = (e3))) -> (~((op (e0) (e1)) = (op (e1) (e1)))) -> (((op (e0) (e2)) = (e3))\/(((op (e1) (e2)) = (e3))\/(((op (e2) (e2)) = (e3))\/((op (e3) (e2)) = (e3))))) -> (~((op (e3) (e0)) = (op (e3) (e2)))) -> (~((op (e2) (e0)) = (op (e2) (e2)))) -> (((op (e3) (e0)) = (e3))\/(((op (e3) (e1)) = (e3))\/(((op (e3) (e2)) = (e3))\/((op (e3) (e3)) = (e3))))) -> (~((op (e3) (e3)) = (e3))) -> (~((op (e0) (e2)) = (op (e3) (e2)))) -> (~((op (e1) (e1)) = (op (e3) (e1)))) -> (~((op (e1) (e1)) = (op (e1) (e3)))) -> (~((op (e0) (e0)) = (op (e2) (e0)))) -> (~((op (e1) (e2)) = (op (e2) (e2)))) -> (((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 (e1) (e0)) = (e3))\/(((op (e1) (e1)) = (e3))\/(((op (e1) (e2)) = (e3))\/((op (e1) (e3)) = (e3))))) -> (((op (e2) (e0)) = (e1))\/(((op (e2) (e1)) = (e1))\/(((op (e2) (e2)) = (e1))\/((op (e2) (e3)) = (e1))))) -> (((op (e0) (e3)) = (e1))\/(((op (e1) (e3)) = (e1))\/(((op (e2) (e3)) = (e1))\/((op (e3) (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 (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 (e2) (e1)) = (op (e3) (e1)))) -> (~((op (e0) (e1)) = (op (e2) (e1)))) -> (~((op (e1) (e1)) = (op (e2) (e1)))) -> (((op (e2) (e1)) = (e0))\/(((op (e2) (e1)) = (e1))\/(((op (e2) (e1)) = (e2))\/((op (e2) (e1)) = (e3))))) -> (~((op (e1) (e3)) = (op (e3) (e3)))) -> (((op (e3) (e0)) = (e1))\/(((op (e3) (e1)) = (e1))\/(((op (e3) (e2)) = (e1))\/((op (e3) (e3)) = (e1))))) -> (~((op (e2) (e0)) = (op (e2) (e1)))) -> ((op (e2) (e0)) = (e2)) -> (((op (e0) (e1)) = (e2))\/(((op (e1) (e1)) = (e2))\/(((op (e2) (e1)) = (e2))\/((op (e3) (e1)) = (e2))))) -> (~((op (e0) (e2)) = (op (e1) (e2)))) -> (((op (e1) (e0)) = (e1))\/(((op (e1) (e1)) = (e1))\/(((op (e1) (e2)) = (e1))\/((op (e1) (e3)) = (e1))))) -> (~((op (e0) (e3)) = (op (e2) (e3)))) -> (~((op (e1) (e2)) = (op (e3) (e2)))) -> (((op (e2) (e3)) = (e0))\/(((op (e2) (e3)) = (e1))\/(((op (e2) (e3)) = (e2))\/((op (e2) (e3)) = (e3))))) -> (~((op (e2) (e0)) = (op (e2) (e3)))) -> (~((op (e1) (e2)) = (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) (e3)) = (e3))\/(((op (e1) (e3)) = (e3))\/(((op (e2) (e3)) = (e3))\/((op (e3) (e3)) = (e3))))) -> (~((op (e3) (e0)) = (op (e3) (e1)))) -> (((op (e0) (e1)) = (e3))\/(((op (e1) (e1)) = (e3))\/(((op (e2) (e1)) = (e3))\/((op (e3) (e1)) = (e3))))) -> (~((e0) = (e2))) -> (~((op (e1) (e1)) = (e1))) -> (~((e0) = (e1))) -> (((op (e0) (e0)) = (e3))\/(((op (e0) (e1)) = (e3))\/(((op (e0) (e2)) = (e3))\/((op (e0) (e3)) = (e3))))) -> ((op (e0) (e0)) = (e1)) -> (~((e1) = (e2))) -> (~((op (e0) (e0)) = (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 (e0) (e2)) = (e0))\/(((op (e1) (e2)) = (e0))\/(((op (e2) (e2)) = (e0))\/((op (e3) (e2)) = (e0))))) -> (((op (e0) (e3)) = (e0))\/(((op (e1) (e3)) = (e0))\/(((op (e2) (e3)) = (e0))\/((op (e3) (e3)) = (e0))))) -> (~((op (e3) (e1)) = (op (e3) (e3)))) -> (~((op (e2) (e2)) = (op (e2) (e3)))) -> ((op (e1) (e0)) = (e0)) -> (~((op (e1) (e0)) = (op (e1) (e3)))) -> (~((op (e0) (e1)) = (op (e0) (e3)))) -> (((op (e3) (e0)) = (e0))\/(((op (e3) (e1)) = (e0))\/(((op (e3) (e2)) = (e0))\/((op (e3) (e3)) = (e0))))) -> (~((op (e2) (e1)) = (e0))) -> (~((op (e2) (e0)) = (e0))) -> (~((op (e0) (e3)) = (e0))) -> (((op (e0) (e0)) = (e0))\/(((op (e0) (e1)) = (e0))\/(((op (e0) (e2)) = (e0))\/((op (e0) (e3)) = (e0))))) -> (~((op (e3) (e0)) = (op (e3) (e3)))) -> (((op (e2) (e2)) = (e0))\/(((op (e2) (e2)) = (e1))\/(((op (e2) (e2)) = (e2))\/((op (e2) (e2)) = (e3))))) -> (~((op (e2) (e2)) = (e2))) -> ((~((op (e3) (e2)) = (e0)))\/((op (e3) (e0)) = (e2))) -> (~((op (e1) (e0)) = (op (e3) (e0)))) -> ((~((op (e3) (e0)) = (e0)))\/((op (e3) (e0)) = (e0))) -> ((op (e3) (e0)) = (e2)) -> (~((e2) = (e3))) -> False). % 18.52/18.75 do 0 intro. intros zenon_H1e0 zenon_H1ed zenon_H13c zenon_H139 zenon_H1ec zenon_H183 zenon_H18f zenon_H62 zenon_H191 zenon_H153 zenon_H145 zenon_H95 zenon_H9a zenon_H10e zenon_H1a6 zenon_H6f zenon_H52 zenon_H165 zenon_H102 zenon_H14f zenon_H160 zenon_H57 zenon_H39 zenon_H2b zenon_He4 zenon_H109 zenon_H16f zenon_H106 zenon_H133 zenon_H1d zenon_H18c zenon_Hf3 zenon_Hc2 zenon_H101 zenon_Haf zenon_H17e zenon_H13e zenon_H1cc zenon_Hd5 zenon_He8 zenon_H1f0 zenon_Hee zenon_H1d8 zenon_H195 zenon_H128 zenon_He2 zenon_H115 zenon_H11f zenon_H5b zenon_H124 zenon_Hdb zenon_Hdf zenon_H136 zenon_H1cf zenon_H1a5 zenon_H149 zenon_H10a zenon_Ha1 zenon_H168 zenon_H7a zenon_H7c zenon_H3f zenon_H2f zenon_H75 zenon_H25 zenon_H6a zenon_H67 zenon_H130 zenon_H6d zenon_H27 zenon_Hd8 zenon_H54 zenon_H1ac zenon_H31 zenon_H30 zenon_H76 zenon_H74 zenon_H71 zenon_H1c4 zenon_H173 zenon_H1a7 zenon_H1fa zenon_H184 zenon_H148 zenon_H12b. % 18.52/18.75 apply (zenon_or_s _ _ zenon_H1e0); [ zenon_intro zenon_H3a | zenon_intro zenon_H1e1 ]. % 18.52/18.75 apply (zenon_L35_); trivial. % 18.52/18.75 apply (zenon_or_s _ _ zenon_H1e1); [ zenon_intro zenon_H9e | zenon_intro zenon_H1e2 ]. % 18.52/18.75 apply (zenon_L263_); trivial. % 18.52/18.75 apply (zenon_or_s _ _ zenon_H1e2); [ zenon_intro zenon_H3b | zenon_intro zenon_H15e ]. % 18.52/18.75 apply (zenon_L313_); trivial. % 18.52/18.75 apply (zenon_L109_); trivial. % 18.52/18.75 (* end of lemma zenon_L314_ *) % 18.52/18.75 assert (zenon_L315_ : ((op (e0) (e0)) = (e1)) -> (~((e0) = (e3))) -> ((~((op (e3) (e0)) = (e0)))\/((op (e3) (e0)) = (e0))) -> (~((op (e1) (e0)) = (op (e3) (e0)))) -> ((~((op (e3) (e2)) = (e0)))\/((op (e3) (e0)) = (e2))) -> (~((op (e2) (e2)) = (e2))) -> (((op (e2) (e2)) = (e0))\/(((op (e2) (e2)) = (e1))\/(((op (e2) (e2)) = (e2))\/((op (e2) (e2)) = (e3))))) -> (~((op (e3) (e0)) = (op (e3) (e3)))) -> (~((e1) = (e2))) -> (((op (e0) (e0)) = (e3))\/(((op (e0) (e1)) = (e3))\/(((op (e0) (e2)) = (e3))\/((op (e0) (e3)) = (e3))))) -> (~((e0) = (e1))) -> (~((op (e1) (e1)) = (e1))) -> (~((e0) = (e2))) -> (((op (e0) (e1)) = (e3))\/(((op (e1) (e1)) = (e3))\/(((op (e2) (e1)) = (e3))\/((op (e3) (e1)) = (e3))))) -> (~((op (e3) (e0)) = (op (e3) (e1)))) -> (~((e2) = (e3))) -> (((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 (e1) (e3)) = (op (e2) (e3)))) -> (~((op (e1) (e2)) = (op (e1) (e3)))) -> (~((op (e2) (e0)) = (op (e2) (e3)))) -> (((op (e2) (e3)) = (e0))\/(((op (e2) (e3)) = (e1))\/(((op (e2) (e3)) = (e2))\/((op (e2) (e3)) = (e3))))) -> (~((op (e1) (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))))) -> (~((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)) = (e2)) -> (~((op (e2) (e0)) = (op (e2) (e1)))) -> (((op (e3) (e0)) = (e1))\/(((op (e3) (e1)) = (e1))\/(((op (e3) (e2)) = (e1))\/((op (e3) (e3)) = (e1))))) -> (~((op (e1) (e3)) = (op (e3) (e3)))) -> (((op (e2) (e1)) = (e0))\/(((op (e2) (e1)) = (e1))\/(((op (e2) (e1)) = (e2))\/((op (e2) (e1)) = (e3))))) -> (~((op (e1) (e1)) = (op (e2) (e1)))) -> (~((op (e0) (e1)) = (op (e2) (e1)))) -> (~((op (e2) (e1)) = (op (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 (e1) (e0)) = (e2))\/(((op (e1) (e1)) = (e2))\/(((op (e1) (e2)) = (e2))\/((op (e1) (e3)) = (e2))))) -> (~((op (e0) (e3)) = (op (e1) (e3)))) -> (((op (e0) (e3)) = (e1))\/(((op (e1) (e3)) = (e1))\/(((op (e2) (e3)) = (e1))\/((op (e3) (e3)) = (e1))))) -> (((op (e2) (e0)) = (e1))\/(((op (e2) (e1)) = (e1))\/(((op (e2) (e2)) = (e1))\/((op (e2) (e3)) = (e1))))) -> (((op (e1) (e0)) = (e3))\/(((op (e1) (e1)) = (e3))\/(((op (e1) (e2)) = (e3))\/((op (e1) (e3)) = (e3))))) -> (((op (e0) (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 (e1) (e2)) = (op (e2) (e2)))) -> (~((op (e0) (e0)) = (op (e2) (e0)))) -> (~((op (e1) (e1)) = (op (e1) (e3)))) -> (~((op (e1) (e1)) = (op (e3) (e1)))) -> (~((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))))) -> (~((op (e2) (e0)) = (op (e2) (e2)))) -> (~((op (e3) (e0)) = (op (e3) (e2)))) -> (((op (e0) (e2)) = (e3))\/(((op (e1) (e2)) = (e3))\/(((op (e2) (e2)) = (e3))\/((op (e3) (e2)) = (e3))))) -> (~((op (e0) (e1)) = (op (e1) (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))))) -> (((op (e3) (e2)) = (e0))\/(((op (e3) (e2)) = (e1))\/(((op (e3) (e2)) = (e2))\/((op (e3) (e2)) = (e3))))) -> (~((op (e3) (e2)) = (op (e3) (e3)))) -> (~((op (e2) (e2)) = (op (e3) (e2)))) -> (((op (e0) (e0)) = (e2))\/(((op (e0) (e1)) = (e2))\/(((op (e0) (e2)) = (e2))\/((op (e0) (e3)) = (e2))))) -> (((op (e0) (e2)) = (e1))\/(((op (e1) (e2)) = (e1))\/(((op (e2) (e2)) = (e1))\/((op (e3) (e2)) = (e1))))) -> (~((op (e0) (e0)) = (op (e0) (e2)))) -> ((~((op (e3) (e1)) = (e0)))\/((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 (e0) (e1)) = (e0))\/(((op (e0) (e2)) = (e0))\/((op (e0) (e3)) = (e0))))) -> (~((op (e0) (e3)) = (e0))) -> (~((op (e2) (e0)) = (e0))) -> (~((op (e2) (e1)) = (e0))) -> (((op (e3) (e0)) = (e0))\/(((op (e3) (e1)) = (e0))\/(((op (e3) (e2)) = (e0))\/((op (e3) (e3)) = (e0))))) -> (~((op (e0) (e1)) = (op (e0) (e3)))) -> (~((op (e1) (e0)) = (op (e1) (e3)))) -> ((op (e1) (e0)) = (e0)) -> (~((op (e2) (e2)) = (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 (e3) (e0)) = (e0))) -> (((op (e0) (e2)) = (e0))\/(((op (e1) (e2)) = (e0))\/(((op (e2) (e2)) = (e0))\/((op (e3) (e2)) = (e0))))) -> (~((op (e1) (e2)) = (e0))) -> (~((op (e0) (e2)) = (e0))) -> (((op (e2) (e0)) = (e0))\/(((op (e2) (e1)) = (e0))\/(((op (e2) (e2)) = (e0))\/((op (e2) (e3)) = (e0))))) -> (~((op (e0) (e0)) = (e0))) -> (~((e1) = (e3))) -> ((op (e3) (e0)) = (e1)) -> ((~((op (e3) (e3)) = (e0)))\/((op (e3) (e0)) = (e3))) -> False). % 18.52/18.75 do 0 intro. intros zenon_H7a zenon_H9a zenon_H184 zenon_H1fa zenon_H1a7 zenon_H173 zenon_H1c4 zenon_H71 zenon_H7c zenon_H168 zenon_Ha1 zenon_H10a zenon_H149 zenon_H1a5 zenon_H1cf zenon_H12b zenon_H136 zenon_Hdf zenon_Hdb zenon_H124 zenon_H5b zenon_H11f zenon_H115 zenon_He2 zenon_H128 zenon_H195 zenon_H1d8 zenon_Hee zenon_H1f0 zenon_He8 zenon_Hd5 zenon_H1cc zenon_H13e zenon_H17e zenon_Haf zenon_H101 zenon_Hc2 zenon_Hf3 zenon_H18c zenon_H1d zenon_H133 zenon_H106 zenon_H16f zenon_H109 zenon_He4 zenon_H2b zenon_H39 zenon_H57 zenon_H160 zenon_H14f zenon_H102 zenon_H165 zenon_H52 zenon_H6f zenon_H1a6 zenon_H10e zenon_H145 zenon_H153 zenon_H191 zenon_H62 zenon_H18f zenon_H183 zenon_H139 zenon_H13c zenon_H1ed zenon_H1e0 zenon_H74 zenon_H76 zenon_H30 zenon_H31 zenon_H1ac zenon_H54 zenon_Hd8 zenon_H27 zenon_H6d zenon_H130 zenon_H67 zenon_H40 zenon_H6a zenon_H25 zenon_H75 zenon_H2f zenon_H3f zenon_H95 zenon_Hac zenon_H1ec. % 18.52/18.75 apply (zenon_or_s _ _ zenon_H1a7); [ zenon_intro zenon_H18b | zenon_intro zenon_H148 ]. % 18.52/18.75 apply (zenon_L271_); trivial. % 18.52/18.75 apply (zenon_L314_); trivial. % 18.52/18.75 (* end of lemma zenon_L315_ *) % 18.52/18.75 assert (zenon_L316_ : ((~((op (e3) (e3)) = (e0)))\/((op (e3) (e0)) = (e3))) -> (~((e1) = (e3))) -> (~((op (e0) (e0)) = (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 (e0) (e2)) = (e0))\/(((op (e1) (e2)) = (e0))\/(((op (e2) (e2)) = (e0))\/((op (e3) (e2)) = (e0))))) -> (~((op (e3) (e0)) = (e0))) -> (((op (e0) (e3)) = (e0))\/(((op (e1) (e3)) = (e0))\/(((op (e2) (e3)) = (e0))\/((op (e3) (e3)) = (e0))))) -> (~((op (e3) (e1)) = (op (e3) (e3)))) -> (~((op (e2) (e2)) = (op (e2) (e3)))) -> ((op (e1) (e0)) = (e0)) -> (~((op (e1) (e0)) = (op (e1) (e3)))) -> (~((op (e0) (e1)) = (op (e0) (e3)))) -> (((op (e3) (e0)) = (e0))\/(((op (e3) (e1)) = (e0))\/(((op (e3) (e2)) = (e0))\/((op (e3) (e3)) = (e0))))) -> (~((op (e2) (e1)) = (e0))) -> (~((op (e2) (e0)) = (e0))) -> (~((op (e0) (e3)) = (e0))) -> (((op (e0) (e0)) = (e0))\/(((op (e0) (e1)) = (e0))\/(((op (e0) (e2)) = (e0))\/((op (e0) (e3)) = (e0))))) -> (((op (e0) (e0)) = (e3))\/(((op (e1) (e0)) = (e3))\/(((op (e2) (e0)) = (e3))\/((op (e3) (e0)) = (e3))))) -> ((~((op (e3) (e1)) = (e0)))\/((op (e3) (e0)) = (e1))) -> (~((op (e0) (e0)) = (op (e0) (e2)))) -> (((op (e0) (e2)) = (e1))\/(((op (e1) (e2)) = (e1))\/(((op (e2) (e2)) = (e1))\/((op (e3) (e2)) = (e1))))) -> (((op (e0) (e0)) = (e2))\/(((op (e0) (e1)) = (e2))\/(((op (e0) (e2)) = (e2))\/((op (e0) (e3)) = (e2))))) -> (~((op (e2) (e2)) = (op (e3) (e2)))) -> (~((op (e3) (e2)) = (op (e3) (e3)))) -> (((op (e3) (e2)) = (e0))\/(((op (e3) (e2)) = (e1))\/(((op (e3) (e2)) = (e2))\/((op (e3) (e2)) = (e3))))) -> (((op (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) (e1)) = (op (e1) (e1)))) -> (((op (e0) (e2)) = (e3))\/(((op (e1) (e2)) = (e3))\/(((op (e2) (e2)) = (e3))\/((op (e3) (e2)) = (e3))))) -> (~((op (e3) (e0)) = (op (e3) (e2)))) -> (~((op (e2) (e0)) = (op (e2) (e2)))) -> (((op (e3) (e0)) = (e3))\/(((op (e3) (e1)) = (e3))\/(((op (e3) (e2)) = (e3))\/((op (e3) (e3)) = (e3))))) -> (~((op (e3) (e3)) = (e3))) -> (~((op (e0) (e2)) = (op (e3) (e2)))) -> (~((op (e1) (e1)) = (op (e3) (e1)))) -> (~((op (e1) (e1)) = (op (e1) (e3)))) -> (~((op (e0) (e0)) = (op (e2) (e0)))) -> (~((op (e1) (e2)) = (op (e2) (e2)))) -> (((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 (e1) (e0)) = (e3))\/(((op (e1) (e1)) = (e3))\/(((op (e1) (e2)) = (e3))\/((op (e1) (e3)) = (e3))))) -> (((op (e2) (e0)) = (e1))\/(((op (e2) (e1)) = (e1))\/(((op (e2) (e2)) = (e1))\/((op (e2) (e3)) = (e1))))) -> (((op (e0) (e3)) = (e1))\/(((op (e1) (e3)) = (e1))\/(((op (e2) (e3)) = (e1))\/((op (e3) (e3)) = (e1))))) -> (~((op (e0) (e3)) = (op (e1) (e3)))) -> (((op (e1) (e0)) = (e2))\/(((op (e1) (e1)) = (e2))\/(((op (e1) (e2)) = (e2))\/((op (e1) (e3)) = (e2))))) -> (~((op (e0) (e3)) = (op (e3) (e3)))) -> (((op (e3) (e3)) = (e0))\/(((op (e3) (e3)) = (e1))\/(((op (e3) (e3)) = (e2))\/((op (e3) (e3)) = (e3))))) -> (~((op (e0) (e1)) = (op (e2) (e1)))) -> (~((op (e1) (e1)) = (op (e2) (e1)))) -> (((op (e2) (e1)) = (e0))\/(((op (e2) (e1)) = (e1))\/(((op (e2) (e1)) = (e2))\/((op (e2) (e1)) = (e3))))) -> (~((op (e1) (e3)) = (op (e3) (e3)))) -> (((op (e3) (e0)) = (e1))\/(((op (e3) (e1)) = (e1))\/(((op (e3) (e2)) = (e1))\/((op (e3) (e3)) = (e1))))) -> (~((op (e2) (e0)) = (op (e2) (e1)))) -> (((op (e0) (e1)) = (e2))\/(((op (e1) (e1)) = (e2))\/(((op (e2) (e1)) = (e2))\/((op (e3) (e1)) = (e2))))) -> (~((op (e0) (e2)) = (op (e1) (e2)))) -> (((op (e1) (e0)) = (e1))\/(((op (e1) (e1)) = (e1))\/(((op (e1) (e2)) = (e1))\/((op (e1) (e3)) = (e1))))) -> (~((op (e1) (e2)) = (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) (e3)) = (e3))\/(((op (e1) (e3)) = (e3))\/(((op (e2) (e3)) = (e3))\/((op (e3) (e3)) = (e3))))) -> (~((e2) = (e3))) -> (~((op (e3) (e0)) = (op (e3) (e1)))) -> (((op (e0) (e1)) = (e3))\/(((op (e1) (e1)) = (e3))\/(((op (e2) (e1)) = (e3))\/((op (e3) (e1)) = (e3))))) -> (~((e0) = (e2))) -> (~((op (e1) (e1)) = (e1))) -> (~((e0) = (e1))) -> (((op (e0) (e0)) = (e3))\/(((op (e0) (e1)) = (e3))\/(((op (e0) (e2)) = (e3))\/((op (e0) (e3)) = (e3))))) -> (~((e1) = (e2))) -> (~((op (e3) (e0)) = (op (e3) (e3)))) -> (((op (e2) (e2)) = (e0))\/(((op (e2) (e2)) = (e1))\/(((op (e2) (e2)) = (e2))\/((op (e2) (e2)) = (e3))))) -> (~((op (e2) (e2)) = (e2))) -> ((~((op (e3) (e2)) = (e0)))\/((op (e3) (e0)) = (e2))) -> (~((op (e1) (e0)) = (op (e3) (e0)))) -> ((~((op (e3) (e0)) = (e0)))\/((op (e3) (e0)) = (e0))) -> (~((e0) = (e3))) -> ((op (e0) (e0)) = (e1)) -> (~((op (e2) (e1)) = (op (e3) (e1)))) -> ((op (e2) (e1)) = (e1)) -> ((op (e1) (e2)) = (e1)) -> (~((op (e1) (e2)) = (op (e3) (e2)))) -> (((op (e2) (e3)) = (e0))\/(((op (e2) (e3)) = (e1))\/(((op (e2) (e3)) = (e2))\/((op (e2) (e3)) = (e3))))) -> ((op (e1) (e3)) = (e2)) -> (~((op (e2) (e3)) = (op (e3) (e3)))) -> (~((op (e2) (e0)) = (op (e2) (e3)))) -> ((op (e2) (e0)) = (e2)) -> (~((op (e0) (e3)) = (op (e2) (e3)))) -> ((op (e0) (e3)) = (e3)) -> False). % 18.52/18.75 do 0 intro. intros zenon_H1ec zenon_H95 zenon_H3f zenon_H2f zenon_H75 zenon_H25 zenon_H6a zenon_H40 zenon_H67 zenon_H130 zenon_H6d zenon_H27 zenon_Hd8 zenon_H54 zenon_H1ac zenon_H31 zenon_H30 zenon_H76 zenon_H74 zenon_H1e0 zenon_H1ed zenon_H13c zenon_H139 zenon_H183 zenon_H18f zenon_H62 zenon_H191 zenon_H153 zenon_H145 zenon_H10e zenon_H1a6 zenon_H6f zenon_H52 zenon_H165 zenon_H102 zenon_H14f zenon_H160 zenon_H57 zenon_H39 zenon_H2b zenon_He4 zenon_H109 zenon_H16f zenon_H106 zenon_H133 zenon_H1d zenon_H18c zenon_Hc2 zenon_H101 zenon_H17e zenon_H13e zenon_H1cc zenon_Hd5 zenon_He8 zenon_H1f0 zenon_H1d8 zenon_H195 zenon_H128 zenon_H124 zenon_Hdb zenon_Hdf zenon_H136 zenon_H12b zenon_H1cf zenon_H1a5 zenon_H149 zenon_H10a zenon_Ha1 zenon_H168 zenon_H7c zenon_H71 zenon_H1c4 zenon_H173 zenon_H1a7 zenon_H1fa zenon_H184 zenon_H9a zenon_H7a zenon_Haf zenon_Ha5 zenon_Hf0 zenon_H115 zenon_H11f zenon_Hd7 zenon_Hf3 zenon_H5b zenon_Hee zenon_He2 zenon_He3. % 18.52/18.75 apply (zenon_or_s _ _ zenon_He8); [ zenon_intro zenon_Hac | zenon_intro zenon_Heb ]. % 18.52/18.75 apply (zenon_L315_); trivial. % 18.52/18.75 apply (zenon_or_s _ _ zenon_Heb); [ zenon_intro zenon_Hae | zenon_intro zenon_Hec ]. % 18.52/18.75 apply (zenon_L42_); trivial. % 18.52/18.75 apply (zenon_or_s _ _ zenon_Hec); [ zenon_intro zenon_Hba | zenon_intro zenon_Hc4 ]. % 18.52/18.75 apply (zenon_L69_); trivial. % 18.52/18.75 apply (zenon_L74_); trivial. % 18.52/18.75 (* end of lemma zenon_L316_ *) % 18.52/18.75 assert (zenon_L317_ : (~((op (e0) (e2)) = (op (e3) (e2)))) -> ((op (e0) (e2)) = (e1)) -> ((op (e3) (e2)) = (e1)) -> False). % 18.52/18.75 do 0 intro. intros zenon_H14f zenon_H122 zenon_Hba. % 18.52/18.75 cut (((op (e0) (e2)) = (e1)) = ((op (e0) (e2)) = (op (e3) (e2)))). % 18.52/18.75 intro zenon_D_pnotp. % 18.52/18.75 apply zenon_H14f. % 18.52/18.75 rewrite <- zenon_D_pnotp. % 18.52/18.75 exact zenon_H122. % 18.52/18.75 cut (((e1) = (op (e3) (e2)))); [idtac | apply NNPP; zenon_intro zenon_H116]. % 18.52/18.75 cut (((op (e0) (e2)) = (op (e0) (e2)))); [idtac | apply NNPP; zenon_intro zenon_H4c]. % 18.52/18.75 congruence. % 18.52/18.75 apply zenon_H4c. apply refl_equal. % 18.52/18.75 apply zenon_H116. apply sym_equal. exact zenon_Hba. % 18.52/18.75 (* end of lemma zenon_L317_ *) % 18.52/18.75 assert (zenon_L318_ : (((op (e0) (e2)) = (e0))\/(((op (e0) (e2)) = (e1))\/(((op (e0) (e2)) = (e2))\/((op (e0) (e2)) = (e3))))) -> (~((op (e0) (e2)) = (e0))) -> ((op (e3) (e2)) = (e1)) -> (~((op (e0) (e2)) = (op (e3) (e2)))) -> (~((e1) = (e2))) -> ((op (e1) (e3)) = (e1)) -> (~((op (e0) (e2)) = (op (e1) (e2)))) -> ((op (e1) (e1)) = (e3)) -> (~((e2) = (e3))) -> ((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)) = (op (e2) (e2)))) -> ((op (e2) (e2)) = (e3)) -> False). % 18.52/18.75 do 0 intro. intros zenon_H1ba zenon_H75 zenon_Hba zenon_H14f zenon_H7c zenon_Hd6 zenon_H195 zenon_H13f zenon_H12b zenon_H27 zenon_H149 zenon_H18c zenon_Ha8 zenon_Haa. % 18.52/18.75 apply (zenon_or_s _ _ zenon_H1ba); [ zenon_intro zenon_H48 | zenon_intro zenon_H1bb ]. % 18.52/18.75 exact (zenon_H75 zenon_H48). % 18.52/18.75 apply (zenon_or_s _ _ zenon_H1bb); [ zenon_intro zenon_H122 | zenon_intro zenon_H1bc ]. % 18.52/18.75 apply (zenon_L317_); trivial. % 18.52/18.75 apply (zenon_or_s _ _ zenon_H1bc); [ zenon_intro zenon_H150 | zenon_intro zenon_Ha9 ]. % 18.52/18.75 apply (zenon_L309_); trivial. % 18.52/18.75 apply (zenon_L40_); trivial. % 18.52/18.75 (* end of lemma zenon_L318_ *) % 18.52/18.75 assert (zenon_L319_ : (((op (e1) (e0)) = (e2))\/(((op (e1) (e1)) = (e2))\/(((op (e1) (e2)) = (e2))\/((op (e1) (e3)) = (e2))))) -> (~((e0) = (e2))) -> (~((op (e0) (e1)) = (op (e1) (e1)))) -> (~((e1) = (e3))) -> (~((e2) = (e3))) -> (((op (e2) (e1)) = (e0))\/(((op (e2) (e1)) = (e1))\/(((op (e2) (e1)) = (e2))\/((op (e2) (e1)) = (e3))))) -> (~((op (e2) (e1)) = (e0))) -> (~((op (e2) (e1)) = (op (e3) (e1)))) -> ((op (e3) (e1)) = (e1)) -> ((op (e0) (e1)) = (e2)) -> (~((op (e0) (e1)) = (op (e2) (e1)))) -> (~((op (e1) (e1)) = (op (e2) (e1)))) -> ((op (e1) (e0)) = (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). % 18.52/18.75 do 0 intro. intros zenon_H18c zenon_H149 zenon_H10e zenon_H95 zenon_H12b zenon_H1cc zenon_H31 zenon_Haf zenon_Hae zenon_H10f zenon_H17e zenon_H13e zenon_H27 zenon_H9a zenon_H16f zenon_Hd6 zenon_H7c. % 18.52/18.75 apply (zenon_or_s _ _ zenon_H18c); [ zenon_intro zenon_H86 | zenon_intro zenon_H18d ]. % 18.52/18.75 apply (zenon_L257_); trivial. % 18.52/18.75 apply (zenon_or_s _ _ zenon_H18d); [ zenon_intro zenon_H110 | zenon_intro zenon_H18e ]. % 18.52/18.75 apply (zenon_L67_); trivial. % 18.52/18.75 apply (zenon_or_s _ _ zenon_H18e); [ zenon_intro zenon_H113 | zenon_intro zenon_Hd7 ]. % 18.52/18.75 apply (zenon_or_s _ _ zenon_H16f); [ zenon_intro zenon_H9e | zenon_intro zenon_H170 ]. % 18.52/18.75 apply (zenon_L263_); trivial. % 18.52/18.75 apply (zenon_or_s _ _ zenon_H170); [ zenon_intro zenon_H13f | zenon_intro zenon_H171 ]. % 18.52/18.75 apply (zenon_L192_); trivial. % 18.52/18.75 apply (zenon_or_s _ _ zenon_H171); [ zenon_intro zenon_H16c | zenon_intro zenon_Hdc ]. % 18.52/18.75 apply (zenon_L116_); trivial. % 18.52/18.75 apply (zenon_L83_); trivial. % 18.52/18.75 apply (zenon_L101_); trivial. % 18.52/18.75 (* end of lemma zenon_L319_ *) % 18.52/18.75 assert (zenon_L320_ : (((op (e2) (e0)) = (e0))\/(((op (e2) (e1)) = (e0))\/(((op (e2) (e2)) = (e0))\/((op (e2) (e3)) = (e0))))) -> (~((op (e2) (e0)) = (e0))) -> (~((op (e2) (e1)) = (e0))) -> ((op (e0) (e2)) = (e3)) -> (~((op (e0) (e2)) = (op (e3) (e2)))) -> ((op (e0) (e2)) = (e2)) -> (~((op (e3) (e2)) = (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 (e2) (e1)) = (e1)) -> (~((op (e2) (e1)) = (op (e3) (e1)))) -> (((op (e3) (e0)) = (e3))\/(((op (e3) (e1)) = (e3))\/(((op (e3) (e2)) = (e3))\/((op (e3) (e3)) = (e3))))) -> (~((e1) = (e3))) -> ((op (e1) (e1)) = (e3)) -> (~((op (e1) (e1)) = (op (e3) (e1)))) -> (~((op (e3) (e3)) = (e3))) -> (((op (e3) (e0)) = (e1))\/(((op (e3) (e1)) = (e1))\/(((op (e3) (e2)) = (e1))\/((op (e3) (e3)) = (e1))))) -> (~((op (e2) (e3)) = (e0))) -> False). % 18.52/18.75 do 0 intro. intros zenon_H2f zenon_H30 zenon_H31 zenon_Ha9 zenon_H14f zenon_H150 zenon_H62 zenon_H18f zenon_H191 zenon_Ha5 zenon_Haf zenon_H165 zenon_H95 zenon_H13f zenon_H160 zenon_H102 zenon_He8 zenon_H32. % 18.52/18.75 apply (zenon_or_s _ _ zenon_H2f); [ zenon_intro zenon_H34 | zenon_intro zenon_H33 ]. % 18.52/18.75 exact (zenon_H30 zenon_H34). % 18.52/18.75 apply (zenon_or_s _ _ zenon_H33); [ zenon_intro zenon_H36 | zenon_intro zenon_H35 ]. % 18.52/18.75 exact (zenon_H31 zenon_H36). % 18.52/18.75 apply (zenon_or_s _ _ zenon_H35); [ zenon_intro zenon_H2c | zenon_intro zenon_H37 ]. % 18.52/18.75 apply (zenon_L291_); trivial. % 18.52/18.75 exact (zenon_H32 zenon_H37). % 18.52/18.75 (* end of lemma zenon_L320_ *) % 18.52/18.75 assert (zenon_L321_ : (((op (e0) (e3)) = (e0))\/(((op (e0) (e3)) = (e1))\/(((op (e0) (e3)) = (e2))\/((op (e0) (e3)) = (e3))))) -> (~((op (e0) (e3)) = (e0))) -> ((op (e2) (e3)) = (e1)) -> (~((op (e0) (e3)) = (op (e2) (e3)))) -> ((op (e3) (e3)) = (e2)) -> (~((op (e0) (e3)) = (op (e3) (e3)))) -> (~((op (e0) (e3)) = (op (e1) (e3)))) -> ((op (e1) (e3)) = (e3)) -> False). % 18.52/18.75 do 0 intro. intros zenon_He4 zenon_H76 zenon_Hf4 zenon_He2 zenon_Hf6 zenon_Hc2 zenon_H1d zenon_Hdc. % 18.52/18.75 apply (zenon_or_s _ _ zenon_He4); [ zenon_intro zenon_H1e | zenon_intro zenon_He5 ]. % 18.52/18.75 exact (zenon_H76 zenon_H1e). % 18.52/18.75 apply (zenon_or_s _ _ zenon_He5); [ zenon_intro zenon_Hc3 | zenon_intro zenon_He6 ]. % 18.52/18.75 apply (zenon_L272_); trivial. % 18.52/18.75 apply (zenon_or_s _ _ zenon_He6); [ zenon_intro zenon_Hcd | zenon_intro zenon_He3 ]. % 18.52/18.75 apply (zenon_L87_); trivial. % 18.52/18.75 apply (zenon_L117_); trivial. % 18.52/18.75 (* end of lemma zenon_L321_ *) % 18.52/18.75 assert (zenon_L322_ : (~((e2) = (e3))) -> (((op (e1) (e0)) = (e1))\/(((op (e1) (e1)) = (e1))\/(((op (e1) (e2)) = (e1))\/((op (e1) (e3)) = (e1))))) -> (~((op (e0) (e3)) = (op (e1) (e3)))) -> (~((op (e3) (e1)) = (e0))) -> (~((op (e3) (e0)) = (e0))) -> (((op (e3) (e0)) = (e0))\/(((op (e3) (e1)) = (e0))\/(((op (e3) (e2)) = (e0))\/((op (e3) (e3)) = (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) (e0)) = (op (e2) (e0)))) -> ((op (e0) (e0)) = (e1)) -> (((op (e2) (e0)) = (e1))\/(((op (e2) (e1)) = (e1))\/(((op (e2) (e2)) = (e1))\/((op (e2) (e3)) = (e1))))) -> (((op (e0) (e1)) = (e1))\/(((op (e1) (e1)) = (e1))\/(((op (e2) (e1)) = (e1))\/((op (e3) (e1)) = (e1))))) -> (~((e0) = (e1))) -> (~((op (e1) (e1)) = (e1))) -> (~((op (e3) (e3)) = (e3))) -> (~((op (e0) (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 (e2) (e0)) = (e0))) -> (~((op (e1) (e3)) = (op (e3) (e3)))) -> ((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 (e1) (e2)) = (e0))\/(((op (e2) (e2)) = (e0))\/((op (e3) (e2)) = (e0))))) -> (~((op (e1) (e2)) = (e0))) -> (~((op (e2) (e2)) = (op (e2) (e3)))) -> (~((op (e3) (e2)) = (e0))) -> (((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))))) -> (~((e0) = (e2))) -> (~((op (e2) (e0)) = (op (e2) (e1)))) -> ((op (e2) (e0)) = (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 (e1) (e1)) = (op (e2) (e1)))) -> (~((op (e0) (e1)) = (op (e2) (e1)))) -> (~((op (e2) (e1)) = (op (e3) (e1)))) -> (~((op (e2) (e1)) = (e0))) -> (((op (e2) (e1)) = (e0))\/(((op (e2) (e1)) = (e1))\/(((op (e2) (e1)) = (e2))\/((op (e2) (e1)) = (e3))))) -> (~((op (e0) (e2)) = (op (e1) (e2)))) -> (((op (e0) (e1)) = (e2))\/(((op (e1) (e1)) = (e2))\/(((op (e2) (e1)) = (e2))\/((op (e3) (e1)) = (e2))))) -> (~((e1) = (e2))) -> (((op (e0) (e0)) = (e3))\/(((op (e0) (e1)) = (e3))\/(((op (e0) (e2)) = (e3))\/((op (e0) (e3)) = (e3))))) -> (~((op (e2) (e3)) = (e0))) -> (~((op (e1) (e1)) = (op (e1) (e3)))) -> ((~((op (e3) (e3)) = (e0)))\/((op (e3) (e0)) = (e3))) -> (~((op (e0) (e0)) = (e0))) -> (((op (e0) (e3)) = (e0))\/(((op (e1) (e3)) = (e0))\/(((op (e2) (e3)) = (e0))\/((op (e3) (e3)) = (e0))))) -> (~((op (e1) (e0)) = (op (e1) (e3)))) -> (~((op (e0) (e1)) = (op (e0) (e3)))) -> (((op (e0) (e0)) = (e0))\/(((op (e0) (e1)) = (e0))\/(((op (e0) (e2)) = (e0))\/((op (e0) (e3)) = (e0))))) -> (((op (e0) (e0)) = (e3))\/(((op (e1) (e0)) = (e3))\/(((op (e2) (e0)) = (e3))\/((op (e3) (e0)) = (e3))))) -> ((~((op (e3) (e1)) = (e0)))\/((op (e3) (e0)) = (e1))) -> (~((op (e0) (e0)) = (op (e0) (e2)))) -> (((op (e0) (e2)) = (e1))\/(((op (e1) (e2)) = (e1))\/(((op (e2) (e2)) = (e1))\/((op (e3) (e2)) = (e1))))) -> (((op (e0) (e0)) = (e2))\/(((op (e0) (e1)) = (e2))\/(((op (e0) (e2)) = (e2))\/((op (e0) (e3)) = (e2))))) -> (~((op (e2) (e2)) = (op (e3) (e2)))) -> (~((op (e3) (e2)) = (op (e3) (e3)))) -> (((op (e3) (e2)) = (e0))\/(((op (e3) (e2)) = (e1))\/(((op (e3) (e2)) = (e2))\/((op (e3) (e2)) = (e3))))) -> (~((op (e0) (e1)) = (op (e1) (e1)))) -> (((op (e0) (e2)) = (e3))\/(((op (e1) (e2)) = (e3))\/(((op (e2) (e2)) = (e3))\/((op (e3) (e2)) = (e3))))) -> (~((op (e3) (e0)) = (op (e3) (e2)))) -> (~((op (e2) (e0)) = (op (e2) (e2)))) -> (((op (e3) (e0)) = (e3))\/(((op (e3) (e1)) = (e3))\/(((op (e3) (e2)) = (e3))\/((op (e3) (e3)) = (e3))))) -> (~((op (e1) (e1)) = (op (e3) (e1)))) -> (~((op (e1) (e2)) = (op (e2) (e2)))) -> (((op (e0) (e3)) = (e0))\/(((op (e0) (e3)) = (e1))\/(((op (e0) (e3)) = (e2))\/((op (e0) (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)) = (e3))\/(((op (e1) (e3)) = (e3))\/(((op (e2) (e3)) = (e3))\/((op (e3) (e3)) = (e3))))) -> (~((op (e3) (e0)) = (op (e3) (e3)))) -> (((op (e2) (e2)) = (e0))\/(((op (e2) (e2)) = (e1))\/(((op (e2) (e2)) = (e2))\/((op (e2) (e2)) = (e3))))) -> (~((op (e2) (e2)) = (e2))) -> ((~((op (e3) (e2)) = (e0)))\/((op (e3) (e0)) = (e2))) -> (~((op (e1) (e0)) = (op (e3) (e0)))) -> ((~((op (e3) (e0)) = (e0)))\/((op (e3) (e0)) = (e0))) -> (~((op (e1) (e2)) = (op (e3) (e2)))) -> (~((op (e0) (e3)) = (op (e2) (e3)))) -> (((op (e2) (e3)) = (e0))\/(((op (e2) (e3)) = (e1))\/(((op (e2) (e3)) = (e2))\/((op (e2) (e3)) = (e3))))) -> (~((op (e0) (e2)) = (op (e3) (e2)))) -> (((op (e0) (e3)) = (e2))\/(((op (e1) (e3)) = (e2))\/(((op (e2) (e3)) = (e2))\/((op (e3) (e3)) = (e2))))) -> (~((op (e2) (e0)) = (op (e2) (e3)))) -> (((op (e3) (e0)) = (e2))\/(((op (e3) (e1)) = (e2))\/(((op (e3) (e2)) = (e2))\/((op (e3) (e3)) = (e2))))) -> (~((op (e1) (e3)) = (op (e2) (e3)))) -> (~((op (e0) (e2)) = (op (e2) (e2)))) -> (((op (e0) (e2)) = (e0))\/(((op (e0) (e2)) = (e1))\/(((op (e0) (e2)) = (e2))\/((op (e0) (e2)) = (e3))))) -> (((op (e2) (e0)) = (e3))\/(((op (e2) (e1)) = (e3))\/(((op (e2) (e2)) = (e3))\/((op (e2) (e3)) = (e3))))) -> (~((op (e0) (e2)) = (e0))) -> (~((op (e0) (e3)) = (e0))) -> False). % 18.52/18.75 do 0 intro. intros zenon_H12b zenon_H128 zenon_H1d zenon_H1ad zenon_H40 zenon_H1ac zenon_H133 zenon_H130 zenon_H39 zenon_H7a zenon_H106 zenon_H109 zenon_Ha1 zenon_H10a zenon_H102 zenon_Hc2 zenon_Hf3 zenon_H101 zenon_H2f zenon_H30 zenon_Hd5 zenon_H15e zenon_He8 zenon_H6a zenon_H25 zenon_H6d zenon_H18b zenon_H1a5 zenon_H1cf zenon_H18c zenon_H149 zenon_H1f0 zenon_Hee zenon_H16f zenon_H9a zenon_H27 zenon_H95 zenon_H13e zenon_H17e zenon_Haf zenon_H31 zenon_H1cc zenon_H195 zenon_H1d8 zenon_H7c zenon_H168 zenon_H32 zenon_H57 zenon_H1ec zenon_H3f zenon_H67 zenon_Hd8 zenon_H54 zenon_H74 zenon_H1e0 zenon_H1ed zenon_H13c zenon_H139 zenon_H183 zenon_H18f zenon_H62 zenon_H191 zenon_H10e zenon_H1a6 zenon_H6f zenon_H52 zenon_H165 zenon_H160 zenon_H2b zenon_He4 zenon_H124 zenon_Hdf zenon_H136 zenon_H71 zenon_H1c4 zenon_H173 zenon_H1a7 zenon_H1fa zenon_H184 zenon_H115 zenon_He2 zenon_H11f zenon_H14f zenon_H145 zenon_H5b zenon_H153 zenon_Hdb zenon_Ha8 zenon_H1ba zenon_He7 zenon_H75 zenon_H76. % 18.52/18.75 apply (zenon_or_s _ _ zenon_H74); [ zenon_intro zenon_H42 | zenon_intro zenon_H77 ]. % 18.52/18.75 exact (zenon_H3f zenon_H42). % 18.52/18.75 apply (zenon_or_s _ _ zenon_H77); [ zenon_intro zenon_H49 | zenon_intro zenon_H78 ]. % 18.52/18.75 apply (zenon_or_s _ _ zenon_H183); [ zenon_intro zenon_H7b | zenon_intro zenon_H186 ]. % 18.52/18.75 apply (zenon_L26_); trivial. % 18.52/18.75 apply (zenon_or_s _ _ zenon_H186); [ zenon_intro zenon_H10f | zenon_intro zenon_H187 ]. % 18.52/18.75 apply (zenon_or_s _ _ zenon_H168); [ zenon_intro zenon_H3a | zenon_intro zenon_H169 ]. % 18.52/18.75 apply (zenon_L35_); trivial. % 18.52/18.75 apply (zenon_or_s _ _ zenon_H169); [ zenon_intro zenon_H99 | zenon_intro zenon_H16a ]. % 18.52/18.75 apply (zenon_L36_); trivial. % 18.52/18.75 apply (zenon_or_s _ _ zenon_H16a); [ zenon_intro zenon_Ha9 | zenon_intro zenon_He3 ]. % 18.52/18.75 apply (zenon_or_s _ _ zenon_H128); [ zenon_intro zenon_H9d | zenon_intro zenon_H129 ]. % 18.52/18.75 apply (zenon_L262_); trivial. % 18.52/18.75 apply (zenon_or_s _ _ zenon_H129); [ zenon_intro zenon_H10d | zenon_intro zenon_H12a ]. % 18.52/18.75 exact (zenon_H10a zenon_H10d). % 18.52/18.75 apply (zenon_or_s _ _ zenon_H12a); [ zenon_intro zenon_Hf0 | zenon_intro zenon_Hd6 ]. % 18.52/18.75 apply (zenon_or_s _ _ zenon_H109); [ zenon_intro zenon_Ha0 | zenon_intro zenon_H10b ]. % 18.52/18.75 apply (zenon_L38_); trivial. % 18.52/18.75 apply (zenon_or_s _ _ zenon_H10b); [ zenon_intro zenon_H10d | zenon_intro zenon_H10c ]. % 18.52/18.75 exact (zenon_H10a zenon_H10d). % 18.52/18.75 apply (zenon_or_s _ _ zenon_H10c); [ zenon_intro zenon_Ha5 | zenon_intro zenon_Hae ]. % 18.52/18.75 apply (zenon_or_s _ _ zenon_H18c); [ zenon_intro zenon_H86 | zenon_intro zenon_H18d ]. % 18.52/18.75 apply (zenon_L257_); trivial. % 18.52/18.75 apply (zenon_or_s _ _ zenon_H18d); [ zenon_intro zenon_H110 | zenon_intro zenon_H18e ]. % 18.52/18.75 apply (zenon_L215_); trivial. % 18.52/18.75 apply (zenon_or_s _ _ zenon_H18e); [ zenon_intro zenon_H113 | zenon_intro zenon_Hd7 ]. % 18.52/18.75 apply (zenon_L68_); trivial. % 18.52/18.75 apply (zenon_or_s _ _ zenon_H16f); [ zenon_intro zenon_H9e | zenon_intro zenon_H170 ]. % 18.52/18.75 apply (zenon_L263_); trivial. % 18.52/18.75 apply (zenon_or_s _ _ zenon_H170); [ zenon_intro zenon_H13f | zenon_intro zenon_H171 ]. % 18.52/18.75 apply (zenon_or_s _ _ zenon_H2f); [ zenon_intro zenon_H34 | zenon_intro zenon_H33 ]. % 18.52/18.75 exact (zenon_H30 zenon_H34). % 18.52/18.75 apply (zenon_or_s _ _ zenon_H33); [ zenon_intro zenon_H36 | zenon_intro zenon_H35 ]. % 18.52/18.75 exact (zenon_H31 zenon_H36). % 18.52/18.75 apply (zenon_or_s _ _ zenon_H35); [ zenon_intro zenon_H2c | zenon_intro zenon_H37 ]. % 18.52/18.75 apply (zenon_L265_); trivial. % 18.52/18.75 exact (zenon_H32 zenon_H37). % 18.52/18.75 apply (zenon_or_s _ _ zenon_H171); [ zenon_intro zenon_H16c | zenon_intro zenon_Hdc ]. % 18.52/18.75 apply (zenon_L167_); trivial. % 18.52/18.75 apply (zenon_L266_); trivial. % 18.52/18.75 apply (zenon_L268_); trivial. % 18.52/18.75 apply (zenon_or_s _ _ zenon_H2f); [ zenon_intro zenon_H34 | zenon_intro zenon_H33 ]. % 18.52/18.75 exact (zenon_H30 zenon_H34). % 18.52/18.75 apply (zenon_or_s _ _ zenon_H33); [ zenon_intro zenon_H36 | zenon_intro zenon_H35 ]. % 18.52/18.75 exact (zenon_H31 zenon_H36). % 18.52/18.75 apply (zenon_or_s _ _ zenon_H35); [ zenon_intro zenon_H2c | zenon_intro zenon_H37 ]. % 18.52/18.75 apply (zenon_L270_); trivial. % 18.52/18.75 exact (zenon_H32 zenon_H37). % 18.52/18.75 apply (zenon_or_s _ _ zenon_H128); [ zenon_intro zenon_H9d | zenon_intro zenon_H129 ]. % 18.52/18.75 apply (zenon_L262_); trivial. % 18.52/18.75 apply (zenon_or_s _ _ zenon_H129); [ zenon_intro zenon_H10d | zenon_intro zenon_H12a ]. % 18.52/18.75 exact (zenon_H10a zenon_H10d). % 18.52/18.75 apply (zenon_or_s _ _ zenon_H12a); [ zenon_intro zenon_Hf0 | zenon_intro zenon_Hd6 ]. % 18.52/18.75 apply (zenon_or_s _ _ zenon_H109); [ zenon_intro zenon_Ha0 | zenon_intro zenon_H10b ]. % 18.52/18.75 apply (zenon_L38_); trivial. % 18.52/18.75 apply (zenon_or_s _ _ zenon_H10b); [ zenon_intro zenon_H10d | zenon_intro zenon_H10c ]. % 18.52/18.75 exact (zenon_H10a zenon_H10d). % 18.52/18.75 apply (zenon_or_s _ _ zenon_H10c); [ zenon_intro zenon_Ha5 | zenon_intro zenon_Hae ]. % 18.52/18.75 apply (zenon_or_s _ _ zenon_H18c); [ zenon_intro zenon_H86 | zenon_intro zenon_H18d ]. % 18.52/18.75 apply (zenon_L257_); trivial. % 18.52/18.75 apply (zenon_or_s _ _ zenon_H18d); [ zenon_intro zenon_H110 | zenon_intro zenon_H18e ]. % 18.52/18.75 apply (zenon_L215_); trivial. % 18.52/18.75 apply (zenon_or_s _ _ zenon_H18e); [ zenon_intro zenon_H113 | zenon_intro zenon_Hd7 ]. % 18.52/18.75 apply (zenon_L68_); trivial. % 18.52/18.75 apply (zenon_L316_); trivial. % 18.52/18.75 apply (zenon_L268_); trivial. % 18.52/18.75 apply (zenon_or_s _ _ zenon_H109); [ zenon_intro zenon_Ha0 | zenon_intro zenon_H10b ]. % 18.52/18.75 apply (zenon_L38_); trivial. % 18.52/18.75 apply (zenon_or_s _ _ zenon_H10b); [ zenon_intro zenon_H10d | zenon_intro zenon_H10c ]. % 18.52/18.75 exact (zenon_H10a zenon_H10d). % 18.52/18.75 apply (zenon_or_s _ _ zenon_H10c); [ zenon_intro zenon_Ha5 | zenon_intro zenon_Hae ]. % 18.52/18.75 apply (zenon_or_s _ _ zenon_H18c); [ zenon_intro zenon_H86 | zenon_intro zenon_H18d ]. % 18.52/18.75 apply (zenon_L257_); trivial. % 18.52/18.75 apply (zenon_or_s _ _ zenon_H18d); [ zenon_intro zenon_H110 | zenon_intro zenon_H18e ]. % 18.52/18.75 apply (zenon_L215_); trivial. % 18.52/18.75 apply (zenon_or_s _ _ zenon_H18e); [ zenon_intro zenon_H113 | zenon_intro zenon_Hd7 ]. % 18.52/18.75 apply (zenon_or_s _ _ zenon_H16f); [ zenon_intro zenon_H9e | zenon_intro zenon_H170 ]. % 18.52/18.75 apply (zenon_L263_); trivial. % 18.52/18.75 apply (zenon_or_s _ _ zenon_H170); [ zenon_intro zenon_H13f | zenon_intro zenon_H171 ]. % 18.52/18.75 apply (zenon_or_s _ _ zenon_He7); [ zenon_intro zenon_H3b | zenon_intro zenon_He9 ]. % 18.52/18.75 apply (zenon_L305_); trivial. % 18.52/18.75 apply (zenon_or_s _ _ zenon_He9); [ zenon_intro zenon_Ha6 | zenon_intro zenon_Hea ]. % 18.52/18.75 apply (zenon_L95_); trivial. % 18.52/18.75 apply (zenon_or_s _ _ zenon_Hea); [ zenon_intro zenon_Haa | zenon_intro zenon_Hdd ]. % 18.52/18.75 apply (zenon_or_s _ _ zenon_He8); [ zenon_intro zenon_Hac | zenon_intro zenon_Heb ]. % 18.52/18.75 apply (zenon_L252_); trivial. % 18.52/18.75 apply (zenon_or_s _ _ zenon_Heb); [ zenon_intro zenon_Hae | zenon_intro zenon_Hec ]. % 18.52/18.75 apply (zenon_L192_); trivial. % 18.52/18.75 apply (zenon_or_s _ _ zenon_Hec); [ zenon_intro zenon_Hba | zenon_intro zenon_Hc4 ]. % 18.52/18.75 apply (zenon_L318_); trivial. % 18.52/18.75 apply (zenon_L50_); trivial. % 18.52/18.75 apply (zenon_L54_); trivial. % 18.52/18.75 apply (zenon_or_s _ _ zenon_H171); [ zenon_intro zenon_H16c | zenon_intro zenon_Hdc ]. % 18.52/18.75 apply (zenon_L116_); trivial. % 18.52/18.75 apply (zenon_L83_); trivial. % 18.52/18.75 apply (zenon_L101_); trivial. % 18.52/18.75 apply (zenon_L319_); trivial. % 18.52/18.75 apply (zenon_or_s _ _ zenon_H187); [ zenon_intro zenon_H150 | zenon_intro zenon_Hcd ]. % 18.52/18.75 apply (zenon_or_s _ _ zenon_H168); [ zenon_intro zenon_H3a | zenon_intro zenon_H169 ]. % 18.52/18.75 apply (zenon_L35_); trivial. % 18.52/18.75 apply (zenon_or_s _ _ zenon_H169); [ zenon_intro zenon_H99 | zenon_intro zenon_H16a ]. % 18.52/18.75 apply (zenon_L36_); trivial. % 18.52/18.75 apply (zenon_or_s _ _ zenon_H16a); [ zenon_intro zenon_Ha9 | zenon_intro zenon_He3 ]. % 18.52/18.75 apply (zenon_or_s _ _ zenon_H128); [ zenon_intro zenon_H9d | zenon_intro zenon_H129 ]. % 18.52/18.75 apply (zenon_L262_); trivial. % 18.52/18.75 apply (zenon_or_s _ _ zenon_H129); [ zenon_intro zenon_H10d | zenon_intro zenon_H12a ]. % 18.52/18.75 exact (zenon_H10a zenon_H10d). % 18.52/18.75 apply (zenon_or_s _ _ zenon_H12a); [ zenon_intro zenon_Hf0 | zenon_intro zenon_Hd6 ]. % 18.52/18.75 apply (zenon_or_s _ _ zenon_H109); [ zenon_intro zenon_Ha0 | zenon_intro zenon_H10b ]. % 18.52/18.75 apply (zenon_L38_); trivial. % 18.52/18.75 apply (zenon_or_s _ _ zenon_H10b); [ zenon_intro zenon_H10d | zenon_intro zenon_H10c ]. % 18.52/18.75 exact (zenon_H10a zenon_H10d). % 18.52/18.75 apply (zenon_or_s _ _ zenon_H10c); [ zenon_intro zenon_Ha5 | zenon_intro zenon_Hae ]. % 18.52/18.75 apply (zenon_or_s _ _ zenon_H18c); [ zenon_intro zenon_H86 | zenon_intro zenon_H18d ]. % 18.52/18.75 apply (zenon_L257_); trivial. % 18.52/18.75 apply (zenon_or_s _ _ zenon_H18d); [ zenon_intro zenon_H110 | zenon_intro zenon_H18e ]. % 18.52/18.75 apply (zenon_L215_); trivial. % 18.52/18.75 apply (zenon_or_s _ _ zenon_H18e); [ zenon_intro zenon_H113 | zenon_intro zenon_Hd7 ]. % 18.52/18.75 apply (zenon_L153_); trivial. % 18.52/18.75 apply (zenon_or_s _ _ zenon_H16f); [ zenon_intro zenon_H9e | zenon_intro zenon_H170 ]. % 18.52/18.75 apply (zenon_L263_); trivial. % 18.52/18.75 apply (zenon_or_s _ _ zenon_H170); [ zenon_intro zenon_H13f | zenon_intro zenon_H171 ]. % 18.52/18.75 apply (zenon_L320_); trivial. % 18.52/18.75 apply (zenon_or_s _ _ zenon_H171); [ zenon_intro zenon_H16c | zenon_intro zenon_Hdc ]. % 18.52/18.75 apply (zenon_L162_); trivial. % 18.52/18.75 apply (zenon_L266_); trivial. % 18.52/18.75 apply (zenon_or_s _ _ zenon_H18c); [ zenon_intro zenon_H86 | zenon_intro zenon_H18d ]. % 18.52/18.75 apply (zenon_L257_); trivial. % 18.52/18.75 apply (zenon_or_s _ _ zenon_H18d); [ zenon_intro zenon_H110 | zenon_intro zenon_H18e ]. % 18.52/18.75 apply (zenon_or_s _ _ zenon_H16f); [ zenon_intro zenon_H9e | zenon_intro zenon_H170 ]. % 18.52/18.75 apply (zenon_L263_); trivial. % 18.52/18.75 apply (zenon_or_s _ _ zenon_H170); [ zenon_intro zenon_H13f | zenon_intro zenon_H171 ]. % 18.52/18.75 apply (zenon_L166_); trivial. % 18.52/18.75 apply (zenon_or_s _ _ zenon_H171); [ zenon_intro zenon_H16c | zenon_intro zenon_Hdc ]. % 18.52/18.75 apply (zenon_L162_); trivial. % 18.52/18.75 apply (zenon_or_s _ _ zenon_H1a5); [ zenon_intro zenon_H99 | zenon_intro zenon_H1a8 ]. % 18.52/18.75 apply (zenon_L36_); trivial. % 18.52/18.75 apply (zenon_or_s _ _ zenon_H1a8); [ zenon_intro zenon_H13f | zenon_intro zenon_H1a9 ]. % 18.52/18.75 apply (zenon_L166_); trivial. % 18.52/18.75 apply (zenon_or_s _ _ zenon_H1a9); [ zenon_intro zenon_Ha6 | zenon_intro zenon_H161 ]. % 18.52/18.75 apply (zenon_or_s _ _ zenon_H106); [ zenon_intro zenon_Hed | zenon_intro zenon_H107 ]. % 18.52/18.75 apply (zenon_L58_); trivial. % 18.52/18.75 apply (zenon_or_s _ _ zenon_H107); [ zenon_intro zenon_Ha5 | zenon_intro zenon_H108 ]. % 18.52/18.75 apply (zenon_L39_); trivial. % 18.52/18.75 apply (zenon_or_s _ _ zenon_H108); [ zenon_intro zenon_Hf1 | zenon_intro zenon_Hf4 ]. % 18.52/18.75 apply (zenon_L59_); trivial. % 18.52/18.75 apply (zenon_or_s _ _ zenon_H153); [ zenon_intro zenon_H148 | zenon_intro zenon_H154 ]. % 18.52/18.75 apply (zenon_L109_); trivial. % 18.52/18.75 apply (zenon_or_s _ _ zenon_H154); [ zenon_intro zenon_H14d | zenon_intro zenon_H155 ]. % 18.52/18.75 apply (zenon_L152_); trivial. % 18.52/18.75 apply (zenon_or_s _ _ zenon_H155); [ zenon_intro zenon_H151 | zenon_intro zenon_Hf6 ]. % 18.52/18.75 apply (zenon_L104_); trivial. % 18.52/18.75 apply (zenon_L321_); trivial. % 18.52/18.75 apply (zenon_L193_); trivial. % 18.52/18.75 apply (zenon_or_s _ _ zenon_H18e); [ zenon_intro zenon_H113 | zenon_intro zenon_Hd7 ]. % 18.52/18.75 apply (zenon_L68_); trivial. % 18.52/18.75 apply (zenon_L284_); trivial. % 18.52/18.75 apply (zenon_L296_); trivial. % 18.52/18.75 apply (zenon_or_s _ _ zenon_H128); [ zenon_intro zenon_H9d | zenon_intro zenon_H129 ]. % 18.52/18.75 apply (zenon_L262_); trivial. % 18.52/18.75 apply (zenon_or_s _ _ zenon_H129); [ zenon_intro zenon_H10d | zenon_intro zenon_H12a ]. % 18.52/18.75 exact (zenon_H10a zenon_H10d). % 18.52/18.75 apply (zenon_or_s _ _ zenon_H12a); [ zenon_intro zenon_Hf0 | zenon_intro zenon_Hd6 ]. % 18.52/18.75 apply (zenon_or_s _ _ zenon_H109); [ zenon_intro zenon_Ha0 | zenon_intro zenon_H10b ]. % 18.52/18.75 apply (zenon_L38_); trivial. % 18.52/18.75 apply (zenon_or_s _ _ zenon_H10b); [ zenon_intro zenon_H10d | zenon_intro zenon_H10c ]. % 18.52/18.75 exact (zenon_H10a zenon_H10d). % 18.52/18.75 apply (zenon_or_s _ _ zenon_H10c); [ zenon_intro zenon_Ha5 | zenon_intro zenon_Hae ]. % 18.52/18.75 apply (zenon_or_s _ _ zenon_H18c); [ zenon_intro zenon_H86 | zenon_intro zenon_H18d ]. % 18.52/18.75 apply (zenon_L257_); trivial. % 18.52/18.75 apply (zenon_or_s _ _ zenon_H18d); [ zenon_intro zenon_H110 | zenon_intro zenon_H18e ]. % 18.52/18.75 apply (zenon_L215_); trivial. % 18.52/18.75 apply (zenon_or_s _ _ zenon_H18e); [ zenon_intro zenon_H113 | zenon_intro zenon_Hd7 ]. % 18.52/18.75 apply (zenon_L153_); trivial. % 18.52/18.75 apply (zenon_L316_); trivial. % 18.52/18.75 apply (zenon_or_s _ _ zenon_H18c); [ zenon_intro zenon_H86 | zenon_intro zenon_H18d ]. % 18.52/18.75 apply (zenon_L257_); trivial. % 18.52/18.75 apply (zenon_or_s _ _ zenon_H18d); [ zenon_intro zenon_H110 | zenon_intro zenon_H18e ]. % 18.52/18.75 apply (zenon_L290_); trivial. % 18.52/18.75 apply (zenon_or_s _ _ zenon_H18e); [ zenon_intro zenon_H113 | zenon_intro zenon_Hd7 ]. % 18.52/18.75 apply (zenon_L68_); trivial. % 18.52/18.75 apply (zenon_L284_); trivial. % 18.52/18.75 apply (zenon_L297_); trivial. % 18.52/18.75 apply (zenon_or_s _ _ zenon_H168); [ zenon_intro zenon_H3a | zenon_intro zenon_H169 ]. % 18.52/18.75 apply (zenon_L35_); trivial. % 18.52/18.75 apply (zenon_or_s _ _ zenon_H169); [ zenon_intro zenon_H99 | zenon_intro zenon_H16a ]. % 18.52/18.75 apply (zenon_L36_); trivial. % 18.52/18.75 apply (zenon_or_s _ _ zenon_H16a); [ zenon_intro zenon_Ha9 | zenon_intro zenon_He3 ]. % 18.52/18.75 apply (zenon_or_s _ _ zenon_H128); [ zenon_intro zenon_H9d | zenon_intro zenon_H129 ]. % 18.52/18.75 apply (zenon_L262_); trivial. % 18.52/18.75 apply (zenon_or_s _ _ zenon_H129); [ zenon_intro zenon_H10d | zenon_intro zenon_H12a ]. % 18.52/18.75 exact (zenon_H10a zenon_H10d). % 18.52/18.75 apply (zenon_or_s _ _ zenon_H12a); [ zenon_intro zenon_Hf0 | zenon_intro zenon_Hd6 ]. % 18.52/18.75 apply (zenon_or_s _ _ zenon_H109); [ zenon_intro zenon_Ha0 | zenon_intro zenon_H10b ]. % 18.52/18.75 apply (zenon_L38_); trivial. % 18.52/18.75 apply (zenon_or_s _ _ zenon_H10b); [ zenon_intro zenon_H10d | zenon_intro zenon_H10c ]. % 18.52/18.75 exact (zenon_H10a zenon_H10d). % 18.52/18.75 apply (zenon_or_s _ _ zenon_H10c); [ zenon_intro zenon_Ha5 | zenon_intro zenon_Hae ]. % 18.52/18.75 apply (zenon_or_s _ _ zenon_H18c); [ zenon_intro zenon_H86 | zenon_intro zenon_H18d ]. % 18.52/18.75 apply (zenon_L257_); trivial. % 18.52/18.75 apply (zenon_or_s _ _ zenon_H18d); [ zenon_intro zenon_H110 | zenon_intro zenon_H18e ]. % 18.52/18.75 apply (zenon_L215_); trivial. % 18.52/18.75 apply (zenon_or_s _ _ zenon_H18e); [ zenon_intro zenon_H113 | zenon_intro zenon_Hd7 ]. % 18.52/18.75 apply (zenon_L68_); trivial. % 18.52/18.75 apply (zenon_L70_); trivial. % 18.52/18.75 apply (zenon_L273_); trivial. % 18.52/18.75 apply (zenon_or_s _ _ zenon_H109); [ zenon_intro zenon_Ha0 | zenon_intro zenon_H10b ]. % 18.52/18.75 apply (zenon_L38_); trivial. % 18.52/18.75 apply (zenon_or_s _ _ zenon_H10b); [ zenon_intro zenon_H10d | zenon_intro zenon_H10c ]. % 18.52/18.75 exact (zenon_H10a zenon_H10d). % 18.52/18.75 apply (zenon_or_s _ _ zenon_H10c); [ zenon_intro zenon_Ha5 | zenon_intro zenon_Hae ]. % 18.52/18.75 apply (zenon_or_s _ _ zenon_H18c); [ zenon_intro zenon_H86 | zenon_intro zenon_H18d ]. % 18.52/18.75 apply (zenon_L257_); trivial. % 18.52/18.75 apply (zenon_or_s _ _ zenon_H18d); [ zenon_intro zenon_H110 | zenon_intro zenon_H18e ]. % 18.52/18.75 apply (zenon_L215_); trivial. % 18.52/18.75 apply (zenon_or_s _ _ zenon_H18e); [ zenon_intro zenon_H113 | zenon_intro zenon_Hd7 ]. % 18.52/18.75 apply (zenon_L280_); trivial. % 18.52/18.75 apply (zenon_L101_); trivial. % 18.52/18.75 apply (zenon_L295_); trivial. % 18.52/18.75 apply (zenon_L81_); trivial. % 18.52/18.75 apply (zenon_or_s _ _ zenon_H78); [ zenon_intro zenon_H48 | zenon_intro zenon_H1e ]. % 18.52/18.75 exact (zenon_H75 zenon_H48). % 18.52/18.75 exact (zenon_H76 zenon_H1e). % 18.52/18.75 (* end of lemma zenon_L322_ *) % 18.52/18.75 assert (zenon_L323_ : (((op (e0) (e0)) = (e0))\/(((op (e0) (e1)) = (e0))\/(((op (e0) (e2)) = (e0))\/((op (e0) (e3)) = (e0))))) -> (~((op (e0) (e3)) = (e0))) -> (~((op (e2) (e0)) = (e0))) -> (~((op (e2) (e1)) = (e0))) -> (((op (e3) (e0)) = (e0))\/(((op (e3) (e1)) = (e0))\/(((op (e3) (e2)) = (e0))\/((op (e3) (e3)) = (e0))))) -> (~((op (e0) (e1)) = (op (e0) (e3)))) -> (~((op (e1) (e0)) = (op (e1) (e3)))) -> ((op (e1) (e0)) = (e0)) -> (~((op (e2) (e2)) = (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 (e0) (e2)) = (e0))\/(((op (e1) (e2)) = (e0))\/(((op (e2) (e2)) = (e0))\/((op (e3) (e2)) = (e0))))) -> (~((op (e1) (e2)) = (e0))) -> (~((op (e0) (e2)) = (e0))) -> (((op (e2) (e0)) = (e0))\/(((op (e2) (e1)) = (e0))\/(((op (e2) (e2)) = (e0))\/((op (e2) (e3)) = (e0))))) -> (~((op (e0) (e0)) = (e0))) -> (~((e1) = (e2))) -> ((op (e0) (e0)) = (e1)) -> ((~((op (e3) (e3)) = (e0)))\/((op (e3) (e0)) = (e3))) -> (((op (e0) (e0)) = (e3))\/(((op (e1) (e0)) = (e3))\/(((op (e2) (e0)) = (e3))\/((op (e3) (e0)) = (e3))))) -> ((~((op (e3) (e1)) = (e0)))\/((op (e3) (e0)) = (e1))) -> (~((op (e0) (e0)) = (op (e0) (e2)))) -> (((op (e0) (e2)) = (e1))\/(((op (e1) (e2)) = (e1))\/(((op (e2) (e2)) = (e1))\/((op (e3) (e2)) = (e1))))) -> (((op (e0) (e0)) = (e2))\/(((op (e0) (e1)) = (e2))\/(((op (e0) (e2)) = (e2))\/((op (e0) (e3)) = (e2))))) -> (~((op (e2) (e2)) = (op (e3) (e2)))) -> (~((op (e3) (e2)) = (op (e3) (e3)))) -> (((op (e3) (e2)) = (e0))\/(((op (e3) (e2)) = (e1))\/(((op (e3) (e2)) = (e2))\/((op (e3) (e2)) = (e3))))) -> (((op (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) (e2)) = (e3))\/(((op (e1) (e2)) = (e3))\/(((op (e2) (e2)) = (e3))\/((op (e3) (e2)) = (e3))))) -> (~((op (e3) (e0)) = (op (e3) (e2)))) -> (~((op (e2) (e0)) = (op (e2) (e2)))) -> (~((op (e1) (e1)) = (op (e1) (e3)))) -> (~((op (e0) (e0)) = (op (e2) (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) (e3)) = (e1))\/(((op (e1) (e3)) = (e1))\/(((op (e2) (e3)) = (e1))\/((op (e3) (e3)) = (e1))))) -> (((op (e3) (e3)) = (e0))\/(((op (e3) (e3)) = (e1))\/(((op (e3) (e3)) = (e2))\/((op (e3) (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 (e1) (e2)) = (op (e3) (e2)))) -> (~((op (e1) (e2)) = (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) (e3)) = (e3))\/(((op (e1) (e3)) = (e3))\/(((op (e2) (e3)) = (e3))\/((op (e3) (e3)) = (e3))))) -> (((op (e0) (e0)) = (e3))\/(((op (e0) (e1)) = (e3))\/(((op (e0) (e2)) = (e3))\/((op (e0) (e3)) = (e3))))) -> (~((op (e3) (e0)) = (op (e3) (e3)))) -> (((op (e2) (e2)) = (e0))\/(((op (e2) (e2)) = (e1))\/(((op (e2) (e2)) = (e2))\/((op (e2) (e2)) = (e3))))) -> (~((op (e2) (e2)) = (e2))) -> ((~((op (e3) (e2)) = (e0)))\/((op (e3) (e0)) = (e2))) -> (~((op (e1) (e0)) = (op (e3) (e0)))) -> ((~((op (e3) (e0)) = (e0)))\/((op (e3) (e0)) = (e0))) -> (~((op (e0) (e2)) = (op (e2) (e2)))) -> (((op (e0) (e2)) = (e0))\/(((op (e0) (e2)) = (e1))\/(((op (e0) (e2)) = (e2))\/((op (e0) (e2)) = (e3))))) -> (((op (e2) (e0)) = (e3))\/(((op (e2) (e1)) = (e3))\/(((op (e2) (e2)) = (e3))\/((op (e2) (e3)) = (e3))))) -> (~((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 (e1) (e1)))) -> (~((e0) = (e2))) -> (((op (e0) (e1)) = (e3))\/(((op (e1) (e1)) = (e3))\/(((op (e2) (e1)) = (e3))\/((op (e3) (e1)) = (e3))))) -> (~((op (e3) (e0)) = (op (e3) (e1)))) -> (~((e2) = (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))))) -> (~((op (e0) (e3)) = (op (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) (e3)) = (op (e2) (e3)))) -> ((op (e2) (e0)) = (e2)) -> (~((op (e2) (e0)) = (op (e2) (e3)))) -> (~((op (e2) (e3)) = (op (e3) (e3)))) -> (((op (e0) (e3)) = (e0))\/(((op (e0) (e3)) = (e1))\/(((op (e0) (e3)) = (e2))\/((op (e0) (e3)) = (e3))))) -> (~((op (e2) (e1)) = (op (e3) (e1)))) -> (~((op (e0) (e1)) = (op (e2) (e1)))) -> (~((op (e1) (e1)) = (op (e2) (e1)))) -> (((op (e2) (e1)) = (e0))\/(((op (e2) (e1)) = (e1))\/(((op (e2) (e1)) = (e2))\/((op (e2) (e1)) = (e3))))) -> (~((op (e1) (e1)) = (op (e3) (e1)))) -> (~((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))))) -> (~((op (e2) (e3)) = (e0))) -> (((op (e1) (e0)) = (e2))\/(((op (e1) (e1)) = (e2))\/(((op (e1) (e2)) = (e2))\/((op (e1) (e3)) = (e2))))) -> (~((op (e0) (e2)) = (op (e1) (e2)))) -> (~((op (e1) (e3)) = (op (e3) (e3)))) -> (((op (e1) (e0)) = (e1))\/(((op (e1) (e1)) = (e1))\/(((op (e1) (e2)) = (e1))\/((op (e1) (e3)) = (e1))))) -> (~((e0) = (e3))) -> (~((e1) = (e3))) -> False). % 18.52/18.75 do 0 intro. intros zenon_H74 zenon_H76 zenon_H30 zenon_H31 zenon_H1ac zenon_H54 zenon_Hd8 zenon_H27 zenon_H6d zenon_H130 zenon_H67 zenon_H6a zenon_H25 zenon_H75 zenon_H2f zenon_H3f zenon_H7c zenon_H7a zenon_H1ec zenon_H1e0 zenon_H1ed zenon_H13c zenon_H139 zenon_H183 zenon_H18f zenon_H62 zenon_H191 zenon_H153 zenon_H145 zenon_H1a6 zenon_H6f zenon_H52 zenon_H57 zenon_H39 zenon_H2b zenon_H106 zenon_H133 zenon_H101 zenon_H1f0 zenon_H1d8 zenon_H115 zenon_H124 zenon_Hdb zenon_Hdf zenon_H136 zenon_H168 zenon_H71 zenon_H1c4 zenon_H173 zenon_H1a7 zenon_H1fa zenon_H184 zenon_Ha8 zenon_H1ba zenon_He7 zenon_Ha1 zenon_H10a zenon_H109 zenon_H10e zenon_H149 zenon_H1a5 zenon_H1cf zenon_H12b zenon_H16f zenon_He8 zenon_Hc2 zenon_H1d zenon_H11f zenon_He2 zenon_Hee zenon_H5b zenon_Hf3 zenon_He4 zenon_Haf zenon_H17e zenon_H13e zenon_H1cc zenon_H160 zenon_H14f zenon_H102 zenon_H165 zenon_H32 zenon_H18c zenon_H195 zenon_Hd5 zenon_H128 zenon_H9a zenon_H95. % 18.52/18.75 apply (zenon_or_s _ _ zenon_H184); [ zenon_intro zenon_H40 | zenon_intro zenon_H44 ]. % 18.52/18.75 apply (zenon_or_s _ _ zenon_H1ed); [ zenon_intro zenon_H1ad | zenon_intro zenon_Hac ]. % 18.52/18.75 apply (zenon_or_s _ _ zenon_H1a7); [ zenon_intro zenon_H18b | zenon_intro zenon_H148 ]. % 18.52/18.75 apply (zenon_or_s _ _ zenon_H1ec); [ zenon_intro zenon_H1ae | zenon_intro zenon_H15e ]. % 18.52/18.75 apply (zenon_L261_); trivial. % 18.52/18.75 apply (zenon_L322_); trivial. % 18.52/18.75 apply (zenon_L314_); trivial. % 18.52/18.75 apply (zenon_L315_); trivial. % 18.52/18.75 apply (zenon_L312_); trivial. % 18.52/18.75 (* end of lemma zenon_L323_ *) % 18.52/18.75 assert (zenon_L324_ : ((~((op (e2) (e3)) = (e0)))\/((op (e2) (e0)) = (e3))) -> (~((e1) = (e3))) -> (~((e0) = (e3))) -> (((op (e1) (e0)) = (e1))\/(((op (e1) (e1)) = (e1))\/(((op (e1) (e2)) = (e1))\/((op (e1) (e3)) = (e1))))) -> (~((op (e1) (e3)) = (op (e3) (e3)))) -> (~((op (e0) (e2)) = (op (e1) (e2)))) -> (((op (e1) (e0)) = (e2))\/(((op (e1) (e1)) = (e2))\/(((op (e1) (e2)) = (e2))\/((op (e1) (e3)) = (e2))))) -> (((op (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 (e2) (e1)) = (e0))\/(((op (e2) (e1)) = (e1))\/(((op (e2) (e1)) = (e2))\/((op (e2) (e1)) = (e3))))) -> (~((op (e1) (e1)) = (op (e2) (e1)))) -> (~((op (e0) (e1)) = (op (e2) (e1)))) -> (~((op (e2) (e1)) = (op (e3) (e1)))) -> (((op (e0) (e3)) = (e0))\/(((op (e0) (e3)) = (e1))\/(((op (e0) (e3)) = (e2))\/((op (e0) (e3)) = (e3))))) -> (~((op (e2) (e3)) = (op (e3) (e3)))) -> (~((op (e2) (e0)) = (op (e2) (e3)))) -> ((op (e2) (e0)) = (e2)) -> (~((op (e0) (e3)) = (op (e2) (e3)))) -> (((op (e2) (e3)) = (e0))\/(((op (e2) (e3)) = (e1))\/(((op (e2) (e3)) = (e2))\/((op (e2) (e3)) = (e3))))) -> (~((op (e0) (e3)) = (op (e1) (e3)))) -> (~((op (e0) (e3)) = (op (e3) (e3)))) -> (((op (e3) (e0)) = (e1))\/(((op (e3) (e1)) = (e1))\/(((op (e3) (e2)) = (e1))\/((op (e3) (e3)) = (e1))))) -> (((op (e1) (e0)) = (e3))\/(((op (e1) (e1)) = (e3))\/(((op (e1) (e2)) = (e3))\/((op (e1) (e3)) = (e3))))) -> (~((e2) = (e3))) -> (~((op (e3) (e0)) = (op (e3) (e1)))) -> (((op (e0) (e1)) = (e3))\/(((op (e1) (e1)) = (e3))\/(((op (e2) (e1)) = (e3))\/((op (e3) (e1)) = (e3))))) -> (~((e0) = (e2))) -> (~((op (e0) (e1)) = (op (e1) (e1)))) -> (((op (e0) (e1)) = (e1))\/(((op (e1) (e1)) = (e1))\/(((op (e2) (e1)) = (e1))\/((op (e3) (e1)) = (e1))))) -> (~((op (e1) (e1)) = (e1))) -> (~((e0) = (e1))) -> (((op (e2) (e0)) = (e3))\/(((op (e2) (e1)) = (e3))\/(((op (e2) (e2)) = (e3))\/((op (e2) (e3)) = (e3))))) -> (((op (e0) (e2)) = (e0))\/(((op (e0) (e2)) = (e1))\/(((op (e0) (e2)) = (e2))\/((op (e0) (e2)) = (e3))))) -> (~((op (e0) (e2)) = (op (e2) (e2)))) -> ((~((op (e3) (e0)) = (e0)))\/((op (e3) (e0)) = (e0))) -> (~((op (e1) (e0)) = (op (e3) (e0)))) -> ((~((op (e3) (e2)) = (e0)))\/((op (e3) (e0)) = (e2))) -> (~((op (e2) (e2)) = (e2))) -> (((op (e2) (e2)) = (e0))\/(((op (e2) (e2)) = (e1))\/(((op (e2) (e2)) = (e2))\/((op (e2) (e2)) = (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) (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 (e1) (e3)) = (op (e2) (e3)))) -> (~((op (e1) (e2)) = (op (e1) (e3)))) -> (~((op (e1) (e2)) = (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 (e3) (e3)) = (e0))\/(((op (e3) (e3)) = (e1))\/(((op (e3) (e3)) = (e2))\/((op (e3) (e3)) = (e3))))) -> (((op (e0) (e3)) = (e1))\/(((op (e1) (e3)) = (e1))\/(((op (e2) (e3)) = (e1))\/((op (e3) (e3)) = (e1))))) -> (((op (e2) (e0)) = (e1))\/(((op (e2) (e1)) = (e1))\/(((op (e2) (e2)) = (e1))\/((op (e2) (e3)) = (e1))))) -> (~((op (e1) (e2)) = (op (e2) (e2)))) -> (~((op (e0) (e0)) = (op (e2) (e0)))) -> (~((op (e1) (e1)) = (op (e1) (e3)))) -> (~((op (e2) (e0)) = (op (e2) (e2)))) -> (~((op (e3) (e0)) = (op (e3) (e2)))) -> (((op (e0) (e2)) = (e3))\/(((op (e1) (e2)) = (e3))\/(((op (e2) (e2)) = (e3))\/((op (e3) (e2)) = (e3))))) -> (((op (e0) (e3)) = (e2))\/(((op (e1) (e3)) = (e2))\/(((op (e2) (e3)) = (e2))\/((op (e3) (e3)) = (e2))))) -> (((op (e3) (e0)) = (e2))\/(((op (e3) (e1)) = (e2))\/(((op (e3) (e2)) = (e2))\/((op (e3) (e3)) = (e2))))) -> (((op (e3) (e2)) = (e0))\/(((op (e3) (e2)) = (e1))\/(((op (e3) (e2)) = (e2))\/((op (e3) (e2)) = (e3))))) -> (~((op (e3) (e2)) = (op (e3) (e3)))) -> (~((op (e2) (e2)) = (op (e3) (e2)))) -> (((op (e0) (e0)) = (e2))\/(((op (e0) (e1)) = (e2))\/(((op (e0) (e2)) = (e2))\/((op (e0) (e3)) = (e2))))) -> (((op (e0) (e2)) = (e1))\/(((op (e1) (e2)) = (e1))\/(((op (e2) (e2)) = (e1))\/((op (e3) (e2)) = (e1))))) -> (~((op (e0) (e0)) = (op (e0) (e2)))) -> ((~((op (e3) (e1)) = (e0)))\/((op (e3) (e0)) = (e1))) -> (((op (e0) (e0)) = (e3))\/(((op (e1) (e0)) = (e3))\/(((op (e2) (e0)) = (e3))\/((op (e3) (e0)) = (e3))))) -> ((~((op (e3) (e3)) = (e0)))\/((op (e3) (e0)) = (e3))) -> ((op (e0) (e0)) = (e1)) -> (~((e1) = (e2))) -> (~((op (e0) (e0)) = (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 (e0) (e2)) = (e0))\/(((op (e1) (e2)) = (e0))\/(((op (e2) (e2)) = (e0))\/((op (e3) (e2)) = (e0))))) -> (((op (e0) (e3)) = (e0))\/(((op (e1) (e3)) = (e0))\/(((op (e2) (e3)) = (e0))\/((op (e3) (e3)) = (e0))))) -> (~((op (e3) (e1)) = (op (e3) (e3)))) -> (~((op (e2) (e2)) = (op (e2) (e3)))) -> ((op (e1) (e0)) = (e0)) -> (~((op (e1) (e0)) = (op (e1) (e3)))) -> (~((op (e0) (e1)) = (op (e0) (e3)))) -> (((op (e3) (e0)) = (e0))\/(((op (e3) (e1)) = (e0))\/(((op (e3) (e2)) = (e0))\/((op (e3) (e3)) = (e0))))) -> (~((op (e2) (e1)) = (e0))) -> (~((op (e2) (e0)) = (e0))) -> (~((op (e0) (e3)) = (e0))) -> (((op (e0) (e0)) = (e0))\/(((op (e0) (e1)) = (e0))\/(((op (e0) (e2)) = (e0))\/((op (e0) (e3)) = (e0))))) -> False). % 18.52/18.75 do 0 intro. intros zenon_H94 zenon_H95 zenon_H9a zenon_H128 zenon_Hd5 zenon_H195 zenon_H18c zenon_H165 zenon_H102 zenon_H14f zenon_H160 zenon_H1cc zenon_H13e zenon_H17e zenon_Haf zenon_He4 zenon_Hf3 zenon_H5b zenon_Hee zenon_He2 zenon_H11f zenon_H1d zenon_Hc2 zenon_He8 zenon_H16f zenon_H12b zenon_H1cf zenon_H1a5 zenon_H149 zenon_H10e zenon_H109 zenon_H10a zenon_Ha1 zenon_He7 zenon_H1ba zenon_Ha8 zenon_H184 zenon_H1fa zenon_H1a7 zenon_H173 zenon_H1c4 zenon_H71 zenon_H168 zenon_H136 zenon_Hdf zenon_Hdb zenon_H124 zenon_H115 zenon_H1d8 zenon_H1f0 zenon_H101 zenon_H133 zenon_H106 zenon_H2b zenon_H39 zenon_H57 zenon_H52 zenon_H6f zenon_H1a6 zenon_H145 zenon_H153 zenon_H191 zenon_H62 zenon_H18f zenon_H183 zenon_H139 zenon_H13c zenon_H1ed zenon_H1e0 zenon_H1ec zenon_H7a zenon_H7c zenon_H3f zenon_H2f zenon_H75 zenon_H25 zenon_H6a zenon_H67 zenon_H130 zenon_H6d zenon_H27 zenon_Hd8 zenon_H54 zenon_H1ac zenon_H31 zenon_H30 zenon_H76 zenon_H74. % 18.52/18.75 apply (zenon_or_s _ _ zenon_H94); [ zenon_intro zenon_H32 | zenon_intro zenon_H3b ]. % 18.52/18.75 apply (zenon_L323_); trivial. % 18.52/18.75 apply (zenon_L313_); trivial. % 18.52/18.75 (* end of lemma zenon_L324_ *) % 18.52/18.75 assert (zenon_L325_ : (((op (e3) (e0)) = (e3))\/(((op (e3) (e1)) = (e3))\/(((op (e3) (e2)) = (e3))\/((op (e3) (e3)) = (e3))))) -> (~((e2) = (e3))) -> ((op (e3) (e0)) = (e2)) -> ((op (e1) (e1)) = (e3)) -> (~((op (e1) (e1)) = (op (e3) (e1)))) -> ((op (e2) (e2)) = (e3)) -> (~((op (e2) (e2)) = (op (e3) (e2)))) -> (~((op (e3) (e3)) = (e3))) -> False). % 18.52/18.75 do 0 intro. intros zenon_H165 zenon_H12b zenon_H148 zenon_H13f zenon_H160 zenon_Haa zenon_H18f zenon_H102. % 18.52/18.75 apply (zenon_or_s _ _ zenon_H165); [ zenon_intro zenon_H15e | zenon_intro zenon_H166 ]. % 18.52/18.75 apply (zenon_L109_); trivial. % 18.52/18.75 apply (zenon_or_s _ _ zenon_H166); [ zenon_intro zenon_H161 | zenon_intro zenon_H167 ]. % 18.52/18.75 apply (zenon_L110_); trivial. % 18.52/18.75 apply (zenon_or_s _ _ zenon_H167); [ zenon_intro zenon_H163 | zenon_intro zenon_H105 ]. % 18.52/18.75 apply (zenon_L180_); trivial. % 18.52/18.75 exact (zenon_H102 zenon_H105). % 18.52/18.75 (* end of lemma zenon_L325_ *) % 18.52/18.75 assert (zenon_L326_ : (((op (e0) (e2)) = (e3))\/(((op (e1) (e2)) = (e3))\/(((op (e2) (e2)) = (e3))\/((op (e3) (e2)) = (e3))))) -> ((op (e2) (e2)) = (e1)) -> ((op (e3) (e2)) = (e0)) -> (~((op (e3) (e3)) = (e3))) -> (~((op (e2) (e2)) = (op (e3) (e2)))) -> (~((op (e1) (e1)) = (op (e3) (e1)))) -> ((op (e3) (e0)) = (e2)) -> (((op (e3) (e0)) = (e3))\/(((op (e3) (e1)) = (e3))\/(((op (e3) (e2)) = (e3))\/((op (e3) (e3)) = (e3))))) -> (((op (e0) (e2)) = (e0))\/(((op (e0) (e2)) = (e1))\/(((op (e0) (e2)) = (e2))\/((op (e0) (e2)) = (e3))))) -> (~((op (e0) (e2)) = (e0))) -> (~((op (e0) (e0)) = (op (e0) (e2)))) -> ((op (e0) (e0)) = (e1)) -> (~((e1) = (e2))) -> ((op (e1) (e3)) = (e1)) -> (~((op (e0) (e2)) = (op (e1) (e2)))) -> ((op (e1) (e1)) = (e3)) -> (~((e2) = (e3))) -> ((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)) = (op (e3) (e2)))) -> False). % 18.52/18.75 do 0 intro. intros zenon_H1a6 zenon_Hf1 zenon_H61 zenon_H102 zenon_H18f zenon_H160 zenon_H148 zenon_H165 zenon_H1ba zenon_H75 zenon_H13c zenon_H7a zenon_H7c zenon_Hd6 zenon_H195 zenon_H13f zenon_H12b zenon_H27 zenon_H149 zenon_H18c zenon_H14f. % 18.52/18.75 apply (zenon_or_s _ _ zenon_H1a6); [ zenon_intro zenon_Ha9 | zenon_intro zenon_H1aa ]. % 18.52/18.75 apply (zenon_L112_); trivial. % 18.52/18.75 apply (zenon_or_s _ _ zenon_H1aa); [ zenon_intro zenon_H16c | zenon_intro zenon_H1ab ]. % 18.52/18.75 apply (zenon_L156_); trivial. % 18.52/18.75 apply (zenon_or_s _ _ zenon_H1ab); [ zenon_intro zenon_Haa | zenon_intro zenon_H163 ]. % 18.52/18.75 apply (zenon_L325_); trivial. % 18.52/18.75 apply (zenon_or_s _ _ zenon_H1ba); [ zenon_intro zenon_H48 | zenon_intro zenon_H1bb ]. % 18.52/18.75 exact (zenon_H75 zenon_H48). % 18.52/18.75 apply (zenon_or_s _ _ zenon_H1bb); [ zenon_intro zenon_H122 | zenon_intro zenon_H1bc ]. % 18.52/18.75 apply (zenon_L92_); trivial. % 18.52/18.75 apply (zenon_or_s _ _ zenon_H1bc); [ zenon_intro zenon_H150 | zenon_intro zenon_Ha9 ]. % 18.52/18.75 apply (zenon_L309_); trivial. % 18.52/18.75 apply (zenon_L111_); trivial. % 18.52/18.75 (* end of lemma zenon_L326_ *) % 18.52/18.75 assert (zenon_L327_ : (((op (e2) (e2)) = (e0))\/(((op (e2) (e2)) = (e1))\/(((op (e2) (e2)) = (e2))\/((op (e2) (e2)) = (e3))))) -> (~((op (e2) (e2)) = (e0))) -> ((op (e3) (e2)) = (e1)) -> (~((op (e2) (e2)) = (op (e3) (e2)))) -> (~((op (e2) (e2)) = (e2))) -> ((op (e2) (e0)) = (e3)) -> (~((op (e2) (e0)) = (op (e2) (e2)))) -> False). % 18.52/18.75 do 0 intro. intros zenon_H1c4 zenon_H81 zenon_Hba zenon_H18f zenon_H173 zenon_H3b zenon_H52. % 18.52/18.75 apply (zenon_or_s _ _ zenon_H1c4); [ zenon_intro zenon_H2c | zenon_intro zenon_H1c5 ]. % 18.52/18.75 exact (zenon_H81 zenon_H2c). % 18.52/18.75 apply (zenon_or_s _ _ zenon_H1c5); [ zenon_intro zenon_Hf1 | zenon_intro zenon_H1c6 ]. % 18.52/18.75 apply (zenon_L185_); trivial. % 18.52/18.75 apply (zenon_or_s _ _ zenon_H1c6); [ zenon_intro zenon_H176 | zenon_intro zenon_Haa ]. % 18.52/18.75 exact (zenon_H173 zenon_H176). % 18.52/18.75 apply (zenon_L168_); trivial. % 18.52/18.75 (* end of lemma zenon_L327_ *) % 18.52/18.75 assert (zenon_L328_ : ((op (e0) (e2)) = (e1)) -> ((op (e0) (e2)) = (e2)) -> (~((e1) = (e2))) -> False). % 18.52/18.75 do 0 intro. intros zenon_H122 zenon_H150 zenon_H7c. % 18.52/18.75 elim (classic ((e2) = (e2))); [ zenon_intro zenon_H7d | zenon_intro zenon_H7e ]. % 18.52/18.75 cut (((e2) = (e2)) = ((e1) = (e2))). % 18.52/18.76 intro zenon_D_pnotp. % 18.52/18.76 apply zenon_H7c. % 18.52/18.76 rewrite <- zenon_D_pnotp. % 18.52/18.76 exact zenon_H7d. % 18.52/18.76 cut (((e2) = (e2))); [idtac | apply NNPP; zenon_intro zenon_H7e]. % 18.52/18.76 cut (((e2) = (e1))); [idtac | apply NNPP; zenon_intro zenon_H7f]. % 18.52/18.76 congruence. % 18.52/18.76 cut (((op (e0) (e2)) = (e1)) = ((e2) = (e1))). % 18.52/18.76 intro zenon_D_pnotp. % 18.52/18.76 apply zenon_H7f. % 18.52/18.76 rewrite <- zenon_D_pnotp. % 18.52/18.76 exact zenon_H122. % 18.52/18.76 cut (((e1) = (e1))); [idtac | apply NNPP; zenon_intro zenon_H79]. % 18.52/18.76 cut (((op (e0) (e2)) = (e2))); [idtac | apply NNPP; zenon_intro zenon_H1fd]. % 18.52/18.76 congruence. % 18.52/18.76 exact (zenon_H1fd zenon_H150). % 18.52/18.76 apply zenon_H79. apply refl_equal. % 18.52/18.76 apply zenon_H7e. apply refl_equal. % 18.52/18.76 apply zenon_H7e. apply refl_equal. % 18.52/18.76 (* end of lemma zenon_L328_ *) % 18.52/18.76 assert (zenon_L329_ : ((~((op (e3) (e3)) = (e0)))\/((op (e3) (e0)) = (e3))) -> (~((op (e0) (e0)) = (e0))) -> (((op (e0) (e0)) = (e2))\/(((op (e0) (e1)) = (e2))\/(((op (e0) (e2)) = (e2))\/((op (e0) (e3)) = (e2))))) -> (~((e1) = (e3))) -> (~((e2) = (e3))) -> (((op (e1) (e0)) = (e1))\/(((op (e1) (e1)) = (e1))\/(((op (e1) (e2)) = (e1))\/((op (e1) (e3)) = (e1))))) -> ((op (e3) (e0)) = (e2)) -> (((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 (e0) (e2)) = (op (e1) (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 (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 (e0) (e3)))) -> (~((op (e1) (e0)) = (op (e1) (e3)))) -> (~((op (e2) (e2)) = (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 (e3) (e0)) = (e0))) -> (((op (e2) (e2)) = (e0))\/(((op (e2) (e2)) = (e1))\/(((op (e2) (e2)) = (e2))\/((op (e2) (e2)) = (e3))))) -> ((op (e2) (e0)) = (e3)) -> (~((op (e2) (e0)) = (op (e2) (e2)))) -> (~((op (e2) (e2)) = (e2))) -> (~((op (e1) (e2)) = (op (e2) (e2)))) -> (((op (e2) (e0)) = (e0))\/(((op (e2) (e1)) = (e0))\/(((op (e2) (e2)) = (e0))\/((op (e2) (e3)) = (e0))))) -> (~((op (e1) (e1)) = (e1))) -> ((op (e1) (e0)) = (e0)) -> (~((e0) = (e1))) -> (~((op (e0) (e1)) = (op (e1) (e1)))) -> (~((op (e0) (e3)) = (op (e1) (e3)))) -> (~((op (e2) (e2)) = (e0))) -> (((op (e0) (e2)) = (e0))\/(((op (e1) (e2)) = (e0))\/(((op (e2) (e2)) = (e0))\/((op (e3) (e2)) = (e0))))) -> (~((op (e0) (e0)) = (op (e0) (e2)))) -> (((op (e0) (e2)) = (e3))\/(((op (e1) (e2)) = (e3))\/(((op (e2) (e2)) = (e3))\/((op (e3) (e2)) = (e3))))) -> (((op (e1) (e0)) = (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)) = (e1))\/(((op (e1) (e2)) = (e1))\/(((op (e2) (e2)) = (e1))\/((op (e3) (e2)) = (e1))))) -> (~((op (e1) (e2)) = (e0))) -> (~((op (e0) (e2)) = (e0))) -> (~((e0) = (e3))) -> (((op (e0) (e0)) = (e3))\/(((op (e0) (e1)) = (e3))\/(((op (e0) (e2)) = (e3))\/((op (e0) (e3)) = (e3))))) -> ((op (e0) (e0)) = (e1)) -> (~((e1) = (e2))) -> (~((op (e0) (e3)) = (e0))) -> (((op (e0) (e0)) = (e0))\/(((op (e0) (e1)) = (e0))\/(((op (e0) (e2)) = (e0))\/((op (e0) (e3)) = (e0))))) -> False). % 18.52/18.76 do 0 intro. intros zenon_H1ec zenon_H3f zenon_H183 zenon_H95 zenon_H12b zenon_H128 zenon_H148 zenon_H165 zenon_H102 zenon_H14f zenon_H160 zenon_H195 zenon_H16f zenon_H30 zenon_H31 zenon_H1ac zenon_H18f zenon_H54 zenon_Hd8 zenon_H6d zenon_H130 zenon_H67 zenon_H40 zenon_H1c4 zenon_H3b zenon_H52 zenon_H173 zenon_H2b zenon_H2f zenon_H10a zenon_H27 zenon_Ha1 zenon_H10e zenon_H1d zenon_H81 zenon_H6a zenon_H13c zenon_H1a6 zenon_H18c zenon_H149 zenon_H1ba zenon_H139 zenon_H25 zenon_H75 zenon_H9a zenon_H168 zenon_H7a zenon_H7c zenon_H76 zenon_H74. % 18.52/18.76 apply (zenon_or_s _ _ zenon_H1ec); [ zenon_intro zenon_H1ae | zenon_intro zenon_H15e ]. % 18.52/18.76 apply (zenon_or_s _ _ zenon_H74); [ zenon_intro zenon_H42 | zenon_intro zenon_H77 ]. % 18.52/18.76 exact (zenon_H3f zenon_H42). % 18.52/18.76 apply (zenon_or_s _ _ zenon_H77); [ zenon_intro zenon_H49 | zenon_intro zenon_H78 ]. % 18.52/18.76 apply (zenon_or_s _ _ zenon_H183); [ zenon_intro zenon_H7b | zenon_intro zenon_H186 ]. % 18.52/18.76 apply (zenon_L26_); trivial. % 18.52/18.76 apply (zenon_or_s _ _ zenon_H186); [ zenon_intro zenon_H10f | zenon_intro zenon_H187 ]. % 18.52/18.76 apply (zenon_or_s _ _ zenon_H168); [ zenon_intro zenon_H3a | zenon_intro zenon_H169 ]. % 18.52/18.76 apply (zenon_L35_); trivial. % 18.52/18.76 apply (zenon_or_s _ _ zenon_H169); [ zenon_intro zenon_H99 | zenon_intro zenon_H16a ]. % 18.52/18.76 apply (zenon_L175_); trivial. % 18.52/18.76 apply (zenon_or_s _ _ zenon_H16a); [ zenon_intro zenon_Ha9 | zenon_intro zenon_He3 ]. % 18.52/18.76 apply (zenon_or_s _ _ zenon_H128); [ zenon_intro zenon_H9d | zenon_intro zenon_H129 ]. % 18.52/18.76 apply (zenon_L262_); trivial. % 18.52/18.76 apply (zenon_or_s _ _ zenon_H129); [ zenon_intro zenon_H10d | zenon_intro zenon_H12a ]. % 18.52/18.76 exact (zenon_H10a zenon_H10d). % 18.52/18.76 apply (zenon_or_s _ _ zenon_H12a); [ zenon_intro zenon_Hf0 | zenon_intro zenon_Hd6 ]. % 18.52/18.76 apply (zenon_L301_); trivial. % 18.52/18.76 apply (zenon_L163_); trivial. % 18.52/18.76 apply (zenon_or_s _ _ zenon_H128); [ zenon_intro zenon_H9d | zenon_intro zenon_H129 ]. % 18.52/18.76 apply (zenon_L262_); trivial. % 18.52/18.76 apply (zenon_or_s _ _ zenon_H129); [ zenon_intro zenon_H10d | zenon_intro zenon_H12a ]. % 18.52/18.76 exact (zenon_H10a zenon_H10d). % 18.52/18.76 apply (zenon_or_s _ _ zenon_H12a); [ zenon_intro zenon_Hf0 | zenon_intro zenon_Hd6 ]. % 18.52/18.76 apply (zenon_L301_); trivial. % 18.52/18.76 apply (zenon_or_s _ _ zenon_H18c); [ zenon_intro zenon_H86 | zenon_intro zenon_H18d ]. % 18.52/18.76 apply (zenon_L33_); trivial. % 18.52/18.76 apply (zenon_or_s _ _ zenon_H18d); [ zenon_intro zenon_H110 | zenon_intro zenon_H18e ]. % 18.52/18.76 apply (zenon_L67_); trivial. % 18.52/18.76 apply (zenon_or_s _ _ zenon_H18e); [ zenon_intro zenon_H113 | zenon_intro zenon_Hd7 ]. % 18.52/18.76 apply (zenon_or_s _ _ zenon_H16f); [ zenon_intro zenon_H9e | zenon_intro zenon_H170 ]. % 18.52/18.76 apply (zenon_L263_); trivial. % 18.52/18.76 apply (zenon_or_s _ _ zenon_H170); [ zenon_intro zenon_H13f | zenon_intro zenon_H171 ]. % 18.52/18.76 apply (zenon_or_s _ _ zenon_H2f); [ zenon_intro zenon_H34 | zenon_intro zenon_H33 ]. % 18.52/18.76 exact (zenon_H30 zenon_H34). % 18.52/18.76 apply (zenon_or_s _ _ zenon_H33); [ zenon_intro zenon_H36 | zenon_intro zenon_H35 ]. % 18.52/18.76 exact (zenon_H31 zenon_H36). % 18.52/18.76 apply (zenon_or_s _ _ zenon_H35); [ zenon_intro zenon_H2c | zenon_intro zenon_H37 ]. % 18.52/18.76 exact (zenon_H81 zenon_H2c). % 18.52/18.76 apply (zenon_or_s _ _ zenon_H6a); [ zenon_intro zenon_H48 | zenon_intro zenon_H6b ]. % 18.52/18.76 exact (zenon_H75 zenon_H48). % 18.52/18.76 apply (zenon_or_s _ _ zenon_H6b); [ zenon_intro zenon_H2a | zenon_intro zenon_H6c ]. % 18.52/18.76 exact (zenon_H25 zenon_H2a). % 18.52/18.76 apply (zenon_or_s _ _ zenon_H6c); [ zenon_intro zenon_H2c | zenon_intro zenon_H61 ]. % 18.52/18.76 exact (zenon_H81 zenon_H2c). % 18.52/18.76 apply (zenon_or_s _ _ zenon_H139); [ zenon_intro zenon_H122 | zenon_intro zenon_H13a ]. % 18.52/18.76 apply (zenon_L92_); trivial. % 18.52/18.76 apply (zenon_or_s _ _ zenon_H13a); [ zenon_intro zenon_Hf0 | zenon_intro zenon_H13b ]. % 18.52/18.76 apply (zenon_L300_); trivial. % 18.52/18.76 apply (zenon_or_s _ _ zenon_H13b); [ zenon_intro zenon_Hf1 | zenon_intro zenon_Hba ]. % 18.52/18.76 apply (zenon_L326_); trivial. % 18.52/18.76 apply (zenon_L327_); trivial. % 18.52/18.76 apply (zenon_or_s _ _ zenon_H171); [ zenon_intro zenon_H16c | zenon_intro zenon_Hdc ]. % 18.52/18.76 apply (zenon_L116_); trivial. % 18.52/18.76 apply (zenon_L117_); trivial. % 18.52/18.76 apply (zenon_L101_); trivial. % 18.52/18.76 apply (zenon_or_s _ _ zenon_H187); [ zenon_intro zenon_H150 | zenon_intro zenon_Hcd ]. % 18.52/18.76 apply (zenon_or_s _ _ zenon_H128); [ zenon_intro zenon_H9d | zenon_intro zenon_H129 ]. % 18.52/18.76 apply (zenon_L262_); trivial. % 18.52/18.76 apply (zenon_or_s _ _ zenon_H129); [ zenon_intro zenon_H10d | zenon_intro zenon_H12a ]. % 18.52/18.76 exact (zenon_H10a zenon_H10d). % 18.52/18.76 apply (zenon_or_s _ _ zenon_H12a); [ zenon_intro zenon_Hf0 | zenon_intro zenon_Hd6 ]. % 18.52/18.76 apply (zenon_L301_); trivial. % 18.52/18.76 apply (zenon_or_s _ _ zenon_H18c); [ zenon_intro zenon_H86 | zenon_intro zenon_H18d ]. % 18.52/18.76 apply (zenon_L257_); trivial. % 18.52/18.76 apply (zenon_or_s _ _ zenon_H18d); [ zenon_intro zenon_H110 | zenon_intro zenon_H18e ]. % 18.52/18.76 apply (zenon_or_s _ _ zenon_H16f); [ zenon_intro zenon_H9e | zenon_intro zenon_H170 ]. % 18.52/18.76 apply (zenon_L107_); trivial. % 18.52/18.76 apply (zenon_or_s _ _ zenon_H170); [ zenon_intro zenon_H13f | zenon_intro zenon_H171 ]. % 18.52/18.76 apply (zenon_L166_); trivial. % 18.52/18.76 apply (zenon_or_s _ _ zenon_H171); [ zenon_intro zenon_H16c | zenon_intro zenon_Hdc ]. % 18.52/18.76 apply (zenon_or_s _ _ zenon_H2f); [ zenon_intro zenon_H34 | zenon_intro zenon_H33 ]. % 18.52/18.76 exact (zenon_H30 zenon_H34). % 18.52/18.76 apply (zenon_or_s _ _ zenon_H33); [ zenon_intro zenon_H36 | zenon_intro zenon_H35 ]. % 18.52/18.76 exact (zenon_H31 zenon_H36). % 18.52/18.76 apply (zenon_or_s _ _ zenon_H35); [ zenon_intro zenon_H2c | zenon_intro zenon_H37 ]. % 18.52/18.76 exact (zenon_H81 zenon_H2c). % 18.52/18.76 apply (zenon_or_s _ _ zenon_H6a); [ zenon_intro zenon_H48 | zenon_intro zenon_H6b ]. % 18.52/18.76 exact (zenon_H75 zenon_H48). % 18.52/18.76 apply (zenon_or_s _ _ zenon_H6b); [ zenon_intro zenon_H2a | zenon_intro zenon_H6c ]. % 18.52/18.76 exact (zenon_H25 zenon_H2a). % 18.52/18.76 apply (zenon_or_s _ _ zenon_H6c); [ zenon_intro zenon_H2c | zenon_intro zenon_H61 ]. % 18.52/18.76 exact (zenon_H81 zenon_H2c). % 18.52/18.76 apply (zenon_or_s _ _ zenon_H139); [ zenon_intro zenon_H122 | zenon_intro zenon_H13a ]. % 18.52/18.76 apply (zenon_L328_); trivial. % 18.52/18.76 apply (zenon_or_s _ _ zenon_H13a); [ zenon_intro zenon_Hf0 | zenon_intro zenon_H13b ]. % 18.52/18.76 apply (zenon_L300_); trivial. % 18.52/18.76 apply (zenon_or_s _ _ zenon_H13b); [ zenon_intro zenon_Hf1 | zenon_intro zenon_Hba ]. % 18.52/18.76 apply (zenon_L156_); trivial. % 18.52/18.76 apply (zenon_L327_); trivial. % 18.52/18.76 apply (zenon_L83_); trivial. % 18.52/18.76 apply (zenon_or_s _ _ zenon_H18e); [ zenon_intro zenon_H113 | zenon_intro zenon_Hd7 ]. % 18.52/18.76 apply (zenon_L153_); trivial. % 18.52/18.76 apply (zenon_L101_); trivial. % 18.52/18.76 apply (zenon_L304_); trivial. % 18.52/18.76 apply (zenon_or_s _ _ zenon_H78); [ zenon_intro zenon_H48 | zenon_intro zenon_H1e ]. % 18.52/18.76 exact (zenon_H75 zenon_H48). % 18.52/18.76 exact (zenon_H76 zenon_H1e). % 18.52/18.76 apply (zenon_L109_); trivial. % 18.52/18.76 (* end of lemma zenon_L329_ *) % 18.52/18.76 assert (zenon_L330_ : (((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 (e3) (e1)) = (e0)))\/((op (e3) (e0)) = (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) (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 (e3) (e0)) = (op (e3) (e2)))) -> (~((op (e1) (e1)) = (op (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) (e3)) = (e1))\/(((op (e1) (e3)) = (e1))\/(((op (e2) (e3)) = (e1))\/((op (e3) (e3)) = (e1))))) -> (((op (e3) (e3)) = (e0))\/(((op (e3) (e3)) = (e1))\/(((op (e3) (e3)) = (e2))\/((op (e3) (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 (e1) (e2)) = (op (e3) (e2)))) -> (~((op (e1) (e2)) = (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) (e3)) = (e3))\/(((op (e1) (e3)) = (e3))\/(((op (e2) (e3)) = (e3))\/((op (e3) (e3)) = (e3))))) -> (~((op (e3) (e0)) = (op (e3) (e3)))) -> ((~((op (e3) (e2)) = (e0)))\/((op (e3) (e0)) = (e2))) -> (~((op (e1) (e0)) = (op (e3) (e0)))) -> ((~((op (e3) (e0)) = (e0)))\/((op (e3) (e0)) = (e0))) -> (~((op (e0) (e2)) = (op (e2) (e2)))) -> (((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) (e1)) = (e3))\/(((op (e1) (e1)) = (e3))\/(((op (e2) (e1)) = (e3))\/((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 (e0) (e3)) = (op (e3) (e3)))) -> (((op (e2) (e3)) = (e0))\/(((op (e2) (e3)) = (e1))\/(((op (e2) (e3)) = (e2))\/((op (e2) (e3)) = (e3))))) -> (~((op (e0) (e3)) = (op (e2) (e3)))) -> (~((op (e2) (e0)) = (op (e2) (e3)))) -> (~((op (e2) (e3)) = (op (e3) (e3)))) -> (((op (e0) (e3)) = (e0))\/(((op (e0) (e3)) = (e1))\/(((op (e0) (e3)) = (e2))\/((op (e0) (e3)) = (e3))))) -> (~((op (e2) (e1)) = (op (e3) (e1)))) -> (~((op (e0) (e1)) = (op (e2) (e1)))) -> (~((op (e1) (e1)) = (op (e2) (e1)))) -> (((op (e2) (e1)) = (e0))\/(((op (e2) (e1)) = (e1))\/(((op (e2) (e1)) = (e2))\/((op (e2) (e1)) = (e3))))) -> (~((op (e1) (e3)) = (op (e3) (e3)))) -> ((~((op (e2) (e3)) = (e0)))\/((op (e2) (e0)) = (e3))) -> ((~((op (e3) (e3)) = (e0)))\/((op (e3) (e0)) = (e3))) -> (~((op (e0) (e0)) = (e0))) -> (((op (e0) (e0)) = (e2))\/(((op (e0) (e1)) = (e2))\/(((op (e0) (e2)) = (e2))\/((op (e0) (e3)) = (e2))))) -> (~((e1) = (e3))) -> (~((e2) = (e3))) -> (((op (e1) (e0)) = (e1))\/(((op (e1) (e1)) = (e1))\/(((op (e1) (e2)) = (e1))\/((op (e1) (e3)) = (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 (e0) (e2)) = (op (e1) (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 (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 (e0) (e3)))) -> (~((op (e1) (e0)) = (op (e1) (e3)))) -> (~((op (e2) (e2)) = (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 (e3) (e0)) = (e0))) -> (((op (e2) (e2)) = (e0))\/(((op (e2) (e2)) = (e1))\/(((op (e2) (e2)) = (e2))\/((op (e2) (e2)) = (e3))))) -> ((op (e2) (e0)) = (e3)) -> (~((op (e2) (e0)) = (op (e2) (e2)))) -> (~((op (e2) (e2)) = (e2))) -> (~((op (e1) (e2)) = (op (e2) (e2)))) -> (((op (e2) (e0)) = (e0))\/(((op (e2) (e1)) = (e0))\/(((op (e2) (e2)) = (e0))\/((op (e2) (e3)) = (e0))))) -> (~((op (e1) (e1)) = (e1))) -> ((op (e1) (e0)) = (e0)) -> (~((e0) = (e1))) -> (~((op (e0) (e1)) = (op (e1) (e1)))) -> (~((op (e0) (e3)) = (op (e1) (e3)))) -> (~((op (e2) (e2)) = (e0))) -> (((op (e0) (e2)) = (e0))\/(((op (e1) (e2)) = (e0))\/(((op (e2) (e2)) = (e0))\/((op (e3) (e2)) = (e0))))) -> (~((op (e0) (e0)) = (op (e0) (e2)))) -> (((op (e0) (e2)) = (e3))\/(((op (e1) (e2)) = (e3))\/(((op (e2) (e2)) = (e3))\/((op (e3) (e2)) = (e3))))) -> (((op (e1) (e0)) = (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)) = (e1))\/(((op (e1) (e2)) = (e1))\/(((op (e2) (e2)) = (e1))\/((op (e3) (e2)) = (e1))))) -> (~((op (e1) (e2)) = (e0))) -> (~((op (e0) (e2)) = (e0))) -> (~((e0) = (e3))) -> (((op (e0) (e0)) = (e3))\/(((op (e0) (e1)) = (e3))\/(((op (e0) (e2)) = (e3))\/((op (e0) (e3)) = (e3))))) -> ((op (e0) (e0)) = (e1)) -> (~((e1) = (e2))) -> (~((op (e0) (e3)) = (e0))) -> (((op (e0) (e0)) = (e0))\/(((op (e0) (e1)) = (e0))\/(((op (e0) (e2)) = (e0))\/((op (e0) (e3)) = (e0))))) -> False). % 18.52/18.76 do 0 intro. intros zenon_H1fe zenon_H1e0 zenon_H1ed zenon_H62 zenon_H191 zenon_H153 zenon_H145 zenon_H6f zenon_H57 zenon_H39 zenon_H106 zenon_H133 zenon_H101 zenon_H1f0 zenon_H1d8 zenon_H115 zenon_H124 zenon_Hdb zenon_Hdf zenon_H136 zenon_H71 zenon_H1a7 zenon_H1fa zenon_H184 zenon_Ha8 zenon_He7 zenon_H109 zenon_H1a5 zenon_H1cf zenon_He8 zenon_Hc2 zenon_H11f zenon_He2 zenon_H5b zenon_Hf3 zenon_He4 zenon_Haf zenon_H17e zenon_H13e zenon_H1cc zenon_Hd5 zenon_H94 zenon_H1ec zenon_H3f zenon_H183 zenon_H95 zenon_H12b zenon_H128 zenon_H165 zenon_H102 zenon_H14f zenon_H160 zenon_H195 zenon_H16f zenon_H30 zenon_H31 zenon_H1ac zenon_H18f zenon_H54 zenon_Hd8 zenon_H6d zenon_H130 zenon_H67 zenon_H40 zenon_H1c4 zenon_H3b zenon_H52 zenon_H173 zenon_H2b zenon_H2f zenon_H10a zenon_H27 zenon_Ha1 zenon_H10e zenon_H1d zenon_H81 zenon_H6a zenon_H13c zenon_H1a6 zenon_H18c zenon_H149 zenon_H1ba zenon_H139 zenon_H25 zenon_H75 zenon_H9a zenon_H168 zenon_H7a zenon_H7c zenon_H76 zenon_H74. % 18.52/18.76 apply (zenon_or_s _ _ zenon_H1fe); [ zenon_intro zenon_H7b | zenon_intro zenon_H1ff ]. % 18.52/18.76 apply (zenon_L26_); trivial. % 18.52/18.76 apply (zenon_or_s _ _ zenon_H1ff); [ zenon_intro zenon_H86 | zenon_intro zenon_H200 ]. % 18.52/18.76 apply (zenon_L33_); trivial. % 18.52/18.76 apply (zenon_or_s _ _ zenon_H200); [ zenon_intro zenon_Hee | zenon_intro zenon_H148 ]. % 18.52/18.76 apply (zenon_L324_); trivial. % 18.52/18.76 apply (zenon_L329_); trivial. % 18.52/18.76 (* end of lemma zenon_L330_ *) % 18.52/18.76 assert (zenon_L331_ : (((op (e0) (e0)) = (e0))\/(((op (e0) (e1)) = (e0))\/(((op (e0) (e2)) = (e0))\/((op (e0) (e3)) = (e0))))) -> (~((op (e0) (e3)) = (e0))) -> (~((e1) = (e2))) -> ((op (e0) (e0)) = (e1)) -> (((op (e0) (e0)) = (e3))\/(((op (e0) (e1)) = (e3))\/(((op (e0) (e2)) = (e3))\/((op (e0) (e3)) = (e3))))) -> (~((e0) = (e3))) -> (~((op (e0) (e2)) = (e0))) -> (~((op (e1) (e2)) = (e0))) -> (((op (e0) (e2)) = (e1))\/(((op (e1) (e2)) = (e1))\/(((op (e2) (e2)) = (e1))\/((op (e3) (e2)) = (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 (e0) (e2)) = (e3))\/(((op (e1) (e2)) = (e3))\/(((op (e2) (e2)) = (e3))\/((op (e3) (e2)) = (e3))))) -> (~((op (e0) (e0)) = (op (e0) (e2)))) -> (((op (e0) (e2)) = (e0))\/(((op (e1) (e2)) = (e0))\/(((op (e2) (e2)) = (e0))\/((op (e3) (e2)) = (e0))))) -> (~((op (e2) (e2)) = (e0))) -> (~((op (e0) (e3)) = (op (e1) (e3)))) -> (~((op (e0) (e1)) = (op (e1) (e1)))) -> (~((e0) = (e1))) -> ((op (e1) (e0)) = (e0)) -> (~((op (e1) (e1)) = (e1))) -> (((op (e2) (e0)) = (e0))\/(((op (e2) (e1)) = (e0))\/(((op (e2) (e2)) = (e0))\/((op (e2) (e3)) = (e0))))) -> (~((op (e1) (e2)) = (op (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 (e3) (e0)) = (e0))) -> (((op (e0) (e3)) = (e0))\/(((op (e1) (e3)) = (e0))\/(((op (e2) (e3)) = (e0))\/((op (e3) (e3)) = (e0))))) -> (~((op (e3) (e1)) = (op (e3) (e3)))) -> (~((op (e2) (e2)) = (op (e2) (e3)))) -> (~((op (e1) (e0)) = (op (e1) (e3)))) -> (~((op (e0) (e1)) = (op (e0) (e3)))) -> (~((op (e2) (e2)) = (op (e3) (e2)))) -> (((op (e3) (e0)) = (e0))\/(((op (e3) (e1)) = (e0))\/(((op (e3) (e2)) = (e0))\/((op (e3) (e3)) = (e0))))) -> (~((op (e2) (e1)) = (e0))) -> (~((op (e2) (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 (e1) (e1)) = (op (e3) (e1)))) -> (~((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))))) -> (((op (e1) (e0)) = (e1))\/(((op (e1) (e1)) = (e1))\/(((op (e1) (e2)) = (e1))\/((op (e1) (e3)) = (e1))))) -> (~((e1) = (e3))) -> (((op (e0) (e0)) = (e2))\/(((op (e0) (e1)) = (e2))\/(((op (e0) (e2)) = (e2))\/((op (e0) (e3)) = (e2))))) -> (~((op (e0) (e0)) = (e0))) -> ((~((op (e3) (e3)) = (e0)))\/((op (e3) (e0)) = (e3))) -> ((~((op (e2) (e3)) = (e0)))\/((op (e2) (e0)) = (e3))) -> (~((op (e1) (e3)) = (op (e3) (e3)))) -> (((op (e2) (e1)) = (e0))\/(((op (e2) (e1)) = (e1))\/(((op (e2) (e1)) = (e2))\/((op (e2) (e1)) = (e3))))) -> (~((op (e1) (e1)) = (op (e2) (e1)))) -> (~((op (e0) (e1)) = (op (e2) (e1)))) -> (~((op (e2) (e1)) = (op (e3) (e1)))) -> (((op (e0) (e3)) = (e0))\/(((op (e0) (e3)) = (e1))\/(((op (e0) (e3)) = (e2))\/((op (e0) (e3)) = (e3))))) -> (~((op (e2) (e3)) = (op (e3) (e3)))) -> (~((op (e2) (e0)) = (op (e2) (e3)))) -> (~((op (e0) (e3)) = (op (e2) (e3)))) -> (((op (e2) (e3)) = (e0))\/(((op (e2) (e3)) = (e1))\/(((op (e2) (e3)) = (e2))\/((op (e2) (e3)) = (e3))))) -> (~((op (e0) (e3)) = (op (e3) (e3)))) -> (((op (e3) (e0)) = (e1))\/(((op (e3) (e1)) = (e1))\/(((op (e3) (e2)) = (e1))\/((op (e3) (e3)) = (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) (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 (e0) (e2)) = (op (e2) (e2)))) -> ((~((op (e3) (e0)) = (e0)))\/((op (e3) (e0)) = (e0))) -> (~((op (e1) (e0)) = (op (e3) (e0)))) -> ((~((op (e3) (e2)) = (e0)))\/((op (e3) (e0)) = (e2))) -> (~((op (e3) (e0)) = (op (e3) (e3)))) -> (((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 (e1) (e3)) = (op (e2) (e3)))) -> (~((op (e1) (e2)) = (op (e1) (e3)))) -> (~((op (e1) (e2)) = (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 (e3) (e3)) = (e0))\/(((op (e3) (e3)) = (e1))\/(((op (e3) (e3)) = (e2))\/((op (e3) (e3)) = (e3))))) -> (((op (e0) (e3)) = (e1))\/(((op (e1) (e3)) = (e1))\/(((op (e2) (e3)) = (e1))\/((op (e3) (e3)) = (e1))))) -> (((op (e2) (e0)) = (e1))\/(((op (e2) (e1)) = (e1))\/(((op (e2) (e2)) = (e1))\/((op (e2) (e3)) = (e1))))) -> (~((op (e0) (e0)) = (op (e2) (e0)))) -> (~((op (e1) (e1)) = (op (e1) (e3)))) -> (~((op (e3) (e0)) = (op (e3) (e2)))) -> (((op (e0) (e3)) = (e2))\/(((op (e1) (e3)) = (e2))\/(((op (e2) (e3)) = (e2))\/((op (e3) (e3)) = (e2))))) -> (((op (e3) (e0)) = (e2))\/(((op (e3) (e1)) = (e2))\/(((op (e3) (e2)) = (e2))\/((op (e3) (e3)) = (e2))))) -> (((op (e3) (e2)) = (e0))\/(((op (e3) (e2)) = (e1))\/(((op (e3) (e2)) = (e2))\/((op (e3) (e2)) = (e3))))) -> (~((op (e3) (e2)) = (op (e3) (e3)))) -> ((~((op (e3) (e1)) = (e0)))\/((op (e3) (e0)) = (e1))) -> (((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 (e3) (e0)) = (e2)) -> (~((e2) = (e3))) -> False). % 18.52/18.76 do 0 intro. intros zenon_H74 zenon_H76 zenon_H7c zenon_H7a zenon_H168 zenon_H9a zenon_H75 zenon_H25 zenon_H139 zenon_H1ba zenon_H149 zenon_H18c zenon_H1a6 zenon_H13c zenon_H6a zenon_H81 zenon_H1d zenon_H10e zenon_Ha1 zenon_H27 zenon_H10a zenon_H2f zenon_H2b zenon_H173 zenon_H52 zenon_H1c4 zenon_H40 zenon_H67 zenon_H130 zenon_H6d zenon_Hd8 zenon_H54 zenon_H18f zenon_H1ac zenon_H31 zenon_H30 zenon_H16f zenon_H195 zenon_H160 zenon_H14f zenon_H102 zenon_H165 zenon_H128 zenon_H95 zenon_H183 zenon_H3f zenon_H1ec zenon_H94 zenon_Hd5 zenon_H1cc zenon_H13e zenon_H17e zenon_Haf zenon_He4 zenon_Hf3 zenon_H5b zenon_He2 zenon_H11f zenon_Hc2 zenon_He8 zenon_H1cf zenon_H1a5 zenon_H109 zenon_He7 zenon_Ha8 zenon_H184 zenon_H1fa zenon_H1a7 zenon_H71 zenon_H136 zenon_Hdf zenon_Hdb zenon_H124 zenon_H115 zenon_H1d8 zenon_H1f0 zenon_H101 zenon_H133 zenon_H106 zenon_H39 zenon_H57 zenon_H6f zenon_H145 zenon_H153 zenon_H191 zenon_H62 zenon_H1ed zenon_H1e0 zenon_H1fe zenon_H148 zenon_H12b. % 18.52/18.76 apply (zenon_or_s _ _ zenon_H1e0); [ zenon_intro zenon_H3a | zenon_intro zenon_H1e1 ]. % 18.52/18.76 apply (zenon_L35_); trivial. % 18.52/18.76 apply (zenon_or_s _ _ zenon_H1e1); [ zenon_intro zenon_H9e | zenon_intro zenon_H1e2 ]. % 18.52/18.76 apply (zenon_L263_); trivial. % 18.52/18.76 apply (zenon_or_s _ _ zenon_H1e2); [ zenon_intro zenon_H3b | zenon_intro zenon_H15e ]. % 18.52/18.76 apply (zenon_L330_); trivial. % 18.52/18.76 apply (zenon_L109_); trivial. % 18.52/18.76 (* end of lemma zenon_L331_ *) % 18.52/18.76 assert (zenon_L332_ : ((op (e2) (e0)) = (e0)) -> ((op (e1) (e0)) = (e0)) -> (~((op (e1) (e0)) = (op (e2) (e0)))) -> False). % 18.52/18.76 do 0 intro. intros zenon_H34 zenon_H27 zenon_H201. % 18.52/18.76 elim (classic ((op (e2) (e0)) = (op (e2) (e0)))); [ zenon_intro zenon_H202 | zenon_intro zenon_H53 ]. % 18.52/18.76 cut (((op (e2) (e0)) = (op (e2) (e0))) = ((op (e1) (e0)) = (op (e2) (e0)))). % 18.52/18.76 intro zenon_D_pnotp. % 18.52/18.76 apply zenon_H201. % 18.52/18.76 rewrite <- zenon_D_pnotp. % 18.52/18.76 exact zenon_H202. % 18.52/18.76 cut (((op (e2) (e0)) = (op (e2) (e0)))); [idtac | apply NNPP; zenon_intro zenon_H53]. % 18.52/18.76 cut (((op (e2) (e0)) = (op (e1) (e0)))); [idtac | apply NNPP; zenon_intro zenon_H203]. % 18.52/18.76 congruence. % 18.52/18.76 cut (((op (e2) (e0)) = (e0)) = ((op (e2) (e0)) = (op (e1) (e0)))). % 18.52/18.76 intro zenon_D_pnotp. % 18.52/18.76 apply zenon_H203. % 18.52/18.76 rewrite <- zenon_D_pnotp. % 18.52/18.76 exact zenon_H34. % 18.52/18.76 cut (((e0) = (op (e1) (e0)))); [idtac | apply NNPP; zenon_intro zenon_H1fc]. % 18.52/18.76 cut (((op (e2) (e0)) = (op (e2) (e0)))); [idtac | apply NNPP; zenon_intro zenon_H53]. % 18.52/18.76 congruence. % 18.52/18.76 apply zenon_H53. apply refl_equal. % 18.52/18.76 apply zenon_H1fc. apply sym_equal. exact zenon_H27. % 18.52/18.76 apply zenon_H53. apply refl_equal. % 18.52/18.76 apply zenon_H53. apply refl_equal. % 18.52/18.76 (* end of lemma zenon_L332_ *) % 18.52/18.76 assert (zenon_L333_ : ((~((op (e0) (e3)) = (e0)))\/((op (e0) (e0)) = (e3))) -> ((~((op (e1) (e1)) = (e0)))\/((op (e1) (e0)) = (e1))) -> (~((e1) = (e2))) -> ((op (e0) (e0)) = (e1)) -> ((~((op (e2) (e3)) = (e0)))\/((op (e2) (e0)) = (e3))) -> (((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))))) -> (((op (e0) (e2)) = (e3))\/(((op (e1) (e2)) = (e3))\/(((op (e2) (e2)) = (e3))\/((op (e3) (e2)) = (e3))))) -> (~((op (e3) (e1)) = (op (e3) (e2)))) -> ((~((op (e3) (e2)) = (e0)))\/((op (e3) (e0)) = (e2))) -> (~((op (e2) (e2)) = (op (e3) (e2)))) -> (((op (e3) (e2)) = (e0))\/(((op (e3) (e2)) = (e1))\/(((op (e3) (e2)) = (e2))\/((op (e3) (e2)) = (e3))))) -> (~((op (e0) (e2)) = (op (e1) (e2)))) -> (((op (e1) (e2)) = (e0))\/(((op (e1) (e2)) = (e1))\/(((op (e1) (e2)) = (e2))\/((op (e1) (e2)) = (e3))))) -> (~((e1) = (e3))) -> (~((e0) = (e3))) -> (~((op (e1) (e1)) = (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) (e3)) = (e0))\/(((op (e2) (e3)) = (e1))\/(((op (e2) (e3)) = (e2))\/((op (e2) (e3)) = (e3))))) -> (~((op (e0) (e3)) = (op (e1) (e3)))) -> (~((op (e0) (e1)) = (op (e1) (e1)))) -> (~((e0) = (e1))) -> (~((op (e0) (e2)) = (op (e2) (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) (e3)) = (e0))\/(((op (e1) (e3)) = (e1))\/(((op (e1) (e3)) = (e2))\/((op (e1) (e3)) = (e3))))) -> (~((op (e1) (e3)) = (op (e2) (e3)))) -> (~((op (e1) (e0)) = (op (e1) (e3)))) -> (~((op (e1) (e3)) = (op (e3) (e3)))) -> (~((op (e0) (e3)) = (op (e2) (e3)))) -> (((op (e0) (e3)) = (e0))\/(((op (e0) (e3)) = (e1))\/(((op (e0) (e3)) = (e2))\/((op (e0) (e3)) = (e3))))) -> (~((op (e2) (e1)) = (op (e3) (e1)))) -> (((op (e2) (e0)) = (e3))\/(((op (e2) (e1)) = (e3))\/(((op (e2) (e2)) = (e3))\/((op (e2) (e3)) = (e3))))) -> (((op (e2) (e0)) = (e1))\/(((op (e2) (e1)) = (e1))\/(((op (e2) (e2)) = (e1))\/((op (e2) (e3)) = (e1))))) -> (~((op (e2) (e3)) = (op (e3) (e3)))) -> (~((op (e3) (e3)) = (e3))) -> (((op (e3) (e3)) = (e0))\/(((op (e3) (e3)) = (e1))\/(((op (e3) (e3)) = (e2))\/((op (e3) (e3)) = (e3))))) -> (~((op (e1) (e2)) = (op (e2) (e2)))) -> (((op (e0) (e1)) = (e1))\/(((op (e1) (e1)) = (e1))\/(((op (e2) (e1)) = (e1))\/((op (e3) (e1)) = (e1))))) -> (~((op (e0) (e0)) = (op (e0) (e3)))) -> ((~((op (e2) (e2)) = (e0)))\/((op (e2) (e0)) = (e2))) -> ((~((op (e3) (e0)) = (e0)))\/((op (e3) (e0)) = (e0))) -> (((op (e0) (e0)) = (e2))\/(((op (e0) (e1)) = (e2))\/(((op (e0) (e2)) = (e2))\/((op (e0) (e3)) = (e2))))) -> (~((op (e2) (e0)) = (op (e3) (e0)))) -> (~((op (e0) (e1)) = (op (e2) (e1)))) -> ((~((op (e1) (e2)) = (e0)))\/((op (e1) (e0)) = (e2))) -> ((~((op (e1) (e3)) = (e0)))\/((op (e1) (e0)) = (e3))) -> (((op (e1) (e1)) = (e0))\/(((op (e1) (e1)) = (e1))\/(((op (e1) (e1)) = (e2))\/((op (e1) (e1)) = (e3))))) -> (~((op (e1) (e1)) = (op (e2) (e1)))) -> (~((op (e0) (e0)) = (op (e0) (e2)))) -> (((op (e0) (e2)) = (e1))\/(((op (e1) (e2)) = (e1))\/(((op (e2) (e2)) = (e1))\/((op (e3) (e2)) = (e1))))) -> (((op (e1) (e0)) = (e1))\/(((op (e1) (e1)) = (e1))\/(((op (e1) (e2)) = (e1))\/((op (e1) (e3)) = (e1))))) -> (((op (e0) (e3)) = (e3))\/(((op (e1) (e3)) = (e3))\/(((op (e2) (e3)) = (e3))\/((op (e3) (e3)) = (e3))))) -> (~((op (e3) (e1)) = (op (e3) (e3)))) -> (((op (e0) (e3)) = (e1))\/(((op (e1) (e3)) = (e1))\/(((op (e2) (e3)) = (e1))\/((op (e3) (e3)) = (e1))))) -> (~((e2) = (e3))) -> (~((op (e1) (e2)) = (op (e1) (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 (e2) (e2)) = (e2))) -> (((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) (e1)) = (op (e3) (e1)))) -> (((op (e3) (e0)) = (e3))\/(((op (e3) (e1)) = (e3))\/(((op (e3) (e2)) = (e3))\/((op (e3) (e3)) = (e3))))) -> (~((e0) = (e2))) -> (~((op (e0) (e2)) = (op (e3) (e2)))) -> (((op (e3) (e0)) = (e2))\/(((op (e3) (e1)) = (e2))\/(((op (e3) (e2)) = (e2))\/((op (e3) (e3)) = (e2))))) -> (~((op (e0) (e0)) = (op (e2) (e0)))) -> ((~((op (e2) (e1)) = (e0)))\/((op (e2) (e0)) = (e1))) -> (((op (e0) (e0)) = (e2))\/(((op (e1) (e0)) = (e2))\/(((op (e2) (e0)) = (e2))\/((op (e3) (e0)) = (e2))))) -> ((~((op (e2) (e0)) = (e0)))\/((op (e2) (e0)) = (e0))) -> (((op (e0) (e0)) = (e3))\/(((op (e1) (e0)) = (e3))\/(((op (e2) (e0)) = (e3))\/((op (e3) (e0)) = (e3))))) -> (((op (e3) (e0)) = (e0))\/(((op (e3) (e1)) = (e0))\/(((op (e3) (e2)) = (e0))\/((op (e3) (e3)) = (e0))))) -> (~((op (e2) (e1)) = (op (e2) (e3)))) -> (((op (e2) (e2)) = (e0))\/(((op (e2) (e2)) = (e1))\/(((op (e2) (e2)) = (e2))\/((op (e2) (e2)) = (e3))))) -> (((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 (e3) (e0)) = (op (e3) (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))))) -> ((~((op (e3) (e3)) = (e0)))\/((op (e3) (e0)) = (e3))) -> ((~((op (e3) (e1)) = (e0)))\/((op (e3) (e0)) = (e1))) -> (~((op (e0) (e0)) = (e0))) -> (((op (e1) (e0)) = (e0))\/(((op (e1) (e1)) = (e0))\/(((op (e1) (e2)) = (e0))\/((op (e1) (e3)) = (e0))))) -> (~((op (e1) (e0)) = (op (e1) (e1)))) -> (((op (e0) (e2)) = (e0))\/(((op (e1) (e2)) = (e0))\/(((op (e2) (e2)) = (e0))\/((op (e3) (e2)) = (e0))))) -> (~((op (e0) (e1)) = (op (e0) (e3)))) -> (~((op (e1) (e1)) = (op (e1) (e3)))) -> (~((op (e2) (e0)) = (op (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) (e0)) = (op (e2) (e2)))) -> (~((op (e1) (e1)) = (op (e1) (e2)))) -> (~((op (e0) (e1)) = (op (e0) (e2)))) -> (~((op (e3) (e0)) = (op (e3) (e3)))) -> (~((op (e2) (e2)) = (op (e2) (e3)))) -> (~((op (e3) (e0)) = (op (e3) (e2)))) -> (((op (e0) (e0)) = (e0))\/(((op (e1) (e0)) = (e0))\/(((op (e2) (e0)) = (e0))\/((op (e3) (e0)) = (e0))))) -> (~((op (e0) (e2)) = (e0))) -> (((op (e0) (e0)) = (e0))\/(((op (e0) (e1)) = (e0))\/(((op (e0) (e2)) = (e0))\/((op (e0) (e3)) = (e0))))) -> (~((op (e1) (e0)) = (op (e3) (e0)))) -> (~((op (e2) (e0)) = (op (e2) (e1)))) -> (~((op (e1) (e0)) = (op (e2) (e0)))) -> ((~((op (e1) (e0)) = (e0)))\/((op (e1) (e0)) = (e0))) -> False). % 18.52/18.76 do 0 intro. intros zenon_H204 zenon_H205 zenon_H7c zenon_H7a zenon_H94 zenon_H2f zenon_H1a5 zenon_H1a6 zenon_H1a4 zenon_H1a7 zenon_H18f zenon_H191 zenon_H195 zenon_H19d zenon_H95 zenon_H9a zenon_H10a zenon_H18c zenon_H115 zenon_H11f zenon_H1d zenon_H10e zenon_Ha1 zenon_Ha8 zenon_He8 zenon_Hc2 zenon_Hdf zenon_Hdb zenon_Hd8 zenon_Hd5 zenon_He2 zenon_He4 zenon_Haf zenon_He7 zenon_H106 zenon_Hf3 zenon_H102 zenon_H101 zenon_H2b zenon_H109 zenon_H189 zenon_H185 zenon_H184 zenon_H183 zenon_H17b zenon_H17e zenon_H178 zenon_H179 zenon_H142 zenon_H13e zenon_H13c zenon_H139 zenon_H128 zenon_H136 zenon_H130 zenon_H133 zenon_H12b zenon_H124 zenon_H145 zenon_H172 zenon_H173 zenon_H16f zenon_H168 zenon_H160 zenon_H165 zenon_H149 zenon_H14f zenon_H153 zenon_H39 zenon_H182 zenon_H1fe zenon_H1ee zenon_H1e0 zenon_H1ac zenon_H1c7 zenon_H1c4 zenon_H1cc zenon_H1ba zenon_H1cf zenon_H1d8 zenon_H1d5 zenon_H1ec zenon_H1ed zenon_H3f zenon_H22 zenon_H45 zenon_H6a zenon_H54 zenon_H57 zenon_H5b zenon_H62 zenon_H67 zenon_H52 zenon_H4f zenon_H4a zenon_H71 zenon_H6d zenon_H6f zenon_H3e zenon_H75 zenon_H74 zenon_H1fa zenon_H1f0 zenon_H201 zenon_H206. % 18.52/18.76 apply (zenon_or_s _ _ zenon_H204); [ zenon_intro zenon_H76 | zenon_intro zenon_H3a ]. % 18.52/18.76 apply (zenon_or_s _ _ zenon_H206); [ zenon_intro zenon_H23 | zenon_intro zenon_H27 ]. % 18.52/18.76 apply (zenon_or_s _ _ zenon_H205); [ zenon_intro zenon_H24 | zenon_intro zenon_H9d ]. % 18.52/18.76 apply (zenon_or_s _ _ zenon_H178); [ zenon_intro zenon_H25 | zenon_intro zenon_H86 ]. % 18.52/18.76 apply (zenon_or_s _ _ zenon_H179); [ zenon_intro zenon_H38 | zenon_intro zenon_H9e ]. % 18.52/18.76 apply (zenon_L24_); trivial. % 18.52/18.76 apply (zenon_or_s _ _ zenon_H1ee); [ zenon_intro zenon_H30 | zenon_intro zenon_H34 ]. % 18.52/18.76 apply (zenon_or_s _ _ zenon_H182); [ zenon_intro zenon_H31 | zenon_intro zenon_Hed ]. % 18.52/18.76 apply (zenon_or_s _ _ zenon_H185); [ zenon_intro zenon_H81 | zenon_intro zenon_Hee ]. % 18.52/18.76 apply (zenon_or_s _ _ zenon_H184); [ zenon_intro zenon_H40 | zenon_intro zenon_H44 ]. % 18.52/18.76 apply (zenon_L7_); trivial. % 18.52/18.76 apply (zenon_or_s _ _ zenon_H1fe); [ zenon_intro zenon_H7b | zenon_intro zenon_H1ff ]. % 18.52/18.76 apply (zenon_L26_); trivial. % 18.52/18.76 apply (zenon_or_s _ _ zenon_H1ff); [ zenon_intro zenon_H86 | zenon_intro zenon_H200 ]. % 18.52/18.76 apply (zenon_L34_); trivial. % 18.52/18.76 apply (zenon_or_s _ _ zenon_H200); [ zenon_intro zenon_Hee | zenon_intro zenon_H148 ]. % 18.52/18.76 apply (zenon_L171_); trivial. % 18.52/18.76 apply (zenon_L100_); trivial. % 18.52/18.76 apply (zenon_L171_); trivial. % 18.52/18.76 apply (zenon_L134_); trivial. % 18.52/18.76 apply (zenon_or_s _ _ zenon_H1fe); [ zenon_intro zenon_H7b | zenon_intro zenon_H1ff ]. % 18.52/18.76 apply (zenon_L26_); trivial. % 18.52/18.76 apply (zenon_or_s _ _ zenon_H1ff); [ zenon_intro zenon_H86 | zenon_intro zenon_H200 ]. % 18.52/18.76 apply (zenon_L256_); trivial. % 18.52/18.76 apply (zenon_or_s _ _ zenon_H200); [ zenon_intro zenon_Hee | zenon_intro zenon_H148 ]. % 18.52/18.76 apply (zenon_L204_); trivial. % 18.52/18.76 apply (zenon_L107_); trivial. % 18.52/18.76 apply (zenon_L256_); trivial. % 18.52/18.76 apply (zenon_L124_); trivial. % 18.52/18.76 apply (zenon_or_s _ _ zenon_H178); [ zenon_intro zenon_H25 | zenon_intro zenon_H86 ]. % 18.52/18.76 apply (zenon_or_s _ _ zenon_H1ee); [ zenon_intro zenon_H30 | zenon_intro zenon_H34 ]. % 18.52/18.76 apply (zenon_or_s _ _ zenon_H182); [ zenon_intro zenon_H31 | zenon_intro zenon_Hed ]. % 18.52/18.76 apply (zenon_or_s _ _ zenon_H185); [ zenon_intro zenon_H81 | zenon_intro zenon_Hee ]. % 18.52/18.76 apply (zenon_or_s _ _ zenon_H94); [ zenon_intro zenon_H32 | zenon_intro zenon_H3b ]. % 18.52/18.76 apply (zenon_or_s _ _ zenon_H184); [ zenon_intro zenon_H40 | zenon_intro zenon_H44 ]. % 18.52/18.76 apply (zenon_or_s _ _ zenon_H1fe); [ zenon_intro zenon_H7b | zenon_intro zenon_H1ff ]. % 18.52/18.76 apply (zenon_L26_); trivial. % 18.52/18.76 apply (zenon_or_s _ _ zenon_H1ff); [ zenon_intro zenon_H86 | zenon_intro zenon_H200 ]. % 18.52/18.76 apply (zenon_L257_); trivial. % 18.52/18.76 apply (zenon_or_s _ _ zenon_H200); [ zenon_intro zenon_Hee | zenon_intro zenon_H148 ]. % 18.52/18.76 apply (zenon_L323_); trivial. % 18.52/18.76 apply (zenon_L331_); trivial. % 18.52/18.76 apply (zenon_L312_); trivial. % 18.52/18.76 apply (zenon_or_s _ _ zenon_H184); [ zenon_intro zenon_H40 | zenon_intro zenon_H44 ]. % 18.52/18.76 apply (zenon_L330_); trivial. % 18.52/18.76 apply (zenon_L312_); trivial. % 18.52/18.76 apply (zenon_L324_); trivial. % 18.52/18.76 apply (zenon_L134_); trivial. % 18.52/18.76 apply (zenon_L332_); trivial. % 18.52/18.76 apply (zenon_L257_); trivial. % 18.52/18.76 apply (zenon_L35_); trivial. % 18.52/18.76 (* end of lemma zenon_L333_ *) % 18.52/18.76 assert (zenon_L334_ : (~((op (e0) (e2)) = (op (e1) (e2)))) -> ((op (e0) (e2)) = (e0)) -> ((op (e1) (e2)) = (e0)) -> False). % 18.52/18.76 do 0 intro. intros zenon_H195 zenon_H48 zenon_H2a. % 18.52/18.76 cut (((op (e0) (e2)) = (e0)) = ((op (e0) (e2)) = (op (e1) (e2)))). % 18.52/18.76 intro zenon_D_pnotp. % 18.52/18.76 apply zenon_H195. % 18.52/18.76 rewrite <- zenon_D_pnotp. % 18.52/18.76 exact zenon_H48. % 18.52/18.76 cut (((e0) = (op (e1) (e2)))); [idtac | apply NNPP; zenon_intro zenon_H207]. % 18.52/18.76 cut (((op (e0) (e2)) = (op (e0) (e2)))); [idtac | apply NNPP; zenon_intro zenon_H4c]. % 18.52/18.76 congruence. % 18.52/18.76 apply zenon_H4c. apply refl_equal. % 18.52/18.76 apply zenon_H207. apply sym_equal. exact zenon_H2a. % 18.52/18.76 (* end of lemma zenon_L334_ *) % 18.52/18.76 assert (zenon_L335_ : (((op (e1) (e0)) = (e0))\/(((op (e1) (e1)) = (e0))\/(((op (e1) (e2)) = (e0))\/((op (e1) (e3)) = (e0))))) -> (~((op (e1) (e0)) = (e0))) -> (~((op (e1) (e1)) = (e0))) -> ((op (e0) (e2)) = (e0)) -> (~((op (e0) (e2)) = (op (e1) (e2)))) -> (~((op (e1) (e3)) = (e0))) -> False). % 18.52/18.76 do 0 intro. intros zenon_H22 zenon_H23 zenon_H24 zenon_H48 zenon_H195 zenon_H38. % 18.52/18.76 apply (zenon_or_s _ _ zenon_H22); [ zenon_intro zenon_H27 | zenon_intro zenon_H26 ]. % 18.52/18.76 exact (zenon_H23 zenon_H27). % 18.52/18.76 apply (zenon_or_s _ _ zenon_H26); [ zenon_intro zenon_H29 | zenon_intro zenon_H28 ]. % 18.52/18.76 exact (zenon_H24 zenon_H29). % 18.52/18.76 apply (zenon_or_s _ _ zenon_H28); [ zenon_intro zenon_H2a | zenon_intro zenon_H1f ]. % 18.52/18.76 apply (zenon_L334_); trivial. % 18.52/18.76 exact (zenon_H38 zenon_H1f). % 18.52/18.76 (* end of lemma zenon_L335_ *) % 18.52/18.76 assert (zenon_L336_ : ((op (e0) (e3)) = (e0)) -> ((op (e0) (e2)) = (e0)) -> (~((op (e0) (e2)) = (op (e0) (e3)))) -> False). % 18.52/18.76 do 0 intro. intros zenon_H1e zenon_H48 zenon_H208. % 18.52/18.76 elim (classic ((op (e0) (e3)) = (op (e0) (e3)))); [ zenon_intro zenon_H55 | zenon_intro zenon_H21 ]. % 18.52/18.76 cut (((op (e0) (e3)) = (op (e0) (e3))) = ((op (e0) (e2)) = (op (e0) (e3)))). % 18.52/18.76 intro zenon_D_pnotp. % 18.52/18.76 apply zenon_H208. % 18.52/18.76 rewrite <- zenon_D_pnotp. % 18.52/18.76 exact zenon_H55. % 18.52/18.76 cut (((op (e0) (e3)) = (op (e0) (e3)))); [idtac | apply NNPP; zenon_intro zenon_H21]. % 18.52/18.76 cut (((op (e0) (e3)) = (op (e0) (e2)))); [idtac | apply NNPP; zenon_intro zenon_H209]. % 18.52/18.76 congruence. % 18.52/18.76 cut (((op (e0) (e3)) = (e0)) = ((op (e0) (e3)) = (op (e0) (e2)))). % 18.52/18.76 intro zenon_D_pnotp. % 18.52/18.76 apply zenon_H209. % 18.52/18.76 rewrite <- zenon_D_pnotp. % 18.52/18.76 exact zenon_H1e. % 18.52/18.76 cut (((e0) = (op (e0) (e2)))); [idtac | apply NNPP; zenon_intro zenon_H20a]. % 18.52/18.76 cut (((op (e0) (e3)) = (op (e0) (e3)))); [idtac | apply NNPP; zenon_intro zenon_H21]. % 18.52/18.76 congruence. % 18.52/18.76 apply zenon_H21. apply refl_equal. % 18.52/18.76 apply zenon_H20a. apply sym_equal. exact zenon_H48. % 18.52/18.76 apply zenon_H21. apply refl_equal. % 18.52/18.76 apply zenon_H21. apply refl_equal. % 18.52/18.76 (* end of lemma zenon_L336_ *) % 18.52/18.76 assert (zenon_L337_ : (((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) (e2)) = (e0))) -> (~((op (e2) (e2)) = (e0))) -> (~((op (e3) (e2)) = (e0))) -> False). % 18.52/18.76 do 0 intro. intros zenon_H6a zenon_H208 zenon_H1e zenon_H25 zenon_H81 zenon_H18b. % 18.52/18.76 apply (zenon_or_s _ _ zenon_H6a); [ zenon_intro zenon_H48 | zenon_intro zenon_H6b ]. % 18.52/18.76 apply (zenon_L336_); trivial. % 18.52/18.76 apply (zenon_or_s _ _ zenon_H6b); [ zenon_intro zenon_H2a | zenon_intro zenon_H6c ]. % 18.52/18.76 exact (zenon_H25 zenon_H2a). % 18.52/18.76 apply (zenon_or_s _ _ zenon_H6c); [ zenon_intro zenon_H2c | zenon_intro zenon_H61 ]. % 18.52/18.76 exact (zenon_H81 zenon_H2c). % 18.52/18.76 exact (zenon_H18b zenon_H61). % 18.52/18.76 (* end of lemma zenon_L337_ *) % 18.52/18.76 assert (zenon_L338_ : (((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 (e1) (e3)) = (e0))) -> (~((op (e0) (e2)) = (op (e1) (e2)))) -> (~((op (e1) (e1)) = (e0))) -> (~((op (e1) (e0)) = (e0))) -> (((op (e1) (e0)) = (e0))\/(((op (e1) (e1)) = (e0))\/(((op (e1) (e2)) = (e0))\/((op (e1) (e3)) = (e0))))) -> (((op (e0) (e2)) = (e0))\/(((op (e1) (e2)) = (e0))\/(((op (e2) (e2)) = (e0))\/((op (e3) (e2)) = (e0))))) -> (~((op (e0) (e2)) = (op (e0) (e3)))) -> (~((op (e1) (e2)) = (e0))) -> (~((op (e2) (e2)) = (e0))) -> (~((op (e3) (e2)) = (e0))) -> False). % 18.52/18.76 do 0 intro. intros zenon_H74 zenon_H3f zenon_H20b zenon_H38 zenon_H195 zenon_H24 zenon_H23 zenon_H22 zenon_H6a zenon_H208 zenon_H25 zenon_H81 zenon_H18b. % 18.52/18.76 apply (zenon_or_s _ _ zenon_H74); [ zenon_intro zenon_H42 | zenon_intro zenon_H77 ]. % 18.52/18.76 exact (zenon_H3f zenon_H42). % 18.52/18.76 apply (zenon_or_s _ _ zenon_H77); [ zenon_intro zenon_H49 | zenon_intro zenon_H78 ]. % 18.52/18.76 exact (zenon_H20b zenon_H49). % 18.52/18.76 apply (zenon_or_s _ _ zenon_H78); [ zenon_intro zenon_H48 | zenon_intro zenon_H1e ]. % 18.52/18.76 apply (zenon_L335_); trivial. % 18.52/18.76 apply (zenon_L337_); trivial. % 18.52/18.76 (* end of lemma zenon_L338_ *) % 18.52/18.76 assert (zenon_L339_ : ((~((op (e3) (e2)) = (e0)))\/((op (e3) (e0)) = (e2))) -> ((op (e3) (e0)) = (e0)) -> (~((e0) = (e2))) -> (~((op (e0) (e0)) = (e0))) -> (~((op (e0) (e1)) = (e0))) -> (((op (e1) (e0)) = (e0))\/(((op (e1) (e1)) = (e0))\/(((op (e1) (e2)) = (e0))\/((op (e1) (e3)) = (e0))))) -> (~((op (e1) (e3)) = (e0))) -> (~((op (e0) (e2)) = (op (e1) (e2)))) -> (~((op (e1) (e1)) = (e0))) -> (~((op (e1) (e0)) = (e0))) -> (((op (e0) (e2)) = (e0))\/(((op (e1) (e2)) = (e0))\/(((op (e2) (e2)) = (e0))\/((op (e3) (e2)) = (e0))))) -> (~((op (e2) (e2)) = (e0))) -> (~((op (e1) (e2)) = (e0))) -> (~((op (e0) (e2)) = (op (e0) (e3)))) -> (((op (e0) (e0)) = (e0))\/(((op (e0) (e1)) = (e0))\/(((op (e0) (e2)) = (e0))\/((op (e0) (e3)) = (e0))))) -> False). % 18.52/18.76 do 0 intro. intros zenon_H1a7 zenon_H44 zenon_H149 zenon_H3f zenon_H20b zenon_H22 zenon_H38 zenon_H195 zenon_H24 zenon_H23 zenon_H6a zenon_H81 zenon_H25 zenon_H208 zenon_H74. % 18.52/18.76 apply (zenon_or_s _ _ zenon_H1a7); [ zenon_intro zenon_H18b | zenon_intro zenon_H148 ]. % 18.52/18.76 apply (zenon_L338_); trivial. % 18.52/18.76 apply (zenon_L100_); trivial. % 18.52/18.76 (* end of lemma zenon_L339_ *) % 18.52/18.76 assert (zenon_L340_ : ((~((op (e3) (e0)) = (e0)))\/((op (e3) (e0)) = (e0))) -> (((op (e0) (e0)) = (e0))\/(((op (e0) (e1)) = (e0))\/(((op (e0) (e2)) = (e0))\/((op (e0) (e3)) = (e0))))) -> (~((op (e0) (e2)) = (op (e0) (e3)))) -> (~((op (e1) (e2)) = (e0))) -> (~((op (e2) (e2)) = (e0))) -> (((op (e0) (e2)) = (e0))\/(((op (e1) (e2)) = (e0))\/(((op (e2) (e2)) = (e0))\/((op (e3) (e2)) = (e0))))) -> (~((op (e1) (e1)) = (e0))) -> (~((op (e0) (e2)) = (op (e1) (e2)))) -> (~((op (e1) (e3)) = (e0))) -> (((op (e1) (e0)) = (e0))\/(((op (e1) (e1)) = (e0))\/(((op (e1) (e2)) = (e0))\/((op (e1) (e3)) = (e0))))) -> (~((op (e0) (e1)) = (e0))) -> (~((e0) = (e2))) -> ((~((op (e3) (e2)) = (e0)))\/((op (e3) (e0)) = (e2))) -> (~((op (e0) (e0)) = (e0))) -> (~((op (e1) (e0)) = (e0))) -> (~((op (e2) (e0)) = (e0))) -> (((op (e0) (e0)) = (e0))\/(((op (e1) (e0)) = (e0))\/(((op (e2) (e0)) = (e0))\/((op (e3) (e0)) = (e0))))) -> False). % 18.52/18.76 do 0 intro. intros zenon_H184 zenon_H74 zenon_H208 zenon_H25 zenon_H81 zenon_H6a zenon_H24 zenon_H195 zenon_H38 zenon_H22 zenon_H20b zenon_H149 zenon_H1a7 zenon_H3f zenon_H23 zenon_H30 zenon_H3e. % 18.52/18.76 apply (zenon_or_s _ _ zenon_H184); [ zenon_intro zenon_H40 | zenon_intro zenon_H44 ]. % 18.52/18.76 apply (zenon_L7_); trivial. % 18.52/18.76 apply (zenon_L339_); trivial. % 18.52/18.76 (* end of lemma zenon_L340_ *) % 18.52/18.76 assert (zenon_L341_ : (~((op (e0) (e0)) = (op (e2) (e0)))) -> ((op (e0) (e0)) = (e2)) -> ((op (e2) (e0)) = (e2)) -> False). % 18.52/18.76 do 0 intro. intros zenon_H39 zenon_H7b zenon_Hee. % 18.52/18.76 cut (((op (e0) (e0)) = (e2)) = ((op (e0) (e0)) = (op (e2) (e0)))). % 18.52/18.76 intro zenon_D_pnotp. % 18.52/18.76 apply zenon_H39. % 18.52/18.76 rewrite <- zenon_D_pnotp. % 18.52/18.76 exact zenon_H7b. % 18.52/18.76 cut (((e2) = (op (e2) (e0)))); [idtac | apply NNPP; zenon_intro zenon_H11e]. % 18.52/18.76 cut (((op (e0) (e0)) = (op (e0) (e0)))); [idtac | apply NNPP; zenon_intro zenon_H3d]. % 18.52/18.76 congruence. % 18.52/18.76 apply zenon_H3d. apply refl_equal. % 18.52/18.76 apply zenon_H11e. apply sym_equal. exact zenon_Hee. % 18.52/18.76 (* end of lemma zenon_L341_ *) % 18.52/18.76 assert (zenon_L342_ : (~((op (e0) (e2)) = (op (e3) (e2)))) -> ((op (e0) (e2)) = (e0)) -> ((op (e3) (e2)) = (e0)) -> False). % 18.52/18.76 do 0 intro. intros zenon_H14f zenon_H48 zenon_H61. % 18.52/18.76 cut (((op (e0) (e2)) = (e0)) = ((op (e0) (e2)) = (op (e3) (e2)))). % 18.52/18.76 intro zenon_D_pnotp. % 18.52/18.76 apply zenon_H14f. % 18.52/18.76 rewrite <- zenon_D_pnotp. % 18.52/18.76 exact zenon_H48. % 18.52/18.76 cut (((e0) = (op (e3) (e2)))); [idtac | apply NNPP; zenon_intro zenon_H66]. % 18.52/18.76 cut (((op (e0) (e2)) = (op (e0) (e2)))); [idtac | apply NNPP; zenon_intro zenon_H4c]. % 18.52/18.76 congruence. % 18.52/18.76 apply zenon_H4c. apply refl_equal. % 18.52/18.76 apply zenon_H66. apply sym_equal. exact zenon_H61. % 18.52/18.76 (* end of lemma zenon_L342_ *) % 18.52/18.76 assert (zenon_L343_ : (((op (e3) (e0)) = (e0))\/(((op (e3) (e1)) = (e0))\/(((op (e3) (e2)) = (e0))\/((op (e3) (e3)) = (e0))))) -> (~((op (e3) (e0)) = (e0))) -> (~((op (e3) (e1)) = (e0))) -> ((op (e0) (e2)) = (e0)) -> (~((op (e0) (e2)) = (op (e3) (e2)))) -> (~((op (e3) (e3)) = (e0))) -> False). % 18.52/18.76 do 0 intro. intros zenon_H1ac zenon_H40 zenon_H1ad zenon_H48 zenon_H14f zenon_H1ae. % 18.52/18.76 apply (zenon_or_s _ _ zenon_H1ac); [ zenon_intro zenon_H44 | zenon_intro zenon_H1af ]. % 18.52/18.76 exact (zenon_H40 zenon_H44). % 18.52/18.76 apply (zenon_or_s _ _ zenon_H1af); [ zenon_intro zenon_H1b1 | zenon_intro zenon_H1b0 ]. % 18.52/18.76 exact (zenon_H1ad zenon_H1b1). % 18.52/18.76 apply (zenon_or_s _ _ zenon_H1b0); [ zenon_intro zenon_H61 | zenon_intro zenon_H60 ]. % 18.52/18.76 apply (zenon_L342_); trivial. % 18.52/18.76 exact (zenon_H1ae zenon_H60). % 18.52/18.76 (* end of lemma zenon_L343_ *) % 18.52/18.76 assert (zenon_L344_ : ((~((op (e3) (e3)) = (e0)))\/((op (e3) (e0)) = (e3))) -> ((op (e3) (e0)) = (e2)) -> (~((e2) = (e3))) -> (~((op (e0) (e0)) = (e0))) -> (~((op (e0) (e1)) = (e0))) -> (((op (e3) (e0)) = (e0))\/(((op (e3) (e1)) = (e0))\/(((op (e3) (e2)) = (e0))\/((op (e3) (e3)) = (e0))))) -> (~((op (e0) (e2)) = (op (e3) (e2)))) -> (~((op (e3) (e1)) = (e0))) -> (~((op (e3) (e0)) = (e0))) -> (((op (e1) (e0)) = (e0))\/(((op (e1) (e1)) = (e0))\/(((op (e1) (e2)) = (e0))\/((op (e1) (e3)) = (e0))))) -> (~((op (e0) (e3)) = (op (e1) (e3)))) -> (~((op (e1) (e2)) = (e0))) -> (~((op (e1) (e1)) = (e0))) -> (~((op (e1) (e0)) = (e0))) -> (((op (e0) (e0)) = (e0))\/(((op (e0) (e1)) = (e0))\/(((op (e0) (e2)) = (e0))\/((op (e0) (e3)) = (e0))))) -> False). % 18.52/18.76 do 0 intro. intros zenon_H1ec zenon_H148 zenon_H12b zenon_H3f zenon_H20b zenon_H1ac zenon_H14f zenon_H1ad zenon_H40 zenon_H22 zenon_H1d zenon_H25 zenon_H24 zenon_H23 zenon_H74. % 18.52/18.76 apply (zenon_or_s _ _ zenon_H1ec); [ zenon_intro zenon_H1ae | zenon_intro zenon_H15e ]. % 18.52/18.76 apply (zenon_or_s _ _ zenon_H74); [ zenon_intro zenon_H42 | zenon_intro zenon_H77 ]. % 18.52/18.76 exact (zenon_H3f zenon_H42). % 18.52/18.76 apply (zenon_or_s _ _ zenon_H77); [ zenon_intro zenon_H49 | zenon_intro zenon_H78 ]. % 18.52/18.76 exact (zenon_H20b zenon_H49). % 18.52/18.76 apply (zenon_or_s _ _ zenon_H78); [ zenon_intro zenon_H48 | zenon_intro zenon_H1e ]. % 18.52/18.76 apply (zenon_L343_); trivial. % 18.52/18.76 apply (zenon_L2_); trivial. % 18.52/18.76 apply (zenon_L109_); trivial. % 18.52/18.76 (* end of lemma zenon_L344_ *) % 18.52/18.76 assert (zenon_L345_ : ((~((op (e3) (e2)) = (e0)))\/((op (e3) (e0)) = (e2))) -> (~((op (e0) (e3)) = (op (e1) (e3)))) -> (~((op (e3) (e0)) = (e0))) -> (~((op (e3) (e1)) = (e0))) -> (~((op (e0) (e2)) = (op (e3) (e2)))) -> (((op (e3) (e0)) = (e0))\/(((op (e3) (e1)) = (e0))\/(((op (e3) (e2)) = (e0))\/((op (e3) (e3)) = (e0))))) -> (~((e2) = (e3))) -> ((~((op (e3) (e3)) = (e0)))\/((op (e3) (e0)) = (e3))) -> (~((op (e0) (e0)) = (e0))) -> (~((op (e0) (e1)) = (e0))) -> (((op (e1) (e0)) = (e0))\/(((op (e1) (e1)) = (e0))\/(((op (e1) (e2)) = (e0))\/((op (e1) (e3)) = (e0))))) -> (~((op (e1) (e3)) = (e0))) -> (~((op (e0) (e2)) = (op (e1) (e2)))) -> (~((op (e1) (e1)) = (e0))) -> (~((op (e1) (e0)) = (e0))) -> (((op (e0) (e2)) = (e0))\/(((op (e1) (e2)) = (e0))\/(((op (e2) (e2)) = (e0))\/((op (e3) (e2)) = (e0))))) -> (~((op (e2) (e2)) = (e0))) -> (~((op (e1) (e2)) = (e0))) -> (~((op (e0) (e2)) = (op (e0) (e3)))) -> (((op (e0) (e0)) = (e0))\/(((op (e0) (e1)) = (e0))\/(((op (e0) (e2)) = (e0))\/((op (e0) (e3)) = (e0))))) -> False). % 18.52/18.76 do 0 intro. intros zenon_H1a7 zenon_H1d zenon_H40 zenon_H1ad zenon_H14f zenon_H1ac zenon_H12b zenon_H1ec zenon_H3f zenon_H20b zenon_H22 zenon_H38 zenon_H195 zenon_H24 zenon_H23 zenon_H6a zenon_H81 zenon_H25 zenon_H208 zenon_H74. % 18.52/18.76 apply (zenon_or_s _ _ zenon_H1a7); [ zenon_intro zenon_H18b | zenon_intro zenon_H148 ]. % 18.52/18.76 apply (zenon_L338_); trivial. % 18.52/18.76 apply (zenon_L344_); trivial. % 18.52/18.76 (* end of lemma zenon_L345_ *) % 18.52/18.76 assert (zenon_L346_ : (~((op (e3) (e0)) = (op (e3) (e1)))) -> ((op (e3) (e0)) = (e0)) -> ((op (e3) (e1)) = (e0)) -> False). % 18.52/18.76 do 0 intro. intros zenon_H1cf zenon_H44 zenon_H1b1. % 18.52/18.76 cut (((op (e3) (e0)) = (e0)) = ((op (e3) (e0)) = (op (e3) (e1)))). % 18.52/18.76 intro zenon_D_pnotp. % 18.52/18.76 apply zenon_H1cf. % 18.52/18.76 rewrite <- zenon_D_pnotp. % 18.52/18.76 exact zenon_H44. % 18.52/18.76 cut (((e0) = (op (e3) (e1)))); [idtac | apply NNPP; zenon_intro zenon_H1eb]. % 18.52/18.76 cut (((op (e3) (e0)) = (op (e3) (e0)))); [idtac | apply NNPP; zenon_intro zenon_H70]. % 18.52/18.76 congruence. % 18.52/18.76 apply zenon_H70. apply refl_equal. % 18.52/18.76 apply zenon_H1eb. apply sym_equal. exact zenon_H1b1. % 18.52/18.76 (* end of lemma zenon_L346_ *) % 18.52/18.76 assert (zenon_L347_ : (((op (e0) (e0)) = (e0))\/(((op (e1) (e0)) = (e0))\/(((op (e2) (e0)) = (e0))\/((op (e3) (e0)) = (e0))))) -> (~((op (e0) (e0)) = (e0))) -> (~((op (e1) (e0)) = (op (e1) (e1)))) -> (~((op (e3) (e1)) = (op (e3) (e2)))) -> (~((op (e2) (e0)) = (op (e2) (e2)))) -> ((op (e1) (e1)) = (e0)) -> (~((op (e1) (e1)) = (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))))) -> (~((op (e3) (e0)) = (op (e3) (e1)))) -> ((op (e3) (e1)) = (e0)) -> False). % 18.52/18.76 do 0 intro. intros zenon_H3e zenon_H3f zenon_H45 zenon_H1a4 zenon_H52 zenon_H29 zenon_H4f zenon_H1e zenon_H208 zenon_H6a zenon_H1cf zenon_H1b1. % 18.52/18.76 apply (zenon_or_s _ _ zenon_H3e); [ zenon_intro zenon_H42 | zenon_intro zenon_H41 ]. % 18.52/18.76 exact (zenon_H3f zenon_H42). % 18.52/18.76 apply (zenon_or_s _ _ zenon_H41); [ zenon_intro zenon_H27 | zenon_intro zenon_H43 ]. % 18.52/18.76 apply (zenon_L8_); trivial. % 18.52/18.76 apply (zenon_or_s _ _ zenon_H43); [ zenon_intro zenon_H34 | zenon_intro zenon_H44 ]. % 18.52/18.76 apply (zenon_or_s _ _ zenon_H6a); [ zenon_intro zenon_H48 | zenon_intro zenon_H6b ]. % 18.52/18.76 apply (zenon_L336_); trivial. % 18.52/18.76 apply (zenon_or_s _ _ zenon_H6b); [ zenon_intro zenon_H2a | zenon_intro zenon_H6c ]. % 18.52/18.76 apply (zenon_L10_); trivial. % 18.52/18.76 apply (zenon_or_s _ _ zenon_H6c); [ zenon_intro zenon_H2c | zenon_intro zenon_H61 ]. % 18.52/18.76 apply (zenon_L11_); trivial. % 18.52/18.76 apply (zenon_L247_); trivial. % 18.52/18.76 apply (zenon_L346_); trivial. % 18.52/18.76 (* end of lemma zenon_L347_ *) % 18.52/18.76 assert (zenon_L348_ : (((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)) = (e0))\/(((op (e1) (e2)) = (e0))\/(((op (e2) (e2)) = (e0))\/((op (e3) (e2)) = (e0))))) -> (~((op (e0) (e2)) = (op (e0) (e3)))) -> (~((op (e1) (e1)) = (op (e1) (e2)))) -> (~((op (e2) (e0)) = (op (e2) (e2)))) -> (~((op (e3) (e1)) = (op (e3) (e2)))) -> (~((op (e1) (e0)) = (op (e1) (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 (e1) (e3)))) -> ((op (e1) (e1)) = (e0)) -> (~((op (e2) (e0)) = (op (e2) (e3)))) -> ((op (e2) (e0)) = (e0)) -> ((op (e3) (e1)) = (e0)) -> (~((op (e3) (e1)) = (op (e3) (e3)))) -> False). % 18.52/18.76 do 0 intro. intros zenon_H67 zenon_H1cf zenon_H6a zenon_H208 zenon_H4f zenon_H52 zenon_H1a4 zenon_H45 zenon_H3f zenon_H3e zenon_H57 zenon_H29 zenon_H5b zenon_H34 zenon_H1b1 zenon_H130. % 18.52/18.76 apply (zenon_or_s _ _ zenon_H67); [ zenon_intro zenon_H1e | zenon_intro zenon_H68 ]. % 18.52/18.76 apply (zenon_L347_); trivial. % 18.52/18.76 apply (zenon_or_s _ _ zenon_H68); [ zenon_intro zenon_H1f | zenon_intro zenon_H69 ]. % 18.52/18.76 apply (zenon_L13_); trivial. % 18.52/18.76 apply (zenon_or_s _ _ zenon_H69); [ zenon_intro zenon_H37 | zenon_intro zenon_H60 ]. % 18.52/18.76 apply (zenon_L14_); trivial. % 18.52/18.76 apply (zenon_L244_); trivial. % 18.52/18.76 (* end of lemma zenon_L348_ *) % 18.52/18.76 assert (zenon_L349_ : (~((op (e3) (e1)) = (op (e3) (e3)))) -> (~((op (e2) (e0)) = (op (e2) (e3)))) -> ((op (e1) (e1)) = (e0)) -> (~((op (e1) (e1)) = (op (e1) (e3)))) -> (((op (e0) (e0)) = (e0))\/(((op (e1) (e0)) = (e0))\/(((op (e2) (e0)) = (e0))\/((op (e3) (e0)) = (e0))))) -> (~((op (e0) (e0)) = (e0))) -> (~((op (e1) (e0)) = (op (e1) (e1)))) -> (~((op (e3) (e1)) = (op (e3) (e2)))) -> (~((op (e2) (e0)) = (op (e2) (e2)))) -> (~((op (e1) (e1)) = (op (e1) (e2)))) -> (~((op (e0) (e2)) = (op (e0) (e3)))) -> (((op (e0) (e2)) = (e0))\/(((op (e1) (e2)) = (e0))\/(((op (e2) (e2)) = (e0))\/((op (e3) (e2)) = (e0))))) -> (((op (e0) (e3)) = (e0))\/(((op (e1) (e3)) = (e0))\/(((op (e2) (e3)) = (e0))\/((op (e3) (e3)) = (e0))))) -> (~((op (e3) (e0)) = (op (e3) (e1)))) -> ((op (e3) (e1)) = (e0)) -> False). % 18.52/18.76 do 0 intro. intros zenon_H130 zenon_H5b zenon_H29 zenon_H57 zenon_H3e zenon_H3f zenon_H45 zenon_H1a4 zenon_H52 zenon_H4f zenon_H208 zenon_H6a zenon_H67 zenon_H1cf zenon_H1b1. % 18.52/18.76 apply (zenon_or_s _ _ zenon_H3e); [ zenon_intro zenon_H42 | zenon_intro zenon_H41 ]. % 18.52/18.76 exact (zenon_H3f zenon_H42). % 18.52/18.76 apply (zenon_or_s _ _ zenon_H41); [ zenon_intro zenon_H27 | zenon_intro zenon_H43 ]. % 18.52/18.76 apply (zenon_L8_); trivial. % 18.52/18.76 apply (zenon_or_s _ _ zenon_H43); [ zenon_intro zenon_H34 | zenon_intro zenon_H44 ]. % 18.52/18.76 apply (zenon_L348_); trivial. % 18.52/18.76 apply (zenon_L346_); trivial. % 18.52/18.76 (* end of lemma zenon_L349_ *) % 18.52/18.76 assert (zenon_L350_ : (((op (e3) (e0)) = (e0))\/(((op (e3) (e1)) = (e0))\/(((op (e3) (e2)) = (e0))\/((op (e3) (e3)) = (e0))))) -> (~((op (e3) (e0)) = (e0))) -> (~((op (e3) (e0)) = (op (e3) (e1)))) -> (((op (e0) (e3)) = (e0))\/(((op (e1) (e3)) = (e0))\/(((op (e2) (e3)) = (e0))\/((op (e3) (e3)) = (e0))))) -> (((op (e0) (e2)) = (e0))\/(((op (e1) (e2)) = (e0))\/(((op (e2) (e2)) = (e0))\/((op (e3) (e2)) = (e0))))) -> (~((op (e0) (e2)) = (op (e0) (e3)))) -> (~((op (e1) (e1)) = (op (e1) (e2)))) -> (~((op (e2) (e0)) = (op (e2) (e2)))) -> (~((op (e3) (e1)) = (op (e3) (e2)))) -> (~((op (e1) (e0)) = (op (e1) (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 (e1) (e3)))) -> ((op (e1) (e1)) = (e0)) -> (~((op (e2) (e0)) = (op (e2) (e3)))) -> (~((op (e3) (e1)) = (op (e3) (e3)))) -> ((op (e0) (e2)) = (e0)) -> (~((op (e0) (e2)) = (op (e3) (e2)))) -> (~((op (e3) (e3)) = (e0))) -> False). % 18.52/18.76 do 0 intro. intros zenon_H1ac zenon_H40 zenon_H1cf zenon_H67 zenon_H6a zenon_H208 zenon_H4f zenon_H52 zenon_H1a4 zenon_H45 zenon_H3f zenon_H3e zenon_H57 zenon_H29 zenon_H5b zenon_H130 zenon_H48 zenon_H14f zenon_H1ae. % 18.52/18.76 apply (zenon_or_s _ _ zenon_H1ac); [ zenon_intro zenon_H44 | zenon_intro zenon_H1af ]. % 18.52/18.76 exact (zenon_H40 zenon_H44). % 18.52/18.76 apply (zenon_or_s _ _ zenon_H1af); [ zenon_intro zenon_H1b1 | zenon_intro zenon_H1b0 ]. % 18.52/18.76 apply (zenon_L349_); trivial. % 18.52/18.76 apply (zenon_or_s _ _ zenon_H1b0); [ zenon_intro zenon_H61 | zenon_intro zenon_H60 ]. % 18.52/18.76 apply (zenon_L342_); trivial. % 18.52/18.76 exact (zenon_H1ae zenon_H60). % 18.52/18.76 (* end of lemma zenon_L350_ *) % 18.52/18.76 assert (zenon_L351_ : (((op (e1) (e0)) = (e0))\/(((op (e1) (e1)) = (e0))\/(((op (e1) (e2)) = (e0))\/((op (e1) (e3)) = (e0))))) -> (~((op (e1) (e0)) = (e0))) -> (~((op (e3) (e3)) = (e0))) -> (~((op (e0) (e2)) = (op (e3) (e2)))) -> ((op (e0) (e2)) = (e0)) -> (~((op (e3) (e1)) = (op (e3) (e3)))) -> (~((op (e2) (e0)) = (op (e2) (e3)))) -> (~((op (e1) (e1)) = (op (e1) (e3)))) -> (((op (e0) (e0)) = (e0))\/(((op (e1) (e0)) = (e0))\/(((op (e2) (e0)) = (e0))\/((op (e3) (e0)) = (e0))))) -> (~((op (e0) (e0)) = (e0))) -> (~((op (e1) (e0)) = (op (e1) (e1)))) -> (~((op (e3) (e1)) = (op (e3) (e2)))) -> (~((op (e2) (e0)) = (op (e2) (e2)))) -> (~((op (e1) (e1)) = (op (e1) (e2)))) -> (~((op (e0) (e2)) = (op (e0) (e3)))) -> (((op (e0) (e2)) = (e0))\/(((op (e1) (e2)) = (e0))\/(((op (e2) (e2)) = (e0))\/((op (e3) (e2)) = (e0))))) -> (((op (e0) (e3)) = (e0))\/(((op (e1) (e3)) = (e0))\/(((op (e2) (e3)) = (e0))\/((op (e3) (e3)) = (e0))))) -> (~((op (e3) (e0)) = (op (e3) (e1)))) -> (~((op (e3) (e0)) = (e0))) -> (((op (e3) (e0)) = (e0))\/(((op (e3) (e1)) = (e0))\/(((op (e3) (e2)) = (e0))\/((op (e3) (e3)) = (e0))))) -> (~((op (e1) (e2)) = (e0))) -> (~((op (e1) (e3)) = (e0))) -> False). % 18.52/18.76 do 0 intro. intros zenon_H22 zenon_H23 zenon_H1ae zenon_H14f zenon_H48 zenon_H130 zenon_H5b zenon_H57 zenon_H3e zenon_H3f zenon_H45 zenon_H1a4 zenon_H52 zenon_H4f zenon_H208 zenon_H6a zenon_H67 zenon_H1cf zenon_H40 zenon_H1ac zenon_H25 zenon_H38. % 18.52/18.76 apply (zenon_or_s _ _ zenon_H22); [ zenon_intro zenon_H27 | zenon_intro zenon_H26 ]. % 18.52/18.76 exact (zenon_H23 zenon_H27). % 18.52/18.76 apply (zenon_or_s _ _ zenon_H26); [ zenon_intro zenon_H29 | zenon_intro zenon_H28 ]. % 18.52/18.76 apply (zenon_L350_); trivial. % 18.52/18.76 apply (zenon_or_s _ _ zenon_H28); [ zenon_intro zenon_H2a | zenon_intro zenon_H1f ]. % 18.52/18.76 exact (zenon_H25 zenon_H2a). % 18.52/18.76 exact (zenon_H38 zenon_H1f). % 18.52/18.76 (* end of lemma zenon_L351_ *) % 18.52/18.76 assert (zenon_L352_ : (((op (e0) (e0)) = (e0))\/(((op (e0) (e1)) = (e0))\/(((op (e0) (e2)) = (e0))\/((op (e0) (e3)) = (e0))))) -> (~((op (e0) (e1)) = (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)) = (op (e3) (e1)))) -> (((op (e0) (e3)) = (e0))\/(((op (e1) (e3)) = (e0))\/(((op (e2) (e3)) = (e0))\/((op (e3) (e3)) = (e0))))) -> (~((op (e1) (e1)) = (op (e1) (e2)))) -> (~((op (e2) (e0)) = (op (e2) (e2)))) -> (~((op (e3) (e1)) = (op (e3) (e2)))) -> (~((op (e1) (e0)) = (op (e1) (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 (e1) (e3)))) -> (~((op (e2) (e0)) = (op (e2) (e3)))) -> (~((op (e3) (e1)) = (op (e3) (e3)))) -> (~((op (e0) (e2)) = (op (e3) (e2)))) -> (~((op (e3) (e3)) = (e0))) -> (~((op (e1) (e0)) = (e0))) -> (((op (e1) (e0)) = (e0))\/(((op (e1) (e1)) = (e0))\/(((op (e1) (e2)) = (e0))\/((op (e1) (e3)) = (e0))))) -> (((op (e0) (e2)) = (e0))\/(((op (e1) (e2)) = (e0))\/(((op (e2) (e2)) = (e0))\/((op (e3) (e2)) = (e0))))) -> (~((op (e0) (e2)) = (op (e0) (e3)))) -> (~((op (e1) (e2)) = (e0))) -> (~((op (e2) (e2)) = (e0))) -> (~((op (e3) (e2)) = (e0))) -> False). % 18.52/18.76 do 0 intro. intros zenon_H74 zenon_H20b zenon_H38 zenon_H1ac zenon_H40 zenon_H1cf zenon_H67 zenon_H4f zenon_H52 zenon_H1a4 zenon_H45 zenon_H3f zenon_H3e zenon_H57 zenon_H5b zenon_H130 zenon_H14f zenon_H1ae zenon_H23 zenon_H22 zenon_H6a zenon_H208 zenon_H25 zenon_H81 zenon_H18b. % 18.52/18.76 apply (zenon_or_s _ _ zenon_H74); [ zenon_intro zenon_H42 | zenon_intro zenon_H77 ]. % 18.52/18.76 exact (zenon_H3f zenon_H42). % 18.52/18.76 apply (zenon_or_s _ _ zenon_H77); [ zenon_intro zenon_H49 | zenon_intro zenon_H78 ]. % 18.52/18.76 exact (zenon_H20b zenon_H49). % 18.52/18.76 apply (zenon_or_s _ _ zenon_H78); [ zenon_intro zenon_H48 | zenon_intro zenon_H1e ]. % 18.52/18.76 apply (zenon_L351_); trivial. % 18.52/18.76 apply (zenon_L337_); trivial. % 18.52/18.76 (* end of lemma zenon_L352_ *) % 18.52/18.76 assert (zenon_L353_ : ((~((op (e3) (e3)) = (e0)))\/((op (e3) (e0)) = (e3))) -> ((op (e3) (e0)) = (e1)) -> (~((e1) = (e3))) -> (~((op (e0) (e0)) = (e0))) -> (~((op (e0) (e1)) = (e0))) -> (((op (e1) (e0)) = (e0))\/(((op (e1) (e1)) = (e0))\/(((op (e1) (e2)) = (e0))\/((op (e1) (e3)) = (e0))))) -> (~((op (e1) (e3)) = (e0))) -> (~((op (e1) (e2)) = (e0))) -> (~((op (e3) (e0)) = (e0))) -> (((op (e0) (e0)) = (e0))\/(((op (e1) (e0)) = (e0))\/(((op (e2) (e0)) = (e0))\/((op (e3) (e0)) = (e0))))) -> (~((op (e3) (e0)) = (op (e3) (e1)))) -> (~((op (e0) (e2)) = (op (e0) (e3)))) -> (~((op (e1) (e1)) = (op (e1) (e2)))) -> (~((op (e2) (e0)) = (op (e2) (e2)))) -> (~((op (e3) (e1)) = (op (e3) (e2)))) -> (((op (e0) (e2)) = (e0))\/(((op (e1) (e2)) = (e0))\/(((op (e2) (e2)) = (e0))\/((op (e3) (e2)) = (e0))))) -> (~((op (e1) (e1)) = (op (e1) (e3)))) -> (~((op (e2) (e0)) = (op (e2) (e3)))) -> (~((op (e3) (e1)) = (op (e3) (e3)))) -> (((op (e0) (e3)) = (e0))\/(((op (e1) (e3)) = (e0))\/(((op (e2) (e3)) = (e0))\/((op (e3) (e3)) = (e0))))) -> (~((op (e1) (e0)) = (op (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 (e1) (e0)) = (e0))) -> (~((op (e3) (e2)) = (e0))) -> (~((op (e2) (e2)) = (e0))) -> (((op (e0) (e0)) = (e0))\/(((op (e0) (e1)) = (e0))\/(((op (e0) (e2)) = (e0))\/((op (e0) (e3)) = (e0))))) -> False). % 18.52/18.76 do 0 intro. intros zenon_H1ec zenon_Hac zenon_H95 zenon_H3f zenon_H20b zenon_H22 zenon_H38 zenon_H25 zenon_H40 zenon_H3e zenon_H1cf zenon_H208 zenon_H4f zenon_H52 zenon_H1a4 zenon_H6a zenon_H57 zenon_H5b zenon_H130 zenon_H67 zenon_H45 zenon_H14f zenon_H1ac zenon_H23 zenon_H18b zenon_H81 zenon_H74. % 18.52/18.76 apply (zenon_or_s _ _ zenon_H1ec); [ zenon_intro zenon_H1ae | zenon_intro zenon_H15e ]. % 18.52/18.76 apply (zenon_L352_); trivial. % 18.52/18.76 apply (zenon_L252_); trivial. % 18.52/18.76 (* end of lemma zenon_L353_ *) % 18.52/18.76 assert (zenon_L354_ : ((op (e1) (e1)) = (e0)) -> ((op (e1) (e1)) = (e2)) -> (~((e0) = (e2))) -> False). % 18.52/18.76 do 0 intro. intros zenon_H29 zenon_H110 zenon_H149. % 18.52/18.76 elim (classic ((e2) = (e2))); [ zenon_intro zenon_H7d | zenon_intro zenon_H7e ]. % 18.52/18.76 cut (((e2) = (e2)) = ((e0) = (e2))). % 18.52/18.76 intro zenon_D_pnotp. % 18.52/18.76 apply zenon_H149. % 18.52/18.76 rewrite <- zenon_D_pnotp. % 18.52/18.76 exact zenon_H7d. % 18.52/18.76 cut (((e2) = (e2))); [idtac | apply NNPP; zenon_intro zenon_H7e]. % 18.52/18.76 cut (((e2) = (e0))); [idtac | apply NNPP; zenon_intro zenon_H14a]. % 18.52/18.76 congruence. % 18.52/18.76 cut (((op (e1) (e1)) = (e0)) = ((e2) = (e0))). % 18.52/18.76 intro zenon_D_pnotp. % 18.52/18.76 apply zenon_H14a. % 18.52/18.76 rewrite <- zenon_D_pnotp. % 18.52/18.76 exact zenon_H29. % 18.52/18.76 cut (((e0) = (e0))); [idtac | apply NNPP; zenon_intro zenon_H82]. % 18.52/18.76 cut (((op (e1) (e1)) = (e2))); [idtac | apply NNPP; zenon_intro zenon_H20c]. % 18.52/18.76 congruence. % 18.52/18.76 exact (zenon_H20c zenon_H110). % 18.52/18.76 apply zenon_H82. apply refl_equal. % 18.52/18.76 apply zenon_H7e. apply refl_equal. % 18.52/18.76 apply zenon_H7e. apply refl_equal. % 18.52/18.76 (* end of lemma zenon_L354_ *) % 18.52/18.76 assert (zenon_L355_ : ((op (e0) (e2)) = (e0)) -> ((op (e0) (e2)) = (e1)) -> (~((e0) = (e1))) -> False). % 18.52/18.76 do 0 intro. intros zenon_H48 zenon_H122 zenon_Ha1. % 18.52/18.76 elim (classic ((e1) = (e1))); [ zenon_intro zenon_Ha2 | zenon_intro zenon_H79 ]. % 18.52/18.76 cut (((e1) = (e1)) = ((e0) = (e1))). % 18.52/18.76 intro zenon_D_pnotp. % 18.52/18.76 apply zenon_Ha1. % 18.52/18.76 rewrite <- zenon_D_pnotp. % 18.52/18.76 exact zenon_Ha2. % 18.52/18.76 cut (((e1) = (e1))); [idtac | apply NNPP; zenon_intro zenon_H79]. % 18.52/18.76 cut (((e1) = (e0))); [idtac | apply NNPP; zenon_intro zenon_Ha3]. % 18.52/18.76 congruence. % 18.52/18.76 cut (((op (e0) (e2)) = (e0)) = ((e1) = (e0))). % 18.52/18.76 intro zenon_D_pnotp. % 18.52/18.76 apply zenon_Ha3. % 18.52/18.76 rewrite <- zenon_D_pnotp. % 18.52/18.76 exact zenon_H48. % 18.52/18.76 cut (((e0) = (e0))); [idtac | apply NNPP; zenon_intro zenon_H82]. % 18.52/18.76 cut (((op (e0) (e2)) = (e1))); [idtac | apply NNPP; zenon_intro zenon_H20d]. % 18.52/18.76 congruence. % 18.52/18.76 exact (zenon_H20d zenon_H122). % 18.52/18.76 apply zenon_H82. apply refl_equal. % 18.52/18.76 apply zenon_H79. apply refl_equal. % 18.52/18.76 apply zenon_H79. apply refl_equal. % 18.52/18.76 (* end of lemma zenon_L355_ *) % 18.52/18.76 assert (zenon_L356_ : (((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) (e0)) = (e1)) -> (((op (e2) (e2)) = (e0))\/(((op (e2) (e2)) = (e1))\/(((op (e2) (e2)) = (e2))\/((op (e2) (e2)) = (e3))))) -> (~((op (e2) (e2)) = (e0))) -> (~((op (e2) (e2)) = (op (e3) (e2)))) -> (~((op (e2) (e2)) = (e2))) -> ((op (e2) (e0)) = (e3)) -> (~((op (e2) (e0)) = (op (e2) (e2)))) -> False). % 18.52/18.76 do 0 intro. intros zenon_H139 zenon_Ha1 zenon_H48 zenon_H7c zenon_H113 zenon_Hed zenon_H1c4 zenon_H81 zenon_H18f zenon_H173 zenon_H3b zenon_H52. % 18.52/18.76 apply (zenon_or_s _ _ zenon_H139); [ zenon_intro zenon_H122 | zenon_intro zenon_H13a ]. % 18.52/18.76 apply (zenon_L355_); trivial. % 18.52/18.76 apply (zenon_or_s _ _ zenon_H13a); [ zenon_intro zenon_Hf0 | zenon_intro zenon_H13b ]. % 18.52/18.76 apply (zenon_L68_); trivial. % 18.52/18.76 apply (zenon_or_s _ _ zenon_H13b); [ zenon_intro zenon_Hf1 | zenon_intro zenon_Hba ]. % 18.52/18.76 apply (zenon_L93_); trivial. % 18.52/18.76 apply (zenon_L327_); trivial. % 18.52/18.76 (* end of lemma zenon_L356_ *) % 18.52/18.76 assert (zenon_L357_ : (~((op (e0) (e1)) = (op (e2) (e1)))) -> ((op (e0) (e1)) = (e1)) -> ((op (e2) (e1)) = (e1)) -> False). % 18.52/18.76 do 0 intro. intros zenon_H17e zenon_Ha0 zenon_Ha5. % 18.52/18.76 cut (((op (e0) (e1)) = (e1)) = ((op (e0) (e1)) = (op (e2) (e1)))). % 18.52/18.76 intro zenon_D_pnotp. % 18.52/18.76 apply zenon_H17e. % 18.52/18.76 rewrite <- zenon_D_pnotp. % 18.52/18.76 exact zenon_Ha0. % 18.52/18.76 cut (((e1) = (op (e2) (e1)))); [idtac | apply NNPP; zenon_intro zenon_Hb3]. % 18.52/18.76 cut (((op (e0) (e1)) = (op (e0) (e1)))); [idtac | apply NNPP; zenon_intro zenon_H112]. % 18.52/18.76 congruence. % 18.52/18.76 apply zenon_H112. apply refl_equal. % 18.52/18.76 apply zenon_Hb3. apply sym_equal. exact zenon_Ha5. % 18.52/18.76 (* end of lemma zenon_L357_ *) % 18.52/18.76 assert (zenon_L358_ : ((op (e0) (e2)) = (e0)) -> ((op (e0) (e2)) = (e3)) -> (~((e0) = (e3))) -> False). % 18.52/18.76 do 0 intro. intros zenon_H48 zenon_Ha9 zenon_H9a. % 18.52/18.76 elim (classic ((e3) = (e3))); [ zenon_intro zenon_H96 | zenon_intro zenon_H85 ]. % 18.52/18.76 cut (((e3) = (e3)) = ((e0) = (e3))). % 18.52/18.76 intro zenon_D_pnotp. % 18.52/18.76 apply zenon_H9a. % 18.52/18.76 rewrite <- zenon_D_pnotp. % 18.52/18.76 exact zenon_H96. % 18.52/18.76 cut (((e3) = (e3))); [idtac | apply NNPP; zenon_intro zenon_H85]. % 18.52/18.76 cut (((e3) = (e0))); [idtac | apply NNPP; zenon_intro zenon_H9b]. % 18.52/18.76 congruence. % 18.52/18.76 cut (((op (e0) (e2)) = (e0)) = ((e3) = (e0))). % 18.52/18.76 intro zenon_D_pnotp. % 18.52/18.76 apply zenon_H9b. % 18.52/18.76 rewrite <- zenon_D_pnotp. % 18.52/18.76 exact zenon_H48. % 18.52/18.76 cut (((e0) = (e0))); [idtac | apply NNPP; zenon_intro zenon_H82]. % 18.52/18.76 cut (((op (e0) (e2)) = (e3))); [idtac | apply NNPP; zenon_intro zenon_H123]. % 18.52/18.76 congruence. % 18.52/18.76 exact (zenon_H123 zenon_Ha9). % 18.52/18.76 apply zenon_H82. apply refl_equal. % 18.52/18.76 apply zenon_H85. apply refl_equal. % 18.52/18.76 apply zenon_H85. apply refl_equal. % 18.52/18.76 (* end of lemma zenon_L358_ *) % 18.52/18.76 assert (zenon_L359_ : ((op (e0) (e3)) = (e1)) -> ((op (e0) (e1)) = (e1)) -> (~((op (e0) (e1)) = (op (e0) (e3)))) -> False). % 18.52/18.76 do 0 intro. intros zenon_Hc3 zenon_Ha0 zenon_H54. % 18.52/18.76 elim (classic ((op (e0) (e3)) = (op (e0) (e3)))); [ zenon_intro zenon_H55 | zenon_intro zenon_H21 ]. % 18.52/18.76 cut (((op (e0) (e3)) = (op (e0) (e3))) = ((op (e0) (e1)) = (op (e0) (e3)))). % 18.52/18.76 intro zenon_D_pnotp. % 18.52/18.76 apply zenon_H54. % 18.52/18.76 rewrite <- zenon_D_pnotp. % 18.52/18.76 exact zenon_H55. % 18.52/18.76 cut (((op (e0) (e3)) = (op (e0) (e3)))); [idtac | apply NNPP; zenon_intro zenon_H21]. % 18.52/18.76 cut (((op (e0) (e3)) = (op (e0) (e1)))); [idtac | apply NNPP; zenon_intro zenon_H56]. % 18.52/18.76 congruence. % 18.52/18.76 cut (((op (e0) (e3)) = (e1)) = ((op (e0) (e3)) = (op (e0) (e1)))). % 18.52/18.76 intro zenon_D_pnotp. % 18.52/18.76 apply zenon_H56. % 18.52/18.76 rewrite <- zenon_D_pnotp. % 18.52/18.76 exact zenon_Hc3. % 18.52/18.76 cut (((e1) = (op (e0) (e1)))); [idtac | apply NNPP; zenon_intro zenon_H20e]. % 18.52/18.76 cut (((op (e0) (e3)) = (op (e0) (e3)))); [idtac | apply NNPP; zenon_intro zenon_H21]. % 18.52/18.76 congruence. % 18.52/18.76 apply zenon_H21. apply refl_equal. % 18.52/18.76 apply zenon_H20e. apply sym_equal. exact zenon_Ha0. % 18.52/18.76 apply zenon_H21. apply refl_equal. % 18.52/18.76 apply zenon_H21. apply refl_equal. % 18.52/18.76 (* end of lemma zenon_L359_ *) % 18.52/18.76 assert (zenon_L360_ : ((op (e1) (e3)) = (e1)) -> ((op (e1) (e0)) = (e1)) -> (~((op (e1) (e0)) = (op (e1) (e3)))) -> False). % 18.52/18.76 do 0 intro. intros zenon_Hd6 zenon_H9d zenon_Hd8. % 18.52/18.76 elim (classic ((op (e1) (e3)) = (op (e1) (e3)))); [ zenon_intro zenon_H58 | zenon_intro zenon_H59 ]. % 18.52/18.76 cut (((op (e1) (e3)) = (op (e1) (e3))) = ((op (e1) (e0)) = (op (e1) (e3)))). % 18.52/18.76 intro zenon_D_pnotp. % 18.52/18.76 apply zenon_Hd8. % 18.52/18.76 rewrite <- zenon_D_pnotp. % 18.52/18.76 exact zenon_H58. % 18.52/18.76 cut (((op (e1) (e3)) = (op (e1) (e3)))); [idtac | apply NNPP; zenon_intro zenon_H59]. % 18.52/18.76 cut (((op (e1) (e3)) = (op (e1) (e0)))); [idtac | apply NNPP; zenon_intro zenon_Hd9]. % 18.52/18.76 congruence. % 18.52/18.76 cut (((op (e1) (e3)) = (e1)) = ((op (e1) (e3)) = (op (e1) (e0)))). % 18.52/18.76 intro zenon_D_pnotp. % 18.52/18.76 apply zenon_Hd9. % 18.52/18.76 rewrite <- zenon_D_pnotp. % 18.52/18.76 exact zenon_Hd6. % 18.52/18.76 cut (((e1) = (op (e1) (e0)))); [idtac | apply NNPP; zenon_intro zenon_H20f]. % 18.52/18.76 cut (((op (e1) (e3)) = (op (e1) (e3)))); [idtac | apply NNPP; zenon_intro zenon_H59]. % 18.52/18.76 congruence. % 18.52/18.76 apply zenon_H59. apply refl_equal. % 18.52/18.76 apply zenon_H20f. apply sym_equal. exact zenon_H9d. % 18.52/18.76 apply zenon_H59. apply refl_equal. % 18.52/18.76 apply zenon_H59. apply refl_equal. % 18.52/18.76 (* end of lemma zenon_L360_ *) % 18.52/18.76 assert (zenon_L361_ : (((op (e2) (e2)) = (e0))\/(((op (e2) (e2)) = (e1))\/(((op (e2) (e2)) = (e2))\/((op (e2) (e2)) = (e3))))) -> (~((op (e2) (e2)) = (e0))) -> (~((op (e2) (e2)) = (op (e2) (e3)))) -> ((op (e2) (e3)) = (e1)) -> (~((op (e2) (e2)) = (e2))) -> (~((op (e2) (e2)) = (op (e3) (e2)))) -> ((op (e3) (e2)) = (e3)) -> False). % 18.52/18.76 do 0 intro. intros zenon_H1c4 zenon_H81 zenon_H6d zenon_Hf4 zenon_H173 zenon_H18f zenon_H163. % 18.52/18.76 apply (zenon_or_s _ _ zenon_H1c4); [ zenon_intro zenon_H2c | zenon_intro zenon_H1c5 ]. % 18.52/18.76 exact (zenon_H81 zenon_H2c). % 18.52/18.76 apply (zenon_or_s _ _ zenon_H1c5); [ zenon_intro zenon_Hf1 | zenon_intro zenon_H1c6 ]. % 18.52/18.76 apply (zenon_L84_); trivial. % 18.52/18.76 apply (zenon_or_s _ _ zenon_H1c6); [ zenon_intro zenon_H176 | zenon_intro zenon_Haa ]. % 18.52/18.76 exact (zenon_H173 zenon_H176). % 18.52/18.76 apply (zenon_L180_); trivial. % 18.52/18.76 (* end of lemma zenon_L361_ *) % 18.52/18.76 assert (zenon_L362_ : (((op (e0) (e3)) = (e1))\/(((op (e1) (e3)) = (e1))\/(((op (e2) (e3)) = (e1))\/((op (e3) (e3)) = (e1))))) -> (~((op (e0) (e1)) = (op (e0) (e3)))) -> ((op (e0) (e1)) = (e1)) -> (~((op (e1) (e0)) = (op (e1) (e3)))) -> ((op (e1) (e0)) = (e1)) -> ((op (e3) (e2)) = (e3)) -> (~((op (e2) (e2)) = (op (e3) (e2)))) -> (~((op (e2) (e2)) = (e2))) -> (~((op (e2) (e2)) = (op (e2) (e3)))) -> (~((op (e2) (e2)) = (e0))) -> (((op (e2) (e2)) = (e0))\/(((op (e2) (e2)) = (e1))\/(((op (e2) (e2)) = (e2))\/((op (e2) (e2)) = (e3))))) -> ((op (e3) (e0)) = (e1)) -> (~((op (e3) (e0)) = (op (e3) (e3)))) -> False). % 18.52/18.76 do 0 intro. intros zenon_H133 zenon_H54 zenon_Ha0 zenon_Hd8 zenon_H9d zenon_H163 zenon_H18f zenon_H173 zenon_H6d zenon_H81 zenon_H1c4 zenon_Hac zenon_H71. % 18.52/18.76 apply (zenon_or_s _ _ zenon_H133); [ zenon_intro zenon_Hc3 | zenon_intro zenon_H134 ]. % 18.52/18.76 apply (zenon_L359_); trivial. % 18.52/18.76 apply (zenon_or_s _ _ zenon_H134); [ zenon_intro zenon_Hd6 | zenon_intro zenon_H135 ]. % 18.52/18.76 apply (zenon_L360_); trivial. % 18.52/18.76 apply (zenon_or_s _ _ zenon_H135); [ zenon_intro zenon_Hf4 | zenon_intro zenon_Hc4 ]. % 18.52/18.76 apply (zenon_L361_); trivial. % 18.52/18.76 apply (zenon_L189_); trivial. % 18.52/18.76 (* end of lemma zenon_L362_ *) % 18.52/18.76 assert (zenon_L363_ : (~((op (e0) (e1)) = (op (e3) (e1)))) -> ((op (e0) (e1)) = (e1)) -> ((op (e3) (e1)) = (e1)) -> False). % 18.52/18.76 do 0 intro. intros zenon_H210 zenon_Ha0 zenon_Hae. % 18.52/18.76 cut (((op (e0) (e1)) = (e1)) = ((op (e0) (e1)) = (op (e3) (e1)))). % 18.52/18.76 intro zenon_D_pnotp. % 18.52/18.76 apply zenon_H210. % 18.52/18.76 rewrite <- zenon_D_pnotp. % 18.52/18.76 exact zenon_Ha0. % 18.52/18.76 cut (((e1) = (op (e3) (e1)))); [idtac | apply NNPP; zenon_intro zenon_H132]. % 18.52/18.76 cut (((op (e0) (e1)) = (op (e0) (e1)))); [idtac | apply NNPP; zenon_intro zenon_H112]. % 18.52/18.76 congruence. % 18.52/18.76 apply zenon_H112. apply refl_equal. % 18.52/18.76 apply zenon_H132. apply sym_equal. exact zenon_Hae. % 18.52/18.76 (* end of lemma zenon_L363_ *) % 18.52/18.76 assert (zenon_L364_ : (~((op (e2) (e1)) = (op (e3) (e1)))) -> ((op (e2) (e1)) = (e2)) -> ((op (e3) (e1)) = (e2)) -> False). % 18.52/18.76 do 0 intro. intros zenon_Haf zenon_H1ca zenon_H14d. % 18.52/18.76 cut (((op (e2) (e1)) = (e2)) = ((op (e2) (e1)) = (op (e3) (e1)))). % 18.52/18.76 intro zenon_D_pnotp. % 18.52/18.76 apply zenon_Haf. % 18.52/18.76 rewrite <- zenon_D_pnotp. % 18.52/18.76 exact zenon_H1ca. % 18.52/18.76 cut (((e2) = (op (e3) (e1)))); [idtac | apply NNPP; zenon_intro zenon_H14e]. % 18.52/18.76 cut (((op (e2) (e1)) = (op (e2) (e1)))); [idtac | apply NNPP; zenon_intro zenon_H211]. % 18.52/18.76 congruence. % 18.52/18.76 apply zenon_H211. apply refl_equal. % 18.52/18.76 apply zenon_H14e. apply sym_equal. exact zenon_H14d. % 18.52/18.76 (* end of lemma zenon_L364_ *) % 18.52/18.76 assert (zenon_L365_ : (((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 (e1) (e3)) = (op (e3) (e3)))) -> ((op (e1) (e3)) = (e1)) -> False). % 18.52/18.76 do 0 intro. intros zenon_He8 zenon_Ha1 zenon_H44 zenon_Ha0 zenon_H210 zenon_Hf1 zenon_H18f zenon_Hd5 zenon_Hd6. % 18.52/18.76 apply (zenon_or_s _ _ zenon_He8); [ zenon_intro zenon_Hac | zenon_intro zenon_Heb ]. % 18.52/18.76 apply (zenon_L41_); trivial. % 18.52/18.76 apply (zenon_or_s _ _ zenon_Heb); [ zenon_intro zenon_Hae | zenon_intro zenon_Hec ]. % 18.52/18.76 apply (zenon_L363_); trivial. % 18.52/18.76 apply (zenon_or_s _ _ zenon_Hec); [ zenon_intro zenon_Hba | zenon_intro zenon_Hc4 ]. % 18.52/18.76 apply (zenon_L185_); trivial. % 18.52/18.76 apply (zenon_L50_); trivial. % 18.52/18.76 (* end of lemma zenon_L365_ *) % 18.52/18.76 assert (zenon_L366_ : (~((op (e1) (e3)) = (op (e2) (e3)))) -> ((op (e1) (e3)) = (e2)) -> ((op (e2) (e3)) = (e2)) -> False). % 18.52/18.76 do 0 intro. intros zenon_Hdb zenon_Hd7 zenon_H11d. % 18.52/18.76 cut (((op (e1) (e3)) = (e2)) = ((op (e1) (e3)) = (op (e2) (e3)))). % 18.52/18.76 intro zenon_D_pnotp. % 18.52/18.76 apply zenon_Hdb. % 18.52/18.76 rewrite <- zenon_D_pnotp. % 18.52/18.76 exact zenon_Hd7. % 18.52/18.76 cut (((e2) = (op (e2) (e3)))); [idtac | apply NNPP; zenon_intro zenon_H1df]. % 18.52/18.76 cut (((op (e1) (e3)) = (op (e1) (e3)))); [idtac | apply NNPP; zenon_intro zenon_H59]. % 18.52/18.76 congruence. % 18.52/18.76 apply zenon_H59. apply refl_equal. % 18.52/18.76 apply zenon_H1df. apply sym_equal. exact zenon_H11d. % 18.52/18.76 (* end of lemma zenon_L366_ *) % 18.52/18.76 assert (zenon_L367_ : (~((op (e0) (e3)) = (op (e2) (e3)))) -> ((op (e0) (e3)) = (e0)) -> ((op (e2) (e3)) = (e0)) -> False). % 18.52/18.76 do 0 intro. intros zenon_He2 zenon_H1e zenon_H37. % 18.52/18.76 cut (((op (e0) (e3)) = (e0)) = ((op (e0) (e3)) = (op (e2) (e3)))). % 18.52/18.76 intro zenon_D_pnotp. % 18.52/18.76 apply zenon_He2. % 18.52/18.76 rewrite <- zenon_D_pnotp. % 18.52/18.76 exact zenon_H1e. % 18.52/18.76 cut (((e0) = (op (e2) (e3)))); [idtac | apply NNPP; zenon_intro zenon_H180]. % 18.52/18.76 cut (((op (e0) (e3)) = (op (e0) (e3)))); [idtac | apply NNPP; zenon_intro zenon_H21]. % 18.52/18.76 congruence. % 18.52/18.76 apply zenon_H21. apply refl_equal. % 18.52/18.76 apply zenon_H180. apply sym_equal. exact zenon_H37. % 18.52/18.76 (* end of lemma zenon_L367_ *) % 18.52/18.76 assert (zenon_L368_ : (((op (e0) (e1)) = (e0))\/(((op (e0) (e1)) = (e1))\/(((op (e0) (e1)) = (e2))\/((op (e0) (e1)) = (e3))))) -> (~((op (e0) (e1)) = (e0))) -> (~((op (e0) (e1)) = (op (e3) (e1)))) -> (~((op (e1) (e1)) = (op (e2) (e1)))) -> (~((op (e0) (e1)) = (op (e2) (e1)))) -> ((op (e3) (e1)) = (e1)) -> (~((op (e2) (e1)) = (op (e3) (e1)))) -> (~((op (e2) (e1)) = (e0))) -> (((op (e2) (e1)) = (e0))\/(((op (e2) (e1)) = (e1))\/(((op (e2) (e1)) = (e2))\/((op (e2) (e1)) = (e3))))) -> (~((op (e0) (e1)) = (op (e1) (e1)))) -> ((op (e1) (e1)) = (e3)) -> False). % 18.52/18.76 do 0 intro. intros zenon_H212 zenon_H20b zenon_H210 zenon_H13e zenon_H17e zenon_Hae zenon_Haf zenon_H31 zenon_H1cc zenon_H10e zenon_H13f. % 18.52/18.76 apply (zenon_or_s _ _ zenon_H212); [ zenon_intro zenon_H49 | zenon_intro zenon_H213 ]. % 18.52/18.76 exact (zenon_H20b zenon_H49). % 18.52/18.76 apply (zenon_or_s _ _ zenon_H213); [ zenon_intro zenon_Ha0 | zenon_intro zenon_H214 ]. % 18.52/18.76 apply (zenon_L363_); trivial. % 18.52/18.76 apply (zenon_or_s _ _ zenon_H214); [ zenon_intro zenon_H10f | zenon_intro zenon_H99 ]. % 18.52/18.76 apply (zenon_L192_); trivial. % 18.52/18.76 apply (zenon_L108_); trivial. % 18.52/18.76 (* end of lemma zenon_L368_ *) % 18.52/18.76 assert (zenon_L369_ : (~((op (op (e1) (e1)) (e1)) = (op (e0) (e1)))) -> ((op (e1) (e1)) = (e0)) -> False). % 18.52/18.76 do 0 intro. intros zenon_H215 zenon_H29. % 18.52/18.76 cut (((e1) = (e1))); [idtac | apply NNPP; zenon_intro zenon_H79]. % 18.52/18.76 cut (((op (e1) (e1)) = (e0))); [idtac | apply NNPP; zenon_intro zenon_H24]. % 18.52/18.76 congruence. % 18.52/18.76 exact (zenon_H24 zenon_H29). % 18.52/18.76 apply zenon_H79. apply refl_equal. % 18.52/18.76 (* end of lemma zenon_L369_ *) % 18.52/18.76 assert (zenon_L370_ : ((op (e0) (e1)) = (e2)) -> ((op (e1) (e1)) = (e0)) -> (~((e2) = (op (op (e1) (e1)) (e1)))) -> False). % 18.52/18.76 do 0 intro. intros zenon_H10f zenon_H29 zenon_H216. % 18.52/18.76 elim (classic ((op (op (e1) (e1)) (e1)) = (op (op (e1) (e1)) (e1)))); [ zenon_intro zenon_H217 | zenon_intro zenon_H218 ]. % 18.52/18.76 cut (((op (op (e1) (e1)) (e1)) = (op (op (e1) (e1)) (e1))) = ((e2) = (op (op (e1) (e1)) (e1)))). % 18.52/18.76 intro zenon_D_pnotp. % 18.52/18.76 apply zenon_H216. % 18.52/18.76 rewrite <- zenon_D_pnotp. % 18.52/18.76 exact zenon_H217. % 18.52/18.76 cut (((op (op (e1) (e1)) (e1)) = (op (op (e1) (e1)) (e1)))); [idtac | apply NNPP; zenon_intro zenon_H218]. % 18.52/18.76 cut (((op (op (e1) (e1)) (e1)) = (e2))); [idtac | apply NNPP; zenon_intro zenon_H219]. % 18.52/18.76 congruence. % 18.52/18.76 cut (((op (e0) (e1)) = (e2)) = ((op (op (e1) (e1)) (e1)) = (e2))). % 18.52/18.76 intro zenon_D_pnotp. % 18.52/18.76 apply zenon_H219. % 18.52/18.76 rewrite <- zenon_D_pnotp. % 18.52/18.76 exact zenon_H10f. % 18.52/18.76 cut (((e2) = (e2))); [idtac | apply NNPP; zenon_intro zenon_H7e]. % 18.52/18.76 cut (((op (e0) (e1)) = (op (op (e1) (e1)) (e1)))); [idtac | apply NNPP; zenon_intro zenon_H21a]. % 18.52/18.76 congruence. % 18.52/18.76 elim (classic ((op (op (e1) (e1)) (e1)) = (op (op (e1) (e1)) (e1)))); [ zenon_intro zenon_H217 | zenon_intro zenon_H218 ]. % 18.52/18.76 cut (((op (op (e1) (e1)) (e1)) = (op (op (e1) (e1)) (e1))) = ((op (e0) (e1)) = (op (op (e1) (e1)) (e1)))). % 18.52/18.76 intro zenon_D_pnotp. % 18.52/18.76 apply zenon_H21a. % 18.52/18.76 rewrite <- zenon_D_pnotp. % 18.52/18.76 exact zenon_H217. % 18.52/18.76 cut (((op (op (e1) (e1)) (e1)) = (op (op (e1) (e1)) (e1)))); [idtac | apply NNPP; zenon_intro zenon_H218]. % 18.52/18.76 cut (((op (op (e1) (e1)) (e1)) = (op (e0) (e1)))); [idtac | apply NNPP; zenon_intro zenon_H215]. % 18.52/18.76 congruence. % 18.52/18.76 apply (zenon_L369_); trivial. % 18.52/18.76 apply zenon_H218. apply refl_equal. % 18.52/18.76 apply zenon_H218. apply refl_equal. % 18.52/18.76 apply zenon_H7e. apply refl_equal. % 18.52/18.76 apply zenon_H218. apply refl_equal. % 18.52/18.76 apply zenon_H218. apply refl_equal. % 18.52/18.76 (* end of lemma zenon_L370_ *) % 18.52/18.76 assert (zenon_L371_ : ((op (e2) (e1)) = (e3)) -> ((op (e0) (e1)) = (e2)) -> ((op (e1) (e1)) = (e0)) -> False). % 18.52/18.76 do 0 intro. intros zenon_Ha6 zenon_H10f zenon_H29. % 18.52/18.76 apply (zenon_notand_s _ _ ax17); [ zenon_intro zenon_H21c | zenon_intro zenon_H21b ]. % 18.52/18.76 elim (classic ((op (op (op (e1) (e1)) (e1)) (e1)) = (op (op (op (e1) (e1)) (e1)) (e1)))); [ zenon_intro zenon_H21d | zenon_intro zenon_H21e ]. % 18.52/18.76 cut (((op (op (op (e1) (e1)) (e1)) (e1)) = (op (op (op (e1) (e1)) (e1)) (e1))) = ((e3) = (op (op (op (e1) (e1)) (e1)) (e1)))). % 18.52/18.76 intro zenon_D_pnotp. % 18.52/18.76 apply zenon_H21c. % 18.52/18.76 rewrite <- zenon_D_pnotp. % 18.52/18.76 exact zenon_H21d. % 18.52/18.76 cut (((op (op (op (e1) (e1)) (e1)) (e1)) = (op (op (op (e1) (e1)) (e1)) (e1)))); [idtac | apply NNPP; zenon_intro zenon_H21e]. % 18.52/18.76 cut (((op (op (op (e1) (e1)) (e1)) (e1)) = (e3))); [idtac | apply NNPP; zenon_intro zenon_H21f]. % 18.52/18.76 congruence. % 18.52/18.76 cut (((op (e2) (e1)) = (e3)) = ((op (op (op (e1) (e1)) (e1)) (e1)) = (e3))). % 18.52/18.76 intro zenon_D_pnotp. % 18.52/18.76 apply zenon_H21f. % 18.52/18.76 rewrite <- zenon_D_pnotp. % 18.52/18.76 exact zenon_Ha6. % 18.52/18.76 cut (((e3) = (e3))); [idtac | apply NNPP; zenon_intro zenon_H85]. % 18.52/18.76 cut (((op (e2) (e1)) = (op (op (op (e1) (e1)) (e1)) (e1)))); [idtac | apply NNPP; zenon_intro zenon_H220]. % 18.52/18.76 congruence. % 18.52/18.76 elim (classic ((op (op (op (e1) (e1)) (e1)) (e1)) = (op (op (op (e1) (e1)) (e1)) (e1)))); [ zenon_intro zenon_H21d | zenon_intro zenon_H21e ]. % 18.52/18.76 cut (((op (op (op (e1) (e1)) (e1)) (e1)) = (op (op (op (e1) (e1)) (e1)) (e1))) = ((op (e2) (e1)) = (op (op (op (e1) (e1)) (e1)) (e1)))). % 18.52/18.76 intro zenon_D_pnotp. % 18.52/18.76 apply zenon_H220. % 18.52/18.76 rewrite <- zenon_D_pnotp. % 18.52/18.76 exact zenon_H21d. % 18.52/18.76 cut (((op (op (op (e1) (e1)) (e1)) (e1)) = (op (op (op (e1) (e1)) (e1)) (e1)))); [idtac | apply NNPP; zenon_intro zenon_H21e]. % 18.52/18.76 cut (((op (op (op (e1) (e1)) (e1)) (e1)) = (op (e2) (e1)))); [idtac | apply NNPP; zenon_intro zenon_H221]. % 18.52/18.76 congruence. % 18.52/18.76 cut (((e1) = (e1))); [idtac | apply NNPP; zenon_intro zenon_H79]. % 18.52/18.76 cut (((op (op (e1) (e1)) (e1)) = (e2))); [idtac | apply NNPP; zenon_intro zenon_H219]. % 18.52/18.76 congruence. % 18.52/18.76 cut (((op (e0) (e1)) = (e2)) = ((op (op (e1) (e1)) (e1)) = (e2))). % 18.52/18.76 intro zenon_D_pnotp. % 18.52/18.76 apply zenon_H219. % 18.52/18.76 rewrite <- zenon_D_pnotp. % 18.52/18.76 exact zenon_H10f. % 18.52/18.76 cut (((e2) = (e2))); [idtac | apply NNPP; zenon_intro zenon_H7e]. % 18.52/18.76 cut (((op (e0) (e1)) = (op (op (e1) (e1)) (e1)))); [idtac | apply NNPP; zenon_intro zenon_H21a]. % 18.52/18.76 congruence. % 18.52/18.76 elim (classic ((op (op (e1) (e1)) (e1)) = (op (op (e1) (e1)) (e1)))); [ zenon_intro zenon_H217 | zenon_intro zenon_H218 ]. % 18.52/18.76 cut (((op (op (e1) (e1)) (e1)) = (op (op (e1) (e1)) (e1))) = ((op (e0) (e1)) = (op (op (e1) (e1)) (e1)))). % 18.52/18.76 intro zenon_D_pnotp. % 18.52/18.76 apply zenon_H21a. % 18.52/18.76 rewrite <- zenon_D_pnotp. % 18.52/18.76 exact zenon_H217. % 18.52/18.76 cut (((op (op (e1) (e1)) (e1)) = (op (op (e1) (e1)) (e1)))); [idtac | apply NNPP; zenon_intro zenon_H218]. % 18.52/18.76 cut (((op (op (e1) (e1)) (e1)) = (op (e0) (e1)))); [idtac | apply NNPP; zenon_intro zenon_H215]. % 18.52/18.76 congruence. % 18.52/18.76 apply (zenon_L369_); trivial. % 18.52/18.76 apply zenon_H218. apply refl_equal. % 18.52/18.76 apply zenon_H218. apply refl_equal. % 18.52/18.76 apply zenon_H7e. apply refl_equal. % 18.52/18.76 apply zenon_H79. apply refl_equal. % 18.52/18.76 apply zenon_H21e. apply refl_equal. % 18.52/18.76 apply zenon_H21e. apply refl_equal. % 18.52/18.76 apply zenon_H85. apply refl_equal. % 18.52/18.76 apply zenon_H21e. apply refl_equal. % 18.52/18.76 apply zenon_H21e. apply refl_equal. % 18.52/18.76 apply (zenon_notand_s _ _ zenon_H21b); [ zenon_intro zenon_H216 | zenon_intro zenon_H46 ]. % 18.52/18.76 apply (zenon_L370_); trivial. % 18.52/18.76 apply zenon_H46. apply sym_equal. exact zenon_H29. % 18.52/18.76 (* end of lemma zenon_L371_ *) % 18.52/18.76 assert (zenon_L372_ : (((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) (e0)) = (op (e2) (e2)))) -> ((op (e2) (e0)) = (e3)) -> (~((op (e3) (e1)) = (op (e3) (e2)))) -> ((op (e3) (e1)) = (e3)) -> False). % 18.52/18.76 do 0 intro. intros zenon_H1a6 zenon_H9a zenon_H48 zenon_H12b zenon_H113 zenon_H52 zenon_H3b zenon_H1a4 zenon_H161. % 18.52/18.76 apply (zenon_or_s _ _ zenon_H1a6); [ zenon_intro zenon_Ha9 | zenon_intro zenon_H1aa ]. % 18.52/18.76 apply (zenon_L358_); trivial. % 18.52/18.76 apply (zenon_or_s _ _ zenon_H1aa); [ zenon_intro zenon_H16c | zenon_intro zenon_H1ab ]. % 18.52/18.76 apply (zenon_L116_); trivial. % 18.52/18.76 apply (zenon_or_s _ _ zenon_H1ab); [ zenon_intro zenon_Haa | zenon_intro zenon_H163 ]. % 18.52/18.76 apply (zenon_L168_); trivial. % 18.52/18.76 apply (zenon_L169_); trivial. % 18.52/18.76 (* end of lemma zenon_L372_ *) % 18.52/18.76 assert (zenon_L373_ : (((op (e0) (e1)) = (e0))\/(((op (e0) (e1)) = (e1))\/(((op (e0) (e1)) = (e2))\/((op (e0) (e1)) = (e3))))) -> (~((op (e0) (e1)) = (e0))) -> ((op (e2) (e1)) = (e1)) -> ((op (e2) (e1)) = (e2)) -> (~((op (e0) (e1)) = (op (e2) (e1)))) -> (~((op (e0) (e1)) = (op (e1) (e1)))) -> ((op (e1) (e1)) = (e3)) -> False). % 18.52/18.76 do 0 intro. intros zenon_H212 zenon_H20b zenon_Ha5 zenon_H1ca zenon_H17e zenon_H10e zenon_H13f. % 18.52/18.76 apply (zenon_or_s _ _ zenon_H212); [ zenon_intro zenon_H49 | zenon_intro zenon_H213 ]. % 18.52/18.76 exact (zenon_H20b zenon_H49). % 18.52/18.76 apply (zenon_or_s _ _ zenon_H213); [ zenon_intro zenon_Ha0 | zenon_intro zenon_H214 ]. % 18.52/18.76 apply (zenon_L357_); trivial. % 18.52/18.76 apply (zenon_or_s _ _ zenon_H214); [ zenon_intro zenon_H10f | zenon_intro zenon_H99 ]. % 18.52/18.76 apply (zenon_L191_); trivial. % 18.52/18.76 apply (zenon_L108_); trivial. % 18.52/18.76 (* end of lemma zenon_L373_ *) % 18.52/18.76 assert (zenon_L374_ : (((op (e0) (e2)) = (e0))\/(((op (e1) (e2)) = (e0))\/(((op (e2) (e2)) = (e0))\/((op (e3) (e2)) = (e0))))) -> (~((e0) = (e1))) -> ((op (e0) (e2)) = (e1)) -> (~((op (e1) (e1)) = (op (e1) (e2)))) -> ((op (e1) (e1)) = (e0)) -> (~((op (e2) (e2)) = (op (e2) (e3)))) -> ((op (e2) (e3)) = (e0)) -> (~((op (e3) (e0)) = (op (e3) (e2)))) -> ((op (e3) (e0)) = (e0)) -> False). % 18.52/18.76 do 0 intro. intros zenon_H6a zenon_Ha1 zenon_H122 zenon_H4f zenon_H29 zenon_H6d zenon_H37 zenon_H6f zenon_H44. % 18.52/18.76 apply (zenon_or_s _ _ zenon_H6a); [ zenon_intro zenon_H48 | zenon_intro zenon_H6b ]. % 18.52/18.76 apply (zenon_L355_); trivial. % 18.52/18.76 apply (zenon_or_s _ _ zenon_H6b); [ zenon_intro zenon_H2a | zenon_intro zenon_H6c ]. % 18.52/18.76 apply (zenon_L10_); trivial. % 18.52/18.76 apply (zenon_or_s _ _ zenon_H6c); [ zenon_intro zenon_H2c | zenon_intro zenon_H61 ]. % 18.52/18.76 apply (zenon_L18_); trivial. % 18.52/18.76 apply (zenon_L19_); trivial. % 18.52/18.76 (* end of lemma zenon_L374_ *) % 18.52/18.76 assert (zenon_L375_ : ((op (e0) (e3)) = (e2)) -> ((op (e0) (e0)) = (e2)) -> (~((op (e0) (e0)) = (op (e0) (e3)))) -> False). % 18.52/18.76 do 0 intro. intros zenon_Hcd zenon_H7b zenon_H189. % 18.52/18.76 elim (classic ((op (e0) (e3)) = (op (e0) (e3)))); [ zenon_intro zenon_H55 | zenon_intro zenon_H21 ]. % 18.52/18.76 cut (((op (e0) (e3)) = (op (e0) (e3))) = ((op (e0) (e0)) = (op (e0) (e3)))). % 18.52/18.76 intro zenon_D_pnotp. % 18.52/18.76 apply zenon_H189. % 18.52/18.76 rewrite <- zenon_D_pnotp. % 18.52/18.76 exact zenon_H55. % 18.52/18.76 cut (((op (e0) (e3)) = (op (e0) (e3)))); [idtac | apply NNPP; zenon_intro zenon_H21]. % 18.52/18.76 cut (((op (e0) (e3)) = (op (e0) (e0)))); [idtac | apply NNPP; zenon_intro zenon_H18a]. % 18.52/18.76 congruence. % 18.52/18.76 cut (((op (e0) (e3)) = (e2)) = ((op (e0) (e3)) = (op (e0) (e0)))). % 18.52/18.76 intro zenon_D_pnotp. % 18.52/18.76 apply zenon_H18a. % 18.52/18.76 rewrite <- zenon_D_pnotp. % 18.52/18.76 exact zenon_Hcd. % 18.52/18.76 cut (((e2) = (op (e0) (e0)))); [idtac | apply NNPP; zenon_intro zenon_H1f9]. % 18.52/18.76 cut (((op (e0) (e3)) = (op (e0) (e3)))); [idtac | apply NNPP; zenon_intro zenon_H21]. % 18.52/18.76 congruence. % 18.52/18.76 apply zenon_H21. apply refl_equal. % 18.52/18.76 apply zenon_H1f9. apply sym_equal. exact zenon_H7b. % 18.52/18.76 apply zenon_H21. apply refl_equal. % 18.52/18.76 apply zenon_H21. apply refl_equal. % 18.52/18.76 (* end of lemma zenon_L375_ *) % 18.52/18.76 assert (zenon_L376_ : (((op (e0) (e1)) = (e2))\/(((op (e1) (e1)) = (e2))\/(((op (e2) (e1)) = (e2))\/((op (e3) (e1)) = (e2))))) -> (~((e2) = (e3))) -> ((op (e0) (e1)) = (e3)) -> (~((e0) = (e2))) -> ((op (e1) (e1)) = (e0)) -> (~((op (e2) (e1)) = (op (e2) (e3)))) -> ((op (e2) (e3)) = (e2)) -> ((op (e3) (e1)) = (e1)) -> (~((e1) = (e2))) -> False). % 18.52/18.76 do 0 intro. intros zenon_H1d8 zenon_H12b zenon_H99 zenon_H149 zenon_H29 zenon_H1c7 zenon_H11d zenon_Hae zenon_H7c. % 18.52/18.76 apply (zenon_or_s _ _ zenon_H1d8); [ zenon_intro zenon_H10f | zenon_intro zenon_H1d9 ]. % 18.52/18.76 apply (zenon_L175_); trivial. % 18.52/18.76 apply (zenon_or_s _ _ zenon_H1d9); [ zenon_intro zenon_H110 | zenon_intro zenon_H1da ]. % 18.52/18.76 apply (zenon_L354_); trivial. % 18.52/18.76 apply (zenon_or_s _ _ zenon_H1da); [ zenon_intro zenon_H1ca | zenon_intro zenon_H14d ]. % 18.52/18.76 apply (zenon_L224_); trivial. % 18.52/18.76 apply (zenon_L152_); trivial. % 18.52/18.76 (* end of lemma zenon_L376_ *) % 18.52/18.76 assert (zenon_L377_ : (((op (e0) (e3)) = (e2))\/(((op (e1) (e3)) = (e2))\/(((op (e2) (e3)) = (e2))\/((op (e3) (e3)) = (e2))))) -> (~((op (e0) (e0)) = (op (e0) (e3)))) -> ((op (e0) (e0)) = (e2)) -> ((op (e1) (e3)) = (e3)) -> (~((e1) = (e2))) -> ((op (e3) (e1)) = (e1)) -> (~((op (e2) (e1)) = (op (e2) (e3)))) -> ((op (e1) (e1)) = (e0)) -> (~((e0) = (e2))) -> ((op (e0) (e1)) = (e3)) -> (~((e2) = (e3))) -> (((op (e0) (e1)) = (e2))\/(((op (e1) (e1)) = (e2))\/(((op (e2) (e1)) = (e2))\/((op (e3) (e1)) = (e2))))) -> ((op (e3) (e0)) = (e2)) -> (~((op (e3) (e0)) = (op (e3) (e3)))) -> False). % 18.52/18.76 do 0 intro. intros zenon_H145 zenon_H189 zenon_H7b zenon_Hdc zenon_H7c zenon_Hae zenon_H1c7 zenon_H29 zenon_H149 zenon_H99 zenon_H12b zenon_H1d8 zenon_H148 zenon_H71. % 18.52/18.76 apply (zenon_or_s _ _ zenon_H145); [ zenon_intro zenon_Hcd | zenon_intro zenon_H146 ]. % 18.52/18.76 apply (zenon_L375_); trivial. % 18.52/18.76 apply (zenon_or_s _ _ zenon_H146); [ zenon_intro zenon_Hd7 | zenon_intro zenon_H147 ]. % 18.52/18.76 apply (zenon_L266_); trivial. % 18.52/18.76 apply (zenon_or_s _ _ zenon_H147); [ zenon_intro zenon_H11d | zenon_intro zenon_Hf6 ]. % 18.52/18.76 apply (zenon_L376_); trivial. % 18.52/18.76 apply (zenon_L114_); trivial. % 18.52/18.76 (* end of lemma zenon_L377_ *) % 18.52/18.76 assert (zenon_L378_ : ((op (e0) (e2)) = (e0)) -> ((op (e0) (e2)) = (e2)) -> (~((e0) = (e2))) -> False). % 18.52/18.76 do 0 intro. intros zenon_H48 zenon_H150 zenon_H149. % 18.52/18.76 elim (classic ((e2) = (e2))); [ zenon_intro zenon_H7d | zenon_intro zenon_H7e ]. % 18.52/18.76 cut (((e2) = (e2)) = ((e0) = (e2))). % 18.52/18.76 intro zenon_D_pnotp. % 18.52/18.76 apply zenon_H149. % 18.52/18.76 rewrite <- zenon_D_pnotp. % 18.52/18.76 exact zenon_H7d. % 18.52/18.76 cut (((e2) = (e2))); [idtac | apply NNPP; zenon_intro zenon_H7e]. % 18.52/18.76 cut (((e2) = (e0))); [idtac | apply NNPP; zenon_intro zenon_H14a]. % 18.52/18.76 congruence. % 18.52/18.76 cut (((op (e0) (e2)) = (e0)) = ((e2) = (e0))). % 18.52/18.76 intro zenon_D_pnotp. % 18.52/18.76 apply zenon_H14a. % 18.52/18.76 rewrite <- zenon_D_pnotp. % 18.52/18.76 exact zenon_H48. % 18.52/18.76 cut (((e0) = (e0))); [idtac | apply NNPP; zenon_intro zenon_H82]. % 18.52/18.76 cut (((op (e0) (e2)) = (e2))); [idtac | apply NNPP; zenon_intro zenon_H1fd]. % 18.52/18.76 congruence. % 18.52/18.76 exact (zenon_H1fd zenon_H150). % 18.52/18.76 apply zenon_H82. apply refl_equal. % 18.52/18.76 apply zenon_H7e. apply refl_equal. % 18.52/18.76 apply zenon_H7e. apply refl_equal. % 18.52/18.76 (* end of lemma zenon_L378_ *) % 18.52/18.76 assert (zenon_L379_ : (((op (e3) (e3)) = (e0))\/(((op (e3) (e3)) = (e1))\/(((op (e3) (e3)) = (e2))\/((op (e3) (e3)) = (e3))))) -> ((op (e0) (e3)) = (e1)) -> ((op (e1) (e3)) = (e2)) -> (~((op (e3) (e1)) = (op (e3) (e3)))) -> ((op (e3) (e1)) = (e1)) -> (~((op (e3) (e2)) = (op (e3) (e3)))) -> ((op (e3) (e2)) = (e2)) -> (~((op (e3) (e3)) = (e3))) -> False). % 18.52/18.76 do 0 intro. intros zenon_H101 zenon_Hc3 zenon_Hd7 zenon_H130 zenon_Hae zenon_H62 zenon_H151 zenon_H102. % 18.52/18.76 apply (zenon_or_s _ _ zenon_H101); [ zenon_intro zenon_H60 | zenon_intro zenon_H103 ]. % 18.52/18.76 apply (zenon_L201_); trivial. % 18.52/18.76 apply (zenon_or_s _ _ zenon_H103); [ zenon_intro zenon_Hc4 | zenon_intro zenon_H104 ]. % 18.52/18.76 apply (zenon_L85_); trivial. % 18.52/18.76 apply (zenon_or_s _ _ zenon_H104); [ zenon_intro zenon_Hf6 | zenon_intro zenon_H105 ]. % 18.52/18.76 apply (zenon_L119_); trivial. % 18.52/18.76 exact (zenon_H102 zenon_H105). % 18.52/18.76 (* end of lemma zenon_L379_ *) % 18.52/18.76 assert (zenon_L380_ : (((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))) -> (((op (e3) (e3)) = (e0))\/(((op (e3) (e3)) = (e1))\/(((op (e3) (e3)) = (e2))\/((op (e3) (e3)) = (e3))))) -> ((op (e0) (e3)) = (e1)) -> ((op (e1) (e3)) = (e2)) -> (~((op (e3) (e1)) = (op (e3) (e3)))) -> ((op (e3) (e1)) = (e1)) -> (~((op (e3) (e2)) = (op (e3) (e3)))) -> (~((op (e3) (e3)) = (e3))) -> False). % 18.52/18.76 do 0 intro. intros zenon_H172 zenon_H149 zenon_H48 zenon_H12b zenon_H16c zenon_H173 zenon_H101 zenon_Hc3 zenon_Hd7 zenon_H130 zenon_Hae zenon_H62 zenon_H102. % 18.52/18.76 apply (zenon_or_s _ _ zenon_H172); [ zenon_intro zenon_H150 | zenon_intro zenon_H174 ]. % 18.52/18.76 apply (zenon_L378_); trivial. % 18.52/18.76 apply (zenon_or_s _ _ zenon_H174); [ zenon_intro zenon_H113 | zenon_intro zenon_H175 ]. % 18.52/18.76 apply (zenon_L116_); trivial. % 18.52/18.76 apply (zenon_or_s _ _ zenon_H175); [ zenon_intro zenon_H176 | zenon_intro zenon_H151 ]. % 18.52/18.76 exact (zenon_H173 zenon_H176). % 18.52/18.76 apply (zenon_L379_); trivial. % 18.52/18.76 (* end of lemma zenon_L380_ *) % 18.52/18.76 assert (zenon_L381_ : (((op (e1) (e0)) = (e3))\/(((op (e1) (e1)) = (e3))\/(((op (e1) (e2)) = (e3))\/((op (e1) (e3)) = (e3))))) -> (~((e1) = (e3))) -> ((op (e1) (e0)) = (e1)) -> ((op (e3) (e1)) = (e3)) -> (~((op (e1) (e1)) = (op (e3) (e1)))) -> (~((op (e3) (e3)) = (e3))) -> (~((op (e3) (e2)) = (op (e3) (e3)))) -> ((op (e3) (e1)) = (e1)) -> (~((op (e3) (e1)) = (op (e3) (e3)))) -> ((op (e0) (e3)) = (e1)) -> (((op (e3) (e3)) = (e0))\/(((op (e3) (e3)) = (e1))\/(((op (e3) (e3)) = (e2))\/((op (e3) (e3)) = (e3))))) -> (~((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 (e1) (e3)) = (e2)) -> (~((e2) = (e3))) -> False). % 18.52/18.76 do 0 intro. intros zenon_H16f zenon_H95 zenon_H9d zenon_H161 zenon_H160 zenon_H102 zenon_H62 zenon_Hae zenon_H130 zenon_Hc3 zenon_H101 zenon_H173 zenon_H48 zenon_H149 zenon_H172 zenon_Hd7 zenon_H12b. % 18.52/18.76 apply (zenon_or_s _ _ zenon_H16f); [ zenon_intro zenon_H9e | zenon_intro zenon_H170 ]. % 18.52/18.76 apply (zenon_L37_); trivial. % 18.52/18.76 apply (zenon_or_s _ _ zenon_H170); [ zenon_intro zenon_H13f | zenon_intro zenon_H171 ]. % 18.52/18.76 apply (zenon_L110_); trivial. % 18.52/18.76 apply (zenon_or_s _ _ zenon_H171); [ zenon_intro zenon_H16c | zenon_intro zenon_Hdc ]. % 18.52/18.76 apply (zenon_L380_); trivial. % 18.52/18.76 apply (zenon_L266_); trivial. % 18.52/18.76 (* end of lemma zenon_L381_ *) % 18.52/18.76 assert (zenon_L382_ : (((op (e1) (e0)) = (e2))\/(((op (e1) (e1)) = (e2))\/(((op (e1) (e2)) = (e2))\/((op (e1) (e3)) = (e2))))) -> (~((e1) = (e2))) -> ((op (e1) (e1)) = (e0)) -> (~((op (e3) (e1)) = (op (e3) (e2)))) -> ((op (e2) (e0)) = (e3)) -> (~((op (e2) (e0)) = (op (e2) (e2)))) -> (~((e0) = (e3))) -> (((op (e0) (e2)) = (e3))\/(((op (e1) (e2)) = (e3))\/(((op (e2) (e2)) = (e3))\/((op (e3) (e2)) = (e3))))) -> (((op (e1) (e0)) = (e3))\/(((op (e1) (e1)) = (e3))\/(((op (e1) (e2)) = (e3))\/((op (e1) (e3)) = (e3))))) -> (~((e1) = (e3))) -> ((op (e1) (e0)) = (e1)) -> ((op (e3) (e1)) = (e3)) -> (~((op (e1) (e1)) = (op (e3) (e1)))) -> (~((op (e3) (e3)) = (e3))) -> (~((op (e3) (e2)) = (op (e3) (e3)))) -> ((op (e3) (e1)) = (e1)) -> (~((op (e3) (e1)) = (op (e3) (e3)))) -> ((op (e0) (e3)) = (e1)) -> (((op (e3) (e3)) = (e0))\/(((op (e3) (e3)) = (e1))\/(((op (e3) (e3)) = (e2))\/((op (e3) (e3)) = (e3))))) -> (~((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))))) -> (~((e2) = (e3))) -> False). % 18.52/18.76 do 0 intro. intros zenon_H18c zenon_H7c zenon_H29 zenon_H1a4 zenon_H3b zenon_H52 zenon_H9a zenon_H1a6 zenon_H16f zenon_H95 zenon_H9d zenon_H161 zenon_H160 zenon_H102 zenon_H62 zenon_Hae zenon_H130 zenon_Hc3 zenon_H101 zenon_H173 zenon_H48 zenon_H149 zenon_H172 zenon_H12b. % 18.52/18.76 apply (zenon_or_s _ _ zenon_H18c); [ zenon_intro zenon_H86 | zenon_intro zenon_H18d ]. % 18.52/18.76 apply (zenon_L123_); trivial. % 18.52/18.76 apply (zenon_or_s _ _ zenon_H18d); [ zenon_intro zenon_H110 | zenon_intro zenon_H18e ]. % 18.52/18.76 apply (zenon_L354_); trivial. % 18.52/18.76 apply (zenon_or_s _ _ zenon_H18e); [ zenon_intro zenon_H113 | zenon_intro zenon_Hd7 ]. % 18.52/18.76 apply (zenon_L372_); trivial. % 18.52/18.76 apply (zenon_L381_); trivial. % 18.52/18.76 (* end of lemma zenon_L382_ *) % 18.52/18.76 assert (zenon_L383_ : ((op (e1) (e2)) = (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) (e0)) = (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) (e0)) = (e2)) -> (~((op (e0) (e0)) = (op (e0) (e3)))) -> (((op (e0) (e3)) = (e2))\/(((op (e1) (e3)) = (e2))\/(((op (e2) (e3)) = (e2))\/((op (e3) (e3)) = (e2))))) -> (~((op (e0) (e1)) = (op (e1) (e1)))) -> (((op (e2) (e1)) = (e0))\/(((op (e2) (e1)) = (e1))\/(((op (e2) (e1)) = (e2))\/((op (e2) (e1)) = (e3))))) -> (~((op (e2) (e1)) = (e0))) -> (~((op (e2) (e1)) = (op (e3) (e1)))) -> (~((op (e0) (e1)) = (op (e2) (e1)))) -> (~((op (e1) (e1)) = (op (e2) (e1)))) -> (~((op (e0) (e1)) = (op (e3) (e1)))) -> (~((op (e0) (e1)) = (e0))) -> (((op (e0) (e1)) = (e0))\/(((op (e0) (e1)) = (e1))\/(((op (e0) (e1)) = (e2))\/((op (e0) (e1)) = (e3))))) -> ((op (e2) (e1)) = (e2)) -> (((op (e1) (e0)) = (e2))\/(((op (e1) (e1)) = (e2))\/(((op (e1) (e2)) = (e2))\/((op (e1) (e3)) = (e2))))) -> (~((e1) = (e2))) -> ((op (e1) (e1)) = (e0)) -> (~((op (e3) (e1)) = (op (e3) (e2)))) -> ((op (e2) (e0)) = (e3)) -> (~((op (e2) (e0)) = (op (e2) (e2)))) -> (~((e0) = (e3))) -> (((op (e0) (e2)) = (e3))\/(((op (e1) (e2)) = (e3))\/(((op (e2) (e2)) = (e3))\/((op (e3) (e2)) = (e3))))) -> (((op (e1) (e0)) = (e3))\/(((op (e1) (e1)) = (e3))\/(((op (e1) (e2)) = (e3))\/((op (e1) (e3)) = (e3))))) -> (~((e1) = (e3))) -> ((op (e1) (e0)) = (e1)) -> (~((op (e1) (e1)) = (op (e3) (e1)))) -> (~((op (e3) (e3)) = (e3))) -> (~((op (e3) (e2)) = (op (e3) (e3)))) -> ((op (e3) (e1)) = (e1)) -> (~((op (e3) (e1)) = (op (e3) (e3)))) -> ((op (e0) (e3)) = (e1)) -> (((op (e3) (e3)) = (e0))\/(((op (e3) (e3)) = (e1))\/(((op (e3) (e3)) = (e2))\/((op (e3) (e3)) = (e3))))) -> (~((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))))) -> (~((e2) = (e3))) -> False). % 18.52/18.76 do 0 intro. intros zenon_H113 zenon_H1a5 zenon_H71 zenon_H148 zenon_H1d8 zenon_H1c7 zenon_H7b zenon_H189 zenon_H145 zenon_H10e zenon_H1cc zenon_H31 zenon_Haf zenon_H17e zenon_H13e zenon_H210 zenon_H20b zenon_H212 zenon_H1ca zenon_H18c zenon_H7c zenon_H29 zenon_H1a4 zenon_H3b zenon_H52 zenon_H9a zenon_H1a6 zenon_H16f zenon_H95 zenon_H9d zenon_H160 zenon_H102 zenon_H62 zenon_Hae zenon_H130 zenon_Hc3 zenon_H101 zenon_H173 zenon_H48 zenon_H149 zenon_H172 zenon_H12b. % 18.52/18.76 apply (zenon_or_s _ _ zenon_H16f); [ zenon_intro zenon_H9e | zenon_intro zenon_H170 ]. % 18.52/18.76 apply (zenon_L37_); trivial. % 18.52/18.76 apply (zenon_or_s _ _ zenon_H170); [ zenon_intro zenon_H13f | zenon_intro zenon_H171 ]. % 18.52/18.76 apply (zenon_L368_); trivial. % 18.52/18.76 apply (zenon_or_s _ _ zenon_H171); [ zenon_intro zenon_H16c | zenon_intro zenon_Hdc ]. % 18.52/18.76 apply (zenon_L116_); trivial. % 18.52/18.76 apply (zenon_or_s _ _ zenon_H1a5); [ zenon_intro zenon_H99 | zenon_intro zenon_H1a8 ]. % 18.52/18.76 apply (zenon_L377_); trivial. % 18.52/18.76 apply (zenon_or_s _ _ zenon_H1a8); [ zenon_intro zenon_H13f | zenon_intro zenon_H1a9 ]. % 18.52/18.76 apply (zenon_L368_); trivial. % 18.52/18.76 apply (zenon_or_s _ _ zenon_H1a9); [ zenon_intro zenon_Ha6 | zenon_intro zenon_H161 ]. % 18.52/18.76 apply (zenon_L207_); trivial. % 18.52/18.76 apply (zenon_L382_); trivial. % 18.52/18.76 (* end of lemma zenon_L383_ *) % 18.52/18.76 assert (zenon_L384_ : ((op (e0) (e1)) = (e3)) -> ((op (e1) (e1)) = (e0)) -> (~((e3) = (op (op (e1) (e1)) (e1)))) -> False). % 18.52/18.76 do 0 intro. intros zenon_H99 zenon_H29 zenon_H222. % 18.52/18.76 elim (classic ((op (op (e1) (e1)) (e1)) = (op (op (e1) (e1)) (e1)))); [ zenon_intro zenon_H217 | zenon_intro zenon_H218 ]. % 18.52/18.76 cut (((op (op (e1) (e1)) (e1)) = (op (op (e1) (e1)) (e1))) = ((e3) = (op (op (e1) (e1)) (e1)))). % 18.52/18.76 intro zenon_D_pnotp. % 18.52/18.76 apply zenon_H222. % 18.52/18.76 rewrite <- zenon_D_pnotp. % 18.52/18.76 exact zenon_H217. % 18.52/18.76 cut (((op (op (e1) (e1)) (e1)) = (op (op (e1) (e1)) (e1)))); [idtac | apply NNPP; zenon_intro zenon_H218]. % 18.52/18.76 cut (((op (op (e1) (e1)) (e1)) = (e3))); [idtac | apply NNPP; zenon_intro zenon_H223]. % 18.52/18.76 congruence. % 18.52/18.76 cut (((op (e0) (e1)) = (e3)) = ((op (op (e1) (e1)) (e1)) = (e3))). % 18.52/18.76 intro zenon_D_pnotp. % 18.52/18.76 apply zenon_H223. % 18.52/18.76 rewrite <- zenon_D_pnotp. % 18.52/18.76 exact zenon_H99. % 18.52/18.76 cut (((e3) = (e3))); [idtac | apply NNPP; zenon_intro zenon_H85]. % 18.52/18.76 cut (((op (e0) (e1)) = (op (op (e1) (e1)) (e1)))); [idtac | apply NNPP; zenon_intro zenon_H21a]. % 18.52/18.76 congruence. % 18.52/18.76 elim (classic ((op (op (e1) (e1)) (e1)) = (op (op (e1) (e1)) (e1)))); [ zenon_intro zenon_H217 | zenon_intro zenon_H218 ]. % 18.52/18.76 cut (((op (op (e1) (e1)) (e1)) = (op (op (e1) (e1)) (e1))) = ((op (e0) (e1)) = (op (op (e1) (e1)) (e1)))). % 18.52/18.76 intro zenon_D_pnotp. % 18.52/18.76 apply zenon_H21a. % 18.52/18.76 rewrite <- zenon_D_pnotp. % 18.52/18.76 exact zenon_H217. % 18.52/18.76 cut (((op (op (e1) (e1)) (e1)) = (op (op (e1) (e1)) (e1)))); [idtac | apply NNPP; zenon_intro zenon_H218]. % 18.52/18.76 cut (((op (op (e1) (e1)) (e1)) = (op (e0) (e1)))); [idtac | apply NNPP; zenon_intro zenon_H215]. % 18.52/18.76 congruence. % 18.52/18.76 apply (zenon_L369_); trivial. % 18.52/18.76 apply zenon_H218. apply refl_equal. % 18.52/18.76 apply zenon_H218. apply refl_equal. % 18.52/18.76 apply zenon_H85. apply refl_equal. % 18.52/18.76 apply zenon_H218. apply refl_equal. % 18.52/18.76 apply zenon_H218. apply refl_equal. % 18.52/18.76 (* end of lemma zenon_L384_ *) % 18.52/18.76 assert (zenon_L385_ : ((op (e3) (e1)) = (e2)) -> ((op (e0) (e1)) = (e3)) -> ((op (e1) (e1)) = (e0)) -> False). % 18.52/18.76 do 0 intro. intros zenon_H14d zenon_H99 zenon_H29. % 18.52/18.76 apply (zenon_notand_s _ _ ax15); [ zenon_intro zenon_H225 | zenon_intro zenon_H224 ]. % 18.52/18.76 elim (classic ((op (op (op (e1) (e1)) (e1)) (e1)) = (op (op (op (e1) (e1)) (e1)) (e1)))); [ zenon_intro zenon_H21d | zenon_intro zenon_H21e ]. % 18.52/18.76 cut (((op (op (op (e1) (e1)) (e1)) (e1)) = (op (op (op (e1) (e1)) (e1)) (e1))) = ((e2) = (op (op (op (e1) (e1)) (e1)) (e1)))). % 18.52/18.76 intro zenon_D_pnotp. % 18.52/18.76 apply zenon_H225. % 18.52/18.76 rewrite <- zenon_D_pnotp. % 18.52/18.76 exact zenon_H21d. % 18.52/18.76 cut (((op (op (op (e1) (e1)) (e1)) (e1)) = (op (op (op (e1) (e1)) (e1)) (e1)))); [idtac | apply NNPP; zenon_intro zenon_H21e]. % 18.52/18.76 cut (((op (op (op (e1) (e1)) (e1)) (e1)) = (e2))); [idtac | apply NNPP; zenon_intro zenon_H226]. % 18.52/18.76 congruence. % 18.52/18.76 cut (((op (e3) (e1)) = (e2)) = ((op (op (op (e1) (e1)) (e1)) (e1)) = (e2))). % 18.52/18.76 intro zenon_D_pnotp. % 18.52/18.76 apply zenon_H226. % 18.52/18.76 rewrite <- zenon_D_pnotp. % 18.52/18.76 exact zenon_H14d. % 18.52/18.76 cut (((e2) = (e2))); [idtac | apply NNPP; zenon_intro zenon_H7e]. % 18.52/18.76 cut (((op (e3) (e1)) = (op (op (op (e1) (e1)) (e1)) (e1)))); [idtac | apply NNPP; zenon_intro zenon_H227]. % 18.52/18.77 congruence. % 18.52/18.77 elim (classic ((op (op (op (e1) (e1)) (e1)) (e1)) = (op (op (op (e1) (e1)) (e1)) (e1)))); [ zenon_intro zenon_H21d | zenon_intro zenon_H21e ]. % 18.52/18.77 cut (((op (op (op (e1) (e1)) (e1)) (e1)) = (op (op (op (e1) (e1)) (e1)) (e1))) = ((op (e3) (e1)) = (op (op (op (e1) (e1)) (e1)) (e1)))). % 18.52/18.77 intro zenon_D_pnotp. % 18.52/18.77 apply zenon_H227. % 18.52/18.77 rewrite <- zenon_D_pnotp. % 18.52/18.77 exact zenon_H21d. % 18.52/18.77 cut (((op (op (op (e1) (e1)) (e1)) (e1)) = (op (op (op (e1) (e1)) (e1)) (e1)))); [idtac | apply NNPP; zenon_intro zenon_H21e]. % 18.52/18.77 cut (((op (op (op (e1) (e1)) (e1)) (e1)) = (op (e3) (e1)))); [idtac | apply NNPP; zenon_intro zenon_H228]. % 18.52/18.77 congruence. % 18.52/18.77 cut (((e1) = (e1))); [idtac | apply NNPP; zenon_intro zenon_H79]. % 18.52/18.77 cut (((op (op (e1) (e1)) (e1)) = (e3))); [idtac | apply NNPP; zenon_intro zenon_H223]. % 18.52/18.77 congruence. % 18.52/18.77 cut (((op (e0) (e1)) = (e3)) = ((op (op (e1) (e1)) (e1)) = (e3))). % 18.52/18.77 intro zenon_D_pnotp. % 18.52/18.77 apply zenon_H223. % 18.52/18.77 rewrite <- zenon_D_pnotp. % 18.52/18.77 exact zenon_H99. % 18.52/18.77 cut (((e3) = (e3))); [idtac | apply NNPP; zenon_intro zenon_H85]. % 18.52/18.77 cut (((op (e0) (e1)) = (op (op (e1) (e1)) (e1)))); [idtac | apply NNPP; zenon_intro zenon_H21a]. % 18.52/18.77 congruence. % 18.52/18.77 elim (classic ((op (op (e1) (e1)) (e1)) = (op (op (e1) (e1)) (e1)))); [ zenon_intro zenon_H217 | zenon_intro zenon_H218 ]. % 18.52/18.77 cut (((op (op (e1) (e1)) (e1)) = (op (op (e1) (e1)) (e1))) = ((op (e0) (e1)) = (op (op (e1) (e1)) (e1)))). % 18.52/18.77 intro zenon_D_pnotp. % 18.52/18.77 apply zenon_H21a. % 18.52/18.77 rewrite <- zenon_D_pnotp. % 18.52/18.77 exact zenon_H217. % 18.52/18.77 cut (((op (op (e1) (e1)) (e1)) = (op (op (e1) (e1)) (e1)))); [idtac | apply NNPP; zenon_intro zenon_H218]. % 18.52/18.77 cut (((op (op (e1) (e1)) (e1)) = (op (e0) (e1)))); [idtac | apply NNPP; zenon_intro zenon_H215]. % 18.52/18.77 congruence. % 18.52/18.77 apply (zenon_L369_); trivial. % 18.52/18.77 apply zenon_H218. apply refl_equal. % 18.52/18.77 apply zenon_H218. apply refl_equal. % 18.52/18.77 apply zenon_H85. apply refl_equal. % 18.52/18.77 apply zenon_H79. apply refl_equal. % 18.52/18.77 apply zenon_H21e. apply refl_equal. % 18.52/18.77 apply zenon_H21e. apply refl_equal. % 18.52/18.77 apply zenon_H7e. apply refl_equal. % 18.52/18.77 apply zenon_H21e. apply refl_equal. % 18.52/18.77 apply zenon_H21e. apply refl_equal. % 18.52/18.77 apply (zenon_notand_s _ _ zenon_H224); [ zenon_intro zenon_H222 | zenon_intro zenon_H46 ]. % 18.52/18.77 apply (zenon_L384_); trivial. % 18.52/18.77 apply zenon_H46. apply sym_equal. exact zenon_H29. % 18.52/18.77 (* end of lemma zenon_L385_ *) % 18.52/18.77 assert (zenon_L386_ : ((op (e2) (e3)) = (e0)) -> ((op (e3) (e3)) = (e2)) -> (~((e0) = (op (op (e3) (e3)) (e3)))) -> False). % 18.52/18.77 do 0 intro. intros zenon_H37 zenon_Hf6 zenon_Hc8. % 18.52/18.77 elim (classic ((op (op (e3) (e3)) (e3)) = (op (op (e3) (e3)) (e3)))); [ zenon_intro zenon_Hc9 | zenon_intro zenon_Hca ]. % 18.52/18.77 cut (((op (op (e3) (e3)) (e3)) = (op (op (e3) (e3)) (e3))) = ((e0) = (op (op (e3) (e3)) (e3)))). % 18.52/18.77 intro zenon_D_pnotp. % 18.52/18.77 apply zenon_Hc8. % 18.52/18.77 rewrite <- zenon_D_pnotp. % 18.52/18.77 exact zenon_Hc9. % 18.52/18.77 cut (((op (op (e3) (e3)) (e3)) = (op (op (e3) (e3)) (e3)))); [idtac | apply NNPP; zenon_intro zenon_Hca]. % 18.52/18.77 cut (((op (op (e3) (e3)) (e3)) = (e0))); [idtac | apply NNPP; zenon_intro zenon_Hcb]. % 18.52/18.77 congruence. % 18.52/18.77 cut (((op (e2) (e3)) = (e0)) = ((op (op (e3) (e3)) (e3)) = (e0))). % 18.52/18.77 intro zenon_D_pnotp. % 18.52/18.77 apply zenon_Hcb. % 18.52/18.77 rewrite <- zenon_D_pnotp. % 18.52/18.77 exact zenon_H37. % 18.52/18.77 cut (((e0) = (e0))); [idtac | apply NNPP; zenon_intro zenon_H82]. % 18.52/18.77 cut (((op (e2) (e3)) = (op (op (e3) (e3)) (e3)))); [idtac | apply NNPP; zenon_intro zenon_Hfa]. % 18.52/18.77 congruence. % 18.52/18.77 elim (classic ((op (op (e3) (e3)) (e3)) = (op (op (e3) (e3)) (e3)))); [ zenon_intro zenon_Hc9 | zenon_intro zenon_Hca ]. % 18.52/18.77 cut (((op (op (e3) (e3)) (e3)) = (op (op (e3) (e3)) (e3))) = ((op (e2) (e3)) = (op (op (e3) (e3)) (e3)))). % 18.52/18.77 intro zenon_D_pnotp. % 18.52/18.77 apply zenon_Hfa. % 18.52/18.77 rewrite <- zenon_D_pnotp. % 18.52/18.77 exact zenon_Hc9. % 18.52/18.77 cut (((op (op (e3) (e3)) (e3)) = (op (op (e3) (e3)) (e3)))); [idtac | apply NNPP; zenon_intro zenon_Hca]. % 18.52/18.77 cut (((op (op (e3) (e3)) (e3)) = (op (e2) (e3)))); [idtac | apply NNPP; zenon_intro zenon_Hf5]. % 18.52/18.77 congruence. % 18.52/18.77 apply (zenon_L61_); trivial. % 18.52/18.77 apply zenon_Hca. apply refl_equal. % 18.52/18.77 apply zenon_Hca. apply refl_equal. % 18.52/18.77 apply zenon_H82. apply refl_equal. % 18.52/18.77 apply zenon_Hca. apply refl_equal. % 18.52/18.77 apply zenon_Hca. apply refl_equal. % 18.52/18.77 (* end of lemma zenon_L386_ *) % 18.52/18.77 assert (zenon_L387_ : ((op (e0) (e3)) = (e1)) -> ((op (e2) (e3)) = (e0)) -> ((op (e3) (e3)) = (e2)) -> False). % 18.52/18.77 do 0 intro. intros zenon_Hc3 zenon_H37 zenon_Hf6. % 18.52/18.77 apply (zenon_notand_s _ _ ax26); [ zenon_intro zenon_H1dd | zenon_intro zenon_H229 ]. % 18.52/18.77 elim (classic ((op (op (op (e3) (e3)) (e3)) (e3)) = (op (op (op (e3) (e3)) (e3)) (e3)))); [ zenon_intro zenon_Hd0 | zenon_intro zenon_Hd1 ]. % 18.52/18.77 cut (((op (op (op (e3) (e3)) (e3)) (e3)) = (op (op (op (e3) (e3)) (e3)) (e3))) = ((e1) = (op (op (op (e3) (e3)) (e3)) (e3)))). % 18.52/18.77 intro zenon_D_pnotp. % 18.52/18.77 apply zenon_H1dd. % 18.52/18.77 rewrite <- zenon_D_pnotp. % 18.52/18.77 exact zenon_Hd0. % 18.52/18.77 cut (((op (op (op (e3) (e3)) (e3)) (e3)) = (op (op (op (e3) (e3)) (e3)) (e3)))); [idtac | apply NNPP; zenon_intro zenon_Hd1]. % 18.52/18.77 cut (((op (op (op (e3) (e3)) (e3)) (e3)) = (e1))); [idtac | apply NNPP; zenon_intro zenon_H1de]. % 18.52/18.77 congruence. % 18.52/18.77 cut (((op (e0) (e3)) = (e1)) = ((op (op (op (e3) (e3)) (e3)) (e3)) = (e1))). % 18.52/18.77 intro zenon_D_pnotp. % 18.52/18.77 apply zenon_H1de. % 18.52/18.77 rewrite <- zenon_D_pnotp. % 18.52/18.77 exact zenon_Hc3. % 18.52/18.77 cut (((e1) = (e1))); [idtac | apply NNPP; zenon_intro zenon_H79]. % 18.52/18.77 cut (((op (e0) (e3)) = (op (op (op (e3) (e3)) (e3)) (e3)))); [idtac | apply NNPP; zenon_intro zenon_Hd3]. % 18.52/18.77 congruence. % 18.52/18.77 elim (classic ((op (op (op (e3) (e3)) (e3)) (e3)) = (op (op (op (e3) (e3)) (e3)) (e3)))); [ zenon_intro zenon_Hd0 | zenon_intro zenon_Hd1 ]. % 18.52/18.77 cut (((op (op (op (e3) (e3)) (e3)) (e3)) = (op (op (op (e3) (e3)) (e3)) (e3))) = ((op (e0) (e3)) = (op (op (op (e3) (e3)) (e3)) (e3)))). % 18.52/18.77 intro zenon_D_pnotp. % 18.52/18.77 apply zenon_Hd3. % 18.52/18.77 rewrite <- zenon_D_pnotp. % 18.52/18.77 exact zenon_Hd0. % 18.52/18.77 cut (((op (op (op (e3) (e3)) (e3)) (e3)) = (op (op (op (e3) (e3)) (e3)) (e3)))); [idtac | apply NNPP; zenon_intro zenon_Hd1]. % 18.52/18.77 cut (((op (op (op (e3) (e3)) (e3)) (e3)) = (op (e0) (e3)))); [idtac | apply NNPP; zenon_intro zenon_Hd4]. % 18.52/18.77 congruence. % 18.52/18.77 cut (((e3) = (e3))); [idtac | apply NNPP; zenon_intro zenon_H85]. % 18.52/18.77 cut (((op (op (e3) (e3)) (e3)) = (e0))); [idtac | apply NNPP; zenon_intro zenon_Hcb]. % 18.52/18.77 congruence. % 18.52/18.77 cut (((op (e2) (e3)) = (e0)) = ((op (op (e3) (e3)) (e3)) = (e0))). % 18.52/18.77 intro zenon_D_pnotp. % 18.52/18.77 apply zenon_Hcb. % 18.52/18.77 rewrite <- zenon_D_pnotp. % 18.52/18.77 exact zenon_H37. % 18.52/18.77 cut (((e0) = (e0))); [idtac | apply NNPP; zenon_intro zenon_H82]. % 18.52/18.77 cut (((op (e2) (e3)) = (op (op (e3) (e3)) (e3)))); [idtac | apply NNPP; zenon_intro zenon_Hfa]. % 18.52/18.77 congruence. % 18.52/18.77 elim (classic ((op (op (e3) (e3)) (e3)) = (op (op (e3) (e3)) (e3)))); [ zenon_intro zenon_Hc9 | zenon_intro zenon_Hca ]. % 18.52/18.77 cut (((op (op (e3) (e3)) (e3)) = (op (op (e3) (e3)) (e3))) = ((op (e2) (e3)) = (op (op (e3) (e3)) (e3)))). % 18.52/18.77 intro zenon_D_pnotp. % 18.52/18.77 apply zenon_Hfa. % 18.52/18.77 rewrite <- zenon_D_pnotp. % 18.52/18.77 exact zenon_Hc9. % 18.52/18.77 cut (((op (op (e3) (e3)) (e3)) = (op (op (e3) (e3)) (e3)))); [idtac | apply NNPP; zenon_intro zenon_Hca]. % 18.52/18.77 cut (((op (op (e3) (e3)) (e3)) = (op (e2) (e3)))); [idtac | apply NNPP; zenon_intro zenon_Hf5]. % 18.52/18.77 congruence. % 18.52/18.77 apply (zenon_L61_); trivial. % 18.52/18.77 apply zenon_Hca. apply refl_equal. % 18.52/18.77 apply zenon_Hca. apply refl_equal. % 18.52/18.77 apply zenon_H82. apply refl_equal. % 18.52/18.77 apply zenon_H85. apply refl_equal. % 18.52/18.77 apply zenon_Hd1. apply refl_equal. % 18.52/18.77 apply zenon_Hd1. apply refl_equal. % 18.52/18.77 apply zenon_H79. apply refl_equal. % 18.52/18.77 apply zenon_Hd1. apply refl_equal. % 18.52/18.77 apply zenon_Hd1. apply refl_equal. % 18.52/18.77 apply (zenon_notand_s _ _ zenon_H229); [ zenon_intro zenon_Hc8 | zenon_intro zenon_H100 ]. % 18.52/18.77 apply (zenon_L386_); trivial. % 18.52/18.77 apply zenon_H100. apply sym_equal. exact zenon_Hf6. % 18.52/18.77 (* end of lemma zenon_L387_ *) % 18.52/18.77 assert (zenon_L388_ : (((op (e2) (e0)) = (e1))\/(((op (e2) (e1)) = (e1))\/(((op (e2) (e2)) = (e1))\/((op (e2) (e3)) = (e1))))) -> (~((op (e2) (e2)) = (op (e3) (e2)))) -> (~((op (e2) (e2)) = (e0))) -> (((op (e2) (e2)) = (e0))\/(((op (e2) (e2)) = (e1))\/(((op (e2) (e2)) = (e2))\/((op (e2) (e2)) = (e3))))) -> (~((e0) = (e1))) -> (((op (e0) (e2)) = (e1))\/(((op (e1) (e2)) = (e1))\/(((op (e2) (e2)) = (e1))\/((op (e3) (e2)) = (e1))))) -> ((op (e2) (e3)) = (e0)) -> (((op (e0) (e3)) = (e2))\/(((op (e1) (e3)) = (e2))\/(((op (e2) (e3)) = (e2))\/((op (e3) (e3)) = (e2))))) -> (~((op (e2) (e2)) = (op (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 (e3) (e3)) = (e3))) -> (~((op (e3) (e1)) = (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 (e2) (e1)) = (op (e2) (e3)))) -> ((op (e1) (e1)) = (e0)) -> (~((e0) = (e2))) -> ((op (e0) (e1)) = (e3)) -> (~((e2) = (e3))) -> (((op (e0) (e1)) = (e2))\/(((op (e1) (e1)) = (e2))\/(((op (e2) (e1)) = (e2))\/((op (e3) (e1)) = (e2))))) -> (~((op (e3) (e2)) = (op (e3) (e3)))) -> ((op (e1) (e2)) = (e2)) -> (((op (e0) (e1)) = (e3))\/(((op (e1) (e1)) = (e3))\/(((op (e2) (e1)) = (e3))\/((op (e3) (e1)) = (e3))))) -> (~((op (e3) (e0)) = (op (e3) (e3)))) -> ((op (e0) (e0)) = (e2)) -> (~((op (e0) (e0)) = (op (e0) (e3)))) -> (~((op (e0) (e1)) = (op (e1) (e1)))) -> (((op (e2) (e1)) = (e0))\/(((op (e2) (e1)) = (e1))\/(((op (e2) (e1)) = (e2))\/((op (e2) (e1)) = (e3))))) -> (~((op (e2) (e1)) = (e0))) -> (~((op (e2) (e1)) = (op (e3) (e1)))) -> (~((op (e0) (e1)) = (op (e2) (e1)))) -> (~((op (e1) (e1)) = (op (e2) (e1)))) -> (~((op (e0) (e1)) = (op (e3) (e1)))) -> (~((op (e0) (e1)) = (e0))) -> (((op (e0) (e1)) = (e0))\/(((op (e0) (e1)) = (e1))\/(((op (e0) (e1)) = (e2))\/((op (e0) (e1)) = (e3))))) -> ((op (e2) (e1)) = (e2)) -> (((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) (e0)) = (op (e2) (e2)))) -> (~((e0) = (e3))) -> (((op (e0) (e2)) = (e3))\/(((op (e1) (e2)) = (e3))\/(((op (e2) (e2)) = (e3))\/((op (e3) (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)) = (op (e3) (e1)))) -> (~((op (e2) (e2)) = (e2))) -> ((op (e0) (e2)) = (e0)) -> (((op (e0) (e2)) = (e2))\/(((op (e1) (e2)) = (e2))\/(((op (e2) (e2)) = (e2))\/((op (e3) (e2)) = (e2))))) -> (((op (e3) (e0)) = (e2))\/(((op (e3) (e1)) = (e2))\/(((op (e3) (e2)) = (e2))\/((op (e3) (e3)) = (e2))))) -> (~((op (e0) (e3)) = (op (e2) (e3)))) -> ((op (e0) (e3)) = (e1)) -> False). % 18.52/18.77 do 0 intro. intros zenon_H106 zenon_H18f zenon_H81 zenon_H1c4 zenon_Ha1 zenon_H139 zenon_H37 zenon_H145 zenon_H6d zenon_Hdc zenon_H95 zenon_H133 zenon_H102 zenon_H130 zenon_H101 zenon_H7c zenon_Hae zenon_H1c7 zenon_H29 zenon_H149 zenon_H99 zenon_H12b zenon_H1d8 zenon_H62 zenon_H113 zenon_H1a5 zenon_H71 zenon_H7b zenon_H189 zenon_H10e zenon_H1cc zenon_H31 zenon_Haf zenon_H17e zenon_H13e zenon_H210 zenon_H20b zenon_H212 zenon_H1ca zenon_H18c zenon_H1a4 zenon_H3b zenon_H52 zenon_H9a zenon_H1a6 zenon_H16f zenon_H9d zenon_H160 zenon_H173 zenon_H48 zenon_H172 zenon_H153 zenon_He2 zenon_Hc3. % 18.52/18.77 apply (zenon_or_s _ _ zenon_H106); [ zenon_intro zenon_Hed | zenon_intro zenon_H107 ]. % 18.52/18.77 apply (zenon_L356_); trivial. % 18.52/18.77 apply (zenon_or_s _ _ zenon_H107); [ zenon_intro zenon_Ha5 | zenon_intro zenon_H108 ]. % 18.52/18.77 apply (zenon_L42_); trivial. % 18.52/18.77 apply (zenon_or_s _ _ zenon_H108); [ zenon_intro zenon_Hf1 | zenon_intro zenon_Hf4 ]. % 18.52/18.77 apply (zenon_or_s _ _ zenon_H153); [ zenon_intro zenon_H148 | zenon_intro zenon_H154 ]. % 18.52/18.77 apply (zenon_L383_); trivial. % 18.52/18.77 apply (zenon_or_s _ _ zenon_H154); [ zenon_intro zenon_H14d | zenon_intro zenon_H155 ]. % 18.52/18.77 apply (zenon_L385_); trivial. % 18.52/18.77 apply (zenon_or_s _ _ zenon_H155); [ zenon_intro zenon_H151 | zenon_intro zenon_Hf6 ]. % 18.52/18.77 apply (zenon_or_s _ _ zenon_H145); [ zenon_intro zenon_Hcd | zenon_intro zenon_H146 ]. % 18.52/18.77 apply (zenon_L86_); trivial. % 18.52/18.77 apply (zenon_or_s _ _ zenon_H146); [ zenon_intro zenon_Hd7 | zenon_intro zenon_H147 ]. % 18.52/18.77 apply (zenon_L379_); trivial. % 18.52/18.77 apply (zenon_or_s _ _ zenon_H147); [ zenon_intro zenon_H11d | zenon_intro zenon_Hf6 ]. % 18.52/18.77 apply (zenon_L376_); trivial. % 18.52/18.77 apply (zenon_L119_); trivial. % 18.52/18.77 apply (zenon_L387_); trivial. % 18.52/18.77 apply (zenon_L272_); trivial. % 18.52/18.77 (* end of lemma zenon_L388_ *) % 18.52/18.77 assert (zenon_L389_ : (~((op (e0) (e1)) = (op (e3) (e1)))) -> ((op (e0) (e1)) = (e2)) -> ((op (e3) (e1)) = (e2)) -> False). % 18.52/18.77 do 0 intro. intros zenon_H210 zenon_H10f zenon_H14d. % 18.52/18.77 cut (((op (e0) (e1)) = (e2)) = ((op (e0) (e1)) = (op (e3) (e1)))). % 18.52/18.77 intro zenon_D_pnotp. % 18.52/18.77 apply zenon_H210. % 18.52/18.77 rewrite <- zenon_D_pnotp. % 18.52/18.77 exact zenon_H10f. % 18.52/18.77 cut (((e2) = (op (e3) (e1)))); [idtac | apply NNPP; zenon_intro zenon_H14e]. % 18.52/18.77 cut (((op (e0) (e1)) = (op (e0) (e1)))); [idtac | apply NNPP; zenon_intro zenon_H112]. % 18.52/18.77 congruence. % 18.52/18.77 apply zenon_H112. apply refl_equal. % 18.52/18.77 apply zenon_H14e. apply sym_equal. exact zenon_H14d. % 18.52/18.77 (* end of lemma zenon_L389_ *) % 18.52/18.77 assert (zenon_L390_ : (((op (e0) (e1)) = (e0))\/(((op (e0) (e1)) = (e1))\/(((op (e0) (e1)) = (e2))\/((op (e0) (e1)) = (e3))))) -> (~((op (e0) (e1)) = (e0))) -> ((op (e2) (e1)) = (e1)) -> (~((op (e0) (e1)) = (op (e2) (e1)))) -> ((op (e3) (e1)) = (e2)) -> (~((op (e0) (e1)) = (op (e3) (e1)))) -> (~((op (e0) (e1)) = (op (e1) (e1)))) -> ((op (e1) (e1)) = (e3)) -> False). % 18.52/18.77 do 0 intro. intros zenon_H212 zenon_H20b zenon_Ha5 zenon_H17e zenon_H14d zenon_H210 zenon_H10e zenon_H13f. % 18.52/18.77 apply (zenon_or_s _ _ zenon_H212); [ zenon_intro zenon_H49 | zenon_intro zenon_H213 ]. % 18.52/18.77 exact (zenon_H20b zenon_H49). % 18.52/18.77 apply (zenon_or_s _ _ zenon_H213); [ zenon_intro zenon_Ha0 | zenon_intro zenon_H214 ]. % 18.52/18.77 apply (zenon_L357_); trivial. % 18.52/18.77 apply (zenon_or_s _ _ zenon_H214); [ zenon_intro zenon_H10f | zenon_intro zenon_H99 ]. % 18.52/18.77 apply (zenon_L389_); trivial. % 18.52/18.77 apply (zenon_L108_); trivial. % 18.52/18.77 (* end of lemma zenon_L390_ *) % 18.52/18.77 assert (zenon_L391_ : (((op (e2) (e0)) = (e2))\/(((op (e2) (e1)) = (e2))\/(((op (e2) (e2)) = (e2))\/((op (e2) (e3)) = (e2))))) -> ((op (e0) (e0)) = (e2)) -> (~((op (e0) (e0)) = (op (e2) (e0)))) -> ((op (e1) (e1)) = (e3)) -> (~((op (e0) (e1)) = (op (e1) (e1)))) -> (~((op (e0) (e1)) = (op (e2) (e1)))) -> ((op (e2) (e1)) = (e1)) -> (~((op (e0) (e1)) = (e0))) -> (((op (e0) (e1)) = (e0))\/(((op (e0) (e1)) = (e1))\/(((op (e0) (e1)) = (e2))\/((op (e0) (e1)) = (e3))))) -> (~((op (e2) (e2)) = (e2))) -> (~((op (e1) (e3)) = (op (e2) (e3)))) -> ((op (e1) (e3)) = (e2)) -> False). % 18.52/18.77 do 0 intro. intros zenon_H1d5 zenon_H7b zenon_H39 zenon_H13f zenon_H10e zenon_H17e zenon_Ha5 zenon_H20b zenon_H212 zenon_H173 zenon_Hdb zenon_Hd7. % 18.52/18.77 apply (zenon_or_s _ _ zenon_H1d5); [ zenon_intro zenon_Hee | zenon_intro zenon_H1d6 ]. % 18.52/18.77 apply (zenon_L341_); trivial. % 18.52/18.77 apply (zenon_or_s _ _ zenon_H1d6); [ zenon_intro zenon_H1ca | zenon_intro zenon_H1d7 ]. % 18.52/18.77 apply (zenon_L373_); trivial. % 18.52/18.77 apply (zenon_or_s _ _ zenon_H1d7); [ zenon_intro zenon_H176 | zenon_intro zenon_H11d ]. % 18.52/18.77 exact (zenon_H173 zenon_H176). % 18.52/18.77 apply (zenon_L366_); trivial. % 18.52/18.77 (* end of lemma zenon_L391_ *) % 18.52/18.77 assert (zenon_L392_ : (((op (e3) (e3)) = (e0))\/(((op (e3) (e3)) = (e1))\/(((op (e3) (e3)) = (e2))\/((op (e3) (e3)) = (e3))))) -> ((op (e0) (e3)) = (e1)) -> ((op (e1) (e3)) = (e2)) -> ((op (e3) (e2)) = (e1)) -> (~((op (e3) (e2)) = (op (e3) (e3)))) -> ((op (e3) (e2)) = (e2)) -> (~((op (e3) (e3)) = (e3))) -> False). % 18.52/18.77 do 0 intro. intros zenon_H101 zenon_Hc3 zenon_Hd7 zenon_Hba zenon_H62 zenon_H151 zenon_H102. % 18.52/18.77 apply (zenon_or_s _ _ zenon_H101); [ zenon_intro zenon_H60 | zenon_intro zenon_H103 ]. % 18.52/18.77 apply (zenon_L201_); trivial. % 18.52/18.77 apply (zenon_or_s _ _ zenon_H103); [ zenon_intro zenon_Hc4 | zenon_intro zenon_H104 ]. % 18.52/18.77 apply (zenon_L147_); trivial. % 18.52/18.77 apply (zenon_or_s _ _ zenon_H104); [ zenon_intro zenon_Hf6 | zenon_intro zenon_H105 ]. % 18.52/18.77 apply (zenon_L119_); trivial. % 18.52/18.77 exact (zenon_H102 zenon_H105). % 18.52/18.77 (* end of lemma zenon_L392_ *) % 18.52/18.77 assert (zenon_L393_ : (((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))) -> (((op (e3) (e0)) = (e1))\/(((op (e3) (e1)) = (e1))\/(((op (e3) (e2)) = (e1))\/((op (e3) (e3)) = (e1))))) -> ((op (e0) (e0)) = (e2)) -> ((op (e2) (e0)) = (e3)) -> (~((op (e3) (e1)) = (op (e3) (e3)))) -> (~((op (e3) (e3)) = (e3))) -> (~((op (e3) (e2)) = (op (e3) (e3)))) -> ((op (e1) (e3)) = (e2)) -> (((op (e3) (e3)) = (e0))\/(((op (e3) (e3)) = (e1))\/(((op (e3) (e3)) = (e2))\/((op (e3) (e3)) = (e3))))) -> (~((op (e0) (e3)) = (op (e3) (e3)))) -> ((op (e0) (e3)) = (e1)) -> False). % 18.52/18.77 do 0 intro. intros zenon_H172 zenon_H149 zenon_H48 zenon_H12b zenon_H16c zenon_H173 zenon_He8 zenon_H7b zenon_H3b zenon_H130 zenon_H102 zenon_H62 zenon_Hd7 zenon_H101 zenon_Hc2 zenon_Hc3. % 18.52/18.77 apply (zenon_or_s _ _ zenon_H172); [ zenon_intro zenon_H150 | zenon_intro zenon_H174 ]. % 18.52/18.77 apply (zenon_L378_); trivial. % 18.52/18.77 apply (zenon_or_s _ _ zenon_H174); [ zenon_intro zenon_H113 | zenon_intro zenon_H175 ]. % 18.52/18.77 apply (zenon_L116_); trivial. % 18.52/18.77 apply (zenon_or_s _ _ zenon_H175); [ zenon_intro zenon_H176 | zenon_intro zenon_H151 ]. % 18.52/18.77 exact (zenon_H173 zenon_H176). % 18.52/18.77 apply (zenon_or_s _ _ zenon_He8); [ zenon_intro zenon_Hac | zenon_intro zenon_Heb ]. % 18.52/18.77 apply (zenon_L308_); trivial. % 18.52/18.77 apply (zenon_or_s _ _ zenon_Heb); [ zenon_intro zenon_Hae | zenon_intro zenon_Hec ]. % 18.52/18.77 apply (zenon_L379_); trivial. % 18.52/18.77 apply (zenon_or_s _ _ zenon_Hec); [ zenon_intro zenon_Hba | zenon_intro zenon_Hc4 ]. % 18.52/18.77 apply (zenon_L392_); trivial. % 18.52/18.77 apply (zenon_L46_); trivial. % 18.52/18.77 (* end of lemma zenon_L393_ *) % 18.52/18.77 assert (zenon_L394_ : (((op (e1) (e0)) = (e3))\/(((op (e1) (e1)) = (e3))\/(((op (e1) (e2)) = (e3))\/((op (e1) (e3)) = (e3))))) -> (~((e1) = (e3))) -> ((op (e1) (e0)) = (e1)) -> (~((op (e0) (e1)) = (op (e1) (e1)))) -> (((op (e2) (e1)) = (e0))\/(((op (e2) (e1)) = (e1))\/(((op (e2) (e1)) = (e2))\/((op (e2) (e1)) = (e3))))) -> (~((op (e2) (e1)) = (e0))) -> (~((op (e2) (e1)) = (op (e3) (e1)))) -> (~((op (e0) (e1)) = (op (e2) (e1)))) -> (~((op (e1) (e1)) = (op (e2) (e1)))) -> (~((op (e0) (e1)) = (op (e3) (e1)))) -> (~((op (e0) (e1)) = (e0))) -> (((op (e0) (e1)) = (e0))\/(((op (e0) (e1)) = (e1))\/(((op (e0) (e1)) = (e2))\/((op (e0) (e1)) = (e3))))) -> (~((op (e3) (e3)) = (e3))) -> (~((op (e3) (e2)) = (op (e3) (e3)))) -> ((op (e3) (e1)) = (e1)) -> (~((op (e3) (e1)) = (op (e3) (e3)))) -> ((op (e0) (e3)) = (e1)) -> (((op (e3) (e3)) = (e0))\/(((op (e3) (e3)) = (e1))\/(((op (e3) (e3)) = (e2))\/((op (e3) (e3)) = (e3))))) -> (~((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 (e1) (e3)) = (e2)) -> (~((e2) = (e3))) -> False). % 18.52/18.77 do 0 intro. intros zenon_H16f zenon_H95 zenon_H9d zenon_H10e zenon_H1cc zenon_H31 zenon_Haf zenon_H17e zenon_H13e zenon_H210 zenon_H20b zenon_H212 zenon_H102 zenon_H62 zenon_Hae zenon_H130 zenon_Hc3 zenon_H101 zenon_H173 zenon_H48 zenon_H149 zenon_H172 zenon_Hd7 zenon_H12b. % 18.52/18.77 apply (zenon_or_s _ _ zenon_H16f); [ zenon_intro zenon_H9e | zenon_intro zenon_H170 ]. % 18.52/18.77 apply (zenon_L37_); trivial. % 18.52/18.77 apply (zenon_or_s _ _ zenon_H170); [ zenon_intro zenon_H13f | zenon_intro zenon_H171 ]. % 18.52/18.77 apply (zenon_L368_); trivial. % 18.52/18.77 apply (zenon_or_s _ _ zenon_H171); [ zenon_intro zenon_H16c | zenon_intro zenon_Hdc ]. % 18.52/18.77 apply (zenon_L380_); trivial. % 18.52/18.77 apply (zenon_L266_); trivial. % 18.52/18.77 (* end of lemma zenon_L394_ *) % 18.52/18.77 assert (zenon_L395_ : (((op (e0) (e1)) = (e1))\/(((op (e1) (e1)) = (e1))\/(((op (e2) (e1)) = (e1))\/((op (e3) (e1)) = (e1))))) -> (~((op (e0) (e1)) = (op (e0) (e3)))) -> (~((op (e1) (e1)) = (e1))) -> (((op (e3) (e0)) = (e1))\/(((op (e3) (e1)) = (e1))\/(((op (e3) (e2)) = (e1))\/((op (e3) (e3)) = (e1))))) -> (~((op (e0) (e3)) = (op (e3) (e3)))) -> (((op (e2) (e0)) = (e2))\/(((op (e2) (e1)) = (e2))\/(((op (e2) (e2)) = (e2))\/((op (e2) (e3)) = (e2))))) -> (~((op (e0) (e0)) = (op (e2) (e0)))) -> (~((op (e1) (e3)) = (op (e2) (e3)))) -> (~((op (e3) (e0)) = (op (e3) (e2)))) -> (~((op (e1) (e1)) = (op (e1) (e2)))) -> (((op (e0) (e2)) = (e0))\/(((op (e1) (e2)) = (e0))\/(((op (e2) (e2)) = (e0))\/((op (e3) (e2)) = (e0))))) -> (~((op (e1) (e2)) = (op (e2) (e2)))) -> ((op (e3) (e0)) = (e0)) -> (~((e1) = (e2))) -> (~((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)) = (op (e0) (e3)))) -> ((op (e0) (e0)) = (e2)) -> (~((op (e3) (e0)) = (op (e3) (e3)))) -> (((op (e0) (e1)) = (e3))\/(((op (e1) (e1)) = (e3))\/(((op (e2) (e1)) = (e3))\/((op (e3) (e1)) = (e3))))) -> (((op (e0) (e1)) = (e2))\/(((op (e1) (e1)) = (e2))\/(((op (e2) (e1)) = (e2))\/((op (e3) (e1)) = (e2))))) -> (~((op (e2) (e1)) = (op (e2) (e3)))) -> (((op (e0) (e3)) = (e1))\/(((op (e1) (e3)) = (e1))\/(((op (e2) (e3)) = (e1))\/((op (e3) (e3)) = (e1))))) -> (~((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)) = (e1))\/(((op (e1) (e2)) = (e1))\/(((op (e2) (e2)) = (e1))\/((op (e3) (e2)) = (e1))))) -> (~((e0) = (e1))) -> (((op (e2) (e2)) = (e0))\/(((op (e2) (e2)) = (e1))\/(((op (e2) (e2)) = (e2))\/((op (e2) (e2)) = (e3))))) -> (~((op (e2) (e2)) = (e0))) -> (~((op (e2) (e2)) = (op (e3) (e2)))) -> (((op (e2) (e0)) = (e1))\/(((op (e2) (e1)) = (e1))\/(((op (e2) (e2)) = (e1))\/((op (e2) (e3)) = (e1))))) -> (~((op (e2) (e0)) = (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 (e1) (e1)) = (e0)) -> (~((op (e3) (e1)) = (op (e3) (e2)))) -> ((op (e2) (e0)) = (e3)) -> (~((op (e2) (e0)) = (op (e2) (e2)))) -> (~((e0) = (e3))) -> (((op (e0) (e2)) = (e3))\/(((op (e1) (e2)) = (e3))\/(((op (e2) (e2)) = (e3))\/((op (e3) (e2)) = (e3))))) -> (~((op (e1) (e1)) = (op (e3) (e1)))) -> (((op (e1) (e0)) = (e3))\/(((op (e1) (e1)) = (e3))\/(((op (e1) (e2)) = (e3))\/((op (e1) (e3)) = (e3))))) -> (~((e1) = (e3))) -> ((op (e1) (e0)) = (e1)) -> (~((op (e0) (e1)) = (op (e1) (e1)))) -> (((op (e2) (e1)) = (e0))\/(((op (e2) (e1)) = (e1))\/(((op (e2) (e1)) = (e2))\/((op (e2) (e1)) = (e3))))) -> (~((op (e2) (e1)) = (e0))) -> (~((op (e2) (e1)) = (op (e3) (e1)))) -> (~((op (e0) (e1)) = (op (e2) (e1)))) -> (~((op (e1) (e1)) = (op (e2) (e1)))) -> (~((op (e0) (e1)) = (op (e3) (e1)))) -> (~((op (e0) (e1)) = (e0))) -> (((op (e0) (e1)) = (e0))\/(((op (e0) (e1)) = (e1))\/(((op (e0) (e1)) = (e2))\/((op (e0) (e1)) = (e3))))) -> (~((op (e3) (e3)) = (e3))) -> (~((op (e3) (e2)) = (op (e3) (e3)))) -> (~((op (e3) (e1)) = (op (e3) (e3)))) -> ((op (e0) (e3)) = (e1)) -> (((op (e3) (e3)) = (e0))\/(((op (e3) (e3)) = (e1))\/(((op (e3) (e3)) = (e2))\/((op (e3) (e3)) = (e3))))) -> (~((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))))) -> (~((e2) = (e3))) -> False). % 18.52/18.77 do 0 intro. intros zenon_H109 zenon_H54 zenon_H10a zenon_He8 zenon_Hc2 zenon_H1d5 zenon_H39 zenon_Hdb zenon_H6f zenon_H4f zenon_H6a zenon_H2b zenon_H44 zenon_H7c zenon_He2 zenon_H153 zenon_H189 zenon_H7b zenon_H71 zenon_H1a5 zenon_H1d8 zenon_H1c7 zenon_H133 zenon_H6d zenon_H145 zenon_H139 zenon_Ha1 zenon_H1c4 zenon_H81 zenon_H18f zenon_H106 zenon_H30 zenon_H2f zenon_H18c zenon_H29 zenon_H1a4 zenon_H3b zenon_H52 zenon_H9a zenon_H1a6 zenon_H160 zenon_H16f zenon_H95 zenon_H9d zenon_H10e zenon_H1cc zenon_H31 zenon_Haf zenon_H17e zenon_H13e zenon_H210 zenon_H20b zenon_H212 zenon_H102 zenon_H62 zenon_H130 zenon_Hc3 zenon_H101 zenon_H173 zenon_H48 zenon_H149 zenon_H172 zenon_H12b. % 18.52/18.77 apply (zenon_or_s _ _ zenon_H109); [ zenon_intro zenon_Ha0 | zenon_intro zenon_H10b ]. % 18.52/18.77 apply (zenon_L359_); trivial. % 18.52/18.77 apply (zenon_or_s _ _ zenon_H10b); [ zenon_intro zenon_H10d | zenon_intro zenon_H10c ]. % 18.52/18.77 exact (zenon_H10a zenon_H10d). % 18.52/18.77 apply (zenon_or_s _ _ zenon_H10c); [ zenon_intro zenon_Ha5 | zenon_intro zenon_Hae ]. % 18.52/18.77 apply (zenon_or_s _ _ zenon_H18c); [ zenon_intro zenon_H86 | zenon_intro zenon_H18d ]. % 18.52/18.77 apply (zenon_L123_); trivial. % 18.52/18.77 apply (zenon_or_s _ _ zenon_H18d); [ zenon_intro zenon_H110 | zenon_intro zenon_H18e ]. % 18.52/18.77 apply (zenon_L354_); trivial. % 18.52/18.77 apply (zenon_or_s _ _ zenon_H18e); [ zenon_intro zenon_H113 | zenon_intro zenon_Hd7 ]. % 18.52/18.77 apply (zenon_or_s _ _ zenon_H1d8); [ zenon_intro zenon_H10f | zenon_intro zenon_H1d9 ]. % 18.52/18.77 apply (zenon_or_s _ _ zenon_H1a5); [ zenon_intro zenon_H99 | zenon_intro zenon_H1a8 ]. % 18.52/18.77 apply (zenon_L175_); trivial. % 18.52/18.77 apply (zenon_or_s _ _ zenon_H1a8); [ zenon_intro zenon_H13f | zenon_intro zenon_H1a9 ]. % 18.52/18.77 apply (zenon_or_s _ _ zenon_He8); [ zenon_intro zenon_Hac | zenon_intro zenon_Heb ]. % 18.52/18.77 apply (zenon_L308_); trivial. % 18.52/18.77 apply (zenon_or_s _ _ zenon_Heb); [ zenon_intro zenon_Hae | zenon_intro zenon_Hec ]. % 18.52/18.77 apply (zenon_L368_); trivial. % 18.52/18.77 apply (zenon_or_s _ _ zenon_Hec); [ zenon_intro zenon_Hba | zenon_intro zenon_Hc4 ]. % 18.52/18.77 apply (zenon_L327_); trivial. % 18.52/18.77 apply (zenon_L46_); trivial. % 18.52/18.77 apply (zenon_or_s _ _ zenon_H1a9); [ zenon_intro zenon_Ha6 | zenon_intro zenon_H161 ]. % 18.52/18.77 apply (zenon_L371_); trivial. % 18.52/18.77 apply (zenon_L372_); trivial. % 18.52/18.77 apply (zenon_or_s _ _ zenon_H1d9); [ zenon_intro zenon_H110 | zenon_intro zenon_H1da ]. % 18.52/18.77 apply (zenon_L354_); trivial. % 18.52/18.77 apply (zenon_or_s _ _ zenon_H1da); [ zenon_intro zenon_H1ca | zenon_intro zenon_H14d ]. % 18.52/18.77 apply (zenon_or_s _ _ zenon_H16f); [ zenon_intro zenon_H9e | zenon_intro zenon_H170 ]. % 18.52/18.77 apply (zenon_L37_); trivial. % 18.52/18.77 apply (zenon_or_s _ _ zenon_H170); [ zenon_intro zenon_H13f | zenon_intro zenon_H171 ]. % 18.52/18.77 apply (zenon_L373_); trivial. % 18.52/18.77 apply (zenon_or_s _ _ zenon_H171); [ zenon_intro zenon_H16c | zenon_intro zenon_Hdc ]. % 18.52/18.77 apply (zenon_L116_); trivial. % 18.52/18.77 apply (zenon_or_s _ _ zenon_H1a5); [ zenon_intro zenon_H99 | zenon_intro zenon_H1a8 ]. % 18.52/18.77 apply (zenon_or_s _ _ zenon_H2f); [ zenon_intro zenon_H34 | zenon_intro zenon_H33 ]. % 18.52/18.77 exact (zenon_H30 zenon_H34). % 18.52/18.77 apply (zenon_or_s _ _ zenon_H33); [ zenon_intro zenon_H36 | zenon_intro zenon_H35 ]. % 18.52/18.77 exact (zenon_H31 zenon_H36). % 18.52/18.77 apply (zenon_or_s _ _ zenon_H35); [ zenon_intro zenon_H2c | zenon_intro zenon_H37 ]. % 18.52/18.77 exact (zenon_H81 zenon_H2c). % 18.52/18.77 apply (zenon_or_s _ _ zenon_H139); [ zenon_intro zenon_H122 | zenon_intro zenon_H13a ]. % 18.52/18.77 apply (zenon_L374_); trivial. % 18.52/18.77 apply (zenon_or_s _ _ zenon_H13a); [ zenon_intro zenon_Hf0 | zenon_intro zenon_H13b ]. % 18.52/18.77 apply (zenon_L300_); trivial. % 18.52/18.77 apply (zenon_or_s _ _ zenon_H13b); [ zenon_intro zenon_Hf1 | zenon_intro zenon_Hba ]. % 18.52/18.77 apply (zenon_or_s _ _ zenon_He8); [ zenon_intro zenon_Hac | zenon_intro zenon_Heb ]. % 18.52/18.77 apply (zenon_L41_); trivial. % 18.52/18.77 apply (zenon_or_s _ _ zenon_Heb); [ zenon_intro zenon_Hae | zenon_intro zenon_Hec ]. % 18.52/18.77 apply (zenon_L388_); trivial. % 18.52/18.77 apply (zenon_or_s _ _ zenon_Hec); [ zenon_intro zenon_Hba | zenon_intro zenon_Hc4 ]. % 18.52/18.77 apply (zenon_L185_); trivial. % 18.52/18.77 apply (zenon_L46_); trivial. % 18.52/18.77 apply (zenon_L327_); trivial. % 18.52/18.77 apply (zenon_or_s _ _ zenon_H1a8); [ zenon_intro zenon_H13f | zenon_intro zenon_H1a9 ]. % 18.52/18.77 apply (zenon_L373_); trivial. % 18.52/18.77 apply (zenon_or_s _ _ zenon_H1a9); [ zenon_intro zenon_Ha6 | zenon_intro zenon_H161 ]. % 18.52/18.77 apply (zenon_L39_); trivial. % 18.52/18.77 apply (zenon_L372_); trivial. % 18.52/18.77 apply (zenon_or_s _ _ zenon_H1a5); [ zenon_intro zenon_H99 | zenon_intro zenon_H1a8 ]. % 18.52/18.77 apply (zenon_L385_); trivial. % 18.52/18.77 apply (zenon_or_s _ _ zenon_H1a8); [ zenon_intro zenon_H13f | zenon_intro zenon_H1a9 ]. % 18.52/18.77 apply (zenon_L390_); trivial. % 18.52/18.77 apply (zenon_or_s _ _ zenon_H1a9); [ zenon_intro zenon_Ha6 | zenon_intro zenon_H161 ]. % 18.52/18.77 apply (zenon_L39_); trivial. % 18.52/18.77 apply (zenon_L372_); trivial. % 18.52/18.77 apply (zenon_or_s _ _ zenon_H16f); [ zenon_intro zenon_H9e | zenon_intro zenon_H170 ]. % 18.52/18.77 apply (zenon_L37_); trivial. % 18.52/18.77 apply (zenon_or_s _ _ zenon_H170); [ zenon_intro zenon_H13f | zenon_intro zenon_H171 ]. % 18.52/18.77 apply (zenon_L391_); trivial. % 18.52/18.77 apply (zenon_or_s _ _ zenon_H171); [ zenon_intro zenon_H16c | zenon_intro zenon_Hdc ]. % 18.52/18.77 apply (zenon_L393_); trivial. % 18.52/18.77 apply (zenon_L266_); trivial. % 18.52/18.77 apply (zenon_or_s _ _ zenon_H18c); [ zenon_intro zenon_H86 | zenon_intro zenon_H18d ]. % 18.52/18.77 apply (zenon_L123_); trivial. % 18.52/18.77 apply (zenon_or_s _ _ zenon_H18d); [ zenon_intro zenon_H110 | zenon_intro zenon_H18e ]. % 18.52/18.77 apply (zenon_L354_); trivial. % 18.52/18.77 apply (zenon_or_s _ _ zenon_H18e); [ zenon_intro zenon_H113 | zenon_intro zenon_Hd7 ]. % 18.52/18.77 apply (zenon_or_s _ _ zenon_H1d8); [ zenon_intro zenon_H10f | zenon_intro zenon_H1d9 ]. % 18.52/18.77 apply (zenon_or_s _ _ zenon_H1a5); [ zenon_intro zenon_H99 | zenon_intro zenon_H1a8 ]. % 18.52/18.77 apply (zenon_L175_); trivial. % 18.52/18.77 apply (zenon_or_s _ _ zenon_H1a8); [ zenon_intro zenon_H13f | zenon_intro zenon_H1a9 ]. % 18.52/18.77 apply (zenon_L368_); trivial. % 18.52/18.77 apply (zenon_or_s _ _ zenon_H1a9); [ zenon_intro zenon_Ha6 | zenon_intro zenon_H161 ]. % 18.52/18.77 apply (zenon_L371_); trivial. % 18.52/18.77 apply (zenon_L372_); trivial. % 18.52/18.77 apply (zenon_or_s _ _ zenon_H1d9); [ zenon_intro zenon_H110 | zenon_intro zenon_H1da ]. % 18.52/18.77 apply (zenon_L354_); trivial. % 18.52/18.77 apply (zenon_or_s _ _ zenon_H1da); [ zenon_intro zenon_H1ca | zenon_intro zenon_H14d ]. % 18.52/18.77 apply (zenon_or_s _ _ zenon_H16f); [ zenon_intro zenon_H9e | zenon_intro zenon_H170 ]. % 18.52/18.77 apply (zenon_L37_); trivial. % 18.52/18.77 apply (zenon_or_s _ _ zenon_H170); [ zenon_intro zenon_H13f | zenon_intro zenon_H171 ]. % 18.52/18.77 apply (zenon_L368_); trivial. % 18.52/18.77 apply (zenon_or_s _ _ zenon_H171); [ zenon_intro zenon_H16c | zenon_intro zenon_Hdc ]. % 18.52/18.77 apply (zenon_L116_); trivial. % 18.52/18.77 apply (zenon_or_s _ _ zenon_H1a5); [ zenon_intro zenon_H99 | zenon_intro zenon_H1a8 ]. % 18.52/18.77 apply (zenon_or_s _ _ zenon_H2f); [ zenon_intro zenon_H34 | zenon_intro zenon_H33 ]. % 18.52/18.77 exact (zenon_H30 zenon_H34). % 18.52/18.77 apply (zenon_or_s _ _ zenon_H33); [ zenon_intro zenon_H36 | zenon_intro zenon_H35 ]. % 18.52/18.77 exact (zenon_H31 zenon_H36). % 18.52/18.77 apply (zenon_or_s _ _ zenon_H35); [ zenon_intro zenon_H2c | zenon_intro zenon_H37 ]. % 18.52/18.77 exact (zenon_H81 zenon_H2c). % 18.52/18.77 apply (zenon_L388_); trivial. % 18.52/18.77 apply (zenon_or_s _ _ zenon_H1a8); [ zenon_intro zenon_H13f | zenon_intro zenon_H1a9 ]. % 18.52/18.77 apply (zenon_L368_); trivial. % 18.52/18.77 apply (zenon_or_s _ _ zenon_H1a9); [ zenon_intro zenon_Ha6 | zenon_intro zenon_H161 ]. % 18.52/18.77 apply (zenon_L207_); trivial. % 18.52/18.77 apply (zenon_L382_); trivial. % 18.52/18.77 apply (zenon_L152_); trivial. % 18.52/18.77 apply (zenon_L394_); trivial. % 18.52/18.77 (* end of lemma zenon_L395_ *) % 18.52/18.77 assert (zenon_L396_ : (((op (e0) (e3)) = (e0))\/(((op (e0) (e3)) = (e1))\/(((op (e0) (e3)) = (e2))\/((op (e0) (e3)) = (e3))))) -> ((op (e2) (e3)) = (e0)) -> (~((e2) = (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) (e3)) = (e0))\/(((op (e3) (e3)) = (e1))\/(((op (e3) (e3)) = (e2))\/((op (e3) (e3)) = (e3))))) -> (~((op (e3) (e1)) = (op (e3) (e3)))) -> (~((op (e3) (e2)) = (op (e3) (e3)))) -> (~((op (e3) (e3)) = (e3))) -> (((op (e0) (e1)) = (e0))\/(((op (e0) (e1)) = (e1))\/(((op (e0) (e1)) = (e2))\/((op (e0) (e1)) = (e3))))) -> (~((op (e0) (e1)) = (e0))) -> (~((op (e0) (e1)) = (op (e3) (e1)))) -> (~((op (e1) (e1)) = (op (e2) (e1)))) -> (~((op (e0) (e1)) = (op (e2) (e1)))) -> (~((op (e2) (e1)) = (op (e3) (e1)))) -> (~((op (e2) (e1)) = (e0))) -> (((op (e2) (e1)) = (e0))\/(((op (e2) (e1)) = (e1))\/(((op (e2) (e1)) = (e2))\/((op (e2) (e1)) = (e3))))) -> (~((op (e0) (e1)) = (op (e1) (e1)))) -> ((op (e1) (e0)) = (e1)) -> (~((e1) = (e3))) -> (((op (e1) (e0)) = (e3))\/(((op (e1) (e1)) = (e3))\/(((op (e1) (e2)) = (e3))\/((op (e1) (e3)) = (e3))))) -> (~((op (e1) (e1)) = (op (e3) (e1)))) -> (((op (e0) (e2)) = (e3))\/(((op (e1) (e2)) = (e3))\/(((op (e2) (e2)) = (e3))\/((op (e3) (e2)) = (e3))))) -> (~((e0) = (e3))) -> (~((op (e2) (e0)) = (op (e2) (e2)))) -> ((op (e2) (e0)) = (e3)) -> (~((op (e3) (e1)) = (op (e3) (e2)))) -> ((op (e1) (e1)) = (e0)) -> (((op (e1) (e0)) = (e2))\/(((op (e1) (e1)) = (e2))\/(((op (e1) (e2)) = (e2))\/((op (e1) (e3)) = (e2))))) -> (((op (e2) (e0)) = (e0))\/(((op (e2) (e1)) = (e0))\/(((op (e2) (e2)) = (e0))\/((op (e2) (e3)) = (e0))))) -> (~((op (e2) (e0)) = (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) (e2)) = (e0))) -> (((op (e2) (e2)) = (e0))\/(((op (e2) (e2)) = (e1))\/(((op (e2) (e2)) = (e2))\/((op (e2) (e2)) = (e3))))) -> (~((e0) = (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 (e2) (e2)) = (op (e2) (e3)))) -> (((op (e0) (e3)) = (e1))\/(((op (e1) (e3)) = (e1))\/(((op (e2) (e3)) = (e1))\/((op (e3) (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) (e1)) = (e3))\/(((op (e1) (e1)) = (e3))\/(((op (e2) (e1)) = (e3))\/((op (e3) (e1)) = (e3))))) -> (~((op (e3) (e0)) = (op (e3) (e3)))) -> ((op (e0) (e0)) = (e2)) -> (~((op (e0) (e0)) = (op (e0) (e3)))) -> (((op (e3) (e0)) = (e2))\/(((op (e3) (e1)) = (e2))\/(((op (e3) (e2)) = (e2))\/((op (e3) (e3)) = (e2))))) -> (~((e1) = (e2))) -> ((op (e3) (e0)) = (e0)) -> (~((op (e1) (e2)) = (op (e2) (e2)))) -> (((op (e0) (e2)) = (e0))\/(((op (e1) (e2)) = (e0))\/(((op (e2) (e2)) = (e0))\/((op (e3) (e2)) = (e0))))) -> (~((op (e1) (e1)) = (op (e1) (e2)))) -> (~((op (e3) (e0)) = (op (e3) (e2)))) -> (~((op (e1) (e3)) = (op (e2) (e3)))) -> (~((op (e0) (e0)) = (op (e2) (e0)))) -> (((op (e2) (e0)) = (e2))\/(((op (e2) (e1)) = (e2))\/(((op (e2) (e2)) = (e2))\/((op (e2) (e3)) = (e2))))) -> (~((op (e0) (e3)) = (op (e3) (e3)))) -> (((op (e3) (e0)) = (e1))\/(((op (e3) (e1)) = (e1))\/(((op (e3) (e2)) = (e1))\/((op (e3) (e3)) = (e1))))) -> (~((op (e1) (e1)) = (e1))) -> (~((op (e0) (e1)) = (op (e0) (e3)))) -> (((op (e0) (e1)) = (e1))\/(((op (e1) (e1)) = (e1))\/(((op (e2) (e1)) = (e1))\/((op (e3) (e1)) = (e1))))) -> ((op (e2) (e3)) = (e2)) -> (~((op (e0) (e3)) = (op (e2) (e3)))) -> (~((op (e0) (e3)) = (op (e1) (e3)))) -> ((op (e1) (e3)) = (e3)) -> False). % 18.52/18.77 do 0 intro. intros zenon_He4 zenon_H37 zenon_H12b zenon_H172 zenon_H149 zenon_H48 zenon_H173 zenon_H101 zenon_H130 zenon_H62 zenon_H102 zenon_H212 zenon_H20b zenon_H210 zenon_H13e zenon_H17e zenon_Haf zenon_H31 zenon_H1cc zenon_H10e zenon_H9d zenon_H95 zenon_H16f zenon_H160 zenon_H1a6 zenon_H9a zenon_H52 zenon_H3b zenon_H1a4 zenon_H29 zenon_H18c zenon_H2f zenon_H30 zenon_H106 zenon_H18f zenon_H81 zenon_H1c4 zenon_Ha1 zenon_H139 zenon_H145 zenon_H6d zenon_H133 zenon_H1c7 zenon_H1d8 zenon_H1a5 zenon_H71 zenon_H7b zenon_H189 zenon_H153 zenon_H7c zenon_H44 zenon_H2b zenon_H6a zenon_H4f zenon_H6f zenon_Hdb zenon_H39 zenon_H1d5 zenon_Hc2 zenon_He8 zenon_H10a zenon_H54 zenon_H109 zenon_H11d zenon_He2 zenon_H1d zenon_Hdc. % 18.52/18.77 apply (zenon_or_s _ _ zenon_He4); [ zenon_intro zenon_H1e | zenon_intro zenon_He5 ]. % 18.52/18.77 apply (zenon_L367_); trivial. % 18.52/18.77 apply (zenon_or_s _ _ zenon_He5); [ zenon_intro zenon_Hc3 | zenon_intro zenon_He6 ]. % 18.52/18.77 apply (zenon_L395_); trivial. % 18.52/18.77 apply (zenon_or_s _ _ zenon_He6); [ zenon_intro zenon_Hcd | zenon_intro zenon_He3 ]. % 18.52/18.77 apply (zenon_L234_); trivial. % 18.52/18.77 apply (zenon_L117_); trivial. % 18.52/18.77 (* end of lemma zenon_L396_ *) % 18.52/18.77 assert (zenon_L397_ : ((op (e3) (e1)) = (e2)) -> (((op (e0) (e3)) = (e0))\/(((op (e0) (e3)) = (e1))\/(((op (e0) (e3)) = (e2))\/((op (e0) (e3)) = (e3))))) -> ((op (e2) (e3)) = (e0)) -> (~((e2) = (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) (e3)) = (e0))\/(((op (e3) (e3)) = (e1))\/(((op (e3) (e3)) = (e2))\/((op (e3) (e3)) = (e3))))) -> (~((op (e3) (e1)) = (op (e3) (e3)))) -> (~((op (e3) (e2)) = (op (e3) (e3)))) -> (~((op (e3) (e3)) = (e3))) -> (((op (e0) (e1)) = (e0))\/(((op (e0) (e1)) = (e1))\/(((op (e0) (e1)) = (e2))\/((op (e0) (e1)) = (e3))))) -> (~((op (e0) (e1)) = (e0))) -> (~((op (e0) (e1)) = (op (e3) (e1)))) -> (~((op (e1) (e1)) = (op (e2) (e1)))) -> (~((op (e0) (e1)) = (op (e2) (e1)))) -> (~((op (e2) (e1)) = (op (e3) (e1)))) -> (~((op (e2) (e1)) = (e0))) -> (((op (e2) (e1)) = (e0))\/(((op (e2) (e1)) = (e1))\/(((op (e2) (e1)) = (e2))\/((op (e2) (e1)) = (e3))))) -> (~((op (e0) (e1)) = (op (e1) (e1)))) -> ((op (e1) (e0)) = (e1)) -> (~((e1) = (e3))) -> (((op (e1) (e0)) = (e3))\/(((op (e1) (e1)) = (e3))\/(((op (e1) (e2)) = (e3))\/((op (e1) (e3)) = (e3))))) -> (~((op (e1) (e1)) = (op (e3) (e1)))) -> (((op (e0) (e2)) = (e3))\/(((op (e1) (e2)) = (e3))\/(((op (e2) (e2)) = (e3))\/((op (e3) (e2)) = (e3))))) -> (~((e0) = (e3))) -> (~((op (e2) (e0)) = (op (e2) (e2)))) -> ((op (e2) (e0)) = (e3)) -> (~((op (e3) (e1)) = (op (e3) (e2)))) -> ((op (e1) (e1)) = (e0)) -> (((op (e1) (e0)) = (e2))\/(((op (e1) (e1)) = (e2))\/(((op (e1) (e2)) = (e2))\/((op (e1) (e3)) = (e2))))) -> (((op (e2) (e0)) = (e0))\/(((op (e2) (e1)) = (e0))\/(((op (e2) (e2)) = (e0))\/((op (e2) (e3)) = (e0))))) -> (~((op (e2) (e0)) = (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) (e2)) = (e0))) -> (((op (e2) (e2)) = (e0))\/(((op (e2) (e2)) = (e1))\/(((op (e2) (e2)) = (e2))\/((op (e2) (e2)) = (e3))))) -> (~((e0) = (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 (e2) (e2)) = (op (e2) (e3)))) -> (((op (e0) (e3)) = (e1))\/(((op (e1) (e3)) = (e1))\/(((op (e2) (e3)) = (e1))\/((op (e3) (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) (e1)) = (e3))\/(((op (e1) (e1)) = (e3))\/(((op (e2) (e1)) = (e3))\/((op (e3) (e1)) = (e3))))) -> (~((op (e3) (e0)) = (op (e3) (e3)))) -> ((op (e0) (e0)) = (e2)) -> (~((op (e0) (e0)) = (op (e0) (e3)))) -> (((op (e3) (e0)) = (e2))\/(((op (e3) (e1)) = (e2))\/(((op (e3) (e2)) = (e2))\/((op (e3) (e3)) = (e2))))) -> (~((e1) = (e2))) -> ((op (e3) (e0)) = (e0)) -> (~((op (e1) (e2)) = (op (e2) (e2)))) -> (((op (e0) (e2)) = (e0))\/(((op (e1) (e2)) = (e0))\/(((op (e2) (e2)) = (e0))\/((op (e3) (e2)) = (e0))))) -> (~((op (e1) (e1)) = (op (e1) (e2)))) -> (~((op (e3) (e0)) = (op (e3) (e2)))) -> (~((op (e1) (e3)) = (op (e2) (e3)))) -> (~((op (e0) (e0)) = (op (e2) (e0)))) -> (((op (e2) (e0)) = (e2))\/(((op (e2) (e1)) = (e2))\/(((op (e2) (e2)) = (e2))\/((op (e2) (e3)) = (e2))))) -> (~((op (e0) (e3)) = (op (e3) (e3)))) -> (((op (e3) (e0)) = (e1))\/(((op (e3) (e1)) = (e1))\/(((op (e3) (e2)) = (e1))\/((op (e3) (e3)) = (e1))))) -> (~((op (e1) (e1)) = (e1))) -> (~((op (e0) (e1)) = (op (e0) (e3)))) -> (((op (e0) (e1)) = (e1))\/(((op (e1) (e1)) = (e1))\/(((op (e2) (e1)) = (e1))\/((op (e3) (e1)) = (e1))))) -> (~((op (e0) (e3)) = (op (e2) (e3)))) -> (~((op (e0) (e3)) = (op (e1) (e3)))) -> ((op (e1) (e3)) = (e3)) -> False). % 18.52/18.77 do 0 intro. intros zenon_H14d zenon_He4 zenon_H37 zenon_H12b zenon_H172 zenon_H149 zenon_H48 zenon_H173 zenon_H101 zenon_H130 zenon_H62 zenon_H102 zenon_H212 zenon_H20b zenon_H210 zenon_H13e zenon_H17e zenon_Haf zenon_H31 zenon_H1cc zenon_H10e zenon_H9d zenon_H95 zenon_H16f zenon_H160 zenon_H1a6 zenon_H9a zenon_H52 zenon_H3b zenon_H1a4 zenon_H29 zenon_H18c zenon_H2f zenon_H30 zenon_H106 zenon_H18f zenon_H81 zenon_H1c4 zenon_Ha1 zenon_H139 zenon_H145 zenon_H6d zenon_H133 zenon_H1c7 zenon_H1d8 zenon_H1a5 zenon_H71 zenon_H7b zenon_H189 zenon_H153 zenon_H7c zenon_H44 zenon_H2b zenon_H6a zenon_H4f zenon_H6f zenon_Hdb zenon_H39 zenon_H1d5 zenon_Hc2 zenon_He8 zenon_H10a zenon_H54 zenon_H109 zenon_He2 zenon_H1d zenon_Hdc. % 18.52/18.77 apply (zenon_or_s _ _ zenon_H1d5); [ zenon_intro zenon_Hee | zenon_intro zenon_H1d6 ]. % 18.52/18.77 apply (zenon_L341_); trivial. % 18.52/18.77 apply (zenon_or_s _ _ zenon_H1d6); [ zenon_intro zenon_H1ca | zenon_intro zenon_H1d7 ]. % 18.52/18.77 apply (zenon_L364_); trivial. % 18.52/18.77 apply (zenon_or_s _ _ zenon_H1d7); [ zenon_intro zenon_H176 | zenon_intro zenon_H11d ]. % 18.52/18.77 exact (zenon_H173 zenon_H176). % 18.52/18.77 apply (zenon_L396_); trivial. % 18.52/18.77 (* end of lemma zenon_L397_ *) % 18.52/18.77 assert (zenon_L398_ : ((op (e3) (e1)) = (e2)) -> (((op (e0) (e3)) = (e0))\/(((op (e0) (e3)) = (e1))\/(((op (e0) (e3)) = (e2))\/((op (e0) (e3)) = (e3))))) -> (~((e2) = (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) (e3)) = (e0))\/(((op (e3) (e3)) = (e1))\/(((op (e3) (e3)) = (e2))\/((op (e3) (e3)) = (e3))))) -> (~((op (e3) (e1)) = (op (e3) (e3)))) -> (~((op (e3) (e2)) = (op (e3) (e3)))) -> (~((op (e3) (e3)) = (e3))) -> (((op (e0) (e1)) = (e0))\/(((op (e0) (e1)) = (e1))\/(((op (e0) (e1)) = (e2))\/((op (e0) (e1)) = (e3))))) -> (~((op (e0) (e1)) = (e0))) -> (~((op (e0) (e1)) = (op (e3) (e1)))) -> (~((op (e1) (e1)) = (op (e2) (e1)))) -> (~((op (e0) (e1)) = (op (e2) (e1)))) -> (~((op (e2) (e1)) = (op (e3) (e1)))) -> (~((op (e2) (e1)) = (e0))) -> (((op (e2) (e1)) = (e0))\/(((op (e2) (e1)) = (e1))\/(((op (e2) (e1)) = (e2))\/((op (e2) (e1)) = (e3))))) -> (~((op (e0) (e1)) = (op (e1) (e1)))) -> ((op (e1) (e0)) = (e1)) -> (~((e1) = (e3))) -> (((op (e1) (e0)) = (e3))\/(((op (e1) (e1)) = (e3))\/(((op (e1) (e2)) = (e3))\/((op (e1) (e3)) = (e3))))) -> (~((op (e1) (e1)) = (op (e3) (e1)))) -> (((op (e0) (e2)) = (e3))\/(((op (e1) (e2)) = (e3))\/(((op (e2) (e2)) = (e3))\/((op (e3) (e2)) = (e3))))) -> (~((e0) = (e3))) -> (~((op (e2) (e0)) = (op (e2) (e2)))) -> ((op (e2) (e0)) = (e3)) -> (~((op (e3) (e1)) = (op (e3) (e2)))) -> ((op (e1) (e1)) = (e0)) -> (((op (e1) (e0)) = (e2))\/(((op (e1) (e1)) = (e2))\/(((op (e1) (e2)) = (e2))\/((op (e1) (e3)) = (e2))))) -> (((op (e2) (e0)) = (e0))\/(((op (e2) (e1)) = (e0))\/(((op (e2) (e2)) = (e0))\/((op (e2) (e3)) = (e0))))) -> (~((op (e2) (e0)) = (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) (e2)) = (e0))) -> (((op (e2) (e2)) = (e0))\/(((op (e2) (e2)) = (e1))\/(((op (e2) (e2)) = (e2))\/((op (e2) (e2)) = (e3))))) -> (~((e0) = (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 (e2) (e2)) = (op (e2) (e3)))) -> (((op (e0) (e3)) = (e1))\/(((op (e1) (e3)) = (e1))\/(((op (e2) (e3)) = (e1))\/((op (e3) (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) (e1)) = (e3))\/(((op (e1) (e1)) = (e3))\/(((op (e2) (e1)) = (e3))\/((op (e3) (e1)) = (e3))))) -> (~((op (e3) (e0)) = (op (e3) (e3)))) -> ((op (e0) (e0)) = (e2)) -> (~((op (e0) (e0)) = (op (e0) (e3)))) -> (((op (e3) (e0)) = (e2))\/(((op (e3) (e1)) = (e2))\/(((op (e3) (e2)) = (e2))\/((op (e3) (e3)) = (e2))))) -> (~((e1) = (e2))) -> ((op (e3) (e0)) = (e0)) -> (~((op (e1) (e2)) = (op (e2) (e2)))) -> (((op (e0) (e2)) = (e0))\/(((op (e1) (e2)) = (e0))\/(((op (e2) (e2)) = (e0))\/((op (e3) (e2)) = (e0))))) -> (~((op (e1) (e1)) = (op (e1) (e2)))) -> (~((op (e3) (e0)) = (op (e3) (e2)))) -> (~((op (e1) (e3)) = (op (e2) (e3)))) -> (~((op (e0) (e0)) = (op (e2) (e0)))) -> (((op (e2) (e0)) = (e2))\/(((op (e2) (e1)) = (e2))\/(((op (e2) (e2)) = (e2))\/((op (e2) (e3)) = (e2))))) -> (~((op (e0) (e3)) = (op (e3) (e3)))) -> (((op (e3) (e0)) = (e1))\/(((op (e3) (e1)) = (e1))\/(((op (e3) (e2)) = (e1))\/((op (e3) (e3)) = (e1))))) -> (~((op (e1) (e1)) = (e1))) -> (~((op (e0) (e1)) = (op (e0) (e3)))) -> (((op (e0) (e1)) = (e1))\/(((op (e1) (e1)) = (e1))\/(((op (e2) (e1)) = (e1))\/((op (e3) (e1)) = (e1))))) -> (~((op (e0) (e3)) = (op (e2) (e3)))) -> (~((op (e0) (e3)) = (op (e1) (e3)))) -> ((op (e1) (e3)) = (e3)) -> False). % 18.52/18.77 do 0 intro. intros zenon_H14d zenon_He4 zenon_H12b zenon_H172 zenon_H149 zenon_H48 zenon_H173 zenon_H101 zenon_H130 zenon_H62 zenon_H102 zenon_H212 zenon_H20b zenon_H210 zenon_H13e zenon_H17e zenon_Haf zenon_H31 zenon_H1cc zenon_H10e zenon_H9d zenon_H95 zenon_H16f zenon_H160 zenon_H1a6 zenon_H9a zenon_H52 zenon_H3b zenon_H1a4 zenon_H29 zenon_H18c zenon_H2f zenon_H30 zenon_H106 zenon_H18f zenon_H81 zenon_H1c4 zenon_Ha1 zenon_H139 zenon_H145 zenon_H6d zenon_H133 zenon_H1c7 zenon_H1d8 zenon_H1a5 zenon_H71 zenon_H7b zenon_H189 zenon_H153 zenon_H7c zenon_H44 zenon_H2b zenon_H6a zenon_H4f zenon_H6f zenon_Hdb zenon_H39 zenon_H1d5 zenon_Hc2 zenon_He8 zenon_H10a zenon_H54 zenon_H109 zenon_He2 zenon_H1d zenon_Hdc. % 18.52/18.77 apply (zenon_or_s _ _ zenon_H2f); [ zenon_intro zenon_H34 | zenon_intro zenon_H33 ]. % 18.52/18.77 exact (zenon_H30 zenon_H34). % 18.52/18.77 apply (zenon_or_s _ _ zenon_H33); [ zenon_intro zenon_H36 | zenon_intro zenon_H35 ]. % 18.52/18.77 exact (zenon_H31 zenon_H36). % 18.52/18.77 apply (zenon_or_s _ _ zenon_H35); [ zenon_intro zenon_H2c | zenon_intro zenon_H37 ]. % 18.52/18.77 exact (zenon_H81 zenon_H2c). % 18.52/18.77 apply (zenon_L397_); trivial. % 18.52/18.77 (* end of lemma zenon_L398_ *) % 18.52/18.77 assert (zenon_L399_ : (((op (e1) (e3)) = (e0))\/(((op (e1) (e3)) = (e1))\/(((op (e1) (e3)) = (e2))\/((op (e1) (e3)) = (e3))))) -> (~((op (e1) (e3)) = (e0))) -> (~((op (e1) (e3)) = (op (e3) (e3)))) -> ((op (e2) (e2)) = (e1)) -> ((op (e0) (e1)) = (e1)) -> ((op (e3) (e1)) = (e2)) -> (((op (e0) (e3)) = (e0))\/(((op (e0) (e3)) = (e1))\/(((op (e0) (e3)) = (e2))\/((op (e0) (e3)) = (e3))))) -> (~((e2) = (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) (e3)) = (e0))\/(((op (e3) (e3)) = (e1))\/(((op (e3) (e3)) = (e2))\/((op (e3) (e3)) = (e3))))) -> (~((op (e3) (e1)) = (op (e3) (e3)))) -> (~((op (e3) (e2)) = (op (e3) (e3)))) -> (~((op (e3) (e3)) = (e3))) -> (((op (e0) (e1)) = (e0))\/(((op (e0) (e1)) = (e1))\/(((op (e0) (e1)) = (e2))\/((op (e0) (e1)) = (e3))))) -> (~((op (e0) (e1)) = (e0))) -> (~((op (e0) (e1)) = (op (e3) (e1)))) -> (~((op (e1) (e1)) = (op (e2) (e1)))) -> (~((op (e0) (e1)) = (op (e2) (e1)))) -> (~((op (e2) (e1)) = (op (e3) (e1)))) -> (~((op (e2) (e1)) = (e0))) -> (((op (e2) (e1)) = (e0))\/(((op (e2) (e1)) = (e1))\/(((op (e2) (e1)) = (e2))\/((op (e2) (e1)) = (e3))))) -> (~((op (e0) (e1)) = (op (e1) (e1)))) -> ((op (e1) (e0)) = (e1)) -> (~((e1) = (e3))) -> (((op (e1) (e0)) = (e3))\/(((op (e1) (e1)) = (e3))\/(((op (e1) (e2)) = (e3))\/((op (e1) (e3)) = (e3))))) -> (~((op (e1) (e1)) = (op (e3) (e1)))) -> (((op (e0) (e2)) = (e3))\/(((op (e1) (e2)) = (e3))\/(((op (e2) (e2)) = (e3))\/((op (e3) (e2)) = (e3))))) -> (~((e0) = (e3))) -> (~((op (e2) (e0)) = (op (e2) (e2)))) -> ((op (e2) (e0)) = (e3)) -> (~((op (e3) (e1)) = (op (e3) (e2)))) -> ((op (e1) (e1)) = (e0)) -> (((op (e1) (e0)) = (e2))\/(((op (e1) (e1)) = (e2))\/(((op (e1) (e2)) = (e2))\/((op (e1) (e3)) = (e2))))) -> (((op (e2) (e0)) = (e0))\/(((op (e2) (e1)) = (e0))\/(((op (e2) (e2)) = (e0))\/((op (e2) (e3)) = (e0))))) -> (~((op (e2) (e0)) = (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) (e2)) = (e0))) -> (((op (e2) (e2)) = (e0))\/(((op (e2) (e2)) = (e1))\/(((op (e2) (e2)) = (e2))\/((op (e2) (e2)) = (e3))))) -> (~((e0) = (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 (e2) (e2)) = (op (e2) (e3)))) -> (((op (e0) (e3)) = (e1))\/(((op (e1) (e3)) = (e1))\/(((op (e2) (e3)) = (e1))\/((op (e3) (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) (e1)) = (e3))\/(((op (e1) (e1)) = (e3))\/(((op (e2) (e1)) = (e3))\/((op (e3) (e1)) = (e3))))) -> (~((op (e3) (e0)) = (op (e3) (e3)))) -> ((op (e0) (e0)) = (e2)) -> (~((op (e0) (e0)) = (op (e0) (e3)))) -> (((op (e3) (e0)) = (e2))\/(((op (e3) (e1)) = (e2))\/(((op (e3) (e2)) = (e2))\/((op (e3) (e3)) = (e2))))) -> (~((e1) = (e2))) -> ((op (e3) (e0)) = (e0)) -> (~((op (e1) (e2)) = (op (e2) (e2)))) -> (((op (e0) (e2)) = (e0))\/(((op (e1) (e2)) = (e0))\/(((op (e2) (e2)) = (e0))\/((op (e3) (e2)) = (e0))))) -> (~((op (e1) (e1)) = (op (e1) (e2)))) -> (~((op (e3) (e0)) = (op (e3) (e2)))) -> (~((op (e1) (e3)) = (op (e2) (e3)))) -> (~((op (e0) (e0)) = (op (e2) (e0)))) -> (((op (e2) (e0)) = (e2))\/(((op (e2) (e1)) = (e2))\/(((op (e2) (e2)) = (e2))\/((op (e2) (e3)) = (e2))))) -> (~((op (e0) (e3)) = (op (e3) (e3)))) -> (((op (e3) (e0)) = (e1))\/(((op (e3) (e1)) = (e1))\/(((op (e3) (e2)) = (e1))\/((op (e3) (e3)) = (e1))))) -> (~((op (e1) (e1)) = (e1))) -> (~((op (e0) (e1)) = (op (e0) (e3)))) -> (((op (e0) (e1)) = (e1))\/(((op (e1) (e1)) = (e1))\/(((op (e2) (e1)) = (e1))\/((op (e3) (e1)) = (e1))))) -> (~((op (e0) (e3)) = (op (e2) (e3)))) -> (~((op (e0) (e3)) = (op (e1) (e3)))) -> False). % 18.52/18.77 do 0 intro. intros zenon_Hdf zenon_H38 zenon_Hd5 zenon_Hf1 zenon_Ha0 zenon_H14d zenon_He4 zenon_H12b zenon_H172 zenon_H149 zenon_H48 zenon_H173 zenon_H101 zenon_H130 zenon_H62 zenon_H102 zenon_H212 zenon_H20b zenon_H210 zenon_H13e zenon_H17e zenon_Haf zenon_H31 zenon_H1cc zenon_H10e zenon_H9d zenon_H95 zenon_H16f zenon_H160 zenon_H1a6 zenon_H9a zenon_H52 zenon_H3b zenon_H1a4 zenon_H29 zenon_H18c zenon_H2f zenon_H30 zenon_H106 zenon_H18f zenon_H81 zenon_H1c4 zenon_Ha1 zenon_H139 zenon_H145 zenon_H6d zenon_H133 zenon_H1c7 zenon_H1d8 zenon_H1a5 zenon_H71 zenon_H7b zenon_H189 zenon_H153 zenon_H7c zenon_H44 zenon_H2b zenon_H6a zenon_H4f zenon_H6f zenon_Hdb zenon_H39 zenon_H1d5 zenon_Hc2 zenon_He8 zenon_H10a zenon_H54 zenon_H109 zenon_He2 zenon_H1d. % 18.52/18.77 apply (zenon_or_s _ _ zenon_H1d5); [ zenon_intro zenon_Hee | zenon_intro zenon_H1d6 ]. % 18.52/18.77 apply (zenon_L341_); trivial. % 18.52/18.77 apply (zenon_or_s _ _ zenon_H1d6); [ zenon_intro zenon_H1ca | zenon_intro zenon_H1d7 ]. % 18.52/18.77 apply (zenon_L364_); trivial. % 18.52/18.77 apply (zenon_or_s _ _ zenon_H1d7); [ zenon_intro zenon_H176 | zenon_intro zenon_H11d ]. % 18.52/18.77 exact (zenon_H173 zenon_H176). % 18.52/18.77 apply (zenon_or_s _ _ zenon_Hdf); [ zenon_intro zenon_H1f | zenon_intro zenon_He0 ]. % 18.52/18.77 exact (zenon_H38 zenon_H1f). % 18.52/18.77 apply (zenon_or_s _ _ zenon_He0); [ zenon_intro zenon_Hd6 | zenon_intro zenon_He1 ]. % 18.52/18.77 apply (zenon_L365_); trivial. % 18.52/18.77 apply (zenon_or_s _ _ zenon_He1); [ zenon_intro zenon_Hd7 | zenon_intro zenon_Hdc ]. % 18.52/18.77 apply (zenon_L366_); trivial. % 18.52/18.77 apply (zenon_L398_); trivial. % 18.52/18.77 (* end of lemma zenon_L399_ *) % 18.52/18.77 assert (zenon_L400_ : (~((op (e3) (e1)) = (op (e3) (e2)))) -> ((op (e3) (e1)) = (e2)) -> ((op (e3) (e2)) = (e2)) -> False). % 18.52/18.77 do 0 intro. intros zenon_H1a4 zenon_H14d zenon_H151. % 18.52/18.77 cut (((op (e3) (e1)) = (e2)) = ((op (e3) (e1)) = (op (e3) (e2)))). % 18.52/18.77 intro zenon_D_pnotp. % 18.52/18.77 apply zenon_H1a4. % 18.52/18.77 rewrite <- zenon_D_pnotp. % 18.52/18.77 exact zenon_H14d. % 18.52/18.77 cut (((e2) = (op (e3) (e2)))); [idtac | apply NNPP; zenon_intro zenon_H152]. % 18.52/18.77 cut (((op (e3) (e1)) = (op (e3) (e1)))); [idtac | apply NNPP; zenon_intro zenon_Hb1]. % 18.52/18.77 congruence. % 18.52/18.77 apply zenon_Hb1. apply refl_equal. % 18.52/18.77 apply zenon_H152. apply sym_equal. exact zenon_H151. % 18.52/18.77 (* end of lemma zenon_L400_ *) % 18.52/18.77 assert (zenon_L401_ : (((op (e3) (e1)) = (e0))\/(((op (e3) (e1)) = (e1))\/(((op (e3) (e1)) = (e2))\/((op (e3) (e1)) = (e3))))) -> (~((op (e3) (e1)) = (e0))) -> (~((op (e3) (e1)) = (op (e3) (e3)))) -> ((op (e3) (e3)) = (e1)) -> ((op (e3) (e2)) = (e2)) -> (~((op (e3) (e1)) = (op (e3) (e2)))) -> ((op (e3) (e2)) = (e3)) -> False). % 18.52/18.77 do 0 intro. intros zenon_H22a zenon_H1ad zenon_H130 zenon_Hc4 zenon_H151 zenon_H1a4 zenon_H163. % 18.52/18.77 apply (zenon_or_s _ _ zenon_H22a); [ zenon_intro zenon_H1b1 | zenon_intro zenon_H22b ]. % 18.52/18.77 exact (zenon_H1ad zenon_H1b1). % 18.52/18.77 apply (zenon_or_s _ _ zenon_H22b); [ zenon_intro zenon_Hae | zenon_intro zenon_H22c ]. % 18.52/18.77 apply (zenon_L85_); trivial. % 18.52/18.77 apply (zenon_or_s _ _ zenon_H22c); [ zenon_intro zenon_H14d | zenon_intro zenon_H161 ]. % 18.52/18.77 apply (zenon_L400_); trivial. % 18.52/18.77 apply (zenon_L169_); trivial. % 18.52/18.77 (* end of lemma zenon_L401_ *) % 18.52/18.77 assert (zenon_L402_ : (~((op (e1) (e3)) = (op (e3) (e3)))) -> ((op (e1) (e3)) = (e2)) -> ((op (e3) (e3)) = (e2)) -> False). % 18.52/18.77 do 0 intro. intros zenon_Hd5 zenon_Hd7 zenon_Hf6. % 18.52/18.77 cut (((op (e1) (e3)) = (e2)) = ((op (e1) (e3)) = (op (e3) (e3)))). % 18.52/18.77 intro zenon_D_pnotp. % 18.52/18.77 apply zenon_Hd5. % 18.52/18.77 rewrite <- zenon_D_pnotp. % 18.52/18.77 exact zenon_Hd7. % 18.52/18.77 cut (((e2) = (op (e3) (e3)))); [idtac | apply NNPP; zenon_intro zenon_H100]. % 18.52/18.77 cut (((op (e1) (e3)) = (op (e1) (e3)))); [idtac | apply NNPP; zenon_intro zenon_H59]. % 18.52/18.77 congruence. % 18.52/18.77 apply zenon_H59. apply refl_equal. % 18.52/18.77 apply zenon_H100. apply sym_equal. exact zenon_Hf6. % 18.52/18.77 (* end of lemma zenon_L402_ *) % 18.52/18.77 assert (zenon_L403_ : ((op (e0) (e1)) = (e1)) -> ((op (e0) (e1)) = (e3)) -> (~((e1) = (e3))) -> False). % 18.52/18.77 do 0 intro. intros zenon_Ha0 zenon_H99 zenon_H95. % 18.52/18.77 elim (classic ((e3) = (e3))); [ zenon_intro zenon_H96 | zenon_intro zenon_H85 ]. % 18.52/18.77 cut (((e3) = (e3)) = ((e1) = (e3))). % 18.52/18.77 intro zenon_D_pnotp. % 18.52/18.77 apply zenon_H95. % 18.52/18.77 rewrite <- zenon_D_pnotp. % 18.52/18.77 exact zenon_H96. % 18.52/18.77 cut (((e3) = (e3))); [idtac | apply NNPP; zenon_intro zenon_H85]. % 18.52/18.77 cut (((e3) = (e1))); [idtac | apply NNPP; zenon_intro zenon_H97]. % 18.52/18.77 congruence. % 18.52/18.77 cut (((op (e0) (e1)) = (e1)) = ((e3) = (e1))). % 18.52/18.77 intro zenon_D_pnotp. % 18.52/18.77 apply zenon_H97. % 18.52/18.77 rewrite <- zenon_D_pnotp. % 18.52/18.77 exact zenon_Ha0. % 18.52/18.77 cut (((e1) = (e1))); [idtac | apply NNPP; zenon_intro zenon_H79]. % 18.52/18.77 cut (((op (e0) (e1)) = (e3))); [idtac | apply NNPP; zenon_intro zenon_H9c]. % 18.52/18.77 congruence. % 18.52/18.77 exact (zenon_H9c zenon_H99). % 18.52/18.77 apply zenon_H79. apply refl_equal. % 18.52/18.77 apply zenon_H85. apply refl_equal. % 18.52/18.77 apply zenon_H85. apply refl_equal. % 18.52/18.77 (* end of lemma zenon_L403_ *) % 18.52/18.77 assert (zenon_L404_ : (((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 (e3) (e3)) = (e1)) -> ((op (e3) (e3)) = (e2)) -> (~((op (e2) (e3)) = (op (e3) (e3)))) -> (~((op (e1) (e3)) = (op (e2) (e3)))) -> ((op (e1) (e3)) = (e3)) -> False). % 18.52/18.77 do 0 intro. intros zenon_H11f zenon_H1e zenon_He2 zenon_Hc4 zenon_Hf6 zenon_Hf3 zenon_Hdb zenon_Hdc. % 18.52/18.77 apply (zenon_or_s _ _ zenon_H11f); [ zenon_intro zenon_H37 | zenon_intro zenon_H120 ]. % 18.52/18.77 apply (zenon_L367_); trivial. % 18.52/18.77 apply (zenon_or_s _ _ zenon_H120); [ zenon_intro zenon_Hf4 | zenon_intro zenon_H121 ]. % 18.52/18.77 apply (zenon_L60_); trivial. % 18.52/18.77 apply (zenon_or_s _ _ zenon_H121); [ zenon_intro zenon_H11d | zenon_intro zenon_Hdd ]. % 18.52/18.77 apply (zenon_L97_); trivial. % 18.52/18.77 apply (zenon_L52_); trivial. % 18.52/18.77 (* end of lemma zenon_L404_ *) % 18.52/18.77 assert (zenon_L405_ : (((op (e0) (e3)) = (e0))\/(((op (e0) (e3)) = (e1))\/(((op (e0) (e3)) = (e2))\/((op (e0) (e3)) = (e3))))) -> (~((op (e1) (e3)) = (op (e2) (e3)))) -> (~((op (e2) (e3)) = (op (e3) (e3)))) -> ((op (e3) (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 (e2) (e3)) = (e0)) -> ((op (e3) (e3)) = (e2)) -> (~((op (e0) (e3)) = (op (e3) (e3)))) -> (~((op (e0) (e3)) = (op (e1) (e3)))) -> ((op (e1) (e3)) = (e3)) -> False). % 18.52/18.77 do 0 intro. intros zenon_He4 zenon_Hdb zenon_Hf3 zenon_Hc4 zenon_He2 zenon_H11f zenon_H37 zenon_Hf6 zenon_Hc2 zenon_H1d zenon_Hdc. % 18.52/18.77 apply (zenon_or_s _ _ zenon_He4); [ zenon_intro zenon_H1e | zenon_intro zenon_He5 ]. % 18.52/18.77 apply (zenon_L404_); trivial. % 18.52/18.77 apply (zenon_or_s _ _ zenon_He5); [ zenon_intro zenon_Hc3 | zenon_intro zenon_He6 ]. % 18.52/18.77 apply (zenon_L387_); trivial. % 18.52/18.77 apply (zenon_or_s _ _ zenon_He6); [ zenon_intro zenon_Hcd | zenon_intro zenon_He3 ]. % 18.52/18.77 apply (zenon_L87_); trivial. % 18.52/18.77 apply (zenon_L117_); trivial. % 18.52/18.77 (* end of lemma zenon_L405_ *) % 18.52/18.77 assert (zenon_L406_ : ((op (e0) (e2)) = (e1)) -> ((op (e0) (e1)) = (e1)) -> (~((op (e0) (e1)) = (op (e0) (e2)))) -> False). % 18.52/18.77 do 0 intro. intros zenon_H122 zenon_Ha0 zenon_H4a. % 18.52/18.77 elim (classic ((op (e0) (e2)) = (op (e0) (e2)))); [ zenon_intro zenon_H4b | zenon_intro zenon_H4c ]. % 18.52/18.77 cut (((op (e0) (e2)) = (op (e0) (e2))) = ((op (e0) (e1)) = (op (e0) (e2)))). % 18.52/18.77 intro zenon_D_pnotp. % 18.52/18.77 apply zenon_H4a. % 18.52/18.77 rewrite <- zenon_D_pnotp. % 18.52/18.77 exact zenon_H4b. % 18.52/18.77 cut (((op (e0) (e2)) = (op (e0) (e2)))); [idtac | apply NNPP; zenon_intro zenon_H4c]. % 18.52/18.77 cut (((op (e0) (e2)) = (op (e0) (e1)))); [idtac | apply NNPP; zenon_intro zenon_H4d]. % 18.52/18.77 congruence. % 18.52/18.77 cut (((op (e0) (e2)) = (e1)) = ((op (e0) (e2)) = (op (e0) (e1)))). % 18.52/18.77 intro zenon_D_pnotp. % 18.52/18.77 apply zenon_H4d. % 18.52/18.77 rewrite <- zenon_D_pnotp. % 18.52/18.77 exact zenon_H122. % 18.52/18.77 cut (((e1) = (op (e0) (e1)))); [idtac | apply NNPP; zenon_intro zenon_H20e]. % 18.52/18.77 cut (((op (e0) (e2)) = (op (e0) (e2)))); [idtac | apply NNPP; zenon_intro zenon_H4c]. % 18.52/18.77 congruence. % 18.52/18.77 apply zenon_H4c. apply refl_equal. % 18.52/18.77 apply zenon_H20e. apply sym_equal. exact zenon_Ha0. % 18.52/18.77 apply zenon_H4c. apply refl_equal. % 18.52/18.77 apply zenon_H4c. apply refl_equal. % 18.52/18.77 (* end of lemma zenon_L406_ *) % 18.52/18.77 assert (zenon_L407_ : (((op (e3) (e0)) = (e1))\/(((op (e3) (e1)) = (e1))\/(((op (e3) (e2)) = (e1))\/((op (e3) (e3)) = (e1))))) -> ((op (e0) (e0)) = (e2)) -> ((op (e2) (e0)) = (e3)) -> ((op (e0) (e1)) = (e1)) -> (~((op (e0) (e1)) = (op (e3) (e1)))) -> ((op (e1) (e2)) = (e1)) -> (~((op (e1) (e2)) = (op (e3) (e2)))) -> (~((op (e2) (e3)) = (op (e3) (e3)))) -> ((op (e2) (e3)) = (e1)) -> False). % 18.52/18.77 do 0 intro. intros zenon_He8 zenon_H7b zenon_H3b zenon_Ha0 zenon_H210 zenon_Hf0 zenon_H115 zenon_Hf3 zenon_Hf4. % 18.52/18.77 apply (zenon_or_s _ _ zenon_He8); [ zenon_intro zenon_Hac | zenon_intro zenon_Heb ]. % 18.52/18.77 apply (zenon_L308_); trivial. % 18.52/18.77 apply (zenon_or_s _ _ zenon_Heb); [ zenon_intro zenon_Hae | zenon_intro zenon_Hec ]. % 18.52/18.77 apply (zenon_L363_); trivial. % 18.52/18.77 apply (zenon_or_s _ _ zenon_Hec); [ zenon_intro zenon_Hba | zenon_intro zenon_Hc4 ]. % 18.52/18.77 apply (zenon_L69_); trivial. % 18.52/18.77 apply (zenon_L60_); trivial. % 18.52/18.77 (* end of lemma zenon_L407_ *) % 18.52/18.77 assert (zenon_L408_ : (((op (e0) (e2)) = (e1))\/(((op (e1) (e2)) = (e1))\/(((op (e2) (e2)) = (e1))\/((op (e3) (e2)) = (e1))))) -> (~((op (e0) (e1)) = (op (e0) (e2)))) -> (~((op (e2) (e3)) = (op (e3) (e3)))) -> (~((op (e1) (e2)) = (op (e3) (e2)))) -> (~((op (e0) (e1)) = (op (e3) (e1)))) -> ((op (e0) (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 (e2) (e3)))) -> ((op (e2) (e3)) = (e1)) -> (((op (e2) (e2)) = (e0))\/(((op (e2) (e2)) = (e1))\/(((op (e2) (e2)) = (e2))\/((op (e2) (e2)) = (e3))))) -> (~((op (e2) (e2)) = (e0))) -> (~((op (e2) (e2)) = (op (e3) (e2)))) -> (~((op (e2) (e2)) = (e2))) -> ((op (e2) (e0)) = (e3)) -> (~((op (e2) (e0)) = (op (e2) (e2)))) -> False). % 18.52/18.77 do 0 intro. intros zenon_H139 zenon_H4a zenon_Hf3 zenon_H115 zenon_H210 zenon_Ha0 zenon_H7b zenon_He8 zenon_H6d zenon_Hf4 zenon_H1c4 zenon_H81 zenon_H18f zenon_H173 zenon_H3b zenon_H52. % 18.52/18.77 apply (zenon_or_s _ _ zenon_H139); [ zenon_intro zenon_H122 | zenon_intro zenon_H13a ]. % 18.52/18.77 apply (zenon_L406_); trivial. % 18.52/18.77 apply (zenon_or_s _ _ zenon_H13a); [ zenon_intro zenon_Hf0 | zenon_intro zenon_H13b ]. % 18.52/18.77 apply (zenon_L407_); trivial. % 18.52/18.77 apply (zenon_or_s _ _ zenon_H13b); [ zenon_intro zenon_Hf1 | zenon_intro zenon_Hba ]. % 18.52/18.77 apply (zenon_L84_); trivial. % 18.52/18.77 apply (zenon_L327_); trivial. % 18.52/18.77 (* end of lemma zenon_L408_ *) % 18.52/18.77 assert (zenon_L409_ : ((op (e1) (e3)) = (e3)) -> (~((op (e0) (e3)) = (op (e1) (e3)))) -> (~((op (e0) (e3)) = (op (e3) (e3)))) -> (((op (e2) (e3)) = (e0))\/(((op (e2) (e3)) = (e1))\/(((op (e2) (e3)) = (e2))\/((op (e2) (e3)) = (e3))))) -> (~((op (e0) (e3)) = (op (e2) (e3)))) -> (~((op (e1) (e3)) = (op (e2) (e3)))) -> (((op (e0) (e3)) = (e0))\/(((op (e0) (e3)) = (e1))\/(((op (e0) (e3)) = (e2))\/((op (e0) (e3)) = (e3))))) -> (((op (e3) (e1)) = (e0))\/(((op (e3) (e1)) = (e1))\/(((op (e3) (e1)) = (e2))\/((op (e3) (e1)) = (e3))))) -> (~((op (e3) (e1)) = (e0))) -> (~((op (e3) (e1)) = (op (e3) (e3)))) -> (~((op (e3) (e1)) = (op (e3) (e2)))) -> (((op (e1) (e3)) = (e0))\/(((op (e1) (e3)) = (e1))\/(((op (e1) (e3)) = (e2))\/((op (e1) (e3)) = (e3))))) -> (~((op (e1) (e3)) = (e0))) -> (~((op (e1) (e3)) = (op (e3) (e3)))) -> (~((e2) = (e3))) -> (((op (e0) (e2)) = (e2))\/(((op (e1) (e2)) = (e2))\/(((op (e2) (e2)) = (e2))\/((op (e3) (e2)) = (e2))))) -> (~((e0) = (e2))) -> ((op (e0) (e2)) = (e0)) -> (((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)) = (e3))) -> (((op (e0) (e1)) = (e0))\/(((op (e0) (e1)) = (e1))\/(((op (e0) (e1)) = (e2))\/((op (e0) (e1)) = (e3))))) -> (~((op (e0) (e1)) = (e0))) -> (~((op (e1) (e1)) = (op (e2) (e1)))) -> (~((op (e0) (e1)) = (op (e2) (e1)))) -> (~((op (e2) (e1)) = (op (e3) (e1)))) -> (~((op (e2) (e1)) = (e0))) -> (((op (e2) (e1)) = (e0))\/(((op (e2) (e1)) = (e1))\/(((op (e2) (e1)) = (e2))\/((op (e2) (e1)) = (e3))))) -> (~((op (e0) (e1)) = (op (e1) (e1)))) -> ((op (e1) (e0)) = (e1)) -> (~((e1) = (e3))) -> (((op (e1) (e0)) = (e3))\/(((op (e1) (e1)) = (e3))\/(((op (e1) (e2)) = (e3))\/((op (e1) (e3)) = (e3))))) -> (~((op (e1) (e1)) = (op (e3) (e1)))) -> (((op (e0) (e2)) = (e3))\/(((op (e1) (e2)) = (e3))\/(((op (e2) (e2)) = (e3))\/((op (e3) (e2)) = (e3))))) -> (~((e0) = (e3))) -> ((op (e1) (e1)) = (e0)) -> (((op (e1) (e0)) = (e2))\/(((op (e1) (e1)) = (e2))\/(((op (e1) (e2)) = (e2))\/((op (e1) (e3)) = (e2))))) -> (((op (e2) (e0)) = (e0))\/(((op (e2) (e1)) = (e0))\/(((op (e2) (e2)) = (e0))\/((op (e2) (e3)) = (e0))))) -> (~((op (e2) (e0)) = (e0))) -> (((op (e2) (e0)) = (e1))\/(((op (e2) (e1)) = (e1))\/(((op (e2) (e2)) = (e1))\/((op (e2) (e3)) = (e1))))) -> (~((e0) = (e1))) -> (((op (e0) (e3)) = (e2))\/(((op (e1) (e3)) = (e2))\/(((op (e2) (e3)) = (e2))\/((op (e3) (e3)) = (e2))))) -> (((op (e0) (e3)) = (e1))\/(((op (e1) (e3)) = (e1))\/(((op (e2) (e3)) = (e1))\/((op (e3) (e3)) = (e1))))) -> (~((op (e2) (e1)) = (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)) = (e3))\/(((op (e2) (e1)) = (e3))\/((op (e3) (e1)) = (e3))))) -> (~((op (e3) (e0)) = (op (e3) (e3)))) -> (~((op (e0) (e0)) = (op (e0) (e3)))) -> (((op (e3) (e0)) = (e2))\/(((op (e3) (e1)) = (e2))\/(((op (e3) (e2)) = (e2))\/((op (e3) (e3)) = (e2))))) -> (~((e1) = (e2))) -> ((op (e3) (e0)) = (e0)) -> (~((op (e1) (e2)) = (op (e2) (e2)))) -> (((op (e0) (e2)) = (e0))\/(((op (e1) (e2)) = (e0))\/(((op (e2) (e2)) = (e0))\/((op (e3) (e2)) = (e0))))) -> (~((op (e1) (e1)) = (op (e1) (e2)))) -> (~((op (e3) (e0)) = (op (e3) (e2)))) -> (~((op (e0) (e0)) = (op (e2) (e0)))) -> (((op (e2) (e0)) = (e2))\/(((op (e2) (e1)) = (e2))\/(((op (e2) (e2)) = (e2))\/((op (e2) (e3)) = (e2))))) -> (~((op (e1) (e1)) = (e1))) -> (~((op (e0) (e1)) = (op (e0) (e3)))) -> (((op (e0) (e1)) = (e1))\/(((op (e1) (e1)) = (e1))\/(((op (e2) (e1)) = (e1))\/((op (e3) (e1)) = (e1))))) -> ((op (e1) (e1)) = (e3)) -> (~((op (e1) (e0)) = (op (e1) (e3)))) -> ((op (e1) (e2)) = (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) (e3)) = (op (e3) (e3)))) -> (~((op (e1) (e2)) = (op (e3) (e2)))) -> (~((op (e0) (e1)) = (op (e3) (e1)))) -> ((op (e0) (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 (e2) (e3)))) -> (((op (e2) (e2)) = (e0))\/(((op (e2) (e2)) = (e1))\/(((op (e2) (e2)) = (e2))\/((op (e2) (e2)) = (e3))))) -> (~((op (e2) (e2)) = (e0))) -> (~((op (e2) (e2)) = (op (e3) (e2)))) -> (~((op (e2) (e2)) = (e2))) -> ((op (e2) (e0)) = (e3)) -> (~((op (e2) (e0)) = (op (e2) (e2)))) -> False). % 18.52/18.77 do 0 intro. intros zenon_Hdc zenon_H1d zenon_Hc2 zenon_H11f zenon_He2 zenon_Hdb zenon_He4 zenon_H22a zenon_H1ad zenon_H130 zenon_H1a4 zenon_Hdf zenon_H38 zenon_Hd5 zenon_H12b zenon_H172 zenon_H149 zenon_H48 zenon_H101 zenon_H62 zenon_H102 zenon_H212 zenon_H20b zenon_H13e zenon_H17e zenon_Haf zenon_H31 zenon_H1cc zenon_H10e zenon_H9d zenon_H95 zenon_H16f zenon_H160 zenon_H1a6 zenon_H9a zenon_H29 zenon_H18c zenon_H2f zenon_H30 zenon_H106 zenon_Ha1 zenon_H145 zenon_H133 zenon_H1c7 zenon_H1d8 zenon_H1a5 zenon_H71 zenon_H189 zenon_H153 zenon_H7c zenon_H44 zenon_H2b zenon_H6a zenon_H4f zenon_H6f zenon_H39 zenon_H1d5 zenon_H10a zenon_H54 zenon_H109 zenon_H13f zenon_Hd8 zenon_H113 zenon_H139 zenon_H4a zenon_Hf3 zenon_H115 zenon_H210 zenon_Ha0 zenon_H7b zenon_He8 zenon_H6d zenon_H1c4 zenon_H81 zenon_H18f zenon_H173 zenon_H3b zenon_H52. % 18.52/18.77 apply (zenon_or_s _ _ zenon_H2f); [ zenon_intro zenon_H34 | zenon_intro zenon_H33 ]. % 18.52/18.77 exact (zenon_H30 zenon_H34). % 18.52/18.77 apply (zenon_or_s _ _ zenon_H33); [ zenon_intro zenon_H36 | zenon_intro zenon_H35 ]. % 18.52/18.77 exact (zenon_H31 zenon_H36). % 18.52/18.77 apply (zenon_or_s _ _ zenon_H35); [ zenon_intro zenon_H2c | zenon_intro zenon_H37 ]. % 18.52/18.77 exact (zenon_H81 zenon_H2c). % 18.52/18.77 apply (zenon_or_s _ _ zenon_H106); [ zenon_intro zenon_Hed | zenon_intro zenon_H107 ]. % 18.52/18.77 apply (zenon_L356_); trivial. % 18.52/18.77 apply (zenon_or_s _ _ zenon_H107); [ zenon_intro zenon_Ha5 | zenon_intro zenon_H108 ]. % 18.52/18.77 apply (zenon_L357_); trivial. % 18.52/18.77 apply (zenon_or_s _ _ zenon_H108); [ zenon_intro zenon_Hf1 | zenon_intro zenon_Hf4 ]. % 18.52/18.77 apply (zenon_or_s _ _ zenon_H1a6); [ zenon_intro zenon_Ha9 | zenon_intro zenon_H1aa ]. % 18.52/18.77 apply (zenon_L358_); trivial. % 18.52/18.77 apply (zenon_or_s _ _ zenon_H1aa); [ zenon_intro zenon_H16c | zenon_intro zenon_H1ab ]. % 18.52/18.77 apply (zenon_L116_); trivial. % 18.52/18.77 apply (zenon_or_s _ _ zenon_H1ab); [ zenon_intro zenon_Haa | zenon_intro zenon_H163 ]. % 18.52/18.77 apply (zenon_L168_); trivial. % 18.52/18.77 apply (zenon_or_s _ _ zenon_He8); [ zenon_intro zenon_Hac | zenon_intro zenon_Heb ]. % 18.52/18.77 apply (zenon_L362_); trivial. % 18.52/18.77 apply (zenon_or_s _ _ zenon_Heb); [ zenon_intro zenon_Hae | zenon_intro zenon_Hec ]. % 18.52/18.77 apply (zenon_L368_); trivial. % 18.52/18.77 apply (zenon_or_s _ _ zenon_Hec); [ zenon_intro zenon_Hba | zenon_intro zenon_Hc4 ]. % 18.52/18.77 apply (zenon_L185_); trivial. % 18.52/18.77 apply (zenon_or_s _ _ zenon_H153); [ zenon_intro zenon_H148 | zenon_intro zenon_H154 ]. % 18.52/18.77 apply (zenon_L100_); trivial. % 18.52/18.77 apply (zenon_or_s _ _ zenon_H154); [ zenon_intro zenon_H14d | zenon_intro zenon_H155 ]. % 18.52/18.77 apply (zenon_L399_); trivial. % 18.52/18.77 apply (zenon_or_s _ _ zenon_H155); [ zenon_intro zenon_H151 | zenon_intro zenon_Hf6 ]. % 18.52/18.77 apply (zenon_L401_); trivial. % 18.52/18.77 apply (zenon_L405_); trivial. % 18.52/18.77 apply (zenon_L408_); trivial. % 18.52/18.77 (* end of lemma zenon_L409_ *) % 18.52/18.77 assert (zenon_L410_ : (~((op (e2) (e2)) = (e2))) -> (~((op (e2) (e2)) = (op (e3) (e2)))) -> (~((op (e2) (e2)) = (e0))) -> (((op (e2) (e2)) = (e0))\/(((op (e2) (e2)) = (e1))\/(((op (e2) (e2)) = (e2))\/((op (e2) (e2)) = (e3))))) -> (~((op (e2) (e2)) = (op (e2) (e3)))) -> (((op (e3) (e0)) = (e1))\/(((op (e3) (e1)) = (e1))\/(((op (e3) (e2)) = (e1))\/((op (e3) (e3)) = (e1))))) -> ((op (e0) (e0)) = (e2)) -> ((op (e0) (e1)) = (e1)) -> (~((op (e0) (e1)) = (op (e3) (e1)))) -> (~((op (e1) (e2)) = (op (e3) (e2)))) -> (~((op (e2) (e3)) = (op (e3) (e3)))) -> (~((op (e0) (e1)) = (op (e0) (e2)))) -> (((op (e0) (e2)) = (e1))\/(((op (e1) (e2)) = (e1))\/(((op (e2) (e2)) = (e1))\/((op (e3) (e2)) = (e1))))) -> (~((op (e1) (e0)) = (op (e1) (e3)))) -> (((op (e0) (e1)) = (e1))\/(((op (e1) (e1)) = (e1))\/(((op (e2) (e1)) = (e1))\/((op (e3) (e1)) = (e1))))) -> (~((op (e0) (e1)) = (op (e0) (e3)))) -> (~((op (e1) (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 (e3) (e0)) = (op (e3) (e2)))) -> (~((op (e1) (e1)) = (op (e1) (e2)))) -> (((op (e0) (e2)) = (e0))\/(((op (e1) (e2)) = (e0))\/(((op (e2) (e2)) = (e0))\/((op (e3) (e2)) = (e0))))) -> (~((op (e1) (e2)) = (op (e2) (e2)))) -> ((op (e3) (e0)) = (e0)) -> (~((e1) = (e2))) -> (((op (e3) (e0)) = (e2))\/(((op (e3) (e1)) = (e2))\/(((op (e3) (e2)) = (e2))\/((op (e3) (e3)) = (e2))))) -> (~((op (e0) (e0)) = (op (e0) (e3)))) -> (~((op (e3) (e0)) = (op (e3) (e3)))) -> (((op (e0) (e1)) = (e3))\/(((op (e1) (e1)) = (e3))\/(((op (e2) (e1)) = (e3))\/((op (e3) (e1)) = (e3))))) -> (((op (e0) (e1)) = (e2))\/(((op (e1) (e1)) = (e2))\/(((op (e2) (e1)) = (e2))\/((op (e3) (e1)) = (e2))))) -> (~((op (e2) (e1)) = (op (e2) (e3)))) -> (((op (e0) (e3)) = (e1))\/(((op (e1) (e3)) = (e1))\/(((op (e2) (e3)) = (e1))\/((op (e3) (e3)) = (e1))))) -> (((op (e0) (e3)) = (e2))\/(((op (e1) (e3)) = (e2))\/(((op (e2) (e3)) = (e2))\/((op (e3) (e3)) = (e2))))) -> (~((e0) = (e1))) -> (((op (e2) (e0)) = (e1))\/(((op (e2) (e1)) = (e1))\/(((op (e2) (e2)) = (e1))\/((op (e2) (e3)) = (e1))))) -> (~((op (e2) (e0)) = (e0))) -> (((op (e2) (e0)) = (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) (e1)) = (e0)) -> (~((op (e1) (e1)) = (op (e3) (e1)))) -> (((op (e1) (e0)) = (e3))\/(((op (e1) (e1)) = (e3))\/(((op (e1) (e2)) = (e3))\/((op (e1) (e3)) = (e3))))) -> (~((e1) = (e3))) -> ((op (e1) (e0)) = (e1)) -> (~((op (e0) (e1)) = (op (e1) (e1)))) -> (((op (e2) (e1)) = (e0))\/(((op (e2) (e1)) = (e1))\/(((op (e2) (e1)) = (e2))\/((op (e2) (e1)) = (e3))))) -> (~((op (e2) (e1)) = (e0))) -> (~((op (e2) (e1)) = (op (e3) (e1)))) -> (~((op (e0) (e1)) = (op (e2) (e1)))) -> (~((op (e1) (e1)) = (op (e2) (e1)))) -> (~((op (e0) (e1)) = (e0))) -> (((op (e0) (e1)) = (e0))\/(((op (e0) (e1)) = (e1))\/(((op (e0) (e1)) = (e2))\/((op (e0) (e1)) = (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))))) -> (~((e0) = (e2))) -> (((op (e0) (e2)) = (e2))\/(((op (e1) (e2)) = (e2))\/(((op (e2) (e2)) = (e2))\/((op (e3) (e2)) = (e2))))) -> (~((op (e1) (e3)) = (op (e3) (e3)))) -> (~((op (e1) (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 (e3) (e1)) = (e0))) -> (((op (e3) (e1)) = (e0))\/(((op (e3) (e1)) = (e1))\/(((op (e3) (e1)) = (e2))\/((op (e3) (e1)) = (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) (e3)) = (op (e2) (e3)))) -> (((op (e2) (e3)) = (e0))\/(((op (e2) (e3)) = (e1))\/(((op (e2) (e3)) = (e2))\/((op (e2) (e3)) = (e3))))) -> (~((op (e0) (e3)) = (op (e3) (e3)))) -> (~((op (e0) (e3)) = (op (e1) (e3)))) -> ((op (e1) (e3)) = (e3)) -> ((op (e2) (e1)) = (e2)) -> (((op (e0) (e2)) = (e3))\/(((op (e1) (e2)) = (e3))\/(((op (e2) (e2)) = (e3))\/((op (e3) (e2)) = (e3))))) -> (~((e0) = (e3))) -> ((op (e0) (e2)) = (e0)) -> (~((e2) = (e3))) -> ((op (e1) (e2)) = (e2)) -> (~((op (e2) (e0)) = (op (e2) (e2)))) -> ((op (e2) (e0)) = (e3)) -> (~((op (e3) (e1)) = (op (e3) (e2)))) -> False). % 18.52/18.77 do 0 intro. intros zenon_H173 zenon_H18f zenon_H81 zenon_H1c4 zenon_H6d zenon_He8 zenon_H7b zenon_Ha0 zenon_H210 zenon_H115 zenon_Hf3 zenon_H4a zenon_H139 zenon_Hd8 zenon_H109 zenon_H54 zenon_H10a zenon_H1d5 zenon_H39 zenon_H6f zenon_H4f zenon_H6a zenon_H2b zenon_H44 zenon_H7c zenon_H153 zenon_H189 zenon_H71 zenon_H1a5 zenon_H1d8 zenon_H1c7 zenon_H133 zenon_H145 zenon_Ha1 zenon_H106 zenon_H30 zenon_H2f zenon_H18c zenon_H29 zenon_H160 zenon_H16f zenon_H95 zenon_H9d zenon_H10e zenon_H1cc zenon_H31 zenon_Haf zenon_H17e zenon_H13e zenon_H20b zenon_H212 zenon_H102 zenon_H62 zenon_H101 zenon_H149 zenon_H172 zenon_Hd5 zenon_H38 zenon_Hdf zenon_H130 zenon_H1ad zenon_H22a zenon_He4 zenon_Hdb zenon_He2 zenon_H11f zenon_Hc2 zenon_H1d zenon_Hdc zenon_H1ca zenon_H1a6 zenon_H9a zenon_H48 zenon_H12b zenon_H113 zenon_H52 zenon_H3b zenon_H1a4. % 18.52/18.77 apply (zenon_or_s _ _ zenon_H1a5); [ zenon_intro zenon_H99 | zenon_intro zenon_H1a8 ]. % 18.52/18.77 apply (zenon_L403_); trivial. % 18.52/18.77 apply (zenon_or_s _ _ zenon_H1a8); [ zenon_intro zenon_H13f | zenon_intro zenon_H1a9 ]. % 18.52/18.77 apply (zenon_L409_); trivial. % 18.52/18.77 apply (zenon_or_s _ _ zenon_H1a9); [ zenon_intro zenon_Ha6 | zenon_intro zenon_H161 ]. % 18.52/18.77 apply (zenon_L207_); trivial. % 18.52/18.77 apply (zenon_L372_); trivial. % 18.52/18.77 (* end of lemma zenon_L410_ *) % 18.52/18.77 assert (zenon_L411_ : ((op (e2) (e2)) = (e1)) -> (~((op (e2) (e2)) = (e2))) -> (~((op (e2) (e2)) = (op (e3) (e2)))) -> (~((op (e2) (e2)) = (e0))) -> (((op (e2) (e2)) = (e0))\/(((op (e2) (e2)) = (e1))\/(((op (e2) (e2)) = (e2))\/((op (e2) (e2)) = (e3))))) -> (~((op (e2) (e2)) = (op (e2) (e3)))) -> (((op (e3) (e0)) = (e1))\/(((op (e3) (e1)) = (e1))\/(((op (e3) (e2)) = (e1))\/((op (e3) (e3)) = (e1))))) -> ((op (e0) (e0)) = (e2)) -> ((op (e0) (e1)) = (e1)) -> (~((op (e0) (e1)) = (op (e3) (e1)))) -> (~((op (e1) (e2)) = (op (e3) (e2)))) -> (~((op (e2) (e3)) = (op (e3) (e3)))) -> (~((op (e0) (e1)) = (op (e0) (e2)))) -> (((op (e0) (e2)) = (e1))\/(((op (e1) (e2)) = (e1))\/(((op (e2) (e2)) = (e1))\/((op (e3) (e2)) = (e1))))) -> (~((op (e1) (e0)) = (op (e1) (e3)))) -> (((op (e0) (e1)) = (e1))\/(((op (e1) (e1)) = (e1))\/(((op (e2) (e1)) = (e1))\/((op (e3) (e1)) = (e1))))) -> (~((op (e0) (e1)) = (op (e0) (e3)))) -> (~((op (e1) (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 (e3) (e0)) = (op (e3) (e2)))) -> (~((op (e1) (e1)) = (op (e1) (e2)))) -> (((op (e0) (e2)) = (e0))\/(((op (e1) (e2)) = (e0))\/(((op (e2) (e2)) = (e0))\/((op (e3) (e2)) = (e0))))) -> (~((op (e1) (e2)) = (op (e2) (e2)))) -> ((op (e3) (e0)) = (e0)) -> (~((e1) = (e2))) -> (((op (e3) (e0)) = (e2))\/(((op (e3) (e1)) = (e2))\/(((op (e3) (e2)) = (e2))\/((op (e3) (e3)) = (e2))))) -> (~((op (e0) (e0)) = (op (e0) (e3)))) -> (~((op (e3) (e0)) = (op (e3) (e3)))) -> (((op (e0) (e1)) = (e3))\/(((op (e1) (e1)) = (e3))\/(((op (e2) (e1)) = (e3))\/((op (e3) (e1)) = (e3))))) -> (((op (e0) (e1)) = (e2))\/(((op (e1) (e1)) = (e2))\/(((op (e2) (e1)) = (e2))\/((op (e3) (e1)) = (e2))))) -> (~((op (e2) (e1)) = (op (e2) (e3)))) -> (((op (e0) (e3)) = (e1))\/(((op (e1) (e3)) = (e1))\/(((op (e2) (e3)) = (e1))\/((op (e3) (e3)) = (e1))))) -> (((op (e0) (e3)) = (e2))\/(((op (e1) (e3)) = (e2))\/(((op (e2) (e3)) = (e2))\/((op (e3) (e3)) = (e2))))) -> (~((e0) = (e1))) -> (((op (e2) (e0)) = (e1))\/(((op (e2) (e1)) = (e1))\/(((op (e2) (e2)) = (e1))\/((op (e2) (e3)) = (e1))))) -> (~((op (e2) (e0)) = (e0))) -> (((op (e2) (e0)) = (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) (e1)) = (e0)) -> (~((op (e1) (e1)) = (op (e3) (e1)))) -> (((op (e1) (e0)) = (e3))\/(((op (e1) (e1)) = (e3))\/(((op (e1) (e2)) = (e3))\/((op (e1) (e3)) = (e3))))) -> (~((e1) = (e3))) -> ((op (e1) (e0)) = (e1)) -> (~((op (e0) (e1)) = (op (e1) (e1)))) -> (((op (e2) (e1)) = (e0))\/(((op (e2) (e1)) = (e1))\/(((op (e2) (e1)) = (e2))\/((op (e2) (e1)) = (e3))))) -> (~((op (e2) (e1)) = (e0))) -> (~((op (e2) (e1)) = (op (e3) (e1)))) -> (~((op (e0) (e1)) = (op (e2) (e1)))) -> (~((op (e1) (e1)) = (op (e2) (e1)))) -> (~((op (e0) (e1)) = (e0))) -> (((op (e0) (e1)) = (e0))\/(((op (e0) (e1)) = (e1))\/(((op (e0) (e1)) = (e2))\/((op (e0) (e1)) = (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))))) -> (~((e0) = (e2))) -> (((op (e0) (e2)) = (e2))\/(((op (e1) (e2)) = (e2))\/(((op (e2) (e2)) = (e2))\/((op (e3) (e2)) = (e2))))) -> (~((op (e1) (e3)) = (op (e3) (e3)))) -> (~((op (e1) (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 (e3) (e1)) = (e0))) -> (((op (e3) (e1)) = (e0))\/(((op (e3) (e1)) = (e1))\/(((op (e3) (e1)) = (e2))\/((op (e3) (e1)) = (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) (e3)) = (op (e2) (e3)))) -> (((op (e2) (e3)) = (e0))\/(((op (e2) (e3)) = (e1))\/(((op (e2) (e3)) = (e2))\/((op (e2) (e3)) = (e3))))) -> (~((op (e0) (e3)) = (op (e3) (e3)))) -> (~((op (e0) (e3)) = (op (e1) (e3)))) -> ((op (e2) (e1)) = (e2)) -> (((op (e0) (e2)) = (e3))\/(((op (e1) (e2)) = (e3))\/(((op (e2) (e2)) = (e3))\/((op (e3) (e2)) = (e3))))) -> (~((e0) = (e3))) -> ((op (e0) (e2)) = (e0)) -> (~((e2) = (e3))) -> ((op (e1) (e2)) = (e2)) -> (~((op (e2) (e0)) = (op (e2) (e2)))) -> ((op (e2) (e0)) = (e3)) -> (~((op (e3) (e1)) = (op (e3) (e2)))) -> False). % 18.52/18.77 do 0 intro. intros zenon_Hf1 zenon_H173 zenon_H18f zenon_H81 zenon_H1c4 zenon_H6d zenon_He8 zenon_H7b zenon_Ha0 zenon_H210 zenon_H115 zenon_Hf3 zenon_H4a zenon_H139 zenon_Hd8 zenon_H109 zenon_H54 zenon_H10a zenon_H1d5 zenon_H39 zenon_H6f zenon_H4f zenon_H6a zenon_H2b zenon_H44 zenon_H7c zenon_H153 zenon_H189 zenon_H71 zenon_H1a5 zenon_H1d8 zenon_H1c7 zenon_H133 zenon_H145 zenon_Ha1 zenon_H106 zenon_H30 zenon_H2f zenon_H18c zenon_H29 zenon_H160 zenon_H16f zenon_H95 zenon_H9d zenon_H10e zenon_H1cc zenon_H31 zenon_Haf zenon_H17e zenon_H13e zenon_H20b zenon_H212 zenon_H102 zenon_H62 zenon_H101 zenon_H149 zenon_H172 zenon_Hd5 zenon_H38 zenon_Hdf zenon_H130 zenon_H1ad zenon_H22a zenon_He4 zenon_Hdb zenon_He2 zenon_H11f zenon_Hc2 zenon_H1d zenon_H1ca zenon_H1a6 zenon_H9a zenon_H48 zenon_H12b zenon_H113 zenon_H52 zenon_H3b zenon_H1a4. % 18.52/18.77 apply (zenon_or_s _ _ zenon_H1a6); [ zenon_intro zenon_Ha9 | zenon_intro zenon_H1aa ]. % 18.52/18.77 apply (zenon_L358_); trivial. % 18.52/18.77 apply (zenon_or_s _ _ zenon_H1aa); [ zenon_intro zenon_H16c | zenon_intro zenon_H1ab ]. % 18.52/18.77 apply (zenon_L116_); trivial. % 18.52/18.77 apply (zenon_or_s _ _ zenon_H1ab); [ zenon_intro zenon_Haa | zenon_intro zenon_H163 ]. % 18.52/18.77 apply (zenon_L168_); trivial. % 18.52/18.77 apply (zenon_or_s _ _ zenon_He8); [ zenon_intro zenon_Hac | zenon_intro zenon_Heb ]. % 18.52/18.77 apply (zenon_L362_); trivial. % 18.52/18.77 apply (zenon_or_s _ _ zenon_Heb); [ zenon_intro zenon_Hae | zenon_intro zenon_Hec ]. % 18.52/18.77 apply (zenon_L363_); trivial. % 18.52/18.77 apply (zenon_or_s _ _ zenon_Hec); [ zenon_intro zenon_Hba | zenon_intro zenon_Hc4 ]. % 18.52/18.77 apply (zenon_L185_); trivial. % 18.52/18.77 apply (zenon_or_s _ _ zenon_H153); [ zenon_intro zenon_H148 | zenon_intro zenon_H154 ]. % 18.52/18.77 apply (zenon_L100_); trivial. % 18.52/18.77 apply (zenon_or_s _ _ zenon_H154); [ zenon_intro zenon_H14d | zenon_intro zenon_H155 ]. % 18.52/18.77 apply (zenon_L399_); trivial. % 18.52/18.77 apply (zenon_or_s _ _ zenon_H155); [ zenon_intro zenon_H151 | zenon_intro zenon_Hf6 ]. % 18.52/18.77 apply (zenon_L401_); trivial. % 18.52/18.77 apply (zenon_or_s _ _ zenon_Hdf); [ zenon_intro zenon_H1f | zenon_intro zenon_He0 ]. % 18.52/18.77 exact (zenon_H38 zenon_H1f). % 18.52/18.77 apply (zenon_or_s _ _ zenon_He0); [ zenon_intro zenon_Hd6 | zenon_intro zenon_He1 ]. % 18.52/18.77 apply (zenon_L50_); trivial. % 18.52/18.77 apply (zenon_or_s _ _ zenon_He1); [ zenon_intro zenon_Hd7 | zenon_intro zenon_Hdc ]. % 18.52/18.77 apply (zenon_L402_); trivial. % 18.52/18.77 apply (zenon_L410_); trivial. % 18.52/18.77 (* end of lemma zenon_L411_ *) % 18.52/18.77 assert (zenon_L412_ : (((op (e2) (e1)) = (e0))\/(((op (e2) (e1)) = (e1))\/(((op (e2) (e1)) = (e2))\/((op (e2) (e1)) = (e3))))) -> (~((op (e2) (e1)) = (e0))) -> ((op (e0) (e1)) = (e1)) -> (~((op (e0) (e1)) = (op (e2) (e1)))) -> (~((op (e2) (e1)) = (op (e2) (e3)))) -> ((op (e2) (e3)) = (e2)) -> ((op (e0) (e1)) = (e2)) -> ((op (e1) (e1)) = (e0)) -> False). % 18.52/18.77 do 0 intro. intros zenon_H1cc zenon_H31 zenon_Ha0 zenon_H17e zenon_H1c7 zenon_H11d zenon_H10f zenon_H29. % 18.52/18.77 apply (zenon_or_s _ _ zenon_H1cc); [ zenon_intro zenon_H36 | zenon_intro zenon_H1cd ]. % 18.52/18.77 exact (zenon_H31 zenon_H36). % 18.52/18.77 apply (zenon_or_s _ _ zenon_H1cd); [ zenon_intro zenon_Ha5 | zenon_intro zenon_H1ce ]. % 18.52/18.77 apply (zenon_L357_); trivial. % 18.52/18.77 apply (zenon_or_s _ _ zenon_H1ce); [ zenon_intro zenon_H1ca | zenon_intro zenon_Ha6 ]. % 18.52/18.77 apply (zenon_L224_); trivial. % 18.52/18.77 apply (zenon_L371_); trivial. % 18.52/18.77 (* end of lemma zenon_L412_ *) % 18.52/18.77 assert (zenon_L413_ : ((op (e2) (e0)) = (e1)) -> ((op (e1) (e0)) = (e1)) -> (~((op (e1) (e0)) = (op (e2) (e0)))) -> False). % 18.52/18.77 do 0 intro. intros zenon_Hed zenon_H9d zenon_H201. % 18.52/18.77 elim (classic ((op (e2) (e0)) = (op (e2) (e0)))); [ zenon_intro zenon_H202 | zenon_intro zenon_H53 ]. % 18.52/18.77 cut (((op (e2) (e0)) = (op (e2) (e0))) = ((op (e1) (e0)) = (op (e2) (e0)))). % 18.52/18.77 intro zenon_D_pnotp. % 18.52/18.77 apply zenon_H201. % 18.52/18.77 rewrite <- zenon_D_pnotp. % 18.52/18.77 exact zenon_H202. % 18.52/18.77 cut (((op (e2) (e0)) = (op (e2) (e0)))); [idtac | apply NNPP; zenon_intro zenon_H53]. % 18.52/18.77 cut (((op (e2) (e0)) = (op (e1) (e0)))); [idtac | apply NNPP; zenon_intro zenon_H203]. % 18.52/18.77 congruence. % 18.52/18.77 cut (((op (e2) (e0)) = (e1)) = ((op (e2) (e0)) = (op (e1) (e0)))). % 18.52/18.77 intro zenon_D_pnotp. % 18.52/18.77 apply zenon_H203. % 18.52/18.77 rewrite <- zenon_D_pnotp. % 18.52/18.77 exact zenon_Hed. % 18.52/18.77 cut (((e1) = (op (e1) (e0)))); [idtac | apply NNPP; zenon_intro zenon_H20f]. % 18.52/18.77 cut (((op (e2) (e0)) = (op (e2) (e0)))); [idtac | apply NNPP; zenon_intro zenon_H53]. % 18.52/18.77 congruence. % 18.52/18.77 apply zenon_H53. apply refl_equal. % 18.52/18.77 apply zenon_H20f. apply sym_equal. exact zenon_H9d. % 18.52/18.77 apply zenon_H53. apply refl_equal. % 18.52/18.78 apply zenon_H53. apply refl_equal. % 18.52/18.78 (* end of lemma zenon_L413_ *) % 18.52/18.78 assert (zenon_L414_ : (((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 (e2) (e3)) = (e1)) -> (~((op (e2) (e3)) = (op (e3) (e3)))) -> (~((op (e3) (e1)) = (op (e3) (e3)))) -> ((op (e3) (e1)) = (e2)) -> (~((op (e3) (e3)) = (e3))) -> False). % 18.52/18.78 do 0 intro. intros zenon_H101 zenon_H71 zenon_H44 zenon_Hf4 zenon_Hf3 zenon_H130 zenon_H14d zenon_H102. % 18.52/18.78 apply (zenon_or_s _ _ zenon_H101); [ zenon_intro zenon_H60 | zenon_intro zenon_H103 ]. % 18.52/18.78 apply (zenon_L21_); trivial. % 18.52/18.78 apply (zenon_or_s _ _ zenon_H103); [ zenon_intro zenon_Hc4 | zenon_intro zenon_H104 ]. % 18.52/18.78 apply (zenon_L60_); trivial. % 18.52/18.78 apply (zenon_or_s _ _ zenon_H104); [ zenon_intro zenon_Hf6 | zenon_intro zenon_H105 ]. % 18.52/18.78 apply (zenon_L102_); trivial. % 18.52/18.78 exact (zenon_H102 zenon_H105). % 18.52/18.78 (* end of lemma zenon_L414_ *) % 18.52/18.78 assert (zenon_L415_ : (((op (e1) (e0)) = (e0))\/(((op (e1) (e1)) = (e0))\/(((op (e1) (e2)) = (e0))\/((op (e1) (e3)) = (e0))))) -> (~((op (e1) (e0)) = (e0))) -> (~((op (e2) (e0)) = (op (e2) (e2)))) -> ((op (e2) (e0)) = (e3)) -> (~((op (e2) (e2)) = (e2))) -> (~((op (e2) (e2)) = (op (e3) (e2)))) -> (~((op (e2) (e2)) = (e0))) -> (((op (e2) (e2)) = (e0))\/(((op (e2) (e2)) = (e1))\/(((op (e2) (e2)) = (e2))\/((op (e2) (e2)) = (e3))))) -> (~((op (e2) (e2)) = (op (e2) (e3)))) -> (((op (e3) (e0)) = (e1))\/(((op (e3) (e1)) = (e1))\/(((op (e3) (e2)) = (e1))\/((op (e3) (e3)) = (e1))))) -> ((op (e0) (e0)) = (e2)) -> ((op (e0) (e1)) = (e1)) -> (~((op (e0) (e1)) = (op (e3) (e1)))) -> (~((op (e1) (e2)) = (op (e3) (e2)))) -> (~((op (e2) (e3)) = (op (e3) (e3)))) -> (~((op (e0) (e1)) = (op (e0) (e2)))) -> (((op (e0) (e2)) = (e1))\/(((op (e1) (e2)) = (e1))\/(((op (e2) (e2)) = (e1))\/((op (e3) (e2)) = (e1))))) -> (~((e0) = (e1))) -> ((op (e3) (e0)) = (e0)) -> (~((op (e0) (e1)) = (op (e2) (e1)))) -> ((op (e1) (e0)) = (e1)) -> (~((op (e1) (e0)) = (op (e2) (e0)))) -> (((op (e2) (e0)) = (e1))\/(((op (e2) (e1)) = (e1))\/(((op (e2) (e2)) = (e1))\/((op (e2) (e3)) = (e1))))) -> (~((op (e2) (e1)) = (e0))) -> (~((op (e2) (e0)) = (e0))) -> (((op (e2) (e0)) = (e0))\/(((op (e2) (e1)) = (e0))\/(((op (e2) (e2)) = (e0))\/((op (e2) (e3)) = (e0))))) -> (((op (e2) (e3)) = (e0))\/(((op (e2) (e3)) = (e1))\/(((op (e2) (e3)) = (e2))\/((op (e2) (e3)) = (e3))))) -> (((op (e3) (e1)) = (e0))\/(((op (e3) (e1)) = (e1))\/(((op (e3) (e1)) = (e2))\/((op (e3) (e1)) = (e3))))) -> (~((op (e3) (e1)) = (e0))) -> (~((op (e1) (e0)) = (op (e1) (e3)))) -> (((op (e1) (e3)) = (e0))\/(((op (e1) (e3)) = (e1))\/(((op (e1) (e3)) = (e2))\/((op (e1) (e3)) = (e3))))) -> (~((op (e1) (e3)) = (op (e3) (e3)))) -> (((op (e0) (e3)) = (e0))\/(((op (e0) (e3)) = (e1))\/(((op (e0) (e3)) = (e2))\/((op (e0) (e3)) = (e3))))) -> (~((e2) = (e3))) -> (((op (e0) (e2)) = (e2))\/(((op (e1) (e2)) = (e2))\/(((op (e2) (e2)) = (e2))\/((op (e3) (e2)) = (e2))))) -> (~((e0) = (e2))) -> ((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) (e3)))) -> (~((op (e3) (e2)) = (op (e3) (e3)))) -> (~((op (e3) (e3)) = (e3))) -> (((op (e0) (e1)) = (e0))\/(((op (e0) (e1)) = (e1))\/(((op (e0) (e1)) = (e2))\/((op (e0) (e1)) = (e3))))) -> (~((op (e0) (e1)) = (e0))) -> (~((op (e1) (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 (e0) (e1)) = (op (e1) (e1)))) -> (~((e1) = (e3))) -> (((op (e1) (e0)) = (e3))\/(((op (e1) (e1)) = (e3))\/(((op (e1) (e2)) = (e3))\/((op (e1) (e3)) = (e3))))) -> (~((op (e1) (e1)) = (op (e3) (e1)))) -> (((op (e0) (e2)) = (e3))\/(((op (e1) (e2)) = (e3))\/(((op (e2) (e2)) = (e3))\/((op (e3) (e2)) = (e3))))) -> (~((e0) = (e3))) -> (~((op (e3) (e1)) = (op (e3) (e2)))) -> (((op (e1) (e0)) = (e2))\/(((op (e1) (e1)) = (e2))\/(((op (e1) (e2)) = (e2))\/((op (e1) (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) (e1)) = (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)) = (e3))\/(((op (e2) (e1)) = (e3))\/((op (e3) (e1)) = (e3))))) -> (~((op (e3) (e0)) = (op (e3) (e3)))) -> (~((op (e0) (e0)) = (op (e0) (e3)))) -> (((op (e3) (e0)) = (e2))\/(((op (e3) (e1)) = (e2))\/(((op (e3) (e2)) = (e2))\/((op (e3) (e3)) = (e2))))) -> (~((e1) = (e2))) -> (~((op (e1) (e2)) = (op (e2) (e2)))) -> (((op (e0) (e2)) = (e0))\/(((op (e1) (e2)) = (e0))\/(((op (e2) (e2)) = (e0))\/((op (e3) (e2)) = (e0))))) -> (~((op (e1) (e1)) = (op (e1) (e2)))) -> (~((op (e3) (e0)) = (op (e3) (e2)))) -> (~((op (e1) (e3)) = (op (e2) (e3)))) -> (~((op (e0) (e0)) = (op (e2) (e0)))) -> (((op (e2) (e0)) = (e2))\/(((op (e2) (e1)) = (e2))\/(((op (e2) (e2)) = (e2))\/((op (e2) (e3)) = (e2))))) -> (~((op (e0) (e3)) = (op (e3) (e3)))) -> (~((op (e1) (e1)) = (e1))) -> (~((op (e0) (e1)) = (op (e0) (e3)))) -> (((op (e0) (e1)) = (e1))\/(((op (e1) (e1)) = (e1))\/(((op (e2) (e1)) = (e1))\/((op (e3) (e1)) = (e1))))) -> (~((op (e0) (e3)) = (op (e2) (e3)))) -> (~((op (e0) (e3)) = (op (e1) (e3)))) -> (~((op (e1) (e2)) = (e0))) -> (~((op (e1) (e3)) = (e0))) -> False). % 18.52/18.78 do 0 intro. intros zenon_H22 zenon_H23 zenon_H52 zenon_H3b zenon_H173 zenon_H18f zenon_H81 zenon_H1c4 zenon_H6d zenon_He8 zenon_H7b zenon_Ha0 zenon_H210 zenon_H115 zenon_Hf3 zenon_H4a zenon_H139 zenon_Ha1 zenon_H44 zenon_H17e zenon_H9d zenon_H201 zenon_H106 zenon_H31 zenon_H30 zenon_H2f zenon_H11f zenon_H22a zenon_H1ad zenon_Hd8 zenon_Hdf zenon_Hd5 zenon_He4 zenon_H12b zenon_H172 zenon_H149 zenon_H48 zenon_H101 zenon_H130 zenon_H62 zenon_H102 zenon_H212 zenon_H20b zenon_H13e zenon_Haf zenon_H1cc zenon_H10e zenon_H95 zenon_H16f zenon_H160 zenon_H1a6 zenon_H9a zenon_H1a4 zenon_H18c zenon_H145 zenon_H133 zenon_H1c7 zenon_H1d8 zenon_H1a5 zenon_H71 zenon_H189 zenon_H153 zenon_H7c zenon_H2b zenon_H6a zenon_H4f zenon_H6f zenon_Hdb zenon_H39 zenon_H1d5 zenon_Hc2 zenon_H10a zenon_H54 zenon_H109 zenon_He2 zenon_H1d zenon_H25 zenon_H38. % 18.52/18.78 apply (zenon_or_s _ _ zenon_H22); [ zenon_intro zenon_H27 | zenon_intro zenon_H26 ]. % 18.52/18.78 exact (zenon_H23 zenon_H27). % 18.52/18.78 apply (zenon_or_s _ _ zenon_H26); [ zenon_intro zenon_H29 | zenon_intro zenon_H28 ]. % 18.52/18.78 apply (zenon_or_s _ _ zenon_H18c); [ zenon_intro zenon_H86 | zenon_intro zenon_H18d ]. % 18.52/18.78 apply (zenon_L123_); trivial. % 18.52/18.78 apply (zenon_or_s _ _ zenon_H18d); [ zenon_intro zenon_H110 | zenon_intro zenon_H18e ]. % 18.52/18.78 apply (zenon_L354_); trivial. % 18.52/18.78 apply (zenon_or_s _ _ zenon_H18e); [ zenon_intro zenon_H113 | zenon_intro zenon_Hd7 ]. % 18.52/18.78 apply (zenon_or_s _ _ zenon_H1d8); [ zenon_intro zenon_H10f | zenon_intro zenon_H1d9 ]. % 18.52/18.78 apply (zenon_or_s _ _ zenon_H106); [ zenon_intro zenon_Hed | zenon_intro zenon_H107 ]. % 18.52/18.78 apply (zenon_L356_); trivial. % 18.52/18.78 apply (zenon_or_s _ _ zenon_H107); [ zenon_intro zenon_Ha5 | zenon_intro zenon_H108 ]. % 18.52/18.78 apply (zenon_L357_); trivial. % 18.52/18.78 apply (zenon_or_s _ _ zenon_H108); [ zenon_intro zenon_Hf1 | zenon_intro zenon_Hf4 ]. % 18.52/18.78 apply (zenon_or_s _ _ zenon_H1d5); [ zenon_intro zenon_Hee | zenon_intro zenon_H1d6 ]. % 18.52/18.78 apply (zenon_L341_); trivial. % 18.52/18.78 apply (zenon_or_s _ _ zenon_H1d6); [ zenon_intro zenon_H1ca | zenon_intro zenon_H1d7 ]. % 18.52/18.78 apply (zenon_L411_); trivial. % 18.52/18.78 apply (zenon_or_s _ _ zenon_H1d7); [ zenon_intro zenon_H176 | zenon_intro zenon_H11d ]. % 18.52/18.78 exact (zenon_H173 zenon_H176). % 18.52/18.78 apply (zenon_L412_); trivial. % 18.52/18.78 apply (zenon_L408_); trivial. % 18.52/18.78 apply (zenon_or_s _ _ zenon_H1d9); [ zenon_intro zenon_H110 | zenon_intro zenon_H1da ]. % 18.52/18.78 apply (zenon_L354_); trivial. % 18.52/18.78 apply (zenon_or_s _ _ zenon_H1da); [ zenon_intro zenon_H1ca | zenon_intro zenon_H14d ]. % 18.52/18.78 apply (zenon_or_s _ _ zenon_H16f); [ zenon_intro zenon_H9e | zenon_intro zenon_H170 ]. % 18.52/18.78 apply (zenon_L37_); trivial. % 18.52/18.78 apply (zenon_or_s _ _ zenon_H170); [ zenon_intro zenon_H13f | zenon_intro zenon_H171 ]. % 18.52/18.78 apply (zenon_or_s _ _ zenon_H106); [ zenon_intro zenon_Hed | zenon_intro zenon_H107 ]. % 18.52/18.78 apply (zenon_L413_); trivial. % 18.52/18.78 apply (zenon_or_s _ _ zenon_H107); [ zenon_intro zenon_Ha5 | zenon_intro zenon_H108 ]. % 18.52/18.78 apply (zenon_L373_); trivial. % 18.52/18.78 apply (zenon_or_s _ _ zenon_H108); [ zenon_intro zenon_Hf1 | zenon_intro zenon_Hf4 ]. % 18.52/18.78 apply (zenon_L411_); trivial. % 18.52/18.78 apply (zenon_L408_); trivial. % 18.52/18.78 apply (zenon_or_s _ _ zenon_H171); [ zenon_intro zenon_H16c | zenon_intro zenon_Hdc ]. % 18.52/18.78 apply (zenon_L116_); trivial. % 18.52/18.78 apply (zenon_L410_); trivial. % 18.52/18.78 apply (zenon_or_s _ _ zenon_H16f); [ zenon_intro zenon_H9e | zenon_intro zenon_H170 ]. % 18.52/18.78 apply (zenon_L37_); trivial. % 18.52/18.78 apply (zenon_or_s _ _ zenon_H170); [ zenon_intro zenon_H13f | zenon_intro zenon_H171 ]. % 18.52/18.78 apply (zenon_or_s _ _ zenon_H106); [ zenon_intro zenon_Hed | zenon_intro zenon_H107 ]. % 18.52/18.78 apply (zenon_L413_); trivial. % 18.52/18.78 apply (zenon_or_s _ _ zenon_H107); [ zenon_intro zenon_Ha5 | zenon_intro zenon_H108 ]. % 18.52/18.78 apply (zenon_L390_); trivial. % 18.52/18.78 apply (zenon_or_s _ _ zenon_H108); [ zenon_intro zenon_Hf1 | zenon_intro zenon_Hf4 ]. % 18.52/18.78 apply (zenon_L399_); trivial. % 18.52/18.78 apply (zenon_L414_); trivial. % 18.52/18.78 apply (zenon_or_s _ _ zenon_H171); [ zenon_intro zenon_H16c | zenon_intro zenon_Hdc ]. % 18.52/18.78 apply (zenon_L116_); trivial. % 18.52/18.78 apply (zenon_L398_); trivial. % 18.52/18.78 apply (zenon_or_s _ _ zenon_H2f); [ zenon_intro zenon_H34 | zenon_intro zenon_H33 ]. % 18.52/18.78 exact (zenon_H30 zenon_H34). % 18.52/18.78 apply (zenon_or_s _ _ zenon_H33); [ zenon_intro zenon_H36 | zenon_intro zenon_H35 ]. % 18.52/18.78 exact (zenon_H31 zenon_H36). % 18.52/18.78 apply (zenon_or_s _ _ zenon_H35); [ zenon_intro zenon_H2c | zenon_intro zenon_H37 ]. % 18.52/18.78 exact (zenon_H81 zenon_H2c). % 18.52/18.78 apply (zenon_or_s _ _ zenon_H106); [ zenon_intro zenon_Hed | zenon_intro zenon_H107 ]. % 18.52/18.78 apply (zenon_L413_); trivial. % 18.52/18.78 apply (zenon_or_s _ _ zenon_H107); [ zenon_intro zenon_Ha5 | zenon_intro zenon_H108 ]. % 18.52/18.78 apply (zenon_L357_); trivial. % 18.52/18.78 apply (zenon_or_s _ _ zenon_H108); [ zenon_intro zenon_Hf1 | zenon_intro zenon_Hf4 ]. % 18.52/18.78 apply (zenon_or_s _ _ zenon_He8); [ zenon_intro zenon_Hac | zenon_intro zenon_Heb ]. % 18.52/18.78 apply (zenon_L41_); trivial. % 18.52/18.78 apply (zenon_or_s _ _ zenon_Heb); [ zenon_intro zenon_Hae | zenon_intro zenon_Hec ]. % 18.52/18.78 apply (zenon_L363_); trivial. % 18.52/18.78 apply (zenon_or_s _ _ zenon_Hec); [ zenon_intro zenon_Hba | zenon_intro zenon_Hc4 ]. % 18.52/18.78 apply (zenon_L185_); trivial. % 18.52/18.78 apply (zenon_L72_); trivial. % 18.52/18.78 apply (zenon_L408_); trivial. % 18.52/18.78 apply (zenon_or_s _ _ zenon_H28); [ zenon_intro zenon_H2a | zenon_intro zenon_H1f ]. % 18.52/18.78 exact (zenon_H25 zenon_H2a). % 18.52/18.78 exact (zenon_H38 zenon_H1f). % 18.52/18.78 (* end of lemma zenon_L415_ *) % 18.52/18.78 assert (zenon_L416_ : (((op (e1) (e0)) = (e0))\/(((op (e1) (e1)) = (e0))\/(((op (e1) (e2)) = (e0))\/((op (e1) (e3)) = (e0))))) -> (~((op (e1) (e0)) = (e0))) -> (~((e2) = (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) (e3)) = (e0))\/(((op (e3) (e3)) = (e1))\/(((op (e3) (e3)) = (e2))\/((op (e3) (e3)) = (e3))))) -> ((op (e0) (e3)) = (e1)) -> (~((op (e3) (e1)) = (op (e3) (e3)))) -> (~((op (e3) (e2)) = (op (e3) (e3)))) -> (~((op (e3) (e3)) = (e3))) -> (((op (e0) (e1)) = (e0))\/(((op (e0) (e1)) = (e1))\/(((op (e0) (e1)) = (e2))\/((op (e0) (e1)) = (e3))))) -> (~((op (e0) (e1)) = (e0))) -> (~((op (e0) (e1)) = (op (e3) (e1)))) -> (~((op (e1) (e1)) = (op (e2) (e1)))) -> (~((op (e0) (e1)) = (op (e2) (e1)))) -> (~((op (e2) (e1)) = (op (e3) (e1)))) -> (~((op (e2) (e1)) = (e0))) -> (((op (e2) (e1)) = (e0))\/(((op (e2) (e1)) = (e1))\/(((op (e2) (e1)) = (e2))\/((op (e2) (e1)) = (e3))))) -> (~((op (e0) (e1)) = (op (e1) (e1)))) -> ((op (e1) (e0)) = (e1)) -> (~((e1) = (e3))) -> (((op (e1) (e0)) = (e3))\/(((op (e1) (e1)) = (e3))\/(((op (e1) (e2)) = (e3))\/((op (e1) (e3)) = (e3))))) -> (~((op (e1) (e1)) = (op (e3) (e1)))) -> (((op (e0) (e2)) = (e3))\/(((op (e1) (e2)) = (e3))\/(((op (e2) (e2)) = (e3))\/((op (e3) (e2)) = (e3))))) -> (~((e0) = (e3))) -> (~((op (e2) (e0)) = (op (e2) (e2)))) -> ((op (e2) (e0)) = (e3)) -> (~((op (e3) (e1)) = (op (e3) (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)) = (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) (e2)) = (e0))) -> (((op (e2) (e2)) = (e0))\/(((op (e2) (e2)) = (e1))\/(((op (e2) (e2)) = (e2))\/((op (e2) (e2)) = (e3))))) -> (~((e0) = (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 (e2) (e2)) = (op (e2) (e3)))) -> (((op (e0) (e3)) = (e1))\/(((op (e1) (e3)) = (e1))\/(((op (e2) (e3)) = (e1))\/((op (e3) (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) (e1)) = (e3))\/(((op (e1) (e1)) = (e3))\/(((op (e2) (e1)) = (e3))\/((op (e3) (e1)) = (e3))))) -> (~((op (e3) (e0)) = (op (e3) (e3)))) -> ((op (e0) (e0)) = (e2)) -> (~((op (e0) (e0)) = (op (e0) (e3)))) -> (((op (e3) (e0)) = (e2))\/(((op (e3) (e1)) = (e2))\/(((op (e3) (e2)) = (e2))\/((op (e3) (e3)) = (e2))))) -> (~((op (e0) (e3)) = (op (e2) (e3)))) -> (~((e1) = (e2))) -> ((op (e3) (e0)) = (e0)) -> (~((op (e1) (e2)) = (op (e2) (e2)))) -> (((op (e0) (e2)) = (e0))\/(((op (e1) (e2)) = (e0))\/(((op (e2) (e2)) = (e0))\/((op (e3) (e2)) = (e0))))) -> (~((op (e1) (e1)) = (op (e1) (e2)))) -> (~((op (e3) (e0)) = (op (e3) (e2)))) -> (~((op (e1) (e3)) = (op (e2) (e3)))) -> (~((op (e0) (e0)) = (op (e2) (e0)))) -> (((op (e2) (e0)) = (e2))\/(((op (e2) (e1)) = (e2))\/(((op (e2) (e2)) = (e2))\/((op (e2) (e3)) = (e2))))) -> (~((op (e0) (e3)) = (op (e3) (e3)))) -> (((op (e3) (e0)) = (e1))\/(((op (e3) (e1)) = (e1))\/(((op (e3) (e2)) = (e1))\/((op (e3) (e3)) = (e1))))) -> (~((op (e1) (e1)) = (e1))) -> (~((op (e0) (e1)) = (op (e0) (e3)))) -> (((op (e0) (e1)) = (e1))\/(((op (e1) (e1)) = (e1))\/(((op (e2) (e1)) = (e1))\/((op (e3) (e1)) = (e1))))) -> (~((op (e1) (e2)) = (e0))) -> (~((op (e1) (e3)) = (e0))) -> False). % 18.52/18.78 do 0 intro. intros zenon_H22 zenon_H23 zenon_H12b zenon_H172 zenon_H149 zenon_H48 zenon_H173 zenon_H101 zenon_Hc3 zenon_H130 zenon_H62 zenon_H102 zenon_H212 zenon_H20b zenon_H210 zenon_H13e zenon_H17e zenon_Haf zenon_H31 zenon_H1cc zenon_H10e zenon_H9d zenon_H95 zenon_H16f zenon_H160 zenon_H1a6 zenon_H9a zenon_H52 zenon_H3b zenon_H1a4 zenon_H18c zenon_H2f zenon_H30 zenon_H106 zenon_H18f zenon_H81 zenon_H1c4 zenon_Ha1 zenon_H139 zenon_H145 zenon_H6d zenon_H133 zenon_H1c7 zenon_H1d8 zenon_H1a5 zenon_H71 zenon_H7b zenon_H189 zenon_H153 zenon_He2 zenon_H7c zenon_H44 zenon_H2b zenon_H6a zenon_H4f zenon_H6f zenon_Hdb zenon_H39 zenon_H1d5 zenon_Hc2 zenon_He8 zenon_H10a zenon_H54 zenon_H109 zenon_H25 zenon_H38. % 18.52/18.78 apply (zenon_or_s _ _ zenon_H22); [ zenon_intro zenon_H27 | zenon_intro zenon_H26 ]. % 18.52/18.78 exact (zenon_H23 zenon_H27). % 18.52/18.78 apply (zenon_or_s _ _ zenon_H26); [ zenon_intro zenon_H29 | zenon_intro zenon_H28 ]. % 18.52/18.78 apply (zenon_L395_); trivial. % 18.52/18.78 apply (zenon_or_s _ _ zenon_H28); [ zenon_intro zenon_H2a | zenon_intro zenon_H1f ]. % 18.52/18.78 exact (zenon_H25 zenon_H2a). % 18.52/18.78 exact (zenon_H38 zenon_H1f). % 18.52/18.78 (* end of lemma zenon_L416_ *) % 18.52/18.78 assert (zenon_L417_ : ((~((op (e2) (e2)) = (e0)))\/((op (e2) (e0)) = (e2))) -> (((op (e2) (e0)) = (e0))\/(((op (e2) (e1)) = (e0))\/(((op (e2) (e2)) = (e0))\/((op (e2) (e3)) = (e0))))) -> (~((op (e2) (e1)) = (e0))) -> (~((op (e2) (e0)) = (e0))) -> ((~((op (e3) (e0)) = (e0)))\/((op (e3) (e0)) = (e0))) -> ((~((op (e3) (e2)) = (e0)))\/((op (e3) (e0)) = (e2))) -> (~((op (e0) (e1)) = (e0))) -> (((op (e0) (e0)) = (e1))\/(((op (e0) (e1)) = (e1))\/(((op (e0) (e2)) = (e1))\/((op (e0) (e3)) = (e1))))) -> (~((op (e0) (e0)) = (op (e2) (e0)))) -> ((op (e0) (e0)) = (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) (e2)) = (op (e2) (e3)))) -> (~((op (e1) (e0)) = (op (e1) (e3)))) -> (~((op (e0) (e1)) = (op (e0) (e3)))) -> (~((op (e0) (e1)) = (op (e3) (e1)))) -> (~((op (e0) (e1)) = (op (e0) (e2)))) -> (~((op (e1) (e2)) = (op (e3) (e2)))) -> (~((op (e2) (e3)) = (op (e3) (e3)))) -> (((op (e2) (e3)) = (e0))\/(((op (e2) (e3)) = (e1))\/(((op (e2) (e3)) = (e2))\/((op (e2) (e3)) = (e3))))) -> (((op (e3) (e1)) = (e0))\/(((op (e3) (e1)) = (e1))\/(((op (e3) (e1)) = (e2))\/((op (e3) (e1)) = (e3))))) -> (~((op (e2) (e1)) = (op (e3) (e1)))) -> (((op (e1) (e3)) = (e0))\/(((op (e1) (e3)) = (e1))\/(((op (e1) (e3)) = (e2))\/((op (e1) (e3)) = (e3))))) -> (~((op (e0) (e3)) = (op (e2) (e3)))) -> (((op (e0) (e1)) = (e1))\/(((op (e1) (e1)) = (e1))\/(((op (e2) (e1)) = (e1))\/((op (e3) (e1)) = (e1))))) -> (((op (e2) (e0)) = (e1))\/(((op (e2) (e1)) = (e1))\/(((op (e2) (e2)) = (e1))\/((op (e2) (e3)) = (e1))))) -> (((op (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)) = (op (e0) (e3)))) -> (((op (e1) (e0)) = (e2))\/(((op (e1) (e1)) = (e2))\/(((op (e1) (e2)) = (e2))\/((op (e1) (e3)) = (e2))))) -> (~((op (e1) (e1)) = (op (e3) (e1)))) -> (((op (e0) (e2)) = (e2))\/(((op (e1) (e2)) = (e2))\/(((op (e2) (e2)) = (e2))\/((op (e3) (e2)) = (e2))))) -> (~((op (e3) (e1)) = (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) (e0)) = (e3))\/(((op (e1) (e1)) = (e3))\/(((op (e1) (e2)) = (e3))\/((op (e1) (e3)) = (e3))))) -> (((op (e3) (e0)) = (e2))\/(((op (e3) (e1)) = (e2))\/(((op (e3) (e2)) = (e2))\/((op (e3) (e3)) = (e2))))) -> (~((op (e1) (e2)) = (op (e2) (e2)))) -> (~((op (e1) (e1)) = (op (e1) (e2)))) -> (~((op (e3) (e0)) = (op (e3) (e2)))) -> (((op (e0) (e2)) = (e0))\/(((op (e1) (e2)) = (e0))\/(((op (e2) (e2)) = (e0))\/((op (e3) (e2)) = (e0))))) -> (~((op (e0) (e3)) = (op (e3) (e3)))) -> (((op (e2) (e1)) = (e0))\/(((op (e2) (e1)) = (e1))\/(((op (e2) (e1)) = (e2))\/((op (e2) (e1)) = (e3))))) -> (~((op (e1) (e1)) = (op (e2) (e1)))) -> (~((op (e0) (e1)) = (op (e1) (e1)))) -> (((op (e0) (e1)) = (e0))\/(((op (e0) (e1)) = (e1))\/(((op (e0) (e1)) = (e2))\/((op (e0) (e1)) = (e3))))) -> (((op (e0) (e2)) = (e3))\/(((op (e1) (e2)) = (e3))\/(((op (e2) (e2)) = (e3))\/((op (e3) (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 (e2) (e0)) = (e2))\/(((op (e2) (e1)) = (e2))\/(((op (e2) (e2)) = (e2))\/((op (e2) (e3)) = (e2))))) -> (~((op (e1) (e1)) = (e1))) -> (~((op (e0) (e3)) = (op (e1) (e3)))) -> (((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 (e3) (e0)) = (e1))\/(((op (e3) (e1)) = (e1))\/(((op (e3) (e2)) = (e1))\/((op (e3) (e3)) = (e1))))) -> (~((op (e1) (e3)) = (e0))) -> (~((e2) = (e3))) -> (~((e0) = (e3))) -> (~((op (e0) (e1)) = (op (e2) (e1)))) -> (~((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) (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 (e1) (e0)) = (op (e2) (e0)))) -> (~((e0) = (e2))) -> ((op (e1) (e0)) = (e1)) -> (~((e1) = (e2))) -> (~((op (e1) (e2)) = (e0))) -> (((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) (e0)) = (e0))\/(((op (e0) (e1)) = (e0))\/(((op (e0) (e2)) = (e0))\/((op (e0) (e3)) = (e0))))) -> ((~((op (e3) (e1)) = (e0)))\/((op (e3) (e0)) = (e1))) -> (~((op (e0) (e0)) = (e0))) -> (~((op (e1) (e0)) = (e0))) -> (((op (e0) (e0)) = (e0))\/(((op (e1) (e0)) = (e0))\/(((op (e2) (e0)) = (e0))\/((op (e3) (e0)) = (e0))))) -> ((~((op (e2) (e3)) = (e0)))\/((op (e2) (e0)) = (e3))) -> False). % 18.52/18.78 do 0 intro. intros zenon_H185 zenon_H2f zenon_H31 zenon_H30 zenon_H184 zenon_H1a7 zenon_H20b zenon_H22d zenon_H39 zenon_H7b zenon_H133 zenon_H71 zenon_H6d zenon_Hd8 zenon_H54 zenon_H210 zenon_H4a zenon_H115 zenon_Hf3 zenon_H11f zenon_H22a zenon_Haf zenon_Hdf zenon_He2 zenon_H109 zenon_H106 zenon_H145 zenon_H1c7 zenon_H1d8 zenon_H189 zenon_H18c zenon_H160 zenon_H172 zenon_H130 zenon_H62 zenon_H102 zenon_H101 zenon_H16f zenon_H153 zenon_H2b zenon_H4f zenon_H6f zenon_H6a zenon_Hc2 zenon_H1cc zenon_H13e zenon_H10e zenon_H212 zenon_H1a6 zenon_H1a4 zenon_H1a5 zenon_H1d5 zenon_H10a zenon_H1d zenon_He4 zenon_Hdb zenon_Hd5 zenon_He8 zenon_H38 zenon_H12b zenon_H9a zenon_H17e zenon_Ha1 zenon_H52 zenon_H1c4 zenon_H173 zenon_H18f zenon_H139 zenon_H201 zenon_H149 zenon_H9d zenon_H7c zenon_H25 zenon_H22 zenon_H3a zenon_H95 zenon_H208 zenon_H74 zenon_H1ed zenon_H3f zenon_H23 zenon_H3e zenon_H94. % 18.52/18.78 apply (zenon_or_s _ _ zenon_H185); [ zenon_intro zenon_H81 | zenon_intro zenon_Hee ]. % 18.52/18.78 apply (zenon_or_s _ _ zenon_H94); [ zenon_intro zenon_H32 | zenon_intro zenon_H3b ]. % 18.52/18.78 apply (zenon_L27_); trivial. % 18.52/18.78 apply (zenon_or_s _ _ zenon_H184); [ zenon_intro zenon_H40 | zenon_intro zenon_H44 ]. % 18.52/18.78 apply (zenon_L7_); trivial. % 18.52/18.78 apply (zenon_or_s _ _ zenon_H1ed); [ zenon_intro zenon_H1ad | zenon_intro zenon_Hac ]. % 18.52/18.78 apply (zenon_or_s _ _ zenon_H1a7); [ zenon_intro zenon_H18b | zenon_intro zenon_H148 ]. % 18.52/18.78 apply (zenon_or_s _ _ zenon_H74); [ zenon_intro zenon_H42 | zenon_intro zenon_H77 ]. % 18.52/18.78 exact (zenon_H3f zenon_H42). % 18.52/18.78 apply (zenon_or_s _ _ zenon_H77); [ zenon_intro zenon_H49 | zenon_intro zenon_H78 ]. % 18.52/18.78 exact (zenon_H20b zenon_H49). % 18.52/18.78 apply (zenon_or_s _ _ zenon_H78); [ zenon_intro zenon_H48 | zenon_intro zenon_H1e ]. % 18.52/18.78 apply (zenon_or_s _ _ zenon_H22d); [ zenon_intro zenon_H7a | zenon_intro zenon_H22e ]. % 18.52/18.78 apply (zenon_L35_); trivial. % 18.52/18.78 apply (zenon_or_s _ _ zenon_H22e); [ zenon_intro zenon_Ha0 | zenon_intro zenon_H22f ]. % 18.52/18.78 apply (zenon_L415_); trivial. % 18.52/18.78 apply (zenon_or_s _ _ zenon_H22f); [ zenon_intro zenon_H122 | zenon_intro zenon_Hc3 ]. % 18.52/18.78 apply (zenon_L355_); trivial. % 18.52/18.78 apply (zenon_L416_); trivial. % 18.52/18.78 apply (zenon_L337_); trivial. % 18.52/18.78 apply (zenon_L100_); trivial. % 18.52/18.78 apply (zenon_L308_); trivial. % 18.52/18.78 apply (zenon_L341_); trivial. % 18.52/18.78 (* end of lemma zenon_L417_ *) % 18.52/18.78 assert (zenon_L418_ : (((op (e3) (e1)) = (e0))\/(((op (e3) (e1)) = (e1))\/(((op (e3) (e1)) = (e2))\/((op (e3) (e1)) = (e3))))) -> (~((op (e3) (e1)) = (e0))) -> ((op (e0) (e1)) = (e1)) -> ((op (e0) (e1)) = (e2)) -> (~((op (e0) (e1)) = (op (e3) (e1)))) -> ((op (e3) (e0)) = (e3)) -> (~((op (e3) (e0)) = (op (e3) (e1)))) -> False). % 18.52/18.78 do 0 intro. intros zenon_H22a zenon_H1ad zenon_Ha0 zenon_H10f zenon_H210 zenon_H15e zenon_H1cf. % 18.52/18.78 apply (zenon_or_s _ _ zenon_H22a); [ zenon_intro zenon_H1b1 | zenon_intro zenon_H22b ]. % 18.52/18.78 exact (zenon_H1ad zenon_H1b1). % 18.52/18.78 apply (zenon_or_s _ _ zenon_H22b); [ zenon_intro zenon_Hae | zenon_intro zenon_H22c ]. % 18.52/18.78 apply (zenon_L363_); trivial. % 18.52/18.78 apply (zenon_or_s _ _ zenon_H22c); [ zenon_intro zenon_H14d | zenon_intro zenon_H161 ]. % 18.52/18.78 apply (zenon_L389_); trivial. % 18.52/18.78 apply (zenon_L193_); trivial. % 18.52/18.78 (* end of lemma zenon_L418_ *) % 18.52/18.78 assert (zenon_L419_ : (((op (e0) (e3)) = (e1))\/(((op (e1) (e3)) = (e1))\/(((op (e2) (e3)) = (e1))\/((op (e3) (e3)) = (e1))))) -> (~((op (e0) (e1)) = (op (e0) (e3)))) -> ((op (e0) (e1)) = (e1)) -> (~((op (e1) (e0)) = (op (e1) (e3)))) -> ((op (e1) (e0)) = (e1)) -> (~((op (e2) (e2)) = (op (e2) (e3)))) -> ((op (e2) (e2)) = (e1)) -> ((op (e3) (e2)) = (e1)) -> (~((op (e3) (e2)) = (op (e3) (e3)))) -> False). % 18.52/18.78 do 0 intro. intros zenon_H133 zenon_H54 zenon_Ha0 zenon_Hd8 zenon_H9d zenon_H6d zenon_Hf1 zenon_Hba zenon_H62. % 18.52/18.78 apply (zenon_or_s _ _ zenon_H133); [ zenon_intro zenon_Hc3 | zenon_intro zenon_H134 ]. % 18.52/18.78 apply (zenon_L359_); trivial. % 18.52/18.78 apply (zenon_or_s _ _ zenon_H134); [ zenon_intro zenon_Hd6 | zenon_intro zenon_H135 ]. % 18.52/18.78 apply (zenon_L360_); trivial. % 18.52/18.78 apply (zenon_or_s _ _ zenon_H135); [ zenon_intro zenon_Hf4 | zenon_intro zenon_Hc4 ]. % 18.52/18.78 apply (zenon_L84_); trivial. % 18.52/18.78 apply (zenon_L147_); trivial. % 18.52/18.78 (* end of lemma zenon_L419_ *) % 18.52/18.78 assert (zenon_L420_ : (~((op (e3) (e0)) = (op (e3) (e2)))) -> ((op (e3) (e0)) = (e2)) -> ((op (e3) (e2)) = (e2)) -> False). % 18.52/18.78 do 0 intro. intros zenon_H6f zenon_H148 zenon_H151. % 18.52/18.78 cut (((op (e3) (e0)) = (e2)) = ((op (e3) (e0)) = (op (e3) (e2)))). % 18.52/18.78 intro zenon_D_pnotp. % 18.52/18.78 apply zenon_H6f. % 18.52/18.78 rewrite <- zenon_D_pnotp. % 18.52/18.78 exact zenon_H148. % 18.52/18.78 cut (((e2) = (op (e3) (e2)))); [idtac | apply NNPP; zenon_intro zenon_H152]. % 18.52/18.78 cut (((op (e3) (e0)) = (op (e3) (e0)))); [idtac | apply NNPP; zenon_intro zenon_H70]. % 18.52/18.78 congruence. % 18.52/18.78 apply zenon_H70. apply refl_equal. % 18.52/18.78 apply zenon_H152. apply sym_equal. exact zenon_H151. % 18.52/18.78 (* end of lemma zenon_L420_ *) % 18.52/18.78 assert (zenon_L421_ : (((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))) -> (~((op (e3) (e0)) = (op (e3) (e2)))) -> ((op (e3) (e0)) = (e2)) -> False). % 18.52/18.78 do 0 intro. intros zenon_H172 zenon_H149 zenon_H48 zenon_H12b zenon_H16c zenon_H173 zenon_H6f zenon_H148. % 18.52/18.78 apply (zenon_or_s _ _ zenon_H172); [ zenon_intro zenon_H150 | zenon_intro zenon_H174 ]. % 18.52/18.78 apply (zenon_L378_); trivial. % 18.52/18.78 apply (zenon_or_s _ _ zenon_H174); [ zenon_intro zenon_H113 | zenon_intro zenon_H175 ]. % 18.52/18.78 apply (zenon_L116_); trivial. % 18.52/18.78 apply (zenon_or_s _ _ zenon_H175); [ zenon_intro zenon_H176 | zenon_intro zenon_H151 ]. % 18.52/18.78 exact (zenon_H173 zenon_H176). % 18.52/18.78 apply (zenon_L420_); trivial. % 18.52/18.78 (* end of lemma zenon_L421_ *) % 18.52/18.78 assert (zenon_L422_ : ((op (e3) (e0)) = (e2)) -> ((op (e0) (e0)) = (e3)) -> (~((e2) = (op (op (e0) (e0)) (e0)))) -> False). % 18.52/18.78 do 0 intro. intros zenon_H148 zenon_H3a zenon_H87. % 18.52/18.78 elim (classic ((op (op (e0) (e0)) (e0)) = (op (op (e0) (e0)) (e0)))); [ zenon_intro zenon_H88 | zenon_intro zenon_H89 ]. % 18.52/18.78 cut (((op (op (e0) (e0)) (e0)) = (op (op (e0) (e0)) (e0))) = ((e2) = (op (op (e0) (e0)) (e0)))). % 18.52/18.78 intro zenon_D_pnotp. % 18.52/18.78 apply zenon_H87. % 18.52/18.78 rewrite <- zenon_D_pnotp. % 18.52/18.78 exact zenon_H88. % 18.52/18.78 cut (((op (op (e0) (e0)) (e0)) = (op (op (e0) (e0)) (e0)))); [idtac | apply NNPP; zenon_intro zenon_H89]. % 18.52/18.78 cut (((op (op (e0) (e0)) (e0)) = (e2))); [idtac | apply NNPP; zenon_intro zenon_H8a]. % 18.52/18.78 congruence. % 18.52/18.78 cut (((op (e3) (e0)) = (e2)) = ((op (op (e0) (e0)) (e0)) = (e2))). % 18.52/18.78 intro zenon_D_pnotp. % 18.52/18.78 apply zenon_H8a. % 18.52/18.78 rewrite <- zenon_D_pnotp. % 18.52/18.78 exact zenon_H148. % 18.52/18.78 cut (((e2) = (e2))); [idtac | apply NNPP; zenon_intro zenon_H7e]. % 18.52/18.78 cut (((op (e3) (e0)) = (op (op (e0) (e0)) (e0)))); [idtac | apply NNPP; zenon_intro zenon_H1e6]. % 18.52/18.78 congruence. % 18.52/18.78 elim (classic ((op (op (e0) (e0)) (e0)) = (op (op (e0) (e0)) (e0)))); [ zenon_intro zenon_H88 | zenon_intro zenon_H89 ]. % 18.52/18.78 cut (((op (op (e0) (e0)) (e0)) = (op (op (e0) (e0)) (e0))) = ((op (e3) (e0)) = (op (op (e0) (e0)) (e0)))). % 18.52/18.78 intro zenon_D_pnotp. % 18.52/18.78 apply zenon_H1e6. % 18.52/18.78 rewrite <- zenon_D_pnotp. % 18.52/18.78 exact zenon_H88. % 18.52/18.78 cut (((op (op (e0) (e0)) (e0)) = (op (op (e0) (e0)) (e0)))); [idtac | apply NNPP; zenon_intro zenon_H89]. % 18.52/18.78 cut (((op (op (e0) (e0)) (e0)) = (op (e3) (e0)))); [idtac | apply NNPP; zenon_intro zenon_H1e3]. % 18.52/18.78 congruence. % 18.52/18.78 apply (zenon_L239_); trivial. % 18.52/18.78 apply zenon_H89. apply refl_equal. % 18.52/18.78 apply zenon_H89. apply refl_equal. % 18.52/18.78 apply zenon_H7e. apply refl_equal. % 18.52/18.78 apply zenon_H89. apply refl_equal. % 18.52/18.78 apply zenon_H89. apply refl_equal. % 18.52/18.78 (* end of lemma zenon_L422_ *) % 18.52/18.78 assert (zenon_L423_ : ((op (e2) (e0)) = (e1)) -> ((op (e3) (e0)) = (e2)) -> ((op (e0) (e0)) = (e3)) -> False). % 18.52/18.78 do 0 intro. intros zenon_Hed zenon_H148 zenon_H3a. % 18.52/18.78 apply (zenon_notand_s _ _ ax6); [ zenon_intro zenon_H1f7 | zenon_intro zenon_H230 ]. % 18.52/18.78 elim (classic ((op (op (op (e0) (e0)) (e0)) (e0)) = (op (op (op (e0) (e0)) (e0)) (e0)))); [ zenon_intro zenon_H8e | zenon_intro zenon_H8f ]. % 18.52/18.78 cut (((op (op (op (e0) (e0)) (e0)) (e0)) = (op (op (op (e0) (e0)) (e0)) (e0))) = ((e1) = (op (op (op (e0) (e0)) (e0)) (e0)))). % 18.52/18.78 intro zenon_D_pnotp. % 18.52/18.78 apply zenon_H1f7. % 18.52/18.78 rewrite <- zenon_D_pnotp. % 18.52/18.78 exact zenon_H8e. % 18.52/18.78 cut (((op (op (op (e0) (e0)) (e0)) (e0)) = (op (op (op (e0) (e0)) (e0)) (e0)))); [idtac | apply NNPP; zenon_intro zenon_H8f]. % 18.52/18.78 cut (((op (op (op (e0) (e0)) (e0)) (e0)) = (e1))); [idtac | apply NNPP; zenon_intro zenon_H1f8]. % 18.52/18.78 congruence. % 18.52/18.78 cut (((op (e2) (e0)) = (e1)) = ((op (op (op (e0) (e0)) (e0)) (e0)) = (e1))). % 18.52/18.78 intro zenon_D_pnotp. % 18.52/18.78 apply zenon_H1f8. % 18.52/18.78 rewrite <- zenon_D_pnotp. % 18.52/18.78 exact zenon_Hed. % 18.52/18.78 cut (((e1) = (e1))); [idtac | apply NNPP; zenon_intro zenon_H79]. % 18.52/18.78 cut (((op (e2) (e0)) = (op (op (op (e0) (e0)) (e0)) (e0)))); [idtac | apply NNPP; zenon_intro zenon_H91]. % 18.52/18.78 congruence. % 18.52/18.78 elim (classic ((op (op (op (e0) (e0)) (e0)) (e0)) = (op (op (op (e0) (e0)) (e0)) (e0)))); [ zenon_intro zenon_H8e | zenon_intro zenon_H8f ]. % 18.52/18.78 cut (((op (op (op (e0) (e0)) (e0)) (e0)) = (op (op (op (e0) (e0)) (e0)) (e0))) = ((op (e2) (e0)) = (op (op (op (e0) (e0)) (e0)) (e0)))). % 18.52/18.78 intro zenon_D_pnotp. % 18.52/18.78 apply zenon_H91. % 18.52/18.78 rewrite <- zenon_D_pnotp. % 18.52/18.78 exact zenon_H8e. % 18.52/18.78 cut (((op (op (op (e0) (e0)) (e0)) (e0)) = (op (op (op (e0) (e0)) (e0)) (e0)))); [idtac | apply NNPP; zenon_intro zenon_H8f]. % 18.52/18.78 cut (((op (op (op (e0) (e0)) (e0)) (e0)) = (op (e2) (e0)))); [idtac | apply NNPP; zenon_intro zenon_H92]. % 18.52/18.78 congruence. % 18.52/18.78 cut (((e0) = (e0))); [idtac | apply NNPP; zenon_intro zenon_H82]. % 18.52/18.78 cut (((op (op (e0) (e0)) (e0)) = (e2))); [idtac | apply NNPP; zenon_intro zenon_H8a]. % 18.52/18.78 congruence. % 18.52/18.78 cut (((op (e3) (e0)) = (e2)) = ((op (op (e0) (e0)) (e0)) = (e2))). % 18.52/18.78 intro zenon_D_pnotp. % 18.52/18.78 apply zenon_H8a. % 18.52/18.78 rewrite <- zenon_D_pnotp. % 18.52/18.78 exact zenon_H148. % 18.52/18.78 cut (((e2) = (e2))); [idtac | apply NNPP; zenon_intro zenon_H7e]. % 18.52/18.78 cut (((op (e3) (e0)) = (op (op (e0) (e0)) (e0)))); [idtac | apply NNPP; zenon_intro zenon_H1e6]. % 18.52/18.78 congruence. % 18.52/18.78 elim (classic ((op (op (e0) (e0)) (e0)) = (op (op (e0) (e0)) (e0)))); [ zenon_intro zenon_H88 | zenon_intro zenon_H89 ]. % 18.52/18.78 cut (((op (op (e0) (e0)) (e0)) = (op (op (e0) (e0)) (e0))) = ((op (e3) (e0)) = (op (op (e0) (e0)) (e0)))). % 18.52/18.78 intro zenon_D_pnotp. % 18.52/18.78 apply zenon_H1e6. % 18.52/18.78 rewrite <- zenon_D_pnotp. % 18.52/18.78 exact zenon_H88. % 18.52/18.78 cut (((op (op (e0) (e0)) (e0)) = (op (op (e0) (e0)) (e0)))); [idtac | apply NNPP; zenon_intro zenon_H89]. % 18.52/18.78 cut (((op (op (e0) (e0)) (e0)) = (op (e3) (e0)))); [idtac | apply NNPP; zenon_intro zenon_H1e3]. % 18.52/18.78 congruence. % 18.52/18.78 apply (zenon_L239_); trivial. % 18.52/18.78 apply zenon_H89. apply refl_equal. % 18.52/18.78 apply zenon_H89. apply refl_equal. % 18.52/18.78 apply zenon_H7e. apply refl_equal. % 18.52/18.78 apply zenon_H82. apply refl_equal. % 18.52/18.78 apply zenon_H8f. apply refl_equal. % 18.52/18.78 apply zenon_H8f. apply refl_equal. % 18.52/18.78 apply zenon_H79. apply refl_equal. % 18.52/18.78 apply zenon_H8f. apply refl_equal. % 18.52/18.78 apply zenon_H8f. apply refl_equal. % 18.52/18.78 apply (zenon_notand_s _ _ zenon_H230); [ zenon_intro zenon_H87 | zenon_intro zenon_H1ea ]. % 18.52/18.78 apply (zenon_L422_); trivial. % 18.52/18.78 apply zenon_H1ea. apply sym_equal. exact zenon_H3a. % 18.52/18.78 (* end of lemma zenon_L423_ *) % 18.52/18.78 assert (zenon_L424_ : (((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)) = (op (e2) (e3)))) -> ((op (e2) (e3)) = (e1)) -> (~((op (e3) (e0)) = (op (e3) (e1)))) -> ((op (e3) (e0)) = (e1)) -> False). % 18.52/18.78 do 0 intro. intros zenon_H109 zenon_H4a zenon_H122 zenon_H10a zenon_H1c7 zenon_Hf4 zenon_H1cf zenon_Hac. % 18.52/18.78 apply (zenon_or_s _ _ zenon_H109); [ zenon_intro zenon_Ha0 | zenon_intro zenon_H10b ]. % 18.52/18.78 apply (zenon_L406_); trivial. % 18.52/18.78 apply (zenon_or_s _ _ zenon_H10b); [ zenon_intro zenon_H10d | zenon_intro zenon_H10c ]. % 18.52/18.78 exact (zenon_H10a zenon_H10d). % 18.52/18.78 apply (zenon_or_s _ _ zenon_H10c); [ zenon_intro zenon_Ha5 | zenon_intro zenon_Hae ]. % 18.52/18.78 apply (zenon_L188_); trivial. % 18.52/18.78 apply (zenon_L242_); trivial. % 18.52/18.78 (* end of lemma zenon_L424_ *) % 18.52/18.78 assert (zenon_L425_ : (((op (e0) (e2)) = (e0))\/(((op (e1) (e2)) = (e0))\/(((op (e2) (e2)) = (e0))\/((op (e3) (e2)) = (e0))))) -> (~((op (e2) (e2)) = (e2))) -> (~((e2) = (e3))) -> (~((e0) = (e2))) -> (((op (e0) (e2)) = (e2))\/(((op (e1) (e2)) = (e2))\/(((op (e2) (e2)) = (e2))\/((op (e3) (e2)) = (e2))))) -> (~((op (e1) (e2)) = (e0))) -> (~((op (e2) (e2)) = (e0))) -> (((op (e2) (e0)) = (e1))\/(((op (e2) (e1)) = (e1))\/(((op (e2) (e2)) = (e1))\/((op (e2) (e3)) = (e1))))) -> ((op (e0) (e0)) = (e3)) -> ((op (e3) (e0)) = (e2)) -> ((op (e0) (e1)) = (e1)) -> (~((op (e0) (e1)) = (op (e2) (e1)))) -> (((op (e0) (e2)) = (e1))\/(((op (e1) (e2)) = (e1))\/(((op (e2) (e2)) = (e1))\/((op (e3) (e2)) = (e1))))) -> (~((op (e3) (e0)) = (op (e3) (e1)))) -> (~((op (e2) (e1)) = (op (e2) (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))))) -> (~((e1) = (e3))) -> ((op (e1) (e2)) = (e3)) -> (~((op (e2) (e2)) = (op (e2) (e3)))) -> (~((op (e3) (e0)) = (op (e3) (e2)))) -> ((op (e3) (e0)) = (e1)) -> False). % 18.52/18.78 do 0 intro. intros zenon_H6a zenon_H173 zenon_H12b zenon_H149 zenon_H172 zenon_H25 zenon_H81 zenon_H106 zenon_H3a zenon_H148 zenon_Ha0 zenon_H17e zenon_H139 zenon_H1cf zenon_H1c7 zenon_H10a zenon_H4a zenon_H109 zenon_H95 zenon_H16c zenon_H6d zenon_H6f zenon_Hac. % 18.52/18.78 apply (zenon_or_s _ _ zenon_H6a); [ zenon_intro zenon_H48 | zenon_intro zenon_H6b ]. % 18.52/18.78 apply (zenon_L421_); trivial. % 18.52/18.78 apply (zenon_or_s _ _ zenon_H6b); [ zenon_intro zenon_H2a | zenon_intro zenon_H6c ]. % 18.52/18.78 exact (zenon_H25 zenon_H2a). % 18.52/18.78 apply (zenon_or_s _ _ zenon_H6c); [ zenon_intro zenon_H2c | zenon_intro zenon_H61 ]. % 18.52/18.78 exact (zenon_H81 zenon_H2c). % 18.52/18.78 apply (zenon_or_s _ _ zenon_H106); [ zenon_intro zenon_Hed | zenon_intro zenon_H107 ]. % 18.52/18.78 apply (zenon_L423_); trivial. % 18.52/18.78 apply (zenon_or_s _ _ zenon_H107); [ zenon_intro zenon_Ha5 | zenon_intro zenon_H108 ]. % 18.52/18.78 apply (zenon_L357_); trivial. % 18.52/18.78 apply (zenon_or_s _ _ zenon_H108); [ zenon_intro zenon_Hf1 | zenon_intro zenon_Hf4 ]. % 18.52/18.78 apply (zenon_L156_); trivial. % 18.52/18.78 apply (zenon_or_s _ _ zenon_H139); [ zenon_intro zenon_H122 | zenon_intro zenon_H13a ]. % 18.52/18.78 apply (zenon_L424_); trivial. % 18.52/18.78 apply (zenon_or_s _ _ zenon_H13a); [ zenon_intro zenon_Hf0 | zenon_intro zenon_H13b ]. % 18.52/18.78 apply (zenon_L167_); trivial. % 18.52/18.78 apply (zenon_or_s _ _ zenon_H13b); [ zenon_intro zenon_Hf1 | zenon_intro zenon_Hba ]. % 18.52/18.78 apply (zenon_L84_); trivial. % 18.52/18.78 apply (zenon_L249_); trivial. % 18.52/18.78 (* end of lemma zenon_L425_ *) % 18.52/18.78 assert (zenon_L426_ : (((op (e0) (e2)) = (e3))\/(((op (e1) (e2)) = (e3))\/(((op (e2) (e2)) = (e3))\/((op (e3) (e2)) = (e3))))) -> (~((op (e0) (e2)) = (op (e3) (e2)))) -> (~((op (e3) (e0)) = (op (e3) (e2)))) -> (~((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))) -> (~((op (e2) (e1)) = (op (e2) (e3)))) -> (~((op (e3) (e0)) = (op (e3) (e1)))) -> (((op (e0) (e2)) = (e1))\/(((op (e1) (e2)) = (e1))\/(((op (e2) (e2)) = (e1))\/((op (e3) (e2)) = (e1))))) -> (~((op (e0) (e1)) = (op (e2) (e1)))) -> ((op (e0) (e0)) = (e3)) -> (((op (e2) (e0)) = (e1))\/(((op (e2) (e1)) = (e1))\/(((op (e2) (e2)) = (e1))\/((op (e2) (e3)) = (e1))))) -> (~((op (e1) (e2)) = (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)) = (e0))\/(((op (e2) (e2)) = (e0))\/((op (e3) (e2)) = (e0))))) -> (~((op (e3) (e3)) = (e3))) -> (~((op (e1) (e1)) = (op (e3) (e1)))) -> ((op (e1) (e1)) = (e3)) -> ((op (e3) (e0)) = (e2)) -> (~((e2) = (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))))) -> (~((op (e0) (e1)) = (op (e0) (e3)))) -> ((op (e0) (e1)) = (e1)) -> (~((op (e1) (e0)) = (op (e1) (e3)))) -> ((op (e1) (e0)) = (e1)) -> (~((op (e2) (e2)) = (op (e3) (e2)))) -> (~((op (e2) (e2)) = (e2))) -> (~((op (e2) (e2)) = (op (e2) (e3)))) -> (~((op (e2) (e2)) = (e0))) -> (((op (e2) (e2)) = (e0))\/(((op (e2) (e2)) = (e1))\/(((op (e2) (e2)) = (e2))\/((op (e2) (e2)) = (e3))))) -> ((op (e3) (e0)) = (e1)) -> (~((op (e3) (e0)) = (op (e3) (e3)))) -> False). % 18.52/18.78 do 0 intro. intros zenon_H1a6 zenon_H14f zenon_H6f zenon_H95 zenon_H109 zenon_H4a zenon_H10a zenon_H1c7 zenon_H1cf zenon_H139 zenon_H17e zenon_H3a zenon_H106 zenon_H25 zenon_H172 zenon_H149 zenon_H6a zenon_H102 zenon_H160 zenon_H13f zenon_H148 zenon_H12b zenon_H165 zenon_H133 zenon_H54 zenon_Ha0 zenon_Hd8 zenon_H9d zenon_H18f zenon_H173 zenon_H6d zenon_H81 zenon_H1c4 zenon_Hac zenon_H71. % 18.52/18.78 apply (zenon_or_s _ _ zenon_H1a6); [ zenon_intro zenon_Ha9 | zenon_intro zenon_H1aa ]. % 18.52/18.78 apply (zenon_L264_); trivial. % 18.52/18.78 apply (zenon_or_s _ _ zenon_H1aa); [ zenon_intro zenon_H16c | zenon_intro zenon_H1ab ]. % 18.52/18.78 apply (zenon_L425_); trivial. % 18.52/18.78 apply (zenon_or_s _ _ zenon_H1ab); [ zenon_intro zenon_Haa | zenon_intro zenon_H163 ]. % 18.52/18.78 apply (zenon_L325_); trivial. % 18.52/18.78 apply (zenon_L362_); trivial. % 18.52/18.78 (* end of lemma zenon_L426_ *) % 18.52/18.78 assert (zenon_L427_ : ((op (e0) (e3)) = (e0)) -> ((op (e0) (e3)) = (e1)) -> (~((e0) = (e1))) -> False). % 18.52/18.78 do 0 intro. intros zenon_H1e zenon_Hc3 zenon_Ha1. % 18.52/18.78 elim (classic ((e1) = (e1))); [ zenon_intro zenon_Ha2 | zenon_intro zenon_H79 ]. % 18.52/18.78 cut (((e1) = (e1)) = ((e0) = (e1))). % 18.52/18.78 intro zenon_D_pnotp. % 18.52/18.78 apply zenon_Ha1. % 18.52/18.78 rewrite <- zenon_D_pnotp. % 18.52/18.78 exact zenon_Ha2. % 18.52/18.78 cut (((e1) = (e1))); [idtac | apply NNPP; zenon_intro zenon_H79]. % 18.52/18.78 cut (((e1) = (e0))); [idtac | apply NNPP; zenon_intro zenon_Ha3]. % 18.52/18.78 congruence. % 18.52/18.78 cut (((op (e0) (e3)) = (e0)) = ((e1) = (e0))). % 18.52/18.78 intro zenon_D_pnotp. % 18.52/18.78 apply zenon_Ha3. % 18.52/18.78 rewrite <- zenon_D_pnotp. % 18.52/18.78 exact zenon_H1e. % 18.52/18.78 cut (((e0) = (e0))); [idtac | apply NNPP; zenon_intro zenon_H82]. % 18.52/18.78 cut (((op (e0) (e3)) = (e1))); [idtac | apply NNPP; zenon_intro zenon_H231]. % 18.52/18.78 congruence. % 18.52/18.78 exact (zenon_H231 zenon_Hc3). % 18.52/18.78 apply zenon_H82. apply refl_equal. % 18.52/18.78 apply zenon_H79. apply refl_equal. % 18.52/18.78 apply zenon_H79. apply refl_equal. % 18.52/18.78 (* end of lemma zenon_L427_ *) % 18.52/18.78 assert (zenon_L428_ : ((op (e0) (e3)) = (e0)) -> ((op (e0) (e3)) = (e2)) -> (~((e0) = (e2))) -> False). % 18.52/18.78 do 0 intro. intros zenon_H1e zenon_Hcd zenon_H149. % 18.52/18.78 elim (classic ((e2) = (e2))); [ zenon_intro zenon_H7d | zenon_intro zenon_H7e ]. % 18.52/18.78 cut (((e2) = (e2)) = ((e0) = (e2))). % 18.52/18.78 intro zenon_D_pnotp. % 18.52/18.78 apply zenon_H149. % 18.52/18.78 rewrite <- zenon_D_pnotp. % 18.52/18.78 exact zenon_H7d. % 18.52/18.78 cut (((e2) = (e2))); [idtac | apply NNPP; zenon_intro zenon_H7e]. % 18.52/18.78 cut (((e2) = (e0))); [idtac | apply NNPP; zenon_intro zenon_H14a]. % 18.52/18.78 congruence. % 18.52/18.78 cut (((op (e0) (e3)) = (e0)) = ((e2) = (e0))). % 18.52/18.78 intro zenon_D_pnotp. % 18.52/18.78 apply zenon_H14a. % 18.52/18.78 rewrite <- zenon_D_pnotp. % 18.52/18.78 exact zenon_H1e. % 18.52/18.78 cut (((e0) = (e0))); [idtac | apply NNPP; zenon_intro zenon_H82]. % 18.52/18.78 cut (((op (e0) (e3)) = (e2))); [idtac | apply NNPP; zenon_intro zenon_H12e]. % 18.52/18.78 congruence. % 18.52/18.78 exact (zenon_H12e zenon_Hcd). % 18.52/18.78 apply zenon_H82. apply refl_equal. % 18.52/18.78 apply zenon_H7e. apply refl_equal. % 18.52/18.78 apply zenon_H7e. apply refl_equal. % 18.52/18.78 (* end of lemma zenon_L428_ *) % 18.52/18.78 assert (zenon_L429_ : (((op (e0) (e3)) = (e2))\/(((op (e1) (e3)) = (e2))\/(((op (e2) (e3)) = (e2))\/((op (e3) (e3)) = (e2))))) -> (~((e0) = (e2))) -> (~((e2) = (e3))) -> (~((op (e2) (e1)) = (op (e2) (e3)))) -> ((op (e2) (e1)) = (e2)) -> (((op (e2) (e3)) = (e0))\/(((op (e2) (e3)) = (e1))\/(((op (e2) (e3)) = (e2))\/((op (e2) (e3)) = (e3))))) -> ((op (e0) (e3)) = (e0)) -> (~((op (e0) (e3)) = (op (e2) (e3)))) -> ((op (e3) (e3)) = (e1)) -> (~((op (e2) (e3)) = (op (e3) (e3)))) -> (~((op (e1) (e3)) = (op (e2) (e3)))) -> ((op (e1) (e3)) = (e3)) -> False). % 18.52/18.78 do 0 intro. intros zenon_H145 zenon_H149 zenon_H12b zenon_H1c7 zenon_H1ca zenon_H11f zenon_H1e zenon_He2 zenon_Hc4 zenon_Hf3 zenon_Hdb zenon_Hdc. % 18.52/18.78 apply (zenon_or_s _ _ zenon_H145); [ zenon_intro zenon_Hcd | zenon_intro zenon_H146 ]. % 18.52/18.78 apply (zenon_L428_); trivial. % 18.52/18.78 apply (zenon_or_s _ _ zenon_H146); [ zenon_intro zenon_Hd7 | zenon_intro zenon_H147 ]. % 18.52/18.78 apply (zenon_L266_); trivial. % 18.52/18.78 apply (zenon_or_s _ _ zenon_H147); [ zenon_intro zenon_H11d | zenon_intro zenon_Hf6 ]. % 18.52/18.78 apply (zenon_L224_); trivial. % 18.52/18.78 apply (zenon_L404_); trivial. % 18.52/18.78 (* end of lemma zenon_L429_ *) % 18.52/18.78 assert (zenon_L430_ : (((op (e0) (e3)) = (e1))\/(((op (e1) (e3)) = (e1))\/(((op (e2) (e3)) = (e1))\/((op (e3) (e3)) = (e1))))) -> (~((e0) = (e1))) -> (~((e1) = (e3))) -> (~((op (e2) (e2)) = (op (e2) (e3)))) -> ((op (e2) (e2)) = (e1)) -> (((op (e0) (e3)) = (e2))\/(((op (e1) (e3)) = (e2))\/(((op (e2) (e3)) = (e2))\/((op (e3) (e3)) = (e2))))) -> (~((e0) = (e2))) -> (~((e2) = (e3))) -> (~((op (e2) (e1)) = (op (e2) (e3)))) -> ((op (e2) (e1)) = (e2)) -> (((op (e2) (e3)) = (e0))\/(((op (e2) (e3)) = (e1))\/(((op (e2) (e3)) = (e2))\/((op (e2) (e3)) = (e3))))) -> ((op (e0) (e3)) = (e0)) -> (~((op (e0) (e3)) = (op (e2) (e3)))) -> (~((op (e2) (e3)) = (op (e3) (e3)))) -> (~((op (e1) (e3)) = (op (e2) (e3)))) -> ((op (e1) (e3)) = (e3)) -> False). % 18.52/18.78 do 0 intro. intros zenon_H133 zenon_Ha1 zenon_H95 zenon_H6d zenon_Hf1 zenon_H145 zenon_H149 zenon_H12b zenon_H1c7 zenon_H1ca zenon_H11f zenon_H1e zenon_He2 zenon_Hf3 zenon_Hdb zenon_Hdc. % 18.52/18.78 apply (zenon_or_s _ _ zenon_H133); [ zenon_intro zenon_Hc3 | zenon_intro zenon_H134 ]. % 18.52/18.78 apply (zenon_L427_); trivial. % 18.52/18.78 apply (zenon_or_s _ _ zenon_H134); [ zenon_intro zenon_Hd6 | zenon_intro zenon_H135 ]. % 18.52/18.78 apply (zenon_L83_); trivial. % 18.52/18.78 apply (zenon_or_s _ _ zenon_H135); [ zenon_intro zenon_Hf4 | zenon_intro zenon_Hc4 ]. % 18.52/18.78 apply (zenon_L84_); trivial. % 18.52/18.78 apply (zenon_L429_); trivial. % 18.52/18.78 (* end of lemma zenon_L430_ *) % 18.52/18.78 assert (zenon_L431_ : ((op (e3) (e2)) = (e0)) -> ((op (e2) (e2)) = (e3)) -> (~((e0) = (op (op (e2) (e2)) (e2)))) -> False). % 18.52/18.78 do 0 intro. intros zenon_H61 zenon_Haa zenon_H1bd. % 18.52/18.78 elim (classic ((op (op (e2) (e2)) (e2)) = (op (op (e2) (e2)) (e2)))); [ zenon_intro zenon_Hb6 | zenon_intro zenon_Hb7 ]. % 18.52/18.78 cut (((op (op (e2) (e2)) (e2)) = (op (op (e2) (e2)) (e2))) = ((e0) = (op (op (e2) (e2)) (e2)))). % 18.52/18.78 intro zenon_D_pnotp. % 18.52/18.78 apply zenon_H1bd. % 18.52/18.78 rewrite <- zenon_D_pnotp. % 18.52/18.78 exact zenon_Hb6. % 18.52/18.78 cut (((op (op (e2) (e2)) (e2)) = (op (op (e2) (e2)) (e2)))); [idtac | apply NNPP; zenon_intro zenon_Hb7]. % 18.52/18.78 cut (((op (op (e2) (e2)) (e2)) = (e0))); [idtac | apply NNPP; zenon_intro zenon_H1be]. % 18.52/18.78 congruence. % 18.52/18.78 cut (((op (e3) (e2)) = (e0)) = ((op (op (e2) (e2)) (e2)) = (e0))). % 18.52/18.78 intro zenon_D_pnotp. % 18.52/18.78 apply zenon_H1be. % 18.52/18.78 rewrite <- zenon_D_pnotp. % 18.52/18.78 exact zenon_H61. % 18.52/18.78 cut (((e0) = (e0))); [idtac | apply NNPP; zenon_intro zenon_H82]. % 18.52/18.78 cut (((op (e3) (e2)) = (op (op (e2) (e2)) (e2)))); [idtac | apply NNPP; zenon_intro zenon_H1b6]. % 18.52/18.78 congruence. % 18.52/18.78 elim (classic ((op (op (e2) (e2)) (e2)) = (op (op (e2) (e2)) (e2)))); [ zenon_intro zenon_Hb6 | zenon_intro zenon_Hb7 ]. % 18.52/18.78 cut (((op (op (e2) (e2)) (e2)) = (op (op (e2) (e2)) (e2))) = ((op (e3) (e2)) = (op (op (e2) (e2)) (e2)))). % 18.52/18.78 intro zenon_D_pnotp. % 18.52/18.78 apply zenon_H1b6. % 18.52/18.78 rewrite <- zenon_D_pnotp. % 18.52/18.78 exact zenon_Hb6. % 18.52/18.78 cut (((op (op (e2) (e2)) (e2)) = (op (op (e2) (e2)) (e2)))); [idtac | apply NNPP; zenon_intro zenon_Hb7]. % 18.52/18.78 cut (((op (op (e2) (e2)) (e2)) = (op (e3) (e2)))); [idtac | apply NNPP; zenon_intro zenon_H1b2]. % 18.52/18.78 congruence. % 18.52/18.78 apply (zenon_L177_); trivial. % 18.52/18.78 apply zenon_Hb7. apply refl_equal. % 18.52/18.78 apply zenon_Hb7. apply refl_equal. % 18.52/18.78 apply zenon_H82. apply refl_equal. % 18.52/18.78 apply zenon_Hb7. apply refl_equal. % 18.52/18.78 apply zenon_Hb7. apply refl_equal. % 18.52/18.78 (* end of lemma zenon_L431_ *) % 18.52/18.78 assert (zenon_L432_ : ((op (e0) (e2)) = (e1)) -> ((op (e3) (e2)) = (e0)) -> ((op (e2) (e2)) = (e3)) -> False). % 18.52/18.78 do 0 intro. intros zenon_H122 zenon_H61 zenon_Haa. % 18.52/18.78 apply (zenon_notand_s _ _ ax20); [ zenon_intro zenon_Hbc | zenon_intro zenon_H232 ]. % 18.52/18.78 elim (classic ((op (op (op (e2) (e2)) (e2)) (e2)) = (op (op (op (e2) (e2)) (e2)) (e2)))); [ zenon_intro zenon_Hbd | zenon_intro zenon_Hbe ]. % 18.52/18.78 cut (((op (op (op (e2) (e2)) (e2)) (e2)) = (op (op (op (e2) (e2)) (e2)) (e2))) = ((e1) = (op (op (op (e2) (e2)) (e2)) (e2)))). % 18.52/18.78 intro zenon_D_pnotp. % 18.52/18.78 apply zenon_Hbc. % 18.52/18.78 rewrite <- zenon_D_pnotp. % 18.52/18.78 exact zenon_Hbd. % 18.52/18.78 cut (((op (op (op (e2) (e2)) (e2)) (e2)) = (op (op (op (e2) (e2)) (e2)) (e2)))); [idtac | apply NNPP; zenon_intro zenon_Hbe]. % 18.52/18.78 cut (((op (op (op (e2) (e2)) (e2)) (e2)) = (e1))); [idtac | apply NNPP; zenon_intro zenon_Hbf]. % 18.52/18.78 congruence. % 18.52/18.78 cut (((op (e0) (e2)) = (e1)) = ((op (op (op (e2) (e2)) (e2)) (e2)) = (e1))). % 18.52/18.78 intro zenon_D_pnotp. % 18.52/18.78 apply zenon_Hbf. % 18.52/18.78 rewrite <- zenon_D_pnotp. % 18.52/18.78 exact zenon_H122. % 18.52/18.78 cut (((e1) = (e1))); [idtac | apply NNPP; zenon_intro zenon_H79]. % 18.52/18.78 cut (((op (e0) (e2)) = (op (op (op (e2) (e2)) (e2)) (e2)))); [idtac | apply NNPP; zenon_intro zenon_H1c2]. % 18.52/18.78 congruence. % 18.52/18.78 elim (classic ((op (op (op (e2) (e2)) (e2)) (e2)) = (op (op (op (e2) (e2)) (e2)) (e2)))); [ zenon_intro zenon_Hbd | zenon_intro zenon_Hbe ]. % 18.52/18.78 cut (((op (op (op (e2) (e2)) (e2)) (e2)) = (op (op (op (e2) (e2)) (e2)) (e2))) = ((op (e0) (e2)) = (op (op (op (e2) (e2)) (e2)) (e2)))). % 18.52/18.78 intro zenon_D_pnotp. % 18.52/18.78 apply zenon_H1c2. % 18.52/18.78 rewrite <- zenon_D_pnotp. % 18.52/18.78 exact zenon_Hbd. % 18.52/18.78 cut (((op (op (op (e2) (e2)) (e2)) (e2)) = (op (op (op (e2) (e2)) (e2)) (e2)))); [idtac | apply NNPP; zenon_intro zenon_Hbe]. % 18.52/18.78 cut (((op (op (op (e2) (e2)) (e2)) (e2)) = (op (e0) (e2)))); [idtac | apply NNPP; zenon_intro zenon_H1c3]. % 18.52/18.78 congruence. % 18.52/18.78 cut (((e2) = (e2))); [idtac | apply NNPP; zenon_intro zenon_H7e]. % 18.52/18.78 cut (((op (op (e2) (e2)) (e2)) = (e0))); [idtac | apply NNPP; zenon_intro zenon_H1be]. % 18.52/18.78 congruence. % 18.52/18.78 cut (((op (e3) (e2)) = (e0)) = ((op (op (e2) (e2)) (e2)) = (e0))). % 18.52/18.78 intro zenon_D_pnotp. % 18.52/18.78 apply zenon_H1be. % 18.52/18.78 rewrite <- zenon_D_pnotp. % 18.52/18.78 exact zenon_H61. % 18.52/18.78 cut (((e0) = (e0))); [idtac | apply NNPP; zenon_intro zenon_H82]. % 18.52/18.78 cut (((op (e3) (e2)) = (op (op (e2) (e2)) (e2)))); [idtac | apply NNPP; zenon_intro zenon_H1b6]. % 18.52/18.78 congruence. % 18.52/18.78 elim (classic ((op (op (e2) (e2)) (e2)) = (op (op (e2) (e2)) (e2)))); [ zenon_intro zenon_Hb6 | zenon_intro zenon_Hb7 ]. % 18.52/18.78 cut (((op (op (e2) (e2)) (e2)) = (op (op (e2) (e2)) (e2))) = ((op (e3) (e2)) = (op (op (e2) (e2)) (e2)))). % 18.52/18.78 intro zenon_D_pnotp. % 18.52/18.78 apply zenon_H1b6. % 18.52/18.78 rewrite <- zenon_D_pnotp. % 18.52/18.78 exact zenon_Hb6. % 18.52/18.78 cut (((op (op (e2) (e2)) (e2)) = (op (op (e2) (e2)) (e2)))); [idtac | apply NNPP; zenon_intro zenon_Hb7]. % 18.52/18.78 cut (((op (op (e2) (e2)) (e2)) = (op (e3) (e2)))); [idtac | apply NNPP; zenon_intro zenon_H1b2]. % 18.52/18.78 congruence. % 18.52/18.78 apply (zenon_L177_); trivial. % 18.52/18.78 apply zenon_Hb7. apply refl_equal. % 18.52/18.78 apply zenon_Hb7. apply refl_equal. % 18.52/18.78 apply zenon_H82. apply refl_equal. % 18.52/18.78 apply zenon_H7e. apply refl_equal. % 18.52/18.78 apply zenon_Hbe. apply refl_equal. % 18.52/18.78 apply zenon_Hbe. apply refl_equal. % 18.52/18.78 apply zenon_H79. apply refl_equal. % 18.52/18.78 apply zenon_Hbe. apply refl_equal. % 18.52/18.78 apply zenon_Hbe. apply refl_equal. % 18.52/18.78 apply (zenon_notand_s _ _ zenon_H232); [ zenon_intro zenon_H1bd | zenon_intro zenon_Hab ]. % 18.52/18.78 apply (zenon_L431_); trivial. % 18.52/18.78 apply zenon_Hab. apply sym_equal. exact zenon_Haa. % 18.52/18.78 (* end of lemma zenon_L432_ *) % 18.52/18.78 assert (zenon_L433_ : (((op (e0) (e2)) = (e3))\/(((op (e1) (e2)) = (e3))\/(((op (e2) (e2)) = (e3))\/((op (e3) (e2)) = (e3))))) -> (~((e1) = (e3))) -> (~((e2) = (e3))) -> ((op (e1) (e2)) = (e2)) -> ((op (e3) (e2)) = (e0)) -> ((op (e0) (e2)) = (e1)) -> (~((op (e3) (e1)) = (op (e3) (e2)))) -> ((op (e3) (e1)) = (e3)) -> False). % 18.52/18.78 do 0 intro. intros zenon_H1a6 zenon_H95 zenon_H12b zenon_H113 zenon_H61 zenon_H122 zenon_H1a4 zenon_H161. % 18.52/18.78 apply (zenon_or_s _ _ zenon_H1a6); [ zenon_intro zenon_Ha9 | zenon_intro zenon_H1aa ]. % 18.52/18.78 apply (zenon_L77_); trivial. % 18.52/18.78 apply (zenon_or_s _ _ zenon_H1aa); [ zenon_intro zenon_H16c | zenon_intro zenon_H1ab ]. % 18.52/18.78 apply (zenon_L116_); trivial. % 18.52/18.78 apply (zenon_or_s _ _ zenon_H1ab); [ zenon_intro zenon_Haa | zenon_intro zenon_H163 ]. % 18.52/18.78 apply (zenon_L432_); trivial. % 18.52/18.78 apply (zenon_L169_); trivial. % 18.52/18.78 (* end of lemma zenon_L433_ *) % 18.52/18.78 assert (zenon_L434_ : (((op (e0) (e2)) = (e1))\/(((op (e1) (e2)) = (e1))\/(((op (e2) (e2)) = (e1))\/((op (e3) (e2)) = (e1))))) -> ((op (e3) (e1)) = (e3)) -> (~((op (e3) (e1)) = (op (e3) (e2)))) -> ((op (e3) (e2)) = (e0)) -> (~((e2) = (e3))) -> (~((e1) = (e3))) -> (((op (e0) (e2)) = (e3))\/(((op (e1) (e2)) = (e3))\/(((op (e2) (e2)) = (e3))\/((op (e3) (e2)) = (e3))))) -> (~((e1) = (e2))) -> ((op (e1) (e2)) = (e2)) -> (~((op (e2) (e2)) = (op (e2) (e3)))) -> ((op (e2) (e3)) = (e1)) -> (~((op (e3) (e0)) = (op (e3) (e2)))) -> ((op (e3) (e0)) = (e1)) -> False). % 18.52/18.78 do 0 intro. intros zenon_H139 zenon_H161 zenon_H1a4 zenon_H61 zenon_H12b zenon_H95 zenon_H1a6 zenon_H7c zenon_H113 zenon_H6d zenon_Hf4 zenon_H6f zenon_Hac. % 18.52/18.78 apply (zenon_or_s _ _ zenon_H139); [ zenon_intro zenon_H122 | zenon_intro zenon_H13a ]. % 18.52/18.78 apply (zenon_L433_); trivial. % 18.52/18.78 apply (zenon_or_s _ _ zenon_H13a); [ zenon_intro zenon_Hf0 | zenon_intro zenon_H13b ]. % 18.52/18.78 apply (zenon_L68_); trivial. % 18.52/18.78 apply (zenon_or_s _ _ zenon_H13b); [ zenon_intro zenon_Hf1 | zenon_intro zenon_Hba ]. % 18.52/18.78 apply (zenon_L84_); trivial. % 18.52/18.78 apply (zenon_L249_); trivial. % 18.52/18.78 (* end of lemma zenon_L434_ *) % 18.52/18.78 assert (zenon_L435_ : (((op (e2) (e0)) = (e1))\/(((op (e2) (e1)) = (e1))\/(((op (e2) (e2)) = (e1))\/((op (e2) (e3)) = (e1))))) -> ((op (e2) (e0)) = (e0)) -> ((op (e0) (e1)) = (e1)) -> (~((op (e0) (e1)) = (op (e2) (e1)))) -> ((op (e1) (e3)) = (e3)) -> (~((op (e1) (e3)) = (op (e2) (e3)))) -> (~((op (e2) (e3)) = (op (e3) (e3)))) -> (~((op (e0) (e3)) = (op (e2) (e3)))) -> ((op (e0) (e3)) = (e0)) -> (((op (e2) (e3)) = (e0))\/(((op (e2) (e3)) = (e1))\/(((op (e2) (e3)) = (e2))\/((op (e2) (e3)) = (e3))))) -> ((op (e2) (e1)) = (e2)) -> (~((op (e2) (e1)) = (op (e2) (e3)))) -> (~((e0) = (e2))) -> (((op (e0) (e3)) = (e2))\/(((op (e1) (e3)) = (e2))\/(((op (e2) (e3)) = (e2))\/((op (e3) (e3)) = (e2))))) -> (~((e0) = (e1))) -> (((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 (e3) (e1)) = (e3)) -> (~((op (e3) (e1)) = (op (e3) (e2)))) -> ((op (e3) (e2)) = (e0)) -> (~((e2) = (e3))) -> (~((e1) = (e3))) -> (((op (e0) (e2)) = (e3))\/(((op (e1) (e2)) = (e3))\/(((op (e2) (e2)) = (e3))\/((op (e3) (e2)) = (e3))))) -> (~((e1) = (e2))) -> ((op (e1) (e2)) = (e2)) -> (~((op (e2) (e2)) = (op (e2) (e3)))) -> (~((op (e3) (e0)) = (op (e3) (e2)))) -> ((op (e3) (e0)) = (e1)) -> False). % 18.52/18.78 do 0 intro. intros zenon_H106 zenon_H34 zenon_Ha0 zenon_H17e zenon_Hdc zenon_Hdb zenon_Hf3 zenon_He2 zenon_H1e zenon_H11f zenon_H1ca zenon_H1c7 zenon_H149 zenon_H145 zenon_Ha1 zenon_H133 zenon_H139 zenon_H161 zenon_H1a4 zenon_H61 zenon_H12b zenon_H95 zenon_H1a6 zenon_H7c zenon_H113 zenon_H6d zenon_H6f zenon_Hac. % 18.52/18.78 apply (zenon_or_s _ _ zenon_H106); [ zenon_intro zenon_Hed | zenon_intro zenon_H107 ]. % 18.52/18.78 apply (zenon_L214_); trivial. % 18.52/18.78 apply (zenon_or_s _ _ zenon_H107); [ zenon_intro zenon_Ha5 | zenon_intro zenon_H108 ]. % 18.52/18.78 apply (zenon_L357_); trivial. % 18.52/18.78 apply (zenon_or_s _ _ zenon_H108); [ zenon_intro zenon_Hf1 | zenon_intro zenon_Hf4 ]. % 18.52/18.78 apply (zenon_L430_); trivial. % 18.52/18.78 apply (zenon_L434_); trivial. % 18.52/18.78 (* end of lemma zenon_L435_ *) % 18.52/18.78 assert (zenon_L436_ : (~((op (e3) (e0)) = (op (e3) (e1)))) -> ((op (e3) (e0)) = (e2)) -> ((op (e3) (e1)) = (e2)) -> False). % 18.52/18.78 do 0 intro. intros zenon_H1cf zenon_H148 zenon_H14d. % 18.52/18.78 cut (((op (e3) (e0)) = (e2)) = ((op (e3) (e0)) = (op (e3) (e1)))). % 18.52/18.78 intro zenon_D_pnotp. % 18.52/18.78 apply zenon_H1cf. % 18.52/18.78 rewrite <- zenon_D_pnotp. % 18.52/18.78 exact zenon_H148. % 18.52/18.78 cut (((e2) = (op (e3) (e1)))); [idtac | apply NNPP; zenon_intro zenon_H14e]. % 18.52/18.78 cut (((op (e3) (e0)) = (op (e3) (e0)))); [idtac | apply NNPP; zenon_intro zenon_H70]. % 18.52/18.78 congruence. % 18.52/18.78 apply zenon_H70. apply refl_equal. % 18.52/18.78 apply zenon_H14e. apply sym_equal. exact zenon_H14d. % 18.52/18.78 (* end of lemma zenon_L436_ *) % 18.52/18.78 assert (zenon_L437_ : (((op (e2) (e2)) = (e0))\/(((op (e2) (e2)) = (e1))\/(((op (e2) (e2)) = (e2))\/((op (e2) (e2)) = (e3))))) -> (~((op (e2) (e2)) = (e0))) -> (~((op (e0) (e2)) = (op (e2) (e2)))) -> (~((op (e2) (e2)) = (e2))) -> ((op (e0) (e2)) = (e1)) -> ((op (e3) (e2)) = (e0)) -> False). % 18.52/18.78 do 0 intro. intros zenon_H1c4 zenon_H81 zenon_Ha8 zenon_H173 zenon_H122 zenon_H61. % 18.52/18.78 apply (zenon_or_s _ _ zenon_H1c4); [ zenon_intro zenon_H2c | zenon_intro zenon_H1c5 ]. % 18.52/18.78 exact (zenon_H81 zenon_H2c). % 18.52/18.78 apply (zenon_or_s _ _ zenon_H1c5); [ zenon_intro zenon_Hf1 | zenon_intro zenon_H1c6 ]. % 18.52/18.78 apply (zenon_L246_); trivial. % 18.52/18.78 apply (zenon_or_s _ _ zenon_H1c6); [ zenon_intro zenon_H176 | zenon_intro zenon_Haa ]. % 18.52/18.78 exact (zenon_H173 zenon_H176). % 18.52/18.78 apply (zenon_L432_); trivial. % 18.52/18.78 (* end of lemma zenon_L437_ *) % 18.52/18.78 assert (zenon_L438_ : (((op (e0) (e2)) = (e0))\/(((op (e1) (e2)) = (e0))\/(((op (e2) (e2)) = (e0))\/((op (e3) (e2)) = (e0))))) -> (~((e0) = (e1))) -> (~((op (e1) (e2)) = (e0))) -> (((op (e2) (e2)) = (e0))\/(((op (e2) (e2)) = (e1))\/(((op (e2) (e2)) = (e2))\/((op (e2) (e2)) = (e3))))) -> (~((op (e2) (e2)) = (e0))) -> (~((op (e0) (e2)) = (op (e2) (e2)))) -> (~((op (e2) (e2)) = (e2))) -> ((op (e0) (e2)) = (e1)) -> False). % 18.52/18.78 do 0 intro. intros zenon_H6a zenon_Ha1 zenon_H25 zenon_H1c4 zenon_H81 zenon_Ha8 zenon_H173 zenon_H122. % 18.52/18.78 apply (zenon_or_s _ _ zenon_H6a); [ zenon_intro zenon_H48 | zenon_intro zenon_H6b ]. % 18.52/18.78 apply (zenon_L355_); trivial. % 18.52/18.78 apply (zenon_or_s _ _ zenon_H6b); [ zenon_intro zenon_H2a | zenon_intro zenon_H6c ]. % 18.52/18.78 exact (zenon_H25 zenon_H2a). % 18.52/18.78 apply (zenon_or_s _ _ zenon_H6c); [ zenon_intro zenon_H2c | zenon_intro zenon_H61 ]. % 18.52/18.78 exact (zenon_H81 zenon_H2c). % 18.52/18.78 apply (zenon_L437_); trivial. % 18.52/18.78 (* end of lemma zenon_L438_ *) % 18.52/18.78 assert (zenon_L439_ : ((~((op (e3) (e2)) = (e0)))\/((op (e3) (e0)) = (e2))) -> ((op (e0) (e0)) = (e3)) -> (~((e0) = (e2))) -> (((op (e0) (e1)) = (e2))\/(((op (e1) (e1)) = (e2))\/(((op (e2) (e1)) = (e2))\/((op (e3) (e1)) = (e2))))) -> ((op (e1) (e0)) = (e1)) -> (((op (e0) (e2)) = (e3))\/(((op (e1) (e2)) = (e3))\/(((op (e2) (e2)) = (e3))\/((op (e3) (e2)) = (e3))))) -> (~((op (e0) (e1)) = (op (e0) (e3)))) -> (~((op (e1) (e0)) = (op (e1) (e3)))) -> (((op (e2) (e2)) = (e0))\/(((op (e2) (e2)) = (e1))\/(((op (e2) (e2)) = (e2))\/((op (e2) (e2)) = (e3))))) -> (~((op (e3) (e0)) = (op (e3) (e3)))) -> (((op (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 (e3) (e0)) = (op (e3) (e2)))) -> (~((op (e2) (e2)) = (e2))) -> (~((e2) = (e3))) -> (((op (e2) (e0)) = (e1))\/(((op (e2) (e1)) = (e1))\/(((op (e2) (e2)) = (e1))\/((op (e2) (e3)) = (e1))))) -> (((op (e0) (e1)) = (e1))\/(((op (e1) (e1)) = (e1))\/(((op (e2) (e1)) = (e1))\/((op (e3) (e1)) = (e1))))) -> (~((op (e2) (e1)) = (op (e2) (e3)))) -> (~((op (e1) (e1)) = (e1))) -> (~((op (e0) (e1)) = (op (e0) (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) (e1)) = (op (e2) (e1)))) -> (~((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) (e1)) = (e3))\/(((op (e1) (e1)) = (e3))\/(((op (e2) (e1)) = (e3))\/((op (e3) (e1)) = (e3))))) -> (((op (e2) (e0)) = (e2))\/(((op (e2) (e1)) = (e2))\/(((op (e2) (e2)) = (e2))\/((op (e2) (e3)) = (e2))))) -> (~((op (e2) (e1)) = (e0))) -> (((op (e2) (e1)) = (e0))\/(((op (e2) (e1)) = (e1))\/(((op (e2) (e1)) = (e2))\/((op (e2) (e1)) = (e3))))) -> (~((e0) = (e1))) -> (((op (e2) (e3)) = (e0))\/(((op (e2) (e3)) = (e1))\/(((op (e2) (e3)) = (e2))\/((op (e2) (e3)) = (e3))))) -> (~((op (e1) (e3)) = (op (e2) (e3)))) -> (~((op (e2) (e3)) = (op (e3) (e3)))) -> (~((op (e0) (e3)) = (op (e2) (e3)))) -> (((op (e0) (e3)) = (e2))\/(((op (e1) (e3)) = (e2))\/(((op (e2) (e3)) = (e2))\/((op (e3) (e3)) = (e2))))) -> (~((e1) = (e2))) -> ((op (e2) (e0)) = (e0)) -> (((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)) = (op (e2) (e2)))) -> (((op (e0) (e0)) = (e1))\/(((op (e0) (e1)) = (e1))\/(((op (e0) (e2)) = (e1))\/((op (e0) (e3)) = (e1))))) -> (((op (e0) (e0)) = (e0))\/(((op (e0) (e1)) = (e0))\/(((op (e0) (e2)) = (e0))\/((op (e0) (e3)) = (e0))))) -> (~((op (e2) (e2)) = (e0))) -> (~((op (e1) (e0)) = (e0))) -> (((op (e3) (e0)) = (e0))\/(((op (e3) (e1)) = (e0))\/(((op (e3) (e2)) = (e0))\/((op (e3) (e3)) = (e0))))) -> (~((op (e0) (e2)) = (op (e3) (e2)))) -> (~((op (e1) (e0)) = (op (e1) (e1)))) -> (((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) (e3)))) -> (~((op (e1) (e1)) = (op (e1) (e3)))) -> (((op (e0) (e2)) = (e0))\/(((op (e1) (e2)) = (e0))\/(((op (e2) (e2)) = (e0))\/((op (e3) (e2)) = (e0))))) -> (~((op (e3) (e1)) = (op (e3) (e2)))) -> (~((op (e2) (e0)) = (op (e2) (e2)))) -> (~((op (e1) (e1)) = (op (e1) (e2)))) -> (~((op (e0) (e2)) = (op (e0) (e3)))) -> (~((op (e3) (e0)) = (op (e3) (e1)))) -> (((op (e0) (e0)) = (e0))\/(((op (e1) (e0)) = (e0))\/(((op (e2) (e0)) = (e0))\/((op (e3) (e0)) = (e0))))) -> (~((op (e3) (e0)) = (e0))) -> (~((op (e1) (e2)) = (e0))) -> (~((op (e1) (e3)) = (e0))) -> (((op (e1) (e0)) = (e0))\/(((op (e1) (e1)) = (e0))\/(((op (e1) (e2)) = (e0))\/((op (e1) (e3)) = (e0))))) -> (~((op (e0) (e1)) = (e0))) -> (~((op (e0) (e0)) = (e0))) -> (~((e1) = (e3))) -> ((op (e3) (e0)) = (e1)) -> ((~((op (e3) (e3)) = (e0)))\/((op (e3) (e0)) = (e3))) -> False). % 18.52/18.78 do 0 intro. intros zenon_H1a7 zenon_H3a zenon_H149 zenon_H1d8 zenon_H9d zenon_H1a6 zenon_H54 zenon_Hd8 zenon_H1c4 zenon_H71 zenon_H133 zenon_H18f zenon_H172 zenon_H6f zenon_H173 zenon_H12b zenon_H106 zenon_H109 zenon_H1c7 zenon_H10a zenon_H4a zenon_H6d zenon_H139 zenon_H17e zenon_H160 zenon_H102 zenon_H165 zenon_H1a5 zenon_H1d5 zenon_H31 zenon_H1cc zenon_Ha1 zenon_H11f zenon_Hdb zenon_Hf3 zenon_He2 zenon_H145 zenon_H7c zenon_H34 zenon_H16f zenon_H18c zenon_Ha8 zenon_H22d zenon_H74 zenon_H81 zenon_H23 zenon_H1ac zenon_H14f zenon_H45 zenon_H67 zenon_H130 zenon_H5b zenon_H57 zenon_H6a zenon_H1a4 zenon_H52 zenon_H4f zenon_H208 zenon_H1cf zenon_H3e zenon_H40 zenon_H25 zenon_H38 zenon_H22 zenon_H20b zenon_H3f zenon_H95 zenon_Hac zenon_H1ec. % 18.52/18.78 apply (zenon_or_s _ _ zenon_H1a7); [ zenon_intro zenon_H18b | zenon_intro zenon_H148 ]. % 18.52/18.78 apply (zenon_L353_); trivial. % 18.52/18.78 apply (zenon_or_s _ _ zenon_H1ec); [ zenon_intro zenon_H1ae | zenon_intro zenon_H15e ]. % 18.52/18.78 apply (zenon_or_s _ _ zenon_H74); [ zenon_intro zenon_H42 | zenon_intro zenon_H77 ]. % 18.52/18.78 exact (zenon_H3f zenon_H42). % 18.52/18.78 apply (zenon_or_s _ _ zenon_H77); [ zenon_intro zenon_H49 | zenon_intro zenon_H78 ]. % 18.52/18.78 exact (zenon_H20b zenon_H49). % 18.52/18.78 apply (zenon_or_s _ _ zenon_H78); [ zenon_intro zenon_H48 | zenon_intro zenon_H1e ]. % 18.52/18.78 apply (zenon_L351_); trivial. % 18.52/18.78 apply (zenon_or_s _ _ zenon_H22d); [ zenon_intro zenon_H7a | zenon_intro zenon_H22e ]. % 18.52/18.78 apply (zenon_L35_); trivial. % 18.52/18.78 apply (zenon_or_s _ _ zenon_H22e); [ zenon_intro zenon_Ha0 | zenon_intro zenon_H22f ]. % 18.52/18.78 apply (zenon_or_s _ _ zenon_H22); [ zenon_intro zenon_H27 | zenon_intro zenon_H26 ]. % 18.52/18.78 exact (zenon_H23 zenon_H27). % 18.52/18.78 apply (zenon_or_s _ _ zenon_H26); [ zenon_intro zenon_H29 | zenon_intro zenon_H28 ]. % 18.52/18.78 apply (zenon_or_s _ _ zenon_H18c); [ zenon_intro zenon_H86 | zenon_intro zenon_H18d ]. % 18.52/18.78 apply (zenon_L241_); trivial. % 18.52/18.78 apply (zenon_or_s _ _ zenon_H18d); [ zenon_intro zenon_H110 | zenon_intro zenon_H18e ]. % 18.52/18.78 apply (zenon_L354_); trivial. % 18.52/18.78 apply (zenon_or_s _ _ zenon_H18e); [ zenon_intro zenon_H113 | zenon_intro zenon_Hd7 ]. % 18.52/18.78 apply (zenon_or_s _ _ zenon_H1d8); [ zenon_intro zenon_H10f | zenon_intro zenon_H1d9 ]. % 18.52/18.78 apply (zenon_or_s _ _ zenon_H16f); [ zenon_intro zenon_H9e | zenon_intro zenon_H170 ]. % 18.52/18.78 apply (zenon_L37_); trivial. % 18.52/18.78 apply (zenon_or_s _ _ zenon_H170); [ zenon_intro zenon_H13f | zenon_intro zenon_H171 ]. % 18.52/18.78 apply (zenon_L426_); trivial. % 18.52/18.78 apply (zenon_or_s _ _ zenon_H171); [ zenon_intro zenon_H16c | zenon_intro zenon_Hdc ]. % 18.52/18.78 apply (zenon_L116_); trivial. % 18.52/18.78 apply (zenon_or_s _ _ zenon_H1a5); [ zenon_intro zenon_H99 | zenon_intro zenon_H1a8 ]. % 18.52/18.78 apply (zenon_L175_); trivial. % 18.52/18.78 apply (zenon_or_s _ _ zenon_H1a8); [ zenon_intro zenon_H13f | zenon_intro zenon_H1a9 ]. % 18.52/18.78 apply (zenon_L426_); trivial. % 18.52/18.78 apply (zenon_or_s _ _ zenon_H1a9); [ zenon_intro zenon_Ha6 | zenon_intro zenon_H161 ]. % 18.52/18.78 apply (zenon_L371_); trivial. % 18.52/18.78 apply (zenon_or_s _ _ zenon_H6a); [ zenon_intro zenon_H48 | zenon_intro zenon_H6b ]. % 18.52/18.78 apply (zenon_L336_); trivial. % 18.52/18.78 apply (zenon_or_s _ _ zenon_H6b); [ zenon_intro zenon_H2a | zenon_intro zenon_H6c ]. % 18.52/18.78 exact (zenon_H25 zenon_H2a). % 18.52/18.78 apply (zenon_or_s _ _ zenon_H6c); [ zenon_intro zenon_H2c | zenon_intro zenon_H61 ]. % 18.52/18.78 exact (zenon_H81 zenon_H2c). % 18.52/18.78 apply (zenon_or_s _ _ zenon_H1d5); [ zenon_intro zenon_Hee | zenon_intro zenon_H1d6 ]. % 18.52/18.78 apply (zenon_L204_); trivial. % 18.52/18.78 apply (zenon_or_s _ _ zenon_H1d6); [ zenon_intro zenon_H1ca | zenon_intro zenon_H1d7 ]. % 18.52/18.78 apply (zenon_L435_); trivial. % 18.52/18.78 apply (zenon_or_s _ _ zenon_H1d7); [ zenon_intro zenon_H176 | zenon_intro zenon_H11d ]. % 18.52/18.78 exact (zenon_H173 zenon_H176). % 18.52/18.78 apply (zenon_L412_); trivial. % 18.52/18.78 apply (zenon_or_s _ _ zenon_H1d9); [ zenon_intro zenon_H110 | zenon_intro zenon_H1da ]. % 18.52/18.78 apply (zenon_L354_); trivial. % 18.52/18.78 apply (zenon_or_s _ _ zenon_H1da); [ zenon_intro zenon_H1ca | zenon_intro zenon_H14d ]. % 18.52/18.78 apply (zenon_or_s _ _ zenon_H16f); [ zenon_intro zenon_H9e | zenon_intro zenon_H170 ]. % 18.52/18.78 apply (zenon_L37_); trivial. % 18.52/18.78 apply (zenon_or_s _ _ zenon_H170); [ zenon_intro zenon_H13f | zenon_intro zenon_H171 ]. % 18.52/18.78 apply (zenon_L426_); trivial. % 18.52/18.78 apply (zenon_or_s _ _ zenon_H171); [ zenon_intro zenon_H16c | zenon_intro zenon_Hdc ]. % 18.52/18.78 apply (zenon_L425_); trivial. % 18.52/18.78 apply (zenon_or_s _ _ zenon_H1a5); [ zenon_intro zenon_H99 | zenon_intro zenon_H1a8 ]. % 18.52/18.78 apply (zenon_L403_); trivial. % 18.52/18.78 apply (zenon_or_s _ _ zenon_H1a8); [ zenon_intro zenon_H13f | zenon_intro zenon_H1a9 ]. % 18.52/18.78 apply (zenon_L426_); trivial. % 18.52/18.78 apply (zenon_or_s _ _ zenon_H1a9); [ zenon_intro zenon_Ha6 | zenon_intro zenon_H161 ]. % 18.52/18.78 apply (zenon_L207_); trivial. % 18.52/18.78 apply (zenon_or_s _ _ zenon_H6a); [ zenon_intro zenon_H48 | zenon_intro zenon_H6b ]. % 18.52/18.78 apply (zenon_L336_); trivial. % 18.52/18.78 apply (zenon_or_s _ _ zenon_H6b); [ zenon_intro zenon_H2a | zenon_intro zenon_H6c ]. % 18.52/18.78 exact (zenon_H25 zenon_H2a). % 18.52/18.78 apply (zenon_or_s _ _ zenon_H6c); [ zenon_intro zenon_H2c | zenon_intro zenon_H61 ]. % 18.52/18.78 exact (zenon_H81 zenon_H2c). % 18.52/18.78 apply (zenon_L435_); trivial. % 18.52/18.78 apply (zenon_L436_); trivial. % 18.52/18.78 apply (zenon_or_s _ _ zenon_H16f); [ zenon_intro zenon_H9e | zenon_intro zenon_H170 ]. % 18.52/18.78 apply (zenon_L37_); trivial. % 18.52/18.78 apply (zenon_or_s _ _ zenon_H170); [ zenon_intro zenon_H13f | zenon_intro zenon_H171 ]. % 18.52/18.78 apply (zenon_L426_); trivial. % 18.52/18.78 apply (zenon_or_s _ _ zenon_H171); [ zenon_intro zenon_H16c | zenon_intro zenon_Hdc ]. % 18.52/18.78 apply (zenon_L425_); trivial. % 18.52/18.78 apply (zenon_L266_); trivial. % 18.52/18.78 apply (zenon_or_s _ _ zenon_H28); [ zenon_intro zenon_H2a | zenon_intro zenon_H1f ]. % 18.52/18.78 exact (zenon_H25 zenon_H2a). % 18.52/18.79 exact (zenon_H38 zenon_H1f). % 18.52/18.79 apply (zenon_or_s _ _ zenon_H22f); [ zenon_intro zenon_H122 | zenon_intro zenon_Hc3 ]. % 18.52/18.79 apply (zenon_L438_); trivial. % 18.52/18.79 apply (zenon_L427_); trivial. % 18.52/18.79 apply (zenon_L109_); trivial. % 18.52/18.79 (* end of lemma zenon_L439_ *) % 18.52/18.79 assert (zenon_L440_ : (~((op (e0) (e3)) = (op (e3) (e3)))) -> ((op (e0) (e3)) = (e0)) -> ((op (e3) (e3)) = (e0)) -> False). % 18.52/18.79 do 0 intro. intros zenon_Hc2 zenon_H1e zenon_H60. % 18.52/18.79 cut (((op (e0) (e3)) = (e0)) = ((op (e0) (e3)) = (op (e3) (e3)))). % 18.52/18.79 intro zenon_D_pnotp. % 18.52/18.79 apply zenon_Hc2. % 18.52/18.79 rewrite <- zenon_D_pnotp. % 18.52/18.79 exact zenon_H1e. % 18.52/18.79 cut (((e0) = (op (e3) (e3)))); [idtac | apply NNPP; zenon_intro zenon_H188]. % 18.52/18.79 cut (((op (e0) (e3)) = (op (e0) (e3)))); [idtac | apply NNPP; zenon_intro zenon_H21]. % 18.52/18.79 congruence. % 18.52/18.79 apply zenon_H21. apply refl_equal. % 18.52/18.79 apply zenon_H188. apply sym_equal. exact zenon_H60. % 18.52/18.79 (* end of lemma zenon_L440_ *) % 18.52/18.79 assert (zenon_L441_ : (((op (e0) (e1)) = (e3))\/(((op (e1) (e1)) = (e3))\/(((op (e2) (e1)) = (e3))\/((op (e3) (e1)) = (e3))))) -> (~((e2) = (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) (e1)) = (e0))) -> (~((op (e2) (e1)) = (op (e3) (e1)))) -> (~((op (e0) (e1)) = (op (e2) (e1)))) -> (~((op (e1) (e1)) = (op (e2) (e1)))) -> (~((op (e3) (e1)) = (e0))) -> (((op (e3) (e1)) = (e0))\/(((op (e3) (e1)) = (e1))\/(((op (e3) (e1)) = (e2))\/((op (e3) (e1)) = (e3))))) -> ((op (e1) (e1)) = (e0)) -> ((op (e0) (e1)) = (e2)) -> ((op (e3) (e0)) = (e3)) -> (~((op (e3) (e0)) = (op (e3) (e1)))) -> False). % 18.52/18.79 do 0 intro. intros zenon_H1a5 zenon_H12b zenon_H210 zenon_H1cc zenon_H31 zenon_Haf zenon_H17e zenon_H13e zenon_H1ad zenon_H22a zenon_H29 zenon_H10f zenon_H15e zenon_H1cf. % 18.52/18.79 apply (zenon_or_s _ _ zenon_H1a5); [ zenon_intro zenon_H99 | zenon_intro zenon_H1a8 ]. % 18.52/18.79 apply (zenon_L175_); trivial. % 18.52/18.79 apply (zenon_or_s _ _ zenon_H1a8); [ zenon_intro zenon_H13f | zenon_intro zenon_H1a9 ]. % 18.52/18.79 apply (zenon_or_s _ _ zenon_H22a); [ zenon_intro zenon_H1b1 | zenon_intro zenon_H22b ]. % 18.52/18.79 exact (zenon_H1ad zenon_H1b1). % 18.52/18.79 apply (zenon_or_s _ _ zenon_H22b); [ zenon_intro zenon_Hae | zenon_intro zenon_H22c ]. % 18.52/18.79 apply (zenon_L192_); trivial. % 18.52/18.79 apply (zenon_or_s _ _ zenon_H22c); [ zenon_intro zenon_H14d | zenon_intro zenon_H161 ]. % 18.52/18.79 apply (zenon_L389_); trivial. % 18.52/18.79 apply (zenon_L193_); trivial. % 18.52/18.79 apply (zenon_or_s _ _ zenon_H1a9); [ zenon_intro zenon_Ha6 | zenon_intro zenon_H161 ]. % 18.52/18.79 apply (zenon_L371_); trivial. % 18.52/18.79 apply (zenon_L193_); trivial. % 18.52/18.79 (* end of lemma zenon_L441_ *) % 18.52/18.79 assert (zenon_L442_ : (((op (e2) (e3)) = (e0))\/(((op (e2) (e3)) = (e1))\/(((op (e2) (e3)) = (e2))\/((op (e2) (e3)) = (e3))))) -> (~((op (e2) (e3)) = (e0))) -> (~((op (e2) (e1)) = (op (e2) (e3)))) -> ((op (e2) (e1)) = (e1)) -> ((op (e3) (e3)) = (e2)) -> (~((op (e2) (e3)) = (op (e3) (e3)))) -> (~((op (e1) (e3)) = (op (e2) (e3)))) -> ((op (e1) (e3)) = (e3)) -> False). % 18.52/18.79 do 0 intro. intros zenon_H11f zenon_H32 zenon_H1c7 zenon_Ha5 zenon_Hf6 zenon_Hf3 zenon_Hdb zenon_Hdc. % 18.52/18.79 apply (zenon_or_s _ _ zenon_H11f); [ zenon_intro zenon_H37 | zenon_intro zenon_H120 ]. % 18.52/18.79 exact (zenon_H32 zenon_H37). % 18.52/18.79 apply (zenon_or_s _ _ zenon_H120); [ zenon_intro zenon_Hf4 | zenon_intro zenon_H121 ]. % 18.52/18.79 apply (zenon_L188_); trivial. % 18.52/18.79 apply (zenon_or_s _ _ zenon_H121); [ zenon_intro zenon_H11d | zenon_intro zenon_Hdd ]. % 18.52/18.79 apply (zenon_L97_); trivial. % 18.52/18.79 apply (zenon_L52_); trivial. % 18.52/18.79 (* end of lemma zenon_L442_ *) % 18.52/18.79 assert (zenon_L443_ : (((op (e0) (e1)) = (e3))\/(((op (e1) (e1)) = (e3))\/(((op (e2) (e1)) = (e3))\/((op (e3) (e1)) = (e3))))) -> ((op (e1) (e1)) = (e0)) -> (~((op (e0) (e1)) = (op (e1) (e1)))) -> (~((op (e0) (e1)) = (op (e3) (e1)))) -> ((op (e3) (e1)) = (e2)) -> (~((op (e0) (e1)) = (op (e2) (e1)))) -> (~((op (e0) (e1)) = (e0))) -> (((op (e0) (e1)) = (e0))\/(((op (e0) (e1)) = (e1))\/(((op (e0) (e1)) = (e2))\/((op (e0) (e1)) = (e3))))) -> (~((e1) = (e3))) -> ((op (e2) (e1)) = (e1)) -> ((op (e3) (e0)) = (e3)) -> (~((op (e3) (e0)) = (op (e3) (e1)))) -> False). % 18.52/18.79 do 0 intro. intros zenon_H1a5 zenon_H29 zenon_H10e zenon_H210 zenon_H14d zenon_H17e zenon_H20b zenon_H212 zenon_H95 zenon_Ha5 zenon_H15e zenon_H1cf. % 18.52/18.79 apply (zenon_or_s _ _ zenon_H1a5); [ zenon_intro zenon_H99 | zenon_intro zenon_H1a8 ]. % 18.52/18.79 apply (zenon_L385_); trivial. % 18.52/18.79 apply (zenon_or_s _ _ zenon_H1a8); [ zenon_intro zenon_H13f | zenon_intro zenon_H1a9 ]. % 18.52/18.79 apply (zenon_L390_); trivial. % 18.52/18.79 apply (zenon_or_s _ _ zenon_H1a9); [ zenon_intro zenon_Ha6 | zenon_intro zenon_H161 ]. % 18.52/18.79 apply (zenon_L39_); trivial. % 18.52/18.79 apply (zenon_L193_); trivial. % 18.52/18.79 (* end of lemma zenon_L443_ *) % 18.52/18.79 assert (zenon_L444_ : (((op (e3) (e0)) = (e0))\/(((op (e3) (e1)) = (e0))\/(((op (e3) (e2)) = (e0))\/((op (e3) (e3)) = (e0))))) -> (~((op (e3) (e0)) = (e0))) -> (~((op (e3) (e1)) = (e0))) -> (~((op (e3) (e2)) = (e0))) -> ((op (e1) (e3)) = (e2)) -> ((op (e0) (e3)) = (e1)) -> False). % 18.52/18.79 do 0 intro. intros zenon_H1ac zenon_H40 zenon_H1ad zenon_H18b zenon_Hd7 zenon_Hc3. % 18.52/18.79 apply (zenon_or_s _ _ zenon_H1ac); [ zenon_intro zenon_H44 | zenon_intro zenon_H1af ]. % 18.52/18.79 exact (zenon_H40 zenon_H44). % 18.52/18.79 apply (zenon_or_s _ _ zenon_H1af); [ zenon_intro zenon_H1b1 | zenon_intro zenon_H1b0 ]. % 18.52/18.79 exact (zenon_H1ad zenon_H1b1). % 18.52/18.79 apply (zenon_or_s _ _ zenon_H1b0); [ zenon_intro zenon_H61 | zenon_intro zenon_H60 ]. % 18.52/18.79 exact (zenon_H18b zenon_H61). % 18.52/18.79 apply (zenon_L201_); trivial. % 18.52/18.79 (* end of lemma zenon_L444_ *) % 18.52/18.79 assert (zenon_L445_ : (((op (e0) (e1)) = (e3))\/(((op (e1) (e1)) = (e3))\/(((op (e2) (e1)) = (e3))\/((op (e3) (e1)) = (e3))))) -> (~((e2) = (e3))) -> (~((op (e0) (e1)) = (op (e1) (e1)))) -> (((op (e2) (e1)) = (e0))\/(((op (e2) (e1)) = (e1))\/(((op (e2) (e1)) = (e2))\/((op (e2) (e1)) = (e3))))) -> (~((op (e2) (e1)) = (e0))) -> (~((op (e2) (e1)) = (op (e3) (e1)))) -> ((op (e3) (e1)) = (e1)) -> (~((op (e0) (e1)) = (op (e2) (e1)))) -> (~((op (e1) (e1)) = (op (e2) (e1)))) -> (~((op (e0) (e1)) = (op (e3) (e1)))) -> (~((op (e0) (e1)) = (e0))) -> (((op (e0) (e1)) = (e0))\/(((op (e0) (e1)) = (e1))\/(((op (e0) (e1)) = (e2))\/((op (e0) (e1)) = (e3))))) -> ((op (e1) (e1)) = (e0)) -> ((op (e0) (e1)) = (e2)) -> ((op (e3) (e0)) = (e3)) -> (~((op (e3) (e0)) = (op (e3) (e1)))) -> False). % 18.52/18.79 do 0 intro. intros zenon_H1a5 zenon_H12b zenon_H10e zenon_H1cc zenon_H31 zenon_Haf zenon_Hae zenon_H17e zenon_H13e zenon_H210 zenon_H20b zenon_H212 zenon_H29 zenon_H10f zenon_H15e zenon_H1cf. % 18.52/18.79 apply (zenon_or_s _ _ zenon_H1a5); [ zenon_intro zenon_H99 | zenon_intro zenon_H1a8 ]. % 18.52/18.79 apply (zenon_L175_); trivial. % 18.52/18.79 apply (zenon_or_s _ _ zenon_H1a8); [ zenon_intro zenon_H13f | zenon_intro zenon_H1a9 ]. % 18.52/18.79 apply (zenon_L368_); trivial. % 18.52/18.79 apply (zenon_or_s _ _ zenon_H1a9); [ zenon_intro zenon_Ha6 | zenon_intro zenon_H161 ]. % 18.52/18.79 apply (zenon_L371_); trivial. % 18.52/18.79 apply (zenon_L193_); trivial. % 18.52/18.79 (* end of lemma zenon_L445_ *) % 18.52/18.79 assert (zenon_L446_ : (((op (e2) (e3)) = (e0))\/(((op (e2) (e3)) = (e1))\/(((op (e2) (e3)) = (e2))\/((op (e2) (e3)) = (e3))))) -> (~((op (e2) (e3)) = (e0))) -> (~((op (e2) (e2)) = (op (e2) (e3)))) -> ((op (e2) (e2)) = (e1)) -> ((op (e3) (e3)) = (e2)) -> (~((op (e2) (e3)) = (op (e3) (e3)))) -> (~((op (e1) (e3)) = (op (e2) (e3)))) -> ((op (e1) (e3)) = (e3)) -> False). % 18.52/18.79 do 0 intro. intros zenon_H11f zenon_H32 zenon_H6d zenon_Hf1 zenon_Hf6 zenon_Hf3 zenon_Hdb zenon_Hdc. % 18.52/18.79 apply (zenon_or_s _ _ zenon_H11f); [ zenon_intro zenon_H37 | zenon_intro zenon_H120 ]. % 18.52/18.79 exact (zenon_H32 zenon_H37). % 18.52/18.79 apply (zenon_or_s _ _ zenon_H120); [ zenon_intro zenon_Hf4 | zenon_intro zenon_H121 ]. % 18.52/18.79 apply (zenon_L84_); trivial. % 18.52/18.79 apply (zenon_or_s _ _ zenon_H121); [ zenon_intro zenon_H11d | zenon_intro zenon_Hdd ]. % 18.52/18.79 apply (zenon_L97_); trivial. % 18.52/18.79 apply (zenon_L52_); trivial. % 18.52/18.79 (* end of lemma zenon_L446_ *) % 18.52/18.79 assert (zenon_L447_ : (((op (e1) (e0)) = (e0))\/(((op (e1) (e1)) = (e0))\/(((op (e1) (e2)) = (e0))\/((op (e1) (e3)) = (e0))))) -> (~((op (e1) (e0)) = (e0))) -> (~((e2) = (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) (e3)) = (e0))\/(((op (e3) (e3)) = (e1))\/(((op (e3) (e3)) = (e2))\/((op (e3) (e3)) = (e3))))) -> ((op (e0) (e3)) = (e1)) -> (~((op (e3) (e1)) = (op (e3) (e3)))) -> (~((op (e3) (e2)) = (op (e3) (e3)))) -> (~((op (e3) (e3)) = (e3))) -> (((op (e0) (e1)) = (e0))\/(((op (e0) (e1)) = (e1))\/(((op (e0) (e1)) = (e2))\/((op (e0) (e1)) = (e3))))) -> (~((op (e0) (e1)) = (e0))) -> (~((op (e0) (e1)) = (op (e3) (e1)))) -> (~((op (e1) (e1)) = (op (e2) (e1)))) -> (~((op (e0) (e1)) = (op (e2) (e1)))) -> (~((op (e2) (e1)) = (op (e3) (e1)))) -> (~((op (e2) (e1)) = (e0))) -> (((op (e2) (e1)) = (e0))\/(((op (e2) (e1)) = (e1))\/(((op (e2) (e1)) = (e2))\/((op (e2) (e1)) = (e3))))) -> (~((op (e0) (e1)) = (op (e1) (e1)))) -> ((op (e1) (e0)) = (e1)) -> (~((e1) = (e3))) -> (((op (e1) (e0)) = (e3))\/(((op (e1) (e1)) = (e3))\/(((op (e1) (e2)) = (e3))\/((op (e1) (e3)) = (e3))))) -> (~((op (e3) (e0)) = (op (e3) (e1)))) -> ((op (e3) (e0)) = (e3)) -> (((op (e2) (e0)) = (e1))\/(((op (e2) (e1)) = (e1))\/(((op (e2) (e2)) = (e1))\/((op (e2) (e3)) = (e1))))) -> (~((e0) = (e1))) -> ((op (e2) (e0)) = (e0)) -> (~((op (e1) (e3)) = (op (e2) (e3)))) -> (~((op (e2) (e3)) = (op (e3) (e3)))) -> (~((op (e2) (e2)) = (op (e2) (e3)))) -> (~((op (e2) (e3)) = (e0))) -> (((op (e2) (e3)) = (e0))\/(((op (e2) (e3)) = (e1))\/(((op (e2) (e3)) = (e2))\/((op (e2) (e3)) = (e3))))) -> (((op (e0) (e3)) = (e2))\/(((op (e1) (e3)) = (e2))\/(((op (e2) (e3)) = (e2))\/((op (e3) (e3)) = (e2))))) -> (((op (e0) (e3)) = (e1))\/(((op (e1) (e3)) = (e1))\/(((op (e2) (e3)) = (e1))\/((op (e3) (e3)) = (e1))))) -> (~((op (e2) (e1)) = (op (e2) (e3)))) -> (~((op (e0) (e0)) = (op (e0) (e3)))) -> ((op (e0) (e0)) = (e2)) -> (((op (e0) (e1)) = (e2))\/(((op (e1) (e1)) = (e2))\/(((op (e2) (e1)) = (e2))\/((op (e3) (e1)) = (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) (e3)) = (op (e2) (e3)))) -> (((op (e0) (e1)) = (e3))\/(((op (e1) (e1)) = (e3))\/(((op (e2) (e1)) = (e3))\/((op (e3) (e1)) = (e3))))) -> (~((e1) = (e2))) -> (((op (e1) (e0)) = (e2))\/(((op (e1) (e1)) = (e2))\/(((op (e1) (e2)) = (e2))\/((op (e1) (e3)) = (e2))))) -> (((op (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) (e0)) = (e0))) -> (~((op (e3) (e1)) = (e0))) -> (~((op (e3) (e2)) = (e0))) -> (~((op (e1) (e1)) = (e1))) -> (~((op (e0) (e1)) = (op (e0) (e3)))) -> (((op (e0) (e1)) = (e1))\/(((op (e1) (e1)) = (e1))\/(((op (e2) (e1)) = (e1))\/((op (e3) (e1)) = (e1))))) -> (~((op (e1) (e2)) = (e0))) -> (~((op (e1) (e3)) = (e0))) -> False). % 18.52/18.79 do 0 intro. intros zenon_H22 zenon_H23 zenon_H12b zenon_H172 zenon_H149 zenon_H48 zenon_H173 zenon_H101 zenon_Hc3 zenon_H130 zenon_H62 zenon_H102 zenon_H212 zenon_H20b zenon_H210 zenon_H13e zenon_H17e zenon_Haf zenon_H31 zenon_H1cc zenon_H10e zenon_H9d zenon_H95 zenon_H16f zenon_H1cf zenon_H15e zenon_H106 zenon_Ha1 zenon_H34 zenon_Hdb zenon_Hf3 zenon_H6d zenon_H32 zenon_H11f zenon_H145 zenon_H133 zenon_H1c7 zenon_H189 zenon_H7b zenon_H1d8 zenon_H71 zenon_H153 zenon_He2 zenon_H1a5 zenon_H7c zenon_H18c zenon_H22a zenon_H1ac zenon_H40 zenon_H1ad zenon_H18b zenon_H10a zenon_H54 zenon_H109 zenon_H25 zenon_H38. % 18.52/18.79 apply (zenon_or_s _ _ zenon_H22); [ zenon_intro zenon_H27 | zenon_intro zenon_H26 ]. % 18.52/18.79 exact (zenon_H23 zenon_H27). % 18.52/18.79 apply (zenon_or_s _ _ zenon_H26); [ zenon_intro zenon_H29 | zenon_intro zenon_H28 ]. % 18.52/18.79 apply (zenon_or_s _ _ zenon_H109); [ zenon_intro zenon_Ha0 | zenon_intro zenon_H10b ]. % 18.52/18.79 apply (zenon_L359_); trivial. % 18.52/18.79 apply (zenon_or_s _ _ zenon_H10b); [ zenon_intro zenon_H10d | zenon_intro zenon_H10c ]. % 18.52/18.79 exact (zenon_H10a zenon_H10d). % 18.52/18.79 apply (zenon_or_s _ _ zenon_H10c); [ zenon_intro zenon_Ha5 | zenon_intro zenon_Hae ]. % 18.52/18.79 apply (zenon_or_s _ _ zenon_H18c); [ zenon_intro zenon_H86 | zenon_intro zenon_H18d ]. % 18.52/18.79 apply (zenon_L123_); trivial. % 18.52/18.79 apply (zenon_or_s _ _ zenon_H18d); [ zenon_intro zenon_H110 | zenon_intro zenon_H18e ]. % 18.52/18.79 apply (zenon_L354_); trivial. % 18.52/18.79 apply (zenon_or_s _ _ zenon_H18e); [ zenon_intro zenon_H113 | zenon_intro zenon_Hd7 ]. % 18.52/18.79 apply (zenon_or_s _ _ zenon_H1d8); [ zenon_intro zenon_H10f | zenon_intro zenon_H1d9 ]. % 18.52/18.79 apply (zenon_L441_); trivial. % 18.52/18.79 apply (zenon_or_s _ _ zenon_H1d9); [ zenon_intro zenon_H110 | zenon_intro zenon_H1da ]. % 18.52/18.79 apply (zenon_L354_); trivial. % 18.52/18.79 apply (zenon_or_s _ _ zenon_H1da); [ zenon_intro zenon_H1ca | zenon_intro zenon_H14d ]. % 18.52/18.79 apply (zenon_or_s _ _ zenon_H16f); [ zenon_intro zenon_H9e | zenon_intro zenon_H170 ]. % 18.52/18.79 apply (zenon_L37_); trivial. % 18.52/18.79 apply (zenon_or_s _ _ zenon_H170); [ zenon_intro zenon_H13f | zenon_intro zenon_H171 ]. % 18.52/18.79 apply (zenon_L373_); trivial. % 18.52/18.79 apply (zenon_or_s _ _ zenon_H171); [ zenon_intro zenon_H16c | zenon_intro zenon_Hdc ]. % 18.52/18.79 apply (zenon_L116_); trivial. % 18.52/18.79 apply (zenon_or_s _ _ zenon_H1ac); [ zenon_intro zenon_H44 | zenon_intro zenon_H1af ]. % 18.52/18.79 exact (zenon_H40 zenon_H44). % 18.52/18.79 apply (zenon_or_s _ _ zenon_H1af); [ zenon_intro zenon_H1b1 | zenon_intro zenon_H1b0 ]. % 18.52/18.79 exact (zenon_H1ad zenon_H1b1). % 18.52/18.79 apply (zenon_or_s _ _ zenon_H1b0); [ zenon_intro zenon_H61 | zenon_intro zenon_H60 ]. % 18.52/18.79 exact (zenon_H18b zenon_H61). % 18.52/18.79 apply (zenon_or_s _ _ zenon_H145); [ zenon_intro zenon_Hcd | zenon_intro zenon_H146 ]. % 18.52/18.79 apply (zenon_L235_); trivial. % 18.52/18.79 apply (zenon_or_s _ _ zenon_H146); [ zenon_intro zenon_Hd7 | zenon_intro zenon_H147 ]. % 18.52/18.79 apply (zenon_L201_); trivial. % 18.52/18.79 apply (zenon_or_s _ _ zenon_H147); [ zenon_intro zenon_H11d | zenon_intro zenon_Hf6 ]. % 18.52/18.79 apply (zenon_L224_); trivial. % 18.52/18.79 apply (zenon_L442_); trivial. % 18.52/18.79 apply (zenon_L443_); trivial. % 18.52/18.79 apply (zenon_L444_); trivial. % 18.52/18.79 apply (zenon_or_s _ _ zenon_H18c); [ zenon_intro zenon_H86 | zenon_intro zenon_H18d ]. % 18.52/18.79 apply (zenon_L123_); trivial. % 18.52/18.79 apply (zenon_or_s _ _ zenon_H18d); [ zenon_intro zenon_H110 | zenon_intro zenon_H18e ]. % 18.52/18.79 apply (zenon_L354_); trivial. % 18.52/18.79 apply (zenon_or_s _ _ zenon_H18e); [ zenon_intro zenon_H113 | zenon_intro zenon_Hd7 ]. % 18.52/18.79 apply (zenon_or_s _ _ zenon_H1d8); [ zenon_intro zenon_H10f | zenon_intro zenon_H1d9 ]. % 18.52/18.79 apply (zenon_L445_); trivial. % 18.52/18.79 apply (zenon_or_s _ _ zenon_H1d9); [ zenon_intro zenon_H110 | zenon_intro zenon_H1da ]. % 18.52/18.79 apply (zenon_L354_); trivial. % 18.52/18.79 apply (zenon_or_s _ _ zenon_H1da); [ zenon_intro zenon_H1ca | zenon_intro zenon_H14d ]. % 18.52/18.79 apply (zenon_or_s _ _ zenon_H16f); [ zenon_intro zenon_H9e | zenon_intro zenon_H170 ]. % 18.52/18.79 apply (zenon_L37_); trivial. % 18.52/18.79 apply (zenon_or_s _ _ zenon_H170); [ zenon_intro zenon_H13f | zenon_intro zenon_H171 ]. % 18.52/18.79 apply (zenon_L368_); trivial. % 18.52/18.79 apply (zenon_or_s _ _ zenon_H171); [ zenon_intro zenon_H16c | zenon_intro zenon_Hdc ]. % 18.52/18.79 apply (zenon_L116_); trivial. % 18.52/18.79 apply (zenon_or_s _ _ zenon_H1a5); [ zenon_intro zenon_H99 | zenon_intro zenon_H1a8 ]. % 18.52/18.79 apply (zenon_or_s _ _ zenon_H106); [ zenon_intro zenon_Hed | zenon_intro zenon_H107 ]. % 18.52/18.79 apply (zenon_L214_); trivial. % 18.52/18.79 apply (zenon_or_s _ _ zenon_H107); [ zenon_intro zenon_Ha5 | zenon_intro zenon_H108 ]. % 18.52/18.79 apply (zenon_L42_); trivial. % 18.52/18.79 apply (zenon_or_s _ _ zenon_H108); [ zenon_intro zenon_Hf1 | zenon_intro zenon_Hf4 ]. % 18.52/18.79 apply (zenon_or_s _ _ zenon_H153); [ zenon_intro zenon_H148 | zenon_intro zenon_H154 ]. % 18.52/18.79 apply (zenon_L377_); trivial. % 18.52/18.79 apply (zenon_or_s _ _ zenon_H154); [ zenon_intro zenon_H14d | zenon_intro zenon_H155 ]. % 18.52/18.79 apply (zenon_L385_); trivial. % 18.52/18.79 apply (zenon_or_s _ _ zenon_H155); [ zenon_intro zenon_H151 | zenon_intro zenon_Hf6 ]. % 18.52/18.79 apply (zenon_or_s _ _ zenon_H145); [ zenon_intro zenon_Hcd | zenon_intro zenon_H146 ]. % 18.52/18.79 apply (zenon_L86_); trivial. % 18.52/18.79 apply (zenon_or_s _ _ zenon_H146); [ zenon_intro zenon_Hd7 | zenon_intro zenon_H147 ]. % 18.52/18.79 apply (zenon_L379_); trivial. % 18.52/18.79 apply (zenon_or_s _ _ zenon_H147); [ zenon_intro zenon_H11d | zenon_intro zenon_Hf6 ]. % 18.52/18.79 apply (zenon_L224_); trivial. % 18.52/18.79 apply (zenon_L446_); trivial. % 18.52/18.79 apply (zenon_L446_); trivial. % 18.52/18.79 apply (zenon_L272_); trivial. % 18.52/18.79 apply (zenon_or_s _ _ zenon_H1a8); [ zenon_intro zenon_H13f | zenon_intro zenon_H1a9 ]. % 18.52/18.79 apply (zenon_L368_); trivial. % 18.52/18.79 apply (zenon_or_s _ _ zenon_H1a9); [ zenon_intro zenon_Ha6 | zenon_intro zenon_H161 ]. % 18.52/18.79 apply (zenon_L207_); trivial. % 18.52/18.79 apply (zenon_L193_); trivial. % 18.52/18.79 apply (zenon_L152_); trivial. % 18.52/18.79 apply (zenon_L394_); trivial. % 18.52/18.79 apply (zenon_or_s _ _ zenon_H28); [ zenon_intro zenon_H2a | zenon_intro zenon_H1f ]. % 18.52/18.79 exact (zenon_H25 zenon_H2a). % 18.52/18.79 exact (zenon_H38 zenon_H1f). % 18.52/18.79 (* end of lemma zenon_L447_ *) % 18.52/18.79 assert (zenon_L448_ : (((op (e0) (e3)) = (e0))\/(((op (e0) (e3)) = (e1))\/(((op (e0) (e3)) = (e2))\/((op (e0) (e3)) = (e3))))) -> ((op (e3) (e3)) = (e0)) -> (~((op (e0) (e3)) = (op (e3) (e3)))) -> (~((op (e1) (e3)) = (e0))) -> (~((op (e1) (e2)) = (e0))) -> (((op (e0) (e1)) = (e1))\/(((op (e1) (e1)) = (e1))\/(((op (e2) (e1)) = (e1))\/((op (e3) (e1)) = (e1))))) -> (~((op (e0) (e1)) = (op (e0) (e3)))) -> (~((op (e1) (e1)) = (e1))) -> (~((op (e3) (e2)) = (e0))) -> (~((op (e3) (e1)) = (e0))) -> (~((op (e3) (e0)) = (e0))) -> (((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 (e1) (e0)) = (e2))\/(((op (e1) (e1)) = (e2))\/(((op (e1) (e2)) = (e2))\/((op (e1) (e3)) = (e2))))) -> (~((e1) = (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 (e3) (e0)) = (op (e3) (e3)))) -> (((op (e0) (e1)) = (e2))\/(((op (e1) (e1)) = (e2))\/(((op (e2) (e1)) = (e2))\/((op (e3) (e1)) = (e2))))) -> ((op (e0) (e0)) = (e2)) -> (~((op (e0) (e0)) = (op (e0) (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) (e3)) = (e2))\/(((op (e1) (e3)) = (e2))\/(((op (e2) (e3)) = (e2))\/((op (e3) (e3)) = (e2))))) -> (((op (e2) (e3)) = (e0))\/(((op (e2) (e3)) = (e1))\/(((op (e2) (e3)) = (e2))\/((op (e2) (e3)) = (e3))))) -> (~((op (e2) (e3)) = (e0))) -> (~((op (e2) (e2)) = (op (e2) (e3)))) -> (~((op (e2) (e3)) = (op (e3) (e3)))) -> (~((op (e1) (e3)) = (op (e2) (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) (e0)) = (e3)) -> (~((op (e3) (e0)) = (op (e3) (e1)))) -> (((op (e1) (e0)) = (e3))\/(((op (e1) (e1)) = (e3))\/(((op (e1) (e2)) = (e3))\/((op (e1) (e3)) = (e3))))) -> (~((e1) = (e3))) -> ((op (e1) (e0)) = (e1)) -> (~((op (e0) (e1)) = (op (e1) (e1)))) -> (((op (e2) (e1)) = (e0))\/(((op (e2) (e1)) = (e1))\/(((op (e2) (e1)) = (e2))\/((op (e2) (e1)) = (e3))))) -> (~((op (e2) (e1)) = (e0))) -> (~((op (e2) (e1)) = (op (e3) (e1)))) -> (~((op (e0) (e1)) = (op (e2) (e1)))) -> (~((op (e1) (e1)) = (op (e2) (e1)))) -> (~((op (e0) (e1)) = (op (e3) (e1)))) -> (~((op (e0) (e1)) = (e0))) -> (((op (e0) (e1)) = (e0))\/(((op (e0) (e1)) = (e1))\/(((op (e0) (e1)) = (e2))\/((op (e0) (e1)) = (e3))))) -> (~((op (e3) (e3)) = (e3))) -> (~((op (e3) (e2)) = (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 (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))))) -> (~((e2) = (e3))) -> (~((op (e1) (e0)) = (e0))) -> (((op (e1) (e0)) = (e0))\/(((op (e1) (e1)) = (e0))\/(((op (e1) (e2)) = (e0))\/((op (e1) (e3)) = (e0))))) -> ((op (e2) (e3)) = (e2)) -> (~((op (e0) (e3)) = (op (e2) (e3)))) -> (~((op (e0) (e3)) = (op (e1) (e3)))) -> ((op (e1) (e3)) = (e3)) -> False). % 18.52/18.79 do 0 intro. intros zenon_He4 zenon_H60 zenon_Hc2 zenon_H38 zenon_H25 zenon_H109 zenon_H54 zenon_H10a zenon_H18b zenon_H1ad zenon_H40 zenon_H1ac zenon_H22a zenon_H18c zenon_H7c zenon_H1a5 zenon_H153 zenon_H71 zenon_H1d8 zenon_H7b zenon_H189 zenon_H1c7 zenon_H133 zenon_H145 zenon_H11f zenon_H32 zenon_H6d zenon_Hf3 zenon_Hdb zenon_H34 zenon_Ha1 zenon_H106 zenon_H15e zenon_H1cf zenon_H16f zenon_H95 zenon_H9d zenon_H10e zenon_H1cc zenon_H31 zenon_Haf zenon_H17e zenon_H13e zenon_H210 zenon_H20b zenon_H212 zenon_H102 zenon_H62 zenon_H130 zenon_H101 zenon_H173 zenon_H48 zenon_H149 zenon_H172 zenon_H12b zenon_H23 zenon_H22 zenon_H11d zenon_He2 zenon_H1d zenon_Hdc. % 18.52/18.79 apply (zenon_or_s _ _ zenon_He4); [ zenon_intro zenon_H1e | zenon_intro zenon_He5 ]. % 18.52/18.79 apply (zenon_L440_); trivial. % 18.52/18.79 apply (zenon_or_s _ _ zenon_He5); [ zenon_intro zenon_Hc3 | zenon_intro zenon_He6 ]. % 18.52/18.79 apply (zenon_L447_); trivial. % 18.52/18.79 apply (zenon_or_s _ _ zenon_He6); [ zenon_intro zenon_Hcd | zenon_intro zenon_He3 ]. % 18.52/18.79 apply (zenon_L234_); trivial. % 18.52/18.79 apply (zenon_L117_); trivial. % 18.52/18.79 (* end of lemma zenon_L448_ *) % 18.52/18.79 assert (zenon_L449_ : (((op (e0) (e3)) = (e0))\/(((op (e0) (e3)) = (e1))\/(((op (e0) (e3)) = (e2))\/((op (e0) (e3)) = (e3))))) -> (~((op (e0) (e3)) = (op (e3) (e3)))) -> (~((op (e1) (e3)) = (e0))) -> (~((op (e1) (e2)) = (e0))) -> (((op (e0) (e1)) = (e1))\/(((op (e1) (e1)) = (e1))\/(((op (e2) (e1)) = (e1))\/((op (e3) (e1)) = (e1))))) -> (~((op (e0) (e1)) = (op (e0) (e3)))) -> (~((op (e1) (e1)) = (e1))) -> (~((op (e3) (e2)) = (e0))) -> (~((op (e3) (e1)) = (e0))) -> (~((op (e3) (e0)) = (e0))) -> (((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 (e1) (e0)) = (e2))\/(((op (e1) (e1)) = (e2))\/(((op (e1) (e2)) = (e2))\/((op (e1) (e3)) = (e2))))) -> (~((e1) = (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 (e3) (e0)) = (op (e3) (e3)))) -> (((op (e0) (e1)) = (e2))\/(((op (e1) (e1)) = (e2))\/(((op (e2) (e1)) = (e2))\/((op (e3) (e1)) = (e2))))) -> ((op (e0) (e0)) = (e2)) -> (~((op (e0) (e0)) = (op (e0) (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) (e3)) = (e2))\/(((op (e1) (e3)) = (e2))\/(((op (e2) (e3)) = (e2))\/((op (e3) (e3)) = (e2))))) -> (((op (e2) (e3)) = (e0))\/(((op (e2) (e3)) = (e1))\/(((op (e2) (e3)) = (e2))\/((op (e2) (e3)) = (e3))))) -> (~((op (e2) (e3)) = (e0))) -> (~((op (e2) (e2)) = (op (e2) (e3)))) -> (~((op (e2) (e3)) = (op (e3) (e3)))) -> (~((op (e1) (e3)) = (op (e2) (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) (e0)) = (e3)) -> (~((op (e3) (e0)) = (op (e3) (e1)))) -> (((op (e1) (e0)) = (e3))\/(((op (e1) (e1)) = (e3))\/(((op (e1) (e2)) = (e3))\/((op (e1) (e3)) = (e3))))) -> (~((e1) = (e3))) -> ((op (e1) (e0)) = (e1)) -> (~((op (e0) (e1)) = (op (e1) (e1)))) -> (((op (e2) (e1)) = (e0))\/(((op (e2) (e1)) = (e1))\/(((op (e2) (e1)) = (e2))\/((op (e2) (e1)) = (e3))))) -> (~((op (e2) (e1)) = (e0))) -> (~((op (e2) (e1)) = (op (e3) (e1)))) -> (~((op (e0) (e1)) = (op (e2) (e1)))) -> (~((op (e1) (e1)) = (op (e2) (e1)))) -> (~((op (e0) (e1)) = (op (e3) (e1)))) -> (~((op (e0) (e1)) = (e0))) -> (((op (e0) (e1)) = (e0))\/(((op (e0) (e1)) = (e1))\/(((op (e0) (e1)) = (e2))\/((op (e0) (e1)) = (e3))))) -> (~((op (e3) (e3)) = (e3))) -> (~((op (e3) (e2)) = (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 (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))))) -> (~((e2) = (e3))) -> (~((op (e1) (e0)) = (e0))) -> (((op (e1) (e0)) = (e0))\/(((op (e1) (e1)) = (e0))\/(((op (e1) (e2)) = (e0))\/((op (e1) (e3)) = (e0))))) -> ((op (e2) (e3)) = (e2)) -> (~((op (e0) (e3)) = (op (e2) (e3)))) -> (~((op (e0) (e3)) = (op (e1) (e3)))) -> ((op (e1) (e3)) = (e3)) -> False). % 18.64/18.79 do 0 intro. intros zenon_He4 zenon_Hc2 zenon_H38 zenon_H25 zenon_H109 zenon_H54 zenon_H10a zenon_H18b zenon_H1ad zenon_H40 zenon_H1ac zenon_H22a zenon_H18c zenon_H7c zenon_H1a5 zenon_H153 zenon_H71 zenon_H1d8 zenon_H7b zenon_H189 zenon_H1c7 zenon_H133 zenon_H145 zenon_H11f zenon_H32 zenon_H6d zenon_Hf3 zenon_Hdb zenon_H34 zenon_Ha1 zenon_H106 zenon_H15e zenon_H1cf zenon_H16f zenon_H95 zenon_H9d zenon_H10e zenon_H1cc zenon_H31 zenon_Haf zenon_H17e zenon_H13e zenon_H210 zenon_H20b zenon_H212 zenon_H102 zenon_H62 zenon_H130 zenon_H101 zenon_H173 zenon_H48 zenon_H149 zenon_H172 zenon_H12b zenon_H23 zenon_H22 zenon_H11d zenon_He2 zenon_H1d zenon_Hdc. % 18.64/18.79 apply (zenon_or_s _ _ zenon_H1ac); [ zenon_intro zenon_H44 | zenon_intro zenon_H1af ]. % 18.64/18.79 exact (zenon_H40 zenon_H44). % 18.64/18.79 apply (zenon_or_s _ _ zenon_H1af); [ zenon_intro zenon_H1b1 | zenon_intro zenon_H1b0 ]. % 18.64/18.79 exact (zenon_H1ad zenon_H1b1). % 18.64/18.79 apply (zenon_or_s _ _ zenon_H1b0); [ zenon_intro zenon_H61 | zenon_intro zenon_H60 ]. % 18.64/18.79 exact (zenon_H18b zenon_H61). % 18.64/18.79 apply (zenon_L448_); trivial. % 18.64/18.79 (* end of lemma zenon_L449_ *) % 18.64/18.79 assert (zenon_L450_ : (((op (e2) (e0)) = (e2))\/(((op (e2) (e1)) = (e2))\/(((op (e2) (e2)) = (e2))\/((op (e2) (e3)) = (e2))))) -> ((op (e3) (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 (e1) (e3)) = (e0))) -> (~((op (e1) (e2)) = (e0))) -> (((op (e0) (e1)) = (e1))\/(((op (e1) (e1)) = (e1))\/(((op (e2) (e1)) = (e1))\/((op (e3) (e1)) = (e1))))) -> (~((op (e0) (e1)) = (op (e0) (e3)))) -> (~((op (e1) (e1)) = (e1))) -> (~((op (e3) (e2)) = (e0))) -> (~((op (e3) (e1)) = (e0))) -> (~((op (e3) (e0)) = (e0))) -> (((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 (e1) (e0)) = (e2))\/(((op (e1) (e1)) = (e2))\/(((op (e1) (e2)) = (e2))\/((op (e1) (e3)) = (e2))))) -> (~((e1) = (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 (e3) (e0)) = (op (e3) (e3)))) -> (((op (e0) (e1)) = (e2))\/(((op (e1) (e1)) = (e2))\/(((op (e2) (e1)) = (e2))\/((op (e3) (e1)) = (e2))))) -> ((op (e0) (e0)) = (e2)) -> (~((op (e0) (e0)) = (op (e0) (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) (e3)) = (e2))\/(((op (e1) (e3)) = (e2))\/(((op (e2) (e3)) = (e2))\/((op (e3) (e3)) = (e2))))) -> (((op (e2) (e3)) = (e0))\/(((op (e2) (e3)) = (e1))\/(((op (e2) (e3)) = (e2))\/((op (e2) (e3)) = (e3))))) -> (~((op (e2) (e3)) = (e0))) -> (~((op (e2) (e2)) = (op (e2) (e3)))) -> (~((op (e2) (e3)) = (op (e3) (e3)))) -> (~((op (e1) (e3)) = (op (e2) (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) (e0)) = (e3)) -> (~((op (e3) (e0)) = (op (e3) (e1)))) -> (((op (e1) (e0)) = (e3))\/(((op (e1) (e1)) = (e3))\/(((op (e1) (e2)) = (e3))\/((op (e1) (e3)) = (e3))))) -> (~((e1) = (e3))) -> ((op (e1) (e0)) = (e1)) -> (~((op (e0) (e1)) = (op (e1) (e1)))) -> (((op (e2) (e1)) = (e0))\/(((op (e2) (e1)) = (e1))\/(((op (e2) (e1)) = (e2))\/((op (e2) (e1)) = (e3))))) -> (~((op (e2) (e1)) = (e0))) -> (~((op (e2) (e1)) = (op (e3) (e1)))) -> (~((op (e0) (e1)) = (op (e2) (e1)))) -> (~((op (e1) (e1)) = (op (e2) (e1)))) -> (~((op (e0) (e1)) = (op (e3) (e1)))) -> (~((op (e0) (e1)) = (e0))) -> (((op (e0) (e1)) = (e0))\/(((op (e0) (e1)) = (e1))\/(((op (e0) (e1)) = (e2))\/((op (e0) (e1)) = (e3))))) -> (~((op (e3) (e3)) = (e3))) -> (~((op (e3) (e2)) = (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 (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))))) -> (~((e2) = (e3))) -> (~((op (e1) (e0)) = (e0))) -> (((op (e1) (e0)) = (e0))\/(((op (e1) (e1)) = (e0))\/(((op (e1) (e2)) = (e0))\/((op (e1) (e3)) = (e0))))) -> (~((op (e0) (e3)) = (op (e2) (e3)))) -> (~((op (e0) (e3)) = (op (e1) (e3)))) -> ((op (e1) (e3)) = (e3)) -> False). % 18.64/18.79 do 0 intro. intros zenon_H1d5 zenon_H14d zenon_He4 zenon_Hc2 zenon_H38 zenon_H25 zenon_H109 zenon_H54 zenon_H10a zenon_H18b zenon_H1ad zenon_H40 zenon_H1ac zenon_H22a zenon_H18c zenon_H7c zenon_H1a5 zenon_H153 zenon_H71 zenon_H1d8 zenon_H7b zenon_H189 zenon_H1c7 zenon_H133 zenon_H145 zenon_H11f zenon_H32 zenon_H6d zenon_Hf3 zenon_Hdb zenon_H34 zenon_Ha1 zenon_H106 zenon_H15e zenon_H1cf zenon_H16f zenon_H95 zenon_H9d zenon_H10e zenon_H1cc zenon_H31 zenon_Haf zenon_H17e zenon_H13e zenon_H210 zenon_H20b zenon_H212 zenon_H102 zenon_H62 zenon_H130 zenon_H101 zenon_H173 zenon_H48 zenon_H149 zenon_H172 zenon_H12b zenon_H23 zenon_H22 zenon_He2 zenon_H1d zenon_Hdc. % 18.64/18.79 apply (zenon_or_s _ _ zenon_H1d5); [ zenon_intro zenon_Hee | zenon_intro zenon_H1d6 ]. % 18.64/18.79 apply (zenon_L204_); trivial. % 18.64/18.79 apply (zenon_or_s _ _ zenon_H1d6); [ zenon_intro zenon_H1ca | zenon_intro zenon_H1d7 ]. % 18.64/18.79 apply (zenon_L364_); trivial. % 18.64/18.79 apply (zenon_or_s _ _ zenon_H1d7); [ zenon_intro zenon_H176 | zenon_intro zenon_H11d ]. % 18.64/18.79 exact (zenon_H173 zenon_H176). % 18.64/18.79 apply (zenon_L449_); trivial. % 18.64/18.79 (* end of lemma zenon_L450_ *) % 18.64/18.79 assert (zenon_L451_ : (((op (e2) (e1)) = (e0))\/(((op (e2) (e1)) = (e1))\/(((op (e2) (e1)) = (e2))\/((op (e2) (e1)) = (e3))))) -> (~((op (e2) (e1)) = (e0))) -> (~((op (e2) (e1)) = (op (e2) (e3)))) -> ((op (e2) (e3)) = (e1)) -> ((op (e3) (e1)) = (e2)) -> (~((op (e2) (e1)) = (op (e3) (e1)))) -> (~((op (e1) (e1)) = (op (e2) (e1)))) -> ((op (e1) (e1)) = (e3)) -> False). % 18.64/18.79 do 0 intro. intros zenon_H1cc zenon_H31 zenon_H1c7 zenon_Hf4 zenon_H14d zenon_Haf zenon_H13e zenon_H13f. % 18.64/18.79 apply (zenon_or_s _ _ zenon_H1cc); [ zenon_intro zenon_H36 | zenon_intro zenon_H1cd ]. % 18.64/18.79 exact (zenon_H31 zenon_H36). % 18.64/18.79 apply (zenon_or_s _ _ zenon_H1cd); [ zenon_intro zenon_Ha5 | zenon_intro zenon_H1ce ]. % 18.64/18.79 apply (zenon_L188_); trivial. % 18.64/18.79 apply (zenon_or_s _ _ zenon_H1ce); [ zenon_intro zenon_H1ca | zenon_intro zenon_Ha6 ]. % 18.64/18.79 apply (zenon_L364_); trivial. % 18.64/18.79 apply (zenon_L95_); trivial. % 18.64/18.79 (* end of lemma zenon_L451_ *) % 18.64/18.79 assert (zenon_L452_ : (((op (e3) (e0)) = (e1))\/(((op (e3) (e1)) = (e1))\/(((op (e3) (e2)) = (e1))\/((op (e3) (e3)) = (e1))))) -> ((~((op (e3) (e3)) = (e0)))\/((op (e3) (e0)) = (e3))) -> (~((op (e0) (e0)) = (e0))) -> (((op (e0) (e0)) = (e0))\/(((op (e1) (e0)) = (e0))\/(((op (e2) (e0)) = (e0))\/((op (e3) (e0)) = (e0))))) -> (~((op (e0) (e2)) = (op (e0) (e3)))) -> (~((op (e1) (e1)) = (op (e1) (e2)))) -> (~((op (e2) (e0)) = (op (e2) (e2)))) -> (~((op (e3) (e1)) = (op (e3) (e2)))) -> (((op (e0) (e2)) = (e0))\/(((op (e1) (e2)) = (e0))\/(((op (e2) (e2)) = (e0))\/((op (e3) (e2)) = (e0))))) -> (~((op (e1) (e1)) = (op (e1) (e3)))) -> (~((op (e2) (e0)) = (op (e2) (e3)))) -> (((op (e0) (e3)) = (e0))\/(((op (e1) (e3)) = (e0))\/(((op (e2) (e3)) = (e0))\/((op (e3) (e3)) = (e0))))) -> (~((op (e1) (e0)) = (op (e1) (e1)))) -> (~((op (e0) (e2)) = (op (e3) (e2)))) -> (~((op (e2) (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 (e0) (e2)) = (op (e2) (e2)))) -> (((op (e3) (e0)) = (e3))\/(((op (e3) (e1)) = (e3))\/(((op (e3) (e2)) = (e3))\/((op (e3) (e3)) = (e3))))) -> (~((op (e1) (e1)) = (op (e3) (e1)))) -> (((op (e0) (e2)) = (e1))\/(((op (e1) (e2)) = (e1))\/(((op (e2) (e2)) = (e1))\/((op (e3) (e2)) = (e1))))) -> (~((op (e0) (e1)) = (op (e0) (e2)))) -> (~((op (e3) (e0)) = (op (e3) (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) (e2)) = (e3))\/(((op (e1) (e2)) = (e3))\/(((op (e2) (e2)) = (e3))\/((op (e3) (e2)) = (e3))))) -> ((op (e0) (e0)) = (e3)) -> ((~((op (e3) (e2)) = (e0)))\/((op (e3) (e0)) = (e2))) -> (~((op (e1) (e0)) = (op (e1) (e3)))) -> ((op (e0) (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 (e1) (e2)) = (e2)) -> (((op (e2) (e0)) = (e2))\/(((op (e2) (e1)) = (e2))\/(((op (e2) (e2)) = (e2))\/((op (e2) (e3)) = (e2))))) -> ((op (e3) (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 (e1) (e3)) = (e0))) -> (~((op (e1) (e2)) = (e0))) -> (((op (e0) (e1)) = (e1))\/(((op (e1) (e1)) = (e1))\/(((op (e2) (e1)) = (e1))\/((op (e3) (e1)) = (e1))))) -> (~((op (e0) (e1)) = (op (e0) (e3)))) -> (~((op (e1) (e1)) = (e1))) -> (~((op (e3) (e2)) = (e0))) -> (~((op (e3) (e1)) = (e0))) -> (~((op (e3) (e0)) = (e0))) -> (((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 (e1) (e0)) = (e2))\/(((op (e1) (e1)) = (e2))\/(((op (e1) (e2)) = (e2))\/((op (e1) (e3)) = (e2))))) -> (~((e1) = (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 (e3) (e0)) = (op (e3) (e3)))) -> (((op (e0) (e1)) = (e2))\/(((op (e1) (e1)) = (e2))\/(((op (e2) (e1)) = (e2))\/((op (e3) (e1)) = (e2))))) -> ((op (e0) (e0)) = (e2)) -> (~((op (e0) (e0)) = (op (e0) (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) (e3)) = (e2))\/(((op (e1) (e3)) = (e2))\/(((op (e2) (e3)) = (e2))\/((op (e3) (e3)) = (e2))))) -> (((op (e2) (e3)) = (e0))\/(((op (e2) (e3)) = (e1))\/(((op (e2) (e3)) = (e2))\/((op (e2) (e3)) = (e3))))) -> (~((op (e2) (e3)) = (e0))) -> (~((op (e2) (e2)) = (op (e2) (e3)))) -> (~((op (e2) (e3)) = (op (e3) (e3)))) -> (~((op (e1) (e3)) = (op (e2) (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) (e0)) = (e3)) -> (~((op (e3) (e0)) = (op (e3) (e1)))) -> (((op (e1) (e0)) = (e3))\/(((op (e1) (e1)) = (e3))\/(((op (e1) (e2)) = (e3))\/((op (e1) (e3)) = (e3))))) -> (~((e1) = (e3))) -> ((op (e1) (e0)) = (e1)) -> (~((op (e0) (e1)) = (op (e1) (e1)))) -> (((op (e2) (e1)) = (e0))\/(((op (e2) (e1)) = (e1))\/(((op (e2) (e1)) = (e2))\/((op (e2) (e1)) = (e3))))) -> (~((op (e2) (e1)) = (e0))) -> (~((op (e2) (e1)) = (op (e3) (e1)))) -> (~((op (e0) (e1)) = (op (e2) (e1)))) -> (~((op (e1) (e1)) = (op (e2) (e1)))) -> (~((op (e0) (e1)) = (op (e3) (e1)))) -> (~((op (e0) (e1)) = (e0))) -> (((op (e0) (e1)) = (e0))\/(((op (e0) (e1)) = (e1))\/(((op (e0) (e1)) = (e2))\/((op (e0) (e1)) = (e3))))) -> (~((op (e3) (e3)) = (e3))) -> (~((op (e3) (e2)) = (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 (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))))) -> (~((e2) = (e3))) -> (~((op (e1) (e0)) = (e0))) -> (((op (e1) (e0)) = (e0))\/(((op (e1) (e1)) = (e0))\/(((op (e1) (e2)) = (e0))\/((op (e1) (e3)) = (e0))))) -> (~((op (e0) (e3)) = (op (e2) (e3)))) -> (~((op (e0) (e3)) = (op (e1) (e3)))) -> False). % 18.64/18.79 do 0 intro. intros zenon_He8 zenon_H1ec zenon_H3f zenon_H3e zenon_H208 zenon_H4f zenon_H52 zenon_H1a4 zenon_H6a zenon_H57 zenon_H5b zenon_H67 zenon_H45 zenon_H14f zenon_H81 zenon_H74 zenon_H22d zenon_Ha8 zenon_H165 zenon_H160 zenon_H139 zenon_H4a zenon_H6f zenon_H18f zenon_H1c4 zenon_H1a6 zenon_H3a zenon_H1a7 zenon_Hd8 zenon_Ha0 zenon_Hdf zenon_Hd5 zenon_H113 zenon_H1d5 zenon_H14d zenon_He4 zenon_Hc2 zenon_H38 zenon_H25 zenon_H109 zenon_H54 zenon_H10a zenon_H18b zenon_H1ad zenon_H40 zenon_H1ac zenon_H22a zenon_H18c zenon_H7c zenon_H1a5 zenon_H153 zenon_H71 zenon_H1d8 zenon_H7b zenon_H189 zenon_H1c7 zenon_H133 zenon_H145 zenon_H11f zenon_H32 zenon_H6d zenon_Hf3 zenon_Hdb zenon_H34 zenon_Ha1 zenon_H106 zenon_H15e zenon_H1cf zenon_H16f zenon_H95 zenon_H9d zenon_H10e zenon_H1cc zenon_H31 zenon_Haf zenon_H17e zenon_H13e zenon_H210 zenon_H20b zenon_H212 zenon_H102 zenon_H62 zenon_H130 zenon_H101 zenon_H173 zenon_H48 zenon_H149 zenon_H172 zenon_H12b zenon_H23 zenon_H22 zenon_He2 zenon_H1d. % 18.64/18.79 apply (zenon_or_s _ _ zenon_H16f); [ zenon_intro zenon_H9e | zenon_intro zenon_H170 ]. % 18.64/18.79 apply (zenon_L37_); trivial. % 18.64/18.79 apply (zenon_or_s _ _ zenon_H170); [ zenon_intro zenon_H13f | zenon_intro zenon_H171 ]. % 18.64/18.79 apply (zenon_or_s _ _ zenon_H106); [ zenon_intro zenon_Hed | zenon_intro zenon_H107 ]. % 18.64/18.79 apply (zenon_L214_); trivial. % 18.64/18.79 apply (zenon_or_s _ _ zenon_H107); [ zenon_intro zenon_Ha5 | zenon_intro zenon_H108 ]. % 18.64/18.79 apply (zenon_L390_); trivial. % 18.64/18.79 apply (zenon_or_s _ _ zenon_H108); [ zenon_intro zenon_Hf1 | zenon_intro zenon_Hf4 ]. % 18.64/18.79 apply (zenon_or_s _ _ zenon_H1d5); [ zenon_intro zenon_Hee | zenon_intro zenon_H1d6 ]. % 18.64/18.79 apply (zenon_L204_); trivial. % 18.64/18.79 apply (zenon_or_s _ _ zenon_H1d6); [ zenon_intro zenon_H1ca | zenon_intro zenon_H1d7 ]. % 18.64/18.79 apply (zenon_L364_); trivial. % 18.64/18.79 apply (zenon_or_s _ _ zenon_H1d7); [ zenon_intro zenon_H176 | zenon_intro zenon_H11d ]. % 18.64/18.79 exact (zenon_H173 zenon_H176). % 18.64/18.79 apply (zenon_or_s _ _ zenon_He8); [ zenon_intro zenon_Hac | zenon_intro zenon_Heb ]. % 18.64/18.79 apply (zenon_L439_); trivial. % 18.64/18.79 apply (zenon_or_s _ _ zenon_Heb); [ zenon_intro zenon_Hae | zenon_intro zenon_Hec ]. % 18.64/18.79 apply (zenon_L368_); trivial. % 18.64/18.79 apply (zenon_or_s _ _ zenon_Hec); [ zenon_intro zenon_Hba | zenon_intro zenon_Hc4 ]. % 18.64/18.79 apply (zenon_L419_); trivial. % 18.64/18.79 apply (zenon_or_s _ _ zenon_Hdf); [ zenon_intro zenon_H1f | zenon_intro zenon_He0 ]. % 18.64/18.79 exact (zenon_H38 zenon_H1f). % 18.64/18.79 apply (zenon_or_s _ _ zenon_He0); [ zenon_intro zenon_Hd6 | zenon_intro zenon_He1 ]. % 18.64/18.79 apply (zenon_L50_); trivial. % 18.64/18.79 apply (zenon_or_s _ _ zenon_He1); [ zenon_intro zenon_Hd7 | zenon_intro zenon_Hdc ]. % 18.64/18.79 apply (zenon_L366_); trivial. % 18.64/18.79 apply (zenon_L450_); trivial. % 18.64/18.79 apply (zenon_L451_); trivial. % 18.64/18.79 apply (zenon_or_s _ _ zenon_H171); [ zenon_intro zenon_H16c | zenon_intro zenon_Hdc ]. % 18.64/18.79 apply (zenon_L116_); trivial. % 18.64/18.79 apply (zenon_L450_); trivial. % 18.64/18.79 (* end of lemma zenon_L452_ *) % 18.64/18.79 assert (zenon_L453_ : (((op (e3) (e1)) = (e0))\/(((op (e3) (e1)) = (e1))\/(((op (e3) (e1)) = (e2))\/((op (e3) (e1)) = (e3))))) -> (~((op (e3) (e1)) = (e0))) -> ((op (e1) (e1)) = (e3)) -> (~((op (e0) (e1)) = (op (e1) (e1)))) -> (((op (e2) (e1)) = (e0))\/(((op (e2) (e1)) = (e1))\/(((op (e2) (e1)) = (e2))\/((op (e2) (e1)) = (e3))))) -> (~((op (e2) (e1)) = (e0))) -> (~((op (e2) (e1)) = (op (e3) (e1)))) -> (~((op (e0) (e1)) = (op (e2) (e1)))) -> (~((op (e1) (e1)) = (op (e2) (e1)))) -> (~((op (e0) (e1)) = (op (e3) (e1)))) -> (~((op (e0) (e1)) = (e0))) -> (((op (e0) (e1)) = (e0))\/(((op (e0) (e1)) = (e1))\/(((op (e0) (e1)) = (e2))\/((op (e0) (e1)) = (e3))))) -> ((op (e3) (e2)) = (e2)) -> (~((op (e3) (e1)) = (op (e3) (e2)))) -> ((op (e3) (e0)) = (e3)) -> (~((op (e3) (e0)) = (op (e3) (e1)))) -> False). % 18.64/18.79 do 0 intro. intros zenon_H22a zenon_H1ad zenon_H13f zenon_H10e zenon_H1cc zenon_H31 zenon_Haf zenon_H17e zenon_H13e zenon_H210 zenon_H20b zenon_H212 zenon_H151 zenon_H1a4 zenon_H15e zenon_H1cf. % 18.64/18.79 apply (zenon_or_s _ _ zenon_H22a); [ zenon_intro zenon_H1b1 | zenon_intro zenon_H22b ]. % 18.64/18.79 exact (zenon_H1ad zenon_H1b1). % 18.64/18.79 apply (zenon_or_s _ _ zenon_H22b); [ zenon_intro zenon_Hae | zenon_intro zenon_H22c ]. % 18.64/18.79 apply (zenon_L368_); trivial. % 18.64/18.79 apply (zenon_or_s _ _ zenon_H22c); [ zenon_intro zenon_H14d | zenon_intro zenon_H161 ]. % 18.64/18.79 apply (zenon_L400_); trivial. % 18.64/18.79 apply (zenon_L193_); trivial. % 18.64/18.79 (* end of lemma zenon_L453_ *) % 18.64/18.79 assert (zenon_L454_ : (((op (e2) (e3)) = (e0))\/(((op (e2) (e3)) = (e1))\/(((op (e2) (e3)) = (e2))\/((op (e2) (e3)) = (e3))))) -> ((op (e1) (e3)) = (e2)) -> ((op (e3) (e3)) = (e1)) -> (~((op (e2) (e3)) = (op (e3) (e3)))) -> (~((op (e2) (e1)) = (op (e2) (e3)))) -> ((op (e2) (e1)) = (e2)) -> (~((op (e0) (e3)) = (op (e2) (e3)))) -> ((op (e0) (e3)) = (e3)) -> False). % 18.64/18.79 do 0 intro. intros zenon_H11f zenon_Hd7 zenon_Hc4 zenon_Hf3 zenon_H1c7 zenon_H1ca zenon_He2 zenon_He3. % 18.64/18.79 apply (zenon_or_s _ _ zenon_H11f); [ zenon_intro zenon_H37 | zenon_intro zenon_H120 ]. % 18.64/18.79 apply (zenon_L72_); trivial. % 18.64/18.79 apply (zenon_or_s _ _ zenon_H120); [ zenon_intro zenon_Hf4 | zenon_intro zenon_H121 ]. % 18.64/18.79 apply (zenon_L60_); trivial. % 18.64/18.79 apply (zenon_or_s _ _ zenon_H121); [ zenon_intro zenon_H11d | zenon_intro zenon_Hdd ]. % 18.64/18.79 apply (zenon_L224_); trivial. % 18.64/18.79 apply (zenon_L54_); trivial. % 18.64/18.79 (* end of lemma zenon_L454_ *) % 18.64/18.79 assert (zenon_L455_ : (((op (e1) (e3)) = (e0))\/(((op (e1) (e3)) = (e1))\/(((op (e1) (e3)) = (e2))\/((op (e1) (e3)) = (e3))))) -> ((op (e3) (e3)) = (e0)) -> (~((op (e1) (e3)) = (op (e3) (e3)))) -> (~((op (e0) (e3)) = (op (e2) (e3)))) -> ((op (e2) (e1)) = (e2)) -> (~((op (e2) (e1)) = (op (e2) (e3)))) -> (~((op (e2) (e3)) = (op (e3) (e3)))) -> ((op (e3) (e3)) = (e1)) -> (((op (e2) (e3)) = (e0))\/(((op (e2) (e3)) = (e1))\/(((op (e2) (e3)) = (e2))\/((op (e2) (e3)) = (e3))))) -> (~((op (e0) (e3)) = (op (e1) (e3)))) -> ((op (e0) (e3)) = (e3)) -> False). % 18.64/18.79 do 0 intro. intros zenon_Hdf zenon_H60 zenon_Hd5 zenon_He2 zenon_H1ca zenon_H1c7 zenon_Hf3 zenon_Hc4 zenon_H11f zenon_H1d zenon_He3. % 18.64/18.79 apply (zenon_or_s _ _ zenon_Hdf); [ zenon_intro zenon_H1f | zenon_intro zenon_He0 ]. % 18.64/18.79 apply (zenon_L136_); trivial. % 18.64/18.79 apply (zenon_or_s _ _ zenon_He0); [ zenon_intro zenon_Hd6 | zenon_intro zenon_He1 ]. % 18.64/18.79 apply (zenon_L50_); trivial. % 18.64/18.79 apply (zenon_or_s _ _ zenon_He1); [ zenon_intro zenon_Hd7 | zenon_intro zenon_Hdc ]. % 18.64/18.79 apply (zenon_L454_); trivial. % 18.64/18.79 apply (zenon_L117_); trivial. % 18.64/18.79 (* end of lemma zenon_L455_ *) % 18.64/18.79 assert (zenon_L456_ : ((~((op (e0) (e2)) = (e0)))\/((op (e0) (e0)) = (e2))) -> ((~((op (e1) (e0)) = (e0)))\/((op (e1) (e0)) = (e0))) -> (~((op (e1) (e0)) = (op (e2) (e0)))) -> (~((op (e2) (e0)) = (op (e2) (e1)))) -> (~((op (e1) (e0)) = (op (e3) (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)) = (op (e3) (e2)))) -> (~((op (e2) (e2)) = (op (e2) (e3)))) -> (~((op (e3) (e0)) = (op (e3) (e3)))) -> (~((op (e0) (e1)) = (op (e0) (e2)))) -> (~((op (e1) (e1)) = (op (e1) (e2)))) -> (~((op (e2) (e0)) = (op (e2) (e2)))) -> (((op (e0) (e3)) = (e0))\/(((op (e1) (e3)) = (e0))\/(((op (e2) (e3)) = (e0))\/((op (e3) (e3)) = (e0))))) -> (~((op (e3) (e2)) = (op (e3) (e3)))) -> (~((op (e2) (e0)) = (op (e2) (e3)))) -> (~((op (e1) (e1)) = (op (e1) (e3)))) -> (~((op (e0) (e1)) = (op (e0) (e3)))) -> (((op (e0) (e2)) = (e0))\/(((op (e1) (e2)) = (e0))\/(((op (e2) (e2)) = (e0))\/((op (e3) (e2)) = (e0))))) -> (~((op (e1) (e0)) = (op (e1) (e1)))) -> (((op (e1) (e0)) = (e0))\/(((op (e1) (e1)) = (e0))\/(((op (e1) (e2)) = (e0))\/((op (e1) (e3)) = (e0))))) -> (~((op (e0) (e0)) = (e0))) -> ((~((op (e3) (e1)) = (e0)))\/((op (e3) (e0)) = (e1))) -> ((~((op (e3) (e3)) = (e0)))\/((op (e3) (e0)) = (e3))) -> (((op (e2) (e0)) = (e2))\/(((op (e2) (e1)) = (e2))\/(((op (e2) (e2)) = (e2))\/((op (e2) (e3)) = (e2))))) -> (((op (e0) (e1)) = (e2))\/(((op (e1) (e1)) = (e2))\/(((op (e2) (e1)) = (e2))\/((op (e3) (e1)) = (e2))))) -> (~((op (e3) (e0)) = (op (e3) (e1)))) -> (((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 (e2) (e2)) = (e0))\/(((op (e2) (e2)) = (e1))\/(((op (e2) (e2)) = (e2))\/((op (e2) (e2)) = (e3))))) -> (~((op (e2) (e1)) = (op (e2) (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 (e2) (e0)) = (e0)))\/((op (e2) (e0)) = (e0))) -> (((op (e0) (e0)) = (e2))\/(((op (e1) (e0)) = (e2))\/(((op (e2) (e0)) = (e2))\/((op (e3) (e0)) = (e2))))) -> ((~((op (e2) (e1)) = (e0)))\/((op (e2) (e0)) = (e1))) -> (~((op (e0) (e0)) = (op (e2) (e0)))) -> (((op (e3) (e0)) = (e2))\/(((op (e3) (e1)) = (e2))\/(((op (e3) (e2)) = (e2))\/((op (e3) (e3)) = (e2))))) -> (~((op (e0) (e2)) = (op (e3) (e2)))) -> (~((e0) = (e2))) -> (((op (e3) (e0)) = (e3))\/(((op (e3) (e1)) = (e3))\/(((op (e3) (e2)) = (e3))\/((op (e3) (e3)) = (e3))))) -> (~((op (e1) (e1)) = (op (e3) (e1)))) -> (((op (e0) (e0)) = (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)) = (e2))) -> (((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) (e2)) = (op (e1) (e3)))) -> (~((e2) = (e3))) -> (((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)) = (e3))\/(((op (e1) (e3)) = (e3))\/(((op (e2) (e3)) = (e3))\/((op (e3) (e3)) = (e3))))) -> (((op (e1) (e0)) = (e1))\/(((op (e1) (e1)) = (e1))\/(((op (e1) (e2)) = (e1))\/((op (e1) (e3)) = (e1))))) -> (((op (e0) (e2)) = (e1))\/(((op (e1) (e2)) = (e1))\/(((op (e2) (e2)) = (e1))\/((op (e3) (e2)) = (e1))))) -> (~((op (e0) (e0)) = (op (e0) (e2)))) -> (~((op (e1) (e1)) = (op (e2) (e1)))) -> (((op (e1) (e1)) = (e0))\/(((op (e1) (e1)) = (e1))\/(((op (e1) (e1)) = (e2))\/((op (e1) (e1)) = (e3))))) -> ((~((op (e1) (e3)) = (e0)))\/((op (e1) (e0)) = (e3))) -> ((~((op (e1) (e2)) = (e0)))\/((op (e1) (e0)) = (e2))) -> (~((op (e0) (e1)) = (op (e2) (e1)))) -> (~((op (e2) (e0)) = (op (e3) (e0)))) -> (((op (e0) (e0)) = (e2))\/(((op (e0) (e1)) = (e2))\/(((op (e0) (e2)) = (e2))\/((op (e0) (e3)) = (e2))))) -> ((~((op (e3) (e0)) = (e0)))\/((op (e3) (e0)) = (e0))) -> ((~((op (e2) (e2)) = (e0)))\/((op (e2) (e0)) = (e2))) -> (~((op (e0) (e0)) = (op (e0) (e3)))) -> (((op (e0) (e1)) = (e1))\/(((op (e1) (e1)) = (e1))\/(((op (e2) (e1)) = (e1))\/((op (e3) (e1)) = (e1))))) -> (~((op (e1) (e2)) = (op (e2) (e2)))) -> (((op (e3) (e3)) = (e0))\/(((op (e3) (e3)) = (e1))\/(((op (e3) (e3)) = (e2))\/((op (e3) (e3)) = (e3))))) -> (~((op (e3) (e3)) = (e3))) -> (~((op (e2) (e3)) = (op (e3) (e3)))) -> (((op (e2) (e0)) = (e1))\/(((op (e2) (e1)) = (e1))\/(((op (e2) (e2)) = (e1))\/((op (e2) (e3)) = (e1))))) -> (((op (e2) (e0)) = (e3))\/(((op (e2) (e1)) = (e3))\/(((op (e2) (e2)) = (e3))\/((op (e2) (e3)) = (e3))))) -> (~((op (e2) (e1)) = (op (e3) (e1)))) -> (((op (e0) (e3)) = (e0))\/(((op (e0) (e3)) = (e1))\/(((op (e0) (e3)) = (e2))\/((op (e0) (e3)) = (e3))))) -> (~((op (e0) (e3)) = (op (e2) (e3)))) -> (~((op (e1) (e3)) = (op (e3) (e3)))) -> (~((op (e1) (e0)) = (op (e1) (e3)))) -> (~((op (e1) (e3)) = (op (e2) (e3)))) -> (((op (e1) (e3)) = (e0))\/(((op (e1) (e3)) = (e1))\/(((op (e1) (e3)) = (e2))\/((op (e1) (e3)) = (e3))))) -> (~((op (e0) (e3)) = (op (e3) (e3)))) -> (((op (e3) (e0)) = (e1))\/(((op (e3) (e1)) = (e1))\/(((op (e3) (e2)) = (e1))\/((op (e3) (e3)) = (e1))))) -> (~((op (e0) (e2)) = (op (e2) (e2)))) -> (~((e0) = (e1))) -> (~((op (e0) (e1)) = (op (e1) (e1)))) -> (~((op (e0) (e3)) = (op (e1) (e3)))) -> (((op (e2) (e3)) = (e0))\/(((op (e2) (e3)) = (e1))\/(((op (e2) (e3)) = (e2))\/((op (e2) (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) (e1)) = (e1))) -> (~((e0) = (e3))) -> (~((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 (e3) (e2)) = (e0))\/(((op (e3) (e2)) = (e1))\/(((op (e3) (e2)) = (e2))\/((op (e3) (e2)) = (e3))))) -> (~((op (e2) (e2)) = (op (e3) (e2)))) -> ((~((op (e3) (e2)) = (e0)))\/((op (e3) (e0)) = (e2))) -> (~((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)) = (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 (e2) (e3)) = (e0)))\/((op (e2) (e0)) = (e3))) -> ((op (e0) (e0)) = (e1)) -> (~((e1) = (e2))) -> ((~((op (e1) (e1)) = (e0)))\/((op (e1) (e0)) = (e1))) -> ((~((op (e0) (e3)) = (e0)))\/((op (e0) (e0)) = (e3))) -> False). % 18.64/18.79 do 0 intro. intros zenon_H233 zenon_H206 zenon_H201 zenon_H1f0 zenon_H1fa zenon_H74 zenon_H3e zenon_H6f zenon_H6d zenon_H71 zenon_H4a zenon_H4f zenon_H52 zenon_H67 zenon_H62 zenon_H5b zenon_H57 zenon_H54 zenon_H6a zenon_H45 zenon_H22 zenon_H3f zenon_H1ed zenon_H1ec zenon_H1d5 zenon_H1d8 zenon_H1cf zenon_H1ba zenon_H1cc zenon_H1c4 zenon_H1c7 zenon_H1ac zenon_H1e0 zenon_H1ee zenon_H1fe zenon_H182 zenon_H39 zenon_H153 zenon_H14f zenon_H149 zenon_H165 zenon_H160 zenon_H168 zenon_H16f zenon_H173 zenon_H172 zenon_H145 zenon_H124 zenon_H12b zenon_H133 zenon_H130 zenon_H136 zenon_H128 zenon_H139 zenon_H13c zenon_H13e zenon_H142 zenon_H179 zenon_H178 zenon_H17e zenon_H17b zenon_H183 zenon_H184 zenon_H185 zenon_H189 zenon_H109 zenon_H2b zenon_H101 zenon_H102 zenon_Hf3 zenon_H106 zenon_He7 zenon_Haf zenon_He4 zenon_He2 zenon_Hd5 zenon_Hd8 zenon_Hdb zenon_Hdf zenon_Hc2 zenon_He8 zenon_Ha8 zenon_Ha1 zenon_H10e zenon_H1d zenon_H11f zenon_H115 zenon_H18c zenon_H10a zenon_H9a zenon_H95 zenon_H19d zenon_H195 zenon_H191 zenon_H18f zenon_H1a7 zenon_H1a4 zenon_H1a6 zenon_H1a5 zenon_H2f zenon_H94 zenon_H7a zenon_H7c zenon_H205 zenon_H204. % 18.64/18.79 apply (zenon_or_s _ _ zenon_H233); [ zenon_intro zenon_H75 | zenon_intro zenon_H7b ]. % 18.64/18.79 apply (zenon_L333_); trivial. % 18.64/18.79 apply (zenon_L26_); trivial. % 18.64/18.79 (* end of lemma zenon_L456_ *) % 18.64/18.79 assert (zenon_L457_ : (((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) (e0)) = (op (e2) (e2)))) -> ((op (e2) (e0)) = (e3)) -> ((op (e3) (e0)) = (e3)) -> (~((op (e3) (e0)) = (op (e3) (e2)))) -> False). % 18.64/18.79 do 0 intro. intros zenon_H1a6 zenon_H9a zenon_H48 zenon_H12b zenon_H113 zenon_H52 zenon_H3b zenon_H15e zenon_H6f. % 18.64/18.79 apply (zenon_or_s _ _ zenon_H1a6); [ zenon_intro zenon_Ha9 | zenon_intro zenon_H1aa ]. % 18.64/18.79 apply (zenon_L358_); trivial. % 18.64/18.79 apply (zenon_or_s _ _ zenon_H1aa); [ zenon_intro zenon_H16c | zenon_intro zenon_H1ab ]. % 18.64/18.79 apply (zenon_L116_); trivial. % 18.64/18.79 apply (zenon_or_s _ _ zenon_H1ab); [ zenon_intro zenon_Haa | zenon_intro zenon_H163 ]. % 18.64/18.79 apply (zenon_L168_); trivial. % 18.64/18.79 apply (zenon_L286_); trivial. % 18.64/18.79 (* end of lemma zenon_L457_ *) % 18.64/18.79 assert (zenon_L458_ : (((op (e2) (e0)) = (e2))\/(((op (e2) (e1)) = (e2))\/(((op (e2) (e2)) = (e2))\/((op (e2) (e3)) = (e2))))) -> (~((e0) = (e2))) -> ((op (e2) (e0)) = (e0)) -> ((op (e0) (e1)) = (e2)) -> (~((op (e0) (e1)) = (op (e2) (e1)))) -> (~((op (e2) (e2)) = (e2))) -> (~((op (e1) (e3)) = (op (e2) (e3)))) -> ((op (e1) (e3)) = (e2)) -> False). % 18.64/18.79 do 0 intro. intros zenon_H1d5 zenon_H149 zenon_H34 zenon_H10f zenon_H17e zenon_H173 zenon_Hdb zenon_Hd7. % 18.64/18.79 apply (zenon_or_s _ _ zenon_H1d5); [ zenon_intro zenon_Hee | zenon_intro zenon_H1d6 ]. % 18.64/18.79 apply (zenon_L204_); trivial. % 18.64/18.79 apply (zenon_or_s _ _ zenon_H1d6); [ zenon_intro zenon_H1ca | zenon_intro zenon_H1d7 ]. % 18.64/18.79 apply (zenon_L191_); trivial. % 18.64/18.79 apply (zenon_or_s _ _ zenon_H1d7); [ zenon_intro zenon_H176 | zenon_intro zenon_H11d ]. % 18.64/18.79 exact (zenon_H173 zenon_H176). % 18.64/18.79 apply (zenon_L366_); trivial. % 18.64/18.79 (* end of lemma zenon_L458_ *) % 18.64/18.79 assert (zenon_L459_ : (((op (e0) (e3)) = (e0))\/(((op (e0) (e3)) = (e1))\/(((op (e0) (e3)) = (e2))\/((op (e0) (e3)) = (e3))))) -> ((op (e3) (e3)) = (e0)) -> (~((op (e0) (e3)) = (op (e3) (e3)))) -> (~((op (e0) (e3)) = (op (e1) (e3)))) -> (((op (e2) (e3)) = (e0))\/(((op (e2) (e3)) = (e1))\/(((op (e2) (e3)) = (e2))\/((op (e2) (e3)) = (e3))))) -> ((op (e1) (e3)) = (e2)) -> ((op (e3) (e3)) = (e1)) -> (~((op (e2) (e3)) = (op (e3) (e3)))) -> (~((op (e2) (e1)) = (op (e2) (e3)))) -> ((op (e2) (e1)) = (e2)) -> (~((op (e0) (e3)) = (op (e2) (e3)))) -> False). % 18.64/18.79 do 0 intro. intros zenon_He4 zenon_H60 zenon_Hc2 zenon_H1d zenon_H11f zenon_Hd7 zenon_Hc4 zenon_Hf3 zenon_H1c7 zenon_H1ca zenon_He2. % 18.64/18.79 apply (zenon_or_s _ _ zenon_He4); [ zenon_intro zenon_H1e | zenon_intro zenon_He5 ]. % 18.64/18.79 apply (zenon_L440_); trivial. % 18.64/18.79 apply (zenon_or_s _ _ zenon_He5); [ zenon_intro zenon_Hc3 | zenon_intro zenon_He6 ]. % 18.64/18.79 apply (zenon_L46_); trivial. % 18.64/18.79 apply (zenon_or_s _ _ zenon_He6); [ zenon_intro zenon_Hcd | zenon_intro zenon_He3 ]. % 18.64/18.79 apply (zenon_L70_); trivial. % 18.64/18.79 apply (zenon_L454_); trivial. % 18.64/18.79 (* end of lemma zenon_L459_ *) % 18.64/18.79 assert (zenon_L460_ : (((op (e3) (e0)) = (e0))\/(((op (e3) (e1)) = (e0))\/(((op (e3) (e2)) = (e0))\/((op (e3) (e3)) = (e0))))) -> (~((op (e3) (e0)) = (e0))) -> (~((op (e3) (e1)) = (e0))) -> (~((op (e3) (e2)) = (e0))) -> (((op (e3) (e0)) = (e1))\/(((op (e3) (e1)) = (e1))\/(((op (e3) (e2)) = (e1))\/((op (e3) (e3)) = (e1))))) -> (~((e1) = (e3))) -> ((op (e3) (e0)) = (e3)) -> ((op (e1) (e1)) = (e3)) -> (~((op (e0) (e1)) = (op (e1) (e1)))) -> (((op (e2) (e1)) = (e0))\/(((op (e2) (e1)) = (e1))\/(((op (e2) (e1)) = (e2))\/((op (e2) (e1)) = (e3))))) -> (~((op (e2) (e1)) = (e0))) -> (~((op (e2) (e1)) = (op (e3) (e1)))) -> (~((op (e0) (e1)) = (op (e2) (e1)))) -> (~((op (e1) (e1)) = (op (e2) (e1)))) -> (~((op (e0) (e1)) = (op (e3) (e1)))) -> (~((op (e0) (e1)) = (e0))) -> (((op (e0) (e1)) = (e0))\/(((op (e0) (e1)) = (e1))\/(((op (e0) (e1)) = (e2))\/((op (e0) (e1)) = (e3))))) -> (~((op (e3) (e2)) = (op (e3) (e3)))) -> ((op (e2) (e2)) = (e1)) -> (~((op (e2) (e2)) = (op (e2) (e3)))) -> ((op (e1) (e0)) = (e1)) -> (~((op (e1) (e0)) = (op (e1) (e3)))) -> ((op (e0) (e1)) = (e1)) -> (~((op (e0) (e1)) = (op (e0) (e3)))) -> (((op (e0) (e3)) = (e1))\/(((op (e1) (e3)) = (e1))\/(((op (e2) (e3)) = (e1))\/((op (e3) (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 (e2) (e3)) = (e0))\/(((op (e2) (e3)) = (e1))\/(((op (e2) (e3)) = (e2))\/((op (e2) (e3)) = (e3))))) -> ((op (e1) (e3)) = (e2)) -> (~((op (e2) (e3)) = (op (e3) (e3)))) -> (~((op (e2) (e1)) = (op (e2) (e3)))) -> ((op (e2) (e1)) = (e2)) -> (~((op (e0) (e3)) = (op (e2) (e3)))) -> False). % 18.64/18.79 do 0 intro. intros zenon_H1ac zenon_H40 zenon_H1ad zenon_H18b zenon_He8 zenon_H95 zenon_H15e zenon_H13f zenon_H10e zenon_H1cc zenon_H31 zenon_Haf zenon_H17e zenon_H13e zenon_H210 zenon_H20b zenon_H212 zenon_H62 zenon_Hf1 zenon_H6d zenon_H9d zenon_Hd8 zenon_Ha0 zenon_H54 zenon_H133 zenon_He4 zenon_Hc2 zenon_H1d zenon_H11f zenon_Hd7 zenon_Hf3 zenon_H1c7 zenon_H1ca zenon_He2. % 18.64/18.79 apply (zenon_or_s _ _ zenon_H1ac); [ zenon_intro zenon_H44 | zenon_intro zenon_H1af ]. % 18.64/18.79 exact (zenon_H40 zenon_H44). % 18.64/18.79 apply (zenon_or_s _ _ zenon_H1af); [ zenon_intro zenon_H1b1 | zenon_intro zenon_H1b0 ]. % 18.64/18.79 exact (zenon_H1ad zenon_H1b1). % 18.64/18.79 apply (zenon_or_s _ _ zenon_H1b0); [ zenon_intro zenon_H61 | zenon_intro zenon_H60 ]. % 18.64/18.79 exact (zenon_H18b zenon_H61). % 18.64/18.79 apply (zenon_or_s _ _ zenon_He8); [ zenon_intro zenon_Hac | zenon_intro zenon_Heb ]. % 18.64/18.79 apply (zenon_L252_); trivial. % 18.64/18.79 apply (zenon_or_s _ _ zenon_Heb); [ zenon_intro zenon_Hae | zenon_intro zenon_Hec ]. % 18.64/18.79 apply (zenon_L368_); trivial. % 18.64/18.79 apply (zenon_or_s _ _ zenon_Hec); [ zenon_intro zenon_Hba | zenon_intro zenon_Hc4 ]. % 18.64/18.79 apply (zenon_L419_); trivial. % 18.64/18.79 apply (zenon_L459_); trivial. % 18.64/18.79 (* end of lemma zenon_L460_ *) % 18.64/18.79 assert (zenon_L461_ : (((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)) -> (~((e1) = (e3))) -> ((op (e1) (e2)) = (e3)) -> ((op (e2) (e0)) = (e1)) -> (((op (e2) (e2)) = (e0))\/(((op (e2) (e2)) = (e1))\/(((op (e2) (e2)) = (e2))\/((op (e2) (e2)) = (e3))))) -> (~((op (e2) (e2)) = (e0))) -> (~((op (e2) (e2)) = (op (e3) (e2)))) -> (~((op (e2) (e2)) = (e2))) -> ((op (e2) (e0)) = (e3)) -> (~((op (e2) (e0)) = (op (e2) (e2)))) -> False). % 18.64/18.79 do 0 intro. intros zenon_H139 zenon_H4a zenon_Ha0 zenon_H95 zenon_H16c zenon_Hed zenon_H1c4 zenon_H81 zenon_H18f zenon_H173 zenon_H3b zenon_H52. % 18.64/18.79 apply (zenon_or_s _ _ zenon_H139); [ zenon_intro zenon_H122 | zenon_intro zenon_H13a ]. % 18.64/18.79 apply (zenon_L406_); trivial. % 18.64/18.79 apply (zenon_or_s _ _ zenon_H13a); [ zenon_intro zenon_Hf0 | zenon_intro zenon_H13b ]. % 18.64/18.79 apply (zenon_L167_); trivial. % 18.64/18.79 apply (zenon_or_s _ _ zenon_H13b); [ zenon_intro zenon_Hf1 | zenon_intro zenon_Hba ]. % 18.64/18.79 apply (zenon_L93_); trivial. % 18.64/18.79 apply (zenon_L327_); trivial. % 18.64/18.79 (* end of lemma zenon_L461_ *) % 18.64/18.79 assert (zenon_L462_ : (((op (e2) (e0)) = (e2))\/(((op (e2) (e1)) = (e2))\/(((op (e2) (e2)) = (e2))\/((op (e2) (e3)) = (e2))))) -> (~((e0) = (e2))) -> ((op (e2) (e0)) = (e0)) -> ((op (e3) (e1)) = (e2)) -> (~((op (e2) (e1)) = (op (e3) (e1)))) -> (~((op (e2) (e2)) = (e2))) -> (~((op (e1) (e3)) = (op (e2) (e3)))) -> ((op (e1) (e3)) = (e2)) -> False). % 18.64/18.79 do 0 intro. intros zenon_H1d5 zenon_H149 zenon_H34 zenon_H14d zenon_Haf zenon_H173 zenon_Hdb zenon_Hd7. % 18.64/18.79 apply (zenon_or_s _ _ zenon_H1d5); [ zenon_intro zenon_Hee | zenon_intro zenon_H1d6 ]. % 18.64/18.79 apply (zenon_L204_); trivial. % 18.64/18.79 apply (zenon_or_s _ _ zenon_H1d6); [ zenon_intro zenon_H1ca | zenon_intro zenon_H1d7 ]. % 18.64/18.79 apply (zenon_L364_); trivial. % 18.64/18.79 apply (zenon_or_s _ _ zenon_H1d7); [ zenon_intro zenon_H176 | zenon_intro zenon_H11d ]. % 18.64/18.79 exact (zenon_H173 zenon_H176). % 18.64/18.79 apply (zenon_L366_); trivial. % 18.64/18.79 (* end of lemma zenon_L462_ *) % 18.64/18.79 assert (zenon_L463_ : (((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 (e1) (e1)) = (e0)))\/((op (e1) (e0)) = (e1))) -> ((~((op (e2) (e3)) = (e0)))\/((op (e2) (e0)) = (e3))) -> (((op (e2) (e0)) = (e0))\/(((op (e2) (e1)) = (e0))\/(((op (e2) (e2)) = (e0))\/((op (e2) (e3)) = (e0))))) -> (~((op (e3) (e1)) = (op (e3) (e2)))) -> ((~((op (e3) (e2)) = (e0)))\/((op (e3) (e0)) = (e2))) -> (((op (e3) (e2)) = (e0))\/(((op (e3) (e2)) = (e1))\/(((op (e3) (e2)) = (e2))\/((op (e3) (e2)) = (e3))))) -> (~((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)) = (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)) = (e3))\/(((op (e2) (e1)) = (e3))\/(((op (e2) (e2)) = (e3))\/((op (e2) (e3)) = (e3))))) -> (~((op (e3) (e3)) = (e3))) -> (((op (e3) (e3)) = (e0))\/(((op (e3) (e3)) = (e1))\/(((op (e3) (e3)) = (e2))\/((op (e3) (e3)) = (e3))))) -> (~((op (e1) (e2)) = (op (e2) (e2)))) -> (((op (e0) (e1)) = (e1))\/(((op (e1) (e1)) = (e1))\/(((op (e2) (e1)) = (e1))\/((op (e3) (e1)) = (e1))))) -> (~((op (e0) (e0)) = (op (e0) (e3)))) -> ((~((op (e2) (e2)) = (e0)))\/((op (e2) (e0)) = (e2))) -> ((~((op (e3) (e0)) = (e0)))\/((op (e3) (e0)) = (e0))) -> (((op (e0) (e0)) = (e2))\/(((op (e0) (e1)) = (e2))\/(((op (e0) (e2)) = (e2))\/((op (e0) (e3)) = (e2))))) -> (~((op (e2) (e0)) = (op (e3) (e0)))) -> ((~((op (e1) (e2)) = (e0)))\/((op (e1) (e0)) = (e2))) -> ((~((op (e1) (e3)) = (e0)))\/((op (e1) (e0)) = (e3))) -> (((op (e1) (e1)) = (e0))\/(((op (e1) (e1)) = (e1))\/(((op (e1) (e1)) = (e2))\/((op (e1) (e1)) = (e3))))) -> (~((op (e0) (e0)) = (op (e0) (e2)))) -> (((op (e1) (e0)) = (e1))\/(((op (e1) (e1)) = (e1))\/(((op (e1) (e2)) = (e1))\/((op (e1) (e3)) = (e1))))) -> (((op (e0) (e3)) = (e3))\/(((op (e1) (e3)) = (e3))\/(((op (e2) (e3)) = (e3))\/((op (e3) (e3)) = (e3))))) -> (~((op (e3) (e1)) = (op (e3) (e3)))) -> (~((op (e1) (e2)) = (op (e1) (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)) = (e3))\/(((op (e0) (e1)) = (e3))\/(((op (e0) (e2)) = (e3))\/((op (e0) (e3)) = (e3))))) -> (~((op (e1) (e1)) = (op (e3) (e1)))) -> (((op (e3) (e0)) = (e3))\/(((op (e3) (e1)) = (e3))\/(((op (e3) (e2)) = (e3))\/((op (e3) (e3)) = (e3))))) -> (~((op (e0) (e2)) = (op (e3) (e2)))) -> (((op (e3) (e0)) = (e2))\/(((op (e3) (e1)) = (e2))\/(((op (e3) (e2)) = (e2))\/((op (e3) (e3)) = (e2))))) -> (~((op (e0) (e0)) = (op (e2) (e0)))) -> ((~((op (e2) (e1)) = (e0)))\/((op (e2) (e0)) = (e1))) -> (((op (e0) (e0)) = (e2))\/(((op (e1) (e0)) = (e2))\/(((op (e2) (e0)) = (e2))\/((op (e3) (e0)) = (e2))))) -> ((~((op (e2) (e0)) = (e0)))\/((op (e2) (e0)) = (e0))) -> (((op (e0) (e0)) = (e3))\/(((op (e1) (e0)) = (e3))\/(((op (e2) (e0)) = (e3))\/((op (e3) (e0)) = (e3))))) -> (((op (e0) (e2)) = (e0))\/(((op (e0) (e2)) = (e1))\/(((op (e0) (e2)) = (e2))\/((op (e0) (e2)) = (e3))))) -> ((~((op (e3) (e3)) = (e0)))\/((op (e3) (e0)) = (e3))) -> ((~((op (e3) (e1)) = (e0)))\/((op (e3) (e0)) = (e1))) -> (~((op (e0) (e0)) = (e0))) -> (~((op (e1) (e0)) = (op (e1) (e1)))) -> (~((op (e2) (e0)) = (op (e2) (e3)))) -> (((op (e0) (e3)) = (e0))\/(((op (e1) (e3)) = (e0))\/(((op (e2) (e3)) = (e0))\/((op (e3) (e3)) = (e0))))) -> (~((op (e1) (e1)) = (op (e1) (e2)))) -> (~((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)) = (e0))\/(((op (e0) (e1)) = (e0))\/(((op (e0) (e2)) = (e0))\/((op (e0) (e3)) = (e0))))) -> (~((op (e1) (e0)) = (op (e3) (e0)))) -> (~((op (e2) (e0)) = (op (e2) (e1)))) -> (~((op (e1) (e0)) = (op (e2) (e0)))) -> ((~((op (e1) (e0)) = (e0)))\/((op (e1) (e0)) = (e0))) -> ((~((op (e0) (e2)) = (e0)))\/((op (e0) (e0)) = (e2))) -> (((op (e0) (e1)) = (e2))\/(((op (e1) (e1)) = (e2))\/(((op (e2) (e1)) = (e2))\/((op (e3) (e1)) = (e2))))) -> (~((op (e1) (e1)) = (op (e1) (e3)))) -> (((op (e0) (e1)) = (e3))\/(((op (e1) (e1)) = (e3))\/(((op (e2) (e1)) = (e3))\/((op (e3) (e1)) = (e3))))) -> (~((op (e2) (e2)) = (op (e3) (e2)))) -> (~((op (e2) (e2)) = (op (e2) (e3)))) -> (((op (e3) (e0)) = (e1))\/(((op (e3) (e1)) = (e1))\/(((op (e3) (e2)) = (e1))\/((op (e3) (e3)) = (e1))))) -> ((op (e0) (e0)) = (e2)) -> (~((op (e0) (e1)) = (op (e3) (e1)))) -> (~((op (e1) (e2)) = (op (e3) (e2)))) -> (~((op (e2) (e3)) = (op (e3) (e3)))) -> (~((op (e0) (e1)) = (op (e0) (e2)))) -> (((op (e0) (e2)) = (e1))\/(((op (e1) (e2)) = (e1))\/(((op (e2) (e2)) = (e1))\/((op (e3) (e2)) = (e1))))) -> (~((e1) = (e3))) -> (~((op (e0) (e1)) = (op (e1) (e1)))) -> (((op (e2) (e1)) = (e0))\/(((op (e2) (e1)) = (e1))\/(((op (e2) (e1)) = (e2))\/((op (e2) (e1)) = (e3))))) -> (~((op (e2) (e1)) = (e0))) -> (~((op (e0) (e1)) = (op (e2) (e1)))) -> (~((op (e1) (e1)) = (op (e2) (e1)))) -> (~((op (e0) (e1)) = (e0))) -> (((op (e0) (e1)) = (e0))\/(((op (e0) (e1)) = (e1))\/(((op (e0) (e1)) = (e2))\/((op (e0) (e1)) = (e3))))) -> (~((op (e3) (e2)) = (op (e3) (e3)))) -> (~((op (e1) (e0)) = (op (e1) (e3)))) -> (~((op (e0) (e1)) = (op (e0) (e3)))) -> (((op (e0) (e3)) = (e1))\/(((op (e1) (e3)) = (e1))\/(((op (e2) (e3)) = (e1))\/((op (e3) (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 (e2) (e3)) = (e0))\/(((op (e2) (e3)) = (e1))\/(((op (e2) (e3)) = (e2))\/((op (e2) (e3)) = (e3))))) -> (~((op (e2) (e1)) = (op (e2) (e3)))) -> (~((op (e0) (e3)) = (op (e2) (e3)))) -> (((op (e2) (e0)) = (e1))\/(((op (e2) (e1)) = (e1))\/(((op (e2) (e2)) = (e1))\/((op (e2) (e3)) = (e1))))) -> (~((op (e3) (e0)) = (op (e3) (e1)))) -> (((op (e1) (e0)) = (e3))\/(((op (e1) (e1)) = (e3))\/(((op (e1) (e2)) = (e3))\/((op (e1) (e3)) = (e3))))) -> (((op (e2) (e0)) = (e2))\/(((op (e2) (e1)) = (e2))\/(((op (e2) (e2)) = (e2))\/((op (e2) (e3)) = (e2))))) -> ((op (e2) (e0)) = (e0)) -> (~((op (e2) (e1)) = (op (e3) (e1)))) -> (~((op (e1) (e3)) = (op (e2) (e3)))) -> (~((op (e2) (e2)) = (e2))) -> (~((op (e0) (e2)) = (op (e2) (e2)))) -> (~((op (e2) (e2)) = (e0))) -> (((op (e2) (e2)) = (e0))\/(((op (e2) (e2)) = (e1))\/(((op (e2) (e2)) = (e2))\/((op (e2) (e2)) = (e3))))) -> (~((e0) = (e1))) -> (((op (e0) (e2)) = (e0))\/(((op (e1) (e2)) = (e0))\/(((op (e2) (e2)) = (e0))\/((op (e3) (e2)) = (e0))))) -> (((op (e1) (e0)) = (e0))\/(((op (e1) (e1)) = (e0))\/(((op (e1) (e2)) = (e0))\/((op (e1) (e3)) = (e0))))) -> (~((op (e1) (e0)) = (e0))) -> (~((op (e3) (e2)) = (e0))) -> (~((op (e3) (e1)) = (e0))) -> (~((op (e3) (e0)) = (e0))) -> (((op (e3) (e0)) = (e0))\/(((op (e3) (e1)) = (e0))\/(((op (e3) (e2)) = (e0))\/((op (e3) (e3)) = (e0))))) -> (((op (e0) (e2)) = (e3))\/(((op (e1) (e2)) = (e3))\/(((op (e2) (e2)) = (e3))\/((op (e3) (e2)) = (e3))))) -> (~((e0) = (e3))) -> ((op (e0) (e2)) = (e0)) -> (~((e2) = (e3))) -> (~((op (e2) (e0)) = (op (e2) (e2)))) -> ((op (e2) (e0)) = (e3)) -> ((op (e3) (e0)) = (e3)) -> (~((op (e3) (e0)) = (op (e3) (e2)))) -> (~((e0) = (e2))) -> ((op (e1) (e0)) = (e1)) -> (~((e1) = (e2))) -> (((op (e1) (e0)) = (e2))\/(((op (e1) (e1)) = (e2))\/(((op (e1) (e2)) = (e2))\/((op (e1) (e3)) = (e2))))) -> (~((op (e1) (e2)) = (e0))) -> (~((op (e1) (e3)) = (e0))) -> False). % 18.64/18.79 do 0 intro. intros zenon_H22d zenon_H204 zenon_H205 zenon_H94 zenon_H2f zenon_H1a4 zenon_H1a7 zenon_H191 zenon_H195 zenon_H19d zenon_H10a zenon_Hdf zenon_Hd5 zenon_He7 zenon_H102 zenon_H101 zenon_H2b zenon_H109 zenon_H189 zenon_H185 zenon_H184 zenon_H183 zenon_H17b zenon_H178 zenon_H179 zenon_H142 zenon_H13c zenon_H128 zenon_H136 zenon_H130 zenon_H124 zenon_H145 zenon_H172 zenon_H168 zenon_H160 zenon_H165 zenon_H14f zenon_H153 zenon_H39 zenon_H182 zenon_H1fe zenon_H1ee zenon_H1e0 zenon_H1ba zenon_H1ec zenon_H1ed zenon_H3f zenon_H45 zenon_H5b zenon_H67 zenon_H4f zenon_H71 zenon_H3e zenon_H74 zenon_H1fa zenon_H1f0 zenon_H201 zenon_H206 zenon_H233 zenon_H1d8 zenon_H57 zenon_H1a5 zenon_H18f zenon_H6d zenon_He8 zenon_H7b zenon_H210 zenon_H115 zenon_Hf3 zenon_H4a zenon_H139 zenon_H95 zenon_H10e zenon_H1cc zenon_H31 zenon_H17e zenon_H13e zenon_H20b zenon_H212 zenon_H62 zenon_Hd8 zenon_H54 zenon_H133 zenon_He4 zenon_Hc2 zenon_H1d zenon_H11f zenon_H1c7 zenon_He2 zenon_H106 zenon_H1cf zenon_H16f zenon_H1d5 zenon_H34 zenon_Haf zenon_Hdb zenon_H173 zenon_Ha8 zenon_H81 zenon_H1c4 zenon_Ha1 zenon_H6a zenon_H22 zenon_H23 zenon_H18b zenon_H1ad zenon_H40 zenon_H1ac zenon_H1a6 zenon_H9a zenon_H48 zenon_H12b zenon_H52 zenon_H3b zenon_H15e zenon_H6f zenon_H149 zenon_H9d zenon_H7c zenon_H18c zenon_H25 zenon_H38. % 18.64/18.79 apply (zenon_or_s _ _ zenon_H22d); [ zenon_intro zenon_H7a | zenon_intro zenon_H22e ]. % 18.64/18.79 apply (zenon_L456_); trivial. % 18.64/18.79 apply (zenon_or_s _ _ zenon_H22e); [ zenon_intro zenon_Ha0 | zenon_intro zenon_H22f ]. % 18.64/18.79 apply (zenon_or_s _ _ zenon_H22); [ zenon_intro zenon_H27 | zenon_intro zenon_H26 ]. % 18.64/18.79 exact (zenon_H23 zenon_H27). % 18.64/18.79 apply (zenon_or_s _ _ zenon_H26); [ zenon_intro zenon_H29 | zenon_intro zenon_H28 ]. % 18.64/18.79 apply (zenon_or_s _ _ zenon_H18c); [ zenon_intro zenon_H86 | zenon_intro zenon_H18d ]. % 18.64/18.79 apply (zenon_L123_); trivial. % 18.64/18.79 apply (zenon_or_s _ _ zenon_H18d); [ zenon_intro zenon_H110 | zenon_intro zenon_H18e ]. % 18.64/18.79 apply (zenon_L354_); trivial. % 18.64/18.79 apply (zenon_or_s _ _ zenon_H18e); [ zenon_intro zenon_H113 | zenon_intro zenon_Hd7 ]. % 18.64/18.79 apply (zenon_L457_); trivial. % 18.64/18.79 apply (zenon_or_s _ _ zenon_H1d8); [ zenon_intro zenon_H10f | zenon_intro zenon_H1d9 ]. % 18.64/18.79 apply (zenon_L458_); trivial. % 18.64/18.79 apply (zenon_or_s _ _ zenon_H1d9); [ zenon_intro zenon_H110 | zenon_intro zenon_H1da ]. % 18.64/18.79 apply (zenon_L283_); trivial. % 18.64/18.79 apply (zenon_or_s _ _ zenon_H1da); [ zenon_intro zenon_H1ca | zenon_intro zenon_H14d ]. % 18.64/18.79 apply (zenon_or_s _ _ zenon_H16f); [ zenon_intro zenon_H9e | zenon_intro zenon_H170 ]. % 18.64/18.79 apply (zenon_L37_); trivial. % 18.64/18.79 apply (zenon_or_s _ _ zenon_H170); [ zenon_intro zenon_H13f | zenon_intro zenon_H171 ]. % 18.64/18.79 apply (zenon_or_s _ _ zenon_H106); [ zenon_intro zenon_Hed | zenon_intro zenon_H107 ]. % 18.64/18.79 apply (zenon_L214_); trivial. % 18.64/18.79 apply (zenon_or_s _ _ zenon_H107); [ zenon_intro zenon_Ha5 | zenon_intro zenon_H108 ]. % 18.64/18.79 apply (zenon_L357_); trivial. % 18.64/18.79 apply (zenon_or_s _ _ zenon_H108); [ zenon_intro zenon_Hf1 | zenon_intro zenon_Hf4 ]. % 18.64/18.79 apply (zenon_L460_); trivial. % 18.64/18.79 apply (zenon_L408_); trivial. % 18.64/18.79 apply (zenon_or_s _ _ zenon_H171); [ zenon_intro zenon_H16c | zenon_intro zenon_Hdc ]. % 18.64/18.79 apply (zenon_or_s _ _ zenon_H1a5); [ zenon_intro zenon_H99 | zenon_intro zenon_H1a8 ]. % 18.64/18.79 apply (zenon_L403_); trivial. % 18.64/18.79 apply (zenon_or_s _ _ zenon_H1a8); [ zenon_intro zenon_H13f | zenon_intro zenon_H1a9 ]. % 18.64/18.79 apply (zenon_or_s _ _ zenon_H106); [ zenon_intro zenon_Hed | zenon_intro zenon_H107 ]. % 18.64/18.79 apply (zenon_L461_); trivial. % 18.64/18.79 apply (zenon_or_s _ _ zenon_H107); [ zenon_intro zenon_Ha5 | zenon_intro zenon_H108 ]. % 18.64/18.79 apply (zenon_L373_); trivial. % 18.64/18.79 apply (zenon_or_s _ _ zenon_H108); [ zenon_intro zenon_Hf1 | zenon_intro zenon_Hf4 ]. % 18.64/18.79 apply (zenon_L460_); trivial. % 18.64/18.79 apply (zenon_L408_); trivial. % 18.64/18.79 apply (zenon_or_s _ _ zenon_H1a9); [ zenon_intro zenon_Ha6 | zenon_intro zenon_H161 ]. % 18.64/18.79 apply (zenon_L207_); trivial. % 18.64/18.79 apply (zenon_L193_); trivial. % 18.64/18.79 apply (zenon_L266_); trivial. % 18.64/18.79 apply (zenon_L462_); trivial. % 18.64/18.79 apply (zenon_or_s _ _ zenon_H28); [ zenon_intro zenon_H2a | zenon_intro zenon_H1f ]. % 18.64/18.79 exact (zenon_H25 zenon_H2a). % 18.64/18.79 exact (zenon_H38 zenon_H1f). % 18.64/18.79 apply (zenon_or_s _ _ zenon_H22f); [ zenon_intro zenon_H122 | zenon_intro zenon_Hc3 ]. % 18.64/18.79 apply (zenon_L438_); trivial. % 18.64/18.79 apply (zenon_or_s _ _ zenon_H22); [ zenon_intro zenon_H27 | zenon_intro zenon_H26 ]. % 18.64/18.79 exact (zenon_H23 zenon_H27). % 18.64/18.79 apply (zenon_or_s _ _ zenon_H26); [ zenon_intro zenon_H29 | zenon_intro zenon_H28 ]. % 18.64/18.79 apply (zenon_or_s _ _ zenon_H18c); [ zenon_intro zenon_H86 | zenon_intro zenon_H18d ]. % 18.64/18.79 apply (zenon_L123_); trivial. % 18.64/18.79 apply (zenon_or_s _ _ zenon_H18d); [ zenon_intro zenon_H110 | zenon_intro zenon_H18e ]. % 18.64/18.79 apply (zenon_L354_); trivial. % 18.64/18.79 apply (zenon_or_s _ _ zenon_H18e); [ zenon_intro zenon_H113 | zenon_intro zenon_Hd7 ]. % 18.64/18.79 apply (zenon_L457_); trivial. % 18.64/18.79 apply (zenon_L444_); trivial. % 18.64/18.79 apply (zenon_or_s _ _ zenon_H28); [ zenon_intro zenon_H2a | zenon_intro zenon_H1f ]. % 18.64/18.79 exact (zenon_H25 zenon_H2a). % 18.64/18.79 exact (zenon_H38 zenon_H1f). % 18.64/18.79 (* end of lemma zenon_L463_ *) % 18.64/18.79 assert (zenon_L464_ : (~((op (e0) (e0)) = (e0))) -> (~((op (e0) (e1)) = (e0))) -> (((op (e0) (e0)) = (e1))\/(((op (e0) (e1)) = (e1))\/(((op (e0) (e2)) = (e1))\/((op (e0) (e3)) = (e1))))) -> (~((op (e1) (e0)) = (e0))) -> ((op (e2) (e0)) = (e0)) -> (((op (e0) (e1)) = (e0))\/(((op (e0) (e1)) = (e1))\/(((op (e0) (e1)) = (e2))\/((op (e0) (e1)) = (e3))))) -> (~((op (e2) (e1)) = (e0))) -> (~((op (e0) (e1)) = (op (e3) (e1)))) -> (~((op (e2) (e2)) = (e0))) -> ((op (e0) (e0)) = (e2)) -> ((op (e2) (e0)) = (e3)) -> ((op (e1) (e0)) = (e1)) -> (~((op (e1) (e2)) = (e0))) -> (~((op (e1) (e3)) = (e0))) -> ((~((op (e0) (e3)) = (e0)))\/((op (e0) (e0)) = (e3))) -> ((~((op (e1) (e1)) = (e0)))\/((op (e1) (e0)) = (e1))) -> (~((e1) = (e2))) -> ((~((op (e2) (e3)) = (e0)))\/((op (e2) (e0)) = (e3))) -> (((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))))) -> (((op (e0) (e2)) = (e3))\/(((op (e1) (e2)) = (e3))\/(((op (e2) (e2)) = (e3))\/((op (e3) (e2)) = (e3))))) -> (~((op (e3) (e1)) = (op (e3) (e2)))) -> ((~((op (e3) (e2)) = (e0)))\/((op (e3) (e0)) = (e2))) -> (~((op (e2) (e2)) = (op (e3) (e2)))) -> (((op (e3) (e2)) = (e0))\/(((op (e3) (e2)) = (e1))\/(((op (e3) (e2)) = (e2))\/((op (e3) (e2)) = (e3))))) -> (~((op (e0) (e2)) = (op (e1) (e2)))) -> (((op (e1) (e2)) = (e0))\/(((op (e1) (e2)) = (e1))\/(((op (e1) (e2)) = (e2))\/((op (e1) (e2)) = (e3))))) -> (~((e1) = (e3))) -> (~((e0) = (e3))) -> (~((op (e1) (e1)) = (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) (e3)) = (e0))\/(((op (e2) (e3)) = (e1))\/(((op (e2) (e3)) = (e2))\/((op (e2) (e3)) = (e3))))) -> (~((op (e0) (e3)) = (op (e1) (e3)))) -> (~((op (e0) (e1)) = (op (e1) (e1)))) -> (~((e0) = (e1))) -> (~((op (e0) (e2)) = (op (e2) (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) (e3)) = (e0))\/(((op (e1) (e3)) = (e1))\/(((op (e1) (e3)) = (e2))\/((op (e1) (e3)) = (e3))))) -> (~((op (e1) (e3)) = (op (e2) (e3)))) -> (~((op (e1) (e0)) = (op (e1) (e3)))) -> (~((op (e1) (e3)) = (op (e3) (e3)))) -> (~((op (e0) (e3)) = (op (e2) (e3)))) -> (((op (e0) (e3)) = (e0))\/(((op (e0) (e3)) = (e1))\/(((op (e0) (e3)) = (e2))\/((op (e0) (e3)) = (e3))))) -> (~((op (e2) (e1)) = (op (e3) (e1)))) -> (((op (e2) (e0)) = (e3))\/(((op (e2) (e1)) = (e3))\/(((op (e2) (e2)) = (e3))\/((op (e2) (e3)) = (e3))))) -> (((op (e2) (e0)) = (e1))\/(((op (e2) (e1)) = (e1))\/(((op (e2) (e2)) = (e1))\/((op (e2) (e3)) = (e1))))) -> (~((op (e2) (e3)) = (op (e3) (e3)))) -> (~((op (e3) (e3)) = (e3))) -> (((op (e3) (e3)) = (e0))\/(((op (e3) (e3)) = (e1))\/(((op (e3) (e3)) = (e2))\/((op (e3) (e3)) = (e3))))) -> (~((op (e1) (e2)) = (op (e2) (e2)))) -> (((op (e0) (e1)) = (e1))\/(((op (e1) (e1)) = (e1))\/(((op (e2) (e1)) = (e1))\/((op (e3) (e1)) = (e1))))) -> (~((op (e0) (e0)) = (op (e0) (e3)))) -> ((~((op (e2) (e2)) = (e0)))\/((op (e2) (e0)) = (e2))) -> ((~((op (e3) (e0)) = (e0)))\/((op (e3) (e0)) = (e0))) -> (((op (e0) (e0)) = (e2))\/(((op (e0) (e1)) = (e2))\/(((op (e0) (e2)) = (e2))\/((op (e0) (e3)) = (e2))))) -> (~((op (e2) (e0)) = (op (e3) (e0)))) -> (~((op (e0) (e1)) = (op (e2) (e1)))) -> ((~((op (e1) (e2)) = (e0)))\/((op (e1) (e0)) = (e2))) -> ((~((op (e1) (e3)) = (e0)))\/((op (e1) (e0)) = (e3))) -> (((op (e1) (e1)) = (e0))\/(((op (e1) (e1)) = (e1))\/(((op (e1) (e1)) = (e2))\/((op (e1) (e1)) = (e3))))) -> (~((op (e1) (e1)) = (op (e2) (e1)))) -> (~((op (e0) (e0)) = (op (e0) (e2)))) -> (((op (e0) (e2)) = (e1))\/(((op (e1) (e2)) = (e1))\/(((op (e2) (e2)) = (e1))\/((op (e3) (e2)) = (e1))))) -> (((op (e1) (e0)) = (e1))\/(((op (e1) (e1)) = (e1))\/(((op (e1) (e2)) = (e1))\/((op (e1) (e3)) = (e1))))) -> (((op (e0) (e3)) = (e3))\/(((op (e1) (e3)) = (e3))\/(((op (e2) (e3)) = (e3))\/((op (e3) (e3)) = (e3))))) -> (~((op (e3) (e1)) = (op (e3) (e3)))) -> (((op (e0) (e3)) = (e1))\/(((op (e1) (e3)) = (e1))\/(((op (e2) (e3)) = (e1))\/((op (e3) (e3)) = (e1))))) -> (~((e2) = (e3))) -> (~((op (e1) (e2)) = (op (e1) (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 (e2) (e2)) = (e2))) -> (((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) (e1)) = (op (e3) (e1)))) -> (((op (e3) (e0)) = (e3))\/(((op (e3) (e1)) = (e3))\/(((op (e3) (e2)) = (e3))\/((op (e3) (e3)) = (e3))))) -> (~((e0) = (e2))) -> (~((op (e0) (e2)) = (op (e3) (e2)))) -> (((op (e3) (e0)) = (e2))\/(((op (e3) (e1)) = (e2))\/(((op (e3) (e2)) = (e2))\/((op (e3) (e3)) = (e2))))) -> (~((op (e0) (e0)) = (op (e2) (e0)))) -> ((~((op (e2) (e1)) = (e0)))\/((op (e2) (e0)) = (e1))) -> (((op (e0) (e0)) = (e2))\/(((op (e1) (e0)) = (e2))\/(((op (e2) (e0)) = (e2))\/((op (e3) (e0)) = (e2))))) -> ((~((op (e2) (e0)) = (e0)))\/((op (e2) (e0)) = (e0))) -> (((op (e0) (e0)) = (e3))\/(((op (e1) (e0)) = (e3))\/(((op (e2) (e0)) = (e3))\/((op (e3) (e0)) = (e3))))) -> (~((op (e2) (e1)) = (op (e2) (e3)))) -> (((op (e2) (e2)) = (e0))\/(((op (e2) (e2)) = (e1))\/(((op (e2) (e2)) = (e2))\/((op (e2) (e2)) = (e3))))) -> (((op (e2) (e1)) = (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 (e3) (e0)) = (op (e3) (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))))) -> ((~((op (e3) (e3)) = (e0)))\/((op (e3) (e0)) = (e3))) -> ((~((op (e3) (e1)) = (e0)))\/((op (e3) (e0)) = (e1))) -> (((op (e1) (e0)) = (e0))\/(((op (e1) (e1)) = (e0))\/(((op (e1) (e2)) = (e0))\/((op (e1) (e3)) = (e0))))) -> (~((op (e1) (e0)) = (op (e1) (e1)))) -> (((op (e0) (e2)) = (e0))\/(((op (e1) (e2)) = (e0))\/(((op (e2) (e2)) = (e0))\/((op (e3) (e2)) = (e0))))) -> (~((op (e0) (e1)) = (op (e0) (e3)))) -> (~((op (e1) (e1)) = (op (e1) (e3)))) -> (~((op (e2) (e0)) = (op (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) (e0)) = (op (e2) (e2)))) -> (~((op (e1) (e1)) = (op (e1) (e2)))) -> (~((op (e0) (e1)) = (op (e0) (e2)))) -> (~((op (e3) (e0)) = (op (e3) (e3)))) -> (~((op (e2) (e2)) = (op (e2) (e3)))) -> (~((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)) = (e0))\/(((op (e0) (e1)) = (e0))\/(((op (e0) (e2)) = (e0))\/((op (e0) (e3)) = (e0))))) -> (~((op (e1) (e0)) = (op (e3) (e0)))) -> (~((op (e2) (e0)) = (op (e2) (e1)))) -> (~((op (e1) (e0)) = (op (e2) (e0)))) -> ((~((op (e1) (e0)) = (e0)))\/((op (e1) (e0)) = (e0))) -> ((~((op (e0) (e2)) = (e0)))\/((op (e0) (e0)) = (e2))) -> (~((op (e0) (e2)) = (op (e0) (e3)))) -> (~((op (e3) (e0)) = (e0))) -> (~((op (e3) (e1)) = (e0))) -> (~((op (e3) (e2)) = (e0))) -> (((op (e3) (e0)) = (e0))\/(((op (e3) (e1)) = (e0))\/(((op (e3) (e2)) = (e0))\/((op (e3) (e3)) = (e0))))) -> False). % 18.64/18.79 do 0 intro. intros zenon_H3f zenon_H20b zenon_H22d zenon_H23 zenon_H34 zenon_H212 zenon_H31 zenon_H210 zenon_H81 zenon_H7b zenon_H3b zenon_H9d zenon_H25 zenon_H38 zenon_H204 zenon_H205 zenon_H7c zenon_H94 zenon_H2f zenon_H1a5 zenon_H1a6 zenon_H1a4 zenon_H1a7 zenon_H18f zenon_H191 zenon_H195 zenon_H19d zenon_H95 zenon_H9a zenon_H10a zenon_H18c zenon_H115 zenon_H11f zenon_H1d zenon_H10e zenon_Ha1 zenon_Ha8 zenon_He8 zenon_Hc2 zenon_Hdf zenon_Hdb zenon_Hd8 zenon_Hd5 zenon_He2 zenon_He4 zenon_Haf zenon_He7 zenon_H106 zenon_Hf3 zenon_H102 zenon_H101 zenon_H2b zenon_H109 zenon_H189 zenon_H185 zenon_H184 zenon_H183 zenon_H17b zenon_H17e zenon_H178 zenon_H179 zenon_H142 zenon_H13e zenon_H13c zenon_H139 zenon_H128 zenon_H136 zenon_H130 zenon_H133 zenon_H12b zenon_H124 zenon_H145 zenon_H172 zenon_H173 zenon_H16f zenon_H168 zenon_H160 zenon_H165 zenon_H149 zenon_H14f zenon_H153 zenon_H39 zenon_H182 zenon_H1fe zenon_H1ee zenon_H1e0 zenon_H1c7 zenon_H1c4 zenon_H1cc zenon_H1ba zenon_H1cf zenon_H1d8 zenon_H1d5 zenon_H1ec zenon_H1ed zenon_H22 zenon_H45 zenon_H6a zenon_H54 zenon_H57 zenon_H5b zenon_H62 zenon_H67 zenon_H52 zenon_H4f zenon_H4a zenon_H71 zenon_H6d zenon_H6f zenon_H3e zenon_H74 zenon_H1fa zenon_H1f0 zenon_H201 zenon_H206 zenon_H233 zenon_H208 zenon_H40 zenon_H1ad zenon_H18b zenon_H1ac. % 18.64/18.79 apply (zenon_or_s _ _ zenon_H1ec); [ zenon_intro zenon_H1ae | zenon_intro zenon_H15e ]. % 18.64/18.79 apply (zenon_L174_); trivial. % 18.64/18.79 apply (zenon_or_s _ _ zenon_H74); [ zenon_intro zenon_H42 | zenon_intro zenon_H77 ]. % 18.64/18.79 exact (zenon_H3f zenon_H42). % 18.64/18.79 apply (zenon_or_s _ _ zenon_H77); [ zenon_intro zenon_H49 | zenon_intro zenon_H78 ]. % 18.64/18.79 exact (zenon_H20b zenon_H49). % 18.64/18.79 apply (zenon_or_s _ _ zenon_H78); [ zenon_intro zenon_H48 | zenon_intro zenon_H1e ]. % 18.64/18.80 apply (zenon_L463_); trivial. % 18.64/18.80 apply (zenon_L337_); trivial. % 18.64/18.80 (* end of lemma zenon_L464_ *) % 18.64/18.80 assert (zenon_L465_ : (((op (e2) (e0)) = (e1))\/(((op (e2) (e1)) = (e1))\/(((op (e2) (e2)) = (e1))\/((op (e2) (e3)) = (e1))))) -> (~((op (e0) (e1)) = (op (e0) (e2)))) -> ((op (e0) (e1)) = (e1)) -> (~((op (e0) (e1)) = (op (e2) (e1)))) -> (((op (e0) (e2)) = (e1))\/(((op (e1) (e2)) = (e1))\/(((op (e2) (e2)) = (e1))\/((op (e3) (e2)) = (e1))))) -> ((op (e3) (e2)) = (e0)) -> (~((op (e0) (e2)) = (op (e2) (e2)))) -> (~((e1) = (e3))) -> ((op (e1) (e2)) = (e3)) -> (~((op (e2) (e2)) = (op (e2) (e3)))) -> (((op (e2) (e2)) = (e0))\/(((op (e2) (e2)) = (e1))\/(((op (e2) (e2)) = (e2))\/((op (e2) (e2)) = (e3))))) -> (~((op (e2) (e2)) = (e0))) -> (~((op (e2) (e2)) = (op (e3) (e2)))) -> (~((op (e2) (e2)) = (e2))) -> ((op (e2) (e0)) = (e3)) -> (~((op (e2) (e0)) = (op (e2) (e2)))) -> False). % 18.64/18.80 do 0 intro. intros zenon_H106 zenon_H4a zenon_Ha0 zenon_H17e zenon_H139 zenon_H61 zenon_Ha8 zenon_H95 zenon_H16c zenon_H6d zenon_H1c4 zenon_H81 zenon_H18f zenon_H173 zenon_H3b zenon_H52. % 18.64/18.80 apply (zenon_or_s _ _ zenon_H106); [ zenon_intro zenon_Hed | zenon_intro zenon_H107 ]. % 18.64/18.80 apply (zenon_L461_); trivial. % 18.64/18.80 apply (zenon_or_s _ _ zenon_H107); [ zenon_intro zenon_Ha5 | zenon_intro zenon_H108 ]. % 18.64/18.80 apply (zenon_L357_); trivial. % 18.64/18.80 apply (zenon_or_s _ _ zenon_H108); [ zenon_intro zenon_Hf1 | zenon_intro zenon_Hf4 ]. % 18.64/18.80 apply (zenon_L156_); trivial. % 18.64/18.80 apply (zenon_or_s _ _ zenon_H139); [ zenon_intro zenon_H122 | zenon_intro zenon_H13a ]. % 18.64/18.80 apply (zenon_L437_); trivial. % 18.64/18.80 apply (zenon_or_s _ _ zenon_H13a); [ zenon_intro zenon_Hf0 | zenon_intro zenon_H13b ]. % 18.64/18.80 apply (zenon_L167_); trivial. % 18.64/18.80 apply (zenon_or_s _ _ zenon_H13b); [ zenon_intro zenon_Hf1 | zenon_intro zenon_Hba ]. % 18.64/18.80 apply (zenon_L84_); trivial. % 18.64/18.80 apply (zenon_L327_); trivial. % 18.64/18.80 (* end of lemma zenon_L465_ *) % 18.64/18.80 assert (zenon_L466_ : (((op (e0) (e2)) = (e0))\/(((op (e0) (e2)) = (e1))\/(((op (e0) (e2)) = (e2))\/((op (e0) (e2)) = (e3))))) -> ((op (e3) (e2)) = (e0)) -> (~((op (e2) (e2)) = (e2))) -> (~((op (e0) (e2)) = (op (e2) (e2)))) -> (~((op (e2) (e2)) = (e0))) -> (((op (e2) (e2)) = (e0))\/(((op (e2) (e2)) = (e1))\/(((op (e2) (e2)) = (e2))\/((op (e2) (e2)) = (e3))))) -> ((op (e1) (e2)) = (e2)) -> (~((op (e0) (e2)) = (op (e1) (e2)))) -> (((op (e3) (e0)) = (e3))\/(((op (e3) (e1)) = (e3))\/(((op (e3) (e2)) = (e3))\/((op (e3) (e3)) = (e3))))) -> (~((e2) = (e3))) -> ((op (e3) (e0)) = (e2)) -> ((op (e1) (e1)) = (e3)) -> (~((op (e1) (e1)) = (op (e3) (e1)))) -> (~((op (e0) (e2)) = (op (e3) (e2)))) -> (~((op (e3) (e3)) = (e3))) -> False). % 18.64/18.80 do 0 intro. intros zenon_H1ba zenon_H61 zenon_H173 zenon_Ha8 zenon_H81 zenon_H1c4 zenon_H113 zenon_H195 zenon_H165 zenon_H12b zenon_H148 zenon_H13f zenon_H160 zenon_H14f zenon_H102. % 18.64/18.80 apply (zenon_or_s _ _ zenon_H1ba); [ zenon_intro zenon_H48 | zenon_intro zenon_H1bb ]. % 18.64/18.80 apply (zenon_L342_); trivial. % 18.64/18.80 apply (zenon_or_s _ _ zenon_H1bb); [ zenon_intro zenon_H122 | zenon_intro zenon_H1bc ]. % 18.64/18.80 apply (zenon_L437_); trivial. % 18.64/18.80 apply (zenon_or_s _ _ zenon_H1bc); [ zenon_intro zenon_H150 | zenon_intro zenon_Ha9 ]. % 18.64/18.80 apply (zenon_L153_); trivial. % 18.64/18.80 apply (zenon_L112_); trivial. % 18.64/18.80 (* end of lemma zenon_L466_ *) % 18.64/18.80 assert (zenon_L467_ : (((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))) -> ((op (e2) (e0)) = (e0)) -> ((op (e3) (e0)) = (e2)) -> (~((op (e3) (e0)) = (op (e3) (e2)))) -> (((op (e0) (e2)) = (e0))\/(((op (e0) (e2)) = (e1))\/(((op (e0) (e2)) = (e2))\/((op (e0) (e2)) = (e3))))) -> (~((op (e0) (e2)) = (op (e2) (e2)))) -> (~((op (e0) (e2)) = (op (e1) (e2)))) -> (((op (e3) (e0)) = (e3))\/(((op (e3) (e1)) = (e3))\/(((op (e3) (e2)) = (e3))\/((op (e3) (e3)) = (e3))))) -> (~((e2) = (e3))) -> ((op (e1) (e1)) = (e3)) -> (~((op (e1) (e1)) = (op (e3) (e1)))) -> (~((op (e0) (e2)) = (op (e3) (e2)))) -> (~((op (e3) (e3)) = (e3))) -> (((op (e1) (e2)) = (e0))\/(((op (e1) (e2)) = (e1))\/(((op (e1) (e2)) = (e2))\/((op (e1) (e2)) = (e3))))) -> (~((op (e1) (e2)) = (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)) = (op (e2) (e1)))) -> (~((e1) = (e3))) -> (((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 (e0) (e1)) = (op (e0) (e2)))) -> (~((op (e2) (e3)) = (op (e3) (e3)))) -> (~((op (e1) (e2)) = (op (e3) (e2)))) -> (~((op (e0) (e1)) = (op (e3) (e1)))) -> ((op (e0) (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 (e2) (e3)))) -> (((op (e2) (e2)) = (e0))\/(((op (e2) (e2)) = (e1))\/(((op (e2) (e2)) = (e2))\/((op (e2) (e2)) = (e3))))) -> (~((op (e2) (e2)) = (e0))) -> (~((op (e2) (e2)) = (op (e3) (e2)))) -> (~((op (e2) (e2)) = (e2))) -> ((op (e2) (e0)) = (e3)) -> (~((op (e2) (e0)) = (op (e2) (e2)))) -> False). % 18.64/18.80 do 0 intro. intros zenon_H6a zenon_H208 zenon_H1e zenon_Ha1 zenon_H34 zenon_H148 zenon_H6f zenon_H1ba zenon_Ha8 zenon_H195 zenon_H165 zenon_H12b zenon_H13f zenon_H160 zenon_H14f zenon_H102 zenon_H19d zenon_H25 zenon_H2b zenon_H106 zenon_H17e zenon_H95 zenon_H172 zenon_H139 zenon_H4a zenon_Hf3 zenon_H115 zenon_H210 zenon_Ha0 zenon_H7b zenon_He8 zenon_H6d zenon_H1c4 zenon_H81 zenon_H18f zenon_H173 zenon_H3b zenon_H52. % 18.64/18.80 apply (zenon_or_s _ _ zenon_H6a); [ zenon_intro zenon_H48 | zenon_intro zenon_H6b ]. % 18.64/18.80 apply (zenon_L336_); trivial. % 18.64/18.80 apply (zenon_or_s _ _ zenon_H6b); [ zenon_intro zenon_H2a | zenon_intro zenon_H6c ]. % 18.64/18.80 exact (zenon_H25 zenon_H2a). % 18.64/18.80 apply (zenon_or_s _ _ zenon_H6c); [ zenon_intro zenon_H2c | zenon_intro zenon_H61 ]. % 18.64/18.80 exact (zenon_H81 zenon_H2c). % 18.64/18.80 apply (zenon_or_s _ _ zenon_H106); [ zenon_intro zenon_Hed | zenon_intro zenon_H107 ]. % 18.64/18.80 apply (zenon_L214_); trivial. % 18.64/18.80 apply (zenon_or_s _ _ zenon_H107); [ zenon_intro zenon_Ha5 | zenon_intro zenon_H108 ]. % 18.64/18.80 apply (zenon_L357_); trivial. % 18.64/18.80 apply (zenon_or_s _ _ zenon_H108); [ zenon_intro zenon_Hf1 | zenon_intro zenon_Hf4 ]. % 18.64/18.80 apply (zenon_or_s _ _ zenon_H172); [ zenon_intro zenon_H150 | zenon_intro zenon_H174 ]. % 18.64/18.80 apply (zenon_or_s _ _ zenon_H19d); [ zenon_intro zenon_H2a | zenon_intro zenon_H19e ]. % 18.64/18.80 exact (zenon_H25 zenon_H2a). % 18.64/18.80 apply (zenon_or_s _ _ zenon_H19e); [ zenon_intro zenon_Hf0 | zenon_intro zenon_H19f ]. % 18.64/18.80 apply (zenon_L59_); trivial. % 18.64/18.80 apply (zenon_or_s _ _ zenon_H19f); [ zenon_intro zenon_H113 | zenon_intro zenon_H16c ]. % 18.64/18.80 apply (zenon_L153_); trivial. % 18.64/18.80 apply (zenon_L465_); trivial. % 18.64/18.80 apply (zenon_or_s _ _ zenon_H174); [ zenon_intro zenon_H113 | zenon_intro zenon_H175 ]. % 18.64/18.80 apply (zenon_L466_); trivial. % 18.64/18.80 apply (zenon_or_s _ _ zenon_H175); [ zenon_intro zenon_H176 | zenon_intro zenon_H151 ]. % 18.64/18.80 exact (zenon_H173 zenon_H176). % 18.64/18.80 apply (zenon_L420_); trivial. % 18.64/18.80 apply (zenon_L408_); trivial. % 18.64/18.80 (* end of lemma zenon_L467_ *) % 18.64/18.80 assert (zenon_L468_ : (((op (e3) (e0)) = (e1))\/(((op (e3) (e1)) = (e1))\/(((op (e3) (e2)) = (e1))\/((op (e3) (e3)) = (e1))))) -> ((op (e0) (e0)) = (e2)) -> ((op (e0) (e1)) = (e1)) -> (~((op (e0) (e1)) = (op (e3) (e1)))) -> (~((op (e2) (e0)) = (op (e2) (e2)))) -> ((op (e2) (e0)) = (e3)) -> (~((op (e2) (e2)) = (e2))) -> (~((op (e2) (e2)) = (op (e3) (e2)))) -> (~((op (e2) (e2)) = (e0))) -> (((op (e2) (e2)) = (e0))\/(((op (e2) (e2)) = (e1))\/(((op (e2) (e2)) = (e2))\/((op (e2) (e2)) = (e3))))) -> (((op (e0) (e3)) = (e2))\/(((op (e1) (e3)) = (e2))\/(((op (e2) (e3)) = (e2))\/((op (e3) (e3)) = (e2))))) -> (~((e0) = (e2))) -> (~((e2) = (e3))) -> (~((op (e2) (e1)) = (op (e2) (e3)))) -> ((op (e2) (e1)) = (e2)) -> (((op (e2) (e3)) = (e0))\/(((op (e2) (e3)) = (e1))\/(((op (e2) (e3)) = (e2))\/((op (e2) (e3)) = (e3))))) -> ((op (e0) (e3)) = (e0)) -> (~((op (e0) (e3)) = (op (e2) (e3)))) -> (~((op (e2) (e3)) = (op (e3) (e3)))) -> (~((op (e1) (e3)) = (op (e2) (e3)))) -> ((op (e1) (e3)) = (e3)) -> False). % 18.65/18.80 do 0 intro. intros zenon_He8 zenon_H7b zenon_Ha0 zenon_H210 zenon_H52 zenon_H3b zenon_H173 zenon_H18f zenon_H81 zenon_H1c4 zenon_H145 zenon_H149 zenon_H12b zenon_H1c7 zenon_H1ca zenon_H11f zenon_H1e zenon_He2 zenon_Hf3 zenon_Hdb zenon_Hdc. % 18.65/18.80 apply (zenon_or_s _ _ zenon_He8); [ zenon_intro zenon_Hac | zenon_intro zenon_Heb ]. % 18.65/18.80 apply (zenon_L308_); trivial. % 18.65/18.80 apply (zenon_or_s _ _ zenon_Heb); [ zenon_intro zenon_Hae | zenon_intro zenon_Hec ]. % 18.65/18.80 apply (zenon_L363_); trivial. % 18.65/18.80 apply (zenon_or_s _ _ zenon_Hec); [ zenon_intro zenon_Hba | zenon_intro zenon_Hc4 ]. % 18.65/18.80 apply (zenon_L327_); trivial. % 18.65/18.80 apply (zenon_L429_); trivial. % 18.65/18.80 (* end of lemma zenon_L468_ *) % 18.65/18.80 assert (zenon_L469_ : (((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) (e2)) = (e0))) -> (((op (e2) (e0)) = (e1))\/(((op (e2) (e1)) = (e1))\/(((op (e2) (e2)) = (e1))\/((op (e2) (e3)) = (e1))))) -> (~((op (e0) (e1)) = (op (e0) (e2)))) -> ((op (e0) (e1)) = (e1)) -> (~((op (e0) (e1)) = (op (e2) (e1)))) -> (((op (e0) (e2)) = (e1))\/(((op (e1) (e2)) = (e1))\/(((op (e2) (e2)) = (e1))\/((op (e3) (e2)) = (e1))))) -> (~((op (e0) (e2)) = (op (e2) (e2)))) -> (~((e1) = (e3))) -> ((op (e1) (e2)) = (e3)) -> (~((op (e2) (e2)) = (op (e2) (e3)))) -> (((op (e2) (e2)) = (e0))\/(((op (e2) (e2)) = (e1))\/(((op (e2) (e2)) = (e2))\/((op (e2) (e2)) = (e3))))) -> (~((op (e2) (e2)) = (e0))) -> (~((op (e2) (e2)) = (op (e3) (e2)))) -> (~((op (e2) (e2)) = (e2))) -> ((op (e2) (e0)) = (e3)) -> (~((op (e2) (e0)) = (op (e2) (e2)))) -> False). % 18.65/18.80 do 0 intro. intros zenon_H6a zenon_H208 zenon_H1e zenon_H25 zenon_H106 zenon_H4a zenon_Ha0 zenon_H17e zenon_H139 zenon_Ha8 zenon_H95 zenon_H16c zenon_H6d zenon_H1c4 zenon_H81 zenon_H18f zenon_H173 zenon_H3b zenon_H52. % 18.65/18.80 apply (zenon_or_s _ _ zenon_H6a); [ zenon_intro zenon_H48 | zenon_intro zenon_H6b ]. % 18.65/18.80 apply (zenon_L336_); trivial. % 18.65/18.80 apply (zenon_or_s _ _ zenon_H6b); [ zenon_intro zenon_H2a | zenon_intro zenon_H6c ]. % 18.65/18.80 exact (zenon_H25 zenon_H2a). % 18.65/18.80 apply (zenon_or_s _ _ zenon_H6c); [ zenon_intro zenon_H2c | zenon_intro zenon_H61 ]. % 18.65/18.80 exact (zenon_H81 zenon_H2c). % 18.65/18.80 apply (zenon_L465_); trivial. % 18.65/18.80 (* end of lemma zenon_L469_ *) % 18.65/18.80 assert (zenon_L470_ : ((op (e0) (e0)) = (e3)) -> (((op (e3) (e0)) = (e0))\/(((op (e3) (e1)) = (e0))\/(((op (e3) (e2)) = (e0))\/((op (e3) (e3)) = (e0))))) -> (~((op (e0) (e2)) = (op (e0) (e3)))) -> ((~((op (e0) (e2)) = (e0)))\/((op (e0) (e0)) = (e2))) -> ((~((op (e1) (e0)) = (e0)))\/((op (e1) (e0)) = (e0))) -> (~((op (e1) (e0)) = (op (e2) (e0)))) -> (~((op (e2) (e0)) = (op (e2) (e1)))) -> (~((op (e1) (e0)) = (op (e3) (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)) = (op (e3) (e2)))) -> (~((op (e2) (e2)) = (op (e2) (e3)))) -> (~((op (e3) (e0)) = (op (e3) (e3)))) -> (~((op (e0) (e1)) = (op (e0) (e2)))) -> (~((op (e1) (e1)) = (op (e1) (e2)))) -> (~((op (e2) (e0)) = (op (e2) (e2)))) -> (((op (e0) (e3)) = (e0))\/(((op (e1) (e3)) = (e0))\/(((op (e2) (e3)) = (e0))\/((op (e3) (e3)) = (e0))))) -> (~((op (e3) (e2)) = (op (e3) (e3)))) -> (~((op (e2) (e0)) = (op (e2) (e3)))) -> (~((op (e1) (e1)) = (op (e1) (e3)))) -> (~((op (e0) (e1)) = (op (e0) (e3)))) -> (((op (e0) (e2)) = (e0))\/(((op (e1) (e2)) = (e0))\/(((op (e2) (e2)) = (e0))\/((op (e3) (e2)) = (e0))))) -> (~((op (e1) (e0)) = (op (e1) (e1)))) -> (((op (e1) (e0)) = (e0))\/(((op (e1) (e1)) = (e0))\/(((op (e1) (e2)) = (e0))\/((op (e1) (e3)) = (e0))))) -> ((~((op (e3) (e1)) = (e0)))\/((op (e3) (e0)) = (e1))) -> ((~((op (e3) (e3)) = (e0)))\/((op (e3) (e0)) = (e3))) -> (((op (e2) (e0)) = (e2))\/(((op (e2) (e1)) = (e2))\/(((op (e2) (e2)) = (e2))\/((op (e2) (e3)) = (e2))))) -> (((op (e0) (e1)) = (e2))\/(((op (e1) (e1)) = (e2))\/(((op (e2) (e1)) = (e2))\/((op (e3) (e1)) = (e2))))) -> (~((op (e3) (e0)) = (op (e3) (e1)))) -> (((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 (e2) (e2)) = (e0))\/(((op (e2) (e2)) = (e1))\/(((op (e2) (e2)) = (e2))\/((op (e2) (e2)) = (e3))))) -> (~((op (e2) (e1)) = (op (e2) (e3)))) -> (((op (e0) (e0)) = (e3))\/(((op (e1) (e0)) = (e3))\/(((op (e2) (e0)) = (e3))\/((op (e3) (e0)) = (e3))))) -> ((~((op (e2) (e0)) = (e0)))\/((op (e2) (e0)) = (e0))) -> (((op (e0) (e0)) = (e2))\/(((op (e1) (e0)) = (e2))\/(((op (e2) (e0)) = (e2))\/((op (e3) (e0)) = (e2))))) -> ((~((op (e2) (e1)) = (e0)))\/((op (e2) (e0)) = (e1))) -> (~((op (e0) (e0)) = (op (e2) (e0)))) -> (((op (e3) (e0)) = (e2))\/(((op (e3) (e1)) = (e2))\/(((op (e3) (e2)) = (e2))\/((op (e3) (e3)) = (e2))))) -> (~((op (e0) (e2)) = (op (e3) (e2)))) -> (~((e0) = (e2))) -> (((op (e3) (e0)) = (e3))\/(((op (e3) (e1)) = (e3))\/(((op (e3) (e2)) = (e3))\/((op (e3) (e3)) = (e3))))) -> (~((op (e1) (e1)) = (op (e3) (e1)))) -> (((op (e0) (e0)) = (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)) = (e2))) -> (((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) (e2)) = (op (e1) (e3)))) -> (~((e2) = (e3))) -> (((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)) = (e3))\/(((op (e1) (e3)) = (e3))\/(((op (e2) (e3)) = (e3))\/((op (e3) (e3)) = (e3))))) -> (((op (e1) (e0)) = (e1))\/(((op (e1) (e1)) = (e1))\/(((op (e1) (e2)) = (e1))\/((op (e1) (e3)) = (e1))))) -> (((op (e0) (e2)) = (e1))\/(((op (e1) (e2)) = (e1))\/(((op (e2) (e2)) = (e1))\/((op (e3) (e2)) = (e1))))) -> (~((op (e0) (e0)) = (op (e0) (e2)))) -> (~((op (e1) (e1)) = (op (e2) (e1)))) -> (((op (e1) (e1)) = (e0))\/(((op (e1) (e1)) = (e1))\/(((op (e1) (e1)) = (e2))\/((op (e1) (e1)) = (e3))))) -> ((~((op (e1) (e3)) = (e0)))\/((op (e1) (e0)) = (e3))) -> ((~((op (e1) (e2)) = (e0)))\/((op (e1) (e0)) = (e2))) -> (~((op (e0) (e1)) = (op (e2) (e1)))) -> (~((op (e2) (e0)) = (op (e3) (e0)))) -> (((op (e0) (e0)) = (e2))\/(((op (e0) (e1)) = (e2))\/(((op (e0) (e2)) = (e2))\/((op (e0) (e3)) = (e2))))) -> ((~((op (e3) (e0)) = (e0)))\/((op (e3) (e0)) = (e0))) -> ((~((op (e2) (e2)) = (e0)))\/((op (e2) (e0)) = (e2))) -> (~((op (e0) (e0)) = (op (e0) (e3)))) -> (((op (e0) (e1)) = (e1))\/(((op (e1) (e1)) = (e1))\/(((op (e2) (e1)) = (e1))\/((op (e3) (e1)) = (e1))))) -> (~((op (e1) (e2)) = (op (e2) (e2)))) -> (((op (e3) (e3)) = (e0))\/(((op (e3) (e3)) = (e1))\/(((op (e3) (e3)) = (e2))\/((op (e3) (e3)) = (e3))))) -> (~((op (e3) (e3)) = (e3))) -> (~((op (e2) (e3)) = (op (e3) (e3)))) -> (((op (e2) (e0)) = (e1))\/(((op (e2) (e1)) = (e1))\/(((op (e2) (e2)) = (e1))\/((op (e2) (e3)) = (e1))))) -> (((op (e2) (e0)) = (e3))\/(((op (e2) (e1)) = (e3))\/(((op (e2) (e2)) = (e3))\/((op (e2) (e3)) = (e3))))) -> (~((op (e2) (e1)) = (op (e3) (e1)))) -> (((op (e0) (e3)) = (e0))\/(((op (e0) (e3)) = (e1))\/(((op (e0) (e3)) = (e2))\/((op (e0) (e3)) = (e3))))) -> (~((op (e0) (e3)) = (op (e2) (e3)))) -> (~((op (e1) (e3)) = (op (e3) (e3)))) -> (~((op (e1) (e0)) = (op (e1) (e3)))) -> (~((op (e1) (e3)) = (op (e2) (e3)))) -> (((op (e1) (e3)) = (e0))\/(((op (e1) (e3)) = (e1))\/(((op (e1) (e3)) = (e2))\/((op (e1) (e3)) = (e3))))) -> (~((op (e0) (e3)) = (op (e3) (e3)))) -> (((op (e3) (e0)) = (e1))\/(((op (e3) (e1)) = (e1))\/(((op (e3) (e2)) = (e1))\/((op (e3) (e3)) = (e1))))) -> (~((op (e0) (e2)) = (op (e2) (e2)))) -> (~((e0) = (e1))) -> (~((op (e0) (e1)) = (op (e1) (e1)))) -> (~((op (e0) (e3)) = (op (e1) (e3)))) -> (((op (e2) (e3)) = (e0))\/(((op (e2) (e3)) = (e1))\/(((op (e2) (e3)) = (e2))\/((op (e2) (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) (e1)) = (e1))) -> (~((e0) = (e3))) -> (~((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 (e3) (e2)) = (e0))\/(((op (e3) (e2)) = (e1))\/(((op (e3) (e2)) = (e2))\/((op (e3) (e2)) = (e3))))) -> (~((op (e2) (e2)) = (op (e3) (e2)))) -> ((~((op (e3) (e2)) = (e0)))\/((op (e3) (e0)) = (e2))) -> (~((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)) = (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 (e2) (e3)) = (e0)))\/((op (e2) (e0)) = (e3))) -> (~((e1) = (e2))) -> ((~((op (e1) (e1)) = (e0)))\/((op (e1) (e0)) = (e1))) -> ((~((op (e0) (e3)) = (e0)))\/((op (e0) (e0)) = (e3))) -> (~((op (e1) (e3)) = (e0))) -> (~((op (e1) (e2)) = (e0))) -> ((op (e1) (e0)) = (e1)) -> ((op (e2) (e0)) = (e3)) -> ((op (e0) (e0)) = (e2)) -> (~((op (e2) (e2)) = (e0))) -> (~((op (e0) (e1)) = (op (e3) (e1)))) -> (~((op (e2) (e1)) = (e0))) -> (((op (e0) (e1)) = (e0))\/(((op (e0) (e1)) = (e1))\/(((op (e0) (e1)) = (e2))\/((op (e0) (e1)) = (e3))))) -> ((op (e2) (e0)) = (e0)) -> (~((op (e1) (e0)) = (e0))) -> (((op (e0) (e0)) = (e1))\/(((op (e0) (e1)) = (e1))\/(((op (e0) (e2)) = (e1))\/((op (e0) (e3)) = (e1))))) -> (~((op (e0) (e1)) = (e0))) -> (~((op (e0) (e0)) = (e0))) -> False). % 18.65/18.80 do 0 intro. intros zenon_H3a zenon_H1ac zenon_H208 zenon_H233 zenon_H206 zenon_H201 zenon_H1f0 zenon_H1fa zenon_H74 zenon_H3e zenon_H6f zenon_H6d zenon_H71 zenon_H4a zenon_H4f zenon_H52 zenon_H67 zenon_H62 zenon_H5b zenon_H57 zenon_H54 zenon_H6a zenon_H45 zenon_H22 zenon_H1ed zenon_H1ec zenon_H1d5 zenon_H1d8 zenon_H1cf zenon_H1ba zenon_H1cc zenon_H1c4 zenon_H1c7 zenon_H1e0 zenon_H1ee zenon_H1fe zenon_H182 zenon_H39 zenon_H153 zenon_H14f zenon_H149 zenon_H165 zenon_H160 zenon_H168 zenon_H16f zenon_H173 zenon_H172 zenon_H145 zenon_H124 zenon_H12b zenon_H133 zenon_H130 zenon_H136 zenon_H128 zenon_H139 zenon_H13c zenon_H13e zenon_H142 zenon_H179 zenon_H178 zenon_H17e zenon_H17b zenon_H183 zenon_H184 zenon_H185 zenon_H189 zenon_H109 zenon_H2b zenon_H101 zenon_H102 zenon_Hf3 zenon_H106 zenon_He7 zenon_Haf zenon_He4 zenon_He2 zenon_Hd5 zenon_Hd8 zenon_Hdb zenon_Hdf zenon_Hc2 zenon_He8 zenon_Ha8 zenon_Ha1 zenon_H10e zenon_H1d zenon_H11f zenon_H115 zenon_H18c zenon_H10a zenon_H9a zenon_H95 zenon_H19d zenon_H195 zenon_H191 zenon_H18f zenon_H1a7 zenon_H1a4 zenon_H1a6 zenon_H1a5 zenon_H2f zenon_H94 zenon_H7c zenon_H205 zenon_H204 zenon_H38 zenon_H25 zenon_H9d zenon_H3b zenon_H7b zenon_H81 zenon_H210 zenon_H31 zenon_H212 zenon_H34 zenon_H23 zenon_H22d zenon_H20b zenon_H3f. % 18.65/18.80 apply (zenon_or_s _ _ zenon_H184); [ zenon_intro zenon_H40 | zenon_intro zenon_H44 ]. % 18.65/18.80 apply (zenon_or_s _ _ zenon_H1ed); [ zenon_intro zenon_H1ad | zenon_intro zenon_Hac ]. % 18.65/18.80 apply (zenon_or_s _ _ zenon_H1a7); [ zenon_intro zenon_H18b | zenon_intro zenon_H148 ]. % 18.65/18.80 apply (zenon_L464_); trivial. % 18.65/18.80 apply (zenon_or_s _ _ zenon_H1ec); [ zenon_intro zenon_H1ae | zenon_intro zenon_H15e ]. % 18.65/18.80 apply (zenon_or_s _ _ zenon_H74); [ zenon_intro zenon_H42 | zenon_intro zenon_H77 ]. % 18.65/18.80 exact (zenon_H3f zenon_H42). % 18.65/18.80 apply (zenon_or_s _ _ zenon_H77); [ zenon_intro zenon_H49 | zenon_intro zenon_H78 ]. % 18.65/18.80 exact (zenon_H20b zenon_H49). % 18.65/18.80 apply (zenon_or_s _ _ zenon_H78); [ zenon_intro zenon_H48 | zenon_intro zenon_H1e ]. % 18.65/18.80 apply (zenon_L343_); trivial. % 18.65/18.80 apply (zenon_or_s _ _ zenon_H22d); [ zenon_intro zenon_H7a | zenon_intro zenon_H22e ]. % 18.65/18.80 apply (zenon_L35_); trivial. % 18.65/18.80 apply (zenon_or_s _ _ zenon_H22e); [ zenon_intro zenon_Ha0 | zenon_intro zenon_H22f ]. % 18.65/18.80 apply (zenon_or_s _ _ zenon_H22); [ zenon_intro zenon_H27 | zenon_intro zenon_H26 ]. % 18.65/18.80 exact (zenon_H23 zenon_H27). % 18.65/18.80 apply (zenon_or_s _ _ zenon_H26); [ zenon_intro zenon_H29 | zenon_intro zenon_H28 ]. % 18.65/18.80 apply (zenon_or_s _ _ zenon_H18c); [ zenon_intro zenon_H86 | zenon_intro zenon_H18d ]. % 18.65/18.80 apply (zenon_L123_); trivial. % 18.65/18.80 apply (zenon_or_s _ _ zenon_H18d); [ zenon_intro zenon_H110 | zenon_intro zenon_H18e ]. % 18.65/18.80 apply (zenon_L354_); trivial. % 18.65/18.80 apply (zenon_or_s _ _ zenon_H18e); [ zenon_intro zenon_H113 | zenon_intro zenon_Hd7 ]. % 18.65/18.80 apply (zenon_or_s _ _ zenon_H1d8); [ zenon_intro zenon_H10f | zenon_intro zenon_H1d9 ]. % 18.65/18.80 apply (zenon_or_s _ _ zenon_H16f); [ zenon_intro zenon_H9e | zenon_intro zenon_H170 ]. % 18.65/18.80 apply (zenon_L37_); trivial. % 18.65/18.80 apply (zenon_or_s _ _ zenon_H170); [ zenon_intro zenon_H13f | zenon_intro zenon_H171 ]. % 18.65/18.80 apply (zenon_L467_); trivial. % 18.65/18.80 apply (zenon_or_s _ _ zenon_H171); [ zenon_intro zenon_H16c | zenon_intro zenon_Hdc ]. % 18.65/18.80 apply (zenon_L116_); trivial. % 18.65/18.80 apply (zenon_or_s _ _ zenon_H1d5); [ zenon_intro zenon_Hee | zenon_intro zenon_H1d6 ]. % 18.65/18.80 apply (zenon_L204_); trivial. % 18.65/18.80 apply (zenon_or_s _ _ zenon_H1d6); [ zenon_intro zenon_H1ca | zenon_intro zenon_H1d7 ]. % 18.65/18.80 apply (zenon_L468_); trivial. % 18.65/18.80 apply (zenon_or_s _ _ zenon_H1d7); [ zenon_intro zenon_H176 | zenon_intro zenon_H11d ]. % 18.65/18.80 exact (zenon_H173 zenon_H176). % 18.65/18.80 apply (zenon_L412_); trivial. % 18.65/18.80 apply (zenon_or_s _ _ zenon_H1d9); [ zenon_intro zenon_H110 | zenon_intro zenon_H1da ]. % 18.65/18.80 apply (zenon_L354_); trivial. % 18.65/18.80 apply (zenon_or_s _ _ zenon_H1da); [ zenon_intro zenon_H1ca | zenon_intro zenon_H14d ]. % 18.65/18.80 apply (zenon_or_s _ _ zenon_H16f); [ zenon_intro zenon_H9e | zenon_intro zenon_H170 ]. % 18.65/18.80 apply (zenon_L37_); trivial. % 18.65/18.80 apply (zenon_or_s _ _ zenon_H170); [ zenon_intro zenon_H13f | zenon_intro zenon_H171 ]. % 18.65/18.80 apply (zenon_L467_); trivial. % 18.65/18.80 apply (zenon_or_s _ _ zenon_H171); [ zenon_intro zenon_H16c | zenon_intro zenon_Hdc ]. % 18.65/18.80 apply (zenon_L116_); trivial. % 18.65/18.80 apply (zenon_L468_); trivial. % 18.65/18.80 apply (zenon_L436_); trivial. % 18.65/18.80 apply (zenon_or_s _ _ zenon_H16f); [ zenon_intro zenon_H9e | zenon_intro zenon_H170 ]. % 18.65/18.80 apply (zenon_L37_); trivial. % 18.65/18.80 apply (zenon_or_s _ _ zenon_H170); [ zenon_intro zenon_H13f | zenon_intro zenon_H171 ]. % 18.65/18.80 apply (zenon_L467_); trivial. % 18.65/18.80 apply (zenon_or_s _ _ zenon_H171); [ zenon_intro zenon_H16c | zenon_intro zenon_Hdc ]. % 18.65/18.80 apply (zenon_L469_); trivial. % 18.65/18.80 apply (zenon_L266_); trivial. % 18.65/18.80 apply (zenon_or_s _ _ zenon_H28); [ zenon_intro zenon_H2a | zenon_intro zenon_H1f ]. % 18.65/18.80 exact (zenon_H25 zenon_H2a). % 18.65/18.80 exact (zenon_H38 zenon_H1f). % 18.65/18.80 apply (zenon_or_s _ _ zenon_H22f); [ zenon_intro zenon_H122 | zenon_intro zenon_Hc3 ]. % 18.65/18.80 apply (zenon_L438_); trivial. % 18.65/18.80 apply (zenon_L427_); trivial. % 18.65/18.80 apply (zenon_L109_); trivial. % 18.65/18.80 apply (zenon_L308_); trivial. % 18.65/18.80 apply (zenon_L127_); trivial. % 18.65/18.80 (* end of lemma zenon_L470_ *) % 18.65/18.80 assert (zenon_L471_ : (((op (e0) (e3)) = (e0))\/(((op (e0) (e3)) = (e1))\/(((op (e0) (e3)) = (e2))\/((op (e0) (e3)) = (e3))))) -> ((op (e3) (e3)) = (e0)) -> ((op (e2) (e3)) = (e1)) -> (~((op (e0) (e3)) = (op (e2) (e3)))) -> ((op (e3) (e3)) = (e2)) -> (~((op (e0) (e3)) = (op (e3) (e3)))) -> (~((op (e0) (e3)) = (op (e1) (e3)))) -> ((op (e1) (e3)) = (e3)) -> False). % 18.65/18.80 do 0 intro. intros zenon_He4 zenon_H60 zenon_Hf4 zenon_He2 zenon_Hf6 zenon_Hc2 zenon_H1d zenon_Hdc. % 18.65/18.80 apply (zenon_or_s _ _ zenon_He4); [ zenon_intro zenon_H1e | zenon_intro zenon_He5 ]. % 18.65/18.80 apply (zenon_L440_); trivial. % 18.65/18.80 apply (zenon_or_s _ _ zenon_He5); [ zenon_intro zenon_Hc3 | zenon_intro zenon_He6 ]. % 18.65/18.80 apply (zenon_L272_); trivial. % 18.65/18.80 apply (zenon_or_s _ _ zenon_He6); [ zenon_intro zenon_Hcd | zenon_intro zenon_He3 ]. % 18.65/18.80 apply (zenon_L87_); trivial. % 18.65/18.80 apply (zenon_L117_); trivial. % 18.65/18.80 (* end of lemma zenon_L471_ *) % 18.65/18.80 assert (zenon_L472_ : ((op (e1) (e3)) = (e3)) -> (~((op (e1) (e3)) = (op (e2) (e3)))) -> (((op (e3) (e0)) = (e0))\/(((op (e3) (e1)) = (e0))\/(((op (e3) (e2)) = (e0))\/((op (e3) (e3)) = (e0))))) -> (~((op (e3) (e0)) = (e0))) -> (~((op (e3) (e2)) = (e0))) -> (((op (e3) (e0)) = (e2))\/(((op (e3) (e1)) = (e2))\/(((op (e3) (e2)) = (e2))\/((op (e3) (e3)) = (e2))))) -> (~((op (e3) (e3)) = (e3))) -> (~((op (e2) (e2)) = (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) (e1)) = (op (e2) (e3)))) -> (~((op (e3) (e1)) = (op (e3) (e2)))) -> (((op (e0) (e1)) = (e0))\/(((op (e0) (e1)) = (e1))\/(((op (e0) (e1)) = (e2))\/((op (e0) (e1)) = (e3))))) -> (~((op (e0) (e1)) = (e0))) -> (~((op (e0) (e1)) = (op (e3) (e1)))) -> (~((op (e1) (e1)) = (op (e2) (e1)))) -> (~((op (e0) (e1)) = (op (e2) (e1)))) -> (~((op (e2) (e1)) = (op (e3) (e1)))) -> (~((op (e2) (e1)) = (e0))) -> (((op (e2) (e1)) = (e0))\/(((op (e2) (e1)) = (e1))\/(((op (e2) (e1)) = (e2))\/((op (e2) (e1)) = (e3))))) -> (~((op (e0) (e1)) = (op (e1) (e1)))) -> (~((op (e3) (e1)) = (e0))) -> (((op (e3) (e1)) = (e0))\/(((op (e3) (e1)) = (e1))\/(((op (e3) (e1)) = (e2))\/((op (e3) (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)))) -> (~((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)) = (e0)))\/((op (e0) (e0)) = (e3))) -> ((~((op (e1) (e1)) = (e0)))\/((op (e1) (e0)) = (e1))) -> ((~((op (e2) (e3)) = (e0)))\/((op (e2) (e0)) = (e3))) -> (((op (e2) (e0)) = (e0))\/(((op (e2) (e1)) = (e0))\/(((op (e2) (e2)) = (e0))\/((op (e2) (e3)) = (e0))))) -> ((~((op (e3) (e2)) = (e0)))\/((op (e3) (e0)) = (e2))) -> (((op (e3) (e2)) = (e0))\/(((op (e3) (e2)) = (e1))\/(((op (e3) (e2)) = (e2))\/((op (e3) (e2)) = (e3))))) -> (~((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)) = (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)) = (e3))\/(((op (e2) (e1)) = (e3))\/(((op (e2) (e2)) = (e3))\/((op (e2) (e3)) = (e3))))) -> (((op (e3) (e3)) = (e0))\/(((op (e3) (e3)) = (e1))\/(((op (e3) (e3)) = (e2))\/((op (e3) (e3)) = (e3))))) -> (~((op (e1) (e2)) = (op (e2) (e2)))) -> (((op (e0) (e1)) = (e1))\/(((op (e1) (e1)) = (e1))\/(((op (e2) (e1)) = (e1))\/((op (e3) (e1)) = (e1))))) -> (~((op (e0) (e0)) = (op (e0) (e3)))) -> ((~((op (e2) (e2)) = (e0)))\/((op (e2) (e0)) = (e2))) -> ((~((op (e3) (e0)) = (e0)))\/((op (e3) (e0)) = (e0))) -> (((op (e0) (e0)) = (e2))\/(((op (e0) (e1)) = (e2))\/(((op (e0) (e2)) = (e2))\/((op (e0) (e3)) = (e2))))) -> (~((op (e2) (e0)) = (op (e3) (e0)))) -> ((~((op (e1) (e2)) = (e0)))\/((op (e1) (e0)) = (e2))) -> ((~((op (e1) (e3)) = (e0)))\/((op (e1) (e0)) = (e3))) -> (((op (e1) (e1)) = (e0))\/(((op (e1) (e1)) = (e1))\/(((op (e1) (e1)) = (e2))\/((op (e1) (e1)) = (e3))))) -> (~((op (e0) (e0)) = (op (e0) (e2)))) -> (((op (e1) (e0)) = (e1))\/(((op (e1) (e1)) = (e1))\/(((op (e1) (e2)) = (e1))\/((op (e1) (e3)) = (e1))))) -> (((op (e0) (e3)) = (e3))\/(((op (e1) (e3)) = (e3))\/(((op (e2) (e3)) = (e3))\/((op (e3) (e3)) = (e3))))) -> (~((op (e3) (e1)) = (op (e3) (e3)))) -> (~((op (e1) (e2)) = (op (e1) (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)) = (e3))\/(((op (e0) (e1)) = (e3))\/(((op (e0) (e2)) = (e3))\/((op (e0) (e3)) = (e3))))) -> (~((op (e0) (e2)) = (op (e3) (e2)))) -> (~((op (e0) (e0)) = (op (e2) (e0)))) -> ((~((op (e2) (e1)) = (e0)))\/((op (e2) (e0)) = (e1))) -> (((op (e0) (e0)) = (e2))\/(((op (e1) (e0)) = (e2))\/(((op (e2) (e0)) = (e2))\/((op (e3) (e0)) = (e2))))) -> ((~((op (e2) (e0)) = (e0)))\/((op (e2) (e0)) = (e0))) -> (((op (e0) (e0)) = (e3))\/(((op (e1) (e0)) = (e3))\/(((op (e2) (e0)) = (e3))\/((op (e3) (e0)) = (e3))))) -> (((op (e0) (e2)) = (e0))\/(((op (e0) (e2)) = (e1))\/(((op (e0) (e2)) = (e2))\/((op (e0) (e2)) = (e3))))) -> ((~((op (e3) (e3)) = (e0)))\/((op (e3) (e0)) = (e3))) -> ((~((op (e3) (e1)) = (e0)))\/((op (e3) (e0)) = (e1))) -> (~((op (e0) (e0)) = (e0))) -> (~((op (e1) (e0)) = (op (e1) (e1)))) -> (~((op (e2) (e0)) = (op (e2) (e3)))) -> (((op (e0) (e3)) = (e0))\/(((op (e1) (e3)) = (e0))\/(((op (e2) (e3)) = (e0))\/((op (e3) (e3)) = (e0))))) -> (~((op (e1) (e1)) = (op (e1) (e2)))) -> (~((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)) = (e0))\/(((op (e0) (e1)) = (e0))\/(((op (e0) (e2)) = (e0))\/((op (e0) (e3)) = (e0))))) -> (~((op (e1) (e0)) = (op (e3) (e0)))) -> (~((op (e2) (e0)) = (op (e2) (e1)))) -> (~((op (e1) (e0)) = (op (e2) (e0)))) -> ((~((op (e1) (e0)) = (e0)))\/((op (e1) (e0)) = (e0))) -> ((~((op (e0) (e2)) = (e0)))\/((op (e0) (e0)) = (e2))) -> (((op (e0) (e1)) = (e2))\/(((op (e1) (e1)) = (e2))\/(((op (e2) (e1)) = (e2))\/((op (e3) (e1)) = (e2))))) -> (~((op (e1) (e1)) = (op (e1) (e3)))) -> (((op (e0) (e1)) = (e3))\/(((op (e1) (e1)) = (e3))\/(((op (e2) (e1)) = (e3))\/((op (e3) (e1)) = (e3))))) -> (~((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)) = (e2)) -> (~((op (e1) (e2)) = (op (e3) (e2)))) -> (~((op (e2) (e3)) = (op (e3) (e3)))) -> (~((op (e0) (e1)) = (op (e0) (e2)))) -> (((op (e0) (e2)) = (e1))\/(((op (e1) (e2)) = (e1))\/(((op (e2) (e2)) = (e1))\/((op (e3) (e2)) = (e1))))) -> (~((e1) = (e3))) -> (~((op (e3) (e2)) = (op (e3) (e3)))) -> (~((op (e1) (e0)) = (op (e1) (e3)))) -> (~((op (e0) (e1)) = (op (e0) (e3)))) -> (((op (e0) (e3)) = (e1))\/(((op (e1) (e3)) = (e1))\/(((op (e2) (e3)) = (e1))\/((op (e3) (e3)) = (e1))))) -> (((op (e2) (e3)) = (e0))\/(((op (e2) (e3)) = (e1))\/(((op (e2) (e3)) = (e2))\/((op (e2) (e3)) = (e3))))) -> (((op (e2) (e0)) = (e1))\/(((op (e2) (e1)) = (e1))\/(((op (e2) (e2)) = (e1))\/((op (e2) (e3)) = (e1))))) -> (((op (e1) (e0)) = (e3))\/(((op (e1) (e1)) = (e3))\/(((op (e1) (e2)) = (e3))\/((op (e1) (e3)) = (e3))))) -> (((op (e2) (e0)) = (e2))\/(((op (e2) (e1)) = (e2))\/(((op (e2) (e2)) = (e2))\/((op (e2) (e3)) = (e2))))) -> ((op (e2) (e0)) = (e0)) -> (~((op (e2) (e2)) = (e2))) -> (~((op (e0) (e2)) = (op (e2) (e2)))) -> (~((op (e2) (e2)) = (e0))) -> (((op (e2) (e2)) = (e0))\/(((op (e2) (e2)) = (e1))\/(((op (e2) (e2)) = (e2))\/((op (e2) (e2)) = (e3))))) -> (~((e0) = (e1))) -> (((op (e0) (e2)) = (e0))\/(((op (e1) (e2)) = (e0))\/(((op (e2) (e2)) = (e0))\/((op (e3) (e2)) = (e0))))) -> (((op (e1) (e0)) = (e0))\/(((op (e1) (e1)) = (e0))\/(((op (e1) (e2)) = (e0))\/((op (e1) (e3)) = (e0))))) -> (~((op (e1) (e0)) = (e0))) -> (((op (e0) (e2)) = (e3))\/(((op (e1) (e2)) = (e3))\/(((op (e2) (e2)) = (e3))\/((op (e3) (e2)) = (e3))))) -> (~((e0) = (e3))) -> ((op (e0) (e2)) = (e0)) -> (~((op (e2) (e0)) = (op (e2) (e2)))) -> (~((op (e3) (e0)) = (op (e3) (e2)))) -> (~((e0) = (e2))) -> ((op (e1) (e0)) = (e1)) -> (~((e1) = (e2))) -> (((op (e1) (e0)) = (e2))\/(((op (e1) (e1)) = (e2))\/(((op (e1) (e2)) = (e2))\/((op (e1) (e3)) = (e2))))) -> (~((op (e1) (e2)) = (e0))) -> (~((op (e1) (e3)) = (e0))) -> (~((op (e2) (e3)) = (e0))) -> (~((op (e0) (e2)) = (op (e0) (e3)))) -> ((op (e0) (e0)) = (e3)) -> ((op (e0) (e1)) = (e1)) -> ((op (e1) (e2)) = (e2)) -> (~((e2) = (e3))) -> ((op (e2) (e1)) = (e2)) -> ((op (e3) (e0)) = (e3)) -> (~((op (e3) (e0)) = (op (e3) (e1)))) -> False). % 18.65/18.80 do 0 intro. intros zenon_Hdc zenon_Hdb zenon_H1ac zenon_H40 zenon_H18b zenon_H153 zenon_H102 zenon_H18f zenon_H160 zenon_H165 zenon_H1c7 zenon_H1a4 zenon_H212 zenon_H20b zenon_H210 zenon_H13e zenon_H17e zenon_Haf zenon_H31 zenon_H1cc zenon_H10e zenon_H1ad zenon_H22a zenon_He4 zenon_He2 zenon_Hc2 zenon_H1d zenon_H22d zenon_H204 zenon_H205 zenon_H94 zenon_H2f zenon_H1a7 zenon_H191 zenon_H195 zenon_H19d zenon_H10a zenon_Hdf zenon_Hd5 zenon_He7 zenon_H101 zenon_H2b zenon_H109 zenon_H189 zenon_H185 zenon_H184 zenon_H183 zenon_H17b zenon_H178 zenon_H179 zenon_H142 zenon_H13c zenon_H128 zenon_H136 zenon_H130 zenon_H124 zenon_H145 zenon_H172 zenon_H168 zenon_H14f zenon_H39 zenon_H182 zenon_H1fe zenon_H1ee zenon_H1e0 zenon_H1ba zenon_H1ec zenon_H1ed zenon_H3f zenon_H45 zenon_H5b zenon_H67 zenon_H4f zenon_H71 zenon_H3e zenon_H74 zenon_H1fa zenon_H1f0 zenon_H201 zenon_H206 zenon_H233 zenon_H1d8 zenon_H57 zenon_H1a5 zenon_H6d zenon_He8 zenon_H7b zenon_H115 zenon_Hf3 zenon_H4a zenon_H139 zenon_H95 zenon_H62 zenon_Hd8 zenon_H54 zenon_H133 zenon_H11f zenon_H106 zenon_H16f zenon_H1d5 zenon_H34 zenon_H173 zenon_Ha8 zenon_H81 zenon_H1c4 zenon_Ha1 zenon_H6a zenon_H22 zenon_H23 zenon_H1a6 zenon_H9a zenon_H48 zenon_H52 zenon_H6f zenon_H149 zenon_H9d zenon_H7c zenon_H18c zenon_H25 zenon_H38 zenon_H32 zenon_H208 zenon_H3a zenon_Ha0 zenon_H113 zenon_H12b zenon_H1ca zenon_H15e zenon_H1cf. % 18.65/18.80 apply (zenon_or_s _ _ zenon_H1a5); [ zenon_intro zenon_H99 | zenon_intro zenon_H1a8 ]. % 18.65/18.80 apply (zenon_L403_); trivial. % 18.65/18.80 apply (zenon_or_s _ _ zenon_H1a8); [ zenon_intro zenon_H13f | zenon_intro zenon_H1a9 ]. % 18.65/18.80 apply (zenon_or_s _ _ zenon_H106); [ zenon_intro zenon_Hed | zenon_intro zenon_H107 ]. % 18.65/18.80 apply (zenon_L413_); trivial. % 18.65/18.80 apply (zenon_or_s _ _ zenon_H107); [ zenon_intro zenon_Ha5 | zenon_intro zenon_H108 ]. % 18.65/18.80 apply (zenon_L357_); trivial. % 18.65/18.80 apply (zenon_or_s _ _ zenon_H108); [ zenon_intro zenon_Hf1 | zenon_intro zenon_Hf4 ]. % 18.65/18.80 apply (zenon_or_s _ _ zenon_He7); [ zenon_intro zenon_H3b | zenon_intro zenon_He9 ]. % 18.65/18.80 apply (zenon_L470_); trivial. % 18.65/18.80 apply (zenon_or_s _ _ zenon_He9); [ zenon_intro zenon_Ha6 | zenon_intro zenon_Hea ]. % 18.65/18.80 apply (zenon_L207_); trivial. % 18.65/18.80 apply (zenon_or_s _ _ zenon_Hea); [ zenon_intro zenon_Haa | zenon_intro zenon_Hdd ]. % 18.65/18.80 apply (zenon_or_s _ _ zenon_H153); [ zenon_intro zenon_H148 | zenon_intro zenon_H154 ]. % 18.65/18.80 apply (zenon_L325_); trivial. % 18.65/18.80 apply (zenon_or_s _ _ zenon_H154); [ zenon_intro zenon_H14d | zenon_intro zenon_H155 ]. % 18.65/18.80 apply (zenon_L452_); trivial. % 18.65/18.80 apply (zenon_or_s _ _ zenon_H155); [ zenon_intro zenon_H151 | zenon_intro zenon_Hf6 ]. % 18.65/18.80 apply (zenon_L453_); trivial. % 18.65/18.80 apply (zenon_L446_); trivial. % 18.65/18.80 apply (zenon_L52_); trivial. % 18.65/18.80 apply (zenon_or_s _ _ zenon_He7); [ zenon_intro zenon_H3b | zenon_intro zenon_He9 ]. % 18.65/18.80 apply (zenon_L463_); trivial. % 18.65/18.80 apply (zenon_or_s _ _ zenon_He9); [ zenon_intro zenon_Ha6 | zenon_intro zenon_Hea ]. % 18.65/18.80 apply (zenon_L95_); trivial. % 18.65/18.80 apply (zenon_or_s _ _ zenon_Hea); [ zenon_intro zenon_Haa | zenon_intro zenon_Hdd ]. % 18.65/18.80 apply (zenon_or_s _ _ zenon_H1ac); [ zenon_intro zenon_H44 | zenon_intro zenon_H1af ]. % 18.65/18.80 exact (zenon_H40 zenon_H44). % 18.65/18.80 apply (zenon_or_s _ _ zenon_H1af); [ zenon_intro zenon_H1b1 | zenon_intro zenon_H1b0 ]. % 18.65/18.80 exact (zenon_H1ad zenon_H1b1). % 18.65/18.80 apply (zenon_or_s _ _ zenon_H1b0); [ zenon_intro zenon_H61 | zenon_intro zenon_H60 ]. % 18.65/18.81 exact (zenon_H18b zenon_H61). % 18.65/18.81 apply (zenon_or_s _ _ zenon_H153); [ zenon_intro zenon_H148 | zenon_intro zenon_H154 ]. % 18.65/18.81 apply (zenon_L325_); trivial. % 18.65/18.81 apply (zenon_or_s _ _ zenon_H154); [ zenon_intro zenon_H14d | zenon_intro zenon_H155 ]. % 18.65/18.81 apply (zenon_L451_); trivial. % 18.65/18.81 apply (zenon_or_s _ _ zenon_H155); [ zenon_intro zenon_H151 | zenon_intro zenon_Hf6 ]. % 18.65/18.81 apply (zenon_L453_); trivial. % 18.65/18.81 apply (zenon_L471_); trivial. % 18.65/18.81 apply (zenon_L52_); trivial. % 18.65/18.81 apply (zenon_or_s _ _ zenon_H1a9); [ zenon_intro zenon_Ha6 | zenon_intro zenon_H161 ]. % 18.65/18.81 apply (zenon_L207_); trivial. % 18.65/18.81 apply (zenon_L193_); trivial. % 18.65/18.81 (* end of lemma zenon_L472_ *) % 18.65/18.81 assert (zenon_L473_ : (((op (e0) (e3)) = (e0))\/(((op (e0) (e3)) = (e1))\/(((op (e0) (e3)) = (e2))\/((op (e0) (e3)) = (e3))))) -> (~((op (e0) (e3)) = (op (e3) (e3)))) -> ((op (e3) (e3)) = (e0)) -> ((op (e2) (e3)) = (e1)) -> (~((op (e0) (e3)) = (op (e2) (e3)))) -> ((op (e2) (e3)) = (e3)) -> False). % 18.65/18.81 do 0 intro. intros zenon_He4 zenon_Hc2 zenon_H60 zenon_Hf4 zenon_He2 zenon_Hdd. % 18.65/18.81 apply (zenon_or_s _ _ zenon_He4); [ zenon_intro zenon_H1e | zenon_intro zenon_He5 ]. % 18.65/18.81 apply (zenon_L440_); trivial. % 18.65/18.81 apply (zenon_or_s _ _ zenon_He5); [ zenon_intro zenon_Hc3 | zenon_intro zenon_He6 ]. % 18.65/18.81 apply (zenon_L272_); trivial. % 18.65/18.81 apply (zenon_or_s _ _ zenon_He6); [ zenon_intro zenon_Hcd | zenon_intro zenon_He3 ]. % 18.65/18.81 apply (zenon_L229_); trivial. % 18.65/18.81 apply (zenon_L54_); trivial. % 18.65/18.81 (* end of lemma zenon_L473_ *) % 18.65/18.81 assert (zenon_L474_ : (((op (e3) (e0)) = (e0))\/(((op (e3) (e1)) = (e0))\/(((op (e3) (e2)) = (e0))\/((op (e3) (e3)) = (e0))))) -> (~((op (e3) (e0)) = (e0))) -> (~((op (e3) (e1)) = (e0))) -> (~((op (e3) (e2)) = (e0))) -> (((op (e0) (e3)) = (e0))\/(((op (e0) (e3)) = (e1))\/(((op (e0) (e3)) = (e2))\/((op (e0) (e3)) = (e3))))) -> (~((op (e0) (e3)) = (op (e3) (e3)))) -> ((op (e2) (e3)) = (e1)) -> (~((op (e0) (e3)) = (op (e2) (e3)))) -> ((op (e2) (e3)) = (e3)) -> False). % 18.65/18.81 do 0 intro. intros zenon_H1ac zenon_H40 zenon_H1ad zenon_H18b zenon_He4 zenon_Hc2 zenon_Hf4 zenon_He2 zenon_Hdd. % 18.65/18.81 apply (zenon_or_s _ _ zenon_H1ac); [ zenon_intro zenon_H44 | zenon_intro zenon_H1af ]. % 18.65/18.81 exact (zenon_H40 zenon_H44). % 18.65/18.81 apply (zenon_or_s _ _ zenon_H1af); [ zenon_intro zenon_H1b1 | zenon_intro zenon_H1b0 ]. % 18.65/18.81 exact (zenon_H1ad zenon_H1b1). % 18.65/18.81 apply (zenon_or_s _ _ zenon_H1b0); [ zenon_intro zenon_H61 | zenon_intro zenon_H60 ]. % 18.65/18.81 exact (zenon_H18b zenon_H61). % 18.65/18.81 apply (zenon_L473_); trivial. % 18.65/18.81 (* end of lemma zenon_L474_ *) % 18.65/18.81 assert (zenon_L475_ : (((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))) -> (((op (e3) (e1)) = (e0))\/(((op (e3) (e1)) = (e1))\/(((op (e3) (e1)) = (e2))\/((op (e3) (e1)) = (e3))))) -> (~((op (e3) (e1)) = (e0))) -> ((op (e1) (e1)) = (e3)) -> (~((op (e0) (e1)) = (op (e1) (e1)))) -> (((op (e2) (e1)) = (e0))\/(((op (e2) (e1)) = (e1))\/(((op (e2) (e1)) = (e2))\/((op (e2) (e1)) = (e3))))) -> (~((op (e2) (e1)) = (e0))) -> (~((op (e2) (e1)) = (op (e3) (e1)))) -> (~((op (e0) (e1)) = (op (e2) (e1)))) -> (~((op (e1) (e1)) = (op (e2) (e1)))) -> (~((op (e0) (e1)) = (op (e3) (e1)))) -> (~((op (e0) (e1)) = (e0))) -> (((op (e0) (e1)) = (e0))\/(((op (e0) (e1)) = (e1))\/(((op (e0) (e1)) = (e2))\/((op (e0) (e1)) = (e3))))) -> (~((op (e3) (e1)) = (op (e3) (e2)))) -> ((op (e3) (e0)) = (e3)) -> (~((op (e3) (e0)) = (op (e3) (e1)))) -> False). % 18.65/18.81 do 0 intro. intros zenon_H172 zenon_H149 zenon_H48 zenon_H12b zenon_H16c zenon_H173 zenon_H22a zenon_H1ad zenon_H13f zenon_H10e zenon_H1cc zenon_H31 zenon_Haf zenon_H17e zenon_H13e zenon_H210 zenon_H20b zenon_H212 zenon_H1a4 zenon_H15e zenon_H1cf. % 18.65/18.81 apply (zenon_or_s _ _ zenon_H172); [ zenon_intro zenon_H150 | zenon_intro zenon_H174 ]. % 18.65/18.81 apply (zenon_L378_); trivial. % 18.65/18.81 apply (zenon_or_s _ _ zenon_H174); [ zenon_intro zenon_H113 | zenon_intro zenon_H175 ]. % 18.65/18.81 apply (zenon_L116_); trivial. % 18.65/18.81 apply (zenon_or_s _ _ zenon_H175); [ zenon_intro zenon_H176 | zenon_intro zenon_H151 ]. % 18.65/18.81 exact (zenon_H173 zenon_H176). % 18.65/18.81 apply (zenon_L453_); trivial. % 18.65/18.81 (* end of lemma zenon_L475_ *) % 18.65/18.81 assert (zenon_L476_ : (((op (e0) (e1)) = (e3))\/(((op (e1) (e1)) = (e3))\/(((op (e2) (e1)) = (e3))\/((op (e3) (e1)) = (e3))))) -> (~((e1) = (e3))) -> ((op (e0) (e1)) = (e1)) -> (~((op (e3) (e1)) = (op (e3) (e2)))) -> (((op (e0) (e1)) = (e0))\/(((op (e0) (e1)) = (e1))\/(((op (e0) (e1)) = (e2))\/((op (e0) (e1)) = (e3))))) -> (~((op (e0) (e1)) = (e0))) -> (~((op (e0) (e1)) = (op (e3) (e1)))) -> (~((op (e1) (e1)) = (op (e2) (e1)))) -> (~((op (e0) (e1)) = (op (e2) (e1)))) -> (~((op (e2) (e1)) = (op (e3) (e1)))) -> (~((op (e2) (e1)) = (e0))) -> (((op (e2) (e1)) = (e0))\/(((op (e2) (e1)) = (e1))\/(((op (e2) (e1)) = (e2))\/((op (e2) (e1)) = (e3))))) -> (~((op (e0) (e1)) = (op (e1) (e1)))) -> (~((op (e3) (e1)) = (e0))) -> (((op (e3) (e1)) = (e0))\/(((op (e3) (e1)) = (e1))\/(((op (e3) (e1)) = (e2))\/((op (e3) (e1)) = (e3))))) -> (~((op (e2) (e2)) = (e2))) -> ((op (e1) (e2)) = (e3)) -> ((op (e0) (e2)) = (e0)) -> (~((e0) = (e2))) -> (((op (e0) (e2)) = (e2))\/(((op (e1) (e2)) = (e2))\/(((op (e2) (e2)) = (e2))\/((op (e3) (e2)) = (e2))))) -> (~((e2) = (e3))) -> ((op (e2) (e1)) = (e2)) -> ((op (e3) (e0)) = (e3)) -> (~((op (e3) (e0)) = (op (e3) (e1)))) -> False). % 18.65/18.81 do 0 intro. intros zenon_H1a5 zenon_H95 zenon_Ha0 zenon_H1a4 zenon_H212 zenon_H20b zenon_H210 zenon_H13e zenon_H17e zenon_Haf zenon_H31 zenon_H1cc zenon_H10e zenon_H1ad zenon_H22a zenon_H173 zenon_H16c zenon_H48 zenon_H149 zenon_H172 zenon_H12b zenon_H1ca zenon_H15e zenon_H1cf. % 18.65/18.81 apply (zenon_or_s _ _ zenon_H1a5); [ zenon_intro zenon_H99 | zenon_intro zenon_H1a8 ]. % 18.65/18.81 apply (zenon_L403_); trivial. % 18.65/18.81 apply (zenon_or_s _ _ zenon_H1a8); [ zenon_intro zenon_H13f | zenon_intro zenon_H1a9 ]. % 18.65/18.81 apply (zenon_L475_); trivial. % 18.65/18.81 apply (zenon_or_s _ _ zenon_H1a9); [ zenon_intro zenon_Ha6 | zenon_intro zenon_H161 ]. % 18.65/18.81 apply (zenon_L207_); trivial. % 18.65/18.81 apply (zenon_L193_); trivial. % 18.65/18.81 (* end of lemma zenon_L476_ *) % 18.65/18.81 assert (zenon_L477_ : (((op (e2) (e0)) = (e2))\/(((op (e2) (e1)) = (e2))\/(((op (e2) (e2)) = (e2))\/((op (e2) (e3)) = (e2))))) -> (~((e0) = (e2))) -> ((op (e2) (e0)) = (e0)) -> (~((op (e2) (e2)) = (e2))) -> (((op (e2) (e1)) = (e0))\/(((op (e2) (e1)) = (e1))\/(((op (e2) (e1)) = (e2))\/((op (e2) (e1)) = (e3))))) -> (~((op (e2) (e1)) = (e0))) -> ((op (e0) (e1)) = (e1)) -> (~((op (e0) (e1)) = (op (e2) (e1)))) -> (~((op (e2) (e1)) = (op (e2) (e3)))) -> ((op (e0) (e1)) = (e2)) -> ((op (e1) (e1)) = (e0)) -> False). % 18.65/18.81 do 0 intro. intros zenon_H1d5 zenon_H149 zenon_H34 zenon_H173 zenon_H1cc zenon_H31 zenon_Ha0 zenon_H17e zenon_H1c7 zenon_H10f zenon_H29. % 18.65/18.81 apply (zenon_or_s _ _ zenon_H1d5); [ zenon_intro zenon_Hee | zenon_intro zenon_H1d6 ]. % 18.65/18.81 apply (zenon_L204_); trivial. % 18.65/18.81 apply (zenon_or_s _ _ zenon_H1d6); [ zenon_intro zenon_H1ca | zenon_intro zenon_H1d7 ]. % 18.65/18.81 apply (zenon_L191_); trivial. % 18.65/18.81 apply (zenon_or_s _ _ zenon_H1d7); [ zenon_intro zenon_H176 | zenon_intro zenon_H11d ]. % 18.65/18.81 exact (zenon_H173 zenon_H176). % 18.65/18.81 apply (zenon_L412_); trivial. % 18.65/18.81 (* end of lemma zenon_L477_ *) % 18.65/18.81 assert (zenon_L478_ : (~((op (e3) (e3)) = (e0))) -> (~((op (e3) (e1)) = (op (e3) (e3)))) -> (~((op (e2) (e0)) = (op (e2) (e3)))) -> ((op (e1) (e1)) = (e0)) -> (~((op (e1) (e1)) = (op (e1) (e3)))) -> (((op (e0) (e0)) = (e0))\/(((op (e1) (e0)) = (e0))\/(((op (e2) (e0)) = (e0))\/((op (e3) (e0)) = (e0))))) -> (~((op (e0) (e0)) = (e0))) -> (~((op (e1) (e0)) = (op (e1) (e1)))) -> (~((op (e3) (e1)) = (op (e3) (e2)))) -> (~((op (e2) (e0)) = (op (e2) (e2)))) -> (~((op (e1) (e1)) = (op (e1) (e2)))) -> (~((op (e0) (e2)) = (op (e0) (e3)))) -> (((op (e0) (e2)) = (e0))\/(((op (e1) (e2)) = (e0))\/(((op (e2) (e2)) = (e0))\/((op (e3) (e2)) = (e0))))) -> (((op (e0) (e3)) = (e0))\/(((op (e1) (e3)) = (e0))\/(((op (e2) (e3)) = (e0))\/((op (e3) (e3)) = (e0))))) -> (~((op (e3) (e0)) = (op (e3) (e1)))) -> (~((op (e3) (e0)) = (e0))) -> (((op (e3) (e0)) = (e0))\/(((op (e3) (e1)) = (e0))\/(((op (e3) (e2)) = (e0))\/((op (e3) (e3)) = (e0))))) -> (~((op (e1) (e2)) = (e0))) -> (((op (e0) (e2)) = (e0))\/(((op (e0) (e2)) = (e1))\/(((op (e0) (e2)) = (e2))\/((op (e0) (e2)) = (e3))))) -> (~((op (e2) (e2)) = (e2))) -> (~((op (e0) (e2)) = (op (e2) (e2)))) -> (~((op (e2) (e2)) = (e0))) -> (((op (e2) (e2)) = (e0))\/(((op (e2) (e2)) = (e1))\/(((op (e2) (e2)) = (e2))\/((op (e2) (e2)) = (e3))))) -> ((op (e1) (e2)) = (e2)) -> (~((op (e0) (e2)) = (op (e1) (e2)))) -> (((op (e3) (e0)) = (e3))\/(((op (e3) (e1)) = (e3))\/(((op (e3) (e2)) = (e3))\/((op (e3) (e3)) = (e3))))) -> (~((e2) = (e3))) -> ((op (e3) (e0)) = (e2)) -> ((op (e1) (e1)) = (e3)) -> (~((op (e1) (e1)) = (op (e3) (e1)))) -> (~((op (e0) (e2)) = (op (e3) (e2)))) -> (~((op (e3) (e3)) = (e3))) -> False). % 18.65/18.81 do 0 intro. intros zenon_H1ae zenon_H130 zenon_H5b zenon_H29 zenon_H57 zenon_H3e zenon_H3f zenon_H45 zenon_H1a4 zenon_H52 zenon_H4f zenon_H208 zenon_H6a zenon_H67 zenon_H1cf zenon_H40 zenon_H1ac zenon_H25 zenon_H1ba zenon_H173 zenon_Ha8 zenon_H81 zenon_H1c4 zenon_H113 zenon_H195 zenon_H165 zenon_H12b zenon_H148 zenon_H13f zenon_H160 zenon_H14f zenon_H102. % 18.65/18.81 apply (zenon_or_s _ _ zenon_H6a); [ zenon_intro zenon_H48 | zenon_intro zenon_H6b ]. % 18.65/18.81 apply (zenon_L350_); trivial. % 18.65/18.81 apply (zenon_or_s _ _ zenon_H6b); [ zenon_intro zenon_H2a | zenon_intro zenon_H6c ]. % 18.65/18.81 exact (zenon_H25 zenon_H2a). % 18.65/18.81 apply (zenon_or_s _ _ zenon_H6c); [ zenon_intro zenon_H2c | zenon_intro zenon_H61 ]. % 18.65/18.81 exact (zenon_H81 zenon_H2c). % 18.65/18.81 apply (zenon_L466_); trivial. % 18.65/18.81 (* end of lemma zenon_L478_ *) % 18.65/18.81 assert (zenon_L479_ : (((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) (e2)) = (e0))) -> (~((op (e2) (e2)) = (e0))) -> (((op (e0) (e2)) = (e2))\/(((op (e1) (e2)) = (e2))\/(((op (e2) (e2)) = (e2))\/((op (e3) (e2)) = (e2))))) -> (~((e1) = (e2))) -> ((op (e3) (e1)) = (e3)) -> (~((op (e3) (e1)) = (op (e3) (e2)))) -> ((op (e0) (e2)) = (e1)) -> (~((e2) = (e3))) -> (~((e1) = (e3))) -> (((op (e0) (e2)) = (e3))\/(((op (e1) (e2)) = (e3))\/(((op (e2) (e2)) = (e3))\/((op (e3) (e2)) = (e3))))) -> (~((op (e2) (e2)) = (e2))) -> (~((op (e3) (e0)) = (op (e3) (e2)))) -> ((op (e3) (e0)) = (e2)) -> False). % 18.65/18.81 do 0 intro. intros zenon_H6a zenon_H208 zenon_H1e zenon_H25 zenon_H81 zenon_H172 zenon_H7c zenon_H161 zenon_H1a4 zenon_H122 zenon_H12b zenon_H95 zenon_H1a6 zenon_H173 zenon_H6f zenon_H148. % 18.65/18.81 apply (zenon_or_s _ _ zenon_H6a); [ zenon_intro zenon_H48 | zenon_intro zenon_H6b ]. % 18.65/18.81 apply (zenon_L336_); trivial. % 18.65/18.81 apply (zenon_or_s _ _ zenon_H6b); [ zenon_intro zenon_H2a | zenon_intro zenon_H6c ]. % 18.65/18.81 exact (zenon_H25 zenon_H2a). % 18.65/18.81 apply (zenon_or_s _ _ zenon_H6c); [ zenon_intro zenon_H2c | zenon_intro zenon_H61 ]. % 18.65/18.81 exact (zenon_H81 zenon_H2c). % 18.65/18.81 apply (zenon_or_s _ _ zenon_H172); [ zenon_intro zenon_H150 | zenon_intro zenon_H174 ]. % 18.65/18.81 apply (zenon_L328_); trivial. % 18.65/18.81 apply (zenon_or_s _ _ zenon_H174); [ zenon_intro zenon_H113 | zenon_intro zenon_H175 ]. % 18.65/18.81 apply (zenon_L433_); trivial. % 18.65/18.81 apply (zenon_or_s _ _ zenon_H175); [ zenon_intro zenon_H176 | zenon_intro zenon_H151 ]. % 18.65/18.81 exact (zenon_H173 zenon_H176). % 18.65/18.81 apply (zenon_L420_); trivial. % 18.65/18.81 (* end of lemma zenon_L479_ *) % 18.65/18.81 assert (zenon_L480_ : (((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 (e3) (e2)) = (e1)) -> ((op (e1) (e3)) = (e2)) -> (~((op (e1) (e3)) = (op (e3) (e3)))) -> (~((op (e3) (e3)) = (e3))) -> False). % 18.65/18.81 do 0 intro. intros zenon_H101 zenon_H1ae zenon_H62 zenon_Hba zenon_Hd7 zenon_Hd5 zenon_H102. % 18.65/18.81 apply (zenon_or_s _ _ zenon_H101); [ zenon_intro zenon_H60 | zenon_intro zenon_H103 ]. % 18.65/18.81 exact (zenon_H1ae zenon_H60). % 18.65/18.81 apply (zenon_or_s _ _ zenon_H103); [ zenon_intro zenon_Hc4 | zenon_intro zenon_H104 ]. % 18.65/18.81 apply (zenon_L147_); trivial. % 18.65/18.81 apply (zenon_or_s _ _ zenon_H104); [ zenon_intro zenon_Hf6 | zenon_intro zenon_H105 ]. % 18.65/18.81 apply (zenon_L402_); trivial. % 18.65/18.81 exact (zenon_H102 zenon_H105). % 18.65/18.81 (* end of lemma zenon_L480_ *) % 18.65/18.81 assert (zenon_L481_ : (((op (e0) (e3)) = (e2))\/(((op (e1) (e3)) = (e2))\/(((op (e2) (e3)) = (e2))\/((op (e3) (e3)) = (e2))))) -> (~((e0) = (e2))) -> ((op (e0) (e3)) = (e0)) -> (~((op (e3) (e3)) = (e3))) -> (~((op (e1) (e3)) = (op (e3) (e3)))) -> ((op (e3) (e2)) = (e1)) -> (~((op (e3) (e2)) = (op (e3) (e3)))) -> (~((op (e3) (e3)) = (e0))) -> (((op (e3) (e3)) = (e0))\/(((op (e3) (e3)) = (e1))\/(((op (e3) (e3)) = (e2))\/((op (e3) (e3)) = (e3))))) -> (~((op (e2) (e1)) = (op (e2) (e3)))) -> ((op (e2) (e1)) = (e2)) -> ((op (e3) (e0)) = (e2)) -> (~((op (e3) (e0)) = (op (e3) (e3)))) -> False). % 18.65/18.81 do 0 intro. intros zenon_H145 zenon_H149 zenon_H1e zenon_H102 zenon_Hd5 zenon_Hba zenon_H62 zenon_H1ae zenon_H101 zenon_H1c7 zenon_H1ca zenon_H148 zenon_H71. % 18.65/18.81 apply (zenon_or_s _ _ zenon_H145); [ zenon_intro zenon_Hcd | zenon_intro zenon_H146 ]. % 18.65/18.81 apply (zenon_L428_); trivial. % 18.65/18.81 apply (zenon_or_s _ _ zenon_H146); [ zenon_intro zenon_Hd7 | zenon_intro zenon_H147 ]. % 18.65/18.81 apply (zenon_L480_); trivial. % 18.65/18.81 apply (zenon_or_s _ _ zenon_H147); [ zenon_intro zenon_H11d | zenon_intro zenon_Hf6 ]. % 18.65/18.81 apply (zenon_L224_); trivial. % 18.65/18.81 apply (zenon_L114_); trivial. % 18.65/18.81 (* end of lemma zenon_L481_ *) % 18.65/18.81 assert (zenon_L482_ : (((op (e2) (e0)) = (e1))\/(((op (e2) (e1)) = (e1))\/(((op (e2) (e2)) = (e1))\/((op (e2) (e3)) = (e1))))) -> ((op (e0) (e0)) = (e3)) -> ((op (e3) (e0)) = (e2)) -> ((op (e0) (e1)) = (e1)) -> (~((op (e0) (e1)) = (op (e2) (e1)))) -> (((op (e0) (e2)) = (e1))\/(((op (e1) (e2)) = (e1))\/(((op (e2) (e2)) = (e1))\/((op (e3) (e2)) = (e1))))) -> ((op (e3) (e2)) = (e0)) -> (~((op (e2) (e2)) = (e2))) -> (~((op (e0) (e2)) = (op (e2) (e2)))) -> (~((op (e2) (e2)) = (e0))) -> (((op (e2) (e2)) = (e0))\/(((op (e2) (e2)) = (e1))\/(((op (e2) (e2)) = (e2))\/((op (e2) (e2)) = (e3))))) -> (~((e1) = (e3))) -> ((op (e1) (e2)) = (e3)) -> (~((op (e2) (e2)) = (op (e2) (e3)))) -> (((op (e3) (e3)) = (e0))\/(((op (e3) (e3)) = (e1))\/(((op (e3) (e3)) = (e2))\/((op (e3) (e3)) = (e3))))) -> (~((op (e3) (e3)) = (e0))) -> (~((op (e3) (e2)) = (op (e3) (e3)))) -> ((op (e1) (e3)) = (e2)) -> (~((op (e1) (e3)) = (op (e3) (e3)))) -> (~((op (e3) (e3)) = (e3))) -> False). % 18.65/18.81 do 0 intro. intros zenon_H106 zenon_H3a zenon_H148 zenon_Ha0 zenon_H17e zenon_H139 zenon_H61 zenon_H173 zenon_Ha8 zenon_H81 zenon_H1c4 zenon_H95 zenon_H16c zenon_H6d zenon_H101 zenon_H1ae zenon_H62 zenon_Hd7 zenon_Hd5 zenon_H102. % 18.65/18.81 apply (zenon_or_s _ _ zenon_H106); [ zenon_intro zenon_Hed | zenon_intro zenon_H107 ]. % 18.65/18.81 apply (zenon_L423_); trivial. % 18.65/18.81 apply (zenon_or_s _ _ zenon_H107); [ zenon_intro zenon_Ha5 | zenon_intro zenon_H108 ]. % 18.65/18.81 apply (zenon_L357_); trivial. % 18.65/18.81 apply (zenon_or_s _ _ zenon_H108); [ zenon_intro zenon_Hf1 | zenon_intro zenon_Hf4 ]. % 18.65/18.81 apply (zenon_L156_); trivial. % 18.65/18.81 apply (zenon_or_s _ _ zenon_H139); [ zenon_intro zenon_H122 | zenon_intro zenon_H13a ]. % 18.65/18.81 apply (zenon_L437_); trivial. % 18.65/18.81 apply (zenon_or_s _ _ zenon_H13a); [ zenon_intro zenon_Hf0 | zenon_intro zenon_H13b ]. % 18.65/18.81 apply (zenon_L167_); trivial. % 18.65/18.81 apply (zenon_or_s _ _ zenon_H13b); [ zenon_intro zenon_Hf1 | zenon_intro zenon_Hba ]. % 18.65/18.81 apply (zenon_L84_); trivial. % 18.65/18.81 apply (zenon_L480_); trivial. % 18.65/18.81 (* end of lemma zenon_L482_ *) % 18.65/18.81 assert (zenon_L483_ : (((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)) = (op (e2) (e3)))) -> ((op (e2) (e3)) = (e1)) -> (~((op (e2) (e2)) = (e2))) -> (~((op (e0) (e2)) = (op (e2) (e2)))) -> ((op (e0) (e2)) = (e3)) -> False). % 18.65/18.81 do 0 intro. intros zenon_H1c4 zenon_H61 zenon_H18f zenon_H6d zenon_Hf4 zenon_H173 zenon_Ha8 zenon_Ha9. % 18.65/18.81 apply (zenon_or_s _ _ zenon_H1c4); [ zenon_intro zenon_H2c | zenon_intro zenon_H1c5 ]. % 18.65/18.81 apply (zenon_L146_); trivial. % 18.65/18.81 apply (zenon_or_s _ _ zenon_H1c5); [ zenon_intro zenon_Hf1 | zenon_intro zenon_H1c6 ]. % 18.65/18.81 apply (zenon_L84_); trivial. % 18.65/18.81 apply (zenon_or_s _ _ zenon_H1c6); [ zenon_intro zenon_H176 | zenon_intro zenon_Haa ]. % 18.65/18.81 exact (zenon_H173 zenon_H176). % 18.65/18.81 apply (zenon_L40_); trivial. % 18.65/18.81 (* end of lemma zenon_L483_ *) % 18.65/18.81 assert (zenon_L484_ : (((op (e0) (e2)) = (e3))\/(((op (e1) (e2)) = (e3))\/(((op (e2) (e2)) = (e3))\/((op (e3) (e2)) = (e3))))) -> (~((op (e0) (e2)) = (op (e2) (e2)))) -> ((op (e3) (e2)) = (e0)) -> (~((e1) = (e3))) -> ((op (e1) (e2)) = (e1)) -> (~((op (e3) (e3)) = (e3))) -> (~((op (e1) (e1)) = (op (e3) (e1)))) -> ((op (e1) (e1)) = (e3)) -> ((op (e3) (e0)) = (e2)) -> (~((e2) = (e3))) -> (((op (e3) (e0)) = (e3))\/(((op (e3) (e1)) = (e3))\/(((op (e3) (e2)) = (e3))\/((op (e3) (e3)) = (e3))))) -> (((op (e2) (e2)) = (e0))\/(((op (e2) (e2)) = (e1))\/(((op (e2) (e2)) = (e2))\/((op (e2) (e2)) = (e3))))) -> (~((op (e2) (e2)) = (e0))) -> (~((op (e2) (e2)) = (op (e2) (e3)))) -> ((op (e2) (e3)) = (e1)) -> (~((op (e2) (e2)) = (e2))) -> (~((op (e2) (e2)) = (op (e3) (e2)))) -> False). % 18.65/18.81 do 0 intro. intros zenon_H1a6 zenon_Ha8 zenon_H61 zenon_H95 zenon_Hf0 zenon_H102 zenon_H160 zenon_H13f zenon_H148 zenon_H12b zenon_H165 zenon_H1c4 zenon_H81 zenon_H6d zenon_Hf4 zenon_H173 zenon_H18f. % 18.65/18.81 apply (zenon_or_s _ _ zenon_H1a6); [ zenon_intro zenon_Ha9 | zenon_intro zenon_H1aa ]. % 18.65/18.81 apply (zenon_L483_); trivial. % 18.65/18.81 apply (zenon_or_s _ _ zenon_H1aa); [ zenon_intro zenon_H16c | zenon_intro zenon_H1ab ]. % 18.65/18.81 apply (zenon_L167_); trivial. % 18.65/18.81 apply (zenon_or_s _ _ zenon_H1ab); [ zenon_intro zenon_Haa | zenon_intro zenon_H163 ]. % 18.65/18.81 apply (zenon_L325_); trivial. % 18.65/18.81 apply (zenon_L361_); trivial. % 18.65/18.81 (* end of lemma zenon_L484_ *) % 18.65/18.81 assert (zenon_L485_ : (((op (e0) (e2)) = (e0))\/(((op (e1) (e2)) = (e0))\/(((op (e2) (e2)) = (e0))\/((op (e3) (e2)) = (e0))))) -> (~((op (e3) (e0)) = (op (e3) (e2)))) -> (~((e2) = (e3))) -> (~((e0) = (e2))) -> (((op (e0) (e2)) = (e2))\/(((op (e1) (e2)) = (e2))\/(((op (e2) (e2)) = (e2))\/((op (e3) (e2)) = (e2))))) -> (~((op (e1) (e2)) = (e0))) -> (((op (e2) (e0)) = (e1))\/(((op (e2) (e1)) = (e1))\/(((op (e2) (e2)) = (e1))\/((op (e2) (e3)) = (e1))))) -> ((op (e0) (e0)) = (e3)) -> ((op (e3) (e0)) = (e2)) -> ((op (e0) (e1)) = (e1)) -> (~((op (e0) (e1)) = (op (e2) (e1)))) -> (((op (e0) (e2)) = (e1))\/(((op (e1) (e2)) = (e1))\/(((op (e2) (e2)) = (e1))\/((op (e3) (e2)) = (e1))))) -> (~((op (e2) (e2)) = (e2))) -> (~((op (e0) (e2)) = (op (e2) (e2)))) -> (~((op (e2) (e2)) = (e0))) -> (((op (e2) (e2)) = (e0))\/(((op (e2) (e2)) = (e1))\/(((op (e2) (e2)) = (e2))\/((op (e2) (e2)) = (e3))))) -> (~((e1) = (e3))) -> ((op (e1) (e2)) = (e3)) -> (~((op (e2) (e2)) = (op (e2) (e3)))) -> (((op (e3) (e3)) = (e0))\/(((op (e3) (e3)) = (e1))\/(((op (e3) (e3)) = (e2))\/((op (e3) (e3)) = (e3))))) -> (~((op (e3) (e3)) = (e0))) -> (~((op (e3) (e2)) = (op (e3) (e3)))) -> ((op (e1) (e3)) = (e2)) -> (~((op (e1) (e3)) = (op (e3) (e3)))) -> (~((op (e3) (e3)) = (e3))) -> False). % 18.65/18.81 do 0 intro. intros zenon_H6a zenon_H6f zenon_H12b zenon_H149 zenon_H172 zenon_H25 zenon_H106 zenon_H3a zenon_H148 zenon_Ha0 zenon_H17e zenon_H139 zenon_H173 zenon_Ha8 zenon_H81 zenon_H1c4 zenon_H95 zenon_H16c zenon_H6d zenon_H101 zenon_H1ae zenon_H62 zenon_Hd7 zenon_Hd5 zenon_H102. % 18.65/18.81 apply (zenon_or_s _ _ zenon_H6a); [ zenon_intro zenon_H48 | zenon_intro zenon_H6b ]. % 18.65/18.81 apply (zenon_L421_); trivial. % 18.65/18.81 apply (zenon_or_s _ _ zenon_H6b); [ zenon_intro zenon_H2a | zenon_intro zenon_H6c ]. % 18.65/18.81 exact (zenon_H25 zenon_H2a). % 18.65/18.81 apply (zenon_or_s _ _ zenon_H6c); [ zenon_intro zenon_H2c | zenon_intro zenon_H61 ]. % 18.65/18.81 exact (zenon_H81 zenon_H2c). % 18.65/18.81 apply (zenon_L482_); trivial. % 18.65/18.81 (* end of lemma zenon_L485_ *) % 18.65/18.81 assert (zenon_L486_ : (~((op (e0) (e0)) = (e0))) -> (~((op (e0) (e1)) = (e0))) -> (((op (e1) (e0)) = (e0))\/(((op (e1) (e1)) = (e0))\/(((op (e1) (e2)) = (e0))\/((op (e1) (e3)) = (e0))))) -> (~((op (e1) (e3)) = (e0))) -> (~((op (e1) (e2)) = (e0))) -> (~((op (e3) (e0)) = (e0))) -> (((op (e0) (e0)) = (e0))\/(((op (e1) (e0)) = (e0))\/(((op (e2) (e0)) = (e0))\/((op (e3) (e0)) = (e0))))) -> (~((op (e3) (e0)) = (op (e3) (e1)))) -> (~((op (e0) (e2)) = (op (e0) (e3)))) -> (~((op (e1) (e1)) = (op (e1) (e2)))) -> (~((op (e2) (e0)) = (op (e2) (e2)))) -> (~((op (e3) (e1)) = (op (e3) (e2)))) -> (((op (e0) (e2)) = (e0))\/(((op (e1) (e2)) = (e0))\/(((op (e2) (e2)) = (e0))\/((op (e3) (e2)) = (e0))))) -> (~((op (e1) (e1)) = (op (e1) (e3)))) -> (~((op (e2) (e0)) = (op (e2) (e3)))) -> (~((op (e3) (e1)) = (op (e3) (e3)))) -> (((op (e0) (e3)) = (e0))\/(((op (e1) (e3)) = (e0))\/(((op (e2) (e3)) = (e0))\/((op (e3) (e3)) = (e0))))) -> (~((op (e1) (e0)) = (op (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 (e1) (e0)) = (e0))) -> (((op (e0) (e0)) = (e1))\/(((op (e0) (e1)) = (e1))\/(((op (e0) (e2)) = (e1))\/((op (e0) (e3)) = (e1))))) -> (~((op (e2) (e1)) = (e0))) -> ((op (e2) (e0)) = (e0)) -> ((op (e0) (e0)) = (e3)) -> (~((op (e2) (e2)) = (e0))) -> ((op (e3) (e0)) = (e2)) -> ((op (e1) (e0)) = (e1)) -> ((~((op (e0) (e3)) = (e0)))\/((op (e0) (e0)) = (e3))) -> ((~((op (e1) (e1)) = (e0)))\/((op (e1) (e0)) = (e1))) -> (~((e1) = (e2))) -> ((~((op (e2) (e3)) = (e0)))\/((op (e2) (e0)) = (e3))) -> (((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))))) -> (((op (e0) (e2)) = (e3))\/(((op (e1) (e2)) = (e3))\/(((op (e2) (e2)) = (e3))\/((op (e3) (e2)) = (e3))))) -> ((~((op (e3) (e2)) = (e0)))\/((op (e3) (e0)) = (e2))) -> (~((op (e2) (e2)) = (op (e3) (e2)))) -> (((op (e3) (e2)) = (e0))\/(((op (e3) (e2)) = (e1))\/(((op (e3) (e2)) = (e2))\/((op (e3) (e2)) = (e3))))) -> (~((op (e0) (e2)) = (op (e1) (e2)))) -> (((op (e1) (e2)) = (e0))\/(((op (e1) (e2)) = (e1))\/(((op (e1) (e2)) = (e2))\/((op (e1) (e2)) = (e3))))) -> (~((e1) = (e3))) -> (~((e0) = (e3))) -> (~((op (e1) (e1)) = (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) (e3)) = (e0))\/(((op (e2) (e3)) = (e1))\/(((op (e2) (e3)) = (e2))\/((op (e2) (e3)) = (e3))))) -> (~((op (e0) (e3)) = (op (e1) (e3)))) -> (~((op (e0) (e1)) = (op (e1) (e1)))) -> (~((e0) = (e1))) -> (~((op (e0) (e2)) = (op (e2) (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) (e3)) = (e0))\/(((op (e1) (e3)) = (e1))\/(((op (e1) (e3)) = (e2))\/((op (e1) (e3)) = (e3))))) -> (~((op (e1) (e3)) = (op (e2) (e3)))) -> (~((op (e1) (e0)) = (op (e1) (e3)))) -> (~((op (e1) (e3)) = (op (e3) (e3)))) -> (~((op (e0) (e3)) = (op (e2) (e3)))) -> (((op (e0) (e3)) = (e0))\/(((op (e0) (e3)) = (e1))\/(((op (e0) (e3)) = (e2))\/((op (e0) (e3)) = (e3))))) -> (~((op (e2) (e1)) = (op (e3) (e1)))) -> (((op (e2) (e0)) = (e3))\/(((op (e2) (e1)) = (e3))\/(((op (e2) (e2)) = (e3))\/((op (e2) (e3)) = (e3))))) -> (((op (e2) (e0)) = (e1))\/(((op (e2) (e1)) = (e1))\/(((op (e2) (e2)) = (e1))\/((op (e2) (e3)) = (e1))))) -> (~((op (e2) (e3)) = (op (e3) (e3)))) -> (~((op (e3) (e3)) = (e3))) -> (((op (e3) (e3)) = (e0))\/(((op (e3) (e3)) = (e1))\/(((op (e3) (e3)) = (e2))\/((op (e3) (e3)) = (e3))))) -> (~((op (e1) (e2)) = (op (e2) (e2)))) -> (((op (e0) (e1)) = (e1))\/(((op (e1) (e1)) = (e1))\/(((op (e2) (e1)) = (e1))\/((op (e3) (e1)) = (e1))))) -> (~((op (e0) (e0)) = (op (e0) (e3)))) -> ((~((op (e2) (e2)) = (e0)))\/((op (e2) (e0)) = (e2))) -> ((~((op (e3) (e0)) = (e0)))\/((op (e3) (e0)) = (e0))) -> (((op (e0) (e0)) = (e2))\/(((op (e0) (e1)) = (e2))\/(((op (e0) (e2)) = (e2))\/((op (e0) (e3)) = (e2))))) -> (~((op (e2) (e0)) = (op (e3) (e0)))) -> (~((op (e0) (e1)) = (op (e2) (e1)))) -> ((~((op (e1) (e2)) = (e0)))\/((op (e1) (e0)) = (e2))) -> ((~((op (e1) (e3)) = (e0)))\/((op (e1) (e0)) = (e3))) -> (((op (e1) (e1)) = (e0))\/(((op (e1) (e1)) = (e1))\/(((op (e1) (e1)) = (e2))\/((op (e1) (e1)) = (e3))))) -> (~((op (e1) (e1)) = (op (e2) (e1)))) -> (~((op (e0) (e0)) = (op (e0) (e2)))) -> (((op (e0) (e2)) = (e1))\/(((op (e1) (e2)) = (e1))\/(((op (e2) (e2)) = (e1))\/((op (e3) (e2)) = (e1))))) -> (((op (e1) (e0)) = (e1))\/(((op (e1) (e1)) = (e1))\/(((op (e1) (e2)) = (e1))\/((op (e1) (e3)) = (e1))))) -> (((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))))) -> (~((e2) = (e3))) -> (~((op (e1) (e2)) = (op (e1) (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 (e2) (e2)) = (e2))) -> (((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) (e1)) = (op (e3) (e1)))) -> (((op (e3) (e0)) = (e3))\/(((op (e3) (e1)) = (e3))\/(((op (e3) (e2)) = (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) (e0)) = (op (e2) (e0)))) -> ((~((op (e2) (e1)) = (e0)))\/((op (e2) (e0)) = (e1))) -> (((op (e0) (e0)) = (e2))\/(((op (e1) (e0)) = (e2))\/(((op (e2) (e0)) = (e2))\/((op (e3) (e0)) = (e2))))) -> ((~((op (e2) (e0)) = (e0)))\/((op (e2) (e0)) = (e0))) -> (((op (e0) (e0)) = (e3))\/(((op (e1) (e0)) = (e3))\/(((op (e2) (e0)) = (e3))\/((op (e3) (e0)) = (e3))))) -> (~((op (e2) (e1)) = (op (e2) (e3)))) -> (((op (e2) (e2)) = (e0))\/(((op (e2) (e2)) = (e1))\/(((op (e2) (e2)) = (e2))\/((op (e2) (e2)) = (e3))))) -> (((op (e2) (e1)) = (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 (e0) (e1)) = (e2))\/(((op (e1) (e1)) = (e2))\/(((op (e2) (e1)) = (e2))\/((op (e3) (e1)) = (e2))))) -> (((op (e2) (e0)) = (e2))\/(((op (e2) (e1)) = (e2))\/(((op (e2) (e2)) = (e2))\/((op (e2) (e3)) = (e2))))) -> ((~((op (e3) (e3)) = (e0)))\/((op (e3) (e0)) = (e3))) -> ((~((op (e3) (e1)) = (e0)))\/((op (e3) (e0)) = (e1))) -> (~((op (e0) (e1)) = (op (e0) (e3)))) -> (~((op (e3) (e2)) = (op (e3) (e3)))) -> (~((op (e0) (e1)) = (op (e0) (e2)))) -> (~((op (e3) (e0)) = (op (e3) (e3)))) -> (~((op (e2) (e2)) = (op (e2) (e3)))) -> (~((op (e3) (e0)) = (op (e3) (e2)))) -> (((op (e0) (e0)) = (e0))\/(((op (e0) (e1)) = (e0))\/(((op (e0) (e2)) = (e0))\/((op (e0) (e3)) = (e0))))) -> (~((op (e1) (e0)) = (op (e3) (e0)))) -> (~((op (e2) (e0)) = (op (e2) (e1)))) -> (~((op (e1) (e0)) = (op (e2) (e0)))) -> ((~((op (e1) (e0)) = (e0)))\/((op (e1) (e0)) = (e0))) -> ((~((op (e0) (e2)) = (e0)))\/((op (e0) (e0)) = (e2))) -> False). % 18.65/18.81 do 0 intro. intros zenon_H3f zenon_H20b zenon_H22 zenon_H38 zenon_H25 zenon_H40 zenon_H3e zenon_H1cf zenon_H208 zenon_H4f zenon_H52 zenon_H1a4 zenon_H6a zenon_H57 zenon_H5b zenon_H130 zenon_H67 zenon_H45 zenon_H14f zenon_H1ac zenon_H23 zenon_H22d zenon_H31 zenon_H34 zenon_H3a zenon_H81 zenon_H148 zenon_H9d zenon_H204 zenon_H205 zenon_H7c zenon_H94 zenon_H2f zenon_H1a5 zenon_H1a6 zenon_H1a7 zenon_H18f zenon_H191 zenon_H195 zenon_H19d zenon_H95 zenon_H9a zenon_H10a zenon_H18c zenon_H115 zenon_H11f zenon_H1d zenon_H10e zenon_Ha1 zenon_Ha8 zenon_He8 zenon_Hc2 zenon_Hdf zenon_Hdb zenon_Hd8 zenon_Hd5 zenon_He2 zenon_He4 zenon_Haf zenon_He7 zenon_H106 zenon_Hf3 zenon_H102 zenon_H101 zenon_H2b zenon_H109 zenon_H189 zenon_H185 zenon_H184 zenon_H183 zenon_H17b zenon_H17e zenon_H178 zenon_H179 zenon_H142 zenon_H13e zenon_H13c zenon_H139 zenon_H128 zenon_H136 zenon_H133 zenon_H12b zenon_H124 zenon_H145 zenon_H172 zenon_H173 zenon_H16f zenon_H168 zenon_H160 zenon_H165 zenon_H149 zenon_H153 zenon_H39 zenon_H182 zenon_H1fe zenon_H1ee zenon_H1e0 zenon_H1c7 zenon_H1c4 zenon_H1cc zenon_H1ba zenon_H1d8 zenon_H1d5 zenon_H1ec zenon_H1ed zenon_H54 zenon_H62 zenon_H4a zenon_H71 zenon_H6d zenon_H6f zenon_H74 zenon_H1fa zenon_H1f0 zenon_H201 zenon_H206 zenon_H233. % 18.65/18.81 apply (zenon_or_s _ _ zenon_H1ec); [ zenon_intro zenon_H1ae | zenon_intro zenon_H15e ]. % 18.65/18.81 apply (zenon_or_s _ _ zenon_H74); [ zenon_intro zenon_H42 | zenon_intro zenon_H77 ]. % 18.65/18.81 exact (zenon_H3f zenon_H42). % 18.65/18.81 apply (zenon_or_s _ _ zenon_H77); [ zenon_intro zenon_H49 | zenon_intro zenon_H78 ]. % 18.65/18.81 exact (zenon_H20b zenon_H49). % 18.65/18.81 apply (zenon_or_s _ _ zenon_H78); [ zenon_intro zenon_H48 | zenon_intro zenon_H1e ]. % 18.65/18.81 apply (zenon_L351_); trivial. % 18.65/18.81 apply (zenon_or_s _ _ zenon_H22d); [ zenon_intro zenon_H7a | zenon_intro zenon_H22e ]. % 18.65/18.81 apply (zenon_L456_); trivial. % 18.65/18.81 apply (zenon_or_s _ _ zenon_H22e); [ zenon_intro zenon_Ha0 | zenon_intro zenon_H22f ]. % 18.65/18.81 apply (zenon_or_s _ _ zenon_H22); [ zenon_intro zenon_H27 | zenon_intro zenon_H26 ]. % 18.65/18.81 exact (zenon_H23 zenon_H27). % 18.65/18.81 apply (zenon_or_s _ _ zenon_H26); [ zenon_intro zenon_H29 | zenon_intro zenon_H28 ]. % 18.65/18.81 apply (zenon_or_s _ _ zenon_H18c); [ zenon_intro zenon_H86 | zenon_intro zenon_H18d ]. % 18.65/18.81 apply (zenon_L123_); trivial. % 18.65/18.81 apply (zenon_or_s _ _ zenon_H18d); [ zenon_intro zenon_H110 | zenon_intro zenon_H18e ]. % 18.65/18.81 apply (zenon_L354_); trivial. % 18.65/18.81 apply (zenon_or_s _ _ zenon_H18e); [ zenon_intro zenon_H113 | zenon_intro zenon_Hd7 ]. % 18.65/18.81 apply (zenon_or_s _ _ zenon_H1d8); [ zenon_intro zenon_H10f | zenon_intro zenon_H1d9 ]. % 18.65/18.81 apply (zenon_L477_); trivial. % 18.65/18.81 apply (zenon_or_s _ _ zenon_H1d9); [ zenon_intro zenon_H110 | zenon_intro zenon_H1da ]. % 18.65/18.81 apply (zenon_L354_); trivial. % 18.65/18.81 apply (zenon_or_s _ _ zenon_H1da); [ zenon_intro zenon_H1ca | zenon_intro zenon_H14d ]. % 18.65/18.81 apply (zenon_or_s _ _ zenon_H16f); [ zenon_intro zenon_H9e | zenon_intro zenon_H170 ]. % 18.65/18.81 apply (zenon_L37_); trivial. % 18.65/18.81 apply (zenon_or_s _ _ zenon_H170); [ zenon_intro zenon_H13f | zenon_intro zenon_H171 ]. % 18.65/18.81 apply (zenon_L478_); trivial. % 18.65/18.81 apply (zenon_or_s _ _ zenon_H171); [ zenon_intro zenon_H16c | zenon_intro zenon_Hdc ]. % 18.65/18.81 apply (zenon_L116_); trivial. % 18.65/18.81 apply (zenon_or_s _ _ zenon_H1a5); [ zenon_intro zenon_H99 | zenon_intro zenon_H1a8 ]. % 18.65/18.81 apply (zenon_L403_); trivial. % 18.65/18.81 apply (zenon_or_s _ _ zenon_H1a8); [ zenon_intro zenon_H13f | zenon_intro zenon_H1a9 ]. % 18.65/18.81 apply (zenon_L478_); trivial. % 18.65/18.81 apply (zenon_or_s _ _ zenon_H1a9); [ zenon_intro zenon_Ha6 | zenon_intro zenon_H161 ]. % 18.65/18.81 apply (zenon_L207_); trivial. % 18.65/18.81 apply (zenon_or_s _ _ zenon_H106); [ zenon_intro zenon_Hed | zenon_intro zenon_H107 ]. % 18.65/18.81 apply (zenon_L423_); trivial. % 18.65/18.81 apply (zenon_or_s _ _ zenon_H107); [ zenon_intro zenon_Ha5 | zenon_intro zenon_H108 ]. % 18.65/18.81 apply (zenon_L357_); trivial. % 18.65/18.81 apply (zenon_or_s _ _ zenon_H108); [ zenon_intro zenon_Hf1 | zenon_intro zenon_Hf4 ]. % 18.65/18.81 apply (zenon_L430_); trivial. % 18.65/18.81 apply (zenon_or_s _ _ zenon_H139); [ zenon_intro zenon_H122 | zenon_intro zenon_H13a ]. % 18.65/18.81 apply (zenon_L479_); trivial. % 18.65/18.81 apply (zenon_or_s _ _ zenon_H13a); [ zenon_intro zenon_Hf0 | zenon_intro zenon_H13b ]. % 18.65/18.81 apply (zenon_L68_); trivial. % 18.65/18.81 apply (zenon_or_s _ _ zenon_H13b); [ zenon_intro zenon_Hf1 | zenon_intro zenon_Hba ]. % 18.65/18.81 apply (zenon_L84_); trivial. % 18.65/18.81 apply (zenon_L481_); trivial. % 18.65/18.81 apply (zenon_L436_); trivial. % 18.65/18.81 apply (zenon_or_s _ _ zenon_H16f); [ zenon_intro zenon_H9e | zenon_intro zenon_H170 ]. % 18.65/18.81 apply (zenon_L37_); trivial. % 18.65/18.81 apply (zenon_or_s _ _ zenon_H170); [ zenon_intro zenon_H13f | zenon_intro zenon_H171 ]. % 18.65/18.81 apply (zenon_or_s _ _ zenon_H6a); [ zenon_intro zenon_H48 | zenon_intro zenon_H6b ]. % 18.65/18.81 apply (zenon_L336_); trivial. % 18.65/18.81 apply (zenon_or_s _ _ zenon_H6b); [ zenon_intro zenon_H2a | zenon_intro zenon_H6c ]. % 18.65/18.81 exact (zenon_H25 zenon_H2a). % 18.65/18.81 apply (zenon_or_s _ _ zenon_H6c); [ zenon_intro zenon_H2c | zenon_intro zenon_H61 ]. % 18.65/18.81 exact (zenon_H81 zenon_H2c). % 18.65/18.81 apply (zenon_or_s _ _ zenon_H106); [ zenon_intro zenon_Hed | zenon_intro zenon_H107 ]. % 18.65/18.81 apply (zenon_L214_); trivial. % 18.65/18.81 apply (zenon_or_s _ _ zenon_H107); [ zenon_intro zenon_Ha5 | zenon_intro zenon_H108 ]. % 18.65/18.81 apply (zenon_L357_); trivial. % 18.65/18.81 apply (zenon_or_s _ _ zenon_H108); [ zenon_intro zenon_Hf1 | zenon_intro zenon_Hf4 ]. % 18.65/18.81 apply (zenon_or_s _ _ zenon_H172); [ zenon_intro zenon_H150 | zenon_intro zenon_H174 ]. % 18.65/18.81 apply (zenon_or_s _ _ zenon_H19d); [ zenon_intro zenon_H2a | zenon_intro zenon_H19e ]. % 18.65/18.81 exact (zenon_H25 zenon_H2a). % 18.65/18.81 apply (zenon_or_s _ _ zenon_H19e); [ zenon_intro zenon_Hf0 | zenon_intro zenon_H19f ]. % 18.65/18.81 apply (zenon_L59_); trivial. % 18.65/18.81 apply (zenon_or_s _ _ zenon_H19f); [ zenon_intro zenon_H113 | zenon_intro zenon_H16c ]. % 18.65/18.81 apply (zenon_L153_); trivial. % 18.65/18.81 apply (zenon_L482_); trivial. % 18.65/18.81 apply (zenon_or_s _ _ zenon_H174); [ zenon_intro zenon_H113 | zenon_intro zenon_H175 ]. % 18.65/18.81 apply (zenon_L466_); trivial. % 18.65/18.81 apply (zenon_or_s _ _ zenon_H175); [ zenon_intro zenon_H176 | zenon_intro zenon_H151 ]. % 18.65/18.81 exact (zenon_H173 zenon_H176). % 18.65/18.81 apply (zenon_L420_); trivial. % 18.65/18.81 apply (zenon_or_s _ _ zenon_H139); [ zenon_intro zenon_H122 | zenon_intro zenon_H13a ]. % 18.65/18.81 apply (zenon_L438_); trivial. % 18.65/18.81 apply (zenon_or_s _ _ zenon_H13a); [ zenon_intro zenon_Hf0 | zenon_intro zenon_H13b ]. % 18.65/18.81 apply (zenon_L484_); trivial. % 18.65/18.81 apply (zenon_or_s _ _ zenon_H13b); [ zenon_intro zenon_Hf1 | zenon_intro zenon_Hba ]. % 18.65/18.81 apply (zenon_L84_); trivial. % 18.65/18.81 apply (zenon_L480_); trivial. % 18.65/18.81 apply (zenon_or_s _ _ zenon_H171); [ zenon_intro zenon_H16c | zenon_intro zenon_Hdc ]. % 18.65/18.81 apply (zenon_L485_); trivial. % 18.65/18.81 apply (zenon_L266_); trivial. % 18.65/18.81 apply (zenon_or_s _ _ zenon_H28); [ zenon_intro zenon_H2a | zenon_intro zenon_H1f ]. % 18.65/18.81 exact (zenon_H25 zenon_H2a). % 18.65/18.81 exact (zenon_H38 zenon_H1f). % 18.65/18.81 apply (zenon_or_s _ _ zenon_H22f); [ zenon_intro zenon_H122 | zenon_intro zenon_Hc3 ]. % 18.65/18.81 apply (zenon_L438_); trivial. % 18.65/18.81 apply (zenon_L427_); trivial. % 18.65/18.81 apply (zenon_L109_); trivial. % 18.65/18.81 (* end of lemma zenon_L486_ *) % 18.65/18.81 assert (zenon_L487_ : (~((op (e3) (e1)) = (op (e3) (e2)))) -> ((~((op (e0) (e2)) = (e0)))\/((op (e0) (e0)) = (e2))) -> ((~((op (e1) (e0)) = (e0)))\/((op (e1) (e0)) = (e0))) -> (~((op (e1) (e0)) = (op (e2) (e0)))) -> (~((op (e2) (e0)) = (op (e2) (e1)))) -> (~((op (e1) (e0)) = (op (e3) (e0)))) -> (((op (e0) (e0)) = (e0))\/(((op (e0) (e1)) = (e0))\/(((op (e0) (e2)) = (e0))\/((op (e0) (e3)) = (e0))))) -> (~((op (e3) (e0)) = (op (e3) (e2)))) -> (~((op (e0) (e1)) = (op (e0) (e2)))) -> ((~((op (e3) (e1)) = (e0)))\/((op (e3) (e0)) = (e1))) -> ((~((op (e3) (e3)) = (e0)))\/((op (e3) (e0)) = (e3))) -> (((op (e0) (e2)) = (e0))\/(((op (e0) (e2)) = (e1))\/(((op (e0) (e2)) = (e2))\/((op (e0) (e2)) = (e3))))) -> (((op (e2) (e2)) = (e0))\/(((op (e2) (e2)) = (e1))\/(((op (e2) (e2)) = (e2))\/((op (e2) (e2)) = (e3))))) -> (((op (e0) (e0)) = (e3))\/(((op (e1) (e0)) = (e3))\/(((op (e2) (e0)) = (e3))\/((op (e3) (e0)) = (e3))))) -> ((~((op (e2) (e0)) = (e0)))\/((op (e2) (e0)) = (e0))) -> (((op (e0) (e0)) = (e2))\/(((op (e1) (e0)) = (e2))\/(((op (e2) (e0)) = (e2))\/((op (e3) (e0)) = (e2))))) -> ((~((op (e2) (e1)) = (e0)))\/((op (e2) (e0)) = (e1))) -> (~((op (e0) (e0)) = (op (e2) (e0)))) -> (((op (e3) (e0)) = (e3))\/(((op (e3) (e1)) = (e3))\/(((op (e3) (e2)) = (e3))\/((op (e3) (e3)) = (e3))))) -> (~((op (e1) (e1)) = (op (e3) (e1)))) -> (((op (e0) (e0)) = (e3))\/(((op (e0) (e1)) = (e3))\/(((op (e0) (e2)) = (e3))\/((op (e0) (e3)) = (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) (e0)) = (e1))\/(((op (e1) (e1)) = (e1))\/(((op (e1) (e2)) = (e1))\/((op (e1) (e3)) = (e1))))) -> (((op (e0) (e2)) = (e1))\/(((op (e1) (e2)) = (e1))\/(((op (e2) (e2)) = (e1))\/((op (e3) (e2)) = (e1))))) -> (~((op (e0) (e0)) = (op (e0) (e2)))) -> (((op (e1) (e1)) = (e0))\/(((op (e1) (e1)) = (e1))\/(((op (e1) (e1)) = (e2))\/((op (e1) (e1)) = (e3))))) -> ((~((op (e1) (e3)) = (e0)))\/((op (e1) (e0)) = (e3))) -> ((~((op (e1) (e2)) = (e0)))\/((op (e1) (e0)) = (e2))) -> (~((op (e2) (e0)) = (op (e3) (e0)))) -> (((op (e0) (e0)) = (e2))\/(((op (e0) (e1)) = (e2))\/(((op (e0) (e2)) = (e2))\/((op (e0) (e3)) = (e2))))) -> ((~((op (e3) (e0)) = (e0)))\/((op (e3) (e0)) = (e0))) -> ((~((op (e2) (e2)) = (e0)))\/((op (e2) (e0)) = (e2))) -> (~((op (e1) (e2)) = (op (e2) (e2)))) -> (((op (e2) (e0)) = (e3))\/(((op (e2) (e1)) = (e3))\/(((op (e2) (e2)) = (e3))\/((op (e2) (e3)) = (e3))))) -> (((op (e0) (e3)) = (e0))\/(((op (e0) (e3)) = (e1))\/(((op (e0) (e3)) = (e2))\/((op (e0) (e3)) = (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) (e3)) = (op (e3) (e3)))) -> (((op (e3) (e0)) = (e1))\/(((op (e3) (e1)) = (e1))\/(((op (e3) (e2)) = (e1))\/((op (e3) (e3)) = (e1))))) -> (~((op (e0) (e2)) = (op (e2) (e2)))) -> (~((op (e0) (e3)) = (op (e1) (e3)))) -> (~((op (e1) (e2)) = (op (e3) (e2)))) -> (~((e0) = (e3))) -> (((op (e1) (e2)) = (e0))\/(((op (e1) (e2)) = (e1))\/(((op (e1) (e2)) = (e2))\/((op (e1) (e2)) = (e3))))) -> (~((op (e0) (e2)) = (op (e1) (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) (e2)) = (e0)))\/((op (e3) (e0)) = (e2))) -> (((op (e0) (e2)) = (e3))\/(((op (e1) (e2)) = (e3))\/(((op (e2) (e2)) = (e3))\/((op (e3) (e2)) = (e3))))) -> (((op (e2) (e0)) = (e0))\/(((op (e2) (e1)) = (e0))\/(((op (e2) (e2)) = (e0))\/((op (e2) (e3)) = (e0))))) -> ((~((op (e2) (e3)) = (e0)))\/((op (e2) (e0)) = (e3))) -> ((~((op (e1) (e1)) = (e0)))\/((op (e1) (e0)) = (e1))) -> ((~((op (e0) (e3)) = (e0)))\/((op (e0) (e0)) = (e3))) -> (~((op (e2) (e2)) = (e0))) -> ((op (e0) (e0)) = (e3)) -> (((op (e0) (e0)) = (e1))\/(((op (e0) (e1)) = (e1))\/(((op (e0) (e2)) = (e1))\/((op (e0) (e3)) = (e1))))) -> (~((op (e0) (e2)) = (op (e3) (e2)))) -> (~((op (e1) (e0)) = (op (e1) (e1)))) -> (((op (e0) (e3)) = (e0))\/(((op (e1) (e3)) = (e0))\/(((op (e2) (e3)) = (e0))\/((op (e3) (e3)) = (e0))))) -> (~((op (e2) (e0)) = (op (e2) (e3)))) -> (~((op (e1) (e1)) = (op (e1) (e3)))) -> (((op (e0) (e2)) = (e0))\/(((op (e1) (e2)) = (e0))\/(((op (e2) (e2)) = (e0))\/((op (e3) (e2)) = (e0))))) -> (~((op (e2) (e0)) = (op (e2) (e2)))) -> (~((op (e1) (e1)) = (op (e1) (e2)))) -> (~((op (e0) (e2)) = (op (e0) (e3)))) -> (((op (e0) (e0)) = (e0))\/(((op (e1) (e0)) = (e0))\/(((op (e2) (e0)) = (e0))\/((op (e3) (e0)) = (e0))))) -> (~((op (e0) (e0)) = (e0))) -> (~((op (e1) (e3)) = (op (e3) (e3)))) -> (((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 (e1) (e0)) = (e0))) -> (~((e2) = (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) (e3)) = (e0))\/(((op (e3) (e3)) = (e1))\/(((op (e3) (e3)) = (e2))\/((op (e3) (e3)) = (e3))))) -> (~((op (e3) (e1)) = (op (e3) (e3)))) -> (~((op (e3) (e2)) = (op (e3) (e3)))) -> (~((op (e3) (e3)) = (e3))) -> (((op (e0) (e1)) = (e0))\/(((op (e0) (e1)) = (e1))\/(((op (e0) (e1)) = (e2))\/((op (e0) (e1)) = (e3))))) -> (~((op (e0) (e1)) = (e0))) -> (~((op (e0) (e1)) = (op (e3) (e1)))) -> (~((op (e1) (e1)) = (op (e2) (e1)))) -> (~((op (e0) (e1)) = (op (e2) (e1)))) -> (~((op (e2) (e1)) = (op (e3) (e1)))) -> (~((op (e2) (e1)) = (e0))) -> (((op (e2) (e1)) = (e0))\/(((op (e2) (e1)) = (e1))\/(((op (e2) (e1)) = (e2))\/((op (e2) (e1)) = (e3))))) -> (~((op (e0) (e1)) = (op (e1) (e1)))) -> ((op (e1) (e0)) = (e1)) -> (~((e1) = (e3))) -> (((op (e1) (e0)) = (e3))\/(((op (e1) (e1)) = (e3))\/(((op (e1) (e2)) = (e3))\/((op (e1) (e3)) = (e3))))) -> (~((op (e3) (e0)) = (op (e3) (e1)))) -> ((op (e3) (e0)) = (e3)) -> (((op (e2) (e0)) = (e1))\/(((op (e2) (e1)) = (e1))\/(((op (e2) (e2)) = (e1))\/((op (e2) (e3)) = (e1))))) -> (~((e0) = (e1))) -> ((op (e2) (e0)) = (e0)) -> (~((op (e1) (e3)) = (op (e2) (e3)))) -> (~((op (e2) (e3)) = (op (e3) (e3)))) -> (~((op (e2) (e2)) = (op (e2) (e3)))) -> (~((op (e2) (e3)) = (e0))) -> (((op (e2) (e3)) = (e0))\/(((op (e2) (e3)) = (e1))\/(((op (e2) (e3)) = (e2))\/((op (e2) (e3)) = (e3))))) -> (((op (e0) (e3)) = (e2))\/(((op (e1) (e3)) = (e2))\/(((op (e2) (e3)) = (e2))\/((op (e3) (e3)) = (e2))))) -> (((op (e0) (e3)) = (e1))\/(((op (e1) (e3)) = (e1))\/(((op (e2) (e3)) = (e1))\/((op (e3) (e3)) = (e1))))) -> (~((op (e2) (e1)) = (op (e2) (e3)))) -> (~((op (e0) (e0)) = (op (e0) (e3)))) -> ((op (e0) (e0)) = (e2)) -> (((op (e0) (e1)) = (e2))\/(((op (e1) (e1)) = (e2))\/(((op (e2) (e1)) = (e2))\/((op (e3) (e1)) = (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) (e3)) = (op (e2) (e3)))) -> (((op (e0) (e1)) = (e3))\/(((op (e1) (e1)) = (e3))\/(((op (e2) (e1)) = (e3))\/((op (e3) (e1)) = (e3))))) -> (~((e1) = (e2))) -> (((op (e1) (e0)) = (e2))\/(((op (e1) (e1)) = (e2))\/(((op (e1) (e2)) = (e2))\/((op (e1) (e3)) = (e2))))) -> (((op (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) (e0)) = (e0))) -> (~((op (e3) (e1)) = (e0))) -> (~((op (e3) (e2)) = (e0))) -> (~((op (e1) (e1)) = (e1))) -> (~((op (e0) (e1)) = (op (e0) (e3)))) -> (((op (e0) (e1)) = (e1))\/(((op (e1) (e1)) = (e1))\/(((op (e2) (e1)) = (e1))\/((op (e3) (e1)) = (e1))))) -> (~((op (e1) (e2)) = (e0))) -> (~((op (e1) (e3)) = (e0))) -> False). % 18.65/18.81 do 0 intro. intros zenon_H1a4 zenon_H233 zenon_H206 zenon_H201 zenon_H1f0 zenon_H1fa zenon_H74 zenon_H6f zenon_H4a zenon_H1ed zenon_H1ec zenon_H1ba zenon_H1c4 zenon_H1e0 zenon_H1ee zenon_H1fe zenon_H182 zenon_H39 zenon_H165 zenon_H160 zenon_H168 zenon_H124 zenon_H136 zenon_H128 zenon_H139 zenon_H13c zenon_H142 zenon_H179 zenon_H178 zenon_H17b zenon_H183 zenon_H184 zenon_H185 zenon_H2b zenon_He7 zenon_He4 zenon_Hd8 zenon_Hdf zenon_Hc2 zenon_He8 zenon_Ha8 zenon_H1d zenon_H115 zenon_H9a zenon_H19d zenon_H195 zenon_H191 zenon_H18f zenon_H1a7 zenon_H1a6 zenon_H2f zenon_H94 zenon_H205 zenon_H204 zenon_H81 zenon_H3a zenon_H22d zenon_H14f zenon_H45 zenon_H67 zenon_H5b zenon_H57 zenon_H6a zenon_H52 zenon_H4f zenon_H208 zenon_H3e zenon_H3f zenon_Hd5 zenon_H1d5 zenon_H22 zenon_H23 zenon_H12b zenon_H172 zenon_H149 zenon_H48 zenon_H173 zenon_H101 zenon_H130 zenon_H62 zenon_H102 zenon_H212 zenon_H20b zenon_H210 zenon_H13e zenon_H17e zenon_Haf zenon_H31 zenon_H1cc zenon_H10e zenon_H9d zenon_H95 zenon_H16f zenon_H1cf zenon_H15e zenon_H106 zenon_Ha1 zenon_H34 zenon_Hdb zenon_Hf3 zenon_H6d zenon_H32 zenon_H11f zenon_H145 zenon_H133 zenon_H1c7 zenon_H189 zenon_H7b zenon_H1d8 zenon_H71 zenon_H153 zenon_He2 zenon_H1a5 zenon_H7c zenon_H18c zenon_H22a zenon_H1ac zenon_H40 zenon_H1ad zenon_H18b zenon_H10a zenon_H54 zenon_H109 zenon_H25 zenon_H38. % 18.65/18.81 apply (zenon_or_s _ _ zenon_H22d); [ zenon_intro zenon_H7a | zenon_intro zenon_H22e ]. % 18.65/18.81 apply (zenon_L35_); trivial. % 18.65/18.81 apply (zenon_or_s _ _ zenon_H22e); [ zenon_intro zenon_Ha0 | zenon_intro zenon_H22f ]. % 18.65/18.81 apply (zenon_or_s _ _ zenon_H22); [ zenon_intro zenon_H27 | zenon_intro zenon_H26 ]. % 18.65/18.81 exact (zenon_H23 zenon_H27). % 18.65/18.81 apply (zenon_or_s _ _ zenon_H26); [ zenon_intro zenon_H29 | zenon_intro zenon_H28 ]. % 18.65/18.81 apply (zenon_or_s _ _ zenon_H18c); [ zenon_intro zenon_H86 | zenon_intro zenon_H18d ]. % 18.65/18.81 apply (zenon_L123_); trivial. % 18.65/18.81 apply (zenon_or_s _ _ zenon_H18d); [ zenon_intro zenon_H110 | zenon_intro zenon_H18e ]. % 18.65/18.81 apply (zenon_L354_); trivial. % 18.65/18.81 apply (zenon_or_s _ _ zenon_H18e); [ zenon_intro zenon_H113 | zenon_intro zenon_Hd7 ]. % 18.65/18.81 apply (zenon_or_s _ _ zenon_H1d8); [ zenon_intro zenon_H10f | zenon_intro zenon_H1d9 ]. % 18.65/18.81 apply (zenon_L418_); trivial. % 18.65/18.81 apply (zenon_or_s _ _ zenon_H1d9); [ zenon_intro zenon_H110 | zenon_intro zenon_H1da ]. % 18.65/18.81 apply (zenon_L354_); trivial. % 18.65/18.81 apply (zenon_or_s _ _ zenon_H1da); [ zenon_intro zenon_H1ca | zenon_intro zenon_H14d ]. % 18.65/18.81 apply (zenon_or_s _ _ zenon_H16f); [ zenon_intro zenon_H9e | zenon_intro zenon_H170 ]. % 18.65/18.81 apply (zenon_L37_); trivial. % 18.65/18.81 apply (zenon_or_s _ _ zenon_H170); [ zenon_intro zenon_H13f | zenon_intro zenon_H171 ]. % 18.65/18.81 apply (zenon_or_s _ _ zenon_H106); [ zenon_intro zenon_Hed | zenon_intro zenon_H107 ]. % 18.65/18.81 apply (zenon_L214_); trivial. % 18.65/18.81 apply (zenon_or_s _ _ zenon_H107); [ zenon_intro zenon_Ha5 | zenon_intro zenon_H108 ]. % 18.65/18.81 apply (zenon_L373_); trivial. % 18.65/18.81 apply (zenon_or_s _ _ zenon_H108); [ zenon_intro zenon_Hf1 | zenon_intro zenon_Hf4 ]. % 18.65/18.81 apply (zenon_or_s _ _ zenon_H1a6); [ zenon_intro zenon_Ha9 | zenon_intro zenon_H1aa ]. % 18.65/18.81 apply (zenon_L358_); trivial. % 18.65/18.81 apply (zenon_or_s _ _ zenon_H1aa); [ zenon_intro zenon_H16c | zenon_intro zenon_H1ab ]. % 18.65/18.81 apply (zenon_L116_); trivial. % 18.65/18.81 apply (zenon_or_s _ _ zenon_H1ab); [ zenon_intro zenon_Haa | zenon_intro zenon_H163 ]. % 18.65/18.81 apply (zenon_or_s _ _ zenon_H1ac); [ zenon_intro zenon_H44 | zenon_intro zenon_H1af ]. % 18.65/18.81 exact (zenon_H40 zenon_H44). % 18.65/18.81 apply (zenon_or_s _ _ zenon_H1af); [ zenon_intro zenon_H1b1 | zenon_intro zenon_H1b0 ]. % 18.65/18.81 exact (zenon_H1ad zenon_H1b1). % 18.65/18.81 apply (zenon_or_s _ _ zenon_H1b0); [ zenon_intro zenon_H61 | zenon_intro zenon_H60 ]. % 18.65/18.81 exact (zenon_H18b zenon_H61). % 18.65/18.81 apply (zenon_or_s _ _ zenon_He8); [ zenon_intro zenon_Hac | zenon_intro zenon_Heb ]. % 18.65/18.81 apply (zenon_L252_); trivial. % 18.65/18.81 apply (zenon_or_s _ _ zenon_Heb); [ zenon_intro zenon_Hae | zenon_intro zenon_Hec ]. % 18.65/18.81 apply (zenon_L368_); trivial. % 18.65/18.81 apply (zenon_or_s _ _ zenon_Hec); [ zenon_intro zenon_Hba | zenon_intro zenon_Hc4 ]. % 18.65/18.81 apply (zenon_L419_); trivial. % 18.65/18.82 apply (zenon_or_s _ _ zenon_H153); [ zenon_intro zenon_H148 | zenon_intro zenon_H154 ]. % 18.65/18.82 apply (zenon_L325_); trivial. % 18.65/18.82 apply (zenon_or_s _ _ zenon_H154); [ zenon_intro zenon_H14d | zenon_intro zenon_H155 ]. % 18.65/18.82 apply (zenon_L452_); trivial. % 18.65/18.82 apply (zenon_or_s _ _ zenon_H155); [ zenon_intro zenon_H151 | zenon_intro zenon_Hf6 ]. % 18.65/18.82 apply (zenon_L453_); trivial. % 18.65/18.82 apply (zenon_or_s _ _ zenon_He4); [ zenon_intro zenon_H1e | zenon_intro zenon_He5 ]. % 18.65/18.82 apply (zenon_L440_); trivial. % 18.65/18.82 apply (zenon_or_s _ _ zenon_He5); [ zenon_intro zenon_Hc3 | zenon_intro zenon_He6 ]. % 18.65/18.82 apply (zenon_L46_); trivial. % 18.65/18.82 apply (zenon_or_s _ _ zenon_He6); [ zenon_intro zenon_Hcd | zenon_intro zenon_He3 ]. % 18.65/18.82 apply (zenon_L87_); trivial. % 18.65/18.82 apply (zenon_L455_); trivial. % 18.65/18.82 apply (zenon_L286_); trivial. % 18.65/18.82 apply (zenon_or_s _ _ zenon_H139); [ zenon_intro zenon_H122 | zenon_intro zenon_H13a ]. % 18.65/18.82 apply (zenon_L438_); trivial. % 18.65/18.82 apply (zenon_or_s _ _ zenon_H13a); [ zenon_intro zenon_Hf0 | zenon_intro zenon_H13b ]. % 18.65/18.82 apply (zenon_L68_); trivial. % 18.65/18.82 apply (zenon_or_s _ _ zenon_H13b); [ zenon_intro zenon_Hf1 | zenon_intro zenon_Hba ]. % 18.65/18.82 apply (zenon_L84_); trivial. % 18.65/18.82 apply (zenon_or_s _ _ zenon_He7); [ zenon_intro zenon_H3b | zenon_intro zenon_He9 ]. % 18.65/18.82 apply (zenon_L327_); trivial. % 18.65/18.82 apply (zenon_or_s _ _ zenon_He9); [ zenon_intro zenon_Ha6 | zenon_intro zenon_Hea ]. % 18.65/18.82 apply (zenon_L95_); trivial. % 18.65/18.82 apply (zenon_or_s _ _ zenon_Hea); [ zenon_intro zenon_Haa | zenon_intro zenon_Hdd ]. % 18.65/18.82 apply (zenon_or_s _ _ zenon_H153); [ zenon_intro zenon_H148 | zenon_intro zenon_H154 ]. % 18.65/18.82 apply (zenon_L325_); trivial. % 18.65/18.82 apply (zenon_or_s _ _ zenon_H154); [ zenon_intro zenon_H14d | zenon_intro zenon_H155 ]. % 18.65/18.82 apply (zenon_L451_); trivial. % 18.65/18.82 apply (zenon_or_s _ _ zenon_H155); [ zenon_intro zenon_H151 | zenon_intro zenon_Hf6 ]. % 18.65/18.82 apply (zenon_L453_); trivial. % 18.65/18.82 apply (zenon_or_s _ _ zenon_Hdf); [ zenon_intro zenon_H1f | zenon_intro zenon_He0 ]. % 18.65/18.82 exact (zenon_H38 zenon_H1f). % 18.65/18.82 apply (zenon_or_s _ _ zenon_He0); [ zenon_intro zenon_Hd6 | zenon_intro zenon_He1 ]. % 18.65/18.82 apply (zenon_L126_); trivial. % 18.65/18.82 apply (zenon_or_s _ _ zenon_He1); [ zenon_intro zenon_Hd7 | zenon_intro zenon_Hdc ]. % 18.65/18.82 apply (zenon_L402_); trivial. % 18.65/18.82 apply (zenon_L472_); trivial. % 18.65/18.82 apply (zenon_L474_); trivial. % 18.65/18.82 apply (zenon_or_s _ _ zenon_H171); [ zenon_intro zenon_H16c | zenon_intro zenon_Hdc ]. % 18.65/18.82 apply (zenon_L476_); trivial. % 18.65/18.82 apply (zenon_L472_); trivial. % 18.65/18.82 apply (zenon_L452_); trivial. % 18.65/18.82 apply (zenon_or_s _ _ zenon_H1d8); [ zenon_intro zenon_H10f | zenon_intro zenon_H1d9 ]. % 18.65/18.82 apply (zenon_L458_); trivial. % 18.65/18.82 apply (zenon_or_s _ _ zenon_H1d9); [ zenon_intro zenon_H110 | zenon_intro zenon_H1da ]. % 18.65/18.82 apply (zenon_L283_); trivial. % 18.65/18.82 apply (zenon_or_s _ _ zenon_H1da); [ zenon_intro zenon_H1ca | zenon_intro zenon_H14d ]. % 18.65/18.82 apply (zenon_or_s _ _ zenon_H16f); [ zenon_intro zenon_H9e | zenon_intro zenon_H170 ]. % 18.65/18.82 apply (zenon_L37_); trivial. % 18.65/18.82 apply (zenon_or_s _ _ zenon_H170); [ zenon_intro zenon_H13f | zenon_intro zenon_H171 ]. % 18.65/18.82 apply (zenon_or_s _ _ zenon_H106); [ zenon_intro zenon_Hed | zenon_intro zenon_H107 ]. % 18.65/18.82 apply (zenon_L413_); trivial. % 18.65/18.82 apply (zenon_or_s _ _ zenon_H107); [ zenon_intro zenon_Ha5 | zenon_intro zenon_H108 ]. % 18.65/18.82 apply (zenon_L373_); trivial. % 18.65/18.82 apply (zenon_or_s _ _ zenon_H108); [ zenon_intro zenon_Hf1 | zenon_intro zenon_Hf4 ]. % 18.65/18.82 apply (zenon_L460_); trivial. % 18.65/18.82 apply (zenon_or_s _ _ zenon_H153); [ zenon_intro zenon_H148 | zenon_intro zenon_H154 ]. % 18.65/18.82 apply (zenon_L486_); trivial. % 18.65/18.82 apply (zenon_or_s _ _ zenon_H154); [ zenon_intro zenon_H14d | zenon_intro zenon_H155 ]. % 18.65/18.82 apply (zenon_L451_); trivial. % 18.65/18.82 apply (zenon_or_s _ _ zenon_H155); [ zenon_intro zenon_H151 | zenon_intro zenon_Hf6 ]. % 18.65/18.82 apply (zenon_L453_); trivial. % 18.65/18.82 apply (zenon_L402_); trivial. % 18.65/18.82 apply (zenon_or_s _ _ zenon_H171); [ zenon_intro zenon_H16c | zenon_intro zenon_Hdc ]. % 18.65/18.82 apply (zenon_L476_); trivial. % 18.65/18.82 apply (zenon_L266_); trivial. % 18.65/18.82 apply (zenon_L462_); trivial. % 18.65/18.82 apply (zenon_or_s _ _ zenon_H28); [ zenon_intro zenon_H2a | zenon_intro zenon_H1f ]. % 18.65/18.82 exact (zenon_H25 zenon_H2a). % 18.65/18.82 exact (zenon_H38 zenon_H1f). % 18.65/18.82 apply (zenon_or_s _ _ zenon_H22f); [ zenon_intro zenon_H122 | zenon_intro zenon_Hc3 ]. % 18.65/18.82 apply (zenon_L355_); trivial. % 18.65/18.82 apply (zenon_L447_); trivial. % 18.65/18.82 (* end of lemma zenon_L487_ *) % 18.65/18.82 assert (zenon_L488_ : ((~((op (e2) (e1)) = (e0)))\/((op (e2) (e0)) = (e1))) -> ((~((op (e2) (e3)) = (e0)))\/((op (e2) (e0)) = (e3))) -> (((op (e0) (e0)) = (e0))\/(((op (e1) (e0)) = (e0))\/(((op (e2) (e0)) = (e0))\/((op (e3) (e0)) = (e0))))) -> (~((op (e1) (e0)) = (e0))) -> (~((op (e0) (e0)) = (e0))) -> ((~((op (e3) (e1)) = (e0)))\/((op (e3) (e0)) = (e1))) -> (((op (e0) (e0)) = (e0))\/(((op (e0) (e1)) = (e0))\/(((op (e0) (e2)) = (e0))\/((op (e0) (e3)) = (e0))))) -> (~((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 (e1) (e2)) = (e0))) -> (~((e1) = (e2))) -> ((op (e1) (e0)) = (e1)) -> (~((e0) = (e2))) -> (~((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 (e3) (e2)))) -> (~((op (e2) (e2)) = (e2))) -> (((op (e2) (e2)) = (e0))\/(((op (e2) (e2)) = (e1))\/(((op (e2) (e2)) = (e2))\/((op (e2) (e2)) = (e3))))) -> (~((op (e2) (e0)) = (op (e2) (e2)))) -> (~((e0) = (e1))) -> (~((op (e0) (e1)) = (op (e2) (e1)))) -> (~((e0) = (e3))) -> (~((e2) = (e3))) -> (((op (e3) (e0)) = (e1))\/(((op (e3) (e1)) = (e1))\/(((op (e3) (e2)) = (e1))\/((op (e3) (e3)) = (e1))))) -> (~((op (e1) (e3)) = (op (e3) (e3)))) -> (~((op (e1) (e3)) = (op (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 (e1) (e1)) = (e1))) -> (((op (e2) (e0)) = (e2))\/(((op (e2) (e1)) = (e2))\/(((op (e2) (e2)) = (e2))\/((op (e2) (e3)) = (e2))))) -> (((op (e0) (e1)) = (e3))\/(((op (e1) (e1)) = (e3))\/(((op (e2) (e1)) = (e3))\/((op (e3) (e1)) = (e3))))) -> (~((op (e3) (e1)) = (op (e3) (e2)))) -> (((op (e0) (e2)) = (e3))\/(((op (e1) (e2)) = (e3))\/(((op (e2) (e2)) = (e3))\/((op (e3) (e2)) = (e3))))) -> (((op (e0) (e1)) = (e0))\/(((op (e0) (e1)) = (e1))\/(((op (e0) (e1)) = (e2))\/((op (e0) (e1)) = (e3))))) -> (~((op (e0) (e1)) = (op (e1) (e1)))) -> (~((op (e1) (e1)) = (op (e2) (e1)))) -> (((op (e2) (e1)) = (e0))\/(((op (e2) (e1)) = (e1))\/(((op (e2) (e1)) = (e2))\/((op (e2) (e1)) = (e3))))) -> (~((op (e0) (e3)) = (op (e3) (e3)))) -> (((op (e0) (e2)) = (e0))\/(((op (e1) (e2)) = (e0))\/(((op (e2) (e2)) = (e0))\/((op (e3) (e2)) = (e0))))) -> (~((op (e3) (e0)) = (op (e3) (e2)))) -> (~((op (e1) (e1)) = (op (e1) (e2)))) -> (~((op (e1) (e2)) = (op (e2) (e2)))) -> (((op (e3) (e0)) = (e2))\/(((op (e3) (e1)) = (e2))\/(((op (e3) (e2)) = (e2))\/((op (e3) (e3)) = (e2))))) -> (((op (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) (e3)) = (e3))) -> (~((op (e3) (e2)) = (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 (e1) (e1)) = (op (e3) (e1)))) -> (((op (e1) (e0)) = (e2))\/(((op (e1) (e1)) = (e2))\/(((op (e1) (e2)) = (e2))\/((op (e1) (e3)) = (e2))))) -> (~((op (e0) (e0)) = (op (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) (e3)) = (e2))\/(((op (e1) (e3)) = (e2))\/(((op (e2) (e3)) = (e2))\/((op (e3) (e3)) = (e2))))) -> (((op (e2) (e0)) = (e1))\/(((op (e2) (e1)) = (e1))\/(((op (e2) (e2)) = (e1))\/((op (e2) (e3)) = (e1))))) -> (((op (e0) (e1)) = (e1))\/(((op (e1) (e1)) = (e1))\/(((op (e2) (e1)) = (e1))\/((op (e3) (e1)) = (e1))))) -> (~((op (e0) (e3)) = (op (e2) (e3)))) -> (((op (e1) (e3)) = (e0))\/(((op (e1) (e3)) = (e1))\/(((op (e1) (e3)) = (e2))\/((op (e1) (e3)) = (e3))))) -> (~((op (e2) (e1)) = (op (e3) (e1)))) -> (((op (e3) (e1)) = (e0))\/(((op (e3) (e1)) = (e1))\/(((op (e3) (e1)) = (e2))\/((op (e3) (e1)) = (e3))))) -> (((op (e2) (e3)) = (e0))\/(((op (e2) (e3)) = (e1))\/(((op (e2) (e3)) = (e2))\/((op (e2) (e3)) = (e3))))) -> (~((op (e2) (e3)) = (op (e3) (e3)))) -> (~((op (e1) (e2)) = (op (e3) (e2)))) -> (~((op (e0) (e1)) = (op (e0) (e2)))) -> (~((op (e0) (e1)) = (op (e3) (e1)))) -> (~((op (e0) (e1)) = (op (e0) (e3)))) -> (~((op (e1) (e0)) = (op (e1) (e3)))) -> (~((op (e2) (e2)) = (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 (e0) (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)) = (e0))) -> ((~((op (e3) (e2)) = (e0)))\/((op (e3) (e0)) = (e2))) -> ((~((op (e3) (e0)) = (e0)))\/((op (e3) (e0)) = (e0))) -> (((op (e2) (e0)) = (e0))\/(((op (e2) (e1)) = (e0))\/(((op (e2) (e2)) = (e0))\/((op (e2) (e3)) = (e0))))) -> ((~((op (e2) (e2)) = (e0)))\/((op (e2) (e0)) = (e2))) -> (((op (e3) (e0)) = (e3))\/(((op (e3) (e1)) = (e3))\/(((op (e3) (e2)) = (e3))\/((op (e3) (e3)) = (e3))))) -> (~((op (e0) (e2)) = (op (e2) (e2)))) -> ((~((op (e3) (e3)) = (e0)))\/((op (e3) (e0)) = (e3))) -> ((~((op (e0) (e3)) = (e0)))\/((op (e0) (e0)) = (e3))) -> ((~((op (e1) (e1)) = (e0)))\/((op (e1) (e0)) = (e1))) -> (((op (e3) (e2)) = (e0))\/(((op (e3) (e2)) = (e1))\/(((op (e3) (e2)) = (e2))\/((op (e3) (e2)) = (e3))))) -> (~((op (e0) (e2)) = (op (e1) (e2)))) -> (((op (e1) (e2)) = (e0))\/(((op (e1) (e2)) = (e1))\/(((op (e1) (e2)) = (e2))\/((op (e1) (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 (e2) (e0)) = (op (e3) (e0)))) -> ((~((op (e1) (e2)) = (e0)))\/((op (e1) (e0)) = (e2))) -> ((~((op (e1) (e3)) = (e0)))\/((op (e1) (e0)) = (e3))) -> (((op (e1) (e1)) = (e0))\/(((op (e1) (e1)) = (e1))\/(((op (e1) (e1)) = (e2))\/((op (e1) (e1)) = (e3))))) -> (~((op (e0) (e0)) = (op (e0) (e2)))) -> (((op (e1) (e0)) = (e1))\/(((op (e1) (e1)) = (e1))\/(((op (e1) (e2)) = (e1))\/((op (e1) (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 (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 (e2) (e0)) = (e0)))\/((op (e2) (e0)) = (e0))) -> (((op (e0) (e0)) = (e3))\/(((op (e1) (e0)) = (e3))\/(((op (e2) (e0)) = (e3))\/((op (e3) (e0)) = (e3))))) -> (((op (e0) (e2)) = (e0))\/(((op (e0) (e2)) = (e1))\/(((op (e0) (e2)) = (e2))\/((op (e0) (e2)) = (e3))))) -> (~((op (e1) (e0)) = (op (e3) (e0)))) -> (~((op (e2) (e0)) = (op (e2) (e1)))) -> ((~((op (e1) (e0)) = (e0)))\/((op (e1) (e0)) = (e0))) -> ((~((op (e0) (e2)) = (e0)))\/((op (e0) (e0)) = (e2))) -> (~((op (e3) (e0)) = (op (e3) (e1)))) -> (~((op (e1) (e1)) = (op (e1) (e3)))) -> (~((op (e2) (e0)) = (op (e2) (e3)))) -> (((op (e0) (e3)) = (e0))\/(((op (e1) (e3)) = (e0))\/(((op (e2) (e3)) = (e0))\/((op (e3) (e3)) = (e0))))) -> (~((op (e1) (e0)) = (op (e1) (e1)))) -> (~((op (e0) (e2)) = (op (e3) (e2)))) -> (((op (e3) (e0)) = (e0))\/(((op (e3) (e1)) = (e0))\/(((op (e3) (e2)) = (e0))\/((op (e3) (e3)) = (e0))))) -> False). % 18.65/18.82 do 0 intro. intros zenon_H182 zenon_H94 zenon_H3e zenon_H23 zenon_H3f zenon_H1ed zenon_H74 zenon_H208 zenon_H95 zenon_H3a zenon_H22 zenon_H25 zenon_H7c zenon_H9d zenon_H149 zenon_H201 zenon_H139 zenon_H18f zenon_H173 zenon_H1c4 zenon_H52 zenon_Ha1 zenon_H17e zenon_H9a zenon_H12b zenon_He8 zenon_Hd5 zenon_Hdb zenon_He4 zenon_H1d zenon_H10a zenon_H1d5 zenon_H1a5 zenon_H1a4 zenon_H1a6 zenon_H212 zenon_H10e zenon_H13e zenon_H1cc zenon_Hc2 zenon_H6a zenon_H6f zenon_H4f zenon_H2b zenon_H153 zenon_H16f zenon_H101 zenon_H102 zenon_H62 zenon_H130 zenon_H172 zenon_H160 zenon_H18c zenon_H189 zenon_H1d8 zenon_H1c7 zenon_H145 zenon_H106 zenon_H109 zenon_He2 zenon_Hdf zenon_Haf zenon_H22a zenon_H11f zenon_Hf3 zenon_H115 zenon_H4a zenon_H210 zenon_H54 zenon_Hd8 zenon_H6d zenon_H71 zenon_H133 zenon_H7b zenon_H39 zenon_H22d zenon_H20b zenon_H1a7 zenon_H184 zenon_H2f zenon_H185 zenon_H165 zenon_Ha8 zenon_H1ec zenon_H204 zenon_H205 zenon_H191 zenon_H195 zenon_H19d zenon_He7 zenon_H183 zenon_H17b zenon_H178 zenon_H179 zenon_H142 zenon_H13c zenon_H128 zenon_H136 zenon_H124 zenon_H168 zenon_H1fe zenon_H1ee zenon_H1e0 zenon_H1ba zenon_H1fa zenon_H1f0 zenon_H206 zenon_H233 zenon_H1cf zenon_H57 zenon_H5b zenon_H67 zenon_H45 zenon_H14f zenon_H1ac. % 18.65/18.82 apply (zenon_or_s _ _ zenon_H179); [ zenon_intro zenon_H38 | zenon_intro zenon_H9e ]. % 18.65/18.82 apply (zenon_or_s _ _ zenon_H1ee); [ zenon_intro zenon_H30 | zenon_intro zenon_H34 ]. % 18.65/18.82 apply (zenon_or_s _ _ zenon_H182); [ zenon_intro zenon_H31 | zenon_intro zenon_Hed ]. % 18.65/18.82 apply (zenon_L417_); trivial. % 18.65/18.82 apply (zenon_L413_); trivial. % 18.65/18.82 apply (zenon_or_s _ _ zenon_H182); [ zenon_intro zenon_H31 | zenon_intro zenon_Hed ]. % 18.65/18.82 apply (zenon_or_s _ _ zenon_H185); [ zenon_intro zenon_H81 | zenon_intro zenon_Hee ]. % 18.65/18.82 apply (zenon_or_s _ _ zenon_H94); [ zenon_intro zenon_H32 | zenon_intro zenon_H3b ]. % 18.65/18.82 apply (zenon_or_s _ _ zenon_H184); [ zenon_intro zenon_H40 | zenon_intro zenon_H44 ]. % 18.65/18.82 apply (zenon_or_s _ _ zenon_H1ed); [ zenon_intro zenon_H1ad | zenon_intro zenon_Hac ]. % 18.65/18.82 apply (zenon_or_s _ _ zenon_H1a7); [ zenon_intro zenon_H18b | zenon_intro zenon_H148 ]. % 18.65/18.82 apply (zenon_or_s _ _ zenon_H1ec); [ zenon_intro zenon_H1ae | zenon_intro zenon_H15e ]. % 18.65/18.82 apply (zenon_L352_); trivial. % 18.65/18.82 apply (zenon_or_s _ _ zenon_H74); [ zenon_intro zenon_H42 | zenon_intro zenon_H77 ]. % 18.65/18.82 exact (zenon_H3f zenon_H42). % 18.65/18.82 apply (zenon_or_s _ _ zenon_H77); [ zenon_intro zenon_H49 | zenon_intro zenon_H78 ]. % 18.65/18.82 exact (zenon_H20b zenon_H49). % 18.65/18.82 apply (zenon_or_s _ _ zenon_H78); [ zenon_intro zenon_H48 | zenon_intro zenon_H1e ]. % 18.65/18.82 apply (zenon_L487_); trivial. % 18.65/18.82 apply (zenon_L337_); trivial. % 18.65/18.82 apply (zenon_L486_); trivial. % 18.65/18.82 apply (zenon_L439_); trivial. % 18.65/18.82 apply (zenon_L127_); trivial. % 18.65/18.82 apply (zenon_L470_); trivial. % 18.65/18.82 apply (zenon_L204_); trivial. % 18.65/18.82 apply (zenon_L214_); trivial. % 18.65/18.82 apply (zenon_L37_); trivial. % 18.65/18.82 (* end of lemma zenon_L488_ *) % 18.65/18.82 assert (zenon_L489_ : (((op (e3) (e0)) = (e0))\/(((op (e3) (e1)) = (e0))\/(((op (e3) (e2)) = (e0))\/((op (e3) (e3)) = (e0))))) -> (~((op (e0) (e2)) = (op (e3) (e2)))) -> (~((op (e1) (e0)) = (op (e1) (e1)))) -> (((op (e0) (e3)) = (e0))\/(((op (e1) (e3)) = (e0))\/(((op (e2) (e3)) = (e0))\/((op (e3) (e3)) = (e0))))) -> (~((op (e2) (e0)) = (op (e2) (e3)))) -> (~((op (e1) (e1)) = (op (e1) (e3)))) -> (~((op (e3) (e0)) = (op (e3) (e1)))) -> ((~((op (e0) (e2)) = (e0)))\/((op (e0) (e0)) = (e2))) -> ((~((op (e1) (e0)) = (e0)))\/((op (e1) (e0)) = (e0))) -> (~((op (e2) (e0)) = (op (e2) (e1)))) -> (~((op (e1) (e0)) = (op (e3) (e0)))) -> (((op (e0) (e2)) = (e0))\/(((op (e0) (e2)) = (e1))\/(((op (e0) (e2)) = (e2))\/((op (e0) (e2)) = (e3))))) -> (((op (e0) (e0)) = (e3))\/(((op (e1) (e0)) = (e3))\/(((op (e2) (e0)) = (e3))\/((op (e3) (e0)) = (e3))))) -> ((~((op (e2) (e0)) = (e0)))\/((op (e2) (e0)) = (e0))) -> (((op (e0) (e0)) = (e2))\/(((op (e1) (e0)) = (e2))\/(((op (e2) (e0)) = (e2))\/((op (e3) (e0)) = (e2))))) -> (((op (e0) (e0)) = (e3))\/(((op (e0) (e1)) = (e3))\/(((op (e0) (e2)) = (e3))\/((op (e0) (e3)) = (e3))))) -> (~((op (e1) (e2)) = (op (e1) (e3)))) -> (((op (e0) (e3)) = (e3))\/(((op (e1) (e3)) = (e3))\/(((op (e2) (e3)) = (e3))\/((op (e3) (e3)) = (e3))))) -> (((op (e1) (e0)) = (e1))\/(((op (e1) (e1)) = (e1))\/(((op (e1) (e2)) = (e1))\/((op (e1) (e3)) = (e1))))) -> (~((op (e0) (e0)) = (op (e0) (e2)))) -> (((op (e1) (e1)) = (e0))\/(((op (e1) (e1)) = (e1))\/(((op (e1) (e1)) = (e2))\/((op (e1) (e1)) = (e3))))) -> ((~((op (e1) (e3)) = (e0)))\/((op (e1) (e0)) = (e3))) -> ((~((op (e1) (e2)) = (e0)))\/((op (e1) (e0)) = (e2))) -> (~((op (e2) (e0)) = (op (e3) (e0)))) -> (((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) (e2)) = (e0))\/(((op (e1) (e2)) = (e1))\/(((op (e1) (e2)) = (e2))\/((op (e1) (e2)) = (e3))))) -> (~((op (e0) (e2)) = (op (e1) (e2)))) -> (((op (e3) (e2)) = (e0))\/(((op (e3) (e2)) = (e1))\/(((op (e3) (e2)) = (e2))\/((op (e3) (e2)) = (e3))))) -> ((~((op (e1) (e1)) = (e0)))\/((op (e1) (e0)) = (e1))) -> ((~((op (e0) (e3)) = (e0)))\/((op (e0) (e0)) = (e3))) -> ((~((op (e3) (e3)) = (e0)))\/((op (e3) (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 (e2) (e2)) = (e0)))\/((op (e2) (e0)) = (e2))) -> (((op (e2) (e0)) = (e0))\/(((op (e2) (e1)) = (e0))\/(((op (e2) (e2)) = (e0))\/((op (e2) (e3)) = (e0))))) -> ((~((op (e3) (e0)) = (e0)))\/((op (e3) (e0)) = (e0))) -> ((~((op (e3) (e2)) = (e0)))\/((op (e3) (e0)) = (e2))) -> (~((op (e0) (e1)) = (e0))) -> (((op (e0) (e0)) = (e1))\/(((op (e0) (e1)) = (e1))\/(((op (e0) (e2)) = (e1))\/((op (e0) (e3)) = (e1))))) -> (~((op (e0) (e0)) = (op (e2) (e0)))) -> ((op (e0) (e0)) = (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) (e2)) = (op (e2) (e3)))) -> (~((op (e1) (e0)) = (op (e1) (e3)))) -> (~((op (e0) (e1)) = (op (e0) (e3)))) -> (~((op (e0) (e1)) = (op (e3) (e1)))) -> (~((op (e0) (e1)) = (op (e0) (e2)))) -> (~((op (e1) (e2)) = (op (e3) (e2)))) -> (~((op (e2) (e3)) = (op (e3) (e3)))) -> (((op (e2) (e3)) = (e0))\/(((op (e2) (e3)) = (e1))\/(((op (e2) (e3)) = (e2))\/((op (e2) (e3)) = (e3))))) -> (((op (e3) (e1)) = (e0))\/(((op (e3) (e1)) = (e1))\/(((op (e3) (e1)) = (e2))\/((op (e3) (e1)) = (e3))))) -> (~((op (e2) (e1)) = (op (e3) (e1)))) -> (((op (e1) (e3)) = (e0))\/(((op (e1) (e3)) = (e1))\/(((op (e1) (e3)) = (e2))\/((op (e1) (e3)) = (e3))))) -> (~((op (e0) (e3)) = (op (e2) (e3)))) -> (((op (e0) (e1)) = (e1))\/(((op (e1) (e1)) = (e1))\/(((op (e2) (e1)) = (e1))\/((op (e3) (e1)) = (e1))))) -> (((op (e2) (e0)) = (e1))\/(((op (e2) (e1)) = (e1))\/(((op (e2) (e2)) = (e1))\/((op (e2) (e3)) = (e1))))) -> (((op (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)) = (op (e0) (e3)))) -> (((op (e1) (e0)) = (e2))\/(((op (e1) (e1)) = (e2))\/(((op (e1) (e2)) = (e2))\/((op (e1) (e3)) = (e2))))) -> (~((op (e1) (e1)) = (op (e3) (e1)))) -> (((op (e0) (e2)) = (e2))\/(((op (e1) (e2)) = (e2))\/(((op (e2) (e2)) = (e2))\/((op (e3) (e2)) = (e2))))) -> (~((op (e3) (e1)) = (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) (e0)) = (e3))\/(((op (e1) (e1)) = (e3))\/(((op (e1) (e2)) = (e3))\/((op (e1) (e3)) = (e3))))) -> (((op (e3) (e0)) = (e2))\/(((op (e3) (e1)) = (e2))\/(((op (e3) (e2)) = (e2))\/((op (e3) (e3)) = (e2))))) -> (~((op (e1) (e2)) = (op (e2) (e2)))) -> (~((op (e1) (e1)) = (op (e1) (e2)))) -> (~((op (e3) (e0)) = (op (e3) (e2)))) -> (((op (e0) (e2)) = (e0))\/(((op (e1) (e2)) = (e0))\/(((op (e2) (e2)) = (e0))\/((op (e3) (e2)) = (e0))))) -> (~((op (e0) (e3)) = (op (e3) (e3)))) -> (((op (e2) (e1)) = (e0))\/(((op (e2) (e1)) = (e1))\/(((op (e2) (e1)) = (e2))\/((op (e2) (e1)) = (e3))))) -> (~((op (e1) (e1)) = (op (e2) (e1)))) -> (~((op (e0) (e1)) = (op (e1) (e1)))) -> (((op (e0) (e1)) = (e0))\/(((op (e0) (e1)) = (e1))\/(((op (e0) (e1)) = (e2))\/((op (e0) (e1)) = (e3))))) -> (((op (e0) (e2)) = (e3))\/(((op (e1) (e2)) = (e3))\/(((op (e2) (e2)) = (e3))\/((op (e3) (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 (e2) (e0)) = (e2))\/(((op (e2) (e1)) = (e2))\/(((op (e2) (e2)) = (e2))\/((op (e2) (e3)) = (e2))))) -> (~((op (e1) (e1)) = (e1))) -> (~((op (e0) (e3)) = (op (e1) (e3)))) -> (((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 (e3) (e0)) = (e1))\/(((op (e3) (e1)) = (e1))\/(((op (e3) (e2)) = (e1))\/((op (e3) (e3)) = (e1))))) -> (~((e2) = (e3))) -> (~((e0) = (e3))) -> (~((op (e0) (e1)) = (op (e2) (e1)))) -> (~((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) (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 (e1) (e0)) = (op (e2) (e0)))) -> (~((e0) = (e2))) -> ((op (e1) (e0)) = (e1)) -> (~((e1) = (e2))) -> (((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) (e0)) = (e0))\/(((op (e0) (e1)) = (e0))\/(((op (e0) (e2)) = (e0))\/((op (e0) (e3)) = (e0))))) -> ((~((op (e3) (e1)) = (e0)))\/((op (e3) (e0)) = (e1))) -> (~((op (e0) (e0)) = (e0))) -> (~((op (e1) (e0)) = (e0))) -> (((op (e0) (e0)) = (e0))\/(((op (e1) (e0)) = (e0))\/(((op (e2) (e0)) = (e0))\/((op (e3) (e0)) = (e0))))) -> ((~((op (e2) (e3)) = (e0)))\/((op (e2) (e0)) = (e3))) -> ((~((op (e2) (e1)) = (e0)))\/((op (e2) (e0)) = (e1))) -> False). % 18.65/18.82 do 0 intro. intros zenon_H1ac zenon_H14f zenon_H45 zenon_H67 zenon_H5b zenon_H57 zenon_H1cf zenon_H233 zenon_H206 zenon_H1f0 zenon_H1fa zenon_H1ba zenon_H1e0 zenon_H1ee zenon_H1fe zenon_H168 zenon_H124 zenon_H136 zenon_H128 zenon_H13c zenon_H142 zenon_H179 zenon_H178 zenon_H17b zenon_H183 zenon_He7 zenon_H19d zenon_H195 zenon_H191 zenon_H205 zenon_H204 zenon_H1ec zenon_Ha8 zenon_H165 zenon_H185 zenon_H2f zenon_H184 zenon_H1a7 zenon_H20b zenon_H22d zenon_H39 zenon_H7b zenon_H133 zenon_H71 zenon_H6d zenon_Hd8 zenon_H54 zenon_H210 zenon_H4a zenon_H115 zenon_Hf3 zenon_H11f zenon_H22a zenon_Haf zenon_Hdf zenon_He2 zenon_H109 zenon_H106 zenon_H145 zenon_H1c7 zenon_H1d8 zenon_H189 zenon_H18c zenon_H160 zenon_H172 zenon_H130 zenon_H62 zenon_H102 zenon_H101 zenon_H16f zenon_H153 zenon_H2b zenon_H4f zenon_H6f zenon_H6a zenon_Hc2 zenon_H1cc zenon_H13e zenon_H10e zenon_H212 zenon_H1a6 zenon_H1a4 zenon_H1a5 zenon_H1d5 zenon_H10a zenon_H1d zenon_He4 zenon_Hdb zenon_Hd5 zenon_He8 zenon_H12b zenon_H9a zenon_H17e zenon_Ha1 zenon_H52 zenon_H1c4 zenon_H173 zenon_H18f zenon_H139 zenon_H201 zenon_H149 zenon_H9d zenon_H7c zenon_H22 zenon_H3a zenon_H95 zenon_H208 zenon_H74 zenon_H1ed zenon_H3f zenon_H23 zenon_H3e zenon_H94 zenon_H182. % 18.65/18.82 apply (zenon_or_s _ _ zenon_H178); [ zenon_intro zenon_H25 | zenon_intro zenon_H86 ]. % 18.65/18.82 apply (zenon_L488_); trivial. % 18.65/18.82 apply (zenon_L123_); trivial. % 18.65/18.82 (* end of lemma zenon_L489_ *) % 18.65/18.82 assert (zenon_L490_ : ((op (e2) (e0)) = (e1)) -> ((op (e0) (e0)) = (e2)) -> (~((e1) = (op (op (e0) (e0)) (e0)))) -> False). % 18.65/18.82 do 0 intro. intros zenon_Hed zenon_H7b zenon_H1e4. % 18.65/18.82 elim (classic ((op (op (e0) (e0)) (e0)) = (op (op (e0) (e0)) (e0)))); [ zenon_intro zenon_H88 | zenon_intro zenon_H89 ]. % 18.65/18.82 cut (((op (op (e0) (e0)) (e0)) = (op (op (e0) (e0)) (e0))) = ((e1) = (op (op (e0) (e0)) (e0)))). % 18.65/18.82 intro zenon_D_pnotp. % 18.65/18.82 apply zenon_H1e4. % 18.65/18.82 rewrite <- zenon_D_pnotp. % 18.65/18.82 exact zenon_H88. % 18.65/18.82 cut (((op (op (e0) (e0)) (e0)) = (op (op (e0) (e0)) (e0)))); [idtac | apply NNPP; zenon_intro zenon_H89]. % 18.65/18.82 cut (((op (op (e0) (e0)) (e0)) = (e1))); [idtac | apply NNPP; zenon_intro zenon_H1e5]. % 18.65/18.82 congruence. % 18.65/18.82 cut (((op (e2) (e0)) = (e1)) = ((op (op (e0) (e0)) (e0)) = (e1))). % 18.65/18.82 intro zenon_D_pnotp. % 18.65/18.82 apply zenon_H1e5. % 18.65/18.82 rewrite <- zenon_D_pnotp. % 18.65/18.82 exact zenon_Hed. % 18.65/18.82 cut (((e1) = (e1))); [idtac | apply NNPP; zenon_intro zenon_H79]. % 18.65/18.82 cut (((op (e2) (e0)) = (op (op (e0) (e0)) (e0)))); [idtac | apply NNPP; zenon_intro zenon_H1f5]. % 18.65/18.82 congruence. % 18.65/18.82 elim (classic ((op (op (e0) (e0)) (e0)) = (op (op (e0) (e0)) (e0)))); [ zenon_intro zenon_H88 | zenon_intro zenon_H89 ]. % 18.65/18.82 cut (((op (op (e0) (e0)) (e0)) = (op (op (e0) (e0)) (e0))) = ((op (e2) (e0)) = (op (op (e0) (e0)) (e0)))). % 18.65/18.82 intro zenon_D_pnotp. % 18.65/18.82 apply zenon_H1f5. % 18.65/18.82 rewrite <- zenon_D_pnotp. % 18.65/18.82 exact zenon_H88. % 18.65/18.82 cut (((op (op (e0) (e0)) (e0)) = (op (op (e0) (e0)) (e0)))); [idtac | apply NNPP; zenon_intro zenon_H89]. % 18.65/18.82 cut (((op (op (e0) (e0)) (e0)) = (op (e2) (e0)))); [idtac | apply NNPP; zenon_intro zenon_H1f4]. % 18.65/18.82 congruence. % 18.65/18.82 apply (zenon_L306_); trivial. % 18.65/18.82 apply zenon_H89. apply refl_equal. % 18.65/18.82 apply zenon_H89. apply refl_equal. % 18.65/18.82 apply zenon_H79. apply refl_equal. % 18.65/18.82 apply zenon_H89. apply refl_equal. % 18.65/18.82 apply zenon_H89. apply refl_equal. % 18.65/18.82 (* end of lemma zenon_L490_ *) % 18.65/18.82 assert (zenon_L491_ : ((op (e1) (e0)) = (e3)) -> ((op (e2) (e0)) = (e1)) -> ((op (e0) (e0)) = (e2)) -> False). % 18.65/18.82 do 0 intro. intros zenon_H9e zenon_Hed zenon_H7b. % 18.65/18.82 apply (zenon_notand_s _ _ ax10); [ zenon_intro zenon_H8d | zenon_intro zenon_H234 ]. % 18.65/18.82 elim (classic ((op (op (op (e0) (e0)) (e0)) (e0)) = (op (op (op (e0) (e0)) (e0)) (e0)))); [ zenon_intro zenon_H8e | zenon_intro zenon_H8f ]. % 18.65/18.82 cut (((op (op (op (e0) (e0)) (e0)) (e0)) = (op (op (op (e0) (e0)) (e0)) (e0))) = ((e3) = (op (op (op (e0) (e0)) (e0)) (e0)))). % 18.65/18.82 intro zenon_D_pnotp. % 18.65/18.82 apply zenon_H8d. % 18.65/18.82 rewrite <- zenon_D_pnotp. % 18.65/18.82 exact zenon_H8e. % 18.65/18.82 cut (((op (op (op (e0) (e0)) (e0)) (e0)) = (op (op (op (e0) (e0)) (e0)) (e0)))); [idtac | apply NNPP; zenon_intro zenon_H8f]. % 18.65/18.82 cut (((op (op (op (e0) (e0)) (e0)) (e0)) = (e3))); [idtac | apply NNPP; zenon_intro zenon_H90]. % 18.65/18.82 congruence. % 18.65/18.82 cut (((op (e1) (e0)) = (e3)) = ((op (op (op (e0) (e0)) (e0)) (e0)) = (e3))). % 18.65/18.82 intro zenon_D_pnotp. % 18.65/18.82 apply zenon_H90. % 18.65/18.82 rewrite <- zenon_D_pnotp. % 18.65/18.82 exact zenon_H9e. % 18.65/18.82 cut (((e3) = (e3))); [idtac | apply NNPP; zenon_intro zenon_H85]. % 18.65/18.82 cut (((op (e1) (e0)) = (op (op (op (e0) (e0)) (e0)) (e0)))); [idtac | apply NNPP; zenon_intro zenon_H1e8]. % 18.65/18.82 congruence. % 18.65/18.82 elim (classic ((op (op (op (e0) (e0)) (e0)) (e0)) = (op (op (op (e0) (e0)) (e0)) (e0)))); [ zenon_intro zenon_H8e | zenon_intro zenon_H8f ]. % 18.65/18.82 cut (((op (op (op (e0) (e0)) (e0)) (e0)) = (op (op (op (e0) (e0)) (e0)) (e0))) = ((op (e1) (e0)) = (op (op (op (e0) (e0)) (e0)) (e0)))). % 18.65/18.82 intro zenon_D_pnotp. % 18.65/18.82 apply zenon_H1e8. % 18.65/18.82 rewrite <- zenon_D_pnotp. % 18.65/18.82 exact zenon_H8e. % 18.65/18.82 cut (((op (op (op (e0) (e0)) (e0)) (e0)) = (op (op (op (e0) (e0)) (e0)) (e0)))); [idtac | apply NNPP; zenon_intro zenon_H8f]. % 18.65/18.82 cut (((op (op (op (e0) (e0)) (e0)) (e0)) = (op (e1) (e0)))); [idtac | apply NNPP; zenon_intro zenon_H1e9]. % 18.65/18.82 congruence. % 18.65/18.82 cut (((e0) = (e0))); [idtac | apply NNPP; zenon_intro zenon_H82]. % 18.65/18.82 cut (((op (op (e0) (e0)) (e0)) = (e1))); [idtac | apply NNPP; zenon_intro zenon_H1e5]. % 18.65/18.82 congruence. % 18.65/18.82 cut (((op (e2) (e0)) = (e1)) = ((op (op (e0) (e0)) (e0)) = (e1))). % 18.65/18.82 intro zenon_D_pnotp. % 18.65/18.82 apply zenon_H1e5. % 18.65/18.82 rewrite <- zenon_D_pnotp. % 18.65/18.82 exact zenon_Hed. % 18.65/18.82 cut (((e1) = (e1))); [idtac | apply NNPP; zenon_intro zenon_H79]. % 18.65/18.82 cut (((op (e2) (e0)) = (op (op (e0) (e0)) (e0)))); [idtac | apply NNPP; zenon_intro zenon_H1f5]. % 18.65/18.82 congruence. % 18.65/18.82 elim (classic ((op (op (e0) (e0)) (e0)) = (op (op (e0) (e0)) (e0)))); [ zenon_intro zenon_H88 | zenon_intro zenon_H89 ]. % 18.65/18.82 cut (((op (op (e0) (e0)) (e0)) = (op (op (e0) (e0)) (e0))) = ((op (e2) (e0)) = (op (op (e0) (e0)) (e0)))). % 18.65/18.82 intro zenon_D_pnotp. % 18.65/18.82 apply zenon_H1f5. % 18.65/18.82 rewrite <- zenon_D_pnotp. % 18.65/18.82 exact zenon_H88. % 18.65/18.82 cut (((op (op (e0) (e0)) (e0)) = (op (op (e0) (e0)) (e0)))); [idtac | apply NNPP; zenon_intro zenon_H89]. % 18.65/18.82 cut (((op (op (e0) (e0)) (e0)) = (op (e2) (e0)))); [idtac | apply NNPP; zenon_intro zenon_H1f4]. % 18.65/18.82 congruence. % 18.65/18.82 apply (zenon_L306_); trivial. % 18.65/18.82 apply zenon_H89. apply refl_equal. % 18.65/18.82 apply zenon_H89. apply refl_equal. % 18.65/18.82 apply zenon_H79. apply refl_equal. % 18.65/18.82 apply zenon_H82. apply refl_equal. % 18.65/18.82 apply zenon_H8f. apply refl_equal. % 18.65/18.82 apply zenon_H8f. apply refl_equal. % 18.65/18.82 apply zenon_H85. apply refl_equal. % 18.65/18.82 apply zenon_H8f. apply refl_equal. % 18.65/18.82 apply zenon_H8f. apply refl_equal. % 18.65/18.82 apply (zenon_notand_s _ _ zenon_H234); [ zenon_intro zenon_H1e4 | zenon_intro zenon_H1f9 ]. % 18.65/18.82 apply (zenon_L490_); trivial. % 18.65/18.82 apply zenon_H1f9. apply sym_equal. exact zenon_H7b. % 18.65/18.82 (* end of lemma zenon_L491_ *) % 18.65/18.82 assert (zenon_L492_ : (((op (e0) (e0)) = (e1))\/(((op (e1) (e0)) = (e1))\/(((op (e2) (e0)) = (e1))\/((op (e3) (e0)) = (e1))))) -> ((~((op (e2) (e1)) = (e0)))\/((op (e2) (e0)) = (e1))) -> ((~((op (e2) (e3)) = (e0)))\/((op (e2) (e0)) = (e3))) -> (((op (e0) (e0)) = (e0))\/(((op (e1) (e0)) = (e0))\/(((op (e2) (e0)) = (e0))\/((op (e3) (e0)) = (e0))))) -> (~((op (e1) (e0)) = (e0))) -> (~((op (e0) (e0)) = (e0))) -> ((~((op (e3) (e1)) = (e0)))\/((op (e3) (e0)) = (e1))) -> (((op (e0) (e0)) = (e0))\/(((op (e0) (e1)) = (e0))\/(((op (e0) (e2)) = (e0))\/((op (e0) (e3)) = (e0))))) -> (~((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))))) -> (~((e1) = (e2))) -> (~((e0) = (e2))) -> (~((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 (e3) (e2)))) -> (~((op (e2) (e2)) = (e2))) -> (((op (e2) (e2)) = (e0))\/(((op (e2) (e2)) = (e1))\/(((op (e2) (e2)) = (e2))\/((op (e2) (e2)) = (e3))))) -> (~((op (e2) (e0)) = (op (e2) (e2)))) -> (~((op (e0) (e1)) = (op (e2) (e1)))) -> (~((e0) = (e3))) -> (~((e2) = (e3))) -> (((op (e3) (e0)) = (e1))\/(((op (e3) (e1)) = (e1))\/(((op (e3) (e2)) = (e1))\/((op (e3) (e3)) = (e1))))) -> (~((op (e1) (e3)) = (op (e3) (e3)))) -> (~((op (e1) (e3)) = (op (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 (e1) (e1)) = (e1))) -> (((op (e2) (e0)) = (e2))\/(((op (e2) (e1)) = (e2))\/(((op (e2) (e2)) = (e2))\/((op (e2) (e3)) = (e2))))) -> (((op (e0) (e1)) = (e3))\/(((op (e1) (e1)) = (e3))\/(((op (e2) (e1)) = (e3))\/((op (e3) (e1)) = (e3))))) -> (~((op (e3) (e1)) = (op (e3) (e2)))) -> (((op (e0) (e2)) = (e3))\/(((op (e1) (e2)) = (e3))\/(((op (e2) (e2)) = (e3))\/((op (e3) (e2)) = (e3))))) -> (((op (e0) (e1)) = (e0))\/(((op (e0) (e1)) = (e1))\/(((op (e0) (e1)) = (e2))\/((op (e0) (e1)) = (e3))))) -> (~((op (e0) (e1)) = (op (e1) (e1)))) -> (~((op (e1) (e1)) = (op (e2) (e1)))) -> (((op (e2) (e1)) = (e0))\/(((op (e2) (e1)) = (e1))\/(((op (e2) (e1)) = (e2))\/((op (e2) (e1)) = (e3))))) -> (~((op (e0) (e3)) = (op (e3) (e3)))) -> (((op (e0) (e2)) = (e0))\/(((op (e1) (e2)) = (e0))\/(((op (e2) (e2)) = (e0))\/((op (e3) (e2)) = (e0))))) -> (~((op (e3) (e0)) = (op (e3) (e2)))) -> (~((op (e1) (e1)) = (op (e1) (e2)))) -> (~((op (e1) (e2)) = (op (e2) (e2)))) -> (((op (e3) (e0)) = (e2))\/(((op (e3) (e1)) = (e2))\/(((op (e3) (e2)) = (e2))\/((op (e3) (e3)) = (e2))))) -> (((op (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) (e3)) = (e3))) -> (~((op (e3) (e2)) = (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 (e1) (e1)) = (op (e3) (e1)))) -> (((op (e1) (e0)) = (e2))\/(((op (e1) (e1)) = (e2))\/(((op (e1) (e2)) = (e2))\/((op (e1) (e3)) = (e2))))) -> (~((op (e0) (e0)) = (op (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) (e3)) = (e2))\/(((op (e1) (e3)) = (e2))\/(((op (e2) (e3)) = (e2))\/((op (e3) (e3)) = (e2))))) -> (((op (e2) (e0)) = (e1))\/(((op (e2) (e1)) = (e1))\/(((op (e2) (e2)) = (e1))\/((op (e2) (e3)) = (e1))))) -> (((op (e0) (e1)) = (e1))\/(((op (e1) (e1)) = (e1))\/(((op (e2) (e1)) = (e1))\/((op (e3) (e1)) = (e1))))) -> (~((op (e0) (e3)) = (op (e2) (e3)))) -> (((op (e1) (e3)) = (e0))\/(((op (e1) (e3)) = (e1))\/(((op (e1) (e3)) = (e2))\/((op (e1) (e3)) = (e3))))) -> (~((op (e2) (e1)) = (op (e3) (e1)))) -> (((op (e3) (e1)) = (e0))\/(((op (e3) (e1)) = (e1))\/(((op (e3) (e1)) = (e2))\/((op (e3) (e1)) = (e3))))) -> (((op (e2) (e3)) = (e0))\/(((op (e2) (e3)) = (e1))\/(((op (e2) (e3)) = (e2))\/((op (e2) (e3)) = (e3))))) -> (~((op (e2) (e3)) = (op (e3) (e3)))) -> (~((op (e1) (e2)) = (op (e3) (e2)))) -> (~((op (e0) (e1)) = (op (e0) (e2)))) -> (~((op (e0) (e1)) = (op (e3) (e1)))) -> (~((op (e0) (e1)) = (op (e0) (e3)))) -> (~((op (e1) (e0)) = (op (e1) (e3)))) -> (~((op (e2) (e2)) = (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 (e0) (e0)) = (op (e2) (e0)))) -> (((op (e0) (e0)) = (e1))\/(((op (e0) (e1)) = (e1))\/(((op (e0) (e2)) = (e1))\/((op (e0) (e3)) = (e1))))) -> (~((op (e0) (e1)) = (e0))) -> ((~((op (e3) (e2)) = (e0)))\/((op (e3) (e0)) = (e2))) -> ((~((op (e3) (e0)) = (e0)))\/((op (e3) (e0)) = (e0))) -> (((op (e2) (e0)) = (e0))\/(((op (e2) (e1)) = (e0))\/(((op (e2) (e2)) = (e0))\/((op (e2) (e3)) = (e0))))) -> ((~((op (e2) (e2)) = (e0)))\/((op (e2) (e0)) = (e2))) -> (((op (e3) (e0)) = (e3))\/(((op (e3) (e1)) = (e3))\/(((op (e3) (e2)) = (e3))\/((op (e3) (e3)) = (e3))))) -> (~((op (e0) (e2)) = (op (e2) (e2)))) -> ((~((op (e3) (e3)) = (e0)))\/((op (e3) (e0)) = (e3))) -> ((~((op (e0) (e3)) = (e0)))\/((op (e0) (e0)) = (e3))) -> ((~((op (e1) (e1)) = (e0)))\/((op (e1) (e0)) = (e1))) -> (((op (e3) (e2)) = (e0))\/(((op (e3) (e2)) = (e1))\/(((op (e3) (e2)) = (e2))\/((op (e3) (e2)) = (e3))))) -> (~((op (e0) (e2)) = (op (e1) (e2)))) -> (((op (e1) (e2)) = (e0))\/(((op (e1) (e2)) = (e1))\/(((op (e1) (e2)) = (e2))\/((op (e1) (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 (e2) (e0)) = (op (e3) (e0)))) -> ((~((op (e1) (e2)) = (e0)))\/((op (e1) (e0)) = (e2))) -> ((~((op (e1) (e3)) = (e0)))\/((op (e1) (e0)) = (e3))) -> (((op (e1) (e1)) = (e0))\/(((op (e1) (e1)) = (e1))\/(((op (e1) (e1)) = (e2))\/((op (e1) (e1)) = (e3))))) -> (~((op (e0) (e0)) = (op (e0) (e2)))) -> (((op (e1) (e0)) = (e1))\/(((op (e1) (e1)) = (e1))\/(((op (e1) (e2)) = (e1))\/((op (e1) (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 (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 (e2) (e0)) = (e0)))\/((op (e2) (e0)) = (e0))) -> (((op (e0) (e0)) = (e3))\/(((op (e1) (e0)) = (e3))\/(((op (e2) (e0)) = (e3))\/((op (e3) (e0)) = (e3))))) -> (((op (e0) (e2)) = (e0))\/(((op (e0) (e2)) = (e1))\/(((op (e0) (e2)) = (e2))\/((op (e0) (e2)) = (e3))))) -> (~((op (e1) (e0)) = (op (e3) (e0)))) -> (~((op (e2) (e0)) = (op (e2) (e1)))) -> ((~((op (e1) (e0)) = (e0)))\/((op (e1) (e0)) = (e0))) -> ((~((op (e0) (e2)) = (e0)))\/((op (e0) (e0)) = (e2))) -> (~((op (e3) (e0)) = (op (e3) (e1)))) -> (~((op (e1) (e1)) = (op (e1) (e3)))) -> (~((op (e2) (e0)) = (op (e2) (e3)))) -> (((op (e0) (e3)) = (e0))\/(((op (e1) (e3)) = (e0))\/(((op (e2) (e3)) = (e0))\/((op (e3) (e3)) = (e0))))) -> (~((op (e1) (e0)) = (op (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) (e0)) = (e2)) -> ((op (e1) (e0)) = (e3)) -> ((op (e3) (e0)) = (e0)) -> (~((e0) = (e1))) -> False). % 18.65/18.82 do 0 intro. intros zenon_H235 zenon_H182 zenon_H94 zenon_H3e zenon_H23 zenon_H3f zenon_H1ed zenon_H74 zenon_H208 zenon_H95 zenon_H3a zenon_H22 zenon_H7c zenon_H149 zenon_H201 zenon_H139 zenon_H18f zenon_H173 zenon_H1c4 zenon_H52 zenon_H17e zenon_H9a zenon_H12b zenon_He8 zenon_Hd5 zenon_Hdb zenon_He4 zenon_H1d zenon_H10a zenon_H1d5 zenon_H1a5 zenon_H1a4 zenon_H1a6 zenon_H212 zenon_H10e zenon_H13e zenon_H1cc zenon_Hc2 zenon_H6a zenon_H6f zenon_H4f zenon_H2b zenon_H153 zenon_H16f zenon_H101 zenon_H102 zenon_H62 zenon_H130 zenon_H172 zenon_H160 zenon_H18c zenon_H189 zenon_H1d8 zenon_H1c7 zenon_H145 zenon_H106 zenon_H109 zenon_He2 zenon_Hdf zenon_Haf zenon_H22a zenon_H11f zenon_Hf3 zenon_H115 zenon_H4a zenon_H210 zenon_H54 zenon_Hd8 zenon_H6d zenon_H71 zenon_H133 zenon_H39 zenon_H22d zenon_H20b zenon_H1a7 zenon_H184 zenon_H2f zenon_H185 zenon_H165 zenon_Ha8 zenon_H1ec zenon_H204 zenon_H205 zenon_H191 zenon_H195 zenon_H19d zenon_He7 zenon_H183 zenon_H17b zenon_H178 zenon_H179 zenon_H142 zenon_H13c zenon_H128 zenon_H136 zenon_H124 zenon_H168 zenon_H1fe zenon_H1ee zenon_H1e0 zenon_H1ba zenon_H1fa zenon_H1f0 zenon_H206 zenon_H233 zenon_H1cf zenon_H57 zenon_H5b zenon_H67 zenon_H45 zenon_H14f zenon_H1ac zenon_H7b zenon_H9e zenon_H44 zenon_Ha1. % 18.65/18.82 apply (zenon_or_s _ _ zenon_H235); [ zenon_intro zenon_H7a | zenon_intro zenon_H236 ]. % 18.65/18.82 apply (zenon_L35_); trivial. % 18.65/18.82 apply (zenon_or_s _ _ zenon_H236); [ zenon_intro zenon_H9d | zenon_intro zenon_H237 ]. % 18.65/18.82 apply (zenon_L489_); trivial. % 18.65/18.82 apply (zenon_or_s _ _ zenon_H237); [ zenon_intro zenon_Hed | zenon_intro zenon_Hac ]. % 18.65/18.82 apply (zenon_L491_); trivial. % 18.65/18.82 apply (zenon_L41_); trivial. % 18.65/18.82 (* end of lemma zenon_L492_ *) % 18.65/18.82 assert (zenon_L493_ : (~((e1) = (e3))) -> ((op (e0) (e0)) = (e3)) -> (((op (e3) (e0)) = (e0))\/(((op (e3) (e1)) = (e0))\/(((op (e3) (e2)) = (e0))\/((op (e3) (e3)) = (e0))))) -> (~((op (e0) (e2)) = (op (e3) (e2)))) -> (~((op (e1) (e0)) = (op (e1) (e1)))) -> (((op (e0) (e3)) = (e0))\/(((op (e1) (e3)) = (e0))\/(((op (e2) (e3)) = (e0))\/((op (e3) (e3)) = (e0))))) -> (~((op (e2) (e0)) = (op (e2) (e3)))) -> (~((op (e1) (e1)) = (op (e1) (e3)))) -> (~((op (e3) (e0)) = (op (e3) (e1)))) -> ((~((op (e0) (e2)) = (e0)))\/((op (e0) (e0)) = (e2))) -> ((~((op (e1) (e0)) = (e0)))\/((op (e1) (e0)) = (e0))) -> (~((op (e2) (e0)) = (op (e2) (e1)))) -> (~((op (e1) (e0)) = (op (e3) (e0)))) -> (((op (e0) (e2)) = (e0))\/(((op (e0) (e2)) = (e1))\/(((op (e0) (e2)) = (e2))\/((op (e0) (e2)) = (e3))))) -> (((op (e0) (e0)) = (e3))\/(((op (e1) (e0)) = (e3))\/(((op (e2) (e0)) = (e3))\/((op (e3) (e0)) = (e3))))) -> ((~((op (e2) (e0)) = (e0)))\/((op (e2) (e0)) = (e0))) -> (((op (e0) (e0)) = (e2))\/(((op (e1) (e0)) = (e2))\/(((op (e2) (e0)) = (e2))\/((op (e3) (e0)) = (e2))))) -> (((op (e0) (e0)) = (e3))\/(((op (e0) (e1)) = (e3))\/(((op (e0) (e2)) = (e3))\/((op (e0) (e3)) = (e3))))) -> (~((op (e1) (e2)) = (op (e1) (e3)))) -> (((op (e0) (e3)) = (e3))\/(((op (e1) (e3)) = (e3))\/(((op (e2) (e3)) = (e3))\/((op (e3) (e3)) = (e3))))) -> (((op (e1) (e0)) = (e1))\/(((op (e1) (e1)) = (e1))\/(((op (e1) (e2)) = (e1))\/((op (e1) (e3)) = (e1))))) -> (~((op (e0) (e0)) = (op (e0) (e2)))) -> (((op (e1) (e1)) = (e0))\/(((op (e1) (e1)) = (e1))\/(((op (e1) (e1)) = (e2))\/((op (e1) (e1)) = (e3))))) -> ((~((op (e1) (e3)) = (e0)))\/((op (e1) (e0)) = (e3))) -> ((~((op (e1) (e2)) = (e0)))\/((op (e1) (e0)) = (e2))) -> (~((op (e2) (e0)) = (op (e3) (e0)))) -> (((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) (e2)) = (e0))\/(((op (e1) (e2)) = (e1))\/(((op (e1) (e2)) = (e2))\/((op (e1) (e2)) = (e3))))) -> (~((op (e0) (e2)) = (op (e1) (e2)))) -> (((op (e3) (e2)) = (e0))\/(((op (e3) (e2)) = (e1))\/(((op (e3) (e2)) = (e2))\/((op (e3) (e2)) = (e3))))) -> ((~((op (e1) (e1)) = (e0)))\/((op (e1) (e0)) = (e1))) -> ((~((op (e0) (e3)) = (e0)))\/((op (e0) (e0)) = (e3))) -> ((~((op (e3) (e3)) = (e0)))\/((op (e3) (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 (e2) (e2)) = (e0)))\/((op (e2) (e0)) = (e2))) -> (((op (e2) (e0)) = (e0))\/(((op (e2) (e1)) = (e0))\/(((op (e2) (e2)) = (e0))\/((op (e2) (e3)) = (e0))))) -> ((~((op (e3) (e0)) = (e0)))\/((op (e3) (e0)) = (e0))) -> ((~((op (e3) (e2)) = (e0)))\/((op (e3) (e0)) = (e2))) -> (~((op (e0) (e1)) = (e0))) -> (((op (e0) (e0)) = (e1))\/(((op (e0) (e1)) = (e1))\/(((op (e0) (e2)) = (e1))\/((op (e0) (e3)) = (e1))))) -> (~((op (e0) (e0)) = (op (e2) (e0)))) -> ((op (e0) (e0)) = (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) (e2)) = (op (e2) (e3)))) -> (~((op (e1) (e0)) = (op (e1) (e3)))) -> (~((op (e0) (e1)) = (op (e0) (e3)))) -> (~((op (e0) (e1)) = (op (e3) (e1)))) -> (~((op (e0) (e1)) = (op (e0) (e2)))) -> (~((op (e1) (e2)) = (op (e3) (e2)))) -> (~((op (e2) (e3)) = (op (e3) (e3)))) -> (((op (e2) (e3)) = (e0))\/(((op (e2) (e3)) = (e1))\/(((op (e2) (e3)) = (e2))\/((op (e2) (e3)) = (e3))))) -> (((op (e3) (e1)) = (e0))\/(((op (e3) (e1)) = (e1))\/(((op (e3) (e1)) = (e2))\/((op (e3) (e1)) = (e3))))) -> (~((op (e2) (e1)) = (op (e3) (e1)))) -> (((op (e1) (e3)) = (e0))\/(((op (e1) (e3)) = (e1))\/(((op (e1) (e3)) = (e2))\/((op (e1) (e3)) = (e3))))) -> (~((op (e0) (e3)) = (op (e2) (e3)))) -> (((op (e0) (e1)) = (e1))\/(((op (e1) (e1)) = (e1))\/(((op (e2) (e1)) = (e1))\/((op (e3) (e1)) = (e1))))) -> (((op (e2) (e0)) = (e1))\/(((op (e2) (e1)) = (e1))\/(((op (e2) (e2)) = (e1))\/((op (e2) (e3)) = (e1))))) -> (((op (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)) = (op (e0) (e3)))) -> (((op (e1) (e0)) = (e2))\/(((op (e1) (e1)) = (e2))\/(((op (e1) (e2)) = (e2))\/((op (e1) (e3)) = (e2))))) -> (~((op (e1) (e1)) = (op (e3) (e1)))) -> (((op (e0) (e2)) = (e2))\/(((op (e1) (e2)) = (e2))\/(((op (e2) (e2)) = (e2))\/((op (e3) (e2)) = (e2))))) -> (~((op (e3) (e1)) = (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) (e0)) = (e3))\/(((op (e1) (e1)) = (e3))\/(((op (e1) (e2)) = (e3))\/((op (e1) (e3)) = (e3))))) -> (((op (e3) (e0)) = (e2))\/(((op (e3) (e1)) = (e2))\/(((op (e3) (e2)) = (e2))\/((op (e3) (e3)) = (e2))))) -> (~((op (e1) (e2)) = (op (e2) (e2)))) -> (~((op (e1) (e1)) = (op (e1) (e2)))) -> (~((op (e3) (e0)) = (op (e3) (e2)))) -> (((op (e0) (e2)) = (e0))\/(((op (e1) (e2)) = (e0))\/(((op (e2) (e2)) = (e0))\/((op (e3) (e2)) = (e0))))) -> (~((op (e0) (e3)) = (op (e3) (e3)))) -> (((op (e2) (e1)) = (e0))\/(((op (e2) (e1)) = (e1))\/(((op (e2) (e1)) = (e2))\/((op (e2) (e1)) = (e3))))) -> (~((op (e1) (e1)) = (op (e2) (e1)))) -> (~((op (e0) (e1)) = (op (e1) (e1)))) -> (((op (e0) (e1)) = (e0))\/(((op (e0) (e1)) = (e1))\/(((op (e0) (e1)) = (e2))\/((op (e0) (e1)) = (e3))))) -> (((op (e0) (e2)) = (e3))\/(((op (e1) (e2)) = (e3))\/(((op (e2) (e2)) = (e3))\/((op (e3) (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 (e2) (e0)) = (e2))\/(((op (e2) (e1)) = (e2))\/(((op (e2) (e2)) = (e2))\/((op (e2) (e3)) = (e2))))) -> (~((op (e1) (e1)) = (e1))) -> (~((op (e0) (e3)) = (op (e1) (e3)))) -> (((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 (e3) (e0)) = (e1))\/(((op (e3) (e1)) = (e1))\/(((op (e3) (e2)) = (e1))\/((op (e3) (e3)) = (e1))))) -> (~((e2) = (e3))) -> (~((e0) = (e3))) -> (~((op (e0) (e1)) = (op (e2) (e1)))) -> (~((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) (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 (e1) (e0)) = (op (e2) (e0)))) -> (~((e0) = (e2))) -> (~((e1) = (e2))) -> (((op (e1) (e0)) = (e0))\/(((op (e1) (e1)) = (e0))\/(((op (e1) (e2)) = (e0))\/((op (e1) (e3)) = (e0))))) -> (~((op (e0) (e2)) = (op (e0) (e3)))) -> (((op (e0) (e0)) = (e0))\/(((op (e0) (e1)) = (e0))\/(((op (e0) (e2)) = (e0))\/((op (e0) (e3)) = (e0))))) -> ((~((op (e3) (e1)) = (e0)))\/((op (e3) (e0)) = (e1))) -> ((~((op (e2) (e3)) = (e0)))\/((op (e2) (e0)) = (e3))) -> ((~((op (e2) (e1)) = (e0)))\/((op (e2) (e0)) = (e1))) -> ((op (e1) (e0)) = (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 (e0) (e0)) = (e0))\/(((op (e1) (e0)) = (e0))\/(((op (e2) (e0)) = (e0))\/((op (e3) (e0)) = (e0))))) -> False). % 18.65/18.82 do 0 intro. intros zenon_H95 zenon_H3a zenon_H1ac zenon_H14f zenon_H45 zenon_H67 zenon_H5b zenon_H57 zenon_H1cf zenon_H233 zenon_H206 zenon_H1f0 zenon_H1fa zenon_H1ba zenon_H1e0 zenon_H1ee zenon_H1fe zenon_H168 zenon_H124 zenon_H136 zenon_H128 zenon_H13c zenon_H142 zenon_H179 zenon_H178 zenon_H17b zenon_H183 zenon_He7 zenon_H19d zenon_H195 zenon_H191 zenon_H205 zenon_H204 zenon_H1ec zenon_Ha8 zenon_H165 zenon_H185 zenon_H2f zenon_H184 zenon_H1a7 zenon_H20b zenon_H22d zenon_H39 zenon_H7b zenon_H133 zenon_H71 zenon_H6d zenon_Hd8 zenon_H54 zenon_H210 zenon_H4a zenon_H115 zenon_Hf3 zenon_H11f zenon_H22a zenon_Haf zenon_Hdf zenon_He2 zenon_H109 zenon_H106 zenon_H145 zenon_H1c7 zenon_H1d8 zenon_H189 zenon_H18c zenon_H160 zenon_H172 zenon_H130 zenon_H62 zenon_H102 zenon_H101 zenon_H16f zenon_H153 zenon_H2b zenon_H4f zenon_H6f zenon_H6a zenon_Hc2 zenon_H1cc zenon_H13e zenon_H10e zenon_H212 zenon_H1a6 zenon_H1a4 zenon_H1a5 zenon_H1d5 zenon_H10a zenon_H1d zenon_He4 zenon_Hdb zenon_Hd5 zenon_He8 zenon_H12b zenon_H9a zenon_H17e zenon_Ha1 zenon_H52 zenon_H1c4 zenon_H173 zenon_H18f zenon_H139 zenon_H201 zenon_H149 zenon_H7c zenon_H22 zenon_H208 zenon_H74 zenon_H1ed zenon_H94 zenon_H182 zenon_H9e zenon_H235 zenon_H3f zenon_H23 zenon_H30 zenon_H3e. % 18.65/18.82 apply (zenon_or_s _ _ zenon_H184); [ zenon_intro zenon_H40 | zenon_intro zenon_H44 ]. % 18.65/18.82 apply (zenon_L7_); trivial. % 18.65/18.82 apply (zenon_L492_); trivial. % 18.65/18.82 (* end of lemma zenon_L493_ *) % 18.65/18.82 assert (zenon_L494_ : (((op (e0) (e0)) = (e1))\/(((op (e1) (e0)) = (e1))\/(((op (e2) (e0)) = (e1))\/((op (e3) (e0)) = (e1))))) -> ((~((op (e2) (e1)) = (e0)))\/((op (e2) (e0)) = (e1))) -> ((~((op (e2) (e3)) = (e0)))\/((op (e2) (e0)) = (e3))) -> (((op (e0) (e0)) = (e0))\/(((op (e1) (e0)) = (e0))\/(((op (e2) (e0)) = (e0))\/((op (e3) (e0)) = (e0))))) -> (~((op (e1) (e0)) = (e0))) -> (~((op (e0) (e0)) = (e0))) -> ((~((op (e3) (e1)) = (e0)))\/((op (e3) (e0)) = (e1))) -> (((op (e0) (e0)) = (e0))\/(((op (e0) (e1)) = (e0))\/(((op (e0) (e2)) = (e0))\/((op (e0) (e3)) = (e0))))) -> (~((op (e0) (e2)) = (op (e0) (e3)))) -> (~((e1) = (e3))) -> (((op (e1) (e0)) = (e0))\/(((op (e1) (e1)) = (e0))\/(((op (e1) (e2)) = (e0))\/((op (e1) (e3)) = (e0))))) -> (~((e1) = (e2))) -> (~((e0) = (e2))) -> (~((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 (e3) (e2)))) -> (~((op (e2) (e2)) = (e2))) -> (((op (e2) (e2)) = (e0))\/(((op (e2) (e2)) = (e1))\/(((op (e2) (e2)) = (e2))\/((op (e2) (e2)) = (e3))))) -> (~((op (e2) (e0)) = (op (e2) (e2)))) -> (~((op (e0) (e1)) = (op (e2) (e1)))) -> (~((e0) = (e3))) -> (~((e2) = (e3))) -> (((op (e3) (e0)) = (e1))\/(((op (e3) (e1)) = (e1))\/(((op (e3) (e2)) = (e1))\/((op (e3) (e3)) = (e1))))) -> (~((op (e1) (e3)) = (op (e3) (e3)))) -> (~((op (e1) (e3)) = (op (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 (e1) (e1)) = (e1))) -> (((op (e2) (e0)) = (e2))\/(((op (e2) (e1)) = (e2))\/(((op (e2) (e2)) = (e2))\/((op (e2) (e3)) = (e2))))) -> (((op (e0) (e1)) = (e3))\/(((op (e1) (e1)) = (e3))\/(((op (e2) (e1)) = (e3))\/((op (e3) (e1)) = (e3))))) -> (~((op (e3) (e1)) = (op (e3) (e2)))) -> (((op (e0) (e2)) = (e3))\/(((op (e1) (e2)) = (e3))\/(((op (e2) (e2)) = (e3))\/((op (e3) (e2)) = (e3))))) -> (((op (e0) (e1)) = (e0))\/(((op (e0) (e1)) = (e1))\/(((op (e0) (e1)) = (e2))\/((op (e0) (e1)) = (e3))))) -> (~((op (e0) (e1)) = (op (e1) (e1)))) -> (~((op (e1) (e1)) = (op (e2) (e1)))) -> (((op (e2) (e1)) = (e0))\/(((op (e2) (e1)) = (e1))\/(((op (e2) (e1)) = (e2))\/((op (e2) (e1)) = (e3))))) -> (~((op (e0) (e3)) = (op (e3) (e3)))) -> (((op (e0) (e2)) = (e0))\/(((op (e1) (e2)) = (e0))\/(((op (e2) (e2)) = (e0))\/((op (e3) (e2)) = (e0))))) -> (~((op (e3) (e0)) = (op (e3) (e2)))) -> (~((op (e1) (e1)) = (op (e1) (e2)))) -> (~((op (e1) (e2)) = (op (e2) (e2)))) -> (((op (e3) (e0)) = (e2))\/(((op (e3) (e1)) = (e2))\/(((op (e3) (e2)) = (e2))\/((op (e3) (e3)) = (e2))))) -> (((op (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) (e3)) = (e3))) -> (~((op (e3) (e2)) = (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 (e1) (e1)) = (op (e3) (e1)))) -> (((op (e1) (e0)) = (e2))\/(((op (e1) (e1)) = (e2))\/(((op (e1) (e2)) = (e2))\/((op (e1) (e3)) = (e2))))) -> (~((op (e0) (e0)) = (op (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) (e3)) = (e2))\/(((op (e1) (e3)) = (e2))\/(((op (e2) (e3)) = (e2))\/((op (e3) (e3)) = (e2))))) -> (((op (e2) (e0)) = (e1))\/(((op (e2) (e1)) = (e1))\/(((op (e2) (e2)) = (e1))\/((op (e2) (e3)) = (e1))))) -> (((op (e0) (e1)) = (e1))\/(((op (e1) (e1)) = (e1))\/(((op (e2) (e1)) = (e1))\/((op (e3) (e1)) = (e1))))) -> (~((op (e0) (e3)) = (op (e2) (e3)))) -> (((op (e1) (e3)) = (e0))\/(((op (e1) (e3)) = (e1))\/(((op (e1) (e3)) = (e2))\/((op (e1) (e3)) = (e3))))) -> (~((op (e2) (e1)) = (op (e3) (e1)))) -> (((op (e3) (e1)) = (e0))\/(((op (e3) (e1)) = (e1))\/(((op (e3) (e1)) = (e2))\/((op (e3) (e1)) = (e3))))) -> (((op (e2) (e3)) = (e0))\/(((op (e2) (e3)) = (e1))\/(((op (e2) (e3)) = (e2))\/((op (e2) (e3)) = (e3))))) -> (~((op (e2) (e3)) = (op (e3) (e3)))) -> (~((op (e1) (e2)) = (op (e3) (e2)))) -> (~((op (e0) (e1)) = (op (e0) (e2)))) -> (~((op (e0) (e1)) = (op (e3) (e1)))) -> (~((op (e0) (e1)) = (op (e0) (e3)))) -> (~((op (e1) (e0)) = (op (e1) (e3)))) -> (~((op (e2) (e2)) = (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 (e0) (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)) = (e0))) -> ((~((op (e3) (e2)) = (e0)))\/((op (e3) (e0)) = (e2))) -> ((~((op (e3) (e0)) = (e0)))\/((op (e3) (e0)) = (e0))) -> (((op (e2) (e0)) = (e0))\/(((op (e2) (e1)) = (e0))\/(((op (e2) (e2)) = (e0))\/((op (e2) (e3)) = (e0))))) -> ((~((op (e2) (e2)) = (e0)))\/((op (e2) (e0)) = (e2))) -> (((op (e3) (e0)) = (e3))\/(((op (e3) (e1)) = (e3))\/(((op (e3) (e2)) = (e3))\/((op (e3) (e3)) = (e3))))) -> (~((op (e0) (e2)) = (op (e2) (e2)))) -> ((~((op (e3) (e3)) = (e0)))\/((op (e3) (e0)) = (e3))) -> ((~((op (e0) (e3)) = (e0)))\/((op (e0) (e0)) = (e3))) -> ((~((op (e1) (e1)) = (e0)))\/((op (e1) (e0)) = (e1))) -> (((op (e3) (e2)) = (e0))\/(((op (e3) (e2)) = (e1))\/(((op (e3) (e2)) = (e2))\/((op (e3) (e2)) = (e3))))) -> (~((op (e0) (e2)) = (op (e1) (e2)))) -> (((op (e1) (e2)) = (e0))\/(((op (e1) (e2)) = (e1))\/(((op (e1) (e2)) = (e2))\/((op (e1) (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 (e2) (e0)) = (op (e3) (e0)))) -> ((~((op (e1) (e2)) = (e0)))\/((op (e1) (e0)) = (e2))) -> ((~((op (e1) (e3)) = (e0)))\/((op (e1) (e0)) = (e3))) -> (((op (e1) (e1)) = (e0))\/(((op (e1) (e1)) = (e1))\/(((op (e1) (e1)) = (e2))\/((op (e1) (e1)) = (e3))))) -> (~((op (e0) (e0)) = (op (e0) (e2)))) -> (((op (e1) (e0)) = (e1))\/(((op (e1) (e1)) = (e1))\/(((op (e1) (e2)) = (e1))\/((op (e1) (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 (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 (e2) (e0)) = (e0)))\/((op (e2) (e0)) = (e0))) -> (((op (e0) (e0)) = (e3))\/(((op (e1) (e0)) = (e3))\/(((op (e2) (e0)) = (e3))\/((op (e3) (e0)) = (e3))))) -> (((op (e0) (e2)) = (e0))\/(((op (e0) (e2)) = (e1))\/(((op (e0) (e2)) = (e2))\/((op (e0) (e2)) = (e3))))) -> (~((op (e1) (e0)) = (op (e3) (e0)))) -> (~((op (e2) (e0)) = (op (e2) (e1)))) -> ((~((op (e1) (e0)) = (e0)))\/((op (e1) (e0)) = (e0))) -> ((~((op (e0) (e2)) = (e0)))\/((op (e0) (e0)) = (e2))) -> (~((op (e3) (e0)) = (op (e3) (e1)))) -> (~((op (e1) (e1)) = (op (e1) (e3)))) -> (~((op (e2) (e0)) = (op (e2) (e3)))) -> (((op (e0) (e3)) = (e0))\/(((op (e1) (e3)) = (e0))\/(((op (e2) (e3)) = (e0))\/((op (e3) (e3)) = (e0))))) -> (~((op (e1) (e0)) = (op (e1) (e1)))) -> (~((op (e0) (e2)) = (op (e3) (e2)))) -> (((op (e3) (e0)) = (e0))\/(((op (e3) (e1)) = (e0))\/(((op (e3) (e2)) = (e0))\/((op (e3) (e3)) = (e0))))) -> (~((e0) = (e1))) -> ((op (e2) (e0)) = (e0)) -> ((op (e1) (e0)) = (e2)) -> ((op (e0) (e0)) = (e3)) -> False). % 18.65/18.82 do 0 intro. intros zenon_H235 zenon_H182 zenon_H94 zenon_H3e zenon_H23 zenon_H3f zenon_H1ed zenon_H74 zenon_H208 zenon_H95 zenon_H22 zenon_H7c zenon_H149 zenon_H201 zenon_H139 zenon_H18f zenon_H173 zenon_H1c4 zenon_H52 zenon_H17e zenon_H9a zenon_H12b zenon_He8 zenon_Hd5 zenon_Hdb zenon_He4 zenon_H1d zenon_H10a zenon_H1d5 zenon_H1a5 zenon_H1a4 zenon_H1a6 zenon_H212 zenon_H10e zenon_H13e zenon_H1cc zenon_Hc2 zenon_H6a zenon_H6f zenon_H4f zenon_H2b zenon_H153 zenon_H16f zenon_H101 zenon_H102 zenon_H62 zenon_H130 zenon_H172 zenon_H160 zenon_H18c zenon_H189 zenon_H1d8 zenon_H1c7 zenon_H145 zenon_H106 zenon_H109 zenon_He2 zenon_Hdf zenon_Haf zenon_H22a zenon_H11f zenon_Hf3 zenon_H115 zenon_H4a zenon_H210 zenon_H54 zenon_Hd8 zenon_H6d zenon_H71 zenon_H133 zenon_H7b zenon_H39 zenon_H22d zenon_H20b zenon_H1a7 zenon_H184 zenon_H2f zenon_H185 zenon_H165 zenon_Ha8 zenon_H1ec zenon_H204 zenon_H205 zenon_H191 zenon_H195 zenon_H19d zenon_He7 zenon_H183 zenon_H17b zenon_H178 zenon_H179 zenon_H142 zenon_H13c zenon_H128 zenon_H136 zenon_H124 zenon_H168 zenon_H1fe zenon_H1ee zenon_H1e0 zenon_H1ba zenon_H1fa zenon_H1f0 zenon_H206 zenon_H233 zenon_H1cf zenon_H57 zenon_H5b zenon_H67 zenon_H45 zenon_H14f zenon_H1ac zenon_Ha1 zenon_H34 zenon_H86 zenon_H3a. % 18.65/18.82 apply (zenon_or_s _ _ zenon_H235); [ zenon_intro zenon_H7a | zenon_intro zenon_H236 ]. % 18.65/18.82 apply (zenon_L35_); trivial. % 18.65/18.82 apply (zenon_or_s _ _ zenon_H236); [ zenon_intro zenon_H9d | zenon_intro zenon_H237 ]. % 18.65/18.82 apply (zenon_L489_); trivial. % 18.65/18.82 apply (zenon_or_s _ _ zenon_H237); [ zenon_intro zenon_Hed | zenon_intro zenon_Hac ]. % 18.65/18.82 apply (zenon_L214_); trivial. % 18.65/18.82 apply (zenon_L241_); trivial. % 18.65/18.82 (* end of lemma zenon_L494_ *) % 18.65/18.82 assert (zenon_L495_ : (((op (e3) (e0)) = (e3))\/(((op (e3) (e1)) = (e3))\/(((op (e3) (e2)) = (e3))\/((op (e3) (e3)) = (e3))))) -> (~((e1) = (e3))) -> ((op (e3) (e0)) = (e1)) -> ((op (e1) (e1)) = (e3)) -> (~((op (e1) (e1)) = (op (e3) (e1)))) -> ((op (e2) (e2)) = (e3)) -> (~((op (e2) (e2)) = (op (e3) (e2)))) -> (~((op (e3) (e3)) = (e3))) -> False). % 18.65/18.82 do 0 intro. intros zenon_H165 zenon_H95 zenon_Hac zenon_H13f zenon_H160 zenon_Haa zenon_H18f zenon_H102. % 18.65/18.82 apply (zenon_or_s _ _ zenon_H165); [ zenon_intro zenon_H15e | zenon_intro zenon_H166 ]. % 18.65/18.82 apply (zenon_L252_); trivial. % 18.65/18.82 apply (zenon_or_s _ _ zenon_H166); [ zenon_intro zenon_H161 | zenon_intro zenon_H167 ]. % 18.65/18.82 apply (zenon_L110_); trivial. % 18.65/18.82 apply (zenon_or_s _ _ zenon_H167); [ zenon_intro zenon_H163 | zenon_intro zenon_H105 ]. % 18.65/18.82 apply (zenon_L180_); trivial. % 18.65/18.82 exact (zenon_H102 zenon_H105). % 18.65/18.82 (* end of lemma zenon_L495_ *) % 18.65/18.82 assert (zenon_L496_ : (((op (e0) (e3)) = (e2))\/(((op (e1) (e3)) = (e2))\/(((op (e2) (e3)) = (e2))\/((op (e3) (e3)) = (e2))))) -> (~((e1) = (e2))) -> ((op (e0) (e3)) = (e1)) -> (~((op (e1) (e1)) = (op (e1) (e3)))) -> ((op (e1) (e1)) = (e2)) -> (~((op (e2) (e1)) = (op (e2) (e3)))) -> ((op (e2) (e1)) = (e2)) -> ((op (e3) (e2)) = (e2)) -> (~((op (e3) (e2)) = (op (e3) (e3)))) -> False). % 18.65/18.82 do 0 intro. intros zenon_H145 zenon_H7c zenon_Hc3 zenon_H57 zenon_H110 zenon_H1c7 zenon_H1ca zenon_H151 zenon_H62. % 18.65/18.82 apply (zenon_or_s _ _ zenon_H145); [ zenon_intro zenon_Hcd | zenon_intro zenon_H146 ]. % 18.65/18.82 apply (zenon_L82_); trivial. % 18.65/18.82 apply (zenon_or_s _ _ zenon_H146); [ zenon_intro zenon_Hd7 | zenon_intro zenon_H147 ]. % 18.65/18.82 apply (zenon_L283_); trivial. % 18.65/18.82 apply (zenon_or_s _ _ zenon_H147); [ zenon_intro zenon_H11d | zenon_intro zenon_Hf6 ]. % 18.65/18.82 apply (zenon_L224_); trivial. % 18.65/18.82 apply (zenon_L119_); trivial. % 18.65/18.82 (* end of lemma zenon_L496_ *) % 18.65/18.82 assert (zenon_L497_ : (((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 (e0) (e3)) = (e2))\/(((op (e1) (e3)) = (e2))\/(((op (e2) (e3)) = (e2))\/((op (e3) (e3)) = (e2))))) -> (~((e1) = (e2))) -> ((op (e0) (e3)) = (e1)) -> (~((op (e1) (e1)) = (op (e1) (e3)))) -> ((op (e1) (e1)) = (e2)) -> (~((op (e2) (e1)) = (op (e2) (e3)))) -> ((op (e2) (e1)) = (e2)) -> (~((op (e3) (e2)) = (op (e3) (e3)))) -> False). % 18.65/18.82 do 0 intro. intros zenon_H172 zenon_H149 zenon_H48 zenon_Hf0 zenon_H173 zenon_H145 zenon_H7c zenon_Hc3 zenon_H57 zenon_H110 zenon_H1c7 zenon_H1ca zenon_H62. % 18.65/18.82 apply (zenon_or_s _ _ zenon_H172); [ zenon_intro zenon_H150 | zenon_intro zenon_H174 ]. % 18.65/18.82 apply (zenon_L378_); trivial. % 18.65/18.82 apply (zenon_or_s _ _ zenon_H174); [ zenon_intro zenon_H113 | zenon_intro zenon_H175 ]. % 18.65/18.82 apply (zenon_L68_); trivial. % 18.65/18.82 apply (zenon_or_s _ _ zenon_H175); [ zenon_intro zenon_H176 | zenon_intro zenon_H151 ]. % 18.65/18.82 exact (zenon_H173 zenon_H176). % 18.65/18.82 apply (zenon_L496_); trivial. % 18.65/18.82 (* end of lemma zenon_L497_ *) % 18.65/18.82 assert (zenon_L498_ : (((op (e2) (e0)) = (e2))\/(((op (e2) (e1)) = (e2))\/(((op (e2) (e2)) = (e2))\/((op (e2) (e3)) = (e2))))) -> ((op (e2) (e0)) = (e0)) -> (~((op (e3) (e2)) = (op (e3) (e3)))) -> (~((op (e2) (e1)) = (op (e2) (e3)))) -> ((op (e1) (e1)) = (e2)) -> (~((op (e1) (e1)) = (op (e1) (e3)))) -> (~((e1) = (e2))) -> (((op (e0) (e3)) = (e2))\/(((op (e1) (e3)) = (e2))\/(((op (e2) (e3)) = (e2))\/((op (e3) (e3)) = (e2))))) -> ((op (e1) (e2)) = (e1)) -> ((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)) = (e2))) -> (((op (e3) (e3)) = (e0))\/(((op (e3) (e3)) = (e1))\/(((op (e3) (e3)) = (e2))\/((op (e3) (e3)) = (e3))))) -> (~((op (e3) (e1)) = (op (e3) (e3)))) -> ((op (e3) (e1)) = (e0)) -> ((op (e0) (e3)) = (e1)) -> (~((op (e0) (e3)) = (op (e3) (e3)))) -> (~((op (e2) (e3)) = (op (e3) (e3)))) -> (~((op (e3) (e3)) = (e3))) -> False). % 18.65/18.82 do 0 intro. intros zenon_H1d5 zenon_H34 zenon_H62 zenon_H1c7 zenon_H110 zenon_H57 zenon_H7c zenon_H145 zenon_Hf0 zenon_H48 zenon_H149 zenon_H172 zenon_H173 zenon_H101 zenon_H130 zenon_H1b1 zenon_Hc3 zenon_Hc2 zenon_Hf3 zenon_H102. % 18.65/18.82 apply (zenon_or_s _ _ zenon_H1d5); [ zenon_intro zenon_Hee | zenon_intro zenon_H1d6 ]. % 18.65/18.82 apply (zenon_L204_); trivial. % 18.65/18.82 apply (zenon_or_s _ _ zenon_H1d6); [ zenon_intro zenon_H1ca | zenon_intro zenon_H1d7 ]. % 18.65/18.82 apply (zenon_L497_); trivial. % 18.65/18.82 apply (zenon_or_s _ _ zenon_H1d7); [ zenon_intro zenon_H176 | zenon_intro zenon_H11d ]. % 18.65/18.82 exact (zenon_H173 zenon_H176). % 18.65/18.82 apply (zenon_L245_); trivial. % 18.65/18.82 (* end of lemma zenon_L498_ *) % 18.65/18.82 assert (zenon_L499_ : (((op (e1) (e1)) = (e0))\/(((op (e1) (e1)) = (e1))\/(((op (e1) (e1)) = (e2))\/((op (e1) (e1)) = (e3))))) -> (~((op (e1) (e1)) = (e0))) -> (~((op (e1) (e1)) = (e1))) -> (~((op (e3) (e2)) = (op (e3) (e3)))) -> ((op (e3) (e2)) = (e2)) -> ((op (e2) (e1)) = (e2)) -> (~((op (e2) (e1)) = (op (e2) (e3)))) -> (~((op (e1) (e1)) = (op (e1) (e3)))) -> ((op (e0) (e3)) = (e1)) -> (~((e1) = (e2))) -> (((op (e0) (e3)) = (e2))\/(((op (e1) (e3)) = (e2))\/(((op (e2) (e3)) = (e2))\/((op (e3) (e3)) = (e2))))) -> (~((op (e0) (e1)) = (op (e1) (e1)))) -> ((op (e0) (e1)) = (e3)) -> False). % 18.65/18.82 do 0 intro. intros zenon_H142 zenon_H24 zenon_H10a zenon_H62 zenon_H151 zenon_H1ca zenon_H1c7 zenon_H57 zenon_Hc3 zenon_H7c zenon_H145 zenon_H10e zenon_H99. % 18.65/18.82 apply (zenon_or_s _ _ zenon_H142); [ zenon_intro zenon_H29 | zenon_intro zenon_H143 ]. % 18.65/18.82 exact (zenon_H24 zenon_H29). % 18.65/18.82 apply (zenon_or_s _ _ zenon_H143); [ zenon_intro zenon_H10d | zenon_intro zenon_H144 ]. % 18.65/18.82 exact (zenon_H10a zenon_H10d). % 18.65/18.82 apply (zenon_or_s _ _ zenon_H144); [ zenon_intro zenon_H110 | zenon_intro zenon_H13f ]. % 18.65/18.82 apply (zenon_L496_); trivial. % 18.65/18.82 apply (zenon_L108_); trivial. % 18.65/18.82 (* end of lemma zenon_L499_ *) % 18.65/18.82 assert (zenon_L500_ : (((op (e3) (e3)) = (e0))\/(((op (e3) (e3)) = (e1))\/(((op (e3) (e3)) = (e2))\/((op (e3) (e3)) = (e3))))) -> ((op (e1) (e3)) = (e2)) -> ((op (e0) (e3)) = (e1)) -> (~((op (e0) (e3)) = (op (e3) (e3)))) -> (~((op (e3) (e1)) = (op (e3) (e3)))) -> ((op (e3) (e1)) = (e2)) -> (~((op (e3) (e3)) = (e3))) -> False). % 18.65/18.82 do 0 intro. intros zenon_H101 zenon_Hd7 zenon_Hc3 zenon_Hc2 zenon_H130 zenon_H14d zenon_H102. % 18.65/18.82 apply (zenon_or_s _ _ zenon_H101); [ zenon_intro zenon_H60 | zenon_intro zenon_H103 ]. % 18.65/18.82 apply (zenon_L201_); trivial. % 18.65/18.82 apply (zenon_or_s _ _ zenon_H103); [ zenon_intro zenon_Hc4 | zenon_intro zenon_H104 ]. % 18.65/18.82 apply (zenon_L46_); trivial. % 18.65/18.82 apply (zenon_or_s _ _ zenon_H104); [ zenon_intro zenon_Hf6 | zenon_intro zenon_H105 ]. % 18.65/18.82 apply (zenon_L102_); trivial. % 18.65/18.82 exact (zenon_H102 zenon_H105). % 18.65/18.82 (* end of lemma zenon_L500_ *) % 18.65/18.82 assert (zenon_L501_ : (~((op (e3) (e3)) = (e3))) -> (~((op (e3) (e1)) = (op (e3) (e3)))) -> (~((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 (e0) (e2)) = (e2))\/(((op (e1) (e2)) = (e2))\/(((op (e2) (e2)) = (e2))\/((op (e3) (e2)) = (e2))))) -> ((op (e0) (e2)) = (e0)) -> ((op (e1) (e2)) = (e1)) -> (((op (e0) (e1)) = (e0))\/(((op (e0) (e1)) = (e1))\/(((op (e0) (e1)) = (e2))\/((op (e0) (e1)) = (e3))))) -> (~((op (e0) (e1)) = (e0))) -> (~((op (e1) (e3)) = (op (e2) (e3)))) -> (~((op (e2) (e2)) = (e2))) -> (~((op (e0) (e1)) = (op (e2) (e1)))) -> ((op (e2) (e0)) = (e0)) -> (~((e0) = (e2))) -> (((op (e2) (e0)) = (e2))\/(((op (e2) (e1)) = (e2))\/(((op (e2) (e2)) = (e2))\/((op (e2) (e3)) = (e2))))) -> (((op (e1) (e1)) = (e0))\/(((op (e1) (e1)) = (e1))\/(((op (e1) (e1)) = (e2))\/((op (e1) (e1)) = (e3))))) -> (~((op (e1) (e1)) = (e0))) -> (~((op (e1) (e1)) = (e1))) -> (~((op (e3) (e2)) = (op (e3) (e3)))) -> (~((op (e2) (e1)) = (op (e2) (e3)))) -> (~((op (e1) (e1)) = (op (e1) (e3)))) -> (~((e1) = (e2))) -> (((op (e0) (e3)) = (e2))\/(((op (e1) (e3)) = (e2))\/(((op (e2) (e3)) = (e2))\/((op (e3) (e3)) = (e2))))) -> (~((op (e0) (e1)) = (op (e1) (e1)))) -> (((op (e0) (e1)) = (e2))\/(((op (e1) (e1)) = (e2))\/(((op (e2) (e1)) = (e2))\/((op (e3) (e1)) = (e2))))) -> ((op (e3) (e1)) = (e0)) -> (~((op (e2) (e3)) = (op (e3) (e3)))) -> (((op (e0) (e0)) = (e1))\/(((op (e1) (e0)) = (e1))\/(((op (e2) (e0)) = (e1))\/((op (e3) (e0)) = (e1))))) -> ((~((op (e2) (e1)) = (e0)))\/((op (e2) (e0)) = (e1))) -> ((~((op (e2) (e3)) = (e0)))\/((op (e2) (e0)) = (e3))) -> (((op (e0) (e0)) = (e0))\/(((op (e1) (e0)) = (e0))\/(((op (e2) (e0)) = (e0))\/((op (e3) (e0)) = (e0))))) -> (~((op (e1) (e0)) = (e0))) -> (~((op (e0) (e0)) = (e0))) -> ((~((op (e3) (e1)) = (e0)))\/((op (e3) (e0)) = (e1))) -> (((op (e0) (e0)) = (e0))\/(((op (e0) (e1)) = (e0))\/(((op (e0) (e2)) = (e0))\/((op (e0) (e3)) = (e0))))) -> (~((op (e0) (e2)) = (op (e0) (e3)))) -> (~((e1) = (e3))) -> (((op (e1) (e0)) = (e0))\/(((op (e1) (e1)) = (e0))\/(((op (e1) (e2)) = (e0))\/((op (e1) (e3)) = (e0))))) -> (~((op (e1) (e0)) = (op (e2) (e0)))) -> (((op (e0) (e2)) = (e1))\/(((op (e1) (e2)) = (e1))\/(((op (e2) (e2)) = (e1))\/((op (e3) (e2)) = (e1))))) -> (~((op (e2) (e2)) = (op (e3) (e2)))) -> (((op (e2) (e2)) = (e0))\/(((op (e2) (e2)) = (e1))\/(((op (e2) (e2)) = (e2))\/((op (e2) (e2)) = (e3))))) -> (~((op (e2) (e0)) = (op (e2) (e2)))) -> (~((e0) = (e3))) -> (~((e2) = (e3))) -> (((op (e3) (e0)) = (e1))\/(((op (e3) (e1)) = (e1))\/(((op (e3) (e2)) = (e1))\/((op (e3) (e3)) = (e1))))) -> (~((op (e1) (e3)) = (op (e3) (e3)))) -> (((op (e0) (e3)) = (e0))\/(((op (e0) (e3)) = (e1))\/(((op (e0) (e3)) = (e2))\/((op (e0) (e3)) = (e3))))) -> (~((op (e0) (e3)) = (op (e1) (e3)))) -> (((op (e0) (e1)) = (e3))\/(((op (e1) (e1)) = (e3))\/(((op (e2) (e1)) = (e3))\/((op (e3) (e1)) = (e3))))) -> (~((op (e3) (e1)) = (op (e3) (e2)))) -> (((op (e0) (e2)) = (e3))\/(((op (e1) (e2)) = (e3))\/(((op (e2) (e2)) = (e3))\/((op (e3) (e2)) = (e3))))) -> (~((op (e1) (e1)) = (op (e2) (e1)))) -> (((op (e2) (e1)) = (e0))\/(((op (e2) (e1)) = (e1))\/(((op (e2) (e1)) = (e2))\/((op (e2) (e1)) = (e3))))) -> (((op (e0) (e2)) = (e0))\/(((op (e1) (e2)) = (e0))\/(((op (e2) (e2)) = (e0))\/((op (e3) (e2)) = (e0))))) -> (~((op (e3) (e0)) = (op (e3) (e2)))) -> (~((op (e1) (e1)) = (op (e1) (e2)))) -> (~((op (e1) (e2)) = (op (e2) (e2)))) -> (((op (e3) (e0)) = (e2))\/(((op (e3) (e1)) = (e2))\/(((op (e3) (e2)) = (e2))\/((op (e3) (e3)) = (e2))))) -> (((op (e1) (e0)) = (e3))\/(((op (e1) (e1)) = (e3))\/(((op (e1) (e2)) = (e3))\/((op (e1) (e3)) = (e3))))) -> (~((op (e1) (e1)) = (op (e3) (e1)))) -> (((op (e1) (e0)) = (e2))\/(((op (e1) (e1)) = (e2))\/(((op (e1) (e2)) = (e2))\/((op (e1) (e3)) = (e2))))) -> (~((op (e0) (e0)) = (op (e0) (e3)))) -> (((op (e2) (e0)) = (e1))\/(((op (e2) (e1)) = (e1))\/(((op (e2) (e2)) = (e1))\/((op (e2) (e3)) = (e1))))) -> (((op (e0) (e1)) = (e1))\/(((op (e1) (e1)) = (e1))\/(((op (e2) (e1)) = (e1))\/((op (e3) (e1)) = (e1))))) -> (~((op (e0) (e3)) = (op (e2) (e3)))) -> (((op (e1) (e3)) = (e0))\/(((op (e1) (e3)) = (e1))\/(((op (e1) (e3)) = (e2))\/((op (e1) (e3)) = (e3))))) -> (~((op (e2) (e1)) = (op (e3) (e1)))) -> (((op (e3) (e1)) = (e0))\/(((op (e3) (e1)) = (e1))\/(((op (e3) (e1)) = (e2))\/((op (e3) (e1)) = (e3))))) -> (((op (e2) (e3)) = (e0))\/(((op (e2) (e3)) = (e1))\/(((op (e2) (e3)) = (e2))\/((op (e2) (e3)) = (e3))))) -> (~((op (e1) (e2)) = (op (e3) (e2)))) -> (~((op (e0) (e1)) = (op (e0) (e2)))) -> (~((op (e0) (e1)) = (op (e3) (e1)))) -> (~((op (e0) (e1)) = (op (e0) (e3)))) -> (~((op (e1) (e0)) = (op (e1) (e3)))) -> (~((op (e2) (e2)) = (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 (e0) (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 (e3) (e2)) = (e0)))\/((op (e3) (e0)) = (e2))) -> ((~((op (e3) (e0)) = (e0)))\/((op (e3) (e0)) = (e0))) -> (((op (e2) (e0)) = (e0))\/(((op (e2) (e1)) = (e0))\/(((op (e2) (e2)) = (e0))\/((op (e2) (e3)) = (e0))))) -> ((~((op (e2) (e2)) = (e0)))\/((op (e2) (e0)) = (e2))) -> (((op (e3) (e0)) = (e3))\/(((op (e3) (e1)) = (e3))\/(((op (e3) (e2)) = (e3))\/((op (e3) (e3)) = (e3))))) -> (~((op (e0) (e2)) = (op (e2) (e2)))) -> ((~((op (e3) (e3)) = (e0)))\/((op (e3) (e0)) = (e3))) -> ((~((op (e0) (e3)) = (e0)))\/((op (e0) (e0)) = (e3))) -> ((~((op (e1) (e1)) = (e0)))\/((op (e1) (e0)) = (e1))) -> (((op (e3) (e2)) = (e0))\/(((op (e3) (e2)) = (e1))\/(((op (e3) (e2)) = (e2))\/((op (e3) (e2)) = (e3))))) -> (~((op (e0) (e2)) = (op (e1) (e2)))) -> (((op (e1) (e2)) = (e0))\/(((op (e1) (e2)) = (e1))\/(((op (e1) (e2)) = (e2))\/((op (e1) (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 (e2) (e0)) = (op (e3) (e0)))) -> ((~((op (e1) (e2)) = (e0)))\/((op (e1) (e0)) = (e2))) -> ((~((op (e1) (e3)) = (e0)))\/((op (e1) (e0)) = (e3))) -> (~((op (e0) (e0)) = (op (e0) (e2)))) -> (((op (e1) (e0)) = (e1))\/(((op (e1) (e1)) = (e1))\/(((op (e1) (e2)) = (e1))\/((op (e1) (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 (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 (e2) (e0)) = (e0)))\/((op (e2) (e0)) = (e0))) -> (((op (e0) (e0)) = (e3))\/(((op (e1) (e0)) = (e3))\/(((op (e2) (e0)) = (e3))\/((op (e3) (e0)) = (e3))))) -> (((op (e0) (e2)) = (e0))\/(((op (e0) (e2)) = (e1))\/(((op (e0) (e2)) = (e2))\/((op (e0) (e2)) = (e3))))) -> (~((op (e1) (e0)) = (op (e3) (e0)))) -> (~((op (e2) (e0)) = (op (e2) (e1)))) -> ((~((op (e1) (e0)) = (e0)))\/((op (e1) (e0)) = (e0))) -> ((~((op (e0) (e2)) = (e0)))\/((op (e0) (e0)) = (e2))) -> (~((op (e2) (e0)) = (op (e2) (e3)))) -> (((op (e0) (e3)) = (e0))\/(((op (e1) (e3)) = (e0))\/(((op (e2) (e3)) = (e0))\/((op (e3) (e3)) = (e0))))) -> (~((op (e1) (e0)) = (op (e1) (e1)))) -> (~((op (e0) (e2)) = (op (e3) (e2)))) -> (((op (e3) (e0)) = (e0))\/(((op (e3) (e1)) = (e0))\/(((op (e3) (e2)) = (e0))\/((op (e3) (e3)) = (e0))))) -> (~((e0) = (e1))) -> ((op (e0) (e0)) = (e3)) -> (~((op (e3) (e0)) = (op (e3) (e1)))) -> ((op (e3) (e0)) = (e1)) -> False). % 18.65/18.82 do 0 intro. intros zenon_H102 zenon_H130 zenon_Hc2 zenon_Hc3 zenon_H101 zenon_H172 zenon_H48 zenon_Hf0 zenon_H212 zenon_H20b zenon_Hdb zenon_H173 zenon_H17e zenon_H34 zenon_H149 zenon_H1d5 zenon_H142 zenon_H24 zenon_H10a zenon_H62 zenon_H1c7 zenon_H57 zenon_H7c zenon_H145 zenon_H10e zenon_H1d8 zenon_H1b1 zenon_Hf3 zenon_H235 zenon_H182 zenon_H94 zenon_H3e zenon_H23 zenon_H3f zenon_H1ed zenon_H74 zenon_H208 zenon_H95 zenon_H22 zenon_H201 zenon_H139 zenon_H18f zenon_H1c4 zenon_H52 zenon_H9a zenon_H12b zenon_He8 zenon_Hd5 zenon_He4 zenon_H1d zenon_H1a5 zenon_H1a4 zenon_H1a6 zenon_H13e zenon_H1cc zenon_H6a zenon_H6f zenon_H4f zenon_H2b zenon_H153 zenon_H16f zenon_H160 zenon_H18c zenon_H189 zenon_H106 zenon_H109 zenon_He2 zenon_Hdf zenon_Haf zenon_H22a zenon_H11f zenon_H115 zenon_H4a zenon_H210 zenon_H54 zenon_Hd8 zenon_H6d zenon_H71 zenon_H133 zenon_H7b zenon_H39 zenon_H22d zenon_H1a7 zenon_H184 zenon_H2f zenon_H185 zenon_H165 zenon_Ha8 zenon_H1ec zenon_H204 zenon_H205 zenon_H191 zenon_H195 zenon_H19d zenon_He7 zenon_H183 zenon_H17b zenon_H178 zenon_H179 zenon_H13c zenon_H128 zenon_H136 zenon_H124 zenon_H168 zenon_H1fe zenon_H1ee zenon_H1e0 zenon_H1ba zenon_H1fa zenon_H1f0 zenon_H206 zenon_H233 zenon_H5b zenon_H67 zenon_H45 zenon_H14f zenon_H1ac zenon_Ha1 zenon_H3a zenon_H1cf zenon_Hac. % 18.65/18.82 apply (zenon_or_s _ _ zenon_H109); [ zenon_intro zenon_Ha0 | zenon_intro zenon_H10b ]. % 18.65/18.82 apply (zenon_L359_); trivial. % 18.65/18.82 apply (zenon_or_s _ _ zenon_H10b); [ zenon_intro zenon_H10d | zenon_intro zenon_H10c ]. % 18.65/18.82 exact (zenon_H10a zenon_H10d). % 18.65/18.82 apply (zenon_or_s _ _ zenon_H10c); [ zenon_intro zenon_Ha5 | zenon_intro zenon_Hae ]. % 18.65/18.82 apply (zenon_or_s _ _ zenon_H18c); [ zenon_intro zenon_H86 | zenon_intro zenon_H18d ]. % 18.65/18.82 apply (zenon_L494_); trivial. % 18.65/18.82 apply (zenon_or_s _ _ zenon_H18d); [ zenon_intro zenon_H110 | zenon_intro zenon_H18e ]. % 18.65/18.82 apply (zenon_L498_); trivial. % 18.65/18.82 apply (zenon_or_s _ _ zenon_H18e); [ zenon_intro zenon_H113 | zenon_intro zenon_Hd7 ]. % 18.65/18.82 apply (zenon_L68_); trivial. % 18.65/18.82 apply (zenon_or_s _ _ zenon_H1d8); [ zenon_intro zenon_H10f | zenon_intro zenon_H1d9 ]. % 18.65/18.82 apply (zenon_L458_); trivial. % 18.65/18.82 apply (zenon_or_s _ _ zenon_H1d9); [ zenon_intro zenon_H110 | zenon_intro zenon_H1da ]. % 18.65/18.82 apply (zenon_L283_); trivial. % 18.65/18.82 apply (zenon_or_s _ _ zenon_H1da); [ zenon_intro zenon_H1ca | zenon_intro zenon_H14d ]. % 18.65/18.82 apply (zenon_or_s _ _ zenon_H172); [ zenon_intro zenon_H150 | zenon_intro zenon_H174 ]. % 18.65/18.82 apply (zenon_L378_); trivial. % 18.65/18.82 apply (zenon_or_s _ _ zenon_H174); [ zenon_intro zenon_H113 | zenon_intro zenon_H175 ]. % 18.65/18.82 apply (zenon_L68_); trivial. % 18.65/18.82 apply (zenon_or_s _ _ zenon_H175); [ zenon_intro zenon_H176 | zenon_intro zenon_H151 ]. % 18.65/18.82 exact (zenon_H173 zenon_H176). % 18.65/18.82 apply (zenon_or_s _ _ zenon_H212); [ zenon_intro zenon_H49 | zenon_intro zenon_H213 ]. % 18.65/18.82 exact (zenon_H20b zenon_H49). % 18.65/18.82 apply (zenon_or_s _ _ zenon_H213); [ zenon_intro zenon_Ha0 | zenon_intro zenon_H214 ]. % 18.65/18.82 apply (zenon_L357_); trivial. % 18.65/18.82 apply (zenon_or_s _ _ zenon_H214); [ zenon_intro zenon_H10f | zenon_intro zenon_H99 ]. % 18.65/18.82 apply (zenon_L458_); trivial. % 18.65/18.82 apply (zenon_L499_); trivial. % 18.65/18.82 apply (zenon_L500_); trivial. % 18.65/18.82 apply (zenon_L242_); trivial. % 18.65/18.82 (* end of lemma zenon_L501_ *) % 18.65/18.82 assert (zenon_L502_ : (~((op (e3) (e2)) = (e0))) -> (~((op (e2) (e2)) = (e0))) -> (~((op (e1) (e2)) = (e0))) -> ((op (e3) (e0)) = (e1)) -> (~((op (e3) (e0)) = (op (e3) (e1)))) -> ((op (e0) (e0)) = (e3)) -> (~((e0) = (e1))) -> (((op (e3) (e0)) = (e0))\/(((op (e3) (e1)) = (e0))\/(((op (e3) (e2)) = (e0))\/((op (e3) (e3)) = (e0))))) -> (~((op (e0) (e2)) = (op (e3) (e2)))) -> (~((op (e1) (e0)) = (op (e1) (e1)))) -> (((op (e0) (e3)) = (e0))\/(((op (e1) (e3)) = (e0))\/(((op (e2) (e3)) = (e0))\/((op (e3) (e3)) = (e0))))) -> (~((op (e2) (e0)) = (op (e2) (e3)))) -> ((~((op (e0) (e2)) = (e0)))\/((op (e0) (e0)) = (e2))) -> ((~((op (e1) (e0)) = (e0)))\/((op (e1) (e0)) = (e0))) -> (~((op (e2) (e0)) = (op (e2) (e1)))) -> (~((op (e1) (e0)) = (op (e3) (e0)))) -> (((op (e0) (e2)) = (e0))\/(((op (e0) (e2)) = (e1))\/(((op (e0) (e2)) = (e2))\/((op (e0) (e2)) = (e3))))) -> (((op (e0) (e0)) = (e3))\/(((op (e1) (e0)) = (e3))\/(((op (e2) (e0)) = (e3))\/((op (e3) (e0)) = (e3))))) -> ((~((op (e2) (e0)) = (e0)))\/((op (e2) (e0)) = (e0))) -> (((op (e0) (e0)) = (e2))\/(((op (e1) (e0)) = (e2))\/(((op (e2) (e0)) = (e2))\/((op (e3) (e0)) = (e2))))) -> (((op (e0) (e0)) = (e3))\/(((op (e0) (e1)) = (e3))\/(((op (e0) (e2)) = (e3))\/((op (e0) (e3)) = (e3))))) -> (~((op (e1) (e2)) = (op (e1) (e3)))) -> (((op (e0) (e3)) = (e3))\/(((op (e1) (e3)) = (e3))\/(((op (e2) (e3)) = (e3))\/((op (e3) (e3)) = (e3))))) -> (((op (e1) (e0)) = (e1))\/(((op (e1) (e1)) = (e1))\/(((op (e1) (e2)) = (e1))\/((op (e1) (e3)) = (e1))))) -> (~((op (e0) (e0)) = (op (e0) (e2)))) -> ((~((op (e1) (e3)) = (e0)))\/((op (e1) (e0)) = (e3))) -> ((~((op (e1) (e2)) = (e0)))\/((op (e1) (e0)) = (e2))) -> (~((op (e2) (e0)) = (op (e3) (e0)))) -> (((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) (e2)) = (e0))\/(((op (e1) (e2)) = (e1))\/(((op (e1) (e2)) = (e2))\/((op (e1) (e2)) = (e3))))) -> (~((op (e0) (e2)) = (op (e1) (e2)))) -> (((op (e3) (e2)) = (e0))\/(((op (e3) (e2)) = (e1))\/(((op (e3) (e2)) = (e2))\/((op (e3) (e2)) = (e3))))) -> ((~((op (e1) (e1)) = (e0)))\/((op (e1) (e0)) = (e1))) -> ((~((op (e0) (e3)) = (e0)))\/((op (e0) (e0)) = (e3))) -> ((~((op (e3) (e3)) = (e0)))\/((op (e3) (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 (e2) (e2)) = (e0)))\/((op (e2) (e0)) = (e2))) -> (((op (e2) (e0)) = (e0))\/(((op (e2) (e1)) = (e0))\/(((op (e2) (e2)) = (e0))\/((op (e2) (e3)) = (e0))))) -> ((~((op (e3) (e0)) = (e0)))\/((op (e3) (e0)) = (e0))) -> ((~((op (e3) (e2)) = (e0)))\/((op (e3) (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) (e3)) = (e1))\/(((op (e1) (e3)) = (e1))\/(((op (e2) (e3)) = (e1))\/((op (e3) (e3)) = (e1))))) -> (~((op (e3) (e0)) = (op (e3) (e3)))) -> (~((op (e2) (e2)) = (op (e2) (e3)))) -> (~((op (e1) (e0)) = (op (e1) (e3)))) -> (~((op (e0) (e1)) = (op (e0) (e3)))) -> (~((op (e0) (e1)) = (op (e3) (e1)))) -> (~((op (e0) (e1)) = (op (e0) (e2)))) -> (~((op (e1) (e2)) = (op (e3) (e2)))) -> (((op (e2) (e3)) = (e0))\/(((op (e2) (e3)) = (e1))\/(((op (e2) (e3)) = (e2))\/((op (e2) (e3)) = (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) (e3)) = (e0))\/(((op (e1) (e3)) = (e1))\/(((op (e1) (e3)) = (e2))\/((op (e1) (e3)) = (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 (e0) (e0)) = (op (e0) (e3)))) -> (((op (e1) (e0)) = (e2))\/(((op (e1) (e1)) = (e2))\/(((op (e1) (e2)) = (e2))\/((op (e1) (e3)) = (e2))))) -> (~((op (e1) (e1)) = (op (e3) (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))))) -> (~((op (e1) (e2)) = (op (e2) (e2)))) -> (~((op (e1) (e1)) = (op (e1) (e2)))) -> (~((op (e3) (e0)) = (op (e3) (e2)))) -> (((op (e0) (e2)) = (e0))\/(((op (e1) (e2)) = (e0))\/(((op (e2) (e2)) = (e0))\/((op (e3) (e2)) = (e0))))) -> (((op (e2) (e1)) = (e0))\/(((op (e2) (e1)) = (e1))\/(((op (e2) (e1)) = (e2))\/((op (e2) (e1)) = (e3))))) -> (~((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 (e0) (e1)) = (e3))\/(((op (e1) (e1)) = (e3))\/(((op (e2) (e1)) = (e3))\/((op (e3) (e1)) = (e3))))) -> (((op (e0) (e3)) = (e0))\/(((op (e0) (e3)) = (e1))\/(((op (e0) (e3)) = (e2))\/((op (e0) (e3)) = (e3))))) -> (~((op (e1) (e3)) = (op (e3) (e3)))) -> (((op (e3) (e0)) = (e1))\/(((op (e3) (e1)) = (e1))\/(((op (e3) (e2)) = (e1))\/((op (e3) (e3)) = (e1))))) -> (~((e2) = (e3))) -> (~((e0) = (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) (e2)) = (op (e3) (e2)))) -> (((op (e0) (e2)) = (e1))\/(((op (e1) (e2)) = (e1))\/(((op (e2) (e2)) = (e1))\/((op (e3) (e2)) = (e1))))) -> (~((op (e1) (e0)) = (op (e2) (e0)))) -> (((op (e1) (e0)) = (e0))\/(((op (e1) (e1)) = (e0))\/(((op (e1) (e2)) = (e0))\/((op (e1) (e3)) = (e0))))) -> (~((e1) = (e3))) -> (~((op (e0) (e2)) = (op (e0) (e3)))) -> (((op (e0) (e0)) = (e0))\/(((op (e0) (e1)) = (e0))\/(((op (e0) (e2)) = (e0))\/((op (e0) (e3)) = (e0))))) -> ((~((op (e3) (e1)) = (e0)))\/((op (e3) (e0)) = (e1))) -> (~((op (e0) (e0)) = (e0))) -> (~((op (e1) (e0)) = (e0))) -> (((op (e0) (e0)) = (e0))\/(((op (e1) (e0)) = (e0))\/(((op (e2) (e0)) = (e0))\/((op (e3) (e0)) = (e0))))) -> ((~((op (e2) (e3)) = (e0)))\/((op (e2) (e0)) = (e3))) -> ((~((op (e2) (e1)) = (e0)))\/((op (e2) (e0)) = (e1))) -> (((op (e0) (e0)) = (e1))\/(((op (e1) (e0)) = (e1))\/(((op (e2) (e0)) = (e1))\/((op (e3) (e0)) = (e1))))) -> (~((op (e2) (e3)) = (op (e3) (e3)))) -> ((op (e3) (e1)) = (e0)) -> (((op (e0) (e1)) = (e2))\/(((op (e1) (e1)) = (e2))\/(((op (e2) (e1)) = (e2))\/((op (e3) (e1)) = (e2))))) -> (~((op (e0) (e1)) = (op (e1) (e1)))) -> (((op (e0) (e3)) = (e2))\/(((op (e1) (e3)) = (e2))\/(((op (e2) (e3)) = (e2))\/((op (e3) (e3)) = (e2))))) -> (~((e1) = (e2))) -> (~((op (e1) (e1)) = (op (e1) (e3)))) -> (~((op (e2) (e1)) = (op (e2) (e3)))) -> (~((op (e3) (e2)) = (op (e3) (e3)))) -> (~((op (e1) (e1)) = (e1))) -> (~((op (e1) (e1)) = (e0))) -> (((op (e1) (e1)) = (e0))\/(((op (e1) (e1)) = (e1))\/(((op (e1) (e1)) = (e2))\/((op (e1) (e1)) = (e3))))) -> (((op (e2) (e0)) = (e2))\/(((op (e2) (e1)) = (e2))\/(((op (e2) (e2)) = (e2))\/((op (e2) (e3)) = (e2))))) -> (~((e0) = (e2))) -> ((op (e2) (e0)) = (e0)) -> (~((op (e0) (e1)) = (op (e2) (e1)))) -> (~((op (e2) (e2)) = (e2))) -> (~((op (e1) (e3)) = (op (e2) (e3)))) -> (~((op (e0) (e1)) = (e0))) -> (((op (e0) (e1)) = (e0))\/(((op (e0) (e1)) = (e1))\/(((op (e0) (e1)) = (e2))\/((op (e0) (e1)) = (e3))))) -> ((op (e1) (e2)) = (e1)) -> ((op (e0) (e2)) = (e0)) -> (((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 (e0) (e3)) = (op (e3) (e3)))) -> (~((op (e3) (e1)) = (op (e3) (e3)))) -> (~((op (e3) (e3)) = (e3))) -> ((op (e1) (e3)) = (e2)) -> (~((op (e0) (e3)) = (op (e1) (e3)))) -> (~((op (e0) (e3)) = (op (e2) (e3)))) -> ((op (e2) (e3)) = (e3)) -> False). % 18.65/18.82 do 0 intro. intros zenon_H18b zenon_H81 zenon_H25 zenon_Hac zenon_H1cf zenon_H3a zenon_Ha1 zenon_H1ac zenon_H14f zenon_H45 zenon_H67 zenon_H5b zenon_H233 zenon_H206 zenon_H1f0 zenon_H1fa zenon_H1ba zenon_H1e0 zenon_H1ee zenon_H1fe zenon_H168 zenon_H124 zenon_H136 zenon_H128 zenon_H13c zenon_H179 zenon_H178 zenon_H17b zenon_H183 zenon_He7 zenon_H19d zenon_H195 zenon_H191 zenon_H205 zenon_H204 zenon_H1ec zenon_Ha8 zenon_H165 zenon_H185 zenon_H2f zenon_H184 zenon_H1a7 zenon_H22d zenon_H39 zenon_H7b zenon_H133 zenon_H71 zenon_H6d zenon_Hd8 zenon_H54 zenon_H210 zenon_H4a zenon_H115 zenon_H11f zenon_H22a zenon_Haf zenon_Hdf zenon_H109 zenon_H106 zenon_H189 zenon_H18c zenon_H160 zenon_H16f zenon_H153 zenon_H2b zenon_H4f zenon_H6f zenon_H6a zenon_H1cc zenon_H13e zenon_H1a6 zenon_H1a4 zenon_H1a5 zenon_He4 zenon_Hd5 zenon_He8 zenon_H12b zenon_H9a zenon_H52 zenon_H1c4 zenon_H18f zenon_H139 zenon_H201 zenon_H22 zenon_H95 zenon_H208 zenon_H74 zenon_H1ed zenon_H3f zenon_H23 zenon_H3e zenon_H94 zenon_H182 zenon_H235 zenon_Hf3 zenon_H1b1 zenon_H1d8 zenon_H10e zenon_H145 zenon_H7c zenon_H57 zenon_H1c7 zenon_H62 zenon_H10a zenon_H24 zenon_H142 zenon_H1d5 zenon_H149 zenon_H34 zenon_H17e zenon_H173 zenon_Hdb zenon_H20b zenon_H212 zenon_Hf0 zenon_H48 zenon_H172 zenon_H101 zenon_Hc2 zenon_H130 zenon_H102 zenon_Hd7 zenon_H1d zenon_He2 zenon_Hdd. % 18.65/18.82 apply (zenon_or_s _ _ zenon_He4); [ zenon_intro zenon_H1e | zenon_intro zenon_He5 ]. % 18.65/18.82 apply (zenon_L337_); trivial. % 18.65/18.82 apply (zenon_or_s _ _ zenon_He5); [ zenon_intro zenon_Hc3 | zenon_intro zenon_He6 ]. % 18.65/18.82 apply (zenon_L501_); trivial. % 18.65/18.82 apply (zenon_or_s _ _ zenon_He6); [ zenon_intro zenon_Hcd | zenon_intro zenon_He3 ]. % 18.65/18.82 apply (zenon_L70_); trivial. % 18.65/18.82 apply (zenon_L54_); trivial. % 18.65/18.82 (* end of lemma zenon_L502_ *) % 18.65/18.82 assert (zenon_L503_ : (((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) (e3)))) -> ((op (e1) (e3)) = (e2)) -> (~((op (e1) (e1)) = (op (e3) (e1)))) -> ((op (e3) (e1)) = (e3)) -> False). % 18.65/18.82 do 0 intro. intros zenon_H142 zenon_H24 zenon_H10a zenon_H57 zenon_Hd7 zenon_H160 zenon_H161. % 18.65/18.82 apply (zenon_or_s _ _ zenon_H142); [ zenon_intro zenon_H29 | zenon_intro zenon_H143 ]. % 18.65/18.82 exact (zenon_H24 zenon_H29). % 18.65/18.82 apply (zenon_or_s _ _ zenon_H143); [ zenon_intro zenon_H10d | zenon_intro zenon_H144 ]. % 18.65/18.82 exact (zenon_H10a zenon_H10d). % 18.65/18.82 apply (zenon_or_s _ _ zenon_H144); [ zenon_intro zenon_H110 | zenon_intro zenon_H13f ]. % 18.65/18.82 apply (zenon_L283_); trivial. % 18.65/18.82 apply (zenon_L110_); trivial. % 18.65/18.82 (* end of lemma zenon_L503_ *) % 18.65/18.82 assert (zenon_L504_ : (~((op (e0) (e3)) = (op (e2) (e3)))) -> (~((op (e0) (e3)) = (op (e1) (e3)))) -> (~((op (e3) (e3)) = (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)) = (e2))\/(((op (e1) (e2)) = (e2))\/(((op (e2) (e2)) = (e2))\/((op (e3) (e2)) = (e2))))) -> ((op (e0) (e2)) = (e0)) -> ((op (e1) (e2)) = (e1)) -> (((op (e0) (e1)) = (e0))\/(((op (e0) (e1)) = (e1))\/(((op (e0) (e1)) = (e2))\/((op (e0) (e1)) = (e3))))) -> (~((op (e0) (e1)) = (e0))) -> (~((op (e1) (e3)) = (op (e2) (e3)))) -> (~((op (e2) (e2)) = (e2))) -> (~((op (e0) (e1)) = (op (e2) (e1)))) -> ((op (e2) (e0)) = (e0)) -> (~((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) (e1)) = (op (e2) (e3)))) -> (~((e1) = (e2))) -> (((op (e0) (e3)) = (e2))\/(((op (e1) (e3)) = (e2))\/(((op (e2) (e3)) = (e2))\/((op (e3) (e3)) = (e2))))) -> (~((op (e0) (e1)) = (op (e1) (e1)))) -> (((op (e0) (e1)) = (e2))\/(((op (e1) (e1)) = (e2))\/(((op (e2) (e1)) = (e2))\/((op (e3) (e1)) = (e2))))) -> ((op (e3) (e1)) = (e0)) -> (~((op (e2) (e3)) = (op (e3) (e3)))) -> (((op (e0) (e0)) = (e1))\/(((op (e1) (e0)) = (e1))\/(((op (e2) (e0)) = (e1))\/((op (e3) (e0)) = (e1))))) -> ((~((op (e2) (e1)) = (e0)))\/((op (e2) (e0)) = (e1))) -> ((~((op (e2) (e3)) = (e0)))\/((op (e2) (e0)) = (e3))) -> (((op (e0) (e0)) = (e0))\/(((op (e1) (e0)) = (e0))\/(((op (e2) (e0)) = (e0))\/((op (e3) (e0)) = (e0))))) -> (~((op (e1) (e0)) = (e0))) -> (~((op (e0) (e0)) = (e0))) -> ((~((op (e3) (e1)) = (e0)))\/((op (e3) (e0)) = (e1))) -> (((op (e0) (e0)) = (e0))\/(((op (e0) (e1)) = (e0))\/(((op (e0) (e2)) = (e0))\/((op (e0) (e3)) = (e0))))) -> (~((op (e0) (e2)) = (op (e0) (e3)))) -> (~((e1) = (e3))) -> (((op (e1) (e0)) = (e0))\/(((op (e1) (e1)) = (e0))\/(((op (e1) (e2)) = (e0))\/((op (e1) (e3)) = (e0))))) -> (~((op (e1) (e0)) = (op (e2) (e0)))) -> (((op (e0) (e2)) = (e1))\/(((op (e1) (e2)) = (e1))\/(((op (e2) (e2)) = (e1))\/((op (e3) (e2)) = (e1))))) -> (~((op (e2) (e2)) = (op (e3) (e2)))) -> (((op (e2) (e2)) = (e0))\/(((op (e2) (e2)) = (e1))\/(((op (e2) (e2)) = (e2))\/((op (e2) (e2)) = (e3))))) -> (~((op (e2) (e0)) = (op (e2) (e2)))) -> (~((e0) = (e3))) -> (((op (e3) (e0)) = (e1))\/(((op (e3) (e1)) = (e1))\/(((op (e3) (e2)) = (e1))\/((op (e3) (e3)) = (e1))))) -> (~((op (e1) (e3)) = (op (e3) (e3)))) -> (((op (e0) (e3)) = (e0))\/(((op (e0) (e3)) = (e1))\/(((op (e0) (e3)) = (e2))\/((op (e0) (e3)) = (e3))))) -> (((op (e0) (e1)) = (e3))\/(((op (e1) (e1)) = (e3))\/(((op (e2) (e1)) = (e3))\/((op (e3) (e1)) = (e3))))) -> (~((op (e3) (e1)) = (op (e3) (e2)))) -> (((op (e0) (e2)) = (e3))\/(((op (e1) (e2)) = (e3))\/(((op (e2) (e2)) = (e3))\/((op (e3) (e2)) = (e3))))) -> (~((op (e1) (e1)) = (op (e2) (e1)))) -> (((op (e2) (e1)) = (e0))\/(((op (e2) (e1)) = (e1))\/(((op (e2) (e1)) = (e2))\/((op (e2) (e1)) = (e3))))) -> (((op (e0) (e2)) = (e0))\/(((op (e1) (e2)) = (e0))\/(((op (e2) (e2)) = (e0))\/((op (e3) (e2)) = (e0))))) -> (~((op (e3) (e0)) = (op (e3) (e2)))) -> (~((op (e1) (e1)) = (op (e1) (e2)))) -> (~((op (e1) (e2)) = (op (e2) (e2)))) -> (((op (e3) (e0)) = (e2))\/(((op (e3) (e1)) = (e2))\/(((op (e3) (e2)) = (e2))\/((op (e3) (e3)) = (e2))))) -> (((op (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) (e0)) = (op (e0) (e3)))) -> (((op (e2) (e0)) = (e1))\/(((op (e2) (e1)) = (e1))\/(((op (e2) (e2)) = (e1))\/((op (e2) (e3)) = (e1))))) -> (((op (e0) (e1)) = (e1))\/(((op (e1) (e1)) = (e1))\/(((op (e2) (e1)) = (e1))\/((op (e3) (e1)) = (e1))))) -> (((op (e1) (e3)) = (e0))\/(((op (e1) (e3)) = (e1))\/(((op (e1) (e3)) = (e2))\/((op (e1) (e3)) = (e3))))) -> (~((op (e2) (e1)) = (op (e3) (e1)))) -> (((op (e3) (e1)) = (e0))\/(((op (e3) (e1)) = (e1))\/(((op (e3) (e1)) = (e2))\/((op (e3) (e1)) = (e3))))) -> (((op (e2) (e3)) = (e0))\/(((op (e2) (e3)) = (e1))\/(((op (e2) (e3)) = (e2))\/((op (e2) (e3)) = (e3))))) -> (~((op (e1) (e2)) = (op (e3) (e2)))) -> (~((op (e0) (e1)) = (op (e0) (e2)))) -> (~((op (e0) (e1)) = (op (e3) (e1)))) -> (~((op (e0) (e1)) = (op (e0) (e3)))) -> (~((op (e1) (e0)) = (op (e1) (e3)))) -> (~((op (e2) (e2)) = (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 (e0) (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 (e3) (e2)) = (e0)))\/((op (e3) (e0)) = (e2))) -> ((~((op (e3) (e0)) = (e0)))\/((op (e3) (e0)) = (e0))) -> (((op (e2) (e0)) = (e0))\/(((op (e2) (e1)) = (e0))\/(((op (e2) (e2)) = (e0))\/((op (e2) (e3)) = (e0))))) -> ((~((op (e2) (e2)) = (e0)))\/((op (e2) (e0)) = (e2))) -> (((op (e3) (e0)) = (e3))\/(((op (e3) (e1)) = (e3))\/(((op (e3) (e2)) = (e3))\/((op (e3) (e3)) = (e3))))) -> (~((op (e0) (e2)) = (op (e2) (e2)))) -> ((~((op (e3) (e3)) = (e0)))\/((op (e3) (e0)) = (e3))) -> ((~((op (e0) (e3)) = (e0)))\/((op (e0) (e0)) = (e3))) -> ((~((op (e1) (e1)) = (e0)))\/((op (e1) (e0)) = (e1))) -> (((op (e3) (e2)) = (e0))\/(((op (e3) (e2)) = (e1))\/(((op (e3) (e2)) = (e2))\/((op (e3) (e2)) = (e3))))) -> (~((op (e0) (e2)) = (op (e1) (e2)))) -> (((op (e1) (e2)) = (e0))\/(((op (e1) (e2)) = (e1))\/(((op (e1) (e2)) = (e2))\/((op (e1) (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 (e2) (e0)) = (op (e3) (e0)))) -> ((~((op (e1) (e2)) = (e0)))\/((op (e1) (e0)) = (e2))) -> ((~((op (e1) (e3)) = (e0)))\/((op (e1) (e0)) = (e3))) -> (~((op (e0) (e0)) = (op (e0) (e2)))) -> (((op (e1) (e0)) = (e1))\/(((op (e1) (e1)) = (e1))\/(((op (e1) (e2)) = (e1))\/((op (e1) (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 (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 (e2) (e0)) = (e0)))\/((op (e2) (e0)) = (e0))) -> (((op (e0) (e0)) = (e3))\/(((op (e1) (e0)) = (e3))\/(((op (e2) (e0)) = (e3))\/((op (e3) (e0)) = (e3))))) -> (((op (e0) (e2)) = (e0))\/(((op (e0) (e2)) = (e1))\/(((op (e0) (e2)) = (e2))\/((op (e0) (e2)) = (e3))))) -> (~((op (e1) (e0)) = (op (e3) (e0)))) -> (~((op (e2) (e0)) = (op (e2) (e1)))) -> ((~((op (e1) (e0)) = (e0)))\/((op (e1) (e0)) = (e0))) -> ((~((op (e0) (e2)) = (e0)))\/((op (e0) (e0)) = (e2))) -> (~((op (e2) (e0)) = (op (e2) (e3)))) -> (((op (e0) (e3)) = (e0))\/(((op (e1) (e3)) = (e0))\/(((op (e2) (e3)) = (e0))\/((op (e3) (e3)) = (e0))))) -> (~((op (e1) (e0)) = (op (e1) (e1)))) -> (~((op (e0) (e2)) = (op (e3) (e2)))) -> (((op (e3) (e0)) = (e0))\/(((op (e3) (e1)) = (e0))\/(((op (e3) (e2)) = (e0))\/((op (e3) (e3)) = (e0))))) -> (~((e0) = (e1))) -> ((op (e0) (e0)) = (e3)) -> (~((op (e3) (e0)) = (op (e3) (e1)))) -> ((op (e3) (e0)) = (e1)) -> (~((op (e1) (e2)) = (e0))) -> (~((op (e2) (e2)) = (e0))) -> (~((op (e3) (e2)) = (e0))) -> ((op (e0) (e1)) = (e1)) -> ((op (e1) (e0)) = (e3)) -> (~((e2) = (e3))) -> ((op (e2) (e1)) = (e2)) -> (((op (e1) (e1)) = (e0))\/(((op (e1) (e1)) = (e1))\/(((op (e1) (e1)) = (e2))\/((op (e1) (e1)) = (e3))))) -> (~((op (e1) (e1)) = (e0))) -> (~((op (e1) (e1)) = (e1))) -> (~((op (e1) (e1)) = (op (e1) (e3)))) -> ((op (e1) (e3)) = (e2)) -> (~((op (e1) (e1)) = (op (e3) (e1)))) -> False). % 18.65/18.83 do 0 intro. intros zenon_He2 zenon_H1d zenon_H102 zenon_H130 zenon_Hc2 zenon_H101 zenon_H172 zenon_H48 zenon_Hf0 zenon_H212 zenon_H20b zenon_Hdb zenon_H173 zenon_H17e zenon_H34 zenon_H149 zenon_H1d5 zenon_H62 zenon_H1c7 zenon_H7c zenon_H145 zenon_H10e zenon_H1d8 zenon_H1b1 zenon_Hf3 zenon_H235 zenon_H182 zenon_H94 zenon_H3e zenon_H23 zenon_H3f zenon_H1ed zenon_H74 zenon_H208 zenon_H95 zenon_H22 zenon_H201 zenon_H139 zenon_H18f zenon_H1c4 zenon_H52 zenon_H9a zenon_He8 zenon_Hd5 zenon_He4 zenon_H1a5 zenon_H1a4 zenon_H1a6 zenon_H13e zenon_H1cc zenon_H6a zenon_H6f zenon_H4f zenon_H2b zenon_H153 zenon_H16f zenon_H18c zenon_H189 zenon_H106 zenon_H109 zenon_Hdf zenon_Haf zenon_H22a zenon_H11f zenon_H115 zenon_H4a zenon_H210 zenon_H54 zenon_Hd8 zenon_H6d zenon_H71 zenon_H133 zenon_H7b zenon_H39 zenon_H22d zenon_H1a7 zenon_H184 zenon_H2f zenon_H185 zenon_H165 zenon_Ha8 zenon_H1ec zenon_H204 zenon_H205 zenon_H191 zenon_H195 zenon_H19d zenon_He7 zenon_H183 zenon_H17b zenon_H178 zenon_H179 zenon_H13c zenon_H128 zenon_H136 zenon_H124 zenon_H168 zenon_H1fe zenon_H1ee zenon_H1e0 zenon_H1ba zenon_H1fa zenon_H1f0 zenon_H206 zenon_H233 zenon_H5b zenon_H67 zenon_H45 zenon_H14f zenon_H1ac zenon_Ha1 zenon_H3a zenon_H1cf zenon_Hac zenon_H25 zenon_H81 zenon_H18b zenon_Ha0 zenon_H9e zenon_H12b zenon_H1ca zenon_H142 zenon_H24 zenon_H10a zenon_H57 zenon_Hd7 zenon_H160. % 18.65/18.83 apply (zenon_or_s _ _ zenon_H1a5); [ zenon_intro zenon_H99 | zenon_intro zenon_H1a8 ]. % 18.65/18.83 apply (zenon_L403_); trivial. % 18.65/18.83 apply (zenon_or_s _ _ zenon_H1a8); [ zenon_intro zenon_H13f | zenon_intro zenon_H1a9 ]. % 18.65/18.83 apply (zenon_or_s _ _ zenon_H106); [ zenon_intro zenon_Hed | zenon_intro zenon_H107 ]. % 18.65/18.83 apply (zenon_L491_); trivial. % 18.65/18.83 apply (zenon_or_s _ _ zenon_H107); [ zenon_intro zenon_Ha5 | zenon_intro zenon_H108 ]. % 18.65/18.83 apply (zenon_L391_); trivial. % 18.65/18.83 apply (zenon_or_s _ _ zenon_H108); [ zenon_intro zenon_Hf1 | zenon_intro zenon_Hf4 ]. % 18.65/18.83 apply (zenon_L59_); trivial. % 18.65/18.83 apply (zenon_or_s _ _ zenon_He7); [ zenon_intro zenon_H3b | zenon_intro zenon_He9 ]. % 18.65/18.83 apply (zenon_L407_); trivial. % 18.65/18.83 apply (zenon_or_s _ _ zenon_He9); [ zenon_intro zenon_Ha6 | zenon_intro zenon_Hea ]. % 18.65/18.83 apply (zenon_L95_); trivial. % 18.65/18.83 apply (zenon_or_s _ _ zenon_Hea); [ zenon_intro zenon_Haa | zenon_intro zenon_Hdd ]. % 18.65/18.83 apply (zenon_L495_); trivial. % 18.65/18.83 apply (zenon_L502_); trivial. % 18.65/18.83 apply (zenon_or_s _ _ zenon_H1a9); [ zenon_intro zenon_Ha6 | zenon_intro zenon_H161 ]. % 18.65/18.83 apply (zenon_L207_); trivial. % 18.65/18.83 apply (zenon_L503_); trivial. % 18.65/18.83 (* end of lemma zenon_L504_ *) % 18.65/18.83 assert (zenon_L505_ : (((op (e2) (e0)) = (e2))\/(((op (e2) (e1)) = (e2))\/(((op (e2) (e2)) = (e2))\/((op (e2) (e3)) = (e2))))) -> ((op (e0) (e0)) = (e2)) -> (~((op (e0) (e0)) = (op (e2) (e0)))) -> ((op (e3) (e1)) = (e2)) -> (~((op (e2) (e1)) = (op (e3) (e1)))) -> (~((op (e2) (e2)) = (e2))) -> (~((op (e1) (e3)) = (op (e2) (e3)))) -> ((op (e1) (e3)) = (e2)) -> False). % 18.65/18.83 do 0 intro. intros zenon_H1d5 zenon_H7b zenon_H39 zenon_H14d zenon_Haf zenon_H173 zenon_Hdb zenon_Hd7. % 18.65/18.83 apply (zenon_or_s _ _ zenon_H1d5); [ zenon_intro zenon_Hee | zenon_intro zenon_H1d6 ]. % 18.65/18.83 apply (zenon_L341_); trivial. % 18.65/18.83 apply (zenon_or_s _ _ zenon_H1d6); [ zenon_intro zenon_H1ca | zenon_intro zenon_H1d7 ]. % 18.65/18.83 apply (zenon_L364_); trivial. % 18.65/18.83 apply (zenon_or_s _ _ zenon_H1d7); [ zenon_intro zenon_H176 | zenon_intro zenon_H11d ]. % 18.65/18.83 exact (zenon_H173 zenon_H176). % 18.65/18.83 apply (zenon_L366_); trivial. % 18.65/18.83 (* end of lemma zenon_L505_ *) % 18.65/18.83 assert (zenon_L506_ : (~((op (e1) (e1)) = (op (e3) (e1)))) -> (~((op (e1) (e1)) = (op (e1) (e3)))) -> (~((op (e1) (e1)) = (e1))) -> (~((op (e1) (e1)) = (e0))) -> (((op (e1) (e1)) = (e0))\/(((op (e1) (e1)) = (e1))\/(((op (e1) (e1)) = (e2))\/((op (e1) (e1)) = (e3))))) -> (~((e2) = (e3))) -> ((op (e1) (e0)) = (e3)) -> ((op (e0) (e1)) = (e1)) -> (~((op (e3) (e2)) = (e0))) -> (~((op (e2) (e2)) = (e0))) -> (~((op (e1) (e2)) = (e0))) -> ((op (e3) (e0)) = (e1)) -> (~((op (e3) (e0)) = (op (e3) (e1)))) -> ((op (e0) (e0)) = (e3)) -> (~((e0) = (e1))) -> (((op (e3) (e0)) = (e0))\/(((op (e3) (e1)) = (e0))\/(((op (e3) (e2)) = (e0))\/((op (e3) (e3)) = (e0))))) -> (~((op (e0) (e2)) = (op (e3) (e2)))) -> (~((op (e1) (e0)) = (op (e1) (e1)))) -> (((op (e0) (e3)) = (e0))\/(((op (e1) (e3)) = (e0))\/(((op (e2) (e3)) = (e0))\/((op (e3) (e3)) = (e0))))) -> (~((op (e2) (e0)) = (op (e2) (e3)))) -> ((~((op (e0) (e2)) = (e0)))\/((op (e0) (e0)) = (e2))) -> ((~((op (e1) (e0)) = (e0)))\/((op (e1) (e0)) = (e0))) -> (~((op (e2) (e0)) = (op (e2) (e1)))) -> (~((op (e1) (e0)) = (op (e3) (e0)))) -> (((op (e0) (e2)) = (e0))\/(((op (e0) (e2)) = (e1))\/(((op (e0) (e2)) = (e2))\/((op (e0) (e2)) = (e3))))) -> (((op (e0) (e0)) = (e3))\/(((op (e1) (e0)) = (e3))\/(((op (e2) (e0)) = (e3))\/((op (e3) (e0)) = (e3))))) -> ((~((op (e2) (e0)) = (e0)))\/((op (e2) (e0)) = (e0))) -> (((op (e0) (e0)) = (e2))\/(((op (e1) (e0)) = (e2))\/(((op (e2) (e0)) = (e2))\/((op (e3) (e0)) = (e2))))) -> (((op (e0) (e0)) = (e3))\/(((op (e0) (e1)) = (e3))\/(((op (e0) (e2)) = (e3))\/((op (e0) (e3)) = (e3))))) -> (~((op (e1) (e2)) = (op (e1) (e3)))) -> (((op (e0) (e3)) = (e3))\/(((op (e1) (e3)) = (e3))\/(((op (e2) (e3)) = (e3))\/((op (e3) (e3)) = (e3))))) -> (((op (e1) (e0)) = (e1))\/(((op (e1) (e1)) = (e1))\/(((op (e1) (e2)) = (e1))\/((op (e1) (e3)) = (e1))))) -> (~((op (e0) (e0)) = (op (e0) (e2)))) -> ((~((op (e1) (e3)) = (e0)))\/((op (e1) (e0)) = (e3))) -> ((~((op (e1) (e2)) = (e0)))\/((op (e1) (e0)) = (e2))) -> (~((op (e2) (e0)) = (op (e3) (e0)))) -> (((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) (e2)) = (e0))\/(((op (e1) (e2)) = (e1))\/(((op (e1) (e2)) = (e2))\/((op (e1) (e2)) = (e3))))) -> (~((op (e0) (e2)) = (op (e1) (e2)))) -> (((op (e3) (e2)) = (e0))\/(((op (e3) (e2)) = (e1))\/(((op (e3) (e2)) = (e2))\/((op (e3) (e2)) = (e3))))) -> ((~((op (e1) (e1)) = (e0)))\/((op (e1) (e0)) = (e1))) -> ((~((op (e0) (e3)) = (e0)))\/((op (e0) (e0)) = (e3))) -> ((~((op (e3) (e3)) = (e0)))\/((op (e3) (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 (e2) (e2)) = (e0)))\/((op (e2) (e0)) = (e2))) -> (((op (e2) (e0)) = (e0))\/(((op (e2) (e1)) = (e0))\/(((op (e2) (e2)) = (e0))\/((op (e2) (e3)) = (e0))))) -> ((~((op (e3) (e0)) = (e0)))\/((op (e3) (e0)) = (e0))) -> ((~((op (e3) (e2)) = (e0)))\/((op (e3) (e0)) = (e2))) -> (((op (e0) (e0)) = (e1))\/(((op (e0) (e1)) = (e1))\/(((op (e0) (e2)) = (e1))\/((op (e0) (e3)) = (e1))))) -> (((op (e0) (e3)) = (e1))\/(((op (e1) (e3)) = (e1))\/(((op (e2) (e3)) = (e1))\/((op (e3) (e3)) = (e1))))) -> (~((op (e3) (e0)) = (op (e3) (e3)))) -> (~((op (e2) (e2)) = (op (e2) (e3)))) -> (~((op (e1) (e0)) = (op (e1) (e3)))) -> (~((op (e0) (e1)) = (op (e0) (e3)))) -> (~((op (e0) (e1)) = (op (e3) (e1)))) -> (~((op (e0) (e1)) = (op (e0) (e2)))) -> (~((op (e1) (e2)) = (op (e3) (e2)))) -> (((op (e2) (e3)) = (e0))\/(((op (e2) (e3)) = (e1))\/(((op (e2) (e3)) = (e2))\/((op (e2) (e3)) = (e3))))) -> (((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) (e1)) = (e1))\/(((op (e1) (e1)) = (e1))\/(((op (e2) (e1)) = (e1))\/((op (e3) (e1)) = (e1))))) -> (((op (e2) (e0)) = (e1))\/(((op (e2) (e1)) = (e1))\/(((op (e2) (e2)) = (e1))\/((op (e2) (e3)) = (e1))))) -> (~((op (e0) (e0)) = (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 (e3) (e0)) = (e2))\/(((op (e3) (e1)) = (e2))\/(((op (e3) (e2)) = (e2))\/((op (e3) (e3)) = (e2))))) -> (~((op (e1) (e2)) = (op (e2) (e2)))) -> (~((op (e1) (e1)) = (op (e1) (e2)))) -> (~((op (e3) (e0)) = (op (e3) (e2)))) -> (((op (e0) (e2)) = (e0))\/(((op (e1) (e2)) = (e0))\/(((op (e2) (e2)) = (e0))\/((op (e3) (e2)) = (e0))))) -> (((op (e2) (e1)) = (e0))\/(((op (e2) (e1)) = (e1))\/(((op (e2) (e1)) = (e2))\/((op (e2) (e1)) = (e3))))) -> (~((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 (e0) (e1)) = (e3))\/(((op (e1) (e1)) = (e3))\/(((op (e2) (e1)) = (e3))\/((op (e3) (e1)) = (e3))))) -> (((op (e0) (e3)) = (e0))\/(((op (e0) (e3)) = (e1))\/(((op (e0) (e3)) = (e2))\/((op (e0) (e3)) = (e3))))) -> (~((op (e1) (e3)) = (op (e3) (e3)))) -> (((op (e3) (e0)) = (e1))\/(((op (e3) (e1)) = (e1))\/(((op (e3) (e2)) = (e1))\/((op (e3) (e3)) = (e1))))) -> (~((e0) = (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) (e2)) = (op (e3) (e2)))) -> (((op (e0) (e2)) = (e1))\/(((op (e1) (e2)) = (e1))\/(((op (e2) (e2)) = (e1))\/((op (e3) (e2)) = (e1))))) -> (~((op (e1) (e0)) = (op (e2) (e0)))) -> (((op (e1) (e0)) = (e0))\/(((op (e1) (e1)) = (e0))\/(((op (e1) (e2)) = (e0))\/((op (e1) (e3)) = (e0))))) -> (~((e1) = (e3))) -> (~((op (e0) (e2)) = (op (e0) (e3)))) -> (((op (e0) (e0)) = (e0))\/(((op (e0) (e1)) = (e0))\/(((op (e0) (e2)) = (e0))\/((op (e0) (e3)) = (e0))))) -> ((~((op (e3) (e1)) = (e0)))\/((op (e3) (e0)) = (e1))) -> (~((op (e0) (e0)) = (e0))) -> (~((op (e1) (e0)) = (e0))) -> (((op (e0) (e0)) = (e0))\/(((op (e1) (e0)) = (e0))\/(((op (e2) (e0)) = (e0))\/((op (e3) (e0)) = (e0))))) -> ((~((op (e2) (e3)) = (e0)))\/((op (e2) (e0)) = (e3))) -> ((~((op (e2) (e1)) = (e0)))\/((op (e2) (e0)) = (e1))) -> (((op (e0) (e0)) = (e1))\/(((op (e1) (e0)) = (e1))\/(((op (e2) (e0)) = (e1))\/((op (e3) (e0)) = (e1))))) -> (~((op (e2) (e3)) = (op (e3) (e3)))) -> ((op (e3) (e1)) = (e0)) -> (((op (e0) (e1)) = (e2))\/(((op (e1) (e1)) = (e2))\/(((op (e2) (e1)) = (e2))\/((op (e3) (e1)) = (e2))))) -> (~((op (e0) (e1)) = (op (e1) (e1)))) -> (((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 (e3) (e2)) = (op (e3) (e3)))) -> (~((e0) = (e2))) -> ((op (e2) (e0)) = (e0)) -> (~((op (e0) (e1)) = (op (e2) (e1)))) -> (~((op (e0) (e1)) = (e0))) -> (((op (e0) (e1)) = (e0))\/(((op (e0) (e1)) = (e1))\/(((op (e0) (e1)) = (e2))\/((op (e0) (e1)) = (e3))))) -> ((op (e1) (e2)) = (e1)) -> ((op (e0) (e2)) = (e0)) -> (((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 (e0) (e3)) = (op (e3) (e3)))) -> (~((op (e3) (e1)) = (op (e3) (e3)))) -> (~((op (e3) (e3)) = (e3))) -> (~((op (e0) (e3)) = (op (e1) (e3)))) -> (~((op (e0) (e3)) = (op (e2) (e3)))) -> (((op (e2) (e0)) = (e2))\/(((op (e2) (e1)) = (e2))\/(((op (e2) (e2)) = (e2))\/((op (e2) (e3)) = (e2))))) -> ((op (e0) (e0)) = (e2)) -> (~((op (e0) (e0)) = (op (e2) (e0)))) -> (~((op (e2) (e1)) = (op (e3) (e1)))) -> (~((op (e2) (e2)) = (e2))) -> (~((op (e1) (e3)) = (op (e2) (e3)))) -> ((op (e1) (e3)) = (e2)) -> False). % 18.65/18.83 do 0 intro. intros zenon_H160 zenon_H57 zenon_H10a zenon_H24 zenon_H142 zenon_H12b zenon_H9e zenon_Ha0 zenon_H18b zenon_H81 zenon_H25 zenon_Hac zenon_H1cf zenon_H3a zenon_Ha1 zenon_H1ac zenon_H14f zenon_H45 zenon_H67 zenon_H5b zenon_H233 zenon_H206 zenon_H1f0 zenon_H1fa zenon_H1ba zenon_H1e0 zenon_H1ee zenon_H1fe zenon_H168 zenon_H124 zenon_H136 zenon_H128 zenon_H13c zenon_H179 zenon_H178 zenon_H17b zenon_H183 zenon_He7 zenon_H19d zenon_H195 zenon_H191 zenon_H205 zenon_H204 zenon_H1ec zenon_Ha8 zenon_H165 zenon_H185 zenon_H2f zenon_H184 zenon_H1a7 zenon_H22d zenon_H133 zenon_H71 zenon_H6d zenon_Hd8 zenon_H54 zenon_H210 zenon_H4a zenon_H115 zenon_H11f zenon_H22a zenon_Hdf zenon_H109 zenon_H106 zenon_H189 zenon_H18c zenon_H16f zenon_H153 zenon_H2b zenon_H4f zenon_H6f zenon_H6a zenon_H1cc zenon_H13e zenon_H1a6 zenon_H1a4 zenon_H1a5 zenon_He4 zenon_Hd5 zenon_He8 zenon_H9a zenon_H52 zenon_H1c4 zenon_H18f zenon_H139 zenon_H201 zenon_H22 zenon_H95 zenon_H208 zenon_H74 zenon_H1ed zenon_H3f zenon_H23 zenon_H3e zenon_H94 zenon_H182 zenon_H235 zenon_Hf3 zenon_H1b1 zenon_H1d8 zenon_H10e zenon_H145 zenon_H7c zenon_H1c7 zenon_H62 zenon_H149 zenon_H34 zenon_H17e zenon_H20b zenon_H212 zenon_Hf0 zenon_H48 zenon_H172 zenon_H101 zenon_Hc2 zenon_H130 zenon_H102 zenon_H1d zenon_He2 zenon_H1d5 zenon_H7b zenon_H39 zenon_Haf zenon_H173 zenon_Hdb zenon_Hd7. % 18.65/18.83 apply (zenon_or_s _ _ zenon_H1d8); [ zenon_intro zenon_H10f | zenon_intro zenon_H1d9 ]. % 18.65/18.83 apply (zenon_L458_); trivial. % 18.65/18.83 apply (zenon_or_s _ _ zenon_H1d9); [ zenon_intro zenon_H110 | zenon_intro zenon_H1da ]. % 18.65/18.83 apply (zenon_L283_); trivial. % 18.65/18.83 apply (zenon_or_s _ _ zenon_H1da); [ zenon_intro zenon_H1ca | zenon_intro zenon_H14d ]. % 18.65/18.83 apply (zenon_L504_); trivial. % 18.65/18.83 apply (zenon_L505_); trivial. % 18.65/18.83 (* end of lemma zenon_L506_ *) % 18.65/18.83 assert (zenon_L507_ : (~((op (op (e1) (e1)) (e1)) = (op (e2) (e1)))) -> ((op (e1) (e1)) = (e2)) -> False). % 18.65/18.83 do 0 intro. intros zenon_H238 zenon_H110. % 18.65/18.83 cut (((e1) = (e1))); [idtac | apply NNPP; zenon_intro zenon_H79]. % 18.65/18.83 cut (((op (e1) (e1)) = (e2))); [idtac | apply NNPP; zenon_intro zenon_H20c]. % 18.65/18.83 congruence. % 18.65/18.83 exact (zenon_H20c zenon_H110). % 18.65/18.83 apply zenon_H79. apply refl_equal. % 18.65/18.83 (* end of lemma zenon_L507_ *) % 18.65/18.83 assert (zenon_L508_ : ((op (e2) (e1)) = (e3)) -> ((op (e1) (e1)) = (e2)) -> (~((e3) = (op (op (e1) (e1)) (e1)))) -> False). % 18.65/18.83 do 0 intro. intros zenon_Ha6 zenon_H110 zenon_H222. % 18.65/18.83 elim (classic ((op (op (e1) (e1)) (e1)) = (op (op (e1) (e1)) (e1)))); [ zenon_intro zenon_H217 | zenon_intro zenon_H218 ]. % 18.65/18.83 cut (((op (op (e1) (e1)) (e1)) = (op (op (e1) (e1)) (e1))) = ((e3) = (op (op (e1) (e1)) (e1)))). % 18.65/18.83 intro zenon_D_pnotp. % 18.65/18.83 apply zenon_H222. % 18.65/18.83 rewrite <- zenon_D_pnotp. % 18.65/18.83 exact zenon_H217. % 18.65/18.83 cut (((op (op (e1) (e1)) (e1)) = (op (op (e1) (e1)) (e1)))); [idtac | apply NNPP; zenon_intro zenon_H218]. % 18.65/18.83 cut (((op (op (e1) (e1)) (e1)) = (e3))); [idtac | apply NNPP; zenon_intro zenon_H223]. % 18.65/18.83 congruence. % 18.65/18.83 cut (((op (e2) (e1)) = (e3)) = ((op (op (e1) (e1)) (e1)) = (e3))). % 18.65/18.83 intro zenon_D_pnotp. % 18.65/18.83 apply zenon_H223. % 18.65/18.83 rewrite <- zenon_D_pnotp. % 18.65/18.83 exact zenon_Ha6. % 18.65/18.83 cut (((e3) = (e3))); [idtac | apply NNPP; zenon_intro zenon_H85]. % 18.65/18.83 cut (((op (e2) (e1)) = (op (op (e1) (e1)) (e1)))); [idtac | apply NNPP; zenon_intro zenon_H239]. % 18.65/18.83 congruence. % 18.65/18.83 elim (classic ((op (op (e1) (e1)) (e1)) = (op (op (e1) (e1)) (e1)))); [ zenon_intro zenon_H217 | zenon_intro zenon_H218 ]. % 18.65/18.83 cut (((op (op (e1) (e1)) (e1)) = (op (op (e1) (e1)) (e1))) = ((op (e2) (e1)) = (op (op (e1) (e1)) (e1)))). % 18.65/18.83 intro zenon_D_pnotp. % 18.65/18.83 apply zenon_H239. % 18.65/18.83 rewrite <- zenon_D_pnotp. % 18.65/18.83 exact zenon_H217. % 18.65/18.83 cut (((op (op (e1) (e1)) (e1)) = (op (op (e1) (e1)) (e1)))); [idtac | apply NNPP; zenon_intro zenon_H218]. % 18.68/18.83 cut (((op (op (e1) (e1)) (e1)) = (op (e2) (e1)))); [idtac | apply NNPP; zenon_intro zenon_H238]. % 18.68/18.83 congruence. % 18.68/18.83 apply (zenon_L507_); trivial. % 18.68/18.83 apply zenon_H218. apply refl_equal. % 18.68/18.83 apply zenon_H218. apply refl_equal. % 18.68/18.83 apply zenon_H85. apply refl_equal. % 18.68/18.83 apply zenon_H218. apply refl_equal. % 18.68/18.83 apply zenon_H218. apply refl_equal. % 18.68/18.83 (* end of lemma zenon_L508_ *) % 18.68/18.83 assert (zenon_L509_ : ((op (e3) (e1)) = (e0)) -> ((op (e2) (e1)) = (e3)) -> ((op (e1) (e1)) = (e2)) -> False). % 18.68/18.83 do 0 intro. intros zenon_H1b1 zenon_Ha6 zenon_H110. % 18.68/18.83 apply (zenon_notand_s _ _ ax13); [ zenon_intro zenon_H23b | zenon_intro zenon_H23a ]. % 18.68/18.83 elim (classic ((op (op (op (e1) (e1)) (e1)) (e1)) = (op (op (op (e1) (e1)) (e1)) (e1)))); [ zenon_intro zenon_H21d | zenon_intro zenon_H21e ]. % 18.68/18.83 cut (((op (op (op (e1) (e1)) (e1)) (e1)) = (op (op (op (e1) (e1)) (e1)) (e1))) = ((e0) = (op (op (op (e1) (e1)) (e1)) (e1)))). % 18.68/18.83 intro zenon_D_pnotp. % 18.68/18.83 apply zenon_H23b. % 18.68/18.83 rewrite <- zenon_D_pnotp. % 18.68/18.83 exact zenon_H21d. % 18.68/18.83 cut (((op (op (op (e1) (e1)) (e1)) (e1)) = (op (op (op (e1) (e1)) (e1)) (e1)))); [idtac | apply NNPP; zenon_intro zenon_H21e]. % 18.68/18.83 cut (((op (op (op (e1) (e1)) (e1)) (e1)) = (e0))); [idtac | apply NNPP; zenon_intro zenon_H23c]. % 18.68/18.83 congruence. % 18.68/18.83 cut (((op (e3) (e1)) = (e0)) = ((op (op (op (e1) (e1)) (e1)) (e1)) = (e0))). % 18.68/18.83 intro zenon_D_pnotp. % 18.68/18.83 apply zenon_H23c. % 18.68/18.83 rewrite <- zenon_D_pnotp. % 18.68/18.83 exact zenon_H1b1. % 18.68/18.83 cut (((e0) = (e0))); [idtac | apply NNPP; zenon_intro zenon_H82]. % 18.68/18.83 cut (((op (e3) (e1)) = (op (op (op (e1) (e1)) (e1)) (e1)))); [idtac | apply NNPP; zenon_intro zenon_H227]. % 18.68/18.83 congruence. % 18.68/18.83 elim (classic ((op (op (op (e1) (e1)) (e1)) (e1)) = (op (op (op (e1) (e1)) (e1)) (e1)))); [ zenon_intro zenon_H21d | zenon_intro zenon_H21e ]. % 18.68/18.83 cut (((op (op (op (e1) (e1)) (e1)) (e1)) = (op (op (op (e1) (e1)) (e1)) (e1))) = ((op (e3) (e1)) = (op (op (op (e1) (e1)) (e1)) (e1)))). % 18.68/18.83 intro zenon_D_pnotp. % 18.68/18.83 apply zenon_H227. % 18.68/18.83 rewrite <- zenon_D_pnotp. % 18.68/18.83 exact zenon_H21d. % 18.68/18.83 cut (((op (op (op (e1) (e1)) (e1)) (e1)) = (op (op (op (e1) (e1)) (e1)) (e1)))); [idtac | apply NNPP; zenon_intro zenon_H21e]. % 18.68/18.83 cut (((op (op (op (e1) (e1)) (e1)) (e1)) = (op (e3) (e1)))); [idtac | apply NNPP; zenon_intro zenon_H228]. % 18.68/18.83 congruence. % 18.68/18.83 cut (((e1) = (e1))); [idtac | apply NNPP; zenon_intro zenon_H79]. % 18.68/18.83 cut (((op (op (e1) (e1)) (e1)) = (e3))); [idtac | apply NNPP; zenon_intro zenon_H223]. % 18.68/18.83 congruence. % 18.68/18.83 cut (((op (e2) (e1)) = (e3)) = ((op (op (e1) (e1)) (e1)) = (e3))). % 18.68/18.83 intro zenon_D_pnotp. % 18.68/18.83 apply zenon_H223. % 18.68/18.83 rewrite <- zenon_D_pnotp. % 18.68/18.83 exact zenon_Ha6. % 18.68/18.83 cut (((e3) = (e3))); [idtac | apply NNPP; zenon_intro zenon_H85]. % 18.68/18.83 cut (((op (e2) (e1)) = (op (op (e1) (e1)) (e1)))); [idtac | apply NNPP; zenon_intro zenon_H239]. % 18.68/18.83 congruence. % 18.68/18.83 elim (classic ((op (op (e1) (e1)) (e1)) = (op (op (e1) (e1)) (e1)))); [ zenon_intro zenon_H217 | zenon_intro zenon_H218 ]. % 18.68/18.83 cut (((op (op (e1) (e1)) (e1)) = (op (op (e1) (e1)) (e1))) = ((op (e2) (e1)) = (op (op (e1) (e1)) (e1)))). % 18.68/18.83 intro zenon_D_pnotp. % 18.68/18.83 apply zenon_H239. % 18.68/18.83 rewrite <- zenon_D_pnotp. % 18.68/18.83 exact zenon_H217. % 18.68/18.83 cut (((op (op (e1) (e1)) (e1)) = (op (op (e1) (e1)) (e1)))); [idtac | apply NNPP; zenon_intro zenon_H218]. % 18.68/18.83 cut (((op (op (e1) (e1)) (e1)) = (op (e2) (e1)))); [idtac | apply NNPP; zenon_intro zenon_H238]. % 18.68/18.83 congruence. % 18.68/18.83 apply (zenon_L507_); trivial. % 18.68/18.83 apply zenon_H218. apply refl_equal. % 18.68/18.83 apply zenon_H218. apply refl_equal. % 18.68/18.83 apply zenon_H85. apply refl_equal. % 18.68/18.83 apply zenon_H79. apply refl_equal. % 18.68/18.83 apply zenon_H21e. apply refl_equal. % 18.68/18.83 apply zenon_H21e. apply refl_equal. % 18.68/18.83 apply zenon_H82. apply refl_equal. % 18.68/18.83 apply zenon_H21e. apply refl_equal. % 18.68/18.83 apply zenon_H21e. apply refl_equal. % 18.68/18.83 apply (zenon_notand_s _ _ zenon_H23a); [ zenon_intro zenon_H222 | zenon_intro zenon_H111 ]. % 18.68/18.83 apply (zenon_L508_); trivial. % 18.68/18.83 apply zenon_H111. apply sym_equal. exact zenon_H110. % 18.68/18.83 (* end of lemma zenon_L509_ *) % 18.68/18.83 assert (zenon_L510_ : (((op (e2) (e1)) = (e0))\/(((op (e2) (e1)) = (e1))\/(((op (e2) (e1)) = (e2))\/((op (e2) (e1)) = (e3))))) -> (~((op (e2) (e1)) = (e0))) -> ((op (e2) (e3)) = (e1)) -> (~((op (e2) (e1)) = (op (e2) (e3)))) -> ((op (e2) (e3)) = (e2)) -> ((op (e3) (e1)) = (e0)) -> ((op (e1) (e1)) = (e2)) -> False). % 18.68/18.83 do 0 intro. intros zenon_H1cc zenon_H31 zenon_Hf4 zenon_H1c7 zenon_H11d zenon_H1b1 zenon_H110. % 18.68/18.83 apply (zenon_or_s _ _ zenon_H1cc); [ zenon_intro zenon_H36 | zenon_intro zenon_H1cd ]. % 18.68/18.83 exact (zenon_H31 zenon_H36). % 18.68/18.83 apply (zenon_or_s _ _ zenon_H1cd); [ zenon_intro zenon_Ha5 | zenon_intro zenon_H1ce ]. % 18.68/18.83 apply (zenon_L188_); trivial. % 18.68/18.83 apply (zenon_or_s _ _ zenon_H1ce); [ zenon_intro zenon_H1ca | zenon_intro zenon_Ha6 ]. % 18.68/18.83 apply (zenon_L224_); trivial. % 18.68/18.83 apply (zenon_L509_); trivial. % 18.68/18.83 (* end of lemma zenon_L510_ *) % 18.68/18.83 assert (zenon_L511_ : (((op (e2) (e2)) = (e0))\/(((op (e2) (e2)) = (e1))\/(((op (e2) (e2)) = (e2))\/((op (e2) (e2)) = (e3))))) -> (~((op (e2) (e2)) = (e0))) -> ((op (e1) (e2)) = (e0)) -> ((op (e0) (e2)) = (e3)) -> (~((op (e2) (e2)) = (e2))) -> ((op (e2) (e0)) = (e3)) -> (~((op (e2) (e0)) = (op (e2) (e2)))) -> False). % 18.68/18.83 do 0 intro. intros zenon_H1c4 zenon_H81 zenon_H2a zenon_Ha9 zenon_H173 zenon_H3b zenon_H52. % 18.68/18.83 apply (zenon_or_s _ _ zenon_H1c4); [ zenon_intro zenon_H2c | zenon_intro zenon_H1c5 ]. % 18.68/18.83 exact (zenon_H81 zenon_H2c). % 18.68/18.83 apply (zenon_or_s _ _ zenon_H1c5); [ zenon_intro zenon_Hf1 | zenon_intro zenon_H1c6 ]. % 18.68/18.83 apply (zenon_L184_); trivial. % 18.68/18.83 apply (zenon_or_s _ _ zenon_H1c6); [ zenon_intro zenon_H176 | zenon_intro zenon_Haa ]. % 18.68/18.83 exact (zenon_H173 zenon_H176). % 18.68/18.83 apply (zenon_L168_); trivial. % 18.68/18.83 (* end of lemma zenon_L511_ *) % 18.68/18.83 assert (zenon_L512_ : (~((op (op (e1) (e1)) (e1)) = (op (e3) (e1)))) -> ((op (e1) (e1)) = (e3)) -> False). % 18.68/18.83 do 0 intro. intros zenon_H23d zenon_H13f. % 18.68/18.83 cut (((e1) = (e1))); [idtac | apply NNPP; zenon_intro zenon_H79]. % 18.68/18.83 cut (((op (e1) (e1)) = (e3))); [idtac | apply NNPP; zenon_intro zenon_H1a1]. % 18.68/18.83 congruence. % 18.68/18.83 exact (zenon_H1a1 zenon_H13f). % 18.68/18.83 apply zenon_H79. apply refl_equal. % 18.68/18.83 (* end of lemma zenon_L512_ *) % 18.68/18.83 assert (zenon_L513_ : ((op (e3) (e1)) = (e2)) -> ((op (e1) (e1)) = (e3)) -> (~((e2) = (op (op (e1) (e1)) (e1)))) -> False). % 18.68/18.83 do 0 intro. intros zenon_H14d zenon_H13f zenon_H216. % 18.68/18.83 elim (classic ((op (op (e1) (e1)) (e1)) = (op (op (e1) (e1)) (e1)))); [ zenon_intro zenon_H217 | zenon_intro zenon_H218 ]. % 18.68/18.83 cut (((op (op (e1) (e1)) (e1)) = (op (op (e1) (e1)) (e1))) = ((e2) = (op (op (e1) (e1)) (e1)))). % 18.68/18.83 intro zenon_D_pnotp. % 18.68/18.83 apply zenon_H216. % 18.68/18.83 rewrite <- zenon_D_pnotp. % 18.68/18.83 exact zenon_H217. % 18.68/18.83 cut (((op (op (e1) (e1)) (e1)) = (op (op (e1) (e1)) (e1)))); [idtac | apply NNPP; zenon_intro zenon_H218]. % 18.68/18.83 cut (((op (op (e1) (e1)) (e1)) = (e2))); [idtac | apply NNPP; zenon_intro zenon_H219]. % 18.68/18.83 congruence. % 18.68/18.83 cut (((op (e3) (e1)) = (e2)) = ((op (op (e1) (e1)) (e1)) = (e2))). % 18.68/18.83 intro zenon_D_pnotp. % 18.68/18.83 apply zenon_H219. % 18.68/18.83 rewrite <- zenon_D_pnotp. % 18.68/18.83 exact zenon_H14d. % 18.68/18.83 cut (((e2) = (e2))); [idtac | apply NNPP; zenon_intro zenon_H7e]. % 18.68/18.83 cut (((op (e3) (e1)) = (op (op (e1) (e1)) (e1)))); [idtac | apply NNPP; zenon_intro zenon_H23e]. % 18.68/18.83 congruence. % 18.68/18.83 elim (classic ((op (op (e1) (e1)) (e1)) = (op (op (e1) (e1)) (e1)))); [ zenon_intro zenon_H217 | zenon_intro zenon_H218 ]. % 18.68/18.83 cut (((op (op (e1) (e1)) (e1)) = (op (op (e1) (e1)) (e1))) = ((op (e3) (e1)) = (op (op (e1) (e1)) (e1)))). % 18.68/18.83 intro zenon_D_pnotp. % 18.68/18.83 apply zenon_H23e. % 18.68/18.83 rewrite <- zenon_D_pnotp. % 18.68/18.83 exact zenon_H217. % 18.68/18.83 cut (((op (op (e1) (e1)) (e1)) = (op (op (e1) (e1)) (e1)))); [idtac | apply NNPP; zenon_intro zenon_H218]. % 18.68/18.83 cut (((op (op (e1) (e1)) (e1)) = (op (e3) (e1)))); [idtac | apply NNPP; zenon_intro zenon_H23d]. % 18.68/18.83 congruence. % 18.68/18.83 apply (zenon_L512_); trivial. % 18.68/18.83 apply zenon_H218. apply refl_equal. % 18.68/18.83 apply zenon_H218. apply refl_equal. % 18.68/18.83 apply zenon_H7e. apply refl_equal. % 18.68/18.83 apply zenon_H218. apply refl_equal. % 18.68/18.83 apply zenon_H218. apply refl_equal. % 18.68/18.83 (* end of lemma zenon_L513_ *) % 18.68/18.83 assert (zenon_L514_ : ((op (e2) (e1)) = (e0)) -> ((op (e3) (e1)) = (e2)) -> ((op (e1) (e1)) = (e3)) -> False). % 18.68/18.83 do 0 intro. intros zenon_H36 zenon_H14d zenon_H13f. % 18.68/18.83 apply (zenon_notand_s _ _ ax12); [ zenon_intro zenon_H23b | zenon_intro zenon_H23f ]. % 18.68/18.83 elim (classic ((op (op (op (e1) (e1)) (e1)) (e1)) = (op (op (op (e1) (e1)) (e1)) (e1)))); [ zenon_intro zenon_H21d | zenon_intro zenon_H21e ]. % 18.68/18.83 cut (((op (op (op (e1) (e1)) (e1)) (e1)) = (op (op (op (e1) (e1)) (e1)) (e1))) = ((e0) = (op (op (op (e1) (e1)) (e1)) (e1)))). % 18.68/18.83 intro zenon_D_pnotp. % 18.68/18.83 apply zenon_H23b. % 18.68/18.83 rewrite <- zenon_D_pnotp. % 18.68/18.83 exact zenon_H21d. % 18.68/18.83 cut (((op (op (op (e1) (e1)) (e1)) (e1)) = (op (op (op (e1) (e1)) (e1)) (e1)))); [idtac | apply NNPP; zenon_intro zenon_H21e]. % 18.68/18.83 cut (((op (op (op (e1) (e1)) (e1)) (e1)) = (e0))); [idtac | apply NNPP; zenon_intro zenon_H23c]. % 18.68/18.83 congruence. % 18.68/18.83 cut (((op (e2) (e1)) = (e0)) = ((op (op (op (e1) (e1)) (e1)) (e1)) = (e0))). % 18.68/18.83 intro zenon_D_pnotp. % 18.68/18.83 apply zenon_H23c. % 18.68/18.83 rewrite <- zenon_D_pnotp. % 18.68/18.83 exact zenon_H36. % 18.68/18.83 cut (((e0) = (e0))); [idtac | apply NNPP; zenon_intro zenon_H82]. % 18.68/18.83 cut (((op (e2) (e1)) = (op (op (op (e1) (e1)) (e1)) (e1)))); [idtac | apply NNPP; zenon_intro zenon_H220]. % 18.68/18.83 congruence. % 18.68/18.83 elim (classic ((op (op (op (e1) (e1)) (e1)) (e1)) = (op (op (op (e1) (e1)) (e1)) (e1)))); [ zenon_intro zenon_H21d | zenon_intro zenon_H21e ]. % 18.68/18.83 cut (((op (op (op (e1) (e1)) (e1)) (e1)) = (op (op (op (e1) (e1)) (e1)) (e1))) = ((op (e2) (e1)) = (op (op (op (e1) (e1)) (e1)) (e1)))). % 18.68/18.83 intro zenon_D_pnotp. % 18.68/18.83 apply zenon_H220. % 18.68/18.83 rewrite <- zenon_D_pnotp. % 18.68/18.83 exact zenon_H21d. % 18.68/18.83 cut (((op (op (op (e1) (e1)) (e1)) (e1)) = (op (op (op (e1) (e1)) (e1)) (e1)))); [idtac | apply NNPP; zenon_intro zenon_H21e]. % 18.68/18.83 cut (((op (op (op (e1) (e1)) (e1)) (e1)) = (op (e2) (e1)))); [idtac | apply NNPP; zenon_intro zenon_H221]. % 18.68/18.83 congruence. % 18.68/18.83 cut (((e1) = (e1))); [idtac | apply NNPP; zenon_intro zenon_H79]. % 18.68/18.83 cut (((op (op (e1) (e1)) (e1)) = (e2))); [idtac | apply NNPP; zenon_intro zenon_H219]. % 18.68/18.83 congruence. % 18.68/18.83 cut (((op (e3) (e1)) = (e2)) = ((op (op (e1) (e1)) (e1)) = (e2))). % 18.68/18.83 intro zenon_D_pnotp. % 18.68/18.83 apply zenon_H219. % 18.68/18.83 rewrite <- zenon_D_pnotp. % 18.68/18.83 exact zenon_H14d. % 18.68/18.83 cut (((e2) = (e2))); [idtac | apply NNPP; zenon_intro zenon_H7e]. % 18.68/18.83 cut (((op (e3) (e1)) = (op (op (e1) (e1)) (e1)))); [idtac | apply NNPP; zenon_intro zenon_H23e]. % 18.68/18.83 congruence. % 18.68/18.83 elim (classic ((op (op (e1) (e1)) (e1)) = (op (op (e1) (e1)) (e1)))); [ zenon_intro zenon_H217 | zenon_intro zenon_H218 ]. % 18.68/18.83 cut (((op (op (e1) (e1)) (e1)) = (op (op (e1) (e1)) (e1))) = ((op (e3) (e1)) = (op (op (e1) (e1)) (e1)))). % 18.68/18.83 intro zenon_D_pnotp. % 18.68/18.83 apply zenon_H23e. % 18.68/18.83 rewrite <- zenon_D_pnotp. % 18.68/18.83 exact zenon_H217. % 18.68/18.83 cut (((op (op (e1) (e1)) (e1)) = (op (op (e1) (e1)) (e1)))); [idtac | apply NNPP; zenon_intro zenon_H218]. % 18.68/18.83 cut (((op (op (e1) (e1)) (e1)) = (op (e3) (e1)))); [idtac | apply NNPP; zenon_intro zenon_H23d]. % 18.68/18.83 congruence. % 18.68/18.83 apply (zenon_L512_); trivial. % 18.68/18.83 apply zenon_H218. apply refl_equal. % 18.68/18.83 apply zenon_H218. apply refl_equal. % 18.68/18.83 apply zenon_H7e. apply refl_equal. % 18.68/18.83 apply zenon_H79. apply refl_equal. % 18.68/18.83 apply zenon_H21e. apply refl_equal. % 18.68/18.83 apply zenon_H21e. apply refl_equal. % 18.68/18.83 apply zenon_H82. apply refl_equal. % 18.68/18.83 apply zenon_H21e. apply refl_equal. % 18.68/18.83 apply zenon_H21e. apply refl_equal. % 18.68/18.83 apply (zenon_notand_s _ _ zenon_H23f); [ zenon_intro zenon_H216 | zenon_intro zenon_H15d ]. % 18.68/18.83 apply (zenon_L513_); trivial. % 18.68/18.83 apply zenon_H15d. apply sym_equal. exact zenon_H13f. % 18.68/18.83 (* end of lemma zenon_L514_ *) % 18.68/18.83 assert (zenon_L515_ : ((op (e0) (e3)) = (e0)) -> ((op (e0) (e3)) = (e3)) -> (~((e0) = (e3))) -> False). % 18.68/18.83 do 0 intro. intros zenon_H1e zenon_He3 zenon_H9a. % 18.68/18.83 elim (classic ((e3) = (e3))); [ zenon_intro zenon_H96 | zenon_intro zenon_H85 ]. % 18.68/18.83 cut (((e3) = (e3)) = ((e0) = (e3))). % 18.68/18.83 intro zenon_D_pnotp. % 18.68/18.83 apply zenon_H9a. % 18.68/18.83 rewrite <- zenon_D_pnotp. % 18.68/18.83 exact zenon_H96. % 18.68/18.83 cut (((e3) = (e3))); [idtac | apply NNPP; zenon_intro zenon_H85]. % 18.68/18.83 cut (((e3) = (e0))); [idtac | apply NNPP; zenon_intro zenon_H9b]. % 18.68/18.83 congruence. % 18.68/18.83 cut (((op (e0) (e3)) = (e0)) = ((e3) = (e0))). % 18.68/18.83 intro zenon_D_pnotp. % 18.68/18.83 apply zenon_H9b. % 18.68/18.83 rewrite <- zenon_D_pnotp. % 18.68/18.83 exact zenon_H1e. % 18.68/18.83 cut (((e0) = (e0))); [idtac | apply NNPP; zenon_intro zenon_H82]. % 18.68/18.83 cut (((op (e0) (e3)) = (e3))); [idtac | apply NNPP; zenon_intro zenon_H12d]. % 18.68/18.83 congruence. % 18.68/18.83 exact (zenon_H12d zenon_He3). % 18.68/18.83 apply zenon_H82. apply refl_equal. % 18.68/18.83 apply zenon_H85. apply refl_equal. % 18.68/18.83 apply zenon_H85. apply refl_equal. % 18.68/18.83 (* end of lemma zenon_L515_ *) % 18.68/18.83 assert (zenon_L516_ : (((op (e1) (e3)) = (e0))\/(((op (e1) (e3)) = (e1))\/(((op (e1) (e3)) = (e2))\/((op (e1) (e3)) = (e3))))) -> (~((op (e1) (e3)) = (e0))) -> ((op (e3) (e3)) = (e1)) -> ((op (e3) (e3)) = (e2)) -> (~((op (e1) (e3)) = (op (e3) (e3)))) -> (~((op (e1) (e3)) = (op (e2) (e3)))) -> ((op (e2) (e3)) = (e3)) -> False). % 18.68/18.83 do 0 intro. intros zenon_Hdf zenon_H38 zenon_Hc4 zenon_Hf6 zenon_Hd5 zenon_Hdb zenon_Hdd. % 18.68/18.83 apply (zenon_or_s _ _ zenon_Hdf); [ zenon_intro zenon_H1f | zenon_intro zenon_He0 ]. % 18.68/18.83 exact (zenon_H38 zenon_H1f). % 18.68/18.83 apply (zenon_or_s _ _ zenon_He0); [ zenon_intro zenon_Hd6 | zenon_intro zenon_He1 ]. % 18.68/18.83 apply (zenon_L50_); trivial. % 18.68/18.83 apply (zenon_or_s _ _ zenon_He1); [ zenon_intro zenon_Hd7 | zenon_intro zenon_Hdc ]. % 18.68/18.83 apply (zenon_L402_); trivial. % 18.68/18.83 apply (zenon_L52_); trivial. % 18.68/18.83 (* end of lemma zenon_L516_ *) % 18.68/18.83 assert (zenon_L517_ : (((op (e0) (e3)) = (e3))\/(((op (e1) (e3)) = (e3))\/(((op (e2) (e3)) = (e3))\/((op (e3) (e3)) = (e3))))) -> (~((e0) = (e3))) -> (~((op (e2) (e3)) = (op (e3) (e3)))) -> (~((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 (e1) (e3)) = (op (e2) (e3)))) -> (~((op (e1) (e3)) = (op (e3) (e3)))) -> ((op (e3) (e3)) = (e2)) -> ((op (e3) (e3)) = (e1)) -> (~((op (e1) (e3)) = (e0))) -> (((op (e1) (e3)) = (e0))\/(((op (e1) (e3)) = (e1))\/(((op (e1) (e3)) = (e2))\/((op (e1) (e3)) = (e3))))) -> (~((op (e3) (e3)) = (e3))) -> False). % 18.68/18.83 do 0 intro. intros zenon_H136 zenon_H9a zenon_Hf3 zenon_He2 zenon_H1e zenon_H11f zenon_Hdb zenon_Hd5 zenon_Hf6 zenon_Hc4 zenon_H38 zenon_Hdf zenon_H102. % 18.68/18.83 apply (zenon_or_s _ _ zenon_H136); [ zenon_intro zenon_He3 | zenon_intro zenon_H137 ]. % 18.68/18.83 apply (zenon_L515_); trivial. % 18.68/18.83 apply (zenon_or_s _ _ zenon_H137); [ zenon_intro zenon_Hdc | zenon_intro zenon_H138 ]. % 18.68/18.83 apply (zenon_L404_); trivial. % 18.68/18.83 apply (zenon_or_s _ _ zenon_H138); [ zenon_intro zenon_Hdd | zenon_intro zenon_H105 ]. % 18.68/18.83 apply (zenon_L516_); trivial. % 18.68/18.83 exact (zenon_H102 zenon_H105). % 18.68/18.83 (* end of lemma zenon_L517_ *) % 18.68/18.83 assert (zenon_L518_ : (((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)) = (e3)) -> ((op (e2) (e1)) = (e0)) -> ((op (e3) (e2)) = (e3)) -> (~((op (e3) (e1)) = (op (e3) (e2)))) -> (~((op (e3) (e1)) = (op (e3) (e3)))) -> (~((op (e3) (e1)) = (e0))) -> (((op (e3) (e1)) = (e0))\/(((op (e3) (e1)) = (e1))\/(((op (e3) (e1)) = (e2))\/((op (e3) (e1)) = (e3))))) -> (((op (e0) (e3)) = (e3))\/(((op (e1) (e3)) = (e3))\/(((op (e2) (e3)) = (e3))\/((op (e3) (e3)) = (e3))))) -> (~((e0) = (e3))) -> (~((op (e2) (e3)) = (op (e3) (e3)))) -> (~((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 (e1) (e3)) = (op (e2) (e3)))) -> (~((op (e1) (e3)) = (op (e3) (e3)))) -> ((op (e3) (e3)) = (e1)) -> (~((op (e1) (e3)) = (e0))) -> (((op (e1) (e3)) = (e0))\/(((op (e1) (e3)) = (e1))\/(((op (e1) (e3)) = (e2))\/((op (e1) (e3)) = (e3))))) -> (~((op (e3) (e3)) = (e3))) -> False). % 18.68/18.83 do 0 intro. intros zenon_H153 zenon_H149 zenon_H44 zenon_H13f zenon_H36 zenon_H163 zenon_H1a4 zenon_H130 zenon_H1ad zenon_H22a zenon_H136 zenon_H9a zenon_Hf3 zenon_He2 zenon_H1e zenon_H11f zenon_Hdb zenon_Hd5 zenon_Hc4 zenon_H38 zenon_Hdf zenon_H102. % 18.68/18.83 apply (zenon_or_s _ _ zenon_H153); [ zenon_intro zenon_H148 | zenon_intro zenon_H154 ]. % 18.68/18.83 apply (zenon_L100_); trivial. % 18.68/18.83 apply (zenon_or_s _ _ zenon_H154); [ zenon_intro zenon_H14d | zenon_intro zenon_H155 ]. % 18.68/18.83 apply (zenon_L514_); trivial. % 18.68/18.83 apply (zenon_or_s _ _ zenon_H155); [ zenon_intro zenon_H151 | zenon_intro zenon_Hf6 ]. % 18.68/18.83 apply (zenon_L401_); trivial. % 18.68/18.83 apply (zenon_L517_); trivial. % 18.68/18.83 (* end of lemma zenon_L518_ *) % 18.68/18.83 assert (zenon_L519_ : (((op (e3) (e0)) = (e1))\/(((op (e3) (e1)) = (e1))\/(((op (e3) (e2)) = (e1))\/((op (e3) (e3)) = (e1))))) -> ((op (e0) (e0)) = (e3)) -> ((op (e1) (e0)) = (e2)) -> ((op (e0) (e1)) = (e1)) -> (~((op (e0) (e1)) = (op (e3) (e1)))) -> (~((op (e2) (e0)) = (op (e2) (e2)))) -> ((op (e2) (e0)) = (e3)) -> (~((op (e2) (e2)) = (e2))) -> (~((op (e2) (e2)) = (op (e3) (e2)))) -> (~((op (e2) (e2)) = (e0))) -> (((op (e2) (e2)) = (e0))\/(((op (e2) (e2)) = (e1))\/(((op (e2) (e2)) = (e2))\/((op (e2) (e2)) = (e3))))) -> (((op (e3) (e0)) = (e2))\/(((op (e3) (e1)) = (e2))\/(((op (e3) (e2)) = (e2))\/((op (e3) (e3)) = (e2))))) -> (~((e0) = (e2))) -> ((op (e3) (e0)) = (e0)) -> ((op (e1) (e1)) = (e3)) -> ((op (e2) (e1)) = (e0)) -> ((op (e3) (e2)) = (e3)) -> (~((op (e3) (e1)) = (op (e3) (e2)))) -> (~((op (e3) (e1)) = (op (e3) (e3)))) -> (~((op (e3) (e1)) = (e0))) -> (((op (e3) (e1)) = (e0))\/(((op (e3) (e1)) = (e1))\/(((op (e3) (e1)) = (e2))\/((op (e3) (e1)) = (e3))))) -> (((op (e0) (e3)) = (e3))\/(((op (e1) (e3)) = (e3))\/(((op (e2) (e3)) = (e3))\/((op (e3) (e3)) = (e3))))) -> (~((e0) = (e3))) -> (~((op (e2) (e3)) = (op (e3) (e3)))) -> (~((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 (e1) (e3)) = (op (e2) (e3)))) -> (~((op (e1) (e3)) = (op (e3) (e3)))) -> (~((op (e1) (e3)) = (e0))) -> (((op (e1) (e3)) = (e0))\/(((op (e1) (e3)) = (e1))\/(((op (e1) (e3)) = (e2))\/((op (e1) (e3)) = (e3))))) -> (~((op (e3) (e3)) = (e3))) -> False). % 18.68/18.83 do 0 intro. intros zenon_He8 zenon_H3a zenon_H86 zenon_Ha0 zenon_H210 zenon_H52 zenon_H3b zenon_H173 zenon_H18f zenon_H81 zenon_H1c4 zenon_H153 zenon_H149 zenon_H44 zenon_H13f zenon_H36 zenon_H163 zenon_H1a4 zenon_H130 zenon_H1ad zenon_H22a zenon_H136 zenon_H9a zenon_Hf3 zenon_He2 zenon_H1e zenon_H11f zenon_Hdb zenon_Hd5 zenon_H38 zenon_Hdf zenon_H102. % 18.68/18.83 apply (zenon_or_s _ _ zenon_He8); [ zenon_intro zenon_Hac | zenon_intro zenon_Heb ]. % 18.68/18.83 apply (zenon_L241_); trivial. % 18.68/18.83 apply (zenon_or_s _ _ zenon_Heb); [ zenon_intro zenon_Hae | zenon_intro zenon_Hec ]. % 18.68/18.83 apply (zenon_L363_); trivial. % 18.68/18.83 apply (zenon_or_s _ _ zenon_Hec); [ zenon_intro zenon_Hba | zenon_intro zenon_Hc4 ]. % 18.68/18.83 apply (zenon_L327_); trivial. % 18.68/18.83 apply (zenon_L518_); trivial. % 18.68/18.83 (* end of lemma zenon_L519_ *) % 18.68/18.83 assert (zenon_L520_ : (((op (e0) (e2)) = (e3))\/(((op (e1) (e2)) = (e3))\/(((op (e2) (e2)) = (e3))\/((op (e3) (e2)) = (e3))))) -> ((op (e1) (e2)) = (e0)) -> (~((e1) = (e3))) -> ((op (e1) (e2)) = (e1)) -> (((op (e3) (e0)) = (e1))\/(((op (e3) (e1)) = (e1))\/(((op (e3) (e2)) = (e1))\/((op (e3) (e3)) = (e1))))) -> ((op (e0) (e0)) = (e3)) -> ((op (e1) (e0)) = (e2)) -> ((op (e0) (e1)) = (e1)) -> (~((op (e0) (e1)) = (op (e3) (e1)))) -> (~((op (e2) (e0)) = (op (e2) (e2)))) -> ((op (e2) (e0)) = (e3)) -> (~((op (e2) (e2)) = (e2))) -> (~((op (e2) (e2)) = (op (e3) (e2)))) -> (~((op (e2) (e2)) = (e0))) -> (((op (e2) (e2)) = (e0))\/(((op (e2) (e2)) = (e1))\/(((op (e2) (e2)) = (e2))\/((op (e2) (e2)) = (e3))))) -> (((op (e3) (e0)) = (e2))\/(((op (e3) (e1)) = (e2))\/(((op (e3) (e2)) = (e2))\/((op (e3) (e3)) = (e2))))) -> (~((e0) = (e2))) -> ((op (e3) (e0)) = (e0)) -> ((op (e1) (e1)) = (e3)) -> ((op (e2) (e1)) = (e0)) -> (~((op (e3) (e1)) = (op (e3) (e2)))) -> (~((op (e3) (e1)) = (op (e3) (e3)))) -> (~((op (e3) (e1)) = (e0))) -> (((op (e3) (e1)) = (e0))\/(((op (e3) (e1)) = (e1))\/(((op (e3) (e1)) = (e2))\/((op (e3) (e1)) = (e3))))) -> (((op (e0) (e3)) = (e3))\/(((op (e1) (e3)) = (e3))\/(((op (e2) (e3)) = (e3))\/((op (e3) (e3)) = (e3))))) -> (~((e0) = (e3))) -> (~((op (e2) (e3)) = (op (e3) (e3)))) -> (~((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 (e1) (e3)) = (op (e2) (e3)))) -> (~((op (e1) (e3)) = (op (e3) (e3)))) -> (~((op (e1) (e3)) = (e0))) -> (((op (e1) (e3)) = (e0))\/(((op (e1) (e3)) = (e1))\/(((op (e1) (e3)) = (e2))\/((op (e1) (e3)) = (e3))))) -> (~((op (e3) (e3)) = (e3))) -> False). % 18.68/18.83 do 0 intro. intros zenon_H1a6 zenon_H2a zenon_H95 zenon_Hf0 zenon_He8 zenon_H3a zenon_H86 zenon_Ha0 zenon_H210 zenon_H52 zenon_H3b zenon_H173 zenon_H18f zenon_H81 zenon_H1c4 zenon_H153 zenon_H149 zenon_H44 zenon_H13f zenon_H36 zenon_H1a4 zenon_H130 zenon_H1ad zenon_H22a zenon_H136 zenon_H9a zenon_Hf3 zenon_He2 zenon_H1e zenon_H11f zenon_Hdb zenon_Hd5 zenon_H38 zenon_Hdf zenon_H102. % 18.68/18.83 apply (zenon_or_s _ _ zenon_H1a6); [ zenon_intro zenon_Ha9 | zenon_intro zenon_H1aa ]. % 18.68/18.83 apply (zenon_L511_); trivial. % 18.68/18.83 apply (zenon_or_s _ _ zenon_H1aa); [ zenon_intro zenon_H16c | zenon_intro zenon_H1ab ]. % 18.68/18.83 apply (zenon_L167_); trivial. % 18.68/18.83 apply (zenon_or_s _ _ zenon_H1ab); [ zenon_intro zenon_Haa | zenon_intro zenon_H163 ]. % 18.68/18.83 apply (zenon_L168_); trivial. % 18.68/18.83 apply (zenon_L519_); trivial. % 18.68/18.83 (* end of lemma zenon_L520_ *) % 18.68/18.83 assert (zenon_L521_ : ((op (e1) (e2)) = (e0)) -> ((op (e1) (e2)) = (e3)) -> (~((e0) = (e3))) -> False). % 18.68/18.83 do 0 intro. intros zenon_H2a zenon_H16c zenon_H9a. % 18.68/18.83 elim (classic ((e3) = (e3))); [ zenon_intro zenon_H96 | zenon_intro zenon_H85 ]. % 18.68/18.83 cut (((e3) = (e3)) = ((e0) = (e3))). % 18.68/18.83 intro zenon_D_pnotp. % 18.68/18.83 apply zenon_H9a. % 18.68/18.83 rewrite <- zenon_D_pnotp. % 18.68/18.83 exact zenon_H96. % 18.68/18.83 cut (((e3) = (e3))); [idtac | apply NNPP; zenon_intro zenon_H85]. % 18.68/18.83 cut (((e3) = (e0))); [idtac | apply NNPP; zenon_intro zenon_H9b]. % 18.68/18.83 congruence. % 18.68/18.83 cut (((op (e1) (e2)) = (e0)) = ((e3) = (e0))). % 18.68/18.83 intro zenon_D_pnotp. % 18.68/18.83 apply zenon_H9b. % 18.68/18.83 rewrite <- zenon_D_pnotp. % 18.68/18.83 exact zenon_H2a. % 18.68/18.83 cut (((e0) = (e0))); [idtac | apply NNPP; zenon_intro zenon_H82]. % 18.68/18.83 cut (((op (e1) (e2)) = (e3))); [idtac | apply NNPP; zenon_intro zenon_H16d]. % 18.68/18.83 congruence. % 18.68/18.83 exact (zenon_H16d zenon_H16c). % 18.68/18.83 apply zenon_H82. apply refl_equal. % 18.68/18.83 apply zenon_H85. apply refl_equal. % 18.68/18.83 apply zenon_H85. apply refl_equal. % 18.68/18.84 (* end of lemma zenon_L521_ *) % 18.68/18.84 assert (zenon_L522_ : (((op (e1) (e1)) = (e0))\/(((op (e1) (e1)) = (e1))\/(((op (e1) (e1)) = (e2))\/((op (e1) (e1)) = (e3))))) -> (~((op (e1) (e1)) = (e0))) -> (~((op (e1) (e1)) = (e1))) -> ((op (e3) (e1)) = (e2)) -> (~((op (e1) (e1)) = (op (e3) (e1)))) -> (~((op (e1) (e1)) = (op (e2) (e1)))) -> ((op (e2) (e1)) = (e3)) -> False). % 18.68/18.84 do 0 intro. intros zenon_H142 zenon_H24 zenon_H10a zenon_H14d zenon_H160 zenon_H13e zenon_Ha6. % 18.68/18.84 apply (zenon_or_s _ _ zenon_H142); [ zenon_intro zenon_H29 | zenon_intro zenon_H143 ]. % 18.68/18.84 exact (zenon_H24 zenon_H29). % 18.68/18.84 apply (zenon_or_s _ _ zenon_H143); [ zenon_intro zenon_H10d | zenon_intro zenon_H144 ]. % 18.68/18.84 exact (zenon_H10a zenon_H10d). % 18.68/18.84 apply (zenon_or_s _ _ zenon_H144); [ zenon_intro zenon_H110 | zenon_intro zenon_H13f ]. % 18.68/18.84 apply (zenon_L164_); trivial. % 18.68/18.84 apply (zenon_L95_); trivial. % 18.68/18.84 (* end of lemma zenon_L522_ *) % 18.68/18.84 assert (zenon_L523_ : (((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) (e0)) = (e2))\/(((op (e3) (e1)) = (e2))\/(((op (e3) (e2)) = (e2))\/((op (e3) (e3)) = (e2))))) -> (~((e0) = (e2))) -> ((op (e3) (e0)) = (e0)) -> ((op (e2) (e1)) = (e3)) -> (~((op (e1) (e1)) = (op (e2) (e1)))) -> (~((op (e1) (e1)) = (op (e3) (e1)))) -> (~((op (e1) (e1)) = (e1))) -> (~((op (e1) (e1)) = (e0))) -> (((op (e1) (e1)) = (e0))\/(((op (e1) (e1)) = (e1))\/(((op (e1) (e1)) = (e2))\/((op (e1) (e1)) = (e3))))) -> ((op (e3) (e2)) = (e3)) -> (~((op (e3) (e1)) = (op (e3) (e2)))) -> (~((op (e3) (e1)) = (op (e3) (e3)))) -> (~((op (e3) (e1)) = (e0))) -> (((op (e3) (e1)) = (e0))\/(((op (e3) (e1)) = (e1))\/(((op (e3) (e1)) = (e2))\/((op (e3) (e1)) = (e3))))) -> (((op (e0) (e3)) = (e3))\/(((op (e1) (e3)) = (e3))\/(((op (e2) (e3)) = (e3))\/((op (e3) (e3)) = (e3))))) -> (~((e0) = (e3))) -> (~((op (e2) (e3)) = (op (e3) (e3)))) -> (~((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 (e1) (e3)) = (op (e2) (e3)))) -> (~((op (e1) (e3)) = (op (e3) (e3)))) -> (~((op (e1) (e3)) = (e0))) -> (((op (e1) (e3)) = (e0))\/(((op (e1) (e3)) = (e1))\/(((op (e1) (e3)) = (e2))\/((op (e1) (e3)) = (e3))))) -> (~((op (e3) (e3)) = (e3))) -> False). % 18.68/18.84 do 0 intro. intros zenon_He8 zenon_Ha1 zenon_Ha0 zenon_H210 zenon_Hf0 zenon_H115 zenon_H153 zenon_H149 zenon_H44 zenon_Ha6 zenon_H13e zenon_H160 zenon_H10a zenon_H24 zenon_H142 zenon_H163 zenon_H1a4 zenon_H130 zenon_H1ad zenon_H22a zenon_H136 zenon_H9a zenon_Hf3 zenon_He2 zenon_H1e zenon_H11f zenon_Hdb zenon_Hd5 zenon_H38 zenon_Hdf zenon_H102. % 18.68/18.84 apply (zenon_or_s _ _ zenon_He8); [ zenon_intro zenon_Hac | zenon_intro zenon_Heb ]. % 18.68/18.84 apply (zenon_L41_); trivial. % 18.68/18.84 apply (zenon_or_s _ _ zenon_Heb); [ zenon_intro zenon_Hae | zenon_intro zenon_Hec ]. % 18.68/18.84 apply (zenon_L363_); trivial. % 18.68/18.84 apply (zenon_or_s _ _ zenon_Hec); [ zenon_intro zenon_Hba | zenon_intro zenon_Hc4 ]. % 18.68/18.84 apply (zenon_L69_); trivial. % 18.68/18.84 apply (zenon_or_s _ _ zenon_H153); [ zenon_intro zenon_H148 | zenon_intro zenon_H154 ]. % 18.68/18.84 apply (zenon_L100_); trivial. % 18.68/18.84 apply (zenon_or_s _ _ zenon_H154); [ zenon_intro zenon_H14d | zenon_intro zenon_H155 ]. % 18.68/18.84 apply (zenon_L522_); trivial. % 18.68/18.84 apply (zenon_or_s _ _ zenon_H155); [ zenon_intro zenon_H151 | zenon_intro zenon_Hf6 ]. % 18.68/18.84 apply (zenon_L401_); trivial. % 18.68/18.84 apply (zenon_L517_); trivial. % 18.68/18.84 (* end of lemma zenon_L523_ *) % 18.68/18.84 assert (zenon_L524_ : (((op (e0) (e2)) = (e3))\/(((op (e1) (e2)) = (e3))\/(((op (e2) (e2)) = (e3))\/((op (e3) (e2)) = (e3))))) -> (~((op (e2) (e2)) = (e2))) -> (~((op (e2) (e2)) = (e0))) -> (((op (e2) (e2)) = (e0))\/(((op (e2) (e2)) = (e1))\/(((op (e2) (e2)) = (e2))\/((op (e2) (e2)) = (e3))))) -> ((op (e1) (e2)) = (e0)) -> (~((op (e2) (e0)) = (op (e2) (e2)))) -> ((op (e2) (e0)) = (e3)) -> (((op (e3) (e0)) = (e1))\/(((op (e3) (e1)) = (e1))\/(((op (e3) (e2)) = (e1))\/((op (e3) (e3)) = (e1))))) -> (~((e0) = (e1))) -> ((op (e0) (e1)) = (e1)) -> (~((op (e0) (e1)) = (op (e3) (e1)))) -> ((op (e1) (e2)) = (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 (e3) (e0)) = (e0)) -> ((op (e2) (e1)) = (e3)) -> (~((op (e1) (e1)) = (op (e2) (e1)))) -> (~((op (e1) (e1)) = (op (e3) (e1)))) -> (~((op (e1) (e1)) = (e1))) -> (~((op (e1) (e1)) = (e0))) -> (((op (e1) (e1)) = (e0))\/(((op (e1) (e1)) = (e1))\/(((op (e1) (e1)) = (e2))\/((op (e1) (e1)) = (e3))))) -> (~((op (e3) (e1)) = (op (e3) (e2)))) -> (~((op (e3) (e1)) = (op (e3) (e3)))) -> (~((op (e3) (e1)) = (e0))) -> (((op (e3) (e1)) = (e0))\/(((op (e3) (e1)) = (e1))\/(((op (e3) (e1)) = (e2))\/((op (e3) (e1)) = (e3))))) -> (((op (e0) (e3)) = (e3))\/(((op (e1) (e3)) = (e3))\/(((op (e2) (e3)) = (e3))\/((op (e3) (e3)) = (e3))))) -> (~((e0) = (e3))) -> (~((op (e2) (e3)) = (op (e3) (e3)))) -> (~((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 (e1) (e3)) = (op (e2) (e3)))) -> (~((op (e1) (e3)) = (op (e3) (e3)))) -> (~((op (e1) (e3)) = (e0))) -> (((op (e1) (e3)) = (e0))\/(((op (e1) (e3)) = (e1))\/(((op (e1) (e3)) = (e2))\/((op (e1) (e3)) = (e3))))) -> (~((op (e3) (e3)) = (e3))) -> False). % 18.68/18.84 do 0 intro. intros zenon_H1a6 zenon_H173 zenon_H81 zenon_H1c4 zenon_H2a zenon_H52 zenon_H3b zenon_He8 zenon_Ha1 zenon_Ha0 zenon_H210 zenon_Hf0 zenon_H115 zenon_H153 zenon_H149 zenon_H44 zenon_Ha6 zenon_H13e zenon_H160 zenon_H10a zenon_H24 zenon_H142 zenon_H1a4 zenon_H130 zenon_H1ad zenon_H22a zenon_H136 zenon_H9a zenon_Hf3 zenon_He2 zenon_H1e zenon_H11f zenon_Hdb zenon_Hd5 zenon_H38 zenon_Hdf zenon_H102. % 18.68/18.84 apply (zenon_or_s _ _ zenon_H1a6); [ zenon_intro zenon_Ha9 | zenon_intro zenon_H1aa ]. % 18.68/18.84 apply (zenon_L511_); trivial. % 18.68/18.84 apply (zenon_or_s _ _ zenon_H1aa); [ zenon_intro zenon_H16c | zenon_intro zenon_H1ab ]. % 18.68/18.84 apply (zenon_L521_); trivial. % 18.68/18.84 apply (zenon_or_s _ _ zenon_H1ab); [ zenon_intro zenon_Haa | zenon_intro zenon_H163 ]. % 18.68/18.84 apply (zenon_L168_); trivial. % 18.68/18.84 apply (zenon_L523_); trivial. % 18.68/18.84 (* end of lemma zenon_L524_ *) % 18.68/18.84 assert (zenon_L525_ : (((op (e0) (e2)) = (e3))\/(((op (e1) (e2)) = (e3))\/(((op (e2) (e2)) = (e3))\/((op (e3) (e2)) = (e3))))) -> (~((op (e2) (e2)) = (e2))) -> (~((op (e2) (e2)) = (e0))) -> (((op (e2) (e2)) = (e0))\/(((op (e2) (e2)) = (e1))\/(((op (e2) (e2)) = (e2))\/((op (e2) (e2)) = (e3))))) -> (~((e0) = (e3))) -> ((op (e1) (e2)) = (e0)) -> (~((op (e2) (e0)) = (op (e2) (e2)))) -> ((op (e2) (e0)) = (e3)) -> (~((op (e3) (e1)) = (op (e3) (e2)))) -> ((op (e3) (e1)) = (e3)) -> False). % 18.68/18.84 do 0 intro. intros zenon_H1a6 zenon_H173 zenon_H81 zenon_H1c4 zenon_H9a zenon_H2a zenon_H52 zenon_H3b zenon_H1a4 zenon_H161. % 18.68/18.84 apply (zenon_or_s _ _ zenon_H1a6); [ zenon_intro zenon_Ha9 | zenon_intro zenon_H1aa ]. % 18.68/18.84 apply (zenon_L511_); trivial. % 18.68/18.84 apply (zenon_or_s _ _ zenon_H1aa); [ zenon_intro zenon_H16c | zenon_intro zenon_H1ab ]. % 18.68/18.84 apply (zenon_L521_); trivial. % 18.68/18.84 apply (zenon_or_s _ _ zenon_H1ab); [ zenon_intro zenon_Haa | zenon_intro zenon_H163 ]. % 18.68/18.84 apply (zenon_L168_); trivial. % 18.68/18.84 apply (zenon_L169_); trivial. % 18.68/18.84 (* end of lemma zenon_L525_ *) % 18.68/18.84 assert (zenon_L526_ : ((~((op (e2) (e1)) = (e0)))\/((op (e2) (e0)) = (e1))) -> ((~((op (e2) (e3)) = (e0)))\/((op (e2) (e0)) = (e3))) -> (((op (e0) (e0)) = (e0))\/(((op (e1) (e0)) = (e0))\/(((op (e2) (e0)) = (e0))\/((op (e3) (e0)) = (e0))))) -> (~((op (e1) (e0)) = (e0))) -> (~((op (e0) (e0)) = (e0))) -> ((~((op (e3) (e1)) = (e0)))\/((op (e3) (e0)) = (e1))) -> (((op (e0) (e0)) = (e0))\/(((op (e0) (e1)) = (e0))\/(((op (e0) (e2)) = (e0))\/((op (e0) (e3)) = (e0))))) -> (~((op (e0) (e2)) = (op (e0) (e3)))) -> (((op (e1) (e0)) = (e0))\/(((op (e1) (e1)) = (e0))\/(((op (e1) (e2)) = (e0))\/((op (e1) (e3)) = (e0))))) -> (~((e1) = (e2))) -> (~((op (e1) (e0)) = (op (e2) (e0)))) -> (~((op (e0) (e1)) = (op (e2) (e1)))) -> (~((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 (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 (e1) (e1)))) -> (((op (e2) (e1)) = (e0))\/(((op (e2) (e1)) = (e1))\/(((op (e2) (e1)) = (e2))\/((op (e2) (e1)) = (e3))))) -> (~((op (e0) (e3)) = (op (e3) (e3)))) -> (((op (e0) (e2)) = (e0))\/(((op (e1) (e2)) = (e0))\/(((op (e2) (e2)) = (e0))\/((op (e3) (e2)) = (e0))))) -> (~((op (e3) (e0)) = (op (e3) (e2)))) -> (~((op (e1) (e1)) = (op (e1) (e2)))) -> (~((op (e1) (e2)) = (op (e2) (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) (e2)) = (op (e3) (e3)))) -> (((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) (e0)) = (op (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) (e3)) = (e2))\/(((op (e1) (e3)) = (e2))\/(((op (e2) (e3)) = (e2))\/((op (e3) (e3)) = (e2))))) -> (((op (e2) (e0)) = (e1))\/(((op (e2) (e1)) = (e1))\/(((op (e2) (e2)) = (e1))\/((op (e2) (e3)) = (e1))))) -> (((op (e0) (e1)) = (e1))\/(((op (e1) (e1)) = (e1))\/(((op (e2) (e1)) = (e1))\/((op (e3) (e1)) = (e1))))) -> (~((op (e2) (e1)) = (op (e3) (e1)))) -> (~((op (e0) (e1)) = (op (e0) (e3)))) -> (~((op (e1) (e0)) = (op (e1) (e3)))) -> (~((op (e2) (e2)) = (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 (e0) (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)) = (e0))) -> ((~((op (e3) (e2)) = (e0)))\/((op (e3) (e0)) = (e2))) -> ((~((op (e3) (e0)) = (e0)))\/((op (e3) (e0)) = (e0))) -> (((op (e2) (e0)) = (e0))\/(((op (e2) (e1)) = (e0))\/(((op (e2) (e2)) = (e0))\/((op (e2) (e3)) = (e0))))) -> ((~((op (e2) (e2)) = (e0)))\/((op (e2) (e0)) = (e2))) -> (((op (e3) (e0)) = (e3))\/(((op (e3) (e1)) = (e3))\/(((op (e3) (e2)) = (e3))\/((op (e3) (e3)) = (e3))))) -> (~((op (e0) (e2)) = (op (e2) (e2)))) -> ((~((op (e3) (e3)) = (e0)))\/((op (e3) (e0)) = (e3))) -> ((~((op (e0) (e3)) = (e0)))\/((op (e0) (e0)) = (e3))) -> ((~((op (e1) (e1)) = (e0)))\/((op (e1) (e0)) = (e1))) -> (((op (e3) (e2)) = (e0))\/(((op (e3) (e2)) = (e1))\/(((op (e3) (e2)) = (e2))\/((op (e3) (e2)) = (e3))))) -> (~((op (e0) (e2)) = (op (e1) (e2)))) -> (((op (e1) (e2)) = (e0))\/(((op (e1) (e2)) = (e1))\/(((op (e1) (e2)) = (e2))\/((op (e1) (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 (e2) (e0)) = (op (e3) (e0)))) -> ((~((op (e1) (e2)) = (e0)))\/((op (e1) (e0)) = (e2))) -> ((~((op (e1) (e3)) = (e0)))\/((op (e1) (e0)) = (e3))) -> (~((op (e0) (e0)) = (op (e0) (e2)))) -> (((op (e1) (e0)) = (e1))\/(((op (e1) (e1)) = (e1))\/(((op (e1) (e2)) = (e1))\/((op (e1) (e3)) = (e1))))) -> (((op (e0) (e0)) = (e3))\/(((op (e0) (e1)) = (e3))\/(((op (e0) (e2)) = (e3))\/((op (e0) (e3)) = (e3))))) -> (((op (e0) (e0)) = (e2))\/(((op (e1) (e0)) = (e2))\/(((op (e2) (e0)) = (e2))\/((op (e3) (e0)) = (e2))))) -> ((~((op (e2) (e0)) = (e0)))\/((op (e2) (e0)) = (e0))) -> (((op (e0) (e0)) = (e3))\/(((op (e1) (e0)) = (e3))\/(((op (e2) (e0)) = (e3))\/((op (e3) (e0)) = (e3))))) -> (((op (e0) (e2)) = (e0))\/(((op (e0) (e2)) = (e1))\/(((op (e0) (e2)) = (e2))\/((op (e0) (e2)) = (e3))))) -> (~((op (e1) (e0)) = (op (e3) (e0)))) -> (~((op (e2) (e0)) = (op (e2) (e1)))) -> ((~((op (e1) (e0)) = (e0)))\/((op (e1) (e0)) = (e0))) -> ((~((op (e0) (e2)) = (e0)))\/((op (e0) (e0)) = (e2))) -> (~((op (e3) (e0)) = (op (e3) (e1)))) -> (~((op (e1) (e1)) = (op (e1) (e3)))) -> (~((op (e2) (e0)) = (op (e2) (e3)))) -> (((op (e0) (e3)) = (e0))\/(((op (e1) (e3)) = (e0))\/(((op (e2) (e3)) = (e0))\/((op (e3) (e3)) = (e0))))) -> (~((op (e1) (e0)) = (op (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 (e3) (e1)) = (op (e3) (e2)))) -> ((op (e1) (e2)) = (e0)) -> (~((e0) = (e3))) -> (((op (e0) (e2)) = (e3))\/(((op (e1) (e2)) = (e3))\/(((op (e2) (e2)) = (e3))\/((op (e3) (e2)) = (e3))))) -> (((op (e3) (e0)) = (e1))\/(((op (e3) (e1)) = (e1))\/(((op (e3) (e2)) = (e1))\/((op (e3) (e3)) = (e1))))) -> (~((e0) = (e1))) -> (~((op (e0) (e1)) = (op (e3) (e1)))) -> (~((op (e1) (e2)) = (op (e3) (e2)))) -> (((op (e3) (e0)) = (e2))\/(((op (e3) (e1)) = (e2))\/(((op (e3) (e2)) = (e2))\/((op (e3) (e3)) = (e2))))) -> (~((e0) = (e2))) -> ((op (e3) (e0)) = (e0)) -> (~((op (e1) (e1)) = (op (e2) (e1)))) -> (~((op (e1) (e1)) = (op (e3) (e1)))) -> (~((op (e1) (e1)) = (e1))) -> (~((op (e1) (e1)) = (e0))) -> (((op (e1) (e1)) = (e0))\/(((op (e1) (e1)) = (e1))\/(((op (e1) (e1)) = (e2))\/((op (e1) (e1)) = (e3))))) -> (~((op (e3) (e1)) = (op (e3) (e3)))) -> (~((op (e3) (e1)) = (e0))) -> (((op (e3) (e1)) = (e0))\/(((op (e3) (e1)) = (e1))\/(((op (e3) (e1)) = (e2))\/((op (e3) (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 (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 (e1) (e3)) = (op (e2) (e3)))) -> (~((op (e1) (e3)) = (op (e3) (e3)))) -> (~((op (e1) (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 (e0) (e0)) = (e3)) -> ((op (e1) (e0)) = (e2)) -> ((op (e2) (e1)) = (e0)) -> (((op (e0) (e1)) = (e3))\/(((op (e1) (e1)) = (e3))\/(((op (e2) (e1)) = (e3))\/((op (e3) (e1)) = (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)) = (op (e1) (e3)))) -> ((op (e2) (e0)) = (e1)) -> (((op (e2) (e2)) = (e0))\/(((op (e2) (e2)) = (e1))\/(((op (e2) (e2)) = (e2))\/((op (e2) (e2)) = (e3))))) -> (~((op (e2) (e2)) = (e0))) -> (~((op (e2) (e2)) = (op (e3) (e2)))) -> (~((op (e2) (e2)) = (e2))) -> ((op (e2) (e0)) = (e3)) -> (~((op (e2) (e0)) = (op (e2) (e2)))) -> False). % 18.68/18.84 do 0 intro. intros zenon_H182 zenon_H94 zenon_H3e zenon_H23 zenon_H3f zenon_H1ed zenon_H74 zenon_H208 zenon_H22 zenon_H7c zenon_H201 zenon_H17e zenon_H12b zenon_He4 zenon_H1d zenon_H1d5 zenon_H212 zenon_H10e zenon_H1cc zenon_Hc2 zenon_H6a zenon_H6f zenon_H4f zenon_H2b zenon_H16f zenon_H101 zenon_H62 zenon_H172 zenon_H18c zenon_H189 zenon_H1d8 zenon_H1c7 zenon_H145 zenon_H106 zenon_H109 zenon_Haf zenon_H54 zenon_Hd8 zenon_H6d zenon_H71 zenon_H133 zenon_H7b zenon_H39 zenon_H22d zenon_H20b zenon_H1a7 zenon_H184 zenon_H2f zenon_H185 zenon_H165 zenon_Ha8 zenon_H1ec zenon_H204 zenon_H205 zenon_H191 zenon_H195 zenon_H19d zenon_He7 zenon_H183 zenon_H17b zenon_H178 zenon_H179 zenon_H13c zenon_H128 zenon_H168 zenon_H1fe zenon_H1ee zenon_H1e0 zenon_H1ba zenon_H1fa zenon_H1f0 zenon_H206 zenon_H233 zenon_H1cf zenon_H57 zenon_H5b zenon_H67 zenon_H45 zenon_H14f zenon_H1ac zenon_H1a4 zenon_H2a zenon_H9a zenon_H1a6 zenon_He8 zenon_Ha1 zenon_H210 zenon_H115 zenon_H153 zenon_H149 zenon_H44 zenon_H13e zenon_H160 zenon_H10a zenon_H24 zenon_H142 zenon_H130 zenon_H1ad zenon_H22a zenon_H136 zenon_Hf3 zenon_He2 zenon_H1e zenon_H11f zenon_Hdb zenon_Hd5 zenon_H38 zenon_Hdf zenon_H102 zenon_H95 zenon_H3a zenon_H86 zenon_H36 zenon_H1a5 zenon_H139 zenon_H4a zenon_Ha0 zenon_H124 zenon_Hed zenon_H1c4 zenon_H81 zenon_H18f zenon_H173 zenon_H3b zenon_H52. % 18.68/18.84 apply (zenon_or_s _ _ zenon_H128); [ zenon_intro zenon_H9d | zenon_intro zenon_H129 ]. % 18.68/18.84 apply (zenon_L489_); trivial. % 18.68/18.84 apply (zenon_or_s _ _ zenon_H129); [ zenon_intro zenon_H10d | zenon_intro zenon_H12a ]. % 18.68/18.84 exact (zenon_H10a zenon_H10d). % 18.68/18.84 apply (zenon_or_s _ _ zenon_H12a); [ zenon_intro zenon_Hf0 | zenon_intro zenon_Hd6 ]. % 18.68/18.84 apply (zenon_or_s _ _ zenon_H1a5); [ zenon_intro zenon_H99 | zenon_intro zenon_H1a8 ]. % 18.68/18.84 apply (zenon_L403_); trivial. % 18.68/18.84 apply (zenon_or_s _ _ zenon_H1a8); [ zenon_intro zenon_H13f | zenon_intro zenon_H1a9 ]. % 18.68/18.84 apply (zenon_L520_); trivial. % 18.68/18.84 apply (zenon_or_s _ _ zenon_H1a9); [ zenon_intro zenon_Ha6 | zenon_intro zenon_H161 ]. % 18.68/18.84 apply (zenon_L524_); trivial. % 18.68/18.84 apply (zenon_L525_); trivial. % 18.68/18.84 apply (zenon_or_s _ _ zenon_H139); [ zenon_intro zenon_H122 | zenon_intro zenon_H13a ]. % 18.68/18.84 apply (zenon_L406_); trivial. % 18.68/18.84 apply (zenon_or_s _ _ zenon_H13a); [ zenon_intro zenon_Hf0 | zenon_intro zenon_H13b ]. % 18.68/18.84 apply (zenon_L78_); trivial. % 18.68/18.84 apply (zenon_or_s _ _ zenon_H13b); [ zenon_intro zenon_Hf1 | zenon_intro zenon_Hba ]. % 18.68/18.84 apply (zenon_L93_); trivial. % 18.68/18.84 apply (zenon_L327_); trivial. % 18.68/18.84 (* end of lemma zenon_L526_ *) % 18.68/18.84 assert (zenon_L527_ : (((op (e1) (e3)) = (e0))\/(((op (e1) (e3)) = (e1))\/(((op (e1) (e3)) = (e2))\/((op (e1) (e3)) = (e3))))) -> ((op (e0) (e3)) = (e0)) -> (~((op (e0) (e3)) = (op (e1) (e3)))) -> ((op (e3) (e3)) = (e1)) -> (~((op (e1) (e3)) = (op (e3) (e3)))) -> ((op (e2) (e3)) = (e2)) -> (~((op (e1) (e3)) = (op (e2) (e3)))) -> ((op (e2) (e3)) = (e3)) -> False). % 18.68/18.84 do 0 intro. intros zenon_Hdf zenon_H1e zenon_H1d zenon_Hc4 zenon_Hd5 zenon_H11d zenon_Hdb zenon_Hdd. % 18.68/18.84 apply (zenon_or_s _ _ zenon_Hdf); [ zenon_intro zenon_H1f | zenon_intro zenon_He0 ]. % 18.68/18.84 apply (zenon_L1_); trivial. % 18.68/18.84 apply (zenon_or_s _ _ zenon_He0); [ zenon_intro zenon_Hd6 | zenon_intro zenon_He1 ]. % 18.68/18.84 apply (zenon_L50_); trivial. % 18.68/18.84 apply (zenon_or_s _ _ zenon_He1); [ zenon_intro zenon_Hd7 | zenon_intro zenon_Hdc ]. % 18.68/18.84 apply (zenon_L366_); trivial. % 18.68/18.84 apply (zenon_L52_); trivial. % 18.68/18.84 (* end of lemma zenon_L527_ *) % 18.68/18.84 assert (zenon_L528_ : (((op (e2) (e2)) = (e0))\/(((op (e2) (e2)) = (e1))\/(((op (e2) (e2)) = (e2))\/((op (e2) (e2)) = (e3))))) -> (~((op (e2) (e2)) = (e0))) -> ((op (e3) (e2)) = (e1)) -> (~((op (e2) (e2)) = (e2))) -> (~((op (e2) (e2)) = (op (e3) (e2)))) -> ((op (e3) (e2)) = (e3)) -> False). % 18.68/18.84 do 0 intro. intros zenon_H1c4 zenon_H81 zenon_Hba zenon_H173 zenon_H18f zenon_H163. % 18.68/18.84 apply (zenon_or_s _ _ zenon_H1c4); [ zenon_intro zenon_H2c | zenon_intro zenon_H1c5 ]. % 18.68/18.84 exact (zenon_H81 zenon_H2c). % 18.68/18.84 apply (zenon_or_s _ _ zenon_H1c5); [ zenon_intro zenon_Hf1 | zenon_intro zenon_H1c6 ]. % 18.68/18.84 apply (zenon_L185_); trivial. % 18.68/18.84 apply (zenon_or_s _ _ zenon_H1c6); [ zenon_intro zenon_H176 | zenon_intro zenon_Haa ]. % 18.68/18.84 exact (zenon_H173 zenon_H176). % 18.68/18.84 apply (zenon_L180_); trivial. % 18.68/18.84 (* end of lemma zenon_L528_ *) % 18.68/18.84 assert (zenon_L529_ : (((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) (e2)) = (op (e3) (e2)))) -> (~((op (e2) (e2)) = (e2))) -> (~((op (e2) (e2)) = (e0))) -> (((op (e2) (e2)) = (e0))\/(((op (e2) (e2)) = (e1))\/(((op (e2) (e2)) = (e2))\/((op (e2) (e2)) = (e3))))) -> (((op (e3) (e0)) = (e2))\/(((op (e3) (e1)) = (e2))\/(((op (e3) (e2)) = (e2))\/((op (e3) (e3)) = (e2))))) -> (~((e0) = (e2))) -> ((op (e3) (e0)) = (e0)) -> ((op (e1) (e1)) = (e3)) -> ((op (e2) (e1)) = (e0)) -> ((op (e3) (e2)) = (e3)) -> (~((op (e3) (e1)) = (op (e3) (e2)))) -> (~((op (e3) (e1)) = (op (e3) (e3)))) -> (~((op (e3) (e1)) = (e0))) -> (((op (e3) (e1)) = (e0))\/(((op (e3) (e1)) = (e1))\/(((op (e3) (e1)) = (e2))\/((op (e3) (e1)) = (e3))))) -> (((op (e0) (e3)) = (e3))\/(((op (e1) (e3)) = (e3))\/(((op (e2) (e3)) = (e3))\/((op (e3) (e3)) = (e3))))) -> (~((e0) = (e3))) -> (~((op (e2) (e3)) = (op (e3) (e3)))) -> (~((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 (e1) (e3)) = (op (e2) (e3)))) -> (~((op (e1) (e3)) = (op (e3) (e3)))) -> (~((op (e1) (e3)) = (e0))) -> (((op (e1) (e3)) = (e0))\/(((op (e1) (e3)) = (e1))\/(((op (e1) (e3)) = (e2))\/((op (e1) (e3)) = (e3))))) -> (~((op (e3) (e3)) = (e3))) -> False). % 18.68/18.84 do 0 intro. intros zenon_He8 zenon_Ha1 zenon_Ha0 zenon_H210 zenon_H18f zenon_H173 zenon_H81 zenon_H1c4 zenon_H153 zenon_H149 zenon_H44 zenon_H13f zenon_H36 zenon_H163 zenon_H1a4 zenon_H130 zenon_H1ad zenon_H22a zenon_H136 zenon_H9a zenon_Hf3 zenon_He2 zenon_H1e zenon_H11f zenon_Hdb zenon_Hd5 zenon_H38 zenon_Hdf zenon_H102. % 18.68/18.84 apply (zenon_or_s _ _ zenon_He8); [ zenon_intro zenon_Hac | zenon_intro zenon_Heb ]. % 18.68/18.84 apply (zenon_L41_); trivial. % 18.68/18.84 apply (zenon_or_s _ _ zenon_Heb); [ zenon_intro zenon_Hae | zenon_intro zenon_Hec ]. % 18.68/18.84 apply (zenon_L363_); trivial. % 18.68/18.84 apply (zenon_or_s _ _ zenon_Hec); [ zenon_intro zenon_Hba | zenon_intro zenon_Hc4 ]. % 18.68/18.84 apply (zenon_L528_); trivial. % 18.68/18.84 apply (zenon_L518_); trivial. % 18.68/18.84 (* end of lemma zenon_L529_ *) % 18.68/18.84 assert (zenon_L530_ : (~((op (e0) (e2)) = (op (e1) (e2)))) -> ((op (e0) (e2)) = (e1)) -> ((op (e1) (e2)) = (e1)) -> False). % 18.68/18.84 do 0 intro. intros zenon_H195 zenon_H122 zenon_Hf0. % 18.68/18.84 cut (((op (e0) (e2)) = (e1)) = ((op (e0) (e2)) = (op (e1) (e2)))). % 18.68/18.84 intro zenon_D_pnotp. % 18.68/18.84 apply zenon_H195. % 18.68/18.84 rewrite <- zenon_D_pnotp. % 18.68/18.84 exact zenon_H122. % 18.68/18.84 cut (((e1) = (op (e1) (e2)))); [idtac | apply NNPP; zenon_intro zenon_H126]. % 18.68/18.84 cut (((op (e0) (e2)) = (op (e0) (e2)))); [idtac | apply NNPP; zenon_intro zenon_H4c]. % 18.68/18.84 congruence. % 18.68/18.84 apply zenon_H4c. apply refl_equal. % 18.68/18.84 apply zenon_H126. apply sym_equal. exact zenon_Hf0. % 18.68/18.84 (* end of lemma zenon_L530_ *) % 18.68/18.84 assert (zenon_L531_ : (((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)) = (e1)) -> (~((op (e1) (e1)) = (e1))) -> ((op (e0) (e2)) = (e1)) -> (~((op (e0) (e2)) = (op (e1) (e2)))) -> (~((op (e1) (e3)) = (op (e3) (e3)))) -> ((op (e3) (e3)) = (e1)) -> False). % 18.68/18.84 do 0 intro. intros zenon_H128 zenon_H201 zenon_Hed zenon_H10a zenon_H122 zenon_H195 zenon_Hd5 zenon_Hc4. % 18.68/18.84 apply (zenon_or_s _ _ zenon_H128); [ zenon_intro zenon_H9d | zenon_intro zenon_H129 ]. % 18.68/18.84 apply (zenon_L413_); trivial. % 18.68/18.84 apply (zenon_or_s _ _ zenon_H129); [ zenon_intro zenon_H10d | zenon_intro zenon_H12a ]. % 18.68/18.84 exact (zenon_H10a zenon_H10d). % 18.68/18.84 apply (zenon_or_s _ _ zenon_H12a); [ zenon_intro zenon_Hf0 | zenon_intro zenon_Hd6 ]. % 18.68/18.84 apply (zenon_L530_); trivial. % 18.68/18.84 apply (zenon_L50_); trivial. % 18.68/18.84 (* end of lemma zenon_L531_ *) % 18.68/18.84 assert (zenon_L532_ : (((op (e0) (e2)) = (e0))\/(((op (e0) (e2)) = (e1))\/(((op (e0) (e2)) = (e2))\/((op (e0) (e2)) = (e3))))) -> ((op (e1) (e2)) = (e0)) -> ((op (e3) (e3)) = (e1)) -> (~((op (e1) (e3)) = (op (e3) (e3)))) -> (~((op (e0) (e2)) = (op (e1) (e2)))) -> (~((op (e1) (e1)) = (e1))) -> ((op (e2) (e0)) = (e1)) -> (~((op (e1) (e0)) = (op (e2) (e0)))) -> (((op (e1) (e0)) = (e1))\/(((op (e1) (e1)) = (e1))\/(((op (e1) (e2)) = (e1))\/((op (e1) (e3)) = (e1))))) -> ((op (e3) (e2)) = (e2)) -> (~((op (e0) (e2)) = (op (e3) (e2)))) -> (~((op (e0) (e2)) = (op (e2) (e2)))) -> ((op (e2) (e2)) = (e3)) -> False). % 18.68/18.84 do 0 intro. intros zenon_H1ba zenon_H2a zenon_Hc4 zenon_Hd5 zenon_H195 zenon_H10a zenon_Hed zenon_H201 zenon_H128 zenon_H151 zenon_H14f zenon_Ha8 zenon_Haa. % 18.68/18.84 apply (zenon_or_s _ _ zenon_H1ba); [ zenon_intro zenon_H48 | zenon_intro zenon_H1bb ]. % 18.68/18.84 apply (zenon_L334_); trivial. % 18.68/18.84 apply (zenon_or_s _ _ zenon_H1bb); [ zenon_intro zenon_H122 | zenon_intro zenon_H1bc ]. % 18.68/18.84 apply (zenon_L531_); trivial. % 18.68/18.84 apply (zenon_or_s _ _ zenon_H1bc); [ zenon_intro zenon_H150 | zenon_intro zenon_Ha9 ]. % 18.68/18.84 apply (zenon_L104_); trivial. % 18.68/18.84 apply (zenon_L40_); trivial. % 18.68/18.84 (* end of lemma zenon_L532_ *) % 18.68/18.84 assert (zenon_L533_ : (((op (e2) (e2)) = (e0))\/(((op (e2) (e2)) = (e1))\/(((op (e2) (e2)) = (e2))\/((op (e2) (e2)) = (e3))))) -> (~((op (e2) (e2)) = (e0))) -> ((op (e0) (e2)) = (e3)) -> (~((op (e2) (e2)) = (e2))) -> (((op (e0) (e2)) = (e0))\/(((op (e0) (e2)) = (e1))\/(((op (e0) (e2)) = (e2))\/((op (e0) (e2)) = (e3))))) -> ((op (e1) (e2)) = (e0)) -> ((op (e3) (e3)) = (e1)) -> (~((op (e1) (e3)) = (op (e3) (e3)))) -> (~((op (e0) (e2)) = (op (e1) (e2)))) -> (~((op (e1) (e1)) = (e1))) -> ((op (e2) (e0)) = (e1)) -> (~((op (e1) (e0)) = (op (e2) (e0)))) -> (((op (e1) (e0)) = (e1))\/(((op (e1) (e1)) = (e1))\/(((op (e1) (e2)) = (e1))\/((op (e1) (e3)) = (e1))))) -> ((op (e3) (e2)) = (e2)) -> (~((op (e0) (e2)) = (op (e3) (e2)))) -> (~((op (e0) (e2)) = (op (e2) (e2)))) -> False). % 18.68/18.84 do 0 intro. intros zenon_H1c4 zenon_H81 zenon_Ha9 zenon_H173 zenon_H1ba zenon_H2a zenon_Hc4 zenon_Hd5 zenon_H195 zenon_H10a zenon_Hed zenon_H201 zenon_H128 zenon_H151 zenon_H14f zenon_Ha8. % 18.68/18.84 apply (zenon_or_s _ _ zenon_H1c4); [ zenon_intro zenon_H2c | zenon_intro zenon_H1c5 ]. % 18.68/18.84 exact (zenon_H81 zenon_H2c). % 18.68/18.84 apply (zenon_or_s _ _ zenon_H1c5); [ zenon_intro zenon_Hf1 | zenon_intro zenon_H1c6 ]. % 18.68/18.84 apply (zenon_L184_); trivial. % 18.68/18.84 apply (zenon_or_s _ _ zenon_H1c6); [ zenon_intro zenon_H176 | zenon_intro zenon_Haa ]. % 18.68/18.84 exact (zenon_H173 zenon_H176). % 18.68/18.84 apply (zenon_L532_); trivial. % 18.68/18.84 (* end of lemma zenon_L533_ *) % 18.68/18.84 assert (zenon_L534_ : (((op (e3) (e0)) = (e1))\/(((op (e3) (e1)) = (e1))\/(((op (e3) (e2)) = (e1))\/((op (e3) (e3)) = (e1))))) -> ((op (e0) (e0)) = (e3)) -> ((op (e1) (e0)) = (e2)) -> ((op (e0) (e1)) = (e1)) -> (~((op (e0) (e1)) = (op (e3) (e1)))) -> (((op (e0) (e2)) = (e0))\/(((op (e0) (e2)) = (e1))\/(((op (e0) (e2)) = (e2))\/((op (e0) (e2)) = (e3))))) -> ((op (e1) (e2)) = (e0)) -> (~((op (e1) (e3)) = (op (e3) (e3)))) -> (~((op (e0) (e2)) = (op (e1) (e2)))) -> (~((op (e1) (e1)) = (e1))) -> ((op (e2) (e0)) = (e1)) -> (~((op (e1) (e0)) = (op (e2) (e0)))) -> (((op (e1) (e0)) = (e1))\/(((op (e1) (e1)) = (e1))\/(((op (e1) (e2)) = (e1))\/((op (e1) (e3)) = (e1))))) -> ((op (e3) (e2)) = (e2)) -> (~((op (e0) (e2)) = (op (e3) (e2)))) -> (~((op (e0) (e2)) = (op (e2) (e2)))) -> ((op (e2) (e2)) = (e3)) -> False). % 18.68/18.84 do 0 intro. intros zenon_He8 zenon_H3a zenon_H86 zenon_Ha0 zenon_H210 zenon_H1ba zenon_H2a zenon_Hd5 zenon_H195 zenon_H10a zenon_Hed zenon_H201 zenon_H128 zenon_H151 zenon_H14f zenon_Ha8 zenon_Haa. % 18.68/18.84 apply (zenon_or_s _ _ zenon_He8); [ zenon_intro zenon_Hac | zenon_intro zenon_Heb ]. % 18.68/18.84 apply (zenon_L241_); trivial. % 18.68/18.84 apply (zenon_or_s _ _ zenon_Heb); [ zenon_intro zenon_Hae | zenon_intro zenon_Hec ]. % 18.68/18.84 apply (zenon_L363_); trivial. % 18.68/18.84 apply (zenon_or_s _ _ zenon_Hec); [ zenon_intro zenon_Hba | zenon_intro zenon_Hc4 ]. % 18.68/18.84 apply (zenon_L179_); trivial. % 18.68/18.84 apply (zenon_L532_); trivial. % 18.68/18.84 (* end of lemma zenon_L534_ *) % 18.68/18.84 assert (zenon_L535_ : (((op (e0) (e2)) = (e3))\/(((op (e1) (e2)) = (e3))\/(((op (e2) (e2)) = (e3))\/((op (e3) (e2)) = (e3))))) -> (~((op (e2) (e2)) = (e2))) -> (~((op (e2) (e2)) = (e0))) -> (((op (e2) (e2)) = (e0))\/(((op (e2) (e2)) = (e1))\/(((op (e2) (e2)) = (e2))\/((op (e2) (e2)) = (e3))))) -> (~((op (e2) (e2)) = (op (e3) (e2)))) -> (~((e1) = (e3))) -> (~((op (e0) (e2)) = (op (e2) (e2)))) -> (~((op (e0) (e2)) = (op (e3) (e2)))) -> ((op (e3) (e2)) = (e2)) -> (((op (e1) (e0)) = (e1))\/(((op (e1) (e1)) = (e1))\/(((op (e1) (e2)) = (e1))\/((op (e1) (e3)) = (e1))))) -> (~((op (e1) (e0)) = (op (e2) (e0)))) -> ((op (e2) (e0)) = (e1)) -> (~((op (e0) (e2)) = (op (e1) (e2)))) -> ((op (e1) (e2)) = (e0)) -> (((op (e0) (e2)) = (e0))\/(((op (e0) (e2)) = (e1))\/(((op (e0) (e2)) = (e2))\/((op (e0) (e2)) = (e3))))) -> ((op (e1) (e0)) = (e2)) -> ((op (e0) (e0)) = (e3)) -> (((op (e3) (e0)) = (e1))\/(((op (e3) (e1)) = (e1))\/(((op (e3) (e2)) = (e1))\/((op (e3) (e3)) = (e1))))) -> (~((e0) = (e1))) -> ((op (e0) (e1)) = (e1)) -> (~((op (e0) (e1)) = (op (e3) (e1)))) -> ((op (e1) (e2)) = (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 (e3) (e0)) = (e0)) -> ((op (e2) (e1)) = (e3)) -> (~((op (e1) (e1)) = (op (e2) (e1)))) -> (~((op (e1) (e1)) = (op (e3) (e1)))) -> (~((op (e1) (e1)) = (e1))) -> (~((op (e1) (e1)) = (e0))) -> (((op (e1) (e1)) = (e0))\/(((op (e1) (e1)) = (e1))\/(((op (e1) (e1)) = (e2))\/((op (e1) (e1)) = (e3))))) -> (~((op (e3) (e1)) = (op (e3) (e2)))) -> (~((op (e3) (e1)) = (op (e3) (e3)))) -> (~((op (e3) (e1)) = (e0))) -> (((op (e3) (e1)) = (e0))\/(((op (e3) (e1)) = (e1))\/(((op (e3) (e1)) = (e2))\/((op (e3) (e1)) = (e3))))) -> (((op (e0) (e3)) = (e3))\/(((op (e1) (e3)) = (e3))\/(((op (e2) (e3)) = (e3))\/((op (e3) (e3)) = (e3))))) -> (~((e0) = (e3))) -> (~((op (e2) (e3)) = (op (e3) (e3)))) -> (~((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 (e1) (e3)) = (op (e2) (e3)))) -> (~((op (e1) (e3)) = (op (e3) (e3)))) -> (~((op (e1) (e3)) = (e0))) -> (((op (e1) (e3)) = (e0))\/(((op (e1) (e3)) = (e1))\/(((op (e1) (e3)) = (e2))\/((op (e1) (e3)) = (e3))))) -> (~((op (e3) (e3)) = (e3))) -> False). % 18.68/18.84 do 0 intro. intros zenon_H1a6 zenon_H173 zenon_H81 zenon_H1c4 zenon_H18f zenon_H95 zenon_Ha8 zenon_H14f zenon_H151 zenon_H128 zenon_H201 zenon_Hed zenon_H195 zenon_H2a zenon_H1ba zenon_H86 zenon_H3a zenon_He8 zenon_Ha1 zenon_Ha0 zenon_H210 zenon_Hf0 zenon_H115 zenon_H153 zenon_H149 zenon_H44 zenon_Ha6 zenon_H13e zenon_H160 zenon_H10a zenon_H24 zenon_H142 zenon_H1a4 zenon_H130 zenon_H1ad zenon_H22a zenon_H136 zenon_H9a zenon_Hf3 zenon_He2 zenon_H1e zenon_H11f zenon_Hdb zenon_Hd5 zenon_H38 zenon_Hdf zenon_H102. % 18.68/18.84 apply (zenon_or_s _ _ zenon_H1a6); [ zenon_intro zenon_Ha9 | zenon_intro zenon_H1aa ]. % 18.68/18.84 apply (zenon_or_s _ _ zenon_He8); [ zenon_intro zenon_Hac | zenon_intro zenon_Heb ]. % 18.68/18.84 apply (zenon_L41_); trivial. % 18.68/18.84 apply (zenon_or_s _ _ zenon_Heb); [ zenon_intro zenon_Hae | zenon_intro zenon_Hec ]. % 18.68/18.84 apply (zenon_L363_); trivial. % 18.68/18.84 apply (zenon_or_s _ _ zenon_Hec); [ zenon_intro zenon_Hba | zenon_intro zenon_Hc4 ]. % 18.68/18.84 apply (zenon_L186_); trivial. % 18.68/18.84 apply (zenon_L533_); trivial. % 18.68/18.84 apply (zenon_or_s _ _ zenon_H1aa); [ zenon_intro zenon_H16c | zenon_intro zenon_H1ab ]. % 18.68/18.84 apply (zenon_L167_); trivial. % 18.68/18.84 apply (zenon_or_s _ _ zenon_H1ab); [ zenon_intro zenon_Haa | zenon_intro zenon_H163 ]. % 18.68/18.84 apply (zenon_L534_); trivial. % 18.68/18.84 apply (zenon_L523_); trivial. % 18.68/18.84 (* end of lemma zenon_L535_ *) % 18.68/18.84 assert (zenon_L536_ : (((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) (e3)) = (e1)) -> (~((op (e0) (e3)) = (op (e3) (e3)))) -> ((op (e2) (e3)) = (e2)) -> (~((op (e0) (e3)) = (op (e2) (e3)))) -> ((op (e2) (e3)) = (e3)) -> False). % 18.68/18.84 do 0 intro. intros zenon_He4 zenon_Hdb zenon_Hd5 zenon_H1d zenon_Hdf zenon_Hc4 zenon_Hc2 zenon_H11d zenon_He2 zenon_Hdd. % 18.68/18.84 apply (zenon_or_s _ _ zenon_He4); [ zenon_intro zenon_H1e | zenon_intro zenon_He5 ]. % 18.68/18.84 apply (zenon_L527_); trivial. % 18.68/18.84 apply (zenon_or_s _ _ zenon_He5); [ zenon_intro zenon_Hc3 | zenon_intro zenon_He6 ]. % 18.68/18.84 apply (zenon_L46_); trivial. % 18.68/18.84 apply (zenon_or_s _ _ zenon_He6); [ zenon_intro zenon_Hcd | zenon_intro zenon_He3 ]. % 18.68/18.84 apply (zenon_L234_); trivial. % 18.68/18.84 apply (zenon_L54_); trivial. % 18.68/18.84 (* end of lemma zenon_L536_ *) % 18.68/18.84 assert (zenon_L537_ : (((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 (e2) (e3)) = (e3)) -> (~((op (e0) (e3)) = (op (e2) (e3)))) -> ((op (e2) (e3)) = (e2)) -> (~((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))))) -> (~((op (e3) (e2)) = (op (e3) (e3)))) -> ((op (e3) (e2)) = (e2)) -> (~((op (e3) (e3)) = (e3))) -> False). % 18.68/18.84 do 0 intro. intros zenon_H101 zenon_H71 zenon_H44 zenon_Hdd zenon_He2 zenon_H11d zenon_Hc2 zenon_Hdf zenon_H1d zenon_Hd5 zenon_Hdb zenon_He4 zenon_H62 zenon_H151 zenon_H102. % 18.68/18.84 apply (zenon_or_s _ _ zenon_H101); [ zenon_intro zenon_H60 | zenon_intro zenon_H103 ]. % 18.68/18.84 apply (zenon_L21_); trivial. % 18.68/18.84 apply (zenon_or_s _ _ zenon_H103); [ zenon_intro zenon_Hc4 | zenon_intro zenon_H104 ]. % 18.68/18.84 apply (zenon_L536_); trivial. % 18.68/18.84 apply (zenon_or_s _ _ zenon_H104); [ zenon_intro zenon_Hf6 | zenon_intro zenon_H105 ]. % 18.68/18.84 apply (zenon_L119_); trivial. % 18.68/18.84 exact (zenon_H102 zenon_H105). % 18.68/18.84 (* end of lemma zenon_L537_ *) % 18.68/18.84 assert (zenon_L538_ : (((op (e2) (e0)) = (e3))\/(((op (e2) (e1)) = (e3))\/(((op (e2) (e2)) = (e3))\/((op (e2) (e3)) = (e3))))) -> ((op (e2) (e1)) = (e0)) -> ((op (e1) (e1)) = (e3)) -> (~((op (e2) (e0)) = (op (e2) (e2)))) -> (~((op (e1) (e3)) = (e0))) -> (((op (e2) (e3)) = (e0))\/(((op (e2) (e3)) = (e1))\/(((op (e2) (e3)) = (e2))\/((op (e2) (e3)) = (e3))))) -> ((op (e0) (e3)) = (e0)) -> (~((op (e2) (e3)) = (op (e3) (e3)))) -> (~((e0) = (e3))) -> (((op (e0) (e3)) = (e3))\/(((op (e1) (e3)) = (e3))\/(((op (e2) (e3)) = (e3))\/((op (e3) (e3)) = (e3))))) -> (((op (e3) (e1)) = (e0))\/(((op (e3) (e1)) = (e1))\/(((op (e3) (e1)) = (e2))\/((op (e3) (e1)) = (e3))))) -> (~((op (e3) (e1)) = (e0))) -> (~((op (e3) (e1)) = (op (e3) (e3)))) -> (~((op (e3) (e1)) = (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 (e3) (e1)))) -> (~((op (e1) (e1)) = (op (e2) (e1)))) -> (~((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 (e1) (e2)) = (e1)) -> (~((e0) = (e1))) -> (~((e1) = (e3))) -> (~((op (e2) (e2)) = (op (e3) (e2)))) -> (((op (e2) (e2)) = (e0))\/(((op (e2) (e2)) = (e1))\/(((op (e2) (e2)) = (e2))\/((op (e2) (e2)) = (e3))))) -> (~((op (e2) (e2)) = (e0))) -> (~((op (e2) (e2)) = (e2))) -> (((op (e0) (e2)) = (e3))\/(((op (e1) (e2)) = (e3))\/(((op (e2) (e2)) = (e3))\/((op (e3) (e2)) = (e3))))) -> (~((op (e0) (e2)) = (op (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 (e2) (e0)) = (e1)) -> (~((op (e1) (e1)) = (e1))) -> (~((op (e0) (e2)) = (op (e1) (e2)))) -> ((op (e1) (e2)) = (e0)) -> (((op (e0) (e2)) = (e0))\/(((op (e0) (e2)) = (e1))\/(((op (e0) (e2)) = (e2))\/((op (e0) (e2)) = (e3))))) -> (~((op (e0) (e1)) = (op (e3) (e1)))) -> ((op (e0) (e1)) = (e1)) -> ((op (e1) (e0)) = (e2)) -> ((op (e0) (e0)) = (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) (e0)) = (op (e3) (e3)))) -> ((op (e3) (e0)) = (e0)) -> (~((op (e0) (e3)) = (op (e2) (e3)))) -> ((op (e2) (e3)) = (e2)) -> (~((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))))) -> (~((op (e3) (e2)) = (op (e3) (e3)))) -> ((op (e3) (e2)) = (e2)) -> (~((op (e3) (e3)) = (e3))) -> False). % 18.68/18.84 do 0 intro. intros zenon_He7 zenon_H36 zenon_H13f zenon_H52 zenon_H38 zenon_H11f zenon_H1e zenon_Hf3 zenon_H9a zenon_H136 zenon_H22a zenon_H1ad zenon_H130 zenon_H1a4 zenon_H142 zenon_H24 zenon_H160 zenon_H13e zenon_H149 zenon_H153 zenon_H115 zenon_Hf0 zenon_Ha1 zenon_H95 zenon_H18f zenon_H1c4 zenon_H81 zenon_H173 zenon_H1a6 zenon_Ha8 zenon_H14f zenon_H128 zenon_H201 zenon_Hed zenon_H10a zenon_H195 zenon_H2a zenon_H1ba zenon_H210 zenon_Ha0 zenon_H86 zenon_H3a zenon_He8 zenon_H101 zenon_H71 zenon_H44 zenon_He2 zenon_H11d zenon_Hc2 zenon_Hdf zenon_H1d zenon_Hd5 zenon_Hdb zenon_He4 zenon_H62 zenon_H151 zenon_H102. % 18.68/18.84 apply (zenon_or_s _ _ zenon_He7); [ zenon_intro zenon_H3b | zenon_intro zenon_He9 ]. % 18.68/18.84 apply (zenon_L520_); trivial. % 18.68/18.84 apply (zenon_or_s _ _ zenon_He9); [ zenon_intro zenon_Ha6 | zenon_intro zenon_Hea ]. % 18.68/18.84 apply (zenon_L535_); trivial. % 18.68/18.84 apply (zenon_or_s _ _ zenon_Hea); [ zenon_intro zenon_Haa | zenon_intro zenon_Hdd ]. % 18.68/18.84 apply (zenon_L534_); trivial. % 18.68/18.84 apply (zenon_L537_); trivial. % 18.68/18.84 (* end of lemma zenon_L538_ *) % 18.68/18.84 assert (zenon_L539_ : (((op (e0) (e3)) = (e2))\/(((op (e1) (e3)) = (e2))\/(((op (e2) (e3)) = (e2))\/((op (e3) (e3)) = (e2))))) -> (~((e0) = (e2))) -> ((op (e0) (e3)) = (e0)) -> (~((op (e1) (e0)) = (op (e1) (e3)))) -> ((op (e1) (e0)) = (e2)) -> (~((op (e2) (e1)) = (op (e2) (e3)))) -> ((op (e2) (e1)) = (e2)) -> ((op (e3) (e1)) = (e2)) -> (~((op (e3) (e1)) = (op (e3) (e3)))) -> False). % 18.68/18.84 do 0 intro. intros zenon_H145 zenon_H149 zenon_H1e zenon_Hd8 zenon_H86 zenon_H1c7 zenon_H1ca zenon_H14d zenon_H130. % 18.68/18.84 apply (zenon_or_s _ _ zenon_H145); [ zenon_intro zenon_Hcd | zenon_intro zenon_H146 ]. % 18.68/18.84 apply (zenon_L428_); trivial. % 18.68/18.84 apply (zenon_or_s _ _ zenon_H146); [ zenon_intro zenon_Hd7 | zenon_intro zenon_H147 ]. % 18.68/18.84 apply (zenon_L51_); trivial. % 18.68/18.84 apply (zenon_or_s _ _ zenon_H147); [ zenon_intro zenon_H11d | zenon_intro zenon_Hf6 ]. % 18.68/18.84 apply (zenon_L224_); trivial. % 18.68/18.84 apply (zenon_L102_); trivial. % 18.68/18.84 (* end of lemma zenon_L539_ *) % 18.68/18.84 assert (zenon_L540_ : (((op (e0) (e3)) = (e2))\/(((op (e1) (e3)) = (e2))\/(((op (e2) (e3)) = (e2))\/((op (e3) (e3)) = (e2))))) -> (~((op (e0) (e0)) = (op (e0) (e3)))) -> ((op (e0) (e0)) = (e2)) -> (~((op (e1) (e0)) = (op (e1) (e3)))) -> ((op (e1) (e0)) = (e2)) -> (~((op (e2) (e1)) = (op (e2) (e3)))) -> ((op (e2) (e1)) = (e2)) -> ((op (e3) (e2)) = (e2)) -> (~((op (e3) (e2)) = (op (e3) (e3)))) -> False). % 18.68/18.84 do 0 intro. intros zenon_H145 zenon_H189 zenon_H7b zenon_Hd8 zenon_H86 zenon_H1c7 zenon_H1ca zenon_H151 zenon_H62. % 18.68/18.84 apply (zenon_or_s _ _ zenon_H145); [ zenon_intro zenon_Hcd | zenon_intro zenon_H146 ]. % 18.68/18.84 apply (zenon_L375_); trivial. % 18.68/18.84 apply (zenon_or_s _ _ zenon_H146); [ zenon_intro zenon_Hd7 | zenon_intro zenon_H147 ]. % 18.68/18.84 apply (zenon_L51_); trivial. % 18.68/18.84 apply (zenon_or_s _ _ zenon_H147); [ zenon_intro zenon_H11d | zenon_intro zenon_Hf6 ]. % 18.68/18.84 apply (zenon_L224_); trivial. % 18.68/18.84 apply (zenon_L119_); trivial. % 18.68/18.84 (* end of lemma zenon_L540_ *) % 18.68/18.84 assert (zenon_L541_ : (((op (e3) (e0)) = (e1))\/(((op (e3) (e1)) = (e1))\/(((op (e3) (e2)) = (e1))\/((op (e3) (e3)) = (e1))))) -> (~((e0) = (e1))) -> ((op (e3) (e0)) = (e0)) -> ((op (e0) (e1)) = (e1)) -> (~((op (e0) (e1)) = (op (e3) (e1)))) -> ((op (e1) (e2)) = (e1)) -> (~((op (e1) (e2)) = (op (e3) (e2)))) -> (((op (e3) (e0)) = (e2))\/(((op (e3) (e1)) = (e2))\/(((op (e3) (e2)) = (e2))\/((op (e3) (e3)) = (e2))))) -> (~((op (e0) (e2)) = (op (e3) (e2)))) -> ((op (e0) (e2)) = (e3)) -> (~((op (e1) (e1)) = (op (e3) (e1)))) -> ((op (e1) (e1)) = (e3)) -> (~((e2) = (e3))) -> (((op (e3) (e0)) = (e3))\/(((op (e3) (e1)) = (e3))\/(((op (e3) (e2)) = (e3))\/((op (e3) (e3)) = (e3))))) -> (~((op (e3) (e1)) = (op (e3) (e3)))) -> (~((e0) = (e2))) -> (~((op (e3) (e2)) = (op (e3) (e3)))) -> ((op (e2) (e1)) = (e2)) -> (~((op (e2) (e1)) = (op (e2) (e3)))) -> ((op (e1) (e0)) = (e2)) -> (~((op (e1) (e0)) = (op (e1) (e3)))) -> ((op (e0) (e0)) = (e2)) -> (~((op (e0) (e0)) = (op (e0) (e3)))) -> (((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))))) -> (~((e0) = (e3))) -> (~((op (e2) (e3)) = (op (e3) (e3)))) -> (~((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 (e1) (e3)) = (op (e2) (e3)))) -> (~((op (e1) (e3)) = (op (e3) (e3)))) -> (~((op (e1) (e3)) = (e0))) -> (((op (e1) (e3)) = (e0))\/(((op (e1) (e3)) = (e1))\/(((op (e1) (e3)) = (e2))\/((op (e1) (e3)) = (e3))))) -> (~((op (e3) (e3)) = (e3))) -> False). % 18.68/18.84 do 0 intro. intros zenon_He8 zenon_Ha1 zenon_H44 zenon_Ha0 zenon_H210 zenon_Hf0 zenon_H115 zenon_H153 zenon_H14f zenon_Ha9 zenon_H160 zenon_H13f zenon_H12b zenon_H165 zenon_H130 zenon_H149 zenon_H62 zenon_H1ca zenon_H1c7 zenon_H86 zenon_Hd8 zenon_H7b zenon_H189 zenon_H145 zenon_H136 zenon_H9a zenon_Hf3 zenon_He2 zenon_H1e zenon_H11f zenon_Hdb zenon_Hd5 zenon_H38 zenon_Hdf zenon_H102. % 18.68/18.84 apply (zenon_or_s _ _ zenon_He8); [ zenon_intro zenon_Hac | zenon_intro zenon_Heb ]. % 18.68/18.84 apply (zenon_L41_); trivial. % 18.68/18.84 apply (zenon_or_s _ _ zenon_Heb); [ zenon_intro zenon_Hae | zenon_intro zenon_Hec ]. % 18.68/18.84 apply (zenon_L363_); trivial. % 18.68/18.84 apply (zenon_or_s _ _ zenon_Hec); [ zenon_intro zenon_Hba | zenon_intro zenon_Hc4 ]. % 18.68/18.84 apply (zenon_L69_); trivial. % 18.68/18.84 apply (zenon_or_s _ _ zenon_H153); [ zenon_intro zenon_H148 | zenon_intro zenon_H154 ]. % 18.68/18.84 apply (zenon_L112_); trivial. % 18.68/18.84 apply (zenon_or_s _ _ zenon_H154); [ zenon_intro zenon_H14d | zenon_intro zenon_H155 ]. % 18.68/18.84 apply (zenon_L539_); trivial. % 18.68/18.84 apply (zenon_or_s _ _ zenon_H155); [ zenon_intro zenon_H151 | zenon_intro zenon_Hf6 ]. % 18.68/18.84 apply (zenon_L540_); trivial. % 18.68/18.84 apply (zenon_L517_); trivial. % 18.68/18.84 (* end of lemma zenon_L541_ *) % 18.68/18.84 assert (zenon_L542_ : ((op (e1) (e2)) = (e0)) -> ((op (e1) (e2)) = (e2)) -> (~((e0) = (e2))) -> False). % 18.68/18.84 do 0 intro. intros zenon_H2a zenon_H113 zenon_H149. % 18.68/18.84 elim (classic ((e2) = (e2))); [ zenon_intro zenon_H7d | zenon_intro zenon_H7e ]. % 18.68/18.84 cut (((e2) = (e2)) = ((e0) = (e2))). % 18.68/18.84 intro zenon_D_pnotp. % 18.68/18.84 apply zenon_H149. % 18.68/18.84 rewrite <- zenon_D_pnotp. % 18.68/18.84 exact zenon_H7d. % 18.68/18.84 cut (((e2) = (e2))); [idtac | apply NNPP; zenon_intro zenon_H7e]. % 18.68/18.84 cut (((e2) = (e0))); [idtac | apply NNPP; zenon_intro zenon_H14a]. % 18.68/18.84 congruence. % 18.68/18.84 cut (((op (e1) (e2)) = (e0)) = ((e2) = (e0))). % 18.68/18.84 intro zenon_D_pnotp. % 18.68/18.84 apply zenon_H14a. % 18.68/18.84 rewrite <- zenon_D_pnotp. % 18.68/18.84 exact zenon_H2a. % 18.68/18.84 cut (((e0) = (e0))); [idtac | apply NNPP; zenon_intro zenon_H82]. % 18.68/18.84 cut (((op (e1) (e2)) = (e2))); [idtac | apply NNPP; zenon_intro zenon_H114]. % 18.68/18.84 congruence. % 18.68/18.84 exact (zenon_H114 zenon_H113). % 18.68/18.84 apply zenon_H82. apply refl_equal. % 18.68/18.84 apply zenon_H7e. apply refl_equal. % 18.68/18.84 apply zenon_H7e. apply refl_equal. % 18.68/18.84 (* end of lemma zenon_L542_ *) % 18.68/18.84 assert (zenon_L543_ : (((op (e0) (e2)) = (e2))\/(((op (e1) (e2)) = (e2))\/(((op (e2) (e2)) = (e2))\/((op (e3) (e2)) = (e2))))) -> (~((op (e3) (e3)) = (e3))) -> (((op (e1) (e3)) = (e0))\/(((op (e1) (e3)) = (e1))\/(((op (e1) (e3)) = (e2))\/((op (e1) (e3)) = (e3))))) -> (~((op (e1) (e3)) = (e0))) -> (~((op (e1) (e3)) = (op (e3) (e3)))) -> (~((op (e1) (e3)) = (op (e2) (e3)))) -> (((op (e2) (e3)) = (e0))\/(((op (e2) (e3)) = (e1))\/(((op (e2) (e3)) = (e2))\/((op (e2) (e3)) = (e3))))) -> ((op (e0) (e3)) = (e0)) -> (~((op (e0) (e3)) = (op (e2) (e3)))) -> (~((op (e2) (e3)) = (op (e3) (e3)))) -> (~((e0) = (e3))) -> (((op (e0) (e3)) = (e3))\/(((op (e1) (e3)) = (e3))\/(((op (e2) (e3)) = (e3))\/((op (e3) (e3)) = (e3))))) -> (((op (e3) (e1)) = (e0))\/(((op (e3) (e1)) = (e1))\/(((op (e3) (e1)) = (e2))\/((op (e3) (e1)) = (e3))))) -> (~((op (e3) (e1)) = (e0))) -> (~((op (e3) (e1)) = (op (e3) (e3)))) -> (~((op (e3) (e1)) = (op (e3) (e2)))) -> ((op (e2) (e1)) = (e0)) -> ((op (e1) (e1)) = (e3)) -> ((op (e3) (e0)) = (e0)) -> (((op (e3) (e0)) = (e2))\/(((op (e3) (e1)) = (e2))\/(((op (e3) (e2)) = (e2))\/((op (e3) (e3)) = (e2))))) -> (((op (e2) (e2)) = (e0))\/(((op (e2) (e2)) = (e1))\/(((op (e2) (e2)) = (e2))\/((op (e2) (e2)) = (e3))))) -> (~((op (e2) (e2)) = (e0))) -> (~((op (e2) (e2)) = (op (e3) (e2)))) -> (~((op (e0) (e1)) = (op (e3) (e1)))) -> ((op (e0) (e1)) = (e1)) -> (~((e0) = (e1))) -> (((op (e3) (e0)) = (e1))\/(((op (e3) (e1)) = (e1))\/(((op (e3) (e2)) = (e1))\/((op (e3) (e3)) = (e1))))) -> (((op (e3) (e2)) = (e0))\/(((op (e3) (e2)) = (e1))\/(((op (e3) (e2)) = (e2))\/((op (e3) (e2)) = (e3))))) -> (~((op (e1) (e2)) = (op (e3) (e2)))) -> (~((op (e0) (e2)) = (op (e3) (e2)))) -> ((op (e1) (e2)) = (e1)) -> (~((op (e1) (e1)) = (op (e3) (e1)))) -> (~((e2) = (e3))) -> (((op (e3) (e0)) = (e3))\/(((op (e3) (e1)) = (e3))\/(((op (e3) (e2)) = (e3))\/((op (e3) (e3)) = (e3))))) -> (((op (e0) (e2)) = (e3))\/(((op (e1) (e2)) = (e3))\/(((op (e2) (e2)) = (e3))\/((op (e3) (e2)) = (e3))))) -> (~((e0) = (e2))) -> ((op (e1) (e2)) = (e0)) -> (~((op (e2) (e2)) = (e2))) -> (((op (e0) (e3)) = (e2))\/(((op (e1) (e3)) = (e2))\/(((op (e2) (e3)) = (e2))\/((op (e3) (e3)) = (e2))))) -> (~((op (e0) (e0)) = (op (e0) (e3)))) -> ((op (e0) (e0)) = (e2)) -> (~((op (e1) (e0)) = (op (e1) (e3)))) -> ((op (e1) (e0)) = (e2)) -> (~((op (e2) (e1)) = (op (e2) (e3)))) -> ((op (e2) (e1)) = (e2)) -> (~((op (e3) (e2)) = (op (e3) (e3)))) -> False). % 18.68/18.84 do 0 intro. intros zenon_H172 zenon_H102 zenon_Hdf zenon_H38 zenon_Hd5 zenon_Hdb zenon_H11f zenon_H1e zenon_He2 zenon_Hf3 zenon_H9a zenon_H136 zenon_H22a zenon_H1ad zenon_H130 zenon_H1a4 zenon_H36 zenon_H13f zenon_H44 zenon_H153 zenon_H1c4 zenon_H81 zenon_H18f zenon_H210 zenon_Ha0 zenon_Ha1 zenon_He8 zenon_H191 zenon_H115 zenon_H14f zenon_Hf0 zenon_H160 zenon_H12b zenon_H165 zenon_H1a6 zenon_H149 zenon_H2a zenon_H173 zenon_H145 zenon_H189 zenon_H7b zenon_Hd8 zenon_H86 zenon_H1c7 zenon_H1ca zenon_H62. % 18.68/18.84 apply (zenon_or_s _ _ zenon_H172); [ zenon_intro zenon_H150 | zenon_intro zenon_H174 ]. % 18.68/18.84 apply (zenon_or_s _ _ zenon_H1a6); [ zenon_intro zenon_Ha9 | zenon_intro zenon_H1aa ]. % 18.68/18.84 apply (zenon_L541_); trivial. % 18.68/18.84 apply (zenon_or_s _ _ zenon_H1aa); [ zenon_intro zenon_H16c | zenon_intro zenon_H1ab ]. % 18.68/18.84 apply (zenon_L521_); trivial. % 18.68/18.84 apply (zenon_or_s _ _ zenon_H1ab); [ zenon_intro zenon_Haa | zenon_intro zenon_H163 ]. % 18.68/18.84 apply (zenon_L181_); trivial. % 18.68/18.84 apply (zenon_L529_); trivial. % 18.68/18.84 apply (zenon_or_s _ _ zenon_H174); [ zenon_intro zenon_H113 | zenon_intro zenon_H175 ]. % 18.68/18.84 apply (zenon_L542_); trivial. % 18.68/18.84 apply (zenon_or_s _ _ zenon_H175); [ zenon_intro zenon_H176 | zenon_intro zenon_H151 ]. % 18.68/18.84 exact (zenon_H173 zenon_H176). % 18.68/18.84 apply (zenon_L540_); trivial. % 18.68/18.84 (* end of lemma zenon_L543_ *) % 18.68/18.84 assert (zenon_L544_ : (((op (e2) (e0)) = (e3))\/(((op (e2) (e1)) = (e3))\/(((op (e2) (e2)) = (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 (e1) (e3)) = (e0))) -> (~((op (e1) (e3)) = (op (e3) (e3)))) -> (((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 (e2) (e3)) = (op (e3) (e3)))) -> (~((e0) = (e3))) -> (((op (e0) (e3)) = (e3))\/(((op (e1) (e3)) = (e3))\/(((op (e2) (e3)) = (e3))\/((op (e3) (e3)) = (e3))))) -> (((op (e3) (e1)) = (e0))\/(((op (e3) (e1)) = (e1))\/(((op (e3) (e1)) = (e2))\/((op (e3) (e1)) = (e3))))) -> (~((op (e3) (e1)) = (e0))) -> (~((op (e3) (e1)) = (op (e3) (e3)))) -> (~((op (e3) (e1)) = (op (e3) (e2)))) -> ((op (e2) (e1)) = (e0)) -> ((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)) = (e0))\/(((op (e2) (e2)) = (e1))\/(((op (e2) (e2)) = (e2))\/((op (e2) (e2)) = (e3))))) -> (~((op (e2) (e2)) = (e0))) -> (~((op (e2) (e2)) = (e2))) -> (~((op (e2) (e0)) = (op (e2) (e2)))) -> (~((op (e0) (e1)) = (op (e3) (e1)))) -> ((op (e0) (e1)) = (e1)) -> ((op (e1) (e0)) = (e2)) -> ((op (e0) (e0)) = (e3)) -> (((op (e3) (e0)) = (e1))\/(((op (e3) (e1)) = (e1))\/(((op (e3) (e2)) = (e1))\/((op (e3) (e3)) = (e1))))) -> ((op (e1) (e2)) = (e1)) -> (~((e1) = (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 (e2) (e2)) = (op (e3) (e2)))) -> (~((op (e0) (e2)) = (op (e3) (e2)))) -> ((op (e0) (e2)) = (e2)) -> ((op (e1) (e2)) = (e0)) -> (~((op (e1) (e2)) = (op (e3) (e2)))) -> (((op (e3) (e2)) = (e0))\/(((op (e3) (e2)) = (e1))\/(((op (e3) (e2)) = (e2))\/((op (e3) (e2)) = (e3))))) -> (~((op (e1) (e3)) = (op (e2) (e3)))) -> ((op (e1) (e3)) = (e3)) -> False). % 18.68/18.84 do 0 intro. intros zenon_He7 zenon_H102 zenon_Hdf zenon_H38 zenon_Hd5 zenon_H11f zenon_H1e zenon_He2 zenon_Hf3 zenon_H9a zenon_H136 zenon_H22a zenon_H1ad zenon_H130 zenon_H1a4 zenon_H36 zenon_H44 zenon_H149 zenon_H153 zenon_H1c4 zenon_H81 zenon_H173 zenon_H52 zenon_H210 zenon_Ha0 zenon_H86 zenon_H3a zenon_He8 zenon_Hf0 zenon_H95 zenon_H1a6 zenon_H13f zenon_H13e zenon_H18f zenon_H14f zenon_H150 zenon_H2a zenon_H115 zenon_H191 zenon_Hdb zenon_Hdc. % 18.68/18.84 apply (zenon_or_s _ _ zenon_He7); [ zenon_intro zenon_H3b | zenon_intro zenon_He9 ]. % 18.68/18.84 apply (zenon_L520_); trivial. % 18.68/18.84 apply (zenon_or_s _ _ zenon_He9); [ zenon_intro zenon_Ha6 | zenon_intro zenon_Hea ]. % 18.68/18.84 apply (zenon_L95_); trivial. % 18.68/18.84 apply (zenon_or_s _ _ zenon_Hea); [ zenon_intro zenon_Haa | zenon_intro zenon_Hdd ]. % 18.68/18.84 apply (zenon_L181_); trivial. % 18.68/18.84 apply (zenon_L52_); trivial. % 18.68/18.84 (* end of lemma zenon_L544_ *) % 18.68/18.84 assert (zenon_L545_ : (((op (e3) (e2)) = (e0))\/(((op (e3) (e2)) = (e1))\/(((op (e3) (e2)) = (e2))\/((op (e3) (e2)) = (e3))))) -> (~((op (e3) (e2)) = (e0))) -> (~((op (e3) (e2)) = (op (e3) (e3)))) -> ((op (e3) (e3)) = (e1)) -> ((op (e3) (e1)) = (e2)) -> (~((op (e3) (e1)) = (op (e3) (e2)))) -> ((op (e3) (e1)) = (e3)) -> False). % 18.68/18.84 do 0 intro. intros zenon_H191 zenon_H18b zenon_H62 zenon_Hc4 zenon_H14d zenon_H1a4 zenon_H161. % 18.68/18.84 apply (zenon_or_s _ _ zenon_H191); [ zenon_intro zenon_H61 | zenon_intro zenon_H192 ]. % 18.68/18.84 exact (zenon_H18b zenon_H61). % 18.68/18.84 apply (zenon_or_s _ _ zenon_H192); [ zenon_intro zenon_Hba | zenon_intro zenon_H193 ]. % 18.68/18.84 apply (zenon_L147_); trivial. % 18.68/18.84 apply (zenon_or_s _ _ zenon_H193); [ zenon_intro zenon_H151 | zenon_intro zenon_H163 ]. % 18.68/18.84 apply (zenon_L400_); trivial. % 18.68/18.84 apply (zenon_L169_); trivial. % 18.68/18.84 (* end of lemma zenon_L545_ *) % 18.68/18.84 assert (zenon_L546_ : (((op (e0) (e1)) = (e3))\/(((op (e1) (e1)) = (e3))\/(((op (e2) (e1)) = (e3))\/((op (e3) (e1)) = (e3))))) -> ((op (e0) (e1)) = (e1)) -> ((op (e2) (e1)) = (e0)) -> (~((op (e1) (e1)) = (op (e2) (e1)))) -> (~((op (e1) (e1)) = (op (e3) (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)) = (e2))\/(((op (e1) (e2)) = (e2))\/(((op (e2) (e2)) = (e2))\/((op (e3) (e2)) = (e2))))) -> (((op (e3) (e2)) = (e0))\/(((op (e3) (e2)) = (e1))\/(((op (e3) (e2)) = (e2))\/((op (e3) (e2)) = (e3))))) -> (~((op (e1) (e2)) = (op (e3) (e2)))) -> ((op (e1) (e2)) = (e0)) -> (~((op (e0) (e2)) = (op (e3) (e2)))) -> (~((op (e2) (e2)) = (op (e3) (e2)))) -> (~((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 (e2) (e2)) = (e0))\/(((op (e2) (e2)) = (e1))\/(((op (e2) (e2)) = (e2))\/((op (e2) (e2)) = (e3))))) -> (~((op (e3) (e2)) = (e0))) -> (~((op (e3) (e2)) = (op (e3) (e3)))) -> (((op (e0) (e2)) = (e3))\/(((op (e1) (e2)) = (e3))\/(((op (e2) (e2)) = (e3))\/((op (e3) (e2)) = (e3))))) -> (~((e1) = (e2))) -> ((op (e1) (e2)) = (e1)) -> (~((op (e2) (e2)) = (e2))) -> (~((op (e3) (e1)) = (op (e3) (e2)))) -> ((op (e3) (e1)) = (e2)) -> False). % 18.68/18.84 do 0 intro. intros zenon_H1a5 zenon_Ha0 zenon_H36 zenon_H13e zenon_H160 zenon_H10a zenon_H24 zenon_H142 zenon_H172 zenon_H191 zenon_H115 zenon_H2a zenon_H14f zenon_H18f zenon_H95 zenon_He8 zenon_Ha1 zenon_H44 zenon_H1c4 zenon_H18b zenon_H62 zenon_H1a6 zenon_H7c zenon_Hf0 zenon_H173 zenon_H1a4 zenon_H14d. % 18.68/18.84 apply (zenon_or_s _ _ zenon_H1a5); [ zenon_intro zenon_H99 | zenon_intro zenon_H1a8 ]. % 18.68/18.84 apply (zenon_L403_); trivial. % 18.68/18.84 apply (zenon_or_s _ _ zenon_H1a8); [ zenon_intro zenon_H13f | zenon_intro zenon_H1a9 ]. % 18.68/18.84 apply (zenon_L514_); trivial. % 18.68/18.84 apply (zenon_or_s _ _ zenon_H1a9); [ zenon_intro zenon_Ha6 | zenon_intro zenon_H161 ]. % 18.68/18.84 apply (zenon_L522_); trivial. % 18.68/18.84 apply (zenon_or_s _ _ zenon_H172); [ zenon_intro zenon_H150 | zenon_intro zenon_H174 ]. % 18.68/18.84 apply (zenon_or_s _ _ zenon_H1a6); [ zenon_intro zenon_Ha9 | zenon_intro zenon_H1aa ]. % 18.68/18.84 apply (zenon_or_s _ _ zenon_He8); [ zenon_intro zenon_Hac | zenon_intro zenon_Heb ]. % 18.68/18.84 apply (zenon_L41_); trivial. % 18.68/18.84 apply (zenon_or_s _ _ zenon_Heb); [ zenon_intro zenon_Hae | zenon_intro zenon_Hec ]. % 18.68/18.84 apply (zenon_L152_); trivial. % 18.68/18.84 apply (zenon_or_s _ _ zenon_Hec); [ zenon_intro zenon_Hba | zenon_intro zenon_Hc4 ]. % 18.68/18.84 apply (zenon_L186_); trivial. % 18.68/18.84 apply (zenon_L545_); trivial. % 18.68/18.84 apply (zenon_or_s _ _ zenon_H1aa); [ zenon_intro zenon_H16c | zenon_intro zenon_H1ab ]. % 18.68/18.84 apply (zenon_L167_); trivial. % 18.68/18.84 apply (zenon_or_s _ _ zenon_H1ab); [ zenon_intro zenon_Haa | zenon_intro zenon_H163 ]. % 18.68/18.84 apply (zenon_L181_); trivial. % 18.68/18.84 apply (zenon_L169_); trivial. % 18.68/18.84 apply (zenon_or_s _ _ zenon_H174); [ zenon_intro zenon_H113 | zenon_intro zenon_H175 ]. % 18.68/18.84 apply (zenon_L68_); trivial. % 18.68/18.84 apply (zenon_or_s _ _ zenon_H175); [ zenon_intro zenon_H176 | zenon_intro zenon_H151 ]. % 18.68/18.84 exact (zenon_H173 zenon_H176). % 18.68/18.84 apply (zenon_L400_); trivial. % 18.68/18.84 (* end of lemma zenon_L546_ *) % 18.68/18.84 assert (zenon_L547_ : (((op (e3) (e2)) = (e0))\/(((op (e3) (e2)) = (e1))\/(((op (e3) (e2)) = (e2))\/((op (e3) (e2)) = (e3))))) -> (~((e1) = (e2))) -> (~((op (e3) (e2)) = (op (e3) (e3)))) -> (~((op (e3) (e2)) = (e0))) -> (((op (e0) (e2)) = (e2))\/(((op (e1) (e2)) = (e2))\/(((op (e2) (e2)) = (e2))\/((op (e3) (e2)) = (e2))))) -> ((op (e2) (e1)) = (e0)) -> (((op (e0) (e1)) = (e3))\/(((op (e1) (e1)) = (e3))\/(((op (e2) (e1)) = (e3))\/((op (e3) (e1)) = (e3))))) -> ((op (e1) (e3)) = (e3)) -> (((op (e0) (e2)) = (e3))\/(((op (e1) (e2)) = (e3))\/(((op (e2) (e2)) = (e3))\/((op (e3) (e2)) = (e3))))) -> (~((op (e2) (e2)) = (e2))) -> (~((op (e2) (e2)) = (e0))) -> (((op (e2) (e2)) = (e0))\/(((op (e2) (e2)) = (e1))\/(((op (e2) (e2)) = (e2))\/((op (e2) (e2)) = (e3))))) -> (~((op (e2) (e2)) = (op (e3) (e2)))) -> (~((e1) = (e3))) -> (~((op (e0) (e2)) = (op (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 (e2) (e0)) = (e1)) -> (~((op (e0) (e2)) = (op (e1) (e2)))) -> ((op (e1) (e2)) = (e0)) -> (((op (e0) (e2)) = (e0))\/(((op (e0) (e2)) = (e1))\/(((op (e0) (e2)) = (e2))\/((op (e0) (e2)) = (e3))))) -> ((op (e1) (e0)) = (e2)) -> ((op (e0) (e0)) = (e3)) -> (((op (e3) (e0)) = (e1))\/(((op (e3) (e1)) = (e1))\/(((op (e3) (e2)) = (e1))\/((op (e3) (e3)) = (e1))))) -> (~((e0) = (e1))) -> ((op (e0) (e1)) = (e1)) -> (~((op (e0) (e1)) = (op (e3) (e1)))) -> ((op (e1) (e2)) = (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 (e3) (e0)) = (e0)) -> ((op (e2) (e1)) = (e3)) -> (~((op (e1) (e1)) = (op (e2) (e1)))) -> (~((op (e1) (e1)) = (op (e3) (e1)))) -> (~((op (e1) (e1)) = (e1))) -> (~((op (e1) (e1)) = (e0))) -> (((op (e1) (e1)) = (e0))\/(((op (e1) (e1)) = (e1))\/(((op (e1) (e1)) = (e2))\/((op (e1) (e1)) = (e3))))) -> (~((op (e3) (e1)) = (op (e3) (e2)))) -> (~((op (e3) (e1)) = (op (e3) (e3)))) -> (~((op (e3) (e1)) = (e0))) -> (((op (e3) (e1)) = (e0))\/(((op (e3) (e1)) = (e1))\/(((op (e3) (e1)) = (e2))\/((op (e3) (e1)) = (e3))))) -> (((op (e0) (e3)) = (e3))\/(((op (e1) (e3)) = (e3))\/(((op (e2) (e3)) = (e3))\/((op (e3) (e3)) = (e3))))) -> (~((e0) = (e3))) -> (~((op (e2) (e3)) = (op (e3) (e3)))) -> (~((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 (e1) (e3)) = (op (e2) (e3)))) -> (~((op (e1) (e3)) = (op (e3) (e3)))) -> (~((op (e1) (e3)) = (e0))) -> (((op (e1) (e3)) = (e0))\/(((op (e1) (e3)) = (e1))\/(((op (e1) (e3)) = (e2))\/((op (e1) (e3)) = (e3))))) -> (~((op (e3) (e3)) = (e3))) -> False). % 18.68/18.84 do 0 intro. intros zenon_H191 zenon_H7c zenon_H62 zenon_H18b zenon_H172 zenon_H36 zenon_H1a5 zenon_Hdc zenon_H1a6 zenon_H173 zenon_H81 zenon_H1c4 zenon_H18f zenon_H95 zenon_Ha8 zenon_H14f zenon_H128 zenon_H201 zenon_Hed zenon_H195 zenon_H2a zenon_H1ba zenon_H86 zenon_H3a zenon_He8 zenon_Ha1 zenon_Ha0 zenon_H210 zenon_Hf0 zenon_H115 zenon_H153 zenon_H149 zenon_H44 zenon_Ha6 zenon_H13e zenon_H160 zenon_H10a zenon_H24 zenon_H142 zenon_H1a4 zenon_H130 zenon_H1ad zenon_H22a zenon_H136 zenon_H9a zenon_Hf3 zenon_He2 zenon_H1e zenon_H11f zenon_Hdb zenon_Hd5 zenon_H38 zenon_Hdf zenon_H102. % 18.68/18.84 apply (zenon_or_s _ _ zenon_H172); [ zenon_intro zenon_H150 | zenon_intro zenon_H174 ]. % 18.68/18.84 apply (zenon_or_s _ _ zenon_H1a6); [ zenon_intro zenon_Ha9 | zenon_intro zenon_H1aa ]. % 18.68/18.84 apply (zenon_or_s _ _ zenon_He8); [ zenon_intro zenon_Hac | zenon_intro zenon_Heb ]. % 18.68/18.84 apply (zenon_L41_); trivial. % 18.68/18.84 apply (zenon_or_s _ _ zenon_Heb); [ zenon_intro zenon_Hae | zenon_intro zenon_Hec ]. % 18.68/18.84 apply (zenon_L363_); trivial. % 18.68/18.84 apply (zenon_or_s _ _ zenon_Hec); [ zenon_intro zenon_Hba | zenon_intro zenon_Hc4 ]. % 18.68/18.84 apply (zenon_L186_); trivial. % 18.68/18.84 apply (zenon_or_s _ _ zenon_H153); [ zenon_intro zenon_H148 | zenon_intro zenon_H154 ]. % 18.68/18.84 apply (zenon_L423_); trivial. % 18.68/18.84 apply (zenon_or_s _ _ zenon_H154); [ zenon_intro zenon_H14d | zenon_intro zenon_H155 ]. % 18.68/18.84 apply (zenon_L546_); trivial. % 18.68/18.84 apply (zenon_or_s _ _ zenon_H155); [ zenon_intro zenon_H151 | zenon_intro zenon_Hf6 ]. % 18.68/18.84 apply (zenon_L533_); trivial. % 18.68/18.84 apply (zenon_L404_); trivial. % 18.68/18.84 apply (zenon_or_s _ _ zenon_H1aa); [ zenon_intro zenon_H16c | zenon_intro zenon_H1ab ]. % 18.68/18.84 apply (zenon_L167_); trivial. % 18.68/18.84 apply (zenon_or_s _ _ zenon_H1ab); [ zenon_intro zenon_Haa | zenon_intro zenon_H163 ]. % 18.68/18.84 apply (zenon_L181_); trivial. % 18.68/18.84 apply (zenon_L523_); trivial. % 18.68/18.84 apply (zenon_or_s _ _ zenon_H174); [ zenon_intro zenon_H113 | zenon_intro zenon_H175 ]. % 18.68/18.84 apply (zenon_L542_); trivial. % 18.68/18.84 apply (zenon_or_s _ _ zenon_H175); [ zenon_intro zenon_H176 | zenon_intro zenon_H151 ]. % 18.68/18.84 exact (zenon_H173 zenon_H176). % 18.68/18.84 apply (zenon_L535_); trivial. % 18.68/18.84 (* end of lemma zenon_L547_ *) % 18.68/18.84 assert (zenon_L548_ : (((op (e0) (e2)) = (e2))\/(((op (e1) (e2)) = (e2))\/(((op (e2) (e2)) = (e2))\/((op (e3) (e2)) = (e2))))) -> ((op (e1) (e3)) = (e3)) -> (~((op (e1) (e3)) = (op (e2) (e3)))) -> (((op (e3) (e2)) = (e0))\/(((op (e3) (e2)) = (e1))\/(((op (e3) (e2)) = (e2))\/((op (e3) (e2)) = (e3))))) -> (~((op (e1) (e2)) = (op (e3) (e2)))) -> (~((op (e0) (e2)) = (op (e3) (e2)))) -> (~((op (e2) (e2)) = (op (e3) (e2)))) -> (~((e2) = (e3))) -> (((op (e0) (e2)) = (e3))\/(((op (e1) (e2)) = (e3))\/(((op (e2) (e2)) = (e3))\/((op (e3) (e2)) = (e3))))) -> (~((op (e2) (e2)) = (e0))) -> (((op (e2) (e2)) = (e0))\/(((op (e2) (e2)) = (e1))\/(((op (e2) (e2)) = (e2))\/((op (e2) (e2)) = (e3))))) -> (~((e0) = (e3))) -> (~((op (e2) (e0)) = (op (e2) (e2)))) -> (~((op (e3) (e1)) = (op (e3) (e2)))) -> ((op (e3) (e1)) = (e3)) -> (((op (e2) (e0)) = (e3))\/(((op (e2) (e1)) = (e3))\/(((op (e2) (e2)) = (e3))\/((op (e2) (e3)) = (e3))))) -> (~((e0) = (e2))) -> ((op (e1) (e2)) = (e0)) -> (~((op (e2) (e2)) = (e2))) -> (((op (e0) (e3)) = (e2))\/(((op (e1) (e3)) = (e2))\/(((op (e2) (e3)) = (e2))\/((op (e3) (e3)) = (e2))))) -> (~((op (e0) (e0)) = (op (e0) (e3)))) -> ((op (e0) (e0)) = (e2)) -> (~((op (e1) (e0)) = (op (e1) (e3)))) -> ((op (e1) (e0)) = (e2)) -> (~((op (e2) (e1)) = (op (e2) (e3)))) -> ((op (e2) (e1)) = (e2)) -> (~((op (e3) (e2)) = (op (e3) (e3)))) -> False). % 18.68/18.84 do 0 intro. intros zenon_H172 zenon_Hdc zenon_Hdb zenon_H191 zenon_H115 zenon_H14f zenon_H18f zenon_H12b zenon_H1a6 zenon_H81 zenon_H1c4 zenon_H9a zenon_H52 zenon_H1a4 zenon_H161 zenon_He7 zenon_H149 zenon_H2a zenon_H173 zenon_H145 zenon_H189 zenon_H7b zenon_Hd8 zenon_H86 zenon_H1c7 zenon_H1ca zenon_H62. % 18.68/18.84 apply (zenon_or_s _ _ zenon_H172); [ zenon_intro zenon_H150 | zenon_intro zenon_H174 ]. % 18.68/18.84 apply (zenon_or_s _ _ zenon_He7); [ zenon_intro zenon_H3b | zenon_intro zenon_He9 ]. % 18.68/18.84 apply (zenon_L525_); trivial. % 18.68/18.84 apply (zenon_or_s _ _ zenon_He9); [ zenon_intro zenon_Ha6 | zenon_intro zenon_Hea ]. % 18.68/18.84 apply (zenon_L207_); trivial. % 18.68/18.84 apply (zenon_or_s _ _ zenon_Hea); [ zenon_intro zenon_Haa | zenon_intro zenon_Hdd ]. % 18.68/18.84 apply (zenon_L181_); trivial. % 18.68/18.84 apply (zenon_L52_); trivial. % 18.68/18.84 apply (zenon_or_s _ _ zenon_H174); [ zenon_intro zenon_H113 | zenon_intro zenon_H175 ]. % 18.68/18.84 apply (zenon_L542_); trivial. % 18.68/18.84 apply (zenon_or_s _ _ zenon_H175); [ zenon_intro zenon_H176 | zenon_intro zenon_H151 ]. % 18.68/18.84 exact (zenon_H173 zenon_H176). % 18.68/18.84 apply (zenon_L540_); trivial. % 18.68/18.84 (* end of lemma zenon_L548_ *) % 18.68/18.84 assert (zenon_L549_ : (((op (e2) (e0)) = (e3))\/(((op (e2) (e1)) = (e3))\/(((op (e2) (e2)) = (e3))\/((op (e2) (e3)) = (e3))))) -> ((op (e3) (e1)) = (e3)) -> (~((op (e2) (e0)) = (op (e2) (e2)))) -> (~((op (e1) (e3)) = (e0))) -> (((op (e2) (e3)) = (e0))\/(((op (e2) (e3)) = (e1))\/(((op (e2) (e3)) = (e2))\/((op (e2) (e3)) = (e3))))) -> ((op (e0) (e3)) = (e0)) -> (~((op (e2) (e3)) = (op (e3) (e3)))) -> (~((e0) = (e3))) -> (((op (e0) (e3)) = (e3))\/(((op (e1) (e3)) = (e3))\/(((op (e2) (e3)) = (e3))\/((op (e3) (e3)) = (e3))))) -> (((op (e3) (e1)) = (e0))\/(((op (e3) (e1)) = (e1))\/(((op (e3) (e1)) = (e2))\/((op (e3) (e1)) = (e3))))) -> (~((op (e3) (e1)) = (e0))) -> (~((op (e3) (e1)) = (op (e3) (e3)))) -> (~((op (e3) (e1)) = (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 (e3) (e1)))) -> (~((op (e1) (e1)) = (op (e2) (e1)))) -> (~((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 (e1) (e2)) = (e1)) -> (~((e0) = (e1))) -> (~((e1) = (e3))) -> (~((op (e2) (e2)) = (op (e3) (e2)))) -> (((op (e2) (e2)) = (e0))\/(((op (e2) (e2)) = (e1))\/(((op (e2) (e2)) = (e2))\/((op (e2) (e2)) = (e3))))) -> (~((op (e2) (e2)) = (e0))) -> (~((op (e2) (e2)) = (e2))) -> (((op (e0) (e2)) = (e3))\/(((op (e1) (e2)) = (e3))\/(((op (e2) (e2)) = (e3))\/((op (e3) (e2)) = (e3))))) -> (~((op (e0) (e2)) = (op (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 (e2) (e0)) = (e1)) -> (~((op (e1) (e1)) = (e1))) -> (~((op (e0) (e2)) = (op (e1) (e2)))) -> ((op (e1) (e2)) = (e0)) -> (((op (e0) (e2)) = (e0))\/(((op (e0) (e2)) = (e1))\/(((op (e0) (e2)) = (e2))\/((op (e0) (e2)) = (e3))))) -> (~((op (e0) (e1)) = (op (e3) (e1)))) -> ((op (e0) (e1)) = (e1)) -> ((op (e1) (e0)) = (e2)) -> ((op (e0) (e0)) = (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) (e0)) = (op (e3) (e3)))) -> ((op (e3) (e0)) = (e0)) -> (~((op (e0) (e3)) = (op (e2) (e3)))) -> ((op (e2) (e3)) = (e2)) -> (~((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))))) -> (~((op (e3) (e2)) = (op (e3) (e3)))) -> ((op (e3) (e2)) = (e2)) -> (~((op (e3) (e3)) = (e3))) -> False). % 18.68/18.85 do 0 intro. intros zenon_He7 zenon_H161 zenon_H52 zenon_H38 zenon_H11f zenon_H1e zenon_Hf3 zenon_H9a zenon_H136 zenon_H22a zenon_H1ad zenon_H130 zenon_H1a4 zenon_H142 zenon_H24 zenon_H160 zenon_H13e zenon_H149 zenon_H153 zenon_H115 zenon_Hf0 zenon_Ha1 zenon_H95 zenon_H18f zenon_H1c4 zenon_H81 zenon_H173 zenon_H1a6 zenon_Ha8 zenon_H14f zenon_H128 zenon_H201 zenon_Hed zenon_H10a zenon_H195 zenon_H2a zenon_H1ba zenon_H210 zenon_Ha0 zenon_H86 zenon_H3a zenon_He8 zenon_H101 zenon_H71 zenon_H44 zenon_He2 zenon_H11d zenon_Hc2 zenon_Hdf zenon_H1d zenon_Hd5 zenon_Hdb zenon_He4 zenon_H62 zenon_H151 zenon_H102. % 18.68/18.85 apply (zenon_or_s _ _ zenon_He7); [ zenon_intro zenon_H3b | zenon_intro zenon_He9 ]. % 18.68/18.85 apply (zenon_L525_); trivial. % 18.68/18.85 apply (zenon_or_s _ _ zenon_He9); [ zenon_intro zenon_Ha6 | zenon_intro zenon_Hea ]. % 18.68/18.85 apply (zenon_L535_); trivial. % 18.68/18.85 apply (zenon_or_s _ _ zenon_Hea); [ zenon_intro zenon_Haa | zenon_intro zenon_Hdd ]. % 18.68/18.85 apply (zenon_L534_); trivial. % 18.68/18.85 apply (zenon_L537_); trivial. % 18.68/18.85 (* end of lemma zenon_L549_ *) % 18.68/18.85 assert (zenon_L550_ : ((op (e1) (e0)) = (e2)) -> (((op (e0) (e0)) = (e0))\/(((op (e1) (e0)) = (e0))\/(((op (e2) (e0)) = (e0))\/((op (e3) (e0)) = (e0))))) -> (~((op (e1) (e0)) = (e0))) -> (~((op (e0) (e0)) = (e0))) -> (((op (e0) (e0)) = (e1))\/(((op (e1) (e0)) = (e1))\/(((op (e2) (e0)) = (e1))\/((op (e3) (e0)) = (e1))))) -> ((op (e1) (e0)) = (e3)) -> ((~((op (e2) (e1)) = (e0)))\/((op (e2) (e0)) = (e1))) -> ((~((op (e2) (e3)) = (e0)))\/((op (e2) (e0)) = (e3))) -> ((~((op (e3) (e1)) = (e0)))\/((op (e3) (e0)) = (e1))) -> (((op (e0) (e0)) = (e0))\/(((op (e0) (e1)) = (e0))\/(((op (e0) (e2)) = (e0))\/((op (e0) (e3)) = (e0))))) -> (~((op (e0) (e2)) = (op (e0) (e3)))) -> (((op (e1) (e0)) = (e0))\/(((op (e1) (e1)) = (e0))\/(((op (e1) (e2)) = (e0))\/((op (e1) (e3)) = (e0))))) -> (~((e1) = (e2))) -> (~((e0) = (e2))) -> (~((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 (e3) (e2)))) -> (~((op (e2) (e2)) = (e2))) -> (((op (e2) (e2)) = (e0))\/(((op (e2) (e2)) = (e1))\/(((op (e2) (e2)) = (e2))\/((op (e2) (e2)) = (e3))))) -> (~((op (e2) (e0)) = (op (e2) (e2)))) -> (~((e0) = (e1))) -> (~((op (e0) (e1)) = (op (e2) (e1)))) -> (~((e0) = (e3))) -> (~((e2) = (e3))) -> (((op (e3) (e0)) = (e1))\/(((op (e3) (e1)) = (e1))\/(((op (e3) (e2)) = (e1))\/((op (e3) (e3)) = (e1))))) -> (~((op (e1) (e3)) = (op (e3) (e3)))) -> (~((op (e1) (e3)) = (op (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 (e1) (e1)) = (e1))) -> (((op (e2) (e0)) = (e2))\/(((op (e2) (e1)) = (e2))\/(((op (e2) (e2)) = (e2))\/((op (e2) (e3)) = (e2))))) -> (((op (e0) (e1)) = (e3))\/(((op (e1) (e1)) = (e3))\/(((op (e2) (e1)) = (e3))\/((op (e3) (e1)) = (e3))))) -> (~((op (e3) (e1)) = (op (e3) (e2)))) -> (((op (e0) (e2)) = (e3))\/(((op (e1) (e2)) = (e3))\/(((op (e2) (e2)) = (e3))\/((op (e3) (e2)) = (e3))))) -> (((op (e0) (e1)) = (e0))\/(((op (e0) (e1)) = (e1))\/(((op (e0) (e1)) = (e2))\/((op (e0) (e1)) = (e3))))) -> (~((op (e0) (e1)) = (op (e1) (e1)))) -> (~((op (e1) (e1)) = (op (e2) (e1)))) -> (((op (e2) (e1)) = (e0))\/(((op (e2) (e1)) = (e1))\/(((op (e2) (e1)) = (e2))\/((op (e2) (e1)) = (e3))))) -> (~((op (e0) (e3)) = (op (e3) (e3)))) -> (((op (e0) (e2)) = (e0))\/(((op (e1) (e2)) = (e0))\/(((op (e2) (e2)) = (e0))\/((op (e3) (e2)) = (e0))))) -> (~((op (e3) (e0)) = (op (e3) (e2)))) -> (~((op (e1) (e1)) = (op (e1) (e2)))) -> (~((op (e1) (e2)) = (op (e2) (e2)))) -> (((op (e3) (e0)) = (e2))\/(((op (e3) (e1)) = (e2))\/(((op (e3) (e2)) = (e2))\/((op (e3) (e3)) = (e2))))) -> (((op (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) (e3)) = (e3))) -> (~((op (e3) (e2)) = (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 (e1) (e1)) = (op (e3) (e1)))) -> (((op (e1) (e0)) = (e2))\/(((op (e1) (e1)) = (e2))\/(((op (e1) (e2)) = (e2))\/((op (e1) (e3)) = (e2))))) -> (~((op (e0) (e0)) = (op (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) (e3)) = (e2))\/(((op (e1) (e3)) = (e2))\/(((op (e2) (e3)) = (e2))\/((op (e3) (e3)) = (e2))))) -> (((op (e2) (e0)) = (e1))\/(((op (e2) (e1)) = (e1))\/(((op (e2) (e2)) = (e1))\/((op (e2) (e3)) = (e1))))) -> (((op (e0) (e1)) = (e1))\/(((op (e1) (e1)) = (e1))\/(((op (e2) (e1)) = (e1))\/((op (e3) (e1)) = (e1))))) -> (~((op (e0) (e3)) = (op (e2) (e3)))) -> (((op (e1) (e3)) = (e0))\/(((op (e1) (e3)) = (e1))\/(((op (e1) (e3)) = (e2))\/((op (e1) (e3)) = (e3))))) -> (~((op (e2) (e1)) = (op (e3) (e1)))) -> (((op (e3) (e1)) = (e0))\/(((op (e3) (e1)) = (e1))\/(((op (e3) (e1)) = (e2))\/((op (e3) (e1)) = (e3))))) -> (((op (e2) (e3)) = (e0))\/(((op (e2) (e3)) = (e1))\/(((op (e2) (e3)) = (e2))\/((op (e2) (e3)) = (e3))))) -> (~((op (e2) (e3)) = (op (e3) (e3)))) -> (~((op (e1) (e2)) = (op (e3) (e2)))) -> (~((op (e0) (e1)) = (op (e0) (e2)))) -> (~((op (e0) (e1)) = (op (e3) (e1)))) -> (~((op (e0) (e1)) = (op (e0) (e3)))) -> (~((op (e1) (e0)) = (op (e1) (e3)))) -> (~((op (e2) (e2)) = (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 (e0) (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)) = (e0))) -> ((~((op (e3) (e2)) = (e0)))\/((op (e3) (e0)) = (e2))) -> ((~((op (e3) (e0)) = (e0)))\/((op (e3) (e0)) = (e0))) -> (((op (e2) (e0)) = (e0))\/(((op (e2) (e1)) = (e0))\/(((op (e2) (e2)) = (e0))\/((op (e2) (e3)) = (e0))))) -> ((~((op (e2) (e2)) = (e0)))\/((op (e2) (e0)) = (e2))) -> (((op (e3) (e0)) = (e3))\/(((op (e3) (e1)) = (e3))\/(((op (e3) (e2)) = (e3))\/((op (e3) (e3)) = (e3))))) -> (~((op (e0) (e2)) = (op (e2) (e2)))) -> ((~((op (e3) (e3)) = (e0)))\/((op (e3) (e0)) = (e3))) -> ((~((op (e0) (e3)) = (e0)))\/((op (e0) (e0)) = (e3))) -> ((~((op (e1) (e1)) = (e0)))\/((op (e1) (e0)) = (e1))) -> (((op (e3) (e2)) = (e0))\/(((op (e3) (e2)) = (e1))\/(((op (e3) (e2)) = (e2))\/((op (e3) (e2)) = (e3))))) -> (~((op (e0) (e2)) = (op (e1) (e2)))) -> (((op (e1) (e2)) = (e0))\/(((op (e1) (e2)) = (e1))\/(((op (e1) (e2)) = (e2))\/((op (e1) (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 (e2) (e0)) = (op (e3) (e0)))) -> ((~((op (e1) (e2)) = (e0)))\/((op (e1) (e0)) = (e2))) -> ((~((op (e1) (e3)) = (e0)))\/((op (e1) (e0)) = (e3))) -> (((op (e1) (e1)) = (e0))\/(((op (e1) (e1)) = (e1))\/(((op (e1) (e1)) = (e2))\/((op (e1) (e1)) = (e3))))) -> (~((op (e0) (e0)) = (op (e0) (e2)))) -> (((op (e1) (e0)) = (e1))\/(((op (e1) (e1)) = (e1))\/(((op (e1) (e2)) = (e1))\/((op (e1) (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 (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 (e2) (e0)) = (e0)))\/((op (e2) (e0)) = (e0))) -> (((op (e0) (e0)) = (e3))\/(((op (e1) (e0)) = (e3))\/(((op (e2) (e0)) = (e3))\/((op (e3) (e0)) = (e3))))) -> (((op (e0) (e2)) = (e0))\/(((op (e0) (e2)) = (e1))\/(((op (e0) (e2)) = (e2))\/((op (e0) (e2)) = (e3))))) -> (~((op (e1) (e0)) = (op (e3) (e0)))) -> (~((op (e2) (e0)) = (op (e2) (e1)))) -> ((~((op (e1) (e0)) = (e0)))\/((op (e1) (e0)) = (e0))) -> ((~((op (e0) (e2)) = (e0)))\/((op (e0) (e0)) = (e2))) -> (~((op (e3) (e0)) = (op (e3) (e1)))) -> (~((op (e1) (e1)) = (op (e1) (e3)))) -> (~((op (e2) (e0)) = (op (e2) (e3)))) -> (((op (e0) (e3)) = (e0))\/(((op (e1) (e3)) = (e0))\/(((op (e2) (e3)) = (e0))\/((op (e3) (e3)) = (e0))))) -> (~((op (e1) (e0)) = (op (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) (e0)) = (e3)) -> (~((e1) = (e3))) -> False). % 18.68/18.85 do 0 intro. intros zenon_H86 zenon_H3e zenon_H23 zenon_H3f zenon_H235 zenon_H9e zenon_H182 zenon_H94 zenon_H1ed zenon_H74 zenon_H208 zenon_H22 zenon_H7c zenon_H149 zenon_H201 zenon_H139 zenon_H18f zenon_H173 zenon_H1c4 zenon_H52 zenon_Ha1 zenon_H17e zenon_H9a zenon_H12b zenon_He8 zenon_Hd5 zenon_Hdb zenon_He4 zenon_H1d zenon_H10a zenon_H1d5 zenon_H1a5 zenon_H1a4 zenon_H1a6 zenon_H212 zenon_H10e zenon_H13e zenon_H1cc zenon_Hc2 zenon_H6a zenon_H6f zenon_H4f zenon_H2b zenon_H153 zenon_H16f zenon_H101 zenon_H102 zenon_H62 zenon_H130 zenon_H172 zenon_H160 zenon_H18c zenon_H189 zenon_H1d8 zenon_H1c7 zenon_H145 zenon_H106 zenon_H109 zenon_He2 zenon_Hdf zenon_Haf zenon_H22a zenon_H11f zenon_Hf3 zenon_H115 zenon_H4a zenon_H210 zenon_H54 zenon_Hd8 zenon_H6d zenon_H71 zenon_H133 zenon_H7b zenon_H39 zenon_H22d zenon_H20b zenon_H1a7 zenon_H184 zenon_H2f zenon_H185 zenon_H165 zenon_Ha8 zenon_H1ec zenon_H204 zenon_H205 zenon_H191 zenon_H195 zenon_H19d zenon_He7 zenon_H183 zenon_H17b zenon_H178 zenon_H179 zenon_H142 zenon_H13c zenon_H128 zenon_H136 zenon_H124 zenon_H168 zenon_H1fe zenon_H1ee zenon_H1e0 zenon_H1ba zenon_H1fa zenon_H1f0 zenon_H206 zenon_H233 zenon_H1cf zenon_H57 zenon_H5b zenon_H67 zenon_H45 zenon_H14f zenon_H1ac zenon_H3a zenon_H95. % 18.68/18.85 apply (zenon_or_s _ _ zenon_H1ee); [ zenon_intro zenon_H30 | zenon_intro zenon_H34 ]. % 18.68/18.85 apply (zenon_L493_); trivial. % 18.68/18.85 apply (zenon_L494_); trivial. % 18.68/18.85 (* end of lemma zenon_L550_ *) % 18.68/18.85 assert (zenon_L551_ : ((op (e2) (e1)) = (e0)) -> ((op (e1) (e1)) = (e2)) -> (~((e0) = (op (op (e1) (e1)) (e1)))) -> False). % 18.68/18.85 do 0 intro. intros zenon_H36 zenon_H110 zenon_H240. % 18.68/18.85 elim (classic ((op (op (e1) (e1)) (e1)) = (op (op (e1) (e1)) (e1)))); [ zenon_intro zenon_H217 | zenon_intro zenon_H218 ]. % 18.68/18.85 cut (((op (op (e1) (e1)) (e1)) = (op (op (e1) (e1)) (e1))) = ((e0) = (op (op (e1) (e1)) (e1)))). % 18.68/18.85 intro zenon_D_pnotp. % 18.68/18.85 apply zenon_H240. % 18.68/18.85 rewrite <- zenon_D_pnotp. % 18.68/18.85 exact zenon_H217. % 18.68/18.85 cut (((op (op (e1) (e1)) (e1)) = (op (op (e1) (e1)) (e1)))); [idtac | apply NNPP; zenon_intro zenon_H218]. % 18.68/18.85 cut (((op (op (e1) (e1)) (e1)) = (e0))); [idtac | apply NNPP; zenon_intro zenon_H241]. % 18.68/18.85 congruence. % 18.68/18.85 cut (((op (e2) (e1)) = (e0)) = ((op (op (e1) (e1)) (e1)) = (e0))). % 18.68/18.85 intro zenon_D_pnotp. % 18.68/18.85 apply zenon_H241. % 18.68/18.85 rewrite <- zenon_D_pnotp. % 18.68/18.85 exact zenon_H36. % 18.68/18.85 cut (((e0) = (e0))); [idtac | apply NNPP; zenon_intro zenon_H82]. % 18.68/18.85 cut (((op (e2) (e1)) = (op (op (e1) (e1)) (e1)))); [idtac | apply NNPP; zenon_intro zenon_H239]. % 18.68/18.85 congruence. % 18.68/18.85 elim (classic ((op (op (e1) (e1)) (e1)) = (op (op (e1) (e1)) (e1)))); [ zenon_intro zenon_H217 | zenon_intro zenon_H218 ]. % 18.68/18.85 cut (((op (op (e1) (e1)) (e1)) = (op (op (e1) (e1)) (e1))) = ((op (e2) (e1)) = (op (op (e1) (e1)) (e1)))). % 18.68/18.85 intro zenon_D_pnotp. % 18.68/18.85 apply zenon_H239. % 18.68/18.85 rewrite <- zenon_D_pnotp. % 18.68/18.85 exact zenon_H217. % 18.68/18.85 cut (((op (op (e1) (e1)) (e1)) = (op (op (e1) (e1)) (e1)))); [idtac | apply NNPP; zenon_intro zenon_H218]. % 18.68/18.85 cut (((op (op (e1) (e1)) (e1)) = (op (e2) (e1)))); [idtac | apply NNPP; zenon_intro zenon_H238]. % 18.68/18.85 congruence. % 18.68/18.85 apply (zenon_L507_); trivial. % 18.68/18.85 apply zenon_H218. apply refl_equal. % 18.68/18.85 apply zenon_H218. apply refl_equal. % 18.68/18.85 apply zenon_H82. apply refl_equal. % 18.68/18.85 apply zenon_H218. apply refl_equal. % 18.68/18.85 apply zenon_H218. apply refl_equal. % 18.68/18.85 (* end of lemma zenon_L551_ *) % 18.68/18.85 assert (zenon_L552_ : ((op (e0) (e1)) = (e3)) -> ((op (e2) (e1)) = (e0)) -> ((op (e1) (e1)) = (e2)) -> False). % 18.68/18.85 do 0 intro. intros zenon_H99 zenon_H36 zenon_H110. % 18.68/18.85 apply (zenon_notand_s _ _ ax16); [ zenon_intro zenon_H21c | zenon_intro zenon_H242 ]. % 18.68/18.85 elim (classic ((op (op (op (e1) (e1)) (e1)) (e1)) = (op (op (op (e1) (e1)) (e1)) (e1)))); [ zenon_intro zenon_H21d | zenon_intro zenon_H21e ]. % 18.68/18.85 cut (((op (op (op (e1) (e1)) (e1)) (e1)) = (op (op (op (e1) (e1)) (e1)) (e1))) = ((e3) = (op (op (op (e1) (e1)) (e1)) (e1)))). % 18.68/18.85 intro zenon_D_pnotp. % 18.68/18.85 apply zenon_H21c. % 18.68/18.85 rewrite <- zenon_D_pnotp. % 18.68/18.85 exact zenon_H21d. % 18.68/18.85 cut (((op (op (op (e1) (e1)) (e1)) (e1)) = (op (op (op (e1) (e1)) (e1)) (e1)))); [idtac | apply NNPP; zenon_intro zenon_H21e]. % 18.68/18.85 cut (((op (op (op (e1) (e1)) (e1)) (e1)) = (e3))); [idtac | apply NNPP; zenon_intro zenon_H21f]. % 18.68/18.85 congruence. % 18.68/18.85 cut (((op (e0) (e1)) = (e3)) = ((op (op (op (e1) (e1)) (e1)) (e1)) = (e3))). % 18.68/18.85 intro zenon_D_pnotp. % 18.68/18.85 apply zenon_H21f. % 18.68/18.85 rewrite <- zenon_D_pnotp. % 18.68/18.85 exact zenon_H99. % 18.68/18.85 cut (((e3) = (e3))); [idtac | apply NNPP; zenon_intro zenon_H85]. % 18.68/18.85 cut (((op (e0) (e1)) = (op (op (op (e1) (e1)) (e1)) (e1)))); [idtac | apply NNPP; zenon_intro zenon_H243]. % 18.68/18.85 congruence. % 18.68/18.85 elim (classic ((op (op (op (e1) (e1)) (e1)) (e1)) = (op (op (op (e1) (e1)) (e1)) (e1)))); [ zenon_intro zenon_H21d | zenon_intro zenon_H21e ]. % 18.68/18.85 cut (((op (op (op (e1) (e1)) (e1)) (e1)) = (op (op (op (e1) (e1)) (e1)) (e1))) = ((op (e0) (e1)) = (op (op (op (e1) (e1)) (e1)) (e1)))). % 18.68/18.85 intro zenon_D_pnotp. % 18.68/18.85 apply zenon_H243. % 18.68/18.85 rewrite <- zenon_D_pnotp. % 18.68/18.85 exact zenon_H21d. % 18.68/18.85 cut (((op (op (op (e1) (e1)) (e1)) (e1)) = (op (op (op (e1) (e1)) (e1)) (e1)))); [idtac | apply NNPP; zenon_intro zenon_H21e]. % 18.68/18.85 cut (((op (op (op (e1) (e1)) (e1)) (e1)) = (op (e0) (e1)))); [idtac | apply NNPP; zenon_intro zenon_H244]. % 18.68/18.85 congruence. % 18.68/18.85 cut (((e1) = (e1))); [idtac | apply NNPP; zenon_intro zenon_H79]. % 18.68/18.85 cut (((op (op (e1) (e1)) (e1)) = (e0))); [idtac | apply NNPP; zenon_intro zenon_H241]. % 18.68/18.85 congruence. % 18.68/18.85 cut (((op (e2) (e1)) = (e0)) = ((op (op (e1) (e1)) (e1)) = (e0))). % 18.68/18.85 intro zenon_D_pnotp. % 18.68/18.85 apply zenon_H241. % 18.68/18.85 rewrite <- zenon_D_pnotp. % 18.68/18.85 exact zenon_H36. % 18.68/18.85 cut (((e0) = (e0))); [idtac | apply NNPP; zenon_intro zenon_H82]. % 18.68/18.85 cut (((op (e2) (e1)) = (op (op (e1) (e1)) (e1)))); [idtac | apply NNPP; zenon_intro zenon_H239]. % 18.68/18.85 congruence. % 18.68/18.85 elim (classic ((op (op (e1) (e1)) (e1)) = (op (op (e1) (e1)) (e1)))); [ zenon_intro zenon_H217 | zenon_intro zenon_H218 ]. % 18.68/18.85 cut (((op (op (e1) (e1)) (e1)) = (op (op (e1) (e1)) (e1))) = ((op (e2) (e1)) = (op (op (e1) (e1)) (e1)))). % 18.68/18.85 intro zenon_D_pnotp. % 18.68/18.85 apply zenon_H239. % 18.68/18.85 rewrite <- zenon_D_pnotp. % 18.68/18.85 exact zenon_H217. % 18.68/18.85 cut (((op (op (e1) (e1)) (e1)) = (op (op (e1) (e1)) (e1)))); [idtac | apply NNPP; zenon_intro zenon_H218]. % 18.68/18.85 cut (((op (op (e1) (e1)) (e1)) = (op (e2) (e1)))); [idtac | apply NNPP; zenon_intro zenon_H238]. % 18.68/18.85 congruence. % 18.68/18.85 apply (zenon_L507_); trivial. % 18.68/18.85 apply zenon_H218. apply refl_equal. % 18.68/18.85 apply zenon_H218. apply refl_equal. % 18.68/18.85 apply zenon_H82. apply refl_equal. % 18.68/18.85 apply zenon_H79. apply refl_equal. % 18.68/18.85 apply zenon_H21e. apply refl_equal. % 18.68/18.85 apply zenon_H21e. apply refl_equal. % 18.68/18.85 apply zenon_H85. apply refl_equal. % 18.68/18.85 apply zenon_H21e. apply refl_equal. % 18.68/18.85 apply zenon_H21e. apply refl_equal. % 18.68/18.85 apply (zenon_notand_s _ _ zenon_H242); [ zenon_intro zenon_H240 | zenon_intro zenon_H111 ]. % 18.68/18.85 apply (zenon_L551_); trivial. % 18.68/18.85 apply zenon_H111. apply sym_equal. exact zenon_H110. % 18.68/18.85 (* end of lemma zenon_L552_ *) % 18.68/18.85 assert (zenon_L553_ : (((op (e2) (e2)) = (e0))\/(((op (e2) (e2)) = (e1))\/(((op (e2) (e2)) = (e2))\/((op (e2) (e2)) = (e3))))) -> (~((op (e2) (e2)) = (e0))) -> ((op (e0) (e2)) = (e1)) -> (~((op (e0) (e2)) = (op (e2) (e2)))) -> (~((op (e2) (e2)) = (e2))) -> (~((op (e2) (e2)) = (op (e3) (e2)))) -> ((op (e3) (e2)) = (e3)) -> False). % 18.68/18.85 do 0 intro. intros zenon_H1c4 zenon_H81 zenon_H122 zenon_Ha8 zenon_H173 zenon_H18f zenon_H163. % 18.68/18.85 apply (zenon_or_s _ _ zenon_H1c4); [ zenon_intro zenon_H2c | zenon_intro zenon_H1c5 ]. % 18.68/18.85 exact (zenon_H81 zenon_H2c). % 18.68/18.85 apply (zenon_or_s _ _ zenon_H1c5); [ zenon_intro zenon_Hf1 | zenon_intro zenon_H1c6 ]. % 18.68/18.85 apply (zenon_L246_); trivial. % 18.68/18.85 apply (zenon_or_s _ _ zenon_H1c6); [ zenon_intro zenon_H176 | zenon_intro zenon_Haa ]. % 18.68/18.85 exact (zenon_H173 zenon_H176). % 18.68/18.85 apply (zenon_L180_); trivial. % 18.68/18.85 (* end of lemma zenon_L553_ *) % 18.68/18.85 assert (zenon_L554_ : (~((e1) = (e3))) -> ((op (e0) (e0)) = (e3)) -> ((op (e2) (e0)) = (e1)) -> ((op (e1) (e0)) = (e2)) -> (~((op (e2) (e2)) = (e0))) -> ((op (e2) (e0)) = (e3)) -> ((~((op (e2) (e1)) = (e0)))\/((op (e2) (e0)) = (e1))) -> ((~((op (e2) (e3)) = (e0)))\/((op (e2) (e0)) = (e3))) -> ((~((op (e3) (e1)) = (e0)))\/((op (e3) (e0)) = (e1))) -> (((op (e0) (e0)) = (e0))\/(((op (e0) (e1)) = (e0))\/(((op (e0) (e2)) = (e0))\/((op (e0) (e3)) = (e0))))) -> (~((op (e0) (e2)) = (op (e0) (e3)))) -> (~((e1) = (e2))) -> (~((e0) = (e2))) -> (~((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 (e3) (e2)))) -> (~((op (e2) (e2)) = (e2))) -> (((op (e2) (e2)) = (e0))\/(((op (e2) (e2)) = (e1))\/(((op (e2) (e2)) = (e2))\/((op (e2) (e2)) = (e3))))) -> (~((op (e2) (e0)) = (op (e2) (e2)))) -> (~((e0) = (e1))) -> (~((op (e0) (e1)) = (op (e2) (e1)))) -> (~((e0) = (e3))) -> (~((e2) = (e3))) -> (((op (e3) (e0)) = (e1))\/(((op (e3) (e1)) = (e1))\/(((op (e3) (e2)) = (e1))\/((op (e3) (e3)) = (e1))))) -> (~((op (e1) (e3)) = (op (e3) (e3)))) -> (~((op (e1) (e3)) = (op (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 (e1) (e1)) = (e1))) -> (((op (e2) (e0)) = (e2))\/(((op (e2) (e1)) = (e2))\/(((op (e2) (e2)) = (e2))\/((op (e2) (e3)) = (e2))))) -> (((op (e0) (e1)) = (e3))\/(((op (e1) (e1)) = (e3))\/(((op (e2) (e1)) = (e3))\/((op (e3) (e1)) = (e3))))) -> (~((op (e3) (e1)) = (op (e3) (e2)))) -> (((op (e0) (e2)) = (e3))\/(((op (e1) (e2)) = (e3))\/(((op (e2) (e2)) = (e3))\/((op (e3) (e2)) = (e3))))) -> (((op (e0) (e1)) = (e0))\/(((op (e0) (e1)) = (e1))\/(((op (e0) (e1)) = (e2))\/((op (e0) (e1)) = (e3))))) -> (~((op (e0) (e1)) = (op (e1) (e1)))) -> (~((op (e1) (e1)) = (op (e2) (e1)))) -> (((op (e2) (e1)) = (e0))\/(((op (e2) (e1)) = (e1))\/(((op (e2) (e1)) = (e2))\/((op (e2) (e1)) = (e3))))) -> (~((op (e0) (e3)) = (op (e3) (e3)))) -> (((op (e0) (e2)) = (e0))\/(((op (e1) (e2)) = (e0))\/(((op (e2) (e2)) = (e0))\/((op (e3) (e2)) = (e0))))) -> (~((op (e3) (e0)) = (op (e3) (e2)))) -> (~((op (e1) (e1)) = (op (e1) (e2)))) -> (~((op (e1) (e2)) = (op (e2) (e2)))) -> (((op (e3) (e0)) = (e2))\/(((op (e3) (e1)) = (e2))\/(((op (e3) (e2)) = (e2))\/((op (e3) (e3)) = (e2))))) -> (((op (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) (e3)) = (e3))) -> (~((op (e3) (e2)) = (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 (e1) (e1)) = (op (e3) (e1)))) -> (((op (e1) (e0)) = (e2))\/(((op (e1) (e1)) = (e2))\/(((op (e1) (e2)) = (e2))\/((op (e1) (e3)) = (e2))))) -> (~((op (e0) (e0)) = (op (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) (e3)) = (e2))\/(((op (e1) (e3)) = (e2))\/(((op (e2) (e3)) = (e2))\/((op (e3) (e3)) = (e2))))) -> (((op (e2) (e0)) = (e1))\/(((op (e2) (e1)) = (e1))\/(((op (e2) (e2)) = (e1))\/((op (e2) (e3)) = (e1))))) -> (((op (e0) (e1)) = (e1))\/(((op (e1) (e1)) = (e1))\/(((op (e2) (e1)) = (e1))\/((op (e3) (e1)) = (e1))))) -> (~((op (e0) (e3)) = (op (e2) (e3)))) -> (((op (e1) (e3)) = (e0))\/(((op (e1) (e3)) = (e1))\/(((op (e1) (e3)) = (e2))\/((op (e1) (e3)) = (e3))))) -> (~((op (e2) (e1)) = (op (e3) (e1)))) -> (((op (e3) (e1)) = (e0))\/(((op (e3) (e1)) = (e1))\/(((op (e3) (e1)) = (e2))\/((op (e3) (e1)) = (e3))))) -> (((op (e2) (e3)) = (e0))\/(((op (e2) (e3)) = (e1))\/(((op (e2) (e3)) = (e2))\/((op (e2) (e3)) = (e3))))) -> (~((op (e2) (e3)) = (op (e3) (e3)))) -> (~((op (e1) (e2)) = (op (e3) (e2)))) -> (~((op (e0) (e1)) = (op (e0) (e2)))) -> (~((op (e0) (e1)) = (op (e3) (e1)))) -> (~((op (e0) (e1)) = (op (e0) (e3)))) -> (~((op (e1) (e0)) = (op (e1) (e3)))) -> (~((op (e2) (e2)) = (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 (e0) (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 (e3) (e2)) = (e0)))\/((op (e3) (e0)) = (e2))) -> ((~((op (e3) (e0)) = (e0)))\/((op (e3) (e0)) = (e0))) -> (((op (e2) (e0)) = (e0))\/(((op (e2) (e1)) = (e0))\/(((op (e2) (e2)) = (e0))\/((op (e2) (e3)) = (e0))))) -> ((~((op (e2) (e2)) = (e0)))\/((op (e2) (e0)) = (e2))) -> (((op (e3) (e0)) = (e3))\/(((op (e3) (e1)) = (e3))\/(((op (e3) (e2)) = (e3))\/((op (e3) (e3)) = (e3))))) -> (~((op (e0) (e2)) = (op (e2) (e2)))) -> ((~((op (e3) (e3)) = (e0)))\/((op (e3) (e0)) = (e3))) -> ((~((op (e0) (e3)) = (e0)))\/((op (e0) (e0)) = (e3))) -> ((~((op (e1) (e1)) = (e0)))\/((op (e1) (e0)) = (e1))) -> (((op (e3) (e2)) = (e0))\/(((op (e3) (e2)) = (e1))\/(((op (e3) (e2)) = (e2))\/((op (e3) (e2)) = (e3))))) -> (((op (e1) (e2)) = (e0))\/(((op (e1) (e2)) = (e1))\/(((op (e1) (e2)) = (e2))\/((op (e1) (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 (e2) (e0)) = (op (e3) (e0)))) -> ((~((op (e1) (e2)) = (e0)))\/((op (e1) (e0)) = (e2))) -> ((~((op (e1) (e3)) = (e0)))\/((op (e1) (e0)) = (e3))) -> (((op (e1) (e1)) = (e0))\/(((op (e1) (e1)) = (e1))\/(((op (e1) (e1)) = (e2))\/((op (e1) (e1)) = (e3))))) -> (~((op (e0) (e0)) = (op (e0) (e2)))) -> (((op (e1) (e0)) = (e1))\/(((op (e1) (e1)) = (e1))\/(((op (e1) (e2)) = (e1))\/((op (e1) (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 (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 (e2) (e0)) = (e0)))\/((op (e2) (e0)) = (e0))) -> (((op (e0) (e0)) = (e3))\/(((op (e1) (e0)) = (e3))\/(((op (e2) (e0)) = (e3))\/((op (e3) (e0)) = (e3))))) -> (((op (e0) (e2)) = (e0))\/(((op (e0) (e2)) = (e1))\/(((op (e0) (e2)) = (e2))\/((op (e0) (e2)) = (e3))))) -> (~((op (e1) (e0)) = (op (e3) (e0)))) -> (~((op (e2) (e0)) = (op (e2) (e1)))) -> ((~((op (e1) (e0)) = (e0)))\/((op (e1) (e0)) = (e0))) -> ((~((op (e0) (e2)) = (e0)))\/((op (e0) (e0)) = (e2))) -> (~((op (e3) (e0)) = (op (e3) (e1)))) -> (~((op (e1) (e1)) = (op (e1) (e3)))) -> (~((op (e2) (e0)) = (op (e2) (e3)))) -> (((op (e0) (e3)) = (e0))\/(((op (e1) (e3)) = (e0))\/(((op (e2) (e3)) = (e0))\/((op (e3) (e3)) = (e0))))) -> (~((op (e1) (e0)) = (op (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) (e1)) = (e0))\/(((op (e1) (e1)) = (e0))\/(((op (e2) (e1)) = (e0))\/((op (e3) (e1)) = (e0))))) -> (~((op (e1) (e1)) = (e0))) -> (~((op (e0) (e2)) = (op (e1) (e2)))) -> (~((op (e1) (e3)) = (e0))) -> (((op (e1) (e0)) = (e0))\/(((op (e1) (e1)) = (e0))\/(((op (e1) (e2)) = (e0))\/((op (e1) (e3)) = (e0))))) -> (~((op (e0) (e1)) = (e0))) -> (~((op (e0) (e0)) = (e0))) -> (~((op (e1) (e0)) = (e0))) -> (~((op (e2) (e0)) = (e0))) -> (((op (e0) (e0)) = (e0))\/(((op (e1) (e0)) = (e0))\/(((op (e2) (e0)) = (e0))\/((op (e3) (e0)) = (e0))))) -> False). % 18.68/18.85 do 0 intro. intros zenon_H95 zenon_H3a zenon_Hed zenon_H86 zenon_H81 zenon_H3b zenon_H182 zenon_H94 zenon_H1ed zenon_H74 zenon_H208 zenon_H7c zenon_H149 zenon_H201 zenon_H139 zenon_H18f zenon_H173 zenon_H1c4 zenon_H52 zenon_Ha1 zenon_H17e zenon_H9a zenon_H12b zenon_He8 zenon_Hd5 zenon_Hdb zenon_He4 zenon_H1d zenon_H10a zenon_H1d5 zenon_H1a5 zenon_H1a4 zenon_H1a6 zenon_H212 zenon_H10e zenon_H13e zenon_H1cc zenon_Hc2 zenon_H6a zenon_H6f zenon_H4f zenon_H2b zenon_H153 zenon_H16f zenon_H101 zenon_H102 zenon_H62 zenon_H130 zenon_H172 zenon_H160 zenon_H18c zenon_H189 zenon_H1d8 zenon_H1c7 zenon_H145 zenon_H106 zenon_H109 zenon_He2 zenon_Hdf zenon_Haf zenon_H22a zenon_H11f zenon_Hf3 zenon_H115 zenon_H4a zenon_H210 zenon_H54 zenon_Hd8 zenon_H6d zenon_H71 zenon_H133 zenon_H7b zenon_H39 zenon_H22d zenon_H1a7 zenon_H184 zenon_H2f zenon_H185 zenon_H165 zenon_Ha8 zenon_H1ec zenon_H204 zenon_H205 zenon_H191 zenon_H19d zenon_He7 zenon_H183 zenon_H17b zenon_H178 zenon_H179 zenon_H142 zenon_H13c zenon_H128 zenon_H136 zenon_H124 zenon_H168 zenon_H1fe zenon_H1ee zenon_H1e0 zenon_H1ba zenon_H1fa zenon_H1f0 zenon_H206 zenon_H233 zenon_H1cf zenon_H57 zenon_H5b zenon_H67 zenon_H45 zenon_H14f zenon_H1ac zenon_H245 zenon_H24 zenon_H195 zenon_H38 zenon_H22 zenon_H20b zenon_H3f zenon_H23 zenon_H30 zenon_H3e. % 18.68/18.85 apply (zenon_or_s _ _ zenon_H184); [ zenon_intro zenon_H40 | zenon_intro zenon_H44 ]. % 18.68/18.85 apply (zenon_L7_); trivial. % 18.68/18.85 apply (zenon_or_s _ _ zenon_H1ed); [ zenon_intro zenon_H1ad | zenon_intro zenon_Hac ]. % 18.68/18.85 apply (zenon_or_s _ _ zenon_H74); [ zenon_intro zenon_H42 | zenon_intro zenon_H77 ]. % 18.68/18.85 exact (zenon_H3f zenon_H42). % 18.68/18.85 apply (zenon_or_s _ _ zenon_H77); [ zenon_intro zenon_H49 | zenon_intro zenon_H78 ]. % 18.68/18.85 exact (zenon_H20b zenon_H49). % 18.68/18.85 apply (zenon_or_s _ _ zenon_H78); [ zenon_intro zenon_H48 | zenon_intro zenon_H1e ]. % 18.68/18.85 apply (zenon_L335_); trivial. % 18.68/18.85 apply (zenon_or_s _ _ zenon_H22d); [ zenon_intro zenon_H7a | zenon_intro zenon_H22e ]. % 18.68/18.85 apply (zenon_L35_); trivial. % 18.68/18.85 apply (zenon_or_s _ _ zenon_H22e); [ zenon_intro zenon_Ha0 | zenon_intro zenon_H22f ]. % 18.68/18.85 apply (zenon_or_s _ _ zenon_H22); [ zenon_intro zenon_H27 | zenon_intro zenon_H26 ]. % 18.68/18.85 exact (zenon_H23 zenon_H27). % 18.68/18.85 apply (zenon_or_s _ _ zenon_H26); [ zenon_intro zenon_H29 | zenon_intro zenon_H28 ]. % 18.68/18.85 exact (zenon_H24 zenon_H29). % 18.68/18.85 apply (zenon_or_s _ _ zenon_H28); [ zenon_intro zenon_H2a | zenon_intro zenon_H1f ]. % 18.68/18.85 apply (zenon_or_s _ _ zenon_H245); [ zenon_intro zenon_H49 | zenon_intro zenon_H246 ]. % 18.68/18.85 exact (zenon_H20b zenon_H49). % 18.68/18.85 apply (zenon_or_s _ _ zenon_H246); [ zenon_intro zenon_H29 | zenon_intro zenon_H247 ]. % 18.68/18.85 exact (zenon_H24 zenon_H29). % 18.68/18.85 apply (zenon_or_s _ _ zenon_H247); [ zenon_intro zenon_H36 | zenon_intro zenon_H1b1 ]. % 18.68/18.85 apply (zenon_L526_); trivial. % 18.68/18.85 exact (zenon_H1ad zenon_H1b1). % 18.68/18.85 exact (zenon_H38 zenon_H1f). % 18.68/18.85 apply (zenon_or_s _ _ zenon_H22f); [ zenon_intro zenon_H122 | zenon_intro zenon_Hc3 ]. % 18.68/18.85 apply (zenon_or_s _ _ zenon_H22); [ zenon_intro zenon_H27 | zenon_intro zenon_H26 ]. % 18.68/18.85 exact (zenon_H23 zenon_H27). % 18.68/18.85 apply (zenon_or_s _ _ zenon_H26); [ zenon_intro zenon_H29 | zenon_intro zenon_H28 ]. % 18.68/18.85 exact (zenon_H24 zenon_H29). % 18.68/18.85 apply (zenon_or_s _ _ zenon_H28); [ zenon_intro zenon_H2a | zenon_intro zenon_H1f ]. % 18.68/18.85 apply (zenon_or_s _ _ zenon_H128); [ zenon_intro zenon_H9d | zenon_intro zenon_H129 ]. % 18.68/18.85 apply (zenon_L413_); trivial. % 18.68/18.85 apply (zenon_or_s _ _ zenon_H129); [ zenon_intro zenon_H10d | zenon_intro zenon_H12a ]. % 18.68/18.85 exact (zenon_H10a zenon_H10d). % 18.68/18.85 apply (zenon_or_s _ _ zenon_H12a); [ zenon_intro zenon_Hf0 | zenon_intro zenon_Hd6 ]. % 18.68/18.85 apply (zenon_L530_); trivial. % 18.68/18.85 apply (zenon_or_s _ _ zenon_H1a6); [ zenon_intro zenon_Ha9 | zenon_intro zenon_H1aa ]. % 18.68/18.85 apply (zenon_L187_); trivial. % 18.68/18.85 apply (zenon_or_s _ _ zenon_H1aa); [ zenon_intro zenon_H16c | zenon_intro zenon_H1ab ]. % 18.68/18.85 apply (zenon_L521_); trivial. % 18.68/18.85 apply (zenon_or_s _ _ zenon_H1ab); [ zenon_intro zenon_Haa | zenon_intro zenon_H163 ]. % 18.68/18.85 apply (zenon_L168_); trivial. % 18.68/18.85 apply (zenon_L553_); trivial. % 18.68/18.85 exact (zenon_H38 zenon_H1f). % 18.68/18.85 apply (zenon_L427_); trivial. % 18.68/18.85 apply (zenon_L41_); trivial. % 18.68/18.85 (* end of lemma zenon_L554_ *) % 18.68/18.85 assert (zenon_L555_ : (((op (e0) (e1)) = (e0))\/(((op (e0) (e1)) = (e1))\/(((op (e0) (e1)) = (e2))\/((op (e0) (e1)) = (e3))))) -> (~((op (e0) (e1)) = (e0))) -> ((op (e3) (e1)) = (e1)) -> (~((op (e0) (e1)) = (op (e3) (e1)))) -> ((op (e2) (e1)) = (e3)) -> (~((op (e1) (e1)) = (op (e2) (e1)))) -> (~((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) (e1)) = (e0)) -> ((op (e1) (e1)) = (e2)) -> False). % 18.68/18.85 do 0 intro. intros zenon_H212 zenon_H20b zenon_Hae zenon_H210 zenon_Ha6 zenon_H13e zenon_H10e zenon_H10a zenon_H24 zenon_H142 zenon_H36 zenon_H110. % 18.68/18.85 apply (zenon_or_s _ _ zenon_H212); [ zenon_intro zenon_H49 | zenon_intro zenon_H213 ]. % 18.68/18.85 exact (zenon_H20b zenon_H49). % 18.68/18.85 apply (zenon_or_s _ _ zenon_H213); [ zenon_intro zenon_Ha0 | zenon_intro zenon_H214 ]. % 18.68/18.85 apply (zenon_L363_); trivial. % 18.68/18.85 apply (zenon_or_s _ _ zenon_H214); [ zenon_intro zenon_H10f | zenon_intro zenon_H99 ]. % 18.68/18.85 apply (zenon_L96_); trivial. % 18.68/18.85 apply (zenon_L552_); trivial. % 18.68/18.85 (* end of lemma zenon_L555_ *) % 18.68/18.85 assert (zenon_L556_ : (((op (e0) (e2)) = (e3))\/(((op (e1) (e2)) = (e3))\/(((op (e2) (e2)) = (e3))\/((op (e3) (e2)) = (e3))))) -> (~((e0) = (e3))) -> (~((op (e0) (e2)) = (op (e3) (e2)))) -> ((op (e0) (e2)) = (e2)) -> ((op (e1) (e2)) = (e0)) -> (~((op (e1) (e2)) = (op (e3) (e2)))) -> (((op (e3) (e2)) = (e0))\/(((op (e3) (e2)) = (e1))\/(((op (e3) (e2)) = (e2))\/((op (e3) (e2)) = (e3))))) -> (((op (e2) (e2)) = (e0))\/(((op (e2) (e2)) = (e1))\/(((op (e2) (e2)) = (e2))\/((op (e2) (e2)) = (e3))))) -> (~((op (e2) (e2)) = (e0))) -> ((op (e3) (e2)) = (e1)) -> (~((op (e2) (e2)) = (e2))) -> (~((op (e2) (e2)) = (op (e3) (e2)))) -> False). % 18.68/18.85 do 0 intro. intros zenon_H1a6 zenon_H9a zenon_H14f zenon_H150 zenon_H2a zenon_H115 zenon_H191 zenon_H1c4 zenon_H81 zenon_Hba zenon_H173 zenon_H18f. % 18.68/18.85 apply (zenon_or_s _ _ zenon_H1a6); [ zenon_intro zenon_Ha9 | zenon_intro zenon_H1aa ]. % 18.68/18.85 apply (zenon_L186_); trivial. % 18.68/18.85 apply (zenon_or_s _ _ zenon_H1aa); [ zenon_intro zenon_H16c | zenon_intro zenon_H1ab ]. % 18.68/18.85 apply (zenon_L521_); trivial. % 18.68/18.85 apply (zenon_or_s _ _ zenon_H1ab); [ zenon_intro zenon_Haa | zenon_intro zenon_H163 ]. % 18.68/18.85 apply (zenon_L181_); trivial. % 18.68/18.85 apply (zenon_L528_); trivial. % 18.68/18.85 (* end of lemma zenon_L556_ *) % 18.68/18.85 assert (zenon_L557_ : (((op (e0) (e2)) = (e2))\/(((op (e1) (e2)) = (e2))\/(((op (e2) (e2)) = (e2))\/((op (e3) (e2)) = (e2))))) -> (~((op (e2) (e2)) = (op (e3) (e2)))) -> ((op (e3) (e2)) = (e1)) -> (~((op (e2) (e2)) = (e0))) -> (((op (e2) (e2)) = (e0))\/(((op (e2) (e2)) = (e1))\/(((op (e2) (e2)) = (e2))\/((op (e2) (e2)) = (e3))))) -> (((op (e3) (e2)) = (e0))\/(((op (e3) (e2)) = (e1))\/(((op (e3) (e2)) = (e2))\/((op (e3) (e2)) = (e3))))) -> (~((op (e1) (e2)) = (op (e3) (e2)))) -> (~((op (e0) (e2)) = (op (e3) (e2)))) -> (~((e0) = (e3))) -> (((op (e0) (e2)) = (e3))\/(((op (e1) (e2)) = (e3))\/(((op (e2) (e2)) = (e3))\/((op (e3) (e2)) = (e3))))) -> (~((e0) = (e2))) -> ((op (e1) (e2)) = (e0)) -> (~((op (e2) (e2)) = (e2))) -> (((op (e0) (e3)) = (e2))\/(((op (e1) (e3)) = (e2))\/(((op (e2) (e3)) = (e2))\/((op (e3) (e3)) = (e2))))) -> (~((op (e0) (e0)) = (op (e0) (e3)))) -> ((op (e0) (e0)) = (e2)) -> (~((op (e1) (e0)) = (op (e1) (e3)))) -> ((op (e1) (e0)) = (e2)) -> (~((op (e2) (e1)) = (op (e2) (e3)))) -> ((op (e2) (e1)) = (e2)) -> (~((op (e3) (e2)) = (op (e3) (e3)))) -> False). % 18.68/18.85 do 0 intro. intros zenon_H172 zenon_H18f zenon_Hba zenon_H81 zenon_H1c4 zenon_H191 zenon_H115 zenon_H14f zenon_H9a zenon_H1a6 zenon_H149 zenon_H2a zenon_H173 zenon_H145 zenon_H189 zenon_H7b zenon_Hd8 zenon_H86 zenon_H1c7 zenon_H1ca zenon_H62. % 18.68/18.85 apply (zenon_or_s _ _ zenon_H172); [ zenon_intro zenon_H150 | zenon_intro zenon_H174 ]. % 18.68/18.85 apply (zenon_L556_); trivial. % 18.68/18.85 apply (zenon_or_s _ _ zenon_H174); [ zenon_intro zenon_H113 | zenon_intro zenon_H175 ]. % 18.68/18.85 apply (zenon_L542_); trivial. % 18.68/18.85 apply (zenon_or_s _ _ zenon_H175); [ zenon_intro zenon_H176 | zenon_intro zenon_H151 ]. % 18.68/18.85 exact (zenon_H173 zenon_H176). % 18.68/18.85 apply (zenon_L540_); trivial. % 18.68/18.85 (* end of lemma zenon_L557_ *) % 18.68/18.85 assert (zenon_L558_ : (((op (e0) (e3)) = (e3))\/(((op (e1) (e3)) = (e3))\/(((op (e2) (e3)) = (e3))\/((op (e3) (e3)) = (e3))))) -> (~((e0) = (e3))) -> ((op (e0) (e3)) = (e0)) -> (~((e1) = (e3))) -> ((op (e1) (e3)) = (e1)) -> ((op (e3) (e2)) = (e2)) -> (~((op (e3) (e2)) = (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 (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 (e2) (e3)) = (e2)) -> (~((op (e0) (e3)) = (op (e2) (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)) = (e3))) -> False). % 18.68/18.85 do 0 intro. intros zenon_H136 zenon_H9a zenon_H1e zenon_H95 zenon_Hd6 zenon_H151 zenon_H62 zenon_He4 zenon_Hdb zenon_Hd5 zenon_H1d zenon_Hdf zenon_Hc2 zenon_H11d zenon_He2 zenon_H44 zenon_H71 zenon_H101 zenon_H102. % 18.68/18.85 apply (zenon_or_s _ _ zenon_H136); [ zenon_intro zenon_He3 | zenon_intro zenon_H137 ]. % 18.68/18.85 apply (zenon_L515_); trivial. % 18.68/18.85 apply (zenon_or_s _ _ zenon_H137); [ zenon_intro zenon_Hdc | zenon_intro zenon_H138 ]. % 18.68/18.85 apply (zenon_L83_); trivial. % 18.68/18.85 apply (zenon_or_s _ _ zenon_H138); [ zenon_intro zenon_Hdd | zenon_intro zenon_H105 ]. % 18.68/18.85 apply (zenon_L537_); trivial. % 18.68/18.85 exact (zenon_H102 zenon_H105). % 18.68/18.85 (* end of lemma zenon_L558_ *) % 18.68/18.85 assert (zenon_L559_ : (((op (e0) (e2)) = (e2))\/(((op (e1) (e2)) = (e2))\/(((op (e2) (e2)) = (e2))\/((op (e3) (e2)) = (e2))))) -> (~((op (e2) (e2)) = (op (e3) (e2)))) -> ((op (e3) (e2)) = (e1)) -> (~((op (e2) (e2)) = (e0))) -> (((op (e2) (e2)) = (e0))\/(((op (e2) (e2)) = (e1))\/(((op (e2) (e2)) = (e2))\/((op (e2) (e2)) = (e3))))) -> (((op (e3) (e2)) = (e0))\/(((op (e3) (e2)) = (e1))\/(((op (e3) (e2)) = (e2))\/((op (e3) (e2)) = (e3))))) -> (~((op (e1) (e2)) = (op (e3) (e2)))) -> (~((op (e0) (e2)) = (op (e3) (e2)))) -> (((op (e0) (e2)) = (e3))\/(((op (e1) (e2)) = (e3))\/(((op (e2) (e2)) = (e3))\/((op (e3) (e2)) = (e3))))) -> (~((e0) = (e2))) -> ((op (e1) (e2)) = (e0)) -> (~((op (e2) (e2)) = (e2))) -> (((op (e0) (e3)) = (e3))\/(((op (e1) (e3)) = (e3))\/(((op (e2) (e3)) = (e3))\/((op (e3) (e3)) = (e3))))) -> (~((e0) = (e3))) -> ((op (e0) (e3)) = (e0)) -> (~((e1) = (e3))) -> ((op (e1) (e3)) = (e1)) -> (~((op (e3) (e2)) = (op (e3) (e3)))) -> (((op (e0) (e3)) = (e0))\/(((op (e0) (e3)) = (e1))\/(((op (e0) (e3)) = (e2))\/((op (e0) (e3)) = (e3))))) -> (~((op (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 (e2) (e3)) = (e2)) -> (~((op (e0) (e3)) = (op (e2) (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)) = (e3))) -> False). % 18.68/18.85 do 0 intro. intros zenon_H172 zenon_H18f zenon_Hba zenon_H81 zenon_H1c4 zenon_H191 zenon_H115 zenon_H14f zenon_H1a6 zenon_H149 zenon_H2a zenon_H173 zenon_H136 zenon_H9a zenon_H1e zenon_H95 zenon_Hd6 zenon_H62 zenon_He4 zenon_Hdb zenon_Hd5 zenon_H1d zenon_Hdf zenon_Hc2 zenon_H11d zenon_He2 zenon_H44 zenon_H71 zenon_H101 zenon_H102. % 18.68/18.85 apply (zenon_or_s _ _ zenon_H172); [ zenon_intro zenon_H150 | zenon_intro zenon_H174 ]. % 18.68/18.85 apply (zenon_L556_); trivial. % 18.68/18.85 apply (zenon_or_s _ _ zenon_H174); [ zenon_intro zenon_H113 | zenon_intro zenon_H175 ]. % 18.68/18.85 apply (zenon_L542_); trivial. % 18.68/18.85 apply (zenon_or_s _ _ zenon_H175); [ zenon_intro zenon_H176 | zenon_intro zenon_H151 ]. % 18.68/18.85 exact (zenon_H173 zenon_H176). % 18.68/18.85 apply (zenon_L558_); trivial. % 18.68/18.85 (* end of lemma zenon_L559_ *) % 18.68/18.85 assert (zenon_L560_ : (((op (e0) (e2)) = (e2))\/(((op (e1) (e2)) = (e2))\/(((op (e2) (e2)) = (e2))\/((op (e3) (e2)) = (e2))))) -> (~((e1) = (e2))) -> ((op (e0) (e2)) = (e1)) -> (~((e0) = (e2))) -> ((op (e1) (e2)) = (e0)) -> (~((op (e2) (e2)) = (e2))) -> (((op (e0) (e3)) = (e3))\/(((op (e1) (e3)) = (e3))\/(((op (e2) (e3)) = (e3))\/((op (e3) (e3)) = (e3))))) -> (~((e0) = (e3))) -> ((op (e0) (e3)) = (e0)) -> (~((e1) = (e3))) -> ((op (e1) (e3)) = (e1)) -> (~((op (e3) (e2)) = (op (e3) (e3)))) -> (((op (e0) (e3)) = (e0))\/(((op (e0) (e3)) = (e1))\/(((op (e0) (e3)) = (e2))\/((op (e0) (e3)) = (e3))))) -> (~((op (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 (e2) (e3)) = (e2)) -> (~((op (e0) (e3)) = (op (e2) (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)) = (e3))) -> False). % 18.68/18.85 do 0 intro. intros zenon_H172 zenon_H7c zenon_H122 zenon_H149 zenon_H2a zenon_H173 zenon_H136 zenon_H9a zenon_H1e zenon_H95 zenon_Hd6 zenon_H62 zenon_He4 zenon_Hdb zenon_Hd5 zenon_H1d zenon_Hdf zenon_Hc2 zenon_H11d zenon_He2 zenon_H44 zenon_H71 zenon_H101 zenon_H102. % 18.68/18.85 apply (zenon_or_s _ _ zenon_H172); [ zenon_intro zenon_H150 | zenon_intro zenon_H174 ]. % 18.68/18.85 apply (zenon_L328_); trivial. % 18.68/18.85 apply (zenon_or_s _ _ zenon_H174); [ zenon_intro zenon_H113 | zenon_intro zenon_H175 ]. % 18.68/18.85 apply (zenon_L542_); trivial. % 18.68/18.85 apply (zenon_or_s _ _ zenon_H175); [ zenon_intro zenon_H176 | zenon_intro zenon_H151 ]. % 18.68/18.85 exact (zenon_H173 zenon_H176). % 18.68/18.85 apply (zenon_L558_); trivial. % 18.68/18.85 (* end of lemma zenon_L560_ *) % 18.68/18.85 assert (zenon_L561_ : (((op (e2) (e0)) = (e2))\/(((op (e2) (e1)) = (e2))\/(((op (e2) (e2)) = (e2))\/((op (e2) (e3)) = (e2))))) -> ((op (e2) (e0)) = (e1)) -> ((op (e0) (e1)) = (e2)) -> (~((op (e0) (e1)) = (op (e2) (e1)))) -> (((op (e0) (e2)) = (e2))\/(((op (e1) (e2)) = (e2))\/(((op (e2) (e2)) = (e2))\/((op (e3) (e2)) = (e2))))) -> (~((e1) = (e2))) -> ((op (e0) (e2)) = (e1)) -> (~((e0) = (e2))) -> ((op (e1) (e2)) = (e0)) -> (~((op (e2) (e2)) = (e2))) -> (((op (e0) (e3)) = (e3))\/(((op (e1) (e3)) = (e3))\/(((op (e2) (e3)) = (e3))\/((op (e3) (e3)) = (e3))))) -> (~((e0) = (e3))) -> ((op (e0) (e3)) = (e0)) -> (~((e1) = (e3))) -> ((op (e1) (e3)) = (e1)) -> (~((op (e3) (e2)) = (op (e3) (e3)))) -> (((op (e0) (e3)) = (e0))\/(((op (e0) (e3)) = (e1))\/(((op (e0) (e3)) = (e2))\/((op (e0) (e3)) = (e3))))) -> (~((op (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) (e3)) = (op (e2) (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)) = (e3))) -> False). % 18.68/18.85 do 0 intro. intros zenon_H1d5 zenon_Hed zenon_H10f zenon_H17e zenon_H172 zenon_H7c zenon_H122 zenon_H149 zenon_H2a zenon_H173 zenon_H136 zenon_H9a zenon_H1e zenon_H95 zenon_Hd6 zenon_H62 zenon_He4 zenon_Hdb zenon_Hd5 zenon_H1d zenon_Hdf zenon_Hc2 zenon_He2 zenon_H44 zenon_H71 zenon_H101 zenon_H102. % 18.68/18.85 apply (zenon_or_s _ _ zenon_H1d5); [ zenon_intro zenon_Hee | zenon_intro zenon_H1d6 ]. % 18.68/18.85 apply (zenon_L58_); trivial. % 18.68/18.85 apply (zenon_or_s _ _ zenon_H1d6); [ zenon_intro zenon_H1ca | zenon_intro zenon_H1d7 ]. % 18.68/18.85 apply (zenon_L191_); trivial. % 18.68/18.85 apply (zenon_or_s _ _ zenon_H1d7); [ zenon_intro zenon_H176 | zenon_intro zenon_H11d ]. % 18.68/18.85 exact (zenon_H173 zenon_H176). % 18.68/18.85 apply (zenon_L560_); trivial. % 18.68/18.85 (* end of lemma zenon_L561_ *) % 18.68/18.85 assert (zenon_L562_ : ((op (e0) (e0)) = (e3)) -> (((op (e3) (e0)) = (e0))\/(((op (e3) (e1)) = (e0))\/(((op (e3) (e2)) = (e0))\/((op (e3) (e3)) = (e0))))) -> (~((op (e0) (e2)) = (op (e3) (e2)))) -> (~((op (e1) (e0)) = (op (e1) (e1)))) -> (((op (e0) (e3)) = (e0))\/(((op (e1) (e3)) = (e0))\/(((op (e2) (e3)) = (e0))\/((op (e3) (e3)) = (e0))))) -> (~((op (e2) (e0)) = (op (e2) (e3)))) -> (~((op (e1) (e1)) = (op (e1) (e3)))) -> (~((op (e3) (e0)) = (op (e3) (e1)))) -> ((~((op (e0) (e2)) = (e0)))\/((op (e0) (e0)) = (e2))) -> ((~((op (e1) (e0)) = (e0)))\/((op (e1) (e0)) = (e0))) -> (~((op (e2) (e0)) = (op (e2) (e1)))) -> (~((op (e1) (e0)) = (op (e3) (e0)))) -> (((op (e0) (e2)) = (e0))\/(((op (e0) (e2)) = (e1))\/(((op (e0) (e2)) = (e2))\/((op (e0) (e2)) = (e3))))) -> (((op (e0) (e0)) = (e3))\/(((op (e1) (e0)) = (e3))\/(((op (e2) (e0)) = (e3))\/((op (e3) (e0)) = (e3))))) -> ((~((op (e2) (e0)) = (e0)))\/((op (e2) (e0)) = (e0))) -> (((op (e0) (e0)) = (e2))\/(((op (e1) (e0)) = (e2))\/(((op (e2) (e0)) = (e2))\/((op (e3) (e0)) = (e2))))) -> (((op (e0) (e0)) = (e3))\/(((op (e0) (e1)) = (e3))\/(((op (e0) (e2)) = (e3))\/((op (e0) (e3)) = (e3))))) -> (~((op (e1) (e2)) = (op (e1) (e3)))) -> (((op (e0) (e3)) = (e3))\/(((op (e1) (e3)) = (e3))\/(((op (e2) (e3)) = (e3))\/((op (e3) (e3)) = (e3))))) -> (((op (e1) (e0)) = (e1))\/(((op (e1) (e1)) = (e1))\/(((op (e1) (e2)) = (e1))\/((op (e1) (e3)) = (e1))))) -> (~((op (e0) (e0)) = (op (e0) (e2)))) -> (((op (e1) (e1)) = (e0))\/(((op (e1) (e1)) = (e1))\/(((op (e1) (e1)) = (e2))\/((op (e1) (e1)) = (e3))))) -> ((~((op (e1) (e3)) = (e0)))\/((op (e1) (e0)) = (e3))) -> ((~((op (e1) (e2)) = (e0)))\/((op (e1) (e0)) = (e2))) -> (~((op (e2) (e0)) = (op (e3) (e0)))) -> (((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) (e2)) = (e0))\/(((op (e1) (e2)) = (e1))\/(((op (e1) (e2)) = (e2))\/((op (e1) (e2)) = (e3))))) -> (~((op (e0) (e2)) = (op (e1) (e2)))) -> (((op (e3) (e2)) = (e0))\/(((op (e3) (e2)) = (e1))\/(((op (e3) (e2)) = (e2))\/((op (e3) (e2)) = (e3))))) -> ((~((op (e1) (e1)) = (e0)))\/((op (e1) (e0)) = (e1))) -> ((~((op (e0) (e3)) = (e0)))\/((op (e0) (e0)) = (e3))) -> ((~((op (e3) (e3)) = (e0)))\/((op (e3) (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 (e2) (e2)) = (e0)))\/((op (e2) (e0)) = (e2))) -> (((op (e2) (e0)) = (e0))\/(((op (e2) (e1)) = (e0))\/(((op (e2) (e2)) = (e0))\/((op (e2) (e3)) = (e0))))) -> ((~((op (e3) (e0)) = (e0)))\/((op (e3) (e0)) = (e0))) -> ((~((op (e3) (e2)) = (e0)))\/((op (e3) (e0)) = (e2))) -> (~((op (e0) (e1)) = (e0))) -> (((op (e0) (e0)) = (e1))\/(((op (e0) (e1)) = (e1))\/(((op (e0) (e2)) = (e1))\/((op (e0) (e3)) = (e1))))) -> (~((op (e0) (e0)) = (op (e2) (e0)))) -> ((op (e0) (e0)) = (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) (e2)) = (op (e2) (e3)))) -> (~((op (e1) (e0)) = (op (e1) (e3)))) -> (~((op (e0) (e1)) = (op (e0) (e3)))) -> (~((op (e0) (e1)) = (op (e3) (e1)))) -> (~((op (e0) (e1)) = (op (e0) (e2)))) -> (~((op (e1) (e2)) = (op (e3) (e2)))) -> (~((op (e2) (e3)) = (op (e3) (e3)))) -> (((op (e2) (e3)) = (e0))\/(((op (e2) (e3)) = (e1))\/(((op (e2) (e3)) = (e2))\/((op (e2) (e3)) = (e3))))) -> (((op (e3) (e1)) = (e0))\/(((op (e3) (e1)) = (e1))\/(((op (e3) (e1)) = (e2))\/((op (e3) (e1)) = (e3))))) -> (~((op (e2) (e1)) = (op (e3) (e1)))) -> (((op (e1) (e3)) = (e0))\/(((op (e1) (e3)) = (e1))\/(((op (e1) (e3)) = (e2))\/((op (e1) (e3)) = (e3))))) -> (~((op (e0) (e3)) = (op (e2) (e3)))) -> (((op (e0) (e1)) = (e1))\/(((op (e1) (e1)) = (e1))\/(((op (e2) (e1)) = (e1))\/((op (e3) (e1)) = (e1))))) -> (((op (e2) (e0)) = (e1))\/(((op (e2) (e1)) = (e1))\/(((op (e2) (e2)) = (e1))\/((op (e2) (e3)) = (e1))))) -> (((op (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)) = (op (e0) (e3)))) -> (((op (e1) (e0)) = (e2))\/(((op (e1) (e1)) = (e2))\/(((op (e1) (e2)) = (e2))\/((op (e1) (e3)) = (e2))))) -> (~((op (e1) (e1)) = (op (e3) (e1)))) -> (((op (e0) (e2)) = (e2))\/(((op (e1) (e2)) = (e2))\/(((op (e2) (e2)) = (e2))\/((op (e3) (e2)) = (e2))))) -> (~((op (e3) (e1)) = (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) (e0)) = (e3))\/(((op (e1) (e1)) = (e3))\/(((op (e1) (e2)) = (e3))\/((op (e1) (e3)) = (e3))))) -> (((op (e3) (e0)) = (e2))\/(((op (e3) (e1)) = (e2))\/(((op (e3) (e2)) = (e2))\/((op (e3) (e3)) = (e2))))) -> (~((op (e1) (e2)) = (op (e2) (e2)))) -> (~((op (e1) (e1)) = (op (e1) (e2)))) -> (~((op (e3) (e0)) = (op (e3) (e2)))) -> (((op (e0) (e2)) = (e0))\/(((op (e1) (e2)) = (e0))\/(((op (e2) (e2)) = (e0))\/((op (e3) (e2)) = (e0))))) -> (~((op (e0) (e3)) = (op (e3) (e3)))) -> (((op (e2) (e1)) = (e0))\/(((op (e2) (e1)) = (e1))\/(((op (e2) (e1)) = (e2))\/((op (e2) (e1)) = (e3))))) -> (~((op (e1) (e1)) = (op (e2) (e1)))) -> (~((op (e0) (e1)) = (op (e1) (e1)))) -> (((op (e0) (e1)) = (e0))\/(((op (e0) (e1)) = (e1))\/(((op (e0) (e1)) = (e2))\/((op (e0) (e1)) = (e3))))) -> (((op (e0) (e2)) = (e3))\/(((op (e1) (e2)) = (e3))\/(((op (e2) (e2)) = (e3))\/((op (e3) (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 (e2) (e0)) = (e2))\/(((op (e2) (e1)) = (e2))\/(((op (e2) (e2)) = (e2))\/((op (e2) (e3)) = (e2))))) -> (~((op (e1) (e1)) = (e1))) -> (~((op (e0) (e3)) = (op (e1) (e3)))) -> (((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 (e3) (e0)) = (e1))\/(((op (e3) (e1)) = (e1))\/(((op (e3) (e2)) = (e1))\/((op (e3) (e3)) = (e1))))) -> (~((op (e0) (e1)) = (op (e2) (e1)))) -> (~((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) (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 (e1) (e0)) = (op (e2) (e0)))) -> (~((e0) = (e2))) -> (~((e1) = (e2))) -> (((op (e1) (e0)) = (e0))\/(((op (e1) (e1)) = (e0))\/(((op (e1) (e2)) = (e0))\/((op (e1) (e3)) = (e0))))) -> (~((op (e0) (e2)) = (op (e0) (e3)))) -> (((op (e0) (e0)) = (e0))\/(((op (e0) (e1)) = (e0))\/(((op (e0) (e2)) = (e0))\/((op (e0) (e3)) = (e0))))) -> ((~((op (e3) (e1)) = (e0)))\/((op (e3) (e0)) = (e1))) -> ((~((op (e2) (e3)) = (e0)))\/((op (e2) (e0)) = (e3))) -> ((~((op (e2) (e1)) = (e0)))\/((op (e2) (e0)) = (e1))) -> (((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 (e0) (e0)) = (e0))\/(((op (e1) (e0)) = (e0))\/(((op (e2) (e0)) = (e0))\/((op (e3) (e0)) = (e0))))) -> ((op (e1) (e0)) = (e2)) -> (~((e2) = (e3))) -> ((op (e1) (e1)) = (e2)) -> (~((e0) = (e3))) -> ((op (e1) (e2)) = (e0)) -> ((op (e1) (e3)) = (e1)) -> (~((e1) = (e3))) -> False). % 18.68/18.85 do 0 intro. intros zenon_H3a zenon_H1ac zenon_H14f zenon_H45 zenon_H67 zenon_H5b zenon_H57 zenon_H1cf zenon_H233 zenon_H206 zenon_H1f0 zenon_H1fa zenon_H1ba zenon_H1e0 zenon_H1ee zenon_H1fe zenon_H168 zenon_H124 zenon_H136 zenon_H128 zenon_H13c zenon_H142 zenon_H179 zenon_H178 zenon_H17b zenon_H183 zenon_He7 zenon_H19d zenon_H195 zenon_H191 zenon_H205 zenon_H204 zenon_H1ec zenon_Ha8 zenon_H165 zenon_H185 zenon_H2f zenon_H184 zenon_H1a7 zenon_H20b zenon_H22d zenon_H39 zenon_H7b zenon_H133 zenon_H71 zenon_H6d zenon_Hd8 zenon_H54 zenon_H210 zenon_H4a zenon_H115 zenon_Hf3 zenon_H11f zenon_H22a zenon_Haf zenon_Hdf zenon_He2 zenon_H109 zenon_H106 zenon_H145 zenon_H1c7 zenon_H1d8 zenon_H189 zenon_H18c zenon_H160 zenon_H172 zenon_H130 zenon_H62 zenon_H102 zenon_H101 zenon_H16f zenon_H153 zenon_H2b zenon_H4f zenon_H6f zenon_H6a zenon_Hc2 zenon_H1cc zenon_H13e zenon_H10e zenon_H212 zenon_H1a6 zenon_H1a4 zenon_H1a5 zenon_H1d5 zenon_H10a zenon_H1d zenon_He4 zenon_Hdb zenon_Hd5 zenon_He8 zenon_H17e zenon_Ha1 zenon_H52 zenon_H1c4 zenon_H173 zenon_H18f zenon_H139 zenon_H201 zenon_H149 zenon_H7c zenon_H22 zenon_H208 zenon_H74 zenon_H1ed zenon_H94 zenon_H182 zenon_H235 zenon_H3f zenon_H23 zenon_H3e zenon_H86 zenon_H12b zenon_H110 zenon_H9a zenon_H2a zenon_Hd6 zenon_H95. % 18.68/18.85 apply (zenon_or_s _ _ zenon_H16f); [ zenon_intro zenon_H9e | zenon_intro zenon_H170 ]. % 18.68/18.85 apply (zenon_L550_); trivial. % 18.68/18.85 apply (zenon_or_s _ _ zenon_H170); [ zenon_intro zenon_H13f | zenon_intro zenon_H171 ]. % 18.68/18.85 apply (zenon_L166_); trivial. % 18.68/18.85 apply (zenon_or_s _ _ zenon_H171); [ zenon_intro zenon_H16c | zenon_intro zenon_Hdc ]. % 18.68/18.85 apply (zenon_L521_); trivial. % 18.68/18.85 apply (zenon_L83_); trivial. % 18.68/18.85 (* end of lemma zenon_L562_ *) % 18.68/18.85 assert (zenon_L563_ : (((op (e0) (e2)) = (e2))\/(((op (e1) (e2)) = (e2))\/(((op (e2) (e2)) = (e2))\/((op (e3) (e2)) = (e2))))) -> (~((e1) = (e2))) -> ((op (e0) (e2)) = (e1)) -> (~((e0) = (e2))) -> ((op (e1) (e2)) = (e0)) -> (~((op (e2) (e2)) = (e2))) -> (((op (e0) (e3)) = (e2))\/(((op (e1) (e3)) = (e2))\/(((op (e2) (e3)) = (e2))\/((op (e3) (e3)) = (e2))))) -> (~((op (e0) (e0)) = (op (e0) (e3)))) -> ((op (e0) (e0)) = (e2)) -> (~((op (e1) (e0)) = (op (e1) (e3)))) -> ((op (e1) (e0)) = (e2)) -> (~((op (e2) (e1)) = (op (e2) (e3)))) -> ((op (e2) (e1)) = (e2)) -> (~((op (e3) (e2)) = (op (e3) (e3)))) -> False). % 18.68/18.85 do 0 intro. intros zenon_H172 zenon_H7c zenon_H122 zenon_H149 zenon_H2a zenon_H173 zenon_H145 zenon_H189 zenon_H7b zenon_Hd8 zenon_H86 zenon_H1c7 zenon_H1ca zenon_H62. % 18.68/18.85 apply (zenon_or_s _ _ zenon_H172); [ zenon_intro zenon_H150 | zenon_intro zenon_H174 ]. % 18.68/18.85 apply (zenon_L328_); trivial. % 18.68/18.85 apply (zenon_or_s _ _ zenon_H174); [ zenon_intro zenon_H113 | zenon_intro zenon_H175 ]. % 18.68/18.85 apply (zenon_L542_); trivial. % 18.68/18.85 apply (zenon_or_s _ _ zenon_H175); [ zenon_intro zenon_H176 | zenon_intro zenon_H151 ]. % 18.68/18.85 exact (zenon_H173 zenon_H176). % 18.68/18.85 apply (zenon_L540_); trivial. % 18.68/18.85 (* end of lemma zenon_L563_ *) % 18.68/18.85 assert (zenon_L564_ : (~((e0) = (e1))) -> ((op (e3) (e0)) = (e0)) -> ((op (e0) (e0)) = (e2)) -> (((op (e3) (e0)) = (e0))\/(((op (e3) (e1)) = (e0))\/(((op (e3) (e2)) = (e0))\/((op (e3) (e3)) = (e0))))) -> (~((op (e0) (e2)) = (op (e3) (e2)))) -> (~((op (e1) (e0)) = (op (e1) (e1)))) -> (((op (e0) (e3)) = (e0))\/(((op (e1) (e3)) = (e0))\/(((op (e2) (e3)) = (e0))\/((op (e3) (e3)) = (e0))))) -> (~((op (e2) (e0)) = (op (e2) (e3)))) -> (~((op (e1) (e1)) = (op (e1) (e3)))) -> (~((op (e3) (e0)) = (op (e3) (e1)))) -> ((~((op (e0) (e2)) = (e0)))\/((op (e0) (e0)) = (e2))) -> ((~((op (e1) (e0)) = (e0)))\/((op (e1) (e0)) = (e0))) -> (~((op (e2) (e0)) = (op (e2) (e1)))) -> (~((op (e1) (e0)) = (op (e3) (e0)))) -> (((op (e0) (e2)) = (e0))\/(((op (e0) (e2)) = (e1))\/(((op (e0) (e2)) = (e2))\/((op (e0) (e2)) = (e3))))) -> (((op (e0) (e0)) = (e3))\/(((op (e1) (e0)) = (e3))\/(((op (e2) (e0)) = (e3))\/((op (e3) (e0)) = (e3))))) -> ((~((op (e2) (e0)) = (e0)))\/((op (e2) (e0)) = (e0))) -> (((op (e0) (e0)) = (e2))\/(((op (e1) (e0)) = (e2))\/(((op (e2) (e0)) = (e2))\/((op (e3) (e0)) = (e2))))) -> (((op (e0) (e0)) = (e3))\/(((op (e0) (e1)) = (e3))\/(((op (e0) (e2)) = (e3))\/((op (e0) (e3)) = (e3))))) -> (~((op (e1) (e2)) = (op (e1) (e3)))) -> (((op (e0) (e3)) = (e3))\/(((op (e1) (e3)) = (e3))\/(((op (e2) (e3)) = (e3))\/((op (e3) (e3)) = (e3))))) -> (((op (e1) (e0)) = (e1))\/(((op (e1) (e1)) = (e1))\/(((op (e1) (e2)) = (e1))\/((op (e1) (e3)) = (e1))))) -> (~((op (e0) (e0)) = (op (e0) (e2)))) -> (((op (e1) (e1)) = (e0))\/(((op (e1) (e1)) = (e1))\/(((op (e1) (e1)) = (e2))\/((op (e1) (e1)) = (e3))))) -> ((~((op (e1) (e3)) = (e0)))\/((op (e1) (e0)) = (e3))) -> ((~((op (e1) (e2)) = (e0)))\/((op (e1) (e0)) = (e2))) -> (~((op (e2) (e0)) = (op (e3) (e0)))) -> (((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) (e2)) = (e0))\/(((op (e1) (e2)) = (e1))\/(((op (e1) (e2)) = (e2))\/((op (e1) (e2)) = (e3))))) -> (~((op (e0) (e2)) = (op (e1) (e2)))) -> (((op (e3) (e2)) = (e0))\/(((op (e3) (e2)) = (e1))\/(((op (e3) (e2)) = (e2))\/((op (e3) (e2)) = (e3))))) -> ((~((op (e1) (e1)) = (e0)))\/((op (e1) (e0)) = (e1))) -> ((~((op (e0) (e3)) = (e0)))\/((op (e0) (e0)) = (e3))) -> ((~((op (e3) (e3)) = (e0)))\/((op (e3) (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 (e2) (e2)) = (e0)))\/((op (e2) (e0)) = (e2))) -> (((op (e2) (e0)) = (e0))\/(((op (e2) (e1)) = (e0))\/(((op (e2) (e2)) = (e0))\/((op (e2) (e3)) = (e0))))) -> ((~((op (e3) (e0)) = (e0)))\/((op (e3) (e0)) = (e0))) -> ((~((op (e3) (e2)) = (e0)))\/((op (e3) (e0)) = (e2))) -> (~((op (e0) (e1)) = (e0))) -> (((op (e0) (e0)) = (e1))\/(((op (e0) (e1)) = (e1))\/(((op (e0) (e2)) = (e1))\/((op (e0) (e3)) = (e1))))) -> (~((op (e0) (e0)) = (op (e2) (e0)))) -> (((op (e0) (e3)) = (e1))\/(((op (e1) (e3)) = (e1))\/(((op (e2) (e3)) = (e1))\/((op (e3) (e3)) = (e1))))) -> (~((op (e3) (e0)) = (op (e3) (e3)))) -> (~((op (e2) (e2)) = (op (e2) (e3)))) -> (~((op (e1) (e0)) = (op (e1) (e3)))) -> (~((op (e0) (e1)) = (op (e0) (e3)))) -> (~((op (e0) (e1)) = (op (e3) (e1)))) -> (~((op (e0) (e1)) = (op (e0) (e2)))) -> (~((op (e1) (e2)) = (op (e3) (e2)))) -> (~((op (e2) (e3)) = (op (e3) (e3)))) -> (((op (e2) (e3)) = (e0))\/(((op (e2) (e3)) = (e1))\/(((op (e2) (e3)) = (e2))\/((op (e2) (e3)) = (e3))))) -> (((op (e3) (e1)) = (e0))\/(((op (e3) (e1)) = (e1))\/(((op (e3) (e1)) = (e2))\/((op (e3) (e1)) = (e3))))) -> (~((op (e2) (e1)) = (op (e3) (e1)))) -> (((op (e1) (e3)) = (e0))\/(((op (e1) (e3)) = (e1))\/(((op (e1) (e3)) = (e2))\/((op (e1) (e3)) = (e3))))) -> (~((op (e0) (e3)) = (op (e2) (e3)))) -> (((op (e0) (e1)) = (e1))\/(((op (e1) (e1)) = (e1))\/(((op (e2) (e1)) = (e1))\/((op (e3) (e1)) = (e1))))) -> (((op (e2) (e0)) = (e1))\/(((op (e2) (e1)) = (e1))\/(((op (e2) (e2)) = (e1))\/((op (e2) (e3)) = (e1))))) -> (((op (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)) = (op (e0) (e3)))) -> (((op (e1) (e0)) = (e2))\/(((op (e1) (e1)) = (e2))\/(((op (e1) (e2)) = (e2))\/((op (e1) (e3)) = (e2))))) -> (~((op (e1) (e1)) = (op (e3) (e1)))) -> (((op (e0) (e2)) = (e2))\/(((op (e1) (e2)) = (e2))\/(((op (e2) (e2)) = (e2))\/((op (e3) (e2)) = (e2))))) -> (~((op (e3) (e1)) = (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) (e0)) = (e3))\/(((op (e1) (e1)) = (e3))\/(((op (e1) (e2)) = (e3))\/((op (e1) (e3)) = (e3))))) -> (((op (e3) (e0)) = (e2))\/(((op (e3) (e1)) = (e2))\/(((op (e3) (e2)) = (e2))\/((op (e3) (e3)) = (e2))))) -> (~((op (e1) (e2)) = (op (e2) (e2)))) -> (~((op (e1) (e1)) = (op (e1) (e2)))) -> (~((op (e3) (e0)) = (op (e3) (e2)))) -> (((op (e0) (e2)) = (e0))\/(((op (e1) (e2)) = (e0))\/(((op (e2) (e2)) = (e0))\/((op (e3) (e2)) = (e0))))) -> (~((op (e0) (e3)) = (op (e3) (e3)))) -> (((op (e2) (e1)) = (e0))\/(((op (e2) (e1)) = (e1))\/(((op (e2) (e1)) = (e2))\/((op (e2) (e1)) = (e3))))) -> (~((op (e1) (e1)) = (op (e2) (e1)))) -> (~((op (e0) (e1)) = (op (e1) (e1)))) -> (((op (e0) (e1)) = (e0))\/(((op (e0) (e1)) = (e1))\/(((op (e0) (e1)) = (e2))\/((op (e0) (e1)) = (e3))))) -> (((op (e0) (e2)) = (e3))\/(((op (e1) (e2)) = (e3))\/(((op (e2) (e2)) = (e3))\/((op (e3) (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 (e2) (e0)) = (e2))\/(((op (e2) (e1)) = (e2))\/(((op (e2) (e2)) = (e2))\/((op (e2) (e3)) = (e2))))) -> (~((op (e1) (e1)) = (e1))) -> (~((op (e0) (e3)) = (op (e1) (e3)))) -> (((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 (e3) (e0)) = (e1))\/(((op (e3) (e1)) = (e1))\/(((op (e3) (e2)) = (e1))\/((op (e3) (e3)) = (e1))))) -> (~((e2) = (e3))) -> (~((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) (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 (e1) (e0)) = (op (e2) (e0)))) -> (~((e0) = (e2))) -> (~((e1) = (e2))) -> (((op (e1) (e0)) = (e0))\/(((op (e1) (e1)) = (e0))\/(((op (e1) (e2)) = (e0))\/((op (e1) (e3)) = (e0))))) -> ((op (e0) (e0)) = (e3)) -> (~((op (e0) (e2)) = (op (e0) (e3)))) -> (((op (e0) (e0)) = (e0))\/(((op (e0) (e1)) = (e0))\/(((op (e0) (e2)) = (e0))\/((op (e0) (e3)) = (e0))))) -> ((~((op (e3) (e1)) = (e0)))\/((op (e3) (e0)) = (e1))) -> (~((op (e0) (e0)) = (e0))) -> (~((op (e1) (e0)) = (e0))) -> (((op (e0) (e0)) = (e0))\/(((op (e1) (e0)) = (e0))\/(((op (e2) (e0)) = (e0))\/((op (e3) (e0)) = (e0))))) -> ((~((op (e2) (e3)) = (e0)))\/((op (e2) (e0)) = (e3))) -> ((~((op (e2) (e1)) = (e0)))\/((op (e2) (e0)) = (e1))) -> (((op (e0) (e0)) = (e1))\/(((op (e1) (e0)) = (e1))\/(((op (e2) (e0)) = (e1))\/((op (e3) (e0)) = (e1))))) -> ((op (e3) (e1)) = (e2)) -> ((op (e2) (e1)) = (e0)) -> (~((e0) = (e3))) -> ((op (e1) (e2)) = (e0)) -> ((op (e1) (e3)) = (e1)) -> (~((e1) = (e3))) -> False). % 18.68/18.85 do 0 intro. intros zenon_Ha1 zenon_H44 zenon_H7b zenon_H1ac zenon_H14f zenon_H45 zenon_H67 zenon_H5b zenon_H57 zenon_H1cf zenon_H233 zenon_H206 zenon_H1f0 zenon_H1fa zenon_H1ba zenon_H1e0 zenon_H1ee zenon_H1fe zenon_H168 zenon_H124 zenon_H136 zenon_H128 zenon_H13c zenon_H142 zenon_H179 zenon_H178 zenon_H17b zenon_H183 zenon_He7 zenon_H19d zenon_H195 zenon_H191 zenon_H205 zenon_H204 zenon_H1ec zenon_Ha8 zenon_H165 zenon_H185 zenon_H2f zenon_H184 zenon_H1a7 zenon_H20b zenon_H22d zenon_H39 zenon_H133 zenon_H71 zenon_H6d zenon_Hd8 zenon_H54 zenon_H210 zenon_H4a zenon_H115 zenon_Hf3 zenon_H11f zenon_H22a zenon_Haf zenon_Hdf zenon_He2 zenon_H109 zenon_H106 zenon_H145 zenon_H1c7 zenon_H1d8 zenon_H189 zenon_H18c zenon_H160 zenon_H172 zenon_H130 zenon_H62 zenon_H102 zenon_H101 zenon_H16f zenon_H153 zenon_H2b zenon_H4f zenon_H6f zenon_H6a zenon_Hc2 zenon_H1cc zenon_H13e zenon_H10e zenon_H212 zenon_H1a6 zenon_H1a4 zenon_H1a5 zenon_H1d5 zenon_H10a zenon_H1d zenon_He4 zenon_Hdb zenon_Hd5 zenon_He8 zenon_H12b zenon_H17e zenon_H52 zenon_H1c4 zenon_H173 zenon_H18f zenon_H139 zenon_H201 zenon_H149 zenon_H7c zenon_H22 zenon_H3a zenon_H208 zenon_H74 zenon_H1ed zenon_H3f zenon_H23 zenon_H3e zenon_H94 zenon_H182 zenon_H235 zenon_H14d zenon_H36 zenon_H9a zenon_H2a zenon_Hd6 zenon_H95. % 18.68/18.85 apply (zenon_or_s _ _ zenon_H16f); [ zenon_intro zenon_H9e | zenon_intro zenon_H170 ]. % 18.68/18.85 apply (zenon_L492_); trivial. % 18.68/18.85 apply (zenon_or_s _ _ zenon_H170); [ zenon_intro zenon_H13f | zenon_intro zenon_H171 ]. % 18.68/18.85 apply (zenon_L514_); trivial. % 18.68/18.85 apply (zenon_or_s _ _ zenon_H171); [ zenon_intro zenon_H16c | zenon_intro zenon_Hdc ]. % 18.68/18.85 apply (zenon_L521_); trivial. % 18.68/18.85 apply (zenon_L83_); trivial. % 18.68/18.85 (* end of lemma zenon_L564_ *) % 18.68/18.85 assert (zenon_L565_ : ((op (e0) (e3)) = (e0)) -> ((op (e2) (e0)) = (e1)) -> ((op (e1) (e0)) = (e2)) -> ((op (e0) (e2)) = (e1)) -> (~((e0) = (e1))) -> ((op (e3) (e0)) = (e0)) -> ((op (e0) (e0)) = (e2)) -> (((op (e3) (e0)) = (e0))\/(((op (e3) (e1)) = (e0))\/(((op (e3) (e2)) = (e0))\/((op (e3) (e3)) = (e0))))) -> (~((op (e0) (e2)) = (op (e3) (e2)))) -> (~((op (e1) (e0)) = (op (e1) (e1)))) -> (((op (e0) (e3)) = (e0))\/(((op (e1) (e3)) = (e0))\/(((op (e2) (e3)) = (e0))\/((op (e3) (e3)) = (e0))))) -> (~((op (e2) (e0)) = (op (e2) (e3)))) -> (~((op (e1) (e1)) = (op (e1) (e3)))) -> (~((op (e3) (e0)) = (op (e3) (e1)))) -> ((~((op (e0) (e2)) = (e0)))\/((op (e0) (e0)) = (e2))) -> ((~((op (e1) (e0)) = (e0)))\/((op (e1) (e0)) = (e0))) -> (~((op (e2) (e0)) = (op (e2) (e1)))) -> (~((op (e1) (e0)) = (op (e3) (e0)))) -> (((op (e0) (e2)) = (e0))\/(((op (e0) (e2)) = (e1))\/(((op (e0) (e2)) = (e2))\/((op (e0) (e2)) = (e3))))) -> (((op (e0) (e0)) = (e3))\/(((op (e1) (e0)) = (e3))\/(((op (e2) (e0)) = (e3))\/((op (e3) (e0)) = (e3))))) -> ((~((op (e2) (e0)) = (e0)))\/((op (e2) (e0)) = (e0))) -> (((op (e0) (e0)) = (e2))\/(((op (e1) (e0)) = (e2))\/(((op (e2) (e0)) = (e2))\/((op (e3) (e0)) = (e2))))) -> (((op (e0) (e0)) = (e3))\/(((op (e0) (e1)) = (e3))\/(((op (e0) (e2)) = (e3))\/((op (e0) (e3)) = (e3))))) -> (~((op (e1) (e2)) = (op (e1) (e3)))) -> (((op (e0) (e3)) = (e3))\/(((op (e1) (e3)) = (e3))\/(((op (e2) (e3)) = (e3))\/((op (e3) (e3)) = (e3))))) -> (((op (e1) (e0)) = (e1))\/(((op (e1) (e1)) = (e1))\/(((op (e1) (e2)) = (e1))\/((op (e1) (e3)) = (e1))))) -> (~((op (e0) (e0)) = (op (e0) (e2)))) -> (((op (e1) (e1)) = (e0))\/(((op (e1) (e1)) = (e1))\/(((op (e1) (e1)) = (e2))\/((op (e1) (e1)) = (e3))))) -> ((~((op (e1) (e3)) = (e0)))\/((op (e1) (e0)) = (e3))) -> ((~((op (e1) (e2)) = (e0)))\/((op (e1) (e0)) = (e2))) -> (~((op (e2) (e0)) = (op (e3) (e0)))) -> (((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) (e2)) = (e0))\/(((op (e1) (e2)) = (e1))\/(((op (e1) (e2)) = (e2))\/((op (e1) (e2)) = (e3))))) -> (~((op (e0) (e2)) = (op (e1) (e2)))) -> (((op (e3) (e2)) = (e0))\/(((op (e3) (e2)) = (e1))\/(((op (e3) (e2)) = (e2))\/((op (e3) (e2)) = (e3))))) -> ((~((op (e1) (e1)) = (e0)))\/((op (e1) (e0)) = (e1))) -> ((~((op (e0) (e3)) = (e0)))\/((op (e0) (e0)) = (e3))) -> ((~((op (e3) (e3)) = (e0)))\/((op (e3) (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 (e2) (e2)) = (e0)))\/((op (e2) (e0)) = (e2))) -> (((op (e2) (e0)) = (e0))\/(((op (e2) (e1)) = (e0))\/(((op (e2) (e2)) = (e0))\/((op (e2) (e3)) = (e0))))) -> ((~((op (e3) (e0)) = (e0)))\/((op (e3) (e0)) = (e0))) -> ((~((op (e3) (e2)) = (e0)))\/((op (e3) (e0)) = (e2))) -> (~((op (e0) (e1)) = (e0))) -> (((op (e0) (e0)) = (e1))\/(((op (e0) (e1)) = (e1))\/(((op (e0) (e2)) = (e1))\/((op (e0) (e3)) = (e1))))) -> (~((op (e0) (e0)) = (op (e2) (e0)))) -> (((op (e0) (e3)) = (e1))\/(((op (e1) (e3)) = (e1))\/(((op (e2) (e3)) = (e1))\/((op (e3) (e3)) = (e1))))) -> (~((op (e3) (e0)) = (op (e3) (e3)))) -> (~((op (e2) (e2)) = (op (e2) (e3)))) -> (~((op (e1) (e0)) = (op (e1) (e3)))) -> (~((op (e0) (e1)) = (op (e0) (e3)))) -> (~((op (e0) (e1)) = (op (e3) (e1)))) -> (~((op (e0) (e1)) = (op (e0) (e2)))) -> (~((op (e1) (e2)) = (op (e3) (e2)))) -> (~((op (e2) (e3)) = (op (e3) (e3)))) -> (((op (e2) (e3)) = (e0))\/(((op (e2) (e3)) = (e1))\/(((op (e2) (e3)) = (e2))\/((op (e2) (e3)) = (e3))))) -> (((op (e3) (e1)) = (e0))\/(((op (e3) (e1)) = (e1))\/(((op (e3) (e1)) = (e2))\/((op (e3) (e1)) = (e3))))) -> (~((op (e2) (e1)) = (op (e3) (e1)))) -> (((op (e1) (e3)) = (e0))\/(((op (e1) (e3)) = (e1))\/(((op (e1) (e3)) = (e2))\/((op (e1) (e3)) = (e3))))) -> (~((op (e0) (e3)) = (op (e2) (e3)))) -> (((op (e0) (e1)) = (e1))\/(((op (e1) (e1)) = (e1))\/(((op (e2) (e1)) = (e1))\/((op (e3) (e1)) = (e1))))) -> (((op (e2) (e0)) = (e1))\/(((op (e2) (e1)) = (e1))\/(((op (e2) (e2)) = (e1))\/((op (e2) (e3)) = (e1))))) -> (((op (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)) = (op (e0) (e3)))) -> (((op (e1) (e0)) = (e2))\/(((op (e1) (e1)) = (e2))\/(((op (e1) (e2)) = (e2))\/((op (e1) (e3)) = (e2))))) -> (~((op (e1) (e1)) = (op (e3) (e1)))) -> (((op (e0) (e2)) = (e2))\/(((op (e1) (e2)) = (e2))\/(((op (e2) (e2)) = (e2))\/((op (e3) (e2)) = (e2))))) -> (~((op (e3) (e1)) = (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) (e0)) = (e3))\/(((op (e1) (e1)) = (e3))\/(((op (e1) (e2)) = (e3))\/((op (e1) (e3)) = (e3))))) -> (((op (e3) (e0)) = (e2))\/(((op (e3) (e1)) = (e2))\/(((op (e3) (e2)) = (e2))\/((op (e3) (e3)) = (e2))))) -> (~((op (e1) (e2)) = (op (e2) (e2)))) -> (~((op (e1) (e1)) = (op (e1) (e2)))) -> (~((op (e3) (e0)) = (op (e3) (e2)))) -> (((op (e0) (e2)) = (e0))\/(((op (e1) (e2)) = (e0))\/(((op (e2) (e2)) = (e0))\/((op (e3) (e2)) = (e0))))) -> (~((op (e0) (e3)) = (op (e3) (e3)))) -> (((op (e2) (e1)) = (e0))\/(((op (e2) (e1)) = (e1))\/(((op (e2) (e1)) = (e2))\/((op (e2) (e1)) = (e3))))) -> (~((op (e1) (e1)) = (op (e2) (e1)))) -> (~((op (e0) (e1)) = (op (e1) (e1)))) -> (((op (e0) (e1)) = (e0))\/(((op (e0) (e1)) = (e1))\/(((op (e0) (e1)) = (e2))\/((op (e0) (e1)) = (e3))))) -> (((op (e0) (e2)) = (e3))\/(((op (e1) (e2)) = (e3))\/(((op (e2) (e2)) = (e3))\/((op (e3) (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 (e2) (e0)) = (e2))\/(((op (e2) (e1)) = (e2))\/(((op (e2) (e2)) = (e2))\/((op (e2) (e3)) = (e2))))) -> (~((op (e1) (e1)) = (e1))) -> (~((op (e0) (e3)) = (op (e1) (e3)))) -> (((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 (e3) (e0)) = (e1))\/(((op (e3) (e1)) = (e1))\/(((op (e3) (e2)) = (e1))\/((op (e3) (e3)) = (e1))))) -> (~((e2) = (e3))) -> (~((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) (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 (e1) (e0)) = (op (e2) (e0)))) -> (~((e0) = (e2))) -> (~((e1) = (e2))) -> (((op (e1) (e0)) = (e0))\/(((op (e1) (e1)) = (e0))\/(((op (e1) (e2)) = (e0))\/((op (e1) (e3)) = (e0))))) -> ((op (e0) (e0)) = (e3)) -> (~((op (e0) (e2)) = (op (e0) (e3)))) -> (((op (e0) (e0)) = (e0))\/(((op (e0) (e1)) = (e0))\/(((op (e0) (e2)) = (e0))\/((op (e0) (e3)) = (e0))))) -> ((~((op (e3) (e1)) = (e0)))\/((op (e3) (e0)) = (e1))) -> (~((op (e0) (e0)) = (e0))) -> (~((op (e1) (e0)) = (e0))) -> (((op (e0) (e0)) = (e0))\/(((op (e1) (e0)) = (e0))\/(((op (e2) (e0)) = (e0))\/((op (e3) (e0)) = (e0))))) -> ((~((op (e2) (e3)) = (e0)))\/((op (e2) (e0)) = (e3))) -> ((~((op (e2) (e1)) = (e0)))\/((op (e2) (e0)) = (e1))) -> (((op (e0) (e0)) = (e1))\/(((op (e1) (e0)) = (e1))\/(((op (e2) (e0)) = (e1))\/((op (e3) (e0)) = (e1))))) -> ((op (e2) (e1)) = (e0)) -> (~((e0) = (e3))) -> ((op (e1) (e2)) = (e0)) -> ((op (e1) (e3)) = (e1)) -> (~((e1) = (e3))) -> False). % 18.68/18.86 do 0 intro. intros zenon_H1e zenon_Hed zenon_H86 zenon_H122 zenon_Ha1 zenon_H44 zenon_H7b zenon_H1ac zenon_H14f zenon_H45 zenon_H67 zenon_H5b zenon_H57 zenon_H1cf zenon_H233 zenon_H206 zenon_H1f0 zenon_H1fa zenon_H1ba zenon_H1e0 zenon_H1ee zenon_H1fe zenon_H168 zenon_H124 zenon_H136 zenon_H128 zenon_H13c zenon_H142 zenon_H179 zenon_H178 zenon_H17b zenon_H183 zenon_He7 zenon_H19d zenon_H195 zenon_H191 zenon_H205 zenon_H204 zenon_H1ec zenon_Ha8 zenon_H165 zenon_H185 zenon_H2f zenon_H184 zenon_H1a7 zenon_H20b zenon_H22d zenon_H39 zenon_H133 zenon_H71 zenon_H6d zenon_Hd8 zenon_H54 zenon_H210 zenon_H4a zenon_H115 zenon_Hf3 zenon_H11f zenon_H22a zenon_Haf zenon_Hdf zenon_He2 zenon_H109 zenon_H106 zenon_H145 zenon_H1c7 zenon_H1d8 zenon_H189 zenon_H18c zenon_H160 zenon_H172 zenon_H130 zenon_H62 zenon_H102 zenon_H101 zenon_H16f zenon_H153 zenon_H2b zenon_H4f zenon_H6f zenon_H6a zenon_Hc2 zenon_H1cc zenon_H13e zenon_H10e zenon_H212 zenon_H1a6 zenon_H1a4 zenon_H1a5 zenon_H1d5 zenon_H10a zenon_H1d zenon_He4 zenon_Hdb zenon_Hd5 zenon_He8 zenon_H12b zenon_H17e zenon_H52 zenon_H1c4 zenon_H173 zenon_H18f zenon_H139 zenon_H201 zenon_H149 zenon_H7c zenon_H22 zenon_H3a zenon_H208 zenon_H74 zenon_H1ed zenon_H3f zenon_H23 zenon_H3e zenon_H94 zenon_H182 zenon_H235 zenon_H36 zenon_H9a zenon_H2a zenon_Hd6 zenon_H95. % 18.68/18.86 apply (zenon_or_s _ _ zenon_H1d8); [ zenon_intro zenon_H10f | zenon_intro zenon_H1d9 ]. % 18.68/18.86 apply (zenon_L561_); trivial. % 18.68/18.86 apply (zenon_or_s _ _ zenon_H1d9); [ zenon_intro zenon_H110 | zenon_intro zenon_H1da ]. % 18.68/18.86 apply (zenon_L562_); trivial. % 18.68/18.86 apply (zenon_or_s _ _ zenon_H1da); [ zenon_intro zenon_H1ca | zenon_intro zenon_H14d ]. % 18.68/18.86 apply (zenon_L563_); trivial. % 18.68/18.86 apply (zenon_L564_); trivial. % 18.68/18.86 (* end of lemma zenon_L565_ *) % 18.68/18.86 assert (zenon_L566_ : (~((op (e3) (e1)) = (e0))) -> ((op (e0) (e3)) = (e0)) -> ((op (e2) (e0)) = (e1)) -> ((op (e1) (e0)) = (e2)) -> ((op (e0) (e2)) = (e1)) -> (~((e0) = (e1))) -> ((op (e3) (e0)) = (e0)) -> ((op (e0) (e0)) = (e2)) -> (((op (e3) (e0)) = (e0))\/(((op (e3) (e1)) = (e0))\/(((op (e3) (e2)) = (e0))\/((op (e3) (e3)) = (e0))))) -> (~((op (e0) (e2)) = (op (e3) (e2)))) -> (~((op (e1) (e0)) = (op (e1) (e1)))) -> (((op (e0) (e3)) = (e0))\/(((op (e1) (e3)) = (e0))\/(((op (e2) (e3)) = (e0))\/((op (e3) (e3)) = (e0))))) -> (~((op (e2) (e0)) = (op (e2) (e3)))) -> (~((op (e1) (e1)) = (op (e1) (e3)))) -> (~((op (e3) (e0)) = (op (e3) (e1)))) -> ((~((op (e0) (e2)) = (e0)))\/((op (e0) (e0)) = (e2))) -> ((~((op (e1) (e0)) = (e0)))\/((op (e1) (e0)) = (e0))) -> (~((op (e2) (e0)) = (op (e2) (e1)))) -> (~((op (e1) (e0)) = (op (e3) (e0)))) -> (((op (e0) (e2)) = (e0))\/(((op (e0) (e2)) = (e1))\/(((op (e0) (e2)) = (e2))\/((op (e0) (e2)) = (e3))))) -> (((op (e0) (e0)) = (e3))\/(((op (e1) (e0)) = (e3))\/(((op (e2) (e0)) = (e3))\/((op (e3) (e0)) = (e3))))) -> ((~((op (e2) (e0)) = (e0)))\/((op (e2) (e0)) = (e0))) -> (((op (e0) (e0)) = (e2))\/(((op (e1) (e0)) = (e2))\/(((op (e2) (e0)) = (e2))\/((op (e3) (e0)) = (e2))))) -> (((op (e0) (e0)) = (e3))\/(((op (e0) (e1)) = (e3))\/(((op (e0) (e2)) = (e3))\/((op (e0) (e3)) = (e3))))) -> (~((op (e1) (e2)) = (op (e1) (e3)))) -> (((op (e0) (e3)) = (e3))\/(((op (e1) (e3)) = (e3))\/(((op (e2) (e3)) = (e3))\/((op (e3) (e3)) = (e3))))) -> (((op (e1) (e0)) = (e1))\/(((op (e1) (e1)) = (e1))\/(((op (e1) (e2)) = (e1))\/((op (e1) (e3)) = (e1))))) -> (~((op (e0) (e0)) = (op (e0) (e2)))) -> (((op (e1) (e1)) = (e0))\/(((op (e1) (e1)) = (e1))\/(((op (e1) (e1)) = (e2))\/((op (e1) (e1)) = (e3))))) -> ((~((op (e1) (e3)) = (e0)))\/((op (e1) (e0)) = (e3))) -> ((~((op (e1) (e2)) = (e0)))\/((op (e1) (e0)) = (e2))) -> (~((op (e2) (e0)) = (op (e3) (e0)))) -> (((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) (e2)) = (e0))\/(((op (e1) (e2)) = (e1))\/(((op (e1) (e2)) = (e2))\/((op (e1) (e2)) = (e3))))) -> (~((op (e0) (e2)) = (op (e1) (e2)))) -> (((op (e3) (e2)) = (e0))\/(((op (e3) (e2)) = (e1))\/(((op (e3) (e2)) = (e2))\/((op (e3) (e2)) = (e3))))) -> ((~((op (e1) (e1)) = (e0)))\/((op (e1) (e0)) = (e1))) -> ((~((op (e0) (e3)) = (e0)))\/((op (e0) (e0)) = (e3))) -> ((~((op (e3) (e3)) = (e0)))\/((op (e3) (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 (e2) (e2)) = (e0)))\/((op (e2) (e0)) = (e2))) -> (((op (e2) (e0)) = (e0))\/(((op (e2) (e1)) = (e0))\/(((op (e2) (e2)) = (e0))\/((op (e2) (e3)) = (e0))))) -> ((~((op (e3) (e0)) = (e0)))\/((op (e3) (e0)) = (e0))) -> ((~((op (e3) (e2)) = (e0)))\/((op (e3) (e0)) = (e2))) -> (~((op (e0) (e1)) = (e0))) -> (((op (e0) (e0)) = (e1))\/(((op (e0) (e1)) = (e1))\/(((op (e0) (e2)) = (e1))\/((op (e0) (e3)) = (e1))))) -> (~((op (e0) (e0)) = (op (e2) (e0)))) -> (((op (e0) (e3)) = (e1))\/(((op (e1) (e3)) = (e1))\/(((op (e2) (e3)) = (e1))\/((op (e3) (e3)) = (e1))))) -> (~((op (e3) (e0)) = (op (e3) (e3)))) -> (~((op (e2) (e2)) = (op (e2) (e3)))) -> (~((op (e1) (e0)) = (op (e1) (e3)))) -> (~((op (e0) (e1)) = (op (e0) (e3)))) -> (~((op (e0) (e1)) = (op (e3) (e1)))) -> (~((op (e0) (e1)) = (op (e0) (e2)))) -> (~((op (e1) (e2)) = (op (e3) (e2)))) -> (~((op (e2) (e3)) = (op (e3) (e3)))) -> (((op (e2) (e3)) = (e0))\/(((op (e2) (e3)) = (e1))\/(((op (e2) (e3)) = (e2))\/((op (e2) (e3)) = (e3))))) -> (((op (e3) (e1)) = (e0))\/(((op (e3) (e1)) = (e1))\/(((op (e3) (e1)) = (e2))\/((op (e3) (e1)) = (e3))))) -> (~((op (e2) (e1)) = (op (e3) (e1)))) -> (((op (e1) (e3)) = (e0))\/(((op (e1) (e3)) = (e1))\/(((op (e1) (e3)) = (e2))\/((op (e1) (e3)) = (e3))))) -> (~((op (e0) (e3)) = (op (e2) (e3)))) -> (((op (e0) (e1)) = (e1))\/(((op (e1) (e1)) = (e1))\/(((op (e2) (e1)) = (e1))\/((op (e3) (e1)) = (e1))))) -> (((op (e2) (e0)) = (e1))\/(((op (e2) (e1)) = (e1))\/(((op (e2) (e2)) = (e1))\/((op (e2) (e3)) = (e1))))) -> (((op (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)) = (op (e0) (e3)))) -> (((op (e1) (e0)) = (e2))\/(((op (e1) (e1)) = (e2))\/(((op (e1) (e2)) = (e2))\/((op (e1) (e3)) = (e2))))) -> (~((op (e1) (e1)) = (op (e3) (e1)))) -> (((op (e0) (e2)) = (e2))\/(((op (e1) (e2)) = (e2))\/(((op (e2) (e2)) = (e2))\/((op (e3) (e2)) = (e2))))) -> (~((op (e3) (e1)) = (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) (e0)) = (e3))\/(((op (e1) (e1)) = (e3))\/(((op (e1) (e2)) = (e3))\/((op (e1) (e3)) = (e3))))) -> (((op (e3) (e0)) = (e2))\/(((op (e3) (e1)) = (e2))\/(((op (e3) (e2)) = (e2))\/((op (e3) (e3)) = (e2))))) -> (~((op (e1) (e2)) = (op (e2) (e2)))) -> (~((op (e1) (e1)) = (op (e1) (e2)))) -> (~((op (e3) (e0)) = (op (e3) (e2)))) -> (((op (e0) (e2)) = (e0))\/(((op (e1) (e2)) = (e0))\/(((op (e2) (e2)) = (e0))\/((op (e3) (e2)) = (e0))))) -> (~((op (e0) (e3)) = (op (e3) (e3)))) -> (((op (e2) (e1)) = (e0))\/(((op (e2) (e1)) = (e1))\/(((op (e2) (e1)) = (e2))\/((op (e2) (e1)) = (e3))))) -> (~((op (e1) (e1)) = (op (e2) (e1)))) -> (~((op (e0) (e1)) = (op (e1) (e1)))) -> (((op (e0) (e1)) = (e0))\/(((op (e0) (e1)) = (e1))\/(((op (e0) (e1)) = (e2))\/((op (e0) (e1)) = (e3))))) -> (((op (e0) (e2)) = (e3))\/(((op (e1) (e2)) = (e3))\/(((op (e2) (e2)) = (e3))\/((op (e3) (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 (e2) (e0)) = (e2))\/(((op (e2) (e1)) = (e2))\/(((op (e2) (e2)) = (e2))\/((op (e2) (e3)) = (e2))))) -> (~((op (e1) (e1)) = (e1))) -> (~((op (e0) (e3)) = (op (e1) (e3)))) -> (((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 (e3) (e0)) = (e1))\/(((op (e3) (e1)) = (e1))\/(((op (e3) (e2)) = (e1))\/((op (e3) (e3)) = (e1))))) -> (~((e2) = (e3))) -> (~((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) (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 (e1) (e0)) = (op (e2) (e0)))) -> (~((e0) = (e2))) -> (~((e1) = (e2))) -> (((op (e1) (e0)) = (e0))\/(((op (e1) (e1)) = (e0))\/(((op (e1) (e2)) = (e0))\/((op (e1) (e3)) = (e0))))) -> ((op (e0) (e0)) = (e3)) -> (~((op (e0) (e2)) = (op (e0) (e3)))) -> (((op (e0) (e0)) = (e0))\/(((op (e0) (e1)) = (e0))\/(((op (e0) (e2)) = (e0))\/((op (e0) (e3)) = (e0))))) -> ((~((op (e3) (e1)) = (e0)))\/((op (e3) (e0)) = (e1))) -> (~((op (e0) (e0)) = (e0))) -> (~((op (e1) (e0)) = (e0))) -> (((op (e0) (e0)) = (e0))\/(((op (e1) (e0)) = (e0))\/(((op (e2) (e0)) = (e0))\/((op (e3) (e0)) = (e0))))) -> ((~((op (e2) (e3)) = (e0)))\/((op (e2) (e0)) = (e3))) -> ((~((op (e2) (e1)) = (e0)))\/((op (e2) (e0)) = (e1))) -> (((op (e0) (e0)) = (e1))\/(((op (e1) (e0)) = (e1))\/(((op (e2) (e0)) = (e1))\/((op (e3) (e0)) = (e1))))) -> (~((e0) = (e3))) -> (~((e1) = (e3))) -> (~((op (e1) (e1)) = (e0))) -> (((op (e0) (e1)) = (e0))\/(((op (e1) (e1)) = (e0))\/(((op (e2) (e1)) = (e0))\/((op (e3) (e1)) = (e0))))) -> (~((op (e1) (e3)) = (e0))) -> False). % 18.68/18.86 do 0 intro. intros zenon_H1ad zenon_H1e zenon_Hed zenon_H86 zenon_H122 zenon_Ha1 zenon_H44 zenon_H7b zenon_H1ac zenon_H14f zenon_H45 zenon_H67 zenon_H5b zenon_H57 zenon_H1cf zenon_H233 zenon_H206 zenon_H1f0 zenon_H1fa zenon_H1ba zenon_H1e0 zenon_H1ee zenon_H1fe zenon_H168 zenon_H124 zenon_H136 zenon_H128 zenon_H13c zenon_H142 zenon_H179 zenon_H178 zenon_H17b zenon_H183 zenon_He7 zenon_H19d zenon_H195 zenon_H191 zenon_H205 zenon_H204 zenon_H1ec zenon_Ha8 zenon_H165 zenon_H185 zenon_H2f zenon_H184 zenon_H1a7 zenon_H20b zenon_H22d zenon_H39 zenon_H133 zenon_H71 zenon_H6d zenon_Hd8 zenon_H54 zenon_H210 zenon_H4a zenon_H115 zenon_Hf3 zenon_H11f zenon_H22a zenon_Haf zenon_Hdf zenon_He2 zenon_H109 zenon_H106 zenon_H145 zenon_H1c7 zenon_H1d8 zenon_H189 zenon_H18c zenon_H160 zenon_H172 zenon_H130 zenon_H62 zenon_H102 zenon_H101 zenon_H16f zenon_H153 zenon_H2b zenon_H4f zenon_H6f zenon_H6a zenon_Hc2 zenon_H1cc zenon_H13e zenon_H10e zenon_H212 zenon_H1a6 zenon_H1a4 zenon_H1a5 zenon_H1d5 zenon_H10a zenon_H1d zenon_He4 zenon_Hdb zenon_Hd5 zenon_He8 zenon_H12b zenon_H17e zenon_H52 zenon_H1c4 zenon_H173 zenon_H18f zenon_H139 zenon_H201 zenon_H149 zenon_H7c zenon_H22 zenon_H3a zenon_H208 zenon_H74 zenon_H1ed zenon_H3f zenon_H23 zenon_H3e zenon_H94 zenon_H182 zenon_H235 zenon_H9a zenon_H95 zenon_H24 zenon_H245 zenon_H38. % 18.68/18.86 apply (zenon_or_s _ _ zenon_H22); [ zenon_intro zenon_H27 | zenon_intro zenon_H26 ]. % 18.68/18.86 exact (zenon_H23 zenon_H27). % 18.68/18.86 apply (zenon_or_s _ _ zenon_H26); [ zenon_intro zenon_H29 | zenon_intro zenon_H28 ]. % 18.68/18.86 exact (zenon_H24 zenon_H29). % 18.68/18.86 apply (zenon_or_s _ _ zenon_H28); [ zenon_intro zenon_H2a | zenon_intro zenon_H1f ]. % 18.68/18.86 apply (zenon_or_s _ _ zenon_H245); [ zenon_intro zenon_H49 | zenon_intro zenon_H246 ]. % 18.68/18.86 exact (zenon_H20b zenon_H49). % 18.68/18.86 apply (zenon_or_s _ _ zenon_H246); [ zenon_intro zenon_H29 | zenon_intro zenon_H247 ]. % 18.68/18.86 exact (zenon_H24 zenon_H29). % 18.68/18.86 apply (zenon_or_s _ _ zenon_H247); [ zenon_intro zenon_H36 | zenon_intro zenon_H1b1 ]. % 18.68/18.86 apply (zenon_or_s _ _ zenon_H128); [ zenon_intro zenon_H9d | zenon_intro zenon_H129 ]. % 18.68/18.86 apply (zenon_L413_); trivial. % 18.68/18.86 apply (zenon_or_s _ _ zenon_H129); [ zenon_intro zenon_H10d | zenon_intro zenon_H12a ]. % 18.68/18.86 exact (zenon_H10a zenon_H10d). % 18.68/18.86 apply (zenon_or_s _ _ zenon_H12a); [ zenon_intro zenon_Hf0 | zenon_intro zenon_Hd6 ]. % 18.68/18.86 apply (zenon_L530_); trivial. % 18.68/18.86 apply (zenon_L565_); trivial. % 18.68/18.86 exact (zenon_H1ad zenon_H1b1). % 18.68/18.86 exact (zenon_H38 zenon_H1f). % 18.68/18.86 (* end of lemma zenon_L566_ *) % 18.68/18.86 assert (zenon_L567_ : (((op (e0) (e0)) = (e0))\/(((op (e1) (e0)) = (e0))\/(((op (e2) (e0)) = (e0))\/((op (e3) (e0)) = (e0))))) -> (~((op (e2) (e0)) = (e0))) -> (~((op (e1) (e0)) = (e0))) -> (~((op (e0) (e0)) = (e0))) -> (~((e1) = (e3))) -> ((op (e0) (e0)) = (e3)) -> ((op (e2) (e0)) = (e1)) -> ((op (e1) (e0)) = (e2)) -> (((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 (e2) (e1)) = (e0)))\/((op (e2) (e0)) = (e1))) -> ((~((op (e2) (e3)) = (e0)))\/((op (e2) (e0)) = (e3))) -> ((~((op (e3) (e1)) = (e0)))\/((op (e3) (e0)) = (e1))) -> (((op (e0) (e0)) = (e0))\/(((op (e0) (e1)) = (e0))\/(((op (e0) (e2)) = (e0))\/((op (e0) (e3)) = (e0))))) -> (~((op (e0) (e2)) = (op (e0) (e3)))) -> (~((e1) = (e2))) -> (~((e0) = (e2))) -> (~((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 (e3) (e2)))) -> (~((op (e2) (e2)) = (e2))) -> (((op (e2) (e2)) = (e0))\/(((op (e2) (e2)) = (e1))\/(((op (e2) (e2)) = (e2))\/((op (e2) (e2)) = (e3))))) -> (~((op (e2) (e0)) = (op (e2) (e2)))) -> (~((e0) = (e1))) -> (~((op (e0) (e1)) = (op (e2) (e1)))) -> (~((e0) = (e3))) -> (~((e2) = (e3))) -> (((op (e3) (e0)) = (e1))\/(((op (e3) (e1)) = (e1))\/(((op (e3) (e2)) = (e1))\/((op (e3) (e3)) = (e1))))) -> (~((op (e1) (e3)) = (op (e3) (e3)))) -> (~((op (e1) (e3)) = (op (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 (e1) (e1)) = (e1))) -> (((op (e2) (e0)) = (e2))\/(((op (e2) (e1)) = (e2))\/(((op (e2) (e2)) = (e2))\/((op (e2) (e3)) = (e2))))) -> (((op (e0) (e1)) = (e3))\/(((op (e1) (e1)) = (e3))\/(((op (e2) (e1)) = (e3))\/((op (e3) (e1)) = (e3))))) -> (~((op (e3) (e1)) = (op (e3) (e2)))) -> (((op (e0) (e2)) = (e3))\/(((op (e1) (e2)) = (e3))\/(((op (e2) (e2)) = (e3))\/((op (e3) (e2)) = (e3))))) -> (((op (e0) (e1)) = (e0))\/(((op (e0) (e1)) = (e1))\/(((op (e0) (e1)) = (e2))\/((op (e0) (e1)) = (e3))))) -> (~((op (e0) (e1)) = (op (e1) (e1)))) -> (~((op (e1) (e1)) = (op (e2) (e1)))) -> (((op (e2) (e1)) = (e0))\/(((op (e2) (e1)) = (e1))\/(((op (e2) (e1)) = (e2))\/((op (e2) (e1)) = (e3))))) -> (~((op (e0) (e3)) = (op (e3) (e3)))) -> (((op (e0) (e2)) = (e0))\/(((op (e1) (e2)) = (e0))\/(((op (e2) (e2)) = (e0))\/((op (e3) (e2)) = (e0))))) -> (~((op (e3) (e0)) = (op (e3) (e2)))) -> (~((op (e1) (e1)) = (op (e1) (e2)))) -> (~((op (e1) (e2)) = (op (e2) (e2)))) -> (((op (e3) (e0)) = (e2))\/(((op (e3) (e1)) = (e2))\/(((op (e3) (e2)) = (e2))\/((op (e3) (e3)) = (e2))))) -> (((op (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) (e3)) = (e3))) -> (~((op (e3) (e2)) = (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 (e1) (e1)) = (op (e3) (e1)))) -> (((op (e1) (e0)) = (e2))\/(((op (e1) (e1)) = (e2))\/(((op (e1) (e2)) = (e2))\/((op (e1) (e3)) = (e2))))) -> (~((op (e0) (e0)) = (op (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) (e3)) = (e2))\/(((op (e1) (e3)) = (e2))\/(((op (e2) (e3)) = (e2))\/((op (e3) (e3)) = (e2))))) -> (((op (e2) (e0)) = (e1))\/(((op (e2) (e1)) = (e1))\/(((op (e2) (e2)) = (e1))\/((op (e2) (e3)) = (e1))))) -> (((op (e0) (e1)) = (e1))\/(((op (e1) (e1)) = (e1))\/(((op (e2) (e1)) = (e1))\/((op (e3) (e1)) = (e1))))) -> (~((op (e0) (e3)) = (op (e2) (e3)))) -> (((op (e1) (e3)) = (e0))\/(((op (e1) (e3)) = (e1))\/(((op (e1) (e3)) = (e2))\/((op (e1) (e3)) = (e3))))) -> (~((op (e2) (e1)) = (op (e3) (e1)))) -> (((op (e3) (e1)) = (e0))\/(((op (e3) (e1)) = (e1))\/(((op (e3) (e1)) = (e2))\/((op (e3) (e1)) = (e3))))) -> (((op (e2) (e3)) = (e0))\/(((op (e2) (e3)) = (e1))\/(((op (e2) (e3)) = (e2))\/((op (e2) (e3)) = (e3))))) -> (~((op (e2) (e3)) = (op (e3) (e3)))) -> (~((op (e1) (e2)) = (op (e3) (e2)))) -> (~((op (e0) (e1)) = (op (e0) (e2)))) -> (~((op (e0) (e1)) = (op (e3) (e1)))) -> (~((op (e0) (e1)) = (op (e0) (e3)))) -> (~((op (e1) (e0)) = (op (e1) (e3)))) -> (~((op (e2) (e2)) = (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 (e0) (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 (e3) (e2)) = (e0)))\/((op (e3) (e0)) = (e2))) -> ((~((op (e3) (e0)) = (e0)))\/((op (e3) (e0)) = (e0))) -> (((op (e2) (e0)) = (e0))\/(((op (e2) (e1)) = (e0))\/(((op (e2) (e2)) = (e0))\/((op (e2) (e3)) = (e0))))) -> ((~((op (e2) (e2)) = (e0)))\/((op (e2) (e0)) = (e2))) -> (((op (e3) (e0)) = (e3))\/(((op (e3) (e1)) = (e3))\/(((op (e3) (e2)) = (e3))\/((op (e3) (e3)) = (e3))))) -> (~((op (e0) (e2)) = (op (e2) (e2)))) -> ((~((op (e3) (e3)) = (e0)))\/((op (e3) (e0)) = (e3))) -> ((~((op (e0) (e3)) = (e0)))\/((op (e0) (e0)) = (e3))) -> ((~((op (e1) (e1)) = (e0)))\/((op (e1) (e0)) = (e1))) -> (((op (e3) (e2)) = (e0))\/(((op (e3) (e2)) = (e1))\/(((op (e3) (e2)) = (e2))\/((op (e3) (e2)) = (e3))))) -> (((op (e1) (e2)) = (e0))\/(((op (e1) (e2)) = (e1))\/(((op (e1) (e2)) = (e2))\/((op (e1) (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 (e2) (e0)) = (op (e3) (e0)))) -> ((~((op (e1) (e2)) = (e0)))\/((op (e1) (e0)) = (e2))) -> ((~((op (e1) (e3)) = (e0)))\/((op (e1) (e0)) = (e3))) -> (((op (e1) (e1)) = (e0))\/(((op (e1) (e1)) = (e1))\/(((op (e1) (e1)) = (e2))\/((op (e1) (e1)) = (e3))))) -> (~((op (e0) (e0)) = (op (e0) (e2)))) -> (((op (e1) (e0)) = (e1))\/(((op (e1) (e1)) = (e1))\/(((op (e1) (e2)) = (e1))\/((op (e1) (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 (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 (e2) (e0)) = (e0)))\/((op (e2) (e0)) = (e0))) -> (((op (e0) (e0)) = (e3))\/(((op (e1) (e0)) = (e3))\/(((op (e2) (e0)) = (e3))\/((op (e3) (e0)) = (e3))))) -> (((op (e0) (e2)) = (e0))\/(((op (e0) (e2)) = (e1))\/(((op (e0) (e2)) = (e2))\/((op (e0) (e2)) = (e3))))) -> (~((op (e1) (e0)) = (op (e3) (e0)))) -> (~((op (e2) (e0)) = (op (e2) (e1)))) -> ((~((op (e1) (e0)) = (e0)))\/((op (e1) (e0)) = (e0))) -> ((~((op (e0) (e2)) = (e0)))\/((op (e0) (e0)) = (e2))) -> (~((op (e3) (e0)) = (op (e3) (e1)))) -> (~((op (e1) (e1)) = (op (e1) (e3)))) -> (~((op (e2) (e0)) = (op (e2) (e3)))) -> (((op (e0) (e3)) = (e0))\/(((op (e1) (e3)) = (e0))\/(((op (e2) (e3)) = (e0))\/((op (e3) (e3)) = (e0))))) -> (~((op (e1) (e0)) = (op (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 (e1) (e1)) = (e0))) -> (~((op (e0) (e2)) = (op (e1) (e2)))) -> (~((op (e1) (e3)) = (e0))) -> (((op (e1) (e0)) = (e0))\/(((op (e1) (e1)) = (e0))\/(((op (e1) (e2)) = (e0))\/((op (e1) (e3)) = (e0))))) -> (~((op (e0) (e1)) = (e0))) -> False). % 18.68/18.86 do 0 intro. intros zenon_H3e zenon_H30 zenon_H23 zenon_H3f zenon_H95 zenon_H3a zenon_Hed zenon_H86 zenon_H235 zenon_H245 zenon_H182 zenon_H94 zenon_H1ed zenon_H74 zenon_H208 zenon_H7c zenon_H149 zenon_H201 zenon_H139 zenon_H18f zenon_H173 zenon_H1c4 zenon_H52 zenon_Ha1 zenon_H17e zenon_H9a zenon_H12b zenon_He8 zenon_Hd5 zenon_Hdb zenon_He4 zenon_H1d zenon_H10a zenon_H1d5 zenon_H1a5 zenon_H1a4 zenon_H1a6 zenon_H212 zenon_H10e zenon_H13e zenon_H1cc zenon_Hc2 zenon_H6a zenon_H6f zenon_H4f zenon_H2b zenon_H153 zenon_H16f zenon_H101 zenon_H102 zenon_H62 zenon_H130 zenon_H172 zenon_H160 zenon_H18c zenon_H189 zenon_H1d8 zenon_H1c7 zenon_H145 zenon_H106 zenon_H109 zenon_He2 zenon_Hdf zenon_Haf zenon_H22a zenon_H11f zenon_Hf3 zenon_H115 zenon_H4a zenon_H210 zenon_H54 zenon_Hd8 zenon_H6d zenon_H71 zenon_H133 zenon_H7b zenon_H39 zenon_H22d zenon_H1a7 zenon_H184 zenon_H2f zenon_H185 zenon_H165 zenon_Ha8 zenon_H1ec zenon_H204 zenon_H205 zenon_H191 zenon_H19d zenon_He7 zenon_H183 zenon_H17b zenon_H178 zenon_H179 zenon_H142 zenon_H13c zenon_H128 zenon_H136 zenon_H124 zenon_H168 zenon_H1fe zenon_H1ee zenon_H1e0 zenon_H1ba zenon_H1fa zenon_H1f0 zenon_H206 zenon_H233 zenon_H1cf zenon_H57 zenon_H5b zenon_H67 zenon_H45 zenon_H14f zenon_H1ac zenon_H24 zenon_H195 zenon_H38 zenon_H22 zenon_H20b. % 18.68/18.86 apply (zenon_or_s _ _ zenon_H185); [ zenon_intro zenon_H81 | zenon_intro zenon_Hee ]. % 18.68/18.86 apply (zenon_or_s _ _ zenon_H184); [ zenon_intro zenon_H40 | zenon_intro zenon_H44 ]. % 18.68/18.86 apply (zenon_L7_); trivial. % 18.68/18.86 apply (zenon_or_s _ _ zenon_H1ed); [ zenon_intro zenon_H1ad | zenon_intro zenon_Hac ]. % 18.68/18.86 apply (zenon_or_s _ _ zenon_H1a7); [ zenon_intro zenon_H18b | zenon_intro zenon_H148 ]. % 18.68/18.86 apply (zenon_or_s _ _ zenon_H74); [ zenon_intro zenon_H42 | zenon_intro zenon_H77 ]. % 18.68/18.86 exact (zenon_H3f zenon_H42). % 18.68/18.86 apply (zenon_or_s _ _ zenon_H77); [ zenon_intro zenon_H49 | zenon_intro zenon_H78 ]. % 18.68/18.86 exact (zenon_H20b zenon_H49). % 18.68/18.86 apply (zenon_or_s _ _ zenon_H78); [ zenon_intro zenon_H48 | zenon_intro zenon_H1e ]. % 18.68/18.86 apply (zenon_L335_); trivial. % 18.68/18.86 apply (zenon_or_s _ _ zenon_H22d); [ zenon_intro zenon_H7a | zenon_intro zenon_H22e ]. % 18.68/18.86 apply (zenon_L35_); trivial. % 18.68/18.86 apply (zenon_or_s _ _ zenon_H22e); [ zenon_intro zenon_Ha0 | zenon_intro zenon_H22f ]. % 18.68/18.86 apply (zenon_or_s _ _ zenon_H22); [ zenon_intro zenon_H27 | zenon_intro zenon_H26 ]. % 18.68/18.86 exact (zenon_H23 zenon_H27). % 18.68/18.86 apply (zenon_or_s _ _ zenon_H26); [ zenon_intro zenon_H29 | zenon_intro zenon_H28 ]. % 18.68/18.86 exact (zenon_H24 zenon_H29). % 18.68/18.86 apply (zenon_or_s _ _ zenon_H28); [ zenon_intro zenon_H2a | zenon_intro zenon_H1f ]. % 18.68/18.86 apply (zenon_or_s _ _ zenon_H245); [ zenon_intro zenon_H49 | zenon_intro zenon_H246 ]. % 18.68/18.86 exact (zenon_H20b zenon_H49). % 18.68/18.86 apply (zenon_or_s _ _ zenon_H246); [ zenon_intro zenon_H29 | zenon_intro zenon_H247 ]. % 18.68/18.86 exact (zenon_H24 zenon_H29). % 18.68/18.86 apply (zenon_or_s _ _ zenon_H247); [ zenon_intro zenon_H36 | zenon_intro zenon_H1b1 ]. % 18.68/18.86 apply (zenon_or_s _ _ zenon_H128); [ zenon_intro zenon_H9d | zenon_intro zenon_H129 ]. % 18.68/18.86 apply (zenon_L489_); trivial. % 18.68/18.86 apply (zenon_or_s _ _ zenon_H129); [ zenon_intro zenon_H10d | zenon_intro zenon_H12a ]. % 18.68/18.86 exact (zenon_H10a zenon_H10d). % 18.68/18.86 apply (zenon_or_s _ _ zenon_H12a); [ zenon_intro zenon_Hf0 | zenon_intro zenon_Hd6 ]. % 18.68/18.86 apply (zenon_or_s _ _ zenon_H1d8); [ zenon_intro zenon_H10f | zenon_intro zenon_H1d9 ]. % 18.68/18.86 apply (zenon_or_s _ _ zenon_H16f); [ zenon_intro zenon_H9e | zenon_intro zenon_H170 ]. % 18.68/18.86 apply (zenon_L492_); trivial. % 18.68/18.86 apply (zenon_or_s _ _ zenon_H170); [ zenon_intro zenon_H13f | zenon_intro zenon_H171 ]. % 18.68/18.86 apply (zenon_or_s _ _ zenon_H1d5); [ zenon_intro zenon_Hee | zenon_intro zenon_H1d6 ]. % 18.68/18.86 apply (zenon_L341_); trivial. % 18.68/18.86 apply (zenon_or_s _ _ zenon_H1d6); [ zenon_intro zenon_H1ca | zenon_intro zenon_H1d7 ]. % 18.68/18.86 apply (zenon_L191_); trivial. % 18.68/18.86 apply (zenon_or_s _ _ zenon_H1d7); [ zenon_intro zenon_H176 | zenon_intro zenon_H11d ]. % 18.68/18.86 exact (zenon_H173 zenon_H176). % 18.68/18.86 apply (zenon_or_s _ _ zenon_H172); [ zenon_intro zenon_H150 | zenon_intro zenon_H174 ]. % 18.68/18.86 apply (zenon_or_s _ _ zenon_He7); [ zenon_intro zenon_H3b | zenon_intro zenon_He9 ]. % 18.68/18.86 apply (zenon_L526_); trivial. % 18.68/18.86 apply (zenon_or_s _ _ zenon_He9); [ zenon_intro zenon_Ha6 | zenon_intro zenon_Hea ]. % 18.68/18.86 apply (zenon_L96_); trivial. % 18.68/18.86 apply (zenon_or_s _ _ zenon_Hea); [ zenon_intro zenon_Haa | zenon_intro zenon_Hdd ]. % 18.68/18.86 apply (zenon_L181_); trivial. % 18.68/18.86 apply (zenon_or_s _ _ zenon_H1a6); [ zenon_intro zenon_Ha9 | zenon_intro zenon_H1aa ]. % 18.68/18.86 apply (zenon_or_s _ _ zenon_He8); [ zenon_intro zenon_Hac | zenon_intro zenon_Heb ]. % 18.68/18.86 apply (zenon_L241_); trivial. % 18.68/18.86 apply (zenon_or_s _ _ zenon_Heb); [ zenon_intro zenon_Hae | zenon_intro zenon_Hec ]. % 18.68/18.86 apply (zenon_L363_); trivial. % 18.68/18.86 apply (zenon_or_s _ _ zenon_Hec); [ zenon_intro zenon_Hba | zenon_intro zenon_Hc4 ]. % 18.68/18.86 apply (zenon_L186_); trivial. % 18.68/18.86 apply (zenon_L527_); trivial. % 18.68/18.86 apply (zenon_or_s _ _ zenon_H1aa); [ zenon_intro zenon_H16c | zenon_intro zenon_H1ab ]. % 18.68/18.86 apply (zenon_L521_); trivial. % 18.68/18.86 apply (zenon_or_s _ _ zenon_H1ab); [ zenon_intro zenon_Haa | zenon_intro zenon_H163 ]. % 18.68/18.86 apply (zenon_L181_); trivial. % 18.68/18.86 apply (zenon_L529_); trivial. % 18.68/18.86 apply (zenon_or_s _ _ zenon_H174); [ zenon_intro zenon_H113 | zenon_intro zenon_H175 ]. % 18.68/18.86 apply (zenon_L68_); trivial. % 18.68/18.86 apply (zenon_or_s _ _ zenon_H175); [ zenon_intro zenon_H176 | zenon_intro zenon_H151 ]. % 18.68/18.86 exact (zenon_H173 zenon_H176). % 18.68/18.86 apply (zenon_L538_); trivial. % 18.68/18.86 apply (zenon_or_s _ _ zenon_H171); [ zenon_intro zenon_H16c | zenon_intro zenon_Hdc ]. % 18.68/18.86 apply (zenon_L167_); trivial. % 18.68/18.86 apply (zenon_or_s _ _ zenon_H1a5); [ zenon_intro zenon_H99 | zenon_intro zenon_H1a8 ]. % 18.68/18.86 apply (zenon_L175_); trivial. % 18.68/18.86 apply (zenon_or_s _ _ zenon_H1a8); [ zenon_intro zenon_H13f | zenon_intro zenon_H1a9 ]. % 18.68/18.86 apply (zenon_or_s _ _ zenon_H1d5); [ zenon_intro zenon_Hee | zenon_intro zenon_H1d6 ]. % 18.68/18.86 apply (zenon_L58_); trivial. % 18.68/18.86 apply (zenon_or_s _ _ zenon_H1d6); [ zenon_intro zenon_H1ca | zenon_intro zenon_H1d7 ]. % 18.68/18.86 apply (zenon_L543_); trivial. % 18.68/18.86 apply (zenon_or_s _ _ zenon_H1d7); [ zenon_intro zenon_H176 | zenon_intro zenon_H11d ]. % 18.68/18.86 exact (zenon_H173 zenon_H176). % 18.68/18.86 apply (zenon_or_s _ _ zenon_H172); [ zenon_intro zenon_H150 | zenon_intro zenon_H174 ]. % 18.68/18.86 apply (zenon_L544_); trivial. % 18.68/18.86 apply (zenon_or_s _ _ zenon_H174); [ zenon_intro zenon_H113 | zenon_intro zenon_H175 ]. % 18.68/18.86 apply (zenon_L542_); trivial. % 18.68/18.86 apply (zenon_or_s _ _ zenon_H175); [ zenon_intro zenon_H176 | zenon_intro zenon_H151 ]. % 18.68/18.86 exact (zenon_H173 zenon_H176). % 18.68/18.86 apply (zenon_L538_); trivial. % 18.68/18.86 apply (zenon_or_s _ _ zenon_H1a9); [ zenon_intro zenon_Ha6 | zenon_intro zenon_H161 ]. % 18.68/18.86 apply (zenon_L547_); trivial. % 18.68/18.86 apply (zenon_or_s _ _ zenon_H1d5); [ zenon_intro zenon_Hee | zenon_intro zenon_H1d6 ]. % 18.68/18.86 apply (zenon_L341_); trivial. % 18.68/18.86 apply (zenon_or_s _ _ zenon_H1d6); [ zenon_intro zenon_H1ca | zenon_intro zenon_H1d7 ]. % 18.68/18.86 apply (zenon_L548_); trivial. % 18.68/18.86 apply (zenon_or_s _ _ zenon_H1d7); [ zenon_intro zenon_H176 | zenon_intro zenon_H11d ]. % 18.68/18.86 exact (zenon_H173 zenon_H176). % 18.68/18.86 apply (zenon_or_s _ _ zenon_H172); [ zenon_intro zenon_H150 | zenon_intro zenon_H174 ]. % 18.68/18.86 apply (zenon_or_s _ _ zenon_He7); [ zenon_intro zenon_H3b | zenon_intro zenon_He9 ]. % 18.68/18.86 apply (zenon_L525_); trivial. % 18.68/18.86 apply (zenon_or_s _ _ zenon_He9); [ zenon_intro zenon_Ha6 | zenon_intro zenon_Hea ]. % 18.68/18.86 apply (zenon_L547_); trivial. % 18.68/18.86 apply (zenon_or_s _ _ zenon_Hea); [ zenon_intro zenon_Haa | zenon_intro zenon_Hdd ]. % 18.68/18.86 apply (zenon_L181_); trivial. % 18.68/18.86 apply (zenon_L52_); trivial. % 18.68/18.86 apply (zenon_or_s _ _ zenon_H174); [ zenon_intro zenon_H113 | zenon_intro zenon_H175 ]. % 18.68/18.86 apply (zenon_L68_); trivial. % 18.68/18.86 apply (zenon_or_s _ _ zenon_H175); [ zenon_intro zenon_H176 | zenon_intro zenon_H151 ]. % 18.68/18.86 exact (zenon_H173 zenon_H176). % 18.68/18.86 apply (zenon_L549_); trivial. % 18.68/18.86 apply (zenon_or_s _ _ zenon_H1d9); [ zenon_intro zenon_H110 | zenon_intro zenon_H1da ]. % 18.68/18.86 apply (zenon_or_s _ _ zenon_H16f); [ zenon_intro zenon_H9e | zenon_intro zenon_H170 ]. % 18.68/18.86 apply (zenon_L550_); trivial. % 18.68/18.86 apply (zenon_or_s _ _ zenon_H170); [ zenon_intro zenon_H13f | zenon_intro zenon_H171 ]. % 18.68/18.86 apply (zenon_L166_); trivial. % 18.68/18.86 apply (zenon_or_s _ _ zenon_H171); [ zenon_intro zenon_H16c | zenon_intro zenon_Hdc ]. % 18.68/18.86 apply (zenon_L521_); trivial. % 18.68/18.86 apply (zenon_or_s _ _ zenon_H1a5); [ zenon_intro zenon_H99 | zenon_intro zenon_H1a8 ]. % 18.68/18.86 apply (zenon_L552_); trivial. % 18.68/18.86 apply (zenon_or_s _ _ zenon_H1a8); [ zenon_intro zenon_H13f | zenon_intro zenon_H1a9 ]. % 18.68/18.86 apply (zenon_L166_); trivial. % 18.68/18.86 apply (zenon_or_s _ _ zenon_H1a9); [ zenon_intro zenon_Ha6 | zenon_intro zenon_H161 ]. % 18.68/18.86 apply (zenon_L547_); trivial. % 18.68/18.86 apply (zenon_or_s _ _ zenon_H1d5); [ zenon_intro zenon_Hee | zenon_intro zenon_H1d6 ]. % 18.68/18.86 apply (zenon_L58_); trivial. % 18.68/18.86 apply (zenon_or_s _ _ zenon_H1d6); [ zenon_intro zenon_H1ca | zenon_intro zenon_H1d7 ]. % 18.68/18.86 apply (zenon_L548_); trivial. % 18.68/18.86 apply (zenon_or_s _ _ zenon_H1d7); [ zenon_intro zenon_H176 | zenon_intro zenon_H11d ]. % 18.68/18.86 exact (zenon_H173 zenon_H176). % 18.68/18.86 apply (zenon_or_s _ _ zenon_H172); [ zenon_intro zenon_H150 | zenon_intro zenon_H174 ]. % 18.68/18.86 apply (zenon_or_s _ _ zenon_He7); [ zenon_intro zenon_H3b | zenon_intro zenon_He9 ]. % 18.68/18.86 apply (zenon_L554_); trivial. % 18.68/18.86 apply (zenon_or_s _ _ zenon_He9); [ zenon_intro zenon_Ha6 | zenon_intro zenon_Hea ]. % 18.68/18.86 apply (zenon_or_s _ _ zenon_H1a6); [ zenon_intro zenon_Ha9 | zenon_intro zenon_H1aa ]. % 18.68/18.86 apply (zenon_or_s _ _ zenon_He8); [ zenon_intro zenon_Hac | zenon_intro zenon_Heb ]. % 18.68/18.86 apply (zenon_L241_); trivial. % 18.68/18.86 apply (zenon_or_s _ _ zenon_Heb); [ zenon_intro zenon_Hae | zenon_intro zenon_Hec ]. % 18.68/18.86 apply (zenon_L555_); trivial. % 18.68/18.86 apply (zenon_or_s _ _ zenon_Hec); [ zenon_intro zenon_Hba | zenon_intro zenon_Hc4 ]. % 18.68/18.86 apply (zenon_L186_); trivial. % 18.68/18.86 apply (zenon_or_s _ _ zenon_H153); [ zenon_intro zenon_H148 | zenon_intro zenon_H154 ]. % 18.68/18.86 apply (zenon_L100_); trivial. % 18.68/18.86 apply (zenon_or_s _ _ zenon_H154); [ zenon_intro zenon_H14d | zenon_intro zenon_H155 ]. % 18.68/18.86 apply (zenon_L545_); trivial. % 18.68/18.86 apply (zenon_or_s _ _ zenon_H155); [ zenon_intro zenon_H151 | zenon_intro zenon_Hf6 ]. % 18.68/18.86 apply (zenon_L533_); trivial. % 18.68/18.86 apply (zenon_L404_); trivial. % 18.68/18.86 apply (zenon_or_s _ _ zenon_H1aa); [ zenon_intro zenon_H16c | zenon_intro zenon_H1ab ]. % 18.68/18.86 apply (zenon_L521_); trivial. % 18.68/18.86 apply (zenon_or_s _ _ zenon_H1ab); [ zenon_intro zenon_Haa | zenon_intro zenon_H163 ]. % 18.68/18.86 apply (zenon_L181_); trivial. % 18.68/18.86 apply (zenon_L169_); trivial. % 18.68/18.86 apply (zenon_or_s _ _ zenon_Hea); [ zenon_intro zenon_Haa | zenon_intro zenon_Hdd ]. % 18.68/18.86 apply (zenon_L181_); trivial. % 18.68/18.86 apply (zenon_L52_); trivial. % 18.68/18.86 apply (zenon_or_s _ _ zenon_H174); [ zenon_intro zenon_H113 | zenon_intro zenon_H175 ]. % 18.68/18.86 apply (zenon_L68_); trivial. % 18.68/18.86 apply (zenon_or_s _ _ zenon_H175); [ zenon_intro zenon_H176 | zenon_intro zenon_H151 ]. % 18.68/18.86 exact (zenon_H173 zenon_H176). % 18.68/18.86 apply (zenon_L549_); trivial. % 18.68/18.86 apply (zenon_or_s _ _ zenon_H1da); [ zenon_intro zenon_H1ca | zenon_intro zenon_H14d ]. % 18.68/18.86 apply (zenon_or_s _ _ zenon_H16f); [ zenon_intro zenon_H9e | zenon_intro zenon_H170 ]. % 18.68/18.86 apply (zenon_L492_); trivial. % 18.68/18.86 apply (zenon_or_s _ _ zenon_H170); [ zenon_intro zenon_H13f | zenon_intro zenon_H171 ]. % 18.68/18.86 apply (zenon_L543_); trivial. % 18.68/18.86 apply (zenon_or_s _ _ zenon_H171); [ zenon_intro zenon_H16c | zenon_intro zenon_Hdc ]. % 18.68/18.86 apply (zenon_L167_); trivial. % 18.68/18.86 apply (zenon_or_s _ _ zenon_H1a5); [ zenon_intro zenon_H99 | zenon_intro zenon_H1a8 ]. % 18.68/18.86 apply (zenon_L403_); trivial. % 18.68/18.86 apply (zenon_or_s _ _ zenon_H1a8); [ zenon_intro zenon_H13f | zenon_intro zenon_H1a9 ]. % 18.68/18.86 apply (zenon_or_s _ _ zenon_H172); [ zenon_intro zenon_H150 | zenon_intro zenon_H174 ]. % 18.68/18.86 apply (zenon_L544_); trivial. % 18.68/18.86 apply (zenon_or_s _ _ zenon_H174); [ zenon_intro zenon_H113 | zenon_intro zenon_H175 ]. % 18.68/18.86 apply (zenon_L68_); trivial. % 18.68/18.86 apply (zenon_or_s _ _ zenon_H175); [ zenon_intro zenon_H176 | zenon_intro zenon_H151 ]. % 18.68/18.86 exact (zenon_H173 zenon_H176). % 18.68/18.86 apply (zenon_L540_); trivial. % 18.68/18.86 apply (zenon_or_s _ _ zenon_H1a9); [ zenon_intro zenon_Ha6 | zenon_intro zenon_H161 ]. % 18.68/18.86 apply (zenon_L207_); trivial. % 18.68/18.86 apply (zenon_L548_); trivial. % 18.68/18.86 apply (zenon_L546_); trivial. % 18.68/18.86 apply (zenon_or_s _ _ zenon_H139); [ zenon_intro zenon_H122 | zenon_intro zenon_H13a ]. % 18.68/18.86 apply (zenon_L406_); trivial. % 18.68/18.86 apply (zenon_or_s _ _ zenon_H13a); [ zenon_intro zenon_Hf0 | zenon_intro zenon_H13b ]. % 18.68/18.86 apply (zenon_L78_); trivial. % 18.68/18.86 apply (zenon_or_s _ _ zenon_H13b); [ zenon_intro zenon_Hf1 | zenon_intro zenon_Hba ]. % 18.68/18.86 apply (zenon_L365_); trivial. % 18.68/18.86 apply (zenon_or_s _ _ zenon_H1d5); [ zenon_intro zenon_Hee | zenon_intro zenon_H1d6 ]. % 18.68/18.86 apply (zenon_L341_); trivial. % 18.68/18.86 apply (zenon_or_s _ _ zenon_H1d6); [ zenon_intro zenon_H1ca | zenon_intro zenon_H1d7 ]. % 18.68/18.86 apply (zenon_L557_); trivial. % 18.68/18.86 apply (zenon_or_s _ _ zenon_H1d7); [ zenon_intro zenon_H176 | zenon_intro zenon_H11d ]. % 18.68/18.86 exact (zenon_H173 zenon_H176). % 18.68/18.86 apply (zenon_L559_); trivial. % 18.68/18.86 exact (zenon_H1ad zenon_H1b1). % 18.68/18.86 exact (zenon_H38 zenon_H1f). % 18.68/18.86 apply (zenon_or_s _ _ zenon_H22f); [ zenon_intro zenon_H122 | zenon_intro zenon_Hc3 ]. % 18.68/18.86 apply (zenon_L566_); trivial. % 18.68/18.86 apply (zenon_L427_); trivial. % 18.68/18.86 apply (zenon_L423_); trivial. % 18.68/18.86 apply (zenon_L241_); trivial. % 18.68/18.86 apply (zenon_L58_); trivial. % 18.68/18.86 (* end of lemma zenon_L567_ *) % 18.68/18.86 assert (zenon_L568_ : (((op (e0) (e0)) = (e0))\/(((op (e1) (e0)) = (e0))\/(((op (e2) (e0)) = (e0))\/((op (e3) (e0)) = (e0))))) -> (~((op (e1) (e0)) = (e0))) -> (~((op (e0) (e0)) = (e0))) -> (((op (e0) (e1)) = (e0))\/(((op (e1) (e1)) = (e0))\/(((op (e2) (e1)) = (e0))\/((op (e3) (e1)) = (e0))))) -> (((op (e0) (e0)) = (e1))\/(((op (e1) (e0)) = (e1))\/(((op (e2) (e0)) = (e1))\/((op (e3) (e0)) = (e1))))) -> ((~((op (e2) (e1)) = (e0)))\/((op (e2) (e0)) = (e1))) -> ((~((op (e3) (e1)) = (e0)))\/((op (e3) (e0)) = (e1))) -> (((op (e0) (e0)) = (e0))\/(((op (e0) (e1)) = (e0))\/(((op (e0) (e2)) = (e0))\/((op (e0) (e3)) = (e0))))) -> (~((op (e0) (e2)) = (op (e0) (e3)))) -> (~((e1) = (e3))) -> ((op (e0) (e0)) = (e3)) -> (~((e1) = (e2))) -> (~((e0) = (e2))) -> (~((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 (e3) (e2)))) -> (~((op (e2) (e2)) = (e2))) -> (((op (e2) (e2)) = (e0))\/(((op (e2) (e2)) = (e1))\/(((op (e2) (e2)) = (e2))\/((op (e2) (e2)) = (e3))))) -> (~((op (e2) (e0)) = (op (e2) (e2)))) -> (~((e0) = (e1))) -> (~((op (e0) (e1)) = (op (e2) (e1)))) -> (~((e0) = (e3))) -> (~((e2) = (e3))) -> (((op (e3) (e0)) = (e1))\/(((op (e3) (e1)) = (e1))\/(((op (e3) (e2)) = (e1))\/((op (e3) (e3)) = (e1))))) -> (~((op (e1) (e3)) = (op (e3) (e3)))) -> (~((op (e1) (e3)) = (op (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 (e1) (e1)) = (e1))) -> (((op (e2) (e0)) = (e2))\/(((op (e2) (e1)) = (e2))\/(((op (e2) (e2)) = (e2))\/((op (e2) (e3)) = (e2))))) -> (((op (e0) (e1)) = (e3))\/(((op (e1) (e1)) = (e3))\/(((op (e2) (e1)) = (e3))\/((op (e3) (e1)) = (e3))))) -> (~((op (e3) (e1)) = (op (e3) (e2)))) -> (((op (e0) (e2)) = (e3))\/(((op (e1) (e2)) = (e3))\/(((op (e2) (e2)) = (e3))\/((op (e3) (e2)) = (e3))))) -> (((op (e0) (e1)) = (e0))\/(((op (e0) (e1)) = (e1))\/(((op (e0) (e1)) = (e2))\/((op (e0) (e1)) = (e3))))) -> (~((op (e0) (e1)) = (op (e1) (e1)))) -> (~((op (e1) (e1)) = (op (e2) (e1)))) -> (((op (e2) (e1)) = (e0))\/(((op (e2) (e1)) = (e1))\/(((op (e2) (e1)) = (e2))\/((op (e2) (e1)) = (e3))))) -> (~((op (e0) (e3)) = (op (e3) (e3)))) -> (((op (e0) (e2)) = (e0))\/(((op (e1) (e2)) = (e0))\/(((op (e2) (e2)) = (e0))\/((op (e3) (e2)) = (e0))))) -> (~((op (e3) (e0)) = (op (e3) (e2)))) -> (~((op (e1) (e1)) = (op (e1) (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 (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) (e1)) = (op (e3) (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) (e0)) = (e2))\/(((op (e1) (e1)) = (e2))\/(((op (e1) (e2)) = (e2))\/((op (e1) (e3)) = (e2))))) -> (~((op (e0) (e0)) = (op (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) (e3)) = (e2))\/(((op (e1) (e3)) = (e2))\/(((op (e2) (e3)) = (e2))\/((op (e3) (e3)) = (e2))))) -> (((op (e2) (e0)) = (e1))\/(((op (e2) (e1)) = (e1))\/(((op (e2) (e2)) = (e1))\/((op (e2) (e3)) = (e1))))) -> (((op (e0) (e1)) = (e1))\/(((op (e1) (e1)) = (e1))\/(((op (e2) (e1)) = (e1))\/((op (e3) (e1)) = (e1))))) -> (~((op (e0) (e3)) = (op (e2) (e3)))) -> (((op (e1) (e3)) = (e0))\/(((op (e1) (e3)) = (e1))\/(((op (e1) (e3)) = (e2))\/((op (e1) (e3)) = (e3))))) -> (~((op (e2) (e1)) = (op (e3) (e1)))) -> (((op (e3) (e1)) = (e0))\/(((op (e3) (e1)) = (e1))\/(((op (e3) (e1)) = (e2))\/((op (e3) (e1)) = (e3))))) -> (((op (e2) (e3)) = (e0))\/(((op (e2) (e3)) = (e1))\/(((op (e2) (e3)) = (e2))\/((op (e2) (e3)) = (e3))))) -> (~((op (e2) (e3)) = (op (e3) (e3)))) -> (~((op (e1) (e2)) = (op (e3) (e2)))) -> (~((op (e0) (e1)) = (op (e0) (e2)))) -> (~((op (e0) (e1)) = (op (e3) (e1)))) -> (~((op (e0) (e1)) = (op (e0) (e3)))) -> (~((op (e1) (e0)) = (op (e1) (e3)))) -> (~((op (e2) (e2)) = (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 (e0) (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)) = (e0))) -> ((~((op (e3) (e2)) = (e0)))\/((op (e3) (e0)) = (e2))) -> ((~((op (e3) (e0)) = (e0)))\/((op (e3) (e0)) = (e0))) -> ((~((op (e2) (e2)) = (e0)))\/((op (e2) (e0)) = (e2))) -> (((op (e3) (e0)) = (e3))\/(((op (e3) (e1)) = (e3))\/(((op (e3) (e2)) = (e3))\/((op (e3) (e3)) = (e3))))) -> (~((op (e0) (e2)) = (op (e2) (e2)))) -> ((~((op (e3) (e3)) = (e0)))\/((op (e3) (e0)) = (e3))) -> ((~((op (e0) (e3)) = (e0)))\/((op (e0) (e0)) = (e3))) -> ((~((op (e1) (e1)) = (e0)))\/((op (e1) (e0)) = (e1))) -> (((op (e3) (e2)) = (e0))\/(((op (e3) (e2)) = (e1))\/(((op (e3) (e2)) = (e2))\/((op (e3) (e2)) = (e3))))) -> (~((op (e0) (e2)) = (op (e1) (e2)))) -> (((op (e1) (e2)) = (e0))\/(((op (e1) (e2)) = (e1))\/(((op (e1) (e2)) = (e2))\/((op (e1) (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 (e2) (e0)) = (op (e3) (e0)))) -> ((~((op (e1) (e2)) = (e0)))\/((op (e1) (e0)) = (e2))) -> ((~((op (e1) (e3)) = (e0)))\/((op (e1) (e0)) = (e3))) -> (((op (e1) (e1)) = (e0))\/(((op (e1) (e1)) = (e1))\/(((op (e1) (e1)) = (e2))\/((op (e1) (e1)) = (e3))))) -> (~((op (e0) (e0)) = (op (e0) (e2)))) -> (((op (e1) (e0)) = (e1))\/(((op (e1) (e1)) = (e1))\/(((op (e1) (e2)) = (e1))\/((op (e1) (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 (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 (e2) (e0)) = (e0)))\/((op (e2) (e0)) = (e0))) -> (((op (e0) (e0)) = (e3))\/(((op (e1) (e0)) = (e3))\/(((op (e2) (e0)) = (e3))\/((op (e3) (e0)) = (e3))))) -> (((op (e0) (e2)) = (e0))\/(((op (e0) (e2)) = (e1))\/(((op (e0) (e2)) = (e2))\/((op (e0) (e2)) = (e3))))) -> (~((op (e1) (e0)) = (op (e3) (e0)))) -> (~((op (e2) (e0)) = (op (e2) (e1)))) -> ((~((op (e1) (e0)) = (e0)))\/((op (e1) (e0)) = (e0))) -> ((~((op (e0) (e2)) = (e0)))\/((op (e0) (e0)) = (e2))) -> (~((op (e3) (e0)) = (op (e3) (e1)))) -> (~((op (e1) (e1)) = (op (e1) (e3)))) -> (~((op (e2) (e0)) = (op (e2) (e3)))) -> (((op (e0) (e3)) = (e0))\/(((op (e1) (e3)) = (e0))\/(((op (e2) (e3)) = (e0))\/((op (e3) (e3)) = (e0))))) -> (~((op (e1) (e0)) = (op (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 (e1) (e0)) = (e0))\/(((op (e1) (e1)) = (e0))\/(((op (e1) (e2)) = (e0))\/((op (e1) (e3)) = (e0))))) -> (~((op (e1) (e2)) = (op (e2) (e2)))) -> (((op (e2) (e0)) = (e0))\/(((op (e2) (e1)) = (e0))\/(((op (e2) (e2)) = (e0))\/((op (e2) (e3)) = (e0))))) -> (~((op (e1) (e1)) = (e0))) -> ((op (e1) (e0)) = (e2)) -> ((~((op (e2) (e3)) = (e0)))\/((op (e2) (e0)) = (e3))) -> False). % 18.68/18.86 do 0 intro. intros zenon_H3e zenon_H23 zenon_H3f zenon_H245 zenon_H235 zenon_H182 zenon_H1ed zenon_H74 zenon_H208 zenon_H95 zenon_H3a zenon_H7c zenon_H149 zenon_H201 zenon_H139 zenon_H18f zenon_H173 zenon_H1c4 zenon_H52 zenon_Ha1 zenon_H17e zenon_H9a zenon_H12b zenon_He8 zenon_Hd5 zenon_Hdb zenon_He4 zenon_H1d zenon_H10a zenon_H1d5 zenon_H1a5 zenon_H1a4 zenon_H1a6 zenon_H212 zenon_H10e zenon_H13e zenon_H1cc zenon_Hc2 zenon_H6a zenon_H6f zenon_H4f zenon_H153 zenon_H16f zenon_H101 zenon_H102 zenon_H62 zenon_H130 zenon_H172 zenon_H160 zenon_H18c zenon_H189 zenon_H1d8 zenon_H1c7 zenon_H145 zenon_H106 zenon_H109 zenon_He2 zenon_Hdf zenon_Haf zenon_H22a zenon_H11f zenon_Hf3 zenon_H115 zenon_H4a zenon_H210 zenon_H54 zenon_Hd8 zenon_H6d zenon_H71 zenon_H133 zenon_H7b zenon_H39 zenon_H22d zenon_H20b zenon_H1a7 zenon_H184 zenon_H185 zenon_H165 zenon_Ha8 zenon_H1ec zenon_H204 zenon_H205 zenon_H191 zenon_H195 zenon_H19d zenon_He7 zenon_H183 zenon_H17b zenon_H178 zenon_H179 zenon_H142 zenon_H13c zenon_H128 zenon_H136 zenon_H124 zenon_H168 zenon_H1fe zenon_H1ee zenon_H1e0 zenon_H1ba zenon_H1fa zenon_H1f0 zenon_H206 zenon_H233 zenon_H1cf zenon_H57 zenon_H5b zenon_H67 zenon_H45 zenon_H14f zenon_H1ac zenon_H22 zenon_H2b zenon_H2f zenon_H24 zenon_H86 zenon_H94. % 18.68/18.86 apply (zenon_or_s _ _ zenon_H179); [ zenon_intro zenon_H38 | zenon_intro zenon_H9e ]. % 18.68/18.86 apply (zenon_or_s _ _ zenon_H1ee); [ zenon_intro zenon_H30 | zenon_intro zenon_H34 ]. % 18.68/18.86 apply (zenon_or_s _ _ zenon_H182); [ zenon_intro zenon_H31 | zenon_intro zenon_Hed ]. % 18.68/18.86 apply (zenon_or_s _ _ zenon_H184); [ zenon_intro zenon_H40 | zenon_intro zenon_H44 ]. % 18.68/18.86 apply (zenon_L7_); trivial. % 18.68/18.86 apply (zenon_or_s _ _ zenon_H235); [ zenon_intro zenon_H7a | zenon_intro zenon_H236 ]. % 18.68/18.86 apply (zenon_L172_); trivial. % 18.68/18.86 apply (zenon_or_s _ _ zenon_H236); [ zenon_intro zenon_H9d | zenon_intro zenon_H237 ]. % 18.68/18.86 apply (zenon_L489_); trivial. % 18.68/18.86 apply (zenon_or_s _ _ zenon_H237); [ zenon_intro zenon_Hed | zenon_intro zenon_Hac ]. % 18.68/18.86 apply (zenon_L567_); trivial. % 18.68/18.86 apply (zenon_L41_); trivial. % 18.68/18.86 apply (zenon_L567_); trivial. % 18.68/18.86 apply (zenon_L494_); trivial. % 18.68/18.86 apply (zenon_L550_); trivial. % 18.68/18.86 (* end of lemma zenon_L568_ *) % 18.68/18.86 assert (zenon_L569_ : (((op (e2) (e1)) = (e0))\/(((op (e2) (e1)) = (e1))\/(((op (e2) (e1)) = (e2))\/((op (e2) (e1)) = (e3))))) -> (~((op (e2) (e1)) = (e0))) -> ((op (e0) (e1)) = (e1)) -> (~((op (e0) (e1)) = (op (e2) (e1)))) -> ((op (e2) (e0)) = (e2)) -> (~((op (e2) (e0)) = (op (e2) (e1)))) -> ((op (e3) (e1)) = (e0)) -> ((op (e1) (e1)) = (e2)) -> False). % 18.68/18.86 do 0 intro. intros zenon_H1cc zenon_H31 zenon_Ha0 zenon_H17e zenon_Hee zenon_H1f0 zenon_H1b1 zenon_H110. % 18.68/18.86 apply (zenon_or_s _ _ zenon_H1cc); [ zenon_intro zenon_H36 | zenon_intro zenon_H1cd ]. % 18.68/18.86 exact (zenon_H31 zenon_H36). % 18.68/18.86 apply (zenon_or_s _ _ zenon_H1cd); [ zenon_intro zenon_Ha5 | zenon_intro zenon_H1ce ]. % 18.68/18.86 apply (zenon_L357_); trivial. % 18.68/18.86 apply (zenon_or_s _ _ zenon_H1ce); [ zenon_intro zenon_H1ca | zenon_intro zenon_Ha6 ]. % 18.68/18.86 apply (zenon_L277_); trivial. % 18.68/18.86 apply (zenon_L509_); trivial. % 18.68/18.86 (* end of lemma zenon_L569_ *) % 18.68/18.86 assert (zenon_L570_ : (((op (e0) (e0)) = (e1))\/(((op (e1) (e0)) = (e1))\/(((op (e2) (e0)) = (e1))\/((op (e3) (e0)) = (e1))))) -> ((~((op (e0) (e3)) = (e0)))\/((op (e0) (e0)) = (e3))) -> ((~((op (e1) (e1)) = (e0)))\/((op (e1) (e0)) = (e1))) -> (~((e1) = (e2))) -> ((~((op (e2) (e3)) = (e0)))\/((op (e2) (e0)) = (e3))) -> (((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))))) -> (((op (e0) (e2)) = (e3))\/(((op (e1) (e2)) = (e3))\/(((op (e2) (e2)) = (e3))\/((op (e3) (e2)) = (e3))))) -> (~((op (e3) (e1)) = (op (e3) (e2)))) -> ((~((op (e3) (e2)) = (e0)))\/((op (e3) (e0)) = (e2))) -> (~((op (e2) (e2)) = (op (e3) (e2)))) -> (((op (e3) (e2)) = (e0))\/(((op (e3) (e2)) = (e1))\/(((op (e3) (e2)) = (e2))\/((op (e3) (e2)) = (e3))))) -> (~((op (e0) (e2)) = (op (e1) (e2)))) -> (((op (e1) (e2)) = (e0))\/(((op (e1) (e2)) = (e1))\/(((op (e1) (e2)) = (e2))\/((op (e1) (e2)) = (e3))))) -> (~((e0) = (e3))) -> (~((op (e1) (e1)) = (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) (e3)) = (e0))\/(((op (e2) (e3)) = (e1))\/(((op (e2) (e3)) = (e2))\/((op (e2) (e3)) = (e3))))) -> (~((op (e0) (e3)) = (op (e1) (e3)))) -> (~((op (e0) (e1)) = (op (e1) (e1)))) -> (~((e0) = (e1))) -> (~((op (e0) (e2)) = (op (e2) (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) (e3)) = (e0))\/(((op (e1) (e3)) = (e1))\/(((op (e1) (e3)) = (e2))\/((op (e1) (e3)) = (e3))))) -> (~((op (e1) (e3)) = (op (e2) (e3)))) -> (~((op (e1) (e0)) = (op (e1) (e3)))) -> (~((op (e1) (e3)) = (op (e3) (e3)))) -> (~((op (e0) (e3)) = (op (e2) (e3)))) -> (((op (e0) (e3)) = (e0))\/(((op (e0) (e3)) = (e1))\/(((op (e0) (e3)) = (e2))\/((op (e0) (e3)) = (e3))))) -> (~((op (e2) (e1)) = (op (e3) (e1)))) -> (((op (e2) (e0)) = (e3))\/(((op (e2) (e1)) = (e3))\/(((op (e2) (e2)) = (e3))\/((op (e2) (e3)) = (e3))))) -> (((op (e2) (e0)) = (e1))\/(((op (e2) (e1)) = (e1))\/(((op (e2) (e2)) = (e1))\/((op (e2) (e3)) = (e1))))) -> (~((op (e2) (e3)) = (op (e3) (e3)))) -> (~((op (e3) (e3)) = (e3))) -> (((op (e3) (e3)) = (e0))\/(((op (e3) (e3)) = (e1))\/(((op (e3) (e3)) = (e2))\/((op (e3) (e3)) = (e3))))) -> (~((op (e1) (e2)) = (op (e2) (e2)))) -> (((op (e0) (e1)) = (e1))\/(((op (e1) (e1)) = (e1))\/(((op (e2) (e1)) = (e1))\/((op (e3) (e1)) = (e1))))) -> (~((op (e0) (e0)) = (op (e0) (e3)))) -> ((~((op (e2) (e2)) = (e0)))\/((op (e2) (e0)) = (e2))) -> ((~((op (e3) (e0)) = (e0)))\/((op (e3) (e0)) = (e0))) -> (((op (e0) (e0)) = (e2))\/(((op (e0) (e1)) = (e2))\/(((op (e0) (e2)) = (e2))\/((op (e0) (e3)) = (e2))))) -> (~((op (e2) (e0)) = (op (e3) (e0)))) -> (~((op (e0) (e1)) = (op (e2) (e1)))) -> ((~((op (e1) (e2)) = (e0)))\/((op (e1) (e0)) = (e2))) -> ((~((op (e1) (e3)) = (e0)))\/((op (e1) (e0)) = (e3))) -> (((op (e1) (e1)) = (e0))\/(((op (e1) (e1)) = (e1))\/(((op (e1) (e1)) = (e2))\/((op (e1) (e1)) = (e3))))) -> (~((op (e1) (e1)) = (op (e2) (e1)))) -> (~((op (e0) (e0)) = (op (e0) (e2)))) -> (((op (e0) (e2)) = (e1))\/(((op (e1) (e2)) = (e1))\/(((op (e2) (e2)) = (e1))\/((op (e3) (e2)) = (e1))))) -> (((op (e1) (e0)) = (e1))\/(((op (e1) (e1)) = (e1))\/(((op (e1) (e2)) = (e1))\/((op (e1) (e3)) = (e1))))) -> (((op (e0) (e3)) = (e3))\/(((op (e1) (e3)) = (e3))\/(((op (e2) (e3)) = (e3))\/((op (e3) (e3)) = (e3))))) -> (~((op (e3) (e1)) = (op (e3) (e3)))) -> (((op (e0) (e3)) = (e1))\/(((op (e1) (e3)) = (e1))\/(((op (e2) (e3)) = (e1))\/((op (e3) (e3)) = (e1))))) -> (~((e2) = (e3))) -> (~((op (e1) (e2)) = (op (e1) (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 (e2) (e2)) = (e2))) -> (((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) (e1)) = (op (e3) (e1)))) -> (((op (e3) (e0)) = (e3))\/(((op (e3) (e1)) = (e3))\/(((op (e3) (e2)) = (e3))\/((op (e3) (e3)) = (e3))))) -> (~((e0) = (e2))) -> (~((op (e0) (e2)) = (op (e3) (e2)))) -> (((op (e3) (e0)) = (e2))\/(((op (e3) (e1)) = (e2))\/(((op (e3) (e2)) = (e2))\/((op (e3) (e3)) = (e2))))) -> (~((op (e0) (e0)) = (op (e2) (e0)))) -> ((~((op (e2) (e1)) = (e0)))\/((op (e2) (e0)) = (e1))) -> (((op (e0) (e0)) = (e2))\/(((op (e1) (e0)) = (e2))\/(((op (e2) (e0)) = (e2))\/((op (e3) (e0)) = (e2))))) -> ((~((op (e2) (e0)) = (e0)))\/((op (e2) (e0)) = (e0))) -> (((op (e0) (e0)) = (e3))\/(((op (e1) (e0)) = (e3))\/(((op (e2) (e0)) = (e3))\/((op (e3) (e0)) = (e3))))) -> (((op (e3) (e0)) = (e0))\/(((op (e3) (e1)) = (e0))\/(((op (e3) (e2)) = (e0))\/((op (e3) (e3)) = (e0))))) -> (~((op (e2) (e1)) = (op (e2) (e3)))) -> (((op (e2) (e2)) = (e0))\/(((op (e2) (e2)) = (e1))\/(((op (e2) (e2)) = (e2))\/((op (e2) (e2)) = (e3))))) -> (((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 (e3) (e0)) = (op (e3) (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))))) -> ((~((op (e3) (e3)) = (e0)))\/((op (e3) (e0)) = (e3))) -> ((~((op (e3) (e1)) = (e0)))\/((op (e3) (e0)) = (e1))) -> (~((op (e0) (e0)) = (e0))) -> (((op (e1) (e0)) = (e0))\/(((op (e1) (e1)) = (e0))\/(((op (e1) (e2)) = (e0))\/((op (e1) (e3)) = (e0))))) -> (~((op (e1) (e0)) = (op (e1) (e1)))) -> (((op (e0) (e2)) = (e0))\/(((op (e1) (e2)) = (e0))\/(((op (e2) (e2)) = (e0))\/((op (e3) (e2)) = (e0))))) -> (~((op (e0) (e1)) = (op (e0) (e3)))) -> (~((op (e1) (e1)) = (op (e1) (e3)))) -> (~((op (e2) (e0)) = (op (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) (e0)) = (op (e2) (e2)))) -> (~((op (e1) (e1)) = (op (e1) (e2)))) -> (~((op (e0) (e1)) = (op (e0) (e2)))) -> (~((op (e3) (e0)) = (op (e3) (e3)))) -> (~((op (e2) (e2)) = (op (e2) (e3)))) -> (~((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)) = (e0))\/(((op (e0) (e1)) = (e0))\/(((op (e0) (e2)) = (e0))\/((op (e0) (e3)) = (e0))))) -> (~((op (e1) (e0)) = (op (e3) (e0)))) -> (~((op (e2) (e0)) = (op (e2) (e1)))) -> (~((op (e1) (e0)) = (op (e2) (e0)))) -> ((~((op (e1) (e0)) = (e0)))\/((op (e1) (e0)) = (e0))) -> ((~((op (e0) (e2)) = (e0)))\/((op (e0) (e0)) = (e2))) -> (~((e1) = (e3))) -> ((op (e1) (e0)) = (e3)) -> ((op (e2) (e0)) = (e3)) -> ((op (e0) (e0)) = (e2)) -> False). % 18.68/18.86 do 0 intro. intros zenon_H235 zenon_H204 zenon_H205 zenon_H7c zenon_H94 zenon_H2f zenon_H1a5 zenon_H1a6 zenon_H1a4 zenon_H1a7 zenon_H18f zenon_H191 zenon_H195 zenon_H19d zenon_H9a zenon_H10a zenon_H18c zenon_H115 zenon_H11f zenon_H1d zenon_H10e zenon_Ha1 zenon_Ha8 zenon_He8 zenon_Hc2 zenon_Hdf zenon_Hdb zenon_Hd8 zenon_Hd5 zenon_He2 zenon_He4 zenon_Haf zenon_He7 zenon_H106 zenon_Hf3 zenon_H102 zenon_H101 zenon_H2b zenon_H109 zenon_H189 zenon_H185 zenon_H184 zenon_H183 zenon_H17b zenon_H17e zenon_H178 zenon_H179 zenon_H142 zenon_H13e zenon_H13c zenon_H139 zenon_H128 zenon_H136 zenon_H130 zenon_H133 zenon_H12b zenon_H124 zenon_H145 zenon_H172 zenon_H173 zenon_H16f zenon_H168 zenon_H160 zenon_H165 zenon_H149 zenon_H14f zenon_H153 zenon_H39 zenon_H182 zenon_H1fe zenon_H1ee zenon_H1e0 zenon_H1ac zenon_H1c7 zenon_H1c4 zenon_H1cc zenon_H1ba zenon_H1cf zenon_H1d8 zenon_H1d5 zenon_H1ec zenon_H1ed zenon_H3f zenon_H22 zenon_H45 zenon_H6a zenon_H54 zenon_H57 zenon_H5b zenon_H62 zenon_H67 zenon_H52 zenon_H4f zenon_H4a zenon_H71 zenon_H6d zenon_H6f zenon_H3e zenon_H74 zenon_H1fa zenon_H1f0 zenon_H201 zenon_H206 zenon_H233 zenon_H95 zenon_H9e zenon_H3b zenon_H7b. % 18.68/18.86 apply (zenon_or_s _ _ zenon_H235); [ zenon_intro zenon_H7a | zenon_intro zenon_H236 ]. % 18.68/18.86 apply (zenon_L456_); trivial. % 18.68/18.86 apply (zenon_or_s _ _ zenon_H236); [ zenon_intro zenon_H9d | zenon_intro zenon_H237 ]. % 18.68/18.86 apply (zenon_L37_); trivial. % 18.68/18.86 apply (zenon_or_s _ _ zenon_H237); [ zenon_intro zenon_Hed | zenon_intro zenon_Hac ]. % 18.68/18.86 apply (zenon_L491_); trivial. % 18.68/18.86 apply (zenon_L308_); trivial. % 18.68/18.86 (* end of lemma zenon_L570_ *) % 18.68/18.86 assert (zenon_L571_ : (((op (e0) (e3)) = (e0))\/(((op (e1) (e3)) = (e0))\/(((op (e2) (e3)) = (e0))\/((op (e3) (e3)) = (e0))))) -> (~((e0) = (e3))) -> ((op (e0) (e3)) = (e3)) -> (~((op (e0) (e3)) = (op (e2) (e3)))) -> (~((op (e2) (e3)) = (op (e3) (e3)))) -> (((op (e2) (e3)) = (e0))\/(((op (e2) (e3)) = (e1))\/(((op (e2) (e3)) = (e2))\/((op (e2) (e3)) = (e3))))) -> ((op (e2) (e1)) = (e2)) -> (~((op (e2) (e1)) = (op (e2) (e3)))) -> ((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 (e2) (e0)) = (op (e2) (e3)))) -> ((op (e2) (e0)) = (e0)) -> ((op (e3) (e1)) = (e0)) -> (~((op (e3) (e1)) = (op (e3) (e3)))) -> False). % 18.68/18.86 do 0 intro. intros zenon_H67 zenon_H9a zenon_He3 zenon_He2 zenon_Hf3 zenon_H11f zenon_H1ca zenon_H1c7 zenon_Hd6 zenon_H7c zenon_H12b zenon_H145 zenon_H5b zenon_H34 zenon_H1b1 zenon_H130. % 18.68/18.86 apply (zenon_or_s _ _ zenon_H67); [ zenon_intro zenon_H1e | zenon_intro zenon_H68 ]. % 18.68/18.86 apply (zenon_L515_); trivial. % 18.68/18.86 apply (zenon_or_s _ _ zenon_H68); [ zenon_intro zenon_H1f | zenon_intro zenon_H69 ]. % 18.68/18.86 apply (zenon_L226_); trivial. % 18.68/18.86 apply (zenon_or_s _ _ zenon_H69); [ zenon_intro zenon_H37 | zenon_intro zenon_H60 ]. % 18.68/18.86 apply (zenon_L14_); trivial. % 18.68/18.86 apply (zenon_L244_); trivial. % 18.68/18.86 (* end of lemma zenon_L571_ *) % 18.68/18.86 assert (zenon_L572_ : (((op (e2) (e1)) = (e0))\/(((op (e2) (e1)) = (e1))\/(((op (e2) (e1)) = (e2))\/((op (e2) (e1)) = (e3))))) -> (~((op (e2) (e1)) = (e0))) -> ((op (e0) (e1)) = (e1)) -> (~((op (e0) (e1)) = (op (e2) (e1)))) -> (~((op (e3) (e1)) = (op (e3) (e3)))) -> ((op (e2) (e0)) = (e0)) -> (~((op (e2) (e0)) = (op (e2) (e3)))) -> (((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) (e1)) = (op (e2) (e3)))) -> (((op (e2) (e3)) = (e0))\/(((op (e2) (e3)) = (e1))\/(((op (e2) (e3)) = (e2))\/((op (e2) (e3)) = (e3))))) -> (~((op (e2) (e3)) = (op (e3) (e3)))) -> (~((op (e0) (e3)) = (op (e2) (e3)))) -> ((op (e0) (e3)) = (e3)) -> (~((e0) = (e3))) -> (((op (e0) (e3)) = (e0))\/(((op (e1) (e3)) = (e0))\/(((op (e2) (e3)) = (e0))\/((op (e3) (e3)) = (e0))))) -> ((op (e3) (e1)) = (e0)) -> ((op (e1) (e1)) = (e2)) -> False). % 18.68/18.86 do 0 intro. intros zenon_H1cc zenon_H31 zenon_Ha0 zenon_H17e zenon_H130 zenon_H34 zenon_H5b zenon_H145 zenon_H12b zenon_H7c zenon_Hd6 zenon_H1c7 zenon_H11f zenon_Hf3 zenon_He2 zenon_He3 zenon_H9a zenon_H67 zenon_H1b1 zenon_H110. % 18.68/18.86 apply (zenon_or_s _ _ zenon_H1cc); [ zenon_intro zenon_H36 | zenon_intro zenon_H1cd ]. % 18.68/18.86 exact (zenon_H31 zenon_H36). % 18.68/18.86 apply (zenon_or_s _ _ zenon_H1cd); [ zenon_intro zenon_Ha5 | zenon_intro zenon_H1ce ]. % 18.68/18.86 apply (zenon_L357_); trivial. % 18.68/18.86 apply (zenon_or_s _ _ zenon_H1ce); [ zenon_intro zenon_H1ca | zenon_intro zenon_Ha6 ]. % 18.68/18.86 apply (zenon_L571_); trivial. % 18.68/18.86 apply (zenon_L509_); trivial. % 18.68/18.86 (* end of lemma zenon_L572_ *) % 18.68/18.86 assert (zenon_L573_ : (((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 (e3) (e3)) = (e3))) -> (~((op (e2) (e3)) = (op (e3) (e3)))) -> (~((op (e0) (e3)) = (op (e3) (e3)))) -> ((op (e3) (e1)) = (e0)) -> (~((op (e3) (e1)) = (op (e3) (e3)))) -> (((op (e3) (e3)) = (e0))\/(((op (e3) (e3)) = (e1))\/(((op (e3) (e3)) = (e2))\/((op (e3) (e3)) = (e3))))) -> ((op (e2) (e3)) = (e2)) -> (~((op (e0) (e3)) = (op (e2) (e3)))) -> ((op (e2) (e3)) = (e3)) -> False). % 18.68/18.86 do 0 intro. intros zenon_He4 zenon_H1f zenon_H1d zenon_H102 zenon_Hf3 zenon_Hc2 zenon_H1b1 zenon_H130 zenon_H101 zenon_H11d zenon_He2 zenon_Hdd. % 18.68/18.86 apply (zenon_or_s _ _ zenon_He4); [ zenon_intro zenon_H1e | zenon_intro zenon_He5 ]. % 18.68/18.86 apply (zenon_L1_); trivial. % 18.68/18.86 apply (zenon_or_s _ _ zenon_He5); [ zenon_intro zenon_Hc3 | zenon_intro zenon_He6 ]. % 18.68/18.86 apply (zenon_L245_); trivial. % 18.68/18.86 apply (zenon_or_s _ _ zenon_He6); [ zenon_intro zenon_Hcd | zenon_intro zenon_He3 ]. % 18.68/18.86 apply (zenon_L234_); trivial. % 18.68/18.86 apply (zenon_L54_); trivial. % 18.68/18.86 (* end of lemma zenon_L573_ *) % 18.68/18.86 assert (zenon_L574_ : (((op (e0) (e3)) = (e3))\/(((op (e1) (e3)) = (e3))\/(((op (e2) (e3)) = (e3))\/((op (e3) (e3)) = (e3))))) -> ((op (e3) (e1)) = (e3)) -> (~((op (e1) (e1)) = (op (e3) (e1)))) -> (((op (e2) (e1)) = (e0))\/(((op (e2) (e1)) = (e1))\/(((op (e2) (e1)) = (e2))\/((op (e2) (e1)) = (e3))))) -> (~((op (e2) (e1)) = (e0))) -> ((op (e0) (e1)) = (e1)) -> (~((op (e0) (e1)) = (op (e2) (e1)))) -> ((op (e2) (e0)) = (e0)) -> (~((op (e2) (e0)) = (op (e2) (e3)))) -> (((op (e0) (e3)) = (e2))\/(((op (e1) (e3)) = (e2))\/(((op (e2) (e3)) = (e2))\/((op (e3) (e3)) = (e2))))) -> (~((e2) = (e3))) -> (~((e1) = (e2))) -> (~((op (e2) (e1)) = (op (e2) (e3)))) -> (((op (e2) (e3)) = (e0))\/(((op (e2) (e3)) = (e1))\/(((op (e2) (e3)) = (e2))\/((op (e2) (e3)) = (e3))))) -> (~((e0) = (e3))) -> (((op (e0) (e3)) = (e0))\/(((op (e1) (e3)) = (e0))\/(((op (e2) (e3)) = (e0))\/((op (e3) (e3)) = (e0))))) -> (~((op (e1) (e1)) = (e1))) -> (~((op (e1) (e1)) = (e0))) -> (((op (e1) (e1)) = (e0))\/(((op (e1) (e1)) = (e1))\/(((op (e1) (e1)) = (e2))\/((op (e1) (e1)) = (e3))))) -> (~((e1) = (e3))) -> ((op (e1) (e3)) = (e1)) -> (~((op (e0) (e3)) = (op (e2) (e3)))) -> ((op (e2) (e3)) = (e2)) -> (((op (e3) (e3)) = (e0))\/(((op (e3) (e3)) = (e1))\/(((op (e3) (e3)) = (e2))\/((op (e3) (e3)) = (e3))))) -> (~((op (e3) (e1)) = (op (e3) (e3)))) -> ((op (e3) (e1)) = (e0)) -> (~((op (e0) (e3)) = (op (e3) (e3)))) -> (~((op (e2) (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 (e3) (e3)) = (e3))) -> False). % 18.68/18.86 do 0 intro. intros zenon_H136 zenon_H161 zenon_H160 zenon_H1cc zenon_H31 zenon_Ha0 zenon_H17e zenon_H34 zenon_H5b zenon_H145 zenon_H12b zenon_H7c zenon_H1c7 zenon_H11f zenon_H9a zenon_H67 zenon_H10a zenon_H24 zenon_H142 zenon_H95 zenon_Hd6 zenon_He2 zenon_H11d zenon_H101 zenon_H130 zenon_H1b1 zenon_Hc2 zenon_Hf3 zenon_H1d zenon_H1f zenon_He4 zenon_H102. % 18.68/18.86 apply (zenon_or_s _ _ zenon_H136); [ zenon_intro zenon_He3 | zenon_intro zenon_H137 ]. % 18.68/18.86 apply (zenon_or_s _ _ zenon_H142); [ zenon_intro zenon_H29 | zenon_intro zenon_H143 ]. % 18.68/18.86 exact (zenon_H24 zenon_H29). % 18.68/18.86 apply (zenon_or_s _ _ zenon_H143); [ zenon_intro zenon_H10d | zenon_intro zenon_H144 ]. % 18.68/18.86 exact (zenon_H10a zenon_H10d). % 18.68/18.86 apply (zenon_or_s _ _ zenon_H144); [ zenon_intro zenon_H110 | zenon_intro zenon_H13f ]. % 18.68/18.86 apply (zenon_L572_); trivial. % 18.68/18.86 apply (zenon_L110_); trivial. % 18.68/18.86 apply (zenon_or_s _ _ zenon_H137); [ zenon_intro zenon_Hdc | zenon_intro zenon_H138 ]. % 18.68/18.86 apply (zenon_L83_); trivial. % 18.68/18.86 apply (zenon_or_s _ _ zenon_H138); [ zenon_intro zenon_Hdd | zenon_intro zenon_H105 ]. % 18.68/18.86 apply (zenon_L573_); trivial. % 18.68/18.86 exact (zenon_H102 zenon_H105). % 18.68/18.86 (* end of lemma zenon_L574_ *) % 18.68/18.86 assert (zenon_L575_ : (((op (e3) (e0)) = (e3))\/(((op (e3) (e1)) = (e3))\/(((op (e3) (e2)) = (e3))\/((op (e3) (e3)) = (e3))))) -> ((op (e3) (e0)) = (e1)) -> (((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 (e2) (e3)) = (op (e3) (e3)))) -> (~((op (e0) (e3)) = (op (e3) (e3)))) -> ((op (e3) (e1)) = (e0)) -> (~((op (e3) (e1)) = (op (e3) (e3)))) -> (((op (e3) (e3)) = (e0))\/(((op (e3) (e3)) = (e1))\/(((op (e3) (e3)) = (e2))\/((op (e3) (e3)) = (e3))))) -> ((op (e2) (e3)) = (e2)) -> (~((op (e0) (e3)) = (op (e2) (e3)))) -> ((op (e1) (e3)) = (e1)) -> (~((e1) = (e3))) -> (((op (e1) (e1)) = (e0))\/(((op (e1) (e1)) = (e1))\/(((op (e1) (e1)) = (e2))\/((op (e1) (e1)) = (e3))))) -> (~((op (e1) (e1)) = (e0))) -> (~((op (e1) (e1)) = (e1))) -> (((op (e0) (e3)) = (e0))\/(((op (e1) (e3)) = (e0))\/(((op (e2) (e3)) = (e0))\/((op (e3) (e3)) = (e0))))) -> (~((e0) = (e3))) -> (((op (e2) (e3)) = (e0))\/(((op (e2) (e3)) = (e1))\/(((op (e2) (e3)) = (e2))\/((op (e2) (e3)) = (e3))))) -> (~((op (e2) (e1)) = (op (e2) (e3)))) -> (~((e1) = (e2))) -> (~((e2) = (e3))) -> (((op (e0) (e3)) = (e2))\/(((op (e1) (e3)) = (e2))\/(((op (e2) (e3)) = (e2))\/((op (e3) (e3)) = (e2))))) -> (~((op (e2) (e0)) = (op (e2) (e3)))) -> ((op (e2) (e0)) = (e0)) -> (~((op (e0) (e1)) = (op (e2) (e1)))) -> ((op (e0) (e1)) = (e1)) -> (~((op (e2) (e1)) = (e0))) -> (((op (e2) (e1)) = (e0))\/(((op (e2) (e1)) = (e1))\/(((op (e2) (e1)) = (e2))\/((op (e2) (e1)) = (e3))))) -> (~((op (e1) (e1)) = (op (e3) (e1)))) -> (((op (e0) (e3)) = (e3))\/(((op (e1) (e3)) = (e3))\/(((op (e2) (e3)) = (e3))\/((op (e3) (e3)) = (e3))))) -> ((op (e2) (e2)) = (e3)) -> (~((op (e2) (e2)) = (op (e3) (e2)))) -> (~((op (e3) (e3)) = (e3))) -> False). % 18.68/18.86 do 0 intro. intros zenon_H165 zenon_Hac zenon_He4 zenon_H1f zenon_H1d zenon_Hf3 zenon_Hc2 zenon_H1b1 zenon_H130 zenon_H101 zenon_H11d zenon_He2 zenon_Hd6 zenon_H95 zenon_H142 zenon_H24 zenon_H10a zenon_H67 zenon_H9a zenon_H11f zenon_H1c7 zenon_H7c zenon_H12b zenon_H145 zenon_H5b zenon_H34 zenon_H17e zenon_Ha0 zenon_H31 zenon_H1cc zenon_H160 zenon_H136 zenon_Haa zenon_H18f zenon_H102. % 18.68/18.86 apply (zenon_or_s _ _ zenon_H165); [ zenon_intro zenon_H15e | zenon_intro zenon_H166 ]. % 18.68/18.86 apply (zenon_L252_); trivial. % 18.68/18.86 apply (zenon_or_s _ _ zenon_H166); [ zenon_intro zenon_H161 | zenon_intro zenon_H167 ]. % 18.68/18.86 apply (zenon_L574_); trivial. % 18.68/18.86 apply (zenon_or_s _ _ zenon_H167); [ zenon_intro zenon_H163 | zenon_intro zenon_H105 ]. % 18.68/18.86 apply (zenon_L180_); trivial. % 18.68/18.86 exact (zenon_H102 zenon_H105). % 18.68/18.86 (* end of lemma zenon_L575_ *) % 18.68/18.86 assert (zenon_L576_ : (((op (e0) (e3)) = (e0))\/(((op (e0) (e3)) = (e1))\/(((op (e0) (e3)) = (e2))\/((op (e0) (e3)) = (e3))))) -> (~((op (e0) (e3)) = (op (e1) (e3)))) -> (~((op (e1) (e2)) = (op (e2) (e2)))) -> ((op (e2) (e2)) = (e1)) -> (~((op (e1) (e1)) = (e1))) -> ((op (e1) (e0)) = (e3)) -> (~((e1) = (e3))) -> (((op (e1) (e0)) = (e1))\/(((op (e1) (e1)) = (e1))\/(((op (e1) (e2)) = (e1))\/((op (e1) (e3)) = (e1))))) -> (~((op (e0) (e3)) = (op (e3) (e3)))) -> (((op (e2) (e3)) = (e0))\/(((op (e2) (e3)) = (e1))\/(((op (e2) (e3)) = (e2))\/((op (e2) (e3)) = (e3))))) -> (~((op (e2) (e0)) = (op (e2) (e3)))) -> ((op (e2) (e0)) = (e0)) -> ((op (e1) (e3)) = (e0)) -> ((op (e3) (e3)) = (e2)) -> (~((op (e2) (e3)) = (op (e3) (e3)))) -> (~((op (e0) (e3)) = (op (e2) (e3)))) -> False). % 18.68/18.86 do 0 intro. intros zenon_He4 zenon_H1d zenon_H2b zenon_Hf1 zenon_H10a zenon_H9e zenon_H95 zenon_H128 zenon_Hc2 zenon_H11f zenon_H5b zenon_H34 zenon_H1f zenon_Hf6 zenon_Hf3 zenon_He2. % 18.68/18.86 apply (zenon_or_s _ _ zenon_He4); [ zenon_intro zenon_H1e | zenon_intro zenon_He5 ]. % 18.68/18.86 apply (zenon_L1_); trivial. % 18.68/18.86 apply (zenon_or_s _ _ zenon_He5); [ zenon_intro zenon_Hc3 | zenon_intro zenon_He6 ]. % 18.68/18.86 apply (zenon_L80_); trivial. % 18.68/18.86 apply (zenon_or_s _ _ zenon_He6); [ zenon_intro zenon_Hcd | zenon_intro zenon_He3 ]. % 18.68/18.86 apply (zenon_L87_); trivial. % 18.68/18.86 apply (zenon_L225_); trivial. % 18.68/18.86 (* end of lemma zenon_L576_ *) % 18.68/18.86 assert (zenon_L577_ : (~((op (e0) (e0)) = (op (e0) (e3)))) -> ((op (e0) (e0)) = (e2)) -> (~((op (e3) (e3)) = (e3))) -> (~((op (e2) (e2)) = (op (e3) (e2)))) -> ((op (e2) (e2)) = (e3)) -> (((op (e0) (e3)) = (e3))\/(((op (e1) (e3)) = (e3))\/(((op (e2) (e3)) = (e3))\/((op (e3) (e3)) = (e3))))) -> (~((op (e1) (e1)) = (op (e3) (e1)))) -> (((op (e2) (e1)) = (e0))\/(((op (e2) (e1)) = (e1))\/(((op (e2) (e1)) = (e2))\/((op (e2) (e1)) = (e3))))) -> (~((op (e2) (e1)) = (e0))) -> ((op (e0) (e1)) = (e1)) -> (~((op (e0) (e1)) = (op (e2) (e1)))) -> (((op (e0) (e3)) = (e2))\/(((op (e1) (e3)) = (e2))\/(((op (e2) (e3)) = (e2))\/((op (e3) (e3)) = (e2))))) -> (~((e2) = (e3))) -> (~((e1) = (e2))) -> (~((op (e2) (e1)) = (op (e2) (e3)))) -> (~((e0) = (e3))) -> (((op (e0) (e3)) = (e0))\/(((op (e1) (e3)) = (e0))\/(((op (e2) (e3)) = (e0))\/((op (e3) (e3)) = (e0))))) -> (~((op (e1) (e1)) = (e0))) -> (((op (e1) (e1)) = (e0))\/(((op (e1) (e1)) = (e1))\/(((op (e1) (e1)) = (e2))\/((op (e1) (e1)) = (e3))))) -> ((op (e1) (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 (e3) (e1)) = (e0)) -> ((op (e3) (e0)) = (e1)) -> (((op (e3) (e0)) = (e3))\/(((op (e3) (e1)) = (e3))\/(((op (e3) (e2)) = (e3))\/((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 (e1) (e2)) = (op (e2) (e2)))) -> ((op (e2) (e2)) = (e1)) -> (~((op (e1) (e1)) = (e1))) -> ((op (e1) (e0)) = (e3)) -> (~((e1) = (e3))) -> (((op (e1) (e0)) = (e1))\/(((op (e1) (e1)) = (e1))\/(((op (e1) (e2)) = (e1))\/((op (e1) (e3)) = (e1))))) -> (~((op (e0) (e3)) = (op (e3) (e3)))) -> (((op (e2) (e3)) = (e0))\/(((op (e2) (e3)) = (e1))\/(((op (e2) (e3)) = (e2))\/((op (e2) (e3)) = (e3))))) -> (~((op (e2) (e0)) = (op (e2) (e3)))) -> ((op (e2) (e0)) = (e0)) -> ((op (e1) (e3)) = (e0)) -> (~((op (e2) (e3)) = (op (e3) (e3)))) -> (~((op (e0) (e3)) = (op (e2) (e3)))) -> False). % 18.68/18.86 do 0 intro. intros zenon_H189 zenon_H7b zenon_H102 zenon_H18f zenon_Haa zenon_H136 zenon_H160 zenon_H1cc zenon_H31 zenon_Ha0 zenon_H17e zenon_H145 zenon_H12b zenon_H7c zenon_H1c7 zenon_H9a zenon_H67 zenon_H24 zenon_H142 zenon_Hd6 zenon_H101 zenon_H130 zenon_H1b1 zenon_Hac zenon_H165 zenon_He4 zenon_H1d zenon_H2b zenon_Hf1 zenon_H10a zenon_H9e zenon_H95 zenon_H128 zenon_Hc2 zenon_H11f zenon_H5b zenon_H34 zenon_H1f zenon_Hf3 zenon_He2. % 18.68/18.86 apply (zenon_or_s _ _ zenon_H145); [ zenon_intro zenon_Hcd | zenon_intro zenon_H146 ]. % 18.68/18.86 apply (zenon_L375_); trivial. % 18.68/18.86 apply (zenon_or_s _ _ zenon_H146); [ zenon_intro zenon_Hd7 | zenon_intro zenon_H147 ]. % 18.68/18.86 apply (zenon_L101_); trivial. % 18.68/18.86 apply (zenon_or_s _ _ zenon_H147); [ zenon_intro zenon_H11d | zenon_intro zenon_Hf6 ]. % 18.68/18.86 apply (zenon_L575_); trivial. % 18.68/18.86 apply (zenon_L576_); trivial. % 18.68/18.86 (* end of lemma zenon_L577_ *) % 18.68/18.86 assert (zenon_L578_ : ((~((op (e0) (e2)) = (e0)))\/((op (e0) (e0)) = (e2))) -> ((~((op (e1) (e0)) = (e0)))\/((op (e1) (e0)) = (e0))) -> (~((op (e1) (e0)) = (op (e2) (e0)))) -> (~((op (e2) (e0)) = (op (e2) (e1)))) -> (~((op (e1) (e0)) = (op (e3) (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)) = (op (e3) (e2)))) -> (~((op (e2) (e2)) = (op (e2) (e3)))) -> (~((op (e3) (e0)) = (op (e3) (e3)))) -> (~((op (e0) (e1)) = (op (e0) (e2)))) -> (~((op (e1) (e1)) = (op (e1) (e2)))) -> (~((op (e2) (e0)) = (op (e2) (e2)))) -> (~((op (e3) (e2)) = (op (e3) (e3)))) -> (~((op (e1) (e1)) = (op (e1) (e3)))) -> (~((op (e0) (e1)) = (op (e0) (e3)))) -> (((op (e0) (e2)) = (e0))\/(((op (e1) (e2)) = (e0))\/(((op (e2) (e2)) = (e0))\/((op (e3) (e2)) = (e0))))) -> (~((op (e1) (e0)) = (op (e1) (e1)))) -> (((op (e1) (e0)) = (e0))\/(((op (e1) (e1)) = (e0))\/(((op (e1) (e2)) = (e0))\/((op (e1) (e3)) = (e0))))) -> (~((op (e0) (e0)) = (e0))) -> ((~((op (e3) (e1)) = (e0)))\/((op (e3) (e0)) = (e1))) -> ((~((op (e3) (e3)) = (e0)))\/((op (e3) (e0)) = (e3))) -> (((op (e2) (e0)) = (e2))\/(((op (e2) (e1)) = (e2))\/(((op (e2) (e2)) = (e2))\/((op (e2) (e3)) = (e2))))) -> (((op (e0) (e1)) = (e2))\/(((op (e1) (e1)) = (e2))\/(((op (e2) (e1)) = (e2))\/((op (e3) (e1)) = (e2))))) -> (~((op (e3) (e0)) = (op (e3) (e1)))) -> (((op (e0) (e2)) = (e0))\/(((op (e0) (e2)) = (e1))\/(((op (e0) (e2)) = (e2))\/((op (e0) (e2)) = (e3))))) -> (((op (e2) (e2)) = (e0))\/(((op (e2) (e2)) = (e1))\/(((op (e2) (e2)) = (e2))\/((op (e2) (e2)) = (e3))))) -> (((op (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 (e2) (e0)) = (e0)))\/((op (e2) (e0)) = (e0))) -> (((op (e0) (e0)) = (e2))\/(((op (e1) (e0)) = (e2))\/(((op (e2) (e0)) = (e2))\/((op (e3) (e0)) = (e2))))) -> ((~((op (e2) (e1)) = (e0)))\/((op (e2) (e0)) = (e1))) -> (~((op (e0) (e0)) = (op (e2) (e0)))) -> (((op (e3) (e0)) = (e2))\/(((op (e3) (e1)) = (e2))\/(((op (e3) (e2)) = (e2))\/((op (e3) (e3)) = (e2))))) -> (~((op (e0) (e2)) = (op (e3) (e2)))) -> (~((e0) = (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)) = (e2))) -> (((op (e0) (e2)) = (e2))\/(((op (e1) (e2)) = (e2))\/(((op (e2) (e2)) = (e2))\/((op (e3) (e2)) = (e2))))) -> (~((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)) = (e1))\/(((op (e1) (e2)) = (e1))\/(((op (e2) (e2)) = (e1))\/((op (e3) (e2)) = (e1))))) -> (~((op (e0) (e0)) = (op (e0) (e2)))) -> (~((op (e1) (e1)) = (op (e2) (e1)))) -> ((~((op (e1) (e3)) = (e0)))\/((op (e1) (e0)) = (e3))) -> ((~((op (e1) (e2)) = (e0)))\/((op (e1) (e0)) = (e2))) -> (~((op (e2) (e0)) = (op (e3) (e0)))) -> (((op (e0) (e0)) = (e2))\/(((op (e0) (e1)) = (e2))\/(((op (e0) (e2)) = (e2))\/((op (e0) (e3)) = (e2))))) -> ((~((op (e3) (e0)) = (e0)))\/((op (e3) (e0)) = (e0))) -> ((~((op (e2) (e2)) = (e0)))\/((op (e2) (e0)) = (e2))) -> (((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)) = (e3))\/(((op (e2) (e1)) = (e3))\/(((op (e2) (e2)) = (e3))\/((op (e2) (e3)) = (e3))))) -> (~((op (e2) (e1)) = (op (e3) (e1)))) -> (~((op (e1) (e0)) = (op (e1) (e3)))) -> (~((op (e1) (e3)) = (op (e2) (e3)))) -> (((op (e1) (e3)) = (e0))\/(((op (e1) (e3)) = (e1))\/(((op (e1) (e3)) = (e2))\/((op (e1) (e3)) = (e3))))) -> (((op (e3) (e0)) = (e1))\/(((op (e3) (e1)) = (e1))\/(((op (e3) (e2)) = (e1))\/((op (e3) (e3)) = (e1))))) -> (~((op (e0) (e2)) = (op (e2) (e2)))) -> (~((e0) = (e1))) -> (~((op (e0) (e1)) = (op (e1) (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)) = (e0))\/(((op (e1) (e2)) = (e1))\/(((op (e1) (e2)) = (e2))\/((op (e1) (e2)) = (e3))))) -> (~((op (e0) (e2)) = (op (e1) (e2)))) -> (((op (e3) (e2)) = (e0))\/(((op (e3) (e2)) = (e1))\/(((op (e3) (e2)) = (e2))\/((op (e3) (e2)) = (e3))))) -> ((~((op (e3) (e2)) = (e0)))\/((op (e3) (e0)) = (e2))) -> (~((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)) = (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 (e2) (e3)) = (e0)))\/((op (e2) (e0)) = (e3))) -> ((~((op (e1) (e1)) = (e0)))\/((op (e1) (e0)) = (e1))) -> ((~((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) (e1)) = (e2)) -> (((op (e3) (e0)) = (e3))\/(((op (e3) (e1)) = (e3))\/(((op (e3) (e2)) = (e3))\/((op (e3) (e3)) = (e3))))) -> ((op (e3) (e0)) = (e1)) -> (((op (e1) (e1)) = (e0))\/(((op (e1) (e1)) = (e1))\/(((op (e1) (e1)) = (e2))\/((op (e1) (e1)) = (e3))))) -> (~((op (e1) (e1)) = (e0))) -> (((op (e0) (e3)) = (e0))\/(((op (e1) (e3)) = (e0))\/(((op (e2) (e3)) = (e0))\/((op (e3) (e3)) = (e0))))) -> (~((e0) = (e3))) -> (~((op (e2) (e1)) = (op (e2) (e3)))) -> (~((e2) = (e3))) -> (~((op (e0) (e1)) = (op (e2) (e1)))) -> ((op (e0) (e1)) = (e1)) -> (~((op (e2) (e1)) = (e0))) -> (((op (e2) (e1)) = (e0))\/(((op (e2) (e1)) = (e1))\/(((op (e2) (e1)) = (e2))\/((op (e2) (e1)) = (e3))))) -> (~((op (e1) (e1)) = (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 (e0) (e0)) = (e2)) -> (~((op (e0) (e0)) = (op (e0) (e3)))) -> (((op (e0) (e3)) = (e2))\/(((op (e1) (e3)) = (e2))\/(((op (e2) (e3)) = (e2))\/((op (e3) (e3)) = (e2))))) -> (~((op (e1) (e3)) = (op (e3) (e3)))) -> (~((e1) = (e2))) -> ((op (e1) (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 (e3) (e1)) = (e0)) -> (~((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 (e1) (e2)) = (op (e2) (e2)))) -> ((op (e2) (e2)) = (e1)) -> (~((op (e1) (e1)) = (e1))) -> ((op (e1) (e0)) = (e3)) -> (~((e1) = (e3))) -> (((op (e1) (e0)) = (e1))\/(((op (e1) (e1)) = (e1))\/(((op (e1) (e2)) = (e1))\/((op (e1) (e3)) = (e1))))) -> (~((op (e0) (e3)) = (op (e3) (e3)))) -> (((op (e2) (e3)) = (e0))\/(((op (e2) (e3)) = (e1))\/(((op (e2) (e3)) = (e2))\/((op (e2) (e3)) = (e3))))) -> (~((op (e2) (e0)) = (op (e2) (e3)))) -> ((op (e2) (e0)) = (e0)) -> ((op (e1) (e3)) = (e0)) -> (~((op (e2) (e3)) = (op (e3) (e3)))) -> (~((op (e0) (e3)) = (op (e2) (e3)))) -> False). % 18.68/18.86 do 0 intro. intros zenon_H233 zenon_H206 zenon_H201 zenon_H1f0 zenon_H1fa zenon_H74 zenon_H3e zenon_H6f zenon_H6d zenon_H71 zenon_H4a zenon_H4f zenon_H52 zenon_H62 zenon_H57 zenon_H54 zenon_H6a zenon_H45 zenon_H22 zenon_H3f zenon_H1ed zenon_H1ec zenon_H1d5 zenon_H1d8 zenon_H1cf zenon_H1ba zenon_H1c4 zenon_H1ac zenon_H1e0 zenon_H1ee zenon_H1fe zenon_H182 zenon_H39 zenon_H153 zenon_H14f zenon_H149 zenon_H168 zenon_H16f zenon_H173 zenon_H172 zenon_H124 zenon_H133 zenon_H139 zenon_H13c zenon_H13e zenon_H179 zenon_H178 zenon_H17b zenon_H183 zenon_H184 zenon_H185 zenon_H109 zenon_H106 zenon_He7 zenon_Haf zenon_Hd8 zenon_Hdb zenon_Hdf zenon_He8 zenon_Ha8 zenon_Ha1 zenon_H10e zenon_H115 zenon_H18c zenon_H19d zenon_H195 zenon_H191 zenon_H1a7 zenon_H1a4 zenon_H1a6 zenon_H1a5 zenon_H2f zenon_H94 zenon_H205 zenon_H204 zenon_H235 zenon_H1ca zenon_H165 zenon_Hac zenon_H142 zenon_H24 zenon_H67 zenon_H9a zenon_H1c7 zenon_H12b zenon_H17e zenon_Ha0 zenon_H31 zenon_H1cc zenon_H160 zenon_H136 zenon_H18f zenon_H7b zenon_H189 zenon_H145 zenon_Hd5 zenon_H7c zenon_Hd6 zenon_H101 zenon_H130 zenon_H1b1 zenon_H102 zenon_He4 zenon_H1d zenon_H2b zenon_Hf1 zenon_H10a zenon_H9e zenon_H95 zenon_H128 zenon_Hc2 zenon_H11f zenon_H5b zenon_H34 zenon_H1f zenon_Hf3 zenon_He2. % 18.68/18.86 apply (zenon_or_s _ _ zenon_He7); [ zenon_intro zenon_H3b | zenon_intro zenon_He9 ]. % 18.68/18.86 apply (zenon_L570_); trivial. % 18.68/18.86 apply (zenon_or_s _ _ zenon_He9); [ zenon_intro zenon_Ha6 | zenon_intro zenon_Hea ]. % 18.68/18.86 apply (zenon_L207_); trivial. % 18.68/18.86 apply (zenon_or_s _ _ zenon_Hea); [ zenon_intro zenon_Haa | zenon_intro zenon_Hdd ]. % 18.68/18.86 apply (zenon_L577_); trivial. % 18.68/18.86 apply (zenon_or_s _ _ zenon_H145); [ zenon_intro zenon_Hcd | zenon_intro zenon_H146 ]. % 18.68/18.86 apply (zenon_L137_); trivial. % 18.68/18.86 apply (zenon_or_s _ _ zenon_H146); [ zenon_intro zenon_Hd7 | zenon_intro zenon_H147 ]. % 18.68/18.86 apply (zenon_L101_); trivial. % 18.68/18.86 apply (zenon_or_s _ _ zenon_H147); [ zenon_intro zenon_H11d | zenon_intro zenon_Hf6 ]. % 18.68/18.86 apply (zenon_L573_); trivial. % 18.68/18.86 apply (zenon_L576_); trivial. % 18.68/18.86 (* end of lemma zenon_L578_ *) % 18.68/18.86 assert (zenon_L579_ : ((op (e3) (e1)) = (e0)) -> ((op (e1) (e1)) = (e3)) -> (~((e0) = (op (op (e1) (e1)) (e1)))) -> False). % 18.68/18.86 do 0 intro. intros zenon_H1b1 zenon_H13f zenon_H240. % 18.68/18.86 elim (classic ((op (op (e1) (e1)) (e1)) = (op (op (e1) (e1)) (e1)))); [ zenon_intro zenon_H217 | zenon_intro zenon_H218 ]. % 18.68/18.86 cut (((op (op (e1) (e1)) (e1)) = (op (op (e1) (e1)) (e1))) = ((e0) = (op (op (e1) (e1)) (e1)))). % 18.68/18.86 intro zenon_D_pnotp. % 18.68/18.86 apply zenon_H240. % 18.68/18.86 rewrite <- zenon_D_pnotp. % 18.68/18.86 exact zenon_H217. % 18.68/18.86 cut (((op (op (e1) (e1)) (e1)) = (op (op (e1) (e1)) (e1)))); [idtac | apply NNPP; zenon_intro zenon_H218]. % 18.68/18.86 cut (((op (op (e1) (e1)) (e1)) = (e0))); [idtac | apply NNPP; zenon_intro zenon_H241]. % 18.68/18.86 congruence. % 18.68/18.86 cut (((op (e3) (e1)) = (e0)) = ((op (op (e1) (e1)) (e1)) = (e0))). % 18.68/18.86 intro zenon_D_pnotp. % 18.68/18.86 apply zenon_H241. % 18.68/18.86 rewrite <- zenon_D_pnotp. % 18.68/18.86 exact zenon_H1b1. % 18.68/18.86 cut (((e0) = (e0))); [idtac | apply NNPP; zenon_intro zenon_H82]. % 18.68/18.86 cut (((op (e3) (e1)) = (op (op (e1) (e1)) (e1)))); [idtac | apply NNPP; zenon_intro zenon_H23e]. % 18.68/18.86 congruence. % 18.68/18.86 elim (classic ((op (op (e1) (e1)) (e1)) = (op (op (e1) (e1)) (e1)))); [ zenon_intro zenon_H217 | zenon_intro zenon_H218 ]. % 18.68/18.86 cut (((op (op (e1) (e1)) (e1)) = (op (op (e1) (e1)) (e1))) = ((op (e3) (e1)) = (op (op (e1) (e1)) (e1)))). % 18.68/18.86 intro zenon_D_pnotp. % 18.68/18.86 apply zenon_H23e. % 18.68/18.86 rewrite <- zenon_D_pnotp. % 18.68/18.86 exact zenon_H217. % 18.68/18.86 cut (((op (op (e1) (e1)) (e1)) = (op (op (e1) (e1)) (e1)))); [idtac | apply NNPP; zenon_intro zenon_H218]. % 18.68/18.86 cut (((op (op (e1) (e1)) (e1)) = (op (e3) (e1)))); [idtac | apply NNPP; zenon_intro zenon_H23d]. % 18.68/18.86 congruence. % 18.68/18.86 apply (zenon_L512_); trivial. % 18.68/18.86 apply zenon_H218. apply refl_equal. % 18.68/18.86 apply zenon_H218. apply refl_equal. % 18.68/18.86 apply zenon_H82. apply refl_equal. % 18.68/18.86 apply zenon_H218. apply refl_equal. % 18.68/18.86 apply zenon_H218. apply refl_equal. % 18.68/18.86 (* end of lemma zenon_L579_ *) % 18.68/18.86 assert (zenon_L580_ : ((op (e0) (e1)) = (e2)) -> ((op (e3) (e1)) = (e0)) -> ((op (e1) (e1)) = (e3)) -> False). % 18.68/18.86 do 0 intro. intros zenon_H10f zenon_H1b1 zenon_H13f. % 18.68/18.86 apply (zenon_notand_s _ _ ax14); [ zenon_intro zenon_H225 | zenon_intro zenon_H248 ]. % 18.68/18.86 elim (classic ((op (op (op (e1) (e1)) (e1)) (e1)) = (op (op (op (e1) (e1)) (e1)) (e1)))); [ zenon_intro zenon_H21d | zenon_intro zenon_H21e ]. % 18.68/18.86 cut (((op (op (op (e1) (e1)) (e1)) (e1)) = (op (op (op (e1) (e1)) (e1)) (e1))) = ((e2) = (op (op (op (e1) (e1)) (e1)) (e1)))). % 18.68/18.86 intro zenon_D_pnotp. % 18.68/18.86 apply zenon_H225. % 18.68/18.86 rewrite <- zenon_D_pnotp. % 18.68/18.86 exact zenon_H21d. % 18.68/18.86 cut (((op (op (op (e1) (e1)) (e1)) (e1)) = (op (op (op (e1) (e1)) (e1)) (e1)))); [idtac | apply NNPP; zenon_intro zenon_H21e]. % 18.68/18.86 cut (((op (op (op (e1) (e1)) (e1)) (e1)) = (e2))); [idtac | apply NNPP; zenon_intro zenon_H226]. % 18.68/18.86 congruence. % 18.68/18.86 cut (((op (e0) (e1)) = (e2)) = ((op (op (op (e1) (e1)) (e1)) (e1)) = (e2))). % 18.68/18.86 intro zenon_D_pnotp. % 18.68/18.86 apply zenon_H226. % 18.68/18.86 rewrite <- zenon_D_pnotp. % 18.68/18.86 exact zenon_H10f. % 18.68/18.86 cut (((e2) = (e2))); [idtac | apply NNPP; zenon_intro zenon_H7e]. % 18.68/18.86 cut (((op (e0) (e1)) = (op (op (op (e1) (e1)) (e1)) (e1)))); [idtac | apply NNPP; zenon_intro zenon_H243]. % 18.68/18.86 congruence. % 18.68/18.86 elim (classic ((op (op (op (e1) (e1)) (e1)) (e1)) = (op (op (op (e1) (e1)) (e1)) (e1)))); [ zenon_intro zenon_H21d | zenon_intro zenon_H21e ]. % 18.68/18.86 cut (((op (op (op (e1) (e1)) (e1)) (e1)) = (op (op (op (e1) (e1)) (e1)) (e1))) = ((op (e0) (e1)) = (op (op (op (e1) (e1)) (e1)) (e1)))). % 18.68/18.86 intro zenon_D_pnotp. % 18.68/18.86 apply zenon_H243. % 18.68/18.86 rewrite <- zenon_D_pnotp. % 18.68/18.86 exact zenon_H21d. % 18.68/18.86 cut (((op (op (op (e1) (e1)) (e1)) (e1)) = (op (op (op (e1) (e1)) (e1)) (e1)))); [idtac | apply NNPP; zenon_intro zenon_H21e]. % 18.68/18.86 cut (((op (op (op (e1) (e1)) (e1)) (e1)) = (op (e0) (e1)))); [idtac | apply NNPP; zenon_intro zenon_H244]. % 18.68/18.86 congruence. % 18.68/18.86 cut (((e1) = (e1))); [idtac | apply NNPP; zenon_intro zenon_H79]. % 18.68/18.86 cut (((op (op (e1) (e1)) (e1)) = (e0))); [idtac | apply NNPP; zenon_intro zenon_H241]. % 18.68/18.86 congruence. % 18.68/18.86 cut (((op (e3) (e1)) = (e0)) = ((op (op (e1) (e1)) (e1)) = (e0))). % 18.68/18.86 intro zenon_D_pnotp. % 18.68/18.86 apply zenon_H241. % 18.68/18.86 rewrite <- zenon_D_pnotp. % 18.68/18.86 exact zenon_H1b1. % 18.68/18.86 cut (((e0) = (e0))); [idtac | apply NNPP; zenon_intro zenon_H82]. % 18.68/18.86 cut (((op (e3) (e1)) = (op (op (e1) (e1)) (e1)))); [idtac | apply NNPP; zenon_intro zenon_H23e]. % 18.68/18.86 congruence. % 18.68/18.86 elim (classic ((op (op (e1) (e1)) (e1)) = (op (op (e1) (e1)) (e1)))); [ zenon_intro zenon_H217 | zenon_intro zenon_H218 ]. % 18.68/18.86 cut (((op (op (e1) (e1)) (e1)) = (op (op (e1) (e1)) (e1))) = ((op (e3) (e1)) = (op (op (e1) (e1)) (e1)))). % 18.68/18.86 intro zenon_D_pnotp. % 18.68/18.86 apply zenon_H23e. % 18.68/18.86 rewrite <- zenon_D_pnotp. % 18.68/18.86 exact zenon_H217. % 18.68/18.86 cut (((op (op (e1) (e1)) (e1)) = (op (op (e1) (e1)) (e1)))); [idtac | apply NNPP; zenon_intro zenon_H218]. % 18.68/18.86 cut (((op (op (e1) (e1)) (e1)) = (op (e3) (e1)))); [idtac | apply NNPP; zenon_intro zenon_H23d]. % 18.68/18.86 congruence. % 18.68/18.86 apply (zenon_L512_); trivial. % 18.68/18.86 apply zenon_H218. apply refl_equal. % 18.68/18.86 apply zenon_H218. apply refl_equal. % 18.68/18.86 apply zenon_H82. apply refl_equal. % 18.68/18.86 apply zenon_H79. apply refl_equal. % 18.68/18.86 apply zenon_H21e. apply refl_equal. % 18.68/18.86 apply zenon_H21e. apply refl_equal. % 18.68/18.86 apply zenon_H7e. apply refl_equal. % 18.68/18.86 apply zenon_H21e. apply refl_equal. % 18.68/18.86 apply zenon_H21e. apply refl_equal. % 18.68/18.86 apply (zenon_notand_s _ _ zenon_H248); [ zenon_intro zenon_H240 | zenon_intro zenon_H15d ]. % 18.68/18.86 apply (zenon_L579_); trivial. % 18.68/18.86 apply zenon_H15d. apply sym_equal. exact zenon_H13f. % 18.68/18.86 (* end of lemma zenon_L580_ *) % 18.68/18.86 assert (zenon_L581_ : (((op (e2) (e0)) = (e1))\/(((op (e2) (e1)) = (e1))\/(((op (e2) (e2)) = (e1))\/((op (e2) (e3)) = (e1))))) -> (~((e0) = (e1))) -> ((op (e3) (e1)) = (e3)) -> (~((op (e3) (e1)) = (op (e3) (e2)))) -> (~((op (e0) (e0)) = (op (e0) (e3)))) -> ((op (e0) (e0)) = (e2)) -> (~((op (e3) (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 (e1) (e1)) = (op (e3) (e1)))) -> (((op (e2) (e1)) = (e0))\/(((op (e2) (e1)) = (e1))\/(((op (e2) (e1)) = (e2))\/((op (e2) (e1)) = (e3))))) -> (~((op (e2) (e1)) = (e0))) -> ((op (e0) (e1)) = (e1)) -> (~((op (e0) (e1)) = (op (e2) (e1)))) -> (((op (e0) (e3)) = (e2))\/(((op (e1) (e3)) = (e2))\/(((op (e2) (e3)) = (e2))\/((op (e3) (e3)) = (e2))))) -> (~((e2) = (e3))) -> (~((e1) = (e2))) -> (~((op (e2) (e1)) = (op (e2) (e3)))) -> (~((e0) = (e3))) -> (((op (e0) (e3)) = (e0))\/(((op (e1) (e3)) = (e0))\/(((op (e2) (e3)) = (e0))\/((op (e3) (e3)) = (e0))))) -> (~((op (e1) (e1)) = (e0))) -> (((op (e1) (e1)) = (e0))\/(((op (e1) (e1)) = (e1))\/(((op (e1) (e1)) = (e2))\/((op (e1) (e1)) = (e3))))) -> (((op (e3) (e3)) = (e0))\/(((op (e3) (e3)) = (e1))\/(((op (e3) (e3)) = (e2))\/((op (e3) (e3)) = (e3))))) -> (~((op (e3) (e1)) = (op (e3) (e3)))) -> ((op (e3) (e1)) = (e0)) -> ((op (e3) (e0)) = (e1)) -> (((op (e3) (e0)) = (e3))\/(((op (e3) (e1)) = (e3))\/(((op (e3) (e2)) = (e3))\/((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 (e1) (e2)) = (op (e2) (e2)))) -> (~((op (e1) (e1)) = (e1))) -> ((op (e1) (e0)) = (e3)) -> (~((e1) = (e3))) -> (((op (e1) (e0)) = (e1))\/(((op (e1) (e1)) = (e1))\/(((op (e1) (e2)) = (e1))\/((op (e1) (e3)) = (e1))))) -> (~((op (e0) (e3)) = (op (e3) (e3)))) -> (((op (e2) (e3)) = (e0))\/(((op (e2) (e3)) = (e1))\/(((op (e2) (e3)) = (e2))\/((op (e2) (e3)) = (e3))))) -> (~((op (e2) (e0)) = (op (e2) (e3)))) -> ((op (e2) (e0)) = (e0)) -> ((op (e1) (e3)) = (e0)) -> (~((op (e2) (e3)) = (op (e3) (e3)))) -> (~((op (e0) (e3)) = (op (e2) (e3)))) -> ((op (e1) (e2)) = (e2)) -> ((op (e0) (e2)) = (e0)) -> (((op (e0) (e2)) = (e3))\/(((op (e1) (e2)) = (e3))\/(((op (e2) (e2)) = (e3))\/((op (e3) (e2)) = (e3))))) -> (~((op (e1) (e3)) = (op (e2) (e3)))) -> ((op (e1) (e3)) = (e1)) -> False). % 18.68/18.86 do 0 intro. intros zenon_H106 zenon_Ha1 zenon_H161 zenon_H1a4 zenon_H189 zenon_H7b zenon_H102 zenon_H18f zenon_H136 zenon_H160 zenon_H1cc zenon_H31 zenon_Ha0 zenon_H17e zenon_H145 zenon_H12b zenon_H7c zenon_H1c7 zenon_H9a zenon_H67 zenon_H24 zenon_H142 zenon_H101 zenon_H130 zenon_H1b1 zenon_Hac zenon_H165 zenon_He4 zenon_H1d zenon_H2b zenon_H10a zenon_H9e zenon_H95 zenon_H128 zenon_Hc2 zenon_H11f zenon_H5b zenon_H34 zenon_H1f zenon_Hf3 zenon_He2 zenon_H113 zenon_H48 zenon_H1a6 zenon_Hdb zenon_Hd6. % 18.68/18.86 apply (zenon_or_s _ _ zenon_H106); [ zenon_intro zenon_Hed | zenon_intro zenon_H107 ]. % 18.68/18.86 apply (zenon_L214_); trivial. % 18.68/18.86 apply (zenon_or_s _ _ zenon_H107); [ zenon_intro zenon_Ha5 | zenon_intro zenon_H108 ]. % 18.68/18.86 apply (zenon_L357_); trivial. % 18.68/18.86 apply (zenon_or_s _ _ zenon_H108); [ zenon_intro zenon_Hf1 | zenon_intro zenon_Hf4 ]. % 18.68/18.86 apply (zenon_or_s _ _ zenon_H1a6); [ zenon_intro zenon_Ha9 | zenon_intro zenon_H1aa ]. % 18.68/18.86 apply (zenon_L358_); trivial. % 18.68/18.86 apply (zenon_or_s _ _ zenon_H1aa); [ zenon_intro zenon_H16c | zenon_intro zenon_H1ab ]. % 18.68/18.86 apply (zenon_L116_); trivial. % 18.68/18.86 apply (zenon_or_s _ _ zenon_H1ab); [ zenon_intro zenon_Haa | zenon_intro zenon_H163 ]. % 18.68/18.86 apply (zenon_L577_); trivial. % 18.68/18.86 apply (zenon_L169_); trivial. % 18.68/18.86 apply (zenon_L126_); trivial. % 18.68/18.86 (* end of lemma zenon_L581_ *) % 18.68/18.86 assert (zenon_L582_ : (~((op (e0) (e3)) = (op (e2) (e3)))) -> (~((op (e2) (e3)) = (op (e3) (e3)))) -> ((op (e1) (e3)) = (e0)) -> ((op (e2) (e0)) = (e0)) -> (~((op (e2) (e0)) = (op (e2) (e3)))) -> (((op (e2) (e3)) = (e0))\/(((op (e2) (e3)) = (e1))\/(((op (e2) (e3)) = (e2))\/((op (e2) (e3)) = (e3))))) -> (~((op (e0) (e3)) = (op (e3) (e3)))) -> (((op (e1) (e0)) = (e1))\/(((op (e1) (e1)) = (e1))\/(((op (e1) (e2)) = (e1))\/((op (e1) (e3)) = (e1))))) -> (~((e1) = (e3))) -> ((op (e1) (e0)) = (e3)) -> (~((op (e1) (e1)) = (e1))) -> (~((op (e1) (e2)) = (op (e2) (e2)))) -> (~((op (e0) (e3)) = (op (e1) (e3)))) -> (((op (e0) (e3)) = (e0))\/(((op (e0) (e3)) = (e1))\/(((op (e0) (e3)) = (e2))\/((op (e0) (e3)) = (e3))))) -> (~((op (e3) (e3)) = (e3))) -> ((op (e3) (e1)) = (e0)) -> (~((op (e3) (e1)) = (op (e3) (e3)))) -> (((op (e3) (e3)) = (e0))\/(((op (e3) (e3)) = (e1))\/(((op (e3) (e3)) = (e2))\/((op (e3) (e3)) = (e3))))) -> (~((e1) = (e2))) -> (~((op (e1) (e3)) = (op (e3) (e3)))) -> (((op (e0) (e3)) = (e2))\/(((op (e1) (e3)) = (e2))\/(((op (e2) (e3)) = (e2))\/((op (e3) (e3)) = (e2))))) -> (~((op (e0) (e0)) = (op (e0) (e3)))) -> ((op (e0) (e0)) = (e2)) -> (~((op (e2) (e2)) = (op (e3) (e2)))) -> (((op (e0) (e3)) = (e3))\/(((op (e1) (e3)) = (e3))\/(((op (e2) (e3)) = (e3))\/((op (e3) (e3)) = (e3))))) -> (~((op (e1) (e1)) = (op (e3) (e1)))) -> (((op (e2) (e1)) = (e0))\/(((op (e2) (e1)) = (e1))\/(((op (e2) (e1)) = (e2))\/((op (e2) (e1)) = (e3))))) -> (~((op (e2) (e1)) = (e0))) -> ((op (e0) (e1)) = (e1)) -> (~((op (e0) (e1)) = (op (e2) (e1)))) -> (~((e2) = (e3))) -> (~((op (e2) (e1)) = (op (e2) (e3)))) -> (~((e0) = (e3))) -> (((op (e0) (e3)) = (e0))\/(((op (e1) (e3)) = (e0))\/(((op (e2) (e3)) = (e0))\/((op (e3) (e3)) = (e0))))) -> (~((op (e1) (e1)) = (e0))) -> (((op (e1) (e1)) = (e0))\/(((op (e1) (e1)) = (e1))\/(((op (e1) (e1)) = (e2))\/((op (e1) (e1)) = (e3))))) -> ((op (e3) (e0)) = (e1)) -> (((op (e3) (e0)) = (e3))\/(((op (e3) (e1)) = (e3))\/(((op (e3) (e2)) = (e3))\/((op (e3) (e3)) = (e3))))) -> ((op (e2) (e1)) = (e2)) -> (((op (e0) (e0)) = (e1))\/(((op (e1) (e0)) = (e1))\/(((op (e2) (e0)) = (e1))\/((op (e3) (e0)) = (e1))))) -> ((~((op (e0) (e3)) = (e0)))\/((op (e0) (e0)) = (e3))) -> ((~((op (e1) (e1)) = (e0)))\/((op (e1) (e0)) = (e1))) -> ((~((op (e2) (e3)) = (e0)))\/((op (e2) (e0)) = (e3))) -> (((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))))) -> (((op (e0) (e2)) = (e3))\/(((op (e1) (e2)) = (e3))\/(((op (e2) (e2)) = (e3))\/((op (e3) (e2)) = (e3))))) -> (~((op (e3) (e1)) = (op (e3) (e2)))) -> ((~((op (e3) (e2)) = (e0)))\/((op (e3) (e0)) = (e2))) -> (((op (e3) (e2)) = (e0))\/(((op (e3) (e2)) = (e1))\/(((op (e3) (e2)) = (e2))\/((op (e3) (e2)) = (e3))))) -> (~((op (e0) (e2)) = (op (e1) (e2)))) -> (((op (e1) (e2)) = (e0))\/(((op (e1) (e2)) = (e1))\/(((op (e1) (e2)) = (e2))\/((op (e1) (e2)) = (e3))))) -> (((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 (e1) (e1)))) -> (~((e0) = (e1))) -> (~((op (e0) (e2)) = (op (e2) (e2)))) -> (((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) (e0)) = (op (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 (e2) (e0)) = (e1))\/(((op (e2) (e1)) = (e1))\/(((op (e2) (e2)) = (e1))\/((op (e2) (e3)) = (e1))))) -> (((op (e0) (e1)) = (e1))\/(((op (e1) (e1)) = (e1))\/(((op (e2) (e1)) = (e1))\/((op (e3) (e1)) = (e1))))) -> ((~((op (e2) (e2)) = (e0)))\/((op (e2) (e0)) = (e2))) -> ((~((op (e3) (e0)) = (e0)))\/((op (e3) (e0)) = (e0))) -> (((op (e0) (e0)) = (e2))\/(((op (e0) (e1)) = (e2))\/(((op (e0) (e2)) = (e2))\/((op (e0) (e3)) = (e2))))) -> (~((op (e2) (e0)) = (op (e3) (e0)))) -> ((~((op (e1) (e2)) = (e0)))\/((op (e1) (e0)) = (e2))) -> ((~((op (e1) (e3)) = (e0)))\/((op (e1) (e0)) = (e3))) -> (~((op (e1) (e1)) = (op (e2) (e1)))) -> (~((op (e0) (e0)) = (op (e0) (e2)))) -> (((op (e0) (e2)) = (e1))\/(((op (e1) (e2)) = (e1))\/(((op (e2) (e2)) = (e1))\/((op (e3) (e2)) = (e1))))) -> (((op (e0) (e3)) = (e1))\/(((op (e1) (e3)) = (e1))\/(((op (e2) (e3)) = (e1))\/((op (e3) (e3)) = (e1))))) -> (~((op (e1) (e2)) = (op (e1) (e3)))) -> (((op (e0) (e2)) = (e2))\/(((op (e1) (e2)) = (e2))\/(((op (e2) (e2)) = (e2))\/((op (e3) (e2)) = (e2))))) -> (~((op (e2) (e2)) = (e2))) -> (((op (e1) (e0)) = (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))))) -> (~((e0) = (e2))) -> (~((op (e0) (e2)) = (op (e3) (e2)))) -> (((op (e3) (e0)) = (e2))\/(((op (e3) (e1)) = (e2))\/(((op (e3) (e2)) = (e2))\/((op (e3) (e3)) = (e2))))) -> (~((op (e0) (e0)) = (op (e2) (e0)))) -> ((~((op (e2) (e1)) = (e0)))\/((op (e2) (e0)) = (e1))) -> (((op (e0) (e0)) = (e2))\/(((op (e1) (e0)) = (e2))\/(((op (e2) (e0)) = (e2))\/((op (e3) (e0)) = (e2))))) -> ((~((op (e2) (e0)) = (e0)))\/((op (e2) (e0)) = (e0))) -> (((op (e0) (e0)) = (e3))\/(((op (e1) (e0)) = (e3))\/(((op (e2) (e0)) = (e3))\/((op (e3) (e0)) = (e3))))) -> (((op (e3) (e0)) = (e0))\/(((op (e3) (e1)) = (e0))\/(((op (e3) (e2)) = (e0))\/((op (e3) (e3)) = (e0))))) -> (((op (e2) (e2)) = (e0))\/(((op (e2) (e2)) = (e1))\/(((op (e2) (e2)) = (e2))\/((op (e2) (e2)) = (e3))))) -> (((op (e0) (e2)) = (e0))\/(((op (e0) (e2)) = (e1))\/(((op (e0) (e2)) = (e2))\/((op (e0) (e2)) = (e3))))) -> (~((op (e3) (e0)) = (op (e3) (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))))) -> ((~((op (e3) (e3)) = (e0)))\/((op (e3) (e0)) = (e3))) -> ((~((op (e3) (e1)) = (e0)))\/((op (e3) (e0)) = (e1))) -> (~((op (e0) (e0)) = (e0))) -> (((op (e1) (e0)) = (e0))\/(((op (e1) (e1)) = (e0))\/(((op (e1) (e2)) = (e0))\/((op (e1) (e3)) = (e0))))) -> (~((op (e1) (e0)) = (op (e1) (e1)))) -> (((op (e0) (e2)) = (e0))\/(((op (e1) (e2)) = (e0))\/(((op (e2) (e2)) = (e0))\/((op (e3) (e2)) = (e0))))) -> (~((op (e0) (e1)) = (op (e0) (e3)))) -> (~((op (e1) (e1)) = (op (e1) (e3)))) -> (~((op (e3) (e2)) = (op (e3) (e3)))) -> (~((op (e2) (e0)) = (op (e2) (e2)))) -> (~((op (e1) (e1)) = (op (e1) (e2)))) -> (~((op (e0) (e1)) = (op (e0) (e2)))) -> (~((op (e3) (e0)) = (op (e3) (e3)))) -> (~((op (e2) (e2)) = (op (e2) (e3)))) -> (~((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)) = (e0))\/(((op (e0) (e1)) = (e0))\/(((op (e0) (e2)) = (e0))\/((op (e0) (e3)) = (e0))))) -> (~((op (e1) (e0)) = (op (e3) (e0)))) -> (~((op (e2) (e0)) = (op (e2) (e1)))) -> (~((op (e1) (e0)) = (op (e2) (e0)))) -> ((~((op (e1) (e0)) = (e0)))\/((op (e1) (e0)) = (e0))) -> ((~((op (e0) (e2)) = (e0)))\/((op (e0) (e0)) = (e2))) -> (~((op (e1) (e3)) = (op (e2) (e3)))) -> ((op (e1) (e3)) = (e1)) -> False). % 18.68/18.86 do 0 intro. intros zenon_He2 zenon_Hf3 zenon_H1f zenon_H34 zenon_H5b zenon_H11f zenon_Hc2 zenon_H128 zenon_H95 zenon_H9e zenon_H10a zenon_H2b zenon_H1d zenon_He4 zenon_H102 zenon_H1b1 zenon_H130 zenon_H101 zenon_H7c zenon_Hd5 zenon_H145 zenon_H189 zenon_H7b zenon_H18f zenon_H136 zenon_H160 zenon_H1cc zenon_H31 zenon_Ha0 zenon_H17e zenon_H12b zenon_H1c7 zenon_H9a zenon_H67 zenon_H24 zenon_H142 zenon_Hac zenon_H165 zenon_H1ca zenon_H235 zenon_H204 zenon_H205 zenon_H94 zenon_H2f zenon_H1a5 zenon_H1a6 zenon_H1a4 zenon_H1a7 zenon_H191 zenon_H195 zenon_H19d zenon_H18c zenon_H115 zenon_H10e zenon_Ha1 zenon_Ha8 zenon_He8 zenon_Hdf zenon_Hd8 zenon_Haf zenon_He7 zenon_H106 zenon_H109 zenon_H185 zenon_H184 zenon_H183 zenon_H17b zenon_H178 zenon_H179 zenon_H13e zenon_H13c zenon_H139 zenon_H133 zenon_H124 zenon_H172 zenon_H173 zenon_H16f zenon_H168 zenon_H149 zenon_H14f zenon_H153 zenon_H39 zenon_H182 zenon_H1fe zenon_H1ee zenon_H1e0 zenon_H1ac zenon_H1c4 zenon_H1ba zenon_H1cf zenon_H1d8 zenon_H1d5 zenon_H1ec zenon_H1ed zenon_H3f zenon_H22 zenon_H45 zenon_H6a zenon_H54 zenon_H57 zenon_H62 zenon_H52 zenon_H4f zenon_H4a zenon_H71 zenon_H6d zenon_H6f zenon_H3e zenon_H74 zenon_H1fa zenon_H1f0 zenon_H201 zenon_H206 zenon_H233 zenon_Hdb zenon_Hd6. % 18.68/18.87 apply (zenon_or_s _ _ zenon_H106); [ zenon_intro zenon_Hed | zenon_intro zenon_H107 ]. % 18.68/18.87 apply (zenon_L491_); trivial. % 18.68/18.87 apply (zenon_or_s _ _ zenon_H107); [ zenon_intro zenon_Ha5 | zenon_intro zenon_H108 ]. % 18.68/18.87 apply (zenon_L357_); trivial. % 18.68/18.87 apply (zenon_or_s _ _ zenon_H108); [ zenon_intro zenon_Hf1 | zenon_intro zenon_Hf4 ]. % 18.68/18.87 apply (zenon_L578_); trivial. % 18.68/18.87 apply (zenon_L126_); trivial. % 18.68/18.87 (* end of lemma zenon_L582_ *) % 18.68/18.87 assert (zenon_L583_ : (((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) (e0)) = (e1)) -> (~((op (e2) (e2)) = (op (e3) (e2)))) -> (((op (e2) (e0)) = (e3))\/(((op (e2) (e1)) = (e3))\/(((op (e2) (e2)) = (e3))\/((op (e2) (e3)) = (e3))))) -> (~((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)) = (e2)) -> (~((op (e0) (e0)) = (op (e2) (e0)))) -> ((op (e3) (e1)) = (e2)) -> (~((op (e2) (e1)) = (op (e3) (e1)))) -> (~((op (e2) (e2)) = (e2))) -> (((op (e0) (e3)) = (e3))\/(((op (e1) (e3)) = (e3))\/(((op (e2) (e3)) = (e3))\/((op (e3) (e3)) = (e3))))) -> (~((op (e1) (e1)) = (op (e3) (e1)))) -> (((op (e2) (e1)) = (e0))\/(((op (e2) (e1)) = (e1))\/(((op (e2) (e1)) = (e2))\/((op (e2) (e1)) = (e3))))) -> (~((op (e2) (e1)) = (e0))) -> ((op (e0) (e1)) = (e1)) -> (~((op (e0) (e1)) = (op (e2) (e1)))) -> ((op (e2) (e0)) = (e0)) -> (~((op (e2) (e0)) = (op (e2) (e3)))) -> (((op (e0) (e3)) = (e2))\/(((op (e1) (e3)) = (e2))\/(((op (e2) (e3)) = (e2))\/((op (e3) (e3)) = (e2))))) -> (~((e2) = (e3))) -> (~((e1) = (e2))) -> (~((op (e2) (e1)) = (op (e2) (e3)))) -> (((op (e2) (e3)) = (e0))\/(((op (e2) (e3)) = (e1))\/(((op (e2) (e3)) = (e2))\/((op (e2) (e3)) = (e3))))) -> (~((e0) = (e3))) -> (((op (e0) (e3)) = (e0))\/(((op (e1) (e3)) = (e0))\/(((op (e2) (e3)) = (e0))\/((op (e3) (e3)) = (e0))))) -> (~((op (e1) (e1)) = (e1))) -> (~((op (e1) (e1)) = (e0))) -> (((op (e1) (e1)) = (e0))\/(((op (e1) (e1)) = (e1))\/(((op (e1) (e1)) = (e2))\/((op (e1) (e1)) = (e3))))) -> (~((e1) = (e3))) -> ((op (e1) (e3)) = (e1)) -> (~((op (e0) (e3)) = (op (e2) (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) (e1)) = (e0)) -> (~((op (e0) (e3)) = (op (e3) (e3)))) -> (~((op (e2) (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 (e3) (e3)) = (e3))) -> False). % 18.68/18.87 do 0 intro. intros zenon_H1a5 zenon_H165 zenon_Hac zenon_H18f zenon_He7 zenon_H149 zenon_H13e zenon_H1d5 zenon_H7b zenon_H39 zenon_H14d zenon_Haf zenon_H173 zenon_H136 zenon_H160 zenon_H1cc zenon_H31 zenon_Ha0 zenon_H17e zenon_H34 zenon_H5b zenon_H145 zenon_H12b zenon_H7c zenon_H1c7 zenon_H11f zenon_H9a zenon_H67 zenon_H10a zenon_H24 zenon_H142 zenon_H95 zenon_Hd6 zenon_He2 zenon_H101 zenon_H130 zenon_H1b1 zenon_Hc2 zenon_Hf3 zenon_H1d zenon_H1f zenon_He4 zenon_H102. % 18.68/18.87 apply (zenon_or_s _ _ zenon_H1a5); [ zenon_intro zenon_H99 | zenon_intro zenon_H1a8 ]. % 18.68/18.87 apply (zenon_L403_); trivial. % 18.68/18.87 apply (zenon_or_s _ _ zenon_H1a8); [ zenon_intro zenon_H13f | zenon_intro zenon_H1a9 ]. % 18.68/18.87 apply (zenon_or_s _ _ zenon_H1d5); [ zenon_intro zenon_Hee | zenon_intro zenon_H1d6 ]. % 18.68/18.87 apply (zenon_L204_); trivial. % 18.68/18.87 apply (zenon_or_s _ _ zenon_H1d6); [ zenon_intro zenon_H1ca | zenon_intro zenon_H1d7 ]. % 18.68/18.87 apply (zenon_L364_); trivial. % 18.68/18.87 apply (zenon_or_s _ _ zenon_H1d7); [ zenon_intro zenon_H176 | zenon_intro zenon_H11d ]. % 18.68/18.87 exact (zenon_H173 zenon_H176). % 18.68/18.87 apply (zenon_or_s _ _ zenon_He7); [ zenon_intro zenon_H3b | zenon_intro zenon_He9 ]. % 18.68/18.87 apply (zenon_L308_); trivial. % 18.68/18.87 apply (zenon_or_s _ _ zenon_He9); [ zenon_intro zenon_Ha6 | zenon_intro zenon_Hea ]. % 18.68/18.87 apply (zenon_L95_); trivial. % 18.68/18.87 apply (zenon_or_s _ _ zenon_Hea); [ zenon_intro zenon_Haa | zenon_intro zenon_Hdd ]. % 18.68/18.87 apply (zenon_L575_); trivial. % 18.68/18.87 apply (zenon_L573_); trivial. % 18.68/18.87 apply (zenon_or_s _ _ zenon_H1a9); [ zenon_intro zenon_Ha6 | zenon_intro zenon_H161 ]. % 18.68/18.87 apply (zenon_L522_); trivial. % 18.68/18.87 apply (zenon_or_s _ _ zenon_H1d5); [ zenon_intro zenon_Hee | zenon_intro zenon_H1d6 ]. % 18.68/18.87 apply (zenon_L341_); trivial. % 18.68/18.87 apply (zenon_or_s _ _ zenon_H1d6); [ zenon_intro zenon_H1ca | zenon_intro zenon_H1d7 ]. % 18.68/18.87 apply (zenon_L364_); trivial. % 18.68/18.87 apply (zenon_or_s _ _ zenon_H1d7); [ zenon_intro zenon_H176 | zenon_intro zenon_H11d ]. % 18.68/18.87 exact (zenon_H173 zenon_H176). % 18.68/18.87 apply (zenon_L574_); trivial. % 18.68/18.87 (* end of lemma zenon_L583_ *) % 18.68/18.87 assert (zenon_L584_ : (((op (e0) (e1)) = (e0))\/(((op (e1) (e1)) = (e0))\/(((op (e2) (e1)) = (e0))\/((op (e3) (e1)) = (e0))))) -> (~((op (e2) (e1)) = (e0))) -> (~((op (e1) (e2)) = (e0))) -> ((op (e3) (e0)) = (e1)) -> (~((op (e3) (e0)) = (op (e3) (e1)))) -> ((op (e0) (e0)) = (e3)) -> (~((e0) = (e1))) -> (((op (e3) (e0)) = (e0))\/(((op (e3) (e1)) = (e0))\/(((op (e3) (e2)) = (e0))\/((op (e3) (e3)) = (e0))))) -> (~((op (e0) (e2)) = (op (e3) (e2)))) -> (~((op (e1) (e0)) = (op (e1) (e1)))) -> (((op (e0) (e3)) = (e0))\/(((op (e1) (e3)) = (e0))\/(((op (e2) (e3)) = (e0))\/((op (e3) (e3)) = (e0))))) -> (~((op (e2) (e0)) = (op (e2) (e3)))) -> ((~((op (e0) (e2)) = (e0)))\/((op (e0) (e0)) = (e2))) -> ((~((op (e1) (e0)) = (e0)))\/((op (e1) (e0)) = (e0))) -> (~((op (e2) (e0)) = (op (e2) (e1)))) -> (~((op (e1) (e0)) = (op (e3) (e0)))) -> (((op (e0) (e2)) = (e0))\/(((op (e0) (e2)) = (e1))\/(((op (e0) (e2)) = (e2))\/((op (e0) (e2)) = (e3))))) -> (((op (e0) (e0)) = (e3))\/(((op (e1) (e0)) = (e3))\/(((op (e2) (e0)) = (e3))\/((op (e3) (e0)) = (e3))))) -> ((~((op (e2) (e0)) = (e0)))\/((op (e2) (e0)) = (e0))) -> (((op (e0) (e0)) = (e2))\/(((op (e1) (e0)) = (e2))\/(((op (e2) (e0)) = (e2))\/((op (e3) (e0)) = (e2))))) -> (((op (e0) (e0)) = (e3))\/(((op (e0) (e1)) = (e3))\/(((op (e0) (e2)) = (e3))\/((op (e0) (e3)) = (e3))))) -> (~((op (e1) (e2)) = (op (e1) (e3)))) -> (((op (e0) (e3)) = (e3))\/(((op (e1) (e3)) = (e3))\/(((op (e2) (e3)) = (e3))\/((op (e3) (e3)) = (e3))))) -> (((op (e1) (e0)) = (e1))\/(((op (e1) (e1)) = (e1))\/(((op (e1) (e2)) = (e1))\/((op (e1) (e3)) = (e1))))) -> (~((op (e0) (e0)) = (op (e0) (e2)))) -> ((~((op (e1) (e3)) = (e0)))\/((op (e1) (e0)) = (e3))) -> ((~((op (e1) (e2)) = (e0)))\/((op (e1) (e0)) = (e2))) -> (~((op (e2) (e0)) = (op (e3) (e0)))) -> (((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) (e2)) = (e0))\/(((op (e1) (e2)) = (e1))\/(((op (e1) (e2)) = (e2))\/((op (e1) (e2)) = (e3))))) -> (~((op (e0) (e2)) = (op (e1) (e2)))) -> (((op (e3) (e2)) = (e0))\/(((op (e3) (e2)) = (e1))\/(((op (e3) (e2)) = (e2))\/((op (e3) (e2)) = (e3))))) -> ((~((op (e1) (e1)) = (e0)))\/((op (e1) (e0)) = (e1))) -> ((~((op (e0) (e3)) = (e0)))\/((op (e0) (e0)) = (e3))) -> ((~((op (e3) (e3)) = (e0)))\/((op (e3) (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 (e2) (e2)) = (e0)))\/((op (e2) (e0)) = (e2))) -> (((op (e2) (e0)) = (e0))\/(((op (e2) (e1)) = (e0))\/(((op (e2) (e2)) = (e0))\/((op (e2) (e3)) = (e0))))) -> ((~((op (e3) (e0)) = (e0)))\/((op (e3) (e0)) = (e0))) -> ((~((op (e3) (e2)) = (e0)))\/((op (e3) (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) (e3)) = (e1))\/(((op (e1) (e3)) = (e1))\/(((op (e2) (e3)) = (e1))\/((op (e3) (e3)) = (e1))))) -> (~((op (e3) (e0)) = (op (e3) (e3)))) -> (~((op (e2) (e2)) = (op (e2) (e3)))) -> (~((op (e1) (e0)) = (op (e1) (e3)))) -> (~((op (e0) (e1)) = (op (e0) (e3)))) -> (~((op (e0) (e1)) = (op (e3) (e1)))) -> (~((op (e0) (e1)) = (op (e0) (e2)))) -> (~((op (e1) (e2)) = (op (e3) (e2)))) -> (((op (e2) (e3)) = (e0))\/(((op (e2) (e3)) = (e1))\/(((op (e2) (e3)) = (e2))\/((op (e2) (e3)) = (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) (e3)) = (e0))\/(((op (e1) (e3)) = (e1))\/(((op (e1) (e3)) = (e2))\/((op (e1) (e3)) = (e3))))) -> (~((op (e0) (e3)) = (op (e2) (e3)))) -> (((op (e0) (e1)) = (e1))\/(((op (e1) (e1)) = (e1))\/(((op (e2) (e1)) = (e1))\/((op (e3) (e1)) = (e1))))) -> (((op (e2) (e0)) = (e1))\/(((op (e2) (e1)) = (e1))\/(((op (e2) (e2)) = (e1))\/((op (e2) (e3)) = (e1))))) -> (~((op (e0) (e0)) = (op (e0) (e3)))) -> (((op (e1) (e0)) = (e2))\/(((op (e1) (e1)) = (e2))\/(((op (e1) (e2)) = (e2))\/((op (e1) (e3)) = (e2))))) -> (~((op (e1) (e1)) = (op (e3) (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))))) -> (~((op (e1) (e2)) = (op (e2) (e2)))) -> (~((op (e1) (e1)) = (op (e1) (e2)))) -> (~((op (e3) (e0)) = (op (e3) (e2)))) -> (((op (e0) (e2)) = (e0))\/(((op (e1) (e2)) = (e0))\/(((op (e2) (e2)) = (e0))\/((op (e3) (e2)) = (e0))))) -> (((op (e2) (e1)) = (e0))\/(((op (e2) (e1)) = (e1))\/(((op (e2) (e1)) = (e2))\/((op (e2) (e1)) = (e3))))) -> (~((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 (e0) (e1)) = (e3))\/(((op (e1) (e1)) = (e3))\/(((op (e2) (e1)) = (e3))\/((op (e3) (e1)) = (e3))))) -> (((op (e0) (e3)) = (e0))\/(((op (e0) (e3)) = (e1))\/(((op (e0) (e3)) = (e2))\/((op (e0) (e3)) = (e3))))) -> (~((op (e1) (e3)) = (op (e3) (e3)))) -> (((op (e3) (e0)) = (e1))\/(((op (e3) (e1)) = (e1))\/(((op (e3) (e2)) = (e1))\/((op (e3) (e3)) = (e1))))) -> (~((e2) = (e3))) -> (~((e0) = (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) (e2)) = (op (e3) (e2)))) -> (((op (e0) (e2)) = (e1))\/(((op (e1) (e2)) = (e1))\/(((op (e2) (e2)) = (e1))\/((op (e3) (e2)) = (e1))))) -> (~((op (e1) (e0)) = (op (e2) (e0)))) -> (((op (e1) (e0)) = (e0))\/(((op (e1) (e1)) = (e0))\/(((op (e1) (e2)) = (e0))\/((op (e1) (e3)) = (e0))))) -> (~((e1) = (e3))) -> (~((op (e0) (e2)) = (op (e0) (e3)))) -> (((op (e0) (e0)) = (e0))\/(((op (e0) (e1)) = (e0))\/(((op (e0) (e2)) = (e0))\/((op (e0) (e3)) = (e0))))) -> ((~((op (e3) (e1)) = (e0)))\/((op (e3) (e0)) = (e1))) -> (~((op (e0) (e0)) = (e0))) -> (~((op (e1) (e0)) = (e0))) -> (((op (e0) (e0)) = (e0))\/(((op (e1) (e0)) = (e0))\/(((op (e2) (e0)) = (e0))\/((op (e3) (e0)) = (e0))))) -> ((~((op (e2) (e3)) = (e0)))\/((op (e2) (e0)) = (e3))) -> ((~((op (e2) (e1)) = (e0)))\/((op (e2) (e0)) = (e1))) -> (((op (e0) (e0)) = (e1))\/(((op (e1) (e0)) = (e1))\/(((op (e2) (e0)) = (e1))\/((op (e3) (e0)) = (e1))))) -> (~((op (e2) (e3)) = (op (e3) (e3)))) -> (((op (e0) (e1)) = (e2))\/(((op (e1) (e1)) = (e2))\/(((op (e2) (e1)) = (e2))\/((op (e3) (e1)) = (e2))))) -> (~((op (e0) (e1)) = (op (e1) (e1)))) -> (((op (e0) (e3)) = (e2))\/(((op (e1) (e3)) = (e2))\/(((op (e2) (e3)) = (e2))\/((op (e3) (e3)) = (e2))))) -> (~((e1) = (e2))) -> (~((op (e1) (e1)) = (op (e1) (e3)))) -> (~((op (e2) (e1)) = (op (e2) (e3)))) -> (~((op (e3) (e2)) = (op (e3) (e3)))) -> (~((op (e1) (e1)) = (e1))) -> (~((op (e1) (e1)) = (e0))) -> (((op (e1) (e1)) = (e0))\/(((op (e1) (e1)) = (e1))\/(((op (e1) (e1)) = (e2))\/((op (e1) (e1)) = (e3))))) -> (((op (e2) (e0)) = (e2))\/(((op (e2) (e1)) = (e2))\/(((op (e2) (e2)) = (e2))\/((op (e2) (e3)) = (e2))))) -> (~((e0) = (e2))) -> ((op (e2) (e0)) = (e0)) -> (~((op (e0) (e1)) = (op (e2) (e1)))) -> (~((op (e2) (e2)) = (e2))) -> (~((op (e1) (e3)) = (op (e2) (e3)))) -> (~((op (e0) (e1)) = (e0))) -> (((op (e0) (e1)) = (e0))\/(((op (e0) (e1)) = (e1))\/(((op (e0) (e1)) = (e2))\/((op (e0) (e1)) = (e3))))) -> ((op (e0) (e2)) = (e0)) -> (((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 (e0) (e3)) = (op (e3) (e3)))) -> (~((op (e3) (e1)) = (op (e3) (e3)))) -> (~((op (e3) (e3)) = (e3))) -> (~((op (e0) (e3)) = (op (e1) (e3)))) -> ((op (e0) (e3)) = (e1)) -> False). % 18.68/18.87 do 0 intro. intros zenon_H245 zenon_H31 zenon_H25 zenon_Hac zenon_H1cf zenon_H3a zenon_Ha1 zenon_H1ac zenon_H14f zenon_H45 zenon_H67 zenon_H5b zenon_H233 zenon_H206 zenon_H1f0 zenon_H1fa zenon_H1ba zenon_H1e0 zenon_H1ee zenon_H1fe zenon_H168 zenon_H124 zenon_H136 zenon_H128 zenon_H13c zenon_H179 zenon_H178 zenon_H17b zenon_H183 zenon_He7 zenon_H19d zenon_H195 zenon_H191 zenon_H205 zenon_H204 zenon_H1ec zenon_Ha8 zenon_H165 zenon_H185 zenon_H2f zenon_H184 zenon_H1a7 zenon_H22d zenon_H39 zenon_H7b zenon_H133 zenon_H71 zenon_H6d zenon_Hd8 zenon_H54 zenon_H210 zenon_H4a zenon_H115 zenon_H11f zenon_H22a zenon_Haf zenon_Hdf zenon_He2 zenon_H109 zenon_H106 zenon_H189 zenon_H18c zenon_H160 zenon_H16f zenon_H153 zenon_H2b zenon_H4f zenon_H6f zenon_H6a zenon_H1cc zenon_H13e zenon_H1a6 zenon_H1a4 zenon_H1a5 zenon_He4 zenon_Hd5 zenon_He8 zenon_H12b zenon_H9a zenon_H52 zenon_H1c4 zenon_H18f zenon_H139 zenon_H201 zenon_H22 zenon_H95 zenon_H208 zenon_H74 zenon_H1ed zenon_H3f zenon_H23 zenon_H3e zenon_H94 zenon_H182 zenon_H235 zenon_Hf3 zenon_H1d8 zenon_H10e zenon_H145 zenon_H7c zenon_H57 zenon_H1c7 zenon_H62 zenon_H10a zenon_H24 zenon_H142 zenon_H1d5 zenon_H149 zenon_H34 zenon_H17e zenon_H173 zenon_Hdb zenon_H20b zenon_H212 zenon_H48 zenon_H172 zenon_H101 zenon_Hc2 zenon_H130 zenon_H102 zenon_H1d zenon_Hc3. % 18.68/18.87 apply (zenon_or_s _ _ zenon_H245); [ zenon_intro zenon_H49 | zenon_intro zenon_H246 ]. % 18.68/18.87 exact (zenon_H20b zenon_H49). % 18.68/18.87 apply (zenon_or_s _ _ zenon_H246); [ zenon_intro zenon_H29 | zenon_intro zenon_H247 ]. % 18.68/18.87 exact (zenon_H24 zenon_H29). % 18.68/18.87 apply (zenon_or_s _ _ zenon_H247); [ zenon_intro zenon_H36 | zenon_intro zenon_H1b1 ]. % 18.68/18.87 exact (zenon_H31 zenon_H36). % 18.68/18.87 apply (zenon_or_s _ _ zenon_H128); [ zenon_intro zenon_H9d | zenon_intro zenon_H129 ]. % 18.68/18.87 apply (zenon_L488_); trivial. % 18.68/18.87 apply (zenon_or_s _ _ zenon_H129); [ zenon_intro zenon_H10d | zenon_intro zenon_H12a ]. % 18.68/18.87 exact (zenon_H10a zenon_H10d). % 18.68/18.87 apply (zenon_or_s _ _ zenon_H12a); [ zenon_intro zenon_Hf0 | zenon_intro zenon_Hd6 ]. % 18.68/18.87 apply (zenon_L501_); trivial. % 18.68/18.87 apply (zenon_L79_); trivial. % 18.68/18.87 (* end of lemma zenon_L584_ *) % 18.68/18.87 assert (zenon_L585_ : ((op (e1) (e0)) = (e3)) -> (~((op (e3) (e2)) = (e0))) -> (~((op (e2) (e2)) = (e0))) -> (((op (e0) (e1)) = (e0))\/(((op (e1) (e1)) = (e0))\/(((op (e2) (e1)) = (e0))\/((op (e3) (e1)) = (e0))))) -> (~((op (e2) (e1)) = (e0))) -> (~((op (e1) (e2)) = (e0))) -> ((op (e3) (e0)) = (e1)) -> (~((op (e3) (e0)) = (op (e3) (e1)))) -> ((op (e0) (e0)) = (e3)) -> (~((e0) = (e1))) -> (((op (e3) (e0)) = (e0))\/(((op (e3) (e1)) = (e0))\/(((op (e3) (e2)) = (e0))\/((op (e3) (e3)) = (e0))))) -> (~((op (e0) (e2)) = (op (e3) (e2)))) -> (~((op (e1) (e0)) = (op (e1) (e1)))) -> (((op (e0) (e3)) = (e0))\/(((op (e1) (e3)) = (e0))\/(((op (e2) (e3)) = (e0))\/((op (e3) (e3)) = (e0))))) -> (~((op (e2) (e0)) = (op (e2) (e3)))) -> ((~((op (e0) (e2)) = (e0)))\/((op (e0) (e0)) = (e2))) -> ((~((op (e1) (e0)) = (e0)))\/((op (e1) (e0)) = (e0))) -> (~((op (e2) (e0)) = (op (e2) (e1)))) -> (~((op (e1) (e0)) = (op (e3) (e0)))) -> (((op (e0) (e2)) = (e0))\/(((op (e0) (e2)) = (e1))\/(((op (e0) (e2)) = (e2))\/((op (e0) (e2)) = (e3))))) -> (((op (e0) (e0)) = (e3))\/(((op (e1) (e0)) = (e3))\/(((op (e2) (e0)) = (e3))\/((op (e3) (e0)) = (e3))))) -> ((~((op (e2) (e0)) = (e0)))\/((op (e2) (e0)) = (e0))) -> (((op (e0) (e0)) = (e2))\/(((op (e1) (e0)) = (e2))\/(((op (e2) (e0)) = (e2))\/((op (e3) (e0)) = (e2))))) -> (((op (e0) (e0)) = (e3))\/(((op (e0) (e1)) = (e3))\/(((op (e0) (e2)) = (e3))\/((op (e0) (e3)) = (e3))))) -> (~((op (e1) (e2)) = (op (e1) (e3)))) -> (((op (e0) (e3)) = (e3))\/(((op (e1) (e3)) = (e3))\/(((op (e2) (e3)) = (e3))\/((op (e3) (e3)) = (e3))))) -> (((op (e1) (e0)) = (e1))\/(((op (e1) (e1)) = (e1))\/(((op (e1) (e2)) = (e1))\/((op (e1) (e3)) = (e1))))) -> (~((op (e0) (e0)) = (op (e0) (e2)))) -> ((~((op (e1) (e3)) = (e0)))\/((op (e1) (e0)) = (e3))) -> ((~((op (e1) (e2)) = (e0)))\/((op (e1) (e0)) = (e2))) -> (~((op (e2) (e0)) = (op (e3) (e0)))) -> (((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) (e2)) = (e0))\/(((op (e1) (e2)) = (e1))\/(((op (e1) (e2)) = (e2))\/((op (e1) (e2)) = (e3))))) -> (~((op (e0) (e2)) = (op (e1) (e2)))) -> (((op (e3) (e2)) = (e0))\/(((op (e3) (e2)) = (e1))\/(((op (e3) (e2)) = (e2))\/((op (e3) (e2)) = (e3))))) -> ((~((op (e1) (e1)) = (e0)))\/((op (e1) (e0)) = (e1))) -> ((~((op (e0) (e3)) = (e0)))\/((op (e0) (e0)) = (e3))) -> ((~((op (e3) (e3)) = (e0)))\/((op (e3) (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 (e2) (e2)) = (e0)))\/((op (e2) (e0)) = (e2))) -> (((op (e2) (e0)) = (e0))\/(((op (e2) (e1)) = (e0))\/(((op (e2) (e2)) = (e0))\/((op (e2) (e3)) = (e0))))) -> ((~((op (e3) (e0)) = (e0)))\/((op (e3) (e0)) = (e0))) -> ((~((op (e3) (e2)) = (e0)))\/((op (e3) (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) (e3)) = (e1))\/(((op (e1) (e3)) = (e1))\/(((op (e2) (e3)) = (e1))\/((op (e3) (e3)) = (e1))))) -> (~((op (e3) (e0)) = (op (e3) (e3)))) -> (~((op (e2) (e2)) = (op (e2) (e3)))) -> (~((op (e1) (e0)) = (op (e1) (e3)))) -> (~((op (e0) (e1)) = (op (e0) (e3)))) -> (~((op (e0) (e1)) = (op (e3) (e1)))) -> (~((op (e0) (e1)) = (op (e0) (e2)))) -> (~((op (e1) (e2)) = (op (e3) (e2)))) -> (((op (e2) (e3)) = (e0))\/(((op (e2) (e3)) = (e1))\/(((op (e2) (e3)) = (e2))\/((op (e2) (e3)) = (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) (e3)) = (e0))\/(((op (e1) (e3)) = (e1))\/(((op (e1) (e3)) = (e2))\/((op (e1) (e3)) = (e3))))) -> (~((op (e0) (e3)) = (op (e2) (e3)))) -> (((op (e0) (e1)) = (e1))\/(((op (e1) (e1)) = (e1))\/(((op (e2) (e1)) = (e1))\/((op (e3) (e1)) = (e1))))) -> (((op (e2) (e0)) = (e1))\/(((op (e2) (e1)) = (e1))\/(((op (e2) (e2)) = (e1))\/((op (e2) (e3)) = (e1))))) -> (~((op (e0) (e0)) = (op (e0) (e3)))) -> (((op (e1) (e0)) = (e2))\/(((op (e1) (e1)) = (e2))\/(((op (e1) (e2)) = (e2))\/((op (e1) (e3)) = (e2))))) -> (~((op (e1) (e1)) = (op (e3) (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))))) -> (~((op (e1) (e2)) = (op (e2) (e2)))) -> (~((op (e1) (e1)) = (op (e1) (e2)))) -> (~((op (e3) (e0)) = (op (e3) (e2)))) -> (((op (e0) (e2)) = (e0))\/(((op (e1) (e2)) = (e0))\/(((op (e2) (e2)) = (e0))\/((op (e3) (e2)) = (e0))))) -> (((op (e2) (e1)) = (e0))\/(((op (e2) (e1)) = (e1))\/(((op (e2) (e1)) = (e2))\/((op (e2) (e1)) = (e3))))) -> (~((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 (e0) (e1)) = (e3))\/(((op (e1) (e1)) = (e3))\/(((op (e2) (e1)) = (e3))\/((op (e3) (e1)) = (e3))))) -> (((op (e0) (e3)) = (e0))\/(((op (e0) (e3)) = (e1))\/(((op (e0) (e3)) = (e2))\/((op (e0) (e3)) = (e3))))) -> (~((op (e1) (e3)) = (op (e3) (e3)))) -> (((op (e3) (e0)) = (e1))\/(((op (e3) (e1)) = (e1))\/(((op (e3) (e2)) = (e1))\/((op (e3) (e3)) = (e1))))) -> (~((e2) = (e3))) -> (~((e0) = (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) (e2)) = (op (e3) (e2)))) -> (((op (e0) (e2)) = (e1))\/(((op (e1) (e2)) = (e1))\/(((op (e2) (e2)) = (e1))\/((op (e3) (e2)) = (e1))))) -> (~((op (e1) (e0)) = (op (e2) (e0)))) -> (((op (e1) (e0)) = (e0))\/(((op (e1) (e1)) = (e0))\/(((op (e1) (e2)) = (e0))\/((op (e1) (e3)) = (e0))))) -> (~((e1) = (e3))) -> (~((op (e0) (e2)) = (op (e0) (e3)))) -> (((op (e0) (e0)) = (e0))\/(((op (e0) (e1)) = (e0))\/(((op (e0) (e2)) = (e0))\/((op (e0) (e3)) = (e0))))) -> ((~((op (e3) (e1)) = (e0)))\/((op (e3) (e0)) = (e1))) -> (~((op (e0) (e0)) = (e0))) -> (~((op (e1) (e0)) = (e0))) -> (((op (e0) (e0)) = (e0))\/(((op (e1) (e0)) = (e0))\/(((op (e2) (e0)) = (e0))\/((op (e3) (e0)) = (e0))))) -> ((~((op (e2) (e3)) = (e0)))\/((op (e2) (e0)) = (e3))) -> ((~((op (e2) (e1)) = (e0)))\/((op (e2) (e0)) = (e1))) -> (((op (e0) (e0)) = (e1))\/(((op (e1) (e0)) = (e1))\/(((op (e2) (e0)) = (e1))\/((op (e3) (e0)) = (e1))))) -> (~((op (e2) (e3)) = (op (e3) (e3)))) -> (((op (e0) (e1)) = (e2))\/(((op (e1) (e1)) = (e2))\/(((op (e2) (e1)) = (e2))\/((op (e3) (e1)) = (e2))))) -> (~((op (e0) (e1)) = (op (e1) (e1)))) -> (((op (e0) (e3)) = (e2))\/(((op (e1) (e3)) = (e2))\/(((op (e2) (e3)) = (e2))\/((op (e3) (e3)) = (e2))))) -> (~((e1) = (e2))) -> (~((op (e1) (e1)) = (op (e1) (e3)))) -> (~((op (e2) (e1)) = (op (e2) (e3)))) -> (~((op (e3) (e2)) = (op (e3) (e3)))) -> (~((op (e1) (e1)) = (e1))) -> (~((op (e1) (e1)) = (e0))) -> (((op (e1) (e1)) = (e0))\/(((op (e1) (e1)) = (e1))\/(((op (e1) (e1)) = (e2))\/((op (e1) (e1)) = (e3))))) -> (((op (e2) (e0)) = (e2))\/(((op (e2) (e1)) = (e2))\/(((op (e2) (e2)) = (e2))\/((op (e2) (e3)) = (e2))))) -> (~((e0) = (e2))) -> ((op (e2) (e0)) = (e0)) -> (~((op (e0) (e1)) = (op (e2) (e1)))) -> (~((op (e2) (e2)) = (e2))) -> (~((op (e1) (e3)) = (op (e2) (e3)))) -> (~((op (e0) (e1)) = (e0))) -> (((op (e0) (e1)) = (e0))\/(((op (e0) (e1)) = (e1))\/(((op (e0) (e1)) = (e2))\/((op (e0) (e1)) = (e3))))) -> ((op (e0) (e2)) = (e0)) -> (((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 (e0) (e3)) = (op (e3) (e3)))) -> (~((op (e3) (e1)) = (op (e3) (e3)))) -> (~((op (e3) (e3)) = (e3))) -> (~((op (e0) (e3)) = (op (e1) (e3)))) -> False). % 18.68/18.87 do 0 intro. intros zenon_H9e zenon_H18b zenon_H81 zenon_H245 zenon_H31 zenon_H25 zenon_Hac zenon_H1cf zenon_H3a zenon_Ha1 zenon_H1ac zenon_H14f zenon_H45 zenon_H67 zenon_H5b zenon_H233 zenon_H206 zenon_H1f0 zenon_H1fa zenon_H1ba zenon_H1e0 zenon_H1ee zenon_H1fe zenon_H168 zenon_H124 zenon_H136 zenon_H128 zenon_H13c zenon_H179 zenon_H178 zenon_H17b zenon_H183 zenon_He7 zenon_H19d zenon_H195 zenon_H191 zenon_H205 zenon_H204 zenon_H1ec zenon_Ha8 zenon_H165 zenon_H185 zenon_H2f zenon_H184 zenon_H1a7 zenon_H22d zenon_H39 zenon_H7b zenon_H133 zenon_H71 zenon_H6d zenon_Hd8 zenon_H54 zenon_H210 zenon_H4a zenon_H115 zenon_H11f zenon_H22a zenon_Haf zenon_Hdf zenon_He2 zenon_H109 zenon_H106 zenon_H189 zenon_H18c zenon_H160 zenon_H16f zenon_H153 zenon_H2b zenon_H4f zenon_H6f zenon_H6a zenon_H1cc zenon_H13e zenon_H1a6 zenon_H1a4 zenon_H1a5 zenon_He4 zenon_Hd5 zenon_He8 zenon_H12b zenon_H9a zenon_H52 zenon_H1c4 zenon_H18f zenon_H139 zenon_H201 zenon_H22 zenon_H95 zenon_H208 zenon_H74 zenon_H1ed zenon_H3f zenon_H23 zenon_H3e zenon_H94 zenon_H182 zenon_H235 zenon_Hf3 zenon_H1d8 zenon_H10e zenon_H145 zenon_H7c zenon_H57 zenon_H1c7 zenon_H62 zenon_H10a zenon_H24 zenon_H142 zenon_H1d5 zenon_H149 zenon_H34 zenon_H17e zenon_H173 zenon_Hdb zenon_H20b zenon_H212 zenon_H48 zenon_H172 zenon_H101 zenon_Hc2 zenon_H130 zenon_H102 zenon_H1d. % 18.68/18.87 apply (zenon_or_s _ _ zenon_H22d); [ zenon_intro zenon_H7a | zenon_intro zenon_H22e ]. % 18.68/18.87 apply (zenon_L456_); trivial. % 18.68/18.87 apply (zenon_or_s _ _ zenon_H22e); [ zenon_intro zenon_Ha0 | zenon_intro zenon_H22f ]. % 18.68/18.87 apply (zenon_or_s _ _ zenon_H22); [ zenon_intro zenon_H27 | zenon_intro zenon_H26 ]. % 18.68/18.87 exact (zenon_H23 zenon_H27). % 18.68/18.87 apply (zenon_or_s _ _ zenon_H26); [ zenon_intro zenon_H29 | zenon_intro zenon_H28 ]. % 18.68/18.87 exact (zenon_H24 zenon_H29). % 18.68/18.87 apply (zenon_or_s _ _ zenon_H28); [ zenon_intro zenon_H2a | zenon_intro zenon_H1f ]. % 18.68/18.87 exact (zenon_H25 zenon_H2a). % 18.68/18.87 apply (zenon_or_s _ _ zenon_H245); [ zenon_intro zenon_H49 | zenon_intro zenon_H246 ]. % 18.68/18.87 exact (zenon_H20b zenon_H49). % 18.68/18.87 apply (zenon_or_s _ _ zenon_H246); [ zenon_intro zenon_H29 | zenon_intro zenon_H247 ]. % 18.68/18.87 exact (zenon_H24 zenon_H29). % 18.68/18.87 apply (zenon_or_s _ _ zenon_H247); [ zenon_intro zenon_H36 | zenon_intro zenon_H1b1 ]. % 18.68/18.87 exact (zenon_H31 zenon_H36). % 18.68/18.87 apply (zenon_or_s _ _ zenon_H128); [ zenon_intro zenon_H9d | zenon_intro zenon_H129 ]. % 18.68/18.87 apply (zenon_L37_); trivial. % 18.68/18.87 apply (zenon_or_s _ _ zenon_H129); [ zenon_intro zenon_H10d | zenon_intro zenon_H12a ]. % 18.68/18.87 exact (zenon_H10a zenon_H10d). % 18.68/18.87 apply (zenon_or_s _ _ zenon_H12a); [ zenon_intro zenon_Hf0 | zenon_intro zenon_Hd6 ]. % 18.68/18.87 apply (zenon_or_s _ _ zenon_H18c); [ zenon_intro zenon_H86 | zenon_intro zenon_H18d ]. % 18.68/18.87 apply (zenon_L494_); trivial. % 18.68/18.87 apply (zenon_or_s _ _ zenon_H18d); [ zenon_intro zenon_H110 | zenon_intro zenon_H18e ]. % 18.68/18.87 apply (zenon_or_s _ _ zenon_H106); [ zenon_intro zenon_Hed | zenon_intro zenon_H107 ]. % 18.68/18.87 apply (zenon_L214_); trivial. % 18.68/18.87 apply (zenon_or_s _ _ zenon_H107); [ zenon_intro zenon_Ha5 | zenon_intro zenon_H108 ]. % 18.68/18.87 apply (zenon_L357_); trivial. % 18.68/18.87 apply (zenon_or_s _ _ zenon_H108); [ zenon_intro zenon_Hf1 | zenon_intro zenon_Hf4 ]. % 18.68/18.87 apply (zenon_L59_); trivial. % 18.68/18.87 apply (zenon_or_s _ _ zenon_H145); [ zenon_intro zenon_Hcd | zenon_intro zenon_H146 ]. % 18.68/18.87 apply (zenon_L137_); trivial. % 18.68/18.87 apply (zenon_or_s _ _ zenon_H146); [ zenon_intro zenon_Hd7 | zenon_intro zenon_H147 ]. % 18.68/18.87 apply (zenon_L506_); trivial. % 18.68/18.87 apply (zenon_or_s _ _ zenon_H147); [ zenon_intro zenon_H11d | zenon_intro zenon_Hf6 ]. % 18.68/18.87 apply (zenon_L510_); trivial. % 18.68/18.87 apply (zenon_L63_); trivial. % 18.68/18.87 apply (zenon_or_s _ _ zenon_H18e); [ zenon_intro zenon_H113 | zenon_intro zenon_Hd7 ]. % 18.68/18.87 apply (zenon_L68_); trivial. % 18.68/18.87 apply (zenon_L506_); trivial. % 18.68/18.87 apply (zenon_or_s _ _ zenon_H18c); [ zenon_intro zenon_H86 | zenon_intro zenon_H18d ]. % 18.68/18.87 apply (zenon_L568_); trivial. % 18.68/18.87 apply (zenon_or_s _ _ zenon_H18d); [ zenon_intro zenon_H110 | zenon_intro zenon_H18e ]. % 18.68/18.87 apply (zenon_or_s _ _ zenon_H1a5); [ zenon_intro zenon_H99 | zenon_intro zenon_H1a8 ]. % 18.68/18.87 apply (zenon_L403_); trivial. % 18.68/18.87 apply (zenon_or_s _ _ zenon_H1a8); [ zenon_intro zenon_H13f | zenon_intro zenon_H1a9 ]. % 18.68/18.87 apply (zenon_L166_); trivial. % 18.68/18.87 apply (zenon_or_s _ _ zenon_H1a9); [ zenon_intro zenon_Ha6 | zenon_intro zenon_H161 ]. % 18.68/18.87 apply (zenon_L509_); trivial. % 18.68/18.87 apply (zenon_or_s _ _ zenon_H106); [ zenon_intro zenon_Hed | zenon_intro zenon_H107 ]. % 18.68/18.87 apply (zenon_L214_); trivial. % 18.68/18.87 apply (zenon_or_s _ _ zenon_H107); [ zenon_intro zenon_Ha5 | zenon_intro zenon_H108 ]. % 18.68/18.87 apply (zenon_L357_); trivial. % 18.68/18.87 apply (zenon_or_s _ _ zenon_H108); [ zenon_intro zenon_Hf1 | zenon_intro zenon_Hf4 ]. % 18.68/18.87 apply (zenon_or_s _ _ zenon_H1d5); [ zenon_intro zenon_Hee | zenon_intro zenon_H1d6 ]. % 18.68/18.87 apply (zenon_L569_); trivial. % 18.68/18.87 apply (zenon_or_s _ _ zenon_H1d6); [ zenon_intro zenon_H1ca | zenon_intro zenon_H1d7 ]. % 18.68/18.87 apply (zenon_L578_); trivial. % 18.68/18.87 apply (zenon_or_s _ _ zenon_H1d7); [ zenon_intro zenon_H176 | zenon_intro zenon_H11d ]. % 18.68/18.87 exact (zenon_H173 zenon_H176). % 18.68/18.87 apply (zenon_L574_); trivial. % 18.68/18.87 apply (zenon_L126_); trivial. % 18.68/18.87 apply (zenon_or_s _ _ zenon_H18e); [ zenon_intro zenon_H113 | zenon_intro zenon_Hd7 ]. % 18.68/18.87 apply (zenon_or_s _ _ zenon_H1d8); [ zenon_intro zenon_H10f | zenon_intro zenon_H1d9 ]. % 18.68/18.87 apply (zenon_or_s _ _ zenon_H1a5); [ zenon_intro zenon_H99 | zenon_intro zenon_H1a8 ]. % 18.68/18.87 apply (zenon_L403_); trivial. % 18.68/18.87 apply (zenon_or_s _ _ zenon_H1a8); [ zenon_intro zenon_H13f | zenon_intro zenon_H1a9 ]. % 18.68/18.87 apply (zenon_L580_); trivial. % 18.68/18.87 apply (zenon_or_s _ _ zenon_H1a9); [ zenon_intro zenon_Ha6 | zenon_intro zenon_H161 ]. % 18.68/18.87 apply (zenon_L96_); trivial. % 18.68/18.87 apply (zenon_L581_); trivial. % 18.68/18.87 apply (zenon_or_s _ _ zenon_H1d9); [ zenon_intro zenon_H110 | zenon_intro zenon_H1da ]. % 18.68/18.87 apply (zenon_or_s _ _ zenon_H1a5); [ zenon_intro zenon_H99 | zenon_intro zenon_H1a8 ]. % 18.68/18.87 apply (zenon_L403_); trivial. % 18.68/18.87 apply (zenon_or_s _ _ zenon_H1a8); [ zenon_intro zenon_H13f | zenon_intro zenon_H1a9 ]. % 18.68/18.87 apply (zenon_L166_); trivial. % 18.68/18.87 apply (zenon_or_s _ _ zenon_H1a9); [ zenon_intro zenon_Ha6 | zenon_intro zenon_H161 ]. % 18.68/18.87 apply (zenon_L509_); trivial. % 18.68/18.87 apply (zenon_L581_); trivial. % 18.68/18.87 apply (zenon_or_s _ _ zenon_H1da); [ zenon_intro zenon_H1ca | zenon_intro zenon_H14d ]. % 18.68/18.87 apply (zenon_L582_); trivial. % 18.68/18.87 apply (zenon_L583_); trivial. % 18.68/18.87 apply (zenon_L101_); trivial. % 18.68/18.87 apply (zenon_or_s _ _ zenon_H22f); [ zenon_intro zenon_H122 | zenon_intro zenon_Hc3 ]. % 18.68/18.87 apply (zenon_L438_); trivial. % 18.68/18.87 apply (zenon_L584_); trivial. % 18.68/18.87 (* end of lemma zenon_L585_ *) % 18.68/18.87 assert (zenon_L586_ : (((op (e0) (e2)) = (e2))\/(((op (e1) (e2)) = (e2))\/(((op (e2) (e2)) = (e2))\/((op (e3) (e2)) = (e2))))) -> (~((e0) = (e2))) -> ((op (e0) (e2)) = (e0)) -> (~((e1) = (e2))) -> ((op (e1) (e2)) = (e1)) -> (~((op (e2) (e2)) = (e2))) -> (~((op (e3) (e0)) = (op (e3) (e2)))) -> ((op (e3) (e0)) = (e2)) -> False). % 18.68/18.87 do 0 intro. intros zenon_H172 zenon_H149 zenon_H48 zenon_H7c zenon_Hf0 zenon_H173 zenon_H6f zenon_H148. % 18.68/18.87 apply (zenon_or_s _ _ zenon_H172); [ zenon_intro zenon_H150 | zenon_intro zenon_H174 ]. % 18.68/18.87 apply (zenon_L378_); trivial. % 18.68/18.87 apply (zenon_or_s _ _ zenon_H174); [ zenon_intro zenon_H113 | zenon_intro zenon_H175 ]. % 18.68/18.87 apply (zenon_L68_); trivial. % 18.68/18.87 apply (zenon_or_s _ _ zenon_H175); [ zenon_intro zenon_H176 | zenon_intro zenon_H151 ]. % 18.68/18.87 exact (zenon_H173 zenon_H176). % 18.68/18.87 apply (zenon_L420_); trivial. % 18.68/18.87 (* end of lemma zenon_L586_ *) % 18.68/18.87 assert (zenon_L587_ : (((op (e0) (e3)) = (e2))\/(((op (e1) (e3)) = (e2))\/(((op (e2) (e3)) = (e2))\/((op (e3) (e3)) = (e2))))) -> (~((op (e3) (e3)) = (e3))) -> (~((op (e0) (e3)) = (op (e3) (e3)))) -> ((op (e1) (e3)) = (e0)) -> (~((op (e1) (e3)) = (op (e3) (e3)))) -> (((op (e3) (e3)) = (e0))\/(((op (e3) (e3)) = (e1))\/(((op (e3) (e3)) = (e2))\/((op (e3) (e3)) = (e3))))) -> (~((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). % 18.68/18.87 do 0 intro. intros zenon_H145 zenon_H102 zenon_Hc2 zenon_H1f zenon_Hd5 zenon_H101 zenon_H7c zenon_Hd6 zenon_H1c7 zenon_H1ca zenon_H148 zenon_H71. % 18.68/18.87 apply (zenon_or_s _ _ zenon_H145); [ zenon_intro zenon_Hcd | zenon_intro zenon_H146 ]. % 18.68/18.87 apply (zenon_L137_); trivial. % 18.68/18.87 apply (zenon_or_s _ _ zenon_H146); [ zenon_intro zenon_Hd7 | zenon_intro zenon_H147 ]. % 18.68/18.87 apply (zenon_L101_); trivial. % 18.68/18.87 apply (zenon_or_s _ _ zenon_H147); [ zenon_intro zenon_H11d | zenon_intro zenon_Hf6 ]. % 18.68/18.87 apply (zenon_L224_); trivial. % 18.68/18.87 apply (zenon_L114_); trivial. % 18.68/18.87 (* end of lemma zenon_L587_ *) % 18.68/18.87 assert (zenon_L588_ : (((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) (e3)) = (e0))\/(((op (e1) (e3)) = (e0))\/(((op (e2) (e3)) = (e0))\/((op (e3) (e3)) = (e0))))) -> (~((e0) = (e3))) -> ((op (e0) (e3)) = (e3)) -> (~((op (e0) (e3)) = (op (e2) (e3)))) -> (~((op (e2) (e3)) = (op (e3) (e3)))) -> (((op (e2) (e3)) = (e0))\/(((op (e2) (e3)) = (e1))\/(((op (e2) (e3)) = (e2))\/((op (e2) (e3)) = (e3))))) -> (~((op (e2) (e1)) = (op (e2) (e3)))) -> ((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 (e2) (e0)) = (op (e2) (e3)))) -> ((op (e2) (e0)) = (e0)) -> (~((op (e3) (e1)) = (op (e3) (e3)))) -> (~((op (e0) (e1)) = (op (e2) (e1)))) -> ((op (e0) (e1)) = (e1)) -> (~((op (e2) (e1)) = (e0))) -> (((op (e2) (e1)) = (e0))\/(((op (e2) (e1)) = (e1))\/(((op (e2) (e1)) = (e2))\/((op (e2) (e1)) = (e3))))) -> ((op (e0) (e1)) = (e2)) -> ((op (e3) (e1)) = (e0)) -> False). % 18.68/18.87 do 0 intro. intros zenon_H142 zenon_H24 zenon_H10a zenon_H67 zenon_H9a zenon_He3 zenon_He2 zenon_Hf3 zenon_H11f zenon_H1c7 zenon_Hd6 zenon_H7c zenon_H12b zenon_H145 zenon_H5b zenon_H34 zenon_H130 zenon_H17e zenon_Ha0 zenon_H31 zenon_H1cc zenon_H10f zenon_H1b1. % 18.68/18.87 apply (zenon_or_s _ _ zenon_H142); [ zenon_intro zenon_H29 | zenon_intro zenon_H143 ]. % 18.68/18.87 exact (zenon_H24 zenon_H29). % 18.68/18.87 apply (zenon_or_s _ _ zenon_H143); [ zenon_intro zenon_H10d | zenon_intro zenon_H144 ]. % 18.68/18.87 exact (zenon_H10a zenon_H10d). % 18.68/18.87 apply (zenon_or_s _ _ zenon_H144); [ zenon_intro zenon_H110 | zenon_intro zenon_H13f ]. % 18.68/18.87 apply (zenon_L572_); trivial. % 18.68/18.87 apply (zenon_L580_); trivial. % 18.68/18.87 (* end of lemma zenon_L588_ *) % 18.68/18.87 assert (zenon_L589_ : (((op (e0) (e1)) = (e0))\/(((op (e1) (e1)) = (e0))\/(((op (e2) (e1)) = (e0))\/((op (e3) (e1)) = (e0))))) -> (~((op (e0) (e1)) = (e0))) -> (((op (e1) (e0)) = (e1))\/(((op (e1) (e1)) = (e1))\/(((op (e1) (e2)) = (e1))\/((op (e1) (e3)) = (e1))))) -> ((op (e1) (e0)) = (e3)) -> (~((op (e3) (e0)) = (op (e3) (e2)))) -> ((op (e0) (e2)) = (e0)) -> (((op (e0) (e2)) = (e2))\/(((op (e1) (e2)) = (e2))\/(((op (e2) (e2)) = (e2))\/((op (e3) (e2)) = (e2))))) -> (((op (e0) (e1)) = (e2))\/(((op (e1) (e1)) = (e2))\/(((op (e2) (e1)) = (e2))\/((op (e3) (e1)) = (e2))))) -> (((op (e1) (e1)) = (e0))\/(((op (e1) (e1)) = (e1))\/(((op (e1) (e1)) = (e2))\/((op (e1) (e1)) = (e3))))) -> (~((op (e1) (e1)) = (e0))) -> (~((op (e1) (e1)) = (e1))) -> (~((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 (e2) (e3)) = (op (e3) (e3)))) -> (~((op (e3) (e1)) = (op (e3) (e3)))) -> (~((op (e0) (e3)) = (op (e2) (e3)))) -> (~((e1) = (e3))) -> (((op (e2) (e1)) = (e0))\/(((op (e2) (e1)) = (e1))\/(((op (e2) (e1)) = (e2))\/((op (e2) (e1)) = (e3))))) -> (~((op (e2) (e1)) = (e0))) -> ((op (e0) (e1)) = (e1)) -> (~((op (e0) (e1)) = (op (e2) (e1)))) -> ((op (e2) (e0)) = (e0)) -> (~((op (e2) (e0)) = (op (e2) (e3)))) -> (~((e2) = (e3))) -> (((op (e2) (e3)) = (e0))\/(((op (e2) (e3)) = (e1))\/(((op (e2) (e3)) = (e2))\/((op (e2) (e3)) = (e3))))) -> (~((e0) = (e3))) -> (((op (e0) (e3)) = (e0))\/(((op (e1) (e3)) = (e0))\/(((op (e2) (e3)) = (e0))\/((op (e3) (e3)) = (e0))))) -> (((op (e0) (e3)) = (e3))\/(((op (e1) (e3)) = (e3))\/(((op (e2) (e3)) = (e3))\/((op (e3) (e3)) = (e3))))) -> (~((op (e2) (e2)) = (e2))) -> (~((op (e2) (e0)) = (op (e2) (e1)))) -> (((op (e2) (e0)) = (e2))\/(((op (e2) (e1)) = (e2))\/(((op (e2) (e2)) = (e2))\/((op (e2) (e3)) = (e2))))) -> (~((op (e3) (e0)) = (op (e3) (e3)))) -> (~((op (e2) (e1)) = (op (e2) (e3)))) -> (~((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 (e1) (e3)) = (e0)) -> (~((op (e0) (e3)) = (op (e3) (e3)))) -> (~((op (e3) (e3)) = (e3))) -> (((op (e0) (e3)) = (e2))\/(((op (e1) (e3)) = (e2))\/(((op (e2) (e3)) = (e2))\/((op (e3) (e3)) = (e2))))) -> (~((op (e3) (e0)) = (op (e3) (e1)))) -> ((op (e3) (e0)) = (e2)) -> False). % 18.68/18.87 do 0 intro. intros zenon_H245 zenon_H20b zenon_H128 zenon_H9e zenon_H6f zenon_H48 zenon_H172 zenon_H1d8 zenon_H142 zenon_H24 zenon_H10a zenon_H149 zenon_He4 zenon_H1d zenon_Hf3 zenon_H130 zenon_He2 zenon_H95 zenon_H1cc zenon_H31 zenon_Ha0 zenon_H17e zenon_H34 zenon_H5b zenon_H12b zenon_H11f zenon_H9a zenon_H67 zenon_H136 zenon_H173 zenon_H1f0 zenon_H1d5 zenon_H71 zenon_H1c7 zenon_H7c zenon_H101 zenon_Hd5 zenon_H1f zenon_Hc2 zenon_H102 zenon_H145 zenon_H1cf zenon_H148. % 18.68/18.87 apply (zenon_or_s _ _ zenon_H245); [ zenon_intro zenon_H49 | zenon_intro zenon_H246 ]. % 18.68/18.87 exact (zenon_H20b zenon_H49). % 18.68/18.87 apply (zenon_or_s _ _ zenon_H246); [ zenon_intro zenon_H29 | zenon_intro zenon_H247 ]. % 18.68/18.87 exact (zenon_H24 zenon_H29). % 18.68/18.87 apply (zenon_or_s _ _ zenon_H247); [ zenon_intro zenon_H36 | zenon_intro zenon_H1b1 ]. % 18.68/18.87 exact (zenon_H31 zenon_H36). % 18.68/18.87 apply (zenon_or_s _ _ zenon_H128); [ zenon_intro zenon_H9d | zenon_intro zenon_H129 ]. % 18.68/18.87 apply (zenon_L37_); trivial. % 18.68/18.87 apply (zenon_or_s _ _ zenon_H129); [ zenon_intro zenon_H10d | zenon_intro zenon_H12a ]. % 18.68/18.87 exact (zenon_H10a zenon_H10d). % 18.68/18.87 apply (zenon_or_s _ _ zenon_H12a); [ zenon_intro zenon_Hf0 | zenon_intro zenon_Hd6 ]. % 18.68/18.87 apply (zenon_L586_); trivial. % 18.68/18.87 apply (zenon_or_s _ _ zenon_H1d8); [ zenon_intro zenon_H10f | zenon_intro zenon_H1d9 ]. % 18.68/18.87 apply (zenon_or_s _ _ zenon_H1d5); [ zenon_intro zenon_Hee | zenon_intro zenon_H1d6 ]. % 18.68/18.87 apply (zenon_L204_); trivial. % 18.68/18.87 apply (zenon_or_s _ _ zenon_H1d6); [ zenon_intro zenon_H1ca | zenon_intro zenon_H1d7 ]. % 18.68/18.87 apply (zenon_L587_); trivial. % 18.68/18.87 apply (zenon_or_s _ _ zenon_H1d7); [ zenon_intro zenon_H176 | zenon_intro zenon_H11d ]. % 18.68/18.87 exact (zenon_H173 zenon_H176). % 18.68/18.87 apply (zenon_or_s _ _ zenon_H136); [ zenon_intro zenon_He3 | zenon_intro zenon_H137 ]. % 18.68/18.87 apply (zenon_L588_); trivial. % 18.68/18.87 apply (zenon_or_s _ _ zenon_H137); [ zenon_intro zenon_Hdc | zenon_intro zenon_H138 ]. % 18.68/18.87 apply (zenon_L83_); trivial. % 18.68/18.87 apply (zenon_or_s _ _ zenon_H138); [ zenon_intro zenon_Hdd | zenon_intro zenon_H105 ]. % 18.68/18.87 apply (zenon_L573_); trivial. % 18.68/18.87 exact (zenon_H102 zenon_H105). % 18.68/18.87 apply (zenon_or_s _ _ zenon_H1d9); [ zenon_intro zenon_H110 | zenon_intro zenon_H1da ]. % 18.68/18.87 apply (zenon_or_s _ _ zenon_H1d5); [ zenon_intro zenon_Hee | zenon_intro zenon_H1d6 ]. % 18.68/18.87 apply (zenon_L569_); trivial. % 18.68/18.87 apply (zenon_or_s _ _ zenon_H1d6); [ zenon_intro zenon_H1ca | zenon_intro zenon_H1d7 ]. % 18.68/18.87 apply (zenon_L587_); trivial. % 18.68/18.87 apply (zenon_or_s _ _ zenon_H1d7); [ zenon_intro zenon_H176 | zenon_intro zenon_H11d ]. % 18.68/18.87 exact (zenon_H173 zenon_H176). % 18.68/18.87 apply (zenon_or_s _ _ zenon_H136); [ zenon_intro zenon_He3 | zenon_intro zenon_H137 ]. % 18.68/18.87 apply (zenon_L572_); trivial. % 18.68/18.87 apply (zenon_or_s _ _ zenon_H137); [ zenon_intro zenon_Hdc | zenon_intro zenon_H138 ]. % 18.68/18.87 apply (zenon_L83_); trivial. % 18.68/18.87 apply (zenon_or_s _ _ zenon_H138); [ zenon_intro zenon_Hdd | zenon_intro zenon_H105 ]. % 18.68/18.87 apply (zenon_L573_); trivial. % 18.68/18.87 exact (zenon_H102 zenon_H105). % 18.68/18.87 apply (zenon_or_s _ _ zenon_H1da); [ zenon_intro zenon_H1ca | zenon_intro zenon_H14d ]. % 18.68/18.87 apply (zenon_L587_); trivial. % 18.68/18.87 apply (zenon_L436_); trivial. % 18.68/18.87 (* end of lemma zenon_L589_ *) % 18.68/18.87 assert (zenon_L590_ : (((op (e0) (e2)) = (e2))\/(((op (e1) (e2)) = (e2))\/(((op (e2) (e2)) = (e2))\/((op (e3) (e2)) = (e2))))) -> (~((e0) = (e2))) -> (~((e1) = (e2))) -> (~((op (e2) (e2)) = (e2))) -> (~((op (e3) (e0)) = (op (e3) (e2)))) -> ((op (e3) (e0)) = (e2)) -> (~((op (e1) (e1)) = (e1))) -> ((~((op (e2) (e1)) = (e0)))\/((op (e2) (e0)) = (e1))) -> ((~((op (e2) (e3)) = (e0)))\/((op (e2) (e0)) = (e3))) -> (((op (e0) (e0)) = (e0))\/(((op (e1) (e0)) = (e0))\/(((op (e2) (e0)) = (e0))\/((op (e3) (e0)) = (e0))))) -> (~((op (e0) (e0)) = (e0))) -> ((~((op (e3) (e1)) = (e0)))\/((op (e3) (e0)) = (e1))) -> (((op (e0) (e0)) = (e0))\/(((op (e0) (e1)) = (e0))\/(((op (e0) (e2)) = (e0))\/((op (e0) (e3)) = (e0))))) -> (~((op (e0) (e2)) = (op (e0) (e3)))) -> (~((e1) = (e3))) -> ((op (e0) (e0)) = (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 (e3) (e2)))) -> (((op (e2) (e2)) = (e0))\/(((op (e2) (e2)) = (e1))\/(((op (e2) (e2)) = (e2))\/((op (e2) (e2)) = (e3))))) -> (~((op (e2) (e0)) = (op (e2) (e2)))) -> (~((e0) = (e1))) -> (~((op (e0) (e1)) = (op (e2) (e1)))) -> (~((e0) = (e3))) -> (~((e2) = (e3))) -> (((op (e3) (e0)) = (e1))\/(((op (e3) (e1)) = (e1))\/(((op (e3) (e2)) = (e1))\/((op (e3) (e3)) = (e1))))) -> (~((op (e1) (e3)) = (op (e3) (e3)))) -> (~((op (e1) (e3)) = (op (e2) (e3)))) -> (((op (e0) (e3)) = (e0))\/(((op (e0) (e3)) = (e1))\/(((op (e0) (e3)) = (e2))\/((op (e0) (e3)) = (e3))))) -> (((op (e2) (e0)) = (e2))\/(((op (e2) (e1)) = (e2))\/(((op (e2) (e2)) = (e2))\/((op (e2) (e3)) = (e2))))) -> (((op (e0) (e1)) = (e3))\/(((op (e1) (e1)) = (e3))\/(((op (e2) (e1)) = (e3))\/((op (e3) (e1)) = (e3))))) -> (~((op (e3) (e1)) = (op (e3) (e2)))) -> (((op (e0) (e2)) = (e3))\/(((op (e1) (e2)) = (e3))\/(((op (e2) (e2)) = (e3))\/((op (e3) (e2)) = (e3))))) -> (((op (e0) (e1)) = (e0))\/(((op (e0) (e1)) = (e1))\/(((op (e0) (e1)) = (e2))\/((op (e0) (e1)) = (e3))))) -> (~((op (e0) (e1)) = (op (e1) (e1)))) -> (~((op (e1) (e1)) = (op (e2) (e1)))) -> (((op (e2) (e1)) = (e0))\/(((op (e2) (e1)) = (e1))\/(((op (e2) (e1)) = (e2))\/((op (e2) (e1)) = (e3))))) -> (~((op (e0) (e3)) = (op (e3) (e3)))) -> (((op (e0) (e2)) = (e0))\/(((op (e1) (e2)) = (e0))\/(((op (e2) (e2)) = (e0))\/((op (e3) (e2)) = (e0))))) -> (~((op (e1) (e1)) = (op (e1) (e2)))) -> (~((op (e1) (e2)) = (op (e2) (e2)))) -> (((op (e3) (e0)) = (e2))\/(((op (e3) (e1)) = (e2))\/(((op (e3) (e2)) = (e2))\/((op (e3) (e3)) = (e2))))) -> (((op (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) (e3)) = (e3))) -> (~((op (e3) (e2)) = (op (e3) (e3)))) -> (~((op (e3) (e1)) = (op (e3) (e3)))) -> (~((op (e1) (e1)) = (op (e3) (e1)))) -> (((op (e1) (e0)) = (e2))\/(((op (e1) (e1)) = (e2))\/(((op (e1) (e2)) = (e2))\/((op (e1) (e3)) = (e2))))) -> (~((op (e0) (e0)) = (op (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) (e3)) = (e2))\/(((op (e1) (e3)) = (e2))\/(((op (e2) (e3)) = (e2))\/((op (e3) (e3)) = (e2))))) -> (((op (e2) (e0)) = (e1))\/(((op (e2) (e1)) = (e1))\/(((op (e2) (e2)) = (e1))\/((op (e2) (e3)) = (e1))))) -> (((op (e0) (e1)) = (e1))\/(((op (e1) (e1)) = (e1))\/(((op (e2) (e1)) = (e1))\/((op (e3) (e1)) = (e1))))) -> (~((op (e0) (e3)) = (op (e2) (e3)))) -> (((op (e1) (e3)) = (e0))\/(((op (e1) (e3)) = (e1))\/(((op (e1) (e3)) = (e2))\/((op (e1) (e3)) = (e3))))) -> (~((op (e2) (e1)) = (op (e3) (e1)))) -> (((op (e3) (e1)) = (e0))\/(((op (e3) (e1)) = (e1))\/(((op (e3) (e1)) = (e2))\/((op (e3) (e1)) = (e3))))) -> (((op (e2) (e3)) = (e0))\/(((op (e2) (e3)) = (e1))\/(((op (e2) (e3)) = (e2))\/((op (e2) (e3)) = (e3))))) -> (~((op (e2) (e3)) = (op (e3) (e3)))) -> (~((op (e1) (e2)) = (op (e3) (e2)))) -> (~((op (e0) (e1)) = (op (e0) (e2)))) -> (~((op (e0) (e1)) = (op (e3) (e1)))) -> (~((op (e0) (e1)) = (op (e0) (e3)))) -> (~((op (e1) (e0)) = (op (e1) (e3)))) -> (~((op (e2) (e2)) = (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 (e0) (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)) = (e0))) -> ((~((op (e3) (e2)) = (e0)))\/((op (e3) (e0)) = (e2))) -> ((~((op (e3) (e0)) = (e0)))\/((op (e3) (e0)) = (e0))) -> (((op (e2) (e0)) = (e0))\/(((op (e2) (e1)) = (e0))\/(((op (e2) (e2)) = (e0))\/((op (e2) (e3)) = (e0))))) -> ((~((op (e2) (e2)) = (e0)))\/((op (e2) (e0)) = (e2))) -> (((op (e3) (e0)) = (e3))\/(((op (e3) (e1)) = (e3))\/(((op (e3) (e2)) = (e3))\/((op (e3) (e3)) = (e3))))) -> (~((op (e0) (e2)) = (op (e2) (e2)))) -> ((~((op (e3) (e3)) = (e0)))\/((op (e3) (e0)) = (e3))) -> ((~((op (e0) (e3)) = (e0)))\/((op (e0) (e0)) = (e3))) -> ((~((op (e1) (e1)) = (e0)))\/((op (e1) (e0)) = (e1))) -> (((op (e3) (e2)) = (e0))\/(((op (e3) (e2)) = (e1))\/(((op (e3) (e2)) = (e2))\/((op (e3) (e2)) = (e3))))) -> (~((op (e0) (e2)) = (op (e1) (e2)))) -> (((op (e1) (e2)) = (e0))\/(((op (e1) (e2)) = (e1))\/(((op (e1) (e2)) = (e2))\/((op (e1) (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 (e2) (e0)) = (op (e3) (e0)))) -> ((~((op (e1) (e2)) = (e0)))\/((op (e1) (e0)) = (e2))) -> ((~((op (e1) (e3)) = (e0)))\/((op (e1) (e0)) = (e3))) -> (((op (e1) (e1)) = (e0))\/(((op (e1) (e1)) = (e1))\/(((op (e1) (e1)) = (e2))\/((op (e1) (e1)) = (e3))))) -> (~((op (e0) (e0)) = (op (e0) (e2)))) -> (((op (e1) (e0)) = (e1))\/(((op (e1) (e1)) = (e1))\/(((op (e1) (e2)) = (e1))\/((op (e1) (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 (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 (e2) (e0)) = (e0)))\/((op (e2) (e0)) = (e0))) -> (((op (e0) (e0)) = (e3))\/(((op (e1) (e0)) = (e3))\/(((op (e2) (e0)) = (e3))\/((op (e3) (e0)) = (e3))))) -> (((op (e0) (e2)) = (e0))\/(((op (e0) (e2)) = (e1))\/(((op (e0) (e2)) = (e2))\/((op (e0) (e2)) = (e3))))) -> (~((op (e1) (e0)) = (op (e3) (e0)))) -> (~((op (e2) (e0)) = (op (e2) (e1)))) -> ((~((op (e1) (e0)) = (e0)))\/((op (e1) (e0)) = (e0))) -> ((~((op (e0) (e2)) = (e0)))\/((op (e0) (e0)) = (e2))) -> (~((op (e3) (e0)) = (op (e3) (e1)))) -> (~((op (e1) (e1)) = (op (e1) (e3)))) -> (~((op (e2) (e0)) = (op (e2) (e3)))) -> (((op (e0) (e3)) = (e0))\/(((op (e1) (e3)) = (e0))\/(((op (e2) (e3)) = (e0))\/((op (e3) (e3)) = (e0))))) -> (~((op (e1) (e0)) = (op (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) (e1)) = (e0))\/(((op (e1) (e1)) = (e0))\/(((op (e2) (e1)) = (e0))\/((op (e3) (e1)) = (e0))))) -> ((op (e1) (e0)) = (e3)) -> (~((op (e2) (e1)) = (e0))) -> ((op (e2) (e0)) = (e0)) -> (((op (e1) (e0)) = (e0))\/(((op (e1) (e1)) = (e0))\/(((op (e1) (e2)) = (e0))\/((op (e1) (e3)) = (e0))))) -> (~((op (e1) (e0)) = (e0))) -> (~((op (e1) (e1)) = (e0))) -> (~((op (e1) (e2)) = (e0))) -> (~((op (e0) (e3)) = (op (e1) (e3)))) -> False). % 18.68/18.87 do 0 intro. intros zenon_H172 zenon_H149 zenon_H7c zenon_H173 zenon_H6f zenon_H148 zenon_H10a zenon_H182 zenon_H94 zenon_H3e zenon_H3f zenon_H1ed zenon_H74 zenon_H208 zenon_H95 zenon_H3a zenon_H201 zenon_H139 zenon_H18f zenon_H1c4 zenon_H52 zenon_Ha1 zenon_H17e zenon_H9a zenon_H12b zenon_He8 zenon_Hd5 zenon_Hdb zenon_He4 zenon_H1d5 zenon_H1a5 zenon_H1a4 zenon_H1a6 zenon_H212 zenon_H10e zenon_H13e zenon_H1cc zenon_Hc2 zenon_H6a zenon_H4f zenon_H2b zenon_H153 zenon_H16f zenon_H101 zenon_H102 zenon_H62 zenon_H130 zenon_H160 zenon_H18c zenon_H189 zenon_H1d8 zenon_H1c7 zenon_H145 zenon_H106 zenon_H109 zenon_He2 zenon_Hdf zenon_Haf zenon_H22a zenon_H11f zenon_Hf3 zenon_H115 zenon_H4a zenon_H210 zenon_H54 zenon_Hd8 zenon_H6d zenon_H71 zenon_H133 zenon_H7b zenon_H39 zenon_H22d zenon_H20b zenon_H1a7 zenon_H184 zenon_H2f zenon_H185 zenon_H165 zenon_Ha8 zenon_H1ec zenon_H204 zenon_H205 zenon_H191 zenon_H195 zenon_H19d zenon_He7 zenon_H183 zenon_H17b zenon_H178 zenon_H179 zenon_H142 zenon_H13c zenon_H128 zenon_H136 zenon_H124 zenon_H168 zenon_H1fe zenon_H1ee zenon_H1e0 zenon_H1ba zenon_H1fa zenon_H1f0 zenon_H206 zenon_H233 zenon_H1cf zenon_H57 zenon_H5b zenon_H67 zenon_H45 zenon_H14f zenon_H1ac zenon_H245 zenon_H9e zenon_H31 zenon_H34 zenon_H22 zenon_H23 zenon_H24 zenon_H25 zenon_H1d. % 18.68/18.87 apply (zenon_or_s _ _ zenon_H74); [ zenon_intro zenon_H42 | zenon_intro zenon_H77 ]. % 18.68/18.87 exact (zenon_H3f zenon_H42). % 18.68/18.87 apply (zenon_or_s _ _ zenon_H77); [ zenon_intro zenon_H49 | zenon_intro zenon_H78 ]. % 18.68/18.87 exact (zenon_H20b zenon_H49). % 18.68/18.87 apply (zenon_or_s _ _ zenon_H78); [ zenon_intro zenon_H48 | zenon_intro zenon_H1e ]. % 18.68/18.87 apply (zenon_or_s _ _ zenon_H22d); [ zenon_intro zenon_H7a | zenon_intro zenon_H22e ]. % 18.68/18.87 apply (zenon_L107_); trivial. % 18.68/18.87 apply (zenon_or_s _ _ zenon_H22e); [ zenon_intro zenon_Ha0 | zenon_intro zenon_H22f ]. % 18.68/18.87 apply (zenon_or_s _ _ zenon_H22); [ zenon_intro zenon_H27 | zenon_intro zenon_H26 ]. % 18.68/18.87 exact (zenon_H23 zenon_H27). % 18.68/18.87 apply (zenon_or_s _ _ zenon_H26); [ zenon_intro zenon_H29 | zenon_intro zenon_H28 ]. % 18.68/18.87 exact (zenon_H24 zenon_H29). % 18.68/18.87 apply (zenon_or_s _ _ zenon_H28); [ zenon_intro zenon_H2a | zenon_intro zenon_H1f ]. % 18.68/18.87 exact (zenon_H25 zenon_H2a). % 18.68/18.87 apply (zenon_L589_); trivial. % 18.68/18.87 apply (zenon_or_s _ _ zenon_H22f); [ zenon_intro zenon_H122 | zenon_intro zenon_Hc3 ]. % 18.68/18.87 apply (zenon_L355_); trivial. % 18.68/18.87 apply (zenon_or_s _ _ zenon_H128); [ zenon_intro zenon_H9d | zenon_intro zenon_H129 ]. % 18.68/18.87 apply (zenon_L488_); trivial. % 18.68/18.87 apply (zenon_or_s _ _ zenon_H129); [ zenon_intro zenon_H10d | zenon_intro zenon_H12a ]. % 18.68/18.87 exact (zenon_H10a zenon_H10d). % 18.68/18.87 apply (zenon_or_s _ _ zenon_H12a); [ zenon_intro zenon_Hf0 | zenon_intro zenon_Hd6 ]. % 18.68/18.87 apply (zenon_L586_); trivial. % 18.68/18.87 apply (zenon_L79_); trivial. % 18.68/18.87 apply (zenon_L2_); trivial. % 18.68/18.87 (* end of lemma zenon_L590_ *) % 18.68/18.87 assert (zenon_L591_ : (~((op (e0) (e0)) = (e0))) -> (~((op (e0) (e1)) = (e0))) -> (~((op (e1) (e0)) = (e0))) -> (~((op (e1) (e1)) = (e0))) -> (~((op (e1) (e2)) = (e0))) -> ((op (e1) (e0)) = (e3)) -> (~((op (e2) (e2)) = (e0))) -> ((op (e3) (e0)) = (e1)) -> ((op (e0) (e0)) = (e3)) -> (((op (e0) (e0)) = (e1))\/(((op (e0) (e1)) = (e1))\/(((op (e0) (e2)) = (e1))\/((op (e0) (e3)) = (e1))))) -> ((op (e0) (e0)) = (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)) = (e0))\/(((op (e0) (e1)) = (e1))\/(((op (e0) (e1)) = (e2))\/((op (e0) (e1)) = (e3))))) -> (~((op (e0) (e2)) = (op (e0) (e3)))) -> ((op (e2) (e0)) = (e0)) -> (((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 (e2) (e1)) = (e0))) -> ((~((op (e0) (e3)) = (e0)))\/((op (e0) (e0)) = (e3))) -> ((~((op (e1) (e1)) = (e0)))\/((op (e1) (e0)) = (e1))) -> (~((e1) = (e2))) -> ((~((op (e2) (e3)) = (e0)))\/((op (e2) (e0)) = (e3))) -> (((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))))) -> (((op (e0) (e2)) = (e3))\/(((op (e1) (e2)) = (e3))\/(((op (e2) (e2)) = (e3))\/((op (e3) (e2)) = (e3))))) -> (~((op (e3) (e1)) = (op (e3) (e2)))) -> ((~((op (e3) (e2)) = (e0)))\/((op (e3) (e0)) = (e2))) -> (~((op (e2) (e2)) = (op (e3) (e2)))) -> (((op (e3) (e2)) = (e0))\/(((op (e3) (e2)) = (e1))\/(((op (e3) (e2)) = (e2))\/((op (e3) (e2)) = (e3))))) -> (~((op (e0) (e2)) = (op (e1) (e2)))) -> (((op (e1) (e2)) = (e0))\/(((op (e1) (e2)) = (e1))\/(((op (e1) (e2)) = (e2))\/((op (e1) (e2)) = (e3))))) -> (~((e1) = (e3))) -> (~((e0) = (e3))) -> (~((op (e1) (e1)) = (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) (e3)) = (e0))\/(((op (e2) (e3)) = (e1))\/(((op (e2) (e3)) = (e2))\/((op (e2) (e3)) = (e3))))) -> (~((op (e0) (e3)) = (op (e1) (e3)))) -> (~((op (e0) (e1)) = (op (e1) (e1)))) -> (~((e0) = (e1))) -> (~((op (e0) (e2)) = (op (e2) (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) (e3)) = (e0))\/(((op (e1) (e3)) = (e1))\/(((op (e1) (e3)) = (e2))\/((op (e1) (e3)) = (e3))))) -> (~((op (e1) (e3)) = (op (e2) (e3)))) -> (~((op (e1) (e0)) = (op (e1) (e3)))) -> (~((op (e1) (e3)) = (op (e3) (e3)))) -> (~((op (e0) (e3)) = (op (e2) (e3)))) -> (((op (e0) (e3)) = (e0))\/(((op (e0) (e3)) = (e1))\/(((op (e0) (e3)) = (e2))\/((op (e0) (e3)) = (e3))))) -> (~((op (e2) (e1)) = (op (e3) (e1)))) -> (((op (e2) (e0)) = (e3))\/(((op (e2) (e1)) = (e3))\/(((op (e2) (e2)) = (e3))\/((op (e2) (e3)) = (e3))))) -> (((op (e2) (e0)) = (e1))\/(((op (e2) (e1)) = (e1))\/(((op (e2) (e2)) = (e1))\/((op (e2) (e3)) = (e1))))) -> (~((op (e2) (e3)) = (op (e3) (e3)))) -> (~((op (e3) (e3)) = (e3))) -> (((op (e3) (e3)) = (e0))\/(((op (e3) (e3)) = (e1))\/(((op (e3) (e3)) = (e2))\/((op (e3) (e3)) = (e3))))) -> (~((op (e1) (e2)) = (op (e2) (e2)))) -> (((op (e0) (e1)) = (e1))\/(((op (e1) (e1)) = (e1))\/(((op (e2) (e1)) = (e1))\/((op (e3) (e1)) = (e1))))) -> (~((op (e0) (e0)) = (op (e0) (e3)))) -> ((~((op (e2) (e2)) = (e0)))\/((op (e2) (e0)) = (e2))) -> ((~((op (e3) (e0)) = (e0)))\/((op (e3) (e0)) = (e0))) -> (((op (e0) (e0)) = (e2))\/(((op (e0) (e1)) = (e2))\/(((op (e0) (e2)) = (e2))\/((op (e0) (e3)) = (e2))))) -> (~((op (e2) (e0)) = (op (e3) (e0)))) -> (~((op (e0) (e1)) = (op (e2) (e1)))) -> ((~((op (e1) (e2)) = (e0)))\/((op (e1) (e0)) = (e2))) -> ((~((op (e1) (e3)) = (e0)))\/((op (e1) (e0)) = (e3))) -> (((op (e1) (e1)) = (e0))\/(((op (e1) (e1)) = (e1))\/(((op (e1) (e1)) = (e2))\/((op (e1) (e1)) = (e3))))) -> (~((op (e1) (e1)) = (op (e2) (e1)))) -> (~((op (e0) (e0)) = (op (e0) (e2)))) -> (((op (e0) (e2)) = (e1))\/(((op (e1) (e2)) = (e1))\/(((op (e2) (e2)) = (e1))\/((op (e3) (e2)) = (e1))))) -> (((op (e1) (e0)) = (e1))\/(((op (e1) (e1)) = (e1))\/(((op (e1) (e2)) = (e1))\/((op (e1) (e3)) = (e1))))) -> (((op (e0) (e3)) = (e3))\/(((op (e1) (e3)) = (e3))\/(((op (e2) (e3)) = (e3))\/((op (e3) (e3)) = (e3))))) -> (~((op (e3) (e1)) = (op (e3) (e3)))) -> (((op (e0) (e3)) = (e1))\/(((op (e1) (e3)) = (e1))\/(((op (e2) (e3)) = (e1))\/((op (e3) (e3)) = (e1))))) -> (~((e2) = (e3))) -> (~((op (e1) (e2)) = (op (e1) (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 (e2) (e2)) = (e2))) -> (((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) (e1)) = (op (e3) (e1)))) -> (((op (e3) (e0)) = (e3))\/(((op (e3) (e1)) = (e3))\/(((op (e3) (e2)) = (e3))\/((op (e3) (e3)) = (e3))))) -> (~((e0) = (e2))) -> (~((op (e0) (e2)) = (op (e3) (e2)))) -> (((op (e3) (e0)) = (e2))\/(((op (e3) (e1)) = (e2))\/(((op (e3) (e2)) = (e2))\/((op (e3) (e3)) = (e2))))) -> (~((op (e0) (e0)) = (op (e2) (e0)))) -> ((~((op (e2) (e1)) = (e0)))\/((op (e2) (e0)) = (e1))) -> (((op (e0) (e0)) = (e2))\/(((op (e1) (e0)) = (e2))\/(((op (e2) (e0)) = (e2))\/((op (e3) (e0)) = (e2))))) -> ((~((op (e2) (e0)) = (e0)))\/((op (e2) (e0)) = (e0))) -> (((op (e0) (e0)) = (e3))\/(((op (e1) (e0)) = (e3))\/(((op (e2) (e0)) = (e3))\/((op (e3) (e0)) = (e3))))) -> (((op (e3) (e0)) = (e0))\/(((op (e3) (e1)) = (e0))\/(((op (e3) (e2)) = (e0))\/((op (e3) (e3)) = (e0))))) -> (~((op (e2) (e1)) = (op (e2) (e3)))) -> (((op (e2) (e2)) = (e0))\/(((op (e2) (e2)) = (e1))\/(((op (e2) (e2)) = (e2))\/((op (e2) (e2)) = (e3))))) -> (((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 (e3) (e0)) = (op (e3) (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))))) -> ((~((op (e3) (e3)) = (e0)))\/((op (e3) (e0)) = (e3))) -> ((~((op (e3) (e1)) = (e0)))\/((op (e3) (e0)) = (e1))) -> (((op (e1) (e0)) = (e0))\/(((op (e1) (e1)) = (e0))\/(((op (e1) (e2)) = (e0))\/((op (e1) (e3)) = (e0))))) -> (~((op (e1) (e0)) = (op (e1) (e1)))) -> (((op (e0) (e2)) = (e0))\/(((op (e1) (e2)) = (e0))\/(((op (e2) (e2)) = (e0))\/((op (e3) (e2)) = (e0))))) -> (~((op (e0) (e1)) = (op (e0) (e3)))) -> (~((op (e1) (e1)) = (op (e1) (e3)))) -> (~((op (e2) (e0)) = (op (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) (e0)) = (op (e2) (e2)))) -> (~((op (e1) (e1)) = (op (e1) (e2)))) -> (~((op (e0) (e1)) = (op (e0) (e2)))) -> (~((op (e3) (e0)) = (op (e3) (e3)))) -> (~((op (e2) (e2)) = (op (e2) (e3)))) -> (~((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)) = (e0))\/(((op (e0) (e1)) = (e0))\/(((op (e0) (e2)) = (e0))\/((op (e0) (e3)) = (e0))))) -> (~((op (e1) (e0)) = (op (e3) (e0)))) -> (~((op (e2) (e0)) = (op (e2) (e1)))) -> (~((op (e1) (e0)) = (op (e2) (e0)))) -> ((~((op (e1) (e0)) = (e0)))\/((op (e1) (e0)) = (e0))) -> ((~((op (e0) (e2)) = (e0)))\/((op (e0) (e0)) = (e2))) -> False). % 18.68/18.87 do 0 intro. intros zenon_H3f zenon_H20b zenon_H23 zenon_H24 zenon_H25 zenon_H9e zenon_H81 zenon_Hac zenon_H3a zenon_H22d zenon_H7b zenon_H210 zenon_H22a zenon_H212 zenon_H208 zenon_H34 zenon_H235 zenon_H245 zenon_H31 zenon_H204 zenon_H205 zenon_H7c zenon_H94 zenon_H2f zenon_H1a5 zenon_H1a6 zenon_H1a4 zenon_H1a7 zenon_H18f zenon_H191 zenon_H195 zenon_H19d zenon_H95 zenon_H9a zenon_H10a zenon_H18c zenon_H115 zenon_H11f zenon_H1d zenon_H10e zenon_Ha1 zenon_Ha8 zenon_He8 zenon_Hc2 zenon_Hdf zenon_Hdb zenon_Hd8 zenon_Hd5 zenon_He2 zenon_He4 zenon_Haf zenon_He7 zenon_H106 zenon_Hf3 zenon_H102 zenon_H101 zenon_H2b zenon_H109 zenon_H189 zenon_H185 zenon_H184 zenon_H183 zenon_H17b zenon_H17e zenon_H178 zenon_H179 zenon_H142 zenon_H13e zenon_H13c zenon_H139 zenon_H128 zenon_H136 zenon_H130 zenon_H133 zenon_H12b zenon_H124 zenon_H145 zenon_H172 zenon_H173 zenon_H16f zenon_H168 zenon_H160 zenon_H165 zenon_H149 zenon_H14f zenon_H153 zenon_H39 zenon_H182 zenon_H1fe zenon_H1ee zenon_H1e0 zenon_H1ac zenon_H1c7 zenon_H1c4 zenon_H1cc zenon_H1ba zenon_H1cf zenon_H1d8 zenon_H1d5 zenon_H1ec zenon_H1ed zenon_H22 zenon_H45 zenon_H6a zenon_H54 zenon_H57 zenon_H5b zenon_H62 zenon_H67 zenon_H52 zenon_H4f zenon_H4a zenon_H71 zenon_H6d zenon_H6f zenon_H3e zenon_H74 zenon_H1fa zenon_H1f0 zenon_H201 zenon_H206 zenon_H233. % 18.68/18.87 apply (zenon_or_s _ _ zenon_H1a7); [ zenon_intro zenon_H18b | zenon_intro zenon_H148 ]. % 18.68/18.87 apply (zenon_or_s _ _ zenon_H74); [ zenon_intro zenon_H42 | zenon_intro zenon_H77 ]. % 18.68/18.87 exact (zenon_H3f zenon_H42). % 18.68/18.87 apply (zenon_or_s _ _ zenon_H77); [ zenon_intro zenon_H49 | zenon_intro zenon_H78 ]. % 18.68/18.87 exact (zenon_H20b zenon_H49). % 18.68/18.87 apply (zenon_or_s _ _ zenon_H78); [ zenon_intro zenon_H48 | zenon_intro zenon_H1e ]. % 18.68/18.87 apply (zenon_L585_); trivial. % 18.68/18.87 apply (zenon_L337_); trivial. % 18.68/18.87 apply (zenon_L590_); trivial. % 18.68/18.87 (* end of lemma zenon_L591_ *) % 18.68/18.87 assert (zenon_L592_ : ((op (e0) (e0)) = (e3)) -> ((~((op (e0) (e2)) = (e0)))\/((op (e0) (e0)) = (e2))) -> ((~((op (e1) (e0)) = (e0)))\/((op (e1) (e0)) = (e0))) -> (~((op (e2) (e0)) = (op (e2) (e1)))) -> (~((op (e1) (e0)) = (op (e3) (e0)))) -> (((op (e0) (e2)) = (e0))\/(((op (e0) (e2)) = (e1))\/(((op (e0) (e2)) = (e2))\/((op (e0) (e2)) = (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 (e0) (e0)) = (e3))\/(((op (e0) (e1)) = (e3))\/(((op (e0) (e2)) = (e3))\/((op (e0) (e3)) = (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) (e0)) = (e1))\/(((op (e1) (e1)) = (e1))\/(((op (e1) (e2)) = (e1))\/((op (e1) (e3)) = (e1))))) -> (~((op (e0) (e0)) = (op (e0) (e2)))) -> (((op (e1) (e1)) = (e0))\/(((op (e1) (e1)) = (e1))\/(((op (e1) (e1)) = (e2))\/((op (e1) (e1)) = (e3))))) -> ((~((op (e1) (e3)) = (e0)))\/((op (e1) (e0)) = (e3))) -> ((~((op (e1) (e2)) = (e0)))\/((op (e1) (e0)) = (e2))) -> (((op (e0) (e0)) = (e2))\/(((op (e0) (e1)) = (e2))\/(((op (e0) (e2)) = (e2))\/((op (e0) (e3)) = (e2))))) -> (((op (e2) (e0)) = (e3))\/(((op (e2) (e1)) = (e3))\/(((op (e2) (e2)) = (e3))\/((op (e2) (e3)) = (e3))))) -> (((op (e1) (e2)) = (e0))\/(((op (e1) (e2)) = (e1))\/(((op (e1) (e2)) = (e2))\/((op (e1) (e2)) = (e3))))) -> (((op (e3) (e2)) = (e0))\/(((op (e3) (e2)) = (e1))\/(((op (e3) (e2)) = (e2))\/((op (e3) (e2)) = (e3))))) -> ((~((op (e1) (e1)) = (e0)))\/((op (e1) (e0)) = (e1))) -> ((~((op (e0) (e3)) = (e0)))\/((op (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 (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) (e3)) = (e1))\/(((op (e1) (e3)) = (e1))\/(((op (e2) (e3)) = (e1))\/((op (e3) (e3)) = (e1))))) -> (~((op (e3) (e0)) = (op (e3) (e3)))) -> (~((op (e2) (e2)) = (op (e2) (e3)))) -> (~((op (e1) (e0)) = (op (e1) (e3)))) -> (~((op (e0) (e1)) = (op (e0) (e3)))) -> (~((op (e0) (e1)) = (op (e3) (e1)))) -> (~((op (e0) (e1)) = (op (e0) (e2)))) -> (~((op (e1) (e2)) = (op (e3) (e2)))) -> (~((op (e2) (e3)) = (op (e3) (e3)))) -> (((op (e2) (e3)) = (e0))\/(((op (e2) (e3)) = (e1))\/(((op (e2) (e3)) = (e2))\/((op (e2) (e3)) = (e3))))) -> (((op (e3) (e1)) = (e0))\/(((op (e3) (e1)) = (e1))\/(((op (e3) (e1)) = (e2))\/((op (e3) (e1)) = (e3))))) -> (~((op (e2) (e1)) = (op (e3) (e1)))) -> (((op (e1) (e3)) = (e0))\/(((op (e1) (e3)) = (e1))\/(((op (e1) (e3)) = (e2))\/((op (e1) (e3)) = (e3))))) -> (~((op (e0) (e3)) = (op (e2) (e3)))) -> (((op (e0) (e1)) = (e1))\/(((op (e1) (e1)) = (e1))\/(((op (e2) (e1)) = (e1))\/((op (e3) (e1)) = (e1))))) -> (((op (e2) (e0)) = (e1))\/(((op (e2) (e1)) = (e1))\/(((op (e2) (e2)) = (e1))\/((op (e2) (e3)) = (e1))))) -> (((op (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)) = (op (e0) (e3)))) -> (((op (e1) (e0)) = (e2))\/(((op (e1) (e1)) = (e2))\/(((op (e1) (e2)) = (e2))\/((op (e1) (e3)) = (e2))))) -> (~((op (e1) (e1)) = (op (e3) (e1)))) -> (((op (e0) (e2)) = (e2))\/(((op (e1) (e2)) = (e2))\/(((op (e2) (e2)) = (e2))\/((op (e3) (e2)) = (e2))))) -> (~((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) (e0)) = (e3))\/(((op (e1) (e1)) = (e3))\/(((op (e1) (e2)) = (e3))\/((op (e1) (e3)) = (e3))))) -> (((op (e3) (e0)) = (e2))\/(((op (e3) (e1)) = (e2))\/(((op (e3) (e2)) = (e2))\/((op (e3) (e3)) = (e2))))) -> (~((op (e1) (e2)) = (op (e2) (e2)))) -> (~((op (e3) (e0)) = (op (e3) (e2)))) -> (~((op (e0) (e3)) = (op (e3) (e3)))) -> (((op (e2) (e1)) = (e0))\/(((op (e2) (e1)) = (e1))\/(((op (e2) (e1)) = (e2))\/((op (e2) (e1)) = (e3))))) -> (~((op (e1) (e1)) = (op (e2) (e1)))) -> (~((op (e0) (e1)) = (op (e1) (e1)))) -> (((op (e0) (e1)) = (e0))\/(((op (e0) (e1)) = (e1))\/(((op (e0) (e1)) = (e2))\/((op (e0) (e1)) = (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 (e2) (e0)) = (e2))\/(((op (e2) (e1)) = (e2))\/(((op (e2) (e2)) = (e2))\/((op (e2) (e3)) = (e2))))) -> (~((op (e1) (e1)) = (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 (e3) (e0)) = (e1))\/(((op (e3) (e1)) = (e1))\/(((op (e3) (e2)) = (e1))\/((op (e3) (e3)) = (e1))))) -> (~((e0) = (e3))) -> (~((op (e0) (e1)) = (op (e2) (e1)))) -> (~((e0) = (e1))) -> (((op (e2) (e2)) = (e0))\/(((op (e2) (e2)) = (e1))\/(((op (e2) (e2)) = (e2))\/((op (e2) (e2)) = (e3))))) -> (~((op (e2) (e2)) = (e2))) -> (~((op (e2) (e2)) = (op (e3) (e2)))) -> (((op (e0) (e2)) = (e1))\/(((op (e1) (e2)) = (e1))\/(((op (e2) (e2)) = (e1))\/((op (e3) (e2)) = (e1))))) -> (~((op (e1) (e0)) = (op (e2) (e0)))) -> (~((e1) = (e2))) -> ((~((op (e2) (e3)) = (e0)))\/((op (e2) (e0)) = (e3))) -> ((~((op (e2) (e1)) = (e0)))\/((op (e2) (e0)) = (e1))) -> (((op (e0) (e0)) = (e1))\/(((op (e1) (e0)) = (e1))\/(((op (e2) (e0)) = (e1))\/((op (e3) (e0)) = (e1))))) -> (((op (e0) (e1)) = (e0))\/(((op (e1) (e1)) = (e0))\/(((op (e2) (e1)) = (e0))\/((op (e3) (e1)) = (e0))))) -> ((~((op (e2) (e2)) = (e0)))\/((op (e2) (e0)) = (e2))) -> ((op (e0) (e0)) = (e2)) -> (~((op (e0) (e0)) = (op (e2) (e0)))) -> (((op (e0) (e0)) = (e0))\/(((op (e1) (e0)) = (e0))\/(((op (e2) (e0)) = (e0))\/((op (e3) (e0)) = (e0))))) -> (~((op (e1) (e0)) = (e0))) -> (~((op (e0) (e0)) = (e0))) -> ((~((op (e3) (e2)) = (e0)))\/((op (e3) (e0)) = (e2))) -> (~((e0) = (e2))) -> (~((op (e0) (e1)) = (e0))) -> (((op (e1) (e0)) = (e0))\/(((op (e1) (e1)) = (e0))\/(((op (e1) (e2)) = (e0))\/((op (e1) (e3)) = (e0))))) -> (~((op (e0) (e2)) = (op (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 (e0) (e0)) = (e0))\/(((op (e0) (e1)) = (e0))\/(((op (e0) (e2)) = (e0))\/((op (e0) (e3)) = (e0))))) -> ((~((op (e3) (e0)) = (e0)))\/((op (e3) (e0)) = (e0))) -> ((~((op (e3) (e1)) = (e0)))\/((op (e3) (e0)) = (e1))) -> (~((e1) = (e3))) -> (~((op (e3) (e0)) = (op (e3) (e1)))) -> (~((op (e1) (e1)) = (op (e1) (e2)))) -> (~((op (e2) (e0)) = (op (e2) (e2)))) -> (~((op (e3) (e1)) = (op (e3) (e2)))) -> (~((op (e1) (e1)) = (op (e1) (e3)))) -> (~((op (e2) (e0)) = (op (e2) (e3)))) -> (~((op (e3) (e1)) = (op (e3) (e3)))) -> (((op (e0) (e3)) = (e0))\/(((op (e1) (e3)) = (e0))\/(((op (e2) (e3)) = (e0))\/((op (e3) (e3)) = (e0))))) -> (~((op (e1) (e0)) = (op (e1) (e1)))) -> ((~((op (e3) (e3)) = (e0)))\/((op (e3) (e0)) = (e3))) -> (~((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) (e3)) = (op (e1) (e3)))) -> (~((op (e2) (e0)) = (op (e3) (e0)))) -> ((~((op (e2) (e0)) = (e0)))\/((op (e2) (e0)) = (e0))) -> False). % 18.68/18.87 do 0 intro. intros zenon_H3a zenon_H233 zenon_H206 zenon_H1f0 zenon_H1fa zenon_H1ba zenon_H1e0 zenon_H1fe zenon_H168 zenon_H124 zenon_H136 zenon_H128 zenon_H13c zenon_H142 zenon_H179 zenon_H178 zenon_H183 zenon_He7 zenon_H19d zenon_H191 zenon_H205 zenon_H204 zenon_Ha8 zenon_H165 zenon_H2f zenon_H22d zenon_H133 zenon_H71 zenon_H6d zenon_Hd8 zenon_H54 zenon_H210 zenon_H4a zenon_H115 zenon_Hf3 zenon_H11f zenon_H22a zenon_Haf zenon_Hdf zenon_He2 zenon_H109 zenon_H106 zenon_H145 zenon_H1c7 zenon_H1d8 zenon_H189 zenon_H18c zenon_H160 zenon_H172 zenon_H62 zenon_H102 zenon_H101 zenon_H16f zenon_H153 zenon_H2b zenon_H6f zenon_Hc2 zenon_H1cc zenon_H13e zenon_H10e zenon_H212 zenon_H1a6 zenon_H1a5 zenon_H1d5 zenon_H10a zenon_He4 zenon_Hdb zenon_Hd5 zenon_He8 zenon_H9a zenon_H17e zenon_Ha1 zenon_H1c4 zenon_H173 zenon_H18f zenon_H139 zenon_H201 zenon_H7c zenon_H94 zenon_H182 zenon_H235 zenon_H245 zenon_H185 zenon_H7b zenon_H39 zenon_H3e zenon_H23 zenon_H3f zenon_H1a7 zenon_H149 zenon_H20b zenon_H22 zenon_H195 zenon_H6a zenon_H208 zenon_H74 zenon_H184 zenon_H1ed zenon_H95 zenon_H1cf zenon_H4f zenon_H52 zenon_H1a4 zenon_H57 zenon_H5b zenon_H130 zenon_H67 zenon_H45 zenon_H1ec zenon_H12b zenon_H1ac zenon_H14f zenon_H1d zenon_H17b zenon_H1ee. % 18.68/18.87 apply (zenon_or_s _ _ zenon_H205); [ zenon_intro zenon_H24 | zenon_intro zenon_H9d ]. % 18.68/18.87 apply (zenon_or_s _ _ zenon_H178); [ zenon_intro zenon_H25 | zenon_intro zenon_H86 ]. % 18.68/18.87 apply (zenon_or_s _ _ zenon_H179); [ zenon_intro zenon_H38 | zenon_intro zenon_H9e ]. % 18.68/18.87 apply (zenon_or_s _ _ zenon_H1ee); [ zenon_intro zenon_H30 | zenon_intro zenon_H34 ]. % 18.68/18.87 apply (zenon_or_s _ _ zenon_H185); [ zenon_intro zenon_H81 | zenon_intro zenon_Hee ]. % 18.68/18.87 apply (zenon_L340_); trivial. % 18.68/18.87 apply (zenon_L341_); trivial. % 18.68/18.87 apply (zenon_or_s _ _ zenon_H185); [ zenon_intro zenon_H81 | zenon_intro zenon_Hee ]. % 18.68/18.87 apply (zenon_or_s _ _ zenon_H184); [ zenon_intro zenon_H40 | zenon_intro zenon_H44 ]. % 18.68/18.87 apply (zenon_or_s _ _ zenon_H1ed); [ zenon_intro zenon_H1ad | zenon_intro zenon_Hac ]. % 18.68/18.87 apply (zenon_L345_); trivial. % 18.68/18.87 apply (zenon_or_s _ _ zenon_H1a7); [ zenon_intro zenon_H18b | zenon_intro zenon_H148 ]. % 18.68/18.87 apply (zenon_L353_); trivial. % 18.68/18.87 apply (zenon_or_s _ _ zenon_H1ec); [ zenon_intro zenon_H1ae | zenon_intro zenon_H15e ]. % 18.68/18.87 apply (zenon_or_s _ _ zenon_H74); [ zenon_intro zenon_H42 | zenon_intro zenon_H77 ]. % 18.68/18.87 exact (zenon_H3f zenon_H42). % 18.68/18.87 apply (zenon_or_s _ _ zenon_H77); [ zenon_intro zenon_H49 | zenon_intro zenon_H78 ]. % 18.68/18.87 exact (zenon_H20b zenon_H49). % 18.68/18.87 apply (zenon_or_s _ _ zenon_H78); [ zenon_intro zenon_H48 | zenon_intro zenon_H1e ]. % 18.68/18.87 apply (zenon_L351_); trivial. % 18.68/18.87 apply (zenon_L2_); trivial. % 18.68/18.87 apply (zenon_L109_); trivial. % 18.68/18.87 apply (zenon_L127_); trivial. % 18.68/18.87 apply (zenon_L204_); trivial. % 18.68/18.87 apply (zenon_or_s _ _ zenon_H1ee); [ zenon_intro zenon_H30 | zenon_intro zenon_H34 ]. % 18.68/18.87 apply (zenon_L493_); trivial. % 18.68/18.87 apply (zenon_or_s _ _ zenon_H182); [ zenon_intro zenon_H31 | zenon_intro zenon_Hed ]. % 18.68/18.87 apply (zenon_or_s _ _ zenon_H185); [ zenon_intro zenon_H81 | zenon_intro zenon_Hee ]. % 18.68/18.87 apply (zenon_or_s _ _ zenon_H235); [ zenon_intro zenon_H7a | zenon_intro zenon_H236 ]. % 18.68/18.87 apply (zenon_L456_); trivial. % 18.68/18.87 apply (zenon_or_s _ _ zenon_H236); [ zenon_intro zenon_H9d | zenon_intro zenon_H237 ]. % 18.68/18.87 apply (zenon_L37_); trivial. % 18.68/18.87 apply (zenon_or_s _ _ zenon_H237); [ zenon_intro zenon_Hed | zenon_intro zenon_Hac ]. % 18.68/18.87 apply (zenon_L214_); trivial. % 18.68/18.87 apply (zenon_L591_); trivial. % 18.68/18.87 apply (zenon_L204_); trivial. % 18.68/18.87 apply (zenon_L214_); trivial. % 18.68/18.87 apply (zenon_L568_); trivial. % 18.68/18.87 apply (zenon_L489_); trivial. % 18.68/18.87 (* end of lemma zenon_L592_ *) % 18.68/18.87 assert (zenon_L593_ : (((op (e3) (e0)) = (e2))\/(((op (e3) (e1)) = (e2))\/(((op (e3) (e2)) = (e2))\/((op (e3) (e3)) = (e2))))) -> (~((e0) = (e2))) -> ((op (e3) (e0)) = (e0)) -> ((op (e0) (e1)) = (e2)) -> (~((op (e0) (e1)) = (op (e3) (e1)))) -> ((op (e3) (e2)) = (e3)) -> (~((op (e3) (e1)) = (op (e3) (e2)))) -> ((op (e3) (e3)) = (e1)) -> (~((op (e3) (e1)) = (op (e3) (e3)))) -> (~((op (e3) (e1)) = (e0))) -> (((op (e3) (e1)) = (e0))\/(((op (e3) (e1)) = (e1))\/(((op (e3) (e1)) = (e2))\/((op (e3) (e1)) = (e3))))) -> (~((op (e1) (e3)) = (op (e3) (e3)))) -> ((op (e1) (e3)) = (e2)) -> False). % 18.68/18.87 do 0 intro. intros zenon_H153 zenon_H149 zenon_H44 zenon_H10f zenon_H210 zenon_H163 zenon_H1a4 zenon_Hc4 zenon_H130 zenon_H1ad zenon_H22a zenon_Hd5 zenon_Hd7. % 18.68/18.87 apply (zenon_or_s _ _ zenon_H153); [ zenon_intro zenon_H148 | zenon_intro zenon_H154 ]. % 18.68/18.87 apply (zenon_L100_); trivial. % 18.68/18.87 apply (zenon_or_s _ _ zenon_H154); [ zenon_intro zenon_H14d | zenon_intro zenon_H155 ]. % 18.68/18.87 apply (zenon_L389_); trivial. % 18.68/18.87 apply (zenon_or_s _ _ zenon_H155); [ zenon_intro zenon_H151 | zenon_intro zenon_Hf6 ]. % 18.68/18.87 apply (zenon_L401_); trivial. % 18.68/18.87 apply (zenon_L402_); trivial. % 18.68/18.87 (* end of lemma zenon_L593_ *) % 18.68/18.87 assert (zenon_L594_ : (((op (e3) (e0)) = (e3))\/(((op (e3) (e1)) = (e3))\/(((op (e3) (e2)) = (e3))\/((op (e3) (e3)) = (e3))))) -> (~((op (e3) (e0)) = (op (e3) (e1)))) -> ((op (e3) (e2)) = (e2)) -> (((op (e0) (e1)) = (e0))\/(((op (e0) (e1)) = (e1))\/(((op (e0) (e1)) = (e2))\/((op (e0) (e1)) = (e3))))) -> (~((op (e0) (e1)) = (e0))) -> (~((op (e1) (e1)) = (op (e2) (e1)))) -> (~((op (e0) (e1)) = (op (e2) (e1)))) -> (~((op (e2) (e1)) = (op (e3) (e1)))) -> (~((op (e2) (e1)) = (e0))) -> (((op (e2) (e1)) = (e0))\/(((op (e2) (e1)) = (e1))\/(((op (e2) (e1)) = (e2))\/((op (e2) (e1)) = (e3))))) -> (~((op (e0) (e1)) = (op (e1) (e1)))) -> ((op (e1) (e1)) = (e3)) -> (~((op (e1) (e1)) = (op (e3) (e1)))) -> ((op (e1) (e3)) = (e2)) -> (~((op (e1) (e3)) = (op (e3) (e3)))) -> (((op (e3) (e1)) = (e0))\/(((op (e3) (e1)) = (e1))\/(((op (e3) (e1)) = (e2))\/((op (e3) (e1)) = (e3))))) -> (~((op (e3) (e1)) = (e0))) -> (~((op (e3) (e1)) = (op (e3) (e3)))) -> ((op (e3) (e3)) = (e1)) -> (~((op (e3) (e1)) = (op (e3) (e2)))) -> (~((op (e0) (e1)) = (op (e3) (e1)))) -> ((op (e0) (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) (e3)) = (e3))) -> False). % 18.68/18.87 do 0 intro. intros zenon_H165 zenon_H1cf zenon_H151 zenon_H212 zenon_H20b zenon_H13e zenon_H17e zenon_Haf zenon_H31 zenon_H1cc zenon_H10e zenon_H13f zenon_H160 zenon_Hd7 zenon_Hd5 zenon_H22a zenon_H1ad zenon_H130 zenon_Hc4 zenon_H1a4 zenon_H210 zenon_H10f zenon_H44 zenon_H149 zenon_H153 zenon_H102. % 18.68/18.87 apply (zenon_or_s _ _ zenon_H165); [ zenon_intro zenon_H15e | zenon_intro zenon_H166 ]. % 18.68/18.87 apply (zenon_L453_); trivial. % 18.68/18.87 apply (zenon_or_s _ _ zenon_H166); [ zenon_intro zenon_H161 | zenon_intro zenon_H167 ]. % 18.68/18.87 apply (zenon_L110_); trivial. % 18.68/18.87 apply (zenon_or_s _ _ zenon_H167); [ zenon_intro zenon_H163 | zenon_intro zenon_H105 ]. % 18.68/18.87 apply (zenon_L593_); trivial. % 18.68/18.87 exact (zenon_H102 zenon_H105). % 18.68/18.87 (* end of lemma zenon_L594_ *) % 18.68/18.87 assert (zenon_L595_ : ((op (e2) (e0)) = (e2)) -> (~((op (e2) (e0)) = (op (e2) (e3)))) -> (((op (e3) (e0)) = (e3))\/(((op (e3) (e1)) = (e3))\/(((op (e3) (e2)) = (e3))\/((op (e3) (e3)) = (e3))))) -> (~((op (e3) (e0)) = (op (e3) (e1)))) -> (((op (e0) (e1)) = (e0))\/(((op (e0) (e1)) = (e1))\/(((op (e0) (e1)) = (e2))\/((op (e0) (e1)) = (e3))))) -> (~((op (e0) (e1)) = (e0))) -> (~((op (e1) (e1)) = (op (e2) (e1)))) -> (~((op (e0) (e1)) = (op (e2) (e1)))) -> (~((op (e2) (e1)) = (op (e3) (e1)))) -> (~((op (e2) (e1)) = (e0))) -> (((op (e2) (e1)) = (e0))\/(((op (e2) (e1)) = (e1))\/(((op (e2) (e1)) = (e2))\/((op (e2) (e1)) = (e3))))) -> (~((op (e0) (e1)) = (op (e1) (e1)))) -> ((op (e1) (e1)) = (e3)) -> (~((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)) = (e0))) -> (~((op (e3) (e1)) = (op (e3) (e3)))) -> (~((op (e3) (e1)) = (op (e3) (e2)))) -> (~((op (e0) (e1)) = (op (e3) (e1)))) -> ((op (e0) (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) (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))))) -> (~((e0) = (e3))) -> (~((op (e2) (e3)) = (op (e3) (e3)))) -> (~((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 (e1) (e3)) = (op (e2) (e3)))) -> (~((op (e1) (e3)) = (op (e3) (e3)))) -> ((op (e3) (e3)) = (e1)) -> (~((op (e1) (e3)) = (e0))) -> (((op (e1) (e3)) = (e0))\/(((op (e1) (e3)) = (e1))\/(((op (e1) (e3)) = (e2))\/((op (e1) (e3)) = (e3))))) -> (~((op (e3) (e3)) = (e3))) -> False). % 18.68/18.87 do 0 intro. intros zenon_Hee zenon_H5b zenon_H165 zenon_H1cf zenon_H212 zenon_H20b zenon_H13e zenon_H17e zenon_Haf zenon_H31 zenon_H1cc zenon_H10e zenon_H13f zenon_H160 zenon_H22a zenon_H1ad zenon_H130 zenon_H1a4 zenon_H210 zenon_H10f zenon_H44 zenon_H149 zenon_H153 zenon_H145 zenon_H136 zenon_H9a zenon_Hf3 zenon_He2 zenon_H1e zenon_H11f zenon_Hdb zenon_Hd5 zenon_Hc4 zenon_H38 zenon_Hdf zenon_H102. % 18.68/18.87 apply (zenon_or_s _ _ zenon_H153); [ zenon_intro zenon_H148 | zenon_intro zenon_H154 ]. % 18.68/18.87 apply (zenon_L100_); trivial. % 18.68/18.87 apply (zenon_or_s _ _ zenon_H154); [ zenon_intro zenon_H14d | zenon_intro zenon_H155 ]. % 18.68/18.87 apply (zenon_L389_); trivial. % 18.68/18.87 apply (zenon_or_s _ _ zenon_H155); [ zenon_intro zenon_H151 | zenon_intro zenon_Hf6 ]. % 18.68/18.87 apply (zenon_or_s _ _ zenon_H145); [ zenon_intro zenon_Hcd | zenon_intro zenon_H146 ]. % 18.68/18.87 apply (zenon_L428_); trivial. % 18.68/18.87 apply (zenon_or_s _ _ zenon_H146); [ zenon_intro zenon_Hd7 | zenon_intro zenon_H147 ]. % 18.68/18.87 apply (zenon_L594_); trivial. % 18.68/18.87 apply (zenon_or_s _ _ zenon_H147); [ zenon_intro zenon_H11d | zenon_intro zenon_Hf6 ]. % 18.68/18.87 apply (zenon_L73_); trivial. % 18.68/18.87 apply (zenon_L517_); trivial. % 18.68/18.87 apply (zenon_L517_); trivial. % 18.68/18.87 (* end of lemma zenon_L595_ *) % 18.68/18.87 assert (zenon_L596_ : (((op (e2) (e1)) = (e0))\/(((op (e2) (e1)) = (e1))\/(((op (e2) (e1)) = (e2))\/((op (e2) (e1)) = (e3))))) -> (~((op (e2) (e1)) = (e0))) -> (~((op (e2) (e1)) = (op (e2) (e3)))) -> ((op (e2) (e3)) = (e1)) -> ((op (e2) (e0)) = (e2)) -> (~((op (e2) (e0)) = (op (e2) (e1)))) -> ((op (e0) (e1)) = (e2)) -> ((op (e1) (e1)) = (e0)) -> False). % 18.68/18.87 do 0 intro. intros zenon_H1cc zenon_H31 zenon_H1c7 zenon_Hf4 zenon_Hee zenon_H1f0 zenon_H10f zenon_H29. % 18.68/18.87 apply (zenon_or_s _ _ zenon_H1cc); [ zenon_intro zenon_H36 | zenon_intro zenon_H1cd ]. % 18.68/18.87 exact (zenon_H31 zenon_H36). % 18.68/18.87 apply (zenon_or_s _ _ zenon_H1cd); [ zenon_intro zenon_Ha5 | zenon_intro zenon_H1ce ]. % 18.68/18.87 apply (zenon_L188_); trivial. % 18.68/18.87 apply (zenon_or_s _ _ zenon_H1ce); [ zenon_intro zenon_H1ca | zenon_intro zenon_Ha6 ]. % 18.68/18.87 apply (zenon_L277_); trivial. % 18.68/18.87 apply (zenon_L371_); trivial. % 18.68/18.87 (* end of lemma zenon_L596_ *) % 18.68/18.87 assert (zenon_L597_ : (((op (e0) (e3)) = (e2))\/(((op (e1) (e3)) = (e2))\/(((op (e2) (e3)) = (e2))\/((op (e3) (e3)) = (e2))))) -> (~((e0) = (e2))) -> ((op (e0) (e3)) = (e0)) -> (~((e2) = (e3))) -> ((op (e1) (e3)) = (e3)) -> (~((op (e2) (e0)) = (op (e2) (e3)))) -> ((op (e2) (e0)) = (e2)) -> ((op (e3) (e2)) = (e2)) -> (~((op (e3) (e2)) = (op (e3) (e3)))) -> False). % 18.68/18.87 do 0 intro. intros zenon_H145 zenon_H149 zenon_H1e zenon_H12b zenon_Hdc zenon_H5b zenon_Hee zenon_H151 zenon_H62. % 18.68/18.87 apply (zenon_or_s _ _ zenon_H145); [ zenon_intro zenon_Hcd | zenon_intro zenon_H146 ]. % 18.68/18.87 apply (zenon_L428_); trivial. % 18.68/18.87 apply (zenon_or_s _ _ zenon_H146); [ zenon_intro zenon_Hd7 | zenon_intro zenon_H147 ]. % 18.68/18.87 apply (zenon_L266_); trivial. % 18.68/18.87 apply (zenon_or_s _ _ zenon_H147); [ zenon_intro zenon_H11d | zenon_intro zenon_Hf6 ]. % 18.68/18.87 apply (zenon_L73_); trivial. % 18.68/18.87 apply (zenon_L119_); trivial. % 18.68/18.87 (* end of lemma zenon_L597_ *) % 18.68/18.87 assert (zenon_L598_ : (((op (e3) (e0)) = (e2))\/(((op (e3) (e1)) = (e2))\/(((op (e3) (e2)) = (e2))\/((op (e3) (e3)) = (e2))))) -> ((op (e3) (e0)) = (e0)) -> ((op (e3) (e1)) = (e3)) -> (~((op (e3) (e1)) = (op (e3) (e2)))) -> (~((op (e3) (e2)) = (e0))) -> (((op (e3) (e2)) = (e0))\/(((op (e3) (e2)) = (e1))\/(((op (e3) (e2)) = (e2))\/((op (e3) (e2)) = (e3))))) -> (~((op (e3) (e2)) = (op (e3) (e3)))) -> ((op (e2) (e0)) = (e2)) -> (~((op (e2) (e0)) = (op (e2) (e3)))) -> ((op (e1) (e3)) = (e3)) -> (~((e2) = (e3))) -> (~((e0) = (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))))) -> (~((e0) = (e3))) -> (~((op (e2) (e3)) = (op (e3) (e3)))) -> (~((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 (e1) (e3)) = (op (e2) (e3)))) -> (~((op (e1) (e3)) = (op (e3) (e3)))) -> ((op (e3) (e3)) = (e1)) -> (~((op (e1) (e3)) = (e0))) -> (((op (e1) (e3)) = (e0))\/(((op (e1) (e3)) = (e1))\/(((op (e1) (e3)) = (e2))\/((op (e1) (e3)) = (e3))))) -> (~((op (e3) (e3)) = (e3))) -> False). % 18.68/18.87 do 0 intro. intros zenon_H153 zenon_H44 zenon_H161 zenon_H1a4 zenon_H18b zenon_H191 zenon_H62 zenon_Hee zenon_H5b zenon_Hdc zenon_H12b zenon_H149 zenon_H145 zenon_H136 zenon_H9a zenon_Hf3 zenon_He2 zenon_H1e zenon_H11f zenon_Hdb zenon_Hd5 zenon_Hc4 zenon_H38 zenon_Hdf zenon_H102. % 18.68/18.87 apply (zenon_or_s _ _ zenon_H153); [ zenon_intro zenon_H148 | zenon_intro zenon_H154 ]. % 18.68/18.87 apply (zenon_L100_); trivial. % 18.68/18.87 apply (zenon_or_s _ _ zenon_H154); [ zenon_intro zenon_H14d | zenon_intro zenon_H155 ]. % 18.68/18.87 apply (zenon_L545_); trivial. % 18.68/18.87 apply (zenon_or_s _ _ zenon_H155); [ zenon_intro zenon_H151 | zenon_intro zenon_Hf6 ]. % 18.68/18.87 apply (zenon_L597_); trivial. % 18.68/18.87 apply (zenon_L517_); trivial. % 18.68/18.87 (* end of lemma zenon_L598_ *) % 18.68/18.87 assert (zenon_L599_ : (((op (e3) (e0)) = (e2))\/(((op (e3) (e1)) = (e2))\/(((op (e3) (e2)) = (e2))\/((op (e3) (e3)) = (e2))))) -> (~((e0) = (e2))) -> ((op (e3) (e0)) = (e0)) -> ((op (e0) (e1)) = (e2)) -> (~((op (e0) (e1)) = (op (e3) (e1)))) -> (~((op (e3) (e1)) = (op (e3) (e2)))) -> (~((op (e3) (e1)) = (op (e3) (e3)))) -> (~((op (e3) (e1)) = (e0))) -> (((op (e3) (e1)) = (e0))\/(((op (e3) (e1)) = (e1))\/(((op (e3) (e1)) = (e2))\/((op (e3) (e1)) = (e3))))) -> ((op (e1) (e3)) = (e2)) -> (~((op (e1) (e1)) = (op (e3) (e1)))) -> ((op (e1) (e1)) = (e3)) -> (~((op (e0) (e1)) = (op (e1) (e1)))) -> (((op (e2) (e1)) = (e0))\/(((op (e2) (e1)) = (e1))\/(((op (e2) (e1)) = (e2))\/((op (e2) (e1)) = (e3))))) -> (~((op (e2) (e1)) = (e0))) -> (~((op (e2) (e1)) = (op (e3) (e1)))) -> (~((op (e0) (e1)) = (op (e2) (e1)))) -> (~((op (e1) (e1)) = (op (e2) (e1)))) -> (~((op (e0) (e1)) = (e0))) -> (((op (e0) (e1)) = (e0))\/(((op (e0) (e1)) = (e1))\/(((op (e0) (e1)) = (e2))\/((op (e0) (e1)) = (e3))))) -> (~((op (e3) (e0)) = (op (e3) (e1)))) -> (((op (e3) (e0)) = (e3))\/(((op (e3) (e1)) = (e3))\/(((op (e3) (e2)) = (e3))\/((op (e3) (e3)) = (e3))))) -> (((op (e0) (e3)) = (e3))\/(((op (e1) (e3)) = (e3))\/(((op (e2) (e3)) = (e3))\/((op (e3) (e3)) = (e3))))) -> (~((e0) = (e3))) -> (~((op (e2) (e3)) = (op (e3) (e3)))) -> (~((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 (e1) (e3)) = (op (e2) (e3)))) -> (~((op (e1) (e3)) = (op (e3) (e3)))) -> ((op (e3) (e3)) = (e1)) -> (~((op (e1) (e3)) = (e0))) -> (((op (e1) (e3)) = (e0))\/(((op (e1) (e3)) = (e1))\/(((op (e1) (e3)) = (e2))\/((op (e1) (e3)) = (e3))))) -> (~((op (e3) (e3)) = (e3))) -> False). % 18.68/18.87 do 0 intro. intros zenon_H153 zenon_H149 zenon_H44 zenon_H10f zenon_H210 zenon_H1a4 zenon_H130 zenon_H1ad zenon_H22a zenon_Hd7 zenon_H160 zenon_H13f zenon_H10e zenon_H1cc zenon_H31 zenon_Haf zenon_H17e zenon_H13e zenon_H20b zenon_H212 zenon_H1cf zenon_H165 zenon_H136 zenon_H9a zenon_Hf3 zenon_He2 zenon_H1e zenon_H11f zenon_Hdb zenon_Hd5 zenon_Hc4 zenon_H38 zenon_Hdf zenon_H102. % 18.68/18.87 apply (zenon_or_s _ _ zenon_H153); [ zenon_intro zenon_H148 | zenon_intro zenon_H154 ]. % 18.68/18.87 apply (zenon_L100_); trivial. % 18.68/18.87 apply (zenon_or_s _ _ zenon_H154); [ zenon_intro zenon_H14d | zenon_intro zenon_H155 ]. % 18.68/18.87 apply (zenon_L389_); trivial. % 18.68/18.87 apply (zenon_or_s _ _ zenon_H155); [ zenon_intro zenon_H151 | zenon_intro zenon_Hf6 ]. % 18.68/18.87 apply (zenon_L594_); trivial. % 18.68/18.87 apply (zenon_L517_); trivial. % 18.68/18.87 (* end of lemma zenon_L599_ *) % 18.68/18.87 assert (zenon_L600_ : (((op (e2) (e0)) = (e1))\/(((op (e2) (e1)) = (e1))\/(((op (e2) (e2)) = (e1))\/((op (e2) (e3)) = (e1))))) -> (~((op (e1) (e0)) = (op (e2) (e0)))) -> ((op (e1) (e0)) = (e1)) -> (~((op (e3) (e3)) = (e3))) -> (((op (e1) (e3)) = (e0))\/(((op (e1) (e3)) = (e1))\/(((op (e1) (e3)) = (e2))\/((op (e1) (e3)) = (e3))))) -> (~((op (e1) (e3)) = (e0))) -> (~((op (e1) (e3)) = (op (e3) (e3)))) -> (~((op (e1) (e3)) = (op (e2) (e3)))) -> (((op (e2) (e3)) = (e0))\/(((op (e2) (e3)) = (e1))\/(((op (e2) (e3)) = (e2))\/((op (e2) (e3)) = (e3))))) -> ((op (e0) (e3)) = (e0)) -> (~((op (e0) (e3)) = (op (e2) (e3)))) -> (~((op (e2) (e3)) = (op (e3) (e3)))) -> (~((e0) = (e3))) -> (((op (e0) (e3)) = (e3))\/(((op (e1) (e3)) = (e3))\/(((op (e2) (e3)) = (e3))\/((op (e3) (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) (e1)) = (e0))\/(((op (e0) (e1)) = (e1))\/(((op (e0) (e1)) = (e2))\/((op (e0) (e1)) = (e3))))) -> (~((op (e0) (e1)) = (e0))) -> (~((op (e1) (e1)) = (op (e2) (e1)))) -> (~((op (e0) (e1)) = (op (e2) (e1)))) -> (~((op (e2) (e1)) = (op (e3) (e1)))) -> (~((op (e0) (e1)) = (op (e1) (e1)))) -> ((op (e1) (e1)) = (e3)) -> (~((op (e1) (e1)) = (op (e3) (e1)))) -> ((op (e1) (e3)) = (e2)) -> (((op (e3) (e1)) = (e0))\/(((op (e3) (e1)) = (e1))\/(((op (e3) (e1)) = (e2))\/((op (e3) (e1)) = (e3))))) -> (~((op (e3) (e1)) = (e0))) -> (~((op (e3) (e1)) = (op (e3) (e3)))) -> (~((op (e3) (e1)) = (op (e3) (e2)))) -> (~((op (e0) (e1)) = (op (e3) (e1)))) -> ((op (e3) (e0)) = (e0)) -> (~((e0) = (e2))) -> (((op (e3) (e0)) = (e2))\/(((op (e3) (e1)) = (e2))\/(((op (e3) (e2)) = (e2))\/((op (e3) (e3)) = (e2))))) -> (~((op (e2) (e2)) = (op (e3) (e2)))) -> ((op (e0) (e1)) = (e1)) -> (~((e0) = (e1))) -> (((op (e3) (e0)) = (e1))\/(((op (e3) (e1)) = (e1))\/(((op (e3) (e2)) = (e1))\/((op (e3) (e3)) = (e1))))) -> (((op (e2) (e1)) = (e0))\/(((op (e2) (e1)) = (e1))\/(((op (e2) (e1)) = (e2))\/((op (e2) (e1)) = (e3))))) -> (~((op (e2) (e1)) = (e0))) -> (~((op (e2) (e1)) = (op (e2) (e3)))) -> ((op (e2) (e0)) = (e2)) -> (~((op (e2) (e0)) = (op (e2) (e1)))) -> ((op (e0) (e1)) = (e2)) -> ((op (e1) (e1)) = (e0)) -> False). % 18.68/18.87 do 0 intro. intros zenon_H106 zenon_H201 zenon_H9d zenon_H102 zenon_Hdf zenon_H38 zenon_Hd5 zenon_Hdb zenon_H11f zenon_H1e zenon_He2 zenon_Hf3 zenon_H9a zenon_H136 zenon_H165 zenon_H1cf zenon_H212 zenon_H20b zenon_H13e zenon_H17e zenon_Haf zenon_H10e zenon_H13f zenon_H160 zenon_Hd7 zenon_H22a zenon_H1ad zenon_H130 zenon_H1a4 zenon_H210 zenon_H44 zenon_H149 zenon_H153 zenon_H18f zenon_Ha0 zenon_Ha1 zenon_He8 zenon_H1cc zenon_H31 zenon_H1c7 zenon_Hee zenon_H1f0 zenon_H10f zenon_H29. % 18.68/18.87 apply (zenon_or_s _ _ zenon_H106); [ zenon_intro zenon_Hed | zenon_intro zenon_H107 ]. % 18.68/18.87 apply (zenon_L413_); trivial. % 18.68/18.87 apply (zenon_or_s _ _ zenon_H107); [ zenon_intro zenon_Ha5 | zenon_intro zenon_H108 ]. % 18.68/18.87 apply (zenon_L357_); trivial. % 18.68/18.87 apply (zenon_or_s _ _ zenon_H108); [ zenon_intro zenon_Hf1 | zenon_intro zenon_Hf4 ]. % 18.68/18.87 apply (zenon_or_s _ _ zenon_He8); [ zenon_intro zenon_Hac | zenon_intro zenon_Heb ]. % 18.68/18.87 apply (zenon_L41_); trivial. % 18.68/18.87 apply (zenon_or_s _ _ zenon_Heb); [ zenon_intro zenon_Hae | zenon_intro zenon_Hec ]. % 18.68/18.87 apply (zenon_L363_); trivial. % 18.68/18.87 apply (zenon_or_s _ _ zenon_Hec); [ zenon_intro zenon_Hba | zenon_intro zenon_Hc4 ]. % 18.68/18.87 apply (zenon_L185_); trivial. % 18.68/18.87 apply (zenon_L599_); trivial. % 18.68/18.87 apply (zenon_L596_); trivial. % 18.68/18.87 (* end of lemma zenon_L600_ *) % 18.68/18.87 assert (zenon_L601_ : (((op (e3) (e0)) = (e2))\/(((op (e3) (e1)) = (e2))\/(((op (e3) (e2)) = (e2))\/((op (e3) (e3)) = (e2))))) -> ((op (e3) (e0)) = (e0)) -> ((op (e0) (e1)) = (e2)) -> (~((op (e0) (e1)) = (op (e3) (e1)))) -> (~((op (e3) (e2)) = (op (e3) (e3)))) -> ((op (e2) (e0)) = (e2)) -> (~((op (e2) (e0)) = (op (e2) (e3)))) -> (~((e2) = (e3))) -> (~((e0) = (e2))) -> (((op (e0) (e3)) = (e2))\/(((op (e1) (e3)) = (e2))\/(((op (e2) (e3)) = (e2))\/((op (e3) (e3)) = (e2))))) -> (((op (e2) (e3)) = (e0))\/(((op (e2) (e3)) = (e1))\/(((op (e2) (e3)) = (e2))\/((op (e2) (e3)) = (e3))))) -> ((op (e0) (e3)) = (e0)) -> (~((op (e0) (e3)) = (op (e2) (e3)))) -> ((op (e3) (e3)) = (e1)) -> (~((op (e2) (e3)) = (op (e3) (e3)))) -> (~((op (e1) (e3)) = (op (e2) (e3)))) -> ((op (e1) (e3)) = (e3)) -> False). % 18.68/18.87 do 0 intro. intros zenon_H153 zenon_H44 zenon_H10f zenon_H210 zenon_H62 zenon_Hee zenon_H5b zenon_H12b zenon_H149 zenon_H145 zenon_H11f zenon_H1e zenon_He2 zenon_Hc4 zenon_Hf3 zenon_Hdb zenon_Hdc. % 18.68/18.87 apply (zenon_or_s _ _ zenon_H153); [ zenon_intro zenon_H148 | zenon_intro zenon_H154 ]. % 18.68/18.87 apply (zenon_L100_); trivial. % 18.68/18.87 apply (zenon_or_s _ _ zenon_H154); [ zenon_intro zenon_H14d | zenon_intro zenon_H155 ]. % 18.68/18.87 apply (zenon_L389_); trivial. % 18.68/18.87 apply (zenon_or_s _ _ zenon_H155); [ zenon_intro zenon_H151 | zenon_intro zenon_Hf6 ]. % 18.68/18.87 apply (zenon_L597_); trivial. % 18.68/18.87 apply (zenon_L404_); trivial. % 18.68/18.87 (* end of lemma zenon_L601_ *) % 18.68/18.87 assert (zenon_L602_ : ((op (e0) (e2)) = (e1)) -> ((op (e2) (e2)) = (e0)) -> (~((e1) = (op (op (e2) (e2)) (e2)))) -> False). % 18.68/18.87 do 0 intro. intros zenon_H122 zenon_H2c zenon_H1b4. % 18.68/18.87 elim (classic ((op (op (e2) (e2)) (e2)) = (op (op (e2) (e2)) (e2)))); [ zenon_intro zenon_Hb6 | zenon_intro zenon_Hb7 ]. % 18.68/18.87 cut (((op (op (e2) (e2)) (e2)) = (op (op (e2) (e2)) (e2))) = ((e1) = (op (op (e2) (e2)) (e2)))). % 18.68/18.87 intro zenon_D_pnotp. % 18.68/18.87 apply zenon_H1b4. % 18.68/18.87 rewrite <- zenon_D_pnotp. % 18.68/18.87 exact zenon_Hb6. % 18.68/18.87 cut (((op (op (e2) (e2)) (e2)) = (op (op (e2) (e2)) (e2)))); [idtac | apply NNPP; zenon_intro zenon_Hb7]. % 18.68/18.87 cut (((op (op (e2) (e2)) (e2)) = (e1))); [idtac | apply NNPP; zenon_intro zenon_H1b5]. % 18.68/18.87 congruence. % 18.68/18.87 cut (((op (e0) (e2)) = (e1)) = ((op (op (e2) (e2)) (e2)) = (e1))). % 18.68/18.87 intro zenon_D_pnotp. % 18.68/18.87 apply zenon_H1b5. % 18.68/18.87 rewrite <- zenon_D_pnotp. % 18.68/18.87 exact zenon_H122. % 18.68/18.87 cut (((e1) = (e1))); [idtac | apply NNPP; zenon_intro zenon_H79]. % 18.68/18.87 cut (((op (e0) (e2)) = (op (op (e2) (e2)) (e2)))); [idtac | apply NNPP; zenon_intro zenon_Hb9]. % 18.68/18.87 congruence. % 18.68/18.87 elim (classic ((op (op (e2) (e2)) (e2)) = (op (op (e2) (e2)) (e2)))); [ zenon_intro zenon_Hb6 | zenon_intro zenon_Hb7 ]. % 18.68/18.87 cut (((op (op (e2) (e2)) (e2)) = (op (op (e2) (e2)) (e2))) = ((op (e0) (e2)) = (op (op (e2) (e2)) (e2)))). % 18.68/18.87 intro zenon_D_pnotp. % 18.68/18.87 apply zenon_Hb9. % 18.68/18.87 rewrite <- zenon_D_pnotp. % 18.68/18.87 exact zenon_Hb6. % 18.68/18.87 cut (((op (op (e2) (e2)) (e2)) = (op (op (e2) (e2)) (e2)))); [idtac | apply NNPP; zenon_intro zenon_Hb7]. % 18.68/18.87 cut (((op (op (e2) (e2)) (e2)) = (op (e0) (e2)))); [idtac | apply NNPP; zenon_intro zenon_Hb4]. % 18.68/18.87 congruence. % 18.68/18.87 apply (zenon_L43_); trivial. % 18.68/18.87 apply zenon_Hb7. apply refl_equal. % 18.68/18.87 apply zenon_Hb7. apply refl_equal. % 18.68/18.87 apply zenon_H79. apply refl_equal. % 18.68/18.87 apply zenon_Hb7. apply refl_equal. % 18.68/18.87 apply zenon_Hb7. apply refl_equal. % 18.68/18.87 (* end of lemma zenon_L602_ *) % 18.68/18.87 assert (zenon_L603_ : ((op (e1) (e2)) = (e3)) -> ((op (e0) (e2)) = (e1)) -> ((op (e2) (e2)) = (e0)) -> False). % 18.68/18.87 do 0 intro. intros zenon_H16c zenon_H122 zenon_H2c. % 18.68/18.87 apply (zenon_notand_s _ _ ax23); [ zenon_intro zenon_H1c0 | zenon_intro zenon_H249 ]. % 18.68/18.87 elim (classic ((op (op (op (e2) (e2)) (e2)) (e2)) = (op (op (op (e2) (e2)) (e2)) (e2)))); [ zenon_intro zenon_Hbd | zenon_intro zenon_Hbe ]. % 18.68/18.87 cut (((op (op (op (e2) (e2)) (e2)) (e2)) = (op (op (op (e2) (e2)) (e2)) (e2))) = ((e3) = (op (op (op (e2) (e2)) (e2)) (e2)))). % 18.68/18.87 intro zenon_D_pnotp. % 18.68/18.87 apply zenon_H1c0. % 18.68/18.87 rewrite <- zenon_D_pnotp. % 18.68/18.87 exact zenon_Hbd. % 18.68/18.87 cut (((op (op (op (e2) (e2)) (e2)) (e2)) = (op (op (op (e2) (e2)) (e2)) (e2)))); [idtac | apply NNPP; zenon_intro zenon_Hbe]. % 18.68/18.87 cut (((op (op (op (e2) (e2)) (e2)) (e2)) = (e3))); [idtac | apply NNPP; zenon_intro zenon_H1c1]. % 18.68/18.87 congruence. % 18.68/18.87 cut (((op (e1) (e2)) = (e3)) = ((op (op (op (e2) (e2)) (e2)) (e2)) = (e3))). % 18.68/18.87 intro zenon_D_pnotp. % 18.68/18.87 apply zenon_H1c1. % 18.68/18.87 rewrite <- zenon_D_pnotp. % 18.68/18.87 exact zenon_H16c. % 18.68/18.87 cut (((e3) = (e3))); [idtac | apply NNPP; zenon_intro zenon_H85]. % 18.68/18.87 cut (((op (e1) (e2)) = (op (op (op (e2) (e2)) (e2)) (e2)))); [idtac | apply NNPP; zenon_intro zenon_H1b8]. % 18.68/18.87 congruence. % 18.68/18.87 elim (classic ((op (op (op (e2) (e2)) (e2)) (e2)) = (op (op (op (e2) (e2)) (e2)) (e2)))); [ zenon_intro zenon_Hbd | zenon_intro zenon_Hbe ]. % 18.68/18.87 cut (((op (op (op (e2) (e2)) (e2)) (e2)) = (op (op (op (e2) (e2)) (e2)) (e2))) = ((op (e1) (e2)) = (op (op (op (e2) (e2)) (e2)) (e2)))). % 18.68/18.87 intro zenon_D_pnotp. % 18.68/18.87 apply zenon_H1b8. % 18.68/18.87 rewrite <- zenon_D_pnotp. % 18.68/18.87 exact zenon_Hbd. % 18.68/18.87 cut (((op (op (op (e2) (e2)) (e2)) (e2)) = (op (op (op (e2) (e2)) (e2)) (e2)))); [idtac | apply NNPP; zenon_intro zenon_Hbe]. % 18.68/18.87 cut (((op (op (op (e2) (e2)) (e2)) (e2)) = (op (e1) (e2)))); [idtac | apply NNPP; zenon_intro zenon_H1b9]. % 18.68/18.87 congruence. % 18.68/18.87 cut (((e2) = (e2))); [idtac | apply NNPP; zenon_intro zenon_H7e]. % 18.68/18.87 cut (((op (op (e2) (e2)) (e2)) = (e1))); [idtac | apply NNPP; zenon_intro zenon_H1b5]. % 18.68/18.87 congruence. % 18.68/18.87 cut (((op (e0) (e2)) = (e1)) = ((op (op (e2) (e2)) (e2)) = (e1))). % 18.68/18.87 intro zenon_D_pnotp. % 18.68/18.87 apply zenon_H1b5. % 18.68/18.87 rewrite <- zenon_D_pnotp. % 18.68/18.87 exact zenon_H122. % 18.68/18.87 cut (((e1) = (e1))); [idtac | apply NNPP; zenon_intro zenon_H79]. % 18.68/18.87 cut (((op (e0) (e2)) = (op (op (e2) (e2)) (e2)))); [idtac | apply NNPP; zenon_intro zenon_Hb9]. % 18.68/18.87 congruence. % 18.68/18.87 elim (classic ((op (op (e2) (e2)) (e2)) = (op (op (e2) (e2)) (e2)))); [ zenon_intro zenon_Hb6 | zenon_intro zenon_Hb7 ]. % 18.68/18.87 cut (((op (op (e2) (e2)) (e2)) = (op (op (e2) (e2)) (e2))) = ((op (e0) (e2)) = (op (op (e2) (e2)) (e2)))). % 18.68/18.87 intro zenon_D_pnotp. % 18.68/18.87 apply zenon_Hb9. % 18.68/18.87 rewrite <- zenon_D_pnotp. % 18.68/18.87 exact zenon_Hb6. % 18.68/18.87 cut (((op (op (e2) (e2)) (e2)) = (op (op (e2) (e2)) (e2)))); [idtac | apply NNPP; zenon_intro zenon_Hb7]. % 18.68/18.87 cut (((op (op (e2) (e2)) (e2)) = (op (e0) (e2)))); [idtac | apply NNPP; zenon_intro zenon_Hb4]. % 18.68/18.88 congruence. % 18.68/18.88 apply (zenon_L43_); trivial. % 18.68/18.88 apply zenon_Hb7. apply refl_equal. % 18.68/18.88 apply zenon_Hb7. apply refl_equal. % 18.68/18.88 apply zenon_H79. apply refl_equal. % 18.68/18.88 apply zenon_H7e. apply refl_equal. % 18.68/18.88 apply zenon_Hbe. apply refl_equal. % 18.68/18.88 apply zenon_Hbe. apply refl_equal. % 18.68/18.88 apply zenon_H85. apply refl_equal. % 18.68/18.88 apply zenon_Hbe. apply refl_equal. % 18.68/18.88 apply zenon_Hbe. apply refl_equal. % 18.68/18.88 apply (zenon_notand_s _ _ zenon_H249); [ zenon_intro zenon_H1b4 | zenon_intro zenon_H2d ]. % 18.68/18.88 apply (zenon_L602_); trivial. % 18.68/18.88 apply zenon_H2d. apply sym_equal. exact zenon_H2c. % 18.68/18.88 (* end of lemma zenon_L603_ *) % 18.68/18.88 assert (zenon_L604_ : (((op (e2) (e0)) = (e0))\/(((op (e2) (e1)) = (e0))\/(((op (e2) (e2)) = (e0))\/((op (e2) (e3)) = (e0))))) -> (~((op (e2) (e0)) = (e0))) -> (~((op (e2) (e1)) = (e0))) -> ((op (e1) (e2)) = (e3)) -> (((op (e0) (e2)) = (e0))\/(((op (e1) (e2)) = (e0))\/(((op (e2) (e2)) = (e0))\/((op (e3) (e2)) = (e0))))) -> (~((e0) = (e1))) -> ((op (e0) (e2)) = (e1)) -> (~((op (e1) (e1)) = (op (e1) (e2)))) -> ((op (e1) (e1)) = (e0)) -> (~((op (e2) (e2)) = (op (e2) (e3)))) -> (~((op (e3) (e0)) = (op (e3) (e2)))) -> ((op (e3) (e0)) = (e0)) -> False). % 18.68/18.88 do 0 intro. intros zenon_H2f zenon_H30 zenon_H31 zenon_H16c zenon_H6a zenon_Ha1 zenon_H122 zenon_H4f zenon_H29 zenon_H6d zenon_H6f zenon_H44. % 18.68/18.88 apply (zenon_or_s _ _ zenon_H2f); [ zenon_intro zenon_H34 | zenon_intro zenon_H33 ]. % 18.68/18.88 exact (zenon_H30 zenon_H34). % 18.68/18.88 apply (zenon_or_s _ _ zenon_H33); [ zenon_intro zenon_H36 | zenon_intro zenon_H35 ]. % 18.68/18.88 exact (zenon_H31 zenon_H36). % 18.68/18.88 apply (zenon_or_s _ _ zenon_H35); [ zenon_intro zenon_H2c | zenon_intro zenon_H37 ]. % 18.68/18.88 apply (zenon_L603_); trivial. % 18.68/18.88 apply (zenon_L374_); trivial. % 18.68/18.88 (* end of lemma zenon_L604_ *) % 18.68/18.88 assert (zenon_L605_ : (((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) (e3)) = (e0))\/(((op (e1) (e3)) = (e1))\/(((op (e1) (e3)) = (e2))\/((op (e1) (e3)) = (e3))))) -> (~((op (e1) (e3)) = (e0))) -> (~((op (e1) (e3)) = (op (e3) (e3)))) -> (~((op (e1) (e3)) = (op (e2) (e3)))) -> (((op (e2) (e3)) = (e0))\/(((op (e2) (e3)) = (e1))\/(((op (e2) (e3)) = (e2))\/((op (e2) (e3)) = (e3))))) -> ((op (e0) (e3)) = (e0)) -> (~((op (e0) (e3)) = (op (e2) (e3)))) -> (~((op (e2) (e3)) = (op (e3) (e3)))) -> (~((e0) = (e3))) -> (((op (e0) (e3)) = (e3))\/(((op (e1) (e3)) = (e3))\/(((op (e2) (e3)) = (e3))\/((op (e3) (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) (e1)) = (e0))\/(((op (e0) (e1)) = (e1))\/(((op (e0) (e1)) = (e2))\/((op (e0) (e1)) = (e3))))) -> (~((op (e0) (e1)) = (e0))) -> (~((op (e1) (e1)) = (op (e2) (e1)))) -> (~((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 (e0) (e1)) = (op (e1) (e1)))) -> (~((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)) = (e0))) -> (~((op (e3) (e1)) = (op (e3) (e3)))) -> (~((op (e3) (e1)) = (op (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 (e0) (e2)) = (op (e3) (e2)))) -> (((op (e3) (e0)) = (e1))\/(((op (e3) (e1)) = (e1))\/(((op (e3) (e2)) = (e1))\/((op (e3) (e3)) = (e1))))) -> ((op (e3) (e0)) = (e0)) -> (~((op (e3) (e0)) = (op (e3) (e2)))) -> (~((op (e2) (e2)) = (op (e2) (e3)))) -> ((op (e1) (e1)) = (e0)) -> (~((op (e1) (e1)) = (op (e1) (e2)))) -> ((op (e0) (e2)) = (e1)) -> (~((e0) = (e1))) -> (((op (e0) (e2)) = (e0))\/(((op (e1) (e2)) = (e0))\/(((op (e2) (e2)) = (e0))\/((op (e3) (e2)) = (e0))))) -> (~((op (e2) (e1)) = (e0))) -> (~((op (e2) (e0)) = (e0))) -> (((op (e2) (e0)) = (e0))\/(((op (e2) (e1)) = (e0))\/(((op (e2) (e2)) = (e0))\/((op (e2) (e3)) = (e0))))) -> ((op (e1) (e3)) = (e2)) -> (~((e2) = (e3))) -> False). % 18.68/18.88 do 0 intro. intros zenon_H16f zenon_H95 zenon_H9d zenon_H102 zenon_Hdf zenon_H38 zenon_Hd5 zenon_Hdb zenon_H11f zenon_H1e zenon_He2 zenon_Hf3 zenon_H9a zenon_H136 zenon_H165 zenon_H1cf zenon_H212 zenon_H20b zenon_H13e zenon_H17e zenon_Haf zenon_H1cc zenon_H10e zenon_H160 zenon_H22a zenon_H1ad zenon_H130 zenon_H1a4 zenon_H210 zenon_H10f zenon_H149 zenon_H153 zenon_H14f zenon_He8 zenon_H44 zenon_H6f zenon_H6d zenon_H29 zenon_H4f zenon_H122 zenon_Ha1 zenon_H6a zenon_H31 zenon_H30 zenon_H2f zenon_Hd7 zenon_H12b. % 18.68/18.88 apply (zenon_or_s _ _ zenon_H16f); [ zenon_intro zenon_H9e | zenon_intro zenon_H170 ]. % 18.68/18.88 apply (zenon_L37_); trivial. % 18.68/18.88 apply (zenon_or_s _ _ zenon_H170); [ zenon_intro zenon_H13f | zenon_intro zenon_H171 ]. % 18.68/18.88 apply (zenon_or_s _ _ zenon_He8); [ zenon_intro zenon_Hac | zenon_intro zenon_Heb ]. % 18.68/18.88 apply (zenon_L41_); trivial. % 18.68/18.88 apply (zenon_or_s _ _ zenon_Heb); [ zenon_intro zenon_Hae | zenon_intro zenon_Hec ]. % 18.68/18.88 apply (zenon_L192_); trivial. % 18.68/18.88 apply (zenon_or_s _ _ zenon_Hec); [ zenon_intro zenon_Hba | zenon_intro zenon_Hc4 ]. % 18.68/18.88 apply (zenon_L317_); trivial. % 18.68/18.88 apply (zenon_L599_); trivial. % 18.68/18.88 apply (zenon_or_s _ _ zenon_H171); [ zenon_intro zenon_H16c | zenon_intro zenon_Hdc ]. % 18.68/18.88 apply (zenon_L604_); trivial. % 18.68/18.88 apply (zenon_L266_); trivial. % 18.68/18.88 (* end of lemma zenon_L605_ *) % 18.68/18.88 assert (zenon_L606_ : (((op (e3) (e2)) = (e0))\/(((op (e3) (e2)) = (e1))\/(((op (e3) (e2)) = (e2))\/((op (e3) (e2)) = (e3))))) -> (~((op (e3) (e2)) = (e0))) -> (~((op (e3) (e2)) = (op (e3) (e3)))) -> ((op (e3) (e3)) = (e1)) -> ((op (e3) (e1)) = (e2)) -> (~((op (e3) (e1)) = (op (e3) (e2)))) -> ((op (e3) (e0)) = (e3)) -> (~((op (e3) (e0)) = (op (e3) (e2)))) -> False). % 18.68/18.88 do 0 intro. intros zenon_H191 zenon_H18b zenon_H62 zenon_Hc4 zenon_H14d zenon_H1a4 zenon_H15e zenon_H6f. % 18.68/18.88 apply (zenon_or_s _ _ zenon_H191); [ zenon_intro zenon_H61 | zenon_intro zenon_H192 ]. % 18.68/18.88 exact (zenon_H18b zenon_H61). % 18.68/18.88 apply (zenon_or_s _ _ zenon_H192); [ zenon_intro zenon_Hba | zenon_intro zenon_H193 ]. % 18.68/18.88 apply (zenon_L147_); trivial. % 18.68/18.88 apply (zenon_or_s _ _ zenon_H193); [ zenon_intro zenon_H151 | zenon_intro zenon_H163 ]. % 18.68/18.88 apply (zenon_L400_); trivial. % 18.68/18.88 apply (zenon_L286_); trivial. % 18.68/18.88 (* end of lemma zenon_L606_ *) % 18.68/18.88 assert (zenon_L607_ : (((op (e3) (e0)) = (e1))\/(((op (e3) (e1)) = (e1))\/(((op (e3) (e2)) = (e1))\/((op (e3) (e3)) = (e1))))) -> (~((e1) = (e3))) -> (~((op (e0) (e1)) = (op (e3) (e1)))) -> ((op (e2) (e2)) = (e1)) -> (~((op (e2) (e2)) = (op (e2) (e3)))) -> ((op (e1) (e0)) = (e1)) -> (~((op (e1) (e0)) = (op (e1) (e3)))) -> ((op (e0) (e1)) = (e1)) -> (~((op (e0) (e1)) = (op (e0) (e3)))) -> (((op (e0) (e3)) = (e1))\/(((op (e1) (e3)) = (e1))\/(((op (e2) (e3)) = (e1))\/((op (e3) (e3)) = (e1))))) -> (((op (e3) (e2)) = (e0))\/(((op (e3) (e2)) = (e1))\/(((op (e3) (e2)) = (e2))\/((op (e3) (e2)) = (e3))))) -> (~((op (e3) (e2)) = (e0))) -> (~((op (e3) (e2)) = (op (e3) (e3)))) -> ((op (e3) (e1)) = (e2)) -> (~((op (e3) (e1)) = (op (e3) (e2)))) -> ((op (e3) (e0)) = (e3)) -> (~((op (e3) (e0)) = (op (e3) (e2)))) -> False). % 18.68/18.88 do 0 intro. intros zenon_He8 zenon_H95 zenon_H210 zenon_Hf1 zenon_H6d zenon_H9d zenon_Hd8 zenon_Ha0 zenon_H54 zenon_H133 zenon_H191 zenon_H18b zenon_H62 zenon_H14d zenon_H1a4 zenon_H15e zenon_H6f. % 18.68/18.88 apply (zenon_or_s _ _ zenon_He8); [ zenon_intro zenon_Hac | zenon_intro zenon_Heb ]. % 18.68/18.88 apply (zenon_L252_); trivial. % 18.68/18.88 apply (zenon_or_s _ _ zenon_Heb); [ zenon_intro zenon_Hae | zenon_intro zenon_Hec ]. % 18.68/18.88 apply (zenon_L363_); trivial. % 18.68/18.88 apply (zenon_or_s _ _ zenon_Hec); [ zenon_intro zenon_Hba | zenon_intro zenon_Hc4 ]. % 18.68/18.88 apply (zenon_L419_); trivial. % 18.68/18.88 apply (zenon_L606_); trivial. % 18.68/18.88 (* end of lemma zenon_L607_ *) % 18.68/18.88 assert (zenon_L608_ : (((op (e3) (e0)) = (e3))\/(((op (e3) (e1)) = (e3))\/(((op (e3) (e2)) = (e3))\/((op (e3) (e3)) = (e3))))) -> (~((op (e3) (e0)) = (op (e3) (e2)))) -> (((op (e0) (e3)) = (e1))\/(((op (e1) (e3)) = (e1))\/(((op (e2) (e3)) = (e1))\/((op (e3) (e3)) = (e1))))) -> (~((op (e0) (e1)) = (op (e0) (e3)))) -> ((op (e0) (e1)) = (e1)) -> (~((op (e1) (e0)) = (op (e1) (e3)))) -> ((op (e1) (e0)) = (e1)) -> (~((op (e2) (e2)) = (op (e2) (e3)))) -> ((op (e2) (e2)) = (e1)) -> (~((op (e0) (e1)) = (op (e3) (e1)))) -> (~((e1) = (e3))) -> (((op (e3) (e0)) = (e1))\/(((op (e3) (e1)) = (e1))\/(((op (e3) (e2)) = (e1))\/((op (e3) (e3)) = (e1))))) -> (~((op (e3) (e1)) = (op (e3) (e2)))) -> ((op (e3) (e1)) = (e2)) -> ((op (e3) (e3)) = (e1)) -> (~((op (e3) (e2)) = (op (e3) (e3)))) -> (~((op (e3) (e2)) = (e0))) -> (((op (e3) (e2)) = (e0))\/(((op (e3) (e2)) = (e1))\/(((op (e3) (e2)) = (e2))\/((op (e3) (e2)) = (e3))))) -> ((op (e1) (e2)) = (e3)) -> (~((op (e1) (e2)) = (op (e3) (e2)))) -> (~((op (e3) (e3)) = (e3))) -> False). % 18.68/18.88 do 0 intro. intros zenon_H165 zenon_H6f zenon_H133 zenon_H54 zenon_Ha0 zenon_Hd8 zenon_H9d zenon_H6d zenon_Hf1 zenon_H210 zenon_H95 zenon_He8 zenon_H1a4 zenon_H14d zenon_Hc4 zenon_H62 zenon_H18b zenon_H191 zenon_H16c zenon_H115 zenon_H102. % 18.68/18.88 apply (zenon_or_s _ _ zenon_H165); [ zenon_intro zenon_H15e | zenon_intro zenon_H166 ]. % 18.68/18.88 apply (zenon_L607_); trivial. % 18.68/18.88 apply (zenon_or_s _ _ zenon_H166); [ zenon_intro zenon_H161 | zenon_intro zenon_H167 ]. % 18.68/18.88 apply (zenon_L545_); trivial. % 18.68/18.88 apply (zenon_or_s _ _ zenon_H167); [ zenon_intro zenon_H163 | zenon_intro zenon_H105 ]. % 18.68/18.88 cut (((op (e1) (e2)) = (e3)) = ((op (e1) (e2)) = (op (e3) (e2)))). % 18.68/18.88 intro zenon_D_pnotp. % 18.68/18.88 apply zenon_H115. % 18.68/18.88 rewrite <- zenon_D_pnotp. % 18.68/18.88 exact zenon_H16c. % 18.68/18.88 cut (((e3) = (op (e3) (e2)))); [idtac | apply NNPP; zenon_intro zenon_H164]. % 18.68/18.88 cut (((op (e1) (e2)) = (op (e1) (e2)))); [idtac | apply NNPP; zenon_intro zenon_H2e]. % 18.68/18.88 congruence. % 18.68/18.88 apply zenon_H2e. apply refl_equal. % 18.68/18.88 apply zenon_H164. apply sym_equal. exact zenon_H163. % 18.68/18.88 exact (zenon_H102 zenon_H105). % 18.68/18.88 (* end of lemma zenon_L608_ *) % 18.68/18.88 assert (zenon_L609_ : (((op (e3) (e0)) = (e2))\/(((op (e3) (e1)) = (e2))\/(((op (e3) (e2)) = (e2))\/((op (e3) (e3)) = (e2))))) -> (~((e0) = (e2))) -> ((op (e3) (e0)) = (e0)) -> (~((op (e3) (e3)) = (e3))) -> (~((op (e1) (e2)) = (op (e3) (e2)))) -> ((op (e1) (e2)) = (e3)) -> (((op (e3) (e2)) = (e0))\/(((op (e3) (e2)) = (e1))\/(((op (e3) (e2)) = (e2))\/((op (e3) (e2)) = (e3))))) -> (~((op (e3) (e2)) = (e0))) -> (~((op (e3) (e2)) = (op (e3) (e3)))) -> (~((op (e3) (e1)) = (op (e3) (e2)))) -> (((op (e3) (e0)) = (e1))\/(((op (e3) (e1)) = (e1))\/(((op (e3) (e2)) = (e1))\/((op (e3) (e3)) = (e1))))) -> (~((e1) = (e3))) -> (~((op (e0) (e1)) = (op (e3) (e1)))) -> ((op (e2) (e2)) = (e1)) -> (~((op (e2) (e2)) = (op (e2) (e3)))) -> ((op (e1) (e0)) = (e1)) -> (~((op (e1) (e0)) = (op (e1) (e3)))) -> ((op (e0) (e1)) = (e1)) -> (~((op (e0) (e1)) = (op (e0) (e3)))) -> (((op (e0) (e3)) = (e1))\/(((op (e1) (e3)) = (e1))\/(((op (e2) (e3)) = (e1))\/((op (e3) (e3)) = (e1))))) -> (~((op (e3) (e0)) = (op (e3) (e2)))) -> (((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 (e1) (e3)) = (e0))\/(((op (e1) (e3)) = (e1))\/(((op (e1) (e3)) = (e2))\/((op (e1) (e3)) = (e3))))) -> (~((op (e1) (e3)) = (e0))) -> ((op (e3) (e3)) = (e1)) -> (~((op (e1) (e3)) = (op (e3) (e3)))) -> (~((op (e1) (e3)) = (op (e2) (e3)))) -> ((op (e2) (e3)) = (e3)) -> False). % 18.68/18.88 do 0 intro. intros zenon_H153 zenon_H149 zenon_H44 zenon_H102 zenon_H115 zenon_H16c zenon_H191 zenon_H18b zenon_H62 zenon_H1a4 zenon_He8 zenon_H95 zenon_H210 zenon_Hf1 zenon_H6d zenon_H9d zenon_Hd8 zenon_Ha0 zenon_H54 zenon_H133 zenon_H6f zenon_H165 zenon_H150 zenon_H14f zenon_Hdf zenon_H38 zenon_Hc4 zenon_Hd5 zenon_Hdb zenon_Hdd. % 18.68/18.88 apply (zenon_or_s _ _ zenon_H153); [ zenon_intro zenon_H148 | zenon_intro zenon_H154 ]. % 18.68/18.88 apply (zenon_L100_); trivial. % 18.68/18.88 apply (zenon_or_s _ _ zenon_H154); [ zenon_intro zenon_H14d | zenon_intro zenon_H155 ]. % 18.68/18.88 apply (zenon_L608_); trivial. % 18.68/18.88 apply (zenon_or_s _ _ zenon_H155); [ zenon_intro zenon_H151 | zenon_intro zenon_Hf6 ]. % 18.68/18.88 apply (zenon_L104_); trivial. % 18.68/18.88 apply (zenon_L516_); trivial. % 18.68/18.88 (* end of lemma zenon_L609_ *) % 18.68/18.88 assert (zenon_L610_ : (((op (e1) (e0)) = (e3))\/(((op (e1) (e1)) = (e3))\/(((op (e1) (e2)) = (e3))\/((op (e1) (e3)) = (e3))))) -> (~((e1) = (e3))) -> ((op (e1) (e0)) = (e1)) -> ((op (e3) (e1)) = (e3)) -> (~((op (e1) (e1)) = (op (e3) (e1)))) -> ((op (e0) (e2)) = (e3)) -> (~((op (e0) (e2)) = (op (e1) (e2)))) -> ((op (e1) (e3)) = (e2)) -> (~((e2) = (e3))) -> False). % 18.68/18.88 do 0 intro. intros zenon_H16f zenon_H95 zenon_H9d zenon_H161 zenon_H160 zenon_Ha9 zenon_H195 zenon_Hd7 zenon_H12b. % 18.68/18.88 apply (zenon_or_s _ _ zenon_H16f); [ zenon_intro zenon_H9e | zenon_intro zenon_H170 ]. % 18.68/18.88 apply (zenon_L37_); trivial. % 18.68/18.88 apply (zenon_or_s _ _ zenon_H170); [ zenon_intro zenon_H13f | zenon_intro zenon_H171 ]. % 18.68/18.88 apply (zenon_L110_); trivial. % 18.68/18.88 apply (zenon_or_s _ _ zenon_H171); [ zenon_intro zenon_H16c | zenon_intro zenon_Hdc ]. % 18.68/18.88 apply (zenon_L162_); trivial. % 18.68/18.88 apply (zenon_L266_); trivial. % 18.68/18.88 (* end of lemma zenon_L610_ *) % 18.68/18.88 assert (zenon_L611_ : (((op (e0) (e2)) = (e0))\/(((op (e0) (e2)) = (e1))\/(((op (e0) (e2)) = (e2))\/((op (e0) (e2)) = (e3))))) -> (~((op (e0) (e2)) = (e0))) -> (((op (e2) (e0)) = (e0))\/(((op (e2) (e1)) = (e0))\/(((op (e2) (e2)) = (e0))\/((op (e2) (e3)) = (e0))))) -> (~((op (e2) (e0)) = (e0))) -> (~((op (e2) (e1)) = (e0))) -> (((op (e0) (e2)) = (e0))\/(((op (e1) (e2)) = (e0))\/(((op (e2) (e2)) = (e0))\/((op (e3) (e2)) = (e0))))) -> (~((e0) = (e1))) -> (~((op (e1) (e1)) = (op (e1) (e2)))) -> ((op (e1) (e1)) = (e0)) -> ((op (e0) (e1)) = (e2)) -> (~((op (e3) (e1)) = (op (e3) (e3)))) -> (~((op (e3) (e1)) = (e0))) -> (((op (e3) (e1)) = (e0))\/(((op (e3) (e1)) = (e1))\/(((op (e3) (e1)) = (e2))\/((op (e3) (e1)) = (e3))))) -> (~((op (e0) (e1)) = (op (e1) (e1)))) -> (((op (e2) (e1)) = (e0))\/(((op (e2) (e1)) = (e1))\/(((op (e2) (e1)) = (e2))\/((op (e2) (e1)) = (e3))))) -> (~((op (e2) (e1)) = (op (e3) (e1)))) -> (~((op (e0) (e1)) = (op (e2) (e1)))) -> (~((op (e1) (e1)) = (op (e2) (e1)))) -> (~((op (e0) (e1)) = (e0))) -> (((op (e0) (e1)) = (e0))\/(((op (e0) (e1)) = (e1))\/(((op (e0) (e1)) = (e2))\/((op (e0) (e1)) = (e3))))) -> (~((op (e3) (e0)) = (op (e3) (e1)))) -> (((op (e0) (e3)) = (e3))\/(((op (e1) (e3)) = (e3))\/(((op (e2) (e3)) = (e3))\/((op (e3) (e3)) = (e3))))) -> (~((e0) = (e3))) -> (~((op (e2) (e3)) = (op (e3) (e3)))) -> (~((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 (e2) (e3)) = (e3)) -> (~((op (e1) (e3)) = (op (e2) (e3)))) -> (~((op (e1) (e3)) = (op (e3) (e3)))) -> ((op (e3) (e3)) = (e1)) -> (~((op (e1) (e3)) = (e0))) -> (((op (e1) (e3)) = (e0))\/(((op (e1) (e3)) = (e1))\/(((op (e1) (e3)) = (e2))\/((op (e1) (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 (e3) (e0)) = (op (e3) (e2)))) -> (((op (e0) (e3)) = (e1))\/(((op (e1) (e3)) = (e1))\/(((op (e2) (e3)) = (e1))\/((op (e3) (e3)) = (e1))))) -> (~((op (e0) (e1)) = (op (e0) (e3)))) -> ((op (e0) (e1)) = (e1)) -> (~((op (e1) (e0)) = (op (e1) (e3)))) -> (~((op (e2) (e2)) = (op (e2) (e3)))) -> ((op (e2) (e2)) = (e1)) -> (~((op (e0) (e1)) = (op (e3) (e1)))) -> (((op (e3) (e0)) = (e1))\/(((op (e3) (e1)) = (e1))\/(((op (e3) (e2)) = (e1))\/((op (e3) (e3)) = (e1))))) -> (~((op (e3) (e1)) = (op (e3) (e2)))) -> (~((op (e3) (e2)) = (op (e3) (e3)))) -> (~((op (e3) (e2)) = (e0))) -> (((op (e3) (e2)) = (e0))\/(((op (e3) (e2)) = (e1))\/(((op (e3) (e2)) = (e2))\/((op (e3) (e2)) = (e3))))) -> ((op (e1) (e2)) = (e3)) -> (~((op (e1) (e2)) = (op (e3) (e2)))) -> (~((op (e3) (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 (e1) (e0)) = (e3))\/(((op (e1) (e1)) = (e3))\/(((op (e1) (e2)) = (e3))\/((op (e1) (e3)) = (e3))))) -> (~((e1) = (e3))) -> ((op (e1) (e0)) = (e1)) -> ((op (e3) (e1)) = (e3)) -> (~((op (e1) (e1)) = (op (e3) (e1)))) -> (~((op (e0) (e2)) = (op (e1) (e2)))) -> ((op (e1) (e3)) = (e2)) -> (~((e2) = (e3))) -> False). % 18.68/18.88 do 0 intro. intros zenon_H1ba zenon_H75 zenon_H2f zenon_H30 zenon_H31 zenon_H6a zenon_Ha1 zenon_H4f zenon_H29 zenon_H10f zenon_H130 zenon_H1ad zenon_H22a zenon_H10e zenon_H1cc zenon_Haf zenon_H17e zenon_H13e zenon_H20b zenon_H212 zenon_H1cf zenon_H136 zenon_H9a zenon_Hf3 zenon_He2 zenon_H1e zenon_H11f zenon_Hdd zenon_Hdb zenon_Hd5 zenon_Hc4 zenon_H38 zenon_Hdf zenon_H14f zenon_H165 zenon_H6f zenon_H133 zenon_H54 zenon_Ha0 zenon_Hd8 zenon_H6d zenon_Hf1 zenon_H210 zenon_He8 zenon_H1a4 zenon_H62 zenon_H18b zenon_H191 zenon_H16c zenon_H115 zenon_H102 zenon_H44 zenon_H149 zenon_H153 zenon_H16f zenon_H95 zenon_H9d zenon_H161 zenon_H160 zenon_H195 zenon_Hd7 zenon_H12b. % 18.68/18.88 apply (zenon_or_s _ _ zenon_H1ba); [ zenon_intro zenon_H48 | zenon_intro zenon_H1bb ]. % 18.68/18.88 exact (zenon_H75 zenon_H48). % 18.68/18.88 apply (zenon_or_s _ _ zenon_H1bb); [ zenon_intro zenon_H122 | zenon_intro zenon_H1bc ]. % 18.68/18.88 apply (zenon_L605_); trivial. % 18.68/18.88 apply (zenon_or_s _ _ zenon_H1bc); [ zenon_intro zenon_H150 | zenon_intro zenon_Ha9 ]. % 18.68/18.88 apply (zenon_L609_); trivial. % 18.68/18.88 apply (zenon_L610_); trivial. % 18.68/18.88 (* end of lemma zenon_L611_ *) % 18.68/18.88 assert (zenon_L612_ : (((op (e2) (e0)) = (e1))\/(((op (e2) (e1)) = (e1))\/(((op (e2) (e2)) = (e1))\/((op (e2) (e3)) = (e1))))) -> (~((e1) = (e2))) -> ((op (e2) (e0)) = (e2)) -> ((op (e0) (e1)) = (e1)) -> (~((op (e0) (e1)) = (op (e2) (e1)))) -> ((op (e1) (e2)) = (e1)) -> (~((op (e1) (e2)) = (op (e2) (e2)))) -> (((op (e2) (e1)) = (e0))\/(((op (e2) (e1)) = (e1))\/(((op (e2) (e1)) = (e2))\/((op (e2) (e1)) = (e3))))) -> (~((op (e2) (e1)) = (e0))) -> (~((op (e2) (e1)) = (op (e2) (e3)))) -> ((op (e3) (e1)) = (e2)) -> (~((op (e2) (e1)) = (op (e3) (e1)))) -> (~((op (e1) (e1)) = (op (e2) (e1)))) -> ((op (e1) (e1)) = (e3)) -> False). % 18.68/18.88 do 0 intro. intros zenon_H106 zenon_H7c zenon_Hee zenon_Ha0 zenon_H17e zenon_Hf0 zenon_H2b zenon_H1cc zenon_H31 zenon_H1c7 zenon_H14d zenon_Haf zenon_H13e zenon_H13f. % 18.68/18.88 apply (zenon_or_s _ _ zenon_H106); [ zenon_intro zenon_Hed | zenon_intro zenon_H107 ]. % 18.68/18.88 apply (zenon_L58_); trivial. % 18.68/18.88 apply (zenon_or_s _ _ zenon_H107); [ zenon_intro zenon_Ha5 | zenon_intro zenon_H108 ]. % 18.68/18.88 apply (zenon_L357_); trivial. % 18.68/18.88 apply (zenon_or_s _ _ zenon_H108); [ zenon_intro zenon_Hf1 | zenon_intro zenon_Hf4 ]. % 18.68/18.88 apply (zenon_L59_); trivial. % 18.68/18.88 apply (zenon_L451_); trivial. % 18.68/18.88 (* end of lemma zenon_L612_ *) % 18.68/18.88 assert (zenon_L613_ : (~((e0) = (e1))) -> ((op (e3) (e0)) = (e0)) -> (~((e1) = (e2))) -> (((op (e3) (e0)) = (e3))\/(((op (e3) (e1)) = (e3))\/(((op (e3) (e2)) = (e3))\/((op (e3) (e3)) = (e3))))) -> (~((op (e3) (e0)) = (op (e3) (e2)))) -> (((op (e0) (e3)) = (e1))\/(((op (e1) (e3)) = (e1))\/(((op (e2) (e3)) = (e1))\/((op (e3) (e3)) = (e1))))) -> (~((op (e0) (e1)) = (op (e0) (e3)))) -> ((op (e0) (e1)) = (e1)) -> (~((op (e1) (e0)) = (op (e1) (e3)))) -> ((op (e1) (e0)) = (e1)) -> (~((op (e2) (e2)) = (op (e2) (e3)))) -> ((op (e2) (e2)) = (e1)) -> (~((op (e0) (e1)) = (op (e3) (e1)))) -> (~((e1) = (e3))) -> (((op (e3) (e0)) = (e1))\/(((op (e3) (e1)) = (e1))\/(((op (e3) (e2)) = (e1))\/((op (e3) (e3)) = (e1))))) -> (~((op (e3) (e1)) = (op (e3) (e2)))) -> ((op (e3) (e1)) = (e2)) -> (~((op (e3) (e2)) = (op (e3) (e3)))) -> (~((op (e3) (e2)) = (e0))) -> (((op (e3) (e2)) = (e0))\/(((op (e3) (e2)) = (e1))\/(((op (e3) (e2)) = (e2))\/((op (e3) (e2)) = (e3))))) -> ((op (e1) (e2)) = (e3)) -> (~((op (e1) (e2)) = (op (e3) (e2)))) -> (~((op (e3) (e3)) = (e3))) -> False). % 18.68/18.88 do 0 intro. intros zenon_Ha1 zenon_H44 zenon_H7c zenon_H165 zenon_H6f zenon_H133 zenon_H54 zenon_Ha0 zenon_Hd8 zenon_H9d zenon_H6d zenon_Hf1 zenon_H210 zenon_H95 zenon_He8 zenon_H1a4 zenon_H14d zenon_H62 zenon_H18b zenon_H191 zenon_H16c zenon_H115 zenon_H102. % 18.68/18.88 apply (zenon_or_s _ _ zenon_He8); [ zenon_intro zenon_Hac | zenon_intro zenon_Heb ]. % 18.68/18.88 apply (zenon_L41_); trivial. % 18.68/18.88 apply (zenon_or_s _ _ zenon_Heb); [ zenon_intro zenon_Hae | zenon_intro zenon_Hec ]. % 18.68/18.88 apply (zenon_L152_); trivial. % 18.68/18.88 apply (zenon_or_s _ _ zenon_Hec); [ zenon_intro zenon_Hba | zenon_intro zenon_Hc4 ]. % 18.68/18.88 apply (zenon_L419_); trivial. % 18.68/18.88 apply (zenon_L608_); trivial. % 18.68/18.88 (* end of lemma zenon_L613_ *) % 18.68/18.88 assert (zenon_L614_ : (((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 (e2) (e2)) = (e1)) -> (~((op (e2) (e2)) = (op (e2) (e3)))) -> ((op (e1) (e0)) = (e1)) -> (~((op (e1) (e0)) = (op (e1) (e3)))) -> ((op (e0) (e1)) = (e1)) -> (~((op (e0) (e1)) = (op (e0) (e3)))) -> (((op (e0) (e3)) = (e1))\/(((op (e1) (e3)) = (e1))\/(((op (e2) (e3)) = (e1))\/((op (e3) (e3)) = (e1))))) -> (((op (e3) (e2)) = (e0))\/(((op (e3) (e2)) = (e1))\/(((op (e3) (e2)) = (e2))\/((op (e3) (e2)) = (e3))))) -> (~((op (e3) (e2)) = (e0))) -> (~((op (e3) (e2)) = (op (e3) (e3)))) -> ((op (e3) (e1)) = (e2)) -> (~((op (e3) (e1)) = (op (e3) (e2)))) -> ((op (e3) (e1)) = (e3)) -> False). % 18.68/18.88 do 0 intro. intros zenon_He8 zenon_Ha1 zenon_H44 zenon_H7c zenon_Hf1 zenon_H6d zenon_H9d zenon_Hd8 zenon_Ha0 zenon_H54 zenon_H133 zenon_H191 zenon_H18b zenon_H62 zenon_H14d zenon_H1a4 zenon_H161. % 18.68/18.88 apply (zenon_or_s _ _ zenon_He8); [ zenon_intro zenon_Hac | zenon_intro zenon_Heb ]. % 18.68/18.88 apply (zenon_L41_); trivial. % 18.68/18.88 apply (zenon_or_s _ _ zenon_Heb); [ zenon_intro zenon_Hae | zenon_intro zenon_Hec ]. % 18.68/18.88 apply (zenon_L152_); trivial. % 18.68/18.88 apply (zenon_or_s _ _ zenon_Hec); [ zenon_intro zenon_Hba | zenon_intro zenon_Hc4 ]. % 18.68/18.88 apply (zenon_L419_); trivial. % 18.68/18.88 apply (zenon_L545_); trivial. % 18.68/18.88 (* end of lemma zenon_L614_ *) % 18.68/18.88 assert (zenon_L615_ : (((op (e2) (e0)) = (e1))\/(((op (e2) (e1)) = (e1))\/(((op (e2) (e2)) = (e1))\/((op (e2) (e3)) = (e1))))) -> ((op (e2) (e0)) = (e2)) -> (~((op (e0) (e1)) = (op (e2) (e1)))) -> ((op (e3) (e1)) = (e3)) -> (~((op (e3) (e1)) = (op (e3) (e2)))) -> (~((op (e3) (e2)) = (op (e3) (e3)))) -> (~((op (e3) (e2)) = (e0))) -> (((op (e3) (e2)) = (e0))\/(((op (e3) (e2)) = (e1))\/(((op (e3) (e2)) = (e2))\/((op (e3) (e2)) = (e3))))) -> (((op (e0) (e3)) = (e1))\/(((op (e1) (e3)) = (e1))\/(((op (e2) (e3)) = (e1))\/((op (e3) (e3)) = (e1))))) -> (~((op (e0) (e1)) = (op (e0) (e3)))) -> ((op (e0) (e1)) = (e1)) -> (~((op (e1) (e0)) = (op (e1) (e3)))) -> ((op (e1) (e0)) = (e1)) -> (~((op (e2) (e2)) = (op (e2) (e3)))) -> (~((e1) = (e2))) -> (~((e0) = (e1))) -> (((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) (e0)) = (op (e3) (e3)))) -> ((op (e3) (e0)) = (e0)) -> (~((op (e2) (e3)) = (op (e3) (e3)))) -> (~((op (e3) (e1)) = (op (e3) (e3)))) -> ((op (e3) (e1)) = (e2)) -> (~((op (e3) (e3)) = (e3))) -> False). % 18.68/18.88 do 0 intro. intros zenon_H106 zenon_Hee zenon_H17e zenon_H161 zenon_H1a4 zenon_H62 zenon_H18b zenon_H191 zenon_H133 zenon_H54 zenon_Ha0 zenon_Hd8 zenon_H9d zenon_H6d zenon_H7c zenon_Ha1 zenon_He8 zenon_H101 zenon_H71 zenon_H44 zenon_Hf3 zenon_H130 zenon_H14d zenon_H102. % 18.68/18.88 apply (zenon_or_s _ _ zenon_H106); [ zenon_intro zenon_Hed | zenon_intro zenon_H107 ]. % 18.68/18.88 apply (zenon_L58_); trivial. % 18.68/18.88 apply (zenon_or_s _ _ zenon_H107); [ zenon_intro zenon_Ha5 | zenon_intro zenon_H108 ]. % 18.68/18.88 apply (zenon_L357_); trivial. % 18.68/18.88 apply (zenon_or_s _ _ zenon_H108); [ zenon_intro zenon_Hf1 | zenon_intro zenon_Hf4 ]. % 18.68/18.88 apply (zenon_L614_); trivial. % 18.68/18.88 apply (zenon_L414_); trivial. % 18.68/18.88 (* end of lemma zenon_L615_ *) % 18.68/18.88 assert (zenon_L616_ : (((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 (e1) (e3)) = (e0))) -> (~((op (e0) (e2)) = (op (e1) (e2)))) -> (~((op (e1) (e1)) = (e0))) -> (~((op (e1) (e0)) = (e0))) -> (((op (e1) (e0)) = (e0))\/(((op (e1) (e1)) = (e0))\/(((op (e1) (e2)) = (e0))\/((op (e1) (e3)) = (e0))))) -> (~((op (e0) (e3)) = (e0))) -> False). % 18.68/18.88 do 0 intro. intros zenon_H74 zenon_H3f zenon_H20b zenon_H38 zenon_H195 zenon_H24 zenon_H23 zenon_H22 zenon_H76. % 18.68/18.88 apply (zenon_or_s _ _ zenon_H74); [ zenon_intro zenon_H42 | zenon_intro zenon_H77 ]. % 18.68/18.88 exact (zenon_H3f zenon_H42). % 18.68/18.88 apply (zenon_or_s _ _ zenon_H77); [ zenon_intro zenon_H49 | zenon_intro zenon_H78 ]. % 18.68/18.88 exact (zenon_H20b zenon_H49). % 18.68/18.88 apply (zenon_or_s _ _ zenon_H78); [ zenon_intro zenon_H48 | zenon_intro zenon_H1e ]. % 18.68/18.88 apply (zenon_L335_); trivial. % 18.68/18.88 exact (zenon_H76 zenon_H1e). % 18.68/18.88 (* end of lemma zenon_L616_ *) % 18.68/18.88 assert (zenon_L617_ : ((~((op (e0) (e2)) = (e0)))\/((op (e0) (e0)) = (e2))) -> ((~((op (e1) (e0)) = (e0)))\/((op (e1) (e0)) = (e0))) -> (~((op (e1) (e0)) = (op (e2) (e0)))) -> (~((op (e2) (e0)) = (op (e2) (e1)))) -> (~((op (e1) (e0)) = (op (e3) (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)) = (op (e3) (e2)))) -> (~((op (e2) (e2)) = (op (e2) (e3)))) -> (~((op (e3) (e0)) = (op (e3) (e3)))) -> (~((op (e0) (e1)) = (op (e0) (e2)))) -> (~((op (e1) (e1)) = (op (e1) (e2)))) -> (~((op (e2) (e0)) = (op (e2) (e2)))) -> (((op (e0) (e3)) = (e0))\/(((op (e1) (e3)) = (e0))\/(((op (e2) (e3)) = (e0))\/((op (e3) (e3)) = (e0))))) -> (~((op (e3) (e2)) = (op (e3) (e3)))) -> (~((op (e2) (e0)) = (op (e2) (e3)))) -> (~((op (e1) (e1)) = (op (e1) (e3)))) -> (~((op (e0) (e1)) = (op (e0) (e3)))) -> (((op (e0) (e2)) = (e0))\/(((op (e1) (e2)) = (e0))\/(((op (e2) (e2)) = (e0))\/((op (e3) (e2)) = (e0))))) -> (~((op (e1) (e0)) = (op (e1) (e1)))) -> (((op (e1) (e0)) = (e0))\/(((op (e1) (e1)) = (e0))\/(((op (e1) (e2)) = (e0))\/((op (e1) (e3)) = (e0))))) -> (~((op (e0) (e0)) = (e0))) -> ((~((op (e3) (e1)) = (e0)))\/((op (e3) (e0)) = (e1))) -> ((~((op (e3) (e3)) = (e0)))\/((op (e3) (e0)) = (e3))) -> (((op (e2) (e0)) = (e2))\/(((op (e2) (e1)) = (e2))\/(((op (e2) (e2)) = (e2))\/((op (e2) (e3)) = (e2))))) -> (((op (e0) (e1)) = (e2))\/(((op (e1) (e1)) = (e2))\/(((op (e2) (e1)) = (e2))\/((op (e3) (e1)) = (e2))))) -> (~((op (e3) (e0)) = (op (e3) (e1)))) -> (((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 (e2) (e2)) = (e0))\/(((op (e2) (e2)) = (e1))\/(((op (e2) (e2)) = (e2))\/((op (e2) (e2)) = (e3))))) -> (~((op (e2) (e1)) = (op (e2) (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 (e2) (e0)) = (e0)))\/((op (e2) (e0)) = (e0))) -> (((op (e0) (e0)) = (e2))\/(((op (e1) (e0)) = (e2))\/(((op (e2) (e0)) = (e2))\/((op (e3) (e0)) = (e2))))) -> ((~((op (e2) (e1)) = (e0)))\/((op (e2) (e0)) = (e1))) -> (~((op (e0) (e0)) = (op (e2) (e0)))) -> (((op (e3) (e0)) = (e2))\/(((op (e3) (e1)) = (e2))\/(((op (e3) (e2)) = (e2))\/((op (e3) (e3)) = (e2))))) -> (~((op (e0) (e2)) = (op (e3) (e2)))) -> (~((e0) = (e2))) -> (((op (e3) (e0)) = (e3))\/(((op (e3) (e1)) = (e3))\/(((op (e3) (e2)) = (e3))\/((op (e3) (e3)) = (e3))))) -> (~((op (e1) (e1)) = (op (e3) (e1)))) -> (((op (e0) (e0)) = (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)) = (e2))) -> (((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) (e2)) = (op (e1) (e3)))) -> (~((e2) = (e3))) -> (((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)) = (e3))\/(((op (e1) (e3)) = (e3))\/(((op (e2) (e3)) = (e3))\/((op (e3) (e3)) = (e3))))) -> (((op (e1) (e0)) = (e1))\/(((op (e1) (e1)) = (e1))\/(((op (e1) (e2)) = (e1))\/((op (e1) (e3)) = (e1))))) -> (((op (e0) (e2)) = (e1))\/(((op (e1) (e2)) = (e1))\/(((op (e2) (e2)) = (e1))\/((op (e3) (e2)) = (e1))))) -> (~((op (e0) (e0)) = (op (e0) (e2)))) -> (~((op (e1) (e1)) = (op (e2) (e1)))) -> (((op (e1) (e1)) = (e0))\/(((op (e1) (e1)) = (e1))\/(((op (e1) (e1)) = (e2))\/((op (e1) (e1)) = (e3))))) -> ((~((op (e1) (e3)) = (e0)))\/((op (e1) (e0)) = (e3))) -> ((~((op (e1) (e2)) = (e0)))\/((op (e1) (e0)) = (e2))) -> (~((op (e0) (e1)) = (op (e2) (e1)))) -> (~((op (e2) (e0)) = (op (e3) (e0)))) -> (((op (e0) (e0)) = (e2))\/(((op (e0) (e1)) = (e2))\/(((op (e0) (e2)) = (e2))\/((op (e0) (e3)) = (e2))))) -> ((~((op (e3) (e0)) = (e0)))\/((op (e3) (e0)) = (e0))) -> ((~((op (e2) (e2)) = (e0)))\/((op (e2) (e0)) = (e2))) -> (~((op (e0) (e0)) = (op (e0) (e3)))) -> (((op (e0) (e1)) = (e1))\/(((op (e1) (e1)) = (e1))\/(((op (e2) (e1)) = (e1))\/((op (e3) (e1)) = (e1))))) -> (~((op (e1) (e2)) = (op (e2) (e2)))) -> (((op (e3) (e3)) = (e0))\/(((op (e3) (e3)) = (e1))\/(((op (e3) (e3)) = (e2))\/((op (e3) (e3)) = (e3))))) -> (~((op (e3) (e3)) = (e3))) -> (~((op (e2) (e3)) = (op (e3) (e3)))) -> (((op (e2) (e0)) = (e1))\/(((op (e2) (e1)) = (e1))\/(((op (e2) (e2)) = (e1))\/((op (e2) (e3)) = (e1))))) -> (((op (e2) (e0)) = (e3))\/(((op (e2) (e1)) = (e3))\/(((op (e2) (e2)) = (e3))\/((op (e2) (e3)) = (e3))))) -> (~((op (e2) (e1)) = (op (e3) (e1)))) -> (((op (e0) (e3)) = (e0))\/(((op (e0) (e3)) = (e1))\/(((op (e0) (e3)) = (e2))\/((op (e0) (e3)) = (e3))))) -> (~((op (e0) (e3)) = (op (e2) (e3)))) -> (~((op (e1) (e3)) = (op (e3) (e3)))) -> (~((op (e1) (e0)) = (op (e1) (e3)))) -> (~((op (e1) (e3)) = (op (e2) (e3)))) -> (((op (e1) (e3)) = (e0))\/(((op (e1) (e3)) = (e1))\/(((op (e1) (e3)) = (e2))\/((op (e1) (e3)) = (e3))))) -> (~((op (e0) (e3)) = (op (e3) (e3)))) -> (((op (e3) (e0)) = (e1))\/(((op (e3) (e1)) = (e1))\/(((op (e3) (e2)) = (e1))\/((op (e3) (e3)) = (e1))))) -> (~((op (e0) (e2)) = (op (e2) (e2)))) -> (~((e0) = (e1))) -> (~((op (e0) (e1)) = (op (e1) (e1)))) -> (~((op (e0) (e3)) = (op (e1) (e3)))) -> (((op (e2) (e3)) = (e0))\/(((op (e2) (e3)) = (e1))\/(((op (e2) (e3)) = (e2))\/((op (e2) (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) (e1)) = (e1))) -> (~((e0) = (e3))) -> (~((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 (e3) (e2)) = (e0))\/(((op (e3) (e2)) = (e1))\/(((op (e3) (e2)) = (e2))\/((op (e3) (e2)) = (e3))))) -> (~((op (e2) (e2)) = (op (e3) (e2)))) -> ((~((op (e3) (e2)) = (e0)))\/((op (e3) (e0)) = (e2))) -> (~((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)) = (e3))\/(((op (e1) (e1)) = (e3))\/(((op (e2) (e1)) = (e3))\/((op (e3) (e1)) = (e3))))) -> ((~((op (e2) (e3)) = (e0)))\/((op (e2) (e0)) = (e3))) -> (~((e1) = (e2))) -> ((~((op (e1) (e1)) = (e0)))\/((op (e1) (e0)) = (e1))) -> ((~((op (e0) (e3)) = (e0)))\/((op (e0) (e0)) = (e3))) -> ((op (e1) (e0)) = (e3)) -> ((op (e0) (e0)) = (e2)) -> (((op (e0) (e0)) = (e1))\/(((op (e1) (e0)) = (e1))\/(((op (e2) (e0)) = (e1))\/((op (e3) (e0)) = (e1))))) -> (~((op (e2) (e0)) = (e0))) -> (((op (e2) (e0)) = (e0))\/(((op (e2) (e1)) = (e0))\/(((op (e2) (e2)) = (e0))\/((op (e2) (e3)) = (e0))))) -> False). % 18.68/18.88 do 0 intro. intros zenon_H233 zenon_H206 zenon_H201 zenon_H1f0 zenon_H1fa zenon_H74 zenon_H3e zenon_H6f zenon_H6d zenon_H71 zenon_H4a zenon_H4f zenon_H52 zenon_H67 zenon_H62 zenon_H5b zenon_H57 zenon_H54 zenon_H6a zenon_H45 zenon_H22 zenon_H3f zenon_H1ed zenon_H1ec zenon_H1d5 zenon_H1d8 zenon_H1cf zenon_H1ba zenon_H1cc zenon_H1c4 zenon_H1c7 zenon_H1ac zenon_H1e0 zenon_H1ee zenon_H1fe zenon_H182 zenon_H39 zenon_H153 zenon_H14f zenon_H149 zenon_H165 zenon_H160 zenon_H168 zenon_H16f zenon_H173 zenon_H172 zenon_H145 zenon_H124 zenon_H12b zenon_H133 zenon_H130 zenon_H136 zenon_H128 zenon_H139 zenon_H13c zenon_H13e zenon_H142 zenon_H179 zenon_H178 zenon_H17e zenon_H17b zenon_H183 zenon_H184 zenon_H185 zenon_H189 zenon_H109 zenon_H2b zenon_H101 zenon_H102 zenon_Hf3 zenon_H106 zenon_He7 zenon_Haf zenon_He4 zenon_He2 zenon_Hd5 zenon_Hd8 zenon_Hdb zenon_Hdf zenon_Hc2 zenon_He8 zenon_Ha8 zenon_Ha1 zenon_H10e zenon_H1d zenon_H11f zenon_H115 zenon_H18c zenon_H10a zenon_H9a zenon_H95 zenon_H19d zenon_H195 zenon_H191 zenon_H18f zenon_H1a7 zenon_H1a4 zenon_H1a6 zenon_H1a5 zenon_H94 zenon_H7c zenon_H205 zenon_H204 zenon_H9e zenon_H7b zenon_H235 zenon_H30 zenon_H2f. % 18.68/18.88 apply (zenon_or_s _ _ zenon_H182); [ zenon_intro zenon_H31 | zenon_intro zenon_Hed ]. % 18.68/18.88 apply (zenon_or_s _ _ zenon_H185); [ zenon_intro zenon_H81 | zenon_intro zenon_Hee ]. % 18.68/18.88 apply (zenon_or_s _ _ zenon_H94); [ zenon_intro zenon_H32 | zenon_intro zenon_H3b ]. % 18.68/18.88 apply (zenon_L27_); trivial. % 18.68/18.88 apply (zenon_L570_); trivial. % 18.68/18.88 apply (zenon_L341_); trivial. % 18.68/18.88 apply (zenon_L491_); trivial. % 18.68/18.88 (* end of lemma zenon_L617_ *) % 18.68/18.88 assert (zenon_L618_ : (((op (e0) (e0)) = (e0))\/(((op (e0) (e1)) = (e0))\/(((op (e0) (e2)) = (e0))\/((op (e0) (e3)) = (e0))))) -> (~((op (e0) (e1)) = (e0))) -> (~((op (e1) (e3)) = (e0))) -> (~((op (e1) (e2)) = (e0))) -> (((op (e3) (e0)) = (e0))\/(((op (e3) (e1)) = (e0))\/(((op (e3) (e2)) = (e0))\/((op (e3) (e3)) = (e0))))) -> (~((op (e3) (e0)) = (e0))) -> (~((op (e3) (e0)) = (op (e3) (e1)))) -> (((op (e0) (e3)) = (e0))\/(((op (e1) (e3)) = (e0))\/(((op (e2) (e3)) = (e0))\/((op (e3) (e3)) = (e0))))) -> (((op (e0) (e2)) = (e0))\/(((op (e1) (e2)) = (e0))\/(((op (e2) (e2)) = (e0))\/((op (e3) (e2)) = (e0))))) -> (~((op (e0) (e2)) = (op (e0) (e3)))) -> (~((op (e1) (e1)) = (op (e1) (e2)))) -> (~((op (e2) (e0)) = (op (e2) (e2)))) -> (~((op (e3) (e1)) = (op (e3) (e2)))) -> (~((op (e1) (e0)) = (op (e1) (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 (e1) (e3)))) -> (~((op (e2) (e0)) = (op (e2) (e3)))) -> (~((op (e3) (e1)) = (op (e3) (e3)))) -> (~((op (e0) (e2)) = (op (e3) (e2)))) -> (~((op (e3) (e3)) = (e0))) -> (~((op (e1) (e0)) = (e0))) -> (((op (e1) (e0)) = (e0))\/(((op (e1) (e1)) = (e0))\/(((op (e1) (e2)) = (e0))\/((op (e1) (e3)) = (e0))))) -> (~((op (e0) (e3)) = (e0))) -> False). % 18.68/18.88 do 0 intro. intros zenon_H74 zenon_H20b zenon_H38 zenon_H25 zenon_H1ac zenon_H40 zenon_H1cf zenon_H67 zenon_H6a zenon_H208 zenon_H4f zenon_H52 zenon_H1a4 zenon_H45 zenon_H3f zenon_H3e zenon_H57 zenon_H5b zenon_H130 zenon_H14f zenon_H1ae zenon_H23 zenon_H22 zenon_H76. % 18.68/18.88 apply (zenon_or_s _ _ zenon_H74); [ zenon_intro zenon_H42 | zenon_intro zenon_H77 ]. % 18.68/18.88 exact (zenon_H3f zenon_H42). % 18.68/18.88 apply (zenon_or_s _ _ zenon_H77); [ zenon_intro zenon_H49 | zenon_intro zenon_H78 ]. % 18.68/18.88 exact (zenon_H20b zenon_H49). % 18.68/18.88 apply (zenon_or_s _ _ zenon_H78); [ zenon_intro zenon_H48 | zenon_intro zenon_H1e ]. % 18.68/18.88 apply (zenon_L351_); trivial. % 18.68/18.88 exact (zenon_H76 zenon_H1e). % 18.68/18.88 (* end of lemma zenon_L618_ *) % 18.68/18.88 assert (zenon_L619_ : (((op (e0) (e3)) = (e0))\/(((op (e1) (e3)) = (e0))\/(((op (e2) (e3)) = (e0))\/((op (e3) (e3)) = (e0))))) -> (~((e0) = (e3))) -> ((op (e0) (e3)) = (e3)) -> (~((op (e1) (e1)) = (op (e1) (e3)))) -> ((op (e1) (e1)) = (e0)) -> (~((op (e2) (e0)) = (op (e2) (e3)))) -> ((op (e2) (e0)) = (e0)) -> ((op (e3) (e2)) = (e0)) -> (~((op (e3) (e2)) = (op (e3) (e3)))) -> False). % 18.68/18.88 do 0 intro. intros zenon_H67 zenon_H9a zenon_He3 zenon_H57 zenon_H29 zenon_H5b zenon_H34 zenon_H61 zenon_H62. % 18.68/18.88 apply (zenon_or_s _ _ zenon_H67); [ zenon_intro zenon_H1e | zenon_intro zenon_H68 ]. % 18.68/18.88 apply (zenon_L515_); trivial. % 18.68/18.88 apply (zenon_or_s _ _ zenon_H68); [ zenon_intro zenon_H1f | zenon_intro zenon_H69 ]. % 18.68/18.88 apply (zenon_L13_); trivial. % 18.68/18.88 apply (zenon_or_s _ _ zenon_H69); [ zenon_intro zenon_H37 | zenon_intro zenon_H60 ]. % 18.68/18.88 apply (zenon_L14_); trivial. % 18.68/18.88 apply (zenon_L15_); trivial. % 18.68/18.88 (* end of lemma zenon_L619_ *) % 18.68/18.88 assert (zenon_L620_ : (((op (e0) (e2)) = (e0))\/(((op (e1) (e2)) = (e0))\/(((op (e2) (e2)) = (e0))\/((op (e3) (e2)) = (e0))))) -> (~((e0) = (e1))) -> ((op (e0) (e2)) = (e1)) -> (~((e0) = (e2))) -> ((op (e1) (e2)) = (e2)) -> (~((op (e2) (e0)) = (op (e2) (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) (e1)) = (op (e1) (e3)))) -> ((op (e1) (e1)) = (e0)) -> (~((op (e2) (e0)) = (op (e2) (e3)))) -> ((op (e2) (e0)) = (e0)) -> (~((op (e3) (e2)) = (op (e3) (e3)))) -> False). % 18.68/18.88 do 0 intro. intros zenon_H6a zenon_Ha1 zenon_H122 zenon_H149 zenon_H113 zenon_H52 zenon_H67 zenon_H9a zenon_He3 zenon_H57 zenon_H29 zenon_H5b zenon_H34 zenon_H62. % 18.68/18.88 apply (zenon_or_s _ _ zenon_H6a); [ zenon_intro zenon_H48 | zenon_intro zenon_H6b ]. % 18.68/18.88 apply (zenon_L355_); trivial. % 18.68/18.88 apply (zenon_or_s _ _ zenon_H6b); [ zenon_intro zenon_H2a | zenon_intro zenon_H6c ]. % 18.68/18.88 apply (zenon_L542_); trivial. % 18.68/18.88 apply (zenon_or_s _ _ zenon_H6c); [ zenon_intro zenon_H2c | zenon_intro zenon_H61 ]. % 18.68/18.88 apply (zenon_L11_); trivial. % 18.68/18.88 apply (zenon_L619_); trivial. % 18.68/18.88 (* end of lemma zenon_L620_ *) % 18.68/18.88 assert (zenon_L621_ : (((op (e2) (e0)) = (e3))\/(((op (e2) (e1)) = (e3))\/(((op (e2) (e2)) = (e3))\/((op (e2) (e3)) = (e3))))) -> (~((op (e3) (e0)) = (op (e3) (e2)))) -> (~((op (e2) (e0)) = (op (e2) (e2)))) -> ((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 (e1) (e3)) = (e2)) -> (~((op (e1) (e3)) = (op (e3) (e3)))) -> (((op (e3) (e1)) = (e0))\/(((op (e3) (e1)) = (e1))\/(((op (e3) (e1)) = (e2))\/((op (e3) (e1)) = (e3))))) -> ((op (e1) (e1)) = (e3)) -> (~((op (e0) (e1)) = (op (e1) (e1)))) -> (((op (e2) (e1)) = (e0))\/(((op (e2) (e1)) = (e1))\/(((op (e2) (e1)) = (e2))\/((op (e2) (e1)) = (e3))))) -> (~((op (e2) (e1)) = (e0))) -> (~((op (e2) (e1)) = (op (e3) (e1)))) -> (~((op (e0) (e1)) = (op (e2) (e1)))) -> (~((op (e1) (e1)) = (op (e2) (e1)))) -> (~((op (e0) (e1)) = (op (e3) (e1)))) -> (~((op (e0) (e1)) = (e0))) -> (((op (e0) (e1)) = (e0))\/(((op (e0) (e1)) = (e1))\/(((op (e0) (e1)) = (e2))\/((op (e0) (e1)) = (e3))))) -> (~((op (e3) (e1)) = (op (e3) (e2)))) -> ((op (e3) (e0)) = (e3)) -> (~((op (e3) (e0)) = (op (e3) (e1)))) -> (~((op (e2) (e1)) = (op (e2) (e3)))) -> (((op (e3) (e0)) = (e3))\/(((op (e3) (e1)) = (e3))\/(((op (e3) (e2)) = (e3))\/((op (e3) (e3)) = (e3))))) -> (~((e2) = (e3))) -> (~((op (e1) (e1)) = (op (e3) (e1)))) -> (~((op (e2) (e2)) = (op (e3) (e2)))) -> (~((op (e3) (e3)) = (e3))) -> (((op (e3) (e0)) = (e2))\/(((op (e3) (e1)) = (e2))\/(((op (e3) (e2)) = (e2))\/((op (e3) (e3)) = (e2))))) -> (((op (e3) (e0)) = (e0))\/(((op (e3) (e1)) = (e0))\/(((op (e3) (e2)) = (e0))\/((op (e3) (e3)) = (e0))))) -> (~((op (e3) (e0)) = (e0))) -> (~((op (e3) (e1)) = (e0))) -> (~((op (e3) (e2)) = (e0))) -> (((op (e0) (e3)) = (e0))\/(((op (e0) (e3)) = (e1))\/(((op (e0) (e3)) = (e2))\/((op (e0) (e3)) = (e3))))) -> (~((op (e0) (e3)) = (op (e3) (e3)))) -> ((op (e2) (e3)) = (e1)) -> (~((op (e0) (e3)) = (op (e2) (e3)))) -> False). % 18.68/18.88 do 0 intro. intros zenon_He7 zenon_H6f zenon_H52 zenon_H113 zenon_H48 zenon_H9a zenon_H1a6 zenon_Hd7 zenon_Hd5 zenon_H22a zenon_H13f zenon_H10e zenon_H1cc zenon_H31 zenon_Haf zenon_H17e zenon_H13e zenon_H210 zenon_H20b zenon_H212 zenon_H1a4 zenon_H15e zenon_H1cf zenon_H1c7 zenon_H165 zenon_H12b zenon_H160 zenon_H18f zenon_H102 zenon_H153 zenon_H1ac zenon_H40 zenon_H1ad zenon_H18b zenon_He4 zenon_Hc2 zenon_Hf4 zenon_He2. % 18.68/18.88 apply (zenon_or_s _ _ zenon_He7); [ zenon_intro zenon_H3b | zenon_intro zenon_He9 ]. % 18.68/18.88 apply (zenon_L457_); trivial. % 18.68/18.88 apply (zenon_or_s _ _ zenon_He9); [ zenon_intro zenon_Ha6 | zenon_intro zenon_Hea ]. % 18.68/18.88 apply (zenon_L95_); trivial. % 18.68/18.88 apply (zenon_or_s _ _ zenon_Hea); [ zenon_intro zenon_Haa | zenon_intro zenon_Hdd ]. % 18.68/18.88 apply (zenon_or_s _ _ zenon_H153); [ zenon_intro zenon_H148 | zenon_intro zenon_H154 ]. % 18.68/18.88 apply (zenon_L325_); trivial. % 18.68/18.88 apply (zenon_or_s _ _ zenon_H154); [ zenon_intro zenon_H14d | zenon_intro zenon_H155 ]. % 18.68/18.88 apply (zenon_L451_); trivial. % 18.68/18.88 apply (zenon_or_s _ _ zenon_H155); [ zenon_intro zenon_H151 | zenon_intro zenon_Hf6 ]. % 18.68/18.88 apply (zenon_L453_); trivial. % 18.68/18.88 apply (zenon_L402_); trivial. % 18.68/18.88 apply (zenon_L474_); trivial. % 18.68/18.88 (* end of lemma zenon_L621_ *) % 18.68/18.88 assert (zenon_L622_ : (((op (e2) (e0)) = (e1))\/(((op (e2) (e1)) = (e1))\/(((op (e2) (e2)) = (e1))\/((op (e2) (e3)) = (e1))))) -> (~((op (e1) (e0)) = (op (e2) (e0)))) -> (~((op (e0) (e1)) = (op (e2) (e1)))) -> (~((op (e3) (e0)) = (op (e3) (e2)))) -> ((op (e3) (e0)) = (e3)) -> (~((op (e3) (e1)) = (op (e3) (e2)))) -> (~((op (e3) (e2)) = (op (e3) (e3)))) -> (~((op (e3) (e2)) = (e0))) -> (((op (e3) (e2)) = (e0))\/(((op (e3) (e2)) = (e1))\/(((op (e3) (e2)) = (e2))\/((op (e3) (e2)) = (e3))))) -> (((op (e0) (e3)) = (e1))\/(((op (e1) (e3)) = (e1))\/(((op (e2) (e3)) = (e1))\/((op (e3) (e3)) = (e1))))) -> (~((op (e0) (e1)) = (op (e0) (e3)))) -> ((op (e0) (e1)) = (e1)) -> (~((op (e1) (e0)) = (op (e1) (e3)))) -> ((op (e1) (e0)) = (e1)) -> (~((op (e2) (e2)) = (op (e2) (e3)))) -> (~((op (e0) (e1)) = (op (e3) (e1)))) -> (~((e1) = (e3))) -> (((op (e3) (e0)) = (e1))\/(((op (e3) (e1)) = (e1))\/(((op (e3) (e2)) = (e1))\/((op (e3) (e3)) = (e1))))) -> (((op (e2) (e1)) = (e0))\/(((op (e2) (e1)) = (e1))\/(((op (e2) (e1)) = (e2))\/((op (e2) (e1)) = (e3))))) -> (~((op (e2) (e1)) = (e0))) -> (~((op (e2) (e1)) = (op (e2) (e3)))) -> ((op (e3) (e1)) = (e2)) -> (~((op (e2) (e1)) = (op (e3) (e1)))) -> (~((op (e1) (e1)) = (op (e2) (e1)))) -> ((op (e1) (e1)) = (e3)) -> False). % 18.68/18.88 do 0 intro. intros zenon_H106 zenon_H201 zenon_H17e zenon_H6f zenon_H15e zenon_H1a4 zenon_H62 zenon_H18b zenon_H191 zenon_H133 zenon_H54 zenon_Ha0 zenon_Hd8 zenon_H9d zenon_H6d zenon_H210 zenon_H95 zenon_He8 zenon_H1cc zenon_H31 zenon_H1c7 zenon_H14d zenon_Haf zenon_H13e zenon_H13f. % 18.68/18.88 apply (zenon_or_s _ _ zenon_H106); [ zenon_intro zenon_Hed | zenon_intro zenon_H107 ]. % 18.68/18.88 apply (zenon_L413_); trivial. % 18.68/18.88 apply (zenon_or_s _ _ zenon_H107); [ zenon_intro zenon_Ha5 | zenon_intro zenon_H108 ]. % 18.68/18.88 apply (zenon_L357_); trivial. % 18.68/18.88 apply (zenon_or_s _ _ zenon_H108); [ zenon_intro zenon_Hf1 | zenon_intro zenon_Hf4 ]. % 18.68/18.88 apply (zenon_L607_); trivial. % 18.68/18.88 apply (zenon_L451_); trivial. % 18.68/18.88 (* end of lemma zenon_L622_ *) % 18.68/18.88 assert (zenon_L623_ : ((~((op (e3) (e3)) = (e0)))\/((op (e3) (e0)) = (e3))) -> ((op (e3) (e0)) = (e2)) -> (~((e2) = (e3))) -> (~((op (e0) (e0)) = (e0))) -> (~((op (e0) (e1)) = (e0))) -> (((op (e1) (e0)) = (e0))\/(((op (e1) (e1)) = (e0))\/(((op (e1) (e2)) = (e0))\/((op (e1) (e3)) = (e0))))) -> (~((op (e1) (e3)) = (e0))) -> (~((op (e1) (e2)) = (e0))) -> (~((op (e3) (e0)) = (e0))) -> (((op (e0) (e0)) = (e0))\/(((op (e1) (e0)) = (e0))\/(((op (e2) (e0)) = (e0))\/((op (e3) (e0)) = (e0))))) -> (~((op (e3) (e0)) = (op (e3) (e1)))) -> (~((op (e0) (e2)) = (op (e0) (e3)))) -> (~((op (e1) (e1)) = (op (e1) (e2)))) -> (~((op (e2) (e0)) = (op (e2) (e2)))) -> (~((op (e3) (e1)) = (op (e3) (e2)))) -> (((op (e0) (e2)) = (e0))\/(((op (e1) (e2)) = (e0))\/(((op (e2) (e2)) = (e0))\/((op (e3) (e2)) = (e0))))) -> (~((op (e1) (e1)) = (op (e1) (e3)))) -> (~((op (e2) (e0)) = (op (e2) (e3)))) -> (~((op (e3) (e1)) = (op (e3) (e3)))) -> (((op (e0) (e3)) = (e0))\/(((op (e1) (e3)) = (e0))\/(((op (e2) (e3)) = (e0))\/((op (e3) (e3)) = (e0))))) -> (~((op (e1) (e0)) = (op (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 (e1) (e0)) = (e0))) -> (~((op (e0) (e3)) = (e0))) -> (((op (e0) (e0)) = (e0))\/(((op (e0) (e1)) = (e0))\/(((op (e0) (e2)) = (e0))\/((op (e0) (e3)) = (e0))))) -> False). % 18.68/18.88 do 0 intro. intros zenon_H1ec zenon_H148 zenon_H12b zenon_H3f zenon_H20b zenon_H22 zenon_H38 zenon_H25 zenon_H40 zenon_H3e zenon_H1cf zenon_H208 zenon_H4f zenon_H52 zenon_H1a4 zenon_H6a zenon_H57 zenon_H5b zenon_H130 zenon_H67 zenon_H45 zenon_H14f zenon_H1ac zenon_H23 zenon_H76 zenon_H74. % 18.68/18.88 apply (zenon_or_s _ _ zenon_H1ec); [ zenon_intro zenon_H1ae | zenon_intro zenon_H15e ]. % 18.68/18.88 apply (zenon_L618_); trivial. % 18.68/18.88 apply (zenon_L109_); trivial. % 18.68/18.88 (* end of lemma zenon_L623_ *) % 18.68/18.88 assert (zenon_L624_ : ((~((op (e3) (e3)) = (e0)))\/((op (e3) (e0)) = (e3))) -> ((op (e3) (e0)) = (e2)) -> (~((e2) = (e3))) -> (~((op (e0) (e0)) = (e0))) -> (~((op (e0) (e1)) = (e0))) -> (((op (e3) (e0)) = (e0))\/(((op (e3) (e1)) = (e0))\/(((op (e3) (e2)) = (e0))\/((op (e3) (e3)) = (e0))))) -> (~((op (e0) (e2)) = (op (e3) (e2)))) -> (~((op (e3) (e1)) = (e0))) -> (~((op (e3) (e0)) = (e0))) -> (~((op (e0) (e3)) = (e0))) -> (((op (e0) (e0)) = (e0))\/(((op (e0) (e1)) = (e0))\/(((op (e0) (e2)) = (e0))\/((op (e0) (e3)) = (e0))))) -> False). % 18.68/18.88 do 0 intro. intros zenon_H1ec zenon_H148 zenon_H12b zenon_H3f zenon_H20b zenon_H1ac zenon_H14f zenon_H1ad zenon_H40 zenon_H76 zenon_H74. % 18.68/18.88 apply (zenon_or_s _ _ zenon_H1ec); [ zenon_intro zenon_H1ae | zenon_intro zenon_H15e ]. % 18.68/18.88 apply (zenon_or_s _ _ zenon_H74); [ zenon_intro zenon_H42 | zenon_intro zenon_H77 ]. % 18.68/18.88 exact (zenon_H3f zenon_H42). % 18.68/18.88 apply (zenon_or_s _ _ zenon_H77); [ zenon_intro zenon_H49 | zenon_intro zenon_H78 ]. % 18.68/18.88 exact (zenon_H20b zenon_H49). % 18.68/18.88 apply (zenon_or_s _ _ zenon_H78); [ zenon_intro zenon_H48 | zenon_intro zenon_H1e ]. % 18.68/18.88 apply (zenon_L343_); trivial. % 18.68/18.88 exact (zenon_H76 zenon_H1e). % 18.68/18.88 apply (zenon_L109_); trivial. % 18.68/18.88 (* end of lemma zenon_L624_ *) % 18.68/18.88 assert (zenon_L625_ : (((op (e0) (e0)) = (e0))\/(((op (e1) (e0)) = (e0))\/(((op (e2) (e0)) = (e0))\/((op (e3) (e0)) = (e0))))) -> (~((op (e1) (e0)) = (e0))) -> (~((op (e0) (e0)) = (e0))) -> (~((op (e0) (e1)) = (e0))) -> (((op (e0) (e0)) = (e1))\/(((op (e0) (e1)) = (e1))\/(((op (e0) (e2)) = (e1))\/((op (e0) (e3)) = (e1))))) -> ((op (e0) (e0)) = (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)) = (e0))\/(((op (e0) (e1)) = (e1))\/(((op (e0) (e1)) = (e2))\/((op (e0) (e1)) = (e3))))) -> ((op (e1) (e0)) = (e1)) -> (~((op (e1) (e2)) = (e0))) -> ((~((op (e0) (e3)) = (e0)))\/((op (e0) (e0)) = (e3))) -> ((~((op (e1) (e1)) = (e0)))\/((op (e1) (e0)) = (e1))) -> (~((e1) = (e2))) -> ((~((op (e2) (e3)) = (e0)))\/((op (e2) (e0)) = (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) (e1)) = (op (e3) (e2)))) -> ((~((op (e3) (e2)) = (e0)))\/((op (e3) (e0)) = (e2))) -> (~((op (e2) (e2)) = (op (e3) (e2)))) -> (((op (e3) (e2)) = (e0))\/(((op (e3) (e2)) = (e1))\/(((op (e3) (e2)) = (e2))\/((op (e3) (e2)) = (e3))))) -> (~((op (e0) (e2)) = (op (e1) (e2)))) -> (((op (e1) (e2)) = (e0))\/(((op (e1) (e2)) = (e1))\/(((op (e1) (e2)) = (e2))\/((op (e1) (e2)) = (e3))))) -> (~((e1) = (e3))) -> (~((e0) = (e3))) -> (~((op (e1) (e1)) = (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) (e3)) = (e0))\/(((op (e2) (e3)) = (e1))\/(((op (e2) (e3)) = (e2))\/((op (e2) (e3)) = (e3))))) -> (~((op (e0) (e3)) = (op (e1) (e3)))) -> (~((op (e0) (e1)) = (op (e1) (e1)))) -> (~((e0) = (e1))) -> (~((op (e0) (e2)) = (op (e2) (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) (e3)) = (e0))\/(((op (e1) (e3)) = (e1))\/(((op (e1) (e3)) = (e2))\/((op (e1) (e3)) = (e3))))) -> (~((op (e1) (e3)) = (op (e2) (e3)))) -> (~((op (e1) (e0)) = (op (e1) (e3)))) -> (~((op (e1) (e3)) = (op (e3) (e3)))) -> (~((op (e0) (e3)) = (op (e2) (e3)))) -> (((op (e0) (e3)) = (e0))\/(((op (e0) (e3)) = (e1))\/(((op (e0) (e3)) = (e2))\/((op (e0) (e3)) = (e3))))) -> (~((op (e2) (e1)) = (op (e3) (e1)))) -> (((op (e2) (e0)) = (e3))\/(((op (e2) (e1)) = (e3))\/(((op (e2) (e2)) = (e3))\/((op (e2) (e3)) = (e3))))) -> (((op (e2) (e0)) = (e1))\/(((op (e2) (e1)) = (e1))\/(((op (e2) (e2)) = (e1))\/((op (e2) (e3)) = (e1))))) -> (~((op (e2) (e3)) = (op (e3) (e3)))) -> (~((op (e3) (e3)) = (e3))) -> (((op (e3) (e3)) = (e0))\/(((op (e3) (e3)) = (e1))\/(((op (e3) (e3)) = (e2))\/((op (e3) (e3)) = (e3))))) -> (~((op (e1) (e2)) = (op (e2) (e2)))) -> (((op (e0) (e1)) = (e1))\/(((op (e1) (e1)) = (e1))\/(((op (e2) (e1)) = (e1))\/((op (e3) (e1)) = (e1))))) -> (~((op (e0) (e0)) = (op (e0) (e3)))) -> ((~((op (e2) (e2)) = (e0)))\/((op (e2) (e0)) = (e2))) -> ((~((op (e3) (e0)) = (e0)))\/((op (e3) (e0)) = (e0))) -> (((op (e0) (e0)) = (e2))\/(((op (e0) (e1)) = (e2))\/(((op (e0) (e2)) = (e2))\/((op (e0) (e3)) = (e2))))) -> (~((op (e2) (e0)) = (op (e3) (e0)))) -> (~((op (e0) (e1)) = (op (e2) (e1)))) -> ((~((op (e1) (e2)) = (e0)))\/((op (e1) (e0)) = (e2))) -> ((~((op (e1) (e3)) = (e0)))\/((op (e1) (e0)) = (e3))) -> (((op (e1) (e1)) = (e0))\/(((op (e1) (e1)) = (e1))\/(((op (e1) (e1)) = (e2))\/((op (e1) (e1)) = (e3))))) -> (~((op (e1) (e1)) = (op (e2) (e1)))) -> (~((op (e0) (e0)) = (op (e0) (e2)))) -> (((op (e0) (e2)) = (e1))\/(((op (e1) (e2)) = (e1))\/(((op (e2) (e2)) = (e1))\/((op (e3) (e2)) = (e1))))) -> (((op (e1) (e0)) = (e1))\/(((op (e1) (e1)) = (e1))\/(((op (e1) (e2)) = (e1))\/((op (e1) (e3)) = (e1))))) -> (((op (e0) (e3)) = (e3))\/(((op (e1) (e3)) = (e3))\/(((op (e2) (e3)) = (e3))\/((op (e3) (e3)) = (e3))))) -> (~((op (e3) (e1)) = (op (e3) (e3)))) -> (((op (e0) (e3)) = (e1))\/(((op (e1) (e3)) = (e1))\/(((op (e2) (e3)) = (e1))\/((op (e3) (e3)) = (e1))))) -> (~((e2) = (e3))) -> (~((op (e1) (e2)) = (op (e1) (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 (e2) (e2)) = (e2))) -> (((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) (e1)) = (op (e3) (e1)))) -> (((op (e3) (e0)) = (e3))\/(((op (e3) (e1)) = (e3))\/(((op (e3) (e2)) = (e3))\/((op (e3) (e3)) = (e3))))) -> (~((e0) = (e2))) -> (~((op (e0) (e2)) = (op (e3) (e2)))) -> (((op (e3) (e0)) = (e2))\/(((op (e3) (e1)) = (e2))\/(((op (e3) (e2)) = (e2))\/((op (e3) (e3)) = (e2))))) -> (~((op (e0) (e0)) = (op (e2) (e0)))) -> ((~((op (e2) (e1)) = (e0)))\/((op (e2) (e0)) = (e1))) -> (((op (e0) (e0)) = (e2))\/(((op (e1) (e0)) = (e2))\/(((op (e2) (e0)) = (e2))\/((op (e3) (e0)) = (e2))))) -> ((~((op (e2) (e0)) = (e0)))\/((op (e2) (e0)) = (e0))) -> (((op (e0) (e0)) = (e3))\/(((op (e1) (e0)) = (e3))\/(((op (e2) (e0)) = (e3))\/((op (e3) (e0)) = (e3))))) -> (((op (e3) (e0)) = (e0))\/(((op (e3) (e1)) = (e0))\/(((op (e3) (e2)) = (e0))\/((op (e3) (e3)) = (e0))))) -> (~((op (e2) (e1)) = (op (e2) (e3)))) -> (((op (e2) (e2)) = (e0))\/(((op (e2) (e2)) = (e1))\/(((op (e2) (e2)) = (e2))\/((op (e2) (e2)) = (e3))))) -> (((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 (e3) (e0)) = (op (e3) (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))))) -> ((~((op (e3) (e3)) = (e0)))\/((op (e3) (e0)) = (e3))) -> ((~((op (e3) (e1)) = (e0)))\/((op (e3) (e0)) = (e1))) -> (((op (e1) (e0)) = (e0))\/(((op (e1) (e1)) = (e0))\/(((op (e1) (e2)) = (e0))\/((op (e1) (e3)) = (e0))))) -> (~((op (e1) (e0)) = (op (e1) (e1)))) -> (((op (e0) (e2)) = (e0))\/(((op (e1) (e2)) = (e0))\/(((op (e2) (e2)) = (e0))\/((op (e3) (e2)) = (e0))))) -> (~((op (e0) (e1)) = (op (e0) (e3)))) -> (~((op (e1) (e1)) = (op (e1) (e3)))) -> (~((op (e2) (e0)) = (op (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) (e0)) = (op (e2) (e2)))) -> (~((op (e1) (e1)) = (op (e1) (e2)))) -> (~((op (e0) (e1)) = (op (e0) (e2)))) -> (~((op (e3) (e0)) = (op (e3) (e3)))) -> (~((op (e2) (e2)) = (op (e2) (e3)))) -> (~((op (e3) (e0)) = (op (e3) (e2)))) -> (((op (e0) (e0)) = (e0))\/(((op (e0) (e1)) = (e0))\/(((op (e0) (e2)) = (e0))\/((op (e0) (e3)) = (e0))))) -> (~((op (e1) (e0)) = (op (e3) (e0)))) -> (~((op (e2) (e0)) = (op (e2) (e1)))) -> (~((op (e1) (e0)) = (op (e2) (e0)))) -> ((~((op (e1) (e0)) = (e0)))\/((op (e1) (e0)) = (e0))) -> ((~((op (e0) (e2)) = (e0)))\/((op (e0) (e0)) = (e2))) -> (~((op (e0) (e3)) = (e0))) -> (((op (e2) (e0)) = (e0))\/(((op (e2) (e1)) = (e0))\/(((op (e2) (e2)) = (e0))\/((op (e2) (e3)) = (e0))))) -> (~((op (e0) (e2)) = (op (e0) (e3)))) -> False). % 18.68/18.88 do 0 intro. intros zenon_H3e zenon_H23 zenon_H3f zenon_H20b zenon_H22d zenon_H7b zenon_H210 zenon_H22a zenon_H212 zenon_H9d zenon_H25 zenon_H204 zenon_H205 zenon_H7c zenon_H94 zenon_H1a5 zenon_H1a6 zenon_H1a4 zenon_H1a7 zenon_H18f zenon_H191 zenon_H195 zenon_H19d zenon_H95 zenon_H9a zenon_H10a zenon_H18c zenon_H115 zenon_H11f zenon_H1d zenon_H10e zenon_Ha1 zenon_Ha8 zenon_He8 zenon_Hc2 zenon_Hdf zenon_Hdb zenon_Hd8 zenon_Hd5 zenon_He2 zenon_He4 zenon_Haf zenon_He7 zenon_H106 zenon_Hf3 zenon_H102 zenon_H101 zenon_H2b zenon_H109 zenon_H189 zenon_H185 zenon_H184 zenon_H183 zenon_H17b zenon_H17e zenon_H178 zenon_H179 zenon_H142 zenon_H13e zenon_H13c zenon_H139 zenon_H128 zenon_H136 zenon_H130 zenon_H133 zenon_H12b zenon_H124 zenon_H145 zenon_H172 zenon_H173 zenon_H16f zenon_H168 zenon_H160 zenon_H165 zenon_H149 zenon_H14f zenon_H153 zenon_H39 zenon_H182 zenon_H1fe zenon_H1ee zenon_H1e0 zenon_H1ac zenon_H1c7 zenon_H1c4 zenon_H1cc zenon_H1ba zenon_H1cf zenon_H1d8 zenon_H1d5 zenon_H1ec zenon_H1ed zenon_H22 zenon_H45 zenon_H6a zenon_H54 zenon_H57 zenon_H5b zenon_H62 zenon_H67 zenon_H52 zenon_H4f zenon_H4a zenon_H71 zenon_H6d zenon_H6f zenon_H74 zenon_H1fa zenon_H1f0 zenon_H201 zenon_H206 zenon_H233 zenon_H76 zenon_H2f zenon_H208. % 18.68/18.88 apply (zenon_or_s _ _ zenon_H179); [ zenon_intro zenon_H38 | zenon_intro zenon_H9e ]. % 18.68/18.88 apply (zenon_or_s _ _ zenon_H1ee); [ zenon_intro zenon_H30 | zenon_intro zenon_H34 ]. % 18.68/18.88 apply (zenon_or_s _ _ zenon_H182); [ zenon_intro zenon_H31 | zenon_intro zenon_Hed ]. % 18.68/18.88 apply (zenon_or_s _ _ zenon_H185); [ zenon_intro zenon_H81 | zenon_intro zenon_Hee ]. % 18.68/18.88 apply (zenon_or_s _ _ zenon_H94); [ zenon_intro zenon_H32 | zenon_intro zenon_H3b ]. % 18.68/18.88 apply (zenon_L27_); trivial. % 18.68/18.88 apply (zenon_or_s _ _ zenon_H184); [ zenon_intro zenon_H40 | zenon_intro zenon_H44 ]. % 18.68/18.88 apply (zenon_L7_); trivial. % 18.68/18.88 apply (zenon_or_s _ _ zenon_H1ed); [ zenon_intro zenon_H1ad | zenon_intro zenon_Hac ]. % 18.68/18.88 apply (zenon_or_s _ _ zenon_H74); [ zenon_intro zenon_H42 | zenon_intro zenon_H77 ]. % 18.68/18.88 exact (zenon_H3f zenon_H42). % 18.68/18.88 apply (zenon_or_s _ _ zenon_H77); [ zenon_intro zenon_H49 | zenon_intro zenon_H78 ]. % 18.68/18.88 exact (zenon_H20b zenon_H49). % 18.68/18.88 apply (zenon_or_s _ _ zenon_H78); [ zenon_intro zenon_H48 | zenon_intro zenon_H1e ]. % 18.68/18.88 apply (zenon_or_s _ _ zenon_H22d); [ zenon_intro zenon_H7a | zenon_intro zenon_H22e ]. % 18.68/18.88 apply (zenon_L456_); trivial. % 18.68/18.88 apply (zenon_or_s _ _ zenon_H22e); [ zenon_intro zenon_Ha0 | zenon_intro zenon_H22f ]. % 18.68/18.88 apply (zenon_L415_); trivial. % 18.68/18.88 apply (zenon_or_s _ _ zenon_H22f); [ zenon_intro zenon_H122 | zenon_intro zenon_Hc3 ]. % 18.68/18.88 apply (zenon_L355_); trivial. % 18.68/18.88 apply (zenon_L416_); trivial. % 18.68/18.88 exact (zenon_H76 zenon_H1e). % 18.68/18.88 apply (zenon_L41_); trivial. % 18.68/18.88 apply (zenon_L341_); trivial. % 18.68/18.88 apply (zenon_L413_); trivial. % 18.68/18.88 apply (zenon_or_s _ _ zenon_H182); [ zenon_intro zenon_H31 | zenon_intro zenon_Hed ]. % 18.68/18.88 apply (zenon_or_s _ _ zenon_H185); [ zenon_intro zenon_H81 | zenon_intro zenon_Hee ]. % 18.68/18.88 apply (zenon_or_s _ _ zenon_H94); [ zenon_intro zenon_H32 | zenon_intro zenon_H3b ]. % 18.68/18.88 apply (zenon_or_s _ _ zenon_H184); [ zenon_intro zenon_H40 | zenon_intro zenon_H44 ]. % 18.68/18.88 apply (zenon_or_s _ _ zenon_H1ed); [ zenon_intro zenon_H1ad | zenon_intro zenon_Hac ]. % 18.68/18.88 apply (zenon_or_s _ _ zenon_H1a7); [ zenon_intro zenon_H18b | zenon_intro zenon_H148 ]. % 18.68/18.88 apply (zenon_or_s _ _ zenon_H1ec); [ zenon_intro zenon_H1ae | zenon_intro zenon_H15e ]. % 18.68/18.88 apply (zenon_L618_); trivial. % 18.68/18.88 apply (zenon_or_s _ _ zenon_H74); [ zenon_intro zenon_H42 | zenon_intro zenon_H77 ]. % 18.68/18.88 exact (zenon_H3f zenon_H42). % 18.68/18.88 apply (zenon_or_s _ _ zenon_H77); [ zenon_intro zenon_H49 | zenon_intro zenon_H78 ]. % 18.68/18.88 exact (zenon_H20b zenon_H49). % 18.68/18.88 apply (zenon_or_s _ _ zenon_H78); [ zenon_intro zenon_H48 | zenon_intro zenon_H1e ]. % 18.68/18.88 apply (zenon_or_s _ _ zenon_H22d); [ zenon_intro zenon_H7a | zenon_intro zenon_H22e ]. % 18.68/18.88 apply (zenon_L26_); trivial. % 18.68/18.88 apply (zenon_or_s _ _ zenon_H22e); [ zenon_intro zenon_Ha0 | zenon_intro zenon_H22f ]. % 18.68/18.88 apply (zenon_or_s _ _ zenon_H168); [ zenon_intro zenon_H3a | zenon_intro zenon_H169 ]. % 18.68/18.88 apply (zenon_L487_); trivial. % 18.68/18.88 apply (zenon_or_s _ _ zenon_H169); [ zenon_intro zenon_H99 | zenon_intro zenon_H16a ]. % 18.68/18.88 apply (zenon_L403_); trivial. % 18.68/18.88 apply (zenon_or_s _ _ zenon_H16a); [ zenon_intro zenon_Ha9 | zenon_intro zenon_He3 ]. % 18.68/18.88 apply (zenon_L358_); trivial. % 18.68/18.88 apply (zenon_or_s _ _ zenon_H22); [ zenon_intro zenon_H27 | zenon_intro zenon_H26 ]. % 18.68/18.88 exact (zenon_H23 zenon_H27). % 18.68/18.88 apply (zenon_or_s _ _ zenon_H26); [ zenon_intro zenon_H29 | zenon_intro zenon_H28 ]. % 18.68/18.88 apply (zenon_or_s _ _ zenon_H18c); [ zenon_intro zenon_H86 | zenon_intro zenon_H18d ]. % 18.68/18.88 apply (zenon_L123_); trivial. % 18.68/18.88 apply (zenon_or_s _ _ zenon_H18d); [ zenon_intro zenon_H110 | zenon_intro zenon_H18e ]. % 18.68/18.88 apply (zenon_L354_); trivial. % 18.68/18.88 apply (zenon_or_s _ _ zenon_H18e); [ zenon_intro zenon_H113 | zenon_intro zenon_Hd7 ]. % 18.68/18.88 apply (zenon_or_s _ _ zenon_H1d8); [ zenon_intro zenon_H10f | zenon_intro zenon_H1d9 ]. % 18.68/18.88 apply (zenon_L418_); trivial. % 18.68/18.88 apply (zenon_or_s _ _ zenon_H1d9); [ zenon_intro zenon_H110 | zenon_intro zenon_H1da ]. % 18.68/18.88 apply (zenon_L354_); trivial. % 18.68/18.88 apply (zenon_or_s _ _ zenon_H1da); [ zenon_intro zenon_H1ca | zenon_intro zenon_H14d ]. % 18.68/18.88 apply (zenon_or_s _ _ zenon_H16f); [ zenon_intro zenon_H9e | zenon_intro zenon_H170 ]. % 18.68/18.88 apply (zenon_L37_); trivial. % 18.68/18.88 apply (zenon_or_s _ _ zenon_H170); [ zenon_intro zenon_H13f | zenon_intro zenon_H171 ]. % 18.68/18.88 apply (zenon_or_s _ _ zenon_H106); [ zenon_intro zenon_Hed | zenon_intro zenon_H107 ]. % 18.68/18.88 apply (zenon_L214_); trivial. % 18.68/18.88 apply (zenon_or_s _ _ zenon_H107); [ zenon_intro zenon_Ha5 | zenon_intro zenon_H108 ]. % 18.68/18.88 apply (zenon_L373_); trivial. % 18.68/18.88 apply (zenon_or_s _ _ zenon_H108); [ zenon_intro zenon_Hf1 | zenon_intro zenon_Hf4 ]. % 18.68/18.88 apply (zenon_or_s _ _ zenon_He7); [ zenon_intro zenon_H3b | zenon_intro zenon_He9 ]. % 18.68/18.88 apply (zenon_L457_); trivial. % 18.68/18.88 apply (zenon_or_s _ _ zenon_He9); [ zenon_intro zenon_Ha6 | zenon_intro zenon_Hea ]. % 18.68/18.88 apply (zenon_L207_); trivial. % 18.68/18.88 apply (zenon_or_s _ _ zenon_Hea); [ zenon_intro zenon_Haa | zenon_intro zenon_Hdd ]. % 18.68/18.88 apply (zenon_or_s _ _ zenon_H1ac); [ zenon_intro zenon_H44 | zenon_intro zenon_H1af ]. % 18.68/18.88 exact (zenon_H40 zenon_H44). % 18.68/18.88 apply (zenon_or_s _ _ zenon_H1af); [ zenon_intro zenon_H1b1 | zenon_intro zenon_H1b0 ]. % 18.68/18.88 exact (zenon_H1ad zenon_H1b1). % 18.68/18.88 apply (zenon_or_s _ _ zenon_H1b0); [ zenon_intro zenon_H61 | zenon_intro zenon_H60 ]. % 18.68/18.88 exact (zenon_H18b zenon_H61). % 18.68/18.88 apply (zenon_or_s _ _ zenon_He8); [ zenon_intro zenon_Hac | zenon_intro zenon_Heb ]. % 18.68/18.88 apply (zenon_L495_); trivial. % 18.68/18.88 apply (zenon_or_s _ _ zenon_Heb); [ zenon_intro zenon_Hae | zenon_intro zenon_Hec ]. % 18.68/18.88 apply (zenon_L368_); trivial. % 18.68/18.88 apply (zenon_or_s _ _ zenon_Hec); [ zenon_intro zenon_Hba | zenon_intro zenon_Hc4 ]. % 18.68/18.88 apply (zenon_L185_); trivial. % 18.68/18.88 apply (zenon_L455_); trivial. % 18.68/18.88 apply (zenon_L54_); trivial. % 18.68/18.88 apply (zenon_or_s _ _ zenon_H139); [ zenon_intro zenon_H122 | zenon_intro zenon_H13a ]. % 18.68/18.88 apply (zenon_L620_); trivial. % 18.68/18.88 apply (zenon_or_s _ _ zenon_H13a); [ zenon_intro zenon_Hf0 | zenon_intro zenon_H13b ]. % 18.68/18.88 apply (zenon_L68_); trivial. % 18.68/18.88 apply (zenon_or_s _ _ zenon_H13b); [ zenon_intro zenon_Hf1 | zenon_intro zenon_Hba ]. % 18.68/18.88 apply (zenon_L84_); trivial. % 18.68/18.88 apply (zenon_or_s _ _ zenon_He7); [ zenon_intro zenon_H3b | zenon_intro zenon_He9 ]. % 18.68/18.88 apply (zenon_L327_); trivial. % 18.68/18.88 apply (zenon_or_s _ _ zenon_He9); [ zenon_intro zenon_Ha6 | zenon_intro zenon_Hea ]. % 18.68/18.88 apply (zenon_L95_); trivial. % 18.68/18.88 apply (zenon_or_s _ _ zenon_Hea); [ zenon_intro zenon_Haa | zenon_intro zenon_Hdd ]. % 18.68/18.88 apply (zenon_or_s _ _ zenon_H153); [ zenon_intro zenon_H148 | zenon_intro zenon_H154 ]. % 18.68/18.88 apply (zenon_L325_); trivial. % 18.68/18.88 apply (zenon_or_s _ _ zenon_H154); [ zenon_intro zenon_H14d | zenon_intro zenon_H155 ]. % 18.68/18.88 apply (zenon_L451_); trivial. % 18.68/18.88 apply (zenon_or_s _ _ zenon_H155); [ zenon_intro zenon_H151 | zenon_intro zenon_Hf6 ]. % 18.68/18.88 apply (zenon_L453_); trivial. % 18.68/18.88 apply (zenon_or_s _ _ zenon_Hdf); [ zenon_intro zenon_H1f | zenon_intro zenon_He0 ]. % 18.68/18.88 exact (zenon_H38 zenon_H1f). % 18.68/18.88 apply (zenon_or_s _ _ zenon_He0); [ zenon_intro zenon_Hd6 | zenon_intro zenon_He1 ]. % 18.68/18.88 apply (zenon_L360_); trivial. % 18.68/18.88 apply (zenon_or_s _ _ zenon_He1); [ zenon_intro zenon_Hd7 | zenon_intro zenon_Hdc ]. % 18.68/18.88 apply (zenon_L621_); trivial. % 18.68/18.88 apply (zenon_L321_); trivial. % 18.68/18.88 apply (zenon_L54_); trivial. % 18.68/18.88 apply (zenon_or_s _ _ zenon_H171); [ zenon_intro zenon_H16c | zenon_intro zenon_Hdc ]. % 18.68/18.88 apply (zenon_L476_); trivial. % 18.68/18.88 apply (zenon_L117_); trivial. % 18.68/18.88 apply (zenon_or_s _ _ zenon_H16f); [ zenon_intro zenon_H9e | zenon_intro zenon_H170 ]. % 18.68/18.88 apply (zenon_L37_); trivial. % 18.68/18.88 apply (zenon_or_s _ _ zenon_H170); [ zenon_intro zenon_H13f | zenon_intro zenon_H171 ]. % 18.68/18.88 apply (zenon_L622_); trivial. % 18.68/18.88 apply (zenon_or_s _ _ zenon_H171); [ zenon_intro zenon_H16c | zenon_intro zenon_Hdc ]. % 18.68/18.88 apply (zenon_L116_); trivial. % 18.68/18.88 apply (zenon_L450_); trivial. % 18.68/18.88 apply (zenon_or_s _ _ zenon_H1d8); [ zenon_intro zenon_H10f | zenon_intro zenon_H1d9 ]. % 18.68/18.88 apply (zenon_L477_); trivial. % 18.68/18.88 apply (zenon_or_s _ _ zenon_H1d9); [ zenon_intro zenon_H110 | zenon_intro zenon_H1da ]. % 18.68/18.88 apply (zenon_L354_); trivial. % 18.68/18.88 apply (zenon_or_s _ _ zenon_H1da); [ zenon_intro zenon_H1ca | zenon_intro zenon_H14d ]. % 18.68/18.88 apply (zenon_or_s _ _ zenon_H16f); [ zenon_intro zenon_H9e | zenon_intro zenon_H170 ]. % 18.68/18.88 apply (zenon_L37_); trivial. % 18.68/18.88 apply (zenon_or_s _ _ zenon_H170); [ zenon_intro zenon_H13f | zenon_intro zenon_H171 ]. % 18.68/18.88 apply (zenon_or_s _ _ zenon_H106); [ zenon_intro zenon_Hed | zenon_intro zenon_H107 ]. % 18.68/18.88 apply (zenon_L413_); trivial. % 18.68/18.88 apply (zenon_or_s _ _ zenon_H107); [ zenon_intro zenon_Ha5 | zenon_intro zenon_H108 ]. % 18.68/18.88 apply (zenon_L391_); trivial. % 18.68/18.88 apply (zenon_or_s _ _ zenon_H108); [ zenon_intro zenon_Hf1 | zenon_intro zenon_Hf4 ]. % 18.68/18.88 apply (zenon_L460_); trivial. % 18.68/18.88 apply (zenon_or_s _ _ zenon_H172); [ zenon_intro zenon_H150 | zenon_intro zenon_H174 ]. % 18.68/18.88 apply (zenon_L378_); trivial. % 18.68/18.88 apply (zenon_or_s _ _ zenon_H174); [ zenon_intro zenon_H113 | zenon_intro zenon_H175 ]. % 18.68/18.88 apply (zenon_L621_); trivial. % 18.68/18.88 apply (zenon_or_s _ _ zenon_H175); [ zenon_intro zenon_H176 | zenon_intro zenon_H151 ]. % 18.68/18.88 exact (zenon_H173 zenon_H176). % 18.68/18.88 apply (zenon_L453_); trivial. % 18.68/18.88 apply (zenon_or_s _ _ zenon_H171); [ zenon_intro zenon_H16c | zenon_intro zenon_Hdc ]. % 18.68/18.88 apply (zenon_L476_); trivial. % 18.68/18.88 apply (zenon_L266_); trivial. % 18.68/18.88 apply (zenon_L462_); trivial. % 18.68/18.88 apply (zenon_or_s _ _ zenon_H28); [ zenon_intro zenon_H2a | zenon_intro zenon_H1f ]. % 18.68/18.88 exact (zenon_H25 zenon_H2a). % 18.68/18.88 exact (zenon_H38 zenon_H1f). % 18.68/18.88 apply (zenon_or_s _ _ zenon_H22f); [ zenon_intro zenon_H122 | zenon_intro zenon_Hc3 ]. % 18.68/18.88 apply (zenon_L355_); trivial. % 18.68/18.88 apply (zenon_L447_); trivial. % 18.68/18.88 exact (zenon_H76 zenon_H1e). % 18.68/18.88 apply (zenon_L623_); trivial. % 18.68/18.88 apply (zenon_or_s _ _ zenon_H1a7); [ zenon_intro zenon_H18b | zenon_intro zenon_H148 ]. % 18.68/18.88 apply (zenon_L353_); trivial. % 18.68/18.88 apply (zenon_L623_); trivial. % 18.68/18.88 apply (zenon_L127_); trivial. % 18.68/18.88 apply (zenon_or_s _ _ zenon_H184); [ zenon_intro zenon_H40 | zenon_intro zenon_H44 ]. % 18.68/18.88 apply (zenon_or_s _ _ zenon_H1ed); [ zenon_intro zenon_H1ad | zenon_intro zenon_Hac ]. % 18.68/18.88 apply (zenon_or_s _ _ zenon_H1a7); [ zenon_intro zenon_H18b | zenon_intro zenon_H148 ]. % 18.68/18.88 apply (zenon_L464_); trivial. % 18.68/18.88 apply (zenon_L624_); trivial. % 18.68/18.88 apply (zenon_L308_); trivial. % 18.68/18.88 apply (zenon_L127_); trivial. % 18.68/18.88 apply (zenon_L204_); trivial. % 18.68/18.88 apply (zenon_L214_); trivial. % 18.68/18.88 apply (zenon_L37_); trivial. % 18.68/18.88 (* end of lemma zenon_L625_ *) % 18.68/18.88 assert (zenon_L626_ : (((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 (e0) (e3)) = (e2))\/(((op (e1) (e3)) = (e2))\/(((op (e2) (e3)) = (e2))\/((op (e3) (e3)) = (e2))))) -> (~((op (e0) (e0)) = (op (e0) (e3)))) -> ((op (e0) (e0)) = (e2)) -> (~((op (e1) (e0)) = (op (e1) (e3)))) -> ((op (e1) (e0)) = (e2)) -> (~((op (e2) (e1)) = (op (e2) (e3)))) -> ((op (e2) (e1)) = (e2)) -> (~((op (e3) (e2)) = (op (e3) (e3)))) -> False). % 18.68/18.88 do 0 intro. intros zenon_H172 zenon_H149 zenon_H48 zenon_H7c zenon_Hf0 zenon_H173 zenon_H145 zenon_H189 zenon_H7b zenon_Hd8 zenon_H86 zenon_H1c7 zenon_H1ca zenon_H62. % 18.68/18.88 apply (zenon_or_s _ _ zenon_H172); [ zenon_intro zenon_H150 | zenon_intro zenon_H174 ]. % 18.68/18.88 apply (zenon_L378_); trivial. % 18.68/18.88 apply (zenon_or_s _ _ zenon_H174); [ zenon_intro zenon_H113 | zenon_intro zenon_H175 ]. % 18.68/18.88 apply (zenon_L68_); trivial. % 18.68/18.88 apply (zenon_or_s _ _ zenon_H175); [ zenon_intro zenon_H176 | zenon_intro zenon_H151 ]. % 18.68/18.88 exact (zenon_H173 zenon_H176). % 18.68/18.88 apply (zenon_L540_); trivial. % 18.68/18.88 (* end of lemma zenon_L626_ *) % 18.68/18.88 assert (zenon_L627_ : (((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 (e0) (e1)) = (e1)) -> (~((op (e3) (e2)) = (op (e3) (e3)))) -> ((op (e1) (e0)) = (e2)) -> (~((op (e1) (e0)) = (op (e1) (e3)))) -> ((op (e0) (e0)) = (e2)) -> (~((op (e0) (e0)) = (op (e0) (e3)))) -> (((op (e0) (e3)) = (e2))\/(((op (e1) (e3)) = (e2))\/(((op (e2) (e3)) = (e2))\/((op (e3) (e3)) = (e2))))) -> ((op (e1) (e2)) = (e1)) -> (~((e1) = (e2))) -> ((op (e0) (e2)) = (e0)) -> (~((e0) = (e2))) -> (((op (e0) (e2)) = (e2))\/(((op (e1) (e2)) = (e2))\/(((op (e2) (e2)) = (e2))\/((op (e3) (e2)) = (e2))))) -> (~((op (e2) (e2)) = (e2))) -> (((op (e2) (e1)) = (e0))\/(((op (e2) (e1)) = (e1))\/(((op (e2) (e1)) = (e2))\/((op (e2) (e1)) = (e3))))) -> (~((op (e2) (e1)) = (e0))) -> ((op (e2) (e3)) = (e1)) -> (~((op (e2) (e1)) = (op (e2) (e3)))) -> ((op (e3) (e1)) = (e0)) -> ((op (e1) (e1)) = (e2)) -> False). % 18.68/18.88 do 0 intro. intros zenon_H1d5 zenon_H1f0 zenon_H17e zenon_Ha0 zenon_H62 zenon_H86 zenon_Hd8 zenon_H7b zenon_H189 zenon_H145 zenon_Hf0 zenon_H7c zenon_H48 zenon_H149 zenon_H172 zenon_H173 zenon_H1cc zenon_H31 zenon_Hf4 zenon_H1c7 zenon_H1b1 zenon_H110. % 18.68/18.88 apply (zenon_or_s _ _ zenon_H1d5); [ zenon_intro zenon_Hee | zenon_intro zenon_H1d6 ]. % 18.68/18.88 apply (zenon_L569_); trivial. % 18.68/18.88 apply (zenon_or_s _ _ zenon_H1d6); [ zenon_intro zenon_H1ca | zenon_intro zenon_H1d7 ]. % 18.68/18.88 apply (zenon_L626_); trivial. % 18.68/18.88 apply (zenon_or_s _ _ zenon_H1d7); [ zenon_intro zenon_H176 | zenon_intro zenon_H11d ]. % 18.68/18.88 exact (zenon_H173 zenon_H176). % 18.68/18.88 apply (zenon_L510_); trivial. % 18.68/18.88 (* end of lemma zenon_L627_ *) % 18.68/18.88 assert (zenon_L628_ : (((op (e1) (e0)) = (e3))\/(((op (e1) (e1)) = (e3))\/(((op (e1) (e2)) = (e3))\/((op (e1) (e3)) = (e3))))) -> ((op (e0) (e0)) = (e2)) -> ((op (e2) (e0)) = (e1)) -> (~((e2) = (e3))) -> ((op (e1) (e1)) = (e2)) -> (~((e1) = (e3))) -> ((op (e1) (e2)) = (e1)) -> (~((op (e0) (e3)) = (op (e1) (e3)))) -> ((op (e0) (e3)) = (e3)) -> False). % 18.68/18.88 do 0 intro. intros zenon_H16f zenon_H7b zenon_Hed zenon_H12b zenon_H110 zenon_H95 zenon_Hf0 zenon_H1d zenon_He3. % 18.68/18.88 apply (zenon_or_s _ _ zenon_H16f); [ zenon_intro zenon_H9e | zenon_intro zenon_H170 ]. % 18.68/18.88 apply (zenon_L491_); trivial. % 18.68/18.88 apply (zenon_or_s _ _ zenon_H170); [ zenon_intro zenon_H13f | zenon_intro zenon_H171 ]. % 18.68/18.88 apply (zenon_L166_); trivial. % 18.68/18.88 apply (zenon_or_s _ _ zenon_H171); [ zenon_intro zenon_H16c | zenon_intro zenon_Hdc ]. % 18.68/18.88 apply (zenon_L167_); trivial. % 18.68/18.88 apply (zenon_L117_); trivial. % 18.68/18.88 (* end of lemma zenon_L628_ *) % 18.68/18.88 assert (zenon_L629_ : (((op (e0) (e1)) = (e2))\/(((op (e1) (e1)) = (e2))\/(((op (e2) (e1)) = (e2))\/((op (e3) (e1)) = (e2))))) -> (~((op (e0) (e3)) = (op (e2) (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)) = (op (e3) (e3)))) -> (~((op (e2) (e3)) = (op (e3) (e3)))) -> (~((op (e3) (e3)) = (e3))) -> ((op (e1) (e3)) = (e0)) -> (((op (e0) (e3)) = (e0))\/(((op (e0) (e3)) = (e1))\/(((op (e0) (e3)) = (e2))\/((op (e0) (e3)) = (e3))))) -> (((op (e1) (e1)) = (e0))\/(((op (e1) (e1)) = (e1))\/(((op (e1) (e1)) = (e2))\/((op (e1) (e1)) = (e3))))) -> (~((op (e1) (e1)) = (e0))) -> (~((op (e1) (e1)) = (e1))) -> (((op (e3) (e0)) = (e3))\/(((op (e3) (e1)) = (e3))\/(((op (e3) (e2)) = (e3))\/((op (e3) (e3)) = (e3))))) -> ((op (e3) (e0)) = (e1)) -> (~((op (e1) (e1)) = (op (e3) (e1)))) -> (~((op (e2) (e2)) = (op (e3) (e2)))) -> (~((op (e0) (e1)) = (op (e1) (e1)))) -> (~((op (e1) (e1)) = (op (e2) (e1)))) -> (((op (e0) (e2)) = (e1))\/(((op (e1) (e2)) = (e1))\/(((op (e2) (e2)) = (e1))\/((op (e3) (e2)) = (e1))))) -> (~((op (e0) (e1)) = (op (e0) (e2)))) -> (~((op (e1) (e2)) = (op (e3) (e2)))) -> (~((op (e0) (e1)) = (op (e3) (e1)))) -> (((op (e3) (e0)) = (e1))\/(((op (e3) (e1)) = (e1))\/(((op (e3) (e2)) = (e1))\/((op (e3) (e3)) = (e1))))) -> (~((op (e2) (e2)) = (op (e2) (e3)))) -> (((op (e2) (e2)) = (e0))\/(((op (e2) (e2)) = (e1))\/(((op (e2) (e2)) = (e2))\/((op (e2) (e2)) = (e3))))) -> (~((op (e2) (e2)) = (e0))) -> (~((op (e2) (e0)) = (op (e2) (e2)))) -> (((op (e2) (e0)) = (e3))\/(((op (e2) (e1)) = (e3))\/(((op (e2) (e2)) = (e3))\/((op (e2) (e3)) = (e3))))) -> (~((op (e0) (e0)) = (op (e2) (e0)))) -> ((op (e2) (e0)) = (e0)) -> (~((e0) = (e1))) -> ((op (e3) (e1)) = (e0)) -> (~((op (e2) (e1)) = (e0))) -> (((op (e2) (e1)) = (e0))\/(((op (e2) (e1)) = (e1))\/(((op (e2) (e1)) = (e2))\/((op (e2) (e1)) = (e3))))) -> ((op (e0) (e1)) = (e1)) -> (~((op (e0) (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 (e1) (e2)) = (op (e2) (e2)))) -> (((op (e1) (e0)) = (e3))\/(((op (e1) (e1)) = (e3))\/(((op (e1) (e2)) = (e3))\/((op (e1) (e3)) = (e3))))) -> (~((e2) = (e3))) -> (~((e1) = (e3))) -> (~((op (e0) (e3)) = (op (e1) (e3)))) -> ((op (e0) (e3)) = (e3)) -> (((op (e2) (e0)) = (e1))\/(((op (e2) (e1)) = (e1))\/(((op (e2) (e2)) = (e1))\/((op (e2) (e3)) = (e1))))) -> (~((op (e3) (e2)) = (op (e3) (e3)))) -> (~((op (e2) (e1)) = (op (e2) (e3)))) -> ((op (e1) (e0)) = (e2)) -> (~((op (e1) (e0)) = (op (e1) (e3)))) -> ((op (e0) (e0)) = (e2)) -> (~((op (e0) (e0)) = (op (e0) (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))))) -> (~((e0) = (e2))) -> ((op (e0) (e2)) = (e0)) -> (~((e1) = (e2))) -> ((op (e1) (e2)) = (e1)) -> (~((op (e2) (e2)) = (e2))) -> (~((op (e3) (e1)) = (op (e3) (e2)))) -> False). % 18.68/18.89 do 0 intro. intros zenon_H1d8 zenon_He2 zenon_H101 zenon_H130 zenon_Hc2 zenon_Hf3 zenon_H102 zenon_H1f zenon_He4 zenon_H142 zenon_H24 zenon_H10a zenon_H165 zenon_Hac zenon_H160 zenon_H18f zenon_H10e zenon_H13e zenon_H139 zenon_H4a zenon_H115 zenon_H210 zenon_He8 zenon_H6d zenon_H1c4 zenon_H81 zenon_H52 zenon_He7 zenon_H39 zenon_H34 zenon_Ha1 zenon_H1b1 zenon_H31 zenon_H1cc zenon_Ha0 zenon_H17e zenon_H1f0 zenon_H1d5 zenon_H2b zenon_H16f zenon_H12b zenon_H95 zenon_H1d zenon_He3 zenon_H106 zenon_H62 zenon_H1c7 zenon_H86 zenon_Hd8 zenon_H7b zenon_H189 zenon_H145 zenon_H172 zenon_H149 zenon_H48 zenon_H7c zenon_Hf0 zenon_H173 zenon_H1a4. % 18.68/18.89 apply (zenon_or_s _ _ zenon_H1d8); [ zenon_intro zenon_H10f | zenon_intro zenon_H1d9 ]. % 18.68/18.89 apply (zenon_or_s _ _ zenon_H106); [ zenon_intro zenon_Hed | zenon_intro zenon_H107 ]. % 18.68/18.89 apply (zenon_L214_); trivial. % 18.68/18.89 apply (zenon_or_s _ _ zenon_H107); [ zenon_intro zenon_Ha5 | zenon_intro zenon_H108 ]. % 18.68/18.89 apply (zenon_L357_); trivial. % 18.68/18.89 apply (zenon_or_s _ _ zenon_H108); [ zenon_intro zenon_Hf1 | zenon_intro zenon_Hf4 ]. % 18.68/18.89 apply (zenon_L59_); trivial. % 18.68/18.89 apply (zenon_or_s _ _ zenon_H1d5); [ zenon_intro zenon_Hee | zenon_intro zenon_H1d6 ]. % 18.68/18.89 apply (zenon_L341_); trivial. % 18.68/18.89 apply (zenon_or_s _ _ zenon_H1d6); [ zenon_intro zenon_H1ca | zenon_intro zenon_H1d7 ]. % 18.68/18.89 apply (zenon_L626_); trivial. % 18.68/18.89 apply (zenon_or_s _ _ zenon_H1d7); [ zenon_intro zenon_H176 | zenon_intro zenon_H11d ]. % 18.68/18.89 exact (zenon_H173 zenon_H176). % 18.68/18.89 apply (zenon_or_s _ _ zenon_He7); [ zenon_intro zenon_H3b | zenon_intro zenon_He9 ]. % 18.68/18.89 apply (zenon_L408_); trivial. % 18.68/18.89 apply (zenon_or_s _ _ zenon_He9); [ zenon_intro zenon_Ha6 | zenon_intro zenon_Hea ]. % 18.68/18.89 apply (zenon_L96_); trivial. % 18.68/18.89 apply (zenon_or_s _ _ zenon_Hea); [ zenon_intro zenon_Haa | zenon_intro zenon_Hdd ]. % 18.68/18.89 apply (zenon_or_s _ _ zenon_H142); [ zenon_intro zenon_H29 | zenon_intro zenon_H143 ]. % 18.68/18.89 exact (zenon_H24 zenon_H29). % 18.68/18.89 apply (zenon_or_s _ _ zenon_H143); [ zenon_intro zenon_H10d | zenon_intro zenon_H144 ]. % 18.68/18.89 exact (zenon_H10a zenon_H10d). % 18.68/18.89 apply (zenon_or_s _ _ zenon_H144); [ zenon_intro zenon_H110 | zenon_intro zenon_H13f ]. % 18.68/18.89 apply (zenon_L627_); trivial. % 18.68/18.89 apply (zenon_L495_); trivial. % 18.68/18.89 apply (zenon_L573_); trivial. % 18.68/18.89 apply (zenon_or_s _ _ zenon_H1d9); [ zenon_intro zenon_H110 | zenon_intro zenon_H1da ]. % 18.68/18.89 apply (zenon_or_s _ _ zenon_H106); [ zenon_intro zenon_Hed | zenon_intro zenon_H107 ]. % 18.68/18.89 apply (zenon_L628_); trivial. % 18.68/18.89 apply (zenon_or_s _ _ zenon_H107); [ zenon_intro zenon_Ha5 | zenon_intro zenon_H108 ]. % 18.68/18.89 apply (zenon_L357_); trivial. % 18.68/18.89 apply (zenon_or_s _ _ zenon_H108); [ zenon_intro zenon_Hf1 | zenon_intro zenon_Hf4 ]. % 18.68/18.89 apply (zenon_L59_); trivial. % 18.68/18.89 apply (zenon_L627_); trivial. % 18.68/18.89 apply (zenon_or_s _ _ zenon_H1da); [ zenon_intro zenon_H1ca | zenon_intro zenon_H14d ]. % 18.68/18.89 apply (zenon_L626_); trivial. % 18.68/18.89 apply (zenon_or_s _ _ zenon_H172); [ zenon_intro zenon_H150 | zenon_intro zenon_H174 ]. % 18.68/18.89 apply (zenon_L378_); trivial. % 18.68/18.89 apply (zenon_or_s _ _ zenon_H174); [ zenon_intro zenon_H113 | zenon_intro zenon_H175 ]. % 18.68/18.89 apply (zenon_L68_); trivial. % 18.68/18.89 apply (zenon_or_s _ _ zenon_H175); [ zenon_intro zenon_H176 | zenon_intro zenon_H151 ]. % 18.68/18.89 exact (zenon_H173 zenon_H176). % 18.68/18.89 apply (zenon_L400_); trivial. % 18.68/18.89 (* end of lemma zenon_L629_ *) % 18.68/18.89 assert (zenon_L630_ : ((op (e0) (e3)) = (e3)) -> (~((op (e1) (e3)) = (op (e2) (e3)))) -> ((~((op (e0) (e2)) = (e0)))\/((op (e0) (e0)) = (e2))) -> ((~((op (e1) (e0)) = (e0)))\/((op (e1) (e0)) = (e0))) -> (~((op (e1) (e0)) = (op (e2) (e0)))) -> (~((op (e2) (e0)) = (op (e2) (e1)))) -> (~((op (e1) (e0)) = (op (e3) (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)) = (op (e3) (e2)))) -> (~((op (e2) (e2)) = (op (e2) (e3)))) -> (~((op (e3) (e0)) = (op (e3) (e3)))) -> (~((op (e0) (e1)) = (op (e0) (e2)))) -> (~((op (e1) (e1)) = (op (e1) (e2)))) -> (~((op (e2) (e0)) = (op (e2) (e2)))) -> (~((op (e3) (e2)) = (op (e3) (e3)))) -> (~((op (e1) (e1)) = (op (e1) (e3)))) -> (~((op (e0) (e1)) = (op (e0) (e3)))) -> (((op (e0) (e2)) = (e0))\/(((op (e1) (e2)) = (e0))\/(((op (e2) (e2)) = (e0))\/((op (e3) (e2)) = (e0))))) -> (~((op (e1) (e0)) = (op (e1) (e1)))) -> (((op (e1) (e0)) = (e0))\/(((op (e1) (e1)) = (e0))\/(((op (e1) (e2)) = (e0))\/((op (e1) (e3)) = (e0))))) -> (~((op (e0) (e0)) = (e0))) -> ((~((op (e3) (e1)) = (e0)))\/((op (e3) (e0)) = (e1))) -> ((~((op (e3) (e3)) = (e0)))\/((op (e3) (e0)) = (e3))) -> (((op (e0) (e1)) = (e2))\/(((op (e1) (e1)) = (e2))\/(((op (e2) (e1)) = (e2))\/((op (e3) (e1)) = (e2))))) -> (~((op (e3) (e0)) = (op (e3) (e1)))) -> (((op (e0) (e2)) = (e0))\/(((op (e0) (e2)) = (e1))\/(((op (e0) (e2)) = (e2))\/((op (e0) (e2)) = (e3))))) -> (((op (e2) (e2)) = (e0))\/(((op (e2) (e2)) = (e1))\/(((op (e2) (e2)) = (e2))\/((op (e2) (e2)) = (e3))))) -> (((op (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 (e2) (e0)) = (e0)))\/((op (e2) (e0)) = (e0))) -> (((op (e0) (e0)) = (e2))\/(((op (e1) (e0)) = (e2))\/(((op (e2) (e0)) = (e2))\/((op (e3) (e0)) = (e2))))) -> ((~((op (e2) (e1)) = (e0)))\/((op (e2) (e0)) = (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)) = (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)) = (e2))\/(((op (e1) (e2)) = (e2))\/(((op (e2) (e2)) = (e2))\/((op (e3) (e2)) = (e2))))) -> (~((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)) = (e1))\/(((op (e1) (e2)) = (e1))\/(((op (e2) (e2)) = (e1))\/((op (e3) (e2)) = (e1))))) -> (~((op (e0) (e0)) = (op (e0) (e2)))) -> ((~((op (e1) (e3)) = (e0)))\/((op (e1) (e0)) = (e3))) -> ((~((op (e1) (e2)) = (e0)))\/((op (e1) (e0)) = (e2))) -> (~((op (e2) (e0)) = (op (e3) (e0)))) -> (((op (e0) (e0)) = (e2))\/(((op (e0) (e1)) = (e2))\/(((op (e0) (e2)) = (e2))\/((op (e0) (e3)) = (e2))))) -> ((~((op (e3) (e0)) = (e0)))\/((op (e3) (e0)) = (e0))) -> ((~((op (e2) (e2)) = (e0)))\/((op (e2) (e0)) = (e2))) -> (((op (e0) (e1)) = (e1))\/(((op (e1) (e1)) = (e1))\/(((op (e2) (e1)) = (e1))\/((op (e3) (e1)) = (e1))))) -> (((op (e2) (e0)) = (e1))\/(((op (e2) (e1)) = (e1))\/(((op (e2) (e2)) = (e1))\/((op (e2) (e3)) = (e1))))) -> (~((op (e1) (e0)) = (op (e1) (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)) = (op (e2) (e2)))) -> (~((e0) = (e1))) -> (~((op (e0) (e1)) = (op (e1) (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)) = (e0))\/(((op (e1) (e2)) = (e1))\/(((op (e1) (e2)) = (e2))\/((op (e1) (e2)) = (e3))))) -> (~((op (e0) (e2)) = (op (e1) (e2)))) -> (((op (e3) (e2)) = (e0))\/(((op (e3) (e2)) = (e1))\/(((op (e3) (e2)) = (e2))\/((op (e3) (e2)) = (e3))))) -> ((~((op (e3) (e2)) = (e0)))\/((op (e3) (e0)) = (e2))) -> (~((op (e3) (e1)) = (op (e3) (e2)))) -> (((op (e0) (e2)) = (e3))\/(((op (e1) (e2)) = (e3))\/(((op (e2) (e2)) = (e3))\/((op (e3) (e2)) = (e3))))) -> (((op (e2) (e0)) = (e0))\/(((op (e2) (e1)) = (e0))\/(((op (e2) (e2)) = (e0))\/((op (e2) (e3)) = (e0))))) -> ((~((op (e2) (e3)) = (e0)))\/((op (e2) (e0)) = (e3))) -> ((~((op (e1) (e1)) = (e0)))\/((op (e1) (e0)) = (e1))) -> ((~((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 (e0) (e0)) = (op (e0) (e3)))) -> (~((op (e1) (e3)) = (op (e3) (e3)))) -> (~((op (e1) (e2)) = (op (e2) (e2)))) -> ((op (e1) (e0)) = (e3)) -> (((op (e1) (e0)) = (e1))\/(((op (e1) (e1)) = (e1))\/(((op (e1) (e2)) = (e1))\/((op (e1) (e3)) = (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 (e3) (e0)) = (e1)) -> (~((op (e2) (e2)) = (op (e3) (e2)))) -> (((op (e2) (e0)) = (e3))\/(((op (e2) (e1)) = (e3))\/(((op (e2) (e2)) = (e3))\/((op (e2) (e3)) = (e3))))) -> (~((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)) = (e2)) -> (~((op (e0) (e0)) = (op (e2) (e0)))) -> (~((op (e2) (e1)) = (op (e3) (e1)))) -> (~((op (e2) (e2)) = (e2))) -> (((op (e0) (e3)) = (e3))\/(((op (e1) (e3)) = (e3))\/(((op (e2) (e3)) = (e3))\/((op (e3) (e3)) = (e3))))) -> (~((op (e1) (e1)) = (op (e3) (e1)))) -> (((op (e2) (e1)) = (e0))\/(((op (e2) (e1)) = (e1))\/(((op (e2) (e1)) = (e2))\/((op (e2) (e1)) = (e3))))) -> (~((op (e2) (e1)) = (e0))) -> ((op (e0) (e1)) = (e1)) -> (~((op (e0) (e1)) = (op (e2) (e1)))) -> ((op (e2) (e0)) = (e0)) -> (~((op (e2) (e0)) = (op (e2) (e3)))) -> (((op (e0) (e3)) = (e2))\/(((op (e1) (e3)) = (e2))\/(((op (e2) (e3)) = (e2))\/((op (e3) (e3)) = (e2))))) -> (~((e2) = (e3))) -> (~((e1) = (e2))) -> (~((op (e2) (e1)) = (op (e2) (e3)))) -> (((op (e2) (e3)) = (e0))\/(((op (e2) (e3)) = (e1))\/(((op (e2) (e3)) = (e2))\/((op (e2) (e3)) = (e3))))) -> (~((e0) = (e3))) -> (((op (e0) (e3)) = (e0))\/(((op (e1) (e3)) = (e0))\/(((op (e2) (e3)) = (e0))\/((op (e3) (e3)) = (e0))))) -> (~((op (e1) (e1)) = (e1))) -> (~((op (e1) (e1)) = (e0))) -> (((op (e1) (e1)) = (e0))\/(((op (e1) (e1)) = (e1))\/(((op (e1) (e1)) = (e2))\/((op (e1) (e1)) = (e3))))) -> (~((e1) = (e3))) -> ((op (e1) (e3)) = (e1)) -> (~((op (e0) (e3)) = (op (e2) (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) (e1)) = (e0)) -> (~((op (e0) (e3)) = (op (e3) (e3)))) -> (~((op (e2) (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 (e3) (e3)) = (e3))) -> False). % 18.68/18.89 do 0 intro. intros zenon_He3 zenon_Hdb zenon_H233 zenon_H206 zenon_H201 zenon_H1f0 zenon_H1fa zenon_H74 zenon_H3e zenon_H6f zenon_H6d zenon_H71 zenon_H4a zenon_H4f zenon_H52 zenon_H62 zenon_H57 zenon_H54 zenon_H6a zenon_H45 zenon_H22 zenon_H3f zenon_H1ed zenon_H1ec zenon_H1d8 zenon_H1cf zenon_H1ba zenon_H1c4 zenon_H1ac zenon_H1e0 zenon_H1ee zenon_H1fe zenon_H182 zenon_H153 zenon_H14f zenon_H168 zenon_H16f zenon_H172 zenon_H124 zenon_H133 zenon_H139 zenon_H13c zenon_H179 zenon_H178 zenon_H17b zenon_H183 zenon_H184 zenon_H185 zenon_H109 zenon_H106 zenon_Hd8 zenon_Hdf zenon_He8 zenon_Ha8 zenon_Ha1 zenon_H10e zenon_H115 zenon_H18c zenon_H19d zenon_H195 zenon_H191 zenon_H1a7 zenon_H1a4 zenon_H1a6 zenon_H2f zenon_H94 zenon_H205 zenon_H204 zenon_H235 zenon_H189 zenon_Hd5 zenon_H2b zenon_H9e zenon_H128 zenon_H1a5 zenon_H165 zenon_Hac zenon_H18f zenon_He7 zenon_H149 zenon_H13e zenon_H1d5 zenon_H7b zenon_H39 zenon_Haf zenon_H173 zenon_H136 zenon_H160 zenon_H1cc zenon_H31 zenon_Ha0 zenon_H17e zenon_H34 zenon_H5b zenon_H145 zenon_H12b zenon_H7c zenon_H1c7 zenon_H11f zenon_H9a zenon_H67 zenon_H10a zenon_H24 zenon_H142 zenon_H95 zenon_Hd6 zenon_He2 zenon_H101 zenon_H130 zenon_H1b1 zenon_Hc2 zenon_Hf3 zenon_H1d zenon_H1f zenon_He4 zenon_H102. % 18.68/18.89 apply (zenon_or_s _ _ zenon_H1d8); [ zenon_intro zenon_H10f | zenon_intro zenon_H1d9 ]. % 18.68/18.89 apply (zenon_L588_); trivial. % 18.68/18.89 apply (zenon_or_s _ _ zenon_H1d9); [ zenon_intro zenon_H110 | zenon_intro zenon_H1da ]. % 18.68/18.89 apply (zenon_L572_); trivial. % 18.68/18.89 apply (zenon_or_s _ _ zenon_H1da); [ zenon_intro zenon_H1ca | zenon_intro zenon_H14d ]. % 18.68/18.89 apply (zenon_L582_); trivial. % 18.68/18.89 apply (zenon_L583_); trivial. % 18.68/18.89 (* end of lemma zenon_L630_ *) % 18.68/18.89 assert (zenon_L631_ : (~((op (e0) (e2)) = (op (e0) (e3)))) -> (((op (e2) (e0)) = (e0))\/(((op (e2) (e1)) = (e0))\/(((op (e2) (e2)) = (e0))\/((op (e2) (e3)) = (e0))))) -> (~((op (e0) (e3)) = (e0))) -> ((~((op (e0) (e2)) = (e0)))\/((op (e0) (e0)) = (e2))) -> ((~((op (e1) (e0)) = (e0)))\/((op (e1) (e0)) = (e0))) -> (~((op (e1) (e0)) = (op (e2) (e0)))) -> (~((op (e2) (e0)) = (op (e2) (e1)))) -> (~((op (e1) (e0)) = (op (e3) (e0)))) -> (((op (e0) (e0)) = (e0))\/(((op (e0) (e1)) = (e0))\/(((op (e0) (e2)) = (e0))\/((op (e0) (e3)) = (e0))))) -> (~((op (e3) (e0)) = (op (e3) (e2)))) -> (~((op (e2) (e2)) = (op (e2) (e3)))) -> (~((op (e3) (e0)) = (op (e3) (e3)))) -> (~((op (e0) (e1)) = (op (e0) (e2)))) -> (~((op (e1) (e1)) = (op (e1) (e2)))) -> (~((op (e2) (e0)) = (op (e2) (e2)))) -> (((op (e0) (e3)) = (e0))\/(((op (e1) (e3)) = (e0))\/(((op (e2) (e3)) = (e0))\/((op (e3) (e3)) = (e0))))) -> (~((op (e3) (e2)) = (op (e3) (e3)))) -> (~((op (e2) (e0)) = (op (e2) (e3)))) -> (~((op (e1) (e1)) = (op (e1) (e3)))) -> (~((op (e0) (e1)) = (op (e0) (e3)))) -> (((op (e0) (e2)) = (e0))\/(((op (e1) (e2)) = (e0))\/(((op (e2) (e2)) = (e0))\/((op (e3) (e2)) = (e0))))) -> (~((op (e1) (e0)) = (op (e1) (e1)))) -> (((op (e1) (e0)) = (e0))\/(((op (e1) (e1)) = (e0))\/(((op (e1) (e2)) = (e0))\/((op (e1) (e3)) = (e0))))) -> ((~((op (e3) (e1)) = (e0)))\/((op (e3) (e0)) = (e1))) -> ((~((op (e3) (e3)) = (e0)))\/((op (e3) (e0)) = (e3))) -> (((op (e2) (e0)) = (e2))\/(((op (e2) (e1)) = (e2))\/(((op (e2) (e2)) = (e2))\/((op (e2) (e3)) = (e2))))) -> (((op (e0) (e1)) = (e2))\/(((op (e1) (e1)) = (e2))\/(((op (e2) (e1)) = (e2))\/((op (e3) (e1)) = (e2))))) -> (~((op (e3) (e0)) = (op (e3) (e1)))) -> (((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 (e2) (e2)) = (e0))\/(((op (e2) (e2)) = (e1))\/(((op (e2) (e2)) = (e2))\/((op (e2) (e2)) = (e3))))) -> (~((op (e2) (e1)) = (op (e2) (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 (e2) (e0)) = (e0)))\/((op (e2) (e0)) = (e0))) -> (((op (e0) (e0)) = (e2))\/(((op (e1) (e0)) = (e2))\/(((op (e2) (e0)) = (e2))\/((op (e3) (e0)) = (e2))))) -> ((~((op (e2) (e1)) = (e0)))\/((op (e2) (e0)) = (e1))) -> (~((op (e0) (e0)) = (op (e2) (e0)))) -> (((op (e3) (e0)) = (e2))\/(((op (e3) (e1)) = (e2))\/(((op (e3) (e2)) = (e2))\/((op (e3) (e3)) = (e2))))) -> (~((op (e0) (e2)) = (op (e3) (e2)))) -> (~((e0) = (e2))) -> (((op (e3) (e0)) = (e3))\/(((op (e3) (e1)) = (e3))\/(((op (e3) (e2)) = (e3))\/((op (e3) (e3)) = (e3))))) -> (~((op (e1) (e1)) = (op (e3) (e1)))) -> (((op (e0) (e0)) = (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)) = (e2))) -> (((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) (e2)) = (op (e1) (e3)))) -> (~((e2) = (e3))) -> (((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)) = (e3))\/(((op (e1) (e3)) = (e3))\/(((op (e2) (e3)) = (e3))\/((op (e3) (e3)) = (e3))))) -> (((op (e1) (e0)) = (e1))\/(((op (e1) (e1)) = (e1))\/(((op (e1) (e2)) = (e1))\/((op (e1) (e3)) = (e1))))) -> (((op (e0) (e2)) = (e1))\/(((op (e1) (e2)) = (e1))\/(((op (e2) (e2)) = (e1))\/((op (e3) (e2)) = (e1))))) -> (~((op (e0) (e0)) = (op (e0) (e2)))) -> (~((op (e1) (e1)) = (op (e2) (e1)))) -> (((op (e1) (e1)) = (e0))\/(((op (e1) (e1)) = (e1))\/(((op (e1) (e1)) = (e2))\/((op (e1) (e1)) = (e3))))) -> ((~((op (e1) (e3)) = (e0)))\/((op (e1) (e0)) = (e3))) -> ((~((op (e1) (e2)) = (e0)))\/((op (e1) (e0)) = (e2))) -> (~((op (e0) (e1)) = (op (e2) (e1)))) -> (~((op (e2) (e0)) = (op (e3) (e0)))) -> (((op (e0) (e0)) = (e2))\/(((op (e0) (e1)) = (e2))\/(((op (e0) (e2)) = (e2))\/((op (e0) (e3)) = (e2))))) -> ((~((op (e3) (e0)) = (e0)))\/((op (e3) (e0)) = (e0))) -> ((~((op (e2) (e2)) = (e0)))\/((op (e2) (e0)) = (e2))) -> (~((op (e0) (e0)) = (op (e0) (e3)))) -> (((op (e0) (e1)) = (e1))\/(((op (e1) (e1)) = (e1))\/(((op (e2) (e1)) = (e1))\/((op (e3) (e1)) = (e1))))) -> (~((op (e1) (e2)) = (op (e2) (e2)))) -> (((op (e3) (e3)) = (e0))\/(((op (e3) (e3)) = (e1))\/(((op (e3) (e3)) = (e2))\/((op (e3) (e3)) = (e3))))) -> (~((op (e3) (e3)) = (e3))) -> (~((op (e2) (e3)) = (op (e3) (e3)))) -> (((op (e2) (e0)) = (e1))\/(((op (e2) (e1)) = (e1))\/(((op (e2) (e2)) = (e1))\/((op (e2) (e3)) = (e1))))) -> (((op (e2) (e0)) = (e3))\/(((op (e2) (e1)) = (e3))\/(((op (e2) (e2)) = (e3))\/((op (e2) (e3)) = (e3))))) -> (~((op (e2) (e1)) = (op (e3) (e1)))) -> (((op (e0) (e3)) = (e0))\/(((op (e0) (e3)) = (e1))\/(((op (e0) (e3)) = (e2))\/((op (e0) (e3)) = (e3))))) -> (~((op (e0) (e3)) = (op (e2) (e3)))) -> (~((op (e1) (e3)) = (op (e3) (e3)))) -> (~((op (e1) (e0)) = (op (e1) (e3)))) -> (~((op (e1) (e3)) = (op (e2) (e3)))) -> (((op (e1) (e3)) = (e0))\/(((op (e1) (e3)) = (e1))\/(((op (e1) (e3)) = (e2))\/((op (e1) (e3)) = (e3))))) -> (~((op (e0) (e3)) = (op (e3) (e3)))) -> (((op (e3) (e0)) = (e1))\/(((op (e3) (e1)) = (e1))\/(((op (e3) (e2)) = (e1))\/((op (e3) (e3)) = (e1))))) -> (~((op (e0) (e2)) = (op (e2) (e2)))) -> (~((e0) = (e1))) -> (~((op (e0) (e1)) = (op (e1) (e1)))) -> (~((op (e0) (e3)) = (op (e1) (e3)))) -> (((op (e2) (e3)) = (e0))\/(((op (e2) (e3)) = (e1))\/(((op (e2) (e3)) = (e2))\/((op (e2) (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) (e1)) = (e1))) -> (~((e0) = (e3))) -> (~((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 (e3) (e2)) = (e0))\/(((op (e3) (e2)) = (e1))\/(((op (e3) (e2)) = (e2))\/((op (e3) (e2)) = (e3))))) -> (~((op (e2) (e2)) = (op (e3) (e2)))) -> ((~((op (e3) (e2)) = (e0)))\/((op (e3) (e0)) = (e2))) -> (~((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)) = (e3))\/(((op (e1) (e1)) = (e3))\/(((op (e2) (e1)) = (e3))\/((op (e3) (e1)) = (e3))))) -> ((~((op (e2) (e3)) = (e0)))\/((op (e2) (e0)) = (e3))) -> (~((e1) = (e2))) -> ((~((op (e1) (e1)) = (e0)))\/((op (e1) (e0)) = (e1))) -> ((~((op (e0) (e3)) = (e0)))\/((op (e0) (e0)) = (e3))) -> ((op (e1) (e0)) = (e1)) -> (((op (e0) (e1)) = (e0))\/(((op (e0) (e1)) = (e1))\/(((op (e0) (e1)) = (e2))\/((op (e0) (e1)) = (e3))))) -> (((op (e3) (e1)) = (e0))\/(((op (e3) (e1)) = (e1))\/(((op (e3) (e1)) = (e2))\/((op (e3) (e1)) = (e3))))) -> (~((op (e0) (e1)) = (op (e3) (e1)))) -> ((op (e0) (e0)) = (e2)) -> (((op (e0) (e0)) = (e1))\/(((op (e0) (e1)) = (e1))\/(((op (e0) (e2)) = (e1))\/((op (e0) (e3)) = (e1))))) -> (~((op (e0) (e1)) = (e0))) -> (~((op (e0) (e0)) = (e0))) -> (~((op (e1) (e0)) = (e0))) -> (((op (e0) (e0)) = (e0))\/(((op (e1) (e0)) = (e0))\/(((op (e2) (e0)) = (e0))\/((op (e3) (e0)) = (e0))))) -> False). % 18.68/18.89 do 0 intro. intros zenon_H208 zenon_H2f zenon_H76 zenon_H233 zenon_H206 zenon_H201 zenon_H1f0 zenon_H1fa zenon_H74 zenon_H6f zenon_H6d zenon_H71 zenon_H4a zenon_H4f zenon_H52 zenon_H67 zenon_H62 zenon_H5b zenon_H57 zenon_H54 zenon_H6a zenon_H45 zenon_H22 zenon_H1ed zenon_H1ec zenon_H1d5 zenon_H1d8 zenon_H1cf zenon_H1ba zenon_H1cc zenon_H1c4 zenon_H1c7 zenon_H1ac zenon_H1e0 zenon_H1ee zenon_H1fe zenon_H182 zenon_H39 zenon_H153 zenon_H14f zenon_H149 zenon_H165 zenon_H160 zenon_H168 zenon_H16f zenon_H173 zenon_H172 zenon_H145 zenon_H124 zenon_H12b zenon_H133 zenon_H130 zenon_H136 zenon_H128 zenon_H139 zenon_H13c zenon_H13e zenon_H142 zenon_H179 zenon_H178 zenon_H17e zenon_H17b zenon_H183 zenon_H184 zenon_H185 zenon_H189 zenon_H109 zenon_H2b zenon_H101 zenon_H102 zenon_Hf3 zenon_H106 zenon_He7 zenon_Haf zenon_He4 zenon_He2 zenon_Hd5 zenon_Hd8 zenon_Hdb zenon_Hdf zenon_Hc2 zenon_He8 zenon_Ha8 zenon_Ha1 zenon_H10e zenon_H1d zenon_H11f zenon_H115 zenon_H18c zenon_H10a zenon_H9a zenon_H95 zenon_H19d zenon_H195 zenon_H191 zenon_H18f zenon_H1a7 zenon_H1a4 zenon_H1a6 zenon_H1a5 zenon_H94 zenon_H7c zenon_H205 zenon_H204 zenon_H9d zenon_H212 zenon_H22a zenon_H210 zenon_H7b zenon_H22d zenon_H20b zenon_H3f zenon_H23 zenon_H3e. % 18.68/18.89 apply (zenon_or_s _ _ zenon_H178); [ zenon_intro zenon_H25 | zenon_intro zenon_H86 ]. % 18.68/18.89 apply (zenon_L625_); trivial. % 18.68/18.89 apply (zenon_L123_); trivial. % 18.68/18.89 (* end of lemma zenon_L631_ *) % 18.68/18.89 assert (zenon_L632_ : (((op (e0) (e1)) = (e0))\/(((op (e1) (e1)) = (e0))\/(((op (e2) (e1)) = (e0))\/((op (e3) (e1)) = (e0))))) -> (~((op (e2) (e1)) = (e0))) -> (((op (e0) (e0)) = (e0))\/(((op (e1) (e0)) = (e0))\/(((op (e2) (e0)) = (e0))\/((op (e3) (e0)) = (e0))))) -> (~((op (e1) (e0)) = (e0))) -> (~((op (e0) (e0)) = (e0))) -> (~((op (e0) (e1)) = (e0))) -> (((op (e0) (e0)) = (e1))\/(((op (e0) (e1)) = (e1))\/(((op (e0) (e2)) = (e1))\/((op (e0) (e3)) = (e1))))) -> (~((op (e0) (e1)) = (op (e3) (e1)))) -> (((op (e3) (e1)) = (e0))\/(((op (e3) (e1)) = (e1))\/(((op (e3) (e1)) = (e2))\/((op (e3) (e1)) = (e3))))) -> (((op (e0) (e1)) = (e0))\/(((op (e0) (e1)) = (e1))\/(((op (e0) (e1)) = (e2))\/((op (e0) (e1)) = (e3))))) -> ((~((op (e0) (e3)) = (e0)))\/((op (e0) (e0)) = (e3))) -> ((~((op (e1) (e1)) = (e0)))\/((op (e1) (e0)) = (e1))) -> ((~((op (e2) (e3)) = (e0)))\/((op (e2) (e0)) = (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) (e1)) = (op (e3) (e2)))) -> ((~((op (e3) (e2)) = (e0)))\/((op (e3) (e0)) = (e2))) -> (~((op (e2) (e2)) = (op (e3) (e2)))) -> (((op (e3) (e2)) = (e0))\/(((op (e3) (e2)) = (e1))\/(((op (e3) (e2)) = (e2))\/((op (e3) (e2)) = (e3))))) -> (~((op (e0) (e2)) = (op (e1) (e2)))) -> (((op (e1) (e2)) = (e0))\/(((op (e1) (e2)) = (e1))\/(((op (e1) (e2)) = (e2))\/((op (e1) (e2)) = (e3))))) -> (~((e1) = (e3))) -> (~((e0) = (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) (e3)) = (e0))\/(((op (e2) (e3)) = (e1))\/(((op (e2) (e3)) = (e2))\/((op (e2) (e3)) = (e3))))) -> (~((e0) = (e1))) -> (~((op (e0) (e2)) = (op (e2) (e2)))) -> (((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) (e0)) = (op (e1) (e3)))) -> (~((op (e1) (e3)) = (op (e3) (e3)))) -> (~((op (e0) (e3)) = (op (e2) (e3)))) -> (((op (e0) (e3)) = (e0))\/(((op (e0) (e3)) = (e1))\/(((op (e0) (e3)) = (e2))\/((op (e0) (e3)) = (e3))))) -> (((op (e2) (e0)) = (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 (e0) (e1)) = (e1))\/(((op (e1) (e1)) = (e1))\/(((op (e2) (e1)) = (e1))\/((op (e3) (e1)) = (e1))))) -> (~((op (e0) (e0)) = (op (e0) (e3)))) -> ((~((op (e2) (e2)) = (e0)))\/((op (e2) (e0)) = (e2))) -> ((~((op (e3) (e0)) = (e0)))\/((op (e3) (e0)) = (e0))) -> (((op (e0) (e0)) = (e2))\/(((op (e0) (e1)) = (e2))\/(((op (e0) (e2)) = (e2))\/((op (e0) (e3)) = (e2))))) -> (~((op (e2) (e0)) = (op (e3) (e0)))) -> (~((op (e0) (e1)) = (op (e2) (e1)))) -> ((~((op (e1) (e2)) = (e0)))\/((op (e1) (e0)) = (e2))) -> ((~((op (e1) (e3)) = (e0)))\/((op (e1) (e0)) = (e3))) -> (~((op (e1) (e1)) = (op (e2) (e1)))) -> (~((op (e0) (e0)) = (op (e0) (e2)))) -> (((op (e0) (e2)) = (e1))\/(((op (e1) (e2)) = (e1))\/(((op (e2) (e2)) = (e1))\/((op (e3) (e2)) = (e1))))) -> (((op (e1) (e0)) = (e1))\/(((op (e1) (e1)) = (e1))\/(((op (e1) (e2)) = (e1))\/((op (e1) (e3)) = (e1))))) -> (((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 (e1) (e2)) = (op (e1) (e3)))) -> (((op (e1) (e0)) = (e3))\/(((op (e1) (e1)) = (e3))\/(((op (e1) (e2)) = (e3))\/((op (e1) (e3)) = (e3))))) -> (((op (e0) (e0)) = (e3))\/(((op (e0) (e1)) = (e3))\/(((op (e0) (e2)) = (e3))\/((op (e0) (e3)) = (e3))))) -> (~((op (e1) (e1)) = (op (e3) (e1)))) -> (((op (e3) (e0)) = (e3))\/(((op (e3) (e1)) = (e3))\/(((op (e3) (e2)) = (e3))\/((op (e3) (e3)) = (e3))))) -> (~((op (e0) (e2)) = (op (e3) (e2)))) -> (((op (e3) (e0)) = (e2))\/(((op (e3) (e1)) = (e2))\/(((op (e3) (e2)) = (e2))\/((op (e3) (e3)) = (e2))))) -> ((~((op (e2) (e1)) = (e0)))\/((op (e2) (e0)) = (e1))) -> (((op (e0) (e0)) = (e2))\/(((op (e1) (e0)) = (e2))\/(((op (e2) (e0)) = (e2))\/((op (e3) (e0)) = (e2))))) -> ((~((op (e2) (e0)) = (e0)))\/((op (e2) (e0)) = (e0))) -> (((op (e0) (e0)) = (e3))\/(((op (e1) (e0)) = (e3))\/(((op (e2) (e0)) = (e3))\/((op (e3) (e0)) = (e3))))) -> (((op (e3) (e0)) = (e0))\/(((op (e3) (e1)) = (e0))\/(((op (e3) (e2)) = (e0))\/((op (e3) (e3)) = (e0))))) -> (((op (e2) (e2)) = (e0))\/(((op (e2) (e2)) = (e1))\/(((op (e2) (e2)) = (e2))\/((op (e2) (e2)) = (e3))))) -> (((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 (e3) (e0)) = (op (e3) (e1)))) -> ((~((op (e3) (e3)) = (e0)))\/((op (e3) (e0)) = (e3))) -> ((~((op (e3) (e1)) = (e0)))\/((op (e3) (e0)) = (e1))) -> (((op (e1) (e0)) = (e0))\/(((op (e1) (e1)) = (e0))\/(((op (e1) (e2)) = (e0))\/((op (e1) (e3)) = (e0))))) -> (~((op (e1) (e0)) = (op (e1) (e1)))) -> (((op (e0) (e2)) = (e0))\/(((op (e1) (e2)) = (e0))\/(((op (e2) (e2)) = (e0))\/((op (e3) (e2)) = (e0))))) -> (~((op (e0) (e1)) = (op (e0) (e3)))) -> (~((op (e2) (e0)) = (op (e2) (e3)))) -> (((op (e0) (e3)) = (e0))\/(((op (e1) (e3)) = (e0))\/(((op (e2) (e3)) = (e0))\/((op (e3) (e3)) = (e0))))) -> (~((op (e2) (e0)) = (op (e2) (e2)))) -> (~((op (e1) (e1)) = (op (e1) (e2)))) -> (~((op (e0) (e1)) = (op (e0) (e2)))) -> (~((op (e3) (e0)) = (op (e3) (e3)))) -> (~((op (e2) (e2)) = (op (e2) (e3)))) -> (~((op (e3) (e0)) = (op (e3) (e2)))) -> (((op (e0) (e0)) = (e0))\/(((op (e0) (e1)) = (e0))\/(((op (e0) (e2)) = (e0))\/((op (e0) (e3)) = (e0))))) -> (~((op (e1) (e0)) = (op (e3) (e0)))) -> (~((op (e2) (e0)) = (op (e2) (e1)))) -> (~((op (e1) (e0)) = (op (e2) (e0)))) -> ((~((op (e1) (e0)) = (e0)))\/((op (e1) (e0)) = (e0))) -> ((~((op (e0) (e2)) = (e0)))\/((op (e0) (e0)) = (e2))) -> (~((op (e0) (e3)) = (e0))) -> (((op (e2) (e0)) = (e0))\/(((op (e2) (e1)) = (e0))\/(((op (e2) (e2)) = (e0))\/((op (e2) (e3)) = (e0))))) -> (~((op (e0) (e2)) = (op (e0) (e3)))) -> (~((op (e3) (e3)) = (e3))) -> (~((op (e2) (e3)) = (op (e3) (e3)))) -> (~((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 (e2) (e2)) = (e2))) -> (~((op (e2) (e1)) = (op (e3) (e1)))) -> (~((op (e0) (e0)) = (op (e2) (e0)))) -> ((op (e0) (e0)) = (e2)) -> (((op (e2) (e0)) = (e2))\/(((op (e2) (e1)) = (e2))\/(((op (e2) (e2)) = (e2))\/((op (e2) (e3)) = (e2))))) -> (((op (e0) (e2)) = (e2))\/(((op (e1) (e2)) = (e2))\/(((op (e2) (e2)) = (e2))\/((op (e3) (e2)) = (e2))))) -> (~((e0) = (e2))) -> ((op (e0) (e2)) = (e0)) -> (((op (e1) (e1)) = (e0))\/(((op (e1) (e1)) = (e1))\/(((op (e1) (e1)) = (e2))\/((op (e1) (e1)) = (e3))))) -> (~((op (e1) (e1)) = (e0))) -> (~((op (e1) (e1)) = (e1))) -> (~((op (e3) (e2)) = (op (e3) (e3)))) -> (~((op (e2) (e1)) = (op (e2) (e3)))) -> (~((op (e1) (e1)) = (op (e1) (e3)))) -> (~((e1) = (e2))) -> (((op (e0) (e3)) = (e2))\/(((op (e1) (e3)) = (e2))\/(((op (e2) (e3)) = (e2))\/((op (e3) (e3)) = (e2))))) -> (~((op (e0) (e1)) = (op (e1) (e1)))) -> ((op (e0) (e1)) = (e3)) -> ((op (e2) (e0)) = (e0)) -> (~((e2) = (e3))) -> (((op (e0) (e1)) = (e2))\/(((op (e1) (e1)) = (e2))\/(((op (e2) (e1)) = (e2))\/((op (e3) (e1)) = (e2))))) -> (~((op (e0) (e3)) = (op (e1) (e3)))) -> ((op (e0) (e3)) = (e1)) -> False). % 18.68/18.89 do 0 intro. intros zenon_H245 zenon_H31 zenon_H3e zenon_H23 zenon_H3f zenon_H20b zenon_H22d zenon_H210 zenon_H22a zenon_H212 zenon_H204 zenon_H205 zenon_H94 zenon_H1a5 zenon_H1a6 zenon_H1a4 zenon_H1a7 zenon_H18f zenon_H191 zenon_H195 zenon_H19d zenon_H95 zenon_H9a zenon_H18c zenon_H115 zenon_H11f zenon_Ha1 zenon_Ha8 zenon_He8 zenon_Hdf zenon_Hdb zenon_Hd8 zenon_Hd5 zenon_He2 zenon_He4 zenon_He7 zenon_H106 zenon_H2b zenon_H109 zenon_H189 zenon_H185 zenon_H184 zenon_H183 zenon_H17b zenon_H17e zenon_H178 zenon_H179 zenon_H13e zenon_H13c zenon_H139 zenon_H128 zenon_H136 zenon_H133 zenon_H124 zenon_H16f zenon_H168 zenon_H160 zenon_H165 zenon_H14f zenon_H153 zenon_H182 zenon_H1fe zenon_H1ee zenon_H1e0 zenon_H1ac zenon_H1c4 zenon_H1cc zenon_H1ba zenon_H1cf zenon_H1ec zenon_H1ed zenon_H22 zenon_H45 zenon_H6a zenon_H54 zenon_H5b zenon_H67 zenon_H52 zenon_H4f zenon_H4a zenon_H71 zenon_H6d zenon_H6f zenon_H74 zenon_H1fa zenon_H1f0 zenon_H201 zenon_H206 zenon_H233 zenon_H76 zenon_H2f zenon_H208 zenon_H102 zenon_Hf3 zenon_Hc2 zenon_H130 zenon_H101 zenon_H173 zenon_Haf zenon_H39 zenon_H7b zenon_H1d5 zenon_H172 zenon_H149 zenon_H48 zenon_H142 zenon_H24 zenon_H10a zenon_H62 zenon_H1c7 zenon_H57 zenon_H7c zenon_H145 zenon_H10e zenon_H99 zenon_H34 zenon_H12b zenon_H1d8 zenon_H1d zenon_Hc3. % 18.68/18.89 apply (zenon_or_s _ _ zenon_H245); [ zenon_intro zenon_H49 | zenon_intro zenon_H246 ]. % 18.68/18.89 exact (zenon_H20b zenon_H49). % 18.68/18.89 apply (zenon_or_s _ _ zenon_H246); [ zenon_intro zenon_H29 | zenon_intro zenon_H247 ]. % 18.68/18.89 exact (zenon_H24 zenon_H29). % 18.68/18.89 apply (zenon_or_s _ _ zenon_H247); [ zenon_intro zenon_H36 | zenon_intro zenon_H1b1 ]. % 18.68/18.89 exact (zenon_H31 zenon_H36). % 18.68/18.89 apply (zenon_or_s _ _ zenon_H128); [ zenon_intro zenon_H9d | zenon_intro zenon_H129 ]. % 18.68/18.89 apply (zenon_L631_); trivial. % 18.68/18.89 apply (zenon_or_s _ _ zenon_H129); [ zenon_intro zenon_H10d | zenon_intro zenon_H12a ]. % 18.68/18.89 exact (zenon_H10a zenon_H10d). % 18.68/18.89 apply (zenon_or_s _ _ zenon_H12a); [ zenon_intro zenon_Hf0 | zenon_intro zenon_Hd6 ]. % 18.68/18.89 apply (zenon_or_s _ _ zenon_H1d8); [ zenon_intro zenon_H10f | zenon_intro zenon_H1d9 ]. % 18.68/18.89 apply (zenon_L175_); trivial. % 18.68/18.89 apply (zenon_or_s _ _ zenon_H1d9); [ zenon_intro zenon_H110 | zenon_intro zenon_H1da ]. % 18.68/18.89 apply (zenon_L498_); trivial. % 18.68/18.89 apply (zenon_or_s _ _ zenon_H1da); [ zenon_intro zenon_H1ca | zenon_intro zenon_H14d ]. % 18.68/18.89 apply (zenon_or_s _ _ zenon_H172); [ zenon_intro zenon_H150 | zenon_intro zenon_H174 ]. % 18.68/18.89 apply (zenon_L378_); trivial. % 18.68/18.89 apply (zenon_or_s _ _ zenon_H174); [ zenon_intro zenon_H113 | zenon_intro zenon_H175 ]. % 18.68/18.89 apply (zenon_L68_); trivial. % 18.68/18.89 apply (zenon_or_s _ _ zenon_H175); [ zenon_intro zenon_H176 | zenon_intro zenon_H151 ]. % 18.68/18.89 exact (zenon_H173 zenon_H176). % 18.68/18.89 apply (zenon_L499_); trivial. % 18.68/18.89 apply (zenon_or_s _ _ zenon_H1d5); [ zenon_intro zenon_Hee | zenon_intro zenon_H1d6 ]. % 18.68/18.89 apply (zenon_L341_); trivial. % 18.68/18.89 apply (zenon_or_s _ _ zenon_H1d6); [ zenon_intro zenon_H1ca | zenon_intro zenon_H1d7 ]. % 18.68/18.89 apply (zenon_L364_); trivial. % 18.68/18.89 apply (zenon_or_s _ _ zenon_H1d7); [ zenon_intro zenon_H176 | zenon_intro zenon_H11d ]. % 18.68/18.89 exact (zenon_H173 zenon_H176). % 18.68/18.89 apply (zenon_L245_); trivial. % 18.68/18.89 apply (zenon_L79_); trivial. % 18.68/18.89 (* end of lemma zenon_L632_ *) % 18.68/18.89 assert (zenon_L633_ : ((op (e0) (e3)) = (e1)) -> ((op (e0) (e3)) = (e3)) -> (~((e1) = (e3))) -> False). % 18.68/18.89 do 0 intro. intros zenon_Hc3 zenon_He3 zenon_H95. % 18.68/18.89 elim (classic ((e3) = (e3))); [ zenon_intro zenon_H96 | zenon_intro zenon_H85 ]. % 18.68/18.89 cut (((e3) = (e3)) = ((e1) = (e3))). % 18.68/18.89 intro zenon_D_pnotp. % 18.68/18.89 apply zenon_H95. % 18.68/18.89 rewrite <- zenon_D_pnotp. % 18.68/18.89 exact zenon_H96. % 18.68/18.89 cut (((e3) = (e3))); [idtac | apply NNPP; zenon_intro zenon_H85]. % 18.68/18.89 cut (((e3) = (e1))); [idtac | apply NNPP; zenon_intro zenon_H97]. % 18.68/18.89 congruence. % 18.68/18.89 cut (((op (e0) (e3)) = (e1)) = ((e3) = (e1))). % 18.68/18.89 intro zenon_D_pnotp. % 18.68/18.89 apply zenon_H97. % 18.68/18.89 rewrite <- zenon_D_pnotp. % 18.68/18.89 exact zenon_Hc3. % 18.68/18.89 cut (((e1) = (e1))); [idtac | apply NNPP; zenon_intro zenon_H79]. % 18.68/18.89 cut (((op (e0) (e3)) = (e3))); [idtac | apply NNPP; zenon_intro zenon_H12d]. % 18.68/18.89 congruence. % 18.68/18.89 exact (zenon_H12d zenon_He3). % 18.68/18.89 apply zenon_H79. apply refl_equal. % 18.68/18.89 apply zenon_H85. apply refl_equal. % 18.68/18.89 apply zenon_H85. apply refl_equal. % 18.68/18.89 (* end of lemma zenon_L633_ *) % 18.68/18.89 assert (zenon_L634_ : (((op (e0) (e0)) = (e1))\/(((op (e1) (e0)) = (e1))\/(((op (e2) (e0)) = (e1))\/((op (e3) (e0)) = (e1))))) -> ((op (e3) (e0)) = (e1)) -> (~((op (e1) (e2)) = (e0))) -> (~((op (e2) (e2)) = (e0))) -> (~((op (e3) (e2)) = (e0))) -> ((op (e1) (e0)) = (e3)) -> (~((op (e0) (e3)) = (op (e1) (e3)))) -> (((op (e0) (e1)) = (e2))\/(((op (e1) (e1)) = (e2))\/(((op (e2) (e1)) = (e2))\/((op (e3) (e1)) = (e2))))) -> (~((e2) = (e3))) -> ((op (e2) (e0)) = (e0)) -> (~((op (e0) (e1)) = (op (e1) (e1)))) -> (((op (e0) (e3)) = (e2))\/(((op (e1) (e3)) = (e2))\/(((op (e2) (e3)) = (e2))\/((op (e3) (e3)) = (e2))))) -> (~((e1) = (e2))) -> (~((op (e1) (e1)) = (op (e1) (e3)))) -> (~((op (e2) (e1)) = (op (e2) (e3)))) -> (~((op (e3) (e2)) = (op (e3) (e3)))) -> (~((op (e1) (e1)) = (e1))) -> (~((op (e1) (e1)) = (e0))) -> (((op (e1) (e1)) = (e0))\/(((op (e1) (e1)) = (e1))\/(((op (e1) (e1)) = (e2))\/((op (e1) (e1)) = (e3))))) -> (~((e0) = (e2))) -> (((op (e0) (e2)) = (e2))\/(((op (e1) (e2)) = (e2))\/(((op (e2) (e2)) = (e2))\/((op (e3) (e2)) = (e2))))) -> (((op (e2) (e0)) = (e2))\/(((op (e2) (e1)) = (e2))\/(((op (e2) (e2)) = (e2))\/((op (e2) (e3)) = (e2))))) -> ((op (e0) (e0)) = (e2)) -> (~((op (e0) (e0)) = (op (e2) (e0)))) -> (~((op (e2) (e1)) = (op (e3) (e1)))) -> (~((op (e2) (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) (e3)) = (op (e3) (e3)))) -> (~((op (e2) (e3)) = (op (e3) (e3)))) -> (~((op (e3) (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 (e0) (e3)) = (e0))) -> ((~((op (e0) (e2)) = (e0)))\/((op (e0) (e0)) = (e2))) -> ((~((op (e1) (e0)) = (e0)))\/((op (e1) (e0)) = (e0))) -> (~((op (e1) (e0)) = (op (e2) (e0)))) -> (~((op (e2) (e0)) = (op (e2) (e1)))) -> (~((op (e1) (e0)) = (op (e3) (e0)))) -> (((op (e0) (e0)) = (e0))\/(((op (e0) (e1)) = (e0))\/(((op (e0) (e2)) = (e0))\/((op (e0) (e3)) = (e0))))) -> (~((op (e3) (e0)) = (op (e3) (e2)))) -> (~((op (e2) (e2)) = (op (e2) (e3)))) -> (~((op (e3) (e0)) = (op (e3) (e3)))) -> (~((op (e0) (e1)) = (op (e0) (e2)))) -> (~((op (e1) (e1)) = (op (e1) (e2)))) -> (~((op (e2) (e0)) = (op (e2) (e2)))) -> (((op (e0) (e3)) = (e0))\/(((op (e1) (e3)) = (e0))\/(((op (e2) (e3)) = (e0))\/((op (e3) (e3)) = (e0))))) -> (~((op (e2) (e0)) = (op (e2) (e3)))) -> (~((op (e0) (e1)) = (op (e0) (e3)))) -> (((op (e0) (e2)) = (e0))\/(((op (e1) (e2)) = (e0))\/(((op (e2) (e2)) = (e0))\/((op (e3) (e2)) = (e0))))) -> (~((op (e1) (e0)) = (op (e1) (e1)))) -> (((op (e1) (e0)) = (e0))\/(((op (e1) (e1)) = (e0))\/(((op (e1) (e2)) = (e0))\/((op (e1) (e3)) = (e0))))) -> ((~((op (e3) (e1)) = (e0)))\/((op (e3) (e0)) = (e1))) -> ((~((op (e3) (e3)) = (e0)))\/((op (e3) (e0)) = (e3))) -> (~((op (e3) (e0)) = (op (e3) (e1)))) -> (((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 (e2) (e2)) = (e0))\/(((op (e2) (e2)) = (e1))\/(((op (e2) (e2)) = (e2))\/((op (e2) (e2)) = (e3))))) -> (((op (e3) (e0)) = (e0))\/(((op (e3) (e1)) = (e0))\/(((op (e3) (e2)) = (e0))\/((op (e3) (e3)) = (e0))))) -> (((op (e0) (e0)) = (e3))\/(((op (e1) (e0)) = (e3))\/(((op (e2) (e0)) = (e3))\/((op (e3) (e0)) = (e3))))) -> ((~((op (e2) (e0)) = (e0)))\/((op (e2) (e0)) = (e0))) -> (((op (e0) (e0)) = (e2))\/(((op (e1) (e0)) = (e2))\/(((op (e2) (e0)) = (e2))\/((op (e3) (e0)) = (e2))))) -> ((~((op (e2) (e1)) = (e0)))\/((op (e2) (e0)) = (e1))) -> (((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)) = (e3))\/(((op (e3) (e1)) = (e3))\/(((op (e3) (e2)) = (e3))\/((op (e3) (e3)) = (e3))))) -> (~((op (e1) (e1)) = (op (e3) (e1)))) -> (((op (e0) (e0)) = (e3))\/(((op (e0) (e1)) = (e3))\/(((op (e0) (e2)) = (e3))\/((op (e0) (e3)) = (e3))))) -> (((op (e1) (e0)) = (e3))\/(((op (e1) (e1)) = (e3))\/(((op (e1) (e2)) = (e3))\/((op (e1) (e3)) = (e3))))) -> (~((op (e1) (e2)) = (op (e1) (e3)))) -> (((op (e0) (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) (e0)) = (e1))\/(((op (e1) (e1)) = (e1))\/(((op (e1) (e2)) = (e1))\/((op (e1) (e3)) = (e1))))) -> (((op (e0) (e2)) = (e1))\/(((op (e1) (e2)) = (e1))\/(((op (e2) (e2)) = (e1))\/((op (e3) (e2)) = (e1))))) -> (~((op (e0) (e0)) = (op (e0) (e2)))) -> (~((op (e1) (e1)) = (op (e2) (e1)))) -> ((~((op (e1) (e3)) = (e0)))\/((op (e1) (e0)) = (e3))) -> ((~((op (e1) (e2)) = (e0)))\/((op (e1) (e0)) = (e2))) -> (~((op (e0) (e1)) = (op (e2) (e1)))) -> (~((op (e2) (e0)) = (op (e3) (e0)))) -> (((op (e0) (e0)) = (e2))\/(((op (e0) (e1)) = (e2))\/(((op (e0) (e2)) = (e2))\/((op (e0) (e3)) = (e2))))) -> ((~((op (e3) (e0)) = (e0)))\/((op (e3) (e0)) = (e0))) -> ((~((op (e2) (e2)) = (e0)))\/((op (e2) (e0)) = (e2))) -> (~((op (e0) (e0)) = (op (e0) (e3)))) -> (((op (e0) (e1)) = (e1))\/(((op (e1) (e1)) = (e1))\/(((op (e2) (e1)) = (e1))\/((op (e3) (e1)) = (e1))))) -> (~((op (e1) (e2)) = (op (e2) (e2)))) -> (((op (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 (e0) (e3)) = (e0))\/(((op (e0) (e3)) = (e1))\/(((op (e0) (e3)) = (e2))\/((op (e0) (e3)) = (e3))))) -> (~((op (e0) (e3)) = (op (e2) (e3)))) -> (~((op (e1) (e3)) = (op (e3) (e3)))) -> (~((op (e1) (e0)) = (op (e1) (e3)))) -> (~((op (e1) (e3)) = (op (e2) (e3)))) -> (((op (e1) (e3)) = (e0))\/(((op (e1) (e3)) = (e1))\/(((op (e1) (e3)) = (e2))\/((op (e1) (e3)) = (e3))))) -> (((op (e3) (e0)) = (e1))\/(((op (e3) (e1)) = (e1))\/(((op (e3) (e2)) = (e1))\/((op (e3) (e3)) = (e1))))) -> (~((op (e0) (e2)) = (op (e2) (e2)))) -> (~((e0) = (e1))) -> (((op (e2) (e3)) = (e0))\/(((op (e2) (e3)) = (e1))\/(((op (e2) (e3)) = (e2))\/((op (e2) (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)) = (e0))\/(((op (e1) (e2)) = (e1))\/(((op (e1) (e2)) = (e2))\/((op (e1) (e2)) = (e3))))) -> (~((op (e0) (e2)) = (op (e1) (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) (e2)) = (e0)))\/((op (e3) (e0)) = (e2))) -> (~((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)) = (e3))\/(((op (e1) (e1)) = (e3))\/(((op (e2) (e1)) = (e3))\/((op (e3) (e1)) = (e3))))) -> ((~((op (e2) (e3)) = (e0)))\/((op (e2) (e0)) = (e3))) -> ((~((op (e1) (e1)) = (e0)))\/((op (e1) (e0)) = (e1))) -> ((~((op (e0) (e3)) = (e0)))\/((op (e0) (e0)) = (e3))) -> (((op (e0) (e1)) = (e0))\/(((op (e0) (e1)) = (e1))\/(((op (e0) (e1)) = (e2))\/((op (e0) (e1)) = (e3))))) -> (((op (e3) (e1)) = (e0))\/(((op (e3) (e1)) = (e1))\/(((op (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) (e1)) = (e0))) -> (~((op (e0) (e0)) = (e0))) -> (~((op (e1) (e0)) = (e0))) -> (((op (e0) (e0)) = (e0))\/(((op (e1) (e0)) = (e0))\/(((op (e2) (e0)) = (e0))\/((op (e3) (e0)) = (e0))))) -> (~((op (e2) (e1)) = (e0))) -> (((op (e0) (e1)) = (e0))\/(((op (e1) (e1)) = (e0))\/(((op (e2) (e1)) = (e0))\/((op (e3) (e1)) = (e0))))) -> (~((e0) = (e3))) -> ((op (e0) (e2)) = (e0)) -> ((op (e0) (e3)) = (e1)) -> (~((e1) = (e3))) -> False). % 18.68/18.89 do 0 intro. intros zenon_H235 zenon_Hac zenon_H25 zenon_H81 zenon_H18b zenon_H9e zenon_H1d zenon_H1d8 zenon_H12b zenon_H34 zenon_H10e zenon_H145 zenon_H7c zenon_H57 zenon_H1c7 zenon_H62 zenon_H10a zenon_H24 zenon_H142 zenon_H149 zenon_H172 zenon_H1d5 zenon_H7b zenon_H39 zenon_Haf zenon_H173 zenon_H101 zenon_H130 zenon_Hc2 zenon_Hf3 zenon_H102 zenon_H208 zenon_H2f zenon_H76 zenon_H233 zenon_H206 zenon_H201 zenon_H1f0 zenon_H1fa zenon_H74 zenon_H6f zenon_H6d zenon_H71 zenon_H4a zenon_H4f zenon_H52 zenon_H67 zenon_H5b zenon_H54 zenon_H6a zenon_H45 zenon_H22 zenon_H1ed zenon_H1ec zenon_H1cf zenon_H1ba zenon_H1cc zenon_H1c4 zenon_H1ac zenon_H1e0 zenon_H1ee zenon_H1fe zenon_H182 zenon_H153 zenon_H14f zenon_H165 zenon_H160 zenon_H168 zenon_H16f zenon_H124 zenon_H133 zenon_H136 zenon_H128 zenon_H139 zenon_H13c zenon_H13e zenon_H179 zenon_H178 zenon_H17e zenon_H17b zenon_H183 zenon_H184 zenon_H185 zenon_H189 zenon_H109 zenon_H2b zenon_H106 zenon_He7 zenon_He4 zenon_He2 zenon_Hd5 zenon_Hd8 zenon_Hdb zenon_Hdf zenon_He8 zenon_Ha8 zenon_Ha1 zenon_H11f zenon_H115 zenon_H18c zenon_H19d zenon_H195 zenon_H191 zenon_H18f zenon_H1a7 zenon_H1a4 zenon_H1a6 zenon_H1a5 zenon_H94 zenon_H205 zenon_H204 zenon_H212 zenon_H22a zenon_H210 zenon_H22d zenon_H20b zenon_H3f zenon_H23 zenon_H3e zenon_H31 zenon_H245 zenon_H9a zenon_H48 zenon_Hc3 zenon_H95. % 18.68/18.89 apply (zenon_or_s _ _ zenon_H168); [ zenon_intro zenon_H3a | zenon_intro zenon_H169 ]. % 18.68/18.89 apply (zenon_L585_); trivial. % 18.68/18.89 apply (zenon_or_s _ _ zenon_H169); [ zenon_intro zenon_H99 | zenon_intro zenon_H16a ]. % 18.68/18.89 apply (zenon_L632_); trivial. % 18.68/18.89 apply (zenon_or_s _ _ zenon_H16a); [ zenon_intro zenon_Ha9 | zenon_intro zenon_He3 ]. % 18.68/18.89 apply (zenon_L358_); trivial. % 18.68/18.89 apply (zenon_L633_); trivial. % 18.68/18.89 (* end of lemma zenon_L634_ *) % 18.68/18.89 assert (zenon_L635_ : (((op (e1) (e0)) = (e0))\/(((op (e1) (e1)) = (e0))\/(((op (e1) (e2)) = (e0))\/((op (e1) (e3)) = (e0))))) -> (~((op (e1) (e0)) = (e0))) -> (~((op (e0) (e2)) = (op (e1) (e2)))) -> (((op (e0) (e1)) = (e0))\/(((op (e1) (e1)) = (e0))\/(((op (e2) (e1)) = (e0))\/((op (e3) (e1)) = (e0))))) -> (~((op (e0) (e1)) = (e0))) -> (((op (e1) (e0)) = (e1))\/(((op (e1) (e1)) = (e1))\/(((op (e1) (e2)) = (e1))\/((op (e1) (e3)) = (e1))))) -> ((op (e1) (e0)) = (e3)) -> (~((op (e3) (e0)) = (op (e3) (e2)))) -> ((op (e0) (e2)) = (e0)) -> (((op (e0) (e2)) = (e2))\/(((op (e1) (e2)) = (e2))\/(((op (e2) (e2)) = (e2))\/((op (e3) (e2)) = (e2))))) -> (((op (e0) (e1)) = (e2))\/(((op (e1) (e1)) = (e2))\/(((op (e2) (e1)) = (e2))\/((op (e3) (e1)) = (e2))))) -> (((op (e1) (e1)) = (e0))\/(((op (e1) (e1)) = (e1))\/(((op (e1) (e1)) = (e2))\/((op (e1) (e1)) = (e3))))) -> (~((op (e1) (e1)) = (e0))) -> (~((op (e1) (e1)) = (e1))) -> (~((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 (e2) (e3)) = (op (e3) (e3)))) -> (~((op (e3) (e1)) = (op (e3) (e3)))) -> (~((op (e0) (e3)) = (op (e2) (e3)))) -> (~((e1) = (e3))) -> (((op (e2) (e1)) = (e0))\/(((op (e2) (e1)) = (e1))\/(((op (e2) (e1)) = (e2))\/((op (e2) (e1)) = (e3))))) -> (~((op (e2) (e1)) = (e0))) -> ((op (e0) (e1)) = (e1)) -> (~((op (e0) (e1)) = (op (e2) (e1)))) -> ((op (e2) (e0)) = (e0)) -> (~((op (e2) (e0)) = (op (e2) (e3)))) -> (~((e2) = (e3))) -> (((op (e2) (e3)) = (e0))\/(((op (e2) (e3)) = (e1))\/(((op (e2) (e3)) = (e2))\/((op (e2) (e3)) = (e3))))) -> (~((e0) = (e3))) -> (((op (e0) (e3)) = (e0))\/(((op (e1) (e3)) = (e0))\/(((op (e2) (e3)) = (e0))\/((op (e3) (e3)) = (e0))))) -> (((op (e0) (e3)) = (e3))\/(((op (e1) (e3)) = (e3))\/(((op (e2) (e3)) = (e3))\/((op (e3) (e3)) = (e3))))) -> (~((op (e2) (e2)) = (e2))) -> (~((op (e2) (e0)) = (op (e2) (e1)))) -> (((op (e2) (e0)) = (e2))\/(((op (e2) (e1)) = (e2))\/(((op (e2) (e2)) = (e2))\/((op (e2) (e3)) = (e2))))) -> (~((op (e3) (e0)) = (op (e3) (e3)))) -> (~((op (e2) (e1)) = (op (e2) (e3)))) -> (~((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 (e0) (e3)) = (op (e3) (e3)))) -> (~((op (e3) (e3)) = (e3))) -> (((op (e0) (e3)) = (e2))\/(((op (e1) (e3)) = (e2))\/(((op (e2) (e3)) = (e2))\/((op (e3) (e3)) = (e2))))) -> (~((op (e3) (e0)) = (op (e3) (e1)))) -> ((op (e3) (e0)) = (e2)) -> False). % 18.68/18.89 do 0 intro. intros zenon_H22 zenon_H23 zenon_H195 zenon_H245 zenon_H20b zenon_H128 zenon_H9e zenon_H6f zenon_H48 zenon_H172 zenon_H1d8 zenon_H142 zenon_H24 zenon_H10a zenon_H149 zenon_He4 zenon_H1d zenon_Hf3 zenon_H130 zenon_He2 zenon_H95 zenon_H1cc zenon_H31 zenon_Ha0 zenon_H17e zenon_H34 zenon_H5b zenon_H12b zenon_H11f zenon_H9a zenon_H67 zenon_H136 zenon_H173 zenon_H1f0 zenon_H1d5 zenon_H71 zenon_H1c7 zenon_H7c zenon_H101 zenon_Hd5 zenon_Hc2 zenon_H102 zenon_H145 zenon_H1cf zenon_H148. % 18.68/18.89 apply (zenon_or_s _ _ zenon_H22); [ zenon_intro zenon_H27 | zenon_intro zenon_H26 ]. % 18.68/18.89 exact (zenon_H23 zenon_H27). % 18.68/18.89 apply (zenon_or_s _ _ zenon_H26); [ zenon_intro zenon_H29 | zenon_intro zenon_H28 ]. % 18.68/18.89 exact (zenon_H24 zenon_H29). % 18.68/18.89 apply (zenon_or_s _ _ zenon_H28); [ zenon_intro zenon_H2a | zenon_intro zenon_H1f ]. % 18.68/18.89 apply (zenon_L334_); trivial. % 18.68/18.89 apply (zenon_L589_); trivial. % 18.68/18.89 (* end of lemma zenon_L635_ *) % 18.68/18.89 assert (zenon_L636_ : (((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))) -> ((op (e3) (e0)) = (e2)) -> (~((op (e3) (e0)) = (op (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 (e0) (e3)) = (op (e1) (e3)))) -> ((op (e0) (e3)) = (e1)) -> False). % 18.68/18.89 do 0 intro. intros zenon_H128 zenon_H95 zenon_H9e zenon_H10a zenon_H148 zenon_H6f zenon_H173 zenon_H7c zenon_H48 zenon_H149 zenon_H172 zenon_H1d zenon_Hc3. % 18.68/18.89 apply (zenon_or_s _ _ zenon_H128); [ zenon_intro zenon_H9d | zenon_intro zenon_H129 ]. % 18.68/18.89 apply (zenon_L37_); trivial. % 18.68/18.89 apply (zenon_or_s _ _ zenon_H129); [ zenon_intro zenon_H10d | zenon_intro zenon_H12a ]. % 18.68/18.89 exact (zenon_H10a zenon_H10d). % 18.68/18.89 apply (zenon_or_s _ _ zenon_H12a); [ zenon_intro zenon_Hf0 | zenon_intro zenon_Hd6 ]. % 18.68/18.89 apply (zenon_L586_); trivial. % 18.68/18.89 apply (zenon_L79_); trivial. % 18.68/18.89 (* end of lemma zenon_L636_ *) % 18.68/18.89 assert (zenon_L637_ : (~((op (e0) (e0)) = (e0))) -> (~((op (e0) (e1)) = (e0))) -> ((~((op (e0) (e2)) = (e0)))\/((op (e0) (e0)) = (e2))) -> ((~((op (e1) (e0)) = (e0)))\/((op (e1) (e0)) = (e0))) -> (~((op (e2) (e0)) = (op (e2) (e1)))) -> (~((op (e1) (e0)) = (op (e3) (e0)))) -> (((op (e0) (e2)) = (e0))\/(((op (e0) (e2)) = (e1))\/(((op (e0) (e2)) = (e2))\/((op (e0) (e2)) = (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 (e0) (e0)) = (e3))\/(((op (e0) (e1)) = (e3))\/(((op (e0) (e2)) = (e3))\/((op (e0) (e3)) = (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) (e0)) = (e1))\/(((op (e1) (e1)) = (e1))\/(((op (e1) (e2)) = (e1))\/((op (e1) (e3)) = (e1))))) -> (~((op (e0) (e0)) = (op (e0) (e2)))) -> (((op (e1) (e1)) = (e0))\/(((op (e1) (e1)) = (e1))\/(((op (e1) (e1)) = (e2))\/((op (e1) (e1)) = (e3))))) -> ((~((op (e1) (e3)) = (e0)))\/((op (e1) (e0)) = (e3))) -> ((~((op (e1) (e2)) = (e0)))\/((op (e1) (e0)) = (e2))) -> (((op (e0) (e0)) = (e2))\/(((op (e0) (e1)) = (e2))\/(((op (e0) (e2)) = (e2))\/((op (e0) (e3)) = (e2))))) -> (((op (e2) (e0)) = (e3))\/(((op (e2) (e1)) = (e3))\/(((op (e2) (e2)) = (e3))\/((op (e2) (e3)) = (e3))))) -> (((op (e1) (e2)) = (e0))\/(((op (e1) (e2)) = (e1))\/(((op (e1) (e2)) = (e2))\/((op (e1) (e2)) = (e3))))) -> (((op (e3) (e2)) = (e0))\/(((op (e3) (e2)) = (e1))\/(((op (e3) (e2)) = (e2))\/((op (e3) (e2)) = (e3))))) -> ((~((op (e1) (e1)) = (e0)))\/((op (e1) (e0)) = (e1))) -> ((~((op (e0) (e3)) = (e0)))\/((op (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 (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) (e3)) = (e1))\/(((op (e1) (e3)) = (e1))\/(((op (e2) (e3)) = (e1))\/((op (e3) (e3)) = (e1))))) -> (~((op (e3) (e0)) = (op (e3) (e3)))) -> (~((op (e2) (e2)) = (op (e2) (e3)))) -> (~((op (e1) (e0)) = (op (e1) (e3)))) -> (~((op (e0) (e1)) = (op (e0) (e3)))) -> (~((op (e0) (e1)) = (op (e3) (e1)))) -> (~((op (e0) (e1)) = (op (e0) (e2)))) -> (~((op (e1) (e2)) = (op (e3) (e2)))) -> (~((op (e2) (e3)) = (op (e3) (e3)))) -> (((op (e2) (e3)) = (e0))\/(((op (e2) (e3)) = (e1))\/(((op (e2) (e3)) = (e2))\/((op (e2) (e3)) = (e3))))) -> (((op (e3) (e1)) = (e0))\/(((op (e3) (e1)) = (e1))\/(((op (e3) (e1)) = (e2))\/((op (e3) (e1)) = (e3))))) -> (~((op (e2) (e1)) = (op (e3) (e1)))) -> (((op (e1) (e3)) = (e0))\/(((op (e1) (e3)) = (e1))\/(((op (e1) (e3)) = (e2))\/((op (e1) (e3)) = (e3))))) -> (~((op (e0) (e3)) = (op (e2) (e3)))) -> (((op (e0) (e1)) = (e1))\/(((op (e1) (e1)) = (e1))\/(((op (e2) (e1)) = (e1))\/((op (e3) (e1)) = (e1))))) -> (((op (e2) (e0)) = (e1))\/(((op (e2) (e1)) = (e1))\/(((op (e2) (e2)) = (e1))\/((op (e2) (e3)) = (e1))))) -> (((op (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)) = (op (e0) (e3)))) -> (((op (e1) (e0)) = (e2))\/(((op (e1) (e1)) = (e2))\/(((op (e1) (e2)) = (e2))\/((op (e1) (e3)) = (e2))))) -> (~((op (e1) (e1)) = (op (e3) (e1)))) -> (((op (e0) (e2)) = (e2))\/(((op (e1) (e2)) = (e2))\/(((op (e2) (e2)) = (e2))\/((op (e3) (e2)) = (e2))))) -> (~((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) (e0)) = (e3))\/(((op (e1) (e1)) = (e3))\/(((op (e1) (e2)) = (e3))\/((op (e1) (e3)) = (e3))))) -> (((op (e3) (e0)) = (e2))\/(((op (e3) (e1)) = (e2))\/(((op (e3) (e2)) = (e2))\/((op (e3) (e3)) = (e2))))) -> (~((op (e1) (e2)) = (op (e2) (e2)))) -> (~((op (e3) (e0)) = (op (e3) (e2)))) -> (~((op (e0) (e3)) = (op (e3) (e3)))) -> (((op (e2) (e1)) = (e0))\/(((op (e2) (e1)) = (e1))\/(((op (e2) (e1)) = (e2))\/((op (e2) (e1)) = (e3))))) -> (~((op (e1) (e1)) = (op (e2) (e1)))) -> (~((op (e0) (e1)) = (op (e1) (e1)))) -> (((op (e0) (e1)) = (e0))\/(((op (e0) (e1)) = (e1))\/(((op (e0) (e1)) = (e2))\/((op (e0) (e1)) = (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 (e2) (e0)) = (e2))\/(((op (e2) (e1)) = (e2))\/(((op (e2) (e2)) = (e2))\/((op (e2) (e3)) = (e2))))) -> (~((op (e1) (e1)) = (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 (e3) (e0)) = (e1))\/(((op (e3) (e1)) = (e1))\/(((op (e3) (e2)) = (e1))\/((op (e3) (e3)) = (e1))))) -> (~((e0) = (e3))) -> (~((op (e0) (e1)) = (op (e2) (e1)))) -> (~((e0) = (e1))) -> (((op (e2) (e2)) = (e0))\/(((op (e2) (e2)) = (e1))\/(((op (e2) (e2)) = (e2))\/((op (e2) (e2)) = (e3))))) -> (~((op (e2) (e2)) = (e2))) -> (~((op (e2) (e2)) = (op (e3) (e2)))) -> (((op (e0) (e2)) = (e1))\/(((op (e1) (e2)) = (e1))\/(((op (e2) (e2)) = (e1))\/((op (e3) (e2)) = (e1))))) -> (~((op (e1) (e0)) = (op (e2) (e0)))) -> ((~((op (e2) (e3)) = (e0)))\/((op (e2) (e0)) = (e3))) -> ((~((op (e2) (e1)) = (e0)))\/((op (e2) (e0)) = (e1))) -> (((op (e0) (e0)) = (e1))\/(((op (e1) (e0)) = (e1))\/(((op (e2) (e0)) = (e1))\/((op (e3) (e0)) = (e1))))) -> (((op (e0) (e1)) = (e0))\/(((op (e1) (e1)) = (e0))\/(((op (e2) (e1)) = (e0))\/((op (e3) (e1)) = (e0))))) -> ((~((op (e2) (e2)) = (e0)))\/((op (e2) (e0)) = (e2))) -> (~((op (e0) (e0)) = (op (e2) (e0)))) -> (((op (e0) (e0)) = (e0))\/(((op (e1) (e0)) = (e0))\/(((op (e2) (e0)) = (e0))\/((op (e3) (e0)) = (e0))))) -> (~((op (e1) (e0)) = (e0))) -> ((~((op (e3) (e2)) = (e0)))\/((op (e3) (e0)) = (e2))) -> (~((e0) = (e2))) -> (((op (e1) (e0)) = (e0))\/(((op (e1) (e1)) = (e0))\/(((op (e1) (e2)) = (e0))\/((op (e1) (e3)) = (e0))))) -> (~((op (e0) (e2)) = (op (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 (e0) (e0)) = (e0))\/(((op (e0) (e1)) = (e0))\/(((op (e0) (e2)) = (e0))\/((op (e0) (e3)) = (e0))))) -> ((~((op (e3) (e0)) = (e0)))\/((op (e3) (e0)) = (e0))) -> ((~((op (e3) (e1)) = (e0)))\/((op (e3) (e0)) = (e1))) -> (~((e1) = (e3))) -> (~((op (e3) (e0)) = (op (e3) (e1)))) -> (~((op (e1) (e1)) = (op (e1) (e2)))) -> (~((op (e2) (e0)) = (op (e2) (e2)))) -> (~((op (e3) (e1)) = (op (e3) (e2)))) -> (~((op (e1) (e1)) = (op (e1) (e3)))) -> (~((op (e2) (e0)) = (op (e2) (e3)))) -> (~((op (e3) (e1)) = (op (e3) (e3)))) -> (((op (e0) (e3)) = (e0))\/(((op (e1) (e3)) = (e0))\/(((op (e2) (e3)) = (e0))\/((op (e3) (e3)) = (e0))))) -> (~((op (e1) (e0)) = (op (e1) (e1)))) -> ((~((op (e3) (e3)) = (e0)))\/((op (e3) (e0)) = (e3))) -> (~((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) (e3)) = (op (e1) (e3)))) -> (~((op (e2) (e0)) = (op (e3) (e0)))) -> ((~((op (e2) (e0)) = (e0)))\/((op (e2) (e0)) = (e0))) -> (~((op (e2) (e1)) = (e0))) -> ((op (e2) (e0)) = (e0)) -> (~((op (e2) (e2)) = (e0))) -> ((op (e3) (e0)) = (e1)) -> ((op (e1) (e0)) = (e3)) -> (~((op (e0) (e3)) = (e0))) -> (~((op (e1) (e2)) = (e0))) -> (~((op (e1) (e1)) = (e0))) -> ((op (e0) (e0)) = (e2)) -> (~((e1) = (e2))) -> False). % 18.68/18.89 do 0 intro. intros zenon_H3f zenon_H20b zenon_H233 zenon_H206 zenon_H1f0 zenon_H1fa zenon_H1ba zenon_H1e0 zenon_H1fe zenon_H168 zenon_H124 zenon_H136 zenon_H128 zenon_H13c zenon_H142 zenon_H179 zenon_H178 zenon_H183 zenon_He7 zenon_H19d zenon_H191 zenon_H205 zenon_H204 zenon_Ha8 zenon_H165 zenon_H2f zenon_H22d zenon_H133 zenon_H71 zenon_H6d zenon_Hd8 zenon_H54 zenon_H210 zenon_H4a zenon_H115 zenon_Hf3 zenon_H11f zenon_H22a zenon_Haf zenon_Hdf zenon_He2 zenon_H109 zenon_H106 zenon_H145 zenon_H1c7 zenon_H1d8 zenon_H189 zenon_H18c zenon_H160 zenon_H172 zenon_H62 zenon_H102 zenon_H101 zenon_H16f zenon_H153 zenon_H2b zenon_H6f zenon_Hc2 zenon_H1cc zenon_H13e zenon_H10e zenon_H212 zenon_H1a6 zenon_H1a5 zenon_H1d5 zenon_H10a zenon_He4 zenon_Hdb zenon_Hd5 zenon_He8 zenon_H9a zenon_H17e zenon_Ha1 zenon_H1c4 zenon_H173 zenon_H18f zenon_H139 zenon_H201 zenon_H94 zenon_H182 zenon_H235 zenon_H245 zenon_H185 zenon_H39 zenon_H3e zenon_H23 zenon_H1a7 zenon_H149 zenon_H22 zenon_H195 zenon_H6a zenon_H208 zenon_H74 zenon_H184 zenon_H1ed zenon_H95 zenon_H1cf zenon_H4f zenon_H52 zenon_H1a4 zenon_H57 zenon_H5b zenon_H130 zenon_H67 zenon_H45 zenon_H1ec zenon_H12b zenon_H1ac zenon_H14f zenon_H1d zenon_H17b zenon_H1ee zenon_H31 zenon_H34 zenon_H81 zenon_Hac zenon_H9e zenon_H76 zenon_H25 zenon_H24 zenon_H7b zenon_H7c. % 18.68/18.89 apply (zenon_or_s _ _ zenon_H1a7); [ zenon_intro zenon_H18b | zenon_intro zenon_H148 ]. % 18.68/18.89 apply (zenon_or_s _ _ zenon_H74); [ zenon_intro zenon_H42 | zenon_intro zenon_H77 ]. % 18.68/18.89 exact (zenon_H3f zenon_H42). % 18.68/18.89 apply (zenon_or_s _ _ zenon_H77); [ zenon_intro zenon_H49 | zenon_intro zenon_H78 ]. % 18.68/18.89 exact (zenon_H20b zenon_H49). % 18.68/18.89 apply (zenon_or_s _ _ zenon_H78); [ zenon_intro zenon_H48 | zenon_intro zenon_H1e ]. % 18.68/18.89 apply (zenon_or_s _ _ zenon_H22d); [ zenon_intro zenon_H7a | zenon_intro zenon_H22e ]. % 18.68/18.89 apply (zenon_L26_); trivial. % 18.68/18.89 apply (zenon_or_s _ _ zenon_H22e); [ zenon_intro zenon_Ha0 | zenon_intro zenon_H22f ]. % 18.68/18.89 apply (zenon_or_s _ _ zenon_H168); [ zenon_intro zenon_H3a | zenon_intro zenon_H169 ]. % 18.68/18.89 apply (zenon_L592_); trivial. % 18.68/18.89 apply (zenon_or_s _ _ zenon_H169); [ zenon_intro zenon_H99 | zenon_intro zenon_H16a ]. % 18.68/18.89 apply (zenon_L403_); trivial. % 18.68/18.89 apply (zenon_or_s _ _ zenon_H16a); [ zenon_intro zenon_Ha9 | zenon_intro zenon_He3 ]. % 18.68/18.89 apply (zenon_L358_); trivial. % 18.68/18.89 apply (zenon_or_s _ _ zenon_H22); [ zenon_intro zenon_H27 | zenon_intro zenon_H26 ]. % 18.68/18.89 exact (zenon_H23 zenon_H27). % 18.68/18.89 apply (zenon_or_s _ _ zenon_H26); [ zenon_intro zenon_H29 | zenon_intro zenon_H28 ]. % 18.68/18.89 exact (zenon_H24 zenon_H29). % 18.68/18.89 apply (zenon_or_s _ _ zenon_H28); [ zenon_intro zenon_H2a | zenon_intro zenon_H1f ]. % 18.68/18.89 exact (zenon_H25 zenon_H2a). % 18.68/18.89 apply (zenon_or_s _ _ zenon_H245); [ zenon_intro zenon_H49 | zenon_intro zenon_H246 ]. % 18.68/18.89 exact (zenon_H20b zenon_H49). % 18.68/18.89 apply (zenon_or_s _ _ zenon_H246); [ zenon_intro zenon_H29 | zenon_intro zenon_H247 ]. % 18.68/18.89 exact (zenon_H24 zenon_H29). % 18.68/18.89 apply (zenon_or_s _ _ zenon_H247); [ zenon_intro zenon_H36 | zenon_intro zenon_H1b1 ]. % 18.68/18.89 exact (zenon_H31 zenon_H36). % 18.68/18.89 apply (zenon_or_s _ _ zenon_H128); [ zenon_intro zenon_H9d | zenon_intro zenon_H129 ]. % 18.68/18.89 apply (zenon_L625_); trivial. % 18.68/18.89 apply (zenon_or_s _ _ zenon_H129); [ zenon_intro zenon_H10d | zenon_intro zenon_H12a ]. % 18.68/18.89 exact (zenon_H10a zenon_H10d). % 18.68/18.89 apply (zenon_or_s _ _ zenon_H12a); [ zenon_intro zenon_Hf0 | zenon_intro zenon_Hd6 ]. % 18.68/18.89 apply (zenon_or_s _ _ zenon_H18c); [ zenon_intro zenon_H86 | zenon_intro zenon_H18d ]. % 18.68/18.89 apply (zenon_L629_); trivial. % 18.68/18.89 apply (zenon_or_s _ _ zenon_H18d); [ zenon_intro zenon_H110 | zenon_intro zenon_H18e ]. % 18.68/18.89 apply (zenon_or_s _ _ zenon_H1a5); [ zenon_intro zenon_H99 | zenon_intro zenon_H1a8 ]. % 18.68/18.89 apply (zenon_L403_); trivial. % 18.68/18.89 apply (zenon_or_s _ _ zenon_H1a8); [ zenon_intro zenon_H13f | zenon_intro zenon_H1a9 ]. % 18.68/18.89 apply (zenon_L166_); trivial. % 18.68/18.89 apply (zenon_or_s _ _ zenon_H1a9); [ zenon_intro zenon_Ha6 | zenon_intro zenon_H161 ]. % 18.68/18.89 apply (zenon_L509_); trivial. % 18.68/18.89 apply (zenon_or_s _ _ zenon_H106); [ zenon_intro zenon_Hed | zenon_intro zenon_H107 ]. % 18.68/18.89 apply (zenon_L491_); trivial. % 18.68/18.89 apply (zenon_or_s _ _ zenon_H107); [ zenon_intro zenon_Ha5 | zenon_intro zenon_H108 ]. % 18.68/18.89 apply (zenon_L357_); trivial. % 18.68/18.89 apply (zenon_or_s _ _ zenon_H108); [ zenon_intro zenon_Hf1 | zenon_intro zenon_Hf4 ]. % 18.68/18.89 apply (zenon_L59_); trivial. % 18.68/18.89 apply (zenon_or_s _ _ zenon_H1d5); [ zenon_intro zenon_Hee | zenon_intro zenon_H1d6 ]. % 18.68/18.89 apply (zenon_L569_); trivial. % 18.68/18.89 apply (zenon_or_s _ _ zenon_H1d6); [ zenon_intro zenon_H1ca | zenon_intro zenon_H1d7 ]. % 18.68/18.89 apply (zenon_or_s _ _ zenon_H145); [ zenon_intro zenon_Hcd | zenon_intro zenon_H146 ]. % 18.68/18.89 apply (zenon_L137_); trivial. % 18.68/18.89 apply (zenon_or_s _ _ zenon_H146); [ zenon_intro zenon_Hd7 | zenon_intro zenon_H147 ]. % 18.68/18.89 apply (zenon_L503_); trivial. % 18.68/18.89 apply (zenon_or_s _ _ zenon_H147); [ zenon_intro zenon_H11d | zenon_intro zenon_Hf6 ]. % 18.68/18.89 apply (zenon_L224_); trivial. % 18.68/18.89 apply (zenon_L225_); trivial. % 18.68/18.89 apply (zenon_or_s _ _ zenon_H1d7); [ zenon_intro zenon_H176 | zenon_intro zenon_H11d ]. % 18.68/18.89 exact (zenon_H173 zenon_H176). % 18.68/18.89 apply (zenon_L510_); trivial. % 18.68/18.89 apply (zenon_or_s _ _ zenon_H18e); [ zenon_intro zenon_H113 | zenon_intro zenon_Hd7 ]. % 18.68/18.89 apply (zenon_L68_); trivial. % 18.68/18.89 apply (zenon_or_s _ _ zenon_H1d8); [ zenon_intro zenon_H10f | zenon_intro zenon_H1d9 ]. % 18.68/18.89 apply (zenon_L458_); trivial. % 18.68/18.89 apply (zenon_or_s _ _ zenon_H1d9); [ zenon_intro zenon_H110 | zenon_intro zenon_H1da ]. % 18.68/18.89 apply (zenon_L283_); trivial. % 18.68/18.89 apply (zenon_or_s _ _ zenon_H1da); [ zenon_intro zenon_H1ca | zenon_intro zenon_H14d ]. % 18.68/18.89 apply (zenon_or_s _ _ zenon_H1a5); [ zenon_intro zenon_H99 | zenon_intro zenon_H1a8 ]. % 18.68/18.89 apply (zenon_L403_); trivial. % 18.68/18.89 apply (zenon_or_s _ _ zenon_H1a8); [ zenon_intro zenon_H13f | zenon_intro zenon_H1a9 ]. % 18.68/18.89 apply (zenon_or_s _ _ zenon_H106); [ zenon_intro zenon_Hed | zenon_intro zenon_H107 ]. % 18.68/18.89 apply (zenon_L214_); trivial. % 18.68/18.89 apply (zenon_or_s _ _ zenon_H107); [ zenon_intro zenon_Ha5 | zenon_intro zenon_H108 ]. % 18.68/18.89 apply (zenon_L373_); trivial. % 18.68/18.89 apply (zenon_or_s _ _ zenon_H108); [ zenon_intro zenon_Hf1 | zenon_intro zenon_Hf4 ]. % 18.68/18.89 apply (zenon_L59_); trivial. % 18.68/18.89 apply (zenon_or_s _ _ zenon_He7); [ zenon_intro zenon_H3b | zenon_intro zenon_He9 ]. % 18.68/18.89 apply (zenon_L408_); trivial. % 18.68/18.89 apply (zenon_or_s _ _ zenon_He9); [ zenon_intro zenon_Ha6 | zenon_intro zenon_Hea ]. % 18.68/18.89 apply (zenon_L207_); trivial. % 18.68/18.89 apply (zenon_or_s _ _ zenon_Hea); [ zenon_intro zenon_Haa | zenon_intro zenon_Hdd ]. % 18.68/18.89 apply (zenon_L495_); trivial. % 18.68/18.89 apply (zenon_L54_); trivial. % 18.68/18.89 apply (zenon_or_s _ _ zenon_H1a9); [ zenon_intro zenon_Ha6 | zenon_intro zenon_H161 ]. % 18.68/18.89 apply (zenon_L207_); trivial. % 18.68/18.89 apply (zenon_L503_); trivial. % 18.68/18.89 apply (zenon_L505_); trivial. % 18.68/18.89 apply (zenon_L630_); trivial. % 18.68/18.89 apply (zenon_or_s _ _ zenon_H22f); [ zenon_intro zenon_H122 | zenon_intro zenon_Hc3 ]. % 18.68/18.89 apply (zenon_L355_); trivial. % 18.68/18.89 apply (zenon_L634_); trivial. % 18.68/18.89 exact (zenon_H76 zenon_H1e). % 18.68/18.89 apply (zenon_or_s _ _ zenon_H74); [ zenon_intro zenon_H42 | zenon_intro zenon_H77 ]. % 18.68/18.89 exact (zenon_H3f zenon_H42). % 18.68/18.89 apply (zenon_or_s _ _ zenon_H77); [ zenon_intro zenon_H49 | zenon_intro zenon_H78 ]. % 18.68/18.89 exact (zenon_H20b zenon_H49). % 18.68/18.89 apply (zenon_or_s _ _ zenon_H78); [ zenon_intro zenon_H48 | zenon_intro zenon_H1e ]. % 18.68/18.89 apply (zenon_or_s _ _ zenon_H22d); [ zenon_intro zenon_H7a | zenon_intro zenon_H22e ]. % 18.68/18.89 apply (zenon_L107_); trivial. % 18.68/18.89 apply (zenon_or_s _ _ zenon_H22e); [ zenon_intro zenon_Ha0 | zenon_intro zenon_H22f ]. % 18.68/18.89 apply (zenon_L635_); trivial. % 18.68/18.89 apply (zenon_or_s _ _ zenon_H22f); [ zenon_intro zenon_H122 | zenon_intro zenon_Hc3 ]. % 18.68/18.89 apply (zenon_L438_); trivial. % 18.68/18.89 apply (zenon_L636_); trivial. % 18.68/18.89 exact (zenon_H76 zenon_H1e). % 18.68/18.89 (* end of lemma zenon_L637_ *) % 18.68/18.89 assert (zenon_L638_ : ((op (e1) (e0)) = (e2)) -> (((op (e0) (e0)) = (e1))\/(((op (e1) (e0)) = (e1))\/(((op (e2) (e0)) = (e1))\/((op (e3) (e0)) = (e1))))) -> (~((op (e0) (e3)) = (op (e1) (e3)))) -> (((op (e0) (e1)) = (e2))\/(((op (e1) (e1)) = (e2))\/(((op (e2) (e1)) = (e2))\/((op (e3) (e1)) = (e2))))) -> (~((e2) = (e3))) -> ((op (e2) (e0)) = (e0)) -> (~((op (e0) (e1)) = (op (e1) (e1)))) -> (((op (e0) (e3)) = (e2))\/(((op (e1) (e3)) = (e2))\/(((op (e2) (e3)) = (e2))\/((op (e3) (e3)) = (e2))))) -> (~((e1) = (e2))) -> (~((op (e1) (e1)) = (op (e1) (e3)))) -> (~((op (e2) (e1)) = (op (e2) (e3)))) -> (~((op (e3) (e2)) = (op (e3) (e3)))) -> (~((op (e1) (e1)) = (e1))) -> (~((op (e1) (e1)) = (e0))) -> (((op (e1) (e1)) = (e0))\/(((op (e1) (e1)) = (e1))\/(((op (e1) (e1)) = (e2))\/((op (e1) (e1)) = (e3))))) -> (~((e0) = (e2))) -> (((op (e0) (e2)) = (e2))\/(((op (e1) (e2)) = (e2))\/(((op (e2) (e2)) = (e2))\/((op (e3) (e2)) = (e2))))) -> (((op (e2) (e0)) = (e2))\/(((op (e2) (e1)) = (e2))\/(((op (e2) (e2)) = (e2))\/((op (e2) (e3)) = (e2))))) -> ((op (e0) (e0)) = (e2)) -> (~((op (e0) (e0)) = (op (e2) (e0)))) -> (~((op (e2) (e1)) = (op (e3) (e1)))) -> (~((op (e2) (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) (e3)) = (op (e3) (e3)))) -> (~((op (e2) (e3)) = (op (e3) (e3)))) -> (~((op (e3) (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 (e0) (e3)) = (e0))) -> ((~((op (e0) (e2)) = (e0)))\/((op (e0) (e0)) = (e2))) -> ((~((op (e1) (e0)) = (e0)))\/((op (e1) (e0)) = (e0))) -> (~((op (e1) (e0)) = (op (e2) (e0)))) -> (~((op (e2) (e0)) = (op (e2) (e1)))) -> (~((op (e1) (e0)) = (op (e3) (e0)))) -> (((op (e0) (e0)) = (e0))\/(((op (e0) (e1)) = (e0))\/(((op (e0) (e2)) = (e0))\/((op (e0) (e3)) = (e0))))) -> (~((op (e3) (e0)) = (op (e3) (e2)))) -> (~((op (e2) (e2)) = (op (e2) (e3)))) -> (~((op (e3) (e0)) = (op (e3) (e3)))) -> (~((op (e0) (e1)) = (op (e0) (e2)))) -> (~((op (e1) (e1)) = (op (e1) (e2)))) -> (~((op (e2) (e0)) = (op (e2) (e2)))) -> (((op (e0) (e3)) = (e0))\/(((op (e1) (e3)) = (e0))\/(((op (e2) (e3)) = (e0))\/((op (e3) (e3)) = (e0))))) -> (~((op (e2) (e0)) = (op (e2) (e3)))) -> (~((op (e0) (e1)) = (op (e0) (e3)))) -> (((op (e0) (e2)) = (e0))\/(((op (e1) (e2)) = (e0))\/(((op (e2) (e2)) = (e0))\/((op (e3) (e2)) = (e0))))) -> (~((op (e1) (e0)) = (op (e1) (e1)))) -> (((op (e1) (e0)) = (e0))\/(((op (e1) (e1)) = (e0))\/(((op (e1) (e2)) = (e0))\/((op (e1) (e3)) = (e0))))) -> ((~((op (e3) (e1)) = (e0)))\/((op (e3) (e0)) = (e1))) -> ((~((op (e3) (e3)) = (e0)))\/((op (e3) (e0)) = (e3))) -> (~((op (e3) (e0)) = (op (e3) (e1)))) -> (((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 (e2) (e2)) = (e0))\/(((op (e2) (e2)) = (e1))\/(((op (e2) (e2)) = (e2))\/((op (e2) (e2)) = (e3))))) -> (((op (e3) (e0)) = (e0))\/(((op (e3) (e1)) = (e0))\/(((op (e3) (e2)) = (e0))\/((op (e3) (e3)) = (e0))))) -> (((op (e0) (e0)) = (e3))\/(((op (e1) (e0)) = (e3))\/(((op (e2) (e0)) = (e3))\/((op (e3) (e0)) = (e3))))) -> ((~((op (e2) (e0)) = (e0)))\/((op (e2) (e0)) = (e0))) -> (((op (e0) (e0)) = (e2))\/(((op (e1) (e0)) = (e2))\/(((op (e2) (e0)) = (e2))\/((op (e3) (e0)) = (e2))))) -> ((~((op (e2) (e1)) = (e0)))\/((op (e2) (e0)) = (e1))) -> (((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)) = (e3))\/(((op (e3) (e1)) = (e3))\/(((op (e3) (e2)) = (e3))\/((op (e3) (e3)) = (e3))))) -> (~((op (e1) (e1)) = (op (e3) (e1)))) -> (((op (e0) (e0)) = (e3))\/(((op (e0) (e1)) = (e3))\/(((op (e0) (e2)) = (e3))\/((op (e0) (e3)) = (e3))))) -> (((op (e1) (e0)) = (e3))\/(((op (e1) (e1)) = (e3))\/(((op (e1) (e2)) = (e3))\/((op (e1) (e3)) = (e3))))) -> (~((op (e1) (e2)) = (op (e1) (e3)))) -> (((op (e0) (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) (e0)) = (e1))\/(((op (e1) (e1)) = (e1))\/(((op (e1) (e2)) = (e1))\/((op (e1) (e3)) = (e1))))) -> (((op (e0) (e2)) = (e1))\/(((op (e1) (e2)) = (e1))\/(((op (e2) (e2)) = (e1))\/((op (e3) (e2)) = (e1))))) -> (~((op (e0) (e0)) = (op (e0) (e2)))) -> (~((op (e1) (e1)) = (op (e2) (e1)))) -> ((~((op (e1) (e3)) = (e0)))\/((op (e1) (e0)) = (e3))) -> ((~((op (e1) (e2)) = (e0)))\/((op (e1) (e0)) = (e2))) -> (~((op (e0) (e1)) = (op (e2) (e1)))) -> (~((op (e2) (e0)) = (op (e3) (e0)))) -> (((op (e0) (e0)) = (e2))\/(((op (e0) (e1)) = (e2))\/(((op (e0) (e2)) = (e2))\/((op (e0) (e3)) = (e2))))) -> ((~((op (e3) (e0)) = (e0)))\/((op (e3) (e0)) = (e0))) -> ((~((op (e2) (e2)) = (e0)))\/((op (e2) (e0)) = (e2))) -> (~((op (e0) (e0)) = (op (e0) (e3)))) -> (((op (e0) (e1)) = (e1))\/(((op (e1) (e1)) = (e1))\/(((op (e2) (e1)) = (e1))\/((op (e3) (e1)) = (e1))))) -> (~((op (e1) (e2)) = (op (e2) (e2)))) -> (((op (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 (e0) (e3)) = (e0))\/(((op (e0) (e3)) = (e1))\/(((op (e0) (e3)) = (e2))\/((op (e0) (e3)) = (e3))))) -> (~((op (e0) (e3)) = (op (e2) (e3)))) -> (~((op (e1) (e3)) = (op (e3) (e3)))) -> (~((op (e1) (e0)) = (op (e1) (e3)))) -> (~((op (e1) (e3)) = (op (e2) (e3)))) -> (((op (e1) (e3)) = (e0))\/(((op (e1) (e3)) = (e1))\/(((op (e1) (e3)) = (e2))\/((op (e1) (e3)) = (e3))))) -> (((op (e3) (e0)) = (e1))\/(((op (e3) (e1)) = (e1))\/(((op (e3) (e2)) = (e1))\/((op (e3) (e3)) = (e1))))) -> (~((op (e0) (e2)) = (op (e2) (e2)))) -> (~((e0) = (e1))) -> (((op (e2) (e3)) = (e0))\/(((op (e2) (e3)) = (e1))\/(((op (e2) (e3)) = (e2))\/((op (e2) (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)) = (e0))\/(((op (e1) (e2)) = (e1))\/(((op (e1) (e2)) = (e2))\/((op (e1) (e2)) = (e3))))) -> (~((op (e0) (e2)) = (op (e1) (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) (e2)) = (e0)))\/((op (e3) (e0)) = (e2))) -> (~((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)) = (e3))\/(((op (e1) (e1)) = (e3))\/(((op (e2) (e1)) = (e3))\/((op (e3) (e1)) = (e3))))) -> ((~((op (e2) (e3)) = (e0)))\/((op (e2) (e0)) = (e3))) -> ((~((op (e1) (e1)) = (e0)))\/((op (e1) (e0)) = (e1))) -> ((~((op (e0) (e3)) = (e0)))\/((op (e0) (e0)) = (e3))) -> (((op (e0) (e1)) = (e0))\/(((op (e0) (e1)) = (e1))\/(((op (e0) (e1)) = (e2))\/((op (e0) (e1)) = (e3))))) -> (((op (e3) (e1)) = (e0))\/(((op (e3) (e1)) = (e1))\/(((op (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) (e1)) = (e0))) -> (~((op (e0) (e0)) = (e0))) -> (~((op (e1) (e0)) = (e0))) -> (((op (e0) (e0)) = (e0))\/(((op (e1) (e0)) = (e0))\/(((op (e2) (e0)) = (e0))\/((op (e3) (e0)) = (e0))))) -> (~((op (e2) (e1)) = (e0))) -> (((op (e0) (e1)) = (e0))\/(((op (e1) (e1)) = (e0))\/(((op (e2) (e1)) = (e0))\/((op (e3) (e1)) = (e0))))) -> (~((e0) = (e3))) -> ((op (e0) (e2)) = (e0)) -> ((op (e0) (e3)) = (e1)) -> (~((e1) = (e3))) -> False). % 18.68/18.90 do 0 intro. intros zenon_H86 zenon_H235 zenon_H1d zenon_H1d8 zenon_H12b zenon_H34 zenon_H10e zenon_H145 zenon_H7c zenon_H57 zenon_H1c7 zenon_H62 zenon_H10a zenon_H24 zenon_H142 zenon_H149 zenon_H172 zenon_H1d5 zenon_H7b zenon_H39 zenon_Haf zenon_H173 zenon_H101 zenon_H130 zenon_Hc2 zenon_Hf3 zenon_H102 zenon_H208 zenon_H2f zenon_H76 zenon_H233 zenon_H206 zenon_H201 zenon_H1f0 zenon_H1fa zenon_H74 zenon_H6f zenon_H6d zenon_H71 zenon_H4a zenon_H4f zenon_H52 zenon_H67 zenon_H5b zenon_H54 zenon_H6a zenon_H45 zenon_H22 zenon_H1ed zenon_H1ec zenon_H1cf zenon_H1ba zenon_H1cc zenon_H1c4 zenon_H1ac zenon_H1e0 zenon_H1ee zenon_H1fe zenon_H182 zenon_H153 zenon_H14f zenon_H165 zenon_H160 zenon_H168 zenon_H16f zenon_H124 zenon_H133 zenon_H136 zenon_H128 zenon_H139 zenon_H13c zenon_H13e zenon_H179 zenon_H178 zenon_H17e zenon_H17b zenon_H183 zenon_H184 zenon_H185 zenon_H189 zenon_H109 zenon_H2b zenon_H106 zenon_He7 zenon_He4 zenon_He2 zenon_Hd5 zenon_Hd8 zenon_Hdb zenon_Hdf zenon_He8 zenon_Ha8 zenon_Ha1 zenon_H11f zenon_H115 zenon_H18c zenon_H19d zenon_H195 zenon_H191 zenon_H18f zenon_H1a7 zenon_H1a4 zenon_H1a6 zenon_H1a5 zenon_H94 zenon_H205 zenon_H204 zenon_H212 zenon_H22a zenon_H210 zenon_H22d zenon_H20b zenon_H3f zenon_H23 zenon_H3e zenon_H31 zenon_H245 zenon_H9a zenon_H48 zenon_Hc3 zenon_H95. % 18.68/18.90 apply (zenon_or_s _ _ zenon_H168); [ zenon_intro zenon_H3a | zenon_intro zenon_H169 ]. % 18.68/18.90 apply (zenon_L494_); trivial. % 18.68/18.90 apply (zenon_or_s _ _ zenon_H169); [ zenon_intro zenon_H99 | zenon_intro zenon_H16a ]. % 18.68/18.90 apply (zenon_L632_); trivial. % 18.68/18.90 apply (zenon_or_s _ _ zenon_H16a); [ zenon_intro zenon_Ha9 | zenon_intro zenon_He3 ]. % 18.68/18.90 apply (zenon_L358_); trivial. % 18.68/18.90 apply (zenon_L633_); trivial. % 18.68/18.90 (* end of lemma zenon_L638_ *) % 18.68/18.90 assert (zenon_L639_ : ((op (e3) (e0)) = (e1)) -> ((op (e1) (e0)) = (e3)) -> (~((op (e2) (e2)) = (e0))) -> ((op (e1) (e0)) = (e2)) -> (((op (e0) (e0)) = (e1))\/(((op (e1) (e0)) = (e1))\/(((op (e2) (e0)) = (e1))\/((op (e3) (e0)) = (e1))))) -> (~((op (e0) (e3)) = (op (e1) (e3)))) -> (((op (e0) (e1)) = (e2))\/(((op (e1) (e1)) = (e2))\/(((op (e2) (e1)) = (e2))\/((op (e3) (e1)) = (e2))))) -> (~((e2) = (e3))) -> ((op (e2) (e0)) = (e0)) -> (~((op (e0) (e1)) = (op (e1) (e1)))) -> (((op (e0) (e3)) = (e2))\/(((op (e1) (e3)) = (e2))\/(((op (e2) (e3)) = (e2))\/((op (e3) (e3)) = (e2))))) -> (~((e1) = (e2))) -> (~((op (e1) (e1)) = (op (e1) (e3)))) -> (~((op (e2) (e1)) = (op (e2) (e3)))) -> (~((op (e3) (e2)) = (op (e3) (e3)))) -> (~((op (e1) (e1)) = (e1))) -> (~((op (e1) (e1)) = (e0))) -> (((op (e1) (e1)) = (e0))\/(((op (e1) (e1)) = (e1))\/(((op (e1) (e1)) = (e2))\/((op (e1) (e1)) = (e3))))) -> (~((e0) = (e2))) -> (((op (e0) (e2)) = (e2))\/(((op (e1) (e2)) = (e2))\/(((op (e2) (e2)) = (e2))\/((op (e3) (e2)) = (e2))))) -> (((op (e2) (e0)) = (e2))\/(((op (e2) (e1)) = (e2))\/(((op (e2) (e2)) = (e2))\/((op (e2) (e3)) = (e2))))) -> ((op (e0) (e0)) = (e2)) -> (~((op (e0) (e0)) = (op (e2) (e0)))) -> (~((op (e2) (e1)) = (op (e3) (e1)))) -> (~((op (e2) (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) (e3)) = (op (e3) (e3)))) -> (~((op (e2) (e3)) = (op (e3) (e3)))) -> (~((op (e3) (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 (e0) (e3)) = (e0))) -> ((~((op (e0) (e2)) = (e0)))\/((op (e0) (e0)) = (e2))) -> ((~((op (e1) (e0)) = (e0)))\/((op (e1) (e0)) = (e0))) -> (~((op (e1) (e0)) = (op (e2) (e0)))) -> (~((op (e2) (e0)) = (op (e2) (e1)))) -> (~((op (e1) (e0)) = (op (e3) (e0)))) -> (((op (e0) (e0)) = (e0))\/(((op (e0) (e1)) = (e0))\/(((op (e0) (e2)) = (e0))\/((op (e0) (e3)) = (e0))))) -> (~((op (e3) (e0)) = (op (e3) (e2)))) -> (~((op (e2) (e2)) = (op (e2) (e3)))) -> (~((op (e3) (e0)) = (op (e3) (e3)))) -> (~((op (e0) (e1)) = (op (e0) (e2)))) -> (~((op (e1) (e1)) = (op (e1) (e2)))) -> (~((op (e2) (e0)) = (op (e2) (e2)))) -> (((op (e0) (e3)) = (e0))\/(((op (e1) (e3)) = (e0))\/(((op (e2) (e3)) = (e0))\/((op (e3) (e3)) = (e0))))) -> (~((op (e2) (e0)) = (op (e2) (e3)))) -> (~((op (e0) (e1)) = (op (e0) (e3)))) -> (((op (e0) (e2)) = (e0))\/(((op (e1) (e2)) = (e0))\/(((op (e2) (e2)) = (e0))\/((op (e3) (e2)) = (e0))))) -> (~((op (e1) (e0)) = (op (e1) (e1)))) -> (((op (e1) (e0)) = (e0))\/(((op (e1) (e1)) = (e0))\/(((op (e1) (e2)) = (e0))\/((op (e1) (e3)) = (e0))))) -> ((~((op (e3) (e1)) = (e0)))\/((op (e3) (e0)) = (e1))) -> ((~((op (e3) (e3)) = (e0)))\/((op (e3) (e0)) = (e3))) -> (~((op (e3) (e0)) = (op (e3) (e1)))) -> (((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 (e2) (e2)) = (e0))\/(((op (e2) (e2)) = (e1))\/(((op (e2) (e2)) = (e2))\/((op (e2) (e2)) = (e3))))) -> (((op (e3) (e0)) = (e0))\/(((op (e3) (e1)) = (e0))\/(((op (e3) (e2)) = (e0))\/((op (e3) (e3)) = (e0))))) -> (((op (e0) (e0)) = (e3))\/(((op (e1) (e0)) = (e3))\/(((op (e2) (e0)) = (e3))\/((op (e3) (e0)) = (e3))))) -> ((~((op (e2) (e0)) = (e0)))\/((op (e2) (e0)) = (e0))) -> (((op (e0) (e0)) = (e2))\/(((op (e1) (e0)) = (e2))\/(((op (e2) (e0)) = (e2))\/((op (e3) (e0)) = (e2))))) -> ((~((op (e2) (e1)) = (e0)))\/((op (e2) (e0)) = (e1))) -> (((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)) = (e3))\/(((op (e3) (e1)) = (e3))\/(((op (e3) (e2)) = (e3))\/((op (e3) (e3)) = (e3))))) -> (~((op (e1) (e1)) = (op (e3) (e1)))) -> (((op (e0) (e0)) = (e3))\/(((op (e0) (e1)) = (e3))\/(((op (e0) (e2)) = (e3))\/((op (e0) (e3)) = (e3))))) -> (((op (e1) (e0)) = (e3))\/(((op (e1) (e1)) = (e3))\/(((op (e1) (e2)) = (e3))\/((op (e1) (e3)) = (e3))))) -> (~((op (e1) (e2)) = (op (e1) (e3)))) -> (((op (e0) (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) (e0)) = (e1))\/(((op (e1) (e1)) = (e1))\/(((op (e1) (e2)) = (e1))\/((op (e1) (e3)) = (e1))))) -> (((op (e0) (e2)) = (e1))\/(((op (e1) (e2)) = (e1))\/(((op (e2) (e2)) = (e1))\/((op (e3) (e2)) = (e1))))) -> (~((op (e0) (e0)) = (op (e0) (e2)))) -> (~((op (e1) (e1)) = (op (e2) (e1)))) -> ((~((op (e1) (e3)) = (e0)))\/((op (e1) (e0)) = (e3))) -> ((~((op (e1) (e2)) = (e0)))\/((op (e1) (e0)) = (e2))) -> (~((op (e0) (e1)) = (op (e2) (e1)))) -> (~((op (e2) (e0)) = (op (e3) (e0)))) -> (((op (e0) (e0)) = (e2))\/(((op (e0) (e1)) = (e2))\/(((op (e0) (e2)) = (e2))\/((op (e0) (e3)) = (e2))))) -> ((~((op (e3) (e0)) = (e0)))\/((op (e3) (e0)) = (e0))) -> ((~((op (e2) (e2)) = (e0)))\/((op (e2) (e0)) = (e2))) -> (~((op (e0) (e0)) = (op (e0) (e3)))) -> (((op (e0) (e1)) = (e1))\/(((op (e1) (e1)) = (e1))\/(((op (e2) (e1)) = (e1))\/((op (e3) (e1)) = (e1))))) -> (~((op (e1) (e2)) = (op (e2) (e2)))) -> (((op (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 (e0) (e3)) = (e0))\/(((op (e0) (e3)) = (e1))\/(((op (e0) (e3)) = (e2))\/((op (e0) (e3)) = (e3))))) -> (~((op (e0) (e3)) = (op (e2) (e3)))) -> (~((op (e1) (e3)) = (op (e3) (e3)))) -> (~((op (e1) (e0)) = (op (e1) (e3)))) -> (~((op (e1) (e3)) = (op (e2) (e3)))) -> (((op (e1) (e3)) = (e0))\/(((op (e1) (e3)) = (e1))\/(((op (e1) (e3)) = (e2))\/((op (e1) (e3)) = (e3))))) -> (((op (e3) (e0)) = (e1))\/(((op (e3) (e1)) = (e1))\/(((op (e3) (e2)) = (e1))\/((op (e3) (e3)) = (e1))))) -> (~((op (e0) (e2)) = (op (e2) (e2)))) -> (~((e0) = (e1))) -> (((op (e2) (e3)) = (e0))\/(((op (e2) (e3)) = (e1))\/(((op (e2) (e3)) = (e2))\/((op (e2) (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)) = (e0))\/(((op (e1) (e2)) = (e1))\/(((op (e1) (e2)) = (e2))\/((op (e1) (e2)) = (e3))))) -> (~((op (e0) (e2)) = (op (e1) (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) (e2)) = (e0)))\/((op (e3) (e0)) = (e2))) -> (~((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)) = (e3))\/(((op (e1) (e1)) = (e3))\/(((op (e2) (e1)) = (e3))\/((op (e3) (e1)) = (e3))))) -> ((~((op (e2) (e3)) = (e0)))\/((op (e2) (e0)) = (e3))) -> ((~((op (e1) (e1)) = (e0)))\/((op (e1) (e0)) = (e1))) -> ((~((op (e0) (e3)) = (e0)))\/((op (e0) (e0)) = (e3))) -> (((op (e0) (e1)) = (e0))\/(((op (e0) (e1)) = (e1))\/(((op (e0) (e1)) = (e2))\/((op (e0) (e1)) = (e3))))) -> (((op (e3) (e1)) = (e0))\/(((op (e3) (e1)) = (e1))\/(((op (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) (e1)) = (e0))) -> (~((op (e0) (e0)) = (e0))) -> (~((op (e1) (e0)) = (e0))) -> (((op (e0) (e0)) = (e0))\/(((op (e1) (e0)) = (e0))\/(((op (e2) (e0)) = (e0))\/((op (e3) (e0)) = (e0))))) -> (~((op (e2) (e1)) = (e0))) -> (((op (e0) (e1)) = (e0))\/(((op (e1) (e1)) = (e0))\/(((op (e2) (e1)) = (e0))\/((op (e3) (e1)) = (e0))))) -> (~((e0) = (e3))) -> ((op (e0) (e2)) = (e0)) -> (~((e1) = (e3))) -> False). % 18.68/18.90 do 0 intro. intros zenon_Hac zenon_H9e zenon_H81 zenon_H86 zenon_H235 zenon_H1d zenon_H1d8 zenon_H12b zenon_H34 zenon_H10e zenon_H145 zenon_H7c zenon_H57 zenon_H1c7 zenon_H62 zenon_H10a zenon_H24 zenon_H142 zenon_H149 zenon_H172 zenon_H1d5 zenon_H7b zenon_H39 zenon_Haf zenon_H173 zenon_H101 zenon_H130 zenon_Hc2 zenon_Hf3 zenon_H102 zenon_H208 zenon_H2f zenon_H76 zenon_H233 zenon_H206 zenon_H201 zenon_H1f0 zenon_H1fa zenon_H74 zenon_H6f zenon_H6d zenon_H71 zenon_H4a zenon_H4f zenon_H52 zenon_H67 zenon_H5b zenon_H54 zenon_H6a zenon_H45 zenon_H22 zenon_H1ed zenon_H1ec zenon_H1cf zenon_H1ba zenon_H1cc zenon_H1c4 zenon_H1ac zenon_H1e0 zenon_H1ee zenon_H1fe zenon_H182 zenon_H153 zenon_H14f zenon_H165 zenon_H160 zenon_H168 zenon_H16f zenon_H124 zenon_H133 zenon_H136 zenon_H128 zenon_H139 zenon_H13c zenon_H13e zenon_H179 zenon_H178 zenon_H17e zenon_H17b zenon_H183 zenon_H184 zenon_H185 zenon_H189 zenon_H109 zenon_H2b zenon_H106 zenon_He7 zenon_He4 zenon_He2 zenon_Hd5 zenon_Hd8 zenon_Hdb zenon_Hdf zenon_He8 zenon_Ha8 zenon_Ha1 zenon_H11f zenon_H115 zenon_H18c zenon_H19d zenon_H195 zenon_H191 zenon_H18f zenon_H1a7 zenon_H1a4 zenon_H1a6 zenon_H1a5 zenon_H94 zenon_H205 zenon_H204 zenon_H212 zenon_H22a zenon_H210 zenon_H22d zenon_H20b zenon_H3f zenon_H23 zenon_H3e zenon_H31 zenon_H245 zenon_H9a zenon_H48 zenon_H95. % 18.68/18.90 apply (zenon_or_s _ _ zenon_H22d); [ zenon_intro zenon_H7a | zenon_intro zenon_H22e ]. % 18.68/18.90 apply (zenon_L456_); trivial. % 18.68/18.90 apply (zenon_or_s _ _ zenon_H22e); [ zenon_intro zenon_Ha0 | zenon_intro zenon_H22f ]. % 18.68/18.90 apply (zenon_or_s _ _ zenon_H168); [ zenon_intro zenon_H3a | zenon_intro zenon_H169 ]. % 18.68/18.90 apply (zenon_L592_); trivial. % 18.68/18.90 apply (zenon_or_s _ _ zenon_H169); [ zenon_intro zenon_H99 | zenon_intro zenon_H16a ]. % 18.68/18.90 apply (zenon_L403_); trivial. % 18.68/18.90 apply (zenon_or_s _ _ zenon_H16a); [ zenon_intro zenon_Ha9 | zenon_intro zenon_He3 ]. % 18.68/18.90 apply (zenon_L358_); trivial. % 18.68/18.90 apply (zenon_or_s _ _ zenon_H22); [ zenon_intro zenon_H27 | zenon_intro zenon_H26 ]. % 18.68/18.90 exact (zenon_H23 zenon_H27). % 18.68/18.90 apply (zenon_or_s _ _ zenon_H26); [ zenon_intro zenon_H29 | zenon_intro zenon_H28 ]. % 18.68/18.90 exact (zenon_H24 zenon_H29). % 18.68/18.90 apply (zenon_or_s _ _ zenon_H28); [ zenon_intro zenon_H2a | zenon_intro zenon_H1f ]. % 18.68/18.90 apply (zenon_L334_); trivial. % 18.68/18.90 apply (zenon_or_s _ _ zenon_H245); [ zenon_intro zenon_H49 | zenon_intro zenon_H246 ]. % 18.68/18.90 exact (zenon_H20b zenon_H49). % 18.68/18.90 apply (zenon_or_s _ _ zenon_H246); [ zenon_intro zenon_H29 | zenon_intro zenon_H247 ]. % 18.68/18.90 exact (zenon_H24 zenon_H29). % 18.68/18.90 apply (zenon_or_s _ _ zenon_H247); [ zenon_intro zenon_H36 | zenon_intro zenon_H1b1 ]. % 18.68/18.90 exact (zenon_H31 zenon_H36). % 18.68/18.90 apply (zenon_or_s _ _ zenon_H128); [ zenon_intro zenon_H9d | zenon_intro zenon_H129 ]. % 18.68/18.90 apply (zenon_L37_); trivial. % 18.68/18.90 apply (zenon_or_s _ _ zenon_H129); [ zenon_intro zenon_H10d | zenon_intro zenon_H12a ]. % 18.68/18.90 exact (zenon_H10a zenon_H10d). % 18.68/18.90 apply (zenon_or_s _ _ zenon_H12a); [ zenon_intro zenon_Hf0 | zenon_intro zenon_Hd6 ]. % 18.68/18.90 apply (zenon_L629_); trivial. % 18.68/18.90 apply (zenon_L630_); trivial. % 18.68/18.90 apply (zenon_or_s _ _ zenon_H22f); [ zenon_intro zenon_H122 | zenon_intro zenon_Hc3 ]. % 18.68/18.90 apply (zenon_L355_); trivial. % 18.68/18.90 apply (zenon_L638_); trivial. % 18.68/18.90 (* end of lemma zenon_L639_ *) % 18.68/18.90 assert (zenon_L640_ : ((op (e2) (e3)) = (e0)) -> ((op (e2) (e1)) = (e0)) -> (~((op (e2) (e1)) = (op (e2) (e3)))) -> False). % 18.68/18.90 do 0 intro. intros zenon_H37 zenon_H36 zenon_H1c7. % 18.68/18.90 elim (classic ((op (e2) (e3)) = (op (e2) (e3)))); [ zenon_intro zenon_H5c | zenon_intro zenon_H5d ]. % 18.68/18.90 cut (((op (e2) (e3)) = (op (e2) (e3))) = ((op (e2) (e1)) = (op (e2) (e3)))). % 18.68/18.90 intro zenon_D_pnotp. % 18.68/18.90 apply zenon_H1c7. % 18.68/18.90 rewrite <- zenon_D_pnotp. % 18.68/18.90 exact zenon_H5c. % 18.68/18.90 cut (((op (e2) (e3)) = (op (e2) (e3)))); [idtac | apply NNPP; zenon_intro zenon_H5d]. % 18.68/18.90 cut (((op (e2) (e3)) = (op (e2) (e1)))); [idtac | apply NNPP; zenon_intro zenon_H1c8]. % 18.68/18.90 congruence. % 18.68/18.90 cut (((op (e2) (e3)) = (e0)) = ((op (e2) (e3)) = (op (e2) (e1)))). % 18.68/18.90 intro zenon_D_pnotp. % 18.68/18.90 apply zenon_H1c8. % 18.68/18.90 rewrite <- zenon_D_pnotp. % 18.68/18.90 exact zenon_H37. % 18.68/18.90 cut (((e0) = (op (e2) (e1)))); [idtac | apply NNPP; zenon_intro zenon_H17f]. % 18.68/18.90 cut (((op (e2) (e3)) = (op (e2) (e3)))); [idtac | apply NNPP; zenon_intro zenon_H5d]. % 18.68/18.90 congruence. % 18.68/18.90 apply zenon_H5d. apply refl_equal. % 18.68/18.90 apply zenon_H17f. apply sym_equal. exact zenon_H36. % 18.68/18.90 apply zenon_H5d. apply refl_equal. % 18.68/18.90 apply zenon_H5d. apply refl_equal. % 18.68/18.90 (* end of lemma zenon_L640_ *) % 18.68/18.90 assert (zenon_L641_ : (((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) (e0)) = (e0)) -> (~((op (e1) (e0)) = (op (e1) (e3)))) -> (~((op (e2) (e1)) = (op (e2) (e3)))) -> ((op (e2) (e1)) = (e0)) -> ((op (e3) (e1)) = (e0)) -> (~((op (e3) (e1)) = (op (e3) (e3)))) -> False). % 18.68/18.90 do 0 intro. intros zenon_H67 zenon_H208 zenon_H48 zenon_H27 zenon_Hd8 zenon_H1c7 zenon_H36 zenon_H1b1 zenon_H130. % 18.68/18.90 apply (zenon_or_s _ _ zenon_H67); [ zenon_intro zenon_H1e | zenon_intro zenon_H68 ]. % 18.68/18.90 apply (zenon_L336_); trivial. % 18.68/18.90 apply (zenon_or_s _ _ zenon_H68); [ zenon_intro zenon_H1f | zenon_intro zenon_H69 ]. % 18.68/18.90 apply (zenon_L258_); trivial. % 18.68/18.90 apply (zenon_or_s _ _ zenon_H69); [ zenon_intro zenon_H37 | zenon_intro zenon_H60 ]. % 18.68/18.90 apply (zenon_L640_); trivial. % 18.68/18.90 apply (zenon_L244_); trivial. % 18.68/18.90 (* end of lemma zenon_L641_ *) % 18.68/18.90 assert (zenon_L642_ : (~((op (e2) (e0)) = (op (e2) (e1)))) -> ((op (e2) (e0)) = (e0)) -> ((op (e2) (e1)) = (e0)) -> False). % 18.68/18.90 do 0 intro. intros zenon_H1f0 zenon_H34 zenon_H36. % 18.68/18.90 cut (((op (e2) (e0)) = (e0)) = ((op (e2) (e0)) = (op (e2) (e1)))). % 18.68/18.90 intro zenon_D_pnotp. % 18.68/18.90 apply zenon_H1f0. % 18.68/18.90 rewrite <- zenon_D_pnotp. % 18.68/18.90 exact zenon_H34. % 18.68/18.90 cut (((e0) = (op (e2) (e1)))); [idtac | apply NNPP; zenon_intro zenon_H17f]. % 18.68/18.90 cut (((op (e2) (e0)) = (op (e2) (e0)))); [idtac | apply NNPP; zenon_intro zenon_H53]. % 18.68/18.90 congruence. % 18.68/18.90 apply zenon_H53. apply refl_equal. % 18.68/18.90 apply zenon_H17f. apply sym_equal. exact zenon_H36. % 18.68/18.90 (* end of lemma zenon_L642_ *) % 18.68/18.90 assert (zenon_L643_ : (((op (e0) (e0)) = (e0))\/(((op (e1) (e0)) = (e0))\/(((op (e2) (e0)) = (e0))\/((op (e3) (e0)) = (e0))))) -> (~((op (e0) (e0)) = (e0))) -> (~((op (e3) (e1)) = (op (e3) (e3)))) -> (~((op (e2) (e1)) = (op (e2) (e3)))) -> (~((op (e1) (e0)) = (op (e1) (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)) = (e0)) -> (~((op (e2) (e0)) = (op (e2) (e1)))) -> (~((op (e3) (e0)) = (op (e3) (e1)))) -> ((op (e3) (e1)) = (e0)) -> False). % 18.68/18.90 do 0 intro. intros zenon_H3e zenon_H3f zenon_H130 zenon_H1c7 zenon_Hd8 zenon_H48 zenon_H208 zenon_H67 zenon_H36 zenon_H1f0 zenon_H1cf zenon_H1b1. % 18.68/18.90 apply (zenon_or_s _ _ zenon_H3e); [ zenon_intro zenon_H42 | zenon_intro zenon_H41 ]. % 18.68/18.90 exact (zenon_H3f zenon_H42). % 18.68/18.90 apply (zenon_or_s _ _ zenon_H41); [ zenon_intro zenon_H27 | zenon_intro zenon_H43 ]. % 18.68/18.90 apply (zenon_L641_); trivial. % 18.68/18.90 apply (zenon_or_s _ _ zenon_H43); [ zenon_intro zenon_H34 | zenon_intro zenon_H44 ]. % 18.68/18.90 apply (zenon_L642_); trivial. % 18.68/18.90 apply (zenon_L346_); trivial. % 18.68/18.90 (* end of lemma zenon_L643_ *) % 18.68/18.90 assert (zenon_L644_ : (~((op (e1) (e0)) = (op (e1) (e2)))) -> ((op (e1) (e0)) = (e0)) -> ((op (e1) (e2)) = (e0)) -> False). % 18.68/18.90 do 0 intro. intros zenon_H24a zenon_H27 zenon_H2a. % 18.68/18.90 cut (((op (e1) (e0)) = (e0)) = ((op (e1) (e0)) = (op (e1) (e2)))). % 18.68/18.90 intro zenon_D_pnotp. % 18.68/18.90 apply zenon_H24a. % 18.68/18.90 rewrite <- zenon_D_pnotp. % 18.68/18.90 exact zenon_H27. % 18.68/18.90 cut (((e0) = (op (e1) (e2)))); [idtac | apply NNPP; zenon_intro zenon_H207]. % 18.68/18.90 cut (((op (e1) (e0)) = (op (e1) (e0)))); [idtac | apply NNPP; zenon_intro zenon_H47]. % 18.68/18.90 congruence. % 18.68/18.90 apply zenon_H47. apply refl_equal. % 18.68/18.90 apply zenon_H207. apply sym_equal. exact zenon_H2a. % 18.68/18.90 (* end of lemma zenon_L644_ *) % 18.68/18.90 assert (zenon_L645_ : ((op (e2) (e2)) = (e0)) -> ((op (e2) (e1)) = (e0)) -> (~((op (e2) (e1)) = (op (e2) (e2)))) -> False). % 18.68/18.90 do 0 intro. intros zenon_H2c zenon_H36 zenon_H24b. % 18.68/18.90 elim (classic ((op (e2) (e2)) = (op (e2) (e2)))); [ zenon_intro zenon_H1a2 | zenon_intro zenon_H190 ]. % 18.68/18.90 cut (((op (e2) (e2)) = (op (e2) (e2))) = ((op (e2) (e1)) = (op (e2) (e2)))). % 18.68/18.90 intro zenon_D_pnotp. % 18.68/18.90 apply zenon_H24b. % 18.68/18.90 rewrite <- zenon_D_pnotp. % 18.68/18.90 exact zenon_H1a2. % 18.68/18.90 cut (((op (e2) (e2)) = (op (e2) (e2)))); [idtac | apply NNPP; zenon_intro zenon_H190]. % 18.68/18.90 cut (((op (e2) (e2)) = (op (e2) (e1)))); [idtac | apply NNPP; zenon_intro zenon_H24c]. % 18.68/18.90 congruence. % 18.68/18.90 cut (((op (e2) (e2)) = (e0)) = ((op (e2) (e2)) = (op (e2) (e1)))). % 18.68/18.90 intro zenon_D_pnotp. % 18.68/18.90 apply zenon_H24c. % 18.68/18.90 rewrite <- zenon_D_pnotp. % 18.68/18.90 exact zenon_H2c. % 18.68/18.90 cut (((e0) = (op (e2) (e1)))); [idtac | apply NNPP; zenon_intro zenon_H17f]. % 18.68/18.90 cut (((op (e2) (e2)) = (op (e2) (e2)))); [idtac | apply NNPP; zenon_intro zenon_H190]. % 18.68/18.90 congruence. % 18.68/18.90 apply zenon_H190. apply refl_equal. % 18.68/18.90 apply zenon_H17f. apply sym_equal. exact zenon_H36. % 18.68/18.90 apply zenon_H190. apply refl_equal. % 18.68/18.90 apply zenon_H190. apply refl_equal. % 18.68/18.90 (* end of lemma zenon_L645_ *) % 18.68/18.90 assert (zenon_L646_ : (((op (e0) (e2)) = (e0))\/(((op (e1) (e2)) = (e0))\/(((op (e2) (e2)) = (e0))\/((op (e3) (e2)) = (e0))))) -> (~((op (e3) (e0)) = (op (e3) (e1)))) -> (~((op (e2) (e0)) = (op (e2) (e1)))) -> (((op (e0) (e3)) = (e0))\/(((op (e1) (e3)) = (e0))\/(((op (e2) (e3)) = (e0))\/((op (e3) (e3)) = (e0))))) -> (~((op (e0) (e2)) = (op (e0) (e3)))) -> (~((op (e1) (e0)) = (op (e1) (e3)))) -> (~((op (e2) (e1)) = (op (e2) (e3)))) -> (~((op (e3) (e1)) = (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) (e0)) = (e0)) -> (~((op (e1) (e0)) = (op (e1) (e2)))) -> (~((op (e2) (e1)) = (op (e2) (e2)))) -> ((op (e2) (e1)) = (e0)) -> (~((op (e3) (e1)) = (op (e3) (e2)))) -> ((op (e3) (e1)) = (e0)) -> False). % 18.68/18.90 do 0 intro. intros zenon_H6a zenon_H1cf zenon_H1f0 zenon_H67 zenon_H208 zenon_Hd8 zenon_H1c7 zenon_H130 zenon_H3f zenon_H3e zenon_H27 zenon_H24a zenon_H24b zenon_H36 zenon_H1a4 zenon_H1b1. % 18.68/18.90 apply (zenon_or_s _ _ zenon_H6a); [ zenon_intro zenon_H48 | zenon_intro zenon_H6b ]. % 18.68/18.90 apply (zenon_L643_); trivial. % 18.68/18.90 apply (zenon_or_s _ _ zenon_H6b); [ zenon_intro zenon_H2a | zenon_intro zenon_H6c ]. % 18.68/18.90 apply (zenon_L644_); trivial. % 18.68/18.90 apply (zenon_or_s _ _ zenon_H6c); [ zenon_intro zenon_H2c | zenon_intro zenon_H61 ]. % 18.68/18.90 apply (zenon_L645_); trivial. % 18.68/18.90 apply (zenon_L247_); trivial. % 18.68/18.90 (* end of lemma zenon_L646_ *) % 18.68/18.90 assert (zenon_L647_ : (~((op (e3) (e1)) = (op (e3) (e2)))) -> (~((op (e2) (e1)) = (op (e2) (e2)))) -> (~((op (e1) (e0)) = (op (e1) (e2)))) -> (((op (e0) (e0)) = (e0))\/(((op (e1) (e0)) = (e0))\/(((op (e2) (e0)) = (e0))\/((op (e3) (e0)) = (e0))))) -> (~((op (e0) (e0)) = (e0))) -> (~((op (e3) (e1)) = (op (e3) (e3)))) -> (~((op (e2) (e1)) = (op (e2) (e3)))) -> (~((op (e1) (e0)) = (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 (e0) (e2)) = (e0))\/(((op (e1) (e2)) = (e0))\/(((op (e2) (e2)) = (e0))\/((op (e3) (e2)) = (e0))))) -> ((op (e2) (e1)) = (e0)) -> (~((op (e2) (e0)) = (op (e2) (e1)))) -> (~((op (e3) (e0)) = (op (e3) (e1)))) -> ((op (e3) (e1)) = (e0)) -> False). % 18.68/18.90 do 0 intro. intros zenon_H1a4 zenon_H24b zenon_H24a zenon_H3e zenon_H3f zenon_H130 zenon_H1c7 zenon_Hd8 zenon_H208 zenon_H67 zenon_H6a zenon_H36 zenon_H1f0 zenon_H1cf zenon_H1b1. % 18.68/18.90 apply (zenon_or_s _ _ zenon_H3e); [ zenon_intro zenon_H42 | zenon_intro zenon_H41 ]. % 18.68/18.90 exact (zenon_H3f zenon_H42). % 18.68/18.90 apply (zenon_or_s _ _ zenon_H41); [ zenon_intro zenon_H27 | zenon_intro zenon_H43 ]. % 18.68/18.90 apply (zenon_L646_); trivial. % 18.68/18.90 apply (zenon_or_s _ _ zenon_H43); [ zenon_intro zenon_H34 | zenon_intro zenon_H44 ]. % 18.68/18.90 apply (zenon_L642_); trivial. % 18.68/18.90 apply (zenon_L346_); trivial. % 18.68/18.90 (* end of lemma zenon_L647_ *) % 18.68/18.90 assert (zenon_L648_ : (((op (e0) (e0)) = (e0))\/(((op (e0) (e1)) = (e0))\/(((op (e0) (e2)) = (e0))\/((op (e0) (e3)) = (e0))))) -> (~((op (e2) (e3)) = (e0))) -> (~((op (e3) (e1)) = (op (e3) (e2)))) -> (~((op (e2) (e1)) = (op (e2) (e2)))) -> (~((op (e1) (e0)) = (op (e1) (e2)))) -> (((op (e0) (e0)) = (e0))\/(((op (e1) (e0)) = (e0))\/(((op (e2) (e0)) = (e0))\/((op (e3) (e0)) = (e0))))) -> (~((op (e0) (e0)) = (e0))) -> (~((op (e3) (e1)) = (op (e3) (e3)))) -> (~((op (e2) (e1)) = (op (e2) (e3)))) -> (~((op (e1) (e0)) = (op (e1) (e3)))) -> (((op (e0) (e3)) = (e0))\/(((op (e1) (e3)) = (e0))\/(((op (e2) (e3)) = (e0))\/((op (e3) (e3)) = (e0))))) -> (~((op (e2) (e0)) = (op (e2) (e1)))) -> (~((op (e3) (e0)) = (op (e3) (e1)))) -> (~((op (e2) (e0)) = (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) (e3)) = (e0))) -> (~((op (e1) (e1)) = (e0))) -> (~((op (e0) (e1)) = (e0))) -> (((op (e0) (e1)) = (e0))\/(((op (e1) (e1)) = (e0))\/(((op (e2) (e1)) = (e0))\/((op (e3) (e1)) = (e0))))) -> (((op (e0) (e2)) = (e0))\/(((op (e1) (e2)) = (e0))\/(((op (e2) (e2)) = (e0))\/((op (e3) (e2)) = (e0))))) -> (~((op (e0) (e2)) = (op (e0) (e3)))) -> (~((op (e1) (e2)) = (e0))) -> (~((op (e2) (e2)) = (e0))) -> (~((op (e3) (e2)) = (e0))) -> False). % 18.68/18.90 do 0 intro. intros zenon_H74 zenon_H32 zenon_H1a4 zenon_H24b zenon_H24a zenon_H3e zenon_H3f zenon_H130 zenon_H1c7 zenon_Hd8 zenon_H67 zenon_H1f0 zenon_H1cf zenon_H30 zenon_H2f zenon_H1ac zenon_H40 zenon_H1ae zenon_H24 zenon_H20b zenon_H245 zenon_H6a zenon_H208 zenon_H25 zenon_H81 zenon_H18b. % 18.68/18.90 apply (zenon_or_s _ _ zenon_H74); [ zenon_intro zenon_H42 | zenon_intro zenon_H77 ]. % 18.68/18.90 exact (zenon_H3f zenon_H42). % 18.68/18.90 apply (zenon_or_s _ _ zenon_H77); [ zenon_intro zenon_H49 | zenon_intro zenon_H78 ]. % 18.68/18.90 exact (zenon_H20b zenon_H49). % 18.68/18.90 apply (zenon_or_s _ _ zenon_H78); [ zenon_intro zenon_H48 | zenon_intro zenon_H1e ]. % 18.68/18.90 apply (zenon_or_s _ _ zenon_H245); [ zenon_intro zenon_H49 | zenon_intro zenon_H246 ]. % 18.68/18.90 exact (zenon_H20b zenon_H49). % 18.68/18.90 apply (zenon_or_s _ _ zenon_H246); [ zenon_intro zenon_H29 | zenon_intro zenon_H247 ]. % 18.68/18.90 exact (zenon_H24 zenon_H29). % 18.68/18.90 apply (zenon_or_s _ _ zenon_H247); [ zenon_intro zenon_H36 | zenon_intro zenon_H1b1 ]. % 18.68/18.90 apply (zenon_or_s _ _ zenon_H1ac); [ zenon_intro zenon_H44 | zenon_intro zenon_H1af ]. % 18.68/18.90 exact (zenon_H40 zenon_H44). % 18.68/18.90 apply (zenon_or_s _ _ zenon_H1af); [ zenon_intro zenon_H1b1 | zenon_intro zenon_H1b0 ]. % 18.68/18.90 apply (zenon_L643_); trivial. % 18.68/18.90 apply (zenon_or_s _ _ zenon_H1b0); [ zenon_intro zenon_H61 | zenon_intro zenon_H60 ]. % 18.68/18.90 exact (zenon_H18b zenon_H61). % 18.68/18.90 exact (zenon_H1ae zenon_H60). % 18.68/18.90 apply (zenon_or_s _ _ zenon_H2f); [ zenon_intro zenon_H34 | zenon_intro zenon_H33 ]. % 18.68/18.90 exact (zenon_H30 zenon_H34). % 18.68/18.90 apply (zenon_or_s _ _ zenon_H33); [ zenon_intro zenon_H36 | zenon_intro zenon_H35 ]. % 18.68/18.90 apply (zenon_L647_); trivial. % 18.68/18.90 apply (zenon_or_s _ _ zenon_H35); [ zenon_intro zenon_H2c | zenon_intro zenon_H37 ]. % 18.68/18.90 exact (zenon_H81 zenon_H2c). % 18.68/18.90 exact (zenon_H32 zenon_H37). % 18.68/18.90 apply (zenon_L337_); trivial. % 18.68/18.90 (* end of lemma zenon_L648_ *) % 18.68/18.90 assert (zenon_L649_ : (((op (e3) (e1)) = (e0))\/(((op (e3) (e1)) = (e1))\/(((op (e3) (e1)) = (e2))\/((op (e3) (e1)) = (e3))))) -> (~((op (e3) (e1)) = (e0))) -> ((op (e1) (e1)) = (e2)) -> ((op (e2) (e1)) = (e0)) -> (((op (e1) (e1)) = (e0))\/(((op (e1) (e1)) = (e1))\/(((op (e1) (e1)) = (e2))\/((op (e1) (e1)) = (e3))))) -> (~((op (e1) (e1)) = (e0))) -> (~((op (e1) (e1)) = (e1))) -> (~((op (e0) (e1)) = (op (e1) (e1)))) -> (~((op (e1) (e1)) = (op (e2) (e1)))) -> ((op (e2) (e1)) = (e3)) -> (~((op (e0) (e1)) = (op (e3) (e1)))) -> (~((op (e0) (e1)) = (e0))) -> (((op (e0) (e1)) = (e0))\/(((op (e0) (e1)) = (e1))\/(((op (e0) (e1)) = (e2))\/((op (e0) (e1)) = (e3))))) -> ((op (e3) (e2)) = (e2)) -> (~((op (e3) (e1)) = (op (e3) (e2)))) -> ((op (e3) (e0)) = (e3)) -> (~((op (e3) (e0)) = (op (e3) (e1)))) -> False). % 18.68/18.90 do 0 intro. intros zenon_H22a zenon_H1ad zenon_H110 zenon_H36 zenon_H142 zenon_H24 zenon_H10a zenon_H10e zenon_H13e zenon_Ha6 zenon_H210 zenon_H20b zenon_H212 zenon_H151 zenon_H1a4 zenon_H15e zenon_H1cf. % 18.68/18.90 apply (zenon_or_s _ _ zenon_H22a); [ zenon_intro zenon_H1b1 | zenon_intro zenon_H22b ]. % 18.68/18.90 exact (zenon_H1ad zenon_H1b1). % 18.68/18.90 apply (zenon_or_s _ _ zenon_H22b); [ zenon_intro zenon_Hae | zenon_intro zenon_H22c ]. % 18.68/18.90 apply (zenon_L555_); trivial. % 18.68/18.90 apply (zenon_or_s _ _ zenon_H22c); [ zenon_intro zenon_H14d | zenon_intro zenon_H161 ]. % 18.68/18.90 apply (zenon_L400_); trivial. % 18.68/18.90 apply (zenon_L193_); trivial. % 18.68/18.90 (* end of lemma zenon_L649_ *) % 18.68/18.90 assert (zenon_L650_ : (((op (e0) (e0)) = (e2))\/(((op (e1) (e0)) = (e2))\/(((op (e2) (e0)) = (e2))\/((op (e3) (e0)) = (e2))))) -> (~((op (e0) (e0)) = (op (e0) (e3)))) -> (~((e0) = (e2))) -> ((op (e1) (e0)) = (e0)) -> (~((e1) = (e2))) -> (((op (e0) (e0)) = (e3))\/(((op (e0) (e1)) = (e3))\/(((op (e0) (e2)) = (e3))\/((op (e0) (e3)) = (e3))))) -> ((op (e2) (e0)) = (e1)) -> (~((e1) = (e3))) -> ((op (e0) (e1)) = (e1)) -> (~((e0) = (e3))) -> ((op (e0) (e2)) = (e0)) -> ((op (e0) (e3)) = (e2)) -> (~((e2) = (e3))) -> False). % 18.68/18.90 do 0 intro. intros zenon_H1fe zenon_H189 zenon_H149 zenon_H27 zenon_H7c zenon_H168 zenon_Hed zenon_H95 zenon_Ha0 zenon_H9a zenon_H48 zenon_Hcd zenon_H12b. % 18.68/18.90 apply (zenon_or_s _ _ zenon_H1fe); [ zenon_intro zenon_H7b | zenon_intro zenon_H1ff ]. % 18.68/18.90 apply (zenon_L375_); trivial. % 18.68/18.90 apply (zenon_or_s _ _ zenon_H1ff); [ zenon_intro zenon_H86 | zenon_intro zenon_H200 ]. % 18.68/18.90 apply (zenon_L257_); trivial. % 18.68/18.90 apply (zenon_or_s _ _ zenon_H200); [ zenon_intro zenon_Hee | zenon_intro zenon_H148 ]. % 18.68/18.90 apply (zenon_L58_); trivial. % 18.68/18.90 apply (zenon_or_s _ _ zenon_H168); [ zenon_intro zenon_H3a | zenon_intro zenon_H169 ]. % 18.68/18.90 apply (zenon_L423_); trivial. % 18.68/18.90 apply (zenon_or_s _ _ zenon_H169); [ zenon_intro zenon_H99 | zenon_intro zenon_H16a ]. % 18.68/18.90 apply (zenon_L403_); trivial. % 18.68/18.90 apply (zenon_or_s _ _ zenon_H16a); [ zenon_intro zenon_Ha9 | zenon_intro zenon_He3 ]. % 18.68/18.90 apply (zenon_L358_); trivial. % 18.68/18.90 apply (zenon_L81_); trivial. % 18.68/18.90 (* end of lemma zenon_L650_ *) % 18.68/18.90 assert (zenon_L651_ : (((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)) = (e1)) -> (~((op (e1) (e1)) = (e1))) -> ((op (e3) (e2)) = (e1)) -> (~((op (e1) (e2)) = (op (e3) (e2)))) -> (~((op (e0) (e3)) = (op (e1) (e3)))) -> ((op (e0) (e3)) = (e1)) -> False). % 18.68/18.90 do 0 intro. intros zenon_H128 zenon_H201 zenon_Hed zenon_H10a zenon_Hba zenon_H115 zenon_H1d zenon_Hc3. % 18.68/18.90 apply (zenon_or_s _ _ zenon_H128); [ zenon_intro zenon_H9d | zenon_intro zenon_H129 ]. % 18.68/18.90 apply (zenon_L413_); trivial. % 18.68/18.90 apply (zenon_or_s _ _ zenon_H129); [ zenon_intro zenon_H10d | zenon_intro zenon_H12a ]. % 18.68/18.90 exact (zenon_H10a zenon_H10d). % 18.68/18.90 apply (zenon_or_s _ _ zenon_H12a); [ zenon_intro zenon_Hf0 | zenon_intro zenon_Hd6 ]. % 18.68/18.90 apply (zenon_L69_); trivial. % 18.68/18.90 apply (zenon_L79_); trivial. % 18.68/18.90 (* end of lemma zenon_L651_ *) % 18.68/18.90 assert (zenon_L652_ : (((op (e0) (e0)) = (e1))\/(((op (e1) (e0)) = (e1))\/(((op (e2) (e0)) = (e1))\/((op (e3) (e0)) = (e1))))) -> (~((op (e0) (e0)) = (op (e0) (e3)))) -> (~((e0) = (e1))) -> ((op (e1) (e0)) = (e0)) -> ((op (e0) (e3)) = (e1)) -> (~((op (e0) (e3)) = (op (e1) (e3)))) -> (~((op (e1) (e2)) = (op (e3) (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))))) -> (~((op (e3) (e0)) = (op (e3) (e2)))) -> ((op (e3) (e2)) = (e1)) -> False). % 18.68/18.90 do 0 intro. intros zenon_H235 zenon_H189 zenon_Ha1 zenon_H27 zenon_Hc3 zenon_H1d zenon_H115 zenon_H10a zenon_H201 zenon_H128 zenon_H6f zenon_Hba. % 18.68/18.90 apply (zenon_or_s _ _ zenon_H235); [ zenon_intro zenon_H7a | zenon_intro zenon_H236 ]. % 18.68/18.90 apply (zenon_L140_); trivial. % 18.68/18.90 apply (zenon_or_s _ _ zenon_H236); [ zenon_intro zenon_H9d | zenon_intro zenon_H237 ]. % 18.68/18.90 apply (zenon_L262_); trivial. % 18.68/18.90 apply (zenon_or_s _ _ zenon_H237); [ zenon_intro zenon_Hed | zenon_intro zenon_Hac ]. % 18.68/18.90 apply (zenon_L651_); trivial. % 18.68/18.90 apply (zenon_L249_); trivial. % 18.68/18.90 (* end of lemma zenon_L652_ *) % 18.68/18.90 assert (zenon_L653_ : (((op (e0) (e3)) = (e0))\/(((op (e0) (e3)) = (e1))\/(((op (e0) (e3)) = (e2))\/((op (e0) (e3)) = (e3))))) -> ((op (e3) (e3)) = (e0)) -> ((op (e3) (e2)) = (e1)) -> (~((op (e3) (e0)) = (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 (e1) (e1)) = (e1))) -> (~((op (e1) (e2)) = (op (e3) (e2)))) -> (~((op (e0) (e3)) = (op (e1) (e3)))) -> ((op (e1) (e0)) = (e0)) -> (~((e0) = (e1))) -> (~((op (e0) (e0)) = (op (e0) (e3)))) -> (((op (e0) (e0)) = (e1))\/(((op (e1) (e0)) = (e1))\/(((op (e2) (e0)) = (e1))\/((op (e3) (e0)) = (e1))))) -> ((op (e3) (e3)) = (e2)) -> (~((op (e0) (e3)) = (op (e3) (e3)))) -> (~((op (e0) (e3)) = (op (e2) (e3)))) -> ((op (e2) (e3)) = (e3)) -> False). % 18.68/18.90 do 0 intro. intros zenon_He4 zenon_H60 zenon_Hba zenon_H6f zenon_H128 zenon_H201 zenon_H10a zenon_H115 zenon_H1d zenon_H27 zenon_Ha1 zenon_H189 zenon_H235 zenon_Hf6 zenon_Hc2 zenon_He2 zenon_Hdd. % 18.68/18.90 apply (zenon_or_s _ _ zenon_He4); [ zenon_intro zenon_H1e | zenon_intro zenon_He5 ]. % 18.68/18.90 apply (zenon_L440_); trivial. % 18.68/18.90 apply (zenon_or_s _ _ zenon_He5); [ zenon_intro zenon_Hc3 | zenon_intro zenon_He6 ]. % 18.68/18.90 apply (zenon_L652_); trivial. % 18.68/18.90 apply (zenon_or_s _ _ zenon_He6); [ zenon_intro zenon_Hcd | zenon_intro zenon_He3 ]. % 18.68/18.90 apply (zenon_L87_); trivial. % 18.68/18.90 apply (zenon_L54_); trivial. % 18.68/18.90 (* end of lemma zenon_L653_ *) % 18.68/18.90 assert (zenon_L654_ : (((op (e0) (e3)) = (e2))\/(((op (e1) (e3)) = (e2))\/(((op (e2) (e3)) = (e2))\/((op (e3) (e3)) = (e2))))) -> ((op (e0) (e0)) = (e2)) -> (~((e1) = (e2))) -> ((op (e1) (e3)) = (e1)) -> (~((op (e2) (e1)) = (op (e2) (e3)))) -> ((op (e2) (e1)) = (e2)) -> (((op (e0) (e3)) = (e0))\/(((op (e0) (e3)) = (e1))\/(((op (e0) (e3)) = (e2))\/((op (e0) (e3)) = (e3))))) -> ((op (e3) (e3)) = (e0)) -> ((op (e3) (e2)) = (e1)) -> (~((op (e3) (e0)) = (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 (e1) (e1)) = (e1))) -> (~((op (e1) (e2)) = (op (e3) (e2)))) -> (~((op (e0) (e3)) = (op (e1) (e3)))) -> ((op (e1) (e0)) = (e0)) -> (~((e0) = (e1))) -> (~((op (e0) (e0)) = (op (e0) (e3)))) -> (((op (e0) (e0)) = (e1))\/(((op (e1) (e0)) = (e1))\/(((op (e2) (e0)) = (e1))\/((op (e3) (e0)) = (e1))))) -> (~((op (e0) (e3)) = (op (e3) (e3)))) -> (~((op (e0) (e3)) = (op (e2) (e3)))) -> ((op (e2) (e3)) = (e3)) -> False). % 18.68/18.90 do 0 intro. intros zenon_H145 zenon_H7b zenon_H7c zenon_Hd6 zenon_H1c7 zenon_H1ca zenon_He4 zenon_H60 zenon_Hba zenon_H6f zenon_H128 zenon_H201 zenon_H10a zenon_H115 zenon_H1d zenon_H27 zenon_Ha1 zenon_H189 zenon_H235 zenon_Hc2 zenon_He2 zenon_Hdd. % 18.68/18.90 apply (zenon_or_s _ _ zenon_H145); [ zenon_intro zenon_Hcd | zenon_intro zenon_H146 ]. % 18.68/18.90 apply (zenon_L375_); trivial. % 18.68/18.90 apply (zenon_or_s _ _ zenon_H146); [ zenon_intro zenon_Hd7 | zenon_intro zenon_H147 ]. % 18.68/18.90 apply (zenon_L101_); trivial. % 18.68/18.90 apply (zenon_or_s _ _ zenon_H147); [ zenon_intro zenon_H11d | zenon_intro zenon_Hf6 ]. % 18.68/18.90 apply (zenon_L224_); trivial. % 18.68/18.90 apply (zenon_L653_); trivial. % 18.68/18.90 (* end of lemma zenon_L654_ *) % 18.68/18.90 assert (zenon_L655_ : (((op (e3) (e0)) = (e0))\/(((op (e3) (e1)) = (e0))\/(((op (e3) (e2)) = (e0))\/((op (e3) (e3)) = (e0))))) -> (~((op (e3) (e0)) = (e0))) -> (~((op (e3) (e1)) = (e0))) -> (~((op (e3) (e2)) = (e0))) -> (((op (e0) (e3)) = (e2))\/(((op (e1) (e3)) = (e2))\/(((op (e2) (e3)) = (e2))\/((op (e3) (e3)) = (e2))))) -> ((op (e0) (e0)) = (e2)) -> (~((e1) = (e2))) -> ((op (e1) (e3)) = (e1)) -> (~((op (e2) (e1)) = (op (e2) (e3)))) -> ((op (e2) (e1)) = (e2)) -> (((op (e0) (e3)) = (e0))\/(((op (e0) (e3)) = (e1))\/(((op (e0) (e3)) = (e2))\/((op (e0) (e3)) = (e3))))) -> ((op (e3) (e2)) = (e1)) -> (~((op (e3) (e0)) = (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 (e1) (e1)) = (e1))) -> (~((op (e1) (e2)) = (op (e3) (e2)))) -> (~((op (e0) (e3)) = (op (e1) (e3)))) -> ((op (e1) (e0)) = (e0)) -> (~((e0) = (e1))) -> (~((op (e0) (e0)) = (op (e0) (e3)))) -> (((op (e0) (e0)) = (e1))\/(((op (e1) (e0)) = (e1))\/(((op (e2) (e0)) = (e1))\/((op (e3) (e0)) = (e1))))) -> (~((op (e0) (e3)) = (op (e3) (e3)))) -> (~((op (e0) (e3)) = (op (e2) (e3)))) -> ((op (e2) (e3)) = (e3)) -> False). % 18.68/18.90 do 0 intro. intros zenon_H1ac zenon_H40 zenon_H1ad zenon_H18b zenon_H145 zenon_H7b zenon_H7c zenon_Hd6 zenon_H1c7 zenon_H1ca zenon_He4 zenon_Hba zenon_H6f zenon_H128 zenon_H201 zenon_H10a zenon_H115 zenon_H1d zenon_H27 zenon_Ha1 zenon_H189 zenon_H235 zenon_Hc2 zenon_He2 zenon_Hdd. % 18.68/18.90 apply (zenon_or_s _ _ zenon_H1ac); [ zenon_intro zenon_H44 | zenon_intro zenon_H1af ]. % 18.68/18.90 exact (zenon_H40 zenon_H44). % 18.68/18.90 apply (zenon_or_s _ _ zenon_H1af); [ zenon_intro zenon_H1b1 | zenon_intro zenon_H1b0 ]. % 18.68/18.90 exact (zenon_H1ad zenon_H1b1). % 18.68/18.90 apply (zenon_or_s _ _ zenon_H1b0); [ zenon_intro zenon_H61 | zenon_intro zenon_H60 ]. % 18.68/18.90 exact (zenon_H18b zenon_H61). % 18.68/18.90 apply (zenon_L654_); trivial. % 18.68/18.90 (* end of lemma zenon_L655_ *) % 18.68/18.90 assert (zenon_L656_ : (((op (e2) (e3)) = (e0))\/(((op (e2) (e3)) = (e1))\/(((op (e2) (e3)) = (e2))\/((op (e2) (e3)) = (e3))))) -> (~((op (e2) (e3)) = (e0))) -> (~((op (e1) (e3)) = (op (e2) (e3)))) -> ((op (e3) (e3)) = (e2)) -> (~((op (e2) (e3)) = (op (e3) (e3)))) -> (((op (e3) (e0)) = (e0))\/(((op (e3) (e1)) = (e0))\/(((op (e3) (e2)) = (e0))\/((op (e3) (e3)) = (e0))))) -> (~((op (e3) (e0)) = (e0))) -> (~((op (e3) (e1)) = (e0))) -> (~((op (e3) (e2)) = (e0))) -> (((op (e0) (e3)) = (e2))\/(((op (e1) (e3)) = (e2))\/(((op (e2) (e3)) = (e2))\/((op (e3) (e3)) = (e2))))) -> ((op (e0) (e0)) = (e2)) -> (~((e1) = (e2))) -> ((op (e1) (e3)) = (e1)) -> (~((op (e2) (e1)) = (op (e2) (e3)))) -> ((op (e2) (e1)) = (e2)) -> (((op (e0) (e3)) = (e0))\/(((op (e0) (e3)) = (e1))\/(((op (e0) (e3)) = (e2))\/((op (e0) (e3)) = (e3))))) -> ((op (e3) (e2)) = (e1)) -> (~((op (e3) (e0)) = (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 (e1) (e1)) = (e1))) -> (~((op (e1) (e2)) = (op (e3) (e2)))) -> (~((op (e0) (e3)) = (op (e1) (e3)))) -> ((op (e1) (e0)) = (e0)) -> (~((e0) = (e1))) -> (~((op (e0) (e0)) = (op (e0) (e3)))) -> (((op (e0) (e0)) = (e1))\/(((op (e1) (e0)) = (e1))\/(((op (e2) (e0)) = (e1))\/((op (e3) (e0)) = (e1))))) -> (~((op (e0) (e3)) = (op (e3) (e3)))) -> (~((op (e0) (e3)) = (op (e2) (e3)))) -> False). % 18.68/18.90 do 0 intro. intros zenon_H11f zenon_H32 zenon_Hdb zenon_Hf6 zenon_Hf3 zenon_H1ac zenon_H40 zenon_H1ad zenon_H18b zenon_H145 zenon_H7b zenon_H7c zenon_Hd6 zenon_H1c7 zenon_H1ca zenon_He4 zenon_Hba zenon_H6f zenon_H128 zenon_H201 zenon_H10a zenon_H115 zenon_H1d zenon_H27 zenon_Ha1 zenon_H189 zenon_H235 zenon_Hc2 zenon_He2. % 18.68/18.90 apply (zenon_or_s _ _ zenon_H11f); [ zenon_intro zenon_H37 | zenon_intro zenon_H120 ]. % 18.68/18.90 exact (zenon_H32 zenon_H37). % 18.68/18.90 apply (zenon_or_s _ _ zenon_H120); [ zenon_intro zenon_Hf4 | zenon_intro zenon_H121 ]. % 18.68/18.90 apply (zenon_L126_); trivial. % 18.68/18.90 apply (zenon_or_s _ _ zenon_H121); [ zenon_intro zenon_H11d | zenon_intro zenon_Hdd ]. % 18.68/18.90 apply (zenon_L97_); trivial. % 18.68/18.90 apply (zenon_L655_); trivial. % 18.68/18.90 (* end of lemma zenon_L656_ *) % 18.68/18.90 assert (zenon_L657_ : (((op (e1) (e0)) = (e3))\/(((op (e1) (e1)) = (e3))\/(((op (e1) (e2)) = (e3))\/((op (e1) (e3)) = (e3))))) -> ((op (e0) (e0)) = (e2)) -> ((op (e2) (e0)) = (e1)) -> ((op (e3) (e1)) = (e2)) -> ((op (e2) (e1)) = (e0)) -> (~((e2) = (e3))) -> ((op (e1) (e2)) = (e2)) -> ((op (e1) (e3)) = (e1)) -> (~((e1) = (e3))) -> False). % 18.68/18.90 do 0 intro. intros zenon_H16f zenon_H7b zenon_Hed zenon_H14d zenon_H36 zenon_H12b zenon_H113 zenon_Hd6 zenon_H95. % 18.68/18.90 apply (zenon_or_s _ _ zenon_H16f); [ zenon_intro zenon_H9e | zenon_intro zenon_H170 ]. % 18.68/18.90 apply (zenon_L491_); trivial. % 18.68/18.90 apply (zenon_or_s _ _ zenon_H170); [ zenon_intro zenon_H13f | zenon_intro zenon_H171 ]. % 18.68/18.90 apply (zenon_L514_); trivial. % 18.68/18.90 apply (zenon_or_s _ _ zenon_H171); [ zenon_intro zenon_H16c | zenon_intro zenon_Hdc ]. % 18.68/18.90 apply (zenon_L116_); trivial. % 18.68/18.90 apply (zenon_L83_); trivial. % 18.68/18.90 (* end of lemma zenon_L657_ *) % 18.68/18.90 assert (zenon_L658_ : (((op (e0) (e1)) = (e3))\/(((op (e1) (e1)) = (e3))\/(((op (e2) (e1)) = (e3))\/((op (e3) (e1)) = (e3))))) -> ((op (e2) (e1)) = (e0)) -> (~((e2) = (e3))) -> ((op (e1) (e1)) = (e2)) -> (~((e1) = (e3))) -> ((op (e2) (e1)) = (e1)) -> ((op (e3) (e0)) = (e3)) -> (~((op (e3) (e0)) = (op (e3) (e1)))) -> False). % 18.68/18.90 do 0 intro. intros zenon_H1a5 zenon_H36 zenon_H12b zenon_H110 zenon_H95 zenon_Ha5 zenon_H15e zenon_H1cf. % 18.68/18.90 apply (zenon_or_s _ _ zenon_H1a5); [ zenon_intro zenon_H99 | zenon_intro zenon_H1a8 ]. % 18.68/18.90 apply (zenon_L552_); trivial. % 18.68/18.90 apply (zenon_or_s _ _ zenon_H1a8); [ zenon_intro zenon_H13f | zenon_intro zenon_H1a9 ]. % 18.68/18.90 apply (zenon_L166_); trivial. % 18.68/18.90 apply (zenon_or_s _ _ zenon_H1a9); [ zenon_intro zenon_Ha6 | zenon_intro zenon_H161 ]. % 18.68/18.90 apply (zenon_L39_); trivial. % 18.68/18.90 apply (zenon_L193_); trivial. % 18.68/18.90 (* end of lemma zenon_L658_ *) % 18.68/18.90 assert (zenon_L659_ : (((op (e0) (e1)) = (e3))\/(((op (e1) (e1)) = (e3))\/(((op (e2) (e1)) = (e3))\/((op (e3) (e1)) = (e3))))) -> (~((e2) = (e3))) -> ((op (e1) (e1)) = (e2)) -> ((op (e2) (e1)) = (e0)) -> (((op (e1) (e1)) = (e0))\/(((op (e1) (e1)) = (e1))\/(((op (e1) (e1)) = (e2))\/((op (e1) (e1)) = (e3))))) -> (~((op (e1) (e1)) = (e0))) -> (~((op (e1) (e1)) = (e1))) -> (~((op (e0) (e1)) = (op (e1) (e1)))) -> (~((op (e1) (e1)) = (op (e2) (e1)))) -> (~((op (e0) (e1)) = (op (e3) (e1)))) -> ((op (e3) (e1)) = (e1)) -> (~((op (e0) (e1)) = (e0))) -> (((op (e0) (e1)) = (e0))\/(((op (e0) (e1)) = (e1))\/(((op (e0) (e1)) = (e2))\/((op (e0) (e1)) = (e3))))) -> ((op (e3) (e0)) = (e3)) -> (~((op (e3) (e0)) = (op (e3) (e1)))) -> False). % 18.68/18.90 do 0 intro. intros zenon_H1a5 zenon_H12b zenon_H110 zenon_H36 zenon_H142 zenon_H24 zenon_H10a zenon_H10e zenon_H13e zenon_H210 zenon_Hae zenon_H20b zenon_H212 zenon_H15e zenon_H1cf. % 18.68/18.90 apply (zenon_or_s _ _ zenon_H1a5); [ zenon_intro zenon_H99 | zenon_intro zenon_H1a8 ]. % 18.68/18.90 apply (zenon_L552_); trivial. % 18.68/18.90 apply (zenon_or_s _ _ zenon_H1a8); [ zenon_intro zenon_H13f | zenon_intro zenon_H1a9 ]. % 18.68/18.90 apply (zenon_L166_); trivial. % 18.68/18.90 apply (zenon_or_s _ _ zenon_H1a9); [ zenon_intro zenon_Ha6 | zenon_intro zenon_H161 ]. % 18.68/18.90 apply (zenon_L555_); trivial. % 18.68/18.90 apply (zenon_L193_); trivial. % 18.68/18.90 (* end of lemma zenon_L659_ *) % 18.68/18.90 assert (zenon_L660_ : (((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)) = (e0))\/(((op (e3) (e3)) = (e1))\/(((op (e3) (e3)) = (e2))\/((op (e3) (e3)) = (e3))))) -> ((op (e0) (e3)) = (e1)) -> ((op (e1) (e3)) = (e2)) -> (~((op (e3) (e1)) = (op (e3) (e3)))) -> ((op (e3) (e1)) = (e1)) -> (~((op (e3) (e2)) = (op (e3) (e3)))) -> (~((op (e3) (e3)) = (e3))) -> False). % 18.68/18.90 do 0 intro. intros zenon_H172 zenon_H149 zenon_H48 zenon_H7c zenon_Hf0 zenon_H173 zenon_H101 zenon_Hc3 zenon_Hd7 zenon_H130 zenon_Hae zenon_H62 zenon_H102. % 18.68/18.90 apply (zenon_or_s _ _ zenon_H172); [ zenon_intro zenon_H150 | zenon_intro zenon_H174 ]. % 18.68/18.90 apply (zenon_L378_); trivial. % 18.68/18.90 apply (zenon_or_s _ _ zenon_H174); [ zenon_intro zenon_H113 | zenon_intro zenon_H175 ]. % 18.68/18.90 apply (zenon_L68_); trivial. % 18.68/18.90 apply (zenon_or_s _ _ zenon_H175); [ zenon_intro zenon_H176 | zenon_intro zenon_H151 ]. % 18.68/18.90 exact (zenon_H173 zenon_H176). % 18.68/18.90 apply (zenon_L379_); trivial. % 18.68/18.90 (* end of lemma zenon_L660_ *) % 18.68/18.90 assert (zenon_L661_ : (((op (e0) (e1)) = (e0))\/(((op (e1) (e1)) = (e0))\/(((op (e2) (e1)) = (e0))\/((op (e3) (e1)) = (e0))))) -> ((op (e0) (e3)) = (e1)) -> (~((op (e0) (e3)) = (op (e1) (e3)))) -> (((op (e0) (e1)) = (e1))\/(((op (e1) (e1)) = (e1))\/(((op (e2) (e1)) = (e1))\/((op (e3) (e1)) = (e1))))) -> (~((op (e0) (e1)) = (op (e0) (e3)))) -> (~((op (e3) (e2)) = (e0))) -> (~((op (e3) (e0)) = (e0))) -> (((op (e3) (e0)) = (e0))\/(((op (e3) (e1)) = (e0))\/(((op (e3) (e2)) = (e0))\/((op (e3) (e3)) = (e0))))) -> (~((e1) = (e3))) -> (((op (e1) (e0)) = (e2))\/(((op (e1) (e1)) = (e2))\/(((op (e1) (e2)) = (e2))\/((op (e1) (e3)) = (e2))))) -> ((op (e1) (e0)) = (e0)) -> (~((op (e3) (e0)) = (op (e3) (e1)))) -> ((op (e3) (e0)) = (e3)) -> (((op (e0) (e1)) = (e0))\/(((op (e0) (e1)) = (e1))\/(((op (e0) (e1)) = (e2))\/((op (e0) (e1)) = (e3))))) -> (~((op (e0) (e1)) = (e0))) -> (~((op (e0) (e1)) = (op (e3) (e1)))) -> (~((op (e1) (e1)) = (op (e2) (e1)))) -> (~((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))))) -> (~((e2) = (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))))) -> (~((e0) = (e2))) -> ((op (e0) (e2)) = (e0)) -> (~((e1) = (e2))) -> (~((op (e2) (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 (e3) (e2)) = (op (e3) (e3)))) -> (~((op (e3) (e3)) = (e3))) -> ((op (e2) (e0)) = (e1)) -> (~((op (e1) (e0)) = (op (e2) (e0)))) -> (((op (e1) (e0)) = (e1))\/(((op (e1) (e1)) = (e1))\/(((op (e1) (e2)) = (e1))\/((op (e1) (e3)) = (e1))))) -> (~((op (e3) (e1)) = (e0))) -> False). % 18.68/18.90 do 0 intro. intros zenon_H245 zenon_Hc3 zenon_H1d zenon_H109 zenon_H54 zenon_H18b zenon_H40 zenon_H1ac zenon_H95 zenon_H18c zenon_H27 zenon_H1cf zenon_H15e zenon_H212 zenon_H20b zenon_H210 zenon_H13e zenon_H10e zenon_H10a zenon_H24 zenon_H142 zenon_H12b zenon_H1a5 zenon_H172 zenon_H149 zenon_H48 zenon_H7c zenon_H173 zenon_H101 zenon_H130 zenon_H62 zenon_H102 zenon_Hed zenon_H201 zenon_H128 zenon_H1ad. % 18.68/18.90 apply (zenon_or_s _ _ zenon_H245); [ zenon_intro zenon_H49 | zenon_intro zenon_H246 ]. % 18.68/18.90 exact (zenon_H20b zenon_H49). % 18.68/18.90 apply (zenon_or_s _ _ zenon_H246); [ zenon_intro zenon_H29 | zenon_intro zenon_H247 ]. % 18.68/18.90 exact (zenon_H24 zenon_H29). % 18.68/18.90 apply (zenon_or_s _ _ zenon_H247); [ zenon_intro zenon_H36 | zenon_intro zenon_H1b1 ]. % 18.68/18.90 apply (zenon_or_s _ _ zenon_H128); [ zenon_intro zenon_H9d | zenon_intro zenon_H129 ]. % 18.68/18.90 apply (zenon_L413_); trivial. % 18.68/18.90 apply (zenon_or_s _ _ zenon_H129); [ zenon_intro zenon_H10d | zenon_intro zenon_H12a ]. % 18.68/18.90 exact (zenon_H10a zenon_H10d). % 18.68/18.90 apply (zenon_or_s _ _ zenon_H12a); [ zenon_intro zenon_Hf0 | zenon_intro zenon_Hd6 ]. % 18.68/18.90 apply (zenon_or_s _ _ zenon_H109); [ zenon_intro zenon_Ha0 | zenon_intro zenon_H10b ]. % 18.68/18.90 apply (zenon_L359_); trivial. % 18.68/18.90 apply (zenon_or_s _ _ zenon_H10b); [ zenon_intro zenon_H10d | zenon_intro zenon_H10c ]. % 18.68/18.90 exact (zenon_H10a zenon_H10d). % 18.68/18.90 apply (zenon_or_s _ _ zenon_H10c); [ zenon_intro zenon_Ha5 | zenon_intro zenon_Hae ]. % 18.68/18.90 apply (zenon_or_s _ _ zenon_H18c); [ zenon_intro zenon_H86 | zenon_intro zenon_H18d ]. % 18.68/18.90 apply (zenon_L257_); trivial. % 18.68/18.90 apply (zenon_or_s _ _ zenon_H18d); [ zenon_intro zenon_H110 | zenon_intro zenon_H18e ]. % 18.68/18.90 apply (zenon_L658_); trivial. % 18.68/18.90 apply (zenon_or_s _ _ zenon_H18e); [ zenon_intro zenon_H113 | zenon_intro zenon_Hd7 ]. % 18.68/18.90 apply (zenon_L68_); trivial. % 18.68/18.90 apply (zenon_L444_); trivial. % 18.68/18.90 apply (zenon_or_s _ _ zenon_H18c); [ zenon_intro zenon_H86 | zenon_intro zenon_H18d ]. % 18.68/18.90 apply (zenon_L257_); trivial. % 18.68/18.90 apply (zenon_or_s _ _ zenon_H18d); [ zenon_intro zenon_H110 | zenon_intro zenon_H18e ]. % 18.68/18.90 apply (zenon_L659_); trivial. % 18.68/18.90 apply (zenon_or_s _ _ zenon_H18e); [ zenon_intro zenon_H113 | zenon_intro zenon_Hd7 ]. % 18.68/18.90 apply (zenon_L68_); trivial. % 18.68/18.90 apply (zenon_L660_); trivial. % 18.68/18.90 apply (zenon_L79_); trivial. % 18.68/18.90 exact (zenon_H1ad zenon_H1b1). % 18.68/18.90 (* end of lemma zenon_L661_ *) % 18.68/18.90 assert (zenon_L662_ : (((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 (e3) (e1)) = (e0))\/(((op (e3) (e1)) = (e1))\/(((op (e3) (e1)) = (e2))\/((op (e3) (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) (e1)) = (e0))) -> ((op (e0) (e0)) = (e2)) -> ((op (e2) (e0)) = (e1)) -> ((op (e1) (e0)) = (e0)) -> ((~((op (e0) (e3)) = (e0)))\/((op (e0) (e0)) = (e3))) -> ((~((op (e1) (e1)) = (e0)))\/((op (e1) (e0)) = (e1))) -> (~((e1) = (e2))) -> ((~((op (e2) (e3)) = (e0)))\/((op (e2) (e0)) = (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)) = (e0)))\/((op (e3) (e0)) = (e2))) -> (~((op (e2) (e2)) = (op (e3) (e2)))) -> (((op (e3) (e2)) = (e0))\/(((op (e3) (e2)) = (e1))\/(((op (e3) (e2)) = (e2))\/((op (e3) (e2)) = (e3))))) -> (~((op (e0) (e2)) = (op (e1) (e2)))) -> (((op (e1) (e2)) = (e0))\/(((op (e1) (e2)) = (e1))\/(((op (e1) (e2)) = (e2))\/((op (e1) (e2)) = (e3))))) -> (~((e1) = (e3))) -> (~((e0) = (e3))) -> (~((op (e1) (e1)) = (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) (e3)) = (e0))\/(((op (e2) (e3)) = (e1))\/(((op (e2) (e3)) = (e2))\/((op (e2) (e3)) = (e3))))) -> (~((op (e0) (e3)) = (op (e1) (e3)))) -> (~((op (e0) (e1)) = (op (e1) (e1)))) -> (~((e0) = (e1))) -> (~((op (e0) (e2)) = (op (e2) (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) (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 (e2) (e3)))) -> (((op (e0) (e3)) = (e0))\/(((op (e0) (e3)) = (e1))\/(((op (e0) (e3)) = (e2))\/((op (e0) (e3)) = (e3))))) -> (~((op (e2) (e1)) = (op (e3) (e1)))) -> (((op (e2) (e0)) = (e3))\/(((op (e2) (e1)) = (e3))\/(((op (e2) (e2)) = (e3))\/((op (e2) (e3)) = (e3))))) -> (((op (e2) (e0)) = (e1))\/(((op (e2) (e1)) = (e1))\/(((op (e2) (e2)) = (e1))\/((op (e2) (e3)) = (e1))))) -> (~((op (e2) (e3)) = (op (e3) (e3)))) -> (~((op (e3) (e3)) = (e3))) -> (((op (e3) (e3)) = (e0))\/(((op (e3) (e3)) = (e1))\/(((op (e3) (e3)) = (e2))\/((op (e3) (e3)) = (e3))))) -> (~((op (e1) (e2)) = (op (e2) (e2)))) -> (((op (e0) (e1)) = (e1))\/(((op (e1) (e1)) = (e1))\/(((op (e2) (e1)) = (e1))\/((op (e3) (e1)) = (e1))))) -> (~((op (e0) (e0)) = (op (e0) (e3)))) -> ((~((op (e2) (e2)) = (e0)))\/((op (e2) (e0)) = (e2))) -> ((~((op (e3) (e0)) = (e0)))\/((op (e3) (e0)) = (e0))) -> (((op (e0) (e0)) = (e2))\/(((op (e0) (e1)) = (e2))\/(((op (e0) (e2)) = (e2))\/((op (e0) (e3)) = (e2))))) -> (~((op (e2) (e0)) = (op (e3) (e0)))) -> (~((op (e0) (e1)) = (op (e2) (e1)))) -> ((~((op (e1) (e2)) = (e0)))\/((op (e1) (e0)) = (e2))) -> ((~((op (e1) (e3)) = (e0)))\/((op (e1) (e0)) = (e3))) -> (((op (e1) (e1)) = (e0))\/(((op (e1) (e1)) = (e1))\/(((op (e1) (e1)) = (e2))\/((op (e1) (e1)) = (e3))))) -> (~((op (e1) (e1)) = (op (e2) (e1)))) -> (~((op (e0) (e0)) = (op (e0) (e2)))) -> (((op (e0) (e2)) = (e1))\/(((op (e1) (e2)) = (e1))\/(((op (e2) (e2)) = (e1))\/((op (e3) (e2)) = (e1))))) -> (((op (e1) (e0)) = (e1))\/(((op (e1) (e1)) = (e1))\/(((op (e1) (e2)) = (e1))\/((op (e1) (e3)) = (e1))))) -> (((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))))) -> (~((e2) = (e3))) -> (~((op (e1) (e2)) = (op (e1) (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 (e2) (e2)) = (e2))) -> (((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) (e1)) = (op (e3) (e1)))) -> (((op (e3) (e0)) = (e3))\/(((op (e3) (e1)) = (e3))\/(((op (e3) (e2)) = (e3))\/((op (e3) (e3)) = (e3))))) -> (~((e0) = (e2))) -> (~((op (e0) (e2)) = (op (e3) (e2)))) -> (((op (e3) (e0)) = (e2))\/(((op (e3) (e1)) = (e2))\/(((op (e3) (e2)) = (e2))\/((op (e3) (e3)) = (e2))))) -> (~((op (e0) (e0)) = (op (e2) (e0)))) -> ((~((op (e2) (e1)) = (e0)))\/((op (e2) (e0)) = (e1))) -> (((op (e0) (e0)) = (e2))\/(((op (e1) (e0)) = (e2))\/(((op (e2) (e0)) = (e2))\/((op (e3) (e0)) = (e2))))) -> ((~((op (e2) (e0)) = (e0)))\/((op (e2) (e0)) = (e0))) -> (((op (e0) (e0)) = (e3))\/(((op (e1) (e0)) = (e3))\/(((op (e2) (e0)) = (e3))\/((op (e3) (e0)) = (e3))))) -> (((op (e2) (e2)) = (e0))\/(((op (e2) (e2)) = (e1))\/(((op (e2) (e2)) = (e2))\/((op (e2) (e2)) = (e3))))) -> (((op (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 (e0) (e1)) = (e2))\/(((op (e1) (e1)) = (e2))\/(((op (e2) (e1)) = (e2))\/((op (e3) (e1)) = (e2))))) -> (((op (e2) (e0)) = (e2))\/(((op (e2) (e1)) = (e2))\/(((op (e2) (e2)) = (e2))\/((op (e2) (e3)) = (e2))))) -> ((~((op (e3) (e3)) = (e0)))\/((op (e3) (e0)) = (e3))) -> ((~((op (e3) (e1)) = (e0)))\/((op (e3) (e0)) = (e1))) -> (((op (e1) (e0)) = (e0))\/(((op (e1) (e1)) = (e0))\/(((op (e1) (e2)) = (e0))\/((op (e1) (e3)) = (e0))))) -> (~((op (e1) (e0)) = (op (e1) (e1)))) -> (~((op (e0) (e1)) = (op (e0) (e3)))) -> (~((op (e1) (e1)) = (op (e1) (e3)))) -> (~((op (e2) (e0)) = (op (e2) (e3)))) -> (~((op (e3) (e2)) = (op (e3) (e3)))) -> (~((op (e2) (e0)) = (op (e2) (e2)))) -> (~((op (e1) (e1)) = (op (e1) (e2)))) -> (~((op (e0) (e1)) = (op (e0) (e2)))) -> (~((op (e3) (e0)) = (op (e3) (e3)))) -> (~((op (e2) (e2)) = (op (e2) (e3)))) -> (~((op (e3) (e0)) = (op (e3) (e2)))) -> (~((op (e1) (e0)) = (op (e3) (e0)))) -> (~((op (e1) (e0)) = (op (e2) (e0)))) -> ((~((op (e1) (e0)) = (e0)))\/((op (e1) (e0)) = (e0))) -> ((~((op (e0) (e2)) = (e0)))\/((op (e0) (e0)) = (e2))) -> (~((op (e0) (e0)) = (e0))) -> (~((op (e0) (e1)) = (e0))) -> (((op (e0) (e1)) = (e0))\/(((op (e1) (e1)) = (e0))\/(((op (e2) (e1)) = (e0))\/((op (e3) (e1)) = (e0))))) -> (~((op (e2) (e0)) = (e0))) -> (~((op (e1) (e0)) = (op (e1) (e2)))) -> (~((op (e2) (e1)) = (op (e2) (e2)))) -> (~((op (e3) (e1)) = (op (e3) (e2)))) -> (((op (e0) (e2)) = (e0))\/(((op (e1) (e2)) = (e0))\/(((op (e2) (e2)) = (e0))\/((op (e3) (e2)) = (e0))))) -> (~((op (e2) (e2)) = (e0))) -> (~((op (e2) (e3)) = (e0))) -> (((op (e2) (e0)) = (e0))\/(((op (e2) (e1)) = (e0))\/(((op (e2) (e2)) = (e0))\/((op (e2) (e3)) = (e0))))) -> (~((op (e3) (e0)) = (e0))) -> (((op (e0) (e0)) = (e0))\/(((op (e1) (e0)) = (e0))\/(((op (e2) (e0)) = (e0))\/((op (e3) (e0)) = (e0))))) -> (~((op (e3) (e0)) = (op (e3) (e1)))) -> (~((op (e2) (e0)) = (op (e2) (e1)))) -> (~((op (e0) (e2)) = (op (e0) (e3)))) -> (~((op (e1) (e0)) = (op (e1) (e3)))) -> (~((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 (e3) (e2)) = (e0))) -> (((op (e3) (e0)) = (e0))\/(((op (e3) (e1)) = (e0))\/(((op (e3) (e2)) = (e0))\/((op (e3) (e3)) = (e0))))) -> (~((op (e1) (e1)) = (e0))) -> (~((op (e1) (e2)) = (e0))) -> (((op (e0) (e0)) = (e0))\/(((op (e0) (e1)) = (e0))\/(((op (e0) (e2)) = (e0))\/((op (e0) (e3)) = (e0))))) -> False). % 18.68/18.90 do 0 intro. intros zenon_H22d zenon_H235 zenon_H22a zenon_H210 zenon_H212 zenon_H1ad zenon_H7b zenon_Hed zenon_H27 zenon_H204 zenon_H205 zenon_H7c zenon_H94 zenon_H1a5 zenon_H1a6 zenon_H1a7 zenon_H18f zenon_H191 zenon_H195 zenon_H19d zenon_H95 zenon_H9a zenon_H10a zenon_H18c zenon_H115 zenon_H11f zenon_H1d zenon_H10e zenon_Ha1 zenon_Ha8 zenon_He8 zenon_Hc2 zenon_Hdf zenon_Hdb zenon_Hd5 zenon_He2 zenon_He4 zenon_Haf zenon_He7 zenon_H106 zenon_Hf3 zenon_H102 zenon_H101 zenon_H2b zenon_H109 zenon_H189 zenon_H185 zenon_H184 zenon_H183 zenon_H17b zenon_H17e zenon_H178 zenon_H179 zenon_H142 zenon_H13e zenon_H13c zenon_H139 zenon_H128 zenon_H136 zenon_H133 zenon_H12b zenon_H124 zenon_H145 zenon_H172 zenon_H173 zenon_H16f zenon_H168 zenon_H160 zenon_H165 zenon_H149 zenon_H14f zenon_H153 zenon_H39 zenon_H182 zenon_H1fe zenon_H1ee zenon_H1e0 zenon_H1c4 zenon_H1cc zenon_H1ba zenon_H1d8 zenon_H1d5 zenon_H1ec zenon_H1ed zenon_H22 zenon_H45 zenon_H54 zenon_H57 zenon_H5b zenon_H62 zenon_H52 zenon_H4f zenon_H4a zenon_H71 zenon_H6d zenon_H6f zenon_H1fa zenon_H201 zenon_H206 zenon_H233 zenon_H3f zenon_H20b zenon_H245 zenon_H30 zenon_H24a zenon_H24b zenon_H1a4 zenon_H6a zenon_H81 zenon_H32 zenon_H2f zenon_H40 zenon_H3e zenon_H1cf zenon_H1f0 zenon_H208 zenon_Hd8 zenon_H1c7 zenon_H130 zenon_H67 zenon_H18b zenon_H1ac zenon_H24 zenon_H25 zenon_H74. % 18.68/18.90 apply (zenon_or_s _ _ zenon_H1ec); [ zenon_intro zenon_H1ae | zenon_intro zenon_H15e ]. % 18.68/18.90 apply (zenon_L648_); trivial. % 18.68/18.90 apply (zenon_or_s _ _ zenon_H74); [ zenon_intro zenon_H42 | zenon_intro zenon_H77 ]. % 18.68/18.90 exact (zenon_H3f zenon_H42). % 18.68/18.90 apply (zenon_or_s _ _ zenon_H77); [ zenon_intro zenon_H49 | zenon_intro zenon_H78 ]. % 18.68/18.90 exact (zenon_H20b zenon_H49). % 18.68/18.90 apply (zenon_or_s _ _ zenon_H78); [ zenon_intro zenon_H48 | zenon_intro zenon_H1e ]. % 18.68/18.90 apply (zenon_or_s _ _ zenon_H22d); [ zenon_intro zenon_H7a | zenon_intro zenon_H22e ]. % 18.68/18.90 apply (zenon_L456_); trivial. % 18.68/18.90 apply (zenon_or_s _ _ zenon_H22e); [ zenon_intro zenon_Ha0 | zenon_intro zenon_H22f ]. % 18.68/18.90 apply (zenon_or_s _ _ zenon_H245); [ zenon_intro zenon_H49 | zenon_intro zenon_H246 ]. % 18.68/18.90 exact (zenon_H20b zenon_H49). % 18.68/18.90 apply (zenon_or_s _ _ zenon_H246); [ zenon_intro zenon_H29 | zenon_intro zenon_H247 ]. % 18.68/18.90 exact (zenon_H24 zenon_H29). % 18.68/18.90 apply (zenon_or_s _ _ zenon_H247); [ zenon_intro zenon_H36 | zenon_intro zenon_H1b1 ]. % 18.68/18.90 apply (zenon_or_s _ _ zenon_H128); [ zenon_intro zenon_H9d | zenon_intro zenon_H129 ]. % 18.68/18.90 apply (zenon_L262_); trivial. % 18.68/18.90 apply (zenon_or_s _ _ zenon_H129); [ zenon_intro zenon_H10d | zenon_intro zenon_H12a ]. % 18.68/18.90 exact (zenon_H10a zenon_H10d). % 18.68/18.90 apply (zenon_or_s _ _ zenon_H12a); [ zenon_intro zenon_Hf0 | zenon_intro zenon_Hd6 ]. % 18.68/18.90 apply (zenon_or_s _ _ zenon_H18c); [ zenon_intro zenon_H86 | zenon_intro zenon_H18d ]. % 18.68/18.90 apply (zenon_L257_); trivial. % 18.68/18.90 apply (zenon_or_s _ _ zenon_H18d); [ zenon_intro zenon_H110 | zenon_intro zenon_H18e ]. % 18.68/18.90 apply (zenon_or_s _ _ zenon_H1a5); [ zenon_intro zenon_H99 | zenon_intro zenon_H1a8 ]. % 18.68/18.90 apply (zenon_L403_); trivial. % 18.68/18.90 apply (zenon_or_s _ _ zenon_H1a8); [ zenon_intro zenon_H13f | zenon_intro zenon_H1a9 ]. % 18.68/18.90 apply (zenon_L166_); trivial. % 18.68/18.90 apply (zenon_or_s _ _ zenon_H1a9); [ zenon_intro zenon_Ha6 | zenon_intro zenon_H161 ]. % 18.68/18.90 apply (zenon_or_s _ _ zenon_H172); [ zenon_intro zenon_H150 | zenon_intro zenon_H174 ]. % 18.68/18.90 apply (zenon_L378_); trivial. % 18.68/18.90 apply (zenon_or_s _ _ zenon_H174); [ zenon_intro zenon_H113 | zenon_intro zenon_H175 ]. % 18.68/18.90 apply (zenon_L68_); trivial. % 18.68/18.90 apply (zenon_or_s _ _ zenon_H175); [ zenon_intro zenon_H176 | zenon_intro zenon_H151 ]. % 18.68/18.90 exact (zenon_H173 zenon_H176). % 18.68/18.90 apply (zenon_L649_); trivial. % 18.68/18.90 apply (zenon_L193_); trivial. % 18.68/18.90 apply (zenon_or_s _ _ zenon_H18e); [ zenon_intro zenon_H113 | zenon_intro zenon_Hd7 ]. % 18.68/18.90 apply (zenon_L68_); trivial. % 18.68/18.90 apply (zenon_or_s _ _ zenon_H1d8); [ zenon_intro zenon_H10f | zenon_intro zenon_H1d9 ]. % 18.68/18.90 apply (zenon_L418_); trivial. % 18.68/18.90 apply (zenon_or_s _ _ zenon_H1d9); [ zenon_intro zenon_H110 | zenon_intro zenon_H1da ]. % 18.68/18.90 apply (zenon_L283_); trivial. % 18.68/18.90 apply (zenon_or_s _ _ zenon_H1da); [ zenon_intro zenon_H1ca | zenon_intro zenon_H14d ]. % 18.68/18.90 apply (zenon_or_s _ _ zenon_H1ac); [ zenon_intro zenon_H44 | zenon_intro zenon_H1af ]. % 18.68/18.90 exact (zenon_H40 zenon_H44). % 18.68/18.90 apply (zenon_or_s _ _ zenon_H1af); [ zenon_intro zenon_H1b1 | zenon_intro zenon_H1b0 ]. % 18.68/18.90 exact (zenon_H1ad zenon_H1b1). % 18.68/18.90 apply (zenon_or_s _ _ zenon_H1b0); [ zenon_intro zenon_H61 | zenon_intro zenon_H60 ]. % 18.68/18.90 exact (zenon_H18b zenon_H61). % 18.68/18.90 apply (zenon_or_s _ _ zenon_He8); [ zenon_intro zenon_Hac | zenon_intro zenon_Heb ]. % 18.68/18.90 apply (zenon_L252_); trivial. % 18.68/18.90 apply (zenon_or_s _ _ zenon_Heb); [ zenon_intro zenon_Hae | zenon_intro zenon_Hec ]. % 18.68/18.90 apply (zenon_L363_); trivial. % 18.68/18.90 apply (zenon_or_s _ _ zenon_Hec); [ zenon_intro zenon_Hba | zenon_intro zenon_Hc4 ]. % 18.68/18.90 apply (zenon_L69_); trivial. % 18.68/18.90 apply (zenon_L459_); trivial. % 18.68/18.90 apply (zenon_or_s _ _ zenon_H16f); [ zenon_intro zenon_H9e | zenon_intro zenon_H170 ]. % 18.68/18.90 apply (zenon_L491_); trivial. % 18.68/18.90 apply (zenon_or_s _ _ zenon_H170); [ zenon_intro zenon_H13f | zenon_intro zenon_H171 ]. % 18.68/18.90 apply (zenon_L514_); trivial. % 18.68/18.90 apply (zenon_or_s _ _ zenon_H171); [ zenon_intro zenon_H16c | zenon_intro zenon_Hdc ]. % 18.68/18.90 apply (zenon_L167_); trivial. % 18.68/18.90 apply (zenon_L266_); trivial. % 18.68/18.90 apply (zenon_or_s _ _ zenon_H18c); [ zenon_intro zenon_H86 | zenon_intro zenon_H18d ]. % 18.68/18.90 apply (zenon_L257_); trivial. % 18.68/18.90 apply (zenon_or_s _ _ zenon_H18d); [ zenon_intro zenon_H110 | zenon_intro zenon_H18e ]. % 18.68/18.90 apply (zenon_or_s _ _ zenon_H16f); [ zenon_intro zenon_H9e | zenon_intro zenon_H170 ]. % 18.68/18.90 apply (zenon_L263_); trivial. % 18.68/18.90 apply (zenon_or_s _ _ zenon_H170); [ zenon_intro zenon_H13f | zenon_intro zenon_H171 ]. % 18.68/18.90 apply (zenon_L166_); trivial. % 18.68/18.90 apply (zenon_or_s _ _ zenon_H171); [ zenon_intro zenon_H16c | zenon_intro zenon_Hdc ]. % 18.68/18.90 apply (zenon_or_s _ _ zenon_H1a5); [ zenon_intro zenon_H99 | zenon_intro zenon_H1a8 ]. % 18.68/18.90 apply (zenon_L552_); trivial. % 18.68/18.90 apply (zenon_or_s _ _ zenon_H1a8); [ zenon_intro zenon_H13f | zenon_intro zenon_H1a9 ]. % 18.68/18.90 apply (zenon_L166_); trivial. % 18.68/18.90 apply (zenon_or_s _ _ zenon_H1a9); [ zenon_intro zenon_Ha6 | zenon_intro zenon_H161 ]. % 18.68/18.90 apply (zenon_or_s _ _ zenon_H172); [ zenon_intro zenon_H150 | zenon_intro zenon_H174 ]. % 18.68/18.90 apply (zenon_L378_); trivial. % 18.68/18.90 apply (zenon_or_s _ _ zenon_H174); [ zenon_intro zenon_H113 | zenon_intro zenon_H175 ]. % 18.68/18.90 apply (zenon_L116_); trivial. % 18.68/18.90 apply (zenon_or_s _ _ zenon_H175); [ zenon_intro zenon_H176 | zenon_intro zenon_H151 ]. % 18.68/18.90 exact (zenon_H173 zenon_H176). % 18.68/18.90 apply (zenon_L649_); trivial. % 18.68/18.90 apply (zenon_L193_); trivial. % 18.68/18.90 apply (zenon_L83_); trivial. % 18.68/18.90 apply (zenon_or_s _ _ zenon_H18e); [ zenon_intro zenon_H113 | zenon_intro zenon_Hd7 ]. % 18.68/18.90 apply (zenon_or_s _ _ zenon_H1d8); [ zenon_intro zenon_H10f | zenon_intro zenon_H1d9 ]. % 18.68/18.90 apply (zenon_L418_); trivial. % 18.68/18.90 apply (zenon_or_s _ _ zenon_H1d9); [ zenon_intro zenon_H110 | zenon_intro zenon_H1da ]. % 18.68/18.90 apply (zenon_L276_); trivial. % 18.68/18.90 apply (zenon_or_s _ _ zenon_H1da); [ zenon_intro zenon_H1ca | zenon_intro zenon_H14d ]. % 18.68/18.90 apply (zenon_or_s _ _ zenon_H139); [ zenon_intro zenon_H122 | zenon_intro zenon_H13a ]. % 18.68/18.90 apply (zenon_L406_); trivial. % 18.68/18.90 apply (zenon_or_s _ _ zenon_H13a); [ zenon_intro zenon_Hf0 | zenon_intro zenon_H13b ]. % 18.68/18.90 apply (zenon_L68_); trivial. % 18.68/18.90 apply (zenon_or_s _ _ zenon_H13b); [ zenon_intro zenon_Hf1 | zenon_intro zenon_Hba ]. % 18.68/18.90 apply (zenon_L93_); trivial. % 18.68/18.90 apply (zenon_or_s _ _ zenon_H145); [ zenon_intro zenon_Hcd | zenon_intro zenon_H146 ]. % 18.68/18.90 apply (zenon_L650_); trivial. % 18.68/18.90 apply (zenon_or_s _ _ zenon_H146); [ zenon_intro zenon_Hd7 | zenon_intro zenon_H147 ]. % 18.68/18.90 apply (zenon_L101_); trivial. % 18.68/18.90 apply (zenon_or_s _ _ zenon_H147); [ zenon_intro zenon_H11d | zenon_intro zenon_Hf6 ]. % 18.68/18.90 apply (zenon_L224_); trivial. % 18.68/18.90 apply (zenon_L656_); trivial. % 18.68/18.90 apply (zenon_L657_); trivial. % 18.68/18.90 apply (zenon_L101_); trivial. % 18.68/18.90 exact (zenon_H1ad zenon_H1b1). % 18.68/18.90 apply (zenon_or_s _ _ zenon_H22f); [ zenon_intro zenon_H122 | zenon_intro zenon_Hc3 ]. % 18.68/18.90 apply (zenon_L355_); trivial. % 18.68/18.90 apply (zenon_L661_); trivial. % 18.68/18.90 apply (zenon_L337_); trivial. % 18.68/18.90 (* end of lemma zenon_L662_ *) % 18.68/18.90 assert (zenon_L663_ : ((~((op (e3) (e3)) = (e0)))\/((op (e3) (e0)) = (e3))) -> ((op (e3) (e0)) = (e1)) -> (~((e1) = (e3))) -> (~((op (e0) (e0)) = (e0))) -> (~((op (e0) (e1)) = (e0))) -> (((op (e0) (e1)) = (e0))\/(((op (e1) (e1)) = (e0))\/(((op (e2) (e1)) = (e0))\/((op (e3) (e1)) = (e0))))) -> (~((op (e2) (e0)) = (e0))) -> (~((op (e1) (e0)) = (op (e1) (e2)))) -> (~((op (e2) (e1)) = (op (e2) (e2)))) -> (~((op (e3) (e1)) = (op (e3) (e2)))) -> (((op (e0) (e2)) = (e0))\/(((op (e1) (e2)) = (e0))\/(((op (e2) (e2)) = (e0))\/((op (e3) (e2)) = (e0))))) -> (~((op (e2) (e2)) = (e0))) -> (~((op (e2) (e3)) = (e0))) -> (((op (e2) (e0)) = (e0))\/(((op (e2) (e1)) = (e0))\/(((op (e2) (e2)) = (e0))\/((op (e2) (e3)) = (e0))))) -> (~((op (e3) (e0)) = (e0))) -> (((op (e0) (e0)) = (e0))\/(((op (e1) (e0)) = (e0))\/(((op (e2) (e0)) = (e0))\/((op (e3) (e0)) = (e0))))) -> (~((op (e3) (e0)) = (op (e3) (e1)))) -> (~((op (e2) (e0)) = (op (e2) (e1)))) -> (~((op (e0) (e2)) = (op (e0) (e3)))) -> (~((op (e1) (e0)) = (op (e1) (e3)))) -> (~((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 (e3) (e2)) = (e0))) -> (((op (e3) (e0)) = (e0))\/(((op (e3) (e1)) = (e0))\/(((op (e3) (e2)) = (e0))\/((op (e3) (e3)) = (e0))))) -> (~((op (e1) (e1)) = (e0))) -> (~((op (e1) (e2)) = (e0))) -> (((op (e0) (e0)) = (e0))\/(((op (e0) (e1)) = (e0))\/(((op (e0) (e2)) = (e0))\/((op (e0) (e3)) = (e0))))) -> False). % 18.68/18.91 do 0 intro. intros zenon_H1ec zenon_Hac zenon_H95 zenon_H3f zenon_H20b zenon_H245 zenon_H30 zenon_H24a zenon_H24b zenon_H1a4 zenon_H6a zenon_H81 zenon_H32 zenon_H2f zenon_H40 zenon_H3e zenon_H1cf zenon_H1f0 zenon_H208 zenon_Hd8 zenon_H1c7 zenon_H130 zenon_H67 zenon_H18b zenon_H1ac zenon_H24 zenon_H25 zenon_H74. % 18.68/18.91 apply (zenon_or_s _ _ zenon_H1ec); [ zenon_intro zenon_H1ae | zenon_intro zenon_H15e ]. % 18.68/18.91 apply (zenon_L648_); trivial. % 18.68/18.91 apply (zenon_L252_); trivial. % 18.68/18.91 (* end of lemma zenon_L663_ *) % 18.68/18.91 assert (zenon_L664_ : (((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 (e3) (e1)) = (e0))\/(((op (e3) (e1)) = (e1))\/(((op (e3) (e1)) = (e2))\/((op (e3) (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 (e0) (e0)) = (e2)) -> ((op (e2) (e0)) = (e1)) -> ((op (e1) (e0)) = (e0)) -> ((~((op (e0) (e3)) = (e0)))\/((op (e0) (e0)) = (e3))) -> ((~((op (e1) (e1)) = (e0)))\/((op (e1) (e0)) = (e1))) -> (~((e1) = (e2))) -> ((~((op (e2) (e3)) = (e0)))\/((op (e2) (e0)) = (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)) = (e0)))\/((op (e3) (e0)) = (e2))) -> (~((op (e2) (e2)) = (op (e3) (e2)))) -> (((op (e3) (e2)) = (e0))\/(((op (e3) (e2)) = (e1))\/(((op (e3) (e2)) = (e2))\/((op (e3) (e2)) = (e3))))) -> (~((op (e0) (e2)) = (op (e1) (e2)))) -> (((op (e1) (e2)) = (e0))\/(((op (e1) (e2)) = (e1))\/(((op (e1) (e2)) = (e2))\/((op (e1) (e2)) = (e3))))) -> (~((e1) = (e3))) -> (~((e0) = (e3))) -> (~((op (e1) (e1)) = (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) (e3)) = (e0))\/(((op (e2) (e3)) = (e1))\/(((op (e2) (e3)) = (e2))\/((op (e2) (e3)) = (e3))))) -> (~((op (e0) (e3)) = (op (e1) (e3)))) -> (~((op (e0) (e1)) = (op (e1) (e1)))) -> (~((e0) = (e1))) -> (~((op (e0) (e2)) = (op (e2) (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) (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 (e2) (e3)))) -> (((op (e0) (e3)) = (e0))\/(((op (e0) (e3)) = (e1))\/(((op (e0) (e3)) = (e2))\/((op (e0) (e3)) = (e3))))) -> (~((op (e2) (e1)) = (op (e3) (e1)))) -> (((op (e2) (e0)) = (e3))\/(((op (e2) (e1)) = (e3))\/(((op (e2) (e2)) = (e3))\/((op (e2) (e3)) = (e3))))) -> (((op (e2) (e0)) = (e1))\/(((op (e2) (e1)) = (e1))\/(((op (e2) (e2)) = (e1))\/((op (e2) (e3)) = (e1))))) -> (~((op (e2) (e3)) = (op (e3) (e3)))) -> (~((op (e3) (e3)) = (e3))) -> (((op (e3) (e3)) = (e0))\/(((op (e3) (e3)) = (e1))\/(((op (e3) (e3)) = (e2))\/((op (e3) (e3)) = (e3))))) -> (~((op (e1) (e2)) = (op (e2) (e2)))) -> (((op (e0) (e1)) = (e1))\/(((op (e1) (e1)) = (e1))\/(((op (e2) (e1)) = (e1))\/((op (e3) (e1)) = (e1))))) -> (~((op (e0) (e0)) = (op (e0) (e3)))) -> ((~((op (e2) (e2)) = (e0)))\/((op (e2) (e0)) = (e2))) -> ((~((op (e3) (e0)) = (e0)))\/((op (e3) (e0)) = (e0))) -> (((op (e0) (e0)) = (e2))\/(((op (e0) (e1)) = (e2))\/(((op (e0) (e2)) = (e2))\/((op (e0) (e3)) = (e2))))) -> (~((op (e2) (e0)) = (op (e3) (e0)))) -> (~((op (e0) (e1)) = (op (e2) (e1)))) -> ((~((op (e1) (e2)) = (e0)))\/((op (e1) (e0)) = (e2))) -> ((~((op (e1) (e3)) = (e0)))\/((op (e1) (e0)) = (e3))) -> (((op (e1) (e1)) = (e0))\/(((op (e1) (e1)) = (e1))\/(((op (e1) (e1)) = (e2))\/((op (e1) (e1)) = (e3))))) -> (~((op (e1) (e1)) = (op (e2) (e1)))) -> (~((op (e0) (e0)) = (op (e0) (e2)))) -> (((op (e0) (e2)) = (e1))\/(((op (e1) (e2)) = (e1))\/(((op (e2) (e2)) = (e1))\/((op (e3) (e2)) = (e1))))) -> (((op (e1) (e0)) = (e1))\/(((op (e1) (e1)) = (e1))\/(((op (e1) (e2)) = (e1))\/((op (e1) (e3)) = (e1))))) -> (((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))))) -> (~((e2) = (e3))) -> (~((op (e1) (e2)) = (op (e1) (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 (e2) (e2)) = (e2))) -> (((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) (e1)) = (op (e3) (e1)))) -> (((op (e3) (e0)) = (e3))\/(((op (e3) (e1)) = (e3))\/(((op (e3) (e2)) = (e3))\/((op (e3) (e3)) = (e3))))) -> (~((e0) = (e2))) -> (~((op (e0) (e2)) = (op (e3) (e2)))) -> (((op (e3) (e0)) = (e2))\/(((op (e3) (e1)) = (e2))\/(((op (e3) (e2)) = (e2))\/((op (e3) (e3)) = (e2))))) -> (~((op (e0) (e0)) = (op (e2) (e0)))) -> ((~((op (e2) (e1)) = (e0)))\/((op (e2) (e0)) = (e1))) -> (((op (e0) (e0)) = (e2))\/(((op (e1) (e0)) = (e2))\/(((op (e2) (e0)) = (e2))\/((op (e3) (e0)) = (e2))))) -> ((~((op (e2) (e0)) = (e0)))\/((op (e2) (e0)) = (e0))) -> (((op (e0) (e0)) = (e3))\/(((op (e1) (e0)) = (e3))\/(((op (e2) (e0)) = (e3))\/((op (e3) (e0)) = (e3))))) -> (((op (e2) (e2)) = (e0))\/(((op (e2) (e2)) = (e1))\/(((op (e2) (e2)) = (e2))\/((op (e2) (e2)) = (e3))))) -> (((op (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 (e0) (e1)) = (e2))\/(((op (e1) (e1)) = (e2))\/(((op (e2) (e1)) = (e2))\/((op (e3) (e1)) = (e2))))) -> (((op (e2) (e0)) = (e2))\/(((op (e2) (e1)) = (e2))\/(((op (e2) (e2)) = (e2))\/((op (e2) (e3)) = (e2))))) -> ((~((op (e3) (e3)) = (e0)))\/((op (e3) (e0)) = (e3))) -> ((~((op (e3) (e1)) = (e0)))\/((op (e3) (e0)) = (e1))) -> (((op (e1) (e0)) = (e0))\/(((op (e1) (e1)) = (e0))\/(((op (e1) (e2)) = (e0))\/((op (e1) (e3)) = (e0))))) -> (~((op (e1) (e0)) = (op (e1) (e1)))) -> (~((op (e0) (e1)) = (op (e0) (e3)))) -> (~((op (e1) (e1)) = (op (e1) (e3)))) -> (~((op (e2) (e0)) = (op (e2) (e3)))) -> (~((op (e3) (e2)) = (op (e3) (e3)))) -> (~((op (e2) (e0)) = (op (e2) (e2)))) -> (~((op (e1) (e1)) = (op (e1) (e2)))) -> (~((op (e0) (e1)) = (op (e0) (e2)))) -> (~((op (e3) (e0)) = (op (e3) (e3)))) -> (~((op (e2) (e2)) = (op (e2) (e3)))) -> (~((op (e3) (e0)) = (op (e3) (e2)))) -> (~((op (e1) (e0)) = (op (e3) (e0)))) -> (~((op (e1) (e0)) = (op (e2) (e0)))) -> ((~((op (e1) (e0)) = (e0)))\/((op (e1) (e0)) = (e0))) -> ((~((op (e0) (e2)) = (e0)))\/((op (e0) (e0)) = (e2))) -> (~((op (e0) (e0)) = (e0))) -> (~((op (e0) (e1)) = (e0))) -> (((op (e0) (e1)) = (e0))\/(((op (e1) (e1)) = (e0))\/(((op (e2) (e1)) = (e0))\/((op (e3) (e1)) = (e0))))) -> (~((op (e2) (e0)) = (e0))) -> (~((op (e1) (e0)) = (op (e1) (e2)))) -> (~((op (e2) (e1)) = (op (e2) (e2)))) -> (~((op (e3) (e1)) = (op (e3) (e2)))) -> (((op (e0) (e2)) = (e0))\/(((op (e1) (e2)) = (e0))\/(((op (e2) (e2)) = (e0))\/((op (e3) (e2)) = (e0))))) -> (~((op (e2) (e2)) = (e0))) -> (~((op (e2) (e3)) = (e0))) -> (((op (e2) (e0)) = (e0))\/(((op (e2) (e1)) = (e0))\/(((op (e2) (e2)) = (e0))\/((op (e2) (e3)) = (e0))))) -> (~((op (e3) (e0)) = (e0))) -> (((op (e0) (e0)) = (e0))\/(((op (e1) (e0)) = (e0))\/(((op (e2) (e0)) = (e0))\/((op (e3) (e0)) = (e0))))) -> (~((op (e3) (e0)) = (op (e3) (e1)))) -> (~((op (e2) (e0)) = (op (e2) (e1)))) -> (~((op (e0) (e2)) = (op (e0) (e3)))) -> (~((op (e1) (e0)) = (op (e1) (e3)))) -> (~((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 (e3) (e0)) = (e0))\/(((op (e3) (e1)) = (e0))\/(((op (e3) (e2)) = (e0))\/((op (e3) (e3)) = (e0))))) -> (~((op (e1) (e1)) = (e0))) -> (~((op (e1) (e2)) = (e0))) -> (((op (e0) (e0)) = (e0))\/(((op (e0) (e1)) = (e0))\/(((op (e0) (e2)) = (e0))\/((op (e0) (e3)) = (e0))))) -> ((op (e0) (e0)) = (e3)) -> False). % 18.68/18.91 do 0 intro. intros zenon_H22d zenon_H235 zenon_H22a zenon_H210 zenon_H212 zenon_H7b zenon_Hed zenon_H27 zenon_H204 zenon_H205 zenon_H7c zenon_H94 zenon_H1a5 zenon_H1a6 zenon_H1a7 zenon_H18f zenon_H191 zenon_H195 zenon_H19d zenon_H95 zenon_H9a zenon_H10a zenon_H18c zenon_H115 zenon_H11f zenon_H1d zenon_H10e zenon_Ha1 zenon_Ha8 zenon_He8 zenon_Hc2 zenon_Hdf zenon_Hdb zenon_Hd5 zenon_He2 zenon_He4 zenon_Haf zenon_He7 zenon_H106 zenon_Hf3 zenon_H102 zenon_H101 zenon_H2b zenon_H109 zenon_H189 zenon_H185 zenon_H184 zenon_H183 zenon_H17b zenon_H17e zenon_H178 zenon_H179 zenon_H142 zenon_H13e zenon_H13c zenon_H139 zenon_H128 zenon_H136 zenon_H133 zenon_H12b zenon_H124 zenon_H145 zenon_H172 zenon_H173 zenon_H16f zenon_H168 zenon_H160 zenon_H165 zenon_H149 zenon_H14f zenon_H153 zenon_H39 zenon_H182 zenon_H1fe zenon_H1ee zenon_H1e0 zenon_H1c4 zenon_H1cc zenon_H1ba zenon_H1d8 zenon_H1d5 zenon_H1ec zenon_H1ed zenon_H22 zenon_H45 zenon_H54 zenon_H57 zenon_H5b zenon_H62 zenon_H52 zenon_H4f zenon_H4a zenon_H71 zenon_H6d zenon_H6f zenon_H1fa zenon_H201 zenon_H206 zenon_H233 zenon_H3f zenon_H20b zenon_H245 zenon_H30 zenon_H24a zenon_H24b zenon_H1a4 zenon_H6a zenon_H81 zenon_H32 zenon_H2f zenon_H40 zenon_H3e zenon_H1cf zenon_H1f0 zenon_H208 zenon_Hd8 zenon_H1c7 zenon_H130 zenon_H67 zenon_H1ac zenon_H24 zenon_H25 zenon_H74 zenon_H3a. % 18.68/18.91 apply (zenon_or_s _ _ zenon_H1ed); [ zenon_intro zenon_H1ad | zenon_intro zenon_Hac ]. % 18.68/18.91 apply (zenon_or_s _ _ zenon_H1a7); [ zenon_intro zenon_H18b | zenon_intro zenon_H148 ]. % 18.68/18.91 apply (zenon_L662_); trivial. % 18.68/18.91 apply (zenon_L423_); trivial. % 18.68/18.91 apply (zenon_or_s _ _ zenon_H1a7); [ zenon_intro zenon_H18b | zenon_intro zenon_H148 ]. % 18.68/18.91 apply (zenon_L663_); trivial. % 18.68/18.91 apply (zenon_L423_); trivial. % 18.68/18.91 (* end of lemma zenon_L664_ *) % 18.68/18.91 assert (zenon_L665_ : (((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) (e0)) = (op (e2) (e2)))) -> ((op (e2) (e0)) = (e3)) -> ((op (e3) (e0)) = (e3)) -> (~((op (e3) (e0)) = (op (e3) (e2)))) -> False). % 18.68/18.91 do 0 intro. intros zenon_H1a6 zenon_H9a zenon_H48 zenon_H95 zenon_Hf0 zenon_H52 zenon_H3b zenon_H15e zenon_H6f. % 18.68/18.91 apply (zenon_or_s _ _ zenon_H1a6); [ zenon_intro zenon_Ha9 | zenon_intro zenon_H1aa ]. % 18.68/18.91 apply (zenon_L358_); trivial. % 18.68/18.91 apply (zenon_or_s _ _ zenon_H1aa); [ zenon_intro zenon_H16c | zenon_intro zenon_H1ab ]. % 18.68/18.91 apply (zenon_L167_); trivial. % 18.68/18.91 apply (zenon_or_s _ _ zenon_H1ab); [ zenon_intro zenon_Haa | zenon_intro zenon_H163 ]. % 18.68/18.91 apply (zenon_L168_); trivial. % 18.68/18.91 apply (zenon_L286_); trivial. % 18.68/18.91 (* end of lemma zenon_L665_ *) % 18.68/18.91 assert (zenon_L666_ : (((op (e1) (e0)) = (e3))\/(((op (e1) (e1)) = (e3))\/(((op (e1) (e2)) = (e3))\/((op (e1) (e3)) = (e3))))) -> ((op (e0) (e0)) = (e2)) -> (~((e2) = (e3))) -> ((op (e1) (e1)) = (e2)) -> (~((op (e2) (e0)) = (op (e2) (e2)))) -> ((op (e2) (e0)) = (e3)) -> (~((op (e2) (e2)) = (e2))) -> (~((op (e2) (e2)) = (op (e3) (e2)))) -> (~((op (e2) (e2)) = (e0))) -> (((op (e2) (e2)) = (e0))\/(((op (e2) (e2)) = (e1))\/(((op (e2) (e2)) = (e2))\/((op (e2) (e2)) = (e3))))) -> ((op (e2) (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 (e1) (e3)) = (e1)) -> (~((e1) = (e3))) -> False). % 18.68/18.91 do 0 intro. intros zenon_H16f zenon_H7b zenon_H12b zenon_H110 zenon_H52 zenon_H3b zenon_H173 zenon_H18f zenon_H81 zenon_H1c4 zenon_Hed zenon_Ha0 zenon_H4a zenon_H139 zenon_Hd6 zenon_H95. % 18.68/18.91 apply (zenon_or_s _ _ zenon_H16f); [ zenon_intro zenon_H9e | zenon_intro zenon_H170 ]. % 18.68/18.91 apply (zenon_L491_); trivial. % 18.68/18.91 apply (zenon_or_s _ _ zenon_H170); [ zenon_intro zenon_H13f | zenon_intro zenon_H171 ]. % 18.68/18.91 apply (zenon_L166_); trivial. % 18.68/18.91 apply (zenon_or_s _ _ zenon_H171); [ zenon_intro zenon_H16c | zenon_intro zenon_Hdc ]. % 18.68/18.91 apply (zenon_L461_); trivial. % 18.68/18.91 apply (zenon_L83_); trivial. % 18.68/18.91 (* end of lemma zenon_L666_ *) % 18.68/18.91 assert (zenon_L667_ : (((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)) = (e1)) -> (~((op (e1) (e1)) = (e1))) -> (~((op (e3) (e0)) = (op (e3) (e2)))) -> ((op (e3) (e0)) = (e3)) -> ((op (e2) (e0)) = (e3)) -> (~((op (e2) (e0)) = (op (e2) (e2)))) -> (~((e1) = (e3))) -> ((op (e0) (e2)) = (e0)) -> (~((e0) = (e3))) -> (((op (e0) (e2)) = (e3))\/(((op (e1) (e2)) = (e3))\/(((op (e2) (e2)) = (e3))\/((op (e3) (e2)) = (e3))))) -> (~((op (e0) (e3)) = (op (e1) (e3)))) -> ((op (e0) (e3)) = (e1)) -> False). % 18.68/18.91 do 0 intro. intros zenon_H128 zenon_H201 zenon_Hed zenon_H10a zenon_H6f zenon_H15e zenon_H3b zenon_H52 zenon_H95 zenon_H48 zenon_H9a zenon_H1a6 zenon_H1d zenon_Hc3. % 18.68/18.91 apply (zenon_or_s _ _ zenon_H128); [ zenon_intro zenon_H9d | zenon_intro zenon_H129 ]. % 18.68/18.91 apply (zenon_L413_); trivial. % 18.68/18.91 apply (zenon_or_s _ _ zenon_H129); [ zenon_intro zenon_H10d | zenon_intro zenon_H12a ]. % 18.68/18.91 exact (zenon_H10a zenon_H10d). % 18.68/18.91 apply (zenon_or_s _ _ zenon_H12a); [ zenon_intro zenon_Hf0 | zenon_intro zenon_Hd6 ]. % 18.68/18.91 apply (zenon_L665_); trivial. % 18.68/18.91 apply (zenon_L79_); trivial. % 18.68/18.91 (* end of lemma zenon_L667_ *) % 18.68/18.91 assert (zenon_L668_ : ((~((op (e3) (e3)) = (e0)))\/((op (e3) (e0)) = (e3))) -> (~((op (e0) (e0)) = (e0))) -> (~((op (e0) (e1)) = (e0))) -> (((op (e0) (e0)) = (e1))\/(((op (e0) (e1)) = (e1))\/(((op (e0) (e2)) = (e1))\/((op (e0) (e3)) = (e1))))) -> (~((op (e1) (e0)) = (op (e2) (e0)))) -> (~((op (e0) (e3)) = (op (e1) (e3)))) -> (~((e0) = (e1))) -> ((op (e1) (e0)) = (e0)) -> (~((op (e1) (e1)) = (e1))) -> (((op (e0) (e2)) = (e3))\/(((op (e1) (e2)) = (e3))\/(((op (e2) (e2)) = (e3))\/((op (e3) (e2)) = (e3))))) -> (~((op (e3) (e0)) = (op (e3) (e2)))) -> ((op (e2) (e0)) = (e3)) -> (~((op (e2) (e0)) = (op (e2) (e2)))) -> (~((e1) = (e3))) -> (~((e0) = (e3))) -> (((op (e1) (e0)) = (e2))\/(((op (e1) (e1)) = (e2))\/(((op (e1) (e2)) = (e2))\/((op (e1) (e3)) = (e2))))) -> (~((e1) = (e2))) -> ((op (e0) (e0)) = (e2)) -> (~((e2) = (e3))) -> (((op (e0) (e2)) = (e1))\/(((op (e1) (e2)) = (e1))\/(((op (e2) (e2)) = (e1))\/((op (e3) (e2)) = (e1))))) -> (~((op (e2) (e2)) = (e0))) -> (~((op (e2) (e2)) = (op (e3) (e2)))) -> (~((op (e2) (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) (e0)) = (e3))\/(((op (e1) (e1)) = (e3))\/(((op (e1) (e2)) = (e3))\/((op (e1) (e3)) = (e3))))) -> (~((e0) = (e2))) -> (((op (e1) (e0)) = (e1))\/(((op (e1) (e1)) = (e1))\/(((op (e1) (e2)) = (e1))\/((op (e1) (e3)) = (e1))))) -> ((op (e2) (e0)) = (e1)) -> (~((op (e0) (e0)) = (op (e2) (e0)))) -> (((op (e0) (e2)) = (e0))\/(((op (e1) (e2)) = (e0))\/(((op (e2) (e2)) = (e0))\/((op (e3) (e2)) = (e0))))) -> (~((op (e1) (e2)) = (e0))) -> (~((op (e0) (e2)) = (op (e0) (e3)))) -> (((op (e0) (e0)) = (e0))\/(((op (e0) (e1)) = (e0))\/(((op (e0) (e2)) = (e0))\/((op (e0) (e3)) = (e0))))) -> (~((op (e3) (e0)) = (e0))) -> (~((op (e3) (e1)) = (e0))) -> (~((op (e3) (e2)) = (e0))) -> (((op (e3) (e0)) = (e0))\/(((op (e3) (e1)) = (e0))\/(((op (e3) (e2)) = (e0))\/((op (e3) (e3)) = (e0))))) -> False). % 18.68/18.91 do 0 intro. intros zenon_H1ec zenon_H3f zenon_H20b zenon_H22d zenon_H201 zenon_H1d zenon_Ha1 zenon_H27 zenon_H10a zenon_H1a6 zenon_H6f zenon_H3b zenon_H52 zenon_H95 zenon_H9a zenon_H18c zenon_H7c zenon_H7b zenon_H12b zenon_H139 zenon_H81 zenon_H18f zenon_H173 zenon_H1c4 zenon_H4a zenon_H16f zenon_H149 zenon_H128 zenon_Hed zenon_H39 zenon_H6a zenon_H25 zenon_H208 zenon_H74 zenon_H40 zenon_H1ad zenon_H18b zenon_H1ac. % 18.68/18.91 apply (zenon_or_s _ _ zenon_H1ec); [ zenon_intro zenon_H1ae | zenon_intro zenon_H15e ]. % 18.68/18.91 apply (zenon_L174_); trivial. % 18.68/18.91 apply (zenon_or_s _ _ zenon_H74); [ zenon_intro zenon_H42 | zenon_intro zenon_H77 ]. % 18.68/18.91 exact (zenon_H3f zenon_H42). % 18.68/18.91 apply (zenon_or_s _ _ zenon_H77); [ zenon_intro zenon_H49 | zenon_intro zenon_H78 ]. % 18.68/18.91 exact (zenon_H20b zenon_H49). % 18.68/18.91 apply (zenon_or_s _ _ zenon_H78); [ zenon_intro zenon_H48 | zenon_intro zenon_H1e ]. % 18.68/18.91 apply (zenon_or_s _ _ zenon_H22d); [ zenon_intro zenon_H7a | zenon_intro zenon_H22e ]. % 18.68/18.91 apply (zenon_L134_); trivial. % 18.68/18.91 apply (zenon_or_s _ _ zenon_H22e); [ zenon_intro zenon_Ha0 | zenon_intro zenon_H22f ]. % 18.68/18.91 apply (zenon_or_s _ _ zenon_H128); [ zenon_intro zenon_H9d | zenon_intro zenon_H129 ]. % 18.68/18.91 apply (zenon_L262_); trivial. % 18.68/18.91 apply (zenon_or_s _ _ zenon_H129); [ zenon_intro zenon_H10d | zenon_intro zenon_H12a ]. % 18.68/18.91 exact (zenon_H10a zenon_H10d). % 18.68/18.91 apply (zenon_or_s _ _ zenon_H12a); [ zenon_intro zenon_Hf0 | zenon_intro zenon_Hd6 ]. % 18.68/18.91 apply (zenon_L665_); trivial. % 18.68/18.91 apply (zenon_or_s _ _ zenon_H18c); [ zenon_intro zenon_H86 | zenon_intro zenon_H18d ]. % 18.68/18.91 apply (zenon_L257_); trivial. % 18.68/18.91 apply (zenon_or_s _ _ zenon_H18d); [ zenon_intro zenon_H110 | zenon_intro zenon_H18e ]. % 18.68/18.91 apply (zenon_L666_); trivial. % 18.68/18.91 apply (zenon_or_s _ _ zenon_H18e); [ zenon_intro zenon_H113 | zenon_intro zenon_Hd7 ]. % 18.68/18.91 apply (zenon_L356_); trivial. % 18.68/18.91 apply (zenon_L101_); trivial. % 18.68/18.91 apply (zenon_or_s _ _ zenon_H22f); [ zenon_intro zenon_H122 | zenon_intro zenon_Hc3 ]. % 18.68/18.91 apply (zenon_L355_); trivial. % 18.68/18.91 apply (zenon_L667_); trivial. % 18.68/18.91 apply (zenon_L337_); trivial. % 18.68/18.91 (* end of lemma zenon_L668_ *) % 18.68/18.91 assert (zenon_L669_ : (~((op (e0) (e3)) = (e0))) -> (((op (e0) (e0)) = (e0))\/(((op (e0) (e1)) = (e0))\/(((op (e0) (e2)) = (e0))\/((op (e0) (e3)) = (e0))))) -> (~((op (e1) (e2)) = (e0))) -> (~((op (e1) (e1)) = (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 (e2) (e1)) = (op (e2) (e3)))) -> (~((op (e1) (e0)) = (op (e1) (e3)))) -> (~((op (e0) (e2)) = (op (e0) (e3)))) -> (~((op (e2) (e0)) = (op (e2) (e1)))) -> (~((op (e3) (e0)) = (op (e3) (e1)))) -> (((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 (e0) (e2)) = (e0))\/(((op (e1) (e2)) = (e0))\/(((op (e2) (e2)) = (e0))\/((op (e3) (e2)) = (e0))))) -> (~((op (e3) (e1)) = (op (e3) (e2)))) -> (~((op (e2) (e1)) = (op (e2) (e2)))) -> (~((op (e1) (e0)) = (op (e1) (e2)))) -> (~((op (e2) (e0)) = (e0))) -> (((op (e0) (e1)) = (e0))\/(((op (e1) (e1)) = (e0))\/(((op (e2) (e1)) = (e0))\/((op (e3) (e1)) = (e0))))) -> (~((op (e0) (e1)) = (e0))) -> (~((op (e0) (e0)) = (e0))) -> ((~((op (e0) (e2)) = (e0)))\/((op (e0) (e0)) = (e2))) -> ((~((op (e1) (e0)) = (e0)))\/((op (e1) (e0)) = (e0))) -> (~((op (e1) (e0)) = (op (e2) (e0)))) -> (~((op (e1) (e0)) = (op (e3) (e0)))) -> (~((op (e3) (e0)) = (op (e3) (e2)))) -> (~((op (e2) (e2)) = (op (e2) (e3)))) -> (~((op (e3) (e0)) = (op (e3) (e3)))) -> (~((op (e0) (e1)) = (op (e0) (e2)))) -> (~((op (e1) (e1)) = (op (e1) (e2)))) -> (~((op (e2) (e0)) = (op (e2) (e2)))) -> (~((op (e3) (e2)) = (op (e3) (e3)))) -> (~((op (e2) (e0)) = (op (e2) (e3)))) -> (~((op (e1) (e1)) = (op (e1) (e3)))) -> (~((op (e0) (e1)) = (op (e0) (e3)))) -> (~((op (e1) (e0)) = (op (e1) (e1)))) -> (((op (e1) (e0)) = (e0))\/(((op (e1) (e1)) = (e0))\/(((op (e1) (e2)) = (e0))\/((op (e1) (e3)) = (e0))))) -> ((~((op (e3) (e1)) = (e0)))\/((op (e3) (e0)) = (e1))) -> ((~((op (e3) (e3)) = (e0)))\/((op (e3) (e0)) = (e3))) -> (((op (e2) (e0)) = (e2))\/(((op (e2) (e1)) = (e2))\/(((op (e2) (e2)) = (e2))\/((op (e2) (e3)) = (e2))))) -> (((op (e0) (e1)) = (e2))\/(((op (e1) (e1)) = (e2))\/(((op (e2) (e1)) = (e2))\/((op (e3) (e1)) = (e2))))) -> (((op (e0) (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 (e2) (e2)) = (e0))\/(((op (e2) (e2)) = (e1))\/(((op (e2) (e2)) = (e2))\/((op (e2) (e2)) = (e3))))) -> (((op (e0) (e0)) = (e3))\/(((op (e1) (e0)) = (e3))\/(((op (e2) (e0)) = (e3))\/((op (e3) (e0)) = (e3))))) -> ((~((op (e2) (e0)) = (e0)))\/((op (e2) (e0)) = (e0))) -> (((op (e0) (e0)) = (e2))\/(((op (e1) (e0)) = (e2))\/(((op (e2) (e0)) = (e2))\/((op (e3) (e0)) = (e2))))) -> ((~((op (e2) (e1)) = (e0)))\/((op (e2) (e0)) = (e1))) -> (~((op (e0) (e0)) = (op (e2) (e0)))) -> (((op (e3) (e0)) = (e2))\/(((op (e3) (e1)) = (e2))\/(((op (e3) (e2)) = (e2))\/((op (e3) (e3)) = (e2))))) -> (~((op (e0) (e2)) = (op (e3) (e2)))) -> (~((e0) = (e2))) -> (((op (e3) (e0)) = (e3))\/(((op (e3) (e1)) = (e3))\/(((op (e3) (e2)) = (e3))\/((op (e3) (e3)) = (e3))))) -> (~((op (e1) (e1)) = (op (e3) (e1)))) -> (((op (e0) (e0)) = (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)) = (e2))) -> (((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) (e2)) = (op (e1) (e3)))) -> (~((e2) = (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) (e0)) = (e1))\/(((op (e1) (e1)) = (e1))\/(((op (e1) (e2)) = (e1))\/((op (e1) (e3)) = (e1))))) -> (((op (e0) (e2)) = (e1))\/(((op (e1) (e2)) = (e1))\/(((op (e2) (e2)) = (e1))\/((op (e3) (e2)) = (e1))))) -> (~((op (e0) (e0)) = (op (e0) (e2)))) -> (~((op (e1) (e1)) = (op (e2) (e1)))) -> (((op (e1) (e1)) = (e0))\/(((op (e1) (e1)) = (e1))\/(((op (e1) (e1)) = (e2))\/((op (e1) (e1)) = (e3))))) -> ((~((op (e1) (e3)) = (e0)))\/((op (e1) (e0)) = (e3))) -> ((~((op (e1) (e2)) = (e0)))\/((op (e1) (e0)) = (e2))) -> (~((op (e0) (e1)) = (op (e2) (e1)))) -> (~((op (e2) (e0)) = (op (e3) (e0)))) -> (((op (e0) (e0)) = (e2))\/(((op (e0) (e1)) = (e2))\/(((op (e0) (e2)) = (e2))\/((op (e0) (e3)) = (e2))))) -> ((~((op (e3) (e0)) = (e0)))\/((op (e3) (e0)) = (e0))) -> ((~((op (e2) (e2)) = (e0)))\/((op (e2) (e0)) = (e2))) -> (~((op (e0) (e0)) = (op (e0) (e3)))) -> (((op (e0) (e1)) = (e1))\/(((op (e1) (e1)) = (e1))\/(((op (e2) (e1)) = (e1))\/((op (e3) (e1)) = (e1))))) -> (~((op (e1) (e2)) = (op (e2) (e2)))) -> (((op (e3) (e3)) = (e0))\/(((op (e3) (e3)) = (e1))\/(((op (e3) (e3)) = (e2))\/((op (e3) (e3)) = (e3))))) -> (~((op (e3) (e3)) = (e3))) -> (~((op (e2) (e3)) = (op (e3) (e3)))) -> (((op (e2) (e0)) = (e1))\/(((op (e2) (e1)) = (e1))\/(((op (e2) (e2)) = (e1))\/((op (e2) (e3)) = (e1))))) -> (((op (e2) (e0)) = (e3))\/(((op (e2) (e1)) = (e3))\/(((op (e2) (e2)) = (e3))\/((op (e2) (e3)) = (e3))))) -> (~((op (e2) (e1)) = (op (e3) (e1)))) -> (((op (e0) (e3)) = (e0))\/(((op (e0) (e3)) = (e1))\/(((op (e0) (e3)) = (e2))\/((op (e0) (e3)) = (e3))))) -> (~((op (e0) (e3)) = (op (e2) (e3)))) -> (~((op (e1) (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) (e3)) = (op (e3) (e3)))) -> (((op (e3) (e0)) = (e1))\/(((op (e3) (e1)) = (e1))\/(((op (e3) (e2)) = (e1))\/((op (e3) (e3)) = (e1))))) -> (~((op (e0) (e2)) = (op (e2) (e2)))) -> (~((e0) = (e1))) -> (~((op (e0) (e1)) = (op (e1) (e1)))) -> (~((op (e0) (e3)) = (op (e1) (e3)))) -> (((op (e2) (e3)) = (e0))\/(((op (e2) (e3)) = (e1))\/(((op (e2) (e3)) = (e2))\/((op (e2) (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) (e1)) = (e1))) -> (~((e0) = (e3))) -> (~((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 (e3) (e2)) = (e0))\/(((op (e3) (e2)) = (e1))\/(((op (e3) (e2)) = (e2))\/((op (e3) (e2)) = (e3))))) -> (~((op (e2) (e2)) = (op (e3) (e2)))) -> ((~((op (e3) (e2)) = (e0)))\/((op (e3) (e0)) = (e2))) -> (((op (e0) (e2)) = (e3))\/(((op (e1) (e2)) = (e3))\/(((op (e2) (e2)) = (e3))\/((op (e3) (e2)) = (e3))))) -> (((op (e0) (e1)) = (e3))\/(((op (e1) (e1)) = (e3))\/(((op (e2) (e1)) = (e3))\/((op (e3) (e1)) = (e3))))) -> ((~((op (e2) (e3)) = (e0)))\/((op (e2) (e0)) = (e3))) -> (~((e1) = (e2))) -> ((~((op (e1) (e1)) = (e0)))\/((op (e1) (e0)) = (e1))) -> ((~((op (e0) (e3)) = (e0)))\/((op (e0) (e0)) = (e3))) -> ((op (e1) (e0)) = (e0)) -> ((op (e2) (e0)) = (e1)) -> ((op (e0) (e0)) = (e2)) -> (((op (e0) (e1)) = (e0))\/(((op (e0) (e1)) = (e1))\/(((op (e0) (e1)) = (e2))\/((op (e0) (e1)) = (e3))))) -> (~((op (e0) (e1)) = (op (e3) (e1)))) -> (((op (e3) (e1)) = (e0))\/(((op (e3) (e1)) = (e1))\/(((op (e3) (e1)) = (e2))\/((op (e3) (e1)) = (e3))))) -> (((op (e0) (e0)) = (e1))\/(((op (e1) (e0)) = (e1))\/(((op (e2) (e0)) = (e1))\/((op (e3) (e0)) = (e1))))) -> (((op (e0) (e0)) = (e1))\/(((op (e0) (e1)) = (e1))\/(((op (e0) (e2)) = (e1))\/((op (e0) (e3)) = (e1))))) -> False). % 18.68/18.91 do 0 intro. intros zenon_H76 zenon_H74 zenon_H25 zenon_H24 zenon_H1ac zenon_H67 zenon_H130 zenon_H1c7 zenon_Hd8 zenon_H208 zenon_H1f0 zenon_H1cf zenon_H3e zenon_H2f zenon_H6a zenon_H1a4 zenon_H24b zenon_H24a zenon_H30 zenon_H245 zenon_H20b zenon_H3f zenon_H233 zenon_H206 zenon_H201 zenon_H1fa zenon_H6f zenon_H6d zenon_H71 zenon_H4a zenon_H4f zenon_H52 zenon_H62 zenon_H5b zenon_H57 zenon_H54 zenon_H45 zenon_H22 zenon_H1ed zenon_H1ec zenon_H1d5 zenon_H1d8 zenon_H1ba zenon_H1cc zenon_H1c4 zenon_H1e0 zenon_H1ee zenon_H1fe zenon_H182 zenon_H39 zenon_H153 zenon_H14f zenon_H149 zenon_H165 zenon_H160 zenon_H168 zenon_H16f zenon_H173 zenon_H172 zenon_H145 zenon_H124 zenon_H12b zenon_H133 zenon_H136 zenon_H128 zenon_H139 zenon_H13c zenon_H13e zenon_H142 zenon_H179 zenon_H178 zenon_H17e zenon_H17b zenon_H183 zenon_H184 zenon_H185 zenon_H189 zenon_H109 zenon_H2b zenon_H101 zenon_H102 zenon_Hf3 zenon_H106 zenon_He7 zenon_Haf zenon_He4 zenon_He2 zenon_Hd5 zenon_Hdb zenon_Hdf zenon_Hc2 zenon_He8 zenon_Ha8 zenon_Ha1 zenon_H10e zenon_H1d zenon_H11f zenon_H115 zenon_H18c zenon_H10a zenon_H9a zenon_H95 zenon_H19d zenon_H195 zenon_H191 zenon_H18f zenon_H1a7 zenon_H1a6 zenon_H1a5 zenon_H94 zenon_H7c zenon_H205 zenon_H204 zenon_H27 zenon_Hed zenon_H7b zenon_H212 zenon_H210 zenon_H22a zenon_H235 zenon_H22d. % 18.68/18.91 apply (zenon_or_s _ _ zenon_H185); [ zenon_intro zenon_H81 | zenon_intro zenon_Hee ]. % 18.68/18.91 apply (zenon_or_s _ _ zenon_H94); [ zenon_intro zenon_H32 | zenon_intro zenon_H3b ]. % 18.68/18.91 apply (zenon_or_s _ _ zenon_H184); [ zenon_intro zenon_H40 | zenon_intro zenon_H44 ]. % 18.68/18.91 apply (zenon_or_s _ _ zenon_H1ed); [ zenon_intro zenon_H1ad | zenon_intro zenon_Hac ]. % 18.68/18.91 apply (zenon_or_s _ _ zenon_H1a7); [ zenon_intro zenon_H18b | zenon_intro zenon_H148 ]. % 18.68/18.91 apply (zenon_L662_); trivial. % 18.68/18.91 apply (zenon_L624_); trivial. % 18.68/18.91 apply (zenon_or_s _ _ zenon_H1a7); [ zenon_intro zenon_H18b | zenon_intro zenon_H148 ]. % 18.68/18.91 apply (zenon_L663_); trivial. % 18.68/18.91 apply (zenon_or_s _ _ zenon_H1e0); [ zenon_intro zenon_H3a | zenon_intro zenon_H1e1 ]. % 18.68/18.91 apply (zenon_L664_); trivial. % 18.68/18.91 apply (zenon_or_s _ _ zenon_H1e1); [ zenon_intro zenon_H9e | zenon_intro zenon_H1e2 ]. % 18.68/18.91 apply (zenon_L491_); trivial. % 18.68/18.91 apply (zenon_or_s _ _ zenon_H1e2); [ zenon_intro zenon_H3b | zenon_intro zenon_H15e ]. % 18.68/18.91 apply (zenon_L308_); trivial. % 18.68/18.91 apply (zenon_L109_); trivial. % 18.68/18.91 apply (zenon_L312_); trivial. % 18.68/18.91 apply (zenon_or_s _ _ zenon_H184); [ zenon_intro zenon_H40 | zenon_intro zenon_H44 ]. % 18.68/18.91 apply (zenon_or_s _ _ zenon_H1ed); [ zenon_intro zenon_H1ad | zenon_intro zenon_Hac ]. % 18.68/18.91 apply (zenon_or_s _ _ zenon_H1a7); [ zenon_intro zenon_H18b | zenon_intro zenon_H148 ]. % 18.68/18.91 apply (zenon_L668_); trivial. % 18.68/18.91 apply (zenon_L624_); trivial. % 18.68/18.91 apply (zenon_L308_); trivial. % 18.68/18.91 apply (zenon_L312_); trivial. % 18.68/18.91 apply (zenon_L58_); trivial. % 18.68/18.91 (* end of lemma zenon_L669_ *) % 18.68/18.91 assert (zenon_L670_ : ((op (e0) (e0)) = (e3)) -> (((op (e0) (e0)) = (e0))\/(((op (e0) (e1)) = (e0))\/(((op (e0) (e2)) = (e0))\/((op (e0) (e3)) = (e0))))) -> (~((op (e1) (e2)) = (e0))) -> (~((op (e1) (e1)) = (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 (e2) (e1)) = (op (e2) (e3)))) -> (~((op (e1) (e0)) = (op (e1) (e3)))) -> (~((op (e0) (e2)) = (op (e0) (e3)))) -> (~((op (e2) (e0)) = (op (e2) (e1)))) -> (~((op (e3) (e0)) = (op (e3) (e1)))) -> (((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 (e0) (e2)) = (e0))\/(((op (e1) (e2)) = (e0))\/(((op (e2) (e2)) = (e0))\/((op (e3) (e2)) = (e0))))) -> (~((op (e3) (e1)) = (op (e3) (e2)))) -> (~((op (e2) (e1)) = (op (e2) (e2)))) -> (~((op (e1) (e0)) = (op (e1) (e2)))) -> (~((op (e2) (e0)) = (e0))) -> (((op (e0) (e1)) = (e0))\/(((op (e1) (e1)) = (e0))\/(((op (e2) (e1)) = (e0))\/((op (e3) (e1)) = (e0))))) -> (~((op (e0) (e1)) = (e0))) -> (~((op (e0) (e0)) = (e0))) -> ((~((op (e0) (e2)) = (e0)))\/((op (e0) (e0)) = (e2))) -> ((~((op (e1) (e0)) = (e0)))\/((op (e1) (e0)) = (e0))) -> (~((op (e1) (e0)) = (op (e2) (e0)))) -> (~((op (e1) (e0)) = (op (e3) (e0)))) -> (~((op (e3) (e0)) = (op (e3) (e2)))) -> (~((op (e2) (e2)) = (op (e2) (e3)))) -> (~((op (e3) (e0)) = (op (e3) (e3)))) -> (~((op (e0) (e1)) = (op (e0) (e2)))) -> (~((op (e1) (e1)) = (op (e1) (e2)))) -> (~((op (e2) (e0)) = (op (e2) (e2)))) -> (~((op (e3) (e2)) = (op (e3) (e3)))) -> (~((op (e2) (e0)) = (op (e2) (e3)))) -> (~((op (e1) (e1)) = (op (e1) (e3)))) -> (~((op (e0) (e1)) = (op (e0) (e3)))) -> (~((op (e1) (e0)) = (op (e1) (e1)))) -> (((op (e1) (e0)) = (e0))\/(((op (e1) (e1)) = (e0))\/(((op (e1) (e2)) = (e0))\/((op (e1) (e3)) = (e0))))) -> ((~((op (e3) (e1)) = (e0)))\/((op (e3) (e0)) = (e1))) -> ((~((op (e3) (e3)) = (e0)))\/((op (e3) (e0)) = (e3))) -> (((op (e2) (e0)) = (e2))\/(((op (e2) (e1)) = (e2))\/(((op (e2) (e2)) = (e2))\/((op (e2) (e3)) = (e2))))) -> (((op (e0) (e1)) = (e2))\/(((op (e1) (e1)) = (e2))\/(((op (e2) (e1)) = (e2))\/((op (e3) (e1)) = (e2))))) -> (((op (e0) (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 (e2) (e2)) = (e0))\/(((op (e2) (e2)) = (e1))\/(((op (e2) (e2)) = (e2))\/((op (e2) (e2)) = (e3))))) -> (((op (e0) (e0)) = (e3))\/(((op (e1) (e0)) = (e3))\/(((op (e2) (e0)) = (e3))\/((op (e3) (e0)) = (e3))))) -> ((~((op (e2) (e0)) = (e0)))\/((op (e2) (e0)) = (e0))) -> (((op (e0) (e0)) = (e2))\/(((op (e1) (e0)) = (e2))\/(((op (e2) (e0)) = (e2))\/((op (e3) (e0)) = (e2))))) -> ((~((op (e2) (e1)) = (e0)))\/((op (e2) (e0)) = (e1))) -> (~((op (e0) (e0)) = (op (e2) (e0)))) -> (((op (e3) (e0)) = (e2))\/(((op (e3) (e1)) = (e2))\/(((op (e3) (e2)) = (e2))\/((op (e3) (e3)) = (e2))))) -> (~((op (e0) (e2)) = (op (e3) (e2)))) -> (~((e0) = (e2))) -> (((op (e3) (e0)) = (e3))\/(((op (e3) (e1)) = (e3))\/(((op (e3) (e2)) = (e3))\/((op (e3) (e3)) = (e3))))) -> (~((op (e1) (e1)) = (op (e3) (e1)))) -> (((op (e0) (e0)) = (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)) = (e2))) -> (((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) (e2)) = (op (e1) (e3)))) -> (~((e2) = (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) (e0)) = (e1))\/(((op (e1) (e1)) = (e1))\/(((op (e1) (e2)) = (e1))\/((op (e1) (e3)) = (e1))))) -> (((op (e0) (e2)) = (e1))\/(((op (e1) (e2)) = (e1))\/(((op (e2) (e2)) = (e1))\/((op (e3) (e2)) = (e1))))) -> (~((op (e0) (e0)) = (op (e0) (e2)))) -> (~((op (e1) (e1)) = (op (e2) (e1)))) -> (((op (e1) (e1)) = (e0))\/(((op (e1) (e1)) = (e1))\/(((op (e1) (e1)) = (e2))\/((op (e1) (e1)) = (e3))))) -> ((~((op (e1) (e3)) = (e0)))\/((op (e1) (e0)) = (e3))) -> ((~((op (e1) (e2)) = (e0)))\/((op (e1) (e0)) = (e2))) -> (~((op (e0) (e1)) = (op (e2) (e1)))) -> (~((op (e2) (e0)) = (op (e3) (e0)))) -> (((op (e0) (e0)) = (e2))\/(((op (e0) (e1)) = (e2))\/(((op (e0) (e2)) = (e2))\/((op (e0) (e3)) = (e2))))) -> ((~((op (e3) (e0)) = (e0)))\/((op (e3) (e0)) = (e0))) -> ((~((op (e2) (e2)) = (e0)))\/((op (e2) (e0)) = (e2))) -> (~((op (e0) (e0)) = (op (e0) (e3)))) -> (((op (e0) (e1)) = (e1))\/(((op (e1) (e1)) = (e1))\/(((op (e2) (e1)) = (e1))\/((op (e3) (e1)) = (e1))))) -> (~((op (e1) (e2)) = (op (e2) (e2)))) -> (((op (e3) (e3)) = (e0))\/(((op (e3) (e3)) = (e1))\/(((op (e3) (e3)) = (e2))\/((op (e3) (e3)) = (e3))))) -> (~((op (e3) (e3)) = (e3))) -> (~((op (e2) (e3)) = (op (e3) (e3)))) -> (((op (e2) (e0)) = (e1))\/(((op (e2) (e1)) = (e1))\/(((op (e2) (e2)) = (e1))\/((op (e2) (e3)) = (e1))))) -> (((op (e2) (e0)) = (e3))\/(((op (e2) (e1)) = (e3))\/(((op (e2) (e2)) = (e3))\/((op (e2) (e3)) = (e3))))) -> (~((op (e2) (e1)) = (op (e3) (e1)))) -> (((op (e0) (e3)) = (e0))\/(((op (e0) (e3)) = (e1))\/(((op (e0) (e3)) = (e2))\/((op (e0) (e3)) = (e3))))) -> (~((op (e0) (e3)) = (op (e2) (e3)))) -> (~((op (e1) (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) (e3)) = (op (e3) (e3)))) -> (((op (e3) (e0)) = (e1))\/(((op (e3) (e1)) = (e1))\/(((op (e3) (e2)) = (e1))\/((op (e3) (e3)) = (e1))))) -> (~((op (e0) (e2)) = (op (e2) (e2)))) -> (~((e0) = (e1))) -> (~((op (e0) (e1)) = (op (e1) (e1)))) -> (~((op (e0) (e3)) = (op (e1) (e3)))) -> (((op (e2) (e3)) = (e0))\/(((op (e2) (e3)) = (e1))\/(((op (e2) (e3)) = (e2))\/((op (e2) (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) (e1)) = (e1))) -> (~((e0) = (e3))) -> (~((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 (e3) (e2)) = (e0))\/(((op (e3) (e2)) = (e1))\/(((op (e3) (e2)) = (e2))\/((op (e3) (e2)) = (e3))))) -> (~((op (e2) (e2)) = (op (e3) (e2)))) -> ((~((op (e3) (e2)) = (e0)))\/((op (e3) (e0)) = (e2))) -> (((op (e0) (e2)) = (e3))\/(((op (e1) (e2)) = (e3))\/(((op (e2) (e2)) = (e3))\/((op (e3) (e2)) = (e3))))) -> (((op (e0) (e1)) = (e3))\/(((op (e1) (e1)) = (e3))\/(((op (e2) (e1)) = (e3))\/((op (e3) (e1)) = (e3))))) -> ((~((op (e2) (e3)) = (e0)))\/((op (e2) (e0)) = (e3))) -> (~((e1) = (e2))) -> ((~((op (e1) (e1)) = (e0)))\/((op (e1) (e0)) = (e1))) -> ((~((op (e0) (e3)) = (e0)))\/((op (e0) (e0)) = (e3))) -> ((op (e1) (e0)) = (e0)) -> ((op (e2) (e0)) = (e1)) -> ((op (e0) (e0)) = (e2)) -> (((op (e0) (e1)) = (e0))\/(((op (e0) (e1)) = (e1))\/(((op (e0) (e1)) = (e2))\/((op (e0) (e1)) = (e3))))) -> (~((op (e0) (e1)) = (op (e3) (e1)))) -> (((op (e3) (e1)) = (e0))\/(((op (e3) (e1)) = (e1))\/(((op (e3) (e1)) = (e2))\/((op (e3) (e1)) = (e3))))) -> (((op (e0) (e0)) = (e1))\/(((op (e1) (e0)) = (e1))\/(((op (e2) (e0)) = (e1))\/((op (e3) (e0)) = (e1))))) -> (((op (e0) (e0)) = (e1))\/(((op (e0) (e1)) = (e1))\/(((op (e0) (e2)) = (e1))\/((op (e0) (e3)) = (e1))))) -> False). % 18.68/18.91 do 0 intro. intros zenon_H3a zenon_H74 zenon_H25 zenon_H24 zenon_H1ac zenon_H67 zenon_H130 zenon_H1c7 zenon_Hd8 zenon_H208 zenon_H1f0 zenon_H1cf zenon_H3e zenon_H2f zenon_H6a zenon_H1a4 zenon_H24b zenon_H24a zenon_H30 zenon_H245 zenon_H20b zenon_H3f zenon_H233 zenon_H206 zenon_H201 zenon_H1fa zenon_H6f zenon_H6d zenon_H71 zenon_H4a zenon_H4f zenon_H52 zenon_H62 zenon_H5b zenon_H57 zenon_H54 zenon_H45 zenon_H22 zenon_H1ed zenon_H1ec zenon_H1d5 zenon_H1d8 zenon_H1ba zenon_H1cc zenon_H1c4 zenon_H1e0 zenon_H1ee zenon_H1fe zenon_H182 zenon_H39 zenon_H153 zenon_H14f zenon_H149 zenon_H165 zenon_H160 zenon_H168 zenon_H16f zenon_H173 zenon_H172 zenon_H145 zenon_H124 zenon_H12b zenon_H133 zenon_H136 zenon_H128 zenon_H139 zenon_H13c zenon_H13e zenon_H142 zenon_H179 zenon_H178 zenon_H17e zenon_H17b zenon_H183 zenon_H184 zenon_H185 zenon_H189 zenon_H109 zenon_H2b zenon_H101 zenon_H102 zenon_Hf3 zenon_H106 zenon_He7 zenon_Haf zenon_He4 zenon_He2 zenon_Hd5 zenon_Hdb zenon_Hdf zenon_Hc2 zenon_He8 zenon_Ha8 zenon_Ha1 zenon_H10e zenon_H1d zenon_H11f zenon_H115 zenon_H18c zenon_H10a zenon_H9a zenon_H95 zenon_H19d zenon_H195 zenon_H191 zenon_H18f zenon_H1a7 zenon_H1a6 zenon_H1a5 zenon_H94 zenon_H7c zenon_H205 zenon_H204 zenon_H27 zenon_Hed zenon_H7b zenon_H212 zenon_H210 zenon_H22a zenon_H235 zenon_H22d. % 18.68/18.91 apply (zenon_or_s _ _ zenon_H185); [ zenon_intro zenon_H81 | zenon_intro zenon_Hee ]. % 18.68/18.91 apply (zenon_or_s _ _ zenon_H94); [ zenon_intro zenon_H32 | zenon_intro zenon_H3b ]. % 18.68/18.91 apply (zenon_or_s _ _ zenon_H184); [ zenon_intro zenon_H40 | zenon_intro zenon_H44 ]. % 18.68/18.91 apply (zenon_L664_); trivial. % 18.68/18.91 apply (zenon_L312_); trivial. % 18.68/18.91 apply (zenon_or_s _ _ zenon_H184); [ zenon_intro zenon_H40 | zenon_intro zenon_H44 ]. % 18.68/18.91 apply (zenon_or_s _ _ zenon_H1ed); [ zenon_intro zenon_H1ad | zenon_intro zenon_Hac ]. % 18.68/18.91 apply (zenon_or_s _ _ zenon_H1a7); [ zenon_intro zenon_H18b | zenon_intro zenon_H148 ]. % 18.68/18.91 apply (zenon_L668_); trivial. % 18.68/18.91 apply (zenon_L423_); trivial. % 18.68/18.91 apply (zenon_L308_); trivial. % 18.68/18.91 apply (zenon_L312_); trivial. % 18.68/18.91 apply (zenon_L58_); trivial. % 18.68/18.91 (* end of lemma zenon_L670_ *) % 18.68/18.91 assert (zenon_L671_ : (((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 (e3) (e1)) = (e0))\/(((op (e3) (e1)) = (e1))\/(((op (e3) (e1)) = (e2))\/((op (e3) (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) (e0)) = (e0)) -> ((~((op (e0) (e3)) = (e0)))\/((op (e0) (e0)) = (e3))) -> ((~((op (e1) (e1)) = (e0)))\/((op (e1) (e0)) = (e1))) -> (~((e1) = (e2))) -> ((~((op (e2) (e3)) = (e0)))\/((op (e2) (e0)) = (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)) = (e0)))\/((op (e3) (e0)) = (e2))) -> (~((op (e2) (e2)) = (op (e3) (e2)))) -> (((op (e3) (e2)) = (e0))\/(((op (e3) (e2)) = (e1))\/(((op (e3) (e2)) = (e2))\/((op (e3) (e2)) = (e3))))) -> (~((op (e0) (e2)) = (op (e1) (e2)))) -> (((op (e1) (e2)) = (e0))\/(((op (e1) (e2)) = (e1))\/(((op (e1) (e2)) = (e2))\/((op (e1) (e2)) = (e3))))) -> (~((e1) = (e3))) -> (~((e0) = (e3))) -> (~((op (e1) (e1)) = (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) (e3)) = (e0))\/(((op (e2) (e3)) = (e1))\/(((op (e2) (e3)) = (e2))\/((op (e2) (e3)) = (e3))))) -> (~((op (e0) (e3)) = (op (e1) (e3)))) -> (~((op (e0) (e1)) = (op (e1) (e1)))) -> (~((e0) = (e1))) -> (~((op (e0) (e2)) = (op (e2) (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) (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 (e2) (e3)))) -> (((op (e0) (e3)) = (e0))\/(((op (e0) (e3)) = (e1))\/(((op (e0) (e3)) = (e2))\/((op (e0) (e3)) = (e3))))) -> (~((op (e2) (e1)) = (op (e3) (e1)))) -> (((op (e2) (e0)) = (e3))\/(((op (e2) (e1)) = (e3))\/(((op (e2) (e2)) = (e3))\/((op (e2) (e3)) = (e3))))) -> (((op (e2) (e0)) = (e1))\/(((op (e2) (e1)) = (e1))\/(((op (e2) (e2)) = (e1))\/((op (e2) (e3)) = (e1))))) -> (~((op (e2) (e3)) = (op (e3) (e3)))) -> (~((op (e3) (e3)) = (e3))) -> (((op (e3) (e3)) = (e0))\/(((op (e3) (e3)) = (e1))\/(((op (e3) (e3)) = (e2))\/((op (e3) (e3)) = (e3))))) -> (~((op (e1) (e2)) = (op (e2) (e2)))) -> (((op (e0) (e1)) = (e1))\/(((op (e1) (e1)) = (e1))\/(((op (e2) (e1)) = (e1))\/((op (e3) (e1)) = (e1))))) -> (~((op (e0) (e0)) = (op (e0) (e3)))) -> ((~((op (e2) (e2)) = (e0)))\/((op (e2) (e0)) = (e2))) -> ((~((op (e3) (e0)) = (e0)))\/((op (e3) (e0)) = (e0))) -> (((op (e0) (e0)) = (e2))\/(((op (e0) (e1)) = (e2))\/(((op (e0) (e2)) = (e2))\/((op (e0) (e3)) = (e2))))) -> (~((op (e2) (e0)) = (op (e3) (e0)))) -> (~((op (e0) (e1)) = (op (e2) (e1)))) -> ((~((op (e1) (e2)) = (e0)))\/((op (e1) (e0)) = (e2))) -> ((~((op (e1) (e3)) = (e0)))\/((op (e1) (e0)) = (e3))) -> (((op (e1) (e1)) = (e0))\/(((op (e1) (e1)) = (e1))\/(((op (e1) (e1)) = (e2))\/((op (e1) (e1)) = (e3))))) -> (~((op (e1) (e1)) = (op (e2) (e1)))) -> (~((op (e0) (e0)) = (op (e0) (e2)))) -> (((op (e0) (e2)) = (e1))\/(((op (e1) (e2)) = (e1))\/(((op (e2) (e2)) = (e1))\/((op (e3) (e2)) = (e1))))) -> (((op (e1) (e0)) = (e1))\/(((op (e1) (e1)) = (e1))\/(((op (e1) (e2)) = (e1))\/((op (e1) (e3)) = (e1))))) -> (((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))))) -> (~((e2) = (e3))) -> (~((op (e1) (e2)) = (op (e1) (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 (e2) (e2)) = (e2))) -> (((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) (e1)) = (op (e3) (e1)))) -> (((op (e3) (e0)) = (e3))\/(((op (e3) (e1)) = (e3))\/(((op (e3) (e2)) = (e3))\/((op (e3) (e3)) = (e3))))) -> (~((e0) = (e2))) -> (~((op (e0) (e2)) = (op (e3) (e2)))) -> (((op (e3) (e0)) = (e2))\/(((op (e3) (e1)) = (e2))\/(((op (e3) (e2)) = (e2))\/((op (e3) (e3)) = (e2))))) -> (~((op (e0) (e0)) = (op (e2) (e0)))) -> ((~((op (e2) (e1)) = (e0)))\/((op (e2) (e0)) = (e1))) -> (((op (e0) (e0)) = (e2))\/(((op (e1) (e0)) = (e2))\/(((op (e2) (e0)) = (e2))\/((op (e3) (e0)) = (e2))))) -> ((~((op (e2) (e0)) = (e0)))\/((op (e2) (e0)) = (e0))) -> (((op (e0) (e0)) = (e3))\/(((op (e1) (e0)) = (e3))\/(((op (e2) (e0)) = (e3))\/((op (e3) (e0)) = (e3))))) -> (((op (e2) (e2)) = (e0))\/(((op (e2) (e2)) = (e1))\/(((op (e2) (e2)) = (e2))\/((op (e2) (e2)) = (e3))))) -> (((op (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 (e0) (e1)) = (e2))\/(((op (e1) (e1)) = (e2))\/(((op (e2) (e1)) = (e2))\/((op (e3) (e1)) = (e2))))) -> (((op (e2) (e0)) = (e2))\/(((op (e2) (e1)) = (e2))\/(((op (e2) (e2)) = (e2))\/((op (e2) (e3)) = (e2))))) -> ((~((op (e3) (e3)) = (e0)))\/((op (e3) (e0)) = (e3))) -> ((~((op (e3) (e1)) = (e0)))\/((op (e3) (e0)) = (e1))) -> (((op (e1) (e0)) = (e0))\/(((op (e1) (e1)) = (e0))\/(((op (e1) (e2)) = (e0))\/((op (e1) (e3)) = (e0))))) -> (~((op (e1) (e0)) = (op (e1) (e1)))) -> (~((op (e0) (e1)) = (op (e0) (e3)))) -> (~((op (e1) (e1)) = (op (e1) (e3)))) -> (~((op (e2) (e0)) = (op (e2) (e3)))) -> (~((op (e3) (e2)) = (op (e3) (e3)))) -> (~((op (e2) (e0)) = (op (e2) (e2)))) -> (~((op (e1) (e1)) = (op (e1) (e2)))) -> (~((op (e0) (e1)) = (op (e0) (e2)))) -> (~((op (e3) (e0)) = (op (e3) (e3)))) -> (~((op (e2) (e2)) = (op (e2) (e3)))) -> (~((op (e3) (e0)) = (op (e3) (e2)))) -> (~((op (e1) (e0)) = (op (e3) (e0)))) -> (~((op (e1) (e0)) = (op (e2) (e0)))) -> ((~((op (e1) (e0)) = (e0)))\/((op (e1) (e0)) = (e0))) -> ((~((op (e0) (e2)) = (e0)))\/((op (e0) (e0)) = (e2))) -> (~((op (e0) (e0)) = (e0))) -> (~((op (e0) (e1)) = (e0))) -> (((op (e0) (e1)) = (e0))\/(((op (e1) (e1)) = (e0))\/(((op (e2) (e1)) = (e0))\/((op (e3) (e1)) = (e0))))) -> (~((op (e2) (e0)) = (e0))) -> (~((op (e1) (e0)) = (op (e1) (e2)))) -> (~((op (e2) (e1)) = (op (e2) (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) (e0)) = (e0))\/(((op (e2) (e1)) = (e0))\/(((op (e2) (e2)) = (e0))\/((op (e2) (e3)) = (e0))))) -> (((op (e0) (e0)) = (e0))\/(((op (e1) (e0)) = (e0))\/(((op (e2) (e0)) = (e0))\/((op (e3) (e0)) = (e0))))) -> (~((op (e3) (e0)) = (op (e3) (e1)))) -> (~((op (e2) (e0)) = (op (e2) (e1)))) -> (~((op (e0) (e2)) = (op (e0) (e3)))) -> (~((op (e1) (e0)) = (op (e1) (e3)))) -> (~((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 (e3) (e0)) = (e0))\/(((op (e3) (e1)) = (e0))\/(((op (e3) (e2)) = (e0))\/((op (e3) (e3)) = (e0))))) -> (~((op (e1) (e1)) = (e0))) -> (~((op (e1) (e2)) = (e0))) -> (((op (e0) (e0)) = (e0))\/(((op (e0) (e1)) = (e0))\/(((op (e0) (e2)) = (e0))\/((op (e0) (e3)) = (e0))))) -> ((op (e0) (e0)) = (e3)) -> ((op (e2) (e0)) = (e3)) -> ((op (e0) (e0)) = (e2)) -> False). % 18.68/18.91 do 0 intro. intros zenon_H22d zenon_H235 zenon_H22a zenon_H210 zenon_H212 zenon_H27 zenon_H204 zenon_H205 zenon_H7c zenon_H94 zenon_H1a5 zenon_H1a6 zenon_H1a7 zenon_H18f zenon_H191 zenon_H195 zenon_H19d zenon_H95 zenon_H9a zenon_H10a zenon_H18c zenon_H115 zenon_H11f zenon_H1d zenon_H10e zenon_Ha1 zenon_Ha8 zenon_He8 zenon_Hc2 zenon_Hdf zenon_Hdb zenon_Hd5 zenon_He2 zenon_He4 zenon_Haf zenon_He7 zenon_H106 zenon_Hf3 zenon_H102 zenon_H101 zenon_H2b zenon_H109 zenon_H189 zenon_H185 zenon_H184 zenon_H183 zenon_H17b zenon_H17e zenon_H178 zenon_H179 zenon_H142 zenon_H13e zenon_H13c zenon_H139 zenon_H128 zenon_H136 zenon_H133 zenon_H12b zenon_H124 zenon_H145 zenon_H172 zenon_H173 zenon_H16f zenon_H168 zenon_H160 zenon_H165 zenon_H149 zenon_H14f zenon_H153 zenon_H39 zenon_H182 zenon_H1fe zenon_H1ee zenon_H1e0 zenon_H1c4 zenon_H1cc zenon_H1ba zenon_H1d8 zenon_H1d5 zenon_H1ec zenon_H1ed zenon_H22 zenon_H45 zenon_H54 zenon_H57 zenon_H5b zenon_H62 zenon_H52 zenon_H4f zenon_H4a zenon_H71 zenon_H6d zenon_H6f zenon_H1fa zenon_H201 zenon_H206 zenon_H233 zenon_H3f zenon_H20b zenon_H245 zenon_H30 zenon_H24a zenon_H24b zenon_H1a4 zenon_H6a zenon_H2f zenon_H3e zenon_H1cf zenon_H1f0 zenon_H208 zenon_Hd8 zenon_H1c7 zenon_H130 zenon_H67 zenon_H1ac zenon_H24 zenon_H25 zenon_H74 zenon_H3a zenon_H3b zenon_H7b. % 18.68/18.91 apply (zenon_or_s _ _ zenon_H235); [ zenon_intro zenon_H7a | zenon_intro zenon_H236 ]. % 18.68/18.91 apply (zenon_L456_); trivial. % 18.68/18.91 apply (zenon_or_s _ _ zenon_H236); [ zenon_intro zenon_H9d | zenon_intro zenon_H237 ]. % 18.68/18.91 apply (zenon_L262_); trivial. % 18.68/18.91 apply (zenon_or_s _ _ zenon_H237); [ zenon_intro zenon_Hed | zenon_intro zenon_Hac ]. % 18.68/18.91 apply (zenon_L670_); trivial. % 18.68/18.91 apply (zenon_L308_); trivial. % 18.68/18.91 (* end of lemma zenon_L671_ *) % 18.68/18.91 assert (zenon_L672_ : ((~((op (e0) (e2)) = (e0)))\/((op (e0) (e0)) = (e2))) -> ((~((op (e1) (e0)) = (e0)))\/((op (e1) (e0)) = (e0))) -> (~((op (e1) (e0)) = (op (e2) (e0)))) -> (~((op (e2) (e0)) = (op (e2) (e1)))) -> (~((op (e1) (e0)) = (op (e3) (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)) = (op (e3) (e2)))) -> (~((op (e2) (e2)) = (op (e2) (e3)))) -> (~((op (e3) (e0)) = (op (e3) (e3)))) -> (~((op (e0) (e1)) = (op (e0) (e2)))) -> (~((op (e1) (e1)) = (op (e1) (e2)))) -> (~((op (e2) (e0)) = (op (e2) (e2)))) -> (((op (e0) (e3)) = (e0))\/(((op (e1) (e3)) = (e0))\/(((op (e2) (e3)) = (e0))\/((op (e3) (e3)) = (e0))))) -> (~((op (e3) (e2)) = (op (e3) (e3)))) -> (~((op (e2) (e0)) = (op (e2) (e3)))) -> (~((op (e1) (e1)) = (op (e1) (e3)))) -> (~((op (e0) (e1)) = (op (e0) (e3)))) -> (((op (e0) (e2)) = (e0))\/(((op (e1) (e2)) = (e0))\/(((op (e2) (e2)) = (e0))\/((op (e3) (e2)) = (e0))))) -> (~((op (e1) (e0)) = (op (e1) (e1)))) -> (((op (e1) (e0)) = (e0))\/(((op (e1) (e1)) = (e0))\/(((op (e1) (e2)) = (e0))\/((op (e1) (e3)) = (e0))))) -> (~((op (e0) (e0)) = (e0))) -> ((~((op (e3) (e1)) = (e0)))\/((op (e3) (e0)) = (e1))) -> ((~((op (e3) (e3)) = (e0)))\/((op (e3) (e0)) = (e3))) -> (((op (e2) (e0)) = (e2))\/(((op (e2) (e1)) = (e2))\/(((op (e2) (e2)) = (e2))\/((op (e2) (e3)) = (e2))))) -> (((op (e0) (e1)) = (e2))\/(((op (e1) (e1)) = (e2))\/(((op (e2) (e1)) = (e2))\/((op (e3) (e1)) = (e2))))) -> (~((op (e3) (e0)) = (op (e3) (e1)))) -> (((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 (e2) (e2)) = (e0))\/(((op (e2) (e2)) = (e1))\/(((op (e2) (e2)) = (e2))\/((op (e2) (e2)) = (e3))))) -> (~((op (e2) (e1)) = (op (e2) (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 (e2) (e0)) = (e0)))\/((op (e2) (e0)) = (e0))) -> (((op (e0) (e0)) = (e2))\/(((op (e1) (e0)) = (e2))\/(((op (e2) (e0)) = (e2))\/((op (e3) (e0)) = (e2))))) -> ((~((op (e2) (e1)) = (e0)))\/((op (e2) (e0)) = (e1))) -> (~((op (e0) (e0)) = (op (e2) (e0)))) -> (((op (e3) (e0)) = (e2))\/(((op (e3) (e1)) = (e2))\/(((op (e3) (e2)) = (e2))\/((op (e3) (e3)) = (e2))))) -> (~((op (e0) (e2)) = (op (e3) (e2)))) -> (~((e0) = (e2))) -> (((op (e3) (e0)) = (e3))\/(((op (e3) (e1)) = (e3))\/(((op (e3) (e2)) = (e3))\/((op (e3) (e3)) = (e3))))) -> (~((op (e1) (e1)) = (op (e3) (e1)))) -> (((op (e0) (e0)) = (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)) = (e2))) -> (((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) (e2)) = (op (e1) (e3)))) -> (~((e2) = (e3))) -> (((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)) = (e3))\/(((op (e1) (e3)) = (e3))\/(((op (e2) (e3)) = (e3))\/((op (e3) (e3)) = (e3))))) -> (((op (e1) (e0)) = (e1))\/(((op (e1) (e1)) = (e1))\/(((op (e1) (e2)) = (e1))\/((op (e1) (e3)) = (e1))))) -> (((op (e0) (e2)) = (e1))\/(((op (e1) (e2)) = (e1))\/(((op (e2) (e2)) = (e1))\/((op (e3) (e2)) = (e1))))) -> (~((op (e0) (e0)) = (op (e0) (e2)))) -> (~((op (e1) (e1)) = (op (e2) (e1)))) -> (((op (e1) (e1)) = (e0))\/(((op (e1) (e1)) = (e1))\/(((op (e1) (e1)) = (e2))\/((op (e1) (e1)) = (e3))))) -> ((~((op (e1) (e3)) = (e0)))\/((op (e1) (e0)) = (e3))) -> ((~((op (e1) (e2)) = (e0)))\/((op (e1) (e0)) = (e2))) -> (~((op (e0) (e1)) = (op (e2) (e1)))) -> (~((op (e2) (e0)) = (op (e3) (e0)))) -> (((op (e0) (e0)) = (e2))\/(((op (e0) (e1)) = (e2))\/(((op (e0) (e2)) = (e2))\/((op (e0) (e3)) = (e2))))) -> ((~((op (e3) (e0)) = (e0)))\/((op (e3) (e0)) = (e0))) -> ((~((op (e2) (e2)) = (e0)))\/((op (e2) (e0)) = (e2))) -> (~((op (e0) (e0)) = (op (e0) (e3)))) -> (((op (e0) (e1)) = (e1))\/(((op (e1) (e1)) = (e1))\/(((op (e2) (e1)) = (e1))\/((op (e3) (e1)) = (e1))))) -> (~((op (e1) (e2)) = (op (e2) (e2)))) -> (((op (e3) (e3)) = (e0))\/(((op (e3) (e3)) = (e1))\/(((op (e3) (e3)) = (e2))\/((op (e3) (e3)) = (e3))))) -> (~((op (e3) (e3)) = (e3))) -> (~((op (e2) (e3)) = (op (e3) (e3)))) -> (((op (e2) (e0)) = (e1))\/(((op (e2) (e1)) = (e1))\/(((op (e2) (e2)) = (e1))\/((op (e2) (e3)) = (e1))))) -> (((op (e2) (e0)) = (e3))\/(((op (e2) (e1)) = (e3))\/(((op (e2) (e2)) = (e3))\/((op (e2) (e3)) = (e3))))) -> (~((op (e2) (e1)) = (op (e3) (e1)))) -> (((op (e0) (e3)) = (e0))\/(((op (e0) (e3)) = (e1))\/(((op (e0) (e3)) = (e2))\/((op (e0) (e3)) = (e3))))) -> (~((op (e0) (e3)) = (op (e2) (e3)))) -> (~((op (e1) (e3)) = (op (e3) (e3)))) -> (~((op (e1) (e0)) = (op (e1) (e3)))) -> (~((op (e1) (e3)) = (op (e2) (e3)))) -> (((op (e1) (e3)) = (e0))\/(((op (e1) (e3)) = (e1))\/(((op (e1) (e3)) = (e2))\/((op (e1) (e3)) = (e3))))) -> (~((op (e0) (e3)) = (op (e3) (e3)))) -> (((op (e3) (e0)) = (e1))\/(((op (e3) (e1)) = (e1))\/(((op (e3) (e2)) = (e1))\/((op (e3) (e3)) = (e1))))) -> (~((op (e0) (e2)) = (op (e2) (e2)))) -> (~((e0) = (e1))) -> (~((op (e0) (e1)) = (op (e1) (e1)))) -> (~((op (e0) (e3)) = (op (e1) (e3)))) -> (((op (e2) (e3)) = (e0))\/(((op (e2) (e3)) = (e1))\/(((op (e2) (e3)) = (e2))\/((op (e2) (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) (e1)) = (e1))) -> (~((e0) = (e3))) -> (~((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 (e3) (e2)) = (e0))\/(((op (e3) (e2)) = (e1))\/(((op (e3) (e2)) = (e2))\/((op (e3) (e2)) = (e3))))) -> (~((op (e2) (e2)) = (op (e3) (e2)))) -> ((~((op (e3) (e2)) = (e0)))\/((op (e3) (e0)) = (e2))) -> (~((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)) = (e3))\/(((op (e1) (e1)) = (e3))\/(((op (e2) (e1)) = (e3))\/((op (e3) (e1)) = (e3))))) -> ((~((op (e2) (e3)) = (e0)))\/((op (e2) (e0)) = (e3))) -> (~((e1) = (e2))) -> ((~((op (e1) (e1)) = (e0)))\/((op (e1) (e0)) = (e1))) -> ((~((op (e0) (e3)) = (e0)))\/((op (e0) (e0)) = (e3))) -> ((op (e1) (e0)) = (e0)) -> ((op (e0) (e0)) = (e3)) -> (~((op (e1) (e2)) = (e0))) -> (~((op (e1) (e1)) = (e0))) -> (~((op (e0) (e2)) = (op (e0) (e3)))) -> (~((op (e2) (e1)) = (op (e2) (e2)))) -> (~((op (e1) (e0)) = (op (e1) (e2)))) -> (((op (e0) (e1)) = (e0))\/(((op (e1) (e1)) = (e0))\/(((op (e2) (e1)) = (e0))\/((op (e3) (e1)) = (e0))))) -> (~((op (e0) (e1)) = (e0))) -> ((op (e0) (e0)) = (e2)) -> (((op (e0) (e1)) = (e0))\/(((op (e0) (e1)) = (e1))\/(((op (e0) (e1)) = (e2))\/((op (e0) (e1)) = (e3))))) -> (~((op (e0) (e1)) = (op (e3) (e1)))) -> (((op (e3) (e1)) = (e0))\/(((op (e3) (e1)) = (e1))\/(((op (e3) (e1)) = (e2))\/((op (e3) (e1)) = (e3))))) -> (((op (e0) (e0)) = (e1))\/(((op (e1) (e0)) = (e1))\/(((op (e2) (e0)) = (e1))\/((op (e3) (e0)) = (e1))))) -> (((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) (e0)) = (e0))\/(((op (e2) (e1)) = (e0))\/(((op (e2) (e2)) = (e0))\/((op (e2) (e3)) = (e0))))) -> False). % 18.68/18.91 do 0 intro. intros zenon_H233 zenon_H206 zenon_H201 zenon_H1f0 zenon_H1fa zenon_H74 zenon_H3e zenon_H6f zenon_H6d zenon_H71 zenon_H4a zenon_H4f zenon_H52 zenon_H67 zenon_H62 zenon_H5b zenon_H57 zenon_H54 zenon_H6a zenon_H45 zenon_H22 zenon_H3f zenon_H1ed zenon_H1ec zenon_H1d5 zenon_H1d8 zenon_H1cf zenon_H1ba zenon_H1cc zenon_H1c4 zenon_H1c7 zenon_H1ac zenon_H1e0 zenon_H1ee zenon_H1fe zenon_H182 zenon_H39 zenon_H153 zenon_H14f zenon_H149 zenon_H165 zenon_H160 zenon_H168 zenon_H16f zenon_H173 zenon_H172 zenon_H145 zenon_H124 zenon_H12b zenon_H133 zenon_H130 zenon_H136 zenon_H128 zenon_H139 zenon_H13c zenon_H13e zenon_H142 zenon_H179 zenon_H178 zenon_H17e zenon_H17b zenon_H183 zenon_H184 zenon_H185 zenon_H189 zenon_H109 zenon_H2b zenon_H101 zenon_H102 zenon_Hf3 zenon_H106 zenon_He7 zenon_Haf zenon_He4 zenon_He2 zenon_Hd5 zenon_Hd8 zenon_Hdb zenon_Hdf zenon_Hc2 zenon_He8 zenon_Ha8 zenon_Ha1 zenon_H10e zenon_H1d zenon_H11f zenon_H115 zenon_H18c zenon_H10a zenon_H9a zenon_H95 zenon_H19d zenon_H195 zenon_H191 zenon_H18f zenon_H1a7 zenon_H1a4 zenon_H1a6 zenon_H1a5 zenon_H94 zenon_H7c zenon_H205 zenon_H204 zenon_H27 zenon_H3a zenon_H25 zenon_H24 zenon_H208 zenon_H24b zenon_H24a zenon_H245 zenon_H20b zenon_H7b zenon_H212 zenon_H210 zenon_H22a zenon_H235 zenon_H22d zenon_H30 zenon_H31 zenon_H81 zenon_H2f. % 18.68/18.91 apply (zenon_or_s _ _ zenon_H94); [ zenon_intro zenon_H32 | zenon_intro zenon_H3b ]. % 18.68/18.91 apply (zenon_L27_); trivial. % 18.68/18.91 apply (zenon_L671_); trivial. % 18.68/18.91 (* end of lemma zenon_L672_ *) % 18.68/18.91 assert (zenon_L673_ : (((op (e1) (e0)) = (e3))\/(((op (e1) (e1)) = (e3))\/(((op (e1) (e2)) = (e3))\/((op (e1) (e3)) = (e3))))) -> (~((e0) = (e3))) -> ((op (e1) (e0)) = (e0)) -> ((op (e3) (e1)) = (e0)) -> ((op (e0) (e1)) = (e2)) -> (~((e1) = (e3))) -> ((op (e1) (e2)) = (e1)) -> ((op (e1) (e3)) = (e2)) -> (~((e2) = (e3))) -> False). % 18.68/18.91 do 0 intro. intros zenon_H16f zenon_H9a zenon_H27 zenon_H1b1 zenon_H10f zenon_H95 zenon_Hf0 zenon_Hd7 zenon_H12b. % 18.68/18.91 apply (zenon_or_s _ _ zenon_H16f); [ zenon_intro zenon_H9e | zenon_intro zenon_H170 ]. % 18.68/18.91 apply (zenon_L263_); trivial. % 18.68/18.91 apply (zenon_or_s _ _ zenon_H170); [ zenon_intro zenon_H13f | zenon_intro zenon_H171 ]. % 18.68/18.91 apply (zenon_L580_); trivial. % 18.68/18.91 apply (zenon_or_s _ _ zenon_H171); [ zenon_intro zenon_H16c | zenon_intro zenon_Hdc ]. % 18.68/18.91 apply (zenon_L167_); trivial. % 18.68/18.91 apply (zenon_L266_); trivial. % 18.68/18.91 (* end of lemma zenon_L673_ *) % 18.68/18.91 assert (zenon_L674_ : (((op (e1) (e0)) = (e2))\/(((op (e1) (e1)) = (e2))\/(((op (e1) (e2)) = (e2))\/((op (e1) (e3)) = (e2))))) -> ((op (e0) (e0)) = (e3)) -> ((op (e3) (e0)) = (e1)) -> (((op (e0) (e1)) = (e2))\/(((op (e1) (e1)) = (e2))\/(((op (e2) (e1)) = (e2))\/((op (e3) (e1)) = (e2))))) -> ((op (e3) (e1)) = (e0)) -> (~((op (e1) (e1)) = (op (e1) (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 (e1) (e0)) = (e0)) -> (~((op (e1) (e1)) = (op (e2) (e1)))) -> (~((op (e2) (e1)) = (op (e3) (e1)))) -> (~((op (e2) (e1)) = (op (e2) (e3)))) -> (~((op (e2) (e1)) = (e0))) -> (((op (e2) (e1)) = (e0))\/(((op (e2) (e1)) = (e1))\/(((op (e2) (e1)) = (e2))\/((op (e2) (e1)) = (e3))))) -> (~((op (e1) (e2)) = (op (e2) (e2)))) -> (~((op (e0) (e1)) = (op (e2) (e1)))) -> ((op (e0) (e1)) = (e1)) -> ((op (e2) (e0)) = (e2)) -> (~((e1) = (e2))) -> (((op (e2) (e0)) = (e1))\/(((op (e2) (e1)) = (e1))\/(((op (e2) (e2)) = (e1))\/((op (e2) (e3)) = (e1))))) -> (~((e1) = (e3))) -> ((op (e1) (e2)) = (e1)) -> (~((e2) = (e3))) -> False). % 18.68/18.91 do 0 intro. intros zenon_H18c zenon_H3a zenon_Hac zenon_H1d8 zenon_H1b1 zenon_H57 zenon_H1f0 zenon_H16f zenon_H9a zenon_H27 zenon_H13e zenon_Haf zenon_H1c7 zenon_H31 zenon_H1cc zenon_H2b zenon_H17e zenon_Ha0 zenon_Hee zenon_H7c zenon_H106 zenon_H95 zenon_Hf0 zenon_H12b. % 18.68/18.91 apply (zenon_or_s _ _ zenon_H18c); [ zenon_intro zenon_H86 | zenon_intro zenon_H18d ]. % 18.68/18.91 apply (zenon_L241_); trivial. % 18.68/18.91 apply (zenon_or_s _ _ zenon_H18d); [ zenon_intro zenon_H110 | zenon_intro zenon_H18e ]. % 18.68/18.91 apply (zenon_L569_); trivial. % 18.68/18.91 apply (zenon_or_s _ _ zenon_H18e); [ zenon_intro zenon_H113 | zenon_intro zenon_Hd7 ]. % 18.68/18.91 apply (zenon_L68_); trivial. % 18.68/18.91 apply (zenon_or_s _ _ zenon_H1d8); [ zenon_intro zenon_H10f | zenon_intro zenon_H1d9 ]. % 18.68/18.91 apply (zenon_L673_); trivial. % 18.68/18.91 apply (zenon_or_s _ _ zenon_H1d9); [ zenon_intro zenon_H110 | zenon_intro zenon_H1da ]. % 18.68/18.91 apply (zenon_L283_); trivial. % 18.68/18.91 apply (zenon_or_s _ _ zenon_H1da); [ zenon_intro zenon_H1ca | zenon_intro zenon_H14d ]. % 18.68/18.91 apply (zenon_L277_); trivial. % 18.68/18.91 apply (zenon_or_s _ _ zenon_H16f); [ zenon_intro zenon_H9e | zenon_intro zenon_H170 ]. % 18.68/18.91 apply (zenon_L263_); trivial. % 18.68/18.91 apply (zenon_or_s _ _ zenon_H170); [ zenon_intro zenon_H13f | zenon_intro zenon_H171 ]. % 18.68/18.91 apply (zenon_L612_); trivial. % 18.68/18.91 apply (zenon_or_s _ _ zenon_H171); [ zenon_intro zenon_H16c | zenon_intro zenon_Hdc ]. % 18.68/18.91 apply (zenon_L167_); trivial. % 18.68/18.91 apply (zenon_L266_); trivial. % 18.68/18.91 (* end of lemma zenon_L674_ *) % 18.68/18.91 assert (zenon_L675_ : (((op (e1) (e0)) = (e3))\/(((op (e1) (e1)) = (e3))\/(((op (e1) (e2)) = (e3))\/((op (e1) (e3)) = (e3))))) -> (~((e0) = (e3))) -> ((op (e1) (e0)) = (e0)) -> ((op (e3) (e1)) = (e0)) -> ((op (e0) (e1)) = (e2)) -> (~((e2) = (e3))) -> ((op (e1) (e2)) = (e2)) -> ((op (e1) (e3)) = (e1)) -> (~((e1) = (e3))) -> False). % 18.68/18.91 do 0 intro. intros zenon_H16f zenon_H9a zenon_H27 zenon_H1b1 zenon_H10f zenon_H12b zenon_H113 zenon_Hd6 zenon_H95. % 18.68/18.91 apply (zenon_or_s _ _ zenon_H16f); [ zenon_intro zenon_H9e | zenon_intro zenon_H170 ]. % 18.68/18.91 apply (zenon_L263_); trivial. % 18.68/18.91 apply (zenon_or_s _ _ zenon_H170); [ zenon_intro zenon_H13f | zenon_intro zenon_H171 ]. % 18.68/18.91 apply (zenon_L580_); trivial. % 18.68/18.91 apply (zenon_or_s _ _ zenon_H171); [ zenon_intro zenon_H16c | zenon_intro zenon_Hdc ]. % 18.68/18.91 apply (zenon_L116_); trivial. % 18.68/18.91 apply (zenon_L83_); trivial. % 18.68/18.91 (* end of lemma zenon_L675_ *) % 18.68/18.91 assert (zenon_L676_ : (((op (e0) (e3)) = (e0))\/(((op (e1) (e3)) = (e0))\/(((op (e2) (e3)) = (e0))\/((op (e3) (e3)) = (e0))))) -> (~((e0) = (e2))) -> ((op (e0) (e3)) = (e2)) -> ((op (e1) (e0)) = (e0)) -> (~((op (e1) (e0)) = (op (e1) (e3)))) -> (~((op (e2) (e2)) = (op (e2) (e3)))) -> ((op (e2) (e2)) = (e0)) -> ((op (e3) (e1)) = (e0)) -> (~((op (e3) (e1)) = (op (e3) (e3)))) -> False). % 18.68/18.91 do 0 intro. intros zenon_H67 zenon_H149 zenon_Hcd zenon_H27 zenon_Hd8 zenon_H6d zenon_H2c zenon_H1b1 zenon_H130. % 18.68/18.91 apply (zenon_or_s _ _ zenon_H67); [ zenon_intro zenon_H1e | zenon_intro zenon_H68 ]. % 18.68/18.91 apply (zenon_L428_); trivial. % 18.68/18.91 apply (zenon_or_s _ _ zenon_H68); [ zenon_intro zenon_H1f | zenon_intro zenon_H69 ]. % 18.68/18.91 apply (zenon_L258_); trivial. % 18.68/18.91 apply (zenon_or_s _ _ zenon_H69); [ zenon_intro zenon_H37 | zenon_intro zenon_H60 ]. % 18.68/18.91 apply (zenon_L18_); trivial. % 18.68/18.91 apply (zenon_L244_); trivial. % 18.68/18.91 (* end of lemma zenon_L676_ *) % 18.68/18.91 assert (zenon_L677_ : (((op (e0) (e1)) = (e2))\/(((op (e1) (e1)) = (e2))\/(((op (e2) (e1)) = (e2))\/((op (e3) (e1)) = (e2))))) -> (~((e1) = (e3))) -> ((op (e1) (e2)) = (e2)) -> (~((e2) = (e3))) -> (~((e0) = (e3))) -> (((op (e1) (e0)) = (e3))\/(((op (e1) (e1)) = (e3))\/(((op (e1) (e2)) = (e3))\/((op (e1) (e3)) = (e3))))) -> (~((op (e2) (e0)) = (op (e2) (e1)))) -> (((op (e2) (e0)) = (e0))\/(((op (e2) (e1)) = (e0))\/(((op (e2) (e2)) = (e0))\/((op (e2) (e3)) = (e0))))) -> (~((op (e2) (e0)) = (e0))) -> (~((op (e2) (e1)) = (e0))) -> (~((op (e3) (e1)) = (op (e3) (e3)))) -> ((op (e2) (e0)) = (e2)) -> (~((op (e2) (e0)) = (op (e2) (e3)))) -> ((op (e1) (e3)) = (e1)) -> (~((e1) = (e2))) -> (((op (e0) (e3)) = (e0))\/(((op (e1) (e3)) = (e0))\/(((op (e2) (e3)) = (e0))\/((op (e3) (e3)) = (e0))))) -> (~((e0) = (e2))) -> ((op (e1) (e0)) = (e0)) -> (~((op (e1) (e0)) = (op (e1) (e3)))) -> (~((op (e2) (e2)) = (op (e2) (e3)))) -> ((op (e3) (e1)) = (e0)) -> (((op (e0) (e3)) = (e2))\/(((op (e1) (e3)) = (e2))\/(((op (e2) (e3)) = (e2))\/((op (e3) (e3)) = (e2))))) -> (~((op (e2) (e3)) = (e0))) -> False). % 18.68/18.91 do 0 intro. intros zenon_H1d8 zenon_H95 zenon_H113 zenon_H12b zenon_H9a zenon_H16f zenon_H1f0 zenon_H2f zenon_H30 zenon_H31 zenon_H130 zenon_Hee zenon_H5b zenon_Hd6 zenon_H7c zenon_H67 zenon_H149 zenon_H27 zenon_Hd8 zenon_H6d zenon_H1b1 zenon_H145 zenon_H32. % 18.68/18.91 apply (zenon_or_s _ _ zenon_H1d8); [ zenon_intro zenon_H10f | zenon_intro zenon_H1d9 ]. % 18.68/18.91 apply (zenon_L675_); trivial. % 18.68/18.91 apply (zenon_or_s _ _ zenon_H1d9); [ zenon_intro zenon_H110 | zenon_intro zenon_H1da ]. % 18.68/18.91 apply (zenon_L276_); trivial. % 18.68/18.91 apply (zenon_or_s _ _ zenon_H1da); [ zenon_intro zenon_H1ca | zenon_intro zenon_H14d ]. % 18.68/18.91 apply (zenon_L277_); trivial. % 18.68/18.91 apply (zenon_or_s _ _ zenon_H2f); [ zenon_intro zenon_H34 | zenon_intro zenon_H33 ]. % 18.68/18.91 exact (zenon_H30 zenon_H34). % 18.68/18.91 apply (zenon_or_s _ _ zenon_H33); [ zenon_intro zenon_H36 | zenon_intro zenon_H35 ]. % 18.68/18.91 exact (zenon_H31 zenon_H36). % 18.68/18.91 apply (zenon_or_s _ _ zenon_H35); [ zenon_intro zenon_H2c | zenon_intro zenon_H37 ]. % 18.68/18.91 apply (zenon_or_s _ _ zenon_H145); [ zenon_intro zenon_Hcd | zenon_intro zenon_H146 ]. % 18.68/18.91 apply (zenon_L676_); trivial. % 18.68/18.91 apply (zenon_or_s _ _ zenon_H146); [ zenon_intro zenon_Hd7 | zenon_intro zenon_H147 ]. % 18.68/18.91 apply (zenon_L101_); trivial. % 18.68/18.91 apply (zenon_or_s _ _ zenon_H147); [ zenon_intro zenon_H11d | zenon_intro zenon_Hf6 ]. % 18.68/18.91 apply (zenon_L73_); trivial. % 18.68/18.91 apply (zenon_L102_); trivial. % 18.68/18.91 exact (zenon_H32 zenon_H37). % 18.68/18.91 (* end of lemma zenon_L677_ *) % 18.68/18.91 assert (zenon_L678_ : (((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 (e1) (e0)) = (e1))\/(((op (e1) (e1)) = (e1))\/(((op (e1) (e2)) = (e1))\/((op (e1) (e3)) = (e1))))) -> (~((e0) = (e1))) -> (~((op (e1) (e1)) = (e1))) -> (((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 (e2) (e3)))) -> (~((op (e2) (e1)) = (op (e3) (e1)))) -> (~((op (e1) (e1)) = (op (e2) (e1)))) -> (~((op (e1) (e1)) = (op (e1) (e3)))) -> ((op (e3) (e0)) = (e1)) -> ((op (e0) (e0)) = (e3)) -> (((op (e1) (e0)) = (e2))\/(((op (e1) (e1)) = (e2))\/(((op (e1) (e2)) = (e2))\/((op (e1) (e3)) = (e2))))) -> (~((op (e0) (e1)) = (op (e2) (e1)))) -> ((op (e0) (e1)) = (e1)) -> (((op (e2) (e1)) = (e0))\/(((op (e2) (e1)) = (e1))\/(((op (e2) (e1)) = (e2))\/((op (e2) (e1)) = (e3))))) -> (~((op (e2) (e3)) = (e0))) -> (((op (e0) (e3)) = (e2))\/(((op (e1) (e3)) = (e2))\/(((op (e2) (e3)) = (e2))\/((op (e3) (e3)) = (e2))))) -> (~((op (e2) (e2)) = (op (e2) (e3)))) -> (~((op (e1) (e0)) = (op (e1) (e3)))) -> ((op (e1) (e0)) = (e0)) -> (~((e0) = (e2))) -> (((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)) = (e2)) -> (~((op (e3) (e1)) = (op (e3) (e3)))) -> (~((op (e2) (e1)) = (e0))) -> (~((op (e2) (e0)) = (e0))) -> (((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)) = (e3))\/(((op (e1) (e1)) = (e3))\/(((op (e1) (e2)) = (e3))\/((op (e1) (e3)) = (e3))))) -> (~((e0) = (e3))) -> (~((e2) = (e3))) -> (~((e1) = (e3))) -> (((op (e0) (e1)) = (e2))\/(((op (e1) (e1)) = (e2))\/(((op (e2) (e1)) = (e2))\/((op (e3) (e1)) = (e2))))) -> (~((e1) = (e2))) -> False). % 18.68/18.91 do 0 intro. intros zenon_H245 zenon_H20b zenon_H24 zenon_H128 zenon_Ha1 zenon_H10a zenon_H106 zenon_H2b zenon_H1c7 zenon_Haf zenon_H13e zenon_H57 zenon_Hac zenon_H3a zenon_H18c zenon_H17e zenon_Ha0 zenon_H1cc zenon_H32 zenon_H145 zenon_H6d zenon_Hd8 zenon_H27 zenon_H149 zenon_H67 zenon_H5b zenon_Hee zenon_H130 zenon_H31 zenon_H30 zenon_H2f zenon_H1f0 zenon_H16f zenon_H9a zenon_H12b zenon_H95 zenon_H1d8 zenon_H7c. % 18.68/18.91 apply (zenon_or_s _ _ zenon_H245); [ zenon_intro zenon_H49 | zenon_intro zenon_H246 ]. % 18.68/18.91 exact (zenon_H20b zenon_H49). % 18.68/18.91 apply (zenon_or_s _ _ zenon_H246); [ zenon_intro zenon_H29 | zenon_intro zenon_H247 ]. % 18.68/18.91 exact (zenon_H24 zenon_H29). % 18.68/18.91 apply (zenon_or_s _ _ zenon_H247); [ zenon_intro zenon_H36 | zenon_intro zenon_H1b1 ]. % 18.68/18.91 exact (zenon_H31 zenon_H36). % 18.68/18.91 apply (zenon_or_s _ _ zenon_H128); [ zenon_intro zenon_H9d | zenon_intro zenon_H129 ]. % 18.68/18.91 apply (zenon_L262_); trivial. % 18.68/18.91 apply (zenon_or_s _ _ zenon_H129); [ zenon_intro zenon_H10d | zenon_intro zenon_H12a ]. % 18.68/18.91 exact (zenon_H10a zenon_H10d). % 18.68/18.91 apply (zenon_or_s _ _ zenon_H12a); [ zenon_intro zenon_Hf0 | zenon_intro zenon_Hd6 ]. % 18.68/18.91 apply (zenon_L674_); trivial. % 18.68/18.91 apply (zenon_or_s _ _ zenon_H18c); [ zenon_intro zenon_H86 | zenon_intro zenon_H18d ]. % 18.68/18.91 apply (zenon_L257_); trivial. % 18.68/18.91 apply (zenon_or_s _ _ zenon_H18d); [ zenon_intro zenon_H110 | zenon_intro zenon_H18e ]. % 18.68/18.91 apply (zenon_L569_); trivial. % 18.68/18.91 apply (zenon_or_s _ _ zenon_H18e); [ zenon_intro zenon_H113 | zenon_intro zenon_Hd7 ]. % 18.68/18.91 apply (zenon_L677_); trivial. % 18.68/18.91 apply (zenon_L101_); trivial. % 18.68/18.91 (* end of lemma zenon_L678_ *) % 18.68/18.91 assert (zenon_L679_ : (~((op (e0) (e2)) = (op (e2) (e2)))) -> ((op (e0) (e2)) = (e0)) -> ((op (e2) (e2)) = (e0)) -> False). % 18.68/18.91 do 0 intro. intros zenon_Ha8 zenon_H48 zenon_H2c. % 18.68/18.92 cut (((op (e0) (e2)) = (e0)) = ((op (e0) (e2)) = (op (e2) (e2)))). % 18.68/18.92 intro zenon_D_pnotp. % 18.68/18.92 apply zenon_Ha8. % 18.68/18.92 rewrite <- zenon_D_pnotp. % 18.68/18.92 exact zenon_H48. % 18.68/18.92 cut (((e0) = (op (e2) (e2)))); [idtac | apply NNPP; zenon_intro zenon_H2d]. % 18.68/18.92 cut (((op (e0) (e2)) = (op (e0) (e2)))); [idtac | apply NNPP; zenon_intro zenon_H4c]. % 18.68/18.92 congruence. % 18.68/18.92 apply zenon_H4c. apply refl_equal. % 18.68/18.92 apply zenon_H2d. apply sym_equal. exact zenon_H2c. % 18.68/18.92 (* end of lemma zenon_L679_ *) % 18.68/18.92 assert (zenon_L680_ : (((op (e0) (e2)) = (e0))\/(((op (e1) (e2)) = (e0))\/(((op (e2) (e2)) = (e0))\/((op (e3) (e2)) = (e0))))) -> (~((e0) = (e2))) -> ((op (e0) (e2)) = (e2)) -> ((op (e1) (e0)) = (e0)) -> (~((op (e1) (e0)) = (op (e1) (e2)))) -> (~((op (e2) (e2)) = (op (e2) (e3)))) -> ((op (e2) (e3)) = (e0)) -> (~((op (e3) (e1)) = (op (e3) (e2)))) -> ((op (e3) (e1)) = (e0)) -> False). % 18.68/18.92 do 0 intro. intros zenon_H6a zenon_H149 zenon_H150 zenon_H27 zenon_H24a zenon_H6d zenon_H37 zenon_H1a4 zenon_H1b1. % 18.68/18.92 apply (zenon_or_s _ _ zenon_H6a); [ zenon_intro zenon_H48 | zenon_intro zenon_H6b ]. % 18.68/18.92 apply (zenon_L378_); trivial. % 18.68/18.92 apply (zenon_or_s _ _ zenon_H6b); [ zenon_intro zenon_H2a | zenon_intro zenon_H6c ]. % 18.68/18.92 apply (zenon_L644_); trivial. % 18.68/18.92 apply (zenon_or_s _ _ zenon_H6c); [ zenon_intro zenon_H2c | zenon_intro zenon_H61 ]. % 18.68/18.92 apply (zenon_L18_); trivial. % 18.68/18.92 apply (zenon_L247_); trivial. % 18.68/18.92 (* end of lemma zenon_L680_ *) % 18.68/18.92 assert (zenon_L681_ : (((op (e0) (e3)) = (e2))\/(((op (e1) (e3)) = (e2))\/(((op (e2) (e3)) = (e2))\/((op (e3) (e3)) = (e2))))) -> (~((op (e0) (e0)) = (op (e0) (e3)))) -> ((op (e0) (e0)) = (e2)) -> (~((op (e1) (e1)) = (op (e1) (e3)))) -> ((op (e1) (e1)) = (e2)) -> (~((op (e2) (e0)) = (op (e2) (e3)))) -> ((op (e2) (e0)) = (e2)) -> ((op (e3) (e2)) = (e2)) -> (~((op (e3) (e2)) = (op (e3) (e3)))) -> False). % 18.68/18.92 do 0 intro. intros zenon_H145 zenon_H189 zenon_H7b zenon_H57 zenon_H110 zenon_H5b zenon_Hee zenon_H151 zenon_H62. % 18.68/18.92 apply (zenon_or_s _ _ zenon_H145); [ zenon_intro zenon_Hcd | zenon_intro zenon_H146 ]. % 18.68/18.92 apply (zenon_L375_); trivial. % 18.68/18.92 apply (zenon_or_s _ _ zenon_H146); [ zenon_intro zenon_Hd7 | zenon_intro zenon_H147 ]. % 18.79/18.92 apply (zenon_L283_); trivial. % 18.79/18.92 apply (zenon_or_s _ _ zenon_H147); [ zenon_intro zenon_H11d | zenon_intro zenon_Hf6 ]. % 18.79/18.92 apply (zenon_L73_); trivial. % 18.79/18.92 apply (zenon_L119_); trivial. % 18.79/18.92 (* end of lemma zenon_L681_ *) % 18.79/18.92 assert (zenon_L682_ : (((op (e2) (e0)) = (e0))\/(((op (e2) (e1)) = (e0))\/(((op (e2) (e2)) = (e0))\/((op (e2) (e3)) = (e0))))) -> (~((op (e2) (e1)) = (op (e2) (e2)))) -> (((op (e0) (e0)) = (e0))\/(((op (e1) (e0)) = (e0))\/(((op (e2) (e0)) = (e0))\/((op (e3) (e0)) = (e0))))) -> (~((op (e0) (e0)) = (e0))) -> (~((op (e1) (e0)) = (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 (e2) (e0)) = (op (e2) (e1)))) -> (~((op (e3) (e0)) = (op (e3) (e1)))) -> (~((op (e0) (e2)) = (op (e2) (e2)))) -> (((op (e2) (e0)) = (e2))\/(((op (e2) (e1)) = (e2))\/(((op (e2) (e2)) = (e2))\/((op (e2) (e3)) = (e2))))) -> (~((op (e2) (e0)) = (op (e2) (e3)))) -> ((op (e0) (e0)) = (e2)) -> (~((op (e0) (e0)) = (op (e0) (e3)))) -> (((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 (e2) (e2)) = (op (e2) (e3)))) -> (~((op (e3) (e1)) = (op (e3) (e2)))) -> (~((op (e3) (e2)) = (op (e3) (e3)))) -> (~((op (e2) (e1)) = (op (e2) (e3)))) -> ((op (e1) (e1)) = (e2)) -> (~((op (e1) (e1)) = (op (e1) (e3)))) -> (~((e1) = (e2))) -> (((op (e0) (e3)) = (e2))\/(((op (e1) (e3)) = (e2))\/(((op (e2) (e3)) = (e2))\/((op (e3) (e3)) = (e2))))) -> ((op (e1) (e2)) = (e1)) -> ((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)) = (e2))) -> (((op (e3) (e3)) = (e0))\/(((op (e3) (e3)) = (e1))\/(((op (e3) (e3)) = (e2))\/((op (e3) (e3)) = (e3))))) -> (~((op (e3) (e1)) = (op (e3) (e3)))) -> ((op (e3) (e1)) = (e0)) -> ((op (e0) (e3)) = (e1)) -> (~((op (e0) (e3)) = (op (e3) (e3)))) -> (~((op (e2) (e3)) = (op (e3) (e3)))) -> (~((op (e3) (e3)) = (e3))) -> False). % 18.79/18.92 do 0 intro. intros zenon_H2f zenon_H24b zenon_H3e zenon_H3f zenon_Hd8 zenon_H208 zenon_H67 zenon_H1f0 zenon_H1cf zenon_Ha8 zenon_H1d5 zenon_H5b zenon_H7b zenon_H189 zenon_H6a zenon_H27 zenon_H24a zenon_H6d zenon_H1a4 zenon_H62 zenon_H1c7 zenon_H110 zenon_H57 zenon_H7c zenon_H145 zenon_Hf0 zenon_H48 zenon_H149 zenon_H172 zenon_H173 zenon_H101 zenon_H130 zenon_H1b1 zenon_Hc3 zenon_Hc2 zenon_Hf3 zenon_H102. % 18.79/18.92 apply (zenon_or_s _ _ zenon_H2f); [ zenon_intro zenon_H34 | zenon_intro zenon_H33 ]. % 18.79/18.92 apply (zenon_L498_); trivial. % 18.79/18.92 apply (zenon_or_s _ _ zenon_H33); [ zenon_intro zenon_H36 | zenon_intro zenon_H35 ]. % 18.79/18.92 apply (zenon_L646_); trivial. % 18.79/18.92 apply (zenon_or_s _ _ zenon_H35); [ zenon_intro zenon_H2c | zenon_intro zenon_H37 ]. % 18.79/18.92 apply (zenon_L679_); trivial. % 18.79/18.92 apply (zenon_or_s _ _ zenon_H1d5); [ zenon_intro zenon_Hee | zenon_intro zenon_H1d6 ]. % 18.79/18.92 apply (zenon_or_s _ _ zenon_H172); [ zenon_intro zenon_H150 | zenon_intro zenon_H174 ]. % 18.79/18.92 apply (zenon_L680_); trivial. % 18.79/18.92 apply (zenon_or_s _ _ zenon_H174); [ zenon_intro zenon_H113 | zenon_intro zenon_H175 ]. % 18.79/18.92 apply (zenon_L68_); trivial. % 18.79/18.92 apply (zenon_or_s _ _ zenon_H175); [ zenon_intro zenon_H176 | zenon_intro zenon_H151 ]. % 18.79/18.92 exact (zenon_H173 zenon_H176). % 18.79/18.92 apply (zenon_L681_); trivial. % 18.79/18.92 apply (zenon_or_s _ _ zenon_H1d6); [ zenon_intro zenon_H1ca | zenon_intro zenon_H1d7 ]. % 18.79/18.92 apply (zenon_L497_); trivial. % 18.79/18.92 apply (zenon_or_s _ _ zenon_H1d7); [ zenon_intro zenon_H176 | zenon_intro zenon_H11d ]. % 18.79/18.92 exact (zenon_H173 zenon_H176). % 18.79/18.92 apply (zenon_L245_); trivial. % 18.79/18.92 (* end of lemma zenon_L682_ *) % 18.79/18.92 assert (zenon_L683_ : (((op (e1) (e0)) = (e3))\/(((op (e1) (e1)) = (e3))\/(((op (e1) (e2)) = (e3))\/((op (e1) (e3)) = (e3))))) -> (~((e0) = (e3))) -> ((op (e1) (e0)) = (e0)) -> (~((e2) = (e3))) -> ((op (e1) (e1)) = (e2)) -> (~((op (e2) (e3)) = (e0))) -> ((op (e0) (e2)) = (e1)) -> (~((op (e2) (e1)) = (e0))) -> (~((op (e2) (e0)) = (e0))) -> (((op (e2) (e0)) = (e0))\/(((op (e2) (e1)) = (e0))\/(((op (e2) (e2)) = (e0))\/((op (e2) (e3)) = (e0))))) -> ((op (e1) (e3)) = (e1)) -> (~((e1) = (e3))) -> False). % 18.79/18.92 do 0 intro. intros zenon_H16f zenon_H9a zenon_H27 zenon_H12b zenon_H110 zenon_H32 zenon_H122 zenon_H31 zenon_H30 zenon_H2f zenon_Hd6 zenon_H95. % 18.79/18.92 apply (zenon_or_s _ _ zenon_H16f); [ zenon_intro zenon_H9e | zenon_intro zenon_H170 ]. % 18.79/18.92 apply (zenon_L263_); trivial. % 18.79/18.92 apply (zenon_or_s _ _ zenon_H170); [ zenon_intro zenon_H13f | zenon_intro zenon_H171 ]. % 18.79/18.92 apply (zenon_L166_); trivial. % 18.79/18.92 apply (zenon_or_s _ _ zenon_H171); [ zenon_intro zenon_H16c | zenon_intro zenon_Hdc ]. % 18.79/18.92 apply (zenon_or_s _ _ zenon_H2f); [ zenon_intro zenon_H34 | zenon_intro zenon_H33 ]. % 18.79/18.92 exact (zenon_H30 zenon_H34). % 18.79/18.92 apply (zenon_or_s _ _ zenon_H33); [ zenon_intro zenon_H36 | zenon_intro zenon_H35 ]. % 18.79/18.92 exact (zenon_H31 zenon_H36). % 18.79/18.92 apply (zenon_or_s _ _ zenon_H35); [ zenon_intro zenon_H2c | zenon_intro zenon_H37 ]. % 18.79/18.92 apply (zenon_L603_); trivial. % 18.79/18.92 exact (zenon_H32 zenon_H37). % 18.79/18.92 apply (zenon_L83_); trivial. % 18.79/18.92 (* end of lemma zenon_L683_ *) % 18.79/18.92 assert (zenon_L684_ : (((op (e0) (e0)) = (e1))\/(((op (e0) (e1)) = (e1))\/(((op (e0) (e2)) = (e1))\/((op (e0) (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 (e1) (e1)) = (op (e1) (e3)))) -> (~((op (e1) (e1)) = (op (e2) (e1)))) -> (~((op (e2) (e1)) = (op (e3) (e1)))) -> (~((op (e2) (e1)) = (op (e2) (e3)))) -> (~((op (e1) (e2)) = (op (e2) (e2)))) -> (((op (e2) (e0)) = (e1))\/(((op (e2) (e1)) = (e1))\/(((op (e2) (e2)) = (e1))\/((op (e2) (e3)) = (e1))))) -> (~((e1) = (e2))) -> (((op (e0) (e1)) = (e2))\/(((op (e1) (e1)) = (e2))\/(((op (e2) (e1)) = (e2))\/((op (e3) (e1)) = (e2))))) -> (~((e1) = (e3))) -> (~((e2) = (e3))) -> (~((e0) = (e3))) -> (((op (e1) (e0)) = (e3))\/(((op (e1) (e1)) = (e3))\/(((op (e1) (e2)) = (e3))\/((op (e1) (e3)) = (e3))))) -> (~((op (e2) (e0)) = (op (e2) (e1)))) -> (((op (e2) (e0)) = (e0))\/(((op (e2) (e1)) = (e0))\/(((op (e2) (e2)) = (e0))\/((op (e2) (e3)) = (e0))))) -> (~((op (e2) (e0)) = (e0))) -> (~((op (e2) (e1)) = (e0))) -> (~((op (e3) (e1)) = (op (e3) (e3)))) -> ((op (e2) (e0)) = (e2)) -> (~((op (e2) (e0)) = (op (e2) (e3)))) -> (((op (e0) (e3)) = (e0))\/(((op (e1) (e3)) = (e0))\/(((op (e2) (e3)) = (e0))\/((op (e3) (e3)) = (e0))))) -> (~((e0) = (e2))) -> ((op (e1) (e0)) = (e0)) -> (~((op (e1) (e0)) = (op (e1) (e3)))) -> (~((op (e2) (e2)) = (op (e2) (e3)))) -> (((op (e0) (e3)) = (e2))\/(((op (e1) (e3)) = (e2))\/(((op (e2) (e3)) = (e2))\/((op (e3) (e3)) = (e2))))) -> (~((op (e2) (e3)) = (e0))) -> ((op (e3) (e0)) = (e1)) -> ((op (e0) (e0)) = (e3)) -> (((op (e1) (e0)) = (e2))\/(((op (e1) (e1)) = (e2))\/(((op (e1) (e2)) = (e2))\/((op (e1) (e3)) = (e2))))) -> (~((op (e0) (e2)) = (op (e1) (e2)))) -> (~((op (e1) (e1)) = (e1))) -> (((op (e1) (e0)) = (e1))\/(((op (e1) (e1)) = (e1))\/(((op (e1) (e2)) = (e1))\/((op (e1) (e3)) = (e1))))) -> (~((op (e1) (e1)) = (e0))) -> (~((op (e0) (e1)) = (e0))) -> (((op (e0) (e1)) = (e0))\/(((op (e1) (e1)) = (e0))\/(((op (e2) (e1)) = (e0))\/((op (e3) (e1)) = (e0))))) -> ((op (e0) (e3)) = (e0)) -> (~((e0) = (e1))) -> False). % 18.79/18.92 do 0 intro. intros zenon_H22d zenon_H1cc zenon_H17e zenon_H57 zenon_H13e zenon_Haf zenon_H1c7 zenon_H2b zenon_H106 zenon_H7c zenon_H1d8 zenon_H95 zenon_H12b zenon_H9a zenon_H16f zenon_H1f0 zenon_H2f zenon_H30 zenon_H31 zenon_H130 zenon_Hee zenon_H5b zenon_H67 zenon_H149 zenon_H27 zenon_Hd8 zenon_H6d zenon_H145 zenon_H32 zenon_Hac zenon_H3a zenon_H18c zenon_H195 zenon_H10a zenon_H128 zenon_H24 zenon_H20b zenon_H245 zenon_H1e zenon_Ha1. % 18.79/18.92 apply (zenon_or_s _ _ zenon_H22d); [ zenon_intro zenon_H7a | zenon_intro zenon_H22e ]. % 18.79/18.92 apply (zenon_L35_); trivial. % 18.79/18.92 apply (zenon_or_s _ _ zenon_H22e); [ zenon_intro zenon_Ha0 | zenon_intro zenon_H22f ]. % 18.79/18.92 apply (zenon_L678_); trivial. % 18.79/18.92 apply (zenon_or_s _ _ zenon_H22f); [ zenon_intro zenon_H122 | zenon_intro zenon_Hc3 ]. % 18.79/18.92 apply (zenon_or_s _ _ zenon_H245); [ zenon_intro zenon_H49 | zenon_intro zenon_H246 ]. % 18.79/18.92 exact (zenon_H20b zenon_H49). % 18.79/18.92 apply (zenon_or_s _ _ zenon_H246); [ zenon_intro zenon_H29 | zenon_intro zenon_H247 ]. % 18.79/18.92 exact (zenon_H24 zenon_H29). % 18.79/18.92 apply (zenon_or_s _ _ zenon_H247); [ zenon_intro zenon_H36 | zenon_intro zenon_H1b1 ]. % 18.79/18.92 exact (zenon_H31 zenon_H36). % 18.79/18.92 apply (zenon_or_s _ _ zenon_H128); [ zenon_intro zenon_H9d | zenon_intro zenon_H129 ]. % 18.79/18.92 apply (zenon_L262_); trivial. % 18.79/18.92 apply (zenon_or_s _ _ zenon_H129); [ zenon_intro zenon_H10d | zenon_intro zenon_H12a ]. % 18.79/18.92 exact (zenon_H10a zenon_H10d). % 18.79/18.92 apply (zenon_or_s _ _ zenon_H12a); [ zenon_intro zenon_Hf0 | zenon_intro zenon_Hd6 ]. % 18.79/18.92 apply (zenon_L530_); trivial. % 18.79/18.92 apply (zenon_or_s _ _ zenon_H18c); [ zenon_intro zenon_H86 | zenon_intro zenon_H18d ]. % 18.79/18.92 apply (zenon_L241_); trivial. % 18.79/18.92 apply (zenon_or_s _ _ zenon_H18d); [ zenon_intro zenon_H110 | zenon_intro zenon_H18e ]. % 18.79/18.92 apply (zenon_L683_); trivial. % 18.79/18.92 apply (zenon_or_s _ _ zenon_H18e); [ zenon_intro zenon_H113 | zenon_intro zenon_Hd7 ]. % 18.79/18.92 apply (zenon_L677_); trivial. % 18.79/18.92 apply (zenon_L101_); trivial. % 18.79/18.92 apply (zenon_L427_); trivial. % 18.79/18.92 (* end of lemma zenon_L684_ *) % 18.79/18.92 assert (zenon_L685_ : (~((op (e0) (e3)) = (op (e1) (e3)))) -> (~((op (e2) (e3)) = (op (e3) (e3)))) -> (~((op (e2) (e2)) = (e2))) -> (((op (e0) (e2)) = (e2))\/(((op (e1) (e2)) = (e2))\/(((op (e2) (e2)) = (e2))\/((op (e3) (e2)) = (e2))))) -> (~((op (e3) (e2)) = (op (e3) (e3)))) -> (~((op (e3) (e1)) = (op (e3) (e2)))) -> (~((op (e1) (e0)) = (op (e1) (e2)))) -> (((op (e0) (e2)) = (e0))\/(((op (e1) (e2)) = (e0))\/(((op (e2) (e2)) = (e0))\/((op (e3) (e2)) = (e0))))) -> (~((op (e0) (e0)) = (op (e0) (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 (e3) (e0)) = (op (e3) (e1)))) -> (~((op (e0) (e2)) = (op (e0) (e3)))) -> (~((op (e0) (e0)) = (e0))) -> (((op (e0) (e0)) = (e0))\/(((op (e1) (e0)) = (e0))\/(((op (e2) (e0)) = (e0))\/((op (e3) (e0)) = (e0))))) -> (~((op (e2) (e1)) = (op (e2) (e2)))) -> (((op (e3) (e3)) = (e0))\/(((op (e3) (e3)) = (e1))\/(((op (e3) (e3)) = (e2))\/((op (e3) (e3)) = (e3))))) -> (~((op (e0) (e3)) = (op (e3) (e3)))) -> (~((op (e3) (e3)) = (e3))) -> ((~((op (e0) (e2)) = (e0)))\/((op (e0) (e0)) = (e2))) -> ((~((op (e1) (e0)) = (e0)))\/((op (e1) (e0)) = (e0))) -> (~((op (e1) (e0)) = (op (e2) (e0)))) -> (~((op (e1) (e0)) = (op (e3) (e0)))) -> (((op (e0) (e0)) = (e0))\/(((op (e0) (e1)) = (e0))\/(((op (e0) (e2)) = (e0))\/((op (e0) (e3)) = (e0))))) -> (~((op (e3) (e0)) = (op (e3) (e2)))) -> (~((op (e3) (e0)) = (op (e3) (e3)))) -> (~((op (e0) (e1)) = (op (e0) (e2)))) -> (~((op (e1) (e1)) = (op (e1) (e2)))) -> (~((op (e2) (e0)) = (op (e2) (e2)))) -> (~((op (e0) (e1)) = (op (e0) (e3)))) -> (~((op (e1) (e0)) = (op (e1) (e1)))) -> (((op (e1) (e0)) = (e0))\/(((op (e1) (e1)) = (e0))\/(((op (e1) (e2)) = (e0))\/((op (e1) (e3)) = (e0))))) -> ((~((op (e3) (e1)) = (e0)))\/((op (e3) (e0)) = (e1))) -> ((~((op (e3) (e3)) = (e0)))\/((op (e3) (e0)) = (e3))) -> (((op (e0) (e2)) = (e0))\/(((op (e0) (e2)) = (e1))\/(((op (e0) (e2)) = (e2))\/((op (e0) (e2)) = (e3))))) -> (((op (e2) (e2)) = (e0))\/(((op (e2) (e2)) = (e1))\/(((op (e2) (e2)) = (e2))\/((op (e2) (e2)) = (e3))))) -> (((op (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 (e2) (e0)) = (e0)))\/((op (e2) (e0)) = (e0))) -> (((op (e0) (e0)) = (e2))\/(((op (e1) (e0)) = (e2))\/(((op (e2) (e0)) = (e2))\/((op (e3) (e0)) = (e2))))) -> ((~((op (e2) (e1)) = (e0)))\/((op (e2) (e0)) = (e1))) -> (~((op (e0) (e0)) = (op (e2) (e0)))) -> (((op (e3) (e0)) = (e2))\/(((op (e3) (e1)) = (e2))\/(((op (e3) (e2)) = (e2))\/((op (e3) (e3)) = (e2))))) -> (~((op (e0) (e2)) = (op (e3) (e2)))) -> (((op (e3) (e0)) = (e3))\/(((op (e3) (e1)) = (e3))\/(((op (e3) (e2)) = (e3))\/((op (e3) (e3)) = (e3))))) -> (~((op (e1) (e1)) = (op (e3) (e1)))) -> (((op (e0) (e0)) = (e3))\/(((op (e0) (e1)) = (e3))\/(((op (e0) (e2)) = (e3))\/((op (e0) (e3)) = (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) (e3)) = (e3))\/(((op (e1) (e3)) = (e3))\/(((op (e2) (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 (e1) (e1)) = (e0))\/(((op (e1) (e1)) = (e1))\/(((op (e1) (e1)) = (e2))\/((op (e1) (e1)) = (e3))))) -> ((~((op (e1) (e3)) = (e0)))\/((op (e1) (e0)) = (e3))) -> ((~((op (e1) (e2)) = (e0)))\/((op (e1) (e0)) = (e2))) -> (~((op (e2) (e0)) = (op (e3) (e0)))) -> (((op (e0) (e0)) = (e2))\/(((op (e0) (e1)) = (e2))\/(((op (e0) (e2)) = (e2))\/((op (e0) (e3)) = (e2))))) -> ((~((op (e3) (e0)) = (e0)))\/((op (e3) (e0)) = (e0))) -> ((~((op (e2) (e2)) = (e0)))\/((op (e2) (e0)) = (e2))) -> (((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 (e0) (e3)) = (e0))\/(((op (e0) (e3)) = (e1))\/(((op (e0) (e3)) = (e2))\/((op (e0) (e3)) = (e3))))) -> (~((op (e0) (e3)) = (op (e2) (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 (e0) (e1)) = (op (e1) (e1)))) -> (((op (e2) (e3)) = (e0))\/(((op (e2) (e3)) = (e1))\/(((op (e2) (e3)) = (e2))\/((op (e2) (e3)) = (e3))))) -> (~((op (e1) (e2)) = (op (e3) (e2)))) -> (((op (e1) (e2)) = (e0))\/(((op (e1) (e2)) = (e1))\/(((op (e1) (e2)) = (e2))\/((op (e1) (e2)) = (e3))))) -> (((op (e3) (e2)) = (e0))\/(((op (e3) (e2)) = (e1))\/(((op (e3) (e2)) = (e2))\/((op (e3) (e2)) = (e3))))) -> (~((op (e2) (e2)) = (op (e3) (e2)))) -> ((~((op (e3) (e2)) = (e0)))\/((op (e3) (e0)) = (e2))) -> (((op (e0) (e2)) = (e3))\/(((op (e1) (e2)) = (e3))\/(((op (e2) (e2)) = (e3))\/((op (e3) (e2)) = (e3))))) -> (((op (e0) (e1)) = (e3))\/(((op (e1) (e1)) = (e3))\/(((op (e2) (e1)) = (e3))\/((op (e3) (e1)) = (e3))))) -> ((~((op (e2) (e3)) = (e0)))\/((op (e2) (e0)) = (e3))) -> ((~((op (e1) (e1)) = (e0)))\/((op (e1) (e0)) = (e1))) -> ((~((op (e0) (e3)) = (e0)))\/((op (e0) (e0)) = (e3))) -> (((op (e0) (e0)) = (e1))\/(((op (e0) (e1)) = (e1))\/(((op (e0) (e2)) = (e1))\/((op (e0) (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 (e1) (e1)) = (op (e1) (e3)))) -> (~((op (e1) (e1)) = (op (e2) (e1)))) -> (~((op (e2) (e1)) = (op (e3) (e1)))) -> (~((op (e2) (e1)) = (op (e2) (e3)))) -> (~((op (e1) (e2)) = (op (e2) (e2)))) -> (((op (e2) (e0)) = (e1))\/(((op (e2) (e1)) = (e1))\/(((op (e2) (e2)) = (e1))\/((op (e2) (e3)) = (e1))))) -> (~((e1) = (e2))) -> (((op (e0) (e1)) = (e2))\/(((op (e1) (e1)) = (e2))\/(((op (e2) (e1)) = (e2))\/((op (e3) (e1)) = (e2))))) -> (~((e1) = (e3))) -> (~((e2) = (e3))) -> (~((e0) = (e3))) -> (((op (e1) (e0)) = (e3))\/(((op (e1) (e1)) = (e3))\/(((op (e1) (e2)) = (e3))\/((op (e1) (e3)) = (e3))))) -> (~((op (e2) (e0)) = (op (e2) (e1)))) -> (((op (e2) (e0)) = (e0))\/(((op (e2) (e1)) = (e0))\/(((op (e2) (e2)) = (e0))\/((op (e2) (e3)) = (e0))))) -> (~((op (e2) (e0)) = (e0))) -> (~((op (e2) (e1)) = (e0))) -> (~((op (e3) (e1)) = (op (e3) (e3)))) -> ((op (e2) (e0)) = (e2)) -> (~((op (e2) (e0)) = (op (e2) (e3)))) -> (((op (e0) (e3)) = (e0))\/(((op (e1) (e3)) = (e0))\/(((op (e2) (e3)) = (e0))\/((op (e3) (e3)) = (e0))))) -> (~((e0) = (e2))) -> ((op (e1) (e0)) = (e0)) -> (~((op (e1) (e0)) = (op (e1) (e3)))) -> (~((op (e2) (e2)) = (op (e2) (e3)))) -> (((op (e0) (e3)) = (e2))\/(((op (e1) (e3)) = (e2))\/(((op (e2) (e3)) = (e2))\/((op (e3) (e3)) = (e2))))) -> (~((op (e2) (e3)) = (e0))) -> ((op (e3) (e0)) = (e1)) -> ((op (e0) (e0)) = (e3)) -> (((op (e1) (e0)) = (e2))\/(((op (e1) (e1)) = (e2))\/(((op (e1) (e2)) = (e2))\/((op (e1) (e3)) = (e2))))) -> (~((op (e0) (e2)) = (op (e1) (e2)))) -> (~((op (e1) (e1)) = (e1))) -> (((op (e1) (e0)) = (e1))\/(((op (e1) (e1)) = (e1))\/(((op (e1) (e2)) = (e1))\/((op (e1) (e3)) = (e1))))) -> (~((op (e1) (e1)) = (e0))) -> (~((op (e0) (e1)) = (e0))) -> (((op (e0) (e1)) = (e0))\/(((op (e1) (e1)) = (e0))\/(((op (e2) (e1)) = (e0))\/((op (e3) (e1)) = (e0))))) -> (~((e0) = (e1))) -> False). % 18.79/18.92 do 0 intro. intros zenon_H1d zenon_Hf3 zenon_H173 zenon_H172 zenon_H62 zenon_H1a4 zenon_H24a zenon_H6a zenon_H189 zenon_H7b zenon_H1d5 zenon_Ha8 zenon_H1cf zenon_H208 zenon_H3f zenon_H3e zenon_H24b zenon_H101 zenon_Hc2 zenon_H102 zenon_H233 zenon_H206 zenon_H201 zenon_H1fa zenon_H74 zenon_H6f zenon_H71 zenon_H4a zenon_H4f zenon_H52 zenon_H54 zenon_H45 zenon_H22 zenon_H1ed zenon_H1ec zenon_H1ba zenon_H1c4 zenon_H1ac zenon_H1e0 zenon_H1ee zenon_H1fe zenon_H182 zenon_H39 zenon_H153 zenon_H14f zenon_H165 zenon_H160 zenon_H168 zenon_H124 zenon_H133 zenon_H136 zenon_H139 zenon_H13c zenon_H142 zenon_H179 zenon_H178 zenon_H17b zenon_H183 zenon_H184 zenon_H185 zenon_H109 zenon_He7 zenon_He4 zenon_He2 zenon_Hd5 zenon_Hdb zenon_Hdf zenon_He8 zenon_H10e zenon_H11f zenon_H115 zenon_H19d zenon_H191 zenon_H18f zenon_H1a7 zenon_H1a6 zenon_H1a5 zenon_H94 zenon_H205 zenon_H204 zenon_H22d zenon_H1cc zenon_H17e zenon_H57 zenon_H13e zenon_Haf zenon_H1c7 zenon_H2b zenon_H106 zenon_H7c zenon_H1d8 zenon_H95 zenon_H12b zenon_H9a zenon_H16f zenon_H1f0 zenon_H2f zenon_H30 zenon_H31 zenon_H130 zenon_Hee zenon_H5b zenon_H67 zenon_H149 zenon_H27 zenon_Hd8 zenon_H6d zenon_H145 zenon_H32 zenon_Hac zenon_H3a zenon_H18c zenon_H195 zenon_H10a zenon_H128 zenon_H24 zenon_H20b zenon_H245 zenon_Ha1. % 18.79/18.92 apply (zenon_or_s _ _ zenon_H74); [ zenon_intro zenon_H42 | zenon_intro zenon_H77 ]. % 18.79/18.92 exact (zenon_H3f zenon_H42). % 18.79/18.92 apply (zenon_or_s _ _ zenon_H77); [ zenon_intro zenon_H49 | zenon_intro zenon_H78 ]. % 18.79/18.92 exact (zenon_H20b zenon_H49). % 18.79/18.92 apply (zenon_or_s _ _ zenon_H78); [ zenon_intro zenon_H48 | zenon_intro zenon_H1e ]. % 18.79/18.92 apply (zenon_or_s _ _ zenon_H22d); [ zenon_intro zenon_H7a | zenon_intro zenon_H22e ]. % 18.79/18.92 apply (zenon_L456_); trivial. % 18.79/18.92 apply (zenon_or_s _ _ zenon_H22e); [ zenon_intro zenon_Ha0 | zenon_intro zenon_H22f ]. % 18.79/18.92 apply (zenon_L678_); trivial. % 18.79/18.92 apply (zenon_or_s _ _ zenon_H22f); [ zenon_intro zenon_H122 | zenon_intro zenon_Hc3 ]. % 18.79/18.92 apply (zenon_L355_); trivial. % 18.79/18.92 apply (zenon_or_s _ _ zenon_H245); [ zenon_intro zenon_H49 | zenon_intro zenon_H246 ]. % 18.79/18.92 exact (zenon_H20b zenon_H49). % 18.79/18.92 apply (zenon_or_s _ _ zenon_H246); [ zenon_intro zenon_H29 | zenon_intro zenon_H247 ]. % 18.79/18.92 exact (zenon_H24 zenon_H29). % 18.79/18.92 apply (zenon_or_s _ _ zenon_H247); [ zenon_intro zenon_H36 | zenon_intro zenon_H1b1 ]. % 18.79/18.92 exact (zenon_H31 zenon_H36). % 18.79/18.92 apply (zenon_or_s _ _ zenon_H128); [ zenon_intro zenon_H9d | zenon_intro zenon_H129 ]. % 18.79/18.92 apply (zenon_L262_); trivial. % 18.79/18.92 apply (zenon_or_s _ _ zenon_H129); [ zenon_intro zenon_H10d | zenon_intro zenon_H12a ]. % 18.79/18.92 exact (zenon_H10a zenon_H10d). % 18.79/18.92 apply (zenon_or_s _ _ zenon_H12a); [ zenon_intro zenon_Hf0 | zenon_intro zenon_Hd6 ]. % 18.79/18.92 apply (zenon_or_s _ _ zenon_H18c); [ zenon_intro zenon_H86 | zenon_intro zenon_H18d ]. % 18.79/18.92 apply (zenon_L257_); trivial. % 18.79/18.92 apply (zenon_or_s _ _ zenon_H18d); [ zenon_intro zenon_H110 | zenon_intro zenon_H18e ]. % 18.79/18.92 apply (zenon_L682_); trivial. % 18.79/18.92 apply (zenon_or_s _ _ zenon_H18e); [ zenon_intro zenon_H113 | zenon_intro zenon_Hd7 ]. % 18.79/18.92 apply (zenon_L68_); trivial. % 18.79/18.92 apply (zenon_or_s _ _ zenon_H1d8); [ zenon_intro zenon_H10f | zenon_intro zenon_H1d9 ]. % 18.79/18.92 apply (zenon_L673_); trivial. % 18.79/18.92 apply (zenon_or_s _ _ zenon_H1d9); [ zenon_intro zenon_H110 | zenon_intro zenon_H1da ]. % 18.79/18.92 apply (zenon_L283_); trivial. % 18.79/18.92 apply (zenon_or_s _ _ zenon_H1da); [ zenon_intro zenon_H1ca | zenon_intro zenon_H14d ]. % 18.79/18.92 apply (zenon_L277_); trivial. % 18.79/18.92 apply (zenon_L500_); trivial. % 18.79/18.92 apply (zenon_L79_); trivial. % 18.79/18.92 apply (zenon_L684_); trivial. % 18.79/18.92 (* end of lemma zenon_L685_ *) % 18.79/18.92 assert (zenon_L686_ : (((op (e2) (e0)) = (e0))\/(((op (e2) (e1)) = (e0))\/(((op (e2) (e2)) = (e0))\/((op (e2) (e3)) = (e0))))) -> (~((op (e2) (e1)) = (e0))) -> (~((op (e2) (e0)) = (e0))) -> (((op (e0) (e0)) = (e1))\/(((op (e0) (e1)) = (e1))\/(((op (e0) (e2)) = (e1))\/((op (e0) (e3)) = (e1))))) -> (((op (e0) (e0)) = (e1))\/(((op (e1) (e0)) = (e1))\/(((op (e2) (e0)) = (e1))\/((op (e3) (e0)) = (e1))))) -> (((op (e3) (e1)) = (e0))\/(((op (e3) (e1)) = (e1))\/(((op (e3) (e1)) = (e2))\/((op (e3) (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 (e0) (e0)) = (e2)) -> (~((op (e0) (e1)) = (e0))) -> (((op (e0) (e1)) = (e0))\/(((op (e1) (e1)) = (e0))\/(((op (e2) (e1)) = (e0))\/((op (e3) (e1)) = (e0))))) -> (~((op (e1) (e0)) = (op (e1) (e2)))) -> (~((op (e2) (e1)) = (op (e2) (e2)))) -> (~((op (e0) (e2)) = (op (e0) (e3)))) -> (~((op (e1) (e1)) = (e0))) -> (~((op (e1) (e2)) = (e0))) -> ((op (e0) (e0)) = (e3)) -> ((op (e1) (e0)) = (e0)) -> ((~((op (e0) (e3)) = (e0)))\/((op (e0) (e0)) = (e3))) -> ((~((op (e1) (e1)) = (e0)))\/((op (e1) (e0)) = (e1))) -> (~((e1) = (e2))) -> ((~((op (e2) (e3)) = (e0)))\/((op (e2) (e0)) = (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) (e1)) = (op (e3) (e2)))) -> ((~((op (e3) (e2)) = (e0)))\/((op (e3) (e0)) = (e2))) -> (~((op (e2) (e2)) = (op (e3) (e2)))) -> (((op (e3) (e2)) = (e0))\/(((op (e3) (e2)) = (e1))\/(((op (e3) (e2)) = (e2))\/((op (e3) (e2)) = (e3))))) -> (~((op (e0) (e2)) = (op (e1) (e2)))) -> (((op (e1) (e2)) = (e0))\/(((op (e1) (e2)) = (e1))\/(((op (e1) (e2)) = (e2))\/((op (e1) (e2)) = (e3))))) -> (~((e1) = (e3))) -> (~((e0) = (e3))) -> (~((op (e1) (e1)) = (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) (e3)) = (e0))\/(((op (e2) (e3)) = (e1))\/(((op (e2) (e3)) = (e2))\/((op (e2) (e3)) = (e3))))) -> (~((op (e0) (e3)) = (op (e1) (e3)))) -> (~((op (e0) (e1)) = (op (e1) (e1)))) -> (~((e0) = (e1))) -> (~((op (e0) (e2)) = (op (e2) (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) (e3)) = (e0))\/(((op (e1) (e3)) = (e1))\/(((op (e1) (e3)) = (e2))\/((op (e1) (e3)) = (e3))))) -> (~((op (e1) (e3)) = (op (e2) (e3)))) -> (~((op (e1) (e0)) = (op (e1) (e3)))) -> (~((op (e1) (e3)) = (op (e3) (e3)))) -> (~((op (e0) (e3)) = (op (e2) (e3)))) -> (((op (e0) (e3)) = (e0))\/(((op (e0) (e3)) = (e1))\/(((op (e0) (e3)) = (e2))\/((op (e0) (e3)) = (e3))))) -> (~((op (e2) (e1)) = (op (e3) (e1)))) -> (((op (e2) (e0)) = (e3))\/(((op (e2) (e1)) = (e3))\/(((op (e2) (e2)) = (e3))\/((op (e2) (e3)) = (e3))))) -> (((op (e2) (e0)) = (e1))\/(((op (e2) (e1)) = (e1))\/(((op (e2) (e2)) = (e1))\/((op (e2) (e3)) = (e1))))) -> (~((op (e2) (e3)) = (op (e3) (e3)))) -> (~((op (e3) (e3)) = (e3))) -> (((op (e3) (e3)) = (e0))\/(((op (e3) (e3)) = (e1))\/(((op (e3) (e3)) = (e2))\/((op (e3) (e3)) = (e3))))) -> (~((op (e1) (e2)) = (op (e2) (e2)))) -> (((op (e0) (e1)) = (e1))\/(((op (e1) (e1)) = (e1))\/(((op (e2) (e1)) = (e1))\/((op (e3) (e1)) = (e1))))) -> (~((op (e0) (e0)) = (op (e0) (e3)))) -> ((~((op (e2) (e2)) = (e0)))\/((op (e2) (e0)) = (e2))) -> ((~((op (e3) (e0)) = (e0)))\/((op (e3) (e0)) = (e0))) -> (((op (e0) (e0)) = (e2))\/(((op (e0) (e1)) = (e2))\/(((op (e0) (e2)) = (e2))\/((op (e0) (e3)) = (e2))))) -> (~((op (e2) (e0)) = (op (e3) (e0)))) -> (~((op (e0) (e1)) = (op (e2) (e1)))) -> ((~((op (e1) (e2)) = (e0)))\/((op (e1) (e0)) = (e2))) -> ((~((op (e1) (e3)) = (e0)))\/((op (e1) (e0)) = (e3))) -> (((op (e1) (e1)) = (e0))\/(((op (e1) (e1)) = (e1))\/(((op (e1) (e1)) = (e2))\/((op (e1) (e1)) = (e3))))) -> (~((op (e1) (e1)) = (op (e2) (e1)))) -> (~((op (e0) (e0)) = (op (e0) (e2)))) -> (((op (e0) (e2)) = (e1))\/(((op (e1) (e2)) = (e1))\/(((op (e2) (e2)) = (e1))\/((op (e3) (e2)) = (e1))))) -> (((op (e1) (e0)) = (e1))\/(((op (e1) (e1)) = (e1))\/(((op (e1) (e2)) = (e1))\/((op (e1) (e3)) = (e1))))) -> (((op (e0) (e3)) = (e3))\/(((op (e1) (e3)) = (e3))\/(((op (e2) (e3)) = (e3))\/((op (e3) (e3)) = (e3))))) -> (~((op (e3) (e1)) = (op (e3) (e3)))) -> (((op (e0) (e3)) = (e1))\/(((op (e1) (e3)) = (e1))\/(((op (e2) (e3)) = (e1))\/((op (e3) (e3)) = (e1))))) -> (~((e2) = (e3))) -> (~((op (e1) (e2)) = (op (e1) (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 (e2) (e2)) = (e2))) -> (((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) (e1)) = (op (e3) (e1)))) -> (((op (e3) (e0)) = (e3))\/(((op (e3) (e1)) = (e3))\/(((op (e3) (e2)) = (e3))\/((op (e3) (e3)) = (e3))))) -> (~((e0) = (e2))) -> (~((op (e0) (e2)) = (op (e3) (e2)))) -> (((op (e3) (e0)) = (e2))\/(((op (e3) (e1)) = (e2))\/(((op (e3) (e2)) = (e2))\/((op (e3) (e3)) = (e2))))) -> (~((op (e0) (e0)) = (op (e2) (e0)))) -> ((~((op (e2) (e1)) = (e0)))\/((op (e2) (e0)) = (e1))) -> (((op (e0) (e0)) = (e2))\/(((op (e1) (e0)) = (e2))\/(((op (e2) (e0)) = (e2))\/((op (e3) (e0)) = (e2))))) -> ((~((op (e2) (e0)) = (e0)))\/((op (e2) (e0)) = (e0))) -> (((op (e0) (e0)) = (e3))\/(((op (e1) (e0)) = (e3))\/(((op (e2) (e0)) = (e3))\/((op (e3) (e0)) = (e3))))) -> (((op (e3) (e0)) = (e0))\/(((op (e3) (e1)) = (e0))\/(((op (e3) (e2)) = (e0))\/((op (e3) (e3)) = (e0))))) -> (~((op (e2) (e1)) = (op (e2) (e3)))) -> (((op (e2) (e2)) = (e0))\/(((op (e2) (e2)) = (e1))\/(((op (e2) (e2)) = (e2))\/((op (e2) (e2)) = (e3))))) -> (((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 (e3) (e0)) = (op (e3) (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))))) -> ((~((op (e3) (e3)) = (e0)))\/((op (e3) (e0)) = (e3))) -> ((~((op (e3) (e1)) = (e0)))\/((op (e3) (e0)) = (e1))) -> (~((op (e0) (e0)) = (e0))) -> (((op (e1) (e0)) = (e0))\/(((op (e1) (e1)) = (e0))\/(((op (e1) (e2)) = (e0))\/((op (e1) (e3)) = (e0))))) -> (~((op (e1) (e0)) = (op (e1) (e1)))) -> (((op (e0) (e2)) = (e0))\/(((op (e1) (e2)) = (e0))\/(((op (e2) (e2)) = (e0))\/((op (e3) (e2)) = (e0))))) -> (~((op (e0) (e1)) = (op (e0) (e3)))) -> (~((op (e1) (e1)) = (op (e1) (e3)))) -> (~((op (e2) (e0)) = (op (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) (e0)) = (op (e2) (e2)))) -> (~((op (e1) (e1)) = (op (e1) (e2)))) -> (~((op (e0) (e1)) = (op (e0) (e2)))) -> (~((op (e3) (e0)) = (op (e3) (e3)))) -> (~((op (e2) (e2)) = (op (e2) (e3)))) -> (~((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)) = (e0))\/(((op (e0) (e1)) = (e0))\/(((op (e0) (e2)) = (e0))\/((op (e0) (e3)) = (e0))))) -> (~((op (e1) (e0)) = (op (e3) (e0)))) -> (~((op (e2) (e0)) = (op (e2) (e1)))) -> (~((op (e1) (e0)) = (op (e2) (e0)))) -> ((~((op (e1) (e0)) = (e0)))\/((op (e1) (e0)) = (e0))) -> ((~((op (e0) (e2)) = (e0)))\/((op (e0) (e0)) = (e2))) -> False). % 18.79/18.92 do 0 intro. intros zenon_H2f zenon_H31 zenon_H30 zenon_H22d zenon_H235 zenon_H22a zenon_H210 zenon_H212 zenon_H7b zenon_H20b zenon_H245 zenon_H24a zenon_H24b zenon_H208 zenon_H24 zenon_H25 zenon_H3a zenon_H27 zenon_H204 zenon_H205 zenon_H7c zenon_H94 zenon_H1a5 zenon_H1a6 zenon_H1a4 zenon_H1a7 zenon_H18f zenon_H191 zenon_H195 zenon_H19d zenon_H95 zenon_H9a zenon_H10a zenon_H18c zenon_H115 zenon_H11f zenon_H1d zenon_H10e zenon_Ha1 zenon_Ha8 zenon_He8 zenon_Hc2 zenon_Hdf zenon_Hdb zenon_Hd8 zenon_Hd5 zenon_He2 zenon_He4 zenon_Haf zenon_He7 zenon_H106 zenon_Hf3 zenon_H102 zenon_H101 zenon_H2b zenon_H109 zenon_H189 zenon_H185 zenon_H184 zenon_H183 zenon_H17b zenon_H17e zenon_H178 zenon_H179 zenon_H142 zenon_H13e zenon_H13c zenon_H139 zenon_H128 zenon_H136 zenon_H130 zenon_H133 zenon_H12b zenon_H124 zenon_H145 zenon_H172 zenon_H173 zenon_H16f zenon_H168 zenon_H160 zenon_H165 zenon_H149 zenon_H14f zenon_H153 zenon_H39 zenon_H182 zenon_H1fe zenon_H1ee zenon_H1e0 zenon_H1ac zenon_H1c7 zenon_H1c4 zenon_H1cc zenon_H1ba zenon_H1cf zenon_H1d8 zenon_H1d5 zenon_H1ec zenon_H1ed zenon_H3f zenon_H22 zenon_H45 zenon_H6a zenon_H54 zenon_H57 zenon_H5b zenon_H62 zenon_H67 zenon_H52 zenon_H4f zenon_H4a zenon_H71 zenon_H6d zenon_H6f zenon_H3e zenon_H74 zenon_H1fa zenon_H1f0 zenon_H201 zenon_H206 zenon_H233. % 18.79/18.92 apply (zenon_or_s _ _ zenon_H185); [ zenon_intro zenon_H81 | zenon_intro zenon_Hee ]. % 18.79/18.92 apply (zenon_L672_); trivial. % 18.79/18.92 apply (zenon_or_s _ _ zenon_H94); [ zenon_intro zenon_H32 | zenon_intro zenon_H3b ]. % 18.79/18.92 apply (zenon_or_s _ _ zenon_H235); [ zenon_intro zenon_H7a | zenon_intro zenon_H236 ]. % 18.79/18.92 apply (zenon_L456_); trivial. % 18.79/18.92 apply (zenon_or_s _ _ zenon_H236); [ zenon_intro zenon_H9d | zenon_intro zenon_H237 ]. % 18.79/18.92 apply (zenon_L262_); trivial. % 18.79/18.92 apply (zenon_or_s _ _ zenon_H237); [ zenon_intro zenon_Hed | zenon_intro zenon_Hac ]. % 18.79/18.92 apply (zenon_L58_); trivial. % 18.79/18.92 apply (zenon_L685_); trivial. % 18.79/18.92 apply (zenon_L671_); trivial. % 18.79/18.92 (* end of lemma zenon_L686_ *) % 18.79/18.92 assert (zenon_L687_ : ((~((op (e0) (e2)) = (e0)))\/((op (e0) (e0)) = (e2))) -> ((~((op (e1) (e0)) = (e0)))\/((op (e1) (e0)) = (e0))) -> (~((op (e1) (e0)) = (op (e2) (e0)))) -> (~((op (e2) (e0)) = (op (e2) (e1)))) -> (~((op (e1) (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) (e2)))) -> (~((op (e2) (e2)) = (op (e2) (e3)))) -> (~((op (e3) (e0)) = (op (e3) (e3)))) -> (~((op (e0) (e1)) = (op (e0) (e2)))) -> (~((op (e1) (e1)) = (op (e1) (e2)))) -> (~((op (e2) (e0)) = (op (e2) (e2)))) -> (((op (e0) (e3)) = (e0))\/(((op (e1) (e3)) = (e0))\/(((op (e2) (e3)) = (e0))\/((op (e3) (e3)) = (e0))))) -> (~((op (e3) (e2)) = (op (e3) (e3)))) -> (~((op (e2) (e0)) = (op (e2) (e3)))) -> (~((op (e1) (e1)) = (op (e1) (e3)))) -> (~((op (e0) (e1)) = (op (e0) (e3)))) -> (((op (e0) (e2)) = (e0))\/(((op (e1) (e2)) = (e0))\/(((op (e2) (e2)) = (e0))\/((op (e3) (e2)) = (e0))))) -> (~((op (e1) (e0)) = (op (e1) (e1)))) -> ((~((op (e3) (e1)) = (e0)))\/((op (e3) (e0)) = (e1))) -> ((~((op (e3) (e3)) = (e0)))\/((op (e3) (e0)) = (e3))) -> (((op (e2) (e0)) = (e2))\/(((op (e2) (e1)) = (e2))\/(((op (e2) (e2)) = (e2))\/((op (e2) (e3)) = (e2))))) -> (((op (e0) (e1)) = (e2))\/(((op (e1) (e1)) = (e2))\/(((op (e2) (e1)) = (e2))\/((op (e3) (e1)) = (e2))))) -> (~((op (e3) (e0)) = (op (e3) (e1)))) -> (((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 (e2) (e2)) = (e0))\/(((op (e2) (e2)) = (e1))\/(((op (e2) (e2)) = (e2))\/((op (e2) (e2)) = (e3))))) -> (~((op (e2) (e1)) = (op (e2) (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 (e2) (e0)) = (e0)))\/((op (e2) (e0)) = (e0))) -> (((op (e0) (e0)) = (e2))\/(((op (e1) (e0)) = (e2))\/(((op (e2) (e0)) = (e2))\/((op (e3) (e0)) = (e2))))) -> ((~((op (e2) (e1)) = (e0)))\/((op (e2) (e0)) = (e1))) -> (~((op (e0) (e0)) = (op (e2) (e0)))) -> (((op (e3) (e0)) = (e2))\/(((op (e3) (e1)) = (e2))\/(((op (e3) (e2)) = (e2))\/((op (e3) (e3)) = (e2))))) -> (~((op (e0) (e2)) = (op (e3) (e2)))) -> (~((e0) = (e2))) -> (((op (e3) (e0)) = (e3))\/(((op (e3) (e1)) = (e3))\/(((op (e3) (e2)) = (e3))\/((op (e3) (e3)) = (e3))))) -> (~((op (e1) (e1)) = (op (e3) (e1)))) -> (((op (e0) (e0)) = (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)) = (e2))) -> (((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) (e2)) = (op (e1) (e3)))) -> (~((e2) = (e3))) -> (((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)) = (e3))\/(((op (e1) (e3)) = (e3))\/(((op (e2) (e3)) = (e3))\/((op (e3) (e3)) = (e3))))) -> (((op (e1) (e0)) = (e1))\/(((op (e1) (e1)) = (e1))\/(((op (e1) (e2)) = (e1))\/((op (e1) (e3)) = (e1))))) -> (((op (e0) (e2)) = (e1))\/(((op (e1) (e2)) = (e1))\/(((op (e2) (e2)) = (e1))\/((op (e3) (e2)) = (e1))))) -> (~((op (e0) (e0)) = (op (e0) (e2)))) -> (~((op (e1) (e1)) = (op (e2) (e1)))) -> (((op (e1) (e1)) = (e0))\/(((op (e1) (e1)) = (e1))\/(((op (e1) (e1)) = (e2))\/((op (e1) (e1)) = (e3))))) -> ((~((op (e1) (e3)) = (e0)))\/((op (e1) (e0)) = (e3))) -> ((~((op (e1) (e2)) = (e0)))\/((op (e1) (e0)) = (e2))) -> (~((op (e0) (e1)) = (op (e2) (e1)))) -> (~((op (e2) (e0)) = (op (e3) (e0)))) -> (((op (e0) (e0)) = (e2))\/(((op (e0) (e1)) = (e2))\/(((op (e0) (e2)) = (e2))\/((op (e0) (e3)) = (e2))))) -> ((~((op (e3) (e0)) = (e0)))\/((op (e3) (e0)) = (e0))) -> ((~((op (e2) (e2)) = (e0)))\/((op (e2) (e0)) = (e2))) -> (~((op (e0) (e0)) = (op (e0) (e3)))) -> (((op (e0) (e1)) = (e1))\/(((op (e1) (e1)) = (e1))\/(((op (e2) (e1)) = (e1))\/((op (e3) (e1)) = (e1))))) -> (~((op (e1) (e2)) = (op (e2) (e2)))) -> (((op (e3) (e3)) = (e0))\/(((op (e3) (e3)) = (e1))\/(((op (e3) (e3)) = (e2))\/((op (e3) (e3)) = (e3))))) -> (~((op (e3) (e3)) = (e3))) -> (~((op (e2) (e3)) = (op (e3) (e3)))) -> (((op (e2) (e0)) = (e1))\/(((op (e2) (e1)) = (e1))\/(((op (e2) (e2)) = (e1))\/((op (e2) (e3)) = (e1))))) -> (((op (e2) (e0)) = (e3))\/(((op (e2) (e1)) = (e3))\/(((op (e2) (e2)) = (e3))\/((op (e2) (e3)) = (e3))))) -> (~((op (e2) (e1)) = (op (e3) (e1)))) -> (((op (e0) (e3)) = (e0))\/(((op (e0) (e3)) = (e1))\/(((op (e0) (e3)) = (e2))\/((op (e0) (e3)) = (e3))))) -> (~((op (e0) (e3)) = (op (e2) (e3)))) -> (~((op (e1) (e3)) = (op (e3) (e3)))) -> (~((op (e1) (e0)) = (op (e1) (e3)))) -> (~((op (e1) (e3)) = (op (e2) (e3)))) -> (((op (e1) (e3)) = (e0))\/(((op (e1) (e3)) = (e1))\/(((op (e1) (e3)) = (e2))\/((op (e1) (e3)) = (e3))))) -> (~((op (e0) (e3)) = (op (e3) (e3)))) -> (((op (e3) (e0)) = (e1))\/(((op (e3) (e1)) = (e1))\/(((op (e3) (e2)) = (e1))\/((op (e3) (e3)) = (e1))))) -> (~((op (e0) (e2)) = (op (e2) (e2)))) -> (~((e0) = (e1))) -> (~((op (e0) (e1)) = (op (e1) (e1)))) -> (~((op (e0) (e3)) = (op (e1) (e3)))) -> (((op (e2) (e3)) = (e0))\/(((op (e2) (e3)) = (e1))\/(((op (e2) (e3)) = (e2))\/((op (e2) (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) (e1)) = (e1))) -> (~((e0) = (e3))) -> (~((e1) = (e3))) -> (((op (e1) (e2)) = (e0))\/(((op (e1) (e2)) = (e1))\/(((op (e1) (e2)) = (e2))\/((op (e1) (e2)) = (e3))))) -> (((op (e3) (e2)) = (e0))\/(((op (e3) (e2)) = (e1))\/(((op (e3) (e2)) = (e2))\/((op (e3) (e2)) = (e3))))) -> (~((op (e2) (e2)) = (op (e3) (e2)))) -> ((~((op (e3) (e2)) = (e0)))\/((op (e3) (e0)) = (e2))) -> (~((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)) = (e3))\/(((op (e1) (e1)) = (e3))\/(((op (e2) (e1)) = (e3))\/((op (e3) (e1)) = (e3))))) -> ((~((op (e2) (e3)) = (e0)))\/((op (e2) (e0)) = (e3))) -> (~((e1) = (e2))) -> ((~((op (e1) (e1)) = (e0)))\/((op (e1) (e0)) = (e1))) -> ((~((op (e0) (e3)) = (e0)))\/((op (e0) (e0)) = (e3))) -> ((op (e0) (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) (e1)) = (e0))\/(((op (e1) (e1)) = (e0))\/(((op (e2) (e1)) = (e0))\/((op (e3) (e1)) = (e0))))) -> (~((op (e0) (e2)) = (op (e0) (e3)))) -> (((op (e0) (e1)) = (e0))\/(((op (e0) (e1)) = (e1))\/(((op (e0) (e1)) = (e2))\/((op (e0) (e1)) = (e3))))) -> (((op (e3) (e1)) = (e0))\/(((op (e3) (e1)) = (e1))\/(((op (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)) = (e0))) -> (~((op (e0) (e1)) = (e0))) -> (((op (e1) (e0)) = (e0))\/(((op (e1) (e1)) = (e0))\/(((op (e1) (e2)) = (e0))\/((op (e1) (e3)) = (e0))))) -> (~((op (e0) (e2)) = (op (e1) (e2)))) -> (((op (e0) (e0)) = (e0))\/(((op (e0) (e1)) = (e0))\/(((op (e0) (e2)) = (e0))\/((op (e0) (e3)) = (e0))))) -> (~((op (e1) (e0)) = (op (e1) (e2)))) -> (~((op (e2) (e1)) = (op (e2) (e2)))) -> False). % 18.79/18.92 do 0 intro. intros zenon_H233 zenon_H206 zenon_H201 zenon_H1f0 zenon_H1fa zenon_H3e zenon_H6f zenon_H6d zenon_H71 zenon_H4a zenon_H4f zenon_H52 zenon_H67 zenon_H62 zenon_H5b zenon_H57 zenon_H54 zenon_H6a zenon_H45 zenon_H1ed zenon_H1ec zenon_H1d5 zenon_H1d8 zenon_H1cf zenon_H1ba zenon_H1cc zenon_H1c4 zenon_H1c7 zenon_H1ac zenon_H1e0 zenon_H1ee zenon_H1fe zenon_H182 zenon_H39 zenon_H153 zenon_H14f zenon_H149 zenon_H165 zenon_H160 zenon_H168 zenon_H16f zenon_H173 zenon_H172 zenon_H145 zenon_H124 zenon_H12b zenon_H133 zenon_H130 zenon_H136 zenon_H128 zenon_H139 zenon_H13c zenon_H13e zenon_H142 zenon_H179 zenon_H178 zenon_H17e zenon_H17b zenon_H183 zenon_H184 zenon_H185 zenon_H189 zenon_H109 zenon_H2b zenon_H101 zenon_H102 zenon_Hf3 zenon_H106 zenon_He7 zenon_Haf zenon_He4 zenon_He2 zenon_Hd5 zenon_Hd8 zenon_Hdb zenon_Hdf zenon_Hc2 zenon_He8 zenon_Ha8 zenon_Ha1 zenon_H10e zenon_H1d zenon_H11f zenon_H115 zenon_H18c zenon_H10a zenon_H9a zenon_H95 zenon_H19d zenon_H191 zenon_H18f zenon_H1a7 zenon_H1a4 zenon_H1a6 zenon_H1a5 zenon_H94 zenon_H7c zenon_H205 zenon_H204 zenon_H7b zenon_H235 zenon_H2f zenon_H245 zenon_H208 zenon_H212 zenon_H22a zenon_H210 zenon_H22d zenon_H3f zenon_H20b zenon_H22 zenon_H195 zenon_H74 zenon_H24a zenon_H24b. % 18.79/18.92 apply (zenon_or_s _ _ zenon_H204); [ zenon_intro zenon_H76 | zenon_intro zenon_H3a ]. % 18.79/18.92 apply (zenon_or_s _ _ zenon_H206); [ zenon_intro zenon_H23 | zenon_intro zenon_H27 ]. % 18.79/18.92 apply (zenon_or_s _ _ zenon_H205); [ zenon_intro zenon_H24 | zenon_intro zenon_H9d ]. % 18.79/18.92 apply (zenon_or_s _ _ zenon_H178); [ zenon_intro zenon_H25 | zenon_intro zenon_H86 ]. % 18.79/18.92 apply (zenon_or_s _ _ zenon_H179); [ zenon_intro zenon_H38 | zenon_intro zenon_H9e ]. % 18.79/18.92 apply (zenon_L616_); trivial. % 18.79/18.92 apply (zenon_or_s _ _ zenon_H1ee); [ zenon_intro zenon_H30 | zenon_intro zenon_H34 ]. % 18.79/18.92 apply (zenon_L617_); trivial. % 18.79/18.92 apply (zenon_or_s _ _ zenon_H182); [ zenon_intro zenon_H31 | zenon_intro zenon_Hed ]. % 18.79/18.92 apply (zenon_or_s _ _ zenon_H185); [ zenon_intro zenon_H81 | zenon_intro zenon_Hee ]. % 18.79/18.92 apply (zenon_or_s _ _ zenon_H235); [ zenon_intro zenon_H7a | zenon_intro zenon_H236 ]. % 18.79/18.92 apply (zenon_L26_); trivial. % 18.79/18.92 apply (zenon_or_s _ _ zenon_H236); [ zenon_intro zenon_H9d | zenon_intro zenon_H237 ]. % 18.79/18.92 apply (zenon_L625_); trivial. % 18.79/18.92 apply (zenon_or_s _ _ zenon_H237); [ zenon_intro zenon_Hed | zenon_intro zenon_Hac ]. % 18.79/18.92 apply (zenon_L491_); trivial. % 18.79/18.92 apply (zenon_L637_); trivial. % 18.79/18.92 apply (zenon_L341_); trivial. % 18.79/18.92 apply (zenon_L491_); trivial. % 18.79/18.92 apply (zenon_or_s _ _ zenon_H179); [ zenon_intro zenon_H38 | zenon_intro zenon_H9e ]. % 18.79/18.92 apply (zenon_L616_); trivial. % 18.79/18.92 apply (zenon_or_s _ _ zenon_H1ee); [ zenon_intro zenon_H30 | zenon_intro zenon_H34 ]. % 18.79/18.92 apply (zenon_L617_); trivial. % 18.79/18.92 apply (zenon_or_s _ _ zenon_H182); [ zenon_intro zenon_H31 | zenon_intro zenon_Hed ]. % 18.79/18.92 apply (zenon_or_s _ _ zenon_H185); [ zenon_intro zenon_H81 | zenon_intro zenon_Hee ]. % 18.79/18.92 apply (zenon_or_s _ _ zenon_H74); [ zenon_intro zenon_H42 | zenon_intro zenon_H77 ]. % 18.79/18.92 exact (zenon_H3f zenon_H42). % 18.79/18.92 apply (zenon_or_s _ _ zenon_H77); [ zenon_intro zenon_H49 | zenon_intro zenon_H78 ]. % 18.79/18.92 exact (zenon_H20b zenon_H49). % 18.79/18.92 apply (zenon_or_s _ _ zenon_H78); [ zenon_intro zenon_H48 | zenon_intro zenon_H1e ]. % 18.79/18.92 apply (zenon_or_s _ _ zenon_H235); [ zenon_intro zenon_H7a | zenon_intro zenon_H236 ]. % 18.79/18.92 apply (zenon_L26_); trivial. % 18.79/18.92 apply (zenon_or_s _ _ zenon_H236); [ zenon_intro zenon_H9d | zenon_intro zenon_H237 ]. % 18.79/18.92 apply (zenon_L631_); trivial. % 18.79/18.92 apply (zenon_or_s _ _ zenon_H237); [ zenon_intro zenon_Hed | zenon_intro zenon_Hac ]. % 18.79/18.92 apply (zenon_L491_); trivial. % 18.79/18.92 apply (zenon_L639_); trivial. % 18.79/18.92 exact (zenon_H76 zenon_H1e). % 18.79/18.92 apply (zenon_L204_); trivial. % 18.79/18.92 apply (zenon_L214_); trivial. % 18.79/18.92 apply (zenon_L631_); trivial. % 18.79/18.92 apply (zenon_or_s _ _ zenon_H205); [ zenon_intro zenon_H24 | zenon_intro zenon_H9d ]. % 18.79/18.92 apply (zenon_or_s _ _ zenon_H178); [ zenon_intro zenon_H25 | zenon_intro zenon_H86 ]. % 18.79/18.92 apply (zenon_or_s _ _ zenon_H1ee); [ zenon_intro zenon_H30 | zenon_intro zenon_H34 ]. % 18.79/18.92 apply (zenon_or_s _ _ zenon_H182); [ zenon_intro zenon_H31 | zenon_intro zenon_Hed ]. % 18.79/18.92 apply (zenon_or_s _ _ zenon_H185); [ zenon_intro zenon_H81 | zenon_intro zenon_Hee ]. % 18.79/18.92 apply (zenon_or_s _ _ zenon_H94); [ zenon_intro zenon_H32 | zenon_intro zenon_H3b ]. % 18.79/18.92 apply (zenon_L27_); trivial. % 18.79/18.92 apply (zenon_or_s _ _ zenon_H235); [ zenon_intro zenon_H7a | zenon_intro zenon_H236 ]. % 18.79/18.92 apply (zenon_L456_); trivial. % 18.79/18.92 apply (zenon_or_s _ _ zenon_H236); [ zenon_intro zenon_H9d | zenon_intro zenon_H237 ]. % 18.79/18.92 apply (zenon_L262_); trivial. % 18.79/18.92 apply (zenon_or_s _ _ zenon_H237); [ zenon_intro zenon_Hed | zenon_intro zenon_Hac ]. % 18.79/18.92 apply (zenon_L669_); trivial. % 18.79/18.92 apply (zenon_L308_); trivial. % 18.79/18.92 apply (zenon_L341_); trivial. % 18.79/18.92 apply (zenon_L669_); trivial. % 18.79/18.92 apply (zenon_L332_); trivial. % 18.79/18.92 apply (zenon_L257_); trivial. % 18.79/18.92 apply (zenon_L262_); trivial. % 18.79/18.92 apply (zenon_or_s _ _ zenon_H206); [ zenon_intro zenon_H23 | zenon_intro zenon_H27 ]. % 18.79/18.92 apply (zenon_L592_); trivial. % 18.79/18.92 apply (zenon_or_s _ _ zenon_H205); [ zenon_intro zenon_H24 | zenon_intro zenon_H9d ]. % 18.79/18.92 apply (zenon_or_s _ _ zenon_H178); [ zenon_intro zenon_H25 | zenon_intro zenon_H86 ]. % 18.79/18.92 apply (zenon_or_s _ _ zenon_H1ee); [ zenon_intro zenon_H30 | zenon_intro zenon_H34 ]. % 18.79/18.92 apply (zenon_or_s _ _ zenon_H182); [ zenon_intro zenon_H31 | zenon_intro zenon_Hed ]. % 18.79/18.92 apply (zenon_L686_); trivial. % 18.79/18.92 apply (zenon_L670_); trivial. % 18.79/18.92 apply (zenon_L332_); trivial. % 18.79/18.92 apply (zenon_L257_); trivial. % 18.79/18.92 apply (zenon_L262_); trivial. % 18.79/18.92 (* end of lemma zenon_L687_ *) % 18.79/18.92 assert (zenon_L688_ : (((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)) = (e1)) -> ((op (e0) (e2)) = (e1)) -> (~((op (e0) (e2)) = (op (e2) (e2)))) -> (((op (e2) (e1)) = (e0))\/(((op (e2) (e1)) = (e1))\/(((op (e2) (e1)) = (e2))\/((op (e2) (e1)) = (e3))))) -> (~((op (e2) (e1)) = (e0))) -> (~((op (e2) (e1)) = (op (e2) (e3)))) -> ((op (e2) (e0)) = (e2)) -> (~((op (e2) (e0)) = (op (e2) (e1)))) -> ((op (e0) (e1)) = (e2)) -> ((op (e1) (e1)) = (e0)) -> False). % 18.79/18.92 do 0 intro. intros zenon_H106 zenon_H7c zenon_Haf zenon_Hae zenon_H122 zenon_Ha8 zenon_H1cc zenon_H31 zenon_H1c7 zenon_Hee zenon_H1f0 zenon_H10f zenon_H29. % 18.79/18.92 apply (zenon_or_s _ _ zenon_H106); [ zenon_intro zenon_Hed | zenon_intro zenon_H107 ]. % 18.79/18.92 apply (zenon_L58_); trivial. % 18.79/18.92 apply (zenon_or_s _ _ zenon_H107); [ zenon_intro zenon_Ha5 | zenon_intro zenon_H108 ]. % 18.79/18.92 apply (zenon_L42_); trivial. % 18.79/18.92 apply (zenon_or_s _ _ zenon_H108); [ zenon_intro zenon_Hf1 | zenon_intro zenon_Hf4 ]. % 18.79/18.92 apply (zenon_L246_); trivial. % 18.79/18.92 apply (zenon_L596_); trivial. % 18.79/18.92 (* end of lemma zenon_L688_ *) % 18.79/18.92 assert (zenon_L689_ : (((op (e0) (e1)) = (e3))\/(((op (e1) (e1)) = (e3))\/(((op (e2) (e1)) = (e3))\/((op (e3) (e1)) = (e3))))) -> ((op (e1) (e1)) = (e0)) -> (~((op (e1) (e1)) = (op (e2) (e1)))) -> (~((op (e2) (e1)) = (op (e3) (e1)))) -> (~((op (e2) (e1)) = (op (e2) (e3)))) -> (~((op (e2) (e1)) = (e0))) -> (((op (e2) (e1)) = (e0))\/(((op (e2) (e1)) = (e1))\/(((op (e2) (e1)) = (e2))\/((op (e2) (e1)) = (e3))))) -> (~((op (e0) (e1)) = (op (e2) (e1)))) -> (~((op (e1) (e0)) = (op (e2) (e0)))) -> (~((op (e3) (e3)) = (e3))) -> ((op (e3) (e1)) = (e2)) -> (~((op (e3) (e1)) = (op (e3) (e3)))) -> (~((op (e2) (e3)) = (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) (e0)) = (e1))\/(((op (e3) (e1)) = (e1))\/(((op (e3) (e2)) = (e1))\/((op (e3) (e3)) = (e1))))) -> (~((e1) = (e3))) -> (~((op (e0) (e1)) = (op (e3) (e1)))) -> (~((op (e2) (e2)) = (op (e2) (e3)))) -> ((op (e1) (e0)) = (e1)) -> (~((op (e1) (e0)) = (op (e1) (e3)))) -> ((op (e0) (e1)) = (e1)) -> (~((op (e0) (e1)) = (op (e0) (e3)))) -> (((op (e0) (e3)) = (e1))\/(((op (e1) (e3)) = (e1))\/(((op (e2) (e3)) = (e1))\/((op (e3) (e3)) = (e1))))) -> (((op (e3) (e2)) = (e0))\/(((op (e3) (e2)) = (e1))\/(((op (e3) (e2)) = (e2))\/((op (e3) (e2)) = (e3))))) -> (~((op (e3) (e2)) = (e0))) -> (~((op (e3) (e2)) = (op (e3) (e3)))) -> (~((op (e3) (e1)) = (op (e3) (e2)))) -> (~((op (e3) (e0)) = (op (e3) (e2)))) -> ((op (e2) (e0)) = (e2)) -> (~((e1) = (e2))) -> (((op (e2) (e0)) = (e1))\/(((op (e2) (e1)) = (e1))\/(((op (e2) (e2)) = (e1))\/((op (e2) (e3)) = (e1))))) -> ((op (e3) (e0)) = (e3)) -> (~((op (e3) (e0)) = (op (e3) (e1)))) -> False). % 18.79/18.92 do 0 intro. intros zenon_H1a5 zenon_H29 zenon_H13e zenon_Haf zenon_H1c7 zenon_H31 zenon_H1cc zenon_H17e zenon_H201 zenon_H102 zenon_H14d zenon_H130 zenon_Hf3 zenon_H44 zenon_H71 zenon_H101 zenon_He8 zenon_H95 zenon_H210 zenon_H6d zenon_H9d zenon_Hd8 zenon_Ha0 zenon_H54 zenon_H133 zenon_H191 zenon_H18b zenon_H62 zenon_H1a4 zenon_H6f zenon_Hee zenon_H7c zenon_H106 zenon_H15e zenon_H1cf. % 18.79/18.92 apply (zenon_or_s _ _ zenon_H1a5); [ zenon_intro zenon_H99 | zenon_intro zenon_H1a8 ]. % 18.79/18.92 apply (zenon_L385_); trivial. % 18.79/18.92 apply (zenon_or_s _ _ zenon_H1a8); [ zenon_intro zenon_H13f | zenon_intro zenon_H1a9 ]. % 18.79/18.92 apply (zenon_L622_); trivial. % 18.79/18.92 apply (zenon_or_s _ _ zenon_H1a9); [ zenon_intro zenon_Ha6 | zenon_intro zenon_H161 ]. % 18.79/18.92 apply (zenon_or_s _ _ zenon_H106); [ zenon_intro zenon_Hed | zenon_intro zenon_H107 ]. % 18.79/18.92 apply (zenon_L58_); trivial. % 18.79/18.92 apply (zenon_or_s _ _ zenon_H107); [ zenon_intro zenon_Ha5 | zenon_intro zenon_H108 ]. % 18.79/18.92 apply (zenon_L39_); trivial. % 18.79/18.92 apply (zenon_or_s _ _ zenon_H108); [ zenon_intro zenon_Hf1 | zenon_intro zenon_Hf4 ]. % 18.79/18.92 apply (zenon_L607_); trivial. % 18.79/18.92 apply (zenon_L414_); trivial. % 18.79/18.92 apply (zenon_L193_); trivial. % 18.79/18.92 (* end of lemma zenon_L689_ *) % 18.79/18.92 assert (zenon_L690_ : (((op (e0) (e1)) = (e2))\/(((op (e1) (e1)) = (e2))\/(((op (e2) (e1)) = (e2))\/((op (e3) (e1)) = (e2))))) -> (~((op (e3) (e1)) = (e0))) -> (((op (e3) (e1)) = (e0))\/(((op (e3) (e1)) = (e1))\/(((op (e3) (e1)) = (e2))\/((op (e3) (e1)) = (e3))))) -> (~((e0) = (e2))) -> (~((op (e2) (e0)) = (op (e2) (e1)))) -> (((op (e0) (e1)) = (e3))\/(((op (e1) (e1)) = (e3))\/(((op (e2) (e1)) = (e3))\/((op (e3) (e1)) = (e3))))) -> ((op (e1) (e1)) = (e0)) -> (~((op (e1) (e1)) = (op (e2) (e1)))) -> (~((op (e2) (e1)) = (op (e3) (e1)))) -> (~((op (e2) (e1)) = (op (e2) (e3)))) -> (~((op (e2) (e1)) = (e0))) -> (((op (e2) (e1)) = (e0))\/(((op (e2) (e1)) = (e1))\/(((op (e2) (e1)) = (e2))\/((op (e2) (e1)) = (e3))))) -> (~((op (e0) (e1)) = (op (e2) (e1)))) -> (~((op (e1) (e0)) = (op (e2) (e0)))) -> (~((op (e3) (e3)) = (e3))) -> (~((op (e3) (e1)) = (op (e3) (e3)))) -> (~((op (e2) (e3)) = (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) (e0)) = (e1))\/(((op (e3) (e1)) = (e1))\/(((op (e3) (e2)) = (e1))\/((op (e3) (e3)) = (e1))))) -> (~((e1) = (e3))) -> (~((op (e0) (e1)) = (op (e3) (e1)))) -> (~((op (e2) (e2)) = (op (e2) (e3)))) -> ((op (e1) (e0)) = (e1)) -> (~((op (e1) (e0)) = (op (e1) (e3)))) -> ((op (e0) (e1)) = (e1)) -> (~((op (e0) (e1)) = (op (e0) (e3)))) -> (((op (e0) (e3)) = (e1))\/(((op (e1) (e3)) = (e1))\/(((op (e2) (e3)) = (e1))\/((op (e3) (e3)) = (e1))))) -> (((op (e3) (e2)) = (e0))\/(((op (e3) (e2)) = (e1))\/(((op (e3) (e2)) = (e2))\/((op (e3) (e2)) = (e3))))) -> (~((op (e3) (e2)) = (e0))) -> (~((op (e3) (e2)) = (op (e3) (e3)))) -> (~((op (e3) (e1)) = (op (e3) (e2)))) -> (~((op (e3) (e0)) = (op (e3) (e2)))) -> ((op (e2) (e0)) = (e2)) -> (~((e1) = (e2))) -> (((op (e2) (e0)) = (e1))\/(((op (e2) (e1)) = (e1))\/(((op (e2) (e2)) = (e1))\/((op (e2) (e3)) = (e1))))) -> ((op (e3) (e0)) = (e3)) -> (~((op (e3) (e0)) = (op (e3) (e1)))) -> False). % 18.79/18.92 do 0 intro. intros zenon_H1d8 zenon_H1ad zenon_H22a zenon_H149 zenon_H1f0 zenon_H1a5 zenon_H29 zenon_H13e zenon_Haf zenon_H1c7 zenon_H31 zenon_H1cc zenon_H17e zenon_H201 zenon_H102 zenon_H130 zenon_Hf3 zenon_H44 zenon_H71 zenon_H101 zenon_He8 zenon_H95 zenon_H210 zenon_H6d zenon_H9d zenon_Hd8 zenon_Ha0 zenon_H54 zenon_H133 zenon_H191 zenon_H18b zenon_H62 zenon_H1a4 zenon_H6f zenon_Hee zenon_H7c zenon_H106 zenon_H15e zenon_H1cf. % 18.79/18.92 apply (zenon_or_s _ _ zenon_H1d8); [ zenon_intro zenon_H10f | zenon_intro zenon_H1d9 ]. % 18.79/18.92 apply (zenon_L418_); trivial. % 18.79/18.92 apply (zenon_or_s _ _ zenon_H1d9); [ zenon_intro zenon_H110 | zenon_intro zenon_H1da ]. % 18.79/18.92 apply (zenon_L354_); trivial. % 18.79/18.92 apply (zenon_or_s _ _ zenon_H1da); [ zenon_intro zenon_H1ca | zenon_intro zenon_H14d ]. % 18.79/18.92 apply (zenon_L277_); trivial. % 18.79/18.92 apply (zenon_L689_); trivial. % 18.79/18.92 (* end of lemma zenon_L690_ *) % 18.79/18.92 assert (zenon_L691_ : (((op (e1) (e0)) = (e0))\/(((op (e1) (e1)) = (e0))\/(((op (e1) (e2)) = (e0))\/((op (e1) (e3)) = (e0))))) -> (~((op (e1) (e0)) = (e0))) -> (~((op (e3) (e0)) = (op (e3) (e1)))) -> ((op (e3) (e0)) = (e3)) -> (((op (e2) (e0)) = (e1))\/(((op (e2) (e1)) = (e1))\/(((op (e2) (e2)) = (e1))\/((op (e2) (e3)) = (e1))))) -> (~((e1) = (e2))) -> ((op (e2) (e0)) = (e2)) -> (~((op (e3) (e0)) = (op (e3) (e2)))) -> (~((op (e3) (e1)) = (op (e3) (e2)))) -> (~((op (e3) (e2)) = (op (e3) (e3)))) -> (~((op (e3) (e2)) = (e0))) -> (((op (e3) (e2)) = (e0))\/(((op (e3) (e2)) = (e1))\/(((op (e3) (e2)) = (e2))\/((op (e3) (e2)) = (e3))))) -> (((op (e0) (e3)) = (e1))\/(((op (e1) (e3)) = (e1))\/(((op (e2) (e3)) = (e1))\/((op (e3) (e3)) = (e1))))) -> (~((op (e0) (e1)) = (op (e0) (e3)))) -> ((op (e0) (e1)) = (e1)) -> (~((op (e1) (e0)) = (op (e1) (e3)))) -> ((op (e1) (e0)) = (e1)) -> (~((op (e2) (e2)) = (op (e2) (e3)))) -> (~((op (e0) (e1)) = (op (e3) (e1)))) -> (~((e1) = (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) (e0)) = (op (e3) (e3)))) -> ((op (e3) (e0)) = (e0)) -> (~((op (e2) (e3)) = (op (e3) (e3)))) -> (~((op (e3) (e1)) = (op (e3) (e3)))) -> (~((op (e3) (e3)) = (e3))) -> (~((op (e1) (e0)) = (op (e2) (e0)))) -> (~((op (e0) (e1)) = (op (e2) (e1)))) -> (((op (e2) (e1)) = (e0))\/(((op (e2) (e1)) = (e1))\/(((op (e2) (e1)) = (e2))\/((op (e2) (e1)) = (e3))))) -> (~((op (e2) (e1)) = (e0))) -> (~((op (e2) (e1)) = (op (e2) (e3)))) -> (~((op (e2) (e1)) = (op (e3) (e1)))) -> (~((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)) = (op (e2) (e1)))) -> (~((e0) = (e2))) -> (((op (e3) (e1)) = (e0))\/(((op (e3) (e1)) = (e1))\/(((op (e3) (e1)) = (e2))\/((op (e3) (e1)) = (e3))))) -> (~((op (e3) (e1)) = (e0))) -> (((op (e0) (e1)) = (e2))\/(((op (e1) (e1)) = (e2))\/(((op (e2) (e1)) = (e2))\/((op (e3) (e1)) = (e2))))) -> (~((op (e1) (e2)) = (e0))) -> (~((op (e1) (e3)) = (e0))) -> False). % 18.79/18.92 do 0 intro. intros zenon_H22 zenon_H23 zenon_H1cf zenon_H15e zenon_H106 zenon_H7c zenon_Hee zenon_H6f zenon_H1a4 zenon_H62 zenon_H18b zenon_H191 zenon_H133 zenon_H54 zenon_Ha0 zenon_Hd8 zenon_H9d zenon_H6d zenon_H210 zenon_H95 zenon_He8 zenon_H101 zenon_H71 zenon_H44 zenon_Hf3 zenon_H130 zenon_H102 zenon_H201 zenon_H17e zenon_H1cc zenon_H31 zenon_H1c7 zenon_Haf zenon_H13e zenon_H1a5 zenon_H1f0 zenon_H149 zenon_H22a zenon_H1ad zenon_H1d8 zenon_H25 zenon_H38. % 18.79/18.92 apply (zenon_or_s _ _ zenon_H22); [ zenon_intro zenon_H27 | zenon_intro zenon_H26 ]. % 18.79/18.92 exact (zenon_H23 zenon_H27). % 18.79/18.92 apply (zenon_or_s _ _ zenon_H26); [ zenon_intro zenon_H29 | zenon_intro zenon_H28 ]. % 18.79/18.92 apply (zenon_L690_); trivial. % 18.79/18.92 apply (zenon_or_s _ _ zenon_H28); [ zenon_intro zenon_H2a | zenon_intro zenon_H1f ]. % 18.79/18.92 exact (zenon_H25 zenon_H2a). % 18.79/18.92 exact (zenon_H38 zenon_H1f). % 18.79/18.92 (* end of lemma zenon_L691_ *) % 18.79/18.92 assert (zenon_L692_ : (((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 (e3) (e1)) = (e0))) -> (~((op (e1) (e1)) = (op (e2) (e1)))) -> (~((op (e2) (e1)) = (op (e3) (e1)))) -> (~((op (e2) (e1)) = (e0))) -> (((op (e2) (e1)) = (e0))\/(((op (e2) (e1)) = (e1))\/(((op (e2) (e1)) = (e2))\/((op (e2) (e1)) = (e3))))) -> (~((e2) = (e3))) -> (~((e0) = (e2))) -> ((op (e2) (e0)) = (e2)) -> (~((op (e2) (e0)) = (op (e2) (e1)))) -> (((op (e0) (e1)) = (e3))\/(((op (e1) (e1)) = (e3))\/(((op (e2) (e1)) = (e3))\/((op (e3) (e1)) = (e3))))) -> ((op (e1) (e1)) = (e0)) -> (~((op (e0) (e1)) = (op (e1) (e1)))) -> (~((op (e0) (e1)) = (op (e3) (e1)))) -> (~((op (e0) (e1)) = (op (e2) (e1)))) -> (~((op (e0) (e1)) = (e0))) -> (((op (e0) (e1)) = (e0))\/(((op (e0) (e1)) = (e1))\/(((op (e0) (e1)) = (e2))\/((op (e0) (e1)) = (e3))))) -> (~((e1) = (e3))) -> ((op (e2) (e1)) = (e1)) -> ((op (e3) (e0)) = (e3)) -> (~((op (e3) (e0)) = (op (e3) (e1)))) -> False). % 18.79/18.92 do 0 intro. intros zenon_H1d8 zenon_H22a zenon_H1ad zenon_H13e zenon_Haf zenon_H31 zenon_H1cc zenon_H12b zenon_H149 zenon_Hee zenon_H1f0 zenon_H1a5 zenon_H29 zenon_H10e zenon_H210 zenon_H17e zenon_H20b zenon_H212 zenon_H95 zenon_Ha5 zenon_H15e zenon_H1cf. % 18.79/18.92 apply (zenon_or_s _ _ zenon_H1d8); [ zenon_intro zenon_H10f | zenon_intro zenon_H1d9 ]. % 18.79/18.92 apply (zenon_L441_); trivial. % 18.79/18.92 apply (zenon_or_s _ _ zenon_H1d9); [ zenon_intro zenon_H110 | zenon_intro zenon_H1da ]. % 18.79/18.92 apply (zenon_L354_); trivial. % 18.79/18.92 apply (zenon_or_s _ _ zenon_H1da); [ zenon_intro zenon_H1ca | zenon_intro zenon_H14d ]. % 18.79/18.92 apply (zenon_L277_); trivial. % 18.79/18.92 apply (zenon_L443_); trivial. % 18.79/18.92 (* end of lemma zenon_L692_ *) % 18.79/18.92 assert (zenon_L693_ : (((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 (e1) (e1)) = (e0)))\/((op (e1) (e0)) = (e1))) -> ((~((op (e2) (e3)) = (e0)))\/((op (e2) (e0)) = (e3))) -> (((op (e2) (e0)) = (e0))\/(((op (e2) (e1)) = (e0))\/(((op (e2) (e2)) = (e0))\/((op (e2) (e3)) = (e0))))) -> (((op (e0) (e2)) = (e3))\/(((op (e1) (e2)) = (e3))\/(((op (e2) (e2)) = (e3))\/((op (e3) (e2)) = (e3))))) -> ((~((op (e3) (e2)) = (e0)))\/((op (e3) (e0)) = (e2))) -> (~((op (e2) (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))))) -> (~((e0) = (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) (e3)) = (e0))\/(((op (e2) (e3)) = (e1))\/(((op (e2) (e3)) = (e2))\/((op (e2) (e3)) = (e3))))) -> (~((op (e0) (e3)) = (op (e1) (e3)))) -> (~((op (e0) (e2)) = (op (e2) (e2)))) -> (~((op (e0) (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) (e3)) = (op (e3) (e3)))) -> (~((op (e0) (e3)) = (op (e2) (e3)))) -> (((op (e0) (e3)) = (e0))\/(((op (e0) (e3)) = (e1))\/(((op (e0) (e3)) = (e2))\/((op (e0) (e3)) = (e3))))) -> (((op (e2) (e0)) = (e3))\/(((op (e2) (e1)) = (e3))\/(((op (e2) (e2)) = (e3))\/((op (e2) (e3)) = (e3))))) -> (~((op (e1) (e2)) = (op (e2) (e2)))) -> (~((op (e0) (e0)) = (op (e0) (e3)))) -> ((~((op (e2) (e2)) = (e0)))\/((op (e2) (e0)) = (e2))) -> ((~((op (e3) (e0)) = (e0)))\/((op (e3) (e0)) = (e0))) -> (((op (e0) (e0)) = (e2))\/(((op (e0) (e1)) = (e2))\/(((op (e0) (e2)) = (e2))\/((op (e0) (e3)) = (e2))))) -> (~((op (e2) (e0)) = (op (e3) (e0)))) -> ((~((op (e1) (e2)) = (e0)))\/((op (e1) (e0)) = (e2))) -> ((~((op (e1) (e3)) = (e0)))\/((op (e1) (e0)) = (e3))) -> (((op (e1) (e1)) = (e0))\/(((op (e1) (e1)) = (e1))\/(((op (e1) (e1)) = (e2))\/((op (e1) (e1)) = (e3))))) -> (~((op (e0) (e0)) = (op (e0) (e2)))) -> (((op (e0) (e2)) = (e1))\/(((op (e1) (e2)) = (e1))\/(((op (e2) (e2)) = (e1))\/((op (e3) (e2)) = (e1))))) -> (((op (e1) (e0)) = (e1))\/(((op (e1) (e1)) = (e1))\/(((op (e1) (e2)) = (e1))\/((op (e1) (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 (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 (e2) (e2)) = (e2))) -> (((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) (e1)) = (op (e3) (e1)))) -> (((op (e3) (e0)) = (e3))\/(((op (e3) (e1)) = (e3))\/(((op (e3) (e2)) = (e3))\/((op (e3) (e3)) = (e3))))) -> (~((op (e0) (e2)) = (op (e3) (e2)))) -> (((op (e3) (e0)) = (e2))\/(((op (e3) (e1)) = (e2))\/(((op (e3) (e2)) = (e2))\/((op (e3) (e3)) = (e2))))) -> (~((op (e0) (e0)) = (op (e2) (e0)))) -> ((~((op (e2) (e1)) = (e0)))\/((op (e2) (e0)) = (e1))) -> (((op (e0) (e0)) = (e2))\/(((op (e1) (e0)) = (e2))\/(((op (e2) (e0)) = (e2))\/((op (e3) (e0)) = (e2))))) -> ((~((op (e2) (e0)) = (e0)))\/((op (e2) (e0)) = (e0))) -> (((op (e0) (e0)) = (e3))\/(((op (e1) (e0)) = (e3))\/(((op (e2) (e0)) = (e3))\/((op (e3) (e0)) = (e3))))) -> (((op (e3) (e0)) = (e0))\/(((op (e3) (e1)) = (e0))\/(((op (e3) (e2)) = (e0))\/((op (e3) (e3)) = (e0))))) -> (((op (e2) (e2)) = (e0))\/(((op (e2) (e2)) = (e1))\/(((op (e2) (e2)) = (e2))\/((op (e2) (e2)) = (e3))))) -> (((op (e0) (e2)) = (e0))\/(((op (e0) (e2)) = (e1))\/(((op (e0) (e2)) = (e2))\/((op (e0) (e2)) = (e3))))) -> (((op (e2) (e0)) = (e2))\/(((op (e2) (e1)) = (e2))\/(((op (e2) (e2)) = (e2))\/((op (e2) (e3)) = (e2))))) -> ((~((op (e3) (e3)) = (e0)))\/((op (e3) (e0)) = (e3))) -> ((~((op (e3) (e1)) = (e0)))\/((op (e3) (e0)) = (e1))) -> (~((op (e0) (e0)) = (e0))) -> (~((op (e1) (e0)) = (op (e1) (e1)))) -> (((op (e0) (e2)) = (e0))\/(((op (e1) (e2)) = (e0))\/(((op (e2) (e2)) = (e0))\/((op (e3) (e2)) = (e0))))) -> (~((op (e1) (e1)) = (op (e1) (e3)))) -> (~((op (e2) (e0)) = (op (e2) (e3)))) -> (((op (e0) (e3)) = (e0))\/(((op (e1) (e3)) = (e0))\/(((op (e2) (e3)) = (e0))\/((op (e3) (e3)) = (e0))))) -> (~((op (e2) (e0)) = (op (e2) (e2)))) -> (~((op (e1) (e1)) = (op (e1) (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 (e1) (e0)) = (op (e3) (e0)))) -> ((~((op (e1) (e0)) = (e0)))\/((op (e1) (e0)) = (e0))) -> ((~((op (e0) (e2)) = (e0)))\/((op (e0) (e0)) = (e2))) -> (~((op (e2) (e1)) = (op (e2) (e3)))) -> (~((op (e1) (e0)) = (op (e2) (e0)))) -> (~((op (e3) (e3)) = (e3))) -> (~((op (e3) (e1)) = (op (e3) (e3)))) -> (~((op (e2) (e3)) = (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) (e0)) = (e1))\/(((op (e3) (e1)) = (e1))\/(((op (e3) (e2)) = (e1))\/((op (e3) (e3)) = (e1))))) -> (~((op (e2) (e2)) = (op (e2) (e3)))) -> ((op (e1) (e0)) = (e1)) -> (~((op (e1) (e0)) = (op (e1) (e3)))) -> (~((op (e0) (e1)) = (op (e0) (e3)))) -> (((op (e0) (e3)) = (e1))\/(((op (e1) (e3)) = (e1))\/(((op (e2) (e3)) = (e1))\/((op (e3) (e3)) = (e1))))) -> (((op (e3) (e2)) = (e0))\/(((op (e3) (e2)) = (e1))\/(((op (e3) (e2)) = (e2))\/((op (e3) (e2)) = (e3))))) -> (~((op (e3) (e2)) = (e0))) -> (~((op (e3) (e2)) = (op (e3) (e3)))) -> (~((op (e3) (e1)) = (op (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) (e3)) = (e0))) -> (~((op (e1) (e2)) = (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)) = (e1))) -> (~((e1) = (e3))) -> (((op (e0) (e1)) = (e0))\/(((op (e0) (e1)) = (e1))\/(((op (e0) (e1)) = (e2))\/((op (e0) (e1)) = (e3))))) -> (~((op (e0) (e1)) = (e0))) -> (~((op (e0) (e1)) = (op (e1) (e1)))) -> (((op (e0) (e1)) = (e2))\/(((op (e1) (e1)) = (e2))\/(((op (e2) (e1)) = (e2))\/((op (e3) (e1)) = (e2))))) -> (~((op (e3) (e0)) = (op (e3) (e1)))) -> ((op (e3) (e0)) = (e3)) -> (((op (e3) (e1)) = (e0))\/(((op (e3) (e1)) = (e1))\/(((op (e3) (e1)) = (e2))\/((op (e3) (e1)) = (e3))))) -> (~((op (e3) (e1)) = (e0))) -> (~((op (e1) (e1)) = (op (e2) (e1)))) -> (~((op (e0) (e1)) = (op (e2) (e1)))) -> (~((op (e2) (e1)) = (op (e3) (e1)))) -> (~((op (e2) (e1)) = (e0))) -> (((op (e2) (e1)) = (e0))\/(((op (e2) (e1)) = (e1))\/(((op (e2) (e1)) = (e2))\/((op (e2) (e1)) = (e3))))) -> (~((op (e0) (e1)) = (op (e3) (e1)))) -> (~((e2) = (e3))) -> (((op (e0) (e1)) = (e3))\/(((op (e1) (e1)) = (e3))\/(((op (e2) (e1)) = (e3))\/((op (e3) (e1)) = (e3))))) -> (~((e0) = (e2))) -> ((op (e2) (e0)) = (e2)) -> (~((op (e2) (e0)) = (op (e2) (e1)))) -> (~((e1) = (e2))) -> (~((op (e1) (e0)) = (e0))) -> (((op (e1) (e0)) = (e0))\/(((op (e1) (e1)) = (e0))\/(((op (e1) (e2)) = (e0))\/((op (e1) (e3)) = (e0))))) -> ((op (e0) (e3)) = (e0)) -> (~((e0) = (e1))) -> False). % 18.79/18.92 do 0 intro. intros zenon_H22d zenon_H204 zenon_H205 zenon_H94 zenon_H2f zenon_H1a6 zenon_H1a7 zenon_H18f zenon_H195 zenon_H19d zenon_H9a zenon_H18c zenon_H115 zenon_H11f zenon_H1d zenon_Ha8 zenon_Hc2 zenon_Hdf zenon_Hdb zenon_Hd5 zenon_He2 zenon_He4 zenon_He7 zenon_H2b zenon_H189 zenon_H185 zenon_H184 zenon_H183 zenon_H17b zenon_H178 zenon_H179 zenon_H142 zenon_H13c zenon_H139 zenon_H128 zenon_H136 zenon_H124 zenon_H145 zenon_H172 zenon_H173 zenon_H16f zenon_H168 zenon_H160 zenon_H165 zenon_H14f zenon_H153 zenon_H39 zenon_H182 zenon_H1fe zenon_H1ee zenon_H1e0 zenon_H1ac zenon_H1c4 zenon_H1ba zenon_H1d5 zenon_H1ec zenon_H1ed zenon_H3f zenon_H45 zenon_H6a zenon_H57 zenon_H5b zenon_H67 zenon_H52 zenon_H4f zenon_H3e zenon_H74 zenon_H1fa zenon_H206 zenon_H233 zenon_H1c7 zenon_H201 zenon_H102 zenon_H130 zenon_Hf3 zenon_H44 zenon_H71 zenon_H101 zenon_He8 zenon_H6d zenon_H9d zenon_Hd8 zenon_H54 zenon_H133 zenon_H191 zenon_H18b zenon_H62 zenon_H1a4 zenon_H6f zenon_H106 zenon_H38 zenon_H25 zenon_H109 zenon_H4a zenon_H10a zenon_H95 zenon_H212 zenon_H20b zenon_H10e zenon_H1d8 zenon_H1cf zenon_H15e zenon_H22a zenon_H1ad zenon_H13e zenon_H17e zenon_Haf zenon_H31 zenon_H1cc zenon_H210 zenon_H12b zenon_H1a5 zenon_H149 zenon_Hee zenon_H1f0 zenon_H7c zenon_H23 zenon_H22 zenon_H1e zenon_Ha1. % 18.79/18.93 apply (zenon_or_s _ _ zenon_H22d); [ zenon_intro zenon_H7a | zenon_intro zenon_H22e ]. % 18.79/18.93 apply (zenon_L456_); trivial. % 18.79/18.93 apply (zenon_or_s _ _ zenon_H22e); [ zenon_intro zenon_Ha0 | zenon_intro zenon_H22f ]. % 18.79/18.93 apply (zenon_L691_); trivial. % 18.79/18.93 apply (zenon_or_s _ _ zenon_H22f); [ zenon_intro zenon_H122 | zenon_intro zenon_Hc3 ]. % 18.79/18.93 apply (zenon_or_s _ _ zenon_H22); [ zenon_intro zenon_H27 | zenon_intro zenon_H26 ]. % 18.79/18.93 exact (zenon_H23 zenon_H27). % 18.79/18.93 apply (zenon_or_s _ _ zenon_H26); [ zenon_intro zenon_H29 | zenon_intro zenon_H28 ]. % 18.79/18.93 apply (zenon_or_s _ _ zenon_H109); [ zenon_intro zenon_Ha0 | zenon_intro zenon_H10b ]. % 18.79/18.93 apply (zenon_L406_); trivial. % 18.79/18.93 apply (zenon_or_s _ _ zenon_H10b); [ zenon_intro zenon_H10d | zenon_intro zenon_H10c ]. % 18.79/18.93 exact (zenon_H10a zenon_H10d). % 18.79/18.93 apply (zenon_or_s _ _ zenon_H10c); [ zenon_intro zenon_Ha5 | zenon_intro zenon_Hae ]. % 18.79/18.93 apply (zenon_L692_); trivial. % 18.79/18.93 apply (zenon_or_s _ _ zenon_H1d8); [ zenon_intro zenon_H10f | zenon_intro zenon_H1d9 ]. % 18.79/18.93 apply (zenon_L441_); trivial. % 18.79/18.93 apply (zenon_or_s _ _ zenon_H1d9); [ zenon_intro zenon_H110 | zenon_intro zenon_H1da ]. % 18.79/18.93 apply (zenon_L354_); trivial. % 18.79/18.93 apply (zenon_or_s _ _ zenon_H1da); [ zenon_intro zenon_H1ca | zenon_intro zenon_H14d ]. % 18.79/18.93 apply (zenon_L277_); trivial. % 18.79/18.93 apply (zenon_L152_); trivial. % 18.79/18.93 apply (zenon_or_s _ _ zenon_H28); [ zenon_intro zenon_H2a | zenon_intro zenon_H1f ]. % 18.79/18.93 exact (zenon_H25 zenon_H2a). % 18.79/18.93 exact (zenon_H38 zenon_H1f). % 18.79/18.93 apply (zenon_L427_); trivial. % 18.79/18.93 (* end of lemma zenon_L693_ *) % 18.79/18.93 assert (zenon_L694_ : (((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) (e2)) = (e0))\/(((op (e1) (e2)) = (e0))\/(((op (e2) (e2)) = (e0))\/((op (e3) (e2)) = (e0))))) -> (~((op (e0) (e2)) = (op (e0) (e3)))) -> (~((op (e1) (e2)) = (e0))) -> (~((op (e2) (e2)) = (e0))) -> (~((op (e3) (e2)) = (e0))) -> False). % 18.79/18.93 do 0 intro. intros zenon_H74 zenon_H3f zenon_H20b zenon_H75 zenon_H6a zenon_H208 zenon_H25 zenon_H81 zenon_H18b. % 18.79/18.93 apply (zenon_or_s _ _ zenon_H74); [ zenon_intro zenon_H42 | zenon_intro zenon_H77 ]. % 18.79/18.93 exact (zenon_H3f zenon_H42). % 18.79/18.93 apply (zenon_or_s _ _ zenon_H77); [ zenon_intro zenon_H49 | zenon_intro zenon_H78 ]. % 18.79/18.93 exact (zenon_H20b zenon_H49). % 18.79/18.93 apply (zenon_or_s _ _ zenon_H78); [ zenon_intro zenon_H48 | zenon_intro zenon_H1e ]. % 18.79/18.93 exact (zenon_H75 zenon_H48). % 18.79/18.93 apply (zenon_L337_); trivial. % 18.79/18.93 (* end of lemma zenon_L694_ *) % 18.79/18.93 assert (zenon_L695_ : (((op (e0) (e0)) = (e0))\/(((op (e1) (e0)) = (e0))\/(((op (e2) (e0)) = (e0))\/((op (e3) (e0)) = (e0))))) -> (~((op (e1) (e0)) = (e0))) -> (~((op (e0) (e0)) = (e0))) -> (~((op (e0) (e1)) = (e0))) -> (~((op (e0) (e2)) = (e0))) -> ((~((op (e0) (e2)) = (e0)))\/((op (e0) (e0)) = (e2))) -> (((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) (e0)) = (op (e1) (e2)))) -> (~((op (e2) (e1)) = (op (e2) (e2)))) -> (((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)) = (e0))\/(((op (e3) (e1)) = (e1))\/(((op (e3) (e1)) = (e2))\/((op (e3) (e1)) = (e3))))) -> (((op (e0) (e1)) = (e0))\/(((op (e0) (e1)) = (e1))\/(((op (e0) (e1)) = (e2))\/((op (e0) (e1)) = (e3))))) -> ((op (e1) (e0)) = (e1)) -> (~((op (e0) (e2)) = (op (e0) (e3)))) -> ((~((op (e1) (e0)) = (e0)))\/((op (e1) (e0)) = (e0))) -> (~((op (e1) (e0)) = (op (e2) (e0)))) -> (~((op (e2) (e0)) = (op (e2) (e1)))) -> (~((op (e1) (e0)) = (op (e3) (e0)))) -> (((op (e0) (e0)) = (e0))\/(((op (e0) (e1)) = (e0))\/(((op (e0) (e2)) = (e0))\/((op (e0) (e3)) = (e0))))) -> (~((op (e3) (e0)) = (op (e3) (e2)))) -> (~((op (e2) (e2)) = (op (e2) (e3)))) -> (~((op (e3) (e0)) = (op (e3) (e3)))) -> (~((op (e0) (e1)) = (op (e0) (e2)))) -> (~((op (e1) (e1)) = (op (e1) (e2)))) -> (~((op (e2) (e0)) = (op (e2) (e2)))) -> (((op (e0) (e3)) = (e0))\/(((op (e1) (e3)) = (e0))\/(((op (e2) (e3)) = (e0))\/((op (e3) (e3)) = (e0))))) -> (~((op (e3) (e2)) = (op (e3) (e3)))) -> (~((op (e2) (e0)) = (op (e2) (e3)))) -> (~((op (e1) (e1)) = (op (e1) (e3)))) -> (~((op (e0) (e1)) = (op (e0) (e3)))) -> (((op (e0) (e2)) = (e0))\/(((op (e1) (e2)) = (e0))\/(((op (e2) (e2)) = (e0))\/((op (e3) (e2)) = (e0))))) -> (~((op (e1) (e0)) = (op (e1) (e1)))) -> (((op (e1) (e0)) = (e0))\/(((op (e1) (e1)) = (e0))\/(((op (e1) (e2)) = (e0))\/((op (e1) (e3)) = (e0))))) -> ((~((op (e3) (e1)) = (e0)))\/((op (e3) (e0)) = (e1))) -> ((~((op (e3) (e3)) = (e0)))\/((op (e3) (e0)) = (e3))) -> (((op (e2) (e0)) = (e2))\/(((op (e2) (e1)) = (e2))\/(((op (e2) (e2)) = (e2))\/((op (e2) (e3)) = (e2))))) -> (((op (e0) (e1)) = (e2))\/(((op (e1) (e1)) = (e2))\/(((op (e2) (e1)) = (e2))\/((op (e3) (e1)) = (e2))))) -> (~((op (e3) (e0)) = (op (e3) (e1)))) -> (((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 (e2) (e2)) = (e0))\/(((op (e2) (e2)) = (e1))\/(((op (e2) (e2)) = (e2))\/((op (e2) (e2)) = (e3))))) -> (~((op (e2) (e1)) = (op (e2) (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 (e2) (e0)) = (e0)))\/((op (e2) (e0)) = (e0))) -> (((op (e0) (e0)) = (e2))\/(((op (e1) (e0)) = (e2))\/(((op (e2) (e0)) = (e2))\/((op (e3) (e0)) = (e2))))) -> ((~((op (e2) (e1)) = (e0)))\/((op (e2) (e0)) = (e1))) -> (((op (e3) (e0)) = (e2))\/(((op (e3) (e1)) = (e2))\/(((op (e3) (e2)) = (e2))\/((op (e3) (e3)) = (e2))))) -> (~((op (e0) (e2)) = (op (e3) (e2)))) -> (~((e0) = (e2))) -> (((op (e3) (e0)) = (e3))\/(((op (e3) (e1)) = (e3))\/(((op (e3) (e2)) = (e3))\/((op (e3) (e3)) = (e3))))) -> (~((op (e1) (e1)) = (op (e3) (e1)))) -> (((op (e0) (e0)) = (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)) = (e2))) -> (((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) (e2)) = (op (e1) (e3)))) -> (~((e2) = (e3))) -> (((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)) = (e3))\/(((op (e1) (e3)) = (e3))\/(((op (e2) (e3)) = (e3))\/((op (e3) (e3)) = (e3))))) -> (((op (e1) (e0)) = (e1))\/(((op (e1) (e1)) = (e1))\/(((op (e1) (e2)) = (e1))\/((op (e1) (e3)) = (e1))))) -> (((op (e0) (e2)) = (e1))\/(((op (e1) (e2)) = (e1))\/(((op (e2) (e2)) = (e1))\/((op (e3) (e2)) = (e1))))) -> (~((op (e0) (e0)) = (op (e0) (e2)))) -> (~((op (e1) (e1)) = (op (e2) (e1)))) -> (((op (e1) (e1)) = (e0))\/(((op (e1) (e1)) = (e1))\/(((op (e1) (e1)) = (e2))\/((op (e1) (e1)) = (e3))))) -> ((~((op (e1) (e3)) = (e0)))\/((op (e1) (e0)) = (e3))) -> ((~((op (e1) (e2)) = (e0)))\/((op (e1) (e0)) = (e2))) -> (~((op (e0) (e1)) = (op (e2) (e1)))) -> (~((op (e2) (e0)) = (op (e3) (e0)))) -> (((op (e0) (e0)) = (e2))\/(((op (e0) (e1)) = (e2))\/(((op (e0) (e2)) = (e2))\/((op (e0) (e3)) = (e2))))) -> ((~((op (e3) (e0)) = (e0)))\/((op (e3) (e0)) = (e0))) -> ((~((op (e2) (e2)) = (e0)))\/((op (e2) (e0)) = (e2))) -> (~((op (e0) (e0)) = (op (e0) (e3)))) -> (((op (e0) (e1)) = (e1))\/(((op (e1) (e1)) = (e1))\/(((op (e2) (e1)) = (e1))\/((op (e3) (e1)) = (e1))))) -> (~((op (e1) (e2)) = (op (e2) (e2)))) -> (((op (e3) (e3)) = (e0))\/(((op (e3) (e3)) = (e1))\/(((op (e3) (e3)) = (e2))\/((op (e3) (e3)) = (e3))))) -> (~((op (e3) (e3)) = (e3))) -> (~((op (e2) (e3)) = (op (e3) (e3)))) -> (((op (e2) (e0)) = (e1))\/(((op (e2) (e1)) = (e1))\/(((op (e2) (e2)) = (e1))\/((op (e2) (e3)) = (e1))))) -> (((op (e2) (e0)) = (e3))\/(((op (e2) (e1)) = (e3))\/(((op (e2) (e2)) = (e3))\/((op (e2) (e3)) = (e3))))) -> (~((op (e2) (e1)) = (op (e3) (e1)))) -> (((op (e0) (e3)) = (e0))\/(((op (e0) (e3)) = (e1))\/(((op (e0) (e3)) = (e2))\/((op (e0) (e3)) = (e3))))) -> (~((op (e0) (e3)) = (op (e2) (e3)))) -> (~((op (e1) (e3)) = (op (e3) (e3)))) -> (~((op (e1) (e0)) = (op (e1) (e3)))) -> (~((op (e1) (e3)) = (op (e2) (e3)))) -> (((op (e1) (e3)) = (e0))\/(((op (e1) (e3)) = (e1))\/(((op (e1) (e3)) = (e2))\/((op (e1) (e3)) = (e3))))) -> (~((op (e0) (e3)) = (op (e3) (e3)))) -> (((op (e3) (e0)) = (e1))\/(((op (e3) (e1)) = (e1))\/(((op (e3) (e2)) = (e1))\/((op (e3) (e3)) = (e1))))) -> (~((op (e0) (e2)) = (op (e2) (e2)))) -> (~((e0) = (e1))) -> (~((op (e0) (e1)) = (op (e1) (e1)))) -> (~((op (e0) (e3)) = (op (e1) (e3)))) -> (((op (e2) (e3)) = (e0))\/(((op (e2) (e3)) = (e1))\/(((op (e2) (e3)) = (e2))\/((op (e2) (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) (e1)) = (e1))) -> (~((e0) = (e3))) -> (~((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 (e3) (e2)) = (e0))\/(((op (e3) (e2)) = (e1))\/(((op (e3) (e2)) = (e2))\/((op (e3) (e2)) = (e3))))) -> (~((op (e2) (e2)) = (op (e3) (e2)))) -> ((~((op (e3) (e2)) = (e0)))\/((op (e3) (e0)) = (e2))) -> (~((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)) = (e3))\/(((op (e1) (e1)) = (e3))\/(((op (e2) (e1)) = (e3))\/((op (e3) (e1)) = (e3))))) -> (~((e1) = (e2))) -> ((~((op (e1) (e1)) = (e0)))\/((op (e1) (e0)) = (e1))) -> ((~((op (e0) (e3)) = (e0)))\/((op (e0) (e0)) = (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)) = (e3)) -> ((~((op (e2) (e3)) = (e0)))\/((op (e2) (e0)) = (e3))) -> False). % 18.79/18.93 do 0 intro. intros zenon_H3e zenon_H23 zenon_H3f zenon_H20b zenon_H75 zenon_H233 zenon_H235 zenon_H245 zenon_H24a zenon_H24b zenon_H22d zenon_H210 zenon_H22a zenon_H212 zenon_H9d zenon_H208 zenon_H206 zenon_H201 zenon_H1f0 zenon_H1fa zenon_H74 zenon_H6f zenon_H6d zenon_H71 zenon_H4a zenon_H4f zenon_H52 zenon_H67 zenon_H62 zenon_H5b zenon_H57 zenon_H54 zenon_H6a zenon_H45 zenon_H22 zenon_H1ed zenon_H1ec zenon_H1d5 zenon_H1d8 zenon_H1cf zenon_H1ba zenon_H1cc zenon_H1c4 zenon_H1c7 zenon_H1ac zenon_H1e0 zenon_H1ee zenon_H1fe zenon_H182 zenon_H153 zenon_H14f zenon_H149 zenon_H165 zenon_H160 zenon_H168 zenon_H16f zenon_H173 zenon_H172 zenon_H145 zenon_H124 zenon_H12b zenon_H133 zenon_H130 zenon_H136 zenon_H128 zenon_H139 zenon_H13c zenon_H13e zenon_H142 zenon_H179 zenon_H178 zenon_H17e zenon_H17b zenon_H183 zenon_H184 zenon_H185 zenon_H189 zenon_H109 zenon_H2b zenon_H101 zenon_H102 zenon_Hf3 zenon_H106 zenon_He7 zenon_Haf zenon_He4 zenon_He2 zenon_Hd5 zenon_Hd8 zenon_Hdb zenon_Hdf zenon_Hc2 zenon_He8 zenon_Ha8 zenon_Ha1 zenon_H10e zenon_H1d zenon_H11f zenon_H115 zenon_H18c zenon_H10a zenon_H9a zenon_H95 zenon_H19d zenon_H195 zenon_H191 zenon_H18f zenon_H1a7 zenon_H1a4 zenon_H1a6 zenon_H1a5 zenon_H7c zenon_H205 zenon_H204 zenon_H2f zenon_H39 zenon_H3a zenon_H94. % 18.79/18.93 apply (zenon_or_s _ _ zenon_H178); [ zenon_intro zenon_H25 | zenon_intro zenon_H86 ]. % 18.79/18.93 apply (zenon_or_s _ _ zenon_H179); [ zenon_intro zenon_H38 | zenon_intro zenon_H9e ]. % 18.79/18.93 apply (zenon_or_s _ _ zenon_H1ee); [ zenon_intro zenon_H30 | zenon_intro zenon_H34 ]. % 18.79/18.93 apply (zenon_or_s _ _ zenon_H182); [ zenon_intro zenon_H31 | zenon_intro zenon_Hed ]. % 18.79/18.93 apply (zenon_or_s _ _ zenon_H185); [ zenon_intro zenon_H81 | zenon_intro zenon_Hee ]. % 18.79/18.93 apply (zenon_or_s _ _ zenon_H94); [ zenon_intro zenon_H32 | zenon_intro zenon_H3b ]. % 18.79/18.93 apply (zenon_L27_); trivial. % 18.79/18.93 apply (zenon_L6_); trivial. % 18.79/18.93 apply (zenon_or_s _ _ zenon_H184); [ zenon_intro zenon_H40 | zenon_intro zenon_H44 ]. % 18.79/18.93 apply (zenon_L7_); trivial. % 18.79/18.93 apply (zenon_or_s _ _ zenon_H1ed); [ zenon_intro zenon_H1ad | zenon_intro zenon_Hac ]. % 18.79/18.93 apply (zenon_or_s _ _ zenon_H1a7); [ zenon_intro zenon_H18b | zenon_intro zenon_H148 ]. % 18.79/18.93 apply (zenon_or_s _ _ zenon_H1ec); [ zenon_intro zenon_H1ae | zenon_intro zenon_H15e ]. % 18.79/18.93 apply (zenon_or_s _ _ zenon_H74); [ zenon_intro zenon_H42 | zenon_intro zenon_H77 ]. % 18.79/18.93 exact (zenon_H3f zenon_H42). % 18.79/18.93 apply (zenon_or_s _ _ zenon_H77); [ zenon_intro zenon_H49 | zenon_intro zenon_H78 ]. % 18.79/18.93 exact (zenon_H20b zenon_H49). % 18.79/18.93 apply (zenon_or_s _ _ zenon_H78); [ zenon_intro zenon_H48 | zenon_intro zenon_H1e ]. % 18.79/18.93 exact (zenon_H75 zenon_H48). % 18.79/18.93 apply (zenon_or_s _ _ zenon_H22d); [ zenon_intro zenon_H7a | zenon_intro zenon_H22e ]. % 18.79/18.93 apply (zenon_L333_); trivial. % 18.79/18.93 apply (zenon_or_s _ _ zenon_H22e); [ zenon_intro zenon_Ha0 | zenon_intro zenon_H22f ]. % 18.79/18.93 apply (zenon_or_s _ _ zenon_H183); [ zenon_intro zenon_H7b | zenon_intro zenon_H186 ]. % 18.79/18.93 apply (zenon_L417_); trivial. % 18.79/18.93 apply (zenon_or_s _ _ zenon_H186); [ zenon_intro zenon_H10f | zenon_intro zenon_H187 ]. % 18.79/18.93 apply (zenon_or_s _ _ zenon_H22); [ zenon_intro zenon_H27 | zenon_intro zenon_H26 ]. % 18.79/18.93 exact (zenon_H23 zenon_H27). % 18.79/18.93 apply (zenon_or_s _ _ zenon_H26); [ zenon_intro zenon_H29 | zenon_intro zenon_H28 ]. % 18.79/18.93 apply (zenon_or_s _ _ zenon_H18c); [ zenon_intro zenon_H86 | zenon_intro zenon_H18d ]. % 18.79/18.93 apply (zenon_L123_); trivial. % 18.79/18.93 apply (zenon_or_s _ _ zenon_H18d); [ zenon_intro zenon_H110 | zenon_intro zenon_H18e ]. % 18.79/18.93 apply (zenon_L354_); trivial. % 18.79/18.93 apply (zenon_or_s _ _ zenon_H18e); [ zenon_intro zenon_H113 | zenon_intro zenon_Hd7 ]. % 18.79/18.93 apply (zenon_or_s _ _ zenon_H16f); [ zenon_intro zenon_H9e | zenon_intro zenon_H170 ]. % 18.79/18.93 apply (zenon_L37_); trivial. % 18.79/18.93 apply (zenon_or_s _ _ zenon_H170); [ zenon_intro zenon_H13f | zenon_intro zenon_H171 ]. % 18.79/18.93 apply (zenon_or_s _ _ zenon_H106); [ zenon_intro zenon_Hed | zenon_intro zenon_H107 ]. % 18.79/18.93 apply (zenon_L413_); trivial. % 18.79/18.93 apply (zenon_or_s _ _ zenon_H107); [ zenon_intro zenon_Ha5 | zenon_intro zenon_H108 ]. % 18.79/18.93 apply (zenon_L357_); trivial. % 18.79/18.93 apply (zenon_or_s _ _ zenon_H108); [ zenon_intro zenon_Hf1 | zenon_intro zenon_Hf4 ]. % 18.79/18.93 apply (zenon_or_s _ _ zenon_He8); [ zenon_intro zenon_Hac | zenon_intro zenon_Heb ]. % 18.79/18.93 apply (zenon_L41_); trivial. % 18.79/18.93 apply (zenon_or_s _ _ zenon_Heb); [ zenon_intro zenon_Hae | zenon_intro zenon_Hec ]. % 18.79/18.93 apply (zenon_L363_); trivial. % 18.79/18.93 apply (zenon_or_s _ _ zenon_Hec); [ zenon_intro zenon_Hba | zenon_intro zenon_Hc4 ]. % 18.79/18.93 apply (zenon_L419_); trivial. % 18.79/18.93 apply (zenon_L595_); trivial. % 18.79/18.93 apply (zenon_L596_); trivial. % 18.79/18.93 apply (zenon_or_s _ _ zenon_H171); [ zenon_intro zenon_H16c | zenon_intro zenon_Hdc ]. % 18.79/18.93 apply (zenon_L116_); trivial. % 18.79/18.93 apply (zenon_or_s _ _ zenon_H1a5); [ zenon_intro zenon_H99 | zenon_intro zenon_H1a8 ]. % 18.79/18.93 apply (zenon_L403_); trivial. % 18.79/18.93 apply (zenon_or_s _ _ zenon_H1a8); [ zenon_intro zenon_H13f | zenon_intro zenon_H1a9 ]. % 18.79/18.93 apply (zenon_or_s _ _ zenon_H106); [ zenon_intro zenon_Hed | zenon_intro zenon_H107 ]. % 18.79/18.93 apply (zenon_L58_); trivial. % 18.79/18.93 apply (zenon_or_s _ _ zenon_H107); [ zenon_intro zenon_Ha5 | zenon_intro zenon_H108 ]. % 18.79/18.93 apply (zenon_L357_); trivial. % 18.79/18.93 apply (zenon_or_s _ _ zenon_H108); [ zenon_intro zenon_Hf1 | zenon_intro zenon_Hf4 ]. % 18.79/18.93 apply (zenon_or_s _ _ zenon_He7); [ zenon_intro zenon_H3b | zenon_intro zenon_He9 ]. % 18.79/18.93 apply (zenon_L6_); trivial. % 18.79/18.93 apply (zenon_or_s _ _ zenon_He9); [ zenon_intro zenon_Ha6 | zenon_intro zenon_Hea ]. % 18.79/18.93 apply (zenon_L371_); trivial. % 18.79/18.93 apply (zenon_or_s _ _ zenon_Hea); [ zenon_intro zenon_Haa | zenon_intro zenon_Hdd ]. % 18.79/18.93 apply (zenon_or_s _ _ zenon_He8); [ zenon_intro zenon_Hac | zenon_intro zenon_Heb ]. % 18.79/18.93 apply (zenon_L495_); trivial. % 18.79/18.93 apply (zenon_or_s _ _ zenon_Heb); [ zenon_intro zenon_Hae | zenon_intro zenon_Hec ]. % 18.79/18.93 apply (zenon_L192_); trivial. % 18.79/18.93 apply (zenon_or_s _ _ zenon_Hec); [ zenon_intro zenon_Hba | zenon_intro zenon_Hc4 ]. % 18.79/18.93 apply (zenon_L419_); trivial. % 18.79/18.93 apply (zenon_L595_); trivial. % 18.79/18.93 apply (zenon_L52_); trivial. % 18.79/18.93 apply (zenon_L596_); trivial. % 18.79/18.93 apply (zenon_or_s _ _ zenon_H1a9); [ zenon_intro zenon_Ha6 | zenon_intro zenon_H161 ]. % 18.79/18.93 apply (zenon_L371_); trivial. % 18.79/18.93 apply (zenon_or_s _ _ zenon_H106); [ zenon_intro zenon_Hed | zenon_intro zenon_H107 ]. % 18.79/18.93 apply (zenon_L413_); trivial. % 18.79/18.93 apply (zenon_or_s _ _ zenon_H107); [ zenon_intro zenon_Ha5 | zenon_intro zenon_H108 ]. % 18.79/18.93 apply (zenon_L357_); trivial. % 18.79/18.93 apply (zenon_or_s _ _ zenon_H108); [ zenon_intro zenon_Hf1 | zenon_intro zenon_Hf4 ]. % 18.79/18.93 apply (zenon_or_s _ _ zenon_He8); [ zenon_intro zenon_Hac | zenon_intro zenon_Heb ]. % 18.79/18.93 apply (zenon_L41_); trivial. % 18.79/18.93 apply (zenon_or_s _ _ zenon_Heb); [ zenon_intro zenon_Hae | zenon_intro zenon_Hec ]. % 18.79/18.93 apply (zenon_L363_); trivial. % 18.79/18.93 apply (zenon_or_s _ _ zenon_Hec); [ zenon_intro zenon_Hba | zenon_intro zenon_Hc4 ]. % 18.79/18.93 apply (zenon_L419_); trivial. % 18.79/18.93 apply (zenon_L598_); trivial. % 18.79/18.93 apply (zenon_L596_); trivial. % 18.79/18.93 apply (zenon_or_s _ _ zenon_H16f); [ zenon_intro zenon_H9e | zenon_intro zenon_H170 ]. % 18.79/18.93 apply (zenon_L37_); trivial. % 18.79/18.93 apply (zenon_or_s _ _ zenon_H170); [ zenon_intro zenon_H13f | zenon_intro zenon_H171 ]. % 18.79/18.93 apply (zenon_L600_); trivial. % 18.79/18.93 apply (zenon_or_s _ _ zenon_H171); [ zenon_intro zenon_H16c | zenon_intro zenon_Hdc ]. % 18.79/18.93 apply (zenon_or_s _ _ zenon_H1a5); [ zenon_intro zenon_H99 | zenon_intro zenon_H1a8 ]. % 18.79/18.93 apply (zenon_L175_); trivial. % 18.79/18.93 apply (zenon_or_s _ _ zenon_H1a8); [ zenon_intro zenon_H13f | zenon_intro zenon_H1a9 ]. % 18.79/18.93 apply (zenon_L600_); trivial. % 18.79/18.93 apply (zenon_or_s _ _ zenon_H1a9); [ zenon_intro zenon_Ha6 | zenon_intro zenon_H161 ]. % 18.79/18.93 apply (zenon_L371_); trivial. % 18.79/18.93 apply (zenon_or_s _ _ zenon_H106); [ zenon_intro zenon_Hed | zenon_intro zenon_H107 ]. % 18.79/18.93 apply (zenon_L58_); trivial. % 18.79/18.93 apply (zenon_or_s _ _ zenon_H107); [ zenon_intro zenon_Ha5 | zenon_intro zenon_H108 ]. % 18.79/18.93 apply (zenon_L357_); trivial. % 18.79/18.93 apply (zenon_or_s _ _ zenon_H108); [ zenon_intro zenon_Hf1 | zenon_intro zenon_Hf4 ]. % 18.79/18.93 apply (zenon_or_s _ _ zenon_He8); [ zenon_intro zenon_Hac | zenon_intro zenon_Heb ]. % 18.79/18.93 apply (zenon_L41_); trivial. % 18.79/18.93 apply (zenon_or_s _ _ zenon_Heb); [ zenon_intro zenon_Hae | zenon_intro zenon_Hec ]. % 18.79/18.93 apply (zenon_L363_); trivial. % 18.79/18.93 apply (zenon_or_s _ _ zenon_Hec); [ zenon_intro zenon_Hba | zenon_intro zenon_Hc4 ]. % 18.79/18.93 apply (zenon_L480_); trivial. % 18.79/18.93 apply (zenon_or_s _ _ zenon_H136); [ zenon_intro zenon_He3 | zenon_intro zenon_H137 ]. % 18.79/18.93 apply (zenon_L74_); trivial. % 18.79/18.93 apply (zenon_or_s _ _ zenon_H137); [ zenon_intro zenon_Hdc | zenon_intro zenon_H138 ]. % 18.79/18.93 apply (zenon_L601_); trivial. % 18.79/18.93 apply (zenon_or_s _ _ zenon_H138); [ zenon_intro zenon_Hdd | zenon_intro zenon_H105 ]. % 18.79/18.93 apply (zenon_L611_); trivial. % 18.79/18.93 exact (zenon_H102 zenon_H105). % 18.79/18.93 apply (zenon_L596_); trivial. % 18.79/18.93 apply (zenon_L266_); trivial. % 18.79/18.93 apply (zenon_or_s _ _ zenon_H28); [ zenon_intro zenon_H2a | zenon_intro zenon_H1f ]. % 18.79/18.93 exact (zenon_H25 zenon_H2a). % 18.79/18.93 exact (zenon_H38 zenon_H1f). % 18.79/18.93 apply (zenon_or_s _ _ zenon_H187); [ zenon_intro zenon_H150 | zenon_intro zenon_Hcd ]. % 18.79/18.93 apply (zenon_or_s _ _ zenon_H22); [ zenon_intro zenon_H27 | zenon_intro zenon_H26 ]. % 18.79/18.93 exact (zenon_H23 zenon_H27). % 18.79/18.93 apply (zenon_or_s _ _ zenon_H26); [ zenon_intro zenon_H29 | zenon_intro zenon_H28 ]. % 18.79/18.93 apply (zenon_or_s _ _ zenon_H18c); [ zenon_intro zenon_H86 | zenon_intro zenon_H18d ]. % 18.79/18.93 apply (zenon_L123_); trivial. % 18.79/18.93 apply (zenon_or_s _ _ zenon_H18d); [ zenon_intro zenon_H110 | zenon_intro zenon_H18e ]. % 18.79/18.93 apply (zenon_L354_); trivial. % 18.79/18.93 apply (zenon_or_s _ _ zenon_H18e); [ zenon_intro zenon_H113 | zenon_intro zenon_Hd7 ]. % 18.79/18.93 apply (zenon_L153_); trivial. % 18.79/18.93 apply (zenon_or_s _ _ zenon_H1d8); [ zenon_intro zenon_H10f | zenon_intro zenon_H1d9 ]. % 18.79/18.93 apply (zenon_or_s _ _ zenon_H16f); [ zenon_intro zenon_H9e | zenon_intro zenon_H170 ]. % 18.79/18.93 apply (zenon_L37_); trivial. % 18.79/18.93 apply (zenon_or_s _ _ zenon_H170); [ zenon_intro zenon_H13f | zenon_intro zenon_H171 ]. % 18.79/18.93 apply (zenon_L600_); trivial. % 18.79/18.93 apply (zenon_or_s _ _ zenon_H171); [ zenon_intro zenon_H16c | zenon_intro zenon_Hdc ]. % 18.79/18.93 apply (zenon_or_s _ _ zenon_H106); [ zenon_intro zenon_Hed | zenon_intro zenon_H107 ]. % 18.79/18.93 apply (zenon_L58_); trivial. % 18.79/18.93 apply (zenon_or_s _ _ zenon_H107); [ zenon_intro zenon_Ha5 | zenon_intro zenon_H108 ]. % 18.79/18.93 apply (zenon_L357_); trivial. % 18.79/18.93 apply (zenon_or_s _ _ zenon_H108); [ zenon_intro zenon_Hf1 | zenon_intro zenon_Hf4 ]. % 18.79/18.93 apply (zenon_or_s _ _ zenon_He8); [ zenon_intro zenon_Hac | zenon_intro zenon_Heb ]. % 18.79/18.93 apply (zenon_L41_); trivial. % 18.79/18.93 apply (zenon_or_s _ _ zenon_Heb); [ zenon_intro zenon_Hae | zenon_intro zenon_Hec ]. % 18.79/18.93 apply (zenon_L363_); trivial. % 18.79/18.93 apply (zenon_or_s _ _ zenon_Hec); [ zenon_intro zenon_Hba | zenon_intro zenon_Hc4 ]. % 18.79/18.93 apply (zenon_L480_); trivial. % 18.79/18.93 apply (zenon_or_s _ _ zenon_H153); [ zenon_intro zenon_H148 | zenon_intro zenon_H154 ]. % 18.79/18.93 apply (zenon_L100_); trivial. % 18.79/18.93 apply (zenon_or_s _ _ zenon_H154); [ zenon_intro zenon_H14d | zenon_intro zenon_H155 ]. % 18.79/18.93 apply (zenon_L608_); trivial. % 18.79/18.93 apply (zenon_or_s _ _ zenon_H155); [ zenon_intro zenon_H151 | zenon_intro zenon_Hf6 ]. % 18.79/18.93 apply (zenon_L104_); trivial. % 18.79/18.93 apply (zenon_L517_); trivial. % 18.79/18.93 apply (zenon_L596_); trivial. % 18.79/18.93 apply (zenon_L266_); trivial. % 18.79/18.93 apply (zenon_or_s _ _ zenon_H1d9); [ zenon_intro zenon_H110 | zenon_intro zenon_H1da ]. % 18.79/18.93 apply (zenon_L283_); trivial. % 18.79/18.93 apply (zenon_or_s _ _ zenon_H1da); [ zenon_intro zenon_H1ca | zenon_intro zenon_H14d ]. % 18.79/18.93 apply (zenon_L277_); trivial. % 18.79/18.93 apply (zenon_or_s _ _ zenon_H16f); [ zenon_intro zenon_H9e | zenon_intro zenon_H170 ]. % 18.79/18.93 apply (zenon_L37_); trivial. % 18.79/18.93 apply (zenon_or_s _ _ zenon_H170); [ zenon_intro zenon_H13f | zenon_intro zenon_H171 ]. % 18.79/18.93 apply (zenon_or_s _ _ zenon_H106); [ zenon_intro zenon_Hed | zenon_intro zenon_H107 ]. % 18.79/18.93 apply (zenon_L413_); trivial. % 18.79/18.93 apply (zenon_or_s _ _ zenon_H107); [ zenon_intro zenon_Ha5 | zenon_intro zenon_H108 ]. % 18.79/18.93 apply (zenon_L390_); trivial. % 18.79/18.93 apply (zenon_or_s _ _ zenon_H108); [ zenon_intro zenon_Hf1 | zenon_intro zenon_Hf4 ]. % 18.79/18.93 apply (zenon_or_s _ _ zenon_He8); [ zenon_intro zenon_Hac | zenon_intro zenon_Heb ]. % 18.79/18.93 apply (zenon_L41_); trivial. % 18.79/18.93 apply (zenon_or_s _ _ zenon_Heb); [ zenon_intro zenon_Hae | zenon_intro zenon_Hec ]. % 18.79/18.93 apply (zenon_L363_); trivial. % 18.79/18.93 apply (zenon_or_s _ _ zenon_Hec); [ zenon_intro zenon_Hba | zenon_intro zenon_Hc4 ]. % 18.79/18.93 apply (zenon_L419_); trivial. % 18.79/18.93 apply (zenon_or_s _ _ zenon_H19d); [ zenon_intro zenon_H2a | zenon_intro zenon_H19e ]. % 18.79/18.93 exact (zenon_H25 zenon_H2a). % 18.79/18.93 apply (zenon_or_s _ _ zenon_H19e); [ zenon_intro zenon_Hf0 | zenon_intro zenon_H19f ]. % 18.79/18.93 apply (zenon_L612_); trivial. % 18.79/18.93 apply (zenon_or_s _ _ zenon_H19f); [ zenon_intro zenon_H113 | zenon_intro zenon_H16c ]. % 18.79/18.93 apply (zenon_L153_); trivial. % 18.79/18.93 apply (zenon_L608_); trivial. % 18.79/18.93 apply (zenon_L414_); trivial. % 18.79/18.93 apply (zenon_or_s _ _ zenon_H171); [ zenon_intro zenon_H16c | zenon_intro zenon_Hdc ]. % 18.79/18.93 apply (zenon_or_s _ _ zenon_H1a5); [ zenon_intro zenon_H99 | zenon_intro zenon_H1a8 ]. % 18.79/18.93 apply (zenon_L385_); trivial. % 18.79/18.93 apply (zenon_or_s _ _ zenon_H1a8); [ zenon_intro zenon_H13f | zenon_intro zenon_H1a9 ]. % 18.79/18.93 apply (zenon_or_s _ _ zenon_H106); [ zenon_intro zenon_Hed | zenon_intro zenon_H107 ]. % 18.79/18.93 apply (zenon_L58_); trivial. % 18.79/18.93 apply (zenon_or_s _ _ zenon_H107); [ zenon_intro zenon_Ha5 | zenon_intro zenon_H108 ]. % 18.79/18.93 apply (zenon_L357_); trivial. % 18.79/18.93 apply (zenon_or_s _ _ zenon_H108); [ zenon_intro zenon_Hf1 | zenon_intro zenon_Hf4 ]. % 18.79/18.93 apply (zenon_L613_); trivial. % 18.79/18.93 apply (zenon_L451_); trivial. % 18.79/18.93 apply (zenon_or_s _ _ zenon_H1a9); [ zenon_intro zenon_Ha6 | zenon_intro zenon_H161 ]. % 18.79/18.93 apply (zenon_or_s _ _ zenon_H106); [ zenon_intro zenon_Hed | zenon_intro zenon_H107 ]. % 18.79/18.93 apply (zenon_L413_); trivial. % 18.79/18.93 apply (zenon_or_s _ _ zenon_H107); [ zenon_intro zenon_Ha5 | zenon_intro zenon_H108 ]. % 18.79/18.93 apply (zenon_L39_); trivial. % 18.79/18.93 apply (zenon_or_s _ _ zenon_H108); [ zenon_intro zenon_Hf1 | zenon_intro zenon_Hf4 ]. % 18.79/18.93 apply (zenon_L613_); trivial. % 18.79/18.93 apply (zenon_L414_); trivial. % 18.79/18.93 apply (zenon_L615_); trivial. % 18.79/18.93 apply (zenon_L266_); trivial. % 18.79/18.93 apply (zenon_or_s _ _ zenon_H28); [ zenon_intro zenon_H2a | zenon_intro zenon_H1f ]. % 18.79/18.93 exact (zenon_H25 zenon_H2a). % 18.79/18.93 exact (zenon_H38 zenon_H1f). % 18.79/18.93 apply (zenon_L428_); trivial. % 18.79/18.93 apply (zenon_or_s _ _ zenon_H22f); [ zenon_intro zenon_H122 | zenon_intro zenon_Hc3 ]. % 18.79/18.93 apply (zenon_or_s _ _ zenon_H183); [ zenon_intro zenon_H7b | zenon_intro zenon_H186 ]. % 18.79/18.93 apply (zenon_L687_); trivial. % 18.79/18.93 apply (zenon_or_s _ _ zenon_H186); [ zenon_intro zenon_H10f | zenon_intro zenon_H187 ]. % 18.79/18.93 apply (zenon_or_s _ _ zenon_H22); [ zenon_intro zenon_H27 | zenon_intro zenon_H26 ]. % 18.79/18.93 exact (zenon_H23 zenon_H27). % 18.79/18.93 apply (zenon_or_s _ _ zenon_H26); [ zenon_intro zenon_H29 | zenon_intro zenon_H28 ]. % 18.79/18.93 apply (zenon_or_s _ _ zenon_H109); [ zenon_intro zenon_Ha0 | zenon_intro zenon_H10b ]. % 18.79/18.93 apply (zenon_L406_); trivial. % 18.79/18.93 apply (zenon_or_s _ _ zenon_H10b); [ zenon_intro zenon_H10d | zenon_intro zenon_H10c ]. % 18.79/18.93 exact (zenon_H10a zenon_H10d). % 18.79/18.93 apply (zenon_or_s _ _ zenon_H10c); [ zenon_intro zenon_Ha5 | zenon_intro zenon_Hae ]. % 18.79/18.93 apply (zenon_or_s _ _ zenon_H18c); [ zenon_intro zenon_H86 | zenon_intro zenon_H18d ]. % 18.79/18.93 apply (zenon_L123_); trivial. % 18.79/18.93 apply (zenon_or_s _ _ zenon_H18d); [ zenon_intro zenon_H110 | zenon_intro zenon_H18e ]. % 18.79/18.93 apply (zenon_L354_); trivial. % 18.79/18.93 apply (zenon_or_s _ _ zenon_H18e); [ zenon_intro zenon_H113 | zenon_intro zenon_Hd7 ]. % 18.79/18.93 apply (zenon_or_s _ _ zenon_H16f); [ zenon_intro zenon_H9e | zenon_intro zenon_H170 ]. % 18.79/18.93 apply (zenon_L37_); trivial. % 18.79/18.93 apply (zenon_or_s _ _ zenon_H170); [ zenon_intro zenon_H13f | zenon_intro zenon_H171 ]. % 18.79/18.93 apply (zenon_or_s _ _ zenon_He8); [ zenon_intro zenon_Hac | zenon_intro zenon_Heb ]. % 18.79/18.93 apply (zenon_L41_); trivial. % 18.79/18.93 apply (zenon_or_s _ _ zenon_Heb); [ zenon_intro zenon_Hae | zenon_intro zenon_Hec ]. % 18.79/18.93 apply (zenon_L42_); trivial. % 18.79/18.93 apply (zenon_or_s _ _ zenon_Hec); [ zenon_intro zenon_Hba | zenon_intro zenon_Hc4 ]. % 18.79/18.93 apply (zenon_L317_); trivial. % 18.79/18.93 apply (zenon_L595_); trivial. % 18.79/18.93 apply (zenon_or_s _ _ zenon_H171); [ zenon_intro zenon_H16c | zenon_intro zenon_Hdc ]. % 18.79/18.93 apply (zenon_L116_); trivial. % 18.79/18.93 apply (zenon_or_s _ _ zenon_He8); [ zenon_intro zenon_Hac | zenon_intro zenon_Heb ]. % 18.79/18.93 apply (zenon_L41_); trivial. % 18.79/18.93 apply (zenon_or_s _ _ zenon_Heb); [ zenon_intro zenon_Hae | zenon_intro zenon_Hec ]. % 18.79/18.93 apply (zenon_L42_); trivial. % 18.79/18.93 apply (zenon_or_s _ _ zenon_Hec); [ zenon_intro zenon_Hba | zenon_intro zenon_Hc4 ]. % 18.79/18.93 apply (zenon_L317_); trivial. % 18.79/18.93 apply (zenon_L601_); trivial. % 18.79/18.93 apply (zenon_L605_); trivial. % 18.79/18.93 apply (zenon_L688_); trivial. % 18.79/18.93 apply (zenon_or_s _ _ zenon_H28); [ zenon_intro zenon_H2a | zenon_intro zenon_H1f ]. % 18.79/18.93 exact (zenon_H25 zenon_H2a). % 18.79/18.93 exact (zenon_H38 zenon_H1f). % 18.79/18.93 apply (zenon_or_s _ _ zenon_H187); [ zenon_intro zenon_H150 | zenon_intro zenon_Hcd ]. % 18.79/18.93 apply (zenon_L328_); trivial. % 18.79/18.93 apply (zenon_L428_); trivial. % 18.79/18.93 apply (zenon_L427_); trivial. % 18.79/18.93 apply (zenon_or_s _ _ zenon_H74); [ zenon_intro zenon_H42 | zenon_intro zenon_H77 ]. % 18.79/18.93 exact (zenon_H3f zenon_H42). % 18.79/18.93 apply (zenon_or_s _ _ zenon_H77); [ zenon_intro zenon_H49 | zenon_intro zenon_H78 ]. % 18.79/18.93 exact (zenon_H20b zenon_H49). % 18.79/18.93 apply (zenon_or_s _ _ zenon_H78); [ zenon_intro zenon_H48 | zenon_intro zenon_H1e ]. % 18.79/18.93 exact (zenon_H75 zenon_H48). % 18.79/18.93 apply (zenon_L693_); trivial. % 18.79/18.93 apply (zenon_L100_); trivial. % 18.79/18.93 apply (zenon_L41_); trivial. % 18.79/18.93 apply (zenon_L413_); trivial. % 18.79/18.93 apply (zenon_or_s _ _ zenon_H182); [ zenon_intro zenon_H31 | zenon_intro zenon_Hed ]. % 18.79/18.93 apply (zenon_or_s _ _ zenon_H185); [ zenon_intro zenon_H81 | zenon_intro zenon_Hee ]. % 18.79/18.93 apply (zenon_or_s _ _ zenon_H184); [ zenon_intro zenon_H40 | zenon_intro zenon_H44 ]. % 18.79/18.93 apply (zenon_or_s _ _ zenon_H1a7); [ zenon_intro zenon_H18b | zenon_intro zenon_H148 ]. % 18.79/18.93 apply (zenon_L694_); trivial. % 18.79/18.93 apply (zenon_L486_); trivial. % 18.79/18.93 apply (zenon_L127_); trivial. % 18.79/18.93 apply (zenon_L204_); trivial. % 18.79/18.93 apply (zenon_L214_); trivial. % 18.79/18.93 apply (zenon_L37_); trivial. % 18.79/18.93 apply (zenon_L123_); trivial. % 18.79/18.93 (* end of lemma zenon_L695_ *) % 18.79/18.93 assert (zenon_L696_ : (((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)) = (e0))\/(((op (e2) (e3)) = (e1))\/(((op (e2) (e3)) = (e2))\/((op (e2) (e3)) = (e3))))) -> ((op (e0) (e3)) = (e0)) -> (~((op (e0) (e3)) = (op (e2) (e3)))) -> ((op (e3) (e3)) = (e1)) -> ((op (e3) (e3)) = (e2)) -> (~((op (e2) (e3)) = (op (e3) (e3)))) -> (~((op (e1) (e3)) = (op (e2) (e3)))) -> False). % 18.79/18.93 do 0 intro. intros zenon_Hdf zenon_H1d zenon_Hd5 zenon_H11f zenon_H1e zenon_He2 zenon_Hc4 zenon_Hf6 zenon_Hf3 zenon_Hdb. % 18.79/18.93 apply (zenon_or_s _ _ zenon_Hdf); [ zenon_intro zenon_H1f | zenon_intro zenon_He0 ]. % 18.79/18.93 apply (zenon_L1_); trivial. % 18.79/18.93 apply (zenon_or_s _ _ zenon_He0); [ zenon_intro zenon_Hd6 | zenon_intro zenon_He1 ]. % 18.79/18.93 apply (zenon_L50_); trivial. % 18.79/18.93 apply (zenon_or_s _ _ zenon_He1); [ zenon_intro zenon_Hd7 | zenon_intro zenon_Hdc ]. % 18.79/18.93 apply (zenon_L402_); trivial. % 18.79/18.93 apply (zenon_L404_); trivial. % 18.79/18.93 (* end of lemma zenon_L696_ *) % 18.79/18.93 assert (zenon_L697_ : (((op (e0) (e0)) = (e3))\/(((op (e0) (e1)) = (e3))\/(((op (e0) (e2)) = (e3))\/((op (e0) (e3)) = (e3))))) -> ((op (e2) (e0)) = (e1)) -> (~((op (e0) (e1)) = (op (e1) (e1)))) -> (~((op (e3) (e3)) = (e3))) -> (~((op (e0) (e2)) = (op (e3) (e2)))) -> (~((op (e1) (e1)) = (op (e3) (e1)))) -> ((op (e1) (e1)) = (e3)) -> ((op (e3) (e0)) = (e2)) -> (~((e2) = (e3))) -> (((op (e3) (e0)) = (e3))\/(((op (e3) (e1)) = (e3))\/(((op (e3) (e2)) = (e3))\/((op (e3) (e3)) = (e3))))) -> ((op (e0) (e3)) = (e0)) -> (~((e0) = (e3))) -> False). % 18.79/18.93 do 0 intro. intros zenon_H168 zenon_Hed zenon_H10e zenon_H102 zenon_H14f zenon_H160 zenon_H13f zenon_H148 zenon_H12b zenon_H165 zenon_H1e zenon_H9a. % 18.79/18.93 apply (zenon_or_s _ _ zenon_H168); [ zenon_intro zenon_H3a | zenon_intro zenon_H169 ]. % 18.79/18.93 apply (zenon_L423_); trivial. % 18.79/18.93 apply (zenon_or_s _ _ zenon_H169); [ zenon_intro zenon_H99 | zenon_intro zenon_H16a ]. % 18.79/18.93 apply (zenon_L108_); trivial. % 18.79/18.93 apply (zenon_or_s _ _ zenon_H16a); [ zenon_intro zenon_Ha9 | zenon_intro zenon_He3 ]. % 18.79/18.93 apply (zenon_L112_); trivial. % 18.79/18.93 apply (zenon_L515_); trivial. % 18.79/18.93 (* end of lemma zenon_L697_ *) % 18.79/18.93 assert (zenon_L698_ : (((op (e0) (e2)) = (e0))\/(((op (e0) (e2)) = (e1))\/(((op (e0) (e2)) = (e2))\/((op (e0) (e2)) = (e3))))) -> (~((op (e0) (e2)) = (op (e1) (e2)))) -> (~((op (e1) (e0)) = (op (e2) (e0)))) -> (((op (e1) (e0)) = (e1))\/(((op (e1) (e1)) = (e1))\/(((op (e1) (e2)) = (e1))\/((op (e1) (e3)) = (e1))))) -> (~((op (e0) (e2)) = (op (e2) (e2)))) -> ((op (e0) (e0)) = (e3)) -> ((op (e1) (e0)) = (e2)) -> ((op (e0) (e2)) = (e2)) -> (~((op (e0) (e1)) = (op (e3) (e1)))) -> (~((op (e2) (e2)) = (e0))) -> (((op (e3) (e0)) = (e2))\/(((op (e3) (e1)) = (e2))\/(((op (e3) (e2)) = (e2))\/((op (e3) (e3)) = (e2))))) -> (~((e0) = (e3))) -> (((op (e3) (e0)) = (e3))\/(((op (e3) (e1)) = (e3))\/(((op (e3) (e2)) = (e3))\/((op (e3) (e3)) = (e3))))) -> (~((e2) = (e3))) -> ((op (e1) (e1)) = (e3)) -> (~((op (e3) (e3)) = (e3))) -> (~((op (e0) (e1)) = (op (e1) (e1)))) -> ((op (e2) (e0)) = (e1)) -> (((op (e0) (e0)) = (e3))\/(((op (e0) (e1)) = (e3))\/(((op (e0) (e2)) = (e3))\/((op (e0) (e3)) = (e3))))) -> (~((op (e2) (e2)) = (e2))) -> ((op (e1) (e2)) = (e1)) -> (~((e1) = (e2))) -> (((op (e0) (e2)) = (e3))\/(((op (e1) (e2)) = (e3))\/(((op (e2) (e2)) = (e3))\/((op (e3) (e2)) = (e3))))) -> (~((op (e3) (e2)) = (op (e3) (e3)))) -> (~((op (e3) (e2)) = (e0))) -> (((op (e2) (e2)) = (e0))\/(((op (e2) (e2)) = (e1))\/(((op (e2) (e2)) = (e2))\/((op (e2) (e2)) = (e3))))) -> ((op (e3) (e0)) = (e0)) -> (~((e0) = (e1))) -> (((op (e3) (e0)) = (e1))\/(((op (e3) (e1)) = (e1))\/(((op (e3) (e2)) = (e1))\/((op (e3) (e3)) = (e1))))) -> (~((e1) = (e3))) -> (~((op (e2) (e2)) = (op (e3) (e2)))) -> (~((op (e0) (e2)) = (op (e3) (e2)))) -> ((op (e1) (e2)) = (e0)) -> (~((op (e1) (e2)) = (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))))) -> (((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 (e3) (e1)))) -> (~((op (e1) (e1)) = (op (e2) (e1)))) -> ((op (e2) (e1)) = (e0)) -> ((op (e0) (e1)) = (e1)) -> (((op (e0) (e1)) = (e3))\/(((op (e1) (e1)) = (e3))\/(((op (e2) (e1)) = (e3))\/((op (e3) (e1)) = (e3))))) -> (~((op (e3) (e1)) = (op (e3) (e2)))) -> (~((op (e3) (e1)) = (op (e3) (e3)))) -> (~((op (e3) (e1)) = (e0))) -> (((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)) = (op (e1) (e3)))) -> (~((op (e1) (e3)) = (op (e3) (e3)))) -> (((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 (e2) (e3)) = (op (e3) (e3)))) -> (~((op (e1) (e3)) = (op (e2) (e3)))) -> False). % 18.79/18.93 do 0 intro. intros zenon_H1ba zenon_H195 zenon_H201 zenon_H128 zenon_Ha8 zenon_H3a zenon_H86 zenon_H150 zenon_H210 zenon_H81 zenon_H153 zenon_H9a zenon_H165 zenon_H12b zenon_H13f zenon_H102 zenon_H10e zenon_Hed zenon_H168 zenon_H173 zenon_Hf0 zenon_H7c zenon_H1a6 zenon_H62 zenon_H18b zenon_H1c4 zenon_H44 zenon_Ha1 zenon_He8 zenon_H95 zenon_H18f zenon_H14f zenon_H2a zenon_H115 zenon_H191 zenon_H172 zenon_H142 zenon_H24 zenon_H10a zenon_H160 zenon_H13e zenon_H36 zenon_Ha0 zenon_H1a5 zenon_H1a4 zenon_H130 zenon_H1ad zenon_H22a zenon_Hdf zenon_H1d zenon_Hd5 zenon_H11f zenon_H1e zenon_He2 zenon_Hf3 zenon_Hdb. % 18.79/18.93 apply (zenon_or_s _ _ zenon_H1a6); [ zenon_intro zenon_Ha9 | zenon_intro zenon_H1aa ]. % 18.79/18.93 apply (zenon_or_s _ _ zenon_He8); [ zenon_intro zenon_Hac | zenon_intro zenon_Heb ]. % 18.79/18.93 apply (zenon_L241_); trivial. % 18.79/18.93 apply (zenon_or_s _ _ zenon_Heb); [ zenon_intro zenon_Hae | zenon_intro zenon_Hec ]. % 18.79/18.93 apply (zenon_L363_); trivial. % 18.79/18.93 apply (zenon_or_s _ _ zenon_Hec); [ zenon_intro zenon_Hba | zenon_intro zenon_Hc4 ]. % 18.79/18.93 apply (zenon_L69_); trivial. % 18.79/18.93 apply (zenon_or_s _ _ zenon_H153); [ zenon_intro zenon_H148 | zenon_intro zenon_H154 ]. % 18.79/18.93 apply (zenon_L423_); trivial. % 18.79/18.93 apply (zenon_or_s _ _ zenon_H154); [ zenon_intro zenon_H14d | zenon_intro zenon_H155 ]. % 18.79/18.93 apply (zenon_L514_); trivial. % 18.79/18.93 apply (zenon_or_s _ _ zenon_H155); [ zenon_intro zenon_H151 | zenon_intro zenon_Hf6 ]. % 18.79/18.93 apply (zenon_L533_); trivial. % 18.79/18.93 apply (zenon_L696_); trivial. % 18.79/18.93 apply (zenon_or_s _ _ zenon_H1aa); [ zenon_intro zenon_H16c | zenon_intro zenon_H1ab ]. % 18.79/18.93 apply (zenon_L521_); trivial. % 18.79/18.93 apply (zenon_or_s _ _ zenon_H1ab); [ zenon_intro zenon_Haa | zenon_intro zenon_H163 ]. % 18.79/18.93 apply (zenon_L181_); trivial. % 18.79/18.93 apply (zenon_or_s _ _ zenon_He8); [ zenon_intro zenon_Hac | zenon_intro zenon_Heb ]. % 18.79/18.93 apply (zenon_L41_); trivial. % 18.79/18.93 apply (zenon_or_s _ _ zenon_Heb); [ zenon_intro zenon_Hae | zenon_intro zenon_Hec ]. % 18.79/18.93 apply (zenon_L363_); trivial. % 18.79/18.93 apply (zenon_or_s _ _ zenon_Hec); [ zenon_intro zenon_Hba | zenon_intro zenon_Hc4 ]. % 18.79/18.93 apply (zenon_L528_); trivial. % 18.79/18.93 apply (zenon_or_s _ _ zenon_H153); [ zenon_intro zenon_H148 | zenon_intro zenon_H154 ]. % 18.79/18.93 apply (zenon_L697_); trivial. % 18.79/18.93 apply (zenon_or_s _ _ zenon_H154); [ zenon_intro zenon_H14d | zenon_intro zenon_H155 ]. % 18.79/18.93 apply (zenon_L546_); trivial. % 18.79/18.93 apply (zenon_or_s _ _ zenon_H155); [ zenon_intro zenon_H151 | zenon_intro zenon_Hf6 ]. % 18.79/18.93 apply (zenon_L401_); trivial. % 18.79/18.93 apply (zenon_L696_); trivial. % 18.79/18.93 (* end of lemma zenon_L698_ *) % 18.79/18.93 assert (zenon_L699_ : (((op (e0) (e2)) = (e3))\/(((op (e1) (e2)) = (e3))\/(((op (e2) (e2)) = (e3))\/((op (e3) (e2)) = (e3))))) -> (~((op (e1) (e3)) = (op (e2) (e3)))) -> (~((op (e2) (e3)) = (op (e3) (e3)))) -> (~((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 (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 (e2) (e2)) = (e0))\/(((op (e2) (e2)) = (e1))\/(((op (e2) (e2)) = (e2))\/((op (e2) (e2)) = (e3))))) -> (~((op (e2) (e2)) = (e0))) -> (~((op (e2) (e2)) = (e2))) -> (((op (e0) (e2)) = (e0))\/(((op (e0) (e2)) = (e1))\/(((op (e0) (e2)) = (e2))\/((op (e0) (e2)) = (e3))))) -> (~((op (e0) (e2)) = (op (e1) (e2)))) -> (~((op (e1) (e1)) = (e1))) -> ((op (e2) (e0)) = (e1)) -> (~((op (e1) (e0)) = (op (e2) (e0)))) -> (((op (e1) (e0)) = (e1))\/(((op (e1) (e1)) = (e1))\/(((op (e1) (e2)) = (e1))\/((op (e1) (e3)) = (e1))))) -> (~((op (e0) (e2)) = (op (e2) (e2)))) -> (~((op (e3) (e2)) = (e0))) -> (~((op (e3) (e2)) = (op (e3) (e3)))) -> ((op (e0) (e0)) = (e3)) -> (((op (e3) (e0)) = (e2))\/(((op (e3) (e1)) = (e2))\/(((op (e3) (e2)) = (e2))\/((op (e3) (e3)) = (e2))))) -> (~((op (e0) (e1)) = (op (e3) (e1)))) -> ((op (e0) (e1)) = (e1)) -> ((op (e1) (e0)) = (e2)) -> (((op (e3) (e0)) = (e1))\/(((op (e3) (e1)) = (e1))\/(((op (e3) (e2)) = (e1))\/((op (e3) (e3)) = (e1))))) -> (~((e1) = (e3))) -> ((op (e1) (e2)) = (e1)) -> (~((op (e2) (e2)) = (op (e3) (e2)))) -> (~((op (e0) (e2)) = (op (e3) (e2)))) -> ((op (e0) (e2)) = (e2)) -> ((op (e1) (e2)) = (e0)) -> (~((op (e1) (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) (e1)) = (e3)) -> False). % 18.79/18.93 do 0 intro. intros zenon_H1a6 zenon_Hdb zenon_Hf3 zenon_He2 zenon_H1e zenon_H11f zenon_Hd5 zenon_H1d zenon_Hdf zenon_H1c4 zenon_H81 zenon_H173 zenon_H1ba zenon_H195 zenon_H10a zenon_Hed zenon_H201 zenon_H128 zenon_Ha8 zenon_H18b zenon_H62 zenon_H3a zenon_H153 zenon_H210 zenon_Ha0 zenon_H86 zenon_He8 zenon_H95 zenon_Hf0 zenon_H18f zenon_H14f zenon_H150 zenon_H2a zenon_H115 zenon_H191 zenon_H1a4 zenon_H161. % 18.79/18.93 apply (zenon_or_s _ _ zenon_H1a6); [ zenon_intro zenon_Ha9 | zenon_intro zenon_H1aa ]. % 18.79/18.93 apply (zenon_or_s _ _ zenon_He8); [ zenon_intro zenon_Hac | zenon_intro zenon_Heb ]. % 18.79/18.93 apply (zenon_L241_); trivial. % 18.79/18.93 apply (zenon_or_s _ _ zenon_Heb); [ zenon_intro zenon_Hae | zenon_intro zenon_Hec ]. % 18.79/18.93 apply (zenon_L363_); trivial. % 18.79/18.93 apply (zenon_or_s _ _ zenon_Hec); [ zenon_intro zenon_Hba | zenon_intro zenon_Hc4 ]. % 18.79/18.93 apply (zenon_L186_); trivial. % 18.79/18.93 apply (zenon_or_s _ _ zenon_H153); [ zenon_intro zenon_H148 | zenon_intro zenon_H154 ]. % 18.79/18.93 apply (zenon_L423_); trivial. % 18.79/18.93 apply (zenon_or_s _ _ zenon_H154); [ zenon_intro zenon_H14d | zenon_intro zenon_H155 ]. % 18.79/18.93 apply (zenon_L545_); trivial. % 18.79/18.93 apply (zenon_or_s _ _ zenon_H155); [ zenon_intro zenon_H151 | zenon_intro zenon_Hf6 ]. % 18.79/18.93 apply (zenon_L533_); trivial. % 18.79/18.93 apply (zenon_L696_); trivial. % 18.79/18.93 apply (zenon_or_s _ _ zenon_H1aa); [ zenon_intro zenon_H16c | zenon_intro zenon_H1ab ]. % 18.79/18.93 apply (zenon_L167_); trivial. % 18.79/18.93 apply (zenon_or_s _ _ zenon_H1ab); [ zenon_intro zenon_Haa | zenon_intro zenon_H163 ]. % 18.79/18.93 apply (zenon_L181_); trivial. % 18.79/18.93 apply (zenon_L169_); trivial. % 18.79/18.93 (* end of lemma zenon_L699_ *) % 18.79/18.93 assert (zenon_L700_ : (((op (e3) (e1)) = (e0))\/(((op (e3) (e1)) = (e1))\/(((op (e3) (e1)) = (e2))\/((op (e3) (e1)) = (e3))))) -> (~((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 (e2) (e1)) = (e0)) -> (~((op (e1) (e1)) = (op (e3) (e1)))) -> (((op (e0) (e2)) = (e2))\/(((op (e1) (e2)) = (e2))\/(((op (e2) (e2)) = (e2))\/((op (e3) (e2)) = (e2))))) -> (~((e0) = (e1))) -> ((op (e3) (e0)) = (e0)) -> (~((e1) = (e2))) -> (((op (e0) (e0)) = (e3))\/(((op (e0) (e1)) = (e3))\/(((op (e0) (e2)) = (e3))\/((op (e0) (e3)) = (e3))))) -> (~((op (e3) (e3)) = (e3))) -> (~((e2) = (e3))) -> (((op (e3) (e0)) = (e3))\/(((op (e3) (e1)) = (e3))\/(((op (e3) (e2)) = (e3))\/((op (e3) (e3)) = (e3))))) -> (~((e0) = (e3))) -> (~((op (e1) (e1)) = (op (e2) (e1)))) -> (~((op (e0) (e1)) = (op (e1) (e1)))) -> ((op (e0) (e1)) = (e2)) -> (~((op (e1) (e1)) = (e0))) -> (((op (e1) (e1)) = (e0))\/(((op (e1) (e1)) = (e1))\/(((op (e1) (e1)) = (e2))\/((op (e1) (e1)) = (e3))))) -> (((op (e0) (e2)) = (e3))\/(((op (e1) (e2)) = (e3))\/(((op (e2) (e2)) = (e3))\/((op (e3) (e2)) = (e3))))) -> (~((op (e1) (e3)) = (op (e2) (e3)))) -> (~((op (e2) (e3)) = (op (e3) (e3)))) -> (~((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 (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 (e2) (e2)) = (e0))\/(((op (e2) (e2)) = (e1))\/(((op (e2) (e2)) = (e2))\/((op (e2) (e2)) = (e3))))) -> (~((op (e2) (e2)) = (e0))) -> (~((op (e2) (e2)) = (e2))) -> (((op (e0) (e2)) = (e0))\/(((op (e0) (e2)) = (e1))\/(((op (e0) (e2)) = (e2))\/((op (e0) (e2)) = (e3))))) -> (~((op (e0) (e2)) = (op (e1) (e2)))) -> (~((op (e1) (e1)) = (e1))) -> ((op (e2) (e0)) = (e1)) -> (~((op (e1) (e0)) = (op (e2) (e0)))) -> (((op (e1) (e0)) = (e1))\/(((op (e1) (e1)) = (e1))\/(((op (e1) (e2)) = (e1))\/((op (e1) (e3)) = (e1))))) -> (~((op (e0) (e2)) = (op (e2) (e2)))) -> (~((op (e3) (e2)) = (e0))) -> (~((op (e3) (e2)) = (op (e3) (e3)))) -> ((op (e0) (e0)) = (e3)) -> (((op (e3) (e0)) = (e2))\/(((op (e3) (e1)) = (e2))\/(((op (e3) (e2)) = (e2))\/((op (e3) (e3)) = (e2))))) -> (~((op (e0) (e1)) = (op (e3) (e1)))) -> ((op (e0) (e1)) = (e1)) -> ((op (e1) (e0)) = (e2)) -> (((op (e3) (e0)) = (e1))\/(((op (e3) (e1)) = (e1))\/(((op (e3) (e2)) = (e1))\/((op (e3) (e3)) = (e1))))) -> (~((e1) = (e3))) -> ((op (e1) (e2)) = (e1)) -> (~((op (e2) (e2)) = (op (e3) (e2)))) -> (~((op (e0) (e2)) = (op (e3) (e2)))) -> ((op (e0) (e2)) = (e2)) -> ((op (e1) (e2)) = (e0)) -> (~((op (e1) (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)))) -> False). % 18.79/18.93 do 0 intro. intros zenon_H22a zenon_H1ad zenon_H130 zenon_H1a5 zenon_H36 zenon_H160 zenon_H172 zenon_Ha1 zenon_H44 zenon_H7c zenon_H168 zenon_H102 zenon_H12b zenon_H165 zenon_H9a zenon_H13e zenon_H10e zenon_H10f zenon_H24 zenon_H142 zenon_H1a6 zenon_Hdb zenon_Hf3 zenon_He2 zenon_H1e zenon_H11f zenon_Hd5 zenon_H1d zenon_Hdf zenon_H1c4 zenon_H81 zenon_H173 zenon_H1ba zenon_H195 zenon_H10a zenon_Hed zenon_H201 zenon_H128 zenon_Ha8 zenon_H18b zenon_H62 zenon_H3a zenon_H153 zenon_H210 zenon_Ha0 zenon_H86 zenon_He8 zenon_H95 zenon_Hf0 zenon_H18f zenon_H14f zenon_H150 zenon_H2a zenon_H115 zenon_H191 zenon_H1a4. % 18.79/18.93 apply (zenon_or_s _ _ zenon_H1a5); [ zenon_intro zenon_H99 | zenon_intro zenon_H1a8 ]. % 18.79/18.93 apply (zenon_L403_); trivial. % 18.79/18.93 apply (zenon_or_s _ _ zenon_H1a8); [ zenon_intro zenon_H13f | zenon_intro zenon_H1a9 ]. % 18.79/18.93 apply (zenon_L698_); trivial. % 18.79/18.93 apply (zenon_or_s _ _ zenon_H1a9); [ zenon_intro zenon_Ha6 | zenon_intro zenon_H161 ]. % 18.79/18.93 apply (zenon_L96_); trivial. % 18.79/18.93 apply (zenon_L699_); trivial. % 18.79/18.93 (* end of lemma zenon_L700_ *) % 18.79/18.93 assert (zenon_L701_ : (((op (e0) (e2)) = (e1))\/(((op (e1) (e2)) = (e1))\/(((op (e2) (e2)) = (e1))\/((op (e3) (e2)) = (e1))))) -> (~((e1) = (e2))) -> (~((op (e1) (e2)) = (op (e1) (e3)))) -> ((op (e1) (e3)) = (e1)) -> (~((op (e1) (e3)) = (op (e3) (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 (e0) (e2)) = (e3))\/(((op (e1) (e2)) = (e3))\/(((op (e2) (e2)) = (e3))\/((op (e3) (e2)) = (e3))))) -> (~((e0) = (e3))) -> (~((op (e0) (e2)) = (op (e3) (e2)))) -> ((op (e0) (e2)) = (e2)) -> ((op (e1) (e2)) = (e0)) -> (~((op (e1) (e2)) = (op (e3) (e2)))) -> (((op (e3) (e2)) = (e0))\/(((op (e3) (e2)) = (e1))\/(((op (e3) (e2)) = (e2))\/((op (e3) (e2)) = (e3))))) -> (((op (e2) (e2)) = (e0))\/(((op (e2) (e2)) = (e1))\/(((op (e2) (e2)) = (e2))\/((op (e2) (e2)) = (e3))))) -> (~((op (e2) (e2)) = (e0))) -> (~((op (e2) (e2)) = (e2))) -> (~((op (e2) (e2)) = (op (e3) (e2)))) -> False). % 18.79/18.93 do 0 intro. intros zenon_H139 zenon_H7c zenon_H124 zenon_Hd6 zenon_Hd5 zenon_H210 zenon_Ha0 zenon_H44 zenon_Ha1 zenon_He8 zenon_H1a6 zenon_H9a zenon_H14f zenon_H150 zenon_H2a zenon_H115 zenon_H191 zenon_H1c4 zenon_H81 zenon_H173 zenon_H18f. % 18.79/18.93 apply (zenon_or_s _ _ zenon_H139); [ zenon_intro zenon_H122 | zenon_intro zenon_H13a ]. % 18.79/18.93 apply (zenon_L328_); trivial. % 18.79/18.93 apply (zenon_or_s _ _ zenon_H13a); [ zenon_intro zenon_Hf0 | zenon_intro zenon_H13b ]. % 18.79/18.93 apply (zenon_L78_); trivial. % 18.79/18.93 apply (zenon_or_s _ _ zenon_H13b); [ zenon_intro zenon_Hf1 | zenon_intro zenon_Hba ]. % 18.79/18.93 apply (zenon_L365_); trivial. % 18.79/18.93 apply (zenon_L556_); trivial. % 18.79/18.93 (* end of lemma zenon_L701_ *) % 18.79/18.93 assert (zenon_L702_ : (((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)) = (op (e3) (e3)))) -> (((op (e0) (e3)) = (e0))\/(((op (e0) (e3)) = (e1))\/(((op (e0) (e3)) = (e2))\/((op (e0) (e3)) = (e3))))) -> (((op (e0) (e3)) = (e3))\/(((op (e1) (e3)) = (e3))\/(((op (e2) (e3)) = (e3))\/((op (e3) (e3)) = (e3))))) -> (~((op (e0) (e1)) = (op (e2) (e1)))) -> (((op (e2) (e0)) = (e2))\/(((op (e2) (e1)) = (e2))\/(((op (e2) (e2)) = (e2))\/((op (e2) (e3)) = (e2))))) -> (~((op (e0) (e0)) = (op (e2) (e0)))) -> (((op (e2) (e0)) = (e3))\/(((op (e2) (e1)) = (e3))\/(((op (e2) (e2)) = (e3))\/((op (e2) (e3)) = (e3))))) -> (~((op (e2) (e0)) = (op (e2) (e2)))) -> (((op (e0) (e0)) = (e0))\/(((op (e1) (e0)) = (e0))\/(((op (e2) (e0)) = (e0))\/((op (e3) (e0)) = (e0))))) -> (~((op (e0) (e0)) = (e0))) -> (~((op (e0) (e2)) = (e0))) -> ((~((op (e0) (e2)) = (e0)))\/((op (e0) (e0)) = (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) (e1)) = (op (e2) (e2)))) -> (((op (e0) (e0)) = (e1))\/(((op (e0) (e1)) = (e1))\/(((op (e0) (e2)) = (e1))\/((op (e0) (e3)) = (e1))))) -> (~((op (e0) (e2)) = (op (e0) (e3)))) -> ((~((op (e1) (e0)) = (e0)))\/((op (e1) (e0)) = (e0))) -> (~((op (e2) (e0)) = (op (e2) (e1)))) -> (~((op (e1) (e0)) = (op (e3) (e0)))) -> (((op (e0) (e0)) = (e0))\/(((op (e0) (e1)) = (e0))\/(((op (e0) (e2)) = (e0))\/((op (e0) (e3)) = (e0))))) -> (~((op (e3) (e0)) = (op (e3) (e2)))) -> (~((op (e2) (e2)) = (op (e2) (e3)))) -> (~((op (e0) (e1)) = (op (e0) (e2)))) -> (~((op (e1) (e1)) = (op (e1) (e2)))) -> (((op (e0) (e3)) = (e0))\/(((op (e1) (e3)) = (e0))\/(((op (e2) (e3)) = (e0))\/((op (e3) (e3)) = (e0))))) -> (~((op (e2) (e0)) = (op (e2) (e3)))) -> (~((op (e1) (e1)) = (op (e1) (e3)))) -> (~((op (e0) (e1)) = (op (e0) (e3)))) -> (((op (e0) (e2)) = (e0))\/(((op (e1) (e2)) = (e0))\/(((op (e2) (e2)) = (e0))\/((op (e3) (e2)) = (e0))))) -> (~((op (e1) (e0)) = (op (e1) (e1)))) -> ((~((op (e3) (e1)) = (e0)))\/((op (e3) (e0)) = (e1))) -> ((~((op (e3) (e3)) = (e0)))\/((op (e3) (e0)) = (e3))) -> (~((op (e3) (e0)) = (op (e3) (e1)))) -> (((op (e2) (e1)) = (e0))\/(((op (e2) (e1)) = (e1))\/(((op (e2) (e1)) = (e2))\/((op (e2) (e1)) = (e3))))) -> (~((op (e2) (e1)) = (op (e2) (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 (e2) (e0)) = (e0)))\/((op (e2) (e0)) = (e0))) -> (((op (e0) (e0)) = (e2))\/(((op (e1) (e0)) = (e2))\/(((op (e2) (e0)) = (e2))\/((op (e3) (e0)) = (e2))))) -> ((~((op (e2) (e1)) = (e0)))\/((op (e2) (e0)) = (e1))) -> (((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)) = (e1))\/(((op (e1) (e3)) = (e1))\/(((op (e2) (e3)) = (e1))\/((op (e3) (e3)) = (e1))))) -> (~((op (e0) (e0)) = (op (e0) (e2)))) -> ((~((op (e1) (e3)) = (e0)))\/((op (e1) (e0)) = (e3))) -> ((~((op (e1) (e2)) = (e0)))\/((op (e1) (e0)) = (e2))) -> (~((op (e2) (e0)) = (op (e3) (e0)))) -> (((op (e0) (e0)) = (e2))\/(((op (e0) (e1)) = (e2))\/(((op (e0) (e2)) = (e2))\/((op (e0) (e3)) = (e2))))) -> ((~((op (e3) (e0)) = (e0)))\/((op (e3) (e0)) = (e0))) -> ((~((op (e2) (e2)) = (e0)))\/((op (e2) (e0)) = (e2))) -> (~((op (e0) (e0)) = (op (e0) (e3)))) -> (((op (e0) (e1)) = (e1))\/(((op (e1) (e1)) = (e1))\/(((op (e2) (e1)) = (e1))\/((op (e3) (e1)) = (e1))))) -> (~((op (e1) (e2)) = (op (e2) (e2)))) -> (((op (e2) (e0)) = (e1))\/(((op (e2) (e1)) = (e1))\/(((op (e2) (e2)) = (e1))\/((op (e2) (e3)) = (e1))))) -> (~((op (e2) (e1)) = (op (e3) (e1)))) -> (~((op (e1) (e0)) = (op (e1) (e3)))) -> (((op (e1) (e0)) = (e2))\/(((op (e1) (e1)) = (e2))\/(((op (e1) (e2)) = (e2))\/((op (e1) (e3)) = (e2))))) -> (((op (e1) (e2)) = (e0))\/(((op (e1) (e2)) = (e1))\/(((op (e1) (e2)) = (e2))\/((op (e1) (e2)) = (e3))))) -> ((~((op (e3) (e2)) = (e0)))\/((op (e3) (e0)) = (e2))) -> ((~((op (e1) (e1)) = (e0)))\/((op (e1) (e0)) = (e1))) -> ((~((op (e0) (e3)) = (e0)))\/((op (e0) (e0)) = (e3))) -> (((op (e2) (e0)) = (e0))\/(((op (e2) (e1)) = (e0))\/(((op (e2) (e2)) = (e0))\/((op (e2) (e3)) = (e0))))) -> ((~((op (e2) (e3)) = (e0)))\/((op (e2) (e0)) = (e3))) -> (~((op (e0) (e3)) = (op (e1) (e3)))) -> (((op (e0) (e1)) = (e0))\/(((op (e1) (e1)) = (e0))\/(((op (e2) (e1)) = (e0))\/((op (e3) (e1)) = (e0))))) -> (~((op (e2) (e2)) = (op (e3) (e2)))) -> (~((op (e2) (e2)) = (e2))) -> (~((op (e2) (e2)) = (e0))) -> (((op (e2) (e2)) = (e0))\/(((op (e2) (e2)) = (e1))\/(((op (e2) (e2)) = (e2))\/((op (e2) (e2)) = (e3))))) -> (((op (e3) (e2)) = (e0))\/(((op (e3) (e2)) = (e1))\/(((op (e3) (e2)) = (e2))\/((op (e3) (e2)) = (e3))))) -> (~((op (e1) (e2)) = (op (e3) (e2)))) -> (~((op (e0) (e2)) = (op (e3) (e2)))) -> (~((e0) = (e3))) -> (((op (e0) (e2)) = (e3))\/(((op (e1) (e2)) = (e3))\/(((op (e2) (e2)) = (e3))\/((op (e3) (e2)) = (e3))))) -> (((op (e3) (e0)) = (e1))\/(((op (e3) (e1)) = (e1))\/(((op (e3) (e2)) = (e1))\/((op (e3) (e3)) = (e1))))) -> (~((e0) = (e1))) -> ((op (e3) (e0)) = (e0)) -> ((op (e0) (e1)) = (e1)) -> (~((op (e0) (e1)) = (op (e3) (e1)))) -> (~((op (e1) (e3)) = (op (e3) (e3)))) -> (~((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) (e1)) = (e2))\/(((op (e1) (e1)) = (e2))\/(((op (e2) (e1)) = (e2))\/((op (e3) (e1)) = (e2))))) -> (~((op (e0) (e1)) = (e0))) -> (((op (e0) (e1)) = (e0))\/(((op (e0) (e1)) = (e1))\/(((op (e0) (e1)) = (e2))\/((op (e0) (e1)) = (e3))))) -> ((op (e1) (e0)) = (e2)) -> (((op (e3) (e0)) = (e2))\/(((op (e3) (e1)) = (e2))\/(((op (e3) (e2)) = (e2))\/((op (e3) (e3)) = (e2))))) -> ((op (e0) (e0)) = (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)) = (op (e2) (e0)))) -> ((op (e2) (e0)) = (e1)) -> (~((op (e0) (e2)) = (op (e1) (e2)))) -> (((op (e0) (e2)) = (e0))\/(((op (e0) (e2)) = (e1))\/(((op (e0) (e2)) = (e2))\/((op (e0) (e2)) = (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 (e0) (e3)) = (op (e2) (e3)))) -> (~((op (e2) (e3)) = (op (e3) (e3)))) -> (~((op (e1) (e3)) = (op (e2) (e3)))) -> (~((e2) = (e3))) -> (((op (e3) (e0)) = (e3))\/(((op (e3) (e1)) = (e3))\/(((op (e3) (e2)) = (e3))\/((op (e3) (e3)) = (e3))))) -> (~((op (e3) (e3)) = (e3))) -> (~((op (e0) (e1)) = (op (e1) (e1)))) -> (((op (e0) (e0)) = (e3))\/(((op (e0) (e1)) = (e3))\/(((op (e0) (e2)) = (e3))\/((op (e0) (e3)) = (e3))))) -> (~((op (e3) (e1)) = (op (e3) (e3)))) -> (((op (e3) (e1)) = (e0))\/(((op (e3) (e1)) = (e1))\/(((op (e3) (e1)) = (e2))\/((op (e3) (e1)) = (e3))))) -> (((op (e0) (e1)) = (e3))\/(((op (e1) (e1)) = (e3))\/(((op (e2) (e1)) = (e3))\/((op (e3) (e1)) = (e3))))) -> (~((op (e1) (e1)) = (op (e2) (e1)))) -> (~((op (e1) (e1)) = (op (e3) (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)) = (e2))\/(((op (e1) (e2)) = (e2))\/(((op (e2) (e2)) = (e2))\/((op (e3) (e2)) = (e2))))) -> (~((e1) = (e3))) -> (~((op (e3) (e2)) = (e0))) -> (~((op (e3) (e2)) = (op (e3) (e3)))) -> (~((op (e3) (e1)) = (op (e3) (e2)))) -> (~((op (e3) (e1)) = (e0))) -> (~((op (e1) (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). % 18.79/18.93 do 0 intro. intros zenon_H101 zenon_H71 zenon_Hc2 zenon_He4 zenon_H136 zenon_H17e zenon_H1d5 zenon_H39 zenon_He7 zenon_H52 zenon_H3e zenon_H3f zenon_H75 zenon_H233 zenon_H235 zenon_H24a zenon_H24b zenon_H22d zenon_H208 zenon_H206 zenon_H1f0 zenon_H1fa zenon_H74 zenon_H6f zenon_H6d zenon_H4a zenon_H4f zenon_H67 zenon_H5b zenon_H57 zenon_H54 zenon_H6a zenon_H45 zenon_H1ed zenon_H1ec zenon_H1cf zenon_H1cc zenon_H1c7 zenon_H1ac zenon_H1e0 zenon_H1ee zenon_H1fe zenon_H182 zenon_H16f zenon_H145 zenon_H133 zenon_H13c zenon_H179 zenon_H178 zenon_H17b zenon_H183 zenon_H184 zenon_H185 zenon_H189 zenon_H109 zenon_H2b zenon_H106 zenon_Haf zenon_Hd8 zenon_H18c zenon_H19d zenon_H1a7 zenon_H205 zenon_H204 zenon_H2f zenon_H94 zenon_H1d zenon_H245 zenon_H18f zenon_H173 zenon_H81 zenon_H1c4 zenon_H191 zenon_H115 zenon_H14f zenon_H9a zenon_H1a6 zenon_He8 zenon_Ha1 zenon_H44 zenon_Ha0 zenon_H210 zenon_Hd5 zenon_H124 zenon_H7c zenon_H139 zenon_H1d8 zenon_H20b zenon_H212 zenon_H86 zenon_H153 zenon_H3a zenon_Ha8 zenon_H128 zenon_H201 zenon_Hed zenon_H195 zenon_H1ba zenon_Hdf zenon_H11f zenon_He2 zenon_Hf3 zenon_Hdb zenon_H12b zenon_H165 zenon_H102 zenon_H10e zenon_H168 zenon_H130 zenon_H22a zenon_H1a5 zenon_H13e zenon_H160 zenon_H10a zenon_H24 zenon_H142 zenon_H172 zenon_H95 zenon_H18b zenon_H62 zenon_H1a4 zenon_H1ad zenon_H23 zenon_H22 zenon_H1e zenon_H149. % 18.79/18.93 apply (zenon_or_s _ _ zenon_H183); [ zenon_intro zenon_H7b | zenon_intro zenon_H186 ]. % 18.79/18.93 apply (zenon_L592_); trivial. % 18.79/18.93 apply (zenon_or_s _ _ zenon_H186); [ zenon_intro zenon_H10f | zenon_intro zenon_H187 ]. % 18.79/18.93 apply (zenon_or_s _ _ zenon_H22); [ zenon_intro zenon_H27 | zenon_intro zenon_H26 ]. % 18.79/18.93 exact (zenon_H23 zenon_H27). % 18.79/18.93 apply (zenon_or_s _ _ zenon_H26); [ zenon_intro zenon_H29 | zenon_intro zenon_H28 ]. % 18.79/18.93 exact (zenon_H24 zenon_H29). % 18.79/18.93 apply (zenon_or_s _ _ zenon_H28); [ zenon_intro zenon_H2a | zenon_intro zenon_H1f ]. % 18.79/18.93 apply (zenon_or_s _ _ zenon_H245); [ zenon_intro zenon_H49 | zenon_intro zenon_H246 ]. % 18.79/18.93 exact (zenon_H20b zenon_H49). % 18.79/18.93 apply (zenon_or_s _ _ zenon_H246); [ zenon_intro zenon_H29 | zenon_intro zenon_H247 ]. % 18.79/18.93 exact (zenon_H24 zenon_H29). % 18.79/18.93 apply (zenon_or_s _ _ zenon_H247); [ zenon_intro zenon_H36 | zenon_intro zenon_H1b1 ]. % 18.79/18.93 apply (zenon_or_s _ _ zenon_H128); [ zenon_intro zenon_H9d | zenon_intro zenon_H129 ]. % 18.79/18.93 apply (zenon_L695_); trivial. % 18.79/18.93 apply (zenon_or_s _ _ zenon_H129); [ zenon_intro zenon_H10d | zenon_intro zenon_H12a ]. % 18.79/18.93 exact (zenon_H10a zenon_H10d). % 18.79/18.93 apply (zenon_or_s _ _ zenon_H12a); [ zenon_intro zenon_Hf0 | zenon_intro zenon_Hd6 ]. % 18.79/18.93 apply (zenon_or_s _ _ zenon_H1a5); [ zenon_intro zenon_H99 | zenon_intro zenon_H1a8 ]. % 18.79/18.93 apply (zenon_L175_); trivial. % 18.79/18.93 apply (zenon_or_s _ _ zenon_H1a8); [ zenon_intro zenon_H13f | zenon_intro zenon_H1a9 ]. % 18.79/18.93 apply (zenon_or_s _ _ zenon_H1d5); [ zenon_intro zenon_Hee | zenon_intro zenon_H1d6 ]. % 18.79/18.93 apply (zenon_L58_); trivial. % 18.79/18.93 apply (zenon_or_s _ _ zenon_H1d6); [ zenon_intro zenon_H1ca | zenon_intro zenon_H1d7 ]. % 18.79/18.93 apply (zenon_L191_); trivial. % 18.79/18.93 apply (zenon_or_s _ _ zenon_H1d7); [ zenon_intro zenon_H176 | zenon_intro zenon_H11d ]. % 18.79/18.93 exact (zenon_H173 zenon_H176). % 18.79/18.93 apply (zenon_or_s _ _ zenon_H172); [ zenon_intro zenon_H150 | zenon_intro zenon_H174 ]. % 18.79/18.93 apply (zenon_L698_); trivial. % 18.79/18.93 apply (zenon_or_s _ _ zenon_H174); [ zenon_intro zenon_H113 | zenon_intro zenon_H175 ]. % 18.79/18.93 apply (zenon_L542_); trivial. % 18.79/18.93 apply (zenon_or_s _ _ zenon_H175); [ zenon_intro zenon_H176 | zenon_intro zenon_H151 ]. % 18.79/18.93 exact (zenon_H173 zenon_H176). % 18.79/18.93 apply (zenon_or_s _ _ zenon_He7); [ zenon_intro zenon_H3b | zenon_intro zenon_He9 ]. % 18.79/18.93 apply (zenon_L6_); trivial. % 18.79/18.93 apply (zenon_or_s _ _ zenon_He9); [ zenon_intro zenon_Ha6 | zenon_intro zenon_Hea ]. % 18.79/18.93 apply (zenon_L96_); trivial. % 18.79/18.93 apply (zenon_or_s _ _ zenon_Hea); [ zenon_intro zenon_Haa | zenon_intro zenon_Hdd ]. % 18.79/18.93 apply (zenon_L534_); trivial. % 18.79/18.93 apply (zenon_L537_); trivial. % 18.79/18.93 apply (zenon_or_s _ _ zenon_H1a9); [ zenon_intro zenon_Ha6 | zenon_intro zenon_H161 ]. % 18.79/18.93 apply (zenon_L96_); trivial. % 18.79/18.93 apply (zenon_or_s _ _ zenon_H1d5); [ zenon_intro zenon_Hee | zenon_intro zenon_H1d6 ]. % 18.79/18.93 apply (zenon_L58_); trivial. % 18.79/18.93 apply (zenon_or_s _ _ zenon_H1d6); [ zenon_intro zenon_H1ca | zenon_intro zenon_H1d7 ]. % 18.79/18.93 apply (zenon_L191_); trivial. % 18.79/18.93 apply (zenon_or_s _ _ zenon_H1d7); [ zenon_intro zenon_H176 | zenon_intro zenon_H11d ]. % 18.79/18.93 exact (zenon_H173 zenon_H176). % 18.79/18.93 apply (zenon_or_s _ _ zenon_H172); [ zenon_intro zenon_H150 | zenon_intro zenon_H174 ]. % 18.79/18.93 apply (zenon_L700_); trivial. % 18.79/18.93 apply (zenon_or_s _ _ zenon_H174); [ zenon_intro zenon_H113 | zenon_intro zenon_H175 ]. % 18.79/18.93 apply (zenon_L68_); trivial. % 18.79/18.93 apply (zenon_or_s _ _ zenon_H175); [ zenon_intro zenon_H176 | zenon_intro zenon_H151 ]. % 18.79/18.93 exact (zenon_H173 zenon_H176). % 18.79/18.93 apply (zenon_or_s _ _ zenon_He7); [ zenon_intro zenon_H3b | zenon_intro zenon_He9 ]. % 18.79/18.93 apply (zenon_L525_); trivial. % 18.79/18.93 apply (zenon_or_s _ _ zenon_He9); [ zenon_intro zenon_Ha6 | zenon_intro zenon_Hea ]. % 18.79/18.93 apply (zenon_L96_); trivial. % 18.79/18.93 apply (zenon_or_s _ _ zenon_Hea); [ zenon_intro zenon_Haa | zenon_intro zenon_Hdd ]. % 18.79/18.93 apply (zenon_L534_); trivial. % 18.79/18.93 apply (zenon_L537_); trivial. % 18.79/18.93 apply (zenon_or_s _ _ zenon_H139); [ zenon_intro zenon_H122 | zenon_intro zenon_H13a ]. % 18.79/18.93 apply (zenon_L561_); trivial. % 18.79/18.93 apply (zenon_or_s _ _ zenon_H13a); [ zenon_intro zenon_Hf0 | zenon_intro zenon_H13b ]. % 18.79/18.93 apply (zenon_L78_); trivial. % 18.79/18.93 apply (zenon_or_s _ _ zenon_H13b); [ zenon_intro zenon_Hf1 | zenon_intro zenon_Hba ]. % 18.79/18.93 apply (zenon_L365_); trivial. % 18.79/18.93 apply (zenon_or_s _ _ zenon_H1d5); [ zenon_intro zenon_Hee | zenon_intro zenon_H1d6 ]. % 18.79/18.93 apply (zenon_L58_); trivial. % 18.79/18.93 apply (zenon_or_s _ _ zenon_H1d6); [ zenon_intro zenon_H1ca | zenon_intro zenon_H1d7 ]. % 18.79/18.93 apply (zenon_L191_); trivial. % 18.79/18.93 apply (zenon_or_s _ _ zenon_H1d7); [ zenon_intro zenon_H176 | zenon_intro zenon_H11d ]. % 18.79/18.93 exact (zenon_H173 zenon_H176). % 18.79/18.93 apply (zenon_L559_); trivial. % 18.79/18.93 exact (zenon_H1ad zenon_H1b1). % 18.79/18.93 apply (zenon_L1_); trivial. % 18.79/18.93 apply (zenon_or_s _ _ zenon_H187); [ zenon_intro zenon_H150 | zenon_intro zenon_Hcd ]. % 18.79/18.93 apply (zenon_or_s _ _ zenon_H22); [ zenon_intro zenon_H27 | zenon_intro zenon_H26 ]. % 18.79/18.93 exact (zenon_H23 zenon_H27). % 18.79/18.93 apply (zenon_or_s _ _ zenon_H26); [ zenon_intro zenon_H29 | zenon_intro zenon_H28 ]. % 18.79/18.93 exact (zenon_H24 zenon_H29). % 18.79/18.93 apply (zenon_or_s _ _ zenon_H28); [ zenon_intro zenon_H2a | zenon_intro zenon_H1f ]. % 18.79/18.93 apply (zenon_or_s _ _ zenon_H245); [ zenon_intro zenon_H49 | zenon_intro zenon_H246 ]. % 18.79/18.93 exact (zenon_H20b zenon_H49). % 18.79/18.93 apply (zenon_or_s _ _ zenon_H246); [ zenon_intro zenon_H29 | zenon_intro zenon_H247 ]. % 18.79/18.93 exact (zenon_H24 zenon_H29). % 18.79/18.93 apply (zenon_or_s _ _ zenon_H247); [ zenon_intro zenon_H36 | zenon_intro zenon_H1b1 ]. % 18.79/18.93 apply (zenon_or_s _ _ zenon_H128); [ zenon_intro zenon_H9d | zenon_intro zenon_H129 ]. % 18.79/18.93 apply (zenon_L413_); trivial. % 18.79/18.93 apply (zenon_or_s _ _ zenon_H129); [ zenon_intro zenon_H10d | zenon_intro zenon_H12a ]. % 18.79/18.93 exact (zenon_H10a zenon_H10d). % 18.79/18.93 apply (zenon_or_s _ _ zenon_H12a); [ zenon_intro zenon_Hf0 | zenon_intro zenon_Hd6 ]. % 18.79/18.93 apply (zenon_or_s _ _ zenon_H1d8); [ zenon_intro zenon_H10f | zenon_intro zenon_H1d9 ]. % 18.79/18.93 apply (zenon_L700_); trivial. % 18.79/18.93 apply (zenon_or_s _ _ zenon_H1d9); [ zenon_intro zenon_H110 | zenon_intro zenon_H1da ]. % 18.79/18.93 apply (zenon_or_s _ _ zenon_H1a5); [ zenon_intro zenon_H99 | zenon_intro zenon_H1a8 ]. % 18.79/18.93 apply (zenon_L403_); trivial. % 18.79/18.93 apply (zenon_or_s _ _ zenon_H1a8); [ zenon_intro zenon_H13f | zenon_intro zenon_H1a9 ]. % 18.79/18.93 apply (zenon_L698_); trivial. % 18.79/18.93 apply (zenon_or_s _ _ zenon_H1a9); [ zenon_intro zenon_Ha6 | zenon_intro zenon_H161 ]. % 18.79/18.93 apply (zenon_or_s _ _ zenon_H1a6); [ zenon_intro zenon_Ha9 | zenon_intro zenon_H1aa ]. % 18.79/18.93 apply (zenon_or_s _ _ zenon_He8); [ zenon_intro zenon_Hac | zenon_intro zenon_Heb ]. % 18.79/18.93 apply (zenon_L241_); trivial. % 18.79/18.93 apply (zenon_or_s _ _ zenon_Heb); [ zenon_intro zenon_Hae | zenon_intro zenon_Hec ]. % 18.79/18.93 apply (zenon_L363_); trivial. % 18.79/18.93 apply (zenon_or_s _ _ zenon_Hec); [ zenon_intro zenon_Hba | zenon_intro zenon_Hc4 ]. % 18.79/18.93 apply (zenon_L69_); trivial. % 18.79/18.93 apply (zenon_or_s _ _ zenon_H153); [ zenon_intro zenon_H148 | zenon_intro zenon_H154 ]. % 18.79/18.93 apply (zenon_L423_); trivial. % 18.79/18.93 apply (zenon_or_s _ _ zenon_H154); [ zenon_intro zenon_H14d | zenon_intro zenon_H155 ]. % 18.79/18.93 apply (zenon_L164_); trivial. % 18.79/18.93 apply (zenon_or_s _ _ zenon_H155); [ zenon_intro zenon_H151 | zenon_intro zenon_Hf6 ]. % 18.79/18.93 apply (zenon_L533_); trivial. % 18.79/18.93 apply (zenon_L696_); trivial. % 18.79/18.93 apply (zenon_or_s _ _ zenon_H1aa); [ zenon_intro zenon_H16c | zenon_intro zenon_H1ab ]. % 18.79/18.93 apply (zenon_L167_); trivial. % 18.79/18.93 apply (zenon_or_s _ _ zenon_H1ab); [ zenon_intro zenon_Haa | zenon_intro zenon_H163 ]. % 18.79/18.93 apply (zenon_L181_); trivial. % 18.79/18.93 apply (zenon_or_s _ _ zenon_He8); [ zenon_intro zenon_Hac | zenon_intro zenon_Heb ]. % 18.79/18.93 apply (zenon_L41_); trivial. % 18.79/18.93 apply (zenon_or_s _ _ zenon_Heb); [ zenon_intro zenon_Hae | zenon_intro zenon_Hec ]. % 18.79/18.93 apply (zenon_L555_); trivial. % 18.79/18.93 apply (zenon_or_s _ _ zenon_Hec); [ zenon_intro zenon_Hba | zenon_intro zenon_Hc4 ]. % 18.79/18.93 apply (zenon_L528_); trivial. % 18.79/18.93 apply (zenon_or_s _ _ zenon_H153); [ zenon_intro zenon_H148 | zenon_intro zenon_H154 ]. % 18.79/18.93 apply (zenon_L100_); trivial. % 18.79/18.93 apply (zenon_or_s _ _ zenon_H154); [ zenon_intro zenon_H14d | zenon_intro zenon_H155 ]. % 18.79/18.93 apply (zenon_L522_); trivial. % 18.79/18.93 apply (zenon_or_s _ _ zenon_H155); [ zenon_intro zenon_H151 | zenon_intro zenon_Hf6 ]. % 18.79/18.93 apply (zenon_L401_); trivial. % 18.79/18.93 apply (zenon_L696_); trivial. % 18.79/18.93 apply (zenon_L699_); trivial. % 18.79/18.94 apply (zenon_or_s _ _ zenon_H1da); [ zenon_intro zenon_H1ca | zenon_intro zenon_H14d ]. % 18.79/18.94 apply (zenon_or_s _ _ zenon_H1a5); [ zenon_intro zenon_H99 | zenon_intro zenon_H1a8 ]. % 18.79/18.94 apply (zenon_L403_); trivial. % 18.79/18.94 apply (zenon_or_s _ _ zenon_H1a8); [ zenon_intro zenon_H13f | zenon_intro zenon_H1a9 ]. % 18.79/18.94 apply (zenon_L698_); trivial. % 18.79/18.94 apply (zenon_or_s _ _ zenon_H1a9); [ zenon_intro zenon_Ha6 | zenon_intro zenon_H161 ]. % 18.79/18.94 apply (zenon_L207_); trivial. % 18.79/18.94 apply (zenon_L699_); trivial. % 18.79/18.94 apply (zenon_L546_); trivial. % 18.79/18.94 apply (zenon_L701_); trivial. % 18.79/18.94 exact (zenon_H1ad zenon_H1b1). % 18.79/18.94 apply (zenon_L1_); trivial. % 18.79/18.94 apply (zenon_L428_); trivial. % 18.79/18.94 (* end of lemma zenon_L702_ *) % 18.79/18.94 assert (zenon_L703_ : (((op (e1) (e0)) = (e0))\/(((op (e1) (e1)) = (e0))\/(((op (e1) (e2)) = (e0))\/((op (e1) (e3)) = (e0))))) -> (~((op (e1) (e0)) = (e0))) -> (~((op (e1) (e1)) = (e0))) -> (~((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 (e3) (e0)) = (e0)) -> (~((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 (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 (e3) (e2)) = (op (e3) (e3)))) -> (~((e1) = (e3))) -> (~((e0) = (e3))) -> (((op (e0) (e3)) = (e3))\/(((op (e1) (e3)) = (e3))\/(((op (e2) (e3)) = (e3))\/((op (e3) (e3)) = (e3))))) -> (~((op (e2) (e2)) = (e2))) -> (~((e0) = (e2))) -> ((op (e0) (e2)) = (e1)) -> (~((e1) = (e2))) -> (((op (e0) (e2)) = (e2))\/(((op (e1) (e2)) = (e2))\/(((op (e2) (e2)) = (e2))\/((op (e3) (e2)) = (e2))))) -> (~((op (e0) (e1)) = (op (e2) (e1)))) -> ((op (e0) (e1)) = (e2)) -> ((op (e2) (e0)) = (e1)) -> (((op (e2) (e0)) = (e2))\/(((op (e2) (e1)) = (e2))\/(((op (e2) (e2)) = (e2))\/((op (e2) (e3)) = (e2))))) -> (~((op (e0) (e2)) = (op (e1) (e2)))) -> (~((op (e1) (e1)) = (e1))) -> (~((op (e1) (e0)) = (op (e2) (e0)))) -> (((op (e1) (e0)) = (e1))\/(((op (e1) (e1)) = (e1))\/(((op (e1) (e2)) = (e1))\/((op (e1) (e3)) = (e1))))) -> (~((op (e0) (e3)) = (op (e1) (e3)))) -> ((op (e0) (e3)) = (e0)) -> False). % 18.79/18.94 do 0 intro. intros zenon_H22 zenon_H23 zenon_H24 zenon_H102 zenon_H101 zenon_H71 zenon_H44 zenon_He2 zenon_Hc2 zenon_Hdf zenon_Hd5 zenon_Hdb zenon_He4 zenon_H62 zenon_H95 zenon_H9a zenon_H136 zenon_H173 zenon_H149 zenon_H122 zenon_H7c zenon_H172 zenon_H17e zenon_H10f zenon_Hed zenon_H1d5 zenon_H195 zenon_H10a zenon_H201 zenon_H128 zenon_H1d zenon_H1e. % 18.79/18.94 apply (zenon_or_s _ _ zenon_H22); [ zenon_intro zenon_H27 | zenon_intro zenon_H26 ]. % 18.79/18.94 exact (zenon_H23 zenon_H27). % 18.79/18.94 apply (zenon_or_s _ _ zenon_H26); [ zenon_intro zenon_H29 | zenon_intro zenon_H28 ]. % 18.79/18.94 exact (zenon_H24 zenon_H29). % 18.79/18.94 apply (zenon_or_s _ _ zenon_H28); [ zenon_intro zenon_H2a | zenon_intro zenon_H1f ]. % 18.79/18.94 apply (zenon_or_s _ _ zenon_H128); [ zenon_intro zenon_H9d | zenon_intro zenon_H129 ]. % 18.79/18.94 apply (zenon_L413_); trivial. % 18.79/18.94 apply (zenon_or_s _ _ zenon_H129); [ zenon_intro zenon_H10d | zenon_intro zenon_H12a ]. % 18.79/18.94 exact (zenon_H10a zenon_H10d). % 18.79/18.94 apply (zenon_or_s _ _ zenon_H12a); [ zenon_intro zenon_Hf0 | zenon_intro zenon_Hd6 ]. % 18.79/18.94 apply (zenon_L530_); trivial. % 18.79/18.94 apply (zenon_L561_); trivial. % 18.79/18.94 apply (zenon_L1_); trivial. % 18.79/18.94 (* end of lemma zenon_L703_ *) % 18.79/18.94 assert (zenon_L704_ : ((~((op (e2) (e3)) = (e0)))\/((op (e2) (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) (e3)) = (e0)))\/((op (e0) (e0)) = (e3))) -> ((~((op (e1) (e1)) = (e0)))\/((op (e1) (e0)) = (e1))) -> (~((e1) = (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 (e3) (e1)) = (op (e3) (e2)))) -> ((~((op (e3) (e2)) = (e0)))\/((op (e3) (e0)) = (e2))) -> (~((op (e2) (e2)) = (op (e3) (e2)))) -> (((op (e3) (e2)) = (e0))\/(((op (e3) (e2)) = (e1))\/(((op (e3) (e2)) = (e2))\/((op (e3) (e2)) = (e3))))) -> (~((op (e0) (e2)) = (op (e1) (e2)))) -> (((op (e1) (e2)) = (e0))\/(((op (e1) (e2)) = (e1))\/(((op (e1) (e2)) = (e2))\/((op (e1) (e2)) = (e3))))) -> (~((e1) = (e3))) -> (~((e0) = (e3))) -> (~((op (e1) (e1)) = (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) (e3)) = (e0))\/(((op (e2) (e3)) = (e1))\/(((op (e2) (e3)) = (e2))\/((op (e2) (e3)) = (e3))))) -> (~((op (e0) (e3)) = (op (e1) (e3)))) -> (~((op (e0) (e1)) = (op (e1) (e1)))) -> (~((op (e0) (e2)) = (op (e2) (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) (e3)) = (e0))\/(((op (e1) (e3)) = (e1))\/(((op (e1) (e3)) = (e2))\/((op (e1) (e3)) = (e3))))) -> (~((op (e1) (e3)) = (op (e2) (e3)))) -> (~((op (e1) (e0)) = (op (e1) (e3)))) -> (~((op (e1) (e3)) = (op (e3) (e3)))) -> (~((op (e0) (e3)) = (op (e2) (e3)))) -> (((op (e0) (e3)) = (e0))\/(((op (e0) (e3)) = (e1))\/(((op (e0) (e3)) = (e2))\/((op (e0) (e3)) = (e3))))) -> (~((op (e2) (e1)) = (op (e3) (e1)))) -> (((op (e2) (e0)) = (e3))\/(((op (e2) (e1)) = (e3))\/(((op (e2) (e2)) = (e3))\/((op (e2) (e3)) = (e3))))) -> (((op (e2) (e0)) = (e1))\/(((op (e2) (e1)) = (e1))\/(((op (e2) (e2)) = (e1))\/((op (e2) (e3)) = (e1))))) -> (~((op (e2) (e3)) = (op (e3) (e3)))) -> (~((op (e3) (e3)) = (e3))) -> (((op (e3) (e3)) = (e0))\/(((op (e3) (e3)) = (e1))\/(((op (e3) (e3)) = (e2))\/((op (e3) (e3)) = (e3))))) -> (~((op (e1) (e2)) = (op (e2) (e2)))) -> (((op (e0) (e1)) = (e1))\/(((op (e1) (e1)) = (e1))\/(((op (e2) (e1)) = (e1))\/((op (e3) (e1)) = (e1))))) -> (~((op (e0) (e0)) = (op (e0) (e3)))) -> ((~((op (e2) (e2)) = (e0)))\/((op (e2) (e0)) = (e2))) -> ((~((op (e3) (e0)) = (e0)))\/((op (e3) (e0)) = (e0))) -> (((op (e0) (e0)) = (e2))\/(((op (e0) (e1)) = (e2))\/(((op (e0) (e2)) = (e2))\/((op (e0) (e3)) = (e2))))) -> (~((op (e2) (e0)) = (op (e3) (e0)))) -> (~((op (e0) (e1)) = (op (e2) (e1)))) -> ((~((op (e1) (e2)) = (e0)))\/((op (e1) (e0)) = (e2))) -> ((~((op (e1) (e3)) = (e0)))\/((op (e1) (e0)) = (e3))) -> (((op (e1) (e1)) = (e0))\/(((op (e1) (e1)) = (e1))\/(((op (e1) (e1)) = (e2))\/((op (e1) (e1)) = (e3))))) -> (~((op (e1) (e1)) = (op (e2) (e1)))) -> (~((op (e0) (e0)) = (op (e0) (e2)))) -> (((op (e0) (e2)) = (e1))\/(((op (e1) (e2)) = (e1))\/(((op (e2) (e2)) = (e1))\/((op (e3) (e2)) = (e1))))) -> (((op (e1) (e0)) = (e1))\/(((op (e1) (e1)) = (e1))\/(((op (e1) (e2)) = (e1))\/((op (e1) (e3)) = (e1))))) -> (((op (e0) (e3)) = (e3))\/(((op (e1) (e3)) = (e3))\/(((op (e2) (e3)) = (e3))\/((op (e3) (e3)) = (e3))))) -> (~((op (e3) (e1)) = (op (e3) (e3)))) -> (((op (e0) (e3)) = (e1))\/(((op (e1) (e3)) = (e1))\/(((op (e2) (e3)) = (e1))\/((op (e3) (e3)) = (e1))))) -> (~((e2) = (e3))) -> (~((op (e1) (e2)) = (op (e1) (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 (e2) (e2)) = (e2))) -> (((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) (e1)) = (op (e3) (e1)))) -> (((op (e3) (e0)) = (e3))\/(((op (e3) (e1)) = (e3))\/(((op (e3) (e2)) = (e3))\/((op (e3) (e3)) = (e3))))) -> (~((e0) = (e2))) -> (~((op (e0) (e2)) = (op (e3) (e2)))) -> (((op (e3) (e0)) = (e2))\/(((op (e3) (e1)) = (e2))\/(((op (e3) (e2)) = (e2))\/((op (e3) (e3)) = (e2))))) -> ((~((op (e2) (e1)) = (e0)))\/((op (e2) (e0)) = (e1))) -> (((op (e0) (e0)) = (e2))\/(((op (e1) (e0)) = (e2))\/(((op (e2) (e0)) = (e2))\/((op (e3) (e0)) = (e2))))) -> ((~((op (e2) (e0)) = (e0)))\/((op (e2) (e0)) = (e0))) -> (((op (e0) (e0)) = (e3))\/(((op (e1) (e0)) = (e3))\/(((op (e2) (e0)) = (e3))\/((op (e3) (e0)) = (e3))))) -> (((op (e3) (e0)) = (e0))\/(((op (e3) (e1)) = (e0))\/(((op (e3) (e2)) = (e0))\/((op (e3) (e3)) = (e0))))) -> (~((op (e2) (e1)) = (op (e2) (e3)))) -> (((op (e2) (e2)) = (e0))\/(((op (e2) (e2)) = (e1))\/(((op (e2) (e2)) = (e2))\/((op (e2) (e2)) = (e3))))) -> (((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 (e3) (e0)) = (op (e3) (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))))) -> ((~((op (e3) (e3)) = (e0)))\/((op (e3) (e0)) = (e3))) -> ((~((op (e3) (e1)) = (e0)))\/((op (e3) (e0)) = (e1))) -> (((op (e1) (e0)) = (e0))\/(((op (e1) (e1)) = (e0))\/(((op (e1) (e2)) = (e0))\/((op (e1) (e3)) = (e0))))) -> (~((op (e1) (e0)) = (op (e1) (e1)))) -> (((op (e0) (e2)) = (e0))\/(((op (e1) (e2)) = (e0))\/(((op (e2) (e2)) = (e0))\/((op (e3) (e2)) = (e0))))) -> (~((op (e0) (e1)) = (op (e0) (e3)))) -> (~((op (e1) (e1)) = (op (e1) (e3)))) -> (~((op (e2) (e0)) = (op (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) (e0)) = (op (e2) (e2)))) -> (~((op (e1) (e1)) = (op (e1) (e2)))) -> (~((op (e0) (e1)) = (op (e0) (e2)))) -> (~((op (e3) (e0)) = (op (e3) (e3)))) -> (~((op (e2) (e2)) = (op (e2) (e3)))) -> (~((op (e3) (e0)) = (op (e3) (e2)))) -> (((op (e0) (e0)) = (e0))\/(((op (e0) (e1)) = (e0))\/(((op (e0) (e2)) = (e0))\/((op (e0) (e3)) = (e0))))) -> (~((op (e1) (e0)) = (op (e3) (e0)))) -> (~((op (e2) (e0)) = (op (e2) (e1)))) -> (~((op (e1) (e0)) = (op (e2) (e0)))) -> ((~((op (e1) (e0)) = (e0)))\/((op (e1) (e0)) = (e0))) -> (~((op (e0) (e2)) = (op (e0) (e3)))) -> (((op (e0) (e1)) = (e0))\/(((op (e0) (e1)) = (e1))\/(((op (e0) (e1)) = (e2))\/((op (e0) (e1)) = (e3))))) -> (((op (e3) (e1)) = (e0))\/(((op (e3) (e1)) = (e1))\/(((op (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 (e2) (e1)) = (op (e2) (e2)))) -> (~((op (e1) (e0)) = (op (e1) (e2)))) -> (((op (e0) (e1)) = (e0))\/(((op (e1) (e1)) = (e0))\/(((op (e2) (e1)) = (e0))\/((op (e3) (e1)) = (e0))))) -> (((op (e0) (e0)) = (e1))\/(((op (e1) (e0)) = (e1))\/(((op (e2) (e0)) = (e1))\/((op (e3) (e0)) = (e1))))) -> ((~((op (e0) (e2)) = (e0)))\/((op (e0) (e0)) = (e2))) -> (~((op (e0) (e2)) = (e0))) -> (~((op (e0) (e1)) = (e0))) -> (~((op (e0) (e0)) = (e0))) -> (~((op (e1) (e0)) = (e0))) -> (((op (e0) (e0)) = (e0))\/(((op (e1) (e0)) = (e0))\/(((op (e2) (e0)) = (e0))\/((op (e3) (e0)) = (e0))))) -> (~((e0) = (e1))) -> ((op (e2) (e0)) = (e0)) -> ((op (e1) (e0)) = (e2)) -> ((op (e0) (e0)) = (e3)) -> False). % 18.79/18.94 do 0 intro. intros zenon_H94 zenon_H39 zenon_H2f zenon_H204 zenon_H205 zenon_H7c zenon_H1a5 zenon_H1a6 zenon_H1a4 zenon_H1a7 zenon_H18f zenon_H191 zenon_H195 zenon_H19d zenon_H95 zenon_H9a zenon_H10a zenon_H18c zenon_H115 zenon_H11f zenon_H1d zenon_H10e zenon_Ha8 zenon_He8 zenon_Hc2 zenon_Hdf zenon_Hdb zenon_Hd8 zenon_Hd5 zenon_He2 zenon_He4 zenon_Haf zenon_He7 zenon_H106 zenon_Hf3 zenon_H102 zenon_H101 zenon_H2b zenon_H109 zenon_H189 zenon_H185 zenon_H184 zenon_H183 zenon_H17b zenon_H17e zenon_H178 zenon_H179 zenon_H142 zenon_H13e zenon_H13c zenon_H139 zenon_H128 zenon_H136 zenon_H130 zenon_H133 zenon_H12b zenon_H124 zenon_H145 zenon_H172 zenon_H173 zenon_H16f zenon_H168 zenon_H160 zenon_H165 zenon_H149 zenon_H14f zenon_H153 zenon_H182 zenon_H1fe zenon_H1ee zenon_H1e0 zenon_H1ac zenon_H1c7 zenon_H1c4 zenon_H1cc zenon_H1ba zenon_H1cf zenon_H1d8 zenon_H1d5 zenon_H1ec zenon_H1ed zenon_H22 zenon_H45 zenon_H6a zenon_H54 zenon_H57 zenon_H5b zenon_H62 zenon_H67 zenon_H52 zenon_H4f zenon_H4a zenon_H71 zenon_H6d zenon_H6f zenon_H74 zenon_H1fa zenon_H1f0 zenon_H201 zenon_H206 zenon_H208 zenon_H212 zenon_H22a zenon_H210 zenon_H22d zenon_H24b zenon_H24a zenon_H245 zenon_H235 zenon_H233 zenon_H75 zenon_H20b zenon_H3f zenon_H23 zenon_H3e zenon_Ha1 zenon_H34 zenon_H86 zenon_H3a. % 18.79/18.94 apply (zenon_or_s _ _ zenon_H235); [ zenon_intro zenon_H7a | zenon_intro zenon_H236 ]. % 18.79/18.94 apply (zenon_L333_); trivial. % 18.79/18.94 apply (zenon_or_s _ _ zenon_H236); [ zenon_intro zenon_H9d | zenon_intro zenon_H237 ]. % 18.79/18.94 apply (zenon_L695_); trivial. % 18.79/18.94 apply (zenon_or_s _ _ zenon_H237); [ zenon_intro zenon_Hed | zenon_intro zenon_Hac ]. % 18.79/18.94 apply (zenon_L214_); trivial. % 18.79/18.94 apply (zenon_L241_); trivial. % 18.79/18.94 (* end of lemma zenon_L704_ *) % 18.79/18.94 assert (zenon_L705_ : (((op (e0) (e0)) = (e0))\/(((op (e1) (e0)) = (e0))\/(((op (e2) (e0)) = (e0))\/((op (e3) (e0)) = (e0))))) -> (~((op (e2) (e0)) = (e0))) -> (~((op (e0) (e0)) = (e0))) -> (((op (e0) (e0)) = (e1))\/(((op (e1) (e0)) = (e1))\/(((op (e2) (e0)) = (e1))\/((op (e3) (e0)) = (e1))))) -> ((op (e1) (e0)) = (e3)) -> ((~((op (e2) (e1)) = (e0)))\/((op (e2) (e0)) = (e1))) -> ((~((op (e2) (e3)) = (e0)))\/((op (e2) (e0)) = (e3))) -> ((~((op (e3) (e1)) = (e0)))\/((op (e3) (e0)) = (e1))) -> (((op (e0) (e0)) = (e0))\/(((op (e0) (e1)) = (e0))\/(((op (e0) (e2)) = (e0))\/((op (e0) (e3)) = (e0))))) -> (~((op (e0) (e2)) = (op (e0) (e3)))) -> (((op (e0) (e2)) = (e1))\/(((op (e1) (e2)) = (e1))\/(((op (e2) (e2)) = (e1))\/((op (e3) (e2)) = (e1))))) -> (~((op (e2) (e2)) = (op (e3) (e2)))) -> (((op (e2) (e2)) = (e0))\/(((op (e2) (e2)) = (e1))\/(((op (e2) (e2)) = (e2))\/((op (e2) (e2)) = (e3))))) -> (~((op (e2) (e0)) = (op (e2) (e2)))) -> (~((e0) = (e1))) -> (~((e2) = (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))))) -> (~((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)) = (e0))\/(((op (e0) (e1)) = (e1))\/(((op (e0) (e1)) = (e2))\/((op (e0) (e1)) = (e3))))) -> (~((op (e0) (e1)) = (op (e1) (e1)))) -> (~((op (e1) (e1)) = (op (e2) (e1)))) -> (((op (e2) (e1)) = (e0))\/(((op (e2) (e1)) = (e1))\/(((op (e2) (e1)) = (e2))\/((op (e2) (e1)) = (e3))))) -> (((op (e0) (e2)) = (e0))\/(((op (e1) (e2)) = (e0))\/(((op (e2) (e2)) = (e0))\/((op (e3) (e2)) = (e0))))) -> (~((op (e3) (e0)) = (op (e3) (e2)))) -> (~((op (e1) (e1)) = (op (e1) (e2)))) -> (~((op (e1) (e2)) = (op (e2) (e2)))) -> (((op (e3) (e0)) = (e2))\/(((op (e3) (e1)) = (e2))\/(((op (e3) (e2)) = (e2))\/((op (e3) (e3)) = (e2))))) -> (((op (e1) (e0)) = (e3))\/(((op (e1) (e1)) = (e3))\/(((op (e1) (e2)) = (e3))\/((op (e1) (e3)) = (e3))))) -> (~((op (e3) (e1)) = (op (e3) (e3)))) -> (~((op (e1) (e1)) = (op (e3) (e1)))) -> (((op (e1) (e0)) = (e2))\/(((op (e1) (e1)) = (e2))\/(((op (e1) (e2)) = (e2))\/((op (e1) (e3)) = (e2))))) -> (~((op (e0) (e0)) = (op (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) (e3)) = (e2))\/(((op (e1) (e3)) = (e2))\/(((op (e2) (e3)) = (e2))\/((op (e3) (e3)) = (e2))))) -> (((op (e2) (e0)) = (e1))\/(((op (e2) (e1)) = (e1))\/(((op (e2) (e2)) = (e1))\/((op (e2) (e3)) = (e1))))) -> (((op (e0) (e1)) = (e1))\/(((op (e1) (e1)) = (e1))\/(((op (e2) (e1)) = (e1))\/((op (e3) (e1)) = (e1))))) -> (~((op (e2) (e1)) = (op (e3) (e1)))) -> (((op (e3) (e1)) = (e0))\/(((op (e3) (e1)) = (e1))\/(((op (e3) (e1)) = (e2))\/((op (e3) (e1)) = (e3))))) -> (((op (e2) (e3)) = (e0))\/(((op (e2) (e3)) = (e1))\/(((op (e2) (e3)) = (e2))\/((op (e2) (e3)) = (e3))))) -> (~((op (e2) (e3)) = (op (e3) (e3)))) -> (~((op (e1) (e2)) = (op (e3) (e2)))) -> (~((op (e0) (e1)) = (op (e0) (e2)))) -> (~((op (e0) (e1)) = (op (e3) (e1)))) -> (~((op (e0) (e1)) = (op (e0) (e3)))) -> (~((op (e1) (e0)) = (op (e1) (e3)))) -> (~((op (e2) (e2)) = (op (e2) (e3)))) -> (((op (e0) (e3)) = (e1))\/(((op (e1) (e3)) = (e1))\/(((op (e2) (e3)) = (e1))\/((op (e3) (e3)) = (e1))))) -> (~((op (e0) (e0)) = (op (e2) (e0)))) -> (((op (e0) (e0)) = (e1))\/(((op (e0) (e1)) = (e1))\/(((op (e0) (e2)) = (e1))\/((op (e0) (e3)) = (e1))))) -> (~((op (e0) (e1)) = (e0))) -> ((~((op (e3) (e2)) = (e0)))\/((op (e3) (e0)) = (e2))) -> ((~((op (e3) (e0)) = (e0)))\/((op (e3) (e0)) = (e0))) -> (((op (e2) (e0)) = (e0))\/(((op (e2) (e1)) = (e0))\/(((op (e2) (e2)) = (e0))\/((op (e2) (e3)) = (e0))))) -> ((~((op (e2) (e2)) = (e0)))\/((op (e2) (e0)) = (e2))) -> (((op (e3) (e0)) = (e3))\/(((op (e3) (e1)) = (e3))\/(((op (e3) (e2)) = (e3))\/((op (e3) (e3)) = (e3))))) -> (~((op (e0) (e2)) = (op (e2) (e2)))) -> ((~((op (e3) (e3)) = (e0)))\/((op (e3) (e0)) = (e3))) -> ((~((op (e0) (e3)) = (e0)))\/((op (e0) (e0)) = (e3))) -> ((~((op (e1) (e1)) = (e0)))\/((op (e1) (e0)) = (e1))) -> (((op (e3) (e2)) = (e0))\/(((op (e3) (e2)) = (e1))\/(((op (e3) (e2)) = (e2))\/((op (e3) (e2)) = (e3))))) -> (((op (e1) (e2)) = (e0))\/(((op (e1) (e2)) = (e1))\/(((op (e1) (e2)) = (e2))\/((op (e1) (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 (e2) (e0)) = (op (e3) (e0)))) -> ((~((op (e1) (e2)) = (e0)))\/((op (e1) (e0)) = (e2))) -> ((~((op (e1) (e3)) = (e0)))\/((op (e1) (e0)) = (e3))) -> (((op (e1) (e1)) = (e0))\/(((op (e1) (e1)) = (e1))\/(((op (e1) (e1)) = (e2))\/((op (e1) (e1)) = (e3))))) -> (~((op (e0) (e0)) = (op (e0) (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) (e0)) = (e2))\/(((op (e1) (e0)) = (e2))\/(((op (e2) (e0)) = (e2))\/((op (e3) (e0)) = (e2))))) -> ((~((op (e2) (e0)) = (e0)))\/((op (e2) (e0)) = (e0))) -> (((op (e0) (e0)) = (e3))\/(((op (e1) (e0)) = (e3))\/(((op (e2) (e0)) = (e3))\/((op (e3) (e0)) = (e3))))) -> (((op (e0) (e2)) = (e0))\/(((op (e0) (e2)) = (e1))\/(((op (e0) (e2)) = (e2))\/((op (e0) (e2)) = (e3))))) -> (~((op (e1) (e0)) = (op (e3) (e0)))) -> (~((op (e2) (e0)) = (op (e2) (e1)))) -> ((~((op (e1) (e0)) = (e0)))\/((op (e1) (e0)) = (e0))) -> ((~((op (e0) (e2)) = (e0)))\/((op (e0) (e0)) = (e2))) -> (~((op (e3) (e0)) = (op (e3) (e1)))) -> (~((op (e1) (e1)) = (op (e1) (e3)))) -> (~((op (e2) (e0)) = (op (e2) (e3)))) -> (((op (e0) (e3)) = (e0))\/(((op (e1) (e3)) = (e0))\/(((op (e2) (e3)) = (e0))\/((op (e3) (e3)) = (e0))))) -> (~((op (e1) (e0)) = (op (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) (e0)) = (e3)) -> (~((op (e0) (e3)) = (op (e1) (e3)))) -> (((op (e1) (e0)) = (e1))\/(((op (e1) (e1)) = (e1))\/(((op (e1) (e2)) = (e1))\/((op (e1) (e3)) = (e1))))) -> (~((op (e1) (e0)) = (op (e2) (e0)))) -> (~((op (e1) (e1)) = (e1))) -> (~((op (e0) (e2)) = (op (e1) (e2)))) -> (((op (e2) (e0)) = (e2))\/(((op (e2) (e1)) = (e2))\/(((op (e2) (e2)) = (e2))\/((op (e2) (e3)) = (e2))))) -> ((op (e2) (e0)) = (e1)) -> (~((op (e0) (e1)) = (op (e2) (e1)))) -> (((op (e0) (e2)) = (e2))\/(((op (e1) (e2)) = (e2))\/(((op (e2) (e2)) = (e2))\/((op (e3) (e2)) = (e2))))) -> (~((op (e2) (e2)) = (e2))) -> (((op (e0) (e3)) = (e3))\/(((op (e1) (e3)) = (e3))\/(((op (e2) (e3)) = (e3))\/((op (e3) (e3)) = (e3))))) -> (~((e0) = (e3))) -> (~((e1) = (e3))) -> (~((op (e3) (e2)) = (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 (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 (e3) (e3)))) -> (~((op (e0) (e3)) = (op (e2) (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)) = (e3))) -> (~((op (e1) (e1)) = (e0))) -> (~((op (e1) (e0)) = (e0))) -> (((op (e1) (e0)) = (e0))\/(((op (e1) (e1)) = (e0))\/(((op (e1) (e2)) = (e0))\/((op (e1) (e3)) = (e0))))) -> (~((e1) = (e2))) -> ((op (e0) (e2)) = (e1)) -> ((op (e0) (e3)) = (e0)) -> (~((e0) = (e2))) -> False). % 18.79/18.94 do 0 intro. intros zenon_H3e zenon_H30 zenon_H3f zenon_H235 zenon_H9e zenon_H182 zenon_H94 zenon_H1ed zenon_H74 zenon_H208 zenon_H139 zenon_H18f zenon_H1c4 zenon_H52 zenon_Ha1 zenon_H12b zenon_He8 zenon_H1a5 zenon_H1a4 zenon_H1a6 zenon_H212 zenon_H10e zenon_H13e zenon_H1cc zenon_H6a zenon_H6f zenon_H4f zenon_H2b zenon_H153 zenon_H16f zenon_H130 zenon_H160 zenon_H18c zenon_H189 zenon_H1d8 zenon_H1c7 zenon_H145 zenon_H106 zenon_H109 zenon_Haf zenon_H22a zenon_H11f zenon_Hf3 zenon_H115 zenon_H4a zenon_H210 zenon_H54 zenon_Hd8 zenon_H6d zenon_H133 zenon_H39 zenon_H22d zenon_H20b zenon_H1a7 zenon_H184 zenon_H2f zenon_H185 zenon_H165 zenon_Ha8 zenon_H1ec zenon_H204 zenon_H205 zenon_H191 zenon_H19d zenon_He7 zenon_H183 zenon_H17b zenon_H178 zenon_H179 zenon_H142 zenon_H13c zenon_H124 zenon_H168 zenon_H1fe zenon_H1ee zenon_H1e0 zenon_H1ba zenon_H1fa zenon_H1f0 zenon_H206 zenon_H233 zenon_H1cf zenon_H57 zenon_H5b zenon_H67 zenon_H45 zenon_H14f zenon_H1ac zenon_H3a zenon_H1d zenon_H128 zenon_H201 zenon_H10a zenon_H195 zenon_H1d5 zenon_Hed zenon_H17e zenon_H172 zenon_H173 zenon_H136 zenon_H9a zenon_H95 zenon_H62 zenon_He4 zenon_Hdb zenon_Hd5 zenon_Hdf zenon_Hc2 zenon_He2 zenon_H44 zenon_H71 zenon_H101 zenon_H102 zenon_H24 zenon_H23 zenon_H22 zenon_H7c zenon_H122 zenon_H1e zenon_H149. % 18.79/18.94 apply (zenon_or_s _ _ zenon_H183); [ zenon_intro zenon_H7b | zenon_intro zenon_H186 ]. % 18.79/18.94 apply (zenon_L493_); trivial. % 18.79/18.94 apply (zenon_or_s _ _ zenon_H186); [ zenon_intro zenon_H10f | zenon_intro zenon_H187 ]. % 18.79/18.94 apply (zenon_L703_); trivial. % 18.79/18.94 apply (zenon_or_s _ _ zenon_H187); [ zenon_intro zenon_H150 | zenon_intro zenon_Hcd ]. % 18.79/18.94 apply (zenon_L328_); trivial. % 18.79/18.94 apply (zenon_L428_); trivial. % 18.79/18.94 (* end of lemma zenon_L705_ *) % 18.79/18.94 assert (zenon_L706_ : (((op (e0) (e0)) = (e0))\/(((op (e1) (e0)) = (e0))\/(((op (e2) (e0)) = (e0))\/((op (e3) (e0)) = (e0))))) -> (~((op (e2) (e0)) = (e0))) -> (~((op (e1) (e0)) = (e0))) -> (~((op (e0) (e0)) = (e0))) -> ((~((op (e0) (e3)) = (e0)))\/((op (e0) (e0)) = (e3))) -> ((~((op (e1) (e1)) = (e0)))\/((op (e1) (e0)) = (e1))) -> (~((e1) = (e2))) -> ((~((op (e2) (e3)) = (e0)))\/((op (e2) (e0)) = (e3))) -> (((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))))) -> (((op (e0) (e2)) = (e3))\/(((op (e1) (e2)) = (e3))\/(((op (e2) (e2)) = (e3))\/((op (e3) (e2)) = (e3))))) -> (~((op (e3) (e1)) = (op (e3) (e2)))) -> ((~((op (e3) (e2)) = (e0)))\/((op (e3) (e0)) = (e2))) -> (~((op (e2) (e2)) = (op (e3) (e2)))) -> (((op (e3) (e2)) = (e0))\/(((op (e3) (e2)) = (e1))\/(((op (e3) (e2)) = (e2))\/((op (e3) (e2)) = (e3))))) -> (~((op (e0) (e2)) = (op (e1) (e2)))) -> (((op (e1) (e2)) = (e0))\/(((op (e1) (e2)) = (e1))\/(((op (e1) (e2)) = (e2))\/((op (e1) (e2)) = (e3))))) -> (~((e1) = (e3))) -> (~((e0) = (e3))) -> (~((op (e1) (e1)) = (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) (e3)) = (e0))\/(((op (e2) (e3)) = (e1))\/(((op (e2) (e3)) = (e2))\/((op (e2) (e3)) = (e3))))) -> (~((op (e0) (e3)) = (op (e1) (e3)))) -> (~((op (e0) (e1)) = (op (e1) (e1)))) -> (~((e0) = (e1))) -> (~((op (e0) (e2)) = (op (e2) (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) (e3)) = (e0))\/(((op (e1) (e3)) = (e1))\/(((op (e1) (e3)) = (e2))\/((op (e1) (e3)) = (e3))))) -> (~((op (e1) (e3)) = (op (e2) (e3)))) -> (~((op (e1) (e0)) = (op (e1) (e3)))) -> (~((op (e1) (e3)) = (op (e3) (e3)))) -> (~((op (e0) (e3)) = (op (e2) (e3)))) -> (((op (e0) (e3)) = (e0))\/(((op (e0) (e3)) = (e1))\/(((op (e0) (e3)) = (e2))\/((op (e0) (e3)) = (e3))))) -> (~((op (e2) (e1)) = (op (e3) (e1)))) -> (((op (e2) (e0)) = (e3))\/(((op (e2) (e1)) = (e3))\/(((op (e2) (e2)) = (e3))\/((op (e2) (e3)) = (e3))))) -> (((op (e2) (e0)) = (e1))\/(((op (e2) (e1)) = (e1))\/(((op (e2) (e2)) = (e1))\/((op (e2) (e3)) = (e1))))) -> (~((op (e2) (e3)) = (op (e3) (e3)))) -> (~((op (e3) (e3)) = (e3))) -> (((op (e3) (e3)) = (e0))\/(((op (e3) (e3)) = (e1))\/(((op (e3) (e3)) = (e2))\/((op (e3) (e3)) = (e3))))) -> (~((op (e1) (e2)) = (op (e2) (e2)))) -> (((op (e0) (e1)) = (e1))\/(((op (e1) (e1)) = (e1))\/(((op (e2) (e1)) = (e1))\/((op (e3) (e1)) = (e1))))) -> (~((op (e0) (e0)) = (op (e0) (e3)))) -> ((~((op (e2) (e2)) = (e0)))\/((op (e2) (e0)) = (e2))) -> ((~((op (e3) (e0)) = (e0)))\/((op (e3) (e0)) = (e0))) -> (((op (e0) (e0)) = (e2))\/(((op (e0) (e1)) = (e2))\/(((op (e0) (e2)) = (e2))\/((op (e0) (e3)) = (e2))))) -> (~((op (e2) (e0)) = (op (e3) (e0)))) -> (~((op (e0) (e1)) = (op (e2) (e1)))) -> ((~((op (e1) (e2)) = (e0)))\/((op (e1) (e0)) = (e2))) -> ((~((op (e1) (e3)) = (e0)))\/((op (e1) (e0)) = (e3))) -> (((op (e1) (e1)) = (e0))\/(((op (e1) (e1)) = (e1))\/(((op (e1) (e1)) = (e2))\/((op (e1) (e1)) = (e3))))) -> (~((op (e1) (e1)) = (op (e2) (e1)))) -> (~((op (e0) (e0)) = (op (e0) (e2)))) -> (((op (e0) (e2)) = (e1))\/(((op (e1) (e2)) = (e1))\/(((op (e2) (e2)) = (e1))\/((op (e3) (e2)) = (e1))))) -> (((op (e1) (e0)) = (e1))\/(((op (e1) (e1)) = (e1))\/(((op (e1) (e2)) = (e1))\/((op (e1) (e3)) = (e1))))) -> (((op (e0) (e3)) = (e3))\/(((op (e1) (e3)) = (e3))\/(((op (e2) (e3)) = (e3))\/((op (e3) (e3)) = (e3))))) -> (~((op (e3) (e1)) = (op (e3) (e3)))) -> (((op (e0) (e3)) = (e1))\/(((op (e1) (e3)) = (e1))\/(((op (e2) (e3)) = (e1))\/((op (e3) (e3)) = (e1))))) -> (~((e2) = (e3))) -> (~((op (e1) (e2)) = (op (e1) (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 (e2) (e2)) = (e2))) -> (((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) (e1)) = (op (e3) (e1)))) -> (((op (e3) (e0)) = (e3))\/(((op (e3) (e1)) = (e3))\/(((op (e3) (e2)) = (e3))\/((op (e3) (e3)) = (e3))))) -> (~((e0) = (e2))) -> (~((op (e0) (e2)) = (op (e3) (e2)))) -> (((op (e3) (e0)) = (e2))\/(((op (e3) (e1)) = (e2))\/(((op (e3) (e2)) = (e2))\/((op (e3) (e3)) = (e2))))) -> (~((op (e0) (e0)) = (op (e2) (e0)))) -> ((~((op (e2) (e1)) = (e0)))\/((op (e2) (e0)) = (e1))) -> (((op (e0) (e0)) = (e2))\/(((op (e1) (e0)) = (e2))\/(((op (e2) (e0)) = (e2))\/((op (e3) (e0)) = (e2))))) -> ((~((op (e2) (e0)) = (e0)))\/((op (e2) (e0)) = (e0))) -> (((op (e0) (e0)) = (e3))\/(((op (e1) (e0)) = (e3))\/(((op (e2) (e0)) = (e3))\/((op (e3) (e0)) = (e3))))) -> (((op (e3) (e0)) = (e0))\/(((op (e3) (e1)) = (e0))\/(((op (e3) (e2)) = (e0))\/((op (e3) (e3)) = (e0))))) -> (~((op (e2) (e1)) = (op (e2) (e3)))) -> (((op (e2) (e2)) = (e0))\/(((op (e2) (e2)) = (e1))\/(((op (e2) (e2)) = (e2))\/((op (e2) (e2)) = (e3))))) -> (((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 (e3) (e0)) = (op (e3) (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))))) -> ((~((op (e3) (e3)) = (e0)))\/((op (e3) (e0)) = (e3))) -> ((~((op (e3) (e1)) = (e0)))\/((op (e3) (e0)) = (e1))) -> (((op (e1) (e0)) = (e0))\/(((op (e1) (e1)) = (e0))\/(((op (e1) (e2)) = (e0))\/((op (e1) (e3)) = (e0))))) -> (~((op (e1) (e0)) = (op (e1) (e1)))) -> (((op (e0) (e2)) = (e0))\/(((op (e1) (e2)) = (e0))\/(((op (e2) (e2)) = (e0))\/((op (e3) (e2)) = (e0))))) -> (~((op (e0) (e1)) = (op (e0) (e3)))) -> (~((op (e1) (e1)) = (op (e1) (e3)))) -> (~((op (e2) (e0)) = (op (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) (e0)) = (op (e2) (e2)))) -> (~((op (e1) (e1)) = (op (e1) (e2)))) -> (~((op (e0) (e1)) = (op (e0) (e2)))) -> (~((op (e3) (e0)) = (op (e3) (e3)))) -> (~((op (e2) (e2)) = (op (e2) (e3)))) -> (~((op (e3) (e0)) = (op (e3) (e2)))) -> (((op (e0) (e0)) = (e0))\/(((op (e0) (e1)) = (e0))\/(((op (e0) (e2)) = (e0))\/((op (e0) (e3)) = (e0))))) -> (~((op (e1) (e0)) = (op (e3) (e0)))) -> (~((op (e2) (e0)) = (op (e2) (e1)))) -> (~((op (e1) (e0)) = (op (e2) (e0)))) -> ((~((op (e1) (e0)) = (e0)))\/((op (e1) (e0)) = (e0))) -> (~((op (e1) (e1)) = (e0))) -> (~((op (e1) (e0)) = (op (e1) (e2)))) -> (~((op (e2) (e1)) = (op (e2) (e2)))) -> ((op (e2) (e0)) = (e1)) -> ((op (e1) (e0)) = (e2)) -> (~((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)) = (e1))\/(((op (e1) (e0)) = (e1))\/(((op (e2) (e0)) = (e1))\/((op (e3) (e0)) = (e1))))) -> (((op (e0) (e1)) = (e0))\/(((op (e0) (e1)) = (e1))\/(((op (e0) (e1)) = (e2))\/((op (e0) (e1)) = (e3))))) -> (((op (e3) (e1)) = (e0))\/(((op (e3) (e1)) = (e1))\/(((op (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) (e2)) = (e0)))\/((op (e0) (e0)) = (e2))) -> ((op (e0) (e0)) = (e3)) -> ((op (e1) (e0)) = (e3)) -> (~((op (e0) (e2)) = (e0))) -> (~((op (e0) (e1)) = (e0))) -> False). % 18.79/18.94 do 0 intro. intros zenon_H3e zenon_H30 zenon_H23 zenon_H3f zenon_H204 zenon_H205 zenon_H7c zenon_H94 zenon_H2f zenon_H1a5 zenon_H1a6 zenon_H1a4 zenon_H1a7 zenon_H18f zenon_H191 zenon_H195 zenon_H19d zenon_H95 zenon_H9a zenon_H10a zenon_H18c zenon_H115 zenon_H11f zenon_H1d zenon_H10e zenon_Ha1 zenon_Ha8 zenon_He8 zenon_Hc2 zenon_Hdf zenon_Hdb zenon_Hd8 zenon_Hd5 zenon_He2 zenon_He4 zenon_Haf zenon_He7 zenon_H106 zenon_Hf3 zenon_H102 zenon_H101 zenon_H2b zenon_H109 zenon_H189 zenon_H185 zenon_H184 zenon_H183 zenon_H17b zenon_H17e zenon_H178 zenon_H179 zenon_H142 zenon_H13e zenon_H13c zenon_H139 zenon_H128 zenon_H136 zenon_H130 zenon_H133 zenon_H12b zenon_H124 zenon_H145 zenon_H172 zenon_H173 zenon_H16f zenon_H168 zenon_H160 zenon_H165 zenon_H149 zenon_H14f zenon_H153 zenon_H39 zenon_H182 zenon_H1fe zenon_H1ee zenon_H1e0 zenon_H1ac zenon_H1c7 zenon_H1c4 zenon_H1cc zenon_H1ba zenon_H1cf zenon_H1d8 zenon_H1d5 zenon_H1ec zenon_H1ed zenon_H22 zenon_H45 zenon_H6a zenon_H54 zenon_H57 zenon_H5b zenon_H62 zenon_H67 zenon_H52 zenon_H4f zenon_H4a zenon_H71 zenon_H6d zenon_H6f zenon_H74 zenon_H1fa zenon_H1f0 zenon_H201 zenon_H206 zenon_H24 zenon_H24a zenon_H24b zenon_Hed zenon_H86 zenon_H208 zenon_H245 zenon_H235 zenon_H212 zenon_H22a zenon_H210 zenon_H22d zenon_H233 zenon_H3a zenon_H9e zenon_H75 zenon_H20b. % 18.79/18.94 apply (zenon_or_s _ _ zenon_H185); [ zenon_intro zenon_H81 | zenon_intro zenon_Hee ]. % 18.79/18.94 apply (zenon_or_s _ _ zenon_H184); [ zenon_intro zenon_H40 | zenon_intro zenon_H44 ]. % 18.79/18.94 apply (zenon_L7_); trivial. % 18.79/18.94 apply (zenon_or_s _ _ zenon_H1ed); [ zenon_intro zenon_H1ad | zenon_intro zenon_Hac ]. % 18.79/18.94 apply (zenon_or_s _ _ zenon_H1a7); [ zenon_intro zenon_H18b | zenon_intro zenon_H148 ]. % 18.79/18.94 apply (zenon_or_s _ _ zenon_H74); [ zenon_intro zenon_H42 | zenon_intro zenon_H77 ]. % 18.79/18.94 exact (zenon_H3f zenon_H42). % 18.79/18.94 apply (zenon_or_s _ _ zenon_H77); [ zenon_intro zenon_H49 | zenon_intro zenon_H78 ]. % 18.79/18.94 exact (zenon_H20b zenon_H49). % 18.79/18.94 apply (zenon_or_s _ _ zenon_H78); [ zenon_intro zenon_H48 | zenon_intro zenon_H1e ]. % 18.79/18.94 exact (zenon_H75 zenon_H48). % 18.79/18.94 apply (zenon_or_s _ _ zenon_H22d); [ zenon_intro zenon_H7a | zenon_intro zenon_H22e ]. % 18.79/18.94 apply (zenon_L333_); trivial. % 18.79/18.94 apply (zenon_or_s _ _ zenon_H22e); [ zenon_intro zenon_Ha0 | zenon_intro zenon_H22f ]. % 18.79/18.94 apply (zenon_L702_); trivial. % 18.79/18.94 apply (zenon_or_s _ _ zenon_H22f); [ zenon_intro zenon_H122 | zenon_intro zenon_Hc3 ]. % 18.79/18.94 apply (zenon_L705_); trivial. % 18.79/18.94 apply (zenon_L427_); trivial. % 18.79/18.94 apply (zenon_L100_); trivial. % 18.79/18.94 apply (zenon_L41_); trivial. % 18.79/18.94 apply (zenon_L58_); trivial. % 18.79/18.94 (* end of lemma zenon_L706_ *) % 18.79/18.94 assert (zenon_L707_ : (((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 (e3) (e1)) = (e0))\/(((op (e3) (e1)) = (e1))\/(((op (e3) (e1)) = (e2))\/((op (e3) (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 (e2) (e1)) = (op (e2) (e2)))) -> (~((op (e0) (e2)) = (op (e0) (e3)))) -> (~((op (e1) (e2)) = (e0))) -> ((~((op (e0) (e3)) = (e0)))\/((op (e0) (e0)) = (e3))) -> ((~((op (e1) (e1)) = (e0)))\/((op (e1) (e0)) = (e1))) -> ((~((op (e2) (e3)) = (e0)))\/((op (e2) (e0)) = (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)) = (e0)))\/((op (e3) (e0)) = (e2))) -> (~((op (e2) (e2)) = (op (e3) (e2)))) -> (((op (e3) (e2)) = (e0))\/(((op (e3) (e2)) = (e1))\/(((op (e3) (e2)) = (e2))\/((op (e3) (e2)) = (e3))))) -> (~((op (e0) (e2)) = (op (e1) (e2)))) -> (((op (e1) (e2)) = (e0))\/(((op (e1) (e2)) = (e1))\/(((op (e1) (e2)) = (e2))\/((op (e1) (e2)) = (e3))))) -> (~((op (e1) (e2)) = (op (e3) (e2)))) -> (((op (e2) (e3)) = (e0))\/(((op (e2) (e3)) = (e1))\/(((op (e2) (e3)) = (e2))\/((op (e2) (e3)) = (e3))))) -> (~((op (e0) (e3)) = (op (e1) (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) (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) (e0)) = (op (e1) (e3)))) -> (~((op (e1) (e3)) = (op (e3) (e3)))) -> (~((op (e0) (e3)) = (op (e2) (e3)))) -> (((op (e0) (e3)) = (e0))\/(((op (e0) (e3)) = (e1))\/(((op (e0) (e3)) = (e2))\/((op (e0) (e3)) = (e3))))) -> (~((op (e2) (e1)) = (op (e3) (e1)))) -> (((op (e2) (e0)) = (e3))\/(((op (e2) (e1)) = (e3))\/(((op (e2) (e2)) = (e3))\/((op (e2) (e3)) = (e3))))) -> (((op (e2) (e0)) = (e1))\/(((op (e2) (e1)) = (e1))\/(((op (e2) (e2)) = (e1))\/((op (e2) (e3)) = (e1))))) -> (~((op (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) (e2)) = (op (e2) (e2)))) -> (((op (e0) (e1)) = (e1))\/(((op (e1) (e1)) = (e1))\/(((op (e2) (e1)) = (e1))\/((op (e3) (e1)) = (e1))))) -> (~((op (e0) (e0)) = (op (e0) (e3)))) -> ((~((op (e2) (e2)) = (e0)))\/((op (e2) (e0)) = (e2))) -> ((~((op (e3) (e0)) = (e0)))\/((op (e3) (e0)) = (e0))) -> (((op (e0) (e0)) = (e2))\/(((op (e0) (e1)) = (e2))\/(((op (e0) (e2)) = (e2))\/((op (e0) (e3)) = (e2))))) -> (~((op (e2) (e0)) = (op (e3) (e0)))) -> (~((op (e0) (e1)) = (op (e2) (e1)))) -> ((~((op (e1) (e2)) = (e0)))\/((op (e1) (e0)) = (e2))) -> ((~((op (e1) (e3)) = (e0)))\/((op (e1) (e0)) = (e3))) -> (((op (e1) (e1)) = (e0))\/(((op (e1) (e1)) = (e1))\/(((op (e1) (e1)) = (e2))\/((op (e1) (e1)) = (e3))))) -> (~((op (e1) (e1)) = (op (e2) (e1)))) -> (~((op (e0) (e0)) = (op (e0) (e2)))) -> (((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 (e3) (e1)) = (op (e3) (e3)))) -> (((op (e0) (e3)) = (e1))\/(((op (e1) (e3)) = (e1))\/(((op (e2) (e3)) = (e1))\/((op (e3) (e3)) = (e1))))) -> (~((op (e1) (e2)) = (op (e1) (e3)))) -> (((op (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 (e2) (e2)) = (e2))) -> (((op (e0) (e0)) = (e3))\/(((op (e0) (e1)) = (e3))\/(((op (e0) (e2)) = (e3))\/((op (e0) (e3)) = (e3))))) -> (~((op (e1) (e1)) = (op (e3) (e1)))) -> (((op (e3) (e0)) = (e3))\/(((op (e3) (e1)) = (e3))\/(((op (e3) (e2)) = (e3))\/((op (e3) (e3)) = (e3))))) -> (~((op (e0) (e2)) = (op (e3) (e2)))) -> (((op (e3) (e0)) = (e2))\/(((op (e3) (e1)) = (e2))\/(((op (e3) (e2)) = (e2))\/((op (e3) (e3)) = (e2))))) -> (~((op (e0) (e0)) = (op (e2) (e0)))) -> ((~((op (e2) (e1)) = (e0)))\/((op (e2) (e0)) = (e1))) -> (((op (e0) (e0)) = (e2))\/(((op (e1) (e0)) = (e2))\/(((op (e2) (e0)) = (e2))\/((op (e3) (e0)) = (e2))))) -> ((~((op (e2) (e0)) = (e0)))\/((op (e2) (e0)) = (e0))) -> (((op (e0) (e0)) = (e3))\/(((op (e1) (e0)) = (e3))\/(((op (e2) (e0)) = (e3))\/((op (e3) (e0)) = (e3))))) -> (((op (e3) (e0)) = (e0))\/(((op (e3) (e1)) = (e0))\/(((op (e3) (e2)) = (e0))\/((op (e3) (e3)) = (e0))))) -> (~((op (e2) (e1)) = (op (e2) (e3)))) -> (((op (e2) (e2)) = (e0))\/(((op (e2) (e2)) = (e1))\/(((op (e2) (e2)) = (e2))\/((op (e2) (e2)) = (e3))))) -> (((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 (e3) (e0)) = (op (e3) (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))))) -> ((~((op (e3) (e3)) = (e0)))\/((op (e3) (e0)) = (e3))) -> ((~((op (e3) (e1)) = (e0)))\/((op (e3) (e0)) = (e1))) -> (~((op (e0) (e0)) = (e0))) -> (((op (e1) (e0)) = (e0))\/(((op (e1) (e1)) = (e0))\/(((op (e1) (e2)) = (e0))\/((op (e1) (e3)) = (e0))))) -> (~((op (e1) (e0)) = (op (e1) (e1)))) -> (~((op (e0) (e1)) = (op (e0) (e3)))) -> (~((op (e1) (e1)) = (op (e1) (e3)))) -> (~((op (e2) (e0)) = (op (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) (e0)) = (op (e2) (e2)))) -> (~((op (e1) (e1)) = (op (e1) (e2)))) -> (~((op (e0) (e1)) = (op (e0) (e2)))) -> (~((op (e3) (e0)) = (op (e3) (e3)))) -> (~((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)) = (e0))\/(((op (e0) (e1)) = (e0))\/(((op (e0) (e2)) = (e0))\/((op (e0) (e3)) = (e0))))) -> (~((op (e1) (e0)) = (op (e3) (e0)))) -> (~((op (e2) (e0)) = (op (e2) (e1)))) -> (~((op (e1) (e0)) = (op (e2) (e0)))) -> ((~((op (e1) (e0)) = (e0)))\/((op (e1) (e0)) = (e0))) -> ((~((op (e0) (e2)) = (e0)))\/((op (e0) (e0)) = (e2))) -> (~((e1) = (e2))) -> (((op (e1) (e0)) = (e3))\/(((op (e1) (e1)) = (e3))\/(((op (e1) (e2)) = (e3))\/((op (e1) (e3)) = (e3))))) -> (~((e0) = (e3))) -> (~((e2) = (e3))) -> (~((e1) = (e3))) -> (~((op (e0) (e1)) = (op (e1) (e1)))) -> ((op (e3) (e0)) = (e1)) -> ((op (e0) (e0)) = (e3)) -> (((op (e1) (e0)) = (e2))\/(((op (e1) (e1)) = (e2))\/(((op (e1) (e2)) = (e2))\/((op (e1) (e3)) = (e2))))) -> (~((op (e1) (e1)) = (e1))) -> (~((e0) = (e1))) -> (((op (e1) (e0)) = (e1))\/(((op (e1) (e1)) = (e1))\/(((op (e1) (e2)) = (e1))\/((op (e1) (e3)) = (e1))))) -> (~((op (e3) (e1)) = (op (e3) (e2)))) -> (~((op (e2) (e2)) = (op (e2) (e3)))) -> (~((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 (e2) (e2)) = (e0))) -> (~((op (e2) (e1)) = (e0))) -> (~((op (e2) (e0)) = (e0))) -> (((op (e2) (e0)) = (e0))\/(((op (e2) (e1)) = (e0))\/(((op (e2) (e2)) = (e0))\/((op (e2) (e3)) = (e0))))) -> (~((op (e1) (e1)) = (e0))) -> (~((op (e0) (e1)) = (e0))) -> (((op (e0) (e1)) = (e0))\/(((op (e1) (e1)) = (e0))\/(((op (e2) (e1)) = (e0))\/((op (e3) (e1)) = (e0))))) -> ((op (e0) (e3)) = (e0)) -> (~((e0) = (e2))) -> False). % 18.79/18.94 do 0 intro. intros zenon_H22d zenon_H235 zenon_H22a zenon_H210 zenon_H212 zenon_H24b zenon_H208 zenon_H25 zenon_H204 zenon_H205 zenon_H94 zenon_H1a5 zenon_H1a6 zenon_H1a7 zenon_H18f zenon_H191 zenon_H195 zenon_H19d zenon_H115 zenon_H11f zenon_H1d zenon_Ha8 zenon_He8 zenon_Hc2 zenon_Hdf zenon_Hdb zenon_Hd8 zenon_Hd5 zenon_He2 zenon_He4 zenon_Haf zenon_He7 zenon_H106 zenon_Hf3 zenon_H102 zenon_H101 zenon_H2b zenon_H109 zenon_H189 zenon_H185 zenon_H184 zenon_H183 zenon_H17b zenon_H17e zenon_H178 zenon_H179 zenon_H142 zenon_H13e zenon_H13c zenon_H139 zenon_H136 zenon_H130 zenon_H133 zenon_H124 zenon_H145 zenon_H172 zenon_H173 zenon_H168 zenon_H160 zenon_H165 zenon_H14f zenon_H153 zenon_H39 zenon_H182 zenon_H1fe zenon_H1ee zenon_H1e0 zenon_H1ac zenon_H1c7 zenon_H1c4 zenon_H1cc zenon_H1ba zenon_H1cf zenon_H1d8 zenon_H1d5 zenon_H1ec zenon_H1ed zenon_H3f zenon_H22 zenon_H45 zenon_H54 zenon_H57 zenon_H5b zenon_H62 zenon_H67 zenon_H52 zenon_H4f zenon_H4a zenon_H71 zenon_H6f zenon_H3e zenon_H74 zenon_H1fa zenon_H1f0 zenon_H201 zenon_H206 zenon_H233 zenon_H7c zenon_H16f zenon_H9a zenon_H12b zenon_H95 zenon_H10e zenon_Hac zenon_H3a zenon_H18c zenon_H10a zenon_Ha1 zenon_H128 zenon_H1a4 zenon_H6d zenon_H24a zenon_H27 zenon_H6a zenon_H81 zenon_H31 zenon_H30 zenon_H2f zenon_H24 zenon_H20b zenon_H245 zenon_H1e zenon_H149. % 18.79/18.94 apply (zenon_or_s _ _ zenon_H183); [ zenon_intro zenon_H7b | zenon_intro zenon_H186 ]. % 18.79/18.94 apply (zenon_L672_); trivial. % 18.79/18.94 apply (zenon_or_s _ _ zenon_H186); [ zenon_intro zenon_H10f | zenon_intro zenon_H187 ]. % 18.79/18.94 apply (zenon_or_s _ _ zenon_H245); [ zenon_intro zenon_H49 | zenon_intro zenon_H246 ]. % 18.79/18.94 exact (zenon_H20b zenon_H49). % 18.79/18.94 apply (zenon_or_s _ _ zenon_H246); [ zenon_intro zenon_H29 | zenon_intro zenon_H247 ]. % 18.79/18.94 exact (zenon_H24 zenon_H29). % 18.79/18.94 apply (zenon_or_s _ _ zenon_H247); [ zenon_intro zenon_H36 | zenon_intro zenon_H1b1 ]. % 18.79/18.94 exact (zenon_H31 zenon_H36). % 18.79/18.94 apply (zenon_or_s _ _ zenon_H128); [ zenon_intro zenon_H9d | zenon_intro zenon_H129 ]. % 18.79/18.94 apply (zenon_L262_); trivial. % 18.79/18.94 apply (zenon_or_s _ _ zenon_H129); [ zenon_intro zenon_H10d | zenon_intro zenon_H12a ]. % 18.79/18.94 exact (zenon_H10a zenon_H10d). % 18.79/18.94 apply (zenon_or_s _ _ zenon_H12a); [ zenon_intro zenon_Hf0 | zenon_intro zenon_Hd6 ]. % 18.79/18.94 apply (zenon_or_s _ _ zenon_H18c); [ zenon_intro zenon_H86 | zenon_intro zenon_H18d ]. % 18.79/18.94 apply (zenon_L257_); trivial. % 18.79/18.94 apply (zenon_or_s _ _ zenon_H18d); [ zenon_intro zenon_H110 | zenon_intro zenon_H18e ]. % 18.79/18.94 apply (zenon_L67_); trivial. % 18.79/18.94 apply (zenon_or_s _ _ zenon_H18e); [ zenon_intro zenon_H113 | zenon_intro zenon_Hd7 ]. % 18.79/18.94 apply (zenon_L68_); trivial. % 18.79/18.94 apply (zenon_L673_); trivial. % 18.79/18.94 apply (zenon_or_s _ _ zenon_H18c); [ zenon_intro zenon_H86 | zenon_intro zenon_H18d ]. % 18.79/18.94 apply (zenon_L241_); trivial. % 18.79/18.94 apply (zenon_or_s _ _ zenon_H18d); [ zenon_intro zenon_H110 | zenon_intro zenon_H18e ]. % 18.79/18.94 apply (zenon_L67_); trivial. % 18.79/18.94 apply (zenon_or_s _ _ zenon_H18e); [ zenon_intro zenon_H113 | zenon_intro zenon_Hd7 ]. % 18.79/18.94 apply (zenon_L675_); trivial. % 18.79/18.94 apply (zenon_L101_); trivial. % 18.79/18.94 apply (zenon_or_s _ _ zenon_H187); [ zenon_intro zenon_H150 | zenon_intro zenon_Hcd ]. % 18.79/18.94 apply (zenon_or_s _ _ zenon_H245); [ zenon_intro zenon_H49 | zenon_intro zenon_H246 ]. % 18.79/18.94 exact (zenon_H20b zenon_H49). % 18.79/18.94 apply (zenon_or_s _ _ zenon_H246); [ zenon_intro zenon_H29 | zenon_intro zenon_H247 ]. % 18.79/18.94 exact (zenon_H24 zenon_H29). % 18.79/18.94 apply (zenon_or_s _ _ zenon_H247); [ zenon_intro zenon_H36 | zenon_intro zenon_H1b1 ]. % 18.79/18.94 exact (zenon_H31 zenon_H36). % 18.79/18.94 apply (zenon_or_s _ _ zenon_H2f); [ zenon_intro zenon_H34 | zenon_intro zenon_H33 ]. % 18.79/18.94 exact (zenon_H30 zenon_H34). % 18.79/18.94 apply (zenon_or_s _ _ zenon_H33); [ zenon_intro zenon_H36 | zenon_intro zenon_H35 ]. % 18.79/18.94 exact (zenon_H31 zenon_H36). % 18.79/18.94 apply (zenon_or_s _ _ zenon_H35); [ zenon_intro zenon_H2c | zenon_intro zenon_H37 ]. % 18.79/18.94 exact (zenon_H81 zenon_H2c). % 18.79/18.94 apply (zenon_L680_); trivial. % 18.79/18.94 apply (zenon_L428_); trivial. % 18.79/18.94 (* end of lemma zenon_L707_ *) % 18.79/18.94 assert (zenon_L708_ : ((~((op (e2) (e2)) = (e0)))\/((op (e2) (e0)) = (e2))) -> (~((e1) = (e2))) -> (((op (e0) (e0)) = (e0))\/(((op (e0) (e1)) = (e0))\/(((op (e0) (e2)) = (e0))\/((op (e0) (e3)) = (e0))))) -> (~((op (e0) (e2)) = (op (e0) (e3)))) -> (~((op (e1) (e2)) = (e0))) -> (((op (e0) (e2)) = (e0))\/(((op (e1) (e2)) = (e0))\/(((op (e2) (e2)) = (e0))\/((op (e3) (e2)) = (e0))))) -> (~((op (e0) (e2)) = (e0))) -> (~((op (e0) (e1)) = (e0))) -> (~((op (e0) (e0)) = (e0))) -> ((op (e0) (e0)) = (e3)) -> ((op (e2) (e0)) = (e1)) -> ((~((op (e3) (e2)) = (e0)))\/((op (e3) (e0)) = (e2))) -> False). % 18.79/18.94 do 0 intro. intros zenon_H185 zenon_H7c zenon_H74 zenon_H208 zenon_H25 zenon_H6a zenon_H75 zenon_H20b zenon_H3f zenon_H3a zenon_Hed zenon_H1a7. % 18.79/18.94 apply (zenon_or_s _ _ zenon_H185); [ zenon_intro zenon_H81 | zenon_intro zenon_Hee ]. % 18.79/18.94 apply (zenon_or_s _ _ zenon_H1a7); [ zenon_intro zenon_H18b | zenon_intro zenon_H148 ]. % 18.79/18.94 apply (zenon_L694_); trivial. % 18.79/18.94 apply (zenon_L423_); trivial. % 18.79/18.94 apply (zenon_L58_); trivial. % 18.79/18.94 (* end of lemma zenon_L708_ *) % 18.79/18.94 assert (zenon_L709_ : (((op (e0) (e0)) = (e3))\/(((op (e0) (e1)) = (e3))\/(((op (e0) (e2)) = (e3))\/((op (e0) (e3)) = (e3))))) -> ((op (e3) (e0)) = (e1)) -> ((op (e1) (e0)) = (e2)) -> (~((e2) = (e3))) -> ((op (e0) (e1)) = (e2)) -> (~((e1) = (e3))) -> ((op (e0) (e2)) = (e1)) -> ((op (e0) (e3)) = (e0)) -> (~((e0) = (e3))) -> False). % 18.79/18.94 do 0 intro. intros zenon_H168 zenon_Hac zenon_H86 zenon_H12b zenon_H10f zenon_H95 zenon_H122 zenon_H1e zenon_H9a. % 18.79/18.94 apply (zenon_or_s _ _ zenon_H168); [ zenon_intro zenon_H3a | zenon_intro zenon_H169 ]. % 18.79/18.94 apply (zenon_L241_); trivial. % 18.79/18.94 apply (zenon_or_s _ _ zenon_H169); [ zenon_intro zenon_H99 | zenon_intro zenon_H16a ]. % 18.79/18.94 apply (zenon_L175_); trivial. % 18.79/18.94 apply (zenon_or_s _ _ zenon_H16a); [ zenon_intro zenon_Ha9 | zenon_intro zenon_He3 ]. % 18.79/18.94 apply (zenon_L77_); trivial. % 18.79/18.94 apply (zenon_L515_); trivial. % 18.79/18.94 (* end of lemma zenon_L709_ *) % 18.79/18.94 assert (zenon_L710_ : (((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 (e2) (e1)) = (e0))) -> (((op (e1) (e0)) = (e1))\/(((op (e1) (e1)) = (e1))\/(((op (e1) (e2)) = (e1))\/((op (e1) (e3)) = (e1))))) -> (~((e0) = (e1))) -> (~((op (e1) (e1)) = (e1))) -> (~((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)) = (e0)) -> ((op (e0) (e2)) = (e1)) -> ((op (e3) (e0)) = (e1)) -> (((op (e0) (e0)) = (e3))\/(((op (e0) (e1)) = (e3))\/(((op (e0) (e2)) = (e3))\/((op (e0) (e3)) = (e3))))) -> (~((op (e0) (e1)) = (op (e1) (e1)))) -> (~((e1) = (e3))) -> (~((e2) = (e3))) -> ((op (e0) (e1)) = (e2)) -> ((op (e1) (e0)) = (e0)) -> (~((e0) = (e3))) -> (((op (e1) (e0)) = (e3))\/(((op (e1) (e1)) = (e3))\/(((op (e1) (e2)) = (e3))\/((op (e1) (e3)) = (e3))))) -> (~((e1) = (e2))) -> False). % 18.79/18.94 do 0 intro. intros zenon_H245 zenon_H20b zenon_H24 zenon_H31 zenon_H128 zenon_Ha1 zenon_H10a zenon_H195 zenon_H18c zenon_H1e zenon_H122 zenon_Hac zenon_H168 zenon_H10e zenon_H95 zenon_H12b zenon_H10f zenon_H27 zenon_H9a zenon_H16f zenon_H7c. % 18.79/18.94 apply (zenon_or_s _ _ zenon_H245); [ zenon_intro zenon_H49 | zenon_intro zenon_H246 ]. % 18.79/18.94 exact (zenon_H20b zenon_H49). % 18.79/18.94 apply (zenon_or_s _ _ zenon_H246); [ zenon_intro zenon_H29 | zenon_intro zenon_H247 ]. % 18.79/18.94 exact (zenon_H24 zenon_H29). % 18.79/18.94 apply (zenon_or_s _ _ zenon_H247); [ zenon_intro zenon_H36 | zenon_intro zenon_H1b1 ]. % 18.79/18.94 exact (zenon_H31 zenon_H36). % 18.79/18.94 apply (zenon_or_s _ _ zenon_H128); [ zenon_intro zenon_H9d | zenon_intro zenon_H129 ]. % 18.79/18.94 apply (zenon_L262_); trivial. % 18.79/18.94 apply (zenon_or_s _ _ zenon_H129); [ zenon_intro zenon_H10d | zenon_intro zenon_H12a ]. % 18.79/18.94 exact (zenon_H10a zenon_H10d). % 18.79/18.94 apply (zenon_or_s _ _ zenon_H12a); [ zenon_intro zenon_Hf0 | zenon_intro zenon_Hd6 ]. % 18.79/18.94 apply (zenon_L530_); trivial. % 18.79/18.94 apply (zenon_or_s _ _ zenon_H18c); [ zenon_intro zenon_H86 | zenon_intro zenon_H18d ]. % 18.79/18.94 apply (zenon_L709_); trivial. % 18.79/18.94 apply (zenon_or_s _ _ zenon_H18d); [ zenon_intro zenon_H110 | zenon_intro zenon_H18e ]. % 18.79/18.94 apply (zenon_L67_); trivial. % 18.79/18.94 apply (zenon_or_s _ _ zenon_H18e); [ zenon_intro zenon_H113 | zenon_intro zenon_Hd7 ]. % 18.79/18.94 apply (zenon_L675_); trivial. % 18.79/18.94 apply (zenon_L101_); trivial. % 18.79/18.94 (* end of lemma zenon_L710_ *) % 18.79/18.94 assert (zenon_L711_ : (~((op (e2) (e1)) = (op (e2) (e2)))) -> (~((op (e1) (e0)) = (op (e1) (e2)))) -> (((op (e0) (e0)) = (e0))\/(((op (e0) (e1)) = (e0))\/(((op (e0) (e2)) = (e0))\/((op (e0) (e3)) = (e0))))) -> (((op (e1) (e0)) = (e0))\/(((op (e1) (e1)) = (e0))\/(((op (e1) (e2)) = (e0))\/((op (e1) (e3)) = (e0))))) -> (~((op (e0) (e0)) = (e0))) -> (((op (e0) (e0)) = (e1))\/(((op (e0) (e1)) = (e1))\/(((op (e0) (e2)) = (e1))\/((op (e0) (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 (e0) (e1)) = (e0))\/(((op (e0) (e1)) = (e1))\/(((op (e0) (e1)) = (e2))\/((op (e0) (e1)) = (e3))))) -> (~((op (e0) (e2)) = (op (e0) (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) (e3)) = (e0)))\/((op (e0) (e0)) = (e3))) -> ((~((op (e1) (e1)) = (e0)))\/((op (e1) (e0)) = (e1))) -> ((~((op (e2) (e3)) = (e0)))\/((op (e2) (e0)) = (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) (e1)) = (op (e3) (e2)))) -> ((~((op (e3) (e2)) = (e0)))\/((op (e3) (e0)) = (e2))) -> (~((op (e2) (e2)) = (op (e3) (e2)))) -> (((op (e3) (e2)) = (e0))\/(((op (e3) (e2)) = (e1))\/(((op (e3) (e2)) = (e2))\/((op (e3) (e2)) = (e3))))) -> (((op (e1) (e2)) = (e0))\/(((op (e1) (e2)) = (e1))\/(((op (e1) (e2)) = (e2))\/((op (e1) (e2)) = (e3))))) -> (~((op (e1) (e2)) = (op (e3) (e2)))) -> (((op (e2) (e3)) = (e0))\/(((op (e2) (e3)) = (e1))\/(((op (e2) (e3)) = (e2))\/((op (e2) (e3)) = (e3))))) -> (~((op (e0) (e3)) = (op (e1) (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) (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) (e0)) = (op (e1) (e3)))) -> (~((op (e1) (e3)) = (op (e3) (e3)))) -> (~((op (e0) (e3)) = (op (e2) (e3)))) -> (((op (e0) (e3)) = (e0))\/(((op (e0) (e3)) = (e1))\/(((op (e0) (e3)) = (e2))\/((op (e0) (e3)) = (e3))))) -> (~((op (e2) (e1)) = (op (e3) (e1)))) -> (((op (e2) (e0)) = (e3))\/(((op (e2) (e1)) = (e3))\/(((op (e2) (e2)) = (e3))\/((op (e2) (e3)) = (e3))))) -> (((op (e2) (e0)) = (e1))\/(((op (e2) (e1)) = (e1))\/(((op (e2) (e2)) = (e1))\/((op (e2) (e3)) = (e1))))) -> (~((op (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) (e2)) = (op (e2) (e2)))) -> (((op (e0) (e1)) = (e1))\/(((op (e1) (e1)) = (e1))\/(((op (e2) (e1)) = (e1))\/((op (e3) (e1)) = (e1))))) -> (~((op (e0) (e0)) = (op (e0) (e3)))) -> ((~((op (e2) (e2)) = (e0)))\/((op (e2) (e0)) = (e2))) -> ((~((op (e3) (e0)) = (e0)))\/((op (e3) (e0)) = (e0))) -> (((op (e0) (e0)) = (e2))\/(((op (e0) (e1)) = (e2))\/(((op (e0) (e2)) = (e2))\/((op (e0) (e3)) = (e2))))) -> (~((op (e2) (e0)) = (op (e3) (e0)))) -> (~((op (e0) (e1)) = (op (e2) (e1)))) -> ((~((op (e1) (e2)) = (e0)))\/((op (e1) (e0)) = (e2))) -> ((~((op (e1) (e3)) = (e0)))\/((op (e1) (e0)) = (e3))) -> (((op (e1) (e1)) = (e0))\/(((op (e1) (e1)) = (e1))\/(((op (e1) (e1)) = (e2))\/((op (e1) (e1)) = (e3))))) -> (~((op (e1) (e1)) = (op (e2) (e1)))) -> (~((op (e0) (e0)) = (op (e0) (e2)))) -> (((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 (e3) (e1)) = (op (e3) (e3)))) -> (((op (e0) (e3)) = (e1))\/(((op (e1) (e3)) = (e1))\/(((op (e2) (e3)) = (e1))\/((op (e3) (e3)) = (e1))))) -> (~((op (e1) (e2)) = (op (e1) (e3)))) -> (((op (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 (e2) (e2)) = (e2))) -> (~((op (e1) (e1)) = (op (e3) (e1)))) -> (((op (e3) (e0)) = (e3))\/(((op (e3) (e1)) = (e3))\/(((op (e3) (e2)) = (e3))\/((op (e3) (e3)) = (e3))))) -> (~((op (e0) (e2)) = (op (e3) (e2)))) -> (((op (e3) (e0)) = (e2))\/(((op (e3) (e1)) = (e2))\/(((op (e3) (e2)) = (e2))\/((op (e3) (e3)) = (e2))))) -> (~((op (e0) (e0)) = (op (e2) (e0)))) -> ((~((op (e2) (e1)) = (e0)))\/((op (e2) (e0)) = (e1))) -> (((op (e0) (e0)) = (e2))\/(((op (e1) (e0)) = (e2))\/(((op (e2) (e0)) = (e2))\/((op (e3) (e0)) = (e2))))) -> ((~((op (e2) (e0)) = (e0)))\/((op (e2) (e0)) = (e0))) -> (((op (e0) (e0)) = (e3))\/(((op (e1) (e0)) = (e3))\/(((op (e2) (e0)) = (e3))\/((op (e3) (e0)) = (e3))))) -> (((op (e3) (e0)) = (e0))\/(((op (e3) (e1)) = (e0))\/(((op (e3) (e2)) = (e0))\/((op (e3) (e3)) = (e0))))) -> (~((op (e2) (e1)) = (op (e2) (e3)))) -> (((op (e2) (e2)) = (e0))\/(((op (e2) (e2)) = (e1))\/(((op (e2) (e2)) = (e2))\/((op (e2) (e2)) = (e3))))) -> (((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 (e3) (e0)) = (op (e3) (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))))) -> ((~((op (e3) (e3)) = (e0)))\/((op (e3) (e0)) = (e3))) -> ((~((op (e3) (e1)) = (e0)))\/((op (e3) (e0)) = (e1))) -> (~((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 (e0) (e3)))) -> (~((op (e1) (e1)) = (op (e1) (e3)))) -> (~((op (e2) (e0)) = (op (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) (e0)) = (op (e2) (e2)))) -> (~((op (e1) (e1)) = (op (e1) (e2)))) -> (~((op (e0) (e1)) = (op (e0) (e2)))) -> (~((op (e3) (e0)) = (op (e3) (e3)))) -> (~((op (e2) (e2)) = (op (e2) (e3)))) -> (~((op (e3) (e0)) = (op (e3) (e2)))) -> (((op (e0) (e0)) = (e0))\/(((op (e1) (e0)) = (e0))\/(((op (e2) (e0)) = (e0))\/((op (e3) (e0)) = (e0))))) -> (~((op (e1) (e0)) = (op (e3) (e0)))) -> (~((op (e2) (e0)) = (op (e2) (e1)))) -> (~((op (e1) (e0)) = (op (e2) (e0)))) -> ((~((op (e1) (e0)) = (e0)))\/((op (e1) (e0)) = (e0))) -> ((~((op (e0) (e2)) = (e0)))\/((op (e0) (e0)) = (e2))) -> (((op (e1) (e0)) = (e3))\/(((op (e1) (e1)) = (e3))\/(((op (e1) (e2)) = (e3))\/((op (e1) (e3)) = (e3))))) -> (~((e0) = (e3))) -> ((op (e1) (e0)) = (e0)) -> (~((e2) = (e3))) -> (~((e1) = (e3))) -> (~((op (e0) (e1)) = (op (e1) (e1)))) -> (((op (e0) (e0)) = (e3))\/(((op (e0) (e1)) = (e3))\/(((op (e0) (e2)) = (e3))\/((op (e0) (e3)) = (e3))))) -> ((op (e3) (e0)) = (e1)) -> (((op (e1) (e0)) = (e2))\/(((op (e1) (e1)) = (e2))\/(((op (e1) (e2)) = (e2))\/((op (e1) (e3)) = (e2))))) -> (~((op (e0) (e2)) = (op (e1) (e2)))) -> (~((op (e1) (e1)) = (e1))) -> (~((e0) = (e1))) -> (((op (e1) (e0)) = (e1))\/(((op (e1) (e1)) = (e1))\/(((op (e1) (e2)) = (e1))\/((op (e1) (e3)) = (e1))))) -> (~((op (e2) (e1)) = (e0))) -> (~((op (e1) (e1)) = (e0))) -> (~((op (e0) (e1)) = (e0))) -> (((op (e0) (e1)) = (e0))\/(((op (e1) (e1)) = (e0))\/(((op (e2) (e1)) = (e0))\/((op (e3) (e1)) = (e0))))) -> (~((e1) = (e2))) -> ((op (e0) (e2)) = (e1)) -> ((op (e0) (e3)) = (e0)) -> (~((e0) = (e2))) -> False). % 18.79/18.94 do 0 intro. intros zenon_H24b zenon_H24a zenon_H74 zenon_H22 zenon_H3f zenon_H22d zenon_H210 zenon_H22a zenon_H212 zenon_H208 zenon_H2f zenon_H235 zenon_H204 zenon_H205 zenon_H94 zenon_H1a5 zenon_H1a6 zenon_H1a4 zenon_H1a7 zenon_H18f zenon_H191 zenon_H19d zenon_H115 zenon_H11f zenon_H1d zenon_Ha8 zenon_He8 zenon_Hc2 zenon_Hdf zenon_Hdb zenon_Hd8 zenon_Hd5 zenon_He2 zenon_He4 zenon_Haf zenon_He7 zenon_H106 zenon_Hf3 zenon_H102 zenon_H101 zenon_H2b zenon_H109 zenon_H189 zenon_H185 zenon_H184 zenon_H183 zenon_H17b zenon_H17e zenon_H178 zenon_H179 zenon_H142 zenon_H13e zenon_H13c zenon_H139 zenon_H136 zenon_H130 zenon_H133 zenon_H124 zenon_H145 zenon_H172 zenon_H173 zenon_H160 zenon_H165 zenon_H14f zenon_H153 zenon_H39 zenon_H182 zenon_H1fe zenon_H1ee zenon_H1e0 zenon_H1ac zenon_H1c7 zenon_H1c4 zenon_H1cc zenon_H1ba zenon_H1cf zenon_H1d8 zenon_H1d5 zenon_H1ec zenon_H1ed zenon_H45 zenon_H6a zenon_H54 zenon_H57 zenon_H5b zenon_H62 zenon_H67 zenon_H52 zenon_H4f zenon_H4a zenon_H71 zenon_H6d zenon_H6f zenon_H3e zenon_H1fa zenon_H1f0 zenon_H201 zenon_H206 zenon_H233 zenon_H16f zenon_H9a zenon_H27 zenon_H12b zenon_H95 zenon_H10e zenon_H168 zenon_Hac zenon_H18c zenon_H195 zenon_H10a zenon_Ha1 zenon_H128 zenon_H31 zenon_H24 zenon_H20b zenon_H245 zenon_H7c zenon_H122 zenon_H1e zenon_H149. % 18.79/18.94 apply (zenon_or_s _ _ zenon_H183); [ zenon_intro zenon_H7b | zenon_intro zenon_H186 ]. % 18.79/18.94 apply (zenon_L687_); trivial. % 18.79/18.94 apply (zenon_or_s _ _ zenon_H186); [ zenon_intro zenon_H10f | zenon_intro zenon_H187 ]. % 18.79/18.94 apply (zenon_L710_); trivial. % 18.79/18.94 apply (zenon_or_s _ _ zenon_H187); [ zenon_intro zenon_H150 | zenon_intro zenon_Hcd ]. % 18.79/18.94 apply (zenon_L328_); trivial. % 18.79/18.94 apply (zenon_L428_); trivial. % 18.79/18.94 (* end of lemma zenon_L711_ *) % 18.79/18.94 assert (zenon_L712_ : (~((op (e0) (e2)) = (e0))) -> ((op (e0) (e0)) = (e3)) -> ((op (e2) (e0)) = (e2)) -> (~((op (e2) (e0)) = (e0))) -> (~((op (e1) (e2)) = (e0))) -> (~((e0) = (e2))) -> (~((e1) = (e2))) -> (((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 (e2) (e1)) = (e0))) -> (((op (e1) (e0)) = (e1))\/(((op (e1) (e1)) = (e1))\/(((op (e1) (e2)) = (e1))\/((op (e1) (e3)) = (e1))))) -> (~((op (e1) (e1)) = (e1))) -> (~((op (e0) (e2)) = (op (e1) (e2)))) -> (((op (e1) (e0)) = (e2))\/(((op (e1) (e1)) = (e2))\/(((op (e1) (e2)) = (e2))\/((op (e1) (e3)) = (e2))))) -> ((op (e3) (e0)) = (e1)) -> (((op (e0) (e0)) = (e3))\/(((op (e0) (e1)) = (e3))\/(((op (e0) (e2)) = (e3))\/((op (e0) (e3)) = (e3))))) -> (~((op (e0) (e1)) = (op (e1) (e1)))) -> (~((e1) = (e3))) -> (~((e2) = (e3))) -> ((op (e1) (e0)) = (e0)) -> (~((e0) = (e3))) -> (((op (e1) (e0)) = (e3))\/(((op (e1) (e1)) = (e3))\/(((op (e1) (e2)) = (e3))\/((op (e1) (e3)) = (e3))))) -> ((~((op (e0) (e2)) = (e0)))\/((op (e0) (e0)) = (e2))) -> ((~((op (e1) (e0)) = (e0)))\/((op (e1) (e0)) = (e0))) -> (~((op (e1) (e0)) = (op (e2) (e0)))) -> (~((op (e2) (e0)) = (op (e2) (e1)))) -> (~((op (e1) (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) (e2)))) -> (~((op (e2) (e2)) = (op (e2) (e3)))) -> (~((op (e3) (e0)) = (op (e3) (e3)))) -> (~((op (e0) (e1)) = (op (e0) (e2)))) -> (~((op (e1) (e1)) = (op (e1) (e2)))) -> (~((op (e2) (e0)) = (op (e2) (e2)))) -> (((op (e0) (e3)) = (e0))\/(((op (e1) (e3)) = (e0))\/(((op (e2) (e3)) = (e0))\/((op (e3) (e3)) = (e0))))) -> (~((op (e3) (e2)) = (op (e3) (e3)))) -> (~((op (e2) (e0)) = (op (e2) (e3)))) -> (~((op (e1) (e1)) = (op (e1) (e3)))) -> (~((op (e0) (e1)) = (op (e0) (e3)))) -> (((op (e0) (e2)) = (e0))\/(((op (e1) (e2)) = (e0))\/(((op (e2) (e2)) = (e0))\/((op (e3) (e2)) = (e0))))) -> (~((op (e1) (e0)) = (op (e1) (e1)))) -> ((~((op (e3) (e1)) = (e0)))\/((op (e3) (e0)) = (e1))) -> ((~((op (e3) (e3)) = (e0)))\/((op (e3) (e0)) = (e3))) -> (((op (e2) (e0)) = (e2))\/(((op (e2) (e1)) = (e2))\/(((op (e2) (e2)) = (e2))\/((op (e2) (e3)) = (e2))))) -> (((op (e0) (e1)) = (e2))\/(((op (e1) (e1)) = (e2))\/(((op (e2) (e1)) = (e2))\/((op (e3) (e1)) = (e2))))) -> (~((op (e3) (e0)) = (op (e3) (e1)))) -> (((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 (e2) (e2)) = (e0))\/(((op (e2) (e2)) = (e1))\/(((op (e2) (e2)) = (e2))\/((op (e2) (e2)) = (e3))))) -> (~((op (e2) (e1)) = (op (e2) (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 (e2) (e0)) = (e0)))\/((op (e2) (e0)) = (e0))) -> (((op (e0) (e0)) = (e2))\/(((op (e1) (e0)) = (e2))\/(((op (e2) (e0)) = (e2))\/((op (e3) (e0)) = (e2))))) -> ((~((op (e2) (e1)) = (e0)))\/((op (e2) (e0)) = (e1))) -> (~((op (e0) (e0)) = (op (e2) (e0)))) -> (((op (e3) (e0)) = (e2))\/(((op (e3) (e1)) = (e2))\/(((op (e3) (e2)) = (e2))\/((op (e3) (e3)) = (e2))))) -> (~((op (e0) (e2)) = (op (e3) (e2)))) -> (((op (e3) (e0)) = (e3))\/(((op (e3) (e1)) = (e3))\/(((op (e3) (e2)) = (e3))\/((op (e3) (e3)) = (e3))))) -> (~((op (e1) (e1)) = (op (e3) (e1)))) -> (~((op (e2) (e2)) = (e2))) -> (((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) (e2)) = (op (e1) (e3)))) -> (((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)) = (e3))\/(((op (e1) (e3)) = (e3))\/(((op (e2) (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 (e1) (e1)) = (op (e2) (e1)))) -> (((op (e1) (e1)) = (e0))\/(((op (e1) (e1)) = (e1))\/(((op (e1) (e1)) = (e2))\/((op (e1) (e1)) = (e3))))) -> ((~((op (e1) (e3)) = (e0)))\/((op (e1) (e0)) = (e3))) -> ((~((op (e1) (e2)) = (e0)))\/((op (e1) (e0)) = (e2))) -> (~((op (e0) (e1)) = (op (e2) (e1)))) -> (~((op (e2) (e0)) = (op (e3) (e0)))) -> (((op (e0) (e0)) = (e2))\/(((op (e0) (e1)) = (e2))\/(((op (e0) (e2)) = (e2))\/((op (e0) (e3)) = (e2))))) -> ((~((op (e3) (e0)) = (e0)))\/((op (e3) (e0)) = (e0))) -> ((~((op (e2) (e2)) = (e0)))\/((op (e2) (e0)) = (e2))) -> (~((op (e0) (e0)) = (op (e0) (e3)))) -> (((op (e0) (e1)) = (e1))\/(((op (e1) (e1)) = (e1))\/(((op (e2) (e1)) = (e1))\/((op (e3) (e1)) = (e1))))) -> (~((op (e1) (e2)) = (op (e2) (e2)))) -> (((op (e3) (e3)) = (e0))\/(((op (e3) (e3)) = (e1))\/(((op (e3) (e3)) = (e2))\/((op (e3) (e3)) = (e3))))) -> (~((op (e3) (e3)) = (e3))) -> (~((op (e2) (e3)) = (op (e3) (e3)))) -> (((op (e2) (e0)) = (e1))\/(((op (e2) (e1)) = (e1))\/(((op (e2) (e2)) = (e1))\/((op (e2) (e3)) = (e1))))) -> (((op (e2) (e0)) = (e3))\/(((op (e2) (e1)) = (e3))\/(((op (e2) (e2)) = (e3))\/((op (e2) (e3)) = (e3))))) -> (~((op (e2) (e1)) = (op (e3) (e1)))) -> (((op (e0) (e3)) = (e0))\/(((op (e0) (e3)) = (e1))\/(((op (e0) (e3)) = (e2))\/((op (e0) (e3)) = (e3))))) -> (~((op (e0) (e3)) = (op (e2) (e3)))) -> (~((op (e1) (e3)) = (op (e3) (e3)))) -> (~((op (e1) (e0)) = (op (e1) (e3)))) -> (~((op (e1) (e3)) = (op (e2) (e3)))) -> (((op (e1) (e3)) = (e0))\/(((op (e1) (e3)) = (e1))\/(((op (e1) (e3)) = (e2))\/((op (e1) (e3)) = (e3))))) -> (~((op (e0) (e3)) = (op (e3) (e3)))) -> (((op (e3) (e0)) = (e1))\/(((op (e3) (e1)) = (e1))\/(((op (e3) (e2)) = (e1))\/((op (e3) (e3)) = (e1))))) -> (~((op (e0) (e2)) = (op (e2) (e2)))) -> (~((op (e0) (e3)) = (op (e1) (e3)))) -> (((op (e2) (e3)) = (e0))\/(((op (e2) (e3)) = (e1))\/(((op (e2) (e3)) = (e2))\/((op (e2) (e3)) = (e3))))) -> (~((op (e1) (e2)) = (op (e3) (e2)))) -> (((op (e1) (e2)) = (e0))\/(((op (e1) (e2)) = (e1))\/(((op (e1) (e2)) = (e2))\/((op (e1) (e2)) = (e3))))) -> (((op (e3) (e2)) = (e0))\/(((op (e3) (e2)) = (e1))\/(((op (e3) (e2)) = (e2))\/((op (e3) (e2)) = (e3))))) -> (~((op (e2) (e2)) = (op (e3) (e2)))) -> ((~((op (e3) (e2)) = (e0)))\/((op (e3) (e0)) = (e2))) -> (~((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)) = (e3))\/(((op (e1) (e1)) = (e3))\/(((op (e2) (e1)) = (e3))\/((op (e3) (e1)) = (e3))))) -> ((~((op (e2) (e3)) = (e0)))\/((op (e2) (e0)) = (e3))) -> ((~((op (e1) (e1)) = (e0)))\/((op (e1) (e0)) = (e1))) -> ((~((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) (e0)) = (e0))\/(((op (e2) (e1)) = (e0))\/(((op (e2) (e2)) = (e0))\/((op (e2) (e3)) = (e0))))) -> (~((op (e0) (e2)) = (op (e0) (e3)))) -> (((op (e0) (e1)) = (e0))\/(((op (e0) (e1)) = (e1))\/(((op (e0) (e1)) = (e2))\/((op (e0) (e1)) = (e3))))) -> (((op (e3) (e1)) = (e0))\/(((op (e3) (e1)) = (e1))\/(((op (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)) = (e0))) -> (((op (e1) (e0)) = (e0))\/(((op (e1) (e1)) = (e0))\/(((op (e1) (e2)) = (e0))\/((op (e1) (e3)) = (e0))))) -> (((op (e0) (e0)) = (e0))\/(((op (e0) (e1)) = (e0))\/(((op (e0) (e2)) = (e0))\/((op (e0) (e3)) = (e0))))) -> (~((op (e1) (e0)) = (op (e1) (e2)))) -> (~((op (e2) (e1)) = (op (e2) (e2)))) -> (~((e0) = (e1))) -> False). % 18.79/18.94 do 0 intro. intros zenon_H75 zenon_H3a zenon_Hee zenon_H30 zenon_H25 zenon_H149 zenon_H7c zenon_H245 zenon_H20b zenon_H24 zenon_H31 zenon_H128 zenon_H10a zenon_H195 zenon_H18c zenon_Hac zenon_H168 zenon_H10e zenon_H95 zenon_H12b zenon_H27 zenon_H9a zenon_H16f zenon_H233 zenon_H206 zenon_H201 zenon_H1f0 zenon_H1fa zenon_H3e zenon_H6f zenon_H6d zenon_H71 zenon_H4a zenon_H4f zenon_H52 zenon_H67 zenon_H62 zenon_H5b zenon_H57 zenon_H54 zenon_H6a zenon_H45 zenon_H1ed zenon_H1ec zenon_H1d5 zenon_H1d8 zenon_H1cf zenon_H1ba zenon_H1cc zenon_H1c4 zenon_H1c7 zenon_H1ac zenon_H1e0 zenon_H1ee zenon_H1fe zenon_H182 zenon_H39 zenon_H153 zenon_H14f zenon_H165 zenon_H160 zenon_H173 zenon_H172 zenon_H145 zenon_H124 zenon_H133 zenon_H130 zenon_H136 zenon_H139 zenon_H13c zenon_H13e zenon_H142 zenon_H179 zenon_H178 zenon_H17e zenon_H17b zenon_H183 zenon_H184 zenon_H185 zenon_H189 zenon_H109 zenon_H2b zenon_H101 zenon_H102 zenon_Hf3 zenon_H106 zenon_He7 zenon_Haf zenon_He4 zenon_He2 zenon_Hd5 zenon_Hd8 zenon_Hdb zenon_Hdf zenon_Hc2 zenon_He8 zenon_Ha8 zenon_H1d zenon_H11f zenon_H115 zenon_H19d zenon_H191 zenon_H18f zenon_H1a7 zenon_H1a4 zenon_H1a6 zenon_H1a5 zenon_H94 zenon_H205 zenon_H204 zenon_H235 zenon_H2f zenon_H208 zenon_H212 zenon_H22a zenon_H210 zenon_H22d zenon_H3f zenon_H22 zenon_H74 zenon_H24a zenon_H24b zenon_Ha1. % 18.79/18.94 apply (zenon_or_s _ _ zenon_H74); [ zenon_intro zenon_H42 | zenon_intro zenon_H77 ]. % 18.79/18.94 exact (zenon_H3f zenon_H42). % 18.79/18.94 apply (zenon_or_s _ _ zenon_H77); [ zenon_intro zenon_H49 | zenon_intro zenon_H78 ]. % 18.79/18.94 exact (zenon_H20b zenon_H49). % 18.79/18.94 apply (zenon_or_s _ _ zenon_H78); [ zenon_intro zenon_H48 | zenon_intro zenon_H1e ]. % 18.79/18.94 exact (zenon_H75 zenon_H48). % 18.79/18.94 apply (zenon_or_s _ _ zenon_H22d); [ zenon_intro zenon_H7a | zenon_intro zenon_H22e ]. % 18.79/18.94 apply (zenon_L333_); trivial. % 18.79/18.94 apply (zenon_or_s _ _ zenon_H22e); [ zenon_intro zenon_Ha0 | zenon_intro zenon_H22f ]. % 18.79/18.94 apply (zenon_or_s _ _ zenon_H183); [ zenon_intro zenon_H7b | zenon_intro zenon_H186 ]. % 18.79/18.94 apply (zenon_L686_); trivial. % 18.79/18.94 apply (zenon_or_s _ _ zenon_H186); [ zenon_intro zenon_H10f | zenon_intro zenon_H187 ]. % 18.79/18.94 apply (zenon_or_s _ _ zenon_H245); [ zenon_intro zenon_H49 | zenon_intro zenon_H246 ]. % 18.79/18.94 exact (zenon_H20b zenon_H49). % 18.79/18.94 apply (zenon_or_s _ _ zenon_H246); [ zenon_intro zenon_H29 | zenon_intro zenon_H247 ]. % 18.79/18.94 exact (zenon_H24 zenon_H29). % 18.79/18.94 apply (zenon_or_s _ _ zenon_H247); [ zenon_intro zenon_H36 | zenon_intro zenon_H1b1 ]. % 18.79/18.94 exact (zenon_H31 zenon_H36). % 18.79/18.94 apply (zenon_or_s _ _ zenon_H128); [ zenon_intro zenon_H9d | zenon_intro zenon_H129 ]. % 18.79/18.94 apply (zenon_L262_); trivial. % 18.79/18.94 apply (zenon_or_s _ _ zenon_H129); [ zenon_intro zenon_H10d | zenon_intro zenon_H12a ]. % 18.79/18.94 exact (zenon_H10a zenon_H10d). % 18.79/18.94 apply (zenon_or_s _ _ zenon_H12a); [ zenon_intro zenon_Hf0 | zenon_intro zenon_Hd6 ]. % 18.79/18.94 apply (zenon_L674_); trivial. % 18.79/18.94 apply (zenon_or_s _ _ zenon_H18c); [ zenon_intro zenon_H86 | zenon_intro zenon_H18d ]. % 18.79/18.94 apply (zenon_L257_); trivial. % 18.79/18.94 apply (zenon_or_s _ _ zenon_H18d); [ zenon_intro zenon_H110 | zenon_intro zenon_H18e ]. % 18.79/18.94 apply (zenon_L569_); trivial. % 18.79/18.94 apply (zenon_or_s _ _ zenon_H18e); [ zenon_intro zenon_H113 | zenon_intro zenon_Hd7 ]. % 18.79/18.94 apply (zenon_L675_); trivial. % 18.79/18.94 apply (zenon_L101_); trivial. % 18.79/18.94 apply (zenon_or_s _ _ zenon_H187); [ zenon_intro zenon_H150 | zenon_intro zenon_Hcd ]. % 18.79/18.94 apply (zenon_or_s _ _ zenon_H245); [ zenon_intro zenon_H49 | zenon_intro zenon_H246 ]. % 18.79/18.94 exact (zenon_H20b zenon_H49). % 18.79/18.94 apply (zenon_or_s _ _ zenon_H246); [ zenon_intro zenon_H29 | zenon_intro zenon_H247 ]. % 18.79/18.94 exact (zenon_H24 zenon_H29). % 18.79/18.94 apply (zenon_or_s _ _ zenon_H247); [ zenon_intro zenon_H36 | zenon_intro zenon_H1b1 ]. % 18.79/18.94 exact (zenon_H31 zenon_H36). % 18.79/18.94 apply (zenon_or_s _ _ zenon_H128); [ zenon_intro zenon_H9d | zenon_intro zenon_H129 ]. % 18.79/18.94 apply (zenon_L262_); trivial. % 18.79/18.94 apply (zenon_or_s _ _ zenon_H129); [ zenon_intro zenon_H10d | zenon_intro zenon_H12a ]. % 18.79/18.94 exact (zenon_H10a zenon_H10d). % 18.79/18.94 apply (zenon_or_s _ _ zenon_H12a); [ zenon_intro zenon_Hf0 | zenon_intro zenon_Hd6 ]. % 18.79/18.94 apply (zenon_L674_); trivial. % 18.79/18.94 apply (zenon_or_s _ _ zenon_H18c); [ zenon_intro zenon_H86 | zenon_intro zenon_H18d ]. % 18.79/18.94 apply (zenon_L241_); trivial. % 18.79/18.94 apply (zenon_or_s _ _ zenon_H18d); [ zenon_intro zenon_H110 | zenon_intro zenon_H18e ]. % 18.79/18.94 apply (zenon_L569_); trivial. % 18.79/18.94 apply (zenon_or_s _ _ zenon_H18e); [ zenon_intro zenon_H113 | zenon_intro zenon_Hd7 ]. % 18.79/18.94 apply (zenon_L153_); trivial. % 18.79/18.94 apply (zenon_L101_); trivial. % 18.79/18.94 apply (zenon_L428_); trivial. % 18.79/18.94 apply (zenon_or_s _ _ zenon_H22f); [ zenon_intro zenon_H122 | zenon_intro zenon_Hc3 ]. % 18.79/18.94 apply (zenon_L711_); trivial. % 18.79/18.94 apply (zenon_L427_); trivial. % 18.79/18.94 (* end of lemma zenon_L712_ *) % 18.79/18.94 assert (zenon_L713_ : (((op (e1) (e0)) = (e1))\/(((op (e1) (e1)) = (e1))\/(((op (e1) (e2)) = (e1))\/((op (e1) (e3)) = (e1))))) -> (~((op (e1) (e0)) = (e1))) -> (~((op (e1) (e1)) = (e1))) -> (~((op (e1) (e2)) = (e1))) -> (~((op (e1) (e3)) = (e1))) -> False). % 18.79/18.94 do 0 intro. intros zenon_H128 zenon_H1ef zenon_H10a zenon_H24d zenon_H24e. % 18.79/18.94 apply (zenon_or_s _ _ zenon_H128); [ zenon_intro zenon_H9d | zenon_intro zenon_H129 ]. % 18.79/18.94 exact (zenon_H1ef zenon_H9d). % 18.79/18.94 apply (zenon_or_s _ _ zenon_H129); [ zenon_intro zenon_H10d | zenon_intro zenon_H12a ]. % 18.79/18.94 exact (zenon_H10a zenon_H10d). % 18.79/18.94 apply (zenon_or_s _ _ zenon_H12a); [ zenon_intro zenon_Hf0 | zenon_intro zenon_Hd6 ]. % 18.79/18.94 exact (zenon_H24d zenon_Hf0). % 18.79/18.94 exact (zenon_H24e zenon_Hd6). % 18.79/18.94 (* end of lemma zenon_L713_ *) % 18.79/18.94 assert (zenon_L714_ : (((op (e0) (e1)) = (e1))\/(((op (e1) (e1)) = (e1))\/(((op (e2) (e1)) = (e1))\/((op (e3) (e1)) = (e1))))) -> (~((op (e0) (e1)) = (e1))) -> (~((op (e1) (e1)) = (e1))) -> (~((op (e2) (e1)) = (e1))) -> (~((op (e3) (e1)) = (e1))) -> False). % 18.79/18.94 do 0 intro. intros zenon_H109 zenon_Ha4 zenon_H10a zenon_H24f zenon_H250. % 18.79/18.94 apply (zenon_or_s _ _ zenon_H109); [ zenon_intro zenon_Ha0 | zenon_intro zenon_H10b ]. % 18.79/18.94 exact (zenon_Ha4 zenon_Ha0). % 18.79/18.94 apply (zenon_or_s _ _ zenon_H10b); [ zenon_intro zenon_H10d | zenon_intro zenon_H10c ]. % 18.79/18.94 exact (zenon_H10a zenon_H10d). % 18.79/18.94 apply (zenon_or_s _ _ zenon_H10c); [ zenon_intro zenon_Ha5 | zenon_intro zenon_Hae ]. % 18.79/18.94 exact (zenon_H24f zenon_Ha5). % 18.79/18.94 exact (zenon_H250 zenon_Hae). % 18.79/18.94 (* end of lemma zenon_L714_ *) % 18.79/18.94 assert (zenon_L715_ : (((op (e0) (e2)) = (e1))\/(((op (e1) (e2)) = (e1))\/(((op (e2) (e2)) = (e1))\/((op (e3) (e2)) = (e1))))) -> (~((op (e0) (e0)) = (op (e0) (e2)))) -> ((op (e0) (e0)) = (e1)) -> (~((op (e1) (e2)) = (e1))) -> (~((op (e2) (e2)) = (e1))) -> (~((op (e3) (e2)) = (e1))) -> False). % 18.79/18.94 do 0 intro. intros zenon_H139 zenon_H13c zenon_H7a zenon_H24d zenon_H198 zenon_H251. % 18.79/18.94 apply (zenon_or_s _ _ zenon_H139); [ zenon_intro zenon_H122 | zenon_intro zenon_H13a ]. % 18.79/18.94 apply (zenon_L92_); trivial. % 18.79/18.94 apply (zenon_or_s _ _ zenon_H13a); [ zenon_intro zenon_Hf0 | zenon_intro zenon_H13b ]. % 18.79/18.94 exact (zenon_H24d zenon_Hf0). % 18.79/18.94 apply (zenon_or_s _ _ zenon_H13b); [ zenon_intro zenon_Hf1 | zenon_intro zenon_Hba ]. % 18.79/18.94 exact (zenon_H198 zenon_Hf1). % 18.79/18.94 exact (zenon_H251 zenon_Hba). % 18.79/18.94 (* end of lemma zenon_L715_ *) % 18.79/18.94 assert (zenon_L716_ : (((op (e0) (e0)) = (e1))\/(((op (e0) (e1)) = (e1))\/(((op (e0) (e2)) = (e1))\/((op (e0) (e3)) = (e1))))) -> (~((op (e3) (e2)) = (e1))) -> (~((op (e2) (e2)) = (e1))) -> (~((op (e1) (e2)) = (e1))) -> (~((op (e0) (e0)) = (op (e0) (e2)))) -> (((op (e0) (e2)) = (e1))\/(((op (e1) (e2)) = (e1))\/(((op (e2) (e2)) = (e1))\/((op (e3) (e2)) = (e1))))) -> (~((op (e0) (e1)) = (e1))) -> (~((op (e0) (e2)) = (e1))) -> (~((op (e0) (e3)) = (e1))) -> False). % 18.79/18.94 do 0 intro. intros zenon_H22d zenon_H251 zenon_H198 zenon_H24d zenon_H13c zenon_H139 zenon_Ha4 zenon_H20d zenon_H231. % 18.79/18.94 apply (zenon_or_s _ _ zenon_H22d); [ zenon_intro zenon_H7a | zenon_intro zenon_H22e ]. % 18.79/18.94 apply (zenon_L715_); trivial. % 18.79/18.94 apply (zenon_or_s _ _ zenon_H22e); [ zenon_intro zenon_Ha0 | zenon_intro zenon_H22f ]. % 18.79/18.95 exact (zenon_Ha4 zenon_Ha0). % 18.79/18.95 apply (zenon_or_s _ _ zenon_H22f); [ zenon_intro zenon_H122 | zenon_intro zenon_Hc3 ]. % 18.79/18.95 exact (zenon_H20d zenon_H122). % 18.79/18.95 exact (zenon_H231 zenon_Hc3). % 18.79/18.95 (* end of lemma zenon_L716_ *) % 18.79/18.95 assert (zenon_L717_ : ((~((op (e3) (e2)) = (e1)))\/((op (e3) (e1)) = (e2))) -> ((op (e3) (e1)) = (e1)) -> (~((e1) = (e2))) -> (((op (e0) (e2)) = (e1))\/(((op (e1) (e2)) = (e1))\/(((op (e2) (e2)) = (e1))\/((op (e3) (e2)) = (e1))))) -> (~((op (e2) (e2)) = (e1))) -> (~((op (e1) (e2)) = (e1))) -> (~((op (e0) (e0)) = (op (e0) (e2)))) -> (~((op (e0) (e1)) = (e1))) -> (~((op (e0) (e2)) = (e1))) -> (~((op (e0) (e3)) = (e1))) -> (((op (e0) (e0)) = (e1))\/(((op (e0) (e1)) = (e1))\/(((op (e0) (e2)) = (e1))\/((op (e0) (e3)) = (e1))))) -> False). % 18.79/18.95 do 0 intro. intros zenon_H252 zenon_Hae zenon_H7c zenon_H139 zenon_H198 zenon_H24d zenon_H13c zenon_Ha4 zenon_H20d zenon_H231 zenon_H22d. % 18.79/18.95 apply (zenon_or_s _ _ zenon_H252); [ zenon_intro zenon_H251 | zenon_intro zenon_H14d ]. % 18.79/18.95 apply (zenon_L716_); trivial. % 18.79/18.95 apply (zenon_L152_); trivial. % 18.79/18.95 (* end of lemma zenon_L717_ *) % 18.79/18.95 assert (zenon_L718_ : ((~((op (e2) (e2)) = (e1)))\/((op (e2) (e1)) = (e2))) -> (~((op (e0) (e1)) = (op (e2) (e1)))) -> ((~((op (e3) (e2)) = (e1)))\/((op (e3) (e1)) = (e2))) -> ((op (e0) (e1)) = (e2)) -> (~((op (e0) (e1)) = (op (e3) (e1)))) -> (((op (e0) (e2)) = (e1))\/(((op (e1) (e2)) = (e1))\/(((op (e2) (e2)) = (e1))\/((op (e3) (e2)) = (e1))))) -> (~((op (e1) (e2)) = (e1))) -> (~((op (e0) (e0)) = (op (e0) (e2)))) -> (~((op (e0) (e1)) = (e1))) -> (((op (e0) (e0)) = (e1))\/(((op (e1) (e0)) = (e1))\/(((op (e2) (e0)) = (e1))\/((op (e3) (e0)) = (e1))))) -> (~((op (e2) (e0)) = (e1))) -> (~((op (e1) (e0)) = (e1))) -> (~((op (e0) (e3)) = (e1))) -> (((op (e0) (e0)) = (e1))\/(((op (e0) (e1)) = (e1))\/(((op (e0) (e2)) = (e1))\/((op (e0) (e3)) = (e1))))) -> ((op (e1) (e1)) = (e3)) -> ((~((op (e3) (e0)) = (e1)))\/((op (e3) (e1)) = (e0))) -> False). % 18.79/18.95 do 0 intro. intros zenon_H253 zenon_H17e zenon_H252 zenon_H10f zenon_H210 zenon_H139 zenon_H24d zenon_H13c zenon_Ha4 zenon_H235 zenon_H1db zenon_H1ef zenon_H231 zenon_H22d zenon_H13f zenon_H254. % 18.79/18.95 apply (zenon_or_s _ _ zenon_H253); [ zenon_intro zenon_H198 | zenon_intro zenon_H1ca ]. % 18.79/18.95 apply (zenon_or_s _ _ zenon_H254); [ zenon_intro zenon_Had | zenon_intro zenon_H1b1 ]. % 18.79/18.95 apply (zenon_or_s _ _ zenon_H252); [ zenon_intro zenon_H251 | zenon_intro zenon_H14d ]. % 18.79/18.95 apply (zenon_or_s _ _ zenon_H22d); [ zenon_intro zenon_H7a | zenon_intro zenon_H22e ]. % 18.79/18.95 apply (zenon_L715_); trivial. % 18.79/18.95 apply (zenon_or_s _ _ zenon_H22e); [ zenon_intro zenon_Ha0 | zenon_intro zenon_H22f ]. % 18.79/18.95 exact (zenon_Ha4 zenon_Ha0). % 18.79/18.95 apply (zenon_or_s _ _ zenon_H22f); [ zenon_intro zenon_H122 | zenon_intro zenon_Hc3 ]. % 18.79/18.95 apply (zenon_or_s _ _ zenon_H235); [ zenon_intro zenon_H7a | zenon_intro zenon_H236 ]. % 18.79/18.95 apply (zenon_L92_); trivial. % 18.79/18.95 apply (zenon_or_s _ _ zenon_H236); [ zenon_intro zenon_H9d | zenon_intro zenon_H237 ]. % 18.79/18.95 exact (zenon_H1ef zenon_H9d). % 18.79/18.95 apply (zenon_or_s _ _ zenon_H237); [ zenon_intro zenon_Hed | zenon_intro zenon_Hac ]. % 18.79/18.95 exact (zenon_H1db zenon_Hed). % 18.79/18.95 exact (zenon_Had zenon_Hac). % 18.79/18.95 exact (zenon_H231 zenon_Hc3). % 18.79/18.95 apply (zenon_L389_); trivial. % 18.79/18.95 apply (zenon_L580_); trivial. % 18.79/18.95 apply (zenon_L191_); trivial. % 18.79/18.95 (* end of lemma zenon_L718_ *) % 18.79/18.95 assert (zenon_L719_ : (((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))))) -> (~((e0) = (e2))) -> ((op (e1) (e0)) = (e0)) -> (~((e2) = (e3))) -> ((op (e1) (e1)) = (e3)) -> ((op (e0) (e2)) = (e2)) -> (~((op (e0) (e2)) = (op (e1) (e2)))) -> (~((e1) = (e2))) -> False). % 18.79/18.95 do 0 intro. intros zenon_H128 zenon_H1ef zenon_H10a zenon_H24d zenon_H18c zenon_H149 zenon_H27 zenon_H12b zenon_H13f zenon_H150 zenon_H195 zenon_H7c. % 18.79/18.95 apply (zenon_or_s _ _ zenon_H128); [ zenon_intro zenon_H9d | zenon_intro zenon_H129 ]. % 18.79/18.95 exact (zenon_H1ef zenon_H9d). % 18.79/18.95 apply (zenon_or_s _ _ zenon_H129); [ zenon_intro zenon_H10d | zenon_intro zenon_H12a ]. % 18.79/18.95 exact (zenon_H10a zenon_H10d). % 18.79/18.95 apply (zenon_or_s _ _ zenon_H12a); [ zenon_intro zenon_Hf0 | zenon_intro zenon_Hd6 ]. % 18.79/18.95 exact (zenon_H24d zenon_Hf0). % 18.79/18.95 apply (zenon_L309_); trivial. % 18.79/18.95 (* end of lemma zenon_L719_ *) % 18.79/18.95 assert (zenon_L720_ : (((op (e0) (e2)) = (e1))\/(((op (e1) (e2)) = (e1))\/(((op (e2) (e2)) = (e1))\/((op (e3) (e2)) = (e1))))) -> (~((op (e0) (e2)) = (e1))) -> (~((op (e1) (e2)) = (op (e1) (e3)))) -> ((op (e1) (e3)) = (e1)) -> (((op (e2) (e2)) = (e0))\/(((op (e2) (e2)) = (e1))\/(((op (e2) (e2)) = (e2))\/((op (e2) (e2)) = (e3))))) -> ((op (e0) (e2)) = (e3)) -> (~((op (e2) (e2)) = (op (e3) (e2)))) -> (~((op (e2) (e2)) = (e2))) -> ((op (e1) (e2)) = (e0)) -> False). % 18.79/18.95 do 0 intro. intros zenon_H139 zenon_H20d zenon_H124 zenon_Hd6 zenon_H1c4 zenon_Ha9 zenon_H18f zenon_H173 zenon_H2a. % 18.79/18.95 apply (zenon_or_s _ _ zenon_H139); [ zenon_intro zenon_H122 | zenon_intro zenon_H13a ]. % 18.79/18.95 exact (zenon_H20d zenon_H122). % 18.79/18.95 apply (zenon_or_s _ _ zenon_H13a); [ zenon_intro zenon_Hf0 | zenon_intro zenon_H13b ]. % 18.79/18.95 apply (zenon_L78_); trivial. % 18.79/18.95 apply (zenon_or_s _ _ zenon_H13b); [ zenon_intro zenon_Hf1 | zenon_intro zenon_Hba ]. % 18.79/18.95 apply (zenon_L184_); trivial. % 18.79/18.95 apply (zenon_L186_); trivial. % 18.79/18.95 (* end of lemma zenon_L720_ *) % 18.79/18.95 assert (zenon_L721_ : (((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) (e2)) = (e1))\/(((op (e1) (e2)) = (e1))\/(((op (e2) (e2)) = (e1))\/((op (e3) (e2)) = (e1))))) -> (~((op (e0) (e2)) = (e1))) -> (~((op (e1) (e2)) = (op (e1) (e3)))) -> (((op (e2) (e2)) = (e0))\/(((op (e2) (e2)) = (e1))\/(((op (e2) (e2)) = (e2))\/((op (e2) (e2)) = (e3))))) -> ((op (e0) (e2)) = (e3)) -> (~((op (e2) (e2)) = (op (e3) (e2)))) -> (~((op (e2) (e2)) = (e2))) -> ((op (e1) (e2)) = (e0)) -> False). % 18.79/18.95 do 0 intro. intros zenon_H128 zenon_H1ef zenon_H10a zenon_H24d zenon_H139 zenon_H20d zenon_H124 zenon_H1c4 zenon_Ha9 zenon_H18f zenon_H173 zenon_H2a. % 18.79/18.95 apply (zenon_or_s _ _ zenon_H128); [ zenon_intro zenon_H9d | zenon_intro zenon_H129 ]. % 18.79/18.95 exact (zenon_H1ef zenon_H9d). % 18.79/18.95 apply (zenon_or_s _ _ zenon_H129); [ zenon_intro zenon_H10d | zenon_intro zenon_H12a ]. % 18.79/18.95 exact (zenon_H10a zenon_H10d). % 18.79/18.95 apply (zenon_or_s _ _ zenon_H12a); [ zenon_intro zenon_Hf0 | zenon_intro zenon_Hd6 ]. % 18.79/18.95 exact (zenon_H24d zenon_Hf0). % 18.79/18.95 apply (zenon_L720_); trivial. % 18.79/18.95 (* end of lemma zenon_L721_ *) % 18.79/18.95 assert (zenon_L722_ : (((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)) = (e1))) -> ((op (e3) (e3)) = (e2)) -> (~((op (e0) (e3)) = (op (e3) (e3)))) -> (~((op (e0) (e3)) = (op (e2) (e3)))) -> ((op (e2) (e3)) = (e3)) -> False). % 18.79/18.95 do 0 intro. intros zenon_He4 zenon_H1f zenon_H1d zenon_H231 zenon_Hf6 zenon_Hc2 zenon_He2 zenon_Hdd. % 18.79/18.95 apply (zenon_or_s _ _ zenon_He4); [ zenon_intro zenon_H1e | zenon_intro zenon_He5 ]. % 18.79/18.95 apply (zenon_L1_); trivial. % 18.79/18.95 apply (zenon_or_s _ _ zenon_He5); [ zenon_intro zenon_Hc3 | zenon_intro zenon_He6 ]. % 18.79/18.95 exact (zenon_H231 zenon_Hc3). % 18.79/18.95 apply (zenon_or_s _ _ zenon_He6); [ zenon_intro zenon_Hcd | zenon_intro zenon_He3 ]. % 18.79/18.95 apply (zenon_L87_); trivial. % 18.79/18.95 apply (zenon_L54_); trivial. % 18.79/18.95 (* end of lemma zenon_L722_ *) % 18.79/18.95 assert (zenon_L723_ : (((op (e1) (e0)) = (e0))\/(((op (e1) (e1)) = (e0))\/(((op (e1) (e2)) = (e0))\/((op (e1) (e3)) = (e0))))) -> (~((e0) = (e2))) -> (~((op (e2) (e0)) = (op (e2) (e3)))) -> (~((op (e1) (e1)) = (op (e1) (e3)))) -> ((op (e0) (e1)) = (e0)) -> (~((op (e0) (e1)) = (op (e0) (e3)))) -> (((op (e0) (e3)) = (e0))\/(((op (e1) (e3)) = (e0))\/(((op (e2) (e3)) = (e0))\/((op (e3) (e3)) = (e0))))) -> (~((op (e1) (e1)) = (op (e1) (e2)))) -> (~((op (e0) (e1)) = (op (e0) (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 (e1) (e2)) = (e1))) -> (((op (e0) (e2)) = (e0))\/(((op (e1) (e2)) = (e0))\/(((op (e2) (e2)) = (e0))\/((op (e3) (e2)) = (e0))))) -> (~((e0) = (e3))) -> (~((op (e2) (e2)) = (e2))) -> (~((op (e2) (e2)) = (op (e3) (e2)))) -> (((op (e2) (e2)) = (e0))\/(((op (e2) (e2)) = (e1))\/(((op (e2) (e2)) = (e2))\/((op (e2) (e2)) = (e3))))) -> (~((op (e1) (e2)) = (op (e1) (e3)))) -> (~((op (e0) (e2)) = (e1))) -> (((op (e0) (e2)) = (e1))\/(((op (e1) (e2)) = (e1))\/(((op (e2) (e2)) = (e1))\/((op (e3) (e2)) = (e1))))) -> ((op (e2) (e0)) = (e0)) -> (~((op (e2) (e0)) = (op (e2) (e2)))) -> (((op (e2) (e0)) = (e3))\/(((op (e2) (e1)) = (e3))\/(((op (e2) (e2)) = (e3))\/((op (e2) (e3)) = (e3))))) -> ((op (e0) (e0)) = (e1)) -> ((op (e1) (e0)) = (e2)) -> ((op (e1) (e1)) = (e3)) -> (~((op (e1) (e1)) = (op (e2) (e1)))) -> ((op (e0) (e2)) = (e3)) -> (~((op (e0) (e2)) = (op (e2) (e2)))) -> (((op (e3) (e3)) = (e0))\/(((op (e3) (e3)) = (e1))\/(((op (e3) (e3)) = (e2))\/((op (e3) (e3)) = (e3))))) -> (~((op (e3) (e2)) = (op (e3) (e3)))) -> (~((op (e3) (e3)) = (e1))) -> (~((op (e0) (e3)) = (op (e2) (e3)))) -> (~((op (e0) (e3)) = (op (e3) (e3)))) -> (~((op (e0) (e3)) = (e1))) -> (~((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)) = (e3))) -> False). % 18.79/18.95 do 0 intro. intros zenon_H22 zenon_H149 zenon_H5b zenon_H57 zenon_H49 zenon_H54 zenon_H67 zenon_H4f zenon_H4a zenon_H128 zenon_H1ef zenon_H10a zenon_H24d zenon_H6a zenon_H9a zenon_H173 zenon_H18f zenon_H1c4 zenon_H124 zenon_H20d zenon_H139 zenon_H34 zenon_H52 zenon_He7 zenon_H7a zenon_H86 zenon_H13f zenon_H13e zenon_Ha9 zenon_Ha8 zenon_H101 zenon_H62 zenon_Hc7 zenon_He2 zenon_Hc2 zenon_H231 zenon_H1d zenon_He4 zenon_H102. % 18.79/18.95 apply (zenon_or_s _ _ zenon_H22); [ zenon_intro zenon_H27 | zenon_intro zenon_H26 ]. % 18.79/18.95 apply (zenon_L257_); trivial. % 18.79/18.95 apply (zenon_or_s _ _ zenon_H26); [ zenon_intro zenon_H29 | zenon_intro zenon_H28 ]. % 18.79/18.95 apply (zenon_L17_); trivial. % 18.79/18.95 apply (zenon_or_s _ _ zenon_H28); [ zenon_intro zenon_H2a | zenon_intro zenon_H1f ]. % 18.79/18.95 apply (zenon_L721_); trivial. % 18.79/18.95 apply (zenon_or_s _ _ zenon_H128); [ zenon_intro zenon_H9d | zenon_intro zenon_H129 ]. % 18.79/18.95 exact (zenon_H1ef zenon_H9d). % 18.79/18.95 apply (zenon_or_s _ _ zenon_H129); [ zenon_intro zenon_H10d | zenon_intro zenon_H12a ]. % 18.79/18.95 exact (zenon_H10a zenon_H10d). % 18.79/18.95 apply (zenon_or_s _ _ zenon_H12a); [ zenon_intro zenon_Hf0 | zenon_intro zenon_Hd6 ]. % 18.79/18.95 exact (zenon_H24d zenon_Hf0). % 18.79/18.95 apply (zenon_or_s _ _ zenon_H6a); [ zenon_intro zenon_H48 | zenon_intro zenon_H6b ]. % 18.79/18.95 apply (zenon_L358_); trivial. % 18.79/18.95 apply (zenon_or_s _ _ zenon_H6b); [ zenon_intro zenon_H2a | zenon_intro zenon_H6c ]. % 18.79/18.95 apply (zenon_L720_); trivial. % 18.79/18.95 apply (zenon_or_s _ _ zenon_H6c); [ zenon_intro zenon_H2c | zenon_intro zenon_H61 ]. % 18.79/18.95 apply (zenon_L11_); trivial. % 18.79/18.95 apply (zenon_or_s _ _ zenon_He7); [ zenon_intro zenon_H3b | zenon_intro zenon_He9 ]. % 18.79/18.95 apply (zenon_L33_); trivial. % 18.79/18.95 apply (zenon_or_s _ _ zenon_He9); [ zenon_intro zenon_Ha6 | zenon_intro zenon_Hea ]. % 18.79/18.95 apply (zenon_L95_); trivial. % 18.79/18.95 apply (zenon_or_s _ _ zenon_Hea); [ zenon_intro zenon_Haa | zenon_intro zenon_Hdd ]. % 18.79/18.95 apply (zenon_L40_); trivial. % 18.79/18.95 apply (zenon_or_s _ _ zenon_H101); [ zenon_intro zenon_H60 | zenon_intro zenon_H103 ]. % 18.79/18.95 apply (zenon_L15_); trivial. % 18.79/18.95 apply (zenon_or_s _ _ zenon_H103); [ zenon_intro zenon_Hc4 | zenon_intro zenon_H104 ]. % 18.79/18.95 exact (zenon_Hc7 zenon_Hc4). % 18.79/18.95 apply (zenon_or_s _ _ zenon_H104); [ zenon_intro zenon_Hf6 | zenon_intro zenon_H105 ]. % 18.79/18.95 apply (zenon_L722_); trivial. % 18.79/18.95 exact (zenon_H102 zenon_H105). % 18.79/18.95 (* end of lemma zenon_L723_ *) % 18.79/18.95 assert (zenon_L724_ : (((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) (e1)) = (op (e1) (e2)))) -> (~((op (e2) (e0)) = (op (e2) (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) (e1)) = (op (e1) (e3)))) -> ((op (e1) (e1)) = (e0)) -> (~((op (e2) (e0)) = (op (e2) (e3)))) -> ((op (e2) (e0)) = (e0)) -> (~((op (e3) (e2)) = (op (e3) (e3)))) -> False). % 18.79/18.95 do 0 intro. intros zenon_H6a zenon_H4a zenon_H49 zenon_H4f zenon_H52 zenon_H67 zenon_H9a zenon_He3 zenon_H57 zenon_H29 zenon_H5b zenon_H34 zenon_H62. % 18.79/18.95 apply (zenon_or_s _ _ zenon_H6a); [ zenon_intro zenon_H48 | zenon_intro zenon_H6b ]. % 18.79/18.95 apply (zenon_L9_); trivial. % 18.79/18.95 apply (zenon_or_s _ _ zenon_H6b); [ zenon_intro zenon_H2a | zenon_intro zenon_H6c ]. % 18.79/18.95 apply (zenon_L10_); trivial. % 18.79/18.95 apply (zenon_or_s _ _ zenon_H6c); [ zenon_intro zenon_H2c | zenon_intro zenon_H61 ]. % 18.79/18.95 apply (zenon_L11_); trivial. % 18.79/18.95 apply (zenon_L619_); trivial. % 18.79/18.95 (* end of lemma zenon_L724_ *) % 18.79/18.95 assert (zenon_L725_ : (((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) (e3)) = (e1))) -> (~((op (e1) (e2)) = (op (e2) (e2)))) -> (~((op (e2) (e1)) = (e1))) -> (~((op (e2) (e0)) = (e1))) -> (((op (e2) (e0)) = (e1))\/(((op (e2) (e1)) = (e1))\/(((op (e2) (e2)) = (e1))\/((op (e2) (e3)) = (e1))))) -> (~((op (e1) (e3)) = (e1))) -> False). % 18.79/18.95 do 0 intro. intros zenon_H128 zenon_H1ef zenon_H10a zenon_H255 zenon_H2b zenon_H24f zenon_H1db zenon_H106 zenon_H24e. % 18.79/18.95 apply (zenon_or_s _ _ zenon_H128); [ zenon_intro zenon_H9d | zenon_intro zenon_H129 ]. % 18.79/18.95 exact (zenon_H1ef zenon_H9d). % 18.79/18.95 apply (zenon_or_s _ _ zenon_H129); [ zenon_intro zenon_H10d | zenon_intro zenon_H12a ]. % 18.79/18.95 exact (zenon_H10a zenon_H10d). % 18.79/18.95 apply (zenon_or_s _ _ zenon_H12a); [ zenon_intro zenon_Hf0 | zenon_intro zenon_Hd6 ]. % 18.79/18.95 apply (zenon_or_s _ _ zenon_H106); [ zenon_intro zenon_Hed | zenon_intro zenon_H107 ]. % 18.79/18.95 exact (zenon_H1db zenon_Hed). % 18.79/18.95 apply (zenon_or_s _ _ zenon_H107); [ zenon_intro zenon_Ha5 | zenon_intro zenon_H108 ]. % 18.79/18.95 exact (zenon_H24f zenon_Ha5). % 18.79/18.95 apply (zenon_or_s _ _ zenon_H108); [ zenon_intro zenon_Hf1 | zenon_intro zenon_Hf4 ]. % 18.79/18.95 apply (zenon_L59_); trivial. % 18.79/18.95 exact (zenon_H255 zenon_Hf4). % 18.79/18.95 exact (zenon_H24e zenon_Hd6). % 18.79/18.95 (* end of lemma zenon_L725_ *) % 18.79/18.95 assert (zenon_L726_ : ((~((op (e1) (e2)) = (e1)))\/((op (e1) (e1)) = (e2))) -> (~((op (e0) (e1)) = (op (e1) (e1)))) -> (((op (e1) (e0)) = (e1))\/(((op (e1) (e1)) = (e1))\/(((op (e1) (e2)) = (e1))\/((op (e1) (e3)) = (e1))))) -> (~((op (e1) (e1)) = (e1))) -> (~((op (e1) (e0)) = (e1))) -> ((~((op (e2) (e0)) = (e1)))\/((op (e2) (e1)) = (e0))) -> ((op (e0) (e1)) = (e0)) -> ((~((op (e3) (e0)) = (e1)))\/((op (e3) (e1)) = (e0))) -> (((op (e0) (e0)) = (e1))\/(((op (e0) (e1)) = (e1))\/(((op (e0) (e2)) = (e1))\/((op (e0) (e3)) = (e1))))) -> (~((op (e0) (e3)) = (e1))) -> (((op (e0) (e0)) = (e1))\/(((op (e1) (e0)) = (e1))\/(((op (e2) (e0)) = (e1))\/((op (e3) (e0)) = (e1))))) -> (~((op (e0) (e1)) = (e1))) -> (~((op (e0) (e0)) = (op (e0) (e2)))) -> (((op (e0) (e2)) = (e1))\/(((op (e1) (e2)) = (e1))\/(((op (e2) (e2)) = (e1))\/((op (e3) (e2)) = (e1))))) -> (~((op (e0) (e1)) = (op (e3) (e1)))) -> ((op (e0) (e1)) = (e2)) -> ((~((op (e3) (e2)) = (e1)))\/((op (e3) (e1)) = (e2))) -> (~((op (e0) (e1)) = (op (e2) (e1)))) -> ((~((op (e2) (e2)) = (e1)))\/((op (e2) (e1)) = (e2))) -> ((~((op (e1) (e3)) = (e1)))\/((op (e1) (e1)) = (e3))) -> False). % 18.79/18.95 do 0 intro. intros zenon_H256 zenon_H10e zenon_H128 zenon_H10a zenon_H1ef zenon_H257 zenon_H49 zenon_H254 zenon_H22d zenon_H231 zenon_H235 zenon_Ha4 zenon_H13c zenon_H139 zenon_H210 zenon_H10f zenon_H252 zenon_H17e zenon_H253 zenon_H258. % 18.79/18.95 apply (zenon_or_s _ _ zenon_H256); [ zenon_intro zenon_H24d | zenon_intro zenon_H110 ]. % 18.79/18.95 apply (zenon_or_s _ _ zenon_H258); [ zenon_intro zenon_H24e | zenon_intro zenon_H13f ]. % 18.79/18.95 apply (zenon_L713_); trivial. % 18.79/18.95 apply (zenon_or_s _ _ zenon_H257); [ zenon_intro zenon_H1db | zenon_intro zenon_H36 ]. % 18.79/18.95 apply (zenon_L718_); trivial. % 18.79/18.95 apply (zenon_L128_); trivial. % 18.79/18.95 apply (zenon_L67_); trivial. % 18.79/18.95 (* end of lemma zenon_L726_ *) % 18.79/18.95 assert (zenon_L727_ : (((op (e2) (e2)) = (e0))\/(((op (e2) (e2)) = (e1))\/(((op (e2) (e2)) = (e2))\/((op (e2) (e2)) = (e3))))) -> (~((op (e2) (e2)) = (op (e2) (e3)))) -> ((op (e2) (e3)) = (e0)) -> (~((op (e2) (e2)) = (e1))) -> (~((op (e2) (e2)) = (e2))) -> (~((op (e0) (e2)) = (op (e2) (e2)))) -> ((op (e0) (e2)) = (e3)) -> False). % 18.79/18.95 do 0 intro. intros zenon_H1c4 zenon_H6d zenon_H37 zenon_H198 zenon_H173 zenon_Ha8 zenon_Ha9. % 18.79/18.95 apply (zenon_or_s _ _ zenon_H1c4); [ zenon_intro zenon_H2c | zenon_intro zenon_H1c5 ]. % 18.79/18.95 apply (zenon_L18_); trivial. % 18.79/18.95 apply (zenon_or_s _ _ zenon_H1c5); [ zenon_intro zenon_Hf1 | zenon_intro zenon_H1c6 ]. % 18.79/18.95 exact (zenon_H198 zenon_Hf1). % 18.79/18.95 apply (zenon_or_s _ _ zenon_H1c6); [ zenon_intro zenon_H176 | zenon_intro zenon_Haa ]. % 18.79/18.95 exact (zenon_H173 zenon_H176). % 18.79/18.95 apply (zenon_L40_); trivial. % 18.79/18.95 (* end of lemma zenon_L727_ *) % 18.79/18.95 assert (zenon_L728_ : (((op (e2) (e0)) = (e0))\/(((op (e2) (e1)) = (e0))\/(((op (e2) (e2)) = (e0))\/((op (e2) (e3)) = (e0))))) -> (~((e0) = (e2))) -> ((op (e2) (e0)) = (e2)) -> ((op (e0) (e1)) = (e0)) -> (~((op (e0) (e1)) = (op (e2) (e1)))) -> ((op (e1) (e2)) = (e0)) -> (~((op (e1) (e2)) = (op (e2) (e2)))) -> (((op (e2) (e2)) = (e0))\/(((op (e2) (e2)) = (e1))\/(((op (e2) (e2)) = (e2))\/((op (e2) (e2)) = (e3))))) -> (~((op (e2) (e2)) = (op (e2) (e3)))) -> (~((op (e2) (e2)) = (e1))) -> (~((op (e2) (e2)) = (e2))) -> (~((op (e0) (e2)) = (op (e2) (e2)))) -> ((op (e0) (e2)) = (e3)) -> False). % 18.79/18.95 do 0 intro. intros zenon_H2f zenon_H149 zenon_Hee zenon_H49 zenon_H17e zenon_H2a zenon_H2b zenon_H1c4 zenon_H6d zenon_H198 zenon_H173 zenon_Ha8 zenon_Ha9. % 18.79/18.95 apply (zenon_or_s _ _ zenon_H2f); [ zenon_intro zenon_H34 | zenon_intro zenon_H33 ]. % 18.79/18.95 apply (zenon_L204_); trivial. % 18.79/18.95 apply (zenon_or_s _ _ zenon_H33); [ zenon_intro zenon_H36 | zenon_intro zenon_H35 ]. % 18.79/18.95 apply (zenon_L128_); trivial. % 18.79/18.95 apply (zenon_or_s _ _ zenon_H35); [ zenon_intro zenon_H2c | zenon_intro zenon_H37 ]. % 18.79/18.95 apply (zenon_L3_); trivial. % 18.79/18.95 apply (zenon_L727_); trivial. % 18.79/18.95 (* end of lemma zenon_L728_ *) % 18.79/18.95 assert (zenon_L729_ : (((op (e2) (e0)) = (e0))\/(((op (e2) (e0)) = (e1))\/(((op (e2) (e0)) = (e2))\/((op (e2) (e0)) = (e3))))) -> (~((op (e2) (e0)) = (op (e2) (e3)))) -> ((op (e2) (e3)) = (e0)) -> (~((op (e2) (e0)) = (e1))) -> ((op (e2) (e1)) = (e2)) -> (~((op (e2) (e0)) = (op (e2) (e1)))) -> ((op (e1) (e0)) = (e2)) -> ((op (e0) (e0)) = (e1)) -> False). % 18.79/18.95 do 0 intro. intros zenon_H259 zenon_H5b zenon_H37 zenon_H1db zenon_H1ca zenon_H1f0 zenon_H86 zenon_H7a. % 18.79/18.95 apply (zenon_or_s _ _ zenon_H259); [ zenon_intro zenon_H34 | zenon_intro zenon_H25a ]. % 18.79/18.95 apply (zenon_L14_); trivial. % 18.79/18.95 apply (zenon_or_s _ _ zenon_H25a); [ zenon_intro zenon_Hed | zenon_intro zenon_H25b ]. % 18.79/18.95 exact (zenon_H1db zenon_Hed). % 18.79/18.95 apply (zenon_or_s _ _ zenon_H25b); [ zenon_intro zenon_Hee | zenon_intro zenon_H3b ]. % 18.79/18.95 apply (zenon_L277_); trivial. % 18.79/18.95 apply (zenon_L33_); trivial. % 18.79/18.95 (* end of lemma zenon_L729_ *) % 18.79/18.95 assert (zenon_L730_ : (((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 (e0) (e1)) = (e0)) -> (~((op (e0) (e1)) = (op (e2) (e1)))) -> ((op (e1) (e2)) = (e0)) -> (~((op (e1) (e2)) = (op (e2) (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) (e0)) = (e1))) -> ((op (e2) (e1)) = (e2)) -> (~((op (e2) (e0)) = (op (e2) (e1)))) -> ((op (e1) (e0)) = (e2)) -> ((op (e0) (e0)) = (e1)) -> False). % 18.79/18.95 do 0 intro. intros zenon_H2f zenon_H17b zenon_H44 zenon_H49 zenon_H17e zenon_H2a zenon_H2b zenon_H259 zenon_H5b zenon_H1db zenon_H1ca zenon_H1f0 zenon_H86 zenon_H7a. % 18.79/18.95 apply (zenon_or_s _ _ zenon_H2f); [ zenon_intro zenon_H34 | zenon_intro zenon_H33 ]. % 18.79/18.95 apply (zenon_L127_); trivial. % 18.79/18.95 apply (zenon_or_s _ _ zenon_H33); [ zenon_intro zenon_H36 | zenon_intro zenon_H35 ]. % 18.79/18.95 apply (zenon_L128_); trivial. % 18.79/18.95 apply (zenon_or_s _ _ zenon_H35); [ zenon_intro zenon_H2c | zenon_intro zenon_H37 ]. % 18.79/18.95 apply (zenon_L3_); trivial. % 18.79/18.95 apply (zenon_L729_); trivial. % 18.79/18.95 (* end of lemma zenon_L730_ *) % 18.79/18.95 assert (zenon_L731_ : (((op (e3) (e0)) = (e0))\/(((op (e3) (e1)) = (e0))\/(((op (e3) (e2)) = (e0))\/((op (e3) (e3)) = (e0))))) -> ((op (e0) (e0)) = (e1)) -> ((op (e1) (e0)) = (e2)) -> (~((op (e2) (e0)) = (op (e2) (e1)))) -> ((op (e2) (e1)) = (e2)) -> (~((op (e2) (e0)) = (e1))) -> (~((op (e2) (e0)) = (op (e2) (e3)))) -> (((op (e2) (e0)) = (e0))\/(((op (e2) (e0)) = (e1))\/(((op (e2) (e0)) = (e2))\/((op (e2) (e0)) = (e3))))) -> (~((op (e1) (e2)) = (op (e2) (e2)))) -> ((op (e1) (e2)) = (e0)) -> (~((op (e0) (e1)) = (op (e2) (e1)))) -> ((op (e0) (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)) -> ((op (e2) (e1)) = (e3)) -> ((op (e0) (e2)) = (e3)) -> (~((op (e0) (e2)) = (op (e2) (e2)))) -> (~((op (e2) (e2)) = (e2))) -> (~((op (e2) (e2)) = (op (e2) (e3)))) -> (~((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)) = (e1)) -> ((op (e0) (e3)) = (e2)) -> False). % 18.79/18.95 do 0 intro. intros zenon_H1ac zenon_H7a zenon_H86 zenon_H1f0 zenon_H1ca zenon_H1db zenon_H5b zenon_H259 zenon_H2b zenon_H2a zenon_H17e zenon_H49 zenon_H17b zenon_H2f zenon_H110 zenon_Ha6 zenon_Ha9 zenon_Ha8 zenon_H173 zenon_H6d zenon_H18f zenon_H1c4 zenon_Hf4 zenon_Hcd. % 18.79/18.95 apply (zenon_or_s _ _ zenon_H1ac); [ zenon_intro zenon_H44 | zenon_intro zenon_H1af ]. % 18.79/18.95 apply (zenon_L730_); trivial. % 18.79/18.95 apply (zenon_or_s _ _ zenon_H1af); [ zenon_intro zenon_H1b1 | zenon_intro zenon_H1b0 ]. % 18.79/18.95 apply (zenon_L509_); trivial. % 18.79/18.95 apply (zenon_or_s _ _ zenon_H1b0); [ zenon_intro zenon_H61 | zenon_intro zenon_H60 ]. % 18.79/18.95 apply (zenon_L483_); trivial. % 18.79/18.95 apply (zenon_L229_); trivial. % 18.79/18.95 (* end of lemma zenon_L731_ *) % 18.79/18.95 assert (zenon_L732_ : (((op (e2) (e0)) = (e1))\/(((op (e2) (e1)) = (e1))\/(((op (e2) (e2)) = (e1))\/((op (e2) (e3)) = (e1))))) -> (~((op (e2) (e0)) = (e1))) -> (~((op (e2) (e1)) = (e1))) -> ((op (e1) (e2)) = (e1)) -> (~((op (e1) (e2)) = (op (e2) (e2)))) -> (((op (e2) (e2)) = (e0))\/(((op (e2) (e2)) = (e1))\/(((op (e2) (e2)) = (e2))\/((op (e2) (e2)) = (e3))))) -> ((op (e3) (e2)) = (e0)) -> (~((op (e2) (e2)) = (op (e3) (e2)))) -> (~((op (e2) (e2)) = (op (e2) (e3)))) -> (~((op (e2) (e2)) = (e2))) -> (~((op (e0) (e2)) = (op (e2) (e2)))) -> ((op (e0) (e2)) = (e3)) -> False). % 18.79/18.95 do 0 intro. intros zenon_H106 zenon_H1db zenon_H24f zenon_Hf0 zenon_H2b zenon_H1c4 zenon_H61 zenon_H18f zenon_H6d zenon_H173 zenon_Ha8 zenon_Ha9. % 18.79/18.95 apply (zenon_or_s _ _ zenon_H106); [ zenon_intro zenon_Hed | zenon_intro zenon_H107 ]. % 18.79/18.95 exact (zenon_H1db zenon_Hed). % 18.79/18.95 apply (zenon_or_s _ _ zenon_H107); [ zenon_intro zenon_Ha5 | zenon_intro zenon_H108 ]. % 18.79/18.95 exact (zenon_H24f zenon_Ha5). % 18.79/18.95 apply (zenon_or_s _ _ zenon_H108); [ zenon_intro zenon_Hf1 | zenon_intro zenon_Hf4 ]. % 18.79/18.95 apply (zenon_L59_); trivial. % 18.79/18.95 apply (zenon_L483_); trivial. % 18.79/18.95 (* end of lemma zenon_L732_ *) % 18.79/18.95 assert (zenon_L733_ : (((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)) = (e3)) -> (~((op (e0) (e2)) = (op (e2) (e2)))) -> (~((op (e2) (e2)) = (e2))) -> (~((op (e2) (e2)) = (op (e2) (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) (e1)) = (e1))) -> (~((op (e2) (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 (e3) (e0)) = (e0))\/(((op (e3) (e1)) = (e0))\/(((op (e3) (e2)) = (e0))\/((op (e3) (e3)) = (e0))))) -> ((op (e0) (e0)) = (e1)) -> ((op (e1) (e0)) = (e2)) -> (~((op (e2) (e0)) = (op (e2) (e1)))) -> ((op (e2) (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) (e1)) = (op (e2) (e1)))) -> ((op (e0) (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)) -> ((op (e2) (e1)) = (e3)) -> ((op (e0) (e3)) = (e2)) -> (~((e0) = (e3))) -> (((op (e0) (e2)) = (e0))\/(((op (e1) (e2)) = (e0))\/(((op (e2) (e2)) = (e0))\/((op (e3) (e2)) = (e0))))) -> (~((op (e1) (e3)) = (e1))) -> False). % 18.79/18.95 do 0 intro. intros zenon_H128 zenon_H1ef zenon_H10a zenon_Ha9 zenon_Ha8 zenon_H173 zenon_H6d zenon_H18f zenon_H1c4 zenon_H2b zenon_H24f zenon_H1db zenon_H106 zenon_H52 zenon_H34 zenon_H1ac zenon_H7a zenon_H86 zenon_H1f0 zenon_H1ca zenon_H5b zenon_H259 zenon_H17e zenon_H49 zenon_H17b zenon_H2f zenon_H110 zenon_Ha6 zenon_Hcd zenon_H9a zenon_H6a zenon_H24e. % 18.79/18.95 apply (zenon_or_s _ _ zenon_H128); [ zenon_intro zenon_H9d | zenon_intro zenon_H129 ]. % 18.79/18.95 exact (zenon_H1ef zenon_H9d). % 18.79/18.95 apply (zenon_or_s _ _ zenon_H129); [ zenon_intro zenon_H10d | zenon_intro zenon_H12a ]. % 18.79/18.95 exact (zenon_H10a zenon_H10d). % 18.79/18.95 apply (zenon_or_s _ _ zenon_H12a); [ zenon_intro zenon_Hf0 | zenon_intro zenon_Hd6 ]. % 18.79/18.95 apply (zenon_or_s _ _ zenon_H6a); [ zenon_intro zenon_H48 | zenon_intro zenon_H6b ]. % 18.79/18.95 apply (zenon_L358_); trivial. % 18.79/18.95 apply (zenon_or_s _ _ zenon_H6b); [ zenon_intro zenon_H2a | zenon_intro zenon_H6c ]. % 18.79/18.95 apply (zenon_or_s _ _ zenon_H106); [ zenon_intro zenon_Hed | zenon_intro zenon_H107 ]. % 18.79/18.95 exact (zenon_H1db zenon_Hed). % 18.79/18.95 apply (zenon_or_s _ _ zenon_H107); [ zenon_intro zenon_Ha5 | zenon_intro zenon_H108 ]. % 18.79/18.95 exact (zenon_H24f zenon_Ha5). % 18.79/18.95 apply (zenon_or_s _ _ zenon_H108); [ zenon_intro zenon_Hf1 | zenon_intro zenon_Hf4 ]. % 18.79/18.95 apply (zenon_L59_); trivial. % 18.79/18.95 apply (zenon_L731_); trivial. % 18.79/18.95 apply (zenon_or_s _ _ zenon_H6c); [ zenon_intro zenon_H2c | zenon_intro zenon_H61 ]. % 18.79/18.95 apply (zenon_L11_); trivial. % 18.79/18.95 apply (zenon_L732_); trivial. % 18.79/18.95 exact (zenon_H24e zenon_Hd6). % 18.79/18.95 (* end of lemma zenon_L733_ *) % 18.79/18.95 assert (zenon_L734_ : (((op (e2) (e0)) = (e3))\/(((op (e2) (e1)) = (e3))\/(((op (e2) (e2)) = (e3))\/((op (e2) (e3)) = (e3))))) -> ((op (e0) (e0)) = (e1)) -> ((op (e1) (e0)) = (e2)) -> ((op (e1) (e1)) = (e2)) -> ((op (e3) (e1)) = (e0)) -> (~((op (e2) (e2)) = (op (e3) (e2)))) -> (~((op (e0) (e2)) = (op (e3) (e2)))) -> ((op (e0) (e2)) = (e2)) -> ((op (e1) (e2)) = (e0)) -> (~((op (e1) (e2)) = (op (e3) (e2)))) -> (((op (e3) (e2)) = (e0))\/(((op (e3) (e2)) = (e1))\/(((op (e3) (e2)) = (e2))\/((op (e3) (e2)) = (e3))))) -> (~((op (e0) (e3)) = (op (e2) (e3)))) -> ((op (e0) (e3)) = (e3)) -> False). % 18.79/18.95 do 0 intro. intros zenon_He7 zenon_H7a zenon_H86 zenon_H110 zenon_H1b1 zenon_H18f zenon_H14f zenon_H150 zenon_H2a zenon_H115 zenon_H191 zenon_He2 zenon_He3. % 18.79/18.95 apply (zenon_or_s _ _ zenon_He7); [ zenon_intro zenon_H3b | zenon_intro zenon_He9 ]. % 18.79/18.95 apply (zenon_L33_); trivial. % 18.79/18.95 apply (zenon_or_s _ _ zenon_He9); [ zenon_intro zenon_Ha6 | zenon_intro zenon_Hea ]. % 18.79/18.95 apply (zenon_L509_); trivial. % 18.79/18.95 apply (zenon_or_s _ _ zenon_Hea); [ zenon_intro zenon_Haa | zenon_intro zenon_Hdd ]. % 18.79/18.95 apply (zenon_L181_); trivial. % 18.79/18.95 apply (zenon_L54_); trivial. % 18.79/18.95 (* end of lemma zenon_L734_ *) % 18.79/18.95 assert (zenon_L735_ : (((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 (e0) (e3)) = (e3)) -> (~((op (e0) (e3)) = (op (e2) (e3)))) -> (((op (e3) (e2)) = (e0))\/(((op (e3) (e2)) = (e1))\/(((op (e3) (e2)) = (e2))\/((op (e3) (e2)) = (e3))))) -> (~((op (e1) (e2)) = (op (e3) (e2)))) -> ((op (e0) (e2)) = (e2)) -> (~((op (e0) (e2)) = (op (e3) (e2)))) -> (~((op (e2) (e2)) = (op (e3) (e2)))) -> ((op (e1) (e1)) = (e2)) -> ((op (e1) (e0)) = (e2)) -> ((op (e0) (e0)) = (e1)) -> (((op (e2) (e0)) = (e3))\/(((op (e2) (e1)) = (e3))\/(((op (e2) (e2)) = (e3))\/((op (e2) (e3)) = (e3))))) -> ((op (e2) (e0)) = (e0)) -> (~((op (e2) (e0)) = (op (e2) (e2)))) -> (~((op (e3) (e1)) = (op (e3) (e2)))) -> ((op (e3) (e1)) = (e0)) -> False). % 18.79/18.95 do 0 intro. intros zenon_H6a zenon_H4a zenon_H49 zenon_He3 zenon_He2 zenon_H191 zenon_H115 zenon_H150 zenon_H14f zenon_H18f zenon_H110 zenon_H86 zenon_H7a zenon_He7 zenon_H34 zenon_H52 zenon_H1a4 zenon_H1b1. % 18.79/18.95 apply (zenon_or_s _ _ zenon_H6a); [ zenon_intro zenon_H48 | zenon_intro zenon_H6b ]. % 18.79/18.95 apply (zenon_L9_); trivial. % 18.79/18.95 apply (zenon_or_s _ _ zenon_H6b); [ zenon_intro zenon_H2a | zenon_intro zenon_H6c ]. % 18.79/18.95 apply (zenon_L734_); trivial. % 18.79/18.95 apply (zenon_or_s _ _ zenon_H6c); [ zenon_intro zenon_H2c | zenon_intro zenon_H61 ]. % 18.79/18.95 apply (zenon_L11_); trivial. % 18.79/18.95 apply (zenon_L247_); trivial. % 18.79/18.95 (* end of lemma zenon_L735_ *) % 18.79/18.95 assert (zenon_L736_ : (((op (e3) (e0)) = (e0))\/(((op (e3) (e1)) = (e0))\/(((op (e3) (e2)) = (e0))\/((op (e3) (e3)) = (e0))))) -> (~((e0) = (e2))) -> ((op (e3) (e0)) = (e2)) -> ((op (e1) (e1)) = (e2)) -> ((op (e2) (e1)) = (e3)) -> ((op (e1) (e2)) = (e0)) -> (~((op (e1) (e2)) = (op (e3) (e2)))) -> ((op (e2) (e3)) = (e1)) -> ((op (e0) (e3)) = (e2)) -> False). % 18.79/18.95 do 0 intro. intros zenon_H1ac zenon_H149 zenon_H148 zenon_H110 zenon_Ha6 zenon_H2a zenon_H115 zenon_Hf4 zenon_Hcd. % 18.79/18.95 apply (zenon_or_s _ _ zenon_H1ac); [ zenon_intro zenon_H44 | zenon_intro zenon_H1af ]. % 18.79/18.95 apply (zenon_L100_); trivial. % 18.79/18.95 apply (zenon_or_s _ _ zenon_H1af); [ zenon_intro zenon_H1b1 | zenon_intro zenon_H1b0 ]. % 18.79/18.95 apply (zenon_L509_); trivial. % 18.79/18.95 apply (zenon_or_s _ _ zenon_H1b0); [ zenon_intro zenon_H61 | zenon_intro zenon_H60 ]. % 18.79/18.95 apply (zenon_L176_); trivial. % 18.79/18.95 apply (zenon_L229_); trivial. % 18.79/18.95 (* end of lemma zenon_L736_ *) % 18.79/18.95 assert (zenon_L737_ : (((op (e1) (e0)) = (e3))\/(((op (e1) (e1)) = (e3))\/(((op (e1) (e2)) = (e3))\/((op (e1) (e3)) = (e3))))) -> ((op (e0) (e0)) = (e1)) -> (~((e1) = (e3))) -> (((op (e2) (e0)) = (e1))\/(((op (e2) (e1)) = (e1))\/(((op (e2) (e2)) = (e1))\/((op (e2) (e3)) = (e1))))) -> (~((op (e2) (e0)) = (e1))) -> (~((op (e2) (e1)) = (e1))) -> ((op (e1) (e2)) = (e1)) -> (~((op (e1) (e2)) = (op (e2) (e2)))) -> (((op (e0) (e3)) = (e2))\/(((op (e1) (e3)) = (e2))\/(((op (e2) (e3)) = (e2))\/((op (e3) (e3)) = (e2))))) -> (~((op (e1) (e2)) = (op (e3) (e2)))) -> ((op (e1) (e2)) = (e0)) -> ((op (e2) (e1)) = (e3)) -> ((op (e1) (e1)) = (e2)) -> (~((e0) = (e2))) -> (((op (e3) (e0)) = (e0))\/(((op (e3) (e1)) = (e0))\/(((op (e3) (e2)) = (e0))\/((op (e3) (e3)) = (e0))))) -> (~((e2) = (e3))) -> (~((op (e2) (e1)) = (op (e2) (e3)))) -> ((op (e2) (e1)) = (e2)) -> ((op (e3) (e0)) = (e2)) -> (~((op (e3) (e0)) = (op (e3) (e3)))) -> False). % 18.79/18.95 do 0 intro. intros zenon_H16f zenon_H7a zenon_H95 zenon_H106 zenon_H1db zenon_H24f zenon_Hf0 zenon_H2b zenon_H145 zenon_H115 zenon_H2a zenon_Ha6 zenon_H110 zenon_H149 zenon_H1ac zenon_H12b zenon_H1c7 zenon_H1ca zenon_H148 zenon_H71. % 18.79/18.95 apply (zenon_or_s _ _ zenon_H16f); [ zenon_intro zenon_H9e | zenon_intro zenon_H170 ]. % 18.79/18.95 apply (zenon_L107_); trivial. % 18.79/18.95 apply (zenon_or_s _ _ zenon_H170); [ zenon_intro zenon_H13f | zenon_intro zenon_H171 ]. % 18.79/18.95 apply (zenon_L166_); trivial. % 18.79/18.95 apply (zenon_or_s _ _ zenon_H171); [ zenon_intro zenon_H16c | zenon_intro zenon_Hdc ]. % 18.79/18.95 apply (zenon_L167_); trivial. % 18.79/18.95 apply (zenon_or_s _ _ zenon_H106); [ zenon_intro zenon_Hed | zenon_intro zenon_H107 ]. % 18.79/18.95 exact (zenon_H1db zenon_Hed). % 18.79/18.95 apply (zenon_or_s _ _ zenon_H107); [ zenon_intro zenon_Ha5 | zenon_intro zenon_H108 ]. % 18.79/18.95 exact (zenon_H24f zenon_Ha5). % 18.79/18.95 apply (zenon_or_s _ _ zenon_H108); [ zenon_intro zenon_Hf1 | zenon_intro zenon_Hf4 ]. % 18.79/18.95 apply (zenon_L59_); trivial. % 18.79/18.95 apply (zenon_or_s _ _ zenon_H145); [ zenon_intro zenon_Hcd | zenon_intro zenon_H146 ]. % 18.79/18.95 apply (zenon_L736_); trivial. % 18.79/18.95 apply (zenon_or_s _ _ zenon_H146); [ zenon_intro zenon_Hd7 | zenon_intro zenon_H147 ]. % 18.79/18.95 apply (zenon_L266_); trivial. % 18.79/18.95 apply (zenon_or_s _ _ zenon_H147); [ zenon_intro zenon_H11d | zenon_intro zenon_Hf6 ]. % 18.79/18.95 apply (zenon_L224_); trivial. % 18.79/18.95 apply (zenon_L114_); trivial. % 18.79/18.95 (* end of lemma zenon_L737_ *) % 18.79/18.95 assert (zenon_L738_ : (((op (e1) (e3)) = (e0))\/(((op (e1) (e3)) = (e1))\/(((op (e1) (e3)) = (e2))\/((op (e1) (e3)) = (e3))))) -> ((op (e3) (e3)) = (e0)) -> (~((op (e1) (e3)) = (e1))) -> ((op (e3) (e3)) = (e2)) -> (~((op (e1) (e3)) = (op (e3) (e3)))) -> (~((op (e0) (e3)) = (op (e1) (e3)))) -> ((op (e0) (e3)) = (e3)) -> False). % 18.79/18.95 do 0 intro. intros zenon_Hdf zenon_H60 zenon_H24e zenon_Hf6 zenon_Hd5 zenon_H1d zenon_He3. % 18.79/18.95 apply (zenon_or_s _ _ zenon_Hdf); [ zenon_intro zenon_H1f | zenon_intro zenon_He0 ]. % 18.79/18.95 apply (zenon_L136_); trivial. % 18.79/18.95 apply (zenon_or_s _ _ zenon_He0); [ zenon_intro zenon_Hd6 | zenon_intro zenon_He1 ]. % 18.79/18.95 exact (zenon_H24e zenon_Hd6). % 18.79/18.95 apply (zenon_or_s _ _ zenon_He1); [ zenon_intro zenon_Hd7 | zenon_intro zenon_Hdc ]. % 18.79/18.95 apply (zenon_L402_); trivial. % 18.79/18.95 apply (zenon_L117_); trivial. % 18.79/18.95 (* end of lemma zenon_L738_ *) % 18.79/18.95 assert (zenon_L739_ : (((op (e0) (e3)) = (e2))\/(((op (e1) (e3)) = (e2))\/(((op (e2) (e3)) = (e2))\/((op (e3) (e3)) = (e2))))) -> (~((e2) = (e3))) -> ((op (e0) (e3)) = (e3)) -> (~((op (e1) (e0)) = (op (e1) (e3)))) -> ((op (e1) (e0)) = (e2)) -> (~((op (e2) (e1)) = (op (e2) (e3)))) -> ((op (e2) (e1)) = (e2)) -> ((op (e3) (e1)) = (e2)) -> (~((op (e3) (e1)) = (op (e3) (e3)))) -> False). % 18.79/18.95 do 0 intro. intros zenon_H145 zenon_H12b zenon_He3 zenon_Hd8 zenon_H86 zenon_H1c7 zenon_H1ca zenon_H14d zenon_H130. % 18.79/18.95 apply (zenon_or_s _ _ zenon_H145); [ zenon_intro zenon_Hcd | zenon_intro zenon_H146 ]. % 18.79/18.95 apply (zenon_L81_); trivial. % 18.79/18.95 apply (zenon_or_s _ _ zenon_H146); [ zenon_intro zenon_Hd7 | zenon_intro zenon_H147 ]. % 18.79/18.95 apply (zenon_L51_); trivial. % 18.79/18.95 apply (zenon_or_s _ _ zenon_H147); [ zenon_intro zenon_H11d | zenon_intro zenon_Hf6 ]. % 18.79/18.95 apply (zenon_L224_); trivial. % 18.79/18.95 apply (zenon_L102_); trivial. % 18.79/18.95 (* end of lemma zenon_L739_ *) % 18.79/18.95 assert (zenon_L740_ : (((op (e1) (e0)) = (e0))\/(((op (e1) (e1)) = (e0))\/(((op (e1) (e2)) = (e0))\/((op (e1) (e3)) = (e0))))) -> (~((op (e3) (e2)) = (op (e3) (e3)))) -> (~((op (e1) (e1)) = (op (e1) (e3)))) -> (~((e0) = (e3))) -> (((op (e0) (e3)) = (e0))\/(((op (e1) (e3)) = (e0))\/(((op (e2) (e3)) = (e0))\/((op (e3) (e3)) = (e0))))) -> (~((op (e1) (e1)) = (op (e1) (e2)))) -> (~((op (e2) (e0)) = (op (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 (e0) (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 (e3) (e1)) = (op (e3) (e2)))) -> (~((op (e2) (e0)) = (op (e2) (e2)))) -> ((op (e2) (e0)) = (e0)) -> (((op (e2) (e0)) = (e3))\/(((op (e2) (e1)) = (e3))\/(((op (e2) (e2)) = (e3))\/((op (e2) (e3)) = (e3))))) -> (~((op (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 (e2) (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 (e3) (e0)) = (op (e3) (e3)))) -> (((op (e3) (e0)) = (e0))\/(((op (e3) (e1)) = (e0))\/(((op (e3) (e2)) = (e0))\/((op (e3) (e3)) = (e0))))) -> (~((e0) = (e2))) -> ((op (e2) (e1)) = (e3)) -> (~((op (e1) (e2)) = (op (e3) (e2)))) -> (~((e1) = (e2))) -> ((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 (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 (e3) (e2)))) -> ((op (e0) (e2)) = (e2)) -> (((op (e0) (e3)) = (e2))\/(((op (e1) (e3)) = (e2))\/(((op (e2) (e3)) = (e2))\/((op (e3) (e3)) = (e2))))) -> (~((e2) = (e3))) -> ((op (e0) (e3)) = (e3)) -> (~((op (e1) (e0)) = (op (e1) (e3)))) -> ((op (e1) (e0)) = (e2)) -> (~((op (e2) (e1)) = (op (e2) (e3)))) -> ((op (e2) (e1)) = (e2)) -> (~((op (e3) (e1)) = (op (e3) (e3)))) -> (((op (e1) (e0)) = (e3))\/(((op (e1) (e1)) = (e3))\/(((op (e1) (e2)) = (e3))\/((op (e1) (e3)) = (e3))))) -> ((op (e0) (e0)) = (e1)) -> ((op (e1) (e1)) = (e2)) -> (~((e1) = (e3))) -> (~((op (e0) (e3)) = (op (e1) (e3)))) -> (((op (e3) (e0)) = (e2))\/(((op (e3) (e1)) = (e2))\/(((op (e3) (e2)) = (e2))\/((op (e3) (e3)) = (e2))))) -> (~((op (e1) (e2)) = (op (e2) (e2)))) -> (~((op (e2) (e1)) = (e1))) -> (~((op (e2) (e0)) = (e1))) -> (((op (e2) (e0)) = (e1))\/(((op (e2) (e1)) = (e1))\/(((op (e2) (e2)) = (e1))\/((op (e2) (e3)) = (e1))))) -> (~((op (e1) (e3)) = (e1))) -> False). % 18.79/18.95 do 0 intro. intros zenon_H22 zenon_H62 zenon_H57 zenon_H9a zenon_H67 zenon_H4f zenon_H1f0 zenon_H5b zenon_H259 zenon_H17e zenon_H17b zenon_H2f zenon_H1a4 zenon_H52 zenon_H34 zenon_He7 zenon_H18f zenon_H191 zenon_He2 zenon_H49 zenon_H4a zenon_H6a zenon_H71 zenon_H1ac zenon_H149 zenon_Ha6 zenon_H115 zenon_H7c zenon_Hae zenon_Hdf zenon_Hd5 zenon_H128 zenon_H1ef zenon_H10a zenon_H14f zenon_H150 zenon_H145 zenon_H12b zenon_He3 zenon_Hd8 zenon_H86 zenon_H1c7 zenon_H1ca zenon_H130 zenon_H16f zenon_H7a zenon_H110 zenon_H95 zenon_H1d zenon_H153 zenon_H2b zenon_H24f zenon_H1db zenon_H106 zenon_H24e. % 18.79/18.95 apply (zenon_or_s _ _ zenon_H22); [ zenon_intro zenon_H27 | zenon_intro zenon_H26 ]. % 18.79/18.95 apply (zenon_L257_); trivial. % 18.79/18.95 apply (zenon_or_s _ _ zenon_H26); [ zenon_intro zenon_H29 | zenon_intro zenon_H28 ]. % 18.79/18.95 apply (zenon_L724_); trivial. % 18.79/18.95 apply (zenon_or_s _ _ zenon_H28); [ zenon_intro zenon_H2a | zenon_intro zenon_H1f ]. % 18.79/18.95 apply (zenon_or_s _ _ zenon_H128); [ zenon_intro zenon_H9d | zenon_intro zenon_H129 ]. % 18.79/18.95 exact (zenon_H1ef zenon_H9d). % 18.79/18.95 apply (zenon_or_s _ _ zenon_H129); [ zenon_intro zenon_H10d | zenon_intro zenon_H12a ]. % 18.79/18.95 exact (zenon_H10a zenon_H10d). % 18.79/18.95 apply (zenon_or_s _ _ zenon_H12a); [ zenon_intro zenon_Hf0 | zenon_intro zenon_Hd6 ]. % 18.79/18.95 apply (zenon_or_s _ _ zenon_H1ac); [ zenon_intro zenon_H44 | zenon_intro zenon_H1af ]. % 18.79/18.95 apply (zenon_L730_); trivial. % 18.79/18.95 apply (zenon_or_s _ _ zenon_H1af); [ zenon_intro zenon_H1b1 | zenon_intro zenon_H1b0 ]. % 18.79/18.95 apply (zenon_L735_); trivial. % 18.79/18.95 apply (zenon_or_s _ _ zenon_H1b0); [ zenon_intro zenon_H61 | zenon_intro zenon_H60 ]. % 18.79/18.95 apply (zenon_L176_); trivial. % 18.79/18.95 apply (zenon_or_s _ _ zenon_H153); [ zenon_intro zenon_H148 | zenon_intro zenon_H154 ]. % 18.79/18.95 apply (zenon_L737_); trivial. % 18.79/18.95 apply (zenon_or_s _ _ zenon_H154); [ zenon_intro zenon_H14d | zenon_intro zenon_H155 ]. % 18.79/18.95 apply (zenon_L152_); trivial. % 18.79/18.95 apply (zenon_or_s _ _ zenon_H155); [ zenon_intro zenon_H151 | zenon_intro zenon_Hf6 ]. % 18.79/18.95 apply (zenon_L104_); trivial. % 18.79/18.95 apply (zenon_L738_); trivial. % 18.79/18.95 exact (zenon_H24e zenon_Hd6). % 18.79/18.95 apply (zenon_or_s _ _ zenon_H128); [ zenon_intro zenon_H9d | zenon_intro zenon_H129 ]. % 18.79/18.95 exact (zenon_H1ef zenon_H9d). % 18.79/18.95 apply (zenon_or_s _ _ zenon_H129); [ zenon_intro zenon_H10d | zenon_intro zenon_H12a ]. % 18.79/18.95 exact (zenon_H10a zenon_H10d). % 18.79/18.95 apply (zenon_or_s _ _ zenon_H12a); [ zenon_intro zenon_Hf0 | zenon_intro zenon_Hd6 ]. % 18.79/18.95 apply (zenon_or_s _ _ zenon_H106); [ zenon_intro zenon_Hed | zenon_intro zenon_H107 ]. % 18.79/18.95 exact (zenon_H1db zenon_Hed). % 18.79/18.95 apply (zenon_or_s _ _ zenon_H107); [ zenon_intro zenon_Ha5 | zenon_intro zenon_H108 ]. % 18.79/18.95 exact (zenon_H24f zenon_Ha5). % 18.79/18.95 apply (zenon_or_s _ _ zenon_H108); [ zenon_intro zenon_Hf1 | zenon_intro zenon_Hf4 ]. % 18.79/18.95 apply (zenon_L59_); trivial. % 18.79/18.95 apply (zenon_or_s _ _ zenon_H153); [ zenon_intro zenon_H148 | zenon_intro zenon_H154 ]. % 18.79/18.95 apply (zenon_L216_); trivial. % 18.79/18.95 apply (zenon_or_s _ _ zenon_H154); [ zenon_intro zenon_H14d | zenon_intro zenon_H155 ]. % 18.79/18.95 apply (zenon_L739_); trivial. % 18.79/18.95 apply (zenon_or_s _ _ zenon_H155); [ zenon_intro zenon_H151 | zenon_intro zenon_Hf6 ]. % 18.79/18.95 apply (zenon_L104_); trivial. % 18.79/18.95 apply (zenon_L63_); trivial. % 18.79/18.95 exact (zenon_H24e zenon_Hd6). % 18.79/18.95 (* end of lemma zenon_L740_ *) % 18.79/18.95 assert (zenon_L741_ : (((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)) = (e1))) -> (((op (e2) (e2)) = (e0))\/(((op (e2) (e2)) = (e1))\/(((op (e2) (e2)) = (e2))\/((op (e2) (e2)) = (e3))))) -> (~((op (e2) (e2)) = (op (e2) (e3)))) -> (~((op (e2) (e2)) = (e2))) -> (~((op (e0) (e2)) = (op (e2) (e2)))) -> ((op (e0) (e2)) = (e3)) -> (((op (e1) (e0)) = (e0))\/(((op (e1) (e1)) = (e0))\/(((op (e1) (e2)) = (e0))\/((op (e1) (e3)) = (e0))))) -> (~((op (e3) (e2)) = (op (e3) (e3)))) -> (~((op (e1) (e1)) = (op (e1) (e3)))) -> (~((e0) = (e3))) -> (((op (e0) (e3)) = (e0))\/(((op (e1) (e3)) = (e0))\/(((op (e2) (e3)) = (e0))\/((op (e3) (e3)) = (e0))))) -> (~((op (e1) (e1)) = (op (e1) (e2)))) -> (~((op (e2) (e0)) = (op (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 (e0) (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 (e3) (e1)) = (op (e3) (e2)))) -> (~((op (e2) (e0)) = (op (e2) (e2)))) -> ((op (e2) (e0)) = (e0)) -> (((op (e2) (e0)) = (e3))\/(((op (e2) (e1)) = (e3))\/(((op (e2) (e2)) = (e3))\/((op (e2) (e3)) = (e3))))) -> (~((op (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 (e2) (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 (e3) (e0)) = (op (e3) (e3)))) -> (((op (e3) (e0)) = (e0))\/(((op (e3) (e1)) = (e0))\/(((op (e3) (e2)) = (e0))\/((op (e3) (e3)) = (e0))))) -> (~((e0) = (e2))) -> ((op (e2) (e1)) = (e3)) -> (~((op (e1) (e2)) = (op (e3) (e2)))) -> (~((e1) = (e2))) -> ((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 (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 (e3) (e2)))) -> ((op (e0) (e2)) = (e2)) -> (((op (e0) (e3)) = (e2))\/(((op (e1) (e3)) = (e2))\/(((op (e2) (e3)) = (e2))\/((op (e3) (e3)) = (e2))))) -> (~((e2) = (e3))) -> (~((op (e1) (e0)) = (op (e1) (e3)))) -> ((op (e1) (e0)) = (e2)) -> (~((op (e2) (e1)) = (op (e2) (e3)))) -> ((op (e2) (e1)) = (e2)) -> (~((op (e3) (e1)) = (op (e3) (e3)))) -> (((op (e1) (e0)) = (e3))\/(((op (e1) (e1)) = (e3))\/(((op (e1) (e2)) = (e3))\/((op (e1) (e3)) = (e3))))) -> ((op (e0) (e0)) = (e1)) -> ((op (e1) (e1)) = (e2)) -> (~((e1) = (e3))) -> (~((op (e0) (e3)) = (op (e1) (e3)))) -> (((op (e3) (e0)) = (e2))\/(((op (e3) (e1)) = (e2))\/(((op (e3) (e2)) = (e2))\/((op (e3) (e3)) = (e2))))) -> (~((op (e1) (e2)) = (op (e2) (e2)))) -> (~((op (e2) (e1)) = (e1))) -> (~((op (e2) (e0)) = (e1))) -> (((op (e2) (e0)) = (e1))\/(((op (e2) (e1)) = (e1))\/(((op (e2) (e2)) = (e1))\/((op (e2) (e3)) = (e1))))) -> (~((op (e1) (e3)) = (e1))) -> False). % 18.79/18.95 do 0 intro. intros zenon_He4 zenon_H54 zenon_H231 zenon_H1c4 zenon_H6d zenon_H173 zenon_Ha8 zenon_Ha9 zenon_H22 zenon_H62 zenon_H57 zenon_H9a zenon_H67 zenon_H4f zenon_H1f0 zenon_H5b zenon_H259 zenon_H17e zenon_H17b zenon_H2f zenon_H1a4 zenon_H52 zenon_H34 zenon_He7 zenon_H18f zenon_H191 zenon_He2 zenon_H49 zenon_H4a zenon_H6a zenon_H71 zenon_H1ac zenon_H149 zenon_Ha6 zenon_H115 zenon_H7c zenon_Hae zenon_Hdf zenon_Hd5 zenon_H128 zenon_H1ef zenon_H10a zenon_H14f zenon_H150 zenon_H145 zenon_H12b zenon_Hd8 zenon_H86 zenon_H1c7 zenon_H1ca zenon_H130 zenon_H16f zenon_H7a zenon_H110 zenon_H95 zenon_H1d zenon_H153 zenon_H2b zenon_H24f zenon_H1db zenon_H106 zenon_H24e. % 18.79/18.95 apply (zenon_or_s _ _ zenon_He4); [ zenon_intro zenon_H1e | zenon_intro zenon_He5 ]. % 18.79/18.95 apply (zenon_L12_); trivial. % 18.79/18.95 apply (zenon_or_s _ _ zenon_He5); [ zenon_intro zenon_Hc3 | zenon_intro zenon_He6 ]. % 18.79/18.95 exact (zenon_H231 zenon_Hc3). % 18.79/18.95 apply (zenon_or_s _ _ zenon_He6); [ zenon_intro zenon_Hcd | zenon_intro zenon_He3 ]. % 18.79/18.95 apply (zenon_L733_); trivial. % 18.79/18.95 apply (zenon_L740_); trivial. % 18.79/18.95 (* end of lemma zenon_L741_ *) % 18.79/18.95 assert (zenon_L742_ : (((op (e3) (e0)) = (e0))\/(((op (e3) (e1)) = (e0))\/(((op (e3) (e2)) = (e0))\/((op (e3) (e3)) = (e0))))) -> (~((op (e3) (e3)) = (e3))) -> (~((op (e2) (e3)) = (op (e3) (e3)))) -> (~((op (e3) (e0)) = (op (e3) (e3)))) -> (((op (e3) (e3)) = (e0))\/(((op (e3) (e3)) = (e1))\/(((op (e3) (e3)) = (e2))\/((op (e3) (e3)) = (e3))))) -> ((op (e1) (e1)) = (e2)) -> ((op (e2) (e1)) = (e3)) -> ((op (e0) (e2)) = (e3)) -> (~((op (e0) (e2)) = (op (e2) (e2)))) -> (~((op (e2) (e2)) = (e2))) -> ((op (e2) (e3)) = (e1)) -> (~((op (e2) (e2)) = (op (e2) (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) (e3)) = (op (e3) (e3)))) -> ((op (e1) (e3)) = (e0)) -> False). % 18.79/18.95 do 0 intro. intros zenon_H1ac zenon_H102 zenon_Hf3 zenon_H71 zenon_H101 zenon_H110 zenon_Ha6 zenon_Ha9 zenon_Ha8 zenon_H173 zenon_Hf4 zenon_H6d zenon_H18f zenon_H1c4 zenon_Hd5 zenon_H1f. % 18.79/18.95 apply (zenon_or_s _ _ zenon_H1ac); [ zenon_intro zenon_H44 | zenon_intro zenon_H1af ]. % 18.79/18.95 apply (zenon_L64_); trivial. % 18.79/18.95 apply (zenon_or_s _ _ zenon_H1af); [ zenon_intro zenon_H1b1 | zenon_intro zenon_H1b0 ]. % 18.79/18.95 apply (zenon_L509_); trivial. % 18.79/18.95 apply (zenon_or_s _ _ zenon_H1b0); [ zenon_intro zenon_H61 | zenon_intro zenon_H60 ]. % 18.79/18.95 apply (zenon_L483_); trivial. % 18.79/18.95 apply (zenon_L136_); trivial. % 18.79/18.95 (* end of lemma zenon_L742_ *) % 18.79/18.95 assert (zenon_L743_ : (((op (e1) (e0)) = (e0))\/(((op (e1) (e1)) = (e0))\/(((op (e1) (e2)) = (e0))\/((op (e1) (e3)) = (e0))))) -> (~((op (e1) (e0)) = (op (e3) (e0)))) -> (((op (e0) (e2)) = (e0))\/(((op (e1) (e2)) = (e0))\/(((op (e2) (e2)) = (e0))\/((op (e3) (e2)) = (e0))))) -> (~((op (e0) (e1)) = (op (e0) (e2)))) -> (~((op (e1) (e1)) = (op (e1) (e2)))) -> (~((op (e3) (e0)) = (op (e3) (e2)))) -> (~((op (e1) (e1)) = (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))))) -> (~((op (e1) (e2)) = (op (e2) (e2)))) -> (~((op (e0) (e1)) = (op (e2) (e1)))) -> ((op (e0) (e1)) = (e0)) -> ((op (e3) (e0)) = (e0)) -> (~((op (e2) (e0)) = (op (e3) (e0)))) -> (((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) (e0)) = (e1))) -> (~((op (e2) (e1)) = (e1))) -> (~((op (e2) (e2)) = (e1))) -> (((op (e3) (e0)) = (e0))\/(((op (e3) (e1)) = (e0))\/(((op (e3) (e2)) = (e0))\/((op (e3) (e3)) = (e0))))) -> (~((op (e3) (e3)) = (e3))) -> (~((op (e2) (e3)) = (op (e3) (e3)))) -> (~((op (e3) (e0)) = (op (e3) (e3)))) -> (((op (e3) (e3)) = (e0))\/(((op (e3) (e3)) = (e1))\/(((op (e3) (e3)) = (e2))\/((op (e3) (e3)) = (e3))))) -> ((op (e1) (e1)) = (e2)) -> ((op (e2) (e1)) = (e3)) -> ((op (e0) (e2)) = (e3)) -> (~((op (e0) (e2)) = (op (e2) (e2)))) -> (~((op (e2) (e2)) = (e2))) -> (~((op (e2) (e2)) = (op (e2) (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) (e3)) = (op (e3) (e3)))) -> False). % 18.79/18.95 do 0 intro. intros zenon_H22 zenon_H1fa zenon_H6a zenon_H4a zenon_H4f zenon_H6f zenon_H57 zenon_H54 zenon_H67 zenon_H2b zenon_H17e zenon_H49 zenon_H44 zenon_H17b zenon_H2f zenon_H106 zenon_H1db zenon_H24f zenon_H198 zenon_H1ac zenon_H102 zenon_Hf3 zenon_H71 zenon_H101 zenon_H110 zenon_Ha6 zenon_Ha9 zenon_Ha8 zenon_H173 zenon_H6d zenon_H18f zenon_H1c4 zenon_Hd5. % 18.79/18.95 apply (zenon_or_s _ _ zenon_H22); [ zenon_intro zenon_H27 | zenon_intro zenon_H26 ]. % 18.79/18.95 apply (zenon_L312_); trivial. % 18.79/18.95 apply (zenon_or_s _ _ zenon_H26); [ zenon_intro zenon_H29 | zenon_intro zenon_H28 ]. % 18.79/18.95 apply (zenon_L22_); trivial. % 18.79/18.95 apply (zenon_or_s _ _ zenon_H28); [ zenon_intro zenon_H2a | zenon_intro zenon_H1f ]. % 18.79/18.95 apply (zenon_or_s _ _ zenon_H2f); [ zenon_intro zenon_H34 | zenon_intro zenon_H33 ]. % 18.79/18.95 apply (zenon_L127_); trivial. % 18.79/18.95 apply (zenon_or_s _ _ zenon_H33); [ zenon_intro zenon_H36 | zenon_intro zenon_H35 ]. % 18.79/18.95 apply (zenon_L128_); trivial. % 18.79/18.95 apply (zenon_or_s _ _ zenon_H35); [ zenon_intro zenon_H2c | zenon_intro zenon_H37 ]. % 18.79/18.95 apply (zenon_L3_); trivial. % 18.79/18.95 apply (zenon_L727_); trivial. % 18.79/18.95 apply (zenon_or_s _ _ zenon_H106); [ zenon_intro zenon_Hed | zenon_intro zenon_H107 ]. % 18.79/18.95 exact (zenon_H1db zenon_Hed). % 18.79/18.95 apply (zenon_or_s _ _ zenon_H107); [ zenon_intro zenon_Ha5 | zenon_intro zenon_H108 ]. % 18.79/18.95 exact (zenon_H24f zenon_Ha5). % 18.79/18.95 apply (zenon_or_s _ _ zenon_H108); [ zenon_intro zenon_Hf1 | zenon_intro zenon_Hf4 ]. % 18.79/18.95 exact (zenon_H198 zenon_Hf1). % 18.79/18.95 apply (zenon_L742_); trivial. % 18.79/18.95 (* end of lemma zenon_L743_ *) % 18.79/18.95 assert (zenon_L744_ : (((op (e0) (e3)) = (e0))\/(((op (e1) (e3)) = (e0))\/(((op (e2) (e3)) = (e0))\/((op (e3) (e3)) = (e0))))) -> (~((e0) = (e3))) -> ((op (e0) (e3)) = (e3)) -> (~((op (e1) (e1)) = (op (e1) (e3)))) -> ((op (e1) (e1)) = (e0)) -> (~((op (e2) (e2)) = (op (e2) (e3)))) -> ((op (e2) (e2)) = (e0)) -> ((op (e3) (e0)) = (e0)) -> (~((op (e3) (e0)) = (op (e3) (e3)))) -> False). % 18.79/18.95 do 0 intro. intros zenon_H67 zenon_H9a zenon_He3 zenon_H57 zenon_H29 zenon_H6d zenon_H2c zenon_H44 zenon_H71. % 18.79/18.95 apply (zenon_or_s _ _ zenon_H67); [ zenon_intro zenon_H1e | zenon_intro zenon_H68 ]. % 18.79/18.95 apply (zenon_L515_); trivial. % 18.79/18.95 apply (zenon_or_s _ _ zenon_H68); [ zenon_intro zenon_H1f | zenon_intro zenon_H69 ]. % 18.79/18.95 apply (zenon_L13_); trivial. % 18.79/18.95 apply (zenon_or_s _ _ zenon_H69); [ zenon_intro zenon_H37 | zenon_intro zenon_H60 ]. % 18.79/18.95 apply (zenon_L18_); trivial. % 18.79/18.95 apply (zenon_L21_); trivial. % 18.79/18.95 (* end of lemma zenon_L744_ *) % 18.79/18.95 assert (zenon_L745_ : (((op (e2) (e0)) = (e0))\/(((op (e2) (e1)) = (e0))\/(((op (e2) (e2)) = (e0))\/((op (e2) (e3)) = (e0))))) -> (~((op (e2) (e0)) = (op (e3) (e0)))) -> (~((op (e0) (e1)) = (op (e2) (e1)))) -> (~((op (e3) (e0)) = (op (e3) (e3)))) -> (~((op (e1) (e1)) = (op (e1) (e3)))) -> ((op (e0) (e3)) = (e3)) -> (~((e0) = (e3))) -> (((op (e0) (e3)) = (e0))\/(((op (e1) (e3)) = (e0))\/(((op (e2) (e3)) = (e0))\/((op (e3) (e3)) = (e0))))) -> (((op (e0) (e2)) = (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) (e1)) = (op (e1) (e2)))) -> ((op (e1) (e1)) = (e0)) -> (~((op (e2) (e2)) = (op (e2) (e3)))) -> (~((op (e3) (e0)) = (op (e3) (e2)))) -> ((op (e3) (e0)) = (e0)) -> False). % 18.79/18.95 do 0 intro. intros zenon_H2f zenon_H17b zenon_H17e zenon_H71 zenon_H57 zenon_He3 zenon_H9a zenon_H67 zenon_H6a zenon_H4a zenon_H49 zenon_H4f zenon_H29 zenon_H6d zenon_H6f zenon_H44. % 18.79/18.95 apply (zenon_or_s _ _ zenon_H2f); [ zenon_intro zenon_H34 | zenon_intro zenon_H33 ]. % 18.79/18.95 apply (zenon_L127_); trivial. % 18.79/18.95 apply (zenon_or_s _ _ zenon_H33); [ zenon_intro zenon_H36 | zenon_intro zenon_H35 ]. % 18.79/18.95 apply (zenon_L128_); trivial. % 18.79/18.95 apply (zenon_or_s _ _ zenon_H35); [ zenon_intro zenon_H2c | zenon_intro zenon_H37 ]. % 18.79/18.95 apply (zenon_L744_); trivial. % 18.79/18.95 apply (zenon_L20_); trivial. % 18.79/18.95 (* end of lemma zenon_L745_ *) % 18.79/18.95 assert (zenon_L746_ : (((op (e2) (e2)) = (e0))\/(((op (e2) (e2)) = (e1))\/(((op (e2) (e2)) = (e2))\/((op (e2) (e2)) = (e3))))) -> (~((op (e2) (e2)) = (op (e2) (e3)))) -> ((op (e2) (e3)) = (e0)) -> (~((op (e2) (e2)) = (e1))) -> (~((op (e2) (e2)) = (e2))) -> (((op (e3) (e2)) = (e0))\/(((op (e3) (e2)) = (e1))\/(((op (e3) (e2)) = (e2))\/((op (e3) (e2)) = (e3))))) -> (~((op (e1) (e2)) = (op (e3) (e2)))) -> ((op (e1) (e2)) = (e0)) -> ((op (e0) (e2)) = (e2)) -> (~((op (e0) (e2)) = (op (e3) (e2)))) -> (~((op (e2) (e2)) = (op (e3) (e2)))) -> False). % 18.79/18.95 do 0 intro. intros zenon_H1c4 zenon_H6d zenon_H37 zenon_H198 zenon_H173 zenon_H191 zenon_H115 zenon_H2a zenon_H150 zenon_H14f zenon_H18f. % 18.79/18.95 apply (zenon_or_s _ _ zenon_H1c4); [ zenon_intro zenon_H2c | zenon_intro zenon_H1c5 ]. % 18.79/18.95 apply (zenon_L18_); trivial. % 18.79/18.95 apply (zenon_or_s _ _ zenon_H1c5); [ zenon_intro zenon_Hf1 | zenon_intro zenon_H1c6 ]. % 18.79/18.95 exact (zenon_H198 zenon_Hf1). % 18.79/18.95 apply (zenon_or_s _ _ zenon_H1c6); [ zenon_intro zenon_H176 | zenon_intro zenon_Haa ]. % 18.79/18.95 exact (zenon_H173 zenon_H176). % 18.79/18.95 apply (zenon_L181_); trivial. % 18.79/18.95 (* end of lemma zenon_L746_ *) % 18.79/18.95 assert (zenon_L747_ : (((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 (e0) (e1)) = (e0)) -> (~((op (e0) (e1)) = (op (e2) (e1)))) -> (~((op (e1) (e2)) = (op (e2) (e2)))) -> (((op (e2) (e2)) = (e0))\/(((op (e2) (e2)) = (e1))\/(((op (e2) (e2)) = (e2))\/((op (e2) (e2)) = (e3))))) -> (~((op (e2) (e2)) = (op (e2) (e3)))) -> (~((op (e2) (e2)) = (e1))) -> (~((op (e2) (e2)) = (e2))) -> (((op (e3) (e2)) = (e0))\/(((op (e3) (e2)) = (e1))\/(((op (e3) (e2)) = (e2))\/((op (e3) (e2)) = (e3))))) -> (~((op (e1) (e2)) = (op (e3) (e2)))) -> ((op (e1) (e2)) = (e0)) -> ((op (e0) (e2)) = (e2)) -> (~((op (e0) (e2)) = (op (e3) (e2)))) -> (~((op (e2) (e2)) = (op (e3) (e2)))) -> False). % 18.79/18.95 do 0 intro. intros zenon_H2f zenon_H17b zenon_H44 zenon_H49 zenon_H17e zenon_H2b zenon_H1c4 zenon_H6d zenon_H198 zenon_H173 zenon_H191 zenon_H115 zenon_H2a zenon_H150 zenon_H14f zenon_H18f. % 18.79/18.95 apply (zenon_or_s _ _ zenon_H2f); [ zenon_intro zenon_H34 | zenon_intro zenon_H33 ]. % 18.79/18.95 apply (zenon_L127_); trivial. % 18.79/18.95 apply (zenon_or_s _ _ zenon_H33); [ zenon_intro zenon_H36 | zenon_intro zenon_H35 ]. % 18.79/18.95 apply (zenon_L128_); trivial. % 18.79/18.95 apply (zenon_or_s _ _ zenon_H35); [ zenon_intro zenon_H2c | zenon_intro zenon_H37 ]. % 18.79/18.95 apply (zenon_L3_); trivial. % 18.79/18.95 apply (zenon_L746_); trivial. % 18.79/18.95 (* end of lemma zenon_L747_ *) % 18.79/18.95 assert (zenon_L748_ : (((op (e0) (e0)) = (e3))\/(((op (e0) (e1)) = (e3))\/(((op (e0) (e2)) = (e3))\/((op (e0) (e3)) = (e3))))) -> (~((e1) = (e3))) -> ((op (e0) (e0)) = (e1)) -> (~((op (e1) (e3)) = (op (e3) (e3)))) -> (~((op (e0) (e2)) = (op (e2) (e2)))) -> ((op (e2) (e1)) = (e3)) -> ((op (e1) (e1)) = (e2)) -> (((op (e3) (e0)) = (e0))\/(((op (e3) (e1)) = (e0))\/(((op (e3) (e2)) = (e0))\/((op (e3) (e3)) = (e0))))) -> (~((op (e0) (e1)) = (op (e0) (e3)))) -> (((op (e1) (e0)) = (e0))\/(((op (e1) (e1)) = (e0))\/(((op (e1) (e2)) = (e0))\/((op (e1) (e3)) = (e0))))) -> (~((op (e1) (e0)) = (op (e3) (e0)))) -> (~((op (e3) (e0)) = (op (e3) (e2)))) -> (~((op (e1) (e1)) = (op (e1) (e2)))) -> (~((op (e0) (e1)) = (op (e0) (e2)))) -> (((op (e0) (e2)) = (e0))\/(((op (e1) (e2)) = (e0))\/(((op (e2) (e2)) = (e0))\/((op (e3) (e2)) = (e0))))) -> (((op (e0) (e3)) = (e0))\/(((op (e1) (e3)) = (e0))\/(((op (e2) (e3)) = (e0))\/((op (e3) (e3)) = (e0))))) -> (~((e0) = (e3))) -> (~((op (e1) (e1)) = (op (e1) (e3)))) -> (~((op (e2) (e2)) = (op (e3) (e2)))) -> (~((op (e0) (e2)) = (op (e3) (e2)))) -> ((op (e0) (e2)) = (e2)) -> (~((op (e1) (e2)) = (op (e3) (e2)))) -> (((op (e3) (e2)) = (e0))\/(((op (e3) (e2)) = (e1))\/(((op (e3) (e2)) = (e2))\/((op (e3) (e2)) = (e3))))) -> (~((op (e2) (e2)) = (e2))) -> (~((op (e2) (e2)) = (op (e2) (e3)))) -> (((op (e2) (e2)) = (e0))\/(((op (e2) (e2)) = (e1))\/(((op (e2) (e2)) = (e2))\/((op (e2) (e2)) = (e3))))) -> (~((op (e1) (e2)) = (op (e2) (e2)))) -> (~((op (e0) (e1)) = (op (e2) (e1)))) -> ((op (e0) (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 (e2) (e0)) = (e1))\/(((op (e2) (e1)) = (e1))\/(((op (e2) (e2)) = (e1))\/((op (e2) (e3)) = (e1))))) -> (~((op (e2) (e0)) = (e1))) -> (~((op (e2) (e1)) = (e1))) -> (~((op (e2) (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) (e0)) = (e0)) -> (~((op (e2) (e3)) = (op (e3) (e3)))) -> (~((op (e3) (e3)) = (e3))) -> False). % 18.79/18.95 do 0 intro. intros zenon_H168 zenon_H95 zenon_H7a zenon_Hd5 zenon_Ha8 zenon_Ha6 zenon_H110 zenon_H1ac zenon_H54 zenon_H22 zenon_H1fa zenon_H6f zenon_H4f zenon_H4a zenon_H6a zenon_H67 zenon_H9a zenon_H57 zenon_H18f zenon_H14f zenon_H150 zenon_H115 zenon_H191 zenon_H173 zenon_H6d zenon_H1c4 zenon_H2b zenon_H17e zenon_H49 zenon_H17b zenon_H2f zenon_H106 zenon_H1db zenon_H24f zenon_H198 zenon_H101 zenon_H71 zenon_H44 zenon_Hf3 zenon_H102. % 18.79/18.95 apply (zenon_or_s _ _ zenon_H168); [ zenon_intro zenon_H3a | zenon_intro zenon_H169 ]. % 18.79/18.95 apply (zenon_L35_); trivial. % 18.79/18.95 apply (zenon_or_s _ _ zenon_H169); [ zenon_intro zenon_H99 | zenon_intro zenon_H16a ]. % 18.79/18.95 apply (zenon_L36_); trivial. % 18.79/18.95 apply (zenon_or_s _ _ zenon_H16a); [ zenon_intro zenon_Ha9 | zenon_intro zenon_He3 ]. % 18.79/18.95 apply (zenon_L743_); trivial. % 18.79/18.95 apply (zenon_or_s _ _ zenon_H22); [ zenon_intro zenon_H27 | zenon_intro zenon_H26 ]. % 18.79/18.95 apply (zenon_L312_); trivial. % 18.79/18.95 apply (zenon_or_s _ _ zenon_H26); [ zenon_intro zenon_H29 | zenon_intro zenon_H28 ]. % 18.79/18.95 apply (zenon_L745_); trivial. % 18.79/18.95 apply (zenon_or_s _ _ zenon_H28); [ zenon_intro zenon_H2a | zenon_intro zenon_H1f ]. % 18.79/18.95 apply (zenon_L747_); trivial. % 18.79/18.95 apply (zenon_or_s _ _ zenon_H106); [ zenon_intro zenon_Hed | zenon_intro zenon_H107 ]. % 18.79/18.95 exact (zenon_H1db zenon_Hed). % 18.79/18.95 apply (zenon_or_s _ _ zenon_H107); [ zenon_intro zenon_Ha5 | zenon_intro zenon_H108 ]. % 18.79/18.95 exact (zenon_H24f zenon_Ha5). % 18.79/18.95 apply (zenon_or_s _ _ zenon_H108); [ zenon_intro zenon_Hf1 | zenon_intro zenon_Hf4 ]. % 18.79/18.95 exact (zenon_H198 zenon_Hf1). % 18.79/18.95 apply (zenon_L64_); trivial. % 18.79/18.95 (* end of lemma zenon_L748_ *) % 18.79/18.95 assert (zenon_L749_ : (((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)) = (e1))) -> ((op (e3) (e3)) = (e0)) -> ((op (e2) (e3)) = (e1)) -> (~((op (e0) (e3)) = (op (e1) (e3)))) -> ((op (e1) (e3)) = (e3)) -> False). % 18.79/18.95 do 0 intro. intros zenon_He4 zenon_Hc2 zenon_H231 zenon_H60 zenon_Hf4 zenon_H1d zenon_Hdc. % 18.79/18.95 apply (zenon_or_s _ _ zenon_He4); [ zenon_intro zenon_H1e | zenon_intro zenon_He5 ]. % 18.79/18.95 apply (zenon_L440_); trivial. % 18.79/18.95 apply (zenon_or_s _ _ zenon_He5); [ zenon_intro zenon_Hc3 | zenon_intro zenon_He6 ]. % 18.79/18.95 exact (zenon_H231 zenon_Hc3). % 18.79/18.95 apply (zenon_or_s _ _ zenon_He6); [ zenon_intro zenon_Hcd | zenon_intro zenon_He3 ]. % 18.79/18.95 apply (zenon_L229_); trivial. % 18.79/18.95 apply (zenon_L117_); trivial. % 18.79/18.95 (* end of lemma zenon_L749_ *) % 18.79/18.95 assert (zenon_L750_ : (~((op (e3) (e3)) = (e3))) -> (~((op (e2) (e3)) = (op (e3) (e3)))) -> (~((op (e3) (e0)) = (op (e3) (e3)))) -> (((op (e3) (e3)) = (e0))\/(((op (e3) (e3)) = (e1))\/(((op (e3) (e3)) = (e2))\/((op (e3) (e3)) = (e3))))) -> (~((op (e2) (e2)) = (e1))) -> (~((op (e2) (e1)) = (e1))) -> (~((op (e2) (e0)) = (e1))) -> (((op (e2) (e0)) = (e1))\/(((op (e2) (e1)) = (e1))\/(((op (e2) (e2)) = (e1))\/((op (e2) (e3)) = (e1))))) -> (((op (e2) (e0)) = (e0))\/(((op (e2) (e1)) = (e0))\/(((op (e2) (e2)) = (e0))\/((op (e2) (e3)) = (e0))))) -> (~((op (e2) (e0)) = (op (e3) (e0)))) -> ((op (e0) (e1)) = (e0)) -> (~((op (e0) (e1)) = (op (e2) (e1)))) -> (~((op (e1) (e2)) = (op (e2) (e2)))) -> (((op (e3) (e2)) = (e0))\/(((op (e3) (e2)) = (e1))\/(((op (e3) (e2)) = (e2))\/((op (e3) (e2)) = (e3))))) -> (~((op (e1) (e2)) = (op (e3) (e2)))) -> ((op (e0) (e2)) = (e2)) -> (~((op (e0) (e2)) = (op (e3) (e2)))) -> (~((op (e1) (e1)) = (op (e1) (e3)))) -> (~((e0) = (e3))) -> (((op (e0) (e3)) = (e0))\/(((op (e1) (e3)) = (e0))\/(((op (e2) (e3)) = (e0))\/((op (e3) (e3)) = (e0))))) -> (((op (e0) (e2)) = (e0))\/(((op (e1) (e2)) = (e0))\/(((op (e2) (e2)) = (e0))\/((op (e3) (e2)) = (e0))))) -> (~((op (e0) (e1)) = (op (e0) (e2)))) -> (~((op (e1) (e1)) = (op (e1) (e2)))) -> (~((op (e3) (e0)) = (op (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 (e0) (e1)) = (op (e0) (e3)))) -> (((op (e3) (e0)) = (e0))\/(((op (e3) (e1)) = (e0))\/(((op (e3) (e2)) = (e0))\/((op (e3) (e3)) = (e0))))) -> (~((op (e1) (e3)) = (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 (e1) (e1)) = (e2)) -> ((op (e2) (e1)) = (e3)) -> ((op (e0) (e2)) = (e3)) -> (~((op (e0) (e2)) = (op (e2) (e2)))) -> (~((op (e2) (e2)) = (e2))) -> (~((op (e2) (e2)) = (op (e2) (e3)))) -> (~((op (e2) (e2)) = (op (e3) (e2)))) -> (((op (e2) (e2)) = (e0))\/(((op (e2) (e2)) = (e1))\/(((op (e2) (e2)) = (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 (e3) (e3)))) -> (~((op (e0) (e3)) = (e1))) -> (~((op (e0) (e3)) = (op (e1) (e3)))) -> ((op (e1) (e3)) = (e3)) -> False). % 18.79/18.95 do 0 intro. intros zenon_H102 zenon_Hf3 zenon_H71 zenon_H101 zenon_H198 zenon_H24f zenon_H1db zenon_H106 zenon_H2f zenon_H17b zenon_H49 zenon_H17e zenon_H2b zenon_H191 zenon_H115 zenon_H150 zenon_H14f zenon_H57 zenon_H9a zenon_H67 zenon_H6a zenon_H4a zenon_H4f zenon_H6f zenon_H1fa zenon_H22 zenon_H54 zenon_H1ac zenon_Hd5 zenon_H7a zenon_H95 zenon_H168 zenon_H110 zenon_Ha6 zenon_Ha9 zenon_Ha8 zenon_H173 zenon_H6d zenon_H18f zenon_H1c4 zenon_He4 zenon_Hc2 zenon_H231 zenon_H1d zenon_Hdc. % 18.79/18.95 apply (zenon_or_s _ _ zenon_H106); [ zenon_intro zenon_Hed | zenon_intro zenon_H107 ]. % 18.79/18.95 exact (zenon_H1db zenon_Hed). % 18.79/18.95 apply (zenon_or_s _ _ zenon_H107); [ zenon_intro zenon_Ha5 | zenon_intro zenon_H108 ]. % 18.79/18.95 exact (zenon_H24f zenon_Ha5). % 18.79/18.95 apply (zenon_or_s _ _ zenon_H108); [ zenon_intro zenon_Hf1 | zenon_intro zenon_Hf4 ]. % 18.79/18.95 exact (zenon_H198 zenon_Hf1). % 18.79/18.95 apply (zenon_or_s _ _ zenon_H1ac); [ zenon_intro zenon_H44 | zenon_intro zenon_H1af ]. % 18.79/18.95 apply (zenon_L748_); trivial. % 18.79/18.95 apply (zenon_or_s _ _ zenon_H1af); [ zenon_intro zenon_H1b1 | zenon_intro zenon_H1b0 ]. % 18.79/18.95 apply (zenon_L509_); trivial. % 18.79/18.95 apply (zenon_or_s _ _ zenon_H1b0); [ zenon_intro zenon_H61 | zenon_intro zenon_H60 ]. % 18.79/18.95 apply (zenon_L483_); trivial. % 18.79/18.95 apply (zenon_L749_); trivial. % 18.79/18.95 (* end of lemma zenon_L750_ *) % 18.79/18.96 assert (zenon_L751_ : (((op (e1) (e0)) = (e3))\/(((op (e1) (e1)) = (e3))\/(((op (e1) (e2)) = (e3))\/((op (e1) (e3)) = (e3))))) -> ((op (e3) (e0)) = (e2)) -> (~((e2) = (e3))) -> ((op (e1) (e2)) = (e1)) -> (~((op (e3) (e3)) = (e3))) -> (~((op (e2) (e3)) = (op (e3) (e3)))) -> (~((op (e3) (e0)) = (op (e3) (e3)))) -> (((op (e3) (e3)) = (e0))\/(((op (e3) (e3)) = (e1))\/(((op (e3) (e3)) = (e2))\/((op (e3) (e3)) = (e3))))) -> (~((op (e2) (e2)) = (e1))) -> (~((op (e2) (e1)) = (e1))) -> (~((op (e2) (e0)) = (e1))) -> (((op (e2) (e0)) = (e1))\/(((op (e2) (e1)) = (e1))\/(((op (e2) (e2)) = (e1))\/((op (e2) (e3)) = (e1))))) -> (((op (e2) (e0)) = (e0))\/(((op (e2) (e1)) = (e0))\/(((op (e2) (e2)) = (e0))\/((op (e2) (e3)) = (e0))))) -> (~((op (e2) (e0)) = (op (e3) (e0)))) -> ((op (e0) (e1)) = (e0)) -> (~((op (e0) (e1)) = (op (e2) (e1)))) -> (~((op (e1) (e2)) = (op (e2) (e2)))) -> (((op (e3) (e2)) = (e0))\/(((op (e3) (e2)) = (e1))\/(((op (e3) (e2)) = (e2))\/((op (e3) (e2)) = (e3))))) -> (~((op (e1) (e2)) = (op (e3) (e2)))) -> ((op (e0) (e2)) = (e2)) -> (~((op (e0) (e2)) = (op (e3) (e2)))) -> (~((op (e1) (e1)) = (op (e1) (e3)))) -> (~((e0) = (e3))) -> (((op (e0) (e3)) = (e0))\/(((op (e1) (e3)) = (e0))\/(((op (e2) (e3)) = (e0))\/((op (e3) (e3)) = (e0))))) -> (((op (e0) (e2)) = (e0))\/(((op (e1) (e2)) = (e0))\/(((op (e2) (e2)) = (e0))\/((op (e3) (e2)) = (e0))))) -> (~((op (e0) (e1)) = (op (e0) (e2)))) -> (~((op (e1) (e1)) = (op (e1) (e2)))) -> (~((op (e3) (e0)) = (op (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 (e0) (e1)) = (op (e0) (e3)))) -> (((op (e3) (e0)) = (e0))\/(((op (e3) (e1)) = (e0))\/(((op (e3) (e2)) = (e0))\/((op (e3) (e3)) = (e0))))) -> (~((op (e1) (e3)) = (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 (e1) (e1)) = (e2)) -> ((op (e2) (e1)) = (e3)) -> ((op (e0) (e2)) = (e3)) -> (~((op (e0) (e2)) = (op (e2) (e2)))) -> (~((op (e2) (e2)) = (e2))) -> (~((op (e2) (e2)) = (op (e2) (e3)))) -> (~((op (e2) (e2)) = (op (e3) (e2)))) -> (((op (e2) (e2)) = (e0))\/(((op (e2) (e2)) = (e1))\/(((op (e2) (e2)) = (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 (e3) (e3)))) -> (~((op (e0) (e3)) = (e1))) -> (~((op (e0) (e3)) = (op (e1) (e3)))) -> False). % 18.79/18.96 do 0 intro. intros zenon_H16f zenon_H148 zenon_H12b zenon_Hf0 zenon_H102 zenon_Hf3 zenon_H71 zenon_H101 zenon_H198 zenon_H24f zenon_H1db zenon_H106 zenon_H2f zenon_H17b zenon_H49 zenon_H17e zenon_H2b zenon_H191 zenon_H115 zenon_H150 zenon_H14f zenon_H57 zenon_H9a zenon_H67 zenon_H6a zenon_H4a zenon_H4f zenon_H6f zenon_H1fa zenon_H22 zenon_H54 zenon_H1ac zenon_Hd5 zenon_H7a zenon_H95 zenon_H168 zenon_H110 zenon_Ha6 zenon_Ha9 zenon_Ha8 zenon_H173 zenon_H6d zenon_H18f zenon_H1c4 zenon_He4 zenon_Hc2 zenon_H231 zenon_H1d. % 18.79/18.96 apply (zenon_or_s _ _ zenon_H16f); [ zenon_intro zenon_H9e | zenon_intro zenon_H170 ]. % 18.79/18.96 apply (zenon_L107_); trivial. % 18.79/18.96 apply (zenon_or_s _ _ zenon_H170); [ zenon_intro zenon_H13f | zenon_intro zenon_H171 ]. % 18.79/18.96 apply (zenon_L166_); trivial. % 18.79/18.96 apply (zenon_or_s _ _ zenon_H171); [ zenon_intro zenon_H16c | zenon_intro zenon_Hdc ]. % 18.79/18.96 apply (zenon_L167_); trivial. % 18.79/18.96 apply (zenon_L750_); trivial. % 18.79/18.96 (* end of lemma zenon_L751_ *) % 18.79/18.96 assert (zenon_L752_ : (((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)) = (e3)) -> (~((op (e0) (e2)) = (op (e2) (e2)))) -> (~((op (e2) (e2)) = (e2))) -> (~((op (e2) (e2)) = (op (e2) (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) (e1)) = (e1))) -> (~((op (e2) (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 (e3) (e0)) = (e0))\/(((op (e3) (e1)) = (e0))\/(((op (e3) (e2)) = (e0))\/((op (e3) (e3)) = (e0))))) -> (~((op (e3) (e3)) = (e3))) -> (~((op (e2) (e3)) = (op (e3) (e3)))) -> (~((op (e3) (e0)) = (op (e3) (e3)))) -> (((op (e3) (e3)) = (e0))\/(((op (e3) (e3)) = (e1))\/(((op (e3) (e3)) = (e2))\/((op (e3) (e3)) = (e3))))) -> ((op (e1) (e1)) = (e2)) -> ((op (e2) (e1)) = (e3)) -> (~((op (e1) (e3)) = (op (e3) (e3)))) -> ((op (e1) (e3)) = (e0)) -> (~((e0) = (e3))) -> (((op (e0) (e2)) = (e0))\/(((op (e1) (e2)) = (e0))\/(((op (e2) (e2)) = (e0))\/((op (e3) (e2)) = (e0))))) -> (~((op (e1) (e3)) = (e1))) -> False). % 18.79/18.96 do 0 intro. intros zenon_H128 zenon_H1ef zenon_H10a zenon_Ha9 zenon_Ha8 zenon_H173 zenon_H6d zenon_H18f zenon_H1c4 zenon_H2b zenon_H24f zenon_H1db zenon_H106 zenon_H52 zenon_H34 zenon_H1ac zenon_H102 zenon_Hf3 zenon_H71 zenon_H101 zenon_H110 zenon_Ha6 zenon_Hd5 zenon_H1f zenon_H9a zenon_H6a zenon_H24e. % 18.79/18.96 apply (zenon_or_s _ _ zenon_H128); [ zenon_intro zenon_H9d | zenon_intro zenon_H129 ]. % 18.79/18.96 exact (zenon_H1ef zenon_H9d). % 18.79/18.96 apply (zenon_or_s _ _ zenon_H129); [ zenon_intro zenon_H10d | zenon_intro zenon_H12a ]. % 18.79/18.96 exact (zenon_H10a zenon_H10d). % 18.79/18.96 apply (zenon_or_s _ _ zenon_H12a); [ zenon_intro zenon_Hf0 | zenon_intro zenon_Hd6 ]. % 18.79/18.96 apply (zenon_or_s _ _ zenon_H6a); [ zenon_intro zenon_H48 | zenon_intro zenon_H6b ]. % 18.79/18.96 apply (zenon_L358_); trivial. % 18.79/18.96 apply (zenon_or_s _ _ zenon_H6b); [ zenon_intro zenon_H2a | zenon_intro zenon_H6c ]. % 18.79/18.96 apply (zenon_or_s _ _ zenon_H106); [ zenon_intro zenon_Hed | zenon_intro zenon_H107 ]. % 18.79/18.96 exact (zenon_H1db zenon_Hed). % 18.79/18.96 apply (zenon_or_s _ _ zenon_H107); [ zenon_intro zenon_Ha5 | zenon_intro zenon_H108 ]. % 18.79/18.96 exact (zenon_H24f zenon_Ha5). % 18.79/18.96 apply (zenon_or_s _ _ zenon_H108); [ zenon_intro zenon_Hf1 | zenon_intro zenon_Hf4 ]. % 18.79/18.96 apply (zenon_L184_); trivial. % 18.79/18.96 apply (zenon_L742_); trivial. % 18.79/18.96 apply (zenon_or_s _ _ zenon_H6c); [ zenon_intro zenon_H2c | zenon_intro zenon_H61 ]. % 18.79/18.96 apply (zenon_L11_); trivial. % 18.79/18.96 apply (zenon_L732_); trivial. % 18.79/18.96 exact (zenon_H24e zenon_Hd6). % 18.79/18.96 (* end of lemma zenon_L752_ *) % 18.79/18.96 assert (zenon_L753_ : (((op (e3) (e0)) = (e2))\/(((op (e3) (e1)) = (e2))\/(((op (e3) (e2)) = (e2))\/((op (e3) (e3)) = (e2))))) -> ((op (e1) (e2)) = (e1)) -> (~((e1) = (e3))) -> (~((e2) = (e3))) -> ((op (e0) (e0)) = (e1)) -> (((op (e1) (e0)) = (e3))\/(((op (e1) (e1)) = (e3))\/(((op (e1) (e2)) = (e3))\/((op (e1) (e3)) = (e3))))) -> ((op (e1) (e1)) = (e2)) -> (~((op (e1) (e1)) = (op (e3) (e1)))) -> ((op (e0) (e2)) = (e2)) -> (~((op (e0) (e2)) = (op (e3) (e2)))) -> (((op (e1) (e3)) = (e0))\/(((op (e1) (e3)) = (e1))\/(((op (e1) (e3)) = (e2))\/((op (e1) (e3)) = (e3))))) -> ((op (e3) (e3)) = (e0)) -> (~((op (e1) (e3)) = (e1))) -> (~((op (e1) (e3)) = (op (e3) (e3)))) -> (~((op (e0) (e3)) = (op (e1) (e3)))) -> ((op (e0) (e3)) = (e3)) -> False). % 18.79/18.96 do 0 intro. intros zenon_H153 zenon_Hf0 zenon_H95 zenon_H12b zenon_H7a zenon_H16f zenon_H110 zenon_H160 zenon_H150 zenon_H14f zenon_Hdf zenon_H60 zenon_H24e zenon_Hd5 zenon_H1d zenon_He3. % 18.79/18.96 apply (zenon_or_s _ _ zenon_H153); [ zenon_intro zenon_H148 | zenon_intro zenon_H154 ]. % 18.79/18.96 apply (zenon_L216_); trivial. % 18.79/18.96 apply (zenon_or_s _ _ zenon_H154); [ zenon_intro zenon_H14d | zenon_intro zenon_H155 ]. % 18.79/18.96 apply (zenon_L164_); trivial. % 18.79/18.96 apply (zenon_or_s _ _ zenon_H155); [ zenon_intro zenon_H151 | zenon_intro zenon_Hf6 ]. % 18.79/18.96 apply (zenon_L104_); trivial. % 18.79/18.96 apply (zenon_L738_); trivial. % 18.79/18.96 (* end of lemma zenon_L753_ *) % 18.79/18.96 assert (zenon_L754_ : (((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) (e3)) = (e3)) -> (~((op (e0) (e3)) = (op (e1) (e3)))) -> (~((e1) = (e3))) -> ((op (e1) (e1)) = (e2)) -> (~((e2) = (e3))) -> ((op (e3) (e0)) = (e2)) -> ((op (e0) (e0)) = (e1)) -> (((op (e1) (e0)) = (e3))\/(((op (e1) (e1)) = (e3))\/(((op (e1) (e2)) = (e3))\/((op (e1) (e3)) = (e3))))) -> (~((op (e1) (e3)) = (e1))) -> False). % 18.79/18.96 do 0 intro. intros zenon_H128 zenon_H1ef zenon_H10a zenon_He3 zenon_H1d zenon_H95 zenon_H110 zenon_H12b zenon_H148 zenon_H7a zenon_H16f zenon_H24e. % 18.79/18.96 apply (zenon_or_s _ _ zenon_H128); [ zenon_intro zenon_H9d | zenon_intro zenon_H129 ]. % 18.79/18.96 exact (zenon_H1ef zenon_H9d). % 18.79/18.96 apply (zenon_or_s _ _ zenon_H129); [ zenon_intro zenon_H10d | zenon_intro zenon_H12a ]. % 18.79/18.96 exact (zenon_H10a zenon_H10d). % 18.79/18.96 apply (zenon_or_s _ _ zenon_H12a); [ zenon_intro zenon_Hf0 | zenon_intro zenon_Hd6 ]. % 18.79/18.96 apply (zenon_L216_); trivial. % 18.79/18.96 exact (zenon_H24e zenon_Hd6). % 18.79/18.96 (* end of lemma zenon_L754_ *) % 18.79/18.96 assert (zenon_L755_ : (~((op (e3) (e3)) = (e3))) -> (~((op (e2) (e3)) = (op (e3) (e3)))) -> (~((op (e3) (e0)) = (op (e3) (e3)))) -> (((op (e3) (e3)) = (e0))\/(((op (e3) (e3)) = (e1))\/(((op (e3) (e3)) = (e2))\/((op (e3) (e3)) = (e3))))) -> (~((op (e2) (e2)) = (e1))) -> (~((op (e2) (e1)) = (e1))) -> (~((op (e2) (e0)) = (e1))) -> (((op (e2) (e0)) = (e1))\/(((op (e2) (e1)) = (e1))\/(((op (e2) (e2)) = (e1))\/((op (e2) (e3)) = (e1))))) -> (((op (e2) (e0)) = (e0))\/(((op (e2) (e1)) = (e0))\/(((op (e2) (e2)) = (e0))\/((op (e2) (e3)) = (e0))))) -> (~((op (e2) (e0)) = (op (e3) (e0)))) -> ((op (e0) (e1)) = (e0)) -> (~((op (e0) (e1)) = (op (e2) (e1)))) -> (~((op (e1) (e2)) = (op (e2) (e2)))) -> (((op (e3) (e2)) = (e0))\/(((op (e3) (e2)) = (e1))\/(((op (e3) (e2)) = (e2))\/((op (e3) (e2)) = (e3))))) -> (~((op (e1) (e2)) = (op (e3) (e2)))) -> ((op (e0) (e2)) = (e2)) -> (~((op (e0) (e2)) = (op (e3) (e2)))) -> (~((op (e1) (e1)) = (op (e1) (e3)))) -> (~((e0) = (e3))) -> (((op (e0) (e3)) = (e0))\/(((op (e1) (e3)) = (e0))\/(((op (e2) (e3)) = (e0))\/((op (e3) (e3)) = (e0))))) -> (((op (e0) (e2)) = (e0))\/(((op (e1) (e2)) = (e0))\/(((op (e2) (e2)) = (e0))\/((op (e3) (e2)) = (e0))))) -> (~((op (e0) (e1)) = (op (e0) (e2)))) -> (~((op (e1) (e1)) = (op (e1) (e2)))) -> (~((op (e3) (e0)) = (op (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 (e0) (e1)) = (op (e0) (e3)))) -> (((op (e3) (e0)) = (e0))\/(((op (e3) (e1)) = (e0))\/(((op (e3) (e2)) = (e0))\/((op (e3) (e3)) = (e0))))) -> (~((op (e1) (e3)) = (op (e3) (e3)))) -> (((op (e0) (e0)) = (e3))\/(((op (e0) (e1)) = (e3))\/(((op (e0) (e2)) = (e3))\/((op (e0) (e3)) = (e3))))) -> ((op (e2) (e1)) = (e3)) -> (~((op (e0) (e2)) = (op (e2) (e2)))) -> (~((op (e2) (e2)) = (e2))) -> (~((op (e2) (e2)) = (op (e2) (e3)))) -> (~((op (e2) (e2)) = (op (e3) (e2)))) -> (((op (e2) (e2)) = (e0))\/(((op (e2) (e2)) = (e1))\/(((op (e2) (e2)) = (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 (e3) (e3)))) -> (~((op (e0) (e3)) = (e1))) -> (((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) (e3)) = (op (e1) (e3)))) -> (~((e1) = (e3))) -> ((op (e1) (e1)) = (e2)) -> (~((e2) = (e3))) -> ((op (e3) (e0)) = (e2)) -> ((op (e0) (e0)) = (e1)) -> (((op (e1) (e0)) = (e3))\/(((op (e1) (e1)) = (e3))\/(((op (e1) (e2)) = (e3))\/((op (e1) (e3)) = (e3))))) -> (~((op (e1) (e3)) = (e1))) -> False). % 18.79/18.96 do 0 intro. intros zenon_H102 zenon_Hf3 zenon_H71 zenon_H101 zenon_H198 zenon_H24f zenon_H1db zenon_H106 zenon_H2f zenon_H17b zenon_H49 zenon_H17e zenon_H2b zenon_H191 zenon_H115 zenon_H150 zenon_H14f zenon_H57 zenon_H9a zenon_H67 zenon_H6a zenon_H4a zenon_H4f zenon_H6f zenon_H1fa zenon_H22 zenon_H54 zenon_H1ac zenon_Hd5 zenon_H168 zenon_Ha6 zenon_Ha8 zenon_H173 zenon_H6d zenon_H18f zenon_H1c4 zenon_He4 zenon_Hc2 zenon_H231 zenon_H128 zenon_H1ef zenon_H10a zenon_H1d zenon_H95 zenon_H110 zenon_H12b zenon_H148 zenon_H7a zenon_H16f zenon_H24e. % 18.79/18.96 apply (zenon_or_s _ _ zenon_H168); [ zenon_intro zenon_H3a | zenon_intro zenon_H169 ]. % 18.79/18.96 apply (zenon_L35_); trivial. % 18.79/18.96 apply (zenon_or_s _ _ zenon_H169); [ zenon_intro zenon_H99 | zenon_intro zenon_H16a ]. % 18.79/18.96 apply (zenon_L36_); trivial. % 18.79/18.96 apply (zenon_or_s _ _ zenon_H16a); [ zenon_intro zenon_Ha9 | zenon_intro zenon_He3 ]. % 18.79/18.96 apply (zenon_or_s _ _ zenon_H128); [ zenon_intro zenon_H9d | zenon_intro zenon_H129 ]. % 18.79/18.96 exact (zenon_H1ef zenon_H9d). % 18.79/18.96 apply (zenon_or_s _ _ zenon_H129); [ zenon_intro zenon_H10d | zenon_intro zenon_H12a ]. % 18.79/18.96 exact (zenon_H10a zenon_H10d). % 18.79/18.96 apply (zenon_or_s _ _ zenon_H12a); [ zenon_intro zenon_Hf0 | zenon_intro zenon_Hd6 ]. % 18.79/18.96 apply (zenon_L751_); trivial. % 18.79/18.96 exact (zenon_H24e zenon_Hd6). % 18.79/18.96 apply (zenon_L754_); trivial. % 18.79/18.96 (* end of lemma zenon_L755_ *) % 18.79/18.96 assert (zenon_L756_ : (((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))))) -> (~((e1) = (e2))) -> ((op (e3) (e1)) = (e1)) -> (((op (e1) (e3)) = (e0))\/(((op (e1) (e3)) = (e1))\/(((op (e1) (e3)) = (e2))\/((op (e1) (e3)) = (e3))))) -> (~((op (e1) (e1)) = (op (e3) (e1)))) -> (((op (e2) (e0)) = (e3))\/(((op (e2) (e1)) = (e3))\/(((op (e2) (e2)) = (e3))\/((op (e2) (e3)) = (e3))))) -> (~((op (e0) (e3)) = (op (e2) (e3)))) -> (~((op (e2) (e0)) = (op (e2) (e2)))) -> (~((op (e2) (e0)) = (op (e2) (e3)))) -> (~((op (e3) (e2)) = (op (e3) (e3)))) -> (~((op (e1) (e0)) = (op (e2) (e0)))) -> (((op (e2) (e0)) = (e2))\/(((op (e2) (e1)) = (e2))\/(((op (e2) (e2)) = (e2))\/((op (e2) (e3)) = (e2))))) -> (~((op (e3) (e1)) = (op (e3) (e3)))) -> (~((op (e2) (e1)) = (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 (e3) (e1)) = (op (e3) (e2)))) -> (((op (e2) (e0)) = (e0))\/(((op (e2) (e0)) = (e1))\/(((op (e2) (e0)) = (e2))\/((op (e2) (e0)) = (e3))))) -> (~((op (e2) (e0)) = (op (e2) (e1)))) -> (~((e0) = (e2))) -> ((op (e2) (e0)) = (e0)) -> (~((op (e3) (e3)) = (e3))) -> (~((op (e2) (e3)) = (op (e3) (e3)))) -> (~((op (e3) (e0)) = (op (e3) (e3)))) -> (((op (e3) (e3)) = (e0))\/(((op (e3) (e3)) = (e1))\/(((op (e3) (e3)) = (e2))\/((op (e3) (e3)) = (e3))))) -> (~((op (e2) (e2)) = (e1))) -> (~((op (e2) (e1)) = (e1))) -> (~((op (e2) (e0)) = (e1))) -> (((op (e2) (e0)) = (e1))\/(((op (e2) (e1)) = (e1))\/(((op (e2) (e2)) = (e1))\/((op (e2) (e3)) = (e1))))) -> (((op (e2) (e0)) = (e0))\/(((op (e2) (e1)) = (e0))\/(((op (e2) (e2)) = (e0))\/((op (e2) (e3)) = (e0))))) -> (~((op (e2) (e0)) = (op (e3) (e0)))) -> ((op (e0) (e1)) = (e0)) -> (~((op (e0) (e1)) = (op (e2) (e1)))) -> (~((op (e1) (e2)) = (op (e2) (e2)))) -> (((op (e3) (e2)) = (e0))\/(((op (e3) (e2)) = (e1))\/(((op (e3) (e2)) = (e2))\/((op (e3) (e2)) = (e3))))) -> (~((op (e1) (e2)) = (op (e3) (e2)))) -> ((op (e0) (e2)) = (e2)) -> (~((op (e0) (e2)) = (op (e3) (e2)))) -> (~((op (e1) (e1)) = (op (e1) (e3)))) -> (~((e0) = (e3))) -> (((op (e0) (e3)) = (e0))\/(((op (e1) (e3)) = (e0))\/(((op (e2) (e3)) = (e0))\/((op (e3) (e3)) = (e0))))) -> (((op (e0) (e2)) = (e0))\/(((op (e1) (e2)) = (e0))\/(((op (e2) (e2)) = (e0))\/((op (e3) (e2)) = (e0))))) -> (~((op (e0) (e1)) = (op (e0) (e2)))) -> (~((op (e1) (e1)) = (op (e1) (e2)))) -> (~((op (e3) (e0)) = (op (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 (e0) (e1)) = (op (e0) (e3)))) -> (((op (e3) (e0)) = (e0))\/(((op (e3) (e1)) = (e0))\/(((op (e3) (e2)) = (e0))\/((op (e3) (e3)) = (e0))))) -> (~((op (e1) (e3)) = (op (e3) (e3)))) -> (((op (e0) (e0)) = (e3))\/(((op (e0) (e1)) = (e3))\/(((op (e0) (e2)) = (e3))\/((op (e0) (e3)) = (e3))))) -> ((op (e2) (e1)) = (e3)) -> (~((op (e0) (e2)) = (op (e2) (e2)))) -> (~((op (e2) (e2)) = (e2))) -> (~((op (e2) (e2)) = (op (e2) (e3)))) -> (~((op (e2) (e2)) = (op (e3) (e2)))) -> (((op (e2) (e2)) = (e0))\/(((op (e2) (e2)) = (e1))\/(((op (e2) (e2)) = (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 (e3) (e3)))) -> (~((op (e0) (e3)) = (e1))) -> (((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) (e3)) = (op (e1) (e3)))) -> (~((e1) = (e3))) -> ((op (e1) (e1)) = (e2)) -> (~((e2) = (e3))) -> ((op (e0) (e0)) = (e1)) -> (((op (e1) (e0)) = (e3))\/(((op (e1) (e1)) = (e3))\/(((op (e1) (e2)) = (e3))\/((op (e1) (e3)) = (e3))))) -> (~((op (e1) (e3)) = (e1))) -> False). % 18.79/18.96 do 0 intro. intros zenon_H1fe zenon_H153 zenon_H7c zenon_Hae zenon_Hdf zenon_H160 zenon_He7 zenon_He2 zenon_H52 zenon_H5b zenon_H62 zenon_H201 zenon_H1d5 zenon_H130 zenon_H1c7 zenon_Hd8 zenon_H145 zenon_H1a4 zenon_H259 zenon_H1f0 zenon_H149 zenon_H34 zenon_H102 zenon_Hf3 zenon_H71 zenon_H101 zenon_H198 zenon_H24f zenon_H1db zenon_H106 zenon_H2f zenon_H17b zenon_H49 zenon_H17e zenon_H2b zenon_H191 zenon_H115 zenon_H150 zenon_H14f zenon_H57 zenon_H9a zenon_H67 zenon_H6a zenon_H4a zenon_H4f zenon_H6f zenon_H1fa zenon_H22 zenon_H54 zenon_H1ac zenon_Hd5 zenon_H168 zenon_Ha6 zenon_Ha8 zenon_H173 zenon_H6d zenon_H18f zenon_H1c4 zenon_He4 zenon_Hc2 zenon_H231 zenon_H128 zenon_H1ef zenon_H10a zenon_H1d zenon_H95 zenon_H110 zenon_H12b zenon_H7a zenon_H16f zenon_H24e. % 18.79/18.96 apply (zenon_or_s _ _ zenon_H1fe); [ zenon_intro zenon_H7b | zenon_intro zenon_H1ff ]. % 18.79/18.96 apply (zenon_L26_); trivial. % 18.79/18.96 apply (zenon_or_s _ _ zenon_H1ff); [ zenon_intro zenon_H86 | zenon_intro zenon_H200 ]. % 18.79/18.96 apply (zenon_or_s _ _ zenon_H168); [ zenon_intro zenon_H3a | zenon_intro zenon_H169 ]. % 18.79/18.96 apply (zenon_L35_); trivial. % 18.79/18.96 apply (zenon_or_s _ _ zenon_H169); [ zenon_intro zenon_H99 | zenon_intro zenon_H16a ]. % 18.79/18.96 apply (zenon_L36_); trivial. % 18.79/18.96 apply (zenon_or_s _ _ zenon_H16a); [ zenon_intro zenon_Ha9 | zenon_intro zenon_He3 ]. % 18.79/18.96 apply (zenon_or_s _ _ zenon_H22); [ zenon_intro zenon_H27 | zenon_intro zenon_H26 ]. % 18.79/18.96 apply (zenon_L332_); trivial. % 18.79/18.96 apply (zenon_or_s _ _ zenon_H26); [ zenon_intro zenon_H29 | zenon_intro zenon_H28 ]. % 18.79/18.96 apply (zenon_L354_); trivial. % 18.79/18.96 apply (zenon_or_s _ _ zenon_H28); [ zenon_intro zenon_H2a | zenon_intro zenon_H1f ]. % 18.79/18.96 apply (zenon_or_s _ _ zenon_H128); [ zenon_intro zenon_H9d | zenon_intro zenon_H129 ]. % 18.79/18.96 exact (zenon_H1ef zenon_H9d). % 18.79/18.96 apply (zenon_or_s _ _ zenon_H129); [ zenon_intro zenon_H10d | zenon_intro zenon_H12a ]. % 18.79/18.96 exact (zenon_H10a zenon_H10d). % 18.79/18.96 apply (zenon_or_s _ _ zenon_H12a); [ zenon_intro zenon_Hf0 | zenon_intro zenon_Hd6 ]. % 18.79/18.96 apply (zenon_or_s _ _ zenon_H1d5); [ zenon_intro zenon_Hee | zenon_intro zenon_H1d6 ]. % 18.79/18.96 apply (zenon_L728_); trivial. % 18.79/18.96 apply (zenon_or_s _ _ zenon_H1d6); [ zenon_intro zenon_H1ca | zenon_intro zenon_H1d7 ]. % 18.79/18.96 apply (zenon_L741_); trivial. % 18.79/18.96 apply (zenon_or_s _ _ zenon_H1d7); [ zenon_intro zenon_H176 | zenon_intro zenon_H11d ]. % 18.79/18.96 exact (zenon_H173 zenon_H176). % 18.79/18.96 apply (zenon_or_s _ _ zenon_H153); [ zenon_intro zenon_H148 | zenon_intro zenon_H154 ]. % 18.79/18.96 apply (zenon_L751_); trivial. % 18.79/18.96 apply (zenon_or_s _ _ zenon_H154); [ zenon_intro zenon_H14d | zenon_intro zenon_H155 ]. % 18.79/18.96 apply (zenon_L152_); trivial. % 18.79/18.96 apply (zenon_or_s _ _ zenon_H155); [ zenon_intro zenon_H151 | zenon_intro zenon_Hf6 ]. % 18.79/18.96 apply (zenon_L104_); trivial. % 18.79/18.96 apply (zenon_L97_); trivial. % 18.79/18.96 exact (zenon_H24e zenon_Hd6). % 18.79/18.96 apply (zenon_L752_); trivial. % 18.79/18.96 apply (zenon_or_s _ _ zenon_H22); [ zenon_intro zenon_H27 | zenon_intro zenon_H26 ]. % 18.79/18.96 apply (zenon_L257_); trivial. % 18.79/18.96 apply (zenon_or_s _ _ zenon_H26); [ zenon_intro zenon_H29 | zenon_intro zenon_H28 ]. % 18.79/18.96 apply (zenon_L724_); trivial. % 18.79/18.96 apply (zenon_or_s _ _ zenon_H28); [ zenon_intro zenon_H2a | zenon_intro zenon_H1f ]. % 18.79/18.96 apply (zenon_or_s _ _ zenon_H128); [ zenon_intro zenon_H9d | zenon_intro zenon_H129 ]. % 18.79/18.96 exact (zenon_H1ef zenon_H9d). % 18.79/18.96 apply (zenon_or_s _ _ zenon_H129); [ zenon_intro zenon_H10d | zenon_intro zenon_H12a ]. % 18.79/18.96 exact (zenon_H10a zenon_H10d). % 18.79/18.96 apply (zenon_or_s _ _ zenon_H12a); [ zenon_intro zenon_Hf0 | zenon_intro zenon_Hd6 ]. % 18.79/18.96 apply (zenon_or_s _ _ zenon_H1ac); [ zenon_intro zenon_H44 | zenon_intro zenon_H1af ]. % 18.79/18.96 apply (zenon_L747_); trivial. % 18.79/18.96 apply (zenon_or_s _ _ zenon_H1af); [ zenon_intro zenon_H1b1 | zenon_intro zenon_H1b0 ]. % 18.79/18.96 apply (zenon_L734_); trivial. % 18.79/18.96 apply (zenon_or_s _ _ zenon_H1b0); [ zenon_intro zenon_H61 | zenon_intro zenon_H60 ]. % 18.79/18.96 apply (zenon_L176_); trivial. % 18.79/18.96 apply (zenon_L753_); trivial. % 18.79/18.96 exact (zenon_H24e zenon_Hd6). % 18.79/18.96 apply (zenon_or_s _ _ zenon_H128); [ zenon_intro zenon_H9d | zenon_intro zenon_H129 ]. % 18.79/18.96 exact (zenon_H1ef zenon_H9d). % 18.79/18.96 apply (zenon_or_s _ _ zenon_H129); [ zenon_intro zenon_H10d | zenon_intro zenon_H12a ]. % 18.79/18.96 exact (zenon_H10a zenon_H10d). % 18.79/18.96 apply (zenon_or_s _ _ zenon_H12a); [ zenon_intro zenon_Hf0 | zenon_intro zenon_Hd6 ]. % 18.79/18.96 apply (zenon_or_s _ _ zenon_H106); [ zenon_intro zenon_Hed | zenon_intro zenon_H107 ]. % 18.79/18.96 exact (zenon_H1db zenon_Hed). % 18.79/18.96 apply (zenon_or_s _ _ zenon_H107); [ zenon_intro zenon_Ha5 | zenon_intro zenon_H108 ]. % 18.79/18.96 exact (zenon_H24f zenon_Ha5). % 18.79/18.96 apply (zenon_or_s _ _ zenon_H108); [ zenon_intro zenon_Hf1 | zenon_intro zenon_Hf4 ]. % 18.79/18.96 exact (zenon_H198 zenon_Hf1). % 18.79/18.96 apply (zenon_L217_); trivial. % 18.79/18.96 exact (zenon_H24e zenon_Hd6). % 18.79/18.96 apply (zenon_or_s _ _ zenon_H200); [ zenon_intro zenon_Hee | zenon_intro zenon_H148 ]. % 18.79/18.96 apply (zenon_L204_); trivial. % 18.79/18.96 apply (zenon_L755_); trivial. % 18.79/18.96 (* end of lemma zenon_L756_ *) % 18.79/18.96 assert (zenon_L757_ : (((op (e1) (e0)) = (e1))\/(((op (e1) (e1)) = (e1))\/(((op (e1) (e2)) = (e1))\/((op (e1) (e3)) = (e1))))) -> (~((op (e1) (e0)) = (e1))) -> (~((op (e1) (e1)) = (e1))) -> (~((op (e3) (e3)) = (e3))) -> ((op (e1) (e3)) = (e0)) -> (~((op (e2) (e3)) = (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) (e2)) = (op (e2) (e2)))) -> ((op (e3) (e1)) = (e1)) -> (~((op (e2) (e1)) = (op (e3) (e1)))) -> ((op (e2) (e0)) = (e2)) -> (~((e1) = (e2))) -> (((op (e2) (e0)) = (e1))\/(((op (e2) (e1)) = (e1))\/(((op (e2) (e2)) = (e1))\/((op (e2) (e3)) = (e1))))) -> (~((op (e1) (e3)) = (e1))) -> False). % 18.79/18.96 do 0 intro. intros zenon_H128 zenon_H1ef zenon_H10a zenon_H102 zenon_H1f zenon_Hf3 zenon_H44 zenon_H71 zenon_H101 zenon_H2b zenon_Hae zenon_Haf zenon_Hee zenon_H7c zenon_H106 zenon_H24e. % 18.79/18.96 apply (zenon_or_s _ _ zenon_H128); [ zenon_intro zenon_H9d | zenon_intro zenon_H129 ]. % 18.79/18.96 exact (zenon_H1ef zenon_H9d). % 18.79/18.96 apply (zenon_or_s _ _ zenon_H129); [ zenon_intro zenon_H10d | zenon_intro zenon_H12a ]. % 18.79/18.96 exact (zenon_H10a zenon_H10d). % 18.79/18.96 apply (zenon_or_s _ _ zenon_H12a); [ zenon_intro zenon_Hf0 | zenon_intro zenon_Hd6 ]. % 18.79/18.96 apply (zenon_L65_); trivial. % 18.79/18.96 exact (zenon_H24e zenon_Hd6). % 18.79/18.96 (* end of lemma zenon_L757_ *) % 18.79/18.96 assert (zenon_L758_ : (((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)) = (e2)) -> ((op (e0) (e2)) = (e3)) -> (~((op (e0) (e2)) = (op (e2) (e2)))) -> (~((op (e2) (e2)) = (e2))) -> (~((op (e2) (e2)) = (e1))) -> (~((op (e2) (e2)) = (op (e2) (e3)))) -> (((op (e2) (e2)) = (e0))\/(((op (e2) (e2)) = (e1))\/(((op (e2) (e2)) = (e2))\/((op (e2) (e2)) = (e3))))) -> (~((op (e0) (e1)) = (op (e2) (e1)))) -> ((op (e0) (e1)) = (e0)) -> (~((e0) = (e2))) -> (((op (e2) (e0)) = (e0))\/(((op (e2) (e1)) = (e0))\/(((op (e2) (e2)) = (e0))\/((op (e2) (e3)) = (e0))))) -> (((op (e1) (e0)) = (e1))\/(((op (e1) (e1)) = (e1))\/(((op (e1) (e2)) = (e1))\/((op (e1) (e3)) = (e1))))) -> (~((op (e1) (e0)) = (e1))) -> (~((op (e1) (e1)) = (e1))) -> (~((op (e3) (e3)) = (e3))) -> (~((op (e2) (e3)) = (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) (e2)) = (op (e2) (e2)))) -> ((op (e3) (e1)) = (e1)) -> (~((op (e2) (e1)) = (op (e3) (e1)))) -> ((op (e2) (e0)) = (e2)) -> (~((e1) = (e2))) -> (((op (e2) (e0)) = (e1))\/(((op (e2) (e1)) = (e1))\/(((op (e2) (e2)) = (e1))\/((op (e2) (e3)) = (e1))))) -> (~((op (e1) (e3)) = (e1))) -> False). % 18.79/18.96 do 0 intro. intros zenon_H22 zenon_H1fa zenon_H110 zenon_Ha9 zenon_Ha8 zenon_H173 zenon_H198 zenon_H6d zenon_H1c4 zenon_H17e zenon_H49 zenon_H149 zenon_H2f zenon_H128 zenon_H1ef zenon_H10a zenon_H102 zenon_Hf3 zenon_H44 zenon_H71 zenon_H101 zenon_H2b zenon_Hae zenon_Haf zenon_Hee zenon_H7c zenon_H106 zenon_H24e. % 18.79/18.96 apply (zenon_or_s _ _ zenon_H22); [ zenon_intro zenon_H27 | zenon_intro zenon_H26 ]. % 18.79/18.96 apply (zenon_L312_); trivial. % 18.79/18.96 apply (zenon_or_s _ _ zenon_H26); [ zenon_intro zenon_H29 | zenon_intro zenon_H28 ]. % 18.79/18.96 apply (zenon_L354_); trivial. % 18.79/18.96 apply (zenon_or_s _ _ zenon_H28); [ zenon_intro zenon_H2a | zenon_intro zenon_H1f ]. % 18.79/18.96 apply (zenon_L728_); trivial. % 18.79/18.96 apply (zenon_L757_); trivial. % 18.79/18.96 (* end of lemma zenon_L758_ *) % 18.79/18.96 assert (zenon_L759_ : (((op (e1) (e3)) = (e0))\/(((op (e1) (e3)) = (e1))\/(((op (e1) (e3)) = (e2))\/((op (e1) (e3)) = (e3))))) -> (~((op (e1) (e3)) = (op (e3) (e3)))) -> (((op (e2) (e2)) = (e0))\/(((op (e2) (e2)) = (e1))\/(((op (e2) (e2)) = (e2))\/((op (e2) (e2)) = (e3))))) -> (~((op (e2) (e2)) = (op (e3) (e2)))) -> (~((op (e2) (e2)) = (op (e2) (e3)))) -> ((op (e2) (e3)) = (e1)) -> (~((op (e2) (e2)) = (e2))) -> (~((op (e0) (e2)) = (op (e2) (e2)))) -> ((op (e0) (e2)) = (e3)) -> ((op (e2) (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 (e2) (e3)) = (op (e3) (e3)))) -> (~((op (e3) (e3)) = (e3))) -> (((op (e3) (e0)) = (e0))\/(((op (e3) (e1)) = (e0))\/(((op (e3) (e2)) = (e0))\/((op (e3) (e3)) = (e0))))) -> (~((op (e1) (e3)) = (e1))) -> (~((op (e1) (e1)) = (op (e1) (e3)))) -> ((op (e1) (e1)) = (e2)) -> (~((op (e1) (e3)) = (op (e2) (e3)))) -> ((op (e2) (e3)) = (e3)) -> False). % 18.79/18.96 do 0 intro. intros zenon_Hdf zenon_Hd5 zenon_H1c4 zenon_H18f zenon_H6d zenon_Hf4 zenon_H173 zenon_Ha8 zenon_Ha9 zenon_Ha6 zenon_H101 zenon_H71 zenon_Hf3 zenon_H102 zenon_H1ac zenon_H24e zenon_H57 zenon_H110 zenon_Hdb zenon_Hdd. % 18.79/18.96 apply (zenon_or_s _ _ zenon_Hdf); [ zenon_intro zenon_H1f | zenon_intro zenon_He0 ]. % 18.79/18.96 apply (zenon_L742_); trivial. % 18.79/18.96 apply (zenon_or_s _ _ zenon_He0); [ zenon_intro zenon_Hd6 | zenon_intro zenon_He1 ]. % 18.79/18.96 exact (zenon_H24e zenon_Hd6). % 18.79/18.96 apply (zenon_or_s _ _ zenon_He1); [ zenon_intro zenon_Hd7 | zenon_intro zenon_Hdc ]. % 18.79/18.96 apply (zenon_L283_); trivial. % 18.79/18.96 apply (zenon_L52_); trivial. % 18.79/18.96 (* end of lemma zenon_L759_ *) % 18.79/18.96 assert (zenon_L760_ : (((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))))) -> (~((e1) = (e3))) -> ((op (e0) (e0)) = (e1)) -> (~((op (e0) (e1)) = (op (e0) (e3)))) -> (((op (e1) (e0)) = (e0))\/(((op (e1) (e1)) = (e0))\/(((op (e1) (e2)) = (e0))\/((op (e1) (e3)) = (e0))))) -> (~((op (e1) (e0)) = (op (e3) (e0)))) -> (~((op (e3) (e0)) = (op (e3) (e2)))) -> (~((op (e1) (e1)) = (op (e1) (e2)))) -> (~((op (e0) (e1)) = (op (e0) (e2)))) -> (((op (e0) (e2)) = (e0))\/(((op (e1) (e2)) = (e0))\/(((op (e2) (e2)) = (e0))\/((op (e3) (e2)) = (e0))))) -> (((op (e0) (e3)) = (e0))\/(((op (e1) (e3)) = (e0))\/(((op (e2) (e3)) = (e0))\/((op (e3) (e3)) = (e0))))) -> (~((e0) = (e3))) -> (~((op (e1) (e2)) = (op (e3) (e2)))) -> (((op (e3) (e2)) = (e0))\/(((op (e3) (e2)) = (e1))\/(((op (e3) (e2)) = (e2))\/((op (e3) (e2)) = (e3))))) -> (~((op (e1) (e2)) = (op (e2) (e2)))) -> (~((op (e0) (e1)) = (op (e2) (e1)))) -> ((op (e0) (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 (e2) (e0)) = (e1))\/(((op (e2) (e1)) = (e1))\/(((op (e2) (e2)) = (e1))\/((op (e2) (e3)) = (e1))))) -> (~((op (e2) (e0)) = (e1))) -> (~((op (e2) (e1)) = (e1))) -> (~((op (e2) (e2)) = (e1))) -> ((op (e1) (e2)) = (e1)) -> (~((e2) = (e3))) -> (((op (e1) (e0)) = (e3))\/(((op (e1) (e1)) = (e3))\/(((op (e1) (e2)) = (e3))\/((op (e1) (e3)) = (e3))))) -> (~((e1) = (e2))) -> ((op (e3) (e1)) = (e1)) -> ((op (e0) (e2)) = (e2)) -> (~((op (e0) (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 (e3) (e3)) = (e0)) -> (~((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 (e1) (e3)) = (op (e2) (e3)))) -> ((op (e1) (e1)) = (e2)) -> (~((op (e1) (e1)) = (op (e1) (e3)))) -> (~((op (e1) (e3)) = (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) (e0)) = (op (e3) (e3)))) -> (((op (e3) (e3)) = (e0))\/(((op (e3) (e3)) = (e1))\/(((op (e3) (e3)) = (e2))\/((op (e3) (e3)) = (e3))))) -> ((op (e2) (e1)) = (e3)) -> ((op (e0) (e2)) = (e3)) -> (~((op (e0) (e2)) = (op (e2) (e2)))) -> (~((op (e2) (e2)) = (e2))) -> ((op (e2) (e3)) = (e1)) -> (~((op (e2) (e2)) = (op (e2) (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) (e3)) = (op (e3) (e3)))) -> (((op (e1) (e3)) = (e0))\/(((op (e1) (e3)) = (e1))\/(((op (e1) (e3)) = (e2))\/((op (e1) (e3)) = (e3))))) -> (~((op (e3) (e3)) = (e3))) -> False). % 18.79/18.96 do 0 intro. intros zenon_H153 zenon_H168 zenon_H95 zenon_H7a zenon_H54 zenon_H22 zenon_H1fa zenon_H6f zenon_H4f zenon_H4a zenon_H6a zenon_H67 zenon_H9a zenon_H115 zenon_H191 zenon_H2b zenon_H17e zenon_H49 zenon_H17b zenon_H2f zenon_H106 zenon_H1db zenon_H24f zenon_H198 zenon_Hf0 zenon_H12b zenon_H16f zenon_H7c zenon_Hae zenon_H150 zenon_H14f zenon_H136 zenon_H1d zenon_H60 zenon_H231 zenon_Hc2 zenon_He4 zenon_Hdb zenon_H110 zenon_H57 zenon_H24e zenon_H1ac zenon_Hf3 zenon_H71 zenon_H101 zenon_Ha6 zenon_Ha9 zenon_Ha8 zenon_H173 zenon_Hf4 zenon_H6d zenon_H18f zenon_H1c4 zenon_Hd5 zenon_Hdf zenon_H102. % 18.79/18.96 apply (zenon_or_s _ _ zenon_H153); [ zenon_intro zenon_H148 | zenon_intro zenon_H154 ]. % 18.79/18.96 apply (zenon_L751_); trivial. % 18.79/18.96 apply (zenon_or_s _ _ zenon_H154); [ zenon_intro zenon_H14d | zenon_intro zenon_H155 ]. % 18.79/18.96 apply (zenon_L152_); trivial. % 18.79/18.96 apply (zenon_or_s _ _ zenon_H155); [ zenon_intro zenon_H151 | zenon_intro zenon_Hf6 ]. % 18.79/18.96 apply (zenon_L104_); trivial. % 18.79/18.96 apply (zenon_or_s _ _ zenon_H136); [ zenon_intro zenon_He3 | zenon_intro zenon_H137 ]. % 18.79/18.96 apply (zenon_L738_); trivial. % 18.79/18.96 apply (zenon_or_s _ _ zenon_H137); [ zenon_intro zenon_Hdc | zenon_intro zenon_H138 ]. % 18.79/18.96 apply (zenon_L749_); trivial. % 18.79/18.96 apply (zenon_or_s _ _ zenon_H138); [ zenon_intro zenon_Hdd | zenon_intro zenon_H105 ]. % 18.79/18.96 apply (zenon_L759_); trivial. % 18.79/18.96 exact (zenon_H102 zenon_H105). % 18.79/18.96 (* end of lemma zenon_L760_ *) % 18.79/18.96 assert (zenon_L761_ : ((op (e0) (e2)) = (e3)) -> (~((op (e0) (e2)) = (op (e2) (e2)))) -> (~((op (e2) (e2)) = (e2))) -> (~((op (e2) (e2)) = (e1))) -> (~((op (e2) (e2)) = (op (e2) (e3)))) -> (((op (e2) (e2)) = (e0))\/(((op (e2) (e2)) = (e1))\/(((op (e2) (e2)) = (e2))\/((op (e2) (e2)) = (e3))))) -> ((op (e2) (e0)) = (e2)) -> (~((op (e2) (e1)) = (op (e3) (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) = (e2))) -> (~((op (e3) (e1)) = (op (e3) (e3)))) -> (~((op (e1) (e0)) = (op (e1) (e3)))) -> ((op (e1) (e0)) = (e0)) -> (((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))))) -> (~((e1) = (e3))) -> ((op (e0) (e0)) = (e1)) -> (~((op (e0) (e1)) = (op (e0) (e3)))) -> (((op (e1) (e0)) = (e0))\/(((op (e1) (e1)) = (e0))\/(((op (e1) (e2)) = (e0))\/((op (e1) (e3)) = (e0))))) -> (~((op (e1) (e0)) = (op (e3) (e0)))) -> (~((op (e3) (e0)) = (op (e3) (e2)))) -> (~((op (e1) (e1)) = (op (e1) (e2)))) -> (~((op (e0) (e1)) = (op (e0) (e2)))) -> (((op (e0) (e2)) = (e0))\/(((op (e1) (e2)) = (e0))\/(((op (e2) (e2)) = (e0))\/((op (e3) (e2)) = (e0))))) -> (((op (e0) (e3)) = (e0))\/(((op (e1) (e3)) = (e0))\/(((op (e2) (e3)) = (e0))\/((op (e3) (e3)) = (e0))))) -> (~((e0) = (e3))) -> (~((op (e1) (e2)) = (op (e3) (e2)))) -> (((op (e3) (e2)) = (e0))\/(((op (e3) (e2)) = (e1))\/(((op (e3) (e2)) = (e2))\/((op (e3) (e2)) = (e3))))) -> (~((op (e1) (e2)) = (op (e2) (e2)))) -> (~((op (e0) (e1)) = (op (e2) (e1)))) -> ((op (e0) (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 (e2) (e0)) = (e1))\/(((op (e2) (e1)) = (e1))\/(((op (e2) (e2)) = (e1))\/((op (e2) (e3)) = (e1))))) -> (~((op (e2) (e0)) = (e1))) -> (~((op (e2) (e1)) = (e1))) -> (~((e2) = (e3))) -> (((op (e1) (e0)) = (e3))\/(((op (e1) (e1)) = (e3))\/(((op (e1) (e2)) = (e3))\/((op (e1) (e3)) = (e3))))) -> (~((e1) = (e2))) -> ((op (e3) (e1)) = (e1)) -> ((op (e0) (e2)) = (e2)) -> (~((op (e0) (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 (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 (e1) (e3)) = (op (e2) (e3)))) -> ((op (e1) (e1)) = (e2)) -> (~((op (e1) (e1)) = (op (e1) (e3)))) -> (((op (e3) (e0)) = (e0))\/(((op (e3) (e1)) = (e0))\/(((op (e3) (e2)) = (e0))\/((op (e3) (e3)) = (e0))))) -> (~((op (e2) (e3)) = (op (e3) (e3)))) -> (~((op (e3) (e0)) = (op (e3) (e3)))) -> (((op (e3) (e3)) = (e0))\/(((op (e3) (e3)) = (e1))\/(((op (e3) (e3)) = (e2))\/((op (e3) (e3)) = (e3))))) -> ((op (e2) (e1)) = (e3)) -> (~((op (e2) (e2)) = (op (e3) (e2)))) -> (~((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)) = (e3))) -> (((op (e0) (e0)) = (e2))\/(((op (e1) (e0)) = (e2))\/(((op (e2) (e0)) = (e2))\/((op (e3) (e0)) = (e2))))) -> (~((op (e1) (e1)) = (op (e3) (e1)))) -> (((op (e2) (e0)) = (e3))\/(((op (e2) (e1)) = (e3))\/(((op (e2) (e2)) = (e3))\/((op (e2) (e3)) = (e3))))) -> (~((op (e0) (e3)) = (op (e2) (e3)))) -> (~((op (e2) (e0)) = (op (e2) (e2)))) -> (~((op (e2) (e0)) = (op (e2) (e3)))) -> (~((op (e3) (e2)) = (op (e3) (e3)))) -> (~((op (e1) (e0)) = (op (e2) (e0)))) -> (((op (e2) (e0)) = (e2))\/(((op (e2) (e1)) = (e2))\/(((op (e2) (e2)) = (e2))\/((op (e2) (e3)) = (e2))))) -> (~((op (e2) (e1)) = (op (e2) (e3)))) -> (((op (e0) (e3)) = (e2))\/(((op (e1) (e3)) = (e2))\/(((op (e2) (e3)) = (e2))\/((op (e3) (e3)) = (e2))))) -> (~((op (e3) (e1)) = (op (e3) (e2)))) -> (((op (e2) (e0)) = (e0))\/(((op (e2) (e0)) = (e1))\/(((op (e2) (e0)) = (e2))\/((op (e2) (e0)) = (e3))))) -> (~((op (e2) (e0)) = (op (e2) (e1)))) -> (~((op (e1) (e3)) = (e1))) -> False). % 18.79/18.96 do 0 intro. intros zenon_Ha9 zenon_Ha8 zenon_H173 zenon_H198 zenon_H6d zenon_H1c4 zenon_Hee zenon_Haf zenon_H10a zenon_H1ef zenon_H128 zenon_H149 zenon_H130 zenon_Hd8 zenon_H27 zenon_H153 zenon_H168 zenon_H95 zenon_H7a zenon_H54 zenon_H22 zenon_H1fa zenon_H6f zenon_H4f zenon_H4a zenon_H6a zenon_H67 zenon_H9a zenon_H115 zenon_H191 zenon_H2b zenon_H17e zenon_H49 zenon_H17b zenon_H2f zenon_H106 zenon_H1db zenon_H24f zenon_H12b zenon_H16f zenon_H7c zenon_Hae zenon_H150 zenon_H14f zenon_H136 zenon_H1d zenon_H231 zenon_Hc2 zenon_He4 zenon_Hdb zenon_H110 zenon_H57 zenon_H1ac zenon_Hf3 zenon_H71 zenon_H101 zenon_Ha6 zenon_H18f zenon_Hd5 zenon_Hdf zenon_H102 zenon_H1fe zenon_H160 zenon_He7 zenon_He2 zenon_H52 zenon_H5b zenon_H62 zenon_H201 zenon_H1d5 zenon_H1c7 zenon_H145 zenon_H1a4 zenon_H259 zenon_H1f0 zenon_H24e. % 18.79/18.96 apply (zenon_or_s _ _ zenon_H128); [ zenon_intro zenon_H9d | zenon_intro zenon_H129 ]. % 18.79/18.96 exact (zenon_H1ef zenon_H9d). % 18.79/18.96 apply (zenon_or_s _ _ zenon_H129); [ zenon_intro zenon_H10d | zenon_intro zenon_H12a ]. % 18.79/18.96 exact (zenon_H10a zenon_H10d). % 18.79/18.96 apply (zenon_or_s _ _ zenon_H12a); [ zenon_intro zenon_Hf0 | zenon_intro zenon_Hd6 ]. % 18.79/18.96 apply (zenon_or_s _ _ zenon_H2f); [ zenon_intro zenon_H34 | zenon_intro zenon_H33 ]. % 18.79/18.96 apply (zenon_L756_); trivial. % 18.79/18.96 apply (zenon_or_s _ _ zenon_H33); [ zenon_intro zenon_H36 | zenon_intro zenon_H35 ]. % 18.79/18.96 apply (zenon_L128_); trivial. % 18.79/18.96 apply (zenon_or_s _ _ zenon_H35); [ zenon_intro zenon_H2c | zenon_intro zenon_H37 ]. % 18.79/18.96 apply (zenon_or_s _ _ zenon_H106); [ zenon_intro zenon_Hed | zenon_intro zenon_H107 ]. % 18.79/18.96 exact (zenon_H1db zenon_Hed). % 18.79/18.96 apply (zenon_or_s _ _ zenon_H107); [ zenon_intro zenon_Ha5 | zenon_intro zenon_H108 ]. % 18.79/18.96 exact (zenon_H24f zenon_Ha5). % 18.79/18.96 apply (zenon_or_s _ _ zenon_H108); [ zenon_intro zenon_Hf1 | zenon_intro zenon_Hf4 ]. % 18.79/18.96 exact (zenon_H198 zenon_Hf1). % 18.79/18.96 apply (zenon_or_s _ _ zenon_H1ac); [ zenon_intro zenon_H44 | zenon_intro zenon_H1af ]. % 18.79/18.96 apply (zenon_L758_); trivial. % 18.79/18.96 apply (zenon_or_s _ _ zenon_H1af); [ zenon_intro zenon_H1b1 | zenon_intro zenon_H1b0 ]. % 18.79/18.96 apply (zenon_L259_); trivial. % 18.79/18.96 apply (zenon_or_s _ _ zenon_H1b0); [ zenon_intro zenon_H61 | zenon_intro zenon_H60 ]. % 18.79/18.96 apply (zenon_L483_); trivial. % 18.79/18.96 apply (zenon_L760_); trivial. % 18.79/18.96 apply (zenon_L727_); trivial. % 18.79/18.96 exact (zenon_H24e zenon_Hd6). % 18.79/18.96 (* end of lemma zenon_L761_ *) % 18.79/18.96 assert (zenon_L762_ : (((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) (e2)) = (e1))) -> False). % 18.79/18.96 do 0 intro. intros zenon_H139 zenon_H95 zenon_Ha9 zenon_H24d zenon_H198 zenon_H251. % 18.79/18.96 apply (zenon_or_s _ _ zenon_H139); [ zenon_intro zenon_H122 | zenon_intro zenon_H13a ]. % 18.79/18.96 apply (zenon_L77_); trivial. % 18.79/18.96 apply (zenon_or_s _ _ zenon_H13a); [ zenon_intro zenon_Hf0 | zenon_intro zenon_H13b ]. % 18.79/18.96 exact (zenon_H24d zenon_Hf0). % 18.79/18.96 apply (zenon_or_s _ _ zenon_H13b); [ zenon_intro zenon_Hf1 | zenon_intro zenon_Hba ]. % 18.79/18.96 exact (zenon_H198 zenon_Hf1). % 18.79/18.96 exact (zenon_H251 zenon_Hba). % 18.79/18.96 (* end of lemma zenon_L762_ *) % 18.79/18.96 assert (zenon_L763_ : ((~((op (e3) (e2)) = (e1)))\/((op (e3) (e1)) = (e2))) -> (~((op (e0) (e1)) = (op (e3) (e1)))) -> (~((op (e0) (e0)) = (e0))) -> (~((op (e1) (e0)) = (op (e1) (e1)))) -> ((op (e1) (e1)) = (e0)) -> (((op (e0) (e2)) = (e0))\/(((op (e1) (e2)) = (e0))\/(((op (e2) (e2)) = (e0))\/((op (e3) (e2)) = (e0))))) -> (~((op (e0) (e1)) = (op (e0) (e3)))) -> (~((op (e1) (e1)) = (op (e1) (e3)))) -> (~((op (e2) (e0)) = (op (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) (e0)) = (op (e2) (e2)))) -> (~((op (e1) (e1)) = (op (e1) (e2)))) -> ((op (e0) (e1)) = (e0)) -> (~((op (e0) (e1)) = (op (e0) (e2)))) -> (((op (e0) (e0)) = (e1))\/(((op (e0) (e1)) = (e1))\/(((op (e0) (e2)) = (e1))\/((op (e0) (e3)) = (e1))))) -> (~((op (e0) (e3)) = (e1))) -> (~((e0) = (e1))) -> (~((op (e0) (e1)) = (e1))) -> (~((e1) = (e3))) -> (~((e2) = (e3))) -> ((op (e0) (e1)) = (e2)) -> (((op (e0) (e2)) = (e1))\/(((op (e1) (e2)) = (e1))\/(((op (e2) (e2)) = (e1))\/((op (e3) (e2)) = (e1))))) -> (~((op (e2) (e2)) = (e1))) -> (~((op (e1) (e2)) = (e1))) -> (((op (e2) (e0)) = (e0))\/(((op (e2) (e1)) = (e0))\/(((op (e2) (e2)) = (e0))\/((op (e2) (e3)) = (e0))))) -> (~((op (e3) (e0)) = (op (e3) (e2)))) -> (~((e0) = (e3))) -> (~((op (e2) (e2)) = (op (e2) (e3)))) -> (~((op (e3) (e0)) = (op (e3) (e3)))) -> (~((op (e0) (e1)) = (op (e2) (e1)))) -> (~((op (e2) (e0)) = (op (e3) (e0)))) -> (((op (e0) (e0)) = (e3))\/(((op (e0) (e1)) = (e3))\/(((op (e0) (e2)) = (e3))\/((op (e0) (e3)) = (e3))))) -> (((op (e0) (e0)) = (e0))\/(((op (e1) (e0)) = (e0))\/(((op (e2) (e0)) = (e0))\/((op (e3) (e0)) = (e0))))) -> False). % 18.79/18.96 do 0 intro. intros zenon_H252 zenon_H210 zenon_H3f zenon_H45 zenon_H29 zenon_H6a zenon_H54 zenon_H57 zenon_H5b zenon_H62 zenon_H67 zenon_H52 zenon_H4f zenon_H49 zenon_H4a zenon_H22d zenon_H231 zenon_Ha1 zenon_Ha4 zenon_H95 zenon_H12b zenon_H10f zenon_H139 zenon_H198 zenon_H24d zenon_H2f zenon_H6f zenon_H9a zenon_H6d zenon_H71 zenon_H17e zenon_H17b zenon_H168 zenon_H3e. % 18.79/18.96 apply (zenon_or_s _ _ zenon_H252); [ zenon_intro zenon_H251 | zenon_intro zenon_H14d ]. % 18.79/18.96 apply (zenon_or_s _ _ zenon_H3e); [ zenon_intro zenon_H42 | zenon_intro zenon_H41 ]. % 18.79/18.96 exact (zenon_H3f zenon_H42). % 18.79/18.96 apply (zenon_or_s _ _ zenon_H41); [ zenon_intro zenon_H27 | zenon_intro zenon_H43 ]. % 18.79/18.96 apply (zenon_L8_); trivial. % 18.79/18.96 apply (zenon_or_s _ _ zenon_H43); [ zenon_intro zenon_H34 | zenon_intro zenon_H44 ]. % 18.79/18.96 apply (zenon_L17_); trivial. % 18.79/18.96 apply (zenon_or_s _ _ zenon_H22d); [ zenon_intro zenon_H7a | zenon_intro zenon_H22e ]. % 18.79/18.96 apply (zenon_or_s _ _ zenon_H168); [ zenon_intro zenon_H3a | zenon_intro zenon_H169 ]. % 18.79/18.96 apply (zenon_L35_); trivial. % 18.79/18.96 apply (zenon_or_s _ _ zenon_H169); [ zenon_intro zenon_H99 | zenon_intro zenon_H16a ]. % 18.79/18.96 apply (zenon_L175_); trivial. % 18.79/18.96 apply (zenon_or_s _ _ zenon_H16a); [ zenon_intro zenon_Ha9 | zenon_intro zenon_He3 ]. % 18.79/18.96 apply (zenon_L762_); trivial. % 18.79/18.96 apply (zenon_L745_); trivial. % 18.79/18.96 apply (zenon_or_s _ _ zenon_H22e); [ zenon_intro zenon_Ha0 | zenon_intro zenon_H22f ]. % 18.79/18.96 exact (zenon_Ha4 zenon_Ha0). % 18.79/18.96 apply (zenon_or_s _ _ zenon_H22f); [ zenon_intro zenon_H122 | zenon_intro zenon_Hc3 ]. % 18.79/18.96 apply (zenon_or_s _ _ zenon_H67); [ zenon_intro zenon_H1e | zenon_intro zenon_H68 ]. % 18.79/18.96 apply (zenon_L12_); trivial. % 18.79/18.96 apply (zenon_or_s _ _ zenon_H68); [ zenon_intro zenon_H1f | zenon_intro zenon_H69 ]. % 18.79/18.96 apply (zenon_L13_); trivial. % 18.79/18.96 apply (zenon_or_s _ _ zenon_H69); [ zenon_intro zenon_H37 | zenon_intro zenon_H60 ]. % 18.79/18.96 apply (zenon_L374_); trivial. % 18.79/18.96 apply (zenon_L21_); trivial. % 18.79/18.96 exact (zenon_H231 zenon_Hc3). % 18.79/18.96 apply (zenon_L389_); trivial. % 18.79/18.96 (* end of lemma zenon_L763_ *) % 18.79/18.96 assert (zenon_L764_ : ((~((op (e0) (e3)) = (e1)))\/((op (e0) (e1)) = (e3))) -> ((~((op (e1) (e2)) = (e1)))\/((op (e1) (e1)) = (e2))) -> (~((op (e0) (e1)) = (op (e1) (e1)))) -> (((op (e1) (e0)) = (e1))\/(((op (e1) (e1)) = (e1))\/(((op (e1) (e2)) = (e1))\/((op (e1) (e3)) = (e1))))) -> (~((op (e1) (e1)) = (e1))) -> ((~((op (e2) (e0)) = (e1)))\/((op (e2) (e1)) = (e0))) -> ((op (e0) (e1)) = (e0)) -> ((~((op (e3) (e0)) = (e1)))\/((op (e3) (e1)) = (e0))) -> (((op (e0) (e0)) = (e1))\/(((op (e0) (e1)) = (e1))\/(((op (e0) (e2)) = (e1))\/((op (e0) (e3)) = (e1))))) -> (((op (e0) (e0)) = (e1))\/(((op (e1) (e0)) = (e1))\/(((op (e2) (e0)) = (e1))\/((op (e3) (e0)) = (e1))))) -> (~((op (e0) (e1)) = (e1))) -> (~((op (e0) (e0)) = (op (e0) (e2)))) -> (((op (e0) (e2)) = (e1))\/(((op (e1) (e2)) = (e1))\/(((op (e2) (e2)) = (e1))\/((op (e3) (e2)) = (e1))))) -> (~((op (e0) (e1)) = (op (e3) (e1)))) -> ((op (e0) (e1)) = (e2)) -> ((~((op (e3) (e2)) = (e1)))\/((op (e3) (e1)) = (e2))) -> (~((op (e0) (e1)) = (op (e2) (e1)))) -> ((~((op (e2) (e2)) = (e1)))\/((op (e2) (e1)) = (e2))) -> ((~((op (e1) (e3)) = (e1)))\/((op (e1) (e1)) = (e3))) -> (~((op (e0) (e0)) = (e0))) -> (~((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 (e0) (e3)))) -> (~((op (e1) (e1)) = (op (e1) (e3)))) -> (~((op (e2) (e0)) = (op (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) (e0)) = (op (e2) (e2)))) -> (~((op (e1) (e1)) = (op (e1) (e2)))) -> (~((op (e0) (e1)) = (op (e0) (e2)))) -> (~((e0) = (e1))) -> (~((e1) = (e3))) -> (~((e2) = (e3))) -> (((op (e2) (e0)) = (e0))\/(((op (e2) (e1)) = (e0))\/(((op (e2) (e2)) = (e0))\/((op (e2) (e3)) = (e0))))) -> (~((op (e3) (e0)) = (op (e3) (e2)))) -> (~((e0) = (e3))) -> (~((op (e2) (e2)) = (op (e2) (e3)))) -> (~((op (e3) (e0)) = (op (e3) (e3)))) -> (~((op (e2) (e0)) = (op (e3) (e0)))) -> (((op (e0) (e0)) = (e3))\/(((op (e0) (e1)) = (e3))\/(((op (e0) (e2)) = (e3))\/((op (e0) (e3)) = (e3))))) -> (((op (e0) (e0)) = (e0))\/(((op (e1) (e0)) = (e0))\/(((op (e2) (e0)) = (e0))\/((op (e3) (e0)) = (e0))))) -> ((~((op (e1) (e0)) = (e1)))\/((op (e1) (e1)) = (e0))) -> False). % 18.79/18.96 do 0 intro. intros zenon_H25c zenon_H256 zenon_H10e zenon_H128 zenon_H10a zenon_H257 zenon_H49 zenon_H254 zenon_H22d zenon_H235 zenon_Ha4 zenon_H13c zenon_H139 zenon_H210 zenon_H10f zenon_H252 zenon_H17e zenon_H253 zenon_H258 zenon_H3f zenon_H45 zenon_H6a zenon_H54 zenon_H57 zenon_H5b zenon_H62 zenon_H67 zenon_H52 zenon_H4f zenon_H4a zenon_Ha1 zenon_H95 zenon_H12b zenon_H2f zenon_H6f zenon_H9a zenon_H6d zenon_H71 zenon_H17b zenon_H168 zenon_H3e zenon_H25d. % 18.79/18.96 apply (zenon_or_s _ _ zenon_H25c); [ zenon_intro zenon_H231 | zenon_intro zenon_H99 ]. % 18.79/18.96 apply (zenon_or_s _ _ zenon_H25d); [ zenon_intro zenon_H1ef | zenon_intro zenon_H29 ]. % 18.79/18.96 apply (zenon_L726_); trivial. % 18.79/18.96 apply (zenon_or_s _ _ zenon_H256); [ zenon_intro zenon_H24d | zenon_intro zenon_H110 ]. % 18.79/18.96 apply (zenon_or_s _ _ zenon_H253); [ zenon_intro zenon_H198 | zenon_intro zenon_H1ca ]. % 18.79/18.96 apply (zenon_L763_); trivial. % 18.79/18.96 apply (zenon_L191_); trivial. % 18.79/18.96 apply (zenon_L67_); trivial. % 18.79/18.96 apply (zenon_L175_); trivial. % 18.79/18.96 (* end of lemma zenon_L764_ *) % 18.79/18.96 assert (zenon_L765_ : (((op (e0) (e0)) = (e2))\/(((op (e0) (e1)) = (e2))\/(((op (e0) (e2)) = (e2))\/((op (e0) (e3)) = (e2))))) -> (~((e1) = (e2))) -> ((~((op (e1) (e0)) = (e1)))\/((op (e1) (e1)) = (e0))) -> (((op (e0) (e0)) = (e0))\/(((op (e1) (e0)) = (e0))\/(((op (e2) (e0)) = (e0))\/((op (e3) (e0)) = (e0))))) -> (~((e0) = (e1))) -> (~((op (e2) (e0)) = (op (e2) (e2)))) -> (~((op (e3) (e2)) = (op (e3) (e3)))) -> (~((op (e2) (e0)) = (op (e2) (e3)))) -> (~((op (e1) (e0)) = (op (e1) (e1)))) -> (~((op (e0) (e0)) = (e0))) -> ((~((op (e1) (e3)) = (e1)))\/((op (e1) (e1)) = (e3))) -> ((~((op (e2) (e2)) = (e1)))\/((op (e2) (e1)) = (e2))) -> ((~((op (e3) (e2)) = (e1)))\/((op (e3) (e1)) = (e2))) -> (~((op (e0) (e1)) = (op (e3) (e1)))) -> (((op (e0) (e2)) = (e1))\/(((op (e1) (e2)) = (e1))\/(((op (e2) (e2)) = (e1))\/((op (e3) (e2)) = (e1))))) -> (~((op (e0) (e0)) = (op (e0) (e2)))) -> (~((op (e0) (e1)) = (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 (e3) (e0)) = (e1)))\/((op (e3) (e1)) = (e0))) -> ((~((op (e2) (e0)) = (e1)))\/((op (e2) (e1)) = (e0))) -> (~((op (e1) (e1)) = (e1))) -> (((op (e1) (e0)) = (e1))\/(((op (e1) (e1)) = (e1))\/(((op (e1) (e2)) = (e1))\/((op (e1) (e3)) = (e1))))) -> (~((op (e0) (e1)) = (op (e1) (e1)))) -> ((~((op (e1) (e2)) = (e1)))\/((op (e1) (e1)) = (e2))) -> ((~((op (e0) (e3)) = (e1)))\/((op (e0) (e1)) = (e3))) -> (((op (e3) (e2)) = (e0))\/(((op (e3) (e2)) = (e1))\/(((op (e3) (e2)) = (e2))\/((op (e3) (e2)) = (e3))))) -> (~((op (e1) (e2)) = (op (e3) (e2)))) -> (~((op (e0) (e2)) = (op (e3) (e2)))) -> (((op (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)) = (op (e3) (e3)))) -> (((op (e2) (e2)) = (e0))\/(((op (e2) (e2)) = (e1))\/(((op (e2) (e2)) = (e2))\/((op (e2) (e2)) = (e3))))) -> (~((op (e2) (e2)) = (op (e3) (e2)))) -> (~((op (e2) (e2)) = (op (e2) (e3)))) -> (~((op (e2) (e2)) = (e2))) -> (~((op (e0) (e2)) = (op (e2) (e2)))) -> ((op (e2) (e1)) = (e3)) -> ((op (e1) (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 (e2) (e3)) = (op (e3) (e3)))) -> (~((op (e3) (e3)) = (e3))) -> (((op (e3) (e0)) = (e0))\/(((op (e3) (e1)) = (e0))\/(((op (e3) (e2)) = (e0))\/((op (e3) (e3)) = (e0))))) -> (~((op (e2) (e2)) = (e1))) -> (~((op (e2) (e1)) = (e1))) -> (~((op (e2) (e0)) = (e1))) -> (((op (e2) (e0)) = (e1))\/(((op (e2) (e1)) = (e1))\/(((op (e2) (e2)) = (e1))\/((op (e2) (e3)) = (e1))))) -> (((op (e2) (e0)) = (e0))\/(((op (e2) (e1)) = (e0))\/(((op (e2) (e2)) = (e0))\/((op (e2) (e3)) = (e0))))) -> (~((op (e2) (e0)) = (op (e3) (e0)))) -> ((op (e3) (e0)) = (e0)) -> ((op (e0) (e1)) = (e0)) -> (~((op (e0) (e1)) = (op (e2) (e1)))) -> (~((op (e1) (e2)) = (op (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 (e1) (e1)) = (op (e1) (e3)))) -> (~((op (e3) (e0)) = (op (e3) (e2)))) -> (~((op (e1) (e1)) = (op (e1) (e2)))) -> (~((op (e0) (e1)) = (op (e0) (e2)))) -> (((op (e0) (e2)) = (e0))\/(((op (e1) (e2)) = (e0))\/(((op (e2) (e2)) = (e0))\/((op (e3) (e2)) = (e0))))) -> (~((op (e1) (e0)) = (op (e3) (e0)))) -> (((op (e1) (e0)) = (e0))\/(((op (e1) (e1)) = (e0))\/(((op (e1) (e2)) = (e0))\/((op (e1) (e3)) = (e0))))) -> (~((e2) = (e3))) -> False). % 18.79/18.96 do 0 intro. intros zenon_H183 zenon_H7c zenon_H25d zenon_H3e zenon_Ha1 zenon_H52 zenon_H62 zenon_H5b zenon_H45 zenon_H3f zenon_H258 zenon_H253 zenon_H252 zenon_H210 zenon_H139 zenon_H13c zenon_Ha4 zenon_H235 zenon_H22d zenon_H254 zenon_H257 zenon_H10a zenon_H128 zenon_H10e zenon_H256 zenon_H25c zenon_H191 zenon_H115 zenon_H14f zenon_H168 zenon_H95 zenon_H7a zenon_H9a zenon_Hd5 zenon_H1c4 zenon_H18f zenon_H6d zenon_H173 zenon_Ha8 zenon_Ha6 zenon_H110 zenon_H101 zenon_H71 zenon_Hf3 zenon_H102 zenon_H1ac zenon_H198 zenon_H24f zenon_H1db zenon_H106 zenon_H2f zenon_H17b zenon_H44 zenon_H49 zenon_H17e zenon_H2b zenon_H67 zenon_H54 zenon_H57 zenon_H6f zenon_H4f zenon_H4a zenon_H6a zenon_H1fa zenon_H22 zenon_H12b. % 18.79/18.96 apply (zenon_or_s _ _ zenon_H183); [ zenon_intro zenon_H7b | zenon_intro zenon_H186 ]. % 18.79/18.96 apply (zenon_L26_); trivial. % 18.79/18.96 apply (zenon_or_s _ _ zenon_H186); [ zenon_intro zenon_H10f | zenon_intro zenon_H187 ]. % 18.79/18.96 apply (zenon_L764_); trivial. % 18.79/18.96 apply (zenon_or_s _ _ zenon_H187); [ zenon_intro zenon_H150 | zenon_intro zenon_Hcd ]. % 18.79/18.96 apply (zenon_L748_); trivial. % 18.79/18.96 apply (zenon_or_s _ _ zenon_H168); [ zenon_intro zenon_H3a | zenon_intro zenon_H169 ]. % 18.79/18.96 apply (zenon_L35_); trivial. % 18.79/18.96 apply (zenon_or_s _ _ zenon_H169); [ zenon_intro zenon_H99 | zenon_intro zenon_H16a ]. % 18.79/18.96 apply (zenon_L36_); trivial. % 18.79/18.96 apply (zenon_or_s _ _ zenon_H16a); [ zenon_intro zenon_Ha9 | zenon_intro zenon_He3 ]. % 18.79/18.96 apply (zenon_L743_); trivial. % 18.79/18.96 apply (zenon_L81_); trivial. % 18.79/18.96 (* end of lemma zenon_L765_ *) % 18.79/18.96 assert (zenon_L766_ : (((op (e0) (e3)) = (e0))\/(((op (e1) (e3)) = (e0))\/(((op (e2) (e3)) = (e0))\/((op (e3) (e3)) = (e0))))) -> (~((e0) = (e3))) -> ((op (e0) (e3)) = (e3)) -> ((op (e1) (e0)) = (e0)) -> (~((op (e1) (e0)) = (op (e1) (e3)))) -> (~((op (e2) (e2)) = (op (e2) (e3)))) -> ((op (e2) (e2)) = (e0)) -> ((op (e3) (e1)) = (e0)) -> (~((op (e3) (e1)) = (op (e3) (e3)))) -> False). % 18.79/18.96 do 0 intro. intros zenon_H67 zenon_H9a zenon_He3 zenon_H27 zenon_Hd8 zenon_H6d zenon_H2c zenon_H1b1 zenon_H130. % 18.79/18.96 apply (zenon_or_s _ _ zenon_H67); [ zenon_intro zenon_H1e | zenon_intro zenon_H68 ]. % 18.79/18.96 apply (zenon_L515_); trivial. % 18.79/18.96 apply (zenon_or_s _ _ zenon_H68); [ zenon_intro zenon_H1f | zenon_intro zenon_H69 ]. % 18.79/18.96 apply (zenon_L258_); trivial. % 18.79/18.96 apply (zenon_or_s _ _ zenon_H69); [ zenon_intro zenon_H37 | zenon_intro zenon_H60 ]. % 18.79/18.96 apply (zenon_L18_); trivial. % 18.79/18.96 apply (zenon_L244_); trivial. % 18.79/18.96 (* end of lemma zenon_L766_ *) % 18.79/18.96 assert (zenon_L767_ : (((op (e1) (e3)) = (e0))\/(((op (e1) (e3)) = (e1))\/(((op (e1) (e3)) = (e2))\/((op (e1) (e3)) = (e3))))) -> ((op (e2) (e3)) = (e0)) -> (~((op (e1) (e3)) = (op (e2) (e3)))) -> (~((op (e1) (e3)) = (e1))) -> ((op (e3) (e3)) = (e2)) -> (~((op (e1) (e3)) = (op (e3) (e3)))) -> (~((op (e0) (e3)) = (op (e1) (e3)))) -> ((op (e0) (e3)) = (e3)) -> False). % 18.79/18.96 do 0 intro. intros zenon_Hdf zenon_H37 zenon_Hdb zenon_H24e zenon_Hf6 zenon_Hd5 zenon_H1d zenon_He3. % 18.79/18.96 apply (zenon_or_s _ _ zenon_Hdf); [ zenon_intro zenon_H1f | zenon_intro zenon_He0 ]. % 18.79/18.96 apply (zenon_L130_); trivial. % 18.79/18.96 apply (zenon_or_s _ _ zenon_He0); [ zenon_intro zenon_Hd6 | zenon_intro zenon_He1 ]. % 18.79/18.96 exact (zenon_H24e zenon_Hd6). % 18.79/18.96 apply (zenon_or_s _ _ zenon_He1); [ zenon_intro zenon_Hd7 | zenon_intro zenon_Hdc ]. % 18.79/18.96 apply (zenon_L402_); trivial. % 18.79/18.96 apply (zenon_L117_); trivial. % 18.79/18.96 (* end of lemma zenon_L767_ *) % 18.79/18.96 assert (zenon_L768_ : (~((op (e1) (e0)) = (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))))) -> (~((e0) = (e2))) -> (~((op (e2) (e0)) = (op (e2) (e1)))) -> (((op (e2) (e0)) = (e0))\/(((op (e2) (e0)) = (e1))\/(((op (e2) (e0)) = (e2))\/((op (e2) (e0)) = (e3))))) -> (~((op (e3) (e1)) = (op (e3) (e2)))) -> (((op (e0) (e3)) = (e2))\/(((op (e1) (e3)) = (e2))\/(((op (e2) (e3)) = (e2))\/((op (e3) (e3)) = (e2))))) -> (~((op (e2) (e1)) = (op (e2) (e3)))) -> (((op (e2) (e0)) = (e2))\/(((op (e2) (e1)) = (e2))\/(((op (e2) (e2)) = (e2))\/((op (e2) (e3)) = (e2))))) -> (~((op (e1) (e0)) = (op (e2) (e0)))) -> (~((op (e0) (e3)) = (op (e2) (e3)))) -> (((op (e2) (e0)) = (e3))\/(((op (e2) (e1)) = (e3))\/(((op (e2) (e2)) = (e3))\/((op (e2) (e3)) = (e3))))) -> ((op (e3) (e1)) = (e1)) -> (((op (e0) (e0)) = (e2))\/(((op (e1) (e0)) = (e2))\/(((op (e2) (e0)) = (e2))\/((op (e3) (e0)) = (e2))))) -> (((op (e1) (e0)) = (e3))\/(((op (e1) (e1)) = (e3))\/(((op (e1) (e2)) = (e3))\/((op (e1) (e3)) = (e3))))) -> (~((e2) = (e3))) -> (~((e1) = (e3))) -> ((op (e1) (e2)) = (e1)) -> (~((op (e2) (e2)) = (op (e3) (e2)))) -> (((op (e0) (e3)) = (e0))\/(((op (e1) (e3)) = (e0))\/(((op (e2) (e3)) = (e0))\/((op (e3) (e3)) = (e0))))) -> (~((e0) = (e3))) -> ((op (e1) (e0)) = (e0)) -> (~((op (e1) (e0)) = (op (e1) (e3)))) -> (~((op (e2) (e2)) = (op (e2) (e3)))) -> (~((op (e3) (e1)) = (op (e3) (e3)))) -> (((op (e0) (e0)) = (e2))\/(((op (e0) (e1)) = (e2))\/(((op (e0) (e2)) = (e2))\/((op (e0) (e3)) = (e2))))) -> (~((e1) = (e2))) -> ((~((op (e1) (e0)) = (e1)))\/((op (e1) (e1)) = (e0))) -> (((op (e0) (e0)) = (e0))\/(((op (e1) (e0)) = (e0))\/(((op (e2) (e0)) = (e0))\/((op (e3) (e0)) = (e0))))) -> (~((e0) = (e1))) -> (~((op (e2) (e0)) = (op (e2) (e2)))) -> (~((op (e3) (e2)) = (op (e3) (e3)))) -> (~((op (e2) (e0)) = (op (e2) (e3)))) -> (~((op (e1) (e0)) = (op (e1) (e1)))) -> (~((op (e0) (e0)) = (e0))) -> ((~((op (e1) (e3)) = (e1)))\/((op (e1) (e1)) = (e3))) -> ((~((op (e2) (e2)) = (e1)))\/((op (e2) (e1)) = (e2))) -> ((~((op (e3) (e2)) = (e1)))\/((op (e3) (e1)) = (e2))) -> (~((op (e0) (e1)) = (op (e3) (e1)))) -> (((op (e0) (e2)) = (e1))\/(((op (e1) (e2)) = (e1))\/(((op (e2) (e2)) = (e1))\/((op (e3) (e2)) = (e1))))) -> (~((op (e0) (e0)) = (op (e0) (e2)))) -> (~((op (e0) (e1)) = (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 (e3) (e0)) = (e1)))\/((op (e3) (e1)) = (e0))) -> ((~((op (e2) (e0)) = (e1)))\/((op (e2) (e1)) = (e0))) -> (~((op (e1) (e1)) = (e1))) -> (((op (e1) (e0)) = (e1))\/(((op (e1) (e1)) = (e1))\/(((op (e1) (e2)) = (e1))\/((op (e1) (e3)) = (e1))))) -> (~((op (e0) (e1)) = (op (e1) (e1)))) -> ((~((op (e1) (e2)) = (e1)))\/((op (e1) (e1)) = (e2))) -> ((~((op (e0) (e3)) = (e1)))\/((op (e0) (e1)) = (e3))) -> (((op (e3) (e2)) = (e0))\/(((op (e3) (e2)) = (e1))\/(((op (e3) (e2)) = (e2))\/((op (e3) (e2)) = (e3))))) -> (~((op (e1) (e2)) = (op (e3) (e2)))) -> (((op (e0) (e0)) = (e3))\/(((op (e0) (e1)) = (e3))\/(((op (e0) (e2)) = (e3))\/((op (e0) (e3)) = (e3))))) -> (((op (e2) (e2)) = (e0))\/(((op (e2) (e2)) = (e1))\/(((op (e2) (e2)) = (e2))\/((op (e2) (e2)) = (e3))))) -> (~((op (e2) (e2)) = (e2))) -> (~((op (e0) (e2)) = (op (e2) (e2)))) -> ((op (e2) (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 (e2) (e3)) = (op (e3) (e3)))) -> (~((op (e3) (e3)) = (e3))) -> (((op (e3) (e0)) = (e0))\/(((op (e3) (e1)) = (e0))\/(((op (e3) (e2)) = (e0))\/((op (e3) (e3)) = (e0))))) -> (~((op (e2) (e2)) = (e1))) -> (~((op (e2) (e1)) = (e1))) -> (~((op (e2) (e0)) = (e1))) -> (((op (e2) (e0)) = (e1))\/(((op (e2) (e1)) = (e1))\/(((op (e2) (e2)) = (e1))\/((op (e2) (e3)) = (e1))))) -> (((op (e2) (e0)) = (e0))\/(((op (e2) (e1)) = (e0))\/(((op (e2) (e2)) = (e0))\/((op (e2) (e3)) = (e0))))) -> (~((op (e2) (e0)) = (op (e3) (e0)))) -> ((op (e0) (e1)) = (e0)) -> (~((op (e0) (e1)) = (op (e2) (e1)))) -> (~((op (e1) (e2)) = (op (e2) (e2)))) -> (~((op (e0) (e1)) = (op (e0) (e3)))) -> (~((op (e1) (e1)) = (op (e1) (e3)))) -> (~((op (e3) (e0)) = (op (e3) (e2)))) -> (~((op (e1) (e1)) = (op (e1) (e2)))) -> (~((op (e0) (e1)) = (op (e0) (e2)))) -> (((op (e0) (e2)) = (e0))\/(((op (e1) (e2)) = (e0))\/(((op (e2) (e2)) = (e0))\/((op (e3) (e2)) = (e0))))) -> (~((op (e1) (e0)) = (op (e3) (e0)))) -> (((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 (e0) (e0)) = (e1)) -> ((op (e1) (e0)) = (e3)) -> ((op (e1) (e1)) = (e2)) -> (~((op (e1) (e1)) = (op (e3) (e1)))) -> ((op (e0) (e2)) = (e2)) -> (~((op (e0) (e2)) = (op (e3) (e2)))) -> (((op (e1) (e3)) = (e0))\/(((op (e1) (e3)) = (e1))\/(((op (e1) (e3)) = (e2))\/((op (e1) (e3)) = (e3))))) -> (~((op (e1) (e3)) = (op (e2) (e3)))) -> (~((op (e1) (e3)) = (e1))) -> (~((op (e1) (e3)) = (op (e3) (e3)))) -> (~((op (e0) (e3)) = (op (e1) (e3)))) -> ((op (e0) (e3)) = (e3)) -> False). % 18.79/18.96 do 0 intro. intros zenon_H1ef zenon_H231 zenon_Hc2 zenon_He4 zenon_H149 zenon_H1f0 zenon_H259 zenon_H1a4 zenon_H145 zenon_H1c7 zenon_H1d5 zenon_H201 zenon_He2 zenon_He7 zenon_Hae zenon_H1fe zenon_H16f zenon_H12b zenon_H95 zenon_Hf0 zenon_H18f zenon_H67 zenon_H9a zenon_H27 zenon_Hd8 zenon_H6d zenon_H130 zenon_H183 zenon_H7c zenon_H25d zenon_H3e zenon_Ha1 zenon_H52 zenon_H62 zenon_H5b zenon_H45 zenon_H3f zenon_H258 zenon_H253 zenon_H252 zenon_H210 zenon_H139 zenon_H13c zenon_Ha4 zenon_H235 zenon_H22d zenon_H254 zenon_H257 zenon_H10a zenon_H128 zenon_H10e zenon_H256 zenon_H25c zenon_H191 zenon_H115 zenon_H168 zenon_H1c4 zenon_H173 zenon_Ha8 zenon_Ha6 zenon_H101 zenon_H71 zenon_Hf3 zenon_H102 zenon_H1ac zenon_H198 zenon_H24f zenon_H1db zenon_H106 zenon_H2f zenon_H17b zenon_H49 zenon_H17e zenon_H2b zenon_H54 zenon_H57 zenon_H6f zenon_H4f zenon_H4a zenon_H6a zenon_H1fa zenon_H22 zenon_H153 zenon_H7a zenon_H9e zenon_H110 zenon_H160 zenon_H150 zenon_H14f zenon_Hdf zenon_Hdb zenon_H24e zenon_Hd5 zenon_H1d zenon_He3. % 18.79/18.96 apply (zenon_or_s _ _ zenon_H2f); [ zenon_intro zenon_H34 | zenon_intro zenon_H33 ]. % 18.79/18.96 apply (zenon_L756_); trivial. % 18.79/18.96 apply (zenon_or_s _ _ zenon_H33); [ zenon_intro zenon_H36 | zenon_intro zenon_H35 ]. % 18.79/18.96 apply (zenon_L128_); trivial. % 18.79/18.96 apply (zenon_or_s _ _ zenon_H35); [ zenon_intro zenon_H2c | zenon_intro zenon_H37 ]. % 18.79/18.96 apply (zenon_or_s _ _ zenon_H1ac); [ zenon_intro zenon_H44 | zenon_intro zenon_H1af ]. % 18.79/18.96 apply (zenon_L765_); trivial. % 18.79/18.96 apply (zenon_or_s _ _ zenon_H1af); [ zenon_intro zenon_H1b1 | zenon_intro zenon_H1b0 ]. % 18.79/18.96 apply (zenon_L766_); trivial. % 18.79/18.96 apply (zenon_or_s _ _ zenon_H1b0); [ zenon_intro zenon_H61 | zenon_intro zenon_H60 ]. % 18.79/18.96 apply (zenon_L146_); trivial. % 18.79/18.96 apply (zenon_L753_); trivial. % 18.79/18.96 apply (zenon_or_s _ _ zenon_H153); [ zenon_intro zenon_H148 | zenon_intro zenon_H154 ]. % 18.79/18.96 apply (zenon_L107_); trivial. % 18.79/18.96 apply (zenon_or_s _ _ zenon_H154); [ zenon_intro zenon_H14d | zenon_intro zenon_H155 ]. % 18.79/18.96 apply (zenon_L164_); trivial. % 18.79/18.96 apply (zenon_or_s _ _ zenon_H155); [ zenon_intro zenon_H151 | zenon_intro zenon_Hf6 ]. % 18.79/18.96 apply (zenon_L104_); trivial. % 18.79/18.96 apply (zenon_L767_); trivial. % 18.79/18.96 (* end of lemma zenon_L768_ *) % 18.79/18.96 assert (zenon_L769_ : (((op (e1) (e0)) = (e0))\/(((op (e1) (e0)) = (e1))\/(((op (e1) (e0)) = (e2))\/((op (e1) (e0)) = (e3))))) -> ((op (e1) (e3)) = (e0)) -> (~((op (e1) (e0)) = (op (e1) (e3)))) -> (~((op (e1) (e0)) = (e1))) -> ((op (e2) (e0)) = (e3)) -> ((op (e3) (e0)) = (e2)) -> ((op (e0) (e0)) = (e1)) -> False). % 18.79/18.96 do 0 intro. intros zenon_H25e zenon_H1f zenon_Hd8 zenon_H1ef zenon_H3b zenon_H148 zenon_H7a. % 18.79/18.96 apply (zenon_or_s _ _ zenon_H25e); [ zenon_intro zenon_H27 | zenon_intro zenon_H25f ]. % 18.79/18.96 apply (zenon_L258_); trivial. % 18.79/18.96 apply (zenon_or_s _ _ zenon_H25f); [ zenon_intro zenon_H9d | zenon_intro zenon_H260 ]. % 18.79/18.96 exact (zenon_H1ef zenon_H9d). % 18.79/18.96 apply (zenon_or_s _ _ zenon_H260); [ zenon_intro zenon_H86 | zenon_intro zenon_H9e ]. % 18.79/18.96 apply (zenon_L33_); trivial. % 18.79/18.96 apply (zenon_L107_); trivial. % 18.79/18.96 (* end of lemma zenon_L769_ *) % 18.79/18.96 assert (zenon_L770_ : (((op (e1) (e0)) = (e0))\/(((op (e1) (e1)) = (e0))\/(((op (e1) (e2)) = (e0))\/((op (e1) (e3)) = (e0))))) -> (~((op (e1) (e0)) = (op (e2) (e0)))) -> (~((op (e3) (e2)) = (op (e3) (e3)))) -> ((op (e2) (e0)) = (e0)) -> (~((op (e2) (e0)) = (op (e2) (e3)))) -> (~((op (e1) (e1)) = (op (e1) (e3)))) -> ((op (e0) (e1)) = (e0)) -> (~((op (e0) (e1)) = (op (e0) (e3)))) -> (((op (e0) (e3)) = (e0))\/(((op (e1) (e3)) = (e0))\/(((op (e2) (e3)) = (e0))\/((op (e3) (e3)) = (e0))))) -> (~((op (e2) (e0)) = (op (e2) (e2)))) -> (~((op (e1) (e1)) = (op (e1) (e2)))) -> (~((op (e0) (e1)) = (op (e0) (e2)))) -> (((op (e0) (e2)) = (e0))\/(((op (e1) (e2)) = (e0))\/(((op (e2) (e2)) = (e0))\/((op (e3) (e2)) = (e0))))) -> (~((op (e1) (e3)) = (e1))) -> (((op (e2) (e0)) = (e1))\/(((op (e2) (e1)) = (e1))\/(((op (e2) (e2)) = (e1))\/((op (e2) (e3)) = (e1))))) -> (~((op (e2) (e0)) = (e1))) -> (~((op (e2) (e1)) = (e1))) -> (~((op (e1) (e2)) = (op (e2) (e2)))) -> (((op (e3) (e0)) = (e0))\/(((op (e3) (e1)) = (e0))\/(((op (e3) (e2)) = (e0))\/((op (e3) (e3)) = (e0))))) -> (~((e0) = (e2))) -> ((op (e1) (e1)) = (e2)) -> ((op (e2) (e1)) = (e3)) -> (~((op (e1) (e2)) = (op (e3) (e2)))) -> ((op (e0) (e3)) = (e2)) -> (~((op (e1) (e1)) = (e1))) -> (((op (e1) (e0)) = (e1))\/(((op (e1) (e1)) = (e1))\/(((op (e1) (e2)) = (e1))\/((op (e1) (e3)) = (e1))))) -> (((op (e1) (e0)) = (e0))\/(((op (e1) (e0)) = (e1))\/(((op (e1) (e0)) = (e2))\/((op (e1) (e0)) = (e3))))) -> (~((op (e1) (e0)) = (op (e1) (e3)))) -> (~((op (e1) (e0)) = (e1))) -> ((op (e2) (e0)) = (e3)) -> ((op (e3) (e0)) = (e2)) -> ((op (e0) (e0)) = (e1)) -> False). % 18.79/18.96 do 0 intro. intros zenon_H22 zenon_H201 zenon_H62 zenon_H34 zenon_H5b zenon_H57 zenon_H49 zenon_H54 zenon_H67 zenon_H52 zenon_H4f zenon_H4a zenon_H6a zenon_H24e zenon_H106 zenon_H1db zenon_H24f zenon_H2b zenon_H1ac zenon_H149 zenon_H110 zenon_Ha6 zenon_H115 zenon_Hcd zenon_H10a zenon_H128 zenon_H25e zenon_Hd8 zenon_H1ef zenon_H3b zenon_H148 zenon_H7a. % 18.79/18.96 apply (zenon_or_s _ _ zenon_H22); [ zenon_intro zenon_H27 | zenon_intro zenon_H26 ]. % 18.79/18.96 apply (zenon_L332_); trivial. % 18.79/18.96 apply (zenon_or_s _ _ zenon_H26); [ zenon_intro zenon_H29 | zenon_intro zenon_H28 ]. % 18.79/18.96 apply (zenon_L17_); trivial. % 18.79/18.96 apply (zenon_or_s _ _ zenon_H28); [ zenon_intro zenon_H2a | zenon_intro zenon_H1f ]. % 18.79/18.96 apply (zenon_or_s _ _ zenon_H128); [ zenon_intro zenon_H9d | zenon_intro zenon_H129 ]. % 18.79/18.96 exact (zenon_H1ef zenon_H9d). % 18.79/18.96 apply (zenon_or_s _ _ zenon_H129); [ zenon_intro zenon_H10d | zenon_intro zenon_H12a ]. % 18.79/18.96 exact (zenon_H10a zenon_H10d). % 18.79/18.96 apply (zenon_or_s _ _ zenon_H12a); [ zenon_intro zenon_Hf0 | zenon_intro zenon_Hd6 ]. % 18.79/18.96 apply (zenon_or_s _ _ zenon_H106); [ zenon_intro zenon_Hed | zenon_intro zenon_H107 ]. % 18.79/18.96 exact (zenon_H1db zenon_Hed). % 18.79/18.96 apply (zenon_or_s _ _ zenon_H107); [ zenon_intro zenon_Ha5 | zenon_intro zenon_H108 ]. % 18.79/18.96 exact (zenon_H24f zenon_Ha5). % 18.79/18.96 apply (zenon_or_s _ _ zenon_H108); [ zenon_intro zenon_Hf1 | zenon_intro zenon_Hf4 ]. % 18.79/18.96 apply (zenon_L59_); trivial. % 18.79/18.96 apply (zenon_L736_); trivial. % 18.79/18.96 exact (zenon_H24e zenon_Hd6). % 18.79/18.96 apply (zenon_L769_); trivial. % 18.79/18.96 (* end of lemma zenon_L770_ *) % 18.79/18.96 assert (zenon_L771_ : (((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)) = (e1))) -> (~((op (e1) (e0)) = (op (e1) (e3)))) -> (((op (e1) (e0)) = (e0))\/(((op (e1) (e0)) = (e1))\/(((op (e1) (e0)) = (e2))\/((op (e1) (e0)) = (e3))))) -> (((op (e1) (e0)) = (e1))\/(((op (e1) (e1)) = (e1))\/(((op (e1) (e2)) = (e1))\/((op (e1) (e3)) = (e1))))) -> (~((op (e1) (e1)) = (e1))) -> ((op (e0) (e3)) = (e2)) -> (~((op (e1) (e2)) = (op (e3) (e2)))) -> ((op (e2) (e1)) = (e3)) -> ((op (e1) (e1)) = (e2)) -> (~((e0) = (e2))) -> (((op (e3) (e0)) = (e0))\/(((op (e3) (e1)) = (e0))\/(((op (e3) (e2)) = (e0))\/((op (e3) (e3)) = (e0))))) -> (~((op (e1) (e2)) = (op (e2) (e2)))) -> (~((op (e2) (e1)) = (e1))) -> (~((op (e2) (e0)) = (e1))) -> (((op (e2) (e0)) = (e1))\/(((op (e2) (e1)) = (e1))\/(((op (e2) (e2)) = (e1))\/((op (e2) (e3)) = (e1))))) -> (~((op (e1) (e3)) = (e1))) -> (((op (e0) (e2)) = (e0))\/(((op (e1) (e2)) = (e0))\/(((op (e2) (e2)) = (e0))\/((op (e3) (e2)) = (e0))))) -> (~((op (e0) (e1)) = (op (e0) (e2)))) -> (~((op (e1) (e1)) = (op (e1) (e2)))) -> (~((op (e2) (e0)) = (op (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) (e1)) = (e0)) -> (~((op (e1) (e1)) = (op (e1) (e3)))) -> (~((op (e2) (e0)) = (op (e2) (e3)))) -> ((op (e2) (e0)) = (e0)) -> (~((op (e3) (e2)) = (op (e3) (e3)))) -> (~((op (e1) (e0)) = (op (e2) (e0)))) -> (((op (e1) (e0)) = (e0))\/(((op (e1) (e1)) = (e0))\/(((op (e1) (e2)) = (e0))\/((op (e1) (e3)) = (e0))))) -> ((op (e3) (e0)) = (e2)) -> (~((e2) = (e3))) -> False). % 18.79/18.96 do 0 intro. intros zenon_H1e0 zenon_H95 zenon_H7a zenon_H1ef zenon_Hd8 zenon_H25e zenon_H128 zenon_H10a zenon_Hcd zenon_H115 zenon_Ha6 zenon_H110 zenon_H149 zenon_H1ac zenon_H2b zenon_H24f zenon_H1db zenon_H106 zenon_H24e zenon_H6a zenon_H4a zenon_H4f zenon_H52 zenon_H67 zenon_H54 zenon_H49 zenon_H57 zenon_H5b zenon_H34 zenon_H62 zenon_H201 zenon_H22 zenon_H148 zenon_H12b. % 18.79/18.96 apply (zenon_or_s _ _ zenon_H1e0); [ zenon_intro zenon_H3a | zenon_intro zenon_H1e1 ]. % 18.79/18.96 apply (zenon_L35_); trivial. % 18.79/18.96 apply (zenon_or_s _ _ zenon_H1e1); [ zenon_intro zenon_H9e | zenon_intro zenon_H1e2 ]. % 18.79/18.96 apply (zenon_L107_); trivial. % 18.79/18.96 apply (zenon_or_s _ _ zenon_H1e2); [ zenon_intro zenon_H3b | zenon_intro zenon_H15e ]. % 18.79/18.96 apply (zenon_L770_); trivial. % 18.79/18.96 apply (zenon_L109_); trivial. % 18.79/18.96 (* end of lemma zenon_L771_ *) % 18.79/18.96 assert (zenon_L772_ : (((op (e0) (e0)) = (e2))\/(((op (e1) (e0)) = (e2))\/(((op (e2) (e0)) = (e2))\/((op (e3) (e0)) = (e2))))) -> (~((op (e0) (e0)) = (op (e0) (e3)))) -> (~((op (e0) (e3)) = (op (e2) (e3)))) -> (~((op (e2) (e0)) = (op (e2) (e1)))) -> (((op (e2) (e0)) = (e0))\/(((op (e2) (e0)) = (e1))\/(((op (e2) (e0)) = (e2))\/((op (e2) (e0)) = (e3))))) -> (~((op (e0) (e1)) = (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 (e2) (e2)) = (e1))) -> (((op (e2) (e0)) = (e2))\/(((op (e2) (e1)) = (e2))\/(((op (e2) (e2)) = (e2))\/((op (e2) (e3)) = (e2))))) -> (~((op (e0) (e2)) = (op (e2) (e2)))) -> (~((op (e2) (e2)) = (e2))) -> (~((op (e2) (e2)) = (op (e2) (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) (e3)) = (e3))) -> (~((op (e2) (e3)) = (op (e3) (e3)))) -> (~((op (e3) (e0)) = (op (e3) (e3)))) -> (((op (e3) (e3)) = (e0))\/(((op (e3) (e3)) = (e1))\/(((op (e3) (e3)) = (e2))\/((op (e3) (e3)) = (e3))))) -> (~((op (e1) (e3)) = (op (e3) (e3)))) -> (~((e0) = (e3))) -> (((op (e0) (e0)) = (e3))\/(((op (e0) (e1)) = (e3))\/(((op (e0) (e2)) = (e3))\/((op (e0) (e3)) = (e3))))) -> (((op (e0) (e0)) = (e3))\/(((op (e1) (e0)) = (e3))\/(((op (e2) (e0)) = (e3))\/((op (e3) (e0)) = (e3))))) -> (~((e1) = (e3))) -> ((op (e0) (e0)) = (e1)) -> (~((op (e1) (e0)) = (e1))) -> (~((op (e1) (e0)) = (op (e1) (e3)))) -> (((op (e1) (e0)) = (e0))\/(((op (e1) (e0)) = (e1))\/(((op (e1) (e0)) = (e2))\/((op (e1) (e0)) = (e3))))) -> (((op (e1) (e0)) = (e1))\/(((op (e1) (e1)) = (e1))\/(((op (e1) (e2)) = (e1))\/((op (e1) (e3)) = (e1))))) -> (~((op (e1) (e1)) = (e1))) -> ((op (e0) (e3)) = (e2)) -> (~((op (e1) (e2)) = (op (e3) (e2)))) -> ((op (e2) (e1)) = (e3)) -> ((op (e1) (e1)) = (e2)) -> (~((e0) = (e2))) -> (((op (e3) (e0)) = (e0))\/(((op (e3) (e1)) = (e0))\/(((op (e3) (e2)) = (e0))\/((op (e3) (e3)) = (e0))))) -> (~((op (e1) (e2)) = (op (e2) (e2)))) -> (~((op (e2) (e1)) = (e1))) -> (~((op (e2) (e0)) = (e1))) -> (((op (e2) (e0)) = (e1))\/(((op (e2) (e1)) = (e1))\/(((op (e2) (e2)) = (e1))\/((op (e2) (e3)) = (e1))))) -> (~((op (e1) (e3)) = (e1))) -> (((op (e0) (e2)) = (e0))\/(((op (e1) (e2)) = (e0))\/(((op (e2) (e2)) = (e0))\/((op (e3) (e2)) = (e0))))) -> (~((op (e0) (e1)) = (op (e0) (e2)))) -> (~((op (e1) (e1)) = (op (e1) (e2)))) -> (~((op (e2) (e0)) = (op (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) (e1)) = (e0)) -> (~((op (e1) (e1)) = (op (e1) (e3)))) -> (~((op (e2) (e0)) = (op (e2) (e3)))) -> ((op (e2) (e0)) = (e0)) -> (~((op (e3) (e2)) = (op (e3) (e3)))) -> (~((op (e1) (e0)) = (op (e2) (e0)))) -> (((op (e1) (e0)) = (e0))\/(((op (e1) (e1)) = (e0))\/(((op (e1) (e2)) = (e0))\/((op (e1) (e3)) = (e0))))) -> (~((e2) = (e3))) -> False). % 18.79/18.96 do 0 intro. intros zenon_H1fe zenon_H189 zenon_He2 zenon_H1f0 zenon_H259 zenon_H17e zenon_H17b zenon_H2f zenon_H198 zenon_H1d5 zenon_Ha8 zenon_H173 zenon_H6d zenon_H18f zenon_H1c4 zenon_H102 zenon_Hf3 zenon_H71 zenon_H101 zenon_Hd5 zenon_H9a zenon_H168 zenon_H1e0 zenon_H95 zenon_H7a zenon_H1ef zenon_Hd8 zenon_H25e zenon_H128 zenon_H10a zenon_Hcd zenon_H115 zenon_Ha6 zenon_H110 zenon_H149 zenon_H1ac zenon_H2b zenon_H24f zenon_H1db zenon_H106 zenon_H24e zenon_H6a zenon_H4a zenon_H4f zenon_H52 zenon_H67 zenon_H54 zenon_H49 zenon_H57 zenon_H5b zenon_H34 zenon_H62 zenon_H201 zenon_H22 zenon_H12b. % 18.79/18.96 apply (zenon_or_s _ _ zenon_H1fe); [ zenon_intro zenon_H7b | zenon_intro zenon_H1ff ]. % 18.79/18.96 apply (zenon_L375_); trivial. % 18.79/18.96 apply (zenon_or_s _ _ zenon_H1ff); [ zenon_intro zenon_H86 | zenon_intro zenon_H200 ]. % 18.79/18.96 apply (zenon_or_s _ _ zenon_H168); [ zenon_intro zenon_H3a | zenon_intro zenon_H169 ]. % 18.79/18.97 apply (zenon_L35_); trivial. % 18.79/18.97 apply (zenon_or_s _ _ zenon_H169); [ zenon_intro zenon_H99 | zenon_intro zenon_H16a ]. % 18.79/18.97 apply (zenon_L36_); trivial. % 18.79/18.97 apply (zenon_or_s _ _ zenon_H16a); [ zenon_intro zenon_Ha9 | zenon_intro zenon_He3 ]. % 18.79/18.97 apply (zenon_or_s _ _ zenon_H22); [ zenon_intro zenon_H27 | zenon_intro zenon_H26 ]. % 18.79/18.97 apply (zenon_L257_); trivial. % 18.79/18.97 apply (zenon_or_s _ _ zenon_H26); [ zenon_intro zenon_H29 | zenon_intro zenon_H28 ]. % 18.79/18.97 apply (zenon_L354_); trivial. % 18.79/18.97 apply (zenon_or_s _ _ zenon_H28); [ zenon_intro zenon_H2a | zenon_intro zenon_H1f ]. % 18.79/18.97 apply (zenon_or_s _ _ zenon_H1d5); [ zenon_intro zenon_Hee | zenon_intro zenon_H1d6 ]. % 18.79/18.97 apply (zenon_L728_); trivial. % 18.79/18.97 apply (zenon_or_s _ _ zenon_H1d6); [ zenon_intro zenon_H1ca | zenon_intro zenon_H1d7 ]. % 18.79/18.97 apply (zenon_L733_); trivial. % 18.79/18.97 apply (zenon_or_s _ _ zenon_H1d7); [ zenon_intro zenon_H176 | zenon_intro zenon_H11d ]. % 18.79/18.97 exact (zenon_H173 zenon_H176). % 18.79/18.97 apply (zenon_L234_); trivial. % 18.79/18.97 apply (zenon_L752_); trivial. % 18.79/18.97 apply (zenon_L81_); trivial. % 18.79/18.97 apply (zenon_or_s _ _ zenon_H200); [ zenon_intro zenon_Hee | zenon_intro zenon_H148 ]. % 18.79/18.97 apply (zenon_L204_); trivial. % 18.79/18.97 apply (zenon_L771_); trivial. % 18.79/18.97 (* end of lemma zenon_L772_ *) % 18.79/18.97 assert (zenon_L773_ : (~((e2) = (e3))) -> (((op (e1) (e0)) = (e0))\/(((op (e1) (e1)) = (e0))\/(((op (e1) (e2)) = (e0))\/((op (e1) (e3)) = (e0))))) -> (~((op (e1) (e0)) = (op (e2) (e0)))) -> (~((op (e3) (e2)) = (op (e3) (e3)))) -> ((op (e2) (e0)) = (e0)) -> (~((op (e2) (e0)) = (op (e2) (e3)))) -> (~((op (e1) (e1)) = (op (e1) (e3)))) -> ((op (e0) (e1)) = (e0)) -> (~((op (e0) (e1)) = (op (e0) (e3)))) -> (((op (e0) (e3)) = (e0))\/(((op (e1) (e3)) = (e0))\/(((op (e2) (e3)) = (e0))\/((op (e3) (e3)) = (e0))))) -> (~((op (e2) (e0)) = (op (e2) (e2)))) -> (~((op (e1) (e1)) = (op (e1) (e2)))) -> (~((op (e0) (e1)) = (op (e0) (e2)))) -> (((op (e0) (e2)) = (e0))\/(((op (e1) (e2)) = (e0))\/(((op (e2) (e2)) = (e0))\/((op (e3) (e2)) = (e0))))) -> (~((op (e1) (e3)) = (e1))) -> (((op (e2) (e0)) = (e1))\/(((op (e2) (e1)) = (e1))\/(((op (e2) (e2)) = (e1))\/((op (e2) (e3)) = (e1))))) -> (~((op (e2) (e0)) = (e1))) -> (~((op (e2) (e1)) = (e1))) -> (~((op (e1) (e2)) = (op (e2) (e2)))) -> (((op (e3) (e0)) = (e0))\/(((op (e3) (e1)) = (e0))\/(((op (e3) (e2)) = (e0))\/((op (e3) (e3)) = (e0))))) -> (~((e0) = (e2))) -> ((op (e1) (e1)) = (e2)) -> ((op (e2) (e1)) = (e3)) -> (~((op (e1) (e2)) = (op (e3) (e2)))) -> (~((op (e1) (e1)) = (e1))) -> (((op (e1) (e0)) = (e1))\/(((op (e1) (e1)) = (e1))\/(((op (e1) (e2)) = (e1))\/((op (e1) (e3)) = (e1))))) -> (((op (e1) (e0)) = (e0))\/(((op (e1) (e0)) = (e1))\/(((op (e1) (e0)) = (e2))\/((op (e1) (e0)) = (e3))))) -> (~((op (e1) (e0)) = (op (e1) (e3)))) -> (~((op (e1) (e0)) = (e1))) -> (~((e1) = (e3))) -> (((op (e0) (e0)) = (e3))\/(((op (e1) (e0)) = (e3))\/(((op (e2) (e0)) = (e3))\/((op (e3) (e0)) = (e3))))) -> (((op (e0) (e0)) = (e3))\/(((op (e0) (e1)) = (e3))\/(((op (e0) (e2)) = (e3))\/((op (e0) (e3)) = (e3))))) -> (~((e0) = (e3))) -> (~((op (e1) (e3)) = (op (e3) (e3)))) -> (((op (e3) (e3)) = (e0))\/(((op (e3) (e3)) = (e1))\/(((op (e3) (e3)) = (e2))\/((op (e3) (e3)) = (e3))))) -> (~((op (e3) (e0)) = (op (e3) (e3)))) -> (~((op (e2) (e3)) = (op (e3) (e3)))) -> (~((op (e3) (e3)) = (e3))) -> (((op (e2) (e2)) = (e0))\/(((op (e2) (e2)) = (e1))\/(((op (e2) (e2)) = (e2))\/((op (e2) (e2)) = (e3))))) -> (~((op (e2) (e2)) = (op (e3) (e2)))) -> (~((op (e2) (e2)) = (op (e2) (e3)))) -> (~((op (e2) (e2)) = (e2))) -> (~((op (e0) (e2)) = (op (e2) (e2)))) -> (((op (e2) (e0)) = (e2))\/(((op (e2) (e1)) = (e2))\/(((op (e2) (e2)) = (e2))\/((op (e2) (e3)) = (e2))))) -> (~((op (e2) (e2)) = (e1))) -> (((op (e2) (e0)) = (e0))\/(((op (e2) (e1)) = (e0))\/(((op (e2) (e2)) = (e0))\/((op (e2) (e3)) = (e0))))) -> (~((op (e2) (e0)) = (op (e3) (e0)))) -> (~((op (e0) (e1)) = (op (e2) (e1)))) -> (((op (e2) (e0)) = (e0))\/(((op (e2) (e0)) = (e1))\/(((op (e2) (e0)) = (e2))\/((op (e2) (e0)) = (e3))))) -> (~((op (e2) (e0)) = (op (e2) (e1)))) -> (~((op (e0) (e3)) = (op (e2) (e3)))) -> (~((op (e0) (e0)) = (op (e0) (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))))) -> (~((e1) = (e2))) -> ((op (e3) (e1)) = (e1)) -> (((op (e1) (e3)) = (e0))\/(((op (e1) (e3)) = (e1))\/(((op (e1) (e3)) = (e2))\/((op (e1) (e3)) = (e3))))) -> (~((op (e1) (e1)) = (op (e3) (e1)))) -> (((op (e2) (e0)) = (e3))\/(((op (e2) (e1)) = (e3))\/(((op (e2) (e2)) = (e3))\/((op (e2) (e3)) = (e3))))) -> (~((op (e3) (e1)) = (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 (e3) (e1)) = (op (e3) (e2)))) -> (((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) (e0)) = (op (e3) (e0)))) -> (((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) (e0)) = (e3))\/(((op (e1) (e1)) = (e3))\/(((op (e1) (e2)) = (e3))\/((op (e1) (e3)) = (e3))))) -> ((~((op (e1) (e2)) = (e1)))\/((op (e1) (e1)) = (e2))) -> (~((op (e0) (e1)) = (op (e1) (e1)))) -> ((~((op (e2) (e0)) = (e1)))\/((op (e2) (e1)) = (e0))) -> ((~((op (e3) (e0)) = (e1)))\/((op (e3) (e1)) = (e0))) -> (((op (e0) (e0)) = (e1))\/(((op (e0) (e1)) = (e1))\/(((op (e0) (e2)) = (e1))\/((op (e0) (e3)) = (e1))))) -> (((op (e0) (e0)) = (e1))\/(((op (e1) (e0)) = (e1))\/(((op (e2) (e0)) = (e1))\/((op (e3) (e0)) = (e1))))) -> (~((op (e0) (e0)) = (op (e0) (e2)))) -> (((op (e0) (e2)) = (e1))\/(((op (e1) (e2)) = (e1))\/(((op (e2) (e2)) = (e1))\/((op (e3) (e2)) = (e1))))) -> (~((op (e0) (e1)) = (op (e3) (e1)))) -> ((~((op (e3) (e2)) = (e1)))\/((op (e3) (e1)) = (e2))) -> ((~((op (e2) (e2)) = (e1)))\/((op (e2) (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) (e1)) = (e1))) -> (~((op (e0) (e2)) = (e1))) -> (~((op (e0) (e3)) = (e1))) -> False). % 18.79/18.97 do 0 intro. intros zenon_H12b zenon_H22 zenon_H201 zenon_H62 zenon_H34 zenon_H5b zenon_H57 zenon_H49 zenon_H54 zenon_H67 zenon_H52 zenon_H4f zenon_H4a zenon_H6a zenon_H24e zenon_H106 zenon_H1db zenon_H24f zenon_H2b zenon_H1ac zenon_H149 zenon_H110 zenon_Ha6 zenon_H115 zenon_H10a zenon_H128 zenon_H25e zenon_Hd8 zenon_H1ef zenon_H95 zenon_H1e0 zenon_H168 zenon_H9a zenon_Hd5 zenon_H101 zenon_H71 zenon_Hf3 zenon_H102 zenon_H1c4 zenon_H18f zenon_H6d zenon_H173 zenon_Ha8 zenon_H1d5 zenon_H198 zenon_H2f zenon_H17b zenon_H17e zenon_H259 zenon_H1f0 zenon_He2 zenon_H189 zenon_H1fe zenon_H153 zenon_H7c zenon_Hae zenon_Hdf zenon_H160 zenon_He7 zenon_H130 zenon_H1c7 zenon_H145 zenon_H1a4 zenon_H191 zenon_H14f zenon_H6f zenon_H1fa zenon_He4 zenon_Hc2 zenon_H1d zenon_H16f zenon_H256 zenon_H10e zenon_H257 zenon_H254 zenon_H22d zenon_H235 zenon_H13c zenon_H139 zenon_H210 zenon_H252 zenon_H253 zenon_H258 zenon_H183 zenon_Ha4 zenon_H20d zenon_H231. % 18.79/18.97 apply (zenon_or_s _ _ zenon_H22d); [ zenon_intro zenon_H7a | zenon_intro zenon_H22e ]. % 18.79/18.97 apply (zenon_or_s _ _ zenon_H183); [ zenon_intro zenon_H7b | zenon_intro zenon_H186 ]. % 18.79/18.97 apply (zenon_L26_); trivial. % 18.79/18.97 apply (zenon_or_s _ _ zenon_H186); [ zenon_intro zenon_H10f | zenon_intro zenon_H187 ]. % 18.79/18.97 apply (zenon_L726_); trivial. % 18.79/18.97 apply (zenon_or_s _ _ zenon_H187); [ zenon_intro zenon_H150 | zenon_intro zenon_Hcd ]. % 18.79/18.97 apply (zenon_L756_); trivial. % 18.79/18.97 apply (zenon_L772_); trivial. % 18.79/18.97 apply (zenon_or_s _ _ zenon_H22e); [ zenon_intro zenon_Ha0 | zenon_intro zenon_H22f ]. % 18.79/18.97 exact (zenon_Ha4 zenon_Ha0). % 18.79/18.97 apply (zenon_or_s _ _ zenon_H22f); [ zenon_intro zenon_H122 | zenon_intro zenon_Hc3 ]. % 18.79/18.97 exact (zenon_H20d zenon_H122). % 18.79/18.97 exact (zenon_H231 zenon_Hc3). % 18.79/18.97 (* end of lemma zenon_L773_ *) % 18.79/18.97 assert (zenon_L774_ : (~((op (e2) (e0)) = (e1))) -> (~((op (e2) (e1)) = (e1))) -> (((op (e3) (e0)) = (e0))\/(((op (e3) (e1)) = (e0))\/(((op (e3) (e2)) = (e0))\/((op (e3) (e3)) = (e0))))) -> (~((op (e1) (e3)) = (e1))) -> (((op (e2) (e0)) = (e1))\/(((op (e2) (e1)) = (e1))\/(((op (e2) (e2)) = (e1))\/((op (e2) (e3)) = (e1))))) -> (~((e1) = (e2))) -> ((op (e2) (e0)) = (e2)) -> (~((op (e2) (e1)) = (op (e3) (e1)))) -> ((op (e3) (e1)) = (e1)) -> (~((op (e1) (e2)) = (op (e2) (e2)))) -> (((op (e3) (e3)) = (e0))\/(((op (e3) (e3)) = (e1))\/(((op (e3) (e3)) = (e2))\/((op (e3) (e3)) = (e3))))) -> (~((op (e3) (e0)) = (op (e3) (e3)))) -> (~((op (e2) (e3)) = (op (e3) (e3)))) -> (~((op (e3) (e3)) = (e3))) -> (~((op (e1) (e1)) = (e1))) -> (~((op (e1) (e0)) = (e1))) -> (((op (e1) (e0)) = (e1))\/(((op (e1) (e1)) = (e1))\/(((op (e1) (e2)) = (e1))\/((op (e1) (e3)) = (e1))))) -> (((op (e2) (e0)) = (e0))\/(((op (e2) (e1)) = (e0))\/(((op (e2) (e2)) = (e0))\/((op (e2) (e3)) = (e0))))) -> (~((e0) = (e2))) -> (~((op (e0) (e1)) = (op (e2) (e1)))) -> (((op (e2) (e2)) = (e0))\/(((op (e2) (e2)) = (e1))\/(((op (e2) (e2)) = (e2))\/((op (e2) (e2)) = (e3))))) -> (~((op (e2) (e2)) = (e1))) -> (~((op (e2) (e2)) = (e2))) -> (~((op (e0) (e2)) = (op (e2) (e2)))) -> ((op (e0) (e2)) = (e3)) -> ((op (e1) (e1)) = (e2)) -> (~((op (e1) (e0)) = (op (e3) (e0)))) -> (((op (e1) (e0)) = (e0))\/(((op (e1) (e1)) = (e0))\/(((op (e1) (e2)) = (e0))\/((op (e1) (e3)) = (e0))))) -> (~((op (e3) (e1)) = (op (e3) (e3)))) -> (~((op (e2) (e2)) = (op (e2) (e3)))) -> (~((op (e1) (e0)) = (op (e1) (e3)))) -> ((op (e1) (e0)) = (e0)) -> ((op (e0) (e1)) = (e0)) -> (~((op (e0) (e1)) = (op (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 (e0) (e3)) = (e2)) -> False). % 18.79/18.97 do 0 intro. intros zenon_H1db zenon_H24f zenon_H1ac zenon_H24e zenon_H106 zenon_H7c zenon_Hee zenon_Haf zenon_Hae zenon_H2b zenon_H101 zenon_H71 zenon_Hf3 zenon_H102 zenon_H10a zenon_H1ef zenon_H128 zenon_H2f zenon_H149 zenon_H17e zenon_H1c4 zenon_H198 zenon_H173 zenon_Ha8 zenon_Ha9 zenon_H110 zenon_H1fa zenon_H22 zenon_H130 zenon_H6d zenon_Hd8 zenon_H27 zenon_H49 zenon_H54 zenon_H67 zenon_H2c zenon_H18f zenon_Hcd. % 18.79/18.97 apply (zenon_or_s _ _ zenon_H106); [ zenon_intro zenon_Hed | zenon_intro zenon_H107 ]. % 18.79/18.97 exact (zenon_H1db zenon_Hed). % 18.79/18.97 apply (zenon_or_s _ _ zenon_H107); [ zenon_intro zenon_Ha5 | zenon_intro zenon_H108 ]. % 18.79/18.97 exact (zenon_H24f zenon_Ha5). % 18.79/18.97 apply (zenon_or_s _ _ zenon_H108); [ zenon_intro zenon_Hf1 | zenon_intro zenon_Hf4 ]. % 18.79/18.97 exact (zenon_H198 zenon_Hf1). % 18.79/18.97 apply (zenon_or_s _ _ zenon_H1ac); [ zenon_intro zenon_H44 | zenon_intro zenon_H1af ]. % 18.79/18.97 apply (zenon_L758_); trivial. % 18.79/18.97 apply (zenon_or_s _ _ zenon_H1af); [ zenon_intro zenon_H1b1 | zenon_intro zenon_H1b0 ]. % 18.79/18.97 apply (zenon_L259_); trivial. % 18.79/18.97 apply (zenon_or_s _ _ zenon_H1b0); [ zenon_intro zenon_H61 | zenon_intro zenon_H60 ]. % 18.79/18.97 apply (zenon_L146_); trivial. % 18.79/18.97 apply (zenon_L229_); trivial. % 18.79/18.97 (* end of lemma zenon_L774_ *) % 18.79/18.97 assert (zenon_L775_ : (((op (e3) (e0)) = (e0))\/(((op (e3) (e1)) = (e0))\/(((op (e3) (e2)) = (e0))\/((op (e3) (e3)) = (e0))))) -> (~((e0) = (e2))) -> ((op (e3) (e0)) = (e2)) -> (~((op (e3) (e1)) = (op (e3) (e3)))) -> (~((op (e2) (e2)) = (op (e2) (e3)))) -> (~((op (e1) (e0)) = (op (e1) (e3)))) -> ((op (e1) (e0)) = (e0)) -> ((op (e0) (e1)) = (e0)) -> (~((op (e0) (e1)) = (op (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 (e2) (e3)) = (e1)) -> ((op (e0) (e3)) = (e2)) -> False). % 18.79/18.97 do 0 intro. intros zenon_H1ac zenon_H149 zenon_H148 zenon_H130 zenon_H6d zenon_Hd8 zenon_H27 zenon_H49 zenon_H54 zenon_H67 zenon_H2c zenon_H18f zenon_Hf4 zenon_Hcd. % 18.79/18.97 apply (zenon_or_s _ _ zenon_H1ac); [ zenon_intro zenon_H44 | zenon_intro zenon_H1af ]. % 18.79/18.97 apply (zenon_L100_); trivial. % 18.79/18.97 apply (zenon_or_s _ _ zenon_H1af); [ zenon_intro zenon_H1b1 | zenon_intro zenon_H1b0 ]. % 18.79/18.97 apply (zenon_L259_); trivial. % 18.79/18.97 apply (zenon_or_s _ _ zenon_H1b0); [ zenon_intro zenon_H61 | zenon_intro zenon_H60 ]. % 18.79/18.97 apply (zenon_L146_); trivial. % 18.79/18.97 apply (zenon_L229_); trivial. % 18.79/18.97 (* end of lemma zenon_L775_ *) % 18.79/18.97 assert (zenon_L776_ : (((op (e0) (e0)) = (e3))\/(((op (e1) (e0)) = (e3))\/(((op (e2) (e0)) = (e3))\/((op (e3) (e0)) = (e3))))) -> (~((op (e1) (e3)) = (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 (e0) (e0)) = (e1)) -> (~((op (e1) (e0)) = (e1))) -> (((op (e1) (e0)) = (e0))\/(((op (e1) (e0)) = (e1))\/(((op (e1) (e0)) = (e2))\/((op (e1) (e0)) = (e3))))) -> (((op (e1) (e0)) = (e1))\/(((op (e1) (e1)) = (e1))\/(((op (e1) (e2)) = (e1))\/((op (e1) (e3)) = (e1))))) -> (~((op (e1) (e1)) = (e1))) -> (~((op (e1) (e2)) = (op (e3) (e2)))) -> ((op (e2) (e1)) = (e3)) -> ((op (e1) (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 (e1) (e1)) = (op (e1) (e2)))) -> (~((op (e1) (e1)) = (op (e1) (e3)))) -> (~((op (e2) (e0)) = (op (e2) (e3)))) -> (~((op (e3) (e2)) = (op (e3) (e3)))) -> (~((op (e1) (e0)) = (op (e2) (e0)))) -> (((op (e1) (e0)) = (e0))\/(((op (e1) (e1)) = (e0))\/(((op (e1) (e2)) = (e0))\/((op (e1) (e3)) = (e0))))) -> (~((op (e0) (e1)) = (op (e2) (e1)))) -> ((op (e0) (e3)) = (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) (e1)) = (op (e0) (e3)))) -> ((op (e0) (e1)) = (e0)) -> ((op (e1) (e0)) = (e0)) -> (~((op (e1) (e0)) = (op (e1) (e3)))) -> (~((op (e3) (e1)) = (op (e3) (e3)))) -> (~((e0) = (e2))) -> (((op (e3) (e0)) = (e0))\/(((op (e3) (e1)) = (e0))\/(((op (e3) (e2)) = (e0))\/((op (e3) (e3)) = (e0))))) -> (((op (e0) (e3)) = (e1))\/(((op (e1) (e3)) = (e1))\/(((op (e2) (e3)) = (e1))\/((op (e3) (e3)) = (e1))))) -> (~((e1) = (e2))) -> (~((e1) = (e3))) -> ((op (e3) (e1)) = (e1)) -> (~((op (e2) (e1)) = (e1))) -> (~((op (e2) (e0)) = (e1))) -> (((op (e2) (e0)) = (e1))\/(((op (e2) (e1)) = (e1))\/(((op (e2) (e2)) = (e1))\/((op (e2) (e3)) = (e1))))) -> (((op (e2) (e2)) = (e0))\/(((op (e2) (e2)) = (e1))\/(((op (e2) (e2)) = (e2))\/((op (e2) (e2)) = (e3))))) -> (~((op (e2) (e2)) = (op (e2) (e3)))) -> (~((op (e1) (e2)) = (op (e2) (e2)))) -> (~((op (e2) (e2)) = (e2))) -> (~((op (e2) (e0)) = (op (e2) (e2)))) -> ((op (e3) (e0)) = (e2)) -> (~((e2) = (e3))) -> False). % 18.79/18.97 do 0 intro. intros zenon_H1e0 zenon_H24e zenon_H16f zenon_H2f zenon_H7a zenon_H1ef zenon_H25e zenon_H128 zenon_H10a zenon_H115 zenon_Ha6 zenon_H110 zenon_H6a zenon_H4a zenon_H4f zenon_H57 zenon_H5b zenon_H62 zenon_H201 zenon_H22 zenon_H17e zenon_Hcd zenon_H18f zenon_H67 zenon_H54 zenon_H49 zenon_H27 zenon_Hd8 zenon_H130 zenon_H149 zenon_H1ac zenon_H133 zenon_H7c zenon_H95 zenon_Hae zenon_H24f zenon_H1db zenon_H106 zenon_H1c4 zenon_H6d zenon_H2b zenon_H173 zenon_H52 zenon_H148 zenon_H12b. % 18.79/18.97 apply (zenon_or_s _ _ zenon_H1e0); [ zenon_intro zenon_H3a | zenon_intro zenon_H1e1 ]. % 18.79/18.97 apply (zenon_L35_); trivial. % 18.79/18.97 apply (zenon_or_s _ _ zenon_H1e1); [ zenon_intro zenon_H9e | zenon_intro zenon_H1e2 ]. % 18.79/18.97 apply (zenon_L107_); trivial. % 18.79/18.97 apply (zenon_or_s _ _ zenon_H1e2); [ zenon_intro zenon_H3b | zenon_intro zenon_H15e ]. % 18.79/18.97 apply (zenon_or_s _ _ zenon_H128); [ zenon_intro zenon_H9d | zenon_intro zenon_H129 ]. % 18.79/18.97 exact (zenon_H1ef zenon_H9d). % 18.79/18.97 apply (zenon_or_s _ _ zenon_H129); [ zenon_intro zenon_H10d | zenon_intro zenon_H12a ]. % 18.79/18.97 exact (zenon_H10a zenon_H10d). % 18.79/18.97 apply (zenon_or_s _ _ zenon_H12a); [ zenon_intro zenon_Hf0 | zenon_intro zenon_Hd6 ]. % 18.79/18.97 apply (zenon_or_s _ _ zenon_H16f); [ zenon_intro zenon_H9e | zenon_intro zenon_H170 ]. % 18.79/18.97 apply (zenon_L107_); trivial. % 18.79/18.97 apply (zenon_or_s _ _ zenon_H170); [ zenon_intro zenon_H13f | zenon_intro zenon_H171 ]. % 18.79/18.97 apply (zenon_L166_); trivial. % 18.79/18.97 apply (zenon_or_s _ _ zenon_H171); [ zenon_intro zenon_H16c | zenon_intro zenon_Hdc ]. % 18.79/18.97 apply (zenon_L167_); trivial. % 18.79/18.97 apply (zenon_or_s _ _ zenon_H2f); [ zenon_intro zenon_H34 | zenon_intro zenon_H33 ]. % 18.79/18.97 apply (zenon_L770_); trivial. % 18.79/18.97 apply (zenon_or_s _ _ zenon_H33); [ zenon_intro zenon_H36 | zenon_intro zenon_H35 ]. % 18.79/18.97 apply (zenon_L128_); trivial. % 18.79/18.97 apply (zenon_or_s _ _ zenon_H35); [ zenon_intro zenon_H2c | zenon_intro zenon_H37 ]. % 18.79/18.97 apply (zenon_or_s _ _ zenon_H106); [ zenon_intro zenon_Hed | zenon_intro zenon_H107 ]. % 18.79/18.97 exact (zenon_H1db zenon_Hed). % 18.79/18.97 apply (zenon_or_s _ _ zenon_H107); [ zenon_intro zenon_Ha5 | zenon_intro zenon_H108 ]. % 18.79/18.97 exact (zenon_H24f zenon_Ha5). % 18.79/18.97 apply (zenon_or_s _ _ zenon_H108); [ zenon_intro zenon_Hf1 | zenon_intro zenon_Hf4 ]. % 18.79/18.97 apply (zenon_L86_); trivial. % 18.79/18.97 apply (zenon_L775_); trivial. % 18.79/18.97 apply (zenon_L300_); trivial. % 18.79/18.97 exact (zenon_H24e zenon_Hd6). % 18.79/18.97 apply (zenon_L109_); trivial. % 18.79/18.97 (* end of lemma zenon_L776_ *) % 18.79/18.97 assert (zenon_L777_ : (~((op (e0) (e3)) = (e1))) -> (~((op (e0) (e2)) = (e1))) -> (~((op (e0) (e1)) = (e1))) -> (((op (e0) (e0)) = (e2))\/(((op (e0) (e1)) = (e2))\/(((op (e0) (e2)) = (e2))\/((op (e0) (e3)) = (e2))))) -> ((~((op (e1) (e3)) = (e1)))\/((op (e1) (e1)) = (e3))) -> ((~((op (e2) (e2)) = (e1)))\/((op (e2) (e1)) = (e2))) -> ((~((op (e3) (e2)) = (e1)))\/((op (e3) (e1)) = (e2))) -> (~((op (e0) (e1)) = (op (e3) (e1)))) -> (((op (e0) (e2)) = (e1))\/(((op (e1) (e2)) = (e1))\/(((op (e2) (e2)) = (e1))\/((op (e3) (e2)) = (e1))))) -> (~((op (e0) (e0)) = (op (e0) (e2)))) -> (((op (e0) (e0)) = (e1))\/(((op (e1) (e0)) = (e1))\/(((op (e2) (e0)) = (e1))\/((op (e3) (e0)) = (e1))))) -> (((op (e0) (e0)) = (e1))\/(((op (e0) (e1)) = (e1))\/(((op (e0) (e2)) = (e1))\/((op (e0) (e3)) = (e1))))) -> ((~((op (e3) (e0)) = (e1)))\/((op (e3) (e1)) = (e0))) -> ((~((op (e2) (e0)) = (e1)))\/((op (e2) (e1)) = (e0))) -> (~((op (e0) (e1)) = (op (e1) (e1)))) -> ((~((op (e1) (e2)) = (e1)))\/((op (e1) (e1)) = (e2))) -> (~((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 (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) (e1)) = (op (e3) (e2)))) -> (((op (e0) (e3)) = (e2))\/(((op (e1) (e3)) = (e2))\/(((op (e2) (e3)) = (e2))\/((op (e3) (e3)) = (e2))))) -> (~((op (e2) (e1)) = (op (e2) (e3)))) -> (((op (e2) (e0)) = (e3))\/(((op (e2) (e1)) = (e3))\/(((op (e2) (e2)) = (e3))\/((op (e2) (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 (e3) (e0)) = (e2))\/(((op (e3) (e1)) = (e2))\/(((op (e3) (e2)) = (e2))\/((op (e3) (e3)) = (e2))))) -> (((op (e0) (e0)) = (e2))\/(((op (e1) (e0)) = (e2))\/(((op (e2) (e0)) = (e2))\/((op (e3) (e0)) = (e2))))) -> (~((op (e0) (e0)) = (op (e0) (e3)))) -> (~((op (e0) (e3)) = (op (e2) (e3)))) -> (~((op (e2) (e0)) = (op (e2) (e1)))) -> (((op (e2) (e0)) = (e0))\/(((op (e2) (e0)) = (e1))\/(((op (e2) (e0)) = (e2))\/((op (e2) (e0)) = (e3))))) -> (~((op (e2) (e0)) = (op (e3) (e0)))) -> (((op (e2) (e0)) = (e2))\/(((op (e2) (e1)) = (e2))\/(((op (e2) (e2)) = (e2))\/((op (e2) (e3)) = (e2))))) -> (~((op (e1) (e3)) = (op (e3) (e3)))) -> (~((e0) = (e3))) -> (((op (e0) (e0)) = (e3))\/(((op (e0) (e1)) = (e3))\/(((op (e0) (e2)) = (e3))\/((op (e0) (e3)) = (e3))))) -> (~((op (e1) (e0)) = (op (e3) (e0)))) -> (~((op (e3) (e3)) = (e3))) -> (~((op (e2) (e3)) = (op (e3) (e3)))) -> (~((op (e3) (e0)) = (op (e3) (e3)))) -> (((op (e3) (e3)) = (e0))\/(((op (e3) (e3)) = (e1))\/(((op (e3) (e3)) = (e2))\/((op (e3) (e3)) = (e3))))) -> (~((op (e2) (e1)) = (op (e3) (e1)))) -> (~((op (e2) (e2)) = (e1))) -> (~((op (e0) (e2)) = (op (e2) (e2)))) -> (((op (e0) (e0)) = (e3))\/(((op (e1) (e0)) = (e3))\/(((op (e2) (e0)) = (e3))\/((op (e3) (e0)) = (e3))))) -> (~((op (e1) (e3)) = (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 (e0) (e0)) = (e1)) -> (~((op (e1) (e0)) = (e1))) -> (((op (e1) (e0)) = (e0))\/(((op (e1) (e0)) = (e1))\/(((op (e1) (e0)) = (e2))\/((op (e1) (e0)) = (e3))))) -> (((op (e1) (e0)) = (e1))\/(((op (e1) (e1)) = (e1))\/(((op (e1) (e2)) = (e1))\/((op (e1) (e3)) = (e1))))) -> (~((op (e1) (e1)) = (e1))) -> (~((op (e1) (e2)) = (op (e3) (e2)))) -> ((op (e2) (e1)) = (e3)) -> ((op (e1) (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 (e1) (e1)) = (op (e1) (e2)))) -> (~((op (e1) (e1)) = (op (e1) (e3)))) -> (~((op (e2) (e0)) = (op (e2) (e3)))) -> (~((op (e3) (e2)) = (op (e3) (e3)))) -> (~((op (e1) (e0)) = (op (e2) (e0)))) -> (((op (e1) (e0)) = (e0))\/(((op (e1) (e1)) = (e0))\/(((op (e1) (e2)) = (e0))\/((op (e1) (e3)) = (e0))))) -> (~((op (e0) (e1)) = (op (e2) (e1)))) -> ((op (e0) (e3)) = (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) (e1)) = (op (e0) (e3)))) -> ((op (e0) (e1)) = (e0)) -> ((op (e1) (e0)) = (e0)) -> (~((op (e1) (e0)) = (op (e1) (e3)))) -> (~((op (e3) (e1)) = (op (e3) (e3)))) -> (~((e0) = (e2))) -> (((op (e3) (e0)) = (e0))\/(((op (e3) (e1)) = (e0))\/(((op (e3) (e2)) = (e0))\/((op (e3) (e3)) = (e0))))) -> (((op (e0) (e3)) = (e1))\/(((op (e1) (e3)) = (e1))\/(((op (e2) (e3)) = (e1))\/((op (e3) (e3)) = (e1))))) -> (~((e1) = (e2))) -> (~((e1) = (e3))) -> ((op (e3) (e1)) = (e1)) -> (~((op (e2) (e1)) = (e1))) -> (~((op (e2) (e0)) = (e1))) -> (((op (e2) (e0)) = (e1))\/(((op (e2) (e1)) = (e1))\/(((op (e2) (e2)) = (e1))\/((op (e2) (e3)) = (e1))))) -> (((op (e2) (e2)) = (e0))\/(((op (e2) (e2)) = (e1))\/(((op (e2) (e2)) = (e2))\/((op (e2) (e2)) = (e3))))) -> (~((op (e2) (e2)) = (op (e2) (e3)))) -> (~((op (e1) (e2)) = (op (e2) (e2)))) -> (~((op (e2) (e2)) = (e2))) -> (~((op (e2) (e0)) = (op (e2) (e2)))) -> (~((e2) = (e3))) -> False). % 18.79/18.97 do 0 intro. intros zenon_H231 zenon_H20d zenon_Ha4 zenon_H183 zenon_H258 zenon_H253 zenon_H252 zenon_H210 zenon_H139 zenon_H13c zenon_H235 zenon_H22d zenon_H254 zenon_H257 zenon_H10e zenon_H256 zenon_H1d zenon_Hc2 zenon_He4 zenon_H6f zenon_H14f zenon_H191 zenon_H1a4 zenon_H145 zenon_H1c7 zenon_He7 zenon_H160 zenon_Hdf zenon_H153 zenon_H1fe zenon_H189 zenon_He2 zenon_H1f0 zenon_H259 zenon_H17b zenon_H1d5 zenon_Hd5 zenon_H9a zenon_H168 zenon_H1fa zenon_H102 zenon_Hf3 zenon_H71 zenon_H101 zenon_Haf zenon_H198 zenon_Ha8 zenon_H1e0 zenon_H24e zenon_H16f zenon_H2f zenon_H7a zenon_H1ef zenon_H25e zenon_H128 zenon_H10a zenon_H115 zenon_Ha6 zenon_H110 zenon_H6a zenon_H4a zenon_H4f zenon_H57 zenon_H5b zenon_H62 zenon_H201 zenon_H22 zenon_H17e zenon_Hcd zenon_H18f zenon_H67 zenon_H54 zenon_H49 zenon_H27 zenon_Hd8 zenon_H130 zenon_H149 zenon_H1ac zenon_H133 zenon_H7c zenon_H95 zenon_Hae zenon_H24f zenon_H1db zenon_H106 zenon_H1c4 zenon_H6d zenon_H2b zenon_H173 zenon_H52 zenon_H12b. % 18.79/18.97 apply (zenon_or_s _ _ zenon_H1fe); [ zenon_intro zenon_H7b | zenon_intro zenon_H1ff ]. % 18.79/18.97 apply (zenon_L375_); trivial. % 18.79/18.97 apply (zenon_or_s _ _ zenon_H1ff); [ zenon_intro zenon_H86 | zenon_intro zenon_H200 ]. % 18.79/18.97 apply (zenon_L257_); trivial. % 18.79/18.97 apply (zenon_or_s _ _ zenon_H200); [ zenon_intro zenon_Hee | zenon_intro zenon_H148 ]. % 18.79/18.97 apply (zenon_or_s _ _ zenon_H168); [ zenon_intro zenon_H3a | zenon_intro zenon_H169 ]. % 18.79/18.97 apply (zenon_L35_); trivial. % 18.79/18.97 apply (zenon_or_s _ _ zenon_H169); [ zenon_intro zenon_H99 | zenon_intro zenon_H16a ]. % 18.79/18.97 apply (zenon_L36_); trivial. % 18.79/18.97 apply (zenon_or_s _ _ zenon_H16a); [ zenon_intro zenon_Ha9 | zenon_intro zenon_He3 ]. % 18.79/18.97 apply (zenon_or_s _ _ zenon_H2f); [ zenon_intro zenon_H34 | zenon_intro zenon_H33 ]. % 18.79/18.97 apply (zenon_L773_); trivial. % 18.79/18.97 apply (zenon_or_s _ _ zenon_H33); [ zenon_intro zenon_H36 | zenon_intro zenon_H35 ]. % 18.79/18.97 apply (zenon_L128_); trivial. % 18.79/18.97 apply (zenon_or_s _ _ zenon_H35); [ zenon_intro zenon_H2c | zenon_intro zenon_H37 ]. % 18.79/18.97 apply (zenon_L774_); trivial. % 18.79/18.97 apply (zenon_L727_); trivial. % 18.79/18.97 apply (zenon_L81_); trivial. % 18.79/18.97 apply (zenon_L776_); trivial. % 18.79/18.97 (* end of lemma zenon_L777_ *) % 18.79/18.97 assert (zenon_L778_ : (~((e2) = (e3))) -> (((op (e1) (e0)) = (e0))\/(((op (e1) (e1)) = (e0))\/(((op (e1) (e2)) = (e0))\/((op (e1) (e3)) = (e0))))) -> (~((op (e1) (e0)) = (op (e3) (e0)))) -> (((op (e0) (e2)) = (e0))\/(((op (e1) (e2)) = (e0))\/(((op (e2) (e2)) = (e0))\/((op (e3) (e2)) = (e0))))) -> (~((op (e0) (e1)) = (op (e0) (e2)))) -> (~((op (e1) (e1)) = (op (e1) (e2)))) -> (~((op (e3) (e0)) = (op (e3) (e2)))) -> (~((op (e1) (e1)) = (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))))) -> (~((op (e1) (e2)) = (op (e2) (e2)))) -> (~((op (e0) (e1)) = (op (e2) (e1)))) -> ((op (e0) (e1)) = (e0)) -> ((op (e3) (e0)) = (e0)) -> (~((op (e2) (e0)) = (op (e3) (e0)))) -> (((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) (e0)) = (e1))) -> (~((op (e2) (e1)) = (e1))) -> (~((op (e2) (e2)) = (e1))) -> (((op (e3) (e0)) = (e0))\/(((op (e3) (e1)) = (e0))\/(((op (e3) (e2)) = (e0))\/((op (e3) (e3)) = (e0))))) -> (~((op (e3) (e3)) = (e3))) -> (~((op (e2) (e3)) = (op (e3) (e3)))) -> (~((op (e3) (e0)) = (op (e3) (e3)))) -> (((op (e3) (e3)) = (e0))\/(((op (e3) (e3)) = (e1))\/(((op (e3) (e3)) = (e2))\/((op (e3) (e3)) = (e3))))) -> ((op (e1) (e1)) = (e2)) -> ((op (e2) (e1)) = (e3)) -> (~((op (e0) (e2)) = (op (e2) (e2)))) -> (~((op (e2) (e2)) = (e2))) -> (~((op (e2) (e2)) = (op (e2) (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) (e3)) = (op (e3) (e3)))) -> (~((e0) = (e3))) -> (~((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 (e1) (e2)) = (op (e3) (e2)))) -> (((op (e3) (e2)) = (e0))\/(((op (e3) (e2)) = (e1))\/(((op (e3) (e2)) = (e2))\/((op (e3) (e2)) = (e3))))) -> ((~((op (e0) (e3)) = (e1)))\/((op (e0) (e1)) = (e3))) -> ((~((op (e1) (e2)) = (e1)))\/((op (e1) (e1)) = (e2))) -> (~((op (e0) (e1)) = (op (e1) (e1)))) -> (((op (e1) (e0)) = (e1))\/(((op (e1) (e1)) = (e1))\/(((op (e1) (e2)) = (e1))\/((op (e1) (e3)) = (e1))))) -> (~((op (e1) (e1)) = (e1))) -> ((~((op (e2) (e0)) = (e1)))\/((op (e2) (e1)) = (e0))) -> ((~((op (e3) (e0)) = (e1)))\/((op (e3) (e1)) = (e0))) -> (((op (e0) (e0)) = (e1))\/(((op (e0) (e1)) = (e1))\/(((op (e0) (e2)) = (e1))\/((op (e0) (e3)) = (e1))))) -> (((op (e0) (e0)) = (e1))\/(((op (e1) (e0)) = (e1))\/(((op (e2) (e0)) = (e1))\/((op (e3) (e0)) = (e1))))) -> (~((op (e0) (e0)) = (op (e0) (e2)))) -> (((op (e0) (e2)) = (e1))\/(((op (e1) (e2)) = (e1))\/(((op (e2) (e2)) = (e1))\/((op (e3) (e2)) = (e1))))) -> (~((op (e0) (e1)) = (op (e3) (e1)))) -> ((~((op (e3) (e2)) = (e1)))\/((op (e3) (e1)) = (e2))) -> ((~((op (e2) (e2)) = (e1)))\/((op (e2) (e1)) = (e2))) -> ((~((op (e1) (e3)) = (e1)))\/((op (e1) (e1)) = (e3))) -> (~((op (e0) (e0)) = (e0))) -> (~((op (e1) (e0)) = (op (e1) (e1)))) -> (~((op (e2) (e0)) = (op (e2) (e3)))) -> (~((op (e3) (e2)) = (op (e3) (e3)))) -> (~((op (e2) (e0)) = (op (e2) (e2)))) -> (~((e0) = (e1))) -> (((op (e0) (e0)) = (e0))\/(((op (e1) (e0)) = (e0))\/(((op (e2) (e0)) = (e0))\/((op (e3) (e0)) = (e0))))) -> ((~((op (e1) (e0)) = (e1)))\/((op (e1) (e1)) = (e0))) -> (~((e1) = (e2))) -> (((op (e0) (e0)) = (e2))\/(((op (e0) (e1)) = (e2))\/(((op (e0) (e2)) = (e2))\/((op (e0) (e3)) = (e2))))) -> (~((op (e0) (e1)) = (e1))) -> (~((op (e0) (e2)) = (e1))) -> (~((op (e0) (e3)) = (e1))) -> False). % 18.79/18.97 do 0 intro. intros zenon_H12b zenon_H22 zenon_H1fa zenon_H6a zenon_H4a zenon_H4f zenon_H6f zenon_H57 zenon_H54 zenon_H67 zenon_H2b zenon_H17e zenon_H49 zenon_H44 zenon_H17b zenon_H2f zenon_H106 zenon_H1db zenon_H24f zenon_H198 zenon_H1ac zenon_H102 zenon_Hf3 zenon_H71 zenon_H101 zenon_H110 zenon_Ha6 zenon_Ha8 zenon_H173 zenon_H6d zenon_H18f zenon_H1c4 zenon_Hd5 zenon_H9a zenon_H95 zenon_H168 zenon_H14f zenon_H115 zenon_H191 zenon_H25c zenon_H256 zenon_H10e zenon_H128 zenon_H10a zenon_H257 zenon_H254 zenon_H22d zenon_H235 zenon_H13c zenon_H139 zenon_H210 zenon_H252 zenon_H253 zenon_H258 zenon_H3f zenon_H45 zenon_H5b zenon_H62 zenon_H52 zenon_Ha1 zenon_H3e zenon_H25d zenon_H7c zenon_H183 zenon_Ha4 zenon_H20d zenon_H231. % 18.79/18.97 apply (zenon_or_s _ _ zenon_H22d); [ zenon_intro zenon_H7a | zenon_intro zenon_H22e ]. % 18.79/18.97 apply (zenon_L765_); trivial. % 18.79/18.97 apply (zenon_or_s _ _ zenon_H22e); [ zenon_intro zenon_Ha0 | zenon_intro zenon_H22f ]. % 18.79/18.97 exact (zenon_Ha4 zenon_Ha0). % 18.79/18.97 apply (zenon_or_s _ _ zenon_H22f); [ zenon_intro zenon_H122 | zenon_intro zenon_Hc3 ]. % 18.79/18.97 exact (zenon_H20d zenon_H122). % 18.79/18.97 exact (zenon_H231 zenon_Hc3). % 18.79/18.97 (* end of lemma zenon_L778_ *) % 18.79/18.97 assert (zenon_L779_ : (((op (e1) (e0)) = (e0))\/(((op (e1) (e1)) = (e0))\/(((op (e1) (e2)) = (e0))\/((op (e1) (e3)) = (e0))))) -> (~((op (e1) (e0)) = (op (e2) (e0)))) -> ((op (e2) (e0)) = (e0)) -> (((op (e0) (e2)) = (e0))\/(((op (e1) (e2)) = (e0))\/(((op (e2) (e2)) = (e0))\/((op (e3) (e2)) = (e0))))) -> (~((op (e0) (e1)) = (op (e0) (e2)))) -> ((op (e0) (e1)) = (e0)) -> (~((op (e1) (e1)) = (op (e1) (e2)))) -> (~((op (e2) (e2)) = (op (e2) (e3)))) -> (~((op (e3) (e0)) = (op (e3) (e2)))) -> (~((op (e1) (e1)) = (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))))) -> (~((op (e2) (e0)) = (op (e2) (e2)))) -> (~((op (e2) (e0)) = (op (e2) (e3)))) -> (~((op (e3) (e2)) = (op (e3) (e3)))) -> (~((op (e1) (e0)) = (op (e1) (e1)))) -> (~((op (e0) (e0)) = (e0))) -> (((op (e0) (e0)) = (e0))\/(((op (e1) (e0)) = (e0))\/(((op (e2) (e0)) = (e0))\/((op (e3) (e0)) = (e0))))) -> (~((op (e1) (e3)) = (e1))) -> (((op (e1) (e0)) = (e3))\/(((op (e1) (e1)) = (e3))\/(((op (e1) (e2)) = (e3))\/((op (e1) (e3)) = (e3))))) -> (~((e1) = (e3))) -> (((op (e2) (e0)) = (e1))\/(((op (e2) (e1)) = (e1))\/(((op (e2) (e2)) = (e1))\/((op (e2) (e3)) = (e1))))) -> (~((op (e2) (e0)) = (e1))) -> (~((op (e2) (e1)) = (e1))) -> (~((op (e1) (e2)) = (op (e2) (e2)))) -> (((op (e0) (e3)) = (e2))\/(((op (e1) (e3)) = (e2))\/(((op (e2) (e3)) = (e2))\/((op (e3) (e3)) = (e2))))) -> (~((op (e1) (e2)) = (op (e3) (e2)))) -> ((op (e2) (e1)) = (e3)) -> ((op (e1) (e1)) = (e2)) -> (~((e0) = (e2))) -> (((op (e3) (e0)) = (e0))\/(((op (e3) (e1)) = (e0))\/(((op (e3) (e2)) = (e0))\/((op (e3) (e3)) = (e0))))) -> (~((e2) = (e3))) -> (~((op (e2) (e1)) = (op (e2) (e3)))) -> ((op (e2) (e1)) = (e2)) -> (~((op (e3) (e0)) = (op (e3) (e3)))) -> (~((op (e1) (e1)) = (e1))) -> (((op (e1) (e0)) = (e1))\/(((op (e1) (e1)) = (e1))\/(((op (e1) (e2)) = (e1))\/((op (e1) (e3)) = (e1))))) -> (((op (e1) (e0)) = (e0))\/(((op (e1) (e0)) = (e1))\/(((op (e1) (e0)) = (e2))\/((op (e1) (e0)) = (e3))))) -> (~((op (e1) (e0)) = (op (e1) (e3)))) -> (~((op (e1) (e0)) = (e1))) -> ((op (e2) (e0)) = (e3)) -> ((op (e3) (e0)) = (e2)) -> ((op (e0) (e0)) = (e1)) -> False). % 18.79/18.97 do 0 intro. intros zenon_H22 zenon_H201 zenon_H34 zenon_H6a zenon_H4a zenon_H49 zenon_H4f zenon_H6d zenon_H6f zenon_H57 zenon_H54 zenon_H67 zenon_H52 zenon_H5b zenon_H62 zenon_H45 zenon_H3f zenon_H3e zenon_H24e zenon_H16f zenon_H95 zenon_H106 zenon_H1db zenon_H24f zenon_H2b zenon_H145 zenon_H115 zenon_Ha6 zenon_H110 zenon_H149 zenon_H1ac zenon_H12b zenon_H1c7 zenon_H1ca zenon_H71 zenon_H10a zenon_H128 zenon_H25e zenon_Hd8 zenon_H1ef zenon_H3b zenon_H148 zenon_H7a. % 18.79/18.97 apply (zenon_or_s _ _ zenon_H22); [ zenon_intro zenon_H27 | zenon_intro zenon_H26 ]. % 18.79/18.97 apply (zenon_L332_); trivial. % 18.79/18.97 apply (zenon_or_s _ _ zenon_H26); [ zenon_intro zenon_H29 | zenon_intro zenon_H28 ]. % 18.79/18.97 apply (zenon_L23_); trivial. % 18.79/18.97 apply (zenon_or_s _ _ zenon_H28); [ zenon_intro zenon_H2a | zenon_intro zenon_H1f ]. % 18.79/18.97 apply (zenon_or_s _ _ zenon_H128); [ zenon_intro zenon_H9d | zenon_intro zenon_H129 ]. % 18.79/18.97 exact (zenon_H1ef zenon_H9d). % 18.79/18.97 apply (zenon_or_s _ _ zenon_H129); [ zenon_intro zenon_H10d | zenon_intro zenon_H12a ]. % 18.79/18.97 exact (zenon_H10a zenon_H10d). % 18.79/18.97 apply (zenon_or_s _ _ zenon_H12a); [ zenon_intro zenon_Hf0 | zenon_intro zenon_Hd6 ]. % 18.79/18.97 apply (zenon_L737_); trivial. % 18.79/18.97 exact (zenon_H24e zenon_Hd6). % 18.79/18.97 apply (zenon_L769_); trivial. % 18.79/18.97 (* end of lemma zenon_L779_ *) % 18.79/18.97 assert (zenon_L780_ : (~((op (e2) (e0)) = (op (e2) (e2)))) -> ((op (e2) (e0)) = (e3)) -> (~((op (e2) (e2)) = (e2))) -> (~((op (e1) (e2)) = (op (e2) (e2)))) -> (~((op (e2) (e2)) = (op (e2) (e3)))) -> (((op (e2) (e2)) = (e0))\/(((op (e2) (e2)) = (e1))\/(((op (e2) (e2)) = (e2))\/((op (e2) (e2)) = (e3))))) -> (((op (e2) (e0)) = (e1))\/(((op (e2) (e1)) = (e1))\/(((op (e2) (e2)) = (e1))\/((op (e2) (e3)) = (e1))))) -> (~((op (e2) (e0)) = (e1))) -> (~((op (e2) (e1)) = (e1))) -> (((op (e0) (e3)) = (e2))\/(((op (e1) (e3)) = (e2))\/(((op (e2) (e3)) = (e2))\/((op (e3) (e3)) = (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) (e1)) = (op (e0) (e3)))) -> ((op (e0) (e1)) = (e0)) -> ((op (e1) (e0)) = (e0)) -> (~((op (e1) (e0)) = (op (e1) (e3)))) -> (~((op (e3) (e1)) = (op (e3) (e3)))) -> (~((e0) = (e2))) -> (((op (e3) (e0)) = (e0))\/(((op (e3) (e1)) = (e0))\/(((op (e3) (e2)) = (e0))\/((op (e3) (e3)) = (e0))))) -> (~((e2) = (e3))) -> (~((op (e2) (e1)) = (op (e2) (e3)))) -> ((op (e2) (e1)) = (e2)) -> ((op (e3) (e0)) = (e2)) -> (~((op (e3) (e0)) = (op (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) (e0)) = (op (e2) (e0)))) -> (((op (e0) (e2)) = (e0))\/(((op (e1) (e2)) = (e0))\/(((op (e2) (e2)) = (e0))\/((op (e3) (e2)) = (e0))))) -> (~((op (e0) (e1)) = (op (e0) (e2)))) -> (~((op (e1) (e1)) = (op (e1) (e2)))) -> (~((op (e3) (e0)) = (op (e3) (e2)))) -> (~((op (e1) (e1)) = (op (e1) (e3)))) -> (~((op (e2) (e0)) = (op (e2) (e3)))) -> (~((op (e3) (e2)) = (op (e3) (e3)))) -> (~((op (e1) (e0)) = (op (e1) (e1)))) -> (~((op (e0) (e0)) = (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))))) -> (~((e1) = (e3))) -> (~((op (e1) (e2)) = (op (e3) (e2)))) -> ((op (e2) (e1)) = (e3)) -> ((op (e1) (e1)) = (e2)) -> (~((op (e1) (e1)) = (e1))) -> (((op (e1) (e0)) = (e1))\/(((op (e1) (e1)) = (e1))\/(((op (e1) (e2)) = (e1))\/((op (e1) (e3)) = (e1))))) -> (((op (e1) (e0)) = (e0))\/(((op (e1) (e0)) = (e1))\/(((op (e1) (e0)) = (e2))\/((op (e1) (e0)) = (e3))))) -> (~((op (e1) (e0)) = (e1))) -> ((op (e0) (e0)) = (e1)) -> (((op (e2) (e0)) = (e0))\/(((op (e2) (e1)) = (e0))\/(((op (e2) (e2)) = (e0))\/((op (e2) (e3)) = (e0))))) -> (~((op (e1) (e3)) = (e1))) -> False). % 18.79/18.97 do 0 intro. intros zenon_H52 zenon_H3b zenon_H173 zenon_H2b zenon_H6d zenon_H1c4 zenon_H106 zenon_H1db zenon_H24f zenon_H145 zenon_H18f zenon_H67 zenon_H54 zenon_H49 zenon_H27 zenon_Hd8 zenon_H130 zenon_H149 zenon_H1ac zenon_H12b zenon_H1c7 zenon_H1ca zenon_H148 zenon_H71 zenon_H17e zenon_H22 zenon_H201 zenon_H6a zenon_H4a zenon_H4f zenon_H6f zenon_H57 zenon_H5b zenon_H62 zenon_H45 zenon_H3f zenon_H3e zenon_H16f zenon_H95 zenon_H115 zenon_Ha6 zenon_H110 zenon_H10a zenon_H128 zenon_H25e zenon_H1ef zenon_H7a zenon_H2f zenon_H24e. % 18.79/18.97 apply (zenon_or_s _ _ zenon_H128); [ zenon_intro zenon_H9d | zenon_intro zenon_H129 ]. % 18.79/18.97 exact (zenon_H1ef zenon_H9d). % 18.79/18.97 apply (zenon_or_s _ _ zenon_H129); [ zenon_intro zenon_H10d | zenon_intro zenon_H12a ]. % 18.79/18.97 exact (zenon_H10a zenon_H10d). % 18.79/18.97 apply (zenon_or_s _ _ zenon_H12a); [ zenon_intro zenon_Hf0 | zenon_intro zenon_Hd6 ]. % 18.79/18.97 apply (zenon_or_s _ _ zenon_H16f); [ zenon_intro zenon_H9e | zenon_intro zenon_H170 ]. % 18.79/18.97 apply (zenon_L107_); trivial. % 18.79/18.97 apply (zenon_or_s _ _ zenon_H170); [ zenon_intro zenon_H13f | zenon_intro zenon_H171 ]. % 18.79/18.97 apply (zenon_L166_); trivial. % 18.79/18.97 apply (zenon_or_s _ _ zenon_H171); [ zenon_intro zenon_H16c | zenon_intro zenon_Hdc ]. % 18.79/18.97 apply (zenon_L167_); trivial. % 18.79/18.97 apply (zenon_or_s _ _ zenon_H2f); [ zenon_intro zenon_H34 | zenon_intro zenon_H33 ]. % 18.79/18.97 apply (zenon_L779_); trivial. % 18.79/18.97 apply (zenon_or_s _ _ zenon_H33); [ zenon_intro zenon_H36 | zenon_intro zenon_H35 ]. % 18.79/18.97 apply (zenon_L128_); trivial. % 18.79/18.97 apply (zenon_or_s _ _ zenon_H35); [ zenon_intro zenon_H2c | zenon_intro zenon_H37 ]. % 18.79/18.97 apply (zenon_or_s _ _ zenon_H106); [ zenon_intro zenon_Hed | zenon_intro zenon_H107 ]. % 18.79/18.97 exact (zenon_H1db zenon_Hed). % 18.79/18.97 apply (zenon_or_s _ _ zenon_H107); [ zenon_intro zenon_Ha5 | zenon_intro zenon_H108 ]. % 18.79/18.97 exact (zenon_H24f zenon_Ha5). % 18.79/18.97 apply (zenon_or_s _ _ zenon_H108); [ zenon_intro zenon_Hf1 | zenon_intro zenon_Hf4 ]. % 18.79/18.97 apply (zenon_L59_); trivial. % 18.79/18.97 apply (zenon_or_s _ _ zenon_H145); [ zenon_intro zenon_Hcd | zenon_intro zenon_H146 ]. % 18.79/18.97 apply (zenon_L775_); trivial. % 18.79/18.97 apply (zenon_or_s _ _ zenon_H146); [ zenon_intro zenon_Hd7 | zenon_intro zenon_H147 ]. % 18.79/18.97 apply (zenon_L266_); trivial. % 18.79/18.97 apply (zenon_or_s _ _ zenon_H147); [ zenon_intro zenon_H11d | zenon_intro zenon_Hf6 ]. % 18.79/18.97 apply (zenon_L224_); trivial. % 18.79/18.97 apply (zenon_L114_); trivial. % 18.79/18.97 apply (zenon_L300_); trivial. % 18.79/18.97 exact (zenon_H24e zenon_Hd6). % 18.79/18.97 (* end of lemma zenon_L780_ *) % 18.79/18.97 assert (zenon_L781_ : (((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 (e1) (e0)) = (op (e1) (e3)))) -> (((op (e1) (e0)) = (e0))\/(((op (e1) (e0)) = (e1))\/(((op (e1) (e0)) = (e2))\/((op (e1) (e0)) = (e3))))) -> (((op (e1) (e0)) = (e1))\/(((op (e1) (e1)) = (e1))\/(((op (e1) (e2)) = (e1))\/((op (e1) (e3)) = (e1))))) -> (~((op (e1) (e1)) = (e1))) -> (~((op (e3) (e0)) = (op (e3) (e3)))) -> ((op (e2) (e1)) = (e2)) -> (~((op (e2) (e1)) = (op (e2) (e3)))) -> (((op (e3) (e0)) = (e0))\/(((op (e3) (e1)) = (e0))\/(((op (e3) (e2)) = (e0))\/((op (e3) (e3)) = (e0))))) -> (~((e0) = (e2))) -> ((op (e1) (e1)) = (e2)) -> ((op (e2) (e1)) = (e3)) -> (~((op (e1) (e2)) = (op (e3) (e2)))) -> (((op (e0) (e3)) = (e2))\/(((op (e1) (e3)) = (e2))\/(((op (e2) (e3)) = (e2))\/((op (e3) (e3)) = (e2))))) -> (~((op (e1) (e2)) = (op (e2) (e2)))) -> (~((op (e2) (e1)) = (e1))) -> (~((op (e2) (e0)) = (e1))) -> (((op (e2) (e0)) = (e1))\/(((op (e2) (e1)) = (e1))\/(((op (e2) (e2)) = (e1))\/((op (e2) (e3)) = (e1))))) -> (~((e1) = (e3))) -> (((op (e1) (e0)) = (e3))\/(((op (e1) (e1)) = (e3))\/(((op (e1) (e2)) = (e3))\/((op (e1) (e3)) = (e3))))) -> (~((op (e1) (e3)) = (e1))) -> (((op (e0) (e0)) = (e0))\/(((op (e1) (e0)) = (e0))\/(((op (e2) (e0)) = (e0))\/((op (e3) (e0)) = (e0))))) -> (~((op (e0) (e0)) = (e0))) -> (~((op (e1) (e0)) = (op (e1) (e1)))) -> (~((op (e3) (e2)) = (op (e3) (e3)))) -> (~((op (e2) (e0)) = (op (e2) (e3)))) -> (~((op (e2) (e0)) = (op (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 (e1) (e1)) = (op (e1) (e3)))) -> (~((op (e3) (e0)) = (op (e3) (e2)))) -> (~((op (e2) (e2)) = (op (e2) (e3)))) -> (~((op (e1) (e1)) = (op (e1) (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 (e2) (e0)) = (e0)) -> (~((op (e1) (e0)) = (op (e2) (e0)))) -> (((op (e1) (e0)) = (e0))\/(((op (e1) (e1)) = (e0))\/(((op (e1) (e2)) = (e0))\/((op (e1) (e3)) = (e0))))) -> ((op (e3) (e0)) = (e2)) -> (~((e2) = (e3))) -> False). % 18.79/18.97 do 0 intro. intros zenon_H1e0 zenon_H7a zenon_H1ef zenon_Hd8 zenon_H25e zenon_H128 zenon_H10a zenon_H71 zenon_H1ca zenon_H1c7 zenon_H1ac zenon_H149 zenon_H110 zenon_Ha6 zenon_H115 zenon_H145 zenon_H2b zenon_H24f zenon_H1db zenon_H106 zenon_H95 zenon_H16f zenon_H24e zenon_H3e zenon_H3f zenon_H45 zenon_H62 zenon_H5b zenon_H52 zenon_H67 zenon_H54 zenon_H57 zenon_H6f zenon_H6d zenon_H4f zenon_H49 zenon_H4a zenon_H6a zenon_H34 zenon_H201 zenon_H22 zenon_H148 zenon_H12b. % 18.79/18.97 apply (zenon_or_s _ _ zenon_H1e0); [ zenon_intro zenon_H3a | zenon_intro zenon_H1e1 ]. % 18.79/18.97 apply (zenon_L35_); trivial. % 18.79/18.97 apply (zenon_or_s _ _ zenon_H1e1); [ zenon_intro zenon_H9e | zenon_intro zenon_H1e2 ]. % 18.79/18.97 apply (zenon_L107_); trivial. % 18.79/18.97 apply (zenon_or_s _ _ zenon_H1e2); [ zenon_intro zenon_H3b | zenon_intro zenon_H15e ]. % 18.79/18.97 apply (zenon_L779_); trivial. % 18.79/18.97 apply (zenon_L109_); trivial. % 18.79/18.97 (* end of lemma zenon_L781_ *) % 18.79/18.97 assert (zenon_L782_ : (((op (e0) (e0)) = (e2))\/(((op (e1) (e0)) = (e2))\/(((op (e2) (e0)) = (e2))\/((op (e3) (e0)) = (e2))))) -> (~((op (e0) (e0)) = (op (e0) (e3)))) -> (~((op (e0) (e2)) = (op (e2) (e2)))) -> (~((op (e2) (e2)) = (e2))) -> (~((op (e2) (e2)) = (op (e2) (e3)))) -> (~((op (e2) (e2)) = (op (e3) (e2)))) -> (((op (e2) (e2)) = (e0))\/(((op (e2) (e2)) = (e1))\/(((op (e2) (e2)) = (e2))\/((op (e2) (e2)) = (e3))))) -> (~((op (e2) (e0)) = (op (e2) (e1)))) -> ((op (e2) (e1)) = (e2)) -> (((op (e2) (e0)) = (e0))\/(((op (e2) (e0)) = (e1))\/(((op (e2) (e0)) = (e2))\/((op (e2) (e0)) = (e3))))) -> (~((op (e0) (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))) -> (((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))))) -> (~((e1) = (e3))) -> ((op (e0) (e0)) = (e1)) -> (~((op (e1) (e0)) = (e1))) -> (~((op (e1) (e0)) = (op (e1) (e3)))) -> (((op (e1) (e0)) = (e0))\/(((op (e1) (e0)) = (e1))\/(((op (e1) (e0)) = (e2))\/((op (e1) (e0)) = (e3))))) -> (((op (e1) (e0)) = (e1))\/(((op (e1) (e1)) = (e1))\/(((op (e1) (e2)) = (e1))\/((op (e1) (e3)) = (e1))))) -> (~((op (e1) (e1)) = (e1))) -> ((op (e0) (e3)) = (e2)) -> (~((op (e1) (e2)) = (op (e3) (e2)))) -> ((op (e2) (e1)) = (e3)) -> ((op (e1) (e1)) = (e2)) -> (~((e0) = (e2))) -> (((op (e3) (e0)) = (e0))\/(((op (e3) (e1)) = (e0))\/(((op (e3) (e2)) = (e0))\/((op (e3) (e3)) = (e0))))) -> (~((op (e1) (e2)) = (op (e2) (e2)))) -> (~((op (e2) (e1)) = (e1))) -> (~((op (e2) (e0)) = (e1))) -> (((op (e2) (e0)) = (e1))\/(((op (e2) (e1)) = (e1))\/(((op (e2) (e2)) = (e1))\/((op (e2) (e3)) = (e1))))) -> (~((op (e1) (e3)) = (e1))) -> (((op (e0) (e2)) = (e0))\/(((op (e1) (e2)) = (e0))\/(((op (e2) (e2)) = (e0))\/((op (e3) (e2)) = (e0))))) -> (~((op (e0) (e1)) = (op (e0) (e2)))) -> (~((op (e1) (e1)) = (op (e1) (e2)))) -> (~((op (e2) (e0)) = (op (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) (e1)) = (e0)) -> (~((op (e1) (e1)) = (op (e1) (e3)))) -> (~((op (e2) (e0)) = (op (e2) (e3)))) -> ((op (e2) (e0)) = (e0)) -> (~((op (e3) (e2)) = (op (e3) (e3)))) -> (~((op (e1) (e0)) = (op (e2) (e0)))) -> (((op (e1) (e0)) = (e0))\/(((op (e1) (e1)) = (e0))\/(((op (e1) (e2)) = (e0))\/((op (e1) (e3)) = (e0))))) -> (~((e2) = (e3))) -> False). % 18.79/18.97 do 0 intro. intros zenon_H1fe zenon_H189 zenon_Ha8 zenon_H173 zenon_H6d zenon_H18f zenon_H1c4 zenon_H1f0 zenon_H1ca zenon_H259 zenon_H17e zenon_H17b zenon_H2f zenon_H9a zenon_H168 zenon_H1e0 zenon_H95 zenon_H7a zenon_H1ef zenon_Hd8 zenon_H25e zenon_H128 zenon_H10a zenon_Hcd zenon_H115 zenon_Ha6 zenon_H110 zenon_H149 zenon_H1ac zenon_H2b zenon_H24f zenon_H1db zenon_H106 zenon_H24e zenon_H6a zenon_H4a zenon_H4f zenon_H52 zenon_H67 zenon_H54 zenon_H49 zenon_H57 zenon_H5b zenon_H34 zenon_H62 zenon_H201 zenon_H22 zenon_H12b. % 18.79/18.97 apply (zenon_or_s _ _ zenon_H1fe); [ zenon_intro zenon_H7b | zenon_intro zenon_H1ff ]. % 18.79/18.97 apply (zenon_L375_); trivial. % 18.79/18.97 apply (zenon_or_s _ _ zenon_H1ff); [ zenon_intro zenon_H86 | zenon_intro zenon_H200 ]. % 18.79/18.97 apply (zenon_or_s _ _ zenon_H168); [ zenon_intro zenon_H3a | zenon_intro zenon_H169 ]. % 18.79/18.97 apply (zenon_L35_); trivial. % 18.79/18.97 apply (zenon_or_s _ _ zenon_H169); [ zenon_intro zenon_H99 | zenon_intro zenon_H16a ]. % 18.79/18.97 apply (zenon_L36_); trivial. % 18.79/18.97 apply (zenon_or_s _ _ zenon_H16a); [ zenon_intro zenon_Ha9 | zenon_intro zenon_He3 ]. % 18.79/18.97 apply (zenon_L733_); trivial. % 18.79/18.97 apply (zenon_L81_); trivial. % 18.79/18.97 apply (zenon_or_s _ _ zenon_H200); [ zenon_intro zenon_Hee | zenon_intro zenon_H148 ]. % 18.79/18.97 apply (zenon_L204_); trivial. % 18.79/18.97 apply (zenon_L771_); trivial. % 18.79/18.97 (* end of lemma zenon_L782_ *) % 18.79/18.97 assert (zenon_L783_ : (((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 (e2) (e0)))) -> (~((op (e3) (e2)) = (op (e3) (e3)))) -> ((op (e2) (e0)) = (e0)) -> (~((op (e2) (e0)) = (op (e2) (e3)))) -> (~((op (e1) (e1)) = (op (e1) (e3)))) -> ((op (e0) (e1)) = (e0)) -> (~((op (e0) (e1)) = (op (e0) (e3)))) -> (((op (e0) (e3)) = (e0))\/(((op (e1) (e3)) = (e0))\/(((op (e2) (e3)) = (e0))\/((op (e3) (e3)) = (e0))))) -> (~((op (e2) (e0)) = (op (e2) (e2)))) -> (~((op (e1) (e1)) = (op (e1) (e2)))) -> (~((op (e0) (e1)) = (op (e0) (e2)))) -> (((op (e0) (e2)) = (e0))\/(((op (e1) (e2)) = (e0))\/(((op (e2) (e2)) = (e0))\/((op (e3) (e2)) = (e0))))) -> (~((op (e1) (e3)) = (e1))) -> (((op (e2) (e0)) = (e1))\/(((op (e2) (e1)) = (e1))\/(((op (e2) (e2)) = (e1))\/((op (e2) (e3)) = (e1))))) -> (~((op (e2) (e0)) = (e1))) -> (~((op (e2) (e1)) = (e1))) -> (~((op (e1) (e2)) = (op (e2) (e2)))) -> (((op (e3) (e0)) = (e0))\/(((op (e3) (e1)) = (e0))\/(((op (e3) (e2)) = (e0))\/((op (e3) (e3)) = (e0))))) -> (~((e0) = (e2))) -> ((op (e1) (e1)) = (e2)) -> ((op (e2) (e1)) = (e3)) -> (~((op (e1) (e2)) = (op (e3) (e2)))) -> (~((op (e1) (e1)) = (e1))) -> (((op (e1) (e0)) = (e1))\/(((op (e1) (e1)) = (e1))\/(((op (e1) (e2)) = (e1))\/((op (e1) (e3)) = (e1))))) -> (((op (e1) (e0)) = (e0))\/(((op (e1) (e0)) = (e1))\/(((op (e1) (e0)) = (e2))\/((op (e1) (e0)) = (e3))))) -> (~((op (e1) (e0)) = (op (e1) (e3)))) -> (~((op (e1) (e0)) = (e1))) -> (~((e1) = (e3))) -> (((op (e0) (e0)) = (e3))\/(((op (e1) (e0)) = (e3))\/(((op (e2) (e0)) = (e3))\/((op (e3) (e0)) = (e3))))) -> (((op (e0) (e0)) = (e3))\/(((op (e0) (e1)) = (e3))\/(((op (e0) (e2)) = (e3))\/((op (e0) (e3)) = (e3))))) -> (~((e0) = (e3))) -> (((op (e2) (e0)) = (e0))\/(((op (e2) (e1)) = (e0))\/(((op (e2) (e2)) = (e0))\/((op (e2) (e3)) = (e0))))) -> (~((op (e2) (e0)) = (op (e3) (e0)))) -> (~((op (e0) (e1)) = (op (e2) (e1)))) -> (((op (e2) (e0)) = (e0))\/(((op (e2) (e0)) = (e1))\/(((op (e2) (e0)) = (e2))\/((op (e2) (e0)) = (e3))))) -> ((op (e2) (e1)) = (e2)) -> (~((op (e2) (e0)) = (op (e2) (e1)))) -> (((op (e2) (e2)) = (e0))\/(((op (e2) (e2)) = (e1))\/(((op (e2) (e2)) = (e2))\/((op (e2) (e2)) = (e3))))) -> (~((op (e2) (e2)) = (op (e3) (e2)))) -> (~((op (e2) (e2)) = (op (e2) (e3)))) -> (~((op (e2) (e2)) = (e2))) -> (~((op (e0) (e2)) = (op (e2) (e2)))) -> (~((op (e0) (e0)) = (op (e0) (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)) = (op (e1) (e3)))) -> (~((op (e3) (e1)) = (op (e3) (e3)))) -> (~((op (e0) (e2)) = (op (e3) (e2)))) -> (~((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)) = (e1)) -> (~((e1) = (e2))) -> (~((op (e0) (e3)) = (op (e2) (e3)))) -> (((op (e3) (e2)) = (e0))\/(((op (e3) (e2)) = (e1))\/(((op (e3) (e2)) = (e2))\/((op (e3) (e2)) = (e3))))) -> (((op (e2) (e0)) = (e3))\/(((op (e2) (e1)) = (e3))\/(((op (e2) (e2)) = (e3))\/((op (e2) (e3)) = (e3))))) -> (~((op (e3) (e1)) = (op (e3) (e2)))) -> (((op (e0) (e3)) = (e0))\/(((op (e0) (e3)) = (e1))\/(((op (e0) (e3)) = (e2))\/((op (e0) (e3)) = (e3))))) -> (~((op (e3) (e0)) = (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) (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 (e0) (e0)) = (e0))) -> (~((op (e1) (e0)) = (op (e1) (e1)))) -> (~((op (e3) (e0)) = (op (e3) (e2)))) -> (((op (e0) (e0)) = (e2))\/(((op (e0) (e1)) = (e2))\/(((op (e0) (e2)) = (e2))\/((op (e0) (e3)) = (e2))))) -> (~((op (e0) (e1)) = (e1))) -> (~((op (e0) (e2)) = (e1))) -> (~((op (e0) (e3)) = (e1))) -> False). % 18.79/18.97 do 0 intro. intros zenon_H22d zenon_H12b zenon_H22 zenon_H201 zenon_H62 zenon_H34 zenon_H5b zenon_H57 zenon_H49 zenon_H54 zenon_H67 zenon_H52 zenon_H4f zenon_H4a zenon_H6a zenon_H24e zenon_H106 zenon_H1db zenon_H24f zenon_H2b zenon_H1ac zenon_H149 zenon_H110 zenon_Ha6 zenon_H115 zenon_H10a zenon_H128 zenon_H25e zenon_Hd8 zenon_H1ef zenon_H95 zenon_H1e0 zenon_H168 zenon_H9a zenon_H2f zenon_H17b zenon_H17e zenon_H259 zenon_H1ca zenon_H1f0 zenon_H1c4 zenon_H18f zenon_H6d zenon_H173 zenon_Ha8 zenon_H189 zenon_H1fe zenon_H153 zenon_H1d zenon_H130 zenon_H14f zenon_Hd5 zenon_Hdf zenon_Hae zenon_H7c zenon_He2 zenon_H191 zenon_He7 zenon_H1a4 zenon_He4 zenon_H71 zenon_H1c7 zenon_H145 zenon_H16f zenon_H3e zenon_H3f zenon_H45 zenon_H6f zenon_H183 zenon_Ha4 zenon_H20d zenon_H231. % 18.79/18.97 apply (zenon_or_s _ _ zenon_H22d); [ zenon_intro zenon_H7a | zenon_intro zenon_H22e ]. % 18.79/18.97 apply (zenon_or_s _ _ zenon_H183); [ zenon_intro zenon_H7b | zenon_intro zenon_H186 ]. % 18.79/18.97 apply (zenon_L26_); trivial. % 18.79/18.97 apply (zenon_or_s _ _ zenon_H186); [ zenon_intro zenon_H10f | zenon_intro zenon_H187 ]. % 18.79/18.97 apply (zenon_L191_); trivial. % 18.79/18.97 apply (zenon_or_s _ _ zenon_H187); [ zenon_intro zenon_H150 | zenon_intro zenon_Hcd ]. % 18.79/18.97 apply (zenon_or_s _ _ zenon_H1fe); [ zenon_intro zenon_H7b | zenon_intro zenon_H1ff ]. % 18.79/18.97 apply (zenon_L26_); trivial. % 18.79/18.97 apply (zenon_or_s _ _ zenon_H1ff); [ zenon_intro zenon_H86 | zenon_intro zenon_H200 ]. % 18.79/18.97 apply (zenon_or_s _ _ zenon_H168); [ zenon_intro zenon_H3a | zenon_intro zenon_H169 ]. % 18.79/18.97 apply (zenon_L35_); trivial. % 18.79/18.97 apply (zenon_or_s _ _ zenon_H169); [ zenon_intro zenon_H99 | zenon_intro zenon_H16a ]. % 18.79/18.97 apply (zenon_L36_); trivial. % 18.79/18.97 apply (zenon_or_s _ _ zenon_H16a); [ zenon_intro zenon_Ha9 | zenon_intro zenon_He3 ]. % 18.79/18.97 apply (zenon_L741_); trivial. % 18.79/18.97 apply (zenon_L740_); trivial. % 18.79/18.97 apply (zenon_or_s _ _ zenon_H200); [ zenon_intro zenon_Hee | zenon_intro zenon_H148 ]. % 18.79/18.97 apply (zenon_L277_); trivial. % 18.79/18.97 apply (zenon_L781_); trivial. % 18.79/18.97 apply (zenon_L782_); trivial. % 18.79/18.97 apply (zenon_or_s _ _ zenon_H22e); [ zenon_intro zenon_Ha0 | zenon_intro zenon_H22f ]. % 18.79/18.97 exact (zenon_Ha4 zenon_Ha0). % 18.79/18.97 apply (zenon_or_s _ _ zenon_H22f); [ zenon_intro zenon_H122 | zenon_intro zenon_Hc3 ]. % 18.79/18.97 exact (zenon_H20d zenon_H122). % 18.79/18.97 exact (zenon_H231 zenon_Hc3). % 18.79/18.97 (* end of lemma zenon_L783_ *) % 18.79/18.97 assert (zenon_L784_ : (((op (e2) (e0)) = (e0))\/(((op (e2) (e0)) = (e1))\/(((op (e2) (e0)) = (e2))\/((op (e2) (e0)) = (e3))))) -> (~((op (e2) (e0)) = (op (e3) (e0)))) -> ((op (e3) (e0)) = (e0)) -> (~((op (e2) (e0)) = (e1))) -> ((op (e2) (e1)) = (e2)) -> (~((op (e2) (e0)) = (op (e2) (e1)))) -> ((op (e1) (e0)) = (e2)) -> ((op (e0) (e0)) = (e1)) -> False). % 18.79/18.97 do 0 intro. intros zenon_H259 zenon_H17b zenon_H44 zenon_H1db zenon_H1ca zenon_H1f0 zenon_H86 zenon_H7a. % 18.79/18.97 apply (zenon_or_s _ _ zenon_H259); [ zenon_intro zenon_H34 | zenon_intro zenon_H25a ]. % 18.79/18.97 apply (zenon_L127_); trivial. % 18.79/18.97 apply (zenon_or_s _ _ zenon_H25a); [ zenon_intro zenon_Hed | zenon_intro zenon_H25b ]. % 18.79/18.97 exact (zenon_H1db zenon_Hed). % 18.79/18.97 apply (zenon_or_s _ _ zenon_H25b); [ zenon_intro zenon_Hee | zenon_intro zenon_H3b ]. % 18.79/18.97 apply (zenon_L277_); trivial. % 18.79/18.97 apply (zenon_L33_); trivial. % 18.79/18.97 (* end of lemma zenon_L784_ *) % 18.79/18.97 assert (zenon_L785_ : (((op (e0) (e0)) = (e2))\/(((op (e1) (e0)) = (e2))\/(((op (e2) (e0)) = (e2))\/((op (e3) (e0)) = (e2))))) -> (~((e1) = (e2))) -> ((op (e0) (e0)) = (e1)) -> (~((op (e2) (e0)) = (e1))) -> (~((op (e2) (e0)) = (op (e3) (e0)))) -> (((op (e2) (e0)) = (e0))\/(((op (e2) (e0)) = (e1))\/(((op (e2) (e0)) = (e2))\/((op (e2) (e0)) = (e3))))) -> ((op (e2) (e1)) = (e2)) -> (~((op (e2) (e0)) = (op (e2) (e1)))) -> ((op (e3) (e0)) = (e0)) -> (~((e0) = (e2))) -> False). % 18.79/18.97 do 0 intro. intros zenon_H1fe zenon_H7c zenon_H7a zenon_H1db zenon_H17b zenon_H259 zenon_H1ca zenon_H1f0 zenon_H44 zenon_H149. % 18.79/18.97 apply (zenon_or_s _ _ zenon_H1fe); [ zenon_intro zenon_H7b | zenon_intro zenon_H1ff ]. % 18.79/18.97 apply (zenon_L26_); trivial. % 18.79/18.97 apply (zenon_or_s _ _ zenon_H1ff); [ zenon_intro zenon_H86 | zenon_intro zenon_H200 ]. % 18.79/18.97 apply (zenon_L784_); trivial. % 18.79/18.97 apply (zenon_or_s _ _ zenon_H200); [ zenon_intro zenon_Hee | zenon_intro zenon_H148 ]. % 18.79/18.97 apply (zenon_L277_); trivial. % 18.79/18.97 apply (zenon_L100_); trivial. % 18.79/18.97 (* end of lemma zenon_L785_ *) % 18.79/18.97 assert (zenon_L786_ : (((op (e0) (e0)) = (e1))\/(((op (e0) (e1)) = (e1))\/(((op (e0) (e2)) = (e1))\/((op (e0) (e3)) = (e1))))) -> (~((e0) = (e2))) -> ((op (e3) (e0)) = (e0)) -> (~((op (e2) (e0)) = (op (e2) (e1)))) -> ((op (e2) (e1)) = (e2)) -> (((op (e2) (e0)) = (e0))\/(((op (e2) (e0)) = (e1))\/(((op (e2) (e0)) = (e2))\/((op (e2) (e0)) = (e3))))) -> (~((op (e2) (e0)) = (op (e3) (e0)))) -> (~((op (e2) (e0)) = (e1))) -> (~((e1) = (e2))) -> (((op (e0) (e0)) = (e2))\/(((op (e1) (e0)) = (e2))\/(((op (e2) (e0)) = (e2))\/((op (e3) (e0)) = (e2))))) -> (~((op (e0) (e1)) = (e1))) -> (~((op (e0) (e2)) = (e1))) -> (~((op (e0) (e3)) = (e1))) -> False). % 18.79/18.97 do 0 intro. intros zenon_H22d zenon_H149 zenon_H44 zenon_H1f0 zenon_H1ca zenon_H259 zenon_H17b zenon_H1db zenon_H7c zenon_H1fe zenon_Ha4 zenon_H20d zenon_H231. % 18.79/18.97 apply (zenon_or_s _ _ zenon_H22d); [ zenon_intro zenon_H7a | zenon_intro zenon_H22e ]. % 18.79/18.97 apply (zenon_L785_); trivial. % 18.79/18.97 apply (zenon_or_s _ _ zenon_H22e); [ zenon_intro zenon_Ha0 | zenon_intro zenon_H22f ]. % 18.79/18.97 exact (zenon_Ha4 zenon_Ha0). % 18.79/18.97 apply (zenon_or_s _ _ zenon_H22f); [ zenon_intro zenon_H122 | zenon_intro zenon_Hc3 ]. % 18.79/18.97 exact (zenon_H20d zenon_H122). % 18.79/18.97 exact (zenon_H231 zenon_Hc3). % 18.79/18.97 (* end of lemma zenon_L786_ *) % 18.79/18.97 assert (zenon_L787_ : (((op (e0) (e3)) = (e1))\/(((op (e1) (e3)) = (e1))\/(((op (e2) (e3)) = (e1))\/((op (e3) (e3)) = (e1))))) -> (~((op (e0) (e3)) = (e1))) -> (~((op (e1) (e2)) = (op (e1) (e3)))) -> ((op (e1) (e2)) = (e1)) -> (~((op (e2) (e3)) = (e1))) -> ((op (e3) (e0)) = (e1)) -> (~((op (e3) (e0)) = (op (e3) (e3)))) -> False). % 18.79/18.97 do 0 intro. intros zenon_H133 zenon_H231 zenon_H124 zenon_Hf0 zenon_H255 zenon_Hac zenon_H71. % 18.79/18.97 apply (zenon_or_s _ _ zenon_H133); [ zenon_intro zenon_Hc3 | zenon_intro zenon_H134 ]. % 18.79/18.97 exact (zenon_H231 zenon_Hc3). % 18.79/18.97 apply (zenon_or_s _ _ zenon_H134); [ zenon_intro zenon_Hd6 | zenon_intro zenon_H135 ]. % 18.79/18.97 apply (zenon_L78_); trivial. % 18.79/18.97 apply (zenon_or_s _ _ zenon_H135); [ zenon_intro zenon_Hf4 | zenon_intro zenon_Hc4 ]. % 18.79/18.97 exact (zenon_H255 zenon_Hf4). % 18.79/18.97 apply (zenon_L189_); trivial. % 18.79/18.97 (* end of lemma zenon_L787_ *) % 18.79/18.97 assert (zenon_L788_ : (((op (e0) (e3)) = (e2))\/(((op (e1) (e3)) = (e2))\/(((op (e2) (e3)) = (e2))\/((op (e3) (e3)) = (e2))))) -> ((op (e3) (e3)) = (e1)) -> ((op (e1) (e3)) = (e0)) -> (~((op (e1) (e1)) = (op (e1) (e3)))) -> ((op (e1) (e1)) = (e2)) -> (~((op (e2) (e1)) = (op (e2) (e3)))) -> ((op (e2) (e1)) = (e2)) -> ((op (e3) (e1)) = (e2)) -> (~((op (e3) (e1)) = (op (e3) (e3)))) -> False). % 18.79/18.97 do 0 intro. intros zenon_H145 zenon_Hc4 zenon_H1f zenon_H57 zenon_H110 zenon_H1c7 zenon_H1ca zenon_H14d zenon_H130. % 18.79/18.97 apply (zenon_or_s _ _ zenon_H145); [ zenon_intro zenon_Hcd | zenon_intro zenon_H146 ]. % 18.79/18.97 apply (zenon_L49_); trivial. % 18.79/18.97 apply (zenon_or_s _ _ zenon_H146); [ zenon_intro zenon_Hd7 | zenon_intro zenon_H147 ]. % 18.79/18.97 apply (zenon_L283_); trivial. % 18.79/18.97 apply (zenon_or_s _ _ zenon_H147); [ zenon_intro zenon_H11d | zenon_intro zenon_Hf6 ]. % 18.79/18.97 apply (zenon_L224_); trivial. % 18.79/18.97 apply (zenon_L102_); trivial. % 18.79/18.97 (* end of lemma zenon_L788_ *) % 18.79/18.97 assert (zenon_L789_ : (((op (e0) (e3)) = (e0))\/(((op (e0) (e3)) = (e1))\/(((op (e0) (e3)) = (e2))\/((op (e0) (e3)) = (e3))))) -> (~((op (e0) (e3)) = (e1))) -> ((op (e3) (e3)) = (e1)) -> ((op (e1) (e3)) = (e0)) -> (~((op (e0) (e3)) = (op (e1) (e3)))) -> ((op (e1) (e3)) = (e3)) -> False). % 18.79/18.97 do 0 intro. intros zenon_He4 zenon_H231 zenon_Hc4 zenon_H1f zenon_H1d zenon_Hdc. % 18.79/18.97 apply (zenon_or_s _ _ zenon_He4); [ zenon_intro zenon_H1e | zenon_intro zenon_He5 ]. % 18.79/18.97 apply (zenon_L1_); trivial. % 18.79/18.97 apply (zenon_or_s _ _ zenon_He5); [ zenon_intro zenon_Hc3 | zenon_intro zenon_He6 ]. % 18.79/18.97 exact (zenon_H231 zenon_Hc3). % 18.79/18.97 apply (zenon_or_s _ _ zenon_He6); [ zenon_intro zenon_Hcd | zenon_intro zenon_He3 ]. % 18.79/18.97 apply (zenon_L49_); trivial. % 18.79/18.97 apply (zenon_L117_); trivial. % 18.79/18.97 (* end of lemma zenon_L789_ *) % 18.79/18.97 assert (zenon_L790_ : (((op (e0) (e3)) = (e3))\/(((op (e1) (e3)) = (e3))\/(((op (e2) (e3)) = (e3))\/((op (e3) (e3)) = (e3))))) -> (~((op (e2) (e3)) = (op (e3) (e3)))) -> ((op (e2) (e0)) = (e0)) -> (~((op (e2) (e0)) = (op (e2) (e3)))) -> (((op (e2) (e3)) = (e0))\/(((op (e2) (e3)) = (e1))\/(((op (e2) (e3)) = (e2))\/((op (e2) (e3)) = (e3))))) -> ((op (e3) (e3)) = (e1)) -> (~((op (e0) (e3)) = (op (e2) (e3)))) -> (~((op (e0) (e3)) = (op (e3) (e3)))) -> ((op (e3) (e3)) = (e2)) -> (~((op (e0) (e3)) = (e1))) -> (~((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 (e3) (e3)) = (e3))) -> False). % 18.79/18.97 do 0 intro. intros zenon_H136 zenon_Hf3 zenon_H34 zenon_H5b zenon_H11f zenon_Hc4 zenon_He2 zenon_Hc2 zenon_Hf6 zenon_H231 zenon_H1d zenon_H1f zenon_He4 zenon_H102. % 18.79/18.97 apply (zenon_or_s _ _ zenon_H136); [ zenon_intro zenon_He3 | zenon_intro zenon_H137 ]. % 18.79/18.97 apply (zenon_L225_); trivial. % 18.79/18.97 apply (zenon_or_s _ _ zenon_H137); [ zenon_intro zenon_Hdc | zenon_intro zenon_H138 ]. % 18.79/18.97 apply (zenon_L789_); trivial. % 18.79/18.97 apply (zenon_or_s _ _ zenon_H138); [ zenon_intro zenon_Hdd | zenon_intro zenon_H105 ]. % 18.79/18.97 apply (zenon_L722_); trivial. % 18.79/18.97 exact (zenon_H102 zenon_H105). % 18.79/18.97 (* end of lemma zenon_L790_ *) % 18.79/18.97 assert (zenon_L791_ : (((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)) = (e1))) -> ((op (e1) (e2)) = (e1)) -> (~((op (e1) (e2)) = (op (e1) (e3)))) -> (((op (e0) (e3)) = (e1))\/(((op (e1) (e3)) = (e1))\/(((op (e2) (e3)) = (e1))\/((op (e3) (e3)) = (e1))))) -> (~((op (e3) (e1)) = (e1))) -> (~((op (e3) (e2)) = (e1))) -> (((op (e3) (e0)) = (e2))\/(((op (e3) (e1)) = (e2))\/(((op (e3) (e2)) = (e2))\/((op (e3) (e3)) = (e2))))) -> ((op (e0) (e0)) = (e1)) -> ((op (e1) (e0)) = (e3)) -> (~((op (e3) (e1)) = (op (e3) (e3)))) -> ((op (e2) (e1)) = (e2)) -> (~((op (e2) (e1)) = (op (e2) (e3)))) -> ((op (e1) (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 (e0) (e2)) = (e2)) -> (~((op (e0) (e2)) = (op (e3) (e2)))) -> (((op (e0) (e3)) = (e3))\/(((op (e1) (e3)) = (e3))\/(((op (e2) (e3)) = (e3))\/((op (e3) (e3)) = (e3))))) -> (~((op (e2) (e3)) = (op (e3) (e3)))) -> ((op (e2) (e0)) = (e0)) -> (~((op (e2) (e0)) = (op (e2) (e3)))) -> (((op (e2) (e3)) = (e0))\/(((op (e2) (e3)) = (e1))\/(((op (e2) (e3)) = (e2))\/((op (e2) (e3)) = (e3))))) -> (~((op (e0) (e3)) = (op (e2) (e3)))) -> (~((op (e0) (e3)) = (op (e3) (e3)))) -> (~((op (e0) (e3)) = (e1))) -> (~((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 (e3) (e3)) = (e3))) -> False). % 18.79/18.97 do 0 intro. intros zenon_He8 zenon_H71 zenon_H255 zenon_Hf0 zenon_H124 zenon_H133 zenon_H250 zenon_H251 zenon_H153 zenon_H7a zenon_H9e zenon_H130 zenon_H1ca zenon_H1c7 zenon_H110 zenon_H57 zenon_H145 zenon_H150 zenon_H14f zenon_H136 zenon_Hf3 zenon_H34 zenon_H5b zenon_H11f zenon_He2 zenon_Hc2 zenon_H231 zenon_H1d zenon_H1f zenon_He4 zenon_H102. % 18.79/18.97 apply (zenon_or_s _ _ zenon_He8); [ zenon_intro zenon_Hac | zenon_intro zenon_Heb ]. % 18.79/18.97 apply (zenon_L787_); trivial. % 18.79/18.97 apply (zenon_or_s _ _ zenon_Heb); [ zenon_intro zenon_Hae | zenon_intro zenon_Hec ]. % 18.79/18.97 exact (zenon_H250 zenon_Hae). % 18.79/18.97 apply (zenon_or_s _ _ zenon_Hec); [ zenon_intro zenon_Hba | zenon_intro zenon_Hc4 ]. % 18.79/18.97 exact (zenon_H251 zenon_Hba). % 18.79/18.97 apply (zenon_or_s _ _ zenon_H153); [ zenon_intro zenon_H148 | zenon_intro zenon_H154 ]. % 18.79/18.97 apply (zenon_L107_); trivial. % 18.79/18.97 apply (zenon_or_s _ _ zenon_H154); [ zenon_intro zenon_H14d | zenon_intro zenon_H155 ]. % 18.79/18.97 apply (zenon_L788_); trivial. % 18.79/18.97 apply (zenon_or_s _ _ zenon_H155); [ zenon_intro zenon_H151 | zenon_intro zenon_Hf6 ]. % 18.79/18.97 apply (zenon_L104_); trivial. % 18.79/18.97 apply (zenon_L790_); trivial. % 18.79/18.97 (* end of lemma zenon_L791_ *) % 18.79/18.97 assert (zenon_L792_ : (((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 (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)) = (e1))) -> (~((op (e0) (e3)) = (op (e3) (e3)))) -> (~((op (e0) (e3)) = (op (e2) (e3)))) -> (((op (e2) (e3)) = (e0))\/(((op (e2) (e3)) = (e1))\/(((op (e2) (e3)) = (e2))\/((op (e2) (e3)) = (e3))))) -> (~((op (e2) (e3)) = (op (e3) (e3)))) -> (((op (e0) (e3)) = (e3))\/(((op (e1) (e3)) = (e3))\/(((op (e2) (e3)) = (e3))\/((op (e3) (e3)) = (e3))))) -> (~((op (e0) (e2)) = (op (e3) (e2)))) -> ((op (e0) (e2)) = (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)) = (e2)) -> (~((op (e2) (e1)) = (op (e2) (e3)))) -> ((op (e2) (e1)) = (e2)) -> ((op (e1) (e0)) = (e3)) -> ((op (e0) (e0)) = (e1)) -> (((op (e3) (e0)) = (e2))\/(((op (e3) (e1)) = (e2))\/(((op (e3) (e2)) = (e2))\/((op (e3) (e3)) = (e2))))) -> (~((op (e3) (e2)) = (e1))) -> (~((op (e3) (e1)) = (e1))) -> (((op (e0) (e3)) = (e1))\/(((op (e1) (e3)) = (e1))\/(((op (e2) (e3)) = (e1))\/((op (e3) (e3)) = (e1))))) -> (~((op (e1) (e2)) = (op (e1) (e3)))) -> ((op (e1) (e2)) = (e1)) -> (~((op (e2) (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 (e2) (e0)) = (op (e2) (e3)))) -> ((op (e2) (e0)) = (e0)) -> ((op (e3) (e1)) = (e0)) -> (~((op (e3) (e1)) = (op (e3) (e3)))) -> False). % 18.79/18.98 do 0 intro. intros zenon_H67 zenon_H54 zenon_H49 zenon_H102 zenon_He4 zenon_H1d zenon_H231 zenon_Hc2 zenon_He2 zenon_H11f zenon_Hf3 zenon_H136 zenon_H14f zenon_H150 zenon_H145 zenon_H57 zenon_H110 zenon_H1c7 zenon_H1ca zenon_H9e zenon_H7a zenon_H153 zenon_H251 zenon_H250 zenon_H133 zenon_H124 zenon_Hf0 zenon_H255 zenon_H71 zenon_He8 zenon_H5b zenon_H34 zenon_H1b1 zenon_H130. % 18.79/18.98 apply (zenon_or_s _ _ zenon_H67); [ zenon_intro zenon_H1e | zenon_intro zenon_H68 ]. % 18.79/18.98 apply (zenon_L12_); trivial. % 18.79/18.98 apply (zenon_or_s _ _ zenon_H68); [ zenon_intro zenon_H1f | zenon_intro zenon_H69 ]. % 18.79/18.98 apply (zenon_L791_); trivial. % 18.79/18.98 apply (zenon_or_s _ _ zenon_H69); [ zenon_intro zenon_H37 | zenon_intro zenon_H60 ]. % 18.79/18.98 apply (zenon_L14_); trivial. % 18.79/18.98 apply (zenon_L244_); trivial. % 18.79/18.98 (* end of lemma zenon_L792_ *) % 18.79/18.98 assert (zenon_L793_ : (((op (e0) (e3)) = (e3))\/(((op (e1) (e3)) = (e3))\/(((op (e2) (e3)) = (e3))\/((op (e3) (e3)) = (e3))))) -> (~((e2) = (e3))) -> (~((op (e0) (e3)) = (op (e2) (e3)))) -> ((op (e2) (e1)) = (e1)) -> (~((op (e2) (e1)) = (op (e2) (e3)))) -> (~((op (e2) (e3)) = (op (e3) (e3)))) -> ((op (e3) (e3)) = (e0)) -> (((op (e2) (e3)) = (e0))\/(((op (e2) (e3)) = (e1))\/(((op (e2) (e3)) = (e2))\/((op (e2) (e3)) = (e3))))) -> ((op (e0) (e0)) = (e1)) -> ((op (e3) (e0)) = (e2)) -> (((op (e1) (e3)) = (e0))\/(((op (e1) (e3)) = (e1))\/(((op (e1) (e3)) = (e2))\/((op (e1) (e3)) = (e3))))) -> ((op (e0) (e3)) = (e2)) -> ((op (e3) (e3)) = (e1)) -> (~((op (e1) (e3)) = (op (e3) (e3)))) -> (~((op (e1) (e0)) = (op (e1) (e3)))) -> (~((op (e1) (e3)) = (op (e2) (e3)))) -> (~((op (e1) (e0)) = (e1))) -> (~((op (e1) (e0)) = (op (e1) (e2)))) -> ((op (e1) (e2)) = (e0)) -> (((op (e1) (e0)) = (e0))\/(((op (e1) (e0)) = (e1))\/(((op (e1) (e0)) = (e2))\/((op (e1) (e0)) = (e3))))) -> (~((op (e3) (e3)) = (e3))) -> False). % 18.79/18.98 do 0 intro. intros zenon_H136 zenon_H12b zenon_He2 zenon_Ha5 zenon_H1c7 zenon_Hf3 zenon_H60 zenon_H11f zenon_H7a zenon_H148 zenon_Hdf zenon_Hcd zenon_Hc4 zenon_Hd5 zenon_Hd8 zenon_Hdb zenon_H1ef zenon_H24a zenon_H2a zenon_H25e zenon_H102. % 18.79/18.98 apply (zenon_or_s _ _ zenon_H136); [ zenon_intro zenon_He3 | zenon_intro zenon_H137 ]. % 18.79/18.98 apply (zenon_L81_); trivial. % 18.79/18.98 apply (zenon_or_s _ _ zenon_H137); [ zenon_intro zenon_Hdc | zenon_intro zenon_H138 ]. % 18.79/18.98 apply (zenon_L235_); trivial. % 18.79/18.98 apply (zenon_or_s _ _ zenon_H138); [ zenon_intro zenon_Hdd | zenon_intro zenon_H105 ]. % 18.79/18.98 apply (zenon_or_s _ _ zenon_H25e); [ zenon_intro zenon_H27 | zenon_intro zenon_H25f ]. % 18.79/18.98 apply (zenon_L644_); trivial. % 18.79/18.98 apply (zenon_or_s _ _ zenon_H25f); [ zenon_intro zenon_H9d | zenon_intro zenon_H260 ]. % 18.79/18.98 exact (zenon_H1ef zenon_H9d). % 18.79/18.98 apply (zenon_or_s _ _ zenon_H260); [ zenon_intro zenon_H86 | zenon_intro zenon_H9e ]. % 18.79/18.98 apply (zenon_L53_); trivial. % 18.79/18.98 apply (zenon_L107_); trivial. % 18.79/18.98 exact (zenon_H102 zenon_H105). % 18.79/18.98 (* end of lemma zenon_L793_ *) % 18.79/18.98 assert (zenon_L794_ : (((op (e0) (e3)) = (e2))\/(((op (e1) (e3)) = (e2))\/(((op (e2) (e3)) = (e2))\/((op (e3) (e3)) = (e2))))) -> (~((op (e3) (e3)) = (e3))) -> (((op (e1) (e0)) = (e0))\/(((op (e1) (e0)) = (e1))\/(((op (e1) (e0)) = (e2))\/((op (e1) (e0)) = (e3))))) -> ((op (e1) (e2)) = (e0)) -> (~((op (e1) (e0)) = (op (e1) (e2)))) -> (~((op (e1) (e0)) = (e1))) -> (~((op (e1) (e3)) = (op (e2) (e3)))) -> (~((op (e1) (e0)) = (op (e1) (e3)))) -> (~((op (e1) (e3)) = (op (e3) (e3)))) -> ((op (e3) (e3)) = (e1)) -> (((op (e1) (e3)) = (e0))\/(((op (e1) (e3)) = (e1))\/(((op (e1) (e3)) = (e2))\/((op (e1) (e3)) = (e3))))) -> ((op (e0) (e0)) = (e1)) -> (((op (e2) (e3)) = (e0))\/(((op (e2) (e3)) = (e1))\/(((op (e2) (e3)) = (e2))\/((op (e2) (e3)) = (e3))))) -> ((op (e3) (e3)) = (e0)) -> (~((op (e2) (e3)) = (op (e3) (e3)))) -> ((op (e2) (e1)) = (e1)) -> (~((op (e0) (e3)) = (op (e2) (e3)))) -> (~((e2) = (e3))) -> (((op (e0) (e3)) = (e3))\/(((op (e1) (e3)) = (e3))\/(((op (e2) (e3)) = (e3))\/((op (e3) (e3)) = (e3))))) -> (~((op (e1) (e1)) = (op (e1) (e3)))) -> ((op (e1) (e1)) = (e2)) -> (~((op (e2) (e1)) = (op (e2) (e3)))) -> ((op (e2) (e1)) = (e2)) -> ((op (e3) (e0)) = (e2)) -> (~((op (e3) (e0)) = (op (e3) (e3)))) -> False). % 18.79/18.98 do 0 intro. intros zenon_H145 zenon_H102 zenon_H25e zenon_H2a zenon_H24a zenon_H1ef zenon_Hdb zenon_Hd8 zenon_Hd5 zenon_Hc4 zenon_Hdf zenon_H7a zenon_H11f zenon_H60 zenon_Hf3 zenon_Ha5 zenon_He2 zenon_H12b zenon_H136 zenon_H57 zenon_H110 zenon_H1c7 zenon_H1ca zenon_H148 zenon_H71. % 18.79/18.98 apply (zenon_or_s _ _ zenon_H145); [ zenon_intro zenon_Hcd | zenon_intro zenon_H146 ]. % 18.79/18.98 apply (zenon_L793_); trivial. % 18.79/18.98 apply (zenon_or_s _ _ zenon_H146); [ zenon_intro zenon_Hd7 | zenon_intro zenon_H147 ]. % 18.79/18.98 apply (zenon_L283_); trivial. % 18.79/18.98 apply (zenon_or_s _ _ zenon_H147); [ zenon_intro zenon_H11d | zenon_intro zenon_Hf6 ]. % 18.79/18.98 apply (zenon_L224_); trivial. % 18.79/18.98 apply (zenon_L114_); trivial. % 18.79/18.98 (* end of lemma zenon_L794_ *) % 18.79/18.98 assert (zenon_L795_ : (((op (e3) (e0)) = (e1))\/(((op (e3) (e1)) = (e1))\/(((op (e3) (e2)) = (e1))\/((op (e3) (e3)) = (e1))))) -> (~((op (e3) (e0)) = (e1))) -> (~((op (e3) (e1)) = (e1))) -> (~((op (e3) (e2)) = (e1))) -> (((op (e0) (e3)) = (e2))\/(((op (e1) (e3)) = (e2))\/(((op (e2) (e3)) = (e2))\/((op (e3) (e3)) = (e2))))) -> (~((op (e3) (e3)) = (e3))) -> (((op (e1) (e0)) = (e0))\/(((op (e1) (e0)) = (e1))\/(((op (e1) (e0)) = (e2))\/((op (e1) (e0)) = (e3))))) -> ((op (e1) (e2)) = (e0)) -> (~((op (e1) (e0)) = (op (e1) (e2)))) -> (~((op (e1) (e0)) = (e1))) -> (~((op (e1) (e3)) = (op (e2) (e3)))) -> (~((op (e1) (e0)) = (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)) = (e1)) -> (((op (e2) (e3)) = (e0))\/(((op (e2) (e3)) = (e1))\/(((op (e2) (e3)) = (e2))\/((op (e2) (e3)) = (e3))))) -> ((op (e3) (e3)) = (e0)) -> (~((op (e2) (e3)) = (op (e3) (e3)))) -> ((op (e2) (e1)) = (e1)) -> (~((op (e0) (e3)) = (op (e2) (e3)))) -> (~((e2) = (e3))) -> (((op (e0) (e3)) = (e3))\/(((op (e1) (e3)) = (e3))\/(((op (e2) (e3)) = (e3))\/((op (e3) (e3)) = (e3))))) -> (~((op (e1) (e1)) = (op (e1) (e3)))) -> ((op (e1) (e1)) = (e2)) -> (~((op (e2) (e1)) = (op (e2) (e3)))) -> ((op (e2) (e1)) = (e2)) -> ((op (e3) (e0)) = (e2)) -> (~((op (e3) (e0)) = (op (e3) (e3)))) -> False). % 18.79/18.98 do 0 intro. intros zenon_He8 zenon_Had zenon_H250 zenon_H251 zenon_H145 zenon_H102 zenon_H25e zenon_H2a zenon_H24a zenon_H1ef zenon_Hdb zenon_Hd8 zenon_Hd5 zenon_Hdf zenon_H7a zenon_H11f zenon_H60 zenon_Hf3 zenon_Ha5 zenon_He2 zenon_H12b zenon_H136 zenon_H57 zenon_H110 zenon_H1c7 zenon_H1ca zenon_H148 zenon_H71. % 18.79/18.98 apply (zenon_or_s _ _ zenon_He8); [ zenon_intro zenon_Hac | zenon_intro zenon_Heb ]. % 18.79/18.98 exact (zenon_Had zenon_Hac). % 18.79/18.98 apply (zenon_or_s _ _ zenon_Heb); [ zenon_intro zenon_Hae | zenon_intro zenon_Hec ]. % 18.79/18.98 exact (zenon_H250 zenon_Hae). % 18.79/18.98 apply (zenon_or_s _ _ zenon_Hec); [ zenon_intro zenon_Hba | zenon_intro zenon_Hc4 ]. % 18.79/18.98 exact (zenon_H251 zenon_Hba). % 18.79/18.98 apply (zenon_L794_); trivial. % 18.79/18.98 (* end of lemma zenon_L795_ *) % 18.79/18.98 assert (zenon_L796_ : (((op (e3) (e0)) = (e1))\/(((op (e3) (e1)) = (e1))\/(((op (e3) (e2)) = (e1))\/((op (e3) (e3)) = (e1))))) -> (~((op (e3) (e0)) = (e1))) -> (~((op (e3) (e1)) = (e1))) -> ((op (e1) (e2)) = (e1)) -> (~((op (e1) (e2)) = (op (e3) (e2)))) -> (((op (e0) (e3)) = (e3))\/(((op (e1) (e3)) = (e3))\/(((op (e2) (e3)) = (e3))\/((op (e3) (e3)) = (e3))))) -> (~((op (e3) (e1)) = (op (e3) (e3)))) -> ((op (e3) (e1)) = (e2)) -> ((op (e2) (e1)) = (e2)) -> (~((e2) = (e3))) -> (((op (e0) (e3)) = (e2))\/(((op (e1) (e3)) = (e2))\/(((op (e2) (e3)) = (e2))\/((op (e3) (e3)) = (e2))))) -> (~((op (e0) (e3)) = (op (e2) (e3)))) -> ((op (e2) (e1)) = (e1)) -> (~((op (e2) (e1)) = (op (e2) (e3)))) -> (~((op (e2) (e3)) = (op (e3) (e3)))) -> ((op (e3) (e3)) = (e0)) -> (((op (e2) (e3)) = (e0))\/(((op (e2) (e3)) = (e1))\/(((op (e2) (e3)) = (e2))\/((op (e2) (e3)) = (e3))))) -> (~((op (e1) (e3)) = (op (e2) (e3)))) -> ((op (e1) (e0)) = (e2)) -> (~((op (e1) (e0)) = (op (e1) (e3)))) -> (~((op (e1) (e3)) = (op (e3) (e3)))) -> ((op (e0) (e3)) = (e2)) -> (((op (e1) (e3)) = (e0))\/(((op (e1) (e3)) = (e1))\/(((op (e1) (e3)) = (e2))\/((op (e1) (e3)) = (e3))))) -> (~((op (e3) (e3)) = (e3))) -> False). % 18.79/18.98 do 0 intro. intros zenon_He8 zenon_Had zenon_H250 zenon_Hf0 zenon_H115 zenon_H136 zenon_H130 zenon_H14d zenon_H1ca zenon_H12b zenon_H145 zenon_He2 zenon_Ha5 zenon_H1c7 zenon_Hf3 zenon_H60 zenon_H11f zenon_Hdb zenon_H86 zenon_Hd8 zenon_Hd5 zenon_Hcd zenon_Hdf zenon_H102. % 18.79/18.98 apply (zenon_or_s _ _ zenon_He8); [ zenon_intro zenon_Hac | zenon_intro zenon_Heb ]. % 18.79/18.98 exact (zenon_Had zenon_Hac). % 18.79/18.98 apply (zenon_or_s _ _ zenon_Heb); [ zenon_intro zenon_Hae | zenon_intro zenon_Hec ]. % 18.79/18.98 exact (zenon_H250 zenon_Hae). % 18.79/18.98 apply (zenon_or_s _ _ zenon_Hec); [ zenon_intro zenon_Hba | zenon_intro zenon_Hc4 ]. % 18.79/18.98 apply (zenon_L69_); trivial. % 18.79/18.98 apply (zenon_or_s _ _ zenon_H136); [ zenon_intro zenon_He3 | zenon_intro zenon_H137 ]. % 18.79/18.98 apply (zenon_L739_); trivial. % 18.79/18.98 apply (zenon_or_s _ _ zenon_H137); [ zenon_intro zenon_Hdc | zenon_intro zenon_H138 ]. % 18.79/18.98 apply (zenon_L235_); trivial. % 18.79/18.98 apply (zenon_or_s _ _ zenon_H138); [ zenon_intro zenon_Hdd | zenon_intro zenon_H105 ]. % 18.79/18.98 apply (zenon_L53_); trivial. % 18.79/18.98 exact (zenon_H102 zenon_H105). % 18.79/18.98 (* end of lemma zenon_L796_ *) % 18.79/18.98 assert (zenon_L797_ : (~((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 (e1) (e0)) = (op (e1) (e3)))) -> ((op (e1) (e0)) = (e2)) -> (~((op (e1) (e3)) = (op (e2) (e3)))) -> (((op (e2) (e3)) = (e0))\/(((op (e2) (e3)) = (e1))\/(((op (e2) (e3)) = (e2))\/((op (e2) (e3)) = (e3))))) -> ((op (e3) (e3)) = (e0)) -> (~((op (e2) (e3)) = (op (e3) (e3)))) -> ((op (e2) (e1)) = (e1)) -> (~((op (e0) (e3)) = (op (e2) (e3)))) -> (((op (e0) (e3)) = (e2))\/(((op (e1) (e3)) = (e2))\/(((op (e2) (e3)) = (e2))\/((op (e3) (e3)) = (e2))))) -> (~((e2) = (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)) = (e1)) -> (~((op (e3) (e1)) = (e1))) -> (~((op (e3) (e0)) = (e1))) -> (((op (e3) (e0)) = (e1))\/(((op (e3) (e1)) = (e1))\/(((op (e3) (e2)) = (e1))\/((op (e3) (e3)) = (e1))))) -> (~((op (e1) (e1)) = (op (e1) (e3)))) -> ((op (e1) (e1)) = (e2)) -> (~((op (e2) (e1)) = (op (e2) (e3)))) -> ((op (e2) (e1)) = (e2)) -> ((op (e3) (e1)) = (e2)) -> (~((op (e3) (e1)) = (op (e3) (e3)))) -> False). % 18.79/18.98 do 0 intro. intros zenon_H102 zenon_Hdf zenon_Hd5 zenon_Hd8 zenon_H86 zenon_Hdb zenon_H11f zenon_H60 zenon_Hf3 zenon_Ha5 zenon_He2 zenon_H145 zenon_H12b zenon_H136 zenon_H115 zenon_Hf0 zenon_H250 zenon_Had zenon_He8 zenon_H57 zenon_H110 zenon_H1c7 zenon_H1ca zenon_H14d zenon_H130. % 18.79/18.98 apply (zenon_or_s _ _ zenon_H145); [ zenon_intro zenon_Hcd | zenon_intro zenon_H146 ]. % 18.79/18.98 apply (zenon_L796_); trivial. % 18.79/18.98 apply (zenon_or_s _ _ zenon_H146); [ zenon_intro zenon_Hd7 | zenon_intro zenon_H147 ]. % 18.79/18.98 apply (zenon_L283_); trivial. % 18.79/18.98 apply (zenon_or_s _ _ zenon_H147); [ zenon_intro zenon_H11d | zenon_intro zenon_Hf6 ]. % 18.79/18.98 apply (zenon_L224_); trivial. % 18.79/18.98 apply (zenon_L102_); trivial. % 18.79/18.98 (* end of lemma zenon_L797_ *) % 18.79/18.98 assert (zenon_L798_ : (((op (e0) (e3)) = (e0))\/(((op (e0) (e3)) = (e1))\/(((op (e0) (e3)) = (e2))\/((op (e0) (e3)) = (e3))))) -> (~((op (e0) (e3)) = (e1))) -> ((op (e3) (e3)) = (e2)) -> (~((op (e0) (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 (e1) (e3)) = (op (e3) (e3)))) -> (~((op (e0) (e3)) = (op (e2) (e3)))) -> ((op (e2) (e1)) = (e2)) -> (~((op (e2) (e1)) = (op (e2) (e3)))) -> (~((op (e2) (e3)) = (op (e3) (e3)))) -> ((op (e3) (e3)) = (e1)) -> (((op (e2) (e3)) = (e0))\/(((op (e2) (e3)) = (e1))\/(((op (e2) (e3)) = (e2))\/((op (e2) (e3)) = (e3))))) -> (~((op (e0) (e3)) = (op (e1) (e3)))) -> False). % 18.79/18.98 do 0 intro. intros zenon_He4 zenon_H231 zenon_Hf6 zenon_Hc2 zenon_Hdf zenon_H60 zenon_Hd5 zenon_He2 zenon_H1ca zenon_H1c7 zenon_Hf3 zenon_Hc4 zenon_H11f zenon_H1d. % 18.79/18.98 apply (zenon_or_s _ _ zenon_He4); [ zenon_intro zenon_H1e | zenon_intro zenon_He5 ]. % 18.79/18.98 apply (zenon_L440_); trivial. % 18.79/18.98 apply (zenon_or_s _ _ zenon_He5); [ zenon_intro zenon_Hc3 | zenon_intro zenon_He6 ]. % 18.79/18.98 exact (zenon_H231 zenon_Hc3). % 18.79/18.98 apply (zenon_or_s _ _ zenon_He6); [ zenon_intro zenon_Hcd | zenon_intro zenon_He3 ]. % 18.79/18.98 apply (zenon_L87_); trivial. % 18.79/18.98 apply (zenon_L455_); trivial. % 18.79/18.98 (* end of lemma zenon_L798_ *) % 18.79/18.98 assert (zenon_L799_ : (((op (e3) (e0)) = (e2))\/(((op (e3) (e1)) = (e2))\/(((op (e3) (e2)) = (e2))\/((op (e3) (e3)) = (e2))))) -> (~((op (e3) (e0)) = (op (e3) (e3)))) -> ((op (e0) (e0)) = (e1)) -> (~((op (e1) (e0)) = (e1))) -> (~((op (e1) (e0)) = (op (e1) (e2)))) -> ((op (e1) (e2)) = (e0)) -> (((op (e1) (e0)) = (e0))\/(((op (e1) (e0)) = (e1))\/(((op (e1) (e0)) = (e2))\/((op (e1) (e0)) = (e3))))) -> (~((op (e3) (e2)) = (e1))) -> (~((op (e3) (e1)) = (op (e3) (e3)))) -> ((op (e1) (e1)) = (e2)) -> (~((op (e1) (e1)) = (op (e1) (e3)))) -> (((op (e3) (e0)) = (e1))\/(((op (e3) (e1)) = (e1))\/(((op (e3) (e2)) = (e1))\/((op (e3) (e3)) = (e1))))) -> (~((op (e3) (e0)) = (e1))) -> (~((op (e3) (e1)) = (e1))) -> ((op (e1) (e2)) = (e1)) -> (~((op (e1) (e2)) = (op (e3) (e2)))) -> (((op (e0) (e3)) = (e3))\/(((op (e1) (e3)) = (e3))\/(((op (e2) (e3)) = (e3))\/((op (e3) (e3)) = (e3))))) -> (~((e2) = (e3))) -> (((op (e0) (e3)) = (e2))\/(((op (e1) (e3)) = (e2))\/(((op (e2) (e3)) = (e2))\/((op (e3) (e3)) = (e2))))) -> ((op (e2) (e1)) = (e1)) -> (~((op (e1) (e3)) = (op (e2) (e3)))) -> ((op (e1) (e0)) = (e2)) -> (~((op (e1) (e0)) = (op (e1) (e3)))) -> (~((op (e3) (e3)) = (e3))) -> ((op (e0) (e2)) = (e2)) -> (~((op (e0) (e2)) = (op (e3) (e2)))) -> (((op (e0) (e3)) = (e0))\/(((op (e0) (e3)) = (e1))\/(((op (e0) (e3)) = (e2))\/((op (e0) (e3)) = (e3))))) -> (~((op (e0) (e3)) = (e1))) -> (~((op (e0) (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 (e1) (e3)) = (op (e3) (e3)))) -> (~((op (e0) (e3)) = (op (e2) (e3)))) -> ((op (e2) (e1)) = (e2)) -> (~((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))))) -> (~((op (e0) (e3)) = (op (e1) (e3)))) -> False). % 18.79/18.98 do 0 intro. intros zenon_H153 zenon_H71 zenon_H7a zenon_H1ef zenon_H24a zenon_H2a zenon_H25e zenon_H251 zenon_H130 zenon_H110 zenon_H57 zenon_He8 zenon_Had zenon_H250 zenon_Hf0 zenon_H115 zenon_H136 zenon_H12b zenon_H145 zenon_Ha5 zenon_Hdb zenon_H86 zenon_Hd8 zenon_H102 zenon_H150 zenon_H14f zenon_He4 zenon_H231 zenon_Hc2 zenon_Hdf zenon_H60 zenon_Hd5 zenon_He2 zenon_H1ca zenon_H1c7 zenon_Hf3 zenon_H11f zenon_H1d. % 18.79/18.98 apply (zenon_or_s _ _ zenon_He8); [ zenon_intro zenon_Hac | zenon_intro zenon_Heb ]. % 18.79/18.98 exact (zenon_Had zenon_Hac). % 18.79/18.98 apply (zenon_or_s _ _ zenon_Heb); [ zenon_intro zenon_Hae | zenon_intro zenon_Hec ]. % 18.79/18.98 exact (zenon_H250 zenon_Hae). % 18.79/18.98 apply (zenon_or_s _ _ zenon_Hec); [ zenon_intro zenon_Hba | zenon_intro zenon_Hc4 ]. % 18.79/18.98 exact (zenon_H251 zenon_Hba). % 18.79/18.98 apply (zenon_or_s _ _ zenon_H153); [ zenon_intro zenon_H148 | zenon_intro zenon_H154 ]. % 18.79/18.98 apply (zenon_L795_); trivial. % 18.79/18.98 apply (zenon_or_s _ _ zenon_H154); [ zenon_intro zenon_H14d | zenon_intro zenon_H155 ]. % 18.79/18.98 apply (zenon_L797_); trivial. % 18.79/18.98 apply (zenon_or_s _ _ zenon_H155); [ zenon_intro zenon_H151 | zenon_intro zenon_Hf6 ]. % 18.79/18.98 apply (zenon_L104_); trivial. % 18.79/18.98 apply (zenon_L798_); trivial. % 18.79/18.98 (* end of lemma zenon_L799_ *) % 18.79/18.98 assert (zenon_L800_ : (((op (e3) (e0)) = (e1))\/(((op (e3) (e1)) = (e1))\/(((op (e3) (e2)) = (e1))\/((op (e3) (e3)) = (e1))))) -> (~((op (e3) (e0)) = (e1))) -> (~((op (e3) (e1)) = (e1))) -> (~((op (e3) (e2)) = (e1))) -> (~((op (e1) (e3)) = (op (e3) (e3)))) -> ((op (e1) (e3)) = (e1)) -> False). % 18.79/18.98 do 0 intro. intros zenon_He8 zenon_Had zenon_H250 zenon_H251 zenon_Hd5 zenon_Hd6. % 18.79/18.98 apply (zenon_or_s _ _ zenon_He8); [ zenon_intro zenon_Hac | zenon_intro zenon_Heb ]. % 18.79/18.98 exact (zenon_Had zenon_Hac). % 18.79/18.98 apply (zenon_or_s _ _ zenon_Heb); [ zenon_intro zenon_Hae | zenon_intro zenon_Hec ]. % 18.79/18.98 exact (zenon_H250 zenon_Hae). % 18.79/18.98 apply (zenon_or_s _ _ zenon_Hec); [ zenon_intro zenon_Hba | zenon_intro zenon_Hc4 ]. % 18.79/18.98 exact (zenon_H251 zenon_Hba). % 18.79/18.98 apply (zenon_L50_); trivial. % 18.79/18.98 (* end of lemma zenon_L800_ *) % 18.79/18.98 assert (zenon_L801_ : (((op (e1) (e0)) = (e1))\/(((op (e1) (e1)) = (e1))\/(((op (e1) (e2)) = (e1))\/((op (e1) (e3)) = (e1))))) -> (~((op (e1) (e0)) = (e1))) -> (~((op (e1) (e1)) = (e1))) -> (~((op (e3) (e3)) = (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)) = (e1))) -> (~((op (e0) (e3)) = (op (e3) (e3)))) -> (~((op (e0) (e3)) = (op (e2) (e3)))) -> (((op (e2) (e3)) = (e0))\/(((op (e2) (e3)) = (e1))\/(((op (e2) (e3)) = (e2))\/((op (e2) (e3)) = (e3))))) -> (~((op (e2) (e0)) = (op (e2) (e3)))) -> ((op (e2) (e0)) = (e0)) -> (~((op (e2) (e3)) = (op (e3) (e3)))) -> (((op (e0) (e3)) = (e3))\/(((op (e1) (e3)) = (e3))\/(((op (e2) (e3)) = (e3))\/((op (e3) (e3)) = (e3))))) -> (~((op (e0) (e2)) = (op (e3) (e2)))) -> ((op (e0) (e2)) = (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)) = (e2)) -> (~((op (e2) (e1)) = (op (e2) (e3)))) -> ((op (e2) (e1)) = (e2)) -> (~((op (e3) (e1)) = (op (e3) (e3)))) -> ((op (e1) (e0)) = (e3)) -> ((op (e0) (e0)) = (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 (e1) (e2)) = (op (e1) (e3)))) -> (~((op (e2) (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 (e3) (e0)) = (e1))) -> (~((op (e3) (e1)) = (e1))) -> (~((op (e3) (e2)) = (e1))) -> (~((op (e1) (e3)) = (op (e3) (e3)))) -> False). % 18.79/18.98 do 0 intro. intros zenon_H128 zenon_H1ef zenon_H10a zenon_H102 zenon_He4 zenon_H1f zenon_H1d zenon_H231 zenon_Hc2 zenon_He2 zenon_H11f zenon_H5b zenon_H34 zenon_Hf3 zenon_H136 zenon_H14f zenon_H150 zenon_H145 zenon_H57 zenon_H110 zenon_H1c7 zenon_H1ca zenon_H130 zenon_H9e zenon_H7a zenon_H153 zenon_H133 zenon_H124 zenon_H255 zenon_H71 zenon_He8 zenon_Had zenon_H250 zenon_H251 zenon_Hd5. % 18.79/18.98 apply (zenon_or_s _ _ zenon_H128); [ zenon_intro zenon_H9d | zenon_intro zenon_H129 ]. % 18.79/18.98 exact (zenon_H1ef zenon_H9d). % 18.79/18.98 apply (zenon_or_s _ _ zenon_H129); [ zenon_intro zenon_H10d | zenon_intro zenon_H12a ]. % 18.79/18.98 exact (zenon_H10a zenon_H10d). % 18.79/18.98 apply (zenon_or_s _ _ zenon_H12a); [ zenon_intro zenon_Hf0 | zenon_intro zenon_Hd6 ]. % 18.79/18.98 apply (zenon_L791_); trivial. % 18.79/18.98 apply (zenon_L800_); trivial. % 18.79/18.98 (* end of lemma zenon_L801_ *) % 18.79/18.98 assert (zenon_L802_ : (((op (e3) (e0)) = (e1))\/(((op (e3) (e1)) = (e1))\/(((op (e3) (e2)) = (e1))\/((op (e3) (e3)) = (e1))))) -> (~((op (e3) (e0)) = (e1))) -> (~((op (e3) (e1)) = (e1))) -> (~((op (e3) (e2)) = (e1))) -> (((op (e0) (e3)) = (e3))\/(((op (e1) (e3)) = (e3))\/(((op (e2) (e3)) = (e3))\/((op (e3) (e3)) = (e3))))) -> (~((e2) = (e3))) -> (~((op (e0) (e3)) = (op (e2) (e3)))) -> ((op (e2) (e1)) = (e1)) -> (~((op (e2) (e1)) = (op (e2) (e3)))) -> (~((op (e2) (e3)) = (op (e3) (e3)))) -> ((op (e3) (e3)) = (e0)) -> (((op (e2) (e3)) = (e0))\/(((op (e2) (e3)) = (e1))\/(((op (e2) (e3)) = (e2))\/((op (e2) (e3)) = (e3))))) -> (~((op (e1) (e3)) = (op (e2) (e3)))) -> ((op (e1) (e0)) = (e2)) -> (~((op (e1) (e0)) = (op (e1) (e3)))) -> (~((op (e1) (e3)) = (op (e3) (e3)))) -> ((op (e0) (e3)) = (e2)) -> (((op (e1) (e3)) = (e0))\/(((op (e1) (e3)) = (e1))\/(((op (e1) (e3)) = (e2))\/((op (e1) (e3)) = (e3))))) -> (~((op (e3) (e3)) = (e3))) -> False). % 18.79/18.98 do 0 intro. intros zenon_He8 zenon_Had zenon_H250 zenon_H251 zenon_H136 zenon_H12b zenon_He2 zenon_Ha5 zenon_H1c7 zenon_Hf3 zenon_H60 zenon_H11f zenon_Hdb zenon_H86 zenon_Hd8 zenon_Hd5 zenon_Hcd zenon_Hdf zenon_H102. % 18.79/18.98 apply (zenon_or_s _ _ zenon_He8); [ zenon_intro zenon_Hac | zenon_intro zenon_Heb ]. % 18.79/18.98 exact (zenon_Had zenon_Hac). % 18.79/18.98 apply (zenon_or_s _ _ zenon_Heb); [ zenon_intro zenon_Hae | zenon_intro zenon_Hec ]. % 18.79/18.98 exact (zenon_H250 zenon_Hae). % 18.79/18.98 apply (zenon_or_s _ _ zenon_Hec); [ zenon_intro zenon_Hba | zenon_intro zenon_Hc4 ]. % 18.79/18.98 exact (zenon_H251 zenon_Hba). % 18.79/18.98 apply (zenon_L236_); trivial. % 18.79/18.98 (* end of lemma zenon_L802_ *) % 18.79/18.98 assert (zenon_L803_ : (((op (e3) (e0)) = (e1))\/(((op (e3) (e1)) = (e1))\/(((op (e3) (e2)) = (e1))\/((op (e3) (e3)) = (e1))))) -> (~((op (e3) (e0)) = (e1))) -> (~((op (e3) (e1)) = (e1))) -> (~((op (e3) (e2)) = (e1))) -> ((op (e0) (e3)) = (e2)) -> ((op (e1) (e3)) = (e0)) -> False). % 18.79/18.98 do 0 intro. intros zenon_He8 zenon_Had zenon_H250 zenon_H251 zenon_Hcd zenon_H1f. % 18.79/18.98 apply (zenon_or_s _ _ zenon_He8); [ zenon_intro zenon_Hac | zenon_intro zenon_Heb ]. % 18.79/18.98 exact (zenon_Had zenon_Hac). % 18.79/18.98 apply (zenon_or_s _ _ zenon_Heb); [ zenon_intro zenon_Hae | zenon_intro zenon_Hec ]. % 18.79/18.98 exact (zenon_H250 zenon_Hae). % 18.79/18.98 apply (zenon_or_s _ _ zenon_Hec); [ zenon_intro zenon_Hba | zenon_intro zenon_Hc4 ]. % 18.79/18.98 exact (zenon_H251 zenon_Hba). % 18.79/18.98 apply (zenon_L49_); trivial. % 18.79/18.98 (* end of lemma zenon_L803_ *) % 18.79/18.98 assert (zenon_L804_ : (((op (e1) (e0)) = (e0))\/(((op (e1) (e1)) = (e0))\/(((op (e1) (e2)) = (e0))\/((op (e1) (e3)) = (e0))))) -> (~((e0) = (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 (e1) (e0)) = (op (e1) (e3)))) -> ((op (e1) (e0)) = (e2)) -> (~((op (e1) (e3)) = (op (e2) (e3)))) -> (((op (e2) (e3)) = (e0))\/(((op (e2) (e3)) = (e1))\/(((op (e2) (e3)) = (e2))\/((op (e2) (e3)) = (e3))))) -> (~((op (e2) (e3)) = (op (e3) (e3)))) -> (~((op (e2) (e1)) = (op (e2) (e3)))) -> ((op (e2) (e1)) = (e1)) -> (~((op (e0) (e3)) = (op (e2) (e3)))) -> (~((e2) = (e3))) -> (((op (e0) (e3)) = (e3))\/(((op (e1) (e3)) = (e3))\/(((op (e2) (e3)) = (e3))\/((op (e3) (e3)) = (e3))))) -> (~((op (e1) (e2)) = (op (e3) (e2)))) -> ((op (e2) (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 (e0) (e1)) = (e0)) -> (~((op (e0) (e1)) = (op (e2) (e1)))) -> (~((op (e1) (e2)) = (op (e2) (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) (e0)) = (e1))) -> ((op (e2) (e1)) = (e2)) -> (~((op (e2) (e0)) = (op (e2) (e1)))) -> ((op (e0) (e0)) = (e1)) -> (((op (e3) (e0)) = (e0))\/(((op (e3) (e1)) = (e0))\/(((op (e3) (e2)) = (e0))\/((op (e3) (e3)) = (e0))))) -> (((op (e3) (e0)) = (e1))\/(((op (e3) (e1)) = (e1))\/(((op (e3) (e2)) = (e1))\/((op (e3) (e3)) = (e1))))) -> (~((op (e3) (e0)) = (e1))) -> (~((op (e3) (e1)) = (e1))) -> (~((op (e3) (e2)) = (e1))) -> ((op (e0) (e3)) = (e2)) -> False). % 18.79/18.98 do 0 intro. intros zenon_H22 zenon_H149 zenon_H102 zenon_Hdf zenon_Hd5 zenon_Hd8 zenon_H86 zenon_Hdb zenon_H11f zenon_Hf3 zenon_H1c7 zenon_Ha5 zenon_He2 zenon_H12b zenon_H136 zenon_H115 zenon_Ha6 zenon_H110 zenon_H2f zenon_H17b zenon_H49 zenon_H17e zenon_H2b zenon_H259 zenon_H5b zenon_H1db zenon_H1ca zenon_H1f0 zenon_H7a zenon_H1ac zenon_He8 zenon_Had zenon_H250 zenon_H251 zenon_Hcd. % 18.79/18.98 apply (zenon_or_s _ _ zenon_H22); [ zenon_intro zenon_H27 | zenon_intro zenon_H26 ]. % 18.79/18.98 apply (zenon_L257_); trivial. % 18.79/18.98 apply (zenon_or_s _ _ zenon_H26); [ zenon_intro zenon_H29 | zenon_intro zenon_H28 ]. % 18.79/18.98 apply (zenon_L354_); trivial. % 18.79/18.98 apply (zenon_or_s _ _ zenon_H28); [ zenon_intro zenon_H2a | zenon_intro zenon_H1f ]. % 18.79/18.98 apply (zenon_or_s _ _ zenon_H1ac); [ zenon_intro zenon_H44 | zenon_intro zenon_H1af ]. % 18.79/18.98 apply (zenon_L730_); trivial. % 18.79/18.98 apply (zenon_or_s _ _ zenon_H1af); [ zenon_intro zenon_H1b1 | zenon_intro zenon_H1b0 ]. % 18.79/18.98 apply (zenon_L509_); trivial. % 18.79/18.98 apply (zenon_or_s _ _ zenon_H1b0); [ zenon_intro zenon_H61 | zenon_intro zenon_H60 ]. % 18.79/18.98 apply (zenon_L176_); trivial. % 18.79/18.98 apply (zenon_L802_); trivial. % 18.79/18.98 apply (zenon_L803_); trivial. % 18.79/18.98 (* end of lemma zenon_L804_ *) % 18.79/18.98 assert (zenon_L805_ : (((op (e3) (e0)) = (e1))\/(((op (e3) (e1)) = (e1))\/(((op (e3) (e2)) = (e1))\/((op (e3) (e3)) = (e1))))) -> (~((op (e3) (e0)) = (e1))) -> (~((op (e3) (e1)) = (e1))) -> (~((op (e3) (e2)) = (e1))) -> (((op (e1) (e3)) = (e0))\/(((op (e1) (e3)) = (e1))\/(((op (e1) (e3)) = (e2))\/((op (e1) (e3)) = (e3))))) -> ((op (e3) (e3)) = (e0)) -> (~((op (e1) (e3)) = (op (e3) (e3)))) -> (~((op (e0) (e3)) = (op (e2) (e3)))) -> ((op (e2) (e1)) = (e2)) -> (~((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))))) -> (~((op (e0) (e3)) = (op (e1) (e3)))) -> ((op (e0) (e3)) = (e3)) -> False). % 18.79/18.98 do 0 intro. intros zenon_He8 zenon_Had zenon_H250 zenon_H251 zenon_Hdf zenon_H60 zenon_Hd5 zenon_He2 zenon_H1ca zenon_H1c7 zenon_Hf3 zenon_H11f zenon_H1d zenon_He3. % 18.79/18.98 apply (zenon_or_s _ _ zenon_He8); [ zenon_intro zenon_Hac | zenon_intro zenon_Heb ]. % 18.79/18.98 exact (zenon_Had zenon_Hac). % 18.79/18.98 apply (zenon_or_s _ _ zenon_Heb); [ zenon_intro zenon_Hae | zenon_intro zenon_Hec ]. % 18.79/18.98 exact (zenon_H250 zenon_Hae). % 18.79/18.98 apply (zenon_or_s _ _ zenon_Hec); [ zenon_intro zenon_Hba | zenon_intro zenon_Hc4 ]. % 18.79/18.98 exact (zenon_H251 zenon_Hba). % 18.79/18.98 apply (zenon_L455_); trivial. % 18.79/18.98 (* end of lemma zenon_L805_ *) % 18.79/18.98 assert (zenon_L806_ : (((op (e3) (e0)) = (e0))\/(((op (e3) (e1)) = (e0))\/(((op (e3) (e2)) = (e0))\/((op (e3) (e3)) = (e0))))) -> ((op (e0) (e0)) = (e1)) -> ((op (e1) (e0)) = (e2)) -> (~((op (e2) (e0)) = (op (e2) (e1)))) -> (~((op (e2) (e0)) = (e1))) -> (~((op (e2) (e0)) = (op (e2) (e3)))) -> (((op (e2) (e0)) = (e0))\/(((op (e2) (e0)) = (e1))\/(((op (e2) (e0)) = (e2))\/((op (e2) (e0)) = (e3))))) -> (~((op (e1) (e2)) = (op (e2) (e2)))) -> (~((op (e0) (e1)) = (op (e2) (e1)))) -> ((op (e0) (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)) -> ((op (e2) (e1)) = (e3)) -> ((op (e1) (e2)) = (e0)) -> (~((op (e1) (e2)) = (op (e3) (e2)))) -> (((op (e3) (e0)) = (e1))\/(((op (e3) (e1)) = (e1))\/(((op (e3) (e2)) = (e1))\/((op (e3) (e3)) = (e1))))) -> (~((op (e3) (e0)) = (e1))) -> (~((op (e3) (e1)) = (e1))) -> (~((op (e3) (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 (e0) (e3)) = (op (e2) (e3)))) -> ((op (e2) (e1)) = (e2)) -> (~((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))))) -> (~((op (e0) (e3)) = (op (e1) (e3)))) -> ((op (e0) (e3)) = (e3)) -> False). % 18.79/18.98 do 0 intro. intros zenon_H1ac zenon_H7a zenon_H86 zenon_H1f0 zenon_H1db zenon_H5b zenon_H259 zenon_H2b zenon_H17e zenon_H49 zenon_H17b zenon_H2f zenon_H110 zenon_Ha6 zenon_H2a zenon_H115 zenon_He8 zenon_Had zenon_H250 zenon_H251 zenon_Hdf zenon_Hd5 zenon_He2 zenon_H1ca zenon_H1c7 zenon_Hf3 zenon_H11f zenon_H1d zenon_He3. % 18.79/18.98 apply (zenon_or_s _ _ zenon_H1ac); [ zenon_intro zenon_H44 | zenon_intro zenon_H1af ]. % 18.79/18.98 apply (zenon_L730_); trivial. % 18.79/18.98 apply (zenon_or_s _ _ zenon_H1af); [ zenon_intro zenon_H1b1 | zenon_intro zenon_H1b0 ]. % 18.79/18.98 apply (zenon_L509_); trivial. % 18.79/18.98 apply (zenon_or_s _ _ zenon_H1b0); [ zenon_intro zenon_H61 | zenon_intro zenon_H60 ]. % 18.79/18.98 apply (zenon_L176_); trivial. % 18.79/18.98 apply (zenon_L805_); trivial. % 18.79/18.98 (* end of lemma zenon_L806_ *) % 18.79/18.98 assert (zenon_L807_ : (((op (e0) (e3)) = (e2))\/(((op (e1) (e3)) = (e2))\/(((op (e2) (e3)) = (e2))\/((op (e3) (e3)) = (e2))))) -> ((op (e1) (e3)) = (e0)) -> (~((op (e3) (e2)) = (e1))) -> (~((op (e3) (e1)) = (e1))) -> (~((op (e3) (e0)) = (e1))) -> (((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)))) -> (~((op (e2) (e3)) = (op (e3) (e3)))) -> ((op (e3) (e3)) = (e1)) -> (((op (e2) (e3)) = (e0))\/(((op (e2) (e3)) = (e1))\/(((op (e2) (e3)) = (e2))\/((op (e2) (e3)) = (e3))))) -> (~((op (e2) (e1)) = (op (e2) (e3)))) -> ((op (e2) (e1)) = (e2)) -> ((op (e3) (e0)) = (e2)) -> (~((op (e3) (e0)) = (op (e3) (e3)))) -> False). % 18.79/18.98 do 0 intro. intros zenon_H145 zenon_H1f zenon_H251 zenon_H250 zenon_Had zenon_He8 zenon_He3 zenon_He2 zenon_Hf3 zenon_Hc4 zenon_H11f zenon_H1c7 zenon_H1ca zenon_H148 zenon_H71. % 18.79/18.98 apply (zenon_or_s _ _ zenon_H145); [ zenon_intro zenon_Hcd | zenon_intro zenon_H146 ]. % 18.79/18.98 apply (zenon_L803_); trivial. % 18.79/18.98 apply (zenon_or_s _ _ zenon_H146); [ zenon_intro zenon_Hd7 | zenon_intro zenon_H147 ]. % 18.79/18.98 apply (zenon_L454_); trivial. % 18.79/18.98 apply (zenon_or_s _ _ zenon_H147); [ zenon_intro zenon_H11d | zenon_intro zenon_Hf6 ]. % 18.79/18.98 apply (zenon_L224_); trivial. % 18.79/18.98 apply (zenon_L114_); trivial. % 18.79/18.98 (* end of lemma zenon_L807_ *) % 18.79/18.98 assert (zenon_L808_ : (((op (e3) (e0)) = (e2))\/(((op (e3) (e1)) = (e2))\/(((op (e3) (e2)) = (e2))\/((op (e3) (e3)) = (e2))))) -> (~((op (e3) (e0)) = (op (e3) (e3)))) -> (((op (e3) (e0)) = (e1))\/(((op (e3) (e1)) = (e1))\/(((op (e3) (e2)) = (e1))\/((op (e3) (e3)) = (e1))))) -> (~((op (e3) (e0)) = (e1))) -> (~((op (e3) (e1)) = (e1))) -> (~((op (e3) (e2)) = (e1))) -> (~((op (e3) (e1)) = (op (e3) (e3)))) -> ((op (e2) (e1)) = (e2)) -> (~((op (e2) (e1)) = (op (e2) (e3)))) -> ((op (e1) (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 (e0) (e2)) = (e2)) -> (~((op (e0) (e2)) = (op (e3) (e2)))) -> (((op (e2) (e3)) = (e0))\/(((op (e2) (e3)) = (e1))\/(((op (e2) (e3)) = (e2))\/((op (e2) (e3)) = (e3))))) -> (~((op (e2) (e0)) = (op (e2) (e3)))) -> ((op (e2) (e0)) = (e0)) -> ((op (e1) (e3)) = (e0)) -> (~((op (e2) (e3)) = (op (e3) (e3)))) -> (~((op (e0) (e3)) = (op (e2) (e3)))) -> ((op (e0) (e3)) = (e3)) -> False). % 18.79/18.98 do 0 intro. intros zenon_H153 zenon_H71 zenon_He8 zenon_Had zenon_H250 zenon_H251 zenon_H130 zenon_H1ca zenon_H1c7 zenon_H110 zenon_H57 zenon_H145 zenon_H150 zenon_H14f zenon_H11f zenon_H5b zenon_H34 zenon_H1f zenon_Hf3 zenon_He2 zenon_He3. % 18.79/18.98 apply (zenon_or_s _ _ zenon_He8); [ zenon_intro zenon_Hac | zenon_intro zenon_Heb ]. % 18.79/18.98 exact (zenon_Had zenon_Hac). % 18.79/18.98 apply (zenon_or_s _ _ zenon_Heb); [ zenon_intro zenon_Hae | zenon_intro zenon_Hec ]. % 18.79/18.98 exact (zenon_H250 zenon_Hae). % 18.79/18.98 apply (zenon_or_s _ _ zenon_Hec); [ zenon_intro zenon_Hba | zenon_intro zenon_Hc4 ]. % 18.79/18.98 exact (zenon_H251 zenon_Hba). % 18.79/18.98 apply (zenon_or_s _ _ zenon_H153); [ zenon_intro zenon_H148 | zenon_intro zenon_H154 ]. % 18.79/18.98 apply (zenon_L807_); trivial. % 18.79/18.98 apply (zenon_or_s _ _ zenon_H154); [ zenon_intro zenon_H14d | zenon_intro zenon_H155 ]. % 18.79/18.98 apply (zenon_L788_); trivial. % 18.79/18.98 apply (zenon_or_s _ _ zenon_H155); [ zenon_intro zenon_H151 | zenon_intro zenon_Hf6 ]. % 18.79/18.98 apply (zenon_L104_); trivial. % 18.79/18.98 apply (zenon_L225_); trivial. % 18.79/18.98 (* end of lemma zenon_L808_ *) % 18.79/18.98 assert (zenon_L809_ : (((op (e1) (e0)) = (e0))\/(((op (e1) (e1)) = (e0))\/(((op (e1) (e2)) = (e0))\/((op (e1) (e3)) = (e0))))) -> (~((op (e1) (e0)) = (op (e2) (e0)))) -> (~((op (e3) (e2)) = (op (e3) (e3)))) -> (~((e0) = (e3))) -> (((op (e0) (e3)) = (e0))\/(((op (e1) (e3)) = (e0))\/(((op (e2) (e3)) = (e0))\/((op (e3) (e3)) = (e0))))) -> (~((op (e2) (e0)) = (op (e2) (e2)))) -> (~((op (e1) (e1)) = (op (e1) (e2)))) -> (~((op (e0) (e1)) = (op (e0) (e2)))) -> (((op (e0) (e2)) = (e0))\/(((op (e1) (e2)) = (e0))\/(((op (e2) (e2)) = (e0))\/((op (e3) (e2)) = (e0))))) -> (~((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 (e1) (e2)) = (op (e3) (e2)))) -> ((op (e2) (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 (e0) (e1)) = (e0)) -> (~((op (e0) (e1)) = (op (e2) (e1)))) -> (~((op (e1) (e2)) = (op (e2) (e2)))) -> (((op (e2) (e0)) = (e0))\/(((op (e2) (e0)) = (e1))\/(((op (e2) (e0)) = (e2))\/((op (e2) (e0)) = (e3))))) -> (~((op (e2) (e0)) = (e1))) -> (~((op (e2) (e0)) = (op (e2) (e1)))) -> ((op (e1) (e0)) = (e2)) -> ((op (e0) (e0)) = (e1)) -> (((op (e3) (e0)) = (e0))\/(((op (e3) (e1)) = (e0))\/(((op (e3) (e2)) = (e0))\/((op (e3) (e3)) = (e0))))) -> (((op (e3) (e0)) = (e2))\/(((op (e3) (e1)) = (e2))\/(((op (e3) (e2)) = (e2))\/((op (e3) (e3)) = (e2))))) -> (~((op (e3) (e0)) = (op (e3) (e3)))) -> (((op (e3) (e0)) = (e1))\/(((op (e3) (e1)) = (e1))\/(((op (e3) (e2)) = (e1))\/((op (e3) (e3)) = (e1))))) -> (~((op (e3) (e0)) = (e1))) -> (~((op (e3) (e1)) = (e1))) -> (~((op (e3) (e2)) = (e1))) -> (~((op (e3) (e1)) = (op (e3) (e3)))) -> ((op (e2) (e1)) = (e2)) -> (~((op (e2) (e1)) = (op (e2) (e3)))) -> ((op (e1) (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 (e0) (e2)) = (e2)) -> (~((op (e0) (e2)) = (op (e3) (e2)))) -> (((op (e2) (e3)) = (e0))\/(((op (e2) (e3)) = (e1))\/(((op (e2) (e3)) = (e2))\/((op (e2) (e3)) = (e3))))) -> (~((op (e2) (e0)) = (op (e2) (e3)))) -> ((op (e2) (e0)) = (e0)) -> (~((op (e2) (e3)) = (op (e3) (e3)))) -> (~((op (e0) (e3)) = (op (e2) (e3)))) -> ((op (e0) (e3)) = (e3)) -> False). % 18.79/18.98 do 0 intro. intros zenon_H22 zenon_H201 zenon_H62 zenon_H9a zenon_H67 zenon_H52 zenon_H4f zenon_H4a zenon_H6a zenon_H1d zenon_Hd5 zenon_Hdf zenon_H115 zenon_Ha6 zenon_H2f zenon_H17b zenon_H49 zenon_H17e zenon_H2b zenon_H259 zenon_H1db zenon_H1f0 zenon_H86 zenon_H7a zenon_H1ac zenon_H153 zenon_H71 zenon_He8 zenon_Had zenon_H250 zenon_H251 zenon_H130 zenon_H1ca zenon_H1c7 zenon_H110 zenon_H57 zenon_H145 zenon_H150 zenon_H14f zenon_H11f zenon_H5b zenon_H34 zenon_Hf3 zenon_He2 zenon_He3. % 18.79/18.98 apply (zenon_or_s _ _ zenon_H22); [ zenon_intro zenon_H27 | zenon_intro zenon_H26 ]. % 18.79/18.98 apply (zenon_L332_); trivial. % 18.79/18.98 apply (zenon_or_s _ _ zenon_H26); [ zenon_intro zenon_H29 | zenon_intro zenon_H28 ]. % 18.79/18.98 apply (zenon_L724_); trivial. % 18.79/18.98 apply (zenon_or_s _ _ zenon_H28); [ zenon_intro zenon_H2a | zenon_intro zenon_H1f ]. % 18.79/18.98 apply (zenon_L806_); trivial. % 18.79/18.98 apply (zenon_L808_); trivial. % 18.79/18.98 (* end of lemma zenon_L809_ *) % 18.79/18.98 assert (zenon_L810_ : (((op (e0) (e3)) = (e2))\/(((op (e1) (e3)) = (e2))\/(((op (e2) (e3)) = (e2))\/((op (e3) (e3)) = (e2))))) -> ((op (e1) (e3)) = (e0)) -> (~((op (e3) (e2)) = (e1))) -> (~((op (e3) (e1)) = (e1))) -> (~((op (e3) (e0)) = (e1))) -> (((op (e3) (e0)) = (e1))\/(((op (e3) (e1)) = (e1))\/(((op (e3) (e2)) = (e1))\/((op (e3) (e3)) = (e1))))) -> (~((op (e1) (e1)) = (op (e1) (e3)))) -> ((op (e1) (e1)) = (e2)) -> (~((op (e2) (e1)) = (op (e2) (e3)))) -> ((op (e2) (e1)) = (e2)) -> ((op (e3) (e0)) = (e2)) -> (~((op (e3) (e0)) = (op (e3) (e3)))) -> False). % 18.79/18.98 do 0 intro. intros zenon_H145 zenon_H1f zenon_H251 zenon_H250 zenon_Had zenon_He8 zenon_H57 zenon_H110 zenon_H1c7 zenon_H1ca zenon_H148 zenon_H71. % 18.79/18.98 apply (zenon_or_s _ _ zenon_H145); [ zenon_intro zenon_Hcd | zenon_intro zenon_H146 ]. % 18.79/18.98 apply (zenon_L803_); trivial. % 18.79/18.98 apply (zenon_or_s _ _ zenon_H146); [ zenon_intro zenon_Hd7 | zenon_intro zenon_H147 ]. % 18.79/18.98 apply (zenon_L283_); trivial. % 18.79/18.98 apply (zenon_or_s _ _ zenon_H147); [ zenon_intro zenon_H11d | zenon_intro zenon_Hf6 ]. % 18.79/18.98 apply (zenon_L224_); trivial. % 18.79/18.98 apply (zenon_L114_); trivial. % 18.79/18.98 (* end of lemma zenon_L810_ *) % 18.79/18.98 assert (zenon_L811_ : (((op (e1) (e0)) = (e0))\/(((op (e1) (e1)) = (e0))\/(((op (e1) (e2)) = (e0))\/((op (e1) (e3)) = (e0))))) -> (~((op (e1) (e0)) = (op (e2) (e0)))) -> ((op (e2) (e0)) = (e0)) -> (((op (e0) (e3)) = (e3))\/(((op (e1) (e3)) = (e3))\/(((op (e2) (e3)) = (e3))\/((op (e3) (e3)) = (e3))))) -> (~((e2) = (e3))) -> (~((op (e0) (e3)) = (op (e2) (e3)))) -> ((op (e2) (e1)) = (e1)) -> (~((op (e2) (e3)) = (op (e3) (e3)))) -> (((op (e2) (e3)) = (e0))\/(((op (e2) (e3)) = (e1))\/(((op (e2) (e3)) = (e2))\/((op (e2) (e3)) = (e3))))) -> ((op (e0) (e0)) = (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) (e0)) = (op (e1) (e3)))) -> (~((op (e1) (e3)) = (op (e2) (e3)))) -> (~((op (e1) (e0)) = (e1))) -> (~((op (e1) (e0)) = (op (e1) (e2)))) -> (((op (e1) (e0)) = (e0))\/(((op (e1) (e0)) = (e1))\/(((op (e1) (e0)) = (e2))\/((op (e1) (e0)) = (e3))))) -> (~((op (e3) (e3)) = (e3))) -> (~((op (e1) (e2)) = (op (e3) (e2)))) -> ((op (e2) (e1)) = (e3)) -> (((op (e0) (e0)) = (e1))\/(((op (e0) (e1)) = (e1))\/(((op (e0) (e2)) = (e1))\/((op (e0) (e3)) = (e1))))) -> (~((e0) = (e2))) -> (~((op (e2) (e0)) = (op (e2) (e1)))) -> (((op (e2) (e0)) = (e0))\/(((op (e2) (e0)) = (e1))\/(((op (e2) (e0)) = (e2))\/((op (e2) (e0)) = (e3))))) -> (~((op (e2) (e0)) = (op (e3) (e0)))) -> (~((op (e2) (e0)) = (e1))) -> (~((e1) = (e2))) -> (((op (e0) (e0)) = (e2))\/(((op (e1) (e0)) = (e2))\/(((op (e2) (e0)) = (e2))\/((op (e3) (e0)) = (e2))))) -> (~((op (e0) (e1)) = (e1))) -> (~((op (e0) (e2)) = (e1))) -> (~((op (e0) (e3)) = (e1))) -> (((op (e3) (e0)) = (e0))\/(((op (e3) (e1)) = (e0))\/(((op (e3) (e2)) = (e0))\/((op (e3) (e3)) = (e0))))) -> (((op (e0) (e3)) = (e2))\/(((op (e1) (e3)) = (e2))\/(((op (e2) (e3)) = (e2))\/((op (e3) (e3)) = (e2))))) -> (~((op (e3) (e2)) = (e1))) -> (~((op (e3) (e1)) = (e1))) -> (~((op (e3) (e0)) = (e1))) -> (((op (e3) (e0)) = (e1))\/(((op (e3) (e1)) = (e1))\/(((op (e3) (e2)) = (e1))\/((op (e3) (e3)) = (e1))))) -> (~((op (e1) (e1)) = (op (e1) (e3)))) -> ((op (e1) (e1)) = (e2)) -> (~((op (e2) (e1)) = (op (e2) (e3)))) -> ((op (e2) (e1)) = (e2)) -> ((op (e3) (e0)) = (e2)) -> (~((op (e3) (e0)) = (op (e3) (e3)))) -> False). % 18.79/18.98 do 0 intro. intros zenon_H22 zenon_H201 zenon_H34 zenon_H136 zenon_H12b zenon_He2 zenon_Ha5 zenon_Hf3 zenon_H11f zenon_H7a zenon_Hdf zenon_Hd5 zenon_Hd8 zenon_Hdb zenon_H1ef zenon_H24a zenon_H25e zenon_H102 zenon_H115 zenon_Ha6 zenon_H22d zenon_H149 zenon_H1f0 zenon_H259 zenon_H17b zenon_H1db zenon_H7c zenon_H1fe zenon_Ha4 zenon_H20d zenon_H231 zenon_H1ac zenon_H145 zenon_H251 zenon_H250 zenon_Had zenon_He8 zenon_H57 zenon_H110 zenon_H1c7 zenon_H1ca zenon_H148 zenon_H71. % 18.79/18.98 apply (zenon_or_s _ _ zenon_H22); [ zenon_intro zenon_H27 | zenon_intro zenon_H26 ]. % 18.79/18.98 apply (zenon_L332_); trivial. % 18.79/18.98 apply (zenon_or_s _ _ zenon_H26); [ zenon_intro zenon_H29 | zenon_intro zenon_H28 ]. % 18.79/18.98 apply (zenon_L354_); trivial. % 18.79/18.98 apply (zenon_or_s _ _ zenon_H28); [ zenon_intro zenon_H2a | zenon_intro zenon_H1f ]. % 18.79/18.98 apply (zenon_or_s _ _ zenon_H1ac); [ zenon_intro zenon_H44 | zenon_intro zenon_H1af ]. % 18.79/18.98 apply (zenon_L786_); trivial. % 18.79/18.98 apply (zenon_or_s _ _ zenon_H1af); [ zenon_intro zenon_H1b1 | zenon_intro zenon_H1b0 ]. % 18.79/18.98 apply (zenon_L509_); trivial. % 18.79/18.98 apply (zenon_or_s _ _ zenon_H1b0); [ zenon_intro zenon_H61 | zenon_intro zenon_H60 ]. % 18.79/18.98 apply (zenon_L176_); trivial. % 18.79/18.98 apply (zenon_L795_); trivial. % 18.79/18.98 apply (zenon_L810_); trivial. % 18.79/18.98 (* end of lemma zenon_L811_ *) % 18.79/18.98 assert (zenon_L812_ : (~((op (e2) (e0)) = (op (e2) (e3)))) -> (~((op (e0) (e2)) = (op (e3) (e2)))) -> ((op (e0) (e2)) = (e2)) -> (~((op (e3) (e1)) = (op (e3) (e3)))) -> (((op (e3) (e0)) = (e2))\/(((op (e3) (e1)) = (e2))\/(((op (e3) (e2)) = (e2))\/((op (e3) (e3)) = (e2))))) -> (~((op (e1) (e2)) = (op (e2) (e2)))) -> (~((op (e0) (e1)) = (op (e2) (e1)))) -> ((op (e0) (e1)) = (e0)) -> (((op (e2) (e0)) = (e0))\/(((op (e2) (e1)) = (e0))\/(((op (e2) (e2)) = (e0))\/((op (e2) (e3)) = (e0))))) -> (~((op (e0) (e3)) = (op (e1) (e3)))) -> (((op (e0) (e2)) = (e0))\/(((op (e1) (e2)) = (e0))\/(((op (e2) (e2)) = (e0))\/((op (e3) (e2)) = (e0))))) -> (~((op (e0) (e1)) = (op (e0) (e2)))) -> (~((op (e1) (e1)) = (op (e1) (e2)))) -> (~((op (e2) (e0)) = (op (e2) (e2)))) -> (((op (e0) (e3)) = (e0))\/(((op (e1) (e3)) = (e0))\/(((op (e2) (e3)) = (e0))\/((op (e3) (e3)) = (e0))))) -> (~((e0) = (e3))) -> (~((op (e3) (e2)) = (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 (e1) (e0)) = (e0))\/(((op (e1) (e1)) = (e0))\/(((op (e1) (e2)) = (e0))\/((op (e1) (e3)) = (e0))))) -> (~((op (e1) (e0)) = (op (e2) (e0)))) -> ((op (e2) (e0)) = (e0)) -> (((op (e0) (e3)) = (e3))\/(((op (e1) (e3)) = (e3))\/(((op (e2) (e3)) = (e3))\/((op (e3) (e3)) = (e3))))) -> (~((e2) = (e3))) -> (~((op (e0) (e3)) = (op (e2) (e3)))) -> ((op (e2) (e1)) = (e1)) -> (~((op (e2) (e3)) = (op (e3) (e3)))) -> (((op (e2) (e3)) = (e0))\/(((op (e2) (e3)) = (e1))\/(((op (e2) (e3)) = (e2))\/((op (e2) (e3)) = (e3))))) -> ((op (e0) (e0)) = (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) (e0)) = (op (e1) (e3)))) -> (~((op (e1) (e3)) = (op (e2) (e3)))) -> (~((op (e1) (e0)) = (e1))) -> (~((op (e1) (e0)) = (op (e1) (e2)))) -> (((op (e1) (e0)) = (e0))\/(((op (e1) (e0)) = (e1))\/(((op (e1) (e0)) = (e2))\/((op (e1) (e0)) = (e3))))) -> (~((op (e3) (e3)) = (e3))) -> (~((op (e1) (e2)) = (op (e3) (e2)))) -> ((op (e2) (e1)) = (e3)) -> (((op (e0) (e0)) = (e1))\/(((op (e0) (e1)) = (e1))\/(((op (e0) (e2)) = (e1))\/((op (e0) (e3)) = (e1))))) -> (~((e0) = (e2))) -> (~((op (e2) (e0)) = (op (e2) (e1)))) -> (((op (e2) (e0)) = (e0))\/(((op (e2) (e0)) = (e1))\/(((op (e2) (e0)) = (e2))\/((op (e2) (e0)) = (e3))))) -> (~((op (e2) (e0)) = (op (e3) (e0)))) -> (~((op (e2) (e0)) = (e1))) -> (~((e1) = (e2))) -> (((op (e0) (e0)) = (e2))\/(((op (e1) (e0)) = (e2))\/(((op (e2) (e0)) = (e2))\/((op (e3) (e0)) = (e2))))) -> (~((op (e0) (e1)) = (e1))) -> (~((op (e0) (e2)) = (e1))) -> (~((op (e0) (e3)) = (e1))) -> (((op (e3) (e0)) = (e0))\/(((op (e3) (e1)) = (e0))\/(((op (e3) (e2)) = (e0))\/((op (e3) (e3)) = (e0))))) -> (((op (e0) (e3)) = (e2))\/(((op (e1) (e3)) = (e2))\/(((op (e2) (e3)) = (e2))\/((op (e3) (e3)) = (e2))))) -> (~((op (e3) (e2)) = (e1))) -> (~((op (e3) (e1)) = (e1))) -> (~((op (e3) (e0)) = (e1))) -> (((op (e3) (e0)) = (e1))\/(((op (e3) (e1)) = (e1))\/(((op (e3) (e2)) = (e1))\/((op (e3) (e3)) = (e1))))) -> (~((op (e1) (e1)) = (op (e1) (e3)))) -> ((op (e1) (e1)) = (e2)) -> (~((op (e2) (e1)) = (op (e2) (e3)))) -> ((op (e2) (e1)) = (e2)) -> (~((op (e3) (e0)) = (op (e3) (e3)))) -> False). % 18.79/18.98 do 0 intro. intros zenon_H5b zenon_H14f zenon_H150 zenon_H130 zenon_H153 zenon_H2b zenon_H17e zenon_H49 zenon_H2f zenon_H1d zenon_H6a zenon_H4a zenon_H4f zenon_H52 zenon_H67 zenon_H9a zenon_H62 zenon_H54 zenon_He4 zenon_H22 zenon_H201 zenon_H34 zenon_H136 zenon_H12b zenon_He2 zenon_Ha5 zenon_Hf3 zenon_H11f zenon_H7a zenon_Hdf zenon_Hd5 zenon_Hd8 zenon_Hdb zenon_H1ef zenon_H24a zenon_H25e zenon_H102 zenon_H115 zenon_Ha6 zenon_H22d zenon_H149 zenon_H1f0 zenon_H259 zenon_H17b zenon_H1db zenon_H7c zenon_H1fe zenon_Ha4 zenon_H20d zenon_H231 zenon_H1ac zenon_H145 zenon_H251 zenon_H250 zenon_Had zenon_He8 zenon_H57 zenon_H110 zenon_H1c7 zenon_H1ca zenon_H71. % 18.79/18.98 apply (zenon_or_s _ _ zenon_H1fe); [ zenon_intro zenon_H7b | zenon_intro zenon_H1ff ]. % 18.79/18.98 apply (zenon_L26_); trivial. % 18.79/18.98 apply (zenon_or_s _ _ zenon_H1ff); [ zenon_intro zenon_H86 | zenon_intro zenon_H200 ]. % 18.79/18.98 apply (zenon_or_s _ _ zenon_He4); [ zenon_intro zenon_H1e | zenon_intro zenon_He5 ]. % 18.79/18.98 apply (zenon_L12_); trivial. % 18.79/18.98 apply (zenon_or_s _ _ zenon_He5); [ zenon_intro zenon_Hc3 | zenon_intro zenon_He6 ]. % 18.79/18.98 exact (zenon_H231 zenon_Hc3). % 18.79/18.98 apply (zenon_or_s _ _ zenon_He6); [ zenon_intro zenon_Hcd | zenon_intro zenon_He3 ]. % 18.79/18.98 apply (zenon_L804_); trivial. % 18.79/18.98 apply (zenon_L809_); trivial. % 18.79/18.98 apply (zenon_or_s _ _ zenon_H200); [ zenon_intro zenon_Hee | zenon_intro zenon_H148 ]. % 18.79/18.98 apply (zenon_L277_); trivial. % 18.79/18.98 apply (zenon_L811_); trivial. % 18.79/18.98 (* end of lemma zenon_L812_ *) % 18.79/18.98 assert (zenon_L813_ : (((op (e3) (e0)) = (e1))\/(((op (e3) (e1)) = (e1))\/(((op (e3) (e2)) = (e1))\/((op (e3) (e3)) = (e1))))) -> (~((op (e3) (e0)) = (e1))) -> (~((op (e3) (e1)) = (e1))) -> (~((op (e3) (e2)) = (e1))) -> (((op (e0) (e3)) = (e3))\/(((op (e1) (e3)) = (e3))\/(((op (e2) (e3)) = (e3))\/((op (e3) (e3)) = (e3))))) -> (~((e2) = (e3))) -> (~((op (e0) (e3)) = (op (e2) (e3)))) -> ((op (e2) (e1)) = (e1)) -> (~((op (e2) (e1)) = (op (e2) (e3)))) -> (~((op (e2) (e3)) = (op (e3) (e3)))) -> ((op (e3) (e3)) = (e0)) -> (((op (e2) (e3)) = (e0))\/(((op (e2) (e3)) = (e1))\/(((op (e2) (e3)) = (e2))\/((op (e2) (e3)) = (e3))))) -> ((op (e0) (e0)) = (e1)) -> ((op (e3) (e0)) = (e2)) -> (((op (e1) (e3)) = (e0))\/(((op (e1) (e3)) = (e1))\/(((op (e1) (e3)) = (e2))\/((op (e1) (e3)) = (e3))))) -> ((op (e0) (e3)) = (e2)) -> (~((op (e1) (e3)) = (op (e3) (e3)))) -> (~((op (e1) (e0)) = (op (e1) (e3)))) -> (~((op (e1) (e3)) = (op (e2) (e3)))) -> (~((op (e1) (e0)) = (e1))) -> (~((op (e1) (e0)) = (op (e1) (e2)))) -> ((op (e1) (e2)) = (e0)) -> (((op (e1) (e0)) = (e0))\/(((op (e1) (e0)) = (e1))\/(((op (e1) (e0)) = (e2))\/((op (e1) (e0)) = (e3))))) -> (~((op (e3) (e3)) = (e3))) -> False). % 18.79/18.98 do 0 intro. intros zenon_He8 zenon_Had zenon_H250 zenon_H251 zenon_H136 zenon_H12b zenon_He2 zenon_Ha5 zenon_H1c7 zenon_Hf3 zenon_H60 zenon_H11f zenon_H7a zenon_H148 zenon_Hdf zenon_Hcd zenon_Hd5 zenon_Hd8 zenon_Hdb zenon_H1ef zenon_H24a zenon_H2a zenon_H25e zenon_H102. % 18.79/18.98 apply (zenon_or_s _ _ zenon_He8); [ zenon_intro zenon_Hac | zenon_intro zenon_Heb ]. % 18.79/18.98 exact (zenon_Had zenon_Hac). % 18.79/18.98 apply (zenon_or_s _ _ zenon_Heb); [ zenon_intro zenon_Hae | zenon_intro zenon_Hec ]. % 18.79/18.98 exact (zenon_H250 zenon_Hae). % 18.79/18.98 apply (zenon_or_s _ _ zenon_Hec); [ zenon_intro zenon_Hba | zenon_intro zenon_Hc4 ]. % 18.79/18.98 exact (zenon_H251 zenon_Hba). % 18.79/18.98 apply (zenon_L793_); trivial. % 18.79/18.98 (* end of lemma zenon_L813_ *) % 18.79/18.98 assert (zenon_L814_ : (((op (e0) (e0)) = (e2))\/(((op (e0) (e1)) = (e2))\/(((op (e0) (e2)) = (e2))\/((op (e0) (e3)) = (e2))))) -> ((~((op (e1) (e0)) = (e1)))\/((op (e1) (e1)) = (e0))) -> (((op (e0) (e0)) = (e0))\/(((op (e1) (e0)) = (e0))\/(((op (e2) (e0)) = (e0))\/((op (e3) (e0)) = (e0))))) -> (((op (e0) (e0)) = (e3))\/(((op (e0) (e1)) = (e3))\/(((op (e0) (e2)) = (e3))\/((op (e0) (e3)) = (e3))))) -> (~((op (e2) (e2)) = (op (e2) (e3)))) -> (~((op (e3) (e0)) = (op (e3) (e2)))) -> (~((e1) = (e3))) -> (~((e0) = (e1))) -> (~((op (e1) (e0)) = (op (e1) (e1)))) -> (~((op (e0) (e0)) = (e0))) -> ((~((op (e1) (e3)) = (e1)))\/((op (e1) (e1)) = (e3))) -> ((~((op (e2) (e2)) = (e1)))\/((op (e2) (e1)) = (e2))) -> ((~((op (e3) (e2)) = (e1)))\/((op (e3) (e1)) = (e2))) -> (~((op (e0) (e1)) = (op (e3) (e1)))) -> (((op (e0) (e2)) = (e1))\/(((op (e1) (e2)) = (e1))\/(((op (e2) (e2)) = (e1))\/((op (e3) (e2)) = (e1))))) -> (~((op (e0) (e0)) = (op (e0) (e2)))) -> (((op (e0) (e0)) = (e1))\/(((op (e1) (e0)) = (e1))\/(((op (e2) (e0)) = (e1))\/((op (e3) (e0)) = (e1))))) -> ((~((op (e3) (e0)) = (e1)))\/((op (e3) (e1)) = (e0))) -> ((~((op (e2) (e0)) = (e1)))\/((op (e2) (e1)) = (e0))) -> (~((op (e1) (e1)) = (e1))) -> (((op (e1) (e0)) = (e1))\/(((op (e1) (e1)) = (e1))\/(((op (e1) (e2)) = (e1))\/((op (e1) (e3)) = (e1))))) -> (~((op (e0) (e1)) = (op (e1) (e1)))) -> ((~((op (e1) (e2)) = (e1)))\/((op (e1) (e1)) = (e2))) -> ((~((op (e0) (e3)) = (e1)))\/((op (e0) (e1)) = (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 (e0) (e2)) = (e1))) -> (~((op (e0) (e1)) = (e1))) -> (~((e1) = (e2))) -> (((op (e0) (e0)) = (e1))\/(((op (e0) (e1)) = (e1))\/(((op (e0) (e2)) = (e1))\/((op (e0) (e3)) = (e1))))) -> (((op (e0) (e3)) = (e0))\/(((op (e0) (e3)) = (e1))\/(((op (e0) (e3)) = (e2))\/((op (e0) (e3)) = (e3))))) -> (~((e0) = (e3))) -> (~((op (e0) (e3)) = (op (e1) (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) (e2)) = (op (e3) (e2)))) -> (((op (e0) (e0)) = (e2))\/(((op (e1) (e0)) = (e2))\/(((op (e2) (e0)) = (e2))\/((op (e3) (e0)) = (e2))))) -> (~((op (e0) (e0)) = (op (e0) (e3)))) -> (~((op (e2) (e0)) = (op (e2) (e1)))) -> ((op (e2) (e1)) = (e2)) -> (~((op (e2) (e0)) = (e1))) -> (((op (e2) (e0)) = (e0))\/(((op (e2) (e0)) = (e1))\/(((op (e2) (e0)) = (e2))\/((op (e2) (e0)) = (e3))))) -> (~((op (e1) (e2)) = (op (e2) (e2)))) -> (~((op (e0) (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) (e0)) = (op (e2) (e0)))) -> (~((op (e3) (e2)) = (op (e3) (e3)))) -> ((op (e2) (e0)) = (e0)) -> (~((op (e2) (e0)) = (op (e2) (e3)))) -> (~((op (e1) (e1)) = (op (e1) (e3)))) -> ((op (e0) (e1)) = (e0)) -> (~((op (e0) (e1)) = (op (e0) (e3)))) -> (((op (e0) (e3)) = (e0))\/(((op (e1) (e3)) = (e0))\/(((op (e2) (e3)) = (e0))\/((op (e3) (e3)) = (e0))))) -> (~((op (e2) (e0)) = (op (e2) (e2)))) -> (~((op (e1) (e1)) = (op (e1) (e2)))) -> (~((op (e0) (e1)) = (op (e0) (e2)))) -> (((op (e0) (e2)) = (e0))\/(((op (e1) (e2)) = (e0))\/(((op (e2) (e2)) = (e0))\/((op (e3) (e2)) = (e0))))) -> (~((op (e3) (e3)) = (e3))) -> (((op (e1) (e0)) = (e0))\/(((op (e1) (e0)) = (e1))\/(((op (e1) (e0)) = (e2))\/((op (e1) (e0)) = (e3))))) -> (~((op (e1) (e0)) = (op (e1) (e2)))) -> (~((op (e1) (e0)) = (e1))) -> (~((op (e1) (e3)) = (op (e2) (e3)))) -> (~((op (e1) (e0)) = (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)) = (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 (e2) (e1)) = (e1)) -> (~((op (e0) (e3)) = (op (e2) (e3)))) -> (~((e2) = (e3))) -> (((op (e0) (e3)) = (e3))\/(((op (e1) (e3)) = (e3))\/(((op (e2) (e3)) = (e3))\/((op (e3) (e3)) = (e3))))) -> (~((op (e1) (e2)) = (op (e3) (e2)))) -> ((op (e2) (e1)) = (e3)) -> ((op (e1) (e1)) = (e2)) -> (~((e0) = (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 (e3) (e0)) = (e1))) -> (~((op (e3) (e1)) = (e1))) -> (~((op (e3) (e2)) = (e1))) -> False). % 18.79/18.98 do 0 intro. intros zenon_H183 zenon_H25d zenon_H3e zenon_H168 zenon_H6d zenon_H6f zenon_H95 zenon_Ha1 zenon_H45 zenon_H3f zenon_H258 zenon_H253 zenon_H252 zenon_H210 zenon_H139 zenon_H13c zenon_H235 zenon_H254 zenon_H257 zenon_H10a zenon_H128 zenon_H10e zenon_H256 zenon_H25c zenon_H71 zenon_H145 zenon_H231 zenon_H20d zenon_Ha4 zenon_H7c zenon_H22d zenon_He4 zenon_H9a zenon_H1d zenon_H153 zenon_H130 zenon_H14f zenon_H1fe zenon_H189 zenon_H1f0 zenon_H1ca zenon_H1db zenon_H259 zenon_H2b zenon_H17e zenon_H17b zenon_H2f zenon_H22 zenon_H201 zenon_H62 zenon_H34 zenon_H5b zenon_H57 zenon_H49 zenon_H54 zenon_H67 zenon_H52 zenon_H4f zenon_H4a zenon_H6a zenon_H102 zenon_H25e zenon_H24a zenon_H1ef zenon_Hdb zenon_Hd8 zenon_Hd5 zenon_Hdf zenon_H7a zenon_H11f zenon_Hf3 zenon_H1c7 zenon_Ha5 zenon_He2 zenon_H12b zenon_H136 zenon_H115 zenon_Ha6 zenon_H110 zenon_H149 zenon_H1ac zenon_He8 zenon_Had zenon_H250 zenon_H251. % 18.79/18.98 apply (zenon_or_s _ _ zenon_H183); [ zenon_intro zenon_H7b | zenon_intro zenon_H186 ]. % 18.79/18.98 apply (zenon_L26_); trivial. % 18.79/18.98 apply (zenon_or_s _ _ zenon_H186); [ zenon_intro zenon_H10f | zenon_intro zenon_H187 ]. % 18.79/18.98 apply (zenon_L764_); trivial. % 18.79/18.98 apply (zenon_or_s _ _ zenon_H187); [ zenon_intro zenon_H150 | zenon_intro zenon_Hcd ]. % 18.79/18.98 apply (zenon_L812_); trivial. % 18.79/18.98 apply (zenon_or_s _ _ zenon_H1fe); [ zenon_intro zenon_H7b | zenon_intro zenon_H1ff ]. % 18.79/18.98 apply (zenon_L375_); trivial. % 18.79/18.98 apply (zenon_or_s _ _ zenon_H1ff); [ zenon_intro zenon_H86 | zenon_intro zenon_H200 ]. % 18.79/18.98 apply (zenon_L804_); trivial. % 18.79/18.98 apply (zenon_or_s _ _ zenon_H200); [ zenon_intro zenon_Hee | zenon_intro zenon_H148 ]. % 18.79/18.98 apply (zenon_L204_); trivial. % 18.79/18.98 apply (zenon_or_s _ _ zenon_H22); [ zenon_intro zenon_H27 | zenon_intro zenon_H26 ]. % 18.79/18.98 apply (zenon_L332_); trivial. % 18.79/18.98 apply (zenon_or_s _ _ zenon_H26); [ zenon_intro zenon_H29 | zenon_intro zenon_H28 ]. % 18.79/18.98 apply (zenon_L17_); trivial. % 18.79/18.98 apply (zenon_or_s _ _ zenon_H28); [ zenon_intro zenon_H2a | zenon_intro zenon_H1f ]. % 18.79/18.98 apply (zenon_or_s _ _ zenon_H1ac); [ zenon_intro zenon_H44 | zenon_intro zenon_H1af ]. % 18.79/18.98 apply (zenon_L100_); trivial. % 18.79/18.98 apply (zenon_or_s _ _ zenon_H1af); [ zenon_intro zenon_H1b1 | zenon_intro zenon_H1b0 ]. % 18.79/18.98 apply (zenon_L509_); trivial. % 18.79/18.98 apply (zenon_or_s _ _ zenon_H1b0); [ zenon_intro zenon_H61 | zenon_intro zenon_H60 ]. % 18.79/18.98 apply (zenon_L176_); trivial. % 18.79/18.98 apply (zenon_L813_); trivial. % 18.79/18.98 apply (zenon_L803_); trivial. % 18.79/18.98 (* end of lemma zenon_L814_ *) % 18.79/18.98 assert (zenon_L815_ : (((op (e0) (e3)) = (e1))\/(((op (e1) (e3)) = (e1))\/(((op (e2) (e3)) = (e1))\/((op (e3) (e3)) = (e1))))) -> (~((op (e0) (e3)) = (e1))) -> (~((op (e1) (e2)) = (op (e1) (e3)))) -> ((op (e1) (e2)) = (e1)) -> (~((op (e2) (e3)) = (e1))) -> ((op (e0) (e3)) = (e2)) -> ((op (e1) (e3)) = (e0)) -> False). % 18.79/18.98 do 0 intro. intros zenon_H133 zenon_H231 zenon_H124 zenon_Hf0 zenon_H255 zenon_Hcd zenon_H1f. % 18.79/18.98 apply (zenon_or_s _ _ zenon_H133); [ zenon_intro zenon_Hc3 | zenon_intro zenon_H134 ]. % 18.79/18.98 exact (zenon_H231 zenon_Hc3). % 18.79/18.98 apply (zenon_or_s _ _ zenon_H134); [ zenon_intro zenon_Hd6 | zenon_intro zenon_H135 ]. % 18.79/18.98 apply (zenon_L78_); trivial. % 18.79/18.98 apply (zenon_or_s _ _ zenon_H135); [ zenon_intro zenon_Hf4 | zenon_intro zenon_Hc4 ]. % 18.79/18.98 exact (zenon_H255 zenon_Hf4). % 18.79/18.98 apply (zenon_L49_); trivial. % 18.79/18.98 (* end of lemma zenon_L815_ *) % 18.79/18.98 assert (zenon_L816_ : (((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 (e2) (e2)) = (e2))) -> (~((op (e2) (e2)) = (op (e3) (e2)))) -> ((op (e0) (e2)) = (e3)) -> (((op (e2) (e2)) = (e0))\/(((op (e2) (e2)) = (e1))\/(((op (e2) (e2)) = (e2))\/((op (e2) (e2)) = (e3))))) -> ((op (e1) (e3)) = (e1)) -> (~((op (e1) (e2)) = (op (e1) (e3)))) -> (~((op (e0) (e2)) = (e1))) -> (((op (e0) (e2)) = (e1))\/(((op (e1) (e2)) = (e1))\/(((op (e2) (e2)) = (e1))\/((op (e3) (e2)) = (e1))))) -> ((op (e2) (e0)) = (e0)) -> (~((op (e2) (e0)) = (op (e2) (e2)))) -> (~((op (e3) (e1)) = (op (e3) (e2)))) -> ((op (e3) (e1)) = (e0)) -> False). % 18.79/18.98 do 0 intro. intros zenon_H6a zenon_H4a zenon_H49 zenon_H173 zenon_H18f zenon_Ha9 zenon_H1c4 zenon_Hd6 zenon_H124 zenon_H20d zenon_H139 zenon_H34 zenon_H52 zenon_H1a4 zenon_H1b1. % 18.79/18.98 apply (zenon_or_s _ _ zenon_H6a); [ zenon_intro zenon_H48 | zenon_intro zenon_H6b ]. % 18.79/18.98 apply (zenon_L9_); trivial. % 18.79/18.98 apply (zenon_or_s _ _ zenon_H6b); [ zenon_intro zenon_H2a | zenon_intro zenon_H6c ]. % 18.79/18.98 apply (zenon_L720_); trivial. % 18.79/18.98 apply (zenon_or_s _ _ zenon_H6c); [ zenon_intro zenon_H2c | zenon_intro zenon_H61 ]. % 18.79/18.98 apply (zenon_L11_); trivial. % 18.79/18.98 apply (zenon_L247_); trivial. % 18.79/18.98 (* end of lemma zenon_L816_ *) % 18.79/18.98 assert (zenon_L817_ : (((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) (e3)) = (e0)) -> ((op (e0) (e3)) = (e2)) -> (~((op (e2) (e3)) = (e1))) -> (~((op (e0) (e3)) = (e1))) -> (((op (e0) (e3)) = (e1))\/(((op (e1) (e3)) = (e1))\/(((op (e2) (e3)) = (e1))\/((op (e3) (e3)) = (e1))))) -> (((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 (e2) (e2)) = (e2))) -> (~((op (e2) (e2)) = (op (e3) (e2)))) -> ((op (e0) (e2)) = (e3)) -> (((op (e2) (e2)) = (e0))\/(((op (e2) (e2)) = (e1))\/(((op (e2) (e2)) = (e2))\/((op (e2) (e2)) = (e3))))) -> (~((op (e1) (e2)) = (op (e1) (e3)))) -> (~((op (e0) (e2)) = (e1))) -> (((op (e0) (e2)) = (e1))\/(((op (e1) (e2)) = (e1))\/(((op (e2) (e2)) = (e1))\/((op (e3) (e2)) = (e1))))) -> ((op (e2) (e0)) = (e0)) -> (~((op (e2) (e0)) = (op (e2) (e2)))) -> (~((op (e3) (e1)) = (op (e3) (e2)))) -> ((op (e3) (e1)) = (e0)) -> False). % 18.79/18.98 do 0 intro. intros zenon_H128 zenon_H1ef zenon_H10a zenon_H1f zenon_Hcd zenon_H255 zenon_H231 zenon_H133 zenon_H6a zenon_H4a zenon_H49 zenon_H173 zenon_H18f zenon_Ha9 zenon_H1c4 zenon_H124 zenon_H20d zenon_H139 zenon_H34 zenon_H52 zenon_H1a4 zenon_H1b1. % 18.79/18.98 apply (zenon_or_s _ _ zenon_H128); [ zenon_intro zenon_H9d | zenon_intro zenon_H129 ]. % 18.79/18.98 exact (zenon_H1ef zenon_H9d). % 18.79/18.98 apply (zenon_or_s _ _ zenon_H129); [ zenon_intro zenon_H10d | zenon_intro zenon_H12a ]. % 18.79/18.98 exact (zenon_H10a zenon_H10d). % 18.79/18.98 apply (zenon_or_s _ _ zenon_H12a); [ zenon_intro zenon_Hf0 | zenon_intro zenon_Hd6 ]. % 18.79/18.98 apply (zenon_L815_); trivial. % 18.79/18.98 apply (zenon_L816_); trivial. % 18.79/18.98 (* end of lemma zenon_L817_ *) % 18.79/18.98 assert (zenon_L818_ : (((op (e0) (e3)) = (e2))\/(((op (e1) (e3)) = (e2))\/(((op (e2) (e3)) = (e2))\/((op (e3) (e3)) = (e2))))) -> ((op (e3) (e1)) = (e0)) -> (~((op (e3) (e1)) = (op (e3) (e2)))) -> (~((op (e2) (e0)) = (op (e2) (e2)))) -> ((op (e2) (e0)) = (e0)) -> (((op (e0) (e2)) = (e1))\/(((op (e1) (e2)) = (e1))\/(((op (e2) (e2)) = (e1))\/((op (e3) (e2)) = (e1))))) -> (~((op (e0) (e2)) = (e1))) -> (~((op (e1) (e2)) = (op (e1) (e3)))) -> (((op (e2) (e2)) = (e0))\/(((op (e2) (e2)) = (e1))\/(((op (e2) (e2)) = (e2))\/((op (e2) (e2)) = (e3))))) -> ((op (e0) (e2)) = (e3)) -> (~((op (e2) (e2)) = (op (e3) (e2)))) -> (~((op (e2) (e2)) = (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) (e3)) = (e1))\/(((op (e1) (e3)) = (e1))\/(((op (e2) (e3)) = (e1))\/((op (e3) (e3)) = (e1))))) -> (~((op (e0) (e3)) = (e1))) -> (~((op (e2) (e3)) = (e1))) -> ((op (e1) (e3)) = (e0)) -> (~((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 (e1) (e1)) = (op (e1) (e3)))) -> ((op (e1) (e1)) = (e2)) -> (~((op (e2) (e1)) = (op (e2) (e3)))) -> ((op (e2) (e1)) = (e2)) -> ((op (e3) (e0)) = (e2)) -> (~((op (e3) (e0)) = (op (e3) (e3)))) -> False). % 18.79/18.98 do 0 intro. intros zenon_H145 zenon_H1b1 zenon_H1a4 zenon_H52 zenon_H34 zenon_H139 zenon_H20d zenon_H124 zenon_H1c4 zenon_Ha9 zenon_H18f zenon_H173 zenon_H49 zenon_H4a zenon_H6a zenon_H133 zenon_H231 zenon_H255 zenon_H1f zenon_H10a zenon_H1ef zenon_H128 zenon_H57 zenon_H110 zenon_H1c7 zenon_H1ca zenon_H148 zenon_H71. % 18.79/18.98 apply (zenon_or_s _ _ zenon_H145); [ zenon_intro zenon_Hcd | zenon_intro zenon_H146 ]. % 18.79/18.98 apply (zenon_L817_); trivial. % 18.79/18.98 apply (zenon_or_s _ _ zenon_H146); [ zenon_intro zenon_Hd7 | zenon_intro zenon_H147 ]. % 18.79/18.98 apply (zenon_L283_); trivial. % 18.79/18.98 apply (zenon_or_s _ _ zenon_H147); [ zenon_intro zenon_H11d | zenon_intro zenon_Hf6 ]. % 18.79/18.98 apply (zenon_L224_); trivial. % 18.79/18.98 apply (zenon_L114_); trivial. % 18.79/18.98 (* end of lemma zenon_L818_ *) % 18.79/18.98 assert (zenon_L819_ : (((op (e0) (e3)) = (e0))\/(((op (e1) (e3)) = (e0))\/(((op (e2) (e3)) = (e0))\/((op (e3) (e3)) = (e0))))) -> (~((op (e0) (e1)) = (op (e0) (e3)))) -> (~((op (e3) (e0)) = (op (e3) (e3)))) -> ((op (e3) (e0)) = (e2)) -> ((op (e2) (e1)) = (e2)) -> (~((op (e2) (e1)) = (op (e2) (e3)))) -> ((op (e1) (e1)) = (e2)) -> (~((op (e1) (e1)) = (op (e1) (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 (e2) (e3)) = (e1))) -> (~((op (e0) (e3)) = (e1))) -> (((op (e0) (e3)) = (e1))\/(((op (e1) (e3)) = (e1))\/(((op (e2) (e3)) = (e1))\/((op (e3) (e3)) = (e1))))) -> (((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 (e2) (e2)) = (op (e3) (e2)))) -> ((op (e0) (e2)) = (e3)) -> (~((op (e1) (e2)) = (op (e1) (e3)))) -> (~((op (e0) (e2)) = (e1))) -> (((op (e0) (e2)) = (e1))\/(((op (e1) (e2)) = (e1))\/(((op (e2) (e2)) = (e1))\/((op (e3) (e2)) = (e1))))) -> ((op (e2) (e0)) = (e0)) -> (~((op (e3) (e1)) = (op (e3) (e2)))) -> (((op (e0) (e3)) = (e2))\/(((op (e1) (e3)) = (e2))\/(((op (e2) (e3)) = (e2))\/((op (e3) (e3)) = (e2))))) -> (~((op (e2) (e0)) = (op (e2) (e2)))) -> ((op (e2) (e0)) = (e3)) -> (~((op (e2) (e2)) = (e2))) -> (~((op (e1) (e2)) = (op (e2) (e2)))) -> ((op (e1) (e2)) = (e1)) -> (~((op (e2) (e2)) = (op (e2) (e3)))) -> (((op (e2) (e2)) = (e0))\/(((op (e2) (e2)) = (e1))\/(((op (e2) (e2)) = (e2))\/((op (e2) (e2)) = (e3))))) -> ((op (e3) (e1)) = (e0)) -> (~((op (e3) (e1)) = (op (e3) (e3)))) -> False). % 18.79/18.98 do 0 intro. intros zenon_H67 zenon_H54 zenon_H71 zenon_H148 zenon_H1ca zenon_H1c7 zenon_H110 zenon_H57 zenon_H128 zenon_H1ef zenon_H10a zenon_H255 zenon_H231 zenon_H133 zenon_H6a zenon_H4a zenon_H49 zenon_H18f zenon_Ha9 zenon_H124 zenon_H20d zenon_H139 zenon_H34 zenon_H1a4 zenon_H145 zenon_H52 zenon_H3b zenon_H173 zenon_H2b zenon_Hf0 zenon_H6d zenon_H1c4 zenon_H1b1 zenon_H130. % 18.79/18.98 apply (zenon_or_s _ _ zenon_H67); [ zenon_intro zenon_H1e | zenon_intro zenon_H68 ]. % 18.79/18.98 apply (zenon_L12_); trivial. % 18.79/18.98 apply (zenon_or_s _ _ zenon_H68); [ zenon_intro zenon_H1f | zenon_intro zenon_H69 ]. % 18.79/18.98 apply (zenon_L818_); trivial. % 18.79/18.98 apply (zenon_or_s _ _ zenon_H69); [ zenon_intro zenon_H37 | zenon_intro zenon_H60 ]. % 18.79/18.98 apply (zenon_L300_); trivial. % 18.79/18.98 apply (zenon_L244_); trivial. % 18.79/18.98 (* end of lemma zenon_L819_ *) % 18.79/18.98 assert (zenon_L820_ : (~((op (e3) (e1)) = (op (e3) (e3)))) -> ((op (e3) (e1)) = (e0)) -> (~((op (e2) (e2)) = (op (e2) (e3)))) -> (~((op (e1) (e2)) = (op (e2) (e2)))) -> ((op (e2) (e0)) = (e3)) -> (~((op (e2) (e0)) = (op (e2) (e2)))) -> (((op (e0) (e3)) = (e2))\/(((op (e1) (e3)) = (e2))\/(((op (e2) (e3)) = (e2))\/((op (e3) (e3)) = (e2))))) -> (~((op (e3) (e1)) = (op (e3) (e2)))) -> ((op (e2) (e0)) = (e0)) -> ((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) (e3)) = (e1))\/(((op (e1) (e3)) = (e1))\/(((op (e2) (e3)) = (e1))\/((op (e3) (e3)) = (e1))))) -> (~((op (e0) (e3)) = (e1))) -> (~((op (e2) (e3)) = (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 (e1) (e1)) = (op (e1) (e3)))) -> ((op (e1) (e1)) = (e2)) -> (~((op (e2) (e1)) = (op (e2) (e3)))) -> ((op (e2) (e1)) = (e2)) -> ((op (e3) (e0)) = (e2)) -> (~((op (e3) (e0)) = (op (e3) (e3)))) -> (~((op (e0) (e1)) = (op (e0) (e3)))) -> (((op (e0) (e3)) = (e0))\/(((op (e1) (e3)) = (e0))\/(((op (e2) (e3)) = (e0))\/((op (e3) (e3)) = (e0))))) -> (((op (e0) (e2)) = (e1))\/(((op (e1) (e2)) = (e1))\/(((op (e2) (e2)) = (e1))\/((op (e3) (e2)) = (e1))))) -> (~((op (e0) (e2)) = (e1))) -> (~((op (e1) (e2)) = (op (e1) (e3)))) -> (((op (e2) (e2)) = (e0))\/(((op (e2) (e2)) = (e1))\/(((op (e2) (e2)) = (e2))\/((op (e2) (e2)) = (e3))))) -> ((op (e0) (e2)) = (e3)) -> (~((op (e2) (e2)) = (op (e3) (e2)))) -> (~((op (e2) (e2)) = (e2))) -> ((op (e1) (e2)) = (e0)) -> False). % 18.79/18.98 do 0 intro. intros zenon_H130 zenon_H1b1 zenon_H6d zenon_H2b zenon_H3b zenon_H52 zenon_H145 zenon_H1a4 zenon_H34 zenon_H49 zenon_H4a zenon_H6a zenon_H133 zenon_H231 zenon_H255 zenon_H10a zenon_H1ef zenon_H128 zenon_H57 zenon_H110 zenon_H1c7 zenon_H1ca zenon_H148 zenon_H71 zenon_H54 zenon_H67 zenon_H139 zenon_H20d zenon_H124 zenon_H1c4 zenon_Ha9 zenon_H18f zenon_H173 zenon_H2a. % 18.79/18.98 apply (zenon_or_s _ _ zenon_H128); [ zenon_intro zenon_H9d | zenon_intro zenon_H129 ]. % 18.79/18.98 exact (zenon_H1ef zenon_H9d). % 18.79/18.98 apply (zenon_or_s _ _ zenon_H129); [ zenon_intro zenon_H10d | zenon_intro zenon_H12a ]. % 18.79/18.98 exact (zenon_H10a zenon_H10d). % 18.79/18.98 apply (zenon_or_s _ _ zenon_H12a); [ zenon_intro zenon_Hf0 | zenon_intro zenon_Hd6 ]. % 18.79/18.98 apply (zenon_L819_); trivial. % 18.79/18.98 apply (zenon_L720_); trivial. % 18.79/18.98 (* end of lemma zenon_L820_ *) % 18.79/18.98 assert (zenon_L821_ : (((op (e0) (e0)) = (e3))\/(((op (e1) (e0)) = (e3))\/(((op (e2) (e0)) = (e3))\/((op (e3) (e0)) = (e3))))) -> (~((e1) = (e3))) -> ((op (e0) (e0)) = (e1)) -> (~((op (e3) (e0)) = (op (e3) (e3)))) -> ((op (e2) (e1)) = (e2)) -> (~((op (e2) (e1)) = (op (e2) (e3)))) -> ((op (e1) (e1)) = (e2)) -> (~((op (e1) (e1)) = (op (e1) (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 (e2) (e3)) = (e1))) -> (~((op (e0) (e3)) = (e1))) -> (((op (e0) (e3)) = (e1))\/(((op (e1) (e3)) = (e1))\/(((op (e2) (e3)) = (e1))\/((op (e3) (e3)) = (e1))))) -> (((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 (e2) (e2)) = (e2))) -> (~((op (e2) (e2)) = (op (e3) (e2)))) -> ((op (e0) (e2)) = (e3)) -> (((op (e2) (e2)) = (e0))\/(((op (e2) (e2)) = (e1))\/(((op (e2) (e2)) = (e2))\/((op (e2) (e2)) = (e3))))) -> (~((op (e1) (e2)) = (op (e1) (e3)))) -> (~((op (e0) (e2)) = (e1))) -> (((op (e0) (e2)) = (e1))\/(((op (e1) (e2)) = (e1))\/(((op (e2) (e2)) = (e1))\/((op (e3) (e2)) = (e1))))) -> ((op (e2) (e0)) = (e0)) -> (~((op (e2) (e0)) = (op (e2) (e2)))) -> (~((op (e3) (e1)) = (op (e3) (e2)))) -> ((op (e3) (e1)) = (e0)) -> (((op (e0) (e3)) = (e2))\/(((op (e1) (e3)) = (e2))\/(((op (e2) (e3)) = (e2))\/((op (e3) (e3)) = (e2))))) -> (~((op (e3) (e1)) = (op (e3) (e3)))) -> (~((op (e2) (e2)) = (op (e2) (e3)))) -> (~((op (e1) (e2)) = (op (e2) (e2)))) -> (~((op (e0) (e1)) = (op (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) (e0)) = (e0))) -> (~((op (e1) (e0)) = (op (e1) (e1)))) -> (~((op (e3) (e2)) = (op (e3) (e3)))) -> (~((op (e2) (e0)) = (op (e2) (e3)))) -> (~((op (e3) (e0)) = (op (e3) (e2)))) -> (~((op (e1) (e1)) = (op (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 (e3) (e0)) = (e2)) -> (~((e2) = (e3))) -> False). % 18.79/18.99 do 0 intro. intros zenon_H1e0 zenon_H95 zenon_H7a zenon_H71 zenon_H1ca zenon_H1c7 zenon_H110 zenon_H57 zenon_H128 zenon_H1ef zenon_H10a zenon_H255 zenon_H231 zenon_H133 zenon_H6a zenon_H4a zenon_H49 zenon_H173 zenon_H18f zenon_Ha9 zenon_H1c4 zenon_H124 zenon_H20d zenon_H139 zenon_H34 zenon_H52 zenon_H1a4 zenon_H1b1 zenon_H145 zenon_H130 zenon_H6d zenon_H2b zenon_H54 zenon_H67 zenon_H3e zenon_H3f zenon_H45 zenon_H62 zenon_H5b zenon_H6f zenon_H4f zenon_H201 zenon_H22 zenon_H148 zenon_H12b. % 18.79/18.99 apply (zenon_or_s _ _ zenon_H1e0); [ zenon_intro zenon_H3a | zenon_intro zenon_H1e1 ]. % 18.79/18.99 apply (zenon_L35_); trivial. % 18.79/18.99 apply (zenon_or_s _ _ zenon_H1e1); [ zenon_intro zenon_H9e | zenon_intro zenon_H1e2 ]. % 18.79/18.99 apply (zenon_L107_); trivial. % 18.79/18.99 apply (zenon_or_s _ _ zenon_H1e2); [ zenon_intro zenon_H3b | zenon_intro zenon_H15e ]. % 18.79/18.99 apply (zenon_or_s _ _ zenon_H22); [ zenon_intro zenon_H27 | zenon_intro zenon_H26 ]. % 18.79/18.99 apply (zenon_L332_); trivial. % 18.79/18.99 apply (zenon_or_s _ _ zenon_H26); [ zenon_intro zenon_H29 | zenon_intro zenon_H28 ]. % 18.79/18.99 apply (zenon_L23_); trivial. % 18.79/18.99 apply (zenon_or_s _ _ zenon_H28); [ zenon_intro zenon_H2a | zenon_intro zenon_H1f ]. % 18.79/18.99 apply (zenon_L820_); trivial. % 18.79/18.99 apply (zenon_L818_); trivial. % 18.79/18.99 apply (zenon_L109_); trivial. % 18.79/18.99 (* end of lemma zenon_L821_ *) % 18.79/18.99 assert (zenon_L822_ : (((op (e3) (e0)) = (e1))\/(((op (e3) (e1)) = (e1))\/(((op (e3) (e2)) = (e1))\/((op (e3) (e3)) = (e1))))) -> (~((e1) = (e3))) -> ((op (e3) (e0)) = (e3)) -> (~((op (e3) (e1)) = (e1))) -> ((op (e1) (e2)) = (e0)) -> (~((op (e2) (e2)) = (e2))) -> (~((op (e2) (e2)) = (op (e3) (e2)))) -> ((op (e0) (e2)) = (e3)) -> (((op (e2) (e2)) = (e0))\/(((op (e2) (e2)) = (e1))\/(((op (e2) (e2)) = (e2))\/((op (e2) (e2)) = (e3))))) -> (((op (e0) (e3)) = (e2))\/(((op (e1) (e3)) = (e2))\/(((op (e2) (e3)) = (e2))\/((op (e3) (e3)) = (e2))))) -> ((op (e1) (e3)) = (e0)) -> (~((op (e1) (e1)) = (op (e1) (e3)))) -> ((op (e1) (e1)) = (e2)) -> (~((op (e2) (e1)) = (op (e2) (e3)))) -> ((op (e2) (e1)) = (e2)) -> ((op (e3) (e1)) = (e2)) -> (~((op (e3) (e1)) = (op (e3) (e3)))) -> False). % 18.79/18.99 do 0 intro. intros zenon_He8 zenon_H95 zenon_H15e zenon_H250 zenon_H2a zenon_H173 zenon_H18f zenon_Ha9 zenon_H1c4 zenon_H145 zenon_H1f zenon_H57 zenon_H110 zenon_H1c7 zenon_H1ca zenon_H14d zenon_H130. % 18.79/18.99 apply (zenon_or_s _ _ zenon_He8); [ zenon_intro zenon_Hac | zenon_intro zenon_Heb ]. % 18.79/18.99 apply (zenon_L252_); trivial. % 18.79/18.99 apply (zenon_or_s _ _ zenon_Heb); [ zenon_intro zenon_Hae | zenon_intro zenon_Hec ]. % 18.79/18.99 exact (zenon_H250 zenon_Hae). % 18.79/18.99 apply (zenon_or_s _ _ zenon_Hec); [ zenon_intro zenon_Hba | zenon_intro zenon_Hc4 ]. % 18.79/18.99 apply (zenon_L186_); trivial. % 18.79/18.99 apply (zenon_L788_); trivial. % 18.79/18.99 (* end of lemma zenon_L822_ *) % 18.79/18.99 assert (zenon_L823_ : (((op (e3) (e0)) = (e2))\/(((op (e3) (e1)) = (e2))\/(((op (e3) (e2)) = (e2))\/((op (e3) (e3)) = (e2))))) -> (~((e2) = (e3))) -> (((op (e1) (e0)) = (e0))\/(((op (e1) (e1)) = (e0))\/(((op (e1) (e2)) = (e0))\/((op (e1) (e3)) = (e0))))) -> (~((op (e1) (e0)) = (op (e2) (e0)))) -> (~((op (e1) (e1)) = (op (e1) (e2)))) -> (~((op (e3) (e0)) = (op (e3) (e2)))) -> (~((op (e2) (e0)) = (op (e2) (e3)))) -> (~((op (e3) (e2)) = (op (e3) (e3)))) -> (~((op (e1) (e0)) = (op (e1) (e1)))) -> (~((op (e0) (e0)) = (e0))) -> (((op (e0) (e0)) = (e0))\/(((op (e1) (e0)) = (e0))\/(((op (e2) (e0)) = (e0))\/((op (e3) (e0)) = (e0))))) -> (((op (e0) (e3)) = (e0))\/(((op (e1) (e3)) = (e0))\/(((op (e2) (e3)) = (e0))\/((op (e3) (e3)) = (e0))))) -> (~((op (e0) (e1)) = (op (e0) (e3)))) -> (~((op (e1) (e2)) = (op (e2) (e2)))) -> (~((op (e2) (e2)) = (op (e2) (e3)))) -> ((op (e3) (e1)) = (e0)) -> (~((op (e3) (e1)) = (op (e3) (e2)))) -> (~((op (e2) (e0)) = (op (e2) (e2)))) -> ((op (e2) (e0)) = (e0)) -> (((op (e0) (e2)) = (e1))\/(((op (e1) (e2)) = (e1))\/(((op (e2) (e2)) = (e1))\/((op (e3) (e2)) = (e1))))) -> (~((op (e0) (e2)) = (e1))) -> (~((op (e1) (e2)) = (op (e1) (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 (e0) (e3)) = (e1))\/(((op (e1) (e3)) = (e1))\/(((op (e2) (e3)) = (e1))\/((op (e3) (e3)) = (e1))))) -> (~((op (e2) (e3)) = (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)) = (op (e3) (e3)))) -> ((op (e0) (e0)) = (e1)) -> (((op (e0) (e0)) = (e3))\/(((op (e1) (e0)) = (e3))\/(((op (e2) (e0)) = (e3))\/((op (e3) (e0)) = (e3))))) -> (~((op (e3) (e1)) = (op (e3) (e3)))) -> ((op (e2) (e1)) = (e2)) -> (~((op (e2) (e1)) = (op (e2) (e3)))) -> ((op (e1) (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) (e2)) = (e0))\/(((op (e2) (e2)) = (e1))\/(((op (e2) (e2)) = (e2))\/((op (e2) (e2)) = (e3))))) -> ((op (e0) (e2)) = (e3)) -> (~((op (e2) (e2)) = (op (e3) (e2)))) -> (~((op (e2) (e2)) = (e2))) -> ((op (e1) (e2)) = (e0)) -> (~((op (e3) (e1)) = (e1))) -> ((op (e3) (e0)) = (e3)) -> (~((e1) = (e3))) -> (((op (e3) (e0)) = (e1))\/(((op (e3) (e1)) = (e1))\/(((op (e3) (e2)) = (e1))\/((op (e3) (e3)) = (e1))))) -> ((op (e0) (e2)) = (e2)) -> (~((op (e0) (e2)) = (op (e3) (e2)))) -> (((op (e0) (e3)) = (e0))\/(((op (e0) (e3)) = (e1))\/(((op (e0) (e3)) = (e2))\/((op (e0) (e3)) = (e3))))) -> ((op (e1) (e3)) = (e0)) -> (~((op (e0) (e3)) = (op (e1) (e3)))) -> (~((op (e0) (e3)) = (e1))) -> (~((op (e0) (e3)) = (op (e3) (e3)))) -> (~((op (e0) (e3)) = (op (e2) (e3)))) -> ((op (e2) (e3)) = (e3)) -> False). % 18.79/18.99 do 0 intro. intros zenon_H153 zenon_H12b zenon_H22 zenon_H201 zenon_H4f zenon_H6f zenon_H5b zenon_H62 zenon_H45 zenon_H3f zenon_H3e zenon_H67 zenon_H54 zenon_H2b zenon_H6d zenon_H1b1 zenon_H1a4 zenon_H52 zenon_H34 zenon_H139 zenon_H20d zenon_H124 zenon_H49 zenon_H4a zenon_H6a zenon_H133 zenon_H255 zenon_H10a zenon_H1ef zenon_H128 zenon_H71 zenon_H7a zenon_H1e0 zenon_H130 zenon_H1ca zenon_H1c7 zenon_H110 zenon_H57 zenon_H145 zenon_H1c4 zenon_Ha9 zenon_H18f zenon_H173 zenon_H2a zenon_H250 zenon_H15e zenon_H95 zenon_He8 zenon_H150 zenon_H14f zenon_He4 zenon_H1f zenon_H1d zenon_H231 zenon_Hc2 zenon_He2 zenon_Hdd. % 18.79/18.99 apply (zenon_or_s _ _ zenon_H153); [ zenon_intro zenon_H148 | zenon_intro zenon_H154 ]. % 18.79/18.99 apply (zenon_L821_); trivial. % 18.79/18.99 apply (zenon_or_s _ _ zenon_H154); [ zenon_intro zenon_H14d | zenon_intro zenon_H155 ]. % 18.79/18.99 apply (zenon_L822_); trivial. % 18.79/18.99 apply (zenon_or_s _ _ zenon_H155); [ zenon_intro zenon_H151 | zenon_intro zenon_Hf6 ]. % 18.79/18.99 apply (zenon_L104_); trivial. % 18.79/18.99 apply (zenon_L722_); trivial. % 18.79/18.99 (* end of lemma zenon_L823_ *) % 18.79/18.99 assert (zenon_L824_ : ((op (e2) (e3)) = (e3)) -> (~((op (e0) (e3)) = (op (e2) (e3)))) -> (~((op (e0) (e3)) = (op (e3) (e3)))) -> (~((op (e0) (e3)) = (e1))) -> (~((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)) = (op (e3) (e2)))) -> ((op (e0) (e2)) = (e2)) -> (((op (e3) (e0)) = (e1))\/(((op (e3) (e1)) = (e1))\/(((op (e3) (e2)) = (e1))\/((op (e3) (e3)) = (e1))))) -> (~((e1) = (e3))) -> ((op (e3) (e0)) = (e3)) -> (~((op (e3) (e1)) = (e1))) -> ((op (e1) (e2)) = (e0)) -> (~((op (e2) (e2)) = (e2))) -> (~((op (e2) (e2)) = (op (e3) (e2)))) -> ((op (e0) (e2)) = (e3)) -> (((op (e2) (e2)) = (e0))\/(((op (e2) (e2)) = (e1))\/(((op (e2) (e2)) = (e2))\/((op (e2) (e2)) = (e3))))) -> (((op (e0) (e3)) = (e2))\/(((op (e1) (e3)) = (e2))\/(((op (e2) (e3)) = (e2))\/((op (e3) (e3)) = (e2))))) -> (~((op (e1) (e1)) = (op (e1) (e3)))) -> ((op (e1) (e1)) = (e2)) -> (~((op (e2) (e1)) = (op (e2) (e3)))) -> ((op (e2) (e1)) = (e2)) -> (((op (e0) (e0)) = (e3))\/(((op (e1) (e0)) = (e3))\/(((op (e2) (e0)) = (e3))\/((op (e3) (e0)) = (e3))))) -> ((op (e0) (e0)) = (e1)) -> (~((op (e3) (e0)) = (op (e3) (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 (e2) (e3)) = (e1))) -> (((op (e0) (e3)) = (e1))\/(((op (e1) (e3)) = (e1))\/(((op (e2) (e3)) = (e1))\/((op (e3) (e3)) = (e1))))) -> (((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)) = (op (e1) (e3)))) -> (~((op (e0) (e2)) = (e1))) -> (((op (e0) (e2)) = (e1))\/(((op (e1) (e2)) = (e1))\/(((op (e2) (e2)) = (e1))\/((op (e3) (e2)) = (e1))))) -> (~((op (e2) (e0)) = (op (e2) (e2)))) -> (~((op (e3) (e1)) = (op (e3) (e2)))) -> (~((op (e2) (e2)) = (op (e2) (e3)))) -> (~((op (e1) (e2)) = (op (e2) (e2)))) -> (~((op (e0) (e1)) = (op (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) (e0)) = (e0))) -> (~((op (e1) (e0)) = (op (e1) (e1)))) -> (~((op (e3) (e2)) = (op (e3) (e3)))) -> (~((op (e3) (e0)) = (op (e3) (e2)))) -> (~((op (e1) (e1)) = (op (e1) (e2)))) -> (~((op (e1) (e0)) = (op (e2) (e0)))) -> (((op (e1) (e0)) = (e0))\/(((op (e1) (e1)) = (e0))\/(((op (e1) (e2)) = (e0))\/((op (e1) (e3)) = (e0))))) -> (~((e2) = (e3))) -> (((op (e3) (e0)) = (e2))\/(((op (e3) (e1)) = (e2))\/(((op (e3) (e2)) = (e2))\/((op (e3) (e3)) = (e2))))) -> (~((op (e2) (e0)) = (op (e2) (e3)))) -> ((op (e2) (e0)) = (e0)) -> ((op (e3) (e1)) = (e0)) -> (~((op (e3) (e1)) = (op (e3) (e3)))) -> False). % 18.79/18.99 do 0 intro. intros zenon_Hdd zenon_He2 zenon_Hc2 zenon_H231 zenon_H1d zenon_He4 zenon_H14f zenon_H150 zenon_He8 zenon_H95 zenon_H15e zenon_H250 zenon_H2a zenon_H173 zenon_H18f zenon_Ha9 zenon_H1c4 zenon_H145 zenon_H57 zenon_H110 zenon_H1c7 zenon_H1ca zenon_H1e0 zenon_H7a zenon_H71 zenon_H128 zenon_H1ef zenon_H10a zenon_H255 zenon_H133 zenon_H6a zenon_H4a zenon_H49 zenon_H124 zenon_H20d zenon_H139 zenon_H52 zenon_H1a4 zenon_H6d zenon_H2b zenon_H54 zenon_H67 zenon_H3e zenon_H3f zenon_H45 zenon_H62 zenon_H6f zenon_H4f zenon_H201 zenon_H22 zenon_H12b zenon_H153 zenon_H5b zenon_H34 zenon_H1b1 zenon_H130. % 18.79/18.99 apply (zenon_or_s _ _ zenon_H67); [ zenon_intro zenon_H1e | zenon_intro zenon_H68 ]. % 18.79/18.99 apply (zenon_L12_); trivial. % 18.79/18.99 apply (zenon_or_s _ _ zenon_H68); [ zenon_intro zenon_H1f | zenon_intro zenon_H69 ]. % 18.79/18.99 apply (zenon_L823_); trivial. % 18.79/18.99 apply (zenon_or_s _ _ zenon_H69); [ zenon_intro zenon_H37 | zenon_intro zenon_H60 ]. % 18.79/18.99 apply (zenon_L14_); trivial. % 18.79/18.99 apply (zenon_L244_); trivial. % 18.79/18.99 (* end of lemma zenon_L824_ *) % 18.79/18.99 assert (zenon_L825_ : (((op (e3) (e0)) = (e1))\/(((op (e3) (e1)) = (e1))\/(((op (e3) (e2)) = (e1))\/((op (e3) (e3)) = (e1))))) -> (~((e1) = (e3))) -> (~((op (e3) (e1)) = (e1))) -> (~((op (e3) (e2)) = (e1))) -> (((op (e3) (e0)) = (e2))\/(((op (e3) (e1)) = (e2))\/(((op (e3) (e2)) = (e2))\/((op (e3) (e3)) = (e2))))) -> (~((e2) = (e3))) -> ((op (e3) (e0)) = (e3)) -> (~((op (e3) (e1)) = (op (e3) (e3)))) -> ((op (e2) (e1)) = (e2)) -> (~((op (e2) (e1)) = (op (e2) (e3)))) -> ((op (e1) (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 (e0) (e2)) = (e2)) -> (~((op (e0) (e2)) = (op (e3) (e2)))) -> (((op (e0) (e3)) = (e3))\/(((op (e1) (e3)) = (e3))\/(((op (e2) (e3)) = (e3))\/((op (e3) (e3)) = (e3))))) -> (~((op (e2) (e3)) = (op (e3) (e3)))) -> ((op (e2) (e0)) = (e0)) -> (~((op (e2) (e0)) = (op (e2) (e3)))) -> (((op (e2) (e3)) = (e0))\/(((op (e2) (e3)) = (e1))\/(((op (e2) (e3)) = (e2))\/((op (e2) (e3)) = (e3))))) -> (~((op (e0) (e3)) = (op (e2) (e3)))) -> (~((op (e0) (e3)) = (op (e3) (e3)))) -> (~((op (e0) (e3)) = (e1))) -> (~((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 (e3) (e3)) = (e3))) -> False). % 18.79/18.99 do 0 intro. intros zenon_He8 zenon_H95 zenon_H250 zenon_H251 zenon_H153 zenon_H12b zenon_H15e zenon_H130 zenon_H1ca zenon_H1c7 zenon_H110 zenon_H57 zenon_H145 zenon_H150 zenon_H14f zenon_H136 zenon_Hf3 zenon_H34 zenon_H5b zenon_H11f zenon_He2 zenon_Hc2 zenon_H231 zenon_H1d zenon_H1f zenon_He4 zenon_H102. % 18.79/18.99 apply (zenon_or_s _ _ zenon_He8); [ zenon_intro zenon_Hac | zenon_intro zenon_Heb ]. % 18.79/18.99 apply (zenon_L252_); trivial. % 18.79/18.99 apply (zenon_or_s _ _ zenon_Heb); [ zenon_intro zenon_Hae | zenon_intro zenon_Hec ]. % 18.79/18.99 exact (zenon_H250 zenon_Hae). % 18.79/18.99 apply (zenon_or_s _ _ zenon_Hec); [ zenon_intro zenon_Hba | zenon_intro zenon_Hc4 ]. % 18.79/18.99 exact (zenon_H251 zenon_Hba). % 18.79/18.99 apply (zenon_or_s _ _ zenon_H153); [ zenon_intro zenon_H148 | zenon_intro zenon_H154 ]. % 18.79/18.99 apply (zenon_L109_); trivial. % 18.79/18.99 apply (zenon_or_s _ _ zenon_H154); [ zenon_intro zenon_H14d | zenon_intro zenon_H155 ]. % 18.79/18.99 apply (zenon_L788_); trivial. % 18.79/18.99 apply (zenon_or_s _ _ zenon_H155); [ zenon_intro zenon_H151 | zenon_intro zenon_Hf6 ]. % 18.79/18.99 apply (zenon_L104_); trivial. % 18.79/18.99 apply (zenon_L790_); trivial. % 18.79/18.99 (* end of lemma zenon_L825_ *) % 18.79/18.99 assert (zenon_L826_ : (~((op (e1) (e3)) = (e1))) -> (((op (e2) (e0)) = (e3))\/(((op (e2) (e1)) = (e3))\/(((op (e2) (e2)) = (e3))\/((op (e2) (e3)) = (e3))))) -> (~((e0) = (e2))) -> (~((op (e0) (e0)) = (op (e0) (e3)))) -> (((op (e0) (e0)) = (e2))\/(((op (e1) (e0)) = (e2))\/(((op (e2) (e0)) = (e2))\/((op (e3) (e0)) = (e2))))) -> (~((e0) = (e3))) -> (((op (e0) (e0)) = (e1))\/(((op (e0) (e1)) = (e1))\/(((op (e0) (e2)) = (e1))\/((op (e0) (e3)) = (e1))))) -> (~((e1) = (e2))) -> (~((op (e0) (e1)) = (e1))) -> ((~((op (e0) (e3)) = (e1)))\/((op (e0) (e1)) = (e3))) -> ((~((op (e1) (e2)) = (e1)))\/((op (e1) (e1)) = (e2))) -> (~((op (e0) (e1)) = (op (e1) (e1)))) -> ((~((op (e2) (e0)) = (e1)))\/((op (e2) (e1)) = (e0))) -> ((~((op (e3) (e0)) = (e1)))\/((op (e3) (e1)) = (e0))) -> (((op (e0) (e0)) = (e1))\/(((op (e1) (e0)) = (e1))\/(((op (e2) (e0)) = (e1))\/((op (e3) (e0)) = (e1))))) -> (~((op (e0) (e0)) = (op (e0) (e2)))) -> (~((op (e0) (e1)) = (op (e3) (e1)))) -> ((~((op (e3) (e2)) = (e1)))\/((op (e3) (e1)) = (e2))) -> ((~((op (e2) (e2)) = (e1)))\/((op (e2) (e1)) = (e2))) -> ((~((op (e1) (e3)) = (e1)))\/((op (e1) (e1)) = (e3))) -> (~((e0) = (e1))) -> (((op (e0) (e0)) = (e3))\/(((op (e0) (e1)) = (e3))\/(((op (e0) (e2)) = (e3))\/((op (e0) (e3)) = (e3))))) -> ((~((op (e1) (e0)) = (e1)))\/((op (e1) (e1)) = (e0))) -> (((op (e0) (e0)) = (e2))\/(((op (e0) (e1)) = (e2))\/(((op (e0) (e2)) = (e2))\/((op (e0) (e3)) = (e2))))) -> (((op (e3) (e2)) = (e0))\/(((op (e3) (e2)) = (e1))\/(((op (e3) (e2)) = (e2))\/((op (e3) (e2)) = (e3))))) -> (((op (e3) (e0)) = (e0))\/(((op (e3) (e1)) = (e0))\/(((op (e3) (e2)) = (e0))\/((op (e3) (e3)) = (e0))))) -> (~((op (e2) (e0)) = (op (e2) (e1)))) -> (~((op (e2) (e0)) = (e1))) -> (((op (e2) (e0)) = (e0))\/(((op (e2) (e0)) = (e1))\/(((op (e2) (e0)) = (e2))\/((op (e2) (e0)) = (e3))))) -> (~((op (e0) (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) (e0)) = (op (e2) (e0)))) -> (~((op (e1) (e1)) = (op (e1) (e2)))) -> (~((op (e3) (e0)) = (op (e3) (e2)))) -> (~((op (e3) (e2)) = (op (e3) (e3)))) -> (~((op (e1) (e0)) = (op (e1) (e1)))) -> (~((op (e0) (e0)) = (e0))) -> (((op (e0) (e0)) = (e0))\/(((op (e1) (e0)) = (e0))\/(((op (e2) (e0)) = (e0))\/((op (e3) (e0)) = (e0))))) -> (((op (e0) (e3)) = (e0))\/(((op (e1) (e3)) = (e0))\/(((op (e2) (e3)) = (e0))\/((op (e3) (e3)) = (e0))))) -> (~((op (e0) (e1)) = (op (e0) (e3)))) -> (~((op (e1) (e2)) = (op (e2) (e2)))) -> (~((op (e2) (e2)) = (op (e2) (e3)))) -> (~((op (e3) (e1)) = (op (e3) (e2)))) -> (~((op (e2) (e0)) = (op (e2) (e2)))) -> (((op (e0) (e2)) = (e1))\/(((op (e1) (e2)) = (e1))\/(((op (e2) (e2)) = (e1))\/((op (e3) (e2)) = (e1))))) -> (~((op (e0) (e2)) = (e1))) -> (~((op (e1) (e2)) = (op (e1) (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 (e0) (e3)) = (e1))\/(((op (e1) (e3)) = (e1))\/(((op (e2) (e3)) = (e1))\/((op (e3) (e3)) = (e1))))) -> (~((op (e2) (e3)) = (e1))) -> (~((op (e1) (e1)) = (e1))) -> (((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 (e2) (e2)) = (e0))\/(((op (e2) (e2)) = (e1))\/(((op (e2) (e2)) = (e2))\/((op (e2) (e2)) = (e3))))) -> ((op (e0) (e2)) = (e3)) -> (~((op (e2) (e2)) = (op (e3) (e2)))) -> (~((op (e2) (e2)) = (e2))) -> (~((op (e3) (e0)) = (op (e3) (e3)))) -> ((op (e0) (e0)) = (e1)) -> (~((op (e1) (e0)) = (e1))) -> (~((op (e1) (e0)) = (op (e1) (e2)))) -> (((op (e1) (e0)) = (e0))\/(((op (e1) (e0)) = (e1))\/(((op (e1) (e0)) = (e2))\/((op (e1) (e0)) = (e3))))) -> (~((op (e3) (e0)) = (e1))) -> (~((op (e1) (e2)) = (op (e3) (e2)))) -> ((op (e2) (e1)) = (e1)) -> (~((op (e1) (e3)) = (op (e2) (e3)))) -> ((op (e1) (e0)) = (e2)) -> (~((op (e1) (e0)) = (op (e1) (e3)))) -> (((op (e1) (e3)) = (e0))\/(((op (e1) (e3)) = (e1))\/(((op (e1) (e3)) = (e2))\/((op (e1) (e3)) = (e3))))) -> (~((op (e1) (e3)) = (op (e3) (e3)))) -> (((op (e3) (e0)) = (e1))\/(((op (e3) (e1)) = (e1))\/(((op (e3) (e2)) = (e1))\/((op (e3) (e3)) = (e1))))) -> (~((e1) = (e3))) -> (~((op (e3) (e1)) = (e1))) -> (~((op (e3) (e2)) = (e1))) -> (((op (e3) (e0)) = (e2))\/(((op (e3) (e1)) = (e2))\/(((op (e3) (e2)) = (e2))\/((op (e3) (e3)) = (e2))))) -> (~((e2) = (e3))) -> (~((op (e3) (e1)) = (op (e3) (e3)))) -> ((op (e2) (e1)) = (e2)) -> (~((op (e2) (e1)) = (op (e2) (e3)))) -> ((op (e1) (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 (e0) (e2)) = (e2)) -> (~((op (e0) (e2)) = (op (e3) (e2)))) -> (((op (e0) (e3)) = (e3))\/(((op (e1) (e3)) = (e3))\/(((op (e2) (e3)) = (e3))\/((op (e3) (e3)) = (e3))))) -> (~((op (e2) (e3)) = (op (e3) (e3)))) -> ((op (e2) (e0)) = (e0)) -> (~((op (e2) (e0)) = (op (e2) (e3)))) -> (((op (e2) (e3)) = (e0))\/(((op (e2) (e3)) = (e1))\/(((op (e2) (e3)) = (e2))\/((op (e2) (e3)) = (e3))))) -> (~((op (e0) (e3)) = (op (e2) (e3)))) -> (~((op (e0) (e3)) = (op (e3) (e3)))) -> (~((op (e0) (e3)) = (e1))) -> (~((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)) = (e3))) -> False). % 18.79/18.99 do 0 intro. intros zenon_H24e zenon_He7 zenon_H149 zenon_H189 zenon_H1fe zenon_H9a zenon_H22d zenon_H7c zenon_Ha4 zenon_H25c zenon_H256 zenon_H10e zenon_H257 zenon_H254 zenon_H235 zenon_H13c zenon_H210 zenon_H252 zenon_H253 zenon_H258 zenon_Ha1 zenon_H168 zenon_H25d zenon_H183 zenon_H191 zenon_H1ac zenon_H1f0 zenon_H1db zenon_H259 zenon_H17e zenon_H17b zenon_H2f zenon_H22 zenon_H201 zenon_H4f zenon_H6f zenon_H62 zenon_H45 zenon_H3f zenon_H3e zenon_H67 zenon_H54 zenon_H2b zenon_H6d zenon_H1a4 zenon_H52 zenon_H139 zenon_H20d zenon_H124 zenon_H49 zenon_H4a zenon_H6a zenon_H133 zenon_H255 zenon_H10a zenon_H128 zenon_H1e0 zenon_H1c4 zenon_Ha9 zenon_H18f zenon_H173 zenon_H71 zenon_H7a zenon_H1ef zenon_H24a zenon_H25e zenon_Had zenon_H115 zenon_Ha5 zenon_Hdb zenon_H86 zenon_Hd8 zenon_Hdf zenon_Hd5 zenon_He8 zenon_H95 zenon_H250 zenon_H251 zenon_H153 zenon_H12b zenon_H130 zenon_H1ca zenon_H1c7 zenon_H110 zenon_H57 zenon_H145 zenon_H150 zenon_H14f zenon_H136 zenon_Hf3 zenon_H34 zenon_H5b zenon_H11f zenon_He2 zenon_Hc2 zenon_H231 zenon_H1d zenon_He4 zenon_H102. % 18.79/18.99 apply (zenon_or_s _ _ zenon_H1e0); [ zenon_intro zenon_H3a | zenon_intro zenon_H1e1 ]. % 18.79/18.99 apply (zenon_L35_); trivial. % 18.79/18.99 apply (zenon_or_s _ _ zenon_H1e1); [ zenon_intro zenon_H9e | zenon_intro zenon_H1e2 ]. % 18.79/18.99 apply (zenon_or_s _ _ zenon_H22); [ zenon_intro zenon_H27 | zenon_intro zenon_H26 ]. % 18.79/18.99 apply (zenon_L332_); trivial. % 18.79/18.99 apply (zenon_or_s _ _ zenon_H26); [ zenon_intro zenon_H29 | zenon_intro zenon_H28 ]. % 18.79/18.99 apply (zenon_L17_); trivial. % 18.79/18.99 apply (zenon_or_s _ _ zenon_H28); [ zenon_intro zenon_H2a | zenon_intro zenon_H1f ]. % 18.79/18.99 apply (zenon_or_s _ _ zenon_H128); [ zenon_intro zenon_H9d | zenon_intro zenon_H129 ]. % 18.79/18.99 exact (zenon_H1ef zenon_H9d). % 18.79/18.99 apply (zenon_or_s _ _ zenon_H129); [ zenon_intro zenon_H10d | zenon_intro zenon_H12a ]. % 18.79/18.99 exact (zenon_H10a zenon_H10d). % 18.79/18.99 apply (zenon_or_s _ _ zenon_H12a); [ zenon_intro zenon_Hf0 | zenon_intro zenon_Hd6 ]. % 18.79/18.99 apply (zenon_or_s _ _ zenon_H1ac); [ zenon_intro zenon_H44 | zenon_intro zenon_H1af ]. % 18.79/18.99 apply (zenon_L730_); trivial. % 18.79/18.99 apply (zenon_or_s _ _ zenon_H1af); [ zenon_intro zenon_H1b1 | zenon_intro zenon_H1b0 ]. % 18.79/18.99 apply (zenon_L792_); trivial. % 18.79/18.99 apply (zenon_or_s _ _ zenon_H1b0); [ zenon_intro zenon_H61 | zenon_intro zenon_H60 ]. % 18.79/18.99 apply (zenon_L176_); trivial. % 18.79/18.99 apply (zenon_L799_); trivial. % 18.79/18.99 exact (zenon_H24e zenon_Hd6). % 18.79/18.99 apply (zenon_L801_); trivial. % 18.79/18.99 apply (zenon_or_s _ _ zenon_H1e2); [ zenon_intro zenon_H3b | zenon_intro zenon_H15e ]. % 18.79/18.99 apply (zenon_L33_); trivial. % 18.79/18.99 apply (zenon_or_s _ _ zenon_H22); [ zenon_intro zenon_H27 | zenon_intro zenon_H26 ]. % 18.79/18.99 apply (zenon_L257_); trivial. % 18.79/18.99 apply (zenon_or_s _ _ zenon_H26); [ zenon_intro zenon_H29 | zenon_intro zenon_H28 ]. % 18.79/18.99 apply (zenon_L354_); trivial. % 18.79/18.99 apply (zenon_or_s _ _ zenon_H28); [ zenon_intro zenon_H2a | zenon_intro zenon_H1f ]. % 18.79/18.99 apply (zenon_or_s _ _ zenon_H128); [ zenon_intro zenon_H9d | zenon_intro zenon_H129 ]. % 18.79/18.99 exact (zenon_H1ef zenon_H9d). % 18.79/18.99 apply (zenon_or_s _ _ zenon_H129); [ zenon_intro zenon_H10d | zenon_intro zenon_H12a ]. % 18.79/18.99 exact (zenon_H10a zenon_H10d). % 18.79/18.99 apply (zenon_or_s _ _ zenon_H12a); [ zenon_intro zenon_Hf0 | zenon_intro zenon_Hd6 ]. % 18.79/18.99 apply (zenon_or_s _ _ zenon_He7); [ zenon_intro zenon_H3b | zenon_intro zenon_He9 ]. % 18.79/18.99 apply (zenon_L33_); trivial. % 18.79/18.99 apply (zenon_or_s _ _ zenon_He9); [ zenon_intro zenon_Ha6 | zenon_intro zenon_Hea ]. % 18.79/18.99 apply (zenon_L814_); trivial. % 18.79/18.99 apply (zenon_or_s _ _ zenon_Hea); [ zenon_intro zenon_Haa | zenon_intro zenon_Hdd ]. % 18.79/18.99 apply (zenon_L181_); trivial. % 18.79/18.99 apply (zenon_or_s _ _ zenon_H1ac); [ zenon_intro zenon_H44 | zenon_intro zenon_H1af ]. % 18.79/18.99 apply (zenon_L730_); trivial. % 18.79/18.99 apply (zenon_or_s _ _ zenon_H1af); [ zenon_intro zenon_H1b1 | zenon_intro zenon_H1b0 ]. % 18.79/18.99 apply (zenon_L824_); trivial. % 18.79/18.99 apply (zenon_or_s _ _ zenon_H1b0); [ zenon_intro zenon_H61 | zenon_intro zenon_H60 ]. % 18.79/18.99 apply (zenon_L176_); trivial. % 18.79/18.99 apply (zenon_L799_); trivial. % 18.79/18.99 exact (zenon_H24e zenon_Hd6). % 18.79/18.99 apply (zenon_L825_); trivial. % 18.79/18.99 (* end of lemma zenon_L826_ *) % 18.79/18.99 assert (zenon_L827_ : (((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)) = (e1))) -> ((op (e1) (e2)) = (e1)) -> (~((op (e1) (e2)) = (op (e1) (e3)))) -> (((op (e0) (e3)) = (e1))\/(((op (e1) (e3)) = (e1))\/(((op (e2) (e3)) = (e1))\/((op (e3) (e3)) = (e1))))) -> (~((op (e3) (e1)) = (e1))) -> (~((op (e3) (e2)) = (e1))) -> (((op (e0) (e3)) = (e0))\/(((op (e0) (e3)) = (e1))\/(((op (e0) (e3)) = (e2))\/((op (e0) (e3)) = (e3))))) -> (~((op (e0) (e3)) = (e1))) -> ((op (e1) (e3)) = (e0)) -> (~((op (e0) (e3)) = (op (e1) (e3)))) -> ((op (e1) (e3)) = (e3)) -> False). % 18.79/18.99 do 0 intro. intros zenon_He8 zenon_H71 zenon_H255 zenon_Hf0 zenon_H124 zenon_H133 zenon_H250 zenon_H251 zenon_He4 zenon_H231 zenon_H1f zenon_H1d zenon_Hdc. % 18.79/18.99 apply (zenon_or_s _ _ zenon_He8); [ zenon_intro zenon_Hac | zenon_intro zenon_Heb ]. % 18.79/18.99 apply (zenon_L787_); trivial. % 18.79/18.99 apply (zenon_or_s _ _ zenon_Heb); [ zenon_intro zenon_Hae | zenon_intro zenon_Hec ]. % 18.79/18.99 exact (zenon_H250 zenon_Hae). % 18.79/18.99 apply (zenon_or_s _ _ zenon_Hec); [ zenon_intro zenon_Hba | zenon_intro zenon_Hc4 ]. % 18.79/18.99 exact (zenon_H251 zenon_Hba). % 18.79/18.99 apply (zenon_L789_); trivial. % 18.79/18.99 (* end of lemma zenon_L827_ *) % 18.79/18.99 assert (zenon_L828_ : (((op (e1) (e0)) = (e3))\/(((op (e1) (e1)) = (e3))\/(((op (e1) (e2)) = (e3))\/((op (e1) (e3)) = (e3))))) -> ((op (e0) (e0)) = (e1)) -> ((op (e3) (e0)) = (e2)) -> (~((e2) = (e3))) -> ((op (e1) (e1)) = (e2)) -> (~((e1) = (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) (e3)) = (e1))) -> ((op (e1) (e2)) = (e1)) -> (~((op (e1) (e2)) = (op (e1) (e3)))) -> (((op (e0) (e3)) = (e1))\/(((op (e1) (e3)) = (e1))\/(((op (e2) (e3)) = (e1))\/((op (e3) (e3)) = (e1))))) -> (~((op (e3) (e1)) = (e1))) -> (~((op (e3) (e2)) = (e1))) -> (((op (e0) (e3)) = (e0))\/(((op (e0) (e3)) = (e1))\/(((op (e0) (e3)) = (e2))\/((op (e0) (e3)) = (e3))))) -> (~((op (e0) (e3)) = (e1))) -> ((op (e1) (e3)) = (e0)) -> (~((op (e0) (e3)) = (op (e1) (e3)))) -> False). % 18.79/18.99 do 0 intro. intros zenon_H16f zenon_H7a zenon_H148 zenon_H12b zenon_H110 zenon_H95 zenon_He8 zenon_H71 zenon_H255 zenon_Hf0 zenon_H124 zenon_H133 zenon_H250 zenon_H251 zenon_He4 zenon_H231 zenon_H1f zenon_H1d. % 18.79/18.99 apply (zenon_or_s _ _ zenon_H16f); [ zenon_intro zenon_H9e | zenon_intro zenon_H170 ]. % 18.79/18.99 apply (zenon_L107_); trivial. % 18.79/18.99 apply (zenon_or_s _ _ zenon_H170); [ zenon_intro zenon_H13f | zenon_intro zenon_H171 ]. % 18.79/18.99 apply (zenon_L166_); trivial. % 18.79/18.99 apply (zenon_or_s _ _ zenon_H171); [ zenon_intro zenon_H16c | zenon_intro zenon_Hdc ]. % 18.79/18.99 apply (zenon_L167_); trivial. % 18.79/18.99 apply (zenon_L827_); trivial. % 18.79/18.99 (* end of lemma zenon_L828_ *) % 18.79/18.99 assert (zenon_L829_ : (((op (e0) (e3)) = (e2))\/(((op (e1) (e3)) = (e2))\/(((op (e2) (e3)) = (e2))\/((op (e3) (e3)) = (e2))))) -> ((op (e3) (e3)) = (e1)) -> ((op (e1) (e3)) = (e0)) -> (~((op (e1) (e1)) = (op (e1) (e3)))) -> ((op (e1) (e1)) = (e2)) -> (~((op (e2) (e0)) = (op (e2) (e3)))) -> ((op (e2) (e0)) = (e2)) -> ((op (e3) (e1)) = (e2)) -> (~((op (e3) (e1)) = (op (e3) (e3)))) -> False). % 18.79/18.99 do 0 intro. intros zenon_H145 zenon_Hc4 zenon_H1f zenon_H57 zenon_H110 zenon_H5b zenon_Hee zenon_H14d zenon_H130. % 18.79/18.99 apply (zenon_or_s _ _ zenon_H145); [ zenon_intro zenon_Hcd | zenon_intro zenon_H146 ]. % 18.79/18.99 apply (zenon_L49_); trivial. % 18.79/18.99 apply (zenon_or_s _ _ zenon_H146); [ zenon_intro zenon_Hd7 | zenon_intro zenon_H147 ]. % 18.79/18.99 apply (zenon_L283_); trivial. % 18.79/18.99 apply (zenon_or_s _ _ zenon_H147); [ zenon_intro zenon_H11d | zenon_intro zenon_Hf6 ]. % 18.79/18.99 apply (zenon_L73_); trivial. % 18.79/18.99 apply (zenon_L102_); trivial. % 18.79/18.99 (* end of lemma zenon_L829_ *) % 18.79/18.99 assert (zenon_L830_ : (((op (e2) (e3)) = (e0))\/(((op (e2) (e3)) = (e1))\/(((op (e2) (e3)) = (e2))\/((op (e2) (e3)) = (e3))))) -> (~((op (e2) (e2)) = (op (e2) (e3)))) -> ((op (e2) (e2)) = (e0)) -> (~((op (e2) (e3)) = (e1))) -> (~((op (e2) (e3)) = (op (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)) = (e1))) -> ((op (e3) (e3)) = (e2)) -> (~((op (e0) (e3)) = (op (e3) (e3)))) -> (~((op (e0) (e3)) = (op (e2) (e3)))) -> False). % 18.79/18.99 do 0 intro. intros zenon_H11f zenon_H6d zenon_H2c zenon_H255 zenon_Hf3 zenon_He4 zenon_H1f zenon_H1d zenon_H231 zenon_Hf6 zenon_Hc2 zenon_He2. % 18.79/18.99 apply (zenon_or_s _ _ zenon_H11f); [ zenon_intro zenon_H37 | zenon_intro zenon_H120 ]. % 18.79/18.99 apply (zenon_L18_); trivial. % 18.79/18.99 apply (zenon_or_s _ _ zenon_H120); [ zenon_intro zenon_Hf4 | zenon_intro zenon_H121 ]. % 18.79/18.99 exact (zenon_H255 zenon_Hf4). % 18.79/18.99 apply (zenon_or_s _ _ zenon_H121); [ zenon_intro zenon_H11d | zenon_intro zenon_Hdd ]. % 18.79/18.99 apply (zenon_L97_); trivial. % 18.79/18.99 apply (zenon_L722_); trivial. % 18.79/18.99 (* end of lemma zenon_L830_ *) % 18.79/18.99 assert (zenon_L831_ : (((op (e3) (e0)) = (e2))\/(((op (e3) (e1)) = (e2))\/(((op (e3) (e2)) = (e2))\/((op (e3) (e3)) = (e2))))) -> (~((op (e3) (e2)) = (e1))) -> (~((op (e3) (e1)) = (e1))) -> (((op (e0) (e3)) = (e1))\/(((op (e1) (e3)) = (e1))\/(((op (e2) (e3)) = (e1))\/((op (e3) (e3)) = (e1))))) -> (~((op (e1) (e2)) = (op (e1) (e3)))) -> ((op (e1) (e2)) = (e1)) -> (~((op (e3) (e0)) = (op (e3) (e3)))) -> (((op (e3) (e0)) = (e1))\/(((op (e3) (e1)) = (e1))\/(((op (e3) (e2)) = (e1))\/((op (e3) (e3)) = (e1))))) -> (~((e1) = (e3))) -> (~((e2) = (e3))) -> ((op (e0) (e0)) = (e1)) -> (((op (e1) (e0)) = (e3))\/(((op (e1) (e1)) = (e3))\/(((op (e1) (e2)) = (e3))\/((op (e1) (e3)) = (e3))))) -> (~((op (e3) (e1)) = (op (e3) (e3)))) -> ((op (e2) (e0)) = (e2)) -> (~((op (e2) (e0)) = (op (e2) (e3)))) -> ((op (e1) (e1)) = (e2)) -> (~((op (e1) (e1)) = (op (e1) (e3)))) -> ((op (e3) (e3)) = (e1)) -> (((op (e0) (e3)) = (e2))\/(((op (e1) (e3)) = (e2))\/(((op (e2) (e3)) = (e2))\/((op (e3) (e3)) = (e2))))) -> ((op (e0) (e2)) = (e2)) -> (~((op (e0) (e2)) = (op (e3) (e2)))) -> (((op (e2) (e3)) = (e0))\/(((op (e2) (e3)) = (e1))\/(((op (e2) (e3)) = (e2))\/((op (e2) (e3)) = (e3))))) -> (~((op (e2) (e2)) = (op (e2) (e3)))) -> ((op (e2) (e2)) = (e0)) -> (~((op (e2) (e3)) = (e1))) -> (~((op (e2) (e3)) = (op (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)) = (e1))) -> (~((op (e0) (e3)) = (op (e3) (e3)))) -> (~((op (e0) (e3)) = (op (e2) (e3)))) -> False). % 18.79/18.99 do 0 intro. intros zenon_H153 zenon_H251 zenon_H250 zenon_H133 zenon_H124 zenon_Hf0 zenon_H71 zenon_He8 zenon_H95 zenon_H12b zenon_H7a zenon_H16f zenon_H130 zenon_Hee zenon_H5b zenon_H110 zenon_H57 zenon_Hc4 zenon_H145 zenon_H150 zenon_H14f zenon_H11f zenon_H6d zenon_H2c zenon_H255 zenon_Hf3 zenon_He4 zenon_H1f zenon_H1d zenon_H231 zenon_Hc2 zenon_He2. % 18.79/18.99 apply (zenon_or_s _ _ zenon_H153); [ zenon_intro zenon_H148 | zenon_intro zenon_H154 ]. % 18.79/18.99 apply (zenon_L828_); trivial. % 18.79/18.99 apply (zenon_or_s _ _ zenon_H154); [ zenon_intro zenon_H14d | zenon_intro zenon_H155 ]. % 18.79/18.99 apply (zenon_L829_); trivial. % 18.79/18.99 apply (zenon_or_s _ _ zenon_H155); [ zenon_intro zenon_H151 | zenon_intro zenon_Hf6 ]. % 18.79/18.99 apply (zenon_L104_); trivial. % 18.79/18.99 apply (zenon_L830_); trivial. % 18.79/18.99 (* end of lemma zenon_L831_ *) % 18.79/18.99 assert (zenon_L832_ : (~((op (e3) (e0)) = (e1))) -> (((op (e3) (e0)) = (e2))\/(((op (e3) (e1)) = (e2))\/(((op (e3) (e2)) = (e2))\/((op (e3) (e3)) = (e2))))) -> (~((op (e3) (e2)) = (e1))) -> (~((op (e3) (e1)) = (e1))) -> (((op (e0) (e3)) = (e1))\/(((op (e1) (e3)) = (e1))\/(((op (e2) (e3)) = (e1))\/((op (e3) (e3)) = (e1))))) -> (~((op (e1) (e2)) = (op (e1) (e3)))) -> ((op (e1) (e2)) = (e1)) -> (~((op (e3) (e0)) = (op (e3) (e3)))) -> (((op (e3) (e0)) = (e1))\/(((op (e3) (e1)) = (e1))\/(((op (e3) (e2)) = (e1))\/((op (e3) (e3)) = (e1))))) -> (~((e1) = (e3))) -> (~((e2) = (e3))) -> ((op (e0) (e0)) = (e1)) -> (((op (e1) (e0)) = (e3))\/(((op (e1) (e1)) = (e3))\/(((op (e1) (e2)) = (e3))\/((op (e1) (e3)) = (e3))))) -> (~((op (e3) (e1)) = (op (e3) (e3)))) -> ((op (e2) (e0)) = (e2)) -> (~((op (e2) (e0)) = (op (e2) (e3)))) -> ((op (e1) (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 (e0) (e2)) = (e2)) -> (~((op (e0) (e2)) = (op (e3) (e2)))) -> (((op (e2) (e3)) = (e0))\/(((op (e2) (e3)) = (e1))\/(((op (e2) (e3)) = (e2))\/((op (e2) (e3)) = (e3))))) -> (~((op (e2) (e2)) = (op (e2) (e3)))) -> ((op (e2) (e2)) = (e0)) -> (~((op (e2) (e3)) = (e1))) -> (~((op (e2) (e3)) = (op (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)) = (e1))) -> (~((op (e0) (e3)) = (op (e3) (e3)))) -> (~((op (e0) (e3)) = (op (e2) (e3)))) -> False). % 18.87/18.99 do 0 intro. intros zenon_Had zenon_H153 zenon_H251 zenon_H250 zenon_H133 zenon_H124 zenon_Hf0 zenon_H71 zenon_He8 zenon_H95 zenon_H12b zenon_H7a zenon_H16f zenon_H130 zenon_Hee zenon_H5b zenon_H110 zenon_H57 zenon_H145 zenon_H150 zenon_H14f zenon_H11f zenon_H6d zenon_H2c zenon_H255 zenon_Hf3 zenon_He4 zenon_H1f zenon_H1d zenon_H231 zenon_Hc2 zenon_He2. % 18.87/18.99 apply (zenon_or_s _ _ zenon_He8); [ zenon_intro zenon_Hac | zenon_intro zenon_Heb ]. % 18.87/18.99 exact (zenon_Had zenon_Hac). % 18.87/18.99 apply (zenon_or_s _ _ zenon_Heb); [ zenon_intro zenon_Hae | zenon_intro zenon_Hec ]. % 18.87/18.99 exact (zenon_H250 zenon_Hae). % 18.87/18.99 apply (zenon_or_s _ _ zenon_Hec); [ zenon_intro zenon_Hba | zenon_intro zenon_Hc4 ]. % 18.87/18.99 exact (zenon_H251 zenon_Hba). % 18.87/18.99 apply (zenon_L831_); trivial. % 18.87/18.99 (* end of lemma zenon_L832_ *) % 18.87/18.99 assert (zenon_L833_ : (((op (e3) (e0)) = (e2))\/(((op (e3) (e1)) = (e2))\/(((op (e3) (e2)) = (e2))\/((op (e3) (e3)) = (e2))))) -> (~((op (e0) (e3)) = (op (e1) (e3)))) -> ((op (e1) (e3)) = (e0)) -> (~((op (e0) (e3)) = (e1))) -> (((op (e0) (e3)) = (e0))\/(((op (e0) (e3)) = (e1))\/(((op (e0) (e3)) = (e2))\/((op (e0) (e3)) = (e3))))) -> (~((op (e3) (e2)) = (e1))) -> (~((op (e3) (e1)) = (e1))) -> (((op (e0) (e3)) = (e1))\/(((op (e1) (e3)) = (e1))\/(((op (e2) (e3)) = (e1))\/((op (e3) (e3)) = (e1))))) -> (~((op (e1) (e2)) = (op (e1) (e3)))) -> ((op (e1) (e2)) = (e1)) -> (~((op (e2) (e3)) = (e1))) -> (~((op (e3) (e0)) = (op (e3) (e3)))) -> (((op (e3) (e0)) = (e1))\/(((op (e3) (e1)) = (e1))\/(((op (e3) (e2)) = (e1))\/((op (e3) (e3)) = (e1))))) -> (~((e1) = (e3))) -> (~((e2) = (e3))) -> ((op (e0) (e0)) = (e1)) -> (((op (e1) (e0)) = (e3))\/(((op (e1) (e1)) = (e3))\/(((op (e1) (e2)) = (e3))\/((op (e1) (e3)) = (e3))))) -> ((op (e1) (e1)) = (e2)) -> (~((op (e1) (e1)) = (op (e3) (e1)))) -> ((op (e0) (e2)) = (e2)) -> (~((op (e0) (e2)) = (op (e3) (e2)))) -> (~((op (e2) (e3)) = (op (e3) (e3)))) -> ((op (e2) (e3)) = (e2)) -> False). % 18.87/18.99 do 0 intro. intros zenon_H153 zenon_H1d zenon_H1f zenon_H231 zenon_He4 zenon_H251 zenon_H250 zenon_H133 zenon_H124 zenon_Hf0 zenon_H255 zenon_H71 zenon_He8 zenon_H95 zenon_H12b zenon_H7a zenon_H16f zenon_H110 zenon_H160 zenon_H150 zenon_H14f zenon_Hf3 zenon_H11d. % 18.87/18.99 apply (zenon_or_s _ _ zenon_H153); [ zenon_intro zenon_H148 | zenon_intro zenon_H154 ]. % 18.87/18.99 apply (zenon_L828_); trivial. % 18.87/18.99 apply (zenon_or_s _ _ zenon_H154); [ zenon_intro zenon_H14d | zenon_intro zenon_H155 ]. % 18.87/18.99 apply (zenon_L164_); trivial. % 18.87/18.99 apply (zenon_or_s _ _ zenon_H155); [ zenon_intro zenon_H151 | zenon_intro zenon_Hf6 ]. % 18.87/18.99 apply (zenon_L104_); trivial. % 18.87/18.99 apply (zenon_L97_); trivial. % 18.87/18.99 (* end of lemma zenon_L833_ *) % 18.87/18.99 assert (zenon_L834_ : (((op (e2) (e0)) = (e0))\/(((op (e2) (e1)) = (e0))\/(((op (e2) (e2)) = (e0))\/((op (e2) (e3)) = (e0))))) -> (~((e0) = (e2))) -> ((op (e2) (e0)) = (e2)) -> ((op (e0) (e1)) = (e0)) -> (~((op (e0) (e1)) = (op (e2) (e1)))) -> (~((op (e1) (e2)) = (op (e2) (e2)))) -> (((op (e2) (e2)) = (e0))\/(((op (e2) (e2)) = (e1))\/(((op (e2) (e2)) = (e2))\/((op (e2) (e2)) = (e3))))) -> (~((op (e2) (e2)) = (op (e2) (e3)))) -> (~((op (e2) (e2)) = (e1))) -> (~((op (e2) (e2)) = (e2))) -> (((op (e3) (e2)) = (e0))\/(((op (e3) (e2)) = (e1))\/(((op (e3) (e2)) = (e2))\/((op (e3) (e2)) = (e3))))) -> (~((op (e1) (e2)) = (op (e3) (e2)))) -> ((op (e1) (e2)) = (e0)) -> ((op (e0) (e2)) = (e2)) -> (~((op (e0) (e2)) = (op (e3) (e2)))) -> (~((op (e2) (e2)) = (op (e3) (e2)))) -> False). % 18.87/18.99 do 0 intro. intros zenon_H2f zenon_H149 zenon_Hee zenon_H49 zenon_H17e zenon_H2b zenon_H1c4 zenon_H6d zenon_H198 zenon_H173 zenon_H191 zenon_H115 zenon_H2a zenon_H150 zenon_H14f zenon_H18f. % 18.87/18.99 apply (zenon_or_s _ _ zenon_H2f); [ zenon_intro zenon_H34 | zenon_intro zenon_H33 ]. % 18.87/18.99 apply (zenon_L204_); trivial. % 18.87/18.99 apply (zenon_or_s _ _ zenon_H33); [ zenon_intro zenon_H36 | zenon_intro zenon_H35 ]. % 18.87/18.99 apply (zenon_L128_); trivial. % 18.87/18.99 apply (zenon_or_s _ _ zenon_H35); [ zenon_intro zenon_H2c | zenon_intro zenon_H37 ]. % 18.87/18.99 apply (zenon_L3_); trivial. % 18.87/18.99 apply (zenon_L746_); trivial. % 18.87/18.99 (* end of lemma zenon_L834_ *) % 18.87/18.99 assert (zenon_L835_ : (((op (e2) (e0)) = (e0))\/(((op (e2) (e1)) = (e0))\/(((op (e2) (e2)) = (e0))\/((op (e2) (e3)) = (e0))))) -> (~((e0) = (e2))) -> ((op (e0) (e1)) = (e0)) -> (~((op (e0) (e1)) = (op (e2) (e1)))) -> (~((op (e0) (e3)) = (op (e2) (e3)))) -> (~((op (e0) (e3)) = (op (e3) (e3)))) -> (~((op (e0) (e3)) = (e1))) -> (~((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)) = (op (e3) (e3)))) -> (~((op (e2) (e3)) = (e1))) -> (~((op (e2) (e2)) = (op (e2) (e3)))) -> (((op (e2) (e3)) = (e0))\/(((op (e2) (e3)) = (e1))\/(((op (e2) (e3)) = (e2))\/((op (e2) (e3)) = (e3))))) -> (~((op (e0) (e2)) = (op (e3) (e2)))) -> ((op (e0) (e2)) = (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)) = (e2)) -> (~((op (e2) (e0)) = (op (e2) (e3)))) -> ((op (e2) (e0)) = (e2)) -> (~((op (e3) (e1)) = (op (e3) (e3)))) -> (((op (e1) (e0)) = (e3))\/(((op (e1) (e1)) = (e3))\/(((op (e1) (e2)) = (e3))\/((op (e1) (e3)) = (e3))))) -> ((op (e0) (e0)) = (e1)) -> (~((e2) = (e3))) -> (~((e1) = (e3))) -> (((op (e3) (e0)) = (e1))\/(((op (e3) (e1)) = (e1))\/(((op (e3) (e2)) = (e1))\/((op (e3) (e3)) = (e1))))) -> (~((op (e3) (e0)) = (op (e3) (e3)))) -> ((op (e1) (e2)) = (e1)) -> (~((op (e1) (e2)) = (op (e1) (e3)))) -> (((op (e0) (e3)) = (e1))\/(((op (e1) (e3)) = (e1))\/(((op (e2) (e3)) = (e1))\/((op (e3) (e3)) = (e1))))) -> (~((op (e3) (e1)) = (e1))) -> (~((op (e3) (e2)) = (e1))) -> (((op (e3) (e0)) = (e2))\/(((op (e3) (e1)) = (e2))\/(((op (e3) (e2)) = (e2))\/((op (e3) (e3)) = (e2))))) -> (~((op (e3) (e0)) = (e1))) -> (~((op (e1) (e3)) = (op (e2) (e3)))) -> ((op (e1) (e3)) = (e0)) -> False). % 18.87/18.99 do 0 intro. intros zenon_H2f zenon_H149 zenon_H49 zenon_H17e zenon_He2 zenon_Hc2 zenon_H231 zenon_H1d zenon_He4 zenon_Hf3 zenon_H255 zenon_H6d zenon_H11f zenon_H14f zenon_H150 zenon_H145 zenon_H57 zenon_H110 zenon_H5b zenon_Hee zenon_H130 zenon_H16f zenon_H7a zenon_H12b zenon_H95 zenon_He8 zenon_H71 zenon_Hf0 zenon_H124 zenon_H133 zenon_H250 zenon_H251 zenon_H153 zenon_Had zenon_Hdb zenon_H1f. % 18.87/18.99 apply (zenon_or_s _ _ zenon_H2f); [ zenon_intro zenon_H34 | zenon_intro zenon_H33 ]. % 18.87/18.99 apply (zenon_L204_); trivial. % 18.87/18.99 apply (zenon_or_s _ _ zenon_H33); [ zenon_intro zenon_H36 | zenon_intro zenon_H35 ]. % 18.87/18.99 apply (zenon_L128_); trivial. % 18.87/18.99 apply (zenon_or_s _ _ zenon_H35); [ zenon_intro zenon_H2c | zenon_intro zenon_H37 ]. % 18.87/18.99 apply (zenon_L832_); trivial. % 18.87/18.99 apply (zenon_L130_); trivial. % 18.87/18.99 (* end of lemma zenon_L835_ *) % 18.87/18.99 assert (zenon_L836_ : (~((op (e1) (e1)) = (op (e3) (e1)))) -> (((op (e0) (e0)) = (e1))\/(((op (e0) (e1)) = (e1))\/(((op (e0) (e2)) = (e1))\/((op (e0) (e3)) = (e1))))) -> (~((op (e2) (e0)) = (op (e2) (e1)))) -> (((op (e2) (e0)) = (e0))\/(((op (e2) (e0)) = (e1))\/(((op (e2) (e0)) = (e2))\/((op (e2) (e0)) = (e3))))) -> (~((op (e2) (e0)) = (op (e3) (e0)))) -> (~((op (e2) (e0)) = (e1))) -> (~((e1) = (e2))) -> (((op (e0) (e0)) = (e2))\/(((op (e1) (e0)) = (e2))\/(((op (e2) (e0)) = (e2))\/((op (e3) (e0)) = (e2))))) -> (~((op (e0) (e1)) = (e1))) -> (~((op (e0) (e2)) = (e1))) -> (((op (e2) (e0)) = (e2))\/(((op (e2) (e1)) = (e2))\/(((op (e2) (e2)) = (e2))\/((op (e2) (e3)) = (e2))))) -> (~((op (e1) (e3)) = (e1))) -> (((op (e2) (e0)) = (e0))\/(((op (e2) (e1)) = (e0))\/(((op (e2) (e2)) = (e0))\/((op (e2) (e3)) = (e0))))) -> ((op (e0) (e1)) = (e0)) -> (~((op (e0) (e1)) = (op (e2) (e1)))) -> (~((op (e0) (e3)) = (op (e2) (e3)))) -> (~((op (e0) (e3)) = (op (e3) (e3)))) -> (~((op (e0) (e3)) = (e1))) -> (~((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)) = (op (e3) (e3)))) -> (~((op (e2) (e3)) = (e1))) -> (~((op (e2) (e2)) = (op (e2) (e3)))) -> (((op (e2) (e3)) = (e0))\/(((op (e2) (e3)) = (e1))\/(((op (e2) (e3)) = (e2))\/((op (e2) (e3)) = (e3))))) -> (~((op (e0) (e2)) = (op (e3) (e2)))) -> ((op (e0) (e2)) = (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)) = (e2)) -> (~((op (e2) (e0)) = (op (e2) (e3)))) -> (~((op (e3) (e1)) = (op (e3) (e3)))) -> (((op (e1) (e0)) = (e3))\/(((op (e1) (e1)) = (e3))\/(((op (e1) (e2)) = (e3))\/((op (e1) (e3)) = (e3))))) -> ((op (e0) (e0)) = (e1)) -> (~((e2) = (e3))) -> (~((e1) = (e3))) -> (((op (e3) (e0)) = (e1))\/(((op (e3) (e1)) = (e1))\/(((op (e3) (e2)) = (e1))\/((op (e3) (e3)) = (e1))))) -> (~((op (e3) (e0)) = (op (e3) (e3)))) -> (~((op (e1) (e2)) = (op (e1) (e3)))) -> (((op (e0) (e3)) = (e1))\/(((op (e1) (e3)) = (e1))\/(((op (e2) (e3)) = (e1))\/((op (e3) (e3)) = (e1))))) -> (~((op (e3) (e1)) = (e1))) -> (~((op (e3) (e2)) = (e1))) -> (((op (e3) (e0)) = (e2))\/(((op (e3) (e1)) = (e2))\/(((op (e3) (e2)) = (e2))\/((op (e3) (e3)) = (e2))))) -> (~((op (e3) (e0)) = (e1))) -> (~((op (e1) (e3)) = (op (e2) (e3)))) -> (~((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 (e1) (e2)) = (op (e2) (e2)))) -> (((op (e2) (e2)) = (e0))\/(((op (e2) (e2)) = (e1))\/(((op (e2) (e2)) = (e2))\/((op (e2) (e2)) = (e3))))) -> (~((op (e2) (e2)) = (e1))) -> (~((op (e2) (e2)) = (e2))) -> (((op (e3) (e2)) = (e0))\/(((op (e3) (e2)) = (e1))\/(((op (e3) (e2)) = (e2))\/((op (e3) (e2)) = (e3))))) -> (~((op (e1) (e2)) = (op (e3) (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) (e1)) = (op (e0) (e3)))) -> (~((op (e3) (e0)) = (op (e3) (e2)))) -> (~((op (e1) (e1)) = (op (e1) (e2)))) -> (~((op (e0) (e1)) = (op (e0) (e2)))) -> (((op (e0) (e2)) = (e0))\/(((op (e1) (e2)) = (e0))\/(((op (e2) (e2)) = (e0))\/((op (e3) (e2)) = (e0))))) -> (~((op (e1) (e0)) = (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). % 18.87/18.99 do 0 intro. intros zenon_H160 zenon_H22d zenon_H1f0 zenon_H259 zenon_H17b zenon_H1db zenon_H7c zenon_H1fe zenon_Ha4 zenon_H20d zenon_H1d5 zenon_H24e zenon_H2f zenon_H49 zenon_H17e zenon_He2 zenon_Hc2 zenon_H231 zenon_H1d zenon_He4 zenon_Hf3 zenon_H255 zenon_H6d zenon_H11f zenon_H14f zenon_H150 zenon_H145 zenon_H57 zenon_H110 zenon_H5b zenon_H130 zenon_H16f zenon_H7a zenon_H12b zenon_H95 zenon_He8 zenon_H71 zenon_H124 zenon_H133 zenon_H250 zenon_H251 zenon_H153 zenon_Had zenon_Hdb zenon_H10a zenon_H1ef zenon_H128 zenon_H2b zenon_H1c4 zenon_H198 zenon_H173 zenon_H191 zenon_H115 zenon_H18f zenon_H67 zenon_H54 zenon_H6f zenon_H4f zenon_H4a zenon_H6a zenon_H1fa zenon_H22 zenon_H44 zenon_H149. % 18.87/18.99 apply (zenon_or_s _ _ zenon_H1fe); [ zenon_intro zenon_H7b | zenon_intro zenon_H1ff ]. % 18.87/18.99 apply (zenon_L26_); trivial. % 18.87/18.99 apply (zenon_or_s _ _ zenon_H1ff); [ zenon_intro zenon_H86 | zenon_intro zenon_H200 ]. % 18.87/18.99 apply (zenon_or_s _ _ zenon_H22); [ zenon_intro zenon_H27 | zenon_intro zenon_H26 ]. % 18.87/18.99 apply (zenon_L257_); trivial. % 18.87/18.99 apply (zenon_or_s _ _ zenon_H26); [ zenon_intro zenon_H29 | zenon_intro zenon_H28 ]. % 18.87/18.99 apply (zenon_L22_); trivial. % 18.87/18.99 apply (zenon_or_s _ _ zenon_H28); [ zenon_intro zenon_H2a | zenon_intro zenon_H1f ]. % 18.87/18.99 apply (zenon_L747_); trivial. % 18.87/18.99 apply (zenon_or_s _ _ zenon_H128); [ zenon_intro zenon_H9d | zenon_intro zenon_H129 ]. % 18.87/18.99 exact (zenon_H1ef zenon_H9d). % 18.87/18.99 apply (zenon_or_s _ _ zenon_H129); [ zenon_intro zenon_H10d | zenon_intro zenon_H12a ]. % 18.87/18.99 exact (zenon_H10a zenon_H10d). % 18.87/18.99 apply (zenon_or_s _ _ zenon_H12a); [ zenon_intro zenon_Hf0 | zenon_intro zenon_Hd6 ]. % 18.87/18.99 apply (zenon_or_s _ _ zenon_H2f); [ zenon_intro zenon_H34 | zenon_intro zenon_H33 ]. % 18.87/18.99 apply (zenon_L127_); trivial. % 18.87/18.99 apply (zenon_or_s _ _ zenon_H33); [ zenon_intro zenon_H36 | zenon_intro zenon_H35 ]. % 18.87/18.99 apply (zenon_L128_); trivial. % 18.87/18.99 apply (zenon_or_s _ _ zenon_H35); [ zenon_intro zenon_H2c | zenon_intro zenon_H37 ]. % 18.87/18.99 apply (zenon_or_s _ _ zenon_H1d5); [ zenon_intro zenon_Hee | zenon_intro zenon_H1d6 ]. % 18.87/18.99 apply (zenon_L832_); trivial. % 18.87/18.99 apply (zenon_or_s _ _ zenon_H1d6); [ zenon_intro zenon_H1ca | zenon_intro zenon_H1d7 ]. % 18.87/18.99 apply (zenon_L786_); trivial. % 18.87/18.99 apply (zenon_or_s _ _ zenon_H1d7); [ zenon_intro zenon_H176 | zenon_intro zenon_H11d ]. % 18.87/18.99 exact (zenon_H173 zenon_H176). % 18.87/18.99 apply (zenon_L833_); trivial. % 18.87/18.99 apply (zenon_L130_); trivial. % 18.87/18.99 exact (zenon_H24e zenon_Hd6). % 18.87/18.99 apply (zenon_or_s _ _ zenon_H200); [ zenon_intro zenon_Hee | zenon_intro zenon_H148 ]. % 18.87/18.99 apply (zenon_or_s _ _ zenon_H22); [ zenon_intro zenon_H27 | zenon_intro zenon_H26 ]. % 18.87/18.99 apply (zenon_L312_); trivial. % 18.87/18.99 apply (zenon_or_s _ _ zenon_H26); [ zenon_intro zenon_H29 | zenon_intro zenon_H28 ]. % 18.87/18.99 apply (zenon_L22_); trivial. % 18.87/18.99 apply (zenon_or_s _ _ zenon_H28); [ zenon_intro zenon_H2a | zenon_intro zenon_H1f ]. % 18.87/18.99 apply (zenon_L834_); trivial. % 18.87/18.99 apply (zenon_or_s _ _ zenon_H128); [ zenon_intro zenon_H9d | zenon_intro zenon_H129 ]. % 18.87/18.99 exact (zenon_H1ef zenon_H9d). % 18.87/18.99 apply (zenon_or_s _ _ zenon_H129); [ zenon_intro zenon_H10d | zenon_intro zenon_H12a ]. % 18.87/18.99 exact (zenon_H10a zenon_H10d). % 18.87/18.99 apply (zenon_or_s _ _ zenon_H12a); [ zenon_intro zenon_Hf0 | zenon_intro zenon_Hd6 ]. % 18.87/18.99 apply (zenon_L835_); trivial. % 18.87/18.99 exact (zenon_H24e zenon_Hd6). % 18.87/18.99 apply (zenon_L100_); trivial. % 18.87/18.99 (* end of lemma zenon_L836_ *) % 18.87/18.99 assert (zenon_L837_ : (((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)) = (e3)) -> (~((op (e0) (e3)) = (op (e1) (e3)))) -> (~((op (e0) (e3)) = (e1))) -> (((op (e0) (e3)) = (e0))\/(((op (e0) (e3)) = (e1))\/(((op (e0) (e3)) = (e2))\/((op (e0) (e3)) = (e3))))) -> (~((op (e3) (e2)) = (e1))) -> (~((op (e3) (e1)) = (e1))) -> (((op (e0) (e3)) = (e1))\/(((op (e1) (e3)) = (e1))\/(((op (e2) (e3)) = (e1))\/((op (e3) (e3)) = (e1))))) -> (~((op (e1) (e2)) = (op (e1) (e3)))) -> (~((op (e2) (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 (e2) (e0)) = (op (e2) (e2)))) -> ((op (e2) (e0)) = (e3)) -> (~((op (e2) (e2)) = (e2))) -> (~((op (e1) (e2)) = (op (e2) (e2)))) -> ((op (e1) (e2)) = (e1)) -> (~((op (e2) (e2)) = (op (e2) (e3)))) -> (((op (e2) (e2)) = (e0))\/(((op (e2) (e2)) = (e1))\/(((op (e2) (e2)) = (e2))\/((op (e2) (e2)) = (e3))))) -> ((op (e3) (e1)) = (e0)) -> (~((op (e3) (e1)) = (op (e3) (e3)))) -> False). % 18.87/18.99 do 0 intro. intros zenon_H67 zenon_H54 zenon_H49 zenon_Hdc zenon_H1d zenon_H231 zenon_He4 zenon_H251 zenon_H250 zenon_H133 zenon_H124 zenon_H255 zenon_H71 zenon_He8 zenon_H52 zenon_H3b zenon_H173 zenon_H2b zenon_Hf0 zenon_H6d zenon_H1c4 zenon_H1b1 zenon_H130. % 18.87/18.99 apply (zenon_or_s _ _ zenon_H67); [ zenon_intro zenon_H1e | zenon_intro zenon_H68 ]. % 18.87/18.99 apply (zenon_L12_); trivial. % 18.87/18.99 apply (zenon_or_s _ _ zenon_H68); [ zenon_intro zenon_H1f | zenon_intro zenon_H69 ]. % 18.87/18.99 apply (zenon_L827_); trivial. % 18.87/18.99 apply (zenon_or_s _ _ zenon_H69); [ zenon_intro zenon_H37 | zenon_intro zenon_H60 ]. % 18.87/18.99 apply (zenon_L300_); trivial. % 18.87/18.99 apply (zenon_L244_); trivial. % 18.87/18.99 (* end of lemma zenon_L837_ *) % 18.87/18.99 assert (zenon_L838_ : (((op (e2) (e0)) = (e3))\/(((op (e2) (e1)) = (e3))\/(((op (e2) (e2)) = (e3))\/((op (e2) (e3)) = (e3))))) -> (~((op (e3) (e1)) = (op (e3) (e3)))) -> ((op (e3) (e1)) = (e0)) -> (((op (e2) (e2)) = (e0))\/(((op (e2) (e2)) = (e1))\/(((op (e2) (e2)) = (e2))\/((op (e2) (e2)) = (e3))))) -> (~((op (e2) (e2)) = (op (e2) (e3)))) -> ((op (e1) (e2)) = (e1)) -> (~((op (e1) (e2)) = (op (e2) (e2)))) -> (~((op (e2) (e2)) = (e2))) -> (~((op (e2) (e0)) = (op (e2) (e2)))) -> (((op (e3) (e0)) = (e1))\/(((op (e3) (e1)) = (e1))\/(((op (e3) (e2)) = (e1))\/((op (e3) (e3)) = (e1))))) -> (~((op (e3) (e0)) = (op (e3) (e3)))) -> (~((op (e2) (e3)) = (e1))) -> (~((op (e1) (e2)) = (op (e1) (e3)))) -> (((op (e0) (e3)) = (e1))\/(((op (e1) (e3)) = (e1))\/(((op (e2) (e3)) = (e1))\/((op (e3) (e3)) = (e1))))) -> (~((op (e3) (e1)) = (e1))) -> (~((op (e3) (e2)) = (e1))) -> (((op (e0) (e3)) = (e0))\/(((op (e0) (e3)) = (e1))\/(((op (e0) (e3)) = (e2))\/((op (e0) (e3)) = (e3))))) -> (~((op (e0) (e3)) = (e1))) -> (~((op (e0) (e3)) = (op (e1) (e3)))) -> ((op (e0) (e1)) = (e0)) -> (~((op (e0) (e1)) = (op (e0) (e3)))) -> (((op (e0) (e3)) = (e0))\/(((op (e1) (e3)) = (e0))\/(((op (e2) (e3)) = (e0))\/((op (e3) (e3)) = (e0))))) -> (~((e1) = (e3))) -> ((op (e2) (e1)) = (e1)) -> (~((op (e2) (e2)) = (op (e3) (e2)))) -> (~((op (e0) (e2)) = (op (e3) (e2)))) -> ((op (e0) (e2)) = (e2)) -> ((op (e1) (e2)) = (e0)) -> (~((op (e1) (e2)) = (op (e3) (e2)))) -> (((op (e3) (e2)) = (e0))\/(((op (e3) (e2)) = (e1))\/(((op (e3) (e2)) = (e2))\/((op (e3) (e2)) = (e3))))) -> (~((op (e1) (e3)) = (op (e2) (e3)))) -> ((op (e1) (e3)) = (e3)) -> False). % 18.87/18.99 do 0 intro. intros zenon_He7 zenon_H130 zenon_H1b1 zenon_H1c4 zenon_H6d zenon_Hf0 zenon_H2b zenon_H173 zenon_H52 zenon_He8 zenon_H71 zenon_H255 zenon_H124 zenon_H133 zenon_H250 zenon_H251 zenon_He4 zenon_H231 zenon_H1d zenon_H49 zenon_H54 zenon_H67 zenon_H95 zenon_Ha5 zenon_H18f zenon_H14f zenon_H150 zenon_H2a zenon_H115 zenon_H191 zenon_Hdb zenon_Hdc. % 18.87/18.99 apply (zenon_or_s _ _ zenon_He7); [ zenon_intro zenon_H3b | zenon_intro zenon_He9 ]. % 18.87/18.99 apply (zenon_L837_); trivial. % 18.87/18.99 apply (zenon_or_s _ _ zenon_He9); [ zenon_intro zenon_Ha6 | zenon_intro zenon_Hea ]. % 18.87/18.99 apply (zenon_L39_); trivial. % 18.87/18.99 apply (zenon_or_s _ _ zenon_Hea); [ zenon_intro zenon_Haa | zenon_intro zenon_Hdd ]. % 18.87/18.99 apply (zenon_L181_); trivial. % 18.87/18.99 apply (zenon_L52_); trivial. % 18.87/18.99 (* end of lemma zenon_L838_ *) % 18.87/18.99 assert (zenon_L839_ : (((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)) = (e1))) -> (~((op (e1) (e3)) = (op (e2) (e3)))) -> (~((op (e0) (e3)) = (op (e2) (e3)))) -> ((op (e2) (e1)) = (e1)) -> (~((op (e2) (e1)) = (op (e2) (e3)))) -> (~((op (e2) (e3)) = (op (e3) (e3)))) -> ((op (e3) (e3)) = (e0)) -> (((op (e2) (e3)) = (e0))\/(((op (e2) (e3)) = (e1))\/(((op (e2) (e3)) = (e2))\/((op (e2) (e3)) = (e3))))) -> (~((op (e0) (e3)) = (op (e1) (e3)))) -> ((op (e1) (e3)) = (e3)) -> False). % 18.87/18.99 do 0 intro. intros zenon_He4 zenon_Hc2 zenon_H231 zenon_Hdb zenon_He2 zenon_Ha5 zenon_H1c7 zenon_Hf3 zenon_H60 zenon_H11f zenon_H1d zenon_Hdc. % 18.87/18.99 apply (zenon_or_s _ _ zenon_He4); [ zenon_intro zenon_H1e | zenon_intro zenon_He5 ]. % 18.87/18.99 apply (zenon_L440_); trivial. % 18.87/18.99 apply (zenon_or_s _ _ zenon_He5); [ zenon_intro zenon_Hc3 | zenon_intro zenon_He6 ]. % 18.87/18.99 exact (zenon_H231 zenon_Hc3). % 18.87/18.99 apply (zenon_or_s _ _ zenon_He6); [ zenon_intro zenon_Hcd | zenon_intro zenon_He3 ]. % 18.87/18.99 apply (zenon_L235_); trivial. % 18.87/18.99 apply (zenon_L117_); trivial. % 18.87/18.99 (* end of lemma zenon_L839_ *) % 18.87/18.99 assert (zenon_L840_ : ((op (e3) (e0)) = (e2)) -> (~((e0) = (e3))) -> (((op (e3) (e0)) = (e0))\/(((op (e3) (e1)) = (e0))\/(((op (e3) (e2)) = (e0))\/((op (e3) (e3)) = (e0))))) -> (~((e0) = (e2))) -> (((op (e1) (e0)) = (e0))\/(((op (e1) (e1)) = (e0))\/(((op (e1) (e2)) = (e0))\/((op (e1) (e3)) = (e0))))) -> (~((op (e1) (e0)) = (op (e3) (e0)))) -> (((op (e0) (e2)) = (e0))\/(((op (e1) (e2)) = (e0))\/(((op (e2) (e2)) = (e0))\/((op (e3) (e2)) = (e0))))) -> (~((op (e0) (e1)) = (op (e0) (e2)))) -> (~((op (e1) (e1)) = (op (e1) (e2)))) -> (~((op (e3) (e0)) = (op (e3) (e2)))) -> (~((op (e2) (e2)) = (e1))) -> (((op (e1) (e0)) = (e1))\/(((op (e1) (e1)) = (e1))\/(((op (e1) (e2)) = (e1))\/((op (e1) (e3)) = (e1))))) -> (~((op (e1) (e0)) = (e1))) -> (~((op (e1) (e1)) = (e1))) -> (~((op (e3) (e0)) = (e1))) -> (((op (e3) (e0)) = (e2))\/(((op (e3) (e1)) = (e2))\/(((op (e3) (e2)) = (e2))\/((op (e3) (e3)) = (e2))))) -> (~((e2) = (e3))) -> ((op (e0) (e0)) = (e1)) -> (((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)) = (e2)) -> (~((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 (e2) (e1)))) -> (((op (e2) (e0)) = (e0))\/(((op (e2) (e1)) = (e0))\/(((op (e2) (e2)) = (e0))\/((op (e2) (e3)) = (e0))))) -> (~((op (e1) (e3)) = (e1))) -> (((op (e2) (e0)) = (e2))\/(((op (e2) (e1)) = (e2))\/(((op (e2) (e2)) = (e2))\/((op (e2) (e3)) = (e2))))) -> (~((op (e0) (e2)) = (e1))) -> (~((op (e0) (e1)) = (e1))) -> (((op (e0) (e0)) = (e2))\/(((op (e1) (e0)) = (e2))\/(((op (e2) (e0)) = (e2))\/((op (e3) (e0)) = (e2))))) -> (~((e1) = (e2))) -> (~((op (e2) (e0)) = (e1))) -> (~((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) (e1)))) -> (((op (e0) (e0)) = (e1))\/(((op (e0) (e1)) = (e1))\/(((op (e0) (e2)) = (e1))\/((op (e0) (e3)) = (e1))))) -> (~((op (e1) (e1)) = (op (e3) (e1)))) -> (((op (e3) (e2)) = (e0))\/(((op (e3) (e2)) = (e1))\/(((op (e3) (e2)) = (e2))\/((op (e3) (e2)) = (e3))))) -> ((op (e0) (e2)) = (e2)) -> (~((op (e0) (e2)) = (op (e3) (e2)))) -> (~((op (e2) (e2)) = (op (e3) (e2)))) -> (~((e1) = (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) (e1)) = (e0)) -> (~((op (e3) (e2)) = (e1))) -> (~((op (e3) (e1)) = (e1))) -> (((op (e0) (e3)) = (e1))\/(((op (e1) (e3)) = (e1))\/(((op (e2) (e3)) = (e1))\/((op (e3) (e3)) = (e1))))) -> (~((op (e1) (e2)) = (op (e1) (e3)))) -> (~((op (e2) (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 (e2) (e0)) = (op (e2) (e2)))) -> (~((op (e2) (e2)) = (e2))) -> (~((op (e1) (e2)) = (op (e2) (e2)))) -> ((op (e1) (e2)) = (e1)) -> (~((op (e2) (e2)) = (op (e2) (e3)))) -> (((op (e2) (e2)) = (e0))\/(((op (e2) (e2)) = (e1))\/(((op (e2) (e2)) = (e2))\/((op (e2) (e2)) = (e3))))) -> (~((op (e3) (e1)) = (op (e3) (e3)))) -> (((op (e2) (e0)) = (e3))\/(((op (e2) (e1)) = (e3))\/(((op (e2) (e2)) = (e3))\/((op (e2) (e3)) = (e3))))) -> ((op (e1) (e2)) = (e0)) -> (~((op (e1) (e2)) = (op (e3) (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)) = (e1))) -> (~((op (e1) (e3)) = (op (e2) (e3)))) -> (~((op (e0) (e3)) = (op (e2) (e3)))) -> ((op (e2) (e1)) = (e1)) -> (~((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))))) -> (~((op (e0) (e3)) = (op (e1) (e3)))) -> False). % 18.87/18.99 do 0 intro. intros zenon_H148 zenon_H9a zenon_H1ac zenon_H149 zenon_H22 zenon_H1fa zenon_H6a zenon_H4a zenon_H4f zenon_H6f zenon_H198 zenon_H128 zenon_H1ef zenon_H10a zenon_Had zenon_H153 zenon_H12b zenon_H7a zenon_H16f zenon_H5b zenon_H110 zenon_H57 zenon_H145 zenon_H17e zenon_H2f zenon_H24e zenon_H1d5 zenon_H20d zenon_Ha4 zenon_H1fe zenon_H7c zenon_H1db zenon_H17b zenon_H259 zenon_H1f0 zenon_H22d zenon_H160 zenon_H191 zenon_H150 zenon_H14f zenon_H18f zenon_H95 zenon_H67 zenon_H54 zenon_H49 zenon_H251 zenon_H250 zenon_H133 zenon_H124 zenon_H255 zenon_H71 zenon_He8 zenon_H52 zenon_H173 zenon_H2b zenon_Hf0 zenon_H6d zenon_H1c4 zenon_H130 zenon_He7 zenon_H2a zenon_H115 zenon_He4 zenon_Hc2 zenon_H231 zenon_Hdb zenon_He2 zenon_Ha5 zenon_H1c7 zenon_Hf3 zenon_H11f zenon_H1d. % 18.87/18.99 apply (zenon_or_s _ _ zenon_H16f); [ zenon_intro zenon_H9e | zenon_intro zenon_H170 ]. % 18.87/18.99 apply (zenon_L107_); trivial. % 18.87/18.99 apply (zenon_or_s _ _ zenon_H170); [ zenon_intro zenon_H13f | zenon_intro zenon_H171 ]. % 18.87/18.99 apply (zenon_L166_); trivial. % 18.87/18.99 apply (zenon_or_s _ _ zenon_H171); [ zenon_intro zenon_H16c | zenon_intro zenon_Hdc ]. % 18.87/18.99 apply (zenon_L521_); trivial. % 18.87/18.99 apply (zenon_or_s _ _ zenon_H1ac); [ zenon_intro zenon_H44 | zenon_intro zenon_H1af ]. % 18.87/18.99 apply (zenon_L836_); trivial. % 18.87/18.99 apply (zenon_or_s _ _ zenon_H1af); [ zenon_intro zenon_H1b1 | zenon_intro zenon_H1b0 ]. % 18.87/18.99 apply (zenon_L838_); trivial. % 18.87/18.99 apply (zenon_or_s _ _ zenon_H1b0); [ zenon_intro zenon_H61 | zenon_intro zenon_H60 ]. % 18.87/18.99 apply (zenon_L176_); trivial. % 18.87/18.99 apply (zenon_L839_); trivial. % 18.87/18.99 (* end of lemma zenon_L840_ *) % 18.87/18.99 assert (zenon_L841_ : (~((op (e2) (e3)) = (op (e3) (e3)))) -> (~((op (e0) (e2)) = (op (e3) (e2)))) -> ((op (e0) (e2)) = (e2)) -> (~((op (e1) (e1)) = (op (e3) (e1)))) -> ((op (e1) (e1)) = (e2)) -> (~((e0) = (e3))) -> (((op (e3) (e0)) = (e0))\/(((op (e3) (e1)) = (e0))\/(((op (e3) (e2)) = (e0))\/((op (e3) (e3)) = (e0))))) -> (~((e0) = (e2))) -> (((op (e1) (e0)) = (e0))\/(((op (e1) (e1)) = (e0))\/(((op (e1) (e2)) = (e0))\/((op (e1) (e3)) = (e0))))) -> (~((op (e1) (e0)) = (op (e3) (e0)))) -> (((op (e0) (e2)) = (e0))\/(((op (e1) (e2)) = (e0))\/(((op (e2) (e2)) = (e0))\/((op (e3) (e2)) = (e0))))) -> (~((op (e0) (e1)) = (op (e0) (e2)))) -> (~((op (e1) (e1)) = (op (e1) (e2)))) -> (~((op (e3) (e0)) = (op (e3) (e2)))) -> (~((op (e2) (e2)) = (e1))) -> (((op (e1) (e0)) = (e1))\/(((op (e1) (e1)) = (e1))\/(((op (e1) (e2)) = (e1))\/((op (e1) (e3)) = (e1))))) -> (~((op (e1) (e0)) = (e1))) -> (~((op (e1) (e1)) = (e1))) -> (~((op (e3) (e0)) = (e1))) -> (((op (e3) (e0)) = (e2))\/(((op (e3) (e1)) = (e2))\/(((op (e3) (e2)) = (e2))\/((op (e3) (e3)) = (e2))))) -> (~((e2) = (e3))) -> ((op (e0) (e0)) = (e1)) -> (((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)) = (op (e1) (e3)))) -> (((op (e0) (e3)) = (e2))\/(((op (e1) (e3)) = (e2))\/(((op (e2) (e3)) = (e2))\/((op (e3) (e3)) = (e2))))) -> (~((op (e0) (e1)) = (op (e2) (e1)))) -> (((op (e2) (e0)) = (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)) = (e1))) -> (~((op (e0) (e1)) = (e1))) -> (((op (e0) (e0)) = (e2))\/(((op (e1) (e0)) = (e2))\/(((op (e2) (e0)) = (e2))\/((op (e3) (e0)) = (e2))))) -> (~((e1) = (e2))) -> (~((op (e2) (e0)) = (e1))) -> (~((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) (e1)))) -> (((op (e0) (e0)) = (e1))\/(((op (e0) (e1)) = (e1))\/(((op (e0) (e2)) = (e1))\/((op (e0) (e3)) = (e1))))) -> (((op (e3) (e2)) = (e0))\/(((op (e3) (e2)) = (e1))\/(((op (e3) (e2)) = (e2))\/((op (e3) (e2)) = (e3))))) -> (~((op (e2) (e2)) = (op (e3) (e2)))) -> (~((e1) = (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) (e1)) = (e0)) -> (~((op (e3) (e2)) = (e1))) -> (~((op (e3) (e1)) = (e1))) -> (((op (e0) (e3)) = (e1))\/(((op (e1) (e3)) = (e1))\/(((op (e2) (e3)) = (e1))\/((op (e3) (e3)) = (e1))))) -> (~((op (e1) (e2)) = (op (e1) (e3)))) -> (~((op (e2) (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 (e2) (e0)) = (op (e2) (e2)))) -> (~((op (e2) (e2)) = (e2))) -> (~((op (e1) (e2)) = (op (e2) (e2)))) -> (~((op (e2) (e2)) = (op (e2) (e3)))) -> (((op (e2) (e2)) = (e0))\/(((op (e2) (e2)) = (e1))\/(((op (e2) (e2)) = (e2))\/((op (e2) (e2)) = (e3))))) -> (~((op (e3) (e1)) = (op (e3) (e3)))) -> (((op (e2) (e0)) = (e3))\/(((op (e2) (e1)) = (e3))\/(((op (e2) (e2)) = (e3))\/((op (e2) (e3)) = (e3))))) -> ((op (e1) (e2)) = (e0)) -> (~((op (e1) (e2)) = (op (e3) (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)) = (e1))) -> (~((op (e1) (e3)) = (op (e2) (e3)))) -> (~((op (e0) (e3)) = (op (e2) (e3)))) -> ((op (e2) (e1)) = (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 (e0) (e0)) = (op (e0) (e3)))) -> ((~((op (e0) (e3)) = (e1)))\/((op (e0) (e1)) = (e3))) -> ((~((op (e1) (e2)) = (e1)))\/((op (e1) (e1)) = (e2))) -> (~((op (e0) (e1)) = (op (e1) (e1)))) -> ((~((op (e2) (e0)) = (e1)))\/((op (e2) (e1)) = (e0))) -> ((~((op (e3) (e0)) = (e1)))\/((op (e3) (e1)) = (e0))) -> (((op (e0) (e0)) = (e1))\/(((op (e1) (e0)) = (e1))\/(((op (e2) (e0)) = (e1))\/((op (e3) (e0)) = (e1))))) -> (~((op (e0) (e0)) = (op (e0) (e2)))) -> (~((op (e0) (e1)) = (op (e3) (e1)))) -> ((~((op (e3) (e2)) = (e1)))\/((op (e3) (e1)) = (e2))) -> ((~((op (e2) (e2)) = (e1)))\/((op (e2) (e1)) = (e2))) -> ((~((op (e1) (e3)) = (e1)))\/((op (e1) (e1)) = (e3))) -> (~((e0) = (e1))) -> (((op (e0) (e0)) = (e3))\/(((op (e0) (e1)) = (e3))\/(((op (e0) (e2)) = (e3))\/((op (e0) (e3)) = (e3))))) -> ((~((op (e1) (e0)) = (e1)))\/((op (e1) (e1)) = (e0))) -> (((op (e0) (e0)) = (e2))\/(((op (e0) (e1)) = (e2))\/(((op (e0) (e2)) = (e2))\/((op (e0) (e3)) = (e2))))) -> (~((op (e1) (e0)) = (op (e2) (e0)))) -> (~((op (e3) (e2)) = (op (e3) (e3)))) -> (~((op (e1) (e0)) = (op (e1) (e1)))) -> (~((op (e0) (e0)) = (e0))) -> (((op (e0) (e0)) = (e0))\/(((op (e1) (e0)) = (e0))\/(((op (e2) (e0)) = (e0))\/((op (e3) (e0)) = (e0))))) -> (~((op (e3) (e1)) = (op (e3) (e2)))) -> (((op (e0) (e2)) = (e1))\/(((op (e1) (e2)) = (e1))\/(((op (e2) (e2)) = (e1))\/((op (e3) (e2)) = (e1))))) -> (((op (e0) (e0)) = (e3))\/(((op (e1) (e0)) = (e3))\/(((op (e2) (e0)) = (e3))\/((op (e3) (e0)) = (e3))))) -> ((op (e0) (e2)) = (e3)) -> (~((op (e1) (e0)) = (op (e1) (e2)))) -> (((op (e1) (e0)) = (e0))\/(((op (e1) (e0)) = (e1))\/(((op (e1) (e0)) = (e2))\/((op (e1) (e0)) = (e3))))) -> ((op (e1) (e0)) = (e2)) -> (~((op (e1) (e0)) = (op (e1) (e3)))) -> (((op (e1) (e3)) = (e0))\/(((op (e1) (e3)) = (e1))\/(((op (e1) (e3)) = (e2))\/((op (e1) (e3)) = (e3))))) -> (~((op (e1) (e3)) = (op (e3) (e3)))) -> (((op (e0) (e3)) = (e3))\/(((op (e1) (e3)) = (e3))\/(((op (e2) (e3)) = (e3))\/((op (e3) (e3)) = (e3))))) -> ((op (e2) (e0)) = (e0)) -> (~((op (e3) (e3)) = (e3))) -> (~((op (e1) (e3)) = (e1))) -> False). % 18.87/18.99 do 0 intro. intros zenon_Hf3 zenon_H14f zenon_H150 zenon_H160 zenon_H110 zenon_H9a zenon_H1ac zenon_H149 zenon_H22 zenon_H1fa zenon_H6a zenon_H4a zenon_H4f zenon_H6f zenon_H198 zenon_H128 zenon_H1ef zenon_H10a zenon_Had zenon_H153 zenon_H12b zenon_H7a zenon_H16f zenon_H5b zenon_H57 zenon_H145 zenon_H17e zenon_H2f zenon_H1d5 zenon_H20d zenon_Ha4 zenon_H1fe zenon_H7c zenon_H1db zenon_H17b zenon_H259 zenon_H1f0 zenon_H22d zenon_H191 zenon_H18f zenon_H95 zenon_H67 zenon_H54 zenon_H49 zenon_H251 zenon_H250 zenon_H133 zenon_H124 zenon_H255 zenon_H71 zenon_He8 zenon_H52 zenon_H173 zenon_H2b zenon_H6d zenon_H1c4 zenon_H130 zenon_He7 zenon_H2a zenon_H115 zenon_He4 zenon_Hc2 zenon_H231 zenon_Hdb zenon_He2 zenon_Ha5 zenon_H1c7 zenon_H11f zenon_H1d zenon_H189 zenon_H25c zenon_H256 zenon_H10e zenon_H257 zenon_H254 zenon_H235 zenon_H13c zenon_H210 zenon_H252 zenon_H253 zenon_H258 zenon_Ha1 zenon_H168 zenon_H25d zenon_H183 zenon_H201 zenon_H62 zenon_H45 zenon_H3f zenon_H3e zenon_H1a4 zenon_H139 zenon_H1e0 zenon_Ha9 zenon_H24a zenon_H25e zenon_H86 zenon_Hd8 zenon_Hdf zenon_Hd5 zenon_H136 zenon_H34 zenon_H102 zenon_H24e. % 18.87/18.99 apply (zenon_or_s _ _ zenon_H128); [ zenon_intro zenon_H9d | zenon_intro zenon_H129 ]. % 18.87/18.99 exact (zenon_H1ef zenon_H9d). % 18.87/18.99 apply (zenon_or_s _ _ zenon_H129); [ zenon_intro zenon_H10d | zenon_intro zenon_H12a ]. % 18.87/18.99 exact (zenon_H10a zenon_H10d). % 18.87/18.99 apply (zenon_or_s _ _ zenon_H12a); [ zenon_intro zenon_Hf0 | zenon_intro zenon_Hd6 ]. % 18.87/18.99 apply (zenon_or_s _ _ zenon_H1d5); [ zenon_intro zenon_Hee | zenon_intro zenon_H1d6 ]. % 18.87/18.99 apply (zenon_L204_); trivial. % 18.87/18.99 apply (zenon_or_s _ _ zenon_H1d6); [ zenon_intro zenon_H1ca | zenon_intro zenon_H1d7 ]. % 18.87/18.99 apply (zenon_L826_); trivial. % 18.87/18.99 apply (zenon_or_s _ _ zenon_H1d7); [ zenon_intro zenon_H176 | zenon_intro zenon_H11d ]. % 18.87/18.99 exact (zenon_H173 zenon_H176). % 18.87/18.99 apply (zenon_or_s _ _ zenon_H153); [ zenon_intro zenon_H148 | zenon_intro zenon_H154 ]. % 18.87/18.99 apply (zenon_L840_); trivial. % 18.87/18.99 apply (zenon_or_s _ _ zenon_H154); [ zenon_intro zenon_H14d | zenon_intro zenon_H155 ]. % 18.87/18.99 apply (zenon_L164_); trivial. % 18.87/18.99 apply (zenon_or_s _ _ zenon_H155); [ zenon_intro zenon_H151 | zenon_intro zenon_Hf6 ]. % 18.87/18.99 apply (zenon_L104_); trivial. % 18.87/18.99 apply (zenon_L97_); trivial. % 18.87/18.99 exact (zenon_H24e zenon_Hd6). % 18.87/18.99 (* end of lemma zenon_L841_ *) % 18.87/18.99 assert (zenon_L842_ : (((op (e1) (e0)) = (e1))\/(((op (e1) (e1)) = (e1))\/(((op (e1) (e2)) = (e1))\/((op (e1) (e3)) = (e1))))) -> (~((op (e1) (e0)) = (e1))) -> (~((op (e1) (e1)) = (e1))) -> (~((op (e3) (e3)) = (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)) = (e1))) -> (~((op (e0) (e3)) = (op (e3) (e3)))) -> (~((op (e0) (e3)) = (op (e2) (e3)))) -> (((op (e2) (e3)) = (e0))\/(((op (e2) (e3)) = (e1))\/(((op (e2) (e3)) = (e2))\/((op (e2) (e3)) = (e3))))) -> (~((op (e2) (e0)) = (op (e2) (e3)))) -> ((op (e2) (e0)) = (e0)) -> (~((op (e2) (e3)) = (op (e3) (e3)))) -> (((op (e0) (e3)) = (e3))\/(((op (e1) (e3)) = (e3))\/(((op (e2) (e3)) = (e3))\/((op (e3) (e3)) = (e3))))) -> (~((op (e0) (e2)) = (op (e3) (e2)))) -> ((op (e0) (e2)) = (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)) = (e2)) -> (~((op (e2) (e1)) = (op (e2) (e3)))) -> ((op (e2) (e1)) = (e2)) -> (~((op (e3) (e1)) = (op (e3) (e3)))) -> ((op (e1) (e0)) = (e3)) -> ((op (e0) (e0)) = (e1)) -> (((op (e3) (e0)) = (e2))\/(((op (e3) (e1)) = (e2))\/(((op (e3) (e2)) = (e2))\/((op (e3) (e3)) = (e2))))) -> (~((op (e3) (e2)) = (e1))) -> (~((op (e3) (e1)) = (e1))) -> (((op (e0) (e3)) = (e1))\/(((op (e1) (e3)) = (e1))\/(((op (e2) (e3)) = (e1))\/((op (e3) (e3)) = (e1))))) -> (~((op (e1) (e2)) = (op (e1) (e3)))) -> (~((op (e2) (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 (e1) (e3)) = (e1))) -> False). % 18.87/19.00 do 0 intro. intros zenon_H128 zenon_H1ef zenon_H10a zenon_H102 zenon_He4 zenon_H1f zenon_H1d zenon_H231 zenon_Hc2 zenon_He2 zenon_H11f zenon_H5b zenon_H34 zenon_Hf3 zenon_H136 zenon_H14f zenon_H150 zenon_H145 zenon_H57 zenon_H110 zenon_H1c7 zenon_H1ca zenon_H130 zenon_H9e zenon_H7a zenon_H153 zenon_H251 zenon_H250 zenon_H133 zenon_H124 zenon_H255 zenon_H71 zenon_He8 zenon_H24e. % 18.87/19.00 apply (zenon_or_s _ _ zenon_H128); [ zenon_intro zenon_H9d | zenon_intro zenon_H129 ]. % 18.87/19.00 exact (zenon_H1ef zenon_H9d). % 18.87/19.00 apply (zenon_or_s _ _ zenon_H129); [ zenon_intro zenon_H10d | zenon_intro zenon_H12a ]. % 18.87/19.00 exact (zenon_H10a zenon_H10d). % 18.87/19.00 apply (zenon_or_s _ _ zenon_H12a); [ zenon_intro zenon_Hf0 | zenon_intro zenon_Hd6 ]. % 18.87/19.00 apply (zenon_L791_); trivial. % 18.87/19.00 exact (zenon_H24e zenon_Hd6). % 18.87/19.00 (* end of lemma zenon_L842_ *) % 18.87/19.00 assert (zenon_L843_ : (((op (e2) (e0)) = (e2))\/(((op (e2) (e1)) = (e2))\/(((op (e2) (e2)) = (e2))\/((op (e2) (e3)) = (e2))))) -> (~((op (e1) (e3)) = (op (e2) (e3)))) -> (~((op (e3) (e0)) = (e1))) -> (~((op (e2) (e2)) = (op (e2) (e3)))) -> (~((op (e0) (e1)) = (op (e2) (e1)))) -> ((op (e0) (e1)) = (e0)) -> (~((e0) = (e2))) -> (((op (e2) (e0)) = (e0))\/(((op (e2) (e1)) = (e0))\/(((op (e2) (e2)) = (e0))\/((op (e2) (e3)) = (e0))))) -> (~((op (e1) (e3)) = (e1))) -> ((op (e1) (e0)) = (e3)) -> (~((op (e3) (e1)) = (op (e3) (e3)))) -> (~((op (e2) (e1)) = (op (e2) (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) (e3)) = (e3))\/(((op (e1) (e3)) = (e3))\/(((op (e2) (e3)) = (e3))\/((op (e3) (e3)) = (e3))))) -> ((op (e2) (e0)) = (e0)) -> (~((op (e2) (e0)) = (op (e2) (e3)))) -> (((op (e2) (e3)) = (e0))\/(((op (e2) (e3)) = (e1))\/(((op (e2) (e3)) = (e2))\/((op (e2) (e3)) = (e3))))) -> (~((op (e0) (e3)) = (op (e2) (e3)))) -> (~((op (e0) (e3)) = (op (e3) (e3)))) -> (~((op (e3) (e3)) = (e3))) -> (~((op (e1) (e1)) = (e1))) -> (~((op (e1) (e0)) = (e1))) -> (((op (e1) (e0)) = (e1))\/(((op (e1) (e1)) = (e1))\/(((op (e1) (e2)) = (e1))\/((op (e1) (e3)) = (e1))))) -> (~((op (e2) (e2)) = (e2))) -> (((op (e3) (e0)) = (e2))\/(((op (e3) (e1)) = (e2))\/(((op (e3) (e2)) = (e2))\/((op (e3) (e3)) = (e2))))) -> (~((op (e0) (e3)) = (op (e1) (e3)))) -> ((op (e1) (e3)) = (e0)) -> (~((op (e0) (e3)) = (e1))) -> (((op (e0) (e3)) = (e0))\/(((op (e0) (e3)) = (e1))\/(((op (e0) (e3)) = (e2))\/((op (e0) (e3)) = (e3))))) -> (~((op (e3) (e2)) = (e1))) -> (~((op (e3) (e1)) = (e1))) -> (((op (e0) (e3)) = (e1))\/(((op (e1) (e3)) = (e1))\/(((op (e2) (e3)) = (e1))\/((op (e3) (e3)) = (e1))))) -> (~((op (e1) (e2)) = (op (e1) (e3)))) -> ((op (e1) (e2)) = (e1)) -> (~((op (e2) (e3)) = (e1))) -> (~((op (e3) (e0)) = (op (e3) (e3)))) -> (((op (e3) (e0)) = (e1))\/(((op (e3) (e1)) = (e1))\/(((op (e3) (e2)) = (e1))\/((op (e3) (e3)) = (e1))))) -> (~((e1) = (e3))) -> (~((e2) = (e3))) -> ((op (e0) (e0)) = (e1)) -> (((op (e1) (e0)) = (e3))\/(((op (e1) (e1)) = (e3))\/(((op (e1) (e2)) = (e3))\/((op (e1) (e3)) = (e3))))) -> ((op (e1) (e1)) = (e2)) -> (~((op (e1) (e1)) = (op (e3) (e1)))) -> ((op (e0) (e2)) = (e2)) -> (~((op (e0) (e2)) = (op (e3) (e2)))) -> (~((op (e2) (e3)) = (op (e3) (e3)))) -> False). % 18.87/19.00 do 0 intro. intros zenon_H1d5 zenon_Hdb zenon_Had zenon_H6d zenon_H17e zenon_H49 zenon_H149 zenon_H2f zenon_H24e zenon_H9e zenon_H130 zenon_H1c7 zenon_H57 zenon_H145 zenon_H136 zenon_H34 zenon_H5b zenon_H11f zenon_He2 zenon_Hc2 zenon_H102 zenon_H10a zenon_H1ef zenon_H128 zenon_H173 zenon_H153 zenon_H1d zenon_H1f zenon_H231 zenon_He4 zenon_H251 zenon_H250 zenon_H133 zenon_H124 zenon_Hf0 zenon_H255 zenon_H71 zenon_He8 zenon_H95 zenon_H12b zenon_H7a zenon_H16f zenon_H110 zenon_H160 zenon_H150 zenon_H14f zenon_Hf3. % 18.87/19.00 apply (zenon_or_s _ _ zenon_H1d5); [ zenon_intro zenon_Hee | zenon_intro zenon_H1d6 ]. % 18.87/19.00 apply (zenon_L835_); trivial. % 18.87/19.00 apply (zenon_or_s _ _ zenon_H1d6); [ zenon_intro zenon_H1ca | zenon_intro zenon_H1d7 ]. % 18.87/19.00 apply (zenon_L842_); trivial. % 18.87/19.00 apply (zenon_or_s _ _ zenon_H1d7); [ zenon_intro zenon_H176 | zenon_intro zenon_H11d ]. % 18.87/19.00 exact (zenon_H173 zenon_H176). % 18.87/19.00 apply (zenon_L833_); trivial. % 18.87/19.00 (* end of lemma zenon_L843_ *) % 18.87/19.00 assert (zenon_L844_ : (~((op (e2) (e3)) = (op (e3) (e3)))) -> (~((op (e0) (e2)) = (op (e3) (e2)))) -> ((op (e0) (e2)) = (e2)) -> (~((op (e1) (e1)) = (op (e3) (e1)))) -> ((op (e1) (e1)) = (e2)) -> (((op (e1) (e0)) = (e3))\/(((op (e1) (e1)) = (e3))\/(((op (e1) (e2)) = (e3))\/((op (e1) (e3)) = (e3))))) -> ((op (e0) (e0)) = (e1)) -> (~((e2) = (e3))) -> (~((e1) = (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) (e3)) = (e1))) -> (~((op (e1) (e2)) = (op (e1) (e3)))) -> (((op (e0) (e3)) = (e1))\/(((op (e1) (e3)) = (e1))\/(((op (e2) (e3)) = (e1))\/((op (e3) (e3)) = (e1))))) -> (~((op (e3) (e1)) = (e1))) -> (~((op (e3) (e2)) = (e1))) -> (((op (e0) (e3)) = (e0))\/(((op (e0) (e3)) = (e1))\/(((op (e0) (e3)) = (e2))\/((op (e0) (e3)) = (e3))))) -> (~((op (e0) (e3)) = (e1))) -> ((op (e1) (e3)) = (e0)) -> (~((op (e0) (e3)) = (op (e1) (e3)))) -> (((op (e3) (e0)) = (e2))\/(((op (e3) (e1)) = (e2))\/(((op (e3) (e2)) = (e2))\/((op (e3) (e3)) = (e2))))) -> (~((op (e2) (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 (e3) (e3)) = (e3))) -> (~((op (e0) (e3)) = (op (e3) (e3)))) -> (~((op (e0) (e3)) = (op (e2) (e3)))) -> (((op (e2) (e3)) = (e0))\/(((op (e2) (e3)) = (e1))\/(((op (e2) (e3)) = (e2))\/((op (e2) (e3)) = (e3))))) -> (~((op (e2) (e0)) = (op (e2) (e3)))) -> ((op (e2) (e0)) = (e0)) -> (((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 (e1) (e1)) = (op (e1) (e3)))) -> (~((op (e2) (e1)) = (op (e2) (e3)))) -> (~((op (e3) (e1)) = (op (e3) (e3)))) -> ((op (e1) (e0)) = (e3)) -> (((op (e2) (e0)) = (e0))\/(((op (e2) (e1)) = (e0))\/(((op (e2) (e2)) = (e0))\/((op (e2) (e3)) = (e0))))) -> (~((e0) = (e2))) -> ((op (e0) (e1)) = (e0)) -> (~((op (e0) (e1)) = (op (e2) (e1)))) -> (~((op (e2) (e2)) = (op (e2) (e3)))) -> (~((op (e3) (e0)) = (e1))) -> (~((op (e1) (e3)) = (op (e2) (e3)))) -> (((op (e2) (e0)) = (e2))\/(((op (e2) (e1)) = (e2))\/(((op (e2) (e2)) = (e2))\/((op (e2) (e3)) = (e2))))) -> (~((op (e1) (e3)) = (e1))) -> False). % 18.87/19.00 do 0 intro. intros zenon_Hf3 zenon_H14f zenon_H150 zenon_H160 zenon_H110 zenon_H16f zenon_H7a zenon_H12b zenon_H95 zenon_He8 zenon_H71 zenon_H255 zenon_H124 zenon_H133 zenon_H250 zenon_H251 zenon_He4 zenon_H231 zenon_H1f zenon_H1d zenon_H153 zenon_H173 zenon_H128 zenon_H1ef zenon_H10a zenon_H102 zenon_Hc2 zenon_He2 zenon_H11f zenon_H5b zenon_H34 zenon_H136 zenon_H145 zenon_H57 zenon_H1c7 zenon_H130 zenon_H9e zenon_H2f zenon_H149 zenon_H49 zenon_H17e zenon_H6d zenon_Had zenon_Hdb zenon_H1d5 zenon_H24e. % 18.87/19.00 apply (zenon_or_s _ _ zenon_H128); [ zenon_intro zenon_H9d | zenon_intro zenon_H129 ]. % 18.87/19.00 exact (zenon_H1ef zenon_H9d). % 18.87/19.00 apply (zenon_or_s _ _ zenon_H129); [ zenon_intro zenon_H10d | zenon_intro zenon_H12a ]. % 18.87/19.00 exact (zenon_H10a zenon_H10d). % 18.87/19.00 apply (zenon_or_s _ _ zenon_H12a); [ zenon_intro zenon_Hf0 | zenon_intro zenon_Hd6 ]. % 18.87/19.00 apply (zenon_L843_); trivial. % 18.87/19.00 exact (zenon_H24e zenon_Hd6). % 18.87/19.00 (* end of lemma zenon_L844_ *) % 18.87/19.00 assert (zenon_L845_ : (((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) (e3)) = (op (e1) (e3)))) -> ((op (e1) (e3)) = (e0)) -> (~((op (e0) (e3)) = (e1))) -> (((op (e0) (e3)) = (e0))\/(((op (e0) (e3)) = (e1))\/(((op (e0) (e3)) = (e2))\/((op (e0) (e3)) = (e3))))) -> (~((op (e3) (e2)) = (e1))) -> (~((op (e3) (e1)) = (e1))) -> (((op (e0) (e3)) = (e1))\/(((op (e1) (e3)) = (e1))\/(((op (e2) (e3)) = (e1))\/((op (e3) (e3)) = (e1))))) -> (~((op (e1) (e2)) = (op (e1) (e3)))) -> (~((op (e2) (e3)) = (e1))) -> (~((op (e3) (e0)) = (op (e3) (e3)))) -> (((op (e3) (e0)) = (e1))\/(((op (e3) (e1)) = (e1))\/(((op (e3) (e2)) = (e1))\/((op (e3) (e3)) = (e1))))) -> (~((e1) = (e3))) -> ((op (e1) (e1)) = (e2)) -> (~((e2) = (e3))) -> ((op (e3) (e0)) = (e2)) -> ((op (e0) (e0)) = (e1)) -> (((op (e1) (e0)) = (e3))\/(((op (e1) (e1)) = (e3))\/(((op (e1) (e2)) = (e3))\/((op (e1) (e3)) = (e3))))) -> (~((op (e1) (e3)) = (e1))) -> False). % 18.87/19.00 do 0 intro. intros zenon_H128 zenon_H1ef zenon_H10a zenon_H1d zenon_H1f zenon_H231 zenon_He4 zenon_H251 zenon_H250 zenon_H133 zenon_H124 zenon_H255 zenon_H71 zenon_He8 zenon_H95 zenon_H110 zenon_H12b zenon_H148 zenon_H7a zenon_H16f zenon_H24e. % 18.87/19.00 apply (zenon_or_s _ _ zenon_H128); [ zenon_intro zenon_H9d | zenon_intro zenon_H129 ]. % 18.87/19.00 exact (zenon_H1ef zenon_H9d). % 18.87/19.00 apply (zenon_or_s _ _ zenon_H129); [ zenon_intro zenon_H10d | zenon_intro zenon_H12a ]. % 18.87/19.00 exact (zenon_H10a zenon_H10d). % 18.87/19.00 apply (zenon_or_s _ _ zenon_H12a); [ zenon_intro zenon_Hf0 | zenon_intro zenon_Hd6 ]. % 18.87/19.00 apply (zenon_L828_); trivial. % 18.87/19.00 exact (zenon_H24e zenon_Hd6). % 18.87/19.00 (* end of lemma zenon_L845_ *) % 18.87/19.00 assert (zenon_L846_ : (~((op (e1) (e0)) = (op (e2) (e0)))) -> ((op (e2) (e0)) = (e0)) -> (~((op (e3) (e2)) = (op (e3) (e3)))) -> (~((op (e1) (e0)) = (op (e1) (e1)))) -> (~((op (e0) (e0)) = (e0))) -> (((op (e0) (e0)) = (e0))\/(((op (e1) (e0)) = (e0))\/(((op (e2) (e0)) = (e0))\/((op (e3) (e0)) = (e0))))) -> (~((e0) = (e3))) -> (((op (e3) (e0)) = (e0))\/(((op (e3) (e1)) = (e0))\/(((op (e3) (e2)) = (e0))\/((op (e3) (e3)) = (e0))))) -> (~((e0) = (e2))) -> (((op (e1) (e0)) = (e0))\/(((op (e1) (e1)) = (e0))\/(((op (e1) (e2)) = (e0))\/((op (e1) (e3)) = (e0))))) -> (~((op (e1) (e0)) = (op (e3) (e0)))) -> (((op (e0) (e2)) = (e0))\/(((op (e1) (e2)) = (e0))\/(((op (e2) (e2)) = (e0))\/((op (e3) (e2)) = (e0))))) -> (~((op (e0) (e1)) = (op (e0) (e2)))) -> (~((op (e1) (e1)) = (op (e1) (e2)))) -> (~((op (e3) (e0)) = (op (e3) (e2)))) -> (~((op (e2) (e2)) = (e1))) -> (~((op (e3) (e0)) = (e1))) -> (((op (e3) (e0)) = (e2))\/(((op (e3) (e1)) = (e2))\/(((op (e3) (e2)) = (e2))\/((op (e3) (e3)) = (e2))))) -> (~((op (e2) (e0)) = (op (e2) (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 (e2) (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 (e0) (e2)) = (e1))) -> (~((op (e0) (e1)) = (e1))) -> (((op (e0) (e0)) = (e2))\/(((op (e1) (e0)) = (e2))\/(((op (e2) (e0)) = (e2))\/((op (e3) (e0)) = (e2))))) -> (~((e1) = (e2))) -> (~((op (e2) (e0)) = (e1))) -> (~((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) (e1)))) -> (((op (e0) (e0)) = (e1))\/(((op (e0) (e1)) = (e1))\/(((op (e0) (e2)) = (e1))\/((op (e0) (e3)) = (e1))))) -> (~((op (e1) (e1)) = (op (e3) (e1)))) -> (((op (e3) (e2)) = (e0))\/(((op (e3) (e2)) = (e1))\/(((op (e3) (e2)) = (e2))\/((op (e3) (e2)) = (e3))))) -> ((op (e0) (e2)) = (e2)) -> (~((op (e0) (e2)) = (op (e3) (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) (e1)) = (op (e0) (e3)))) -> ((op (e0) (e1)) = (e0)) -> (~((op (e2) (e0)) = (op (e2) (e2)))) -> (~((op (e2) (e2)) = (e2))) -> (~((op (e1) (e2)) = (op (e2) (e2)))) -> (~((op (e2) (e2)) = (op (e2) (e3)))) -> (((op (e2) (e2)) = (e0))\/(((op (e2) (e2)) = (e1))\/(((op (e2) (e2)) = (e2))\/((op (e2) (e2)) = (e3))))) -> (~((op (e3) (e1)) = (op (e3) (e3)))) -> (((op (e2) (e0)) = (e3))\/(((op (e2) (e1)) = (e3))\/(((op (e2) (e2)) = (e3))\/((op (e2) (e3)) = (e3))))) -> (~((op (e1) (e2)) = (op (e3) (e2)))) -> (~((op (e0) (e3)) = (op (e3) (e3)))) -> (~((op (e1) (e3)) = (op (e2) (e3)))) -> (~((op (e0) (e3)) = (op (e2) (e3)))) -> ((op (e2) (e1)) = (e1)) -> (~((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))))) -> (((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) (e3)) = (op (e1) (e3)))) -> (~((op (e0) (e3)) = (e1))) -> (((op (e0) (e3)) = (e0))\/(((op (e0) (e3)) = (e1))\/(((op (e0) (e3)) = (e2))\/((op (e0) (e3)) = (e3))))) -> (~((op (e3) (e2)) = (e1))) -> (~((op (e3) (e1)) = (e1))) -> (((op (e0) (e3)) = (e1))\/(((op (e1) (e3)) = (e1))\/(((op (e2) (e3)) = (e1))\/((op (e3) (e3)) = (e1))))) -> (~((op (e1) (e2)) = (op (e1) (e3)))) -> (~((op (e2) (e3)) = (e1))) -> (~((op (e3) (e0)) = (op (e3) (e3)))) -> (((op (e3) (e0)) = (e1))\/(((op (e3) (e1)) = (e1))\/(((op (e3) (e2)) = (e1))\/((op (e3) (e3)) = (e1))))) -> (~((e1) = (e3))) -> ((op (e1) (e1)) = (e2)) -> (~((e2) = (e3))) -> ((op (e3) (e0)) = (e2)) -> ((op (e0) (e0)) = (e1)) -> (((op (e1) (e0)) = (e3))\/(((op (e1) (e1)) = (e3))\/(((op (e1) (e2)) = (e3))\/((op (e1) (e3)) = (e3))))) -> (~((op (e1) (e3)) = (e1))) -> False). % 18.87/19.00 do 0 intro. intros zenon_H201 zenon_H34 zenon_H62 zenon_H45 zenon_H3f zenon_H3e zenon_H9a zenon_H1ac zenon_H149 zenon_H22 zenon_H1fa zenon_H6a zenon_H4a zenon_H4f zenon_H6f zenon_H198 zenon_Had zenon_H153 zenon_H5b zenon_H57 zenon_H145 zenon_H17e zenon_H2f zenon_H1d5 zenon_H20d zenon_Ha4 zenon_H1fe zenon_H7c zenon_H1db zenon_H17b zenon_H259 zenon_H1f0 zenon_H22d zenon_H160 zenon_H191 zenon_H150 zenon_H14f zenon_H18f zenon_H67 zenon_H54 zenon_H49 zenon_H52 zenon_H173 zenon_H2b zenon_H6d zenon_H1c4 zenon_H130 zenon_He7 zenon_H115 zenon_Hc2 zenon_Hdb zenon_He2 zenon_Ha5 zenon_H1c7 zenon_Hf3 zenon_H11f zenon_H128 zenon_H1ef zenon_H10a zenon_H1d zenon_H231 zenon_He4 zenon_H251 zenon_H250 zenon_H133 zenon_H124 zenon_H255 zenon_H71 zenon_He8 zenon_H95 zenon_H110 zenon_H12b zenon_H148 zenon_H7a zenon_H16f zenon_H24e. % 18.87/19.00 apply (zenon_or_s _ _ zenon_H22); [ zenon_intro zenon_H27 | zenon_intro zenon_H26 ]. % 18.87/19.00 apply (zenon_L332_); trivial. % 18.87/19.00 apply (zenon_or_s _ _ zenon_H26); [ zenon_intro zenon_H29 | zenon_intro zenon_H28 ]. % 18.87/19.00 apply (zenon_L23_); trivial. % 18.87/19.00 apply (zenon_or_s _ _ zenon_H28); [ zenon_intro zenon_H2a | zenon_intro zenon_H1f ]. % 18.87/19.00 apply (zenon_or_s _ _ zenon_H128); [ zenon_intro zenon_H9d | zenon_intro zenon_H129 ]. % 18.87/19.00 exact (zenon_H1ef zenon_H9d). % 18.87/19.00 apply (zenon_or_s _ _ zenon_H129); [ zenon_intro zenon_H10d | zenon_intro zenon_H12a ]. % 18.87/19.00 exact (zenon_H10a zenon_H10d). % 18.87/19.00 apply (zenon_or_s _ _ zenon_H12a); [ zenon_intro zenon_Hf0 | zenon_intro zenon_Hd6 ]. % 18.87/19.00 apply (zenon_L840_); trivial. % 18.87/19.00 exact (zenon_H24e zenon_Hd6). % 18.87/19.00 apply (zenon_L845_); trivial. % 18.87/19.00 (* end of lemma zenon_L846_ *) % 18.87/19.00 assert (zenon_L847_ : (~((op (e3) (e0)) = (op (e3) (e1)))) -> ((op (e3) (e1)) = (e3)) -> (~((op (e3) (e3)) = (e3))) -> (((op (e0) (e3)) = (e3))\/(((op (e1) (e3)) = (e3))\/(((op (e2) (e3)) = (e3))\/((op (e3) (e3)) = (e3))))) -> (((op (e0) (e0)) = (e3))\/(((op (e1) (e0)) = (e3))\/(((op (e2) (e0)) = (e3))\/((op (e3) (e0)) = (e3))))) -> (~((op (e0) (e0)) = (op (e0) (e3)))) -> ((~((op (e0) (e3)) = (e1)))\/((op (e0) (e1)) = (e3))) -> ((~((op (e1) (e2)) = (e1)))\/((op (e1) (e1)) = (e2))) -> (~((op (e0) (e1)) = (op (e1) (e1)))) -> ((~((op (e2) (e0)) = (e1)))\/((op (e2) (e1)) = (e0))) -> ((~((op (e3) (e0)) = (e1)))\/((op (e3) (e1)) = (e0))) -> (((op (e0) (e0)) = (e1))\/(((op (e1) (e0)) = (e1))\/(((op (e2) (e0)) = (e1))\/((op (e3) (e0)) = (e1))))) -> (~((op (e0) (e0)) = (op (e0) (e2)))) -> (~((op (e0) (e1)) = (op (e3) (e1)))) -> ((~((op (e3) (e2)) = (e1)))\/((op (e3) (e1)) = (e2))) -> ((~((op (e2) (e2)) = (e1)))\/((op (e2) (e1)) = (e2))) -> ((~((op (e1) (e3)) = (e1)))\/((op (e1) (e1)) = (e3))) -> (~((e0) = (e1))) -> (((op (e0) (e0)) = (e3))\/(((op (e0) (e1)) = (e3))\/(((op (e0) (e2)) = (e3))\/((op (e0) (e3)) = (e3))))) -> ((~((op (e1) (e0)) = (e1)))\/((op (e1) (e1)) = (e0))) -> (((op (e0) (e0)) = (e2))\/(((op (e0) (e1)) = (e2))\/(((op (e0) (e2)) = (e2))\/((op (e0) (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 (e1) (e0)) = (op (e1) (e2)))) -> (((op (e1) (e0)) = (e0))\/(((op (e1) (e0)) = (e1))\/(((op (e1) (e0)) = (e2))\/((op (e1) (e0)) = (e3))))) -> (~((op (e1) (e0)) = (op (e1) (e3)))) -> (((op (e1) (e3)) = (e0))\/(((op (e1) (e3)) = (e1))\/(((op (e1) (e3)) = (e2))\/((op (e1) (e3)) = (e3))))) -> (~((op (e1) (e3)) = (op (e3) (e3)))) -> (~((op (e1) (e0)) = (op (e2) (e0)))) -> ((op (e2) (e0)) = (e0)) -> (~((op (e3) (e2)) = (op (e3) (e3)))) -> (~((op (e1) (e0)) = (op (e1) (e1)))) -> (~((op (e0) (e0)) = (e0))) -> (((op (e0) (e0)) = (e0))\/(((op (e1) (e0)) = (e0))\/(((op (e2) (e0)) = (e0))\/((op (e3) (e0)) = (e0))))) -> (~((e0) = (e3))) -> (((op (e3) (e0)) = (e0))\/(((op (e3) (e1)) = (e0))\/(((op (e3) (e2)) = (e0))\/((op (e3) (e3)) = (e0))))) -> (~((e0) = (e2))) -> (((op (e1) (e0)) = (e0))\/(((op (e1) (e1)) = (e0))\/(((op (e1) (e2)) = (e0))\/((op (e1) (e3)) = (e0))))) -> (~((op (e1) (e0)) = (op (e3) (e0)))) -> (((op (e0) (e2)) = (e0))\/(((op (e1) (e2)) = (e0))\/(((op (e2) (e2)) = (e0))\/((op (e3) (e2)) = (e0))))) -> (~((op (e0) (e1)) = (op (e0) (e2)))) -> (~((op (e1) (e1)) = (op (e1) (e2)))) -> (~((op (e3) (e0)) = (op (e3) (e2)))) -> (~((op (e2) (e2)) = (e1))) -> (~((op (e3) (e0)) = (e1))) -> (((op (e3) (e0)) = (e2))\/(((op (e3) (e1)) = (e2))\/(((op (e3) (e2)) = (e2))\/((op (e3) (e3)) = (e2))))) -> (~((op (e2) (e0)) = (op (e2) (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 (e2) (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 (e0) (e2)) = (e1))) -> (~((op (e0) (e1)) = (e1))) -> (((op (e0) (e0)) = (e2))\/(((op (e1) (e0)) = (e2))\/(((op (e2) (e0)) = (e2))\/((op (e3) (e0)) = (e2))))) -> (~((e1) = (e2))) -> (~((op (e2) (e0)) = (e1))) -> (~((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) (e1)))) -> (((op (e0) (e0)) = (e1))\/(((op (e0) (e1)) = (e1))\/(((op (e0) (e2)) = (e1))\/((op (e0) (e3)) = (e1))))) -> (~((op (e1) (e1)) = (op (e3) (e1)))) -> (((op (e3) (e2)) = (e0))\/(((op (e3) (e2)) = (e1))\/(((op (e3) (e2)) = (e2))\/((op (e3) (e2)) = (e3))))) -> ((op (e0) (e2)) = (e2)) -> (~((op (e0) (e2)) = (op (e3) (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) (e1)) = (op (e0) (e3)))) -> ((op (e0) (e1)) = (e0)) -> (~((op (e2) (e0)) = (op (e2) (e2)))) -> (~((op (e2) (e2)) = (e2))) -> (~((op (e1) (e2)) = (op (e2) (e2)))) -> (~((op (e2) (e2)) = (op (e2) (e3)))) -> (((op (e2) (e2)) = (e0))\/(((op (e2) (e2)) = (e1))\/(((op (e2) (e2)) = (e2))\/((op (e2) (e2)) = (e3))))) -> (~((op (e3) (e1)) = (op (e3) (e3)))) -> (((op (e2) (e0)) = (e3))\/(((op (e2) (e1)) = (e3))\/(((op (e2) (e2)) = (e3))\/((op (e2) (e3)) = (e3))))) -> (~((op (e1) (e2)) = (op (e3) (e2)))) -> (~((op (e0) (e3)) = (op (e3) (e3)))) -> (~((op (e1) (e3)) = (op (e2) (e3)))) -> (~((op (e0) (e3)) = (op (e2) (e3)))) -> ((op (e2) (e1)) = (e1)) -> (~((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))))) -> (((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) (e3)) = (op (e1) (e3)))) -> (~((op (e0) (e3)) = (e1))) -> (((op (e0) (e3)) = (e0))\/(((op (e0) (e3)) = (e1))\/(((op (e0) (e3)) = (e2))\/((op (e0) (e3)) = (e3))))) -> (~((op (e3) (e2)) = (e1))) -> (~((op (e3) (e1)) = (e1))) -> (((op (e0) (e3)) = (e1))\/(((op (e1) (e3)) = (e1))\/(((op (e2) (e3)) = (e1))\/((op (e3) (e3)) = (e1))))) -> (~((op (e1) (e2)) = (op (e1) (e3)))) -> (~((op (e2) (e3)) = (e1))) -> (~((op (e3) (e0)) = (op (e3) (e3)))) -> (((op (e3) (e0)) = (e1))\/(((op (e3) (e1)) = (e1))\/(((op (e3) (e2)) = (e1))\/((op (e3) (e3)) = (e1))))) -> (~((e1) = (e3))) -> ((op (e1) (e1)) = (e2)) -> (~((e2) = (e3))) -> ((op (e0) (e0)) = (e1)) -> (((op (e1) (e0)) = (e3))\/(((op (e1) (e1)) = (e3))\/(((op (e1) (e2)) = (e3))\/((op (e1) (e3)) = (e3))))) -> (~((op (e1) (e3)) = (e1))) -> False). % 18.87/19.00 do 0 intro. intros zenon_H1cf zenon_H161 zenon_H102 zenon_H136 zenon_H1e0 zenon_H189 zenon_H25c zenon_H256 zenon_H10e zenon_H257 zenon_H254 zenon_H235 zenon_H13c zenon_H210 zenon_H252 zenon_H253 zenon_H258 zenon_Ha1 zenon_H168 zenon_H25d zenon_H183 zenon_H1a4 zenon_H139 zenon_H24a zenon_H25e zenon_Hd8 zenon_Hdf zenon_Hd5 zenon_H201 zenon_H34 zenon_H62 zenon_H45 zenon_H3f zenon_H3e zenon_H9a zenon_H1ac zenon_H149 zenon_H22 zenon_H1fa zenon_H6a zenon_H4a zenon_H4f zenon_H6f zenon_H198 zenon_Had zenon_H153 zenon_H5b zenon_H57 zenon_H145 zenon_H17e zenon_H2f zenon_H1d5 zenon_H20d zenon_Ha4 zenon_H1fe zenon_H7c zenon_H1db zenon_H17b zenon_H259 zenon_H1f0 zenon_H22d zenon_H160 zenon_H191 zenon_H150 zenon_H14f zenon_H18f zenon_H67 zenon_H54 zenon_H49 zenon_H52 zenon_H173 zenon_H2b zenon_H6d zenon_H1c4 zenon_H130 zenon_He7 zenon_H115 zenon_Hc2 zenon_Hdb zenon_He2 zenon_Ha5 zenon_H1c7 zenon_Hf3 zenon_H11f zenon_H128 zenon_H1ef zenon_H10a zenon_H1d zenon_H231 zenon_He4 zenon_H251 zenon_H250 zenon_H133 zenon_H124 zenon_H255 zenon_H71 zenon_He8 zenon_H95 zenon_H110 zenon_H12b zenon_H7a zenon_H16f zenon_H24e. % 18.87/19.00 apply (zenon_or_s _ _ zenon_H1fe); [ zenon_intro zenon_H7b | zenon_intro zenon_H1ff ]. % 18.87/19.00 apply (zenon_L26_); trivial. % 18.87/19.00 apply (zenon_or_s _ _ zenon_H1ff); [ zenon_intro zenon_H86 | zenon_intro zenon_H200 ]. % 18.87/19.00 apply (zenon_or_s _ _ zenon_H168); [ zenon_intro zenon_H3a | zenon_intro zenon_H169 ]. % 18.87/19.00 apply (zenon_L35_); trivial. % 18.87/19.00 apply (zenon_or_s _ _ zenon_H169); [ zenon_intro zenon_H99 | zenon_intro zenon_H16a ]. % 18.87/19.00 apply (zenon_L36_); trivial. % 18.87/19.00 apply (zenon_or_s _ _ zenon_H16a); [ zenon_intro zenon_Ha9 | zenon_intro zenon_He3 ]. % 18.87/19.00 apply (zenon_or_s _ _ zenon_H1e0); [ zenon_intro zenon_H3a | zenon_intro zenon_H1e1 ]. % 18.87/19.00 apply (zenon_L35_); trivial. % 18.87/19.00 apply (zenon_or_s _ _ zenon_H1e1); [ zenon_intro zenon_H9e | zenon_intro zenon_H1e2 ]. % 18.87/19.00 apply (zenon_or_s _ _ zenon_H22); [ zenon_intro zenon_H27 | zenon_intro zenon_H26 ]. % 18.87/19.00 apply (zenon_L257_); trivial. % 18.87/19.00 apply (zenon_or_s _ _ zenon_H26); [ zenon_intro zenon_H29 | zenon_intro zenon_H28 ]. % 18.87/19.00 apply (zenon_L23_); trivial. % 18.87/19.00 apply (zenon_or_s _ _ zenon_H28); [ zenon_intro zenon_H2a | zenon_intro zenon_H1f ]. % 18.87/19.00 apply (zenon_L841_); trivial. % 18.87/19.00 apply (zenon_L844_); trivial. % 18.87/19.00 apply (zenon_or_s _ _ zenon_H1e2); [ zenon_intro zenon_H3b | zenon_intro zenon_H15e ]. % 18.87/19.00 apply (zenon_L33_); trivial. % 18.87/19.00 apply (zenon_L193_); trivial. % 18.87/19.00 apply (zenon_or_s _ _ zenon_H1e0); [ zenon_intro zenon_H3a | zenon_intro zenon_H1e1 ]. % 18.87/19.00 apply (zenon_L35_); trivial. % 18.87/19.00 apply (zenon_or_s _ _ zenon_H1e1); [ zenon_intro zenon_H9e | zenon_intro zenon_H1e2 ]. % 18.87/19.00 apply (zenon_or_s _ _ zenon_H22); [ zenon_intro zenon_H27 | zenon_intro zenon_H26 ]. % 18.87/19.00 apply (zenon_L332_); trivial. % 18.87/19.00 apply (zenon_or_s _ _ zenon_H26); [ zenon_intro zenon_H29 | zenon_intro zenon_H28 ]. % 18.87/19.00 apply (zenon_L724_); trivial. % 18.87/19.00 apply (zenon_or_s _ _ zenon_H28); [ zenon_intro zenon_H2a | zenon_intro zenon_H1f ]. % 18.87/19.00 apply (zenon_L211_); trivial. % 18.87/19.00 apply (zenon_L844_); trivial. % 18.87/19.00 apply (zenon_or_s _ _ zenon_H1e2); [ zenon_intro zenon_H3b | zenon_intro zenon_H15e ]. % 18.87/19.00 apply (zenon_L33_); trivial. % 18.87/19.00 apply (zenon_L193_); trivial. % 18.87/19.00 apply (zenon_or_s _ _ zenon_H200); [ zenon_intro zenon_Hee | zenon_intro zenon_H148 ]. % 18.87/19.00 apply (zenon_L204_); trivial. % 18.87/19.00 apply (zenon_L846_); trivial. % 18.87/19.00 (* end of lemma zenon_L847_ *) % 18.87/19.00 assert (zenon_L848_ : (((op (e1) (e3)) = (e0))\/(((op (e1) (e3)) = (e1))\/(((op (e1) (e3)) = (e2))\/((op (e1) (e3)) = (e3))))) -> (~((op (e2) (e3)) = (e1))) -> ((op (e2) (e2)) = (e0)) -> (~((op (e2) (e2)) = (op (e2) (e3)))) -> (~((op (e0) (e2)) = (op (e3) (e2)))) -> ((op (e0) (e2)) = (e2)) -> (((op (e0) (e3)) = (e2))\/(((op (e1) (e3)) = (e2))\/(((op (e2) (e3)) = (e2))\/((op (e3) (e3)) = (e2))))) -> ((op (e3) (e3)) = (e1)) -> (~((op (e1) (e1)) = (op (e1) (e3)))) -> ((op (e1) (e1)) = (e2)) -> (~((op (e2) (e0)) = (op (e2) (e3)))) -> ((op (e2) (e0)) = (e2)) -> (~((op (e3) (e1)) = (op (e3) (e3)))) -> (((op (e1) (e0)) = (e3))\/(((op (e1) (e1)) = (e3))\/(((op (e1) (e2)) = (e3))\/((op (e1) (e3)) = (e3))))) -> ((op (e0) (e0)) = (e1)) -> (~((e2) = (e3))) -> (~((e1) = (e3))) -> (((op (e3) (e0)) = (e1))\/(((op (e3) (e1)) = (e1))\/(((op (e3) (e2)) = (e1))\/((op (e3) (e3)) = (e1))))) -> (~((op (e3) (e0)) = (op (e3) (e3)))) -> ((op (e1) (e2)) = (e1)) -> (~((op (e1) (e2)) = (op (e1) (e3)))) -> (((op (e0) (e3)) = (e1))\/(((op (e1) (e3)) = (e1))\/(((op (e2) (e3)) = (e1))\/((op (e3) (e3)) = (e1))))) -> (~((op (e3) (e1)) = (e1))) -> (~((op (e3) (e2)) = (e1))) -> (((op (e3) (e0)) = (e2))\/(((op (e3) (e1)) = (e2))\/(((op (e3) (e2)) = (e2))\/((op (e3) (e3)) = (e2))))) -> (~((op (e1) (e3)) = (e1))) -> ((op (e3) (e3)) = (e2)) -> (~((op (e1) (e3)) = (op (e3) (e3)))) -> (((op (e0) (e3)) = (e0))\/(((op (e0) (e3)) = (e1))\/(((op (e0) (e3)) = (e2))\/((op (e0) (e3)) = (e3))))) -> (~((op (e0) (e3)) = (op (e3) (e3)))) -> (~((op (e0) (e3)) = (e1))) -> (~((op (e1) (e3)) = (op (e2) (e3)))) -> (~((op (e0) (e3)) = (op (e2) (e3)))) -> ((op (e2) (e1)) = (e1)) -> (~((op (e2) (e1)) = (op (e2) (e3)))) -> (~((op (e2) (e3)) = (op (e3) (e3)))) -> ((op (e3) (e3)) = (e0)) -> (((op (e2) (e3)) = (e0))\/(((op (e2) (e3)) = (e1))\/(((op (e2) (e3)) = (e2))\/((op (e2) (e3)) = (e3))))) -> (~((op (e0) (e3)) = (op (e1) (e3)))) -> False). % 18.87/19.00 do 0 intro. intros zenon_Hdf zenon_H255 zenon_H2c zenon_H6d zenon_H14f zenon_H150 zenon_H145 zenon_Hc4 zenon_H57 zenon_H110 zenon_H5b zenon_Hee zenon_H130 zenon_H16f zenon_H7a zenon_H12b zenon_H95 zenon_He8 zenon_H71 zenon_Hf0 zenon_H124 zenon_H133 zenon_H250 zenon_H251 zenon_H153 zenon_H24e zenon_Hf6 zenon_Hd5 zenon_He4 zenon_Hc2 zenon_H231 zenon_Hdb zenon_He2 zenon_Ha5 zenon_H1c7 zenon_Hf3 zenon_H60 zenon_H11f zenon_H1d. % 18.87/19.00 apply (zenon_or_s _ _ zenon_Hdf); [ zenon_intro zenon_H1f | zenon_intro zenon_He0 ]. % 18.87/19.00 apply (zenon_L831_); trivial. % 18.87/19.00 apply (zenon_or_s _ _ zenon_He0); [ zenon_intro zenon_Hd6 | zenon_intro zenon_He1 ]. % 18.87/19.00 exact (zenon_H24e zenon_Hd6). % 18.87/19.00 apply (zenon_or_s _ _ zenon_He1); [ zenon_intro zenon_Hd7 | zenon_intro zenon_Hdc ]. % 18.87/19.00 apply (zenon_L402_); trivial. % 18.87/19.00 apply (zenon_L839_); trivial. % 18.87/19.00 (* end of lemma zenon_L848_ *) % 18.87/19.00 assert (zenon_L849_ : (((op (e3) (e0)) = (e0))\/(((op (e3) (e1)) = (e0))\/(((op (e3) (e2)) = (e0))\/((op (e3) (e3)) = (e0))))) -> (~((e0) = (e2))) -> (((op (e1) (e0)) = (e0))\/(((op (e1) (e1)) = (e0))\/(((op (e1) (e2)) = (e0))\/((op (e1) (e3)) = (e0))))) -> (~((op (e1) (e0)) = (op (e3) (e0)))) -> (((op (e0) (e2)) = (e0))\/(((op (e1) (e2)) = (e0))\/(((op (e2) (e2)) = (e0))\/((op (e3) (e2)) = (e0))))) -> (~((op (e0) (e1)) = (op (e0) (e2)))) -> (~((op (e1) (e1)) = (op (e1) (e2)))) -> (~((op (e3) (e0)) = (op (e3) (e2)))) -> (~((op (e1) (e2)) = (op (e3) (e2)))) -> (((op (e3) (e2)) = (e0))\/(((op (e3) (e2)) = (e1))\/(((op (e3) (e2)) = (e2))\/((op (e3) (e2)) = (e3))))) -> (~((op (e2) (e2)) = (e2))) -> (~((op (e2) (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 (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)) = (op (e2) (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 (e0) (e2)) = (e1))) -> (~((op (e0) (e1)) = (e1))) -> (((op (e0) (e0)) = (e2))\/(((op (e1) (e0)) = (e2))\/(((op (e2) (e0)) = (e2))\/((op (e3) (e0)) = (e2))))) -> (~((e1) = (e2))) -> (~((op (e2) (e0)) = (e1))) -> (~((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) (e1)))) -> (((op (e0) (e0)) = (e1))\/(((op (e0) (e1)) = (e1))\/(((op (e0) (e2)) = (e1))\/((op (e0) (e3)) = (e1))))) -> (~((op (e1) (e0)) = (op (e1) (e3)))) -> ((op (e1) (e0)) = (e0)) -> ((op (e0) (e1)) = (e0)) -> (~((op (e0) (e1)) = (op (e0) (e3)))) -> (((op (e0) (e3)) = (e0))\/(((op (e1) (e3)) = (e0))\/(((op (e2) (e3)) = (e0))\/((op (e3) (e3)) = (e0))))) -> (~((op (e2) (e2)) = (op (e3) (e2)))) -> (~((op (e3) (e0)) = (e1))) -> ((op (e1) (e0)) = (e3)) -> (~((op (e1) (e1)) = (op (e3) (e1)))) -> (((op (e1) (e3)) = (e0))\/(((op (e1) (e3)) = (e1))\/(((op (e1) (e3)) = (e2))\/((op (e1) (e3)) = (e3))))) -> (~((op (e2) (e3)) = (e1))) -> ((op (e2) (e2)) = (e0)) -> (~((op (e2) (e2)) = (op (e2) (e3)))) -> (~((op (e0) (e2)) = (op (e3) (e2)))) -> ((op (e0) (e2)) = (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)) = (e2)) -> (~((op (e2) (e0)) = (op (e2) (e3)))) -> ((op (e2) (e0)) = (e2)) -> (~((op (e3) (e1)) = (op (e3) (e3)))) -> (((op (e1) (e0)) = (e3))\/(((op (e1) (e1)) = (e3))\/(((op (e1) (e2)) = (e3))\/((op (e1) (e3)) = (e3))))) -> ((op (e0) (e0)) = (e1)) -> (~((e2) = (e3))) -> (~((e1) = (e3))) -> (((op (e3) (e0)) = (e1))\/(((op (e3) (e1)) = (e1))\/(((op (e3) (e2)) = (e1))\/((op (e3) (e3)) = (e1))))) -> (~((op (e3) (e0)) = (op (e3) (e3)))) -> ((op (e1) (e2)) = (e1)) -> (~((op (e1) (e2)) = (op (e1) (e3)))) -> (((op (e0) (e3)) = (e1))\/(((op (e1) (e3)) = (e1))\/(((op (e2) (e3)) = (e1))\/((op (e3) (e3)) = (e1))))) -> (~((op (e3) (e1)) = (e1))) -> (~((op (e3) (e2)) = (e1))) -> (((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)))) -> (((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)) = (e1))) -> (~((op (e1) (e3)) = (op (e2) (e3)))) -> (~((op (e0) (e3)) = (op (e2) (e3)))) -> ((op (e2) (e1)) = (e1)) -> (~((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))))) -> (~((op (e0) (e3)) = (op (e1) (e3)))) -> False). % 18.87/19.00 do 0 intro. intros zenon_H1ac zenon_H149 zenon_H22 zenon_H1fa zenon_H6a zenon_H4a zenon_H4f zenon_H6f zenon_H115 zenon_H191 zenon_H173 zenon_H198 zenon_H1c4 zenon_H2b zenon_H128 zenon_H1ef zenon_H10a zenon_H17e zenon_H2f zenon_H1d5 zenon_H20d zenon_Ha4 zenon_H1fe zenon_H7c zenon_H1db zenon_H17b zenon_H259 zenon_H1f0 zenon_H22d zenon_Hd8 zenon_H27 zenon_H49 zenon_H54 zenon_H67 zenon_H18f zenon_Had zenon_H9e zenon_H160 zenon_Hdf zenon_H255 zenon_H2c zenon_H6d zenon_H14f zenon_H150 zenon_H145 zenon_H57 zenon_H110 zenon_H5b zenon_Hee zenon_H130 zenon_H16f zenon_H7a zenon_H12b zenon_H95 zenon_He8 zenon_H71 zenon_Hf0 zenon_H124 zenon_H133 zenon_H250 zenon_H251 zenon_H153 zenon_H24e zenon_Hd5 zenon_He4 zenon_Hc2 zenon_H231 zenon_Hdb zenon_He2 zenon_Ha5 zenon_H1c7 zenon_Hf3 zenon_H11f zenon_H1d. % 18.87/19.00 apply (zenon_or_s _ _ zenon_H1ac); [ zenon_intro zenon_H44 | zenon_intro zenon_H1af ]. % 18.87/19.00 apply (zenon_L836_); trivial. % 18.87/19.00 apply (zenon_or_s _ _ zenon_H1af); [ zenon_intro zenon_H1b1 | zenon_intro zenon_H1b0 ]. % 18.87/19.00 apply (zenon_L259_); trivial. % 18.87/19.00 apply (zenon_or_s _ _ zenon_H1b0); [ zenon_intro zenon_H61 | zenon_intro zenon_H60 ]. % 18.87/19.00 apply (zenon_L146_); trivial. % 18.87/19.00 apply (zenon_or_s _ _ zenon_He8); [ zenon_intro zenon_Hac | zenon_intro zenon_Heb ]. % 18.87/19.00 exact (zenon_Had zenon_Hac). % 18.87/19.00 apply (zenon_or_s _ _ zenon_Heb); [ zenon_intro zenon_Hae | zenon_intro zenon_Hec ]. % 18.87/19.00 exact (zenon_H250 zenon_Hae). % 18.87/19.00 apply (zenon_or_s _ _ zenon_Hec); [ zenon_intro zenon_Hba | zenon_intro zenon_Hc4 ]. % 18.87/19.00 exact (zenon_H251 zenon_Hba). % 18.87/19.00 apply (zenon_or_s _ _ zenon_H153); [ zenon_intro zenon_H148 | zenon_intro zenon_H154 ]. % 18.87/19.00 apply (zenon_L107_); trivial. % 18.87/19.00 apply (zenon_or_s _ _ zenon_H154); [ zenon_intro zenon_H14d | zenon_intro zenon_H155 ]. % 18.87/19.00 apply (zenon_L164_); trivial. % 18.87/19.00 apply (zenon_or_s _ _ zenon_H155); [ zenon_intro zenon_H151 | zenon_intro zenon_Hf6 ]. % 18.87/19.00 apply (zenon_L104_); trivial. % 18.87/19.00 apply (zenon_L848_); trivial. % 18.87/19.00 (* end of lemma zenon_L849_ *) % 18.87/19.00 assert (zenon_L850_ : (((op (e1) (e3)) = (e0))\/(((op (e1) (e3)) = (e1))\/(((op (e1) (e3)) = (e2))\/((op (e1) (e3)) = (e3))))) -> ((op (e0) (e3)) = (e2)) -> (~((op (e1) (e3)) = (op (e3) (e3)))) -> ((op (e3) (e3)) = (e1)) -> ((op (e2) (e3)) = (e0)) -> (~((op (e1) (e3)) = (op (e2) (e3)))) -> ((op (e2) (e3)) = (e3)) -> False). % 18.87/19.00 do 0 intro. intros zenon_Hdf zenon_Hcd zenon_Hd5 zenon_Hc4 zenon_H37 zenon_Hdb zenon_Hdd. % 18.87/19.00 apply (zenon_or_s _ _ zenon_Hdf); [ zenon_intro zenon_H1f | zenon_intro zenon_He0 ]. % 18.87/19.00 apply (zenon_L49_); trivial. % 18.87/19.00 apply (zenon_or_s _ _ zenon_He0); [ zenon_intro zenon_Hd6 | zenon_intro zenon_He1 ]. % 18.87/19.00 apply (zenon_L50_); trivial. % 18.87/19.00 apply (zenon_or_s _ _ zenon_He1); [ zenon_intro zenon_Hd7 | zenon_intro zenon_Hdc ]. % 18.87/19.00 apply (zenon_L72_); trivial. % 18.87/19.00 apply (zenon_L52_); trivial. % 18.87/19.00 (* end of lemma zenon_L850_ *) % 18.87/19.00 assert (zenon_L851_ : (((op (e3) (e0)) = (e1))\/(((op (e3) (e1)) = (e1))\/(((op (e3) (e2)) = (e1))\/((op (e3) (e3)) = (e1))))) -> (~((op (e3) (e0)) = (e1))) -> (~((op (e3) (e1)) = (e1))) -> (~((op (e3) (e2)) = (e1))) -> (((op (e1) (e3)) = (e0))\/(((op (e1) (e3)) = (e1))\/(((op (e1) (e3)) = (e2))\/((op (e1) (e3)) = (e3))))) -> ((op (e0) (e3)) = (e2)) -> (~((op (e1) (e3)) = (op (e3) (e3)))) -> ((op (e2) (e3)) = (e0)) -> (~((op (e1) (e3)) = (op (e2) (e3)))) -> ((op (e2) (e3)) = (e3)) -> False). % 18.87/19.00 do 0 intro. intros zenon_He8 zenon_Had zenon_H250 zenon_H251 zenon_Hdf zenon_Hcd zenon_Hd5 zenon_H37 zenon_Hdb zenon_Hdd. % 18.87/19.00 apply (zenon_or_s _ _ zenon_He8); [ zenon_intro zenon_Hac | zenon_intro zenon_Heb ]. % 18.87/19.00 exact (zenon_Had zenon_Hac). % 18.87/19.00 apply (zenon_or_s _ _ zenon_Heb); [ zenon_intro zenon_Hae | zenon_intro zenon_Hec ]. % 18.87/19.00 exact (zenon_H250 zenon_Hae). % 18.87/19.00 apply (zenon_or_s _ _ zenon_Hec); [ zenon_intro zenon_Hba | zenon_intro zenon_Hc4 ]. % 18.87/19.00 exact (zenon_H251 zenon_Hba). % 18.87/19.00 apply (zenon_L850_); trivial. % 18.87/19.00 (* end of lemma zenon_L851_ *) % 18.87/19.00 assert (zenon_L852_ : (((op (e0) (e3)) = (e0))\/(((op (e0) (e3)) = (e1))\/(((op (e0) (e3)) = (e2))\/((op (e0) (e3)) = (e3))))) -> (~((op (e0) (e3)) = (e1))) -> (~((op (e1) (e3)) = (op (e2) (e3)))) -> ((op (e2) (e3)) = (e0)) -> (~((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)) = (e1))) -> (~((op (e3) (e1)) = (e1))) -> (~((op (e3) (e0)) = (e1))) -> (((op (e3) (e0)) = (e1))\/(((op (e3) (e1)) = (e1))\/(((op (e3) (e2)) = (e1))\/((op (e3) (e3)) = (e1))))) -> (~((op (e0) (e3)) = (op (e2) (e3)))) -> ((op (e2) (e3)) = (e3)) -> False). % 18.87/19.00 do 0 intro. intros zenon_He4 zenon_H231 zenon_Hdb zenon_H37 zenon_Hd5 zenon_Hdf zenon_H251 zenon_H250 zenon_Had zenon_He8 zenon_He2 zenon_Hdd. % 18.87/19.00 apply (zenon_or_s _ _ zenon_He4); [ zenon_intro zenon_H1e | zenon_intro zenon_He5 ]. % 18.87/19.00 apply (zenon_L367_); trivial. % 18.87/19.00 apply (zenon_or_s _ _ zenon_He5); [ zenon_intro zenon_Hc3 | zenon_intro zenon_He6 ]. % 18.87/19.00 exact (zenon_H231 zenon_Hc3). % 18.87/19.00 apply (zenon_or_s _ _ zenon_He6); [ zenon_intro zenon_Hcd | zenon_intro zenon_He3 ]. % 18.87/19.00 apply (zenon_L851_); trivial. % 18.87/19.00 apply (zenon_L54_); trivial. % 18.87/19.00 (* end of lemma zenon_L852_ *) % 18.87/19.00 assert (zenon_L853_ : (((op (e2) (e0)) = (e0))\/(((op (e2) (e1)) = (e0))\/(((op (e2) (e2)) = (e0))\/((op (e2) (e3)) = (e0))))) -> (~((e0) = (e2))) -> ((op (e2) (e0)) = (e2)) -> ((op (e0) (e1)) = (e0)) -> (~((op (e0) (e1)) = (op (e2) (e1)))) -> ((op (e1) (e2)) = (e0)) -> (((op (e2) (e2)) = (e0))\/(((op (e2) (e2)) = (e1))\/(((op (e2) (e2)) = (e2))\/((op (e2) (e2)) = (e3))))) -> (~((op (e2) (e2)) = (op (e2) (e3)))) -> ((op (e1) (e2)) = (e1)) -> (~((op (e1) (e2)) = (op (e2) (e2)))) -> (~((op (e2) (e2)) = (e2))) -> ((op (e2) (e0)) = (e3)) -> (~((op (e2) (e0)) = (op (e2) (e2)))) -> False). % 18.87/19.00 do 0 intro. intros zenon_H2f zenon_H149 zenon_Hee zenon_H49 zenon_H17e zenon_H2a zenon_H1c4 zenon_H6d zenon_Hf0 zenon_H2b zenon_H173 zenon_H3b zenon_H52. % 18.87/19.00 apply (zenon_or_s _ _ zenon_H2f); [ zenon_intro zenon_H34 | zenon_intro zenon_H33 ]. % 18.87/19.00 apply (zenon_L204_); trivial. % 18.87/19.00 apply (zenon_or_s _ _ zenon_H33); [ zenon_intro zenon_H36 | zenon_intro zenon_H35 ]. % 18.87/19.00 apply (zenon_L128_); trivial. % 18.87/19.00 apply (zenon_or_s _ _ zenon_H35); [ zenon_intro zenon_H2c | zenon_intro zenon_H37 ]. % 18.87/19.00 apply (zenon_L3_); trivial. % 18.87/19.00 apply (zenon_L300_); trivial. % 18.87/19.00 (* end of lemma zenon_L853_ *) % 18.87/19.00 assert (zenon_L854_ : (((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) (e0)) = (op (e2) (e2)))) -> ((op (e2) (e0)) = (e3)) -> (~((op (e2) (e2)) = (e2))) -> (~((op (e1) (e2)) = (op (e2) (e2)))) -> (~((op (e2) (e2)) = (op (e2) (e3)))) -> (((op (e2) (e2)) = (e0))\/(((op (e2) (e2)) = (e1))\/(((op (e2) (e2)) = (e2))\/((op (e2) (e2)) = (e3))))) -> ((op (e1) (e2)) = (e0)) -> (~((op (e0) (e1)) = (op (e2) (e1)))) -> ((op (e0) (e1)) = (e0)) -> ((op (e2) (e0)) = (e2)) -> (~((e0) = (e2))) -> (((op (e2) (e0)) = (e0))\/(((op (e2) (e1)) = (e0))\/(((op (e2) (e2)) = (e0))\/((op (e2) (e3)) = (e0))))) -> (~((op (e1) (e3)) = (e1))) -> False). % 18.87/19.00 do 0 intro. intros zenon_H128 zenon_H1ef zenon_H10a zenon_H52 zenon_H3b zenon_H173 zenon_H2b zenon_H6d zenon_H1c4 zenon_H2a zenon_H17e zenon_H49 zenon_Hee zenon_H149 zenon_H2f zenon_H24e. % 18.87/19.00 apply (zenon_or_s _ _ zenon_H128); [ zenon_intro zenon_H9d | zenon_intro zenon_H129 ]. % 18.87/19.00 exact (zenon_H1ef zenon_H9d). % 18.87/19.00 apply (zenon_or_s _ _ zenon_H129); [ zenon_intro zenon_H10d | zenon_intro zenon_H12a ]. % 18.87/19.00 exact (zenon_H10a zenon_H10d). % 18.87/19.00 apply (zenon_or_s _ _ zenon_H12a); [ zenon_intro zenon_Hf0 | zenon_intro zenon_Hd6 ]. % 18.87/19.00 apply (zenon_L853_); trivial. % 18.87/19.00 exact (zenon_H24e zenon_Hd6). % 18.87/19.00 (* end of lemma zenon_L854_ *) % 18.87/19.00 assert (zenon_L855_ : (((op (e1) (e0)) = (e0))\/(((op (e1) (e1)) = (e0))\/(((op (e1) (e2)) = (e0))\/((op (e1) (e3)) = (e0))))) -> (~((op (e1) (e0)) = (op (e3) (e0)))) -> (~((e0) = (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) (e0)) = (op (e2) (e2)))) -> ((op (e2) (e0)) = (e3)) -> (~((op (e2) (e2)) = (e2))) -> (~((op (e1) (e2)) = (op (e2) (e2)))) -> (~((op (e2) (e2)) = (op (e2) (e3)))) -> (((op (e2) (e2)) = (e0))\/(((op (e2) (e2)) = (e1))\/(((op (e2) (e2)) = (e2))\/((op (e2) (e2)) = (e3))))) -> (~((op (e3) (e0)) = (e1))) -> (((op (e3) (e0)) = (e2))\/(((op (e3) (e1)) = (e2))\/(((op (e3) (e2)) = (e2))\/((op (e3) (e3)) = (e2))))) -> (~((op (e3) (e2)) = (e1))) -> (~((op (e3) (e1)) = (e1))) -> (((op (e0) (e3)) = (e1))\/(((op (e1) (e3)) = (e1))\/(((op (e2) (e3)) = (e1))\/((op (e3) (e3)) = (e1))))) -> (~((op (e1) (e2)) = (op (e1) (e3)))) -> (~((op (e3) (e0)) = (op (e3) (e3)))) -> (((op (e3) (e0)) = (e1))\/(((op (e3) (e1)) = (e1))\/(((op (e3) (e2)) = (e1))\/((op (e3) (e3)) = (e1))))) -> (~((e1) = (e3))) -> (~((e2) = (e3))) -> ((op (e0) (e0)) = (e1)) -> (((op (e1) (e0)) = (e3))\/(((op (e1) (e1)) = (e3))\/(((op (e1) (e2)) = (e3))\/((op (e1) (e3)) = (e3))))) -> (~((op (e3) (e1)) = (op (e3) (e3)))) -> ((op (e2) (e0)) = (e2)) -> (~((op (e2) (e0)) = (op (e2) (e3)))) -> ((op (e1) (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 (e0) (e2)) = (e2)) -> (~((op (e0) (e2)) = (op (e3) (e2)))) -> (((op (e2) (e3)) = (e0))\/(((op (e2) (e3)) = (e1))\/(((op (e2) (e3)) = (e2))\/((op (e2) (e3)) = (e3))))) -> (~((op (e2) (e3)) = (e1))) -> (~((op (e2) (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 (e0) (e3)) = (e1))) -> (~((op (e0) (e3)) = (op (e3) (e3)))) -> (~((op (e0) (e3)) = (op (e2) (e3)))) -> (~((op (e0) (e1)) = (op (e2) (e1)))) -> ((op (e0) (e1)) = (e0)) -> ((op (e3) (e0)) = (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) (e3)) = (e1))) -> False). % 18.87/19.00 do 0 intro. intros zenon_H22 zenon_H1fa zenon_H149 zenon_H128 zenon_H1ef zenon_H10a zenon_H52 zenon_H3b zenon_H173 zenon_H2b zenon_H6d zenon_H1c4 zenon_Had zenon_H153 zenon_H251 zenon_H250 zenon_H133 zenon_H124 zenon_H71 zenon_He8 zenon_H95 zenon_H12b zenon_H7a zenon_H16f zenon_H130 zenon_Hee zenon_H5b zenon_H110 zenon_H57 zenon_H145 zenon_H150 zenon_H14f zenon_H11f zenon_H255 zenon_Hf3 zenon_He4 zenon_H1d zenon_H231 zenon_Hc2 zenon_He2 zenon_H17e zenon_H49 zenon_H44 zenon_H17b zenon_H2f zenon_H24e. % 18.87/19.00 apply (zenon_or_s _ _ zenon_H22); [ zenon_intro zenon_H27 | zenon_intro zenon_H26 ]. % 18.87/19.00 apply (zenon_L312_); trivial. % 18.87/19.00 apply (zenon_or_s _ _ zenon_H26); [ zenon_intro zenon_H29 | zenon_intro zenon_H28 ]. % 18.87/19.00 apply (zenon_L354_); trivial. % 18.87/19.00 apply (zenon_or_s _ _ zenon_H28); [ zenon_intro zenon_H2a | zenon_intro zenon_H1f ]. % 18.87/19.00 apply (zenon_L854_); trivial. % 18.87/19.00 apply (zenon_or_s _ _ zenon_H128); [ zenon_intro zenon_H9d | zenon_intro zenon_H129 ]. % 18.87/19.00 exact (zenon_H1ef zenon_H9d). % 18.87/19.00 apply (zenon_or_s _ _ zenon_H129); [ zenon_intro zenon_H10d | zenon_intro zenon_H12a ]. % 18.87/19.00 exact (zenon_H10a zenon_H10d). % 18.87/19.00 apply (zenon_or_s _ _ zenon_H12a); [ zenon_intro zenon_Hf0 | zenon_intro zenon_Hd6 ]. % 18.87/19.00 apply (zenon_or_s _ _ zenon_H2f); [ zenon_intro zenon_H34 | zenon_intro zenon_H33 ]. % 18.87/19.00 apply (zenon_L127_); trivial. % 18.87/19.00 apply (zenon_or_s _ _ zenon_H33); [ zenon_intro zenon_H36 | zenon_intro zenon_H35 ]. % 18.87/19.00 apply (zenon_L128_); trivial. % 18.87/19.00 apply (zenon_or_s _ _ zenon_H35); [ zenon_intro zenon_H2c | zenon_intro zenon_H37 ]. % 18.87/19.00 apply (zenon_L832_); trivial. % 18.87/19.00 apply (zenon_L300_); trivial. % 18.87/19.00 exact (zenon_H24e zenon_Hd6). % 18.87/19.00 (* end of lemma zenon_L855_ *) % 18.87/19.00 assert (zenon_L856_ : (((op (e3) (e0)) = (e1))\/(((op (e3) (e1)) = (e1))\/(((op (e3) (e2)) = (e1))\/((op (e3) (e3)) = (e1))))) -> (~((op (e3) (e0)) = (e1))) -> (~((op (e3) (e1)) = (e1))) -> ((op (e1) (e2)) = (e1)) -> (~((op (e1) (e2)) = (op (e3) (e2)))) -> (((op (e0) (e3)) = (e2))\/(((op (e1) (e3)) = (e2))\/(((op (e2) (e3)) = (e2))\/((op (e3) (e3)) = (e2))))) -> ((op (e1) (e3)) = (e0)) -> (~((op (e1) (e1)) = (op (e1) (e3)))) -> ((op (e1) (e1)) = (e2)) -> (~((op (e2) (e0)) = (op (e2) (e3)))) -> ((op (e2) (e0)) = (e2)) -> ((op (e3) (e1)) = (e2)) -> (~((op (e3) (e1)) = (op (e3) (e3)))) -> False). % 18.87/19.00 do 0 intro. intros zenon_He8 zenon_Had zenon_H250 zenon_Hf0 zenon_H115 zenon_H145 zenon_H1f zenon_H57 zenon_H110 zenon_H5b zenon_Hee zenon_H14d zenon_H130. % 18.87/19.00 apply (zenon_or_s _ _ zenon_He8); [ zenon_intro zenon_Hac | zenon_intro zenon_Heb ]. % 18.87/19.00 exact (zenon_Had zenon_Hac). % 18.87/19.00 apply (zenon_or_s _ _ zenon_Heb); [ zenon_intro zenon_Hae | zenon_intro zenon_Hec ]. % 18.87/19.00 exact (zenon_H250 zenon_Hae). % 18.87/19.00 apply (zenon_or_s _ _ zenon_Hec); [ zenon_intro zenon_Hba | zenon_intro zenon_Hc4 ]. % 18.87/19.00 apply (zenon_L69_); trivial. % 18.87/19.00 apply (zenon_L829_); trivial. % 18.87/19.00 (* end of lemma zenon_L856_ *) % 18.87/19.00 assert (zenon_L857_ : (((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) (e1)) = (e2)) -> (~((op (e1) (e1)) = (op (e1) (e3)))) -> ((op (e1) (e3)) = (e0)) -> (~((op (e1) (e2)) = (op (e3) (e2)))) -> (~((op (e3) (e1)) = (e1))) -> (~((op (e3) (e0)) = (e1))) -> (((op (e3) (e0)) = (e1))\/(((op (e3) (e1)) = (e1))\/(((op (e3) (e2)) = (e1))\/((op (e3) (e3)) = (e1))))) -> (((op (e0) (e3)) = (e2))\/(((op (e1) (e3)) = (e2))\/(((op (e2) (e3)) = (e2))\/((op (e3) (e3)) = (e2))))) -> (~((e2) = (e3))) -> ((op (e0) (e3)) = (e3)) -> (~((e1) = (e2))) -> (~((op (e2) (e0)) = (op (e2) (e3)))) -> ((op (e2) (e0)) = (e2)) -> ((op (e3) (e1)) = (e2)) -> (~((op (e3) (e1)) = (op (e3) (e3)))) -> False). % 18.87/19.00 do 0 intro. intros zenon_H128 zenon_H1ef zenon_H10a zenon_H110 zenon_H57 zenon_H1f zenon_H115 zenon_H250 zenon_Had zenon_He8 zenon_H145 zenon_H12b zenon_He3 zenon_H7c zenon_H5b zenon_Hee zenon_H14d zenon_H130. % 18.87/19.00 apply (zenon_or_s _ _ zenon_H128); [ zenon_intro zenon_H9d | zenon_intro zenon_H129 ]. % 18.87/19.00 exact (zenon_H1ef zenon_H9d). % 18.87/19.00 apply (zenon_or_s _ _ zenon_H129); [ zenon_intro zenon_H10d | zenon_intro zenon_H12a ]. % 18.87/19.00 exact (zenon_H10a zenon_H10d). % 18.87/19.00 apply (zenon_or_s _ _ zenon_H12a); [ zenon_intro zenon_Hf0 | zenon_intro zenon_Hd6 ]. % 18.87/19.00 apply (zenon_L856_); trivial. % 18.87/19.00 apply (zenon_L103_); trivial. % 18.87/19.00 (* end of lemma zenon_L857_ *) % 18.87/19.00 assert (zenon_L858_ : (((op (e3) (e0)) = (e2))\/(((op (e3) (e1)) = (e2))\/(((op (e3) (e2)) = (e2))\/((op (e3) (e3)) = (e2))))) -> ((op (e0) (e0)) = (e1)) -> ((op (e1) (e0)) = (e3)) -> (~((op (e3) (e1)) = (op (e3) (e3)))) -> ((op (e2) (e0)) = (e2)) -> (~((op (e2) (e0)) = (op (e2) (e3)))) -> (~((e1) = (e2))) -> ((op (e0) (e3)) = (e3)) -> (~((e2) = (e3))) -> (((op (e0) (e3)) = (e2))\/(((op (e1) (e3)) = (e2))\/(((op (e2) (e3)) = (e2))\/((op (e3) (e3)) = (e2))))) -> (((op (e3) (e0)) = (e1))\/(((op (e3) (e1)) = (e1))\/(((op (e3) (e2)) = (e1))\/((op (e3) (e3)) = (e1))))) -> (~((op (e3) (e0)) = (e1))) -> (~((op (e3) (e1)) = (e1))) -> (~((op (e1) (e2)) = (op (e3) (e2)))) -> (~((op (e1) (e1)) = (op (e1) (e3)))) -> ((op (e1) (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) (e2)) = (e2)) -> (~((op (e0) (e2)) = (op (e3) (e2)))) -> (((op (e2) (e3)) = (e0))\/(((op (e2) (e3)) = (e1))\/(((op (e2) (e3)) = (e2))\/((op (e2) (e3)) = (e3))))) -> (~((op (e2) (e2)) = (op (e2) (e3)))) -> ((op (e2) (e2)) = (e0)) -> (~((op (e2) (e3)) = (e1))) -> (~((op (e2) (e3)) = (op (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)) = (e1))) -> (~((op (e0) (e3)) = (op (e3) (e3)))) -> (~((op (e0) (e3)) = (op (e2) (e3)))) -> False). % 18.87/19.00 do 0 intro. intros zenon_H153 zenon_H7a zenon_H9e zenon_H130 zenon_Hee zenon_H5b zenon_H7c zenon_He3 zenon_H12b zenon_H145 zenon_He8 zenon_Had zenon_H250 zenon_H115 zenon_H57 zenon_H110 zenon_H10a zenon_H1ef zenon_H128 zenon_H150 zenon_H14f zenon_H11f zenon_H6d zenon_H2c zenon_H255 zenon_Hf3 zenon_He4 zenon_H1f zenon_H1d zenon_H231 zenon_Hc2 zenon_He2. % 18.87/19.00 apply (zenon_or_s _ _ zenon_H153); [ zenon_intro zenon_H148 | zenon_intro zenon_H154 ]. % 18.87/19.00 apply (zenon_L107_); trivial. % 18.87/19.00 apply (zenon_or_s _ _ zenon_H154); [ zenon_intro zenon_H14d | zenon_intro zenon_H155 ]. % 18.87/19.00 apply (zenon_L857_); trivial. % 18.87/19.00 apply (zenon_or_s _ _ zenon_H155); [ zenon_intro zenon_H151 | zenon_intro zenon_Hf6 ]. % 18.87/19.00 apply (zenon_L104_); trivial. % 18.87/19.00 apply (zenon_L830_); trivial. % 18.87/19.00 (* end of lemma zenon_L858_ *) % 18.87/19.00 assert (zenon_L859_ : (((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 (e0) (e2)) = (e0))\/(((op (e1) (e2)) = (e0))\/(((op (e2) (e2)) = (e0))\/((op (e3) (e2)) = (e0))))) -> (~((op (e0) (e1)) = (op (e0) (e2)))) -> (~((op (e1) (e1)) = (op (e1) (e2)))) -> (~((op (e3) (e0)) = (op (e3) (e2)))) -> (~((op (e0) (e1)) = (op (e0) (e3)))) -> (((op (e0) (e3)) = (e0))\/(((op (e1) (e3)) = (e0))\/(((op (e2) (e3)) = (e0))\/((op (e3) (e3)) = (e0))))) -> (~((op (e2) (e2)) = (op (e3) (e2)))) -> (((op (e3) (e2)) = (e0))\/(((op (e3) (e2)) = (e1))\/(((op (e3) (e2)) = (e2))\/((op (e3) (e2)) = (e3))))) -> (~((op (e2) (e2)) = (e2))) -> (~((op (e2) (e2)) = (e1))) -> (((op (e2) (e2)) = (e0))\/(((op (e2) (e2)) = (e1))\/(((op (e2) (e2)) = (e2))\/((op (e2) (e2)) = (e3))))) -> (~((op (e1) (e2)) = (op (e2) (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 (e3) (e0)) = (e0)) -> ((op (e0) (e1)) = (e0)) -> (~((op (e0) (e1)) = (op (e2) (e1)))) -> (~((op (e0) (e3)) = (op (e2) (e3)))) -> (~((op (e0) (e3)) = (op (e3) (e3)))) -> (~((op (e0) (e3)) = (e1))) -> (~((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)) = (op (e3) (e3)))) -> (~((op (e2) (e3)) = (e1))) -> (~((op (e2) (e2)) = (op (e2) (e3)))) -> (((op (e2) (e3)) = (e0))\/(((op (e2) (e3)) = (e1))\/(((op (e2) (e3)) = (e2))\/((op (e2) (e3)) = (e3))))) -> (~((op (e0) (e2)) = (op (e3) (e2)))) -> ((op (e0) (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 (e1) (e1)) = (e2)) -> (~((op (e1) (e1)) = (op (e1) (e3)))) -> (~((op (e1) (e2)) = (op (e3) (e2)))) -> (~((op (e3) (e1)) = (e1))) -> (~((op (e3) (e0)) = (e1))) -> (((op (e3) (e0)) = (e1))\/(((op (e3) (e1)) = (e1))\/(((op (e3) (e2)) = (e1))\/((op (e3) (e3)) = (e1))))) -> (((op (e0) (e3)) = (e2))\/(((op (e1) (e3)) = (e2))\/(((op (e2) (e3)) = (e2))\/((op (e3) (e3)) = (e2))))) -> (~((e2) = (e3))) -> ((op (e0) (e3)) = (e3)) -> (~((e1) = (e2))) -> (~((op (e2) (e0)) = (op (e2) (e3)))) -> ((op (e2) (e0)) = (e2)) -> (~((op (e3) (e1)) = (op (e3) (e3)))) -> ((op (e1) (e0)) = (e3)) -> ((op (e0) (e0)) = (e1)) -> (((op (e3) (e0)) = (e2))\/(((op (e3) (e1)) = (e2))\/(((op (e3) (e2)) = (e2))\/((op (e3) (e3)) = (e2))))) -> (~((op (e1) (e3)) = (op (e2) (e3)))) -> False). % 18.87/19.00 do 0 intro. intros zenon_H22 zenon_H1fa zenon_H71 zenon_H6a zenon_H4a zenon_H4f zenon_H6f zenon_H54 zenon_H67 zenon_H18f zenon_H191 zenon_H173 zenon_H198 zenon_H1c4 zenon_H2b zenon_H149 zenon_H2f zenon_H17b zenon_H44 zenon_H49 zenon_H17e zenon_He2 zenon_Hc2 zenon_H231 zenon_H1d zenon_He4 zenon_Hf3 zenon_H255 zenon_H6d zenon_H11f zenon_H14f zenon_H150 zenon_H128 zenon_H1ef zenon_H10a zenon_H110 zenon_H57 zenon_H115 zenon_H250 zenon_Had zenon_He8 zenon_H145 zenon_H12b zenon_He3 zenon_H7c zenon_H5b zenon_Hee zenon_H130 zenon_H9e zenon_H7a zenon_H153 zenon_Hdb. % 18.87/19.00 apply (zenon_or_s _ _ zenon_H22); [ zenon_intro zenon_H27 | zenon_intro zenon_H26 ]. % 18.87/19.00 apply (zenon_L312_); trivial. % 18.87/19.00 apply (zenon_or_s _ _ zenon_H26); [ zenon_intro zenon_H29 | zenon_intro zenon_H28 ]. % 18.87/19.00 apply (zenon_L22_); trivial. % 18.87/19.00 apply (zenon_or_s _ _ zenon_H28); [ zenon_intro zenon_H2a | zenon_intro zenon_H1f ]. % 18.87/19.00 apply (zenon_L834_); trivial. % 18.87/19.00 apply (zenon_or_s _ _ zenon_H2f); [ zenon_intro zenon_H34 | zenon_intro zenon_H33 ]. % 18.87/19.00 apply (zenon_L127_); trivial. % 18.87/19.00 apply (zenon_or_s _ _ zenon_H33); [ zenon_intro zenon_H36 | zenon_intro zenon_H35 ]. % 18.87/19.00 apply (zenon_L128_); trivial. % 18.87/19.00 apply (zenon_or_s _ _ zenon_H35); [ zenon_intro zenon_H2c | zenon_intro zenon_H37 ]. % 18.87/19.00 apply (zenon_L858_); trivial. % 18.87/19.00 apply (zenon_L130_); trivial. % 18.87/19.00 (* end of lemma zenon_L859_ *) % 18.87/19.00 assert (zenon_L860_ : (((op (e3) (e0)) = (e0))\/(((op (e3) (e1)) = (e0))\/(((op (e3) (e2)) = (e0))\/((op (e3) (e3)) = (e0))))) -> ((op (e1) (e0)) = (e3)) -> (~((e1) = (e2))) -> (~((op (e1) (e2)) = (op (e3) (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) (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) = (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)) = (e1))) -> (~((op (e2) (e2)) = (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) (e1)) = (op (e1) (e2)))) -> (~((op (e0) (e1)) = (op (e0) (e2)))) -> (((op (e0) (e2)) = (e0))\/(((op (e1) (e2)) = (e0))\/(((op (e2) (e2)) = (e0))\/((op (e3) (e2)) = (e0))))) -> (~((op (e1) (e0)) = (op (e3) (e0)))) -> (((op (e1) (e0)) = (e0))\/(((op (e1) (e1)) = (e0))\/(((op (e1) (e2)) = (e0))\/((op (e1) (e3)) = (e0))))) -> (~((op (e1) (e0)) = (op (e1) (e3)))) -> ((op (e1) (e0)) = (e0)) -> ((op (e0) (e1)) = (e0)) -> (~((op (e0) (e1)) = (op (e0) (e3)))) -> (((op (e0) (e3)) = (e0))\/(((op (e1) (e3)) = (e0))\/(((op (e2) (e3)) = (e0))\/((op (e3) (e3)) = (e0))))) -> (~((op (e2) (e2)) = (op (e3) (e2)))) -> (~((op (e3) (e0)) = (e1))) -> ((op (e0) (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 (e2) (e3)) = (e1))) -> ((op (e2) (e2)) = (e0)) -> (~((op (e2) (e2)) = (op (e2) (e3)))) -> (~((op (e0) (e2)) = (op (e3) (e2)))) -> ((op (e0) (e2)) = (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)) = (e2)) -> (~((op (e2) (e0)) = (op (e2) (e3)))) -> ((op (e2) (e0)) = (e2)) -> (~((op (e3) (e1)) = (op (e3) (e3)))) -> (((op (e1) (e0)) = (e3))\/(((op (e1) (e1)) = (e3))\/(((op (e1) (e2)) = (e3))\/((op (e1) (e3)) = (e3))))) -> ((op (e0) (e0)) = (e1)) -> (~((e2) = (e3))) -> (~((e1) = (e3))) -> (((op (e3) (e0)) = (e1))\/(((op (e3) (e1)) = (e1))\/(((op (e3) (e2)) = (e1))\/((op (e3) (e3)) = (e1))))) -> (~((op (e3) (e0)) = (op (e3) (e3)))) -> ((op (e1) (e2)) = (e1)) -> (~((op (e1) (e2)) = (op (e1) (e3)))) -> (((op (e0) (e3)) = (e1))\/(((op (e1) (e3)) = (e1))\/(((op (e2) (e3)) = (e1))\/((op (e3) (e3)) = (e1))))) -> (~((op (e3) (e1)) = (e1))) -> (~((op (e3) (e2)) = (e1))) -> (((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)))) -> (((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)) = (e1))) -> (~((op (e1) (e3)) = (op (e2) (e3)))) -> (~((op (e0) (e3)) = (op (e2) (e3)))) -> ((op (e2) (e1)) = (e1)) -> (~((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))))) -> (~((op (e0) (e3)) = (op (e1) (e3)))) -> False). % 18.87/19.00 do 0 intro. intros zenon_H1ac zenon_H9e zenon_H7c zenon_H115 zenon_H10a zenon_H1ef zenon_H128 zenon_H17e zenon_H17b zenon_H2f zenon_H149 zenon_H2b zenon_H1c4 zenon_H198 zenon_H173 zenon_H191 zenon_H6f zenon_H4f zenon_H4a zenon_H6a zenon_H1fa zenon_H22 zenon_Hd8 zenon_H27 zenon_H49 zenon_H54 zenon_H67 zenon_H18f zenon_Had zenon_He3 zenon_H160 zenon_Hdf zenon_H255 zenon_H2c zenon_H6d zenon_H14f zenon_H150 zenon_H145 zenon_H57 zenon_H110 zenon_H5b zenon_Hee zenon_H130 zenon_H16f zenon_H7a zenon_H12b zenon_H95 zenon_He8 zenon_H71 zenon_Hf0 zenon_H124 zenon_H133 zenon_H250 zenon_H251 zenon_H153 zenon_H24e zenon_Hd5 zenon_He4 zenon_Hc2 zenon_H231 zenon_Hdb zenon_He2 zenon_Ha5 zenon_H1c7 zenon_Hf3 zenon_H11f zenon_H1d. % 18.87/19.00 apply (zenon_or_s _ _ zenon_H1ac); [ zenon_intro zenon_H44 | zenon_intro zenon_H1af ]. % 18.87/19.00 apply (zenon_L859_); trivial. % 18.87/19.00 apply (zenon_or_s _ _ zenon_H1af); [ zenon_intro zenon_H1b1 | zenon_intro zenon_H1b0 ]. % 18.87/19.00 apply (zenon_L259_); trivial. % 18.87/19.00 apply (zenon_or_s _ _ zenon_H1b0); [ zenon_intro zenon_H61 | zenon_intro zenon_H60 ]. % 18.87/19.00 apply (zenon_L146_); trivial. % 18.87/19.00 apply (zenon_or_s _ _ zenon_He8); [ zenon_intro zenon_Hac | zenon_intro zenon_Heb ]. % 18.87/19.00 exact (zenon_Had zenon_Hac). % 18.87/19.00 apply (zenon_or_s _ _ zenon_Heb); [ zenon_intro zenon_Hae | zenon_intro zenon_Hec ]. % 18.87/19.00 exact (zenon_H250 zenon_Hae). % 18.87/19.00 apply (zenon_or_s _ _ zenon_Hec); [ zenon_intro zenon_Hba | zenon_intro zenon_Hc4 ]. % 18.87/19.00 exact (zenon_H251 zenon_Hba). % 18.87/19.00 apply (zenon_or_s _ _ zenon_H153); [ zenon_intro zenon_H148 | zenon_intro zenon_H154 ]. % 18.87/19.00 apply (zenon_L216_); trivial. % 18.87/19.00 apply (zenon_or_s _ _ zenon_H154); [ zenon_intro zenon_H14d | zenon_intro zenon_H155 ]. % 18.87/19.00 apply (zenon_L164_); trivial. % 18.87/19.00 apply (zenon_or_s _ _ zenon_H155); [ zenon_intro zenon_H151 | zenon_intro zenon_Hf6 ]. % 18.87/19.00 apply (zenon_L104_); trivial. % 18.87/19.00 apply (zenon_L848_); trivial. % 18.87/19.00 (* end of lemma zenon_L860_ *) % 18.87/19.00 assert (zenon_L861_ : (((op (e0) (e0)) = (e3))\/(((op (e1) (e0)) = (e3))\/(((op (e2) (e0)) = (e3))\/((op (e3) (e0)) = (e3))))) -> (~((e1) = (e3))) -> ((op (e0) (e0)) = (e1)) -> (~((op (e2) (e0)) = (op (e2) (e2)))) -> ((op (e2) (e2)) = (e3)) -> ((op (e3) (e0)) = (e2)) -> (~((e2) = (e3))) -> False). % 18.87/19.00 do 0 intro. intros zenon_H1e0 zenon_H95 zenon_H7a zenon_H52 zenon_Haa zenon_H148 zenon_H12b. % 18.87/19.00 apply (zenon_or_s _ _ zenon_H1e0); [ zenon_intro zenon_H3a | zenon_intro zenon_H1e1 ]. % 18.87/19.00 apply (zenon_L35_); trivial. % 18.87/19.00 apply (zenon_or_s _ _ zenon_H1e1); [ zenon_intro zenon_H9e | zenon_intro zenon_H1e2 ]. % 18.87/19.00 apply (zenon_L107_); trivial. % 18.87/19.00 apply (zenon_or_s _ _ zenon_H1e2); [ zenon_intro zenon_H3b | zenon_intro zenon_H15e ]. % 18.87/19.00 apply (zenon_L168_); trivial. % 18.87/19.00 apply (zenon_L109_); trivial. % 18.87/19.00 (* end of lemma zenon_L861_ *) % 18.87/19.00 assert (zenon_L862_ : (((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 (e0) (e3)) = (e2)) -> (~((op (e2) (e3)) = (e1))) -> ((op (e1) (e2)) = (e1)) -> (~((op (e1) (e2)) = (op (e1) (e3)))) -> (~((op (e0) (e3)) = (e1))) -> (((op (e0) (e3)) = (e1))\/(((op (e1) (e3)) = (e1))\/(((op (e2) (e3)) = (e1))\/((op (e3) (e3)) = (e1))))) -> (~((op (e2) (e0)) = (op (e2) (e3)))) -> ((op (e2) (e0)) = (e0)) -> ((op (e3) (e1)) = (e0)) -> (~((op (e3) (e1)) = (op (e3) (e3)))) -> False). % 18.87/19.00 do 0 intro. intros zenon_H67 zenon_H54 zenon_H49 zenon_Hcd zenon_H255 zenon_Hf0 zenon_H124 zenon_H231 zenon_H133 zenon_H5b zenon_H34 zenon_H1b1 zenon_H130. % 18.87/19.00 apply (zenon_or_s _ _ zenon_H67); [ zenon_intro zenon_H1e | zenon_intro zenon_H68 ]. % 18.87/19.00 apply (zenon_L12_); trivial. % 18.87/19.00 apply (zenon_or_s _ _ zenon_H68); [ zenon_intro zenon_H1f | zenon_intro zenon_H69 ]. % 18.87/19.00 apply (zenon_L815_); trivial. % 18.87/19.00 apply (zenon_or_s _ _ zenon_H69); [ zenon_intro zenon_H37 | zenon_intro zenon_H60 ]. % 18.87/19.00 apply (zenon_L14_); trivial. % 18.87/19.00 apply (zenon_L244_); trivial. % 18.87/19.00 (* end of lemma zenon_L862_ *) % 18.87/19.00 assert (zenon_L863_ : (((op (e3) (e0)) = (e0))\/(((op (e3) (e1)) = (e0))\/(((op (e3) (e2)) = (e0))\/((op (e3) (e3)) = (e0))))) -> ((op (e0) (e0)) = (e1)) -> (~((op (e2) (e0)) = (op (e2) (e1)))) -> ((op (e2) (e1)) = (e2)) -> (~((op (e2) (e0)) = (e1))) -> (((op (e2) (e0)) = (e0))\/(((op (e2) (e0)) = (e1))\/(((op (e2) (e0)) = (e2))\/((op (e2) (e0)) = (e3))))) -> (~((op (e1) (e2)) = (op (e2) (e2)))) -> (~((op (e0) (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 (e3) (e1)) = (op (e3) (e3)))) -> ((op (e2) (e0)) = (e0)) -> (~((op (e2) (e0)) = (op (e2) (e3)))) -> (((op (e0) (e3)) = (e1))\/(((op (e1) (e3)) = (e1))\/(((op (e2) (e3)) = (e1))\/((op (e3) (e3)) = (e1))))) -> (~((op (e0) (e3)) = (e1))) -> (~((op (e1) (e2)) = (op (e1) (e3)))) -> ((op (e1) (e2)) = (e1)) -> (~((op (e2) (e3)) = (e1))) -> ((op (e0) (e1)) = (e0)) -> (~((op (e0) (e1)) = (op (e0) (e3)))) -> (((op (e0) (e3)) = (e0))\/(((op (e1) (e3)) = (e0))\/(((op (e2) (e3)) = (e0))\/((op (e3) (e3)) = (e0))))) -> ((op (e1) (e2)) = (e0)) -> (~((op (e1) (e2)) = (op (e3) (e2)))) -> (((op (e3) (e0)) = (e1))\/(((op (e3) (e1)) = (e1))\/(((op (e3) (e2)) = (e1))\/((op (e3) (e3)) = (e1))))) -> (~((op (e3) (e0)) = (e1))) -> (~((op (e3) (e1)) = (e1))) -> (~((op (e3) (e2)) = (e1))) -> (((op (e0) (e3)) = (e3))\/(((op (e1) (e3)) = (e3))\/(((op (e2) (e3)) = (e3))\/((op (e3) (e3)) = (e3))))) -> (~((e2) = (e3))) -> (~((op (e0) (e3)) = (op (e2) (e3)))) -> ((op (e2) (e1)) = (e1)) -> (~((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))))) -> (~((op (e1) (e3)) = (op (e2) (e3)))) -> ((op (e1) (e0)) = (e2)) -> (~((op (e1) (e0)) = (op (e1) (e3)))) -> (~((op (e1) (e3)) = (op (e3) (e3)))) -> ((op (e0) (e3)) = (e2)) -> (((op (e1) (e3)) = (e0))\/(((op (e1) (e3)) = (e1))\/(((op (e1) (e3)) = (e2))\/((op (e1) (e3)) = (e3))))) -> (~((op (e3) (e3)) = (e3))) -> False). % 18.87/19.00 do 0 intro. intros zenon_H1ac zenon_H7a zenon_H1f0 zenon_H1ca zenon_H1db zenon_H259 zenon_H2b zenon_H17e zenon_H17b zenon_H2f zenon_H130 zenon_H34 zenon_H5b zenon_H133 zenon_H231 zenon_H124 zenon_Hf0 zenon_H255 zenon_H49 zenon_H54 zenon_H67 zenon_H2a zenon_H115 zenon_He8 zenon_Had zenon_H250 zenon_H251 zenon_H136 zenon_H12b zenon_He2 zenon_Ha5 zenon_H1c7 zenon_Hf3 zenon_H11f zenon_Hdb zenon_H86 zenon_Hd8 zenon_Hd5 zenon_Hcd zenon_Hdf zenon_H102. % 18.87/19.00 apply (zenon_or_s _ _ zenon_H1ac); [ zenon_intro zenon_H44 | zenon_intro zenon_H1af ]. % 18.87/19.00 apply (zenon_L730_); trivial. % 18.87/19.00 apply (zenon_or_s _ _ zenon_H1af); [ zenon_intro zenon_H1b1 | zenon_intro zenon_H1b0 ]. % 18.87/19.00 apply (zenon_L862_); trivial. % 18.87/19.00 apply (zenon_or_s _ _ zenon_H1b0); [ zenon_intro zenon_H61 | zenon_intro zenon_H60 ]. % 18.87/19.00 apply (zenon_L176_); trivial. % 18.87/19.00 apply (zenon_L802_); trivial. % 18.87/19.00 (* end of lemma zenon_L863_ *) % 18.87/19.00 assert (zenon_L864_ : (((op (e1) (e0)) = (e0))\/(((op (e1) (e1)) = (e0))\/(((op (e1) (e2)) = (e0))\/((op (e1) (e3)) = (e0))))) -> (~((op (e1) (e0)) = (op (e2) (e0)))) -> (~((op (e3) (e2)) = (op (e3) (e3)))) -> (~((op (e1) (e1)) = (op (e1) (e3)))) -> (~((op (e2) (e0)) = (op (e2) (e2)))) -> (~((op (e1) (e1)) = (op (e1) (e2)))) -> (~((op (e0) (e1)) = (op (e0) (e2)))) -> (((op (e0) (e2)) = (e0))\/(((op (e1) (e2)) = (e0))\/(((op (e2) (e2)) = (e0))\/((op (e3) (e2)) = (e0))))) -> (~((op (e1) (e3)) = (op (e3) (e3)))) -> (((op (e3) (e0)) = (e0))\/(((op (e3) (e1)) = (e0))\/(((op (e3) (e2)) = (e0))\/((op (e3) (e3)) = (e0))))) -> (~((e0) = (e2))) -> (~((op (e3) (e1)) = (op (e3) (e3)))) -> ((op (e2) (e0)) = (e0)) -> (~((op (e2) (e0)) = (op (e2) (e3)))) -> (((op (e0) (e3)) = (e1))\/(((op (e1) (e3)) = (e1))\/(((op (e2) (e3)) = (e1))\/((op (e3) (e3)) = (e1))))) -> (~((op (e0) (e3)) = (e1))) -> (~((op (e1) (e2)) = (op (e1) (e3)))) -> (~((op (e2) (e3)) = (e1))) -> ((op (e0) (e1)) = (e0)) -> (~((op (e0) (e1)) = (op (e0) (e3)))) -> (((op (e0) (e3)) = (e0))\/(((op (e1) (e3)) = (e0))\/(((op (e2) (e3)) = (e0))\/((op (e3) (e3)) = (e0))))) -> (~((op (e1) (e2)) = (op (e3) (e2)))) -> (((op (e0) (e3)) = (e3))\/(((op (e1) (e3)) = (e3))\/(((op (e2) (e3)) = (e3))\/((op (e3) (e3)) = (e3))))) -> (~((e2) = (e3))) -> (~((op (e0) (e3)) = (op (e2) (e3)))) -> ((op (e2) (e1)) = (e1)) -> (~((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))))) -> ((op (e0) (e0)) = (e1)) -> ((op (e3) (e0)) = (e2)) -> (((op (e1) (e3)) = (e0))\/(((op (e1) (e3)) = (e1))\/(((op (e1) (e3)) = (e2))\/((op (e1) (e3)) = (e3))))) -> (~((op (e1) (e0)) = (op (e1) (e3)))) -> (~((op (e1) (e3)) = (op (e2) (e3)))) -> (~((op (e1) (e0)) = (e1))) -> (~((op (e1) (e0)) = (op (e1) (e2)))) -> (((op (e1) (e0)) = (e0))\/(((op (e1) (e0)) = (e1))\/(((op (e1) (e0)) = (e2))\/((op (e1) (e0)) = (e3))))) -> (~((op (e3) (e3)) = (e3))) -> (~((op (e1) (e1)) = (e1))) -> (((op (e1) (e0)) = (e1))\/(((op (e1) (e1)) = (e1))\/(((op (e1) (e2)) = (e1))\/((op (e1) (e3)) = (e1))))) -> (((op (e3) (e0)) = (e1))\/(((op (e3) (e1)) = (e1))\/(((op (e3) (e2)) = (e1))\/((op (e3) (e3)) = (e1))))) -> (~((op (e3) (e0)) = (e1))) -> (~((op (e3) (e1)) = (e1))) -> (~((op (e3) (e2)) = (e1))) -> ((op (e0) (e3)) = (e2)) -> False). % 18.87/19.00 do 0 intro. intros zenon_H22 zenon_H201 zenon_H62 zenon_H57 zenon_H52 zenon_H4f zenon_H4a zenon_H6a zenon_Hd5 zenon_H1ac zenon_H149 zenon_H130 zenon_H34 zenon_H5b zenon_H133 zenon_H231 zenon_H124 zenon_H255 zenon_H49 zenon_H54 zenon_H67 zenon_H115 zenon_H136 zenon_H12b zenon_He2 zenon_Ha5 zenon_H1c7 zenon_Hf3 zenon_H11f zenon_H7a zenon_H148 zenon_Hdf zenon_Hd8 zenon_Hdb zenon_H1ef zenon_H24a zenon_H25e zenon_H102 zenon_H10a zenon_H128 zenon_He8 zenon_Had zenon_H250 zenon_H251 zenon_Hcd. % 18.87/19.00 apply (zenon_or_s _ _ zenon_H22); [ zenon_intro zenon_H27 | zenon_intro zenon_H26 ]. % 18.87/19.00 apply (zenon_L332_); trivial. % 18.87/19.00 apply (zenon_or_s _ _ zenon_H26); [ zenon_intro zenon_H29 | zenon_intro zenon_H28 ]. % 18.87/19.00 apply (zenon_L17_); trivial. % 18.87/19.00 apply (zenon_or_s _ _ zenon_H28); [ zenon_intro zenon_H2a | zenon_intro zenon_H1f ]. % 18.87/19.00 apply (zenon_or_s _ _ zenon_H128); [ zenon_intro zenon_H9d | zenon_intro zenon_H129 ]. % 18.87/19.00 exact (zenon_H1ef zenon_H9d). % 18.87/19.00 apply (zenon_or_s _ _ zenon_H129); [ zenon_intro zenon_H10d | zenon_intro zenon_H12a ]. % 18.87/19.01 exact (zenon_H10a zenon_H10d). % 18.87/19.01 apply (zenon_or_s _ _ zenon_H12a); [ zenon_intro zenon_Hf0 | zenon_intro zenon_Hd6 ]. % 18.87/19.01 apply (zenon_or_s _ _ zenon_H1ac); [ zenon_intro zenon_H44 | zenon_intro zenon_H1af ]. % 18.87/19.01 apply (zenon_L100_); trivial. % 18.87/19.01 apply (zenon_or_s _ _ zenon_H1af); [ zenon_intro zenon_H1b1 | zenon_intro zenon_H1b0 ]. % 18.87/19.01 apply (zenon_L862_); trivial. % 18.87/19.01 apply (zenon_or_s _ _ zenon_H1b0); [ zenon_intro zenon_H61 | zenon_intro zenon_H60 ]. % 18.87/19.01 apply (zenon_L176_); trivial. % 18.87/19.01 apply (zenon_L813_); trivial. % 18.87/19.01 apply (zenon_L800_); trivial. % 18.87/19.01 apply (zenon_L803_); trivial. % 18.87/19.01 (* end of lemma zenon_L864_ *) % 18.87/19.01 assert (zenon_L865_ : (((op (e0) (e0)) = (e2))\/(((op (e1) (e0)) = (e2))\/(((op (e2) (e0)) = (e2))\/((op (e3) (e0)) = (e2))))) -> (~((op (e0) (e0)) = (op (e0) (e3)))) -> (~((op (e2) (e2)) = (e2))) -> (~((op (e2) (e0)) = (op (e2) (e1)))) -> (~((op (e2) (e0)) = (e1))) -> (((op (e2) (e0)) = (e0))\/(((op (e2) (e0)) = (e1))\/(((op (e2) (e0)) = (e2))\/((op (e2) (e0)) = (e3))))) -> (~((op (e1) (e2)) = (op (e2) (e2)))) -> (~((op (e0) (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 (e2) (e0)) = (e2))\/(((op (e2) (e1)) = (e2))\/(((op (e2) (e2)) = (e2))\/((op (e2) (e3)) = (e2))))) -> (~((op (e1) (e3)) = (e1))) -> (((op (e1) (e0)) = (e0))\/(((op (e1) (e1)) = (e0))\/(((op (e1) (e2)) = (e0))\/((op (e1) (e3)) = (e0))))) -> (~((op (e1) (e0)) = (op (e2) (e0)))) -> (~((op (e3) (e2)) = (op (e3) (e3)))) -> (~((op (e1) (e1)) = (op (e1) (e3)))) -> (~((op (e2) (e0)) = (op (e2) (e2)))) -> (~((op (e1) (e1)) = (op (e1) (e2)))) -> (~((op (e0) (e1)) = (op (e0) (e2)))) -> (((op (e0) (e2)) = (e0))\/(((op (e1) (e2)) = (e0))\/(((op (e2) (e2)) = (e0))\/((op (e3) (e2)) = (e0))))) -> (~((op (e1) (e3)) = (op (e3) (e3)))) -> (((op (e3) (e0)) = (e0))\/(((op (e3) (e1)) = (e0))\/(((op (e3) (e2)) = (e0))\/((op (e3) (e3)) = (e0))))) -> (~((e0) = (e2))) -> (~((op (e3) (e1)) = (op (e3) (e3)))) -> ((op (e2) (e0)) = (e0)) -> (~((op (e2) (e0)) = (op (e2) (e3)))) -> (((op (e0) (e3)) = (e1))\/(((op (e1) (e3)) = (e1))\/(((op (e2) (e3)) = (e1))\/((op (e3) (e3)) = (e1))))) -> (~((op (e0) (e3)) = (e1))) -> (~((op (e1) (e2)) = (op (e1) (e3)))) -> (~((op (e2) (e3)) = (e1))) -> ((op (e0) (e1)) = (e0)) -> (~((op (e0) (e1)) = (op (e0) (e3)))) -> (((op (e0) (e3)) = (e0))\/(((op (e1) (e3)) = (e0))\/(((op (e2) (e3)) = (e0))\/((op (e3) (e3)) = (e0))))) -> (~((op (e1) (e2)) = (op (e3) (e2)))) -> (((op (e0) (e3)) = (e3))\/(((op (e1) (e3)) = (e3))\/(((op (e2) (e3)) = (e3))\/((op (e3) (e3)) = (e3))))) -> (~((e2) = (e3))) -> (~((op (e0) (e3)) = (op (e2) (e3)))) -> ((op (e2) (e1)) = (e1)) -> (~((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))))) -> ((op (e0) (e0)) = (e1)) -> (((op (e1) (e3)) = (e0))\/(((op (e1) (e3)) = (e1))\/(((op (e1) (e3)) = (e2))\/((op (e1) (e3)) = (e3))))) -> (~((op (e1) (e0)) = (op (e1) (e3)))) -> (~((op (e1) (e3)) = (op (e2) (e3)))) -> (~((op (e1) (e0)) = (e1))) -> (~((op (e1) (e0)) = (op (e1) (e2)))) -> (((op (e1) (e0)) = (e0))\/(((op (e1) (e0)) = (e1))\/(((op (e1) (e0)) = (e2))\/((op (e1) (e0)) = (e3))))) -> (~((op (e3) (e3)) = (e3))) -> (~((op (e1) (e1)) = (e1))) -> (((op (e1) (e0)) = (e1))\/(((op (e1) (e1)) = (e1))\/(((op (e1) (e2)) = (e1))\/((op (e1) (e3)) = (e1))))) -> (((op (e3) (e0)) = (e1))\/(((op (e3) (e1)) = (e1))\/(((op (e3) (e2)) = (e1))\/((op (e3) (e3)) = (e1))))) -> (~((op (e3) (e0)) = (e1))) -> (~((op (e3) (e1)) = (e1))) -> (~((op (e3) (e2)) = (e1))) -> ((op (e0) (e3)) = (e2)) -> False). % 18.87/19.01 do 0 intro. intros zenon_H1fe zenon_H189 zenon_H173 zenon_H1f0 zenon_H1db zenon_H259 zenon_H2b zenon_H17e zenon_H17b zenon_H2f zenon_H1d5 zenon_H24e zenon_H22 zenon_H201 zenon_H62 zenon_H57 zenon_H52 zenon_H4f zenon_H4a zenon_H6a zenon_Hd5 zenon_H1ac zenon_H149 zenon_H130 zenon_H34 zenon_H5b zenon_H133 zenon_H231 zenon_H124 zenon_H255 zenon_H49 zenon_H54 zenon_H67 zenon_H115 zenon_H136 zenon_H12b zenon_He2 zenon_Ha5 zenon_H1c7 zenon_Hf3 zenon_H11f zenon_H7a zenon_Hdf zenon_Hd8 zenon_Hdb zenon_H1ef zenon_H24a zenon_H25e zenon_H102 zenon_H10a zenon_H128 zenon_He8 zenon_Had zenon_H250 zenon_H251 zenon_Hcd. % 18.87/19.01 apply (zenon_or_s _ _ zenon_H1fe); [ zenon_intro zenon_H7b | zenon_intro zenon_H1ff ]. % 18.87/19.01 apply (zenon_L375_); trivial. % 18.87/19.01 apply (zenon_or_s _ _ zenon_H1ff); [ zenon_intro zenon_H86 | zenon_intro zenon_H200 ]. % 18.87/19.01 apply (zenon_or_s _ _ zenon_H22); [ zenon_intro zenon_H27 | zenon_intro zenon_H26 ]. % 18.87/19.01 apply (zenon_L257_); trivial. % 18.87/19.01 apply (zenon_or_s _ _ zenon_H26); [ zenon_intro zenon_H29 | zenon_intro zenon_H28 ]. % 18.87/19.01 apply (zenon_L17_); trivial. % 18.87/19.01 apply (zenon_or_s _ _ zenon_H28); [ zenon_intro zenon_H2a | zenon_intro zenon_H1f ]. % 18.87/19.01 apply (zenon_or_s _ _ zenon_H128); [ zenon_intro zenon_H9d | zenon_intro zenon_H129 ]. % 18.87/19.01 exact (zenon_H1ef zenon_H9d). % 18.87/19.01 apply (zenon_or_s _ _ zenon_H129); [ zenon_intro zenon_H10d | zenon_intro zenon_H12a ]. % 18.87/19.01 exact (zenon_H10a zenon_H10d). % 18.87/19.01 apply (zenon_or_s _ _ zenon_H12a); [ zenon_intro zenon_Hf0 | zenon_intro zenon_Hd6 ]. % 18.87/19.01 apply (zenon_or_s _ _ zenon_H1d5); [ zenon_intro zenon_Hee | zenon_intro zenon_H1d6 ]. % 18.87/19.01 apply (zenon_L204_); trivial. % 18.87/19.01 apply (zenon_or_s _ _ zenon_H1d6); [ zenon_intro zenon_H1ca | zenon_intro zenon_H1d7 ]. % 18.87/19.01 apply (zenon_L863_); trivial. % 18.87/19.01 apply (zenon_or_s _ _ zenon_H1d7); [ zenon_intro zenon_H176 | zenon_intro zenon_H11d ]. % 18.87/19.01 exact (zenon_H173 zenon_H176). % 18.87/19.01 apply (zenon_L234_); trivial. % 18.87/19.01 exact (zenon_H24e zenon_Hd6). % 18.87/19.01 apply (zenon_L803_); trivial. % 18.87/19.01 apply (zenon_or_s _ _ zenon_H200); [ zenon_intro zenon_Hee | zenon_intro zenon_H148 ]. % 18.87/19.01 apply (zenon_L204_); trivial. % 18.87/19.01 apply (zenon_L864_); trivial. % 18.87/19.01 (* end of lemma zenon_L865_ *) % 18.87/19.01 assert (zenon_L866_ : (~((op (e3) (e2)) = (e1))) -> (~((op (e3) (e1)) = (e1))) -> (~((op (e3) (e0)) = (e1))) -> (((op (e3) (e0)) = (e1))\/(((op (e3) (e1)) = (e1))\/(((op (e3) (e2)) = (e1))\/((op (e3) (e3)) = (e1))))) -> (((op (e1) (e0)) = (e1))\/(((op (e1) (e1)) = (e1))\/(((op (e1) (e2)) = (e1))\/((op (e1) (e3)) = (e1))))) -> (~((op (e1) (e1)) = (e1))) -> (~((op (e3) (e3)) = (e3))) -> (((op (e1) (e0)) = (e0))\/(((op (e1) (e0)) = (e1))\/(((op (e1) (e0)) = (e2))\/((op (e1) (e0)) = (e3))))) -> (~((op (e1) (e0)) = (op (e1) (e2)))) -> (~((op (e1) (e0)) = (e1))) -> (~((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 (e2) (e3)) = (e0))\/(((op (e2) (e3)) = (e1))\/(((op (e2) (e3)) = (e2))\/((op (e2) (e3)) = (e3))))) -> (~((op (e2) (e3)) = (op (e3) (e3)))) -> (~((op (e2) (e1)) = (op (e2) (e3)))) -> ((op (e2) (e1)) = (e1)) -> (~((op (e0) (e3)) = (op (e2) (e3)))) -> (~((e2) = (e3))) -> (((op (e0) (e3)) = (e3))\/(((op (e1) (e3)) = (e3))\/(((op (e2) (e3)) = (e3))\/((op (e3) (e3)) = (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) (e1)) = (op (e0) (e3)))) -> ((op (e0) (e1)) = (e0)) -> (~((op (e2) (e3)) = (e1))) -> (~((op (e1) (e2)) = (op (e1) (e3)))) -> (((op (e0) (e3)) = (e1))\/(((op (e1) (e3)) = (e1))\/(((op (e2) (e3)) = (e1))\/((op (e3) (e3)) = (e1))))) -> (~((op (e2) (e0)) = (op (e2) (e3)))) -> ((op (e2) (e0)) = (e0)) -> (~((op (e3) (e1)) = (op (e3) (e3)))) -> (~((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 (e0) (e2)) = (e0))\/(((op (e1) (e2)) = (e0))\/(((op (e2) (e2)) = (e0))\/((op (e3) (e2)) = (e0))))) -> (~((op (e0) (e1)) = (op (e0) (e2)))) -> (~((op (e1) (e1)) = (op (e1) (e2)))) -> (~((op (e2) (e0)) = (op (e2) (e2)))) -> (~((op (e1) (e1)) = (op (e1) (e3)))) -> (~((op (e3) (e2)) = (op (e3) (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) (e3)) = (e1))) -> (((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 (e2) (e0)) = (op (e3) (e0)))) -> (~((op (e0) (e1)) = (op (e2) (e1)))) -> (~((op (e1) (e2)) = (op (e2) (e2)))) -> (((op (e2) (e0)) = (e0))\/(((op (e2) (e0)) = (e1))\/(((op (e2) (e0)) = (e2))\/((op (e2) (e0)) = (e3))))) -> (~((op (e2) (e0)) = (e1))) -> (~((op (e2) (e0)) = (op (e2) (e1)))) -> (~((op (e2) (e2)) = (e2))) -> (~((op (e0) (e0)) = (op (e0) (e3)))) -> (((op (e0) (e0)) = (e2))\/(((op (e1) (e0)) = (e2))\/(((op (e2) (e0)) = (e2))\/((op (e3) (e0)) = (e2))))) -> (~((op (e3) (e0)) = (op (e3) (e1)))) -> ((op (e3) (e1)) = (e3)) -> (((op (e0) (e0)) = (e3))\/(((op (e1) (e0)) = (e3))\/(((op (e2) (e0)) = (e3))\/((op (e3) (e0)) = (e3))))) -> ((~((op (e0) (e3)) = (e1)))\/((op (e0) (e1)) = (e3))) -> ((~((op (e1) (e2)) = (e1)))\/((op (e1) (e1)) = (e2))) -> (~((op (e0) (e1)) = (op (e1) (e1)))) -> ((~((op (e2) (e0)) = (e1)))\/((op (e2) (e1)) = (e0))) -> ((~((op (e3) (e0)) = (e1)))\/((op (e3) (e1)) = (e0))) -> (((op (e0) (e0)) = (e1))\/(((op (e1) (e0)) = (e1))\/(((op (e2) (e0)) = (e1))\/((op (e3) (e0)) = (e1))))) -> (~((op (e0) (e0)) = (op (e0) (e2)))) -> (~((op (e0) (e1)) = (op (e3) (e1)))) -> ((~((op (e3) (e2)) = (e1)))\/((op (e3) (e1)) = (e2))) -> ((~((op (e2) (e2)) = (e1)))\/((op (e2) (e1)) = (e2))) -> ((~((op (e1) (e3)) = (e1)))\/((op (e1) (e1)) = (e3))) -> (~((e0) = (e1))) -> (((op (e0) (e0)) = (e3))\/(((op (e0) (e1)) = (e3))\/(((op (e0) (e2)) = (e3))\/((op (e0) (e3)) = (e3))))) -> ((~((op (e1) (e0)) = (e1)))\/((op (e1) (e1)) = (e0))) -> (((op (e0) (e0)) = (e2))\/(((op (e0) (e1)) = (e2))\/(((op (e0) (e2)) = (e2))\/((op (e0) (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 (e1) (e0)) = (op (e1) (e1)))) -> (~((op (e0) (e0)) = (e0))) -> (((op (e0) (e0)) = (e0))\/(((op (e1) (e0)) = (e0))\/(((op (e2) (e0)) = (e0))\/((op (e3) (e0)) = (e0))))) -> (~((e0) = (e3))) -> (~((op (e1) (e0)) = (op (e3) (e0)))) -> (~((op (e3) (e0)) = (op (e3) (e2)))) -> (~((op (e2) (e2)) = (e1))) -> (((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))))) -> (~((e1) = (e2))) -> (((op (e0) (e0)) = (e1))\/(((op (e0) (e1)) = (e1))\/(((op (e0) (e2)) = (e1))\/((op (e0) (e3)) = (e1))))) -> (~((op (e1) (e1)) = (op (e3) (e1)))) -> (((op (e3) (e2)) = (e0))\/(((op (e3) (e2)) = (e1))\/(((op (e3) (e2)) = (e2))\/((op (e3) (e2)) = (e3))))) -> (~((op (e0) (e2)) = (op (e3) (e2)))) -> (~((op (e2) (e2)) = (op (e3) (e2)))) -> (~((op (e2) (e2)) = (op (e2) (e3)))) -> (((op (e2) (e2)) = (e0))\/(((op (e2) (e2)) = (e1))\/(((op (e2) (e2)) = (e2))\/((op (e2) (e2)) = (e3))))) -> (((op (e2) (e0)) = (e3))\/(((op (e2) (e1)) = (e3))\/(((op (e2) (e2)) = (e3))\/((op (e2) (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))))) -> (~((op (e3) (e0)) = (op (e3) (e3)))) -> (~((e1) = (e3))) -> ((op (e1) (e1)) = (e2)) -> (((op (e1) (e0)) = (e3))\/(((op (e1) (e1)) = (e3))\/(((op (e1) (e2)) = (e3))\/((op (e1) (e3)) = (e3))))) -> (~((op (e0) (e1)) = (e1))) -> (~((op (e0) (e2)) = (e1))) -> (~((op (e0) (e3)) = (e1))) -> False). % 18.87/19.01 do 0 intro. intros zenon_H251 zenon_H250 zenon_Had zenon_He8 zenon_H128 zenon_H10a zenon_H102 zenon_H25e zenon_H24a zenon_H1ef zenon_Hdb zenon_Hd8 zenon_Hdf zenon_H11f zenon_Hf3 zenon_H1c7 zenon_Ha5 zenon_He2 zenon_H12b zenon_H136 zenon_H115 zenon_H67 zenon_H54 zenon_H49 zenon_H255 zenon_H124 zenon_H133 zenon_H5b zenon_H34 zenon_H130 zenon_H149 zenon_H1ac zenon_Hd5 zenon_H6a zenon_H4a zenon_H4f zenon_H52 zenon_H57 zenon_H62 zenon_H201 zenon_H22 zenon_H24e zenon_H1d5 zenon_H2f zenon_H17b zenon_H17e zenon_H2b zenon_H259 zenon_H1db zenon_H1f0 zenon_H173 zenon_H189 zenon_H1fe zenon_H1cf zenon_H161 zenon_H1e0 zenon_H25c zenon_H256 zenon_H10e zenon_H257 zenon_H254 zenon_H235 zenon_H13c zenon_H210 zenon_H252 zenon_H253 zenon_H258 zenon_Ha1 zenon_H168 zenon_H25d zenon_H183 zenon_H1a4 zenon_H139 zenon_H45 zenon_H3f zenon_H3e zenon_H9a zenon_H1fa zenon_H6f zenon_H198 zenon_H153 zenon_H145 zenon_H7c zenon_H22d zenon_H160 zenon_H191 zenon_H14f zenon_H18f zenon_H6d zenon_H1c4 zenon_He7 zenon_Hc2 zenon_H1d zenon_He4 zenon_H71 zenon_H95 zenon_H110 zenon_H16f zenon_Ha4 zenon_H20d zenon_H231. % 18.87/19.01 apply (zenon_or_s _ _ zenon_H22d); [ zenon_intro zenon_H7a | zenon_intro zenon_H22e ]. % 18.87/19.01 apply (zenon_or_s _ _ zenon_H183); [ zenon_intro zenon_H7b | zenon_intro zenon_H186 ]. % 18.87/19.01 apply (zenon_L26_); trivial. % 18.87/19.01 apply (zenon_or_s _ _ zenon_H186); [ zenon_intro zenon_H10f | zenon_intro zenon_H187 ]. % 18.87/19.01 apply (zenon_L764_); trivial. % 18.87/19.01 apply (zenon_or_s _ _ zenon_H187); [ zenon_intro zenon_H150 | zenon_intro zenon_Hcd ]. % 18.87/19.01 apply (zenon_L847_); trivial. % 18.87/19.01 apply (zenon_L865_); trivial. % 18.87/19.01 apply (zenon_or_s _ _ zenon_H22e); [ zenon_intro zenon_Ha0 | zenon_intro zenon_H22f ]. % 18.87/19.01 exact (zenon_Ha4 zenon_Ha0). % 18.87/19.01 apply (zenon_or_s _ _ zenon_H22f); [ zenon_intro zenon_H122 | zenon_intro zenon_Hc3 ]. % 18.87/19.01 exact (zenon_H20d zenon_H122). % 18.87/19.01 exact (zenon_H231 zenon_Hc3). % 18.87/19.01 (* end of lemma zenon_L866_ *) % 18.87/19.01 assert (zenon_L867_ : (((op (e2) (e0)) = (e3))\/(((op (e2) (e1)) = (e3))\/(((op (e2) (e2)) = (e3))\/((op (e2) (e3)) = (e3))))) -> (~((op (e2) (e0)) = (op (e2) (e2)))) -> (~((op (e2) (e2)) = (e2))) -> (~((op (e1) (e2)) = (op (e2) (e2)))) -> ((op (e1) (e2)) = (e1)) -> (~((op (e2) (e2)) = (op (e2) (e3)))) -> (((op (e2) (e2)) = (e0))\/(((op (e2) (e2)) = (e1))\/(((op (e2) (e2)) = (e2))\/((op (e2) (e2)) = (e3))))) -> ((op (e1) (e2)) = (e0)) -> (~((op (e0) (e1)) = (op (e2) (e1)))) -> ((op (e0) (e1)) = (e0)) -> ((op (e2) (e0)) = (e2)) -> (~((e0) = (e2))) -> (((op (e2) (e0)) = (e0))\/(((op (e2) (e1)) = (e0))\/(((op (e2) (e2)) = (e0))\/((op (e2) (e3)) = (e0))))) -> (~((e1) = (e3))) -> ((op (e2) (e1)) = (e1)) -> ((op (e0) (e2)) = (e3)) -> (~((op (e0) (e2)) = (op (e2) (e2)))) -> (((op (e3) (e0)) = (e1))\/(((op (e3) (e1)) = (e1))\/(((op (e3) (e2)) = (e1))\/((op (e3) (e3)) = (e1))))) -> (~((op (e3) (e0)) = (e1))) -> (~((op (e3) (e1)) = (e1))) -> (~((op (e3) (e2)) = (e1))) -> (((op (e1) (e3)) = (e0))\/(((op (e1) (e3)) = (e1))\/(((op (e1) (e3)) = (e2))\/((op (e1) (e3)) = (e3))))) -> ((op (e0) (e3)) = (e2)) -> (~((op (e1) (e3)) = (op (e3) (e3)))) -> ((op (e2) (e3)) = (e0)) -> (~((op (e1) (e3)) = (op (e2) (e3)))) -> False). % 18.87/19.01 do 0 intro. intros zenon_He7 zenon_H52 zenon_H173 zenon_H2b zenon_Hf0 zenon_H6d zenon_H1c4 zenon_H2a zenon_H17e zenon_H49 zenon_Hee zenon_H149 zenon_H2f zenon_H95 zenon_Ha5 zenon_Ha9 zenon_Ha8 zenon_He8 zenon_Had zenon_H250 zenon_H251 zenon_Hdf zenon_Hcd zenon_Hd5 zenon_H37 zenon_Hdb. % 18.87/19.01 apply (zenon_or_s _ _ zenon_He7); [ zenon_intro zenon_H3b | zenon_intro zenon_He9 ]. % 18.87/19.01 apply (zenon_L853_); trivial. % 18.87/19.01 apply (zenon_or_s _ _ zenon_He9); [ zenon_intro zenon_Ha6 | zenon_intro zenon_Hea ]. % 18.87/19.01 apply (zenon_L39_); trivial. % 18.87/19.01 apply (zenon_or_s _ _ zenon_Hea); [ zenon_intro zenon_Haa | zenon_intro zenon_Hdd ]. % 18.87/19.01 apply (zenon_L40_); trivial. % 18.87/19.01 apply (zenon_L851_); trivial. % 18.87/19.01 (* end of lemma zenon_L867_ *) % 18.87/19.01 assert (zenon_L868_ : (((op (e0) (e0)) = (e3))\/(((op (e0) (e1)) = (e3))\/(((op (e0) (e2)) = (e3))\/((op (e0) (e3)) = (e3))))) -> ((op (e0) (e0)) = (e1)) -> (~((e0) = (e3))) -> (~((op (e1) (e3)) = (op (e2) (e3)))) -> (((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)) = (op (e3) (e1)))) -> ((op (e2) (e1)) = (e1)) -> (~((op (e0) (e1)) = (op (e2) (e1)))) -> ((op (e0) (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)) = (e1))\/(((op (e1) (e1)) = (e1))\/(((op (e1) (e2)) = (e1))\/((op (e1) (e3)) = (e1))))) -> (~((op (e1) (e0)) = (e1))) -> (~((op (e1) (e1)) = (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) (e2)) = (e1))) -> (~((op (e3) (e1)) = (e1))) -> (~((op (e3) (e0)) = (e1))) -> (~((op (e0) (e2)) = (op (e2) (e2)))) -> (~((e1) = (e3))) -> (~((e0) = (e2))) -> ((op (e2) (e0)) = (e2)) -> (((op (e2) (e2)) = (e0))\/(((op (e2) (e2)) = (e1))\/(((op (e2) (e2)) = (e2))\/((op (e2) (e2)) = (e3))))) -> (~((op (e2) (e2)) = (op (e2) (e3)))) -> (~((op (e1) (e2)) = (op (e2) (e2)))) -> (~((op (e2) (e2)) = (e2))) -> (~((op (e2) (e0)) = (op (e2) (e2)))) -> (((op (e2) (e0)) = (e3))\/(((op (e2) (e1)) = (e3))\/(((op (e2) (e2)) = (e3))\/((op (e2) (e3)) = (e3))))) -> (~((op (e1) (e3)) = (e1))) -> ((op (e1) (e1)) = (e2)) -> (~((op (e1) (e0)) = (op (e3) (e0)))) -> (((op (e1) (e0)) = (e0))\/(((op (e1) (e1)) = (e0))\/(((op (e1) (e2)) = (e0))\/((op (e1) (e3)) = (e0))))) -> ((op (e0) (e3)) = (e2)) -> (~((e2) = (e3))) -> False). % 18.87/19.01 do 0 intro. intros zenon_H168 zenon_H7a zenon_H9a zenon_Hdb zenon_He8 zenon_Ha1 zenon_H44 zenon_Haf zenon_Ha5 zenon_H17e zenon_H49 zenon_H17b zenon_H2f zenon_H128 zenon_H1ef zenon_H10a zenon_Hd5 zenon_Hdf zenon_H251 zenon_H250 zenon_Had zenon_Ha8 zenon_H95 zenon_H149 zenon_Hee zenon_H1c4 zenon_H6d zenon_H2b zenon_H173 zenon_H52 zenon_He7 zenon_H24e zenon_H110 zenon_H1fa zenon_H22 zenon_Hcd zenon_H12b. % 18.87/19.01 apply (zenon_or_s _ _ zenon_H168); [ zenon_intro zenon_H3a | zenon_intro zenon_H169 ]. % 18.87/19.01 apply (zenon_L35_); trivial. % 18.87/19.01 apply (zenon_or_s _ _ zenon_H169); [ zenon_intro zenon_H99 | zenon_intro zenon_H16a ]. % 18.87/19.01 apply (zenon_L36_); trivial. % 18.87/19.01 apply (zenon_or_s _ _ zenon_H16a); [ zenon_intro zenon_Ha9 | zenon_intro zenon_He3 ]. % 18.87/19.01 apply (zenon_or_s _ _ zenon_H22); [ zenon_intro zenon_H27 | zenon_intro zenon_H26 ]. % 18.87/19.01 apply (zenon_L312_); trivial. % 18.87/19.01 apply (zenon_or_s _ _ zenon_H26); [ zenon_intro zenon_H29 | zenon_intro zenon_H28 ]. % 18.87/19.01 apply (zenon_L354_); trivial. % 18.87/19.01 apply (zenon_or_s _ _ zenon_H28); [ zenon_intro zenon_H2a | zenon_intro zenon_H1f ]. % 18.87/19.01 apply (zenon_or_s _ _ zenon_H128); [ zenon_intro zenon_H9d | zenon_intro zenon_H129 ]. % 18.87/19.01 exact (zenon_H1ef zenon_H9d). % 18.87/19.01 apply (zenon_or_s _ _ zenon_H129); [ zenon_intro zenon_H10d | zenon_intro zenon_H12a ]. % 18.87/19.01 exact (zenon_H10a zenon_H10d). % 18.87/19.01 apply (zenon_or_s _ _ zenon_H12a); [ zenon_intro zenon_Hf0 | zenon_intro zenon_Hd6 ]. % 18.87/19.01 apply (zenon_or_s _ _ zenon_H2f); [ zenon_intro zenon_H34 | zenon_intro zenon_H33 ]. % 18.87/19.01 apply (zenon_L127_); trivial. % 18.87/19.01 apply (zenon_or_s _ _ zenon_H33); [ zenon_intro zenon_H36 | zenon_intro zenon_H35 ]. % 18.87/19.01 apply (zenon_L128_); trivial. % 18.87/19.01 apply (zenon_or_s _ _ zenon_H35); [ zenon_intro zenon_H2c | zenon_intro zenon_H37 ]. % 18.87/19.01 apply (zenon_L3_); trivial. % 18.87/19.01 apply (zenon_L867_); trivial. % 18.87/19.01 exact (zenon_H24e zenon_Hd6). % 18.87/19.01 apply (zenon_L131_); trivial. % 18.87/19.01 apply (zenon_L81_); trivial. % 18.87/19.01 (* end of lemma zenon_L868_ *) % 18.87/19.01 assert (zenon_L869_ : (((op (e3) (e0)) = (e1))\/(((op (e3) (e1)) = (e1))\/(((op (e3) (e2)) = (e1))\/((op (e3) (e3)) = (e1))))) -> (~((op (e3) (e0)) = (e1))) -> (~((op (e3) (e1)) = (e1))) -> ((op (e2) (e2)) = (e0)) -> ((op (e0) (e2)) = (e3)) -> (~((op (e1) (e3)) = (op (e3) (e3)))) -> ((op (e1) (e3)) = (e1)) -> False). % 18.87/19.01 do 0 intro. intros zenon_He8 zenon_Had zenon_H250 zenon_H2c zenon_Ha9 zenon_Hd5 zenon_Hd6. % 18.87/19.01 apply (zenon_or_s _ _ zenon_He8); [ zenon_intro zenon_Hac | zenon_intro zenon_Heb ]. % 18.87/19.01 exact (zenon_Had zenon_Hac). % 18.87/19.01 apply (zenon_or_s _ _ zenon_Heb); [ zenon_intro zenon_Hae | zenon_intro zenon_Hec ]. % 18.87/19.01 exact (zenon_H250 zenon_Hae). % 18.87/19.01 apply (zenon_or_s _ _ zenon_Hec); [ zenon_intro zenon_Hba | zenon_intro zenon_Hc4 ]. % 18.87/19.01 apply (zenon_L45_); trivial. % 18.87/19.01 apply (zenon_L50_); trivial. % 18.87/19.01 (* end of lemma zenon_L869_ *) % 18.87/19.01 assert (zenon_L870_ : (((op (e1) (e3)) = (e0))\/(((op (e1) (e3)) = (e1))\/(((op (e1) (e3)) = (e2))\/((op (e1) (e3)) = (e3))))) -> ((op (e3) (e3)) = (e0)) -> (~((op (e1) (e3)) = (op (e3) (e3)))) -> ((op (e0) (e2)) = (e3)) -> ((op (e2) (e2)) = (e0)) -> (~((op (e3) (e1)) = (e1))) -> (~((op (e3) (e0)) = (e1))) -> (((op (e3) (e0)) = (e1))\/(((op (e3) (e1)) = (e1))\/(((op (e3) (e2)) = (e1))\/((op (e3) (e3)) = (e1))))) -> (~((op (e1) (e1)) = (op (e1) (e3)))) -> ((op (e1) (e1)) = (e2)) -> (~((op (e1) (e3)) = (op (e2) (e3)))) -> ((op (e2) (e3)) = (e3)) -> False). % 18.87/19.01 do 0 intro. intros zenon_Hdf zenon_H60 zenon_Hd5 zenon_Ha9 zenon_H2c zenon_H250 zenon_Had zenon_He8 zenon_H57 zenon_H110 zenon_Hdb zenon_Hdd. % 18.87/19.01 apply (zenon_or_s _ _ zenon_Hdf); [ zenon_intro zenon_H1f | zenon_intro zenon_He0 ]. % 18.87/19.01 apply (zenon_L136_); trivial. % 18.87/19.01 apply (zenon_or_s _ _ zenon_He0); [ zenon_intro zenon_Hd6 | zenon_intro zenon_He1 ]. % 18.87/19.01 apply (zenon_L869_); trivial. % 18.87/19.01 apply (zenon_or_s _ _ zenon_He1); [ zenon_intro zenon_Hd7 | zenon_intro zenon_Hdc ]. % 18.87/19.01 apply (zenon_L283_); trivial. % 18.87/19.01 apply (zenon_L52_); trivial. % 18.87/19.01 (* end of lemma zenon_L870_ *) % 18.87/19.01 assert (zenon_L871_ : (((op (e0) (e3)) = (e3))\/(((op (e1) (e3)) = (e3))\/(((op (e2) (e3)) = (e3))\/((op (e3) (e3)) = (e3))))) -> (~((e2) = (e3))) -> (~((op (e0) (e3)) = (op (e2) (e3)))) -> ((op (e0) (e3)) = (e2)) -> ((op (e2) (e1)) = (e1)) -> (~((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))))) -> (~((op (e1) (e3)) = (op (e2) (e3)))) -> ((op (e1) (e1)) = (e2)) -> (~((op (e1) (e1)) = (op (e1) (e3)))) -> (((op (e3) (e0)) = (e1))\/(((op (e3) (e1)) = (e1))\/(((op (e3) (e2)) = (e1))\/((op (e3) (e3)) = (e1))))) -> (~((op (e3) (e0)) = (e1))) -> (~((op (e3) (e1)) = (e1))) -> ((op (e2) (e2)) = (e0)) -> ((op (e0) (e2)) = (e3)) -> (~((op (e1) (e3)) = (op (e3) (e3)))) -> ((op (e3) (e3)) = (e0)) -> (((op (e1) (e3)) = (e0))\/(((op (e1) (e3)) = (e1))\/(((op (e1) (e3)) = (e2))\/((op (e1) (e3)) = (e3))))) -> (~((op (e3) (e3)) = (e3))) -> False). % 18.87/19.01 do 0 intro. intros zenon_H136 zenon_H12b zenon_He2 zenon_Hcd zenon_Ha5 zenon_H1c7 zenon_Hf3 zenon_H11f zenon_Hdb zenon_H110 zenon_H57 zenon_He8 zenon_Had zenon_H250 zenon_H2c zenon_Ha9 zenon_Hd5 zenon_H60 zenon_Hdf zenon_H102. % 18.87/19.01 apply (zenon_or_s _ _ zenon_H136); [ zenon_intro zenon_He3 | zenon_intro zenon_H137 ]. % 18.87/19.01 apply (zenon_L81_); trivial. % 18.87/19.01 apply (zenon_or_s _ _ zenon_H137); [ zenon_intro zenon_Hdc | zenon_intro zenon_H138 ]. % 18.87/19.01 apply (zenon_L235_); trivial. % 18.87/19.01 apply (zenon_or_s _ _ zenon_H138); [ zenon_intro zenon_Hdd | zenon_intro zenon_H105 ]. % 18.87/19.01 apply (zenon_L870_); trivial. % 18.87/19.01 exact (zenon_H102 zenon_H105). % 18.87/19.01 (* end of lemma zenon_L871_ *) % 18.87/19.01 assert (zenon_L872_ : (((op (e3) (e0)) = (e0))\/(((op (e3) (e1)) = (e0))\/(((op (e3) (e2)) = (e0))\/((op (e3) (e3)) = (e0))))) -> (~((e2) = (e3))) -> ((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 (e1) (e1)) = (e2)) -> (~((op (e1) (e3)) = (e1))) -> (((op (e2) (e0)) = (e3))\/(((op (e2) (e1)) = (e3))\/(((op (e2) (e2)) = (e3))\/((op (e2) (e3)) = (e3))))) -> (~((op (e2) (e0)) = (op (e2) (e2)))) -> (~((op (e2) (e2)) = (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)) -> (~((e0) = (e2))) -> (~((e1) = (e3))) -> (~((op (e0) (e2)) = (op (e2) (e2)))) -> (~((op (e3) (e0)) = (e1))) -> (~((op (e3) (e1)) = (e1))) -> (~((op (e3) (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 (e1) (e1)) = (e1))) -> (~((op (e1) (e0)) = (e1))) -> (((op (e1) (e0)) = (e1))\/(((op (e1) (e1)) = (e1))\/(((op (e1) (e2)) = (e1))\/((op (e1) (e3)) = (e1))))) -> (((op (e2) (e0)) = (e0))\/(((op (e2) (e1)) = (e0))\/(((op (e2) (e2)) = (e0))\/((op (e2) (e3)) = (e0))))) -> (~((op (e2) (e0)) = (op (e3) (e0)))) -> (~((op (e0) (e1)) = (op (e2) (e1)))) -> (~((op (e2) (e1)) = (op (e3) (e1)))) -> (~((e0) = (e1))) -> (((op (e3) (e0)) = (e1))\/(((op (e3) (e1)) = (e1))\/(((op (e3) (e2)) = (e1))\/((op (e3) (e3)) = (e1))))) -> (~((e0) = (e3))) -> ((op (e0) (e0)) = (e1)) -> (((op (e0) (e0)) = (e3))\/(((op (e0) (e1)) = (e3))\/(((op (e0) (e2)) = (e3))\/((op (e0) (e3)) = (e3))))) -> (~((op (e3) (e1)) = (op (e3) (e3)))) -> (~((op (e2) (e2)) = (op (e2) (e3)))) -> (~((op (e1) (e0)) = (op (e1) (e3)))) -> ((op (e1) (e0)) = (e0)) -> ((op (e0) (e1)) = (e0)) -> (~((op (e0) (e1)) = (op (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 (e0) (e3)) = (e0))\/(((op (e0) (e3)) = (e1))\/(((op (e0) (e3)) = (e2))\/((op (e0) (e3)) = (e3))))) -> (~((op (e0) (e3)) = (op (e3) (e3)))) -> (~((op (e0) (e3)) = (e1))) -> (~((op (e1) (e3)) = (op (e2) (e3)))) -> (~((op (e0) (e3)) = (op (e2) (e3)))) -> ((op (e2) (e1)) = (e1)) -> (~((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))))) -> (~((op (e0) (e3)) = (op (e1) (e3)))) -> ((op (e1) (e3)) = (e3)) -> False). % 18.87/19.01 do 0 intro. intros zenon_H1ac zenon_H12b zenon_Hcd zenon_H22 zenon_H1fa zenon_H110 zenon_H24e zenon_He7 zenon_H52 zenon_H173 zenon_H2b zenon_H1c4 zenon_Hee zenon_H149 zenon_H95 zenon_Ha8 zenon_Had zenon_H250 zenon_H251 zenon_Hdf zenon_Hd5 zenon_H10a zenon_H1ef zenon_H128 zenon_H2f zenon_H17b zenon_H17e zenon_Haf zenon_Ha1 zenon_He8 zenon_H9a zenon_H7a zenon_H168 zenon_H130 zenon_H6d zenon_Hd8 zenon_H27 zenon_H49 zenon_H54 zenon_H67 zenon_H2c zenon_H18f zenon_He4 zenon_Hc2 zenon_H231 zenon_Hdb zenon_He2 zenon_Ha5 zenon_H1c7 zenon_Hf3 zenon_H11f zenon_H1d zenon_Hdc. % 18.87/19.01 apply (zenon_or_s _ _ zenon_H1ac); [ zenon_intro zenon_H44 | zenon_intro zenon_H1af ]. % 18.87/19.01 apply (zenon_L868_); trivial. % 18.87/19.01 apply (zenon_or_s _ _ zenon_H1af); [ zenon_intro zenon_H1b1 | zenon_intro zenon_H1b0 ]. % 18.87/19.01 apply (zenon_L259_); trivial. % 18.87/19.01 apply (zenon_or_s _ _ zenon_H1b0); [ zenon_intro zenon_H61 | zenon_intro zenon_H60 ]. % 18.87/19.01 apply (zenon_L146_); trivial. % 18.87/19.01 apply (zenon_L839_); trivial. % 18.87/19.01 (* end of lemma zenon_L872_ *) % 18.87/19.01 assert (zenon_L873_ : (((op (e0) (e3)) = (e3))\/(((op (e1) (e3)) = (e3))\/(((op (e2) (e3)) = (e3))\/((op (e3) (e3)) = (e3))))) -> (~((op (e0) (e3)) = (op (e1) (e3)))) -> ((op (e2) (e1)) = (e2)) -> (~((op (e3) (e2)) = (e1))) -> (~((op (e0) (e3)) = (op (e2) (e3)))) -> ((op (e0) (e3)) = (e2)) -> ((op (e2) (e1)) = (e1)) -> (~((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))))) -> (~((op (e1) (e3)) = (op (e2) (e3)))) -> ((op (e1) (e1)) = (e2)) -> (~((op (e1) (e1)) = (op (e1) (e3)))) -> (((op (e3) (e0)) = (e1))\/(((op (e3) (e1)) = (e1))\/(((op (e3) (e2)) = (e1))\/((op (e3) (e3)) = (e1))))) -> (~((op (e3) (e0)) = (e1))) -> (~((op (e3) (e1)) = (e1))) -> ((op (e2) (e2)) = (e0)) -> ((op (e0) (e2)) = (e3)) -> (~((op (e1) (e3)) = (op (e3) (e3)))) -> ((op (e3) (e3)) = (e0)) -> (((op (e1) (e3)) = (e0))\/(((op (e1) (e3)) = (e1))\/(((op (e1) (e3)) = (e2))\/((op (e1) (e3)) = (e3))))) -> (~((op (e3) (e3)) = (e3))) -> False). % 18.87/19.01 do 0 intro. intros zenon_H136 zenon_H1d zenon_H1ca zenon_H251 zenon_He2 zenon_Hcd zenon_Ha5 zenon_H1c7 zenon_Hf3 zenon_H11f zenon_Hdb zenon_H110 zenon_H57 zenon_He8 zenon_Had zenon_H250 zenon_H2c zenon_Ha9 zenon_Hd5 zenon_H60 zenon_Hdf zenon_H102. % 18.87/19.01 apply (zenon_or_s _ _ zenon_H136); [ zenon_intro zenon_He3 | zenon_intro zenon_H137 ]. % 18.87/19.01 apply (zenon_L805_); trivial. % 18.87/19.01 apply (zenon_or_s _ _ zenon_H137); [ zenon_intro zenon_Hdc | zenon_intro zenon_H138 ]. % 18.87/19.01 apply (zenon_L235_); trivial. % 18.87/19.01 apply (zenon_or_s _ _ zenon_H138); [ zenon_intro zenon_Hdd | zenon_intro zenon_H105 ]. % 18.87/19.01 apply (zenon_L870_); trivial. % 18.87/19.01 exact (zenon_H102 zenon_H105). % 18.87/19.01 (* end of lemma zenon_L873_ *) % 18.87/19.01 assert (zenon_L874_ : (((op (e0) (e3)) = (e2))\/(((op (e1) (e3)) = (e2))\/(((op (e2) (e3)) = (e2))\/((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 (e3) (e3)) = (e0)) -> (~((op (e1) (e3)) = (op (e3) (e3)))) -> ((op (e0) (e2)) = (e3)) -> ((op (e2) (e2)) = (e0)) -> (~((op (e3) (e1)) = (e1))) -> (~((op (e3) (e0)) = (e1))) -> (((op (e3) (e0)) = (e1))\/(((op (e3) (e1)) = (e1))\/(((op (e3) (e2)) = (e1))\/((op (e3) (e3)) = (e1))))) -> (~((op (e1) (e3)) = (op (e2) (e3)))) -> (((op (e2) (e3)) = (e0))\/(((op (e2) (e3)) = (e1))\/(((op (e2) (e3)) = (e2))\/((op (e2) (e3)) = (e3))))) -> (~((op (e2) (e3)) = (op (e3) (e3)))) -> ((op (e2) (e1)) = (e1)) -> (~((op (e0) (e3)) = (op (e2) (e3)))) -> (~((op (e3) (e2)) = (e1))) -> (~((op (e0) (e3)) = (op (e1) (e3)))) -> (((op (e0) (e3)) = (e3))\/(((op (e1) (e3)) = (e3))\/(((op (e2) (e3)) = (e3))\/((op (e3) (e3)) = (e3))))) -> (~((op (e1) (e1)) = (op (e1) (e3)))) -> ((op (e1) (e1)) = (e2)) -> (~((op (e2) (e1)) = (op (e2) (e3)))) -> ((op (e2) (e1)) = (e2)) -> ((op (e3) (e0)) = (e2)) -> (~((op (e3) (e0)) = (op (e3) (e3)))) -> False). % 18.87/19.01 do 0 intro. intros zenon_H145 zenon_H102 zenon_Hdf zenon_H60 zenon_Hd5 zenon_Ha9 zenon_H2c zenon_H250 zenon_Had zenon_He8 zenon_Hdb zenon_H11f zenon_Hf3 zenon_Ha5 zenon_He2 zenon_H251 zenon_H1d zenon_H136 zenon_H57 zenon_H110 zenon_H1c7 zenon_H1ca zenon_H148 zenon_H71. % 18.87/19.01 apply (zenon_or_s _ _ zenon_H145); [ zenon_intro zenon_Hcd | zenon_intro zenon_H146 ]. % 18.87/19.01 apply (zenon_L873_); trivial. % 18.87/19.01 apply (zenon_or_s _ _ zenon_H146); [ zenon_intro zenon_Hd7 | zenon_intro zenon_H147 ]. % 18.87/19.01 apply (zenon_L283_); trivial. % 18.87/19.01 apply (zenon_or_s _ _ zenon_H147); [ zenon_intro zenon_H11d | zenon_intro zenon_Hf6 ]. % 18.87/19.01 apply (zenon_L224_); trivial. % 18.87/19.01 apply (zenon_L114_); trivial. % 18.87/19.01 (* end of lemma zenon_L874_ *) % 18.87/19.01 assert (zenon_L875_ : (((op (e3) (e0)) = (e0))\/(((op (e3) (e1)) = (e0))\/(((op (e3) (e2)) = (e0))\/((op (e3) (e3)) = (e0))))) -> (~((op (e0) (e3)) = (e1))) -> (~((op (e0) (e2)) = (e1))) -> (~((op (e0) (e1)) = (e1))) -> (((op (e0) (e0)) = (e2))\/(((op (e1) (e0)) = (e2))\/(((op (e2) (e0)) = (e2))\/((op (e3) (e0)) = (e2))))) -> (~((e1) = (e2))) -> (~((op (e2) (e0)) = (e1))) -> (~((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) (e1)))) -> (~((e0) = (e2))) -> (((op (e0) (e0)) = (e1))\/(((op (e0) (e1)) = (e1))\/(((op (e0) (e2)) = (e1))\/((op (e0) (e3)) = (e1))))) -> (~((op (e3) (e1)) = (op (e3) (e3)))) -> (~((op (e2) (e2)) = (op (e2) (e3)))) -> (~((op (e1) (e0)) = (op (e1) (e3)))) -> ((op (e1) (e0)) = (e0)) -> ((op (e0) (e1)) = (e0)) -> (~((op (e0) (e1)) = (op (e0) (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)) = (e2))\/(((op (e1) (e3)) = (e2))\/(((op (e2) (e3)) = (e2))\/((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) (e2)) = (e3)) -> ((op (e2) (e2)) = (e0)) -> (~((op (e3) (e1)) = (e1))) -> (~((op (e3) (e0)) = (e1))) -> (((op (e3) (e0)) = (e1))\/(((op (e3) (e1)) = (e1))\/(((op (e3) (e2)) = (e1))\/((op (e3) (e3)) = (e1))))) -> (~((op (e1) (e3)) = (op (e2) (e3)))) -> (((op (e2) (e3)) = (e0))\/(((op (e2) (e3)) = (e1))\/(((op (e2) (e3)) = (e2))\/((op (e2) (e3)) = (e3))))) -> (~((op (e2) (e3)) = (op (e3) (e3)))) -> ((op (e2) (e1)) = (e1)) -> (~((op (e0) (e3)) = (op (e2) (e3)))) -> (~((op (e3) (e2)) = (e1))) -> (~((op (e0) (e3)) = (op (e1) (e3)))) -> (((op (e0) (e3)) = (e3))\/(((op (e1) (e3)) = (e3))\/(((op (e2) (e3)) = (e3))\/((op (e3) (e3)) = (e3))))) -> (~((op (e1) (e1)) = (op (e1) (e3)))) -> ((op (e1) (e1)) = (e2)) -> (~((op (e2) (e1)) = (op (e2) (e3)))) -> ((op (e2) (e1)) = (e2)) -> ((op (e3) (e0)) = (e2)) -> (~((op (e3) (e0)) = (op (e3) (e3)))) -> False). % 18.87/19.01 do 0 intro. intros zenon_H1ac zenon_H231 zenon_H20d zenon_Ha4 zenon_H1fe zenon_H7c zenon_H1db zenon_H17b zenon_H259 zenon_H1f0 zenon_H149 zenon_H22d zenon_H130 zenon_H6d zenon_Hd8 zenon_H27 zenon_H49 zenon_H54 zenon_H67 zenon_H18f zenon_H145 zenon_H102 zenon_Hdf zenon_Hd5 zenon_Ha9 zenon_H2c zenon_H250 zenon_Had zenon_He8 zenon_Hdb zenon_H11f zenon_Hf3 zenon_Ha5 zenon_He2 zenon_H251 zenon_H1d zenon_H136 zenon_H57 zenon_H110 zenon_H1c7 zenon_H1ca zenon_H148 zenon_H71. % 18.87/19.01 apply (zenon_or_s _ _ zenon_H1ac); [ zenon_intro zenon_H44 | zenon_intro zenon_H1af ]. % 18.87/19.01 apply (zenon_L786_); trivial. % 18.87/19.01 apply (zenon_or_s _ _ zenon_H1af); [ zenon_intro zenon_H1b1 | zenon_intro zenon_H1b0 ]. % 18.87/19.01 apply (zenon_L259_); trivial. % 18.87/19.01 apply (zenon_or_s _ _ zenon_H1b0); [ zenon_intro zenon_H61 | zenon_intro zenon_H60 ]. % 18.87/19.01 apply (zenon_L146_); trivial. % 18.87/19.01 apply (zenon_L874_); trivial. % 18.87/19.01 (* end of lemma zenon_L875_ *) % 18.87/19.01 assert (zenon_L876_ : ((op (e3) (e0)) = (e2)) -> (~((op (e2) (e0)) = (op (e2) (e2)))) -> (~((op (e2) (e2)) = (e2))) -> (~((op (e1) (e2)) = (op (e2) (e2)))) -> (~((op (e2) (e2)) = (op (e2) (e3)))) -> (((op (e2) (e2)) = (e0))\/(((op (e2) (e2)) = (e1))\/(((op (e2) (e2)) = (e2))\/((op (e2) (e2)) = (e3))))) -> (((op (e2) (e0)) = (e2))\/(((op (e2) (e1)) = (e2))\/(((op (e2) (e2)) = (e2))\/((op (e2) (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) (e0)) = (e3))\/(((op (e0) (e1)) = (e3))\/(((op (e0) (e2)) = (e3))\/((op (e0) (e3)) = (e3))))) -> ((op (e0) (e0)) = (e1)) -> (~((e0) = (e3))) -> (~((e0) = (e1))) -> (~((op (e2) (e1)) = (op (e3) (e1)))) -> (~((op (e0) (e1)) = (op (e2) (e1)))) -> (((op (e2) (e0)) = (e0))\/(((op (e2) (e1)) = (e0))\/(((op (e2) (e2)) = (e0))\/((op (e2) (e3)) = (e0))))) -> (((op (e1) (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 (e2) (e2)))) -> (~((e1) = (e3))) -> (((op (e2) (e0)) = (e3))\/(((op (e2) (e1)) = (e3))\/(((op (e2) (e2)) = (e3))\/((op (e2) (e3)) = (e3))))) -> (~((op (e1) (e0)) = (op (e3) (e0)))) -> (((op (e1) (e0)) = (e0))\/(((op (e1) (e1)) = (e0))\/(((op (e1) (e2)) = (e0))\/((op (e1) (e3)) = (e0))))) -> (~((op (e3) (e0)) = (op (e3) (e3)))) -> (~((op (e2) (e1)) = (op (e2) (e3)))) -> ((op (e1) (e1)) = (e2)) -> (~((op (e1) (e1)) = (op (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 (e3) (e2)) = (e1))) -> ((op (e2) (e1)) = (e1)) -> (~((op (e2) (e3)) = (op (e3) (e3)))) -> (((op (e2) (e3)) = (e0))\/(((op (e2) (e3)) = (e1))\/(((op (e2) (e3)) = (e2))\/((op (e2) (e3)) = (e3))))) -> (~((op (e1) (e3)) = (op (e2) (e3)))) -> (((op (e3) (e0)) = (e1))\/(((op (e3) (e1)) = (e1))\/(((op (e3) (e2)) = (e1))\/((op (e3) (e3)) = (e1))))) -> (~((op (e3) (e0)) = (e1))) -> (~((op (e3) (e1)) = (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)) = (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) (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) (e0)) = (e0)) -> (~((op (e1) (e0)) = (op (e1) (e3)))) -> (~((op (e3) (e1)) = (op (e3) (e3)))) -> (((op (e0) (e0)) = (e1))\/(((op (e0) (e1)) = (e1))\/(((op (e0) (e2)) = (e1))\/((op (e0) (e3)) = (e1))))) -> (~((e0) = (e2))) -> (~((op (e2) (e0)) = (op (e2) (e1)))) -> (((op (e2) (e0)) = (e0))\/(((op (e2) (e0)) = (e1))\/(((op (e2) (e0)) = (e2))\/((op (e2) (e0)) = (e3))))) -> (~((op (e2) (e0)) = (op (e3) (e0)))) -> (~((op (e2) (e0)) = (e1))) -> (~((e1) = (e2))) -> (((op (e0) (e0)) = (e2))\/(((op (e1) (e0)) = (e2))\/(((op (e2) (e0)) = (e2))\/((op (e3) (e0)) = (e2))))) -> (~((op (e0) (e1)) = (e1))) -> (~((op (e0) (e2)) = (e1))) -> (~((op (e0) (e3)) = (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)) = (op (e0) (e3)))) -> (~((op (e1) (e0)) = (op (e2) (e0)))) -> (~((op (e3) (e2)) = (op (e3) (e3)))) -> (~((op (e1) (e1)) = (op (e1) (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 (e2) (e3)))) -> (((op (e0) (e3)) = (e1))\/(((op (e1) (e3)) = (e1))\/(((op (e2) (e3)) = (e1))\/((op (e3) (e3)) = (e1))))) -> (~((op (e1) (e2)) = (op (e1) (e3)))) -> (~((op (e2) (e3)) = (e1))) -> (~((op (e1) (e2)) = (op (e3) (e2)))) -> (~((op (e1) (e0)) = (op (e1) (e2)))) -> (((op (e1) (e0)) = (e0))\/(((op (e1) (e0)) = (e1))\/(((op (e1) (e0)) = (e2))\/((op (e1) (e0)) = (e3))))) -> (((op (e1) (e0)) = (e3))\/(((op (e1) (e1)) = (e3))\/(((op (e1) (e2)) = (e3))\/((op (e1) (e3)) = (e3))))) -> (~((op (e1) (e3)) = (e1))) -> (((op (e0) (e0)) = (e3))\/(((op (e1) (e0)) = (e3))\/(((op (e2) (e0)) = (e3))\/((op (e3) (e0)) = (e3))))) -> ((op (e0) (e3)) = (e2)) -> (~((e2) = (e3))) -> False). % 18.87/19.01 do 0 intro. intros zenon_H148 zenon_H52 zenon_H173 zenon_H2b zenon_H6d zenon_H1c4 zenon_H1d5 zenon_Hc2 zenon_He4 zenon_H168 zenon_H7a zenon_H9a zenon_Ha1 zenon_Haf zenon_H17e zenon_H2f zenon_H128 zenon_H1ef zenon_H10a zenon_Ha8 zenon_H95 zenon_He7 zenon_H1fa zenon_H22 zenon_H71 zenon_H1c7 zenon_H110 zenon_H57 zenon_H136 zenon_H1d zenon_H251 zenon_Ha5 zenon_Hf3 zenon_H11f zenon_Hdb zenon_He8 zenon_Had zenon_H250 zenon_Hd5 zenon_Hdf zenon_H102 zenon_H145 zenon_H18f zenon_H67 zenon_H54 zenon_H49 zenon_H27 zenon_Hd8 zenon_H130 zenon_H22d zenon_H149 zenon_H1f0 zenon_H259 zenon_H17b zenon_H1db zenon_H7c zenon_H1fe zenon_Ha4 zenon_H20d zenon_H231 zenon_H1ac zenon_He2 zenon_H189 zenon_H201 zenon_H62 zenon_H4f zenon_H4a zenon_H6a zenon_H5b zenon_H133 zenon_H124 zenon_H255 zenon_H115 zenon_H24a zenon_H25e zenon_H16f zenon_H24e zenon_H1e0 zenon_Hcd zenon_H12b. % 18.87/19.01 apply (zenon_or_s _ _ zenon_H168); [ zenon_intro zenon_H3a | zenon_intro zenon_H169 ]. % 18.87/19.01 apply (zenon_L35_); trivial. % 18.87/19.01 apply (zenon_or_s _ _ zenon_H169); [ zenon_intro zenon_H99 | zenon_intro zenon_H16a ]. % 18.87/19.01 apply (zenon_L36_); trivial. % 18.87/19.01 apply (zenon_or_s _ _ zenon_H16a); [ zenon_intro zenon_Ha9 | zenon_intro zenon_He3 ]. % 18.87/19.01 apply (zenon_or_s _ _ zenon_H1e0); [ zenon_intro zenon_H3a | zenon_intro zenon_H1e1 ]. % 18.87/19.01 apply (zenon_L35_); trivial. % 18.87/19.01 apply (zenon_or_s _ _ zenon_H1e1); [ zenon_intro zenon_H9e | zenon_intro zenon_H1e2 ]. % 18.87/19.01 apply (zenon_L107_); trivial. % 18.87/19.01 apply (zenon_or_s _ _ zenon_H1e2); [ zenon_intro zenon_H3b | zenon_intro zenon_H15e ]. % 18.87/19.01 apply (zenon_or_s _ _ zenon_H128); [ zenon_intro zenon_H9d | zenon_intro zenon_H129 ]. % 18.87/19.01 exact (zenon_H1ef zenon_H9d). % 18.87/19.01 apply (zenon_or_s _ _ zenon_H129); [ zenon_intro zenon_H10d | zenon_intro zenon_H12a ]. % 18.87/19.01 exact (zenon_H10a zenon_H10d). % 18.87/19.01 apply (zenon_or_s _ _ zenon_H12a); [ zenon_intro zenon_Hf0 | zenon_intro zenon_Hd6 ]. % 18.87/19.01 apply (zenon_or_s _ _ zenon_H16f); [ zenon_intro zenon_H9e | zenon_intro zenon_H170 ]. % 18.87/19.01 apply (zenon_L107_); trivial. % 18.87/19.01 apply (zenon_or_s _ _ zenon_H170); [ zenon_intro zenon_H13f | zenon_intro zenon_H171 ]. % 18.87/19.01 apply (zenon_L166_); trivial. % 18.87/19.01 apply (zenon_or_s _ _ zenon_H171); [ zenon_intro zenon_H16c | zenon_intro zenon_Hdc ]. % 18.87/19.01 apply (zenon_L167_); trivial. % 18.87/19.01 apply (zenon_or_s _ _ zenon_H2f); [ zenon_intro zenon_H34 | zenon_intro zenon_H33 ]. % 18.87/19.01 apply (zenon_L865_); trivial. % 18.87/19.01 apply (zenon_or_s _ _ zenon_H33); [ zenon_intro zenon_H36 | zenon_intro zenon_H35 ]. % 18.87/19.01 apply (zenon_L128_); trivial. % 18.87/19.01 apply (zenon_or_s _ _ zenon_H35); [ zenon_intro zenon_H2c | zenon_intro zenon_H37 ]. % 18.87/19.01 apply (zenon_or_s _ _ zenon_H1d5); [ zenon_intro zenon_Hee | zenon_intro zenon_H1d6 ]. % 18.87/19.01 apply (zenon_L872_); trivial. % 18.87/19.01 apply (zenon_or_s _ _ zenon_H1d6); [ zenon_intro zenon_H1ca | zenon_intro zenon_H1d7 ]. % 18.87/19.01 apply (zenon_L875_); trivial. % 18.87/19.01 apply (zenon_or_s _ _ zenon_H1d7); [ zenon_intro zenon_H176 | zenon_intro zenon_H11d ]. % 18.87/19.01 exact (zenon_H173 zenon_H176). % 18.87/19.01 apply (zenon_L234_); trivial. % 18.87/19.01 apply (zenon_L300_); trivial. % 18.87/19.01 exact (zenon_H24e zenon_Hd6). % 18.87/19.01 apply (zenon_L109_); trivial. % 18.87/19.01 apply (zenon_L81_); trivial. % 18.87/19.01 (* end of lemma zenon_L876_ *) % 18.87/19.01 assert (zenon_L877_ : (~((op (e3) (e0)) = (op (e3) (e1)))) -> ((op (e3) (e1)) = (e3)) -> ((~((op (e0) (e3)) = (e1)))\/((op (e0) (e1)) = (e3))) -> ((~((op (e1) (e2)) = (e1)))\/((op (e1) (e1)) = (e2))) -> (~((op (e0) (e1)) = (op (e1) (e1)))) -> ((~((op (e2) (e0)) = (e1)))\/((op (e2) (e1)) = (e0))) -> ((~((op (e3) (e0)) = (e1)))\/((op (e3) (e1)) = (e0))) -> (((op (e0) (e0)) = (e1))\/(((op (e1) (e0)) = (e1))\/(((op (e2) (e0)) = (e1))\/((op (e3) (e0)) = (e1))))) -> (~((op (e0) (e0)) = (op (e0) (e2)))) -> (~((op (e0) (e1)) = (op (e3) (e1)))) -> ((~((op (e3) (e2)) = (e1)))\/((op (e3) (e1)) = (e2))) -> ((~((op (e2) (e2)) = (e1)))\/((op (e2) (e1)) = (e2))) -> ((~((op (e1) (e3)) = (e1)))\/((op (e1) (e1)) = (e3))) -> ((~((op (e1) (e0)) = (e1)))\/((op (e1) (e1)) = (e0))) -> (((op (e0) (e0)) = (e2))\/(((op (e0) (e1)) = (e2))\/(((op (e0) (e2)) = (e2))\/((op (e0) (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 (e1) (e0)) = (op (e1) (e1)))) -> (~((op (e0) (e0)) = (e0))) -> (((op (e0) (e0)) = (e0))\/(((op (e1) (e0)) = (e0))\/(((op (e2) (e0)) = (e0))\/((op (e3) (e0)) = (e0))))) -> (~((op (e3) (e0)) = (op (e3) (e2)))) -> (~((op (e2) (e2)) = (e1))) -> (((op (e3) (e0)) = (e2))\/(((op (e3) (e1)) = (e2))\/(((op (e3) (e2)) = (e2))\/((op (e3) (e3)) = (e2))))) -> (~((op (e1) (e1)) = (op (e3) (e1)))) -> (((op (e3) (e2)) = (e0))\/(((op (e3) (e2)) = (e1))\/(((op (e3) (e2)) = (e2))\/((op (e3) (e2)) = (e3))))) -> (~((op (e0) (e2)) = (op (e3) (e2)))) -> (~((op (e2) (e0)) = (op (e2) (e2)))) -> (~((op (e2) (e2)) = (e2))) -> (~((op (e1) (e2)) = (op (e2) (e2)))) -> (~((op (e2) (e2)) = (op (e2) (e3)))) -> (((op (e2) (e2)) = (e0))\/(((op (e2) (e2)) = (e1))\/(((op (e2) (e2)) = (e2))\/((op (e2) (e2)) = (e3))))) -> (((op (e2) (e0)) = (e2))\/(((op (e2) (e1)) = (e2))\/(((op (e2) (e2)) = (e2))\/((op (e2) (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) (e0)) = (e3))\/(((op (e0) (e1)) = (e3))\/(((op (e0) (e2)) = (e3))\/((op (e0) (e3)) = (e3))))) -> ((op (e0) (e0)) = (e1)) -> (~((e0) = (e3))) -> (~((e0) = (e1))) -> (~((op (e2) (e1)) = (op (e3) (e1)))) -> (~((op (e0) (e1)) = (op (e2) (e1)))) -> (((op (e2) (e0)) = (e0))\/(((op (e2) (e1)) = (e0))\/(((op (e2) (e2)) = (e0))\/((op (e2) (e3)) = (e0))))) -> (((op (e1) (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 (e2) (e2)))) -> (~((e1) = (e3))) -> (((op (e2) (e0)) = (e3))\/(((op (e2) (e1)) = (e3))\/(((op (e2) (e2)) = (e3))\/((op (e2) (e3)) = (e3))))) -> (~((op (e1) (e0)) = (op (e3) (e0)))) -> (((op (e1) (e0)) = (e0))\/(((op (e1) (e1)) = (e0))\/(((op (e1) (e2)) = (e0))\/((op (e1) (e3)) = (e0))))) -> (~((op (e3) (e0)) = (op (e3) (e3)))) -> (~((op (e2) (e1)) = (op (e2) (e3)))) -> ((op (e1) (e1)) = (e2)) -> (~((op (e1) (e1)) = (op (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 (e3) (e2)) = (e1))) -> ((op (e2) (e1)) = (e1)) -> (~((op (e2) (e3)) = (op (e3) (e3)))) -> (((op (e2) (e3)) = (e0))\/(((op (e2) (e3)) = (e1))\/(((op (e2) (e3)) = (e2))\/((op (e2) (e3)) = (e3))))) -> (~((op (e1) (e3)) = (op (e2) (e3)))) -> (((op (e3) (e0)) = (e1))\/(((op (e3) (e1)) = (e1))\/(((op (e3) (e2)) = (e1))\/((op (e3) (e3)) = (e1))))) -> (~((op (e3) (e0)) = (e1))) -> (~((op (e3) (e1)) = (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)) = (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) (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) (e0)) = (e0)) -> (~((op (e1) (e0)) = (op (e1) (e3)))) -> (~((op (e3) (e1)) = (op (e3) (e3)))) -> (((op (e0) (e0)) = (e1))\/(((op (e0) (e1)) = (e1))\/(((op (e0) (e2)) = (e1))\/((op (e0) (e3)) = (e1))))) -> (~((e0) = (e2))) -> (~((op (e2) (e0)) = (op (e2) (e1)))) -> (((op (e2) (e0)) = (e0))\/(((op (e2) (e0)) = (e1))\/(((op (e2) (e0)) = (e2))\/((op (e2) (e0)) = (e3))))) -> (~((op (e2) (e0)) = (op (e3) (e0)))) -> (~((op (e2) (e0)) = (e1))) -> (~((e1) = (e2))) -> (((op (e0) (e0)) = (e2))\/(((op (e1) (e0)) = (e2))\/(((op (e2) (e0)) = (e2))\/((op (e3) (e0)) = (e2))))) -> (~((op (e0) (e1)) = (e1))) -> (~((op (e0) (e2)) = (e1))) -> (~((op (e0) (e3)) = (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)) = (op (e0) (e3)))) -> (~((op (e1) (e0)) = (op (e2) (e0)))) -> (~((op (e3) (e2)) = (op (e3) (e3)))) -> (~((op (e1) (e1)) = (op (e1) (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 (e2) (e3)))) -> (((op (e0) (e3)) = (e1))\/(((op (e1) (e3)) = (e1))\/(((op (e2) (e3)) = (e1))\/((op (e3) (e3)) = (e1))))) -> (~((op (e1) (e2)) = (op (e1) (e3)))) -> (~((op (e2) (e3)) = (e1))) -> (~((op (e1) (e2)) = (op (e3) (e2)))) -> (~((op (e1) (e0)) = (op (e1) (e2)))) -> (((op (e1) (e0)) = (e0))\/(((op (e1) (e0)) = (e1))\/(((op (e1) (e0)) = (e2))\/((op (e1) (e0)) = (e3))))) -> (((op (e1) (e0)) = (e3))\/(((op (e1) (e1)) = (e3))\/(((op (e1) (e2)) = (e3))\/((op (e1) (e3)) = (e3))))) -> (~((op (e1) (e3)) = (e1))) -> (((op (e0) (e0)) = (e3))\/(((op (e1) (e0)) = (e3))\/(((op (e2) (e0)) = (e3))\/((op (e3) (e0)) = (e3))))) -> (~((e2) = (e3))) -> False). % 18.87/19.01 do 0 intro. intros zenon_H1cf zenon_H161 zenon_H25c zenon_H256 zenon_H10e zenon_H257 zenon_H254 zenon_H235 zenon_H13c zenon_H210 zenon_H252 zenon_H253 zenon_H258 zenon_H25d zenon_H183 zenon_H1a4 zenon_H139 zenon_H45 zenon_H3f zenon_H3e zenon_H6f zenon_H198 zenon_H153 zenon_H160 zenon_H191 zenon_H14f zenon_H52 zenon_H173 zenon_H2b zenon_H6d zenon_H1c4 zenon_H1d5 zenon_Hc2 zenon_He4 zenon_H168 zenon_H7a zenon_H9a zenon_Ha1 zenon_Haf zenon_H17e zenon_H2f zenon_H128 zenon_H1ef zenon_H10a zenon_Ha8 zenon_H95 zenon_He7 zenon_H1fa zenon_H22 zenon_H71 zenon_H1c7 zenon_H110 zenon_H57 zenon_H136 zenon_H1d zenon_H251 zenon_Ha5 zenon_Hf3 zenon_H11f zenon_Hdb zenon_He8 zenon_Had zenon_H250 zenon_Hd5 zenon_Hdf zenon_H102 zenon_H145 zenon_H18f zenon_H67 zenon_H54 zenon_H49 zenon_H27 zenon_Hd8 zenon_H130 zenon_H22d zenon_H149 zenon_H1f0 zenon_H259 zenon_H17b zenon_H1db zenon_H7c zenon_H1fe zenon_Ha4 zenon_H20d zenon_H231 zenon_H1ac zenon_He2 zenon_H189 zenon_H201 zenon_H62 zenon_H4f zenon_H4a zenon_H6a zenon_H5b zenon_H133 zenon_H124 zenon_H255 zenon_H115 zenon_H24a zenon_H25e zenon_H16f zenon_H24e zenon_H1e0 zenon_H12b. % 18.87/19.01 apply (zenon_or_s _ _ zenon_H183); [ zenon_intro zenon_H7b | zenon_intro zenon_H186 ]. % 18.87/19.01 apply (zenon_L26_); trivial. % 18.87/19.01 apply (zenon_or_s _ _ zenon_H186); [ zenon_intro zenon_H10f | zenon_intro zenon_H187 ]. % 18.87/19.01 apply (zenon_L726_); trivial. % 18.87/19.01 apply (zenon_or_s _ _ zenon_H187); [ zenon_intro zenon_H150 | zenon_intro zenon_Hcd ]. % 18.87/19.01 apply (zenon_or_s _ _ zenon_H1fe); [ zenon_intro zenon_H7b | zenon_intro zenon_H1ff ]. % 18.87/19.01 apply (zenon_L26_); trivial. % 18.87/19.01 apply (zenon_or_s _ _ zenon_H1ff); [ zenon_intro zenon_H86 | zenon_intro zenon_H200 ]. % 18.87/19.01 apply (zenon_L257_); trivial. % 18.87/19.01 apply (zenon_or_s _ _ zenon_H200); [ zenon_intro zenon_Hee | zenon_intro zenon_H148 ]. % 18.87/19.01 apply (zenon_or_s _ _ zenon_H168); [ zenon_intro zenon_H3a | zenon_intro zenon_H169 ]. % 18.87/19.01 apply (zenon_L35_); trivial. % 18.87/19.01 apply (zenon_or_s _ _ zenon_H169); [ zenon_intro zenon_H99 | zenon_intro zenon_H16a ]. % 18.87/19.01 apply (zenon_L36_); trivial. % 18.87/19.01 apply (zenon_or_s _ _ zenon_H16a); [ zenon_intro zenon_Ha9 | zenon_intro zenon_He3 ]. % 18.87/19.01 apply (zenon_or_s _ _ zenon_H1e0); [ zenon_intro zenon_H3a | zenon_intro zenon_H1e1 ]. % 18.87/19.01 apply (zenon_L35_); trivial. % 18.87/19.01 apply (zenon_or_s _ _ zenon_H1e1); [ zenon_intro zenon_H9e | zenon_intro zenon_H1e2 ]. % 18.87/19.01 apply (zenon_or_s _ _ zenon_H128); [ zenon_intro zenon_H9d | zenon_intro zenon_H129 ]. % 18.87/19.01 exact (zenon_H1ef zenon_H9d). % 18.87/19.01 apply (zenon_or_s _ _ zenon_H129); [ zenon_intro zenon_H10d | zenon_intro zenon_H12a ]. % 18.87/19.01 exact (zenon_H10a zenon_H10d). % 18.87/19.01 apply (zenon_or_s _ _ zenon_H12a); [ zenon_intro zenon_Hf0 | zenon_intro zenon_Hd6 ]. % 18.87/19.01 apply (zenon_or_s _ _ zenon_H2f); [ zenon_intro zenon_H34 | zenon_intro zenon_H33 ]. % 18.87/19.01 apply (zenon_L847_); trivial. % 18.87/19.01 apply (zenon_or_s _ _ zenon_H33); [ zenon_intro zenon_H36 | zenon_intro zenon_H35 ]. % 18.87/19.01 apply (zenon_L128_); trivial. % 18.87/19.01 apply (zenon_or_s _ _ zenon_H35); [ zenon_intro zenon_H2c | zenon_intro zenon_H37 ]. % 18.87/19.01 apply (zenon_L849_); trivial. % 18.87/19.01 apply (zenon_or_s _ _ zenon_He7); [ zenon_intro zenon_H3b | zenon_intro zenon_He9 ]. % 18.87/19.01 apply (zenon_L300_); trivial. % 18.87/19.01 apply (zenon_or_s _ _ zenon_He9); [ zenon_intro zenon_Ha6 | zenon_intro zenon_Hea ]. % 18.87/19.01 apply (zenon_L39_); trivial. % 18.87/19.01 apply (zenon_or_s _ _ zenon_Hea); [ zenon_intro zenon_Haa | zenon_intro zenon_Hdd ]. % 18.87/19.01 apply (zenon_L40_); trivial. % 18.87/19.01 apply (zenon_L852_); trivial. % 18.87/19.01 exact (zenon_H24e zenon_Hd6). % 18.87/19.01 apply (zenon_or_s _ _ zenon_H1e2); [ zenon_intro zenon_H3b | zenon_intro zenon_H15e ]. % 18.87/19.01 apply (zenon_or_s _ _ zenon_H128); [ zenon_intro zenon_H9d | zenon_intro zenon_H129 ]. % 18.87/19.01 exact (zenon_H1ef zenon_H9d). % 18.87/19.01 apply (zenon_or_s _ _ zenon_H129); [ zenon_intro zenon_H10d | zenon_intro zenon_H12a ]. % 18.87/19.01 exact (zenon_H10a zenon_H10d). % 18.87/19.01 apply (zenon_or_s _ _ zenon_H12a); [ zenon_intro zenon_Hf0 | zenon_intro zenon_Hd6 ]. % 18.87/19.01 apply (zenon_or_s _ _ zenon_H16f); [ zenon_intro zenon_H9e | zenon_intro zenon_H170 ]. % 18.87/19.01 apply (zenon_or_s _ _ zenon_H2f); [ zenon_intro zenon_H34 | zenon_intro zenon_H33 ]. % 18.87/19.01 apply (zenon_L204_); trivial. % 18.87/19.01 apply (zenon_or_s _ _ zenon_H33); [ zenon_intro zenon_H36 | zenon_intro zenon_H35 ]. % 18.87/19.01 apply (zenon_L128_); trivial. % 18.87/19.01 apply (zenon_or_s _ _ zenon_H35); [ zenon_intro zenon_H2c | zenon_intro zenon_H37 ]. % 18.87/19.01 apply (zenon_L849_); trivial. % 18.87/19.01 apply (zenon_L300_); trivial. % 18.87/19.01 apply (zenon_or_s _ _ zenon_H170); [ zenon_intro zenon_H13f | zenon_intro zenon_H171 ]. % 18.87/19.01 apply (zenon_L166_); trivial. % 18.87/19.01 apply (zenon_or_s _ _ zenon_H171); [ zenon_intro zenon_H16c | zenon_intro zenon_Hdc ]. % 18.87/19.01 apply (zenon_L167_); trivial. % 18.87/19.01 apply (zenon_or_s _ _ zenon_H2f); [ zenon_intro zenon_H34 | zenon_intro zenon_H33 ]. % 18.87/19.01 apply (zenon_L847_); trivial. % 18.87/19.01 apply (zenon_or_s _ _ zenon_H33); [ zenon_intro zenon_H36 | zenon_intro zenon_H35 ]. % 18.87/19.01 apply (zenon_L128_); trivial. % 18.87/19.01 apply (zenon_or_s _ _ zenon_H35); [ zenon_intro zenon_H2c | zenon_intro zenon_H37 ]. % 18.87/19.01 apply (zenon_or_s _ _ zenon_H1ac); [ zenon_intro zenon_H44 | zenon_intro zenon_H1af ]. % 18.87/19.01 apply (zenon_L855_); trivial. % 18.87/19.01 apply (zenon_or_s _ _ zenon_H1af); [ zenon_intro zenon_H1b1 | zenon_intro zenon_H1b0 ]. % 18.87/19.01 apply (zenon_L837_); trivial. % 18.87/19.01 apply (zenon_or_s _ _ zenon_H1b0); [ zenon_intro zenon_H61 | zenon_intro zenon_H60 ]. % 18.87/19.01 apply (zenon_L146_); trivial. % 18.87/19.01 apply (zenon_L839_); trivial. % 18.87/19.01 apply (zenon_L300_); trivial. % 18.87/19.01 exact (zenon_H24e zenon_Hd6). % 18.87/19.01 apply (zenon_L193_); trivial. % 18.87/19.01 apply (zenon_or_s _ _ zenon_H1e0); [ zenon_intro zenon_H3a | zenon_intro zenon_H1e1 ]. % 18.87/19.01 apply (zenon_L35_); trivial. % 18.87/19.01 apply (zenon_or_s _ _ zenon_H1e1); [ zenon_intro zenon_H9e | zenon_intro zenon_H1e2 ]. % 18.87/19.01 apply (zenon_or_s _ _ zenon_H128); [ zenon_intro zenon_H9d | zenon_intro zenon_H129 ]. % 18.87/19.01 exact (zenon_H1ef zenon_H9d). % 18.87/19.01 apply (zenon_or_s _ _ zenon_H129); [ zenon_intro zenon_H10d | zenon_intro zenon_H12a ]. % 18.87/19.01 exact (zenon_H10a zenon_H10d). % 18.87/19.01 apply (zenon_or_s _ _ zenon_H12a); [ zenon_intro zenon_Hf0 | zenon_intro zenon_Hd6 ]. % 18.87/19.01 apply (zenon_or_s _ _ zenon_H2f); [ zenon_intro zenon_H34 | zenon_intro zenon_H33 ]. % 18.87/19.01 apply (zenon_L204_); trivial. % 18.87/19.01 apply (zenon_or_s _ _ zenon_H33); [ zenon_intro zenon_H36 | zenon_intro zenon_H35 ]. % 18.87/19.01 apply (zenon_L128_); trivial. % 18.87/19.01 apply (zenon_or_s _ _ zenon_H35); [ zenon_intro zenon_H2c | zenon_intro zenon_H37 ]. % 18.87/19.01 apply (zenon_L860_); trivial. % 18.87/19.01 apply (zenon_or_s _ _ zenon_He7); [ zenon_intro zenon_H3b | zenon_intro zenon_He9 ]. % 18.87/19.01 apply (zenon_L300_); trivial. % 18.87/19.01 apply (zenon_or_s _ _ zenon_He9); [ zenon_intro zenon_Ha6 | zenon_intro zenon_Hea ]. % 18.87/19.01 apply (zenon_L39_); trivial. % 18.87/19.01 apply (zenon_or_s _ _ zenon_Hea); [ zenon_intro zenon_Haa | zenon_intro zenon_Hdd ]. % 18.87/19.01 apply (zenon_or_s _ _ zenon_H153); [ zenon_intro zenon_H148 | zenon_intro zenon_H154 ]. % 18.87/19.01 apply (zenon_L861_); trivial. % 18.87/19.01 apply (zenon_or_s _ _ zenon_H154); [ zenon_intro zenon_H14d | zenon_intro zenon_H155 ]. % 18.87/19.01 apply (zenon_L164_); trivial. % 18.87/19.01 apply (zenon_or_s _ _ zenon_H155); [ zenon_intro zenon_H151 | zenon_intro zenon_Hf6 ]. % 18.87/19.01 apply (zenon_L104_); trivial. % 18.87/19.01 apply (zenon_L767_); trivial. % 18.87/19.01 apply (zenon_L54_); trivial. % 18.87/19.01 exact (zenon_H24e zenon_Hd6). % 18.87/19.01 apply (zenon_or_s _ _ zenon_H1e2); [ zenon_intro zenon_H3b | zenon_intro zenon_H15e ]. % 18.87/19.01 apply (zenon_or_s _ _ zenon_H128); [ zenon_intro zenon_H9d | zenon_intro zenon_H129 ]. % 18.87/19.01 exact (zenon_H1ef zenon_H9d). % 18.87/19.01 apply (zenon_or_s _ _ zenon_H129); [ zenon_intro zenon_H10d | zenon_intro zenon_H12a ]. % 18.87/19.01 exact (zenon_H10a zenon_H10d). % 18.87/19.01 apply (zenon_or_s _ _ zenon_H12a); [ zenon_intro zenon_Hf0 | zenon_intro zenon_Hd6 ]. % 18.87/19.01 apply (zenon_or_s _ _ zenon_H16f); [ zenon_intro zenon_H9e | zenon_intro zenon_H170 ]. % 18.87/19.01 apply (zenon_or_s _ _ zenon_H2f); [ zenon_intro zenon_H34 | zenon_intro zenon_H33 ]. % 18.87/19.01 apply (zenon_L847_); trivial. % 18.87/19.01 apply (zenon_or_s _ _ zenon_H33); [ zenon_intro zenon_H36 | zenon_intro zenon_H35 ]. % 18.87/19.01 apply (zenon_L128_); trivial. % 18.87/19.01 apply (zenon_or_s _ _ zenon_H35); [ zenon_intro zenon_H2c | zenon_intro zenon_H37 ]. % 18.87/19.01 apply (zenon_L860_); trivial. % 18.87/19.01 apply (zenon_L300_); trivial. % 18.87/19.01 apply (zenon_or_s _ _ zenon_H170); [ zenon_intro zenon_H13f | zenon_intro zenon_H171 ]. % 18.87/19.01 apply (zenon_L166_); trivial. % 18.87/19.01 apply (zenon_or_s _ _ zenon_H171); [ zenon_intro zenon_H16c | zenon_intro zenon_Hdc ]. % 18.87/19.01 apply (zenon_L167_); trivial. % 18.87/19.01 apply (zenon_L117_); trivial. % 18.87/19.01 exact (zenon_H24e zenon_Hd6). % 18.87/19.01 apply (zenon_L193_); trivial. % 18.87/19.01 apply (zenon_or_s _ _ zenon_H1e0); [ zenon_intro zenon_H3a | zenon_intro zenon_H1e1 ]. % 18.87/19.01 apply (zenon_L35_); trivial. % 18.87/19.01 apply (zenon_or_s _ _ zenon_H1e1); [ zenon_intro zenon_H9e | zenon_intro zenon_H1e2 ]. % 18.87/19.01 apply (zenon_L107_); trivial. % 18.87/19.01 apply (zenon_or_s _ _ zenon_H1e2); [ zenon_intro zenon_H3b | zenon_intro zenon_H15e ]. % 18.87/19.01 apply (zenon_or_s _ _ zenon_H128); [ zenon_intro zenon_H9d | zenon_intro zenon_H129 ]. % 18.87/19.01 exact (zenon_H1ef zenon_H9d). % 18.87/19.01 apply (zenon_or_s _ _ zenon_H129); [ zenon_intro zenon_H10d | zenon_intro zenon_H12a ]. % 18.87/19.01 exact (zenon_H10a zenon_H10d). % 18.87/19.01 apply (zenon_or_s _ _ zenon_H12a); [ zenon_intro zenon_Hf0 | zenon_intro zenon_Hd6 ]. % 18.87/19.01 apply (zenon_or_s _ _ zenon_H16f); [ zenon_intro zenon_H9e | zenon_intro zenon_H170 ]. % 18.87/19.01 apply (zenon_L107_); trivial. % 18.87/19.01 apply (zenon_or_s _ _ zenon_H170); [ zenon_intro zenon_H13f | zenon_intro zenon_H171 ]. % 18.87/19.01 apply (zenon_L166_); trivial. % 18.87/19.01 apply (zenon_or_s _ _ zenon_H171); [ zenon_intro zenon_H16c | zenon_intro zenon_Hdc ]. % 18.87/19.01 apply (zenon_L167_); trivial. % 18.87/19.01 apply (zenon_or_s _ _ zenon_H2f); [ zenon_intro zenon_H34 | zenon_intro zenon_H33 ]. % 18.87/19.01 apply (zenon_L846_); trivial. % 18.87/19.01 apply (zenon_or_s _ _ zenon_H33); [ zenon_intro zenon_H36 | zenon_intro zenon_H35 ]. % 18.87/19.01 apply (zenon_L128_); trivial. % 18.87/19.01 apply (zenon_or_s _ _ zenon_H35); [ zenon_intro zenon_H2c | zenon_intro zenon_H37 ]. % 18.87/19.01 apply (zenon_or_s _ _ zenon_H1ac); [ zenon_intro zenon_H44 | zenon_intro zenon_H1af ]. % 18.87/19.01 apply (zenon_L100_); trivial. % 18.87/19.01 apply (zenon_or_s _ _ zenon_H1af); [ zenon_intro zenon_H1b1 | zenon_intro zenon_H1b0 ]. % 18.87/19.01 apply (zenon_L259_); trivial. % 18.87/19.01 apply (zenon_or_s _ _ zenon_H1b0); [ zenon_intro zenon_H61 | zenon_intro zenon_H60 ]. % 18.87/19.01 apply (zenon_L146_); trivial. % 18.87/19.01 apply (zenon_L839_); trivial. % 18.87/19.01 apply (zenon_L300_); trivial. % 18.87/19.01 exact (zenon_H24e zenon_Hd6). % 18.87/19.01 apply (zenon_L109_); trivial. % 18.87/19.01 apply (zenon_or_s _ _ zenon_H1fe); [ zenon_intro zenon_H7b | zenon_intro zenon_H1ff ]. % 18.87/19.01 apply (zenon_L375_); trivial. % 18.87/19.01 apply (zenon_or_s _ _ zenon_H1ff); [ zenon_intro zenon_H86 | zenon_intro zenon_H200 ]. % 18.87/19.01 apply (zenon_L257_); trivial. % 18.87/19.01 apply (zenon_or_s _ _ zenon_H200); [ zenon_intro zenon_Hee | zenon_intro zenon_H148 ]. % 18.87/19.01 apply (zenon_or_s _ _ zenon_H168); [ zenon_intro zenon_H3a | zenon_intro zenon_H169 ]. % 18.87/19.01 apply (zenon_L35_); trivial. % 18.87/19.01 apply (zenon_or_s _ _ zenon_H169); [ zenon_intro zenon_H99 | zenon_intro zenon_H16a ]. % 18.87/19.01 apply (zenon_L36_); trivial. % 18.87/19.01 apply (zenon_or_s _ _ zenon_H16a); [ zenon_intro zenon_Ha9 | zenon_intro zenon_He3 ]. % 18.87/19.01 apply (zenon_or_s _ _ zenon_H128); [ zenon_intro zenon_H9d | zenon_intro zenon_H129 ]. % 18.87/19.01 exact (zenon_H1ef zenon_H9d). % 18.87/19.01 apply (zenon_or_s _ _ zenon_H129); [ zenon_intro zenon_H10d | zenon_intro zenon_H12a ]. % 18.87/19.01 exact (zenon_H10a zenon_H10d). % 18.87/19.01 apply (zenon_or_s _ _ zenon_H12a); [ zenon_intro zenon_Hf0 | zenon_intro zenon_Hd6 ]. % 18.87/19.01 apply (zenon_or_s _ _ zenon_H2f); [ zenon_intro zenon_H34 | zenon_intro zenon_H33 ]. % 18.87/19.01 apply (zenon_L866_); trivial. % 18.87/19.01 apply (zenon_or_s _ _ zenon_H33); [ zenon_intro zenon_H36 | zenon_intro zenon_H35 ]. % 18.87/19.01 apply (zenon_L128_); trivial. % 18.87/19.01 apply (zenon_or_s _ _ zenon_H35); [ zenon_intro zenon_H2c | zenon_intro zenon_H37 ]. % 18.87/19.01 apply (zenon_or_s _ _ zenon_H1ac); [ zenon_intro zenon_H44 | zenon_intro zenon_H1af ]. % 18.87/19.01 apply (zenon_L868_); trivial. % 18.87/19.01 apply (zenon_or_s _ _ zenon_H1af); [ zenon_intro zenon_H1b1 | zenon_intro zenon_H1b0 ]. % 18.87/19.01 apply (zenon_L259_); trivial. % 18.87/19.01 apply (zenon_or_s _ _ zenon_H1b0); [ zenon_intro zenon_H61 | zenon_intro zenon_H60 ]. % 18.87/19.01 apply (zenon_L146_); trivial. % 18.87/19.01 apply (zenon_L871_); trivial. % 18.87/19.01 apply (zenon_or_s _ _ zenon_He7); [ zenon_intro zenon_H3b | zenon_intro zenon_He9 ]. % 18.87/19.01 apply (zenon_L300_); trivial. % 18.87/19.01 apply (zenon_or_s _ _ zenon_He9); [ zenon_intro zenon_Ha6 | zenon_intro zenon_Hea ]. % 18.87/19.01 apply (zenon_L39_); trivial. % 18.87/19.01 apply (zenon_or_s _ _ zenon_Hea); [ zenon_intro zenon_Haa | zenon_intro zenon_Hdd ]. % 18.87/19.01 apply (zenon_L40_); trivial. % 18.87/19.01 apply (zenon_L851_); trivial. % 18.87/19.01 exact (zenon_H24e zenon_Hd6). % 18.87/19.01 apply (zenon_L81_); trivial. % 18.87/19.01 apply (zenon_L876_); trivial. % 18.87/19.01 (* end of lemma zenon_L877_ *) % 18.87/19.01 assert (zenon_L878_ : (~((op (e0) (e3)) = (op (e1) (e3)))) -> ((op (e1) (e3)) = (e0)) -> (~((op (e0) (e3)) = (e1))) -> (((op (e0) (e3)) = (e0))\/(((op (e0) (e3)) = (e1))\/(((op (e0) (e3)) = (e2))\/((op (e0) (e3)) = (e3))))) -> (~((op (e3) (e2)) = (e1))) -> (~((op (e3) (e1)) = (e1))) -> (((op (e0) (e3)) = (e1))\/(((op (e1) (e3)) = (e1))\/(((op (e2) (e3)) = (e1))\/((op (e3) (e3)) = (e1))))) -> (~((op (e1) (e2)) = (op (e1) (e3)))) -> (~((op (e2) (e3)) = (e1))) -> (~((op (e3) (e0)) = (op (e3) (e3)))) -> (((op (e3) (e0)) = (e1))\/(((op (e3) (e1)) = (e1))\/(((op (e3) (e2)) = (e1))\/((op (e3) (e3)) = (e1))))) -> (~((e1) = (e3))) -> ((op (e1) (e1)) = (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) (e0)) = (e1))) -> (~((op (e2) (e2)) = (op (e2) (e3)))) -> (~((op (e0) (e1)) = (op (e2) (e1)))) -> ((op (e0) (e1)) = (e0)) -> (~((e0) = (e2))) -> (((op (e2) (e0)) = (e0))\/(((op (e2) (e1)) = (e0))\/(((op (e2) (e2)) = (e0))\/((op (e2) (e3)) = (e0))))) -> (~((op (e3) (e1)) = (op (e3) (e3)))) -> (~((op (e2) (e1)) = (op (e2) (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) (e3)) = (e3))\/(((op (e1) (e3)) = (e3))\/(((op (e2) (e3)) = (e3))\/((op (e3) (e3)) = (e3))))) -> ((op (e2) (e0)) = (e0)) -> (~((op (e2) (e0)) = (op (e2) (e3)))) -> (((op (e2) (e3)) = (e0))\/(((op (e2) (e3)) = (e1))\/(((op (e2) (e3)) = (e2))\/((op (e2) (e3)) = (e3))))) -> (~((op (e0) (e3)) = (op (e2) (e3)))) -> (~((op (e0) (e3)) = (op (e3) (e3)))) -> (~((op (e3) (e3)) = (e3))) -> (~((op (e1) (e1)) = (e1))) -> (~((op (e1) (e0)) = (e1))) -> (((op (e1) (e0)) = (e1))\/(((op (e1) (e1)) = (e1))\/(((op (e1) (e2)) = (e1))\/((op (e1) (e3)) = (e1))))) -> (~((op (e2) (e2)) = (e2))) -> (((op (e3) (e0)) = (e2))\/(((op (e3) (e1)) = (e2))\/(((op (e3) (e2)) = (e2))\/((op (e3) (e3)) = (e2))))) -> ((op (e0) (e0)) = (e1)) -> (((op (e1) (e0)) = (e3))\/(((op (e1) (e1)) = (e3))\/(((op (e1) (e2)) = (e3))\/((op (e1) (e3)) = (e3))))) -> (~((op (e1) (e1)) = (op (e3) (e1)))) -> ((op (e0) (e2)) = (e2)) -> (~((op (e0) (e2)) = (op (e3) (e2)))) -> (~((op (e2) (e3)) = (op (e3) (e3)))) -> (~((op (e1) (e3)) = (e1))) -> False). % 18.87/19.01 do 0 intro. intros zenon_H1d zenon_H1f zenon_H231 zenon_He4 zenon_H251 zenon_H250 zenon_H133 zenon_H124 zenon_H255 zenon_H71 zenon_He8 zenon_H95 zenon_H110 zenon_H12b zenon_H1d5 zenon_Hdb zenon_Had zenon_H6d zenon_H17e zenon_H49 zenon_H149 zenon_H2f zenon_H130 zenon_H1c7 zenon_H57 zenon_H145 zenon_H136 zenon_H34 zenon_H5b zenon_H11f zenon_He2 zenon_Hc2 zenon_H102 zenon_H10a zenon_H1ef zenon_H128 zenon_H173 zenon_H153 zenon_H7a zenon_H16f zenon_H160 zenon_H150 zenon_H14f zenon_Hf3 zenon_H24e. % 18.87/19.01 apply (zenon_or_s _ _ zenon_H128); [ zenon_intro zenon_H9d | zenon_intro zenon_H129 ]. % 18.87/19.01 exact (zenon_H1ef zenon_H9d). % 18.87/19.01 apply (zenon_or_s _ _ zenon_H129); [ zenon_intro zenon_H10d | zenon_intro zenon_H12a ]. % 18.87/19.01 exact (zenon_H10a zenon_H10d). % 18.87/19.01 apply (zenon_or_s _ _ zenon_H12a); [ zenon_intro zenon_Hf0 | zenon_intro zenon_Hd6 ]. % 18.87/19.01 apply (zenon_or_s _ _ zenon_H16f); [ zenon_intro zenon_H9e | zenon_intro zenon_H170 ]. % 18.87/19.01 apply (zenon_L843_); trivial. % 18.87/19.01 apply (zenon_or_s _ _ zenon_H170); [ zenon_intro zenon_H13f | zenon_intro zenon_H171 ]. % 18.87/19.01 apply (zenon_L166_); trivial. % 18.87/19.01 apply (zenon_or_s _ _ zenon_H171); [ zenon_intro zenon_H16c | zenon_intro zenon_Hdc ]. % 18.87/19.01 apply (zenon_L167_); trivial. % 18.87/19.01 apply (zenon_L827_); trivial. % 18.87/19.01 exact (zenon_H24e zenon_Hd6). % 18.87/19.01 (* end of lemma zenon_L878_ *) % 18.87/19.01 assert (zenon_L879_ : (((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)) = (op (e2) (e3)))) -> (~((op (e1) (e1)) = (op (e1) (e3)))) -> (~((op (e0) (e1)) = (op (e0) (e3)))) -> (~((op (e2) (e0)) = (op (e2) (e2)))) -> (~((op (e0) (e1)) = (op (e2) (e1)))) -> (~((op (e3) (e0)) = (op (e3) (e3)))) -> (((op (e3) (e0)) = (e1))\/(((op (e3) (e1)) = (e1))\/(((op (e3) (e2)) = (e1))\/((op (e3) (e3)) = (e1))))) -> (~((e0) = (e1))) -> (~((op (e2) (e1)) = (op (e3) (e1)))) -> ((op (e2) (e1)) = (e1)) -> ((op (e0) (e2)) = (e3)) -> ((op (e0) (e3)) = (e2)) -> (~((e0) = (e2))) -> (((op (e0) (e3)) = (e0))\/(((op (e1) (e3)) = (e0))\/(((op (e2) (e3)) = (e0))\/((op (e3) (e3)) = (e0))))) -> (((op (e0) (e2)) = (e0))\/(((op (e1) (e2)) = (e0))\/(((op (e2) (e2)) = (e0))\/((op (e3) (e2)) = (e0))))) -> (~((op (e0) (e1)) = (op (e0) (e2)))) -> ((op (e0) (e1)) = (e0)) -> (~((op (e1) (e1)) = (op (e1) (e2)))) -> ((op (e1) (e1)) = (e0)) -> (~((op (e2) (e2)) = (op (e2) (e3)))) -> (~((op (e3) (e0)) = (op (e3) (e2)))) -> ((op (e3) (e0)) = (e0)) -> False). % 18.87/19.01 do 0 intro. intros zenon_H2f zenon_H62 zenon_H5b zenon_H57 zenon_H54 zenon_H52 zenon_H17e zenon_H71 zenon_He8 zenon_Ha1 zenon_Haf zenon_Ha5 zenon_Ha9 zenon_Hcd zenon_H149 zenon_H67 zenon_H6a zenon_H4a zenon_H49 zenon_H4f zenon_H29 zenon_H6d zenon_H6f zenon_H44. % 18.87/19.01 apply (zenon_or_s _ _ zenon_H2f); [ zenon_intro zenon_H34 | zenon_intro zenon_H33 ]. % 18.87/19.01 apply (zenon_L17_); trivial. % 18.87/19.01 apply (zenon_or_s _ _ zenon_H33); [ zenon_intro zenon_H36 | zenon_intro zenon_H35 ]. % 18.87/19.01 apply (zenon_L128_); trivial. % 18.87/19.01 apply (zenon_or_s _ _ zenon_H35); [ zenon_intro zenon_H2c | zenon_intro zenon_H37 ]. % 18.87/19.01 apply (zenon_or_s _ _ zenon_H67); [ zenon_intro zenon_H1e | zenon_intro zenon_H68 ]. % 18.87/19.01 apply (zenon_L428_); trivial. % 18.87/19.01 apply (zenon_or_s _ _ zenon_H68); [ zenon_intro zenon_H1f | zenon_intro zenon_H69 ]. % 18.87/19.01 apply (zenon_L129_); trivial. % 18.87/19.01 apply (zenon_or_s _ _ zenon_H69); [ zenon_intro zenon_H37 | zenon_intro zenon_H60 ]. % 18.87/19.01 apply (zenon_L20_); trivial. % 18.87/19.01 apply (zenon_L21_); trivial. % 18.87/19.01 apply (zenon_L20_); trivial. % 18.87/19.01 (* end of lemma zenon_L879_ *) % 18.87/19.01 assert (zenon_L880_ : (~((e0) = (e2))) -> ((op (e3) (e0)) = (e0)) -> (((op (e0) (e0)) = (e3))\/(((op (e0) (e1)) = (e3))\/(((op (e0) (e2)) = (e3))\/((op (e0) (e3)) = (e3))))) -> (~((e0) = (e3))) -> (~((op (e1) (e3)) = (op (e2) (e3)))) -> (((op (e3) (e0)) = (e1))\/(((op (e3) (e1)) = (e1))\/(((op (e3) (e2)) = (e1))\/((op (e3) (e3)) = (e1))))) -> (~((e0) = (e1))) -> (~((op (e2) (e1)) = (op (e3) (e1)))) -> ((op (e2) (e1)) = (e1)) -> (~((op (e0) (e1)) = (op (e2) (e1)))) -> ((op (e0) (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)) = (e1))\/(((op (e1) (e1)) = (e1))\/(((op (e1) (e2)) = (e1))\/((op (e1) (e3)) = (e1))))) -> (~((op (e1) (e0)) = (e1))) -> (~((op (e1) (e1)) = (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) (e2)) = (e1))) -> (~((op (e3) (e1)) = (e1))) -> (~((op (e3) (e0)) = (e1))) -> (~((op (e0) (e2)) = (op (e2) (e2)))) -> (~((e1) = (e3))) -> (((op (e2) (e2)) = (e0))\/(((op (e2) (e2)) = (e1))\/(((op (e2) (e2)) = (e2))\/((op (e2) (e2)) = (e3))))) -> (~((op (e2) (e2)) = (op (e2) (e3)))) -> (~((op (e1) (e2)) = (op (e2) (e2)))) -> (~((op (e2) (e2)) = (e2))) -> (~((op (e2) (e0)) = (op (e2) (e2)))) -> (((op (e2) (e0)) = (e3))\/(((op (e2) (e1)) = (e3))\/(((op (e2) (e2)) = (e3))\/((op (e2) (e3)) = (e3))))) -> (~((op (e1) (e3)) = (e1))) -> ((op (e1) (e1)) = (e2)) -> (~((op (e1) (e0)) = (op (e3) (e0)))) -> (((op (e1) (e0)) = (e0))\/(((op (e1) (e1)) = (e0))\/(((op (e1) (e2)) = (e0))\/((op (e1) (e3)) = (e0))))) -> (~((e2) = (e3))) -> (~((op (e0) (e3)) = (op (e2) (e3)))) -> (((op (e2) (e0)) = (e0))\/(((op (e2) (e0)) = (e1))\/(((op (e2) (e0)) = (e2))\/((op (e2) (e0)) = (e3))))) -> (~((op (e2) (e0)) = (op (e2) (e3)))) -> (~((op (e2) (e0)) = (e1))) -> (~((op (e2) (e0)) = (op (e2) (e1)))) -> (((op (e2) (e0)) = (e2))\/(((op (e2) (e1)) = (e2))\/(((op (e2) (e2)) = (e2))\/((op (e2) (e3)) = (e2))))) -> (~((op (e3) (e2)) = (op (e3) (e3)))) -> (~((op (e1) (e1)) = (op (e1) (e3)))) -> (~((op (e0) (e1)) = (op (e0) (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) (e2)) = (e0))\/(((op (e1) (e2)) = (e0))\/(((op (e2) (e2)) = (e0))\/((op (e3) (e2)) = (e0))))) -> (~((op (e0) (e1)) = (op (e0) (e2)))) -> (~((op (e1) (e1)) = (op (e1) (e2)))) -> (~((op (e3) (e0)) = (op (e3) (e2)))) -> (~((op (e0) (e0)) = (op (e0) (e3)))) -> (((op (e0) (e0)) = (e2))\/(((op (e1) (e0)) = (e2))\/(((op (e2) (e0)) = (e2))\/((op (e3) (e0)) = (e2))))) -> (~((op (e1) (e1)) = (op (e3) (e1)))) -> (((op (e0) (e0)) = (e1))\/(((op (e0) (e1)) = (e1))\/(((op (e0) (e2)) = (e1))\/((op (e0) (e3)) = (e1))))) -> (~((e1) = (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 (e2) (e3)) = (op (e3) (e3)))) -> (~((op (e2) (e3)) = (e1))) -> (((op (e2) (e3)) = (e0))\/(((op (e2) (e3)) = (e1))\/(((op (e2) (e3)) = (e2))\/((op (e2) (e3)) = (e3))))) -> (~((op (e0) (e2)) = (op (e3) (e2)))) -> (((op (e0) (e3)) = (e2))\/(((op (e1) (e3)) = (e2))\/(((op (e2) (e3)) = (e2))\/((op (e3) (e3)) = (e2))))) -> (~((op (e3) (e1)) = (op (e3) (e3)))) -> (((op (e1) (e0)) = (e3))\/(((op (e1) (e1)) = (e3))\/(((op (e1) (e2)) = (e3))\/((op (e1) (e3)) = (e3))))) -> (~((op (e1) (e2)) = (op (e1) (e3)))) -> (((op (e0) (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 (e2) (e2)) = (e1))) -> (((op (e3) (e2)) = (e0))\/(((op (e3) (e2)) = (e1))\/(((op (e3) (e2)) = (e2))\/((op (e3) (e2)) = (e3))))) -> (~((op (e1) (e2)) = (op (e3) (e2)))) -> (~((op (e2) (e2)) = (op (e3) (e2)))) -> ((~((op (e1) (e2)) = (e1)))\/((op (e1) (e1)) = (e2))) -> (~((op (e0) (e1)) = (op (e1) (e1)))) -> ((~((op (e2) (e0)) = (e1)))\/((op (e2) (e1)) = (e0))) -> ((~((op (e3) (e0)) = (e1)))\/((op (e3) (e1)) = (e0))) -> (((op (e0) (e0)) = (e1))\/(((op (e1) (e0)) = (e1))\/(((op (e2) (e0)) = (e1))\/((op (e3) (e0)) = (e1))))) -> (~((op (e0) (e0)) = (op (e0) (e2)))) -> (((op (e0) (e2)) = (e1))\/(((op (e1) (e2)) = (e1))\/(((op (e2) (e2)) = (e1))\/((op (e3) (e2)) = (e1))))) -> (~((op (e0) (e1)) = (op (e3) (e1)))) -> ((~((op (e3) (e2)) = (e1)))\/((op (e3) (e1)) = (e2))) -> ((~((op (e2) (e2)) = (e1)))\/((op (e2) (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) (e1)) = (e1))) -> (~((op (e0) (e2)) = (e1))) -> (~((op (e0) (e3)) = (e1))) -> False). % 18.87/19.02 do 0 intro. intros zenon_H149 zenon_H44 zenon_H168 zenon_H9a zenon_Hdb zenon_He8 zenon_Ha1 zenon_Haf zenon_Ha5 zenon_H17e zenon_H49 zenon_H17b zenon_H2f zenon_H128 zenon_H1ef zenon_H10a zenon_Hd5 zenon_Hdf zenon_H251 zenon_H250 zenon_Had zenon_Ha8 zenon_H95 zenon_H1c4 zenon_H6d zenon_H2b zenon_H173 zenon_H52 zenon_He7 zenon_H24e zenon_H110 zenon_H1fa zenon_H22 zenon_H12b zenon_He2 zenon_H259 zenon_H5b zenon_H1db zenon_H1f0 zenon_H1d5 zenon_H62 zenon_H57 zenon_H54 zenon_H71 zenon_H67 zenon_H6a zenon_H4a zenon_H4f zenon_H6f zenon_H189 zenon_H1fe zenon_H160 zenon_H22d zenon_H7c zenon_Hc2 zenon_H1d zenon_He4 zenon_Hf3 zenon_H255 zenon_H11f zenon_H14f zenon_H145 zenon_H130 zenon_H16f zenon_H124 zenon_H133 zenon_H153 zenon_H198 zenon_H191 zenon_H115 zenon_H18f zenon_H256 zenon_H10e zenon_H257 zenon_H254 zenon_H235 zenon_H13c zenon_H139 zenon_H210 zenon_H252 zenon_H253 zenon_H258 zenon_H183 zenon_Ha4 zenon_H20d zenon_H231. % 18.87/19.02 apply (zenon_or_s _ _ zenon_H22d); [ zenon_intro zenon_H7a | zenon_intro zenon_H22e ]. % 18.87/19.02 apply (zenon_or_s _ _ zenon_H183); [ zenon_intro zenon_H7b | zenon_intro zenon_H186 ]. % 18.87/19.02 apply (zenon_L26_); trivial. % 18.87/19.02 apply (zenon_or_s _ _ zenon_H186); [ zenon_intro zenon_H10f | zenon_intro zenon_H187 ]. % 18.87/19.02 apply (zenon_L726_); trivial. % 18.87/19.02 apply (zenon_or_s _ _ zenon_H187); [ zenon_intro zenon_H150 | zenon_intro zenon_Hcd ]. % 18.87/19.02 apply (zenon_L836_); trivial. % 18.87/19.02 apply (zenon_or_s _ _ zenon_H1fe); [ zenon_intro zenon_H7b | zenon_intro zenon_H1ff ]. % 18.87/19.02 apply (zenon_L375_); trivial. % 18.87/19.02 apply (zenon_or_s _ _ zenon_H1ff); [ zenon_intro zenon_H86 | zenon_intro zenon_H200 ]. % 18.87/19.02 apply (zenon_or_s _ _ zenon_H168); [ zenon_intro zenon_H3a | zenon_intro zenon_H169 ]. % 18.87/19.02 apply (zenon_L35_); trivial. % 18.87/19.02 apply (zenon_or_s _ _ zenon_H169); [ zenon_intro zenon_H99 | zenon_intro zenon_H16a ]. % 18.87/19.02 apply (zenon_L36_); trivial. % 18.87/19.02 apply (zenon_or_s _ _ zenon_H16a); [ zenon_intro zenon_Ha9 | zenon_intro zenon_He3 ]. % 18.87/19.02 apply (zenon_or_s _ _ zenon_H22); [ zenon_intro zenon_H27 | zenon_intro zenon_H26 ]. % 18.87/19.02 apply (zenon_L312_); trivial. % 18.87/19.02 apply (zenon_or_s _ _ zenon_H26); [ zenon_intro zenon_H29 | zenon_intro zenon_H28 ]. % 18.87/19.02 apply (zenon_L879_); trivial. % 18.87/19.02 apply (zenon_or_s _ _ zenon_H28); [ zenon_intro zenon_H2a | zenon_intro zenon_H1f ]. % 18.87/19.02 apply (zenon_or_s _ _ zenon_H128); [ zenon_intro zenon_H9d | zenon_intro zenon_H129 ]. % 18.87/19.02 exact (zenon_H1ef zenon_H9d). % 18.87/19.02 apply (zenon_or_s _ _ zenon_H129); [ zenon_intro zenon_H10d | zenon_intro zenon_H12a ]. % 18.87/19.02 exact (zenon_H10a zenon_H10d). % 18.87/19.02 apply (zenon_or_s _ _ zenon_H12a); [ zenon_intro zenon_Hf0 | zenon_intro zenon_Hd6 ]. % 18.87/19.02 apply (zenon_or_s _ _ zenon_H2f); [ zenon_intro zenon_H34 | zenon_intro zenon_H33 ]. % 18.87/19.02 apply (zenon_L127_); trivial. % 18.87/19.02 apply (zenon_or_s _ _ zenon_H33); [ zenon_intro zenon_H36 | zenon_intro zenon_H35 ]. % 18.87/19.02 apply (zenon_L128_); trivial. % 18.87/19.02 apply (zenon_or_s _ _ zenon_H35); [ zenon_intro zenon_H2c | zenon_intro zenon_H37 ]. % 18.87/19.02 apply (zenon_L3_); trivial. % 18.87/19.02 apply (zenon_or_s _ _ zenon_H1d5); [ zenon_intro zenon_Hee | zenon_intro zenon_H1d6 ]. % 18.87/19.02 apply (zenon_L867_); trivial. % 18.87/19.02 apply (zenon_or_s _ _ zenon_H1d6); [ zenon_intro zenon_H1ca | zenon_intro zenon_H1d7 ]. % 18.87/19.02 apply (zenon_L729_); trivial. % 18.87/19.02 apply (zenon_or_s _ _ zenon_H1d7); [ zenon_intro zenon_H176 | zenon_intro zenon_H11d ]. % 18.87/19.02 exact (zenon_H173 zenon_H176). % 18.87/19.02 apply (zenon_L234_); trivial. % 18.87/19.02 exact (zenon_H24e zenon_Hd6). % 18.87/19.02 apply (zenon_L803_); trivial. % 18.87/19.02 apply (zenon_L81_); trivial. % 18.87/19.02 apply (zenon_or_s _ _ zenon_H200); [ zenon_intro zenon_Hee | zenon_intro zenon_H148 ]. % 18.87/19.02 apply (zenon_L868_); trivial. % 18.87/19.02 apply (zenon_L100_); trivial. % 18.87/19.02 apply (zenon_or_s _ _ zenon_H22e); [ zenon_intro zenon_Ha0 | zenon_intro zenon_H22f ]. % 18.87/19.02 exact (zenon_Ha4 zenon_Ha0). % 18.87/19.02 apply (zenon_or_s _ _ zenon_H22f); [ zenon_intro zenon_H122 | zenon_intro zenon_Hc3 ]. % 18.87/19.02 exact (zenon_H20d zenon_H122). % 18.87/19.02 exact (zenon_H231 zenon_Hc3). % 18.87/19.02 (* end of lemma zenon_L880_ *) % 18.87/19.02 assert (zenon_L881_ : (((op (e1) (e0)) = (e0))\/(((op (e1) (e1)) = (e0))\/(((op (e1) (e2)) = (e0))\/((op (e1) (e3)) = (e0))))) -> (~((op (e1) (e0)) = (op (e2) (e0)))) -> (~((op (e3) (e2)) = (op (e3) (e3)))) -> (~((op (e1) (e1)) = (op (e1) (e2)))) -> (((op (e0) (e3)) = (e0))\/(((op (e1) (e3)) = (e0))\/(((op (e2) (e3)) = (e0))\/((op (e3) (e3)) = (e0))))) -> (~((op (e0) (e1)) = (op (e0) (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 (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)) = (e1))) -> (~((op (e0) (e3)) = (op (e3) (e3)))) -> (~((op (e0) (e3)) = (op (e2) (e3)))) -> (((op (e2) (e3)) = (e0))\/(((op (e2) (e3)) = (e1))\/(((op (e2) (e3)) = (e2))\/((op (e2) (e3)) = (e3))))) -> (~((op (e2) (e0)) = (op (e2) (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) (e2)) = (op (e3) (e2)))) -> ((op (e0) (e2)) = (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)) = (e2)) -> (~((op (e2) (e1)) = (op (e2) (e3)))) -> ((op (e2) (e1)) = (e2)) -> (~((op (e3) (e1)) = (op (e3) (e3)))) -> ((op (e1) (e0)) = (e3)) -> ((op (e0) (e0)) = (e1)) -> (((op (e3) (e0)) = (e2))\/(((op (e3) (e1)) = (e2))\/(((op (e3) (e2)) = (e2))\/((op (e3) (e3)) = (e2))))) -> (~((op (e3) (e2)) = (e1))) -> (~((op (e3) (e1)) = (e1))) -> (((op (e0) (e3)) = (e1))\/(((op (e1) (e3)) = (e1))\/(((op (e2) (e3)) = (e1))\/((op (e3) (e3)) = (e1))))) -> (~((op (e2) (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)) = (e0))\/(((op (e1) (e2)) = (e0))\/(((op (e2) (e2)) = (e0))\/((op (e3) (e2)) = (e0))))) -> (~((op (e0) (e1)) = (op (e0) (e2)))) -> ((op (e0) (e1)) = (e0)) -> (~((op (e2) (e2)) = (e2))) -> (~((op (e2) (e2)) = (op (e3) (e2)))) -> ((op (e0) (e2)) = (e3)) -> (((op (e2) (e2)) = (e0))\/(((op (e2) (e2)) = (e1))\/(((op (e2) (e2)) = (e2))\/((op (e2) (e2)) = (e3))))) -> (~((op (e1) (e2)) = (op (e1) (e3)))) -> (~((op (e0) (e2)) = (e1))) -> (((op (e0) (e2)) = (e1))\/(((op (e1) (e2)) = (e1))\/(((op (e2) (e2)) = (e1))\/((op (e3) (e2)) = (e1))))) -> ((op (e2) (e0)) = (e0)) -> (~((op (e2) (e0)) = (op (e2) (e2)))) -> (~((op (e3) (e1)) = (op (e3) (e2)))) -> ((op (e3) (e1)) = (e0)) -> False). % 18.87/19.02 do 0 intro. intros zenon_H22 zenon_H201 zenon_H62 zenon_H4f zenon_H67 zenon_H54 zenon_H128 zenon_H1ef zenon_H10a zenon_H102 zenon_He4 zenon_H1d zenon_H231 zenon_Hc2 zenon_He2 zenon_H11f zenon_H5b zenon_Hf3 zenon_H136 zenon_H14f zenon_H150 zenon_H145 zenon_H57 zenon_H110 zenon_H1c7 zenon_H1ca zenon_H130 zenon_H9e zenon_H7a zenon_H153 zenon_H251 zenon_H250 zenon_H133 zenon_H255 zenon_H71 zenon_He8 zenon_H6a zenon_H4a zenon_H49 zenon_H173 zenon_H18f zenon_Ha9 zenon_H1c4 zenon_H124 zenon_H20d zenon_H139 zenon_H34 zenon_H52 zenon_H1a4 zenon_H1b1. % 18.87/19.02 apply (zenon_or_s _ _ zenon_H22); [ zenon_intro zenon_H27 | zenon_intro zenon_H26 ]. % 18.87/19.02 apply (zenon_L332_); trivial. % 18.87/19.02 apply (zenon_or_s _ _ zenon_H26); [ zenon_intro zenon_H29 | zenon_intro zenon_H28 ]. % 18.87/19.02 apply (zenon_L17_); trivial. % 18.87/19.02 apply (zenon_or_s _ _ zenon_H28); [ zenon_intro zenon_H2a | zenon_intro zenon_H1f ]. % 18.87/19.02 apply (zenon_or_s _ _ zenon_H128); [ zenon_intro zenon_H9d | zenon_intro zenon_H129 ]. % 18.87/19.02 exact (zenon_H1ef zenon_H9d). % 18.87/19.02 apply (zenon_or_s _ _ zenon_H129); [ zenon_intro zenon_H10d | zenon_intro zenon_H12a ]. % 18.87/19.02 exact (zenon_H10a zenon_H10d). % 18.87/19.02 apply (zenon_or_s _ _ zenon_H12a); [ zenon_intro zenon_Hf0 | zenon_intro zenon_Hd6 ]. % 18.87/19.02 apply (zenon_L792_); trivial. % 18.87/19.02 apply (zenon_L720_); trivial. % 18.87/19.02 apply (zenon_or_s _ _ zenon_H128); [ zenon_intro zenon_H9d | zenon_intro zenon_H129 ]. % 18.87/19.02 exact (zenon_H1ef zenon_H9d). % 18.87/19.02 apply (zenon_or_s _ _ zenon_H129); [ zenon_intro zenon_H10d | zenon_intro zenon_H12a ]. % 18.87/19.02 exact (zenon_H10a zenon_H10d). % 18.87/19.02 apply (zenon_or_s _ _ zenon_H12a); [ zenon_intro zenon_Hf0 | zenon_intro zenon_Hd6 ]. % 18.87/19.02 apply (zenon_L791_); trivial. % 18.87/19.02 apply (zenon_L816_); trivial. % 18.87/19.02 (* end of lemma zenon_L881_ *) % 18.87/19.02 assert (zenon_L882_ : (((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 (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)) = (e1))) -> (~((op (e0) (e3)) = (op (e3) (e3)))) -> (~((op (e0) (e3)) = (op (e2) (e3)))) -> (((op (e2) (e3)) = (e0))\/(((op (e2) (e3)) = (e1))\/(((op (e2) (e3)) = (e2))\/((op (e2) (e3)) = (e3))))) -> ((op (e2) (e0)) = (e0)) -> (~((op (e2) (e3)) = (op (e3) (e3)))) -> (((op (e0) (e3)) = (e3))\/(((op (e1) (e3)) = (e3))\/(((op (e2) (e3)) = (e3))\/((op (e3) (e3)) = (e3))))) -> (~((op (e0) (e2)) = (op (e3) (e2)))) -> ((op (e0) (e2)) = (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)) = (e2)) -> (~((op (e2) (e1)) = (op (e2) (e3)))) -> ((op (e3) (e0)) = (e3)) -> (~((e2) = (e3))) -> (((op (e3) (e0)) = (e2))\/(((op (e3) (e1)) = (e2))\/(((op (e3) (e2)) = (e2))\/((op (e3) (e3)) = (e2))))) -> (~((op (e3) (e2)) = (e1))) -> (~((op (e3) (e1)) = (e1))) -> (~((e1) = (e3))) -> (((op (e3) (e0)) = (e1))\/(((op (e3) (e1)) = (e1))\/(((op (e3) (e2)) = (e1))\/((op (e3) (e3)) = (e1))))) -> ((op (e0) (e0)) = (e1)) -> ((op (e1) (e0)) = (e2)) -> (~((op (e2) (e0)) = (op (e2) (e1)))) -> ((op (e2) (e1)) = (e2)) -> (~((op (e2) (e0)) = (e1))) -> (~((op (e2) (e0)) = (op (e2) (e3)))) -> (((op (e2) (e0)) = (e0))\/(((op (e2) (e0)) = (e1))\/(((op (e2) (e0)) = (e2))\/((op (e2) (e0)) = (e3))))) -> ((op (e3) (e1)) = (e0)) -> (~((op (e3) (e1)) = (op (e3) (e3)))) -> False). % 18.87/19.02 do 0 intro. intros zenon_H67 zenon_H54 zenon_H49 zenon_H102 zenon_He4 zenon_H1d zenon_H231 zenon_Hc2 zenon_He2 zenon_H11f zenon_H34 zenon_Hf3 zenon_H136 zenon_H14f zenon_H150 zenon_H145 zenon_H57 zenon_H110 zenon_H1c7 zenon_H15e zenon_H12b zenon_H153 zenon_H251 zenon_H250 zenon_H95 zenon_He8 zenon_H7a zenon_H86 zenon_H1f0 zenon_H1ca zenon_H1db zenon_H5b zenon_H259 zenon_H1b1 zenon_H130. % 18.87/19.02 apply (zenon_or_s _ _ zenon_H67); [ zenon_intro zenon_H1e | zenon_intro zenon_H68 ]. % 18.87/19.02 apply (zenon_L12_); trivial. % 18.87/19.02 apply (zenon_or_s _ _ zenon_H68); [ zenon_intro zenon_H1f | zenon_intro zenon_H69 ]. % 18.87/19.02 apply (zenon_L825_); trivial. % 18.87/19.02 apply (zenon_or_s _ _ zenon_H69); [ zenon_intro zenon_H37 | zenon_intro zenon_H60 ]. % 18.87/19.02 apply (zenon_L729_); trivial. % 18.87/19.02 apply (zenon_L244_); trivial. % 18.87/19.02 (* end of lemma zenon_L882_ *) % 18.87/19.02 assert (zenon_L883_ : (((op (e0) (e0)) = (e3))\/(((op (e1) (e0)) = (e3))\/(((op (e2) (e0)) = (e3))\/((op (e3) (e0)) = (e3))))) -> (~((op (e3) (e1)) = (op (e3) (e2)))) -> (~((op (e2) (e0)) = (op (e2) (e2)))) -> (((op (e0) (e2)) = (e1))\/(((op (e1) (e2)) = (e1))\/(((op (e2) (e2)) = (e1))\/((op (e3) (e2)) = (e1))))) -> (~((op (e0) (e2)) = (e1))) -> (~((op (e1) (e2)) = (op (e1) (e3)))) -> (((op (e2) (e2)) = (e0))\/(((op (e2) (e2)) = (e1))\/(((op (e2) (e2)) = (e2))\/((op (e2) (e2)) = (e3))))) -> ((op (e0) (e2)) = (e3)) -> (~((op (e2) (e2)) = (op (e3) (e2)))) -> (~((op (e2) (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 (e3) (e0)) = (op (e3) (e3)))) -> (~((op (e2) (e3)) = (e1))) -> (((op (e0) (e3)) = (e1))\/(((op (e1) (e3)) = (e1))\/(((op (e2) (e3)) = (e1))\/((op (e3) (e3)) = (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 (e1) (e1)) = (op (e1) (e2)))) -> (~((op (e3) (e2)) = (op (e3) (e3)))) -> (~((op (e1) (e0)) = (op (e2) (e0)))) -> (((op (e1) (e0)) = (e0))\/(((op (e1) (e1)) = (e0))\/(((op (e1) (e2)) = (e0))\/((op (e1) (e3)) = (e0))))) -> (((op (e0) (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 (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)) = (e1))) -> (~((op (e0) (e3)) = (op (e3) (e3)))) -> (~((op (e0) (e3)) = (op (e2) (e3)))) -> (((op (e2) (e3)) = (e0))\/(((op (e2) (e3)) = (e1))\/(((op (e2) (e3)) = (e2))\/((op (e2) (e3)) = (e3))))) -> ((op (e2) (e0)) = (e0)) -> (~((op (e2) (e3)) = (op (e3) (e3)))) -> (((op (e0) (e3)) = (e3))\/(((op (e1) (e3)) = (e3))\/(((op (e2) (e3)) = (e3))\/((op (e3) (e3)) = (e3))))) -> (~((op (e0) (e2)) = (op (e3) (e2)))) -> ((op (e0) (e2)) = (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)) = (e2)) -> (~((op (e2) (e1)) = (op (e2) (e3)))) -> (~((e2) = (e3))) -> (((op (e3) (e0)) = (e2))\/(((op (e3) (e1)) = (e2))\/(((op (e3) (e2)) = (e2))\/((op (e3) (e3)) = (e2))))) -> (~((op (e3) (e2)) = (e1))) -> (~((op (e3) (e1)) = (e1))) -> (~((e1) = (e3))) -> (((op (e3) (e0)) = (e1))\/(((op (e3) (e1)) = (e1))\/(((op (e3) (e2)) = (e1))\/((op (e3) (e3)) = (e1))))) -> ((op (e0) (e0)) = (e1)) -> ((op (e1) (e0)) = (e2)) -> (~((op (e2) (e0)) = (op (e2) (e1)))) -> ((op (e2) (e1)) = (e2)) -> (~((op (e2) (e0)) = (e1))) -> (~((op (e2) (e0)) = (op (e2) (e3)))) -> (((op (e2) (e0)) = (e0))\/(((op (e2) (e0)) = (e1))\/(((op (e2) (e0)) = (e2))\/((op (e2) (e0)) = (e3))))) -> ((op (e3) (e1)) = (e0)) -> (~((op (e3) (e1)) = (op (e3) (e3)))) -> False). % 18.87/19.02 do 0 intro. intros zenon_H1e0 zenon_H1a4 zenon_H52 zenon_H139 zenon_H20d zenon_H124 zenon_H1c4 zenon_Ha9 zenon_H18f zenon_H173 zenon_H4a zenon_H6a zenon_H71 zenon_H255 zenon_H133 zenon_H10a zenon_H1ef zenon_H128 zenon_H4f zenon_H62 zenon_H201 zenon_H22 zenon_H67 zenon_H54 zenon_H49 zenon_H102 zenon_He4 zenon_H1d zenon_H231 zenon_Hc2 zenon_He2 zenon_H11f zenon_H34 zenon_Hf3 zenon_H136 zenon_H14f zenon_H150 zenon_H145 zenon_H57 zenon_H110 zenon_H1c7 zenon_H12b zenon_H153 zenon_H251 zenon_H250 zenon_H95 zenon_He8 zenon_H7a zenon_H86 zenon_H1f0 zenon_H1ca zenon_H1db zenon_H5b zenon_H259 zenon_H1b1 zenon_H130. % 18.87/19.02 apply (zenon_or_s _ _ zenon_H1e0); [ zenon_intro zenon_H3a | zenon_intro zenon_H1e1 ]. % 18.87/19.02 apply (zenon_L35_); trivial. % 18.87/19.02 apply (zenon_or_s _ _ zenon_H1e1); [ zenon_intro zenon_H9e | zenon_intro zenon_H1e2 ]. % 18.87/19.02 apply (zenon_L881_); trivial. % 18.87/19.02 apply (zenon_or_s _ _ zenon_H1e2); [ zenon_intro zenon_H3b | zenon_intro zenon_H15e ]. % 18.87/19.02 apply (zenon_L33_); trivial. % 18.87/19.02 apply (zenon_L882_); trivial. % 18.87/19.02 (* end of lemma zenon_L883_ *) % 18.87/19.02 assert (zenon_L884_ : (((op (e0) (e0)) = (e3))\/(((op (e1) (e0)) = (e3))\/(((op (e2) (e0)) = (e3))\/((op (e3) (e0)) = (e3))))) -> (~((op (e1) (e3)) = (e1))) -> (((op (e1) (e0)) = (e3))\/(((op (e1) (e1)) = (e3))\/(((op (e1) (e2)) = (e3))\/((op (e1) (e3)) = (e3))))) -> ((op (e0) (e0)) = (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) (e1)) = (op (e0) (e3)))) -> ((op (e0) (e1)) = (e0)) -> (~((op (e0) (e3)) = (op (e1) (e3)))) -> (~((op (e0) (e3)) = (e1))) -> (((op (e0) (e3)) = (e0))\/(((op (e0) (e3)) = (e1))\/(((op (e0) (e3)) = (e2))\/((op (e0) (e3)) = (e3))))) -> (~((op (e3) (e2)) = (e1))) -> (~((op (e3) (e1)) = (e1))) -> (((op (e0) (e3)) = (e1))\/(((op (e1) (e3)) = (e1))\/(((op (e2) (e3)) = (e1))\/((op (e3) (e3)) = (e1))))) -> (~((op (e1) (e2)) = (op (e1) (e3)))) -> (~((op (e2) (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 (e2) (e0)) = (op (e2) (e2)))) -> (~((op (e2) (e2)) = (e2))) -> (~((op (e1) (e2)) = (op (e2) (e2)))) -> (~((op (e2) (e2)) = (op (e2) (e3)))) -> (((op (e2) (e2)) = (e0))\/(((op (e2) (e2)) = (e1))\/(((op (e2) (e2)) = (e2))\/((op (e2) (e2)) = (e3))))) -> ((op (e3) (e1)) = (e0)) -> (~((op (e3) (e1)) = (op (e3) (e3)))) -> (~((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)) = (e2)) -> (~((e2) = (e3))) -> False). % 18.87/19.02 do 0 intro. intros zenon_H1e0 zenon_H24e zenon_H16f zenon_H7a zenon_H110 zenon_H95 zenon_H67 zenon_H54 zenon_H49 zenon_H1d zenon_H231 zenon_He4 zenon_H251 zenon_H250 zenon_H133 zenon_H124 zenon_H255 zenon_H71 zenon_He8 zenon_H52 zenon_H173 zenon_H2b zenon_H6d zenon_H1c4 zenon_H1b1 zenon_H130 zenon_H10a zenon_H1ef zenon_H128 zenon_H148 zenon_H12b. % 18.87/19.02 apply (zenon_or_s _ _ zenon_H1e0); [ zenon_intro zenon_H3a | zenon_intro zenon_H1e1 ]. % 18.87/19.02 apply (zenon_L35_); trivial. % 18.87/19.02 apply (zenon_or_s _ _ zenon_H1e1); [ zenon_intro zenon_H9e | zenon_intro zenon_H1e2 ]. % 18.87/19.02 apply (zenon_L107_); trivial. % 18.87/19.02 apply (zenon_or_s _ _ zenon_H1e2); [ zenon_intro zenon_H3b | zenon_intro zenon_H15e ]. % 18.87/19.02 apply (zenon_or_s _ _ zenon_H128); [ zenon_intro zenon_H9d | zenon_intro zenon_H129 ]. % 18.87/19.02 exact (zenon_H1ef zenon_H9d). % 18.87/19.02 apply (zenon_or_s _ _ zenon_H129); [ zenon_intro zenon_H10d | zenon_intro zenon_H12a ]. % 18.87/19.02 exact (zenon_H10a zenon_H10d). % 18.87/19.02 apply (zenon_or_s _ _ zenon_H12a); [ zenon_intro zenon_Hf0 | zenon_intro zenon_Hd6 ]. % 18.87/19.02 apply (zenon_or_s _ _ zenon_H16f); [ zenon_intro zenon_H9e | zenon_intro zenon_H170 ]. % 18.87/19.02 apply (zenon_L107_); trivial. % 18.87/19.02 apply (zenon_or_s _ _ zenon_H170); [ zenon_intro zenon_H13f | zenon_intro zenon_H171 ]. % 18.87/19.02 apply (zenon_L166_); trivial. % 18.87/19.02 apply (zenon_or_s _ _ zenon_H171); [ zenon_intro zenon_H16c | zenon_intro zenon_Hdc ]. % 18.87/19.02 apply (zenon_L167_); trivial. % 18.87/19.02 apply (zenon_L837_); trivial. % 18.87/19.02 exact (zenon_H24e zenon_Hd6). % 18.87/19.02 apply (zenon_L109_); trivial. % 18.87/19.02 (* end of lemma zenon_L884_ *) % 18.87/19.02 assert (zenon_L885_ : (((op (e0) (e0)) = (e2))\/(((op (e1) (e0)) = (e2))\/(((op (e2) (e0)) = (e2))\/((op (e3) (e0)) = (e2))))) -> (~((e1) = (e2))) -> (~((op (e3) (e1)) = (op (e3) (e2)))) -> (((op (e2) (e0)) = (e3))\/(((op (e2) (e1)) = (e3))\/(((op (e2) (e2)) = (e3))\/((op (e2) (e3)) = (e3))))) -> (~((op (e2) (e2)) = (op (e3) (e2)))) -> (~((op (e0) (e2)) = (op (e3) (e2)))) -> ((op (e0) (e2)) = (e2)) -> (~((op (e1) (e2)) = (op (e3) (e2)))) -> (((op (e3) (e2)) = (e0))\/(((op (e3) (e2)) = (e1))\/(((op (e3) (e2)) = (e2))\/((op (e3) (e2)) = (e3))))) -> (~((op (e0) (e3)) = (op (e2) (e3)))) -> (~((op (e0) (e1)) = (op (e0) (e2)))) -> (((op (e0) (e2)) = (e0))\/(((op (e1) (e2)) = (e0))\/(((op (e2) (e2)) = (e0))\/((op (e3) (e2)) = (e0))))) -> (~((op (e2) (e2)) = (e1))) -> (~((e0) = (e3))) -> ((op (e2) (e1)) = (e1)) -> (~((op (e1) (e3)) = (op (e2) (e3)))) -> (~((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))))) -> (((op (e0) (e2)) = (e1))\/(((op (e1) (e2)) = (e1))\/(((op (e2) (e2)) = (e1))\/((op (e3) (e2)) = (e1))))) -> (~((op (e0) (e2)) = (e1))) -> (~((op (e1) (e1)) = (op (e1) (e2)))) -> (~((op (e3) (e2)) = (op (e3) (e3)))) -> (~((op (e1) (e0)) = (op (e2) (e0)))) -> (((op (e1) (e0)) = (e0))\/(((op (e1) (e1)) = (e0))\/(((op (e1) (e2)) = (e0))\/((op (e1) (e3)) = (e0))))) -> (~((op (e3) (e3)) = (e3))) -> (~((op (e0) (e3)) = (op (e3) (e3)))) -> (((op (e2) (e3)) = (e0))\/(((op (e2) (e3)) = (e1))\/(((op (e2) (e3)) = (e2))\/((op (e2) (e3)) = (e3))))) -> (((op (e0) (e3)) = (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 (e1) (e1)) = (op (e1) (e3)))) -> (~((op (e2) (e1)) = (op (e2) (e3)))) -> (~((op (e2) (e0)) = (op (e2) (e1)))) -> (~((op (e2) (e0)) = (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 (e0) (e0)) = (e3))\/(((op (e0) (e1)) = (e3))\/(((op (e0) (e2)) = (e3))\/((op (e0) (e3)) = (e3))))) -> (~((e0) = (e2))) -> ((op (e2) (e0)) = (e0)) -> (((op (e0) (e0)) = (e3))\/(((op (e1) (e0)) = (e3))\/(((op (e2) (e0)) = (e3))\/((op (e3) (e0)) = (e3))))) -> (~((op (e1) (e3)) = (e1))) -> (((op (e1) (e0)) = (e3))\/(((op (e1) (e1)) = (e3))\/(((op (e1) (e2)) = (e3))\/((op (e1) (e3)) = (e3))))) -> ((op (e0) (e0)) = (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) (e1)) = (op (e0) (e3)))) -> ((op (e0) (e1)) = (e0)) -> (~((op (e0) (e3)) = (op (e1) (e3)))) -> (~((op (e0) (e3)) = (e1))) -> (((op (e0) (e3)) = (e0))\/(((op (e0) (e3)) = (e1))\/(((op (e0) (e3)) = (e2))\/((op (e0) (e3)) = (e3))))) -> (~((op (e3) (e2)) = (e1))) -> (~((op (e3) (e1)) = (e1))) -> (((op (e0) (e3)) = (e1))\/(((op (e1) (e3)) = (e1))\/(((op (e2) (e3)) = (e1))\/((op (e3) (e3)) = (e1))))) -> (~((op (e1) (e2)) = (op (e1) (e3)))) -> (~((op (e2) (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 (e2) (e0)) = (op (e2) (e2)))) -> (~((op (e2) (e2)) = (e2))) -> (~((op (e1) (e2)) = (op (e2) (e2)))) -> (~((op (e2) (e2)) = (op (e2) (e3)))) -> (((op (e2) (e2)) = (e0))\/(((op (e2) (e2)) = (e1))\/(((op (e2) (e2)) = (e2))\/((op (e2) (e2)) = (e3))))) -> ((op (e3) (e1)) = (e0)) -> (~((op (e3) (e1)) = (op (e3) (e3)))) -> (~((op (e1) (e1)) = (e1))) -> (~((op (e1) (e0)) = (e1))) -> (((op (e1) (e0)) = (e1))\/(((op (e1) (e1)) = (e1))\/(((op (e1) (e2)) = (e1))\/((op (e1) (e3)) = (e1))))) -> (~((e2) = (e3))) -> False). % 18.87/19.02 do 0 intro. intros zenon_H1fe zenon_H7c zenon_H1a4 zenon_He7 zenon_H18f zenon_H14f zenon_H150 zenon_H115 zenon_H191 zenon_He2 zenon_H4a zenon_H6a zenon_H198 zenon_H9a zenon_Ha5 zenon_Hdb zenon_Hf3 zenon_H160 zenon_H153 zenon_H139 zenon_H20d zenon_H4f zenon_H62 zenon_H201 zenon_H22 zenon_H102 zenon_Hc2 zenon_H11f zenon_H136 zenon_H145 zenon_H57 zenon_H1c7 zenon_H1f0 zenon_H1db zenon_H5b zenon_H259 zenon_H1d5 zenon_H168 zenon_H149 zenon_H34 zenon_H1e0 zenon_H24e zenon_H16f zenon_H7a zenon_H110 zenon_H95 zenon_H67 zenon_H54 zenon_H49 zenon_H1d zenon_H231 zenon_He4 zenon_H251 zenon_H250 zenon_H133 zenon_H124 zenon_H255 zenon_H71 zenon_He8 zenon_H52 zenon_H173 zenon_H2b zenon_H6d zenon_H1c4 zenon_H1b1 zenon_H130 zenon_H10a zenon_H1ef zenon_H128 zenon_H12b. % 18.87/19.02 apply (zenon_or_s _ _ zenon_H1fe); [ zenon_intro zenon_H7b | zenon_intro zenon_H1ff ]. % 18.87/19.02 apply (zenon_L26_); trivial. % 18.87/19.02 apply (zenon_or_s _ _ zenon_H1ff); [ zenon_intro zenon_H86 | zenon_intro zenon_H200 ]. % 18.87/19.02 apply (zenon_or_s _ _ zenon_H168); [ zenon_intro zenon_H3a | zenon_intro zenon_H169 ]. % 18.87/19.02 apply (zenon_L35_); trivial. % 18.87/19.02 apply (zenon_or_s _ _ zenon_H169); [ zenon_intro zenon_H99 | zenon_intro zenon_H16a ]. % 18.87/19.02 apply (zenon_L36_); trivial. % 18.87/19.02 apply (zenon_or_s _ _ zenon_H16a); [ zenon_intro zenon_Ha9 | zenon_intro zenon_He3 ]. % 18.87/19.02 apply (zenon_or_s _ _ zenon_H22); [ zenon_intro zenon_H27 | zenon_intro zenon_H26 ]. % 18.87/19.02 apply (zenon_L332_); trivial. % 18.87/19.02 apply (zenon_or_s _ _ zenon_H26); [ zenon_intro zenon_H29 | zenon_intro zenon_H28 ]. % 18.87/19.02 apply (zenon_L17_); trivial. % 18.87/19.02 apply (zenon_or_s _ _ zenon_H28); [ zenon_intro zenon_H2a | zenon_intro zenon_H1f ]. % 18.87/19.02 apply (zenon_or_s _ _ zenon_H128); [ zenon_intro zenon_H9d | zenon_intro zenon_H129 ]. % 18.87/19.02 exact (zenon_H1ef zenon_H9d). % 18.87/19.02 apply (zenon_or_s _ _ zenon_H129); [ zenon_intro zenon_H10d | zenon_intro zenon_H12a ]. % 18.87/19.02 exact (zenon_H10a zenon_H10d). % 18.87/19.02 apply (zenon_or_s _ _ zenon_H12a); [ zenon_intro zenon_Hf0 | zenon_intro zenon_Hd6 ]. % 18.87/19.02 apply (zenon_or_s _ _ zenon_H16f); [ zenon_intro zenon_H9e | zenon_intro zenon_H170 ]. % 18.87/19.02 apply (zenon_or_s _ _ zenon_H1d5); [ zenon_intro zenon_Hee | zenon_intro zenon_H1d6 ]. % 18.87/19.02 apply (zenon_L204_); trivial. % 18.87/19.02 apply (zenon_or_s _ _ zenon_H1d6); [ zenon_intro zenon_H1ca | zenon_intro zenon_H1d7 ]. % 18.87/19.02 apply (zenon_L881_); trivial. % 18.87/19.02 apply (zenon_or_s _ _ zenon_H1d7); [ zenon_intro zenon_H176 | zenon_intro zenon_H11d ]. % 18.87/19.02 exact (zenon_H173 zenon_H176). % 18.87/19.02 apply (zenon_or_s _ _ zenon_H67); [ zenon_intro zenon_H1e | zenon_intro zenon_H68 ]. % 18.87/19.02 apply (zenon_L12_); trivial. % 18.87/19.02 apply (zenon_or_s _ _ zenon_H68); [ zenon_intro zenon_H1f | zenon_intro zenon_H69 ]. % 18.87/19.02 apply (zenon_L833_); trivial. % 18.87/19.02 apply (zenon_or_s _ _ zenon_H69); [ zenon_intro zenon_H37 | zenon_intro zenon_H60 ]. % 18.87/19.02 apply (zenon_L746_); trivial. % 18.87/19.02 apply (zenon_L244_); trivial. % 18.87/19.02 apply (zenon_or_s _ _ zenon_H170); [ zenon_intro zenon_H13f | zenon_intro zenon_H171 ]. % 18.87/19.02 apply (zenon_L166_); trivial. % 18.87/19.02 apply (zenon_or_s _ _ zenon_H171); [ zenon_intro zenon_H16c | zenon_intro zenon_Hdc ]. % 18.87/19.02 apply (zenon_L521_); trivial. % 18.87/19.02 apply (zenon_L838_); trivial. % 18.87/19.02 exact (zenon_H24e zenon_Hd6). % 18.87/19.02 apply (zenon_or_s _ _ zenon_H128); [ zenon_intro zenon_H9d | zenon_intro zenon_H129 ]. % 18.87/19.02 exact (zenon_H1ef zenon_H9d). % 18.87/19.02 apply (zenon_or_s _ _ zenon_H129); [ zenon_intro zenon_H10d | zenon_intro zenon_H12a ]. % 18.87/19.02 exact (zenon_H10a zenon_H10d). % 18.87/19.02 apply (zenon_or_s _ _ zenon_H12a); [ zenon_intro zenon_Hf0 | zenon_intro zenon_Hd6 ]. % 18.87/19.02 apply (zenon_or_s _ _ zenon_H1d5); [ zenon_intro zenon_Hee | zenon_intro zenon_H1d6 ]. % 18.87/19.02 apply (zenon_L204_); trivial. % 18.87/19.02 apply (zenon_or_s _ _ zenon_H1d6); [ zenon_intro zenon_H1ca | zenon_intro zenon_H1d7 ]. % 18.87/19.02 apply (zenon_L883_); trivial. % 18.87/19.02 apply (zenon_or_s _ _ zenon_H1d7); [ zenon_intro zenon_H176 | zenon_intro zenon_H11d ]. % 18.87/19.02 exact (zenon_H173 zenon_H176). % 18.87/19.02 apply (zenon_L833_); trivial. % 18.87/19.02 exact (zenon_H24e zenon_Hd6). % 18.87/19.02 apply (zenon_L735_); trivial. % 18.87/19.02 apply (zenon_or_s _ _ zenon_H200); [ zenon_intro zenon_Hee | zenon_intro zenon_H148 ]. % 18.87/19.02 apply (zenon_L204_); trivial. % 18.87/19.02 apply (zenon_L884_); trivial. % 18.87/19.02 (* end of lemma zenon_L885_ *) % 18.87/19.02 assert (zenon_L886_ : (((op (e1) (e0)) = (e1))\/(((op (e1) (e1)) = (e1))\/(((op (e1) (e2)) = (e1))\/((op (e1) (e3)) = (e1))))) -> (~((op (e1) (e0)) = (e1))) -> (~((op (e1) (e1)) = (e1))) -> (~((op (e3) (e1)) = (op (e3) (e3)))) -> ((op (e3) (e1)) = (e0)) -> ((op (e2) (e0)) = (e0)) -> (~((op (e2) (e0)) = (op (e2) (e3)))) -> (((op (e0) (e3)) = (e1))\/(((op (e1) (e3)) = (e1))\/(((op (e2) (e3)) = (e1))\/((op (e3) (e3)) = (e1))))) -> (~((op (e0) (e3)) = (e1))) -> (~((op (e2) (e3)) = (e1))) -> ((op (e0) (e3)) = (e2)) -> ((op (e0) (e1)) = (e0)) -> (~((op (e0) (e1)) = (op (e0) (e3)))) -> (((op (e0) (e3)) = (e0))\/(((op (e1) (e3)) = (e0))\/(((op (e2) (e3)) = (e0))\/((op (e3) (e3)) = (e0))))) -> (((op (e0) (e2)) = (e1))\/(((op (e1) (e2)) = (e1))\/(((op (e2) (e2)) = (e1))\/((op (e3) (e2)) = (e1))))) -> (~((op (e0) (e2)) = (e1))) -> (~((op (e1) (e2)) = (op (e1) (e3)))) -> (((op (e2) (e2)) = (e0))\/(((op (e2) (e2)) = (e1))\/(((op (e2) (e2)) = (e2))\/((op (e2) (e2)) = (e3))))) -> ((op (e0) (e2)) = (e3)) -> (~((op (e2) (e2)) = (op (e3) (e2)))) -> (~((op (e2) (e2)) = (e2))) -> ((op (e1) (e2)) = (e0)) -> False). % 18.87/19.02 do 0 intro. intros zenon_H128 zenon_H1ef zenon_H10a zenon_H130 zenon_H1b1 zenon_H34 zenon_H5b zenon_H133 zenon_H231 zenon_H255 zenon_Hcd zenon_H49 zenon_H54 zenon_H67 zenon_H139 zenon_H20d zenon_H124 zenon_H1c4 zenon_Ha9 zenon_H18f zenon_H173 zenon_H2a. % 18.87/19.02 apply (zenon_or_s _ _ zenon_H128); [ zenon_intro zenon_H9d | zenon_intro zenon_H129 ]. % 18.87/19.02 exact (zenon_H1ef zenon_H9d). % 18.87/19.02 apply (zenon_or_s _ _ zenon_H129); [ zenon_intro zenon_H10d | zenon_intro zenon_H12a ]. % 18.87/19.02 exact (zenon_H10a zenon_H10d). % 18.87/19.02 apply (zenon_or_s _ _ zenon_H12a); [ zenon_intro zenon_Hf0 | zenon_intro zenon_Hd6 ]. % 18.87/19.02 apply (zenon_L862_); trivial. % 18.87/19.02 apply (zenon_L720_); trivial. % 18.87/19.02 (* end of lemma zenon_L886_ *) % 18.87/19.02 assert (zenon_L887_ : (((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) (e1)) = (e0)) -> (~((op (e3) (e1)) = (op (e3) (e2)))) -> (~((op (e2) (e0)) = (op (e2) (e2)))) -> ((op (e2) (e0)) = (e0)) -> (((op (e0) (e2)) = (e1))\/(((op (e1) (e2)) = (e1))\/(((op (e2) (e2)) = (e1))\/((op (e3) (e2)) = (e1))))) -> (~((op (e0) (e2)) = (e1))) -> (~((op (e1) (e2)) = (op (e1) (e3)))) -> (((op (e2) (e2)) = (e0))\/(((op (e2) (e2)) = (e1))\/(((op (e2) (e2)) = (e2))\/((op (e2) (e2)) = (e3))))) -> (~((op (e2) (e2)) = (op (e3) (e2)))) -> (~((op (e2) (e2)) = (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) (e3)) = (e1))\/(((op (e1) (e3)) = (e1))\/(((op (e2) (e3)) = (e1))\/((op (e3) (e3)) = (e1))))) -> (~((op (e0) (e3)) = (e1))) -> (~((op (e2) (e3)) = (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) (e1)) = (op (e3) (e3)))) -> (~((op (e2) (e0)) = (op (e2) (e3)))) -> (~((op (e0) (e1)) = (op (e0) (e3)))) -> (((op (e0) (e3)) = (e0))\/(((op (e1) (e3)) = (e0))\/(((op (e2) (e3)) = (e0))\/((op (e3) (e3)) = (e0))))) -> (~((op (e1) (e1)) = (op (e1) (e2)))) -> (~((op (e1) (e1)) = (op (e1) (e3)))) -> (~((op (e3) (e2)) = (op (e3) (e3)))) -> (~((op (e1) (e0)) = (op (e2) (e0)))) -> (((op (e1) (e0)) = (e0))\/(((op (e1) (e1)) = (e0))\/(((op (e1) (e2)) = (e0))\/((op (e1) (e3)) = (e0))))) -> ((op (e0) (e3)) = (e2)) -> (~((e2) = (e3))) -> False). % 18.87/19.02 do 0 intro. intros zenon_H168 zenon_H95 zenon_H7a zenon_H9a zenon_H1b1 zenon_H1a4 zenon_H52 zenon_H34 zenon_H139 zenon_H20d zenon_H124 zenon_H1c4 zenon_H18f zenon_H173 zenon_H49 zenon_H4a zenon_H6a zenon_H133 zenon_H231 zenon_H255 zenon_H10a zenon_H1ef zenon_H128 zenon_H130 zenon_H5b zenon_H54 zenon_H67 zenon_H4f zenon_H57 zenon_H62 zenon_H201 zenon_H22 zenon_Hcd zenon_H12b. % 18.87/19.02 apply (zenon_or_s _ _ zenon_H168); [ zenon_intro zenon_H3a | zenon_intro zenon_H169 ]. % 18.87/19.02 apply (zenon_L35_); trivial. % 18.87/19.02 apply (zenon_or_s _ _ zenon_H169); [ zenon_intro zenon_H99 | zenon_intro zenon_H16a ]. % 18.87/19.02 apply (zenon_L36_); trivial. % 18.87/19.02 apply (zenon_or_s _ _ zenon_H16a); [ zenon_intro zenon_Ha9 | zenon_intro zenon_He3 ]. % 18.87/19.02 apply (zenon_or_s _ _ zenon_H22); [ zenon_intro zenon_H27 | zenon_intro zenon_H26 ]. % 18.87/19.02 apply (zenon_L332_); trivial. % 18.87/19.02 apply (zenon_or_s _ _ zenon_H26); [ zenon_intro zenon_H29 | zenon_intro zenon_H28 ]. % 18.87/19.02 apply (zenon_L17_); trivial. % 18.87/19.02 apply (zenon_or_s _ _ zenon_H28); [ zenon_intro zenon_H2a | zenon_intro zenon_H1f ]. % 18.87/19.02 apply (zenon_L886_); trivial. % 18.87/19.02 apply (zenon_L817_); trivial. % 18.87/19.02 apply (zenon_L81_); trivial. % 18.87/19.02 (* end of lemma zenon_L887_ *) % 18.87/19.02 assert (zenon_L888_ : (~((e2) = (e3))) -> (((op (e1) (e0)) = (e0))\/(((op (e1) (e1)) = (e0))\/(((op (e1) (e2)) = (e0))\/((op (e1) (e3)) = (e0))))) -> (~((op (e1) (e0)) = (op (e2) (e0)))) -> (~((op (e3) (e2)) = (op (e3) (e3)))) -> (~((op (e1) (e1)) = (op (e1) (e3)))) -> (~((op (e1) (e1)) = (op (e1) (e2)))) -> (((op (e0) (e3)) = (e0))\/(((op (e1) (e3)) = (e0))\/(((op (e2) (e3)) = (e0))\/((op (e3) (e3)) = (e0))))) -> (~((op (e0) (e1)) = (op (e0) (e3)))) -> (~((op (e2) (e0)) = (op (e2) (e3)))) -> (~((op (e3) (e1)) = (op (e3) (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 (e2) (e3)) = (e1))) -> (((op (e0) (e3)) = (e1))\/(((op (e1) (e3)) = (e1))\/(((op (e2) (e3)) = (e1))\/((op (e3) (e3)) = (e1))))) -> (((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 (e2) (e2)) = (e2))) -> (~((op (e2) (e2)) = (op (e3) (e2)))) -> (((op (e2) (e2)) = (e0))\/(((op (e2) (e2)) = (e1))\/(((op (e2) (e2)) = (e2))\/((op (e2) (e2)) = (e3))))) -> (~((op (e1) (e2)) = (op (e1) (e3)))) -> (((op (e0) (e2)) = (e1))\/(((op (e1) (e2)) = (e1))\/(((op (e2) (e2)) = (e1))\/((op (e3) (e2)) = (e1))))) -> ((op (e2) (e0)) = (e0)) -> (~((op (e2) (e0)) = (op (e2) (e2)))) -> (~((op (e3) (e1)) = (op (e3) (e2)))) -> ((op (e3) (e1)) = (e0)) -> (~((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 (e1) (e0)) = (e2))\/(((op (e2) (e0)) = (e2))\/((op (e3) (e0)) = (e2))))) -> (~((e1) = (e2))) -> (((op (e2) (e0)) = (e3))\/(((op (e2) (e1)) = (e3))\/(((op (e2) (e2)) = (e3))\/((op (e2) (e3)) = (e3))))) -> (~((op (e0) (e2)) = (op (e3) (e2)))) -> (~((op (e1) (e2)) = (op (e3) (e2)))) -> (((op (e3) (e2)) = (e0))\/(((op (e3) (e2)) = (e1))\/(((op (e3) (e2)) = (e2))\/((op (e3) (e2)) = (e3))))) -> (~((op (e0) (e3)) = (op (e2) (e3)))) -> (~((op (e2) (e2)) = (e1))) -> ((op (e2) (e1)) = (e1)) -> (~((op (e1) (e3)) = (op (e2) (e3)))) -> (~((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))))) -> (~((op (e3) (e3)) = (e3))) -> (~((op (e0) (e3)) = (op (e3) (e3)))) -> (((op (e2) (e3)) = (e0))\/(((op (e2) (e3)) = (e1))\/(((op (e2) (e3)) = (e2))\/((op (e2) (e3)) = (e3))))) -> (((op (e0) (e3)) = (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 (e2) (e1)) = (op (e2) (e3)))) -> (~((op (e2) (e0)) = (op (e2) (e1)))) -> (~((op (e2) (e0)) = (e1))) -> (((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))))) -> (~((e0) = (e2))) -> (((op (e0) (e0)) = (e3))\/(((op (e1) (e0)) = (e3))\/(((op (e2) (e0)) = (e3))\/((op (e3) (e0)) = (e3))))) -> (~((op (e1) (e3)) = (e1))) -> (((op (e1) (e0)) = (e3))\/(((op (e1) (e1)) = (e3))\/(((op (e1) (e2)) = (e3))\/((op (e1) (e3)) = (e3))))) -> ((op (e1) (e1)) = (e2)) -> (~((op (e0) (e3)) = (op (e1) (e3)))) -> (((op (e0) (e3)) = (e0))\/(((op (e0) (e3)) = (e1))\/(((op (e0) (e3)) = (e2))\/((op (e0) (e3)) = (e3))))) -> (~((op (e3) (e2)) = (e1))) -> (~((op (e3) (e1)) = (e1))) -> (~((op (e3) (e0)) = (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 (e2) (e2)) = (op (e2) (e3)))) -> ((~((op (e1) (e2)) = (e1)))\/((op (e1) (e1)) = (e2))) -> (~((op (e0) (e1)) = (op (e1) (e1)))) -> ((~((op (e2) (e0)) = (e1)))\/((op (e2) (e1)) = (e0))) -> ((~((op (e3) (e0)) = (e1)))\/((op (e3) (e1)) = (e0))) -> (((op (e0) (e0)) = (e1))\/(((op (e0) (e1)) = (e1))\/(((op (e0) (e2)) = (e1))\/((op (e0) (e3)) = (e1))))) -> (((op (e0) (e0)) = (e1))\/(((op (e1) (e0)) = (e1))\/(((op (e2) (e0)) = (e1))\/((op (e3) (e0)) = (e1))))) -> (~((op (e0) (e0)) = (op (e0) (e2)))) -> (~((op (e0) (e1)) = (op (e3) (e1)))) -> ((~((op (e3) (e2)) = (e1)))\/((op (e3) (e1)) = (e2))) -> (~((op (e0) (e1)) = (op (e2) (e1)))) -> ((~((op (e2) (e2)) = (e1)))\/((op (e2) (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) (e1)) = (e1))) -> (~((op (e0) (e2)) = (e1))) -> (~((op (e0) (e3)) = (e1))) -> False). % 18.87/19.02 do 0 intro. intros zenon_H12b zenon_H22 zenon_H201 zenon_H62 zenon_H57 zenon_H4f zenon_H67 zenon_H54 zenon_H5b zenon_H130 zenon_H128 zenon_H1ef zenon_H10a zenon_H255 zenon_H133 zenon_H6a zenon_H4a zenon_H49 zenon_H173 zenon_H18f zenon_H1c4 zenon_H124 zenon_H139 zenon_H34 zenon_H52 zenon_H1a4 zenon_H1b1 zenon_H9a zenon_H95 zenon_H168 zenon_H1fe zenon_H7c zenon_He7 zenon_H14f zenon_H115 zenon_H191 zenon_He2 zenon_H198 zenon_Ha5 zenon_Hdb zenon_Hf3 zenon_H160 zenon_H153 zenon_H102 zenon_Hc2 zenon_H11f zenon_H136 zenon_H145 zenon_H1c7 zenon_H1f0 zenon_H1db zenon_H259 zenon_H1d5 zenon_H149 zenon_H1e0 zenon_H24e zenon_H16f zenon_H110 zenon_H1d zenon_He4 zenon_H251 zenon_H250 zenon_H71 zenon_He8 zenon_H2b zenon_H6d zenon_H256 zenon_H10e zenon_H257 zenon_H254 zenon_H22d zenon_H235 zenon_H13c zenon_H210 zenon_H252 zenon_H17e zenon_H253 zenon_H258 zenon_H183 zenon_Ha4 zenon_H20d zenon_H231. % 18.87/19.02 apply (zenon_or_s _ _ zenon_H22d); [ zenon_intro zenon_H7a | zenon_intro zenon_H22e ]. % 18.87/19.02 apply (zenon_or_s _ _ zenon_H183); [ zenon_intro zenon_H7b | zenon_intro zenon_H186 ]. % 18.87/19.02 apply (zenon_L26_); trivial. % 18.87/19.02 apply (zenon_or_s _ _ zenon_H186); [ zenon_intro zenon_H10f | zenon_intro zenon_H187 ]. % 18.87/19.02 apply (zenon_L726_); trivial. % 18.87/19.02 apply (zenon_or_s _ _ zenon_H187); [ zenon_intro zenon_H150 | zenon_intro zenon_Hcd ]. % 18.87/19.02 apply (zenon_L885_); trivial. % 18.87/19.02 apply (zenon_L887_); trivial. % 18.87/19.02 apply (zenon_or_s _ _ zenon_H22e); [ zenon_intro zenon_Ha0 | zenon_intro zenon_H22f ]. % 18.87/19.02 exact (zenon_Ha4 zenon_Ha0). % 18.87/19.02 apply (zenon_or_s _ _ zenon_H22f); [ zenon_intro zenon_H122 | zenon_intro zenon_Hc3 ]. % 18.87/19.02 exact (zenon_H20d zenon_H122). % 18.87/19.02 exact (zenon_H231 zenon_Hc3). % 18.87/19.02 (* end of lemma zenon_L888_ *) % 18.87/19.02 assert (zenon_L889_ : (((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) (e0)) = (op (e1) (e2)))) -> (~((op (e3) (e1)) = (op (e3) (e3)))) -> (~((op (e2) (e2)) = (op (e2) (e3)))) -> (~((op (e1) (e0)) = (op (e1) (e3)))) -> ((op (e1) (e0)) = (e0)) -> ((op (e0) (e3)) = (e2)) -> (~((e0) = (e2))) -> (((op (e0) (e3)) = (e0))\/(((op (e1) (e3)) = (e0))\/(((op (e2) (e3)) = (e0))\/((op (e3) (e3)) = (e0))))) -> (~((op (e3) (e1)) = (op (e3) (e2)))) -> ((op (e3) (e1)) = (e0)) -> False). % 18.87/19.02 do 0 intro. intros zenon_H6a zenon_H4a zenon_H49 zenon_H24a zenon_H130 zenon_H6d zenon_Hd8 zenon_H27 zenon_Hcd zenon_H149 zenon_H67 zenon_H1a4 zenon_H1b1. % 18.87/19.02 apply (zenon_or_s _ _ zenon_H6a); [ zenon_intro zenon_H48 | zenon_intro zenon_H6b ]. % 18.87/19.02 apply (zenon_L9_); trivial. % 18.87/19.02 apply (zenon_or_s _ _ zenon_H6b); [ zenon_intro zenon_H2a | zenon_intro zenon_H6c ]. % 18.87/19.02 apply (zenon_L644_); trivial. % 18.87/19.02 apply (zenon_or_s _ _ zenon_H6c); [ zenon_intro zenon_H2c | zenon_intro zenon_H61 ]. % 18.87/19.02 apply (zenon_L676_); trivial. % 18.87/19.02 apply (zenon_L247_); trivial. % 18.87/19.02 (* end of lemma zenon_L889_ *) % 18.87/19.02 assert (zenon_L890_ : (((op (e1) (e0)) = (e0))\/(((op (e1) (e1)) = (e0))\/(((op (e1) (e2)) = (e0))\/((op (e1) (e3)) = (e0))))) -> (~((op (e1) (e0)) = (op (e2) (e0)))) -> (~((e0) = (e2))) -> (((op (e0) (e3)) = (e3))\/(((op (e1) (e3)) = (e3))\/(((op (e2) (e3)) = (e3))\/((op (e3) (e3)) = (e3))))) -> (~((e2) = (e3))) -> (~((op (e0) (e3)) = (op (e2) (e3)))) -> ((op (e2) (e1)) = (e1)) -> (~((op (e2) (e3)) = (op (e3) (e3)))) -> (((op (e2) (e3)) = (e0))\/(((op (e2) (e3)) = (e1))\/(((op (e2) (e3)) = (e2))\/((op (e2) (e3)) = (e3))))) -> ((op (e0) (e0)) = (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) (e0)) = (op (e1) (e3)))) -> (~((op (e1) (e3)) = (op (e2) (e3)))) -> (~((op (e1) (e0)) = (e1))) -> (~((op (e1) (e0)) = (op (e1) (e2)))) -> (((op (e1) (e0)) = (e0))\/(((op (e1) (e0)) = (e1))\/(((op (e1) (e0)) = (e2))\/((op (e1) (e0)) = (e3))))) -> (~((op (e3) (e3)) = (e3))) -> (~((op (e1) (e2)) = (op (e3) (e2)))) -> (~((op (e3) (e1)) = (op (e3) (e3)))) -> (~((op (e2) (e2)) = (op (e2) (e3)))) -> (~((op (e1) (e2)) = (op (e2) (e2)))) -> ((op (e2) (e0)) = (e3)) -> (~((op (e2) (e0)) = (op (e2) (e2)))) -> (~((op (e3) (e1)) = (op (e3) (e2)))) -> ((op (e2) (e0)) = (e0)) -> ((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) (e3)) = (e1))\/(((op (e1) (e3)) = (e1))\/(((op (e2) (e3)) = (e1))\/((op (e3) (e3)) = (e1))))) -> (~((op (e0) (e3)) = (e1))) -> (~((op (e2) (e3)) = (e1))) -> (~((op (e1) (e1)) = (e1))) -> (((op (e1) (e0)) = (e1))\/(((op (e1) (e1)) = (e1))\/(((op (e1) (e2)) = (e1))\/((op (e1) (e3)) = (e1))))) -> (~((op (e0) (e1)) = (op (e0) (e3)))) -> (((op (e0) (e3)) = (e0))\/(((op (e1) (e3)) = (e0))\/(((op (e2) (e3)) = (e0))\/((op (e3) (e3)) = (e0))))) -> (((op (e0) (e2)) = (e1))\/(((op (e1) (e2)) = (e1))\/(((op (e2) (e2)) = (e1))\/((op (e3) (e2)) = (e1))))) -> (~((op (e0) (e2)) = (e1))) -> (~((op (e1) (e2)) = (op (e1) (e3)))) -> (((op (e2) (e2)) = (e0))\/(((op (e2) (e2)) = (e1))\/(((op (e2) (e2)) = (e2))\/((op (e2) (e2)) = (e3))))) -> ((op (e0) (e2)) = (e3)) -> (~((op (e2) (e2)) = (op (e3) (e2)))) -> (~((op (e2) (e2)) = (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) (e3)) = (e2))\/(((op (e1) (e3)) = (e2))\/(((op (e2) (e3)) = (e2))\/((op (e3) (e3)) = (e2))))) -> (~((op (e3) (e2)) = (e1))) -> (~((op (e3) (e1)) = (e1))) -> (~((op (e3) (e0)) = (e1))) -> (((op (e3) (e0)) = (e1))\/(((op (e3) (e1)) = (e1))\/(((op (e3) (e2)) = (e1))\/((op (e3) (e3)) = (e1))))) -> (~((op (e1) (e1)) = (op (e1) (e3)))) -> ((op (e1) (e1)) = (e2)) -> (~((op (e2) (e1)) = (op (e2) (e3)))) -> ((op (e2) (e1)) = (e2)) -> ((op (e3) (e0)) = (e2)) -> (~((op (e3) (e0)) = (op (e3) (e3)))) -> False). % 18.87/19.02 do 0 intro. intros zenon_H22 zenon_H201 zenon_H149 zenon_H136 zenon_H12b zenon_He2 zenon_Ha5 zenon_Hf3 zenon_H11f zenon_H7a zenon_Hdf zenon_Hd5 zenon_Hd8 zenon_Hdb zenon_H1ef zenon_H24a zenon_H25e zenon_H102 zenon_H115 zenon_H130 zenon_H6d zenon_H2b zenon_H3b zenon_H52 zenon_H1a4 zenon_H34 zenon_H49 zenon_H4a zenon_H6a zenon_H133 zenon_H231 zenon_H255 zenon_H10a zenon_H128 zenon_H54 zenon_H67 zenon_H139 zenon_H20d zenon_H124 zenon_H1c4 zenon_Ha9 zenon_H18f zenon_H173 zenon_H17b zenon_H1ac zenon_H145 zenon_H251 zenon_H250 zenon_Had zenon_He8 zenon_H57 zenon_H110 zenon_H1c7 zenon_H1ca zenon_H148 zenon_H71. % 18.87/19.02 apply (zenon_or_s _ _ zenon_H22); [ zenon_intro zenon_H27 | zenon_intro zenon_H26 ]. % 18.87/19.02 apply (zenon_L332_); trivial. % 18.87/19.02 apply (zenon_or_s _ _ zenon_H26); [ zenon_intro zenon_H29 | zenon_intro zenon_H28 ]. % 18.87/19.02 apply (zenon_L354_); trivial. % 18.87/19.02 apply (zenon_or_s _ _ zenon_H28); [ zenon_intro zenon_H2a | zenon_intro zenon_H1f ]. % 18.87/19.02 apply (zenon_or_s _ _ zenon_H1ac); [ zenon_intro zenon_H44 | zenon_intro zenon_H1af ]. % 18.87/19.02 apply (zenon_L127_); trivial. % 18.87/19.02 apply (zenon_or_s _ _ zenon_H1af); [ zenon_intro zenon_H1b1 | zenon_intro zenon_H1b0 ]. % 18.87/19.02 apply (zenon_L820_); trivial. % 18.87/19.02 apply (zenon_or_s _ _ zenon_H1b0); [ zenon_intro zenon_H61 | zenon_intro zenon_H60 ]. % 18.87/19.02 apply (zenon_L176_); trivial. % 18.87/19.02 apply (zenon_L795_); trivial. % 18.87/19.02 apply (zenon_L810_); trivial. % 18.87/19.02 (* end of lemma zenon_L890_ *) % 18.87/19.02 assert (zenon_L891_ : (((op (e0) (e0)) = (e3))\/(((op (e1) (e0)) = (e3))\/(((op (e2) (e0)) = (e3))\/((op (e3) (e0)) = (e3))))) -> (~((e1) = (e3))) -> (~((op (e1) (e3)) = (op (e3) (e3)))) -> (~((op (e3) (e2)) = (e1))) -> (~((op (e3) (e1)) = (e1))) -> (~((op (e3) (e0)) = (e1))) -> (((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 (e1) (e2)) = (op (e1) (e3)))) -> (((op (e0) (e2)) = (e1))\/(((op (e1) (e2)) = (e1))\/(((op (e2) (e2)) = (e1))\/((op (e3) (e2)) = (e1))))) -> (((op (e1) (e0)) = (e1))\/(((op (e1) (e1)) = (e1))\/(((op (e1) (e2)) = (e1))\/((op (e1) (e3)) = (e1))))) -> (~((op (e1) (e1)) = (e1))) -> (~((op (e2) (e3)) = (e1))) -> (((op (e0) (e3)) = (e1))\/(((op (e1) (e3)) = (e1))\/(((op (e2) (e3)) = (e1))\/((op (e3) (e3)) = (e1))))) -> (((op (e0) (e2)) = (e0))\/(((op (e1) (e2)) = (e0))\/(((op (e2) (e2)) = (e0))\/((op (e3) (e2)) = (e0))))) -> (~((op (e0) (e1)) = (op (e0) (e2)))) -> (~((op (e3) (e1)) = (op (e3) (e2)))) -> (~((op (e1) (e2)) = (op (e3) (e2)))) -> (((op (e1) (e0)) = (e0))\/(((op (e1) (e0)) = (e1))\/(((op (e1) (e0)) = (e2))\/((op (e1) (e0)) = (e3))))) -> (~((op (e1) (e0)) = (op (e1) (e2)))) -> (~((op (e1) (e0)) = (e1))) -> ((op (e0) (e0)) = (e1)) -> (~((op (e1) (e0)) = (op (e2) (e0)))) -> (((op (e1) (e0)) = (e0))\/(((op (e1) (e1)) = (e0))\/(((op (e1) (e2)) = (e0))\/((op (e1) (e3)) = (e0))))) -> (~((op (e0) (e1)) = (op (e2) (e1)))) -> (~((op (e3) (e0)) = (op (e3) (e3)))) -> ((op (e2) (e1)) = (e2)) -> (~((op (e2) (e1)) = (op (e2) (e3)))) -> ((op (e1) (e1)) = (e2)) -> (~((op (e1) (e1)) = (op (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 (e0) (e3)) = (op (e2) (e3)))) -> ((op (e2) (e1)) = (e1)) -> (~((op (e2) (e3)) = (op (e3) (e3)))) -> (((op (e2) (e3)) = (e0))\/(((op (e2) (e3)) = (e1))\/(((op (e2) (e3)) = (e2))\/((op (e2) (e3)) = (e3))))) -> (~((op (e1) (e3)) = (op (e2) (e3)))) -> ((op (e0) (e2)) = (e3)) -> (((op (e1) (e3)) = (e0))\/(((op (e1) (e3)) = (e1))\/(((op (e1) (e3)) = (e2))\/((op (e1) (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)) = (op (e3) (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) (e1)) = (e0)) -> ((op (e1) (e0)) = (e0)) -> (~((op (e1) (e0)) = (op (e1) (e3)))) -> (~((op (e3) (e1)) = (op (e3) (e3)))) -> (((op (e0) (e0)) = (e1))\/(((op (e0) (e1)) = (e1))\/(((op (e0) (e2)) = (e1))\/((op (e0) (e3)) = (e1))))) -> (~((e0) = (e2))) -> (~((op (e2) (e0)) = (op (e2) (e1)))) -> (((op (e2) (e0)) = (e0))\/(((op (e2) (e0)) = (e1))\/(((op (e2) (e0)) = (e2))\/((op (e2) (e0)) = (e3))))) -> (~((op (e2) (e0)) = (op (e3) (e0)))) -> (~((op (e2) (e0)) = (e1))) -> (~((e1) = (e2))) -> (((op (e0) (e0)) = (e2))\/(((op (e1) (e0)) = (e2))\/(((op (e2) (e0)) = (e2))\/((op (e3) (e0)) = (e2))))) -> (~((op (e0) (e1)) = (e1))) -> (~((op (e0) (e2)) = (e1))) -> (~((op (e0) (e3)) = (e1))) -> (((op (e3) (e0)) = (e0))\/(((op (e3) (e1)) = (e0))\/(((op (e3) (e2)) = (e0))\/((op (e3) (e3)) = (e0))))) -> (((op (e2) (e2)) = (e0))\/(((op (e2) (e2)) = (e1))\/(((op (e2) (e2)) = (e2))\/((op (e2) (e2)) = (e3))))) -> (~((op (e2) (e2)) = (op (e2) (e3)))) -> (~((op (e1) (e2)) = (op (e2) (e2)))) -> (~((op (e2) (e2)) = (e2))) -> (~((op (e2) (e0)) = (op (e2) (e2)))) -> ((op (e3) (e0)) = (e2)) -> (~((e2) = (e3))) -> False). % 18.87/19.02 do 0 intro. intros zenon_H1e0 zenon_H95 zenon_Hd5 zenon_H251 zenon_H250 zenon_Had zenon_He8 zenon_H2f zenon_H124 zenon_H139 zenon_H128 zenon_H10a zenon_H255 zenon_H133 zenon_H6a zenon_H4a zenon_H1a4 zenon_H115 zenon_H25e zenon_H24a zenon_H1ef zenon_H7a zenon_H201 zenon_H22 zenon_H17e zenon_H71 zenon_H1ca zenon_H1c7 zenon_H110 zenon_H57 zenon_H136 zenon_H1d zenon_He2 zenon_Ha5 zenon_Hf3 zenon_H11f zenon_Hdb zenon_Ha9 zenon_Hdf zenon_H102 zenon_H145 zenon_H18f zenon_H67 zenon_H54 zenon_H49 zenon_H27 zenon_Hd8 zenon_H130 zenon_H22d zenon_H149 zenon_H1f0 zenon_H259 zenon_H17b zenon_H1db zenon_H7c zenon_H1fe zenon_Ha4 zenon_H20d zenon_H231 zenon_H1ac zenon_H1c4 zenon_H6d zenon_H2b zenon_H173 zenon_H52 zenon_H148 zenon_H12b. % 18.87/19.02 apply (zenon_or_s _ _ zenon_H1e0); [ zenon_intro zenon_H3a | zenon_intro zenon_H1e1 ]. % 18.87/19.02 apply (zenon_L35_); trivial. % 18.87/19.02 apply (zenon_or_s _ _ zenon_H1e1); [ zenon_intro zenon_H9e | zenon_intro zenon_H1e2 ]. % 18.87/19.02 apply (zenon_L107_); trivial. % 18.87/19.02 apply (zenon_or_s _ _ zenon_H1e2); [ zenon_intro zenon_H3b | zenon_intro zenon_H15e ]. % 18.87/19.02 apply (zenon_or_s _ _ zenon_H128); [ zenon_intro zenon_H9d | zenon_intro zenon_H129 ]. % 18.87/19.02 exact (zenon_H1ef zenon_H9d). % 18.87/19.02 apply (zenon_or_s _ _ zenon_H129); [ zenon_intro zenon_H10d | zenon_intro zenon_H12a ]. % 18.87/19.02 exact (zenon_H10a zenon_H10d). % 18.87/19.02 apply (zenon_or_s _ _ zenon_H12a); [ zenon_intro zenon_Hf0 | zenon_intro zenon_Hd6 ]. % 18.87/19.02 apply (zenon_or_s _ _ zenon_H2f); [ zenon_intro zenon_H34 | zenon_intro zenon_H33 ]. % 18.87/19.02 apply (zenon_L890_); trivial. % 18.87/19.02 apply (zenon_or_s _ _ zenon_H33); [ zenon_intro zenon_H36 | zenon_intro zenon_H35 ]. % 18.87/19.02 apply (zenon_L128_); trivial. % 18.87/19.02 apply (zenon_or_s _ _ zenon_H35); [ zenon_intro zenon_H2c | zenon_intro zenon_H37 ]. % 18.87/19.02 apply (zenon_L875_); trivial. % 18.87/19.02 apply (zenon_L300_); trivial. % 18.87/19.02 apply (zenon_L800_); trivial. % 18.87/19.02 apply (zenon_L109_); trivial. % 18.87/19.02 (* end of lemma zenon_L891_ *) % 18.87/19.02 assert (zenon_L892_ : (((op (e0) (e3)) = (e2))\/(((op (e1) (e3)) = (e2))\/(((op (e2) (e3)) = (e2))\/((op (e3) (e3)) = (e2))))) -> ((op (e1) (e3)) = (e0)) -> ((op (e0) (e3)) = (e3)) -> (~((op (e0) (e3)) = (op (e2) (e3)))) -> (~((op (e2) (e3)) = (op (e3) (e3)))) -> ((op (e3) (e3)) = (e1)) -> (((op (e2) (e3)) = (e0))\/(((op (e2) (e3)) = (e1))\/(((op (e2) (e3)) = (e2))\/((op (e2) (e3)) = (e3))))) -> (~((op (e2) (e1)) = (op (e2) (e3)))) -> ((op (e2) (e1)) = (e2)) -> ((op (e3) (e0)) = (e2)) -> (~((op (e3) (e0)) = (op (e3) (e3)))) -> False). % 18.87/19.02 do 0 intro. intros zenon_H145 zenon_H1f zenon_He3 zenon_He2 zenon_Hf3 zenon_Hc4 zenon_H11f zenon_H1c7 zenon_H1ca zenon_H148 zenon_H71. % 18.87/19.02 apply (zenon_or_s _ _ zenon_H145); [ zenon_intro zenon_Hcd | zenon_intro zenon_H146 ]. % 18.87/19.02 apply (zenon_L49_); trivial. % 18.87/19.02 apply (zenon_or_s _ _ zenon_H146); [ zenon_intro zenon_Hd7 | zenon_intro zenon_H147 ]. % 18.87/19.02 apply (zenon_L454_); trivial. % 18.87/19.02 apply (zenon_or_s _ _ zenon_H147); [ zenon_intro zenon_H11d | zenon_intro zenon_Hf6 ]. % 18.87/19.02 apply (zenon_L224_); trivial. % 18.87/19.02 apply (zenon_L114_); trivial. % 18.87/19.02 (* end of lemma zenon_L892_ *) % 18.87/19.02 assert (zenon_L893_ : (((op (e0) (e3)) = (e1))\/(((op (e1) (e3)) = (e1))\/(((op (e2) (e3)) = (e1))\/((op (e3) (e3)) = (e1))))) -> (~((op (e0) (e3)) = (e1))) -> ((op (e2) (e0)) = (e0)) -> (~((op (e2) (e0)) = (op (e2) (e3)))) -> (~((e1) = (e2))) -> (~((e2) = (e3))) -> (~((op (e2) (e3)) = (e1))) -> (((op (e0) (e3)) = (e2))\/(((op (e1) (e3)) = (e2))\/(((op (e2) (e3)) = (e2))\/((op (e3) (e3)) = (e2))))) -> ((op (e1) (e3)) = (e0)) -> ((op (e0) (e3)) = (e3)) -> (~((op (e0) (e3)) = (op (e2) (e3)))) -> (~((op (e2) (e3)) = (op (e3) (e3)))) -> (((op (e2) (e3)) = (e0))\/(((op (e2) (e3)) = (e1))\/(((op (e2) (e3)) = (e2))\/((op (e2) (e3)) = (e3))))) -> (~((op (e2) (e1)) = (op (e2) (e3)))) -> ((op (e2) (e1)) = (e2)) -> ((op (e3) (e0)) = (e2)) -> (~((op (e3) (e0)) = (op (e3) (e3)))) -> False). % 18.87/19.02 do 0 intro. intros zenon_H133 zenon_H231 zenon_H34 zenon_H5b zenon_H7c zenon_H12b zenon_H255 zenon_H145 zenon_H1f zenon_He3 zenon_He2 zenon_Hf3 zenon_H11f zenon_H1c7 zenon_H1ca zenon_H148 zenon_H71. % 18.87/19.02 apply (zenon_or_s _ _ zenon_H133); [ zenon_intro zenon_Hc3 | zenon_intro zenon_H134 ]. % 18.87/19.02 exact (zenon_H231 zenon_Hc3). % 18.87/19.02 apply (zenon_or_s _ _ zenon_H134); [ zenon_intro zenon_Hd6 | zenon_intro zenon_H135 ]. % 18.87/19.02 apply (zenon_L226_); trivial. % 18.87/19.02 apply (zenon_or_s _ _ zenon_H135); [ zenon_intro zenon_Hf4 | zenon_intro zenon_Hc4 ]. % 18.87/19.02 exact (zenon_H255 zenon_Hf4). % 18.87/19.02 apply (zenon_L892_); trivial. % 18.87/19.02 (* end of lemma zenon_L893_ *) % 18.87/19.02 assert (zenon_L894_ : (((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 (e3) (e0)) = (op (e3) (e3)))) -> ((op (e3) (e0)) = (e2)) -> ((op (e2) (e1)) = (e2)) -> (~((op (e2) (e1)) = (op (e2) (e3)))) -> (((op (e2) (e3)) = (e0))\/(((op (e2) (e3)) = (e1))\/(((op (e2) (e3)) = (e2))\/((op (e2) (e3)) = (e3))))) -> (~((op (e2) (e3)) = (op (e3) (e3)))) -> (~((op (e0) (e3)) = (op (e2) (e3)))) -> ((op (e0) (e3)) = (e3)) -> (((op (e0) (e3)) = (e2))\/(((op (e1) (e3)) = (e2))\/(((op (e2) (e3)) = (e2))\/((op (e3) (e3)) = (e2))))) -> (~((op (e2) (e3)) = (e1))) -> (~((e2) = (e3))) -> (~((e1) = (e2))) -> (~((op (e0) (e3)) = (e1))) -> (((op (e0) (e3)) = (e1))\/(((op (e1) (e3)) = (e1))\/(((op (e2) (e3)) = (e1))\/((op (e3) (e3)) = (e1))))) -> (~((op (e2) (e0)) = (op (e2) (e3)))) -> ((op (e2) (e0)) = (e0)) -> ((op (e3) (e1)) = (e0)) -> (~((op (e3) (e1)) = (op (e3) (e3)))) -> False). % 18.87/19.02 do 0 intro. intros zenon_H67 zenon_H54 zenon_H49 zenon_H71 zenon_H148 zenon_H1ca zenon_H1c7 zenon_H11f zenon_Hf3 zenon_He2 zenon_He3 zenon_H145 zenon_H255 zenon_H12b zenon_H7c zenon_H231 zenon_H133 zenon_H5b zenon_H34 zenon_H1b1 zenon_H130. % 18.87/19.02 apply (zenon_or_s _ _ zenon_H67); [ zenon_intro zenon_H1e | zenon_intro zenon_H68 ]. % 18.87/19.02 apply (zenon_L12_); trivial. % 18.87/19.02 apply (zenon_or_s _ _ zenon_H68); [ zenon_intro zenon_H1f | zenon_intro zenon_H69 ]. % 18.87/19.02 apply (zenon_L893_); trivial. % 18.87/19.02 apply (zenon_or_s _ _ zenon_H69); [ zenon_intro zenon_H37 | zenon_intro zenon_H60 ]. % 18.87/19.02 apply (zenon_L14_); trivial. % 18.87/19.02 apply (zenon_L244_); trivial. % 18.87/19.02 (* end of lemma zenon_L894_ *) % 18.87/19.02 assert (zenon_L895_ : (((op (e0) (e0)) = (e3))\/(((op (e0) (e1)) = (e3))\/(((op (e0) (e2)) = (e3))\/((op (e0) (e3)) = (e3))))) -> ((op (e1) (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 (e1) (e0)) = (op (e2) (e0)))) -> (~((op (e1) (e1)) = (op (e1) (e2)))) -> (~((op (e3) (e0)) = (op (e3) (e2)))) -> (~((op (e3) (e2)) = (op (e3) (e3)))) -> (~((op (e1) (e0)) = (op (e1) (e1)))) -> (~((op (e0) (e0)) = (e0))) -> (((op (e0) (e0)) = (e0))\/(((op (e1) (e0)) = (e0))\/(((op (e2) (e0)) = (e0))\/((op (e3) (e0)) = (e0))))) -> (~((op (e1) (e2)) = (op (e2) (e2)))) -> (~((op (e2) (e2)) = (op (e2) (e3)))) -> (~((op (e3) (e1)) = (op (e3) (e2)))) -> (~((op (e2) (e0)) = (op (e2) (e2)))) -> (((op (e0) (e2)) = (e1))\/(((op (e1) (e2)) = (e1))\/(((op (e2) (e2)) = (e1))\/((op (e3) (e2)) = (e1))))) -> (~((op (e0) (e2)) = (e1))) -> (~((op (e1) (e2)) = (op (e1) (e3)))) -> (((op (e2) (e2)) = (e0))\/(((op (e2) (e2)) = (e1))\/(((op (e2) (e2)) = (e2))\/((op (e2) (e2)) = (e3))))) -> (~((op (e2) (e2)) = (op (e3) (e2)))) -> (~((op (e2) (e2)) = (e2))) -> (~((op (e0) (e1)) = (op (e0) (e2)))) -> (((op (e0) (e2)) = (e0))\/(((op (e1) (e2)) = (e0))\/(((op (e2) (e2)) = (e0))\/((op (e3) (e2)) = (e0))))) -> (~((op (e1) (e1)) = (e1))) -> (~((op (e1) (e0)) = (e1))) -> (((op (e1) (e0)) = (e1))\/(((op (e1) (e1)) = (e1))\/(((op (e1) (e2)) = (e1))\/((op (e1) (e3)) = (e1))))) -> (~((op (e1) (e1)) = (op (e1) (e3)))) -> ((op (e1) (e1)) = (e2)) -> ((op (e0) (e0)) = (e1)) -> (~((e1) = (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) (e1)) = (op (e0) (e3)))) -> ((op (e0) (e1)) = (e0)) -> (~((op (e3) (e0)) = (op (e3) (e3)))) -> ((op (e3) (e0)) = (e2)) -> ((op (e2) (e1)) = (e2)) -> (~((op (e2) (e1)) = (op (e2) (e3)))) -> (((op (e2) (e3)) = (e0))\/(((op (e2) (e3)) = (e1))\/(((op (e2) (e3)) = (e2))\/((op (e2) (e3)) = (e3))))) -> (~((op (e2) (e3)) = (op (e3) (e3)))) -> (~((op (e0) (e3)) = (op (e2) (e3)))) -> (((op (e0) (e3)) = (e2))\/(((op (e1) (e3)) = (e2))\/(((op (e2) (e3)) = (e2))\/((op (e3) (e3)) = (e2))))) -> (~((op (e2) (e3)) = (e1))) -> (~((e2) = (e3))) -> (~((e1) = (e2))) -> (~((op (e0) (e3)) = (e1))) -> (((op (e0) (e3)) = (e1))\/(((op (e1) (e3)) = (e1))\/(((op (e2) (e3)) = (e1))\/((op (e3) (e3)) = (e1))))) -> (~((op (e2) (e0)) = (op (e2) (e3)))) -> ((op (e2) (e0)) = (e0)) -> ((op (e3) (e1)) = (e0)) -> (~((op (e3) (e1)) = (op (e3) (e3)))) -> False). % 18.87/19.02 do 0 intro. intros zenon_H168 zenon_H13f zenon_H10e zenon_H22 zenon_H201 zenon_H4f zenon_H6f zenon_H62 zenon_H45 zenon_H3f zenon_H3e zenon_H2b zenon_H6d zenon_H1a4 zenon_H52 zenon_H139 zenon_H20d zenon_H124 zenon_H1c4 zenon_H18f zenon_H173 zenon_H4a zenon_H6a zenon_H10a zenon_H1ef zenon_H128 zenon_H57 zenon_H110 zenon_H7a zenon_H95 zenon_H1e0 zenon_H67 zenon_H54 zenon_H49 zenon_H71 zenon_H148 zenon_H1ca zenon_H1c7 zenon_H11f zenon_Hf3 zenon_He2 zenon_H145 zenon_H255 zenon_H12b zenon_H7c zenon_H231 zenon_H133 zenon_H5b zenon_H34 zenon_H1b1 zenon_H130. % 18.87/19.02 apply (zenon_or_s _ _ zenon_H168); [ zenon_intro zenon_H3a | zenon_intro zenon_H169 ]. % 18.87/19.02 apply (zenon_L35_); trivial. % 18.87/19.02 apply (zenon_or_s _ _ zenon_H169); [ zenon_intro zenon_H99 | zenon_intro zenon_H16a ]. % 18.87/19.02 apply (zenon_L108_); trivial. % 18.87/19.02 apply (zenon_or_s _ _ zenon_H16a); [ zenon_intro zenon_Ha9 | zenon_intro zenon_He3 ]. % 18.87/19.02 apply (zenon_L821_); trivial. % 18.87/19.02 apply (zenon_L894_); trivial. % 18.87/19.02 (* end of lemma zenon_L895_ *) % 18.87/19.02 assert (zenon_L896_ : (((op (e3) (e0)) = (e0))\/(((op (e3) (e1)) = (e0))\/(((op (e3) (e2)) = (e0))\/((op (e3) (e3)) = (e0))))) -> (~((e0) = (e2))) -> (~((op (e3) (e1)) = (op (e3) (e3)))) -> ((op (e2) (e0)) = (e0)) -> (~((op (e2) (e0)) = (op (e2) (e3)))) -> (((op (e0) (e3)) = (e1))\/(((op (e1) (e3)) = (e1))\/(((op (e2) (e3)) = (e1))\/((op (e3) (e3)) = (e1))))) -> (~((op (e0) (e3)) = (e1))) -> (~((e1) = (e2))) -> (~((e2) = (e3))) -> (~((op (e2) (e3)) = (e1))) -> (((op (e0) (e3)) = (e2))\/(((op (e1) (e3)) = (e2))\/(((op (e2) (e3)) = (e2))\/((op (e3) (e3)) = (e2))))) -> ((op (e3) (e0)) = (e2)) -> (~((op (e3) (e0)) = (op (e3) (e3)))) -> ((op (e0) (e1)) = (e0)) -> (~((op (e0) (e1)) = (op (e0) (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))))) -> (~((e1) = (e3))) -> ((op (e0) (e0)) = (e1)) -> ((op (e1) (e1)) = (e2)) -> (~((op (e1) (e1)) = (op (e1) (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 (e0) (e2)) = (e0))\/(((op (e1) (e2)) = (e0))\/(((op (e2) (e2)) = (e0))\/((op (e3) (e2)) = (e0))))) -> (~((op (e0) (e1)) = (op (e0) (e2)))) -> (~((op (e2) (e2)) = (e2))) -> (~((op (e2) (e2)) = (op (e3) (e2)))) -> (((op (e2) (e2)) = (e0))\/(((op (e2) (e2)) = (e1))\/(((op (e2) (e2)) = (e2))\/((op (e2) (e2)) = (e3))))) -> (~((op (e1) (e2)) = (op (e1) (e3)))) -> (~((op (e0) (e2)) = (e1))) -> (((op (e0) (e2)) = (e1))\/(((op (e1) (e2)) = (e1))\/(((op (e2) (e2)) = (e1))\/((op (e3) (e2)) = (e1))))) -> (~((op (e2) (e0)) = (op (e2) (e2)))) -> (~((op (e3) (e1)) = (op (e3) (e2)))) -> (~((op (e2) (e2)) = (op (e2) (e3)))) -> (~((op (e1) (e2)) = (op (e2) (e2)))) -> (((op (e0) (e0)) = (e0))\/(((op (e1) (e0)) = (e0))\/(((op (e2) (e0)) = (e0))\/((op (e3) (e0)) = (e0))))) -> (~((op (e0) (e0)) = (e0))) -> (~((op (e1) (e0)) = (op (e1) (e1)))) -> (~((op (e3) (e2)) = (op (e3) (e3)))) -> (~((op (e3) (e0)) = (op (e3) (e2)))) -> (~((op (e1) (e1)) = (op (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 (e0) (e1)) = (op (e1) (e1)))) -> ((op (e1) (e1)) = (e3)) -> (((op (e0) (e0)) = (e3))\/(((op (e0) (e1)) = (e3))\/(((op (e0) (e2)) = (e3))\/((op (e0) (e3)) = (e3))))) -> ((op (e1) (e2)) = (e0)) -> (~((op (e1) (e2)) = (op (e3) (e2)))) -> (((op (e3) (e0)) = (e1))\/(((op (e3) (e1)) = (e1))\/(((op (e3) (e2)) = (e1))\/((op (e3) (e3)) = (e1))))) -> (~((op (e3) (e0)) = (e1))) -> (~((op (e3) (e1)) = (e1))) -> (~((op (e3) (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 (e0) (e3)) = (op (e2) (e3)))) -> ((op (e2) (e1)) = (e2)) -> (~((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))))) -> (~((op (e0) (e3)) = (op (e1) (e3)))) -> ((op (e0) (e3)) = (e3)) -> False). % 18.87/19.02 do 0 intro. intros zenon_H1ac zenon_H149 zenon_H130 zenon_H34 zenon_H5b zenon_H133 zenon_H231 zenon_H7c zenon_H12b zenon_H255 zenon_H145 zenon_H148 zenon_H71 zenon_H49 zenon_H54 zenon_H67 zenon_H1e0 zenon_H95 zenon_H7a zenon_H110 zenon_H57 zenon_H128 zenon_H1ef zenon_H10a zenon_H6a zenon_H4a zenon_H173 zenon_H18f zenon_H1c4 zenon_H124 zenon_H20d zenon_H139 zenon_H52 zenon_H1a4 zenon_H6d zenon_H2b zenon_H3e zenon_H3f zenon_H45 zenon_H62 zenon_H6f zenon_H4f zenon_H201 zenon_H22 zenon_H10e zenon_H13f zenon_H168 zenon_H2a zenon_H115 zenon_He8 zenon_Had zenon_H250 zenon_H251 zenon_Hdf zenon_Hd5 zenon_He2 zenon_H1ca zenon_H1c7 zenon_Hf3 zenon_H11f zenon_H1d zenon_He3. % 18.87/19.02 apply (zenon_or_s _ _ zenon_H1ac); [ zenon_intro zenon_H44 | zenon_intro zenon_H1af ]. % 18.87/19.02 apply (zenon_L100_); trivial. % 18.87/19.02 apply (zenon_or_s _ _ zenon_H1af); [ zenon_intro zenon_H1b1 | zenon_intro zenon_H1b0 ]. % 18.87/19.02 apply (zenon_L895_); trivial. % 18.87/19.02 apply (zenon_or_s _ _ zenon_H1b0); [ zenon_intro zenon_H61 | zenon_intro zenon_H60 ]. % 18.87/19.02 apply (zenon_L176_); trivial. % 18.87/19.02 apply (zenon_L805_); trivial. % 18.87/19.02 (* end of lemma zenon_L896_ *) % 18.87/19.02 assert (zenon_L897_ : (~((e0) = (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 (e1) (e2)) = (op (e3) (e2)))) -> (((op (e0) (e0)) = (e3))\/(((op (e0) (e1)) = (e3))\/(((op (e0) (e2)) = (e3))\/((op (e0) (e3)) = (e3))))) -> ((op (e1) (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 (e1) (e0)) = (op (e2) (e0)))) -> (~((op (e1) (e1)) = (op (e1) (e2)))) -> (~((op (e3) (e0)) = (op (e3) (e2)))) -> (~((op (e3) (e2)) = (op (e3) (e3)))) -> (~((op (e1) (e0)) = (op (e1) (e1)))) -> (~((op (e0) (e0)) = (e0))) -> (((op (e0) (e0)) = (e0))\/(((op (e1) (e0)) = (e0))\/(((op (e2) (e0)) = (e0))\/((op (e3) (e0)) = (e0))))) -> (~((op (e1) (e2)) = (op (e2) (e2)))) -> (~((op (e2) (e2)) = (op (e2) (e3)))) -> (~((op (e3) (e1)) = (op (e3) (e2)))) -> (~((op (e2) (e0)) = (op (e2) (e2)))) -> (((op (e0) (e2)) = (e1))\/(((op (e1) (e2)) = (e1))\/(((op (e2) (e2)) = (e1))\/((op (e3) (e2)) = (e1))))) -> (~((op (e0) (e2)) = (e1))) -> (~((op (e1) (e2)) = (op (e1) (e3)))) -> (((op (e2) (e2)) = (e0))\/(((op (e2) (e2)) = (e1))\/(((op (e2) (e2)) = (e2))\/((op (e2) (e2)) = (e3))))) -> (~((op (e2) (e2)) = (op (e3) (e2)))) -> (~((op (e2) (e2)) = (e2))) -> (~((op (e0) (e1)) = (op (e0) (e2)))) -> (((op (e0) (e2)) = (e0))\/(((op (e1) (e2)) = (e0))\/(((op (e2) (e2)) = (e0))\/((op (e3) (e2)) = (e0))))) -> (~((op (e1) (e1)) = (e1))) -> (~((op (e1) (e0)) = (e1))) -> (((op (e1) (e0)) = (e1))\/(((op (e1) (e1)) = (e1))\/(((op (e1) (e2)) = (e1))\/((op (e1) (e3)) = (e1))))) -> ((op (e0) (e0)) = (e1)) -> (~((e1) = (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) (e1)) = (op (e0) (e3)))) -> ((op (e0) (e1)) = (e0)) -> ((op (e3) (e0)) = (e2)) -> (~((op (e2) (e3)) = (e1))) -> (~((e2) = (e3))) -> (~((e1) = (e2))) -> (~((op (e0) (e3)) = (e1))) -> (((op (e0) (e3)) = (e1))\/(((op (e1) (e3)) = (e1))\/(((op (e2) (e3)) = (e1))\/((op (e3) (e3)) = (e1))))) -> (~((e0) = (e2))) -> (((op (e3) (e0)) = (e0))\/(((op (e3) (e1)) = (e0))\/(((op (e3) (e2)) = (e0))\/((op (e3) (e3)) = (e0))))) -> (((op (e3) (e0)) = (e2))\/(((op (e3) (e1)) = (e2))\/(((op (e3) (e2)) = (e2))\/((op (e3) (e3)) = (e2))))) -> (~((op (e3) (e0)) = (op (e3) (e3)))) -> (((op (e3) (e0)) = (e1))\/(((op (e3) (e1)) = (e1))\/(((op (e3) (e2)) = (e1))\/((op (e3) (e3)) = (e1))))) -> (~((op (e3) (e0)) = (e1))) -> (~((op (e3) (e1)) = (e1))) -> (~((op (e3) (e2)) = (e1))) -> (~((op (e3) (e1)) = (op (e3) (e3)))) -> ((op (e2) (e1)) = (e2)) -> (~((op (e2) (e1)) = (op (e2) (e3)))) -> ((op (e1) (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 (e0) (e2)) = (e2)) -> (~((op (e0) (e2)) = (op (e3) (e2)))) -> (((op (e2) (e3)) = (e0))\/(((op (e2) (e3)) = (e1))\/(((op (e2) (e3)) = (e2))\/((op (e2) (e3)) = (e3))))) -> (~((op (e2) (e0)) = (op (e2) (e3)))) -> ((op (e2) (e0)) = (e0)) -> (~((op (e2) (e3)) = (op (e3) (e3)))) -> (~((op (e0) (e3)) = (op (e2) (e3)))) -> ((op (e0) (e3)) = (e3)) -> False). % 18.87/19.03 do 0 intro. intros zenon_H9a zenon_H1d zenon_Hd5 zenon_Hdf zenon_H115 zenon_H168 zenon_H13f zenon_H10e zenon_H22 zenon_H201 zenon_H4f zenon_H6f zenon_H62 zenon_H45 zenon_H3f zenon_H3e zenon_H2b zenon_H6d zenon_H1a4 zenon_H52 zenon_H139 zenon_H20d zenon_H124 zenon_H1c4 zenon_H18f zenon_H173 zenon_H4a zenon_H6a zenon_H10a zenon_H1ef zenon_H128 zenon_H7a zenon_H95 zenon_H1e0 zenon_H67 zenon_H54 zenon_H49 zenon_H148 zenon_H255 zenon_H12b zenon_H7c zenon_H231 zenon_H133 zenon_H149 zenon_H1ac zenon_H153 zenon_H71 zenon_He8 zenon_Had zenon_H250 zenon_H251 zenon_H130 zenon_H1ca zenon_H1c7 zenon_H110 zenon_H57 zenon_H145 zenon_H150 zenon_H14f zenon_H11f zenon_H5b zenon_H34 zenon_Hf3 zenon_He2 zenon_He3. % 18.87/19.03 apply (zenon_or_s _ _ zenon_H22); [ zenon_intro zenon_H27 | zenon_intro zenon_H26 ]. % 18.87/19.03 apply (zenon_L332_); trivial. % 18.87/19.03 apply (zenon_or_s _ _ zenon_H26); [ zenon_intro zenon_H29 | zenon_intro zenon_H28 ]. % 18.87/19.03 apply (zenon_L724_); trivial. % 18.87/19.03 apply (zenon_or_s _ _ zenon_H28); [ zenon_intro zenon_H2a | zenon_intro zenon_H1f ]. % 18.87/19.03 apply (zenon_L896_); trivial. % 18.87/19.03 apply (zenon_L808_); trivial. % 18.87/19.03 (* end of lemma zenon_L897_ *) % 18.87/19.03 assert (zenon_L898_ : (((op (e2) (e0)) = (e0))\/(((op (e2) (e1)) = (e0))\/(((op (e2) (e2)) = (e0))\/((op (e2) (e3)) = (e0))))) -> (~((op (e2) (e0)) = (op (e2) (e3)))) -> (~((op (e0) (e2)) = (op (e3) (e2)))) -> ((op (e0) (e2)) = (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)) = (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) (e3)) = (e1))\/(((op (e1) (e3)) = (e1))\/(((op (e2) (e3)) = (e1))\/((op (e3) (e3)) = (e1))))) -> (~((op (e0) (e3)) = (e1))) -> (~((e1) = (e2))) -> (~((e2) = (e3))) -> (~((op (e2) (e3)) = (e1))) -> (((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)) = (e1))\/(((op (e1) (e1)) = (e1))\/(((op (e1) (e2)) = (e1))\/((op (e1) (e3)) = (e1))))) -> (~((op (e1) (e0)) = (e1))) -> (~((op (e1) (e1)) = (e1))) -> (((op (e0) (e2)) = (e0))\/(((op (e1) (e2)) = (e0))\/(((op (e2) (e2)) = (e0))\/((op (e3) (e2)) = (e0))))) -> (~((op (e0) (e1)) = (op (e0) (e2)))) -> (~((op (e1) (e2)) = (op (e1) (e3)))) -> (~((op (e0) (e2)) = (e1))) -> (((op (e0) (e2)) = (e1))\/(((op (e1) (e2)) = (e1))\/(((op (e2) (e2)) = (e1))\/((op (e3) (e2)) = (e1))))) -> (~((op (e3) (e1)) = (op (e3) (e2)))) -> (((op (e0) (e0)) = (e0))\/(((op (e1) (e0)) = (e0))\/(((op (e2) (e0)) = (e0))\/((op (e3) (e0)) = (e0))))) -> (~((op (e0) (e0)) = (e0))) -> (~((op (e1) (e0)) = (op (e1) (e1)))) -> (~((op (e3) (e2)) = (op (e3) (e3)))) -> (~((op (e3) (e0)) = (op (e3) (e2)))) -> (~((op (e1) (e1)) = (op (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 (e0) (e1)) = (op (e1) (e1)))) -> ((op (e1) (e1)) = (e3)) -> (((op (e0) (e0)) = (e3))\/(((op (e0) (e1)) = (e3))\/(((op (e0) (e2)) = (e3))\/((op (e0) (e3)) = (e3))))) -> (~((op (e1) (e2)) = (op (e3) (e2)))) -> (~((e0) = (e3))) -> (~((op (e0) (e1)) = (op (e2) (e1)))) -> ((op (e0) (e3)) = (e3)) -> (~((op (e0) (e3)) = (op (e1) (e3)))) -> (((op (e2) (e3)) = (e0))\/(((op (e2) (e3)) = (e1))\/(((op (e2) (e3)) = (e2))\/((op (e2) (e3)) = (e3))))) -> (~((op (e2) (e3)) = (op (e3) (e3)))) -> (~((op (e2) (e1)) = (op (e2) (e3)))) -> ((op (e2) (e1)) = (e2)) -> (~((op (e0) (e3)) = (op (e2) (e3)))) -> (~((op (e1) (e3)) = (op (e3) (e3)))) -> (((op (e1) (e3)) = (e0))\/(((op (e1) (e3)) = (e1))\/(((op (e1) (e3)) = (e2))\/((op (e1) (e3)) = (e3))))) -> (~((op (e3) (e2)) = (e1))) -> (~((op (e3) (e1)) = (e1))) -> (~((op (e3) (e0)) = (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) (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) (e0)) = (e0)) -> (~((op (e1) (e0)) = (op (e1) (e3)))) -> (~((op (e3) (e1)) = (op (e3) (e3)))) -> ((op (e3) (e0)) = (e2)) -> (~((e0) = (e2))) -> (((op (e3) (e0)) = (e0))\/(((op (e3) (e1)) = (e0))\/(((op (e3) (e2)) = (e0))\/((op (e3) (e3)) = (e0))))) -> (((op (e2) (e2)) = (e0))\/(((op (e2) (e2)) = (e1))\/(((op (e2) (e2)) = (e2))\/((op (e2) (e2)) = (e3))))) -> (~((op (e2) (e2)) = (op (e2) (e3)))) -> ((op (e1) (e2)) = (e1)) -> (~((op (e1) (e2)) = (op (e2) (e2)))) -> (~((op (e2) (e2)) = (e2))) -> ((op (e2) (e0)) = (e3)) -> (~((op (e2) (e0)) = (op (e2) (e2)))) -> False). % 18.87/19.03 do 0 intro. intros zenon_H2f zenon_H5b zenon_H14f zenon_H150 zenon_H145 zenon_H57 zenon_H110 zenon_H71 zenon_H153 zenon_H133 zenon_H231 zenon_H7c zenon_H12b zenon_H255 zenon_H1e0 zenon_H95 zenon_H7a zenon_H128 zenon_H1ef zenon_H10a zenon_H6a zenon_H4a zenon_H124 zenon_H20d zenon_H139 zenon_H1a4 zenon_H3e zenon_H3f zenon_H45 zenon_H62 zenon_H6f zenon_H4f zenon_H201 zenon_H22 zenon_H10e zenon_H13f zenon_H168 zenon_H115 zenon_H9a zenon_H17e zenon_He3 zenon_H1d zenon_H11f zenon_Hf3 zenon_H1c7 zenon_H1ca zenon_He2 zenon_Hd5 zenon_Hdf zenon_H251 zenon_H250 zenon_Had zenon_He8 zenon_H18f zenon_H67 zenon_H54 zenon_H49 zenon_H27 zenon_Hd8 zenon_H130 zenon_H148 zenon_H149 zenon_H1ac zenon_H1c4 zenon_H6d zenon_Hf0 zenon_H2b zenon_H173 zenon_H3b zenon_H52. % 18.87/19.03 apply (zenon_or_s _ _ zenon_H2f); [ zenon_intro zenon_H34 | zenon_intro zenon_H33 ]. % 18.87/19.03 apply (zenon_L897_); trivial. % 18.87/19.03 apply (zenon_or_s _ _ zenon_H33); [ zenon_intro zenon_H36 | zenon_intro zenon_H35 ]. % 18.87/19.03 apply (zenon_L128_); trivial. % 18.87/19.03 apply (zenon_or_s _ _ zenon_H35); [ zenon_intro zenon_H2c | zenon_intro zenon_H37 ]. % 18.87/19.03 apply (zenon_or_s _ _ zenon_H1ac); [ zenon_intro zenon_H44 | zenon_intro zenon_H1af ]. % 18.87/19.03 apply (zenon_L100_); trivial. % 18.87/19.03 apply (zenon_or_s _ _ zenon_H1af); [ zenon_intro zenon_H1b1 | zenon_intro zenon_H1b0 ]. % 18.87/19.03 apply (zenon_L259_); trivial. % 18.87/19.03 apply (zenon_or_s _ _ zenon_H1b0); [ zenon_intro zenon_H61 | zenon_intro zenon_H60 ]. % 18.87/19.03 apply (zenon_L146_); trivial. % 18.87/19.03 apply (zenon_L805_); trivial. % 18.87/19.03 apply (zenon_L300_); trivial. % 18.87/19.03 (* end of lemma zenon_L898_ *) % 18.87/19.03 assert (zenon_L899_ : (((op (e2) (e0)) = (e3))\/(((op (e2) (e1)) = (e3))\/(((op (e2) (e2)) = (e3))\/((op (e2) (e3)) = (e3))))) -> (~((op (e0) (e3)) = (op (e1) (e3)))) -> (((op (e2) (e3)) = (e0))\/(((op (e2) (e3)) = (e1))\/(((op (e2) (e3)) = (e2))\/((op (e2) (e3)) = (e3))))) -> (~((op (e2) (e3)) = (op (e3) (e3)))) -> (~((op (e2) (e1)) = (op (e2) (e3)))) -> ((op (e2) (e1)) = (e2)) -> (~((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)) = (e1))) -> (~((op (e3) (e1)) = (e1))) -> (~((op (e3) (e0)) = (e1))) -> (((op (e3) (e0)) = (e1))\/(((op (e3) (e1)) = (e1))\/(((op (e3) (e2)) = (e1))\/((op (e3) (e3)) = (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 (e0) (e1)) = (e0)) -> (~((op (e0) (e1)) = (op (e2) (e1)))) -> (~((op (e1) (e2)) = (op (e2) (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) (e0)) = (e1))) -> (~((op (e2) (e0)) = (op (e2) (e1)))) -> ((op (e1) (e0)) = (e2)) -> ((op (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) (e2)) = (op (e3) (e2)))) -> ((op (e0) (e2)) = (e2)) -> ((op (e1) (e2)) = (e0)) -> (~((op (e1) (e2)) = (op (e3) (e2)))) -> (((op (e3) (e2)) = (e0))\/(((op (e3) (e2)) = (e1))\/(((op (e3) (e2)) = (e2))\/((op (e3) (e2)) = (e3))))) -> (~((op (e0) (e3)) = (op (e2) (e3)))) -> ((op (e0) (e3)) = (e3)) -> False). % 18.87/19.03 do 0 intro. intros zenon_He7 zenon_H1d zenon_H11f zenon_Hf3 zenon_H1c7 zenon_H1ca zenon_Hd5 zenon_Hdf zenon_H251 zenon_H250 zenon_Had zenon_He8 zenon_H110 zenon_H2f zenon_H17b zenon_H49 zenon_H17e zenon_H2b zenon_H259 zenon_H5b zenon_H1db zenon_H1f0 zenon_H86 zenon_H7a zenon_H1ac zenon_H18f zenon_H14f zenon_H150 zenon_H2a zenon_H115 zenon_H191 zenon_He2 zenon_He3. % 18.87/19.03 apply (zenon_or_s _ _ zenon_He7); [ zenon_intro zenon_H3b | zenon_intro zenon_He9 ]. % 18.87/19.03 apply (zenon_L33_); trivial. % 18.87/19.03 apply (zenon_or_s _ _ zenon_He9); [ zenon_intro zenon_Ha6 | zenon_intro zenon_Hea ]. % 18.87/19.03 apply (zenon_L806_); trivial. % 18.87/19.03 apply (zenon_or_s _ _ zenon_Hea); [ zenon_intro zenon_Haa | zenon_intro zenon_Hdd ]. % 18.87/19.03 apply (zenon_L181_); trivial. % 18.87/19.03 apply (zenon_L54_); trivial. % 18.87/19.03 (* end of lemma zenon_L899_ *) % 18.87/19.03 assert (zenon_L900_ : (((op (e0) (e0)) = (e3))\/(((op (e1) (e0)) = (e3))\/(((op (e2) (e0)) = (e3))\/((op (e3) (e0)) = (e3))))) -> (~((e1) = (e3))) -> (~((op (e3) (e0)) = (op (e3) (e3)))) -> ((op (e2) (e1)) = (e2)) -> (~((op (e2) (e1)) = (op (e2) (e3)))) -> ((op (e1) (e1)) = (e2)) -> (~((op (e1) (e1)) = (op (e1) (e3)))) -> (((op (e3) (e0)) = (e1))\/(((op (e3) (e1)) = (e1))\/(((op (e3) (e2)) = (e1))\/((op (e3) (e3)) = (e1))))) -> (~((op (e3) (e0)) = (e1))) -> (~((op (e3) (e1)) = (e1))) -> (~((op (e3) (e2)) = (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)) = (op (e3) (e0)))) -> (~((op (e2) (e2)) = (e2))) -> (~((op (e2) (e2)) = (op (e3) (e2)))) -> ((op (e0) (e2)) = (e3)) -> (((op (e2) (e2)) = (e0))\/(((op (e2) (e2)) = (e1))\/(((op (e2) (e2)) = (e2))\/((op (e2) (e2)) = (e3))))) -> (~((op (e1) (e2)) = (op (e1) (e3)))) -> (~((op (e0) (e2)) = (e1))) -> (((op (e0) (e2)) = (e1))\/(((op (e1) (e2)) = (e1))\/(((op (e2) (e2)) = (e1))\/((op (e3) (e2)) = (e1))))) -> (((op (e0) (e3)) = (e0))\/(((op (e1) (e3)) = (e0))\/(((op (e2) (e3)) = (e0))\/((op (e3) (e3)) = (e0))))) -> (~((op (e0) (e1)) = (op (e0) (e3)))) -> (((op (e1) (e0)) = (e1))\/(((op (e1) (e1)) = (e1))\/(((op (e1) (e2)) = (e1))\/((op (e1) (e3)) = (e1))))) -> (~((op (e1) (e1)) = (e1))) -> (~((op (e2) (e3)) = (e1))) -> (~((op (e0) (e3)) = (e1))) -> (((op (e0) (e3)) = (e1))\/(((op (e1) (e3)) = (e1))\/(((op (e2) (e3)) = (e1))\/((op (e3) (e3)) = (e1))))) -> (((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 (e2) (e0)) = (e0)) -> (~((op (e3) (e1)) = (op (e3) (e2)))) -> (~((op (e2) (e0)) = (op (e2) (e2)))) -> (~((op (e1) (e2)) = (op (e2) (e2)))) -> (~((op (e2) (e2)) = (op (e2) (e3)))) -> (~((op (e3) (e1)) = (op (e3) (e3)))) -> (~((op (e1) (e2)) = (op (e3) (e2)))) -> (~((op (e3) (e3)) = (e3))) -> (((op (e1) (e0)) = (e0))\/(((op (e1) (e0)) = (e1))\/(((op (e1) (e0)) = (e2))\/((op (e1) (e0)) = (e3))))) -> (~((op (e1) (e0)) = (op (e1) (e2)))) -> (~((op (e1) (e0)) = (e1))) -> (~((op (e1) (e3)) = (op (e2) (e3)))) -> (~((op (e1) (e0)) = (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)) = (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)) = (e1)) -> (~((op (e0) (e3)) = (op (e2) (e3)))) -> (((op (e0) (e3)) = (e3))\/(((op (e1) (e3)) = (e3))\/(((op (e2) (e3)) = (e3))\/((op (e3) (e3)) = (e3))))) -> (~((e0) = (e2))) -> (~((op (e1) (e0)) = (op (e2) (e0)))) -> (((op (e1) (e0)) = (e0))\/(((op (e1) (e1)) = (e0))\/(((op (e1) (e2)) = (e0))\/((op (e1) (e3)) = (e0))))) -> ((op (e3) (e0)) = (e2)) -> (~((e2) = (e3))) -> False). % 18.87/19.03 do 0 intro. intros zenon_H1e0 zenon_H95 zenon_H71 zenon_H1ca zenon_H1c7 zenon_H110 zenon_H57 zenon_He8 zenon_Had zenon_H250 zenon_H251 zenon_H145 zenon_H1ac zenon_H17b zenon_H173 zenon_H18f zenon_Ha9 zenon_H1c4 zenon_H124 zenon_H20d zenon_H139 zenon_H67 zenon_H54 zenon_H128 zenon_H10a zenon_H255 zenon_H231 zenon_H133 zenon_H6a zenon_H4a zenon_H49 zenon_H34 zenon_H1a4 zenon_H52 zenon_H2b zenon_H6d zenon_H130 zenon_H115 zenon_H102 zenon_H25e zenon_H24a zenon_H1ef zenon_Hdb zenon_Hd8 zenon_Hd5 zenon_Hdf zenon_H7a zenon_H11f zenon_Hf3 zenon_Ha5 zenon_He2 zenon_H136 zenon_H149 zenon_H201 zenon_H22 zenon_H148 zenon_H12b. % 18.87/19.03 apply (zenon_or_s _ _ zenon_H1e0); [ zenon_intro zenon_H3a | zenon_intro zenon_H1e1 ]. % 18.87/19.03 apply (zenon_L35_); trivial. % 18.87/19.03 apply (zenon_or_s _ _ zenon_H1e1); [ zenon_intro zenon_H9e | zenon_intro zenon_H1e2 ]. % 18.87/19.03 apply (zenon_L107_); trivial. % 18.87/19.03 apply (zenon_or_s _ _ zenon_H1e2); [ zenon_intro zenon_H3b | zenon_intro zenon_H15e ]. % 18.87/19.03 apply (zenon_L890_); trivial. % 18.87/19.03 apply (zenon_L109_); trivial. % 18.87/19.03 (* end of lemma zenon_L900_ *) % 18.87/19.03 assert (zenon_L901_ : (((op (e1) (e0)) = (e1))\/(((op (e1) (e1)) = (e1))\/(((op (e1) (e2)) = (e1))\/((op (e1) (e3)) = (e1))))) -> (~((op (e1) (e0)) = (e1))) -> (~((op (e1) (e1)) = (e1))) -> (~((op (e3) (e3)) = (e3))) -> (((op (e1) (e3)) = (e0))\/(((op (e1) (e3)) = (e1))\/(((op (e1) (e3)) = (e2))\/((op (e1) (e3)) = (e3))))) -> ((op (e0) (e3)) = (e2)) -> (~((op (e1) (e3)) = (op (e3) (e3)))) -> (~((op (e1) (e0)) = (op (e1) (e3)))) -> ((op (e1) (e0)) = (e2)) -> (~((op (e1) (e3)) = (op (e2) (e3)))) -> (((op (e2) (e3)) = (e0))\/(((op (e2) (e3)) = (e1))\/(((op (e2) (e3)) = (e2))\/((op (e2) (e3)) = (e3))))) -> (~((op (e2) (e3)) = (op (e3) (e3)))) -> (~((op (e2) (e1)) = (op (e2) (e3)))) -> ((op (e2) (e1)) = (e1)) -> (~((op (e0) (e3)) = (op (e2) (e3)))) -> (~((e2) = (e3))) -> (((op (e0) (e3)) = (e3))\/(((op (e1) (e3)) = (e3))\/(((op (e2) (e3)) = (e3))\/((op (e3) (e3)) = (e3))))) -> (~((op (e3) (e2)) = (e1))) -> (~((op (e3) (e1)) = (e1))) -> (~((op (e3) (e0)) = (e1))) -> (((op (e3) (e0)) = (e1))\/(((op (e3) (e1)) = (e1))\/(((op (e3) (e2)) = (e1))\/((op (e3) (e3)) = (e1))))) -> (~((op (e1) (e2)) = (op (e3) (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) (e1)) = (e0)) -> (~((op (e2) (e3)) = (e1))) -> (~((op (e0) (e3)) = (e1))) -> (((op (e0) (e3)) = (e1))\/(((op (e1) (e3)) = (e1))\/(((op (e2) (e3)) = (e1))\/((op (e3) (e3)) = (e1))))) -> (~((op (e2) (e0)) = (op (e2) (e3)))) -> ((op (e2) (e0)) = (e0)) -> (~((op (e3) (e1)) = (op (e3) (e3)))) -> (((op (e2) (e0)) = (e0))\/(((op (e2) (e1)) = (e0))\/(((op (e2) (e2)) = (e0))\/((op (e2) (e3)) = (e0))))) -> (~((op (e2) (e0)) = (op (e3) (e0)))) -> (~((op (e0) (e1)) = (op (e2) (e1)))) -> (~((op (e1) (e2)) = (op (e2) (e2)))) -> (((op (e2) (e0)) = (e0))\/(((op (e2) (e0)) = (e1))\/(((op (e2) (e0)) = (e2))\/((op (e2) (e0)) = (e3))))) -> (~((op (e2) (e0)) = (e1))) -> ((op (e2) (e1)) = (e2)) -> (~((op (e2) (e0)) = (op (e2) (e1)))) -> ((op (e0) (e0)) = (e1)) -> (((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) (e2)) = (e1))) -> (~((op (e1) (e2)) = (op (e1) (e3)))) -> (((op (e2) (e2)) = (e0))\/(((op (e2) (e2)) = (e1))\/(((op (e2) (e2)) = (e2))\/((op (e2) (e2)) = (e3))))) -> ((op (e0) (e2)) = (e3)) -> (~((op (e2) (e2)) = (op (e3) (e2)))) -> (~((op (e2) (e2)) = (e2))) -> ((op (e1) (e2)) = (e0)) -> False). % 18.87/19.03 do 0 intro. intros zenon_H128 zenon_H1ef zenon_H10a zenon_H102 zenon_Hdf zenon_Hcd zenon_Hd5 zenon_Hd8 zenon_H86 zenon_Hdb zenon_H11f zenon_Hf3 zenon_H1c7 zenon_Ha5 zenon_He2 zenon_H12b zenon_H136 zenon_H251 zenon_H250 zenon_Had zenon_He8 zenon_H115 zenon_H67 zenon_H54 zenon_H49 zenon_H255 zenon_H231 zenon_H133 zenon_H5b zenon_H34 zenon_H130 zenon_H2f zenon_H17b zenon_H17e zenon_H2b zenon_H259 zenon_H1db zenon_H1ca zenon_H1f0 zenon_H7a zenon_H1ac zenon_H139 zenon_H20d zenon_H124 zenon_H1c4 zenon_Ha9 zenon_H18f zenon_H173 zenon_H2a. % 18.87/19.03 apply (zenon_or_s _ _ zenon_H128); [ zenon_intro zenon_H9d | zenon_intro zenon_H129 ]. % 18.87/19.03 exact (zenon_H1ef zenon_H9d). % 18.87/19.03 apply (zenon_or_s _ _ zenon_H129); [ zenon_intro zenon_H10d | zenon_intro zenon_H12a ]. % 18.87/19.03 exact (zenon_H10a zenon_H10d). % 18.87/19.03 apply (zenon_or_s _ _ zenon_H12a); [ zenon_intro zenon_Hf0 | zenon_intro zenon_Hd6 ]. % 18.87/19.03 apply (zenon_L863_); trivial. % 18.87/19.03 apply (zenon_L720_); trivial. % 18.87/19.03 (* end of lemma zenon_L901_ *) % 18.87/19.03 assert (zenon_L902_ : (((op (e0) (e0)) = (e2))\/(((op (e1) (e0)) = (e2))\/(((op (e2) (e0)) = (e2))\/((op (e3) (e0)) = (e2))))) -> (~((op (e0) (e0)) = (op (e0) (e3)))) -> ((op (e1) (e1)) = (e2)) -> (~((op (e2) (e2)) = (e2))) -> (~((op (e2) (e2)) = (op (e3) (e2)))) -> (((op (e2) (e2)) = (e0))\/(((op (e2) (e2)) = (e1))\/(((op (e2) (e2)) = (e2))\/((op (e2) (e2)) = (e3))))) -> (~((op (e0) (e2)) = (e1))) -> (((op (e0) (e2)) = (e1))\/(((op (e1) (e2)) = (e1))\/(((op (e2) (e2)) = (e1))\/((op (e3) (e2)) = (e1))))) -> (~((op (e2) (e0)) = (op (e2) (e1)))) -> ((op (e2) (e1)) = (e2)) -> (~((op (e2) (e0)) = (e1))) -> (((op (e2) (e0)) = (e0))\/(((op (e2) (e0)) = (e1))\/(((op (e2) (e0)) = (e2))\/((op (e2) (e0)) = (e3))))) -> (~((op (e1) (e2)) = (op (e2) (e2)))) -> (~((op (e0) (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)) = (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)) = (op (e2) (e0)))) -> (~((op (e3) (e2)) = (op (e3) (e3)))) -> (~((op (e1) (e1)) = (op (e1) (e3)))) -> (~((op (e2) (e0)) = (op (e2) (e2)))) -> (~((op (e1) (e1)) = (op (e1) (e2)))) -> (~((op (e0) (e1)) = (op (e0) (e2)))) -> (((op (e0) (e2)) = (e0))\/(((op (e1) (e2)) = (e0))\/(((op (e2) (e2)) = (e0))\/((op (e3) (e2)) = (e0))))) -> (~((op (e1) (e3)) = (op (e3) (e3)))) -> (((op (e3) (e0)) = (e0))\/(((op (e3) (e1)) = (e0))\/(((op (e3) (e2)) = (e0))\/((op (e3) (e3)) = (e0))))) -> (~((e0) = (e2))) -> (~((op (e3) (e1)) = (op (e3) (e3)))) -> ((op (e2) (e0)) = (e0)) -> (~((op (e2) (e0)) = (op (e2) (e3)))) -> (((op (e0) (e3)) = (e1))\/(((op (e1) (e3)) = (e1))\/(((op (e2) (e3)) = (e1))\/((op (e3) (e3)) = (e1))))) -> (~((op (e0) (e3)) = (e1))) -> (~((op (e1) (e2)) = (op (e1) (e3)))) -> (~((op (e2) (e3)) = (e1))) -> ((op (e0) (e1)) = (e0)) -> (~((op (e0) (e1)) = (op (e0) (e3)))) -> (((op (e0) (e3)) = (e0))\/(((op (e1) (e3)) = (e0))\/(((op (e2) (e3)) = (e0))\/((op (e3) (e3)) = (e0))))) -> (~((op (e1) (e2)) = (op (e3) (e2)))) -> (((op (e0) (e3)) = (e3))\/(((op (e1) (e3)) = (e3))\/(((op (e2) (e3)) = (e3))\/((op (e3) (e3)) = (e3))))) -> (~((e2) = (e3))) -> (~((op (e0) (e3)) = (op (e2) (e3)))) -> ((op (e2) (e1)) = (e1)) -> (~((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))))) -> ((op (e0) (e0)) = (e1)) -> (((op (e1) (e3)) = (e0))\/(((op (e1) (e3)) = (e1))\/(((op (e1) (e3)) = (e2))\/((op (e1) (e3)) = (e3))))) -> (~((op (e1) (e0)) = (op (e1) (e3)))) -> (~((op (e1) (e3)) = (op (e2) (e3)))) -> (~((op (e1) (e0)) = (e1))) -> (~((op (e1) (e0)) = (op (e1) (e2)))) -> (((op (e1) (e0)) = (e0))\/(((op (e1) (e0)) = (e1))\/(((op (e1) (e0)) = (e2))\/((op (e1) (e0)) = (e3))))) -> (~((op (e3) (e3)) = (e3))) -> (~((op (e1) (e1)) = (e1))) -> (((op (e1) (e0)) = (e1))\/(((op (e1) (e1)) = (e1))\/(((op (e1) (e2)) = (e1))\/((op (e1) (e3)) = (e1))))) -> (((op (e3) (e0)) = (e1))\/(((op (e3) (e1)) = (e1))\/(((op (e3) (e2)) = (e1))\/((op (e3) (e3)) = (e1))))) -> (~((op (e3) (e0)) = (e1))) -> (~((op (e3) (e1)) = (e1))) -> (~((op (e3) (e2)) = (e1))) -> ((op (e0) (e3)) = (e2)) -> False). % 18.87/19.03 do 0 intro. intros zenon_H1fe zenon_H189 zenon_H110 zenon_H173 zenon_H18f zenon_H1c4 zenon_H20d zenon_H139 zenon_H1f0 zenon_H1ca zenon_H1db zenon_H259 zenon_H2b zenon_H17e zenon_H17b zenon_H2f zenon_H9a zenon_H95 zenon_H168 zenon_H22 zenon_H201 zenon_H62 zenon_H57 zenon_H52 zenon_H4f zenon_H4a zenon_H6a zenon_Hd5 zenon_H1ac zenon_H149 zenon_H130 zenon_H34 zenon_H5b zenon_H133 zenon_H231 zenon_H124 zenon_H255 zenon_H49 zenon_H54 zenon_H67 zenon_H115 zenon_H136 zenon_H12b zenon_He2 zenon_Ha5 zenon_H1c7 zenon_Hf3 zenon_H11f zenon_H7a zenon_Hdf zenon_Hd8 zenon_Hdb zenon_H1ef zenon_H24a zenon_H25e zenon_H102 zenon_H10a zenon_H128 zenon_He8 zenon_Had zenon_H250 zenon_H251 zenon_Hcd. % 18.87/19.03 apply (zenon_or_s _ _ zenon_H1fe); [ zenon_intro zenon_H7b | zenon_intro zenon_H1ff ]. % 18.87/19.03 apply (zenon_L375_); trivial. % 18.87/19.03 apply (zenon_or_s _ _ zenon_H1ff); [ zenon_intro zenon_H86 | zenon_intro zenon_H200 ]. % 18.87/19.03 apply (zenon_or_s _ _ zenon_H168); [ zenon_intro zenon_H3a | zenon_intro zenon_H169 ]. % 18.87/19.03 apply (zenon_L35_); trivial. % 18.87/19.03 apply (zenon_or_s _ _ zenon_H169); [ zenon_intro zenon_H99 | zenon_intro zenon_H16a ]. % 18.87/19.03 apply (zenon_L36_); trivial. % 18.87/19.03 apply (zenon_or_s _ _ zenon_H16a); [ zenon_intro zenon_Ha9 | zenon_intro zenon_He3 ]. % 18.87/19.03 apply (zenon_or_s _ _ zenon_H22); [ zenon_intro zenon_H27 | zenon_intro zenon_H26 ]. % 18.87/19.03 apply (zenon_L332_); trivial. % 18.87/19.03 apply (zenon_or_s _ _ zenon_H26); [ zenon_intro zenon_H29 | zenon_intro zenon_H28 ]. % 18.87/19.03 apply (zenon_L354_); trivial. % 18.87/19.03 apply (zenon_or_s _ _ zenon_H28); [ zenon_intro zenon_H2a | zenon_intro zenon_H1f ]. % 18.87/19.03 apply (zenon_L901_); trivial. % 18.87/19.03 apply (zenon_L803_); trivial. % 18.87/19.03 apply (zenon_L81_); trivial. % 18.87/19.03 apply (zenon_or_s _ _ zenon_H200); [ zenon_intro zenon_Hee | zenon_intro zenon_H148 ]. % 18.87/19.03 apply (zenon_L204_); trivial. % 18.87/19.03 apply (zenon_L864_); trivial. % 18.87/19.03 (* end of lemma zenon_L902_ *) % 18.87/19.03 assert (zenon_L903_ : (((op (e0) (e3)) = (e1))\/(((op (e1) (e3)) = (e1))\/(((op (e2) (e3)) = (e1))\/((op (e3) (e3)) = (e1))))) -> (~((op (e0) (e3)) = (e1))) -> ((op (e1) (e2)) = (e0)) -> (~((op (e2) (e2)) = (e2))) -> (~((op (e2) (e2)) = (op (e3) (e2)))) -> ((op (e0) (e2)) = (e3)) -> (((op (e2) (e2)) = (e0))\/(((op (e2) (e2)) = (e1))\/(((op (e2) (e2)) = (e2))\/((op (e2) (e2)) = (e3))))) -> (~((op (e1) (e2)) = (op (e1) (e3)))) -> (~((op (e0) (e2)) = (e1))) -> (((op (e0) (e2)) = (e1))\/(((op (e1) (e2)) = (e1))\/(((op (e2) (e2)) = (e1))\/((op (e3) (e2)) = (e1))))) -> (~((op (e2) (e3)) = (e1))) -> (((op (e0) (e3)) = (e2))\/(((op (e1) (e3)) = (e2))\/(((op (e2) (e3)) = (e2))\/((op (e3) (e3)) = (e2))))) -> ((op (e1) (e3)) = (e0)) -> (~((op (e1) (e1)) = (op (e1) (e3)))) -> ((op (e1) (e1)) = (e2)) -> (~((op (e2) (e1)) = (op (e2) (e3)))) -> ((op (e2) (e1)) = (e2)) -> ((op (e3) (e1)) = (e2)) -> (~((op (e3) (e1)) = (op (e3) (e3)))) -> False). % 18.87/19.03 do 0 intro. intros zenon_H133 zenon_H231 zenon_H2a zenon_H173 zenon_H18f zenon_Ha9 zenon_H1c4 zenon_H124 zenon_H20d zenon_H139 zenon_H255 zenon_H145 zenon_H1f zenon_H57 zenon_H110 zenon_H1c7 zenon_H1ca zenon_H14d zenon_H130. % 18.87/19.03 apply (zenon_or_s _ _ zenon_H133); [ zenon_intro zenon_Hc3 | zenon_intro zenon_H134 ]. % 18.87/19.03 exact (zenon_H231 zenon_Hc3). % 18.87/19.03 apply (zenon_or_s _ _ zenon_H134); [ zenon_intro zenon_Hd6 | zenon_intro zenon_H135 ]. % 18.87/19.03 apply (zenon_L720_); trivial. % 18.87/19.03 apply (zenon_or_s _ _ zenon_H135); [ zenon_intro zenon_Hf4 | zenon_intro zenon_Hc4 ]. % 18.87/19.03 exact (zenon_H255 zenon_Hf4). % 18.87/19.03 apply (zenon_L788_); trivial. % 18.87/19.03 (* end of lemma zenon_L903_ *) % 18.87/19.03 assert (zenon_L904_ : (((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)) -> (~((op (e0) (e1)) = (op (e1) (e1)))) -> ((op (e3) (e1)) = (e0)) -> (~((op (e3) (e1)) = (op (e3) (e2)))) -> (~((op (e2) (e0)) = (op (e2) (e2)))) -> ((op (e2) (e0)) = (e0)) -> (((op (e0) (e3)) = (e1))\/(((op (e1) (e3)) = (e1))\/(((op (e2) (e3)) = (e1))\/((op (e3) (e3)) = (e1))))) -> (~((op (e0) (e3)) = (e1))) -> (~((op (e2) (e2)) = (e2))) -> (~((op (e2) (e2)) = (op (e3) (e2)))) -> (((op (e2) (e2)) = (e0))\/(((op (e2) (e2)) = (e1))\/(((op (e2) (e2)) = (e2))\/((op (e2) (e2)) = (e3))))) -> (~((op (e1) (e2)) = (op (e1) (e3)))) -> (~((op (e0) (e2)) = (e1))) -> (((op (e0) (e2)) = (e1))\/(((op (e1) (e2)) = (e1))\/(((op (e2) (e2)) = (e1))\/((op (e3) (e2)) = (e1))))) -> (~((op (e2) (e3)) = (e1))) -> (~((op (e1) (e1)) = (op (e1) (e3)))) -> ((op (e1) (e1)) = (e2)) -> ((op (e0) (e2)) = (e2)) -> (~((e0) = (e2))) -> (((op (e0) (e2)) = (e0))\/(((op (e1) (e2)) = (e0))\/(((op (e2) (e2)) = (e0))\/((op (e3) (e2)) = (e0))))) -> (((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 (e2) (e0)) = (op (e2) (e3)))) -> (~((op (e0) (e1)) = (op (e0) (e2)))) -> (~((op (e1) (e1)) = (op (e1) (e2)))) -> (~((op (e3) (e2)) = (op (e3) (e3)))) -> (~((op (e1) (e0)) = (op (e2) (e0)))) -> (((op (e1) (e0)) = (e0))\/(((op (e1) (e1)) = (e0))\/(((op (e1) (e2)) = (e0))\/((op (e1) (e3)) = (e0))))) -> (((op (e0) (e3)) = (e2))\/(((op (e1) (e3)) = (e2))\/(((op (e2) (e3)) = (e2))\/((op (e3) (e3)) = (e2))))) -> (~((e2) = (e3))) -> (~((op (e1) (e0)) = (op (e1) (e3)))) -> ((op (e1) (e0)) = (e2)) -> (~((op (e2) (e1)) = (op (e2) (e3)))) -> ((op (e2) (e1)) = (e2)) -> ((op (e3) (e1)) = (e2)) -> (~((op (e3) (e1)) = (op (e3) (e3)))) -> False). % 18.87/19.03 do 0 intro. intros zenon_H168 zenon_H95 zenon_H7a zenon_H13f zenon_H10e zenon_H1b1 zenon_H1a4 zenon_H52 zenon_H34 zenon_H133 zenon_H231 zenon_H173 zenon_H18f zenon_H1c4 zenon_H124 zenon_H20d zenon_H139 zenon_H255 zenon_H57 zenon_H110 zenon_H150 zenon_H149 zenon_H6a zenon_H67 zenon_H54 zenon_H49 zenon_H5b zenon_H4a zenon_H4f zenon_H62 zenon_H201 zenon_H22 zenon_H145 zenon_H12b zenon_Hd8 zenon_H86 zenon_H1c7 zenon_H1ca zenon_H14d zenon_H130. % 18.87/19.03 apply (zenon_or_s _ _ zenon_H168); [ zenon_intro zenon_H3a | zenon_intro zenon_H169 ]. % 18.87/19.03 apply (zenon_L35_); trivial. % 18.87/19.03 apply (zenon_or_s _ _ zenon_H169); [ zenon_intro zenon_H99 | zenon_intro zenon_H16a ]. % 18.87/19.03 apply (zenon_L108_); trivial. % 18.87/19.03 apply (zenon_or_s _ _ zenon_H16a); [ zenon_intro zenon_Ha9 | zenon_intro zenon_He3 ]. % 18.87/19.03 apply (zenon_or_s _ _ zenon_H22); [ zenon_intro zenon_H27 | zenon_intro zenon_H26 ]. % 18.87/19.03 apply (zenon_L332_); trivial. % 18.87/19.03 apply (zenon_or_s _ _ zenon_H26); [ zenon_intro zenon_H29 | zenon_intro zenon_H28 ]. % 18.87/19.03 apply (zenon_L17_); trivial. % 18.87/19.03 apply (zenon_or_s _ _ zenon_H28); [ zenon_intro zenon_H2a | zenon_intro zenon_H1f ]. % 18.87/19.03 apply (zenon_or_s _ _ zenon_H67); [ zenon_intro zenon_H1e | zenon_intro zenon_H68 ]. % 18.87/19.03 apply (zenon_L12_); trivial. % 18.87/19.03 apply (zenon_or_s _ _ zenon_H68); [ zenon_intro zenon_H1f | zenon_intro zenon_H69 ]. % 18.87/19.03 apply (zenon_L903_); trivial. % 18.87/19.03 apply (zenon_or_s _ _ zenon_H69); [ zenon_intro zenon_H37 | zenon_intro zenon_H60 ]. % 18.87/19.03 apply (zenon_L14_); trivial. % 18.87/19.03 apply (zenon_L244_); trivial. % 18.87/19.03 apply (zenon_or_s _ _ zenon_H6a); [ zenon_intro zenon_H48 | zenon_intro zenon_H6b ]. % 18.87/19.03 apply (zenon_L378_); trivial. % 18.87/19.03 apply (zenon_or_s _ _ zenon_H6b); [ zenon_intro zenon_H2a | zenon_intro zenon_H6c ]. % 18.87/19.03 apply (zenon_L903_); trivial. % 18.87/19.03 apply (zenon_or_s _ _ zenon_H6c); [ zenon_intro zenon_H2c | zenon_intro zenon_H61 ]. % 18.87/19.03 apply (zenon_L11_); trivial. % 18.87/19.03 apply (zenon_L247_); trivial. % 18.87/19.03 apply (zenon_L739_); trivial. % 18.87/19.03 (* end of lemma zenon_L904_ *) % 18.87/19.03 assert (zenon_L905_ : (((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)) = (e1)) -> (~((op (e3) (e1)) = (op (e3) (e3)))) -> ((op (e2) (e1)) = (e2)) -> (~((op (e2) (e1)) = (op (e2) (e3)))) -> ((op (e1) (e0)) = (e2)) -> (~((op (e1) (e0)) = (op (e1) (e3)))) -> (~((e2) = (e3))) -> (((op (e0) (e3)) = (e2))\/(((op (e1) (e3)) = (e2))\/(((op (e2) (e3)) = (e2))\/((op (e3) (e3)) = (e2))))) -> (((op (e1) (e0)) = (e0))\/(((op (e1) (e1)) = (e0))\/(((op (e1) (e2)) = (e0))\/((op (e1) (e3)) = (e0))))) -> (~((op (e1) (e0)) = (op (e2) (e0)))) -> (~((op (e3) (e2)) = (op (e3) (e3)))) -> (~((op (e1) (e1)) = (op (e1) (e2)))) -> (~((op (e0) (e1)) = (op (e0) (e2)))) -> ((op (e0) (e1)) = (e0)) -> (~((op (e0) (e1)) = (op (e0) (e3)))) -> (((op (e0) (e3)) = (e0))\/(((op (e1) (e3)) = (e0))\/(((op (e2) (e3)) = (e0))\/((op (e3) (e3)) = (e0))))) -> (((op (e0) (e2)) = (e0))\/(((op (e1) (e2)) = (e0))\/(((op (e2) (e2)) = (e0))\/((op (e3) (e2)) = (e0))))) -> (~((e0) = (e2))) -> ((op (e1) (e1)) = (e2)) -> (~((op (e1) (e1)) = (op (e1) (e3)))) -> (~((op (e2) (e3)) = (e1))) -> (((op (e0) (e2)) = (e1))\/(((op (e1) (e2)) = (e1))\/(((op (e2) (e2)) = (e1))\/((op (e3) (e2)) = (e1))))) -> (~((op (e0) (e2)) = (e1))) -> (~((op (e1) (e2)) = (op (e1) (e3)))) -> (((op (e2) (e2)) = (e0))\/(((op (e2) (e2)) = (e1))\/(((op (e2) (e2)) = (e2))\/((op (e2) (e2)) = (e3))))) -> (~((op (e2) (e2)) = (op (e3) (e2)))) -> (~((op (e2) (e2)) = (e2))) -> (~((op (e0) (e3)) = (e1))) -> (((op (e0) (e3)) = (e1))\/(((op (e1) (e3)) = (e1))\/(((op (e2) (e3)) = (e1))\/((op (e3) (e3)) = (e1))))) -> (~((op (e2) (e0)) = (op (e2) (e2)))) -> (~((op (e3) (e1)) = (op (e3) (e2)))) -> ((op (e3) (e1)) = (e0)) -> (~((op (e0) (e1)) = (op (e1) (e1)))) -> ((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 (e0) (e2)) = (e2)) -> (~((op (e0) (e2)) = (op (e3) (e2)))) -> (((op (e2) (e3)) = (e0))\/(((op (e2) (e3)) = (e1))\/(((op (e2) (e3)) = (e2))\/((op (e2) (e3)) = (e3))))) -> (~((op (e2) (e0)) = (op (e2) (e3)))) -> ((op (e2) (e0)) = (e0)) -> ((op (e1) (e3)) = (e0)) -> (~((op (e2) (e3)) = (op (e3) (e3)))) -> (~((op (e0) (e3)) = (op (e2) (e3)))) -> ((op (e0) (e3)) = (e3)) -> False). % 18.87/19.03 do 0 intro. intros zenon_H153 zenon_H71 zenon_Hc4 zenon_H130 zenon_H1ca zenon_H1c7 zenon_H86 zenon_Hd8 zenon_H12b zenon_H145 zenon_H22 zenon_H201 zenon_H62 zenon_H4f zenon_H4a zenon_H49 zenon_H54 zenon_H67 zenon_H6a zenon_H149 zenon_H110 zenon_H57 zenon_H255 zenon_H139 zenon_H20d zenon_H124 zenon_H1c4 zenon_H18f zenon_H173 zenon_H231 zenon_H133 zenon_H52 zenon_H1a4 zenon_H1b1 zenon_H10e zenon_H13f zenon_H7a zenon_H95 zenon_H168 zenon_H150 zenon_H14f zenon_H11f zenon_H5b zenon_H34 zenon_H1f zenon_Hf3 zenon_He2 zenon_He3. % 18.87/19.03 apply (zenon_or_s _ _ zenon_H153); [ zenon_intro zenon_H148 | zenon_intro zenon_H154 ]. % 18.87/19.03 apply (zenon_L892_); trivial. % 18.87/19.03 apply (zenon_or_s _ _ zenon_H154); [ zenon_intro zenon_H14d | zenon_intro zenon_H155 ]. % 18.87/19.03 apply (zenon_L904_); trivial. % 18.87/19.03 apply (zenon_or_s _ _ zenon_H155); [ zenon_intro zenon_H151 | zenon_intro zenon_Hf6 ]. % 18.87/19.03 apply (zenon_L104_); trivial. % 18.87/19.03 apply (zenon_L225_); trivial. % 18.87/19.03 (* end of lemma zenon_L905_ *) % 18.87/19.03 assert (zenon_L906_ : (((op (e3) (e0)) = (e1))\/(((op (e3) (e1)) = (e1))\/(((op (e3) (e2)) = (e1))\/((op (e3) (e3)) = (e1))))) -> ((op (e1) (e2)) = (e1)) -> (~((op (e3) (e1)) = (e1))) -> (~((op (e3) (e2)) = (e1))) -> (((op (e3) (e0)) = (e2))\/(((op (e3) (e1)) = (e2))\/(((op (e3) (e2)) = (e2))\/((op (e3) (e3)) = (e2))))) -> (~((op (e3) (e0)) = (op (e3) (e3)))) -> (~((op (e3) (e1)) = (op (e3) (e3)))) -> ((op (e2) (e1)) = (e2)) -> (~((op (e2) (e1)) = (op (e2) (e3)))) -> ((op (e1) (e0)) = (e2)) -> (~((op (e1) (e0)) = (op (e1) (e3)))) -> (~((e2) = (e3))) -> (((op (e0) (e3)) = (e2))\/(((op (e1) (e3)) = (e2))\/(((op (e2) (e3)) = (e2))\/((op (e3) (e3)) = (e2))))) -> (((op (e1) (e0)) = (e0))\/(((op (e1) (e1)) = (e0))\/(((op (e1) (e2)) = (e0))\/((op (e1) (e3)) = (e0))))) -> (~((op (e1) (e0)) = (op (e2) (e0)))) -> (~((op (e3) (e2)) = (op (e3) (e3)))) -> (~((op (e1) (e1)) = (op (e1) (e2)))) -> (~((op (e0) (e1)) = (op (e0) (e2)))) -> ((op (e0) (e1)) = (e0)) -> (~((op (e0) (e1)) = (op (e0) (e3)))) -> (((op (e0) (e3)) = (e0))\/(((op (e1) (e3)) = (e0))\/(((op (e2) (e3)) = (e0))\/((op (e3) (e3)) = (e0))))) -> (((op (e0) (e2)) = (e0))\/(((op (e1) (e2)) = (e0))\/(((op (e2) (e2)) = (e0))\/((op (e3) (e2)) = (e0))))) -> (~((e0) = (e2))) -> ((op (e1) (e1)) = (e2)) -> (~((op (e1) (e1)) = (op (e1) (e3)))) -> (~((op (e2) (e3)) = (e1))) -> (((op (e0) (e2)) = (e1))\/(((op (e1) (e2)) = (e1))\/(((op (e2) (e2)) = (e1))\/((op (e3) (e2)) = (e1))))) -> (~((op (e0) (e2)) = (e1))) -> (~((op (e1) (e2)) = (op (e1) (e3)))) -> (((op (e2) (e2)) = (e0))\/(((op (e2) (e2)) = (e1))\/(((op (e2) (e2)) = (e2))\/((op (e2) (e2)) = (e3))))) -> (~((op (e2) (e2)) = (op (e3) (e2)))) -> (~((op (e2) (e2)) = (e2))) -> (~((op (e0) (e3)) = (e1))) -> (((op (e0) (e3)) = (e1))\/(((op (e1) (e3)) = (e1))\/(((op (e2) (e3)) = (e1))\/((op (e3) (e3)) = (e1))))) -> (~((op (e2) (e0)) = (op (e2) (e2)))) -> (~((op (e3) (e1)) = (op (e3) (e2)))) -> ((op (e3) (e1)) = (e0)) -> (~((op (e0) (e1)) = (op (e1) (e1)))) -> ((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 (e0) (e2)) = (e2)) -> (~((op (e0) (e2)) = (op (e3) (e2)))) -> (((op (e2) (e3)) = (e0))\/(((op (e2) (e3)) = (e1))\/(((op (e2) (e3)) = (e2))\/((op (e2) (e3)) = (e3))))) -> (~((op (e2) (e0)) = (op (e2) (e3)))) -> ((op (e2) (e0)) = (e0)) -> ((op (e1) (e3)) = (e0)) -> (~((op (e2) (e3)) = (op (e3) (e3)))) -> (~((op (e0) (e3)) = (op (e2) (e3)))) -> ((op (e0) (e3)) = (e3)) -> False). % 18.87/19.03 do 0 intro. intros zenon_He8 zenon_Hf0 zenon_H250 zenon_H251 zenon_H153 zenon_H71 zenon_H130 zenon_H1ca zenon_H1c7 zenon_H86 zenon_Hd8 zenon_H12b zenon_H145 zenon_H22 zenon_H201 zenon_H62 zenon_H4f zenon_H4a zenon_H49 zenon_H54 zenon_H67 zenon_H6a zenon_H149 zenon_H110 zenon_H57 zenon_H255 zenon_H139 zenon_H20d zenon_H124 zenon_H1c4 zenon_H18f zenon_H173 zenon_H231 zenon_H133 zenon_H52 zenon_H1a4 zenon_H1b1 zenon_H10e zenon_H13f zenon_H7a zenon_H95 zenon_H168 zenon_H150 zenon_H14f zenon_H11f zenon_H5b zenon_H34 zenon_H1f zenon_Hf3 zenon_He2 zenon_He3. % 18.87/19.03 apply (zenon_or_s _ _ zenon_He8); [ zenon_intro zenon_Hac | zenon_intro zenon_Heb ]. % 18.87/19.03 apply (zenon_L787_); trivial. % 18.87/19.03 apply (zenon_or_s _ _ zenon_Heb); [ zenon_intro zenon_Hae | zenon_intro zenon_Hec ]. % 18.87/19.03 exact (zenon_H250 zenon_Hae). % 18.87/19.03 apply (zenon_or_s _ _ zenon_Hec); [ zenon_intro zenon_Hba | zenon_intro zenon_Hc4 ]. % 18.87/19.03 exact (zenon_H251 zenon_Hba). % 18.87/19.03 apply (zenon_L905_); trivial. % 18.87/19.03 (* end of lemma zenon_L906_ *) % 18.87/19.03 assert (zenon_L907_ : ((op (e0) (e3)) = (e3)) -> (~((op (e0) (e3)) = (op (e2) (e3)))) -> (~((op (e2) (e3)) = (op (e3) (e3)))) -> ((op (e2) (e0)) = (e0)) -> (((op (e2) (e3)) = (e0))\/(((op (e2) (e3)) = (e1))\/(((op (e2) (e3)) = (e2))\/((op (e2) (e3)) = (e3))))) -> (~((op (e0) (e2)) = (op (e3) (e2)))) -> ((op (e0) (e2)) = (e2)) -> (((op (e0) (e0)) = (e3))\/(((op (e0) (e1)) = (e3))\/(((op (e0) (e2)) = (e3))\/((op (e0) (e3)) = (e3))))) -> (~((e1) = (e3))) -> ((op (e1) (e1)) = (e3)) -> (~((op (e0) (e1)) = (op (e1) (e1)))) -> (~((op (e3) (e1)) = (op (e3) (e2)))) -> (~((op (e2) (e0)) = (op (e2) (e2)))) -> (((op (e0) (e3)) = (e1))\/(((op (e1) (e3)) = (e1))\/(((op (e2) (e3)) = (e1))\/((op (e3) (e3)) = (e1))))) -> (~((op (e0) (e3)) = (e1))) -> (~((op (e2) (e2)) = (e2))) -> (~((op (e2) (e2)) = (op (e3) (e2)))) -> (((op (e2) (e2)) = (e0))\/(((op (e2) (e2)) = (e1))\/(((op (e2) (e2)) = (e2))\/((op (e2) (e2)) = (e3))))) -> (~((op (e1) (e2)) = (op (e1) (e3)))) -> (~((op (e0) (e2)) = (e1))) -> (((op (e0) (e2)) = (e1))\/(((op (e1) (e2)) = (e1))\/(((op (e2) (e2)) = (e1))\/((op (e3) (e2)) = (e1))))) -> (~((op (e2) (e3)) = (e1))) -> (~((op (e1) (e1)) = (op (e1) (e3)))) -> ((op (e1) (e1)) = (e2)) -> (~((e0) = (e2))) -> (((op (e0) (e2)) = (e0))\/(((op (e1) (e2)) = (e0))\/(((op (e2) (e2)) = (e0))\/((op (e3) (e2)) = (e0))))) -> (((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 (e0) (e1)) = (op (e0) (e2)))) -> (~((op (e1) (e1)) = (op (e1) (e2)))) -> (~((op (e3) (e2)) = (op (e3) (e3)))) -> (~((op (e1) (e0)) = (op (e2) (e0)))) -> (((op (e1) (e0)) = (e0))\/(((op (e1) (e1)) = (e0))\/(((op (e1) (e2)) = (e0))\/((op (e1) (e3)) = (e0))))) -> (((op (e0) (e3)) = (e2))\/(((op (e1) (e3)) = (e2))\/(((op (e2) (e3)) = (e2))\/((op (e3) (e3)) = (e2))))) -> (~((e2) = (e3))) -> (~((op (e1) (e0)) = (op (e1) (e3)))) -> (~((op (e2) (e1)) = (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) (e2)) = (e1))) -> (~((op (e3) (e1)) = (e1))) -> ((op (e1) (e2)) = (e1)) -> (((op (e3) (e0)) = (e1))\/(((op (e3) (e1)) = (e1))\/(((op (e3) (e2)) = (e1))\/((op (e3) (e3)) = (e1))))) -> ((op (e0) (e0)) = (e1)) -> ((op (e1) (e0)) = (e2)) -> (~((op (e2) (e0)) = (op (e2) (e1)))) -> ((op (e2) (e1)) = (e2)) -> (~((op (e2) (e0)) = (e1))) -> (~((op (e2) (e0)) = (op (e2) (e3)))) -> (((op (e2) (e0)) = (e0))\/(((op (e2) (e0)) = (e1))\/(((op (e2) (e0)) = (e2))\/((op (e2) (e0)) = (e3))))) -> ((op (e3) (e1)) = (e0)) -> (~((op (e3) (e1)) = (op (e3) (e3)))) -> False). % 18.87/19.03 do 0 intro. intros zenon_He3 zenon_He2 zenon_Hf3 zenon_H34 zenon_H11f zenon_H14f zenon_H150 zenon_H168 zenon_H95 zenon_H13f zenon_H10e zenon_H1a4 zenon_H52 zenon_H133 zenon_H231 zenon_H173 zenon_H18f zenon_H1c4 zenon_H124 zenon_H20d zenon_H139 zenon_H255 zenon_H57 zenon_H110 zenon_H149 zenon_H6a zenon_H67 zenon_H54 zenon_H49 zenon_H4a zenon_H4f zenon_H62 zenon_H201 zenon_H22 zenon_H145 zenon_H12b zenon_Hd8 zenon_H1c7 zenon_H71 zenon_H153 zenon_H251 zenon_H250 zenon_Hf0 zenon_He8 zenon_H7a zenon_H86 zenon_H1f0 zenon_H1ca zenon_H1db zenon_H5b zenon_H259 zenon_H1b1 zenon_H130. % 18.87/19.03 apply (zenon_or_s _ _ zenon_H67); [ zenon_intro zenon_H1e | zenon_intro zenon_H68 ]. % 18.87/19.03 apply (zenon_L12_); trivial. % 18.87/19.03 apply (zenon_or_s _ _ zenon_H68); [ zenon_intro zenon_H1f | zenon_intro zenon_H69 ]. % 18.87/19.03 apply (zenon_L906_); trivial. % 18.87/19.03 apply (zenon_or_s _ _ zenon_H69); [ zenon_intro zenon_H37 | zenon_intro zenon_H60 ]. % 18.87/19.03 apply (zenon_L729_); trivial. % 18.87/19.03 apply (zenon_L244_); trivial. % 18.87/19.03 (* end of lemma zenon_L907_ *) % 18.87/19.03 assert (zenon_L908_ : (((op (e0) (e0)) = (e2))\/(((op (e1) (e0)) = (e2))\/(((op (e2) (e0)) = (e2))\/((op (e3) (e0)) = (e2))))) -> (~((e0) = (e3))) -> (~((op (e0) (e2)) = (op (e3) (e2)))) -> ((op (e0) (e2)) = (e2)) -> (~((op (e1) (e0)) = (op (e1) (e3)))) -> (((op (e3) (e0)) = (e2))\/(((op (e3) (e1)) = (e2))\/(((op (e3) (e2)) = (e2))\/((op (e3) (e3)) = (e2))))) -> (~((op (e3) (e2)) = (e1))) -> (~((op (e3) (e1)) = (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) (e0)) = (e1))) -> (((op (e2) (e0)) = (e0))\/(((op (e2) (e0)) = (e1))\/(((op (e2) (e0)) = (e2))\/((op (e2) (e0)) = (e3))))) -> (~((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) (e3)) = (e3))\/(((op (e1) (e3)) = (e3))\/(((op (e2) (e3)) = (e3))\/((op (e3) (e3)) = (e3))))) -> (~((e0) = (e2))) -> (((op (e0) (e0)) = (e3))\/(((op (e0) (e1)) = (e3))\/(((op (e0) (e2)) = (e3))\/((op (e0) (e3)) = (e3))))) -> ((op (e1) (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 (e1) (e0)) = (op (e2) (e0)))) -> (~((op (e1) (e1)) = (op (e1) (e2)))) -> (~((op (e3) (e0)) = (op (e3) (e2)))) -> (~((op (e3) (e2)) = (op (e3) (e3)))) -> (~((op (e1) (e0)) = (op (e1) (e1)))) -> (~((op (e0) (e0)) = (e0))) -> (((op (e0) (e0)) = (e0))\/(((op (e1) (e0)) = (e0))\/(((op (e2) (e0)) = (e0))\/((op (e3) (e0)) = (e0))))) -> (~((op (e1) (e2)) = (op (e2) (e2)))) -> (~((op (e2) (e2)) = (op (e2) (e3)))) -> (~((op (e3) (e1)) = (op (e3) (e2)))) -> (~((op (e2) (e0)) = (op (e2) (e2)))) -> (((op (e0) (e2)) = (e1))\/(((op (e1) (e2)) = (e1))\/(((op (e2) (e2)) = (e1))\/((op (e3) (e2)) = (e1))))) -> (~((op (e0) (e2)) = (e1))) -> (~((op (e1) (e2)) = (op (e1) (e3)))) -> (((op (e2) (e2)) = (e0))\/(((op (e2) (e2)) = (e1))\/(((op (e2) (e2)) = (e2))\/((op (e2) (e2)) = (e3))))) -> (~((op (e2) (e2)) = (op (e3) (e2)))) -> (~((op (e2) (e2)) = (e2))) -> (~((op (e0) (e1)) = (op (e0) (e2)))) -> (((op (e0) (e2)) = (e0))\/(((op (e1) (e2)) = (e0))\/(((op (e2) (e2)) = (e0))\/((op (e3) (e2)) = (e0))))) -> (~((op (e1) (e1)) = (e1))) -> (~((op (e1) (e0)) = (e1))) -> (((op (e1) (e0)) = (e1))\/(((op (e1) (e1)) = (e1))\/(((op (e1) (e2)) = (e1))\/((op (e1) (e3)) = (e1))))) -> (~((op (e1) (e1)) = (op (e1) (e3)))) -> ((op (e1) (e1)) = (e2)) -> ((op (e0) (e0)) = (e1)) -> (~((e1) = (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) (e1)) = (op (e0) (e3)))) -> ((op (e0) (e1)) = (e0)) -> (~((op (e3) (e0)) = (op (e3) (e3)))) -> ((op (e2) (e1)) = (e2)) -> (~((op (e2) (e1)) = (op (e2) (e3)))) -> (((op (e2) (e3)) = (e0))\/(((op (e2) (e3)) = (e1))\/(((op (e2) (e3)) = (e2))\/((op (e2) (e3)) = (e3))))) -> (~((op (e2) (e3)) = (op (e3) (e3)))) -> (~((op (e0) (e3)) = (op (e2) (e3)))) -> (((op (e0) (e3)) = (e2))\/(((op (e1) (e3)) = (e2))\/(((op (e2) (e3)) = (e2))\/((op (e3) (e3)) = (e2))))) -> (~((op (e2) (e3)) = (e1))) -> (~((e2) = (e3))) -> (~((e1) = (e2))) -> (~((op (e0) (e3)) = (e1))) -> (((op (e0) (e3)) = (e1))\/(((op (e1) (e3)) = (e1))\/(((op (e2) (e3)) = (e1))\/((op (e3) (e3)) = (e1))))) -> (~((op (e2) (e0)) = (op (e2) (e3)))) -> ((op (e2) (e0)) = (e0)) -> ((op (e3) (e1)) = (e0)) -> (~((op (e3) (e1)) = (op (e3) (e3)))) -> False). % 18.87/19.03 do 0 intro. intros zenon_H1fe zenon_H9a zenon_H14f zenon_H150 zenon_Hd8 zenon_H153 zenon_H251 zenon_H250 zenon_He8 zenon_H1f0 zenon_H1db zenon_H259 zenon_H102 zenon_He4 zenon_H1d zenon_Hc2 zenon_H136 zenon_H149 zenon_H168 zenon_H13f zenon_H10e zenon_H22 zenon_H201 zenon_H4f zenon_H6f zenon_H62 zenon_H45 zenon_H3f zenon_H3e zenon_H2b zenon_H6d zenon_H1a4 zenon_H52 zenon_H139 zenon_H20d zenon_H124 zenon_H1c4 zenon_H18f zenon_H173 zenon_H4a zenon_H6a zenon_H10a zenon_H1ef zenon_H128 zenon_H57 zenon_H110 zenon_H7a zenon_H95 zenon_H1e0 zenon_H67 zenon_H54 zenon_H49 zenon_H71 zenon_H1ca zenon_H1c7 zenon_H11f zenon_Hf3 zenon_He2 zenon_H145 zenon_H255 zenon_H12b zenon_H7c zenon_H231 zenon_H133 zenon_H5b zenon_H34 zenon_H1b1 zenon_H130. % 18.87/19.03 apply (zenon_or_s _ _ zenon_H1fe); [ zenon_intro zenon_H7b | zenon_intro zenon_H1ff ]. % 18.87/19.03 apply (zenon_L26_); trivial. % 18.87/19.03 apply (zenon_or_s _ _ zenon_H1ff); [ zenon_intro zenon_H86 | zenon_intro zenon_H200 ]. % 18.87/19.03 apply (zenon_or_s _ _ zenon_H168); [ zenon_intro zenon_H3a | zenon_intro zenon_H169 ]. % 18.87/19.03 apply (zenon_L35_); trivial. % 18.87/19.03 apply (zenon_or_s _ _ zenon_H169); [ zenon_intro zenon_H99 | zenon_intro zenon_H16a ]. % 18.87/19.03 apply (zenon_L36_); trivial. % 18.87/19.03 apply (zenon_or_s _ _ zenon_H16a); [ zenon_intro zenon_Ha9 | zenon_intro zenon_He3 ]. % 18.87/19.03 apply (zenon_L883_); trivial. % 18.87/19.03 apply (zenon_or_s _ _ zenon_H128); [ zenon_intro zenon_H9d | zenon_intro zenon_H129 ]. % 18.87/19.03 exact (zenon_H1ef zenon_H9d). % 18.87/19.03 apply (zenon_or_s _ _ zenon_H129); [ zenon_intro zenon_H10d | zenon_intro zenon_H12a ]. % 18.87/19.03 exact (zenon_H10a zenon_H10d). % 18.87/19.03 apply (zenon_or_s _ _ zenon_H12a); [ zenon_intro zenon_Hf0 | zenon_intro zenon_Hd6 ]. % 18.87/19.03 apply (zenon_L907_); trivial. % 18.87/19.03 apply (zenon_L571_); trivial. % 18.87/19.03 apply (zenon_or_s _ _ zenon_H200); [ zenon_intro zenon_Hee | zenon_intro zenon_H148 ]. % 18.87/19.03 apply (zenon_L204_); trivial. % 18.87/19.03 apply (zenon_L895_); trivial. % 18.87/19.03 (* end of lemma zenon_L908_ *) % 18.87/19.03 assert (zenon_L909_ : (((op (e2) (e0)) = (e0))\/(((op (e2) (e1)) = (e0))\/(((op (e2) (e2)) = (e0))\/((op (e2) (e3)) = (e0))))) -> (~((op (e2) (e0)) = (op (e2) (e3)))) -> (((op (e0) (e3)) = (e1))\/(((op (e1) (e3)) = (e1))\/(((op (e2) (e3)) = (e1))\/((op (e3) (e3)) = (e1))))) -> (~((op (e0) (e3)) = (e1))) -> (~((e1) = (e2))) -> (~((e2) = (e3))) -> (~((op (e2) (e3)) = (e1))) -> (((op (e0) (e3)) = (e2))\/(((op (e1) (e3)) = (e2))\/(((op (e2) (e3)) = (e2))\/((op (e3) (e3)) = (e2))))) -> (~((op (e0) (e3)) = (op (e2) (e3)))) -> (~((op (e2) (e3)) = (op (e3) (e3)))) -> (((op (e2) (e3)) = (e0))\/(((op (e2) (e3)) = (e1))\/(((op (e2) (e3)) = (e2))\/((op (e2) (e3)) = (e3))))) -> (~((op (e2) (e1)) = (op (e2) (e3)))) -> ((op (e2) (e1)) = (e2)) -> (~((op (e3) (e0)) = (op (e3) (e3)))) -> (~((op (e0) (e1)) = (op (e0) (e3)))) -> (((op (e0) (e0)) = (e3))\/(((op (e1) (e0)) = (e3))\/(((op (e2) (e0)) = (e3))\/((op (e3) (e0)) = (e3))))) -> (~((e1) = (e3))) -> ((op (e0) (e0)) = (e1)) -> ((op (e1) (e1)) = (e2)) -> (~((op (e1) (e1)) = (op (e1) (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 (e0) (e1)) = (op (e0) (e2)))) -> (~((op (e2) (e2)) = (e2))) -> (~((op (e2) (e2)) = (op (e3) (e2)))) -> (((op (e2) (e2)) = (e0))\/(((op (e2) (e2)) = (e1))\/(((op (e2) (e2)) = (e2))\/((op (e2) (e2)) = (e3))))) -> (~((op (e1) (e2)) = (op (e1) (e3)))) -> (~((op (e0) (e2)) = (e1))) -> (((op (e0) (e2)) = (e1))\/(((op (e1) (e2)) = (e1))\/(((op (e2) (e2)) = (e1))\/((op (e3) (e2)) = (e1))))) -> (~((op (e2) (e0)) = (op (e2) (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) (e0)) = (e0))) -> (~((op (e1) (e0)) = (op (e1) (e1)))) -> (~((op (e3) (e2)) = (op (e3) (e3)))) -> (~((op (e3) (e0)) = (op (e3) (e2)))) -> (~((op (e1) (e1)) = (op (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 (e0) (e1)) = (op (e1) (e1)))) -> ((op (e1) (e1)) = (e3)) -> (((op (e0) (e0)) = (e3))\/(((op (e0) (e1)) = (e3))\/(((op (e0) (e2)) = (e3))\/((op (e0) (e3)) = (e3))))) -> (((op (e0) (e3)) = (e3))\/(((op (e1) (e3)) = (e3))\/(((op (e2) (e3)) = (e3))\/((op (e3) (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))))) -> (~((op (e3) (e3)) = (e3))) -> (((op (e2) (e0)) = (e0))\/(((op (e2) (e0)) = (e1))\/(((op (e2) (e0)) = (e2))\/((op (e2) (e0)) = (e3))))) -> (~((op (e2) (e0)) = (e1))) -> (~((op (e2) (e0)) = (op (e2) (e1)))) -> (((op (e3) (e0)) = (e1))\/(((op (e3) (e1)) = (e1))\/(((op (e3) (e2)) = (e1))\/((op (e3) (e3)) = (e1))))) -> (~((op (e3) (e1)) = (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) (e0)) = (e2))\/(((op (e1) (e0)) = (e2))\/(((op (e2) (e0)) = (e2))\/((op (e3) (e0)) = (e2))))) -> ((op (e0) (e1)) = (e0)) -> (~((op (e0) (e1)) = (op (e2) (e1)))) -> (~((op (e3) (e1)) = (op (e3) (e3)))) -> (~((op (e1) (e0)) = (op (e1) (e3)))) -> ((op (e0) (e3)) = (e3)) -> (~((e0) = (e3))) -> (((op (e0) (e3)) = (e0))\/(((op (e1) (e3)) = (e0))\/(((op (e2) (e3)) = (e0))\/((op (e3) (e3)) = (e0))))) -> (((op (e0) (e2)) = (e0))\/(((op (e1) (e2)) = (e0))\/(((op (e2) (e2)) = (e0))\/((op (e3) (e2)) = (e0))))) -> (~((e0) = (e2))) -> ((op (e0) (e2)) = (e2)) -> ((op (e1) (e0)) = (e0)) -> (~((op (e1) (e0)) = (op (e1) (e2)))) -> (~((op (e2) (e2)) = (op (e2) (e3)))) -> (~((op (e3) (e1)) = (op (e3) (e2)))) -> ((op (e3) (e1)) = (e0)) -> False). % 18.87/19.03 do 0 intro. intros zenon_H2f zenon_H5b zenon_H133 zenon_H231 zenon_H7c zenon_H12b zenon_H255 zenon_H145 zenon_He2 zenon_Hf3 zenon_H11f zenon_H1c7 zenon_H1ca zenon_H71 zenon_H54 zenon_H1e0 zenon_H95 zenon_H7a zenon_H110 zenon_H57 zenon_H128 zenon_H1ef zenon_H10a zenon_H4a zenon_H173 zenon_H18f zenon_H1c4 zenon_H124 zenon_H20d zenon_H139 zenon_H52 zenon_H2b zenon_H3e zenon_H3f zenon_H45 zenon_H62 zenon_H6f zenon_H4f zenon_H201 zenon_H22 zenon_H10e zenon_H13f zenon_H168 zenon_H136 zenon_Hc2 zenon_H1d zenon_He4 zenon_H102 zenon_H259 zenon_H1db zenon_H1f0 zenon_He8 zenon_H250 zenon_H251 zenon_H153 zenon_H14f zenon_H1fe zenon_H49 zenon_H17e zenon_H130 zenon_Hd8 zenon_He3 zenon_H9a zenon_H67 zenon_H6a zenon_H149 zenon_H150 zenon_H27 zenon_H24a zenon_H6d zenon_H1a4 zenon_H1b1. % 18.87/19.03 apply (zenon_or_s _ _ zenon_H2f); [ zenon_intro zenon_H34 | zenon_intro zenon_H33 ]. % 18.87/19.03 apply (zenon_L908_); trivial. % 18.87/19.03 apply (zenon_or_s _ _ zenon_H33); [ zenon_intro zenon_H36 | zenon_intro zenon_H35 ]. % 18.87/19.03 apply (zenon_L128_); trivial. % 18.87/19.03 apply (zenon_or_s _ _ zenon_H35); [ zenon_intro zenon_H2c | zenon_intro zenon_H37 ]. % 18.87/19.03 apply (zenon_L766_); trivial. % 18.87/19.03 apply (zenon_L680_); trivial. % 18.87/19.03 (* end of lemma zenon_L909_ *) % 18.87/19.03 assert (zenon_L910_ : (((op (e0) (e0)) = (e3))\/(((op (e0) (e1)) = (e3))\/(((op (e0) (e2)) = (e3))\/((op (e0) (e3)) = (e3))))) -> (~((e0) = (e3))) -> (((op (e1) (e0)) = (e0))\/(((op (e1) (e1)) = (e0))\/(((op (e1) (e2)) = (e0))\/((op (e1) (e3)) = (e0))))) -> (~((op (e1) (e0)) = (op (e2) (e0)))) -> (~((op (e1) (e1)) = (op (e1) (e2)))) -> (~((op (e3) (e0)) = (op (e3) (e2)))) -> (~((op (e3) (e2)) = (op (e3) (e3)))) -> (~((op (e1) (e0)) = (op (e1) (e1)))) -> (~((op (e0) (e0)) = (e0))) -> (((op (e0) (e0)) = (e0))\/(((op (e1) (e0)) = (e0))\/(((op (e2) (e0)) = (e0))\/((op (e3) (e0)) = (e0))))) -> (~((op (e1) (e2)) = (op (e2) (e2)))) -> (~((op (e2) (e2)) = (op (e2) (e3)))) -> (~((op (e3) (e1)) = (op (e3) (e2)))) -> (~((op (e2) (e0)) = (op (e2) (e2)))) -> (((op (e0) (e2)) = (e1))\/(((op (e1) (e2)) = (e1))\/(((op (e2) (e2)) = (e1))\/((op (e3) (e2)) = (e1))))) -> (~((op (e0) (e2)) = (e1))) -> (~((op (e1) (e2)) = (op (e1) (e3)))) -> (((op (e2) (e2)) = (e0))\/(((op (e2) (e2)) = (e1))\/(((op (e2) (e2)) = (e2))\/((op (e2) (e2)) = (e3))))) -> (~((op (e2) (e2)) = (op (e3) (e2)))) -> (~((op (e2) (e2)) = (e2))) -> (~((op (e0) (e1)) = (op (e0) (e2)))) -> (((op (e0) (e2)) = (e0))\/(((op (e1) (e2)) = (e0))\/(((op (e2) (e2)) = (e0))\/((op (e3) (e2)) = (e0))))) -> (~((op (e1) (e1)) = (e1))) -> (~((op (e1) (e0)) = (e1))) -> (((op (e1) (e0)) = (e1))\/(((op (e1) (e1)) = (e1))\/(((op (e1) (e2)) = (e1))\/((op (e1) (e3)) = (e1))))) -> (~((op (e1) (e1)) = (op (e1) (e3)))) -> ((op (e1) (e1)) = (e2)) -> ((op (e0) (e0)) = (e1)) -> (~((e1) = (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) (e1)) = (op (e0) (e3)))) -> ((op (e0) (e1)) = (e0)) -> (~((op (e3) (e0)) = (op (e3) (e3)))) -> ((op (e3) (e0)) = (e2)) -> ((op (e2) (e1)) = (e2)) -> (~((op (e2) (e1)) = (op (e2) (e3)))) -> (((op (e2) (e3)) = (e0))\/(((op (e2) (e3)) = (e1))\/(((op (e2) (e3)) = (e2))\/((op (e2) (e3)) = (e3))))) -> (~((op (e2) (e3)) = (op (e3) (e3)))) -> (~((op (e0) (e3)) = (op (e2) (e3)))) -> (((op (e0) (e3)) = (e2))\/(((op (e1) (e3)) = (e2))\/(((op (e2) (e3)) = (e2))\/((op (e3) (e3)) = (e2))))) -> (~((op (e2) (e3)) = (e1))) -> (~((e2) = (e3))) -> (~((e1) = (e2))) -> (~((op (e0) (e3)) = (e1))) -> (((op (e0) (e3)) = (e1))\/(((op (e1) (e3)) = (e1))\/(((op (e2) (e3)) = (e1))\/((op (e3) (e3)) = (e1))))) -> (~((op (e2) (e0)) = (op (e2) (e3)))) -> ((op (e2) (e0)) = (e0)) -> ((op (e3) (e1)) = (e0)) -> (~((op (e3) (e1)) = (op (e3) (e3)))) -> False). % 18.87/19.03 do 0 intro. intros zenon_H168 zenon_H9a zenon_H22 zenon_H201 zenon_H4f zenon_H6f zenon_H62 zenon_H45 zenon_H3f zenon_H3e zenon_H2b zenon_H6d zenon_H1a4 zenon_H52 zenon_H139 zenon_H20d zenon_H124 zenon_H1c4 zenon_H18f zenon_H173 zenon_H4a zenon_H6a zenon_H10a zenon_H1ef zenon_H128 zenon_H57 zenon_H110 zenon_H7a zenon_H95 zenon_H1e0 zenon_H67 zenon_H54 zenon_H49 zenon_H71 zenon_H148 zenon_H1ca zenon_H1c7 zenon_H11f zenon_Hf3 zenon_He2 zenon_H145 zenon_H255 zenon_H12b zenon_H7c zenon_H231 zenon_H133 zenon_H5b zenon_H34 zenon_H1b1 zenon_H130. % 18.87/19.03 apply (zenon_or_s _ _ zenon_H168); [ zenon_intro zenon_H3a | zenon_intro zenon_H169 ]. % 18.87/19.03 apply (zenon_L35_); trivial. % 18.87/19.03 apply (zenon_or_s _ _ zenon_H169); [ zenon_intro zenon_H99 | zenon_intro zenon_H16a ]. % 18.87/19.03 apply (zenon_L36_); trivial. % 18.87/19.03 apply (zenon_or_s _ _ zenon_H16a); [ zenon_intro zenon_Ha9 | zenon_intro zenon_He3 ]. % 18.87/19.03 apply (zenon_L821_); trivial. % 18.87/19.03 apply (zenon_L894_); trivial. % 18.87/19.03 (* end of lemma zenon_L910_ *) % 18.87/19.03 assert (zenon_L911_ : (((op (e0) (e0)) = (e3))\/(((op (e1) (e0)) = (e3))\/(((op (e2) (e0)) = (e3))\/((op (e3) (e0)) = (e3))))) -> (~((e1) = (e3))) -> (~((op (e1) (e3)) = (op (e3) (e3)))) -> (~((op (e3) (e2)) = (e1))) -> (~((op (e3) (e1)) = (e1))) -> (~((op (e3) (e0)) = (e1))) -> (((op (e3) (e0)) = (e1))\/(((op (e3) (e1)) = (e1))\/(((op (e3) (e2)) = (e1))\/((op (e3) (e3)) = (e1))))) -> (~((op (e1) (e2)) = (op (e3) (e2)))) -> (((op (e1) (e0)) = (e0))\/(((op (e1) (e0)) = (e1))\/(((op (e1) (e0)) = (e2))\/((op (e1) (e0)) = (e3))))) -> (~((op (e1) (e0)) = (op (e1) (e2)))) -> (~((op (e1) (e0)) = (e1))) -> (~((op (e1) (e0)) = (op (e1) (e3)))) -> ((op (e0) (e0)) = (e1)) -> (~((op (e1) (e0)) = (op (e2) (e0)))) -> (((op (e1) (e0)) = (e0))\/(((op (e1) (e1)) = (e0))\/(((op (e1) (e2)) = (e0))\/((op (e1) (e3)) = (e0))))) -> (((op (e0) (e3)) = (e0))\/(((op (e0) (e3)) = (e1))\/(((op (e0) (e3)) = (e2))\/((op (e0) (e3)) = (e3))))) -> (~((op (e0) (e1)) = (op (e0) (e3)))) -> (~((op (e3) (e2)) = (op (e3) (e3)))) -> (~((e0) = (e3))) -> (((op (e0) (e3)) = (e0))\/(((op (e1) (e3)) = (e0))\/(((op (e2) (e3)) = (e0))\/((op (e3) (e3)) = (e0))))) -> (~((op (e1) (e1)) = (op (e1) (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)) = (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 (e3) (e1)) = (op (e3) (e3)))) -> ((op (e0) (e2)) = (e2)) -> (~((op (e0) (e2)) = (op (e3) (e2)))) -> (~((op (e2) (e0)) = (op (e2) (e3)))) -> ((op (e0) (e1)) = (e0)) -> (~((op (e0) (e1)) = (op (e2) (e1)))) -> (~((op (e3) (e0)) = (op (e3) (e3)))) -> ((op (e2) (e1)) = (e2)) -> (~((op (e2) (e1)) = (op (e2) (e3)))) -> ((op (e1) (e1)) = (e2)) -> (~((op (e1) (e1)) = (op (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 (e0) (e3)) = (op (e2) (e3)))) -> ((op (e2) (e1)) = (e1)) -> (~((op (e2) (e3)) = (op (e3) (e3)))) -> (((op (e2) (e3)) = (e0))\/(((op (e2) (e3)) = (e1))\/(((op (e2) (e3)) = (e2))\/((op (e2) (e3)) = (e3))))) -> (~((op (e1) (e3)) = (op (e2) (e3)))) -> ((op (e0) (e2)) = (e3)) -> (((op (e1) (e3)) = (e0))\/(((op (e1) (e3)) = (e1))\/(((op (e1) (e3)) = (e2))\/((op (e1) (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)) = (op (e3) (e2)))) -> ((op (e2) (e1)) = (e3)) -> (((op (e0) (e0)) = (e1))\/(((op (e0) (e1)) = (e1))\/(((op (e0) (e2)) = (e1))\/((op (e0) (e3)) = (e1))))) -> (~((e0) = (e2))) -> (~((op (e2) (e0)) = (op (e2) (e1)))) -> (((op (e2) (e0)) = (e0))\/(((op (e2) (e0)) = (e1))\/(((op (e2) (e0)) = (e2))\/((op (e2) (e0)) = (e3))))) -> (~((op (e2) (e0)) = (op (e3) (e0)))) -> (~((op (e2) (e0)) = (e1))) -> (~((e1) = (e2))) -> (((op (e0) (e0)) = (e2))\/(((op (e1) (e0)) = (e2))\/(((op (e2) (e0)) = (e2))\/((op (e3) (e0)) = (e2))))) -> (~((op (e0) (e1)) = (e1))) -> (~((op (e0) (e2)) = (e1))) -> (~((op (e0) (e3)) = (e1))) -> (((op (e3) (e0)) = (e0))\/(((op (e3) (e1)) = (e0))\/(((op (e3) (e2)) = (e0))\/((op (e3) (e3)) = (e0))))) -> (((op (e2) (e2)) = (e0))\/(((op (e2) (e2)) = (e1))\/(((op (e2) (e2)) = (e2))\/((op (e2) (e2)) = (e3))))) -> (~((op (e2) (e2)) = (op (e2) (e3)))) -> (~((op (e1) (e2)) = (op (e2) (e2)))) -> (~((op (e2) (e2)) = (e2))) -> (~((op (e2) (e0)) = (op (e2) (e2)))) -> (~((op (e1) (e1)) = (e1))) -> (((op (e1) (e0)) = (e1))\/(((op (e1) (e1)) = (e1))\/(((op (e1) (e2)) = (e1))\/((op (e1) (e3)) = (e1))))) -> ((op (e3) (e0)) = (e2)) -> (~((e2) = (e3))) -> False). % 18.87/19.03 do 0 intro. intros zenon_H1e0 zenon_H95 zenon_Hd5 zenon_H251 zenon_H250 zenon_Had zenon_He8 zenon_H115 zenon_H25e zenon_H24a zenon_H1ef zenon_Hd8 zenon_H7a zenon_H201 zenon_H22 zenon_He4 zenon_H54 zenon_H62 zenon_H9a zenon_H67 zenon_H4f zenon_H4a zenon_H6a zenon_H2f zenon_H153 zenon_H130 zenon_H150 zenon_H14f zenon_H5b zenon_H49 zenon_H17e zenon_H71 zenon_H1ca zenon_H1c7 zenon_H110 zenon_H57 zenon_H136 zenon_H1d zenon_He2 zenon_Ha5 zenon_Hf3 zenon_H11f zenon_Hdb zenon_Ha9 zenon_Hdf zenon_H102 zenon_H145 zenon_H18f zenon_Ha6 zenon_H22d zenon_H149 zenon_H1f0 zenon_H259 zenon_H17b zenon_H1db zenon_H7c zenon_H1fe zenon_Ha4 zenon_H20d zenon_H231 zenon_H1ac zenon_H1c4 zenon_H6d zenon_H2b zenon_H173 zenon_H52 zenon_H10a zenon_H128 zenon_H148 zenon_H12b. % 18.87/19.03 apply (zenon_or_s _ _ zenon_H1e0); [ zenon_intro zenon_H3a | zenon_intro zenon_H1e1 ]. % 18.87/19.03 apply (zenon_L35_); trivial. % 18.87/19.03 apply (zenon_or_s _ _ zenon_H1e1); [ zenon_intro zenon_H9e | zenon_intro zenon_H1e2 ]. % 18.87/19.03 apply (zenon_L107_); trivial. % 18.87/19.03 apply (zenon_or_s _ _ zenon_H1e2); [ zenon_intro zenon_H3b | zenon_intro zenon_H15e ]. % 18.87/19.03 apply (zenon_or_s _ _ zenon_H128); [ zenon_intro zenon_H9d | zenon_intro zenon_H129 ]. % 18.87/19.03 exact (zenon_H1ef zenon_H9d). % 18.87/19.03 apply (zenon_or_s _ _ zenon_H129); [ zenon_intro zenon_H10d | zenon_intro zenon_H12a ]. % 18.87/19.03 exact (zenon_H10a zenon_H10d). % 18.87/19.03 apply (zenon_or_s _ _ zenon_H12a); [ zenon_intro zenon_Hf0 | zenon_intro zenon_Hd6 ]. % 18.87/19.03 apply (zenon_or_s _ _ zenon_H2f); [ zenon_intro zenon_H34 | zenon_intro zenon_H33 ]. % 18.87/19.03 apply (zenon_L812_); trivial. % 18.87/19.03 apply (zenon_or_s _ _ zenon_H33); [ zenon_intro zenon_H36 | zenon_intro zenon_H35 ]. % 18.87/19.03 apply (zenon_L128_); trivial. % 18.87/19.03 apply (zenon_or_s _ _ zenon_H35); [ zenon_intro zenon_H2c | zenon_intro zenon_H37 ]. % 18.87/19.03 apply (zenon_or_s _ _ zenon_H1ac); [ zenon_intro zenon_H44 | zenon_intro zenon_H1af ]. % 18.87/19.03 apply (zenon_L786_); trivial. % 18.87/19.03 apply (zenon_or_s _ _ zenon_H1af); [ zenon_intro zenon_H1b1 | zenon_intro zenon_H1b0 ]. % 18.87/19.03 apply (zenon_L509_); trivial. % 18.87/19.03 apply (zenon_or_s _ _ zenon_H1b0); [ zenon_intro zenon_H61 | zenon_intro zenon_H60 ]. % 18.87/19.03 apply (zenon_L146_); trivial. % 18.87/19.03 apply (zenon_L874_); trivial. % 18.87/19.03 apply (zenon_L300_); trivial. % 18.87/19.03 apply (zenon_L800_); trivial. % 18.87/19.03 apply (zenon_L109_); trivial. % 18.87/19.03 (* end of lemma zenon_L911_ *) % 18.87/19.03 assert (zenon_L912_ : (((op (e1) (e0)) = (e0))\/(((op (e1) (e1)) = (e0))\/(((op (e1) (e2)) = (e0))\/((op (e1) (e3)) = (e0))))) -> (~((op (e1) (e0)) = (op (e2) (e0)))) -> (~((op (e3) (e2)) = (op (e3) (e3)))) -> ((op (e2) (e0)) = (e0)) -> (~((op (e2) (e0)) = (op (e2) (e3)))) -> (~((op (e1) (e1)) = (op (e1) (e3)))) -> (~((e0) = (e3))) -> (((op (e0) (e3)) = (e0))\/(((op (e1) (e3)) = (e0))\/(((op (e2) (e3)) = (e0))\/((op (e3) (e3)) = (e0))))) -> (~((op (e2) (e0)) = (op (e2) (e2)))) -> (~((op (e1) (e1)) = (op (e1) (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) (e3)) = (e3))\/(((op (e1) (e3)) = (e3))\/(((op (e2) (e3)) = (e3))\/((op (e3) (e3)) = (e3))))) -> (~((e2) = (e3))) -> ((op (e2) (e1)) = (e1)) -> ((op (e0) (e0)) = (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) (e0)) = (op (e1) (e3)))) -> (~((op (e1) (e3)) = (op (e2) (e3)))) -> (~((op (e1) (e0)) = (e1))) -> (~((op (e1) (e0)) = (op (e1) (e2)))) -> (((op (e1) (e0)) = (e0))\/(((op (e1) (e0)) = (e1))\/(((op (e1) (e0)) = (e2))\/((op (e1) (e0)) = (e3))))) -> (~((op (e3) (e3)) = (e3))) -> (~((op (e1) (e2)) = (op (e3) (e2)))) -> ((op (e2) (e1)) = (e3)) -> ((op (e1) (e1)) = (e2)) -> (~((e0) = (e2))) -> (((op (e3) (e0)) = (e0))\/(((op (e3) (e1)) = (e0))\/(((op (e3) (e2)) = (e0))\/((op (e3) (e3)) = (e0))))) -> (((op (e0) (e3)) = (e2))\/(((op (e1) (e3)) = (e2))\/(((op (e2) (e3)) = (e2))\/((op (e3) (e3)) = (e2))))) -> (~((op (e3) (e2)) = (e1))) -> (~((op (e3) (e1)) = (e1))) -> (~((op (e3) (e0)) = (e1))) -> (((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)))) -> (~((op (e2) (e3)) = (op (e3) (e3)))) -> (((op (e2) (e3)) = (e0))\/(((op (e2) (e3)) = (e1))\/(((op (e2) (e3)) = (e2))\/((op (e2) (e3)) = (e3))))) -> (~((op (e2) (e1)) = (op (e2) (e3)))) -> ((op (e2) (e1)) = (e2)) -> ((op (e3) (e0)) = (e2)) -> (~((op (e3) (e0)) = (op (e3) (e3)))) -> False). % 18.87/19.03 do 0 intro. intros zenon_H22 zenon_H201 zenon_H62 zenon_H34 zenon_H5b zenon_H57 zenon_H9a zenon_H67 zenon_H52 zenon_H4f zenon_H49 zenon_H4a zenon_H6a zenon_H136 zenon_H12b zenon_Ha5 zenon_H7a zenon_Hdf zenon_Hd5 zenon_Hd8 zenon_Hdb zenon_H1ef zenon_H24a zenon_H25e zenon_H102 zenon_H115 zenon_Ha6 zenon_H110 zenon_H149 zenon_H1ac zenon_H145 zenon_H251 zenon_H250 zenon_Had zenon_He8 zenon_He3 zenon_He2 zenon_Hf3 zenon_H11f zenon_H1c7 zenon_H1ca zenon_H148 zenon_H71. % 18.87/19.03 apply (zenon_or_s _ _ zenon_H22); [ zenon_intro zenon_H27 | zenon_intro zenon_H26 ]. % 18.87/19.03 apply (zenon_L332_); trivial. % 18.87/19.03 apply (zenon_or_s _ _ zenon_H26); [ zenon_intro zenon_H29 | zenon_intro zenon_H28 ]. % 18.87/19.03 apply (zenon_L724_); trivial. % 18.87/19.03 apply (zenon_or_s _ _ zenon_H28); [ zenon_intro zenon_H2a | zenon_intro zenon_H1f ]. % 18.87/19.03 apply (zenon_or_s _ _ zenon_H1ac); [ zenon_intro zenon_H44 | zenon_intro zenon_H1af ]. % 18.87/19.03 apply (zenon_L100_); trivial. % 18.87/19.03 apply (zenon_or_s _ _ zenon_H1af); [ zenon_intro zenon_H1b1 | zenon_intro zenon_H1b0 ]. % 18.87/19.03 apply (zenon_L509_); trivial. % 18.87/19.03 apply (zenon_or_s _ _ zenon_H1b0); [ zenon_intro zenon_H61 | zenon_intro zenon_H60 ]. % 18.87/19.03 apply (zenon_L176_); trivial. % 18.87/19.03 apply (zenon_or_s _ _ zenon_He8); [ zenon_intro zenon_Hac | zenon_intro zenon_Heb ]. % 18.87/19.03 exact (zenon_Had zenon_Hac). % 18.87/19.03 apply (zenon_or_s _ _ zenon_Heb); [ zenon_intro zenon_Hae | zenon_intro zenon_Hec ]. % 18.87/19.03 exact (zenon_H250 zenon_Hae). % 18.87/19.03 apply (zenon_or_s _ _ zenon_Hec); [ zenon_intro zenon_Hba | zenon_intro zenon_Hc4 ]. % 18.87/19.03 exact (zenon_H251 zenon_Hba). % 18.87/19.03 apply (zenon_or_s _ _ zenon_H145); [ zenon_intro zenon_Hcd | zenon_intro zenon_H146 ]. % 18.87/19.03 apply (zenon_L793_); trivial. % 18.87/19.03 apply (zenon_or_s _ _ zenon_H146); [ zenon_intro zenon_Hd7 | zenon_intro zenon_H147 ]. % 18.87/19.03 apply (zenon_L454_); trivial. % 18.87/19.03 apply (zenon_or_s _ _ zenon_H147); [ zenon_intro zenon_H11d | zenon_intro zenon_Hf6 ]. % 18.87/19.03 apply (zenon_L224_); trivial. % 18.87/19.03 apply (zenon_L114_); trivial. % 18.87/19.03 apply (zenon_or_s _ _ zenon_He8); [ zenon_intro zenon_Hac | zenon_intro zenon_Heb ]. % 18.87/19.03 exact (zenon_Had zenon_Hac). % 18.87/19.03 apply (zenon_or_s _ _ zenon_Heb); [ zenon_intro zenon_Hae | zenon_intro zenon_Hec ]. % 18.87/19.03 exact (zenon_H250 zenon_Hae). % 18.87/19.03 apply (zenon_or_s _ _ zenon_Hec); [ zenon_intro zenon_Hba | zenon_intro zenon_Hc4 ]. % 18.87/19.03 exact (zenon_H251 zenon_Hba). % 18.87/19.03 apply (zenon_L807_); trivial. % 18.87/19.03 (* end of lemma zenon_L912_ *) % 18.87/19.03 assert (zenon_L913_ : (((op (e0) (e0)) = (e3))\/(((op (e1) (e0)) = (e3))\/(((op (e2) (e0)) = (e3))\/((op (e3) (e0)) = (e3))))) -> (~((e1) = (e3))) -> (~((op (e1) (e3)) = (op (e3) (e3)))) -> (~((op (e3) (e2)) = (e1))) -> (~((op (e3) (e1)) = (e1))) -> (~((op (e3) (e0)) = (e1))) -> (((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)) = (op (e3) (e3)))) -> (((op (e0) (e3)) = (e2))\/(((op (e1) (e3)) = (e2))\/(((op (e2) (e3)) = (e2))\/((op (e3) (e3)) = (e2))))) -> (~((op (e1) (e2)) = (op (e3) (e2)))) -> (~((op (e3) (e3)) = (e3))) -> (((op (e1) (e0)) = (e0))\/(((op (e1) (e0)) = (e1))\/(((op (e1) (e0)) = (e2))\/((op (e1) (e0)) = (e3))))) -> (~((op (e1) (e0)) = (op (e1) (e2)))) -> (~((op (e1) (e0)) = (e1))) -> (~((op (e1) (e3)) = (op (e2) (e3)))) -> (~((op (e1) (e0)) = (op (e1) (e3)))) -> ((op (e0) (e0)) = (e1)) -> ((op (e2) (e1)) = (e1)) -> (((op (e0) (e3)) = (e3))\/(((op (e1) (e3)) = (e3))\/(((op (e2) (e3)) = (e3))\/((op (e3) (e3)) = (e3))))) -> (((op (e0) (e2)) = (e0))\/(((op (e1) (e2)) = (e0))\/(((op (e2) (e2)) = (e0))\/((op (e3) (e2)) = (e0))))) -> (~((op (e0) (e1)) = (op (e0) (e2)))) -> (~((op (e1) (e1)) = (op (e1) (e2)))) -> (((op (e0) (e3)) = (e0))\/(((op (e1) (e3)) = (e0))\/(((op (e2) (e3)) = (e0))\/((op (e3) (e3)) = (e0))))) -> (~((e0) = (e3))) -> (~((op (e1) (e1)) = (op (e1) (e3)))) -> (~((op (e2) (e0)) = (op (e2) (e3)))) -> (~((op (e3) (e2)) = (op (e3) (e3)))) -> (~((op (e1) (e0)) = (op (e2) (e0)))) -> (((op (e1) (e0)) = (e0))\/(((op (e1) (e1)) = (e0))\/(((op (e1) (e2)) = (e0))\/((op (e1) (e3)) = (e0))))) -> ((op (e0) (e1)) = (e0)) -> (~((op (e0) (e1)) = (op (e2) (e1)))) -> ((op (e0) (e3)) = (e3)) -> (~((op (e0) (e3)) = (op (e1) (e3)))) -> (((op (e2) (e3)) = (e0))\/(((op (e2) (e3)) = (e1))\/(((op (e2) (e3)) = (e2))\/((op (e2) (e3)) = (e3))))) -> (~((op (e2) (e3)) = (op (e3) (e3)))) -> (~((op (e2) (e1)) = (op (e2) (e3)))) -> ((op (e2) (e1)) = (e2)) -> (~((op (e0) (e3)) = (op (e2) (e3)))) -> (((op (e1) (e3)) = (e0))\/(((op (e1) (e3)) = (e1))\/(((op (e1) (e3)) = (e2))\/((op (e1) (e3)) = (e3))))) -> (~((op (e2) (e2)) = (op (e3) (e2)))) -> ((op (e2) (e1)) = (e3)) -> ((op (e1) (e1)) = (e2)) -> (~((e0) = (e2))) -> (((op (e3) (e0)) = (e0))\/(((op (e3) (e1)) = (e0))\/(((op (e3) (e2)) = (e0))\/((op (e3) (e3)) = (e0))))) -> (((op (e2) (e2)) = (e0))\/(((op (e2) (e2)) = (e1))\/(((op (e2) (e2)) = (e2))\/((op (e2) (e2)) = (e3))))) -> (~((op (e2) (e2)) = (op (e2) (e3)))) -> (~((op (e1) (e2)) = (op (e2) (e2)))) -> (~((op (e2) (e2)) = (e2))) -> (~((op (e2) (e0)) = (op (e2) (e2)))) -> (~((op (e1) (e1)) = (e1))) -> (((op (e1) (e0)) = (e1))\/(((op (e1) (e1)) = (e1))\/(((op (e1) (e2)) = (e1))\/((op (e1) (e3)) = (e1))))) -> ((op (e3) (e0)) = (e2)) -> (~((e2) = (e3))) -> False). % 18.87/19.04 do 0 intro. intros zenon_H1e0 zenon_H95 zenon_Hd5 zenon_H251 zenon_H250 zenon_Had zenon_He8 zenon_H2f zenon_H71 zenon_H145 zenon_H115 zenon_H102 zenon_H25e zenon_H24a zenon_H1ef zenon_Hdb zenon_Hd8 zenon_H7a zenon_Ha5 zenon_H136 zenon_H6a zenon_H4a zenon_H4f zenon_H67 zenon_H9a zenon_H57 zenon_H5b zenon_H62 zenon_H201 zenon_H22 zenon_H49 zenon_H17e zenon_He3 zenon_H1d zenon_H11f zenon_Hf3 zenon_H1c7 zenon_H1ca zenon_He2 zenon_Hdf zenon_H18f zenon_Ha6 zenon_H110 zenon_H149 zenon_H1ac zenon_H1c4 zenon_H6d zenon_H2b zenon_H173 zenon_H52 zenon_H10a zenon_H128 zenon_H148 zenon_H12b. % 18.87/19.04 apply (zenon_or_s _ _ zenon_H1e0); [ zenon_intro zenon_H3a | zenon_intro zenon_H1e1 ]. % 18.87/19.04 apply (zenon_L35_); trivial. % 18.87/19.04 apply (zenon_or_s _ _ zenon_H1e1); [ zenon_intro zenon_H9e | zenon_intro zenon_H1e2 ]. % 18.87/19.04 apply (zenon_L107_); trivial. % 18.87/19.04 apply (zenon_or_s _ _ zenon_H1e2); [ zenon_intro zenon_H3b | zenon_intro zenon_H15e ]. % 18.87/19.04 apply (zenon_or_s _ _ zenon_H128); [ zenon_intro zenon_H9d | zenon_intro zenon_H129 ]. % 18.87/19.04 exact (zenon_H1ef zenon_H9d). % 18.87/19.04 apply (zenon_or_s _ _ zenon_H129); [ zenon_intro zenon_H10d | zenon_intro zenon_H12a ]. % 18.87/19.04 exact (zenon_H10a zenon_H10d). % 18.87/19.04 apply (zenon_or_s _ _ zenon_H12a); [ zenon_intro zenon_Hf0 | zenon_intro zenon_Hd6 ]. % 18.87/19.04 apply (zenon_or_s _ _ zenon_H2f); [ zenon_intro zenon_H34 | zenon_intro zenon_H33 ]. % 18.87/19.04 apply (zenon_L912_); trivial. % 18.87/19.04 apply (zenon_or_s _ _ zenon_H33); [ zenon_intro zenon_H36 | zenon_intro zenon_H35 ]. % 18.87/19.04 apply (zenon_L128_); trivial. % 18.87/19.04 apply (zenon_or_s _ _ zenon_H35); [ zenon_intro zenon_H2c | zenon_intro zenon_H37 ]. % 18.87/19.04 apply (zenon_or_s _ _ zenon_H1ac); [ zenon_intro zenon_H44 | zenon_intro zenon_H1af ]. % 18.87/19.04 apply (zenon_L100_); trivial. % 18.87/19.04 apply (zenon_or_s _ _ zenon_H1af); [ zenon_intro zenon_H1b1 | zenon_intro zenon_H1b0 ]. % 18.87/19.04 apply (zenon_L509_); trivial. % 18.87/19.04 apply (zenon_or_s _ _ zenon_H1b0); [ zenon_intro zenon_H61 | zenon_intro zenon_H60 ]. % 18.87/19.04 apply (zenon_L146_); trivial. % 18.87/19.04 apply (zenon_L805_); trivial. % 18.87/19.04 apply (zenon_L300_); trivial. % 18.87/19.04 apply (zenon_L800_); trivial. % 18.87/19.04 apply (zenon_L109_); trivial. % 18.87/19.04 (* end of lemma zenon_L913_ *) % 18.87/19.04 assert (zenon_L914_ : (~((op (e0) (e0)) = (op (e0) (e3)))) -> (~((op (e2) (e0)) = (op (e2) (e3)))) -> (((op (e0) (e0)) = (e3))\/(((op (e0) (e1)) = (e3))\/(((op (e0) (e2)) = (e3))\/((op (e0) (e3)) = (e3))))) -> (~((e0) = (e3))) -> (((op (e1) (e0)) = (e1))\/(((op (e1) (e1)) = (e1))\/(((op (e1) (e2)) = (e1))\/((op (e1) (e3)) = (e1))))) -> (~((op (e1) (e1)) = (e1))) -> (~((op (e2) (e0)) = (op (e2) (e2)))) -> (~((op (e2) (e2)) = (e2))) -> (~((op (e1) (e2)) = (op (e2) (e2)))) -> (~((op (e2) (e2)) = (op (e2) (e3)))) -> (((op (e2) (e2)) = (e0))\/(((op (e2) (e2)) = (e1))\/(((op (e2) (e2)) = (e2))\/((op (e2) (e2)) = (e3))))) -> (((op (e3) (e0)) = (e0))\/(((op (e3) (e1)) = (e0))\/(((op (e3) (e2)) = (e0))\/((op (e3) (e3)) = (e0))))) -> (~((e0) = (e2))) -> ((op (e2) (e1)) = (e3)) -> (~((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 (e2) (e1)) = (e2)) -> (~((op (e0) (e3)) = (op (e2) (e3)))) -> ((op (e2) (e1)) = (e1)) -> (~((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))))) -> (~((op (e1) (e3)) = (op (e2) (e3)))) -> ((op (e1) (e1)) = (e2)) -> (~((op (e1) (e1)) = (op (e1) (e3)))) -> (((op (e1) (e3)) = (e0))\/(((op (e1) (e3)) = (e1))\/(((op (e1) (e3)) = (e2))\/((op (e1) (e3)) = (e3))))) -> (~((op (e3) (e3)) = (e3))) -> (~((op (e0) (e1)) = (op (e2) (e1)))) -> ((op (e0) (e1)) = (e0)) -> (((op (e1) (e0)) = (e0))\/(((op (e1) (e1)) = (e0))\/(((op (e1) (e2)) = (e0))\/((op (e1) (e3)) = (e0))))) -> (~((op (e1) (e0)) = (op (e2) (e0)))) -> ((op (e0) (e0)) = (e1)) -> (~((op (e1) (e0)) = (op (e1) (e3)))) -> (~((op (e1) (e0)) = (e1))) -> (~((op (e1) (e0)) = (op (e1) (e2)))) -> (((op (e1) (e0)) = (e0))\/(((op (e1) (e0)) = (e1))\/(((op (e1) (e0)) = (e2))\/((op (e1) (e0)) = (e3))))) -> (~((op (e1) (e2)) = (op (e3) (e2)))) -> (((op (e0) (e0)) = (e1))\/(((op (e0) (e1)) = (e1))\/(((op (e0) (e2)) = (e1))\/((op (e0) (e3)) = (e1))))) -> (~((op (e2) (e0)) = (op (e2) (e1)))) -> (((op (e2) (e0)) = (e0))\/(((op (e2) (e0)) = (e1))\/(((op (e2) (e0)) = (e2))\/((op (e2) (e0)) = (e3))))) -> (~((op (e2) (e0)) = (op (e3) (e0)))) -> (~((op (e2) (e0)) = (e1))) -> (~((e1) = (e2))) -> (((op (e0) (e0)) = (e2))\/(((op (e1) (e0)) = (e2))\/(((op (e2) (e0)) = (e2))\/((op (e3) (e0)) = (e2))))) -> (~((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 (e3) (e0)) = (op (e3) (e3)))) -> (((op (e2) (e0)) = (e0))\/(((op (e2) (e1)) = (e0))\/(((op (e2) (e2)) = (e0))\/((op (e2) (e3)) = (e0))))) -> (((op (e3) (e0)) = (e1))\/(((op (e3) (e1)) = (e1))\/(((op (e3) (e2)) = (e1))\/((op (e3) (e3)) = (e1))))) -> (~((op (e3) (e0)) = (e1))) -> (~((op (e3) (e1)) = (e1))) -> (~((op (e3) (e2)) = (e1))) -> (~((op (e1) (e3)) = (op (e3) (e3)))) -> (~((e1) = (e3))) -> (((op (e0) (e0)) = (e3))\/(((op (e1) (e0)) = (e3))\/(((op (e2) (e0)) = (e3))\/((op (e3) (e0)) = (e3))))) -> ((op (e0) (e3)) = (e2)) -> (~((e2) = (e3))) -> False). % 18.87/19.04 do 0 intro. intros zenon_H189 zenon_H5b zenon_H168 zenon_H9a zenon_H128 zenon_H10a zenon_H52 zenon_H173 zenon_H2b zenon_H6d zenon_H1c4 zenon_H1ac zenon_H149 zenon_Ha6 zenon_H18f zenon_H136 zenon_H1d zenon_H1ca zenon_He2 zenon_Ha5 zenon_H1c7 zenon_Hf3 zenon_H11f zenon_Hdb zenon_H110 zenon_H57 zenon_Hdf zenon_H102 zenon_H17e zenon_H49 zenon_H22 zenon_H201 zenon_H7a zenon_Hd8 zenon_H1ef zenon_H24a zenon_H25e zenon_H115 zenon_H22d zenon_H1f0 zenon_H259 zenon_H17b zenon_H1db zenon_H7c zenon_H1fe zenon_Ha4 zenon_H20d zenon_H231 zenon_H145 zenon_H71 zenon_H2f zenon_He8 zenon_Had zenon_H250 zenon_H251 zenon_Hd5 zenon_H95 zenon_H1e0 zenon_Hcd zenon_H12b. % 18.87/19.04 apply (zenon_or_s _ _ zenon_H1fe); [ zenon_intro zenon_H7b | zenon_intro zenon_H1ff ]. % 18.87/19.04 apply (zenon_L375_); trivial. % 18.87/19.04 apply (zenon_or_s _ _ zenon_H1ff); [ zenon_intro zenon_H86 | zenon_intro zenon_H200 ]. % 18.87/19.04 apply (zenon_L804_); trivial. % 18.87/19.04 apply (zenon_or_s _ _ zenon_H200); [ zenon_intro zenon_Hee | zenon_intro zenon_H148 ]. % 18.87/19.04 apply (zenon_L277_); trivial. % 18.87/19.04 apply (zenon_or_s _ _ zenon_H168); [ zenon_intro zenon_H3a | zenon_intro zenon_H169 ]. % 18.87/19.04 apply (zenon_L35_); trivial. % 18.87/19.04 apply (zenon_or_s _ _ zenon_H169); [ zenon_intro zenon_H99 | zenon_intro zenon_H16a ]. % 18.87/19.04 apply (zenon_L36_); trivial. % 18.87/19.04 apply (zenon_or_s _ _ zenon_H16a); [ zenon_intro zenon_Ha9 | zenon_intro zenon_He3 ]. % 18.87/19.04 apply (zenon_or_s _ _ zenon_H1e0); [ zenon_intro zenon_H3a | zenon_intro zenon_H1e1 ]. % 18.87/19.04 apply (zenon_L35_); trivial. % 18.87/19.04 apply (zenon_or_s _ _ zenon_H1e1); [ zenon_intro zenon_H9e | zenon_intro zenon_H1e2 ]. % 18.87/19.04 apply (zenon_L107_); trivial. % 18.87/19.04 apply (zenon_or_s _ _ zenon_H1e2); [ zenon_intro zenon_H3b | zenon_intro zenon_H15e ]. % 18.87/19.04 apply (zenon_or_s _ _ zenon_H128); [ zenon_intro zenon_H9d | zenon_intro zenon_H129 ]. % 18.87/19.04 exact (zenon_H1ef zenon_H9d). % 18.87/19.04 apply (zenon_or_s _ _ zenon_H129); [ zenon_intro zenon_H10d | zenon_intro zenon_H12a ]. % 18.87/19.04 exact (zenon_H10a zenon_H10d). % 18.87/19.04 apply (zenon_or_s _ _ zenon_H12a); [ zenon_intro zenon_Hf0 | zenon_intro zenon_Hd6 ]. % 18.87/19.04 apply (zenon_or_s _ _ zenon_H2f); [ zenon_intro zenon_H34 | zenon_intro zenon_H33 ]. % 18.87/19.04 apply (zenon_L811_); trivial. % 18.87/19.04 apply (zenon_or_s _ _ zenon_H33); [ zenon_intro zenon_H36 | zenon_intro zenon_H35 ]. % 18.87/19.04 apply (zenon_L128_); trivial. % 18.87/19.04 apply (zenon_or_s _ _ zenon_H35); [ zenon_intro zenon_H2c | zenon_intro zenon_H37 ]. % 18.87/19.04 apply (zenon_or_s _ _ zenon_H1ac); [ zenon_intro zenon_H44 | zenon_intro zenon_H1af ]. % 18.87/19.04 apply (zenon_L100_); trivial. % 18.87/19.04 apply (zenon_or_s _ _ zenon_H1af); [ zenon_intro zenon_H1b1 | zenon_intro zenon_H1b0 ]. % 18.87/19.04 apply (zenon_L509_); trivial. % 18.87/19.04 apply (zenon_or_s _ _ zenon_H1b0); [ zenon_intro zenon_H61 | zenon_intro zenon_H60 ]. % 18.87/19.04 apply (zenon_L146_); trivial. % 18.87/19.04 apply (zenon_L873_); trivial. % 18.87/19.04 apply (zenon_L300_); trivial. % 18.87/19.04 apply (zenon_L800_); trivial. % 18.87/19.04 apply (zenon_L109_); trivial. % 18.87/19.04 apply (zenon_L81_); trivial. % 18.87/19.04 (* end of lemma zenon_L914_ *) % 18.87/19.04 assert (zenon_L915_ : (~((op (e3) (e2)) = (e1))) -> (~((op (e3) (e1)) = (e1))) -> (~((op (e3) (e0)) = (e1))) -> (((op (e3) (e0)) = (e1))\/(((op (e3) (e1)) = (e1))\/(((op (e3) (e2)) = (e1))\/((op (e3) (e3)) = (e1))))) -> (((op (e3) (e0)) = (e0))\/(((op (e3) (e1)) = (e0))\/(((op (e3) (e2)) = (e0))\/((op (e3) (e3)) = (e0))))) -> (~((e0) = (e2))) -> ((op (e1) (e1)) = (e2)) -> ((op (e2) (e1)) = (e3)) -> (~((op (e1) (e2)) = (op (e3) (e2)))) -> (((op (e0) (e3)) = (e3))\/(((op (e1) (e3)) = (e3))\/(((op (e2) (e3)) = (e3))\/((op (e3) (e3)) = (e3))))) -> (~((e2) = (e3))) -> (~((op (e0) (e3)) = (op (e2) (e3)))) -> ((op (e2) (e1)) = (e1)) -> (~((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))))) -> (((op (e1) (e3)) = (e0))\/(((op (e1) (e3)) = (e1))\/(((op (e1) (e3)) = (e2))\/((op (e1) (e3)) = (e3))))) -> (~((op (e1) (e3)) = (op (e3) (e3)))) -> (~((op (e1) (e0)) = (op (e1) (e3)))) -> (~((op (e1) (e3)) = (op (e2) (e3)))) -> (~((op (e1) (e0)) = (e1))) -> (~((op (e1) (e0)) = (op (e1) (e2)))) -> (((op (e1) (e0)) = (e0))\/(((op (e1) (e0)) = (e1))\/(((op (e1) (e0)) = (e2))\/((op (e1) (e0)) = (e3))))) -> (~((op (e3) (e3)) = (e3))) -> (((op (e0) (e2)) = (e0))\/(((op (e1) (e2)) = (e0))\/(((op (e2) (e2)) = (e0))\/((op (e3) (e2)) = (e0))))) -> (~((op (e0) (e1)) = (op (e0) (e2)))) -> (~((op (e1) (e1)) = (op (e1) (e2)))) -> (~((op (e2) (e0)) = (op (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) (e1)) = (e0)) -> (~((op (e1) (e1)) = (op (e1) (e3)))) -> (~((op (e2) (e0)) = (op (e2) (e3)))) -> ((op (e2) (e0)) = (e0)) -> (~((op (e3) (e2)) = (op (e3) (e3)))) -> (~((op (e1) (e0)) = (op (e2) (e0)))) -> (((op (e1) (e0)) = (e0))\/(((op (e1) (e1)) = (e0))\/(((op (e1) (e2)) = (e0))\/((op (e1) (e3)) = (e0))))) -> (((op (e2) (e0)) = (e0))\/(((op (e2) (e1)) = (e0))\/(((op (e2) (e2)) = (e0))\/((op (e2) (e3)) = (e0))))) -> (~((op (e2) (e0)) = (op (e3) (e0)))) -> (~((op (e0) (e1)) = (op (e2) (e1)))) -> (~((op (e1) (e2)) = (op (e2) (e2)))) -> (((op (e2) (e0)) = (e0))\/(((op (e2) (e0)) = (e1))\/(((op (e2) (e0)) = (e2))\/((op (e2) (e0)) = (e3))))) -> (~((op (e2) (e0)) = (e1))) -> ((op (e2) (e1)) = (e2)) -> (~((op (e2) (e0)) = (op (e2) (e1)))) -> (~((op (e0) (e0)) = (op (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 (e3) (e1)) = (op (e3) (e3)))) -> (((op (e3) (e0)) = (e2))\/(((op (e3) (e1)) = (e2))\/(((op (e3) (e2)) = (e2))\/((op (e3) (e3)) = (e2))))) -> (~((op (e0) (e3)) = (op (e1) (e3)))) -> (~((e0) = (e3))) -> (((op (e0) (e3)) = (e0))\/(((op (e0) (e3)) = (e1))\/(((op (e0) (e3)) = (e2))\/((op (e0) (e3)) = (e3))))) -> (((op (e0) (e0)) = (e1))\/(((op (e0) (e1)) = (e1))\/(((op (e0) (e2)) = (e1))\/((op (e0) (e3)) = (e1))))) -> (~((e1) = (e2))) -> (((op (e0) (e3)) = (e2))\/(((op (e1) (e3)) = (e2))\/(((op (e2) (e3)) = (e2))\/((op (e3) (e3)) = (e2))))) -> (~((op (e3) (e0)) = (op (e3) (e3)))) -> ((~((op (e0) (e3)) = (e1)))\/((op (e0) (e1)) = (e3))) -> ((~((op (e1) (e2)) = (e1)))\/((op (e1) (e1)) = (e2))) -> (~((op (e0) (e1)) = (op (e1) (e1)))) -> (((op (e1) (e0)) = (e1))\/(((op (e1) (e1)) = (e1))\/(((op (e1) (e2)) = (e1))\/((op (e1) (e3)) = (e1))))) -> (~((op (e1) (e1)) = (e1))) -> ((~((op (e2) (e0)) = (e1)))\/((op (e2) (e1)) = (e0))) -> ((~((op (e3) (e0)) = (e1)))\/((op (e3) (e1)) = (e0))) -> (((op (e0) (e0)) = (e1))\/(((op (e1) (e0)) = (e1))\/(((op (e2) (e0)) = (e1))\/((op (e3) (e0)) = (e1))))) -> (~((op (e0) (e0)) = (op (e0) (e2)))) -> (((op (e0) (e2)) = (e1))\/(((op (e1) (e2)) = (e1))\/(((op (e2) (e2)) = (e1))\/((op (e3) (e2)) = (e1))))) -> (~((op (e0) (e1)) = (op (e3) (e1)))) -> ((~((op (e3) (e2)) = (e1)))\/((op (e3) (e1)) = (e2))) -> ((~((op (e2) (e2)) = (e1)))\/((op (e2) (e1)) = (e2))) -> ((~((op (e1) (e3)) = (e1)))\/((op (e1) (e1)) = (e3))) -> (~((op (e0) (e0)) = (e0))) -> (~((op (e1) (e0)) = (op (e1) (e1)))) -> (~((e0) = (e1))) -> (~((e1) = (e3))) -> (~((op (e3) (e0)) = (op (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) (e0)) = (e0))\/(((op (e1) (e0)) = (e0))\/(((op (e2) (e0)) = (e0))\/((op (e3) (e0)) = (e0))))) -> ((~((op (e1) (e0)) = (e1)))\/((op (e1) (e1)) = (e0))) -> (((op (e0) (e0)) = (e2))\/(((op (e0) (e1)) = (e2))\/(((op (e0) (e2)) = (e2))\/((op (e0) (e3)) = (e2))))) -> (~((op (e0) (e1)) = (e1))) -> (~((op (e0) (e2)) = (e1))) -> (~((op (e0) (e3)) = (e1))) -> False). % 18.87/19.04 do 0 intro. intros zenon_H251 zenon_H250 zenon_Had zenon_He8 zenon_H1ac zenon_H149 zenon_H110 zenon_Ha6 zenon_H115 zenon_H136 zenon_H12b zenon_He2 zenon_Ha5 zenon_H1c7 zenon_Hf3 zenon_H11f zenon_Hdf zenon_Hd5 zenon_Hd8 zenon_Hdb zenon_H1ef zenon_H24a zenon_H25e zenon_H102 zenon_H6a zenon_H4a zenon_H4f zenon_H52 zenon_H67 zenon_H54 zenon_H49 zenon_H57 zenon_H5b zenon_H34 zenon_H62 zenon_H201 zenon_H22 zenon_H2f zenon_H17b zenon_H17e zenon_H2b zenon_H259 zenon_H1db zenon_H1ca zenon_H1f0 zenon_H189 zenon_H1fe zenon_H14f zenon_H130 zenon_H153 zenon_H1d zenon_H9a zenon_He4 zenon_H22d zenon_H7c zenon_H145 zenon_H71 zenon_H25c zenon_H256 zenon_H10e zenon_H128 zenon_H10a zenon_H257 zenon_H254 zenon_H235 zenon_H13c zenon_H139 zenon_H210 zenon_H252 zenon_H253 zenon_H258 zenon_H3f zenon_H45 zenon_Ha1 zenon_H95 zenon_H6f zenon_H6d zenon_H168 zenon_H3e zenon_H25d zenon_H183 zenon_Ha4 zenon_H20d zenon_H231. % 18.87/19.04 apply (zenon_or_s _ _ zenon_H22d); [ zenon_intro zenon_H7a | zenon_intro zenon_H22e ]. % 18.87/19.04 apply (zenon_L814_); trivial. % 18.87/19.04 apply (zenon_or_s _ _ zenon_H22e); [ zenon_intro zenon_Ha0 | zenon_intro zenon_H22f ]. % 18.87/19.04 exact (zenon_Ha4 zenon_Ha0). % 18.87/19.04 apply (zenon_or_s _ _ zenon_H22f); [ zenon_intro zenon_H122 | zenon_intro zenon_Hc3 ]. % 18.87/19.04 exact (zenon_H20d zenon_H122). % 18.87/19.04 exact (zenon_H231 zenon_Hc3). % 18.87/19.04 (* end of lemma zenon_L915_ *) % 18.87/19.04 assert (zenon_L916_ : (~((op (e1) (e1)) = (op (e3) (e1)))) -> (~((op (e0) (e0)) = (e0))) -> (~((e1) = (e2))) -> ((~((op (e0) (e3)) = (e1)))\/((op (e0) (e1)) = (e3))) -> ((~((op (e1) (e2)) = (e1)))\/((op (e1) (e1)) = (e2))) -> (~((op (e0) (e1)) = (op (e1) (e1)))) -> (((op (e1) (e0)) = (e1))\/(((op (e1) (e1)) = (e1))\/(((op (e1) (e2)) = (e1))\/((op (e1) (e3)) = (e1))))) -> (~((op (e1) (e1)) = (e1))) -> ((~((op (e2) (e0)) = (e1)))\/((op (e2) (e1)) = (e0))) -> ((op (e0) (e1)) = (e0)) -> ((~((op (e3) (e0)) = (e1)))\/((op (e3) (e1)) = (e0))) -> (((op (e0) (e0)) = (e1))\/(((op (e0) (e1)) = (e1))\/(((op (e0) (e2)) = (e1))\/((op (e0) (e3)) = (e1))))) -> (((op (e0) (e0)) = (e1))\/(((op (e1) (e0)) = (e1))\/(((op (e2) (e0)) = (e1))\/((op (e3) (e0)) = (e1))))) -> (~((op (e0) (e1)) = (e1))) -> (~((op (e0) (e0)) = (op (e0) (e2)))) -> (((op (e0) (e2)) = (e1))\/(((op (e1) (e2)) = (e1))\/(((op (e2) (e2)) = (e1))\/((op (e3) (e2)) = (e1))))) -> (~((op (e0) (e1)) = (op (e3) (e1)))) -> ((~((op (e3) (e2)) = (e1)))\/((op (e3) (e1)) = (e2))) -> (~((op (e0) (e1)) = (op (e2) (e1)))) -> ((~((op (e2) (e2)) = (e1)))\/((op (e2) (e1)) = (e2))) -> ((~((op (e1) (e3)) = (e1)))\/((op (e1) (e1)) = (e3))) -> (~((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 (e0) (e3)))) -> (~((op (e1) (e1)) = (op (e1) (e3)))) -> (~((op (e2) (e0)) = (op (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) (e0)) = (op (e2) (e2)))) -> (~((op (e1) (e1)) = (op (e1) (e2)))) -> (~((op (e0) (e1)) = (op (e0) (e2)))) -> (~((e0) = (e1))) -> (~((e1) = (e3))) -> (~((e2) = (e3))) -> (((op (e2) (e0)) = (e0))\/(((op (e2) (e1)) = (e0))\/(((op (e2) (e2)) = (e0))\/((op (e2) (e3)) = (e0))))) -> (~((op (e3) (e0)) = (op (e3) (e2)))) -> (~((e0) = (e3))) -> (~((op (e2) (e2)) = (op (e2) (e3)))) -> (~((op (e3) (e0)) = (op (e3) (e3)))) -> (~((op (e2) (e0)) = (op (e3) (e0)))) -> (((op (e0) (e0)) = (e3))\/(((op (e0) (e1)) = (e3))\/(((op (e0) (e2)) = (e3))\/((op (e0) (e3)) = (e3))))) -> (((op (e0) (e0)) = (e0))\/(((op (e1) (e0)) = (e0))\/(((op (e2) (e0)) = (e0))\/((op (e3) (e0)) = (e0))))) -> ((~((op (e1) (e0)) = (e1)))\/((op (e1) (e1)) = (e0))) -> (((op (e0) (e0)) = (e3))\/(((op (e1) (e0)) = (e3))\/(((op (e2) (e0)) = (e3))\/((op (e3) (e0)) = (e3))))) -> (~((op (e1) (e0)) = (e1))) -> (~((op (e2) (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 (e0) (e3)) = (e0))\/(((op (e0) (e3)) = (e1))\/(((op (e0) (e3)) = (e2))\/((op (e0) (e3)) = (e3))))) -> (~((op (e1) (e0)) = (op (e2) (e0)))) -> (~((op (e0) (e3)) = (op (e1) (e3)))) -> (((op (e0) (e3)) = (e2))\/(((op (e1) (e3)) = (e2))\/(((op (e2) (e3)) = (e2))\/((op (e3) (e3)) = (e2))))) -> (~((op (e3) (e1)) = (op (e3) (e3)))) -> (~((op (e0) (e2)) = (op (e3) (e2)))) -> (((op (e3) (e0)) = (e2))\/(((op (e3) (e1)) = (e2))\/(((op (e3) (e2)) = (e2))\/((op (e3) (e3)) = (e2))))) -> ((op (e1) (e1)) = (e2)) -> (((op (e3) (e0)) = (e0))\/(((op (e3) (e1)) = (e0))\/(((op (e3) (e2)) = (e0))\/((op (e3) (e3)) = (e0))))) -> (((op (e0) (e3)) = (e3))\/(((op (e1) (e3)) = (e3))\/(((op (e2) (e3)) = (e3))\/((op (e3) (e3)) = (e3))))) -> (~((op (e3) (e3)) = (e3))) -> (~((op (e1) (e3)) = (op (e3) (e3)))) -> (~((op (e1) (e0)) = (op (e1) (e3)))) -> (((op (e1) (e3)) = (e0))\/(((op (e1) (e3)) = (e1))\/(((op (e1) (e3)) = (e2))\/((op (e1) (e3)) = (e3))))) -> (~((op (e2) (e3)) = (op (e3) (e3)))) -> (~((op (e2) (e1)) = (op (e2) (e3)))) -> ((op (e2) (e1)) = (e1)) -> (~((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))))) -> (((op (e3) (e0)) = (e1))\/(((op (e3) (e1)) = (e1))\/(((op (e3) (e2)) = (e1))\/((op (e3) (e3)) = (e1))))) -> (~((op (e1) (e2)) = (op (e3) (e2)))) -> ((op (e2) (e1)) = (e3)) -> (~((op (e1) (e2)) = (op (e2) (e2)))) -> (((op (e2) (e0)) = (e0))\/(((op (e2) (e0)) = (e1))\/(((op (e2) (e0)) = (e2))\/((op (e2) (e0)) = (e3))))) -> (~((op (e2) (e0)) = (e1))) -> (((op (e1) (e0)) = (e0))\/(((op (e1) (e1)) = (e0))\/(((op (e1) (e2)) = (e0))\/((op (e1) (e3)) = (e0))))) -> (~((op (e0) (e3)) = (e1))) -> (~((op (e0) (e2)) = (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) (e0)) = (e0))\/(((op (e1) (e0)) = (e1))\/(((op (e1) (e0)) = (e2))\/((op (e1) (e0)) = (e3))))) -> ((op (e2) (e1)) = (e2)) -> (~((op (e2) (e0)) = (op (e2) (e1)))) -> (~((e0) = (e2))) -> (~((op (e0) (e0)) = (op (e0) (e3)))) -> (((op (e0) (e0)) = (e2))\/(((op (e0) (e1)) = (e2))\/(((op (e0) (e2)) = (e2))\/((op (e0) (e3)) = (e2))))) -> (~((op (e2) (e1)) = (op (e3) (e1)))) -> ((~((op (e3) (e1)) = (e1)))\/((op (e3) (e1)) = (e1))) -> False). % 18.87/19.04 do 0 intro. intros zenon_H160 zenon_H3f zenon_H7c zenon_H25c zenon_H256 zenon_H10e zenon_H128 zenon_H10a zenon_H257 zenon_H49 zenon_H254 zenon_H22d zenon_H235 zenon_Ha4 zenon_H13c zenon_H139 zenon_H210 zenon_H252 zenon_H17e zenon_H253 zenon_H258 zenon_H45 zenon_H6a zenon_H54 zenon_H57 zenon_H5b zenon_H62 zenon_H67 zenon_H52 zenon_H4f zenon_H4a zenon_Ha1 zenon_H95 zenon_H12b zenon_H2f zenon_H6f zenon_H9a zenon_H6d zenon_H71 zenon_H17b zenon_H168 zenon_H3e zenon_H25d zenon_H1e0 zenon_H1ef zenon_H173 zenon_H1c4 zenon_H18f zenon_He4 zenon_H201 zenon_H1d zenon_H145 zenon_H130 zenon_H14f zenon_H153 zenon_H110 zenon_H1ac zenon_H136 zenon_H102 zenon_Hd5 zenon_Hd8 zenon_Hdf zenon_Hf3 zenon_H1c7 zenon_Ha5 zenon_He2 zenon_Hdb zenon_H11f zenon_He8 zenon_H115 zenon_Ha6 zenon_H2b zenon_H259 zenon_H1db zenon_H22 zenon_H231 zenon_H20d zenon_H1fe zenon_H24a zenon_H25e zenon_H1ca zenon_H1f0 zenon_H149 zenon_H189 zenon_H183 zenon_Haf zenon_H261. % 18.87/19.04 apply (zenon_or_s _ _ zenon_H254); [ zenon_intro zenon_Had | zenon_intro zenon_H1b1 ]. % 18.87/19.04 apply (zenon_or_s _ _ zenon_H261); [ zenon_intro zenon_H250 | zenon_intro zenon_Hae ]. % 18.87/19.04 apply (zenon_or_s _ _ zenon_H252); [ zenon_intro zenon_H251 | zenon_intro zenon_H14d ]. % 18.87/19.04 apply (zenon_or_s _ _ zenon_H3e); [ zenon_intro zenon_H42 | zenon_intro zenon_H41 ]. % 18.87/19.04 exact (zenon_H3f zenon_H42). % 18.87/19.04 apply (zenon_or_s _ _ zenon_H41); [ zenon_intro zenon_H27 | zenon_intro zenon_H43 ]. % 18.87/19.04 apply (zenon_or_s _ _ zenon_H22d); [ zenon_intro zenon_H7a | zenon_intro zenon_H22e ]. % 18.87/19.04 apply (zenon_or_s _ _ zenon_H183); [ zenon_intro zenon_H7b | zenon_intro zenon_H186 ]. % 18.87/19.04 apply (zenon_L26_); trivial. % 18.87/19.04 apply (zenon_or_s _ _ zenon_H186); [ zenon_intro zenon_H10f | zenon_intro zenon_H187 ]. % 18.87/19.04 apply (zenon_L764_); trivial. % 18.87/19.04 apply (zenon_or_s _ _ zenon_H187); [ zenon_intro zenon_H150 | zenon_intro zenon_Hcd ]. % 18.87/19.04 apply (zenon_or_s _ _ zenon_H1fe); [ zenon_intro zenon_H7b | zenon_intro zenon_H1ff ]. % 18.87/19.04 apply (zenon_L26_); trivial. % 18.87/19.04 apply (zenon_or_s _ _ zenon_H1ff); [ zenon_intro zenon_H86 | zenon_intro zenon_H200 ]. % 18.87/19.04 apply (zenon_L257_); trivial. % 18.87/19.04 apply (zenon_or_s _ _ zenon_H200); [ zenon_intro zenon_Hee | zenon_intro zenon_H148 ]. % 18.87/19.04 apply (zenon_L277_); trivial. % 18.87/19.04 apply (zenon_or_s _ _ zenon_H168); [ zenon_intro zenon_H3a | zenon_intro zenon_H169 ]. % 18.87/19.04 apply (zenon_L35_); trivial. % 18.87/19.04 apply (zenon_or_s _ _ zenon_H169); [ zenon_intro zenon_H99 | zenon_intro zenon_H16a ]. % 18.87/19.04 apply (zenon_L36_); trivial. % 18.87/19.04 apply (zenon_or_s _ _ zenon_H16a); [ zenon_intro zenon_Ha9 | zenon_intro zenon_He3 ]. % 18.87/19.04 apply (zenon_L911_); trivial. % 18.87/19.04 apply (zenon_L913_); trivial. % 18.87/19.04 apply (zenon_L914_); trivial. % 18.87/19.04 apply (zenon_or_s _ _ zenon_H22e); [ zenon_intro zenon_Ha0 | zenon_intro zenon_H22f ]. % 18.87/19.04 exact (zenon_Ha4 zenon_Ha0). % 18.87/19.04 apply (zenon_or_s _ _ zenon_H22f); [ zenon_intro zenon_H122 | zenon_intro zenon_Hc3 ]. % 18.87/19.04 exact (zenon_H20d zenon_H122). % 18.87/19.04 exact (zenon_H231 zenon_Hc3). % 18.87/19.04 apply (zenon_or_s _ _ zenon_H43); [ zenon_intro zenon_H34 | zenon_intro zenon_H44 ]. % 18.87/19.04 apply (zenon_L915_); trivial. % 18.87/19.04 apply (zenon_L786_); trivial. % 18.87/19.04 apply (zenon_L164_); trivial. % 18.87/19.04 apply (zenon_L42_); trivial. % 18.87/19.04 apply (zenon_L509_); trivial. % 18.87/19.04 (* end of lemma zenon_L916_ *) % 18.87/19.04 assert (zenon_L917_ : ((~((op (e2) (e1)) = (e1)))\/((op (e2) (e1)) = (e1))) -> (((op (e0) (e1)) = (e3))\/(((op (e1) (e1)) = (e3))\/(((op (e2) (e1)) = (e3))\/((op (e3) (e1)) = (e3))))) -> (~((op (e1) (e0)) = (op (e1) (e2)))) -> (((op (e3) (e0)) = (e1))\/(((op (e3) (e1)) = (e1))\/(((op (e3) (e2)) = (e1))\/((op (e3) (e3)) = (e1))))) -> (((op (e2) (e3)) = (e0))\/(((op (e2) (e3)) = (e1))\/(((op (e2) (e3)) = (e2))\/((op (e2) (e3)) = (e3))))) -> (~((op (e1) (e2)) = (op (e1) (e3)))) -> (~((op (e3) (e0)) = (op (e3) (e1)))) -> ((~((op (e2) (e3)) = (e1)))\/((op (e2) (e1)) = (e3))) -> (((op (e0) (e1)) = (e1))\/(((op (e1) (e1)) = (e1))\/(((op (e2) (e1)) = (e1))\/((op (e3) (e1)) = (e1))))) -> (~((op (e0) (e1)) = (e1))) -> (~((op (e0) (e0)) = (op (e0) (e3)))) -> (~((op (e0) (e2)) = (e1))) -> (((op (e1) (e0)) = (e0))\/(((op (e1) (e0)) = (e1))\/(((op (e1) (e0)) = (e2))\/((op (e1) (e0)) = (e3))))) -> (((op (e0) (e0)) = (e3))\/(((op (e1) (e0)) = (e3))\/(((op (e2) (e0)) = (e3))\/((op (e3) (e0)) = (e3))))) -> (((op (e0) (e3)) = (e1))\/(((op (e1) (e3)) = (e1))\/(((op (e2) (e3)) = (e1))\/((op (e3) (e3)) = (e1))))) -> (~((e0) = (e2))) -> ((~((op (e0) (e3)) = (e1)))\/((op (e0) (e1)) = (e3))) -> (~((op (e1) (e0)) = (op (e1) (e1)))) -> (~((e0) = (e1))) -> (((op (e0) (e0)) = (e0))\/(((op (e1) (e0)) = (e0))\/(((op (e2) (e0)) = (e0))\/((op (e3) (e0)) = (e0))))) -> ((~((op (e1) (e0)) = (e1)))\/((op (e1) (e1)) = (e0))) -> (((op (e0) (e0)) = (e2))\/(((op (e0) (e1)) = (e2))\/(((op (e0) (e2)) = (e2))\/((op (e0) (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 (e2) (e1)) = (op (e3) (e1)))) -> (~((op (e1) (e1)) = (op (e3) (e1)))) -> (~((op (e1) (e0)) = (op (e2) (e0)))) -> ((op (e1) (e1)) = (e2)) -> (((op (e2) (e0)) = (e0))\/(((op (e2) (e1)) = (e0))\/(((op (e2) (e2)) = (e0))\/((op (e2) (e3)) = (e0))))) -> (~((op (e2) (e2)) = (op (e2) (e3)))) -> (~((op (e2) (e2)) = (e2))) -> (~((op (e0) (e2)) = (op (e2) (e2)))) -> (((op (e2) (e2)) = (e0))\/(((op (e2) (e2)) = (e1))\/(((op (e2) (e2)) = (e2))\/((op (e2) (e2)) = (e3))))) -> (((op (e0) (e3)) = (e0))\/(((op (e0) (e3)) = (e1))\/(((op (e0) (e3)) = (e2))\/((op (e0) (e3)) = (e3))))) -> (~((op (e1) (e1)) = (op (e1) (e3)))) -> (~((op (e3) (e2)) = (op (e3) (e3)))) -> (((op (e0) (e3)) = (e0))\/(((op (e1) (e3)) = (e0))\/(((op (e2) (e3)) = (e0))\/((op (e3) (e3)) = (e0))))) -> (~((op (e1) (e1)) = (op (e1) (e2)))) -> (~((op (e0) (e1)) = (op (e0) (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) (e2)) = (op (e3) (e2)))) -> (~((op (e1) (e2)) = (op (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)) = (e2))\/(((op (e3) (e1)) = (e2))\/(((op (e3) (e2)) = (e2))\/((op (e3) (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))))) -> (~((e2) = (e3))) -> (~((op (e2) (e1)) = (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 (e1) (e0)) = (e3))\/(((op (e1) (e1)) = (e3))\/(((op (e1) (e2)) = (e3))\/((op (e1) (e3)) = (e3))))) -> (~((op (e1) (e0)) = (op (e1) (e3)))) -> (~((op (e3) (e1)) = (op (e3) (e3)))) -> (((op (e1) (e0)) = (e0))\/(((op (e1) (e1)) = (e0))\/(((op (e1) (e2)) = (e0))\/((op (e1) (e3)) = (e0))))) -> (((op (e0) (e2)) = (e0))\/(((op (e1) (e2)) = (e0))\/(((op (e2) (e2)) = (e0))\/((op (e3) (e2)) = (e0))))) -> (~((op (e2) (e0)) = (op (e2) (e2)))) -> (((op (e3) (e0)) = (e0))\/(((op (e3) (e1)) = (e0))\/(((op (e3) (e2)) = (e0))\/((op (e3) (e3)) = (e0))))) -> (~((op (e2) (e2)) = (op (e3) (e2)))) -> (~((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) (e1)))) -> (~((op (e2) (e0)) = (op (e2) (e3)))) -> (~((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 (e3) (e0)))) -> (~((op (e3) (e0)) = (op (e3) (e2)))) -> (((op (e3) (e3)) = (e0))\/(((op (e3) (e3)) = (e1))\/(((op (e3) (e3)) = (e2))\/((op (e3) (e3)) = (e3))))) -> (~((op (e3) (e3)) = (e3))) -> (~((op (e2) (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) (e0)) = (e2))\/(((op (e1) (e0)) = (e2))\/(((op (e2) (e0)) = (e2))\/((op (e3) (e0)) = (e2))))) -> (~((e0) = (e3))) -> (~((e1) = (e3))) -> ((~((op (e1) (e3)) = (e1)))\/((op (e1) (e1)) = (e3))) -> ((~((op (e2) (e2)) = (e1)))\/((op (e2) (e1)) = (e2))) -> (~((op (e0) (e1)) = (op (e2) (e1)))) -> ((~((op (e3) (e2)) = (e1)))\/((op (e3) (e1)) = (e2))) -> (~((op (e0) (e1)) = (op (e3) (e1)))) -> (((op (e0) (e2)) = (e1))\/(((op (e1) (e2)) = (e1))\/(((op (e2) (e2)) = (e1))\/((op (e3) (e2)) = (e1))))) -> (~((op (e0) (e0)) = (op (e0) (e2)))) -> (((op (e0) (e0)) = (e1))\/(((op (e1) (e0)) = (e1))\/(((op (e2) (e0)) = (e1))\/((op (e3) (e0)) = (e1))))) -> (~((op (e0) (e3)) = (e1))) -> (((op (e0) (e0)) = (e1))\/(((op (e0) (e1)) = (e1))\/(((op (e0) (e2)) = (e1))\/((op (e0) (e3)) = (e1))))) -> ((~((op (e3) (e0)) = (e1)))\/((op (e3) (e1)) = (e0))) -> ((op (e0) (e1)) = (e0)) -> ((~((op (e2) (e0)) = (e1)))\/((op (e2) (e1)) = (e0))) -> (~((op (e0) (e1)) = (op (e1) (e1)))) -> ((~((op (e1) (e2)) = (e1)))\/((op (e1) (e1)) = (e2))) -> (~((e1) = (e2))) -> (~((op (e0) (e0)) = (e0))) -> ((~((op (e3) (e1)) = (e1)))\/((op (e3) (e1)) = (e1))) -> (~((op (e1) (e0)) = (e1))) -> (~((op (e1) (e1)) = (e1))) -> (((op (e2) (e0)) = (e1))\/(((op (e2) (e1)) = (e1))\/(((op (e2) (e2)) = (e1))\/((op (e2) (e3)) = (e1))))) -> (~((op (e1) (e2)) = (op (e2) (e2)))) -> (((op (e1) (e0)) = (e1))\/(((op (e1) (e1)) = (e1))\/(((op (e1) (e2)) = (e1))\/((op (e1) (e3)) = (e1))))) -> False). % 18.87/19.04 do 0 intro. intros zenon_H262 zenon_H1a5 zenon_H24a zenon_He8 zenon_H11f zenon_H124 zenon_H1cf zenon_H263 zenon_H109 zenon_Ha4 zenon_H189 zenon_H20d zenon_H25e zenon_H1e0 zenon_H133 zenon_H149 zenon_H25c zenon_H45 zenon_Ha1 zenon_H3e zenon_H25d zenon_H183 zenon_H136 zenon_Hdb zenon_Haf zenon_H160 zenon_H201 zenon_H110 zenon_H2f zenon_H6d zenon_H173 zenon_Ha8 zenon_H1c4 zenon_He4 zenon_H57 zenon_H62 zenon_H67 zenon_H4f zenon_H4a zenon_H1a4 zenon_H191 zenon_H14f zenon_H115 zenon_He2 zenon_He7 zenon_H153 zenon_Hd5 zenon_H1d zenon_Hdf zenon_H12b zenon_H1c7 zenon_H71 zenon_H145 zenon_H16f zenon_Hd8 zenon_H130 zenon_H22 zenon_H6a zenon_H52 zenon_H1ac zenon_H18f zenon_H17b zenon_H259 zenon_H1f0 zenon_H5b zenon_H54 zenon_H168 zenon_H1fa zenon_H6f zenon_H101 zenon_H102 zenon_Hf3 zenon_Hc2 zenon_H1d5 zenon_H1fe zenon_H9a zenon_H95 zenon_H258 zenon_H253 zenon_H17e zenon_H252 zenon_H210 zenon_H139 zenon_H13c zenon_H235 zenon_H231 zenon_H22d zenon_H254 zenon_H49 zenon_H257 zenon_H10e zenon_H256 zenon_H7c zenon_H3f zenon_H261 zenon_H1ef zenon_H10a zenon_H106 zenon_H2b zenon_H128. % 18.87/19.04 apply (zenon_or_s _ _ zenon_H258); [ zenon_intro zenon_H24e | zenon_intro zenon_H13f ]. % 18.87/19.04 apply (zenon_or_s _ _ zenon_H257); [ zenon_intro zenon_H1db | zenon_intro zenon_H36 ]. % 18.87/19.04 apply (zenon_or_s _ _ zenon_H262); [ zenon_intro zenon_H24f | zenon_intro zenon_Ha5 ]. % 18.87/19.04 apply (zenon_or_s _ _ zenon_H253); [ zenon_intro zenon_H198 | zenon_intro zenon_H1ca ]. % 18.87/19.04 apply (zenon_or_s _ _ zenon_H263); [ zenon_intro zenon_H255 | zenon_intro zenon_Ha6 ]. % 18.87/19.04 apply (zenon_L725_); trivial. % 18.87/19.04 apply (zenon_or_s _ _ zenon_H261); [ zenon_intro zenon_H250 | zenon_intro zenon_Hae ]. % 18.87/19.04 apply (zenon_L714_); trivial. % 18.87/19.04 apply (zenon_or_s _ _ zenon_H3e); [ zenon_intro zenon_H42 | zenon_intro zenon_H41 ]. % 18.87/19.04 exact (zenon_H3f zenon_H42). % 18.87/19.04 apply (zenon_or_s _ _ zenon_H41); [ zenon_intro zenon_H27 | zenon_intro zenon_H43 ]. % 18.87/19.04 apply (zenon_or_s _ _ zenon_H22d); [ zenon_intro zenon_H7a | zenon_intro zenon_H22e ]. % 18.87/19.04 apply (zenon_or_s _ _ zenon_H183); [ zenon_intro zenon_H7b | zenon_intro zenon_H186 ]. % 18.87/19.04 apply (zenon_L26_); trivial. % 18.87/19.04 apply (zenon_or_s _ _ zenon_H186); [ zenon_intro zenon_H10f | zenon_intro zenon_H187 ]. % 18.87/19.04 apply (zenon_L726_); trivial. % 18.87/19.04 apply (zenon_or_s _ _ zenon_H187); [ zenon_intro zenon_H150 | zenon_intro zenon_Hcd ]. % 18.87/19.04 apply (zenon_or_s _ _ zenon_H1fe); [ zenon_intro zenon_H7b | zenon_intro zenon_H1ff ]. % 18.87/19.04 apply (zenon_L26_); trivial. % 18.87/19.04 apply (zenon_or_s _ _ zenon_H1ff); [ zenon_intro zenon_H86 | zenon_intro zenon_H200 ]. % 18.87/19.04 apply (zenon_L257_); trivial. % 18.87/19.04 apply (zenon_or_s _ _ zenon_H200); [ zenon_intro zenon_Hee | zenon_intro zenon_H148 ]. % 18.87/19.04 apply (zenon_or_s _ _ zenon_H168); [ zenon_intro zenon_H3a | zenon_intro zenon_H169 ]. % 18.87/19.04 apply (zenon_L35_); trivial. % 18.87/19.04 apply (zenon_or_s _ _ zenon_H169); [ zenon_intro zenon_H99 | zenon_intro zenon_H16a ]. % 18.87/19.04 apply (zenon_L36_); trivial. % 18.87/19.04 apply (zenon_or_s _ _ zenon_H16a); [ zenon_intro zenon_Ha9 | zenon_intro zenon_He3 ]. % 18.87/19.04 apply (zenon_L761_); trivial. % 18.87/19.04 apply (zenon_or_s _ _ zenon_H128); [ zenon_intro zenon_H9d | zenon_intro zenon_H129 ]. % 18.87/19.04 exact (zenon_H1ef zenon_H9d). % 18.87/19.04 apply (zenon_or_s _ _ zenon_H129); [ zenon_intro zenon_H10d | zenon_intro zenon_H12a ]. % 18.87/19.04 exact (zenon_H10a zenon_H10d). % 18.87/19.04 apply (zenon_or_s _ _ zenon_H12a); [ zenon_intro zenon_Hf0 | zenon_intro zenon_Hd6 ]. % 18.87/19.04 apply (zenon_or_s _ _ zenon_H16f); [ zenon_intro zenon_H9e | zenon_intro zenon_H170 ]. % 18.87/19.04 apply (zenon_L768_); trivial. % 18.87/19.04 apply (zenon_or_s _ _ zenon_H170); [ zenon_intro zenon_H13f | zenon_intro zenon_H171 ]. % 18.87/19.04 apply (zenon_L166_); trivial. % 18.87/19.04 apply (zenon_or_s _ _ zenon_H171); [ zenon_intro zenon_H16c | zenon_intro zenon_Hdc ]. % 18.87/19.04 apply (zenon_L167_); trivial. % 18.87/19.04 apply (zenon_L117_); trivial. % 18.87/19.04 exact (zenon_H24e zenon_Hd6). % 18.87/19.04 apply (zenon_L755_); trivial. % 18.87/19.04 apply (zenon_L777_); trivial. % 18.87/19.04 apply (zenon_or_s _ _ zenon_H22e); [ zenon_intro zenon_Ha0 | zenon_intro zenon_H22f ]. % 18.87/19.04 exact (zenon_Ha4 zenon_Ha0). % 18.87/19.04 apply (zenon_or_s _ _ zenon_H22f); [ zenon_intro zenon_H122 | zenon_intro zenon_Hc3 ]. % 18.87/19.04 exact (zenon_H20d zenon_H122). % 18.87/19.04 exact (zenon_H231 zenon_Hc3). % 18.87/19.04 apply (zenon_or_s _ _ zenon_H43); [ zenon_intro zenon_H34 | zenon_intro zenon_H44 ]. % 18.87/19.04 apply (zenon_L773_); trivial. % 18.87/19.04 apply (zenon_L778_); trivial. % 18.87/19.04 apply (zenon_or_s _ _ zenon_H263); [ zenon_intro zenon_H255 | zenon_intro zenon_Ha6 ]. % 18.87/19.04 apply (zenon_L725_); trivial. % 18.87/19.04 apply (zenon_or_s _ _ zenon_H261); [ zenon_intro zenon_H250 | zenon_intro zenon_Hae ]. % 18.87/19.04 apply (zenon_L714_); trivial. % 18.87/19.04 apply (zenon_or_s _ _ zenon_H3e); [ zenon_intro zenon_H42 | zenon_intro zenon_H41 ]. % 18.87/19.04 exact (zenon_H3f zenon_H42). % 18.87/19.04 apply (zenon_or_s _ _ zenon_H41); [ zenon_intro zenon_H27 | zenon_intro zenon_H43 ]. % 18.87/19.04 apply (zenon_or_s _ _ zenon_H22d); [ zenon_intro zenon_H7a | zenon_intro zenon_H22e ]. % 18.87/19.04 apply (zenon_or_s _ _ zenon_H1fe); [ zenon_intro zenon_H7b | zenon_intro zenon_H1ff ]. % 18.87/19.04 apply (zenon_L26_); trivial. % 18.87/19.04 apply (zenon_or_s _ _ zenon_H1ff); [ zenon_intro zenon_H86 | zenon_intro zenon_H200 ]. % 18.87/19.04 apply (zenon_L257_); trivial. % 18.87/19.04 apply (zenon_or_s _ _ zenon_H200); [ zenon_intro zenon_Hee | zenon_intro zenon_H148 ]. % 18.87/19.04 apply (zenon_L277_); trivial. % 18.87/19.04 apply (zenon_or_s _ _ zenon_H1e0); [ zenon_intro zenon_H3a | zenon_intro zenon_H1e1 ]. % 18.87/19.04 apply (zenon_L35_); trivial. % 18.87/19.04 apply (zenon_or_s _ _ zenon_H1e1); [ zenon_intro zenon_H9e | zenon_intro zenon_H1e2 ]. % 18.87/19.04 apply (zenon_L107_); trivial. % 18.87/19.04 apply (zenon_or_s _ _ zenon_H1e2); [ zenon_intro zenon_H3b | zenon_intro zenon_H15e ]. % 18.87/19.04 apply (zenon_L780_); trivial. % 18.87/19.04 apply (zenon_L109_); trivial. % 18.87/19.04 apply (zenon_or_s _ _ zenon_H22e); [ zenon_intro zenon_Ha0 | zenon_intro zenon_H22f ]. % 18.87/19.04 exact (zenon_Ha4 zenon_Ha0). % 18.87/19.04 apply (zenon_or_s _ _ zenon_H22f); [ zenon_intro zenon_H122 | zenon_intro zenon_Hc3 ]. % 18.87/19.04 exact (zenon_H20d zenon_H122). % 18.87/19.04 exact (zenon_H231 zenon_Hc3). % 18.87/19.04 apply (zenon_or_s _ _ zenon_H43); [ zenon_intro zenon_H34 | zenon_intro zenon_H44 ]. % 18.87/19.04 apply (zenon_L783_); trivial. % 18.87/19.04 apply (zenon_L786_); trivial. % 18.87/19.04 apply (zenon_or_s _ _ zenon_H253); [ zenon_intro zenon_H198 | zenon_intro zenon_H1ca ]. % 18.87/19.04 apply (zenon_or_s _ _ zenon_H263); [ zenon_intro zenon_H255 | zenon_intro zenon_Ha6 ]. % 18.87/19.04 apply (zenon_or_s _ _ zenon_H254); [ zenon_intro zenon_Had | zenon_intro zenon_H1b1 ]. % 18.87/19.04 apply (zenon_or_s _ _ zenon_H261); [ zenon_intro zenon_H250 | zenon_intro zenon_Hae ]. % 18.87/19.04 apply (zenon_or_s _ _ zenon_H252); [ zenon_intro zenon_H251 | zenon_intro zenon_H14d ]. % 18.87/19.04 apply (zenon_or_s _ _ zenon_H3e); [ zenon_intro zenon_H42 | zenon_intro zenon_H41 ]. % 18.87/19.04 exact (zenon_H3f zenon_H42). % 18.87/19.04 apply (zenon_or_s _ _ zenon_H41); [ zenon_intro zenon_H27 | zenon_intro zenon_H43 ]. % 18.87/19.04 apply (zenon_or_s _ _ zenon_H22d); [ zenon_intro zenon_H7a | zenon_intro zenon_H22e ]. % 18.87/19.04 apply (zenon_or_s _ _ zenon_H1a5); [ zenon_intro zenon_H99 | zenon_intro zenon_H1a8 ]. % 18.87/19.04 apply (zenon_L36_); trivial. % 18.87/19.04 apply (zenon_or_s _ _ zenon_H1a8); [ zenon_intro zenon_H13f | zenon_intro zenon_H1a9 ]. % 18.87/19.04 apply (zenon_L166_); trivial. % 18.87/19.04 apply (zenon_or_s _ _ zenon_H1a9); [ zenon_intro zenon_Ha6 | zenon_intro zenon_H161 ]. % 18.87/19.04 apply (zenon_L39_); trivial. % 18.87/19.04 apply (zenon_L877_); trivial. % 18.87/19.04 apply (zenon_or_s _ _ zenon_H22e); [ zenon_intro zenon_Ha0 | zenon_intro zenon_H22f ]. % 18.87/19.04 exact (zenon_Ha4 zenon_Ha0). % 18.87/19.04 apply (zenon_or_s _ _ zenon_H22f); [ zenon_intro zenon_H122 | zenon_intro zenon_Hc3 ]. % 18.87/19.04 exact (zenon_H20d zenon_H122). % 18.87/19.04 exact (zenon_H231 zenon_Hc3). % 18.87/19.04 apply (zenon_or_s _ _ zenon_H43); [ zenon_intro zenon_H34 | zenon_intro zenon_H44 ]. % 18.87/19.04 apply (zenon_or_s _ _ zenon_H22d); [ zenon_intro zenon_H7a | zenon_intro zenon_H22e ]. % 18.87/19.04 apply (zenon_or_s _ _ zenon_H183); [ zenon_intro zenon_H7b | zenon_intro zenon_H186 ]. % 18.87/19.04 apply (zenon_L26_); trivial. % 18.87/19.04 apply (zenon_or_s _ _ zenon_H186); [ zenon_intro zenon_H10f | zenon_intro zenon_H187 ]. % 18.87/19.04 apply (zenon_L764_); trivial. % 18.87/19.04 apply (zenon_or_s _ _ zenon_H187); [ zenon_intro zenon_H150 | zenon_intro zenon_Hcd ]. % 18.87/19.04 apply (zenon_or_s _ _ zenon_H1fe); [ zenon_intro zenon_H7b | zenon_intro zenon_H1ff ]. % 18.87/19.04 apply (zenon_L26_); trivial. % 18.87/19.04 apply (zenon_or_s _ _ zenon_H1ff); [ zenon_intro zenon_H86 | zenon_intro zenon_H200 ]. % 18.87/19.04 apply (zenon_or_s _ _ zenon_H168); [ zenon_intro zenon_H3a | zenon_intro zenon_H169 ]. % 18.87/19.04 apply (zenon_L35_); trivial. % 18.87/19.04 apply (zenon_or_s _ _ zenon_H169); [ zenon_intro zenon_H99 | zenon_intro zenon_H16a ]. % 18.87/19.04 apply (zenon_L36_); trivial. % 18.87/19.04 apply (zenon_or_s _ _ zenon_H16a); [ zenon_intro zenon_Ha9 | zenon_intro zenon_He3 ]. % 18.87/19.04 apply (zenon_or_s _ _ zenon_H22); [ zenon_intro zenon_H27 | zenon_intro zenon_H26 ]. % 18.87/19.04 apply (zenon_L257_); trivial. % 18.87/19.04 apply (zenon_or_s _ _ zenon_H26); [ zenon_intro zenon_H29 | zenon_intro zenon_H28 ]. % 18.87/19.04 apply (zenon_L23_); trivial. % 18.87/19.04 apply (zenon_or_s _ _ zenon_H28); [ zenon_intro zenon_H2a | zenon_intro zenon_H1f ]. % 18.87/19.04 apply (zenon_L841_); trivial. % 18.87/19.04 apply (zenon_L878_); trivial. % 18.87/19.04 apply (zenon_or_s _ _ zenon_H22); [ zenon_intro zenon_H27 | zenon_intro zenon_H26 ]. % 18.87/19.04 apply (zenon_L332_); trivial. % 18.87/19.04 apply (zenon_or_s _ _ zenon_H26); [ zenon_intro zenon_H29 | zenon_intro zenon_H28 ]. % 18.87/19.04 apply (zenon_L17_); trivial. % 18.87/19.04 apply (zenon_or_s _ _ zenon_H28); [ zenon_intro zenon_H2a | zenon_intro zenon_H1f ]. % 18.87/19.04 apply (zenon_L211_); trivial. % 18.87/19.04 apply (zenon_L878_); trivial. % 18.87/19.04 apply (zenon_or_s _ _ zenon_H200); [ zenon_intro zenon_Hee | zenon_intro zenon_H148 ]. % 18.87/19.04 apply (zenon_L204_); trivial. % 18.87/19.04 apply (zenon_L846_); trivial. % 18.87/19.04 apply (zenon_L865_); trivial. % 18.87/19.04 apply (zenon_or_s _ _ zenon_H22e); [ zenon_intro zenon_Ha0 | zenon_intro zenon_H22f ]. % 18.87/19.04 exact (zenon_Ha4 zenon_Ha0). % 18.87/19.04 apply (zenon_or_s _ _ zenon_H22f); [ zenon_intro zenon_H122 | zenon_intro zenon_Hc3 ]. % 18.87/19.04 exact (zenon_H20d zenon_H122). % 18.87/19.04 exact (zenon_H231 zenon_Hc3). % 18.87/19.04 apply (zenon_L880_); trivial. % 18.87/19.04 apply (zenon_L164_); trivial. % 18.87/19.04 apply (zenon_L42_); trivial. % 18.87/19.04 apply (zenon_or_s _ _ zenon_H261); [ zenon_intro zenon_H250 | zenon_intro zenon_Hae ]. % 18.87/19.04 apply (zenon_or_s _ _ zenon_H252); [ zenon_intro zenon_H251 | zenon_intro zenon_H14d ]. % 18.87/19.04 apply (zenon_or_s _ _ zenon_H3e); [ zenon_intro zenon_H42 | zenon_intro zenon_H41 ]. % 18.87/19.04 exact (zenon_H3f zenon_H42). % 18.87/19.04 apply (zenon_or_s _ _ zenon_H41); [ zenon_intro zenon_H27 | zenon_intro zenon_H43 ]. % 18.87/19.04 apply (zenon_or_s _ _ zenon_H22d); [ zenon_intro zenon_H7a | zenon_intro zenon_H22e ]. % 18.87/19.04 apply (zenon_or_s _ _ zenon_H183); [ zenon_intro zenon_H7b | zenon_intro zenon_H186 ]. % 18.87/19.04 apply (zenon_L26_); trivial. % 18.87/19.04 apply (zenon_or_s _ _ zenon_H186); [ zenon_intro zenon_H10f | zenon_intro zenon_H187 ]. % 18.87/19.04 apply (zenon_L764_); trivial. % 18.87/19.04 apply (zenon_or_s _ _ zenon_H187); [ zenon_intro zenon_H150 | zenon_intro zenon_Hcd ]. % 18.87/19.04 apply (zenon_or_s _ _ zenon_H2f); [ zenon_intro zenon_H34 | zenon_intro zenon_H33 ]. % 18.87/19.04 apply (zenon_L888_); trivial. % 18.87/19.04 apply (zenon_or_s _ _ zenon_H33); [ zenon_intro zenon_H36 | zenon_intro zenon_H35 ]. % 18.87/19.04 apply (zenon_L128_); trivial. % 18.87/19.04 apply (zenon_or_s _ _ zenon_H35); [ zenon_intro zenon_H2c | zenon_intro zenon_H37 ]. % 18.87/19.04 apply (zenon_L259_); trivial. % 18.87/19.04 apply (zenon_L680_); trivial. % 18.87/19.04 apply (zenon_L889_); trivial. % 18.87/19.04 apply (zenon_or_s _ _ zenon_H22e); [ zenon_intro zenon_Ha0 | zenon_intro zenon_H22f ]. % 18.87/19.04 exact (zenon_Ha4 zenon_Ha0). % 18.87/19.04 apply (zenon_or_s _ _ zenon_H22f); [ zenon_intro zenon_H122 | zenon_intro zenon_Hc3 ]. % 18.87/19.04 exact (zenon_H20d zenon_H122). % 18.87/19.04 exact (zenon_H231 zenon_Hc3). % 18.87/19.04 apply (zenon_or_s _ _ zenon_H43); [ zenon_intro zenon_H34 | zenon_intro zenon_H44 ]. % 18.87/19.04 apply (zenon_L888_); trivial. % 18.87/19.04 apply (zenon_L346_); trivial. % 18.87/19.04 apply (zenon_L164_); trivial. % 18.87/19.04 apply (zenon_L42_); trivial. % 18.87/19.04 apply (zenon_L39_); trivial. % 18.87/19.04 apply (zenon_or_s _ _ zenon_H263); [ zenon_intro zenon_H255 | zenon_intro zenon_Ha6 ]. % 18.87/19.04 apply (zenon_or_s _ _ zenon_H254); [ zenon_intro zenon_Had | zenon_intro zenon_H1b1 ]. % 18.87/19.04 apply (zenon_or_s _ _ zenon_H261); [ zenon_intro zenon_H250 | zenon_intro zenon_Hae ]. % 18.87/19.04 apply (zenon_or_s _ _ zenon_H252); [ zenon_intro zenon_H251 | zenon_intro zenon_H14d ]. % 18.87/19.04 apply (zenon_or_s _ _ zenon_H3e); [ zenon_intro zenon_H42 | zenon_intro zenon_H41 ]. % 18.87/19.04 exact (zenon_H3f zenon_H42). % 18.87/19.04 apply (zenon_or_s _ _ zenon_H41); [ zenon_intro zenon_H27 | zenon_intro zenon_H43 ]. % 18.87/19.04 apply (zenon_or_s _ _ zenon_H22d); [ zenon_intro zenon_H7a | zenon_intro zenon_H22e ]. % 18.87/19.04 apply (zenon_or_s _ _ zenon_H183); [ zenon_intro zenon_H7b | zenon_intro zenon_H186 ]. % 18.87/19.04 apply (zenon_L26_); trivial. % 18.87/19.04 apply (zenon_or_s _ _ zenon_H186); [ zenon_intro zenon_H10f | zenon_intro zenon_H187 ]. % 18.87/19.04 apply (zenon_L764_); trivial. % 18.87/19.04 apply (zenon_or_s _ _ zenon_H187); [ zenon_intro zenon_H150 | zenon_intro zenon_Hcd ]. % 18.87/19.04 apply (zenon_or_s _ _ zenon_H1fe); [ zenon_intro zenon_H7b | zenon_intro zenon_H1ff ]. % 18.87/19.04 apply (zenon_L26_); trivial. % 18.87/19.04 apply (zenon_or_s _ _ zenon_H1ff); [ zenon_intro zenon_H86 | zenon_intro zenon_H200 ]. % 18.87/19.04 apply (zenon_L257_); trivial. % 18.87/19.04 apply (zenon_or_s _ _ zenon_H200); [ zenon_intro zenon_Hee | zenon_intro zenon_H148 ]. % 18.87/19.04 apply (zenon_L277_); trivial. % 18.87/19.04 apply (zenon_or_s _ _ zenon_H168); [ zenon_intro zenon_H3a | zenon_intro zenon_H169 ]. % 18.87/19.04 apply (zenon_L35_); trivial. % 18.87/19.04 apply (zenon_or_s _ _ zenon_H169); [ zenon_intro zenon_H99 | zenon_intro zenon_H16a ]. % 18.87/19.04 apply (zenon_L36_); trivial. % 18.87/19.04 apply (zenon_or_s _ _ zenon_H16a); [ zenon_intro zenon_Ha9 | zenon_intro zenon_He3 ]. % 18.87/19.04 apply (zenon_L891_); trivial. % 18.87/19.04 apply (zenon_or_s _ _ zenon_H1e0); [ zenon_intro zenon_H3a | zenon_intro zenon_H1e1 ]. % 18.87/19.04 apply (zenon_L35_); trivial. % 18.87/19.04 apply (zenon_or_s _ _ zenon_H1e1); [ zenon_intro zenon_H9e | zenon_intro zenon_H1e2 ]. % 18.87/19.04 apply (zenon_L107_); trivial. % 18.87/19.04 apply (zenon_or_s _ _ zenon_H1e2); [ zenon_intro zenon_H3b | zenon_intro zenon_H15e ]. % 18.87/19.04 apply (zenon_or_s _ _ zenon_H128); [ zenon_intro zenon_H9d | zenon_intro zenon_H129 ]. % 18.87/19.04 exact (zenon_H1ef zenon_H9d). % 18.87/19.04 apply (zenon_or_s _ _ zenon_H129); [ zenon_intro zenon_H10d | zenon_intro zenon_H12a ]. % 18.87/19.04 exact (zenon_H10a zenon_H10d). % 18.87/19.04 apply (zenon_or_s _ _ zenon_H12a); [ zenon_intro zenon_Hf0 | zenon_intro zenon_Hd6 ]. % 18.87/19.04 apply (zenon_or_s _ _ zenon_H16f); [ zenon_intro zenon_H9e | zenon_intro zenon_H170 ]. % 18.87/19.04 apply (zenon_L107_); trivial. % 18.87/19.04 apply (zenon_or_s _ _ zenon_H170); [ zenon_intro zenon_H13f | zenon_intro zenon_H171 ]. % 18.87/19.04 apply (zenon_L898_); trivial. % 18.87/19.04 apply (zenon_or_s _ _ zenon_H171); [ zenon_intro zenon_H16c | zenon_intro zenon_Hdc ]. % 18.87/19.04 apply (zenon_L167_); trivial. % 18.87/19.04 apply (zenon_L117_); trivial. % 18.87/19.04 exact (zenon_H24e zenon_Hd6). % 18.87/19.04 apply (zenon_L109_); trivial. % 18.87/19.04 apply (zenon_or_s _ _ zenon_H1fe); [ zenon_intro zenon_H7b | zenon_intro zenon_H1ff ]. % 18.87/19.04 apply (zenon_L375_); trivial. % 18.87/19.04 apply (zenon_or_s _ _ zenon_H1ff); [ zenon_intro zenon_H86 | zenon_intro zenon_H200 ]. % 18.87/19.04 apply (zenon_L257_); trivial. % 18.87/19.04 apply (zenon_or_s _ _ zenon_H200); [ zenon_intro zenon_Hee | zenon_intro zenon_H148 ]. % 18.87/19.04 apply (zenon_L277_); trivial. % 18.87/19.04 apply (zenon_or_s _ _ zenon_H168); [ zenon_intro zenon_H3a | zenon_intro zenon_H169 ]. % 18.87/19.04 apply (zenon_L35_); trivial. % 18.87/19.04 apply (zenon_or_s _ _ zenon_H169); [ zenon_intro zenon_H99 | zenon_intro zenon_H16a ]. % 18.87/19.04 apply (zenon_L36_); trivial. % 18.87/19.04 apply (zenon_or_s _ _ zenon_H16a); [ zenon_intro zenon_Ha9 | zenon_intro zenon_He3 ]. % 18.87/19.04 apply (zenon_L891_); trivial. % 18.87/19.04 apply (zenon_L81_); trivial. % 18.87/19.04 apply (zenon_or_s _ _ zenon_H22e); [ zenon_intro zenon_Ha0 | zenon_intro zenon_H22f ]. % 18.87/19.04 exact (zenon_Ha4 zenon_Ha0). % 18.87/19.04 apply (zenon_or_s _ _ zenon_H22f); [ zenon_intro zenon_H122 | zenon_intro zenon_Hc3 ]. % 18.87/19.04 exact (zenon_H20d zenon_H122). % 18.87/19.04 exact (zenon_H231 zenon_Hc3). % 18.87/19.04 apply (zenon_or_s _ _ zenon_H43); [ zenon_intro zenon_H34 | zenon_intro zenon_H44 ]. % 18.87/19.04 apply (zenon_or_s _ _ zenon_H22d); [ zenon_intro zenon_H7a | zenon_intro zenon_H22e ]. % 18.87/19.04 apply (zenon_or_s _ _ zenon_H183); [ zenon_intro zenon_H7b | zenon_intro zenon_H186 ]. % 18.87/19.04 apply (zenon_L26_); trivial. % 18.87/19.04 apply (zenon_or_s _ _ zenon_H186); [ zenon_intro zenon_H10f | zenon_intro zenon_H187 ]. % 18.87/19.04 apply (zenon_L726_); trivial. % 18.87/19.04 apply (zenon_or_s _ _ zenon_H187); [ zenon_intro zenon_H150 | zenon_intro zenon_Hcd ]. % 18.87/19.04 apply (zenon_or_s _ _ zenon_H1fe); [ zenon_intro zenon_H7b | zenon_intro zenon_H1ff ]. % 18.87/19.04 apply (zenon_L26_); trivial. % 18.87/19.04 apply (zenon_or_s _ _ zenon_H1ff); [ zenon_intro zenon_H86 | zenon_intro zenon_H200 ]. % 18.87/19.04 apply (zenon_or_s _ _ zenon_H168); [ zenon_intro zenon_H3a | zenon_intro zenon_H169 ]. % 18.87/19.04 apply (zenon_L35_); trivial. % 18.87/19.04 apply (zenon_or_s _ _ zenon_H169); [ zenon_intro zenon_H99 | zenon_intro zenon_H16a ]. % 18.87/19.04 apply (zenon_L36_); trivial. % 18.87/19.04 apply (zenon_or_s _ _ zenon_H16a); [ zenon_intro zenon_Ha9 | zenon_intro zenon_He3 ]. % 18.87/19.04 apply (zenon_L826_); trivial. % 18.87/19.04 apply (zenon_or_s _ _ zenon_H1e0); [ zenon_intro zenon_H3a | zenon_intro zenon_H1e1 ]. % 18.87/19.04 apply (zenon_L35_); trivial. % 18.87/19.04 apply (zenon_or_s _ _ zenon_H1e1); [ zenon_intro zenon_H9e | zenon_intro zenon_H1e2 ]. % 18.87/19.04 apply (zenon_or_s _ _ zenon_H22); [ zenon_intro zenon_H27 | zenon_intro zenon_H26 ]. % 18.87/19.04 apply (zenon_L332_); trivial. % 18.87/19.04 apply (zenon_or_s _ _ zenon_H26); [ zenon_intro zenon_H29 | zenon_intro zenon_H28 ]. % 18.87/19.04 apply (zenon_L17_); trivial. % 18.87/19.04 apply (zenon_or_s _ _ zenon_H28); [ zenon_intro zenon_H2a | zenon_intro zenon_H1f ]. % 18.87/19.04 apply (zenon_L899_); trivial. % 18.87/19.04 apply (zenon_L801_); trivial. % 18.87/19.04 apply (zenon_or_s _ _ zenon_H1e2); [ zenon_intro zenon_H3b | zenon_intro zenon_H15e ]. % 18.87/19.04 apply (zenon_L33_); trivial. % 18.87/19.04 apply (zenon_or_s _ _ zenon_H22); [ zenon_intro zenon_H27 | zenon_intro zenon_H26 ]. % 18.87/19.04 apply (zenon_L257_); trivial. % 18.87/19.04 apply (zenon_or_s _ _ zenon_H26); [ zenon_intro zenon_H29 | zenon_intro zenon_H28 ]. % 18.87/19.04 apply (zenon_L724_); trivial. % 18.87/19.04 apply (zenon_or_s _ _ zenon_H28); [ zenon_intro zenon_H2a | zenon_intro zenon_H1f ]. % 18.87/19.04 apply (zenon_L899_); trivial. % 18.87/19.04 apply (zenon_L825_); trivial. % 18.87/19.04 apply (zenon_or_s _ _ zenon_H200); [ zenon_intro zenon_Hee | zenon_intro zenon_H148 ]. % 18.87/19.04 apply (zenon_L204_); trivial. % 18.87/19.04 apply (zenon_or_s _ _ zenon_H168); [ zenon_intro zenon_H3a | zenon_intro zenon_H169 ]. % 18.87/19.04 apply (zenon_L35_); trivial. % 18.87/19.04 apply (zenon_or_s _ _ zenon_H169); [ zenon_intro zenon_H99 | zenon_intro zenon_H16a ]. % 18.87/19.04 apply (zenon_L36_); trivial. % 18.87/19.04 apply (zenon_or_s _ _ zenon_H16a); [ zenon_intro zenon_Ha9 | zenon_intro zenon_He3 ]. % 18.87/19.04 apply (zenon_L900_); trivial. % 18.87/19.04 apply (zenon_or_s _ _ zenon_H22); [ zenon_intro zenon_H27 | zenon_intro zenon_H26 ]. % 18.87/19.04 apply (zenon_L332_); trivial. % 18.87/19.04 apply (zenon_or_s _ _ zenon_H26); [ zenon_intro zenon_H29 | zenon_intro zenon_H28 ]. % 18.87/19.04 apply (zenon_L724_); trivial. % 18.87/19.04 apply (zenon_or_s _ _ zenon_H28); [ zenon_intro zenon_H2a | zenon_intro zenon_H1f ]. % 18.87/19.04 apply (zenon_or_s _ _ zenon_H16f); [ zenon_intro zenon_H9e | zenon_intro zenon_H170 ]. % 18.87/19.04 apply (zenon_L107_); trivial. % 18.87/19.04 apply (zenon_or_s _ _ zenon_H170); [ zenon_intro zenon_H13f | zenon_intro zenon_H171 ]. % 18.87/19.04 apply (zenon_L896_); trivial. % 18.87/19.04 apply (zenon_or_s _ _ zenon_H171); [ zenon_intro zenon_H16c | zenon_intro zenon_Hdc ]. % 18.87/19.04 apply (zenon_L521_); trivial. % 18.87/19.04 apply (zenon_L117_); trivial. % 18.87/19.04 apply (zenon_L808_); trivial. % 18.87/19.04 apply (zenon_L902_); trivial. % 18.87/19.04 apply (zenon_or_s _ _ zenon_H22e); [ zenon_intro zenon_Ha0 | zenon_intro zenon_H22f ]. % 18.87/19.04 exact (zenon_Ha4 zenon_Ha0). % 18.87/19.04 apply (zenon_or_s _ _ zenon_H22f); [ zenon_intro zenon_H122 | zenon_intro zenon_Hc3 ]. % 18.87/19.04 exact (zenon_H20d zenon_H122). % 18.87/19.04 exact (zenon_H231 zenon_Hc3). % 18.87/19.04 apply (zenon_L786_); trivial. % 18.87/19.04 apply (zenon_L164_); trivial. % 18.87/19.04 apply (zenon_L42_); trivial. % 18.87/19.04 apply (zenon_or_s _ _ zenon_H261); [ zenon_intro zenon_H250 | zenon_intro zenon_Hae ]. % 18.87/19.04 apply (zenon_or_s _ _ zenon_H252); [ zenon_intro zenon_H251 | zenon_intro zenon_H14d ]. % 18.87/19.04 apply (zenon_or_s _ _ zenon_H3e); [ zenon_intro zenon_H42 | zenon_intro zenon_H41 ]. % 18.87/19.04 exact (zenon_H3f zenon_H42). % 18.87/19.04 apply (zenon_or_s _ _ zenon_H41); [ zenon_intro zenon_H27 | zenon_intro zenon_H43 ]. % 18.87/19.04 apply (zenon_or_s _ _ zenon_H22d); [ zenon_intro zenon_H7a | zenon_intro zenon_H22e ]. % 18.87/19.04 apply (zenon_or_s _ _ zenon_H183); [ zenon_intro zenon_H7b | zenon_intro zenon_H186 ]. % 18.87/19.04 apply (zenon_L26_); trivial. % 18.87/19.04 apply (zenon_or_s _ _ zenon_H186); [ zenon_intro zenon_H10f | zenon_intro zenon_H187 ]. % 18.87/19.04 apply (zenon_L764_); trivial. % 18.87/19.04 apply (zenon_or_s _ _ zenon_H187); [ zenon_intro zenon_H150 | zenon_intro zenon_Hcd ]. % 18.87/19.04 apply (zenon_or_s _ _ zenon_H1fe); [ zenon_intro zenon_H7b | zenon_intro zenon_H1ff ]. % 18.87/19.04 apply (zenon_L26_); trivial. % 18.87/19.04 apply (zenon_or_s _ _ zenon_H1ff); [ zenon_intro zenon_H86 | zenon_intro zenon_H200 ]. % 18.87/19.04 apply (zenon_L257_); trivial. % 18.87/19.04 apply (zenon_or_s _ _ zenon_H200); [ zenon_intro zenon_Hee | zenon_intro zenon_H148 ]. % 18.87/19.04 apply (zenon_L277_); trivial. % 18.87/19.04 apply (zenon_or_s _ _ zenon_H168); [ zenon_intro zenon_H3a | zenon_intro zenon_H169 ]. % 18.87/19.04 apply (zenon_L35_); trivial. % 18.87/19.04 apply (zenon_or_s _ _ zenon_H169); [ zenon_intro zenon_H99 | zenon_intro zenon_H16a ]. % 18.87/19.04 apply (zenon_L36_); trivial. % 18.87/19.04 apply (zenon_or_s _ _ zenon_H16a); [ zenon_intro zenon_Ha9 | zenon_intro zenon_He3 ]. % 18.87/19.04 apply (zenon_or_s _ _ zenon_H1e0); [ zenon_intro zenon_H3a | zenon_intro zenon_H1e1 ]. % 18.87/19.04 apply (zenon_L35_); trivial. % 18.87/19.04 apply (zenon_or_s _ _ zenon_H1e1); [ zenon_intro zenon_H9e | zenon_intro zenon_H1e2 ]. % 18.87/19.04 apply (zenon_L107_); trivial. % 18.87/19.04 apply (zenon_or_s _ _ zenon_H1e2); [ zenon_intro zenon_H3b | zenon_intro zenon_H15e ]. % 18.87/19.04 apply (zenon_or_s _ _ zenon_H128); [ zenon_intro zenon_H9d | zenon_intro zenon_H129 ]. % 18.87/19.04 exact (zenon_H1ef zenon_H9d). % 18.87/19.04 apply (zenon_or_s _ _ zenon_H129); [ zenon_intro zenon_H10d | zenon_intro zenon_H12a ]. % 18.87/19.04 exact (zenon_H10a zenon_H10d). % 18.87/19.04 apply (zenon_or_s _ _ zenon_H12a); [ zenon_intro zenon_Hf0 | zenon_intro zenon_Hd6 ]. % 18.87/19.04 apply (zenon_or_s _ _ zenon_H2f); [ zenon_intro zenon_H34 | zenon_intro zenon_H33 ]. % 18.87/19.04 apply (zenon_L821_); trivial. % 18.87/19.04 apply (zenon_or_s _ _ zenon_H33); [ zenon_intro zenon_H36 | zenon_intro zenon_H35 ]. % 18.87/19.04 apply (zenon_L128_); trivial. % 18.87/19.04 apply (zenon_or_s _ _ zenon_H35); [ zenon_intro zenon_H2c | zenon_intro zenon_H37 ]. % 18.87/19.04 apply (zenon_L259_); trivial. % 18.87/19.04 apply (zenon_L300_); trivial. % 18.87/19.04 exact (zenon_H24e zenon_Hd6). % 18.87/19.04 apply (zenon_L109_); trivial. % 18.87/19.04 apply (zenon_or_s _ _ zenon_H128); [ zenon_intro zenon_H9d | zenon_intro zenon_H129 ]. % 18.87/19.04 exact (zenon_H1ef zenon_H9d). % 18.87/19.04 apply (zenon_or_s _ _ zenon_H129); [ zenon_intro zenon_H10d | zenon_intro zenon_H12a ]. % 18.87/19.04 exact (zenon_H10a zenon_H10d). % 18.87/19.04 apply (zenon_or_s _ _ zenon_H12a); [ zenon_intro zenon_Hf0 | zenon_intro zenon_Hd6 ]. % 18.87/19.04 apply (zenon_or_s _ _ zenon_H16f); [ zenon_intro zenon_H9e | zenon_intro zenon_H170 ]. % 18.87/19.04 apply (zenon_L107_); trivial. % 18.87/19.04 apply (zenon_or_s _ _ zenon_H170); [ zenon_intro zenon_H13f | zenon_intro zenon_H171 ]. % 18.87/19.04 apply (zenon_L909_); trivial. % 18.87/19.04 apply (zenon_or_s _ _ zenon_H171); [ zenon_intro zenon_H16c | zenon_intro zenon_Hdc ]. % 18.87/19.04 apply (zenon_L167_); trivial. % 18.87/19.04 apply (zenon_L117_); trivial. % 18.87/19.04 exact (zenon_H24e zenon_Hd6). % 18.87/19.04 apply (zenon_or_s _ _ zenon_H1fe); [ zenon_intro zenon_H7b | zenon_intro zenon_H1ff ]. % 18.87/19.04 apply (zenon_L375_); trivial. % 18.87/19.04 apply (zenon_or_s _ _ zenon_H1ff); [ zenon_intro zenon_H86 | zenon_intro zenon_H200 ]. % 18.87/19.04 apply (zenon_L257_); trivial. % 18.87/19.04 apply (zenon_or_s _ _ zenon_H200); [ zenon_intro zenon_Hee | zenon_intro zenon_H148 ]. % 18.87/19.04 apply (zenon_L277_); trivial. % 18.87/19.04 apply (zenon_or_s _ _ zenon_H168); [ zenon_intro zenon_H3a | zenon_intro zenon_H169 ]. % 18.87/19.04 apply (zenon_L35_); trivial. % 18.87/19.04 apply (zenon_or_s _ _ zenon_H169); [ zenon_intro zenon_H99 | zenon_intro zenon_H16a ]. % 18.87/19.04 apply (zenon_L36_); trivial. % 18.87/19.04 apply (zenon_or_s _ _ zenon_H16a); [ zenon_intro zenon_Ha9 | zenon_intro zenon_He3 ]. % 18.87/19.04 apply (zenon_or_s _ _ zenon_H1e0); [ zenon_intro zenon_H3a | zenon_intro zenon_H1e1 ]. % 18.87/19.04 apply (zenon_L35_); trivial. % 18.87/19.04 apply (zenon_or_s _ _ zenon_H1e1); [ zenon_intro zenon_H9e | zenon_intro zenon_H1e2 ]. % 18.87/19.04 apply (zenon_L107_); trivial. % 18.87/19.04 apply (zenon_or_s _ _ zenon_H1e2); [ zenon_intro zenon_H3b | zenon_intro zenon_H15e ]. % 18.87/19.04 apply (zenon_or_s _ _ zenon_H128); [ zenon_intro zenon_H9d | zenon_intro zenon_H129 ]. % 18.87/19.04 exact (zenon_H1ef zenon_H9d). % 18.87/19.04 apply (zenon_or_s _ _ zenon_H129); [ zenon_intro zenon_H10d | zenon_intro zenon_H12a ]. % 18.87/19.04 exact (zenon_H10a zenon_H10d). % 18.87/19.04 apply (zenon_or_s _ _ zenon_H12a); [ zenon_intro zenon_Hf0 | zenon_intro zenon_Hd6 ]. % 18.87/19.04 apply (zenon_or_s _ _ zenon_H2f); [ zenon_intro zenon_H34 | zenon_intro zenon_H33 ]. % 18.87/19.04 apply (zenon_L819_); trivial. % 18.87/19.04 apply (zenon_or_s _ _ zenon_H33); [ zenon_intro zenon_H36 | zenon_intro zenon_H35 ]. % 18.87/19.04 apply (zenon_L128_); trivial. % 18.87/19.04 apply (zenon_or_s _ _ zenon_H35); [ zenon_intro zenon_H2c | zenon_intro zenon_H37 ]. % 18.87/19.04 apply (zenon_L676_); trivial. % 18.87/19.04 apply (zenon_L300_); trivial. % 18.87/19.04 exact (zenon_H24e zenon_Hd6). % 18.87/19.04 apply (zenon_L109_); trivial. % 18.87/19.04 apply (zenon_L81_); trivial. % 18.87/19.04 apply (zenon_or_s _ _ zenon_H22e); [ zenon_intro zenon_Ha0 | zenon_intro zenon_H22f ]. % 18.87/19.04 exact (zenon_Ha4 zenon_Ha0). % 18.87/19.04 apply (zenon_or_s _ _ zenon_H22f); [ zenon_intro zenon_H122 | zenon_intro zenon_Hc3 ]. % 18.87/19.04 exact (zenon_H20d zenon_H122). % 18.87/19.04 exact (zenon_H231 zenon_Hc3). % 18.87/19.04 apply (zenon_or_s _ _ zenon_H43); [ zenon_intro zenon_H34 | zenon_intro zenon_H44 ]. % 18.87/19.04 apply (zenon_or_s _ _ zenon_H22d); [ zenon_intro zenon_H7a | zenon_intro zenon_H22e ]. % 18.87/19.04 apply (zenon_or_s _ _ zenon_H183); [ zenon_intro zenon_H7b | zenon_intro zenon_H186 ]. % 18.87/19.04 apply (zenon_L26_); trivial. % 18.87/19.04 apply (zenon_or_s _ _ zenon_H186); [ zenon_intro zenon_H10f | zenon_intro zenon_H187 ]. % 18.87/19.04 apply (zenon_L726_); trivial. % 18.87/19.04 apply (zenon_or_s _ _ zenon_H187); [ zenon_intro zenon_H150 | zenon_intro zenon_Hcd ]. % 18.87/19.04 apply (zenon_or_s _ _ zenon_H1fe); [ zenon_intro zenon_H7b | zenon_intro zenon_H1ff ]. % 18.87/19.04 apply (zenon_L26_); trivial. % 18.87/19.04 apply (zenon_or_s _ _ zenon_H1ff); [ zenon_intro zenon_H86 | zenon_intro zenon_H200 ]. % 18.87/19.04 apply (zenon_or_s _ _ zenon_H1e0); [ zenon_intro zenon_H3a | zenon_intro zenon_H1e1 ]. % 18.87/19.04 apply (zenon_L35_); trivial. % 18.87/19.04 apply (zenon_or_s _ _ zenon_H1e1); [ zenon_intro zenon_H9e | zenon_intro zenon_H1e2 ]. % 18.87/19.04 apply (zenon_or_s _ _ zenon_H128); [ zenon_intro zenon_H9d | zenon_intro zenon_H129 ]. % 18.87/19.04 exact (zenon_H1ef zenon_H9d). % 18.87/19.04 apply (zenon_or_s _ _ zenon_H129); [ zenon_intro zenon_H10d | zenon_intro zenon_H12a ]. % 18.87/19.04 exact (zenon_H10a zenon_H10d). % 18.87/19.04 apply (zenon_or_s _ _ zenon_H12a); [ zenon_intro zenon_Hf0 | zenon_intro zenon_Hd6 ]. % 18.87/19.04 apply (zenon_L792_); trivial. % 18.87/19.04 exact (zenon_H24e zenon_Hd6). % 18.87/19.04 apply (zenon_or_s _ _ zenon_H1e2); [ zenon_intro zenon_H3b | zenon_intro zenon_H15e ]. % 18.87/19.04 apply (zenon_L33_); trivial. % 18.87/19.04 apply (zenon_L882_); trivial. % 18.87/19.04 apply (zenon_or_s _ _ zenon_H200); [ zenon_intro zenon_Hee | zenon_intro zenon_H148 ]. % 18.87/19.04 apply (zenon_L204_); trivial. % 18.87/19.04 apply (zenon_L910_); trivial. % 18.87/19.04 apply (zenon_L887_); trivial. % 18.87/19.04 apply (zenon_or_s _ _ zenon_H22e); [ zenon_intro zenon_Ha0 | zenon_intro zenon_H22f ]. % 18.87/19.04 exact (zenon_Ha4 zenon_Ha0). % 18.87/19.04 apply (zenon_or_s _ _ zenon_H22f); [ zenon_intro zenon_H122 | zenon_intro zenon_Hc3 ]. % 18.87/19.04 exact (zenon_H20d zenon_H122). % 18.87/19.04 exact (zenon_H231 zenon_Hc3). % 18.87/19.04 apply (zenon_L346_); trivial. % 18.87/19.04 apply (zenon_L164_); trivial. % 18.87/19.04 apply (zenon_L42_); trivial. % 18.87/19.04 apply (zenon_L916_); trivial. % 18.87/19.04 apply (zenon_L128_); trivial. % 18.87/19.04 apply (zenon_L166_); trivial. % 18.87/19.04 (* end of lemma zenon_L917_ *) % 18.87/19.04 assert (zenon_L918_ : (((op (e1) (e0)) = (e2))\/(((op (e1) (e1)) = (e2))\/(((op (e1) (e2)) = (e2))\/((op (e1) (e3)) = (e2))))) -> ((op (e0) (e0)) = (e1)) -> ((op (e2) (e0)) = (e3)) -> (((op (e1) (e0)) = (e1))\/(((op (e1) (e1)) = (e1))\/(((op (e1) (e2)) = (e1))\/((op (e1) (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 (e1) (e1)) = (e1))) -> (~((op (e1) (e0)) = (e1))) -> ((~((op (e3) (e1)) = (e1)))\/((op (e3) (e1)) = (e1))) -> (~((op (e0) (e0)) = (e0))) -> ((~((op (e1) (e2)) = (e1)))\/((op (e1) (e1)) = (e2))) -> (~((op (e0) (e1)) = (op (e1) (e1)))) -> ((~((op (e2) (e0)) = (e1)))\/((op (e2) (e1)) = (e0))) -> ((op (e0) (e1)) = (e0)) -> ((~((op (e3) (e0)) = (e1)))\/((op (e3) (e1)) = (e0))) -> (((op (e0) (e0)) = (e1))\/(((op (e0) (e1)) = (e1))\/(((op (e0) (e2)) = (e1))\/((op (e0) (e3)) = (e1))))) -> (~((op (e0) (e3)) = (e1))) -> (((op (e0) (e0)) = (e1))\/(((op (e1) (e0)) = (e1))\/(((op (e2) (e0)) = (e1))\/((op (e3) (e0)) = (e1))))) -> (~((op (e0) (e0)) = (op (e0) (e2)))) -> (((op (e0) (e2)) = (e1))\/(((op (e1) (e2)) = (e1))\/(((op (e2) (e2)) = (e1))\/((op (e3) (e2)) = (e1))))) -> (~((op (e0) (e1)) = (op (e3) (e1)))) -> ((~((op (e3) (e2)) = (e1)))\/((op (e3) (e1)) = (e2))) -> (~((op (e0) (e1)) = (op (e2) (e1)))) -> ((~((op (e2) (e2)) = (e1)))\/((op (e2) (e1)) = (e2))) -> ((~((op (e1) (e3)) = (e1)))\/((op (e1) (e1)) = (e3))) -> (~((e1) = (e3))) -> (~((e0) = (e3))) -> (((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 (e0) (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) (e2)))) -> (~((op (e1) (e0)) = (op (e3) (e0)))) -> (((op (e0) (e0)) = (e3))\/(((op (e0) (e1)) = (e3))\/(((op (e0) (e2)) = (e3))\/((op (e0) (e3)) = (e3))))) -> (~((op (e0) (e1)) = (op (e0) (e3)))) -> (~((op (e2) (e0)) = (op (e2) (e3)))) -> (~((op (e2) (e0)) = (op (e2) (e1)))) -> (((op (e2) (e0)) = (e0))\/(((op (e2) (e0)) = (e1))\/(((op (e2) (e0)) = (e2))\/((op (e2) (e0)) = (e3))))) -> (~((op (e2) (e0)) = (op (e3) (e0)))) -> (~((op (e2) (e2)) = (op (e3) (e2)))) -> (((op (e3) (e0)) = (e0))\/(((op (e3) (e1)) = (e0))\/(((op (e3) (e2)) = (e0))\/((op (e3) (e3)) = (e0))))) -> (~((op (e2) (e0)) = (op (e2) (e2)))) -> (((op (e0) (e2)) = (e0))\/(((op (e1) (e2)) = (e0))\/(((op (e2) (e2)) = (e0))\/((op (e3) (e2)) = (e0))))) -> (((op (e1) (e0)) = (e0))\/(((op (e1) (e1)) = (e0))\/(((op (e1) (e2)) = (e0))\/((op (e1) (e3)) = (e0))))) -> (~((op (e3) (e1)) = (op (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 (e0) (e3)) = (e2))\/(((op (e1) (e3)) = (e2))\/(((op (e2) (e3)) = (e2))\/((op (e3) (e3)) = (e2))))) -> (~((op (e3) (e0)) = (op (e3) (e3)))) -> (~((op (e2) (e1)) = (op (e2) (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 (e3) (e0)) = (e2))\/(((op (e3) (e1)) = (e2))\/(((op (e3) (e2)) = (e2))\/((op (e3) (e3)) = (e2))))) -> (((op (e2) (e0)) = (e3))\/(((op (e2) (e1)) = (e3))\/(((op (e2) (e2)) = (e3))\/((op (e2) (e3)) = (e3))))) -> (~((op (e0) (e3)) = (op (e2) (e3)))) -> (~((op (e1) (e2)) = (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) (e1)) = (op (e3) (e2)))) -> (~((op (e0) (e1)) = (op (e0) (e2)))) -> (~((op (e1) (e1)) = (op (e1) (e2)))) -> (((op (e0) (e3)) = (e0))\/(((op (e1) (e3)) = (e0))\/(((op (e2) (e3)) = (e0))\/((op (e3) (e3)) = (e0))))) -> (~((op (e3) (e2)) = (op (e3) (e3)))) -> (~((op (e1) (e1)) = (op (e1) (e3)))) -> (((op (e0) (e3)) = (e0))\/(((op (e0) (e3)) = (e1))\/(((op (e0) (e3)) = (e2))\/((op (e0) (e3)) = (e3))))) -> (((op (e2) (e2)) = (e0))\/(((op (e2) (e2)) = (e1))\/(((op (e2) (e2)) = (e2))\/((op (e2) (e2)) = (e3))))) -> (~((op (e0) (e2)) = (op (e2) (e2)))) -> (~((op (e2) (e2)) = (e2))) -> (~((op (e2) (e2)) = (op (e2) (e3)))) -> (((op (e2) (e0)) = (e0))\/(((op (e2) (e1)) = (e0))\/(((op (e2) (e2)) = (e0))\/((op (e2) (e3)) = (e0))))) -> (~((op (e1) (e0)) = (op (e2) (e0)))) -> (~((op (e1) (e1)) = (op (e3) (e1)))) -> (~((op (e2) (e1)) = (op (e3) (e1)))) -> (~((op (e1) (e3)) = (op (e2) (e3)))) -> (((op (e0) (e3)) = (e3))\/(((op (e1) (e3)) = (e3))\/(((op (e2) (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)) = (e1)))\/((op (e1) (e1)) = (e0))) -> (((op (e0) (e0)) = (e0))\/(((op (e1) (e0)) = (e0))\/(((op (e2) (e0)) = (e0))\/((op (e3) (e0)) = (e0))))) -> (~((e0) = (e1))) -> (~((op (e1) (e0)) = (op (e1) (e1)))) -> ((~((op (e0) (e3)) = (e1)))\/((op (e0) (e1)) = (e3))) -> (~((e0) = (e2))) -> (((op (e0) (e3)) = (e1))\/(((op (e1) (e3)) = (e1))\/(((op (e2) (e3)) = (e1))\/((op (e3) (e3)) = (e1))))) -> (((op (e0) (e0)) = (e3))\/(((op (e1) (e0)) = (e3))\/(((op (e2) (e0)) = (e3))\/((op (e3) (e0)) = (e3))))) -> (((op (e1) (e0)) = (e0))\/(((op (e1) (e0)) = (e1))\/(((op (e1) (e0)) = (e2))\/((op (e1) (e0)) = (e3))))) -> (~((op (e0) (e2)) = (e1))) -> (~((op (e0) (e0)) = (op (e0) (e3)))) -> (~((op (e0) (e1)) = (e1))) -> (((op (e0) (e1)) = (e1))\/(((op (e1) (e1)) = (e1))\/(((op (e2) (e1)) = (e1))\/((op (e3) (e1)) = (e1))))) -> ((~((op (e2) (e3)) = (e1)))\/((op (e2) (e1)) = (e3))) -> (~((op (e3) (e0)) = (op (e3) (e1)))) -> (~((op (e1) (e2)) = (op (e1) (e3)))) -> (((op (e2) (e3)) = (e0))\/(((op (e2) (e3)) = (e1))\/(((op (e2) (e3)) = (e2))\/((op (e2) (e3)) = (e3))))) -> (((op (e3) (e0)) = (e1))\/(((op (e3) (e1)) = (e1))\/(((op (e3) (e2)) = (e1))\/((op (e3) (e3)) = (e1))))) -> (~((op (e1) (e0)) = (op (e1) (e2)))) -> (((op (e0) (e1)) = (e3))\/(((op (e1) (e1)) = (e3))\/(((op (e2) (e1)) = (e3))\/((op (e3) (e1)) = (e3))))) -> ((~((op (e2) (e1)) = (e1)))\/((op (e2) (e1)) = (e1))) -> ((op (e0) (e2)) = (e2)) -> (~((op (e0) (e2)) = (op (e1) (e2)))) -> ((op (e1) (e3)) = (e1)) -> (~((e1) = (e2))) -> False). % 18.87/19.05 do 0 intro. intros zenon_H18c zenon_H7a zenon_H3b zenon_H128 zenon_H2b zenon_H106 zenon_H10a zenon_H1ef zenon_H261 zenon_H3f zenon_H256 zenon_H10e zenon_H257 zenon_H49 zenon_H254 zenon_H22d zenon_H231 zenon_H235 zenon_H13c zenon_H139 zenon_H210 zenon_H252 zenon_H17e zenon_H253 zenon_H258 zenon_H95 zenon_H9a zenon_H1fe zenon_H1d5 zenon_Hc2 zenon_Hf3 zenon_H102 zenon_H101 zenon_H6f zenon_H1fa zenon_H168 zenon_H54 zenon_H5b zenon_H1f0 zenon_H259 zenon_H17b zenon_H18f zenon_H1ac zenon_H52 zenon_H6a zenon_H22 zenon_H130 zenon_Hd8 zenon_H16f zenon_H145 zenon_H71 zenon_H1c7 zenon_H12b zenon_Hdf zenon_H1d zenon_Hd5 zenon_H153 zenon_He7 zenon_He2 zenon_H115 zenon_H14f zenon_H191 zenon_H1a4 zenon_H4a zenon_H4f zenon_H67 zenon_H62 zenon_H57 zenon_He4 zenon_H1c4 zenon_Ha8 zenon_H173 zenon_H6d zenon_H2f zenon_H201 zenon_H160 zenon_Haf zenon_Hdb zenon_H136 zenon_H183 zenon_H25d zenon_H3e zenon_Ha1 zenon_H45 zenon_H25c zenon_H149 zenon_H133 zenon_H1e0 zenon_H25e zenon_H20d zenon_H189 zenon_Ha4 zenon_H109 zenon_H263 zenon_H1cf zenon_H124 zenon_H11f zenon_He8 zenon_H24a zenon_H1a5 zenon_H262 zenon_H150 zenon_H195 zenon_Hd6 zenon_H7c. % 18.87/19.05 apply (zenon_or_s _ _ zenon_H18c); [ zenon_intro zenon_H86 | zenon_intro zenon_H18d ]. % 18.87/19.05 apply (zenon_L33_); trivial. % 18.87/19.05 apply (zenon_or_s _ _ zenon_H18d); [ zenon_intro zenon_H110 | zenon_intro zenon_H18e ]. % 18.87/19.05 apply (zenon_L917_); trivial. % 18.87/19.05 apply (zenon_or_s _ _ zenon_H18e); [ zenon_intro zenon_H113 | zenon_intro zenon_Hd7 ]. % 18.87/19.05 apply (zenon_L153_); trivial. % 18.87/19.05 apply (zenon_L101_); trivial. % 18.87/19.05 (* end of lemma zenon_L918_ *) % 18.87/19.05 assert (zenon_L919_ : (((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)) = (e2))\/(((op (e1) (e3)) = (e2))\/(((op (e2) (e3)) = (e2))\/((op (e3) (e3)) = (e2))))) -> (~((e2) = (e3))) -> (~((e1) = (e2))) -> (~((op (e2) (e1)) = (op (e2) (e3)))) -> ((op (e2) (e1)) = (e2)) -> (((op (e2) (e3)) = (e0))\/(((op (e2) (e3)) = (e1))\/(((op (e2) (e3)) = (e2))\/((op (e2) (e3)) = (e3))))) -> (~((op (e2) (e0)) = (op (e2) (e3)))) -> ((op (e2) (e0)) = (e0)) -> ((op (e1) (e3)) = (e0)) -> (~((op (e2) (e3)) = (op (e3) (e3)))) -> (~((op (e0) (e3)) = (op (e2) (e3)))) -> ((op (e0) (e3)) = (e3)) -> False). % 18.87/19.05 do 0 intro. intros zenon_H128 zenon_H1ef zenon_H10a zenon_H24d zenon_H145 zenon_H12b zenon_H7c zenon_H1c7 zenon_H1ca zenon_H11f zenon_H5b zenon_H34 zenon_H1f zenon_Hf3 zenon_He2 zenon_He3. % 18.87/19.05 apply (zenon_or_s _ _ zenon_H128); [ zenon_intro zenon_H9d | zenon_intro zenon_H129 ]. % 18.87/19.05 exact (zenon_H1ef zenon_H9d). % 18.87/19.05 apply (zenon_or_s _ _ zenon_H129); [ zenon_intro zenon_H10d | zenon_intro zenon_H12a ]. % 18.87/19.05 exact (zenon_H10a zenon_H10d). % 18.87/19.05 apply (zenon_or_s _ _ zenon_H12a); [ zenon_intro zenon_Hf0 | zenon_intro zenon_Hd6 ]. % 18.87/19.05 exact (zenon_H24d zenon_Hf0). % 18.87/19.05 apply (zenon_L226_); trivial. % 18.87/19.05 (* end of lemma zenon_L919_ *) % 18.87/19.05 assert (zenon_L920_ : (~((op (e1) (e2)) = (e1))) -> (((op (e1) (e0)) = (e2))\/(((op (e1) (e1)) = (e2))\/(((op (e1) (e2)) = (e2))\/((op (e1) (e3)) = (e2))))) -> ((op (e0) (e0)) = (e1)) -> ((op (e2) (e0)) = (e3)) -> (((op (e1) (e0)) = (e1))\/(((op (e1) (e1)) = (e1))\/(((op (e1) (e2)) = (e1))\/((op (e1) (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 (e1) (e1)) = (e1))) -> (~((op (e1) (e0)) = (e1))) -> ((~((op (e3) (e1)) = (e1)))\/((op (e3) (e1)) = (e1))) -> (~((op (e0) (e0)) = (e0))) -> ((~((op (e1) (e2)) = (e1)))\/((op (e1) (e1)) = (e2))) -> (~((op (e0) (e1)) = (op (e1) (e1)))) -> ((~((op (e2) (e0)) = (e1)))\/((op (e2) (e1)) = (e0))) -> ((op (e0) (e1)) = (e0)) -> ((~((op (e3) (e0)) = (e1)))\/((op (e3) (e1)) = (e0))) -> (((op (e0) (e0)) = (e1))\/(((op (e0) (e1)) = (e1))\/(((op (e0) (e2)) = (e1))\/((op (e0) (e3)) = (e1))))) -> (~((op (e0) (e3)) = (e1))) -> (((op (e0) (e0)) = (e1))\/(((op (e1) (e0)) = (e1))\/(((op (e2) (e0)) = (e1))\/((op (e3) (e0)) = (e1))))) -> (~((op (e0) (e0)) = (op (e0) (e2)))) -> (((op (e0) (e2)) = (e1))\/(((op (e1) (e2)) = (e1))\/(((op (e2) (e2)) = (e1))\/((op (e3) (e2)) = (e1))))) -> (~((op (e0) (e1)) = (op (e3) (e1)))) -> ((~((op (e3) (e2)) = (e1)))\/((op (e3) (e1)) = (e2))) -> (~((op (e0) (e1)) = (op (e2) (e1)))) -> ((~((op (e2) (e2)) = (e1)))\/((op (e2) (e1)) = (e2))) -> ((~((op (e1) (e3)) = (e1)))\/((op (e1) (e1)) = (e3))) -> (~((e1) = (e3))) -> (~((e0) = (e3))) -> (((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 (e0) (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) (e2)))) -> (~((op (e1) (e0)) = (op (e3) (e0)))) -> (((op (e0) (e0)) = (e3))\/(((op (e0) (e1)) = (e3))\/(((op (e0) (e2)) = (e3))\/((op (e0) (e3)) = (e3))))) -> (~((op (e0) (e1)) = (op (e0) (e3)))) -> (~((op (e2) (e0)) = (op (e2) (e3)))) -> (~((op (e2) (e0)) = (op (e2) (e1)))) -> (((op (e2) (e0)) = (e0))\/(((op (e2) (e0)) = (e1))\/(((op (e2) (e0)) = (e2))\/((op (e2) (e0)) = (e3))))) -> (~((op (e2) (e0)) = (op (e3) (e0)))) -> (~((op (e2) (e2)) = (op (e3) (e2)))) -> (((op (e3) (e0)) = (e0))\/(((op (e3) (e1)) = (e0))\/(((op (e3) (e2)) = (e0))\/((op (e3) (e3)) = (e0))))) -> (~((op (e2) (e0)) = (op (e2) (e2)))) -> (((op (e0) (e2)) = (e0))\/(((op (e1) (e2)) = (e0))\/(((op (e2) (e2)) = (e0))\/((op (e3) (e2)) = (e0))))) -> (((op (e1) (e0)) = (e0))\/(((op (e1) (e1)) = (e0))\/(((op (e1) (e2)) = (e0))\/((op (e1) (e3)) = (e0))))) -> (~((op (e3) (e1)) = (op (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 (e0) (e3)) = (e2))\/(((op (e1) (e3)) = (e2))\/(((op (e2) (e3)) = (e2))\/((op (e3) (e3)) = (e2))))) -> (~((op (e3) (e0)) = (op (e3) (e3)))) -> (~((op (e2) (e1)) = (op (e2) (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 (e3) (e0)) = (e2))\/(((op (e3) (e1)) = (e2))\/(((op (e3) (e2)) = (e2))\/((op (e3) (e3)) = (e2))))) -> (((op (e2) (e0)) = (e3))\/(((op (e2) (e1)) = (e3))\/(((op (e2) (e2)) = (e3))\/((op (e2) (e3)) = (e3))))) -> (~((op (e0) (e3)) = (op (e2) (e3)))) -> (~((op (e1) (e2)) = (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) (e1)) = (op (e3) (e2)))) -> (~((op (e0) (e1)) = (op (e0) (e2)))) -> (~((op (e1) (e1)) = (op (e1) (e2)))) -> (((op (e0) (e3)) = (e0))\/(((op (e1) (e3)) = (e0))\/(((op (e2) (e3)) = (e0))\/((op (e3) (e3)) = (e0))))) -> (~((op (e3) (e2)) = (op (e3) (e3)))) -> (~((op (e1) (e1)) = (op (e1) (e3)))) -> (((op (e0) (e3)) = (e0))\/(((op (e0) (e3)) = (e1))\/(((op (e0) (e3)) = (e2))\/((op (e0) (e3)) = (e3))))) -> (((op (e2) (e2)) = (e0))\/(((op (e2) (e2)) = (e1))\/(((op (e2) (e2)) = (e2))\/((op (e2) (e2)) = (e3))))) -> (~((op (e0) (e2)) = (op (e2) (e2)))) -> (~((op (e2) (e2)) = (e2))) -> (~((op (e2) (e2)) = (op (e2) (e3)))) -> (((op (e2) (e0)) = (e0))\/(((op (e2) (e1)) = (e0))\/(((op (e2) (e2)) = (e0))\/((op (e2) (e3)) = (e0))))) -> (~((op (e1) (e0)) = (op (e2) (e0)))) -> (~((op (e1) (e1)) = (op (e3) (e1)))) -> (~((op (e2) (e1)) = (op (e3) (e1)))) -> (~((op (e1) (e3)) = (op (e2) (e3)))) -> (((op (e0) (e3)) = (e3))\/(((op (e1) (e3)) = (e3))\/(((op (e2) (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)) = (e1)))\/((op (e1) (e1)) = (e0))) -> (((op (e0) (e0)) = (e0))\/(((op (e1) (e0)) = (e0))\/(((op (e2) (e0)) = (e0))\/((op (e3) (e0)) = (e0))))) -> (~((e0) = (e1))) -> (~((op (e1) (e0)) = (op (e1) (e1)))) -> ((~((op (e0) (e3)) = (e1)))\/((op (e0) (e1)) = (e3))) -> (~((e0) = (e2))) -> (((op (e0) (e3)) = (e1))\/(((op (e1) (e3)) = (e1))\/(((op (e2) (e3)) = (e1))\/((op (e3) (e3)) = (e1))))) -> (((op (e0) (e0)) = (e3))\/(((op (e1) (e0)) = (e3))\/(((op (e2) (e0)) = (e3))\/((op (e3) (e0)) = (e3))))) -> (((op (e1) (e0)) = (e0))\/(((op (e1) (e0)) = (e1))\/(((op (e1) (e0)) = (e2))\/((op (e1) (e0)) = (e3))))) -> (~((op (e0) (e2)) = (e1))) -> (~((op (e0) (e0)) = (op (e0) (e3)))) -> (~((op (e0) (e1)) = (e1))) -> (((op (e0) (e1)) = (e1))\/(((op (e1) (e1)) = (e1))\/(((op (e2) (e1)) = (e1))\/((op (e3) (e1)) = (e1))))) -> ((~((op (e2) (e3)) = (e1)))\/((op (e2) (e1)) = (e3))) -> (~((op (e3) (e0)) = (op (e3) (e1)))) -> (~((op (e1) (e2)) = (op (e1) (e3)))) -> (((op (e2) (e3)) = (e0))\/(((op (e2) (e3)) = (e1))\/(((op (e2) (e3)) = (e2))\/((op (e2) (e3)) = (e3))))) -> (((op (e3) (e0)) = (e1))\/(((op (e3) (e1)) = (e1))\/(((op (e3) (e2)) = (e1))\/((op (e3) (e3)) = (e1))))) -> (~((op (e1) (e0)) = (op (e1) (e2)))) -> (((op (e0) (e1)) = (e3))\/(((op (e1) (e1)) = (e3))\/(((op (e2) (e1)) = (e3))\/((op (e3) (e1)) = (e3))))) -> ((~((op (e2) (e1)) = (e1)))\/((op (e2) (e1)) = (e1))) -> ((op (e0) (e2)) = (e2)) -> (~((op (e0) (e2)) = (op (e1) (e2)))) -> (~((e1) = (e2))) -> False). % 18.87/19.05 do 0 intro. intros zenon_H24d zenon_H18c zenon_H7a zenon_H3b zenon_H128 zenon_H2b zenon_H106 zenon_H10a zenon_H1ef zenon_H261 zenon_H3f zenon_H256 zenon_H10e zenon_H257 zenon_H49 zenon_H254 zenon_H22d zenon_H231 zenon_H235 zenon_H13c zenon_H139 zenon_H210 zenon_H252 zenon_H17e zenon_H253 zenon_H258 zenon_H95 zenon_H9a zenon_H1fe zenon_H1d5 zenon_Hc2 zenon_Hf3 zenon_H102 zenon_H101 zenon_H6f zenon_H1fa zenon_H168 zenon_H54 zenon_H5b zenon_H1f0 zenon_H259 zenon_H17b zenon_H18f zenon_H1ac zenon_H52 zenon_H6a zenon_H22 zenon_H130 zenon_Hd8 zenon_H16f zenon_H145 zenon_H71 zenon_H1c7 zenon_H12b zenon_Hdf zenon_H1d zenon_Hd5 zenon_H153 zenon_He7 zenon_He2 zenon_H115 zenon_H14f zenon_H191 zenon_H1a4 zenon_H4a zenon_H4f zenon_H67 zenon_H62 zenon_H57 zenon_He4 zenon_H1c4 zenon_Ha8 zenon_H173 zenon_H6d zenon_H2f zenon_H201 zenon_H160 zenon_Haf zenon_Hdb zenon_H136 zenon_H183 zenon_H25d zenon_H3e zenon_Ha1 zenon_H45 zenon_H25c zenon_H149 zenon_H133 zenon_H1e0 zenon_H25e zenon_H20d zenon_H189 zenon_Ha4 zenon_H109 zenon_H263 zenon_H1cf zenon_H124 zenon_H11f zenon_He8 zenon_H24a zenon_H1a5 zenon_H262 zenon_H150 zenon_H195 zenon_H7c. % 18.87/19.05 apply (zenon_or_s _ _ zenon_H128); [ zenon_intro zenon_H9d | zenon_intro zenon_H129 ]. % 18.87/19.05 exact (zenon_H1ef zenon_H9d). % 18.87/19.05 apply (zenon_or_s _ _ zenon_H129); [ zenon_intro zenon_H10d | zenon_intro zenon_H12a ]. % 18.87/19.05 exact (zenon_H10a zenon_H10d). % 18.87/19.05 apply (zenon_or_s _ _ zenon_H12a); [ zenon_intro zenon_Hf0 | zenon_intro zenon_Hd6 ]. % 18.87/19.05 exact (zenon_H24d zenon_Hf0). % 18.87/19.05 apply (zenon_L918_); trivial. % 18.87/19.05 (* end of lemma zenon_L920_ *) % 18.87/19.05 assert (zenon_L921_ : (((op (e1) (e0)) = (e0))\/(((op (e1) (e1)) = (e0))\/(((op (e1) (e2)) = (e0))\/((op (e1) (e3)) = (e0))))) -> (~((op (e1) (e0)) = (op (e2) (e0)))) -> ((op (e2) (e0)) = (e0)) -> (~((op (e3) (e0)) = (op (e3) (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)) -> (~((op (e1) (e1)) = (op (e1) (e2)))) -> (~((op (e2) (e2)) = (op (e2) (e3)))) -> (~((op (e3) (e0)) = (op (e3) (e2)))) -> (~((op (e1) (e1)) = (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))))) -> (~((op (e2) (e0)) = (op (e2) (e2)))) -> (~((op (e2) (e0)) = (op (e2) (e3)))) -> (~((op (e3) (e2)) = (op (e3) (e3)))) -> (~((op (e1) (e0)) = (op (e1) (e1)))) -> (~((op (e0) (e0)) = (e0))) -> (((op (e0) (e0)) = (e0))\/(((op (e1) (e0)) = (e0))\/(((op (e2) (e0)) = (e0))\/((op (e3) (e0)) = (e0))))) -> (~((op (e2) (e2)) = (e2))) -> (~((op (e2) (e2)) = (op (e3) (e2)))) -> ((op (e0) (e2)) = (e3)) -> (((op (e2) (e2)) = (e0))\/(((op (e2) (e2)) = (e1))\/(((op (e2) (e2)) = (e2))\/((op (e2) (e2)) = (e3))))) -> (~((op (e1) (e2)) = (op (e1) (e3)))) -> (~((op (e0) (e2)) = (e1))) -> (((op (e0) (e2)) = (e1))\/(((op (e1) (e2)) = (e1))\/(((op (e2) (e2)) = (e1))\/((op (e3) (e2)) = (e1))))) -> (~((op (e1) (e2)) = (e1))) -> (~((op (e1) (e1)) = (e1))) -> (((op (e1) (e0)) = (e1))\/(((op (e1) (e1)) = (e1))\/(((op (e1) (e2)) = (e1))\/((op (e1) (e3)) = (e1))))) -> (((op (e1) (e0)) = (e0))\/(((op (e1) (e0)) = (e1))\/(((op (e1) (e0)) = (e2))\/((op (e1) (e0)) = (e3))))) -> (~((op (e1) (e0)) = (op (e1) (e3)))) -> (~((op (e1) (e0)) = (e1))) -> ((op (e2) (e0)) = (e3)) -> ((op (e3) (e0)) = (e2)) -> ((op (e0) (e0)) = (e1)) -> False). % 18.87/19.05 do 0 intro. intros zenon_H22 zenon_H201 zenon_H34 zenon_H71 zenon_H6a zenon_H4a zenon_H49 zenon_H4f zenon_H6d zenon_H6f zenon_H57 zenon_H54 zenon_H67 zenon_H52 zenon_H5b zenon_H62 zenon_H45 zenon_H3f zenon_H3e zenon_H173 zenon_H18f zenon_Ha9 zenon_H1c4 zenon_H124 zenon_H20d zenon_H139 zenon_H24d zenon_H10a zenon_H128 zenon_H25e zenon_Hd8 zenon_H1ef zenon_H3b zenon_H148 zenon_H7a. % 18.87/19.05 apply (zenon_or_s _ _ zenon_H22); [ zenon_intro zenon_H27 | zenon_intro zenon_H26 ]. % 18.87/19.05 apply (zenon_L332_); trivial. % 18.87/19.05 apply (zenon_or_s _ _ zenon_H26); [ zenon_intro zenon_H29 | zenon_intro zenon_H28 ]. % 18.87/19.05 apply (zenon_L23_); trivial. % 18.87/19.05 apply (zenon_or_s _ _ zenon_H28); [ zenon_intro zenon_H2a | zenon_intro zenon_H1f ]. % 18.87/19.05 apply (zenon_L721_); trivial. % 18.87/19.05 apply (zenon_L769_); trivial. % 18.87/19.05 (* end of lemma zenon_L921_ *) % 18.87/19.05 assert (zenon_L922_ : (((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) (e0)) = (e1))\/(((op (e3) (e1)) = (e1))\/(((op (e3) (e2)) = (e1))\/((op (e3) (e3)) = (e1))))) -> (~((op (e3) (e0)) = (e1))) -> (~((op (e3) (e1)) = (e1))) -> (~((op (e3) (e2)) = (e1))) -> (~((op (e1) (e3)) = (op (e3) (e3)))) -> False). % 18.87/19.05 do 0 intro. intros zenon_H128 zenon_H1ef zenon_H10a zenon_H24d zenon_He8 zenon_Had zenon_H250 zenon_H251 zenon_Hd5. % 18.87/19.05 apply (zenon_or_s _ _ zenon_H128); [ zenon_intro zenon_H9d | zenon_intro zenon_H129 ]. % 18.87/19.05 exact (zenon_H1ef zenon_H9d). % 18.87/19.05 apply (zenon_or_s _ _ zenon_H129); [ zenon_intro zenon_H10d | zenon_intro zenon_H12a ]. % 18.87/19.05 exact (zenon_H10a zenon_H10d). % 18.87/19.05 apply (zenon_or_s _ _ zenon_H12a); [ zenon_intro zenon_Hf0 | zenon_intro zenon_Hd6 ]. % 18.87/19.05 exact (zenon_H24d zenon_Hf0). % 18.87/19.05 apply (zenon_L800_); trivial. % 18.87/19.05 (* end of lemma zenon_L922_ *) % 18.87/19.05 assert (zenon_L923_ : (((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)))) -> ((op (e3) (e2)) = (e1)) -> (~((op (e3) (e1)) = (op (e3) (e3)))) -> ((op (e3) (e1)) = (e2)) -> (~((op (e3) (e3)) = (e3))) -> False). % 18.87/19.05 do 0 intro. intros zenon_H101 zenon_H61 zenon_H62 zenon_Hba zenon_H130 zenon_H14d zenon_H102. % 18.87/19.05 apply (zenon_or_s _ _ zenon_H101); [ zenon_intro zenon_H60 | zenon_intro zenon_H103 ]. % 18.87/19.05 apply (zenon_L15_); trivial. % 18.87/19.05 apply (zenon_or_s _ _ zenon_H103); [ zenon_intro zenon_Hc4 | zenon_intro zenon_H104 ]. % 18.87/19.05 apply (zenon_L147_); trivial. % 18.87/19.05 apply (zenon_or_s _ _ zenon_H104); [ zenon_intro zenon_Hf6 | zenon_intro zenon_H105 ]. % 18.87/19.05 apply (zenon_L102_); trivial. % 18.87/19.05 exact (zenon_H102 zenon_H105). % 18.87/19.05 (* end of lemma zenon_L923_ *) % 18.87/19.05 assert (zenon_L924_ : (((op (e3) (e0)) = (e1))\/(((op (e3) (e1)) = (e1))\/(((op (e3) (e2)) = (e1))\/((op (e3) (e3)) = (e1))))) -> (~((op (e3) (e0)) = (e1))) -> (~((op (e3) (e1)) = (e1))) -> (~((op (e3) (e3)) = (e3))) -> ((op (e3) (e1)) = (e2)) -> (~((op (e3) (e1)) = (op (e3) (e3)))) -> (~((op (e3) (e2)) = (op (e3) (e3)))) -> ((op (e3) (e2)) = (e0)) -> (((op (e3) (e3)) = (e0))\/(((op (e3) (e3)) = (e1))\/(((op (e3) (e3)) = (e2))\/((op (e3) (e3)) = (e3))))) -> ((op (e0) (e3)) = (e2)) -> ((op (e1) (e3)) = (e0)) -> False). % 18.87/19.05 do 0 intro. intros zenon_He8 zenon_Had zenon_H250 zenon_H102 zenon_H14d zenon_H130 zenon_H62 zenon_H61 zenon_H101 zenon_Hcd zenon_H1f. % 18.87/19.05 apply (zenon_or_s _ _ zenon_He8); [ zenon_intro zenon_Hac | zenon_intro zenon_Heb ]. % 18.87/19.05 exact (zenon_Had zenon_Hac). % 18.87/19.05 apply (zenon_or_s _ _ zenon_Heb); [ zenon_intro zenon_Hae | zenon_intro zenon_Hec ]. % 18.87/19.05 exact (zenon_H250 zenon_Hae). % 18.87/19.05 apply (zenon_or_s _ _ zenon_Hec); [ zenon_intro zenon_Hba | zenon_intro zenon_Hc4 ]. % 18.87/19.05 apply (zenon_L923_); trivial. % 18.87/19.05 apply (zenon_L49_); trivial. % 18.87/19.05 (* end of lemma zenon_L924_ *) % 18.87/19.05 assert (zenon_L925_ : (((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 (e2) (e2)) = (e2))) -> (~((op (e2) (e2)) = (op (e3) (e2)))) -> (((op (e2) (e2)) = (e0))\/(((op (e2) (e2)) = (e1))\/(((op (e2) (e2)) = (e2))\/((op (e2) (e2)) = (e3))))) -> (~((op (e1) (e2)) = (op (e1) (e3)))) -> (~((op (e0) (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 (e3) (e3)))) -> ((op (e0) (e2)) = (e3)) -> (((op (e3) (e0)) = (e1))\/(((op (e3) (e1)) = (e1))\/(((op (e3) (e2)) = (e1))\/((op (e3) (e3)) = (e1))))) -> (~((op (e3) (e0)) = (e1))) -> (~((op (e3) (e1)) = (e1))) -> (~((op (e3) (e3)) = (e3))) -> ((op (e3) (e1)) = (e2)) -> (~((op (e3) (e1)) = (op (e3) (e3)))) -> (~((op (e3) (e2)) = (op (e3) (e3)))) -> (((op (e3) (e3)) = (e0))\/(((op (e3) (e3)) = (e1))\/(((op (e3) (e3)) = (e2))\/((op (e3) (e3)) = (e3))))) -> ((op (e0) (e3)) = (e2)) -> ((op (e1) (e3)) = (e0)) -> False). % 18.87/19.05 do 0 intro. intros zenon_H6a zenon_H4a zenon_H49 zenon_H173 zenon_H18f zenon_H1c4 zenon_H124 zenon_H20d zenon_H139 zenon_Hd6 zenon_Hd5 zenon_Ha9 zenon_He8 zenon_Had zenon_H250 zenon_H102 zenon_H14d zenon_H130 zenon_H62 zenon_H101 zenon_Hcd zenon_H1f. % 18.87/19.05 apply (zenon_or_s _ _ zenon_H6a); [ zenon_intro zenon_H48 | zenon_intro zenon_H6b ]. % 18.87/19.05 apply (zenon_L9_); trivial. % 18.87/19.05 apply (zenon_or_s _ _ zenon_H6b); [ zenon_intro zenon_H2a | zenon_intro zenon_H6c ]. % 18.87/19.05 apply (zenon_L720_); trivial. % 18.87/19.05 apply (zenon_or_s _ _ zenon_H6c); [ zenon_intro zenon_H2c | zenon_intro zenon_H61 ]. % 18.87/19.05 apply (zenon_L869_); trivial. % 18.87/19.05 apply (zenon_L924_); trivial. % 18.87/19.05 (* end of lemma zenon_L925_ *) % 18.87/19.05 assert (zenon_L926_ : (((op (e1) (e0)) = (e0))\/(((op (e1) (e1)) = (e0))\/(((op (e1) (e2)) = (e0))\/((op (e1) (e3)) = (e0))))) -> (~((op (e1) (e0)) = (op (e2) (e0)))) -> ((op (e2) (e0)) = (e0)) -> (~((op (e2) (e0)) = (op (e2) (e3)))) -> (~((op (e1) (e1)) = (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))))) -> (~((op (e2) (e0)) = (op (e2) (e2)))) -> (~((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)) = (e1))) -> (~((op (e1) (e1)) = (e1))) -> (~((op (e1) (e2)) = (e1))) -> (((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 (e2) (e2)) = (e2))) -> (~((op (e2) (e2)) = (op (e3) (e2)))) -> (((op (e2) (e2)) = (e0))\/(((op (e2) (e2)) = (e1))\/(((op (e2) (e2)) = (e2))\/((op (e2) (e2)) = (e3))))) -> (~((op (e1) (e2)) = (op (e1) (e3)))) -> (~((op (e0) (e2)) = (e1))) -> (((op (e0) (e2)) = (e1))\/(((op (e1) (e2)) = (e1))\/(((op (e2) (e2)) = (e1))\/((op (e3) (e2)) = (e1))))) -> (~((op (e1) (e3)) = (op (e3) (e3)))) -> ((op (e0) (e2)) = (e3)) -> (((op (e3) (e0)) = (e1))\/(((op (e3) (e1)) = (e1))\/(((op (e3) (e2)) = (e1))\/((op (e3) (e3)) = (e1))))) -> (~((op (e3) (e0)) = (e1))) -> (~((op (e3) (e1)) = (e1))) -> (~((op (e3) (e3)) = (e3))) -> ((op (e3) (e1)) = (e2)) -> (~((op (e3) (e1)) = (op (e3) (e3)))) -> (~((op (e3) (e2)) = (op (e3) (e3)))) -> (((op (e3) (e3)) = (e0))\/(((op (e3) (e3)) = (e1))\/(((op (e3) (e3)) = (e2))\/((op (e3) (e3)) = (e3))))) -> ((op (e0) (e3)) = (e2)) -> False). % 18.87/19.05 do 0 intro. intros zenon_H22 zenon_H201 zenon_H34 zenon_H5b zenon_H57 zenon_H54 zenon_H67 zenon_H52 zenon_H4f zenon_H128 zenon_H1ef zenon_H10a zenon_H24d zenon_H6a zenon_H4a zenon_H49 zenon_H173 zenon_H18f zenon_H1c4 zenon_H124 zenon_H20d zenon_H139 zenon_Hd5 zenon_Ha9 zenon_He8 zenon_Had zenon_H250 zenon_H102 zenon_H14d zenon_H130 zenon_H62 zenon_H101 zenon_Hcd. % 18.87/19.05 apply (zenon_or_s _ _ zenon_H22); [ zenon_intro zenon_H27 | zenon_intro zenon_H26 ]. % 18.87/19.05 apply (zenon_L332_); trivial. % 18.87/19.05 apply (zenon_or_s _ _ zenon_H26); [ zenon_intro zenon_H29 | zenon_intro zenon_H28 ]. % 18.87/19.05 apply (zenon_L17_); trivial. % 18.87/19.05 apply (zenon_or_s _ _ zenon_H28); [ zenon_intro zenon_H2a | zenon_intro zenon_H1f ]. % 18.87/19.05 apply (zenon_L721_); trivial. % 18.87/19.05 apply (zenon_or_s _ _ zenon_H128); [ zenon_intro zenon_H9d | zenon_intro zenon_H129 ]. % 18.87/19.05 exact (zenon_H1ef zenon_H9d). % 18.87/19.05 apply (zenon_or_s _ _ zenon_H129); [ zenon_intro zenon_H10d | zenon_intro zenon_H12a ]. % 18.87/19.05 exact (zenon_H10a zenon_H10d). % 18.87/19.05 apply (zenon_or_s _ _ zenon_H12a); [ zenon_intro zenon_Hf0 | zenon_intro zenon_Hd6 ]. % 18.87/19.05 exact (zenon_H24d zenon_Hf0). % 18.87/19.05 apply (zenon_L925_); trivial. % 18.87/19.05 (* end of lemma zenon_L926_ *) % 18.87/19.05 assert (zenon_L927_ : (((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)) = (e2))\/(((op (e1) (e3)) = (e2))\/(((op (e2) (e3)) = (e2))\/((op (e3) (e3)) = (e2))))) -> (~((e2) = (e3))) -> ((op (e0) (e3)) = (e3)) -> (~((e1) = (e2))) -> (~((op (e2) (e0)) = (op (e2) (e3)))) -> ((op (e2) (e0)) = (e2)) -> ((op (e3) (e1)) = (e2)) -> (~((op (e3) (e1)) = (op (e3) (e3)))) -> False). % 18.87/19.05 do 0 intro. intros zenon_H128 zenon_H1ef zenon_H10a zenon_H24d zenon_H145 zenon_H12b zenon_He3 zenon_H7c zenon_H5b zenon_Hee zenon_H14d zenon_H130. % 18.87/19.05 apply (zenon_or_s _ _ zenon_H128); [ zenon_intro zenon_H9d | zenon_intro zenon_H129 ]. % 18.87/19.05 exact (zenon_H1ef zenon_H9d). % 18.87/19.05 apply (zenon_or_s _ _ zenon_H129); [ zenon_intro zenon_H10d | zenon_intro zenon_H12a ]. % 18.87/19.05 exact (zenon_H10a zenon_H10d). % 18.87/19.05 apply (zenon_or_s _ _ zenon_H12a); [ zenon_intro zenon_Hf0 | zenon_intro zenon_Hd6 ]. % 18.87/19.05 exact (zenon_H24d zenon_Hf0). % 18.87/19.05 apply (zenon_L103_); trivial. % 18.87/19.05 (* end of lemma zenon_L927_ *) % 18.87/19.05 assert (zenon_L928_ : (((op (e3) (e0)) = (e1))\/(((op (e3) (e1)) = (e1))\/(((op (e3) (e2)) = (e1))\/((op (e3) (e3)) = (e1))))) -> (~((op (e3) (e0)) = (e1))) -> (~((op (e3) (e1)) = (e1))) -> (~((op (e3) (e3)) = (e3))) -> ((op (e3) (e1)) = (e2)) -> (~((op (e3) (e1)) = (op (e3) (e3)))) -> (~((op (e3) (e2)) = (op (e3) (e3)))) -> ((op (e3) (e2)) = (e0)) -> (((op (e3) (e3)) = (e0))\/(((op (e3) (e3)) = (e1))\/(((op (e3) (e3)) = (e2))\/((op (e3) (e3)) = (e3))))) -> (~((op (e1) (e3)) = (op (e3) (e3)))) -> ((op (e1) (e3)) = (e1)) -> False). % 18.87/19.05 do 0 intro. intros zenon_He8 zenon_Had zenon_H250 zenon_H102 zenon_H14d zenon_H130 zenon_H62 zenon_H61 zenon_H101 zenon_Hd5 zenon_Hd6. % 18.87/19.05 apply (zenon_or_s _ _ zenon_He8); [ zenon_intro zenon_Hac | zenon_intro zenon_Heb ]. % 18.87/19.05 exact (zenon_Had zenon_Hac). % 18.87/19.05 apply (zenon_or_s _ _ zenon_Heb); [ zenon_intro zenon_Hae | zenon_intro zenon_Hec ]. % 18.87/19.05 exact (zenon_H250 zenon_Hae). % 18.87/19.05 apply (zenon_or_s _ _ zenon_Hec); [ zenon_intro zenon_Hba | zenon_intro zenon_Hc4 ]. % 18.87/19.05 apply (zenon_L923_); trivial. % 18.87/19.05 apply (zenon_L50_); trivial. % 18.87/19.05 (* end of lemma zenon_L928_ *) % 18.87/19.05 assert (zenon_L929_ : (((op (e0) (e2)) = (e0))\/(((op (e1) (e2)) = (e0))\/(((op (e2) (e2)) = (e0))\/((op (e3) (e2)) = (e0))))) -> (~((e0) = (e2))) -> ((op (e0) (e2)) = (e2)) -> (~((op (e2) (e2)) = (e2))) -> (~((op (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 (e1) (e3)))) -> (~((op (e0) (e2)) = (e1))) -> (((op (e0) (e2)) = (e1))\/(((op (e1) (e2)) = (e1))\/(((op (e2) (e2)) = (e1))\/((op (e3) (e2)) = (e1))))) -> ((op (e0) (e2)) = (e3)) -> (((op (e3) (e0)) = (e1))\/(((op (e3) (e1)) = (e1))\/(((op (e3) (e2)) = (e1))\/((op (e3) (e3)) = (e1))))) -> (~((op (e3) (e0)) = (e1))) -> (~((op (e3) (e1)) = (e1))) -> (~((op (e3) (e3)) = (e3))) -> ((op (e3) (e1)) = (e2)) -> (~((op (e3) (e1)) = (op (e3) (e3)))) -> (~((op (e3) (e2)) = (op (e3) (e3)))) -> (((op (e3) (e3)) = (e0))\/(((op (e3) (e3)) = (e1))\/(((op (e3) (e3)) = (e2))\/((op (e3) (e3)) = (e3))))) -> (~((op (e1) (e3)) = (op (e3) (e3)))) -> ((op (e1) (e3)) = (e1)) -> False). % 18.87/19.05 do 0 intro. intros zenon_H6a zenon_H149 zenon_H150 zenon_H173 zenon_H18f zenon_H1c4 zenon_H124 zenon_H20d zenon_H139 zenon_Ha9 zenon_He8 zenon_Had zenon_H250 zenon_H102 zenon_H14d zenon_H130 zenon_H62 zenon_H101 zenon_Hd5 zenon_Hd6. % 18.87/19.05 apply (zenon_or_s _ _ zenon_H6a); [ zenon_intro zenon_H48 | zenon_intro zenon_H6b ]. % 18.87/19.05 apply (zenon_L378_); trivial. % 18.87/19.05 apply (zenon_or_s _ _ zenon_H6b); [ zenon_intro zenon_H2a | zenon_intro zenon_H6c ]. % 18.87/19.05 apply (zenon_L720_); trivial. % 18.87/19.05 apply (zenon_or_s _ _ zenon_H6c); [ zenon_intro zenon_H2c | zenon_intro zenon_H61 ]. % 18.87/19.05 apply (zenon_L869_); trivial. % 18.87/19.05 apply (zenon_L928_); trivial. % 18.87/19.05 (* end of lemma zenon_L929_ *) % 18.87/19.05 assert (zenon_L930_ : (((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) (e2)) = (e0))\/(((op (e1) (e2)) = (e0))\/(((op (e2) (e2)) = (e0))\/((op (e3) (e2)) = (e0))))) -> (~((e0) = (e2))) -> ((op (e0) (e2)) = (e2)) -> (~((op (e2) (e2)) = (e2))) -> (~((op (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 (e1) (e3)))) -> (~((op (e0) (e2)) = (e1))) -> (((op (e0) (e2)) = (e1))\/(((op (e1) (e2)) = (e1))\/(((op (e2) (e2)) = (e1))\/((op (e3) (e2)) = (e1))))) -> ((op (e0) (e2)) = (e3)) -> (((op (e3) (e0)) = (e1))\/(((op (e3) (e1)) = (e1))\/(((op (e3) (e2)) = (e1))\/((op (e3) (e3)) = (e1))))) -> (~((op (e3) (e0)) = (e1))) -> (~((op (e3) (e1)) = (e1))) -> (~((op (e3) (e3)) = (e3))) -> ((op (e3) (e1)) = (e2)) -> (~((op (e3) (e1)) = (op (e3) (e3)))) -> (~((op (e3) (e2)) = (op (e3) (e3)))) -> (((op (e3) (e3)) = (e0))\/(((op (e3) (e3)) = (e1))\/(((op (e3) (e3)) = (e2))\/((op (e3) (e3)) = (e3))))) -> (~((op (e1) (e3)) = (op (e3) (e3)))) -> False). % 18.87/19.05 do 0 intro. intros zenon_H128 zenon_H1ef zenon_H10a zenon_H24d zenon_H6a zenon_H149 zenon_H150 zenon_H173 zenon_H18f zenon_H1c4 zenon_H124 zenon_H20d zenon_H139 zenon_Ha9 zenon_He8 zenon_Had zenon_H250 zenon_H102 zenon_H14d zenon_H130 zenon_H62 zenon_H101 zenon_Hd5. % 18.87/19.05 apply (zenon_or_s _ _ zenon_H128); [ zenon_intro zenon_H9d | zenon_intro zenon_H129 ]. % 18.87/19.05 exact (zenon_H1ef zenon_H9d). % 18.87/19.05 apply (zenon_or_s _ _ zenon_H129); [ zenon_intro zenon_H10d | zenon_intro zenon_H12a ]. % 18.87/19.05 exact (zenon_H10a zenon_H10d). % 18.87/19.05 apply (zenon_or_s _ _ zenon_H12a); [ zenon_intro zenon_Hf0 | zenon_intro zenon_Hd6 ]. % 18.87/19.05 exact (zenon_H24d zenon_Hf0). % 18.87/19.05 apply (zenon_L929_); trivial. % 18.87/19.05 (* end of lemma zenon_L930_ *) % 18.87/19.05 assert (zenon_L931_ : (((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)) -> (~((op (e0) (e1)) = (op (e1) (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) (e2)) = (op (e3) (e3)))) -> (~((op (e3) (e3)) = (e3))) -> (~((op (e3) (e1)) = (e1))) -> (~((op (e3) (e0)) = (e1))) -> (((op (e3) (e0)) = (e1))\/(((op (e3) (e1)) = (e1))\/(((op (e3) (e2)) = (e1))\/((op (e3) (e3)) = (e1))))) -> (((op (e0) (e2)) = (e1))\/(((op (e1) (e2)) = (e1))\/(((op (e2) (e2)) = (e1))\/((op (e3) (e2)) = (e1))))) -> (~((op (e0) (e2)) = (e1))) -> (~((op (e1) (e2)) = (op (e1) (e3)))) -> (((op (e2) (e2)) = (e0))\/(((op (e2) (e2)) = (e1))\/(((op (e2) (e2)) = (e2))\/((op (e2) (e2)) = (e3))))) -> (~((op (e2) (e2)) = (op (e3) (e2)))) -> (~((op (e2) (e2)) = (e2))) -> ((op (e0) (e2)) = (e2)) -> (~((e0) = (e2))) -> (((op (e0) (e2)) = (e0))\/(((op (e1) (e2)) = (e0))\/(((op (e2) (e2)) = (e0))\/((op (e3) (e2)) = (e0))))) -> (~((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 (e0) (e3)) = (e2))\/(((op (e1) (e3)) = (e2))\/(((op (e2) (e3)) = (e2))\/((op (e3) (e3)) = (e2))))) -> (~((e2) = (e3))) -> (~((op (e1) (e0)) = (op (e1) (e3)))) -> ((op (e1) (e0)) = (e2)) -> (~((op (e2) (e1)) = (op (e2) (e3)))) -> ((op (e2) (e1)) = (e2)) -> ((op (e3) (e1)) = (e2)) -> (~((op (e3) (e1)) = (op (e3) (e3)))) -> False). % 18.87/19.05 do 0 intro. intros zenon_H168 zenon_H95 zenon_H7a zenon_H13f zenon_H10e zenon_Hd5 zenon_H101 zenon_H62 zenon_H102 zenon_H250 zenon_Had zenon_He8 zenon_H139 zenon_H20d zenon_H124 zenon_H1c4 zenon_H18f zenon_H173 zenon_H150 zenon_H149 zenon_H6a zenon_H24d zenon_H10a zenon_H1ef zenon_H128 zenon_H145 zenon_H12b zenon_Hd8 zenon_H86 zenon_H1c7 zenon_H1ca zenon_H14d zenon_H130. % 18.87/19.05 apply (zenon_or_s _ _ zenon_H168); [ zenon_intro zenon_H3a | zenon_intro zenon_H169 ]. % 18.87/19.05 apply (zenon_L35_); trivial. % 18.87/19.05 apply (zenon_or_s _ _ zenon_H169); [ zenon_intro zenon_H99 | zenon_intro zenon_H16a ]. % 18.87/19.05 apply (zenon_L108_); trivial. % 18.87/19.05 apply (zenon_or_s _ _ zenon_H16a); [ zenon_intro zenon_Ha9 | zenon_intro zenon_He3 ]. % 18.87/19.05 apply (zenon_L930_); trivial. % 18.87/19.05 apply (zenon_L739_); trivial. % 18.87/19.05 (* end of lemma zenon_L931_ *) % 18.87/19.05 assert (zenon_L932_ : (((op (e2) (e0)) = (e0))\/(((op (e2) (e0)) = (e1))\/(((op (e2) (e0)) = (e2))\/((op (e2) (e0)) = (e3))))) -> ((op (e2) (e2)) = (e0)) -> (~((op (e2) (e0)) = (e1))) -> (~((op (e2) (e0)) = (op (e2) (e3)))) -> ((op (e2) (e3)) = (e2)) -> ((op (e2) (e2)) = (e3)) -> (~((op (e2) (e0)) = (op (e2) (e2)))) -> False). % 18.87/19.05 do 0 intro. intros zenon_H259 zenon_H2c zenon_H1db zenon_H5b zenon_H11d zenon_Haa zenon_H52. % 18.87/19.05 apply (zenon_or_s _ _ zenon_H259); [ zenon_intro zenon_H34 | zenon_intro zenon_H25a ]. % 18.87/19.05 apply (zenon_L11_); trivial. % 18.87/19.05 apply (zenon_or_s _ _ zenon_H25a); [ zenon_intro zenon_Hed | zenon_intro zenon_H25b ]. % 18.87/19.05 exact (zenon_H1db zenon_Hed). % 18.87/19.05 apply (zenon_or_s _ _ zenon_H25b); [ zenon_intro zenon_Hee | zenon_intro zenon_H3b ]. % 18.87/19.05 apply (zenon_L73_); trivial. % 18.87/19.05 apply (zenon_L168_); trivial. % 18.87/19.05 (* end of lemma zenon_L932_ *) % 18.87/19.05 assert (zenon_L933_ : (((op (e2) (e0)) = (e2))\/(((op (e2) (e1)) = (e2))\/(((op (e2) (e2)) = (e2))\/((op (e2) (e3)) = (e2))))) -> (~((op (e3) (e1)) = (op (e3) (e3)))) -> (~((op (e2) (e1)) = (op (e2) (e3)))) -> ((op (e1) (e0)) = (e2)) -> (~((op (e1) (e0)) = (op (e1) (e3)))) -> (~((e2) = (e3))) -> (((op (e0) (e3)) = (e2))\/(((op (e1) (e3)) = (e2))\/(((op (e2) (e3)) = (e2))\/((op (e3) (e3)) = (e2))))) -> (((op (e1) (e0)) = (e1))\/(((op (e1) (e1)) = (e1))\/(((op (e1) (e2)) = (e1))\/((op (e1) (e3)) = (e1))))) -> (~((op (e1) (e0)) = (e1))) -> (~((op (e1) (e1)) = (e1))) -> (~((op (e1) (e2)) = (e1))) -> (((op (e0) (e2)) = (e0))\/(((op (e1) (e2)) = (e0))\/(((op (e2) (e2)) = (e0))\/((op (e3) (e2)) = (e0))))) -> (~((e0) = (e2))) -> (~((op (e2) (e2)) = (op (e3) (e2)))) -> (((op (e2) (e2)) = (e0))\/(((op (e2) (e2)) = (e1))\/(((op (e2) (e2)) = (e2))\/((op (e2) (e2)) = (e3))))) -> (~((op (e1) (e2)) = (op (e1) (e3)))) -> (~((op (e0) (e2)) = (e1))) -> (((op (e0) (e2)) = (e1))\/(((op (e1) (e2)) = (e1))\/(((op (e2) (e2)) = (e1))\/((op (e3) (e2)) = (e1))))) -> (((op (e3) (e0)) = (e1))\/(((op (e3) (e1)) = (e1))\/(((op (e3) (e2)) = (e1))\/((op (e3) (e3)) = (e1))))) -> (~((op (e3) (e0)) = (e1))) -> (~((op (e3) (e1)) = (e1))) -> (~((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 (e1) (e3)) = (op (e3) (e3)))) -> (~((op (e0) (e1)) = (op (e1) (e1)))) -> ((op (e1) (e1)) = (e3)) -> (((op (e0) (e0)) = (e3))\/(((op (e0) (e1)) = (e3))\/(((op (e0) (e2)) = (e3))\/((op (e0) (e3)) = (e3))))) -> (~((op (e2) (e2)) = (e2))) -> (((op (e2) (e0)) = (e3))\/(((op (e2) (e1)) = (e3))\/(((op (e2) (e2)) = (e3))\/((op (e2) (e3)) = (e3))))) -> (~((e1) = (e2))) -> ((op (e1) (e3)) = (e1)) -> (~((op (e0) (e2)) = (op (e1) (e2)))) -> ((op (e0) (e2)) = (e2)) -> (~((op (e1) (e1)) = (op (e3) (e1)))) -> ((op (e3) (e1)) = (e2)) -> ((op (e0) (e0)) = (e1)) -> (((op (e1) (e0)) = (e2))\/(((op (e1) (e1)) = (e2))\/(((op (e1) (e2)) = (e2))\/((op (e1) (e3)) = (e2))))) -> (~((e1) = (e3))) -> ((op (e2) (e1)) = (e1)) -> (~((op (e2) (e0)) = (op (e2) (e2)))) -> (~((op (e2) (e0)) = (op (e2) (e3)))) -> (~((op (e2) (e0)) = (e1))) -> ((op (e2) (e2)) = (e0)) -> (((op (e2) (e0)) = (e0))\/(((op (e2) (e0)) = (e1))\/(((op (e2) (e0)) = (e2))\/((op (e2) (e0)) = (e3))))) -> (~((op (e0) (e3)) = (op (e2) (e3)))) -> ((op (e0) (e3)) = (e3)) -> False). % 18.87/19.05 do 0 intro. intros zenon_H1d5 zenon_H130 zenon_H1c7 zenon_H86 zenon_Hd8 zenon_H12b zenon_H145 zenon_H128 zenon_H1ef zenon_H10a zenon_H24d zenon_H6a zenon_H149 zenon_H18f zenon_H1c4 zenon_H124 zenon_H20d zenon_H139 zenon_He8 zenon_Had zenon_H250 zenon_H102 zenon_H62 zenon_H101 zenon_Hd5 zenon_H10e zenon_H13f zenon_H168 zenon_H173 zenon_He7 zenon_H7c zenon_Hd6 zenon_H195 zenon_H150 zenon_H160 zenon_H14d zenon_H7a zenon_H18c zenon_H95 zenon_Ha5 zenon_H52 zenon_H5b zenon_H1db zenon_H2c zenon_H259 zenon_He2 zenon_He3. % 18.87/19.05 apply (zenon_or_s _ _ zenon_H1d5); [ zenon_intro zenon_Hee | zenon_intro zenon_H1d6 ]. % 18.87/19.05 apply (zenon_L103_); trivial. % 18.87/19.05 apply (zenon_or_s _ _ zenon_H1d6); [ zenon_intro zenon_H1ca | zenon_intro zenon_H1d7 ]. % 18.87/19.05 apply (zenon_L931_); trivial. % 18.87/19.05 apply (zenon_or_s _ _ zenon_H1d7); [ zenon_intro zenon_H176 | zenon_intro zenon_H11d ]. % 18.87/19.05 exact (zenon_H173 zenon_H176). % 18.87/19.05 apply (zenon_or_s _ _ zenon_He7); [ zenon_intro zenon_H3b | zenon_intro zenon_He9 ]. % 18.87/19.05 apply (zenon_L165_); trivial. % 18.87/19.05 apply (zenon_or_s _ _ zenon_He9); [ zenon_intro zenon_Ha6 | zenon_intro zenon_Hea ]. % 18.87/19.05 apply (zenon_L39_); trivial. % 18.87/19.05 apply (zenon_or_s _ _ zenon_Hea); [ zenon_intro zenon_Haa | zenon_intro zenon_Hdd ]. % 18.87/19.05 apply (zenon_L932_); trivial. % 18.87/19.05 apply (zenon_L54_); trivial. % 18.87/19.05 (* end of lemma zenon_L933_ *) % 18.87/19.05 assert (zenon_L934_ : (((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 (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) (e3)) = (e3))) -> (~((op (e3) (e1)) = (e1))) -> (~((op (e3) (e0)) = (e1))) -> (((op (e3) (e0)) = (e1))\/(((op (e3) (e1)) = (e1))\/(((op (e3) (e2)) = (e1))\/((op (e3) (e3)) = (e1))))) -> (((op (e0) (e2)) = (e1))\/(((op (e1) (e2)) = (e1))\/(((op (e2) (e2)) = (e1))\/((op (e3) (e2)) = (e1))))) -> (~((op (e0) (e2)) = (e1))) -> (~((op (e1) (e2)) = (op (e1) (e3)))) -> (((op (e2) (e2)) = (e0))\/(((op (e2) (e2)) = (e1))\/(((op (e2) (e2)) = (e2))\/((op (e2) (e2)) = (e3))))) -> (~((op (e2) (e2)) = (op (e3) (e2)))) -> (~((op (e2) (e2)) = (e2))) -> ((op (e0) (e2)) = (e2)) -> (~((e0) = (e2))) -> (((op (e0) (e2)) = (e0))\/(((op (e1) (e2)) = (e0))\/(((op (e2) (e2)) = (e0))\/((op (e3) (e2)) = (e0))))) -> (((op (e1) (e0)) = (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)) = (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)) -> ((op (e3) (e1)) = (e2)) -> (~((op (e3) (e1)) = (op (e3) (e3)))) -> False). % 18.87/19.05 do 0 intro. intros zenon_H168 zenon_H95 zenon_H7a zenon_H9a zenon_H49 zenon_Hd5 zenon_H101 zenon_H62 zenon_H102 zenon_H250 zenon_Had zenon_He8 zenon_H139 zenon_H20d zenon_H124 zenon_H1c4 zenon_H18f zenon_H173 zenon_H150 zenon_H149 zenon_H6a zenon_H128 zenon_H1ef zenon_H10a zenon_H24d zenon_H145 zenon_H12b zenon_H7c zenon_H5b zenon_Hee zenon_H14d zenon_H130. % 18.87/19.05 apply (zenon_or_s _ _ zenon_H168); [ zenon_intro zenon_H3a | zenon_intro zenon_H169 ]. % 18.87/19.05 apply (zenon_L35_); trivial. % 18.87/19.05 apply (zenon_or_s _ _ zenon_H169); [ zenon_intro zenon_H99 | zenon_intro zenon_H16a ]. % 18.87/19.05 apply (zenon_L36_); trivial. % 18.87/19.05 apply (zenon_or_s _ _ zenon_H16a); [ zenon_intro zenon_Ha9 | zenon_intro zenon_He3 ]. % 18.87/19.05 apply (zenon_L930_); trivial. % 18.87/19.05 apply (zenon_L927_); trivial. % 18.87/19.05 (* end of lemma zenon_L934_ *) % 18.87/19.05 assert (zenon_L935_ : (((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)) -> (~((op (e0) (e1)) = (op (e1) (e1)))) -> ((op (e3) (e0)) = (e0)) -> (~((op (e3) (e0)) = (op (e3) (e2)))) -> (~((op (e2) (e2)) = (op (e2) (e3)))) -> ((op (e1) (e1)) = (e0)) -> (~((op (e1) (e1)) = (op (e1) (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) (e3)) = (e0))\/(((op (e1) (e3)) = (e0))\/(((op (e2) (e3)) = (e0))\/((op (e3) (e3)) = (e0))))) -> (~((e0) = (e2))) -> ((op (e2) (e1)) = (e1)) -> (~((op (e2) (e1)) = (op (e3) (e1)))) -> (~((e0) = (e1))) -> (((op (e3) (e0)) = (e1))\/(((op (e3) (e1)) = (e1))\/(((op (e3) (e2)) = (e1))\/((op (e3) (e3)) = (e1))))) -> (~((op (e3) (e0)) = (op (e3) (e3)))) -> (~((op (e0) (e1)) = (op (e2) (e1)))) -> (~((op (e2) (e0)) = (op (e2) (e2)))) -> (~((op (e0) (e1)) = (op (e0) (e3)))) -> (~((op (e1) (e1)) = (op (e1) (e3)))) -> (~((op (e2) (e0)) = (op (e2) (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) (e3)) = (e2)) -> (~((e2) = (e3))) -> False). % 18.87/19.05 do 0 intro. intros zenon_H168 zenon_H95 zenon_H7a zenon_H13f zenon_H10e zenon_H44 zenon_H6f zenon_H6d zenon_H29 zenon_H4f zenon_H49 zenon_H4a zenon_H6a zenon_H67 zenon_H149 zenon_Ha5 zenon_Haf zenon_Ha1 zenon_He8 zenon_H71 zenon_H17e zenon_H52 zenon_H54 zenon_H57 zenon_H5b zenon_H62 zenon_H2f zenon_Hcd zenon_H12b. % 18.87/19.05 apply (zenon_or_s _ _ zenon_H168); [ zenon_intro zenon_H3a | zenon_intro zenon_H169 ]. % 18.87/19.05 apply (zenon_L35_); trivial. % 18.87/19.05 apply (zenon_or_s _ _ zenon_H169); [ zenon_intro zenon_H99 | zenon_intro zenon_H16a ]. % 18.87/19.05 apply (zenon_L108_); trivial. % 18.87/19.05 apply (zenon_or_s _ _ zenon_H16a); [ zenon_intro zenon_Ha9 | zenon_intro zenon_He3 ]. % 18.87/19.05 apply (zenon_L879_); trivial. % 18.87/19.05 apply (zenon_L81_); trivial. % 18.87/19.05 (* end of lemma zenon_L935_ *) % 18.87/19.05 assert (zenon_L936_ : (((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 (e1) (e1)) = (e3)) -> (~((op (e1) (e2)) = (op (e2) (e2)))) -> (((op (e0) (e2)) = (e2))\/(((op (e1) (e2)) = (e2))\/(((op (e2) (e2)) = (e2))\/((op (e3) (e2)) = (e2))))) -> (~((op (e2) (e2)) = (op (e3) (e2)))) -> (~((op (e0) (e2)) = (op (e3) (e2)))) -> (~((op (e1) (e2)) = (op (e3) (e2)))) -> (((op (e3) (e2)) = (e0))\/(((op (e3) (e2)) = (e1))\/(((op (e3) (e2)) = (e2))\/((op (e3) (e2)) = (e3))))) -> (~((op (e2) (e2)) = (e1))) -> (~((op (e2) (e2)) = (op (e2) (e3)))) -> (((op (e2) (e2)) = (e0))\/(((op (e2) (e2)) = (e1))\/(((op (e2) (e2)) = (e2))\/((op (e2) (e2)) = (e3))))) -> (~((e0) = (e2))) -> ((op (e1) (e2)) = (e0)) -> (~((op (e2) (e2)) = (e2))) -> (~((op (e3) (e1)) = (op (e3) (e2)))) -> ((op (e3) (e1)) = (e2)) -> False). % 18.87/19.05 do 0 intro. intros zenon_H2f zenon_H17b zenon_H44 zenon_H13f zenon_H2b zenon_H172 zenon_H18f zenon_H14f zenon_H115 zenon_H191 zenon_H198 zenon_H6d zenon_H1c4 zenon_H149 zenon_H2a zenon_H173 zenon_H1a4 zenon_H14d. % 18.87/19.05 apply (zenon_or_s _ _ zenon_H2f); [ zenon_intro zenon_H34 | zenon_intro zenon_H33 ]. % 18.87/19.05 apply (zenon_L127_); trivial. % 18.87/19.05 apply (zenon_or_s _ _ zenon_H33); [ zenon_intro zenon_H36 | zenon_intro zenon_H35 ]. % 18.87/19.05 apply (zenon_L514_); trivial. % 18.87/19.05 apply (zenon_or_s _ _ zenon_H35); [ zenon_intro zenon_H2c | zenon_intro zenon_H37 ]. % 18.87/19.05 apply (zenon_L3_); trivial. % 18.87/19.05 apply (zenon_or_s _ _ zenon_H172); [ zenon_intro zenon_H150 | zenon_intro zenon_H174 ]. % 18.87/19.05 apply (zenon_L746_); trivial. % 18.87/19.05 apply (zenon_or_s _ _ zenon_H174); [ zenon_intro zenon_H113 | zenon_intro zenon_H175 ]. % 18.87/19.05 apply (zenon_L542_); trivial. % 18.87/19.05 apply (zenon_or_s _ _ zenon_H175); [ zenon_intro zenon_H176 | zenon_intro zenon_H151 ]. % 18.87/19.05 exact (zenon_H173 zenon_H176). % 18.87/19.05 apply (zenon_L400_); trivial. % 18.87/19.05 (* end of lemma zenon_L936_ *) % 18.87/19.05 assert (zenon_L937_ : (~((op (e1) (e3)) = (op (e2) (e3)))) -> (((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)) = (op (e3) (e1)))) -> ((op (e2) (e1)) = (e1)) -> (~((op (e0) (e1)) = (op (e2) (e1)))) -> ((op (e0) (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 (e1) (e2)) = (op (e2) (e2)))) -> (((op (e0) (e2)) = (e2))\/(((op (e1) (e2)) = (e2))\/(((op (e2) (e2)) = (e2))\/((op (e3) (e2)) = (e2))))) -> (~((op (e2) (e2)) = (op (e3) (e2)))) -> (~((op (e0) (e2)) = (op (e3) (e2)))) -> (~((op (e1) (e2)) = (op (e3) (e2)))) -> (((op (e3) (e2)) = (e0))\/(((op (e3) (e2)) = (e1))\/(((op (e3) (e2)) = (e2))\/((op (e3) (e2)) = (e3))))) -> (~((op (e2) (e2)) = (e1))) -> (~((op (e2) (e2)) = (op (e2) (e3)))) -> (((op (e2) (e2)) = (e0))\/(((op (e2) (e2)) = (e1))\/(((op (e2) (e2)) = (e2))\/((op (e2) (e2)) = (e3))))) -> (~((e0) = (e2))) -> (~((op (e2) (e2)) = (e2))) -> (~((op (e3) (e1)) = (op (e3) (e2)))) -> ((op (e3) (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 (e0) (e1)) = (op (e1) (e1)))) -> (~((op (e3) (e0)) = (op (e3) (e2)))) -> (~((op (e1) (e1)) = (op (e1) (e2)))) -> (~((op (e0) (e1)) = (op (e0) (e2)))) -> (((op (e0) (e2)) = (e0))\/(((op (e1) (e2)) = (e0))\/(((op (e2) (e2)) = (e0))\/((op (e3) (e2)) = (e0))))) -> (((op (e0) (e3)) = (e0))\/(((op (e1) (e3)) = (e0))\/(((op (e2) (e3)) = (e0))\/((op (e3) (e3)) = (e0))))) -> (~((op (e3) (e0)) = (op (e3) (e3)))) -> (~((op (e2) (e0)) = (op (e2) (e2)))) -> (~((op (e0) (e1)) = (op (e0) (e3)))) -> (~((op (e1) (e1)) = (op (e1) (e3)))) -> (~((op (e2) (e0)) = (op (e2) (e3)))) -> (~((op (e3) (e2)) = (op (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 (e0) (e3)) = (e2)) -> (~((e2) = (e3))) -> False). % 18.87/19.05 do 0 intro. intros zenon_Hdb zenon_He8 zenon_Ha1 zenon_H44 zenon_Haf zenon_Ha5 zenon_H17e zenon_H49 zenon_H17b zenon_H2f zenon_H13f zenon_H2b zenon_H172 zenon_H18f zenon_H14f zenon_H115 zenon_H191 zenon_H198 zenon_H6d zenon_H1c4 zenon_H149 zenon_H173 zenon_H1a4 zenon_H14d zenon_H168 zenon_H95 zenon_H7a zenon_H10e zenon_H6f zenon_H4f zenon_H4a zenon_H6a zenon_H67 zenon_H71 zenon_H52 zenon_H54 zenon_H57 zenon_H5b zenon_H62 zenon_H1fa zenon_H22 zenon_Hcd zenon_H12b. % 18.87/19.05 apply (zenon_or_s _ _ zenon_H168); [ zenon_intro zenon_H3a | zenon_intro zenon_H169 ]. % 18.87/19.05 apply (zenon_L35_); trivial. % 18.87/19.05 apply (zenon_or_s _ _ zenon_H169); [ zenon_intro zenon_H99 | zenon_intro zenon_H16a ]. % 18.87/19.05 apply (zenon_L108_); trivial. % 18.87/19.05 apply (zenon_or_s _ _ zenon_H16a); [ zenon_intro zenon_Ha9 | zenon_intro zenon_He3 ]. % 18.87/19.05 apply (zenon_or_s _ _ zenon_H22); [ zenon_intro zenon_H27 | zenon_intro zenon_H26 ]. % 18.87/19.05 apply (zenon_L312_); trivial. % 18.87/19.05 apply (zenon_or_s _ _ zenon_H26); [ zenon_intro zenon_H29 | zenon_intro zenon_H28 ]. % 18.87/19.05 apply (zenon_L935_); trivial. % 18.87/19.05 apply (zenon_or_s _ _ zenon_H28); [ zenon_intro zenon_H2a | zenon_intro zenon_H1f ]. % 18.87/19.05 apply (zenon_L936_); trivial. % 18.87/19.05 apply (zenon_L131_); trivial. % 18.87/19.05 apply (zenon_L81_); trivial. % 18.87/19.05 (* end of lemma zenon_L937_ *) % 18.87/19.05 assert (zenon_L938_ : (((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) (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 (e2) (e2)) = (e2))) -> (~((op (e2) (e2)) = (op (e3) (e2)))) -> ((op (e0) (e2)) = (e3)) -> (((op (e2) (e2)) = (e0))\/(((op (e2) (e2)) = (e1))\/(((op (e2) (e2)) = (e2))\/((op (e2) (e2)) = (e3))))) -> (~((op (e1) (e2)) = (op (e1) (e3)))) -> (~((op (e0) (e2)) = (e1))) -> (((op (e0) (e2)) = (e1))\/(((op (e1) (e2)) = (e1))\/(((op (e2) (e2)) = (e1))\/((op (e3) (e2)) = (e1))))) -> ((op (e2) (e0)) = (e0)) -> (~((op (e2) (e0)) = (op (e2) (e2)))) -> (~((op (e3) (e1)) = (op (e3) (e2)))) -> ((op (e3) (e1)) = (e0)) -> False). % 18.87/19.05 do 0 intro. intros zenon_H128 zenon_H1ef zenon_H10a zenon_H24d zenon_H6a zenon_H4a zenon_H49 zenon_H173 zenon_H18f zenon_Ha9 zenon_H1c4 zenon_H124 zenon_H20d zenon_H139 zenon_H34 zenon_H52 zenon_H1a4 zenon_H1b1. % 18.87/19.05 apply (zenon_or_s _ _ zenon_H128); [ zenon_intro zenon_H9d | zenon_intro zenon_H129 ]. % 18.87/19.05 exact (zenon_H1ef zenon_H9d). % 18.87/19.05 apply (zenon_or_s _ _ zenon_H129); [ zenon_intro zenon_H10d | zenon_intro zenon_H12a ]. % 18.87/19.05 exact (zenon_H10a zenon_H10d). % 18.87/19.05 apply (zenon_or_s _ _ zenon_H12a); [ zenon_intro zenon_Hf0 | zenon_intro zenon_Hd6 ]. % 18.87/19.05 exact (zenon_H24d zenon_Hf0). % 18.87/19.05 apply (zenon_L816_); trivial. % 18.87/19.05 (* end of lemma zenon_L938_ *) % 18.87/19.05 assert (zenon_L939_ : (((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) (e1)) = (e2)) -> (~((op (e2) (e0)) = (op (e2) (e1)))) -> (~((op (e3) (e0)) = (op (e3) (e1)))) -> ((op (e3) (e1)) = (e2)) -> False). % 18.87/19.05 do 0 intro. intros zenon_H1fe zenon_H7c zenon_H7a zenon_H149 zenon_H27 zenon_H1ca zenon_H1f0 zenon_H1cf zenon_H14d. % 18.87/19.05 apply (zenon_or_s _ _ zenon_H1fe); [ zenon_intro zenon_H7b | zenon_intro zenon_H1ff ]. % 18.87/19.05 apply (zenon_L26_); trivial. % 18.87/19.05 apply (zenon_or_s _ _ zenon_H1ff); [ zenon_intro zenon_H86 | zenon_intro zenon_H200 ]. % 18.87/19.05 apply (zenon_L257_); trivial. % 18.87/19.05 apply (zenon_or_s _ _ zenon_H200); [ zenon_intro zenon_Hee | zenon_intro zenon_H148 ]. % 18.87/19.05 apply (zenon_L277_); trivial. % 18.87/19.05 apply (zenon_L436_); trivial. % 18.87/19.05 (* end of lemma zenon_L939_ *) % 18.87/19.05 assert (zenon_L940_ : (((op (e0) (e0)) = (e1))\/(((op (e0) (e1)) = (e1))\/(((op (e0) (e2)) = (e1))\/((op (e0) (e3)) = (e1))))) -> ((op (e3) (e1)) = (e2)) -> (~((op (e3) (e0)) = (op (e3) (e1)))) -> (~((op (e2) (e0)) = (op (e2) (e1)))) -> ((op (e2) (e1)) = (e2)) -> ((op (e1) (e0)) = (e0)) -> (~((e0) = (e2))) -> (~((e1) = (e2))) -> (((op (e0) (e0)) = (e2))\/(((op (e1) (e0)) = (e2))\/(((op (e2) (e0)) = (e2))\/((op (e3) (e0)) = (e2))))) -> (~((op (e0) (e1)) = (e1))) -> (~((op (e0) (e2)) = (e1))) -> (~((op (e0) (e3)) = (e1))) -> False). % 18.87/19.05 do 0 intro. intros zenon_H22d zenon_H14d zenon_H1cf zenon_H1f0 zenon_H1ca zenon_H27 zenon_H149 zenon_H7c zenon_H1fe zenon_Ha4 zenon_H20d zenon_H231. % 18.87/19.05 apply (zenon_or_s _ _ zenon_H22d); [ zenon_intro zenon_H7a | zenon_intro zenon_H22e ]. % 18.87/19.05 apply (zenon_L939_); trivial. % 18.87/19.05 apply (zenon_or_s _ _ zenon_H22e); [ zenon_intro zenon_Ha0 | zenon_intro zenon_H22f ]. % 18.87/19.05 exact (zenon_Ha4 zenon_Ha0). % 18.87/19.05 apply (zenon_or_s _ _ zenon_H22f); [ zenon_intro zenon_H122 | zenon_intro zenon_Hc3 ]. % 18.87/19.05 exact (zenon_H20d zenon_H122). % 18.87/19.05 exact (zenon_H231 zenon_Hc3). % 18.87/19.05 (* end of lemma zenon_L940_ *) % 18.87/19.05 assert (zenon_L941_ : (((op (e2) (e0)) = (e0))\/(((op (e2) (e1)) = (e0))\/(((op (e2) (e2)) = (e0))\/((op (e2) (e3)) = (e0))))) -> (~((op (e2) (e0)) = (op (e2) (e3)))) -> (((op (e0) (e3)) = (e1))\/(((op (e1) (e3)) = (e1))\/(((op (e2) (e3)) = (e1))\/((op (e3) (e3)) = (e1))))) -> (~((op (e0) (e3)) = (e1))) -> (~((e1) = (e2))) -> (~((e2) = (e3))) -> (~((op (e2) (e3)) = (e1))) -> (((op (e0) (e3)) = (e2))\/(((op (e1) (e3)) = (e2))\/(((op (e2) (e3)) = (e2))\/((op (e3) (e3)) = (e2))))) -> (~((op (e0) (e3)) = (op (e2) (e3)))) -> (~((op (e2) (e3)) = (op (e3) (e3)))) -> (((op (e2) (e3)) = (e0))\/(((op (e2) (e3)) = (e1))\/(((op (e2) (e3)) = (e2))\/((op (e2) (e3)) = (e3))))) -> (~((op (e2) (e1)) = (op (e2) (e3)))) -> ((op (e2) (e1)) = (e2)) -> ((op (e3) (e0)) = (e2)) -> (~((op (e3) (e0)) = (op (e3) (e3)))) -> (((op (e0) (e0)) = (e3))\/(((op (e1) (e0)) = (e3))\/(((op (e2) (e0)) = (e3))\/((op (e3) (e0)) = (e3))))) -> (~((e1) = (e3))) -> ((op (e0) (e0)) = (e1)) -> ((op (e1) (e1)) = (e2)) -> (~((op (e1) (e1)) = (op (e1) (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 (e0) (e1)) = (op (e0) (e2)))) -> (~((op (e2) (e2)) = (e2))) -> (~((op (e2) (e2)) = (op (e3) (e2)))) -> (((op (e2) (e2)) = (e0))\/(((op (e2) (e2)) = (e1))\/(((op (e2) (e2)) = (e2))\/((op (e2) (e2)) = (e3))))) -> (~((op (e1) (e2)) = (op (e1) (e3)))) -> (~((op (e0) (e2)) = (e1))) -> (((op (e0) (e2)) = (e1))\/(((op (e1) (e2)) = (e1))\/(((op (e2) (e2)) = (e1))\/((op (e3) (e2)) = (e1))))) -> (~((op (e2) (e0)) = (op (e2) (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) (e0)) = (e0))) -> (~((op (e1) (e0)) = (op (e1) (e1)))) -> (~((op (e3) (e2)) = (op (e3) (e3)))) -> (~((op (e3) (e0)) = (op (e3) (e2)))) -> (~((op (e1) (e1)) = (op (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 (e0) (e1)) = (op (e1) (e1)))) -> ((op (e1) (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 (e3) (e1)) = (op (e3) (e3)))) -> (~((op (e1) (e0)) = (op (e1) (e3)))) -> ((op (e0) (e1)) = (e0)) -> (~((op (e0) (e1)) = (op (e0) (e3)))) -> (((op (e0) (e3)) = (e0))\/(((op (e1) (e3)) = (e0))\/(((op (e2) (e3)) = (e0))\/((op (e3) (e3)) = (e0))))) -> (((op (e0) (e2)) = (e0))\/(((op (e1) (e2)) = (e0))\/(((op (e2) (e2)) = (e0))\/((op (e3) (e2)) = (e0))))) -> (~((e0) = (e2))) -> ((op (e0) (e2)) = (e2)) -> ((op (e1) (e0)) = (e0)) -> (~((op (e1) (e0)) = (op (e1) (e2)))) -> (~((op (e2) (e2)) = (op (e2) (e3)))) -> (~((op (e3) (e1)) = (op (e3) (e2)))) -> ((op (e3) (e1)) = (e0)) -> False). % 18.87/19.05 do 0 intro. intros zenon_H2f zenon_H5b zenon_H133 zenon_H231 zenon_H7c zenon_H12b zenon_H255 zenon_H145 zenon_He2 zenon_Hf3 zenon_H11f zenon_H1c7 zenon_H1ca zenon_H148 zenon_H71 zenon_H1e0 zenon_H95 zenon_H7a zenon_H110 zenon_H57 zenon_H128 zenon_H1ef zenon_H10a zenon_H4a zenon_H173 zenon_H18f zenon_H1c4 zenon_H124 zenon_H20d zenon_H139 zenon_H52 zenon_H2b zenon_H3e zenon_H3f zenon_H45 zenon_H62 zenon_H6f zenon_H4f zenon_H201 zenon_H22 zenon_H10e zenon_H13f zenon_H168 zenon_H17e zenon_H130 zenon_Hd8 zenon_H49 zenon_H54 zenon_H67 zenon_H6a zenon_H149 zenon_H150 zenon_H27 zenon_H24a zenon_H6d zenon_H1a4 zenon_H1b1. % 18.87/19.05 apply (zenon_or_s _ _ zenon_H2f); [ zenon_intro zenon_H34 | zenon_intro zenon_H33 ]. % 18.87/19.05 apply (zenon_L895_); trivial. % 18.87/19.05 apply (zenon_or_s _ _ zenon_H33); [ zenon_intro zenon_H36 | zenon_intro zenon_H35 ]. % 18.87/19.05 apply (zenon_L128_); trivial. % 18.87/19.05 apply (zenon_or_s _ _ zenon_H35); [ zenon_intro zenon_H2c | zenon_intro zenon_H37 ]. % 18.87/19.05 apply (zenon_L259_); trivial. % 18.87/19.05 apply (zenon_L680_); trivial. % 18.87/19.05 (* end of lemma zenon_L941_ *) % 18.87/19.05 assert (zenon_L942_ : (~((op (e1) (e2)) = (e1))) -> (((op (e1) (e0)) = (e2))\/(((op (e1) (e1)) = (e2))\/(((op (e1) (e2)) = (e2))\/((op (e1) (e3)) = (e2))))) -> ((op (e2) (e0)) = (e3)) -> ((op (e3) (e1)) = (e0)) -> (~((op (e3) (e1)) = (op (e3) (e2)))) -> (~((op (e2) (e2)) = (op (e2) (e3)))) -> (~((op (e1) (e0)) = (op (e1) (e2)))) -> ((op (e1) (e0)) = (e0)) -> (~((e0) = (e2))) -> (((op (e0) (e2)) = (e0))\/(((op (e1) (e2)) = (e0))\/(((op (e2) (e2)) = (e0))\/((op (e3) (e2)) = (e0))))) -> (((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) (e0)) = (op (e1) (e3)))) -> (~((op (e3) (e1)) = (op (e3) (e3)))) -> (~((op (e0) (e1)) = (op (e2) (e1)))) -> (((op (e0) (e0)) = (e3))\/(((op (e0) (e1)) = (e3))\/(((op (e0) (e2)) = (e3))\/((op (e0) (e3)) = (e3))))) -> ((op (e1) (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 (e1) (e0)) = (op (e2) (e0)))) -> (~((op (e1) (e1)) = (op (e1) (e2)))) -> (~((op (e3) (e0)) = (op (e3) (e2)))) -> (~((op (e3) (e2)) = (op (e3) (e3)))) -> (~((op (e1) (e0)) = (op (e1) (e1)))) -> (~((op (e0) (e0)) = (e0))) -> (((op (e0) (e0)) = (e0))\/(((op (e1) (e0)) = (e0))\/(((op (e2) (e0)) = (e0))\/((op (e3) (e0)) = (e0))))) -> (~((op (e1) (e2)) = (op (e2) (e2)))) -> (~((op (e2) (e0)) = (op (e2) (e2)))) -> (((op (e0) (e2)) = (e1))\/(((op (e1) (e2)) = (e1))\/(((op (e2) (e2)) = (e1))\/((op (e3) (e2)) = (e1))))) -> (~((op (e0) (e2)) = (e1))) -> (~((op (e1) (e2)) = (op (e1) (e3)))) -> (((op (e2) (e2)) = (e0))\/(((op (e2) (e2)) = (e1))\/(((op (e2) (e2)) = (e2))\/((op (e2) (e2)) = (e3))))) -> (~((op (e2) (e2)) = (op (e3) (e2)))) -> (~((op (e2) (e2)) = (e2))) -> (~((op (e0) (e1)) = (op (e0) (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 (e1) (e1)) = (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 (e3) (e0)) = (op (e3) (e3)))) -> ((op (e3) (e0)) = (e2)) -> ((op (e2) (e1)) = (e2)) -> (~((op (e2) (e1)) = (op (e2) (e3)))) -> (((op (e2) (e3)) = (e0))\/(((op (e2) (e3)) = (e1))\/(((op (e2) (e3)) = (e2))\/((op (e2) (e3)) = (e3))))) -> (~((op (e2) (e3)) = (op (e3) (e3)))) -> (~((op (e0) (e3)) = (op (e2) (e3)))) -> (((op (e0) (e3)) = (e2))\/(((op (e1) (e3)) = (e2))\/(((op (e2) (e3)) = (e2))\/((op (e3) (e3)) = (e2))))) -> (~((op (e2) (e3)) = (e1))) -> (~((e2) = (e3))) -> (~((op (e0) (e3)) = (e1))) -> (((op (e0) (e3)) = (e1))\/(((op (e1) (e3)) = (e1))\/(((op (e2) (e3)) = (e1))\/((op (e3) (e3)) = (e1))))) -> (~((op (e2) (e0)) = (op (e2) (e3)))) -> (((op (e2) (e0)) = (e0))\/(((op (e2) (e1)) = (e0))\/(((op (e2) (e2)) = (e0))\/((op (e2) (e3)) = (e0))))) -> ((op (e0) (e2)) = (e2)) -> (~((op (e0) (e2)) = (op (e1) (e2)))) -> (~((e1) = (e2))) -> False). % 18.87/19.05 do 0 intro. intros zenon_H24d zenon_H18c zenon_H3b zenon_H1b1 zenon_H1a4 zenon_H6d zenon_H24a zenon_H27 zenon_H149 zenon_H6a zenon_H67 zenon_H54 zenon_H49 zenon_Hd8 zenon_H130 zenon_H17e zenon_H168 zenon_H13f zenon_H10e zenon_H22 zenon_H201 zenon_H4f zenon_H6f zenon_H62 zenon_H45 zenon_H3f zenon_H3e zenon_H2b zenon_H52 zenon_H139 zenon_H20d zenon_H124 zenon_H1c4 zenon_H18f zenon_H173 zenon_H4a zenon_H10a zenon_H1ef zenon_H128 zenon_H57 zenon_H7a zenon_H95 zenon_H1e0 zenon_H71 zenon_H148 zenon_H1ca zenon_H1c7 zenon_H11f zenon_Hf3 zenon_He2 zenon_H145 zenon_H255 zenon_H12b zenon_H231 zenon_H133 zenon_H5b zenon_H2f zenon_H150 zenon_H195 zenon_H7c. % 18.87/19.05 apply (zenon_or_s _ _ zenon_H128); [ zenon_intro zenon_H9d | zenon_intro zenon_H129 ]. % 18.87/19.05 exact (zenon_H1ef zenon_H9d). % 18.87/19.05 apply (zenon_or_s _ _ zenon_H129); [ zenon_intro zenon_H10d | zenon_intro zenon_H12a ]. % 18.87/19.05 exact (zenon_H10a zenon_H10d). % 18.87/19.05 apply (zenon_or_s _ _ zenon_H12a); [ zenon_intro zenon_Hf0 | zenon_intro zenon_Hd6 ]. % 18.87/19.05 exact (zenon_H24d zenon_Hf0). % 18.87/19.05 apply (zenon_or_s _ _ zenon_H18c); [ zenon_intro zenon_H86 | zenon_intro zenon_H18d ]. % 18.87/19.05 apply (zenon_L33_); trivial. % 18.87/19.05 apply (zenon_or_s _ _ zenon_H18d); [ zenon_intro zenon_H110 | zenon_intro zenon_H18e ]. % 18.87/19.05 apply (zenon_L941_); trivial. % 18.87/19.05 apply (zenon_or_s _ _ zenon_H18e); [ zenon_intro zenon_H113 | zenon_intro zenon_Hd7 ]. % 18.87/19.05 apply (zenon_L153_); trivial. % 18.87/19.05 apply (zenon_L101_); trivial. % 18.87/19.05 (* end of lemma zenon_L942_ *) % 18.87/19.05 assert (zenon_L943_ : (((op (e0) (e0)) = (e0))\/(((op (e1) (e0)) = (e0))\/(((op (e2) (e0)) = (e0))\/((op (e3) (e0)) = (e0))))) -> (~((op (e0) (e0)) = (e0))) -> (~((op (e1) (e0)) = (op (e1) (e1)))) -> (~((op (e3) (e2)) = (op (e3) (e3)))) -> (~((op (e2) (e0)) = (op (e2) (e3)))) -> ((op (e1) (e1)) = (e0)) -> (~((op (e1) (e1)) = (op (e1) (e3)))) -> ((op (e0) (e1)) = (e0)) -> (~((op (e0) (e1)) = (op (e0) (e3)))) -> (((op (e0) (e3)) = (e0))\/(((op (e1) (e3)) = (e0))\/(((op (e2) (e3)) = (e0))\/((op (e3) (e3)) = (e0))))) -> (~((op (e2) (e0)) = (op (e2) (e2)))) -> (~((op (e1) (e1)) = (op (e1) (e2)))) -> (~((op (e0) (e1)) = (op (e0) (e2)))) -> (((op (e0) (e2)) = (e0))\/(((op (e1) (e2)) = (e0))\/(((op (e2) (e2)) = (e0))\/((op (e3) (e2)) = (e0))))) -> (~((op (e3) (e0)) = (op (e3) (e1)))) -> ((op (e3) (e1)) = (e0)) -> False). % 18.87/19.05 do 0 intro. intros zenon_H3e zenon_H3f zenon_H45 zenon_H62 zenon_H5b zenon_H29 zenon_H57 zenon_H49 zenon_H54 zenon_H67 zenon_H52 zenon_H4f zenon_H4a zenon_H6a zenon_H1cf zenon_H1b1. % 18.87/19.05 apply (zenon_or_s _ _ zenon_H3e); [ zenon_intro zenon_H42 | zenon_intro zenon_H41 ]. % 18.87/19.05 exact (zenon_H3f zenon_H42). % 18.87/19.05 apply (zenon_or_s _ _ zenon_H41); [ zenon_intro zenon_H27 | zenon_intro zenon_H43 ]. % 18.87/19.05 apply (zenon_L8_); trivial. % 18.87/19.05 apply (zenon_or_s _ _ zenon_H43); [ zenon_intro zenon_H34 | zenon_intro zenon_H44 ]. % 18.87/19.05 apply (zenon_L17_); trivial. % 18.87/19.05 apply (zenon_L346_); trivial. % 18.87/19.05 (* end of lemma zenon_L943_ *) % 18.87/19.05 assert (zenon_L944_ : (((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 (e2) (e0)))) -> (~((op (e3) (e2)) = (op (e3) (e3)))) -> (~((op (e1) (e1)) = (op (e1) (e3)))) -> (~((op (e1) (e1)) = (op (e1) (e2)))) -> (((op (e0) (e3)) = (e0))\/(((op (e1) (e3)) = (e0))\/(((op (e2) (e3)) = (e0))\/((op (e3) (e3)) = (e0))))) -> (~((op (e0) (e1)) = (op (e0) (e3)))) -> (~((op (e2) (e0)) = (op (e2) (e3)))) -> (~((op (e3) (e1)) = (op (e3) (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 (e2) (e3)) = (e1))) -> (((op (e0) (e3)) = (e1))\/(((op (e1) (e3)) = (e1))\/(((op (e2) (e3)) = (e1))\/((op (e3) (e3)) = (e1))))) -> (((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 (e2) (e2)) = (e2))) -> (~((op (e2) (e2)) = (op (e3) (e2)))) -> (((op (e2) (e2)) = (e0))\/(((op (e2) (e2)) = (e1))\/(((op (e2) (e2)) = (e2))\/((op (e2) (e2)) = (e3))))) -> (~((op (e1) (e2)) = (op (e1) (e3)))) -> (((op (e0) (e2)) = (e1))\/(((op (e1) (e2)) = (e1))\/(((op (e2) (e2)) = (e1))\/((op (e3) (e2)) = (e1))))) -> ((op (e2) (e0)) = (e0)) -> (~((op (e2) (e0)) = (op (e2) (e2)))) -> (~((op (e3) (e1)) = (op (e3) (e2)))) -> ((op (e3) (e1)) = (e0)) -> (~((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 (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 (e2) (e1)) = (e1)) -> (~((op (e0) (e2)) = (op (e3) (e2)))) -> (~((op (e1) (e2)) = (op (e3) (e2)))) -> (((op (e3) (e2)) = (e0))\/(((op (e3) (e2)) = (e1))\/(((op (e3) (e2)) = (e2))\/((op (e3) (e2)) = (e3))))) -> (((op (e0) (e0)) = (e0))\/(((op (e1) (e0)) = (e0))\/(((op (e2) (e0)) = (e0))\/((op (e3) (e0)) = (e0))))) -> (~((op (e0) (e0)) = (e0))) -> (~((op (e1) (e0)) = (op (e1) (e1)))) -> (~((op (e3) (e0)) = (op (e3) (e1)))) -> (~((e0) = (e2))) -> (~((op (e0) (e1)) = (op (e1) (e1)))) -> ((op (e1) (e1)) = (e3)) -> (~((op (e2) (e0)) = (op (e2) (e1)))) -> (~((op (e1) (e2)) = (e1))) -> (~((op (e3) (e0)) = (op (e3) (e3)))) -> ((op (e2) (e1)) = (e2)) -> (~((op (e2) (e1)) = (op (e2) (e3)))) -> (((op (e2) (e3)) = (e0))\/(((op (e2) (e3)) = (e1))\/(((op (e2) (e3)) = (e2))\/((op (e2) (e3)) = (e3))))) -> (~((op (e2) (e3)) = (op (e3) (e3)))) -> (~((op (e0) (e3)) = (op (e2) (e3)))) -> (((op (e0) (e3)) = (e2))\/(((op (e1) (e3)) = (e2))\/(((op (e2) (e3)) = (e2))\/((op (e3) (e3)) = (e2))))) -> (~((e1) = (e2))) -> (((op (e0) (e0)) = (e2))\/(((op (e0) (e1)) = (e2))\/(((op (e0) (e2)) = (e2))\/((op (e0) (e3)) = (e2))))) -> (~((op (e0) (e1)) = (e1))) -> (~((op (e0) (e2)) = (e1))) -> (~((op (e0) (e3)) = (e1))) -> False). % 18.87/19.05 do 0 intro. intros zenon_H22d zenon_H12b zenon_H22 zenon_H201 zenon_H62 zenon_H57 zenon_H4f zenon_H67 zenon_H54 zenon_H5b zenon_H130 zenon_H128 zenon_H1ef zenon_H10a zenon_H255 zenon_H133 zenon_H6a zenon_H4a zenon_H49 zenon_H173 zenon_H18f zenon_H1c4 zenon_H124 zenon_H139 zenon_H34 zenon_H52 zenon_H1a4 zenon_H1b1 zenon_H9a zenon_H95 zenon_H168 zenon_H1fe zenon_He7 zenon_Ha5 zenon_H14f zenon_H115 zenon_H191 zenon_H3e zenon_H3f zenon_H45 zenon_H1cf zenon_H149 zenon_H10e zenon_H13f zenon_H1f0 zenon_H24d zenon_H71 zenon_H1ca zenon_H1c7 zenon_H11f zenon_Hf3 zenon_He2 zenon_H145 zenon_H7c zenon_H183 zenon_Ha4 zenon_H20d zenon_H231. % 18.87/19.05 apply (zenon_or_s _ _ zenon_H22d); [ zenon_intro zenon_H7a | zenon_intro zenon_H22e ]. % 18.87/19.05 apply (zenon_or_s _ _ zenon_H183); [ zenon_intro zenon_H7b | zenon_intro zenon_H186 ]. % 18.87/19.05 apply (zenon_L26_); trivial. % 18.87/19.05 apply (zenon_or_s _ _ zenon_H186); [ zenon_intro zenon_H10f | zenon_intro zenon_H187 ]. % 18.87/19.05 apply (zenon_L580_); trivial. % 18.87/19.05 apply (zenon_or_s _ _ zenon_H187); [ zenon_intro zenon_H150 | zenon_intro zenon_Hcd ]. % 18.87/19.05 apply (zenon_or_s _ _ zenon_H1fe); [ zenon_intro zenon_H7b | zenon_intro zenon_H1ff ]. % 18.87/19.05 apply (zenon_L26_); trivial. % 18.87/19.05 apply (zenon_or_s _ _ zenon_H1ff); [ zenon_intro zenon_H86 | zenon_intro zenon_H200 ]. % 18.87/19.05 apply (zenon_or_s _ _ zenon_H168); [ zenon_intro zenon_H3a | zenon_intro zenon_H169 ]. % 18.87/19.05 apply (zenon_L35_); trivial. % 18.87/19.05 apply (zenon_or_s _ _ zenon_H169); [ zenon_intro zenon_H99 | zenon_intro zenon_H16a ]. % 18.87/19.05 apply (zenon_L108_); trivial. % 18.87/19.05 apply (zenon_or_s _ _ zenon_H16a); [ zenon_intro zenon_Ha9 | zenon_intro zenon_He3 ]. % 18.87/19.05 apply (zenon_L938_); trivial. % 18.87/19.05 apply (zenon_or_s _ _ zenon_H22); [ zenon_intro zenon_H27 | zenon_intro zenon_H26 ]. % 18.87/19.05 apply (zenon_L257_); trivial. % 18.87/19.05 apply (zenon_or_s _ _ zenon_H26); [ zenon_intro zenon_H29 | zenon_intro zenon_H28 ]. % 18.87/19.05 apply (zenon_L943_); trivial. % 18.87/19.05 apply (zenon_or_s _ _ zenon_H28); [ zenon_intro zenon_H2a | zenon_intro zenon_H1f ]. % 18.87/19.05 apply (zenon_L211_); trivial. % 18.87/19.05 apply (zenon_L919_); trivial. % 18.87/19.05 apply (zenon_or_s _ _ zenon_H200); [ zenon_intro zenon_Hee | zenon_intro zenon_H148 ]. % 18.87/19.05 apply (zenon_L277_); trivial. % 18.87/19.05 apply (zenon_or_s _ _ zenon_H168); [ zenon_intro zenon_H3a | zenon_intro zenon_H169 ]. % 18.87/19.05 apply (zenon_L35_); trivial. % 18.87/19.05 apply (zenon_or_s _ _ zenon_H169); [ zenon_intro zenon_H99 | zenon_intro zenon_H16a ]. % 18.87/19.05 apply (zenon_L36_); trivial. % 18.87/19.05 apply (zenon_or_s _ _ zenon_H16a); [ zenon_intro zenon_Ha9 | zenon_intro zenon_He3 ]. % 18.87/19.05 apply (zenon_L938_); trivial. % 18.87/19.05 apply (zenon_L894_); trivial. % 18.87/19.05 apply (zenon_L887_); trivial. % 18.87/19.05 apply (zenon_or_s _ _ zenon_H22e); [ zenon_intro zenon_Ha0 | zenon_intro zenon_H22f ]. % 18.87/19.05 exact (zenon_Ha4 zenon_Ha0). % 18.87/19.05 apply (zenon_or_s _ _ zenon_H22f); [ zenon_intro zenon_H122 | zenon_intro zenon_Hc3 ]. % 18.87/19.05 exact (zenon_H20d zenon_H122). % 18.87/19.05 exact (zenon_H231 zenon_Hc3). % 18.87/19.05 (* end of lemma zenon_L944_ *) % 18.87/19.05 assert (zenon_L945_ : (((op (e1) (e0)) = (e1))\/(((op (e1) (e1)) = (e1))\/(((op (e1) (e2)) = (e1))\/((op (e1) (e3)) = (e1))))) -> (~((op (e1) (e1)) = (e1))) -> (~((op (e1) (e0)) = (e1))) -> (~((op (e1) (e2)) = (op (e2) (e2)))) -> (((op (e2) (e0)) = (e1))\/(((op (e2) (e1)) = (e1))\/(((op (e2) (e2)) = (e1))\/((op (e2) (e3)) = (e1))))) -> ((~((op (e1) (e2)) = (e1)))\/((op (e1) (e1)) = (e2))) -> ((~((op (e2) (e0)) = (e1)))\/((op (e2) (e1)) = (e0))) -> ((~((op (e1) (e3)) = (e1)))\/((op (e1) (e1)) = (e3))) -> (((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) (e2)))) -> (~((op (e1) (e0)) = (op (e3) (e0)))) -> (((op (e2) (e0)) = (e0))\/(((op (e2) (e0)) = (e1))\/(((op (e2) (e0)) = (e2))\/((op (e2) (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) (e1)) = (op (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 (e0) (e3)) = (e2))\/(((op (e1) (e3)) = (e2))\/(((op (e2) (e3)) = (e2))\/((op (e3) (e3)) = (e2))))) -> (~((op (e3) (e0)) = (op (e3) (e3)))) -> (~((op (e2) (e1)) = (op (e2) (e3)))) -> (((op (e1) (e3)) = (e0))\/(((op (e1) (e3)) = (e1))\/(((op (e1) (e3)) = (e2))\/((op (e1) (e3)) = (e3))))) -> (~((op (e1) (e3)) = (op (e3) (e3)))) -> (((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)) = (e0))\/(((op (e3) (e2)) = (e1))\/(((op (e3) (e2)) = (e2))\/((op (e3) (e2)) = (e3))))) -> (~((op (e3) (e1)) = (op (e3) (e2)))) -> (~((op (e2) (e2)) = (op (e2) (e3)))) -> (((op (e2) (e0)) = (e0))\/(((op (e2) (e1)) = (e0))\/(((op (e2) (e2)) = (e0))\/((op (e2) (e3)) = (e0))))) -> (~((op (e1) (e0)) = (op (e2) (e0)))) -> (~((op (e2) (e1)) = (op (e3) (e1)))) -> (~((op (e1) (e3)) = (op (e2) (e3)))) -> (((op (e0) (e3)) = (e3))\/(((op (e1) (e3)) = (e3))\/(((op (e2) (e3)) = (e3))\/((op (e3) (e3)) = (e3))))) -> ((~((op (e1) (e0)) = (e1)))\/((op (e1) (e1)) = (e0))) -> (((op (e0) (e0)) = (e0))\/(((op (e1) (e0)) = (e0))\/(((op (e2) (e0)) = (e0))\/((op (e3) (e0)) = (e0))))) -> (~((e0) = (e1))) -> (~((op (e1) (e0)) = (op (e1) (e1)))) -> ((~((op (e0) (e3)) = (e1)))\/((op (e0) (e1)) = (e3))) -> (((op (e0) (e3)) = (e1))\/(((op (e1) (e3)) = (e1))\/(((op (e2) (e3)) = (e1))\/((op (e3) (e3)) = (e1))))) -> (((op (e0) (e0)) = (e3))\/(((op (e1) (e0)) = (e3))\/(((op (e2) (e0)) = (e3))\/((op (e3) (e0)) = (e3))))) -> (((op (e1) (e0)) = (e0))\/(((op (e1) (e0)) = (e1))\/(((op (e1) (e0)) = (e2))\/((op (e1) (e0)) = (e3))))) -> ((~((op (e2) (e3)) = (e1)))\/((op (e2) (e1)) = (e3))) -> (~((op (e3) (e0)) = (op (e3) (e1)))) -> (((op (e2) (e3)) = (e0))\/(((op (e2) (e3)) = (e1))\/(((op (e2) (e3)) = (e2))\/((op (e2) (e3)) = (e3))))) -> (((op (e3) (e0)) = (e1))\/(((op (e3) (e1)) = (e1))\/(((op (e3) (e2)) = (e1))\/((op (e3) (e3)) = (e1))))) -> (~((op (e1) (e0)) = (op (e1) (e2)))) -> (((op (e0) (e1)) = (e3))\/(((op (e1) (e1)) = (e3))\/(((op (e2) (e1)) = (e3))\/((op (e3) (e1)) = (e3))))) -> ((~((op (e2) (e1)) = (e1)))\/((op (e2) (e1)) = (e1))) -> (((op (e0) (e2)) = (e0))\/(((op (e1) (e2)) = (e0))\/(((op (e2) (e2)) = (e0))\/((op (e3) (e2)) = (e0))))) -> (~((op (e0) (e1)) = (op (e0) (e3)))) -> (~((op (e1) (e1)) = (op (e1) (e3)))) -> (~((op (e2) (e0)) = (op (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) (e0)) = (op (e2) (e2)))) -> (~((op (e1) (e1)) = (op (e1) (e2)))) -> (~((op (e0) (e1)) = (op (e0) (e2)))) -> (~((op (e1) (e2)) = (op (e1) (e3)))) -> (((op (e2) (e2)) = (e0))\/(((op (e2) (e2)) = (e1))\/(((op (e2) (e2)) = (e2))\/((op (e2) (e2)) = (e3))))) -> (~((op (e2) (e2)) = (e2))) -> (~((op (e2) (e2)) = (op (e3) (e2)))) -> (((op (e2) (e0)) = (e3))\/(((op (e2) (e1)) = (e3))\/(((op (e2) (e2)) = (e3))\/((op (e2) (e3)) = (e3))))) -> (((op (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 (e3) (e3)) = (e0))\/(((op (e3) (e3)) = (e1))\/(((op (e3) (e3)) = (e2))\/((op (e3) (e3)) = (e3))))) -> (~((op (e0) (e2)) = (op (e2) (e2)))) -> (~((op (e1) (e1)) = (op (e2) (e1)))) -> (((op (e1) (e0)) = (e0))\/(((op (e1) (e1)) = (e0))\/(((op (e1) (e2)) = (e0))\/((op (e1) (e3)) = (e0))))) -> ((op (e0) (e1)) = (e0)) -> (~((e0) = (e3))) -> (((op (e0) (e0)) = (e2))\/(((op (e0) (e1)) = (e2))\/(((op (e0) (e2)) = (e2))\/((op (e0) (e3)) = (e2))))) -> (~((op (e0) (e0)) = (op (e0) (e3)))) -> (~((op (e2) (e0)) = (op (e2) (e1)))) -> (((op (e0) (e0)) = (e3))\/(((op (e0) (e1)) = (e3))\/(((op (e0) (e2)) = (e3))\/((op (e0) (e3)) = (e3))))) -> (~((op (e1) (e1)) = (op (e3) (e1)))) -> (~((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))))) -> (~((op (e0) (e1)) = (op (e1) (e1)))) -> (~((e1) = (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)) = (op (e1) (e2)))) -> (~((e2) = (e3))) -> (~((e0) = (e2))) -> ((~((op (e3) (e0)) = (e1)))\/((op (e3) (e1)) = (e0))) -> (((op (e0) (e0)) = (e1))\/(((op (e1) (e0)) = (e1))\/(((op (e2) (e0)) = (e1))\/((op (e3) (e0)) = (e1))))) -> (~((op (e0) (e1)) = (op (e3) (e1)))) -> (~((op (e0) (e1)) = (op (e2) (e1)))) -> ((~((op (e2) (e2)) = (e1)))\/((op (e2) (e1)) = (e2))) -> (~((op (e0) (e0)) = (e0))) -> ((~((op (e3) (e3)) = (e1)))\/((op (e3) (e1)) = (e3))) -> (((op (e0) (e1)) = (e1))\/(((op (e1) (e1)) = (e1))\/(((op (e2) (e1)) = (e1))\/((op (e3) (e1)) = (e1))))) -> (~((op (e0) (e1)) = (e1))) -> ((~((op (e3) (e2)) = (e1)))\/((op (e3) (e1)) = (e2))) -> (~((e1) = (e2))) -> (((op (e0) (e2)) = (e1))\/(((op (e1) (e2)) = (e1))\/(((op (e2) (e2)) = (e1))\/((op (e3) (e2)) = (e1))))) -> (~((op (e0) (e0)) = (op (e0) (e2)))) -> (~((op (e0) (e2)) = (e1))) -> (~((op (e0) (e3)) = (e1))) -> (((op (e0) (e0)) = (e1))\/(((op (e0) (e1)) = (e1))\/(((op (e0) (e2)) = (e1))\/((op (e0) (e3)) = (e1))))) -> ((~((op (e3) (e1)) = (e1)))\/((op (e3) (e1)) = (e1))) -> (((op (e0) (e2)) = (e2))\/(((op (e1) (e2)) = (e2))\/(((op (e2) (e2)) = (e2))\/((op (e3) (e2)) = (e2))))) -> False). % 18.87/19.05 do 0 intro. intros zenon_H128 zenon_H10a zenon_H1ef zenon_H2b zenon_H106 zenon_H256 zenon_H257 zenon_H258 zenon_H1d5 zenon_Hf3 zenon_H6f zenon_H1fa zenon_H259 zenon_H17b zenon_H1ac zenon_H130 zenon_Hd8 zenon_H16f zenon_H145 zenon_H71 zenon_H1c7 zenon_Hdf zenon_Hd5 zenon_H153 zenon_H115 zenon_H191 zenon_H1a4 zenon_H6d zenon_H2f zenon_H201 zenon_Haf zenon_Hdb zenon_H136 zenon_H25d zenon_H3e zenon_Ha1 zenon_H45 zenon_H25c zenon_H133 zenon_H1e0 zenon_H25e zenon_H263 zenon_H1cf zenon_H11f zenon_He8 zenon_H24a zenon_H1a5 zenon_H262 zenon_H6a zenon_H54 zenon_H57 zenon_H5b zenon_H62 zenon_H67 zenon_H52 zenon_H4f zenon_H4a zenon_H124 zenon_H1c4 zenon_H173 zenon_H18f zenon_He7 zenon_He4 zenon_He2 zenon_Hc2 zenon_H1d zenon_H101 zenon_Ha8 zenon_H13e zenon_H22 zenon_H49 zenon_H9a zenon_H183 zenon_H189 zenon_H1f0 zenon_H168 zenon_H160 zenon_H14f zenon_H102 zenon_H165 zenon_H10e zenon_H95 zenon_H1fe zenon_H18c zenon_H195 zenon_H12b zenon_H149 zenon_H254 zenon_H235 zenon_H210 zenon_H17e zenon_H253 zenon_H3f zenon_H264 zenon_H109 zenon_Ha4 zenon_H252 zenon_H7c zenon_H139 zenon_H13c zenon_H20d zenon_H231 zenon_H22d zenon_H261 zenon_H172. % 18.87/19.05 apply (zenon_or_s _ _ zenon_H256); [ zenon_intro zenon_H24d | zenon_intro zenon_H110 ]. % 18.87/19.05 apply (zenon_or_s _ _ zenon_H258); [ zenon_intro zenon_H24e | zenon_intro zenon_H13f ]. % 18.87/19.05 apply (zenon_L713_); trivial. % 18.87/19.05 apply (zenon_or_s _ _ zenon_H257); [ zenon_intro zenon_H1db | zenon_intro zenon_H36 ]. % 18.87/19.05 apply (zenon_or_s _ _ zenon_H262); [ zenon_intro zenon_H24f | zenon_intro zenon_Ha5 ]. % 18.87/19.05 apply (zenon_or_s _ _ zenon_H253); [ zenon_intro zenon_H198 | zenon_intro zenon_H1ca ]. % 18.87/19.05 apply (zenon_or_s _ _ zenon_H261); [ zenon_intro zenon_H250 | zenon_intro zenon_Hae ]. % 18.87/19.05 apply (zenon_L714_); trivial. % 18.87/19.05 apply (zenon_L717_); trivial. % 18.87/19.05 apply (zenon_or_s _ _ zenon_H264); [ zenon_intro zenon_Hc7 | zenon_intro zenon_H161 ]. % 18.87/19.05 apply (zenon_or_s _ _ zenon_H3e); [ zenon_intro zenon_H42 | zenon_intro zenon_H41 ]. % 18.87/19.05 exact (zenon_H3f zenon_H42). % 18.87/19.05 apply (zenon_or_s _ _ zenon_H41); [ zenon_intro zenon_H27 | zenon_intro zenon_H43 ]. % 18.87/19.05 apply (zenon_or_s _ _ zenon_H22d); [ zenon_intro zenon_H7a | zenon_intro zenon_H22e ]. % 18.87/19.05 apply (zenon_or_s _ _ zenon_H183); [ zenon_intro zenon_H7b | zenon_intro zenon_H186 ]. % 18.87/19.05 apply (zenon_L26_); trivial. % 18.87/19.05 apply (zenon_or_s _ _ zenon_H186); [ zenon_intro zenon_H10f | zenon_intro zenon_H187 ]. % 18.87/19.05 apply (zenon_L718_); trivial. % 18.87/19.05 apply (zenon_or_s _ _ zenon_H187); [ zenon_intro zenon_H150 | zenon_intro zenon_Hcd ]. % 18.87/19.05 apply (zenon_L719_); trivial. % 18.87/19.05 apply (zenon_or_s _ _ zenon_H1fe); [ zenon_intro zenon_H7b | zenon_intro zenon_H1ff ]. % 18.87/19.05 apply (zenon_L375_); trivial. % 18.87/19.05 apply (zenon_or_s _ _ zenon_H1ff); [ zenon_intro zenon_H86 | zenon_intro zenon_H200 ]. % 18.87/19.05 apply (zenon_L257_); trivial. % 18.87/19.05 apply (zenon_or_s _ _ zenon_H200); [ zenon_intro zenon_Hee | zenon_intro zenon_H148 ]. % 18.87/19.05 apply (zenon_L277_); trivial. % 18.87/19.05 apply (zenon_L113_); trivial. % 18.87/19.05 apply (zenon_or_s _ _ zenon_H22e); [ zenon_intro zenon_Ha0 | zenon_intro zenon_H22f ]. % 18.87/19.05 exact (zenon_Ha4 zenon_Ha0). % 18.87/19.05 apply (zenon_or_s _ _ zenon_H22f); [ zenon_intro zenon_H122 | zenon_intro zenon_Hc3 ]. % 18.87/19.05 exact (zenon_H20d zenon_H122). % 18.87/19.05 exact (zenon_H231 zenon_Hc3). % 18.87/19.05 apply (zenon_or_s _ _ zenon_H43); [ zenon_intro zenon_H34 | zenon_intro zenon_H44 ]. % 18.87/19.05 apply (zenon_or_s _ _ zenon_H22d); [ zenon_intro zenon_H7a | zenon_intro zenon_H22e ]. % 18.87/19.05 apply (zenon_or_s _ _ zenon_H183); [ zenon_intro zenon_H7b | zenon_intro zenon_H186 ]. % 18.87/19.05 apply (zenon_L26_); trivial. % 18.87/19.05 apply (zenon_or_s _ _ zenon_H186); [ zenon_intro zenon_H10f | zenon_intro zenon_H187 ]. % 18.87/19.05 apply (zenon_L191_); trivial. % 18.87/19.05 apply (zenon_or_s _ _ zenon_H187); [ zenon_intro zenon_H150 | zenon_intro zenon_Hcd ]. % 18.87/19.05 apply (zenon_or_s _ _ zenon_H1fe); [ zenon_intro zenon_H7b | zenon_intro zenon_H1ff ]. % 18.87/19.05 apply (zenon_L26_); trivial. % 18.87/19.05 apply (zenon_or_s _ _ zenon_H1ff); [ zenon_intro zenon_H86 | zenon_intro zenon_H200 ]. % 18.87/19.05 apply (zenon_or_s _ _ zenon_H168); [ zenon_intro zenon_H3a | zenon_intro zenon_H169 ]. % 18.87/19.05 apply (zenon_L35_); trivial. % 18.87/19.06 apply (zenon_or_s _ _ zenon_H169); [ zenon_intro zenon_H99 | zenon_intro zenon_H16a ]. % 18.87/19.06 apply (zenon_L36_); trivial. % 18.87/19.06 apply (zenon_or_s _ _ zenon_H16a); [ zenon_intro zenon_Ha9 | zenon_intro zenon_He3 ]. % 18.87/19.06 apply (zenon_L723_); trivial. % 18.87/19.06 apply (zenon_or_s _ _ zenon_H22); [ zenon_intro zenon_H27 | zenon_intro zenon_H26 ]. % 18.87/19.06 apply (zenon_L257_); trivial. % 18.87/19.06 apply (zenon_or_s _ _ zenon_H26); [ zenon_intro zenon_H29 | zenon_intro zenon_H28 ]. % 18.87/19.06 apply (zenon_L724_); trivial. % 18.87/19.06 apply (zenon_or_s _ _ zenon_H28); [ zenon_intro zenon_H2a | zenon_intro zenon_H1f ]. % 18.87/19.06 apply (zenon_or_s _ _ zenon_H128); [ zenon_intro zenon_H9d | zenon_intro zenon_H129 ]. % 18.87/19.06 exact (zenon_H1ef zenon_H9d). % 18.87/19.06 apply (zenon_or_s _ _ zenon_H129); [ zenon_intro zenon_H10d | zenon_intro zenon_H12a ]. % 18.87/19.06 exact (zenon_H10a zenon_H10d). % 18.87/19.06 apply (zenon_or_s _ _ zenon_H12a); [ zenon_intro zenon_Hf0 | zenon_intro zenon_Hd6 ]. % 18.87/19.06 exact (zenon_H24d zenon_Hf0). % 18.87/19.06 apply (zenon_or_s _ _ zenon_He7); [ zenon_intro zenon_H3b | zenon_intro zenon_He9 ]. % 18.87/19.06 apply (zenon_L918_); trivial. % 18.87/19.06 apply (zenon_or_s _ _ zenon_He9); [ zenon_intro zenon_Ha6 | zenon_intro zenon_Hea ]. % 18.87/19.06 apply (zenon_L95_); trivial. % 18.87/19.06 apply (zenon_or_s _ _ zenon_Hea); [ zenon_intro zenon_Haa | zenon_intro zenon_Hdd ]. % 18.87/19.06 apply (zenon_L181_); trivial. % 18.87/19.06 apply (zenon_L54_); trivial. % 18.87/19.06 apply (zenon_L919_); trivial. % 18.87/19.06 apply (zenon_or_s _ _ zenon_H200); [ zenon_intro zenon_Hee | zenon_intro zenon_H148 ]. % 18.87/19.06 apply (zenon_L204_); trivial. % 18.87/19.06 apply (zenon_or_s _ _ zenon_H1e0); [ zenon_intro zenon_H3a | zenon_intro zenon_H1e1 ]. % 18.87/19.06 apply (zenon_L35_); trivial. % 18.87/19.06 apply (zenon_or_s _ _ zenon_H1e1); [ zenon_intro zenon_H9e | zenon_intro zenon_H1e2 ]. % 18.87/19.06 apply (zenon_L107_); trivial. % 18.87/19.06 apply (zenon_or_s _ _ zenon_H1e2); [ zenon_intro zenon_H3b | zenon_intro zenon_H15e ]. % 18.87/19.06 apply (zenon_L920_); trivial. % 18.87/19.06 apply (zenon_L109_); trivial. % 18.87/19.06 apply (zenon_or_s _ _ zenon_H1fe); [ zenon_intro zenon_H7b | zenon_intro zenon_H1ff ]. % 18.87/19.06 apply (zenon_L375_); trivial. % 18.87/19.06 apply (zenon_or_s _ _ zenon_H1ff); [ zenon_intro zenon_H86 | zenon_intro zenon_H200 ]. % 18.87/19.06 apply (zenon_or_s _ _ zenon_H168); [ zenon_intro zenon_H3a | zenon_intro zenon_H169 ]. % 18.87/19.06 apply (zenon_L35_); trivial. % 18.87/19.06 apply (zenon_or_s _ _ zenon_H169); [ zenon_intro zenon_H99 | zenon_intro zenon_H16a ]. % 18.87/19.06 apply (zenon_L108_); trivial. % 18.87/19.06 apply (zenon_or_s _ _ zenon_H16a); [ zenon_intro zenon_Ha9 | zenon_intro zenon_He3 ]. % 18.87/19.06 apply (zenon_L723_); trivial. % 18.87/19.06 apply (zenon_L81_); trivial. % 18.87/19.06 apply (zenon_or_s _ _ zenon_H200); [ zenon_intro zenon_Hee | zenon_intro zenon_H148 ]. % 18.87/19.06 apply (zenon_L277_); trivial. % 18.87/19.06 apply (zenon_or_s _ _ zenon_H168); [ zenon_intro zenon_H3a | zenon_intro zenon_H169 ]. % 18.87/19.06 apply (zenon_L35_); trivial. % 18.87/19.06 apply (zenon_or_s _ _ zenon_H169); [ zenon_intro zenon_H99 | zenon_intro zenon_H16a ]. % 18.87/19.06 apply (zenon_L36_); trivial. % 18.87/19.06 apply (zenon_or_s _ _ zenon_H16a); [ zenon_intro zenon_Ha9 | zenon_intro zenon_He3 ]. % 18.87/19.06 apply (zenon_or_s _ _ zenon_H1e0); [ zenon_intro zenon_H3a | zenon_intro zenon_H1e1 ]. % 18.87/19.06 apply (zenon_L35_); trivial. % 18.87/19.06 apply (zenon_or_s _ _ zenon_H1e1); [ zenon_intro zenon_H9e | zenon_intro zenon_H1e2 ]. % 18.87/19.06 apply (zenon_L107_); trivial. % 18.87/19.06 apply (zenon_or_s _ _ zenon_H1e2); [ zenon_intro zenon_H3b | zenon_intro zenon_H15e ]. % 18.87/19.06 apply (zenon_L921_); trivial. % 18.87/19.06 apply (zenon_L109_); trivial. % 18.87/19.06 apply (zenon_L81_); trivial. % 18.87/19.06 apply (zenon_or_s _ _ zenon_H22e); [ zenon_intro zenon_Ha0 | zenon_intro zenon_H22f ]. % 18.87/19.06 exact (zenon_Ha4 zenon_Ha0). % 18.87/19.06 apply (zenon_or_s _ _ zenon_H22f); [ zenon_intro zenon_H122 | zenon_intro zenon_Hc3 ]. % 18.87/19.06 exact (zenon_H20d zenon_H122). % 18.87/19.06 exact (zenon_H231 zenon_Hc3). % 18.87/19.06 apply (zenon_L786_); trivial. % 18.87/19.06 apply (zenon_L110_); trivial. % 18.87/19.06 apply (zenon_or_s _ _ zenon_H253); [ zenon_intro zenon_H198 | zenon_intro zenon_H1ca ]. % 18.87/19.06 apply (zenon_or_s _ _ zenon_H263); [ zenon_intro zenon_H255 | zenon_intro zenon_Ha6 ]. % 18.87/19.06 apply (zenon_or_s _ _ zenon_H254); [ zenon_intro zenon_Had | zenon_intro zenon_H1b1 ]. % 18.87/19.06 apply (zenon_or_s _ _ zenon_H261); [ zenon_intro zenon_H250 | zenon_intro zenon_Hae ]. % 18.87/19.06 apply (zenon_or_s _ _ zenon_H252); [ zenon_intro zenon_H251 | zenon_intro zenon_H14d ]. % 18.87/19.06 apply (zenon_L922_); trivial. % 18.87/19.06 apply (zenon_or_s _ _ zenon_H3e); [ zenon_intro zenon_H42 | zenon_intro zenon_H41 ]. % 18.87/19.06 exact (zenon_H3f zenon_H42). % 18.87/19.06 apply (zenon_or_s _ _ zenon_H41); [ zenon_intro zenon_H27 | zenon_intro zenon_H43 ]. % 18.87/19.06 apply (zenon_or_s _ _ zenon_H22d); [ zenon_intro zenon_H7a | zenon_intro zenon_H22e ]. % 18.87/19.06 apply (zenon_or_s _ _ zenon_H183); [ zenon_intro zenon_H7b | zenon_intro zenon_H186 ]. % 18.87/19.06 apply (zenon_L26_); trivial. % 18.87/19.06 apply (zenon_or_s _ _ zenon_H186); [ zenon_intro zenon_H10f | zenon_intro zenon_H187 ]. % 18.87/19.06 apply (zenon_L389_); trivial. % 18.87/19.06 apply (zenon_or_s _ _ zenon_H187); [ zenon_intro zenon_H150 | zenon_intro zenon_Hcd ]. % 18.87/19.06 apply (zenon_L719_); trivial. % 18.87/19.06 apply (zenon_or_s _ _ zenon_H1fe); [ zenon_intro zenon_H7b | zenon_intro zenon_H1ff ]. % 18.87/19.06 apply (zenon_L375_); trivial. % 18.87/19.06 apply (zenon_or_s _ _ zenon_H1ff); [ zenon_intro zenon_H86 | zenon_intro zenon_H200 ]. % 18.87/19.06 apply (zenon_L257_); trivial. % 18.87/19.06 apply (zenon_or_s _ _ zenon_H200); [ zenon_intro zenon_Hee | zenon_intro zenon_H148 ]. % 18.87/19.06 apply (zenon_or_s _ _ zenon_H168); [ zenon_intro zenon_H3a | zenon_intro zenon_H169 ]. % 18.87/19.06 apply (zenon_L35_); trivial. % 18.87/19.06 apply (zenon_or_s _ _ zenon_H169); [ zenon_intro zenon_H99 | zenon_intro zenon_H16a ]. % 18.87/19.06 apply (zenon_L36_); trivial. % 18.87/19.06 apply (zenon_or_s _ _ zenon_H16a); [ zenon_intro zenon_Ha9 | zenon_intro zenon_He3 ]. % 18.87/19.06 apply (zenon_or_s _ _ zenon_H128); [ zenon_intro zenon_H9d | zenon_intro zenon_H129 ]. % 18.87/19.06 exact (zenon_H1ef zenon_H9d). % 18.87/19.06 apply (zenon_or_s _ _ zenon_H129); [ zenon_intro zenon_H10d | zenon_intro zenon_H12a ]. % 18.87/19.06 exact (zenon_H10a zenon_H10d). % 18.87/19.06 apply (zenon_or_s _ _ zenon_H12a); [ zenon_intro zenon_Hf0 | zenon_intro zenon_Hd6 ]. % 18.87/19.06 exact (zenon_H24d zenon_Hf0). % 18.87/19.06 apply (zenon_or_s _ _ zenon_H2f); [ zenon_intro zenon_H34 | zenon_intro zenon_H33 ]. % 18.87/19.06 apply (zenon_L926_); trivial. % 18.87/19.06 apply (zenon_or_s _ _ zenon_H33); [ zenon_intro zenon_H36 | zenon_intro zenon_H35 ]. % 18.87/19.06 apply (zenon_L128_); trivial. % 18.87/19.06 apply (zenon_or_s _ _ zenon_H35); [ zenon_intro zenon_H2c | zenon_intro zenon_H37 ]. % 18.87/19.06 apply (zenon_L869_); trivial. % 18.87/19.06 apply (zenon_L727_); trivial. % 18.87/19.06 apply (zenon_L927_); trivial. % 18.87/19.06 apply (zenon_L436_); trivial. % 18.87/19.06 apply (zenon_or_s _ _ zenon_H22e); [ zenon_intro zenon_Ha0 | zenon_intro zenon_H22f ]. % 18.87/19.06 exact (zenon_Ha4 zenon_Ha0). % 18.87/19.06 apply (zenon_or_s _ _ zenon_H22f); [ zenon_intro zenon_H122 | zenon_intro zenon_Hc3 ]. % 18.87/19.06 exact (zenon_H20d zenon_H122). % 18.87/19.06 exact (zenon_H231 zenon_Hc3). % 18.87/19.06 apply (zenon_or_s _ _ zenon_H43); [ zenon_intro zenon_H34 | zenon_intro zenon_H44 ]. % 18.87/19.06 apply (zenon_or_s _ _ zenon_H22d); [ zenon_intro zenon_H7a | zenon_intro zenon_H22e ]. % 18.87/19.06 apply (zenon_or_s _ _ zenon_H183); [ zenon_intro zenon_H7b | zenon_intro zenon_H186 ]. % 18.87/19.06 apply (zenon_L26_); trivial. % 18.87/19.06 apply (zenon_or_s _ _ zenon_H186); [ zenon_intro zenon_H10f | zenon_intro zenon_H187 ]. % 18.87/19.06 apply (zenon_L726_); trivial. % 18.87/19.06 apply (zenon_or_s _ _ zenon_H187); [ zenon_intro zenon_H150 | zenon_intro zenon_Hcd ]. % 18.87/19.06 apply (zenon_or_s _ _ zenon_H1fe); [ zenon_intro zenon_H7b | zenon_intro zenon_H1ff ]. % 18.87/19.06 apply (zenon_L26_); trivial. % 18.87/19.06 apply (zenon_or_s _ _ zenon_H1ff); [ zenon_intro zenon_H86 | zenon_intro zenon_H200 ]. % 18.87/19.06 apply (zenon_or_s _ _ zenon_H168); [ zenon_intro zenon_H3a | zenon_intro zenon_H169 ]. % 18.87/19.06 apply (zenon_L35_); trivial. % 18.87/19.06 apply (zenon_or_s _ _ zenon_H169); [ zenon_intro zenon_H99 | zenon_intro zenon_H16a ]. % 18.87/19.06 apply (zenon_L108_); trivial. % 18.87/19.06 apply (zenon_or_s _ _ zenon_H16a); [ zenon_intro zenon_Ha9 | zenon_intro zenon_He3 ]. % 18.87/19.06 apply (zenon_L930_); trivial. % 18.87/19.06 apply (zenon_or_s _ _ zenon_H128); [ zenon_intro zenon_H9d | zenon_intro zenon_H129 ]. % 18.87/19.06 exact (zenon_H1ef zenon_H9d). % 18.87/19.06 apply (zenon_or_s _ _ zenon_H129); [ zenon_intro zenon_H10d | zenon_intro zenon_H12a ]. % 18.87/19.06 exact (zenon_H10a zenon_H10d). % 18.87/19.06 apply (zenon_or_s _ _ zenon_H12a); [ zenon_intro zenon_Hf0 | zenon_intro zenon_Hd6 ]. % 18.87/19.06 exact (zenon_H24d zenon_Hf0). % 18.87/19.06 apply (zenon_or_s _ _ zenon_H6a); [ zenon_intro zenon_H48 | zenon_intro zenon_H6b ]. % 18.87/19.06 apply (zenon_L378_); trivial. % 18.87/19.06 apply (zenon_or_s _ _ zenon_H6b); [ zenon_intro zenon_H2a | zenon_intro zenon_H6c ]. % 18.87/19.06 apply (zenon_L211_); trivial. % 18.87/19.06 apply (zenon_or_s _ _ zenon_H6c); [ zenon_intro zenon_H2c | zenon_intro zenon_H61 ]. % 18.87/19.06 apply (zenon_L933_); trivial. % 18.87/19.06 apply (zenon_L928_); trivial. % 18.87/19.06 apply (zenon_or_s _ _ zenon_H200); [ zenon_intro zenon_Hee | zenon_intro zenon_H148 ]. % 18.87/19.06 apply (zenon_L934_); trivial. % 18.87/19.06 apply (zenon_L436_); trivial. % 18.87/19.06 apply (zenon_or_s _ _ zenon_H168); [ zenon_intro zenon_H3a | zenon_intro zenon_H169 ]. % 18.87/19.06 apply (zenon_L35_); trivial. % 18.87/19.06 apply (zenon_or_s _ _ zenon_H169); [ zenon_intro zenon_H99 | zenon_intro zenon_H16a ]. % 18.87/19.06 apply (zenon_L36_); trivial. % 18.87/19.06 apply (zenon_or_s _ _ zenon_H16a); [ zenon_intro zenon_Ha9 | zenon_intro zenon_He3 ]. % 18.87/19.06 apply (zenon_L926_); trivial. % 18.87/19.06 apply (zenon_L81_); trivial. % 18.87/19.06 apply (zenon_or_s _ _ zenon_H22e); [ zenon_intro zenon_Ha0 | zenon_intro zenon_H22f ]. % 18.87/19.06 exact (zenon_Ha4 zenon_Ha0). % 18.87/19.06 apply (zenon_or_s _ _ zenon_H22f); [ zenon_intro zenon_H122 | zenon_intro zenon_Hc3 ]. % 18.87/19.06 exact (zenon_H20d zenon_H122). % 18.87/19.06 exact (zenon_H231 zenon_Hc3). % 18.87/19.06 apply (zenon_or_s _ _ zenon_H22d); [ zenon_intro zenon_H7a | zenon_intro zenon_H22e ]. % 18.87/19.06 apply (zenon_or_s _ _ zenon_H183); [ zenon_intro zenon_H7b | zenon_intro zenon_H186 ]. % 18.87/19.06 apply (zenon_L26_); trivial. % 18.87/19.06 apply (zenon_or_s _ _ zenon_H186); [ zenon_intro zenon_H10f | zenon_intro zenon_H187 ]. % 18.87/19.06 apply (zenon_L389_); trivial. % 18.87/19.06 apply (zenon_or_s _ _ zenon_H187); [ zenon_intro zenon_H150 | zenon_intro zenon_Hcd ]. % 18.87/19.06 apply (zenon_or_s _ _ zenon_H1fe); [ zenon_intro zenon_H7b | zenon_intro zenon_H1ff ]. % 18.87/19.06 apply (zenon_L26_); trivial. % 18.87/19.06 apply (zenon_or_s _ _ zenon_H1ff); [ zenon_intro zenon_H86 | zenon_intro zenon_H200 ]. % 18.87/19.06 apply (zenon_or_s _ _ zenon_H168); [ zenon_intro zenon_H3a | zenon_intro zenon_H169 ]. % 18.87/19.06 apply (zenon_L35_); trivial. % 18.87/19.06 apply (zenon_or_s _ _ zenon_H169); [ zenon_intro zenon_H99 | zenon_intro zenon_H16a ]. % 18.87/19.06 apply (zenon_L108_); trivial. % 18.87/19.06 apply (zenon_or_s _ _ zenon_H16a); [ zenon_intro zenon_Ha9 | zenon_intro zenon_He3 ]. % 18.87/19.06 apply (zenon_L930_); trivial. % 18.87/19.06 apply (zenon_or_s _ _ zenon_H22); [ zenon_intro zenon_H27 | zenon_intro zenon_H26 ]. % 18.87/19.06 apply (zenon_L312_); trivial. % 18.87/19.06 apply (zenon_or_s _ _ zenon_H26); [ zenon_intro zenon_H29 | zenon_intro zenon_H28 ]. % 18.87/19.06 apply (zenon_L745_); trivial. % 18.87/19.06 apply (zenon_or_s _ _ zenon_H28); [ zenon_intro zenon_H2a | zenon_intro zenon_H1f ]. % 18.87/19.06 apply (zenon_L211_); trivial. % 18.87/19.06 apply (zenon_or_s _ _ zenon_H128); [ zenon_intro zenon_H9d | zenon_intro zenon_H129 ]. % 18.87/19.06 exact (zenon_H1ef zenon_H9d). % 18.87/19.06 apply (zenon_or_s _ _ zenon_H129); [ zenon_intro zenon_H10d | zenon_intro zenon_H12a ]. % 18.87/19.06 exact (zenon_H10a zenon_H10d). % 18.87/19.06 apply (zenon_or_s _ _ zenon_H12a); [ zenon_intro zenon_Hf0 | zenon_intro zenon_Hd6 ]. % 18.87/19.06 exact (zenon_H24d zenon_Hf0). % 18.87/19.06 apply (zenon_or_s _ _ zenon_H2f); [ zenon_intro zenon_H34 | zenon_intro zenon_H33 ]. % 18.87/19.06 apply (zenon_L127_); trivial. % 18.87/19.06 apply (zenon_or_s _ _ zenon_H33); [ zenon_intro zenon_H36 | zenon_intro zenon_H35 ]. % 18.87/19.06 apply (zenon_L514_); trivial. % 18.87/19.06 apply (zenon_or_s _ _ zenon_H35); [ zenon_intro zenon_H2c | zenon_intro zenon_H37 ]. % 18.87/19.06 apply (zenon_L933_); trivial. % 18.87/19.06 apply (zenon_L130_); trivial. % 18.87/19.06 apply (zenon_or_s _ _ zenon_H200); [ zenon_intro zenon_Hee | zenon_intro zenon_H148 ]. % 18.87/19.06 apply (zenon_L934_); trivial. % 18.87/19.06 apply (zenon_L100_); trivial. % 18.87/19.06 apply (zenon_L937_); trivial. % 18.87/19.06 apply (zenon_or_s _ _ zenon_H22e); [ zenon_intro zenon_Ha0 | zenon_intro zenon_H22f ]. % 18.87/19.06 exact (zenon_Ha4 zenon_Ha0). % 18.87/19.06 apply (zenon_or_s _ _ zenon_H22f); [ zenon_intro zenon_H122 | zenon_intro zenon_Hc3 ]. % 18.87/19.06 exact (zenon_H20d zenon_H122). % 18.87/19.06 exact (zenon_H231 zenon_Hc3). % 18.87/19.06 apply (zenon_L42_); trivial. % 18.87/19.06 apply (zenon_or_s _ _ zenon_H252); [ zenon_intro zenon_H251 | zenon_intro zenon_H14d ]. % 18.87/19.06 apply (zenon_L716_); trivial. % 18.87/19.06 apply (zenon_or_s _ _ zenon_H3e); [ zenon_intro zenon_H42 | zenon_intro zenon_H41 ]. % 18.87/19.06 exact (zenon_H3f zenon_H42). % 18.87/19.06 apply (zenon_or_s _ _ zenon_H41); [ zenon_intro zenon_H27 | zenon_intro zenon_H43 ]. % 18.87/19.06 apply (zenon_or_s _ _ zenon_H22d); [ zenon_intro zenon_H7a | zenon_intro zenon_H22e ]. % 18.87/19.06 apply (zenon_or_s _ _ zenon_H183); [ zenon_intro zenon_H7b | zenon_intro zenon_H186 ]. % 18.87/19.06 apply (zenon_L26_); trivial. % 18.87/19.06 apply (zenon_or_s _ _ zenon_H186); [ zenon_intro zenon_H10f | zenon_intro zenon_H187 ]. % 18.87/19.06 apply (zenon_L389_); trivial. % 18.87/19.06 apply (zenon_or_s _ _ zenon_H187); [ zenon_intro zenon_H150 | zenon_intro zenon_Hcd ]. % 18.87/19.06 apply (zenon_L719_); trivial. % 18.87/19.06 apply (zenon_L889_); trivial. % 18.87/19.06 apply (zenon_or_s _ _ zenon_H22e); [ zenon_intro zenon_Ha0 | zenon_intro zenon_H22f ]. % 18.87/19.06 exact (zenon_Ha4 zenon_Ha0). % 18.87/19.06 apply (zenon_or_s _ _ zenon_H22f); [ zenon_intro zenon_H122 | zenon_intro zenon_Hc3 ]. % 18.87/19.06 exact (zenon_H20d zenon_H122). % 18.87/19.06 exact (zenon_H231 zenon_Hc3). % 18.87/19.06 apply (zenon_or_s _ _ zenon_H43); [ zenon_intro zenon_H34 | zenon_intro zenon_H44 ]. % 18.87/19.06 apply (zenon_or_s _ _ zenon_H22d); [ zenon_intro zenon_H7a | zenon_intro zenon_H22e ]. % 18.87/19.06 apply (zenon_or_s _ _ zenon_H183); [ zenon_intro zenon_H7b | zenon_intro zenon_H186 ]. % 18.87/19.06 apply (zenon_L26_); trivial. % 18.87/19.06 apply (zenon_or_s _ _ zenon_H186); [ zenon_intro zenon_H10f | zenon_intro zenon_H187 ]. % 18.87/19.06 apply (zenon_L580_); trivial. % 18.87/19.06 apply (zenon_or_s _ _ zenon_H187); [ zenon_intro zenon_H150 | zenon_intro zenon_Hcd ]. % 18.87/19.06 apply (zenon_or_s _ _ zenon_H1fe); [ zenon_intro zenon_H7b | zenon_intro zenon_H1ff ]. % 18.87/19.06 apply (zenon_L26_); trivial. % 18.87/19.06 apply (zenon_or_s _ _ zenon_H1ff); [ zenon_intro zenon_H86 | zenon_intro zenon_H200 ]. % 18.87/19.06 apply (zenon_or_s _ _ zenon_H168); [ zenon_intro zenon_H3a | zenon_intro zenon_H169 ]. % 18.87/19.06 apply (zenon_L35_); trivial. % 18.87/19.06 apply (zenon_or_s _ _ zenon_H169); [ zenon_intro zenon_H99 | zenon_intro zenon_H16a ]. % 18.87/19.06 apply (zenon_L108_); trivial. % 18.87/19.06 apply (zenon_or_s _ _ zenon_H16a); [ zenon_intro zenon_Ha9 | zenon_intro zenon_He3 ]. % 18.87/19.06 apply (zenon_L938_); trivial. % 18.87/19.06 apply (zenon_L248_); trivial. % 18.87/19.06 apply (zenon_or_s _ _ zenon_H200); [ zenon_intro zenon_Hee | zenon_intro zenon_H148 ]. % 18.87/19.06 apply (zenon_L204_); trivial. % 18.87/19.06 apply (zenon_L436_); trivial. % 18.87/19.06 apply (zenon_L887_); trivial. % 18.87/19.06 apply (zenon_or_s _ _ zenon_H22e); [ zenon_intro zenon_Ha0 | zenon_intro zenon_H22f ]. % 18.87/19.06 exact (zenon_Ha4 zenon_Ha0). % 18.87/19.06 apply (zenon_or_s _ _ zenon_H22f); [ zenon_intro zenon_H122 | zenon_intro zenon_Hc3 ]. % 18.87/19.06 exact (zenon_H20d zenon_H122). % 18.87/19.06 exact (zenon_H231 zenon_Hc3). % 18.87/19.06 apply (zenon_L346_); trivial. % 18.87/19.06 apply (zenon_L39_); trivial. % 18.87/19.06 apply (zenon_or_s _ _ zenon_H263); [ zenon_intro zenon_H255 | zenon_intro zenon_Ha6 ]. % 18.87/19.06 apply (zenon_or_s _ _ zenon_H254); [ zenon_intro zenon_Had | zenon_intro zenon_H1b1 ]. % 18.87/19.06 apply (zenon_or_s _ _ zenon_H261); [ zenon_intro zenon_H250 | zenon_intro zenon_Hae ]. % 18.87/19.06 apply (zenon_or_s _ _ zenon_H252); [ zenon_intro zenon_H251 | zenon_intro zenon_H14d ]. % 18.87/19.06 apply (zenon_L922_); trivial. % 18.87/19.06 apply (zenon_or_s _ _ zenon_H3e); [ zenon_intro zenon_H42 | zenon_intro zenon_H41 ]. % 18.87/19.06 exact (zenon_H3f zenon_H42). % 18.87/19.06 apply (zenon_or_s _ _ zenon_H41); [ zenon_intro zenon_H27 | zenon_intro zenon_H43 ]. % 18.87/19.06 apply (zenon_L940_); trivial. % 18.87/19.06 apply (zenon_or_s _ _ zenon_H43); [ zenon_intro zenon_H34 | zenon_intro zenon_H44 ]. % 18.87/19.06 apply (zenon_or_s _ _ zenon_H22d); [ zenon_intro zenon_H7a | zenon_intro zenon_H22e ]. % 18.87/19.06 apply (zenon_or_s _ _ zenon_H183); [ zenon_intro zenon_H7b | zenon_intro zenon_H186 ]. % 18.87/19.06 apply (zenon_L26_); trivial. % 18.87/19.06 apply (zenon_or_s _ _ zenon_H186); [ zenon_intro zenon_H10f | zenon_intro zenon_H187 ]. % 18.87/19.06 apply (zenon_L389_); trivial. % 18.87/19.06 apply (zenon_or_s _ _ zenon_H187); [ zenon_intro zenon_H150 | zenon_intro zenon_Hcd ]. % 18.87/19.06 apply (zenon_or_s _ _ zenon_H1fe); [ zenon_intro zenon_H7b | zenon_intro zenon_H1ff ]. % 18.87/19.06 apply (zenon_L26_); trivial. % 18.87/19.06 apply (zenon_or_s _ _ zenon_H1ff); [ zenon_intro zenon_H86 | zenon_intro zenon_H200 ]. % 18.87/19.06 apply (zenon_L931_); trivial. % 18.87/19.06 apply (zenon_or_s _ _ zenon_H200); [ zenon_intro zenon_Hee | zenon_intro zenon_H148 ]. % 18.87/19.06 apply (zenon_L277_); trivial. % 18.87/19.06 apply (zenon_L436_); trivial. % 18.87/19.06 apply (zenon_or_s _ _ zenon_H1fe); [ zenon_intro zenon_H7b | zenon_intro zenon_H1ff ]. % 18.87/19.06 apply (zenon_L375_); trivial. % 18.87/19.06 apply (zenon_or_s _ _ zenon_H1ff); [ zenon_intro zenon_H86 | zenon_intro zenon_H200 ]. % 18.87/19.06 apply (zenon_or_s _ _ zenon_H168); [ zenon_intro zenon_H3a | zenon_intro zenon_H169 ]. % 18.87/19.06 apply (zenon_L35_); trivial. % 18.87/19.06 apply (zenon_or_s _ _ zenon_H169); [ zenon_intro zenon_H99 | zenon_intro zenon_H16a ]. % 18.87/19.06 apply (zenon_L36_); trivial. % 18.87/19.06 apply (zenon_or_s _ _ zenon_H16a); [ zenon_intro zenon_Ha9 | zenon_intro zenon_He3 ]. % 18.87/19.06 apply (zenon_L926_); trivial. % 18.87/19.06 apply (zenon_L739_); trivial. % 18.87/19.06 apply (zenon_or_s _ _ zenon_H200); [ zenon_intro zenon_Hee | zenon_intro zenon_H148 ]. % 18.87/19.06 apply (zenon_L204_); trivial. % 18.87/19.06 apply (zenon_L436_); trivial. % 18.87/19.06 apply (zenon_or_s _ _ zenon_H22e); [ zenon_intro zenon_Ha0 | zenon_intro zenon_H22f ]. % 18.87/19.06 exact (zenon_Ha4 zenon_Ha0). % 18.87/19.06 apply (zenon_or_s _ _ zenon_H22f); [ zenon_intro zenon_H122 | zenon_intro zenon_Hc3 ]. % 18.87/19.06 exact (zenon_H20d zenon_H122). % 18.87/19.06 exact (zenon_H231 zenon_Hc3). % 18.87/19.06 apply (zenon_L786_); trivial. % 18.87/19.06 apply (zenon_L42_); trivial. % 18.87/19.06 apply (zenon_or_s _ _ zenon_H3e); [ zenon_intro zenon_H42 | zenon_intro zenon_H41 ]. % 18.87/19.06 exact (zenon_H3f zenon_H42). % 18.87/19.06 apply (zenon_or_s _ _ zenon_H41); [ zenon_intro zenon_H27 | zenon_intro zenon_H43 ]. % 18.87/19.06 apply (zenon_or_s _ _ zenon_H22d); [ zenon_intro zenon_H7a | zenon_intro zenon_H22e ]. % 18.87/19.06 apply (zenon_or_s _ _ zenon_H183); [ zenon_intro zenon_H7b | zenon_intro zenon_H186 ]. % 18.87/19.06 apply (zenon_L26_); trivial. % 18.87/19.06 apply (zenon_or_s _ _ zenon_H186); [ zenon_intro zenon_H10f | zenon_intro zenon_H187 ]. % 18.87/19.06 apply (zenon_L580_); trivial. % 18.87/19.06 apply (zenon_or_s _ _ zenon_H187); [ zenon_intro zenon_H150 | zenon_intro zenon_Hcd ]. % 18.87/19.06 apply (zenon_or_s _ _ zenon_H1fe); [ zenon_intro zenon_H7b | zenon_intro zenon_H1ff ]. % 18.87/19.06 apply (zenon_L26_); trivial. % 18.87/19.06 apply (zenon_or_s _ _ zenon_H1ff); [ zenon_intro zenon_H86 | zenon_intro zenon_H200 ]. % 18.87/19.06 apply (zenon_L257_); trivial. % 18.87/19.06 apply (zenon_or_s _ _ zenon_H200); [ zenon_intro zenon_Hee | zenon_intro zenon_H148 ]. % 18.87/19.06 apply (zenon_L277_); trivial. % 18.87/19.06 apply (zenon_or_s _ _ zenon_H1e0); [ zenon_intro zenon_H3a | zenon_intro zenon_H1e1 ]. % 18.87/19.06 apply (zenon_L35_); trivial. % 18.87/19.06 apply (zenon_or_s _ _ zenon_H1e1); [ zenon_intro zenon_H9e | zenon_intro zenon_H1e2 ]. % 18.87/19.06 apply (zenon_L107_); trivial. % 18.87/19.06 apply (zenon_or_s _ _ zenon_H1e2); [ zenon_intro zenon_H3b | zenon_intro zenon_H15e ]. % 18.87/19.06 apply (zenon_L942_); trivial. % 18.87/19.06 apply (zenon_L109_); trivial. % 18.87/19.06 apply (zenon_L889_); trivial. % 18.87/19.06 apply (zenon_or_s _ _ zenon_H22e); [ zenon_intro zenon_Ha0 | zenon_intro zenon_H22f ]. % 18.87/19.06 exact (zenon_Ha4 zenon_Ha0). % 18.87/19.06 apply (zenon_or_s _ _ zenon_H22f); [ zenon_intro zenon_H122 | zenon_intro zenon_Hc3 ]. % 18.87/19.06 exact (zenon_H20d zenon_H122). % 18.87/19.06 exact (zenon_H231 zenon_Hc3). % 18.87/19.06 apply (zenon_or_s _ _ zenon_H43); [ zenon_intro zenon_H34 | zenon_intro zenon_H44 ]. % 18.87/19.06 apply (zenon_L944_); trivial. % 18.87/19.06 apply (zenon_L346_); trivial. % 18.87/19.06 apply (zenon_L39_); trivial. % 18.87/19.06 apply (zenon_L128_); trivial. % 18.87/19.06 apply (zenon_L917_); trivial. % 18.87/19.06 (* end of lemma zenon_L945_ *) % 18.87/19.06 assert (zenon_L946_ : (((op (e0) (e0)) = (e1))\/(((op (e0) (e1)) = (e1))\/(((op (e0) (e2)) = (e1))\/((op (e0) (e3)) = (e1))))) -> (~((op (e0) (e0)) = (e1))) -> (~((op (e0) (e1)) = (e1))) -> (~((e0) = (e1))) -> ((op (e0) (e2)) = (e0)) -> (~((op (e0) (e3)) = (e1))) -> False). % 18.87/19.06 do 0 intro. intros zenon_H22d zenon_H84 zenon_Ha4 zenon_Ha1 zenon_H48 zenon_H231. % 18.87/19.06 apply (zenon_or_s _ _ zenon_H22d); [ zenon_intro zenon_H7a | zenon_intro zenon_H22e ]. % 18.87/19.06 exact (zenon_H84 zenon_H7a). % 18.87/19.06 apply (zenon_or_s _ _ zenon_H22e); [ zenon_intro zenon_Ha0 | zenon_intro zenon_H22f ]. % 18.87/19.06 exact (zenon_Ha4 zenon_Ha0). % 18.87/19.06 apply (zenon_or_s _ _ zenon_H22f); [ zenon_intro zenon_H122 | zenon_intro zenon_Hc3 ]. % 18.87/19.06 apply (zenon_L355_); trivial. % 18.87/19.06 exact (zenon_H231 zenon_Hc3). % 18.87/19.06 (* end of lemma zenon_L946_ *) % 18.87/19.06 assert (zenon_L947_ : (((op (e0) (e0)) = (e1))\/(((op (e0) (e1)) = (e1))\/(((op (e0) (e2)) = (e1))\/((op (e0) (e3)) = (e1))))) -> (~((op (e0) (e0)) = (e1))) -> (~((op (e0) (e1)) = (e1))) -> (~((op (e0) (e2)) = (e1))) -> ((op (e0) (e3)) = (e0)) -> (~((e0) = (e1))) -> False). % 18.87/19.06 do 0 intro. intros zenon_H22d zenon_H84 zenon_Ha4 zenon_H20d zenon_H1e zenon_Ha1. % 18.87/19.06 apply (zenon_or_s _ _ zenon_H22d); [ zenon_intro zenon_H7a | zenon_intro zenon_H22e ]. % 18.87/19.06 exact (zenon_H84 zenon_H7a). % 18.87/19.06 apply (zenon_or_s _ _ zenon_H22e); [ zenon_intro zenon_Ha0 | zenon_intro zenon_H22f ]. % 18.87/19.06 exact (zenon_Ha4 zenon_Ha0). % 18.87/19.06 apply (zenon_or_s _ _ zenon_H22f); [ zenon_intro zenon_H122 | zenon_intro zenon_Hc3 ]. % 18.87/19.06 exact (zenon_H20d zenon_H122). % 18.87/19.06 apply (zenon_L427_); trivial. % 18.87/19.06 (* end of lemma zenon_L947_ *) % 18.87/19.06 assert (zenon_L948_ : (((op (e0) (e0)) = (e1))\/(((op (e1) (e0)) = (e1))\/(((op (e2) (e0)) = (e1))\/((op (e3) (e0)) = (e1))))) -> (~((op (e0) (e0)) = (e1))) -> (~((op (e1) (e0)) = (e1))) -> (~((op (e2) (e0)) = (e1))) -> (~((op (e3) (e0)) = (e1))) -> False). % 18.87/19.06 do 0 intro. intros zenon_H235 zenon_H84 zenon_H1ef zenon_H1db zenon_Had. % 18.87/19.06 apply (zenon_or_s _ _ zenon_H235); [ zenon_intro zenon_H7a | zenon_intro zenon_H236 ]. % 18.87/19.06 exact (zenon_H84 zenon_H7a). % 18.87/19.06 apply (zenon_or_s _ _ zenon_H236); [ zenon_intro zenon_H9d | zenon_intro zenon_H237 ]. % 18.87/19.06 exact (zenon_H1ef zenon_H9d). % 18.87/19.06 apply (zenon_or_s _ _ zenon_H237); [ zenon_intro zenon_Hed | zenon_intro zenon_Hac ]. % 18.87/19.06 exact (zenon_H1db zenon_Hed). % 18.87/19.06 exact (zenon_Had zenon_Hac). % 18.87/19.06 (* end of lemma zenon_L948_ *) % 18.87/19.06 assert (zenon_L949_ : (((op (e1) (e0)) = (e1))\/(((op (e1) (e1)) = (e1))\/(((op (e1) (e2)) = (e1))\/((op (e1) (e3)) = (e1))))) -> (~((op (e1) (e1)) = (e1))) -> (~((op (e1) (e2)) = (op (e2) (e2)))) -> (((op (e2) (e0)) = (e1))\/(((op (e2) (e1)) = (e1))\/(((op (e2) (e2)) = (e1))\/((op (e2) (e3)) = (e1))))) -> ((~((op (e1) (e2)) = (e1)))\/((op (e1) (e1)) = (e2))) -> ((~((op (e2) (e0)) = (e1)))\/((op (e2) (e1)) = (e0))) -> ((~((op (e1) (e3)) = (e1)))\/((op (e1) (e1)) = (e3))) -> (((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) (e2)))) -> (~((op (e1) (e0)) = (op (e3) (e0)))) -> (((op (e2) (e0)) = (e0))\/(((op (e2) (e0)) = (e1))\/(((op (e2) (e0)) = (e2))\/((op (e2) (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) (e1)) = (op (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 (e0) (e3)) = (e2))\/(((op (e1) (e3)) = (e2))\/(((op (e2) (e3)) = (e2))\/((op (e3) (e3)) = (e2))))) -> (~((op (e3) (e0)) = (op (e3) (e3)))) -> (~((op (e2) (e1)) = (op (e2) (e3)))) -> (((op (e1) (e3)) = (e0))\/(((op (e1) (e3)) = (e1))\/(((op (e1) (e3)) = (e2))\/((op (e1) (e3)) = (e3))))) -> (~((op (e1) (e3)) = (op (e3) (e3)))) -> (((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)) = (e0))\/(((op (e3) (e2)) = (e1))\/(((op (e3) (e2)) = (e2))\/((op (e3) (e2)) = (e3))))) -> (~((op (e3) (e1)) = (op (e3) (e2)))) -> (~((op (e2) (e2)) = (op (e2) (e3)))) -> (((op (e2) (e0)) = (e0))\/(((op (e2) (e1)) = (e0))\/(((op (e2) (e2)) = (e0))\/((op (e2) (e3)) = (e0))))) -> (~((op (e1) (e0)) = (op (e2) (e0)))) -> (~((op (e2) (e1)) = (op (e3) (e1)))) -> (~((op (e1) (e3)) = (op (e2) (e3)))) -> (((op (e0) (e3)) = (e3))\/(((op (e1) (e3)) = (e3))\/(((op (e2) (e3)) = (e3))\/((op (e3) (e3)) = (e3))))) -> ((~((op (e1) (e0)) = (e1)))\/((op (e1) (e1)) = (e0))) -> (((op (e0) (e0)) = (e0))\/(((op (e1) (e0)) = (e0))\/(((op (e2) (e0)) = (e0))\/((op (e3) (e0)) = (e0))))) -> (~((e0) = (e1))) -> (~((op (e1) (e0)) = (op (e1) (e1)))) -> ((~((op (e0) (e3)) = (e1)))\/((op (e0) (e1)) = (e3))) -> (((op (e0) (e3)) = (e1))\/(((op (e1) (e3)) = (e1))\/(((op (e2) (e3)) = (e1))\/((op (e3) (e3)) = (e1))))) -> (((op (e0) (e0)) = (e3))\/(((op (e1) (e0)) = (e3))\/(((op (e2) (e0)) = (e3))\/((op (e3) (e0)) = (e3))))) -> (((op (e1) (e0)) = (e0))\/(((op (e1) (e0)) = (e1))\/(((op (e1) (e0)) = (e2))\/((op (e1) (e0)) = (e3))))) -> ((~((op (e2) (e3)) = (e1)))\/((op (e2) (e1)) = (e3))) -> (~((op (e3) (e0)) = (op (e3) (e1)))) -> (((op (e2) (e3)) = (e0))\/(((op (e2) (e3)) = (e1))\/(((op (e2) (e3)) = (e2))\/((op (e2) (e3)) = (e3))))) -> (((op (e3) (e0)) = (e1))\/(((op (e3) (e1)) = (e1))\/(((op (e3) (e2)) = (e1))\/((op (e3) (e3)) = (e1))))) -> (~((op (e1) (e0)) = (op (e1) (e2)))) -> (((op (e0) (e1)) = (e3))\/(((op (e1) (e1)) = (e3))\/(((op (e2) (e1)) = (e3))\/((op (e3) (e1)) = (e3))))) -> ((~((op (e2) (e1)) = (e1)))\/((op (e2) (e1)) = (e1))) -> (((op (e0) (e2)) = (e0))\/(((op (e1) (e2)) = (e0))\/(((op (e2) (e2)) = (e0))\/((op (e3) (e2)) = (e0))))) -> (~((op (e0) (e1)) = (op (e0) (e3)))) -> (~((op (e1) (e1)) = (op (e1) (e3)))) -> (~((op (e2) (e0)) = (op (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) (e0)) = (op (e2) (e2)))) -> (~((op (e1) (e1)) = (op (e1) (e2)))) -> (~((op (e0) (e1)) = (op (e0) (e2)))) -> (~((op (e1) (e2)) = (op (e1) (e3)))) -> (((op (e2) (e2)) = (e0))\/(((op (e2) (e2)) = (e1))\/(((op (e2) (e2)) = (e2))\/((op (e2) (e2)) = (e3))))) -> (~((op (e2) (e2)) = (e2))) -> (~((op (e2) (e2)) = (op (e3) (e2)))) -> (((op (e2) (e0)) = (e3))\/(((op (e2) (e1)) = (e3))\/(((op (e2) (e2)) = (e3))\/((op (e2) (e3)) = (e3))))) -> (((op (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 (e3) (e3)) = (e0))\/(((op (e3) (e3)) = (e1))\/(((op (e3) (e3)) = (e2))\/((op (e3) (e3)) = (e3))))) -> (~((op (e0) (e2)) = (op (e2) (e2)))) -> (~((op (e1) (e1)) = (op (e2) (e1)))) -> (((op (e1) (e0)) = (e0))\/(((op (e1) (e1)) = (e0))\/(((op (e1) (e2)) = (e0))\/((op (e1) (e3)) = (e0))))) -> ((op (e0) (e1)) = (e0)) -> (~((e0) = (e3))) -> (((op (e0) (e0)) = (e2))\/(((op (e0) (e1)) = (e2))\/(((op (e0) (e2)) = (e2))\/((op (e0) (e3)) = (e2))))) -> (~((op (e0) (e0)) = (op (e0) (e3)))) -> (~((op (e2) (e0)) = (op (e2) (e1)))) -> (((op (e0) (e0)) = (e3))\/(((op (e0) (e1)) = (e3))\/(((op (e0) (e2)) = (e3))\/((op (e0) (e3)) = (e3))))) -> (~((op (e1) (e1)) = (op (e3) (e1)))) -> (~((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))))) -> (~((op (e0) (e1)) = (op (e1) (e1)))) -> (~((e1) = (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)) = (op (e1) (e2)))) -> (~((e2) = (e3))) -> (~((e0) = (e2))) -> ((~((op (e3) (e0)) = (e1)))\/((op (e3) (e1)) = (e0))) -> (((op (e0) (e0)) = (e1))\/(((op (e1) (e0)) = (e1))\/(((op (e2) (e0)) = (e1))\/((op (e3) (e0)) = (e1))))) -> (~((op (e0) (e1)) = (op (e3) (e1)))) -> (~((op (e0) (e1)) = (op (e2) (e1)))) -> ((~((op (e2) (e2)) = (e1)))\/((op (e2) (e1)) = (e2))) -> (~((op (e0) (e0)) = (e0))) -> ((~((op (e3) (e3)) = (e1)))\/((op (e3) (e1)) = (e3))) -> (((op (e0) (e1)) = (e1))\/(((op (e1) (e1)) = (e1))\/(((op (e2) (e1)) = (e1))\/((op (e3) (e1)) = (e1))))) -> (~((op (e0) (e1)) = (e1))) -> ((~((op (e3) (e2)) = (e1)))\/((op (e3) (e1)) = (e2))) -> (~((e1) = (e2))) -> (((op (e0) (e2)) = (e1))\/(((op (e1) (e2)) = (e1))\/(((op (e2) (e2)) = (e1))\/((op (e3) (e2)) = (e1))))) -> (~((op (e0) (e0)) = (op (e0) (e2)))) -> (~((op (e0) (e2)) = (e1))) -> (((op (e0) (e0)) = (e1))\/(((op (e0) (e1)) = (e1))\/(((op (e0) (e2)) = (e1))\/((op (e0) (e3)) = (e1))))) -> ((~((op (e3) (e1)) = (e1)))\/((op (e3) (e1)) = (e1))) -> (((op (e0) (e2)) = (e2))\/(((op (e1) (e2)) = (e2))\/(((op (e2) (e2)) = (e2))\/((op (e3) (e2)) = (e2))))) -> False). % 18.87/19.06 do 0 intro. intros zenon_H128 zenon_H10a zenon_H2b zenon_H106 zenon_H256 zenon_H257 zenon_H258 zenon_H1d5 zenon_Hf3 zenon_H6f zenon_H1fa zenon_H259 zenon_H17b zenon_H1ac zenon_H130 zenon_Hd8 zenon_H16f zenon_H145 zenon_H71 zenon_H1c7 zenon_Hdf zenon_Hd5 zenon_H153 zenon_H115 zenon_H191 zenon_H1a4 zenon_H6d zenon_H2f zenon_H201 zenon_Haf zenon_Hdb zenon_H136 zenon_H25d zenon_H3e zenon_Ha1 zenon_H45 zenon_H25c zenon_H133 zenon_H1e0 zenon_H25e zenon_H263 zenon_H1cf zenon_H11f zenon_He8 zenon_H24a zenon_H1a5 zenon_H262 zenon_H6a zenon_H54 zenon_H57 zenon_H5b zenon_H62 zenon_H67 zenon_H52 zenon_H4f zenon_H4a zenon_H124 zenon_H1c4 zenon_H173 zenon_H18f zenon_He7 zenon_He4 zenon_He2 zenon_Hc2 zenon_H1d zenon_H101 zenon_Ha8 zenon_H13e zenon_H22 zenon_H49 zenon_H9a zenon_H183 zenon_H189 zenon_H1f0 zenon_H168 zenon_H160 zenon_H14f zenon_H102 zenon_H165 zenon_H10e zenon_H95 zenon_H1fe zenon_H18c zenon_H195 zenon_H12b zenon_H149 zenon_H254 zenon_H235 zenon_H210 zenon_H17e zenon_H253 zenon_H3f zenon_H264 zenon_H109 zenon_Ha4 zenon_H252 zenon_H7c zenon_H139 zenon_H13c zenon_H20d zenon_H22d zenon_H261 zenon_H172. % 18.87/19.06 apply (zenon_or_s _ _ zenon_H25c); [ zenon_intro zenon_H231 | zenon_intro zenon_H99 ]. % 18.87/19.06 apply (zenon_or_s _ _ zenon_H25d); [ zenon_intro zenon_H1ef | zenon_intro zenon_H29 ]. % 18.87/19.06 apply (zenon_L945_); trivial. % 18.87/19.06 apply (zenon_L23_); trivial. % 18.87/19.06 apply (zenon_L36_); trivial. % 18.87/19.06 (* end of lemma zenon_L949_ *) % 18.87/19.06 assert (zenon_L950_ : (((op (e0) (e0)) = (e0))\/(((op (e0) (e1)) = (e0))\/(((op (e0) (e2)) = (e0))\/((op (e0) (e3)) = (e0))))) -> ((~((op (e3) (e1)) = (e1)))\/((op (e3) (e1)) = (e1))) -> (~((op (e0) (e0)) = (op (e0) (e2)))) -> (((op (e0) (e2)) = (e1))\/(((op (e1) (e2)) = (e1))\/(((op (e2) (e2)) = (e1))\/((op (e3) (e2)) = (e1))))) -> ((~((op (e3) (e2)) = (e1)))\/((op (e3) (e1)) = (e2))) -> (((op (e0) (e1)) = (e1))\/(((op (e1) (e1)) = (e1))\/(((op (e2) (e1)) = (e1))\/((op (e3) (e1)) = (e1))))) -> ((~((op (e3) (e3)) = (e1)))\/((op (e3) (e1)) = (e3))) -> ((~((op (e2) (e2)) = (e1)))\/((op (e2) (e1)) = (e2))) -> (~((op (e0) (e1)) = (op (e2) (e1)))) -> (~((op (e0) (e1)) = (op (e3) (e1)))) -> (((op (e0) (e0)) = (e1))\/(((op (e1) (e0)) = (e1))\/(((op (e2) (e0)) = (e1))\/((op (e3) (e0)) = (e1))))) -> ((~((op (e3) (e0)) = (e1)))\/((op (e3) (e1)) = (e0))) -> (~((e2) = (e3))) -> (~((op (e0) (e2)) = (op (e1) (e2)))) -> (((op (e1) (e0)) = (e2))\/(((op (e1) (e1)) = (e2))\/(((op (e1) (e2)) = (e2))\/((op (e1) (e3)) = (e2))))) -> (((op (e0) (e0)) = (e2))\/(((op (e1) (e0)) = (e2))\/(((op (e2) (e0)) = (e2))\/((op (e3) (e0)) = (e2))))) -> (~((e1) = (e3))) -> (((op (e3) (e0)) = (e3))\/(((op (e3) (e1)) = (e3))\/(((op (e3) (e2)) = (e3))\/((op (e3) (e3)) = (e3))))) -> (~((op (e0) (e2)) = (op (e3) (e2)))) -> (~((op (e1) (e1)) = (op (e3) (e1)))) -> (((op (e0) (e0)) = (e3))\/(((op (e0) (e1)) = (e3))\/(((op (e0) (e2)) = (e3))\/((op (e0) (e3)) = (e3))))) -> (~((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) (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 (e2) (e0)) = (e3))\/(((op (e2) (e1)) = (e3))\/(((op (e2) (e2)) = (e3))\/((op (e2) (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 (e1) (e3)))) -> (~((op (e0) (e1)) = (op (e0) (e2)))) -> (~((op (e1) (e1)) = (op (e1) (e2)))) -> (~((op (e2) (e0)) = (op (e2) (e2)))) -> (~((op (e0) (e1)) = (op (e0) (e3)))) -> ((~((op (e2) (e1)) = (e1)))\/((op (e2) (e1)) = (e1))) -> (((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)) = (e0))\/(((op (e2) (e3)) = (e1))\/(((op (e2) (e3)) = (e2))\/((op (e2) (e3)) = (e3))))) -> ((~((op (e2) (e3)) = (e1)))\/((op (e2) (e1)) = (e3))) -> (((op (e1) (e0)) = (e0))\/(((op (e1) (e0)) = (e1))\/(((op (e1) (e0)) = (e2))\/((op (e1) (e0)) = (e3))))) -> (((op (e0) (e0)) = (e3))\/(((op (e1) (e0)) = (e3))\/(((op (e2) (e0)) = (e3))\/((op (e3) (e0)) = (e3))))) -> (((op (e0) (e3)) = (e1))\/(((op (e1) (e3)) = (e1))\/(((op (e2) (e3)) = (e1))\/((op (e3) (e3)) = (e1))))) -> ((~((op (e0) (e3)) = (e1)))\/((op (e0) (e1)) = (e3))) -> (~((op (e1) (e0)) = (op (e1) (e1)))) -> ((~((op (e1) (e0)) = (e1)))\/((op (e1) (e1)) = (e0))) -> (((op (e0) (e3)) = (e3))\/(((op (e1) (e3)) = (e3))\/(((op (e2) (e3)) = (e3))\/((op (e3) (e3)) = (e3))))) -> (~((op (e1) (e3)) = (op (e2) (e3)))) -> (~((op (e2) (e1)) = (op (e3) (e1)))) -> (~((op (e1) (e0)) = (op (e2) (e0)))) -> (((op (e3) (e2)) = (e0))\/(((op (e3) (e2)) = (e1))\/(((op (e3) (e2)) = (e2))\/((op (e3) (e2)) = (e3))))) -> (~((op (e1) (e2)) = (op (e3) (e2)))) -> (((op (e3) (e0)) = (e2))\/(((op (e3) (e1)) = (e2))\/(((op (e3) (e2)) = (e2))\/((op (e3) (e3)) = (e2))))) -> (~((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)) = (op (e3) (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))))) -> (~((op (e2) (e0)) = (op (e3) (e0)))) -> (((op (e2) (e0)) = (e0))\/(((op (e2) (e0)) = (e1))\/(((op (e2) (e0)) = (e2))\/((op (e2) (e0)) = (e3))))) -> (~((op (e1) (e0)) = (op (e3) (e0)))) -> (~((op (e3) (e0)) = (op (e3) (e2)))) -> ((~((op (e1) (e3)) = (e1)))\/((op (e1) (e1)) = (e3))) -> ((~((op (e2) (e0)) = (e1)))\/((op (e2) (e1)) = (e0))) -> ((~((op (e1) (e2)) = (e1)))\/((op (e1) (e1)) = (e2))) -> (((op (e2) (e0)) = (e1))\/(((op (e2) (e1)) = (e1))\/(((op (e2) (e2)) = (e1))\/((op (e2) (e3)) = (e1))))) -> (~((op (e1) (e2)) = (op (e2) (e2)))) -> ((op (e3) (e1)) = (e0)) -> (~((op (e3) (e0)) = (op (e3) (e1)))) -> (((op (e1) (e0)) = (e1))\/(((op (e1) (e1)) = (e1))\/(((op (e1) (e2)) = (e1))\/((op (e1) (e3)) = (e1))))) -> (~((op (e1) (e0)) = (e1))) -> (~((op (e1) (e1)) = (e1))) -> (~((op (e3) (e3)) = (e3))) -> (~((op (e2) (e3)) = (op (e3) (e3)))) -> (~((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 (e2) (e2)) = (e2))) -> (((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 (e1) (e1)) = (op (e1) (e3)))) -> ((op (e1) (e1)) = (e2)) -> (~((op (e2) (e1)) = (op (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) (e3)) = (e1))) -> (((op (e0) (e0)) = (e2))\/(((op (e0) (e1)) = (e2))\/(((op (e0) (e2)) = (e2))\/((op (e0) (e3)) = (e2))))) -> (((op (e2) (e0)) = (e0))\/(((op (e2) (e1)) = (e0))\/(((op (e2) (e2)) = (e0))\/((op (e2) (e3)) = (e0))))) -> (~((op (e2) (e1)) = (op (e2) (e2)))) -> (((op (e0) (e0)) = (e0))\/(((op (e1) (e0)) = (e0))\/(((op (e2) (e0)) = (e0))\/((op (e3) (e0)) = (e0))))) -> (~((op (e0) (e0)) = (e0))) -> (~((op (e1) (e0)) = (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 (e2) (e0)) = (op (e2) (e1)))) -> (~((op (e0) (e2)) = (op (e2) (e2)))) -> (~((op (e2) (e0)) = (op (e2) (e3)))) -> (~((op (e0) (e0)) = (op (e0) (e3)))) -> (((op (e0) (e2)) = (e0))\/(((op (e1) (e2)) = (e0))\/(((op (e2) (e2)) = (e0))\/((op (e3) (e2)) = (e0))))) -> (~((op (e1) (e0)) = (op (e1) (e2)))) -> (~((op (e2) (e2)) = (op (e2) (e3)))) -> (~((op (e3) (e1)) = (op (e3) (e2)))) -> (~((op (e0) (e1)) = (op (e1) (e1)))) -> (((op (e0) (e0)) = (e1))\/(((op (e0) (e1)) = (e1))\/(((op (e0) (e2)) = (e1))\/((op (e0) (e3)) = (e1))))) -> (~((op (e0) (e0)) = (e1))) -> (~((op (e0) (e1)) = (e1))) -> (~((op (e0) (e2)) = (e1))) -> (~((e0) = (e1))) -> False). % 18.87/19.06 do 0 intro. intros zenon_H74 zenon_H261 zenon_H13c zenon_H139 zenon_H252 zenon_H109 zenon_H264 zenon_H253 zenon_H17e zenon_H210 zenon_H235 zenon_H254 zenon_H12b zenon_H195 zenon_H18c zenon_H1fe zenon_H95 zenon_H165 zenon_H14f zenon_H160 zenon_H168 zenon_H9a zenon_H22 zenon_H13e zenon_H1d zenon_He2 zenon_He4 zenon_He7 zenon_H18f zenon_H1c4 zenon_H124 zenon_H4a zenon_H4f zenon_H52 zenon_H54 zenon_H262 zenon_H1a5 zenon_He8 zenon_H11f zenon_H263 zenon_H25e zenon_H1e0 zenon_H133 zenon_H25c zenon_H45 zenon_H25d zenon_H136 zenon_Hdb zenon_Haf zenon_H201 zenon_H191 zenon_H115 zenon_H153 zenon_Hd5 zenon_Hdf zenon_H71 zenon_H16f zenon_H1ac zenon_H17b zenon_H259 zenon_H1fa zenon_H6f zenon_H258 zenon_H257 zenon_H256 zenon_H106 zenon_H2b zenon_H1b1 zenon_H1cf zenon_H128 zenon_H1ef zenon_H10a zenon_H102 zenon_Hf3 zenon_Hc2 zenon_H130 zenon_H101 zenon_H173 zenon_H172 zenon_H149 zenon_H145 zenon_H7c zenon_H57 zenon_H110 zenon_H1c7 zenon_H62 zenon_H1d5 zenon_H24e zenon_H183 zenon_H2f zenon_H24b zenon_H3e zenon_H3f zenon_Hd8 zenon_H208 zenon_H67 zenon_H1f0 zenon_Ha8 zenon_H5b zenon_H189 zenon_H6a zenon_H24a zenon_H6d zenon_H1a4 zenon_H10e zenon_H22d zenon_H84 zenon_Ha4 zenon_H20d zenon_Ha1. % 18.87/19.06 apply (zenon_or_s _ _ zenon_H74); [ zenon_intro zenon_H42 | zenon_intro zenon_H77 ]. % 18.87/19.06 exact (zenon_H3f zenon_H42). % 18.87/19.06 apply (zenon_or_s _ _ zenon_H77); [ zenon_intro zenon_H49 | zenon_intro zenon_H78 ]. % 18.87/19.06 apply (zenon_L949_); trivial. % 18.87/19.06 apply (zenon_or_s _ _ zenon_H78); [ zenon_intro zenon_H48 | zenon_intro zenon_H1e ]. % 18.87/19.06 apply (zenon_or_s _ _ zenon_H3e); [ zenon_intro zenon_H42 | zenon_intro zenon_H41 ]. % 18.87/19.06 exact (zenon_H3f zenon_H42). % 18.87/19.06 apply (zenon_or_s _ _ zenon_H41); [ zenon_intro zenon_H27 | zenon_intro zenon_H43 ]. % 18.87/19.06 apply (zenon_or_s _ _ zenon_H22d); [ zenon_intro zenon_H7a | zenon_intro zenon_H22e ]. % 18.87/19.06 exact (zenon_H84 zenon_H7a). % 18.87/19.06 apply (zenon_or_s _ _ zenon_H22e); [ zenon_intro zenon_Ha0 | zenon_intro zenon_H22f ]. % 18.87/19.06 exact (zenon_Ha4 zenon_Ha0). % 18.87/19.06 apply (zenon_or_s _ _ zenon_H22f); [ zenon_intro zenon_H122 | zenon_intro zenon_Hc3 ]. % 18.87/19.06 exact (zenon_H20d zenon_H122). % 18.87/19.06 apply (zenon_or_s _ _ zenon_H183); [ zenon_intro zenon_H7b | zenon_intro zenon_H186 ]. % 18.87/19.06 apply (zenon_or_s _ _ zenon_H128); [ zenon_intro zenon_H9d | zenon_intro zenon_H129 ]. % 18.87/19.06 exact (zenon_H1ef zenon_H9d). % 18.87/19.06 apply (zenon_or_s _ _ zenon_H129); [ zenon_intro zenon_H10d | zenon_intro zenon_H12a ]. % 18.87/19.06 exact (zenon_H10a zenon_H10d). % 18.87/19.06 apply (zenon_or_s _ _ zenon_H12a); [ zenon_intro zenon_Hf0 | zenon_intro zenon_Hd6 ]. % 18.87/19.06 apply (zenon_L682_); trivial. % 18.87/19.06 exact (zenon_H24e zenon_Hd6). % 18.87/19.06 apply (zenon_or_s _ _ zenon_H186); [ zenon_intro zenon_H10f | zenon_intro zenon_H187 ]. % 18.87/19.06 apply (zenon_L67_); trivial. % 18.87/19.06 apply (zenon_or_s _ _ zenon_H187); [ zenon_intro zenon_H150 | zenon_intro zenon_Hcd ]. % 18.87/19.06 apply (zenon_L378_); trivial. % 18.87/19.06 apply (zenon_L82_); trivial. % 18.87/19.06 apply (zenon_or_s _ _ zenon_H43); [ zenon_intro zenon_H34 | zenon_intro zenon_H44 ]. % 18.87/19.06 apply (zenon_or_s _ _ zenon_H22d); [ zenon_intro zenon_H7a | zenon_intro zenon_H22e ]. % 18.87/19.06 exact (zenon_H84 zenon_H7a). % 18.87/19.06 apply (zenon_or_s _ _ zenon_H22e); [ zenon_intro zenon_Ha0 | zenon_intro zenon_H22f ]. % 18.87/19.06 exact (zenon_Ha4 zenon_Ha0). % 18.87/19.06 apply (zenon_or_s _ _ zenon_H22f); [ zenon_intro zenon_H122 | zenon_intro zenon_Hc3 ]. % 18.87/19.06 exact (zenon_H20d zenon_H122). % 18.87/19.06 apply (zenon_or_s _ _ zenon_H128); [ zenon_intro zenon_H9d | zenon_intro zenon_H129 ]. % 18.87/19.06 exact (zenon_H1ef zenon_H9d). % 18.87/19.06 apply (zenon_or_s _ _ zenon_H129); [ zenon_intro zenon_H10d | zenon_intro zenon_H12a ]. % 18.87/19.06 exact (zenon_H10a zenon_H10d). % 18.87/19.06 apply (zenon_or_s _ _ zenon_H12a); [ zenon_intro zenon_Hf0 | zenon_intro zenon_Hd6 ]. % 18.87/19.06 apply (zenon_L498_); trivial. % 18.87/19.06 exact (zenon_H24e zenon_Hd6). % 18.87/19.06 apply (zenon_L346_); trivial. % 18.87/19.06 apply (zenon_L947_); trivial. % 18.87/19.06 (* end of lemma zenon_L950_ *) % 18.87/19.06 assert (zenon_L951_ : ((~((op (e2) (e3)) = (e1)))\/((op (e2) (e1)) = (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) (e0)) = (e1))\/(((op (e2) (e1)) = (e1))\/(((op (e2) (e2)) = (e1))\/((op (e2) (e3)) = (e1))))) -> False). % 18.87/19.06 do 0 intro. intros zenon_H263 zenon_H13f zenon_H13e zenon_H1db zenon_H24f zenon_H198 zenon_H106. % 18.87/19.06 apply (zenon_or_s _ _ zenon_H263); [ zenon_intro zenon_H255 | zenon_intro zenon_Ha6 ]. % 18.87/19.06 apply (zenon_or_s _ _ zenon_H106); [ zenon_intro zenon_Hed | zenon_intro zenon_H107 ]. % 18.87/19.06 exact (zenon_H1db zenon_Hed). % 18.87/19.06 apply (zenon_or_s _ _ zenon_H107); [ zenon_intro zenon_Ha5 | zenon_intro zenon_H108 ]. % 18.87/19.06 exact (zenon_H24f zenon_Ha5). % 18.87/19.06 apply (zenon_or_s _ _ zenon_H108); [ zenon_intro zenon_Hf1 | zenon_intro zenon_Hf4 ]. % 18.87/19.06 exact (zenon_H198 zenon_Hf1). % 18.87/19.06 exact (zenon_H255 zenon_Hf4). % 18.87/19.06 apply (zenon_L95_); trivial. % 18.87/19.06 (* end of lemma zenon_L951_ *) % 18.87/19.06 assert (zenon_L952_ : (((op (e3) (e0)) = (e1))\/(((op (e3) (e1)) = (e1))\/(((op (e3) (e2)) = (e1))\/((op (e3) (e3)) = (e1))))) -> (~((op (e3) (e0)) = (e1))) -> (~((op (e3) (e1)) = (e1))) -> (~((op (e3) (e2)) = (e1))) -> (~((op (e3) (e3)) = (e1))) -> False). % 18.87/19.06 do 0 intro. intros zenon_He8 zenon_Had zenon_H250 zenon_H251 zenon_Hc7. % 18.87/19.06 apply (zenon_or_s _ _ zenon_He8); [ zenon_intro zenon_Hac | zenon_intro zenon_Heb ]. % 18.87/19.06 exact (zenon_Had zenon_Hac). % 18.87/19.06 apply (zenon_or_s _ _ zenon_Heb); [ zenon_intro zenon_Hae | zenon_intro zenon_Hec ]. % 18.87/19.06 exact (zenon_H250 zenon_Hae). % 18.87/19.06 apply (zenon_or_s _ _ zenon_Hec); [ zenon_intro zenon_Hba | zenon_intro zenon_Hc4 ]. % 18.87/19.06 exact (zenon_H251 zenon_Hba). % 18.87/19.06 exact (zenon_Hc7 zenon_Hc4). % 18.87/19.06 (* end of lemma zenon_L952_ *) % 18.87/19.06 assert (zenon_L953_ : ((~((op (e3) (e0)) = (e1)))\/((op (e3) (e1)) = (e0))) -> ((~((op (e3) (e2)) = (e1)))\/((op (e3) (e1)) = (e2))) -> ((op (e0) (e1)) = (e2)) -> (~((op (e0) (e1)) = (op (e3) (e1)))) -> (((op (e3) (e0)) = (e1))\/(((op (e3) (e1)) = (e1))\/(((op (e3) (e2)) = (e1))\/((op (e3) (e3)) = (e1))))) -> (~((op (e1) (e1)) = (op (e3) (e1)))) -> ((op (e1) (e1)) = (e3)) -> ((~((op (e3) (e3)) = (e1)))\/((op (e3) (e1)) = (e3))) -> (~((op (e2) (e1)) = (op (e3) (e1)))) -> ((op (e2) (e1)) = (e1)) -> ((~((op (e3) (e1)) = (e1)))\/((op (e3) (e1)) = (e1))) -> False). % 18.87/19.06 do 0 intro. intros zenon_H254 zenon_H252 zenon_H10f zenon_H210 zenon_He8 zenon_H160 zenon_H13f zenon_H264 zenon_Haf zenon_Ha5 zenon_H261. % 18.87/19.06 apply (zenon_or_s _ _ zenon_H254); [ zenon_intro zenon_Had | zenon_intro zenon_H1b1 ]. % 18.87/19.06 apply (zenon_or_s _ _ zenon_H261); [ zenon_intro zenon_H250 | zenon_intro zenon_Hae ]. % 18.87/19.06 apply (zenon_or_s _ _ zenon_H252); [ zenon_intro zenon_H251 | zenon_intro zenon_H14d ]. % 18.87/19.06 apply (zenon_or_s _ _ zenon_H264); [ zenon_intro zenon_Hc7 | zenon_intro zenon_H161 ]. % 18.87/19.06 apply (zenon_L952_); trivial. % 18.87/19.06 apply (zenon_L110_); trivial. % 18.87/19.06 apply (zenon_L389_); trivial. % 18.87/19.06 apply (zenon_L42_); trivial. % 18.87/19.06 apply (zenon_L580_); trivial. % 18.87/19.06 (* end of lemma zenon_L953_ *) % 18.87/19.06 assert (zenon_L954_ : ((~((op (e2) (e1)) = (e1)))\/((op (e2) (e1)) = (e1))) -> ((~((op (e3) (e1)) = (e1)))\/((op (e3) (e1)) = (e1))) -> (~((op (e2) (e1)) = (op (e3) (e1)))) -> ((~((op (e3) (e3)) = (e1)))\/((op (e3) (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) (e1)) = (op (e3) (e1)))) -> ((~((op (e3) (e2)) = (e1)))\/((op (e3) (e1)) = (e2))) -> ((~((op (e3) (e0)) = (e1)))\/((op (e3) (e1)) = (e0))) -> ((~((op (e2) (e3)) = (e1)))\/((op (e2) (e1)) = (e3))) -> ((op (e1) (e1)) = (e3)) -> (~((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 (e0) (e1)) = (op (e2) (e1)))) -> ((op (e0) (e1)) = (e2)) -> ((~((op (e2) (e2)) = (e1)))\/((op (e2) (e1)) = (e2))) -> False). % 18.87/19.06 do 0 intro. intros zenon_H262 zenon_H261 zenon_Haf zenon_H264 zenon_H160 zenon_He8 zenon_H210 zenon_H252 zenon_H254 zenon_H263 zenon_H13f zenon_H13e zenon_H1db zenon_H106 zenon_H17e zenon_H10f zenon_H253. % 18.87/19.06 apply (zenon_or_s _ _ zenon_H262); [ zenon_intro zenon_H24f | zenon_intro zenon_Ha5 ]. % 18.87/19.06 apply (zenon_or_s _ _ zenon_H253); [ zenon_intro zenon_H198 | zenon_intro zenon_H1ca ]. % 18.87/19.06 apply (zenon_L951_); trivial. % 18.87/19.06 apply (zenon_L191_); trivial. % 18.87/19.06 apply (zenon_L953_); trivial. % 18.87/19.06 (* end of lemma zenon_L954_ *) % 18.87/19.06 assert (zenon_L955_ : (((op (e2) (e2)) = (e0))\/(((op (e2) (e2)) = (e1))\/(((op (e2) (e2)) = (e2))\/((op (e2) (e2)) = (e3))))) -> (~((op (e2) (e1)) = (op (e2) (e2)))) -> ((op (e2) (e1)) = (e0)) -> (~((op (e2) (e2)) = (e1))) -> (~((op (e2) (e2)) = (e2))) -> (~((op (e2) (e2)) = (op (e3) (e2)))) -> ((op (e3) (e2)) = (e3)) -> False). % 18.87/19.06 do 0 intro. intros zenon_H1c4 zenon_H24b zenon_H36 zenon_H198 zenon_H173 zenon_H18f zenon_H163. % 18.87/19.06 apply (zenon_or_s _ _ zenon_H1c4); [ zenon_intro zenon_H2c | zenon_intro zenon_H1c5 ]. % 18.87/19.06 apply (zenon_L645_); trivial. % 18.87/19.06 apply (zenon_or_s _ _ zenon_H1c5); [ zenon_intro zenon_Hf1 | zenon_intro zenon_H1c6 ]. % 18.87/19.06 exact (zenon_H198 zenon_Hf1). % 18.87/19.06 apply (zenon_or_s _ _ zenon_H1c6); [ zenon_intro zenon_H176 | zenon_intro zenon_Haa ]. % 18.87/19.06 exact (zenon_H173 zenon_H176). % 18.87/19.06 apply (zenon_L180_); trivial. % 18.87/19.06 (* end of lemma zenon_L955_ *) % 18.87/19.06 assert (zenon_L956_ : (((op (e2) (e0)) = (e1))\/(((op (e2) (e1)) = (e1))\/(((op (e2) (e2)) = (e1))\/((op (e2) (e3)) = (e1))))) -> (~((op (e1) (e0)) = (op (e2) (e0)))) -> ((op (e1) (e0)) = (e1)) -> (~((op (e2) (e1)) = (e1))) -> (~((op (e2) (e2)) = (e1))) -> (~((op (e2) (e3)) = (e1))) -> False). % 18.87/19.06 do 0 intro. intros zenon_H106 zenon_H201 zenon_H9d zenon_H24f zenon_H198 zenon_H255. % 18.87/19.06 apply (zenon_or_s _ _ zenon_H106); [ zenon_intro zenon_Hed | zenon_intro zenon_H107 ]. % 18.87/19.06 apply (zenon_L413_); trivial. % 18.87/19.06 apply (zenon_or_s _ _ zenon_H107); [ zenon_intro zenon_Ha5 | zenon_intro zenon_H108 ]. % 18.87/19.06 exact (zenon_H24f zenon_Ha5). % 18.87/19.06 apply (zenon_or_s _ _ zenon_H108); [ zenon_intro zenon_Hf1 | zenon_intro zenon_Hf4 ]. % 18.87/19.06 exact (zenon_H198 zenon_Hf1). % 18.87/19.06 exact (zenon_H255 zenon_Hf4). % 18.87/19.06 (* end of lemma zenon_L956_ *) % 18.87/19.06 assert (zenon_L957_ : ((~((op (e2) (e2)) = (e1)))\/((op (e2) (e1)) = (e2))) -> (~((op (e0) (e1)) = (op (e2) (e1)))) -> (((op (e1) (e0)) = (e1))\/(((op (e1) (e1)) = (e1))\/(((op (e1) (e2)) = (e1))\/((op (e1) (e3)) = (e1))))) -> (~((op (e1) (e3)) = (e1))) -> (~((op (e1) (e2)) = (e1))) -> (~((op (e1) (e1)) = (e1))) -> (~((op (e1) (e0)) = (op (e2) (e0)))) -> (~((op (e2) (e1)) = (e1))) -> (((op (e2) (e0)) = (e1))\/(((op (e2) (e1)) = (e1))\/(((op (e2) (e2)) = (e1))\/((op (e2) (e3)) = (e1))))) -> ((op (e1) (e1)) = (e0)) -> ((op (e0) (e1)) = (e2)) -> ((~((op (e2) (e3)) = (e1)))\/((op (e2) (e1)) = (e3))) -> False). % 18.87/19.06 do 0 intro. intros zenon_H253 zenon_H17e zenon_H128 zenon_H24e zenon_H24d zenon_H10a zenon_H201 zenon_H24f zenon_H106 zenon_H29 zenon_H10f zenon_H263. % 18.87/19.06 apply (zenon_or_s _ _ zenon_H253); [ zenon_intro zenon_H198 | zenon_intro zenon_H1ca ]. % 18.87/19.06 apply (zenon_or_s _ _ zenon_H263); [ zenon_intro zenon_H255 | zenon_intro zenon_Ha6 ]. % 18.87/19.06 apply (zenon_or_s _ _ zenon_H128); [ zenon_intro zenon_H9d | zenon_intro zenon_H129 ]. % 18.87/19.06 apply (zenon_L956_); trivial. % 18.87/19.06 apply (zenon_or_s _ _ zenon_H129); [ zenon_intro zenon_H10d | zenon_intro zenon_H12a ]. % 18.87/19.06 exact (zenon_H10a zenon_H10d). % 18.87/19.06 apply (zenon_or_s _ _ zenon_H12a); [ zenon_intro zenon_Hf0 | zenon_intro zenon_Hd6 ]. % 18.87/19.06 exact (zenon_H24d zenon_Hf0). % 18.87/19.06 exact (zenon_H24e zenon_Hd6). % 18.87/19.06 apply (zenon_L371_); trivial. % 18.87/19.06 apply (zenon_L191_); trivial. % 18.87/19.06 (* end of lemma zenon_L957_ *) % 18.87/19.06 assert (zenon_L958_ : (((op (e0) (e2)) = (e0))\/(((op (e1) (e2)) = (e0))\/(((op (e2) (e2)) = (e0))\/((op (e3) (e2)) = (e0))))) -> (~((e0) = (e1))) -> (~((op (e1) (e1)) = (op (e1) (e2)))) -> ((op (e1) (e1)) = (e0)) -> ((op (e2) (e0)) = (e0)) -> (~((op (e2) (e0)) = (op (e2) (e2)))) -> (((op (e0) (e2)) = (e3))\/(((op (e1) (e2)) = (e3))\/(((op (e2) (e2)) = (e3))\/((op (e3) (e2)) = (e3))))) -> (~((e1) = (e3))) -> (~((e2) = (e3))) -> ((op (e1) (e2)) = (e2)) -> ((op (e0) (e2)) = (e1)) -> (~((op (e3) (e1)) = (op (e3) (e2)))) -> ((op (e3) (e1)) = (e3)) -> False). % 18.87/19.06 do 0 intro. intros zenon_H6a zenon_Ha1 zenon_H4f zenon_H29 zenon_H34 zenon_H52 zenon_H1a6 zenon_H95 zenon_H12b zenon_H113 zenon_H122 zenon_H1a4 zenon_H161. % 18.87/19.06 apply (zenon_or_s _ _ zenon_H6a); [ zenon_intro zenon_H48 | zenon_intro zenon_H6b ]. % 18.87/19.06 apply (zenon_L355_); trivial. % 18.87/19.06 apply (zenon_or_s _ _ zenon_H6b); [ zenon_intro zenon_H2a | zenon_intro zenon_H6c ]. % 18.87/19.06 apply (zenon_L10_); trivial. % 18.87/19.06 apply (zenon_or_s _ _ zenon_H6c); [ zenon_intro zenon_H2c | zenon_intro zenon_H61 ]. % 18.87/19.06 apply (zenon_L11_); trivial. % 18.87/19.06 apply (zenon_L433_); trivial. % 18.87/19.06 (* end of lemma zenon_L958_ *) % 18.87/19.06 assert (zenon_L959_ : (((op (e1) (e0)) = (e2))\/(((op (e1) (e1)) = (e2))\/(((op (e1) (e2)) = (e2))\/((op (e1) (e3)) = (e2))))) -> (~((e1) = (e2))) -> ((op (e1) (e0)) = (e1)) -> (~((op (e0) (e1)) = (op (e1) (e1)))) -> ((op (e3) (e1)) = (e3)) -> (~((op (e3) (e1)) = (op (e3) (e2)))) -> ((op (e0) (e2)) = (e1)) -> (~((e2) = (e3))) -> (~((e1) = (e3))) -> (((op (e0) (e2)) = (e3))\/(((op (e1) (e2)) = (e3))\/(((op (e2) (e2)) = (e3))\/((op (e3) (e2)) = (e3))))) -> (~((op (e2) (e0)) = (op (e2) (e2)))) -> ((op (e1) (e1)) = (e0)) -> (~((op (e1) (e1)) = (op (e1) (e2)))) -> (~((e0) = (e1))) -> (((op (e0) (e2)) = (e0))\/(((op (e1) (e2)) = (e0))\/(((op (e2) (e2)) = (e0))\/((op (e3) (e2)) = (e0))))) -> (((op (e2) (e0)) = (e2))\/(((op (e2) (e1)) = (e2))\/(((op (e2) (e2)) = (e2))\/((op (e2) (e3)) = (e2))))) -> (~((e0) = (e2))) -> ((op (e2) (e0)) = (e0)) -> ((op (e0) (e1)) = (e2)) -> (~((op (e0) (e1)) = (op (e2) (e1)))) -> (~((op (e2) (e2)) = (e2))) -> (~((op (e1) (e3)) = (op (e2) (e3)))) -> False). % 18.87/19.06 do 0 intro. intros zenon_H18c zenon_H7c zenon_H9d zenon_H10e zenon_H161 zenon_H1a4 zenon_H122 zenon_H12b zenon_H95 zenon_H1a6 zenon_H52 zenon_H29 zenon_H4f zenon_Ha1 zenon_H6a zenon_H1d5 zenon_H149 zenon_H34 zenon_H10f zenon_H17e zenon_H173 zenon_Hdb. % 18.87/19.06 apply (zenon_or_s _ _ zenon_H18c); [ zenon_intro zenon_H86 | zenon_intro zenon_H18d ]. % 18.87/19.06 apply (zenon_L123_); trivial. % 18.87/19.06 apply (zenon_or_s _ _ zenon_H18d); [ zenon_intro zenon_H110 | zenon_intro zenon_H18e ]. % 18.87/19.06 apply (zenon_L67_); trivial. % 18.87/19.06 apply (zenon_or_s _ _ zenon_H18e); [ zenon_intro zenon_H113 | zenon_intro zenon_Hd7 ]. % 18.87/19.06 apply (zenon_L958_); trivial. % 18.87/19.06 apply (zenon_L458_); trivial. % 18.87/19.06 (* end of lemma zenon_L959_ *) % 18.87/19.06 assert (zenon_L960_ : (((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))) -> (~((op (e1) (e2)) = (e1))) -> (~((op (e1) (e3)) = (e1))) -> False). % 18.87/19.06 do 0 intro. intros zenon_H128 zenon_H95 zenon_H9e zenon_H10a zenon_H24d zenon_H24e. % 18.87/19.06 apply (zenon_or_s _ _ zenon_H128); [ zenon_intro zenon_H9d | zenon_intro zenon_H129 ]. % 18.87/19.06 apply (zenon_L37_); trivial. % 18.87/19.06 apply (zenon_or_s _ _ zenon_H129); [ zenon_intro zenon_H10d | zenon_intro zenon_H12a ]. % 18.87/19.06 exact (zenon_H10a zenon_H10d). % 18.87/19.06 apply (zenon_or_s _ _ zenon_H12a); [ zenon_intro zenon_Hf0 | zenon_intro zenon_Hd6 ]. % 18.87/19.06 exact (zenon_H24d zenon_Hf0). % 18.87/19.06 exact (zenon_H24e zenon_Hd6). % 18.87/19.06 (* end of lemma zenon_L960_ *) % 18.87/19.06 assert (zenon_L961_ : (((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) (e1)) = (op (e1) (e3)))) -> ((op (e1) (e1)) = (e0)) -> (~((op (e2) (e1)) = (op (e2) (e3)))) -> ((op (e2) (e1)) = (e0)) -> ((op (e3) (e0)) = (e0)) -> (~((op (e3) (e0)) = (op (e3) (e3)))) -> False). % 18.87/19.06 do 0 intro. intros zenon_H67 zenon_H208 zenon_H48 zenon_H57 zenon_H29 zenon_H1c7 zenon_H36 zenon_H44 zenon_H71. % 18.87/19.06 apply (zenon_or_s _ _ zenon_H67); [ zenon_intro zenon_H1e | zenon_intro zenon_H68 ]. % 18.87/19.06 apply (zenon_L336_); trivial. % 18.87/19.06 apply (zenon_or_s _ _ zenon_H68); [ zenon_intro zenon_H1f | zenon_intro zenon_H69 ]. % 18.87/19.06 apply (zenon_L13_); trivial. % 18.87/19.06 apply (zenon_or_s _ _ zenon_H69); [ zenon_intro zenon_H37 | zenon_intro zenon_H60 ]. % 18.87/19.06 apply (zenon_L640_); trivial. % 18.87/19.06 apply (zenon_L21_); trivial. % 18.87/19.06 (* end of lemma zenon_L961_ *) % 18.87/19.06 assert (zenon_L962_ : (((op (e0) (e0)) = (e0))\/(((op (e1) (e0)) = (e0))\/(((op (e2) (e0)) = (e0))\/((op (e3) (e0)) = (e0))))) -> (~((op (e0) (e0)) = (e0))) -> (~((op (e1) (e0)) = (op (e1) (e1)))) -> (~((op (e2) (e0)) = (op (e2) (e1)))) -> (((op (e0) (e3)) = (e0))\/(((op (e1) (e3)) = (e0))\/(((op (e2) (e3)) = (e0))\/((op (e3) (e3)) = (e0))))) -> (~((op (e0) (e2)) = (op (e0) (e3)))) -> ((op (e0) (e2)) = (e0)) -> (~((op (e1) (e1)) = (op (e1) (e3)))) -> ((op (e1) (e1)) = (e0)) -> (~((op (e2) (e1)) = (op (e2) (e3)))) -> ((op (e2) (e1)) = (e0)) -> (~((op (e3) (e0)) = (op (e3) (e3)))) -> False). % 18.87/19.06 do 0 intro. intros zenon_H3e zenon_H3f zenon_H45 zenon_H1f0 zenon_H67 zenon_H208 zenon_H48 zenon_H57 zenon_H29 zenon_H1c7 zenon_H36 zenon_H71. % 18.87/19.06 apply (zenon_or_s _ _ zenon_H3e); [ zenon_intro zenon_H42 | zenon_intro zenon_H41 ]. % 18.87/19.06 exact (zenon_H3f zenon_H42). % 18.87/19.06 apply (zenon_or_s _ _ zenon_H41); [ zenon_intro zenon_H27 | zenon_intro zenon_H43 ]. % 18.87/19.06 apply (zenon_L8_); trivial. % 18.87/19.06 apply (zenon_or_s _ _ zenon_H43); [ zenon_intro zenon_H34 | zenon_intro zenon_H44 ]. % 18.87/19.06 apply (zenon_L642_); trivial. % 18.87/19.06 apply (zenon_L961_); trivial. % 18.87/19.06 (* end of lemma zenon_L962_ *) % 18.87/19.06 assert (zenon_L963_ : (((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) (e1)) = (op (e1) (e2)))) -> ((op (e1) (e1)) = (e0)) -> (~((op (e2) (e1)) = (op (e2) (e2)))) -> ((op (e2) (e1)) = (e0)) -> (~((op (e3) (e0)) = (op (e3) (e2)))) -> ((op (e3) (e0)) = (e0)) -> False). % 18.87/19.06 do 0 intro. intros zenon_H6a zenon_H208 zenon_H1e zenon_H4f zenon_H29 zenon_H24b zenon_H36 zenon_H6f zenon_H44. % 18.87/19.06 apply (zenon_or_s _ _ zenon_H6a); [ zenon_intro zenon_H48 | zenon_intro zenon_H6b ]. % 18.87/19.06 apply (zenon_L336_); trivial. % 18.87/19.06 apply (zenon_or_s _ _ zenon_H6b); [ zenon_intro zenon_H2a | zenon_intro zenon_H6c ]. % 18.87/19.06 apply (zenon_L10_); trivial. % 18.87/19.06 apply (zenon_or_s _ _ zenon_H6c); [ zenon_intro zenon_H2c | zenon_intro zenon_H61 ]. % 18.87/19.06 apply (zenon_L645_); trivial. % 18.87/19.06 apply (zenon_L19_); trivial. % 18.87/19.06 (* end of lemma zenon_L963_ *) % 18.87/19.06 assert (zenon_L964_ : (((op (e0) (e0)) = (e0))\/(((op (e1) (e0)) = (e0))\/(((op (e2) (e0)) = (e0))\/((op (e3) (e0)) = (e0))))) -> (~((op (e0) (e0)) = (e0))) -> (~((op (e1) (e0)) = (op (e1) (e1)))) -> (~((op (e2) (e0)) = (op (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 (e1) (e1)) = (op (e1) (e2)))) -> ((op (e1) (e1)) = (e0)) -> (~((op (e2) (e1)) = (op (e2) (e2)))) -> ((op (e2) (e1)) = (e0)) -> (~((op (e3) (e0)) = (op (e3) (e2)))) -> False). % 18.87/19.06 do 0 intro. intros zenon_H3e zenon_H3f zenon_H45 zenon_H1f0 zenon_H6a zenon_H208 zenon_H1e zenon_H4f zenon_H29 zenon_H24b zenon_H36 zenon_H6f. % 18.87/19.06 apply (zenon_or_s _ _ zenon_H3e); [ zenon_intro zenon_H42 | zenon_intro zenon_H41 ]. % 18.87/19.06 exact (zenon_H3f zenon_H42). % 18.87/19.06 apply (zenon_or_s _ _ zenon_H41); [ zenon_intro zenon_H27 | zenon_intro zenon_H43 ]. % 18.87/19.06 apply (zenon_L8_); trivial. % 18.87/19.06 apply (zenon_or_s _ _ zenon_H43); [ zenon_intro zenon_H34 | zenon_intro zenon_H44 ]. % 18.87/19.06 apply (zenon_L642_); trivial. % 18.87/19.06 apply (zenon_L963_); trivial. % 18.87/19.06 (* end of lemma zenon_L964_ *) % 18.87/19.06 assert (zenon_L965_ : (((op (e0) (e0)) = (e0))\/(((op (e0) (e1)) = (e0))\/(((op (e0) (e2)) = (e0))\/((op (e0) (e3)) = (e0))))) -> (~((op (e0) (e1)) = (op (e2) (e1)))) -> (~((op (e3) (e0)) = (op (e3) (e3)))) -> (~((op (e2) (e1)) = (op (e2) (e3)))) -> (~((op (e1) (e1)) = (op (e1) (e3)))) -> (((op (e0) (e3)) = (e0))\/(((op (e1) (e3)) = (e0))\/(((op (e2) (e3)) = (e0))\/((op (e3) (e3)) = (e0))))) -> (((op (e0) (e0)) = (e0))\/(((op (e1) (e0)) = (e0))\/(((op (e2) (e0)) = (e0))\/((op (e3) (e0)) = (e0))))) -> (~((op (e0) (e0)) = (e0))) -> (~((op (e1) (e0)) = (op (e1) (e1)))) -> (~((op (e2) (e0)) = (op (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 (e1) (e1)) = (op (e1) (e2)))) -> ((op (e1) (e1)) = (e0)) -> (~((op (e2) (e1)) = (op (e2) (e2)))) -> ((op (e2) (e1)) = (e0)) -> (~((op (e3) (e0)) = (op (e3) (e2)))) -> False). % 18.87/19.06 do 0 intro. intros zenon_H74 zenon_H17e zenon_H71 zenon_H1c7 zenon_H57 zenon_H67 zenon_H3e zenon_H3f zenon_H45 zenon_H1f0 zenon_H6a zenon_H208 zenon_H4f zenon_H29 zenon_H24b zenon_H36 zenon_H6f. % 18.87/19.06 apply (zenon_or_s _ _ zenon_H74); [ zenon_intro zenon_H42 | zenon_intro zenon_H77 ]. % 18.87/19.06 exact (zenon_H3f zenon_H42). % 18.87/19.06 apply (zenon_or_s _ _ zenon_H77); [ zenon_intro zenon_H49 | zenon_intro zenon_H78 ]. % 18.87/19.06 apply (zenon_L128_); trivial. % 18.87/19.06 apply (zenon_or_s _ _ zenon_H78); [ zenon_intro zenon_H48 | zenon_intro zenon_H1e ]. % 18.87/19.06 apply (zenon_L962_); trivial. % 18.87/19.06 apply (zenon_L964_); trivial. % 18.87/19.06 (* end of lemma zenon_L965_ *) % 18.87/19.06 assert (zenon_L966_ : ((~((op (e2) (e0)) = (e1)))\/((op (e2) (e1)) = (e0))) -> (~((op (e0) (e0)) = (e0))) -> (((op (e0) (e0)) = (e0))\/(((op (e1) (e0)) = (e0))\/(((op (e2) (e0)) = (e0))\/((op (e3) (e0)) = (e0))))) -> (~((op (e0) (e2)) = (op (e0) (e3)))) -> (~((op (e1) (e1)) = (op (e1) (e3)))) -> (~((op (e2) (e1)) = (op (e2) (e3)))) -> (~((op (e3) (e0)) = (op (e3) (e3)))) -> (((op (e0) (e3)) = (e0))\/(((op (e1) (e3)) = (e0))\/(((op (e2) (e3)) = (e0))\/((op (e3) (e3)) = (e0))))) -> (~((op (e2) (e0)) = (op (e2) (e1)))) -> ((op (e1) (e1)) = (e0)) -> (~((op (e1) (e0)) = (op (e1) (e1)))) -> (~((op (e1) (e1)) = (op (e1) (e2)))) -> (~((op (e2) (e1)) = (op (e2) (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) (e0)) = (e0))\/(((op (e0) (e1)) = (e0))\/(((op (e0) (e2)) = (e0))\/((op (e0) (e3)) = (e0))))) -> ((~((op (e2) (e2)) = (e1)))\/((op (e2) (e1)) = (e2))) -> ((op (e0) (e1)) = (e2)) -> (~((op (e0) (e1)) = (op (e2) (e1)))) -> (((op (e2) (e0)) = (e1))\/(((op (e2) (e1)) = (e1))\/(((op (e2) (e2)) = (e1))\/((op (e2) (e3)) = (e1))))) -> (~((op (e1) (e1)) = (op (e2) (e1)))) -> ((op (e1) (e1)) = (e3)) -> ((~((op (e2) (e3)) = (e1)))\/((op (e2) (e1)) = (e3))) -> ((~((op (e3) (e0)) = (e1)))\/((op (e3) (e1)) = (e0))) -> ((~((op (e3) (e2)) = (e1)))\/((op (e3) (e1)) = (e2))) -> (~((op (e0) (e1)) = (op (e3) (e1)))) -> (((op (e3) (e0)) = (e1))\/(((op (e3) (e1)) = (e1))\/(((op (e3) (e2)) = (e1))\/((op (e3) (e3)) = (e1))))) -> (~((op (e1) (e1)) = (op (e3) (e1)))) -> ((~((op (e3) (e3)) = (e1)))\/((op (e3) (e1)) = (e3))) -> (~((op (e2) (e1)) = (op (e3) (e1)))) -> ((~((op (e3) (e1)) = (e1)))\/((op (e3) (e1)) = (e1))) -> ((~((op (e2) (e1)) = (e1)))\/((op (e2) (e1)) = (e1))) -> False). % 18.87/19.06 do 0 intro. intros zenon_H257 zenon_H3f zenon_H3e zenon_H208 zenon_H57 zenon_H1c7 zenon_H71 zenon_H67 zenon_H1f0 zenon_H29 zenon_H45 zenon_H4f zenon_H24b zenon_H6f zenon_H6a zenon_H74 zenon_H253 zenon_H10f zenon_H17e zenon_H106 zenon_H13e zenon_H13f zenon_H263 zenon_H254 zenon_H252 zenon_H210 zenon_He8 zenon_H160 zenon_H264 zenon_Haf zenon_H261 zenon_H262. % 18.87/19.06 apply (zenon_or_s _ _ zenon_H257); [ zenon_intro zenon_H1db | zenon_intro zenon_H36 ]. % 18.87/19.06 apply (zenon_L954_); trivial. % 18.87/19.06 apply (zenon_L965_); trivial. % 18.87/19.06 (* end of lemma zenon_L966_ *) % 18.87/19.06 assert (zenon_L967_ : (((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) (e3)) = (e1))) -> (~((op (e0) (e3)) = (op (e1) (e3)))) -> (((op (e0) (e3)) = (e0))\/(((op (e0) (e3)) = (e1))\/(((op (e0) (e3)) = (e2))\/((op (e0) (e3)) = (e3))))) -> (~((op (e1) (e3)) = (e1))) -> ((op (e3) (e3)) = (e2)) -> (~((op (e1) (e3)) = (op (e3) (e3)))) -> (~((op (e1) (e3)) = (op (e2) (e3)))) -> ((op (e2) (e3)) = (e3)) -> False). % 18.87/19.06 do 0 intro. intros zenon_Hdf zenon_He2 zenon_Hc2 zenon_H231 zenon_H1d zenon_He4 zenon_H24e zenon_Hf6 zenon_Hd5 zenon_Hdb zenon_Hdd. % 18.87/19.06 apply (zenon_or_s _ _ zenon_Hdf); [ zenon_intro zenon_H1f | zenon_intro zenon_He0 ]. % 18.87/19.06 apply (zenon_L722_); trivial. % 18.87/19.06 apply (zenon_or_s _ _ zenon_He0); [ zenon_intro zenon_Hd6 | zenon_intro zenon_He1 ]. % 18.87/19.06 exact (zenon_H24e zenon_Hd6). % 18.87/19.06 apply (zenon_or_s _ _ zenon_He1); [ zenon_intro zenon_Hd7 | zenon_intro zenon_Hdc ]. % 18.87/19.06 apply (zenon_L402_); trivial. % 18.87/19.06 apply (zenon_L52_); trivial. % 18.87/19.06 (* end of lemma zenon_L967_ *) % 18.87/19.06 assert (zenon_L968_ : (((op (e0) (e3)) = (e3))\/(((op (e1) (e3)) = (e3))\/(((op (e2) (e3)) = (e3))\/((op (e3) (e3)) = (e3))))) -> (~((op (e3) (e0)) = (op (e3) (e3)))) -> ((op (e3) (e0)) = (e0)) -> ((op (e2) (e2)) = (e0)) -> (~((op (e2) (e2)) = (op (e2) (e3)))) -> ((op (e1) (e1)) = (e0)) -> (~((op (e1) (e1)) = (op (e1) (e3)))) -> (~((e0) = (e3))) -> (((op (e0) (e3)) = (e0))\/(((op (e1) (e3)) = (e0))\/(((op (e2) (e3)) = (e0))\/((op (e3) (e3)) = (e0))))) -> (~((op (e2) (e3)) = (op (e3) (e3)))) -> ((op (e3) (e3)) = (e1)) -> ((op (e0) (e3)) = (e0)) -> (((op (e2) (e3)) = (e0))\/(((op (e2) (e3)) = (e1))\/(((op (e2) (e3)) = (e2))\/((op (e2) (e3)) = (e3))))) -> (~((op (e1) (e3)) = (op (e2) (e3)))) -> (~((op (e1) (e3)) = (op (e3) (e3)))) -> ((op (e3) (e3)) = (e2)) -> (~((op (e1) (e3)) = (e1))) -> (((op (e0) (e3)) = (e0))\/(((op (e0) (e3)) = (e1))\/(((op (e0) (e3)) = (e2))\/((op (e0) (e3)) = (e3))))) -> (~((op (e0) (e3)) = (op (e1) (e3)))) -> (~((op (e0) (e3)) = (e1))) -> (~((op (e0) (e3)) = (op (e3) (e3)))) -> (~((op (e0) (e3)) = (op (e2) (e3)))) -> (((op (e1) (e3)) = (e0))\/(((op (e1) (e3)) = (e1))\/(((op (e1) (e3)) = (e2))\/((op (e1) (e3)) = (e3))))) -> (~((op (e3) (e3)) = (e3))) -> False). % 18.87/19.06 do 0 intro. intros zenon_H136 zenon_H71 zenon_H44 zenon_H2c zenon_H6d zenon_H29 zenon_H57 zenon_H9a zenon_H67 zenon_Hf3 zenon_Hc4 zenon_H1e zenon_H11f zenon_Hdb zenon_Hd5 zenon_Hf6 zenon_H24e zenon_He4 zenon_H1d zenon_H231 zenon_Hc2 zenon_He2 zenon_Hdf zenon_H102. % 18.87/19.06 apply (zenon_or_s _ _ zenon_H136); [ zenon_intro zenon_He3 | zenon_intro zenon_H137 ]. % 18.87/19.06 apply (zenon_L744_); trivial. % 18.87/19.06 apply (zenon_or_s _ _ zenon_H137); [ zenon_intro zenon_Hdc | zenon_intro zenon_H138 ]. % 18.87/19.06 apply (zenon_L404_); trivial. % 18.87/19.06 apply (zenon_or_s _ _ zenon_H138); [ zenon_intro zenon_Hdd | zenon_intro zenon_H105 ]. % 18.87/19.06 apply (zenon_L967_); trivial. % 18.87/19.06 exact (zenon_H102 zenon_H105). % 18.87/19.06 (* end of lemma zenon_L968_ *) % 18.87/19.06 assert (zenon_L969_ : (((op (e3) (e0)) = (e1))\/(((op (e3) (e1)) = (e1))\/(((op (e3) (e2)) = (e1))\/((op (e3) (e3)) = (e1))))) -> (~((op (e3) (e0)) = (e1))) -> (~((op (e3) (e1)) = (e1))) -> (~((op (e3) (e2)) = (e1))) -> (((op (e0) (e3)) = (e2))\/(((op (e1) (e3)) = (e2))\/(((op (e2) (e3)) = (e2))\/((op (e3) (e3)) = (e2))))) -> (~((e0) = (e2))) -> (~((e2) = (e3))) -> ((op (e1) (e3)) = (e3)) -> (~((op (e2) (e0)) = (op (e2) (e2)))) -> ((op (e2) (e2)) = (e3)) -> (~((op (e2) (e0)) = (op (e2) (e3)))) -> (~((op (e2) (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 (e3) (e0)) = (op (e3) (e3)))) -> ((op (e3) (e0)) = (e0)) -> ((op (e2) (e2)) = (e0)) -> (~((op (e2) (e2)) = (op (e2) (e3)))) -> ((op (e1) (e1)) = (e0)) -> (~((op (e1) (e1)) = (op (e1) (e3)))) -> (~((e0) = (e3))) -> (((op (e0) (e3)) = (e0))\/(((op (e1) (e3)) = (e0))\/(((op (e2) (e3)) = (e0))\/((op (e3) (e3)) = (e0))))) -> (~((op (e2) (e3)) = (op (e3) (e3)))) -> ((op (e0) (e3)) = (e0)) -> (((op (e2) (e3)) = (e0))\/(((op (e2) (e3)) = (e1))\/(((op (e2) (e3)) = (e2))\/((op (e2) (e3)) = (e3))))) -> (~((op (e1) (e3)) = (op (e2) (e3)))) -> (~((op (e1) (e3)) = (op (e3) (e3)))) -> (~((op (e1) (e3)) = (e1))) -> (((op (e0) (e3)) = (e0))\/(((op (e0) (e3)) = (e1))\/(((op (e0) (e3)) = (e2))\/((op (e0) (e3)) = (e3))))) -> (~((op (e0) (e3)) = (op (e1) (e3)))) -> (~((op (e0) (e3)) = (e1))) -> (~((op (e0) (e3)) = (op (e3) (e3)))) -> (~((op (e0) (e3)) = (op (e2) (e3)))) -> (((op (e1) (e3)) = (e0))\/(((op (e1) (e3)) = (e1))\/(((op (e1) (e3)) = (e2))\/((op (e1) (e3)) = (e3))))) -> (~((op (e3) (e3)) = (e3))) -> False). % 18.95/19.07 do 0 intro. intros zenon_He8 zenon_Had zenon_H250 zenon_H251 zenon_H145 zenon_H149 zenon_H12b zenon_Hdc zenon_H52 zenon_Haa zenon_H5b zenon_H1db zenon_H259 zenon_H136 zenon_H71 zenon_H44 zenon_H2c zenon_H6d zenon_H29 zenon_H57 zenon_H9a zenon_H67 zenon_Hf3 zenon_H1e zenon_H11f zenon_Hdb zenon_Hd5 zenon_H24e zenon_He4 zenon_H1d zenon_H231 zenon_Hc2 zenon_He2 zenon_Hdf zenon_H102. % 18.95/19.07 apply (zenon_or_s _ _ zenon_He8); [ zenon_intro zenon_Hac | zenon_intro zenon_Heb ]. % 18.95/19.07 exact (zenon_Had zenon_Hac). % 18.95/19.07 apply (zenon_or_s _ _ zenon_Heb); [ zenon_intro zenon_Hae | zenon_intro zenon_Hec ]. % 18.95/19.07 exact (zenon_H250 zenon_Hae). % 18.95/19.07 apply (zenon_or_s _ _ zenon_Hec); [ zenon_intro zenon_Hba | zenon_intro zenon_Hc4 ]. % 18.95/19.07 exact (zenon_H251 zenon_Hba). % 18.95/19.07 apply (zenon_or_s _ _ zenon_H145); [ zenon_intro zenon_Hcd | zenon_intro zenon_H146 ]. % 18.95/19.07 apply (zenon_L428_); trivial. % 18.95/19.07 apply (zenon_or_s _ _ zenon_H146); [ zenon_intro zenon_Hd7 | zenon_intro zenon_H147 ]. % 18.95/19.07 apply (zenon_L266_); trivial. % 18.95/19.07 apply (zenon_or_s _ _ zenon_H147); [ zenon_intro zenon_H11d | zenon_intro zenon_Hf6 ]. % 18.95/19.07 apply (zenon_L932_); trivial. % 18.95/19.07 apply (zenon_L968_); trivial. % 18.95/19.07 (* end of lemma zenon_L969_ *) % 18.95/19.07 assert (zenon_L970_ : (((op (e1) (e0)) = (e3))\/(((op (e1) (e1)) = (e3))\/(((op (e1) (e2)) = (e3))\/((op (e1) (e3)) = (e3))))) -> (~((op (e1) (e1)) = (e1))) -> (((op (e1) (e0)) = (e1))\/(((op (e1) (e1)) = (e1))\/(((op (e1) (e2)) = (e1))\/((op (e1) (e3)) = (e1))))) -> ((~((op (e2) (e1)) = (e1)))\/((op (e2) (e1)) = (e1))) -> ((~((op (e3) (e1)) = (e1)))\/((op (e3) (e1)) = (e1))) -> (~((op (e2) (e1)) = (op (e3) (e1)))) -> ((~((op (e3) (e3)) = (e1)))\/((op (e3) (e1)) = (e3))) -> (~((op (e1) (e1)) = (op (e3) (e1)))) -> (~((op (e0) (e1)) = (op (e3) (e1)))) -> ((~((op (e3) (e2)) = (e1)))\/((op (e3) (e1)) = (e2))) -> ((~((op (e3) (e0)) = (e1)))\/((op (e3) (e1)) = (e0))) -> ((~((op (e2) (e3)) = (e1)))\/((op (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))))) -> ((op (e0) (e1)) = (e2)) -> ((~((op (e2) (e2)) = (e1)))\/((op (e2) (e1)) = (e2))) -> ((~((op (e2) (e0)) = (e1)))\/((op (e2) (e1)) = (e0))) -> ((op (e1) (e2)) = (e2)) -> (((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) (e1)) = (op (e2) (e2)))) -> (~((op (e1) (e1)) = (op (e1) (e2)))) -> (~((op (e0) (e2)) = (op (e0) (e3)))) -> (((op (e0) (e2)) = (e0))\/(((op (e1) (e2)) = (e0))\/(((op (e2) (e2)) = (e0))\/((op (e3) (e2)) = (e0))))) -> (~((op (e2) (e0)) = (op (e2) (e1)))) -> (~((op (e1) (e0)) = (op (e1) (e1)))) -> (~((op (e0) (e0)) = (e0))) -> (((op (e0) (e0)) = (e0))\/(((op (e1) (e0)) = (e0))\/(((op (e2) (e0)) = (e0))\/((op (e3) (e0)) = (e0))))) -> (~((op (e2) (e1)) = (op (e2) (e3)))) -> (~((op (e0) (e1)) = (op (e2) (e1)))) -> (((op (e0) (e0)) = (e0))\/(((op (e0) (e1)) = (e0))\/(((op (e0) (e2)) = (e0))\/((op (e0) (e3)) = (e0))))) -> ((op (e3) (e1)) = (e3)) -> (~((op (e3) (e1)) = (op (e3) (e2)))) -> (((op (e3) (e0)) = (e1))\/(((op (e3) (e1)) = (e1))\/(((op (e3) (e2)) = (e1))\/((op (e3) (e3)) = (e1))))) -> (~((op (e3) (e0)) = (e1))) -> (~((op (e3) (e1)) = (e1))) -> (~((op (e3) (e2)) = (e1))) -> (((op (e0) (e3)) = (e2))\/(((op (e1) (e3)) = (e2))\/(((op (e2) (e3)) = (e2))\/((op (e3) (e3)) = (e2))))) -> (~((e0) = (e2))) -> (~((e2) = (e3))) -> (~((op (e2) (e0)) = (op (e2) (e2)))) -> (~((op (e2) (e0)) = (op (e2) (e3)))) -> (~((op (e2) (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 (e3) (e0)) = (op (e3) (e3)))) -> ((op (e3) (e0)) = (e0)) -> (~((op (e2) (e2)) = (op (e2) (e3)))) -> ((op (e1) (e1)) = (e0)) -> (~((op (e1) (e1)) = (op (e1) (e3)))) -> (~((e0) = (e3))) -> (((op (e0) (e3)) = (e0))\/(((op (e1) (e3)) = (e0))\/(((op (e2) (e3)) = (e0))\/((op (e3) (e3)) = (e0))))) -> (~((op (e2) (e3)) = (op (e3) (e3)))) -> (((op (e2) (e3)) = (e0))\/(((op (e2) (e3)) = (e1))\/(((op (e2) (e3)) = (e2))\/((op (e2) (e3)) = (e3))))) -> (~((op (e1) (e3)) = (op (e2) (e3)))) -> (~((op (e1) (e3)) = (op (e3) (e3)))) -> (~((op (e1) (e3)) = (e1))) -> (((op (e0) (e3)) = (e0))\/(((op (e0) (e3)) = (e1))\/(((op (e0) (e3)) = (e2))\/((op (e0) (e3)) = (e3))))) -> (~((op (e0) (e3)) = (op (e1) (e3)))) -> (~((op (e0) (e3)) = (e1))) -> (~((op (e0) (e3)) = (op (e3) (e3)))) -> (((op (e1) (e3)) = (e0))\/(((op (e1) (e3)) = (e1))\/(((op (e1) (e3)) = (e2))\/((op (e1) (e3)) = (e3))))) -> (~((op (e3) (e3)) = (e3))) -> ((op (e0) (e2)) = (e1)) -> (((op (e0) (e2)) = (e1))\/(((op (e1) (e2)) = (e1))\/(((op (e2) (e2)) = (e1))\/((op (e3) (e2)) = (e1))))) -> (~((e1) = (e3))) -> (~((op (e1) (e2)) = (e1))) -> (~((op (e2) (e2)) = (e1))) -> (((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). % 18.95/19.07 do 0 intro. intros zenon_H16f zenon_H10a zenon_H128 zenon_H262 zenon_H261 zenon_Haf zenon_H264 zenon_H160 zenon_H210 zenon_H252 zenon_H254 zenon_H263 zenon_H13e zenon_H106 zenon_H10f zenon_H253 zenon_H257 zenon_H113 zenon_H2f zenon_H17b zenon_H6f zenon_H24b zenon_H4f zenon_H208 zenon_H6a zenon_H1f0 zenon_H45 zenon_H3f zenon_H3e zenon_H1c7 zenon_H17e zenon_H74 zenon_H161 zenon_H1a4 zenon_He8 zenon_Had zenon_H250 zenon_H251 zenon_H145 zenon_H149 zenon_H12b zenon_H52 zenon_H5b zenon_H1db zenon_H259 zenon_H136 zenon_H71 zenon_H44 zenon_H6d zenon_H29 zenon_H57 zenon_H9a zenon_H67 zenon_Hf3 zenon_H11f zenon_Hdb zenon_Hd5 zenon_H24e zenon_He4 zenon_H1d zenon_H231 zenon_Hc2 zenon_Hdf zenon_H102 zenon_H122 zenon_H139 zenon_H95 zenon_H24d zenon_H198 zenon_H1a6 zenon_He2 zenon_H1e. % 18.95/19.07 apply (zenon_or_s _ _ zenon_H16f); [ zenon_intro zenon_H9e | zenon_intro zenon_H170 ]. % 18.95/19.07 apply (zenon_L960_); trivial. % 18.95/19.07 apply (zenon_or_s _ _ zenon_H170); [ zenon_intro zenon_H13f | zenon_intro zenon_H171 ]. % 18.95/19.07 apply (zenon_L966_); trivial. % 18.95/19.07 apply (zenon_or_s _ _ zenon_H171); [ zenon_intro zenon_H16c | zenon_intro zenon_Hdc ]. % 18.95/19.07 apply (zenon_L116_); trivial. % 18.95/19.07 apply (zenon_or_s _ _ zenon_H2f); [ zenon_intro zenon_H34 | zenon_intro zenon_H33 ]. % 18.95/19.07 apply (zenon_L127_); trivial. % 18.95/19.07 apply (zenon_or_s _ _ zenon_H33); [ zenon_intro zenon_H36 | zenon_intro zenon_H35 ]. % 18.95/19.07 apply (zenon_L965_); trivial. % 18.95/19.07 apply (zenon_or_s _ _ zenon_H35); [ zenon_intro zenon_H2c | zenon_intro zenon_H37 ]. % 18.95/19.07 apply (zenon_or_s _ _ zenon_H1a6); [ zenon_intro zenon_Ha9 | zenon_intro zenon_H1aa ]. % 18.95/19.07 apply (zenon_L762_); trivial. % 18.95/19.07 apply (zenon_or_s _ _ zenon_H1aa); [ zenon_intro zenon_H16c | zenon_intro zenon_H1ab ]. % 18.95/19.07 apply (zenon_L603_); trivial. % 18.95/19.07 apply (zenon_or_s _ _ zenon_H1ab); [ zenon_intro zenon_Haa | zenon_intro zenon_H163 ]. % 18.95/19.07 apply (zenon_L969_); trivial. % 18.95/19.07 apply (zenon_L169_); trivial. % 18.95/19.07 apply (zenon_L367_); trivial. % 18.95/19.07 (* end of lemma zenon_L970_ *) % 18.95/19.07 assert (zenon_L971_ : (((op (e3) (e0)) = (e1))\/(((op (e3) (e1)) = (e1))\/(((op (e3) (e2)) = (e1))\/((op (e3) (e3)) = (e1))))) -> (~((op (e3) (e0)) = (e1))) -> (~((op (e3) (e1)) = (e1))) -> (~((op (e3) (e2)) = (e1))) -> ((op (e2) (e3)) = (e0)) -> ((op (e1) (e3)) = (e2)) -> False). % 18.95/19.07 do 0 intro. intros zenon_He8 zenon_Had zenon_H250 zenon_H251 zenon_H37 zenon_Hd7. % 18.95/19.07 apply (zenon_or_s _ _ zenon_He8); [ zenon_intro zenon_Hac | zenon_intro zenon_Heb ]. % 18.95/19.07 exact (zenon_Had zenon_Hac). % 18.95/19.07 apply (zenon_or_s _ _ zenon_Heb); [ zenon_intro zenon_Hae | zenon_intro zenon_Hec ]. % 18.95/19.07 exact (zenon_H250 zenon_Hae). % 18.95/19.07 apply (zenon_or_s _ _ zenon_Hec); [ zenon_intro zenon_Hba | zenon_intro zenon_Hc4 ]. % 18.95/19.07 exact (zenon_H251 zenon_Hba). % 18.95/19.07 apply (zenon_L72_); trivial. % 18.95/19.07 (* end of lemma zenon_L971_ *) % 18.95/19.07 assert (zenon_L972_ : ((~((op (e1) (e2)) = (e1)))\/((op (e1) (e1)) = (e2))) -> ((~((op (e2) (e2)) = (e1)))\/((op (e2) (e1)) = (e2))) -> (~((op (e0) (e1)) = (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)) = (op (e2) (e0)))) -> (((op (e2) (e0)) = (e1))\/(((op (e2) (e1)) = (e1))\/(((op (e2) (e2)) = (e1))\/((op (e2) (e3)) = (e1))))) -> ((op (e1) (e1)) = (e0)) -> ((op (e0) (e1)) = (e2)) -> ((~((op (e2) (e3)) = (e1)))\/((op (e2) (e1)) = (e3))) -> (~((op (e0) (e0)) = (e0))) -> ((~((op (e3) (e2)) = (e1)))\/((op (e3) (e1)) = (e2))) -> (~((op (e0) (e1)) = (op (e3) (e1)))) -> (~((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 (e0) (e3)))) -> (~((op (e1) (e1)) = (op (e1) (e3)))) -> (~((op (e2) (e0)) = (op (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) (e0)) = (op (e2) (e2)))) -> (~((op (e1) (e1)) = (op (e1) (e2)))) -> (~((op (e0) (e1)) = (op (e0) (e2)))) -> (((op (e0) (e0)) = (e1))\/(((op (e0) (e1)) = (e1))\/(((op (e0) (e2)) = (e1))\/((op (e0) (e3)) = (e1))))) -> (~((op (e0) (e3)) = (e1))) -> (~((e0) = (e1))) -> (~((op (e0) (e1)) = (e1))) -> (~((e1) = (e3))) -> (~((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 (e3) (e0)) = (op (e3) (e2)))) -> (~((e0) = (e3))) -> (~((op (e2) (e2)) = (op (e2) (e3)))) -> (~((op (e3) (e0)) = (op (e3) (e3)))) -> (~((op (e2) (e0)) = (op (e3) (e0)))) -> (((op (e0) (e0)) = (e3))\/(((op (e0) (e1)) = (e3))\/(((op (e0) (e2)) = (e3))\/((op (e0) (e3)) = (e3))))) -> (((op (e0) (e0)) = (e0))\/(((op (e1) (e0)) = (e0))\/(((op (e2) (e0)) = (e0))\/((op (e3) (e0)) = (e0))))) -> (~((op (e0) (e0)) = (e1))) -> (((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 (e2) (e3)) = (e0))\/(((op (e2) (e3)) = (e1))\/(((op (e2) (e3)) = (e2))\/((op (e2) (e3)) = (e3))))) -> (~((op (e2) (e3)) = (op (e3) (e3)))) -> (~((op (e0) (e3)) = (op (e2) (e3)))) -> (((op (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))))) -> (~((op (e3) (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) (e1)) = (e1)))\/((op (e2) (e1)) = (e1))) -> ((~((op (e3) (e1)) = (e1)))\/((op (e3) (e1)) = (e1))) -> (~((op (e2) (e1)) = (op (e3) (e1)))) -> ((~((op (e3) (e3)) = (e1)))\/((op (e3) (e1)) = (e3))) -> (~((op (e1) (e1)) = (op (e3) (e1)))) -> ((~((op (e3) (e0)) = (e1)))\/((op (e3) (e1)) = (e0))) -> (~((op (e1) (e1)) = (op (e2) (e1)))) -> (((op (e0) (e0)) = (e0))\/(((op (e0) (e1)) = (e0))\/(((op (e0) (e2)) = (e0))\/((op (e0) (e3)) = (e0))))) -> (~((op (e2) (e1)) = (op (e2) (e2)))) -> (~((op (e2) (e0)) = (op (e2) (e1)))) -> (~((op (e2) (e1)) = (op (e2) (e3)))) -> (~((op (e0) (e2)) = (op (e0) (e3)))) -> ((~((op (e2) (e0)) = (e1)))\/((op (e2) (e1)) = (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) (e1)) = (op (e3) (e2)))) -> (((op (e0) (e2)) = (e3))\/(((op (e1) (e2)) = (e3))\/(((op (e2) (e2)) = (e3))\/((op (e3) (e2)) = (e3))))) -> (((op (e2) (e0)) = (e2))\/(((op (e2) (e1)) = (e2))\/(((op (e2) (e2)) = (e2))\/((op (e2) (e3)) = (e2))))) -> (~((op (e1) (e3)) = (op (e2) (e3)))) -> (~((op (e2) (e2)) = (e2))) -> (~((e0) = (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)) = (op (e3) (e1)))) -> (~((op (e3) (e1)) = (op (e3) (e3)))) -> ((~((op (e1) (e3)) = (e1)))\/((op (e1) (e1)) = (e3))) -> False). % 18.95/19.07 do 0 intro. intros zenon_H256 zenon_H253 zenon_H17e zenon_H128 zenon_H10a zenon_H201 zenon_H106 zenon_H29 zenon_H10f zenon_H263 zenon_H3f zenon_H252 zenon_H210 zenon_H45 zenon_H6a zenon_H54 zenon_H57 zenon_H5b zenon_H62 zenon_H67 zenon_H52 zenon_H4f zenon_H4a zenon_H22d zenon_H231 zenon_Ha1 zenon_Ha4 zenon_H95 zenon_H12b zenon_H139 zenon_H2f zenon_H6f zenon_H9a zenon_H6d zenon_H71 zenon_H17b zenon_H168 zenon_H3e zenon_H84 zenon_H16f zenon_H145 zenon_H11f zenon_Hf3 zenon_He2 zenon_Hdf zenon_Hd5 zenon_H1d zenon_Hc2 zenon_He4 zenon_H102 zenon_H136 zenon_H259 zenon_H262 zenon_H261 zenon_Haf zenon_H264 zenon_H160 zenon_H254 zenon_H13e zenon_H74 zenon_H24b zenon_H1f0 zenon_H1c7 zenon_H208 zenon_H257 zenon_H235 zenon_H7c zenon_H10e zenon_H1a4 zenon_H1a6 zenon_H1d5 zenon_Hdb zenon_H173 zenon_H149 zenon_H18c zenon_He8 zenon_H1cf zenon_H130 zenon_H258. % 18.95/19.07 apply (zenon_or_s _ _ zenon_H256); [ zenon_intro zenon_H24d | zenon_intro zenon_H110 ]. % 18.95/19.07 apply (zenon_or_s _ _ zenon_H258); [ zenon_intro zenon_H24e | zenon_intro zenon_H13f ]. % 18.95/19.07 apply (zenon_or_s _ _ zenon_H257); [ zenon_intro zenon_H1db | zenon_intro zenon_H36 ]. % 18.95/19.07 apply (zenon_or_s _ _ zenon_H262); [ zenon_intro zenon_H24f | zenon_intro zenon_Ha5 ]. % 18.95/19.07 apply (zenon_L957_); trivial. % 18.95/19.07 apply (zenon_or_s _ _ zenon_H253); [ zenon_intro zenon_H198 | zenon_intro zenon_H1ca ]. % 18.95/19.07 apply (zenon_or_s _ _ zenon_H254); [ zenon_intro zenon_Had | zenon_intro zenon_H1b1 ]. % 18.95/19.07 apply (zenon_or_s _ _ zenon_H261); [ zenon_intro zenon_H250 | zenon_intro zenon_Hae ]. % 18.95/19.07 apply (zenon_or_s _ _ zenon_H252); [ zenon_intro zenon_H251 | zenon_intro zenon_H14d ]. % 18.95/19.07 apply (zenon_or_s _ _ zenon_H264); [ zenon_intro zenon_Hc7 | zenon_intro zenon_H161 ]. % 18.95/19.07 apply (zenon_L952_); trivial. % 18.95/19.07 apply (zenon_or_s _ _ zenon_H74); [ zenon_intro zenon_H42 | zenon_intro zenon_H77 ]. % 18.95/19.07 exact (zenon_H3f zenon_H42). % 18.95/19.07 apply (zenon_or_s _ _ zenon_H77); [ zenon_intro zenon_H49 | zenon_intro zenon_H78 ]. % 18.95/19.07 apply (zenon_L763_); trivial. % 18.95/19.07 apply (zenon_or_s _ _ zenon_H78); [ zenon_intro zenon_H48 | zenon_intro zenon_H1e ]. % 18.95/19.07 apply (zenon_L946_); trivial. % 18.95/19.07 apply (zenon_or_s _ _ zenon_H3e); [ zenon_intro zenon_H42 | zenon_intro zenon_H41 ]. % 18.95/19.07 exact (zenon_H3f zenon_H42). % 18.95/19.07 apply (zenon_or_s _ _ zenon_H41); [ zenon_intro zenon_H27 | zenon_intro zenon_H43 ]. % 18.95/19.07 apply (zenon_L8_); trivial. % 18.95/19.07 apply (zenon_or_s _ _ zenon_H43); [ zenon_intro zenon_H34 | zenon_intro zenon_H44 ]. % 18.95/19.07 apply (zenon_or_s _ _ zenon_H22d); [ zenon_intro zenon_H7a | zenon_intro zenon_H22e ]. % 18.95/19.07 exact (zenon_H84 zenon_H7a). % 18.95/19.07 apply (zenon_or_s _ _ zenon_H22e); [ zenon_intro zenon_Ha0 | zenon_intro zenon_H22f ]. % 18.95/19.07 exact (zenon_Ha4 zenon_Ha0). % 18.95/19.07 apply (zenon_or_s _ _ zenon_H22f); [ zenon_intro zenon_H122 | zenon_intro zenon_Hc3 ]. % 18.95/19.07 apply (zenon_or_s _ _ zenon_H235); [ zenon_intro zenon_H7a | zenon_intro zenon_H236 ]. % 18.95/19.07 exact (zenon_H84 zenon_H7a). % 18.95/19.07 apply (zenon_or_s _ _ zenon_H236); [ zenon_intro zenon_H9d | zenon_intro zenon_H237 ]. % 18.95/19.07 apply (zenon_L959_); trivial. % 18.95/19.07 apply (zenon_or_s _ _ zenon_H237); [ zenon_intro zenon_Hed | zenon_intro zenon_Hac ]. % 18.95/19.07 exact (zenon_H1db zenon_Hed). % 18.95/19.07 exact (zenon_Had zenon_Hac). % 18.95/19.07 exact (zenon_H231 zenon_Hc3). % 18.95/19.07 apply (zenon_or_s _ _ zenon_H22d); [ zenon_intro zenon_H7a | zenon_intro zenon_H22e ]. % 18.95/19.07 exact (zenon_H84 zenon_H7a). % 18.95/19.07 apply (zenon_or_s _ _ zenon_H22e); [ zenon_intro zenon_Ha0 | zenon_intro zenon_H22f ]. % 18.95/19.07 exact (zenon_Ha4 zenon_Ha0). % 18.95/19.07 apply (zenon_or_s _ _ zenon_H22f); [ zenon_intro zenon_H122 | zenon_intro zenon_Hc3 ]. % 18.95/19.07 apply (zenon_or_s _ _ zenon_H235); [ zenon_intro zenon_H7a | zenon_intro zenon_H236 ]. % 18.95/19.07 exact (zenon_H84 zenon_H7a). % 18.95/19.07 apply (zenon_or_s _ _ zenon_H236); [ zenon_intro zenon_H9d | zenon_intro zenon_H237 ]. % 18.95/19.07 apply (zenon_or_s _ _ zenon_H18c); [ zenon_intro zenon_H86 | zenon_intro zenon_H18d ]. % 18.95/19.07 apply (zenon_L123_); trivial. % 18.95/19.07 apply (zenon_or_s _ _ zenon_H18d); [ zenon_intro zenon_H110 | zenon_intro zenon_H18e ]. % 18.95/19.07 apply (zenon_L354_); trivial. % 18.95/19.07 apply (zenon_or_s _ _ zenon_H18e); [ zenon_intro zenon_H113 | zenon_intro zenon_Hd7 ]. % 18.95/19.07 apply (zenon_L970_); trivial. % 18.95/19.07 apply (zenon_or_s _ _ zenon_H16f); [ zenon_intro zenon_H9e | zenon_intro zenon_H170 ]. % 18.95/19.07 apply (zenon_L37_); trivial. % 18.95/19.07 apply (zenon_or_s _ _ zenon_H170); [ zenon_intro zenon_H13f | zenon_intro zenon_H171 ]. % 18.95/19.07 apply (zenon_L110_); trivial. % 18.95/19.07 apply (zenon_or_s _ _ zenon_H171); [ zenon_intro zenon_H16c | zenon_intro zenon_Hdc ]. % 18.95/19.07 apply (zenon_or_s _ _ zenon_H2f); [ zenon_intro zenon_H34 | zenon_intro zenon_H33 ]. % 18.95/19.07 apply (zenon_L458_); trivial. % 18.95/19.07 apply (zenon_or_s _ _ zenon_H33); [ zenon_intro zenon_H36 | zenon_intro zenon_H35 ]. % 18.95/19.07 apply (zenon_L963_); trivial. % 18.95/19.07 apply (zenon_or_s _ _ zenon_H35); [ zenon_intro zenon_H2c | zenon_intro zenon_H37 ]. % 18.95/19.07 apply (zenon_L603_); trivial. % 18.95/19.07 apply (zenon_L971_); trivial. % 18.95/19.07 apply (zenon_L266_); trivial. % 18.95/19.07 apply (zenon_or_s _ _ zenon_H237); [ zenon_intro zenon_Hed | zenon_intro zenon_Hac ]. % 18.95/19.07 exact (zenon_H1db zenon_Hed). % 18.95/19.07 exact (zenon_Had zenon_Hac). % 18.95/19.07 exact (zenon_H231 zenon_Hc3). % 18.95/19.07 apply (zenon_L389_); trivial. % 18.95/19.07 apply (zenon_L42_); trivial. % 18.95/19.07 apply (zenon_L349_); trivial. % 18.95/19.07 apply (zenon_L191_); trivial. % 18.95/19.07 apply (zenon_L965_); trivial. % 18.95/19.07 apply (zenon_L966_); trivial. % 18.95/19.07 apply (zenon_L354_); trivial. % 18.95/19.07 (* end of lemma zenon_L972_ *) % 18.95/19.07 assert (zenon_L973_ : (((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) (e3)) = (e1))) -> (~((op (e3) (e2)) = (op (e3) (e3)))) -> ((op (e3) (e2)) = (e2)) -> (~((op (e3) (e3)) = (e3))) -> False). % 18.95/19.07 do 0 intro. intros zenon_H101 zenon_H71 zenon_H44 zenon_Hc7 zenon_H62 zenon_H151 zenon_H102. % 18.95/19.07 apply (zenon_or_s _ _ zenon_H101); [ zenon_intro zenon_H60 | zenon_intro zenon_H103 ]. % 18.95/19.07 apply (zenon_L21_); trivial. % 18.95/19.07 apply (zenon_or_s _ _ zenon_H103); [ zenon_intro zenon_Hc4 | zenon_intro zenon_H104 ]. % 18.95/19.07 exact (zenon_Hc7 zenon_Hc4). % 18.95/19.07 apply (zenon_or_s _ _ zenon_H104); [ zenon_intro zenon_Hf6 | zenon_intro zenon_H105 ]. % 18.95/19.07 apply (zenon_L119_); trivial. % 18.95/19.07 exact (zenon_H102 zenon_H105). % 18.95/19.07 (* end of lemma zenon_L973_ *) % 18.95/19.07 assert (zenon_L974_ : (((op (e0) (e2)) = (e2))\/(((op (e1) (e2)) = (e2))\/(((op (e2) (e2)) = (e2))\/((op (e3) (e2)) = (e2))))) -> (~((e1) = (e2))) -> ((op (e0) (e2)) = (e1)) -> (~((e0) = (e2))) -> ((op (e1) (e2)) = (e0)) -> (~((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) (e3)) = (e1))) -> (~((op (e3) (e2)) = (op (e3) (e3)))) -> (~((op (e3) (e3)) = (e3))) -> False). % 18.95/19.07 do 0 intro. intros zenon_H172 zenon_H7c zenon_H122 zenon_H149 zenon_H2a zenon_H173 zenon_H101 zenon_H71 zenon_H44 zenon_Hc7 zenon_H62 zenon_H102. % 18.95/19.07 apply (zenon_or_s _ _ zenon_H172); [ zenon_intro zenon_H150 | zenon_intro zenon_H174 ]. % 18.95/19.07 apply (zenon_L328_); trivial. % 18.95/19.07 apply (zenon_or_s _ _ zenon_H174); [ zenon_intro zenon_H113 | zenon_intro zenon_H175 ]. % 18.95/19.07 apply (zenon_L542_); trivial. % 18.95/19.07 apply (zenon_or_s _ _ zenon_H175); [ zenon_intro zenon_H176 | zenon_intro zenon_H151 ]. % 18.95/19.07 exact (zenon_H173 zenon_H176). % 18.95/19.07 apply (zenon_L973_); trivial. % 18.95/19.07 (* end of lemma zenon_L974_ *) % 18.95/19.07 assert (zenon_L975_ : ((~((op (e0) (e3)) = (e1)))\/((op (e0) (e1)) = (e3))) -> (((op (e1) (e0)) = (e1))\/(((op (e1) (e1)) = (e1))\/(((op (e1) (e2)) = (e1))\/((op (e1) (e3)) = (e1))))) -> (~((op (e1) (e1)) = (e1))) -> (~((op (e0) (e0)) = (e0))) -> (((op (e0) (e0)) = (e1))\/(((op (e0) (e1)) = (e1))\/(((op (e0) (e2)) = (e1))\/((op (e0) (e3)) = (e1))))) -> (~((e0) = (e1))) -> (~((op (e0) (e1)) = (e1))) -> (~((op (e0) (e0)) = (e1))) -> (((op (e1) (e0)) = (e0))\/(((op (e1) (e1)) = (e0))\/(((op (e1) (e2)) = (e0))\/((op (e1) (e3)) = (e0))))) -> (((op (e3) (e3)) = (e0))\/(((op (e3) (e3)) = (e1))\/(((op (e3) (e3)) = (e2))\/((op (e3) (e3)) = (e3))))) -> (((op (e0) (e2)) = (e2))\/(((op (e1) (e2)) = (e2))\/(((op (e2) (e2)) = (e2))\/((op (e3) (e2)) = (e2))))) -> ((~((op (e1) (e3)) = (e1)))\/((op (e1) (e1)) = (e3))) -> (~((op (e3) (e1)) = (op (e3) (e3)))) -> (~((op (e3) (e0)) = (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 (e3) (e1)) = (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 (e2) (e0)) = (e1)))\/((op (e2) (e1)) = (e0))) -> (~((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)) = (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 (e3) (e3)) = (e3))) -> (((op (e0) (e3)) = (e0))\/(((op (e0) (e3)) = (e1))\/(((op (e0) (e3)) = (e2))\/((op (e0) (e3)) = (e3))))) -> (~((op (e0) (e3)) = (op (e3) (e3)))) -> (~((op (e0) (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 (e0) (e3)) = (op (e2) (e3)))) -> (~((op (e2) (e3)) = (op (e3) (e3)))) -> (((op (e2) (e3)) = (e0))\/(((op (e2) (e3)) = (e1))\/(((op (e2) (e3)) = (e2))\/((op (e2) (e3)) = (e3))))) -> (((op (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) (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 (e2) (e0)) = (op (e3) (e0)))) -> (~((op (e3) (e0)) = (op (e3) (e3)))) -> (~((op (e2) (e2)) = (op (e2) (e3)))) -> (~((e0) = (e3))) -> (~((op (e3) (e0)) = (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 (e0) (e1)) = (op (e0) (e2)))) -> (~((op (e1) (e1)) = (op (e1) (e2)))) -> (~((op (e2) (e0)) = (op (e2) (e2)))) -> (((op (e0) (e3)) = (e0))\/(((op (e1) (e3)) = (e0))\/(((op (e2) (e3)) = (e0))\/((op (e3) (e3)) = (e0))))) -> (~((op (e3) (e2)) = (op (e3) (e3)))) -> (~((op (e2) (e0)) = (op (e2) (e3)))) -> (~((op (e1) (e1)) = (op (e1) (e3)))) -> (~((op (e0) (e1)) = (op (e0) (e3)))) -> (~((op (e1) (e0)) = (op (e1) (e1)))) -> (~((op (e1) (e0)) = (op (e2) (e0)))) -> ((~((op (e1) (e2)) = (e1)))\/((op (e1) (e1)) = (e2))) -> (~((op (e1) (e0)) = (op (e3) (e0)))) -> (~((op (e2) (e0)) = (op (e2) (e1)))) -> (~((e0) = (e2))) -> (~((e2) = (e3))) -> (((op (e0) (e2)) = (e0))\/(((op (e1) (e2)) = (e0))\/(((op (e2) (e2)) = (e0))\/((op (e3) (e2)) = (e0))))) -> (~((e1) = (e3))) -> (((op (e2) (e2)) = (e0))\/(((op (e2) (e2)) = (e1))\/(((op (e2) (e2)) = (e2))\/((op (e2) (e2)) = (e3))))) -> (~((op (e2) (e2)) = (op (e3) (e2)))) -> (~((op (e2) (e2)) = (e2))) -> (((op (e0) (e2)) = (e3))\/(((op (e1) (e2)) = (e3))\/(((op (e2) (e2)) = (e3))\/((op (e3) (e2)) = (e3))))) -> (~((op (e2) (e1)) = (op (e2) (e2)))) -> (~((op (e0) (e2)) = (op (e0) (e3)))) -> (~((e1) = (e2))) -> (((op (e1) (e0)) = (e2))\/(((op (e1) (e1)) = (e2))\/(((op (e1) (e2)) = (e2))\/((op (e1) (e3)) = (e2))))) -> ((~((op (e2) (e2)) = (e1)))\/((op (e2) (e1)) = (e2))) -> ((op (e0) (e1)) = (e2)) -> (~((op (e0) (e1)) = (op (e2) (e1)))) -> (((op (e2) (e0)) = (e1))\/(((op (e2) (e1)) = (e1))\/(((op (e2) (e2)) = (e1))\/((op (e2) (e3)) = (e1))))) -> (~((op (e1) (e1)) = (op (e2) (e1)))) -> ((~((op (e2) (e3)) = (e1)))\/((op (e2) (e1)) = (e3))) -> ((~((op (e3) (e0)) = (e1)))\/((op (e3) (e1)) = (e0))) -> ((~((op (e3) (e2)) = (e1)))\/((op (e3) (e1)) = (e2))) -> (~((op (e0) (e1)) = (op (e3) (e1)))) -> (((op (e3) (e0)) = (e1))\/(((op (e3) (e1)) = (e1))\/(((op (e3) (e2)) = (e1))\/((op (e3) (e3)) = (e1))))) -> (~((op (e1) (e1)) = (op (e3) (e1)))) -> ((~((op (e3) (e3)) = (e1)))\/((op (e3) (e1)) = (e3))) -> (~((op (e2) (e1)) = (op (e3) (e1)))) -> ((~((op (e3) (e1)) = (e1)))\/((op (e3) (e1)) = (e1))) -> ((~((op (e2) (e1)) = (e1)))\/((op (e2) (e1)) = (e1))) -> ((~((op (e1) (e0)) = (e1)))\/((op (e1) (e1)) = (e0))) -> False). % 18.95/19.07 do 0 intro. intros zenon_H25c zenon_H128 zenon_H10a zenon_H3f zenon_H22d zenon_Ha1 zenon_Ha4 zenon_H84 zenon_H22 zenon_H101 zenon_H172 zenon_H258 zenon_H130 zenon_H1cf zenon_Hdb zenon_H1d5 zenon_H1a4 zenon_H10e zenon_H235 zenon_H257 zenon_H1c7 zenon_H74 zenon_H259 zenon_H136 zenon_H102 zenon_He4 zenon_Hc2 zenon_H1d zenon_Hd5 zenon_Hdf zenon_He2 zenon_Hf3 zenon_H11f zenon_H145 zenon_H16f zenon_H3e zenon_H168 zenon_H17b zenon_H71 zenon_H6d zenon_H9a zenon_H6f zenon_H2f zenon_H139 zenon_H4a zenon_H4f zenon_H52 zenon_H67 zenon_H62 zenon_H5b zenon_H57 zenon_H54 zenon_H45 zenon_H201 zenon_H256 zenon_H1fa zenon_H1f0 zenon_H149 zenon_H12b zenon_H6a zenon_H95 zenon_H1c4 zenon_H18f zenon_H173 zenon_H1a6 zenon_H24b zenon_H208 zenon_H7c zenon_H18c zenon_H253 zenon_H10f zenon_H17e zenon_H106 zenon_H13e zenon_H263 zenon_H254 zenon_H252 zenon_H210 zenon_He8 zenon_H160 zenon_H264 zenon_Haf zenon_H261 zenon_H262 zenon_H25d. % 18.95/19.07 apply (zenon_or_s _ _ zenon_H25c); [ zenon_intro zenon_H231 | zenon_intro zenon_H99 ]. % 18.95/19.07 apply (zenon_or_s _ _ zenon_H25d); [ zenon_intro zenon_H1ef | zenon_intro zenon_H29 ]. % 18.95/19.07 apply (zenon_or_s _ _ zenon_H256); [ zenon_intro zenon_H24d | zenon_intro zenon_H110 ]. % 18.95/19.07 apply (zenon_or_s _ _ zenon_H258); [ zenon_intro zenon_H24e | zenon_intro zenon_H13f ]. % 18.95/19.07 apply (zenon_L713_); trivial. % 18.95/19.07 apply (zenon_or_s _ _ zenon_H257); [ zenon_intro zenon_H1db | zenon_intro zenon_H36 ]. % 18.95/19.07 apply (zenon_L954_); trivial. % 18.95/19.07 apply (zenon_or_s _ _ zenon_H253); [ zenon_intro zenon_H198 | zenon_intro zenon_H1ca ]. % 18.95/19.07 apply (zenon_or_s _ _ zenon_H264); [ zenon_intro zenon_Hc7 | zenon_intro zenon_H161 ]. % 18.95/19.07 apply (zenon_or_s _ _ zenon_H74); [ zenon_intro zenon_H42 | zenon_intro zenon_H77 ]. % 18.95/19.07 exact (zenon_H3f zenon_H42). % 18.95/19.07 apply (zenon_or_s _ _ zenon_H77); [ zenon_intro zenon_H49 | zenon_intro zenon_H78 ]. % 18.95/19.07 apply (zenon_L128_); trivial. % 18.95/19.07 apply (zenon_or_s _ _ zenon_H78); [ zenon_intro zenon_H48 | zenon_intro zenon_H1e ]. % 18.95/19.07 apply (zenon_L946_); trivial. % 18.95/19.07 apply (zenon_or_s _ _ zenon_H3e); [ zenon_intro zenon_H42 | zenon_intro zenon_H41 ]. % 18.95/19.07 exact (zenon_H3f zenon_H42). % 18.95/19.07 apply (zenon_or_s _ _ zenon_H41); [ zenon_intro zenon_H27 | zenon_intro zenon_H43 ]. % 18.95/19.07 apply (zenon_or_s _ _ zenon_H22d); [ zenon_intro zenon_H7a | zenon_intro zenon_H22e ]. % 18.95/19.07 exact (zenon_H84 zenon_H7a). % 18.95/19.07 apply (zenon_or_s _ _ zenon_H22e); [ zenon_intro zenon_Ha0 | zenon_intro zenon_H22f ]. % 18.95/19.07 exact (zenon_Ha4 zenon_Ha0). % 18.95/19.07 apply (zenon_or_s _ _ zenon_H22f); [ zenon_intro zenon_H122 | zenon_intro zenon_Hc3 ]. % 18.95/19.07 apply (zenon_or_s _ _ zenon_H128); [ zenon_intro zenon_H9d | zenon_intro zenon_H129 ]. % 18.95/19.07 exact (zenon_H1ef zenon_H9d). % 18.95/19.07 apply (zenon_or_s _ _ zenon_H129); [ zenon_intro zenon_H10d | zenon_intro zenon_H12a ]. % 18.95/19.07 exact (zenon_H10a zenon_H10d). % 18.95/19.07 apply (zenon_or_s _ _ zenon_H12a); [ zenon_intro zenon_Hf0 | zenon_intro zenon_Hd6 ]. % 18.95/19.07 exact (zenon_H24d zenon_Hf0). % 18.95/19.07 apply (zenon_or_s _ _ zenon_H18c); [ zenon_intro zenon_H86 | zenon_intro zenon_H18d ]. % 18.95/19.07 apply (zenon_L257_); trivial. % 18.95/19.07 apply (zenon_or_s _ _ zenon_H18d); [ zenon_intro zenon_H110 | zenon_intro zenon_H18e ]. % 18.95/19.07 apply (zenon_L166_); trivial. % 18.95/19.07 apply (zenon_or_s _ _ zenon_H18e); [ zenon_intro zenon_H113 | zenon_intro zenon_Hd7 ]. % 18.95/19.07 apply (zenon_or_s _ _ zenon_H6a); [ zenon_intro zenon_H48 | zenon_intro zenon_H6b ]. % 18.95/19.07 apply (zenon_L336_); trivial. % 18.95/19.07 apply (zenon_or_s _ _ zenon_H6b); [ zenon_intro zenon_H2a | zenon_intro zenon_H6c ]. % 18.95/19.07 apply (zenon_L542_); trivial. % 18.95/19.07 apply (zenon_or_s _ _ zenon_H6c); [ zenon_intro zenon_H2c | zenon_intro zenon_H61 ]. % 18.95/19.07 apply (zenon_L645_); trivial. % 18.95/19.07 apply (zenon_or_s _ _ zenon_H1a6); [ zenon_intro zenon_Ha9 | zenon_intro zenon_H1aa ]. % 18.95/19.07 apply (zenon_L77_); trivial. % 18.95/19.07 apply (zenon_or_s _ _ zenon_H1aa); [ zenon_intro zenon_H16c | zenon_intro zenon_H1ab ]. % 18.95/19.07 apply (zenon_L116_); trivial. % 18.95/19.07 apply (zenon_or_s _ _ zenon_H1ab); [ zenon_intro zenon_Haa | zenon_intro zenon_H163 ]. % 18.95/19.07 apply (zenon_L432_); trivial. % 18.95/19.07 apply (zenon_L955_); trivial. % 18.95/19.07 apply (zenon_L101_); trivial. % 18.95/19.07 exact (zenon_H231 zenon_Hc3). % 18.95/19.07 apply (zenon_or_s _ _ zenon_H43); [ zenon_intro zenon_H34 | zenon_intro zenon_H44 ]. % 18.95/19.07 apply (zenon_L642_); trivial. % 18.95/19.07 apply (zenon_or_s _ _ zenon_H22d); [ zenon_intro zenon_H7a | zenon_intro zenon_H22e ]. % 18.95/19.07 exact (zenon_H84 zenon_H7a). % 18.95/19.07 apply (zenon_or_s _ _ zenon_H22e); [ zenon_intro zenon_Ha0 | zenon_intro zenon_H22f ]. % 18.95/19.07 exact (zenon_Ha4 zenon_Ha0). % 18.95/19.07 apply (zenon_or_s _ _ zenon_H22f); [ zenon_intro zenon_H122 | zenon_intro zenon_Hc3 ]. % 18.95/19.07 apply (zenon_or_s _ _ zenon_H22); [ zenon_intro zenon_H27 | zenon_intro zenon_H26 ]. % 18.95/19.07 apply (zenon_L312_); trivial. % 18.95/19.07 apply (zenon_or_s _ _ zenon_H26); [ zenon_intro zenon_H29 | zenon_intro zenon_H28 ]. % 18.95/19.07 apply (zenon_L972_); trivial. % 18.95/19.07 apply (zenon_or_s _ _ zenon_H28); [ zenon_intro zenon_H2a | zenon_intro zenon_H1f ]. % 18.95/19.07 apply (zenon_L974_); trivial. % 18.95/19.07 apply (zenon_L1_); trivial. % 18.95/19.07 exact (zenon_H231 zenon_Hc3). % 18.95/19.07 apply (zenon_L110_); trivial. % 18.95/19.07 apply (zenon_L191_); trivial. % 18.95/19.07 apply (zenon_L67_); trivial. % 18.95/19.07 apply (zenon_L972_); trivial. % 18.95/19.07 apply (zenon_L175_); trivial. % 18.95/19.07 (* end of lemma zenon_L975_ *) % 18.95/19.07 assert (zenon_L976_ : (((op (e0) (e0)) = (e1))\/(((op (e0) (e1)) = (e1))\/(((op (e0) (e2)) = (e1))\/((op (e0) (e3)) = (e1))))) -> (~((op (e0) (e0)) = (e1))) -> (~((op (e0) (e1)) = (e1))) -> (~((op (e0) (e2)) = (e1))) -> (((op (e3) (e0)) = (e1))\/(((op (e3) (e1)) = (e1))\/(((op (e3) (e2)) = (e1))\/((op (e3) (e3)) = (e1))))) -> (~((op (e3) (e0)) = (e1))) -> (~((op (e3) (e1)) = (e1))) -> (~((op (e3) (e2)) = (e1))) -> (~((op (e0) (e3)) = (op (e3) (e3)))) -> False). % 18.95/19.07 do 0 intro. intros zenon_H22d zenon_H84 zenon_Ha4 zenon_H20d zenon_He8 zenon_Had zenon_H250 zenon_H251 zenon_Hc2. % 18.95/19.07 apply (zenon_or_s _ _ zenon_H22d); [ zenon_intro zenon_H7a | zenon_intro zenon_H22e ]. % 18.95/19.07 exact (zenon_H84 zenon_H7a). % 18.95/19.07 apply (zenon_or_s _ _ zenon_H22e); [ zenon_intro zenon_Ha0 | zenon_intro zenon_H22f ]. % 18.95/19.07 exact (zenon_Ha4 zenon_Ha0). % 18.95/19.07 apply (zenon_or_s _ _ zenon_H22f); [ zenon_intro zenon_H122 | zenon_intro zenon_Hc3 ]. % 18.95/19.07 exact (zenon_H20d zenon_H122). % 18.95/19.07 apply (zenon_or_s _ _ zenon_He8); [ zenon_intro zenon_Hac | zenon_intro zenon_Heb ]. % 18.95/19.07 exact (zenon_Had zenon_Hac). % 18.95/19.07 apply (zenon_or_s _ _ zenon_Heb); [ zenon_intro zenon_Hae | zenon_intro zenon_Hec ]. % 18.95/19.07 exact (zenon_H250 zenon_Hae). % 18.95/19.07 apply (zenon_or_s _ _ zenon_Hec); [ zenon_intro zenon_Hba | zenon_intro zenon_Hc4 ]. % 18.95/19.07 exact (zenon_H251 zenon_Hba). % 18.95/19.07 apply (zenon_L46_); trivial. % 18.95/19.07 (* end of lemma zenon_L976_ *) % 18.95/19.07 assert (zenon_L977_ : ((~((op (e3) (e2)) = (e1)))\/((op (e3) (e1)) = (e2))) -> ((op (e2) (e1)) = (e2)) -> (~((op (e2) (e1)) = (op (e3) (e1)))) -> (~((op (e0) (e0)) = (e1))) -> (~((op (e0) (e1)) = (e1))) -> (~((op (e0) (e2)) = (e1))) -> (((op (e3) (e0)) = (e1))\/(((op (e3) (e1)) = (e1))\/(((op (e3) (e2)) = (e1))\/((op (e3) (e3)) = (e1))))) -> (~((op (e0) (e3)) = (op (e3) (e3)))) -> (~((op (e3) (e1)) = (e1))) -> (~((op (e3) (e0)) = (e1))) -> (((op (e0) (e0)) = (e1))\/(((op (e0) (e1)) = (e1))\/(((op (e0) (e2)) = (e1))\/((op (e0) (e3)) = (e1))))) -> False). % 18.95/19.07 do 0 intro. intros zenon_H252 zenon_H1ca zenon_Haf zenon_H84 zenon_Ha4 zenon_H20d zenon_He8 zenon_Hc2 zenon_H250 zenon_Had zenon_H22d. % 18.95/19.07 apply (zenon_or_s _ _ zenon_H252); [ zenon_intro zenon_H251 | zenon_intro zenon_H14d ]. % 18.95/19.07 apply (zenon_L976_); trivial. % 18.95/19.07 apply (zenon_L364_); trivial. % 18.95/19.07 (* end of lemma zenon_L977_ *) % 18.95/19.07 assert (zenon_L978_ : (((op (e0) (e0)) = (e1))\/(((op (e0) (e1)) = (e1))\/(((op (e0) (e2)) = (e1))\/((op (e0) (e3)) = (e1))))) -> (~((op (e0) (e0)) = (e1))) -> (~((op (e0) (e1)) = (e1))) -> (~((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)))) -> (~((op (e3) (e0)) = (op (e3) (e2)))) -> (~((op (e2) (e1)) = (op (e2) (e2)))) -> ((op (e1) (e1)) = (e0)) -> (~((op (e1) (e1)) = (op (e1) (e2)))) -> (~((op (e0) (e2)) = (op (e0) (e3)))) -> (((op (e0) (e2)) = (e0))\/(((op (e1) (e2)) = (e0))\/(((op (e2) (e2)) = (e0))\/((op (e3) (e2)) = (e0))))) -> (~((op (e2) (e0)) = (op (e2) (e1)))) -> (~((op (e1) (e0)) = (op (e1) (e1)))) -> (~((op (e0) (e0)) = (e0))) -> (((op (e0) (e0)) = (e0))\/(((op (e1) (e0)) = (e0))\/(((op (e2) (e0)) = (e0))\/((op (e3) (e0)) = (e0))))) -> (((op (e0) (e3)) = (e0))\/(((op (e1) (e3)) = (e0))\/(((op (e2) (e3)) = (e0))\/((op (e3) (e3)) = (e0))))) -> (~((op (e1) (e1)) = (op (e1) (e3)))) -> (~((op (e2) (e1)) = (op (e2) (e3)))) -> (~((op (e0) (e1)) = (op (e2) (e1)))) -> (((op (e0) (e0)) = (e0))\/(((op (e0) (e1)) = (e0))\/(((op (e0) (e2)) = (e0))\/((op (e0) (e3)) = (e0))))) -> ((op (e0) (e2)) = (e0)) -> (~((op (e0) (e2)) = (op (e2) (e2)))) -> (((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) (e2)) = (op (e3) (e3)))) -> (~((op (e3) (e3)) = (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))))) -> False). % 18.95/19.07 do 0 intro. intros zenon_H22d zenon_H84 zenon_Ha4 zenon_H20d zenon_H2f zenon_H17b zenon_H6f zenon_H24b zenon_H29 zenon_H4f zenon_H208 zenon_H6a zenon_H1f0 zenon_H45 zenon_H3f zenon_H3e zenon_H67 zenon_H57 zenon_H1c7 zenon_H17e zenon_H74 zenon_H48 zenon_Ha8 zenon_H153 zenon_H149 zenon_H7c zenon_Hae zenon_H102 zenon_H62 zenon_Hc7 zenon_H44 zenon_H71 zenon_H101. % 18.95/19.07 apply (zenon_or_s _ _ zenon_H22d); [ zenon_intro zenon_H7a | zenon_intro zenon_H22e ]. % 18.95/19.07 exact (zenon_H84 zenon_H7a). % 18.95/19.07 apply (zenon_or_s _ _ zenon_H22e); [ zenon_intro zenon_Ha0 | zenon_intro zenon_H22f ]. % 18.95/19.07 exact (zenon_Ha4 zenon_Ha0). % 18.95/19.07 apply (zenon_or_s _ _ zenon_H22f); [ zenon_intro zenon_H122 | zenon_intro zenon_Hc3 ]. % 18.95/19.07 exact (zenon_H20d zenon_H122). % 18.95/19.07 apply (zenon_or_s _ _ zenon_H2f); [ zenon_intro zenon_H34 | zenon_intro zenon_H33 ]. % 18.95/19.07 apply (zenon_L127_); trivial. % 18.95/19.07 apply (zenon_or_s _ _ zenon_H33); [ zenon_intro zenon_H36 | zenon_intro zenon_H35 ]. % 18.95/19.07 apply (zenon_L965_); trivial. % 18.95/19.07 apply (zenon_or_s _ _ zenon_H35); [ zenon_intro zenon_H2c | zenon_intro zenon_H37 ]. % 18.95/19.07 apply (zenon_L679_); trivial. % 18.95/19.07 apply (zenon_or_s _ _ zenon_H153); [ zenon_intro zenon_H148 | zenon_intro zenon_H154 ]. % 18.95/19.07 apply (zenon_L100_); trivial. % 18.95/19.07 apply (zenon_or_s _ _ zenon_H154); [ zenon_intro zenon_H14d | zenon_intro zenon_H155 ]. % 18.95/19.07 apply (zenon_L152_); trivial. % 18.95/19.07 apply (zenon_or_s _ _ zenon_H155); [ zenon_intro zenon_H151 | zenon_intro zenon_Hf6 ]. % 18.95/19.07 apply (zenon_L973_); trivial. % 18.95/19.07 apply (zenon_L387_); trivial. % 18.95/19.07 (* end of lemma zenon_L978_ *) % 18.95/19.07 assert (zenon_L979_ : (((op (e2) (e3)) = (e0))\/(((op (e2) (e3)) = (e1))\/(((op (e2) (e3)) = (e2))\/((op (e2) (e3)) = (e3))))) -> ((op (e3) (e3)) = (e0)) -> (~((op (e2) (e3)) = (op (e3) (e3)))) -> (~((op (e2) (e3)) = (e1))) -> ((op (e0) (e3)) = (e2)) -> (~((op (e0) (e3)) = (op (e2) (e3)))) -> (~((op (e1) (e3)) = (op (e2) (e3)))) -> ((op (e1) (e3)) = (e3)) -> False). % 18.95/19.07 do 0 intro. intros zenon_H11f zenon_H60 zenon_Hf3 zenon_H255 zenon_Hcd zenon_He2 zenon_Hdb zenon_Hdc. % 18.95/19.07 apply (zenon_or_s _ _ zenon_H11f); [ zenon_intro zenon_H37 | zenon_intro zenon_H120 ]. % 18.95/19.07 apply (zenon_L219_); trivial. % 18.95/19.07 apply (zenon_or_s _ _ zenon_H120); [ zenon_intro zenon_Hf4 | zenon_intro zenon_H121 ]. % 18.95/19.07 exact (zenon_H255 zenon_Hf4). % 18.95/19.07 apply (zenon_or_s _ _ zenon_H121); [ zenon_intro zenon_H11d | zenon_intro zenon_Hdd ]. % 18.95/19.07 apply (zenon_L234_); trivial. % 18.95/19.07 apply (zenon_L52_); trivial. % 18.95/19.07 (* end of lemma zenon_L979_ *) % 18.95/19.07 assert (zenon_L980_ : (((op (e2) (e3)) = (e0))\/(((op (e2) (e3)) = (e1))\/(((op (e2) (e3)) = (e2))\/((op (e2) (e3)) = (e3))))) -> ((op (e0) (e3)) = (e1)) -> (~((op (e2) (e3)) = (e1))) -> ((op (e3) (e3)) = (e2)) -> (~((op (e2) (e3)) = (op (e3) (e3)))) -> (~((op (e1) (e3)) = (op (e2) (e3)))) -> ((op (e1) (e3)) = (e3)) -> False). % 18.95/19.07 do 0 intro. intros zenon_H11f zenon_Hc3 zenon_H255 zenon_Hf6 zenon_Hf3 zenon_Hdb zenon_Hdc. % 18.96/19.07 apply (zenon_or_s _ _ zenon_H11f); [ zenon_intro zenon_H37 | zenon_intro zenon_H120 ]. % 18.96/19.07 apply (zenon_L387_); trivial. % 18.96/19.07 apply (zenon_or_s _ _ zenon_H120); [ zenon_intro zenon_Hf4 | zenon_intro zenon_H121 ]. % 18.96/19.07 exact (zenon_H255 zenon_Hf4). % 18.96/19.07 apply (zenon_or_s _ _ zenon_H121); [ zenon_intro zenon_H11d | zenon_intro zenon_Hdd ]. % 18.96/19.07 apply (zenon_L97_); trivial. % 18.96/19.07 apply (zenon_L52_); trivial. % 18.96/19.07 (* end of lemma zenon_L980_ *) % 18.96/19.07 assert (zenon_L981_ : (((op (e1) (e0)) = (e3))\/(((op (e1) (e1)) = (e3))\/(((op (e1) (e2)) = (e3))\/((op (e1) (e3)) = (e3))))) -> (~((e1) = (e3))) -> ((op (e1) (e0)) = (e1)) -> ((op (e0) (e1)) = (e3)) -> (~((op (e0) (e1)) = (op (e1) (e1)))) -> (~((op (e3) (e3)) = (e3))) -> (~((op (e3) (e2)) = (op (e3) (e3)))) -> ((op (e3) (e1)) = (e1)) -> (~((op (e3) (e1)) = (op (e3) (e3)))) -> ((op (e0) (e3)) = (e1)) -> (((op (e3) (e3)) = (e0))\/(((op (e3) (e3)) = (e1))\/(((op (e3) (e3)) = (e2))\/((op (e3) (e3)) = (e3))))) -> (~((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 (e1) (e3)) = (e2)) -> (~((e2) = (e3))) -> False). % 18.96/19.07 do 0 intro. intros zenon_H16f zenon_H95 zenon_H9d zenon_H99 zenon_H10e zenon_H102 zenon_H62 zenon_Hae zenon_H130 zenon_Hc3 zenon_H101 zenon_H173 zenon_H48 zenon_H149 zenon_H172 zenon_Hd7 zenon_H12b. % 18.96/19.07 apply (zenon_or_s _ _ zenon_H16f); [ zenon_intro zenon_H9e | zenon_intro zenon_H170 ]. % 18.96/19.07 apply (zenon_L37_); trivial. % 18.96/19.07 apply (zenon_or_s _ _ zenon_H170); [ zenon_intro zenon_H13f | zenon_intro zenon_H171 ]. % 18.96/19.07 apply (zenon_L108_); trivial. % 18.96/19.07 apply (zenon_or_s _ _ zenon_H171); [ zenon_intro zenon_H16c | zenon_intro zenon_Hdc ]. % 18.96/19.07 apply (zenon_L380_); trivial. % 18.96/19.07 apply (zenon_L266_); trivial. % 18.96/19.07 (* end of lemma zenon_L981_ *) % 18.96/19.07 assert (zenon_L982_ : (~((op (e2) (e0)) = (e1))) -> ((op (e1) (e1)) = (e0)) -> (((op (e0) (e0)) = (e0))\/(((op (e0) (e1)) = (e0))\/(((op (e0) (e2)) = (e0))\/((op (e0) (e3)) = (e0))))) -> (~((op (e2) (e1)) = (op (e2) (e2)))) -> (~((op (e0) (e2)) = (op (e0) (e3)))) -> ((op (e0) (e1)) = (e3)) -> (((op (e0) (e2)) = (e2))\/(((op (e1) (e2)) = (e2))\/(((op (e2) (e2)) = (e2))\/((op (e3) (e2)) = (e2))))) -> ((~((op (e3) (e1)) = (e1)))\/((op (e3) (e1)) = (e1))) -> (~((op (e0) (e0)) = (op (e0) (e2)))) -> (((op (e0) (e2)) = (e1))\/(((op (e1) (e2)) = (e1))\/(((op (e2) (e2)) = (e1))\/((op (e3) (e2)) = (e1))))) -> (~((e1) = (e2))) -> (((op (e0) (e1)) = (e1))\/(((op (e1) (e1)) = (e1))\/(((op (e2) (e1)) = (e1))\/((op (e3) (e1)) = (e1))))) -> ((~((op (e3) (e3)) = (e1)))\/((op (e3) (e1)) = (e3))) -> ((~((op (e2) (e2)) = (e1)))\/((op (e2) (e1)) = (e2))) -> (~((op (e0) (e1)) = (op (e2) (e1)))) -> (~((op (e0) (e1)) = (op (e3) (e1)))) -> (((op (e0) (e0)) = (e1))\/(((op (e1) (e0)) = (e1))\/(((op (e2) (e0)) = (e1))\/((op (e3) (e0)) = (e1))))) -> ((~((op (e3) (e0)) = (e1)))\/((op (e3) (e1)) = (e0))) -> (~((e0) = (e2))) -> (~((e2) = (e3))) -> (~((op (e0) (e2)) = (op (e1) (e2)))) -> (((op (e1) (e0)) = (e2))\/(((op (e1) (e1)) = (e2))\/(((op (e1) (e2)) = (e2))\/((op (e1) (e3)) = (e2))))) -> (((op (e0) (e0)) = (e2))\/(((op (e1) (e0)) = (e2))\/(((op (e2) (e0)) = (e2))\/((op (e3) (e0)) = (e2))))) -> (~((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 (e3) (e3)) = (e3))) -> (~((op (e0) (e2)) = (op (e3) (e2)))) -> (~((op (e1) (e1)) = (op (e3) (e1)))) -> (((op (e0) (e0)) = (e3))\/(((op (e0) (e1)) = (e3))\/(((op (e0) (e2)) = (e3))\/((op (e0) (e3)) = (e3))))) -> (~((op (e2) (e0)) = (op (e2) (e1)))) -> (~((op (e0) (e0)) = (op (e0) (e3)))) -> (((op (e0) (e0)) = (e2))\/(((op (e0) (e1)) = (e2))\/(((op (e0) (e2)) = (e2))\/((op (e0) (e3)) = (e2))))) -> (~((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) (e2)) = (op (e2) (e2)))) -> (((op (e3) (e3)) = (e0))\/(((op (e3) (e3)) = (e1))\/(((op (e3) (e3)) = (e2))\/((op (e3) (e3)) = (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 (e2) (e0)) = (e3))\/(((op (e2) (e1)) = (e3))\/(((op (e2) (e2)) = (e3))\/((op (e2) (e3)) = (e3))))) -> (~((op (e2) (e2)) = (op (e3) (e2)))) -> (~((op (e2) (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 (e0) (e1)) = (op (e0) (e2)))) -> (~((op (e1) (e1)) = (op (e1) (e2)))) -> (~((op (e2) (e0)) = (op (e2) (e2)))) -> (((op (e0) (e3)) = (e0))\/(((op (e1) (e3)) = (e0))\/(((op (e2) (e3)) = (e0))\/((op (e3) (e3)) = (e0))))) -> (~((op (e3) (e2)) = (op (e3) (e3)))) -> (~((op (e2) (e0)) = (op (e2) (e3)))) -> (~((op (e1) (e1)) = (op (e1) (e3)))) -> (~((op (e0) (e1)) = (op (e0) (e3)))) -> (((op (e0) (e2)) = (e0))\/(((op (e1) (e2)) = (e0))\/(((op (e2) (e2)) = (e0))\/((op (e3) (e2)) = (e0))))) -> ((~((op (e2) (e1)) = (e1)))\/((op (e2) (e1)) = (e1))) -> (((op (e0) (e1)) = (e3))\/(((op (e1) (e1)) = (e3))\/(((op (e2) (e1)) = (e3))\/((op (e3) (e1)) = (e3))))) -> (~((op (e1) (e0)) = (op (e1) (e2)))) -> (((op (e2) (e3)) = (e0))\/(((op (e2) (e3)) = (e1))\/(((op (e2) (e3)) = (e2))\/((op (e2) (e3)) = (e3))))) -> (~((op (e3) (e0)) = (op (e3) (e1)))) -> ((~((op (e2) (e3)) = (e1)))\/((op (e2) (e1)) = (e3))) -> (((op (e1) (e0)) = (e0))\/(((op (e1) (e0)) = (e1))\/(((op (e1) (e0)) = (e2))\/((op (e1) (e0)) = (e3))))) -> (((op (e0) (e0)) = (e3))\/(((op (e1) (e0)) = (e3))\/(((op (e2) (e0)) = (e3))\/((op (e3) (e0)) = (e3))))) -> (((op (e0) (e3)) = (e1))\/(((op (e1) (e3)) = (e1))\/(((op (e2) (e3)) = (e1))\/((op (e3) (e3)) = (e1))))) -> ((~((op (e0) (e3)) = (e1)))\/((op (e0) (e1)) = (e3))) -> (~((op (e1) (e0)) = (op (e1) (e1)))) -> (~((e0) = (e1))) -> (((op (e0) (e0)) = (e0))\/(((op (e1) (e0)) = (e0))\/(((op (e2) (e0)) = (e0))\/((op (e3) (e0)) = (e0))))) -> ((~((op (e1) (e0)) = (e1)))\/((op (e1) (e1)) = (e0))) -> (((op (e0) (e3)) = (e3))\/(((op (e1) (e3)) = (e3))\/(((op (e2) (e3)) = (e3))\/((op (e3) (e3)) = (e3))))) -> (~((op (e1) (e3)) = (op (e2) (e3)))) -> (~((op (e1) (e0)) = (op (e2) (e0)))) -> (((op (e2) (e0)) = (e0))\/(((op (e2) (e1)) = (e0))\/(((op (e2) (e2)) = (e0))\/((op (e2) (e3)) = (e0))))) -> (~((op (e2) (e2)) = (op (e2) (e3)))) -> (~((op (e3) (e1)) = (op (e3) (e2)))) -> (((op (e3) (e2)) = (e0))\/(((op (e3) (e2)) = (e1))\/(((op (e3) (e2)) = (e2))\/((op (e3) (e2)) = (e3))))) -> (~((op (e1) (e2)) = (op (e3) (e2)))) -> (((op (e3) (e0)) = (e2))\/(((op (e3) (e1)) = (e2))\/(((op (e3) (e2)) = (e2))\/((op (e3) (e3)) = (e2))))) -> (~((op (e1) (e3)) = (op (e3) (e3)))) -> (((op (e1) (e3)) = (e0))\/(((op (e1) (e3)) = (e1))\/(((op (e1) (e3)) = (e2))\/((op (e1) (e3)) = (e3))))) -> (~((op (e2) (e1)) = (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 (e1) (e0)) = (e3))\/(((op (e1) (e1)) = (e3))\/(((op (e1) (e2)) = (e3))\/((op (e1) (e3)) = (e3))))) -> (~((op (e1) (e0)) = (op (e1) (e3)))) -> (~((op (e3) (e1)) = (op (e3) (e3)))) -> (((op (e3) (e0)) = (e0))\/(((op (e3) (e1)) = (e0))\/(((op (e3) (e2)) = (e0))\/((op (e3) (e3)) = (e0))))) -> (~((op (e2) (e0)) = (op (e3) (e0)))) -> (((op (e2) (e0)) = (e0))\/(((op (e2) (e0)) = (e1))\/(((op (e2) (e0)) = (e2))\/((op (e2) (e0)) = (e3))))) -> (~((op (e1) (e0)) = (op (e3) (e0)))) -> (~((op (e3) (e0)) = (op (e3) (e2)))) -> (~((op (e2) (e3)) = (op (e3) (e3)))) -> (((op (e2) (e0)) = (e2))\/(((op (e2) (e1)) = (e2))\/(((op (e2) (e2)) = (e2))\/((op (e2) (e3)) = (e2))))) -> ((~((op (e1) (e3)) = (e1)))\/((op (e1) (e1)) = (e3))) -> ((~((op (e2) (e0)) = (e1)))\/((op (e2) (e1)) = (e0))) -> ((~((op (e1) (e2)) = (e1)))\/((op (e1) (e1)) = (e2))) -> (((op (e2) (e0)) = (e1))\/(((op (e2) (e1)) = (e1))\/(((op (e2) (e2)) = (e1))\/((op (e2) (e3)) = (e1))))) -> (~((op (e1) (e2)) = (op (e2) (e2)))) -> (~((op (e1) (e1)) = (e1))) -> (((op (e1) (e0)) = (e1))\/(((op (e1) (e1)) = (e1))\/(((op (e1) (e2)) = (e1))\/((op (e1) (e3)) = (e1))))) -> (~((op (e0) (e0)) = (e0))) -> (~((op (e1) (e3)) = (e1))) -> (~((op (e1) (e2)) = (e1))) -> (((op (e0) (e1)) = (e2))\/(((op (e1) (e1)) = (e2))\/(((op (e2) (e1)) = (e2))\/((op (e3) (e1)) = (e2))))) -> (((op (e0) (e2)) = (e3))\/(((op (e1) (e2)) = (e3))\/(((op (e2) (e2)) = (e3))\/((op (e3) (e2)) = (e3))))) -> (((op (e0) (e0)) = (e1))\/(((op (e0) (e1)) = (e1))\/(((op (e0) (e2)) = (e1))\/((op (e0) (e3)) = (e1))))) -> (~((op (e0) (e3)) = (op (e3) (e3)))) -> (((op (e3) (e0)) = (e1))\/(((op (e3) (e1)) = (e1))\/(((op (e3) (e2)) = (e1))\/((op (e3) (e3)) = (e1))))) -> (~((op (e0) (e2)) = (e1))) -> (~((op (e0) (e1)) = (e1))) -> (~((op (e0) (e0)) = (e1))) -> (~((op (e2) (e1)) = (op (e3) (e1)))) -> ((op (e2) (e1)) = (e2)) -> ((~((op (e3) (e2)) = (e1)))\/((op (e3) (e1)) = (e2))) -> False). % 18.96/19.07 do 0 intro. intros zenon_H1db zenon_H29 zenon_H74 zenon_H24b zenon_H208 zenon_H99 zenon_H172 zenon_H261 zenon_H13c zenon_H139 zenon_H7c zenon_H109 zenon_H264 zenon_H253 zenon_H17e zenon_H210 zenon_H235 zenon_H254 zenon_H149 zenon_H12b zenon_H195 zenon_H18c zenon_H1fe zenon_H95 zenon_H10e zenon_H165 zenon_H102 zenon_H14f zenon_H160 zenon_H168 zenon_H1f0 zenon_H189 zenon_H183 zenon_H9a zenon_H22 zenon_H13e zenon_Ha8 zenon_H101 zenon_H1d zenon_He2 zenon_He4 zenon_He7 zenon_H18f zenon_H173 zenon_H1c4 zenon_H124 zenon_H4a zenon_H4f zenon_H52 zenon_H67 zenon_H62 zenon_H5b zenon_H57 zenon_H54 zenon_H6a zenon_H262 zenon_H1a5 zenon_H24a zenon_H11f zenon_H1cf zenon_H263 zenon_H25e zenon_H1e0 zenon_H133 zenon_H25c zenon_H45 zenon_Ha1 zenon_H3e zenon_H25d zenon_H136 zenon_Hdb zenon_H201 zenon_H2f zenon_H6d zenon_H1a4 zenon_H191 zenon_H115 zenon_H153 zenon_Hd5 zenon_Hdf zenon_H1c7 zenon_H71 zenon_H145 zenon_H16f zenon_Hd8 zenon_H130 zenon_H1ac zenon_H17b zenon_H259 zenon_H1fa zenon_H6f zenon_Hf3 zenon_H1d5 zenon_H258 zenon_H257 zenon_H256 zenon_H106 zenon_H2b zenon_H10a zenon_H128 zenon_H3f zenon_H24e zenon_H24d zenon_H1d8 zenon_H1a6 zenon_H22d zenon_Hc2 zenon_He8 zenon_H20d zenon_Ha4 zenon_H84 zenon_Haf zenon_H1ca zenon_H252. % 18.96/19.07 apply (zenon_or_s _ _ zenon_H263); [ zenon_intro zenon_H255 | zenon_intro zenon_Ha6 ]. % 18.96/19.07 apply (zenon_or_s _ _ zenon_H254); [ zenon_intro zenon_Had | zenon_intro zenon_H1b1 ]. % 18.96/19.07 apply (zenon_or_s _ _ zenon_H261); [ zenon_intro zenon_H250 | zenon_intro zenon_Hae ]. % 18.96/19.07 apply (zenon_L977_); trivial. % 18.96/19.07 apply (zenon_or_s _ _ zenon_H264); [ zenon_intro zenon_Hc7 | zenon_intro zenon_H161 ]. % 18.96/19.07 apply (zenon_or_s _ _ zenon_H74); [ zenon_intro zenon_H42 | zenon_intro zenon_H77 ]. % 18.96/19.07 exact (zenon_H3f zenon_H42). % 18.96/19.07 apply (zenon_or_s _ _ zenon_H77); [ zenon_intro zenon_H49 | zenon_intro zenon_H78 ]. % 18.96/19.07 apply (zenon_L949_); trivial. % 18.96/19.07 apply (zenon_or_s _ _ zenon_H78); [ zenon_intro zenon_H48 | zenon_intro zenon_H1e ]. % 18.96/19.07 apply (zenon_or_s _ _ zenon_H22d); [ zenon_intro zenon_H7a | zenon_intro zenon_H22e ]. % 18.96/19.07 exact (zenon_H84 zenon_H7a). % 18.96/19.07 apply (zenon_or_s _ _ zenon_H22e); [ zenon_intro zenon_Ha0 | zenon_intro zenon_H22f ]. % 18.96/19.07 exact (zenon_Ha4 zenon_Ha0). % 18.96/19.07 apply (zenon_or_s _ _ zenon_H22f); [ zenon_intro zenon_H122 | zenon_intro zenon_Hc3 ]. % 18.96/19.07 exact (zenon_H20d zenon_H122). % 18.96/19.07 apply (zenon_or_s _ _ zenon_H235); [ zenon_intro zenon_H7a | zenon_intro zenon_H236 ]. % 18.96/19.07 exact (zenon_H84 zenon_H7a). % 18.96/19.07 apply (zenon_or_s _ _ zenon_H236); [ zenon_intro zenon_H9d | zenon_intro zenon_H237 ]. % 18.96/19.07 apply (zenon_or_s _ _ zenon_H18c); [ zenon_intro zenon_H86 | zenon_intro zenon_H18d ]. % 18.96/19.07 apply (zenon_L123_); trivial. % 18.96/19.07 apply (zenon_or_s _ _ zenon_H18d); [ zenon_intro zenon_H110 | zenon_intro zenon_H18e ]. % 18.96/19.07 apply (zenon_L354_); trivial. % 18.96/19.07 apply (zenon_or_s _ _ zenon_H18e); [ zenon_intro zenon_H113 | zenon_intro zenon_Hd7 ]. % 18.96/19.07 apply (zenon_or_s _ _ zenon_H16f); [ zenon_intro zenon_H9e | zenon_intro zenon_H170 ]. % 18.96/19.07 apply (zenon_L37_); trivial. % 18.96/19.07 apply (zenon_or_s _ _ zenon_H170); [ zenon_intro zenon_H13f | zenon_intro zenon_H171 ]. % 18.96/19.07 apply (zenon_L108_); trivial. % 18.96/19.07 apply (zenon_or_s _ _ zenon_H171); [ zenon_intro zenon_H16c | zenon_intro zenon_Hdc ]. % 18.96/19.07 apply (zenon_L116_); trivial. % 18.96/19.07 apply (zenon_or_s _ _ zenon_H1ac); [ zenon_intro zenon_H44 | zenon_intro zenon_H1af ]. % 18.96/19.07 apply (zenon_L978_); trivial. % 18.96/19.07 apply (zenon_or_s _ _ zenon_H1af); [ zenon_intro zenon_H1b1 | zenon_intro zenon_H1b0 ]. % 18.96/19.07 apply (zenon_L349_); trivial. % 18.96/19.07 apply (zenon_or_s _ _ zenon_H1b0); [ zenon_intro zenon_H61 | zenon_intro zenon_H60 ]. % 18.96/19.07 apply (zenon_L342_); trivial. % 18.96/19.07 apply (zenon_or_s _ _ zenon_H145); [ zenon_intro zenon_Hcd | zenon_intro zenon_H146 ]. % 18.96/19.07 apply (zenon_L979_); trivial. % 18.96/19.07 apply (zenon_or_s _ _ zenon_H146); [ zenon_intro zenon_Hd7 | zenon_intro zenon_H147 ]. % 18.96/19.07 apply (zenon_L201_); trivial. % 18.96/19.07 apply (zenon_or_s _ _ zenon_H147); [ zenon_intro zenon_H11d | zenon_intro zenon_Hf6 ]. % 18.96/19.07 apply (zenon_L224_); trivial. % 18.96/19.07 apply (zenon_L980_); trivial. % 18.96/19.07 apply (zenon_L981_); trivial. % 18.96/19.07 apply (zenon_or_s _ _ zenon_H237); [ zenon_intro zenon_Hed | zenon_intro zenon_Hac ]. % 18.96/19.07 exact (zenon_H1db zenon_Hed). % 18.96/19.07 exact (zenon_Had zenon_Hac). % 18.96/19.07 apply (zenon_L947_); trivial. % 18.96/19.07 apply (zenon_or_s _ _ zenon_H74); [ zenon_intro zenon_H42 | zenon_intro zenon_H77 ]. % 18.96/19.07 exact (zenon_H3f zenon_H42). % 18.96/19.07 apply (zenon_or_s _ _ zenon_H77); [ zenon_intro zenon_H49 | zenon_intro zenon_H78 ]. % 18.96/19.07 apply (zenon_L23_); trivial. % 18.96/19.07 apply (zenon_or_s _ _ zenon_H78); [ zenon_intro zenon_H48 | zenon_intro zenon_H1e ]. % 18.96/19.07 apply (zenon_or_s _ _ zenon_H22d); [ zenon_intro zenon_H7a | zenon_intro zenon_H22e ]. % 18.96/19.07 exact (zenon_H84 zenon_H7a). % 18.96/19.07 apply (zenon_or_s _ _ zenon_H22e); [ zenon_intro zenon_Ha0 | zenon_intro zenon_H22f ]. % 18.96/19.07 exact (zenon_Ha4 zenon_Ha0). % 18.96/19.07 apply (zenon_or_s _ _ zenon_H22f); [ zenon_intro zenon_H122 | zenon_intro zenon_Hc3 ]. % 18.96/19.07 exact (zenon_H20d zenon_H122). % 18.96/19.07 apply (zenon_or_s _ _ zenon_H235); [ zenon_intro zenon_H7a | zenon_intro zenon_H236 ]. % 18.96/19.07 exact (zenon_H84 zenon_H7a). % 18.96/19.07 apply (zenon_or_s _ _ zenon_H236); [ zenon_intro zenon_H9d | zenon_intro zenon_H237 ]. % 18.96/19.07 apply (zenon_or_s _ _ zenon_H183); [ zenon_intro zenon_H7b | zenon_intro zenon_H186 ]. % 18.96/19.07 apply (zenon_or_s _ _ zenon_H18c); [ zenon_intro zenon_H86 | zenon_intro zenon_H18d ]. % 18.96/19.07 apply (zenon_L123_); trivial. % 18.96/19.07 apply (zenon_or_s _ _ zenon_H18d); [ zenon_intro zenon_H110 | zenon_intro zenon_H18e ]. % 18.96/19.07 apply (zenon_L354_); trivial. % 18.96/19.07 apply (zenon_or_s _ _ zenon_H18e); [ zenon_intro zenon_H113 | zenon_intro zenon_Hd7 ]. % 18.96/19.07 apply (zenon_or_s _ _ zenon_H16f); [ zenon_intro zenon_H9e | zenon_intro zenon_H170 ]. % 18.96/19.07 apply (zenon_L960_); trivial. % 18.96/19.07 apply (zenon_or_s _ _ zenon_H170); [ zenon_intro zenon_H13f | zenon_intro zenon_H171 ]. % 18.96/19.07 apply (zenon_L108_); trivial. % 18.96/19.07 apply (zenon_or_s _ _ zenon_H171); [ zenon_intro zenon_H16c | zenon_intro zenon_Hdc ]. % 18.96/19.07 apply (zenon_L116_); trivial. % 18.96/19.07 apply (zenon_or_s _ _ zenon_H145); [ zenon_intro zenon_Hcd | zenon_intro zenon_H146 ]. % 18.96/19.07 apply (zenon_L375_); trivial. % 18.96/19.07 apply (zenon_or_s _ _ zenon_H146); [ zenon_intro zenon_Hd7 | zenon_intro zenon_H147 ]. % 18.96/19.07 apply (zenon_L381_); trivial. % 18.96/19.07 apply (zenon_or_s _ _ zenon_H147); [ zenon_intro zenon_H11d | zenon_intro zenon_Hf6 ]. % 18.96/19.07 apply (zenon_L376_); trivial. % 18.96/19.07 apply (zenon_L980_); trivial. % 18.96/19.07 apply (zenon_L381_); trivial. % 18.96/19.07 apply (zenon_or_s _ _ zenon_H186); [ zenon_intro zenon_H10f | zenon_intro zenon_H187 ]. % 18.96/19.07 apply (zenon_L975_); trivial. % 18.96/19.07 apply (zenon_or_s _ _ zenon_H187); [ zenon_intro zenon_H150 | zenon_intro zenon_Hcd ]. % 18.96/19.07 apply (zenon_L378_); trivial. % 18.96/19.07 apply (zenon_L82_); trivial. % 18.96/19.07 apply (zenon_or_s _ _ zenon_H237); [ zenon_intro zenon_Hed | zenon_intro zenon_Hac ]. % 18.96/19.07 exact (zenon_H1db zenon_Hed). % 18.96/19.07 exact (zenon_Had zenon_Hac). % 18.96/19.07 apply (zenon_L947_); trivial. % 18.96/19.07 apply (zenon_L349_); trivial. % 18.96/19.07 apply (zenon_L207_); trivial. % 18.96/19.07 (* end of lemma zenon_L982_ *) % 18.96/19.07 assert (zenon_L983_ : ((~((op (e3) (e1)) = (e1)))\/((op (e3) (e1)) = (e1))) -> ((op (e0) (e1)) = (e1)) -> (~((op (e0) (e1)) = (op (e3) (e1)))) -> (((op (e1) (e0)) = (e1))\/(((op (e1) (e1)) = (e1))\/(((op (e1) (e2)) = (e1))\/((op (e1) (e3)) = (e1))))) -> (~((op (e3) (e0)) = (e1))) -> (~((op (e1) (e3)) = (op (e3) (e3)))) -> (((op (e3) (e0)) = (e1))\/(((op (e3) (e1)) = (e1))\/(((op (e3) (e2)) = (e1))\/((op (e3) (e3)) = (e1))))) -> (~((op (e1) (e2)) = (e1))) -> (~((op (e1) (e1)) = (e1))) -> (~((op (e1) (e0)) = (e1))) -> (~((op (e2) (e1)) = (op (e3) (e1)))) -> ((op (e2) (e1)) = (e2)) -> ((~((op (e3) (e2)) = (e1)))\/((op (e3) (e1)) = (e2))) -> False). % 18.96/19.07 do 0 intro. intros zenon_H261 zenon_Ha0 zenon_H210 zenon_H128 zenon_Had zenon_Hd5 zenon_He8 zenon_H24d zenon_H10a zenon_H1ef zenon_Haf zenon_H1ca zenon_H252. % 18.96/19.07 apply (zenon_or_s _ _ zenon_H261); [ zenon_intro zenon_H250 | zenon_intro zenon_Hae ]. % 18.96/19.07 apply (zenon_or_s _ _ zenon_H252); [ zenon_intro zenon_H251 | zenon_intro zenon_H14d ]. % 18.96/19.07 apply (zenon_L922_); trivial. % 18.96/19.07 apply (zenon_L364_); trivial. % 18.96/19.07 apply (zenon_L363_); trivial. % 18.96/19.07 (* end of lemma zenon_L983_ *) % 18.96/19.07 assert (zenon_L984_ : ((~((op (e0) (e1)) = (e1)))\/((op (e0) (e1)) = (e1))) -> (((op (e1) (e0)) = (e1))\/(((op (e1) (e1)) = (e1))\/(((op (e1) (e2)) = (e1))\/((op (e1) (e3)) = (e1))))) -> (~((op (e1) (e1)) = (e1))) -> (~((op (e1) (e2)) = (op (e2) (e2)))) -> (((op (e2) (e0)) = (e1))\/(((op (e2) (e1)) = (e1))\/(((op (e2) (e2)) = (e1))\/((op (e2) (e3)) = (e1))))) -> ((~((op (e1) (e2)) = (e1)))\/((op (e1) (e1)) = (e2))) -> ((~((op (e2) (e0)) = (e1)))\/((op (e2) (e1)) = (e0))) -> ((~((op (e1) (e3)) = (e1)))\/((op (e1) (e1)) = (e3))) -> (((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) (e2)))) -> (~((op (e1) (e0)) = (op (e3) (e0)))) -> (((op (e2) (e0)) = (e0))\/(((op (e2) (e0)) = (e1))\/(((op (e2) (e0)) = (e2))\/((op (e2) (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) (e1)) = (op (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 (e0) (e3)) = (e2))\/(((op (e1) (e3)) = (e2))\/(((op (e2) (e3)) = (e2))\/((op (e3) (e3)) = (e2))))) -> (~((op (e3) (e0)) = (op (e3) (e3)))) -> (~((op (e2) (e1)) = (op (e2) (e3)))) -> (((op (e1) (e3)) = (e0))\/(((op (e1) (e3)) = (e1))\/(((op (e1) (e3)) = (e2))\/((op (e1) (e3)) = (e3))))) -> (~((op (e1) (e3)) = (op (e3) (e3)))) -> (((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)) = (e0))\/(((op (e3) (e2)) = (e1))\/(((op (e3) (e2)) = (e2))\/((op (e3) (e2)) = (e3))))) -> (~((op (e3) (e1)) = (op (e3) (e2)))) -> (~((op (e2) (e2)) = (op (e2) (e3)))) -> (((op (e2) (e0)) = (e0))\/(((op (e2) (e1)) = (e0))\/(((op (e2) (e2)) = (e0))\/((op (e2) (e3)) = (e0))))) -> (~((op (e1) (e0)) = (op (e2) (e0)))) -> (~((op (e2) (e1)) = (op (e3) (e1)))) -> (~((op (e1) (e3)) = (op (e2) (e3)))) -> (((op (e0) (e3)) = (e3))\/(((op (e1) (e3)) = (e3))\/(((op (e2) (e3)) = (e3))\/((op (e3) (e3)) = (e3))))) -> ((~((op (e1) (e0)) = (e1)))\/((op (e1) (e1)) = (e0))) -> (((op (e0) (e0)) = (e0))\/(((op (e1) (e0)) = (e0))\/(((op (e2) (e0)) = (e0))\/((op (e3) (e0)) = (e0))))) -> (~((e0) = (e1))) -> (~((op (e1) (e0)) = (op (e1) (e1)))) -> ((~((op (e0) (e3)) = (e1)))\/((op (e0) (e1)) = (e3))) -> (((op (e0) (e3)) = (e1))\/(((op (e1) (e3)) = (e1))\/(((op (e2) (e3)) = (e1))\/((op (e3) (e3)) = (e1))))) -> (((op (e0) (e0)) = (e3))\/(((op (e1) (e0)) = (e3))\/(((op (e2) (e0)) = (e3))\/((op (e3) (e0)) = (e3))))) -> (((op (e1) (e0)) = (e0))\/(((op (e1) (e0)) = (e1))\/(((op (e1) (e0)) = (e2))\/((op (e1) (e0)) = (e3))))) -> ((~((op (e2) (e3)) = (e1)))\/((op (e2) (e1)) = (e3))) -> (~((op (e3) (e0)) = (op (e3) (e1)))) -> (((op (e2) (e3)) = (e0))\/(((op (e2) (e3)) = (e1))\/(((op (e2) (e3)) = (e2))\/((op (e2) (e3)) = (e3))))) -> (((op (e3) (e0)) = (e1))\/(((op (e3) (e1)) = (e1))\/(((op (e3) (e2)) = (e1))\/((op (e3) (e3)) = (e1))))) -> (~((op (e1) (e0)) = (op (e1) (e2)))) -> (((op (e0) (e1)) = (e3))\/(((op (e1) (e1)) = (e3))\/(((op (e2) (e1)) = (e3))\/((op (e3) (e1)) = (e3))))) -> ((~((op (e2) (e1)) = (e1)))\/((op (e2) (e1)) = (e1))) -> (((op (e0) (e2)) = (e0))\/(((op (e1) (e2)) = (e0))\/(((op (e2) (e2)) = (e0))\/((op (e3) (e2)) = (e0))))) -> (~((op (e0) (e1)) = (op (e0) (e3)))) -> (~((op (e1) (e1)) = (op (e1) (e3)))) -> (~((op (e2) (e0)) = (op (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) (e0)) = (op (e2) (e2)))) -> (~((op (e1) (e1)) = (op (e1) (e2)))) -> (~((op (e0) (e1)) = (op (e0) (e2)))) -> (~((op (e1) (e2)) = (op (e1) (e3)))) -> (((op (e2) (e2)) = (e0))\/(((op (e2) (e2)) = (e1))\/(((op (e2) (e2)) = (e2))\/((op (e2) (e2)) = (e3))))) -> (~((op (e2) (e2)) = (e2))) -> (~((op (e2) (e2)) = (op (e3) (e2)))) -> (((op (e2) (e0)) = (e3))\/(((op (e2) (e1)) = (e3))\/(((op (e2) (e2)) = (e3))\/((op (e2) (e3)) = (e3))))) -> (((op (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 (e3) (e3)) = (e0))\/(((op (e3) (e3)) = (e1))\/(((op (e3) (e3)) = (e2))\/((op (e3) (e3)) = (e3))))) -> (~((op (e0) (e2)) = (op (e2) (e2)))) -> (~((op (e1) (e1)) = (op (e2) (e1)))) -> (((op (e1) (e0)) = (e0))\/(((op (e1) (e1)) = (e0))\/(((op (e1) (e2)) = (e0))\/((op (e1) (e3)) = (e0))))) -> ((op (e0) (e1)) = (e0)) -> (~((e0) = (e3))) -> (((op (e0) (e0)) = (e2))\/(((op (e0) (e1)) = (e2))\/(((op (e0) (e2)) = (e2))\/((op (e0) (e3)) = (e2))))) -> (~((op (e0) (e0)) = (op (e0) (e3)))) -> (~((op (e2) (e0)) = (op (e2) (e1)))) -> (((op (e0) (e0)) = (e3))\/(((op (e0) (e1)) = (e3))\/(((op (e0) (e2)) = (e3))\/((op (e0) (e3)) = (e3))))) -> (~((op (e1) (e1)) = (op (e3) (e1)))) -> (~((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))))) -> (~((op (e0) (e1)) = (op (e1) (e1)))) -> (~((e1) = (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)) = (op (e1) (e2)))) -> (~((e2) = (e3))) -> (~((e0) = (e2))) -> ((~((op (e3) (e0)) = (e1)))\/((op (e3) (e1)) = (e0))) -> (((op (e0) (e0)) = (e1))\/(((op (e1) (e0)) = (e1))\/(((op (e2) (e0)) = (e1))\/((op (e3) (e0)) = (e1))))) -> (~((op (e0) (e1)) = (op (e3) (e1)))) -> (~((op (e0) (e1)) = (op (e2) (e1)))) -> ((~((op (e2) (e2)) = (e1)))\/((op (e2) (e1)) = (e2))) -> (~((op (e0) (e0)) = (e0))) -> ((~((op (e3) (e3)) = (e1)))\/((op (e3) (e1)) = (e3))) -> (((op (e0) (e1)) = (e1))\/(((op (e1) (e1)) = (e1))\/(((op (e2) (e1)) = (e1))\/((op (e3) (e1)) = (e1))))) -> ((~((op (e3) (e2)) = (e1)))\/((op (e3) (e1)) = (e2))) -> (~((e1) = (e2))) -> (((op (e0) (e2)) = (e1))\/(((op (e1) (e2)) = (e1))\/(((op (e2) (e2)) = (e1))\/((op (e3) (e2)) = (e1))))) -> (~((op (e0) (e0)) = (op (e0) (e2)))) -> (((op (e0) (e0)) = (e1))\/(((op (e0) (e1)) = (e1))\/(((op (e0) (e2)) = (e1))\/((op (e0) (e3)) = (e1))))) -> ((~((op (e3) (e1)) = (e1)))\/((op (e3) (e1)) = (e1))) -> (((op (e0) (e2)) = (e2))\/(((op (e1) (e2)) = (e2))\/(((op (e2) (e2)) = (e2))\/((op (e3) (e2)) = (e2))))) -> ((~((op (e0) (e2)) = (e1)))\/((op (e0) (e1)) = (e2))) -> False). % 18.96/19.07 do 0 intro. intros zenon_H265 zenon_H128 zenon_H10a zenon_H2b zenon_H106 zenon_H256 zenon_H257 zenon_H258 zenon_H1d5 zenon_Hf3 zenon_H6f zenon_H1fa zenon_H259 zenon_H17b zenon_H1ac zenon_H130 zenon_Hd8 zenon_H16f zenon_H145 zenon_H71 zenon_H1c7 zenon_Hdf zenon_Hd5 zenon_H153 zenon_H115 zenon_H191 zenon_H1a4 zenon_H6d zenon_H2f zenon_H201 zenon_Haf zenon_Hdb zenon_H136 zenon_H25d zenon_H3e zenon_Ha1 zenon_H45 zenon_H25c zenon_H133 zenon_H1e0 zenon_H25e zenon_H263 zenon_H1cf zenon_H11f zenon_He8 zenon_H24a zenon_H1a5 zenon_H262 zenon_H6a zenon_H54 zenon_H57 zenon_H5b zenon_H62 zenon_H67 zenon_H52 zenon_H4f zenon_H4a zenon_H124 zenon_H1c4 zenon_H173 zenon_H18f zenon_He7 zenon_He4 zenon_He2 zenon_Hc2 zenon_H1d zenon_H101 zenon_Ha8 zenon_H13e zenon_H22 zenon_H49 zenon_H9a zenon_H183 zenon_H189 zenon_H1f0 zenon_H168 zenon_H160 zenon_H14f zenon_H102 zenon_H165 zenon_H10e zenon_H95 zenon_H1fe zenon_H18c zenon_H195 zenon_H12b zenon_H149 zenon_H254 zenon_H235 zenon_H210 zenon_H17e zenon_H253 zenon_H3f zenon_H264 zenon_H109 zenon_H252 zenon_H7c zenon_H139 zenon_H13c zenon_H22d zenon_H261 zenon_H172 zenon_H266. % 18.96/19.07 apply (zenon_or_s _ _ zenon_H265); [ zenon_intro zenon_Ha4 | zenon_intro zenon_Ha0 ]. % 18.96/19.07 apply (zenon_or_s _ _ zenon_H266); [ zenon_intro zenon_H20d | zenon_intro zenon_H10f ]. % 18.96/19.07 apply (zenon_L949_); trivial. % 18.96/19.07 apply (zenon_L764_); trivial. % 18.96/19.07 apply (zenon_L38_); trivial. % 18.96/19.07 (* end of lemma zenon_L984_ *) % 18.96/19.07 assert (zenon_L985_ : ((~((op (e3) (e0)) = (e1)))\/((op (e3) (e1)) = (e0))) -> ((op (e2) (e1)) = (e3)) -> ((op (e1) (e1)) = (e2)) -> (~((op (e0) (e0)) = (e1))) -> (~((op (e1) (e0)) = (e1))) -> (~((op (e2) (e0)) = (e1))) -> (((op (e0) (e0)) = (e1))\/(((op (e1) (e0)) = (e1))\/(((op (e2) (e0)) = (e1))\/((op (e3) (e0)) = (e1))))) -> False). % 18.96/19.07 do 0 intro. intros zenon_H254 zenon_Ha6 zenon_H110 zenon_H84 zenon_H1ef zenon_H1db zenon_H235. % 18.96/19.07 apply (zenon_or_s _ _ zenon_H254); [ zenon_intro zenon_Had | zenon_intro zenon_H1b1 ]. % 18.96/19.07 apply (zenon_L948_); trivial. % 18.96/19.07 apply (zenon_L509_); trivial. % 18.96/19.07 (* end of lemma zenon_L985_ *) % 18.96/19.07 assert (zenon_L986_ : (((op (e2) (e0)) = (e1))\/(((op (e2) (e1)) = (e1))\/(((op (e2) (e2)) = (e1))\/((op (e2) (e3)) = (e1))))) -> (~((e1) = (e2))) -> ((op (e2) (e0)) = (e2)) -> (~((op (e2) (e1)) = (e1))) -> (~((op (e2) (e2)) = (e1))) -> (~((op (e2) (e3)) = (e1))) -> False). % 18.96/19.07 do 0 intro. intros zenon_H106 zenon_H7c zenon_Hee zenon_H24f zenon_H198 zenon_H255. % 18.96/19.07 apply (zenon_or_s _ _ zenon_H106); [ zenon_intro zenon_Hed | zenon_intro zenon_H107 ]. % 18.96/19.07 apply (zenon_L58_); trivial. % 18.96/19.07 apply (zenon_or_s _ _ zenon_H107); [ zenon_intro zenon_Ha5 | zenon_intro zenon_H108 ]. % 18.96/19.07 exact (zenon_H24f zenon_Ha5). % 18.96/19.07 apply (zenon_or_s _ _ zenon_H108); [ zenon_intro zenon_Hf1 | zenon_intro zenon_Hf4 ]. % 18.96/19.07 exact (zenon_H198 zenon_Hf1). % 18.96/19.07 exact (zenon_H255 zenon_Hf4). % 18.96/19.07 (* end of lemma zenon_L986_ *) % 18.96/19.07 assert (zenon_L987_ : (((op (e1) (e0)) = (e0))\/(((op (e1) (e1)) = (e0))\/(((op (e1) (e2)) = (e0))\/((op (e1) (e3)) = (e0))))) -> (~((op (e1) (e0)) = (op (e3) (e0)))) -> ((op (e3) (e0)) = (e0)) -> ((op (e2) (e1)) = (e0)) -> (~((op (e2) (e1)) = (op (e2) (e3)))) -> (~((op (e1) (e1)) = (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 (e0) (e2)) = (e0)) -> (~((op (e0) (e2)) = (op (e1) (e2)))) -> (((op (e1) (e0)) = (e1))\/(((op (e1) (e1)) = (e1))\/(((op (e1) (e2)) = (e1))\/((op (e1) (e3)) = (e1))))) -> (~((op (e1) (e0)) = (e1))) -> (~((op (e1) (e1)) = (e1))) -> (~((op (e0) (e3)) = (op (e1) (e3)))) -> (~((op (e0) (e3)) = (e1))) -> (((op (e0) (e3)) = (e0))\/(((op (e0) (e3)) = (e1))\/(((op (e0) (e3)) = (e2))\/((op (e0) (e3)) = (e3))))) -> (~((op (e3) (e2)) = (e1))) -> (~((op (e3) (e1)) = (e1))) -> (((op (e0) (e3)) = (e1))\/(((op (e1) (e3)) = (e1))\/(((op (e2) (e3)) = (e1))\/((op (e3) (e3)) = (e1))))) -> (~((op (e1) (e2)) = (op (e1) (e3)))) -> (~((op (e2) (e3)) = (e1))) -> (~((op (e3) (e0)) = (op (e3) (e3)))) -> (((op (e3) (e0)) = (e1))\/(((op (e3) (e1)) = (e1))\/(((op (e3) (e2)) = (e1))\/((op (e3) (e3)) = (e1))))) -> (~((e1) = (e3))) -> (~((op (e1) (e1)) = (op (e3) (e1)))) -> ((op (e3) (e1)) = (e3)) -> ((op (e2) (e0)) = (e1)) -> ((op (e0) (e0)) = (e2)) -> (((op (e1) (e0)) = (e3))\/(((op (e1) (e1)) = (e3))\/(((op (e1) (e2)) = (e3))\/((op (e1) (e3)) = (e3))))) -> (~((op (e1) (e3)) = (e1))) -> False). % 18.96/19.08 do 0 intro. intros zenon_H22 zenon_H1fa zenon_H44 zenon_H36 zenon_H1c7 zenon_H57 zenon_H208 zenon_H67 zenon_H48 zenon_H195 zenon_H128 zenon_H1ef zenon_H10a zenon_H1d zenon_H231 zenon_He4 zenon_H251 zenon_H250 zenon_H133 zenon_H124 zenon_H255 zenon_H71 zenon_He8 zenon_H95 zenon_H160 zenon_H161 zenon_Hed zenon_H7b zenon_H16f zenon_H24e. % 18.96/19.08 apply (zenon_or_s _ _ zenon_H22); [ zenon_intro zenon_H27 | zenon_intro zenon_H26 ]. % 18.96/19.08 apply (zenon_L312_); trivial. % 18.96/19.08 apply (zenon_or_s _ _ zenon_H26); [ zenon_intro zenon_H29 | zenon_intro zenon_H28 ]. % 18.96/19.08 apply (zenon_L961_); trivial. % 18.96/19.08 apply (zenon_or_s _ _ zenon_H28); [ zenon_intro zenon_H2a | zenon_intro zenon_H1f ]. % 18.96/19.08 apply (zenon_L334_); trivial. % 18.96/19.08 apply (zenon_or_s _ _ zenon_H128); [ zenon_intro zenon_H9d | zenon_intro zenon_H129 ]. % 18.96/19.08 exact (zenon_H1ef zenon_H9d). % 18.96/19.08 apply (zenon_or_s _ _ zenon_H129); [ zenon_intro zenon_H10d | zenon_intro zenon_H12a ]. % 18.96/19.08 exact (zenon_H10a zenon_H10d). % 18.96/19.08 apply (zenon_or_s _ _ zenon_H12a); [ zenon_intro zenon_Hf0 | zenon_intro zenon_Hd6 ]. % 18.96/19.08 apply (zenon_or_s _ _ zenon_H16f); [ zenon_intro zenon_H9e | zenon_intro zenon_H170 ]. % 18.96/19.08 apply (zenon_L491_); trivial. % 18.96/19.08 apply (zenon_or_s _ _ zenon_H170); [ zenon_intro zenon_H13f | zenon_intro zenon_H171 ]. % 18.96/19.08 apply (zenon_L110_); trivial. % 18.96/19.08 apply (zenon_or_s _ _ zenon_H171); [ zenon_intro zenon_H16c | zenon_intro zenon_Hdc ]. % 18.96/19.08 apply (zenon_L167_); trivial. % 18.96/19.08 apply (zenon_L827_); trivial. % 18.96/19.08 exact (zenon_H24e zenon_Hd6). % 18.96/19.08 (* end of lemma zenon_L987_ *) % 18.96/19.08 assert (zenon_L988_ : (((op (e3) (e0)) = (e0))\/(((op (e3) (e0)) = (e1))\/(((op (e3) (e0)) = (e2))\/((op (e3) (e0)) = (e3))))) -> ((op (e3) (e2)) = (e0)) -> (~((op (e3) (e0)) = (e1))) -> ((op (e3) (e2)) = (e2)) -> (~((op (e3) (e0)) = (op (e3) (e2)))) -> ((op (e3) (e1)) = (e3)) -> (~((op (e3) (e0)) = (op (e3) (e1)))) -> False). % 18.96/19.08 do 0 intro. intros zenon_H267 zenon_H61 zenon_Had zenon_H151 zenon_H6f zenon_H161 zenon_H1cf. % 18.96/19.08 apply (zenon_or_s _ _ zenon_H267); [ zenon_intro zenon_H44 | zenon_intro zenon_H268 ]. % 18.96/19.08 apply (zenon_L19_); trivial. % 18.96/19.08 apply (zenon_or_s _ _ zenon_H268); [ zenon_intro zenon_Hac | zenon_intro zenon_H269 ]. % 18.96/19.08 exact (zenon_Had zenon_Hac). % 18.96/19.08 apply (zenon_or_s _ _ zenon_H269); [ zenon_intro zenon_H148 | zenon_intro zenon_H15e ]. % 18.96/19.08 apply (zenon_L420_); trivial. % 18.96/19.08 apply (zenon_L193_); trivial. % 18.96/19.08 (* end of lemma zenon_L988_ *) % 18.96/19.08 assert (zenon_L989_ : (((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)) = (e1))) -> ((op (e1) (e3)) = (e2)) -> (((op (e1) (e3)) = (e0))\/(((op (e1) (e3)) = (e1))\/(((op (e1) (e3)) = (e2))\/((op (e1) (e3)) = (e3))))) -> ((op (e3) (e3)) = (e0)) -> (~((op (e1) (e3)) = (op (e3) (e3)))) -> (~((op (e0) (e3)) = (op (e2) (e3)))) -> ((op (e2) (e1)) = (e2)) -> (~((op (e2) (e1)) = (op (e2) (e3)))) -> (~((op (e2) (e3)) = (op (e3) (e3)))) -> ((op (e3) (e3)) = (e1)) -> (((op (e2) (e3)) = (e0))\/(((op (e2) (e3)) = (e1))\/(((op (e2) (e3)) = (e2))\/((op (e2) (e3)) = (e3))))) -> (~((op (e0) (e3)) = (op (e1) (e3)))) -> False). % 18.96/19.08 do 0 intro. intros zenon_He4 zenon_Hc2 zenon_H231 zenon_Hd7 zenon_Hdf zenon_H60 zenon_Hd5 zenon_He2 zenon_H1ca zenon_H1c7 zenon_Hf3 zenon_Hc4 zenon_H11f zenon_H1d. % 18.96/19.08 apply (zenon_or_s _ _ zenon_He4); [ zenon_intro zenon_H1e | zenon_intro zenon_He5 ]. % 18.96/19.08 apply (zenon_L440_); trivial. % 18.96/19.08 apply (zenon_or_s _ _ zenon_He5); [ zenon_intro zenon_Hc3 | zenon_intro zenon_He6 ]. % 18.96/19.08 exact (zenon_H231 zenon_Hc3). % 18.96/19.08 apply (zenon_or_s _ _ zenon_He6); [ zenon_intro zenon_Hcd | zenon_intro zenon_He3 ]. % 18.96/19.08 apply (zenon_L70_); trivial. % 18.96/19.08 apply (zenon_L455_); trivial. % 18.96/19.08 (* end of lemma zenon_L989_ *) % 18.96/19.08 assert (zenon_L990_ : (((op (e0) (e2)) = (e2))\/(((op (e1) (e2)) = (e2))\/(((op (e2) (e2)) = (e2))\/((op (e3) (e2)) = (e2))))) -> (~((e0) = (e2))) -> (~((e1) = (e2))) -> ((op (e1) (e2)) = (e1)) -> (~((op (e2) (e2)) = (e2))) -> (((op (e3) (e0)) = (e0))\/(((op (e3) (e1)) = (e0))\/(((op (e3) (e2)) = (e0))\/((op (e3) (e3)) = (e0))))) -> (~((op (e1) (e3)) = (e1))) -> (((op (e1) (e0)) = (e3))\/(((op (e1) (e1)) = (e3))\/(((op (e1) (e2)) = (e3))\/((op (e1) (e3)) = (e3))))) -> ((op (e0) (e0)) = (e2)) -> ((op (e2) (e0)) = (e1)) -> (~((op (e1) (e1)) = (op (e3) (e1)))) -> (~((e1) = (e3))) -> (~((op (e3) (e0)) = (op (e3) (e3)))) -> (~((op (e1) (e2)) = (op (e1) (e3)))) -> (((op (e0) (e3)) = (e1))\/(((op (e1) (e3)) = (e1))\/(((op (e2) (e3)) = (e1))\/((op (e3) (e3)) = (e1))))) -> (~((op (e1) (e1)) = (e1))) -> (~((op (e1) (e0)) = (e1))) -> (((op (e1) (e0)) = (e1))\/(((op (e1) (e1)) = (e1))\/(((op (e1) (e2)) = (e1))\/((op (e1) (e3)) = (e1))))) -> (~((op (e0) (e2)) = (op (e1) (e2)))) -> ((op (e0) (e2)) = (e0)) -> (~((op (e1) (e1)) = (op (e1) (e3)))) -> (~((op (e1) (e0)) = (op (e3) (e0)))) -> (((op (e1) (e0)) = (e0))\/(((op (e1) (e1)) = (e0))\/(((op (e1) (e2)) = (e0))\/((op (e1) (e3)) = (e0))))) -> (~((op (e3) (e1)) = (op (e3) (e2)))) -> ((op (e2) (e1)) = (e0)) -> (~((op (e2) (e1)) = (op (e2) (e2)))) -> (~((op (e1) (e0)) = (op (e1) (e2)))) -> ((op (e1) (e0)) = (e0)) -> (((op (e0) (e0)) = (e0))\/(((op (e1) (e0)) = (e0))\/(((op (e2) (e0)) = (e0))\/((op (e3) (e0)) = (e0))))) -> (~((op (e0) (e0)) = (e0))) -> (~((op (e3) (e1)) = (op (e3) (e3)))) -> (~((op (e1) (e0)) = (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 (e2) (e0)) = (op (e2) (e1)))) -> (((op (e0) (e2)) = (e0))\/(((op (e1) (e2)) = (e0))\/(((op (e2) (e2)) = (e0))\/((op (e3) (e2)) = (e0))))) -> (~((op (e3) (e0)) = (op (e3) (e1)))) -> ((op (e3) (e1)) = (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))))) -> (~((op (e3) (e0)) = (e1))) -> (~((op (e3) (e1)) = (e1))) -> (~((op (e3) (e2)) = (e1))) -> (((op (e0) (e3)) = (e2))\/(((op (e1) (e3)) = (e2))\/(((op (e2) (e3)) = (e2))\/((op (e3) (e3)) = (e2))))) -> ((op (e1) (e3)) = (e3)) -> (~((op (e1) (e3)) = (op (e2) (e3)))) -> (~((op (e2) (e3)) = (e1))) -> (((op (e0) (e3)) = (e0))\/(((op (e0) (e3)) = (e1))\/(((op (e0) (e3)) = (e2))\/((op (e0) (e3)) = (e3))))) -> (~((op (e0) (e3)) = (e1))) -> (~((op (e0) (e3)) = (op (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 (e2) (e3)))) -> ((op (e2) (e1)) = (e2)) -> (~((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))))) -> (~((op (e0) (e3)) = (op (e1) (e3)))) -> False). % 18.96/19.08 do 0 intro. intros zenon_H172 zenon_H149 zenon_H7c zenon_Hf0 zenon_H173 zenon_H1ac zenon_H24e zenon_H16f zenon_H7b zenon_Hed zenon_H160 zenon_H95 zenon_H71 zenon_H124 zenon_H133 zenon_H10a zenon_H1ef zenon_H128 zenon_H195 zenon_H48 zenon_H57 zenon_H1fa zenon_H22 zenon_H1a4 zenon_H36 zenon_H24b zenon_H24a zenon_H27 zenon_H3e zenon_H3f zenon_H130 zenon_Hd8 zenon_H208 zenon_H67 zenon_H1f0 zenon_H6a zenon_H1cf zenon_H161 zenon_H6f zenon_H267 zenon_He8 zenon_Had zenon_H250 zenon_H251 zenon_H145 zenon_Hdc zenon_Hdb zenon_H255 zenon_He4 zenon_H231 zenon_Hc2 zenon_Hdf zenon_Hd5 zenon_He2 zenon_H1ca zenon_H1c7 zenon_Hf3 zenon_H11f zenon_H1d. % 18.96/19.08 apply (zenon_or_s _ _ zenon_H172); [ zenon_intro zenon_H150 | zenon_intro zenon_H174 ]. % 18.96/19.08 apply (zenon_L378_); trivial. % 18.96/19.08 apply (zenon_or_s _ _ zenon_H174); [ zenon_intro zenon_H113 | zenon_intro zenon_H175 ]. % 18.96/19.08 apply (zenon_L68_); trivial. % 18.96/19.08 apply (zenon_or_s _ _ zenon_H175); [ zenon_intro zenon_H176 | zenon_intro zenon_H151 ]. % 18.96/19.08 exact (zenon_H173 zenon_H176). % 18.96/19.08 apply (zenon_or_s _ _ zenon_H1ac); [ zenon_intro zenon_H44 | zenon_intro zenon_H1af ]. % 18.96/19.08 apply (zenon_L987_); trivial. % 18.96/19.08 apply (zenon_or_s _ _ zenon_H1af); [ zenon_intro zenon_H1b1 | zenon_intro zenon_H1b0 ]. % 18.96/19.08 apply (zenon_L646_); trivial. % 18.96/19.08 apply (zenon_or_s _ _ zenon_H1b0); [ zenon_intro zenon_H61 | zenon_intro zenon_H60 ]. % 18.96/19.08 apply (zenon_L988_); trivial. % 18.96/19.08 apply (zenon_or_s _ _ zenon_He8); [ zenon_intro zenon_Hac | zenon_intro zenon_Heb ]. % 18.96/19.08 exact (zenon_Had zenon_Hac). % 18.96/19.08 apply (zenon_or_s _ _ zenon_Heb); [ zenon_intro zenon_Hae | zenon_intro zenon_Hec ]. % 18.96/19.08 exact (zenon_H250 zenon_Hae). % 18.96/19.08 apply (zenon_or_s _ _ zenon_Hec); [ zenon_intro zenon_Hba | zenon_intro zenon_Hc4 ]. % 18.96/19.08 exact (zenon_H251 zenon_Hba). % 18.96/19.08 apply (zenon_or_s _ _ zenon_H145); [ zenon_intro zenon_Hcd | zenon_intro zenon_H146 ]. % 18.96/19.08 apply (zenon_L979_); trivial. % 18.96/19.08 apply (zenon_or_s _ _ zenon_H146); [ zenon_intro zenon_Hd7 | zenon_intro zenon_H147 ]. % 18.96/19.08 apply (zenon_L989_); trivial. % 18.96/19.08 apply (zenon_or_s _ _ zenon_H147); [ zenon_intro zenon_H11d | zenon_intro zenon_Hf6 ]. % 18.96/19.08 apply (zenon_L224_); trivial. % 18.96/19.08 apply (zenon_L798_); trivial. % 18.96/19.08 (* end of lemma zenon_L990_ *) % 18.96/19.08 assert (zenon_L991_ : (((op (e0) (e3)) = (e0))\/(((op (e0) (e3)) = (e1))\/(((op (e0) (e3)) = (e2))\/((op (e0) (e3)) = (e3))))) -> ((op (e3) (e3)) = (e0)) -> (~((op (e0) (e3)) = (op (e3) (e3)))) -> (~((op (e0) (e3)) = (e1))) -> ((op (e2) (e3)) = (e2)) -> (~((op (e0) (e3)) = (op (e2) (e3)))) -> (~((op (e0) (e3)) = (op (e1) (e3)))) -> ((op (e1) (e3)) = (e3)) -> False). % 18.96/19.08 do 0 intro. intros zenon_He4 zenon_H60 zenon_Hc2 zenon_H231 zenon_H11d zenon_He2 zenon_H1d zenon_Hdc. % 18.96/19.08 apply (zenon_or_s _ _ zenon_He4); [ zenon_intro zenon_H1e | zenon_intro zenon_He5 ]. % 18.96/19.08 apply (zenon_L440_); trivial. % 18.96/19.08 apply (zenon_or_s _ _ zenon_He5); [ zenon_intro zenon_Hc3 | zenon_intro zenon_He6 ]. % 18.96/19.08 exact (zenon_H231 zenon_Hc3). % 18.96/19.08 apply (zenon_or_s _ _ zenon_He6); [ zenon_intro zenon_Hcd | zenon_intro zenon_He3 ]. % 18.96/19.08 apply (zenon_L234_); trivial. % 18.96/19.08 apply (zenon_L117_); trivial. % 18.96/19.08 (* end of lemma zenon_L991_ *) % 18.96/19.08 assert (zenon_L992_ : (((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)) = (e1)) -> (~((op (e1) (e1)) = (e1))) -> (~((op (e1) (e2)) = (e1))) -> (((op (e3) (e0)) = (e1))\/(((op (e3) (e1)) = (e1))\/(((op (e3) (e2)) = (e1))\/((op (e3) (e3)) = (e1))))) -> (~((op (e3) (e0)) = (e1))) -> (~((op (e3) (e1)) = (e1))) -> (~((op (e3) (e2)) = (e1))) -> (~((op (e1) (e3)) = (op (e3) (e3)))) -> False). % 18.96/19.08 do 0 intro. intros zenon_H128 zenon_H201 zenon_Hed zenon_H10a zenon_H24d zenon_He8 zenon_Had zenon_H250 zenon_H251 zenon_Hd5. % 18.96/19.08 apply (zenon_or_s _ _ zenon_H128); [ zenon_intro zenon_H9d | zenon_intro zenon_H129 ]. % 18.96/19.08 apply (zenon_L413_); trivial. % 18.96/19.08 apply (zenon_or_s _ _ zenon_H129); [ zenon_intro zenon_H10d | zenon_intro zenon_H12a ]. % 18.96/19.08 exact (zenon_H10a zenon_H10d). % 18.96/19.08 apply (zenon_or_s _ _ zenon_H12a); [ zenon_intro zenon_Hf0 | zenon_intro zenon_Hd6 ]. % 18.96/19.08 exact (zenon_H24d zenon_Hf0). % 18.96/19.08 apply (zenon_L800_); trivial. % 18.96/19.08 (* end of lemma zenon_L992_ *) % 18.96/19.08 assert (zenon_L993_ : (((op (e0) (e0)) = (e1))\/(((op (e1) (e0)) = (e1))\/(((op (e2) (e0)) = (e1))\/((op (e3) (e0)) = (e1))))) -> (~((op (e0) (e0)) = (e1))) -> (~((op (e2) (e3)) = (e1))) -> (~((op (e2) (e2)) = (e1))) -> (~((op (e2) (e1)) = (e1))) -> (((op (e2) (e0)) = (e1))\/(((op (e2) (e1)) = (e1))\/(((op (e2) (e2)) = (e1))\/((op (e2) (e3)) = (e1))))) -> (~((op (e1) (e3)) = (op (e3) (e3)))) -> (~((op (e3) (e2)) = (e1))) -> (~((op (e3) (e1)) = (e1))) -> (((op (e3) (e0)) = (e1))\/(((op (e3) (e1)) = (e1))\/(((op (e3) (e2)) = (e1))\/((op (e3) (e3)) = (e1))))) -> (~((op (e1) (e2)) = (e1))) -> (~((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))))) -> (~((op (e3) (e0)) = (e1))) -> False). % 18.96/19.08 do 0 intro. intros zenon_H235 zenon_H84 zenon_H255 zenon_H198 zenon_H24f zenon_H106 zenon_Hd5 zenon_H251 zenon_H250 zenon_He8 zenon_H24d zenon_H10a zenon_H201 zenon_H128 zenon_Had. % 18.96/19.08 apply (zenon_or_s _ _ zenon_H235); [ zenon_intro zenon_H7a | zenon_intro zenon_H236 ]. % 18.96/19.08 exact (zenon_H84 zenon_H7a). % 18.96/19.08 apply (zenon_or_s _ _ zenon_H236); [ zenon_intro zenon_H9d | zenon_intro zenon_H237 ]. % 18.96/19.08 apply (zenon_L956_); trivial. % 18.96/19.08 apply (zenon_or_s _ _ zenon_H237); [ zenon_intro zenon_Hed | zenon_intro zenon_Hac ]. % 18.96/19.08 apply (zenon_L992_); trivial. % 18.96/19.08 exact (zenon_Had zenon_Hac). % 18.96/19.08 (* end of lemma zenon_L993_ *) % 18.96/19.08 assert (zenon_L994_ : ((~((op (e3) (e1)) = (e1)))\/((op (e3) (e1)) = (e1))) -> ((op (e0) (e1)) = (e1)) -> (((op (e0) (e0)) = (e1))\/(((op (e1) (e0)) = (e1))\/(((op (e2) (e0)) = (e1))\/((op (e3) (e0)) = (e1))))) -> (~((op (e1) (e1)) = (e1))) -> (~((op (e1) (e2)) = (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) (e0)) = (e1))) -> (((op (e1) (e0)) = (e1))\/(((op (e1) (e1)) = (e1))\/(((op (e1) (e2)) = (e1))\/((op (e1) (e3)) = (e1))))) -> (~((op (e1) (e0)) = (op (e2) (e0)))) -> (~((op (e2) (e1)) = (e1))) -> (~((op (e2) (e2)) = (e1))) -> (~((op (e2) (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)) = (op (e3) (e1)))) -> ((op (e0) (e1)) = (e2)) -> ((~((op (e3) (e2)) = (e1)))\/((op (e3) (e1)) = (e2))) -> False). % 18.96/19.08 do 0 intro. intros zenon_H261 zenon_Ha0 zenon_H235 zenon_H10a zenon_H24d zenon_He8 zenon_Hd5 zenon_Had zenon_H128 zenon_H201 zenon_H24f zenon_H198 zenon_H255 zenon_H106 zenon_H84 zenon_H210 zenon_H10f zenon_H252. % 18.96/19.08 apply (zenon_or_s _ _ zenon_H261); [ zenon_intro zenon_H250 | zenon_intro zenon_Hae ]. % 18.96/19.08 apply (zenon_or_s _ _ zenon_H252); [ zenon_intro zenon_H251 | zenon_intro zenon_H14d ]. % 18.96/19.08 apply (zenon_L993_); trivial. % 18.96/19.08 apply (zenon_L389_); trivial. % 18.96/19.08 apply (zenon_L363_); trivial. % 18.96/19.08 (* end of lemma zenon_L994_ *) % 18.96/19.08 assert (zenon_L995_ : ((~((op (e2) (e2)) = (e1)))\/((op (e2) (e1)) = (e2))) -> (~((op (e0) (e1)) = (op (e2) (e1)))) -> ((~((op (e3) (e0)) = (e1)))\/((op (e3) (e1)) = (e0))) -> ((op (e1) (e1)) = (e3)) -> ((~((op (e3) (e2)) = (e1)))\/((op (e3) (e1)) = (e2))) -> ((op (e0) (e1)) = (e2)) -> (~((op (e0) (e1)) = (op (e3) (e1)))) -> (~((op (e0) (e0)) = (e1))) -> (((op (e2) (e0)) = (e1))\/(((op (e2) (e1)) = (e1))\/(((op (e2) (e2)) = (e1))\/((op (e2) (e3)) = (e1))))) -> (~((op (e2) (e1)) = (e1))) -> (~((op (e1) (e0)) = (op (e2) (e0)))) -> (((op (e1) (e0)) = (e1))\/(((op (e1) (e1)) = (e1))\/(((op (e1) (e2)) = (e1))\/((op (e1) (e3)) = (e1))))) -> (~((op (e1) (e3)) = (op (e3) (e3)))) -> (((op (e3) (e0)) = (e1))\/(((op (e3) (e1)) = (e1))\/(((op (e3) (e2)) = (e1))\/((op (e3) (e3)) = (e1))))) -> (~((op (e1) (e2)) = (e1))) -> (~((op (e1) (e1)) = (e1))) -> (((op (e0) (e0)) = (e1))\/(((op (e1) (e0)) = (e1))\/(((op (e2) (e0)) = (e1))\/((op (e3) (e0)) = (e1))))) -> ((op (e0) (e1)) = (e1)) -> ((~((op (e3) (e1)) = (e1)))\/((op (e3) (e1)) = (e1))) -> (~((op (e1) (e1)) = (op (e2) (e1)))) -> ((~((op (e2) (e3)) = (e1)))\/((op (e2) (e1)) = (e3))) -> False). % 18.96/19.08 do 0 intro. intros zenon_H253 zenon_H17e zenon_H254 zenon_H13f zenon_H252 zenon_H10f zenon_H210 zenon_H84 zenon_H106 zenon_H24f zenon_H201 zenon_H128 zenon_Hd5 zenon_He8 zenon_H24d zenon_H10a zenon_H235 zenon_Ha0 zenon_H261 zenon_H13e zenon_H263. % 18.96/19.08 apply (zenon_or_s _ _ zenon_H253); [ zenon_intro zenon_H198 | zenon_intro zenon_H1ca ]. % 18.96/19.08 apply (zenon_or_s _ _ zenon_H263); [ zenon_intro zenon_H255 | zenon_intro zenon_Ha6 ]. % 18.96/19.08 apply (zenon_or_s _ _ zenon_H254); [ zenon_intro zenon_Had | zenon_intro zenon_H1b1 ]. % 18.96/19.08 apply (zenon_L994_); trivial. % 18.96/19.08 apply (zenon_L580_); trivial. % 18.96/19.08 apply (zenon_L95_); trivial. % 18.96/19.08 apply (zenon_L191_); trivial. % 18.96/19.08 (* end of lemma zenon_L995_ *) % 18.96/19.08 assert (zenon_L996_ : ((~((op (e2) (e1)) = (e1)))\/((op (e2) (e1)) = (e1))) -> ((~((op (e2) (e3)) = (e1)))\/((op (e2) (e1)) = (e3))) -> (~((op (e1) (e1)) = (op (e2) (e1)))) -> ((~((op (e3) (e1)) = (e1)))\/((op (e3) (e1)) = (e1))) -> ((op (e0) (e1)) = (e1)) -> (((op (e0) (e0)) = (e1))\/(((op (e1) (e0)) = (e1))\/(((op (e2) (e0)) = (e1))\/((op (e3) (e0)) = (e1))))) -> (~((op (e1) (e1)) = (e1))) -> (~((op (e1) (e2)) = (e1))) -> (((op (e3) (e0)) = (e1))\/(((op (e3) (e1)) = (e1))\/(((op (e3) (e2)) = (e1))\/((op (e3) (e3)) = (e1))))) -> (~((op (e1) (e3)) = (op (e3) (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)) = (e1))\/(((op (e2) (e1)) = (e1))\/(((op (e2) (e2)) = (e1))\/((op (e2) (e3)) = (e1))))) -> (~((op (e0) (e0)) = (e1))) -> (~((op (e0) (e1)) = (op (e3) (e1)))) -> ((op (e0) (e1)) = (e2)) -> ((~((op (e3) (e2)) = (e1)))\/((op (e3) (e1)) = (e2))) -> ((op (e1) (e1)) = (e3)) -> ((~((op (e3) (e0)) = (e1)))\/((op (e3) (e1)) = (e0))) -> (~((op (e0) (e1)) = (op (e2) (e1)))) -> ((~((op (e2) (e2)) = (e1)))\/((op (e2) (e1)) = (e2))) -> False). % 18.96/19.08 do 0 intro. intros zenon_H262 zenon_H263 zenon_H13e zenon_H261 zenon_Ha0 zenon_H235 zenon_H10a zenon_H24d zenon_He8 zenon_Hd5 zenon_H128 zenon_H201 zenon_H106 zenon_H84 zenon_H210 zenon_H10f zenon_H252 zenon_H13f zenon_H254 zenon_H17e zenon_H253. % 18.96/19.08 apply (zenon_or_s _ _ zenon_H262); [ zenon_intro zenon_H24f | zenon_intro zenon_Ha5 ]. % 18.96/19.08 apply (zenon_L995_); trivial. % 18.96/19.08 apply (zenon_L357_); trivial. % 18.96/19.08 (* end of lemma zenon_L996_ *) % 18.96/19.08 assert (zenon_L997_ : ((~((op (e1) (e2)) = (e1)))\/((op (e1) (e1)) = (e2))) -> (~((op (e0) (e1)) = (op (e1) (e1)))) -> (((op (e1) (e0)) = (e1))\/(((op (e1) (e1)) = (e1))\/(((op (e1) (e2)) = (e1))\/((op (e1) (e3)) = (e1))))) -> (~((op (e1) (e1)) = (e1))) -> (~((op (e1) (e0)) = (e1))) -> ((~((op (e2) (e1)) = (e1)))\/((op (e2) (e1)) = (e1))) -> ((~((op (e2) (e3)) = (e1)))\/((op (e2) (e1)) = (e3))) -> (~((op (e1) (e1)) = (op (e2) (e1)))) -> ((~((op (e3) (e1)) = (e1)))\/((op (e3) (e1)) = (e1))) -> ((op (e0) (e1)) = (e1)) -> (((op (e0) (e0)) = (e1))\/(((op (e1) (e0)) = (e1))\/(((op (e2) (e0)) = (e1))\/((op (e3) (e0)) = (e1))))) -> (((op (e3) (e0)) = (e1))\/(((op (e3) (e1)) = (e1))\/(((op (e3) (e2)) = (e1))\/((op (e3) (e3)) = (e1))))) -> (~((op (e1) (e3)) = (op (e3) (e3)))) -> (~((op (e1) (e0)) = (op (e2) (e0)))) -> (((op (e2) (e0)) = (e1))\/(((op (e2) (e1)) = (e1))\/(((op (e2) (e2)) = (e1))\/((op (e2) (e3)) = (e1))))) -> (~((op (e0) (e0)) = (e1))) -> (~((op (e0) (e1)) = (op (e3) (e1)))) -> ((op (e0) (e1)) = (e2)) -> ((~((op (e3) (e2)) = (e1)))\/((op (e3) (e1)) = (e2))) -> ((~((op (e3) (e0)) = (e1)))\/((op (e3) (e1)) = (e0))) -> (~((op (e0) (e1)) = (op (e2) (e1)))) -> ((~((op (e2) (e2)) = (e1)))\/((op (e2) (e1)) = (e2))) -> ((~((op (e1) (e3)) = (e1)))\/((op (e1) (e1)) = (e3))) -> False). % 18.96/19.08 do 0 intro. intros zenon_H256 zenon_H10e zenon_H128 zenon_H10a zenon_H1ef zenon_H262 zenon_H263 zenon_H13e zenon_H261 zenon_Ha0 zenon_H235 zenon_He8 zenon_Hd5 zenon_H201 zenon_H106 zenon_H84 zenon_H210 zenon_H10f zenon_H252 zenon_H254 zenon_H17e zenon_H253 zenon_H258. % 18.96/19.08 apply (zenon_or_s _ _ zenon_H256); [ zenon_intro zenon_H24d | zenon_intro zenon_H110 ]. % 18.96/19.08 apply (zenon_or_s _ _ zenon_H258); [ zenon_intro zenon_H24e | zenon_intro zenon_H13f ]. % 18.96/19.08 apply (zenon_L713_); trivial. % 18.96/19.08 apply (zenon_L996_); trivial. % 18.96/19.08 apply (zenon_L67_); trivial. % 18.96/19.08 (* end of lemma zenon_L997_ *) % 18.96/19.08 assert (zenon_L998_ : (((op (e0) (e3)) = (e0))\/(((op (e1) (e3)) = (e0))\/(((op (e2) (e3)) = (e0))\/((op (e3) (e3)) = (e0))))) -> (~((e0) = (e2))) -> ((op (e0) (e3)) = (e2)) -> (~((op (e3) (e2)) = (e1))) -> (~((op (e3) (e1)) = (e1))) -> (~((op (e3) (e0)) = (e1))) -> (((op (e3) (e0)) = (e1))\/(((op (e3) (e1)) = (e1))\/(((op (e3) (e2)) = (e1))\/((op (e3) (e3)) = (e1))))) -> (~((op (e2) (e1)) = (op (e2) (e3)))) -> ((op (e2) (e1)) = (e0)) -> ((op (e3) (e0)) = (e0)) -> (~((op (e3) (e0)) = (op (e3) (e3)))) -> False). % 18.96/19.08 do 0 intro. intros zenon_H67 zenon_H149 zenon_Hcd zenon_H251 zenon_H250 zenon_Had zenon_He8 zenon_H1c7 zenon_H36 zenon_H44 zenon_H71. % 18.96/19.08 apply (zenon_or_s _ _ zenon_H67); [ zenon_intro zenon_H1e | zenon_intro zenon_H68 ]. % 18.96/19.08 apply (zenon_L428_); trivial. % 18.96/19.08 apply (zenon_or_s _ _ zenon_H68); [ zenon_intro zenon_H1f | zenon_intro zenon_H69 ]. % 18.96/19.08 apply (zenon_L803_); trivial. % 18.96/19.08 apply (zenon_or_s _ _ zenon_H69); [ zenon_intro zenon_H37 | zenon_intro zenon_H60 ]. % 18.96/19.08 apply (zenon_L640_); trivial. % 18.96/19.08 apply (zenon_L21_); trivial. % 18.96/19.08 (* end of lemma zenon_L998_ *) % 18.96/19.08 assert (zenon_L999_ : (~((op (e3) (e0)) = (op (e3) (e3)))) -> ((op (e3) (e0)) = (e0)) -> ((op (e2) (e1)) = (e0)) -> (~((op (e2) (e1)) = (op (e2) (e3)))) -> (((op (e3) (e0)) = (e1))\/(((op (e3) (e1)) = (e1))\/(((op (e3) (e2)) = (e1))\/((op (e3) (e3)) = (e1))))) -> (~((op (e3) (e1)) = (e1))) -> (~((op (e3) (e2)) = (e1))) -> (~((e0) = (e2))) -> (((op (e0) (e3)) = (e0))\/(((op (e1) (e3)) = (e0))\/(((op (e2) (e3)) = (e0))\/((op (e3) (e3)) = (e0))))) -> ((op (e0) (e2)) = (e0)) -> ((~((op (e1) (e2)) = (e1)))\/((op (e1) (e1)) = (e2))) -> (~((op (e0) (e1)) = (op (e1) (e1)))) -> (((op (e1) (e0)) = (e1))\/(((op (e1) (e1)) = (e1))\/(((op (e1) (e2)) = (e1))\/((op (e1) (e3)) = (e1))))) -> (~((op (e1) (e1)) = (e1))) -> (~((op (e1) (e0)) = (e1))) -> ((~((op (e2) (e1)) = (e1)))\/((op (e2) (e1)) = (e1))) -> ((~((op (e2) (e3)) = (e1)))\/((op (e2) (e1)) = (e3))) -> (~((op (e1) (e1)) = (op (e2) (e1)))) -> ((~((op (e3) (e1)) = (e1)))\/((op (e3) (e1)) = (e1))) -> ((op (e0) (e1)) = (e1)) -> (((op (e0) (e0)) = (e1))\/(((op (e1) (e0)) = (e1))\/(((op (e2) (e0)) = (e1))\/((op (e3) (e0)) = (e1))))) -> (~((op (e1) (e3)) = (op (e3) (e3)))) -> (~((op (e1) (e0)) = (op (e2) (e0)))) -> (((op (e2) (e0)) = (e1))\/(((op (e2) (e1)) = (e1))\/(((op (e2) (e2)) = (e1))\/((op (e2) (e3)) = (e1))))) -> (~((op (e0) (e0)) = (e1))) -> (~((op (e0) (e1)) = (op (e3) (e1)))) -> ((~((op (e3) (e2)) = (e1)))\/((op (e3) (e1)) = (e2))) -> ((~((op (e3) (e0)) = (e1)))\/((op (e3) (e1)) = (e0))) -> (~((op (e0) (e1)) = (op (e2) (e1)))) -> ((~((op (e2) (e2)) = (e1)))\/((op (e2) (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 (e1) (e0)) = (op (e3) (e0)))) -> (~((op (e1) (e1)) = (op (e1) (e3)))) -> (~((op (e0) (e2)) = (op (e0) (e3)))) -> (~((op (e0) (e2)) = (op (e1) (e2)))) -> (~((op (e0) (e3)) = (op (e1) (e3)))) -> (~((op (e0) (e3)) = (e1))) -> (((op (e0) (e3)) = (e0))\/(((op (e0) (e3)) = (e1))\/(((op (e0) (e3)) = (e2))\/((op (e0) (e3)) = (e3))))) -> (((op (e0) (e3)) = (e1))\/(((op (e1) (e3)) = (e1))\/(((op (e2) (e3)) = (e1))\/((op (e3) (e3)) = (e1))))) -> (~((op (e1) (e2)) = (op (e1) (e3)))) -> (~((op (e2) (e3)) = (e1))) -> (~((e1) = (e3))) -> ((op (e1) (e1)) = (e2)) -> (~((e2) = (e3))) -> (((op (e1) (e0)) = (e3))\/(((op (e1) (e1)) = (e3))\/(((op (e1) (e2)) = (e3))\/((op (e1) (e3)) = (e3))))) -> (~((op (e1) (e3)) = (e1))) -> (((op (e0) (e0)) = (e2))\/(((op (e0) (e1)) = (e2))\/(((op (e0) (e2)) = (e2))\/((op (e0) (e3)) = (e2))))) -> (~((op (e3) (e0)) = (e1))) -> False). % 18.96/19.08 do 0 intro. intros zenon_H71 zenon_H44 zenon_H36 zenon_H1c7 zenon_He8 zenon_H250 zenon_H251 zenon_H149 zenon_H67 zenon_H48 zenon_H256 zenon_H10e zenon_H128 zenon_H10a zenon_H1ef zenon_H262 zenon_H263 zenon_H13e zenon_H261 zenon_Ha0 zenon_H235 zenon_Hd5 zenon_H201 zenon_H106 zenon_H84 zenon_H210 zenon_H252 zenon_H254 zenon_H17e zenon_H253 zenon_H258 zenon_H22 zenon_H1fa zenon_H57 zenon_H208 zenon_H195 zenon_H1d zenon_H231 zenon_He4 zenon_H133 zenon_H124 zenon_H255 zenon_H95 zenon_H110 zenon_H12b zenon_H16f zenon_H24e zenon_H183 zenon_Had. % 18.96/19.08 apply (zenon_or_s _ _ zenon_H235); [ zenon_intro zenon_H7a | zenon_intro zenon_H236 ]. % 18.96/19.08 exact (zenon_H84 zenon_H7a). % 18.96/19.08 apply (zenon_or_s _ _ zenon_H236); [ zenon_intro zenon_H9d | zenon_intro zenon_H237 ]. % 18.96/19.08 exact (zenon_H1ef zenon_H9d). % 18.96/19.08 apply (zenon_or_s _ _ zenon_H237); [ zenon_intro zenon_Hed | zenon_intro zenon_Hac ]. % 18.96/19.08 apply (zenon_or_s _ _ zenon_H183); [ zenon_intro zenon_H7b | zenon_intro zenon_H186 ]. % 18.96/19.08 apply (zenon_or_s _ _ zenon_H22); [ zenon_intro zenon_H27 | zenon_intro zenon_H26 ]. % 18.96/19.08 apply (zenon_L312_); trivial. % 18.96/19.08 apply (zenon_or_s _ _ zenon_H26); [ zenon_intro zenon_H29 | zenon_intro zenon_H28 ]. % 18.96/19.08 apply (zenon_L961_); trivial. % 18.96/19.08 apply (zenon_or_s _ _ zenon_H28); [ zenon_intro zenon_H2a | zenon_intro zenon_H1f ]. % 18.96/19.08 apply (zenon_L334_); trivial. % 18.96/19.08 apply (zenon_or_s _ _ zenon_H128); [ zenon_intro zenon_H9d | zenon_intro zenon_H129 ]. % 18.96/19.08 exact (zenon_H1ef zenon_H9d). % 18.96/19.08 apply (zenon_or_s _ _ zenon_H129); [ zenon_intro zenon_H10d | zenon_intro zenon_H12a ]. % 18.96/19.08 exact (zenon_H10a zenon_H10d). % 18.96/19.08 apply (zenon_or_s _ _ zenon_H12a); [ zenon_intro zenon_Hf0 | zenon_intro zenon_Hd6 ]. % 18.96/19.08 apply (zenon_or_s _ _ zenon_H16f); [ zenon_intro zenon_H9e | zenon_intro zenon_H170 ]. % 18.96/19.08 apply (zenon_L491_); trivial. % 18.96/19.08 apply (zenon_or_s _ _ zenon_H170); [ zenon_intro zenon_H13f | zenon_intro zenon_H171 ]. % 18.96/19.08 apply (zenon_L166_); trivial. % 18.96/19.08 apply (zenon_or_s _ _ zenon_H171); [ zenon_intro zenon_H16c | zenon_intro zenon_Hdc ]. % 18.96/19.08 apply (zenon_L167_); trivial. % 18.96/19.08 apply (zenon_L827_); trivial. % 18.96/19.08 exact (zenon_H24e zenon_Hd6). % 18.96/19.08 apply (zenon_or_s _ _ zenon_H186); [ zenon_intro zenon_H10f | zenon_intro zenon_H187 ]. % 18.96/19.08 apply (zenon_L997_); trivial. % 18.96/19.08 apply (zenon_or_s _ _ zenon_H187); [ zenon_intro zenon_H150 | zenon_intro zenon_Hcd ]. % 18.96/19.08 apply (zenon_L378_); trivial. % 18.96/19.08 apply (zenon_L998_); trivial. % 18.96/19.08 exact (zenon_Had zenon_Hac). % 18.96/19.08 (* end of lemma zenon_L999_ *) % 18.96/19.08 assert (zenon_L1000_ : (((op (e2) (e2)) = (e0))\/(((op (e2) (e2)) = (e1))\/(((op (e2) (e2)) = (e2))\/((op (e2) (e2)) = (e3))))) -> ((op (e1) (e2)) = (e0)) -> (~((op (e1) (e2)) = (op (e2) (e2)))) -> (~((op (e2) (e2)) = (e1))) -> (~((op (e2) (e2)) = (e2))) -> (~((op (e0) (e2)) = (op (e2) (e2)))) -> ((op (e0) (e2)) = (e3)) -> False). % 18.96/19.08 do 0 intro. intros zenon_H1c4 zenon_H2a zenon_H2b zenon_H198 zenon_H173 zenon_Ha8 zenon_Ha9. % 18.96/19.08 apply (zenon_or_s _ _ zenon_H1c4); [ zenon_intro zenon_H2c | zenon_intro zenon_H1c5 ]. % 18.96/19.08 apply (zenon_L3_); trivial. % 18.96/19.08 apply (zenon_or_s _ _ zenon_H1c5); [ zenon_intro zenon_Hf1 | zenon_intro zenon_H1c6 ]. % 18.96/19.08 exact (zenon_H198 zenon_Hf1). % 18.96/19.08 apply (zenon_or_s _ _ zenon_H1c6); [ zenon_intro zenon_H176 | zenon_intro zenon_Haa ]. % 18.96/19.08 exact (zenon_H173 zenon_H176). % 18.96/19.08 apply (zenon_L40_); trivial. % 18.96/19.08 (* end of lemma zenon_L1000_ *) % 18.96/19.08 assert (zenon_L1001_ : (((op (e0) (e2)) = (e3))\/(((op (e1) (e2)) = (e3))\/(((op (e2) (e2)) = (e3))\/((op (e3) (e2)) = (e3))))) -> (~((op (e2) (e2)) = (e2))) -> (~((op (e2) (e2)) = (e1))) -> (~((op (e1) (e2)) = (op (e2) (e2)))) -> (((op (e2) (e2)) = (e0))\/(((op (e2) (e2)) = (e1))\/(((op (e2) (e2)) = (e2))\/((op (e2) (e2)) = (e3))))) -> (~((e1) = (e3))) -> ((op (e1) (e2)) = (e1)) -> (~((op (e0) (e2)) = (op (e2) (e2)))) -> (((op (e3) (e2)) = (e0))\/(((op (e3) (e2)) = (e1))\/(((op (e3) (e2)) = (e2))\/((op (e3) (e2)) = (e3))))) -> (~((op (e1) (e2)) = (op (e3) (e2)))) -> ((op (e1) (e2)) = (e0)) -> (~((op (e0) (e2)) = (op (e3) (e2)))) -> (~((op (e2) (e2)) = (op (e3) (e2)))) -> (~((op (e0) (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) (e1)) = (op (e3) (e2)))) -> ((op (e3) (e1)) = (e3)) -> False). % 18.96/19.08 do 0 intro. intros zenon_H1a6 zenon_H173 zenon_H198 zenon_H2b zenon_H1c4 zenon_H95 zenon_Hf0 zenon_Ha8 zenon_H191 zenon_H115 zenon_H2a zenon_H14f zenon_H18f zenon_H20d zenon_H195 zenon_H1ba zenon_H1a4 zenon_H161. % 18.96/19.08 apply (zenon_or_s _ _ zenon_H1a6); [ zenon_intro zenon_Ha9 | zenon_intro zenon_H1aa ]. % 18.96/19.08 apply (zenon_L1000_); trivial. % 18.96/19.08 apply (zenon_or_s _ _ zenon_H1aa); [ zenon_intro zenon_H16c | zenon_intro zenon_H1ab ]. % 18.96/19.08 apply (zenon_L167_); trivial. % 18.96/19.08 apply (zenon_or_s _ _ zenon_H1ab); [ zenon_intro zenon_Haa | zenon_intro zenon_H163 ]. % 18.96/19.08 apply (zenon_or_s _ _ zenon_H1ba); [ zenon_intro zenon_H48 | zenon_intro zenon_H1bb ]. % 18.96/19.08 apply (zenon_L334_); trivial. % 18.96/19.08 apply (zenon_or_s _ _ zenon_H1bb); [ zenon_intro zenon_H122 | zenon_intro zenon_H1bc ]. % 18.96/19.08 exact (zenon_H20d zenon_H122). % 18.96/19.08 apply (zenon_or_s _ _ zenon_H1bc); [ zenon_intro zenon_H150 | zenon_intro zenon_Ha9 ]. % 18.96/19.08 apply (zenon_L181_); trivial. % 18.96/19.08 apply (zenon_L40_); trivial. % 18.96/19.08 apply (zenon_L169_); trivial. % 18.96/19.08 (* end of lemma zenon_L1001_ *) % 18.96/19.08 assert (zenon_L1002_ : (((op (e2) (e0)) = (e1))\/(((op (e2) (e1)) = (e1))\/(((op (e2) (e2)) = (e1))\/((op (e2) (e3)) = (e1))))) -> ((op (e0) (e0)) = (e2)) -> ((op (e1) (e0)) = (e3)) -> ((op (e0) (e1)) = (e1)) -> (~((op (e0) (e1)) = (op (e2) (e1)))) -> ((op (e1) (e2)) = (e1)) -> (~((op (e1) (e2)) = (op (e2) (e2)))) -> (~((op (e2) (e3)) = (op (e3) (e3)))) -> ((op (e3) (e3)) = (e1)) -> False). % 18.96/19.08 do 0 intro. intros zenon_H106 zenon_H7b zenon_H9e zenon_Ha0 zenon_H17e zenon_Hf0 zenon_H2b zenon_Hf3 zenon_Hc4. % 18.96/19.08 apply (zenon_or_s _ _ zenon_H106); [ zenon_intro zenon_Hed | zenon_intro zenon_H107 ]. % 18.96/19.08 apply (zenon_L491_); trivial. % 18.96/19.08 apply (zenon_or_s _ _ zenon_H107); [ zenon_intro zenon_Ha5 | zenon_intro zenon_H108 ]. % 18.96/19.08 apply (zenon_L357_); trivial. % 18.96/19.08 apply (zenon_or_s _ _ zenon_H108); [ zenon_intro zenon_Hf1 | zenon_intro zenon_Hf4 ]. % 18.96/19.08 apply (zenon_L59_); trivial. % 18.96/19.08 apply (zenon_L60_); trivial. % 18.96/19.08 (* end of lemma zenon_L1002_ *) % 18.96/19.08 assert (zenon_L1003_ : (((op (e3) (e0)) = (e1))\/(((op (e3) (e1)) = (e1))\/(((op (e3) (e2)) = (e1))\/((op (e3) (e3)) = (e1))))) -> (~((op (e3) (e0)) = (e1))) -> (~((op (e3) (e1)) = (e1))) -> (~((op (e3) (e2)) = (e1))) -> (((op (e2) (e2)) = (e0))\/(((op (e2) (e2)) = (e1))\/(((op (e2) (e2)) = (e2))\/((op (e2) (e2)) = (e3))))) -> ((op (e0) (e2)) = (e3)) -> (~((op (e0) (e2)) = (op (e3) (e2)))) -> ((op (e0) (e2)) = (e2)) -> (~((op (e3) (e2)) = (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 (e2) (e2)) = (e1))) -> (~((op (e2) (e2)) = (e2))) -> ((op (e2) (e0)) = (e3)) -> (~((op (e2) (e0)) = (op (e2) (e2)))) -> False). % 18.96/19.08 do 0 intro. intros zenon_He8 zenon_Had zenon_H250 zenon_H251 zenon_H1c4 zenon_Ha9 zenon_H14f zenon_H150 zenon_H62 zenon_H18f zenon_H191 zenon_H198 zenon_H173 zenon_H3b zenon_H52. % 18.96/19.08 apply (zenon_or_s _ _ zenon_He8); [ zenon_intro zenon_Hac | zenon_intro zenon_Heb ]. % 18.96/19.08 exact (zenon_Had zenon_Hac). % 18.96/19.08 apply (zenon_or_s _ _ zenon_Heb); [ zenon_intro zenon_Hae | zenon_intro zenon_Hec ]. % 18.96/19.08 exact (zenon_H250 zenon_Hae). % 18.96/19.08 apply (zenon_or_s _ _ zenon_Hec); [ zenon_intro zenon_Hba | zenon_intro zenon_Hc4 ]. % 18.96/19.08 exact (zenon_H251 zenon_Hba). % 18.96/19.08 apply (zenon_or_s _ _ zenon_H1c4); [ zenon_intro zenon_H2c | zenon_intro zenon_H1c5 ]. % 18.96/19.08 apply (zenon_L148_); trivial. % 18.96/19.08 apply (zenon_or_s _ _ zenon_H1c5); [ zenon_intro zenon_Hf1 | zenon_intro zenon_H1c6 ]. % 18.96/19.08 exact (zenon_H198 zenon_Hf1). % 18.96/19.08 apply (zenon_or_s _ _ zenon_H1c6); [ zenon_intro zenon_H176 | zenon_intro zenon_Haa ]. % 18.96/19.08 exact (zenon_H173 zenon_H176). % 18.96/19.08 apply (zenon_L168_); trivial. % 18.96/19.08 (* end of lemma zenon_L1003_ *) % 18.96/19.08 assert (zenon_L1004_ : (((op (e0) (e0)) = (e3))\/(((op (e1) (e0)) = (e3))\/(((op (e2) (e0)) = (e3))\/((op (e3) (e0)) = (e3))))) -> (~((op (e1) (e3)) = (e1))) -> (((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 (e2) (e3)) = (op (e3) (e3)))) -> (~((op (e1) (e2)) = (op (e2) (e2)))) -> (~((op (e0) (e1)) = (op (e2) (e1)))) -> ((op (e0) (e1)) = (e1)) -> (((op (e2) (e0)) = (e1))\/(((op (e2) (e1)) = (e1))\/(((op (e2) (e2)) = (e1))\/((op (e2) (e3)) = (e1))))) -> ((op (e2) (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))))) -> (~((op (e2) (e0)) = (op (e2) (e2)))) -> (~((op (e2) (e2)) = (e2))) -> (~((op (e2) (e2)) = (e1))) -> (((op (e3) (e2)) = (e0))\/(((op (e3) (e2)) = (e1))\/(((op (e3) (e2)) = (e2))\/((op (e3) (e2)) = (e3))))) -> (~((op (e2) (e2)) = (op (e3) (e2)))) -> (~((op (e3) (e2)) = (op (e3) (e3)))) -> ((op (e0) (e2)) = (e2)) -> (~((op (e0) (e2)) = (op (e3) (e2)))) -> ((op (e0) (e2)) = (e3)) -> (((op (e2) (e2)) = (e0))\/(((op (e2) (e2)) = (e1))\/(((op (e2) (e2)) = (e2))\/((op (e2) (e2)) = (e3))))) -> (~((op (e3) (e2)) = (e1))) -> (~((op (e3) (e1)) = (e1))) -> (~((op (e3) (e0)) = (e1))) -> (((op (e3) (e0)) = (e1))\/(((op (e3) (e1)) = (e1))\/(((op (e3) (e2)) = (e1))\/((op (e3) (e3)) = (e1))))) -> ((op (e3) (e0)) = (e2)) -> (~((e2) = (e3))) -> False). % 18.96/19.08 do 0 intro. intros zenon_H1e0 zenon_H24e zenon_H26a zenon_H3f zenon_H84 zenon_Hf3 zenon_H2b zenon_H17e zenon_Ha0 zenon_H106 zenon_Hed zenon_H10a zenon_H1ef zenon_H128 zenon_H52 zenon_H173 zenon_H198 zenon_H191 zenon_H18f zenon_H62 zenon_H150 zenon_H14f zenon_Ha9 zenon_H1c4 zenon_H251 zenon_H250 zenon_Had zenon_He8 zenon_H148 zenon_H12b. % 18.96/19.08 apply (zenon_or_s _ _ zenon_H1e0); [ zenon_intro zenon_H3a | zenon_intro zenon_H1e1 ]. % 18.96/19.08 apply (zenon_L423_); trivial. % 18.96/19.08 apply (zenon_or_s _ _ zenon_H1e1); [ zenon_intro zenon_H9e | zenon_intro zenon_H1e2 ]. % 18.96/19.08 apply (zenon_or_s _ _ zenon_H128); [ zenon_intro zenon_H9d | zenon_intro zenon_H129 ]. % 18.96/19.08 exact (zenon_H1ef zenon_H9d). % 18.96/19.08 apply (zenon_or_s _ _ zenon_H129); [ zenon_intro zenon_H10d | zenon_intro zenon_H12a ]. % 18.96/19.08 exact (zenon_H10a zenon_H10d). % 18.96/19.08 apply (zenon_or_s _ _ zenon_H12a); [ zenon_intro zenon_Hf0 | zenon_intro zenon_Hd6 ]. % 18.96/19.08 apply (zenon_or_s _ _ zenon_He8); [ zenon_intro zenon_Hac | zenon_intro zenon_Heb ]. % 18.96/19.08 exact (zenon_Had zenon_Hac). % 18.96/19.08 apply (zenon_or_s _ _ zenon_Heb); [ zenon_intro zenon_Hae | zenon_intro zenon_Hec ]. % 18.96/19.08 exact (zenon_H250 zenon_Hae). % 18.96/19.08 apply (zenon_or_s _ _ zenon_Hec); [ zenon_intro zenon_Hba | zenon_intro zenon_Hc4 ]. % 18.96/19.08 exact (zenon_H251 zenon_Hba). % 18.96/19.08 apply (zenon_or_s _ _ zenon_H26a); [ zenon_intro zenon_H42 | zenon_intro zenon_H26b ]. % 18.96/19.08 exact (zenon_H3f zenon_H42). % 18.96/19.08 apply (zenon_or_s _ _ zenon_H26b); [ zenon_intro zenon_H7a | zenon_intro zenon_H26c ]. % 18.96/19.08 exact (zenon_H84 zenon_H7a). % 18.96/19.08 apply (zenon_or_s _ _ zenon_H26c); [ zenon_intro zenon_H7b | zenon_intro zenon_H3a ]. % 18.96/19.08 apply (zenon_L1002_); trivial. % 18.96/19.08 apply (zenon_L423_); trivial. % 18.96/19.08 exact (zenon_H24e zenon_Hd6). % 18.96/19.08 apply (zenon_or_s _ _ zenon_H1e2); [ zenon_intro zenon_H3b | zenon_intro zenon_H15e ]. % 18.96/19.08 apply (zenon_L1003_); trivial. % 18.96/19.08 apply (zenon_L109_); trivial. % 18.96/19.08 (* end of lemma zenon_L1004_ *) % 18.96/19.08 assert (zenon_L1005_ : (((op (e0) (e0)) = (e3))\/(((op (e0) (e1)) = (e3))\/(((op (e0) (e2)) = (e3))\/((op (e0) (e3)) = (e3))))) -> (~((e1) = (e3))) -> (~((e2) = (e3))) -> ((op (e3) (e0)) = (e2)) -> (((op (e3) (e0)) = (e1))\/(((op (e3) (e1)) = (e1))\/(((op (e3) (e2)) = (e1))\/((op (e3) (e3)) = (e1))))) -> (~((op (e3) (e0)) = (e1))) -> (~((op (e3) (e1)) = (e1))) -> (~((op (e3) (e2)) = (e1))) -> (((op (e2) (e2)) = (e0))\/(((op (e2) (e2)) = (e1))\/(((op (e2) (e2)) = (e2))\/((op (e2) (e2)) = (e3))))) -> (~((op (e0) (e2)) = (op (e3) (e2)))) -> ((op (e0) (e2)) = (e2)) -> (~((op (e3) (e2)) = (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 (e2) (e2)) = (e1))) -> (~((op (e2) (e2)) = (e2))) -> (~((op (e2) (e0)) = (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) (e0)) = (e1)) -> (((op (e2) (e0)) = (e1))\/(((op (e2) (e1)) = (e1))\/(((op (e2) (e2)) = (e1))\/((op (e2) (e3)) = (e1))))) -> ((op (e0) (e1)) = (e1)) -> (~((op (e0) (e1)) = (op (e2) (e1)))) -> (~((op (e1) (e2)) = (op (e2) (e2)))) -> (~((op (e2) (e3)) = (op (e3) (e3)))) -> (~((op (e0) (e0)) = (e1))) -> (~((op (e0) (e0)) = (e0))) -> (((op (e0) (e0)) = (e0))\/(((op (e0) (e0)) = (e1))\/(((op (e0) (e0)) = (e2))\/((op (e0) (e0)) = (e3))))) -> (~((op (e1) (e3)) = (e1))) -> (((op (e0) (e0)) = (e3))\/(((op (e1) (e0)) = (e3))\/(((op (e2) (e0)) = (e3))\/((op (e3) (e0)) = (e3))))) -> ((op (e0) (e3)) = (e0)) -> (~((e0) = (e3))) -> False). % 18.96/19.08 do 0 intro. intros zenon_H168 zenon_H95 zenon_H12b zenon_H148 zenon_He8 zenon_Had zenon_H250 zenon_H251 zenon_H1c4 zenon_H14f zenon_H150 zenon_H62 zenon_H18f zenon_H191 zenon_H198 zenon_H173 zenon_H52 zenon_H128 zenon_H1ef zenon_H10a zenon_Hed zenon_H106 zenon_Ha0 zenon_H17e zenon_H2b zenon_Hf3 zenon_H84 zenon_H3f zenon_H26a zenon_H24e zenon_H1e0 zenon_H1e zenon_H9a. % 18.96/19.08 apply (zenon_or_s _ _ zenon_H168); [ zenon_intro zenon_H3a | zenon_intro zenon_H169 ]. % 18.96/19.08 apply (zenon_L423_); trivial. % 18.96/19.08 apply (zenon_or_s _ _ zenon_H169); [ zenon_intro zenon_H99 | zenon_intro zenon_H16a ]. % 18.96/19.08 apply (zenon_L403_); trivial. % 18.96/19.08 apply (zenon_or_s _ _ zenon_H16a); [ zenon_intro zenon_Ha9 | zenon_intro zenon_He3 ]. % 18.96/19.08 apply (zenon_L1004_); trivial. % 18.96/19.08 apply (zenon_L515_); trivial. % 18.96/19.08 (* end of lemma zenon_L1005_ *) % 18.96/19.08 assert (zenon_L1006_ : (((op (e0) (e3)) = (e3))\/(((op (e1) (e3)) = (e3))\/(((op (e2) (e3)) = (e3))\/((op (e3) (e3)) = (e3))))) -> (~((e0) = (e3))) -> (~((op (e2) (e3)) = (op (e3) (e3)))) -> ((op (e3) (e3)) = (e1)) -> ((op (e0) (e3)) = (e0)) -> (((op (e2) (e3)) = (e0))\/(((op (e2) (e3)) = (e1))\/(((op (e2) (e3)) = (e2))\/((op (e2) (e3)) = (e3))))) -> (~((op (e1) (e3)) = (op (e2) (e3)))) -> (~((op (e1) (e3)) = (op (e3) (e3)))) -> ((op (e3) (e3)) = (e2)) -> (~((op (e1) (e3)) = (e1))) -> (((op (e0) (e3)) = (e0))\/(((op (e0) (e3)) = (e1))\/(((op (e0) (e3)) = (e2))\/((op (e0) (e3)) = (e3))))) -> (~((op (e0) (e3)) = (op (e1) (e3)))) -> (~((op (e0) (e3)) = (e1))) -> (~((op (e0) (e3)) = (op (e3) (e3)))) -> (~((op (e0) (e3)) = (op (e2) (e3)))) -> (((op (e1) (e3)) = (e0))\/(((op (e1) (e3)) = (e1))\/(((op (e1) (e3)) = (e2))\/((op (e1) (e3)) = (e3))))) -> (~((op (e3) (e3)) = (e3))) -> False). % 18.96/19.08 do 0 intro. intros zenon_H136 zenon_H9a zenon_Hf3 zenon_Hc4 zenon_H1e zenon_H11f zenon_Hdb zenon_Hd5 zenon_Hf6 zenon_H24e zenon_He4 zenon_H1d zenon_H231 zenon_Hc2 zenon_He2 zenon_Hdf zenon_H102. % 18.96/19.08 apply (zenon_or_s _ _ zenon_H136); [ zenon_intro zenon_He3 | zenon_intro zenon_H137 ]. % 18.96/19.08 apply (zenon_L515_); trivial. % 18.96/19.08 apply (zenon_or_s _ _ zenon_H137); [ zenon_intro zenon_Hdc | zenon_intro zenon_H138 ]. % 18.96/19.08 apply (zenon_L404_); trivial. % 18.96/19.08 apply (zenon_or_s _ _ zenon_H138); [ zenon_intro zenon_Hdd | zenon_intro zenon_H105 ]. % 18.96/19.08 apply (zenon_L967_); trivial. % 18.96/19.08 exact (zenon_H102 zenon_H105). % 18.96/19.08 (* end of lemma zenon_L1006_ *) % 18.96/19.08 assert (zenon_L1007_ : (((op (e3) (e0)) = (e2))\/(((op (e3) (e1)) = (e2))\/(((op (e3) (e2)) = (e2))\/((op (e3) (e3)) = (e2))))) -> (((op (e0) (e0)) = (e3))\/(((op (e1) (e0)) = (e3))\/(((op (e2) (e0)) = (e3))\/((op (e3) (e0)) = (e3))))) -> (((op (e0) (e0)) = (e0))\/(((op (e0) (e0)) = (e1))\/(((op (e0) (e0)) = (e2))\/((op (e0) (e0)) = (e3))))) -> (~((op (e0) (e0)) = (e0))) -> (~((op (e0) (e0)) = (e1))) -> (~((op (e1) (e2)) = (op (e2) (e2)))) -> (~((op (e0) (e1)) = (op (e2) (e1)))) -> ((op (e0) (e1)) = (e1)) -> (((op (e2) (e0)) = (e1))\/(((op (e2) (e1)) = (e1))\/(((op (e2) (e2)) = (e1))\/((op (e2) (e3)) = (e1))))) -> ((op (e2) (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))))) -> (~((op (e2) (e0)) = (op (e2) (e2)))) -> (~((op (e2) (e2)) = (e2))) -> (~((op (e2) (e2)) = (e1))) -> (((op (e3) (e2)) = (e0))\/(((op (e3) (e2)) = (e1))\/(((op (e3) (e2)) = (e2))\/((op (e3) (e2)) = (e3))))) -> (~((op (e2) (e2)) = (op (e3) (e2)))) -> (~((op (e3) (e2)) = (op (e3) (e3)))) -> ((op (e0) (e2)) = (e2)) -> (~((op (e0) (e2)) = (op (e3) (e2)))) -> (((op (e2) (e2)) = (e0))\/(((op (e2) (e2)) = (e1))\/(((op (e2) (e2)) = (e2))\/((op (e2) (e2)) = (e3))))) -> (~((op (e3) (e2)) = (e1))) -> (~((op (e3) (e1)) = (e1))) -> (((op (e3) (e0)) = (e1))\/(((op (e3) (e1)) = (e1))\/(((op (e3) (e2)) = (e1))\/((op (e3) (e3)) = (e1))))) -> (~((e2) = (e3))) -> (~((e1) = (e3))) -> (((op (e0) (e0)) = (e3))\/(((op (e0) (e1)) = (e3))\/(((op (e0) (e2)) = (e3))\/((op (e0) (e3)) = (e3))))) -> ((op (e1) (e1)) = (e2)) -> (~((op (e1) (e1)) = (op (e3) (e1)))) -> (~((op (e3) (e0)) = (op (e3) (e1)))) -> ((op (e3) (e1)) = (e3)) -> (~((op (e3) (e0)) = (op (e3) (e2)))) -> (~((op (e3) (e0)) = (e1))) -> ((op (e3) (e2)) = (e0)) -> (((op (e3) (e0)) = (e0))\/(((op (e3) (e0)) = (e1))\/(((op (e3) (e0)) = (e2))\/((op (e3) (e0)) = (e3))))) -> (((op (e0) (e3)) = (e3))\/(((op (e1) (e3)) = (e3))\/(((op (e2) (e3)) = (e3))\/((op (e3) (e3)) = (e3))))) -> (~((e0) = (e3))) -> (~((op (e2) (e3)) = (op (e3) (e3)))) -> ((op (e0) (e3)) = (e0)) -> (((op (e2) (e3)) = (e0))\/(((op (e2) (e3)) = (e1))\/(((op (e2) (e3)) = (e2))\/((op (e2) (e3)) = (e3))))) -> (~((op (e1) (e3)) = (op (e2) (e3)))) -> (~((op (e1) (e3)) = (op (e3) (e3)))) -> (~((op (e1) (e3)) = (e1))) -> (((op (e0) (e3)) = (e0))\/(((op (e0) (e3)) = (e1))\/(((op (e0) (e3)) = (e2))\/((op (e0) (e3)) = (e3))))) -> (~((op (e0) (e3)) = (op (e1) (e3)))) -> (~((op (e0) (e3)) = (e1))) -> (~((op (e0) (e3)) = (op (e3) (e3)))) -> (~((op (e0) (e3)) = (op (e2) (e3)))) -> (((op (e1) (e3)) = (e0))\/(((op (e1) (e3)) = (e1))\/(((op (e1) (e3)) = (e2))\/((op (e1) (e3)) = (e3))))) -> (~((op (e3) (e3)) = (e3))) -> False). % 18.96/19.08 do 0 intro. intros zenon_H153 zenon_H1e0 zenon_H26a zenon_H3f zenon_H84 zenon_H2b zenon_H17e zenon_Ha0 zenon_H106 zenon_Hed zenon_H10a zenon_H1ef zenon_H128 zenon_H52 zenon_H173 zenon_H198 zenon_H191 zenon_H18f zenon_H62 zenon_H150 zenon_H14f zenon_H1c4 zenon_H251 zenon_H250 zenon_He8 zenon_H12b zenon_H95 zenon_H168 zenon_H110 zenon_H160 zenon_H1cf zenon_H161 zenon_H6f zenon_Had zenon_H61 zenon_H267 zenon_H136 zenon_H9a zenon_Hf3 zenon_H1e zenon_H11f zenon_Hdb zenon_Hd5 zenon_H24e zenon_He4 zenon_H1d zenon_H231 zenon_Hc2 zenon_He2 zenon_Hdf zenon_H102. % 18.96/19.08 apply (zenon_or_s _ _ zenon_He8); [ zenon_intro zenon_Hac | zenon_intro zenon_Heb ]. % 18.96/19.08 exact (zenon_Had zenon_Hac). % 18.96/19.08 apply (zenon_or_s _ _ zenon_Heb); [ zenon_intro zenon_Hae | zenon_intro zenon_Hec ]. % 18.96/19.08 exact (zenon_H250 zenon_Hae). % 18.96/19.08 apply (zenon_or_s _ _ zenon_Hec); [ zenon_intro zenon_Hba | zenon_intro zenon_Hc4 ]. % 18.96/19.08 exact (zenon_H251 zenon_Hba). % 18.96/19.08 apply (zenon_or_s _ _ zenon_H153); [ zenon_intro zenon_H148 | zenon_intro zenon_H154 ]. % 18.96/19.08 apply (zenon_L1005_); trivial. % 18.96/19.08 apply (zenon_or_s _ _ zenon_H154); [ zenon_intro zenon_H14d | zenon_intro zenon_H155 ]. % 18.96/19.08 apply (zenon_L164_); trivial. % 18.96/19.08 apply (zenon_or_s _ _ zenon_H155); [ zenon_intro zenon_H151 | zenon_intro zenon_Hf6 ]. % 18.96/19.08 apply (zenon_L988_); trivial. % 18.96/19.08 apply (zenon_L1006_); trivial. % 18.96/19.08 (* end of lemma zenon_L1007_ *) % 18.96/19.08 assert (zenon_L1008_ : (((op (e0) (e0)) = (e1))\/(((op (e1) (e0)) = (e1))\/(((op (e2) (e0)) = (e1))\/((op (e3) (e0)) = (e1))))) -> (~((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 (e3) (e1)) = (op (e3) (e2)))) -> (((op (e0) (e2)) = (e0))\/(((op (e0) (e2)) = (e1))\/(((op (e0) (e2)) = (e2))\/((op (e0) (e2)) = (e3))))) -> (~((op (e0) (e2)) = (op (e1) (e2)))) -> (~((op (e0) (e2)) = (e1))) -> (~((op (e1) (e2)) = (op (e3) (e2)))) -> (~((op (e0) (e2)) = (op (e2) (e2)))) -> (((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)) = (e0)) -> (((op (e0) (e2)) = (e2))\/(((op (e1) (e2)) = (e2))\/(((op (e2) (e2)) = (e2))\/((op (e3) (e2)) = (e2))))) -> (~((op (e3) (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 (e0) (e3)) = (op (e3) (e3)))) -> (~((op (e0) (e3)) = (e1))) -> (~((op (e0) (e3)) = (op (e1) (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)) = (op (e2) (e3)))) -> (((op (e2) (e3)) = (e0))\/(((op (e2) (e3)) = (e1))\/(((op (e2) (e3)) = (e2))\/((op (e2) (e3)) = (e3))))) -> ((op (e0) (e3)) = (e0)) -> (~((op (e2) (e3)) = (op (e3) (e3)))) -> (~((e0) = (e3))) -> (((op (e0) (e3)) = (e3))\/(((op (e1) (e3)) = (e3))\/(((op (e2) (e3)) = (e3))\/((op (e3) (e3)) = (e3))))) -> (~((op (e1) (e1)) = (op (e3) (e1)))) -> ((op (e1) (e1)) = (e2)) -> (((op (e0) (e0)) = (e3))\/(((op (e0) (e1)) = (e3))\/(((op (e0) (e2)) = (e3))\/((op (e0) (e3)) = (e3))))) -> (~((e1) = (e3))) -> (~((e2) = (e3))) -> (((op (e3) (e0)) = (e1))\/(((op (e3) (e1)) = (e1))\/(((op (e3) (e2)) = (e1))\/((op (e3) (e3)) = (e1))))) -> (~((op (e3) (e1)) = (e1))) -> (~((op (e3) (e2)) = (e1))) -> (((op (e2) (e2)) = (e0))\/(((op (e2) (e2)) = (e1))\/(((op (e2) (e2)) = (e2))\/((op (e2) (e2)) = (e3))))) -> (~((op (e0) (e2)) = (op (e3) (e2)))) -> (~((op (e3) (e2)) = (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 (e2) (e2)) = (e1))) -> (~((op (e2) (e0)) = (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) (e0)) = (e1))\/(((op (e2) (e1)) = (e1))\/(((op (e2) (e2)) = (e1))\/((op (e2) (e3)) = (e1))))) -> ((op (e0) (e1)) = (e1)) -> (~((op (e0) (e1)) = (op (e2) (e1)))) -> (~((op (e1) (e2)) = (op (e2) (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 (e0) (e0)) = (e3))\/(((op (e1) (e0)) = (e3))\/(((op (e2) (e0)) = (e3))\/((op (e3) (e0)) = (e3))))) -> (((op (e3) (e0)) = (e2))\/(((op (e3) (e1)) = (e2))\/(((op (e3) (e2)) = (e2))\/((op (e3) (e3)) = (e2))))) -> (~((e1) = (e2))) -> (~((op (e2) (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 (e3) (e1)) = (e3)) -> (~((op (e3) (e0)) = (op (e3) (e1)))) -> (~((op (e3) (e0)) = (e1))) -> False). % 18.96/19.08 do 0 intro. intros zenon_H235 zenon_H24e zenon_H6a zenon_H208 zenon_H1a4 zenon_H1ba zenon_H195 zenon_H20d zenon_H115 zenon_Ha8 zenon_H1a6 zenon_H24b zenon_H36 zenon_H172 zenon_H102 zenon_Hdf zenon_He2 zenon_Hc2 zenon_H231 zenon_H1d zenon_He4 zenon_Hd5 zenon_Hdb zenon_H11f zenon_H1e zenon_Hf3 zenon_H9a zenon_H136 zenon_H160 zenon_H110 zenon_H168 zenon_H95 zenon_H12b zenon_He8 zenon_H250 zenon_H251 zenon_H1c4 zenon_H14f zenon_H62 zenon_H18f zenon_H191 zenon_H198 zenon_H52 zenon_H128 zenon_H1ef zenon_H10a zenon_H106 zenon_Ha0 zenon_H17e zenon_H2b zenon_H84 zenon_H3f zenon_H26a zenon_H1e0 zenon_H153 zenon_H7c zenon_H173 zenon_H267 zenon_H6f zenon_H161 zenon_H1cf zenon_Had. % 18.96/19.08 apply (zenon_or_s _ _ zenon_H235); [ zenon_intro zenon_H7a | zenon_intro zenon_H236 ]. % 18.96/19.08 exact (zenon_H84 zenon_H7a). % 18.96/19.08 apply (zenon_or_s _ _ zenon_H236); [ zenon_intro zenon_H9d | zenon_intro zenon_H237 ]. % 18.96/19.08 exact (zenon_H1ef zenon_H9d). % 18.96/19.08 apply (zenon_or_s _ _ zenon_H237); [ zenon_intro zenon_Hed | zenon_intro zenon_Hac ]. % 18.96/19.08 apply (zenon_or_s _ _ zenon_H128); [ zenon_intro zenon_H9d | zenon_intro zenon_H129 ]. % 18.96/19.08 exact (zenon_H1ef zenon_H9d). % 18.96/19.08 apply (zenon_or_s _ _ zenon_H129); [ zenon_intro zenon_H10d | zenon_intro zenon_H12a ]. % 18.96/19.08 exact (zenon_H10a zenon_H10d). % 18.96/19.08 apply (zenon_or_s _ _ zenon_H12a); [ zenon_intro zenon_Hf0 | zenon_intro zenon_Hd6 ]. % 18.96/19.08 apply (zenon_or_s _ _ zenon_H6a); [ zenon_intro zenon_H48 | zenon_intro zenon_H6b ]. % 18.96/19.08 apply (zenon_L336_); trivial. % 18.96/19.08 apply (zenon_or_s _ _ zenon_H6b); [ zenon_intro zenon_H2a | zenon_intro zenon_H6c ]. % 18.96/19.08 apply (zenon_L1001_); trivial. % 18.96/19.08 apply (zenon_or_s _ _ zenon_H6c); [ zenon_intro zenon_H2c | zenon_intro zenon_H61 ]. % 18.96/19.08 apply (zenon_L645_); trivial. % 18.96/19.08 apply (zenon_or_s _ _ zenon_H172); [ zenon_intro zenon_H150 | zenon_intro zenon_H174 ]. % 18.96/19.08 apply (zenon_L1007_); trivial. % 18.96/19.08 apply (zenon_or_s _ _ zenon_H174); [ zenon_intro zenon_H113 | zenon_intro zenon_H175 ]. % 18.96/19.08 apply (zenon_L68_); trivial. % 18.96/19.08 apply (zenon_or_s _ _ zenon_H175); [ zenon_intro zenon_H176 | zenon_intro zenon_H151 ]. % 18.96/19.08 exact (zenon_H173 zenon_H176). % 18.96/19.08 apply (zenon_L988_); trivial. % 18.96/19.08 exact (zenon_H24e zenon_Hd6). % 18.96/19.08 exact (zenon_Had zenon_Hac). % 18.96/19.08 (* end of lemma zenon_L1008_ *) % 18.96/19.08 assert (zenon_L1009_ : (((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 (e3) (e0)) = (e0)) -> ((op (e2) (e1)) = (e0)) -> (~((op (e2) (e1)) = (op (e2) (e3)))) -> (~((op (e1) (e1)) = (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 (e0) (e2)) = (e0)) -> (~((op (e0) (e2)) = (op (e1) (e2)))) -> (((op (e1) (e0)) = (e1))\/(((op (e1) (e1)) = (e1))\/(((op (e1) (e2)) = (e1))\/((op (e1) (e3)) = (e1))))) -> (~((op (e1) (e0)) = (e1))) -> (~((op (e1) (e1)) = (e1))) -> (~((op (e0) (e3)) = (op (e1) (e3)))) -> (~((op (e0) (e3)) = (e1))) -> (((op (e0) (e3)) = (e0))\/(((op (e0) (e3)) = (e1))\/(((op (e0) (e3)) = (e2))\/((op (e0) (e3)) = (e3))))) -> (~((op (e3) (e2)) = (e1))) -> (~((op (e3) (e1)) = (e1))) -> (~((op (e3) (e0)) = (e1))) -> (((op (e3) (e0)) = (e1))\/(((op (e3) (e1)) = (e1))\/(((op (e3) (e2)) = (e1))\/((op (e3) (e3)) = (e1))))) -> (~((e1) = (e3))) -> (~((op (e1) (e1)) = (op (e2) (e1)))) -> ((op (e2) (e1)) = (e3)) -> ((op (e2) (e0)) = (e1)) -> ((op (e0) (e0)) = (e2)) -> (((op (e1) (e0)) = (e3))\/(((op (e1) (e1)) = (e3))\/(((op (e1) (e2)) = (e3))\/((op (e1) (e3)) = (e3))))) -> (~((op (e1) (e3)) = (e1))) -> False). % 18.96/19.08 do 0 intro. intros zenon_H22 zenon_H1fa zenon_H71 zenon_H44 zenon_H36 zenon_H1c7 zenon_H57 zenon_H208 zenon_H67 zenon_H48 zenon_H195 zenon_H128 zenon_H1ef zenon_H10a zenon_H1d zenon_H231 zenon_He4 zenon_H251 zenon_H250 zenon_Had zenon_He8 zenon_H95 zenon_H13e zenon_Ha6 zenon_Hed zenon_H7b zenon_H16f zenon_H24e. % 18.96/19.08 apply (zenon_or_s _ _ zenon_H22); [ zenon_intro zenon_H27 | zenon_intro zenon_H26 ]. % 18.96/19.08 apply (zenon_L312_); trivial. % 18.96/19.08 apply (zenon_or_s _ _ zenon_H26); [ zenon_intro zenon_H29 | zenon_intro zenon_H28 ]. % 18.96/19.08 apply (zenon_L961_); trivial. % 18.96/19.08 apply (zenon_or_s _ _ zenon_H28); [ zenon_intro zenon_H2a | zenon_intro zenon_H1f ]. % 18.96/19.08 apply (zenon_L334_); trivial. % 18.96/19.08 apply (zenon_or_s _ _ zenon_H128); [ zenon_intro zenon_H9d | zenon_intro zenon_H129 ]. % 18.96/19.08 exact (zenon_H1ef zenon_H9d). % 18.96/19.08 apply (zenon_or_s _ _ zenon_H129); [ zenon_intro zenon_H10d | zenon_intro zenon_H12a ]. % 18.96/19.08 exact (zenon_H10a zenon_H10d). % 18.96/19.08 apply (zenon_or_s _ _ zenon_H12a); [ zenon_intro zenon_Hf0 | zenon_intro zenon_Hd6 ]. % 18.96/19.08 apply (zenon_or_s _ _ zenon_H16f); [ zenon_intro zenon_H9e | zenon_intro zenon_H170 ]. % 18.96/19.08 apply (zenon_L491_); trivial. % 18.96/19.08 apply (zenon_or_s _ _ zenon_H170); [ zenon_intro zenon_H13f | zenon_intro zenon_H171 ]. % 18.96/19.08 apply (zenon_L95_); trivial. % 18.96/19.08 apply (zenon_or_s _ _ zenon_H171); [ zenon_intro zenon_H16c | zenon_intro zenon_Hdc ]. % 18.96/19.08 apply (zenon_L167_); trivial. % 18.96/19.08 apply (zenon_or_s _ _ zenon_He8); [ zenon_intro zenon_Hac | zenon_intro zenon_Heb ]. % 18.96/19.08 exact (zenon_Had zenon_Hac). % 18.96/19.08 apply (zenon_or_s _ _ zenon_Heb); [ zenon_intro zenon_Hae | zenon_intro zenon_Hec ]. % 18.96/19.08 exact (zenon_H250 zenon_Hae). % 18.96/19.08 apply (zenon_or_s _ _ zenon_Hec); [ zenon_intro zenon_Hba | zenon_intro zenon_Hc4 ]. % 18.96/19.08 exact (zenon_H251 zenon_Hba). % 18.96/19.08 apply (zenon_L789_); trivial. % 18.96/19.08 exact (zenon_H24e zenon_Hd6). % 18.96/19.08 (* end of lemma zenon_L1009_ *) % 18.96/19.08 assert (zenon_L1010_ : (((op (e0) (e2)) = (e2))\/(((op (e1) (e2)) = (e2))\/(((op (e2) (e2)) = (e2))\/((op (e3) (e2)) = (e2))))) -> (~((e0) = (e2))) -> (~((e1) = (e2))) -> ((op (e1) (e2)) = (e1)) -> (~((op (e2) (e2)) = (e2))) -> (((op (e3) (e0)) = (e0))\/(((op (e3) (e1)) = (e0))\/(((op (e3) (e2)) = (e0))\/((op (e3) (e3)) = (e0))))) -> (~((op (e1) (e3)) = (e1))) -> (((op (e1) (e0)) = (e3))\/(((op (e1) (e1)) = (e3))\/(((op (e1) (e2)) = (e3))\/((op (e1) (e3)) = (e3))))) -> ((op (e0) (e0)) = (e2)) -> ((op (e2) (e0)) = (e1)) -> (~((op (e1) (e1)) = (op (e3) (e1)))) -> (~((e1) = (e3))) -> (~((op (e3) (e0)) = (op (e3) (e3)))) -> (~((op (e1) (e2)) = (op (e1) (e3)))) -> (((op (e0) (e3)) = (e1))\/(((op (e1) (e3)) = (e1))\/(((op (e2) (e3)) = (e1))\/((op (e3) (e3)) = (e1))))) -> (~((op (e1) (e1)) = (e1))) -> (~((op (e1) (e0)) = (e1))) -> (((op (e1) (e0)) = (e1))\/(((op (e1) (e1)) = (e1))\/(((op (e1) (e2)) = (e1))\/((op (e1) (e3)) = (e1))))) -> (~((op (e0) (e2)) = (op (e1) (e2)))) -> ((op (e0) (e2)) = (e0)) -> (~((op (e1) (e1)) = (op (e1) (e3)))) -> (~((op (e1) (e0)) = (op (e3) (e0)))) -> (((op (e1) (e0)) = (e0))\/(((op (e1) (e1)) = (e0))\/(((op (e1) (e2)) = (e0))\/((op (e1) (e3)) = (e0))))) -> (~((op (e3) (e1)) = (op (e3) (e2)))) -> ((op (e2) (e1)) = (e0)) -> (~((op (e2) (e1)) = (op (e2) (e2)))) -> (~((op (e1) (e0)) = (op (e1) (e2)))) -> ((op (e1) (e0)) = (e0)) -> (((op (e0) (e0)) = (e0))\/(((op (e1) (e0)) = (e0))\/(((op (e2) (e0)) = (e0))\/((op (e3) (e0)) = (e0))))) -> (~((op (e0) (e0)) = (e0))) -> (~((op (e3) (e1)) = (op (e3) (e3)))) -> (~((op (e1) (e0)) = (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 (e2) (e0)) = (op (e2) (e1)))) -> (((op (e0) (e2)) = (e0))\/(((op (e1) (e2)) = (e0))\/(((op (e2) (e2)) = (e0))\/((op (e3) (e2)) = (e0))))) -> (~((op (e3) (e0)) = (op (e3) (e1)))) -> ((op (e3) (e1)) = (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))))) -> (~((op (e3) (e0)) = (e1))) -> (~((op (e3) (e1)) = (e1))) -> (~((op (e3) (e2)) = (e1))) -> (((op (e0) (e3)) = (e2))\/(((op (e1) (e3)) = (e2))\/(((op (e2) (e3)) = (e2))\/((op (e3) (e3)) = (e2))))) -> (~((op (e1) (e3)) = (op (e2) (e3)))) -> (~((op (e2) (e3)) = (e1))) -> (((op (e0) (e3)) = (e0))\/(((op (e0) (e3)) = (e1))\/(((op (e0) (e3)) = (e2))\/((op (e0) (e3)) = (e3))))) -> (~((op (e0) (e3)) = (e1))) -> (~((op (e0) (e3)) = (op (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 (e2) (e3)))) -> ((op (e2) (e1)) = (e2)) -> (~((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))))) -> (~((op (e0) (e3)) = (op (e1) (e3)))) -> False). % 18.96/19.08 do 0 intro. intros zenon_H172 zenon_H149 zenon_H7c zenon_Hf0 zenon_H173 zenon_H1ac zenon_H24e zenon_H16f zenon_H7b zenon_Hed zenon_H160 zenon_H95 zenon_H71 zenon_H124 zenon_H133 zenon_H10a zenon_H1ef zenon_H128 zenon_H195 zenon_H48 zenon_H57 zenon_H1fa zenon_H22 zenon_H1a4 zenon_H36 zenon_H24b zenon_H24a zenon_H27 zenon_H3e zenon_H3f zenon_H130 zenon_Hd8 zenon_H208 zenon_H67 zenon_H1f0 zenon_H6a zenon_H1cf zenon_H161 zenon_H6f zenon_H267 zenon_He8 zenon_Had zenon_H250 zenon_H251 zenon_H145 zenon_Hdb zenon_H255 zenon_He4 zenon_H231 zenon_Hc2 zenon_Hdf zenon_Hd5 zenon_He2 zenon_H1ca zenon_H1c7 zenon_Hf3 zenon_H11f zenon_H1d. % 18.96/19.08 apply (zenon_or_s _ _ zenon_H16f); [ zenon_intro zenon_H9e | zenon_intro zenon_H170 ]. % 18.96/19.08 apply (zenon_L491_); trivial. % 18.96/19.08 apply (zenon_or_s _ _ zenon_H170); [ zenon_intro zenon_H13f | zenon_intro zenon_H171 ]. % 18.96/19.08 apply (zenon_L110_); trivial. % 18.96/19.08 apply (zenon_or_s _ _ zenon_H171); [ zenon_intro zenon_H16c | zenon_intro zenon_Hdc ]. % 18.96/19.08 apply (zenon_L167_); trivial. % 18.96/19.08 apply (zenon_L990_); trivial. % 18.96/19.08 (* end of lemma zenon_L1010_ *) % 18.96/19.08 assert (zenon_L1011_ : (((op (e3) (e0)) = (e1))\/(((op (e3) (e1)) = (e1))\/(((op (e3) (e2)) = (e1))\/((op (e3) (e3)) = (e1))))) -> (~((op (e3) (e0)) = (e1))) -> (~((op (e3) (e1)) = (e1))) -> (~((op (e3) (e2)) = (e1))) -> (((op (e0) (e3)) = (e2))\/(((op (e1) (e3)) = (e2))\/(((op (e2) (e3)) = (e2))\/((op (e3) (e3)) = (e2))))) -> (~((e0) = (e2))) -> (~((op (e1) (e1)) = (op (e1) (e3)))) -> ((op (e1) (e1)) = (e2)) -> (~((op (e2) (e1)) = (op (e2) (e3)))) -> ((op (e2) (e1)) = (e2)) -> (((op (e0) (e3)) = (e3))\/(((op (e1) (e3)) = (e3))\/(((op (e2) (e3)) = (e3))\/((op (e3) (e3)) = (e3))))) -> (~((e0) = (e3))) -> (~((op (e2) (e3)) = (op (e3) (e3)))) -> ((op (e0) (e3)) = (e0)) -> (((op (e2) (e3)) = (e0))\/(((op (e2) (e3)) = (e1))\/(((op (e2) (e3)) = (e2))\/((op (e2) (e3)) = (e3))))) -> (~((op (e1) (e3)) = (op (e2) (e3)))) -> (~((op (e1) (e3)) = (op (e3) (e3)))) -> (~((op (e1) (e3)) = (e1))) -> (((op (e0) (e3)) = (e0))\/(((op (e0) (e3)) = (e1))\/(((op (e0) (e3)) = (e2))\/((op (e0) (e3)) = (e3))))) -> (~((op (e0) (e3)) = (op (e1) (e3)))) -> (~((op (e0) (e3)) = (e1))) -> (~((op (e0) (e3)) = (op (e3) (e3)))) -> (~((op (e0) (e3)) = (op (e2) (e3)))) -> (((op (e1) (e3)) = (e0))\/(((op (e1) (e3)) = (e1))\/(((op (e1) (e3)) = (e2))\/((op (e1) (e3)) = (e3))))) -> (~((op (e3) (e3)) = (e3))) -> False). % 18.96/19.08 do 0 intro. intros zenon_He8 zenon_Had zenon_H250 zenon_H251 zenon_H145 zenon_H149 zenon_H57 zenon_H110 zenon_H1c7 zenon_H1ca zenon_H136 zenon_H9a zenon_Hf3 zenon_H1e zenon_H11f zenon_Hdb zenon_Hd5 zenon_H24e zenon_He4 zenon_H1d zenon_H231 zenon_Hc2 zenon_He2 zenon_Hdf zenon_H102. % 18.96/19.08 apply (zenon_or_s _ _ zenon_He8); [ zenon_intro zenon_Hac | zenon_intro zenon_Heb ]. % 18.96/19.08 exact (zenon_Had zenon_Hac). % 18.96/19.08 apply (zenon_or_s _ _ zenon_Heb); [ zenon_intro zenon_Hae | zenon_intro zenon_Hec ]. % 18.96/19.08 exact (zenon_H250 zenon_Hae). % 18.96/19.08 apply (zenon_or_s _ _ zenon_Hec); [ zenon_intro zenon_Hba | zenon_intro zenon_Hc4 ]. % 18.96/19.08 exact (zenon_H251 zenon_Hba). % 18.96/19.08 apply (zenon_or_s _ _ zenon_H145); [ zenon_intro zenon_Hcd | zenon_intro zenon_H146 ]. % 18.96/19.08 apply (zenon_L428_); trivial. % 18.96/19.08 apply (zenon_or_s _ _ zenon_H146); [ zenon_intro zenon_Hd7 | zenon_intro zenon_H147 ]. % 18.96/19.08 apply (zenon_L283_); trivial. % 18.96/19.08 apply (zenon_or_s _ _ zenon_H147); [ zenon_intro zenon_H11d | zenon_intro zenon_Hf6 ]. % 18.96/19.08 apply (zenon_L224_); trivial. % 18.96/19.08 apply (zenon_L1006_); trivial. % 18.96/19.08 (* end of lemma zenon_L1011_ *) % 18.96/19.08 assert (zenon_L1012_ : ((~((op (e2) (e1)) = (e1)))\/((op (e2) (e1)) = (e1))) -> ((op (e0) (e1)) = (e1)) -> (~((op (e0) (e1)) = (op (e2) (e1)))) -> (((op (e1) (e0)) = (e1))\/(((op (e1) (e1)) = (e1))\/(((op (e1) (e2)) = (e1))\/((op (e1) (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 (e1) (e1)) = (e1))) -> (~((op (e1) (e0)) = (e1))) -> ((~((op (e3) (e0)) = (e1)))\/((op (e3) (e1)) = (e0))) -> ((op (e1) (e1)) = (e2)) -> (~((op (e0) (e0)) = (e1))) -> (((op (e0) (e0)) = (e1))\/(((op (e1) (e0)) = (e1))\/(((op (e2) (e0)) = (e1))\/((op (e3) (e0)) = (e1))))) -> ((~((op (e2) (e3)) = (e1)))\/((op (e2) (e1)) = (e3))) -> ((~((op (e3) (e3)) = (e1)))\/((op (e3) (e1)) = (e3))) -> (~((op (e0) (e0)) = (e0))) -> (~((e0) = (e1))) -> ((~((op (e1) (e3)) = (e1)))\/((op (e1) (e1)) = (e3))) -> ((~((op (e2) (e2)) = (e1)))\/((op (e2) (e1)) = (e2))) -> ((~((op (e3) (e2)) = (e1)))\/((op (e3) (e1)) = (e2))) -> (~((op (e0) (e1)) = (op (e3) (e1)))) -> (~((op (e1) (e0)) = (op (e2) (e0)))) -> ((~((op (e3) (e1)) = (e1)))\/((op (e3) (e1)) = (e1))) -> (~((op (e1) (e1)) = (op (e2) (e1)))) -> ((~((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) (e0)) = (op (e0) (e3)))) -> (((op (e0) (e0)) = (e3))\/(((op (e0) (e1)) = (e3))\/(((op (e0) (e2)) = (e3))\/((op (e0) (e3)) = (e3))))) -> (~((e2) = (e3))) -> (~((e0) = (e3))) -> (((op (e0) (e0)) = (e2))\/(((op (e1) (e0)) = (e2))\/(((op (e2) (e0)) = (e2))\/((op (e3) (e0)) = (e2))))) -> (~((op (e0) (e1)) = (op (e1) (e1)))) -> (~((e1) = (e2))) -> (((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 (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))))) -> (~((op (e1) (e2)) = (op (e1) (e3)))) -> (~((op (e0) (e3)) = (e1))) -> (((op (e0) (e3)) = (e0))\/(((op (e0) (e3)) = (e1))\/(((op (e0) (e3)) = (e2))\/((op (e0) (e3)) = (e3))))) -> (~((op (e0) (e3)) = (op (e1) (e3)))) -> (~((op (e0) (e2)) = (op (e1) (e2)))) -> (~((op (e0) (e2)) = (op (e0) (e3)))) -> (~((op (e1) (e1)) = (op (e1) (e3)))) -> (~((op (e2) (e1)) = (op (e2) (e3)))) -> (~((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)) = (op (e3) (e0)))) -> (((op (e0) (e2)) = (e0))\/(((op (e1) (e2)) = (e0))\/(((op (e2) (e2)) = (e0))\/((op (e3) (e2)) = (e0))))) -> (~((op (e3) (e1)) = (op (e3) (e2)))) -> (~((op (e2) (e1)) = (op (e2) (e2)))) -> (~((op (e1) (e0)) = (op (e1) (e2)))) -> (~((op (e3) (e1)) = (op (e3) (e3)))) -> (~((op (e1) (e0)) = (op (e1) (e3)))) -> (~((op (e2) (e0)) = (op (e2) (e1)))) -> (~((op (e3) (e0)) = (op (e3) (e1)))) -> (((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)) = (op (e3) (e2)))) -> (((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)) = (op (e2) (e3)))) -> (~((op (e2) (e3)) = (op (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 (e3) (e3)))) -> (((op (e0) (e3)) = (e2))\/(((op (e1) (e3)) = (e2))\/(((op (e2) (e3)) = (e2))\/((op (e3) (e3)) = (e2))))) -> (((op (e3) (e0)) = (e0))\/(((op (e3) (e1)) = (e0))\/(((op (e3) (e2)) = (e0))\/((op (e3) (e3)) = (e0))))) -> (~((op (e2) (e2)) = (e2))) -> (~((e0) = (e2))) -> (((op (e2) (e0)) = (e2))\/(((op (e2) (e1)) = (e2))\/(((op (e2) (e2)) = (e2))\/((op (e2) (e3)) = (e2))))) -> (~((e1) = (e3))) -> (~((op (e1) (e1)) = (op (e3) (e1)))) -> (((op (e0) (e0)) = (e0))\/(((op (e0) (e0)) = (e1))\/(((op (e0) (e0)) = (e2))\/((op (e0) (e0)) = (e3))))) -> (~((op (e3) (e2)) = (op (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 (e0) (e3)) = (e3))\/(((op (e1) (e3)) = (e3))\/(((op (e2) (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 (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 (e0) (e2)) = (e1))\/(((op (e0) (e2)) = (e2))\/((op (e0) (e2)) = (e3))))) -> (~((op (e1) (e2)) = (op (e3) (e2)))) -> (~((op (e0) (e2)) = (op (e3) (e2)))) -> (~((op (e2) (e2)) = (op (e3) (e2)))) -> (((op (e3) (e2)) = (e0))\/(((op (e3) (e2)) = (e1))\/(((op (e3) (e2)) = (e2))\/((op (e3) (e2)) = (e3))))) -> (~((op (e0) (e2)) = (e1))) -> (((op (e0) (e2)) = (e3))\/(((op (e1) (e2)) = (e3))\/(((op (e2) (e2)) = (e3))\/((op (e3) (e2)) = (e3))))) -> (((op (e0) (e0)) = (e0))\/(((op (e0) (e1)) = (e0))\/(((op (e0) (e2)) = (e0))\/((op (e0) (e3)) = (e0))))) -> (((op (e3) (e0)) = (e1))\/(((op (e3) (e1)) = (e1))\/(((op (e3) (e2)) = (e1))\/((op (e3) (e3)) = (e1))))) -> (((op (e0) (e1)) = (e3))\/(((op (e1) (e1)) = (e3))\/(((op (e2) (e1)) = (e3))\/((op (e3) (e1)) = (e3))))) -> (~((op (e2) (e1)) = (op (e3) (e1)))) -> ((~((op (e2) (e0)) = (e1)))\/((op (e2) (e1)) = (e0))) -> False). % 18.96/19.08 do 0 intro. intros zenon_H262 zenon_Ha0 zenon_H17e zenon_H128 zenon_H2b zenon_H106 zenon_H10a zenon_H1ef zenon_H254 zenon_H110 zenon_H84 zenon_H235 zenon_H263 zenon_H264 zenon_H3f zenon_Ha1 zenon_H258 zenon_H253 zenon_H252 zenon_H210 zenon_H201 zenon_H261 zenon_H13e zenon_H256 zenon_H183 zenon_H189 zenon_H168 zenon_H12b zenon_H9a zenon_H1fe zenon_H10e zenon_H7c zenon_H172 zenon_H22 zenon_H16f zenon_H133 zenon_H124 zenon_H231 zenon_He4 zenon_H1d zenon_H195 zenon_H208 zenon_H57 zenon_H1c7 zenon_H71 zenon_H67 zenon_H1fa zenon_H6a zenon_H1a4 zenon_H24b zenon_H24a zenon_H130 zenon_Hd8 zenon_H1f0 zenon_H1cf zenon_H3e zenon_H267 zenon_H6f zenon_H11f zenon_Hdb zenon_He2 zenon_Hf3 zenon_Hd5 zenon_Hdf zenon_Hc2 zenon_H145 zenon_H1ac zenon_H173 zenon_H149 zenon_H1d5 zenon_H95 zenon_H160 zenon_H26a zenon_H62 zenon_H52 zenon_H1e0 zenon_H136 zenon_H102 zenon_H153 zenon_H1c4 zenon_Ha8 zenon_H1ba zenon_H115 zenon_H14f zenon_H18f zenon_H191 zenon_H20d zenon_H1a6 zenon_H74 zenon_He8 zenon_H1a5 zenon_Haf zenon_H257. % 18.96/19.08 apply (zenon_or_s _ _ zenon_H258); [ zenon_intro zenon_H24e | zenon_intro zenon_H13f ]. % 18.96/19.08 apply (zenon_or_s _ _ zenon_H257); [ zenon_intro zenon_H1db | zenon_intro zenon_H36 ]. % 18.96/19.08 apply (zenon_or_s _ _ zenon_H262); [ zenon_intro zenon_H24f | zenon_intro zenon_Ha5 ]. % 18.96/19.08 apply (zenon_or_s _ _ zenon_H263); [ zenon_intro zenon_H255 | zenon_intro zenon_Ha6 ]. % 18.96/19.08 apply (zenon_L725_); trivial. % 18.96/19.08 apply (zenon_L985_); trivial. % 18.96/19.08 apply (zenon_L357_); trivial. % 18.96/19.08 apply (zenon_or_s _ _ zenon_H262); [ zenon_intro zenon_H24f | zenon_intro zenon_Ha5 ]. % 18.96/19.08 apply (zenon_or_s _ _ zenon_H253); [ zenon_intro zenon_H198 | zenon_intro zenon_H1ca ]. % 18.96/19.08 apply (zenon_or_s _ _ zenon_H263); [ zenon_intro zenon_H255 | zenon_intro zenon_Ha6 ]. % 18.96/19.08 apply (zenon_or_s _ _ zenon_H254); [ zenon_intro zenon_Had | zenon_intro zenon_H1b1 ]. % 18.96/19.08 apply (zenon_or_s _ _ zenon_H261); [ zenon_intro zenon_H250 | zenon_intro zenon_Hae ]. % 18.96/19.08 apply (zenon_or_s _ _ zenon_H252); [ zenon_intro zenon_H251 | zenon_intro zenon_H14d ]. % 18.96/19.08 apply (zenon_or_s _ _ zenon_H264); [ zenon_intro zenon_Hc7 | zenon_intro zenon_H161 ]. % 18.96/19.08 apply (zenon_L952_); trivial. % 18.96/19.08 apply (zenon_or_s _ _ zenon_H74); [ zenon_intro zenon_H42 | zenon_intro zenon_H77 ]. % 18.96/19.08 exact (zenon_H3f zenon_H42). % 18.96/19.08 apply (zenon_or_s _ _ zenon_H77); [ zenon_intro zenon_H49 | zenon_intro zenon_H78 ]. % 18.96/19.08 apply (zenon_L38_); trivial. % 18.96/19.08 apply (zenon_or_s _ _ zenon_H78); [ zenon_intro zenon_H48 | zenon_intro zenon_H1e ]. % 18.96/19.08 apply (zenon_or_s _ _ zenon_H3e); [ zenon_intro zenon_H42 | zenon_intro zenon_H41 ]. % 18.96/19.08 exact (zenon_H3f zenon_H42). % 18.96/19.08 apply (zenon_or_s _ _ zenon_H41); [ zenon_intro zenon_H27 | zenon_intro zenon_H43 ]. % 18.96/19.08 apply (zenon_or_s _ _ zenon_H235); [ zenon_intro zenon_H7a | zenon_intro zenon_H236 ]. % 18.96/19.08 exact (zenon_H84 zenon_H7a). % 18.96/19.08 apply (zenon_or_s _ _ zenon_H236); [ zenon_intro zenon_H9d | zenon_intro zenon_H237 ]. % 18.96/19.08 exact (zenon_H1ef zenon_H9d). % 18.96/19.08 apply (zenon_or_s _ _ zenon_H237); [ zenon_intro zenon_Hed | zenon_intro zenon_Hac ]. % 18.96/19.08 apply (zenon_or_s _ _ zenon_H183); [ zenon_intro zenon_H7b | zenon_intro zenon_H186 ]. % 18.96/19.08 apply (zenon_or_s _ _ zenon_H128); [ zenon_intro zenon_H9d | zenon_intro zenon_H129 ]. % 18.96/19.08 exact (zenon_H1ef zenon_H9d). % 18.96/19.08 apply (zenon_or_s _ _ zenon_H129); [ zenon_intro zenon_H10d | zenon_intro zenon_H12a ]. % 18.96/19.08 exact (zenon_H10a zenon_H10d). % 18.96/19.08 apply (zenon_or_s _ _ zenon_H12a); [ zenon_intro zenon_Hf0 | zenon_intro zenon_Hd6 ]. % 18.96/19.08 apply (zenon_or_s _ _ zenon_H16f); [ zenon_intro zenon_H9e | zenon_intro zenon_H170 ]. % 18.96/19.08 apply (zenon_L491_); trivial. % 18.96/19.08 apply (zenon_or_s _ _ zenon_H170); [ zenon_intro zenon_H13f | zenon_intro zenon_H171 ]. % 18.96/19.08 apply (zenon_L110_); trivial. % 18.96/19.08 apply (zenon_or_s _ _ zenon_H171); [ zenon_intro zenon_H16c | zenon_intro zenon_Hdc ]. % 18.96/19.08 apply (zenon_L167_); trivial. % 18.96/19.08 apply (zenon_or_s _ _ zenon_H1d5); [ zenon_intro zenon_Hee | zenon_intro zenon_H1d6 ]. % 18.96/19.08 apply (zenon_L986_); trivial. % 18.96/19.08 apply (zenon_or_s _ _ zenon_H1d6); [ zenon_intro zenon_H1ca | zenon_intro zenon_H1d7 ]. % 18.96/19.08 apply (zenon_L990_); trivial. % 18.96/19.08 apply (zenon_or_s _ _ zenon_H1d7); [ zenon_intro zenon_H176 | zenon_intro zenon_H11d ]. % 18.96/19.08 exact (zenon_H173 zenon_H176). % 18.96/19.08 apply (zenon_or_s _ _ zenon_H172); [ zenon_intro zenon_H150 | zenon_intro zenon_H174 ]. % 18.96/19.08 apply (zenon_L378_); trivial. % 18.96/19.08 apply (zenon_or_s _ _ zenon_H174); [ zenon_intro zenon_H113 | zenon_intro zenon_H175 ]. % 18.96/19.08 apply (zenon_L68_); trivial. % 18.96/19.08 apply (zenon_or_s _ _ zenon_H175); [ zenon_intro zenon_H176 | zenon_intro zenon_H151 ]. % 18.96/19.08 exact (zenon_H173 zenon_H176). % 18.96/19.08 apply (zenon_or_s _ _ zenon_H1ac); [ zenon_intro zenon_H44 | zenon_intro zenon_H1af ]. % 18.96/19.08 apply (zenon_L987_); trivial. % 18.96/19.08 apply (zenon_or_s _ _ zenon_H1af); [ zenon_intro zenon_H1b1 | zenon_intro zenon_H1b0 ]. % 18.96/19.08 apply (zenon_L641_); trivial. % 18.96/19.08 apply (zenon_or_s _ _ zenon_H1b0); [ zenon_intro zenon_H61 | zenon_intro zenon_H60 ]. % 18.96/19.08 apply (zenon_L988_); trivial. % 18.96/19.08 apply (zenon_L991_); trivial. % 18.96/19.08 exact (zenon_H24e zenon_Hd6). % 18.96/19.08 apply (zenon_or_s _ _ zenon_H186); [ zenon_intro zenon_H10f | zenon_intro zenon_H187 ]. % 18.96/19.08 apply (zenon_L67_); trivial. % 18.96/19.08 apply (zenon_or_s _ _ zenon_H187); [ zenon_intro zenon_H150 | zenon_intro zenon_Hcd ]. % 18.96/19.08 apply (zenon_L378_); trivial. % 18.96/19.08 apply (zenon_L650_); trivial. % 18.96/19.08 exact (zenon_Had zenon_Hac). % 18.96/19.08 apply (zenon_or_s _ _ zenon_H43); [ zenon_intro zenon_H34 | zenon_intro zenon_H44 ]. % 18.96/19.08 apply (zenon_L642_); trivial. % 18.96/19.08 apply (zenon_L999_); trivial. % 18.96/19.08 apply (zenon_L1008_); trivial. % 18.96/19.08 apply (zenon_L164_); trivial. % 18.96/19.08 apply (zenon_L363_); trivial. % 18.96/19.08 apply (zenon_L647_); trivial. % 18.96/19.08 apply (zenon_or_s _ _ zenon_H254); [ zenon_intro zenon_Had | zenon_intro zenon_H1b1 ]. % 18.96/19.08 apply (zenon_or_s _ _ zenon_H261); [ zenon_intro zenon_H250 | zenon_intro zenon_Hae ]. % 18.96/19.08 apply (zenon_or_s _ _ zenon_H252); [ zenon_intro zenon_H251 | zenon_intro zenon_H14d ]. % 18.96/19.08 apply (zenon_or_s _ _ zenon_H264); [ zenon_intro zenon_Hc7 | zenon_intro zenon_H161 ]. % 18.96/19.08 apply (zenon_L952_); trivial. % 18.96/19.08 apply (zenon_or_s _ _ zenon_H74); [ zenon_intro zenon_H42 | zenon_intro zenon_H77 ]. % 18.96/19.08 exact (zenon_H3f zenon_H42). % 18.96/19.08 apply (zenon_or_s _ _ zenon_H77); [ zenon_intro zenon_H49 | zenon_intro zenon_H78 ]. % 18.96/19.08 apply (zenon_L128_); trivial. % 18.96/19.08 apply (zenon_or_s _ _ zenon_H78); [ zenon_intro zenon_H48 | zenon_intro zenon_H1e ]. % 18.96/19.08 apply (zenon_or_s _ _ zenon_H3e); [ zenon_intro zenon_H42 | zenon_intro zenon_H41 ]. % 18.96/19.08 exact (zenon_H3f zenon_H42). % 18.96/19.08 apply (zenon_or_s _ _ zenon_H41); [ zenon_intro zenon_H27 | zenon_intro zenon_H43 ]. % 18.96/19.08 apply (zenon_or_s _ _ zenon_H235); [ zenon_intro zenon_H7a | zenon_intro zenon_H236 ]. % 18.96/19.08 exact (zenon_H84 zenon_H7a). % 18.96/19.08 apply (zenon_or_s _ _ zenon_H236); [ zenon_intro zenon_H9d | zenon_intro zenon_H237 ]. % 18.96/19.08 exact (zenon_H1ef zenon_H9d). % 18.96/19.08 apply (zenon_or_s _ _ zenon_H237); [ zenon_intro zenon_Hed | zenon_intro zenon_Hac ]. % 18.96/19.08 apply (zenon_or_s _ _ zenon_H183); [ zenon_intro zenon_H7b | zenon_intro zenon_H186 ]. % 18.96/19.08 apply (zenon_or_s _ _ zenon_H128); [ zenon_intro zenon_H9d | zenon_intro zenon_H129 ]. % 18.96/19.08 exact (zenon_H1ef zenon_H9d). % 18.96/19.08 apply (zenon_or_s _ _ zenon_H129); [ zenon_intro zenon_H10d | zenon_intro zenon_H12a ]. % 18.96/19.09 exact (zenon_H10a zenon_H10d). % 18.96/19.09 apply (zenon_or_s _ _ zenon_H12a); [ zenon_intro zenon_Hf0 | zenon_intro zenon_Hd6 ]. % 18.96/19.09 apply (zenon_or_s _ _ zenon_H16f); [ zenon_intro zenon_H9e | zenon_intro zenon_H170 ]. % 18.96/19.09 apply (zenon_L491_); trivial. % 18.96/19.09 apply (zenon_or_s _ _ zenon_H170); [ zenon_intro zenon_H13f | zenon_intro zenon_H171 ]. % 18.96/19.09 apply (zenon_L166_); trivial. % 18.96/19.09 apply (zenon_or_s _ _ zenon_H171); [ zenon_intro zenon_H16c | zenon_intro zenon_Hdc ]. % 18.96/19.09 apply (zenon_L167_); trivial. % 18.96/19.09 apply (zenon_or_s _ _ zenon_H1d5); [ zenon_intro zenon_Hee | zenon_intro zenon_H1d6 ]. % 18.96/19.09 apply (zenon_L58_); trivial. % 18.96/19.09 apply (zenon_or_s _ _ zenon_H1d6); [ zenon_intro zenon_H1ca | zenon_intro zenon_H1d7 ]. % 18.96/19.09 apply (zenon_L207_); trivial. % 18.96/19.09 apply (zenon_or_s _ _ zenon_H1d7); [ zenon_intro zenon_H176 | zenon_intro zenon_H11d ]. % 18.96/19.09 exact (zenon_H173 zenon_H176). % 18.96/19.09 apply (zenon_or_s _ _ zenon_H172); [ zenon_intro zenon_H150 | zenon_intro zenon_H174 ]. % 18.96/19.09 apply (zenon_L378_); trivial. % 18.96/19.09 apply (zenon_or_s _ _ zenon_H174); [ zenon_intro zenon_H113 | zenon_intro zenon_H175 ]. % 18.96/19.09 apply (zenon_L68_); trivial. % 18.96/19.09 apply (zenon_or_s _ _ zenon_H175); [ zenon_intro zenon_H176 | zenon_intro zenon_H151 ]. % 18.96/19.09 exact (zenon_H173 zenon_H176). % 18.96/19.09 apply (zenon_or_s _ _ zenon_H1ac); [ zenon_intro zenon_H44 | zenon_intro zenon_H1af ]. % 18.96/19.09 apply (zenon_L1009_); trivial. % 18.96/19.09 apply (zenon_or_s _ _ zenon_H1af); [ zenon_intro zenon_H1b1 | zenon_intro zenon_H1b0 ]. % 18.96/19.09 apply (zenon_L643_); trivial. % 18.96/19.09 apply (zenon_or_s _ _ zenon_H1b0); [ zenon_intro zenon_H61 | zenon_intro zenon_H60 ]. % 18.96/19.09 apply (zenon_L988_); trivial. % 18.96/19.09 apply (zenon_L991_); trivial. % 18.96/19.09 exact (zenon_H24e zenon_Hd6). % 18.96/19.09 apply (zenon_or_s _ _ zenon_H186); [ zenon_intro zenon_H10f | zenon_intro zenon_H187 ]. % 18.96/19.09 apply (zenon_L67_); trivial. % 18.96/19.09 apply (zenon_or_s _ _ zenon_H187); [ zenon_intro zenon_H150 | zenon_intro zenon_Hcd ]. % 18.96/19.09 apply (zenon_L378_); trivial. % 18.96/19.09 apply (zenon_L650_); trivial. % 18.96/19.09 exact (zenon_Had zenon_Hac). % 18.96/19.09 apply (zenon_or_s _ _ zenon_H43); [ zenon_intro zenon_H34 | zenon_intro zenon_H44 ]. % 18.96/19.09 apply (zenon_L642_); trivial. % 18.96/19.09 apply (zenon_or_s _ _ zenon_H235); [ zenon_intro zenon_H7a | zenon_intro zenon_H236 ]. % 18.96/19.09 exact (zenon_H84 zenon_H7a). % 18.96/19.09 apply (zenon_or_s _ _ zenon_H236); [ zenon_intro zenon_H9d | zenon_intro zenon_H237 ]. % 18.96/19.09 exact (zenon_H1ef zenon_H9d). % 18.96/19.09 apply (zenon_or_s _ _ zenon_H237); [ zenon_intro zenon_Hed | zenon_intro zenon_Hac ]. % 18.96/19.09 apply (zenon_or_s _ _ zenon_H183); [ zenon_intro zenon_H7b | zenon_intro zenon_H186 ]. % 18.96/19.09 apply (zenon_L1009_); trivial. % 18.96/19.09 apply (zenon_or_s _ _ zenon_H186); [ zenon_intro zenon_H10f | zenon_intro zenon_H187 ]. % 18.96/19.09 apply (zenon_L997_); trivial. % 18.96/19.09 apply (zenon_or_s _ _ zenon_H187); [ zenon_intro zenon_H150 | zenon_intro zenon_Hcd ]. % 18.96/19.09 apply (zenon_L378_); trivial. % 18.96/19.09 apply (zenon_L998_); trivial. % 18.96/19.09 exact (zenon_Had zenon_Hac). % 18.96/19.09 apply (zenon_L1008_); trivial. % 18.96/19.09 apply (zenon_L164_); trivial. % 18.96/19.09 apply (zenon_L363_); trivial. % 18.96/19.09 apply (zenon_L509_); trivial. % 18.96/19.09 apply (zenon_or_s _ _ zenon_H263); [ zenon_intro zenon_H255 | zenon_intro zenon_Ha6 ]. % 18.96/19.09 apply (zenon_or_s _ _ zenon_H254); [ zenon_intro zenon_Had | zenon_intro zenon_H1b1 ]. % 18.96/19.09 apply (zenon_or_s _ _ zenon_H261); [ zenon_intro zenon_H250 | zenon_intro zenon_Hae ]. % 18.96/19.09 apply (zenon_or_s _ _ zenon_H252); [ zenon_intro zenon_H251 | zenon_intro zenon_H14d ]. % 18.96/19.09 apply (zenon_or_s _ _ zenon_H74); [ zenon_intro zenon_H42 | zenon_intro zenon_H77 ]. % 18.96/19.09 exact (zenon_H3f zenon_H42). % 18.96/19.09 apply (zenon_or_s _ _ zenon_H77); [ zenon_intro zenon_H49 | zenon_intro zenon_H78 ]. % 18.96/19.09 apply (zenon_L38_); trivial. % 18.96/19.09 apply (zenon_or_s _ _ zenon_H78); [ zenon_intro zenon_H48 | zenon_intro zenon_H1e ]. % 18.96/19.09 apply (zenon_or_s _ _ zenon_H3e); [ zenon_intro zenon_H42 | zenon_intro zenon_H41 ]. % 18.96/19.09 exact (zenon_H3f zenon_H42). % 18.96/19.09 apply (zenon_or_s _ _ zenon_H41); [ zenon_intro zenon_H27 | zenon_intro zenon_H43 ]. % 18.96/19.09 apply (zenon_or_s _ _ zenon_H235); [ zenon_intro zenon_H7a | zenon_intro zenon_H236 ]. % 18.96/19.09 exact (zenon_H84 zenon_H7a). % 18.96/19.09 apply (zenon_or_s _ _ zenon_H236); [ zenon_intro zenon_H9d | zenon_intro zenon_H237 ]. % 18.96/19.09 exact (zenon_H1ef zenon_H9d). % 18.96/19.09 apply (zenon_or_s _ _ zenon_H237); [ zenon_intro zenon_Hed | zenon_intro zenon_Hac ]. % 18.96/19.09 apply (zenon_or_s _ _ zenon_H183); [ zenon_intro zenon_H7b | zenon_intro zenon_H186 ]. % 18.96/19.09 apply (zenon_or_s _ _ zenon_H128); [ zenon_intro zenon_H9d | zenon_intro zenon_H129 ]. % 18.96/19.09 exact (zenon_H1ef zenon_H9d). % 18.96/19.09 apply (zenon_or_s _ _ zenon_H129); [ zenon_intro zenon_H10d | zenon_intro zenon_H12a ]. % 18.96/19.09 exact (zenon_H10a zenon_H10d). % 18.96/19.09 apply (zenon_or_s _ _ zenon_H12a); [ zenon_intro zenon_Hf0 | zenon_intro zenon_Hd6 ]. % 18.96/19.09 apply (zenon_or_s _ _ zenon_H1a5); [ zenon_intro zenon_H99 | zenon_intro zenon_H1a8 ]. % 18.96/19.09 apply (zenon_L403_); trivial. % 18.96/19.09 apply (zenon_or_s _ _ zenon_H1a8); [ zenon_intro zenon_H13f | zenon_intro zenon_H1a9 ]. % 18.96/19.09 apply (zenon_L166_); trivial. % 18.96/19.09 apply (zenon_or_s _ _ zenon_H1a9); [ zenon_intro zenon_Ha6 | zenon_intro zenon_H161 ]. % 18.96/19.09 apply (zenon_L207_); trivial. % 18.96/19.09 apply (zenon_L1010_); trivial. % 18.96/19.09 exact (zenon_H24e zenon_Hd6). % 18.96/19.09 apply (zenon_or_s _ _ zenon_H186); [ zenon_intro zenon_H10f | zenon_intro zenon_H187 ]. % 18.96/19.09 apply (zenon_L191_); trivial. % 18.96/19.09 apply (zenon_or_s _ _ zenon_H187); [ zenon_intro zenon_H150 | zenon_intro zenon_Hcd ]. % 18.96/19.09 apply (zenon_L378_); trivial. % 18.96/19.09 apply (zenon_L650_); trivial. % 18.96/19.09 exact (zenon_Had zenon_Hac). % 18.96/19.09 apply (zenon_or_s _ _ zenon_H43); [ zenon_intro zenon_H34 | zenon_intro zenon_H44 ]. % 18.96/19.09 apply (zenon_L642_); trivial. % 18.96/19.09 apply (zenon_L999_); trivial. % 18.96/19.09 apply (zenon_L1011_); trivial. % 18.96/19.09 apply (zenon_L364_); trivial. % 18.96/19.09 apply (zenon_L363_); trivial. % 18.96/19.09 apply (zenon_L647_); trivial. % 18.96/19.09 apply (zenon_L207_); trivial. % 18.96/19.09 apply (zenon_L357_); trivial. % 18.96/19.09 apply (zenon_L166_); trivial. % 18.96/19.09 (* end of lemma zenon_L1012_ *) % 18.96/19.09 assert (zenon_L1013_ : (((op (e2) (e0)) = (e0))\/(((op (e2) (e0)) = (e1))\/(((op (e2) (e0)) = (e2))\/((op (e2) (e0)) = (e3))))) -> ((op (e2) (e2)) = (e0)) -> (~((op (e2) (e0)) = (e1))) -> ((op (e2) (e1)) = (e2)) -> (~((op (e2) (e0)) = (op (e2) (e1)))) -> ((op (e2) (e2)) = (e3)) -> (~((op (e2) (e0)) = (op (e2) (e2)))) -> False). % 18.96/19.09 do 0 intro. intros zenon_H259 zenon_H2c zenon_H1db zenon_H1ca zenon_H1f0 zenon_Haa zenon_H52. % 18.96/19.09 apply (zenon_or_s _ _ zenon_H259); [ zenon_intro zenon_H34 | zenon_intro zenon_H25a ]. % 18.96/19.09 apply (zenon_L11_); trivial. % 18.96/19.09 apply (zenon_or_s _ _ zenon_H25a); [ zenon_intro zenon_Hed | zenon_intro zenon_H25b ]. % 18.96/19.09 exact (zenon_H1db zenon_Hed). % 18.96/19.09 apply (zenon_or_s _ _ zenon_H25b); [ zenon_intro zenon_Hee | zenon_intro zenon_H3b ]. % 18.96/19.09 apply (zenon_L277_); trivial. % 18.96/19.09 apply (zenon_L168_); trivial. % 18.96/19.09 (* end of lemma zenon_L1013_ *) % 18.96/19.09 assert (zenon_L1014_ : (((op (e0) (e2)) = (e3))\/(((op (e1) (e2)) = (e3))\/(((op (e2) (e2)) = (e3))\/((op (e3) (e2)) = (e3))))) -> (~((op (e3) (e3)) = (e3))) -> (~((op (e1) (e1)) = (op (e3) (e1)))) -> ((op (e1) (e1)) = (e3)) -> ((op (e3) (e0)) = (e1)) -> (~((e1) = (e3))) -> (((op (e3) (e0)) = (e3))\/(((op (e3) (e1)) = (e3))\/(((op (e3) (e2)) = (e3))\/((op (e3) (e3)) = (e3))))) -> (~((e2) = (e3))) -> (~((op (e2) (e0)) = (op (e2) (e2)))) -> (~((op (e2) (e0)) = (op (e2) (e1)))) -> ((op (e2) (e1)) = (e2)) -> (~((op (e2) (e0)) = (e1))) -> (((op (e2) (e0)) = (e0))\/(((op (e2) (e0)) = (e1))\/(((op (e2) (e0)) = (e2))\/((op (e2) (e0)) = (e3))))) -> (((op (e0) (e2)) = (e0))\/(((op (e0) (e2)) = (e1))\/(((op (e0) (e2)) = (e2))\/((op (e0) (e2)) = (e3))))) -> ((op (e2) (e2)) = (e0)) -> (~((op (e0) (e2)) = (op (e2) (e2)))) -> (~((op (e0) (e2)) = (e1))) -> ((op (e1) (e2)) = (e2)) -> (~((op (e0) (e2)) = (op (e1) (e2)))) -> (~((op (e0) (e2)) = (op (e3) (e2)))) -> False). % 18.96/19.09 do 0 intro. intros zenon_H1a6 zenon_H102 zenon_H160 zenon_H13f zenon_Hac zenon_H95 zenon_H165 zenon_H12b zenon_H52 zenon_H1f0 zenon_H1ca zenon_H1db zenon_H259 zenon_H1ba zenon_H2c zenon_Ha8 zenon_H20d zenon_H113 zenon_H195 zenon_H14f. % 18.96/19.09 apply (zenon_or_s _ _ zenon_H1a6); [ zenon_intro zenon_Ha9 | zenon_intro zenon_H1aa ]. % 18.96/19.09 apply (zenon_L264_); trivial. % 18.96/19.09 apply (zenon_or_s _ _ zenon_H1aa); [ zenon_intro zenon_H16c | zenon_intro zenon_H1ab ]. % 18.96/19.09 apply (zenon_L116_); trivial. % 18.96/19.09 apply (zenon_or_s _ _ zenon_H1ab); [ zenon_intro zenon_Haa | zenon_intro zenon_H163 ]. % 18.96/19.09 apply (zenon_L1013_); trivial. % 18.96/19.09 apply (zenon_or_s _ _ zenon_H1ba); [ zenon_intro zenon_H48 | zenon_intro zenon_H1bb ]. % 18.96/19.09 apply (zenon_L679_); trivial. % 18.96/19.09 apply (zenon_or_s _ _ zenon_H1bb); [ zenon_intro zenon_H122 | zenon_intro zenon_H1bc ]. % 18.96/19.09 exact (zenon_H20d zenon_H122). % 18.96/19.09 apply (zenon_or_s _ _ zenon_H1bc); [ zenon_intro zenon_H150 | zenon_intro zenon_Ha9 ]. % 18.96/19.09 apply (zenon_L153_); trivial. % 18.96/19.09 apply (zenon_L111_); trivial. % 18.96/19.09 (* end of lemma zenon_L1014_ *) % 18.96/19.09 assert (zenon_L1015_ : (((op (e2) (e0)) = (e0))\/(((op (e2) (e0)) = (e1))\/(((op (e2) (e0)) = (e2))\/((op (e2) (e0)) = (e3))))) -> (~((op (e2) (e0)) = (op (e2) (e3)))) -> ((op (e2) (e3)) = (e0)) -> (~((op (e2) (e0)) = (e1))) -> ((op (e2) (e1)) = (e2)) -> (~((op (e2) (e0)) = (op (e2) (e1)))) -> ((op (e2) (e2)) = (e3)) -> (~((op (e2) (e0)) = (op (e2) (e2)))) -> False). % 18.96/19.09 do 0 intro. intros zenon_H259 zenon_H5b zenon_H37 zenon_H1db zenon_H1ca zenon_H1f0 zenon_Haa zenon_H52. % 18.96/19.09 apply (zenon_or_s _ _ zenon_H259); [ zenon_intro zenon_H34 | zenon_intro zenon_H25a ]. % 18.96/19.09 apply (zenon_L14_); trivial. % 18.96/19.09 apply (zenon_or_s _ _ zenon_H25a); [ zenon_intro zenon_Hed | zenon_intro zenon_H25b ]. % 18.96/19.09 exact (zenon_H1db zenon_Hed). % 18.96/19.09 apply (zenon_or_s _ _ zenon_H25b); [ zenon_intro zenon_Hee | zenon_intro zenon_H3b ]. % 18.96/19.09 apply (zenon_L277_); trivial. % 18.96/19.09 apply (zenon_L168_); trivial. % 18.96/19.09 (* end of lemma zenon_L1015_ *) % 18.96/19.09 assert (zenon_L1016_ : (((op (e2) (e0)) = (e0))\/(((op (e2) (e1)) = (e0))\/(((op (e2) (e2)) = (e0))\/((op (e2) (e3)) = (e0))))) -> (((op (e0) (e3)) = (e2))\/(((op (e1) (e3)) = (e2))\/(((op (e2) (e3)) = (e2))\/((op (e3) (e3)) = (e2))))) -> (~((e1) = (e2))) -> ((op (e1) (e3)) = (e1)) -> (((op (e2) (e3)) = (e0))\/(((op (e2) (e3)) = (e1))\/(((op (e2) (e3)) = (e2))\/((op (e2) (e3)) = (e3))))) -> (~((op (e2) (e3)) = (op (e3) (e3)))) -> (~((e0) = (e3))) -> (~((op (e3) (e1)) = (op (e3) (e3)))) -> ((op (e3) (e1)) = (e0)) -> (~((op (e2) (e1)) = (op (e2) (e3)))) -> (~((op (e1) (e0)) = (op (e1) (e3)))) -> ((op (e1) (e0)) = (e0)) -> ((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 (e0) (e2)) = (op (e3) (e2)))) -> (~((op (e0) (e2)) = (op (e1) (e2)))) -> ((op (e1) (e2)) = (e2)) -> (~((op (e0) (e2)) = (e1))) -> (~((op (e0) (e2)) = (op (e2) (e2)))) -> (((op (e0) (e2)) = (e0))\/(((op (e0) (e2)) = (e1))\/(((op (e0) (e2)) = (e2))\/((op (e0) (e2)) = (e3))))) -> (((op (e3) (e0)) = (e3))\/(((op (e3) (e1)) = (e3))\/(((op (e3) (e2)) = (e3))\/((op (e3) (e3)) = (e3))))) -> (~((e1) = (e3))) -> ((op (e1) (e1)) = (e3)) -> (~((op (e1) (e1)) = (op (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 (e0) (e0)) = (e2)) -> ((op (e3) (e0)) = (e1)) -> (~((e2) = (e3))) -> (~((op (e2) (e0)) = (op (e2) (e2)))) -> (~((op (e2) (e0)) = (op (e2) (e1)))) -> ((op (e2) (e1)) = (e2)) -> (~((op (e2) (e0)) = (e1))) -> (~((op (e2) (e0)) = (op (e2) (e3)))) -> (((op (e2) (e0)) = (e0))\/(((op (e2) (e0)) = (e1))\/(((op (e2) (e0)) = (e2))\/((op (e2) (e0)) = (e3))))) -> (~((op (e0) (e3)) = (op (e2) (e3)))) -> ((op (e0) (e3)) = (e3)) -> False). % 18.96/19.09 do 0 intro. intros zenon_H2f zenon_H145 zenon_H7c zenon_Hd6 zenon_H11f zenon_Hf3 zenon_H9a zenon_H130 zenon_H1b1 zenon_H1c7 zenon_Hd8 zenon_H27 zenon_H48 zenon_H208 zenon_H67 zenon_H14f zenon_H195 zenon_H113 zenon_H20d zenon_Ha8 zenon_H1ba zenon_H165 zenon_H95 zenon_H13f zenon_H160 zenon_H102 zenon_H1a6 zenon_He7 zenon_H7b zenon_Hac zenon_H12b zenon_H52 zenon_H1f0 zenon_H1ca zenon_H1db zenon_H5b zenon_H259 zenon_He2 zenon_He3. % 18.96/19.09 apply (zenon_or_s _ _ zenon_H2f); [ zenon_intro zenon_H34 | zenon_intro zenon_H33 ]. % 18.96/19.09 apply (zenon_L571_); trivial. % 18.96/19.09 apply (zenon_or_s _ _ zenon_H33); [ zenon_intro zenon_H36 | zenon_intro zenon_H35 ]. % 18.96/19.09 apply (zenon_L641_); trivial. % 18.96/19.09 apply (zenon_or_s _ _ zenon_H35); [ zenon_intro zenon_H2c | zenon_intro zenon_H37 ]. % 18.96/19.09 apply (zenon_L1014_); trivial. % 18.96/19.09 apply (zenon_or_s _ _ zenon_He7); [ zenon_intro zenon_H3b | zenon_intro zenon_He9 ]. % 18.96/19.09 apply (zenon_L308_); trivial. % 18.96/19.09 apply (zenon_or_s _ _ zenon_He9); [ zenon_intro zenon_Ha6 | zenon_intro zenon_Hea ]. % 18.96/19.09 apply (zenon_L207_); trivial. % 18.96/19.09 apply (zenon_or_s _ _ zenon_Hea); [ zenon_intro zenon_Haa | zenon_intro zenon_Hdd ]. % 18.96/19.09 apply (zenon_L1015_); trivial. % 18.96/19.09 apply (zenon_L54_); trivial. % 18.96/19.09 (* end of lemma zenon_L1016_ *) % 18.96/19.09 assert (zenon_L1017_ : (((op (e0) (e3)) = (e0))\/(((op (e0) (e3)) = (e1))\/(((op (e0) (e3)) = (e2))\/((op (e0) (e3)) = (e3))))) -> ((op (e2) (e3)) = (e0)) -> (~((op (e0) (e3)) = (e1))) -> ((op (e3) (e3)) = (e2)) -> (~((op (e0) (e3)) = (op (e3) (e3)))) -> (((op (e2) (e0)) = (e0))\/(((op (e2) (e1)) = (e0))\/(((op (e2) (e2)) = (e0))\/((op (e2) (e3)) = (e0))))) -> (((op (e0) (e3)) = (e2))\/(((op (e1) (e3)) = (e2))\/(((op (e2) (e3)) = (e2))\/((op (e3) (e3)) = (e2))))) -> (~((e1) = (e2))) -> ((op (e1) (e3)) = (e1)) -> (((op (e2) (e3)) = (e0))\/(((op (e2) (e3)) = (e1))\/(((op (e2) (e3)) = (e2))\/((op (e2) (e3)) = (e3))))) -> (~((op (e2) (e3)) = (op (e3) (e3)))) -> (~((e0) = (e3))) -> (~((op (e3) (e1)) = (op (e3) (e3)))) -> ((op (e3) (e1)) = (e0)) -> (~((op (e2) (e1)) = (op (e2) (e3)))) -> (~((op (e1) (e0)) = (op (e1) (e3)))) -> ((op (e1) (e0)) = (e0)) -> ((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 (e0) (e2)) = (op (e3) (e2)))) -> (~((op (e0) (e2)) = (op (e1) (e2)))) -> ((op (e1) (e2)) = (e2)) -> (~((op (e0) (e2)) = (e1))) -> (~((op (e0) (e2)) = (op (e2) (e2)))) -> (((op (e0) (e2)) = (e0))\/(((op (e0) (e2)) = (e1))\/(((op (e0) (e2)) = (e2))\/((op (e0) (e2)) = (e3))))) -> (((op (e3) (e0)) = (e3))\/(((op (e3) (e1)) = (e3))\/(((op (e3) (e2)) = (e3))\/((op (e3) (e3)) = (e3))))) -> (~((e1) = (e3))) -> ((op (e1) (e1)) = (e3)) -> (~((op (e1) (e1)) = (op (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 (e0) (e0)) = (e2)) -> ((op (e3) (e0)) = (e1)) -> (~((e2) = (e3))) -> (~((op (e2) (e0)) = (op (e2) (e2)))) -> (~((op (e2) (e0)) = (op (e2) (e1)))) -> ((op (e2) (e1)) = (e2)) -> (~((op (e2) (e0)) = (e1))) -> (~((op (e2) (e0)) = (op (e2) (e3)))) -> (((op (e2) (e0)) = (e0))\/(((op (e2) (e0)) = (e1))\/(((op (e2) (e0)) = (e2))\/((op (e2) (e0)) = (e3))))) -> (~((op (e0) (e3)) = (op (e2) (e3)))) -> False). % 18.96/19.09 do 0 intro. intros zenon_He4 zenon_H37 zenon_H231 zenon_Hf6 zenon_Hc2 zenon_H2f zenon_H145 zenon_H7c zenon_Hd6 zenon_H11f zenon_Hf3 zenon_H9a zenon_H130 zenon_H1b1 zenon_H1c7 zenon_Hd8 zenon_H27 zenon_H48 zenon_H208 zenon_H67 zenon_H14f zenon_H195 zenon_H113 zenon_H20d zenon_Ha8 zenon_H1ba zenon_H165 zenon_H95 zenon_H13f zenon_H160 zenon_H102 zenon_H1a6 zenon_He7 zenon_H7b zenon_Hac zenon_H12b zenon_H52 zenon_H1f0 zenon_H1ca zenon_H1db zenon_H5b zenon_H259 zenon_He2. % 18.96/19.09 apply (zenon_or_s _ _ zenon_He4); [ zenon_intro zenon_H1e | zenon_intro zenon_He5 ]. % 18.96/19.09 apply (zenon_L367_); trivial. % 18.96/19.09 apply (zenon_or_s _ _ zenon_He5); [ zenon_intro zenon_Hc3 | zenon_intro zenon_He6 ]. % 18.96/19.09 exact (zenon_H231 zenon_Hc3). % 18.96/19.09 apply (zenon_or_s _ _ zenon_He6); [ zenon_intro zenon_Hcd | zenon_intro zenon_He3 ]. % 18.96/19.09 apply (zenon_L87_); trivial. % 18.96/19.09 apply (zenon_L1016_); trivial. % 18.96/19.09 (* end of lemma zenon_L1017_ *) % 18.96/19.09 assert (zenon_L1018_ : ((~((op (e1) (e0)) = (e1)))\/((op (e1) (e1)) = (e0))) -> ((~((op (e1) (e3)) = (e1)))\/((op (e1) (e1)) = (e3))) -> ((~((op (e2) (e2)) = (e1)))\/((op (e2) (e1)) = (e2))) -> (~((op (e0) (e1)) = (op (e2) (e1)))) -> ((~((op (e3) (e0)) = (e1)))\/((op (e3) (e1)) = (e0))) -> ((~((op (e3) (e2)) = (e1)))\/((op (e3) (e1)) = (e2))) -> ((op (e0) (e1)) = (e2)) -> (~((op (e0) (e1)) = (op (e3) (e1)))) -> (~((op (e0) (e0)) = (e1))) -> (((op (e2) (e0)) = (e1))\/(((op (e2) (e1)) = (e1))\/(((op (e2) (e2)) = (e1))\/((op (e2) (e3)) = (e1))))) -> (~((op (e1) (e0)) = (op (e2) (e0)))) -> (~((op (e1) (e3)) = (op (e3) (e3)))) -> (((op (e3) (e0)) = (e1))\/(((op (e3) (e1)) = (e1))\/(((op (e3) (e2)) = (e1))\/((op (e3) (e3)) = (e1))))) -> (((op (e0) (e0)) = (e1))\/(((op (e1) (e0)) = (e1))\/(((op (e2) (e0)) = (e1))\/((op (e3) (e0)) = (e1))))) -> ((op (e0) (e1)) = (e1)) -> ((~((op (e3) (e1)) = (e1)))\/((op (e3) (e1)) = (e1))) -> (~((op (e1) (e1)) = (op (e2) (e1)))) -> ((~((op (e2) (e3)) = (e1)))\/((op (e2) (e1)) = (e3))) -> ((~((op (e2) (e1)) = (e1)))\/((op (e2) (e1)) = (e1))) -> (~((op (e1) (e1)) = (e1))) -> (((op (e1) (e0)) = (e1))\/(((op (e1) (e1)) = (e1))\/(((op (e1) (e2)) = (e1))\/((op (e1) (e3)) = (e1))))) -> (~((op (e0) (e1)) = (op (e1) (e1)))) -> ((~((op (e1) (e2)) = (e1)))\/((op (e1) (e1)) = (e2))) -> False). % 18.96/19.09 do 0 intro. intros zenon_H25d zenon_H258 zenon_H253 zenon_H17e zenon_H254 zenon_H252 zenon_H10f zenon_H210 zenon_H84 zenon_H106 zenon_H201 zenon_Hd5 zenon_He8 zenon_H235 zenon_Ha0 zenon_H261 zenon_H13e zenon_H263 zenon_H262 zenon_H10a zenon_H128 zenon_H10e zenon_H256. % 18.96/19.09 apply (zenon_or_s _ _ zenon_H25d); [ zenon_intro zenon_H1ef | zenon_intro zenon_H29 ]. % 18.96/19.09 apply (zenon_L997_); trivial. % 18.96/19.09 apply (zenon_or_s _ _ zenon_H256); [ zenon_intro zenon_H24d | zenon_intro zenon_H110 ]. % 18.96/19.09 apply (zenon_or_s _ _ zenon_H258); [ zenon_intro zenon_H24e | zenon_intro zenon_H13f ]. % 18.96/19.09 apply (zenon_or_s _ _ zenon_H262); [ zenon_intro zenon_H24f | zenon_intro zenon_Ha5 ]. % 18.96/19.09 apply (zenon_L957_); trivial. % 18.96/19.09 apply (zenon_L357_); trivial. % 18.96/19.09 apply (zenon_L996_); trivial. % 18.96/19.09 apply (zenon_L67_); trivial. % 18.96/19.09 (* end of lemma zenon_L1018_ *) % 18.96/19.09 assert (zenon_L1019_ : (((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 (e2) (e0)) = (e0))\/(((op (e2) (e1)) = (e0))\/(((op (e2) (e2)) = (e0))\/((op (e2) (e3)) = (e0))))) -> (~((op (e1) (e0)) = (op (e2) (e0)))) -> (~((op (e3) (e1)) = (op (e3) (e2)))) -> (~((op (e2) (e1)) = (op (e2) (e2)))) -> (~((op (e1) (e0)) = (op (e1) (e2)))) -> (((op (e0) (e0)) = (e0))\/(((op (e1) (e0)) = (e0))\/(((op (e2) (e0)) = (e0))\/((op (e3) (e0)) = (e0))))) -> (~((op (e0) (e0)) = (e0))) -> (~((op (e2) (e1)) = (op (e2) (e3)))) -> (~((op (e0) (e2)) = (op (e0) (e3)))) -> (~((op (e2) (e0)) = (op (e2) (e1)))) -> (~((op (e3) (e0)) = (op (e3) (e1)))) -> (((op (e0) (e2)) = (e0))\/(((op (e1) (e2)) = (e0))\/(((op (e2) (e2)) = (e0))\/((op (e3) (e2)) = (e0))))) -> (~((op (e3) (e1)) = (op (e3) (e3)))) -> ((op (e3) (e1)) = (e0)) -> (~((op (e2) (e2)) = (op (e2) (e3)))) -> (~((op (e1) (e0)) = (op (e1) (e3)))) -> ((op (e1) (e0)) = (e0)) -> (~((e0) = (e2))) -> (((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 (e2) (e3)) = (op (e3) (e3)))) -> (~((op (e1) (e3)) = (op (e3) (e3)))) -> ((op (e0) (e3)) = (e2)) -> (~((op (e0) (e3)) = (op (e3) (e3)))) -> (~((op (e3) (e3)) = (e3))) -> False). % 18.96/19.09 do 0 intro. intros zenon_H128 zenon_H1ef zenon_H10a zenon_H24d zenon_H2f zenon_H201 zenon_H1a4 zenon_H24b zenon_H24a zenon_H3e zenon_H3f zenon_H1c7 zenon_H208 zenon_H1f0 zenon_H1cf zenon_H6a zenon_H130 zenon_H1b1 zenon_H6d zenon_Hd8 zenon_H27 zenon_H149 zenon_H67 zenon_H101 zenon_Hf3 zenon_Hd5 zenon_Hcd zenon_Hc2 zenon_H102. % 18.96/19.09 apply (zenon_or_s _ _ zenon_H128); [ zenon_intro zenon_H9d | zenon_intro zenon_H129 ]. % 18.96/19.09 exact (zenon_H1ef zenon_H9d). % 18.96/19.09 apply (zenon_or_s _ _ zenon_H129); [ zenon_intro zenon_H10d | zenon_intro zenon_H12a ]. % 18.96/19.09 exact (zenon_H10a zenon_H10d). % 18.96/19.09 apply (zenon_or_s _ _ zenon_H12a); [ zenon_intro zenon_Hf0 | zenon_intro zenon_Hd6 ]. % 18.96/19.09 exact (zenon_H24d zenon_Hf0). % 18.96/19.09 apply (zenon_or_s _ _ zenon_H2f); [ zenon_intro zenon_H34 | zenon_intro zenon_H33 ]. % 18.96/19.09 apply (zenon_L332_); trivial. % 18.96/19.09 apply (zenon_or_s _ _ zenon_H33); [ zenon_intro zenon_H36 | zenon_intro zenon_H35 ]. % 18.96/19.09 apply (zenon_L646_); trivial. % 18.96/19.09 apply (zenon_or_s _ _ zenon_H35); [ zenon_intro zenon_H2c | zenon_intro zenon_H37 ]. % 18.96/19.09 apply (zenon_L676_); trivial. % 18.96/19.09 apply (zenon_L275_); trivial. % 18.96/19.09 (* end of lemma zenon_L1019_ *) % 18.96/19.09 assert (zenon_L1020_ : (((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 (e2) (e3)) = (e3)) -> (~((op (e0) (e3)) = (op (e2) (e3)))) -> (~((op (e0) (e3)) = (op (e3) (e3)))) -> (~((op (e0) (e3)) = (e1))) -> (~((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 (e3) (e3)) = (e3))) -> False). % 18.96/19.09 do 0 intro. intros zenon_H101 zenon_Hd5 zenon_Hc7 zenon_Hdd zenon_He2 zenon_Hc2 zenon_H231 zenon_H1d zenon_H1f zenon_He4 zenon_H102. % 18.96/19.09 apply (zenon_or_s _ _ zenon_H101); [ zenon_intro zenon_H60 | zenon_intro zenon_H103 ]. % 18.96/19.09 apply (zenon_L136_); trivial. % 18.96/19.09 apply (zenon_or_s _ _ zenon_H103); [ zenon_intro zenon_Hc4 | zenon_intro zenon_H104 ]. % 18.96/19.09 exact (zenon_Hc7 zenon_Hc4). % 18.96/19.09 apply (zenon_or_s _ _ zenon_H104); [ zenon_intro zenon_Hf6 | zenon_intro zenon_H105 ]. % 18.96/19.09 apply (zenon_L722_); trivial. % 18.96/19.09 exact (zenon_H102 zenon_H105). % 18.96/19.09 (* end of lemma zenon_L1020_ *) % 18.96/19.09 assert (zenon_L1021_ : (((op (e0) (e0)) = (e1))\/(((op (e1) (e0)) = (e1))\/(((op (e2) (e0)) = (e1))\/((op (e3) (e0)) = (e1))))) -> (~((op (e0) (e0)) = (e1))) -> (~((op (e2) (e3)) = (e1))) -> (((op (e3) (e0)) = (e1))\/(((op (e3) (e1)) = (e1))\/(((op (e3) (e2)) = (e1))\/((op (e3) (e3)) = (e1))))) -> (~((op (e3) (e1)) = (e1))) -> (~((op (e3) (e2)) = (op (e3) (e3)))) -> (~((op (e2) (e2)) = (op (e2) (e3)))) -> (~((op (e1) (e0)) = (op (e1) (e3)))) -> ((op (e0) (e1)) = (e1)) -> (~((op (e0) (e1)) = (op (e0) (e3)))) -> (((op (e0) (e3)) = (e1))\/(((op (e1) (e3)) = (e1))\/(((op (e2) (e3)) = (e1))\/((op (e3) (e3)) = (e1))))) -> (~((op (e3) (e3)) = (e1))) -> (~((op (e2) (e1)) = (e1))) -> (((op (e2) (e0)) = (e1))\/(((op (e2) (e1)) = (e1))\/(((op (e2) (e2)) = (e1))\/((op (e2) (e3)) = (e1))))) -> (~((op (e2) (e0)) = (e1))) -> (~((op (e3) (e0)) = (e1))) -> False). % 18.96/19.09 do 0 intro. intros zenon_H235 zenon_H84 zenon_H255 zenon_He8 zenon_H250 zenon_H62 zenon_H6d zenon_Hd8 zenon_Ha0 zenon_H54 zenon_H133 zenon_Hc7 zenon_H24f zenon_H106 zenon_H1db zenon_Had. % 18.96/19.09 apply (zenon_or_s _ _ zenon_H235); [ zenon_intro zenon_H7a | zenon_intro zenon_H236 ]. % 18.96/19.09 exact (zenon_H84 zenon_H7a). % 18.96/19.09 apply (zenon_or_s _ _ zenon_H236); [ zenon_intro zenon_H9d | zenon_intro zenon_H237 ]. % 18.96/19.09 apply (zenon_or_s _ _ zenon_H106); [ zenon_intro zenon_Hed | zenon_intro zenon_H107 ]. % 18.96/19.09 exact (zenon_H1db zenon_Hed). % 18.96/19.09 apply (zenon_or_s _ _ zenon_H107); [ zenon_intro zenon_Ha5 | zenon_intro zenon_H108 ]. % 18.96/19.09 exact (zenon_H24f zenon_Ha5). % 18.96/19.09 apply (zenon_or_s _ _ zenon_H108); [ zenon_intro zenon_Hf1 | zenon_intro zenon_Hf4 ]. % 18.96/19.09 apply (zenon_or_s _ _ zenon_He8); [ zenon_intro zenon_Hac | zenon_intro zenon_Heb ]. % 18.96/19.09 exact (zenon_Had zenon_Hac). % 18.96/19.09 apply (zenon_or_s _ _ zenon_Heb); [ zenon_intro zenon_Hae | zenon_intro zenon_Hec ]. % 18.96/19.09 exact (zenon_H250 zenon_Hae). % 18.96/19.09 apply (zenon_or_s _ _ zenon_Hec); [ zenon_intro zenon_Hba | zenon_intro zenon_Hc4 ]. % 18.96/19.09 apply (zenon_L419_); trivial. % 18.96/19.09 exact (zenon_Hc7 zenon_Hc4). % 18.96/19.09 exact (zenon_H255 zenon_Hf4). % 18.96/19.09 apply (zenon_or_s _ _ zenon_H237); [ zenon_intro zenon_Hed | zenon_intro zenon_Hac ]. % 18.96/19.09 exact (zenon_H1db zenon_Hed). % 18.96/19.09 exact (zenon_Had zenon_Hac). % 18.96/19.09 (* end of lemma zenon_L1021_ *) % 18.96/19.09 assert (zenon_L1022_ : ((~((op (e3) (e1)) = (e1)))\/((op (e3) (e1)) = (e1))) -> (~((op (e0) (e1)) = (op (e3) (e1)))) -> (((op (e0) (e0)) = (e1))\/(((op (e1) (e0)) = (e1))\/(((op (e2) (e0)) = (e1))\/((op (e3) (e0)) = (e1))))) -> (~((op (e2) (e0)) = (e1))) -> (~((op (e2) (e1)) = (e1))) -> (((op (e3) (e0)) = (e1))\/(((op (e3) (e1)) = (e1))\/(((op (e3) (e2)) = (e1))\/((op (e3) (e3)) = (e1))))) -> (~((op (e0) (e1)) = (op (e0) (e3)))) -> ((op (e0) (e1)) = (e1)) -> (~((op (e1) (e0)) = (op (e1) (e3)))) -> (~((op (e2) (e2)) = (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 (e3) (e0)) = (e1))) -> (~((op (e2) (e3)) = (e1))) -> (((op (e2) (e0)) = (e1))\/(((op (e2) (e1)) = (e1))\/(((op (e2) (e2)) = (e1))\/((op (e2) (e3)) = (e1))))) -> (~((op (e0) (e0)) = (e1))) -> (~((op (e1) (e1)) = (op (e3) (e1)))) -> ((op (e1) (e1)) = (e3)) -> ((~((op (e3) (e3)) = (e1)))\/((op (e3) (e1)) = (e3))) -> False). % 18.96/19.09 do 0 intro. intros zenon_H261 zenon_H210 zenon_H235 zenon_H1db zenon_H24f zenon_He8 zenon_H54 zenon_Ha0 zenon_Hd8 zenon_H6d zenon_H62 zenon_H133 zenon_Had zenon_H255 zenon_H106 zenon_H84 zenon_H160 zenon_H13f zenon_H264. % 18.96/19.09 apply (zenon_or_s _ _ zenon_H261); [ zenon_intro zenon_H250 | zenon_intro zenon_Hae ]. % 18.96/19.09 apply (zenon_or_s _ _ zenon_H264); [ zenon_intro zenon_Hc7 | zenon_intro zenon_H161 ]. % 18.96/19.09 apply (zenon_L1021_); trivial. % 18.96/19.09 apply (zenon_L110_); trivial. % 18.96/19.09 apply (zenon_L363_); trivial. % 18.96/19.09 (* end of lemma zenon_L1022_ *) % 18.96/19.09 assert (zenon_L1023_ : ((~((op (e2) (e3)) = (e1)))\/((op (e2) (e1)) = (e3))) -> (~((op (e1) (e1)) = (op (e2) (e1)))) -> ((~((op (e3) (e1)) = (e1)))\/((op (e3) (e1)) = (e1))) -> (~((op (e0) (e1)) = (op (e3) (e1)))) -> (((op (e0) (e0)) = (e1))\/(((op (e1) (e0)) = (e1))\/(((op (e2) (e0)) = (e1))\/((op (e3) (e0)) = (e1))))) -> (~((op (e2) (e0)) = (e1))) -> (~((op (e2) (e1)) = (e1))) -> (((op (e3) (e0)) = (e1))\/(((op (e3) (e1)) = (e1))\/(((op (e3) (e2)) = (e1))\/((op (e3) (e3)) = (e1))))) -> (~((op (e0) (e1)) = (op (e0) (e3)))) -> ((op (e0) (e1)) = (e1)) -> (~((op (e1) (e0)) = (op (e1) (e3)))) -> (~((op (e2) (e2)) = (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) (e0)) = (e1))\/(((op (e2) (e1)) = (e1))\/(((op (e2) (e2)) = (e1))\/((op (e2) (e3)) = (e1))))) -> (~((op (e0) (e0)) = (e1))) -> (~((op (e1) (e1)) = (op (e3) (e1)))) -> ((op (e1) (e1)) = (e3)) -> ((~((op (e3) (e3)) = (e1)))\/((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) (e1)))) -> (~((op (e0) (e2)) = (op (e0) (e3)))) -> (~((op (e1) (e1)) = (op (e1) (e2)))) -> (~((op (e2) (e0)) = (op (e2) (e2)))) -> (~((op (e3) (e1)) = (op (e3) (e2)))) -> (((op (e0) (e2)) = (e0))\/(((op (e1) (e2)) = (e0))\/(((op (e2) (e2)) = (e0))\/((op (e3) (e2)) = (e0))))) -> (~((op (e1) (e1)) = (op (e1) (e3)))) -> (~((op (e2) (e0)) = (op (e2) (e3)))) -> (~((op (e3) (e1)) = (op (e3) (e3)))) -> (((op (e0) (e3)) = (e0))\/(((op (e1) (e3)) = (e0))\/(((op (e2) (e3)) = (e0))\/((op (e3) (e3)) = (e0))))) -> ((op (e1) (e1)) = (e0)) -> (~((op (e1) (e0)) = (op (e1) (e1)))) -> (~((op (e0) (e0)) = (e0))) -> ((~((op (e3) (e0)) = (e1)))\/((op (e3) (e1)) = (e0))) -> False). % 18.96/19.09 do 0 intro. intros zenon_H263 zenon_H13e zenon_H261 zenon_H210 zenon_H235 zenon_H1db zenon_H24f zenon_He8 zenon_H54 zenon_Ha0 zenon_Hd8 zenon_H6d zenon_H62 zenon_H133 zenon_H106 zenon_H84 zenon_H160 zenon_H13f zenon_H264 zenon_H3e zenon_H1cf zenon_H208 zenon_H4f zenon_H52 zenon_H1a4 zenon_H6a zenon_H57 zenon_H5b zenon_H130 zenon_H67 zenon_H29 zenon_H45 zenon_H3f zenon_H254. % 18.96/19.09 apply (zenon_or_s _ _ zenon_H263); [ zenon_intro zenon_H255 | zenon_intro zenon_Ha6 ]. % 18.96/19.09 apply (zenon_or_s _ _ zenon_H254); [ zenon_intro zenon_Had | zenon_intro zenon_H1b1 ]. % 18.96/19.09 apply (zenon_L1022_); trivial. % 18.96/19.09 apply (zenon_L349_); trivial. % 18.96/19.09 apply (zenon_L95_); trivial. % 18.96/19.09 (* end of lemma zenon_L1023_ *) % 18.96/19.09 assert (zenon_L1024_ : (((op (e1) (e0)) = (e0))\/(((op (e1) (e1)) = (e0))\/(((op (e1) (e2)) = (e0))\/((op (e1) (e3)) = (e0))))) -> (~((op (e1) (e0)) = (op (e2) (e0)))) -> ((op (e2) (e0)) = (e0)) -> ((~((op (e3) (e0)) = (e1)))\/((op (e3) (e1)) = (e0))) -> (~((op (e0) (e0)) = (e0))) -> (~((op (e1) (e0)) = (op (e1) (e1)))) -> (((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) (e3)))) -> (~((op (e1) (e1)) = (op (e1) (e3)))) -> (((op (e0) (e2)) = (e0))\/(((op (e1) (e2)) = (e0))\/(((op (e2) (e2)) = (e0))\/((op (e3) (e2)) = (e0))))) -> (~((op (e3) (e1)) = (op (e3) (e2)))) -> (~((op (e2) (e0)) = (op (e2) (e2)))) -> (~((op (e1) (e1)) = (op (e1) (e2)))) -> (~((op (e0) (e2)) = (op (e0) (e3)))) -> (~((op (e3) (e0)) = (op (e3) (e1)))) -> (((op (e0) (e0)) = (e0))\/(((op (e1) (e0)) = (e0))\/(((op (e2) (e0)) = (e0))\/((op (e3) (e0)) = (e0))))) -> ((~((op (e3) (e3)) = (e1)))\/((op (e3) (e1)) = (e3))) -> (~((op (e1) (e1)) = (op (e3) (e1)))) -> (~((op (e0) (e0)) = (e1))) -> (((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))))) -> (~((op (e3) (e2)) = (op (e3) (e3)))) -> (~((op (e2) (e2)) = (op (e2) (e3)))) -> (~((op (e1) (e0)) = (op (e1) (e3)))) -> ((op (e0) (e1)) = (e1)) -> (~((op (e0) (e1)) = (op (e0) (e3)))) -> (((op (e3) (e0)) = (e1))\/(((op (e3) (e1)) = (e1))\/(((op (e3) (e2)) = (e1))\/((op (e3) (e3)) = (e1))))) -> (~((op (e2) (e1)) = (e1))) -> (~((op (e2) (e0)) = (e1))) -> (((op (e0) (e0)) = (e1))\/(((op (e1) (e0)) = (e1))\/(((op (e2) (e0)) = (e1))\/((op (e3) (e0)) = (e1))))) -> (~((op (e0) (e1)) = (op (e3) (e1)))) -> ((~((op (e3) (e1)) = (e1)))\/((op (e3) (e1)) = (e1))) -> (~((op (e1) (e1)) = (op (e2) (e1)))) -> ((~((op (e2) (e3)) = (e1)))\/((op (e2) (e1)) = (e3))) -> (~((e1) = (e2))) -> (~((e0) = (e2))) -> ((op (e1) (e1)) = (e3)) -> (~((e2) = (e3))) -> ((op (e3) (e0)) = (e1)) -> ((op (e0) (e0)) = (e3)) -> (((op (e1) (e0)) = (e2))\/(((op (e1) (e1)) = (e2))\/(((op (e1) (e2)) = (e2))\/((op (e1) (e3)) = (e2))))) -> (~((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 (e0) (e3)) = (op (e1) (e3)))) -> ((op (e0) (e3)) = (e0)) -> False). % 18.96/19.09 do 0 intro. intros zenon_H22 zenon_H201 zenon_H34 zenon_H254 zenon_H3f zenon_H45 zenon_H67 zenon_H130 zenon_H5b zenon_H57 zenon_H6a zenon_H1a4 zenon_H52 zenon_H4f zenon_H208 zenon_H1cf zenon_H3e zenon_H264 zenon_H160 zenon_H84 zenon_H106 zenon_H133 zenon_H62 zenon_H6d zenon_Hd8 zenon_Ha0 zenon_H54 zenon_He8 zenon_H24f zenon_H1db zenon_H235 zenon_H210 zenon_H261 zenon_H13e zenon_H263 zenon_H7c zenon_H149 zenon_H13f zenon_H12b zenon_Hac zenon_H3a zenon_H18c zenon_H24d zenon_H10a zenon_H1ef zenon_H128 zenon_H1d zenon_H1e. % 18.96/19.09 apply (zenon_or_s _ _ zenon_H22); [ zenon_intro zenon_H27 | zenon_intro zenon_H26 ]. % 18.96/19.09 apply (zenon_L332_); trivial. % 18.96/19.09 apply (zenon_or_s _ _ zenon_H26); [ zenon_intro zenon_H29 | zenon_intro zenon_H28 ]. % 18.96/19.09 apply (zenon_L1023_); trivial. % 18.96/19.09 apply (zenon_or_s _ _ zenon_H28); [ zenon_intro zenon_H2a | zenon_intro zenon_H1f ]. % 18.96/19.09 apply (zenon_or_s _ _ zenon_H128); [ zenon_intro zenon_H9d | zenon_intro zenon_H129 ]. % 18.96/19.09 exact (zenon_H1ef zenon_H9d). % 18.96/19.09 apply (zenon_or_s _ _ zenon_H129); [ zenon_intro zenon_H10d | zenon_intro zenon_H12a ]. % 18.96/19.09 exact (zenon_H10a zenon_H10d). % 18.96/19.09 apply (zenon_or_s _ _ zenon_H12a); [ zenon_intro zenon_Hf0 | zenon_intro zenon_Hd6 ]. % 18.96/19.09 exact (zenon_H24d zenon_Hf0). % 18.96/19.09 apply (zenon_or_s _ _ zenon_H18c); [ zenon_intro zenon_H86 | zenon_intro zenon_H18d ]. % 18.96/19.09 apply (zenon_L241_); trivial. % 18.96/19.09 apply (zenon_or_s _ _ zenon_H18d); [ zenon_intro zenon_H110 | zenon_intro zenon_H18e ]. % 18.96/19.09 apply (zenon_L166_); trivial. % 18.96/19.09 apply (zenon_or_s _ _ zenon_H18e); [ zenon_intro zenon_H113 | zenon_intro zenon_Hd7 ]. % 18.96/19.09 apply (zenon_L542_); trivial. % 18.96/19.09 apply (zenon_L101_); trivial. % 18.96/19.09 apply (zenon_L1_); trivial. % 18.96/19.09 (* end of lemma zenon_L1024_ *) % 18.96/19.09 assert (zenon_L1025_ : (((op (e1) (e0)) = (e0))\/(((op (e1) (e1)) = (e0))\/(((op (e1) (e2)) = (e0))\/((op (e1) (e3)) = (e0))))) -> (~((op (e1) (e0)) = (op (e2) (e0)))) -> ((op (e2) (e0)) = (e0)) -> ((~((op (e3) (e0)) = (e1)))\/((op (e3) (e1)) = (e0))) -> (~((op (e0) (e0)) = (e0))) -> (~((op (e1) (e0)) = (op (e1) (e1)))) -> (((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) (e3)))) -> (~((op (e1) (e1)) = (op (e1) (e3)))) -> (((op (e0) (e2)) = (e0))\/(((op (e1) (e2)) = (e0))\/(((op (e2) (e2)) = (e0))\/((op (e3) (e2)) = (e0))))) -> (~((op (e3) (e1)) = (op (e3) (e2)))) -> (~((op (e2) (e0)) = (op (e2) (e2)))) -> (~((op (e1) (e1)) = (op (e1) (e2)))) -> (~((op (e0) (e2)) = (op (e0) (e3)))) -> (~((op (e3) (e0)) = (op (e3) (e1)))) -> (((op (e0) (e0)) = (e0))\/(((op (e1) (e0)) = (e0))\/(((op (e2) (e0)) = (e0))\/((op (e3) (e0)) = (e0))))) -> ((~((op (e3) (e3)) = (e1)))\/((op (e3) (e1)) = (e3))) -> ((op (e1) (e1)) = (e3)) -> (~((op (e1) (e1)) = (op (e3) (e1)))) -> (~((op (e0) (e0)) = (e1))) -> (((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))))) -> (~((op (e3) (e2)) = (op (e3) (e3)))) -> (~((op (e2) (e2)) = (op (e2) (e3)))) -> (~((op (e1) (e0)) = (op (e1) (e3)))) -> ((op (e0) (e1)) = (e1)) -> (~((op (e0) (e1)) = (op (e0) (e3)))) -> (((op (e3) (e0)) = (e1))\/(((op (e3) (e1)) = (e1))\/(((op (e3) (e2)) = (e1))\/((op (e3) (e3)) = (e1))))) -> (~((op (e2) (e1)) = (e1))) -> (~((op (e2) (e0)) = (e1))) -> (((op (e0) (e0)) = (e1))\/(((op (e1) (e0)) = (e1))\/(((op (e2) (e0)) = (e1))\/((op (e3) (e0)) = (e1))))) -> (~((op (e0) (e1)) = (op (e3) (e1)))) -> ((~((op (e3) (e1)) = (e1)))\/((op (e3) (e1)) = (e1))) -> (~((op (e1) (e1)) = (op (e2) (e1)))) -> ((~((op (e2) (e3)) = (e1)))\/((op (e2) (e1)) = (e3))) -> (~((op (e2) (e2)) = (e2))) -> (~((op (e2) (e2)) = (op (e3) (e2)))) -> ((op (e0) (e2)) = (e3)) -> (((op (e2) (e2)) = (e0))\/(((op (e2) (e2)) = (e1))\/(((op (e2) (e2)) = (e2))\/((op (e2) (e2)) = (e3))))) -> (~((op (e1) (e2)) = (op (e1) (e3)))) -> (~((op (e0) (e2)) = (e1))) -> (((op (e0) (e2)) = (e1))\/(((op (e1) (e2)) = (e1))\/(((op (e2) (e2)) = (e1))\/((op (e3) (e2)) = (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 (e0) (e3)) = (op (e1) (e3)))) -> ((op (e0) (e3)) = (e0)) -> False). % 18.96/19.09 do 0 intro. intros zenon_H22 zenon_H201 zenon_H34 zenon_H254 zenon_H3f zenon_H45 zenon_H67 zenon_H130 zenon_H5b zenon_H57 zenon_H6a zenon_H1a4 zenon_H52 zenon_H4f zenon_H208 zenon_H1cf zenon_H3e zenon_H264 zenon_H13f zenon_H160 zenon_H84 zenon_H106 zenon_H133 zenon_H62 zenon_H6d zenon_Hd8 zenon_Ha0 zenon_H54 zenon_He8 zenon_H24f zenon_H1db zenon_H235 zenon_H210 zenon_H261 zenon_H13e zenon_H263 zenon_H173 zenon_H18f zenon_Ha9 zenon_H1c4 zenon_H124 zenon_H20d zenon_H139 zenon_H24d zenon_H10a zenon_H1ef zenon_H128 zenon_H1d zenon_H1e. % 18.96/19.09 apply (zenon_or_s _ _ zenon_H22); [ zenon_intro zenon_H27 | zenon_intro zenon_H26 ]. % 18.96/19.09 apply (zenon_L332_); trivial. % 18.96/19.09 apply (zenon_or_s _ _ zenon_H26); [ zenon_intro zenon_H29 | zenon_intro zenon_H28 ]. % 18.96/19.09 apply (zenon_L1023_); trivial. % 18.96/19.09 apply (zenon_or_s _ _ zenon_H28); [ zenon_intro zenon_H2a | zenon_intro zenon_H1f ]. % 18.96/19.09 apply (zenon_L721_); trivial. % 18.96/19.09 apply (zenon_L1_); trivial. % 18.96/19.09 (* end of lemma zenon_L1025_ *) % 18.96/19.09 assert (zenon_L1026_ : (((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)) = (e0))\/(((op (e1) (e3)) = (e0))\/(((op (e2) (e3)) = (e0))\/((op (e3) (e3)) = (e0))))) -> (~((e0) = (e3))) -> ((op (e0) (e3)) = (e3)) -> (~((op (e0) (e3)) = (op (e2) (e3)))) -> (~((op (e2) (e3)) = (op (e3) (e3)))) -> (((op (e2) (e3)) = (e0))\/(((op (e2) (e3)) = (e1))\/(((op (e2) (e3)) = (e2))\/((op (e2) (e3)) = (e3))))) -> ((op (e2) (e1)) = (e2)) -> (~((op (e2) (e1)) = (op (e2) (e3)))) -> (~((e1) = (e2))) -> (~((e2) = (e3))) -> (((op (e0) (e3)) = (e2))\/(((op (e1) (e3)) = (e2))\/(((op (e2) (e3)) = (e2))\/((op (e3) (e3)) = (e2))))) -> (~((op (e2) (e0)) = (op (e2) (e3)))) -> ((op (e2) (e0)) = (e0)) -> ((op (e3) (e1)) = (e0)) -> (~((op (e3) (e1)) = (op (e3) (e3)))) -> False). % 18.96/19.09 do 0 intro. intros zenon_H128 zenon_H1ef zenon_H10a zenon_H24d zenon_H67 zenon_H9a zenon_He3 zenon_He2 zenon_Hf3 zenon_H11f zenon_H1ca zenon_H1c7 zenon_H7c zenon_H12b zenon_H145 zenon_H5b zenon_H34 zenon_H1b1 zenon_H130. % 18.96/19.09 apply (zenon_or_s _ _ zenon_H128); [ zenon_intro zenon_H9d | zenon_intro zenon_H129 ]. % 18.96/19.09 exact (zenon_H1ef zenon_H9d). % 18.96/19.09 apply (zenon_or_s _ _ zenon_H129); [ zenon_intro zenon_H10d | zenon_intro zenon_H12a ]. % 18.96/19.09 exact (zenon_H10a zenon_H10d). % 18.96/19.09 apply (zenon_or_s _ _ zenon_H12a); [ zenon_intro zenon_Hf0 | zenon_intro zenon_Hd6 ]. % 18.96/19.09 exact (zenon_H24d zenon_Hf0). % 18.96/19.09 apply (zenon_L571_); trivial. % 18.96/19.09 (* end of lemma zenon_L1026_ *) % 18.96/19.09 assert (zenon_L1027_ : ((~((op (e3) (e1)) = (e1)))\/((op (e3) (e1)) = (e1))) -> ((op (e0) (e1)) = (e1)) -> (~((op (e0) (e1)) = (op (e3) (e1)))) -> (((op (e0) (e0)) = (e1))\/(((op (e1) (e0)) = (e1))\/(((op (e2) (e0)) = (e1))\/((op (e3) (e0)) = (e1))))) -> (~((op (e1) (e1)) = (e1))) -> (~((op (e1) (e2)) = (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) (e0)) = (e1))) -> (((op (e1) (e0)) = (e1))\/(((op (e1) (e1)) = (e1))\/(((op (e1) (e2)) = (e1))\/((op (e1) (e3)) = (e1))))) -> (~((op (e1) (e0)) = (op (e2) (e0)))) -> (~((op (e2) (e1)) = (e1))) -> (~((op (e2) (e2)) = (e1))) -> (~((op (e2) (e3)) = (e1))) -> (((op (e2) (e0)) = (e1))\/(((op (e2) (e1)) = (e1))\/(((op (e2) (e2)) = (e1))\/((op (e2) (e3)) = (e1))))) -> (~((op (e0) (e0)) = (e1))) -> ((op (e1) (e1)) = (e3)) -> ((op (e2) (e1)) = (e0)) -> ((~((op (e3) (e2)) = (e1)))\/((op (e3) (e1)) = (e2))) -> False). % 18.96/19.09 do 0 intro. intros zenon_H261 zenon_Ha0 zenon_H210 zenon_H235 zenon_H10a zenon_H24d zenon_He8 zenon_Hd5 zenon_Had zenon_H128 zenon_H201 zenon_H24f zenon_H198 zenon_H255 zenon_H106 zenon_H84 zenon_H13f zenon_H36 zenon_H252. % 18.96/19.09 apply (zenon_or_s _ _ zenon_H261); [ zenon_intro zenon_H250 | zenon_intro zenon_Hae ]. % 18.96/19.09 apply (zenon_or_s _ _ zenon_H252); [ zenon_intro zenon_H251 | zenon_intro zenon_H14d ]. % 18.96/19.09 apply (zenon_L993_); trivial. % 18.96/19.09 apply (zenon_L514_); trivial. % 18.96/19.09 apply (zenon_L363_); trivial. % 18.96/19.09 (* end of lemma zenon_L1027_ *) % 18.96/19.09 assert (zenon_L1028_ : ((~((op (e2) (e0)) = (e1)))\/((op (e2) (e1)) = (e0))) -> (~((op (e2) (e1)) = (op (e2) (e3)))) -> (~((op (e3) (e0)) = (op (e3) (e3)))) -> (~((op (e2) (e0)) = (op (e2) (e1)))) -> (~((op (e2) (e1)) = (op (e2) (e2)))) -> (~((op (e3) (e0)) = (op (e3) (e2)))) -> (((op (e0) (e0)) = (e0))\/(((op (e0) (e1)) = (e0))\/(((op (e0) (e2)) = (e0))\/((op (e0) (e3)) = (e0))))) -> ((~((op (e2) (e3)) = (e1)))\/((op (e2) (e1)) = (e3))) -> (~((op (e1) (e1)) = (op (e2) (e1)))) -> ((~((op (e3) (e1)) = (e1)))\/((op (e3) (e1)) = (e1))) -> (~((op (e0) (e1)) = (op (e3) (e1)))) -> (((op (e0) (e0)) = (e1))\/(((op (e1) (e0)) = (e1))\/(((op (e2) (e0)) = (e1))\/((op (e3) (e0)) = (e1))))) -> (((op (e3) (e0)) = (e1))\/(((op (e3) (e1)) = (e1))\/(((op (e3) (e2)) = (e1))\/((op (e3) (e3)) = (e1))))) -> (~((op (e0) (e1)) = (op (e0) (e3)))) -> ((op (e0) (e1)) = (e1)) -> (~((op (e1) (e0)) = (op (e1) (e3)))) -> (~((op (e2) (e2)) = (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) (e0)) = (e1))\/(((op (e2) (e1)) = (e1))\/(((op (e2) (e2)) = (e1))\/((op (e2) (e3)) = (e1))))) -> (~((op (e0) (e0)) = (e1))) -> (~((op (e1) (e1)) = (op (e3) (e1)))) -> ((op (e1) (e1)) = (e3)) -> ((~((op (e3) (e3)) = (e1)))\/((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) (e1)))) -> (~((op (e0) (e2)) = (op (e0) (e3)))) -> (~((op (e1) (e1)) = (op (e1) (e2)))) -> (~((op (e2) (e0)) = (op (e2) (e2)))) -> (~((op (e3) (e1)) = (op (e3) (e2)))) -> (((op (e0) (e2)) = (e0))\/(((op (e1) (e2)) = (e0))\/(((op (e2) (e2)) = (e0))\/((op (e3) (e2)) = (e0))))) -> (~((op (e1) (e1)) = (op (e1) (e3)))) -> (~((op (e2) (e0)) = (op (e2) (e3)))) -> (~((op (e3) (e1)) = (op (e3) (e3)))) -> (((op (e0) (e3)) = (e0))\/(((op (e1) (e3)) = (e0))\/(((op (e2) (e3)) = (e0))\/((op (e3) (e3)) = (e0))))) -> ((op (e1) (e1)) = (e0)) -> (~((op (e1) (e0)) = (op (e1) (e1)))) -> (~((op (e0) (e0)) = (e0))) -> ((~((op (e3) (e0)) = (e1)))\/((op (e3) (e1)) = (e0))) -> (~((op (e0) (e1)) = (op (e2) (e1)))) -> ((~((op (e2) (e1)) = (e1)))\/((op (e2) (e1)) = (e1))) -> False). % 18.96/19.09 do 0 intro. intros zenon_H257 zenon_H1c7 zenon_H71 zenon_H1f0 zenon_H24b zenon_H6f zenon_H74 zenon_H263 zenon_H13e zenon_H261 zenon_H210 zenon_H235 zenon_He8 zenon_H54 zenon_Ha0 zenon_Hd8 zenon_H6d zenon_H62 zenon_H133 zenon_H106 zenon_H84 zenon_H160 zenon_H13f zenon_H264 zenon_H3e zenon_H1cf zenon_H208 zenon_H4f zenon_H52 zenon_H1a4 zenon_H6a zenon_H57 zenon_H5b zenon_H130 zenon_H67 zenon_H29 zenon_H45 zenon_H3f zenon_H254 zenon_H17e zenon_H262. % 18.96/19.09 apply (zenon_or_s _ _ zenon_H257); [ zenon_intro zenon_H1db | zenon_intro zenon_H36 ]. % 18.96/19.09 apply (zenon_or_s _ _ zenon_H262); [ zenon_intro zenon_H24f | zenon_intro zenon_Ha5 ]. % 18.96/19.09 apply (zenon_L1023_); trivial. % 18.96/19.09 apply (zenon_L357_); trivial. % 18.96/19.09 apply (zenon_L965_); trivial. % 18.96/19.09 (* end of lemma zenon_L1028_ *) % 18.96/19.09 assert (zenon_L1029_ : (((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) (e3)))) -> ((op (e3) (e0)) = (e0)) -> (~((op (e2) (e1)) = (op (e2) (e3)))) -> ((op (e1) (e1)) = (e0)) -> (~((op (e1) (e1)) = (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 (e0) (e2)) = (op (e2) (e2)))) -> (((op (e2) (e0)) = (e3))\/(((op (e2) (e1)) = (e3))\/(((op (e2) (e2)) = (e3))\/((op (e2) (e3)) = (e3))))) -> ((op (e3) (e1)) = (e3)) -> (~((op (e3) (e1)) = (op (e3) (e2)))) -> ((op (e1) (e2)) = (e2)) -> ((op (e0) (e2)) = (e0)) -> (~((e0) = (e3))) -> (((op (e0) (e2)) = (e3))\/(((op (e1) (e2)) = (e3))\/(((op (e2) (e2)) = (e3))\/((op (e3) (e2)) = (e3))))) -> (~((e2) = (e3))) -> (~((op (e2) (e0)) = (op (e2) (e2)))) -> (~((op (e2) (e0)) = (op (e2) (e1)))) -> ((op (e2) (e1)) = (e2)) -> (~((op (e2) (e0)) = (e1))) -> (~((op (e2) (e0)) = (op (e2) (e3)))) -> (((op (e2) (e0)) = (e0))\/(((op (e2) (e0)) = (e1))\/(((op (e2) (e0)) = (e2))\/((op (e2) (e0)) = (e3))))) -> (~((op (e1) (e3)) = (op (e2) (e3)))) -> ((op (e1) (e3)) = (e3)) -> False). % 18.96/19.09 do 0 intro. intros zenon_H2f zenon_H17b zenon_H71 zenon_H44 zenon_H1c7 zenon_H29 zenon_H57 zenon_H208 zenon_H67 zenon_Ha8 zenon_He7 zenon_H161 zenon_H1a4 zenon_H113 zenon_H48 zenon_H9a zenon_H1a6 zenon_H12b zenon_H52 zenon_H1f0 zenon_H1ca zenon_H1db zenon_H5b zenon_H259 zenon_Hdb zenon_Hdc. % 18.96/19.09 apply (zenon_or_s _ _ zenon_H2f); [ zenon_intro zenon_H34 | zenon_intro zenon_H33 ]. % 18.96/19.09 apply (zenon_L127_); trivial. % 18.96/19.09 apply (zenon_or_s _ _ zenon_H33); [ zenon_intro zenon_H36 | zenon_intro zenon_H35 ]. % 18.96/19.09 apply (zenon_L961_); trivial. % 18.96/19.09 apply (zenon_or_s _ _ zenon_H35); [ zenon_intro zenon_H2c | zenon_intro zenon_H37 ]. % 18.96/19.09 apply (zenon_L679_); trivial. % 18.96/19.09 apply (zenon_or_s _ _ zenon_He7); [ zenon_intro zenon_H3b | zenon_intro zenon_He9 ]. % 18.96/19.09 apply (zenon_L372_); trivial. % 18.96/19.09 apply (zenon_or_s _ _ zenon_He9); [ zenon_intro zenon_Ha6 | zenon_intro zenon_Hea ]. % 18.96/19.09 apply (zenon_L207_); trivial. % 18.96/19.09 apply (zenon_or_s _ _ zenon_Hea); [ zenon_intro zenon_Haa | zenon_intro zenon_Hdd ]. % 18.96/19.09 apply (zenon_L1015_); trivial. % 18.96/19.09 apply (zenon_L52_); trivial. % 18.96/19.09 (* end of lemma zenon_L1029_ *) % 18.96/19.09 assert (zenon_L1030_ : (((op (e0) (e3)) = (e0))\/(((op (e1) (e3)) = (e0))\/(((op (e2) (e3)) = (e0))\/((op (e3) (e3)) = (e0))))) -> (~((e0) = (e2))) -> ((op (e0) (e3)) = (e2)) -> (~((op (e1) (e1)) = (op (e1) (e3)))) -> ((op (e1) (e1)) = (e0)) -> (~((op (e2) (e0)) = (op (e2) (e3)))) -> ((op (e2) (e0)) = (e0)) -> ((op (e3) (e1)) = (e0)) -> (~((op (e3) (e1)) = (op (e3) (e3)))) -> False). % 18.96/19.09 do 0 intro. intros zenon_H67 zenon_H149 zenon_Hcd zenon_H57 zenon_H29 zenon_H5b zenon_H34 zenon_H1b1 zenon_H130. % 18.96/19.09 apply (zenon_or_s _ _ zenon_H67); [ zenon_intro zenon_H1e | zenon_intro zenon_H68 ]. % 18.96/19.09 apply (zenon_L428_); trivial. % 18.96/19.09 apply (zenon_or_s _ _ zenon_H68); [ zenon_intro zenon_H1f | zenon_intro zenon_H69 ]. % 18.96/19.09 apply (zenon_L13_); trivial. % 18.96/19.09 apply (zenon_or_s _ _ zenon_H69); [ zenon_intro zenon_H37 | zenon_intro zenon_H60 ]. % 18.96/19.09 apply (zenon_L14_); trivial. % 18.96/19.09 apply (zenon_L244_); trivial. % 18.96/19.09 (* end of lemma zenon_L1030_ *) % 18.96/19.09 assert (zenon_L1031_ : (((op (e1) (e0)) = (e3))\/(((op (e1) (e1)) = (e3))\/(((op (e1) (e2)) = (e3))\/((op (e1) (e3)) = (e3))))) -> (~((e1) = (e3))) -> ((op (e1) (e0)) = (e1)) -> ((~((op (e2) (e1)) = (e1)))\/((op (e2) (e1)) = (e1))) -> (~((op (e0) (e1)) = (op (e2) (e1)))) -> ((~((op (e3) (e0)) = (e1)))\/((op (e3) (e1)) = (e0))) -> (~((op (e0) (e0)) = (e0))) -> (~((op (e1) (e0)) = (op (e1) (e1)))) -> (((op (e0) (e2)) = (e0))\/(((op (e1) (e2)) = (e0))\/(((op (e2) (e2)) = (e0))\/((op (e3) (e2)) = (e0))))) -> (~((op (e1) (e1)) = (op (e1) (e2)))) -> (~((op (e3) (e0)) = (op (e3) (e1)))) -> (((op (e0) (e0)) = (e0))\/(((op (e1) (e0)) = (e0))\/(((op (e2) (e0)) = (e0))\/((op (e3) (e0)) = (e0))))) -> ((~((op (e3) (e3)) = (e1)))\/((op (e3) (e1)) = (e3))) -> (~((op (e1) (e1)) = (op (e3) (e1)))) -> (~((op (e0) (e0)) = (e1))) -> (((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))))) -> (~((op (e3) (e2)) = (op (e3) (e3)))) -> (~((op (e2) (e2)) = (op (e2) (e3)))) -> (~((op (e1) (e0)) = (op (e1) (e3)))) -> ((op (e0) (e1)) = (e1)) -> (~((op (e0) (e1)) = (op (e0) (e3)))) -> (((op (e3) (e0)) = (e1))\/(((op (e3) (e1)) = (e1))\/(((op (e3) (e2)) = (e1))\/((op (e3) (e3)) = (e1))))) -> (((op (e0) (e0)) = (e1))\/(((op (e1) (e0)) = (e1))\/(((op (e2) (e0)) = (e1))\/((op (e3) (e0)) = (e1))))) -> (~((op (e0) (e1)) = (op (e3) (e1)))) -> ((~((op (e3) (e1)) = (e1)))\/((op (e3) (e1)) = (e1))) -> (~((op (e1) (e1)) = (op (e2) (e1)))) -> ((~((op (e2) (e3)) = (e1)))\/((op (e2) (e1)) = (e3))) -> (((op (e0) (e0)) = (e0))\/(((op (e0) (e1)) = (e0))\/(((op (e0) (e2)) = (e0))\/((op (e0) (e3)) = (e0))))) -> (~((op (e3) (e0)) = (op (e3) (e2)))) -> (~((op (e2) (e1)) = (op (e2) (e2)))) -> ((~((op (e2) (e0)) = (e1)))\/((op (e2) (e1)) = (e0))) -> (((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) (e0)) = (e1))) -> ((op (e2) (e1)) = (e2)) -> (~((op (e2) (e0)) = (op (e2) (e1)))) -> (~((op (e2) (e0)) = (op (e2) (e2)))) -> (~((e2) = (e3))) -> (((op (e0) (e2)) = (e3))\/(((op (e1) (e2)) = (e3))\/(((op (e2) (e2)) = (e3))\/((op (e3) (e2)) = (e3))))) -> (~((e0) = (e3))) -> ((op (e1) (e2)) = (e2)) -> (~((op (e3) (e1)) = (op (e3) (e2)))) -> ((op (e3) (e1)) = (e3)) -> (((op (e2) (e0)) = (e3))\/(((op (e2) (e1)) = (e3))\/(((op (e2) (e2)) = (e3))\/((op (e2) (e3)) = (e3))))) -> (~((op (e0) (e2)) = (op (e2) (e2)))) -> (~((op (e0) (e2)) = (op (e0) (e3)))) -> (~((op (e2) (e1)) = (op (e2) (e3)))) -> (~((op (e3) (e0)) = (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))))) -> (~((op (e3) (e1)) = (op (e3) (e3)))) -> ((op (e2) (e0)) = (e0)) -> (~((op (e2) (e0)) = (op (e2) (e3)))) -> ((op (e1) (e1)) = (e0)) -> (~((op (e1) (e1)) = (op (e1) (e3)))) -> (~((e0) = (e2))) -> (((op (e0) (e3)) = (e0))\/(((op (e1) (e3)) = (e0))\/(((op (e2) (e3)) = (e0))\/((op (e3) (e3)) = (e0))))) -> ((op (e0) (e2)) = (e0)) -> (~((op (e0) (e2)) = (op (e3) (e2)))) -> (((op (e2) (e3)) = (e0))\/(((op (e2) (e3)) = (e1))\/(((op (e2) (e3)) = (e2))\/((op (e2) (e3)) = (e3))))) -> (~((op (e2) (e3)) = (op (e3) (e3)))) -> (~((op (e2) (e3)) = (e1))) -> ((op (e0) (e3)) = (e2)) -> (~((op (e0) (e3)) = (op (e2) (e3)))) -> (~((op (e1) (e3)) = (op (e2) (e3)))) -> False). % 18.96/19.09 do 0 intro. intros zenon_H16f zenon_H95 zenon_H9d zenon_H262 zenon_H17e zenon_H254 zenon_H3f zenon_H45 zenon_H6a zenon_H4f zenon_H1cf zenon_H3e zenon_H264 zenon_H160 zenon_H84 zenon_H106 zenon_H133 zenon_H62 zenon_H6d zenon_Hd8 zenon_Ha0 zenon_H54 zenon_He8 zenon_H235 zenon_H210 zenon_H261 zenon_H13e zenon_H263 zenon_H74 zenon_H6f zenon_H24b zenon_H257 zenon_H1ac zenon_H259 zenon_H1db zenon_H1ca zenon_H1f0 zenon_H52 zenon_H12b zenon_H1a6 zenon_H9a zenon_H113 zenon_H1a4 zenon_H161 zenon_He7 zenon_Ha8 zenon_H208 zenon_H1c7 zenon_H71 zenon_H17b zenon_H2f zenon_H130 zenon_H34 zenon_H5b zenon_H29 zenon_H57 zenon_H149 zenon_H67 zenon_H48 zenon_H14f zenon_H11f zenon_Hf3 zenon_H255 zenon_Hcd zenon_He2 zenon_Hdb. % 18.96/19.09 apply (zenon_or_s _ _ zenon_H16f); [ zenon_intro zenon_H9e | zenon_intro zenon_H170 ]. % 18.96/19.09 apply (zenon_L37_); trivial. % 18.96/19.09 apply (zenon_or_s _ _ zenon_H170); [ zenon_intro zenon_H13f | zenon_intro zenon_H171 ]. % 18.96/19.09 apply (zenon_L1028_); trivial. % 18.96/19.09 apply (zenon_or_s _ _ zenon_H171); [ zenon_intro zenon_H16c | zenon_intro zenon_Hdc ]. % 18.96/19.09 apply (zenon_L116_); trivial. % 18.96/19.09 apply (zenon_or_s _ _ zenon_H1ac); [ zenon_intro zenon_H44 | zenon_intro zenon_H1af ]. % 18.96/19.09 apply (zenon_L1029_); trivial. % 18.96/19.09 apply (zenon_or_s _ _ zenon_H1af); [ zenon_intro zenon_H1b1 | zenon_intro zenon_H1b0 ]. % 18.96/19.09 apply (zenon_L1030_); trivial. % 18.96/19.09 apply (zenon_or_s _ _ zenon_H1b0); [ zenon_intro zenon_H61 | zenon_intro zenon_H60 ]. % 18.96/19.09 apply (zenon_L342_); trivial. % 18.96/19.09 apply (zenon_L979_); trivial. % 18.96/19.09 (* end of lemma zenon_L1031_ *) % 18.96/19.09 assert (zenon_L1032_ : (((op (e2) (e0)) = (e1))\/(((op (e2) (e1)) = (e1))\/(((op (e2) (e2)) = (e1))\/((op (e2) (e3)) = (e1))))) -> (~((op (e2) (e0)) = (e1))) -> (~((op (e2) (e1)) = (e1))) -> ((op (e1) (e2)) = (e3)) -> ((op (e3) (e2)) = (e0)) -> (~((op (e2) (e3)) = (e1))) -> False). % 18.96/19.09 do 0 intro. intros zenon_H106 zenon_H1db zenon_H24f zenon_H16c zenon_H61 zenon_H255. % 18.96/19.09 apply (zenon_or_s _ _ zenon_H106); [ zenon_intro zenon_Hed | zenon_intro zenon_H107 ]. % 18.96/19.09 exact (zenon_H1db zenon_Hed). % 18.96/19.09 apply (zenon_or_s _ _ zenon_H107); [ zenon_intro zenon_Ha5 | zenon_intro zenon_H108 ]. % 18.96/19.09 exact (zenon_H24f zenon_Ha5). % 18.96/19.09 apply (zenon_or_s _ _ zenon_H108); [ zenon_intro zenon_Hf1 | zenon_intro zenon_Hf4 ]. % 18.96/19.09 apply (zenon_L156_); trivial. % 18.96/19.09 exact (zenon_H255 zenon_Hf4). % 18.96/19.09 (* end of lemma zenon_L1032_ *) % 18.96/19.09 assert (zenon_L1033_ : (((op (e0) (e2)) = (e0))\/(((op (e1) (e2)) = (e0))\/(((op (e2) (e2)) = (e0))\/((op (e3) (e2)) = (e0))))) -> (~((e0) = (e2))) -> ((op (e0) (e2)) = (e2)) -> (~((e0) = (e3))) -> ((op (e2) (e0)) = (e0)) -> (~((op (e2) (e0)) = (op (e2) (e2)))) -> (((op (e2) (e0)) = (e1))\/(((op (e2) (e1)) = (e1))\/(((op (e2) (e2)) = (e1))\/((op (e2) (e3)) = (e1))))) -> (~((op (e2) (e0)) = (e1))) -> (~((op (e2) (e1)) = (e1))) -> ((op (e1) (e2)) = (e3)) -> (~((op (e2) (e3)) = (e1))) -> False). % 18.96/19.09 do 0 intro. intros zenon_H6a zenon_H149 zenon_H150 zenon_H9a zenon_H34 zenon_H52 zenon_H106 zenon_H1db zenon_H24f zenon_H16c zenon_H255. % 18.96/19.09 apply (zenon_or_s _ _ zenon_H6a); [ zenon_intro zenon_H48 | zenon_intro zenon_H6b ]. % 18.96/19.09 apply (zenon_L378_); trivial. % 18.96/19.09 apply (zenon_or_s _ _ zenon_H6b); [ zenon_intro zenon_H2a | zenon_intro zenon_H6c ]. % 18.96/19.09 apply (zenon_L521_); trivial. % 18.96/19.09 apply (zenon_or_s _ _ zenon_H6c); [ zenon_intro zenon_H2c | zenon_intro zenon_H61 ]. % 18.96/19.09 apply (zenon_L11_); trivial. % 18.96/19.09 apply (zenon_L1032_); trivial. % 18.96/19.09 (* end of lemma zenon_L1033_ *) % 18.96/19.09 assert (zenon_L1034_ : (((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) (e1)) = (op (e2) (e2)))) -> ((op (e1) (e1)) = (e0)) -> (~((op (e1) (e1)) = (op (e1) (e2)))) -> (~((op (e0) (e2)) = (op (e0) (e3)))) -> (((op (e0) (e2)) = (e0))\/(((op (e1) (e2)) = (e0))\/(((op (e2) (e2)) = (e0))\/((op (e3) (e2)) = (e0))))) -> (~((op (e2) (e0)) = (op (e2) (e1)))) -> (~((op (e1) (e0)) = (op (e1) (e1)))) -> (~((op (e0) (e0)) = (e0))) -> (((op (e0) (e0)) = (e0))\/(((op (e1) (e0)) = (e0))\/(((op (e2) (e0)) = (e0))\/((op (e3) (e0)) = (e0))))) -> (((op (e0) (e3)) = (e0))\/(((op (e1) (e3)) = (e0))\/(((op (e2) (e3)) = (e0))\/((op (e3) (e3)) = (e0))))) -> (~((op (e1) (e1)) = (op (e1) (e3)))) -> (~((op (e2) (e1)) = (op (e2) (e3)))) -> (~((op (e3) (e0)) = (op (e3) (e3)))) -> (~((op (e0) (e1)) = (op (e2) (e1)))) -> (((op (e0) (e0)) = (e0))\/(((op (e0) (e1)) = (e0))\/(((op (e0) (e2)) = (e0))\/((op (e0) (e3)) = (e0))))) -> ((op (e0) (e2)) = (e0)) -> (~((op (e0) (e2)) = (op (e2) (e2)))) -> (((op (e3) (e0)) = (e1))\/(((op (e3) (e1)) = (e1))\/(((op (e3) (e2)) = (e1))\/((op (e3) (e3)) = (e1))))) -> (~((op (e3) (e0)) = (e1))) -> (~((op (e3) (e1)) = (e1))) -> (~((op (e3) (e2)) = (e1))) -> ((op (e1) (e3)) = (e2)) -> False). % 18.96/19.09 do 0 intro. intros zenon_H2f zenon_H17b zenon_H44 zenon_H6f zenon_H24b zenon_H29 zenon_H4f zenon_H208 zenon_H6a zenon_H1f0 zenon_H45 zenon_H3f zenon_H3e zenon_H67 zenon_H57 zenon_H1c7 zenon_H71 zenon_H17e zenon_H74 zenon_H48 zenon_Ha8 zenon_He8 zenon_Had zenon_H250 zenon_H251 zenon_Hd7. % 18.96/19.09 apply (zenon_or_s _ _ zenon_H2f); [ zenon_intro zenon_H34 | zenon_intro zenon_H33 ]. % 18.96/19.09 apply (zenon_L127_); trivial. % 18.96/19.09 apply (zenon_or_s _ _ zenon_H33); [ zenon_intro zenon_H36 | zenon_intro zenon_H35 ]. % 18.96/19.09 apply (zenon_L965_); trivial. % 18.96/19.09 apply (zenon_or_s _ _ zenon_H35); [ zenon_intro zenon_H2c | zenon_intro zenon_H37 ]. % 18.96/19.09 apply (zenon_L679_); trivial. % 18.96/19.09 apply (zenon_L971_); trivial. % 18.96/19.09 (* end of lemma zenon_L1034_ *) % 18.96/19.09 assert (zenon_L1035_ : (((op (e3) (e0)) = (e0))\/(((op (e3) (e1)) = (e0))\/(((op (e3) (e2)) = (e0))\/((op (e3) (e3)) = (e0))))) -> (~((op (e0) (e2)) = (op (e2) (e2)))) -> ((op (e0) (e2)) = (e0)) -> (((op (e0) (e0)) = (e0))\/(((op (e0) (e1)) = (e0))\/(((op (e0) (e2)) = (e0))\/((op (e0) (e3)) = (e0))))) -> (~((op (e0) (e1)) = (op (e2) (e1)))) -> (~((op (e3) (e0)) = (op (e3) (e3)))) -> (~((op (e2) (e0)) = (op (e2) (e1)))) -> (~((op (e2) (e1)) = (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)) = (op (e3) (e3)))) -> ((op (e2) (e0)) = (e0)) -> (~((op (e2) (e0)) = (op (e2) (e3)))) -> ((op (e1) (e1)) = (e0)) -> (~((op (e1) (e1)) = (op (e1) (e3)))) -> (((op (e0) (e0)) = (e0))\/(((op (e1) (e0)) = (e0))\/(((op (e2) (e0)) = (e0))\/((op (e3) (e0)) = (e0))))) -> (~((op (e0) (e0)) = (e0))) -> (~((op (e1) (e0)) = (op (e1) (e1)))) -> (~((op (e3) (e1)) = (op (e3) (e2)))) -> (~((op (e2) (e0)) = (op (e2) (e2)))) -> (~((op (e1) (e1)) = (op (e1) (e2)))) -> (~((op (e0) (e2)) = (op (e0) (e3)))) -> (((op (e0) (e2)) = (e0))\/(((op (e1) (e2)) = (e0))\/(((op (e2) (e2)) = (e0))\/((op (e3) (e2)) = (e0))))) -> (((op (e0) (e3)) = (e0))\/(((op (e1) (e3)) = (e0))\/(((op (e2) (e3)) = (e0))\/((op (e3) (e3)) = (e0))))) -> (~((op (e3) (e0)) = (op (e3) (e1)))) -> ((op (e3) (e1)) = (e3)) -> (~((op (e3) (e0)) = (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)) = (e1))\/(((op (e3) (e1)) = (e1))\/(((op (e3) (e2)) = (e1))\/((op (e3) (e3)) = (e1))))) -> (~((op (e3) (e0)) = (e1))) -> (~((op (e3) (e1)) = (e1))) -> (~((op (e3) (e2)) = (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)) = (e1))) -> ((op (e1) (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 (e0) (e3)) = (op (e2) (e3)))) -> ((op (e2) (e1)) = (e2)) -> (~((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))))) -> (~((op (e0) (e3)) = (op (e1) (e3)))) -> False). % 18.96/19.09 do 0 intro. intros zenon_H1ac zenon_Ha8 zenon_H48 zenon_H74 zenon_H17e zenon_H71 zenon_H1f0 zenon_H24b zenon_H17b zenon_H2f zenon_H130 zenon_H34 zenon_H5b zenon_H29 zenon_H57 zenon_H3e zenon_H3f zenon_H45 zenon_H1a4 zenon_H52 zenon_H4f zenon_H208 zenon_H6a zenon_H67 zenon_H1cf zenon_H161 zenon_H6f zenon_H151 zenon_H267 zenon_He8 zenon_Had zenon_H250 zenon_H251 zenon_He4 zenon_Hc2 zenon_H231 zenon_Hd7 zenon_Hdf zenon_Hd5 zenon_He2 zenon_H1ca zenon_H1c7 zenon_Hf3 zenon_H11f zenon_H1d. % 18.96/19.09 apply (zenon_or_s _ _ zenon_H1ac); [ zenon_intro zenon_H44 | zenon_intro zenon_H1af ]. % 18.96/19.09 apply (zenon_L1034_); trivial. % 18.96/19.09 apply (zenon_or_s _ _ zenon_H1af); [ zenon_intro zenon_H1b1 | zenon_intro zenon_H1b0 ]. % 18.96/19.09 apply (zenon_L348_); trivial. % 18.96/19.09 apply (zenon_or_s _ _ zenon_H1b0); [ zenon_intro zenon_H61 | zenon_intro zenon_H60 ]. % 18.96/19.09 apply (zenon_L988_); trivial. % 18.96/19.09 apply (zenon_or_s _ _ zenon_He8); [ zenon_intro zenon_Hac | zenon_intro zenon_Heb ]. % 18.96/19.09 exact (zenon_Had zenon_Hac). % 18.96/19.09 apply (zenon_or_s _ _ zenon_Heb); [ zenon_intro zenon_Hae | zenon_intro zenon_Hec ]. % 18.96/19.09 exact (zenon_H250 zenon_Hae). % 18.96/19.09 apply (zenon_or_s _ _ zenon_Hec); [ zenon_intro zenon_Hba | zenon_intro zenon_Hc4 ]. % 18.96/19.09 exact (zenon_H251 zenon_Hba). % 18.96/19.09 apply (zenon_L989_); trivial. % 18.96/19.09 (* end of lemma zenon_L1035_ *) % 18.96/19.09 assert (zenon_L1036_ : (((op (e1) (e0)) = (e3))\/(((op (e1) (e1)) = (e3))\/(((op (e1) (e2)) = (e3))\/((op (e1) (e3)) = (e3))))) -> (~((e1) = (e3))) -> ((op (e1) (e0)) = (e1)) -> ((~((op (e3) (e3)) = (e1)))\/((op (e3) (e1)) = (e3))) -> (~((op (e1) (e1)) = (op (e3) (e1)))) -> (~((op (e0) (e0)) = (e1))) -> (((op (e0) (e3)) = (e1))\/(((op (e1) (e3)) = (e1))\/(((op (e2) (e3)) = (e1))\/((op (e3) (e3)) = (e1))))) -> (~((op (e3) (e2)) = (op (e3) (e3)))) -> (~((op (e2) (e2)) = (op (e2) (e3)))) -> (~((op (e1) (e0)) = (op (e1) (e3)))) -> ((op (e0) (e1)) = (e1)) -> (~((op (e0) (e1)) = (op (e0) (e3)))) -> (((op (e0) (e0)) = (e1))\/(((op (e1) (e0)) = (e1))\/(((op (e2) (e0)) = (e1))\/((op (e3) (e0)) = (e1))))) -> (~((op (e0) (e1)) = (op (e3) (e1)))) -> ((~((op (e3) (e1)) = (e1)))\/((op (e3) (e1)) = (e1))) -> (~((op (e0) (e3)) = (op (e1) (e3)))) -> (((op (e2) (e3)) = (e0))\/(((op (e2) (e3)) = (e1))\/(((op (e2) (e3)) = (e2))\/((op (e2) (e3)) = (e3))))) -> (~((op (e2) (e3)) = (op (e3) (e3)))) -> (~((op (e2) (e1)) = (op (e2) (e3)))) -> ((op (e2) (e1)) = (e2)) -> (~((op (e0) (e3)) = (op (e2) (e3)))) -> (~((op (e1) (e3)) = (op (e3) (e3)))) -> (((op (e1) (e3)) = (e0))\/(((op (e1) (e3)) = (e1))\/(((op (e1) (e3)) = (e2))\/((op (e1) (e3)) = (e3))))) -> (~((op (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 (e3) (e2)) = (e1))) -> (~((op (e3) (e1)) = (e1))) -> (~((op (e3) (e0)) = (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) (e0)) = (op (e3) (e2)))) -> ((op (e3) (e1)) = (e3)) -> (~((op (e3) (e0)) = (op (e3) (e1)))) -> (((op (e0) (e3)) = (e0))\/(((op (e1) (e3)) = (e0))\/(((op (e2) (e3)) = (e0))\/((op (e3) (e3)) = (e0))))) -> (((op (e0) (e2)) = (e0))\/(((op (e1) (e2)) = (e0))\/(((op (e2) (e2)) = (e0))\/((op (e3) (e2)) = (e0))))) -> (~((op (e0) (e2)) = (op (e0) (e3)))) -> (~((op (e1) (e1)) = (op (e1) (e2)))) -> (~((op (e2) (e0)) = (op (e2) (e2)))) -> (~((op (e3) (e1)) = (op (e3) (e2)))) -> (~((op (e1) (e0)) = (op (e1) (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 (e1) (e3)))) -> ((op (e1) (e1)) = (e0)) -> (~((op (e2) (e0)) = (op (e2) (e3)))) -> ((op (e2) (e0)) = (e0)) -> (~((op (e3) (e1)) = (op (e3) (e3)))) -> (((op (e2) (e0)) = (e0))\/(((op (e2) (e1)) = (e0))\/(((op (e2) (e2)) = (e0))\/((op (e2) (e3)) = (e0))))) -> (~((op (e2) (e0)) = (op (e3) (e0)))) -> (~((op (e2) (e1)) = (op (e2) (e2)))) -> (~((op (e2) (e0)) = (op (e2) (e1)))) -> (~((op (e3) (e0)) = (op (e3) (e3)))) -> (~((op (e0) (e1)) = (op (e2) (e1)))) -> (((op (e0) (e0)) = (e0))\/(((op (e0) (e1)) = (e0))\/(((op (e0) (e2)) = (e0))\/((op (e0) (e3)) = (e0))))) -> ((op (e0) (e2)) = (e0)) -> (~((op (e0) (e2)) = (op (e2) (e2)))) -> (((op (e3) (e0)) = (e0))\/(((op (e3) (e1)) = (e0))\/(((op (e3) (e2)) = (e0))\/((op (e3) (e3)) = (e0))))) -> (~((op (e2) (e2)) = (e2))) -> (~((e0) = (e2))) -> (~((e0) = (e3))) -> (((op (e2) (e0)) = (e1))\/(((op (e2) (e1)) = (e1))\/(((op (e2) (e2)) = (e1))\/((op (e2) (e3)) = (e1))))) -> (~((op (e2) (e0)) = (e1))) -> (~((op (e2) (e1)) = (e1))) -> (~((op (e2) (e3)) = (e1))) -> (((op (e0) (e2)) = (e2))\/(((op (e1) (e2)) = (e2))\/(((op (e2) (e2)) = (e2))\/((op (e3) (e2)) = (e2))))) -> ((op (e1) (e3)) = (e2)) -> (~((e2) = (e3))) -> False). % 18.96/19.09 do 0 intro. intros zenon_H16f zenon_H95 zenon_H9d zenon_H264 zenon_H160 zenon_H84 zenon_H133 zenon_H62 zenon_H6d zenon_Hd8 zenon_Ha0 zenon_H54 zenon_H235 zenon_H210 zenon_H261 zenon_H1d zenon_H11f zenon_Hf3 zenon_H1c7 zenon_H1ca zenon_He2 zenon_Hd5 zenon_Hdf zenon_H231 zenon_Hc2 zenon_He4 zenon_H251 zenon_H250 zenon_Had zenon_He8 zenon_H267 zenon_H6f zenon_H161 zenon_H1cf zenon_H67 zenon_H6a zenon_H208 zenon_H4f zenon_H52 zenon_H1a4 zenon_H45 zenon_H3f zenon_H3e zenon_H57 zenon_H29 zenon_H5b zenon_H34 zenon_H130 zenon_H2f zenon_H17b zenon_H24b zenon_H1f0 zenon_H71 zenon_H17e zenon_H74 zenon_H48 zenon_Ha8 zenon_H1ac zenon_H173 zenon_H149 zenon_H9a zenon_H106 zenon_H1db zenon_H24f zenon_H255 zenon_H172 zenon_Hd7 zenon_H12b. % 18.96/19.09 apply (zenon_or_s _ _ zenon_H16f); [ zenon_intro zenon_H9e | zenon_intro zenon_H170 ]. % 18.96/19.09 apply (zenon_L37_); trivial. % 18.96/19.09 apply (zenon_or_s _ _ zenon_H170); [ zenon_intro zenon_H13f | zenon_intro zenon_H171 ]. % 18.96/19.09 apply (zenon_L1022_); trivial. % 18.96/19.09 apply (zenon_or_s _ _ zenon_H171); [ zenon_intro zenon_H16c | zenon_intro zenon_Hdc ]. % 18.96/19.09 apply (zenon_or_s _ _ zenon_H172); [ zenon_intro zenon_H150 | zenon_intro zenon_H174 ]. % 18.96/19.09 apply (zenon_L1033_); trivial. % 18.96/19.09 apply (zenon_or_s _ _ zenon_H174); [ zenon_intro zenon_H113 | zenon_intro zenon_H175 ]. % 18.96/19.09 apply (zenon_L116_); trivial. % 18.96/19.09 apply (zenon_or_s _ _ zenon_H175); [ zenon_intro zenon_H176 | zenon_intro zenon_H151 ]. % 18.96/19.09 exact (zenon_H173 zenon_H176). % 18.96/19.09 apply (zenon_L1035_); trivial. % 18.96/19.09 apply (zenon_L266_); trivial. % 18.96/19.09 (* end of lemma zenon_L1036_ *) % 18.96/19.09 assert (zenon_L1037_ : (((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) = (e3))) -> ((op (e2) (e0)) = (e0)) -> (~((op (e2) (e0)) = (op (e2) (e2)))) -> (((op (e2) (e0)) = (e1))\/(((op (e2) (e1)) = (e1))\/(((op (e2) (e2)) = (e1))\/((op (e2) (e3)) = (e1))))) -> (~((op (e2) (e0)) = (e1))) -> (~((op (e2) (e1)) = (e1))) -> ((op (e1) (e2)) = (e3)) -> (~((op (e2) (e3)) = (e1))) -> False). % 18.96/19.09 do 0 intro. intros zenon_H6a zenon_H208 zenon_H1e zenon_H9a zenon_H34 zenon_H52 zenon_H106 zenon_H1db zenon_H24f zenon_H16c zenon_H255. % 18.96/19.09 apply (zenon_or_s _ _ zenon_H6a); [ zenon_intro zenon_H48 | zenon_intro zenon_H6b ]. % 18.96/19.09 apply (zenon_L336_); trivial. % 18.96/19.09 apply (zenon_or_s _ _ zenon_H6b); [ zenon_intro zenon_H2a | zenon_intro zenon_H6c ]. % 18.96/19.09 apply (zenon_L521_); trivial. % 18.96/19.09 apply (zenon_or_s _ _ zenon_H6c); [ zenon_intro zenon_H2c | zenon_intro zenon_H61 ]. % 18.96/19.09 apply (zenon_L11_); trivial. % 18.96/19.09 apply (zenon_L1032_); trivial. % 18.96/19.09 (* end of lemma zenon_L1037_ *) % 18.96/19.09 assert (zenon_L1038_ : (((op (e3) (e0)) = (e1))\/(((op (e3) (e1)) = (e1))\/(((op (e3) (e2)) = (e1))\/((op (e3) (e3)) = (e1))))) -> (~((op (e3) (e0)) = (e1))) -> (~((op (e3) (e1)) = (e1))) -> (~((op (e3) (e2)) = (op (e3) (e3)))) -> ((op (e2) (e2)) = (e1)) -> (~((op (e2) (e2)) = (op (e2) (e3)))) -> ((op (e1) (e0)) = (e1)) -> (~((op (e1) (e0)) = (op (e1) (e3)))) -> ((op (e0) (e1)) = (e1)) -> (~((op (e0) (e1)) = (op (e0) (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))))) -> (~((e0) = (e2))) -> (~((e2) = (e3))) -> (~((op (e2) (e1)) = (op (e2) (e3)))) -> ((op (e2) (e1)) = (e2)) -> (((op (e2) (e3)) = (e0))\/(((op (e2) (e3)) = (e1))\/(((op (e2) (e3)) = (e2))\/((op (e2) (e3)) = (e3))))) -> ((op (e0) (e3)) = (e0)) -> (~((op (e0) (e3)) = (op (e2) (e3)))) -> (~((op (e2) (e3)) = (op (e3) (e3)))) -> (~((op (e1) (e3)) = (op (e2) (e3)))) -> ((op (e1) (e3)) = (e3)) -> False). % 18.96/19.09 do 0 intro. intros zenon_He8 zenon_Had zenon_H250 zenon_H62 zenon_Hf1 zenon_H6d zenon_H9d zenon_Hd8 zenon_Ha0 zenon_H54 zenon_H133 zenon_H145 zenon_H149 zenon_H12b zenon_H1c7 zenon_H1ca zenon_H11f zenon_H1e zenon_He2 zenon_Hf3 zenon_Hdb zenon_Hdc. % 18.96/19.09 apply (zenon_or_s _ _ zenon_He8); [ zenon_intro zenon_Hac | zenon_intro zenon_Heb ]. % 18.96/19.09 exact (zenon_Had zenon_Hac). % 18.96/19.09 apply (zenon_or_s _ _ zenon_Heb); [ zenon_intro zenon_Hae | zenon_intro zenon_Hec ]. % 18.96/19.09 exact (zenon_H250 zenon_Hae). % 18.96/19.09 apply (zenon_or_s _ _ zenon_Hec); [ zenon_intro zenon_Hba | zenon_intro zenon_Hc4 ]. % 18.96/19.09 apply (zenon_L419_); trivial. % 18.96/19.09 apply (zenon_L429_); trivial. % 18.96/19.09 (* end of lemma zenon_L1038_ *) % 18.96/19.09 assert (zenon_L1039_ : (((op (e0) (e2)) = (e1))\/(((op (e1) (e2)) = (e1))\/(((op (e2) (e2)) = (e1))\/((op (e3) (e2)) = (e1))))) -> (~((op (e0) (e2)) = (e1))) -> (~((op (e1) (e2)) = (e1))) -> (~((op (e2) (e2)) = (op (e2) (e3)))) -> ((op (e2) (e3)) = (e1)) -> (~((op (e3) (e2)) = (e1))) -> False). % 18.96/19.09 do 0 intro. intros zenon_H139 zenon_H20d zenon_H24d zenon_H6d zenon_Hf4 zenon_H251. % 18.96/19.09 apply (zenon_or_s _ _ zenon_H139); [ zenon_intro zenon_H122 | zenon_intro zenon_H13a ]. % 18.96/19.09 exact (zenon_H20d zenon_H122). % 18.96/19.09 apply (zenon_or_s _ _ zenon_H13a); [ zenon_intro zenon_Hf0 | zenon_intro zenon_H13b ]. % 18.96/19.10 exact (zenon_H24d zenon_Hf0). % 18.96/19.10 apply (zenon_or_s _ _ zenon_H13b); [ zenon_intro zenon_Hf1 | zenon_intro zenon_Hba ]. % 18.96/19.10 apply (zenon_L84_); trivial. % 18.96/19.10 exact (zenon_H251 zenon_Hba). % 18.96/19.10 (* end of lemma zenon_L1039_ *) % 18.96/19.10 assert (zenon_L1040_ : (((op (e2) (e0)) = (e1))\/(((op (e2) (e1)) = (e1))\/(((op (e2) (e2)) = (e1))\/((op (e2) (e3)) = (e1))))) -> (~((op (e2) (e0)) = (e1))) -> (~((op (e2) (e1)) = (e1))) -> ((op (e1) (e3)) = (e3)) -> (~((op (e1) (e3)) = (op (e2) (e3)))) -> (~((op (e2) (e3)) = (op (e3) (e3)))) -> (~((op (e0) (e3)) = (op (e2) (e3)))) -> ((op (e0) (e3)) = (e0)) -> (((op (e2) (e3)) = (e0))\/(((op (e2) (e3)) = (e1))\/(((op (e2) (e3)) = (e2))\/((op (e2) (e3)) = (e3))))) -> ((op (e2) (e1)) = (e2)) -> (~((op (e2) (e1)) = (op (e2) (e3)))) -> (~((e2) = (e3))) -> (~((e0) = (e2))) -> (((op (e0) (e3)) = (e2))\/(((op (e1) (e3)) = (e2))\/(((op (e2) (e3)) = (e2))\/((op (e3) (e3)) = (e2))))) -> (((op (e0) (e3)) = (e1))\/(((op (e1) (e3)) = (e1))\/(((op (e2) (e3)) = (e1))\/((op (e3) (e3)) = (e1))))) -> (~((op (e0) (e1)) = (op (e0) (e3)))) -> ((op (e0) (e1)) = (e1)) -> (~((op (e1) (e0)) = (op (e1) (e3)))) -> ((op (e1) (e0)) = (e1)) -> (~((op (e3) (e2)) = (op (e3) (e3)))) -> (~((op (e3) (e1)) = (e1))) -> (~((op (e3) (e0)) = (e1))) -> (((op (e3) (e0)) = (e1))\/(((op (e3) (e1)) = (e1))\/(((op (e3) (e2)) = (e1))\/((op (e3) (e3)) = (e1))))) -> (((op (e0) (e2)) = (e1))\/(((op (e1) (e2)) = (e1))\/(((op (e2) (e2)) = (e1))\/((op (e3) (e2)) = (e1))))) -> (~((op (e0) (e2)) = (e1))) -> (~((op (e1) (e2)) = (e1))) -> (~((op (e2) (e2)) = (op (e2) (e3)))) -> (~((op (e3) (e2)) = (e1))) -> False). % 18.96/19.10 do 0 intro. intros zenon_H106 zenon_H1db zenon_H24f zenon_Hdc zenon_Hdb zenon_Hf3 zenon_He2 zenon_H1e zenon_H11f zenon_H1ca zenon_H1c7 zenon_H12b zenon_H149 zenon_H145 zenon_H133 zenon_H54 zenon_Ha0 zenon_Hd8 zenon_H9d zenon_H62 zenon_H250 zenon_Had zenon_He8 zenon_H139 zenon_H20d zenon_H24d zenon_H6d zenon_H251. % 18.96/19.10 apply (zenon_or_s _ _ zenon_H106); [ zenon_intro zenon_Hed | zenon_intro zenon_H107 ]. % 18.96/19.10 exact (zenon_H1db zenon_Hed). % 18.96/19.10 apply (zenon_or_s _ _ zenon_H107); [ zenon_intro zenon_Ha5 | zenon_intro zenon_H108 ]. % 18.96/19.10 exact (zenon_H24f zenon_Ha5). % 18.96/19.10 apply (zenon_or_s _ _ zenon_H108); [ zenon_intro zenon_Hf1 | zenon_intro zenon_Hf4 ]. % 18.96/19.10 apply (zenon_L1038_); trivial. % 18.96/19.10 apply (zenon_L1039_); trivial. % 18.96/19.10 (* end of lemma zenon_L1040_ *) % 18.96/19.10 assert (zenon_L1041_ : (((op (e3) (e0)) = (e2))\/(((op (e3) (e1)) = (e2))\/(((op (e3) (e2)) = (e2))\/((op (e3) (e3)) = (e2))))) -> (~((e0) = (e2))) -> ((op (e2) (e1)) = (e2)) -> (~((op (e2) (e1)) = (op (e3) (e1)))) -> ((op (e0) (e2)) = (e2)) -> (~((op (e0) (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) (e3)))) -> ((op (e3) (e0)) = (e0)) -> ((op (e2) (e2)) = (e0)) -> (~((op (e2) (e2)) = (op (e2) (e3)))) -> ((op (e1) (e1)) = (e0)) -> (~((op (e1) (e1)) = (op (e1) (e3)))) -> (~((e0) = (e3))) -> (((op (e0) (e3)) = (e0))\/(((op (e1) (e3)) = (e0))\/(((op (e2) (e3)) = (e0))\/((op (e3) (e3)) = (e0))))) -> (~((op (e2) (e3)) = (op (e3) (e3)))) -> ((op (e3) (e3)) = (e1)) -> ((op (e0) (e3)) = (e0)) -> (((op (e2) (e3)) = (e0))\/(((op (e2) (e3)) = (e1))\/(((op (e2) (e3)) = (e2))\/((op (e2) (e3)) = (e3))))) -> (~((op (e1) (e3)) = (op (e2) (e3)))) -> (~((op (e1) (e3)) = (op (e3) (e3)))) -> (~((op (e1) (e3)) = (e1))) -> (((op (e0) (e3)) = (e0))\/(((op (e0) (e3)) = (e1))\/(((op (e0) (e3)) = (e2))\/((op (e0) (e3)) = (e3))))) -> (~((op (e0) (e3)) = (op (e1) (e3)))) -> (~((op (e0) (e3)) = (e1))) -> (~((op (e0) (e3)) = (op (e3) (e3)))) -> (~((op (e0) (e3)) = (op (e2) (e3)))) -> (((op (e1) (e3)) = (e0))\/(((op (e1) (e3)) = (e1))\/(((op (e1) (e3)) = (e2))\/((op (e1) (e3)) = (e3))))) -> (~((op (e3) (e3)) = (e3))) -> False). % 18.96/19.10 do 0 intro. intros zenon_H153 zenon_H149 zenon_H1ca zenon_Haf zenon_H150 zenon_H14f zenon_H136 zenon_H71 zenon_H44 zenon_H2c zenon_H6d zenon_H29 zenon_H57 zenon_H9a zenon_H67 zenon_Hf3 zenon_Hc4 zenon_H1e zenon_H11f zenon_Hdb zenon_Hd5 zenon_H24e zenon_He4 zenon_H1d zenon_H231 zenon_Hc2 zenon_He2 zenon_Hdf zenon_H102. % 18.96/19.10 apply (zenon_or_s _ _ zenon_H153); [ zenon_intro zenon_H148 | zenon_intro zenon_H154 ]. % 18.96/19.10 apply (zenon_L100_); trivial. % 18.96/19.10 apply (zenon_or_s _ _ zenon_H154); [ zenon_intro zenon_H14d | zenon_intro zenon_H155 ]. % 18.96/19.10 apply (zenon_L364_); trivial. % 18.96/19.10 apply (zenon_or_s _ _ zenon_H155); [ zenon_intro zenon_H151 | zenon_intro zenon_Hf6 ]. % 18.96/19.10 apply (zenon_L104_); trivial. % 18.96/19.10 apply (zenon_L968_); trivial. % 18.96/19.10 (* end of lemma zenon_L1041_ *) % 18.96/19.10 assert (zenon_L1042_ : (((op (e1) (e0)) = (e3))\/(((op (e1) (e1)) = (e3))\/(((op (e1) (e2)) = (e3))\/((op (e1) (e3)) = (e3))))) -> (~((e1) = (e3))) -> ((op (e1) (e0)) = (e1)) -> ((~((op (e3) (e3)) = (e1)))\/((op (e3) (e1)) = (e3))) -> (~((op (e1) (e1)) = (op (e3) (e1)))) -> (~((op (e0) (e0)) = (e1))) -> (((op (e2) (e0)) = (e1))\/(((op (e2) (e1)) = (e1))\/(((op (e2) (e2)) = (e1))\/((op (e2) (e3)) = (e1))))) -> (~((op (e2) (e3)) = (e1))) -> (~((op (e3) (e0)) = (e1))) -> (((op (e0) (e3)) = (e1))\/(((op (e1) (e3)) = (e1))\/(((op (e2) (e3)) = (e1))\/((op (e3) (e3)) = (e1))))) -> (~((op (e3) (e2)) = (op (e3) (e3)))) -> (~((op (e2) (e2)) = (op (e2) (e3)))) -> (~((op (e1) (e0)) = (op (e1) (e3)))) -> ((op (e0) (e1)) = (e1)) -> (~((op (e0) (e1)) = (op (e0) (e3)))) -> (((op (e3) (e0)) = (e1))\/(((op (e3) (e1)) = (e1))\/(((op (e3) (e2)) = (e1))\/((op (e3) (e3)) = (e1))))) -> (~((op (e2) (e1)) = (e1))) -> (~((op (e2) (e0)) = (e1))) -> (((op (e0) (e0)) = (e1))\/(((op (e1) (e0)) = (e1))\/(((op (e2) (e0)) = (e1))\/((op (e3) (e0)) = (e1))))) -> (~((op (e0) (e1)) = (op (e3) (e1)))) -> ((~((op (e3) (e1)) = (e1)))\/((op (e3) (e1)) = (e1))) -> ((op (e0) (e2)) = (e3)) -> (~((op (e0) (e2)) = (op (e1) (e2)))) -> ((op (e1) (e3)) = (e2)) -> (~((e2) = (e3))) -> False). % 18.96/19.10 do 0 intro. intros zenon_H16f zenon_H95 zenon_H9d zenon_H264 zenon_H160 zenon_H84 zenon_H106 zenon_H255 zenon_Had zenon_H133 zenon_H62 zenon_H6d zenon_Hd8 zenon_Ha0 zenon_H54 zenon_He8 zenon_H24f zenon_H1db zenon_H235 zenon_H210 zenon_H261 zenon_Ha9 zenon_H195 zenon_Hd7 zenon_H12b. % 18.96/19.10 apply (zenon_or_s _ _ zenon_H16f); [ zenon_intro zenon_H9e | zenon_intro zenon_H170 ]. % 18.96/19.10 apply (zenon_L37_); trivial. % 18.96/19.10 apply (zenon_or_s _ _ zenon_H170); [ zenon_intro zenon_H13f | zenon_intro zenon_H171 ]. % 18.96/19.10 apply (zenon_L1022_); trivial. % 18.96/19.10 apply (zenon_or_s _ _ zenon_H171); [ zenon_intro zenon_H16c | zenon_intro zenon_Hdc ]. % 18.96/19.10 apply (zenon_L162_); trivial. % 18.96/19.10 apply (zenon_L266_); trivial. % 18.96/19.10 (* end of lemma zenon_L1042_ *) % 18.96/19.10 assert (zenon_L1043_ : (((op (e0) (e2)) = (e0))\/(((op (e0) (e2)) = (e1))\/(((op (e0) (e2)) = (e2))\/((op (e0) (e2)) = (e3))))) -> (~((op (e0) (e2)) = (op (e2) (e2)))) -> (~((op (e0) (e2)) = (e1))) -> (~((op (e3) (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 (e0) (e3)) = (op (e3) (e3)))) -> (~((op (e0) (e3)) = (e1))) -> (~((op (e0) (e3)) = (op (e1) (e3)))) -> (((op (e0) (e3)) = (e0))\/(((op (e0) (e3)) = (e1))\/(((op (e0) (e3)) = (e2))\/((op (e0) (e3)) = (e3))))) -> (~((op (e1) (e3)) = (e1))) -> (~((op (e1) (e3)) = (op (e3) (e3)))) -> (~((op (e1) (e3)) = (op (e2) (e3)))) -> (((op (e2) (e3)) = (e0))\/(((op (e2) (e3)) = (e1))\/(((op (e2) (e3)) = (e2))\/((op (e2) (e3)) = (e3))))) -> ((op (e0) (e3)) = (e0)) -> ((op (e3) (e3)) = (e1)) -> (~((op (e2) (e3)) = (op (e3) (e3)))) -> (((op (e0) (e3)) = (e0))\/(((op (e1) (e3)) = (e0))\/(((op (e2) (e3)) = (e0))\/((op (e3) (e3)) = (e0))))) -> (~((e0) = (e3))) -> (~((op (e1) (e1)) = (op (e1) (e3)))) -> ((op (e1) (e1)) = (e0)) -> ((op (e2) (e2)) = (e0)) -> ((op (e3) (e0)) = (e0)) -> (~((op (e3) (e0)) = (op (e3) (e3)))) -> (((op (e0) (e3)) = (e3))\/(((op (e1) (e3)) = (e3))\/(((op (e2) (e3)) = (e3))\/((op (e3) (e3)) = (e3))))) -> (~((op (e0) (e2)) = (op (e3) (e2)))) -> (~((op (e2) (e1)) = (op (e3) (e1)))) -> ((op (e2) (e1)) = (e2)) -> (~((e0) = (e2))) -> (((op (e3) (e0)) = (e2))\/(((op (e3) (e1)) = (e2))\/(((op (e3) (e2)) = (e2))\/((op (e3) (e3)) = (e2))))) -> (((op (e1) (e0)) = (e3))\/(((op (e1) (e1)) = (e3))\/(((op (e1) (e2)) = (e3))\/((op (e1) (e3)) = (e3))))) -> (~((e1) = (e3))) -> ((op (e1) (e0)) = (e1)) -> ((~((op (e3) (e3)) = (e1)))\/((op (e3) (e1)) = (e3))) -> (~((op (e1) (e1)) = (op (e3) (e1)))) -> (~((op (e0) (e0)) = (e1))) -> (((op (e2) (e0)) = (e1))\/(((op (e2) (e1)) = (e1))\/(((op (e2) (e2)) = (e1))\/((op (e2) (e3)) = (e1))))) -> (~((op (e2) (e3)) = (e1))) -> (~((op (e3) (e0)) = (e1))) -> (((op (e0) (e3)) = (e1))\/(((op (e1) (e3)) = (e1))\/(((op (e2) (e3)) = (e1))\/((op (e3) (e3)) = (e1))))) -> (~((op (e3) (e2)) = (op (e3) (e3)))) -> (~((op (e2) (e2)) = (op (e2) (e3)))) -> (~((op (e1) (e0)) = (op (e1) (e3)))) -> ((op (e0) (e1)) = (e1)) -> (~((op (e0) (e1)) = (op (e0) (e3)))) -> (((op (e3) (e0)) = (e1))\/(((op (e3) (e1)) = (e1))\/(((op (e3) (e2)) = (e1))\/((op (e3) (e3)) = (e1))))) -> (~((op (e2) (e1)) = (e1))) -> (~((op (e2) (e0)) = (e1))) -> (((op (e0) (e0)) = (e1))\/(((op (e1) (e0)) = (e1))\/(((op (e2) (e0)) = (e1))\/((op (e3) (e0)) = (e1))))) -> (~((op (e0) (e1)) = (op (e3) (e1)))) -> ((~((op (e3) (e1)) = (e1)))\/((op (e3) (e1)) = (e1))) -> (~((op (e0) (e2)) = (op (e1) (e2)))) -> ((op (e1) (e3)) = (e2)) -> (~((e2) = (e3))) -> False). % 18.96/19.10 do 0 intro. intros zenon_H1ba zenon_Ha8 zenon_H20d zenon_H102 zenon_Hdf zenon_He2 zenon_Hc2 zenon_H231 zenon_H1d zenon_He4 zenon_H24e zenon_Hd5 zenon_Hdb zenon_H11f zenon_H1e zenon_Hc4 zenon_Hf3 zenon_H67 zenon_H9a zenon_H57 zenon_H29 zenon_H2c zenon_H44 zenon_H71 zenon_H136 zenon_H14f zenon_Haf zenon_H1ca zenon_H149 zenon_H153 zenon_H16f zenon_H95 zenon_H9d zenon_H264 zenon_H160 zenon_H84 zenon_H106 zenon_H255 zenon_Had zenon_H133 zenon_H62 zenon_H6d zenon_Hd8 zenon_Ha0 zenon_H54 zenon_He8 zenon_H24f zenon_H1db zenon_H235 zenon_H210 zenon_H261 zenon_H195 zenon_Hd7 zenon_H12b. % 18.96/19.10 apply (zenon_or_s _ _ zenon_H1ba); [ zenon_intro zenon_H48 | zenon_intro zenon_H1bb ]. % 18.96/19.10 apply (zenon_L679_); trivial. % 18.96/19.10 apply (zenon_or_s _ _ zenon_H1bb); [ zenon_intro zenon_H122 | zenon_intro zenon_H1bc ]. % 18.96/19.10 exact (zenon_H20d zenon_H122). % 18.96/19.10 apply (zenon_or_s _ _ zenon_H1bc); [ zenon_intro zenon_H150 | zenon_intro zenon_Ha9 ]. % 18.96/19.10 apply (zenon_L1041_); trivial. % 18.96/19.10 apply (zenon_L1042_); trivial. % 18.96/19.10 (* end of lemma zenon_L1043_ *) % 18.96/19.10 assert (zenon_L1044_ : (((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) (e1)) = (op (e2) (e2)))) -> (~((op (e1) (e1)) = (op (e1) (e2)))) -> (~((op (e0) (e2)) = (op (e0) (e3)))) -> (((op (e0) (e2)) = (e0))\/(((op (e1) (e2)) = (e0))\/(((op (e2) (e2)) = (e0))\/((op (e3) (e2)) = (e0))))) -> (~((op (e2) (e0)) = (op (e2) (e1)))) -> (~((op (e1) (e0)) = (op (e1) (e1)))) -> (~((op (e0) (e0)) = (e0))) -> (((op (e0) (e0)) = (e0))\/(((op (e1) (e0)) = (e0))\/(((op (e2) (e0)) = (e0))\/((op (e3) (e0)) = (e0))))) -> (~((op (e2) (e1)) = (op (e2) (e3)))) -> (~((op (e0) (e1)) = (op (e2) (e1)))) -> (((op (e0) (e0)) = (e0))\/(((op (e0) (e1)) = (e0))\/(((op (e0) (e2)) = (e0))\/((op (e0) (e3)) = (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 (e3) (e3)))) -> (~((op (e0) (e3)) = (e1))) -> (~((op (e0) (e3)) = (op (e1) (e3)))) -> (((op (e0) (e3)) = (e0))\/(((op (e0) (e3)) = (e1))\/(((op (e0) (e3)) = (e2))\/((op (e0) (e3)) = (e3))))) -> (~((op (e1) (e3)) = (e1))) -> (~((op (e1) (e3)) = (op (e3) (e3)))) -> (~((op (e1) (e3)) = (op (e2) (e3)))) -> (((op (e2) (e3)) = (e0))\/(((op (e2) (e3)) = (e1))\/(((op (e2) (e3)) = (e2))\/((op (e2) (e3)) = (e3))))) -> (~((op (e2) (e3)) = (op (e3) (e3)))) -> (((op (e0) (e3)) = (e0))\/(((op (e1) (e3)) = (e0))\/(((op (e2) (e3)) = (e0))\/((op (e3) (e3)) = (e0))))) -> (~((e0) = (e3))) -> (~((op (e1) (e1)) = (op (e1) (e3)))) -> ((op (e1) (e1)) = (e0)) -> (~((op (e2) (e2)) = (op (e2) (e3)))) -> ((op (e3) (e0)) = (e0)) -> (~((op (e3) (e0)) = (op (e3) (e3)))) -> (((op (e0) (e3)) = (e3))\/(((op (e1) (e3)) = (e3))\/(((op (e2) (e3)) = (e3))\/((op (e3) (e3)) = (e3))))) -> (~((op (e0) (e2)) = (op (e3) (e2)))) -> ((op (e0) (e2)) = (e2)) -> (~((op (e2) (e1)) = (op (e3) (e1)))) -> ((op (e2) (e1)) = (e2)) -> (~((e0) = (e2))) -> (((op (e3) (e0)) = (e2))\/(((op (e3) (e1)) = (e2))\/(((op (e3) (e2)) = (e2))\/((op (e3) (e3)) = (e2))))) -> (~((op (e3) (e2)) = (e1))) -> (~((op (e3) (e1)) = (e1))) -> (~((op (e3) (e0)) = (e1))) -> (((op (e3) (e0)) = (e1))\/(((op (e3) (e1)) = (e1))\/(((op (e3) (e2)) = (e1))\/((op (e3) (e3)) = (e1))))) -> (~((op (e0) (e3)) = (op (e2) (e3)))) -> ((op (e0) (e3)) = (e0)) -> False). % 18.96/19.10 do 0 intro. intros zenon_H2f zenon_H17b zenon_H6f zenon_H24b zenon_H4f zenon_H208 zenon_H6a zenon_H1f0 zenon_H45 zenon_H3f zenon_H3e zenon_H1c7 zenon_H17e zenon_H74 zenon_H102 zenon_Hdf zenon_Hc2 zenon_H231 zenon_H1d zenon_He4 zenon_H24e zenon_Hd5 zenon_Hdb zenon_H11f zenon_Hf3 zenon_H67 zenon_H9a zenon_H57 zenon_H29 zenon_H6d zenon_H44 zenon_H71 zenon_H136 zenon_H14f zenon_H150 zenon_Haf zenon_H1ca zenon_H149 zenon_H153 zenon_H251 zenon_H250 zenon_Had zenon_He8 zenon_He2 zenon_H1e. % 18.96/19.10 apply (zenon_or_s _ _ zenon_H2f); [ zenon_intro zenon_H34 | zenon_intro zenon_H33 ]. % 18.96/19.10 apply (zenon_L127_); trivial. % 18.96/19.10 apply (zenon_or_s _ _ zenon_H33); [ zenon_intro zenon_H36 | zenon_intro zenon_H35 ]. % 18.96/19.10 apply (zenon_L965_); trivial. % 18.96/19.10 apply (zenon_or_s _ _ zenon_H35); [ zenon_intro zenon_H2c | zenon_intro zenon_H37 ]. % 18.96/19.10 apply (zenon_or_s _ _ zenon_He8); [ zenon_intro zenon_Hac | zenon_intro zenon_Heb ]. % 18.96/19.10 exact (zenon_Had zenon_Hac). % 18.96/19.10 apply (zenon_or_s _ _ zenon_Heb); [ zenon_intro zenon_Hae | zenon_intro zenon_Hec ]. % 18.96/19.10 exact (zenon_H250 zenon_Hae). % 18.96/19.10 apply (zenon_or_s _ _ zenon_Hec); [ zenon_intro zenon_Hba | zenon_intro zenon_Hc4 ]. % 18.96/19.10 exact (zenon_H251 zenon_Hba). % 18.96/19.10 apply (zenon_L1041_); trivial. % 18.96/19.10 apply (zenon_L367_); trivial. % 18.96/19.10 (* end of lemma zenon_L1044_ *) % 18.96/19.10 assert (zenon_L1045_ : (~((op (e0) (e0)) = (e0))) -> (((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)) = (op (e3) (e3)))) -> (~((op (e0) (e1)) = (op (e0) (e2)))) -> (~((op (e1) (e1)) = (op (e1) (e2)))) -> (~((op (e2) (e0)) = (op (e2) (e2)))) -> (((op (e0) (e3)) = (e0))\/(((op (e1) (e3)) = (e0))\/(((op (e2) (e3)) = (e0))\/((op (e3) (e3)) = (e0))))) -> (~((op (e2) (e0)) = (op (e2) (e3)))) -> (~((op (e1) (e1)) = (op (e1) (e3)))) -> (((op (e0) (e2)) = (e0))\/(((op (e1) (e2)) = (e0))\/(((op (e2) (e2)) = (e0))\/((op (e3) (e2)) = (e0))))) -> ((op (e1) (e1)) = (e0)) -> (~((op (e1) (e0)) = (op (e1) (e1)))) -> (((op (e1) (e0)) = (e2))\/(((op (e1) (e1)) = (e2))\/(((op (e1) (e2)) = (e2))\/((op (e1) (e3)) = (e2))))) -> (((op (e1) (e0)) = (e1))\/(((op (e1) (e1)) = (e1))\/(((op (e1) (e2)) = (e1))\/((op (e1) (e3)) = (e1))))) -> (~((op (e1) (e3)) = (e1))) -> (~((op (e1) (e2)) = (e1))) -> (~((op (e1) (e1)) = (e1))) -> (~((e1) = (e3))) -> ((~((op (e2) (e0)) = (e1)))\/((op (e2) (e1)) = (e0))) -> (~((op (e2) (e1)) = (op (e2) (e3)))) -> (~((op (e2) (e0)) = (op (e2) (e1)))) -> (~((op (e2) (e1)) = (op (e2) (e2)))) -> (((op (e0) (e0)) = (e0))\/(((op (e0) (e1)) = (e0))\/(((op (e0) (e2)) = (e0))\/((op (e0) (e3)) = (e0))))) -> ((~((op (e2) (e3)) = (e1)))\/((op (e2) (e1)) = (e3))) -> (~((op (e1) (e1)) = (op (e2) (e1)))) -> ((~((op (e3) (e1)) = (e1)))\/((op (e3) (e1)) = (e1))) -> (~((op (e0) (e1)) = (op (e3) (e1)))) -> (~((op (e1) (e1)) = (op (e3) (e1)))) -> ((~((op (e3) (e3)) = (e1)))\/((op (e3) (e1)) = (e3))) -> (~((op (e3) (e0)) = (op (e3) (e1)))) -> (~((op (e0) (e2)) = (op (e0) (e3)))) -> (~((op (e3) (e1)) = (op (e3) (e2)))) -> (~((op (e3) (e1)) = (op (e3) (e3)))) -> ((~((op (e3) (e0)) = (e1)))\/((op (e3) (e1)) = (e0))) -> (~((op (e0) (e1)) = (op (e2) (e1)))) -> ((~((op (e2) (e1)) = (e1)))\/((op (e2) (e1)) = (e1))) -> (~((e2) = (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 (e3) (e0)) = (e0))\/(((op (e3) (e0)) = (e1))\/(((op (e3) (e0)) = (e2))\/((op (e3) (e0)) = (e3))))) -> (~((op (e0) (e3)) = (op (e3) (e3)))) -> (~((op (e0) (e3)) = (e1))) -> (~((op (e0) (e3)) = (op (e1) (e3)))) -> (((op (e1) (e3)) = (e0))\/(((op (e1) (e3)) = (e1))\/(((op (e1) (e3)) = (e2))\/((op (e1) (e3)) = (e3))))) -> (~((op (e1) (e3)) = (op (e3) (e3)))) -> (((op (e0) (e3)) = (e0))\/(((op (e0) (e3)) = (e1))\/(((op (e0) (e3)) = (e2))\/((op (e0) (e3)) = (e3))))) -> (~((op (e2) (e2)) = (e2))) -> (((op (e3) (e0)) = (e0))\/(((op (e3) (e1)) = (e0))\/(((op (e3) (e2)) = (e0))\/((op (e3) (e3)) = (e0))))) -> (~((op (e2) (e3)) = (op (e3) (e3)))) -> (~((op (e0) (e3)) = (op (e2) (e3)))) -> (((op (e2) (e3)) = (e0))\/(((op (e2) (e3)) = (e1))\/(((op (e2) (e3)) = (e2))\/((op (e2) (e3)) = (e3))))) -> (((op (e1) (e0)) = (e3))\/(((op (e1) (e1)) = (e3))\/(((op (e1) (e2)) = (e3))\/((op (e1) (e3)) = (e3))))) -> (~((op (e0) (e2)) = (op (e3) (e2)))) -> (~((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 (e1) (e3)) = (op (e2) (e3)))) -> (((op (e2) (e0)) = (e0))\/(((op (e2) (e0)) = (e1))\/(((op (e2) (e0)) = (e2))\/((op (e2) (e0)) = (e3))))) -> ((op (e2) (e1)) = (e2)) -> (~((e0) = (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) = (e2))) -> (~((e1) = (e2))) -> (((op (e0) (e0)) = (e2))\/(((op (e0) (e1)) = (e2))\/(((op (e0) (e2)) = (e2))\/((op (e0) (e3)) = (e2))))) -> (~((op (e0) (e0)) = (op (e0) (e3)))) -> (((op (e0) (e2)) = (e0))\/(((op (e0) (e2)) = (e1))\/(((op (e0) (e2)) = (e2))\/((op (e0) (e2)) = (e3))))) -> (~((op (e0) (e2)) = (op (e1) (e2)))) -> (~((op (e2) (e1)) = (op (e3) (e1)))) -> (((op (e0) (e3)) = (e3))\/(((op (e1) (e3)) = (e3))\/(((op (e2) (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 (e0) (e2)) = (e1))\/(((op (e1) (e2)) = (e1))\/(((op (e2) (e2)) = (e1))\/((op (e3) (e2)) = (e1))))) -> (~((op (e0) (e2)) = (e1))) -> (~((op (e0) (e0)) = (e1))) -> (((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))))) -> (~((op (e3) (e2)) = (op (e3) (e3)))) -> (~((op (e2) (e2)) = (op (e2) (e3)))) -> (~((op (e1) (e0)) = (op (e1) (e3)))) -> ((op (e0) (e1)) = (e1)) -> (~((op (e0) (e1)) = (op (e0) (e3)))) -> (((op (e3) (e0)) = (e1))\/(((op (e3) (e1)) = (e1))\/(((op (e3) (e2)) = (e1))\/((op (e3) (e3)) = (e1))))) -> (~((op (e2) (e1)) = (e1))) -> (~((op (e2) (e0)) = (e1))) -> (((op (e0) (e0)) = (e1))\/(((op (e1) (e0)) = (e1))\/(((op (e2) (e0)) = (e1))\/((op (e3) (e0)) = (e1))))) -> ((~((op (e3) (e2)) = (e1)))\/((op (e3) (e1)) = (e2))) -> False). % 18.96/19.10 do 0 intro. intros zenon_H3f zenon_H3e zenon_H6f zenon_H71 zenon_H4a zenon_H4f zenon_H52 zenon_H67 zenon_H5b zenon_H57 zenon_H6a zenon_H29 zenon_H45 zenon_H18c zenon_H128 zenon_H24e zenon_H24d zenon_H10a zenon_H95 zenon_H257 zenon_H1c7 zenon_H1f0 zenon_H24b zenon_H74 zenon_H263 zenon_H13e zenon_H261 zenon_H210 zenon_H160 zenon_H264 zenon_H1cf zenon_H208 zenon_H1a4 zenon_H130 zenon_H254 zenon_H17e zenon_H262 zenon_H12b zenon_H145 zenon_H172 zenon_H267 zenon_Hc2 zenon_H231 zenon_H1d zenon_Hdf zenon_Hd5 zenon_He4 zenon_H173 zenon_H1ac zenon_Hf3 zenon_He2 zenon_H11f zenon_H16f zenon_H14f zenon_H17b zenon_Ha8 zenon_He7 zenon_Hdb zenon_H259 zenon_H1ca zenon_H9a zenon_H1a6 zenon_H2f zenon_H149 zenon_H7c zenon_H183 zenon_H189 zenon_H1ba zenon_H195 zenon_Haf zenon_H136 zenon_H102 zenon_H153 zenon_H139 zenon_H20d zenon_H84 zenon_H106 zenon_H133 zenon_H62 zenon_H6d zenon_Hd8 zenon_Ha0 zenon_H54 zenon_He8 zenon_H24f zenon_H1db zenon_H235 zenon_H252. % 18.96/19.10 apply (zenon_or_s _ _ zenon_H263); [ zenon_intro zenon_H255 | zenon_intro zenon_Ha6 ]. % 18.96/19.10 apply (zenon_or_s _ _ zenon_H254); [ zenon_intro zenon_Had | zenon_intro zenon_H1b1 ]. % 18.96/19.10 apply (zenon_or_s _ _ zenon_H261); [ zenon_intro zenon_H250 | zenon_intro zenon_Hae ]. % 18.96/19.10 apply (zenon_or_s _ _ zenon_H252); [ zenon_intro zenon_H251 | zenon_intro zenon_H14d ]. % 18.96/19.10 apply (zenon_or_s _ _ zenon_H264); [ zenon_intro zenon_Hc7 | zenon_intro zenon_H161 ]. % 18.96/19.10 apply (zenon_L1021_); trivial. % 18.96/19.10 apply (zenon_or_s _ _ zenon_H74); [ zenon_intro zenon_H42 | zenon_intro zenon_H77 ]. % 18.96/19.10 exact (zenon_H3f zenon_H42). % 18.96/19.10 apply (zenon_or_s _ _ zenon_H77); [ zenon_intro zenon_H49 | zenon_intro zenon_H78 ]. % 18.96/19.10 apply (zenon_L23_); trivial. % 18.96/19.10 apply (zenon_or_s _ _ zenon_H78); [ zenon_intro zenon_H48 | zenon_intro zenon_H1e ]. % 18.96/19.10 apply (zenon_or_s _ _ zenon_H3e); [ zenon_intro zenon_H42 | zenon_intro zenon_H41 ]. % 18.96/19.10 exact (zenon_H3f zenon_H42). % 18.96/19.10 apply (zenon_or_s _ _ zenon_H41); [ zenon_intro zenon_H27 | zenon_intro zenon_H43 ]. % 18.96/19.10 apply (zenon_L8_); trivial. % 18.96/19.10 apply (zenon_or_s _ _ zenon_H43); [ zenon_intro zenon_H34 | zenon_intro zenon_H44 ]. % 18.96/19.10 apply (zenon_or_s _ _ zenon_H235); [ zenon_intro zenon_H7a | zenon_intro zenon_H236 ]. % 18.96/19.10 exact (zenon_H84 zenon_H7a). % 18.96/19.10 apply (zenon_or_s _ _ zenon_H236); [ zenon_intro zenon_H9d | zenon_intro zenon_H237 ]. % 18.96/19.10 apply (zenon_or_s _ _ zenon_H18c); [ zenon_intro zenon_H86 | zenon_intro zenon_H18d ]. % 18.96/19.10 apply (zenon_L123_); trivial. % 18.96/19.10 apply (zenon_or_s _ _ zenon_H18d); [ zenon_intro zenon_H110 | zenon_intro zenon_H18e ]. % 18.96/19.10 apply (zenon_L354_); trivial. % 18.96/19.10 apply (zenon_or_s _ _ zenon_H18e); [ zenon_intro zenon_H113 | zenon_intro zenon_Hd7 ]. % 18.96/19.10 apply (zenon_or_s _ _ zenon_H16f); [ zenon_intro zenon_H9e | zenon_intro zenon_H170 ]. % 18.96/19.10 apply (zenon_L960_); trivial. % 18.96/19.10 apply (zenon_or_s _ _ zenon_H170); [ zenon_intro zenon_H13f | zenon_intro zenon_H171 ]. % 18.96/19.10 apply (zenon_L1028_); trivial. % 18.96/19.10 apply (zenon_or_s _ _ zenon_H171); [ zenon_intro zenon_H16c | zenon_intro zenon_Hdc ]. % 18.96/19.10 apply (zenon_L116_); trivial. % 18.96/19.10 apply (zenon_or_s _ _ zenon_H1ac); [ zenon_intro zenon_H44 | zenon_intro zenon_H1af ]. % 18.96/19.10 apply (zenon_L1029_); trivial. % 18.96/19.10 apply (zenon_or_s _ _ zenon_H1af); [ zenon_intro zenon_H1b1 | zenon_intro zenon_H1b0 ]. % 18.96/19.10 apply (zenon_L349_); trivial. % 18.96/19.10 apply (zenon_or_s _ _ zenon_H1b0); [ zenon_intro zenon_H61 | zenon_intro zenon_H60 ]. % 18.96/19.10 apply (zenon_L342_); trivial. % 18.96/19.10 apply (zenon_or_s _ _ zenon_He8); [ zenon_intro zenon_Hac | zenon_intro zenon_Heb ]. % 18.96/19.10 exact (zenon_Had zenon_Hac). % 18.96/19.10 apply (zenon_or_s _ _ zenon_Heb); [ zenon_intro zenon_Hae | zenon_intro zenon_Hec ]. % 18.96/19.10 exact (zenon_H250 zenon_Hae). % 18.96/19.10 apply (zenon_or_s _ _ zenon_Hec); [ zenon_intro zenon_Hba | zenon_intro zenon_Hc4 ]. % 18.96/19.10 exact (zenon_H251 zenon_Hba). % 18.96/19.10 apply (zenon_or_s _ _ zenon_H145); [ zenon_intro zenon_Hcd | zenon_intro zenon_H146 ]. % 18.96/19.10 apply (zenon_L1031_); trivial. % 18.96/19.10 apply (zenon_or_s _ _ zenon_H146); [ zenon_intro zenon_Hd7 | zenon_intro zenon_H147 ]. % 18.96/19.10 apply (zenon_L1036_); trivial. % 18.96/19.10 apply (zenon_or_s _ _ zenon_H147); [ zenon_intro zenon_H11d | zenon_intro zenon_Hf6 ]. % 18.96/19.10 apply (zenon_L224_); trivial. % 18.96/19.10 apply (zenon_L798_); trivial. % 18.96/19.10 apply (zenon_L1036_); trivial. % 18.96/19.10 apply (zenon_or_s _ _ zenon_H237); [ zenon_intro zenon_Hed | zenon_intro zenon_Hac ]. % 18.96/19.10 exact (zenon_H1db zenon_Hed). % 18.96/19.10 exact (zenon_Had zenon_Hac). % 18.96/19.10 apply (zenon_or_s _ _ zenon_H235); [ zenon_intro zenon_H7a | zenon_intro zenon_H236 ]. % 18.96/19.10 exact (zenon_H84 zenon_H7a). % 18.96/19.10 apply (zenon_or_s _ _ zenon_H236); [ zenon_intro zenon_H9d | zenon_intro zenon_H237 ]. % 18.96/19.10 apply (zenon_or_s _ _ zenon_H18c); [ zenon_intro zenon_H86 | zenon_intro zenon_H18d ]. % 18.96/19.10 apply (zenon_L123_); trivial. % 18.96/19.10 apply (zenon_or_s _ _ zenon_H18d); [ zenon_intro zenon_H110 | zenon_intro zenon_H18e ]. % 18.96/19.10 apply (zenon_L354_); trivial. % 18.96/19.10 apply (zenon_or_s _ _ zenon_H18e); [ zenon_intro zenon_H113 | zenon_intro zenon_Hd7 ]. % 18.96/19.10 apply (zenon_or_s _ _ zenon_H16f); [ zenon_intro zenon_H9e | zenon_intro zenon_H170 ]. % 18.96/19.10 apply (zenon_L960_); trivial. % 18.96/19.10 apply (zenon_or_s _ _ zenon_H170); [ zenon_intro zenon_H13f | zenon_intro zenon_H171 ]. % 18.96/19.10 apply (zenon_L1022_); trivial. % 18.96/19.10 apply (zenon_or_s _ _ zenon_H171); [ zenon_intro zenon_H16c | zenon_intro zenon_Hdc ]. % 18.96/19.10 apply (zenon_L116_); trivial. % 18.96/19.10 apply (zenon_L1029_); trivial. % 18.96/19.10 apply (zenon_L1034_); trivial. % 18.96/19.10 apply (zenon_or_s _ _ zenon_H237); [ zenon_intro zenon_Hed | zenon_intro zenon_Hac ]. % 18.96/19.10 exact (zenon_H1db zenon_Hed). % 18.96/19.10 exact (zenon_Had zenon_Hac). % 18.96/19.10 apply (zenon_or_s _ _ zenon_H3e); [ zenon_intro zenon_H42 | zenon_intro zenon_H41 ]. % 18.96/19.10 exact (zenon_H3f zenon_H42). % 18.96/19.10 apply (zenon_or_s _ _ zenon_H41); [ zenon_intro zenon_H27 | zenon_intro zenon_H43 ]. % 18.96/19.10 apply (zenon_L8_); trivial. % 18.96/19.10 apply (zenon_or_s _ _ zenon_H43); [ zenon_intro zenon_H34 | zenon_intro zenon_H44 ]. % 18.96/19.10 apply (zenon_or_s _ _ zenon_H235); [ zenon_intro zenon_H7a | zenon_intro zenon_H236 ]. % 18.96/19.10 exact (zenon_H84 zenon_H7a). % 18.96/19.10 apply (zenon_or_s _ _ zenon_H236); [ zenon_intro zenon_H9d | zenon_intro zenon_H237 ]. % 18.96/19.10 apply (zenon_or_s _ _ zenon_H16f); [ zenon_intro zenon_H9e | zenon_intro zenon_H170 ]. % 18.96/19.10 apply (zenon_L37_); trivial. % 18.96/19.10 apply (zenon_or_s _ _ zenon_H170); [ zenon_intro zenon_H13f | zenon_intro zenon_H171 ]. % 18.96/19.10 apply (zenon_L1022_); trivial. % 18.96/19.10 apply (zenon_or_s _ _ zenon_H171); [ zenon_intro zenon_H16c | zenon_intro zenon_Hdc ]. % 18.96/19.10 apply (zenon_L1037_); trivial. % 18.96/19.10 apply (zenon_L1040_); trivial. % 18.96/19.10 apply (zenon_or_s _ _ zenon_H237); [ zenon_intro zenon_Hed | zenon_intro zenon_Hac ]. % 18.96/19.10 exact (zenon_H1db zenon_Hed). % 18.96/19.10 exact (zenon_Had zenon_Hac). % 18.96/19.10 apply (zenon_or_s _ _ zenon_H235); [ zenon_intro zenon_H7a | zenon_intro zenon_H236 ]. % 18.96/19.10 exact (zenon_H84 zenon_H7a). % 18.96/19.10 apply (zenon_or_s _ _ zenon_H236); [ zenon_intro zenon_H9d | zenon_intro zenon_H237 ]. % 18.96/19.10 apply (zenon_or_s _ _ zenon_H183); [ zenon_intro zenon_H7b | zenon_intro zenon_H186 ]. % 18.96/19.10 apply (zenon_or_s _ _ zenon_H2f); [ zenon_intro zenon_H34 | zenon_intro zenon_H33 ]. % 18.96/19.10 apply (zenon_L127_); trivial. % 18.96/19.10 apply (zenon_or_s _ _ zenon_H33); [ zenon_intro zenon_H36 | zenon_intro zenon_H35 ]. % 18.96/19.10 apply (zenon_L965_); trivial. % 18.96/19.10 apply (zenon_or_s _ _ zenon_H35); [ zenon_intro zenon_H2c | zenon_intro zenon_H37 ]. % 18.96/19.10 apply (zenon_or_s _ _ zenon_He8); [ zenon_intro zenon_Hac | zenon_intro zenon_Heb ]. % 18.96/19.10 exact (zenon_Had zenon_Hac). % 18.96/19.10 apply (zenon_or_s _ _ zenon_Heb); [ zenon_intro zenon_Hae | zenon_intro zenon_Hec ]. % 18.96/19.10 exact (zenon_H250 zenon_Hae). % 18.96/19.10 apply (zenon_or_s _ _ zenon_Hec); [ zenon_intro zenon_Hba | zenon_intro zenon_Hc4 ]. % 18.96/19.10 exact (zenon_H251 zenon_Hba). % 18.96/19.10 apply (zenon_or_s _ _ zenon_H145); [ zenon_intro zenon_Hcd | zenon_intro zenon_H146 ]. % 18.96/19.10 apply (zenon_L375_); trivial. % 18.96/19.10 apply (zenon_or_s _ _ zenon_H146); [ zenon_intro zenon_Hd7 | zenon_intro zenon_H147 ]. % 18.96/19.10 apply (zenon_L1043_); trivial. % 18.96/19.10 apply (zenon_or_s _ _ zenon_H147); [ zenon_intro zenon_H11d | zenon_intro zenon_Hf6 ]. % 18.96/19.10 apply (zenon_L224_); trivial. % 18.96/19.10 apply (zenon_L968_); trivial. % 18.96/19.10 apply (zenon_L367_); trivial. % 18.96/19.10 apply (zenon_or_s _ _ zenon_H186); [ zenon_intro zenon_H10f | zenon_intro zenon_H187 ]. % 18.96/19.10 apply (zenon_L191_); trivial. % 18.96/19.10 apply (zenon_or_s _ _ zenon_H187); [ zenon_intro zenon_H150 | zenon_intro zenon_Hcd ]. % 18.96/19.10 apply (zenon_L1044_); trivial. % 18.96/19.10 apply (zenon_L428_); trivial. % 18.96/19.10 apply (zenon_or_s _ _ zenon_H237); [ zenon_intro zenon_Hed | zenon_intro zenon_Hac ]. % 18.96/19.10 exact (zenon_H1db zenon_Hed). % 18.96/19.10 exact (zenon_Had zenon_Hac). % 18.96/19.10 apply (zenon_L364_); trivial. % 18.96/19.10 apply (zenon_L363_); trivial. % 18.96/19.10 apply (zenon_L349_); trivial. % 18.96/19.10 apply (zenon_L207_); trivial. % 18.96/19.10 (* end of lemma zenon_L1045_ *) % 18.96/19.10 assert (zenon_L1046_ : (((op (e2) (e0)) = (e1))\/(((op (e2) (e1)) = (e1))\/(((op (e2) (e2)) = (e1))\/((op (e2) (e3)) = (e1))))) -> (~((op (e2) (e0)) = (e1))) -> (~((op (e2) (e1)) = (e1))) -> (~((op (e2) (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) (e0)) = (e0)) -> (~((op (e2) (e3)) = (op (e3) (e3)))) -> (~((op (e3) (e1)) = (op (e3) (e3)))) -> ((op (e3) (e1)) = (e2)) -> (~((op (e3) (e3)) = (e3))) -> False). % 18.96/19.10 do 0 intro. intros zenon_H106 zenon_H1db zenon_H24f zenon_H198 zenon_H101 zenon_H71 zenon_H44 zenon_Hf3 zenon_H130 zenon_H14d zenon_H102. % 18.96/19.10 apply (zenon_or_s _ _ zenon_H106); [ zenon_intro zenon_Hed | zenon_intro zenon_H107 ]. % 18.96/19.10 exact (zenon_H1db zenon_Hed). % 18.96/19.10 apply (zenon_or_s _ _ zenon_H107); [ zenon_intro zenon_Ha5 | zenon_intro zenon_H108 ]. % 18.96/19.10 exact (zenon_H24f zenon_Ha5). % 18.96/19.10 apply (zenon_or_s _ _ zenon_H108); [ zenon_intro zenon_Hf1 | zenon_intro zenon_Hf4 ]. % 18.96/19.10 exact (zenon_H198 zenon_Hf1). % 18.96/19.10 apply (zenon_L414_); trivial. % 18.96/19.10 (* end of lemma zenon_L1046_ *) % 18.96/19.10 assert (zenon_L1047_ : (~((op (e3) (e0)) = (e1))) -> (((op (e1) (e0)) = (e2))\/(((op (e1) (e1)) = (e2))\/(((op (e1) (e2)) = (e2))\/((op (e1) (e3)) = (e2))))) -> (~((e1) = (e2))) -> (~((op (e0) (e3)) = (op (e1) (e3)))) -> (~((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 (e3) (e2)) = (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 (e0) (e2)) = (e0))\/(((op (e1) (e2)) = (e0))\/(((op (e2) (e2)) = (e0))\/((op (e3) (e2)) = (e0))))) -> (~((op (e0) (e2)) = (op (e0) (e3)))) -> (~((op (e1) (e1)) = (op (e1) (e2)))) -> (~((op (e2) (e0)) = (op (e2) (e2)))) -> (~((op (e3) (e1)) = (op (e3) (e2)))) -> (~((op (e1) (e0)) = (op (e1) (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 (e1) (e3)))) -> ((op (e1) (e1)) = (e0)) -> (~((op (e2) (e0)) = (op (e2) (e3)))) -> (((op (e3) (e0)) = (e0))\/(((op (e3) (e1)) = (e0))\/(((op (e3) (e2)) = (e0))\/((op (e3) (e3)) = (e0))))) -> (~((op (e1) (e2)) = (e1))) -> (~((op (e0) (e2)) = (e1))) -> (((op (e0) (e2)) = (e1))\/(((op (e1) (e2)) = (e1))\/(((op (e2) (e2)) = (e1))\/((op (e3) (e2)) = (e1))))) -> (~((e2) = (e3))) -> ((~((op (e2) (e0)) = (e1)))\/((op (e2) (e1)) = (e0))) -> (~((op (e2) (e1)) = (op (e2) (e3)))) -> (~((op (e2) (e0)) = (op (e2) (e1)))) -> (~((op (e2) (e1)) = (op (e2) (e2)))) -> (~((op (e3) (e0)) = (op (e3) (e2)))) -> (((op (e0) (e0)) = (e0))\/(((op (e0) (e1)) = (e0))\/(((op (e0) (e2)) = (e0))\/((op (e0) (e3)) = (e0))))) -> ((~((op (e2) (e3)) = (e1)))\/((op (e2) (e1)) = (e3))) -> (~((op (e1) (e1)) = (op (e2) (e1)))) -> ((~((op (e3) (e1)) = (e1)))\/((op (e3) (e1)) = (e1))) -> (~((op (e0) (e1)) = (op (e3) (e1)))) -> (((op (e0) (e0)) = (e1))\/(((op (e1) (e0)) = (e1))\/(((op (e2) (e0)) = (e1))\/((op (e3) (e0)) = (e1))))) -> (((op (e3) (e0)) = (e1))\/(((op (e3) (e1)) = (e1))\/(((op (e3) (e2)) = (e1))\/((op (e3) (e3)) = (e1))))) -> (~((op (e0) (e1)) = (op (e0) (e3)))) -> ((op (e0) (e1)) = (e1)) -> (~((op (e1) (e0)) = (op (e1) (e3)))) -> (~((op (e2) (e2)) = (op (e2) (e3)))) -> (((op (e0) (e3)) = (e1))\/(((op (e1) (e3)) = (e1))\/(((op (e2) (e3)) = (e1))\/((op (e3) (e3)) = (e1))))) -> (~((op (e0) (e0)) = (e1))) -> (~((op (e1) (e1)) = (op (e3) (e1)))) -> ((~((op (e3) (e3)) = (e1)))\/((op (e3) (e1)) = (e3))) -> ((~((op (e3) (e0)) = (e1)))\/((op (e3) (e1)) = (e0))) -> (~((op (e0) (e1)) = (op (e2) (e1)))) -> ((~((op (e2) (e1)) = (e1)))\/((op (e2) (e1)) = (e1))) -> (((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) (e0)) = (e2))\/(((op (e2) (e1)) = (e2))\/(((op (e2) (e2)) = (e2))\/((op (e2) (e3)) = (e2))))) -> (~((e0) = (e2))) -> (~((op (e2) (e1)) = (op (e3) (e1)))) -> (~((op (e2) (e2)) = (e2))) -> (~((op (e1) (e3)) = (op (e2) (e3)))) -> (((op (e2) (e0)) = (e1))\/(((op (e2) (e1)) = (e1))\/(((op (e2) (e2)) = (e1))\/((op (e2) (e3)) = (e1))))) -> (~((op (e2) (e0)) = (e1))) -> (~((op (e2) (e1)) = (e1))) -> (~((op (e2) (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 (e2) (e3)) = (op (e3) (e3)))) -> (~((op (e3) (e1)) = (op (e3) (e3)))) -> ((op (e3) (e1)) = (e2)) -> (~((op (e3) (e3)) = (e3))) -> False). % 18.96/19.10 do 0 intro. intros zenon_Had zenon_H18c zenon_H7c zenon_H1d zenon_H231 zenon_Hc2 zenon_He4 zenon_H62 zenon_H67 zenon_H1cf zenon_H6a zenon_H208 zenon_H4f zenon_H52 zenon_H1a4 zenon_H45 zenon_H3f zenon_H3e zenon_H57 zenon_H29 zenon_H5b zenon_H1ac zenon_H24d zenon_H20d zenon_H139 zenon_H12b zenon_H257 zenon_H1c7 zenon_H1f0 zenon_H24b zenon_H6f zenon_H74 zenon_H263 zenon_H13e zenon_H261 zenon_H210 zenon_H235 zenon_He8 zenon_H54 zenon_Ha0 zenon_Hd8 zenon_H6d zenon_H133 zenon_H84 zenon_H160 zenon_H264 zenon_H254 zenon_H17e zenon_H262 zenon_H128 zenon_H95 zenon_H10a zenon_H24e zenon_H16f zenon_H1d5 zenon_H149 zenon_Haf zenon_H173 zenon_Hdb zenon_H106 zenon_H1db zenon_H24f zenon_H198 zenon_H101 zenon_H71 zenon_Hf3 zenon_H130 zenon_H14d zenon_H102. % 18.96/19.10 apply (zenon_or_s _ _ zenon_H3e); [ zenon_intro zenon_H42 | zenon_intro zenon_H41 ]. % 18.96/19.10 exact (zenon_H3f zenon_H42). % 18.96/19.10 apply (zenon_or_s _ _ zenon_H41); [ zenon_intro zenon_H27 | zenon_intro zenon_H43 ]. % 18.96/19.10 apply (zenon_L8_); trivial. % 18.96/19.10 apply (zenon_or_s _ _ zenon_H43); [ zenon_intro zenon_H34 | zenon_intro zenon_H44 ]. % 18.96/19.10 apply (zenon_or_s _ _ zenon_H235); [ zenon_intro zenon_H7a | zenon_intro zenon_H236 ]. % 18.96/19.10 exact (zenon_H84 zenon_H7a). % 18.96/19.10 apply (zenon_or_s _ _ zenon_H236); [ zenon_intro zenon_H9d | zenon_intro zenon_H237 ]. % 18.96/19.10 apply (zenon_or_s _ _ zenon_H18c); [ zenon_intro zenon_H86 | zenon_intro zenon_H18d ]. % 18.96/19.10 apply (zenon_L123_); trivial. % 18.96/19.10 apply (zenon_or_s _ _ zenon_H18d); [ zenon_intro zenon_H110 | zenon_intro zenon_H18e ]. % 18.96/19.10 apply (zenon_L354_); trivial. % 18.96/19.10 apply (zenon_or_s _ _ zenon_H18e); [ zenon_intro zenon_H113 | zenon_intro zenon_Hd7 ]. % 18.96/19.10 apply (zenon_or_s _ _ zenon_H16f); [ zenon_intro zenon_H9e | zenon_intro zenon_H170 ]. % 18.96/19.10 apply (zenon_L960_); trivial. % 18.96/19.10 apply (zenon_or_s _ _ zenon_H170); [ zenon_intro zenon_H13f | zenon_intro zenon_H171 ]. % 18.96/19.10 apply (zenon_L1028_); trivial. % 18.96/19.10 apply (zenon_or_s _ _ zenon_H171); [ zenon_intro zenon_H16c | zenon_intro zenon_Hdc ]. % 18.96/19.10 apply (zenon_L116_); trivial. % 18.96/19.10 apply (zenon_or_s _ _ zenon_H106); [ zenon_intro zenon_Hed | zenon_intro zenon_H107 ]. % 18.96/19.10 exact (zenon_H1db zenon_Hed). % 18.96/19.10 apply (zenon_or_s _ _ zenon_H107); [ zenon_intro zenon_Ha5 | zenon_intro zenon_H108 ]. % 18.96/19.10 exact (zenon_H24f zenon_Ha5). % 18.96/19.10 apply (zenon_or_s _ _ zenon_H108); [ zenon_intro zenon_Hf1 | zenon_intro zenon_Hf4 ]. % 18.96/19.10 exact (zenon_H198 zenon_Hf1). % 18.96/19.10 apply (zenon_or_s _ _ zenon_H139); [ zenon_intro zenon_H122 | zenon_intro zenon_H13a ]. % 18.96/19.10 exact (zenon_H20d zenon_H122). % 18.96/19.10 apply (zenon_or_s _ _ zenon_H13a); [ zenon_intro zenon_Hf0 | zenon_intro zenon_H13b ]. % 18.96/19.10 exact (zenon_H24d zenon_Hf0). % 18.96/19.10 apply (zenon_or_s _ _ zenon_H13b); [ zenon_intro zenon_Hf1 | zenon_intro zenon_Hba ]. % 18.96/19.10 exact (zenon_H198 zenon_Hf1). % 18.96/19.10 apply (zenon_or_s _ _ zenon_H1ac); [ zenon_intro zenon_H44 | zenon_intro zenon_H1af ]. % 18.96/19.10 apply (zenon_L414_); trivial. % 18.96/19.10 apply (zenon_or_s _ _ zenon_H1af); [ zenon_intro zenon_H1b1 | zenon_intro zenon_H1b0 ]. % 18.96/19.10 apply (zenon_L348_); trivial. % 18.96/19.10 apply (zenon_or_s _ _ zenon_H1b0); [ zenon_intro zenon_H61 | zenon_intro zenon_H60 ]. % 18.96/19.10 apply (zenon_L923_); trivial. % 18.96/19.10 apply (zenon_L749_); trivial. % 18.96/19.10 apply (zenon_L462_); trivial. % 18.96/19.10 apply (zenon_or_s _ _ zenon_H237); [ zenon_intro zenon_Hed | zenon_intro zenon_Hac ]. % 18.96/19.10 exact (zenon_H1db zenon_Hed). % 18.96/19.10 exact (zenon_Had zenon_Hac). % 18.96/19.10 apply (zenon_L1046_); trivial. % 18.96/19.10 (* end of lemma zenon_L1047_ *) % 18.96/19.10 assert (zenon_L1048_ : (((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) (e0)) = (e2))\/(((op (e2) (e1)) = (e2))\/(((op (e2) (e2)) = (e2))\/((op (e2) (e3)) = (e2))))) -> (~((op (e0) (e1)) = (op (e0) (e3)))) -> (~((op (e1) (e0)) = (op (e1) (e3)))) -> (~((op (e2) (e2)) = (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 (e0) (e2)) = (e1))) -> (((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 (e3) (e3)) = (e3))) -> (((op (e0) (e3)) = (e3))\/(((op (e1) (e3)) = (e3))\/(((op (e2) (e3)) = (e3))\/((op (e3) (e3)) = (e3))))) -> (~((op (e2) (e1)) = (op (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) (e0)) = (op (e0) (e3)))) -> (((op (e0) (e0)) = (e2))\/(((op (e0) (e1)) = (e2))\/(((op (e0) (e2)) = (e2))\/((op (e0) (e3)) = (e2))))) -> (~((e1) = (e2))) -> (((op (e2) (e0)) = (e0))\/(((op (e2) (e1)) = (e0))\/(((op (e2) (e2)) = (e0))\/((op (e2) (e3)) = (e0))))) -> (((op (e0) (e2)) = (e3))\/(((op (e1) (e2)) = (e3))\/(((op (e2) (e2)) = (e3))\/((op (e3) (e2)) = (e3))))) -> (~((e0) = (e3))) -> (((op (e2) (e0)) = (e0))\/(((op (e2) (e0)) = (e1))\/(((op (e2) (e0)) = (e2))\/((op (e2) (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 (e0) (e2)) = (op (e2) (e2)))) -> (~((op (e2) (e0)) = (op (e3) (e0)))) -> (~((op (e0) (e2)) = (op (e3) (e2)))) -> (((op (e1) (e0)) = (e3))\/(((op (e1) (e1)) = (e3))\/(((op (e1) (e2)) = (e3))\/((op (e1) (e3)) = (e3))))) -> (((op (e2) (e3)) = (e0))\/(((op (e2) (e3)) = (e1))\/(((op (e2) (e3)) = (e2))\/((op (e2) (e3)) = (e3))))) -> (~((op (e0) (e3)) = (op (e2) (e3)))) -> (~((op (e2) (e3)) = (op (e3) (e3)))) -> (((op (e3) (e0)) = (e0))\/(((op (e3) (e1)) = (e0))\/(((op (e3) (e2)) = (e0))\/((op (e3) (e3)) = (e0))))) -> (~((op (e2) (e2)) = (e2))) -> (((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)) = (op (e1) (e3)))) -> (~((op (e0) (e3)) = (e1))) -> (~((op (e0) (e3)) = (op (e3) (e3)))) -> (((op (e3) (e0)) = (e0))\/(((op (e3) (e0)) = (e1))\/(((op (e3) (e0)) = (e2))\/((op (e3) (e0)) = (e3))))) -> (((op (e0) (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))))) -> (~((e2) = (e3))) -> (~((op (e3) (e1)) = (op (e3) (e3)))) -> (~((op (e3) (e1)) = (op (e3) (e2)))) -> (~((op (e0) (e2)) = (op (e0) (e3)))) -> (~((op (e3) (e0)) = (op (e3) (e1)))) -> ((~((op (e3) (e3)) = (e1)))\/((op (e3) (e1)) = (e3))) -> (~((op (e1) (e1)) = (op (e3) (e1)))) -> (((op (e0) (e0)) = (e0))\/(((op (e0) (e1)) = (e0))\/(((op (e0) (e2)) = (e0))\/((op (e0) (e3)) = (e0))))) -> (~((op (e2) (e1)) = (op (e2) (e2)))) -> (~((op (e2) (e0)) = (op (e2) (e1)))) -> (~((op (e2) (e1)) = (op (e2) (e3)))) -> ((~((op (e2) (e0)) = (e1)))\/((op (e2) (e1)) = (e0))) -> (~((e1) = (e3))) -> (((op (e1) (e0)) = (e2))\/(((op (e1) (e1)) = (e2))\/(((op (e1) (e2)) = (e2))\/((op (e1) (e3)) = (e2))))) -> (~((op (e1) (e0)) = (op (e1) (e1)))) -> (((op (e0) (e2)) = (e0))\/(((op (e1) (e2)) = (e0))\/(((op (e2) (e2)) = (e0))\/((op (e3) (e2)) = (e0))))) -> (~((op (e1) (e1)) = (op (e1) (e3)))) -> (~((op (e2) (e0)) = (op (e2) (e3)))) -> (((op (e0) (e3)) = (e0))\/(((op (e1) (e3)) = (e0))\/(((op (e2) (e3)) = (e0))\/((op (e3) (e3)) = (e0))))) -> (~((op (e2) (e0)) = (op (e2) (e2)))) -> (~((op (e1) (e1)) = (op (e1) (e2)))) -> (~((op (e0) (e1)) = (op (e0) (e2)))) -> (~((op (e3) (e0)) = (op (e3) (e3)))) -> (~((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)) = (e0))) -> ((op (e1) (e1)) = (e0)) -> (~((e0) = (e2))) -> ((~((op (e1) (e2)) = (e1)))\/((op (e1) (e1)) = (e2))) -> (~((op (e0) (e1)) = (op (e1) (e1)))) -> (((op (e1) (e0)) = (e1))\/(((op (e1) (e1)) = (e1))\/(((op (e1) (e2)) = (e1))\/((op (e1) (e3)) = (e1))))) -> (~((op (e1) (e1)) = (e1))) -> ((~((op (e2) (e1)) = (e1)))\/((op (e2) (e1)) = (e1))) -> ((~((op (e2) (e3)) = (e1)))\/((op (e2) (e1)) = (e3))) -> (~((op (e1) (e1)) = (op (e2) (e1)))) -> ((~((op (e3) (e1)) = (e1)))\/((op (e3) (e1)) = (e1))) -> ((op (e0) (e1)) = (e1)) -> (((op (e0) (e0)) = (e1))\/(((op (e1) (e0)) = (e1))\/(((op (e2) (e0)) = (e1))\/((op (e3) (e0)) = (e1))))) -> (((op (e3) (e0)) = (e1))\/(((op (e3) (e1)) = (e1))\/(((op (e3) (e2)) = (e1))\/((op (e3) (e3)) = (e1))))) -> (~((op (e1) (e3)) = (op (e3) (e3)))) -> (~((op (e1) (e0)) = (op (e2) (e0)))) -> (((op (e2) (e0)) = (e1))\/(((op (e2) (e1)) = (e1))\/(((op (e2) (e2)) = (e1))\/((op (e2) (e3)) = (e1))))) -> (~((op (e0) (e0)) = (e1))) -> (~((op (e0) (e1)) = (op (e3) (e1)))) -> ((~((op (e3) (e2)) = (e1)))\/((op (e3) (e1)) = (e2))) -> ((~((op (e3) (e0)) = (e1)))\/((op (e3) (e1)) = (e0))) -> (~((op (e0) (e1)) = (op (e2) (e1)))) -> ((~((op (e2) (e2)) = (e1)))\/((op (e2) (e1)) = (e2))) -> ((~((op (e1) (e3)) = (e1)))\/((op (e1) (e1)) = (e3))) -> ((~((op (e1) (e0)) = (e1)))\/((op (e1) (e1)) = (e0))) -> False). % 18.99/19.10 do 0 intro. intros zenon_H1d8 zenon_H101 zenon_H1d5 zenon_H54 zenon_Hd8 zenon_H6d zenon_H62 zenon_H133 zenon_H20d zenon_H139 zenon_H153 zenon_H102 zenon_H136 zenon_Haf zenon_H195 zenon_H1ba zenon_H189 zenon_H183 zenon_H7c zenon_H2f zenon_H1a6 zenon_H9a zenon_H259 zenon_Hdb zenon_He7 zenon_Ha8 zenon_H17b zenon_H14f zenon_H16f zenon_H11f zenon_He2 zenon_Hf3 zenon_H1ac zenon_H173 zenon_He4 zenon_Hdf zenon_H1d zenon_H231 zenon_Hc2 zenon_H267 zenon_H172 zenon_H145 zenon_H12b zenon_H130 zenon_H1a4 zenon_H208 zenon_H1cf zenon_H264 zenon_H160 zenon_H74 zenon_H24b zenon_H1f0 zenon_H1c7 zenon_H257 zenon_H95 zenon_H18c zenon_H45 zenon_H6a zenon_H57 zenon_H5b zenon_H67 zenon_H52 zenon_H4f zenon_H4a zenon_H71 zenon_H6f zenon_H3e zenon_H3f zenon_H29 zenon_H149 zenon_H256 zenon_H10e zenon_H128 zenon_H10a zenon_H262 zenon_H263 zenon_H13e zenon_H261 zenon_Ha0 zenon_H235 zenon_He8 zenon_Hd5 zenon_H201 zenon_H106 zenon_H84 zenon_H210 zenon_H252 zenon_H254 zenon_H17e zenon_H253 zenon_H258 zenon_H25d. % 18.99/19.10 apply (zenon_or_s _ _ zenon_H256); [ zenon_intro zenon_H24d | zenon_intro zenon_H110 ]. % 18.99/19.10 apply (zenon_or_s _ _ zenon_H258); [ zenon_intro zenon_H24e | zenon_intro zenon_H13f ]. % 18.99/19.10 apply (zenon_or_s _ _ zenon_H257); [ zenon_intro zenon_H1db | zenon_intro zenon_H36 ]. % 18.99/19.10 apply (zenon_or_s _ _ zenon_H262); [ zenon_intro zenon_H24f | zenon_intro zenon_Ha5 ]. % 18.99/19.10 apply (zenon_or_s _ _ zenon_H253); [ zenon_intro zenon_H198 | zenon_intro zenon_H1ca ]. % 18.99/19.10 apply (zenon_or_s _ _ zenon_H254); [ zenon_intro zenon_Had | zenon_intro zenon_H1b1 ]. % 18.99/19.10 apply (zenon_or_s _ _ zenon_H1d8); [ zenon_intro zenon_H10f | zenon_intro zenon_H1d9 ]. % 18.99/19.10 apply (zenon_L1018_); trivial. % 18.99/19.10 apply (zenon_or_s _ _ zenon_H1d9); [ zenon_intro zenon_H110 | zenon_intro zenon_H1da ]. % 18.99/19.10 apply (zenon_L354_); trivial. % 18.99/19.10 apply (zenon_or_s _ _ zenon_H1da); [ zenon_intro zenon_H1ca | zenon_intro zenon_H14d ]. % 18.99/19.10 apply (zenon_L1045_); trivial. % 18.99/19.10 apply (zenon_L1047_); trivial. % 18.99/19.10 apply (zenon_L349_); trivial. % 18.99/19.10 apply (zenon_L1045_); trivial. % 18.99/19.10 apply (zenon_L357_); trivial. % 18.99/19.10 apply (zenon_L965_); trivial. % 18.99/19.10 apply (zenon_L1028_); trivial. % 18.99/19.10 apply (zenon_L354_); trivial. % 18.99/19.10 (* end of lemma zenon_L1048_ *) % 18.99/19.10 assert (zenon_L1049_ : (((op (e1) (e0)) = (e2))\/(((op (e1) (e1)) = (e2))\/(((op (e1) (e2)) = (e2))\/((op (e1) (e3)) = (e2))))) -> (~((op (e1) (e0)) = (e2))) -> (~((op (e1) (e1)) = (e2))) -> (~((op (e1) (e2)) = (e2))) -> (~((op (e1) (e3)) = (e2))) -> False). % 18.99/19.10 do 0 intro. intros zenon_H18c zenon_H177 zenon_H20c zenon_H114 zenon_H14c. % 18.99/19.10 apply (zenon_or_s _ _ zenon_H18c); [ zenon_intro zenon_H86 | zenon_intro zenon_H18d ]. % 18.99/19.10 exact (zenon_H177 zenon_H86). % 18.99/19.10 apply (zenon_or_s _ _ zenon_H18d); [ zenon_intro zenon_H110 | zenon_intro zenon_H18e ]. % 18.99/19.10 exact (zenon_H20c zenon_H110). % 18.99/19.10 apply (zenon_or_s _ _ zenon_H18e); [ zenon_intro zenon_H113 | zenon_intro zenon_Hd7 ]. % 18.99/19.10 exact (zenon_H114 zenon_H113). % 18.99/19.10 exact (zenon_H14c zenon_Hd7). % 18.99/19.10 (* end of lemma zenon_L1049_ *) % 18.99/19.10 assert (zenon_L1050_ : (((op (e0) (e0)) = (e2))\/(((op (e0) (e1)) = (e2))\/(((op (e0) (e2)) = (e2))\/((op (e0) (e3)) = (e2))))) -> (~((op (e0) (e0)) = (e2))) -> (~((op (e0) (e1)) = (e2))) -> (~((op (e0) (e2)) = (e2))) -> (((op (e2) (e0)) = (e2))\/(((op (e2) (e1)) = (e2))\/(((op (e2) (e2)) = (e2))\/((op (e2) (e3)) = (e2))))) -> (~((op (e2) (e0)) = (e2))) -> (~((op (e2) (e1)) = (e2))) -> (~((op (e2) (e2)) = (e2))) -> (~((op (e0) (e3)) = (op (e2) (e3)))) -> False). % 18.99/19.10 do 0 intro. intros zenon_H183 zenon_H80 zenon_H26d zenon_H1fd zenon_H1d5 zenon_Hef zenon_H26e zenon_H173 zenon_He2. % 18.99/19.10 apply (zenon_or_s _ _ zenon_H183); [ zenon_intro zenon_H7b | zenon_intro zenon_H186 ]. % 18.99/19.10 exact (zenon_H80 zenon_H7b). % 18.99/19.10 apply (zenon_or_s _ _ zenon_H186); [ zenon_intro zenon_H10f | zenon_intro zenon_H187 ]. % 18.99/19.10 exact (zenon_H26d zenon_H10f). % 18.99/19.10 apply (zenon_or_s _ _ zenon_H187); [ zenon_intro zenon_H150 | zenon_intro zenon_Hcd ]. % 18.99/19.10 exact (zenon_H1fd zenon_H150). % 18.99/19.10 apply (zenon_or_s _ _ zenon_H1d5); [ zenon_intro zenon_Hee | zenon_intro zenon_H1d6 ]. % 18.99/19.10 exact (zenon_Hef zenon_Hee). % 18.99/19.10 apply (zenon_or_s _ _ zenon_H1d6); [ zenon_intro zenon_H1ca | zenon_intro zenon_H1d7 ]. % 18.99/19.10 exact (zenon_H26e zenon_H1ca). % 18.99/19.10 apply (zenon_or_s _ _ zenon_H1d7); [ zenon_intro zenon_H176 | zenon_intro zenon_H11d ]. % 18.99/19.10 exact (zenon_H173 zenon_H176). % 18.99/19.10 apply (zenon_L234_); trivial. % 18.99/19.10 (* end of lemma zenon_L1050_ *) % 18.99/19.10 assert (zenon_L1051_ : (((op (e0) (e0)) = (e2))\/(((op (e1) (e0)) = (e2))\/(((op (e2) (e0)) = (e2))\/((op (e3) (e0)) = (e2))))) -> (~((op (e0) (e0)) = (e2))) -> (~((op (e1) (e0)) = (e2))) -> (~((op (e3) (e1)) = (e2))) -> (~((op (e2) (e0)) = (op (e2) (e1)))) -> (~((op (e1) (e1)) = (e2))) -> (~((op (e0) (e1)) = (e2))) -> (((op (e0) (e1)) = (e2))\/(((op (e1) (e1)) = (e2))\/(((op (e2) (e1)) = (e2))\/((op (e3) (e1)) = (e2))))) -> (~((op (e3) (e0)) = (e2))) -> False). % 18.99/19.10 do 0 intro. intros zenon_H1fe zenon_H80 zenon_H177 zenon_H194 zenon_H1f0 zenon_H20c zenon_H26d zenon_H1d8 zenon_H14b. % 18.99/19.10 apply (zenon_or_s _ _ zenon_H1fe); [ zenon_intro zenon_H7b | zenon_intro zenon_H1ff ]. % 18.99/19.10 exact (zenon_H80 zenon_H7b). % 18.99/19.10 apply (zenon_or_s _ _ zenon_H1ff); [ zenon_intro zenon_H86 | zenon_intro zenon_H200 ]. % 18.99/19.10 exact (zenon_H177 zenon_H86). % 18.99/19.10 apply (zenon_or_s _ _ zenon_H200); [ zenon_intro zenon_Hee | zenon_intro zenon_H148 ]. % 18.99/19.10 apply (zenon_or_s _ _ zenon_H1d8); [ zenon_intro zenon_H10f | zenon_intro zenon_H1d9 ]. % 18.99/19.10 exact (zenon_H26d zenon_H10f). % 18.99/19.10 apply (zenon_or_s _ _ zenon_H1d9); [ zenon_intro zenon_H110 | zenon_intro zenon_H1da ]. % 18.99/19.10 exact (zenon_H20c zenon_H110). % 18.99/19.10 apply (zenon_or_s _ _ zenon_H1da); [ zenon_intro zenon_H1ca | zenon_intro zenon_H14d ]. % 18.99/19.10 apply (zenon_L277_); trivial. % 18.99/19.10 exact (zenon_H194 zenon_H14d). % 18.99/19.10 exact (zenon_H14b zenon_H148). % 18.99/19.10 (* end of lemma zenon_L1051_ *) % 18.99/19.10 assert (zenon_L1052_ : ((~((op (e3) (e1)) = (e2)))\/((op (e3) (e2)) = (e1))) -> ((op (e2) (e2)) = (e1)) -> (~((op (e2) (e2)) = (op (e3) (e2)))) -> (~((op (e0) (e0)) = (e2))) -> (~((op (e1) (e0)) = (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)) = (e2))) -> (~((op (e0) (e1)) = (e2))) -> (~((op (e3) (e0)) = (e2))) -> (((op (e0) (e0)) = (e2))\/(((op (e1) (e0)) = (e2))\/(((op (e2) (e0)) = (e2))\/((op (e3) (e0)) = (e2))))) -> False). % 18.99/19.10 do 0 intro. intros zenon_H26f zenon_Hf1 zenon_H18f zenon_H80 zenon_H177 zenon_H1d8 zenon_H1f0 zenon_H20c zenon_H26d zenon_H14b zenon_H1fe. % 18.99/19.10 apply (zenon_or_s _ _ zenon_H26f); [ zenon_intro zenon_H194 | zenon_intro zenon_Hba ]. % 18.99/19.10 apply (zenon_L1051_); trivial. % 18.99/19.10 apply (zenon_L185_); trivial. % 18.99/19.10 (* end of lemma zenon_L1052_ *) % 18.99/19.10 assert (zenon_L1053_ : ((~((op (e3) (e0)) = (e2)))\/((op (e3) (e2)) = (e0))) -> ((op (e1) (e2)) = (e3)) -> (((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) (e0)) = (op (e2) (e1)))) -> (((op (e0) (e1)) = (e2))\/(((op (e1) (e1)) = (e2))\/(((op (e2) (e1)) = (e2))\/((op (e3) (e1)) = (e2))))) -> (~((op (e1) (e0)) = (e2))) -> (~((op (e0) (e0)) = (e2))) -> (~((op (e2) (e2)) = (op (e3) (e2)))) -> ((op (e2) (e2)) = (e1)) -> ((~((op (e3) (e1)) = (e2)))\/((op (e3) (e2)) = (e1))) -> False). % 18.99/19.10 do 0 intro. intros zenon_H270 zenon_H16c zenon_H1fe zenon_H26d zenon_H20c zenon_H1f0 zenon_H1d8 zenon_H177 zenon_H80 zenon_H18f zenon_Hf1 zenon_H26f. % 18.99/19.10 apply (zenon_or_s _ _ zenon_H270); [ zenon_intro zenon_H14b | zenon_intro zenon_H61 ]. % 18.99/19.10 apply (zenon_L1052_); trivial. % 18.99/19.10 apply (zenon_L156_); trivial. % 18.99/19.10 (* end of lemma zenon_L1053_ *) % 18.99/19.10 assert (zenon_L1054_ : ((~((op (e2) (e1)) = (e2)))\/((op (e2) (e2)) = (e1))) -> ((~((op (e3) (e1)) = (e2)))\/((op (e3) (e2)) = (e1))) -> (~((op (e2) (e2)) = (op (e3) (e2)))) -> (~((op (e1) (e0)) = (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)) = (e2))) -> (((op (e0) (e0)) = (e2))\/(((op (e1) (e0)) = (e2))\/(((op (e2) (e0)) = (e2))\/((op (e3) (e0)) = (e2))))) -> ((op (e1) (e2)) = (e3)) -> ((~((op (e3) (e0)) = (e2)))\/((op (e3) (e2)) = (e0))) -> (~((op (e0) (e0)) = (e2))) -> (~((op (e0) (e1)) = (e2))) -> (~((op (e0) (e2)) = (e2))) -> (((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)) = (e2))) -> (~((op (e2) (e0)) = (e2))) -> (((op (e0) (e0)) = (e2))\/(((op (e0) (e1)) = (e2))\/(((op (e0) (e2)) = (e2))\/((op (e0) (e3)) = (e2))))) -> False). % 18.99/19.10 do 0 intro. intros zenon_H271 zenon_H26f zenon_H18f zenon_H177 zenon_H1d8 zenon_H1f0 zenon_H20c zenon_H1fe zenon_H16c zenon_H270 zenon_H80 zenon_H26d zenon_H1fd zenon_H1d5 zenon_He2 zenon_H173 zenon_Hef zenon_H183. % 18.99/19.10 apply (zenon_or_s _ _ zenon_H271); [ zenon_intro zenon_H26e | zenon_intro zenon_Hf1 ]. % 18.99/19.10 apply (zenon_L1050_); trivial. % 18.99/19.10 apply (zenon_L1053_); trivial. % 18.99/19.10 (* end of lemma zenon_L1054_ *) % 18.99/19.10 assert (zenon_L1055_ : (((op (e0) (e2)) = (e2))\/(((op (e1) (e2)) = (e2))\/(((op (e2) (e2)) = (e2))\/((op (e3) (e2)) = (e2))))) -> (~((op (e0) (e2)) = (e2))) -> (~((op (e1) (e2)) = (e2))) -> (~((op (e2) (e2)) = (e2))) -> (~((op (e3) (e2)) = (e2))) -> False). % 18.99/19.10 do 0 intro. intros zenon_H172 zenon_H1fd zenon_H114 zenon_H173 zenon_H272. % 18.99/19.10 apply (zenon_or_s _ _ zenon_H172); [ zenon_intro zenon_H150 | zenon_intro zenon_H174 ]. % 18.99/19.10 exact (zenon_H1fd zenon_H150). % 18.99/19.10 apply (zenon_or_s _ _ zenon_H174); [ zenon_intro zenon_H113 | zenon_intro zenon_H175 ]. % 18.99/19.10 exact (zenon_H114 zenon_H113). % 18.99/19.10 apply (zenon_or_s _ _ zenon_H175); [ zenon_intro zenon_H176 | zenon_intro zenon_H151 ]. % 18.99/19.10 exact (zenon_H173 zenon_H176). % 18.99/19.10 exact (zenon_H272 zenon_H151). % 18.99/19.10 (* end of lemma zenon_L1055_ *) % 18.99/19.10 assert (zenon_L1056_ : (((op (e0) (e1)) = (e2))\/(((op (e1) (e1)) = (e2))\/(((op (e2) (e1)) = (e2))\/((op (e3) (e1)) = (e2))))) -> (~((op (e0) (e1)) = (e2))) -> (~((op (e1) (e1)) = (e2))) -> (~((op (e2) (e1)) = (e2))) -> (~((op (e3) (e1)) = (op (e3) (e2)))) -> ((op (e3) (e2)) = (e2)) -> False). % 18.99/19.10 do 0 intro. intros zenon_H1d8 zenon_H26d zenon_H20c zenon_H26e zenon_H1a4 zenon_H151. % 18.99/19.10 apply (zenon_or_s _ _ zenon_H1d8); [ zenon_intro zenon_H10f | zenon_intro zenon_H1d9 ]. % 18.99/19.10 exact (zenon_H26d zenon_H10f). % 18.99/19.10 apply (zenon_or_s _ _ zenon_H1d9); [ zenon_intro zenon_H110 | zenon_intro zenon_H1da ]. % 18.99/19.10 exact (zenon_H20c zenon_H110). % 18.99/19.10 apply (zenon_or_s _ _ zenon_H1da); [ zenon_intro zenon_H1ca | zenon_intro zenon_H14d ]. % 18.99/19.10 exact (zenon_H26e zenon_H1ca). % 18.99/19.10 apply (zenon_L400_); trivial. % 18.99/19.10 (* end of lemma zenon_L1056_ *) % 18.99/19.10 assert (zenon_L1057_ : ((~((op (e3) (e2)) = (e2)))\/((op (e3) (e2)) = (e2))) -> (~((op (e0) (e1)) = (e2))) -> (~((op (e1) (e1)) = (e2))) -> (~((op (e2) (e1)) = (e2))) -> (~((op (e3) (e1)) = (op (e3) (e2)))) -> (((op (e0) (e1)) = (e2))\/(((op (e1) (e1)) = (e2))\/(((op (e2) (e1)) = (e2))\/((op (e3) (e1)) = (e2))))) -> (~((op (e0) (e2)) = (e2))) -> (~((op (e1) (e2)) = (e2))) -> (~((op (e2) (e2)) = (e2))) -> (((op (e0) (e2)) = (e2))\/(((op (e1) (e2)) = (e2))\/(((op (e2) (e2)) = (e2))\/((op (e3) (e2)) = (e2))))) -> False). % 18.99/19.10 do 0 intro. intros zenon_H273 zenon_H26d zenon_H20c zenon_H26e zenon_H1a4 zenon_H1d8 zenon_H1fd zenon_H114 zenon_H173 zenon_H172. % 18.99/19.10 apply (zenon_or_s _ _ zenon_H273); [ zenon_intro zenon_H272 | zenon_intro zenon_H151 ]. % 18.99/19.10 apply (zenon_L1055_); trivial. % 18.99/19.10 apply (zenon_L1056_); trivial. % 18.99/19.10 (* end of lemma zenon_L1057_ *) % 18.99/19.10 assert (zenon_L1058_ : ((~((op (e3) (e0)) = (e2)))\/((op (e3) (e2)) = (e0))) -> ((op (e2) (e2)) = (e0)) -> (((op (e0) (e0)) = (e2))\/(((op (e1) (e0)) = (e2))\/(((op (e2) (e0)) = (e2))\/((op (e3) (e0)) = (e2))))) -> (~((op (e0) (e1)) = (e2))) -> (~((op (e1) (e1)) = (e2))) -> (~((op (e2) (e0)) = (op (e2) (e1)))) -> (((op (e0) (e1)) = (e2))\/(((op (e1) (e1)) = (e2))\/(((op (e2) (e1)) = (e2))\/((op (e3) (e1)) = (e2))))) -> (~((op (e1) (e0)) = (e2))) -> (~((op (e0) (e0)) = (e2))) -> (~((op (e2) (e2)) = (op (e3) (e2)))) -> ((op (e2) (e2)) = (e1)) -> ((~((op (e3) (e1)) = (e2)))\/((op (e3) (e2)) = (e1))) -> False). % 18.99/19.10 do 0 intro. intros zenon_H270 zenon_H2c zenon_H1fe zenon_H26d zenon_H20c zenon_H1f0 zenon_H1d8 zenon_H177 zenon_H80 zenon_H18f zenon_Hf1 zenon_H26f. % 18.99/19.10 apply (zenon_or_s _ _ zenon_H270); [ zenon_intro zenon_H14b | zenon_intro zenon_H61 ]. % 18.99/19.10 apply (zenon_L1052_); trivial. % 18.99/19.10 apply (zenon_L146_); trivial. % 18.99/19.10 (* end of lemma zenon_L1058_ *) % 18.99/19.10 assert (zenon_L1059_ : (((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)) = (e2))) -> (~((op (e0) (e2)) = (e2))) -> (~((op (e0) (e3)) = (e2))) -> False). % 18.99/19.10 do 0 intro. intros zenon_H183 zenon_H7c zenon_H7a zenon_H26d zenon_H1fd zenon_H12e. % 18.99/19.10 apply (zenon_or_s _ _ zenon_H183); [ zenon_intro zenon_H7b | zenon_intro zenon_H186 ]. % 18.99/19.10 apply (zenon_L26_); trivial. % 18.99/19.10 apply (zenon_or_s _ _ zenon_H186); [ zenon_intro zenon_H10f | zenon_intro zenon_H187 ]. % 18.99/19.10 exact (zenon_H26d zenon_H10f). % 18.99/19.10 apply (zenon_or_s _ _ zenon_H187); [ zenon_intro zenon_H150 | zenon_intro zenon_Hcd ]. % 18.99/19.10 exact (zenon_H1fd zenon_H150). % 18.99/19.10 exact (zenon_H12e zenon_Hcd). % 18.99/19.10 (* end of lemma zenon_L1059_ *) % 18.99/19.10 assert (zenon_L1060_ : (((op (e0) (e0)) = (e2))\/(((op (e0) (e1)) = (e2))\/(((op (e0) (e2)) = (e2))\/((op (e0) (e3)) = (e2))))) -> (~((op (e0) (e0)) = (e2))) -> (~((op (e0) (e1)) = (e2))) -> (~((op (e0) (e2)) = (e2))) -> ((op (e0) (e3)) = (e1)) -> (~((e1) = (e2))) -> False). % 18.99/19.10 do 0 intro. intros zenon_H183 zenon_H80 zenon_H26d zenon_H1fd zenon_Hc3 zenon_H7c. % 18.99/19.10 apply (zenon_or_s _ _ zenon_H183); [ zenon_intro zenon_H7b | zenon_intro zenon_H186 ]. % 18.99/19.10 exact (zenon_H80 zenon_H7b). % 18.99/19.10 apply (zenon_or_s _ _ zenon_H186); [ zenon_intro zenon_H10f | zenon_intro zenon_H187 ]. % 18.99/19.10 exact (zenon_H26d zenon_H10f). % 18.99/19.10 apply (zenon_or_s _ _ zenon_H187); [ zenon_intro zenon_H150 | zenon_intro zenon_Hcd ]. % 18.99/19.10 exact (zenon_H1fd zenon_H150). % 18.99/19.10 apply (zenon_L82_); trivial. % 18.99/19.10 (* end of lemma zenon_L1060_ *) % 18.99/19.10 assert (zenon_L1061_ : (((op (e0) (e0)) = (e2))\/(((op (e0) (e1)) = (e2))\/(((op (e0) (e2)) = (e2))\/((op (e0) (e3)) = (e2))))) -> (~((op (e0) (e0)) = (e2))) -> (~((op (e0) (e1)) = (e2))) -> (~((op (e0) (e2)) = (e2))) -> ((op (e0) (e3)) = (e0)) -> (~((e0) = (e2))) -> False). % 18.99/19.10 do 0 intro. intros zenon_H183 zenon_H80 zenon_H26d zenon_H1fd zenon_H1e zenon_H149. % 18.99/19.10 apply (zenon_or_s _ _ zenon_H183); [ zenon_intro zenon_H7b | zenon_intro zenon_H186 ]. % 18.99/19.10 exact (zenon_H80 zenon_H7b). % 18.99/19.10 apply (zenon_or_s _ _ zenon_H186); [ zenon_intro zenon_H10f | zenon_intro zenon_H187 ]. % 18.99/19.10 exact (zenon_H26d zenon_H10f). % 18.99/19.10 apply (zenon_or_s _ _ zenon_H187); [ zenon_intro zenon_H150 | zenon_intro zenon_Hcd ]. % 18.99/19.10 exact (zenon_H1fd zenon_H150). % 18.99/19.10 apply (zenon_L428_); trivial. % 18.99/19.10 (* end of lemma zenon_L1061_ *) % 18.99/19.10 assert (zenon_L1062_ : (((op (e2) (e0)) = (e2))\/(((op (e2) (e1)) = (e2))\/(((op (e2) (e2)) = (e2))\/((op (e2) (e3)) = (e2))))) -> (~((op (e2) (e0)) = (e2))) -> (~((op (e2) (e1)) = (e2))) -> (~((op (e2) (e2)) = (e2))) -> (~((op (e2) (e3)) = (e2))) -> False). % 18.99/19.10 do 0 intro. intros zenon_H1d5 zenon_Hef zenon_H26e zenon_H173 zenon_H274. % 18.99/19.10 apply (zenon_or_s _ _ zenon_H1d5); [ zenon_intro zenon_Hee | zenon_intro zenon_H1d6 ]. % 18.99/19.10 exact (zenon_Hef zenon_Hee). % 18.99/19.10 apply (zenon_or_s _ _ zenon_H1d6); [ zenon_intro zenon_H1ca | zenon_intro zenon_H1d7 ]. % 18.99/19.10 exact (zenon_H26e zenon_H1ca). % 18.99/19.10 apply (zenon_or_s _ _ zenon_H1d7); [ zenon_intro zenon_H176 | zenon_intro zenon_H11d ]. % 18.99/19.10 exact (zenon_H173 zenon_H176). % 18.99/19.10 exact (zenon_H274 zenon_H11d). % 18.99/19.10 (* end of lemma zenon_L1062_ *) % 18.99/19.10 assert (zenon_L1063_ : (((op (e0) (e1)) = (e2))\/(((op (e1) (e1)) = (e2))\/(((op (e2) (e1)) = (e2))\/((op (e3) (e1)) = (e2))))) -> (~((op (e0) (e1)) = (e2))) -> (~((op (e1) (e1)) = (e2))) -> (~((op (e2) (e1)) = (e2))) -> (~((op (e3) (e1)) = (e2))) -> False). % 18.99/19.10 do 0 intro. intros zenon_H1d8 zenon_H26d zenon_H20c zenon_H26e zenon_H194. % 18.99/19.10 apply (zenon_or_s _ _ zenon_H1d8); [ zenon_intro zenon_H10f | zenon_intro zenon_H1d9 ]. % 18.99/19.10 exact (zenon_H26d zenon_H10f). % 18.99/19.10 apply (zenon_or_s _ _ zenon_H1d9); [ zenon_intro zenon_H110 | zenon_intro zenon_H1da ]. % 18.99/19.10 exact (zenon_H20c zenon_H110). % 18.99/19.10 apply (zenon_or_s _ _ zenon_H1da); [ zenon_intro zenon_H1ca | zenon_intro zenon_H14d ]. % 18.99/19.10 exact (zenon_H26e zenon_H1ca). % 18.99/19.10 exact (zenon_H194 zenon_H14d). % 18.99/19.10 (* end of lemma zenon_L1063_ *) % 18.99/19.10 assert (zenon_L1064_ : (((op (e1) (e0)) = (e0))\/(((op (e1) (e0)) = (e1))\/(((op (e1) (e0)) = (e2))\/((op (e1) (e0)) = (e3))))) -> (~((op (e1) (e0)) = (op (e3) (e0)))) -> ((op (e3) (e0)) = (e0)) -> (~((op (e1) (e0)) = (op (e2) (e0)))) -> (~((op (e1) (e0)) = (e2))) -> ((op (e2) (e0)) = (e1)) -> ((op (e0) (e0)) = (e2)) -> False). % 18.99/19.10 do 0 intro. intros zenon_H25e zenon_H1fa zenon_H44 zenon_H201 zenon_H177 zenon_Hed zenon_H7b. % 18.99/19.10 apply (zenon_or_s _ _ zenon_H25e); [ zenon_intro zenon_H27 | zenon_intro zenon_H25f ]. % 18.99/19.10 apply (zenon_L312_); trivial. % 18.99/19.10 apply (zenon_or_s _ _ zenon_H25f); [ zenon_intro zenon_H9d | zenon_intro zenon_H260 ]. % 18.99/19.10 apply (zenon_L413_); trivial. % 18.99/19.10 apply (zenon_or_s _ _ zenon_H260); [ zenon_intro zenon_H86 | zenon_intro zenon_H9e ]. % 18.99/19.10 exact (zenon_H177 zenon_H86). % 18.99/19.10 apply (zenon_L491_); trivial. % 18.99/19.10 (* end of lemma zenon_L1064_ *) % 18.99/19.10 assert (zenon_L1065_ : (((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 (e1) (e3)) = (op (e2) (e3)))) -> ((op (e1) (e3)) = (e2)) -> False). % 18.99/19.10 do 0 intro. intros zenon_H1d5 zenon_Hef zenon_H26e zenon_H173 zenon_Hdb zenon_Hd7. % 18.99/19.10 apply (zenon_or_s _ _ zenon_H1d5); [ zenon_intro zenon_Hee | zenon_intro zenon_H1d6 ]. % 18.99/19.10 exact (zenon_Hef zenon_Hee). % 18.99/19.10 apply (zenon_or_s _ _ zenon_H1d6); [ zenon_intro zenon_H1ca | zenon_intro zenon_H1d7 ]. % 18.99/19.10 exact (zenon_H26e zenon_H1ca). % 18.99/19.10 apply (zenon_or_s _ _ zenon_H1d7); [ zenon_intro zenon_H176 | zenon_intro zenon_H11d ]. % 18.99/19.10 exact (zenon_H173 zenon_H176). % 18.99/19.10 apply (zenon_L366_); trivial. % 18.99/19.10 (* end of lemma zenon_L1065_ *) % 18.99/19.10 assert (zenon_L1066_ : (((op (e1) (e0)) = (e2))\/(((op (e1) (e1)) = (e2))\/(((op (e1) (e2)) = (e2))\/((op (e1) (e3)) = (e2))))) -> (~((op (e1) (e0)) = (e2))) -> (~((e0) = (e2))) -> ((op (e1) (e1)) = (e0)) -> (~((op (e1) (e2)) = (e2))) -> (((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 (e1) (e3)) = (op (e2) (e3)))) -> False). % 18.99/19.10 do 0 intro. intros zenon_H18c zenon_H177 zenon_H149 zenon_H29 zenon_H114 zenon_H1d5 zenon_Hef zenon_H26e zenon_H173 zenon_Hdb. % 18.99/19.10 apply (zenon_or_s _ _ zenon_H18c); [ zenon_intro zenon_H86 | zenon_intro zenon_H18d ]. % 18.99/19.10 exact (zenon_H177 zenon_H86). % 18.99/19.10 apply (zenon_or_s _ _ zenon_H18d); [ zenon_intro zenon_H110 | zenon_intro zenon_H18e ]. % 18.99/19.10 apply (zenon_L354_); trivial. % 18.99/19.10 apply (zenon_or_s _ _ zenon_H18e); [ zenon_intro zenon_H113 | zenon_intro zenon_Hd7 ]. % 18.99/19.10 exact (zenon_H114 zenon_H113). % 18.99/19.10 apply (zenon_L1065_); trivial. % 18.99/19.10 (* end of lemma zenon_L1066_ *) % 18.99/19.10 assert (zenon_L1067_ : (((op (e3) (e3)) = (e0))\/(((op (e3) (e3)) = (e1))\/(((op (e3) (e3)) = (e2))\/((op (e3) (e3)) = (e3))))) -> (~((op (e3) (e1)) = (op (e3) (e3)))) -> ((op (e3) (e1)) = (e0)) -> (~((op (e3) (e0)) = (op (e3) (e3)))) -> ((op (e3) (e0)) = (e1)) -> (~((op (e3) (e3)) = (e2))) -> (~((op (e3) (e3)) = (e3))) -> False). % 18.99/19.10 do 0 intro. intros zenon_H101 zenon_H130 zenon_H1b1 zenon_H71 zenon_Hac zenon_Hf7 zenon_H102. % 18.99/19.10 apply (zenon_or_s _ _ zenon_H101); [ zenon_intro zenon_H60 | zenon_intro zenon_H103 ]. % 18.99/19.10 apply (zenon_L244_); trivial. % 18.99/19.10 apply (zenon_or_s _ _ zenon_H103); [ zenon_intro zenon_Hc4 | zenon_intro zenon_H104 ]. % 18.99/19.10 apply (zenon_L189_); trivial. % 18.99/19.10 apply (zenon_or_s _ _ zenon_H104); [ zenon_intro zenon_Hf6 | zenon_intro zenon_H105 ]. % 18.99/19.10 exact (zenon_Hf7 zenon_Hf6). % 18.99/19.10 exact (zenon_H102 zenon_H105). % 18.99/19.10 (* end of lemma zenon_L1067_ *) % 18.99/19.10 assert (zenon_L1068_ : (((op (e3) (e3)) = (e0))\/(((op (e3) (e3)) = (e1))\/(((op (e3) (e3)) = (e2))\/((op (e3) (e3)) = (e3))))) -> ((op (e3) (e2)) = (e0)) -> ((op (e0) (e3)) = (e1)) -> (~((op (e0) (e3)) = (op (e3) (e3)))) -> (~((op (e3) (e2)) = (op (e3) (e3)))) -> ((op (e3) (e2)) = (e2)) -> (~((op (e3) (e3)) = (e3))) -> False). % 18.99/19.10 do 0 intro. intros zenon_H101 zenon_H61 zenon_Hc3 zenon_Hc2 zenon_H62 zenon_H151 zenon_H102. % 18.99/19.10 apply (zenon_or_s _ _ zenon_H101); [ zenon_intro zenon_H60 | zenon_intro zenon_H103 ]. % 18.99/19.10 apply (zenon_L15_); trivial. % 18.99/19.10 apply (zenon_or_s _ _ zenon_H103); [ zenon_intro zenon_Hc4 | zenon_intro zenon_H104 ]. % 18.99/19.10 apply (zenon_L46_); trivial. % 18.99/19.10 apply (zenon_or_s _ _ zenon_H104); [ zenon_intro zenon_Hf6 | zenon_intro zenon_H105 ]. % 18.99/19.10 apply (zenon_L119_); trivial. % 18.99/19.10 exact (zenon_H102 zenon_H105). % 18.99/19.11 (* end of lemma zenon_L1068_ *) % 18.99/19.11 assert (zenon_L1069_ : (((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) (e0)) = (op (e3) (e3)))) -> ((op (e3) (e0)) = (e1)) -> ((op (e2) (e3)) = (e1)) -> ((op (e1) (e3)) = (e0)) -> (~((op (e3) (e3)) = (e3))) -> False). % 18.99/19.11 do 0 intro. intros zenon_H101 zenon_H62 zenon_H61 zenon_H71 zenon_Hac zenon_Hf4 zenon_H1f zenon_H102. % 18.99/19.11 apply (zenon_or_s _ _ zenon_H101); [ zenon_intro zenon_H60 | zenon_intro zenon_H103 ]. % 18.99/19.11 apply (zenon_L15_); trivial. % 18.99/19.11 apply (zenon_or_s _ _ zenon_H103); [ zenon_intro zenon_Hc4 | zenon_intro zenon_H104 ]. % 18.99/19.11 apply (zenon_L189_); trivial. % 18.99/19.11 apply (zenon_or_s _ _ zenon_H104); [ zenon_intro zenon_Hf6 | zenon_intro zenon_H105 ]. % 18.99/19.11 apply (zenon_L63_); trivial. % 18.99/19.11 exact (zenon_H102 zenon_H105). % 18.99/19.11 (* end of lemma zenon_L1069_ *) % 18.99/19.11 assert (zenon_L1070_ : (((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 (e3) (e0)) = (op (e3) (e3)))) -> ((op (e3) (e0)) = (e1)) -> (((op (e3) (e3)) = (e0))\/(((op (e3) (e3)) = (e1))\/(((op (e3) (e3)) = (e2))\/((op (e3) (e3)) = (e3))))) -> (~((op (e3) (e3)) = (e3))) -> ((op (e1) (e2)) = (e1)) -> (~((op (e1) (e2)) = (op (e1) (e3)))) -> (~((op (e0) (e3)) = (op (e3) (e3)))) -> ((op (e3) (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) (e1)) = (e0)) -> ((op (e3) (e2)) = (e0)) -> (~((op (e3) (e2)) = (op (e3) (e3)))) -> False). % 18.99/19.11 do 0 intro. intros zenon_H67 zenon_H208 zenon_H48 zenon_H71 zenon_Hac zenon_H101 zenon_H102 zenon_Hf0 zenon_H124 zenon_Hc2 zenon_H151 zenon_H133 zenon_H1c7 zenon_H36 zenon_H61 zenon_H62. % 18.99/19.11 apply (zenon_or_s _ _ zenon_H67); [ zenon_intro zenon_H1e | zenon_intro zenon_H68 ]. % 18.99/19.11 apply (zenon_L336_); trivial. % 18.99/19.11 apply (zenon_or_s _ _ zenon_H68); [ zenon_intro zenon_H1f | zenon_intro zenon_H69 ]. % 18.99/19.11 apply (zenon_or_s _ _ zenon_H133); [ zenon_intro zenon_Hc3 | zenon_intro zenon_H134 ]. % 18.99/19.11 apply (zenon_L1068_); trivial. % 18.99/19.11 apply (zenon_or_s _ _ zenon_H134); [ zenon_intro zenon_Hd6 | zenon_intro zenon_H135 ]. % 18.99/19.11 apply (zenon_L78_); trivial. % 18.99/19.11 apply (zenon_or_s _ _ zenon_H135); [ zenon_intro zenon_Hf4 | zenon_intro zenon_Hc4 ]. % 18.99/19.11 apply (zenon_L1069_); trivial. % 18.99/19.11 apply (zenon_L189_); trivial. % 18.99/19.11 apply (zenon_or_s _ _ zenon_H69); [ zenon_intro zenon_H37 | zenon_intro zenon_H60 ]. % 18.99/19.11 apply (zenon_L640_); trivial. % 18.99/19.11 apply (zenon_L15_); trivial. % 18.99/19.11 (* end of lemma zenon_L1070_ *) % 18.99/19.11 assert (zenon_L1071_ : (((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)) = (e0)) -> ((op (e2) (e1)) = (e1)) -> (~((op (e0) (e1)) = (op (e2) (e1)))) -> (~((op (e0) (e1)) = (e2))) -> ((op (e2) (e1)) = (e0)) -> ((op (e1) (e1)) = (e2)) -> False). % 18.99/19.11 do 0 intro. intros zenon_H212 zenon_H4a zenon_H48 zenon_Ha5 zenon_H17e zenon_H26d zenon_H36 zenon_H110. % 18.99/19.11 apply (zenon_or_s _ _ zenon_H212); [ zenon_intro zenon_H49 | zenon_intro zenon_H213 ]. % 18.99/19.11 apply (zenon_L9_); trivial. % 18.99/19.11 apply (zenon_or_s _ _ zenon_H213); [ zenon_intro zenon_Ha0 | zenon_intro zenon_H214 ]. % 18.99/19.11 apply (zenon_L357_); trivial. % 18.99/19.11 apply (zenon_or_s _ _ zenon_H214); [ zenon_intro zenon_H10f | zenon_intro zenon_H99 ]. % 18.99/19.11 exact (zenon_H26d zenon_H10f). % 18.99/19.11 apply (zenon_L552_); trivial. % 18.99/19.11 (* end of lemma zenon_L1071_ *) % 18.99/19.11 assert (zenon_L1072_ : (((op (e1) (e0)) = (e2))\/(((op (e1) (e1)) = (e2))\/(((op (e1) (e2)) = (e2))\/((op (e1) (e3)) = (e2))))) -> (~((op (e1) (e0)) = (e2))) -> ((op (e2) (e1)) = (e0)) -> (~((op (e0) (e1)) = (e2))) -> (~((op (e0) (e1)) = (op (e2) (e1)))) -> ((op (e2) (e1)) = (e1)) -> ((op (e0) (e2)) = (e0)) -> (~((op (e0) (e1)) = (op (e0) (e2)))) -> (((op (e0) (e1)) = (e0))\/(((op (e0) (e1)) = (e1))\/(((op (e0) (e1)) = (e2))\/((op (e0) (e1)) = (e3))))) -> (~((op (e1) (e2)) = (e2))) -> (((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 (e1) (e3)) = (op (e2) (e3)))) -> False). % 18.99/19.11 do 0 intro. intros zenon_H18c zenon_H177 zenon_H36 zenon_H26d zenon_H17e zenon_Ha5 zenon_H48 zenon_H4a zenon_H212 zenon_H114 zenon_H1d5 zenon_Hef zenon_H26e zenon_H173 zenon_Hdb. % 18.99/19.11 apply (zenon_or_s _ _ zenon_H18c); [ zenon_intro zenon_H86 | zenon_intro zenon_H18d ]. % 18.99/19.11 exact (zenon_H177 zenon_H86). % 18.99/19.11 apply (zenon_or_s _ _ zenon_H18d); [ zenon_intro zenon_H110 | zenon_intro zenon_H18e ]. % 18.99/19.11 apply (zenon_L1071_); trivial. % 18.99/19.11 apply (zenon_or_s _ _ zenon_H18e); [ zenon_intro zenon_H113 | zenon_intro zenon_Hd7 ]. % 18.99/19.11 exact (zenon_H114 zenon_H113). % 18.99/19.11 apply (zenon_L1065_); trivial. % 18.99/19.11 (* end of lemma zenon_L1072_ *) % 18.99/19.11 assert (zenon_L1073_ : (((op (e0) (e1)) = (e2))\/(((op (e1) (e1)) = (e2))\/(((op (e2) (e1)) = (e2))\/((op (e3) (e1)) = (e2))))) -> (~((e2) = (e3))) -> ((op (e2) (e1)) = (e0)) -> ((op (e0) (e1)) = (e3)) -> (~((op (e2) (e1)) = (op (e2) (e3)))) -> ((op (e2) (e3)) = (e2)) -> ((op (e3) (e1)) = (e1)) -> (~((e1) = (e2))) -> False). % 18.99/19.11 do 0 intro. intros zenon_H1d8 zenon_H12b zenon_H36 zenon_H99 zenon_H1c7 zenon_H11d zenon_Hae zenon_H7c. % 18.99/19.11 apply (zenon_or_s _ _ zenon_H1d8); [ zenon_intro zenon_H10f | zenon_intro zenon_H1d9 ]. % 18.99/19.11 apply (zenon_L175_); trivial. % 18.99/19.11 apply (zenon_or_s _ _ zenon_H1d9); [ zenon_intro zenon_H110 | zenon_intro zenon_H1da ]. % 18.99/19.11 apply (zenon_L552_); trivial. % 18.99/19.11 apply (zenon_or_s _ _ zenon_H1da); [ zenon_intro zenon_H1ca | zenon_intro zenon_H14d ]. % 18.99/19.11 apply (zenon_L224_); trivial. % 18.99/19.11 apply (zenon_L152_); trivial. % 18.99/19.11 (* end of lemma zenon_L1073_ *) % 18.99/19.11 assert (zenon_L1074_ : (((op (e0) (e1)) = (e0))\/(((op (e0) (e1)) = (e1))\/(((op (e0) (e1)) = (e2))\/((op (e0) (e1)) = (e3))))) -> (~((op (e0) (e1)) = (op (e2) (e1)))) -> (~((op (e0) (e1)) = (op (e3) (e1)))) -> (~((op (e0) (e1)) = (e2))) -> (((op (e0) (e1)) = (e2))\/(((op (e1) (e1)) = (e2))\/(((op (e2) (e1)) = (e2))\/((op (e3) (e1)) = (e2))))) -> (~((e2) = (e3))) -> ((op (e2) (e1)) = (e0)) -> (~((op (e2) (e1)) = (op (e2) (e3)))) -> ((op (e2) (e3)) = (e2)) -> ((op (e3) (e1)) = (e1)) -> (~((e1) = (e2))) -> False). % 18.99/19.11 do 0 intro. intros zenon_H212 zenon_H17e zenon_H210 zenon_H26d zenon_H1d8 zenon_H12b zenon_H36 zenon_H1c7 zenon_H11d zenon_Hae zenon_H7c. % 18.99/19.11 apply (zenon_or_s _ _ zenon_H212); [ zenon_intro zenon_H49 | zenon_intro zenon_H213 ]. % 18.99/19.11 apply (zenon_L128_); trivial. % 18.99/19.11 apply (zenon_or_s _ _ zenon_H213); [ zenon_intro zenon_Ha0 | zenon_intro zenon_H214 ]. % 18.99/19.11 apply (zenon_L363_); trivial. % 18.99/19.11 apply (zenon_or_s _ _ zenon_H214); [ zenon_intro zenon_H10f | zenon_intro zenon_H99 ]. % 18.99/19.11 exact (zenon_H26d zenon_H10f). % 18.99/19.11 apply (zenon_L1073_); trivial. % 18.99/19.11 (* end of lemma zenon_L1074_ *) % 18.99/19.11 assert (zenon_L1075_ : (((op (e2) (e0)) = (e2))\/(((op (e2) (e1)) = (e2))\/(((op (e2) (e2)) = (e2))\/((op (e2) (e3)) = (e2))))) -> (~((op (e2) (e0)) = (e2))) -> (~((op (e2) (e1)) = (e2))) -> (~((op (e2) (e2)) = (e2))) -> (((op (e0) (e1)) = (e0))\/(((op (e0) (e1)) = (e1))\/(((op (e0) (e1)) = (e2))\/((op (e0) (e1)) = (e3))))) -> (~((op (e0) (e1)) = (op (e2) (e1)))) -> (~((op (e0) (e1)) = (op (e3) (e1)))) -> (~((op (e0) (e1)) = (e2))) -> (((op (e0) (e1)) = (e2))\/(((op (e1) (e1)) = (e2))\/(((op (e2) (e1)) = (e2))\/((op (e3) (e1)) = (e2))))) -> (~((e2) = (e3))) -> ((op (e2) (e1)) = (e0)) -> (~((op (e2) (e1)) = (op (e2) (e3)))) -> ((op (e3) (e1)) = (e1)) -> (~((e1) = (e2))) -> False). % 18.99/19.11 do 0 intro. intros zenon_H1d5 zenon_Hef zenon_H26e zenon_H173 zenon_H212 zenon_H17e zenon_H210 zenon_H26d zenon_H1d8 zenon_H12b zenon_H36 zenon_H1c7 zenon_Hae zenon_H7c. % 18.99/19.11 apply (zenon_or_s _ _ zenon_H1d5); [ zenon_intro zenon_Hee | zenon_intro zenon_H1d6 ]. % 18.99/19.11 exact (zenon_Hef zenon_Hee). % 18.99/19.11 apply (zenon_or_s _ _ zenon_H1d6); [ zenon_intro zenon_H1ca | zenon_intro zenon_H1d7 ]. % 18.99/19.11 exact (zenon_H26e zenon_H1ca). % 18.99/19.11 apply (zenon_or_s _ _ zenon_H1d7); [ zenon_intro zenon_H176 | zenon_intro zenon_H11d ]. % 18.99/19.11 exact (zenon_H173 zenon_H176). % 18.99/19.11 apply (zenon_L1074_); trivial. % 18.99/19.11 (* end of lemma zenon_L1075_ *) % 18.99/19.11 assert (zenon_L1076_ : (((op (e0) (e1)) = (e1))\/(((op (e1) (e1)) = (e1))\/(((op (e2) (e1)) = (e1))\/((op (e3) (e1)) = (e1))))) -> (~((op (e0) (e1)) = (op (e0) (e3)))) -> ((op (e0) (e3)) = (e1)) -> (~((op (e1) (e1)) = (e1))) -> (~((op (e1) (e3)) = (op (e2) (e3)))) -> (~((op (e1) (e2)) = (e2))) -> (~((op (e0) (e1)) = (op (e0) (e2)))) -> ((op (e0) (e2)) = (e0)) -> (~((op (e1) (e0)) = (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 (e2) (e0)) = (e2))) -> (~((op (e2) (e1)) = (e2))) -> (~((op (e2) (e2)) = (e2))) -> (((op (e0) (e1)) = (e0))\/(((op (e0) (e1)) = (e1))\/(((op (e0) (e1)) = (e2))\/((op (e0) (e1)) = (e3))))) -> (~((op (e0) (e1)) = (op (e2) (e1)))) -> (~((op (e0) (e1)) = (op (e3) (e1)))) -> (~((op (e0) (e1)) = (e2))) -> (((op (e0) (e1)) = (e2))\/(((op (e1) (e1)) = (e2))\/(((op (e2) (e1)) = (e2))\/((op (e3) (e1)) = (e2))))) -> (~((e2) = (e3))) -> ((op (e2) (e1)) = (e0)) -> (~((op (e2) (e1)) = (op (e2) (e3)))) -> (~((e1) = (e2))) -> False). % 18.99/19.11 do 0 intro. intros zenon_H109 zenon_H54 zenon_Hc3 zenon_H10a zenon_Hdb zenon_H114 zenon_H4a zenon_H48 zenon_H177 zenon_H18c zenon_H1d5 zenon_Hef zenon_H26e zenon_H173 zenon_H212 zenon_H17e zenon_H210 zenon_H26d zenon_H1d8 zenon_H12b zenon_H36 zenon_H1c7 zenon_H7c. % 18.99/19.11 apply (zenon_or_s _ _ zenon_H109); [ zenon_intro zenon_Ha0 | zenon_intro zenon_H10b ]. % 18.99/19.11 apply (zenon_L359_); trivial. % 18.99/19.11 apply (zenon_or_s _ _ zenon_H10b); [ zenon_intro zenon_H10d | zenon_intro zenon_H10c ]. % 18.99/19.11 exact (zenon_H10a zenon_H10d). % 18.99/19.11 apply (zenon_or_s _ _ zenon_H10c); [ zenon_intro zenon_Ha5 | zenon_intro zenon_Hae ]. % 18.99/19.11 apply (zenon_L1072_); trivial. % 18.99/19.11 apply (zenon_L1075_); trivial. % 18.99/19.11 (* end of lemma zenon_L1076_ *) % 18.99/19.11 assert (zenon_L1077_ : (((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) (e3)) = (e0))\/(((op (e3) (e3)) = (e1))\/(((op (e3) (e3)) = (e2))\/((op (e3) (e3)) = (e3))))) -> (~((op (e3) (e1)) = (op (e3) (e3)))) -> ((op (e3) (e1)) = (e0)) -> ((op (e0) (e3)) = (e1)) -> (~((op (e0) (e3)) = (op (e3) (e3)))) -> (~((op (e2) (e3)) = (op (e3) (e3)))) -> (~((op (e3) (e3)) = (e3))) -> False). % 18.99/19.11 do 0 intro. intros zenon_H1d5 zenon_Hef zenon_H26e zenon_H173 zenon_H101 zenon_H130 zenon_H1b1 zenon_Hc3 zenon_Hc2 zenon_Hf3 zenon_H102. % 18.99/19.11 apply (zenon_or_s _ _ zenon_H1d5); [ zenon_intro zenon_Hee | zenon_intro zenon_H1d6 ]. % 18.99/19.11 exact (zenon_Hef zenon_Hee). % 18.99/19.11 apply (zenon_or_s _ _ zenon_H1d6); [ zenon_intro zenon_H1ca | zenon_intro zenon_H1d7 ]. % 18.99/19.11 exact (zenon_H26e zenon_H1ca). % 18.99/19.11 apply (zenon_or_s _ _ zenon_H1d7); [ zenon_intro zenon_H176 | zenon_intro zenon_H11d ]. % 18.99/19.11 exact (zenon_H173 zenon_H176). % 18.99/19.11 apply (zenon_L245_); trivial. % 18.99/19.11 (* end of lemma zenon_L1077_ *) % 18.99/19.11 assert (zenon_L1078_ : (((op (e0) (e1)) = (e0))\/(((op (e1) (e1)) = (e0))\/(((op (e2) (e1)) = (e0))\/((op (e3) (e1)) = (e0))))) -> ((op (e1) (e0)) = (e0)) -> (~((op (e1) (e0)) = (op (e1) (e1)))) -> (~((e1) = (e2))) -> (~((op (e2) (e1)) = (op (e2) (e3)))) -> (~((e2) = (e3))) -> (((op (e0) (e1)) = (e2))\/(((op (e1) (e1)) = (e2))\/(((op (e2) (e1)) = (e2))\/((op (e3) (e1)) = (e2))))) -> (~((op (e0) (e1)) = (e2))) -> (~((op (e0) (e1)) = (op (e3) (e1)))) -> (~((op (e0) (e1)) = (op (e2) (e1)))) -> (((op (e0) (e1)) = (e0))\/(((op (e0) (e1)) = (e1))\/(((op (e0) (e1)) = (e2))\/((op (e0) (e1)) = (e3))))) -> (((op (e1) (e0)) = (e2))\/(((op (e1) (e1)) = (e2))\/(((op (e1) (e2)) = (e2))\/((op (e1) (e3)) = (e2))))) -> (~((op (e1) (e0)) = (e2))) -> ((op (e0) (e2)) = (e0)) -> (~((op (e0) (e1)) = (op (e0) (e2)))) -> (~((op (e1) (e2)) = (e2))) -> (~((op (e1) (e3)) = (op (e2) (e3)))) -> (~((op (e1) (e1)) = (e1))) -> (~((op (e0) (e1)) = (op (e0) (e3)))) -> (((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) (e0)) = (e2))) -> (~((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 (e3) (e1)) = (op (e3) (e3)))) -> ((op (e0) (e3)) = (e1)) -> (~((op (e0) (e3)) = (op (e3) (e3)))) -> (~((op (e2) (e3)) = (op (e3) (e3)))) -> (~((op (e3) (e3)) = (e3))) -> False). % 18.99/19.11 do 0 intro. intros zenon_H245 zenon_H27 zenon_H45 zenon_H7c zenon_H1c7 zenon_H12b zenon_H1d8 zenon_H26d zenon_H210 zenon_H17e zenon_H212 zenon_H18c zenon_H177 zenon_H48 zenon_H4a zenon_H114 zenon_Hdb zenon_H10a zenon_H54 zenon_H109 zenon_H1d5 zenon_Hef zenon_H26e zenon_H173 zenon_H101 zenon_H130 zenon_Hc3 zenon_Hc2 zenon_Hf3 zenon_H102. % 18.99/19.11 apply (zenon_or_s _ _ zenon_H245); [ zenon_intro zenon_H49 | zenon_intro zenon_H246 ]. % 18.99/19.11 apply (zenon_L9_); trivial. % 18.99/19.11 apply (zenon_or_s _ _ zenon_H246); [ zenon_intro zenon_H29 | zenon_intro zenon_H247 ]. % 18.99/19.11 apply (zenon_L8_); trivial. % 18.99/19.11 apply (zenon_or_s _ _ zenon_H247); [ zenon_intro zenon_H36 | zenon_intro zenon_H1b1 ]. % 18.99/19.11 apply (zenon_L1076_); trivial. % 18.99/19.11 apply (zenon_L1077_); trivial. % 18.99/19.11 (* end of lemma zenon_L1078_ *) % 18.99/19.11 assert (zenon_L1079_ : (((op (e1) (e3)) = (e0))\/(((op (e1) (e3)) = (e1))\/(((op (e1) (e3)) = (e2))\/((op (e1) (e3)) = (e3))))) -> ((op (e3) (e3)) = (e0)) -> (~((op (e1) (e3)) = (op (e3) (e3)))) -> ((op (e2) (e3)) = (e1)) -> (~((op (e1) (e3)) = (op (e2) (e3)))) -> (~((op (e1) (e3)) = (e2))) -> (~((op (e0) (e3)) = (op (e1) (e3)))) -> ((op (e0) (e3)) = (e3)) -> False). % 18.99/19.11 do 0 intro. intros zenon_Hdf zenon_H60 zenon_Hd5 zenon_Hf4 zenon_Hdb zenon_H14c zenon_H1d zenon_He3. % 18.99/19.11 apply (zenon_or_s _ _ zenon_Hdf); [ zenon_intro zenon_H1f | zenon_intro zenon_He0 ]. % 18.99/19.11 apply (zenon_L136_); trivial. % 18.99/19.11 apply (zenon_or_s _ _ zenon_He0); [ zenon_intro zenon_Hd6 | zenon_intro zenon_He1 ]. % 18.99/19.11 apply (zenon_L126_); trivial. % 18.99/19.11 apply (zenon_or_s _ _ zenon_He1); [ zenon_intro zenon_Hd7 | zenon_intro zenon_Hdc ]. % 18.99/19.11 exact (zenon_H14c zenon_Hd7). % 18.99/19.11 apply (zenon_L117_); trivial. % 18.99/19.11 (* end of lemma zenon_L1079_ *) % 18.99/19.11 assert (zenon_L1080_ : (((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 (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 (e2) (e2)) = (e2))) -> (~((op (e2) (e1)) = (e2))) -> (~((op (e2) (e0)) = (e2))) -> (((op (e2) (e0)) = (e2))\/(((op (e2) (e1)) = (e2))\/(((op (e2) (e2)) = (e2))\/((op (e2) (e3)) = (e2))))) -> (((op (e0) (e1)) = (e1))\/(((op (e1) (e1)) = (e1))\/(((op (e2) (e1)) = (e1))\/((op (e3) (e1)) = (e1))))) -> (~((op (e0) (e1)) = (op (e0) (e3)))) -> (~((op (e1) (e1)) = (e1))) -> (~((op (e1) (e2)) = (e2))) -> (~((op (e0) (e1)) = (op (e0) (e2)))) -> ((op (e0) (e2)) = (e0)) -> (~((op (e1) (e0)) = (e2))) -> (((op (e1) (e0)) = (e2))\/(((op (e1) (e1)) = (e2))\/(((op (e1) (e2)) = (e2))\/((op (e1) (e3)) = (e2))))) -> (((op (e0) (e1)) = (e0))\/(((op (e0) (e1)) = (e1))\/(((op (e0) (e1)) = (e2))\/((op (e0) (e1)) = (e3))))) -> (~((op (e0) (e1)) = (op (e2) (e1)))) -> (~((op (e0) (e1)) = (op (e3) (e1)))) -> (~((op (e0) (e1)) = (e2))) -> (((op (e0) (e1)) = (e2))\/(((op (e1) (e1)) = (e2))\/(((op (e2) (e1)) = (e2))\/((op (e3) (e1)) = (e2))))) -> (~((e2) = (e3))) -> (~((op (e2) (e1)) = (op (e2) (e3)))) -> (~((e1) = (e2))) -> (~((op (e1) (e0)) = (op (e1) (e1)))) -> ((op (e1) (e0)) = (e0)) -> (((op (e0) (e1)) = (e0))\/(((op (e1) (e1)) = (e0))\/(((op (e2) (e1)) = (e0))\/((op (e3) (e1)) = (e0))))) -> (~((op (e1) (e2)) = (op (e1) (e3)))) -> ((op (e1) (e2)) = (e1)) -> ((op (e0) (e3)) = (e3)) -> (~((op (e0) (e3)) = (op (e1) (e3)))) -> (~((op (e1) (e3)) = (e2))) -> (~((op (e1) (e3)) = (op (e2) (e3)))) -> (~((op (e1) (e3)) = (op (e3) (e3)))) -> ((op (e3) (e3)) = (e0)) -> (((op (e1) (e3)) = (e0))\/(((op (e1) (e3)) = (e1))\/(((op (e1) (e3)) = (e2))\/((op (e1) (e3)) = (e3))))) -> ((op (e3) (e0)) = (e1)) -> (~((op (e3) (e0)) = (op (e3) (e3)))) -> False). % 18.99/19.11 do 0 intro. intros zenon_H133 zenon_H102 zenon_Hf3 zenon_Hc2 zenon_H130 zenon_H101 zenon_H173 zenon_H26e zenon_Hef zenon_H1d5 zenon_H109 zenon_H54 zenon_H10a zenon_H114 zenon_H4a zenon_H48 zenon_H177 zenon_H18c zenon_H212 zenon_H17e zenon_H210 zenon_H26d zenon_H1d8 zenon_H12b zenon_H1c7 zenon_H7c zenon_H45 zenon_H27 zenon_H245 zenon_H124 zenon_Hf0 zenon_He3 zenon_H1d zenon_H14c zenon_Hdb zenon_Hd5 zenon_H60 zenon_Hdf zenon_Hac zenon_H71. % 18.99/19.11 apply (zenon_or_s _ _ zenon_H133); [ zenon_intro zenon_Hc3 | zenon_intro zenon_H134 ]. % 18.99/19.11 apply (zenon_L1078_); trivial. % 18.99/19.11 apply (zenon_or_s _ _ zenon_H134); [ zenon_intro zenon_Hd6 | zenon_intro zenon_H135 ]. % 18.99/19.11 apply (zenon_L78_); trivial. % 18.99/19.11 apply (zenon_or_s _ _ zenon_H135); [ zenon_intro zenon_Hf4 | zenon_intro zenon_Hc4 ]. % 18.99/19.11 apply (zenon_L1079_); trivial. % 18.99/19.11 apply (zenon_L189_); trivial. % 18.99/19.11 (* end of lemma zenon_L1080_ *) % 18.99/19.11 assert (zenon_L1081_ : (((op (e0) (e3)) = (e0))\/(((op (e0) (e3)) = (e1))\/(((op (e0) (e3)) = (e2))\/((op (e0) (e3)) = (e3))))) -> ((op (e2) (e3)) = (e1)) -> (~((op (e0) (e3)) = (op (e2) (e3)))) -> (~((op (e0) (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 (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 (e2) (e2)) = (e2))) -> (~((op (e2) (e1)) = (e2))) -> (~((op (e2) (e0)) = (e2))) -> (((op (e2) (e0)) = (e2))\/(((op (e2) (e1)) = (e2))\/(((op (e2) (e2)) = (e2))\/((op (e2) (e3)) = (e2))))) -> (((op (e0) (e1)) = (e1))\/(((op (e1) (e1)) = (e1))\/(((op (e2) (e1)) = (e1))\/((op (e3) (e1)) = (e1))))) -> (~((op (e0) (e1)) = (op (e0) (e3)))) -> (~((op (e1) (e1)) = (e1))) -> (~((op (e1) (e2)) = (e2))) -> (~((op (e0) (e1)) = (op (e0) (e2)))) -> ((op (e0) (e2)) = (e0)) -> (~((op (e1) (e0)) = (e2))) -> (((op (e1) (e0)) = (e2))\/(((op (e1) (e1)) = (e2))\/(((op (e1) (e2)) = (e2))\/((op (e1) (e3)) = (e2))))) -> (((op (e0) (e1)) = (e0))\/(((op (e0) (e1)) = (e1))\/(((op (e0) (e1)) = (e2))\/((op (e0) (e1)) = (e3))))) -> (~((op (e0) (e1)) = (op (e2) (e1)))) -> (~((op (e0) (e1)) = (op (e3) (e1)))) -> (~((op (e0) (e1)) = (e2))) -> (((op (e0) (e1)) = (e2))\/(((op (e1) (e1)) = (e2))\/(((op (e2) (e1)) = (e2))\/((op (e3) (e1)) = (e2))))) -> (~((e2) = (e3))) -> (~((op (e2) (e1)) = (op (e2) (e3)))) -> (~((e1) = (e2))) -> (~((op (e1) (e0)) = (op (e1) (e1)))) -> ((op (e1) (e0)) = (e0)) -> (((op (e0) (e1)) = (e0))\/(((op (e1) (e1)) = (e0))\/(((op (e2) (e1)) = (e0))\/((op (e3) (e1)) = (e0))))) -> (~((op (e1) (e2)) = (op (e1) (e3)))) -> ((op (e1) (e2)) = (e1)) -> (~((op (e0) (e3)) = (op (e1) (e3)))) -> (~((op (e1) (e3)) = (e2))) -> (~((op (e1) (e3)) = (op (e2) (e3)))) -> (~((op (e1) (e3)) = (op (e3) (e3)))) -> ((op (e3) (e3)) = (e0)) -> (((op (e1) (e3)) = (e0))\/(((op (e1) (e3)) = (e1))\/(((op (e1) (e3)) = (e2))\/((op (e1) (e3)) = (e3))))) -> ((op (e3) (e0)) = (e1)) -> (~((op (e3) (e0)) = (op (e3) (e3)))) -> False). % 18.99/19.11 do 0 intro. intros zenon_He4 zenon_Hf4 zenon_He2 zenon_H12e zenon_H133 zenon_H102 zenon_Hf3 zenon_Hc2 zenon_H130 zenon_H101 zenon_H173 zenon_H26e zenon_Hef zenon_H1d5 zenon_H109 zenon_H54 zenon_H10a zenon_H114 zenon_H4a zenon_H48 zenon_H177 zenon_H18c zenon_H212 zenon_H17e zenon_H210 zenon_H26d zenon_H1d8 zenon_H12b zenon_H1c7 zenon_H7c zenon_H45 zenon_H27 zenon_H245 zenon_H124 zenon_Hf0 zenon_H1d zenon_H14c zenon_Hdb zenon_Hd5 zenon_H60 zenon_Hdf zenon_Hac zenon_H71. % 18.99/19.11 apply (zenon_or_s _ _ zenon_He4); [ zenon_intro zenon_H1e | zenon_intro zenon_He5 ]. % 18.99/19.11 apply (zenon_L440_); trivial. % 18.99/19.11 apply (zenon_or_s _ _ zenon_He5); [ zenon_intro zenon_Hc3 | zenon_intro zenon_He6 ]. % 18.99/19.11 apply (zenon_L272_); trivial. % 18.99/19.11 apply (zenon_or_s _ _ zenon_He6); [ zenon_intro zenon_Hcd | zenon_intro zenon_He3 ]. % 18.99/19.11 exact (zenon_H12e zenon_Hcd). % 18.99/19.11 apply (zenon_L1080_); trivial. % 18.99/19.11 (* end of lemma zenon_L1081_ *) % 18.99/19.11 assert (zenon_L1082_ : ((op (e2) (e1)) = (e0)) -> (((op (e1) (e3)) = (e0))\/(((op (e1) (e3)) = (e1))\/(((op (e1) (e3)) = (e2))\/((op (e1) (e3)) = (e3))))) -> ((op (e3) (e3)) = (e0)) -> (~((op (e1) (e3)) = (op (e3) (e3)))) -> (~((op (e1) (e3)) = (op (e2) (e3)))) -> (~((op (e1) (e3)) = (e2))) -> (~((op (e0) (e3)) = (op (e1) (e3)))) -> ((op (e1) (e2)) = (e1)) -> (~((op (e1) (e2)) = (op (e1) (e3)))) -> (((op (e0) (e1)) = (e0))\/(((op (e1) (e1)) = (e0))\/(((op (e2) (e1)) = (e0))\/((op (e3) (e1)) = (e0))))) -> ((op (e1) (e0)) = (e0)) -> (~((op (e1) (e0)) = (op (e1) (e1)))) -> (~((e1) = (e2))) -> (~((op (e2) (e1)) = (op (e2) (e3)))) -> (~((e2) = (e3))) -> (((op (e0) (e1)) = (e2))\/(((op (e1) (e1)) = (e2))\/(((op (e2) (e1)) = (e2))\/((op (e3) (e1)) = (e2))))) -> (~((op (e0) (e1)) = (e2))) -> (~((op (e0) (e1)) = (op (e3) (e1)))) -> (~((op (e0) (e1)) = (op (e2) (e1)))) -> (((op (e0) (e1)) = (e0))\/(((op (e0) (e1)) = (e1))\/(((op (e0) (e1)) = (e2))\/((op (e0) (e1)) = (e3))))) -> (((op (e1) (e0)) = (e2))\/(((op (e1) (e1)) = (e2))\/(((op (e1) (e2)) = (e2))\/((op (e1) (e3)) = (e2))))) -> (~((op (e1) (e0)) = (e2))) -> ((op (e0) (e2)) = (e0)) -> (~((op (e0) (e1)) = (op (e0) (e2)))) -> (~((op (e1) (e2)) = (e2))) -> (~((op (e1) (e1)) = (e1))) -> (~((op (e0) (e1)) = (op (e0) (e3)))) -> (((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) (e0)) = (e2))) -> (~((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 (e3) (e1)) = (op (e3) (e3)))) -> (~((op (e0) (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 (e0) (e3)) = (op (e2) (e3)))) -> (((op (e0) (e3)) = (e0))\/(((op (e0) (e3)) = (e1))\/(((op (e0) (e3)) = (e2))\/((op (e0) (e3)) = (e3))))) -> ((op (e3) (e0)) = (e1)) -> (~((op (e3) (e0)) = (op (e3) (e3)))) -> False). % 18.99/19.11 do 0 intro. intros zenon_H36 zenon_Hdf zenon_H60 zenon_Hd5 zenon_Hdb zenon_H14c zenon_H1d zenon_Hf0 zenon_H124 zenon_H245 zenon_H27 zenon_H45 zenon_H7c zenon_H1c7 zenon_H12b zenon_H1d8 zenon_H26d zenon_H210 zenon_H17e zenon_H212 zenon_H18c zenon_H177 zenon_H48 zenon_H4a zenon_H114 zenon_H10a zenon_H54 zenon_H109 zenon_H1d5 zenon_Hef zenon_H26e zenon_H173 zenon_H101 zenon_H130 zenon_Hc2 zenon_Hf3 zenon_H102 zenon_H133 zenon_H12e zenon_He2 zenon_He4 zenon_Hac zenon_H71. % 18.99/19.11 apply (zenon_or_s _ _ zenon_H133); [ zenon_intro zenon_Hc3 | zenon_intro zenon_H134 ]. % 18.99/19.11 apply (zenon_L1076_); trivial. % 18.99/19.11 apply (zenon_or_s _ _ zenon_H134); [ zenon_intro zenon_Hd6 | zenon_intro zenon_H135 ]. % 18.99/19.11 apply (zenon_L78_); trivial. % 18.99/19.11 apply (zenon_or_s _ _ zenon_H135); [ zenon_intro zenon_Hf4 | zenon_intro zenon_Hc4 ]. % 18.99/19.11 apply (zenon_L1081_); trivial. % 18.99/19.11 apply (zenon_L189_); trivial. % 18.99/19.11 (* end of lemma zenon_L1082_ *) % 18.99/19.11 assert (zenon_L1083_ : (((op (e0) (e1)) = (e2))\/(((op (e1) (e1)) = (e2))\/(((op (e2) (e1)) = (e2))\/((op (e3) (e1)) = (e2))))) -> (~((op (e0) (e1)) = (e2))) -> (~((op (e1) (e1)) = (op (e1) (e3)))) -> ((op (e1) (e3)) = (e2)) -> (~((op (e2) (e1)) = (e2))) -> (~((op (e3) (e1)) = (op (e3) (e2)))) -> ((op (e3) (e2)) = (e2)) -> False). % 18.99/19.11 do 0 intro. intros zenon_H1d8 zenon_H26d zenon_H57 zenon_Hd7 zenon_H26e zenon_H1a4 zenon_H151. % 18.99/19.11 apply (zenon_or_s _ _ zenon_H1d8); [ zenon_intro zenon_H10f | zenon_intro zenon_H1d9 ]. % 18.99/19.11 exact (zenon_H26d zenon_H10f). % 18.99/19.11 apply (zenon_or_s _ _ zenon_H1d9); [ zenon_intro zenon_H110 | zenon_intro zenon_H1da ]. % 18.99/19.11 apply (zenon_L283_); trivial. % 18.99/19.11 apply (zenon_or_s _ _ zenon_H1da); [ zenon_intro zenon_H1ca | zenon_intro zenon_H14d ]. % 18.99/19.11 exact (zenon_H26e zenon_H1ca). % 18.99/19.11 apply (zenon_L400_); trivial. % 18.99/19.11 (* end of lemma zenon_L1083_ *) % 18.99/19.11 assert (zenon_L1084_ : (((op (e1) (e0)) = (e2))\/(((op (e1) (e1)) = (e2))\/(((op (e1) (e2)) = (e2))\/((op (e1) (e3)) = (e2))))) -> (~((op (e3) (e3)) = (e3))) -> ((op (e1) (e3)) = (e0)) -> (~((op (e2) (e3)) = (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) (e2)) = (op (e2) (e2)))) -> ((op (e1) (e2)) = (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)) = (e0)) -> (~((op (e0) (e1)) = (op (e2) (e1)))) -> ((op (e2) (e1)) = (e0)) -> (((op (e1) (e0)) = (e0))\/(((op (e1) (e0)) = (e1))\/(((op (e1) (e0)) = (e2))\/((op (e1) (e0)) = (e3))))) -> (~((op (e1) (e0)) = (op (e3) (e0)))) -> (~((op (e1) (e0)) = (op (e2) (e0)))) -> (~((op (e1) (e0)) = (e2))) -> ((op (e0) (e0)) = (e2)) -> (((op (e2) (e0)) = (e1))\/(((op (e2) (e1)) = (e1))\/(((op (e2) (e2)) = (e1))\/((op (e2) (e3)) = (e1))))) -> (~((op (e1) (e2)) = (e2))) -> (((op (e0) (e1)) = (e2))\/(((op (e1) (e1)) = (e2))\/(((op (e2) (e1)) = (e2))\/((op (e3) (e1)) = (e2))))) -> (~((op (e0) (e1)) = (e2))) -> (~((op (e1) (e1)) = (op (e1) (e3)))) -> (~((op (e2) (e1)) = (e2))) -> (~((op (e3) (e1)) = (op (e3) (e2)))) -> ((op (e3) (e2)) = (e2)) -> False). % 18.99/19.11 do 0 intro. intros zenon_H18c zenon_H102 zenon_H1f zenon_Hf3 zenon_H44 zenon_H71 zenon_H101 zenon_H2b zenon_Hf0 zenon_H212 zenon_H4a zenon_H48 zenon_H17e zenon_H36 zenon_H25e zenon_H1fa zenon_H201 zenon_H177 zenon_H7b zenon_H106 zenon_H114 zenon_H1d8 zenon_H26d zenon_H57 zenon_H26e zenon_H1a4 zenon_H151. % 18.99/19.11 apply (zenon_or_s _ _ zenon_H18c); [ zenon_intro zenon_H86 | zenon_intro zenon_H18d ]. % 18.99/19.11 exact (zenon_H177 zenon_H86). % 18.99/19.11 apply (zenon_or_s _ _ zenon_H18d); [ zenon_intro zenon_H110 | zenon_intro zenon_H18e ]. % 18.99/19.11 apply (zenon_or_s _ _ zenon_H106); [ zenon_intro zenon_Hed | zenon_intro zenon_H107 ]. % 18.99/19.11 apply (zenon_L1064_); trivial. % 18.99/19.11 apply (zenon_or_s _ _ zenon_H107); [ zenon_intro zenon_Ha5 | zenon_intro zenon_H108 ]. % 18.99/19.11 apply (zenon_L1071_); trivial. % 18.99/19.11 apply (zenon_or_s _ _ zenon_H108); [ zenon_intro zenon_Hf1 | zenon_intro zenon_Hf4 ]. % 18.99/19.11 apply (zenon_L59_); trivial. % 18.99/19.11 apply (zenon_L64_); trivial. % 18.99/19.11 apply (zenon_or_s _ _ zenon_H18e); [ zenon_intro zenon_H113 | zenon_intro zenon_Hd7 ]. % 18.99/19.11 exact (zenon_H114 zenon_H113). % 18.99/19.11 apply (zenon_L1083_); trivial. % 18.99/19.11 (* end of lemma zenon_L1084_ *) % 18.99/19.11 assert (zenon_L1085_ : (((op (e0) (e0)) = (e2))\/(((op (e0) (e1)) = (e2))\/(((op (e0) (e2)) = (e2))\/((op (e0) (e3)) = (e2))))) -> ((op (e3) (e0)) = (e0)) -> (~((op (e3) (e0)) = (op (e3) (e1)))) -> (((op (e1) (e0)) = (e2))\/(((op (e1) (e1)) = (e2))\/(((op (e1) (e2)) = (e2))\/((op (e1) (e3)) = (e2))))) -> (~((op (e3) (e3)) = (e3))) -> (~((op (e2) (e3)) = (op (e3) (e3)))) -> (~((op (e3) (e0)) = (op (e3) (e3)))) -> (((op (e3) (e3)) = (e0))\/(((op (e3) (e3)) = (e1))\/(((op (e3) (e3)) = (e2))\/((op (e3) (e3)) = (e3))))) -> (~((op (e1) (e2)) = (op (e2) (e2)))) -> ((op (e1) (e2)) = (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)) = (e0)) -> (~((op (e0) (e1)) = (op (e2) (e1)))) -> (((op (e1) (e0)) = (e0))\/(((op (e1) (e0)) = (e1))\/(((op (e1) (e0)) = (e2))\/((op (e1) (e0)) = (e3))))) -> (~((op (e1) (e0)) = (op (e3) (e0)))) -> (~((op (e1) (e0)) = (op (e2) (e0)))) -> (~((op (e1) (e0)) = (e2))) -> (((op (e2) (e0)) = (e1))\/(((op (e2) (e1)) = (e1))\/(((op (e2) (e2)) = (e1))\/((op (e2) (e3)) = (e1))))) -> (~((op (e1) (e2)) = (e2))) -> (((op (e0) (e1)) = (e2))\/(((op (e1) (e1)) = (e2))\/(((op (e2) (e1)) = (e2))\/((op (e3) (e1)) = (e2))))) -> (~((op (e1) (e1)) = (op (e1) (e3)))) -> (~((op (e2) (e1)) = (e2))) -> (~((op (e3) (e1)) = (op (e3) (e2)))) -> ((op (e3) (e2)) = (e2)) -> (((op (e0) (e1)) = (e0))\/(((op (e1) (e1)) = (e0))\/(((op (e2) (e1)) = (e0))\/((op (e3) (e1)) = (e0))))) -> (~((op (e0) (e2)) = (op (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 (e2) (e2)) = (e2))) -> (~((op (e1) (e3)) = (op (e2) (e3)))) -> (((op (e1) (e0)) = (e0))\/(((op (e1) (e1)) = (e0))\/(((op (e1) (e2)) = (e0))\/((op (e1) (e3)) = (e0))))) -> (~((op (e0) (e1)) = (e2))) -> (~((op (e0) (e2)) = (e2))) -> (~((op (e0) (e3)) = (e2))) -> False). % 18.99/19.11 do 0 intro. intros zenon_H183 zenon_H44 zenon_H1cf zenon_H18c zenon_H102 zenon_Hf3 zenon_H71 zenon_H101 zenon_H2b zenon_Hf0 zenon_H212 zenon_H4a zenon_H48 zenon_H17e zenon_H25e zenon_H1fa zenon_H201 zenon_H177 zenon_H106 zenon_H114 zenon_H1d8 zenon_H57 zenon_H26e zenon_H1a4 zenon_H151 zenon_H245 zenon_H195 zenon_H149 zenon_H1d5 zenon_Hef zenon_H173 zenon_Hdb zenon_H22 zenon_H26d zenon_H1fd zenon_H12e. % 18.99/19.11 apply (zenon_or_s _ _ zenon_H183); [ zenon_intro zenon_H7b | zenon_intro zenon_H186 ]. % 18.99/19.11 apply (zenon_or_s _ _ zenon_H22); [ zenon_intro zenon_H27 | zenon_intro zenon_H26 ]. % 18.99/19.11 apply (zenon_L312_); trivial. % 18.99/19.11 apply (zenon_or_s _ _ zenon_H26); [ zenon_intro zenon_H29 | zenon_intro zenon_H28 ]. % 18.99/19.11 apply (zenon_L1066_); trivial. % 18.99/19.11 apply (zenon_or_s _ _ zenon_H28); [ zenon_intro zenon_H2a | zenon_intro zenon_H1f ]. % 18.99/19.11 apply (zenon_L334_); trivial. % 18.99/19.11 apply (zenon_or_s _ _ zenon_H245); [ zenon_intro zenon_H49 | zenon_intro zenon_H246 ]. % 18.99/19.11 apply (zenon_L9_); trivial. % 18.99/19.11 apply (zenon_or_s _ _ zenon_H246); [ zenon_intro zenon_H29 | zenon_intro zenon_H247 ]. % 18.99/19.11 apply (zenon_L13_); trivial. % 18.99/19.11 apply (zenon_or_s _ _ zenon_H247); [ zenon_intro zenon_H36 | zenon_intro zenon_H1b1 ]. % 18.99/19.11 apply (zenon_L1084_); trivial. % 18.99/19.11 apply (zenon_L346_); trivial. % 18.99/19.11 apply (zenon_or_s _ _ zenon_H186); [ zenon_intro zenon_H10f | zenon_intro zenon_H187 ]. % 18.99/19.11 exact (zenon_H26d zenon_H10f). % 18.99/19.11 apply (zenon_or_s _ _ zenon_H187); [ zenon_intro zenon_H150 | zenon_intro zenon_Hcd ]. % 18.99/19.11 exact (zenon_H1fd zenon_H150). % 18.99/19.11 exact (zenon_H12e zenon_Hcd). % 18.99/19.11 (* end of lemma zenon_L1085_ *) % 18.99/19.11 assert (zenon_L1086_ : (((op (e3) (e0)) = (e0))\/(((op (e3) (e1)) = (e0))\/(((op (e3) (e2)) = (e0))\/((op (e3) (e3)) = (e0))))) -> (~((op (e0) (e2)) = (e2))) -> (((op (e1) (e0)) = (e0))\/(((op (e1) (e1)) = (e0))\/(((op (e1) (e2)) = (e0))\/((op (e1) (e3)) = (e0))))) -> (~((e0) = (e2))) -> (~((op (e0) (e2)) = (op (e1) (e2)))) -> (~((op (e3) (e1)) = (op (e3) (e2)))) -> (~((op (e1) (e1)) = (op (e1) (e3)))) -> (((op (e2) (e0)) = (e1))\/(((op (e2) (e1)) = (e1))\/(((op (e2) (e2)) = (e1))\/((op (e2) (e3)) = (e1))))) -> (~((op (e1) (e0)) = (op (e2) (e0)))) -> (~((op (e1) (e0)) = (op (e3) (e0)))) -> (((op (e1) (e0)) = (e0))\/(((op (e1) (e0)) = (e1))\/(((op (e1) (e0)) = (e2))\/((op (e1) (e0)) = (e3))))) -> (~((op (e1) (e2)) = (op (e2) (e2)))) -> (~((op (e3) (e0)) = (op (e3) (e1)))) -> (((op (e0) (e0)) = (e2))\/(((op (e0) (e1)) = (e2))\/(((op (e0) (e2)) = (e2))\/((op (e0) (e3)) = (e2))))) -> (~((op (e3) (e3)) = (e2))) -> (~((op (e3) (e2)) = (op (e3) (e3)))) -> ((op (e2) (e1)) = (e0)) -> ((op (e3) (e2)) = (e2)) -> (~((op (e0) (e2)) = (op (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 (e2) (e3)) = (e1)) -> (~((op (e0) (e3)) = (op (e2) (e3)))) -> (~((op (e0) (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 (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 (e2) (e2)) = (e2))) -> (~((op (e2) (e1)) = (e2))) -> (~((op (e2) (e0)) = (e2))) -> (((op (e2) (e0)) = (e2))\/(((op (e2) (e1)) = (e2))\/(((op (e2) (e2)) = (e2))\/((op (e2) (e3)) = (e2))))) -> (((op (e0) (e1)) = (e1))\/(((op (e1) (e1)) = (e1))\/(((op (e2) (e1)) = (e1))\/((op (e3) (e1)) = (e1))))) -> (~((op (e0) (e1)) = (op (e0) (e3)))) -> (~((op (e1) (e1)) = (e1))) -> (~((op (e1) (e2)) = (e2))) -> (~((op (e0) (e1)) = (op (e0) (e2)))) -> ((op (e0) (e2)) = (e0)) -> (~((op (e1) (e0)) = (e2))) -> (((op (e1) (e0)) = (e2))\/(((op (e1) (e1)) = (e2))\/(((op (e1) (e2)) = (e2))\/((op (e1) (e3)) = (e2))))) -> (((op (e0) (e1)) = (e0))\/(((op (e0) (e1)) = (e1))\/(((op (e0) (e1)) = (e2))\/((op (e0) (e1)) = (e3))))) -> (~((op (e0) (e1)) = (op (e2) (e1)))) -> (~((op (e0) (e1)) = (op (e3) (e1)))) -> (~((op (e0) (e1)) = (e2))) -> (((op (e0) (e1)) = (e2))\/(((op (e1) (e1)) = (e2))\/(((op (e2) (e1)) = (e2))\/((op (e3) (e1)) = (e2))))) -> (~((e2) = (e3))) -> (~((op (e2) (e1)) = (op (e2) (e3)))) -> (~((e1) = (e2))) -> (~((op (e1) (e0)) = (op (e1) (e1)))) -> ((op (e1) (e0)) = (e0)) -> (((op (e0) (e1)) = (e0))\/(((op (e1) (e1)) = (e0))\/(((op (e2) (e1)) = (e0))\/((op (e3) (e1)) = (e0))))) -> (~((op (e1) (e2)) = (op (e1) (e3)))) -> ((op (e1) (e2)) = (e1)) -> (~((op (e0) (e3)) = (op (e1) (e3)))) -> (~((op (e1) (e3)) = (e2))) -> (~((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) (e0)) = (op (e3) (e3)))) -> False). % 18.99/19.11 do 0 intro. intros zenon_H1ac zenon_H1fd zenon_H22 zenon_H149 zenon_H195 zenon_H1a4 zenon_H57 zenon_H106 zenon_H201 zenon_H1fa zenon_H25e zenon_H2b zenon_H1cf zenon_H183 zenon_Hf7 zenon_H62 zenon_H36 zenon_H151 zenon_H208 zenon_H67 zenon_He4 zenon_Hf4 zenon_He2 zenon_H12e zenon_H133 zenon_H102 zenon_Hf3 zenon_Hc2 zenon_H130 zenon_H101 zenon_H173 zenon_H26e zenon_Hef zenon_H1d5 zenon_H109 zenon_H54 zenon_H10a zenon_H114 zenon_H4a zenon_H48 zenon_H177 zenon_H18c zenon_H212 zenon_H17e zenon_H210 zenon_H26d zenon_H1d8 zenon_H12b zenon_H1c7 zenon_H7c zenon_H45 zenon_H27 zenon_H245 zenon_H124 zenon_Hf0 zenon_H1d zenon_H14c zenon_Hdb zenon_Hd5 zenon_Hdf zenon_Hac zenon_H71. % 18.99/19.11 apply (zenon_or_s _ _ zenon_H1ac); [ zenon_intro zenon_H44 | zenon_intro zenon_H1af ]. % 18.99/19.11 apply (zenon_L1085_); trivial. % 18.99/19.11 apply (zenon_or_s _ _ zenon_H1af); [ zenon_intro zenon_H1b1 | zenon_intro zenon_H1b0 ]. % 18.99/19.11 apply (zenon_L1067_); trivial. % 18.99/19.11 apply (zenon_or_s _ _ zenon_H1b0); [ zenon_intro zenon_H61 | zenon_intro zenon_H60 ]. % 18.99/19.11 apply (zenon_L1070_); trivial. % 18.99/19.11 apply (zenon_L1081_); trivial. % 18.99/19.11 (* end of lemma zenon_L1086_ *) % 18.99/19.11 assert (zenon_L1087_ : (~((op (e3) (e3)) = (e3))) -> (~((op (e3) (e3)) = (e2))) -> ((op (e3) (e0)) = (e1)) -> (~((op (e3) (e0)) = (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 (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 (e0) (e3)) = (op (e1) (e3)))) -> ((op (e1) (e2)) = (e1)) -> (~((op (e1) (e2)) = (op (e1) (e3)))) -> (((op (e0) (e1)) = (e0))\/(((op (e1) (e1)) = (e0))\/(((op (e2) (e1)) = (e0))\/((op (e3) (e1)) = (e0))))) -> ((op (e1) (e0)) = (e0)) -> (~((op (e1) (e0)) = (op (e1) (e1)))) -> (~((e1) = (e2))) -> (~((op (e2) (e1)) = (op (e2) (e3)))) -> (~((e2) = (e3))) -> (((op (e0) (e1)) = (e2))\/(((op (e1) (e1)) = (e2))\/(((op (e2) (e1)) = (e2))\/((op (e3) (e1)) = (e2))))) -> (~((op (e0) (e1)) = (op (e3) (e1)))) -> (~((op (e0) (e1)) = (op (e2) (e1)))) -> (((op (e0) (e1)) = (e0))\/(((op (e0) (e1)) = (e1))\/(((op (e0) (e1)) = (e2))\/((op (e0) (e1)) = (e3))))) -> (((op (e1) (e0)) = (e2))\/(((op (e1) (e1)) = (e2))\/(((op (e1) (e2)) = (e2))\/((op (e1) (e3)) = (e2))))) -> (~((op (e1) (e0)) = (e2))) -> ((op (e0) (e2)) = (e0)) -> (~((op (e0) (e1)) = (op (e0) (e2)))) -> (~((op (e1) (e1)) = (e1))) -> (~((op (e0) (e1)) = (op (e0) (e3)))) -> (((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) (e0)) = (e2))) -> (~((op (e2) (e1)) = (e2))) -> (~((op (e2) (e2)) = (e2))) -> (~((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)) = (op (e2) (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 (e0) (e2)) = (op (e0) (e3)))) -> ((op (e3) (e2)) = (e2)) -> (~((op (e3) (e2)) = (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 (e1) (e2)) = (op (e2) (e2)))) -> (((op (e1) (e0)) = (e0))\/(((op (e1) (e0)) = (e1))\/(((op (e1) (e0)) = (e2))\/((op (e1) (e0)) = (e3))))) -> (~((op (e1) (e0)) = (op (e3) (e0)))) -> (~((op (e1) (e0)) = (op (e2) (e0)))) -> (((op (e2) (e0)) = (e1))\/(((op (e2) (e1)) = (e1))\/(((op (e2) (e2)) = (e1))\/((op (e2) (e3)) = (e1))))) -> (~((op (e1) (e1)) = (op (e1) (e3)))) -> (~((op (e3) (e1)) = (op (e3) (e2)))) -> (~((op (e0) (e2)) = (op (e1) (e2)))) -> (~((e0) = (e2))) -> (((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 (e1) (e2)) = (e2))) -> (~((op (e1) (e3)) = (e2))) -> (~((op (e0) (e1)) = (e2))) -> (~((op (e0) (e2)) = (e2))) -> (~((op (e0) (e3)) = (e2))) -> False). % 18.99/19.11 do 0 intro. intros zenon_H102 zenon_Hf7 zenon_Hac zenon_H71 zenon_H130 zenon_H101 zenon_Hdf zenon_Hd5 zenon_Hdb zenon_H1d zenon_Hf0 zenon_H124 zenon_H245 zenon_H27 zenon_H45 zenon_H7c zenon_H1c7 zenon_H12b zenon_H1d8 zenon_H210 zenon_H17e zenon_H212 zenon_H18c zenon_H177 zenon_H48 zenon_H4a zenon_H10a zenon_H54 zenon_H109 zenon_H1d5 zenon_Hef zenon_H26e zenon_H173 zenon_Hc2 zenon_Hf3 zenon_H133 zenon_He2 zenon_He4 zenon_H67 zenon_H208 zenon_H151 zenon_H62 zenon_H183 zenon_H1cf zenon_H2b zenon_H25e zenon_H1fa zenon_H201 zenon_H106 zenon_H57 zenon_H1a4 zenon_H195 zenon_H149 zenon_H22 zenon_H1ac zenon_H114 zenon_H14c zenon_H26d zenon_H1fd zenon_H12e. % 18.99/19.11 apply (zenon_or_s _ _ zenon_H183); [ zenon_intro zenon_H7b | zenon_intro zenon_H186 ]. % 18.99/19.11 apply (zenon_or_s _ _ zenon_H245); [ zenon_intro zenon_H49 | zenon_intro zenon_H246 ]. % 18.99/19.11 apply (zenon_L9_); trivial. % 18.99/19.11 apply (zenon_or_s _ _ zenon_H246); [ zenon_intro zenon_H29 | zenon_intro zenon_H247 ]. % 18.99/19.11 apply (zenon_L1066_); trivial. % 18.99/19.11 apply (zenon_or_s _ _ zenon_H247); [ zenon_intro zenon_H36 | zenon_intro zenon_H1b1 ]. % 18.99/19.11 apply (zenon_or_s _ _ zenon_H18c); [ zenon_intro zenon_H86 | zenon_intro zenon_H18d ]. % 18.99/19.11 exact (zenon_H177 zenon_H86). % 18.99/19.11 apply (zenon_or_s _ _ zenon_H18d); [ zenon_intro zenon_H110 | zenon_intro zenon_H18e ]. % 18.99/19.11 apply (zenon_or_s _ _ zenon_H106); [ zenon_intro zenon_Hed | zenon_intro zenon_H107 ]. % 18.99/19.11 apply (zenon_or_s _ _ zenon_H1ac); [ zenon_intro zenon_H44 | zenon_intro zenon_H1af ]. % 18.99/19.11 apply (zenon_L1064_); trivial. % 18.99/19.11 apply (zenon_or_s _ _ zenon_H1af); [ zenon_intro zenon_H1b1 | zenon_intro zenon_H1b0 ]. % 18.99/19.11 apply (zenon_L1067_); trivial. % 18.99/19.11 apply (zenon_or_s _ _ zenon_H1b0); [ zenon_intro zenon_H61 | zenon_intro zenon_H60 ]. % 18.99/19.11 apply (zenon_L1070_); trivial. % 18.99/19.11 apply (zenon_L1082_); trivial. % 18.99/19.11 apply (zenon_or_s _ _ zenon_H107); [ zenon_intro zenon_Ha5 | zenon_intro zenon_H108 ]. % 18.99/19.11 apply (zenon_L1071_); trivial. % 18.99/19.11 apply (zenon_or_s _ _ zenon_H108); [ zenon_intro zenon_Hf1 | zenon_intro zenon_Hf4 ]. % 18.99/19.11 apply (zenon_L59_); trivial. % 18.99/19.11 apply (zenon_L1086_); trivial. % 18.99/19.11 apply (zenon_or_s _ _ zenon_H18e); [ zenon_intro zenon_H113 | zenon_intro zenon_Hd7 ]. % 18.99/19.11 exact (zenon_H114 zenon_H113). % 18.99/19.11 exact (zenon_H14c zenon_Hd7). % 18.99/19.11 apply (zenon_L1067_); trivial. % 18.99/19.11 apply (zenon_or_s _ _ zenon_H186); [ zenon_intro zenon_H10f | zenon_intro zenon_H187 ]. % 18.99/19.11 exact (zenon_H26d zenon_H10f). % 18.99/19.11 apply (zenon_or_s _ _ zenon_H187); [ zenon_intro zenon_H150 | zenon_intro zenon_Hcd ]. % 18.99/19.11 exact (zenon_H1fd zenon_H150). % 18.99/19.11 exact (zenon_H12e zenon_Hcd). % 18.99/19.11 (* end of lemma zenon_L1087_ *) % 18.99/19.11 assert (zenon_L1088_ : (((op (e1) (e3)) = (e0))\/(((op (e1) (e3)) = (e1))\/(((op (e1) (e3)) = (e2))\/((op (e1) (e3)) = (e3))))) -> ((op (e2) (e3)) = (e0)) -> (~((op (e1) (e3)) = (op (e2) (e3)))) -> ((op (e3) (e3)) = (e1)) -> (~((op (e1) (e3)) = (op (e3) (e3)))) -> (~((op (e1) (e3)) = (e2))) -> (~((op (e0) (e3)) = (op (e1) (e3)))) -> ((op (e0) (e3)) = (e3)) -> False). % 18.99/19.11 do 0 intro. intros zenon_Hdf zenon_H37 zenon_Hdb zenon_Hc4 zenon_Hd5 zenon_H14c zenon_H1d zenon_He3. % 18.99/19.11 apply (zenon_or_s _ _ zenon_Hdf); [ zenon_intro zenon_H1f | zenon_intro zenon_He0 ]. % 18.99/19.11 apply (zenon_L130_); trivial. % 18.99/19.11 apply (zenon_or_s _ _ zenon_He0); [ zenon_intro zenon_Hd6 | zenon_intro zenon_He1 ]. % 18.99/19.11 apply (zenon_L50_); trivial. % 18.99/19.11 apply (zenon_or_s _ _ zenon_He1); [ zenon_intro zenon_Hd7 | zenon_intro zenon_Hdc ]. % 18.99/19.11 exact (zenon_H14c zenon_Hd7). % 18.99/19.11 apply (zenon_L117_); trivial. % 18.99/19.11 (* end of lemma zenon_L1088_ *) % 18.99/19.11 assert (zenon_L1089_ : (((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)) = (e2))) -> (((op (e1) (e3)) = (e0))\/(((op (e1) (e3)) = (e1))\/(((op (e1) (e3)) = (e2))\/((op (e1) (e3)) = (e3))))) -> ((op (e2) (e3)) = (e0)) -> (~((op (e1) (e3)) = (op (e2) (e3)))) -> ((op (e3) (e3)) = (e1)) -> (~((op (e1) (e3)) = (op (e3) (e3)))) -> (~((op (e1) (e3)) = (e2))) -> (~((op (e0) (e3)) = (op (e1) (e3)))) -> False). % 18.99/19.11 do 0 intro. intros zenon_He4 zenon_He2 zenon_Hc2 zenon_H12e zenon_Hdf zenon_H37 zenon_Hdb zenon_Hc4 zenon_Hd5 zenon_H14c zenon_H1d. % 18.99/19.11 apply (zenon_or_s _ _ zenon_He4); [ zenon_intro zenon_H1e | zenon_intro zenon_He5 ]. % 18.99/19.11 apply (zenon_L367_); trivial. % 18.99/19.11 apply (zenon_or_s _ _ zenon_He5); [ zenon_intro zenon_Hc3 | zenon_intro zenon_He6 ]. % 18.99/19.11 apply (zenon_L46_); trivial. % 18.99/19.11 apply (zenon_or_s _ _ zenon_He6); [ zenon_intro zenon_Hcd | zenon_intro zenon_He3 ]. % 18.99/19.11 exact (zenon_H12e zenon_Hcd). % 18.99/19.11 apply (zenon_L1088_); trivial. % 18.99/19.11 (* end of lemma zenon_L1089_ *) % 18.99/19.11 assert (zenon_L1090_ : (((op (e3) (e0)) = (e1))\/(((op (e3) (e1)) = (e1))\/(((op (e3) (e2)) = (e1))\/((op (e3) (e3)) = (e1))))) -> (~((op (e0) (e2)) = (e2))) -> (~((op (e0) (e1)) = (e2))) -> (~((op (e1) (e2)) = (e2))) -> (((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))))) -> (~((e0) = (e2))) -> (~((op (e0) (e2)) = (op (e1) (e2)))) -> (~((op (e3) (e1)) = (op (e3) (e2)))) -> (~((op (e1) (e1)) = (op (e1) (e3)))) -> (((op (e2) (e0)) = (e1))\/(((op (e2) (e1)) = (e1))\/(((op (e2) (e2)) = (e1))\/((op (e2) (e3)) = (e1))))) -> (~((op (e1) (e0)) = (op (e2) (e0)))) -> (~((op (e1) (e0)) = (op (e3) (e0)))) -> (((op (e1) (e0)) = (e0))\/(((op (e1) (e0)) = (e1))\/(((op (e1) (e0)) = (e2))\/((op (e1) (e0)) = (e3))))) -> (~((op (e1) (e2)) = (op (e2) (e2)))) -> (~((op (e3) (e0)) = (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 (e3) (e2)) = (e2)) -> (~((op (e0) (e2)) = (op (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 (e2) (e3)) = (op (e3) (e3)))) -> (~((op (e2) (e2)) = (e2))) -> (~((op (e2) (e1)) = (e2))) -> (~((op (e2) (e0)) = (e2))) -> (((op (e2) (e0)) = (e2))\/(((op (e2) (e1)) = (e2))\/(((op (e2) (e2)) = (e2))\/((op (e2) (e3)) = (e2))))) -> (((op (e0) (e1)) = (e1))\/(((op (e1) (e1)) = (e1))\/(((op (e2) (e1)) = (e1))\/((op (e3) (e1)) = (e1))))) -> (~((op (e0) (e1)) = (op (e0) (e3)))) -> (~((op (e1) (e1)) = (e1))) -> (~((op (e0) (e1)) = (op (e0) (e2)))) -> ((op (e0) (e2)) = (e0)) -> (~((op (e1) (e0)) = (e2))) -> (((op (e1) (e0)) = (e2))\/(((op (e1) (e1)) = (e2))\/(((op (e1) (e2)) = (e2))\/((op (e1) (e3)) = (e2))))) -> (((op (e0) (e1)) = (e0))\/(((op (e0) (e1)) = (e1))\/(((op (e0) (e1)) = (e2))\/((op (e0) (e1)) = (e3))))) -> (~((op (e0) (e1)) = (op (e2) (e1)))) -> (((op (e0) (e1)) = (e2))\/(((op (e1) (e1)) = (e2))\/(((op (e2) (e1)) = (e2))\/((op (e3) (e1)) = (e2))))) -> (~((e2) = (e3))) -> (~((op (e2) (e1)) = (op (e2) (e3)))) -> (~((e1) = (e2))) -> (~((op (e1) (e0)) = (op (e1) (e1)))) -> ((op (e1) (e0)) = (e0)) -> (((op (e0) (e1)) = (e0))\/(((op (e1) (e1)) = (e0))\/(((op (e2) (e1)) = (e0))\/((op (e3) (e1)) = (e0))))) -> (~((op (e1) (e2)) = (op (e1) (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)) = (op (e3) (e3)))) -> (~((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 (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)) = (e2))) -> (((op (e1) (e3)) = (e0))\/(((op (e1) (e3)) = (e1))\/(((op (e1) (e3)) = (e2))\/((op (e1) (e3)) = (e3))))) -> ((op (e2) (e3)) = (e0)) -> (~((op (e1) (e3)) = (op (e2) (e3)))) -> (~((op (e1) (e3)) = (op (e3) (e3)))) -> (~((op (e1) (e3)) = (e2))) -> (~((op (e0) (e3)) = (op (e1) (e3)))) -> False). % 18.99/19.11 do 0 intro. intros zenon_He8 zenon_H1fd zenon_H26d zenon_H114 zenon_H1ac zenon_H22 zenon_H149 zenon_H195 zenon_H1a4 zenon_H57 zenon_H106 zenon_H201 zenon_H1fa zenon_H25e zenon_H2b zenon_H1cf zenon_H183 zenon_H62 zenon_H151 zenon_H208 zenon_H67 zenon_H133 zenon_Hf3 zenon_H173 zenon_H26e zenon_Hef zenon_H1d5 zenon_H109 zenon_H54 zenon_H10a zenon_H4a zenon_H48 zenon_H177 zenon_H18c zenon_H212 zenon_H17e zenon_H1d8 zenon_H12b zenon_H1c7 zenon_H7c zenon_H45 zenon_H27 zenon_H245 zenon_H124 zenon_H101 zenon_H130 zenon_H71 zenon_Hf7 zenon_H102 zenon_Ha0 zenon_H210 zenon_Hf0 zenon_H115 zenon_He4 zenon_He2 zenon_Hc2 zenon_H12e zenon_Hdf zenon_H37 zenon_Hdb zenon_Hd5 zenon_H14c zenon_H1d. % 18.99/19.11 apply (zenon_or_s _ _ zenon_He8); [ zenon_intro zenon_Hac | zenon_intro zenon_Heb ]. % 18.99/19.11 apply (zenon_L1087_); trivial. % 18.99/19.11 apply (zenon_or_s _ _ zenon_Heb); [ zenon_intro zenon_Hae | zenon_intro zenon_Hec ]. % 18.99/19.11 apply (zenon_L363_); trivial. % 18.99/19.11 apply (zenon_or_s _ _ zenon_Hec); [ zenon_intro zenon_Hba | zenon_intro zenon_Hc4 ]. % 18.99/19.11 apply (zenon_L69_); trivial. % 18.99/19.11 apply (zenon_L1089_); trivial. % 18.99/19.11 (* end of lemma zenon_L1090_ *) % 18.99/19.11 assert (zenon_L1091_ : (~((op (e1) (e0)) = (op (e1) (e3)))) -> (~((op (e0) (e3)) = (op (e1) (e3)))) -> (~((op (e1) (e3)) = (e2))) -> (~((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) (e3)) = (e2))) -> (~((op (e0) (e3)) = (op (e3) (e3)))) -> (~((op (e0) (e3)) = (op (e2) (e3)))) -> (((op (e0) (e3)) = (e0))\/(((op (e0) (e3)) = (e1))\/(((op (e0) (e3)) = (e2))\/((op (e0) (e3)) = (e3))))) -> (~((op (e1) (e2)) = (op (e3) (e2)))) -> ((op (e1) (e2)) = (e1)) -> (~((op (e0) (e1)) = (op (e3) (e1)))) -> ((op (e0) (e1)) = (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 (e1) (e2)) = (op (e1) (e3)))) -> (((op (e0) (e1)) = (e0))\/(((op (e1) (e1)) = (e0))\/(((op (e2) (e1)) = (e0))\/((op (e3) (e1)) = (e0))))) -> ((op (e1) (e0)) = (e0)) -> (~((op (e1) (e0)) = (op (e1) (e1)))) -> (~((e1) = (e2))) -> (~((op (e2) (e1)) = (op (e2) (e3)))) -> (~((e2) = (e3))) -> (((op (e0) (e1)) = (e2))\/(((op (e1) (e1)) = (e2))\/(((op (e2) (e1)) = (e2))\/((op (e3) (e1)) = (e2))))) -> (~((op (e0) (e1)) = (op (e2) (e1)))) -> (((op (e0) (e1)) = (e0))\/(((op (e0) (e1)) = (e1))\/(((op (e0) (e1)) = (e2))\/((op (e0) (e1)) = (e3))))) -> (((op (e1) (e0)) = (e2))\/(((op (e1) (e1)) = (e2))\/(((op (e1) (e2)) = (e2))\/((op (e1) (e3)) = (e2))))) -> (~((op (e1) (e0)) = (e2))) -> ((op (e0) (e2)) = (e0)) -> (~((op (e0) (e1)) = (op (e0) (e2)))) -> (~((op (e1) (e1)) = (e1))) -> (~((op (e0) (e1)) = (op (e0) (e3)))) -> (((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) (e0)) = (e2))) -> (~((op (e2) (e1)) = (e2))) -> (~((op (e2) (e2)) = (e2))) -> (~((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) (e2)) = (op (e0) (e3)))) -> ((op (e3) (e2)) = (e2)) -> (~((op (e3) (e2)) = (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 (e1) (e2)) = (op (e2) (e2)))) -> (((op (e1) (e0)) = (e0))\/(((op (e1) (e0)) = (e1))\/(((op (e1) (e0)) = (e2))\/((op (e1) (e0)) = (e3))))) -> (~((op (e1) (e0)) = (op (e3) (e0)))) -> (~((op (e1) (e0)) = (op (e2) (e0)))) -> (((op (e2) (e0)) = (e1))\/(((op (e2) (e1)) = (e1))\/(((op (e2) (e2)) = (e1))\/((op (e2) (e3)) = (e1))))) -> (~((op (e1) (e1)) = (op (e1) (e3)))) -> (~((op (e3) (e1)) = (op (e3) (e2)))) -> (~((op (e0) (e2)) = (op (e1) (e2)))) -> (~((e0) = (e2))) -> (((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 (e1) (e2)) = (e2))) -> (~((op (e0) (e1)) = (e2))) -> (~((op (e0) (e2)) = (e2))) -> (((op (e3) (e0)) = (e1))\/(((op (e3) (e1)) = (e1))\/(((op (e3) (e2)) = (e1))\/((op (e3) (e3)) = (e1))))) -> ((op (e3) (e1)) = (e0)) -> (~((op (e3) (e1)) = (op (e3) (e3)))) -> False). % 18.99/19.11 do 0 intro. intros zenon_Hd8 zenon_H1d zenon_H14c zenon_Hd5 zenon_Hdb zenon_Hdf zenon_H12e zenon_Hc2 zenon_He2 zenon_He4 zenon_H115 zenon_Hf0 zenon_H210 zenon_Ha0 zenon_H102 zenon_Hf7 zenon_H71 zenon_H101 zenon_H124 zenon_H245 zenon_H27 zenon_H45 zenon_H7c zenon_H1c7 zenon_H12b zenon_H1d8 zenon_H17e zenon_H212 zenon_H18c zenon_H177 zenon_H48 zenon_H4a zenon_H10a zenon_H54 zenon_H109 zenon_H1d5 zenon_Hef zenon_H26e zenon_H173 zenon_Hf3 zenon_H133 zenon_H67 zenon_H208 zenon_H151 zenon_H62 zenon_H183 zenon_H1cf zenon_H2b zenon_H25e zenon_H1fa zenon_H201 zenon_H106 zenon_H57 zenon_H1a4 zenon_H195 zenon_H149 zenon_H22 zenon_H1ac zenon_H114 zenon_H26d zenon_H1fd zenon_He8 zenon_H1b1 zenon_H130. % 18.99/19.11 apply (zenon_or_s _ _ zenon_H67); [ zenon_intro zenon_H1e | zenon_intro zenon_H68 ]. % 18.99/19.11 apply (zenon_L336_); trivial. % 18.99/19.11 apply (zenon_or_s _ _ zenon_H68); [ zenon_intro zenon_H1f | zenon_intro zenon_H69 ]. % 18.99/19.11 apply (zenon_L258_); trivial. % 18.99/19.11 apply (zenon_or_s _ _ zenon_H69); [ zenon_intro zenon_H37 | zenon_intro zenon_H60 ]. % 18.99/19.11 apply (zenon_L1090_); trivial. % 18.99/19.11 apply (zenon_L244_); trivial. % 18.99/19.11 (* end of lemma zenon_L1091_ *) % 18.99/19.11 assert (zenon_L1092_ : (((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 (e1) (e3)) = (op (e3) (e3)))) -> (~((op (e1) (e3)) = (e2))) -> (~((op (e0) (e3)) = (op (e1) (e3)))) -> ((op (e0) (e3)) = (e3)) -> False). % 18.99/19.11 do 0 intro. intros zenon_Hdf zenon_H60 zenon_Hc4 zenon_Hd5 zenon_H14c zenon_H1d zenon_He3. % 18.99/19.11 apply (zenon_or_s _ _ zenon_Hdf); [ zenon_intro zenon_H1f | zenon_intro zenon_He0 ]. % 18.99/19.11 apply (zenon_L136_); trivial. % 18.99/19.11 apply (zenon_or_s _ _ zenon_He0); [ zenon_intro zenon_Hd6 | zenon_intro zenon_He1 ]. % 18.99/19.11 apply (zenon_L50_); trivial. % 18.99/19.11 apply (zenon_or_s _ _ zenon_He1); [ zenon_intro zenon_Hd7 | zenon_intro zenon_Hdc ]. % 18.99/19.11 exact (zenon_H14c zenon_Hd7). % 18.99/19.11 apply (zenon_L117_); trivial. % 18.99/19.11 (* end of lemma zenon_L1092_ *) % 18.99/19.11 assert (zenon_L1093_ : (((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)) = (e2))) -> (((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 (e1) (e3)) = (op (e3) (e3)))) -> (~((op (e1) (e3)) = (e2))) -> (~((op (e0) (e3)) = (op (e1) (e3)))) -> False). % 18.99/19.11 do 0 intro. intros zenon_He4 zenon_Hc2 zenon_H12e zenon_Hdf zenon_H60 zenon_Hc4 zenon_Hd5 zenon_H14c zenon_H1d. % 18.99/19.11 apply (zenon_or_s _ _ zenon_He4); [ zenon_intro zenon_H1e | zenon_intro zenon_He5 ]. % 18.99/19.11 apply (zenon_L440_); trivial. % 18.99/19.11 apply (zenon_or_s _ _ zenon_He5); [ zenon_intro zenon_Hc3 | zenon_intro zenon_He6 ]. % 18.99/19.11 apply (zenon_L46_); trivial. % 18.99/19.11 apply (zenon_or_s _ _ zenon_He6); [ zenon_intro zenon_Hcd | zenon_intro zenon_He3 ]. % 18.99/19.11 exact (zenon_H12e zenon_Hcd). % 18.99/19.11 apply (zenon_L1092_); trivial. % 18.99/19.11 (* end of lemma zenon_L1093_ *) % 18.99/19.11 assert (zenon_L1094_ : (((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) (e3)))) -> ((op (e2) (e3)) = (e1)) -> (~((op (e2) (e1)) = (e2))) -> ((op (e3) (e1)) = (e0)) -> ((op (e1) (e1)) = (e2)) -> False). % 18.99/19.11 do 0 intro. intros zenon_H1cc zenon_H34 zenon_H1f0 zenon_H1c7 zenon_Hf4 zenon_H26e zenon_H1b1 zenon_H110. % 18.99/19.11 apply (zenon_or_s _ _ zenon_H1cc); [ zenon_intro zenon_H36 | zenon_intro zenon_H1cd ]. % 18.99/19.11 apply (zenon_L642_); trivial. % 18.99/19.11 apply (zenon_or_s _ _ zenon_H1cd); [ zenon_intro zenon_Ha5 | zenon_intro zenon_H1ce ]. % 18.99/19.11 apply (zenon_L188_); trivial. % 18.99/19.11 apply (zenon_or_s _ _ zenon_H1ce); [ zenon_intro zenon_H1ca | zenon_intro zenon_Ha6 ]. % 18.99/19.11 exact (zenon_H26e zenon_H1ca). % 18.99/19.11 apply (zenon_L509_); trivial. % 18.99/19.11 (* end of lemma zenon_L1094_ *) % 18.99/19.11 assert (zenon_L1095_ : (((op (e1) (e0)) = (e2))\/(((op (e1) (e1)) = (e2))\/(((op (e1) (e2)) = (e2))\/((op (e1) (e3)) = (e2))))) -> (~((op (e1) (e0)) = (e2))) -> ((op (e3) (e1)) = (e0)) -> (~((op (e2) (e1)) = (op (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))))) -> (~((op (e1) (e2)) = (op (e2) (e2)))) -> ((op (e1) (e2)) = (e1)) -> (~((op (e0) (e1)) = (op (e2) (e1)))) -> ((op (e0) (e1)) = (e1)) -> (~((e0) = (e1))) -> (((op (e2) (e0)) = (e1))\/(((op (e2) (e1)) = (e1))\/(((op (e2) (e2)) = (e1))\/((op (e2) (e3)) = (e1))))) -> (~((op (e1) (e2)) = (e2))) -> (((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 (e1) (e3)) = (op (e2) (e3)))) -> False). % 18.99/19.11 do 0 intro. intros zenon_H18c zenon_H177 zenon_H1b1 zenon_H1c7 zenon_H1f0 zenon_H34 zenon_H1cc zenon_H2b zenon_Hf0 zenon_H17e zenon_Ha0 zenon_Ha1 zenon_H106 zenon_H114 zenon_H1d5 zenon_Hef zenon_H26e zenon_H173 zenon_Hdb. % 18.99/19.11 apply (zenon_or_s _ _ zenon_H18c); [ zenon_intro zenon_H86 | zenon_intro zenon_H18d ]. % 18.99/19.11 exact (zenon_H177 zenon_H86). % 18.99/19.11 apply (zenon_or_s _ _ zenon_H18d); [ zenon_intro zenon_H110 | zenon_intro zenon_H18e ]. % 18.99/19.11 apply (zenon_or_s _ _ zenon_H106); [ zenon_intro zenon_Hed | zenon_intro zenon_H107 ]. % 18.99/19.11 apply (zenon_L214_); trivial. % 18.99/19.11 apply (zenon_or_s _ _ zenon_H107); [ zenon_intro zenon_Ha5 | zenon_intro zenon_H108 ]. % 18.99/19.11 apply (zenon_L357_); trivial. % 18.99/19.11 apply (zenon_or_s _ _ zenon_H108); [ zenon_intro zenon_Hf1 | zenon_intro zenon_Hf4 ]. % 18.99/19.11 apply (zenon_L59_); trivial. % 18.99/19.11 apply (zenon_L1094_); trivial. % 18.99/19.11 apply (zenon_or_s _ _ zenon_H18e); [ zenon_intro zenon_H113 | zenon_intro zenon_Hd7 ]. % 18.99/19.11 exact (zenon_H114 zenon_H113). % 18.99/19.11 apply (zenon_L1065_); trivial. % 18.99/19.11 (* end of lemma zenon_L1095_ *) % 18.99/19.11 assert (zenon_L1096_ : (((op (e0) (e1)) = (e0))\/(((op (e1) (e1)) = (e0))\/(((op (e2) (e1)) = (e0))\/((op (e3) (e1)) = (e0))))) -> (~((op (e1) (e1)) = (op (e1) (e3)))) -> ((op (e1) (e3)) = (e0)) -> (((op (e1) (e0)) = (e2))\/(((op (e1) (e1)) = (e2))\/(((op (e1) (e2)) = (e2))\/((op (e1) (e3)) = (e2))))) -> (~((op (e1) (e0)) = (e2))) -> (~((op (e2) (e1)) = (op (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))))) -> (~((op (e1) (e2)) = (op (e2) (e2)))) -> ((op (e1) (e2)) = (e1)) -> (~((op (e0) (e1)) = (op (e2) (e1)))) -> ((op (e0) (e1)) = (e1)) -> (~((e0) = (e1))) -> (((op (e2) (e0)) = (e1))\/(((op (e2) (e1)) = (e1))\/(((op (e2) (e2)) = (e1))\/((op (e2) (e3)) = (e1))))) -> (~((op (e1) (e2)) = (e2))) -> (((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 (e1) (e3)) = (op (e2) (e3)))) -> False). % 18.99/19.11 do 0 intro. intros zenon_H245 zenon_H57 zenon_H1f zenon_H18c zenon_H177 zenon_H1c7 zenon_H1f0 zenon_H34 zenon_H1cc zenon_H2b zenon_Hf0 zenon_H17e zenon_Ha0 zenon_Ha1 zenon_H106 zenon_H114 zenon_H1d5 zenon_Hef zenon_H26e zenon_H173 zenon_Hdb. % 18.99/19.11 apply (zenon_or_s _ _ zenon_H245); [ zenon_intro zenon_H49 | zenon_intro zenon_H246 ]. % 18.99/19.11 apply (zenon_L38_); trivial. % 18.99/19.11 apply (zenon_or_s _ _ zenon_H246); [ zenon_intro zenon_H29 | zenon_intro zenon_H247 ]. % 18.99/19.11 apply (zenon_L13_); trivial. % 18.99/19.11 apply (zenon_or_s _ _ zenon_H247); [ zenon_intro zenon_H36 | zenon_intro zenon_H1b1 ]. % 18.99/19.11 apply (zenon_L642_); trivial. % 18.99/19.11 apply (zenon_L1095_); trivial. % 18.99/19.11 (* end of lemma zenon_L1096_ *) % 18.99/19.11 assert (zenon_L1097_ : (((op (e1) (e0)) = (e0))\/(((op (e1) (e1)) = (e0))\/(((op (e1) (e2)) = (e0))\/((op (e1) (e3)) = (e0))))) -> (~((op (e1) (e0)) = (op (e2) (e0)))) -> (~((e0) = (e2))) -> ((op (e0) (e2)) = (e0)) -> (~((op (e0) (e2)) = (op (e1) (e2)))) -> (((op (e0) (e1)) = (e0))\/(((op (e1) (e1)) = (e0))\/(((op (e2) (e1)) = (e0))\/((op (e3) (e1)) = (e0))))) -> (~((op (e1) (e1)) = (op (e1) (e3)))) -> (((op (e1) (e0)) = (e2))\/(((op (e1) (e1)) = (e2))\/(((op (e1) (e2)) = (e2))\/((op (e1) (e3)) = (e2))))) -> (~((op (e1) (e0)) = (e2))) -> (~((op (e2) (e1)) = (op (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))))) -> (~((op (e1) (e2)) = (op (e2) (e2)))) -> ((op (e1) (e2)) = (e1)) -> (~((op (e0) (e1)) = (op (e2) (e1)))) -> ((op (e0) (e1)) = (e1)) -> (~((e0) = (e1))) -> (((op (e2) (e0)) = (e1))\/(((op (e2) (e1)) = (e1))\/(((op (e2) (e2)) = (e1))\/((op (e2) (e3)) = (e1))))) -> (~((op (e1) (e2)) = (e2))) -> (((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 (e1) (e3)) = (op (e2) (e3)))) -> False). % 18.99/19.11 do 0 intro. intros zenon_H22 zenon_H201 zenon_H149 zenon_H48 zenon_H195 zenon_H245 zenon_H57 zenon_H18c zenon_H177 zenon_H1c7 zenon_H1f0 zenon_H34 zenon_H1cc zenon_H2b zenon_Hf0 zenon_H17e zenon_Ha0 zenon_Ha1 zenon_H106 zenon_H114 zenon_H1d5 zenon_Hef zenon_H26e zenon_H173 zenon_Hdb. % 18.99/19.11 apply (zenon_or_s _ _ zenon_H22); [ zenon_intro zenon_H27 | zenon_intro zenon_H26 ]. % 18.99/19.11 apply (zenon_L332_); trivial. % 18.99/19.11 apply (zenon_or_s _ _ zenon_H26); [ zenon_intro zenon_H29 | zenon_intro zenon_H28 ]. % 18.99/19.11 apply (zenon_L1066_); trivial. % 18.99/19.11 apply (zenon_or_s _ _ zenon_H28); [ zenon_intro zenon_H2a | zenon_intro zenon_H1f ]. % 18.99/19.11 apply (zenon_L334_); trivial. % 18.99/19.11 apply (zenon_L1096_); trivial. % 18.99/19.11 (* end of lemma zenon_L1097_ *) % 18.99/19.11 assert (zenon_L1098_ : (((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)) = (op (e1) (e3)))) -> ((op (e1) (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 (e2) (e0)) = (e2))) -> (~((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 (e3) (e1)) = (op (e3) (e3)))) -> ((op (e0) (e3)) = (e1)) -> (~((op (e0) (e3)) = (op (e3) (e3)))) -> (~((op (e2) (e3)) = (op (e3) (e3)))) -> (~((op (e3) (e3)) = (e3))) -> False). % 18.99/19.11 do 0 intro. intros zenon_H245 zenon_H4a zenon_H48 zenon_H57 zenon_H1f zenon_H34 zenon_H1f0 zenon_H1d5 zenon_Hef zenon_H26e zenon_H173 zenon_H101 zenon_H130 zenon_Hc3 zenon_Hc2 zenon_Hf3 zenon_H102. % 18.99/19.11 apply (zenon_or_s _ _ zenon_H245); [ zenon_intro zenon_H49 | zenon_intro zenon_H246 ]. % 18.99/19.11 apply (zenon_L9_); trivial. % 18.99/19.11 apply (zenon_or_s _ _ zenon_H246); [ zenon_intro zenon_H29 | zenon_intro zenon_H247 ]. % 18.99/19.11 apply (zenon_L13_); trivial. % 18.99/19.11 apply (zenon_or_s _ _ zenon_H247); [ zenon_intro zenon_H36 | zenon_intro zenon_H1b1 ]. % 18.99/19.11 apply (zenon_L642_); trivial. % 18.99/19.11 apply (zenon_L1077_); trivial. % 18.99/19.11 (* end of lemma zenon_L1098_ *) % 18.99/19.11 assert (zenon_L1099_ : (((op (e1) (e0)) = (e0))\/(((op (e1) (e1)) = (e0))\/(((op (e1) (e2)) = (e0))\/((op (e1) (e3)) = (e0))))) -> (~((op (e1) (e0)) = (op (e2) (e0)))) -> (~((op (e1) (e3)) = (op (e2) (e3)))) -> (~((op (e1) (e2)) = (e2))) -> (~((e0) = (e2))) -> (~((op (e1) (e0)) = (e2))) -> (((op (e1) (e0)) = (e2))\/(((op (e1) (e1)) = (e2))\/(((op (e1) (e2)) = (e2))\/((op (e1) (e3)) = (e2))))) -> (~((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)) = (op (e0) (e2)))) -> ((op (e0) (e2)) = (e0)) -> (~((op (e1) (e1)) = (op (e1) (e3)))) -> ((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 (e2) (e0)) = (e2))) -> (~((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 (e3) (e1)) = (op (e3) (e3)))) -> ((op (e0) (e3)) = (e1)) -> (~((op (e0) (e3)) = (op (e3) (e3)))) -> (~((op (e2) (e3)) = (op (e3) (e3)))) -> (~((op (e3) (e3)) = (e3))) -> False). % 18.99/19.11 do 0 intro. intros zenon_H22 zenon_H201 zenon_Hdb zenon_H114 zenon_H149 zenon_H177 zenon_H18c zenon_H195 zenon_H245 zenon_H4a zenon_H48 zenon_H57 zenon_H34 zenon_H1f0 zenon_H1d5 zenon_Hef zenon_H26e zenon_H173 zenon_H101 zenon_H130 zenon_Hc3 zenon_Hc2 zenon_Hf3 zenon_H102. % 18.99/19.11 apply (zenon_or_s _ _ zenon_H22); [ zenon_intro zenon_H27 | zenon_intro zenon_H26 ]. % 18.99/19.11 apply (zenon_L332_); trivial. % 18.99/19.11 apply (zenon_or_s _ _ zenon_H26); [ zenon_intro zenon_H29 | zenon_intro zenon_H28 ]. % 18.99/19.11 apply (zenon_L1066_); trivial. % 18.99/19.11 apply (zenon_or_s _ _ zenon_H28); [ zenon_intro zenon_H2a | zenon_intro zenon_H1f ]. % 18.99/19.11 apply (zenon_L334_); trivial. % 18.99/19.11 apply (zenon_L1098_); trivial. % 18.99/19.11 (* end of lemma zenon_L1099_ *) % 18.99/19.11 assert (zenon_L1100_ : (((op (e0) (e0)) = (e1))\/(((op (e0) (e1)) = (e1))\/(((op (e0) (e2)) = (e1))\/((op (e0) (e3)) = (e1))))) -> (~((op (e0) (e3)) = (e2))) -> (~((op (e0) (e2)) = (e2))) -> (~((op (e0) (e1)) = (e2))) -> (~((e1) = (e2))) -> (((op (e0) (e0)) = (e2))\/(((op (e0) (e1)) = (e2))\/(((op (e0) (e2)) = (e2))\/((op (e0) (e3)) = (e2))))) -> (((op (e2) (e0)) = (e1))\/(((op (e2) (e1)) = (e1))\/(((op (e2) (e2)) = (e1))\/((op (e2) (e3)) = (e1))))) -> (~((e0) = (e1))) -> (~((op (e0) (e1)) = (op (e2) (e1)))) -> (~((op (e1) (e2)) = (op (e2) (e2)))) -> (((op (e2) (e1)) = (e0))\/(((op (e2) (e1)) = (e1))\/(((op (e2) (e1)) = (e2))\/((op (e2) (e1)) = (e3))))) -> (~((op (e2) (e1)) = (op (e2) (e3)))) -> ((op (e1) (e2)) = (e1)) -> (((op (e1) (e0)) = (e0))\/(((op (e1) (e1)) = (e0))\/(((op (e1) (e2)) = (e0))\/((op (e1) (e3)) = (e0))))) -> (~((op (e1) (e0)) = (op (e2) (e0)))) -> (~((op (e1) (e3)) = (op (e2) (e3)))) -> (~((op (e1) (e2)) = (e2))) -> (~((e0) = (e2))) -> (~((op (e1) (e0)) = (e2))) -> (((op (e1) (e0)) = (e2))\/(((op (e1) (e1)) = (e2))\/(((op (e1) (e2)) = (e2))\/((op (e1) (e3)) = (e2))))) -> (~((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)) = (op (e0) (e2)))) -> ((op (e0) (e2)) = (e0)) -> (~((op (e1) (e1)) = (op (e1) (e3)))) -> ((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 (e2) (e0)) = (e2))) -> (~((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 (e3) (e1)) = (op (e3) (e3)))) -> (~((op (e0) (e3)) = (op (e3) (e3)))) -> (~((op (e2) (e3)) = (op (e3) (e3)))) -> (~((op (e3) (e3)) = (e3))) -> False). % 18.99/19.11 do 0 intro. intros zenon_H22d zenon_H12e zenon_H1fd zenon_H26d zenon_H7c zenon_H183 zenon_H106 zenon_Ha1 zenon_H17e zenon_H2b zenon_H1cc zenon_H1c7 zenon_Hf0 zenon_H22 zenon_H201 zenon_Hdb zenon_H114 zenon_H149 zenon_H177 zenon_H18c zenon_H195 zenon_H245 zenon_H4a zenon_H48 zenon_H57 zenon_H34 zenon_H1f0 zenon_H1d5 zenon_Hef zenon_H26e zenon_H173 zenon_H101 zenon_H130 zenon_Hc2 zenon_Hf3 zenon_H102. % 18.99/19.11 apply (zenon_or_s _ _ zenon_H22d); [ zenon_intro zenon_H7a | zenon_intro zenon_H22e ]. % 18.99/19.11 apply (zenon_L1059_); trivial. % 18.99/19.11 apply (zenon_or_s _ _ zenon_H22e); [ zenon_intro zenon_Ha0 | zenon_intro zenon_H22f ]. % 18.99/19.11 apply (zenon_L1097_); trivial. % 18.99/19.12 apply (zenon_or_s _ _ zenon_H22f); [ zenon_intro zenon_H122 | zenon_intro zenon_Hc3 ]. % 18.99/19.12 apply (zenon_L530_); trivial. % 18.99/19.12 apply (zenon_L1099_); trivial. % 18.99/19.12 (* end of lemma zenon_L1100_ *) % 18.99/19.12 assert (zenon_L1101_ : ((~((op (e1) (e2)) = (e2)))\/((op (e1) (e2)) = (e2))) -> ((~((op (e2) (e0)) = (e2)))\/((op (e2) (e2)) = (e0))) -> (~((op (e0) (e2)) = (op (e2) (e2)))) -> ((~((op (e2) (e3)) = (e2)))\/((op (e2) (e2)) = (e3))) -> (((op (e0) (e2)) = (e2))\/(((op (e1) (e2)) = (e2))\/(((op (e2) (e2)) = (e2))\/((op (e3) (e2)) = (e2))))) -> (~((op (e0) (e2)) = (e2))) -> ((~((op (e3) (e3)) = (e2)))\/((op (e3) (e2)) = (e3))) -> (~((op (e2) (e2)) = (op (e3) (e2)))) -> (~((op (e0) (e0)) = (e0))) -> (((op (e0) (e0)) = (e1))\/(((op (e0) (e1)) = (e1))\/(((op (e0) (e2)) = (e1))\/((op (e0) (e3)) = (e1))))) -> (~((e0) = (e1))) -> (~((op (e1) (e0)) = (op (e1) (e1)))) -> (((op (e1) (e0)) = (e0))\/(((op (e1) (e0)) = (e1))\/(((op (e1) (e0)) = (e2))\/((op (e1) (e0)) = (e3))))) -> (~((op (e1) (e0)) = (e2))) -> (~((op (e1) (e0)) = (op (e2) (e0)))) -> (~((op (e1) (e0)) = (op (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 (e1) (e3)) = (op (e2) (e3)))) -> (~((e0) = (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))))) -> (~((e2) = (e3))) -> (((op (e0) (e1)) = (e2))\/(((op (e1) (e1)) = (e2))\/(((op (e2) (e1)) = (e2))\/((op (e3) (e1)) = (e2))))) -> (~((op (e0) (e1)) = (op (e3) (e1)))) -> (((op (e0) (e1)) = (e0))\/(((op (e0) (e1)) = (e1))\/(((op (e0) (e1)) = (e2))\/((op (e0) (e1)) = (e3))))) -> (~((op (e0) (e1)) = (op (e2) (e1)))) -> (~((op (e1) (e1)) = (e1))) -> (~((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))))) -> (~((op (e2) (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)) = (op (e2) (e3)))) -> (((op (e0) (e3)) = (e1))\/(((op (e1) (e3)) = (e1))\/(((op (e2) (e3)) = (e1))\/((op (e3) (e3)) = (e1))))) -> ((op (e1) (e2)) = (e1)) -> (~((op (e1) (e2)) = (op (e1) (e3)))) -> (~((op (e3) (e2)) = (op (e3) (e3)))) -> (~((op (e0) (e3)) = (op (e3) (e3)))) -> (~((op (e2) (e1)) = (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) (e0)) = (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) (e2)) = (op (e2) (e2)))) -> (((op (e1) (e0)) = (e0))\/(((op (e1) (e1)) = (e0))\/(((op (e1) (e2)) = (e0))\/((op (e1) (e3)) = (e0))))) -> (~((op (e1) (e1)) = (op (e1) (e3)))) -> (~((op (e3) (e1)) = (op (e3) (e2)))) -> (((op (e2) (e0)) = (e1))\/(((op (e2) (e1)) = (e1))\/(((op (e2) (e2)) = (e1))\/((op (e2) (e3)) = (e1))))) -> (~((op (e3) (e0)) = (op (e3) (e1)))) -> (~((op (e0) (e2)) = (op (e1) (e2)))) -> (~((op (e1) (e2)) = (op (e3) (e2)))) -> (((op (e3) (e0)) = (e1))\/(((op (e3) (e1)) = (e1))\/(((op (e3) (e2)) = (e1))\/((op (e3) (e3)) = (e1))))) -> (~((op (e1) (e0)) = (op (e1) (e3)))) -> ((op (e0) (e2)) = (e0)) -> (~((op (e0) (e2)) = (op (e0) (e3)))) -> (~((op (e0) (e2)) = (op (e3) (e2)))) -> (((op (e0) (e0)) = (e1))\/(((op (e1) (e0)) = (e1))\/(((op (e2) (e0)) = (e1))\/((op (e3) (e0)) = (e1))))) -> (~((e1) = (e2))) -> (~((op (e0) (e1)) = (e2))) -> (~((op (e0) (e3)) = (e2))) -> (((op (e0) (e0)) = (e2))\/(((op (e0) (e1)) = (e2))\/(((op (e0) (e2)) = (e2))\/((op (e0) (e3)) = (e2))))) -> (((op (e2) (e1)) = (e0))\/(((op (e2) (e1)) = (e1))\/(((op (e2) (e1)) = (e2))\/((op (e2) (e1)) = (e3))))) -> (~((op (e2) (e0)) = (op (e2) (e1)))) -> (((op (e0) (e0)) = (e0))\/(((op (e1) (e0)) = (e0))\/(((op (e2) (e0)) = (e0))\/((op (e3) (e0)) = (e0))))) -> ((~((op (e3) (e2)) = (e2)))\/((op (e3) (e2)) = (e2))) -> (~((op (e2) (e2)) = (e2))) -> (((op (e2) (e0)) = (e2))\/(((op (e2) (e1)) = (e2))\/(((op (e2) (e2)) = (e2))\/((op (e2) (e3)) = (e2))))) -> ((~((op (e2) (e1)) = (e2)))\/((op (e2) (e2)) = (e1))) -> (~((e1) = (e3))) -> ((~((op (e1) (e3)) = (e2)))\/((op (e1) (e2)) = (e3))) -> False). % 18.99/19.12 do 0 intro. intros zenon_H275 zenon_H276 zenon_Ha8 zenon_H277 zenon_H172 zenon_H1fd zenon_H278 zenon_H18f zenon_H3f zenon_H22d zenon_Ha1 zenon_H45 zenon_H25e zenon_H177 zenon_H201 zenon_H1fa zenon_H4a zenon_H18c zenon_Hdb zenon_H149 zenon_H1ac zenon_H109 zenon_H12b zenon_H1d8 zenon_H210 zenon_H212 zenon_H17e zenon_H10a zenon_H54 zenon_He4 zenon_H245 zenon_Hf3 zenon_Hdf zenon_H1d zenon_Hd5 zenon_He2 zenon_H133 zenon_Hf0 zenon_H124 zenon_H62 zenon_Hc2 zenon_H1c7 zenon_H67 zenon_H130 zenon_H71 zenon_H102 zenon_H101 zenon_H2b zenon_H22 zenon_H57 zenon_H1a4 zenon_H106 zenon_H1cf zenon_H195 zenon_H115 zenon_He8 zenon_Hd8 zenon_H48 zenon_H208 zenon_H14f zenon_H235 zenon_H7c zenon_H26d zenon_H12e zenon_H183 zenon_H1cc zenon_H1f0 zenon_H3e zenon_H273 zenon_H173 zenon_H1d5 zenon_H271 zenon_H95 zenon_H279. % 18.99/19.12 apply (zenon_or_s _ _ zenon_H275); [ zenon_intro zenon_H114 | zenon_intro zenon_H113 ]. % 18.99/19.12 apply (zenon_or_s _ _ zenon_H279); [ zenon_intro zenon_H14c | zenon_intro zenon_H16c ]. % 18.99/19.12 apply (zenon_or_s _ _ zenon_H276); [ zenon_intro zenon_Hef | zenon_intro zenon_H2c ]. % 18.99/19.12 apply (zenon_or_s _ _ zenon_H271); [ zenon_intro zenon_H26e | zenon_intro zenon_Hf1 ]. % 18.99/19.12 apply (zenon_or_s _ _ zenon_H277); [ zenon_intro zenon_H274 | zenon_intro zenon_Haa ]. % 18.99/19.12 apply (zenon_L1062_); trivial. % 18.99/19.12 apply (zenon_or_s _ _ zenon_H273); [ zenon_intro zenon_H272 | zenon_intro zenon_H151 ]. % 18.99/19.12 apply (zenon_L1055_); trivial. % 18.99/19.12 apply (zenon_or_s _ _ zenon_H278); [ zenon_intro zenon_Hf7 | zenon_intro zenon_H163 ]. % 18.99/19.12 apply (zenon_or_s _ _ zenon_H3e); [ zenon_intro zenon_H42 | zenon_intro zenon_H41 ]. % 18.99/19.12 exact (zenon_H3f zenon_H42). % 18.99/19.12 apply (zenon_or_s _ _ zenon_H41); [ zenon_intro zenon_H27 | zenon_intro zenon_H43 ]. % 18.99/19.12 apply (zenon_or_s _ _ zenon_H22d); [ zenon_intro zenon_H7a | zenon_intro zenon_H22e ]. % 18.99/19.12 apply (zenon_L1059_); trivial. % 18.99/19.12 apply (zenon_or_s _ _ zenon_H22e); [ zenon_intro zenon_Ha0 | zenon_intro zenon_H22f ]. % 18.99/19.12 apply (zenon_or_s _ _ zenon_H235); [ zenon_intro zenon_H7a | zenon_intro zenon_H236 ]. % 18.99/19.12 apply (zenon_L1059_); trivial. % 18.99/19.12 apply (zenon_or_s _ _ zenon_H236); [ zenon_intro zenon_H9d | zenon_intro zenon_H237 ]. % 18.99/19.12 apply (zenon_L262_); trivial. % 18.99/19.12 apply (zenon_or_s _ _ zenon_H237); [ zenon_intro zenon_Hed | zenon_intro zenon_Hac ]. % 18.99/19.12 apply (zenon_or_s _ _ zenon_H183); [ zenon_intro zenon_H7b | zenon_intro zenon_H186 ]. % 18.99/19.12 apply (zenon_or_s _ _ zenon_H245); [ zenon_intro zenon_H49 | zenon_intro zenon_H246 ]. % 18.99/19.12 apply (zenon_L38_); trivial. % 18.99/19.12 apply (zenon_or_s _ _ zenon_H246); [ zenon_intro zenon_H29 | zenon_intro zenon_H247 ]. % 18.99/19.12 apply (zenon_L8_); trivial. % 18.99/19.12 apply (zenon_or_s _ _ zenon_H247); [ zenon_intro zenon_H36 | zenon_intro zenon_H1b1 ]. % 18.99/19.12 apply (zenon_or_s _ _ zenon_H1d5); [ zenon_intro zenon_Hee | zenon_intro zenon_H1d6 ]. % 18.99/19.12 exact (zenon_Hef zenon_Hee). % 18.99/19.12 apply (zenon_or_s _ _ zenon_H1d6); [ zenon_intro zenon_H1ca | zenon_intro zenon_H1d7 ]. % 18.99/19.12 exact (zenon_H26e zenon_H1ca). % 18.99/19.12 apply (zenon_or_s _ _ zenon_H1d7); [ zenon_intro zenon_H176 | zenon_intro zenon_H11d ]. % 18.99/19.12 exact (zenon_H173 zenon_H176). % 18.99/19.12 apply (zenon_or_s _ _ zenon_H1ac); [ zenon_intro zenon_H44 | zenon_intro zenon_H1af ]. % 18.99/19.12 apply (zenon_L1064_); trivial. % 18.99/19.12 apply (zenon_or_s _ _ zenon_H1af); [ zenon_intro zenon_H1b1 | zenon_intro zenon_H1b0 ]. % 18.99/19.12 apply (zenon_L1091_); trivial. % 18.99/19.12 apply (zenon_or_s _ _ zenon_H1b0); [ zenon_intro zenon_H61 | zenon_intro zenon_H60 ]. % 18.99/19.12 apply (zenon_L342_); trivial. % 18.99/19.12 apply (zenon_or_s _ _ zenon_He8); [ zenon_intro zenon_Hac | zenon_intro zenon_Heb ]. % 18.99/19.12 apply (zenon_L1082_); trivial. % 18.99/19.12 apply (zenon_or_s _ _ zenon_Heb); [ zenon_intro zenon_Hae | zenon_intro zenon_Hec ]. % 18.99/19.12 apply (zenon_L1074_); trivial. % 18.99/19.12 apply (zenon_or_s _ _ zenon_Hec); [ zenon_intro zenon_Hba | zenon_intro zenon_Hc4 ]. % 18.99/19.12 apply (zenon_L69_); trivial. % 18.99/19.12 apply (zenon_L1093_); trivial. % 18.99/19.12 apply (zenon_L1091_); trivial. % 18.99/19.12 apply (zenon_or_s _ _ zenon_H186); [ zenon_intro zenon_H10f | zenon_intro zenon_H187 ]. % 18.99/19.12 exact (zenon_H26d zenon_H10f). % 18.99/19.12 apply (zenon_or_s _ _ zenon_H187); [ zenon_intro zenon_H150 | zenon_intro zenon_Hcd ]. % 18.99/19.12 exact (zenon_H1fd zenon_H150). % 18.99/19.12 exact (zenon_H12e zenon_Hcd). % 18.99/19.12 apply (zenon_L1087_); trivial. % 18.99/19.12 apply (zenon_or_s _ _ zenon_H22f); [ zenon_intro zenon_H122 | zenon_intro zenon_Hc3 ]. % 18.99/19.12 apply (zenon_L355_); trivial. % 18.99/19.12 apply (zenon_L1078_); trivial. % 18.99/19.12 apply (zenon_or_s _ _ zenon_H43); [ zenon_intro zenon_H34 | zenon_intro zenon_H44 ]. % 18.99/19.12 apply (zenon_L1100_); trivial. % 18.99/19.12 apply (zenon_L1085_); trivial. % 18.99/19.12 apply (zenon_L180_); trivial. % 18.99/19.12 apply (zenon_L59_); trivial. % 18.99/19.12 apply (zenon_L679_); trivial. % 18.99/19.12 apply (zenon_L167_); trivial. % 18.99/19.12 apply (zenon_L68_); trivial. % 18.99/19.12 (* end of lemma zenon_L1101_ *) % 18.99/19.12 assert (zenon_L1102_ : (((op (e3) (e3)) = (e0))\/(((op (e3) (e3)) = (e1))\/(((op (e3) (e3)) = (e2))\/((op (e3) (e3)) = (e3))))) -> (~((op (e3) (e1)) = (op (e3) (e3)))) -> ((op (e3) (e1)) = (e0)) -> ((op (e1) (e3)) = (e1)) -> (~((op (e1) (e3)) = (op (e3) (e3)))) -> (~((op (e3) (e3)) = (e2))) -> (~((op (e3) (e3)) = (e3))) -> False). % 18.99/19.12 do 0 intro. intros zenon_H101 zenon_H130 zenon_H1b1 zenon_Hd6 zenon_Hd5 zenon_Hf7 zenon_H102. % 18.99/19.12 apply (zenon_or_s _ _ zenon_H101); [ zenon_intro zenon_H60 | zenon_intro zenon_H103 ]. % 18.99/19.12 apply (zenon_L244_); trivial. % 18.99/19.12 apply (zenon_or_s _ _ zenon_H103); [ zenon_intro zenon_Hc4 | zenon_intro zenon_H104 ]. % 18.99/19.12 apply (zenon_L50_); trivial. % 18.99/19.12 apply (zenon_or_s _ _ zenon_H104); [ zenon_intro zenon_Hf6 | zenon_intro zenon_H105 ]. % 18.99/19.12 exact (zenon_Hf7 zenon_Hf6). % 18.99/19.12 exact (zenon_H102 zenon_H105). % 18.99/19.12 (* end of lemma zenon_L1102_ *) % 18.99/19.12 assert (zenon_L1103_ : (((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 (e3) (e2)) = (e1)) -> (~((op (e1) (e2)) = (op (e3) (e2)))) -> (((op (e3) (e3)) = (e0))\/(((op (e3) (e3)) = (e1))\/(((op (e3) (e3)) = (e2))\/((op (e3) (e3)) = (e3))))) -> (~((op (e3) (e1)) = (op (e3) (e3)))) -> ((op (e3) (e1)) = (e0)) -> (~((op (e1) (e3)) = (op (e3) (e3)))) -> (~((op (e3) (e3)) = (e2))) -> (~((op (e3) (e3)) = (e3))) -> False). % 18.99/19.12 do 0 intro. intros zenon_H128 zenon_Ha1 zenon_H27 zenon_H10a zenon_Hba zenon_H115 zenon_H101 zenon_H130 zenon_H1b1 zenon_Hd5 zenon_Hf7 zenon_H102. % 18.99/19.12 apply (zenon_or_s _ _ zenon_H128); [ zenon_intro zenon_H9d | zenon_intro zenon_H129 ]. % 18.99/19.12 apply (zenon_L262_); trivial. % 18.99/19.12 apply (zenon_or_s _ _ zenon_H129); [ zenon_intro zenon_H10d | zenon_intro zenon_H12a ]. % 18.99/19.12 exact (zenon_H10a zenon_H10d). % 18.99/19.12 apply (zenon_or_s _ _ zenon_H12a); [ zenon_intro zenon_Hf0 | zenon_intro zenon_Hd6 ]. % 18.99/19.12 apply (zenon_L69_); trivial. % 18.99/19.12 apply (zenon_L1102_); trivial. % 18.99/19.12 (* end of lemma zenon_L1103_ *) % 18.99/19.12 assert (zenon_L1104_ : (((op (e0) (e3)) = (e2))\/(((op (e1) (e3)) = (e2))\/(((op (e2) (e3)) = (e2))\/((op (e3) (e3)) = (e2))))) -> (~((op (e0) (e3)) = (e2))) -> (~((op (e3) (e3)) = (e3))) -> ((op (e3) (e2)) = (e1)) -> (~((op (e3) (e2)) = (op (e3) (e3)))) -> ((op (e0) (e3)) = (e1)) -> (((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) (e3)) = (e2))) -> False). % 18.99/19.12 do 0 intro. intros zenon_H145 zenon_H12e zenon_H102 zenon_Hba zenon_H62 zenon_Hc3 zenon_H101 zenon_H1c7 zenon_H1ca zenon_Hf7. % 18.99/19.12 apply (zenon_or_s _ _ zenon_H145); [ zenon_intro zenon_Hcd | zenon_intro zenon_H146 ]. % 18.99/19.12 exact (zenon_H12e zenon_Hcd). % 18.99/19.12 apply (zenon_or_s _ _ zenon_H146); [ zenon_intro zenon_Hd7 | zenon_intro zenon_H147 ]. % 18.99/19.12 apply (zenon_or_s _ _ zenon_H101); [ zenon_intro zenon_H60 | zenon_intro zenon_H103 ]. % 18.99/19.12 apply (zenon_L201_); trivial. % 18.99/19.12 apply (zenon_or_s _ _ zenon_H103); [ zenon_intro zenon_Hc4 | zenon_intro zenon_H104 ]. % 18.99/19.12 apply (zenon_L147_); trivial. % 18.99/19.12 apply (zenon_or_s _ _ zenon_H104); [ zenon_intro zenon_Hf6 | zenon_intro zenon_H105 ]. % 18.99/19.12 exact (zenon_Hf7 zenon_Hf6). % 18.99/19.12 exact (zenon_H102 zenon_H105). % 18.99/19.12 apply (zenon_or_s _ _ zenon_H147); [ zenon_intro zenon_H11d | zenon_intro zenon_Hf6 ]. % 18.99/19.12 apply (zenon_L224_); trivial. % 18.99/19.12 exact (zenon_Hf7 zenon_Hf6). % 18.99/19.12 (* end of lemma zenon_L1104_ *) % 18.99/19.12 assert (zenon_L1105_ : (((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)) = (e0)) -> ((op (e2) (e1)) = (e1)) -> (~((op (e0) (e1)) = (op (e2) (e1)))) -> (~((op (e0) (e1)) = (e2))) -> ((op (e3) (e1)) = (e2)) -> ((op (e1) (e1)) = (e0)) -> False). % 18.99/19.12 do 0 intro. intros zenon_H212 zenon_H4a zenon_H48 zenon_Ha5 zenon_H17e zenon_H26d zenon_H14d zenon_H29. % 18.99/19.12 apply (zenon_or_s _ _ zenon_H212); [ zenon_intro zenon_H49 | zenon_intro zenon_H213 ]. % 18.99/19.12 apply (zenon_L9_); trivial. % 18.99/19.12 apply (zenon_or_s _ _ zenon_H213); [ zenon_intro zenon_Ha0 | zenon_intro zenon_H214 ]. % 18.99/19.12 apply (zenon_L357_); trivial. % 18.99/19.12 apply (zenon_or_s _ _ zenon_H214); [ zenon_intro zenon_H10f | zenon_intro zenon_H99 ]. % 18.99/19.12 exact (zenon_H26d zenon_H10f). % 18.99/19.12 apply (zenon_L385_); trivial. % 18.99/19.12 (* end of lemma zenon_L1105_ *) % 18.99/19.12 assert (zenon_L1106_ : (((op (e0) (e3)) = (e2))\/(((op (e1) (e3)) = (e2))\/(((op (e2) (e3)) = (e2))\/((op (e3) (e3)) = (e2))))) -> (~((op (e0) (e3)) = (e2))) -> (~((op (e3) (e3)) = (e3))) -> ((op (e3) (e1)) = (e1)) -> (~((op (e3) (e1)) = (op (e3) (e3)))) -> ((op (e0) (e3)) = (e1)) -> (((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) (e3)) = (e2))) -> False). % 18.99/19.12 do 0 intro. intros zenon_H145 zenon_H12e zenon_H102 zenon_Hae zenon_H130 zenon_Hc3 zenon_H101 zenon_H1c7 zenon_H1ca zenon_Hf7. % 18.99/19.12 apply (zenon_or_s _ _ zenon_H145); [ zenon_intro zenon_Hcd | zenon_intro zenon_H146 ]. % 18.99/19.12 exact (zenon_H12e zenon_Hcd). % 18.99/19.12 apply (zenon_or_s _ _ zenon_H146); [ zenon_intro zenon_Hd7 | zenon_intro zenon_H147 ]. % 18.99/19.12 apply (zenon_or_s _ _ zenon_H101); [ zenon_intro zenon_H60 | zenon_intro zenon_H103 ]. % 18.99/19.12 apply (zenon_L201_); trivial. % 18.99/19.12 apply (zenon_or_s _ _ zenon_H103); [ zenon_intro zenon_Hc4 | zenon_intro zenon_H104 ]. % 18.99/19.12 apply (zenon_L85_); trivial. % 18.99/19.12 apply (zenon_or_s _ _ zenon_H104); [ zenon_intro zenon_Hf6 | zenon_intro zenon_H105 ]. % 18.99/19.12 exact (zenon_Hf7 zenon_Hf6). % 18.99/19.12 exact (zenon_H102 zenon_H105). % 18.99/19.12 apply (zenon_or_s _ _ zenon_H147); [ zenon_intro zenon_H11d | zenon_intro zenon_Hf6 ]. % 18.99/19.12 apply (zenon_L224_); trivial. % 18.99/19.12 exact (zenon_Hf7 zenon_Hf6). % 18.99/19.12 (* end of lemma zenon_L1106_ *) % 18.99/19.12 assert (zenon_L1107_ : (((op (e0) (e1)) = (e2))\/(((op (e1) (e1)) = (e2))\/(((op (e2) (e1)) = (e2))\/((op (e3) (e1)) = (e2))))) -> (~((op (e0) (e1)) = (e2))) -> (~((op (e1) (e1)) = (e2))) -> (~((op (e3) (e3)) = (e2))) -> (~((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)) = (e1)) -> (~((op (e3) (e1)) = (op (e3) (e3)))) -> (~((op (e3) (e3)) = (e3))) -> (~((op (e0) (e3)) = (e2))) -> (((op (e0) (e3)) = (e2))\/(((op (e1) (e3)) = (e2))\/(((op (e2) (e3)) = (e2))\/((op (e3) (e3)) = (e2))))) -> ((op (e3) (e1)) = (e1)) -> (~((e1) = (e2))) -> False). % 18.99/19.12 do 0 intro. intros zenon_H1d8 zenon_H26d zenon_H20c zenon_Hf7 zenon_H1c7 zenon_H101 zenon_Hc3 zenon_H130 zenon_H102 zenon_H12e zenon_H145 zenon_Hae zenon_H7c. % 18.99/19.12 apply (zenon_or_s _ _ zenon_H1d8); [ zenon_intro zenon_H10f | zenon_intro zenon_H1d9 ]. % 18.99/19.12 exact (zenon_H26d zenon_H10f). % 18.99/19.12 apply (zenon_or_s _ _ zenon_H1d9); [ zenon_intro zenon_H110 | zenon_intro zenon_H1da ]. % 18.99/19.12 exact (zenon_H20c zenon_H110). % 18.99/19.12 apply (zenon_or_s _ _ zenon_H1da); [ zenon_intro zenon_H1ca | zenon_intro zenon_H14d ]. % 18.99/19.12 apply (zenon_L1106_); trivial. % 18.99/19.12 apply (zenon_L152_); trivial. % 18.99/19.12 (* end of lemma zenon_L1107_ *) % 18.99/19.12 assert (zenon_L1108_ : (((op (e0) (e1)) = (e1))\/(((op (e1) (e1)) = (e1))\/(((op (e2) (e1)) = (e1))\/((op (e3) (e1)) = (e1))))) -> (~((op (e0) (e1)) = (op (e0) (e3)))) -> (~((op (e1) (e1)) = (e1))) -> ((op (e1) (e1)) = (e0)) -> (~((op (e0) (e1)) = (op (e2) (e1)))) -> ((op (e0) (e2)) = (e0)) -> (~((op (e0) (e1)) = (op (e0) (e2)))) -> (((op (e0) (e1)) = (e0))\/(((op (e0) (e1)) = (e1))\/(((op (e0) (e1)) = (e2))\/((op (e0) (e1)) = (e3))))) -> ((op (e3) (e2)) = (e1)) -> (~((op (e3) (e2)) = (op (e3) (e3)))) -> (((op (e0) (e1)) = (e2))\/(((op (e1) (e1)) = (e2))\/(((op (e2) (e1)) = (e2))\/((op (e3) (e1)) = (e2))))) -> (~((op (e0) (e1)) = (e2))) -> (~((op (e1) (e1)) = (e2))) -> (~((op (e3) (e3)) = (e2))) -> (~((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)) = (e1)) -> (~((op (e3) (e1)) = (op (e3) (e3)))) -> (~((op (e3) (e3)) = (e3))) -> (~((op (e0) (e3)) = (e2))) -> (((op (e0) (e3)) = (e2))\/(((op (e1) (e3)) = (e2))\/(((op (e2) (e3)) = (e2))\/((op (e3) (e3)) = (e2))))) -> (~((e1) = (e2))) -> False). % 18.99/19.12 do 0 intro. intros zenon_H109 zenon_H54 zenon_H10a zenon_H29 zenon_H17e zenon_H48 zenon_H4a zenon_H212 zenon_Hba zenon_H62 zenon_H1d8 zenon_H26d zenon_H20c zenon_Hf7 zenon_H1c7 zenon_H101 zenon_Hc3 zenon_H130 zenon_H102 zenon_H12e zenon_H145 zenon_H7c. % 18.99/19.12 apply (zenon_or_s _ _ zenon_H109); [ zenon_intro zenon_Ha0 | zenon_intro zenon_H10b ]. % 18.99/19.12 apply (zenon_L359_); trivial. % 18.99/19.12 apply (zenon_or_s _ _ zenon_H10b); [ zenon_intro zenon_H10d | zenon_intro zenon_H10c ]. % 18.99/19.12 exact (zenon_H10a zenon_H10d). % 18.99/19.12 apply (zenon_or_s _ _ zenon_H10c); [ zenon_intro zenon_Ha5 | zenon_intro zenon_Hae ]. % 18.99/19.12 apply (zenon_or_s _ _ zenon_H1d8); [ zenon_intro zenon_H10f | zenon_intro zenon_H1d9 ]. % 18.99/19.12 exact (zenon_H26d zenon_H10f). % 18.99/19.12 apply (zenon_or_s _ _ zenon_H1d9); [ zenon_intro zenon_H110 | zenon_intro zenon_H1da ]. % 18.99/19.12 exact (zenon_H20c zenon_H110). % 18.99/19.12 apply (zenon_or_s _ _ zenon_H1da); [ zenon_intro zenon_H1ca | zenon_intro zenon_H14d ]. % 18.99/19.12 apply (zenon_L1104_); trivial. % 18.99/19.12 apply (zenon_L1105_); trivial. % 18.99/19.12 apply (zenon_L1107_); trivial. % 18.99/19.12 (* end of lemma zenon_L1108_ *) % 18.99/19.12 assert (zenon_L1109_ : (((op (e0) (e3)) = (e1))\/(((op (e1) (e3)) = (e1))\/(((op (e2) (e3)) = (e1))\/((op (e3) (e3)) = (e1))))) -> (~((op (e3) (e3)) = (e2))) -> ((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 (e3) (e3)) = (e3))) -> (~((op (e0) (e3)) = (e2))) -> (((op (e0) (e3)) = (e2))\/(((op (e1) (e3)) = (e2))\/(((op (e2) (e3)) = (e2))\/((op (e3) (e3)) = (e2))))) -> (~((op (e1) (e0)) = (op (e1) (e3)))) -> ((op (e1) (e0)) = (e1)) -> (~((op (e2) (e2)) = (op (e2) (e3)))) -> ((op (e2) (e2)) = (e1)) -> ((op (e3) (e2)) = (e1)) -> (~((op (e3) (e2)) = (op (e3) (e3)))) -> False). % 18.99/19.12 do 0 intro. intros zenon_H133 zenon_Hf7 zenon_H1ca zenon_H1c7 zenon_H101 zenon_H102 zenon_H12e zenon_H145 zenon_Hd8 zenon_H9d zenon_H6d zenon_Hf1 zenon_Hba zenon_H62. % 18.99/19.12 apply (zenon_or_s _ _ zenon_H133); [ zenon_intro zenon_Hc3 | zenon_intro zenon_H134 ]. % 18.99/19.12 apply (zenon_L1104_); trivial. % 18.99/19.12 apply (zenon_or_s _ _ zenon_H134); [ zenon_intro zenon_Hd6 | zenon_intro zenon_H135 ]. % 18.99/19.12 apply (zenon_L360_); trivial. % 18.99/19.12 apply (zenon_or_s _ _ zenon_H135); [ zenon_intro zenon_Hf4 | zenon_intro zenon_Hc4 ]. % 18.99/19.12 apply (zenon_L84_); trivial. % 18.99/19.12 apply (zenon_L147_); trivial. % 18.99/19.12 (* end of lemma zenon_L1109_ *) % 18.99/19.12 assert (zenon_L1110_ : (((op (e2) (e0)) = (e2))\/(((op (e2) (e1)) = (e2))\/(((op (e2) (e2)) = (e2))\/((op (e2) (e3)) = (e2))))) -> (~((op (e2) (e0)) = (e2))) -> (~((op (e3) (e2)) = (op (e3) (e3)))) -> ((op (e3) (e2)) = (e1)) -> ((op (e2) (e2)) = (e1)) -> (~((op (e2) (e2)) = (op (e2) (e3)))) -> ((op (e1) (e0)) = (e1)) -> (~((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)) = (e2))) -> (~((op (e2) (e1)) = (op (e2) (e3)))) -> (~((op (e3) (e3)) = (e2))) -> (((op (e0) (e3)) = (e1))\/(((op (e1) (e3)) = (e1))\/(((op (e2) (e3)) = (e1))\/((op (e3) (e3)) = (e1))))) -> (~((op (e2) (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 (e3) (e1)) = (e0)) -> ((op (e0) (e3)) = (e1)) -> (~((op (e0) (e3)) = (op (e3) (e3)))) -> (~((op (e2) (e3)) = (op (e3) (e3)))) -> (~((op (e3) (e3)) = (e3))) -> False). % 18.99/19.12 do 0 intro. intros zenon_H1d5 zenon_Hef zenon_H62 zenon_Hba zenon_Hf1 zenon_H6d zenon_H9d zenon_Hd8 zenon_H145 zenon_H12e zenon_H1c7 zenon_Hf7 zenon_H133 zenon_H173 zenon_H101 zenon_H130 zenon_H1b1 zenon_Hc3 zenon_Hc2 zenon_Hf3 zenon_H102. % 18.99/19.12 apply (zenon_or_s _ _ zenon_H1d5); [ zenon_intro zenon_Hee | zenon_intro zenon_H1d6 ]. % 18.99/19.12 exact (zenon_Hef zenon_Hee). % 18.99/19.12 apply (zenon_or_s _ _ zenon_H1d6); [ zenon_intro zenon_H1ca | zenon_intro zenon_H1d7 ]. % 18.99/19.12 apply (zenon_L1109_); trivial. % 18.99/19.12 apply (zenon_or_s _ _ zenon_H1d7); [ zenon_intro zenon_H176 | zenon_intro zenon_H11d ]. % 18.99/19.12 exact (zenon_H173 zenon_H176). % 18.99/19.12 apply (zenon_L245_); trivial. % 18.99/19.12 (* end of lemma zenon_L1110_ *) % 18.99/19.12 assert (zenon_L1111_ : (((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)) = (op (e1) (e3)))) -> ((op (e1) (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 (e2) (e0)) = (e2))) -> (~((op (e3) (e2)) = (op (e3) (e3)))) -> ((op (e3) (e2)) = (e1)) -> ((op (e2) (e2)) = (e1)) -> (~((op (e2) (e2)) = (op (e2) (e3)))) -> ((op (e1) (e0)) = (e1)) -> (~((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)) = (e2))) -> (~((op (e2) (e1)) = (op (e2) (e3)))) -> (~((op (e3) (e3)) = (e2))) -> (((op (e0) (e3)) = (e1))\/(((op (e1) (e3)) = (e1))\/(((op (e2) (e3)) = (e1))\/((op (e3) (e3)) = (e1))))) -> (~((op (e2) (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) (e3)) = (e1)) -> (~((op (e0) (e3)) = (op (e3) (e3)))) -> (~((op (e2) (e3)) = (op (e3) (e3)))) -> (~((op (e3) (e3)) = (e3))) -> False). % 18.99/19.12 do 0 intro. intros zenon_H245 zenon_H4a zenon_H48 zenon_H57 zenon_H1f zenon_H34 zenon_H1f0 zenon_H1d5 zenon_Hef zenon_H62 zenon_Hba zenon_Hf1 zenon_H6d zenon_H9d zenon_Hd8 zenon_H145 zenon_H12e zenon_H1c7 zenon_Hf7 zenon_H133 zenon_H173 zenon_H101 zenon_H130 zenon_Hc3 zenon_Hc2 zenon_Hf3 zenon_H102. % 18.99/19.12 apply (zenon_or_s _ _ zenon_H245); [ zenon_intro zenon_H49 | zenon_intro zenon_H246 ]. % 18.99/19.12 apply (zenon_L9_); trivial. % 18.99/19.12 apply (zenon_or_s _ _ zenon_H246); [ zenon_intro zenon_H29 | zenon_intro zenon_H247 ]. % 18.99/19.12 apply (zenon_L13_); trivial. % 18.99/19.12 apply (zenon_or_s _ _ zenon_H247); [ zenon_intro zenon_H36 | zenon_intro zenon_H1b1 ]. % 18.99/19.12 apply (zenon_L642_); trivial. % 18.99/19.12 apply (zenon_L1110_); trivial. % 18.99/19.12 (* end of lemma zenon_L1111_ *) % 18.99/19.12 assert (zenon_L1112_ : (((op (e0) (e0)) = (e1))\/(((op (e1) (e0)) = (e1))\/(((op (e2) (e0)) = (e1))\/((op (e3) (e0)) = (e1))))) -> (~((op (e0) (e0)) = (op (e0) (e3)))) -> (~((op (e3) (e3)) = (e3))) -> (~((op (e2) (e3)) = (op (e3) (e3)))) -> (~((op (e0) (e3)) = (op (e3) (e3)))) -> ((op (e0) (e3)) = (e1)) -> (~((op (e3) (e1)) = (op (e3) (e3)))) -> (((op (e3) (e3)) = (e0))\/(((op (e3) (e3)) = (e1))\/(((op (e3) (e3)) = (e2))\/((op (e3) (e3)) = (e3))))) -> (~((op (e2) (e2)) = (e2))) -> (((op (e0) (e3)) = (e1))\/(((op (e1) (e3)) = (e1))\/(((op (e2) (e3)) = (e1))\/((op (e3) (e3)) = (e1))))) -> (~((op (e3) (e3)) = (e2))) -> (~((op (e2) (e1)) = (op (e2) (e3)))) -> (~((op (e0) (e3)) = (e2))) -> (((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)) = (op (e2) (e3)))) -> ((op (e2) (e2)) = (e1)) -> (~((op (e3) (e2)) = (op (e3) (e3)))) -> (~((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) (e2)) = (e0)) -> (~((op (e0) (e1)) = (op (e0) (e2)))) -> (((op (e0) (e1)) = (e0))\/(((op (e1) (e1)) = (e0))\/(((op (e2) (e1)) = (e0))\/((op (e3) (e1)) = (e0))))) -> ((op (e2) (e2)) = (e3)) -> (((op (e0) (e1)) = (e1))\/(((op (e1) (e1)) = (e1))\/(((op (e2) (e1)) = (e1))\/((op (e3) (e1)) = (e1))))) -> (~((op (e0) (e1)) = (op (e0) (e3)))) -> (~((op (e1) (e1)) = (e1))) -> (~((op (e0) (e1)) = (op (e2) (e1)))) -> (((op (e0) (e1)) = (e0))\/(((op (e0) (e1)) = (e1))\/(((op (e0) (e1)) = (e2))\/((op (e0) (e1)) = (e3))))) -> (((op (e0) (e1)) = (e2))\/(((op (e1) (e1)) = (e2))\/(((op (e2) (e1)) = (e2))\/((op (e3) (e1)) = (e2))))) -> (~((op (e0) (e1)) = (e2))) -> (~((op (e1) (e1)) = (e2))) -> (~((e1) = (e2))) -> (((op (e1) (e0)) = (e0))\/(((op (e1) (e1)) = (e0))\/(((op (e1) (e2)) = (e0))\/((op (e1) (e3)) = (e0))))) -> (~((e0) = (e1))) -> ((op (e2) (e0)) = (e0)) -> (~((op (e3) (e0)) = (op (e3) (e2)))) -> ((op (e3) (e2)) = (e1)) -> False). % 18.99/19.12 do 0 intro. intros zenon_H235 zenon_H189 zenon_H102 zenon_Hf3 zenon_Hc2 zenon_Hc3 zenon_H130 zenon_H101 zenon_H173 zenon_H133 zenon_Hf7 zenon_H1c7 zenon_H12e zenon_H145 zenon_Hd8 zenon_H6d zenon_Hf1 zenon_H62 zenon_Hef zenon_H1d5 zenon_H1f0 zenon_H57 zenon_H48 zenon_H4a zenon_H245 zenon_Haa zenon_H109 zenon_H54 zenon_H10a zenon_H17e zenon_H212 zenon_H1d8 zenon_H26d zenon_H20c zenon_H7c zenon_H22 zenon_Ha1 zenon_H34 zenon_H6f zenon_Hba. % 18.99/19.12 apply (zenon_or_s _ _ zenon_H235); [ zenon_intro zenon_H7a | zenon_intro zenon_H236 ]. % 18.99/19.12 apply (zenon_L140_); trivial. % 18.99/19.12 apply (zenon_or_s _ _ zenon_H236); [ zenon_intro zenon_H9d | zenon_intro zenon_H237 ]. % 18.99/19.12 apply (zenon_or_s _ _ zenon_H22); [ zenon_intro zenon_H27 | zenon_intro zenon_H26 ]. % 18.99/19.12 apply (zenon_L262_); trivial. % 18.99/19.12 apply (zenon_or_s _ _ zenon_H26); [ zenon_intro zenon_H29 | zenon_intro zenon_H28 ]. % 18.99/19.12 apply (zenon_L1108_); trivial. % 18.99/19.12 apply (zenon_or_s _ _ zenon_H28); [ zenon_intro zenon_H2a | zenon_intro zenon_H1f ]. % 18.99/19.12 apply (zenon_L179_); trivial. % 18.99/19.12 apply (zenon_L1111_); trivial. % 18.99/19.12 apply (zenon_or_s _ _ zenon_H237); [ zenon_intro zenon_Hed | zenon_intro zenon_Hac ]. % 18.99/19.12 apply (zenon_L214_); trivial. % 18.99/19.12 apply (zenon_L249_); trivial. % 18.99/19.12 (* end of lemma zenon_L1112_ *) % 18.99/19.12 assert (zenon_L1113_ : (~((op (e3) (e0)) = (op (e3) (e2)))) -> ((op (e2) (e0)) = (e0)) -> (~((e0) = (e1))) -> (((op (e1) (e0)) = (e0))\/(((op (e1) (e1)) = (e0))\/(((op (e1) (e2)) = (e0))\/((op (e1) (e3)) = (e0))))) -> (~((e1) = (e2))) -> (~((op (e1) (e1)) = (e2))) -> (~((op (e0) (e1)) = (e2))) -> (((op (e0) (e1)) = (e2))\/(((op (e1) (e1)) = (e2))\/(((op (e2) (e1)) = (e2))\/((op (e3) (e1)) = (e2))))) -> (((op (e0) (e1)) = (e0))\/(((op (e0) (e1)) = (e1))\/(((op (e0) (e1)) = (e2))\/((op (e0) (e1)) = (e3))))) -> (~((op (e0) (e1)) = (op (e2) (e1)))) -> (~((op (e1) (e1)) = (e1))) -> (~((op (e0) (e1)) = (op (e0) (e3)))) -> (((op (e0) (e1)) = (e1))\/(((op (e1) (e1)) = (e1))\/(((op (e2) (e1)) = (e1))\/((op (e3) (e1)) = (e1))))) -> ((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 (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) (e3)) = (e2))\/(((op (e1) (e3)) = (e2))\/(((op (e2) (e3)) = (e2))\/((op (e3) (e3)) = (e2))))) -> (~((op (e0) (e3)) = (e2))) -> (~((op (e2) (e1)) = (op (e2) (e3)))) -> (~((op (e3) (e3)) = (e2))) -> (((op (e0) (e3)) = (e1))\/(((op (e1) (e3)) = (e1))\/(((op (e2) (e3)) = (e1))\/((op (e3) (e3)) = (e1))))) -> (~((op (e2) (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) (e3)) = (op (e3) (e3)))) -> (~((op (e2) (e3)) = (op (e3) (e3)))) -> (~((op (e3) (e3)) = (e3))) -> (~((op (e0) (e0)) = (op (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 (e1) (e0)) = (e1)) -> (~((op (e2) (e2)) = (op (e2) (e3)))) -> ((op (e2) (e2)) = (e1)) -> ((op (e3) (e2)) = (e1)) -> (~((op (e3) (e2)) = (op (e3) (e3)))) -> False). % 18.99/19.12 do 0 intro. intros zenon_H6f zenon_H34 zenon_Ha1 zenon_H22 zenon_H7c zenon_H20c zenon_H26d zenon_H1d8 zenon_H212 zenon_H17e zenon_H10a zenon_H54 zenon_H109 zenon_Haa zenon_H245 zenon_H4a zenon_H48 zenon_H57 zenon_H1f0 zenon_H1d5 zenon_Hef zenon_H145 zenon_H12e zenon_H1c7 zenon_Hf7 zenon_H133 zenon_H173 zenon_H101 zenon_H130 zenon_Hc2 zenon_Hf3 zenon_H102 zenon_H189 zenon_H235 zenon_Hd8 zenon_H9d zenon_H6d zenon_Hf1 zenon_Hba zenon_H62. % 18.99/19.12 apply (zenon_or_s _ _ zenon_H133); [ zenon_intro zenon_Hc3 | zenon_intro zenon_H134 ]. % 18.99/19.12 apply (zenon_L1112_); trivial. % 18.99/19.12 apply (zenon_or_s _ _ zenon_H134); [ zenon_intro zenon_Hd6 | zenon_intro zenon_H135 ]. % 18.99/19.12 apply (zenon_L360_); trivial. % 18.99/19.12 apply (zenon_or_s _ _ zenon_H135); [ zenon_intro zenon_Hf4 | zenon_intro zenon_Hc4 ]. % 18.99/19.12 apply (zenon_L84_); trivial. % 18.99/19.12 apply (zenon_L147_); trivial. % 18.99/19.12 (* end of lemma zenon_L1113_ *) % 18.99/19.12 assert (zenon_L1114_ : (((op (e1) (e1)) = (e0))\/(((op (e1) (e1)) = (e1))\/(((op (e1) (e1)) = (e2))\/((op (e1) (e1)) = (e3))))) -> ((op (e0) (e1)) = (e3)) -> (~((op (e1) (e1)) = (e1))) -> (~((op (e1) (e1)) = (e2))) -> ((op (e2) (e1)) = (e0)) -> ((op (e3) (e1)) = (e2)) -> False). % 18.99/19.12 do 0 intro. intros zenon_H142 zenon_H99 zenon_H10a zenon_H20c zenon_H36 zenon_H14d. % 18.99/19.12 apply (zenon_or_s _ _ zenon_H142); [ zenon_intro zenon_H29 | zenon_intro zenon_H143 ]. % 18.99/19.12 apply (zenon_L385_); trivial. % 18.99/19.12 apply (zenon_or_s _ _ zenon_H143); [ zenon_intro zenon_H10d | zenon_intro zenon_H144 ]. % 18.99/19.12 exact (zenon_H10a zenon_H10d). % 18.99/19.12 apply (zenon_or_s _ _ zenon_H144); [ zenon_intro zenon_H110 | zenon_intro zenon_H13f ]. % 18.99/19.12 exact (zenon_H20c zenon_H110). % 18.99/19.12 apply (zenon_L514_); trivial. % 18.99/19.12 (* end of lemma zenon_L1114_ *) % 18.99/19.12 assert (zenon_L1115_ : (((op (e0) (e1)) = (e0))\/(((op (e0) (e1)) = (e1))\/(((op (e0) (e1)) = (e2))\/((op (e0) (e1)) = (e3))))) -> ((op (e2) (e1)) = (e1)) -> (~((op (e0) (e1)) = (op (e2) (e1)))) -> (~((op (e0) (e1)) = (e2))) -> (((op (e1) (e1)) = (e0))\/(((op (e1) (e1)) = (e1))\/(((op (e1) (e1)) = (e2))\/((op (e1) (e1)) = (e3))))) -> (~((op (e1) (e1)) = (e1))) -> (~((op (e1) (e1)) = (e2))) -> ((op (e2) (e1)) = (e0)) -> ((op (e3) (e1)) = (e2)) -> False). % 18.99/19.12 do 0 intro. intros zenon_H212 zenon_Ha5 zenon_H17e zenon_H26d zenon_H142 zenon_H10a zenon_H20c zenon_H36 zenon_H14d. % 18.99/19.12 apply (zenon_or_s _ _ zenon_H212); [ zenon_intro zenon_H49 | zenon_intro zenon_H213 ]. % 18.99/19.12 apply (zenon_L128_); trivial. % 18.99/19.12 apply (zenon_or_s _ _ zenon_H213); [ zenon_intro zenon_Ha0 | zenon_intro zenon_H214 ]. % 18.99/19.12 apply (zenon_L357_); trivial. % 18.99/19.12 apply (zenon_or_s _ _ zenon_H214); [ zenon_intro zenon_H10f | zenon_intro zenon_H99 ]. % 18.99/19.12 exact (zenon_H26d zenon_H10f). % 18.99/19.12 apply (zenon_L1114_); trivial. % 18.99/19.12 (* end of lemma zenon_L1115_ *) % 18.99/19.12 assert (zenon_L1116_ : (((op (e0) (e1)) = (e2))\/(((op (e1) (e1)) = (e2))\/(((op (e2) (e1)) = (e2))\/((op (e3) (e1)) = (e2))))) -> (~((op (e0) (e1)) = (e2))) -> (~((op (e1) (e1)) = (e2))) -> (~((op (e3) (e2)) = (op (e3) (e3)))) -> ((op (e3) (e2)) = (e1)) -> ((op (e2) (e2)) = (e1)) -> (~((op (e2) (e2)) = (op (e2) (e3)))) -> ((op (e1) (e0)) = (e1)) -> (~((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)) = (e2))) -> (~((op (e3) (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) (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)) = (e0)) -> False). % 18.99/19.12 do 0 intro. intros zenon_H1d8 zenon_H26d zenon_H20c zenon_H62 zenon_Hba zenon_Hf1 zenon_H6d zenon_H9d zenon_Hd8 zenon_H145 zenon_H12e zenon_H102 zenon_H101 zenon_H1c7 zenon_Hf7 zenon_H133 zenon_H99 zenon_H29. % 18.99/19.12 apply (zenon_or_s _ _ zenon_H1d8); [ zenon_intro zenon_H10f | zenon_intro zenon_H1d9 ]. % 18.99/19.12 exact (zenon_H26d zenon_H10f). % 18.99/19.12 apply (zenon_or_s _ _ zenon_H1d9); [ zenon_intro zenon_H110 | zenon_intro zenon_H1da ]. % 18.99/19.12 exact (zenon_H20c zenon_H110). % 18.99/19.12 apply (zenon_or_s _ _ zenon_H1da); [ zenon_intro zenon_H1ca | zenon_intro zenon_H14d ]. % 18.99/19.12 apply (zenon_L1109_); trivial. % 18.99/19.12 apply (zenon_L385_); trivial. % 18.99/19.12 (* end of lemma zenon_L1116_ *) % 18.99/19.12 assert (zenon_L1117_ : (((op (e0) (e1)) = (e2))\/(((op (e1) (e1)) = (e2))\/(((op (e2) (e1)) = (e2))\/((op (e3) (e1)) = (e2))))) -> (~((op (e0) (e1)) = (e2))) -> (~((op (e3) (e3)) = (e2))) -> (~((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)) = (e1)) -> (~((op (e3) (e2)) = (op (e3) (e3)))) -> ((op (e3) (e2)) = (e1)) -> (~((op (e3) (e3)) = (e3))) -> (~((op (e0) (e3)) = (e2))) -> (((op (e0) (e3)) = (e2))\/(((op (e1) (e3)) = (e2))\/(((op (e2) (e3)) = (e2))\/((op (e3) (e3)) = (e2))))) -> (((op (e1) (e1)) = (e0))\/(((op (e1) (e1)) = (e1))\/(((op (e1) (e1)) = (e2))\/((op (e1) (e1)) = (e3))))) -> ((op (e0) (e1)) = (e3)) -> (~((op (e1) (e1)) = (e1))) -> (~((op (e1) (e1)) = (e2))) -> ((op (e2) (e1)) = (e0)) -> False). % 18.99/19.12 do 0 intro. intros zenon_H1d8 zenon_H26d zenon_Hf7 zenon_H1c7 zenon_H101 zenon_Hc3 zenon_H62 zenon_Hba zenon_H102 zenon_H12e zenon_H145 zenon_H142 zenon_H99 zenon_H10a zenon_H20c zenon_H36. % 18.99/19.12 apply (zenon_or_s _ _ zenon_H1d8); [ zenon_intro zenon_H10f | zenon_intro zenon_H1d9 ]. % 18.99/19.12 exact (zenon_H26d zenon_H10f). % 18.99/19.12 apply (zenon_or_s _ _ zenon_H1d9); [ zenon_intro zenon_H110 | zenon_intro zenon_H1da ]. % 18.99/19.12 exact (zenon_H20c zenon_H110). % 18.99/19.12 apply (zenon_or_s _ _ zenon_H1da); [ zenon_intro zenon_H1ca | zenon_intro zenon_H14d ]. % 18.99/19.12 apply (zenon_L1104_); trivial. % 18.99/19.12 apply (zenon_L1114_); trivial. % 18.99/19.12 (* end of lemma zenon_L1117_ *) % 18.99/19.12 assert (zenon_L1118_ : (((op (e0) (e1)) = (e0))\/(((op (e1) (e1)) = (e0))\/(((op (e2) (e1)) = (e0))\/((op (e3) (e1)) = (e0))))) -> (~((e0) = (e3))) -> (~((op (e1) (e1)) = (op (e1) (e3)))) -> ((op (e1) (e3)) = (e0)) -> (~((op (e1) (e1)) = (e2))) -> (~((op (e1) (e1)) = (e1))) -> ((op (e0) (e1)) = (e3)) -> (((op (e1) (e1)) = (e0))\/(((op (e1) (e1)) = (e1))\/(((op (e1) (e1)) = (e2))\/((op (e1) (e1)) = (e3))))) -> (((op (e0) (e3)) = (e2))\/(((op (e1) (e3)) = (e2))\/(((op (e2) (e3)) = (e2))\/((op (e3) (e3)) = (e2))))) -> (~((op (e0) (e3)) = (e2))) -> (~((op (e3) (e3)) = (e3))) -> ((op (e3) (e2)) = (e1)) -> (~((op (e3) (e2)) = (op (e3) (e3)))) -> ((op (e0) (e3)) = (e1)) -> (((op (e3) (e3)) = (e0))\/(((op (e3) (e3)) = (e1))\/(((op (e3) (e3)) = (e2))\/((op (e3) (e3)) = (e3))))) -> (~((op (e2) (e1)) = (op (e2) (e3)))) -> (~((op (e3) (e3)) = (e2))) -> (~((op (e0) (e1)) = (e2))) -> (((op (e0) (e1)) = (e2))\/(((op (e1) (e1)) = (e2))\/(((op (e2) (e1)) = (e2))\/((op (e3) (e1)) = (e2))))) -> (~((op (e3) (e0)) = (op (e3) (e1)))) -> ((op (e3) (e0)) = (e0)) -> False). % 18.99/19.12 do 0 intro. intros zenon_H245 zenon_H9a zenon_H57 zenon_H1f zenon_H20c zenon_H10a zenon_H99 zenon_H142 zenon_H145 zenon_H12e zenon_H102 zenon_Hba zenon_H62 zenon_Hc3 zenon_H101 zenon_H1c7 zenon_Hf7 zenon_H26d zenon_H1d8 zenon_H1cf zenon_H44. % 18.99/19.12 apply (zenon_or_s _ _ zenon_H245); [ zenon_intro zenon_H49 | zenon_intro zenon_H246 ]. % 18.99/19.12 apply (zenon_L36_); trivial. % 18.99/19.12 apply (zenon_or_s _ _ zenon_H246); [ zenon_intro zenon_H29 | zenon_intro zenon_H247 ]. % 18.99/19.12 apply (zenon_L13_); trivial. % 18.99/19.12 apply (zenon_or_s _ _ zenon_H247); [ zenon_intro zenon_H36 | zenon_intro zenon_H1b1 ]. % 18.99/19.12 apply (zenon_L1117_); trivial. % 18.99/19.12 apply (zenon_L346_); trivial. % 18.99/19.12 (* end of lemma zenon_L1118_ *) % 18.99/19.12 assert (zenon_L1119_ : (((op (e1) (e0)) = (e0))\/(((op (e1) (e1)) = (e0))\/(((op (e1) (e2)) = (e0))\/((op (e1) (e3)) = (e0))))) -> (~((op (e1) (e0)) = (op (e3) (e0)))) -> (((op (e0) (e3)) = (e1))\/(((op (e1) (e3)) = (e1))\/(((op (e2) (e3)) = (e1))\/((op (e3) (e3)) = (e1))))) -> (~((op (e1) (e0)) = (op (e1) (e3)))) -> ((op (e1) (e0)) = (e1)) -> (~((op (e2) (e2)) = (op (e2) (e3)))) -> ((op (e2) (e2)) = (e1)) -> ((op (e2) (e2)) = (e3)) -> (((op (e0) (e1)) = (e0))\/(((op (e1) (e1)) = (e0))\/(((op (e2) (e1)) = (e0))\/((op (e3) (e1)) = (e0))))) -> (~((e0) = (e3))) -> (~((op (e1) (e1)) = (op (e1) (e3)))) -> (~((op (e1) (e1)) = (e2))) -> (~((op (e1) (e1)) = (e1))) -> ((op (e0) (e1)) = (e3)) -> (((op (e1) (e1)) = (e0))\/(((op (e1) (e1)) = (e1))\/(((op (e1) (e1)) = (e2))\/((op (e1) (e1)) = (e3))))) -> (((op (e0) (e3)) = (e2))\/(((op (e1) (e3)) = (e2))\/(((op (e2) (e3)) = (e2))\/((op (e3) (e3)) = (e2))))) -> (~((op (e0) (e3)) = (e2))) -> (~((op (e3) (e3)) = (e3))) -> ((op (e3) (e2)) = (e1)) -> (~((op (e3) (e2)) = (op (e3) (e3)))) -> ((op (e0) (e3)) = (e1)) -> (((op (e3) (e3)) = (e0))\/(((op (e3) (e3)) = (e1))\/(((op (e3) (e3)) = (e2))\/((op (e3) (e3)) = (e3))))) -> (~((op (e2) (e1)) = (op (e2) (e3)))) -> (~((op (e3) (e3)) = (e2))) -> (~((op (e0) (e1)) = (e2))) -> (((op (e0) (e1)) = (e2))\/(((op (e1) (e1)) = (e2))\/(((op (e2) (e1)) = (e2))\/((op (e3) (e1)) = (e2))))) -> (~((op (e3) (e0)) = (op (e3) (e1)))) -> ((op (e3) (e0)) = (e0)) -> False). % 18.99/19.12 do 0 intro. intros zenon_H22 zenon_H1fa zenon_H133 zenon_Hd8 zenon_H9d zenon_H6d zenon_Hf1 zenon_Haa zenon_H245 zenon_H9a zenon_H57 zenon_H20c zenon_H10a zenon_H99 zenon_H142 zenon_H145 zenon_H12e zenon_H102 zenon_Hba zenon_H62 zenon_Hc3 zenon_H101 zenon_H1c7 zenon_Hf7 zenon_H26d zenon_H1d8 zenon_H1cf zenon_H44. % 18.99/19.12 apply (zenon_or_s _ _ zenon_H22); [ zenon_intro zenon_H27 | zenon_intro zenon_H26 ]. % 18.99/19.12 apply (zenon_L312_); trivial. % 18.99/19.12 apply (zenon_or_s _ _ zenon_H26); [ zenon_intro zenon_H29 | zenon_intro zenon_H28 ]. % 18.99/19.12 apply (zenon_L1116_); trivial. % 18.99/19.12 apply (zenon_or_s _ _ zenon_H28); [ zenon_intro zenon_H2a | zenon_intro zenon_H1f ]. % 18.99/19.12 apply (zenon_L179_); trivial. % 18.99/19.12 apply (zenon_L1118_); trivial. % 18.99/19.12 (* end of lemma zenon_L1119_ *) % 18.99/19.12 assert (zenon_L1120_ : (((op (e0) (e0)) = (e2))\/(((op (e0) (e1)) = (e2))\/(((op (e0) (e2)) = (e2))\/((op (e0) (e3)) = (e2))))) -> ((op (e2) (e0)) = (e1)) -> (~((op (e1) (e0)) = (e2))) -> (~((op (e1) (e0)) = (op (e2) (e0)))) -> ((op (e3) (e0)) = (e0)) -> (~((op (e1) (e0)) = (op (e3) (e0)))) -> (((op (e1) (e0)) = (e0))\/(((op (e1) (e0)) = (e1))\/(((op (e1) (e0)) = (e2))\/((op (e1) (e0)) = (e3))))) -> (~((op (e0) (e1)) = (e2))) -> (~((op (e0) (e2)) = (e2))) -> (~((op (e0) (e3)) = (e2))) -> False). % 18.99/19.12 do 0 intro. intros zenon_H183 zenon_Hed zenon_H177 zenon_H201 zenon_H44 zenon_H1fa zenon_H25e zenon_H26d zenon_H1fd zenon_H12e. % 18.99/19.12 apply (zenon_or_s _ _ zenon_H183); [ zenon_intro zenon_H7b | zenon_intro zenon_H186 ]. % 18.99/19.12 apply (zenon_L1064_); trivial. % 18.99/19.12 apply (zenon_or_s _ _ zenon_H186); [ zenon_intro zenon_H10f | zenon_intro zenon_H187 ]. % 18.99/19.12 exact (zenon_H26d zenon_H10f). % 18.99/19.12 apply (zenon_or_s _ _ zenon_H187); [ zenon_intro zenon_H150 | zenon_intro zenon_Hcd ]. % 18.99/19.12 exact (zenon_H1fd zenon_H150). % 18.99/19.12 exact (zenon_H12e zenon_Hcd). % 18.99/19.12 (* end of lemma zenon_L1120_ *) % 18.99/19.12 assert (zenon_L1121_ : (((op (e0) (e0)) = (e1))\/(((op (e1) (e0)) = (e1))\/(((op (e2) (e0)) = (e1))\/((op (e3) (e0)) = (e1))))) -> (~((op (e0) (e0)) = (op (e0) (e3)))) -> (~((e1) = (e2))) -> (((op (e0) (e3)) = (e2))\/(((op (e1) (e3)) = (e2))\/(((op (e2) (e3)) = (e2))\/((op (e3) (e3)) = (e2))))) -> (~((op (e3) (e3)) = (e3))) -> (~((op (e3) (e1)) = (op (e3) (e3)))) -> ((op (e0) (e3)) = (e1)) -> (((op (e3) (e3)) = (e0))\/(((op (e3) (e3)) = (e1))\/(((op (e3) (e3)) = (e2))\/((op (e3) (e3)) = (e3))))) -> (~((op (e2) (e1)) = (op (e2) (e3)))) -> (~((op (e3) (e3)) = (e2))) -> (~((op (e1) (e1)) = (e2))) -> (((op (e0) (e1)) = (e2))\/(((op (e1) (e1)) = (e2))\/(((op (e2) (e1)) = (e2))\/((op (e3) (e1)) = (e2))))) -> (((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)) = (e0)) -> (~((op (e0) (e1)) = (op (e2) (e1)))) -> (((op (e1) (e0)) = (e0))\/(((op (e1) (e1)) = (e0))\/(((op (e1) (e2)) = (e0))\/((op (e1) (e3)) = (e0))))) -> (((op (e0) (e3)) = (e1))\/(((op (e1) (e3)) = (e1))\/(((op (e2) (e3)) = (e1))\/((op (e3) (e3)) = (e1))))) -> (~((op (e1) (e0)) = (op (e1) (e3)))) -> (~((op (e2) (e2)) = (op (e2) (e3)))) -> ((op (e2) (e2)) = (e1)) -> ((op (e2) (e2)) = (e3)) -> (((op (e0) (e1)) = (e0))\/(((op (e1) (e1)) = (e0))\/(((op (e2) (e1)) = (e0))\/((op (e3) (e1)) = (e0))))) -> (~((e0) = (e3))) -> (~((op (e1) (e1)) = (op (e1) (e3)))) -> (~((op (e1) (e1)) = (e1))) -> (((op (e1) (e1)) = (e0))\/(((op (e1) (e1)) = (e1))\/(((op (e1) (e1)) = (e2))\/((op (e1) (e1)) = (e3))))) -> ((op (e3) (e2)) = (e1)) -> (~((op (e3) (e2)) = (op (e3) (e3)))) -> (~((op (e3) (e0)) = (op (e3) (e1)))) -> (~((op (e0) (e1)) = (op (e0) (e3)))) -> (((op (e0) (e1)) = (e1))\/(((op (e1) (e1)) = (e1))\/(((op (e2) (e1)) = (e1))\/((op (e3) (e1)) = (e1))))) -> (~((op (e0) (e3)) = (e2))) -> (~((op (e0) (e2)) = (e2))) -> (~((op (e0) (e1)) = (e2))) -> (((op (e1) (e0)) = (e0))\/(((op (e1) (e0)) = (e1))\/(((op (e1) (e0)) = (e2))\/((op (e1) (e0)) = (e3))))) -> (~((op (e1) (e0)) = (op (e3) (e0)))) -> (~((op (e1) (e0)) = (op (e2) (e0)))) -> (~((op (e1) (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). % 18.99/19.12 do 0 intro. intros zenon_H235 zenon_H189 zenon_H7c zenon_H145 zenon_H102 zenon_H130 zenon_Hc3 zenon_H101 zenon_H1c7 zenon_Hf7 zenon_H20c zenon_H1d8 zenon_H212 zenon_H4a zenon_H48 zenon_H17e zenon_H22 zenon_H133 zenon_Hd8 zenon_H6d zenon_Hf1 zenon_Haa zenon_H245 zenon_H9a zenon_H57 zenon_H10a zenon_H142 zenon_Hba zenon_H62 zenon_H1cf zenon_H54 zenon_H109 zenon_H12e zenon_H1fd zenon_H26d zenon_H25e zenon_H1fa zenon_H201 zenon_H177 zenon_H183 zenon_H44 zenon_Ha1. % 18.99/19.12 apply (zenon_or_s _ _ zenon_H235); [ zenon_intro zenon_H7a | zenon_intro zenon_H236 ]. % 18.99/19.12 apply (zenon_L140_); trivial. % 18.99/19.12 apply (zenon_or_s _ _ zenon_H236); [ zenon_intro zenon_H9d | zenon_intro zenon_H237 ]. % 18.99/19.12 apply (zenon_or_s _ _ zenon_H109); [ zenon_intro zenon_Ha0 | zenon_intro zenon_H10b ]. % 18.99/19.12 apply (zenon_L359_); trivial. % 18.99/19.12 apply (zenon_or_s _ _ zenon_H10b); [ zenon_intro zenon_H10d | zenon_intro zenon_H10c ]. % 18.99/19.12 exact (zenon_H10a zenon_H10d). % 18.99/19.12 apply (zenon_or_s _ _ zenon_H10c); [ zenon_intro zenon_Ha5 | zenon_intro zenon_Hae ]. % 18.99/19.12 apply (zenon_or_s _ _ zenon_H212); [ zenon_intro zenon_H49 | zenon_intro zenon_H213 ]. % 18.99/19.12 apply (zenon_L9_); trivial. % 18.99/19.12 apply (zenon_or_s _ _ zenon_H213); [ zenon_intro zenon_Ha0 | zenon_intro zenon_H214 ]. % 18.99/19.12 apply (zenon_L357_); trivial. % 18.99/19.12 apply (zenon_or_s _ _ zenon_H214); [ zenon_intro zenon_H10f | zenon_intro zenon_H99 ]. % 18.99/19.12 exact (zenon_H26d zenon_H10f). % 18.99/19.12 apply (zenon_L1119_); trivial. % 18.99/19.12 apply (zenon_L1107_); trivial. % 18.99/19.12 apply (zenon_or_s _ _ zenon_H237); [ zenon_intro zenon_Hed | zenon_intro zenon_Hac ]. % 18.99/19.12 apply (zenon_L1120_); trivial. % 18.99/19.12 apply (zenon_L41_); trivial. % 18.99/19.12 (* end of lemma zenon_L1121_ *) % 18.99/19.12 assert (zenon_L1122_ : (~((e0) = (e1))) -> ((op (e3) (e0)) = (e0)) -> (((op (e0) (e0)) = (e2))\/(((op (e0) (e1)) = (e2))\/(((op (e0) (e2)) = (e2))\/((op (e0) (e3)) = (e2))))) -> (~((op (e1) (e0)) = (e2))) -> (~((op (e1) (e0)) = (op (e2) (e0)))) -> (~((op (e1) (e0)) = (op (e3) (e0)))) -> (((op (e1) (e0)) = (e0))\/(((op (e1) (e0)) = (e1))\/(((op (e1) (e0)) = (e2))\/((op (e1) (e0)) = (e3))))) -> (~((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 (e0) (e1)) = (op (e0) (e3)))) -> (~((op (e3) (e0)) = (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) (e1)) = (op (e1) (e3)))) -> (~((e0) = (e3))) -> (((op (e0) (e1)) = (e0))\/(((op (e1) (e1)) = (e0))\/(((op (e2) (e1)) = (e0))\/((op (e3) (e1)) = (e0))))) -> ((op (e2) (e2)) = (e3)) -> (((op (e0) (e3)) = (e1))\/(((op (e1) (e3)) = (e1))\/(((op (e2) (e3)) = (e1))\/((op (e3) (e3)) = (e1))))) -> (((op (e1) (e0)) = (e0))\/(((op (e1) (e1)) = (e0))\/(((op (e1) (e2)) = (e0))\/((op (e1) (e3)) = (e0))))) -> (~((op (e0) (e1)) = (op (e2) (e1)))) -> ((op (e0) (e2)) = (e0)) -> (~((op (e0) (e1)) = (op (e0) (e2)))) -> (((op (e0) (e1)) = (e0))\/(((op (e0) (e1)) = (e1))\/(((op (e0) (e1)) = (e2))\/((op (e0) (e1)) = (e3))))) -> (((op (e0) (e1)) = (e2))\/(((op (e1) (e1)) = (e2))\/(((op (e2) (e1)) = (e2))\/((op (e3) (e1)) = (e2))))) -> (~((op (e1) (e1)) = (e2))) -> (~((op (e3) (e3)) = (e2))) -> (~((op (e2) (e1)) = (op (e2) (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)) = (e3))) -> (((op (e0) (e3)) = (e2))\/(((op (e1) (e3)) = (e2))\/(((op (e2) (e3)) = (e2))\/((op (e3) (e3)) = (e2))))) -> (~((e1) = (e2))) -> (~((op (e0) (e0)) = (op (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 (e1) (e0)) = (e1)) -> (~((op (e2) (e2)) = (op (e2) (e3)))) -> ((op (e2) (e2)) = (e1)) -> ((op (e3) (e2)) = (e1)) -> (~((op (e3) (e2)) = (op (e3) (e3)))) -> False). % 18.99/19.12 do 0 intro. intros zenon_Ha1 zenon_H44 zenon_H183 zenon_H177 zenon_H201 zenon_H1fa zenon_H25e zenon_H26d zenon_H1fd zenon_H12e zenon_H109 zenon_H54 zenon_H1cf zenon_H142 zenon_H10a zenon_H57 zenon_H9a zenon_H245 zenon_Haa zenon_H133 zenon_H22 zenon_H17e zenon_H48 zenon_H4a zenon_H212 zenon_H1d8 zenon_H20c zenon_Hf7 zenon_H1c7 zenon_H101 zenon_H130 zenon_H102 zenon_H145 zenon_H7c zenon_H189 zenon_H235 zenon_Hd8 zenon_H9d zenon_H6d zenon_Hf1 zenon_Hba zenon_H62. % 18.99/19.12 apply (zenon_or_s _ _ zenon_H133); [ zenon_intro zenon_Hc3 | zenon_intro zenon_H134 ]. % 18.99/19.12 apply (zenon_L1121_); trivial. % 18.99/19.12 apply (zenon_or_s _ _ zenon_H134); [ zenon_intro zenon_Hd6 | zenon_intro zenon_H135 ]. % 18.99/19.12 apply (zenon_L360_); trivial. % 18.99/19.12 apply (zenon_or_s _ _ zenon_H135); [ zenon_intro zenon_Hf4 | zenon_intro zenon_Hc4 ]. % 18.99/19.12 apply (zenon_L84_); trivial. % 18.99/19.12 apply (zenon_L147_); trivial. % 18.99/19.12 (* end of lemma zenon_L1122_ *) % 18.99/19.12 assert (zenon_L1123_ : (((op (e0) (e3)) = (e1))\/(((op (e1) (e3)) = (e1))\/(((op (e2) (e3)) = (e1))\/((op (e3) (e3)) = (e1))))) -> (~((op (e3) (e3)) = (e2))) -> ((op (e2) (e1)) = (e2)) -> (~((op (e2) (e1)) = (op (e2) (e3)))) -> (~((op (e0) (e3)) = (e2))) -> (((op (e0) (e3)) = (e2))\/(((op (e1) (e3)) = (e2))\/(((op (e2) (e3)) = (e2))\/((op (e3) (e3)) = (e2))))) -> (~((op (e1) (e0)) = (op (e1) (e3)))) -> ((op (e1) (e0)) = (e1)) -> (~((op (e3) (e3)) = (e3))) -> ((op (e1) (e3)) = (e0)) -> (~((op (e2) (e3)) = (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)) = (e1)) -> (~((op (e3) (e2)) = (op (e3) (e3)))) -> False). % 18.99/19.12 do 0 intro. intros zenon_H133 zenon_Hf7 zenon_H1ca zenon_H1c7 zenon_H12e zenon_H145 zenon_Hd8 zenon_H9d zenon_H102 zenon_H1f zenon_Hf3 zenon_H44 zenon_H71 zenon_H101 zenon_Hba zenon_H62. % 18.99/19.12 apply (zenon_or_s _ _ zenon_H133); [ zenon_intro zenon_Hc3 | zenon_intro zenon_H134 ]. % 18.99/19.12 apply (zenon_L1104_); trivial. % 18.99/19.12 apply (zenon_or_s _ _ zenon_H134); [ zenon_intro zenon_Hd6 | zenon_intro zenon_H135 ]. % 18.99/19.12 apply (zenon_L360_); trivial. % 18.99/19.12 apply (zenon_or_s _ _ zenon_H135); [ zenon_intro zenon_Hf4 | zenon_intro zenon_Hc4 ]. % 18.99/19.12 apply (zenon_L64_); trivial. % 18.99/19.12 apply (zenon_L147_); trivial. % 18.99/19.12 (* end of lemma zenon_L1123_ *) % 18.99/19.12 assert (zenon_L1124_ : (((op (e0) (e1)) = (e1))\/(((op (e1) (e1)) = (e1))\/(((op (e2) (e1)) = (e1))\/((op (e3) (e1)) = (e1))))) -> (~((op (e0) (e1)) = (op (e0) (e3)))) -> ((op (e2) (e1)) = (e0)) -> (~((op (e1) (e1)) = (e1))) -> (((op (e1) (e1)) = (e0))\/(((op (e1) (e1)) = (e1))\/(((op (e1) (e1)) = (e2))\/((op (e1) (e1)) = (e3))))) -> (~((op (e0) (e1)) = (op (e2) (e1)))) -> (((op (e0) (e1)) = (e0))\/(((op (e0) (e1)) = (e1))\/(((op (e0) (e1)) = (e2))\/((op (e0) (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)) -> ((op (e1) (e3)) = (e0)) -> (~((op (e2) (e3)) = (op (e3) (e3)))) -> ((op (e3) (e0)) = (e0)) -> (~((op (e3) (e0)) = (op (e3) (e3)))) -> ((op (e3) (e2)) = (e1)) -> (~((op (e3) (e2)) = (op (e3) (e3)))) -> (((op (e0) (e1)) = (e2))\/(((op (e1) (e1)) = (e2))\/(((op (e2) (e1)) = (e2))\/((op (e3) (e1)) = (e2))))) -> (~((op (e0) (e1)) = (e2))) -> (~((op (e1) (e1)) = (e2))) -> (~((op (e3) (e3)) = (e2))) -> (~((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)) = (e1)) -> (~((op (e3) (e1)) = (op (e3) (e3)))) -> (~((op (e3) (e3)) = (e3))) -> (~((op (e0) (e3)) = (e2))) -> (((op (e0) (e3)) = (e2))\/(((op (e1) (e3)) = (e2))\/(((op (e2) (e3)) = (e2))\/((op (e3) (e3)) = (e2))))) -> (~((e1) = (e2))) -> False). % 18.99/19.12 do 0 intro. intros zenon_H109 zenon_H54 zenon_H36 zenon_H10a zenon_H142 zenon_H17e zenon_H212 zenon_H133 zenon_Hd8 zenon_H9d zenon_H1f zenon_Hf3 zenon_H44 zenon_H71 zenon_Hba zenon_H62 zenon_H1d8 zenon_H26d zenon_H20c zenon_Hf7 zenon_H1c7 zenon_H101 zenon_Hc3 zenon_H130 zenon_H102 zenon_H12e zenon_H145 zenon_H7c. % 18.99/19.12 apply (zenon_or_s _ _ zenon_H109); [ zenon_intro zenon_Ha0 | zenon_intro zenon_H10b ]. % 18.99/19.12 apply (zenon_L359_); trivial. % 18.99/19.12 apply (zenon_or_s _ _ zenon_H10b); [ zenon_intro zenon_H10d | zenon_intro zenon_H10c ]. % 18.99/19.12 exact (zenon_H10a zenon_H10d). % 18.99/19.12 apply (zenon_or_s _ _ zenon_H10c); [ zenon_intro zenon_Ha5 | zenon_intro zenon_Hae ]. % 18.99/19.12 apply (zenon_or_s _ _ zenon_H1d8); [ zenon_intro zenon_H10f | zenon_intro zenon_H1d9 ]. % 18.99/19.12 exact (zenon_H26d zenon_H10f). % 18.99/19.12 apply (zenon_or_s _ _ zenon_H1d9); [ zenon_intro zenon_H110 | zenon_intro zenon_H1da ]. % 18.99/19.12 exact (zenon_H20c zenon_H110). % 18.99/19.12 apply (zenon_or_s _ _ zenon_H1da); [ zenon_intro zenon_H1ca | zenon_intro zenon_H14d ]. % 18.99/19.12 apply (zenon_L1123_); trivial. % 18.99/19.12 apply (zenon_L1115_); trivial. % 18.99/19.12 apply (zenon_L1107_); trivial. % 18.99/19.12 (* end of lemma zenon_L1124_ *) % 18.99/19.12 assert (zenon_L1125_ : (~((e1) = (e2))) -> (((op (e0) (e3)) = (e2))\/(((op (e1) (e3)) = (e2))\/(((op (e2) (e3)) = (e2))\/((op (e3) (e3)) = (e2))))) -> (~((op (e0) (e3)) = (e2))) -> (~((op (e3) (e1)) = (op (e3) (e3)))) -> (~((op (e2) (e1)) = (op (e2) (e3)))) -> (~((op (e3) (e3)) = (e2))) -> (~((op (e1) (e1)) = (e2))) -> (~((op (e0) (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 (e0) (e1)) = (e0))\/(((op (e0) (e1)) = (e1))\/(((op (e0) (e1)) = (e2))\/((op (e0) (e1)) = (e3))))) -> (~((op (e0) (e1)) = (op (e2) (e1)))) -> (((op (e1) (e1)) = (e0))\/(((op (e1) (e1)) = (e1))\/(((op (e1) (e1)) = (e2))\/((op (e1) (e1)) = (e3))))) -> (~((op (e1) (e1)) = (e1))) -> ((op (e2) (e1)) = (e0)) -> (~((op (e0) (e1)) = (op (e0) (e3)))) -> (((op (e0) (e1)) = (e1))\/(((op (e1) (e1)) = (e1))\/(((op (e2) (e1)) = (e1))\/((op (e3) (e1)) = (e1))))) -> (~((op (e1) (e0)) = (op (e1) (e3)))) -> ((op (e1) (e0)) = (e1)) -> (~((op (e3) (e3)) = (e3))) -> ((op (e1) (e3)) = (e0)) -> (~((op (e2) (e3)) = (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)) = (e1)) -> (~((op (e3) (e2)) = (op (e3) (e3)))) -> False). % 18.99/19.12 do 0 intro. intros zenon_H7c zenon_H145 zenon_H12e zenon_H130 zenon_H1c7 zenon_Hf7 zenon_H20c zenon_H26d zenon_H1d8 zenon_H133 zenon_H212 zenon_H17e zenon_H142 zenon_H10a zenon_H36 zenon_H54 zenon_H109 zenon_Hd8 zenon_H9d zenon_H102 zenon_H1f zenon_Hf3 zenon_H44 zenon_H71 zenon_H101 zenon_Hba zenon_H62. % 18.99/19.12 apply (zenon_or_s _ _ zenon_H133); [ zenon_intro zenon_Hc3 | zenon_intro zenon_H134 ]. % 18.99/19.12 apply (zenon_L1124_); trivial. % 18.99/19.12 apply (zenon_or_s _ _ zenon_H134); [ zenon_intro zenon_Hd6 | zenon_intro zenon_H135 ]. % 18.99/19.12 apply (zenon_L360_); trivial. % 18.99/19.12 apply (zenon_or_s _ _ zenon_H135); [ zenon_intro zenon_Hf4 | zenon_intro zenon_Hc4 ]. % 18.99/19.12 apply (zenon_L64_); trivial. % 18.99/19.12 apply (zenon_L147_); trivial. % 18.99/19.12 (* end of lemma zenon_L1125_ *) % 18.99/19.12 assert (zenon_L1126_ : (((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 (e1) (e3)) = (op (e2) (e3)))) -> (~((op (e1) (e3)) = (e2))) -> (~((op (e0) (e3)) = (op (e1) (e3)))) -> ((op (e0) (e3)) = (e3)) -> False). % 18.99/19.12 do 0 intro. intros zenon_Hdf zenon_H37 zenon_Hf4 zenon_Hdb zenon_H14c zenon_H1d zenon_He3. % 18.99/19.12 apply (zenon_or_s _ _ zenon_Hdf); [ zenon_intro zenon_H1f | zenon_intro zenon_He0 ]. % 18.99/19.12 apply (zenon_L130_); trivial. % 18.99/19.12 apply (zenon_or_s _ _ zenon_He0); [ zenon_intro zenon_Hd6 | zenon_intro zenon_He1 ]. % 18.99/19.12 apply (zenon_L126_); trivial. % 18.99/19.12 apply (zenon_or_s _ _ zenon_He1); [ zenon_intro zenon_Hd7 | zenon_intro zenon_Hdc ]. % 18.99/19.12 exact (zenon_H14c zenon_Hd7). % 18.99/19.12 apply (zenon_L117_); trivial. % 18.99/19.12 (* end of lemma zenon_L1126_ *) % 18.99/19.12 assert (zenon_L1127_ : (((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)) = (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 (e1) (e3)) = (op (e2) (e3)))) -> (~((op (e1) (e3)) = (e2))) -> (~((op (e0) (e3)) = (op (e1) (e3)))) -> False). % 18.99/19.12 do 0 intro. intros zenon_He4 zenon_He2 zenon_H12e zenon_Hdf zenon_H37 zenon_Hf4 zenon_Hdb zenon_H14c zenon_H1d. % 18.99/19.12 apply (zenon_or_s _ _ zenon_He4); [ zenon_intro zenon_H1e | zenon_intro zenon_He5 ]. % 18.99/19.12 apply (zenon_L367_); trivial. % 18.99/19.12 apply (zenon_or_s _ _ zenon_He5); [ zenon_intro zenon_Hc3 | zenon_intro zenon_He6 ]. % 18.99/19.12 apply (zenon_L272_); trivial. % 18.99/19.12 apply (zenon_or_s _ _ zenon_He6); [ zenon_intro zenon_Hcd | zenon_intro zenon_He3 ]. % 18.99/19.12 exact (zenon_H12e zenon_Hcd). % 18.99/19.12 apply (zenon_L1126_); trivial. % 18.99/19.12 (* end of lemma zenon_L1127_ *) % 18.99/19.12 assert (zenon_L1128_ : (((op (e0) (e0)) = (e1))\/(((op (e1) (e0)) = (e1))\/(((op (e2) (e0)) = (e1))\/((op (e3) (e0)) = (e1))))) -> (~((op (e0) (e3)) = (e2))) -> (~((op (e0) (e2)) = (e2))) -> (~((op (e0) (e1)) = (e2))) -> (~((e1) = (e2))) -> (((op (e0) (e0)) = (e2))\/(((op (e0) (e1)) = (e2))\/(((op (e0) (e2)) = (e2))\/((op (e0) (e3)) = (e2))))) -> (~((op (e3) (e2)) = (op (e3) (e3)))) -> ((op (e3) (e2)) = (e1)) -> (~((op (e2) (e2)) = (op (e2) (e3)))) -> (~((op (e1) (e0)) = (op (e1) (e3)))) -> ((op (e0) (e1)) = (e1)) -> (~((op (e0) (e1)) = (op (e0) (e3)))) -> (((op (e0) (e3)) = (e1))\/(((op (e1) (e3)) = (e1))\/(((op (e2) (e3)) = (e1))\/((op (e3) (e3)) = (e1))))) -> ((op (e2) (e2)) = (e1)) -> (~((op (e2) (e0)) = (op (e2) (e2)))) -> ((op (e3) (e0)) = (e0)) -> (~((e0) = (e1))) -> False). % 18.99/19.12 do 0 intro. intros zenon_H235 zenon_H12e zenon_H1fd zenon_H26d zenon_H7c zenon_H183 zenon_H62 zenon_Hba zenon_H6d zenon_Hd8 zenon_Ha0 zenon_H54 zenon_H133 zenon_Hf1 zenon_H52 zenon_H44 zenon_Ha1. % 18.99/19.12 apply (zenon_or_s _ _ zenon_H235); [ zenon_intro zenon_H7a | zenon_intro zenon_H236 ]. % 18.99/19.12 apply (zenon_L1059_); trivial. % 18.99/19.12 apply (zenon_or_s _ _ zenon_H236); [ zenon_intro zenon_H9d | zenon_intro zenon_H237 ]. % 18.99/19.12 apply (zenon_L419_); trivial. % 18.99/19.12 apply (zenon_or_s _ _ zenon_H237); [ zenon_intro zenon_Hed | zenon_intro zenon_Hac ]. % 18.99/19.12 apply (zenon_L93_); trivial. % 18.99/19.12 apply (zenon_L41_); trivial. % 18.99/19.12 (* end of lemma zenon_L1128_ *) % 18.99/19.12 assert (zenon_L1129_ : (((op (e3) (e0)) = (e1))\/(((op (e3) (e1)) = (e1))\/(((op (e3) (e2)) = (e1))\/((op (e3) (e3)) = (e1))))) -> (~((op (e0) (e1)) = (op (e3) (e1)))) -> (~((e0) = (e1))) -> ((op (e3) (e0)) = (e0)) -> (~((op (e2) (e0)) = (op (e2) (e2)))) -> ((op (e2) (e2)) = (e1)) -> (((op (e0) (e3)) = (e1))\/(((op (e1) (e3)) = (e1))\/(((op (e2) (e3)) = (e1))\/((op (e3) (e3)) = (e1))))) -> (~((op (e0) (e1)) = (op (e0) (e3)))) -> ((op (e0) (e1)) = (e1)) -> (~((op (e1) (e0)) = (op (e1) (e3)))) -> (~((op (e2) (e2)) = (op (e2) (e3)))) -> (~((op (e3) (e2)) = (op (e3) (e3)))) -> (((op (e0) (e0)) = (e2))\/(((op (e0) (e1)) = (e2))\/(((op (e0) (e2)) = (e2))\/((op (e0) (e3)) = (e2))))) -> (~((e1) = (e2))) -> (~((op (e0) (e1)) = (e2))) -> (~((op (e0) (e2)) = (e2))) -> (((op (e0) (e0)) = (e1))\/(((op (e1) (e0)) = (e1))\/(((op (e2) (e0)) = (e1))\/((op (e3) (e0)) = (e1))))) -> (((op (e0) (e3)) = (e0))\/(((op (e0) (e3)) = (e1))\/(((op (e0) (e3)) = (e2))\/((op (e0) (e3)) = (e3))))) -> (~((op (e0) (e3)) = (op (e2) (e3)))) -> (~((op (e0) (e3)) = (op (e3) (e3)))) -> (~((op (e0) (e3)) = (e2))) -> (((op (e1) (e3)) = (e0))\/(((op (e1) (e3)) = (e1))\/(((op (e1) (e3)) = (e2))\/((op (e1) (e3)) = (e3))))) -> ((op (e2) (e3)) = (e0)) -> (~((op (e1) (e3)) = (op (e2) (e3)))) -> (~((op (e1) (e3)) = (op (e3) (e3)))) -> (~((op (e1) (e3)) = (e2))) -> (~((op (e0) (e3)) = (op (e1) (e3)))) -> False). % 18.99/19.12 do 0 intro. intros zenon_He8 zenon_H210 zenon_Ha1 zenon_H44 zenon_H52 zenon_Hf1 zenon_H133 zenon_H54 zenon_Ha0 zenon_Hd8 zenon_H6d zenon_H62 zenon_H183 zenon_H7c zenon_H26d zenon_H1fd zenon_H235 zenon_He4 zenon_He2 zenon_Hc2 zenon_H12e zenon_Hdf zenon_H37 zenon_Hdb zenon_Hd5 zenon_H14c zenon_H1d. % 18.99/19.12 apply (zenon_or_s _ _ zenon_He8); [ zenon_intro zenon_Hac | zenon_intro zenon_Heb ]. % 18.99/19.12 apply (zenon_L41_); trivial. % 18.99/19.12 apply (zenon_or_s _ _ zenon_Heb); [ zenon_intro zenon_Hae | zenon_intro zenon_Hec ]. % 18.99/19.12 apply (zenon_L363_); trivial. % 18.99/19.12 apply (zenon_or_s _ _ zenon_Hec); [ zenon_intro zenon_Hba | zenon_intro zenon_Hc4 ]. % 18.99/19.12 apply (zenon_L1128_); trivial. % 18.99/19.12 apply (zenon_L1089_); trivial. % 18.99/19.12 (* end of lemma zenon_L1129_ *) % 18.99/19.12 assert (zenon_L1130_ : (((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) (e3)))) -> (((op (e0) (e3)) = (e2))\/(((op (e1) (e3)) = (e2))\/(((op (e2) (e3)) = (e2))\/((op (e3) (e3)) = (e2))))) -> (~((op (e3) (e1)) = (op (e3) (e3)))) -> (~((op (e2) (e1)) = (op (e2) (e3)))) -> (~((op (e3) (e3)) = (e2))) -> (~((op (e1) (e1)) = (e2))) -> (((op (e0) (e1)) = (e2))\/(((op (e1) (e1)) = (e2))\/(((op (e2) (e1)) = (e2))\/((op (e3) (e1)) = (e2))))) -> (((op (e1) (e1)) = (e0))\/(((op (e1) (e1)) = (e1))\/(((op (e1) (e1)) = (e2))\/((op (e1) (e1)) = (e3))))) -> (~((op (e1) (e1)) = (e1))) -> (((op (e0) (e1)) = (e1))\/(((op (e1) (e1)) = (e1))\/(((op (e2) (e1)) = (e1))\/((op (e3) (e1)) = (e1))))) -> ((op (e1) (e0)) = (e1)) -> (~((op (e3) (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)) = (e1)) -> (~((op (e0) (e2)) = (op (e0) (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) (e3)))) -> (~((e0) = (e3))) -> (((op (e0) (e1)) = (e0))\/(((op (e1) (e1)) = (e0))\/(((op (e2) (e1)) = (e0))\/((op (e3) (e1)) = (e0))))) -> ((op (e2) (e2)) = (e3)) -> (((op (e1) (e0)) = (e0))\/(((op (e1) (e1)) = (e0))\/(((op (e1) (e2)) = (e0))\/((op (e1) (e3)) = (e0))))) -> (~((op (e0) (e0)) = (op (e0) (e3)))) -> ((op (e0) (e0)) = (e2)) -> (~((op (e0) (e2)) = (op (e2) (e2)))) -> (((op (e2) (e0)) = (e1))\/(((op (e2) (e1)) = (e1))\/(((op (e2) (e2)) = (e1))\/((op (e2) (e3)) = (e1))))) -> (((op (e1) (e0)) = (e0))\/(((op (e1) (e0)) = (e1))\/(((op (e1) (e0)) = (e2))\/((op (e1) (e0)) = (e3))))) -> (~((op (e1) (e0)) = (op (e3) (e0)))) -> (~((op (e1) (e0)) = (op (e2) (e0)))) -> (~((op (e1) (e0)) = (e2))) -> ((op (e1) (e1)) = (e0)) -> ((op (e3) (e1)) = (e2)) -> (~((op (e0) (e1)) = (op (e2) (e1)))) -> ((op (e0) (e2)) = (e0)) -> (~((op (e0) (e1)) = (op (e0) (e2)))) -> (((op (e0) (e1)) = (e0))\/(((op (e0) (e1)) = (e1))\/(((op (e0) (e1)) = (e2))\/((op (e0) (e1)) = (e3))))) -> (~((op (e1) (e3)) = (op (e3) (e3)))) -> (~((op (e0) (e3)) = (op (e3) (e3)))) -> (((op (e0) (e0)) = (e1))\/(((op (e1) (e0)) = (e1))\/(((op (e2) (e0)) = (e1))\/((op (e3) (e0)) = (e1))))) -> (~((op (e0) (e2)) = (e2))) -> (~((op (e0) (e1)) = (e2))) -> (~((e1) = (e2))) -> (((op (e0) (e0)) = (e2))\/(((op (e0) (e1)) = (e2))\/(((op (e0) (e2)) = (e2))\/((op (e0) (e3)) = (e2))))) -> (~((op (e3) (e2)) = (op (e3) (e3)))) -> (~((op (e2) (e2)) = (op (e2) (e3)))) -> (~((op (e1) (e0)) = (op (e1) (e3)))) -> ((op (e0) (e1)) = (e1)) -> (~((op (e0) (e1)) = (op (e0) (e3)))) -> (((op (e0) (e3)) = (e1))\/(((op (e1) (e3)) = (e1))\/(((op (e2) (e3)) = (e1))\/((op (e3) (e3)) = (e1))))) -> (~((op (e2) (e0)) = (op (e2) (e2)))) -> ((op (e3) (e0)) = (e0)) -> (~((e0) = (e1))) -> (~((op (e0) (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 (e0) (e3)) = (e1))\/(((op (e0) (e3)) = (e2))\/((op (e0) (e3)) = (e3))))) -> (~((op (e0) (e3)) = (op (e2) (e3)))) -> (~((op (e0) (e3)) = (e2))) -> (((op (e1) (e3)) = (e0))\/(((op (e1) (e3)) = (e1))\/(((op (e1) (e3)) = (e2))\/((op (e1) (e3)) = (e3))))) -> (~((op (e1) (e3)) = (op (e2) (e3)))) -> (~((op (e1) (e3)) = (e2))) -> (~((op (e0) (e3)) = (op (e1) (e3)))) -> False). % 18.99/19.12 do 0 intro. intros zenon_H2f zenon_H17b zenon_H71 zenon_H145 zenon_H130 zenon_H1c7 zenon_Hf7 zenon_H20c zenon_H1d8 zenon_H142 zenon_H10a zenon_H109 zenon_H9d zenon_H102 zenon_Hf3 zenon_H101 zenon_Hba zenon_H208 zenon_H67 zenon_H1cf zenon_H57 zenon_H9a zenon_H245 zenon_Haa zenon_H22 zenon_H189 zenon_H7b zenon_Ha8 zenon_H106 zenon_H25e zenon_H1fa zenon_H201 zenon_H177 zenon_H29 zenon_H14d zenon_H17e zenon_H48 zenon_H4a zenon_H212 zenon_Hd5 zenon_Hc2 zenon_H235 zenon_H1fd zenon_H26d zenon_H7c zenon_H183 zenon_H62 zenon_H6d zenon_Hd8 zenon_Ha0 zenon_H54 zenon_H133 zenon_H52 zenon_H44 zenon_Ha1 zenon_H210 zenon_He8 zenon_He4 zenon_He2 zenon_H12e zenon_Hdf zenon_Hdb zenon_H14c zenon_H1d. % 18.99/19.12 apply (zenon_or_s _ _ zenon_H2f); [ zenon_intro zenon_H34 | zenon_intro zenon_H33 ]. % 18.99/19.12 apply (zenon_L127_); trivial. % 18.99/19.12 apply (zenon_or_s _ _ zenon_H33); [ zenon_intro zenon_H36 | zenon_intro zenon_H35 ]. % 18.99/19.12 apply (zenon_or_s _ _ zenon_H106); [ zenon_intro zenon_Hed | zenon_intro zenon_H107 ]. % 18.99/19.12 apply (zenon_L1064_); trivial. % 18.99/19.12 apply (zenon_or_s _ _ zenon_H107); [ zenon_intro zenon_Ha5 | zenon_intro zenon_H108 ]. % 18.99/19.12 apply (zenon_L1115_); trivial. % 18.99/19.12 apply (zenon_or_s _ _ zenon_H108); [ zenon_intro zenon_Hf1 | zenon_intro zenon_Hf4 ]. % 18.99/19.12 apply (zenon_L1122_); trivial. % 18.99/19.12 apply (zenon_or_s _ _ zenon_H67); [ zenon_intro zenon_H1e | zenon_intro zenon_H68 ]. % 18.99/19.12 apply (zenon_L336_); trivial. % 18.99/19.12 apply (zenon_or_s _ _ zenon_H68); [ zenon_intro zenon_H1f | zenon_intro zenon_H69 ]. % 18.99/19.12 apply (zenon_L1125_); trivial. % 18.99/19.12 apply (zenon_or_s _ _ zenon_H69); [ zenon_intro zenon_H37 | zenon_intro zenon_H60 ]. % 18.99/19.12 apply (zenon_L1127_); trivial. % 18.99/19.12 apply (zenon_L21_); trivial. % 18.99/19.12 apply (zenon_or_s _ _ zenon_H35); [ zenon_intro zenon_H2c | zenon_intro zenon_H37 ]. % 18.99/19.12 apply (zenon_L679_); trivial. % 18.99/19.12 apply (zenon_or_s _ _ zenon_H106); [ zenon_intro zenon_Hed | zenon_intro zenon_H107 ]. % 18.99/19.12 apply (zenon_L1120_); trivial. % 18.99/19.12 apply (zenon_or_s _ _ zenon_H107); [ zenon_intro zenon_Ha5 | zenon_intro zenon_H108 ]. % 18.99/19.12 apply (zenon_L1105_); trivial. % 18.99/19.12 apply (zenon_or_s _ _ zenon_H108); [ zenon_intro zenon_Hf1 | zenon_intro zenon_Hf4 ]. % 18.99/19.12 apply (zenon_L1129_); trivial. % 18.99/19.12 apply (zenon_L1127_); trivial. % 18.99/19.12 (* end of lemma zenon_L1130_ *) % 18.99/19.12 assert (zenon_L1131_ : (((op (e3) (e3)) = (e0))\/(((op (e3) (e3)) = (e1))\/(((op (e3) (e3)) = (e2))\/((op (e3) (e3)) = (e3))))) -> ((op (e0) (e3)) = (e3)) -> (~((op (e0) (e3)) = (op (e1) (e3)))) -> (~((op (e1) (e3)) = (e2))) -> (~((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 (e2) (e3)) = (e1)) -> (~((op (e2) (e3)) = (op (e3) (e3)))) -> (~((op (e3) (e3)) = (e2))) -> (~((op (e3) (e3)) = (e3))) -> False). % 18.99/19.12 do 0 intro. intros zenon_H101 zenon_He3 zenon_H1d zenon_H14c zenon_Hdb zenon_Hd5 zenon_Hdf zenon_Hf4 zenon_Hf3 zenon_Hf7 zenon_H102. % 18.99/19.12 apply (zenon_or_s _ _ zenon_H101); [ zenon_intro zenon_H60 | zenon_intro zenon_H103 ]. % 18.99/19.12 apply (zenon_L1079_); trivial. % 18.99/19.12 apply (zenon_or_s _ _ zenon_H103); [ zenon_intro zenon_Hc4 | zenon_intro zenon_H104 ]. % 18.99/19.12 apply (zenon_L60_); trivial. % 18.99/19.12 apply (zenon_or_s _ _ zenon_H104); [ zenon_intro zenon_Hf6 | zenon_intro zenon_H105 ]. % 18.99/19.12 exact (zenon_Hf7 zenon_Hf6). % 18.99/19.12 exact (zenon_H102 zenon_H105). % 18.99/19.12 (* end of lemma zenon_L1131_ *) % 18.99/19.12 assert (zenon_L1132_ : (((op (e0) (e3)) = (e0))\/(((op (e0) (e3)) = (e1))\/(((op (e0) (e3)) = (e2))\/((op (e0) (e3)) = (e3))))) -> ((op (e1) (e3)) = (e0)) -> ((op (e2) (e3)) = (e2)) -> (~((op (e0) (e3)) = (op (e3) (e3)))) -> ((op (e3) (e1)) = (e0)) -> (~((op (e3) (e1)) = (op (e3) (e3)))) -> (~((op (e0) (e3)) = (e2))) -> (((op (e3) (e3)) = (e0))\/(((op (e3) (e3)) = (e1))\/(((op (e3) (e3)) = (e2))\/((op (e3) (e3)) = (e3))))) -> (~((op (e0) (e3)) = (op (e1) (e3)))) -> (~((op (e1) (e3)) = (e2))) -> (~((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 (e2) (e3)) = (e1)) -> (~((op (e2) (e3)) = (op (e3) (e3)))) -> (~((op (e3) (e3)) = (e2))) -> (~((op (e3) (e3)) = (e3))) -> False). % 18.99/19.12 do 0 intro. intros zenon_He4 zenon_H1f zenon_H11d zenon_Hc2 zenon_H1b1 zenon_H130 zenon_H12e zenon_H101 zenon_H1d zenon_H14c zenon_Hdb zenon_Hd5 zenon_Hdf zenon_Hf4 zenon_Hf3 zenon_Hf7 zenon_H102. % 18.99/19.12 apply (zenon_or_s _ _ zenon_He4); [ zenon_intro zenon_H1e | zenon_intro zenon_He5 ]. % 18.99/19.12 apply (zenon_L1_); trivial. % 18.99/19.12 apply (zenon_or_s _ _ zenon_He5); [ zenon_intro zenon_Hc3 | zenon_intro zenon_He6 ]. % 19.02/19.13 apply (zenon_L245_); trivial. % 19.02/19.13 apply (zenon_or_s _ _ zenon_He6); [ zenon_intro zenon_Hcd | zenon_intro zenon_He3 ]. % 19.02/19.13 exact (zenon_H12e zenon_Hcd). % 19.02/19.13 apply (zenon_L1131_); trivial. % 19.02/19.13 (* end of lemma zenon_L1132_ *) % 19.02/19.13 assert (zenon_L1133_ : (((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 (e2) (e3)))) -> (~((op (e0) (e3)) = (e2))) -> (((op (e1) (e3)) = (e0))\/(((op (e1) (e3)) = (e1))\/(((op (e1) (e3)) = (e2))\/((op (e1) (e3)) = (e3))))) -> ((op (e3) (e3)) = (e0)) -> (~((op (e1) (e3)) = (op (e3) (e3)))) -> ((op (e2) (e3)) = (e1)) -> (~((op (e1) (e3)) = (op (e2) (e3)))) -> (~((op (e1) (e3)) = (e2))) -> (~((op (e0) (e3)) = (op (e1) (e3)))) -> False). % 19.02/19.13 do 0 intro. intros zenon_He4 zenon_Hc2 zenon_He2 zenon_H12e zenon_Hdf zenon_H60 zenon_Hd5 zenon_Hf4 zenon_Hdb zenon_H14c zenon_H1d. % 19.02/19.13 apply (zenon_or_s _ _ zenon_He4); [ zenon_intro zenon_H1e | zenon_intro zenon_He5 ]. % 19.02/19.13 apply (zenon_L440_); trivial. % 19.02/19.13 apply (zenon_or_s _ _ zenon_He5); [ zenon_intro zenon_Hc3 | zenon_intro zenon_He6 ]. % 19.02/19.13 apply (zenon_L272_); trivial. % 19.02/19.13 apply (zenon_or_s _ _ zenon_He6); [ zenon_intro zenon_Hcd | zenon_intro zenon_He3 ]. % 19.02/19.13 exact (zenon_H12e zenon_Hcd). % 19.02/19.13 apply (zenon_L1079_); trivial. % 19.02/19.13 (* end of lemma zenon_L1133_ *) % 19.02/19.13 assert (zenon_L1134_ : (((op (e2) (e0)) = (e2))\/(((op (e2) (e1)) = (e2))\/(((op (e2) (e2)) = (e2))\/((op (e2) (e3)) = (e2))))) -> (~((op (e2) (e0)) = (e2))) -> (((op (e0) (e3)) = (e2))\/(((op (e1) (e3)) = (e2))\/(((op (e2) (e3)) = (e2))\/((op (e3) (e3)) = (e2))))) -> (~((op (e0) (e3)) = (e2))) -> (~((op (e2) (e1)) = (op (e2) (e3)))) -> (~((op (e3) (e3)) = (e2))) -> (~((op (e2) (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 (e0) (e3)) = (op (e3) (e3)))) -> ((op (e3) (e1)) = (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) (e0)) = (op (e1) (e3)))) -> ((op (e1) (e0)) = (e1)) -> (~((op (e2) (e2)) = (op (e2) (e3)))) -> ((op (e2) (e2)) = (e1)) -> ((op (e3) (e2)) = (e1)) -> (~((op (e3) (e2)) = (op (e3) (e3)))) -> False). % 19.02/19.13 do 0 intro. intros zenon_H1d5 zenon_Hef zenon_H145 zenon_H12e zenon_H1c7 zenon_Hf7 zenon_H173 zenon_H133 zenon_H102 zenon_Hf3 zenon_Hc2 zenon_H1b1 zenon_H130 zenon_H101 zenon_Hd8 zenon_H9d zenon_H6d zenon_Hf1 zenon_Hba zenon_H62. % 19.02/19.13 apply (zenon_or_s _ _ zenon_H1d5); [ zenon_intro zenon_Hee | zenon_intro zenon_H1d6 ]. % 19.02/19.13 exact (zenon_Hef zenon_Hee). % 19.02/19.13 apply (zenon_or_s _ _ zenon_H1d6); [ zenon_intro zenon_H1ca | zenon_intro zenon_H1d7 ]. % 19.02/19.13 apply (zenon_L1109_); trivial. % 19.02/19.13 apply (zenon_or_s _ _ zenon_H1d7); [ zenon_intro zenon_H176 | zenon_intro zenon_H11d ]. % 19.02/19.13 exact (zenon_H173 zenon_H176). % 19.02/19.13 apply (zenon_or_s _ _ zenon_H133); [ zenon_intro zenon_Hc3 | zenon_intro zenon_H134 ]. % 19.02/19.13 apply (zenon_L245_); trivial. % 19.02/19.13 apply (zenon_or_s _ _ zenon_H134); [ zenon_intro zenon_Hd6 | zenon_intro zenon_H135 ]. % 19.02/19.13 apply (zenon_L360_); trivial. % 19.02/19.13 apply (zenon_or_s _ _ zenon_H135); [ zenon_intro zenon_Hf4 | zenon_intro zenon_Hc4 ]. % 19.02/19.13 apply (zenon_L84_); trivial. % 19.02/19.13 apply (zenon_L147_); trivial. % 19.02/19.13 (* end of lemma zenon_L1134_ *) % 19.02/19.13 assert (zenon_L1135_ : (((op (e0) (e1)) = (e0))\/(((op (e1) (e1)) = (e0))\/(((op (e2) (e1)) = (e0))\/((op (e3) (e1)) = (e0))))) -> (~((e0) = (e1))) -> ((op (e0) (e1)) = (e1)) -> (~((op (e1) (e1)) = (op (e1) (e3)))) -> (~((op (e3) (e2)) = (op (e3) (e3)))) -> ((op (e3) (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 (e2) (e3)) = (op (e3) (e3)))) -> ((op (e1) (e3)) = (e0)) -> (~((op (e3) (e3)) = (e3))) -> ((op (e1) (e0)) = (e1)) -> (~((op (e1) (e0)) = (op (e1) (e3)))) -> (((op (e0) (e1)) = (e1))\/(((op (e1) (e1)) = (e1))\/(((op (e2) (e1)) = (e1))\/((op (e3) (e1)) = (e1))))) -> (~((op (e0) (e1)) = (op (e0) (e3)))) -> (~((op (e1) (e1)) = (e1))) -> (((op (e1) (e1)) = (e0))\/(((op (e1) (e1)) = (e1))\/(((op (e1) (e1)) = (e2))\/((op (e1) (e1)) = (e3))))) -> (~((op (e0) (e1)) = (op (e2) (e1)))) -> (((op (e0) (e1)) = (e0))\/(((op (e0) (e1)) = (e1))\/(((op (e0) (e1)) = (e2))\/((op (e0) (e1)) = (e3))))) -> (((op (e0) (e3)) = (e1))\/(((op (e1) (e3)) = (e1))\/(((op (e2) (e3)) = (e1))\/((op (e3) (e3)) = (e1))))) -> (((op (e0) (e1)) = (e2))\/(((op (e1) (e1)) = (e2))\/(((op (e2) (e1)) = (e2))\/((op (e3) (e1)) = (e2))))) -> (~((op (e0) (e1)) = (e2))) -> (~((op (e1) (e1)) = (e2))) -> (~((op (e3) (e3)) = (e2))) -> (~((op (e2) (e1)) = (op (e2) (e3)))) -> (~((op (e3) (e1)) = (op (e3) (e3)))) -> (~((op (e0) (e3)) = (e2))) -> (((op (e0) (e3)) = (e2))\/(((op (e1) (e3)) = (e2))\/(((op (e2) (e3)) = (e2))\/((op (e3) (e3)) = (e2))))) -> (~((e1) = (e2))) -> (~((op (e3) (e0)) = (op (e3) (e1)))) -> ((op (e3) (e0)) = (e0)) -> False). % 19.02/19.13 do 0 intro. intros zenon_H245 zenon_Ha1 zenon_Ha0 zenon_H57 zenon_H62 zenon_Hba zenon_H101 zenon_H71 zenon_Hf3 zenon_H1f zenon_H102 zenon_H9d zenon_Hd8 zenon_H109 zenon_H54 zenon_H10a zenon_H142 zenon_H17e zenon_H212 zenon_H133 zenon_H1d8 zenon_H26d zenon_H20c zenon_Hf7 zenon_H1c7 zenon_H130 zenon_H12e zenon_H145 zenon_H7c zenon_H1cf zenon_H44. % 19.02/19.13 apply (zenon_or_s _ _ zenon_H245); [ zenon_intro zenon_H49 | zenon_intro zenon_H246 ]. % 19.02/19.13 apply (zenon_L38_); trivial. % 19.02/19.13 apply (zenon_or_s _ _ zenon_H246); [ zenon_intro zenon_H29 | zenon_intro zenon_H247 ]. % 19.02/19.13 apply (zenon_L13_); trivial. % 19.02/19.13 apply (zenon_or_s _ _ zenon_H247); [ zenon_intro zenon_H36 | zenon_intro zenon_H1b1 ]. % 19.02/19.13 apply (zenon_L1125_); trivial. % 19.02/19.13 apply (zenon_L346_); trivial. % 19.02/19.13 (* end of lemma zenon_L1135_ *) % 19.02/19.13 assert (zenon_L1136_ : (((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)) = (op (e1) (e3)))) -> (~((e1) = (e2))) -> (((op (e0) (e3)) = (e2))\/(((op (e1) (e3)) = (e2))\/(((op (e2) (e3)) = (e2))\/((op (e3) (e3)) = (e2))))) -> (~((op (e0) (e3)) = (e2))) -> (~((op (e3) (e3)) = (e3))) -> (~((op (e3) (e1)) = (op (e3) (e3)))) -> ((op (e0) (e3)) = (e1)) -> (((op (e3) (e3)) = (e0))\/(((op (e3) (e3)) = (e1))\/(((op (e3) (e3)) = (e2))\/((op (e3) (e3)) = (e3))))) -> (~((op (e2) (e1)) = (op (e2) (e3)))) -> (~((op (e3) (e3)) = (e2))) -> (~((op (e1) (e1)) = (e2))) -> (~((op (e0) (e1)) = (e2))) -> (((op (e0) (e1)) = (e2))\/(((op (e1) (e1)) = (e2))\/(((op (e2) (e1)) = (e2))\/((op (e3) (e1)) = (e2))))) -> (~((op (e3) (e2)) = (op (e3) (e3)))) -> ((op (e3) (e2)) = (e1)) -> (~((op (e3) (e0)) = (op (e3) (e3)))) -> (~((op (e2) (e3)) = (op (e3) (e3)))) -> ((op (e1) (e3)) = (e0)) -> ((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)) = (e0))\/(((op (e0) (e1)) = (e1))\/(((op (e0) (e1)) = (e2))\/((op (e0) (e1)) = (e3))))) -> (~((op (e0) (e1)) = (op (e2) (e1)))) -> (((op (e1) (e1)) = (e0))\/(((op (e1) (e1)) = (e1))\/(((op (e1) (e1)) = (e2))\/((op (e1) (e1)) = (e3))))) -> (~((op (e1) (e1)) = (e1))) -> (~((op (e0) (e1)) = (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 (e3) (e0)) = (e0)) -> False). % 19.02/19.13 do 0 intro. intros zenon_H245 zenon_H4a zenon_H48 zenon_H57 zenon_H7c zenon_H145 zenon_H12e zenon_H102 zenon_H130 zenon_Hc3 zenon_H101 zenon_H1c7 zenon_Hf7 zenon_H20c zenon_H26d zenon_H1d8 zenon_H62 zenon_Hba zenon_H71 zenon_Hf3 zenon_H1f zenon_H9d zenon_Hd8 zenon_H133 zenon_H212 zenon_H17e zenon_H142 zenon_H10a zenon_H54 zenon_H109 zenon_H1cf zenon_H44. % 19.02/19.13 apply (zenon_or_s _ _ zenon_H245); [ zenon_intro zenon_H49 | zenon_intro zenon_H246 ]. % 19.02/19.13 apply (zenon_L9_); trivial. % 19.02/19.13 apply (zenon_or_s _ _ zenon_H246); [ zenon_intro zenon_H29 | zenon_intro zenon_H247 ]. % 19.02/19.13 apply (zenon_L13_); trivial. % 19.02/19.13 apply (zenon_or_s _ _ zenon_H247); [ zenon_intro zenon_H36 | zenon_intro zenon_H1b1 ]. % 19.02/19.13 apply (zenon_L1124_); trivial. % 19.02/19.13 apply (zenon_L346_); trivial. % 19.02/19.13 (* end of lemma zenon_L1136_ *) % 19.02/19.13 assert (zenon_L1137_ : (((op (e2) (e3)) = (e0))\/(((op (e2) (e3)) = (e1))\/(((op (e2) (e3)) = (e2))\/((op (e2) (e3)) = (e3))))) -> ((op (e3) (e3)) = (e2)) -> ((op (e0) (e3)) = (e1)) -> (~((op (e2) (e1)) = (op (e2) (e3)))) -> ((op (e2) (e1)) = (e1)) -> (~((op (e2) (e3)) = (e2))) -> (~((op (e1) (e3)) = (op (e2) (e3)))) -> ((op (e1) (e3)) = (e3)) -> False). % 19.02/19.13 do 0 intro. intros zenon_H11f zenon_Hf6 zenon_Hc3 zenon_H1c7 zenon_Ha5 zenon_H274 zenon_Hdb zenon_Hdc. % 19.02/19.13 apply (zenon_or_s _ _ zenon_H11f); [ zenon_intro zenon_H37 | zenon_intro zenon_H120 ]. % 19.02/19.13 apply (zenon_L387_); trivial. % 19.02/19.13 apply (zenon_or_s _ _ zenon_H120); [ zenon_intro zenon_Hf4 | zenon_intro zenon_H121 ]. % 19.02/19.13 apply (zenon_L188_); trivial. % 19.02/19.13 apply (zenon_or_s _ _ zenon_H121); [ zenon_intro zenon_H11d | zenon_intro zenon_Hdd ]. % 19.02/19.13 exact (zenon_H274 zenon_H11d). % 19.02/19.13 apply (zenon_L52_); trivial. % 19.02/19.13 (* end of lemma zenon_L1137_ *) % 19.02/19.13 assert (zenon_L1138_ : (((op (e3) (e0)) = (e2))\/(((op (e3) (e1)) = (e2))\/(((op (e3) (e2)) = (e2))\/((op (e3) (e3)) = (e2))))) -> (~((op (e3) (e0)) = (e2))) -> (~((op (e3) (e1)) = (e2))) -> (~((op (e3) (e2)) = (e2))) -> (((op (e2) (e3)) = (e0))\/(((op (e2) (e3)) = (e1))\/(((op (e2) (e3)) = (e2))\/((op (e2) (e3)) = (e3))))) -> ((op (e0) (e3)) = (e1)) -> (~((op (e2) (e1)) = (op (e2) (e3)))) -> ((op (e2) (e1)) = (e1)) -> (~((op (e2) (e3)) = (e2))) -> (~((op (e1) (e3)) = (op (e2) (e3)))) -> ((op (e1) (e3)) = (e3)) -> False). % 19.02/19.13 do 0 intro. intros zenon_H153 zenon_H14b zenon_H194 zenon_H272 zenon_H11f zenon_Hc3 zenon_H1c7 zenon_Ha5 zenon_H274 zenon_Hdb zenon_Hdc. % 19.02/19.13 apply (zenon_or_s _ _ zenon_H153); [ zenon_intro zenon_H148 | zenon_intro zenon_H154 ]. % 19.02/19.13 exact (zenon_H14b zenon_H148). % 19.02/19.13 apply (zenon_or_s _ _ zenon_H154); [ zenon_intro zenon_H14d | zenon_intro zenon_H155 ]. % 19.02/19.13 exact (zenon_H194 zenon_H14d). % 19.02/19.13 apply (zenon_or_s _ _ zenon_H155); [ zenon_intro zenon_H151 | zenon_intro zenon_Hf6 ]. % 19.02/19.13 exact (zenon_H272 zenon_H151). % 19.02/19.13 apply (zenon_L1137_); trivial. % 19.02/19.13 (* end of lemma zenon_L1138_ *) % 19.02/19.13 assert (zenon_L1139_ : (((op (e1) (e0)) = (e3))\/(((op (e1) (e1)) = (e3))\/(((op (e1) (e2)) = (e3))\/((op (e1) (e3)) = (e3))))) -> (~((e1) = (e3))) -> ((op (e1) (e0)) = (e1)) -> ((op (e0) (e1)) = (e3)) -> (~((op (e0) (e1)) = (op (e1) (e1)))) -> (~((e2) = (e3))) -> ((op (e1) (e2)) = (e2)) -> (((op (e3) (e0)) = (e2))\/(((op (e3) (e1)) = (e2))\/(((op (e3) (e2)) = (e2))\/((op (e3) (e3)) = (e2))))) -> (~((op (e3) (e0)) = (e2))) -> (~((op (e3) (e1)) = (e2))) -> (~((op (e3) (e2)) = (e2))) -> (((op (e2) (e3)) = (e0))\/(((op (e2) (e3)) = (e1))\/(((op (e2) (e3)) = (e2))\/((op (e2) (e3)) = (e3))))) -> ((op (e0) (e3)) = (e1)) -> (~((op (e2) (e1)) = (op (e2) (e3)))) -> ((op (e2) (e1)) = (e1)) -> (~((op (e2) (e3)) = (e2))) -> (~((op (e1) (e3)) = (op (e2) (e3)))) -> False). % 19.02/19.13 do 0 intro. intros zenon_H16f zenon_H95 zenon_H9d zenon_H99 zenon_H10e zenon_H12b zenon_H113 zenon_H153 zenon_H14b zenon_H194 zenon_H272 zenon_H11f zenon_Hc3 zenon_H1c7 zenon_Ha5 zenon_H274 zenon_Hdb. % 19.02/19.13 apply (zenon_or_s _ _ zenon_H16f); [ zenon_intro zenon_H9e | zenon_intro zenon_H170 ]. % 19.02/19.13 apply (zenon_L37_); trivial. % 19.02/19.13 apply (zenon_or_s _ _ zenon_H170); [ zenon_intro zenon_H13f | zenon_intro zenon_H171 ]. % 19.02/19.13 apply (zenon_L108_); trivial. % 19.02/19.13 apply (zenon_or_s _ _ zenon_H171); [ zenon_intro zenon_H16c | zenon_intro zenon_Hdc ]. % 19.02/19.13 apply (zenon_L116_); trivial. % 19.02/19.13 apply (zenon_L1138_); trivial. % 19.02/19.13 (* end of lemma zenon_L1139_ *) % 19.02/19.13 assert (zenon_L1140_ : (((op (e1) (e0)) = (e1))\/(((op (e1) (e1)) = (e1))\/(((op (e1) (e2)) = (e1))\/((op (e1) (e3)) = (e1))))) -> ((op (e3) (e0)) = (e1)) -> (((op (e1) (e0)) = (e3))\/(((op (e1) (e1)) = (e3))\/(((op (e1) (e2)) = (e3))\/((op (e1) (e3)) = (e3))))) -> ((op (e0) (e1)) = (e3)) -> (~((op (e0) (e1)) = (op (e1) (e1)))) -> ((op (e1) (e2)) = (e2)) -> (((op (e3) (e0)) = (e2))\/(((op (e3) (e1)) = (e2))\/(((op (e3) (e2)) = (e2))\/((op (e3) (e3)) = (e2))))) -> (~((op (e3) (e0)) = (e2))) -> (~((op (e3) (e1)) = (e2))) -> (~((op (e3) (e2)) = (e2))) -> (((op (e2) (e3)) = (e0))\/(((op (e2) (e3)) = (e1))\/(((op (e2) (e3)) = (e2))\/((op (e2) (e3)) = (e3))))) -> (~((op (e2) (e3)) = (e2))) -> ((~((op (e1) (e3)) = (e2)))\/((op (e1) (e2)) = (e3))) -> (~((e1) = (e3))) -> ((~((op (e2) (e1)) = (e2)))\/((op (e2) (e2)) = (e1))) -> (((op (e2) (e0)) = (e2))\/(((op (e2) (e1)) = (e2))\/(((op (e2) (e2)) = (e2))\/((op (e2) (e3)) = (e2))))) -> (~((op (e2) (e2)) = (e2))) -> ((~((op (e3) (e2)) = (e2)))\/((op (e3) (e2)) = (e2))) -> (((op (e0) (e0)) = (e0))\/(((op (e1) (e0)) = (e0))\/(((op (e2) (e0)) = (e0))\/((op (e3) (e0)) = (e0))))) -> (~((op (e2) (e0)) = (op (e2) (e1)))) -> (((op (e2) (e1)) = (e0))\/(((op (e2) (e1)) = (e1))\/(((op (e2) (e1)) = (e2))\/((op (e2) (e1)) = (e3))))) -> (((op (e0) (e0)) = (e2))\/(((op (e0) (e1)) = (e2))\/(((op (e0) (e2)) = (e2))\/((op (e0) (e3)) = (e2))))) -> (~((op (e0) (e3)) = (e2))) -> (~((op (e0) (e1)) = (e2))) -> (~((e1) = (e2))) -> (((op (e0) (e0)) = (e1))\/(((op (e1) (e0)) = (e1))\/(((op (e2) (e0)) = (e1))\/((op (e3) (e0)) = (e1))))) -> (~((op (e0) (e2)) = (op (e3) (e2)))) -> (~((op (e0) (e2)) = (op (e0) (e3)))) -> ((op (e0) (e2)) = (e0)) -> (~((op (e1) (e0)) = (op (e1) (e3)))) -> (((op (e3) (e0)) = (e1))\/(((op (e3) (e1)) = (e1))\/(((op (e3) (e2)) = (e1))\/((op (e3) (e3)) = (e1))))) -> (~((op (e1) (e2)) = (op (e3) (e2)))) -> (~((op (e0) (e2)) = (op (e1) (e2)))) -> (~((op (e3) (e0)) = (op (e3) (e1)))) -> (((op (e2) (e0)) = (e1))\/(((op (e2) (e1)) = (e1))\/(((op (e2) (e2)) = (e1))\/((op (e2) (e3)) = (e1))))) -> (~((op (e3) (e1)) = (op (e3) (e2)))) -> (~((op (e1) (e1)) = (op (e1) (e3)))) -> (((op (e1) (e0)) = (e0))\/(((op (e1) (e1)) = (e0))\/(((op (e1) (e2)) = (e0))\/((op (e1) (e3)) = (e0))))) -> (~((op (e1) (e2)) = (op (e2) (e2)))) -> (((op (e3) (e3)) = (e0))\/(((op (e3) (e3)) = (e1))\/(((op (e3) (e3)) = (e2))\/((op (e3) (e3)) = (e3))))) -> (~((op (e3) (e3)) = (e3))) -> (~((op (e3) (e0)) = (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 (e2) (e1)) = (op (e2) (e3)))) -> (~((op (e0) (e3)) = (op (e3) (e3)))) -> (~((op (e3) (e2)) = (op (e3) (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) (e3)) = (op (e2) (e3)))) -> (~((op (e1) (e3)) = (op (e3) (e3)))) -> (((op (e1) (e3)) = (e0))\/(((op (e1) (e3)) = (e1))\/(((op (e1) (e3)) = (e2))\/((op (e1) (e3)) = (e3))))) -> (~((op (e2) (e3)) = (op (e3) (e3)))) -> (((op (e0) (e1)) = (e0))\/(((op (e1) (e1)) = (e0))\/(((op (e2) (e1)) = (e0))\/((op (e3) (e1)) = (e0))))) -> (((op (e0) (e3)) = (e0))\/(((op (e0) (e3)) = (e1))\/(((op (e0) (e3)) = (e2))\/((op (e0) (e3)) = (e3))))) -> (~((op (e0) (e1)) = (op (e0) (e3)))) -> (~((op (e1) (e1)) = (e1))) -> (~((op (e0) (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 (e0) (e1)) = (e2))\/(((op (e1) (e1)) = (e2))\/(((op (e2) (e1)) = (e2))\/((op (e3) (e1)) = (e2))))) -> (~((e2) = (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))))) -> (~((e0) = (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) (e1)) = (op (e0) (e2)))) -> (~((op (e1) (e0)) = (op (e3) (e0)))) -> (~((op (e1) (e0)) = (op (e2) (e0)))) -> (~((op (e1) (e0)) = (e2))) -> (((op (e1) (e0)) = (e0))\/(((op (e1) (e0)) = (e1))\/(((op (e1) (e0)) = (e2))\/((op (e1) (e0)) = (e3))))) -> (~((op (e1) (e0)) = (op (e1) (e1)))) -> (~((e0) = (e1))) -> (((op (e0) (e0)) = (e1))\/(((op (e0) (e1)) = (e1))\/(((op (e0) (e2)) = (e1))\/((op (e0) (e3)) = (e1))))) -> (~((op (e0) (e0)) = (e0))) -> (~((op (e2) (e2)) = (op (e3) (e2)))) -> ((~((op (e3) (e3)) = (e2)))\/((op (e3) (e2)) = (e3))) -> (~((op (e0) (e2)) = (e2))) -> (((op (e0) (e2)) = (e2))\/(((op (e1) (e2)) = (e2))\/(((op (e2) (e2)) = (e2))\/((op (e3) (e2)) = (e2))))) -> ((~((op (e2) (e3)) = (e2)))\/((op (e2) (e2)) = (e3))) -> (~((op (e0) (e2)) = (op (e2) (e2)))) -> ((~((op (e2) (e0)) = (e2)))\/((op (e2) (e2)) = (e0))) -> ((~((op (e1) (e2)) = (e2)))\/((op (e1) (e2)) = (e2))) -> (~((op (e0) (e3)) = (op (e1) (e3)))) -> ((op (e0) (e3)) = (e1)) -> False). % 19.02/19.13 do 0 intro. intros zenon_H128 zenon_Hac zenon_H16f zenon_H99 zenon_H10e zenon_H113 zenon_H153 zenon_H14b zenon_H194 zenon_H272 zenon_H11f zenon_H274 zenon_H279 zenon_H95 zenon_H271 zenon_H1d5 zenon_H173 zenon_H273 zenon_H3e zenon_H1f0 zenon_H1cc zenon_H183 zenon_H12e zenon_H26d zenon_H7c zenon_H235 zenon_H14f zenon_H208 zenon_H48 zenon_Hd8 zenon_He8 zenon_H115 zenon_H195 zenon_H1cf zenon_H106 zenon_H1a4 zenon_H57 zenon_H22 zenon_H2b zenon_H101 zenon_H102 zenon_H71 zenon_H130 zenon_H67 zenon_H1c7 zenon_Hc2 zenon_H62 zenon_H124 zenon_H133 zenon_He2 zenon_Hd5 zenon_Hdf zenon_Hf3 zenon_H245 zenon_He4 zenon_H54 zenon_H10a zenon_H17e zenon_H212 zenon_H210 zenon_H1d8 zenon_H12b zenon_H109 zenon_H1ac zenon_H149 zenon_Hdb zenon_H18c zenon_H4a zenon_H1fa zenon_H201 zenon_H177 zenon_H25e zenon_H45 zenon_Ha1 zenon_H22d zenon_H3f zenon_H18f zenon_H278 zenon_H1fd zenon_H172 zenon_H277 zenon_Ha8 zenon_H276 zenon_H275 zenon_H1d zenon_Hc3. % 19.02/19.13 apply (zenon_or_s _ _ zenon_H128); [ zenon_intro zenon_H9d | zenon_intro zenon_H129 ]. % 19.02/19.13 apply (zenon_or_s _ _ zenon_H109); [ zenon_intro zenon_Ha0 | zenon_intro zenon_H10b ]. % 19.02/19.13 apply (zenon_L359_); trivial. % 19.02/19.13 apply (zenon_or_s _ _ zenon_H10b); [ zenon_intro zenon_H10d | zenon_intro zenon_H10c ]. % 19.02/19.13 exact (zenon_H10a zenon_H10d). % 19.02/19.13 apply (zenon_or_s _ _ zenon_H10c); [ zenon_intro zenon_Ha5 | zenon_intro zenon_Hae ]. % 19.02/19.13 apply (zenon_L1139_); trivial. % 19.02/19.13 apply (zenon_L242_); trivial. % 19.02/19.13 apply (zenon_or_s _ _ zenon_H129); [ zenon_intro zenon_H10d | zenon_intro zenon_H12a ]. % 19.02/19.13 exact (zenon_H10a zenon_H10d). % 19.02/19.13 apply (zenon_or_s _ _ zenon_H12a); [ zenon_intro zenon_Hf0 | zenon_intro zenon_Hd6 ]. % 19.02/19.13 apply (zenon_L1101_); trivial. % 19.02/19.13 apply (zenon_L79_); trivial. % 19.02/19.13 (* end of lemma zenon_L1140_ *) % 19.02/19.13 assert (zenon_L1141_ : ((op (e2) (e1)) = (e1)) -> (((op (e1) (e0)) = (e1))\/(((op (e1) (e1)) = (e1))\/(((op (e1) (e2)) = (e1))\/((op (e1) (e3)) = (e1))))) -> ((op (e3) (e0)) = (e1)) -> (((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)) = (e2)) -> (((op (e3) (e0)) = (e2))\/(((op (e3) (e1)) = (e2))\/(((op (e3) (e2)) = (e2))\/((op (e3) (e3)) = (e2))))) -> (~((op (e3) (e0)) = (e2))) -> (~((op (e3) (e1)) = (e2))) -> (~((op (e3) (e2)) = (e2))) -> (((op (e2) (e3)) = (e0))\/(((op (e2) (e3)) = (e1))\/(((op (e2) (e3)) = (e2))\/((op (e2) (e3)) = (e3))))) -> (~((op (e2) (e3)) = (e2))) -> ((~((op (e1) (e3)) = (e2)))\/((op (e1) (e2)) = (e3))) -> (~((e1) = (e3))) -> ((~((op (e2) (e1)) = (e2)))\/((op (e2) (e2)) = (e1))) -> (((op (e2) (e0)) = (e2))\/(((op (e2) (e1)) = (e2))\/(((op (e2) (e2)) = (e2))\/((op (e2) (e3)) = (e2))))) -> (~((op (e2) (e2)) = (e2))) -> ((~((op (e3) (e2)) = (e2)))\/((op (e3) (e2)) = (e2))) -> (((op (e0) (e0)) = (e0))\/(((op (e1) (e0)) = (e0))\/(((op (e2) (e0)) = (e0))\/((op (e3) (e0)) = (e0))))) -> (~((op (e2) (e0)) = (op (e2) (e1)))) -> (((op (e2) (e1)) = (e0))\/(((op (e2) (e1)) = (e1))\/(((op (e2) (e1)) = (e2))\/((op (e2) (e1)) = (e3))))) -> (((op (e0) (e0)) = (e2))\/(((op (e0) (e1)) = (e2))\/(((op (e0) (e2)) = (e2))\/((op (e0) (e3)) = (e2))))) -> (~((op (e0) (e3)) = (e2))) -> (~((op (e0) (e1)) = (e2))) -> (~((e1) = (e2))) -> (((op (e0) (e0)) = (e1))\/(((op (e1) (e0)) = (e1))\/(((op (e2) (e0)) = (e1))\/((op (e3) (e0)) = (e1))))) -> (~((op (e0) (e2)) = (op (e3) (e2)))) -> (~((op (e0) (e2)) = (op (e0) (e3)))) -> ((op (e0) (e2)) = (e0)) -> (~((op (e1) (e0)) = (op (e1) (e3)))) -> (((op (e3) (e0)) = (e1))\/(((op (e3) (e1)) = (e1))\/(((op (e3) (e2)) = (e1))\/((op (e3) (e3)) = (e1))))) -> (~((op (e1) (e2)) = (op (e3) (e2)))) -> (~((op (e0) (e2)) = (op (e1) (e2)))) -> (~((op (e3) (e0)) = (op (e3) (e1)))) -> (((op (e2) (e0)) = (e1))\/(((op (e2) (e1)) = (e1))\/(((op (e2) (e2)) = (e1))\/((op (e2) (e3)) = (e1))))) -> (~((op (e3) (e1)) = (op (e3) (e2)))) -> (~((op (e1) (e1)) = (op (e1) (e3)))) -> (((op (e1) (e0)) = (e0))\/(((op (e1) (e1)) = (e0))\/(((op (e1) (e2)) = (e0))\/((op (e1) (e3)) = (e0))))) -> (~((op (e1) (e2)) = (op (e2) (e2)))) -> (((op (e3) (e3)) = (e0))\/(((op (e3) (e3)) = (e1))\/(((op (e3) (e3)) = (e2))\/((op (e3) (e3)) = (e3))))) -> (~((op (e3) (e3)) = (e3))) -> (~((op (e3) (e0)) = (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 (e2) (e1)) = (op (e2) (e3)))) -> (~((op (e0) (e3)) = (op (e3) (e3)))) -> (~((op (e3) (e2)) = (op (e3) (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) (e3)) = (op (e2) (e3)))) -> (~((op (e1) (e3)) = (op (e3) (e3)))) -> (((op (e1) (e3)) = (e0))\/(((op (e1) (e3)) = (e1))\/(((op (e1) (e3)) = (e2))\/((op (e1) (e3)) = (e3))))) -> (~((op (e2) (e3)) = (op (e3) (e3)))) -> (((op (e0) (e1)) = (e0))\/(((op (e1) (e1)) = (e0))\/(((op (e2) (e1)) = (e0))\/((op (e3) (e1)) = (e0))))) -> (((op (e0) (e3)) = (e0))\/(((op (e0) (e3)) = (e1))\/(((op (e0) (e3)) = (e2))\/((op (e0) (e3)) = (e3))))) -> (~((op (e0) (e1)) = (op (e0) (e3)))) -> (~((op (e1) (e1)) = (e1))) -> (~((op (e0) (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 (e0) (e1)) = (e2))\/(((op (e1) (e1)) = (e2))\/(((op (e2) (e1)) = (e2))\/((op (e3) (e1)) = (e2))))) -> (~((e2) = (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))))) -> (~((e0) = (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) (e1)) = (op (e0) (e2)))) -> (~((op (e1) (e0)) = (op (e3) (e0)))) -> (~((op (e1) (e0)) = (op (e2) (e0)))) -> (~((op (e1) (e0)) = (e2))) -> (((op (e1) (e0)) = (e0))\/(((op (e1) (e0)) = (e1))\/(((op (e1) (e0)) = (e2))\/((op (e1) (e0)) = (e3))))) -> (~((op (e1) (e0)) = (op (e1) (e1)))) -> (~((e0) = (e1))) -> (((op (e0) (e0)) = (e1))\/(((op (e0) (e1)) = (e1))\/(((op (e0) (e2)) = (e1))\/((op (e0) (e3)) = (e1))))) -> (~((op (e0) (e0)) = (e0))) -> (~((op (e2) (e2)) = (op (e3) (e2)))) -> ((~((op (e3) (e3)) = (e2)))\/((op (e3) (e2)) = (e3))) -> (~((op (e0) (e2)) = (e2))) -> (((op (e0) (e2)) = (e2))\/(((op (e1) (e2)) = (e2))\/(((op (e2) (e2)) = (e2))\/((op (e3) (e2)) = (e2))))) -> ((~((op (e2) (e3)) = (e2)))\/((op (e2) (e2)) = (e3))) -> (~((op (e0) (e2)) = (op (e2) (e2)))) -> ((~((op (e2) (e0)) = (e2)))\/((op (e2) (e2)) = (e0))) -> ((~((op (e1) (e2)) = (e2)))\/((op (e1) (e2)) = (e2))) -> (~((op (e0) (e3)) = (op (e1) (e3)))) -> ((op (e0) (e3)) = (e1)) -> False). % 19.02/19.13 do 0 intro. intros zenon_Ha5 zenon_H128 zenon_Hac zenon_H16f zenon_H10e zenon_H113 zenon_H153 zenon_H14b zenon_H194 zenon_H272 zenon_H11f zenon_H274 zenon_H279 zenon_H95 zenon_H271 zenon_H1d5 zenon_H173 zenon_H273 zenon_H3e zenon_H1f0 zenon_H1cc zenon_H183 zenon_H12e zenon_H26d zenon_H7c zenon_H235 zenon_H14f zenon_H208 zenon_H48 zenon_Hd8 zenon_He8 zenon_H115 zenon_H195 zenon_H1cf zenon_H106 zenon_H1a4 zenon_H57 zenon_H22 zenon_H2b zenon_H101 zenon_H102 zenon_H71 zenon_H130 zenon_H67 zenon_H1c7 zenon_Hc2 zenon_H62 zenon_H124 zenon_H133 zenon_He2 zenon_Hd5 zenon_Hdf zenon_Hf3 zenon_H245 zenon_He4 zenon_H54 zenon_H10a zenon_H17e zenon_H212 zenon_H210 zenon_H1d8 zenon_H12b zenon_H109 zenon_H1ac zenon_H149 zenon_Hdb zenon_H18c zenon_H4a zenon_H1fa zenon_H201 zenon_H177 zenon_H25e zenon_H45 zenon_Ha1 zenon_H22d zenon_H3f zenon_H18f zenon_H278 zenon_H1fd zenon_H172 zenon_H277 zenon_Ha8 zenon_H276 zenon_H275 zenon_H1d zenon_Hc3. % 19.02/19.13 apply (zenon_or_s _ _ zenon_H212); [ zenon_intro zenon_H49 | zenon_intro zenon_H213 ]. % 19.02/19.13 apply (zenon_L9_); trivial. % 19.02/19.13 apply (zenon_or_s _ _ zenon_H213); [ zenon_intro zenon_Ha0 | zenon_intro zenon_H214 ]. % 19.02/19.13 apply (zenon_L357_); trivial. % 19.02/19.13 apply (zenon_or_s _ _ zenon_H214); [ zenon_intro zenon_H10f | zenon_intro zenon_H99 ]. % 19.02/19.13 exact (zenon_H26d zenon_H10f). % 19.02/19.13 apply (zenon_L1140_); trivial. % 19.02/19.13 (* end of lemma zenon_L1141_ *) % 19.02/19.13 assert (zenon_L1142_ : ((op (e0) (e3)) = (e1)) -> (~((op (e0) (e3)) = (op (e1) (e3)))) -> ((~((op (e1) (e2)) = (e2)))\/((op (e1) (e2)) = (e2))) -> ((~((op (e2) (e0)) = (e2)))\/((op (e2) (e2)) = (e0))) -> (~((op (e0) (e2)) = (op (e2) (e2)))) -> ((~((op (e2) (e3)) = (e2)))\/((op (e2) (e2)) = (e3))) -> (((op (e0) (e2)) = (e2))\/(((op (e1) (e2)) = (e2))\/(((op (e2) (e2)) = (e2))\/((op (e3) (e2)) = (e2))))) -> (~((op (e0) (e2)) = (e2))) -> ((~((op (e3) (e3)) = (e2)))\/((op (e3) (e2)) = (e3))) -> (~((op (e2) (e2)) = (op (e3) (e2)))) -> (~((op (e0) (e0)) = (e0))) -> (((op (e0) (e0)) = (e1))\/(((op (e0) (e1)) = (e1))\/(((op (e0) (e2)) = (e1))\/((op (e0) (e3)) = (e1))))) -> (~((e0) = (e1))) -> (~((op (e1) (e0)) = (op (e1) (e1)))) -> (((op (e1) (e0)) = (e0))\/(((op (e1) (e0)) = (e1))\/(((op (e1) (e0)) = (e2))\/((op (e1) (e0)) = (e3))))) -> (~((op (e1) (e0)) = (e2))) -> (~((op (e1) (e0)) = (op (e2) (e0)))) -> (~((op (e1) (e0)) = (op (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 (e1) (e3)) = (op (e2) (e3)))) -> (~((e0) = (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))))) -> (~((e2) = (e3))) -> (((op (e0) (e1)) = (e2))\/(((op (e1) (e1)) = (e2))\/(((op (e2) (e1)) = (e2))\/((op (e3) (e1)) = (e2))))) -> (~((op (e0) (e1)) = (op (e3) (e1)))) -> (((op (e0) (e1)) = (e0))\/(((op (e0) (e1)) = (e1))\/(((op (e0) (e1)) = (e2))\/((op (e0) (e1)) = (e3))))) -> (~((op (e0) (e1)) = (op (e2) (e1)))) -> (~((op (e1) (e1)) = (e1))) -> (~((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))))) -> (~((op (e2) (e3)) = (op (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 (e2) (e3)))) -> (((op (e0) (e3)) = (e1))\/(((op (e1) (e3)) = (e1))\/(((op (e2) (e3)) = (e1))\/((op (e3) (e3)) = (e1))))) -> (~((op (e1) (e2)) = (op (e1) (e3)))) -> (~((op (e3) (e2)) = (op (e3) (e3)))) -> (~((op (e0) (e3)) = (op (e3) (e3)))) -> (~((op (e2) (e1)) = (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) (e0)) = (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) (e2)) = (op (e2) (e2)))) -> (((op (e1) (e0)) = (e0))\/(((op (e1) (e1)) = (e0))\/(((op (e1) (e2)) = (e0))\/((op (e1) (e3)) = (e0))))) -> (~((op (e1) (e1)) = (op (e1) (e3)))) -> (~((op (e3) (e1)) = (op (e3) (e2)))) -> (((op (e2) (e0)) = (e1))\/(((op (e2) (e1)) = (e1))\/(((op (e2) (e2)) = (e1))\/((op (e2) (e3)) = (e1))))) -> (~((op (e0) (e2)) = (op (e1) (e2)))) -> (~((op (e1) (e2)) = (op (e3) (e2)))) -> (((op (e3) (e0)) = (e1))\/(((op (e3) (e1)) = (e1))\/(((op (e3) (e2)) = (e1))\/((op (e3) (e3)) = (e1))))) -> (~((op (e1) (e0)) = (op (e1) (e3)))) -> ((op (e0) (e2)) = (e0)) -> (~((op (e0) (e2)) = (op (e0) (e3)))) -> (~((op (e0) (e2)) = (op (e3) (e2)))) -> (((op (e0) (e0)) = (e1))\/(((op (e1) (e0)) = (e1))\/(((op (e2) (e0)) = (e1))\/((op (e3) (e0)) = (e1))))) -> (~((e1) = (e2))) -> (~((op (e0) (e1)) = (e2))) -> (~((op (e0) (e3)) = (e2))) -> (((op (e0) (e0)) = (e2))\/(((op (e0) (e1)) = (e2))\/(((op (e0) (e2)) = (e2))\/((op (e0) (e3)) = (e2))))) -> (((op (e2) (e1)) = (e0))\/(((op (e2) (e1)) = (e1))\/(((op (e2) (e1)) = (e2))\/((op (e2) (e1)) = (e3))))) -> (~((op (e2) (e0)) = (op (e2) (e1)))) -> (((op (e0) (e0)) = (e0))\/(((op (e1) (e0)) = (e0))\/(((op (e2) (e0)) = (e0))\/((op (e3) (e0)) = (e0))))) -> ((~((op (e3) (e2)) = (e2)))\/((op (e3) (e2)) = (e2))) -> (~((op (e2) (e2)) = (e2))) -> (((op (e2) (e0)) = (e2))\/(((op (e2) (e1)) = (e2))\/(((op (e2) (e2)) = (e2))\/((op (e2) (e3)) = (e2))))) -> ((~((op (e2) (e1)) = (e2)))\/((op (e2) (e2)) = (e1))) -> (~((e1) = (e3))) -> ((~((op (e1) (e3)) = (e2)))\/((op (e1) (e2)) = (e3))) -> (~((op (e2) (e3)) = (e2))) -> (((op (e2) (e3)) = (e0))\/(((op (e2) (e3)) = (e1))\/(((op (e2) (e3)) = (e2))\/((op (e2) (e3)) = (e3))))) -> (~((op (e3) (e2)) = (e2))) -> (~((op (e3) (e1)) = (e2))) -> (~((op (e3) (e0)) = (e2))) -> (((op (e3) (e0)) = (e2))\/(((op (e3) (e1)) = (e2))\/(((op (e3) (e2)) = (e2))\/((op (e3) (e3)) = (e2))))) -> ((op (e1) (e2)) = (e2)) -> (~((op (e0) (e1)) = (op (e1) (e1)))) -> (((op (e1) (e0)) = (e3))\/(((op (e1) (e1)) = (e3))\/(((op (e1) (e2)) = (e3))\/((op (e1) (e3)) = (e3))))) -> (((op (e1) (e0)) = (e1))\/(((op (e1) (e1)) = (e1))\/(((op (e1) (e2)) = (e1))\/((op (e1) (e3)) = (e1))))) -> (~((op (e3) (e0)) = (op (e3) (e1)))) -> ((op (e3) (e0)) = (e1)) -> False). % 19.02/19.13 do 0 intro. intros zenon_Hc3 zenon_H1d zenon_H275 zenon_H276 zenon_Ha8 zenon_H277 zenon_H172 zenon_H1fd zenon_H278 zenon_H18f zenon_H3f zenon_H22d zenon_Ha1 zenon_H45 zenon_H25e zenon_H177 zenon_H201 zenon_H1fa zenon_H4a zenon_H18c zenon_Hdb zenon_H149 zenon_H1ac zenon_H109 zenon_H12b zenon_H1d8 zenon_H210 zenon_H212 zenon_H17e zenon_H10a zenon_H54 zenon_He4 zenon_H245 zenon_Hf3 zenon_Hdf zenon_Hd5 zenon_He2 zenon_H133 zenon_H124 zenon_H62 zenon_Hc2 zenon_H1c7 zenon_H67 zenon_H130 zenon_H71 zenon_H102 zenon_H101 zenon_H2b zenon_H22 zenon_H57 zenon_H1a4 zenon_H106 zenon_H195 zenon_H115 zenon_He8 zenon_Hd8 zenon_H48 zenon_H208 zenon_H14f zenon_H235 zenon_H7c zenon_H26d zenon_H12e zenon_H183 zenon_H1cc zenon_H1f0 zenon_H3e zenon_H273 zenon_H173 zenon_H1d5 zenon_H271 zenon_H95 zenon_H279 zenon_H274 zenon_H11f zenon_H272 zenon_H194 zenon_H14b zenon_H153 zenon_H113 zenon_H10e zenon_H16f zenon_H128 zenon_H1cf zenon_Hac. % 19.02/19.13 apply (zenon_or_s _ _ zenon_H109); [ zenon_intro zenon_Ha0 | zenon_intro zenon_H10b ]. % 19.02/19.13 apply (zenon_L359_); trivial. % 19.02/19.13 apply (zenon_or_s _ _ zenon_H10b); [ zenon_intro zenon_H10d | zenon_intro zenon_H10c ]. % 19.02/19.13 exact (zenon_H10a zenon_H10d). % 19.02/19.13 apply (zenon_or_s _ _ zenon_H10c); [ zenon_intro zenon_Ha5 | zenon_intro zenon_Hae ]. % 19.02/19.13 apply (zenon_L1141_); trivial. % 19.02/19.13 apply (zenon_L242_); trivial. % 19.02/19.13 (* end of lemma zenon_L1142_ *) % 19.02/19.13 assert (zenon_L1143_ : (((op (e2) (e3)) = (e0))\/(((op (e2) (e3)) = (e1))\/(((op (e2) (e3)) = (e2))\/((op (e2) (e3)) = (e3))))) -> (~((op (e2) (e3)) = (op (e3) (e3)))) -> (~((op (e0) (e3)) = (op (e1) (e3)))) -> (~((op (e1) (e3)) = (e2))) -> (~((op (e1) (e3)) = (op (e2) (e3)))) -> (~((op (e1) (e3)) = (op (e3) (e3)))) -> ((op (e3) (e3)) = (e0)) -> (((op (e1) (e3)) = (e0))\/(((op (e1) (e3)) = (e1))\/(((op (e1) (e3)) = (e2))\/((op (e1) (e3)) = (e3))))) -> (~((op (e2) (e3)) = (e2))) -> (~((op (e0) (e3)) = (op (e2) (e3)))) -> ((op (e0) (e3)) = (e3)) -> False). % 19.02/19.13 do 0 intro. intros zenon_H11f zenon_Hf3 zenon_H1d zenon_H14c zenon_Hdb zenon_Hd5 zenon_H60 zenon_Hdf zenon_H274 zenon_He2 zenon_He3. % 19.02/19.13 apply (zenon_or_s _ _ zenon_H11f); [ zenon_intro zenon_H37 | zenon_intro zenon_H120 ]. % 19.02/19.13 apply (zenon_L219_); trivial. % 19.02/19.13 apply (zenon_or_s _ _ zenon_H120); [ zenon_intro zenon_Hf4 | zenon_intro zenon_H121 ]. % 19.02/19.13 apply (zenon_L1079_); trivial. % 19.02/19.13 apply (zenon_or_s _ _ zenon_H121); [ zenon_intro zenon_H11d | zenon_intro zenon_Hdd ]. % 19.02/19.13 exact (zenon_H274 zenon_H11d). % 19.02/19.13 apply (zenon_L54_); trivial. % 19.02/19.13 (* end of lemma zenon_L1143_ *) % 19.02/19.13 assert (zenon_L1144_ : ((op (e3) (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 (e1) (e0)) = (e3))\/(((op (e1) (e1)) = (e3))\/(((op (e1) (e2)) = (e3))\/((op (e1) (e3)) = (e3))))) -> (~((op (e0) (e1)) = (op (e1) (e1)))) -> ((op (e1) (e2)) = (e2)) -> (((op (e3) (e0)) = (e2))\/(((op (e3) (e1)) = (e2))\/(((op (e3) (e2)) = (e2))\/((op (e3) (e3)) = (e2))))) -> (~((op (e3) (e0)) = (e2))) -> (~((op (e3) (e1)) = (e2))) -> (~((op (e3) (e2)) = (e2))) -> ((~((op (e1) (e3)) = (e2)))\/((op (e1) (e2)) = (e3))) -> (~((e1) = (e3))) -> ((~((op (e2) (e1)) = (e2)))\/((op (e2) (e2)) = (e1))) -> (((op (e2) (e0)) = (e2))\/(((op (e2) (e1)) = (e2))\/(((op (e2) (e2)) = (e2))\/((op (e2) (e3)) = (e2))))) -> (~((op (e2) (e2)) = (e2))) -> ((~((op (e3) (e2)) = (e2)))\/((op (e3) (e2)) = (e2))) -> (((op (e0) (e0)) = (e0))\/(((op (e1) (e0)) = (e0))\/(((op (e2) (e0)) = (e0))\/((op (e3) (e0)) = (e0))))) -> (~((op (e2) (e0)) = (op (e2) (e1)))) -> (((op (e2) (e1)) = (e0))\/(((op (e2) (e1)) = (e1))\/(((op (e2) (e1)) = (e2))\/((op (e2) (e1)) = (e3))))) -> (((op (e0) (e0)) = (e2))\/(((op (e0) (e1)) = (e2))\/(((op (e0) (e2)) = (e2))\/((op (e0) (e3)) = (e2))))) -> (~((op (e0) (e1)) = (e2))) -> (~((e1) = (e2))) -> (((op (e0) (e0)) = (e1))\/(((op (e1) (e0)) = (e1))\/(((op (e2) (e0)) = (e1))\/((op (e3) (e0)) = (e1))))) -> (~((op (e0) (e2)) = (op (e3) (e2)))) -> (~((op (e0) (e2)) = (op (e0) (e3)))) -> ((op (e0) (e2)) = (e0)) -> (~((op (e1) (e0)) = (op (e1) (e3)))) -> (((op (e3) (e0)) = (e1))\/(((op (e3) (e1)) = (e1))\/(((op (e3) (e2)) = (e1))\/((op (e3) (e3)) = (e1))))) -> (~((op (e1) (e2)) = (op (e3) (e2)))) -> (~((op (e0) (e2)) = (op (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 (e1) (e1)) = (op (e1) (e3)))) -> (((op (e1) (e0)) = (e0))\/(((op (e1) (e1)) = (e0))\/(((op (e1) (e2)) = (e0))\/((op (e1) (e3)) = (e0))))) -> (~((op (e1) (e2)) = (op (e2) (e2)))) -> (((op (e3) (e3)) = (e0))\/(((op (e3) (e3)) = (e1))\/(((op (e3) (e3)) = (e2))\/((op (e3) (e3)) = (e3))))) -> (~((op (e3) (e3)) = (e3))) -> (~((op (e3) (e0)) = (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 (e2) (e1)) = (op (e2) (e3)))) -> (~((op (e0) (e3)) = (op (e3) (e3)))) -> (~((op (e3) (e2)) = (op (e3) (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) (e1)) = (e0))\/(((op (e1) (e1)) = (e0))\/(((op (e2) (e1)) = (e0))\/((op (e3) (e1)) = (e0))))) -> (((op (e0) (e3)) = (e0))\/(((op (e0) (e3)) = (e1))\/(((op (e0) (e3)) = (e2))\/((op (e0) (e3)) = (e3))))) -> (~((op (e0) (e1)) = (op (e0) (e3)))) -> (~((op (e1) (e1)) = (e1))) -> (~((op (e0) (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 (e0) (e1)) = (e2))\/(((op (e1) (e1)) = (e2))\/(((op (e2) (e1)) = (e2))\/((op (e3) (e1)) = (e2))))) -> (~((e2) = (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))))) -> (~((e0) = (e2))) -> (((op (e1) (e0)) = (e2))\/(((op (e1) (e1)) = (e2))\/(((op (e1) (e2)) = (e2))\/((op (e1) (e3)) = (e2))))) -> (~((op (e0) (e1)) = (op (e0) (e2)))) -> (~((op (e1) (e0)) = (op (e3) (e0)))) -> (~((op (e1) (e0)) = (op (e2) (e0)))) -> (~((op (e1) (e0)) = (e2))) -> (((op (e1) (e0)) = (e0))\/(((op (e1) (e0)) = (e1))\/(((op (e1) (e0)) = (e2))\/((op (e1) (e0)) = (e3))))) -> (~((op (e1) (e0)) = (op (e1) (e1)))) -> (~((e0) = (e1))) -> (((op (e0) (e0)) = (e1))\/(((op (e0) (e1)) = (e1))\/(((op (e0) (e2)) = (e1))\/((op (e0) (e3)) = (e1))))) -> (~((op (e0) (e0)) = (e0))) -> (~((op (e2) (e2)) = (op (e3) (e2)))) -> ((~((op (e3) (e3)) = (e2)))\/((op (e3) (e2)) = (e3))) -> (~((op (e0) (e2)) = (e2))) -> (((op (e0) (e2)) = (e2))\/(((op (e1) (e2)) = (e2))\/(((op (e2) (e2)) = (e2))\/((op (e3) (e2)) = (e2))))) -> ((~((op (e2) (e3)) = (e2)))\/((op (e2) (e2)) = (e3))) -> (~((op (e0) (e2)) = (op (e2) (e2)))) -> ((~((op (e2) (e0)) = (e2)))\/((op (e2) (e2)) = (e0))) -> ((~((op (e1) (e2)) = (e2)))\/((op (e1) (e2)) = (e2))) -> (~((op (e0) (e3)) = (e2))) -> (((op (e2) (e3)) = (e0))\/(((op (e2) (e3)) = (e1))\/(((op (e2) (e3)) = (e2))\/((op (e2) (e3)) = (e3))))) -> (~((op (e2) (e3)) = (op (e3) (e3)))) -> (~((op (e0) (e3)) = (op (e1) (e3)))) -> (~((op (e1) (e3)) = (e2))) -> (~((op (e1) (e3)) = (op (e2) (e3)))) -> (~((op (e1) (e3)) = (op (e3) (e3)))) -> ((op (e3) (e3)) = (e0)) -> (((op (e1) (e3)) = (e0))\/(((op (e1) (e3)) = (e1))\/(((op (e1) (e3)) = (e2))\/((op (e1) (e3)) = (e3))))) -> (~((op (e2) (e3)) = (e2))) -> (~((op (e0) (e3)) = (op (e2) (e3)))) -> False). % 19.02/19.13 do 0 intro. intros zenon_Hac zenon_H1cf zenon_H128 zenon_H16f zenon_H10e zenon_H113 zenon_H153 zenon_H14b zenon_H194 zenon_H272 zenon_H279 zenon_H95 zenon_H271 zenon_H1d5 zenon_H173 zenon_H273 zenon_H3e zenon_H1f0 zenon_H1cc zenon_H183 zenon_H26d zenon_H7c zenon_H235 zenon_H14f zenon_H208 zenon_H48 zenon_Hd8 zenon_He8 zenon_H115 zenon_H195 zenon_H106 zenon_H1a4 zenon_H57 zenon_H22 zenon_H2b zenon_H101 zenon_H102 zenon_H71 zenon_H130 zenon_H67 zenon_H1c7 zenon_Hc2 zenon_H62 zenon_H124 zenon_H133 zenon_H245 zenon_He4 zenon_H54 zenon_H10a zenon_H17e zenon_H212 zenon_H210 zenon_H1d8 zenon_H12b zenon_H109 zenon_H1ac zenon_H149 zenon_H18c zenon_H4a zenon_H1fa zenon_H201 zenon_H177 zenon_H25e zenon_H45 zenon_Ha1 zenon_H22d zenon_H3f zenon_H18f zenon_H278 zenon_H1fd zenon_H172 zenon_H277 zenon_Ha8 zenon_H276 zenon_H275 zenon_H12e zenon_H11f zenon_Hf3 zenon_H1d zenon_H14c zenon_Hdb zenon_Hd5 zenon_H60 zenon_Hdf zenon_H274 zenon_He2. % 19.02/19.13 apply (zenon_or_s _ _ zenon_He4); [ zenon_intro zenon_H1e | zenon_intro zenon_He5 ]. % 19.02/19.13 apply (zenon_L440_); trivial. % 19.02/19.13 apply (zenon_or_s _ _ zenon_He5); [ zenon_intro zenon_Hc3 | zenon_intro zenon_He6 ]. % 19.02/19.13 apply (zenon_L1142_); trivial. % 19.02/19.13 apply (zenon_or_s _ _ zenon_He6); [ zenon_intro zenon_Hcd | zenon_intro zenon_He3 ]. % 19.02/19.13 exact (zenon_H12e zenon_Hcd). % 19.02/19.13 apply (zenon_L1143_); trivial. % 19.02/19.13 (* end of lemma zenon_L1144_ *) % 19.02/19.13 assert (zenon_L1145_ : (((op (e2) (e0)) = (e0))\/(((op (e2) (e0)) = (e1))\/(((op (e2) (e0)) = (e2))\/((op (e2) (e0)) = (e3))))) -> (~((op (e2) (e0)) = (op (e2) (e3)))) -> ((op (e2) (e3)) = (e0)) -> ((op (e2) (e2)) = (e1)) -> (~((op (e2) (e0)) = (op (e2) (e2)))) -> (~((op (e2) (e0)) = (e2))) -> ((op (e3) (e0)) = (e1)) -> ((op (e0) (e0)) = (e2)) -> False). % 19.02/19.13 do 0 intro. intros zenon_H259 zenon_H5b zenon_H37 zenon_Hf1 zenon_H52 zenon_Hef zenon_Hac zenon_H7b. % 19.02/19.13 apply (zenon_or_s _ _ zenon_H259); [ zenon_intro zenon_H34 | zenon_intro zenon_H25a ]. % 19.02/19.13 apply (zenon_L14_); trivial. % 19.02/19.13 apply (zenon_or_s _ _ zenon_H25a); [ zenon_intro zenon_Hed | zenon_intro zenon_H25b ]. % 19.02/19.13 apply (zenon_L93_); trivial. % 19.02/19.13 apply (zenon_or_s _ _ zenon_H25b); [ zenon_intro zenon_Hee | zenon_intro zenon_H3b ]. % 19.02/19.13 exact (zenon_Hef zenon_Hee). % 19.02/19.13 apply (zenon_L308_); trivial. % 19.02/19.13 (* end of lemma zenon_L1145_ *) % 19.02/19.13 assert (zenon_L1146_ : (((op (e2) (e0)) = (e0))\/(((op (e2) (e1)) = (e0))\/(((op (e2) (e2)) = (e0))\/((op (e2) (e3)) = (e0))))) -> (~((op (e1) (e0)) = (op (e2) (e0)))) -> (~((op (e3) (e1)) = (op (e3) (e3)))) -> ((op (e3) (e1)) = (e0)) -> (~((op (e2) (e1)) = (op (e2) (e3)))) -> (~((op (e1) (e0)) = (op (e1) (e3)))) -> ((op (e1) (e0)) = (e0)) -> (~((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 (e2) (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)) = (e1)) -> (~((op (e2) (e0)) = (op (e2) (e2)))) -> (~((op (e2) (e0)) = (e2))) -> ((op (e3) (e0)) = (e1)) -> ((op (e0) (e0)) = (e2)) -> False). % 19.02/19.13 do 0 intro. intros zenon_H2f zenon_H201 zenon_H130 zenon_H1b1 zenon_H1c7 zenon_Hd8 zenon_H27 zenon_H208 zenon_H67 zenon_H48 zenon_Ha8 zenon_H259 zenon_H5b zenon_Hf1 zenon_H52 zenon_Hef zenon_Hac zenon_H7b. % 19.02/19.13 apply (zenon_or_s _ _ zenon_H2f); [ zenon_intro zenon_H34 | zenon_intro zenon_H33 ]. % 19.02/19.13 apply (zenon_L332_); trivial. % 19.02/19.13 apply (zenon_or_s _ _ zenon_H33); [ zenon_intro zenon_H36 | zenon_intro zenon_H35 ]. % 19.02/19.13 apply (zenon_L641_); trivial. % 19.02/19.13 apply (zenon_or_s _ _ zenon_H35); [ zenon_intro zenon_H2c | zenon_intro zenon_H37 ]. % 19.02/19.13 apply (zenon_L679_); trivial. % 19.02/19.13 apply (zenon_L1145_); trivial. % 19.02/19.13 (* end of lemma zenon_L1146_ *) % 19.02/19.13 assert (zenon_L1147_ : (((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) (e1)) = (op (e0) (e3)))) -> ((op (e0) (e1)) = (e1)) -> (~((op (e0) (e3)) = (e2))) -> (~((op (e0) (e3)) = (op (e2) (e3)))) -> ((op (e2) (e3)) = (e3)) -> False). % 19.02/19.13 do 0 intro. intros zenon_He4 zenon_H1f zenon_H1d zenon_H54 zenon_Ha0 zenon_H12e zenon_He2 zenon_Hdd. % 19.02/19.13 apply (zenon_or_s _ _ zenon_He4); [ zenon_intro zenon_H1e | zenon_intro zenon_He5 ]. % 19.02/19.13 apply (zenon_L1_); trivial. % 19.02/19.13 apply (zenon_or_s _ _ zenon_He5); [ zenon_intro zenon_Hc3 | zenon_intro zenon_He6 ]. % 19.02/19.13 apply (zenon_L359_); trivial. % 19.02/19.13 apply (zenon_or_s _ _ zenon_He6); [ zenon_intro zenon_Hcd | zenon_intro zenon_He3 ]. % 19.02/19.13 exact (zenon_H12e zenon_Hcd). % 19.02/19.13 apply (zenon_L54_); trivial. % 19.02/19.13 (* end of lemma zenon_L1147_ *) % 19.02/19.13 assert (zenon_L1148_ : (((op (e2) (e3)) = (e0))\/(((op (e2) (e3)) = (e1))\/(((op (e2) (e3)) = (e2))\/((op (e2) (e3)) = (e3))))) -> (~((op (e1) (e3)) = (e2))) -> (~((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) (e3)) = (op (e3) (e3)))) -> ((op (e3) (e3)) = (e1)) -> (~((op (e2) (e3)) = (op (e3) (e3)))) -> (~((op (e2) (e3)) = (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) (e1)) = (op (e0) (e3)))) -> ((op (e0) (e1)) = (e1)) -> (~((op (e0) (e3)) = (e2))) -> (~((op (e0) (e3)) = (op (e2) (e3)))) -> False). % 19.02/19.13 do 0 intro. intros zenon_H11f zenon_H14c zenon_Hd5 zenon_Hdb zenon_Hdf zenon_Hc2 zenon_Hc4 zenon_Hf3 zenon_H274 zenon_He4 zenon_H1f zenon_H1d zenon_H54 zenon_Ha0 zenon_H12e zenon_He2. % 19.02/19.13 apply (zenon_or_s _ _ zenon_H11f); [ zenon_intro zenon_H37 | zenon_intro zenon_H120 ]. % 19.02/19.13 apply (zenon_L1089_); trivial. % 19.02/19.13 apply (zenon_or_s _ _ zenon_H120); [ zenon_intro zenon_Hf4 | zenon_intro zenon_H121 ]. % 19.02/19.13 apply (zenon_L60_); trivial. % 19.02/19.13 apply (zenon_or_s _ _ zenon_H121); [ zenon_intro zenon_H11d | zenon_intro zenon_Hdd ]. % 19.02/19.13 exact (zenon_H274 zenon_H11d). % 19.02/19.13 apply (zenon_L1147_); trivial. % 19.02/19.13 (* end of lemma zenon_L1148_ *) % 19.02/19.13 assert (zenon_L1149_ : (((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)) = (op (e3) (e1)))) -> ((op (e2) (e2)) = (e1)) -> (~((op (e2) (e2)) = (op (e3) (e2)))) -> (((op (e2) (e3)) = (e0))\/(((op (e2) (e3)) = (e1))\/(((op (e2) (e3)) = (e2))\/((op (e2) (e3)) = (e3))))) -> (~((op (e1) (e3)) = (e2))) -> (~((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) (e3)) = (op (e3) (e3)))) -> (~((op (e2) (e3)) = (op (e3) (e3)))) -> (~((op (e2) (e3)) = (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) (e1)) = (op (e0) (e3)))) -> ((op (e0) (e1)) = (e1)) -> (~((op (e0) (e3)) = (e2))) -> (~((op (e0) (e3)) = (op (e2) (e3)))) -> False). % 19.02/19.13 do 0 intro. intros zenon_He8 zenon_Ha1 zenon_H44 zenon_H210 zenon_Hf1 zenon_H18f zenon_H11f zenon_H14c zenon_Hd5 zenon_Hdb zenon_Hdf zenon_Hc2 zenon_Hf3 zenon_H274 zenon_He4 zenon_H1f zenon_H1d zenon_H54 zenon_Ha0 zenon_H12e zenon_He2. % 19.02/19.13 apply (zenon_or_s _ _ zenon_He8); [ zenon_intro zenon_Hac | zenon_intro zenon_Heb ]. % 19.02/19.13 apply (zenon_L41_); trivial. % 19.02/19.13 apply (zenon_or_s _ _ zenon_Heb); [ zenon_intro zenon_Hae | zenon_intro zenon_Hec ]. % 19.02/19.13 apply (zenon_L363_); trivial. % 19.02/19.13 apply (zenon_or_s _ _ zenon_Hec); [ zenon_intro zenon_Hba | zenon_intro zenon_Hc4 ]. % 19.02/19.13 apply (zenon_L185_); trivial. % 19.02/19.13 apply (zenon_L1148_); trivial. % 19.02/19.13 (* end of lemma zenon_L1149_ *) % 19.02/19.13 assert (zenon_L1150_ : (((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 (e2) (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 (e3) (e2)))) -> (~((op (e0) (e3)) = (op (e1) (e3)))) -> (~((op (e1) (e3)) = (e2))) -> (~((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) (e3)) = (e2))) -> (~((op (e0) (e3)) = (op (e3) (e3)))) -> (~((op (e0) (e3)) = (op (e2) (e3)))) -> (((op (e0) (e3)) = (e0))\/(((op (e0) (e3)) = (e1))\/(((op (e0) (e3)) = (e2))\/((op (e0) (e3)) = (e3))))) -> (((op (e0) (e0)) = (e1))\/(((op (e1) (e0)) = (e1))\/(((op (e2) (e0)) = (e1))\/((op (e3) (e0)) = (e1))))) -> (~((op (e0) (e2)) = (e2))) -> (~((op (e0) (e1)) = (e2))) -> (~((e1) = (e2))) -> (((op (e0) (e0)) = (e2))\/(((op (e0) (e1)) = (e2))\/(((op (e0) (e2)) = (e2))\/((op (e0) (e3)) = (e2))))) -> (~((op (e3) (e2)) = (op (e3) (e3)))) -> (~((op (e2) (e2)) = (op (e2) (e3)))) -> (~((op (e1) (e0)) = (op (e1) (e3)))) -> ((op (e0) (e1)) = (e1)) -> (~((op (e0) (e1)) = (op (e0) (e3)))) -> (((op (e0) (e3)) = (e1))\/(((op (e1) (e3)) = (e1))\/(((op (e2) (e3)) = (e1))\/((op (e3) (e3)) = (e1))))) -> ((op (e2) (e2)) = (e1)) -> (~((op (e2) (e0)) = (op (e2) (e2)))) -> (~((e0) = (e1))) -> (~((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)) = (e0)) -> (~((op (e3) (e0)) = (op (e3) (e3)))) -> False). % 19.02/19.13 do 0 intro. intros zenon_H67 zenon_H208 zenon_H48 zenon_H274 zenon_Hf3 zenon_H11f zenon_H18f zenon_H1d zenon_H14c zenon_Hd5 zenon_Hdb zenon_Hdf zenon_H12e zenon_Hc2 zenon_He2 zenon_He4 zenon_H235 zenon_H1fd zenon_H26d zenon_H7c zenon_H183 zenon_H62 zenon_H6d zenon_Hd8 zenon_Ha0 zenon_H54 zenon_H133 zenon_Hf1 zenon_H52 zenon_Ha1 zenon_H210 zenon_He8 zenon_H44 zenon_H71. % 19.02/19.13 apply (zenon_or_s _ _ zenon_H67); [ zenon_intro zenon_H1e | zenon_intro zenon_H68 ]. % 19.02/19.13 apply (zenon_L336_); trivial. % 19.02/19.13 apply (zenon_or_s _ _ zenon_H68); [ zenon_intro zenon_H1f | zenon_intro zenon_H69 ]. % 19.02/19.13 apply (zenon_L1149_); trivial. % 19.02/19.13 apply (zenon_or_s _ _ zenon_H69); [ zenon_intro zenon_H37 | zenon_intro zenon_H60 ]. % 19.02/19.13 apply (zenon_L1129_); trivial. % 19.02/19.13 apply (zenon_L21_); trivial. % 19.02/19.13 (* end of lemma zenon_L1150_ *) % 19.02/19.13 assert (zenon_L1151_ : (((op (e2) (e3)) = (e0))\/(((op (e2) (e3)) = (e1))\/(((op (e2) (e3)) = (e2))\/((op (e2) (e3)) = (e3))))) -> ((op (e0) (e3)) = (e1)) -> ((op (e3) (e3)) = (e2)) -> ((op (e1) (e3)) = (e0)) -> (~((op (e2) (e3)) = (e2))) -> (~((op (e1) (e3)) = (op (e2) (e3)))) -> ((op (e1) (e3)) = (e3)) -> False). % 19.02/19.13 do 0 intro. intros zenon_H11f zenon_Hc3 zenon_Hf6 zenon_H1f zenon_H274 zenon_Hdb zenon_Hdc. % 19.02/19.13 apply (zenon_or_s _ _ zenon_H11f); [ zenon_intro zenon_H37 | zenon_intro zenon_H120 ]. % 19.02/19.13 apply (zenon_L387_); trivial. % 19.02/19.13 apply (zenon_or_s _ _ zenon_H120); [ zenon_intro zenon_Hf4 | zenon_intro zenon_H121 ]. % 19.02/19.13 apply (zenon_L63_); trivial. % 19.02/19.13 apply (zenon_or_s _ _ zenon_H121); [ zenon_intro zenon_H11d | zenon_intro zenon_Hdd ]. % 19.02/19.13 exact (zenon_H274 zenon_H11d). % 19.02/19.13 apply (zenon_L52_); trivial. % 19.02/19.13 (* end of lemma zenon_L1151_ *) % 19.02/19.13 assert (zenon_L1152_ : (((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)) = (e0)) -> ((op (e2) (e3)) = (e3)) -> (~((op (e0) (e3)) = (op (e2) (e3)))) -> (~((op (e0) (e3)) = (e2))) -> (~((op (e0) (e1)) = (op (e0) (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) (e1)) = (e2))) -> (((op (e1) (e0)) = (e3))\/(((op (e1) (e1)) = (e3))\/(((op (e1) (e2)) = (e3))\/((op (e1) (e3)) = (e3))))) -> (~((e1) = (e3))) -> ((op (e1) (e0)) = (e1)) -> (~((op (e0) (e1)) = (op (e1) (e1)))) -> (~((e2) = (e3))) -> ((op (e1) (e2)) = (e2)) -> (((op (e3) (e0)) = (e2))\/(((op (e3) (e1)) = (e2))\/(((op (e3) (e2)) = (e2))\/((op (e3) (e3)) = (e2))))) -> (~((op (e3) (e0)) = (e2))) -> (~((op (e3) (e1)) = (e2))) -> (~((op (e3) (e2)) = (e2))) -> (((op (e2) (e3)) = (e0))\/(((op (e2) (e3)) = (e1))\/(((op (e2) (e3)) = (e2))\/((op (e2) (e3)) = (e3))))) -> ((op (e0) (e3)) = (e1)) -> (~((op (e2) (e1)) = (op (e2) (e3)))) -> ((op (e2) (e1)) = (e1)) -> (~((op (e2) (e3)) = (e2))) -> (~((op (e1) (e3)) = (op (e2) (e3)))) -> False). % 19.02/19.13 do 0 intro. intros zenon_H212 zenon_H4a zenon_H48 zenon_Hdd zenon_He2 zenon_H12e zenon_H54 zenon_H1d zenon_H1f zenon_He4 zenon_H26d zenon_H16f zenon_H95 zenon_H9d zenon_H10e zenon_H12b zenon_H113 zenon_H153 zenon_H14b zenon_H194 zenon_H272 zenon_H11f zenon_Hc3 zenon_H1c7 zenon_Ha5 zenon_H274 zenon_Hdb. % 19.02/19.13 apply (zenon_or_s _ _ zenon_H212); [ zenon_intro zenon_H49 | zenon_intro zenon_H213 ]. % 19.02/19.13 apply (zenon_L9_); trivial. % 19.02/19.13 apply (zenon_or_s _ _ zenon_H213); [ zenon_intro zenon_Ha0 | zenon_intro zenon_H214 ]. % 19.02/19.13 apply (zenon_L1147_); trivial. % 19.02/19.13 apply (zenon_or_s _ _ zenon_H214); [ zenon_intro zenon_H10f | zenon_intro zenon_H99 ]. % 19.02/19.13 exact (zenon_H26d zenon_H10f). % 19.02/19.13 apply (zenon_L1139_); trivial. % 19.02/19.13 (* end of lemma zenon_L1152_ *) % 19.02/19.13 assert (zenon_L1153_ : (((op (e0) (e3)) = (e3))\/(((op (e1) (e3)) = (e3))\/(((op (e2) (e3)) = (e3))\/((op (e3) (e3)) = (e3))))) -> (~((op (e1) (e3)) = (op (e2) (e3)))) -> (~((op (e2) (e3)) = (e2))) -> ((op (e2) (e1)) = (e1)) -> (~((op (e2) (e1)) = (op (e2) (e3)))) -> ((op (e0) (e3)) = (e1)) -> (((op (e2) (e3)) = (e0))\/(((op (e2) (e3)) = (e1))\/(((op (e2) (e3)) = (e2))\/((op (e2) (e3)) = (e3))))) -> (~((op (e3) (e2)) = (e2))) -> (~((op (e3) (e1)) = (e2))) -> (~((op (e3) (e0)) = (e2))) -> (((op (e3) (e0)) = (e2))\/(((op (e3) (e1)) = (e2))\/(((op (e3) (e2)) = (e2))\/((op (e3) (e3)) = (e2))))) -> ((op (e1) (e2)) = (e2)) -> (~((e2) = (e3))) -> (~((op (e0) (e1)) = (op (e1) (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) (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) (e1)) = (op (e0) (e3)))) -> (~((op (e0) (e3)) = (e2))) -> (~((op (e0) (e3)) = (op (e2) (e3)))) -> ((op (e0) (e2)) = (e0)) -> (~((op (e0) (e1)) = (op (e0) (e2)))) -> (((op (e0) (e1)) = (e0))\/(((op (e0) (e1)) = (e1))\/(((op (e0) (e1)) = (e2))\/((op (e0) (e1)) = (e3))))) -> (~((op (e3) (e3)) = (e3))) -> False). % 19.02/19.13 do 0 intro. intros zenon_H136 zenon_Hdb zenon_H274 zenon_Ha5 zenon_H1c7 zenon_Hc3 zenon_H11f zenon_H272 zenon_H194 zenon_H14b zenon_H153 zenon_H113 zenon_H12b zenon_H10e zenon_H9d zenon_H95 zenon_H16f zenon_H26d zenon_He4 zenon_H1f zenon_H1d zenon_H54 zenon_H12e zenon_He2 zenon_H48 zenon_H4a zenon_H212 zenon_H102. % 19.02/19.13 apply (zenon_or_s _ _ zenon_H153); [ zenon_intro zenon_H148 | zenon_intro zenon_H154 ]. % 19.02/19.13 exact (zenon_H14b zenon_H148). % 19.02/19.13 apply (zenon_or_s _ _ zenon_H154); [ zenon_intro zenon_H14d | zenon_intro zenon_H155 ]. % 19.02/19.13 exact (zenon_H194 zenon_H14d). % 19.02/19.13 apply (zenon_or_s _ _ zenon_H155); [ zenon_intro zenon_H151 | zenon_intro zenon_Hf6 ]. % 19.02/19.13 exact (zenon_H272 zenon_H151). % 19.02/19.13 apply (zenon_or_s _ _ zenon_H136); [ zenon_intro zenon_He3 | zenon_intro zenon_H137 ]. % 19.02/19.13 apply (zenon_L633_); trivial. % 19.02/19.13 apply (zenon_or_s _ _ zenon_H137); [ zenon_intro zenon_Hdc | zenon_intro zenon_H138 ]. % 19.02/19.13 apply (zenon_L1151_); trivial. % 19.02/19.13 apply (zenon_or_s _ _ zenon_H138); [ zenon_intro zenon_Hdd | zenon_intro zenon_H105 ]. % 19.02/19.13 apply (zenon_L1152_); trivial. % 19.02/19.13 exact (zenon_H102 zenon_H105). % 19.02/19.13 (* end of lemma zenon_L1153_ *) % 19.02/19.13 assert (zenon_L1154_ : (((op (e0) (e1)) = (e1))\/(((op (e1) (e1)) = (e1))\/(((op (e2) (e1)) = (e1))\/((op (e3) (e1)) = (e1))))) -> (~((op (e1) (e1)) = (e1))) -> (~((op (e3) (e3)) = (e3))) -> (((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)) = (e0)) -> (~((op (e0) (e3)) = (op (e2) (e3)))) -> (~((op (e0) (e3)) = (e2))) -> (~((op (e0) (e1)) = (op (e0) (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) (e1)) = (e2))) -> (((op (e1) (e0)) = (e3))\/(((op (e1) (e1)) = (e3))\/(((op (e1) (e2)) = (e3))\/((op (e1) (e3)) = (e3))))) -> (~((e1) = (e3))) -> ((op (e1) (e0)) = (e1)) -> (~((op (e0) (e1)) = (op (e1) (e1)))) -> (~((e2) = (e3))) -> ((op (e1) (e2)) = (e2)) -> (((op (e3) (e0)) = (e2))\/(((op (e3) (e1)) = (e2))\/(((op (e3) (e2)) = (e2))\/((op (e3) (e3)) = (e2))))) -> (~((op (e3) (e0)) = (e2))) -> (~((op (e3) (e1)) = (e2))) -> (~((op (e3) (e2)) = (e2))) -> (((op (e2) (e3)) = (e0))\/(((op (e2) (e3)) = (e1))\/(((op (e2) (e3)) = (e2))\/((op (e2) (e3)) = (e3))))) -> ((op (e0) (e3)) = (e1)) -> (~((op (e2) (e1)) = (op (e2) (e3)))) -> (~((op (e2) (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) (e0)) = (op (e3) (e1)))) -> ((op (e3) (e0)) = (e1)) -> False). % 19.02/19.13 do 0 intro. intros zenon_H109 zenon_H10a zenon_H102 zenon_H212 zenon_H4a zenon_H48 zenon_He2 zenon_H12e zenon_H54 zenon_H1d zenon_H1f zenon_He4 zenon_H26d zenon_H16f zenon_H95 zenon_H9d zenon_H10e zenon_H12b zenon_H113 zenon_H153 zenon_H14b zenon_H194 zenon_H272 zenon_H11f zenon_Hc3 zenon_H1c7 zenon_H274 zenon_Hdb zenon_H136 zenon_H1cf zenon_Hac. % 19.02/19.13 apply (zenon_or_s _ _ zenon_H109); [ zenon_intro zenon_Ha0 | zenon_intro zenon_H10b ]. % 19.02/19.13 apply (zenon_L359_); trivial. % 19.02/19.13 apply (zenon_or_s _ _ zenon_H10b); [ zenon_intro zenon_H10d | zenon_intro zenon_H10c ]. % 19.02/19.13 exact (zenon_H10a zenon_H10d). % 19.02/19.13 apply (zenon_or_s _ _ zenon_H10c); [ zenon_intro zenon_Ha5 | zenon_intro zenon_Hae ]. % 19.02/19.13 apply (zenon_L1153_); trivial. % 19.02/19.13 apply (zenon_L242_); trivial. % 19.02/19.13 (* end of lemma zenon_L1154_ *) % 19.02/19.13 assert (zenon_L1155_ : (((op (e0) (e3)) = (e1))\/(((op (e1) (e3)) = (e1))\/(((op (e2) (e3)) = (e1))\/((op (e3) (e3)) = (e1))))) -> ((op (e3) (e0)) = (e1)) -> (~((op (e3) (e0)) = (op (e3) (e1)))) -> (((op (e0) (e3)) = (e3))\/(((op (e1) (e3)) = (e3))\/(((op (e2) (e3)) = (e3))\/((op (e3) (e3)) = (e3))))) -> (~((op (e2) (e1)) = (op (e2) (e3)))) -> (~((op (e3) (e2)) = (e2))) -> (~((op (e3) (e1)) = (e2))) -> (~((op (e3) (e0)) = (e2))) -> (((op (e3) (e0)) = (e2))\/(((op (e3) (e1)) = (e2))\/(((op (e3) (e2)) = (e2))\/((op (e3) (e3)) = (e2))))) -> ((op (e1) (e2)) = (e2)) -> (~((e2) = (e3))) -> (~((op (e0) (e1)) = (op (e1) (e1)))) -> (~((e1) = (e3))) -> (((op (e1) (e0)) = (e3))\/(((op (e1) (e1)) = (e3))\/(((op (e1) (e2)) = (e3))\/((op (e1) (e3)) = (e3))))) -> (~((op (e0) (e1)) = (e2))) -> ((op (e0) (e2)) = (e0)) -> (~((op (e0) (e1)) = (op (e0) (e2)))) -> (((op (e0) (e1)) = (e0))\/(((op (e0) (e1)) = (e1))\/(((op (e0) (e1)) = (e2))\/((op (e0) (e1)) = (e3))))) -> (~((op (e3) (e3)) = (e3))) -> (~((op (e1) (e1)) = (e1))) -> (((op (e0) (e1)) = (e1))\/(((op (e1) (e1)) = (e1))\/(((op (e2) (e1)) = (e1))\/((op (e3) (e1)) = (e1))))) -> (~((op (e1) (e0)) = (op (e1) (e3)))) -> ((op (e1) (e0)) = (e1)) -> (~((op (e2) (e2)) = (op (e2) (e3)))) -> ((op (e2) (e2)) = (e1)) -> (((op (e2) (e3)) = (e0))\/(((op (e2) (e3)) = (e1))\/(((op (e2) (e3)) = (e2))\/((op (e2) (e3)) = (e3))))) -> (~((op (e1) (e3)) = (e2))) -> (~((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) (e3)) = (op (e3) (e3)))) -> (~((op (e2) (e3)) = (op (e3) (e3)))) -> (~((op (e2) (e3)) = (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) (e1)) = (op (e0) (e3)))) -> ((op (e0) (e1)) = (e1)) -> (~((op (e0) (e3)) = (e2))) -> (~((op (e0) (e3)) = (op (e2) (e3)))) -> False). % 19.02/19.13 do 0 intro. intros zenon_H133 zenon_Hac zenon_H1cf zenon_H136 zenon_H1c7 zenon_H272 zenon_H194 zenon_H14b zenon_H153 zenon_H113 zenon_H12b zenon_H10e zenon_H95 zenon_H16f zenon_H26d zenon_H48 zenon_H4a zenon_H212 zenon_H102 zenon_H10a zenon_H109 zenon_Hd8 zenon_H9d zenon_H6d zenon_Hf1 zenon_H11f zenon_H14c zenon_Hd5 zenon_Hdb zenon_Hdf zenon_Hc2 zenon_Hf3 zenon_H274 zenon_He4 zenon_H1f zenon_H1d zenon_H54 zenon_Ha0 zenon_H12e zenon_He2. % 19.02/19.13 apply (zenon_or_s _ _ zenon_H133); [ zenon_intro zenon_Hc3 | zenon_intro zenon_H134 ]. % 19.02/19.13 apply (zenon_L1154_); trivial. % 19.02/19.13 apply (zenon_or_s _ _ zenon_H134); [ zenon_intro zenon_Hd6 | zenon_intro zenon_H135 ]. % 19.02/19.13 apply (zenon_L360_); trivial. % 19.02/19.13 apply (zenon_or_s _ _ zenon_H135); [ zenon_intro zenon_Hf4 | zenon_intro zenon_Hc4 ]. % 19.02/19.13 apply (zenon_L84_); trivial. % 19.02/19.13 apply (zenon_L1148_); trivial. % 19.02/19.13 (* end of lemma zenon_L1155_ *) % 19.02/19.13 assert (zenon_L1156_ : (((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 (e0) (e3)) = (e2))) -> ((op (e0) (e1)) = (e1)) -> (~((op (e0) (e1)) = (op (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)) = (e2))) -> (~((op (e2) (e3)) = (op (e3) (e3)))) -> (~((op (e0) (e3)) = (op (e3) (e3)))) -> (((op (e1) (e3)) = (e0))\/(((op (e1) (e3)) = (e1))\/(((op (e1) (e3)) = (e2))\/((op (e1) (e3)) = (e3))))) -> (~((op (e1) (e3)) = (op (e2) (e3)))) -> (~((op (e1) (e3)) = (op (e3) (e3)))) -> (~((op (e1) (e3)) = (e2))) -> (((op (e2) (e3)) = (e0))\/(((op (e2) (e3)) = (e1))\/(((op (e2) (e3)) = (e2))\/((op (e2) (e3)) = (e3))))) -> ((op (e2) (e2)) = (e1)) -> (~((op (e2) (e2)) = (op (e2) (e3)))) -> ((op (e1) (e0)) = (e1)) -> (~((op (e1) (e0)) = (op (e1) (e3)))) -> (((op (e0) (e1)) = (e1))\/(((op (e1) (e1)) = (e1))\/(((op (e2) (e1)) = (e1))\/((op (e3) (e1)) = (e1))))) -> (~((op (e1) (e1)) = (e1))) -> (~((op (e3) (e3)) = (e3))) -> (((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)) = (e0)) -> (~((op (e0) (e1)) = (e2))) -> (((op (e1) (e0)) = (e3))\/(((op (e1) (e1)) = (e3))\/(((op (e1) (e2)) = (e3))\/((op (e1) (e3)) = (e3))))) -> (~((e1) = (e3))) -> (~((op (e0) (e1)) = (op (e1) (e1)))) -> (~((e2) = (e3))) -> ((op (e1) (e2)) = (e2)) -> (((op (e3) (e0)) = (e2))\/(((op (e3) (e1)) = (e2))\/(((op (e3) (e2)) = (e2))\/((op (e3) (e3)) = (e2))))) -> (~((op (e3) (e0)) = (e2))) -> (~((op (e3) (e1)) = (e2))) -> (~((op (e3) (e2)) = (e2))) -> (~((op (e2) (e1)) = (op (e2) (e3)))) -> (((op (e0) (e3)) = (e3))\/(((op (e1) (e3)) = (e3))\/(((op (e2) (e3)) = (e3))\/((op (e3) (e3)) = (e3))))) -> (~((op (e3) (e0)) = (op (e3) (e1)))) -> ((op (e3) (e0)) = (e1)) -> (((op (e0) (e3)) = (e1))\/(((op (e1) (e3)) = (e1))\/(((op (e2) (e3)) = (e1))\/((op (e3) (e3)) = (e1))))) -> (~((op (e2) (e0)) = (op (e2) (e3)))) -> ((op (e2) (e0)) = (e0)) -> ((op (e3) (e1)) = (e0)) -> (~((op (e3) (e1)) = (op (e3) (e3)))) -> False). % 19.02/19.13 do 0 intro. intros zenon_H67 zenon_H208 zenon_He2 zenon_H12e zenon_Ha0 zenon_H54 zenon_H1d zenon_He4 zenon_H274 zenon_Hf3 zenon_Hc2 zenon_Hdf zenon_Hdb zenon_Hd5 zenon_H14c zenon_H11f zenon_Hf1 zenon_H6d zenon_H9d zenon_Hd8 zenon_H109 zenon_H10a zenon_H102 zenon_H212 zenon_H4a zenon_H48 zenon_H26d zenon_H16f zenon_H95 zenon_H10e zenon_H12b zenon_H113 zenon_H153 zenon_H14b zenon_H194 zenon_H272 zenon_H1c7 zenon_H136 zenon_H1cf zenon_Hac zenon_H133 zenon_H5b zenon_H34 zenon_H1b1 zenon_H130. % 19.02/19.13 apply (zenon_or_s _ _ zenon_H67); [ zenon_intro zenon_H1e | zenon_intro zenon_H68 ]. % 19.02/19.13 apply (zenon_L336_); trivial. % 19.02/19.13 apply (zenon_or_s _ _ zenon_H68); [ zenon_intro zenon_H1f | zenon_intro zenon_H69 ]. % 19.02/19.13 apply (zenon_L1155_); trivial. % 19.02/19.13 apply (zenon_or_s _ _ zenon_H69); [ zenon_intro zenon_H37 | zenon_intro zenon_H60 ]. % 19.02/19.13 apply (zenon_L14_); trivial. % 19.02/19.13 apply (zenon_L244_); trivial. % 19.02/19.13 (* end of lemma zenon_L1156_ *) % 19.02/19.13 assert (zenon_L1157_ : (((op (e3) (e0)) = (e1))\/(((op (e3) (e1)) = (e1))\/(((op (e3) (e2)) = (e1))\/((op (e3) (e3)) = (e1))))) -> (~((op (e3) (e1)) = (op (e3) (e3)))) -> ((op (e3) (e1)) = (e0)) -> ((op (e2) (e0)) = (e0)) -> (~((op (e2) (e0)) = (op (e2) (e3)))) -> (((op (e0) (e3)) = (e1))\/(((op (e1) (e3)) = (e1))\/(((op (e2) (e3)) = (e1))\/((op (e3) (e3)) = (e1))))) -> (~((op (e3) (e0)) = (op (e3) (e1)))) -> (((op (e0) (e3)) = (e3))\/(((op (e1) (e3)) = (e3))\/(((op (e2) (e3)) = (e3))\/((op (e3) (e3)) = (e3))))) -> (~((op (e2) (e1)) = (op (e2) (e3)))) -> (~((op (e3) (e2)) = (e2))) -> (~((op (e3) (e1)) = (e2))) -> (~((op (e3) (e0)) = (e2))) -> (((op (e3) (e0)) = (e2))\/(((op (e3) (e1)) = (e2))\/(((op (e3) (e2)) = (e2))\/((op (e3) (e3)) = (e2))))) -> ((op (e1) (e2)) = (e2)) -> (~((e2) = (e3))) -> (~((op (e0) (e1)) = (op (e1) (e1)))) -> (~((e1) = (e3))) -> (((op (e1) (e0)) = (e3))\/(((op (e1) (e1)) = (e3))\/(((op (e1) (e2)) = (e3))\/((op (e1) (e3)) = (e3))))) -> (~((op (e0) (e1)) = (e2))) -> ((op (e0) (e2)) = (e0)) -> (~((op (e0) (e1)) = (op (e0) (e2)))) -> (((op (e0) (e1)) = (e0))\/(((op (e0) (e1)) = (e1))\/(((op (e0) (e1)) = (e2))\/((op (e0) (e1)) = (e3))))) -> (~((op (e3) (e3)) = (e3))) -> (~((op (e1) (e1)) = (e1))) -> (((op (e0) (e1)) = (e1))\/(((op (e1) (e1)) = (e1))\/(((op (e2) (e1)) = (e1))\/((op (e3) (e1)) = (e1))))) -> (~((op (e1) (e0)) = (op (e1) (e3)))) -> ((op (e1) (e0)) = (e1)) -> (~((op (e2) (e2)) = (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) (e1)) = (op (e3) (e1)))) -> ((op (e2) (e2)) = (e1)) -> (~((op (e2) (e2)) = (op (e3) (e2)))) -> (((op (e2) (e3)) = (e0))\/(((op (e2) (e3)) = (e1))\/(((op (e2) (e3)) = (e2))\/((op (e2) (e3)) = (e3))))) -> (~((op (e1) (e3)) = (e2))) -> (~((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) (e3)) = (op (e3) (e3)))) -> (~((op (e2) (e3)) = (op (e3) (e3)))) -> (~((op (e2) (e3)) = (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) (e1)) = (op (e0) (e3)))) -> ((op (e0) (e1)) = (e1)) -> (~((op (e0) (e3)) = (e2))) -> (~((op (e0) (e3)) = (op (e2) (e3)))) -> False). % 19.02/19.14 do 0 intro. intros zenon_He8 zenon_H130 zenon_H1b1 zenon_H34 zenon_H5b zenon_H133 zenon_H1cf zenon_H136 zenon_H1c7 zenon_H272 zenon_H194 zenon_H14b zenon_H153 zenon_H113 zenon_H12b zenon_H10e zenon_H95 zenon_H16f zenon_H26d zenon_H48 zenon_H4a zenon_H212 zenon_H102 zenon_H10a zenon_H109 zenon_Hd8 zenon_H9d zenon_H6d zenon_H208 zenon_H67 zenon_H210 zenon_Hf1 zenon_H18f zenon_H11f zenon_H14c zenon_Hd5 zenon_Hdb zenon_Hdf zenon_Hc2 zenon_Hf3 zenon_H274 zenon_He4 zenon_H1f zenon_H1d zenon_H54 zenon_Ha0 zenon_H12e zenon_He2. % 19.02/19.14 apply (zenon_or_s _ _ zenon_He8); [ zenon_intro zenon_Hac | zenon_intro zenon_Heb ]. % 19.02/19.14 apply (zenon_L1156_); trivial. % 19.02/19.14 apply (zenon_or_s _ _ zenon_Heb); [ zenon_intro zenon_Hae | zenon_intro zenon_Hec ]. % 19.02/19.14 apply (zenon_L363_); trivial. % 19.02/19.14 apply (zenon_or_s _ _ zenon_Hec); [ zenon_intro zenon_Hba | zenon_intro zenon_Hc4 ]. % 19.02/19.14 apply (zenon_L185_); trivial. % 19.02/19.14 apply (zenon_L1148_); trivial. % 19.02/19.14 (* end of lemma zenon_L1157_ *) % 19.02/19.14 assert (zenon_L1158_ : (~((op (e0) (e3)) = (op (e2) (e3)))) -> (~((op (e2) (e3)) = (e2))) -> (~((op (e1) (e3)) = (op (e2) (e3)))) -> (~((op (e2) (e3)) = (op (e3) (e3)))) -> (((op (e2) (e3)) = (e0))\/(((op (e2) (e3)) = (e1))\/(((op (e2) (e3)) = (e2))\/((op (e2) (e3)) = (e3))))) -> ((~((op (e1) (e2)) = (e2)))\/((op (e1) (e2)) = (e2))) -> ((~((op (e2) (e0)) = (e2)))\/((op (e2) (e2)) = (e0))) -> (~((op (e0) (e2)) = (op (e2) (e2)))) -> ((~((op (e2) (e3)) = (e2)))\/((op (e2) (e2)) = (e3))) -> (((op (e0) (e2)) = (e2))\/(((op (e1) (e2)) = (e2))\/(((op (e2) (e2)) = (e2))\/((op (e3) (e2)) = (e2))))) -> (~((op (e0) (e2)) = (e2))) -> ((~((op (e3) (e3)) = (e2)))\/((op (e3) (e2)) = (e3))) -> (~((op (e2) (e2)) = (op (e3) (e2)))) -> (~((op (e0) (e0)) = (e0))) -> (((op (e0) (e0)) = (e1))\/(((op (e0) (e1)) = (e1))\/(((op (e0) (e2)) = (e1))\/((op (e0) (e3)) = (e1))))) -> (~((e0) = (e1))) -> (~((op (e1) (e0)) = (op (e1) (e1)))) -> (((op (e1) (e0)) = (e0))\/(((op (e1) (e0)) = (e1))\/(((op (e1) (e0)) = (e2))\/((op (e1) (e0)) = (e3))))) -> (~((op (e1) (e0)) = (e2))) -> (~((op (e1) (e0)) = (op (e2) (e0)))) -> (~((op (e1) (e0)) = (op (e3) (e0)))) -> (~((op (e0) (e1)) = (op (e0) (e2)))) -> (((op (e1) (e0)) = (e2))\/(((op (e1) (e1)) = (e2))\/(((op (e1) (e2)) = (e2))\/((op (e1) (e3)) = (e2))))) -> (~((e0) = (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))))) -> (~((e2) = (e3))) -> (((op (e0) (e1)) = (e2))\/(((op (e1) (e1)) = (e2))\/(((op (e2) (e1)) = (e2))\/((op (e3) (e1)) = (e2))))) -> (((op (e0) (e1)) = (e0))\/(((op (e0) (e1)) = (e1))\/(((op (e0) (e1)) = (e2))\/((op (e0) (e1)) = (e3))))) -> (~((op (e0) (e1)) = (op (e2) (e1)))) -> (~((op (e1) (e1)) = (e1))) -> (((op (e0) (e1)) = (e0))\/(((op (e1) (e1)) = (e0))\/(((op (e2) (e1)) = (e0))\/((op (e3) (e1)) = (e0))))) -> (~((op (e1) (e2)) = (op (e1) (e3)))) -> (~((op (e2) (e1)) = (op (e2) (e3)))) -> (((op (e0) (e3)) = (e0))\/(((op (e1) (e3)) = (e0))\/(((op (e2) (e3)) = (e0))\/((op (e3) (e3)) = (e0))))) -> (~((op (e3) (e1)) = (op (e3) (e3)))) -> (~((op (e3) (e0)) = (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) (e2)) = (op (e2) (e2)))) -> (((op (e1) (e0)) = (e0))\/(((op (e1) (e1)) = (e0))\/(((op (e1) (e2)) = (e0))\/((op (e1) (e3)) = (e0))))) -> (~((op (e1) (e1)) = (op (e1) (e3)))) -> (~((op (e3) (e1)) = (op (e3) (e2)))) -> (((op (e2) (e0)) = (e1))\/(((op (e2) (e1)) = (e1))\/(((op (e2) (e2)) = (e1))\/((op (e2) (e3)) = (e1))))) -> (~((op (e0) (e2)) = (op (e1) (e2)))) -> (~((op (e1) (e2)) = (op (e3) (e2)))) -> (((op (e3) (e0)) = (e1))\/(((op (e3) (e1)) = (e1))\/(((op (e3) (e2)) = (e1))\/((op (e3) (e3)) = (e1))))) -> ((op (e0) (e2)) = (e0)) -> (~((op (e0) (e2)) = (op (e0) (e3)))) -> (~((op (e0) (e2)) = (op (e3) (e2)))) -> (((op (e0) (e0)) = (e1))\/(((op (e1) (e0)) = (e1))\/(((op (e2) (e0)) = (e1))\/((op (e3) (e0)) = (e1))))) -> (~((e1) = (e2))) -> (~((op (e0) (e1)) = (e2))) -> (((op (e0) (e0)) = (e2))\/(((op (e0) (e1)) = (e2))\/(((op (e0) (e2)) = (e2))\/((op (e0) (e3)) = (e2))))) -> (((op (e2) (e1)) = (e0))\/(((op (e2) (e1)) = (e1))\/(((op (e2) (e1)) = (e2))\/((op (e2) (e1)) = (e3))))) -> (~((op (e2) (e0)) = (op (e2) (e1)))) -> (((op (e0) (e0)) = (e0))\/(((op (e1) (e0)) = (e0))\/(((op (e2) (e0)) = (e0))\/((op (e3) (e0)) = (e0))))) -> ((~((op (e3) (e2)) = (e2)))\/((op (e3) (e2)) = (e2))) -> (~((op (e2) (e2)) = (e2))) -> (((op (e2) (e0)) = (e2))\/(((op (e2) (e1)) = (e2))\/(((op (e2) (e2)) = (e2))\/((op (e2) (e3)) = (e2))))) -> ((~((op (e2) (e1)) = (e2)))\/((op (e2) (e2)) = (e1))) -> (~((e1) = (e3))) -> ((~((op (e1) (e3)) = (e2)))\/((op (e1) (e2)) = (e3))) -> (~((op (e3) (e2)) = (e2))) -> (~((op (e3) (e1)) = (e2))) -> (~((op (e3) (e0)) = (e2))) -> (((op (e3) (e0)) = (e2))\/(((op (e3) (e1)) = (e2))\/(((op (e3) (e2)) = (e2))\/((op (e3) (e3)) = (e2))))) -> ((op (e1) (e2)) = (e2)) -> (~((op (e0) (e1)) = (op (e1) (e1)))) -> (((op (e1) (e0)) = (e3))\/(((op (e1) (e1)) = (e3))\/(((op (e1) (e2)) = (e3))\/((op (e1) (e3)) = (e3))))) -> (((op (e1) (e0)) = (e1))\/(((op (e1) (e1)) = (e1))\/(((op (e1) (e2)) = (e1))\/((op (e1) (e3)) = (e1))))) -> (~((op (e3) (e0)) = (op (e3) (e1)))) -> (~((op (e0) (e1)) = (op (e3) (e1)))) -> (~((op (e3) (e2)) = (op (e3) (e3)))) -> ((op (e2) (e2)) = (e1)) -> (~((op (e2) (e2)) = (op (e2) (e3)))) -> ((op (e1) (e0)) = (e1)) -> (~((op (e1) (e0)) = (op (e1) (e3)))) -> ((op (e0) (e1)) = (e1)) -> (~((op (e0) (e1)) = (op (e0) (e3)))) -> (((op (e0) (e3)) = (e1))\/(((op (e1) (e3)) = (e1))\/(((op (e2) (e3)) = (e1))\/((op (e3) (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)) = (e2))) -> (((op (e1) (e3)) = (e0))\/(((op (e1) (e3)) = (e1))\/(((op (e1) (e3)) = (e2))\/((op (e1) (e3)) = (e3))))) -> ((op (e3) (e3)) = (e0)) -> (~((op (e1) (e3)) = (op (e3) (e3)))) -> (~((op (e1) (e3)) = (e2))) -> (~((op (e0) (e3)) = (op (e1) (e3)))) -> False). % 19.02/19.14 do 0 intro. intros zenon_He2 zenon_H274 zenon_Hdb zenon_Hf3 zenon_H11f zenon_H275 zenon_H276 zenon_Ha8 zenon_H277 zenon_H172 zenon_H1fd zenon_H278 zenon_H18f zenon_H3f zenon_H22d zenon_Ha1 zenon_H45 zenon_H25e zenon_H177 zenon_H201 zenon_H1fa zenon_H4a zenon_H18c zenon_H149 zenon_H1ac zenon_H109 zenon_H12b zenon_H1d8 zenon_H212 zenon_H17e zenon_H10a zenon_H245 zenon_H124 zenon_H1c7 zenon_H67 zenon_H130 zenon_H71 zenon_H102 zenon_H101 zenon_H2b zenon_H22 zenon_H57 zenon_H1a4 zenon_H106 zenon_H195 zenon_H115 zenon_He8 zenon_H48 zenon_H208 zenon_H14f zenon_H235 zenon_H7c zenon_H26d zenon_H183 zenon_H1cc zenon_H1f0 zenon_H3e zenon_H273 zenon_H173 zenon_H1d5 zenon_H271 zenon_H95 zenon_H279 zenon_H272 zenon_H194 zenon_H14b zenon_H153 zenon_H113 zenon_H10e zenon_H16f zenon_H128 zenon_H1cf zenon_H210 zenon_H62 zenon_Hf1 zenon_H6d zenon_H9d zenon_Hd8 zenon_Ha0 zenon_H54 zenon_H133 zenon_He4 zenon_Hc2 zenon_H12e zenon_Hdf zenon_H60 zenon_Hd5 zenon_H14c zenon_H1d. % 19.02/19.14 apply (zenon_or_s _ _ zenon_He8); [ zenon_intro zenon_Hac | zenon_intro zenon_Heb ]. % 19.02/19.14 apply (zenon_L1144_); trivial. % 19.02/19.14 apply (zenon_or_s _ _ zenon_Heb); [ zenon_intro zenon_Hae | zenon_intro zenon_Hec ]. % 19.02/19.14 apply (zenon_L363_); trivial. % 19.02/19.14 apply (zenon_or_s _ _ zenon_Hec); [ zenon_intro zenon_Hba | zenon_intro zenon_Hc4 ]. % 19.02/19.14 apply (zenon_L419_); trivial. % 19.02/19.14 apply (zenon_L1093_); trivial. % 19.02/19.14 (* end of lemma zenon_L1158_ *) % 19.02/19.14 assert (zenon_L1159_ : (((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)) = (op (e2) (e3)))) -> (~((op (e2) (e3)) = (e2))) -> (~((op (e0) (e3)) = (op (e2) (e3)))) -> ((op (e0) (e3)) = (e3)) -> False). % 19.02/19.14 do 0 intro. intros zenon_H11f zenon_H1f zenon_Hd6 zenon_Hdb zenon_H274 zenon_He2 zenon_He3. % 19.02/19.14 apply (zenon_or_s _ _ zenon_H11f); [ zenon_intro zenon_H37 | zenon_intro zenon_H120 ]. % 19.02/19.14 apply (zenon_L130_); trivial. % 19.02/19.14 apply (zenon_or_s _ _ zenon_H120); [ zenon_intro zenon_Hf4 | zenon_intro zenon_H121 ]. % 19.02/19.14 apply (zenon_L126_); trivial. % 19.02/19.14 apply (zenon_or_s _ _ zenon_H121); [ zenon_intro zenon_H11d | zenon_intro zenon_Hdd ]. % 19.02/19.14 exact (zenon_H274 zenon_H11d). % 19.02/19.14 apply (zenon_L54_); trivial. % 19.02/19.14 (* end of lemma zenon_L1159_ *) % 19.02/19.14 assert (zenon_L1160_ : (((op (e0) (e3)) = (e0))\/(((op (e1) (e3)) = (e0))\/(((op (e2) (e3)) = (e0))\/((op (e3) (e3)) = (e0))))) -> (~((e0) = (e3))) -> ((op (e1) (e3)) = (e1)) -> (~((op (e2) (e0)) = (op (e2) (e3)))) -> ((op (e2) (e0)) = (e0)) -> (((op (e2) (e3)) = (e0))\/(((op (e2) (e3)) = (e1))\/(((op (e2) (e3)) = (e2))\/((op (e2) (e3)) = (e3))))) -> (~((op (e2) (e3)) = (op (e3) (e3)))) -> (~((op (e0) (e3)) = (op (e1) (e3)))) -> (~((op (e1) (e3)) = (e2))) -> (~((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 (e2) (e3)) = (e2))) -> (~((op (e0) (e3)) = (op (e2) (e3)))) -> ((op (e0) (e3)) = (e3)) -> False). % 19.02/19.14 do 0 intro. intros zenon_H67 zenon_H9a zenon_Hd6 zenon_H5b zenon_H34 zenon_H11f zenon_Hf3 zenon_H1d zenon_H14c zenon_Hdb zenon_Hd5 zenon_Hdf zenon_H274 zenon_He2 zenon_He3. % 19.02/19.14 apply (zenon_or_s _ _ zenon_H67); [ zenon_intro zenon_H1e | zenon_intro zenon_H68 ]. % 19.02/19.14 apply (zenon_L515_); trivial. % 19.02/19.14 apply (zenon_or_s _ _ zenon_H68); [ zenon_intro zenon_H1f | zenon_intro zenon_H69 ]. % 19.02/19.14 apply (zenon_L1159_); trivial. % 19.02/19.14 apply (zenon_or_s _ _ zenon_H69); [ zenon_intro zenon_H37 | zenon_intro zenon_H60 ]. % 19.02/19.14 apply (zenon_L14_); trivial. % 19.02/19.14 apply (zenon_L1143_); trivial. % 19.02/19.14 (* end of lemma zenon_L1160_ *) % 19.02/19.14 assert (zenon_L1161_ : (((op (e0) (e3)) = (e3))\/(((op (e1) (e3)) = (e3))\/(((op (e2) (e3)) = (e3))\/((op (e3) (e3)) = (e3))))) -> (~((op (e2) (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 (e1) (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) (e0)) = (e0)) -> (~((op (e2) (e0)) = (op (e2) (e3)))) -> (~((e0) = (e3))) -> (((op (e0) (e3)) = (e0))\/(((op (e1) (e3)) = (e0))\/(((op (e2) (e3)) = (e0))\/((op (e3) (e3)) = (e0))))) -> (~((e1) = (e3))) -> ((op (e1) (e3)) = (e1)) -> (~((op (e0) (e3)) = (op (e2) (e3)))) -> (~((op (e0) (e3)) = (e2))) -> ((op (e0) (e1)) = (e1)) -> (~((op (e0) (e1)) = (op (e0) (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 (e3) (e3)) = (e3))) -> False). % 19.02/19.14 do 0 intro. intros zenon_H136 zenon_H274 zenon_Hdf zenon_Hd5 zenon_Hdb zenon_H14c zenon_Hf3 zenon_H11f zenon_H34 zenon_H5b zenon_H9a zenon_H67 zenon_H95 zenon_Hd6 zenon_He2 zenon_H12e zenon_Ha0 zenon_H54 zenon_H1d zenon_H1f zenon_He4 zenon_H102. % 19.02/19.14 apply (zenon_or_s _ _ zenon_H136); [ zenon_intro zenon_He3 | zenon_intro zenon_H137 ]. % 19.02/19.14 apply (zenon_L1160_); trivial. % 19.02/19.14 apply (zenon_or_s _ _ zenon_H137); [ zenon_intro zenon_Hdc | zenon_intro zenon_H138 ]. % 19.02/19.14 apply (zenon_L83_); trivial. % 19.02/19.14 apply (zenon_or_s _ _ zenon_H138); [ zenon_intro zenon_Hdd | zenon_intro zenon_H105 ]. % 19.02/19.14 apply (zenon_L1147_); trivial. % 19.02/19.14 exact (zenon_H102 zenon_H105). % 19.02/19.14 (* end of lemma zenon_L1161_ *) % 19.02/19.14 assert (zenon_L1162_ : (((op (e1) (e0)) = (e1))\/(((op (e1) (e1)) = (e1))\/(((op (e1) (e2)) = (e1))\/((op (e1) (e3)) = (e1))))) -> ((op (e2) (e2)) = (e1)) -> (~((op (e2) (e2)) = (op (e2) (e3)))) -> (((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)) = (e2)) -> (((op (e3) (e0)) = (e2))\/(((op (e3) (e1)) = (e2))\/(((op (e3) (e2)) = (e2))\/((op (e3) (e3)) = (e2))))) -> (~((op (e3) (e0)) = (e2))) -> (~((op (e3) (e1)) = (e2))) -> (~((op (e3) (e2)) = (e2))) -> ((op (e3) (e0)) = (e1)) -> ((~((op (e1) (e3)) = (e2)))\/((op (e1) (e2)) = (e3))) -> ((~((op (e2) (e1)) = (e2)))\/((op (e2) (e2)) = (e1))) -> (((op (e2) (e0)) = (e2))\/(((op (e2) (e1)) = (e2))\/(((op (e2) (e2)) = (e2))\/((op (e2) (e3)) = (e2))))) -> (~((op (e2) (e2)) = (e2))) -> ((~((op (e3) (e2)) = (e2)))\/((op (e3) (e2)) = (e2))) -> (((op (e0) (e0)) = (e0))\/(((op (e1) (e0)) = (e0))\/(((op (e2) (e0)) = (e0))\/((op (e3) (e0)) = (e0))))) -> (~((op (e2) (e0)) = (op (e2) (e1)))) -> (((op (e2) (e1)) = (e0))\/(((op (e2) (e1)) = (e1))\/(((op (e2) (e1)) = (e2))\/((op (e2) (e1)) = (e3))))) -> (((op (e0) (e0)) = (e2))\/(((op (e0) (e1)) = (e2))\/(((op (e0) (e2)) = (e2))\/((op (e0) (e3)) = (e2))))) -> (~((op (e0) (e1)) = (e2))) -> (~((e1) = (e2))) -> (((op (e0) (e0)) = (e1))\/(((op (e1) (e0)) = (e1))\/(((op (e2) (e0)) = (e1))\/((op (e3) (e0)) = (e1))))) -> (~((op (e0) (e2)) = (op (e3) (e2)))) -> (~((op (e0) (e2)) = (op (e0) (e3)))) -> ((op (e0) (e2)) = (e0)) -> (~((op (e1) (e0)) = (op (e1) (e3)))) -> (((op (e3) (e0)) = (e1))\/(((op (e3) (e1)) = (e1))\/(((op (e3) (e2)) = (e1))\/((op (e3) (e3)) = (e1))))) -> (~((op (e1) (e2)) = (op (e3) (e2)))) -> (~((op (e0) (e2)) = (op (e1) (e2)))) -> (~((op (e3) (e0)) = (op (e3) (e1)))) -> (((op (e2) (e0)) = (e1))\/(((op (e2) (e1)) = (e1))\/(((op (e2) (e2)) = (e1))\/((op (e2) (e3)) = (e1))))) -> (~((op (e3) (e1)) = (op (e3) (e2)))) -> (~((op (e1) (e1)) = (op (e1) (e3)))) -> (((op (e1) (e0)) = (e0))\/(((op (e1) (e1)) = (e0))\/(((op (e1) (e2)) = (e0))\/((op (e1) (e3)) = (e0))))) -> (~((op (e1) (e2)) = (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) (e1)) = (op (e3) (e3)))) -> (~((op (e2) (e1)) = (op (e2) (e3)))) -> (~((op (e0) (e3)) = (op (e3) (e3)))) -> (~((op (e3) (e2)) = (op (e3) (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) (e1)) = (e0))\/(((op (e1) (e1)) = (e0))\/(((op (e2) (e1)) = (e0))\/((op (e3) (e1)) = (e0))))) -> (~((op (e1) (e1)) = (e1))) -> (~((op (e0) (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 (e0) (e1)) = (e2))\/(((op (e1) (e1)) = (e2))\/(((op (e2) (e1)) = (e2))\/((op (e3) (e1)) = (e2))))) -> (~((e2) = (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))))) -> (~((e0) = (e2))) -> (((op (e1) (e0)) = (e2))\/(((op (e1) (e1)) = (e2))\/(((op (e1) (e2)) = (e2))\/((op (e1) (e3)) = (e2))))) -> (~((op (e0) (e1)) = (op (e0) (e2)))) -> (~((op (e1) (e0)) = (op (e3) (e0)))) -> (~((op (e1) (e0)) = (op (e2) (e0)))) -> (~((op (e1) (e0)) = (e2))) -> (((op (e1) (e0)) = (e0))\/(((op (e1) (e0)) = (e1))\/(((op (e1) (e0)) = (e2))\/((op (e1) (e0)) = (e3))))) -> (~((op (e1) (e0)) = (op (e1) (e1)))) -> (~((e0) = (e1))) -> (((op (e0) (e0)) = (e1))\/(((op (e0) (e1)) = (e1))\/(((op (e0) (e2)) = (e1))\/((op (e0) (e3)) = (e1))))) -> (~((op (e0) (e0)) = (e0))) -> (~((op (e2) (e2)) = (op (e3) (e2)))) -> ((~((op (e3) (e3)) = (e2)))\/((op (e3) (e2)) = (e3))) -> (~((op (e0) (e2)) = (e2))) -> (((op (e0) (e2)) = (e2))\/(((op (e1) (e2)) = (e2))\/(((op (e2) (e2)) = (e2))\/((op (e3) (e2)) = (e2))))) -> ((~((op (e2) (e3)) = (e2)))\/((op (e2) (e2)) = (e3))) -> (~((op (e0) (e2)) = (op (e2) (e2)))) -> ((~((op (e2) (e0)) = (e2)))\/((op (e2) (e2)) = (e0))) -> ((~((op (e1) (e2)) = (e2)))\/((op (e1) (e2)) = (e2))) -> (((op (e0) (e3)) = (e3))\/(((op (e1) (e3)) = (e3))\/(((op (e2) (e3)) = (e3))\/((op (e3) (e3)) = (e3))))) -> (~((op (e2) (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 (e1) (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) (e0)) = (e0)) -> (~((op (e2) (e0)) = (op (e2) (e3)))) -> (~((e0) = (e3))) -> (((op (e0) (e3)) = (e0))\/(((op (e1) (e3)) = (e0))\/(((op (e2) (e3)) = (e0))\/((op (e3) (e3)) = (e0))))) -> (~((e1) = (e3))) -> (~((op (e0) (e3)) = (op (e2) (e3)))) -> (~((op (e0) (e3)) = (e2))) -> ((op (e0) (e1)) = (e1)) -> (~((op (e0) (e1)) = (op (e0) (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 (e3) (e3)) = (e3))) -> False). % 19.02/19.14 do 0 intro. intros zenon_H128 zenon_Hf1 zenon_H6d zenon_H16f zenon_H10e zenon_H113 zenon_H153 zenon_H14b zenon_H194 zenon_H272 zenon_Hac zenon_H279 zenon_H271 zenon_H1d5 zenon_H173 zenon_H273 zenon_H3e zenon_H1f0 zenon_H1cc zenon_H183 zenon_H26d zenon_H7c zenon_H235 zenon_H14f zenon_H208 zenon_H48 zenon_Hd8 zenon_He8 zenon_H115 zenon_H195 zenon_H1cf zenon_H106 zenon_H1a4 zenon_H57 zenon_H22 zenon_H2b zenon_H101 zenon_H71 zenon_H130 zenon_H1c7 zenon_Hc2 zenon_H62 zenon_H124 zenon_H133 zenon_H245 zenon_H10a zenon_H17e zenon_H212 zenon_H210 zenon_H1d8 zenon_H12b zenon_H109 zenon_H1ac zenon_H149 zenon_H18c zenon_H4a zenon_H1fa zenon_H201 zenon_H177 zenon_H25e zenon_H45 zenon_Ha1 zenon_H22d zenon_H3f zenon_H18f zenon_H278 zenon_H1fd zenon_H172 zenon_H277 zenon_Ha8 zenon_H276 zenon_H275 zenon_H136 zenon_H274 zenon_Hdf zenon_Hd5 zenon_Hdb zenon_H14c zenon_Hf3 zenon_H11f zenon_H34 zenon_H5b zenon_H9a zenon_H67 zenon_H95 zenon_He2 zenon_H12e zenon_Ha0 zenon_H54 zenon_H1d zenon_H1f zenon_He4 zenon_H102. % 19.02/19.14 apply (zenon_or_s _ _ zenon_H128); [ zenon_intro zenon_H9d | zenon_intro zenon_H129 ]. % 19.02/19.14 apply (zenon_L1155_); trivial. % 19.02/19.14 apply (zenon_or_s _ _ zenon_H129); [ zenon_intro zenon_H10d | zenon_intro zenon_H12a ]. % 19.02/19.14 exact (zenon_H10a zenon_H10d). % 19.02/19.14 apply (zenon_or_s _ _ zenon_H12a); [ zenon_intro zenon_Hf0 | zenon_intro zenon_Hd6 ]. % 19.02/19.14 apply (zenon_L1101_); trivial. % 19.02/19.14 apply (zenon_L1161_); trivial. % 19.02/19.14 (* end of lemma zenon_L1162_ *) % 19.02/19.14 assert (zenon_L1163_ : (((op (e3) (e0)) = (e2))\/(((op (e3) (e1)) = (e2))\/(((op (e3) (e2)) = (e2))\/((op (e3) (e3)) = (e2))))) -> (~((op (e3) (e0)) = (e2))) -> (~((e1) = (e2))) -> ((op (e3) (e1)) = (e1)) -> (~((op (e3) (e2)) = (e2))) -> (((op (e2) (e3)) = (e0))\/(((op (e2) (e3)) = (e1))\/(((op (e2) (e3)) = (e2))\/((op (e2) (e3)) = (e3))))) -> ((op (e0) (e3)) = (e1)) -> ((op (e1) (e3)) = (e0)) -> (~((op (e2) (e3)) = (e2))) -> (~((op (e1) (e3)) = (op (e2) (e3)))) -> ((op (e1) (e3)) = (e3)) -> False). % 19.02/19.14 do 0 intro. intros zenon_H153 zenon_H14b zenon_H7c zenon_Hae zenon_H272 zenon_H11f zenon_Hc3 zenon_H1f zenon_H274 zenon_Hdb zenon_Hdc. % 19.02/19.14 apply (zenon_or_s _ _ zenon_H153); [ zenon_intro zenon_H148 | zenon_intro zenon_H154 ]. % 19.02/19.14 exact (zenon_H14b zenon_H148). % 19.02/19.14 apply (zenon_or_s _ _ zenon_H154); [ zenon_intro zenon_H14d | zenon_intro zenon_H155 ]. % 19.02/19.14 apply (zenon_L152_); trivial. % 19.02/19.14 apply (zenon_or_s _ _ zenon_H155); [ zenon_intro zenon_H151 | zenon_intro zenon_Hf6 ]. % 19.02/19.14 exact (zenon_H272 zenon_H151). % 19.02/19.14 apply (zenon_L1151_); trivial. % 19.02/19.14 (* end of lemma zenon_L1163_ *) % 19.02/19.14 assert (zenon_L1164_ : (((op (e2) (e3)) = (e0))\/(((op (e2) (e3)) = (e1))\/(((op (e2) (e3)) = (e2))\/((op (e2) (e3)) = (e3))))) -> ((op (e3) (e3)) = (e0)) -> (~((op (e2) (e3)) = (op (e3) (e3)))) -> (~((op (e2) (e2)) = (op (e2) (e3)))) -> ((op (e2) (e2)) = (e1)) -> (~((op (e2) (e3)) = (e2))) -> (~((op (e1) (e3)) = (op (e2) (e3)))) -> ((op (e1) (e3)) = (e3)) -> False). % 19.02/19.14 do 0 intro. intros zenon_H11f zenon_H60 zenon_Hf3 zenon_H6d zenon_Hf1 zenon_H274 zenon_Hdb zenon_Hdc. % 19.02/19.14 apply (zenon_or_s _ _ zenon_H11f); [ zenon_intro zenon_H37 | zenon_intro zenon_H120 ]. % 19.02/19.14 apply (zenon_L219_); trivial. % 19.02/19.14 apply (zenon_or_s _ _ zenon_H120); [ zenon_intro zenon_Hf4 | zenon_intro zenon_H121 ]. % 19.02/19.14 apply (zenon_L84_); trivial. % 19.02/19.14 apply (zenon_or_s _ _ zenon_H121); [ zenon_intro zenon_H11d | zenon_intro zenon_Hdd ]. % 19.02/19.14 exact (zenon_H274 zenon_H11d). % 19.02/19.14 apply (zenon_L52_); trivial. % 19.02/19.14 (* end of lemma zenon_L1164_ *) % 19.02/19.14 assert (zenon_L1165_ : (((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)) = (e1)) -> (~((op (e3) (e2)) = (e2))) -> ((op (e3) (e1)) = (e1)) -> (~((e1) = (e2))) -> (~((op (e3) (e0)) = (e2))) -> (((op (e3) (e0)) = (e2))\/(((op (e3) (e1)) = (e2))\/(((op (e3) (e2)) = (e2))\/((op (e3) (e3)) = (e2))))) -> (~((op (e2) (e0)) = (op (e2) (e3)))) -> ((op (e2) (e0)) = (e0)) -> (((op (e2) (e3)) = (e0))\/(((op (e2) (e3)) = (e1))\/(((op (e2) (e3)) = (e2))\/((op (e2) (e3)) = (e3))))) -> (~((op (e2) (e3)) = (op (e3) (e3)))) -> (~((op (e2) (e2)) = (op (e2) (e3)))) -> ((op (e2) (e2)) = (e1)) -> (~((op (e2) (e3)) = (e2))) -> (~((op (e1) (e3)) = (op (e2) (e3)))) -> ((op (e1) (e3)) = (e3)) -> False). % 19.02/19.14 do 0 intro. intros zenon_H67 zenon_H208 zenon_H48 zenon_Hc3 zenon_H272 zenon_Hae zenon_H7c zenon_H14b zenon_H153 zenon_H5b zenon_H34 zenon_H11f zenon_Hf3 zenon_H6d zenon_Hf1 zenon_H274 zenon_Hdb zenon_Hdc. % 19.02/19.14 apply (zenon_or_s _ _ zenon_H67); [ zenon_intro zenon_H1e | zenon_intro zenon_H68 ]. % 19.02/19.14 apply (zenon_L336_); trivial. % 19.02/19.14 apply (zenon_or_s _ _ zenon_H68); [ zenon_intro zenon_H1f | zenon_intro zenon_H69 ]. % 19.02/19.14 apply (zenon_L1163_); trivial. % 19.02/19.14 apply (zenon_or_s _ _ zenon_H69); [ zenon_intro zenon_H37 | zenon_intro zenon_H60 ]. % 19.02/19.14 apply (zenon_L14_); trivial. % 19.02/19.14 apply (zenon_L1164_); trivial. % 19.02/19.14 (* end of lemma zenon_L1165_ *) % 19.02/19.14 assert (zenon_L1166_ : (((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)))) -> (~((op (e1) (e1)) = (e1))) -> (~((e1) = (e3))) -> (((op (e1) (e0)) = (e1))\/(((op (e1) (e1)) = (e1))\/(((op (e1) (e2)) = (e1))\/((op (e1) (e3)) = (e1))))) -> ((op (e0) (e1)) = (e3)) -> (~((op (e0) (e1)) = (op (e1) (e1)))) -> (~((e2) = (e3))) -> ((op (e1) (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)) = (e1)) -> (~((op (e3) (e2)) = (e2))) -> ((op (e3) (e1)) = (e1)) -> (~((e1) = (e2))) -> (~((op (e3) (e0)) = (e2))) -> (((op (e3) (e0)) = (e2))\/(((op (e3) (e1)) = (e2))\/(((op (e3) (e2)) = (e2))\/((op (e3) (e3)) = (e2))))) -> (~((op (e2) (e0)) = (op (e2) (e3)))) -> ((op (e2) (e0)) = (e0)) -> (((op (e2) (e3)) = (e0))\/(((op (e2) (e3)) = (e1))\/(((op (e2) (e3)) = (e2))\/((op (e2) (e3)) = (e3))))) -> (~((op (e2) (e3)) = (op (e3) (e3)))) -> (~((op (e2) (e2)) = (op (e2) (e3)))) -> ((op (e2) (e2)) = (e1)) -> (~((op (e2) (e3)) = (e2))) -> (~((op (e1) (e3)) = (op (e2) (e3)))) -> False). % 19.02/19.14 do 0 intro. intros zenon_H16f zenon_H1d zenon_H2b zenon_H10a zenon_H95 zenon_H128 zenon_H99 zenon_H10e zenon_H12b zenon_H113 zenon_H67 zenon_H208 zenon_H48 zenon_Hc3 zenon_H272 zenon_Hae zenon_H7c zenon_H14b zenon_H153 zenon_H5b zenon_H34 zenon_H11f zenon_Hf3 zenon_H6d zenon_Hf1 zenon_H274 zenon_Hdb. % 19.02/19.14 apply (zenon_or_s _ _ zenon_H16f); [ zenon_intro zenon_H9e | zenon_intro zenon_H170 ]. % 19.02/19.14 apply (zenon_L80_); trivial. % 19.02/19.14 apply (zenon_or_s _ _ zenon_H170); [ zenon_intro zenon_H13f | zenon_intro zenon_H171 ]. % 19.02/19.14 apply (zenon_L108_); trivial. % 19.02/19.14 apply (zenon_or_s _ _ zenon_H171); [ zenon_intro zenon_H16c | zenon_intro zenon_Hdc ]. % 19.02/19.14 apply (zenon_L116_); trivial. % 19.02/19.14 apply (zenon_L1165_); trivial. % 19.02/19.14 (* end of lemma zenon_L1166_ *) % 19.02/19.14 assert (zenon_L1167_ : (((op (e0) (e1)) = (e1))\/(((op (e1) (e1)) = (e1))\/(((op (e2) (e1)) = (e1))\/((op (e3) (e1)) = (e1))))) -> (~((op (e0) (e1)) = (op (e0) (e3)))) -> (~((op (e2) (e1)) = (op (e2) (e3)))) -> (~((op (e3) (e1)) = (e2))) -> ((op (e1) (e0)) = (e1)) -> (((op (e1) (e0)) = (e3))\/(((op (e1) (e1)) = (e3))\/(((op (e1) (e2)) = (e3))\/((op (e1) (e3)) = (e3))))) -> (~((op (e0) (e3)) = (op (e1) (e3)))) -> (~((op (e1) (e2)) = (op (e2) (e2)))) -> (~((op (e1) (e1)) = (e1))) -> (~((e1) = (e3))) -> (((op (e1) (e0)) = (e1))\/(((op (e1) (e1)) = (e1))\/(((op (e1) (e2)) = (e1))\/((op (e1) (e3)) = (e1))))) -> ((op (e0) (e1)) = (e3)) -> (~((op (e0) (e1)) = (op (e1) (e1)))) -> (~((e2) = (e3))) -> ((op (e1) (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)) = (e1)) -> (~((op (e3) (e2)) = (e2))) -> (~((e1) = (e2))) -> (~((op (e3) (e0)) = (e2))) -> (((op (e3) (e0)) = (e2))\/(((op (e3) (e1)) = (e2))\/(((op (e3) (e2)) = (e2))\/((op (e3) (e3)) = (e2))))) -> (~((op (e2) (e0)) = (op (e2) (e3)))) -> ((op (e2) (e0)) = (e0)) -> (((op (e2) (e3)) = (e0))\/(((op (e2) (e3)) = (e1))\/(((op (e2) (e3)) = (e2))\/((op (e2) (e3)) = (e3))))) -> (~((op (e2) (e3)) = (op (e3) (e3)))) -> (~((op (e2) (e2)) = (op (e2) (e3)))) -> ((op (e2) (e2)) = (e1)) -> (~((op (e2) (e3)) = (e2))) -> (~((op (e1) (e3)) = (op (e2) (e3)))) -> False). % 19.02/19.14 do 0 intro. intros zenon_H109 zenon_H54 zenon_H1c7 zenon_H194 zenon_H9d zenon_H16f zenon_H1d zenon_H2b zenon_H10a zenon_H95 zenon_H128 zenon_H99 zenon_H10e zenon_H12b zenon_H113 zenon_H67 zenon_H208 zenon_H48 zenon_Hc3 zenon_H272 zenon_H7c zenon_H14b zenon_H153 zenon_H5b zenon_H34 zenon_H11f zenon_Hf3 zenon_H6d zenon_Hf1 zenon_H274 zenon_Hdb. % 19.02/19.14 apply (zenon_or_s _ _ zenon_H109); [ zenon_intro zenon_Ha0 | zenon_intro zenon_H10b ]. % 19.02/19.14 apply (zenon_L359_); trivial. % 19.02/19.14 apply (zenon_or_s _ _ zenon_H10b); [ zenon_intro zenon_H10d | zenon_intro zenon_H10c ]. % 19.02/19.14 exact (zenon_H10a zenon_H10d). % 19.02/19.14 apply (zenon_or_s _ _ zenon_H10c); [ zenon_intro zenon_Ha5 | zenon_intro zenon_Hae ]. % 19.02/19.14 apply (zenon_L1139_); trivial. % 19.02/19.14 apply (zenon_L1166_); trivial. % 19.02/19.14 (* end of lemma zenon_L1167_ *) % 19.02/19.14 assert (zenon_L1168_ : (((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)) = (e1)) -> (~((op (e0) (e1)) = (op (e3) (e1)))) -> (~((op (e0) (e1)) = (e2))) -> (((op (e0) (e1)) = (e1))\/(((op (e1) (e1)) = (e1))\/(((op (e2) (e1)) = (e1))\/((op (e3) (e1)) = (e1))))) -> (~((op (e0) (e1)) = (op (e0) (e3)))) -> (~((op (e2) (e1)) = (op (e2) (e3)))) -> (~((op (e3) (e1)) = (e2))) -> ((op (e1) (e0)) = (e1)) -> (((op (e1) (e0)) = (e3))\/(((op (e1) (e1)) = (e3))\/(((op (e1) (e2)) = (e3))\/((op (e1) (e3)) = (e3))))) -> (~((op (e0) (e3)) = (op (e1) (e3)))) -> (~((op (e1) (e2)) = (op (e2) (e2)))) -> (~((op (e1) (e1)) = (e1))) -> (~((e1) = (e3))) -> (((op (e1) (e0)) = (e1))\/(((op (e1) (e1)) = (e1))\/(((op (e1) (e2)) = (e1))\/((op (e1) (e3)) = (e1))))) -> (~((op (e0) (e1)) = (op (e1) (e1)))) -> (~((e2) = (e3))) -> ((op (e1) (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)) = (e1)) -> (~((op (e3) (e2)) = (e2))) -> (~((e1) = (e2))) -> (~((op (e3) (e0)) = (e2))) -> (((op (e3) (e0)) = (e2))\/(((op (e3) (e1)) = (e2))\/(((op (e3) (e2)) = (e2))\/((op (e3) (e3)) = (e2))))) -> (~((op (e2) (e0)) = (op (e2) (e3)))) -> ((op (e2) (e0)) = (e0)) -> (((op (e2) (e3)) = (e0))\/(((op (e2) (e3)) = (e1))\/(((op (e2) (e3)) = (e2))\/((op (e2) (e3)) = (e3))))) -> (~((op (e2) (e3)) = (op (e3) (e3)))) -> (~((op (e2) (e2)) = (op (e2) (e3)))) -> ((op (e2) (e2)) = (e1)) -> (~((op (e2) (e3)) = (e2))) -> (~((op (e1) (e3)) = (op (e2) (e3)))) -> False). % 19.02/19.14 do 0 intro. intros zenon_H212 zenon_H4a zenon_Hae zenon_H210 zenon_H26d zenon_H109 zenon_H54 zenon_H1c7 zenon_H194 zenon_H9d zenon_H16f zenon_H1d zenon_H2b zenon_H10a zenon_H95 zenon_H128 zenon_H10e zenon_H12b zenon_H113 zenon_H67 zenon_H208 zenon_H48 zenon_Hc3 zenon_H272 zenon_H7c zenon_H14b zenon_H153 zenon_H5b zenon_H34 zenon_H11f zenon_Hf3 zenon_H6d zenon_Hf1 zenon_H274 zenon_Hdb. % 19.02/19.14 apply (zenon_or_s _ _ zenon_H212); [ zenon_intro zenon_H49 | zenon_intro zenon_H213 ]. % 19.02/19.14 apply (zenon_L9_); trivial. % 19.02/19.14 apply (zenon_or_s _ _ zenon_H213); [ zenon_intro zenon_Ha0 | zenon_intro zenon_H214 ]. % 19.02/19.14 apply (zenon_L363_); trivial. % 19.02/19.14 apply (zenon_or_s _ _ zenon_H214); [ zenon_intro zenon_H10f | zenon_intro zenon_H99 ]. % 19.02/19.14 exact (zenon_H26d zenon_H10f). % 19.02/19.14 apply (zenon_L1167_); trivial. % 19.02/19.14 (* end of lemma zenon_L1168_ *) % 19.02/19.14 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 (e1) (e3)) = (e3)) -> (~((op (e1) (e3)) = (op (e2) (e3)))) -> (~((op (e2) (e3)) = (e2))) -> ((op (e1) (e3)) = (e0)) -> (((op (e2) (e3)) = (e0))\/(((op (e2) (e3)) = (e1))\/(((op (e2) (e3)) = (e2))\/((op (e2) (e3)) = (e3))))) -> (~((op (e3) (e2)) = (e2))) -> (~((e1) = (e2))) -> (~((op (e3) (e0)) = (e2))) -> (((op (e3) (e0)) = (e2))\/(((op (e3) (e1)) = (e2))\/(((op (e3) (e2)) = (e2))\/((op (e3) (e3)) = (e2))))) -> ((op (e2) (e2)) = (e1)) -> (~((op (e2) (e2)) = (op (e3) (e2)))) -> (~((op (e0) (e3)) = (op (e3) (e3)))) -> ((op (e0) (e3)) = (e1)) -> False). % 19.02/19.14 do 0 intro. intros zenon_He8 zenon_Ha1 zenon_H44 zenon_Hdc zenon_Hdb zenon_H274 zenon_H1f zenon_H11f zenon_H272 zenon_H7c zenon_H14b zenon_H153 zenon_Hf1 zenon_H18f zenon_Hc2 zenon_Hc3. % 19.02/19.14 apply (zenon_or_s _ _ zenon_He8); [ zenon_intro zenon_Hac | zenon_intro zenon_Heb ]. % 19.02/19.14 apply (zenon_L41_); trivial. % 19.02/19.14 apply (zenon_or_s _ _ zenon_Heb); [ zenon_intro zenon_Hae | zenon_intro zenon_Hec ]. % 19.02/19.14 apply (zenon_L1163_); trivial. % 19.02/19.14 apply (zenon_or_s _ _ zenon_Hec); [ zenon_intro zenon_Hba | zenon_intro zenon_Hc4 ]. % 19.02/19.14 apply (zenon_L185_); trivial. % 19.02/19.14 apply (zenon_L46_); trivial. % 19.02/19.14 (* end of lemma zenon_L1169_ *) % 19.02/19.14 assert (zenon_L1170_ : (((op (e1) (e0)) = (e3))\/(((op (e1) (e1)) = (e3))\/(((op (e1) (e2)) = (e3))\/((op (e1) (e3)) = (e3))))) -> (~((e1) = (e3))) -> ((op (e1) (e0)) = (e1)) -> ((op (e0) (e1)) = (e3)) -> (~((op (e0) (e1)) = (op (e1) (e1)))) -> (~((e2) = (e3))) -> ((op (e1) (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) (e3)) = (op (e2) (e3)))) -> (~((op (e2) (e3)) = (e2))) -> ((op (e1) (e3)) = (e0)) -> (((op (e2) (e3)) = (e0))\/(((op (e2) (e3)) = (e1))\/(((op (e2) (e3)) = (e2))\/((op (e2) (e3)) = (e3))))) -> (~((op (e3) (e2)) = (e2))) -> (~((e1) = (e2))) -> (~((op (e3) (e0)) = (e2))) -> (((op (e3) (e0)) = (e2))\/(((op (e3) (e1)) = (e2))\/(((op (e3) (e2)) = (e2))\/((op (e3) (e3)) = (e2))))) -> ((op (e2) (e2)) = (e1)) -> (~((op (e2) (e2)) = (op (e3) (e2)))) -> (~((op (e0) (e3)) = (op (e3) (e3)))) -> ((op (e0) (e3)) = (e1)) -> False). % 19.02/19.14 do 0 intro. intros zenon_H16f zenon_H95 zenon_H9d zenon_H99 zenon_H10e zenon_H12b zenon_H113 zenon_He8 zenon_Ha1 zenon_H44 zenon_Hdb zenon_H274 zenon_H1f zenon_H11f zenon_H272 zenon_H7c zenon_H14b zenon_H153 zenon_Hf1 zenon_H18f zenon_Hc2 zenon_Hc3. % 19.02/19.14 apply (zenon_or_s _ _ zenon_H16f); [ zenon_intro zenon_H9e | zenon_intro zenon_H170 ]. % 19.02/19.14 apply (zenon_L37_); trivial. % 19.02/19.14 apply (zenon_or_s _ _ zenon_H170); [ zenon_intro zenon_H13f | zenon_intro zenon_H171 ]. % 19.02/19.14 apply (zenon_L108_); trivial. % 19.02/19.14 apply (zenon_or_s _ _ zenon_H171); [ zenon_intro zenon_H16c | zenon_intro zenon_Hdc ]. % 19.02/19.14 apply (zenon_L116_); trivial. % 19.02/19.14 apply (zenon_L1169_); trivial. % 19.02/19.14 (* end of lemma zenon_L1170_ *) % 19.02/19.14 assert (zenon_L1171_ : (((op (e0) (e1)) = (e0))\/(((op (e0) (e1)) = (e1))\/(((op (e0) (e1)) = (e2))\/((op (e0) (e1)) = (e3))))) -> ((op (e2) (e1)) = (e0)) -> (~((op (e0) (e1)) = (op (e2) (e1)))) -> ((op (e2) (e3)) = (e3)) -> (~((op (e0) (e3)) = (op (e2) (e3)))) -> (~((op (e0) (e3)) = (e2))) -> (~((op (e0) (e1)) = (op (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 (e0) (e1)) = (e2))) -> (((op (e1) (e0)) = (e3))\/(((op (e1) (e1)) = (e3))\/(((op (e1) (e2)) = (e3))\/((op (e1) (e3)) = (e3))))) -> (~((e1) = (e3))) -> ((op (e1) (e0)) = (e1)) -> (~((op (e0) (e1)) = (op (e1) (e1)))) -> (~((e2) = (e3))) -> ((op (e1) (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) (e3)) = (op (e2) (e3)))) -> (~((op (e2) (e3)) = (e2))) -> ((op (e1) (e3)) = (e0)) -> (((op (e2) (e3)) = (e0))\/(((op (e2) (e3)) = (e1))\/(((op (e2) (e3)) = (e2))\/((op (e2) (e3)) = (e3))))) -> (~((op (e3) (e2)) = (e2))) -> (~((e1) = (e2))) -> (~((op (e3) (e0)) = (e2))) -> (((op (e3) (e0)) = (e2))\/(((op (e3) (e1)) = (e2))\/(((op (e3) (e2)) = (e2))\/((op (e3) (e3)) = (e2))))) -> ((op (e2) (e2)) = (e1)) -> (~((op (e2) (e2)) = (op (e3) (e2)))) -> (~((op (e0) (e3)) = (op (e3) (e3)))) -> ((op (e0) (e3)) = (e1)) -> False). % 19.02/19.14 do 0 intro. intros zenon_H212 zenon_H36 zenon_H17e zenon_Hdd zenon_He2 zenon_H12e zenon_H54 zenon_H1d zenon_He4 zenon_H26d zenon_H16f zenon_H95 zenon_H9d zenon_H10e zenon_H12b zenon_H113 zenon_He8 zenon_Ha1 zenon_H44 zenon_Hdb zenon_H274 zenon_H1f zenon_H11f zenon_H272 zenon_H7c zenon_H14b zenon_H153 zenon_Hf1 zenon_H18f zenon_Hc2 zenon_Hc3. % 19.02/19.14 apply (zenon_or_s _ _ zenon_H212); [ zenon_intro zenon_H49 | zenon_intro zenon_H213 ]. % 19.02/19.14 apply (zenon_L128_); trivial. % 19.02/19.14 apply (zenon_or_s _ _ zenon_H213); [ zenon_intro zenon_Ha0 | zenon_intro zenon_H214 ]. % 19.02/19.14 apply (zenon_L1147_); trivial. % 19.02/19.14 apply (zenon_or_s _ _ zenon_H214); [ zenon_intro zenon_H10f | zenon_intro zenon_H99 ]. % 19.02/19.14 exact (zenon_H26d zenon_H10f). % 19.02/19.14 apply (zenon_L1170_); trivial. % 19.02/19.14 (* end of lemma zenon_L1171_ *) % 19.02/19.14 assert (zenon_L1172_ : (((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)) = (op (e1) (e3)))) -> (~((op (e3) (e3)) = (e3))) -> (((op (e0) (e1)) = (e0))\/(((op (e0) (e1)) = (e1))\/(((op (e0) (e1)) = (e2))\/((op (e0) (e1)) = (e3))))) -> (~((op (e0) (e1)) = (op (e2) (e1)))) -> (~((op (e0) (e3)) = (op (e2) (e3)))) -> (~((op (e0) (e3)) = (e2))) -> (~((op (e0) (e1)) = (op (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 (e0) (e1)) = (e2))) -> (((op (e1) (e0)) = (e3))\/(((op (e1) (e1)) = (e3))\/(((op (e1) (e2)) = (e3))\/((op (e1) (e3)) = (e3))))) -> (~((e1) = (e3))) -> ((op (e1) (e0)) = (e1)) -> (~((op (e0) (e1)) = (op (e1) (e1)))) -> (~((e2) = (e3))) -> ((op (e1) (e2)) = (e2)) -> (((op (e3) (e0)) = (e1))\/(((op (e3) (e1)) = (e1))\/(((op (e3) (e2)) = (e1))\/((op (e3) (e3)) = (e1))))) -> (~((e0) = (e1))) -> (~((op (e1) (e3)) = (op (e2) (e3)))) -> (~((op (e2) (e3)) = (e2))) -> ((op (e1) (e3)) = (e0)) -> (((op (e2) (e3)) = (e0))\/(((op (e2) (e3)) = (e1))\/(((op (e2) (e3)) = (e2))\/((op (e2) (e3)) = (e3))))) -> (~((op (e3) (e2)) = (e2))) -> (~((e1) = (e2))) -> (~((op (e3) (e0)) = (e2))) -> (((op (e3) (e0)) = (e2))\/(((op (e3) (e1)) = (e2))\/(((op (e3) (e2)) = (e2))\/((op (e3) (e3)) = (e2))))) -> ((op (e2) (e2)) = (e1)) -> (~((op (e2) (e2)) = (op (e3) (e2)))) -> (~((op (e0) (e3)) = (op (e3) (e3)))) -> ((op (e0) (e3)) = (e1)) -> (((op (e0) (e3)) = (e3))\/(((op (e1) (e3)) = (e3))\/(((op (e2) (e3)) = (e3))\/((op (e3) (e3)) = (e3))))) -> (~((op (e3) (e1)) = (e2))) -> (~((op (e3) (e0)) = (op (e3) (e1)))) -> ((op (e3) (e0)) = (e0)) -> False). % 19.02/19.14 do 0 intro. intros zenon_H245 zenon_H4a zenon_H48 zenon_H57 zenon_H102 zenon_H212 zenon_H17e zenon_He2 zenon_H12e zenon_H54 zenon_H1d zenon_He4 zenon_H26d zenon_H16f zenon_H95 zenon_H9d zenon_H10e zenon_H12b zenon_H113 zenon_He8 zenon_Ha1 zenon_Hdb zenon_H274 zenon_H1f zenon_H11f zenon_H272 zenon_H7c zenon_H14b zenon_H153 zenon_Hf1 zenon_H18f zenon_Hc2 zenon_Hc3 zenon_H136 zenon_H194 zenon_H1cf zenon_H44. % 19.02/19.14 apply (zenon_or_s _ _ zenon_H245); [ zenon_intro zenon_H49 | zenon_intro zenon_H246 ]. % 19.02/19.14 apply (zenon_L9_); trivial. % 19.02/19.14 apply (zenon_or_s _ _ zenon_H246); [ zenon_intro zenon_H29 | zenon_intro zenon_H247 ]. % 19.02/19.14 apply (zenon_L13_); trivial. % 19.02/19.14 apply (zenon_or_s _ _ zenon_H247); [ zenon_intro zenon_H36 | zenon_intro zenon_H1b1 ]. % 19.02/19.14 apply (zenon_or_s _ _ zenon_H153); [ zenon_intro zenon_H148 | zenon_intro zenon_H154 ]. % 19.02/19.14 exact (zenon_H14b zenon_H148). % 19.02/19.14 apply (zenon_or_s _ _ zenon_H154); [ zenon_intro zenon_H14d | zenon_intro zenon_H155 ]. % 19.02/19.14 exact (zenon_H194 zenon_H14d). % 19.02/19.14 apply (zenon_or_s _ _ zenon_H155); [ zenon_intro zenon_H151 | zenon_intro zenon_Hf6 ]. % 19.02/19.14 exact (zenon_H272 zenon_H151). % 19.02/19.14 apply (zenon_or_s _ _ zenon_H136); [ zenon_intro zenon_He3 | zenon_intro zenon_H137 ]. % 19.02/19.14 apply (zenon_L633_); trivial. % 19.02/19.14 apply (zenon_or_s _ _ zenon_H137); [ zenon_intro zenon_Hdc | zenon_intro zenon_H138 ]. % 19.02/19.14 apply (zenon_L1151_); trivial. % 19.02/19.14 apply (zenon_or_s _ _ zenon_H138); [ zenon_intro zenon_Hdd | zenon_intro zenon_H105 ]. % 19.02/19.14 apply (zenon_L1171_); trivial. % 19.02/19.14 exact (zenon_H102 zenon_H105). % 19.02/19.14 apply (zenon_L346_); trivial. % 19.02/19.14 (* end of lemma zenon_L1172_ *) % 19.02/19.14 assert (zenon_L1173_ : (((op (e3) (e0)) = (e2))\/(((op (e3) (e1)) = (e2))\/(((op (e3) (e2)) = (e2))\/((op (e3) (e3)) = (e2))))) -> (~((op (e3) (e0)) = (e2))) -> (~((op (e3) (e1)) = (e2))) -> (~((op (e3) (e2)) = (e2))) -> ((op (e0) (e3)) = (e1)) -> ((op (e2) (e3)) = (e0)) -> False). % 19.02/19.14 do 0 intro. intros zenon_H153 zenon_H14b zenon_H194 zenon_H272 zenon_Hc3 zenon_H37. % 19.02/19.14 apply (zenon_or_s _ _ zenon_H153); [ zenon_intro zenon_H148 | zenon_intro zenon_H154 ]. % 19.02/19.14 exact (zenon_H14b zenon_H148). % 19.02/19.14 apply (zenon_or_s _ _ zenon_H154); [ zenon_intro zenon_H14d | zenon_intro zenon_H155 ]. % 19.02/19.14 exact (zenon_H194 zenon_H14d). % 19.02/19.14 apply (zenon_or_s _ _ zenon_H155); [ zenon_intro zenon_H151 | zenon_intro zenon_Hf6 ]. % 19.02/19.14 exact (zenon_H272 zenon_H151). % 19.02/19.14 apply (zenon_L387_); trivial. % 19.02/19.14 (* end of lemma zenon_L1173_ *) % 19.02/19.14 assert (zenon_L1174_ : (((op (e0) (e3)) = (e2))\/(((op (e1) (e3)) = (e2))\/(((op (e2) (e3)) = (e2))\/((op (e3) (e3)) = (e2))))) -> (~((op (e0) (e3)) = (e2))) -> (~((op (e1) (e3)) = (e2))) -> (~((op (e2) (e3)) = (e2))) -> ((op (e3) (e2)) = (e2)) -> (~((op (e3) (e2)) = (op (e3) (e3)))) -> False). % 19.02/19.14 do 0 intro. intros zenon_H145 zenon_H12e zenon_H14c zenon_H274 zenon_H151 zenon_H62. % 19.02/19.14 apply (zenon_or_s _ _ zenon_H145); [ zenon_intro zenon_Hcd | zenon_intro zenon_H146 ]. % 19.02/19.14 exact (zenon_H12e zenon_Hcd). % 19.02/19.14 apply (zenon_or_s _ _ zenon_H146); [ zenon_intro zenon_Hd7 | zenon_intro zenon_H147 ]. % 19.02/19.14 exact (zenon_H14c zenon_Hd7). % 19.02/19.14 apply (zenon_or_s _ _ zenon_H147); [ zenon_intro zenon_H11d | zenon_intro zenon_Hf6 ]. % 19.02/19.14 exact (zenon_H274 zenon_H11d). % 19.02/19.14 apply (zenon_L119_); trivial. % 19.02/19.14 (* end of lemma zenon_L1174_ *) % 19.02/19.14 assert (zenon_L1175_ : (((op (e0) (e3)) = (e2))\/(((op (e1) (e3)) = (e2))\/(((op (e2) (e3)) = (e2))\/((op (e3) (e3)) = (e2))))) -> (~((op (e0) (e3)) = (e2))) -> (~((e1) = (e2))) -> ((op (e1) (e3)) = (e1)) -> (~((op (e2) (e1)) = (op (e2) (e3)))) -> ((op (e2) (e1)) = (e2)) -> (~((op (e3) (e3)) = (e2))) -> False). % 19.02/19.14 do 0 intro. intros zenon_H145 zenon_H12e zenon_H7c zenon_Hd6 zenon_H1c7 zenon_H1ca zenon_Hf7. % 19.02/19.14 apply (zenon_or_s _ _ zenon_H145); [ zenon_intro zenon_Hcd | zenon_intro zenon_H146 ]. % 19.02/19.14 exact (zenon_H12e zenon_Hcd). % 19.02/19.14 apply (zenon_or_s _ _ zenon_H146); [ zenon_intro zenon_Hd7 | zenon_intro zenon_H147 ]. % 19.02/19.14 apply (zenon_L101_); trivial. % 19.02/19.14 apply (zenon_or_s _ _ zenon_H147); [ zenon_intro zenon_H11d | zenon_intro zenon_Hf6 ]. % 19.02/19.14 apply (zenon_L224_); trivial. % 19.02/19.14 exact (zenon_Hf7 zenon_Hf6). % 19.02/19.14 (* end of lemma zenon_L1175_ *) % 19.02/19.14 assert (zenon_L1176_ : (((op (e0) (e1)) = (e2))\/(((op (e1) (e1)) = (e2))\/(((op (e2) (e1)) = (e2))\/((op (e3) (e1)) = (e2))))) -> (~((op (e0) (e1)) = (e2))) -> (~((op (e1) (e1)) = (e2))) -> (~((op (e3) (e3)) = (e2))) -> (~((op (e2) (e1)) = (op (e2) (e3)))) -> ((op (e1) (e3)) = (e1)) -> (~((e1) = (e2))) -> (~((op (e0) (e3)) = (e2))) -> (((op (e0) (e3)) = (e2))\/(((op (e1) (e3)) = (e2))\/(((op (e2) (e3)) = (e2))\/((op (e3) (e3)) = (e2))))) -> (~((op (e3) (e1)) = (e2))) -> False). % 19.02/19.14 do 0 intro. intros zenon_H1d8 zenon_H26d zenon_H20c zenon_Hf7 zenon_H1c7 zenon_Hd6 zenon_H7c zenon_H12e zenon_H145 zenon_H194. % 19.02/19.14 apply (zenon_or_s _ _ zenon_H1d8); [ zenon_intro zenon_H10f | zenon_intro zenon_H1d9 ]. % 19.02/19.14 exact (zenon_H26d zenon_H10f). % 19.02/19.14 apply (zenon_or_s _ _ zenon_H1d9); [ zenon_intro zenon_H110 | zenon_intro zenon_H1da ]. % 19.02/19.14 exact (zenon_H20c zenon_H110). % 19.02/19.14 apply (zenon_or_s _ _ zenon_H1da); [ zenon_intro zenon_H1ca | zenon_intro zenon_H14d ]. % 19.02/19.14 apply (zenon_L1175_); trivial. % 19.02/19.14 exact (zenon_H194 zenon_H14d). % 19.02/19.14 (* end of lemma zenon_L1176_ *) % 19.02/19.14 assert (zenon_L1177_ : (((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 (e2) (e2)) = (e1)) -> (~((op (e1) (e2)) = (op (e2) (e2)))) -> (((op (e0) (e1)) = (e2))\/(((op (e1) (e1)) = (e2))\/(((op (e2) (e1)) = (e2))\/((op (e3) (e1)) = (e2))))) -> (~((op (e0) (e1)) = (e2))) -> (~((op (e1) (e1)) = (e2))) -> (~((op (e3) (e3)) = (e2))) -> (~((op (e2) (e1)) = (op (e2) (e3)))) -> (~((e1) = (e2))) -> (~((op (e0) (e3)) = (e2))) -> (((op (e0) (e3)) = (e2))\/(((op (e1) (e3)) = (e2))\/(((op (e2) (e3)) = (e2))\/((op (e3) (e3)) = (e2))))) -> (~((op (e3) (e1)) = (e2))) -> False). % 19.02/19.14 do 0 intro. intros zenon_H128 zenon_Ha1 zenon_H27 zenon_H10a zenon_Hf1 zenon_H2b zenon_H1d8 zenon_H26d zenon_H20c zenon_Hf7 zenon_H1c7 zenon_H7c zenon_H12e zenon_H145 zenon_H194. % 19.02/19.14 apply (zenon_or_s _ _ zenon_H128); [ zenon_intro zenon_H9d | zenon_intro zenon_H129 ]. % 19.02/19.14 apply (zenon_L262_); trivial. % 19.02/19.14 apply (zenon_or_s _ _ zenon_H129); [ zenon_intro zenon_H10d | zenon_intro zenon_H12a ]. % 19.02/19.14 exact (zenon_H10a zenon_H10d). % 19.02/19.14 apply (zenon_or_s _ _ zenon_H12a); [ zenon_intro zenon_Hf0 | zenon_intro zenon_Hd6 ]. % 19.02/19.14 apply (zenon_L59_); trivial. % 19.02/19.14 apply (zenon_L1176_); trivial. % 19.02/19.14 (* end of lemma zenon_L1177_ *) % 19.02/19.14 assert (zenon_L1178_ : (((op (e2) (e3)) = (e0))\/(((op (e2) (e3)) = (e1))\/(((op (e2) (e3)) = (e2))\/((op (e2) (e3)) = (e3))))) -> ((op (e3) (e3)) = (e1)) -> ((op (e1) (e3)) = (e2)) -> (~((op (e3) (e3)) = (e3))) -> ((op (e1) (e3)) = (e0)) -> (~((op (e2) (e3)) = (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) (e1)) = (op (e2) (e3)))) -> ((op (e2) (e1)) = (e2)) -> (~((op (e0) (e3)) = (op (e2) (e3)))) -> ((op (e0) (e3)) = (e3)) -> False). % 19.02/19.14 do 0 intro. intros zenon_H11f zenon_Hc4 zenon_Hd7 zenon_H102 zenon_H1f zenon_Hf3 zenon_H44 zenon_H71 zenon_H101 zenon_H1c7 zenon_H1ca zenon_He2 zenon_He3. % 19.02/19.14 apply (zenon_or_s _ _ zenon_H11f); [ zenon_intro zenon_H37 | zenon_intro zenon_H120 ]. % 19.02/19.14 apply (zenon_L72_); trivial. % 19.02/19.14 apply (zenon_or_s _ _ zenon_H120); [ zenon_intro zenon_Hf4 | zenon_intro zenon_H121 ]. % 19.02/19.14 apply (zenon_L64_); trivial. % 19.02/19.14 apply (zenon_or_s _ _ zenon_H121); [ zenon_intro zenon_H11d | zenon_intro zenon_Hdd ]. % 19.02/19.14 apply (zenon_L224_); trivial. % 19.02/19.14 apply (zenon_L54_); trivial. % 19.02/19.14 (* end of lemma zenon_L1178_ *) % 19.02/19.14 assert (zenon_L1179_ : (((op (e0) (e3)) = (e3))\/(((op (e1) (e3)) = (e3))\/(((op (e2) (e3)) = (e3))\/((op (e3) (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 (e3) (e0)) = (op (e3) (e3)))) -> ((op (e3) (e0)) = (e0)) -> (~((op (e2) (e3)) = (op (e3) (e3)))) -> ((op (e3) (e3)) = (e1)) -> (((op (e2) (e3)) = (e0))\/(((op (e2) (e3)) = (e1))\/(((op (e2) (e3)) = (e2))\/((op (e2) (e3)) = (e3))))) -> (~((e2) = (e3))) -> ((op (e1) (e3)) = (e2)) -> (~((op (e0) (e3)) = (op (e2) (e3)))) -> (~((op (e0) (e3)) = (e2))) -> ((op (e0) (e1)) = (e1)) -> (~((op (e0) (e1)) = (op (e0) (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 (e3) (e3)) = (e3))) -> False). % 19.02/19.14 do 0 intro. intros zenon_H136 zenon_H1ca zenon_H1c7 zenon_H101 zenon_H71 zenon_H44 zenon_Hf3 zenon_Hc4 zenon_H11f zenon_H12b zenon_Hd7 zenon_He2 zenon_H12e zenon_Ha0 zenon_H54 zenon_H1d zenon_H1f zenon_He4 zenon_H102. % 19.02/19.14 apply (zenon_or_s _ _ zenon_H136); [ zenon_intro zenon_He3 | zenon_intro zenon_H137 ]. % 19.02/19.14 apply (zenon_L1178_); trivial. % 19.02/19.14 apply (zenon_or_s _ _ zenon_H137); [ zenon_intro zenon_Hdc | zenon_intro zenon_H138 ]. % 19.02/19.14 apply (zenon_L266_); trivial. % 19.02/19.14 apply (zenon_or_s _ _ zenon_H138); [ zenon_intro zenon_Hdd | zenon_intro zenon_H105 ]. % 19.02/19.14 apply (zenon_L1147_); trivial. % 19.02/19.14 exact (zenon_H102 zenon_H105). % 19.02/19.14 (* end of lemma zenon_L1179_ *) % 19.02/19.14 assert (zenon_L1180_ : (((op (e0) (e3)) = (e2))\/(((op (e1) (e3)) = (e2))\/(((op (e2) (e3)) = (e2))\/((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 (e1) (e3)) = (e0)) -> (~((op (e0) (e3)) = (op (e1) (e3)))) -> (~((op (e0) (e1)) = (op (e0) (e3)))) -> ((op (e0) (e1)) = (e1)) -> (~((op (e0) (e3)) = (e2))) -> (~((op (e0) (e3)) = (op (e2) (e3)))) -> (~((e2) = (e3))) -> (((op (e2) (e3)) = (e0))\/(((op (e2) (e3)) = (e1))\/(((op (e2) (e3)) = (e2))\/((op (e2) (e3)) = (e3))))) -> ((op (e3) (e3)) = (e1)) -> (~((op (e2) (e3)) = (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 (e0) (e3)) = (e3))\/(((op (e1) (e3)) = (e3))\/(((op (e2) (e3)) = (e3))\/((op (e3) (e3)) = (e3))))) -> (~((op (e2) (e1)) = (op (e2) (e3)))) -> ((op (e2) (e1)) = (e2)) -> (~((op (e3) (e3)) = (e2))) -> False). % 19.02/19.14 do 0 intro. intros zenon_H145 zenon_H102 zenon_He4 zenon_H1f zenon_H1d zenon_H54 zenon_Ha0 zenon_H12e zenon_He2 zenon_H12b zenon_H11f zenon_Hc4 zenon_Hf3 zenon_H44 zenon_H71 zenon_H101 zenon_H136 zenon_H1c7 zenon_H1ca zenon_Hf7. % 19.02/19.14 apply (zenon_or_s _ _ zenon_H145); [ zenon_intro zenon_Hcd | zenon_intro zenon_H146 ]. % 19.02/19.14 exact (zenon_H12e zenon_Hcd). % 19.02/19.14 apply (zenon_or_s _ _ zenon_H146); [ zenon_intro zenon_Hd7 | zenon_intro zenon_H147 ]. % 19.02/19.14 apply (zenon_L1179_); trivial. % 19.02/19.14 apply (zenon_or_s _ _ zenon_H147); [ zenon_intro zenon_H11d | zenon_intro zenon_Hf6 ]. % 19.02/19.14 apply (zenon_L224_); trivial. % 19.02/19.14 exact (zenon_Hf7 zenon_Hf6). % 19.02/19.14 (* end of lemma zenon_L1180_ *) % 19.02/19.14 assert (zenon_L1181_ : (~((op (e3) (e3)) = (e2))) -> (~((op (e2) (e1)) = (op (e2) (e3)))) -> (((op (e0) (e3)) = (e3))\/(((op (e1) (e3)) = (e3))\/(((op (e2) (e3)) = (e3))\/((op (e3) (e3)) = (e3))))) -> (((op (e3) (e3)) = (e0))\/(((op (e3) (e3)) = (e1))\/(((op (e3) (e3)) = (e2))\/((op (e3) (e3)) = (e3))))) -> (~((op (e3) (e0)) = (op (e3) (e3)))) -> ((op (e3) (e0)) = (e0)) -> (~((op (e2) (e3)) = (op (e3) (e3)))) -> (((op (e2) (e3)) = (e0))\/(((op (e2) (e3)) = (e1))\/(((op (e2) (e3)) = (e2))\/((op (e2) (e3)) = (e3))))) -> (~((e2) = (e3))) -> (~((op (e0) (e3)) = (op (e2) (e3)))) -> (~((op (e0) (e3)) = (e2))) -> ((op (e0) (e1)) = (e1)) -> (~((op (e0) (e1)) = (op (e0) (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 (e3) (e3)) = (e3))) -> (((op (e0) (e3)) = (e2))\/(((op (e1) (e3)) = (e2))\/(((op (e2) (e3)) = (e2))\/((op (e3) (e3)) = (e2))))) -> (~((e1) = (e2))) -> (~((op (e3) (e1)) = (op (e3) (e3)))) -> (~((op (e1) (e1)) = (e2))) -> (~((op (e0) (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 (e0) (e1)) = (e0))\/(((op (e0) (e1)) = (e1))\/(((op (e0) (e1)) = (e2))\/((op (e0) (e1)) = (e3))))) -> (~((op (e0) (e1)) = (op (e2) (e1)))) -> (((op (e1) (e1)) = (e0))\/(((op (e1) (e1)) = (e1))\/(((op (e1) (e1)) = (e2))\/((op (e1) (e1)) = (e3))))) -> (~((op (e1) (e1)) = (e1))) -> ((op (e2) (e1)) = (e0)) -> (((op (e0) (e1)) = (e1))\/(((op (e1) (e1)) = (e1))\/(((op (e2) (e1)) = (e1))\/((op (e3) (e1)) = (e1))))) -> (~((op (e1) (e0)) = (op (e1) (e3)))) -> ((op (e1) (e0)) = (e1)) -> (~((op (e3) (e2)) = (op (e3) (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 (e3) (e1)) = (e2))) -> False). % 19.02/19.14 do 0 intro. intros zenon_Hf7 zenon_H1c7 zenon_H136 zenon_H101 zenon_H71 zenon_H44 zenon_Hf3 zenon_H11f zenon_H12b zenon_He2 zenon_H12e zenon_Ha0 zenon_H54 zenon_H1d zenon_H1f zenon_He4 zenon_H102 zenon_H145 zenon_H7c zenon_H130 zenon_H20c zenon_H26d zenon_H1d8 zenon_H133 zenon_H212 zenon_H17e zenon_H142 zenon_H10a zenon_H36 zenon_H109 zenon_Hd8 zenon_H9d zenon_H62 zenon_H210 zenon_Ha1 zenon_He8 zenon_H194. % 19.02/19.14 apply (zenon_or_s _ _ zenon_H1d8); [ zenon_intro zenon_H10f | zenon_intro zenon_H1d9 ]. % 19.02/19.14 exact (zenon_H26d zenon_H10f). % 19.02/19.14 apply (zenon_or_s _ _ zenon_H1d9); [ zenon_intro zenon_H110 | zenon_intro zenon_H1da ]. % 19.02/19.14 exact (zenon_H20c zenon_H110). % 19.02/19.14 apply (zenon_or_s _ _ zenon_H1da); [ zenon_intro zenon_H1ca | zenon_intro zenon_H14d ]. % 19.02/19.14 apply (zenon_or_s _ _ zenon_He8); [ zenon_intro zenon_Hac | zenon_intro zenon_Heb ]. % 19.02/19.14 apply (zenon_L41_); trivial. % 19.02/19.14 apply (zenon_or_s _ _ zenon_Heb); [ zenon_intro zenon_Hae | zenon_intro zenon_Hec ]. % 19.02/19.14 apply (zenon_L363_); trivial. % 19.02/19.14 apply (zenon_or_s _ _ zenon_Hec); [ zenon_intro zenon_Hba | zenon_intro zenon_Hc4 ]. % 19.02/19.14 apply (zenon_L1125_); trivial. % 19.02/19.14 apply (zenon_L1180_); trivial. % 19.02/19.14 exact (zenon_H194 zenon_H14d). % 19.02/19.14 (* end of lemma zenon_L1181_ *) % 19.02/19.14 assert (zenon_L1182_ : (((op (e0) (e3)) = (e2))\/(((op (e1) (e3)) = (e2))\/(((op (e2) (e3)) = (e2))\/((op (e3) (e3)) = (e2))))) -> (~((op (e0) (e3)) = (e2))) -> ((op (e3) (e3)) = (e1)) -> ((op (e2) (e3)) = (e0)) -> (~((op (e2) (e1)) = (op (e2) (e3)))) -> ((op (e2) (e1)) = (e2)) -> (~((op (e3) (e3)) = (e2))) -> False). % 19.02/19.14 do 0 intro. intros zenon_H145 zenon_H12e zenon_Hc4 zenon_H37 zenon_H1c7 zenon_H1ca zenon_Hf7. % 19.02/19.14 apply (zenon_or_s _ _ zenon_H145); [ zenon_intro zenon_Hcd | zenon_intro zenon_H146 ]. % 19.02/19.14 exact (zenon_H12e zenon_Hcd). % 19.02/19.14 apply (zenon_or_s _ _ zenon_H146); [ zenon_intro zenon_Hd7 | zenon_intro zenon_H147 ]. % 19.02/19.14 apply (zenon_L72_); trivial. % 19.02/19.14 apply (zenon_or_s _ _ zenon_H147); [ zenon_intro zenon_H11d | zenon_intro zenon_Hf6 ]. % 19.02/19.14 apply (zenon_L224_); trivial. % 19.02/19.14 exact (zenon_Hf7 zenon_Hf6). % 19.02/19.14 (* end of lemma zenon_L1182_ *) % 19.02/19.14 assert (zenon_L1183_ : (((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)) = (op (e3) (e3)))) -> ((op (e2) (e2)) = (e1)) -> (~((op (e2) (e2)) = (op (e2) (e3)))) -> ((op (e1) (e0)) = (e1)) -> (~((op (e1) (e0)) = (op (e1) (e3)))) -> (~((op (e3) (e3)) = (e3))) -> (((op (e3) (e3)) = (e0))\/(((op (e3) (e3)) = (e1))\/(((op (e3) (e3)) = (e2))\/((op (e3) (e3)) = (e3))))) -> (((op (e0) (e3)) = (e1))\/(((op (e1) (e3)) = (e1))\/(((op (e2) (e3)) = (e1))\/((op (e3) (e3)) = (e1))))) -> (((op (e0) (e3)) = (e2))\/(((op (e1) (e3)) = (e2))\/(((op (e2) (e3)) = (e2))\/((op (e3) (e3)) = (e2))))) -> (~((op (e0) (e3)) = (e2))) -> ((op (e2) (e3)) = (e0)) -> (~((op (e2) (e1)) = (op (e2) (e3)))) -> ((op (e2) (e1)) = (e2)) -> (~((op (e3) (e3)) = (e2))) -> False). % 19.02/19.14 do 0 intro. intros zenon_He8 zenon_Ha1 zenon_H44 zenon_Ha0 zenon_H210 zenon_H62 zenon_Hf1 zenon_H6d zenon_H9d zenon_Hd8 zenon_H102 zenon_H101 zenon_H133 zenon_H145 zenon_H12e zenon_H37 zenon_H1c7 zenon_H1ca zenon_Hf7. % 19.02/19.14 apply (zenon_or_s _ _ zenon_He8); [ zenon_intro zenon_Hac | zenon_intro zenon_Heb ]. % 19.02/19.14 apply (zenon_L41_); trivial. % 19.02/19.14 apply (zenon_or_s _ _ zenon_Heb); [ zenon_intro zenon_Hae | zenon_intro zenon_Hec ]. % 19.02/19.14 apply (zenon_L363_); trivial. % 19.02/19.14 apply (zenon_or_s _ _ zenon_Hec); [ zenon_intro zenon_Hba | zenon_intro zenon_Hc4 ]. % 19.02/19.14 apply (zenon_L1109_); trivial. % 19.02/19.14 apply (zenon_L1182_); trivial. % 19.02/19.14 (* end of lemma zenon_L1183_ *) % 19.02/19.14 assert (zenon_L1184_ : (((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) (e3)))) -> (((op (e0) (e3)) = (e3))\/(((op (e1) (e3)) = (e3))\/(((op (e2) (e3)) = (e3))\/((op (e3) (e3)) = (e3))))) -> (~((op (e2) (e3)) = (op (e3) (e3)))) -> (((op (e2) (e3)) = (e0))\/(((op (e2) (e3)) = (e1))\/(((op (e2) (e3)) = (e2))\/((op (e2) (e3)) = (e3))))) -> (~((e2) = (e3))) -> (~((op (e0) (e3)) = (op (e2) (e3)))) -> (~((op (e0) (e1)) = (op (e0) (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) (e1)) = (op (e3) (e3)))) -> (~((op (e1) (e1)) = (e2))) -> (~((op (e0) (e1)) = (e2))) -> (((op (e0) (e1)) = (e2))\/(((op (e1) (e1)) = (e2))\/(((op (e2) (e1)) = (e2))\/((op (e3) (e1)) = (e2))))) -> (((op (e0) (e1)) = (e0))\/(((op (e0) (e1)) = (e1))\/(((op (e0) (e1)) = (e2))\/((op (e0) (e1)) = (e3))))) -> (~((op (e0) (e1)) = (op (e2) (e1)))) -> (((op (e1) (e1)) = (e0))\/(((op (e1) (e1)) = (e1))\/(((op (e1) (e1)) = (e2))\/((op (e1) (e1)) = (e3))))) -> (~((op (e1) (e1)) = (e1))) -> (((op (e0) (e1)) = (e1))\/(((op (e1) (e1)) = (e1))\/(((op (e2) (e1)) = (e1))\/((op (e3) (e1)) = (e1))))) -> (~((op (e3) (e1)) = (e2))) -> (~((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 (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)))) -> (~((op (e3) (e2)) = (op (e3) (e3)))) -> ((op (e2) (e2)) = (e1)) -> (~((op (e2) (e2)) = (op (e2) (e3)))) -> ((op (e1) (e0)) = (e1)) -> (~((op (e1) (e0)) = (op (e1) (e3)))) -> (~((op (e3) (e3)) = (e3))) -> (((op (e3) (e3)) = (e0))\/(((op (e3) (e3)) = (e1))\/(((op (e3) (e3)) = (e2))\/((op (e3) (e3)) = (e3))))) -> (((op (e0) (e3)) = (e1))\/(((op (e1) (e3)) = (e1))\/(((op (e2) (e3)) = (e1))\/((op (e3) (e3)) = (e1))))) -> (((op (e0) (e3)) = (e2))\/(((op (e1) (e3)) = (e2))\/(((op (e2) (e3)) = (e2))\/((op (e3) (e3)) = (e2))))) -> (~((op (e0) (e3)) = (e2))) -> (~((op (e2) (e1)) = (op (e2) (e3)))) -> ((op (e2) (e1)) = (e2)) -> (~((op (e3) (e3)) = (e2))) -> False). % 19.02/19.14 do 0 intro. intros zenon_H2f zenon_H17b zenon_H71 zenon_H136 zenon_Hf3 zenon_H11f zenon_H12b zenon_He2 zenon_H54 zenon_H1d zenon_He4 zenon_H7c zenon_H130 zenon_H20c zenon_H26d zenon_H1d8 zenon_H212 zenon_H17e zenon_H142 zenon_H10a zenon_H109 zenon_H194 zenon_H208 zenon_H67 zenon_H48 zenon_Ha8 zenon_He8 zenon_Ha1 zenon_H44 zenon_Ha0 zenon_H210 zenon_H62 zenon_Hf1 zenon_H6d zenon_H9d zenon_Hd8 zenon_H102 zenon_H101 zenon_H133 zenon_H145 zenon_H12e zenon_H1c7 zenon_H1ca zenon_Hf7. % 19.02/19.14 apply (zenon_or_s _ _ zenon_H2f); [ zenon_intro zenon_H34 | zenon_intro zenon_H33 ]. % 19.02/19.14 apply (zenon_L127_); trivial. % 19.02/19.14 apply (zenon_or_s _ _ zenon_H33); [ zenon_intro zenon_H36 | zenon_intro zenon_H35 ]. % 19.02/19.14 apply (zenon_or_s _ _ zenon_H67); [ zenon_intro zenon_H1e | zenon_intro zenon_H68 ]. % 19.02/19.14 apply (zenon_L336_); trivial. % 19.02/19.14 apply (zenon_or_s _ _ zenon_H68); [ zenon_intro zenon_H1f | zenon_intro zenon_H69 ]. % 19.02/19.14 apply (zenon_L1181_); trivial. % 19.02/19.14 apply (zenon_or_s _ _ zenon_H69); [ zenon_intro zenon_H37 | zenon_intro zenon_H60 ]. % 19.02/19.14 apply (zenon_L640_); trivial. % 19.02/19.14 apply (zenon_L21_); trivial. % 19.02/19.14 apply (zenon_or_s _ _ zenon_H35); [ zenon_intro zenon_H2c | zenon_intro zenon_H37 ]. % 19.02/19.14 apply (zenon_L679_); trivial. % 19.02/19.14 apply (zenon_L1183_); trivial. % 19.02/19.14 (* end of lemma zenon_L1184_ *) % 19.02/19.14 assert (zenon_L1185_ : (((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)) = (op (e1) (e3)))) -> ((op (e1) (e3)) = (e0)) -> ((op (e2) (e0)) = (e0)) -> (~((op (e2) (e0)) = (op (e2) (e1)))) -> (((op (e3) (e3)) = (e0))\/(((op (e3) (e3)) = (e1))\/(((op (e3) (e3)) = (e2))\/((op (e3) (e3)) = (e3))))) -> (~((op (e3) (e1)) = (op (e3) (e3)))) -> (~((op (e3) (e0)) = (op (e3) (e3)))) -> ((op (e3) (e0)) = (e1)) -> (~((op (e3) (e3)) = (e2))) -> (~((op (e3) (e3)) = (e3))) -> False). % 19.02/19.14 do 0 intro. intros zenon_H245 zenon_H4a zenon_H48 zenon_H57 zenon_H1f zenon_H34 zenon_H1f0 zenon_H101 zenon_H130 zenon_H71 zenon_Hac zenon_Hf7 zenon_H102. % 19.02/19.14 apply (zenon_or_s _ _ zenon_H245); [ zenon_intro zenon_H49 | zenon_intro zenon_H246 ]. % 19.02/19.14 apply (zenon_L9_); trivial. % 19.02/19.14 apply (zenon_or_s _ _ zenon_H246); [ zenon_intro zenon_H29 | zenon_intro zenon_H247 ]. % 19.02/19.14 apply (zenon_L13_); trivial. % 19.02/19.14 apply (zenon_or_s _ _ zenon_H247); [ zenon_intro zenon_H36 | zenon_intro zenon_H1b1 ]. % 19.02/19.14 apply (zenon_L642_); trivial. % 19.02/19.14 apply (zenon_L1067_); trivial. % 19.02/19.14 (* end of lemma zenon_L1185_ *) % 19.02/19.14 assert (zenon_L1186_ : (((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)) = (op (e1) (e3)))) -> ((op (e1) (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 (e2) (e0)) = (e2))) -> (((op (e0) (e3)) = (e2))\/(((op (e1) (e3)) = (e2))\/(((op (e2) (e3)) = (e2))\/((op (e3) (e3)) = (e2))))) -> (~((op (e0) (e3)) = (e2))) -> (~((op (e2) (e1)) = (op (e2) (e3)))) -> (~((op (e3) (e3)) = (e2))) -> (~((op (e2) (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 (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 (e1) (e0)) = (op (e1) (e3)))) -> ((op (e1) (e0)) = (e1)) -> (~((op (e2) (e2)) = (op (e2) (e3)))) -> ((op (e2) (e2)) = (e1)) -> ((op (e3) (e2)) = (e1)) -> (~((op (e3) (e2)) = (op (e3) (e3)))) -> False). % 19.02/19.14 do 0 intro. intros zenon_H245 zenon_H4a zenon_H48 zenon_H57 zenon_H1f zenon_H34 zenon_H1f0 zenon_H1d5 zenon_Hef zenon_H145 zenon_H12e zenon_H1c7 zenon_Hf7 zenon_H173 zenon_H133 zenon_H102 zenon_Hf3 zenon_Hc2 zenon_H130 zenon_H101 zenon_Hd8 zenon_H9d zenon_H6d zenon_Hf1 zenon_Hba zenon_H62. % 19.02/19.14 apply (zenon_or_s _ _ zenon_H245); [ zenon_intro zenon_H49 | zenon_intro zenon_H246 ]. % 19.02/19.14 apply (zenon_L9_); trivial. % 19.02/19.14 apply (zenon_or_s _ _ zenon_H246); [ zenon_intro zenon_H29 | zenon_intro zenon_H247 ]. % 19.02/19.14 apply (zenon_L13_); trivial. % 19.02/19.14 apply (zenon_or_s _ _ zenon_H247); [ zenon_intro zenon_H36 | zenon_intro zenon_H1b1 ]. % 19.02/19.14 apply (zenon_L642_); trivial. % 19.02/19.14 apply (zenon_L1134_); trivial. % 19.02/19.14 (* end of lemma zenon_L1186_ *) % 19.02/19.14 assert (zenon_L1187_ : (((op (e0) (e3)) = (e3))\/(((op (e1) (e3)) = (e3))\/(((op (e2) (e3)) = (e3))\/((op (e3) (e3)) = (e3))))) -> ((op (e2) (e1)) = (e2)) -> (~((op (e2) (e1)) = (op (e2) (e3)))) -> (~((op (e2) (e3)) = (op (e3) (e3)))) -> ((op (e3) (e3)) = (e1)) -> (((op (e2) (e3)) = (e0))\/(((op (e2) (e3)) = (e1))\/(((op (e2) (e3)) = (e2))\/((op (e2) (e3)) = (e3))))) -> (~((e2) = (e3))) -> ((op (e1) (e3)) = (e2)) -> (~((op (e0) (e3)) = (op (e2) (e3)))) -> (~((op (e0) (e3)) = (e2))) -> ((op (e0) (e1)) = (e1)) -> (~((op (e0) (e1)) = (op (e0) (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 (e3) (e3)) = (e3))) -> False). % 19.02/19.14 do 0 intro. intros zenon_H136 zenon_H1ca zenon_H1c7 zenon_Hf3 zenon_Hc4 zenon_H11f zenon_H12b zenon_Hd7 zenon_He2 zenon_H12e zenon_Ha0 zenon_H54 zenon_H1d zenon_H1f zenon_He4 zenon_H102. % 19.02/19.14 apply (zenon_or_s _ _ zenon_H136); [ zenon_intro zenon_He3 | zenon_intro zenon_H137 ]. % 19.02/19.14 apply (zenon_L454_); trivial. % 19.02/19.14 apply (zenon_or_s _ _ zenon_H137); [ zenon_intro zenon_Hdc | zenon_intro zenon_H138 ]. % 19.02/19.14 apply (zenon_L266_); trivial. % 19.02/19.14 apply (zenon_or_s _ _ zenon_H138); [ zenon_intro zenon_Hdd | zenon_intro zenon_H105 ]. % 19.02/19.14 apply (zenon_L1147_); trivial. % 19.02/19.14 exact (zenon_H102 zenon_H105). % 19.02/19.14 (* end of lemma zenon_L1187_ *) % 19.02/19.14 assert (zenon_L1188_ : (((op (e0) (e3)) = (e2))\/(((op (e1) (e3)) = (e2))\/(((op (e2) (e3)) = (e2))\/((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 (e1) (e3)) = (e0)) -> (~((op (e0) (e3)) = (op (e1) (e3)))) -> (~((op (e0) (e1)) = (op (e0) (e3)))) -> ((op (e0) (e1)) = (e1)) -> (~((op (e0) (e3)) = (e2))) -> (~((op (e0) (e3)) = (op (e2) (e3)))) -> (~((e2) = (e3))) -> (((op (e2) (e3)) = (e0))\/(((op (e2) (e3)) = (e1))\/(((op (e2) (e3)) = (e2))\/((op (e2) (e3)) = (e3))))) -> ((op (e3) (e3)) = (e1)) -> (~((op (e2) (e3)) = (op (e3) (e3)))) -> (((op (e0) (e3)) = (e3))\/(((op (e1) (e3)) = (e3))\/(((op (e2) (e3)) = (e3))\/((op (e3) (e3)) = (e3))))) -> (~((op (e2) (e1)) = (op (e2) (e3)))) -> ((op (e2) (e1)) = (e2)) -> (~((op (e3) (e3)) = (e2))) -> False). % 19.02/19.14 do 0 intro. intros zenon_H145 zenon_H102 zenon_He4 zenon_H1f zenon_H1d zenon_H54 zenon_Ha0 zenon_H12e zenon_He2 zenon_H12b zenon_H11f zenon_Hc4 zenon_Hf3 zenon_H136 zenon_H1c7 zenon_H1ca zenon_Hf7. % 19.02/19.14 apply (zenon_or_s _ _ zenon_H145); [ zenon_intro zenon_Hcd | zenon_intro zenon_H146 ]. % 19.02/19.14 exact (zenon_H12e zenon_Hcd). % 19.02/19.14 apply (zenon_or_s _ _ zenon_H146); [ zenon_intro zenon_Hd7 | zenon_intro zenon_H147 ]. % 19.02/19.14 apply (zenon_L1187_); trivial. % 19.02/19.14 apply (zenon_or_s _ _ zenon_H147); [ zenon_intro zenon_H11d | zenon_intro zenon_Hf6 ]. % 19.02/19.14 apply (zenon_L224_); trivial. % 19.02/19.14 exact (zenon_Hf7 zenon_Hf6). % 19.02/19.14 (* end of lemma zenon_L1188_ *) % 19.02/19.14 assert (zenon_L1189_ : (((op (e3) (e0)) = (e1))\/(((op (e3) (e1)) = (e1))\/(((op (e3) (e2)) = (e1))\/((op (e3) (e3)) = (e1))))) -> (~((op (e3) (e0)) = (op (e3) (e3)))) -> (~((op (e0) (e1)) = (op (e3) (e1)))) -> (~((op (e3) (e2)) = (op (e3) (e3)))) -> ((op (e2) (e2)) = (e1)) -> (~((op (e2) (e2)) = (op (e2) (e3)))) -> ((op (e1) (e0)) = (e1)) -> (~((op (e1) (e0)) = (op (e1) (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)) = (op (e3) (e3)))) -> (((op (e0) (e3)) = (e1))\/(((op (e1) (e3)) = (e1))\/(((op (e2) (e3)) = (e1))\/((op (e3) (e3)) = (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 (e2) (e0)) = (op (e2) (e1)))) -> ((op (e2) (e0)) = (e0)) -> (~((op (e1) (e1)) = (op (e1) (e3)))) -> ((op (e0) (e2)) = (e0)) -> (~((op (e0) (e1)) = (op (e0) (e2)))) -> (((op (e0) (e1)) = (e0))\/(((op (e1) (e1)) = (e0))\/(((op (e2) (e1)) = (e0))\/((op (e3) (e1)) = (e0))))) -> (((op (e0) (e3)) = (e2))\/(((op (e1) (e3)) = (e2))\/(((op (e2) (e3)) = (e2))\/((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 (e1) (e3)) = (e0)) -> (~((op (e0) (e3)) = (op (e1) (e3)))) -> (~((op (e0) (e1)) = (op (e0) (e3)))) -> ((op (e0) (e1)) = (e1)) -> (~((op (e0) (e3)) = (e2))) -> (~((op (e0) (e3)) = (op (e2) (e3)))) -> (~((e2) = (e3))) -> (((op (e2) (e3)) = (e0))\/(((op (e2) (e3)) = (e1))\/(((op (e2) (e3)) = (e2))\/((op (e2) (e3)) = (e3))))) -> (~((op (e2) (e3)) = (op (e3) (e3)))) -> (((op (e0) (e3)) = (e3))\/(((op (e1) (e3)) = (e3))\/(((op (e2) (e3)) = (e3))\/((op (e3) (e3)) = (e3))))) -> (~((op (e2) (e1)) = (op (e2) (e3)))) -> ((op (e2) (e1)) = (e2)) -> (~((op (e3) (e3)) = (e2))) -> False). % 19.02/19.14 do 0 intro. intros zenon_He8 zenon_H71 zenon_H210 zenon_H62 zenon_Hf1 zenon_H6d zenon_H9d zenon_Hd8 zenon_H101 zenon_H130 zenon_Hc2 zenon_H133 zenon_H173 zenon_Hef zenon_H1d5 zenon_H1f0 zenon_H34 zenon_H57 zenon_H48 zenon_H4a zenon_H245 zenon_H145 zenon_H102 zenon_He4 zenon_H1f zenon_H1d zenon_H54 zenon_Ha0 zenon_H12e zenon_He2 zenon_H12b zenon_H11f zenon_Hf3 zenon_H136 zenon_H1c7 zenon_H1ca zenon_Hf7. % 19.02/19.14 apply (zenon_or_s _ _ zenon_He8); [ zenon_intro zenon_Hac | zenon_intro zenon_Heb ]. % 19.02/19.14 apply (zenon_L1185_); trivial. % 19.02/19.14 apply (zenon_or_s _ _ zenon_Heb); [ zenon_intro zenon_Hae | zenon_intro zenon_Hec ]. % 19.02/19.14 apply (zenon_L363_); trivial. % 19.02/19.14 apply (zenon_or_s _ _ zenon_Hec); [ zenon_intro zenon_Hba | zenon_intro zenon_Hc4 ]. % 19.02/19.14 apply (zenon_L1186_); trivial. % 19.02/19.14 apply (zenon_L1188_); trivial. % 19.02/19.14 (* end of lemma zenon_L1189_ *) % 19.02/19.14 assert (zenon_L1190_ : (((op (e0) (e3)) = (e0))\/(((op (e1) (e3)) = (e0))\/(((op (e2) (e3)) = (e0))\/((op (e3) (e3)) = (e0))))) -> (~((op (e0) (e2)) = (op (e0) (e3)))) -> (~((op (e3) (e3)) = (e2))) -> ((op (e2) (e1)) = (e2)) -> (~((op (e2) (e1)) = (op (e2) (e3)))) -> (((op (e0) (e3)) = (e3))\/(((op (e1) (e3)) = (e3))\/(((op (e2) (e3)) = (e3))\/((op (e3) (e3)) = (e3))))) -> (~((op (e2) (e3)) = (op (e3) (e3)))) -> (((op (e2) (e3)) = (e0))\/(((op (e2) (e3)) = (e1))\/(((op (e2) (e3)) = (e2))\/((op (e2) (e3)) = (e3))))) -> (~((e2) = (e3))) -> (~((op (e0) (e3)) = (op (e2) (e3)))) -> (~((op (e0) (e3)) = (e2))) -> ((op (e0) (e1)) = (e1)) -> (~((op (e0) (e1)) = (op (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 (e3) (e3)) = (e3))) -> (((op (e0) (e3)) = (e2))\/(((op (e1) (e3)) = (e2))\/(((op (e2) (e3)) = (e2))\/((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)) = (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 (e2) (e2)) = (e2))) -> (((op (e0) (e3)) = (e1))\/(((op (e1) (e3)) = (e1))\/(((op (e2) (e3)) = (e1))\/((op (e3) (e3)) = (e1))))) -> (~((op (e0) (e3)) = (op (e3) (e3)))) -> (((op (e3) (e3)) = (e0))\/(((op (e3) (e3)) = (e1))\/(((op (e3) (e3)) = (e2))\/((op (e3) (e3)) = (e3))))) -> (~((op (e1) (e0)) = (op (e1) (e3)))) -> ((op (e1) (e0)) = (e1)) -> (~((op (e2) (e2)) = (op (e2) (e3)))) -> ((op (e2) (e2)) = (e1)) -> (~((op (e3) (e2)) = (op (e3) (e3)))) -> (~((op (e0) (e1)) = (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 (e2) (e0)) = (op (e2) (e3)))) -> ((op (e2) (e0)) = (e0)) -> ((op (e3) (e1)) = (e0)) -> (~((op (e3) (e1)) = (op (e3) (e3)))) -> False). % 19.02/19.14 do 0 intro. intros zenon_H67 zenon_H208 zenon_Hf7 zenon_H1ca zenon_H1c7 zenon_H136 zenon_Hf3 zenon_H11f zenon_H12b zenon_He2 zenon_H12e zenon_Ha0 zenon_H54 zenon_H1d zenon_He4 zenon_H102 zenon_H145 zenon_H245 zenon_H4a zenon_H48 zenon_H57 zenon_H1f0 zenon_H1d5 zenon_Hef zenon_H173 zenon_H133 zenon_Hc2 zenon_H101 zenon_Hd8 zenon_H9d zenon_H6d zenon_Hf1 zenon_H62 zenon_H210 zenon_H71 zenon_He8 zenon_H5b zenon_H34 zenon_H1b1 zenon_H130. % 19.02/19.14 apply (zenon_or_s _ _ zenon_H67); [ zenon_intro zenon_H1e | zenon_intro zenon_H68 ]. % 19.02/19.14 apply (zenon_L336_); trivial. % 19.02/19.14 apply (zenon_or_s _ _ zenon_H68); [ zenon_intro zenon_H1f | zenon_intro zenon_H69 ]. % 19.02/19.14 apply (zenon_L1189_); trivial. % 19.02/19.14 apply (zenon_or_s _ _ zenon_H69); [ zenon_intro zenon_H37 | zenon_intro zenon_H60 ]. % 19.02/19.14 apply (zenon_L14_); trivial. % 19.02/19.14 apply (zenon_L244_); trivial. % 19.02/19.14 (* end of lemma zenon_L1190_ *) % 19.02/19.14 assert (zenon_L1191_ : (((op (e0) (e3)) = (e2))\/(((op (e1) (e3)) = (e2))\/(((op (e2) (e3)) = (e2))\/((op (e3) (e3)) = (e2))))) -> (~((op (e0) (e3)) = (e2))) -> ((op (e3) (e3)) = (e0)) -> ((op (e0) (e3)) = (e1)) -> (~((op (e2) (e1)) = (op (e2) (e3)))) -> ((op (e2) (e1)) = (e2)) -> (~((op (e3) (e3)) = (e2))) -> False). % 19.02/19.14 do 0 intro. intros zenon_H145 zenon_H12e zenon_H60 zenon_Hc3 zenon_H1c7 zenon_H1ca zenon_Hf7. % 19.02/19.14 apply (zenon_or_s _ _ zenon_H145); [ zenon_intro zenon_Hcd | zenon_intro zenon_H146 ]. % 19.02/19.14 exact (zenon_H12e zenon_Hcd). % 19.02/19.14 apply (zenon_or_s _ _ zenon_H146); [ zenon_intro zenon_Hd7 | zenon_intro zenon_H147 ]. % 19.02/19.14 apply (zenon_L201_); trivial. % 19.02/19.14 apply (zenon_or_s _ _ zenon_H147); [ zenon_intro zenon_H11d | zenon_intro zenon_Hf6 ]. % 19.02/19.14 apply (zenon_L224_); trivial. % 19.02/19.14 exact (zenon_Hf7 zenon_Hf6). % 19.02/19.14 (* end of lemma zenon_L1191_ *) % 19.02/19.14 assert (zenon_L1192_ : (((op (e0) (e3)) = (e0))\/(((op (e0) (e3)) = (e1))\/(((op (e0) (e3)) = (e2))\/((op (e0) (e3)) = (e3))))) -> (~((op (e0) (e3)) = (op (e3) (e3)))) -> ((op (e3) (e3)) = (e0)) -> (~((op (e0) (e3)) = (e2))) -> (((op (e2) (e3)) = (e0))\/(((op (e2) (e3)) = (e1))\/(((op (e2) (e3)) = (e2))\/((op (e2) (e3)) = (e3))))) -> ((op (e1) (e3)) = (e2)) -> ((op (e3) (e3)) = (e1)) -> (~((op (e2) (e3)) = (op (e3) (e3)))) -> (~((op (e2) (e1)) = (op (e2) (e3)))) -> ((op (e2) (e1)) = (e2)) -> (~((op (e0) (e3)) = (op (e2) (e3)))) -> False). % 19.02/19.14 do 0 intro. intros zenon_He4 zenon_Hc2 zenon_H60 zenon_H12e zenon_H11f zenon_Hd7 zenon_Hc4 zenon_Hf3 zenon_H1c7 zenon_H1ca zenon_He2. % 19.02/19.14 apply (zenon_or_s _ _ zenon_He4); [ zenon_intro zenon_H1e | zenon_intro zenon_He5 ]. % 19.02/19.14 apply (zenon_L440_); trivial. % 19.02/19.14 apply (zenon_or_s _ _ zenon_He5); [ zenon_intro zenon_Hc3 | zenon_intro zenon_He6 ]. % 19.02/19.14 apply (zenon_L201_); trivial. % 19.02/19.14 apply (zenon_or_s _ _ zenon_He6); [ zenon_intro zenon_Hcd | zenon_intro zenon_He3 ]. % 19.02/19.14 exact (zenon_H12e zenon_Hcd). % 19.02/19.14 apply (zenon_L454_); trivial. % 19.02/19.14 (* end of lemma zenon_L1192_ *) % 19.02/19.14 assert (zenon_L1193_ : (((op (e0) (e3)) = (e2))\/(((op (e1) (e3)) = (e2))\/(((op (e2) (e3)) = (e2))\/((op (e3) (e3)) = (e2))))) -> (~((op (e0) (e3)) = (op (e2) (e3)))) -> (~((op (e2) (e3)) = (op (e3) (e3)))) -> ((op (e3) (e3)) = (e1)) -> (((op (e2) (e3)) = (e0))\/(((op (e2) (e3)) = (e1))\/(((op (e2) (e3)) = (e2))\/((op (e2) (e3)) = (e3))))) -> (~((op (e0) (e3)) = (e2))) -> ((op (e3) (e3)) = (e0)) -> (~((op (e0) (e3)) = (op (e3) (e3)))) -> (((op (e0) (e3)) = (e0))\/(((op (e0) (e3)) = (e1))\/(((op (e0) (e3)) = (e2))\/((op (e0) (e3)) = (e3))))) -> (~((op (e2) (e1)) = (op (e2) (e3)))) -> ((op (e2) (e1)) = (e2)) -> (~((op (e3) (e3)) = (e2))) -> False). % 19.02/19.14 do 0 intro. intros zenon_H145 zenon_He2 zenon_Hf3 zenon_Hc4 zenon_H11f zenon_H12e zenon_H60 zenon_Hc2 zenon_He4 zenon_H1c7 zenon_H1ca zenon_Hf7. % 19.02/19.14 apply (zenon_or_s _ _ zenon_H145); [ zenon_intro zenon_Hcd | zenon_intro zenon_H146 ]. % 19.02/19.14 exact (zenon_H12e zenon_Hcd). % 19.02/19.14 apply (zenon_or_s _ _ zenon_H146); [ zenon_intro zenon_Hd7 | zenon_intro zenon_H147 ]. % 19.02/19.14 apply (zenon_L1192_); trivial. % 19.02/19.14 apply (zenon_or_s _ _ zenon_H147); [ zenon_intro zenon_H11d | zenon_intro zenon_Hf6 ]. % 19.02/19.14 apply (zenon_L224_); trivial. % 19.02/19.14 exact (zenon_Hf7 zenon_Hf6). % 19.02/19.14 (* end of lemma zenon_L1193_ *) % 19.02/19.14 assert (zenon_L1194_ : (((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 (e2) (e2)) = (op (e2) (e3)))) -> ((op (e2) (e2)) = (e1)) -> (((op (e0) (e3)) = (e2))\/(((op (e1) (e3)) = (e2))\/(((op (e2) (e3)) = (e2))\/((op (e3) (e3)) = (e2))))) -> (~((op (e0) (e3)) = (op (e2) (e3)))) -> (~((op (e2) (e3)) = (op (e3) (e3)))) -> (((op (e2) (e3)) = (e0))\/(((op (e2) (e3)) = (e1))\/(((op (e2) (e3)) = (e2))\/((op (e2) (e3)) = (e3))))) -> (~((op (e0) (e3)) = (e2))) -> ((op (e3) (e3)) = (e0)) -> (~((op (e0) (e3)) = (op (e3) (e3)))) -> (((op (e0) (e3)) = (e0))\/(((op (e0) (e3)) = (e1))\/(((op (e0) (e3)) = (e2))\/((op (e0) (e3)) = (e3))))) -> (~((op (e2) (e1)) = (op (e2) (e3)))) -> ((op (e2) (e1)) = (e2)) -> (~((op (e3) (e3)) = (e2))) -> False). % 19.02/19.14 do 0 intro. intros zenon_H133 zenon_Hd8 zenon_H9d zenon_H6d zenon_Hf1 zenon_H145 zenon_He2 zenon_Hf3 zenon_H11f zenon_H12e zenon_H60 zenon_Hc2 zenon_He4 zenon_H1c7 zenon_H1ca zenon_Hf7. % 19.02/19.14 apply (zenon_or_s _ _ zenon_H133); [ zenon_intro zenon_Hc3 | zenon_intro zenon_H134 ]. % 19.02/19.14 apply (zenon_L1191_); trivial. % 19.02/19.14 apply (zenon_or_s _ _ zenon_H134); [ zenon_intro zenon_Hd6 | zenon_intro zenon_H135 ]. % 19.02/19.14 apply (zenon_L360_); trivial. % 19.02/19.15 apply (zenon_or_s _ _ zenon_H135); [ zenon_intro zenon_Hf4 | zenon_intro zenon_Hc4 ]. % 19.02/19.15 apply (zenon_L84_); trivial. % 19.02/19.15 apply (zenon_L1193_); trivial. % 19.02/19.15 (* end of lemma zenon_L1194_ *) % 19.02/19.15 assert (zenon_L1195_ : (((op (e3) (e0)) = (e1))\/(((op (e3) (e1)) = (e1))\/(((op (e3) (e2)) = (e1))\/((op (e3) (e3)) = (e1))))) -> (~((e0) = (e1))) -> ((op (e3) (e0)) = (e0)) -> (~((op (e3) (e1)) = (op (e3) (e3)))) -> (~((op (e3) (e2)) = (op (e3) (e3)))) -> ((op (e2) (e2)) = (e1)) -> (~((op (e2) (e2)) = (op (e2) (e3)))) -> ((op (e1) (e0)) = (e1)) -> (~((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)) = (e2))) -> (~((op (e3) (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 (e2) (e1)) = (e2)) -> (~((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)) = (e1)) -> False). % 19.02/19.15 do 0 intro. intros zenon_He8 zenon_Ha1 zenon_H44 zenon_H130 zenon_H62 zenon_Hf1 zenon_H6d zenon_H9d zenon_Hd8 zenon_H145 zenon_H12e zenon_H102 zenon_H101 zenon_H1c7 zenon_H1ca zenon_Hf7 zenon_H133 zenon_Hc2 zenon_Hc3. % 19.02/19.15 apply (zenon_or_s _ _ zenon_He8); [ zenon_intro zenon_Hac | zenon_intro zenon_Heb ]. % 19.02/19.15 apply (zenon_L41_); trivial. % 19.02/19.15 apply (zenon_or_s _ _ zenon_Heb); [ zenon_intro zenon_Hae | zenon_intro zenon_Hec ]. % 19.02/19.15 apply (zenon_L1106_); trivial. % 19.02/19.15 apply (zenon_or_s _ _ zenon_Hec); [ zenon_intro zenon_Hba | zenon_intro zenon_Hc4 ]. % 19.02/19.15 apply (zenon_L1109_); trivial. % 19.02/19.15 apply (zenon_L46_); trivial. % 19.02/19.15 (* end of lemma zenon_L1195_ *) % 19.02/19.15 assert (zenon_L1196_ : (((op (e3) (e0)) = (e1))\/(((op (e3) (e1)) = (e1))\/(((op (e3) (e2)) = (e1))\/((op (e3) (e3)) = (e1))))) -> (~((op (e3) (e0)) = (op (e3) (e3)))) -> ((op (e2) (e1)) = (e2)) -> (~((op (e3) (e3)) = (e3))) -> (~((op (e2) (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 (e2) (e2)) = (e2))) -> (((op (e0) (e3)) = (e1))\/(((op (e1) (e3)) = (e1))\/(((op (e2) (e3)) = (e1))\/((op (e3) (e3)) = (e1))))) -> (~((op (e3) (e3)) = (e2))) -> (~((op (e2) (e1)) = (op (e2) (e3)))) -> (~((op (e0) (e3)) = (e2))) -> (((op (e0) (e3)) = (e2))\/(((op (e1) (e3)) = (e2))\/(((op (e2) (e3)) = (e2))\/((op (e3) (e3)) = (e2))))) -> (~((op (e1) (e0)) = (op (e1) (e3)))) -> ((op (e1) (e0)) = (e1)) -> (~((op (e2) (e2)) = (op (e2) (e3)))) -> ((op (e2) (e2)) = (e1)) -> (~((op (e3) (e2)) = (op (e3) (e3)))) -> (~((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 (e2) (e0)) = (e0)) -> ((op (e1) (e3)) = (e0)) -> (~((op (e1) (e1)) = (op (e1) (e3)))) -> ((op (e0) (e2)) = (e0)) -> (~((op (e0) (e1)) = (op (e0) (e2)))) -> (((op (e0) (e1)) = (e0))\/(((op (e1) (e1)) = (e0))\/(((op (e2) (e1)) = (e0))\/((op (e3) (e1)) = (e0))))) -> (~((op (e0) (e3)) = (op (e3) (e3)))) -> ((op (e0) (e3)) = (e1)) -> False). % 19.02/19.15 do 0 intro. intros zenon_He8 zenon_H71 zenon_H1ca zenon_H102 zenon_Hf3 zenon_H130 zenon_H101 zenon_H173 zenon_H133 zenon_Hf7 zenon_H1c7 zenon_H12e zenon_H145 zenon_Hd8 zenon_H9d zenon_H6d zenon_Hf1 zenon_H62 zenon_Hef zenon_H1d5 zenon_H1f0 zenon_H34 zenon_H1f zenon_H57 zenon_H48 zenon_H4a zenon_H245 zenon_Hc2 zenon_Hc3. % 19.02/19.15 apply (zenon_or_s _ _ zenon_He8); [ zenon_intro zenon_Hac | zenon_intro zenon_Heb ]. % 19.02/19.15 apply (zenon_L1185_); trivial. % 19.02/19.15 apply (zenon_or_s _ _ zenon_Heb); [ zenon_intro zenon_Hae | zenon_intro zenon_Hec ]. % 19.02/19.15 apply (zenon_L1106_); trivial. % 19.02/19.15 apply (zenon_or_s _ _ zenon_Hec); [ zenon_intro zenon_Hba | zenon_intro zenon_Hc4 ]. % 19.02/19.15 apply (zenon_L1111_); trivial. % 19.02/19.15 apply (zenon_L46_); trivial. % 19.02/19.15 (* end of lemma zenon_L1196_ *) % 19.02/19.15 assert (zenon_L1197_ : (((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 (e0) (e3)) = (op (e3) (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 (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 (e3) (e2)) = (op (e3) (e3)))) -> ((op (e2) (e2)) = (e1)) -> (~((op (e2) (e2)) = (op (e2) (e3)))) -> ((op (e1) (e0)) = (e1)) -> (~((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)) = (e2))) -> (~((op (e2) (e1)) = (op (e2) (e3)))) -> (~((op (e3) (e3)) = (e2))) -> (((op (e0) (e3)) = (e1))\/(((op (e1) (e3)) = (e1))\/(((op (e2) (e3)) = (e1))\/((op (e3) (e3)) = (e1))))) -> (~((op (e2) (e2)) = (e2))) -> (((op (e3) (e3)) = (e0))\/(((op (e3) (e3)) = (e1))\/(((op (e3) (e3)) = (e2))\/((op (e3) (e3)) = (e3))))) -> (~((op (e2) (e3)) = (op (e3) (e3)))) -> (~((op (e3) (e3)) = (e3))) -> ((op (e2) (e1)) = (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)) = (op (e2) (e3)))) -> ((op (e2) (e0)) = (e0)) -> ((op (e3) (e1)) = (e0)) -> (~((op (e3) (e1)) = (op (e3) (e3)))) -> False). % 19.02/19.15 do 0 intro. intros zenon_H67 zenon_H208 zenon_Hc3 zenon_Hc2 zenon_H245 zenon_H4a zenon_H48 zenon_H57 zenon_H1f0 zenon_H1d5 zenon_Hef zenon_H62 zenon_Hf1 zenon_H6d zenon_H9d zenon_Hd8 zenon_H145 zenon_H12e zenon_H1c7 zenon_Hf7 zenon_H133 zenon_H173 zenon_H101 zenon_Hf3 zenon_H102 zenon_H1ca zenon_H71 zenon_He8 zenon_H5b zenon_H34 zenon_H1b1 zenon_H130. % 19.02/19.15 apply (zenon_or_s _ _ zenon_H67); [ zenon_intro zenon_H1e | zenon_intro zenon_H68 ]. % 19.02/19.15 apply (zenon_L336_); trivial. % 19.02/19.15 apply (zenon_or_s _ _ zenon_H68); [ zenon_intro zenon_H1f | zenon_intro zenon_H69 ]. % 19.02/19.15 apply (zenon_L1196_); trivial. % 19.02/19.15 apply (zenon_or_s _ _ zenon_H69); [ zenon_intro zenon_H37 | zenon_intro zenon_H60 ]. % 19.02/19.15 apply (zenon_L14_); trivial. % 19.02/19.15 apply (zenon_L244_); trivial. % 19.02/19.15 (* end of lemma zenon_L1197_ *) % 19.02/19.15 assert (zenon_L1198_ : (((op (e3) (e0)) = (e0))\/(((op (e3) (e1)) = (e0))\/(((op (e3) (e2)) = (e0))\/((op (e3) (e3)) = (e0))))) -> (~((e0) = (e1))) -> (~((op (e3) (e1)) = (op (e3) (e3)))) -> ((op (e2) (e0)) = (e0)) -> (~((op (e2) (e0)) = (op (e2) (e3)))) -> (((op (e3) (e0)) = (e1))\/(((op (e3) (e1)) = (e1))\/(((op (e3) (e2)) = (e1))\/((op (e3) (e3)) = (e1))))) -> (~((op (e3) (e0)) = (op (e3) (e3)))) -> (~((op (e3) (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)) = (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 (e2) (e2)) = (op (e2) (e3)))) -> ((op (e2) (e2)) = (e1)) -> (~((op (e3) (e2)) = (op (e3) (e3)))) -> (~((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)) = (e0))\/(((op (e1) (e1)) = (e0))\/(((op (e2) (e1)) = (e0))\/((op (e3) (e1)) = (e0))))) -> (~((op (e0) (e3)) = (op (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) (e2)) = (e0)) -> (~((op (e0) (e2)) = (op (e3) (e2)))) -> (((op (e0) (e3)) = (e2))\/(((op (e1) (e3)) = (e2))\/(((op (e2) (e3)) = (e2))\/((op (e3) (e3)) = (e2))))) -> (~((op (e0) (e3)) = (e2))) -> ((op (e0) (e3)) = (e1)) -> (~((op (e2) (e1)) = (op (e2) (e3)))) -> ((op (e2) (e1)) = (e2)) -> (~((op (e3) (e3)) = (e2))) -> False). % 19.02/19.15 do 0 intro. intros zenon_H1ac zenon_Ha1 zenon_H130 zenon_H34 zenon_H5b zenon_He8 zenon_H71 zenon_H102 zenon_Hf3 zenon_H101 zenon_H173 zenon_H133 zenon_Hd8 zenon_H9d zenon_H6d zenon_Hf1 zenon_H62 zenon_Hef zenon_H1d5 zenon_H1f0 zenon_H57 zenon_H4a zenon_H245 zenon_Hc2 zenon_H208 zenon_H67 zenon_H48 zenon_H14f zenon_H145 zenon_H12e zenon_Hc3 zenon_H1c7 zenon_H1ca zenon_Hf7. % 19.02/19.15 apply (zenon_or_s _ _ zenon_H1ac); [ zenon_intro zenon_H44 | zenon_intro zenon_H1af ]. % 19.02/19.15 apply (zenon_L1195_); trivial. % 19.02/19.15 apply (zenon_or_s _ _ zenon_H1af); [ zenon_intro zenon_H1b1 | zenon_intro zenon_H1b0 ]. % 19.02/19.15 apply (zenon_L1197_); trivial. % 19.02/19.15 apply (zenon_or_s _ _ zenon_H1b0); [ zenon_intro zenon_H61 | zenon_intro zenon_H60 ]. % 19.02/19.15 apply (zenon_L342_); trivial. % 19.02/19.15 apply (zenon_L1191_); trivial. % 19.02/19.15 (* end of lemma zenon_L1198_ *) % 19.02/19.15 assert (zenon_L1199_ : (((op (e0) (e0)) = (e1))\/(((op (e0) (e1)) = (e1))\/(((op (e0) (e2)) = (e1))\/((op (e0) (e3)) = (e1))))) -> (~((op (e2) (e0)) = (op (e2) (e2)))) -> (~((op (e0) (e1)) = (op (e3) (e1)))) -> ((op (e0) (e2)) = (e0)) -> (((op (e0) (e3)) = (e0))\/(((op (e1) (e3)) = (e0))\/(((op (e2) (e3)) = (e0))\/((op (e3) (e3)) = (e0))))) -> (~((op (e0) (e2)) = (op (e0) (e3)))) -> (((op (e0) (e1)) = (e1))\/(((op (e1) (e1)) = (e1))\/(((op (e2) (e1)) = (e1))\/((op (e3) (e1)) = (e1))))) -> (~((op (e1) (e1)) = (e1))) -> (((op (e1) (e1)) = (e0))\/(((op (e1) (e1)) = (e1))\/(((op (e1) (e1)) = (e2))\/((op (e1) (e1)) = (e3))))) -> (~((op (e0) (e1)) = (op (e2) (e1)))) -> (((op (e0) (e1)) = (e0))\/(((op (e0) (e1)) = (e1))\/(((op (e0) (e1)) = (e2))\/((op (e0) (e1)) = (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) (e1)) = (op (e0) (e3)))) -> (~((op (e0) (e3)) = (op (e2) (e3)))) -> (~((e2) = (e3))) -> (((op (e2) (e3)) = (e0))\/(((op (e2) (e3)) = (e1))\/(((op (e2) (e3)) = (e2))\/((op (e2) (e3)) = (e3))))) -> (~((op (e2) (e3)) = (op (e3) (e3)))) -> (((op (e0) (e3)) = (e3))\/(((op (e1) (e3)) = (e3))\/(((op (e2) (e3)) = (e3))\/((op (e3) (e3)) = (e3))))) -> (~((op (e3) (e0)) = (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))))) -> (~((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)) = (op (e0) (e3)))) -> (~((op (e3) (e1)) = (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 (e2) (e2)) = (e1)) -> (~((op (e2) (e2)) = (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 (e3) (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) (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 (e1) (e1)) = (e2))) -> (((op (e0) (e1)) = (e2))\/(((op (e1) (e1)) = (e2))\/(((op (e2) (e1)) = (e2))\/((op (e3) (e1)) = (e2))))) -> (~((op (e0) (e3)) = (e2))) -> (~((op (e0) (e2)) = (e2))) -> (~((op (e0) (e1)) = (e2))) -> (((op (e1) (e0)) = (e0))\/(((op (e1) (e0)) = (e1))\/(((op (e1) (e0)) = (e2))\/((op (e1) (e0)) = (e3))))) -> (~((op (e1) (e0)) = (op (e3) (e0)))) -> (~((op (e1) (e0)) = (op (e2) (e0)))) -> (~((op (e1) (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). % 19.02/19.15 do 0 intro. intros zenon_H22d zenon_H52 zenon_H210 zenon_H48 zenon_H67 zenon_H208 zenon_H109 zenon_H10a zenon_H142 zenon_H17e zenon_H212 zenon_H7c zenon_He4 zenon_H1d zenon_H54 zenon_He2 zenon_H12b zenon_H11f zenon_Hf3 zenon_H136 zenon_H71 zenon_H17b zenon_H2f zenon_Ha8 zenon_H235 zenon_H189 zenon_H194 zenon_He8 zenon_H130 zenon_H62 zenon_Hf1 zenon_H6d zenon_Hd8 zenon_H145 zenon_H102 zenon_H101 zenon_H1c7 zenon_Hf7 zenon_H133 zenon_Hc2 zenon_H20c zenon_H1d8 zenon_H12e zenon_H1fd zenon_H26d zenon_H25e zenon_H1fa zenon_H201 zenon_H177 zenon_H183 zenon_H44 zenon_Ha1. % 19.02/19.15 apply (zenon_or_s _ _ zenon_H22d); [ zenon_intro zenon_H7a | zenon_intro zenon_H22e ]. % 19.02/19.15 apply (zenon_L1059_); trivial. % 19.02/19.15 apply (zenon_or_s _ _ zenon_H22e); [ zenon_intro zenon_Ha0 | zenon_intro zenon_H22f ]. % 19.02/19.15 apply (zenon_or_s _ _ zenon_H235); [ zenon_intro zenon_H7a | zenon_intro zenon_H236 ]. % 19.02/19.15 apply (zenon_L1059_); trivial. % 19.02/19.15 apply (zenon_or_s _ _ zenon_H236); [ zenon_intro zenon_H9d | zenon_intro zenon_H237 ]. % 19.02/19.15 apply (zenon_or_s _ _ zenon_H1d8); [ zenon_intro zenon_H10f | zenon_intro zenon_H1d9 ]. % 19.02/19.15 exact (zenon_H26d zenon_H10f). % 19.02/19.15 apply (zenon_or_s _ _ zenon_H1d9); [ zenon_intro zenon_H110 | zenon_intro zenon_H1da ]. % 19.02/19.15 exact (zenon_H20c zenon_H110). % 19.02/19.15 apply (zenon_or_s _ _ zenon_H1da); [ zenon_intro zenon_H1ca | zenon_intro zenon_H14d ]. % 19.02/19.15 apply (zenon_L1184_); trivial. % 19.02/19.15 exact (zenon_H194 zenon_H14d). % 19.02/19.15 apply (zenon_or_s _ _ zenon_H237); [ zenon_intro zenon_Hed | zenon_intro zenon_Hac ]. % 19.02/19.15 apply (zenon_L93_); trivial. % 19.02/19.15 apply (zenon_L41_); trivial. % 19.02/19.15 apply (zenon_or_s _ _ zenon_H22f); [ zenon_intro zenon_H122 | zenon_intro zenon_Hc3 ]. % 19.02/19.15 apply (zenon_L246_); trivial. % 19.02/19.15 apply (zenon_or_s _ _ zenon_H235); [ zenon_intro zenon_H7a | zenon_intro zenon_H236 ]. % 19.02/19.15 apply (zenon_L140_); trivial. % 19.02/19.15 apply (zenon_or_s _ _ zenon_H236); [ zenon_intro zenon_H9d | zenon_intro zenon_H237 ]. % 19.02/19.15 apply (zenon_or_s _ _ zenon_H1d8); [ zenon_intro zenon_H10f | zenon_intro zenon_H1d9 ]. % 19.02/19.15 exact (zenon_H26d zenon_H10f). % 19.02/19.15 apply (zenon_or_s _ _ zenon_H1d9); [ zenon_intro zenon_H110 | zenon_intro zenon_H1da ]. % 19.02/19.15 exact (zenon_H20c zenon_H110). % 19.02/19.15 apply (zenon_or_s _ _ zenon_H1da); [ zenon_intro zenon_H1ca | zenon_intro zenon_H14d ]. % 19.02/19.15 apply (zenon_L1195_); trivial. % 19.02/19.15 exact (zenon_H194 zenon_H14d). % 19.02/19.15 apply (zenon_or_s _ _ zenon_H237); [ zenon_intro zenon_Hed | zenon_intro zenon_Hac ]. % 19.02/19.15 apply (zenon_L1120_); trivial. % 19.02/19.15 apply (zenon_L41_); trivial. % 19.02/19.15 (* end of lemma zenon_L1199_ *) % 19.02/19.15 assert (zenon_L1200_ : ((op (e2) (e2)) = (e3)) -> (~((op (e0) (e0)) = (e0))) -> (((op (e1) (e0)) = (e1))\/(((op (e1) (e1)) = (e1))\/(((op (e1) (e2)) = (e1))\/((op (e1) (e3)) = (e1))))) -> (~((op (e0) (e1)) = (e2))) -> (~((op (e1) (e1)) = (e2))) -> (((op (e0) (e3)) = (e2))\/(((op (e1) (e3)) = (e2))\/(((op (e2) (e3)) = (e2))\/((op (e3) (e3)) = (e2))))) -> (~((op (e2) (e1)) = (op (e2) (e3)))) -> (~((e1) = (e2))) -> (~((op (e0) (e3)) = (e2))) -> (~((op (e3) (e1)) = (e2))) -> (((op (e0) (e1)) = (e2))\/(((op (e1) (e1)) = (e2))\/(((op (e2) (e1)) = (e2))\/((op (e3) (e1)) = (e2))))) -> ((op (e2) (e2)) = (e1)) -> (~((op (e1) (e2)) = (op (e2) (e2)))) -> (~((op (e1) (e1)) = (e1))) -> (~((e0) = (e1))) -> (((op (e2) (e0)) = (e0))\/(((op (e2) (e1)) = (e0))\/(((op (e2) (e2)) = (e0))\/((op (e2) (e3)) = (e0))))) -> (~((op (e2) (e2)) = (op (e2) (e3)))) -> (~((op (e0) (e2)) = (op (e2) (e2)))) -> (~((op (e0) (e2)) = (op (e0) (e3)))) -> ((op (e0) (e2)) = (e0)) -> (~((op (e0) (e1)) = (op (e3) (e1)))) -> (~((op (e0) (e1)) = (op (e0) (e3)))) -> (~((op (e0) (e1)) = (op (e2) (e1)))) -> (((op (e1) (e1)) = (e0))\/(((op (e1) (e1)) = (e1))\/(((op (e1) (e1)) = (e2))\/((op (e1) (e1)) = (e3))))) -> (((op (e0) (e1)) = (e0))\/(((op (e0) (e1)) = (e1))\/(((op (e0) (e1)) = (e2))\/((op (e0) (e1)) = (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) (e0)) = (op (e1) (e3)))) -> (~((op (e2) (e3)) = (op (e3) (e3)))) -> (~((op (e3) (e0)) = (op (e3) (e3)))) -> (((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 (e1) (e1)) = (e1))\/(((op (e2) (e1)) = (e1))\/((op (e3) (e1)) = (e1))))) -> (((op (e2) (e3)) = (e0))\/(((op (e2) (e3)) = (e1))\/(((op (e2) (e3)) = (e2))\/((op (e2) (e3)) = (e3))))) -> (~((op (e0) (e3)) = (op (e2) (e3)))) -> (~((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) (e3)) = (e3))\/(((op (e1) (e3)) = (e3))\/(((op (e2) (e3)) = (e3))\/((op (e3) (e3)) = (e3))))) -> (((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 (e2) (e0)) = (op (e3) (e0)))) -> (~((op (e2) (e0)) = (op (e2) (e3)))) -> (((op (e0) (e1)) = (e0))\/(((op (e1) (e1)) = (e0))\/(((op (e2) (e1)) = (e0))\/((op (e3) (e1)) = (e0))))) -> (~((op (e2) (e0)) = (op (e2) (e1)))) -> (~((op (e1) (e1)) = (op (e1) (e3)))) -> (~((op (e0) (e1)) = (op (e0) (e2)))) -> (~((op (e2) (e0)) = (e2))) -> (~((op (e2) (e2)) = (e2))) -> (~((op (e0) (e3)) = (op (e3) (e3)))) -> (((op (e2) (e0)) = (e2))\/(((op (e2) (e1)) = (e2))\/(((op (e2) (e2)) = (e2))\/((op (e2) (e3)) = (e2))))) -> (~((op (e0) (e2)) = (op (e3) (e2)))) -> (((op (e3) (e0)) = (e0))\/(((op (e3) (e1)) = (e0))\/(((op (e3) (e2)) = (e0))\/((op (e3) (e3)) = (e0))))) -> ((~((op (e1) (e3)) = (e2)))\/((op (e1) (e2)) = (e3))) -> (~((e1) = (e3))) -> ((~((op (e2) (e1)) = (e2)))\/((op (e2) (e2)) = (e1))) -> ((~((op (e3) (e2)) = (e2)))\/((op (e3) (e2)) = (e2))) -> (((op (e0) (e0)) = (e0))\/(((op (e1) (e0)) = (e0))\/(((op (e2) (e0)) = (e0))\/((op (e3) (e0)) = (e0))))) -> (((op (e2) (e1)) = (e0))\/(((op (e2) (e1)) = (e1))\/(((op (e2) (e1)) = (e2))\/((op (e2) (e1)) = (e3))))) -> (((op (e0) (e0)) = (e1))\/(((op (e1) (e0)) = (e1))\/(((op (e2) (e0)) = (e1))\/((op (e3) (e0)) = (e1))))) -> (~((op (e1) (e2)) = (op (e3) (e2)))) -> (~((op (e0) (e2)) = (op (e1) (e2)))) -> (~((op (e3) (e0)) = (op (e3) (e1)))) -> (((op (e2) (e0)) = (e1))\/(((op (e2) (e1)) = (e1))\/(((op (e2) (e2)) = (e1))\/((op (e2) (e3)) = (e1))))) -> (~((op (e3) (e1)) = (op (e3) (e2)))) -> (((op (e1) (e0)) = (e0))\/(((op (e1) (e1)) = (e0))\/(((op (e1) (e2)) = (e0))\/((op (e1) (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))))) -> (~((e0) = (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 (e3) (e0)))) -> (~((op (e1) (e0)) = (op (e2) (e0)))) -> (~((op (e1) (e0)) = (e2))) -> (((op (e1) (e0)) = (e0))\/(((op (e1) (e0)) = (e1))\/(((op (e1) (e0)) = (e2))\/((op (e1) (e0)) = (e3))))) -> (~((op (e1) (e0)) = (op (e1) (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) (e3)) = (e2)))\/((op (e3) (e2)) = (e3))) -> (((op (e0) (e2)) = (e2))\/(((op (e1) (e2)) = (e2))\/(((op (e2) (e2)) = (e2))\/((op (e3) (e2)) = (e2))))) -> ((~((op (e2) (e3)) = (e2)))\/((op (e2) (e2)) = (e3))) -> ((~((op (e2) (e0)) = (e2)))\/((op (e2) (e2)) = (e0))) -> ((~((op (e1) (e2)) = (e2)))\/((op (e1) (e2)) = (e2))) -> (~((op (e0) (e2)) = (e2))) -> (((op (e0) (e0)) = (e2))\/(((op (e0) (e1)) = (e2))\/(((op (e0) (e2)) = (e2))\/((op (e0) (e3)) = (e2))))) -> (~((op (e0) (e0)) = (op (e0) (e3)))) -> (~((op (e2) (e0)) = (op (e2) (e2)))) -> False). % 19.02/19.15 do 0 intro. intros zenon_Haa zenon_H3f zenon_H128 zenon_H26d zenon_H20c zenon_H145 zenon_H1c7 zenon_H7c zenon_H12e zenon_H194 zenon_H1d8 zenon_Hf1 zenon_H2b zenon_H10a zenon_Ha1 zenon_H2f zenon_H6d zenon_Ha8 zenon_H208 zenon_H48 zenon_H210 zenon_H54 zenon_H17e zenon_H142 zenon_H212 zenon_H62 zenon_H102 zenon_H101 zenon_Hd8 zenon_Hf3 zenon_H71 zenon_H133 zenon_H130 zenon_H109 zenon_H11f zenon_He2 zenon_H12b zenon_He4 zenon_H1d zenon_H136 zenon_He8 zenon_H67 zenon_H17b zenon_H5b zenon_H245 zenon_H1f0 zenon_H57 zenon_H4a zenon_Hef zenon_H173 zenon_Hc2 zenon_H1d5 zenon_H14f zenon_H1ac zenon_H279 zenon_H95 zenon_H271 zenon_H273 zenon_H3e zenon_H1cc zenon_H235 zenon_H115 zenon_H195 zenon_H1cf zenon_H106 zenon_H1a4 zenon_H22 zenon_H124 zenon_Hd5 zenon_Hdf zenon_H149 zenon_Hdb zenon_H18c zenon_H1fa zenon_H201 zenon_H177 zenon_H25e zenon_H45 zenon_H22d zenon_H18f zenon_H278 zenon_H172 zenon_H277 zenon_H276 zenon_H275 zenon_H1fd zenon_H183 zenon_H189 zenon_H52. % 19.02/19.15 apply (zenon_or_s _ _ zenon_H278); [ zenon_intro zenon_Hf7 | zenon_intro zenon_H163 ]. % 19.02/19.15 apply (zenon_or_s _ _ zenon_H3e); [ zenon_intro zenon_H42 | zenon_intro zenon_H41 ]. % 19.02/19.15 exact (zenon_H3f zenon_H42). % 19.02/19.15 apply (zenon_or_s _ _ zenon_H41); [ zenon_intro zenon_H27 | zenon_intro zenon_H43 ]. % 19.02/19.15 apply (zenon_L1177_); trivial. % 19.02/19.15 apply (zenon_or_s _ _ zenon_H43); [ zenon_intro zenon_H34 | zenon_intro zenon_H44 ]. % 19.02/19.15 apply (zenon_or_s _ _ zenon_H22d); [ zenon_intro zenon_H7a | zenon_intro zenon_H22e ]. % 19.02/19.15 apply (zenon_L1059_); trivial. % 19.02/19.15 apply (zenon_or_s _ _ zenon_H22e); [ zenon_intro zenon_Ha0 | zenon_intro zenon_H22f ]. % 19.02/19.15 apply (zenon_or_s _ _ zenon_H235); [ zenon_intro zenon_H7a | zenon_intro zenon_H236 ]. % 19.02/19.15 apply (zenon_L1059_); trivial. % 19.02/19.15 apply (zenon_or_s _ _ zenon_H236); [ zenon_intro zenon_H9d | zenon_intro zenon_H237 ]. % 19.02/19.15 apply (zenon_or_s _ _ zenon_H1d8); [ zenon_intro zenon_H10f | zenon_intro zenon_H1d9 ]. % 19.02/19.15 exact (zenon_H26d zenon_H10f). % 19.02/19.15 apply (zenon_or_s _ _ zenon_H1d9); [ zenon_intro zenon_H110 | zenon_intro zenon_H1da ]. % 19.02/19.15 exact (zenon_H20c zenon_H110). % 19.02/19.15 apply (zenon_or_s _ _ zenon_H1da); [ zenon_intro zenon_H1ca | zenon_intro zenon_H14d ]. % 19.02/19.15 apply (zenon_or_s _ _ zenon_H1ac); [ zenon_intro zenon_H44 | zenon_intro zenon_H1af ]. % 19.02/19.15 apply (zenon_L1184_); trivial. % 19.02/19.15 apply (zenon_or_s _ _ zenon_H1af); [ zenon_intro zenon_H1b1 | zenon_intro zenon_H1b0 ]. % 19.02/19.15 apply (zenon_L1190_); trivial. % 19.02/19.15 apply (zenon_or_s _ _ zenon_H1b0); [ zenon_intro zenon_H61 | zenon_intro zenon_H60 ]. % 19.02/19.15 apply (zenon_L342_); trivial. % 19.02/19.15 apply (zenon_L1194_); trivial. % 19.02/19.15 exact (zenon_H194 zenon_H14d). % 19.02/19.15 apply (zenon_or_s _ _ zenon_H237); [ zenon_intro zenon_Hed | zenon_intro zenon_Hac ]. % 19.02/19.15 apply (zenon_L214_); trivial. % 19.02/19.15 apply (zenon_or_s _ _ zenon_H128); [ zenon_intro zenon_H9d | zenon_intro zenon_H129 ]. % 19.02/19.15 apply (zenon_or_s _ _ zenon_H1d8); [ zenon_intro zenon_H10f | zenon_intro zenon_H1d9 ]. % 19.02/19.15 exact (zenon_H26d zenon_H10f). % 19.02/19.15 apply (zenon_or_s _ _ zenon_H1d9); [ zenon_intro zenon_H110 | zenon_intro zenon_H1da ]. % 19.02/19.15 exact (zenon_H20c zenon_H110). % 19.02/19.15 apply (zenon_or_s _ _ zenon_H1da); [ zenon_intro zenon_H1ca | zenon_intro zenon_H14d ]. % 19.02/19.15 apply (zenon_or_s _ _ zenon_H1ac); [ zenon_intro zenon_H44 | zenon_intro zenon_H1af ]. % 19.02/19.15 apply (zenon_L41_); trivial. % 19.02/19.15 apply (zenon_or_s _ _ zenon_H1af); [ zenon_intro zenon_H1b1 | zenon_intro zenon_H1b0 ]. % 19.02/19.15 apply (zenon_L1067_); trivial. % 19.02/19.15 apply (zenon_or_s _ _ zenon_H1b0); [ zenon_intro zenon_H61 | zenon_intro zenon_H60 ]. % 19.02/19.15 apply (zenon_L342_); trivial. % 19.02/19.15 apply (zenon_L1194_); trivial. % 19.02/19.15 exact (zenon_H194 zenon_H14d). % 19.02/19.15 apply (zenon_or_s _ _ zenon_H129); [ zenon_intro zenon_H10d | zenon_intro zenon_H12a ]. % 19.02/19.15 exact (zenon_H10a zenon_H10d). % 19.02/19.15 apply (zenon_or_s _ _ zenon_H12a); [ zenon_intro zenon_Hf0 | zenon_intro zenon_Hd6 ]. % 19.02/19.15 apply (zenon_L1101_); trivial. % 19.02/19.15 apply (zenon_L1176_); trivial. % 19.02/19.15 apply (zenon_or_s _ _ zenon_H22f); [ zenon_intro zenon_H122 | zenon_intro zenon_Hc3 ]. % 19.02/19.15 apply (zenon_L246_); trivial. % 19.02/19.15 apply (zenon_or_s _ _ zenon_H128); [ zenon_intro zenon_H9d | zenon_intro zenon_H129 ]. % 19.02/19.15 apply (zenon_or_s _ _ zenon_H1d8); [ zenon_intro zenon_H10f | zenon_intro zenon_H1d9 ]. % 19.02/19.15 exact (zenon_H26d zenon_H10f). % 19.02/19.15 apply (zenon_or_s _ _ zenon_H1d9); [ zenon_intro zenon_H110 | zenon_intro zenon_H1da ]. % 19.02/19.15 exact (zenon_H20c zenon_H110). % 19.02/19.15 apply (zenon_or_s _ _ zenon_H1da); [ zenon_intro zenon_H1ca | zenon_intro zenon_H14d ]. % 19.02/19.15 apply (zenon_L1198_); trivial. % 19.02/19.15 exact (zenon_H194 zenon_H14d). % 19.02/19.15 apply (zenon_or_s _ _ zenon_H129); [ zenon_intro zenon_H10d | zenon_intro zenon_H12a ]. % 19.02/19.15 exact (zenon_H10a zenon_H10d). % 19.02/19.15 apply (zenon_or_s _ _ zenon_H12a); [ zenon_intro zenon_Hf0 | zenon_intro zenon_Hd6 ]. % 19.02/19.15 apply (zenon_L1101_); trivial. % 19.02/19.15 apply (zenon_L79_); trivial. % 19.02/19.15 apply (zenon_L1199_); trivial. % 19.02/19.15 apply (zenon_L180_); trivial. % 19.02/19.15 (* end of lemma zenon_L1200_ *) % 19.02/19.15 assert (zenon_L1201_ : (((op (e0) (e0)) = (e1))\/(((op (e1) (e0)) = (e1))\/(((op (e2) (e0)) = (e1))\/((op (e3) (e0)) = (e1))))) -> (~((op (e0) (e3)) = (e2))) -> (~((op (e0) (e2)) = (e2))) -> (~((op (e0) (e1)) = (e2))) -> (~((e1) = (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) (e2)) = (e1)) -> (~((op (e2) (e0)) = (op (e2) (e2)))) -> (~((op (e3) (e0)) = (op (e3) (e2)))) -> ((op (e3) (e2)) = (e1)) -> False). % 19.02/19.15 do 0 intro. intros zenon_H235 zenon_H12e zenon_H1fd zenon_H26d zenon_H7c zenon_H183 zenon_Ha1 zenon_H27 zenon_Hf1 zenon_H52 zenon_H6f zenon_Hba. % 19.02/19.15 apply (zenon_or_s _ _ zenon_H235); [ zenon_intro zenon_H7a | zenon_intro zenon_H236 ]. % 19.02/19.15 apply (zenon_L1059_); trivial. % 19.02/19.15 apply (zenon_or_s _ _ zenon_H236); [ zenon_intro zenon_H9d | zenon_intro zenon_H237 ]. % 19.02/19.15 apply (zenon_L262_); trivial. % 19.02/19.15 apply (zenon_or_s _ _ zenon_H237); [ zenon_intro zenon_Hed | zenon_intro zenon_Hac ]. % 19.02/19.15 apply (zenon_L93_); trivial. % 19.02/19.15 apply (zenon_L249_); trivial. % 19.02/19.15 (* end of lemma zenon_L1201_ *) % 19.02/19.15 assert (zenon_L1202_ : ((~((op (e3) (e3)) = (e2)))\/((op (e3) (e2)) = (e3))) -> (~((op (e2) (e2)) = (op (e3) (e2)))) -> (~((op (e0) (e0)) = (e0))) -> (((op (e0) (e0)) = (e1))\/(((op (e1) (e0)) = (e1))\/(((op (e2) (e0)) = (e1))\/((op (e3) (e0)) = (e1))))) -> ((op (e3) (e2)) = (e1)) -> (~((op (e3) (e0)) = (op (e3) (e2)))) -> ((op (e2) (e2)) = (e1)) -> (~((op (e2) (e0)) = (op (e2) (e2)))) -> (~((e0) = (e1))) -> (~((e1) = (e2))) -> (~((op (e0) (e1)) = (e2))) -> (~((op (e0) (e2)) = (e2))) -> (~((op (e0) (e3)) = (e2))) -> (((op (e0) (e0)) = (e2))\/(((op (e0) (e1)) = (e2))\/(((op (e0) (e2)) = (e2))\/((op (e0) (e3)) = (e2))))) -> (((op (e0) (e1)) = (e1))\/(((op (e1) (e1)) = (e1))\/(((op (e2) (e1)) = (e1))\/((op (e3) (e1)) = (e1))))) -> (~((op (e3) (e1)) = (op (e3) (e3)))) -> (~((op (e1) (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 (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 (e0) (e1)) = (e0))\/(((op (e0) (e1)) = (e1))\/(((op (e0) (e1)) = (e2))\/((op (e0) (e1)) = (e3))))) -> (~((op (e0) (e1)) = (op (e2) (e1)))) -> ((op (e0) (e2)) = (e0)) -> (~((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)) = (e1))) -> (~((op (e0) (e1)) = (op (e0) (e3)))) -> ((op (e2) (e2)) = (e3)) -> (((op (e0) (e1)) = (e0))\/(((op (e1) (e1)) = (e0))\/(((op (e2) (e1)) = (e0))\/((op (e3) (e1)) = (e0))))) -> (~((op (e2) (e0)) = (e2))) -> (((op (e0) (e3)) = (e1))\/(((op (e1) (e3)) = (e1))\/(((op (e2) (e3)) = (e1))\/((op (e3) (e3)) = (e1))))) -> (~((op (e2) (e2)) = (op (e2) (e3)))) -> (~((op (e1) (e0)) = (op (e1) (e3)))) -> (~((op (e2) (e2)) = (e2))) -> (~((op (e2) (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 (e2) (e0)) = (op (e2) (e1)))) -> (~((op (e1) (e1)) = (op (e1) (e3)))) -> (((op (e1) (e0)) = (e0))\/(((op (e1) (e1)) = (e0))\/(((op (e1) (e2)) = (e0))\/((op (e1) (e3)) = (e0))))) -> (~((op (e0) (e0)) = (op (e0) (e3)))) -> (((op (e1) (e0)) = (e0))\/(((op (e1) (e0)) = (e1))\/(((op (e1) (e0)) = (e2))\/((op (e1) (e0)) = (e3))))) -> (~((op (e1) (e0)) = (e2))) -> (~((op (e1) (e0)) = (op (e2) (e0)))) -> (~((op (e1) (e0)) = (op (e3) (e0)))) -> (~((op (e3) (e0)) = (op (e3) (e1)))) -> (((op (e1) (e1)) = (e0))\/(((op (e1) (e1)) = (e1))\/(((op (e1) (e1)) = (e2))\/((op (e1) (e1)) = (e3))))) -> (~((e0) = (e3))) -> (((op (e0) (e0)) = (e0))\/(((op (e1) (e0)) = (e0))\/(((op (e2) (e0)) = (e0))\/((op (e3) (e0)) = (e0))))) -> False). % 19.02/19.15 do 0 intro. intros zenon_H278 zenon_H18f zenon_H3f zenon_H235 zenon_Hba zenon_H6f zenon_Hf1 zenon_H52 zenon_Ha1 zenon_H7c zenon_H26d zenon_H1fd zenon_H12e zenon_H183 zenon_H109 zenon_H130 zenon_H20c zenon_H145 zenon_H1c7 zenon_H62 zenon_H102 zenon_H101 zenon_H212 zenon_H17e zenon_H48 zenon_H4a zenon_H1d8 zenon_H10a zenon_H54 zenon_Haa zenon_H245 zenon_Hef zenon_H133 zenon_H6d zenon_Hd8 zenon_H173 zenon_Hf3 zenon_Hc2 zenon_H1d5 zenon_H1f0 zenon_H57 zenon_H22 zenon_H189 zenon_H25e zenon_H177 zenon_H201 zenon_H1fa zenon_H1cf zenon_H142 zenon_H9a zenon_H3e. % 19.02/19.15 apply (zenon_or_s _ _ zenon_H278); [ zenon_intro zenon_Hf7 | zenon_intro zenon_H163 ]. % 19.02/19.15 apply (zenon_or_s _ _ zenon_H3e); [ zenon_intro zenon_H42 | zenon_intro zenon_H41 ]. % 19.02/19.15 exact (zenon_H3f zenon_H42). % 19.02/19.15 apply (zenon_or_s _ _ zenon_H41); [ zenon_intro zenon_H27 | zenon_intro zenon_H43 ]. % 19.02/19.15 apply (zenon_L1201_); trivial. % 19.02/19.15 apply (zenon_or_s _ _ zenon_H43); [ zenon_intro zenon_H34 | zenon_intro zenon_H44 ]. % 19.02/19.15 apply (zenon_or_s _ _ zenon_H235); [ zenon_intro zenon_H7a | zenon_intro zenon_H236 ]. % 19.02/19.15 apply (zenon_L1059_); trivial. % 19.02/19.15 apply (zenon_or_s _ _ zenon_H236); [ zenon_intro zenon_H9d | zenon_intro zenon_H237 ]. % 19.02/19.15 apply (zenon_L1113_); trivial. % 19.02/19.15 apply (zenon_or_s _ _ zenon_H237); [ zenon_intro zenon_Hed | zenon_intro zenon_Hac ]. % 19.02/19.15 apply (zenon_L93_); trivial. % 19.02/19.15 apply (zenon_L249_); trivial. % 19.02/19.15 apply (zenon_or_s _ _ zenon_H235); [ zenon_intro zenon_H7a | zenon_intro zenon_H236 ]. % 19.02/19.15 apply (zenon_L1059_); trivial. % 19.02/19.15 apply (zenon_or_s _ _ zenon_H236); [ zenon_intro zenon_H9d | zenon_intro zenon_H237 ]. % 19.02/19.15 apply (zenon_L1122_); trivial. % 19.02/19.15 apply (zenon_or_s _ _ zenon_H237); [ zenon_intro zenon_Hed | zenon_intro zenon_Hac ]. % 19.02/19.15 apply (zenon_L93_); trivial. % 19.02/19.15 apply (zenon_L249_); trivial. % 19.02/19.15 apply (zenon_L180_); trivial. % 19.02/19.15 (* end of lemma zenon_L1202_ *) % 19.02/19.15 assert (zenon_L1203_ : ((~((op (e3) (e1)) = (e2)))\/((op (e3) (e2)) = (e1))) -> (~((e0) = (e3))) -> (~((op (e3) (e0)) = (op (e3) (e2)))) -> (~((op (e2) (e0)) = (op (e2) (e2)))) -> (~((op (e0) (e0)) = (op (e0) (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 (e1) (e2)) = (e2))) -> ((~((op (e2) (e0)) = (e2)))\/((op (e2) (e2)) = (e0))) -> ((~((op (e2) (e3)) = (e2)))\/((op (e2) (e2)) = (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 (e2) (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) (e1)))) -> (((op (e1) (e0)) = (e0))\/(((op (e1) (e0)) = (e1))\/(((op (e1) (e0)) = (e2))\/((op (e1) (e0)) = (e3))))) -> (~((op (e1) (e0)) = (e2))) -> (~((op (e1) (e0)) = (op (e2) (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) (e3)) = (op (e2) (e3)))) -> (~((e0) = (e2))) -> (((op (e1) (e3)) = (e0))\/(((op (e1) (e3)) = (e1))\/(((op (e1) (e3)) = (e2))\/((op (e1) (e3)) = (e3))))) -> (~((op (e1) (e3)) = (op (e3) (e3)))) -> (~((op (e1) (e2)) = (op (e1) (e3)))) -> (((op (e1) (e0)) = (e0))\/(((op (e1) (e1)) = (e0))\/(((op (e1) (e2)) = (e0))\/((op (e1) (e3)) = (e0))))) -> (~((op (e3) (e1)) = (op (e3) (e2)))) -> (((op (e2) (e0)) = (e1))\/(((op (e2) (e1)) = (e1))\/(((op (e2) (e2)) = (e1))\/((op (e2) (e3)) = (e1))))) -> (~((op (e3) (e0)) = (op (e3) (e1)))) -> (~((op (e0) (e2)) = (op (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) (e1)) = (e0))\/(((op (e2) (e1)) = (e1))\/(((op (e2) (e1)) = (e2))\/((op (e2) (e1)) = (e3))))) -> (((op (e0) (e0)) = (e0))\/(((op (e1) (e0)) = (e0))\/(((op (e2) (e0)) = (e0))\/((op (e3) (e0)) = (e0))))) -> ((~((op (e3) (e2)) = (e2)))\/((op (e3) (e2)) = (e2))) -> ((~((op (e2) (e1)) = (e2)))\/((op (e2) (e2)) = (e1))) -> (~((e1) = (e3))) -> ((~((op (e1) (e3)) = (e2)))\/((op (e1) (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 (e2) (e0)) = (e2))\/(((op (e2) (e1)) = (e2))\/(((op (e2) (e2)) = (e2))\/((op (e2) (e3)) = (e2))))) -> (~((op (e0) (e3)) = (op (e3) (e3)))) -> (~((op (e2) (e2)) = (e2))) -> (~((op (e2) (e0)) = (e2))) -> (~((op (e0) (e1)) = (op (e0) (e2)))) -> (~((op (e1) (e1)) = (op (e1) (e3)))) -> (~((op (e2) (e0)) = (op (e2) (e1)))) -> (((op (e0) (e1)) = (e0))\/(((op (e1) (e1)) = (e0))\/(((op (e2) (e1)) = (e0))\/((op (e3) (e1)) = (e0))))) -> (~((op (e2) (e0)) = (op (e2) (e3)))) -> (~((op (e2) (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 (e0) (e3)) = (e3))\/(((op (e1) (e3)) = (e3))\/(((op (e2) (e3)) = (e3))\/((op (e3) (e3)) = (e3))))) -> (~((op (e0) (e3)) = (op (e1) (e3)))) -> (((op (e0) (e3)) = (e0))\/(((op (e0) (e3)) = (e1))\/(((op (e0) (e3)) = (e2))\/((op (e0) (e3)) = (e3))))) -> (~((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)) = (e1))\/(((op (e1) (e1)) = (e1))\/(((op (e2) (e1)) = (e1))\/((op (e3) (e1)) = (e1))))) -> (~((op (e3) (e1)) = (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 (e2) (e3)) = (op (e3) (e3)))) -> (~((op (e1) (e0)) = (op (e1) (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 (e0) (e1)) = (e0))\/(((op (e0) (e1)) = (e1))\/(((op (e0) (e1)) = (e2))\/((op (e0) (e1)) = (e3))))) -> (((op (e1) (e1)) = (e0))\/(((op (e1) (e1)) = (e1))\/(((op (e1) (e1)) = (e2))\/((op (e1) (e1)) = (e3))))) -> (~((op (e0) (e1)) = (op (e2) (e1)))) -> (~((op (e0) (e1)) = (op (e0) (e3)))) -> (~((op (e0) (e1)) = (op (e3) (e1)))) -> ((op (e0) (e2)) = (e0)) -> (~((op (e0) (e2)) = (op (e0) (e3)))) -> (~((op (e0) (e2)) = (op (e2) (e2)))) -> (~((op (e2) (e2)) = (op (e2) (e3)))) -> (((op (e2) (e0)) = (e0))\/(((op (e2) (e1)) = (e0))\/(((op (e2) (e2)) = (e0))\/((op (e2) (e3)) = (e0))))) -> (~((e0) = (e1))) -> (~((op (e1) (e1)) = (e1))) -> (~((op (e1) (e2)) = (op (e2) (e2)))) -> ((op (e2) (e2)) = (e1)) -> (((op (e0) (e1)) = (e2))\/(((op (e1) (e1)) = (e2))\/(((op (e2) (e1)) = (e2))\/((op (e3) (e1)) = (e2))))) -> (~((op (e0) (e3)) = (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))))) -> (~((op (e1) (e1)) = (e2))) -> (~((op (e0) (e1)) = (e2))) -> (((op (e1) (e0)) = (e1))\/(((op (e1) (e1)) = (e1))\/(((op (e1) (e2)) = (e1))\/((op (e1) (e3)) = (e1))))) -> (~((op (e0) (e0)) = (e0))) -> ((op (e2) (e2)) = (e3)) -> False). % 19.02/19.15 do 0 intro. intros zenon_H26f zenon_H9a zenon_H6f zenon_H52 zenon_H189 zenon_H183 zenon_H1fd zenon_H275 zenon_H276 zenon_H277 zenon_H172 zenon_H278 zenon_H18f zenon_H22d zenon_H45 zenon_H25e zenon_H177 zenon_H201 zenon_H1fa zenon_H18c zenon_Hdb zenon_H149 zenon_Hdf zenon_Hd5 zenon_H124 zenon_H22 zenon_H1a4 zenon_H106 zenon_H1cf zenon_H195 zenon_H115 zenon_H235 zenon_H1cc zenon_H3e zenon_H273 zenon_H271 zenon_H95 zenon_H279 zenon_H1ac zenon_H14f zenon_H1d5 zenon_Hc2 zenon_H173 zenon_Hef zenon_H4a zenon_H57 zenon_H1f0 zenon_H245 zenon_H5b zenon_H17b zenon_H67 zenon_He8 zenon_H136 zenon_H1d zenon_He4 zenon_H12b zenon_He2 zenon_H11f zenon_H109 zenon_H130 zenon_H133 zenon_H71 zenon_Hf3 zenon_Hd8 zenon_H101 zenon_H102 zenon_H62 zenon_H212 zenon_H142 zenon_H17e zenon_H54 zenon_H210 zenon_H48 zenon_H208 zenon_Ha8 zenon_H6d zenon_H2f zenon_Ha1 zenon_H10a zenon_H2b zenon_Hf1 zenon_H1d8 zenon_H12e zenon_H7c zenon_H1c7 zenon_H145 zenon_H20c zenon_H26d zenon_H128 zenon_H3f zenon_Haa. % 19.02/19.15 apply (zenon_or_s _ _ zenon_H26f); [ zenon_intro zenon_H194 | zenon_intro zenon_Hba ]. % 19.02/19.15 apply (zenon_L1200_); trivial. % 19.02/19.15 apply (zenon_L1202_); trivial. % 19.02/19.15 (* end of lemma zenon_L1203_ *) % 19.02/19.15 assert (zenon_L1204_ : (((op (e0) (e1)) = (e2))\/(((op (e1) (e1)) = (e2))\/(((op (e2) (e1)) = (e2))\/((op (e3) (e1)) = (e2))))) -> (~((op (e1) (e1)) = (e2))) -> (~((op (e0) (e1)) = (e2))) -> (~((op (e0) (e0)) = (e0))) -> (~((op (e0) (e0)) = (op (e0) (e3)))) -> (~((e0) = (e1))) -> (~((op (e1) (e0)) = (op (e1) (e1)))) -> (((op (e1) (e0)) = (e1))\/(((op (e1) (e1)) = (e1))\/(((op (e1) (e2)) = (e1))\/((op (e1) (e3)) = (e1))))) -> (((op (e1) (e0)) = (e3))\/(((op (e1) (e1)) = (e3))\/(((op (e1) (e2)) = (e3))\/((op (e1) (e3)) = (e3))))) -> ((op (e1) (e2)) = (e2)) -> ((~((op (e1) (e3)) = (e2)))\/((op (e1) (e2)) = (e3))) -> (~((e1) = (e3))) -> ((~((op (e2) (e1)) = (e2)))\/((op (e2) (e2)) = (e1))) -> ((~((op (e3) (e2)) = (e2)))\/((op (e3) (e2)) = (e2))) -> (((op (e0) (e0)) = (e0))\/(((op (e1) (e0)) = (e0))\/(((op (e2) (e0)) = (e0))\/((op (e3) (e0)) = (e0))))) -> (~((op (e2) (e0)) = (op (e2) (e1)))) -> (((op (e2) (e1)) = (e0))\/(((op (e2) (e1)) = (e1))\/(((op (e2) (e1)) = (e2))\/((op (e2) (e1)) = (e3))))) -> (((op (e0) (e0)) = (e1))\/(((op (e1) (e0)) = (e1))\/(((op (e2) (e0)) = (e1))\/((op (e3) (e0)) = (e1))))) -> (~((op (e0) (e2)) = (op (e3) (e2)))) -> (~((op (e0) (e2)) = (op (e0) (e3)))) -> ((op (e0) (e2)) = (e0)) -> (~((op (e1) (e0)) = (op (e1) (e3)))) -> (((op (e3) (e0)) = (e1))\/(((op (e3) (e1)) = (e1))\/(((op (e3) (e2)) = (e1))\/((op (e3) (e3)) = (e1))))) -> (~((op (e1) (e2)) = (op (e3) (e2)))) -> (~((op (e0) (e2)) = (op (e1) (e2)))) -> (~((op (e3) (e0)) = (op (e3) (e1)))) -> (((op (e2) (e0)) = (e1))\/(((op (e2) (e1)) = (e1))\/(((op (e2) (e2)) = (e1))\/((op (e2) (e3)) = (e1))))) -> (~((op (e3) (e1)) = (op (e3) (e2)))) -> (~((op (e1) (e1)) = (op (e1) (e3)))) -> (((op (e1) (e0)) = (e0))\/(((op (e1) (e1)) = (e0))\/(((op (e1) (e2)) = (e0))\/((op (e1) (e3)) = (e0))))) -> (~((op (e1) (e2)) = (op (e2) (e2)))) -> (((op (e3) (e3)) = (e0))\/(((op (e3) (e3)) = (e1))\/(((op (e3) (e3)) = (e2))\/((op (e3) (e3)) = (e3))))) -> (~((op (e3) (e3)) = (e3))) -> (~((op (e3) (e0)) = (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 (e2) (e1)) = (op (e2) (e3)))) -> (~((op (e0) (e3)) = (op (e3) (e3)))) -> (~((op (e3) (e2)) = (op (e3) (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) (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 (e2) (e3)) = (op (e3) (e3)))) -> (((op (e0) (e1)) = (e0))\/(((op (e1) (e1)) = (e0))\/(((op (e2) (e1)) = (e0))\/((op (e3) (e1)) = (e0))))) -> (((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)) = (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)))) -> (~((e2) = (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))))) -> (~((e0) = (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) (e1)) = (op (e0) (e2)))) -> (~((op (e1) (e0)) = (op (e3) (e0)))) -> (~((op (e1) (e0)) = (e2))) -> (((op (e1) (e0)) = (e0))\/(((op (e1) (e0)) = (e1))\/(((op (e1) (e0)) = (e2))\/((op (e1) (e0)) = (e3))))) -> (((op (e0) (e0)) = (e1))\/(((op (e0) (e1)) = (e1))\/(((op (e0) (e2)) = (e1))\/((op (e0) (e3)) = (e1))))) -> (~((op (e2) (e2)) = (op (e3) (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 (e2) (e3)) = (e2)))\/((op (e2) (e2)) = (e3))) -> (~((op (e0) (e2)) = (op (e2) (e2)))) -> ((~((op (e2) (e0)) = (e2)))\/((op (e2) (e2)) = (e0))) -> ((~((op (e1) (e2)) = (e2)))\/((op (e1) (e2)) = (e2))) -> (~((op (e1) (e1)) = (e1))) -> (~((op (e1) (e0)) = (op (e2) (e0)))) -> (~((op (e3) (e0)) = (op (e3) (e2)))) -> (~((e1) = (e2))) -> (~((op (e0) (e2)) = (e2))) -> (~((op (e0) (e3)) = (e2))) -> (((op (e0) (e0)) = (e2))\/(((op (e0) (e1)) = (e2))\/(((op (e0) (e2)) = (e2))\/((op (e0) (e3)) = (e2))))) -> (~((op (e2) (e2)) = (op (e2) (e3)))) -> (((op (e0) (e3)) = (e2))\/(((op (e1) (e3)) = (e2))\/(((op (e2) (e3)) = (e2))\/((op (e3) (e3)) = (e2))))) -> (((op (e2) (e0)) = (e0))\/(((op (e2) (e1)) = (e0))\/(((op (e2) (e2)) = (e0))\/((op (e2) (e3)) = (e0))))) -> (~((op (e2) (e0)) = (op (e2) (e2)))) -> (((op (e1) (e1)) = (e0))\/(((op (e1) (e1)) = (e1))\/(((op (e1) (e1)) = (e2))\/((op (e1) (e1)) = (e3))))) -> (~((e0) = (e3))) -> (~((op (e1) (e3)) = (e2))) -> (~((op (e2) (e0)) = (op (e3) (e0)))) -> ((~((op (e3) (e1)) = (e2)))\/((op (e3) (e2)) = (e1))) -> (~((op (e2) (e2)) = (e2))) -> (((op (e2) (e0)) = (e2))\/(((op (e2) (e1)) = (e2))\/(((op (e2) (e2)) = (e2))\/((op (e2) (e3)) = (e2))))) -> (((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)) = (op (e2) (e3)))) -> (~((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)) = (e0))\/(((op (e2) (e3)) = (e1))\/(((op (e2) (e3)) = (e2))\/((op (e2) (e3)) = (e3))))) -> ((~((op (e3) (e0)) = (e2)))\/((op (e3) (e2)) = (e0))) -> False). % 19.02/19.15 do 0 intro. intros zenon_H1d8 zenon_H20c zenon_H26d zenon_H3f zenon_H189 zenon_Ha1 zenon_H45 zenon_H128 zenon_H16f zenon_H113 zenon_H279 zenon_H95 zenon_H271 zenon_H273 zenon_H3e zenon_H1f0 zenon_H1cc zenon_H235 zenon_H14f zenon_H208 zenon_H48 zenon_Hd8 zenon_He8 zenon_H115 zenon_H195 zenon_H1cf zenon_H106 zenon_H1a4 zenon_H57 zenon_H22 zenon_H2b zenon_H101 zenon_H102 zenon_H71 zenon_H130 zenon_H67 zenon_H1c7 zenon_Hc2 zenon_H62 zenon_H124 zenon_H133 zenon_He2 zenon_Hd5 zenon_H1d zenon_Hdf zenon_Hf3 zenon_H245 zenon_He4 zenon_H54 zenon_H17e zenon_H212 zenon_H210 zenon_H12b zenon_H109 zenon_H1ac zenon_H149 zenon_Hdb zenon_H18c zenon_H4a zenon_H1fa zenon_H177 zenon_H25e zenon_H22d zenon_H18f zenon_H278 zenon_H172 zenon_H277 zenon_Ha8 zenon_H276 zenon_H275 zenon_H10a zenon_H201 zenon_H6f zenon_H7c zenon_H1fd zenon_H12e zenon_H183 zenon_H6d zenon_H145 zenon_H2f zenon_H52 zenon_H142 zenon_H9a zenon_H14c zenon_H17b zenon_H26f zenon_H173 zenon_H1d5 zenon_H136 zenon_H259 zenon_H5b zenon_H10e zenon_H153 zenon_H11f zenon_H270. % 19.02/19.15 apply (zenon_or_s _ _ zenon_H276); [ zenon_intro zenon_Hef | zenon_intro zenon_H2c ]. % 19.02/19.15 apply (zenon_or_s _ _ zenon_H271); [ zenon_intro zenon_H26e | zenon_intro zenon_Hf1 ]. % 19.02/19.15 apply (zenon_or_s _ _ zenon_H277); [ zenon_intro zenon_H274 | zenon_intro zenon_Haa ]. % 19.02/19.15 apply (zenon_L1062_); trivial. % 19.02/19.15 apply (zenon_or_s _ _ zenon_H26f); [ zenon_intro zenon_H194 | zenon_intro zenon_Hba ]. % 19.02/19.15 apply (zenon_L1063_); trivial. % 19.02/19.15 apply (zenon_or_s _ _ zenon_H278); [ zenon_intro zenon_Hf7 | zenon_intro zenon_H163 ]. % 19.02/19.15 apply (zenon_or_s _ _ zenon_H3e); [ zenon_intro zenon_H42 | zenon_intro zenon_H41 ]. % 19.02/19.15 exact (zenon_H3f zenon_H42). % 19.02/19.15 apply (zenon_or_s _ _ zenon_H41); [ zenon_intro zenon_H27 | zenon_intro zenon_H43 ]. % 19.02/19.15 apply (zenon_or_s _ _ zenon_H22d); [ zenon_intro zenon_H7a | zenon_intro zenon_H22e ]. % 19.02/19.15 apply (zenon_L1059_); trivial. % 19.02/19.15 apply (zenon_or_s _ _ zenon_H22e); [ zenon_intro zenon_Ha0 | zenon_intro zenon_H22f ]. % 19.02/19.15 apply (zenon_or_s _ _ zenon_H235); [ zenon_intro zenon_H7a | zenon_intro zenon_H236 ]. % 19.02/19.15 apply (zenon_L1059_); trivial. % 19.02/19.15 apply (zenon_or_s _ _ zenon_H236); [ zenon_intro zenon_H9d | zenon_intro zenon_H237 ]. % 19.02/19.15 apply (zenon_L262_); trivial. % 19.02/19.15 apply (zenon_or_s _ _ zenon_H237); [ zenon_intro zenon_Hed | zenon_intro zenon_Hac ]. % 19.02/19.15 apply (zenon_or_s _ _ zenon_H183); [ zenon_intro zenon_H7b | zenon_intro zenon_H186 ]. % 19.02/19.15 apply (zenon_or_s _ _ zenon_H245); [ zenon_intro zenon_H49 | zenon_intro zenon_H246 ]. % 19.02/19.15 apply (zenon_L38_); trivial. % 19.02/19.15 apply (zenon_or_s _ _ zenon_H246); [ zenon_intro zenon_H29 | zenon_intro zenon_H247 ]. % 19.02/19.15 apply (zenon_L8_); trivial. % 19.02/19.15 apply (zenon_or_s _ _ zenon_H247); [ zenon_intro zenon_H36 | zenon_intro zenon_H1b1 ]. % 19.02/19.15 apply (zenon_or_s _ _ zenon_H128); [ zenon_intro zenon_H9d | zenon_intro zenon_H129 ]. % 19.02/19.15 apply (zenon_L413_); trivial. % 19.02/19.15 apply (zenon_or_s _ _ zenon_H129); [ zenon_intro zenon_H10d | zenon_intro zenon_H12a ]. % 19.02/19.15 exact (zenon_H10a zenon_H10d). % 19.02/19.15 apply (zenon_or_s _ _ zenon_H12a); [ zenon_intro zenon_Hf0 | zenon_intro zenon_Hd6 ]. % 19.02/19.15 apply (zenon_L1101_); trivial. % 19.02/19.15 apply (zenon_or_s _ _ zenon_H1d8); [ zenon_intro zenon_H10f | zenon_intro zenon_H1d9 ]. % 19.02/19.15 exact (zenon_H26d zenon_H10f). % 19.02/19.15 apply (zenon_or_s _ _ zenon_H1d9); [ zenon_intro zenon_H110 | zenon_intro zenon_H1da ]. % 19.02/19.15 exact (zenon_H20c zenon_H110). % 19.02/19.15 apply (zenon_or_s _ _ zenon_H1da); [ zenon_intro zenon_H1ca | zenon_intro zenon_H14d ]. % 19.02/19.15 exact (zenon_H26e zenon_H1ca). % 19.02/19.15 apply (zenon_L657_); trivial. % 19.02/19.15 apply (zenon_L1103_); trivial. % 19.02/19.15 apply (zenon_or_s _ _ zenon_H186); [ zenon_intro zenon_H10f | zenon_intro zenon_H187 ]. % 19.02/19.15 exact (zenon_H26d zenon_H10f). % 19.02/19.15 apply (zenon_or_s _ _ zenon_H187); [ zenon_intro zenon_H150 | zenon_intro zenon_Hcd ]. % 19.02/19.15 exact (zenon_H1fd zenon_H150). % 19.02/19.15 exact (zenon_H12e zenon_Hcd). % 19.02/19.15 apply (zenon_L249_); trivial. % 19.02/19.15 apply (zenon_or_s _ _ zenon_H22f); [ zenon_intro zenon_H122 | zenon_intro zenon_Hc3 ]. % 19.02/19.15 apply (zenon_L355_); trivial. % 19.02/19.15 apply (zenon_L652_); trivial. % 19.02/19.15 apply (zenon_or_s _ _ zenon_H43); [ zenon_intro zenon_H34 | zenon_intro zenon_H44 ]. % 19.02/19.15 apply (zenon_or_s _ _ zenon_H22d); [ zenon_intro zenon_H7a | zenon_intro zenon_H22e ]. % 19.02/19.15 apply (zenon_L1059_); trivial. % 19.02/19.15 apply (zenon_or_s _ _ zenon_H22e); [ zenon_intro zenon_Ha0 | zenon_intro zenon_H22f ]. % 19.02/19.15 apply (zenon_or_s _ _ zenon_H235); [ zenon_intro zenon_H7a | zenon_intro zenon_H236 ]. % 19.02/19.15 apply (zenon_L1059_); trivial. % 19.02/19.15 apply (zenon_or_s _ _ zenon_H236); [ zenon_intro zenon_H9d | zenon_intro zenon_H237 ]. % 19.02/19.15 apply (zenon_or_s _ _ zenon_H183); [ zenon_intro zenon_H7b | zenon_intro zenon_H186 ]. % 19.02/19.15 apply (zenon_or_s _ _ zenon_H22); [ zenon_intro zenon_H27 | zenon_intro zenon_H26 ]. % 19.02/19.15 apply (zenon_L332_); trivial. % 19.02/19.15 apply (zenon_or_s _ _ zenon_H26); [ zenon_intro zenon_H29 | zenon_intro zenon_H28 ]. % 19.02/19.15 apply (zenon_or_s _ _ zenon_H1d8); [ zenon_intro zenon_H10f | zenon_intro zenon_H1d9 ]. % 19.02/19.15 exact (zenon_H26d zenon_H10f). % 19.02/19.15 apply (zenon_or_s _ _ zenon_H1d9); [ zenon_intro zenon_H110 | zenon_intro zenon_H1da ]. % 19.02/19.15 exact (zenon_H20c zenon_H110). % 19.02/19.15 apply (zenon_or_s _ _ zenon_H1da); [ zenon_intro zenon_H1ca | zenon_intro zenon_H14d ]. % 19.02/19.15 exact (zenon_H26e zenon_H1ca). % 19.02/19.15 apply (zenon_or_s _ _ zenon_H106); [ zenon_intro zenon_Hed | zenon_intro zenon_H107 ]. % 19.02/19.15 apply (zenon_L214_); trivial. % 19.02/19.15 apply (zenon_or_s _ _ zenon_H107); [ zenon_intro zenon_Ha5 | zenon_intro zenon_H108 ]. % 19.02/19.15 apply (zenon_L357_); trivial. % 19.02/19.15 apply (zenon_or_s _ _ zenon_H108); [ zenon_intro zenon_Hf1 | zenon_intro zenon_Hf4 ]. % 19.02/19.15 apply (zenon_L1113_); trivial. % 19.02/19.15 apply (zenon_or_s _ _ zenon_H1d5); [ zenon_intro zenon_Hee | zenon_intro zenon_H1d6 ]. % 19.02/19.15 exact (zenon_Hef zenon_Hee). % 19.02/19.15 apply (zenon_or_s _ _ zenon_H1d6); [ zenon_intro zenon_H1ca | zenon_intro zenon_H1d7 ]. % 19.02/19.15 exact (zenon_H26e zenon_H1ca). % 19.02/19.15 apply (zenon_or_s _ _ zenon_H1d7); [ zenon_intro zenon_H176 | zenon_intro zenon_H11d ]. % 19.02/19.15 exact (zenon_H173 zenon_H176). % 19.02/19.15 apply (zenon_or_s _ _ zenon_H1ac); [ zenon_intro zenon_H44 | zenon_intro zenon_H1af ]. % 19.02/19.15 apply (zenon_L1130_); trivial. % 19.02/19.15 apply (zenon_or_s _ _ zenon_H1af); [ zenon_intro zenon_H1b1 | zenon_intro zenon_H1b0 ]. % 19.02/19.15 apply (zenon_or_s _ _ zenon_H67); [ zenon_intro zenon_H1e | zenon_intro zenon_H68 ]. % 19.02/19.15 apply (zenon_L336_); trivial. % 19.02/19.15 apply (zenon_or_s _ _ zenon_H68); [ zenon_intro zenon_H1f | zenon_intro zenon_H69 ]. % 19.02/19.15 apply (zenon_L1132_); trivial. % 19.02/19.15 apply (zenon_or_s _ _ zenon_H69); [ zenon_intro zenon_H37 | zenon_intro zenon_H60 ]. % 19.02/19.15 apply (zenon_L1127_); trivial. % 19.02/19.15 apply (zenon_L1133_); trivial. % 19.02/19.15 apply (zenon_or_s _ _ zenon_H1b0); [ zenon_intro zenon_H61 | zenon_intro zenon_H60 ]. % 19.02/19.15 apply (zenon_L342_); trivial. % 19.02/19.15 apply (zenon_L1133_); trivial. % 19.02/19.15 apply (zenon_or_s _ _ zenon_H28); [ zenon_intro zenon_H2a | zenon_intro zenon_H1f ]. % 19.02/19.15 apply (zenon_L179_); trivial. % 19.02/19.15 apply (zenon_or_s _ _ zenon_H245); [ zenon_intro zenon_H49 | zenon_intro zenon_H246 ]. % 19.02/19.15 apply (zenon_L9_); trivial. % 19.02/19.15 apply (zenon_or_s _ _ zenon_H246); [ zenon_intro zenon_H29 | zenon_intro zenon_H247 ]. % 19.02/19.15 apply (zenon_L13_); trivial. % 19.02/19.15 apply (zenon_or_s _ _ zenon_H247); [ zenon_intro zenon_H36 | zenon_intro zenon_H1b1 ]. % 19.02/19.15 apply (zenon_L642_); trivial. % 19.02/19.15 apply (zenon_or_s _ _ zenon_H106); [ zenon_intro zenon_Hed | zenon_intro zenon_H107 ]. % 19.02/19.15 apply (zenon_L413_); trivial. % 19.02/19.15 apply (zenon_or_s _ _ zenon_H107); [ zenon_intro zenon_Ha5 | zenon_intro zenon_H108 ]. % 19.02/19.15 apply (zenon_L357_); trivial. % 19.02/19.15 apply (zenon_or_s _ _ zenon_H108); [ zenon_intro zenon_Hf1 | zenon_intro zenon_Hf4 ]. % 19.02/19.15 apply (zenon_L1134_); trivial. % 19.02/19.15 apply (zenon_or_s _ _ zenon_H1d5); [ zenon_intro zenon_Hee | zenon_intro zenon_H1d6 ]. % 19.02/19.15 exact (zenon_Hef zenon_Hee). % 19.02/19.15 apply (zenon_or_s _ _ zenon_H1d6); [ zenon_intro zenon_H1ca | zenon_intro zenon_H1d7 ]. % 19.02/19.15 exact (zenon_H26e zenon_H1ca). % 19.02/19.15 apply (zenon_or_s _ _ zenon_H1d7); [ zenon_intro zenon_H176 | zenon_intro zenon_H11d ]. % 19.02/19.15 exact (zenon_H173 zenon_H176). % 19.02/19.15 apply (zenon_L1132_); trivial. % 19.02/19.15 apply (zenon_or_s _ _ zenon_H186); [ zenon_intro zenon_H10f | zenon_intro zenon_H187 ]. % 19.02/19.15 exact (zenon_H26d zenon_H10f). % 19.02/19.15 apply (zenon_or_s _ _ zenon_H187); [ zenon_intro zenon_H150 | zenon_intro zenon_Hcd ]. % 19.02/19.15 exact (zenon_H1fd zenon_H150). % 19.02/19.15 exact (zenon_H12e zenon_Hcd). % 19.02/19.15 apply (zenon_or_s _ _ zenon_H237); [ zenon_intro zenon_Hed | zenon_intro zenon_Hac ]. % 19.02/19.15 apply (zenon_L214_); trivial. % 19.02/19.15 apply (zenon_L249_); trivial. % 19.02/19.15 apply (zenon_or_s _ _ zenon_H22f); [ zenon_intro zenon_H122 | zenon_intro zenon_Hc3 ]. % 19.02/19.15 apply (zenon_L317_); trivial. % 19.02/19.15 apply (zenon_or_s _ _ zenon_H22); [ zenon_intro zenon_H27 | zenon_intro zenon_H26 ]. % 19.02/19.15 apply (zenon_L332_); trivial. % 19.02/19.15 apply (zenon_or_s _ _ zenon_H26); [ zenon_intro zenon_H29 | zenon_intro zenon_H28 ]. % 19.02/19.15 apply (zenon_L1108_); trivial. % 19.02/19.15 apply (zenon_or_s _ _ zenon_H28); [ zenon_intro zenon_H2a | zenon_intro zenon_H1f ]. % 19.02/19.15 apply (zenon_L334_); trivial. % 19.02/19.15 apply (zenon_L1098_); trivial. % 19.02/19.15 apply (zenon_or_s _ _ zenon_H22d); [ zenon_intro zenon_H7a | zenon_intro zenon_H22e ]. % 19.02/19.15 apply (zenon_L1059_); trivial. % 19.02/19.15 apply (zenon_or_s _ _ zenon_H22e); [ zenon_intro zenon_Ha0 | zenon_intro zenon_H22f ]. % 19.02/19.15 apply (zenon_or_s _ _ zenon_H235); [ zenon_intro zenon_H7a | zenon_intro zenon_H236 ]. % 19.02/19.15 apply (zenon_L1059_); trivial. % 19.02/19.15 apply (zenon_or_s _ _ zenon_H236); [ zenon_intro zenon_H9d | zenon_intro zenon_H237 ]. % 19.02/19.15 apply (zenon_or_s _ _ zenon_H183); [ zenon_intro zenon_H7b | zenon_intro zenon_H186 ]. % 19.02/19.15 apply (zenon_or_s _ _ zenon_H22); [ zenon_intro zenon_H27 | zenon_intro zenon_H26 ]. % 19.02/19.15 apply (zenon_L262_); trivial. % 19.02/19.15 apply (zenon_or_s _ _ zenon_H26); [ zenon_intro zenon_H29 | zenon_intro zenon_H28 ]. % 19.02/19.15 apply (zenon_or_s _ _ zenon_H1d8); [ zenon_intro zenon_H10f | zenon_intro zenon_H1d9 ]. % 19.02/19.15 exact (zenon_H26d zenon_H10f). % 19.02/19.15 apply (zenon_or_s _ _ zenon_H1d9); [ zenon_intro zenon_H110 | zenon_intro zenon_H1da ]. % 19.02/19.15 exact (zenon_H20c zenon_H110). % 19.02/19.15 apply (zenon_or_s _ _ zenon_H1da); [ zenon_intro zenon_H1ca | zenon_intro zenon_H14d ]. % 19.02/19.15 exact (zenon_H26e zenon_H1ca). % 19.02/19.15 apply (zenon_L1130_); trivial. % 19.02/19.15 apply (zenon_or_s _ _ zenon_H28); [ zenon_intro zenon_H2a | zenon_intro zenon_H1f ]. % 19.02/19.15 apply (zenon_L334_); trivial. % 19.02/19.15 apply (zenon_L1135_); trivial. % 19.02/19.15 apply (zenon_or_s _ _ zenon_H186); [ zenon_intro zenon_H10f | zenon_intro zenon_H187 ]. % 19.02/19.15 exact (zenon_H26d zenon_H10f). % 19.02/19.15 apply (zenon_or_s _ _ zenon_H187); [ zenon_intro zenon_H150 | zenon_intro zenon_Hcd ]. % 19.02/19.15 exact (zenon_H1fd zenon_H150). % 19.02/19.15 exact (zenon_H12e zenon_Hcd). % 19.02/19.15 apply (zenon_or_s _ _ zenon_H237); [ zenon_intro zenon_Hed | zenon_intro zenon_Hac ]. % 19.02/19.15 apply (zenon_L1120_); trivial. % 19.02/19.15 apply (zenon_L249_); trivial. % 19.02/19.15 apply (zenon_or_s _ _ zenon_H22f); [ zenon_intro zenon_H122 | zenon_intro zenon_Hc3 ]. % 19.02/19.15 apply (zenon_L355_); trivial. % 19.02/19.15 apply (zenon_or_s _ _ zenon_H235); [ zenon_intro zenon_H7a | zenon_intro zenon_H236 ]. % 19.02/19.15 apply (zenon_L140_); trivial. % 19.02/19.15 apply (zenon_or_s _ _ zenon_H236); [ zenon_intro zenon_H9d | zenon_intro zenon_H237 ]. % 19.02/19.15 apply (zenon_or_s _ _ zenon_H22); [ zenon_intro zenon_H27 | zenon_intro zenon_H26 ]. % 19.02/19.15 apply (zenon_L262_); trivial. % 19.02/19.15 apply (zenon_or_s _ _ zenon_H26); [ zenon_intro zenon_H29 | zenon_intro zenon_H28 ]. % 19.02/19.15 apply (zenon_L1108_); trivial. % 19.02/19.15 apply (zenon_or_s _ _ zenon_H28); [ zenon_intro zenon_H2a | zenon_intro zenon_H1f ]. % 19.02/19.15 apply (zenon_L179_); trivial. % 19.02/19.15 apply (zenon_L1136_); trivial. % 19.02/19.15 apply (zenon_or_s _ _ zenon_H237); [ zenon_intro zenon_Hed | zenon_intro zenon_Hac ]. % 19.02/19.15 apply (zenon_L1120_); trivial. % 19.02/19.15 apply (zenon_L41_); trivial. % 19.02/19.15 apply (zenon_L180_); trivial. % 19.02/19.15 apply (zenon_or_s _ _ zenon_H277); [ zenon_intro zenon_H274 | zenon_intro zenon_Haa ]. % 19.02/19.15 apply (zenon_or_s _ _ zenon_H270); [ zenon_intro zenon_H14b | zenon_intro zenon_H61 ]. % 19.02/19.15 apply (zenon_or_s _ _ zenon_H26f); [ zenon_intro zenon_H194 | zenon_intro zenon_Hba ]. % 19.02/19.15 apply (zenon_or_s _ _ zenon_H273); [ zenon_intro zenon_H272 | zenon_intro zenon_H151 ]. % 19.02/19.15 apply (zenon_or_s _ _ zenon_H3e); [ zenon_intro zenon_H42 | zenon_intro zenon_H41 ]. % 19.02/19.15 exact (zenon_H3f zenon_H42). % 19.02/19.15 apply (zenon_or_s _ _ zenon_H41); [ zenon_intro zenon_H27 | zenon_intro zenon_H43 ]. % 19.02/19.15 apply (zenon_or_s _ _ zenon_H22d); [ zenon_intro zenon_H7a | zenon_intro zenon_H22e ]. % 19.02/19.15 apply (zenon_L1059_); trivial. % 19.02/19.15 apply (zenon_or_s _ _ zenon_H22e); [ zenon_intro zenon_Ha0 | zenon_intro zenon_H22f ]. % 19.02/19.15 apply (zenon_or_s _ _ zenon_H235); [ zenon_intro zenon_H7a | zenon_intro zenon_H236 ]. % 19.02/19.15 apply (zenon_L1059_); trivial. % 19.02/19.15 apply (zenon_or_s _ _ zenon_H236); [ zenon_intro zenon_H9d | zenon_intro zenon_H237 ]. % 19.02/19.15 apply (zenon_L262_); trivial. % 19.02/19.15 apply (zenon_or_s _ _ zenon_H237); [ zenon_intro zenon_Hed | zenon_intro zenon_Hac ]. % 19.02/19.15 apply (zenon_L93_); trivial. % 19.02/19.15 apply (zenon_or_s _ _ zenon_H183); [ zenon_intro zenon_H7b | zenon_intro zenon_H186 ]. % 19.02/19.15 apply (zenon_or_s _ _ zenon_H245); [ zenon_intro zenon_H49 | zenon_intro zenon_H246 ]. % 19.02/19.15 apply (zenon_L38_); trivial. % 19.02/19.15 apply (zenon_or_s _ _ zenon_H246); [ zenon_intro zenon_H29 | zenon_intro zenon_H247 ]. % 19.02/19.15 apply (zenon_L8_); trivial. % 19.02/19.15 apply (zenon_or_s _ _ zenon_H247); [ zenon_intro zenon_H36 | zenon_intro zenon_H1b1 ]. % 19.02/19.15 apply (zenon_or_s _ _ zenon_H1ac); [ zenon_intro zenon_H44 | zenon_intro zenon_H1af ]. % 19.02/19.15 apply (zenon_L41_); trivial. % 19.02/19.15 apply (zenon_or_s _ _ zenon_H1af); [ zenon_intro zenon_H1b1 | zenon_intro zenon_H1b0 ]. % 19.02/19.15 apply (zenon_L641_); trivial. % 19.02/19.15 apply (zenon_or_s _ _ zenon_H1b0); [ zenon_intro zenon_H61 | zenon_intro zenon_H60 ]. % 19.02/19.15 apply (zenon_L342_); trivial. % 19.02/19.15 apply (zenon_L1144_); trivial. % 19.02/19.15 apply (zenon_L1146_); trivial. % 19.02/19.15 apply (zenon_or_s _ _ zenon_H186); [ zenon_intro zenon_H10f | zenon_intro zenon_H187 ]. % 19.02/19.15 exact (zenon_H26d zenon_H10f). % 19.02/19.15 apply (zenon_or_s _ _ zenon_H187); [ zenon_intro zenon_H150 | zenon_intro zenon_Hcd ]. % 19.02/19.15 exact (zenon_H1fd zenon_H150). % 19.02/19.15 exact (zenon_H12e zenon_Hcd). % 19.02/19.15 apply (zenon_or_s _ _ zenon_H22f); [ zenon_intro zenon_H122 | zenon_intro zenon_Hc3 ]. % 19.02/19.15 apply (zenon_L246_); trivial. % 19.02/19.15 apply (zenon_or_s _ _ zenon_H235); [ zenon_intro zenon_H7a | zenon_intro zenon_H236 ]. % 19.02/19.15 apply (zenon_L140_); trivial. % 19.02/19.15 apply (zenon_or_s _ _ zenon_H236); [ zenon_intro zenon_H9d | zenon_intro zenon_H237 ]. % 19.02/19.15 apply (zenon_L262_); trivial. % 19.02/19.15 apply (zenon_or_s _ _ zenon_H237); [ zenon_intro zenon_Hed | zenon_intro zenon_Hac ]. % 19.02/19.15 apply (zenon_L93_); trivial. % 19.02/19.15 apply (zenon_L1142_); trivial. % 19.02/19.15 apply (zenon_or_s _ _ zenon_H43); [ zenon_intro zenon_H34 | zenon_intro zenon_H44 ]. % 19.02/19.15 apply (zenon_or_s _ _ zenon_H22d); [ zenon_intro zenon_H7a | zenon_intro zenon_H22e ]. % 19.02/19.15 apply (zenon_L1059_); trivial. % 19.02/19.15 apply (zenon_or_s _ _ zenon_H22e); [ zenon_intro zenon_Ha0 | zenon_intro zenon_H22f ]. % 19.02/19.15 apply (zenon_or_s _ _ zenon_H235); [ zenon_intro zenon_H7a | zenon_intro zenon_H236 ]. % 19.02/19.15 apply (zenon_L1059_); trivial. % 19.02/19.15 apply (zenon_or_s _ _ zenon_H236); [ zenon_intro zenon_H9d | zenon_intro zenon_H237 ]. % 19.02/19.15 apply (zenon_or_s _ _ zenon_H1ac); [ zenon_intro zenon_H44 | zenon_intro zenon_H1af ]. % 19.02/19.15 apply (zenon_L1150_); trivial. % 19.02/19.15 apply (zenon_or_s _ _ zenon_H1af); [ zenon_intro zenon_H1b1 | zenon_intro zenon_H1b0 ]. % 19.02/19.15 apply (zenon_or_s _ _ zenon_H67); [ zenon_intro zenon_H1e | zenon_intro zenon_H68 ]. % 19.02/19.15 apply (zenon_L336_); trivial. % 19.02/19.15 apply (zenon_or_s _ _ zenon_H68); [ zenon_intro zenon_H1f | zenon_intro zenon_H69 ]. % 19.02/19.15 apply (zenon_L1157_); trivial. % 19.02/19.15 apply (zenon_or_s _ _ zenon_H69); [ zenon_intro zenon_H37 | zenon_intro zenon_H60 ]. % 19.02/19.15 apply (zenon_L14_); trivial. % 19.02/19.15 apply (zenon_L1158_); trivial. % 19.02/19.15 apply (zenon_or_s _ _ zenon_H1b0); [ zenon_intro zenon_H61 | zenon_intro zenon_H60 ]. % 19.02/19.15 apply (zenon_L342_); trivial. % 19.02/19.15 apply (zenon_L1158_); trivial. % 19.02/19.15 apply (zenon_or_s _ _ zenon_H237); [ zenon_intro zenon_Hed | zenon_intro zenon_Hac ]. % 19.02/19.15 apply (zenon_L93_); trivial. % 19.02/19.15 apply (zenon_or_s _ _ zenon_H22); [ zenon_intro zenon_H27 | zenon_intro zenon_H26 ]. % 19.02/19.15 apply (zenon_L332_); trivial. % 19.02/19.15 apply (zenon_or_s _ _ zenon_H26); [ zenon_intro zenon_H29 | zenon_intro zenon_H28 ]. % 19.02/19.15 apply (zenon_or_s _ _ zenon_H67); [ zenon_intro zenon_H1e | zenon_intro zenon_H68 ]. % 19.02/19.15 apply (zenon_L336_); trivial. % 19.02/19.15 apply (zenon_or_s _ _ zenon_H68); [ zenon_intro zenon_H1f | zenon_intro zenon_H69 ]. % 19.02/19.15 apply (zenon_L13_); trivial. % 19.02/19.15 apply (zenon_or_s _ _ zenon_H69); [ zenon_intro zenon_H37 | zenon_intro zenon_H60 ]. % 19.02/19.15 apply (zenon_L14_); trivial. % 19.02/19.15 apply (zenon_L1144_); trivial. % 19.02/19.15 apply (zenon_or_s _ _ zenon_H28); [ zenon_intro zenon_H2a | zenon_intro zenon_H1f ]. % 19.02/19.15 apply (zenon_L334_); trivial. % 19.02/19.15 apply (zenon_L1162_); trivial. % 19.02/19.15 apply (zenon_or_s _ _ zenon_H22f); [ zenon_intro zenon_H122 | zenon_intro zenon_Hc3 ]. % 19.02/19.15 apply (zenon_L355_); trivial. % 19.02/19.15 apply (zenon_or_s _ _ zenon_H235); [ zenon_intro zenon_H7a | zenon_intro zenon_H236 ]. % 19.02/19.15 apply (zenon_L140_); trivial. % 19.02/19.15 apply (zenon_or_s _ _ zenon_H236); [ zenon_intro zenon_H9d | zenon_intro zenon_H237 ]. % 19.02/19.15 apply (zenon_or_s _ _ zenon_H109); [ zenon_intro zenon_Ha0 | zenon_intro zenon_H10b ]. % 19.02/19.15 apply (zenon_L359_); trivial. % 19.02/19.15 apply (zenon_or_s _ _ zenon_H10b); [ zenon_intro zenon_H10d | zenon_intro zenon_H10c ]. % 19.02/19.15 exact (zenon_H10a zenon_H10d). % 19.02/19.15 apply (zenon_or_s _ _ zenon_H10c); [ zenon_intro zenon_Ha5 | zenon_intro zenon_Hae ]. % 19.02/19.15 apply (zenon_or_s _ _ zenon_He8); [ zenon_intro zenon_Hac | zenon_intro zenon_Heb ]. % 19.02/19.15 apply (zenon_L1141_); trivial. % 19.02/19.15 apply (zenon_or_s _ _ zenon_Heb); [ zenon_intro zenon_Hae | zenon_intro zenon_Hec ]. % 19.02/19.15 apply (zenon_L1168_); trivial. % 19.02/19.15 apply (zenon_or_s _ _ zenon_Hec); [ zenon_intro zenon_Hba | zenon_intro zenon_Hc4 ]. % 19.02/19.15 apply (zenon_L185_); trivial. % 19.02/19.15 apply (zenon_L46_); trivial. % 19.02/19.15 apply (zenon_L1168_); trivial. % 19.02/19.15 apply (zenon_or_s _ _ zenon_H237); [ zenon_intro zenon_Hed | zenon_intro zenon_Hac ]. % 19.02/19.15 apply (zenon_L214_); trivial. % 19.02/19.15 apply (zenon_L1142_); trivial. % 19.02/19.15 apply (zenon_or_s _ _ zenon_H22d); [ zenon_intro zenon_H7a | zenon_intro zenon_H22e ]. % 19.02/19.15 apply (zenon_L1059_); trivial. % 19.02/19.15 apply (zenon_or_s _ _ zenon_H22e); [ zenon_intro zenon_Ha0 | zenon_intro zenon_H22f ]. % 19.02/19.15 apply (zenon_L1150_); trivial. % 19.02/19.15 apply (zenon_or_s _ _ zenon_H22f); [ zenon_intro zenon_H122 | zenon_intro zenon_Hc3 ]. % 19.02/19.15 apply (zenon_L246_); trivial. % 19.02/19.15 apply (zenon_or_s _ _ zenon_H235); [ zenon_intro zenon_H7a | zenon_intro zenon_H236 ]. % 19.02/19.15 apply (zenon_L140_); trivial. % 19.02/19.15 apply (zenon_or_s _ _ zenon_H236); [ zenon_intro zenon_H9d | zenon_intro zenon_H237 ]. % 19.02/19.15 apply (zenon_or_s _ _ zenon_H2f); [ zenon_intro zenon_H34 | zenon_intro zenon_H33 ]. % 19.02/19.15 apply (zenon_L127_); trivial. % 19.02/19.15 apply (zenon_or_s _ _ zenon_H33); [ zenon_intro zenon_H36 | zenon_intro zenon_H35 ]. % 19.02/19.15 apply (zenon_or_s _ _ zenon_H67); [ zenon_intro zenon_H1e | zenon_intro zenon_H68 ]. % 19.02/19.15 apply (zenon_L336_); trivial. % 19.02/19.15 apply (zenon_or_s _ _ zenon_H68); [ zenon_intro zenon_H1f | zenon_intro zenon_H69 ]. % 19.02/19.15 apply (zenon_L1172_); trivial. % 19.02/19.15 apply (zenon_or_s _ _ zenon_H69); [ zenon_intro zenon_H37 | zenon_intro zenon_H60 ]. % 19.02/19.15 apply (zenon_L640_); trivial. % 19.02/19.15 apply (zenon_L21_); trivial. % 19.02/19.15 apply (zenon_or_s _ _ zenon_H35); [ zenon_intro zenon_H2c | zenon_intro zenon_H37 ]. % 19.02/19.15 apply (zenon_L679_); trivial. % 19.02/19.15 apply (zenon_L1173_); trivial. % 19.02/19.15 apply (zenon_or_s _ _ zenon_H237); [ zenon_intro zenon_Hed | zenon_intro zenon_Hac ]. % 19.02/19.15 apply (zenon_L93_); trivial. % 19.02/19.15 apply (zenon_L41_); trivial. % 19.02/19.15 apply (zenon_L1174_); trivial. % 19.02/19.15 apply (zenon_L185_); trivial. % 19.02/19.15 apply (zenon_L342_); trivial. % 19.02/19.15 apply (zenon_L1203_); trivial. % 19.02/19.15 apply (zenon_L679_); trivial. % 19.02/19.15 (* end of lemma zenon_L1204_ *) % 19.02/19.15 assert (zenon_L1205_ : ((~((op (e2) (e1)) = (e2)))\/((op (e2) (e2)) = (e1))) -> ((op (e1) (e2)) = (e1)) -> (~((op (e1) (e2)) = (op (e2) (e2)))) -> (~((op (e0) (e0)) = (e2))) -> (~((op (e0) (e1)) = (e2))) -> (~((op (e0) (e2)) = (e2))) -> (((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)) = (e2))) -> (~((op (e2) (e0)) = (e2))) -> (((op (e0) (e0)) = (e2))\/(((op (e0) (e1)) = (e2))\/(((op (e0) (e2)) = (e2))\/((op (e0) (e3)) = (e2))))) -> False). % 19.02/19.16 do 0 intro. intros zenon_H271 zenon_Hf0 zenon_H2b zenon_H80 zenon_H26d zenon_H1fd zenon_H1d5 zenon_He2 zenon_H173 zenon_Hef zenon_H183. % 19.02/19.16 apply (zenon_or_s _ _ zenon_H271); [ zenon_intro zenon_H26e | zenon_intro zenon_Hf1 ]. % 19.02/19.16 apply (zenon_L1050_); trivial. % 19.02/19.16 apply (zenon_L59_); trivial. % 19.02/19.16 (* end of lemma zenon_L1205_ *) % 19.02/19.16 assert (zenon_L1206_ : ((~((op (e3) (e2)) = (e2)))\/((op (e3) (e2)) = (e2))) -> (~((op (e0) (e3)) = (e2))) -> (~((op (e1) (e3)) = (e2))) -> (~((op (e2) (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 (e0) (e2)) = (e2))) -> (~((op (e1) (e2)) = (e2))) -> (~((op (e2) (e2)) = (e2))) -> (((op (e0) (e2)) = (e2))\/(((op (e1) (e2)) = (e2))\/(((op (e2) (e2)) = (e2))\/((op (e3) (e2)) = (e2))))) -> False). % 19.02/19.16 do 0 intro. intros zenon_H273 zenon_H12e zenon_H14c zenon_H274 zenon_H62 zenon_H145 zenon_H1fd zenon_H114 zenon_H173 zenon_H172. % 19.02/19.16 apply (zenon_or_s _ _ zenon_H273); [ zenon_intro zenon_H272 | zenon_intro zenon_H151 ]. % 19.02/19.16 apply (zenon_L1055_); trivial. % 19.02/19.16 apply (zenon_L1174_); trivial. % 19.02/19.16 (* end of lemma zenon_L1206_ *) % 19.02/19.16 assert (zenon_L1207_ : ((~((op (e3) (e3)) = (e2)))\/((op (e3) (e2)) = (e3))) -> ((op (e2) (e2)) = (e3)) -> (~((op (e2) (e2)) = (op (e3) (e2)))) -> (~((op (e0) (e0)) = (e2))) -> (~((op (e1) (e0)) = (e2))) -> (((op (e0) (e3)) = (e2))\/(((op (e1) (e3)) = (e2))\/(((op (e2) (e3)) = (e2))\/((op (e3) (e3)) = (e2))))) -> (~((op (e2) (e0)) = (op (e2) (e3)))) -> (~((op (e1) (e3)) = (e2))) -> (~((op (e0) (e3)) = (e2))) -> (~((op (e3) (e0)) = (e2))) -> (((op (e0) (e0)) = (e2))\/(((op (e1) (e0)) = (e2))\/(((op (e2) (e0)) = (e2))\/((op (e3) (e0)) = (e2))))) -> False). % 19.02/19.16 do 0 intro. intros zenon_H278 zenon_Haa zenon_H18f zenon_H80 zenon_H177 zenon_H145 zenon_H5b zenon_H14c zenon_H12e zenon_H14b zenon_H1fe. % 19.02/19.16 apply (zenon_or_s _ _ zenon_H278); [ zenon_intro zenon_Hf7 | zenon_intro zenon_H163 ]. % 19.02/19.16 apply (zenon_or_s _ _ zenon_H1fe); [ zenon_intro zenon_H7b | zenon_intro zenon_H1ff ]. % 19.02/19.16 exact (zenon_H80 zenon_H7b). % 19.02/19.16 apply (zenon_or_s _ _ zenon_H1ff); [ zenon_intro zenon_H86 | zenon_intro zenon_H200 ]. % 19.02/19.16 exact (zenon_H177 zenon_H86). % 19.02/19.16 apply (zenon_or_s _ _ zenon_H200); [ zenon_intro zenon_Hee | zenon_intro zenon_H148 ]. % 19.02/19.16 apply (zenon_or_s _ _ zenon_H145); [ zenon_intro zenon_Hcd | zenon_intro zenon_H146 ]. % 19.02/19.16 exact (zenon_H12e zenon_Hcd). % 19.02/19.16 apply (zenon_or_s _ _ zenon_H146); [ zenon_intro zenon_Hd7 | zenon_intro zenon_H147 ]. % 19.02/19.16 exact (zenon_H14c zenon_Hd7). % 19.02/19.16 apply (zenon_or_s _ _ zenon_H147); [ zenon_intro zenon_H11d | zenon_intro zenon_Hf6 ]. % 19.02/19.16 apply (zenon_L73_); trivial. % 19.02/19.16 exact (zenon_Hf7 zenon_Hf6). % 19.02/19.16 exact (zenon_H14b zenon_H148). % 19.02/19.16 apply (zenon_L180_); trivial. % 19.02/19.16 (* end of lemma zenon_L1207_ *) % 19.02/19.16 assert (zenon_L1208_ : ((~((op (e3) (e0)) = (e2)))\/((op (e3) (e2)) = (e0))) -> ((op (e2) (e2)) = (e0)) -> (((op (e0) (e0)) = (e2))\/(((op (e1) (e0)) = (e2))\/(((op (e2) (e0)) = (e2))\/((op (e3) (e0)) = (e2))))) -> (~((op (e0) (e3)) = (e2))) -> (~((op (e1) (e3)) = (e2))) -> (~((op (e2) (e0)) = (op (e2) (e3)))) -> (((op (e0) (e3)) = (e2))\/(((op (e1) (e3)) = (e2))\/(((op (e2) (e3)) = (e2))\/((op (e3) (e3)) = (e2))))) -> (~((op (e1) (e0)) = (e2))) -> (~((op (e0) (e0)) = (e2))) -> (~((op (e2) (e2)) = (op (e3) (e2)))) -> ((op (e2) (e2)) = (e3)) -> ((~((op (e3) (e3)) = (e2)))\/((op (e3) (e2)) = (e3))) -> False). % 19.02/19.16 do 0 intro. intros zenon_H270 zenon_H2c zenon_H1fe zenon_H12e zenon_H14c zenon_H5b zenon_H145 zenon_H177 zenon_H80 zenon_H18f zenon_Haa zenon_H278. % 19.02/19.16 apply (zenon_or_s _ _ zenon_H270); [ zenon_intro zenon_H14b | zenon_intro zenon_H61 ]. % 19.02/19.16 apply (zenon_L1207_); trivial. % 19.02/19.16 apply (zenon_L146_); trivial. % 19.02/19.16 (* end of lemma zenon_L1208_ *) % 19.02/19.16 assert (zenon_L1209_ : (((op (e3) (e0)) = (e1))\/(((op (e3) (e1)) = (e1))\/(((op (e3) (e2)) = (e1))\/((op (e3) (e3)) = (e1))))) -> ((op (e0) (e0)) = (e3)) -> ((op (e1) (e0)) = (e2)) -> (~((op (e2) (e1)) = (op (e3) (e1)))) -> ((op (e2) (e1)) = (e1)) -> ((op (e1) (e2)) = (e0)) -> (((op (e2) (e0)) = (e0))\/(((op (e2) (e0)) = (e1))\/(((op (e2) (e0)) = (e2))\/((op (e2) (e0)) = (e3))))) -> ((op (e2) (e1)) = (e0)) -> (~((op (e2) (e0)) = (op (e2) (e1)))) -> (~((op (e1) (e3)) = (op (e3) (e3)))) -> (~((op (e0) (e2)) = (op (e1) (e2)))) -> ((op (e0) (e2)) = (e1)) -> (~((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))))) -> (~((op (e2) (e0)) = (e2))) -> ((op (e2) (e2)) = (e3)) -> (~((op (e2) (e0)) = (op (e2) (e2)))) -> False). % 19.02/19.16 do 0 intro. intros zenon_He8 zenon_H3a zenon_H86 zenon_Haf zenon_Ha5 zenon_H2a zenon_H259 zenon_H36 zenon_H1f0 zenon_Hd5 zenon_H195 zenon_H122 zenon_H10a zenon_H201 zenon_H128 zenon_Hef zenon_Haa zenon_H52. % 19.02/19.16 apply (zenon_or_s _ _ zenon_He8); [ zenon_intro zenon_Hac | zenon_intro zenon_Heb ]. % 19.02/19.16 apply (zenon_L241_); trivial. % 19.02/19.16 apply (zenon_or_s _ _ zenon_Heb); [ zenon_intro zenon_Hae | zenon_intro zenon_Hec ]. % 19.02/19.16 apply (zenon_L42_); trivial. % 19.02/19.16 apply (zenon_or_s _ _ zenon_Hec); [ zenon_intro zenon_Hba | zenon_intro zenon_Hc4 ]. % 19.02/19.16 apply (zenon_L179_); trivial. % 19.02/19.16 apply (zenon_or_s _ _ zenon_H259); [ zenon_intro zenon_H34 | zenon_intro zenon_H25a ]. % 19.02/19.16 apply (zenon_L642_); trivial. % 19.02/19.16 apply (zenon_or_s _ _ zenon_H25a); [ zenon_intro zenon_Hed | zenon_intro zenon_H25b ]. % 19.02/19.16 apply (zenon_L531_); trivial. % 19.02/19.16 apply (zenon_or_s _ _ zenon_H25b); [ zenon_intro zenon_Hee | zenon_intro zenon_H3b ]. % 19.02/19.16 exact (zenon_Hef zenon_Hee). % 19.02/19.16 apply (zenon_L168_); trivial. % 19.02/19.16 (* end of lemma zenon_L1209_ *) % 19.02/19.16 assert (zenon_L1210_ : (((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) (e3)) = (e2))) -> (~((op (e3) (e3)) = (e3))) -> False). % 19.02/19.16 do 0 intro. intros zenon_H101 zenon_H71 zenon_H44 zenon_H130 zenon_Hae zenon_Hf7 zenon_H102. % 19.02/19.16 apply (zenon_or_s _ _ zenon_H101); [ zenon_intro zenon_H60 | zenon_intro zenon_H103 ]. % 19.02/19.16 apply (zenon_L21_); trivial. % 19.02/19.16 apply (zenon_or_s _ _ zenon_H103); [ zenon_intro zenon_Hc4 | zenon_intro zenon_H104 ]. % 19.02/19.16 apply (zenon_L85_); trivial. % 19.02/19.16 apply (zenon_or_s _ _ zenon_H104); [ zenon_intro zenon_Hf6 | zenon_intro zenon_H105 ]. % 19.02/19.16 exact (zenon_Hf7 zenon_Hf6). % 19.02/19.16 exact (zenon_H102 zenon_H105). % 19.02/19.16 (* end of lemma zenon_L1210_ *) % 19.02/19.16 assert (zenon_L1211_ : (((op (e2) (e0)) = (e0))\/(((op (e2) (e1)) = (e0))\/(((op (e2) (e2)) = (e0))\/((op (e2) (e3)) = (e0))))) -> (~((op (e2) (e0)) = (op (e3) (e0)))) -> (~((op (e2) (e0)) = (op (e2) (e2)))) -> ((op (e2) (e2)) = (e3)) -> (~((op (e2) (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 (e0) (e2)) = (op (e1) (e2)))) -> (~((op (e2) (e0)) = (op (e2) (e1)))) -> (((op (e2) (e0)) = (e0))\/(((op (e2) (e0)) = (e1))\/(((op (e2) (e0)) = (e2))\/((op (e2) (e0)) = (e3))))) -> ((op (e2) (e1)) = (e1)) -> (~((op (e2) (e1)) = (op (e3) (e1)))) -> ((op (e1) (e2)) = (e0)) -> (~((op (e1) (e2)) = (op (e2) (e2)))) -> (((op (e3) (e0)) = (e1))\/(((op (e3) (e1)) = (e1))\/(((op (e3) (e2)) = (e1))\/((op (e3) (e3)) = (e1))))) -> ((op (e0) (e0)) = (e3)) -> ((op (e1) (e0)) = (e2)) -> (~((op (e3) (e3)) = (e3))) -> (~((op (e3) (e3)) = (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 (e0) (e2)) = (e1)) -> (~((op (e0) (e2)) = (op (e3) (e2)))) -> (((op (e0) (e3)) = (e0))\/(((op (e0) (e3)) = (e1))\/(((op (e0) (e3)) = (e2))\/((op (e0) (e3)) = (e3))))) -> (~((op (e0) (e3)) = (op (e2) (e3)))) -> (~((op (e0) (e3)) = (op (e3) (e3)))) -> (~((op (e0) (e3)) = (e2))) -> (((op (e1) (e3)) = (e0))\/(((op (e1) (e3)) = (e1))\/(((op (e1) (e3)) = (e2))\/((op (e1) (e3)) = (e3))))) -> (~((op (e1) (e3)) = (op (e2) (e3)))) -> (~((op (e1) (e3)) = (op (e3) (e3)))) -> (~((op (e1) (e3)) = (e2))) -> (~((op (e0) (e3)) = (op (e1) (e3)))) -> False). % 19.02/19.16 do 0 intro. intros zenon_H2f zenon_H17b zenon_H52 zenon_Haa zenon_Hef zenon_H128 zenon_H201 zenon_H10a zenon_H195 zenon_H1f0 zenon_H259 zenon_Ha5 zenon_Haf zenon_H2a zenon_H2b zenon_He8 zenon_H3a zenon_H86 zenon_H102 zenon_Hf7 zenon_H130 zenon_H44 zenon_H71 zenon_H101 zenon_H122 zenon_H14f zenon_He4 zenon_He2 zenon_Hc2 zenon_H12e zenon_Hdf zenon_Hdb zenon_Hd5 zenon_H14c zenon_H1d. % 19.02/19.16 apply (zenon_or_s _ _ zenon_H2f); [ zenon_intro zenon_H34 | zenon_intro zenon_H33 ]. % 19.02/19.16 apply (zenon_L127_); trivial. % 19.02/19.16 apply (zenon_or_s _ _ zenon_H33); [ zenon_intro zenon_H36 | zenon_intro zenon_H35 ]. % 19.02/19.16 apply (zenon_L1209_); trivial. % 19.02/19.16 apply (zenon_or_s _ _ zenon_H35); [ zenon_intro zenon_H2c | zenon_intro zenon_H37 ]. % 19.02/19.16 apply (zenon_L3_); trivial. % 19.02/19.16 apply (zenon_or_s _ _ zenon_He8); [ zenon_intro zenon_Hac | zenon_intro zenon_Heb ]. % 19.02/19.16 apply (zenon_L241_); trivial. % 19.02/19.16 apply (zenon_or_s _ _ zenon_Heb); [ zenon_intro zenon_Hae | zenon_intro zenon_Hec ]. % 19.02/19.16 apply (zenon_L1210_); trivial. % 19.02/19.16 apply (zenon_or_s _ _ zenon_Hec); [ zenon_intro zenon_Hba | zenon_intro zenon_Hc4 ]. % 19.02/19.16 apply (zenon_L317_); trivial. % 19.02/19.16 apply (zenon_L1089_); trivial. % 19.02/19.16 (* end of lemma zenon_L1211_ *) % 19.02/19.16 assert (zenon_L1212_ : (((op (e0) (e0)) = (e2))\/(((op (e1) (e0)) = (e2))\/(((op (e2) (e0)) = (e2))\/((op (e3) (e0)) = (e2))))) -> (~((op (e0) (e0)) = (e2))) -> (~((op (e0) (e3)) = (op (e1) (e3)))) -> (~((op (e1) (e3)) = (e2))) -> (~((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 (e1) (e2)) = (e0)) -> ((op (e2) (e2)) = (e3)) -> (((op (e3) (e3)) = (e0))\/(((op (e3) (e3)) = (e1))\/(((op (e3) (e3)) = (e2))\/((op (e3) (e3)) = (e3))))) -> (~((op (e3) (e0)) = (op (e3) (e3)))) -> ((op (e3) (e0)) = (e0)) -> (~((op (e3) (e1)) = (op (e3) (e3)))) -> (~((op (e3) (e3)) = (e2))) -> (~((op (e3) (e3)) = (e3))) -> (~((e0) = (e1))) -> (((op (e3) (e0)) = (e1))\/(((op (e3) (e1)) = (e1))\/(((op (e3) (e2)) = (e1))\/((op (e3) (e3)) = (e1))))) -> (~((op (e1) (e2)) = (op (e2) (e2)))) -> (~((op (e0) (e1)) = (op (e2) (e1)))) -> ((op (e0) (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) (e2)) = (e1)) -> (~((e1) = (e3))) -> (~((e0) = (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) (e3)) = (e2))) -> (~((op (e0) (e3)) = (op (e3) (e3)))) -> (~((op (e0) (e3)) = (op (e2) (e3)))) -> (((op (e0) (e3)) = (e0))\/(((op (e0) (e3)) = (e1))\/(((op (e0) (e3)) = (e2))\/((op (e0) (e3)) = (e3))))) -> (~((op (e0) (e2)) = (op (e3) (e2)))) -> (~((op (e2) (e1)) = (op (e3) (e1)))) -> (((op (e2) (e0)) = (e0))\/(((op (e2) (e0)) = (e1))\/(((op (e2) (e0)) = (e2))\/((op (e2) (e0)) = (e3))))) -> (~((op (e2) (e0)) = (op (e2) (e1)))) -> (~((op (e0) (e2)) = (op (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))))) -> (~((op (e2) (e0)) = (op (e2) (e2)))) -> (((op (e0) (e0)) = (e3))\/(((op (e0) (e1)) = (e3))\/(((op (e0) (e2)) = (e3))\/((op (e0) (e3)) = (e3))))) -> (~((op (e2) (e0)) = (e2))) -> (~((op (e3) (e0)) = (e2))) -> False). % 19.02/19.16 do 0 intro. intros zenon_H1fe zenon_H80 zenon_H1d zenon_H14c zenon_Hd5 zenon_Hdb zenon_Hdf zenon_H2a zenon_Haa zenon_H101 zenon_H71 zenon_H44 zenon_H130 zenon_Hf7 zenon_H102 zenon_Ha1 zenon_He8 zenon_H2b zenon_H17e zenon_H49 zenon_H17b zenon_H2f zenon_H122 zenon_H95 zenon_H9a zenon_H109 zenon_H4a zenon_H12e zenon_Hc2 zenon_He2 zenon_He4 zenon_H14f zenon_Haf zenon_H259 zenon_H1f0 zenon_H195 zenon_H10a zenon_H201 zenon_H128 zenon_H52 zenon_H168 zenon_Hef zenon_H14b. % 19.02/19.16 apply (zenon_or_s _ _ zenon_H1fe); [ zenon_intro zenon_H7b | zenon_intro zenon_H1ff ]. % 19.02/19.16 exact (zenon_H80 zenon_H7b). % 19.02/19.16 apply (zenon_or_s _ _ zenon_H1ff); [ zenon_intro zenon_H86 | zenon_intro zenon_H200 ]. % 19.02/19.16 apply (zenon_or_s _ _ zenon_H168); [ zenon_intro zenon_H3a | zenon_intro zenon_H169 ]. % 19.02/19.16 apply (zenon_or_s _ _ zenon_H109); [ zenon_intro zenon_Ha0 | zenon_intro zenon_H10b ]. % 19.02/19.16 apply (zenon_L406_); trivial. % 19.02/19.16 apply (zenon_or_s _ _ zenon_H10b); [ zenon_intro zenon_H10d | zenon_intro zenon_H10c ]. % 19.02/19.16 exact (zenon_H10a zenon_H10d). % 19.02/19.16 apply (zenon_or_s _ _ zenon_H10c); [ zenon_intro zenon_Ha5 | zenon_intro zenon_Hae ]. % 19.02/19.16 apply (zenon_L1211_); trivial. % 19.02/19.16 apply (zenon_L1210_); trivial. % 19.02/19.16 apply (zenon_or_s _ _ zenon_H169); [ zenon_intro zenon_H99 | zenon_intro zenon_H16a ]. % 19.02/19.16 apply (zenon_L36_); trivial. % 19.02/19.16 apply (zenon_or_s _ _ zenon_H16a); [ zenon_intro zenon_Ha9 | zenon_intro zenon_He3 ]. % 19.02/19.16 apply (zenon_L77_); trivial. % 19.02/19.16 apply (zenon_or_s _ _ zenon_H2f); [ zenon_intro zenon_H34 | zenon_intro zenon_H33 ]. % 19.02/19.16 apply (zenon_L127_); trivial. % 19.02/19.16 apply (zenon_or_s _ _ zenon_H33); [ zenon_intro zenon_H36 | zenon_intro zenon_H35 ]. % 19.02/19.16 apply (zenon_L128_); trivial. % 19.02/19.16 apply (zenon_or_s _ _ zenon_H35); [ zenon_intro zenon_H2c | zenon_intro zenon_H37 ]. % 19.02/19.16 apply (zenon_L3_); trivial. % 19.02/19.16 apply (zenon_or_s _ _ zenon_He8); [ zenon_intro zenon_Hac | zenon_intro zenon_Heb ]. % 19.02/19.16 apply (zenon_L41_); trivial. % 19.02/19.16 apply (zenon_or_s _ _ zenon_Heb); [ zenon_intro zenon_Hae | zenon_intro zenon_Hec ]. % 19.02/19.16 apply (zenon_L1210_); trivial. % 19.02/19.16 apply (zenon_or_s _ _ zenon_Hec); [ zenon_intro zenon_Hba | zenon_intro zenon_Hc4 ]. % 19.02/19.16 apply (zenon_L179_); trivial. % 19.02/19.16 apply (zenon_L1088_); trivial. % 19.02/19.16 apply (zenon_or_s _ _ zenon_H200); [ zenon_intro zenon_Hee | zenon_intro zenon_H148 ]. % 19.02/19.16 exact (zenon_Hef zenon_Hee). % 19.02/19.16 exact (zenon_H14b zenon_H148). % 19.02/19.16 (* end of lemma zenon_L1212_ *) % 19.02/19.16 assert (zenon_L1213_ : (((op (e1) (e1)) = (e0))\/(((op (e1) (e1)) = (e1))\/(((op (e1) (e1)) = (e2))\/((op (e1) (e1)) = (e3))))) -> (~((op (e1) (e1)) = (op (e1) (e2)))) -> ((op (e1) (e2)) = (e0)) -> (~((op (e1) (e1)) = (e1))) -> (~((op (e1) (e1)) = (e2))) -> ((op (e0) (e1)) = (e2)) -> ((op (e3) (e1)) = (e0)) -> False). % 19.02/19.16 do 0 intro. intros zenon_H142 zenon_H4f zenon_H2a zenon_H10a zenon_H20c zenon_H10f zenon_H1b1. % 19.02/19.16 apply (zenon_or_s _ _ zenon_H142); [ zenon_intro zenon_H29 | zenon_intro zenon_H143 ]. % 19.02/19.16 apply (zenon_L10_); trivial. % 19.02/19.16 apply (zenon_or_s _ _ zenon_H143); [ zenon_intro zenon_H10d | zenon_intro zenon_H144 ]. % 19.02/19.16 exact (zenon_H10a zenon_H10d). % 19.02/19.16 apply (zenon_or_s _ _ zenon_H144); [ zenon_intro zenon_H110 | zenon_intro zenon_H13f ]. % 19.02/19.16 exact (zenon_H20c zenon_H110). % 19.02/19.16 apply (zenon_L580_); trivial. % 19.02/19.16 (* end of lemma zenon_L1213_ *) % 19.02/19.16 assert (zenon_L1214_ : (((op (e0) (e0)) = (e0))\/(((op (e0) (e0)) = (e1))\/(((op (e0) (e0)) = (e2))\/((op (e0) (e0)) = (e3))))) -> (~((op (e0) (e0)) = (e0))) -> (~((op (e0) (e0)) = (op (e0) (e2)))) -> ((op (e0) (e2)) = (e1)) -> (~((op (e0) (e0)) = (e2))) -> ((op (e1) (e0)) = (e2)) -> ((op (e3) (e0)) = (e1)) -> False). % 19.02/19.16 do 0 intro. intros zenon_H26a zenon_H3f zenon_H13c zenon_H122 zenon_H80 zenon_H86 zenon_Hac. % 19.02/19.16 apply (zenon_or_s _ _ zenon_H26a); [ zenon_intro zenon_H42 | zenon_intro zenon_H26b ]. % 19.02/19.16 exact (zenon_H3f zenon_H42). % 19.02/19.16 apply (zenon_or_s _ _ zenon_H26b); [ zenon_intro zenon_H7a | zenon_intro zenon_H26c ]. % 19.02/19.16 apply (zenon_L92_); trivial. % 19.02/19.16 apply (zenon_or_s _ _ zenon_H26c); [ zenon_intro zenon_H7b | zenon_intro zenon_H3a ]. % 19.02/19.16 exact (zenon_H80 zenon_H7b). % 19.02/19.16 apply (zenon_L241_); trivial. % 19.02/19.16 (* end of lemma zenon_L1214_ *) % 19.02/19.16 assert (zenon_L1215_ : (((op (e1) (e1)) = (e0))\/(((op (e1) (e1)) = (e1))\/(((op (e1) (e1)) = (e2))\/((op (e1) (e1)) = (e3))))) -> (~((op (e2) (e1)) = (e2))) -> ((op (e2) (e3)) = (e1)) -> (~((op (e2) (e1)) = (op (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))))) -> (~((op (e1) (e1)) = (e1))) -> (~((op (e1) (e1)) = (e2))) -> ((op (e0) (e1)) = (e2)) -> ((op (e3) (e1)) = (e0)) -> False). % 19.02/19.16 do 0 intro. intros zenon_H142 zenon_H26e zenon_Hf4 zenon_H1c7 zenon_H1f0 zenon_H34 zenon_H1cc zenon_H10a zenon_H20c zenon_H10f zenon_H1b1. % 19.02/19.16 apply (zenon_or_s _ _ zenon_H142); [ zenon_intro zenon_H29 | zenon_intro zenon_H143 ]. % 19.02/19.16 apply (zenon_or_s _ _ zenon_H1cc); [ zenon_intro zenon_H36 | zenon_intro zenon_H1cd ]. % 19.02/19.16 apply (zenon_L642_); trivial. % 19.02/19.16 apply (zenon_or_s _ _ zenon_H1cd); [ zenon_intro zenon_Ha5 | zenon_intro zenon_H1ce ]. % 19.02/19.16 apply (zenon_L188_); trivial. % 19.02/19.16 apply (zenon_or_s _ _ zenon_H1ce); [ zenon_intro zenon_H1ca | zenon_intro zenon_Ha6 ]. % 19.02/19.16 exact (zenon_H26e zenon_H1ca). % 19.02/19.16 apply (zenon_L371_); trivial. % 19.02/19.16 apply (zenon_or_s _ _ zenon_H143); [ zenon_intro zenon_H10d | zenon_intro zenon_H144 ]. % 19.02/19.16 exact (zenon_H10a zenon_H10d). % 19.02/19.16 apply (zenon_or_s _ _ zenon_H144); [ zenon_intro zenon_H110 | zenon_intro zenon_H13f ]. % 19.02/19.16 exact (zenon_H20c zenon_H110). % 19.02/19.16 apply (zenon_L580_); trivial. % 19.02/19.16 (* end of lemma zenon_L1215_ *) % 19.02/19.16 assert (zenon_L1216_ : ((~((op (e2) (e0)) = (e2)))\/((op (e2) (e2)) = (e0))) -> ((~((op (e2) (e3)) = (e2)))\/((op (e2) (e2)) = (e3))) -> ((~((op (e3) (e3)) = (e2)))\/((op (e3) (e2)) = (e3))) -> (~((op (e2) (e2)) = (op (e3) (e2)))) -> (~((op (e0) (e0)) = (e0))) -> (((op (e0) (e0)) = (e0))\/(((op (e1) (e0)) = (e0))\/(((op (e2) (e0)) = (e0))\/((op (e3) (e0)) = (e0))))) -> (~((op (e0) (e0)) = (e2))) -> (~((e0) = (e1))) -> (~((op (e1) (e1)) = (e1))) -> (((op (e3) (e0)) = (e0))\/(((op (e3) (e1)) = (e0))\/(((op (e3) (e2)) = (e0))\/((op (e3) (e3)) = (e0))))) -> (((op (e0) (e0)) = (e0))\/(((op (e0) (e0)) = (e1))\/(((op (e0) (e0)) = (e2))\/((op (e0) (e0)) = (e3))))) -> (~((op (e0) (e0)) = (op (e0) (e2)))) -> (~((op (e1) (e2)) = (op (e3) (e2)))) -> (~((op (e1) (e1)) = (op (e1) (e2)))) -> (~((op (e1) (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 (e0) (e1)) = (op (e2) (e1)))) -> (~((e1) = (e3))) -> (~((e0) = (e3))) -> (~((op (e0) (e1)) = (op (e0) (e2)))) -> ((op (e0) (e2)) = (e1)) -> (((op (e2) (e0)) = (e0))\/(((op (e2) (e1)) = (e0))\/(((op (e2) (e2)) = (e0))\/((op (e2) (e3)) = (e0))))) -> (((op (e3) (e3)) = (e0))\/(((op (e3) (e3)) = (e1))\/(((op (e3) (e3)) = (e2))\/((op (e3) (e3)) = (e3))))) -> (~((op (e3) (e3)) = (e3))) -> (~((op (e3) (e1)) = (op (e3) (e3)))) -> (~((op (e3) (e0)) = (op (e3) (e3)))) -> (~((op (e0) (e2)) = (op (e3) (e2)))) -> (((op (e0) (e3)) = (e0))\/(((op (e0) (e3)) = (e1))\/(((op (e0) (e3)) = (e2))\/((op (e0) (e3)) = (e3))))) -> (~((op (e1) (e3)) = (op (e2) (e3)))) -> (~((op (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) (e2)) = (op (e2) (e2)))) -> (~((op (e2) (e1)) = (op (e3) (e1)))) -> (((op (e2) (e0)) = (e0))\/(((op (e2) (e0)) = (e1))\/(((op (e2) (e0)) = (e2))\/((op (e2) (e0)) = (e3))))) -> (~((op (e2) (e0)) = (op (e2) (e2)))) -> (~((op (e1) (e0)) = (op (e2) (e0)))) -> (~((op (e0) (e2)) = (op (e1) (e2)))) -> (~((op (e1) (e3)) = (op (e3) (e3)))) -> (((op (e1) (e0)) = (e1))\/(((op (e1) (e1)) = (e1))\/(((op (e1) (e2)) = (e1))\/((op (e1) (e3)) = (e1))))) -> (~((op (e2) (e0)) = (op (e2) (e1)))) -> (((op (e3) (e0)) = (e1))\/(((op (e3) (e1)) = (e1))\/(((op (e3) (e2)) = (e1))\/((op (e3) (e3)) = (e1))))) -> (~((op (e2) (e0)) = (op (e3) (e0)))) -> (((op (e0) (e1)) = (e1))\/(((op (e1) (e1)) = (e1))\/(((op (e2) (e1)) = (e1))\/((op (e3) (e1)) = (e1))))) -> (((op (e0) (e0)) = (e2))\/(((op (e1) (e0)) = (e2))\/(((op (e2) (e0)) = (e2))\/((op (e3) (e0)) = (e2))))) -> (((op (e2) (e0)) = (e1))\/(((op (e2) (e1)) = (e1))\/(((op (e2) (e2)) = (e1))\/((op (e2) (e3)) = (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) (e2)) = (op (e2) (e2)))) -> (((op (e0) (e0)) = (e2))\/(((op (e0) (e1)) = (e2))\/(((op (e0) (e2)) = (e2))\/((op (e0) (e3)) = (e2))))) -> ((op (e1) (e2)) = (e0)) -> (~((op (e1) (e0)) = (op (e1) (e2)))) -> (~((e2) = (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) (e0)) = (e0))\/(((op (e0) (e1)) = (e0))\/(((op (e0) (e2)) = (e0))\/((op (e0) (e3)) = (e0))))) -> ((~((op (e3) (e0)) = (e2)))\/((op (e3) (e2)) = (e0))) -> (((op (e0) (e2)) = (e2))\/(((op (e1) (e2)) = (e2))\/(((op (e2) (e2)) = (e2))\/((op (e3) (e2)) = (e2))))) -> (~((op (e2) (e2)) = (e2))) -> (~((op (e1) (e2)) = (e2))) -> (~((op (e0) (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 (e1) (e3)) = (e2))) -> (~((op (e0) (e3)) = (e2))) -> ((~((op (e3) (e2)) = (e2)))\/((op (e3) (e2)) = (e2))) -> ((~((op (e2) (e1)) = (e2)))\/((op (e2) (e2)) = (e1))) -> False). % 19.02/19.16 do 0 intro. intros zenon_H276 zenon_H277 zenon_H278 zenon_H18f zenon_H3f zenon_H3e zenon_H80 zenon_Ha1 zenon_H10a zenon_H1ac zenon_H26a zenon_H13c zenon_H115 zenon_H4f zenon_H20c zenon_H142 zenon_H168 zenon_H17e zenon_H95 zenon_H9a zenon_H4a zenon_H122 zenon_H2f zenon_H101 zenon_H102 zenon_H130 zenon_H71 zenon_H14f zenon_He4 zenon_Hdb zenon_H1d zenon_Hdf zenon_Hc2 zenon_He2 zenon_H2b zenon_Haf zenon_H259 zenon_H52 zenon_H201 zenon_H195 zenon_Hd5 zenon_H128 zenon_H1f0 zenon_He8 zenon_H17b zenon_H109 zenon_H1fe zenon_H106 zenon_H1c7 zenon_H1cc zenon_Ha8 zenon_H183 zenon_H2a zenon_H24a zenon_H12b zenon_H245 zenon_H54 zenon_H74 zenon_H270 zenon_H172 zenon_H173 zenon_H114 zenon_H1fd zenon_H145 zenon_H62 zenon_H14c zenon_H12e zenon_H273 zenon_H271. % 19.02/19.16 apply (zenon_or_s _ _ zenon_H276); [ zenon_intro zenon_Hef | zenon_intro zenon_H2c ]. % 19.02/19.16 apply (zenon_or_s _ _ zenon_H271); [ zenon_intro zenon_H26e | zenon_intro zenon_Hf1 ]. % 19.02/19.16 apply (zenon_or_s _ _ zenon_H277); [ zenon_intro zenon_H274 | zenon_intro zenon_Haa ]. % 19.02/19.16 apply (zenon_L1206_); trivial. % 19.02/19.16 apply (zenon_or_s _ _ zenon_H270); [ zenon_intro zenon_H14b | zenon_intro zenon_H61 ]. % 19.02/19.16 apply (zenon_or_s _ _ zenon_H278); [ zenon_intro zenon_Hf7 | zenon_intro zenon_H163 ]. % 19.02/19.16 apply (zenon_or_s _ _ zenon_H74); [ zenon_intro zenon_H42 | zenon_intro zenon_H77 ]. % 19.02/19.16 exact (zenon_H3f zenon_H42). % 19.02/19.16 apply (zenon_or_s _ _ zenon_H77); [ zenon_intro zenon_H49 | zenon_intro zenon_H78 ]. % 19.02/19.16 apply (zenon_or_s _ _ zenon_H3e); [ zenon_intro zenon_H42 | zenon_intro zenon_H41 ]. % 19.02/19.16 exact (zenon_H3f zenon_H42). % 19.02/19.16 apply (zenon_or_s _ _ zenon_H41); [ zenon_intro zenon_H27 | zenon_intro zenon_H43 ]. % 19.02/19.16 apply (zenon_L644_); trivial. % 19.02/19.16 apply (zenon_or_s _ _ zenon_H43); [ zenon_intro zenon_H34 | zenon_intro zenon_H44 ]. % 19.02/19.16 apply (zenon_or_s _ _ zenon_H183); [ zenon_intro zenon_H7b | zenon_intro zenon_H186 ]. % 19.02/19.16 exact (zenon_H80 zenon_H7b). % 19.02/19.16 apply (zenon_or_s _ _ zenon_H186); [ zenon_intro zenon_H10f | zenon_intro zenon_H187 ]. % 19.02/19.16 apply (zenon_or_s _ _ zenon_H1fe); [ zenon_intro zenon_H7b | zenon_intro zenon_H1ff ]. % 19.02/19.16 exact (zenon_H80 zenon_H7b). % 19.02/19.16 apply (zenon_or_s _ _ zenon_H1ff); [ zenon_intro zenon_H86 | zenon_intro zenon_H200 ]. % 19.02/19.16 apply (zenon_or_s _ _ zenon_H109); [ zenon_intro zenon_Ha0 | zenon_intro zenon_H10b ]. % 19.02/19.16 apply (zenon_L38_); trivial. % 19.02/19.16 apply (zenon_or_s _ _ zenon_H10b); [ zenon_intro zenon_H10d | zenon_intro zenon_H10c ]. % 19.02/19.16 exact (zenon_H10a zenon_H10d). % 19.02/19.16 apply (zenon_or_s _ _ zenon_H10c); [ zenon_intro zenon_Ha5 | zenon_intro zenon_Hae ]. % 19.02/19.16 apply (zenon_or_s _ _ zenon_H1ac); [ zenon_intro zenon_H44 | zenon_intro zenon_H1af ]. % 19.02/19.16 apply (zenon_L1212_); trivial. % 19.02/19.16 apply (zenon_or_s _ _ zenon_H1af); [ zenon_intro zenon_H1b1 | zenon_intro zenon_H1b0 ]. % 19.02/19.16 apply (zenon_L1213_); trivial. % 19.02/19.16 apply (zenon_or_s _ _ zenon_H1b0); [ zenon_intro zenon_H61 | zenon_intro zenon_H60 ]. % 19.02/19.16 apply (zenon_L176_); trivial. % 19.02/19.16 apply (zenon_or_s _ _ zenon_He8); [ zenon_intro zenon_Hac | zenon_intro zenon_Heb ]. % 19.02/19.16 apply (zenon_L1214_); trivial. % 19.02/19.16 apply (zenon_or_s _ _ zenon_Heb); [ zenon_intro zenon_Hae | zenon_intro zenon_Hec ]. % 19.02/19.16 apply (zenon_L42_); trivial. % 19.02/19.16 apply (zenon_or_s _ _ zenon_Hec); [ zenon_intro zenon_Hba | zenon_intro zenon_Hc4 ]. % 19.02/19.16 apply (zenon_L179_); trivial. % 19.02/19.16 apply (zenon_L1093_); trivial. % 19.02/19.16 apply (zenon_or_s _ _ zenon_H106); [ zenon_intro zenon_Hed | zenon_intro zenon_H107 ]. % 19.02/19.16 apply (zenon_L214_); trivial. % 19.02/19.16 apply (zenon_or_s _ _ zenon_H107); [ zenon_intro zenon_Ha5 | zenon_intro zenon_H108 ]. % 19.02/19.16 apply (zenon_L42_); trivial. % 19.02/19.16 apply (zenon_or_s _ _ zenon_H108); [ zenon_intro zenon_Hf1 | zenon_intro zenon_Hf4 ]. % 19.02/19.16 apply (zenon_L246_); trivial. % 19.02/19.16 apply (zenon_or_s _ _ zenon_H1ac); [ zenon_intro zenon_H44 | zenon_intro zenon_H1af ]. % 19.02/19.16 apply (zenon_L1210_); trivial. % 19.02/19.16 apply (zenon_or_s _ _ zenon_H1af); [ zenon_intro zenon_H1b1 | zenon_intro zenon_H1b0 ]. % 19.02/19.16 apply (zenon_L1215_); trivial. % 19.02/19.16 apply (zenon_or_s _ _ zenon_H1b0); [ zenon_intro zenon_H61 | zenon_intro zenon_H60 ]. % 19.02/19.16 apply (zenon_L432_); trivial. % 19.02/19.16 apply (zenon_L1133_); trivial. % 19.02/19.16 apply (zenon_or_s _ _ zenon_H200); [ zenon_intro zenon_Hee | zenon_intro zenon_H148 ]. % 19.02/19.16 exact (zenon_Hef zenon_Hee). % 19.02/19.16 exact (zenon_H14b zenon_H148). % 19.02/19.16 apply (zenon_or_s _ _ zenon_H187); [ zenon_intro zenon_H150 | zenon_intro zenon_Hcd ]. % 19.02/19.16 exact (zenon_H1fd zenon_H150). % 19.02/19.16 exact (zenon_H12e zenon_Hcd). % 19.02/19.16 apply (zenon_L1212_); trivial. % 19.02/19.16 apply (zenon_or_s _ _ zenon_H78); [ zenon_intro zenon_H48 | zenon_intro zenon_H1e ]. % 19.02/19.16 apply (zenon_L334_); trivial. % 19.02/19.16 apply (zenon_or_s _ _ zenon_H3e); [ zenon_intro zenon_H42 | zenon_intro zenon_H41 ]. % 19.02/19.16 exact (zenon_H3f zenon_H42). % 19.02/19.16 apply (zenon_or_s _ _ zenon_H41); [ zenon_intro zenon_H27 | zenon_intro zenon_H43 ]. % 19.02/19.16 apply (zenon_L644_); trivial. % 19.02/19.16 apply (zenon_or_s _ _ zenon_H43); [ zenon_intro zenon_H34 | zenon_intro zenon_H44 ]. % 19.02/19.16 apply (zenon_or_s _ _ zenon_H183); [ zenon_intro zenon_H7b | zenon_intro zenon_H186 ]. % 19.02/19.16 exact (zenon_H80 zenon_H7b). % 19.02/19.16 apply (zenon_or_s _ _ zenon_H186); [ zenon_intro zenon_H10f | zenon_intro zenon_H187 ]. % 19.02/19.16 apply (zenon_or_s _ _ zenon_H245); [ zenon_intro zenon_H49 | zenon_intro zenon_H246 ]. % 19.02/19.16 apply (zenon_L12_); trivial. % 19.02/19.16 apply (zenon_or_s _ _ zenon_H246); [ zenon_intro zenon_H29 | zenon_intro zenon_H247 ]. % 19.02/19.16 apply (zenon_L10_); trivial. % 19.02/19.16 apply (zenon_or_s _ _ zenon_H247); [ zenon_intro zenon_H36 | zenon_intro zenon_H1b1 ]. % 19.02/19.16 apply (zenon_L642_); trivial. % 19.02/19.16 apply (zenon_L1213_); trivial. % 19.02/19.16 apply (zenon_or_s _ _ zenon_H187); [ zenon_intro zenon_H150 | zenon_intro zenon_Hcd ]. % 19.02/19.16 exact (zenon_H1fd zenon_H150). % 19.02/19.16 exact (zenon_H12e zenon_Hcd). % 19.02/19.16 apply (zenon_or_s _ _ zenon_H183); [ zenon_intro zenon_H7b | zenon_intro zenon_H186 ]. % 19.02/19.16 exact (zenon_H80 zenon_H7b). % 19.02/19.16 apply (zenon_or_s _ _ zenon_H186); [ zenon_intro zenon_H10f | zenon_intro zenon_H187 ]. % 19.02/19.16 apply (zenon_or_s _ _ zenon_H1fe); [ zenon_intro zenon_H7b | zenon_intro zenon_H1ff ]. % 19.02/19.16 exact (zenon_H80 zenon_H7b). % 19.02/19.16 apply (zenon_or_s _ _ zenon_H1ff); [ zenon_intro zenon_H86 | zenon_intro zenon_H200 ]. % 19.02/19.16 apply (zenon_or_s _ _ zenon_H168); [ zenon_intro zenon_H3a | zenon_intro zenon_H169 ]. % 19.02/19.16 apply (zenon_or_s _ _ zenon_H109); [ zenon_intro zenon_Ha0 | zenon_intro zenon_H10b ]. % 19.02/19.16 apply (zenon_L406_); trivial. % 19.02/19.16 apply (zenon_or_s _ _ zenon_H10b); [ zenon_intro zenon_H10d | zenon_intro zenon_H10c ]. % 19.02/19.16 exact (zenon_H10a zenon_H10d). % 19.02/19.16 apply (zenon_or_s _ _ zenon_H10c); [ zenon_intro zenon_Ha5 | zenon_intro zenon_Hae ]. % 19.02/19.16 apply (zenon_or_s _ _ zenon_H2f); [ zenon_intro zenon_H34 | zenon_intro zenon_H33 ]. % 19.02/19.16 apply (zenon_L127_); trivial. % 19.02/19.16 apply (zenon_or_s _ _ zenon_H33); [ zenon_intro zenon_H36 | zenon_intro zenon_H35 ]. % 19.02/19.16 apply (zenon_L1209_); trivial. % 19.02/19.16 apply (zenon_or_s _ _ zenon_H35); [ zenon_intro zenon_H2c | zenon_intro zenon_H37 ]. % 19.02/19.16 apply (zenon_L3_); trivial. % 19.02/19.16 apply (zenon_L367_); trivial. % 19.02/19.16 apply (zenon_L1210_); trivial. % 19.02/19.16 apply (zenon_or_s _ _ zenon_H169); [ zenon_intro zenon_H99 | zenon_intro zenon_H16a ]. % 19.02/19.16 apply (zenon_L175_); trivial. % 19.02/19.16 apply (zenon_or_s _ _ zenon_H16a); [ zenon_intro zenon_Ha9 | zenon_intro zenon_He3 ]. % 19.02/19.16 apply (zenon_L77_); trivial. % 19.02/19.16 apply (zenon_L515_); trivial. % 19.02/19.16 apply (zenon_or_s _ _ zenon_H200); [ zenon_intro zenon_Hee | zenon_intro zenon_H148 ]. % 19.02/19.16 exact (zenon_Hef zenon_Hee). % 19.02/19.16 exact (zenon_H14b zenon_H148). % 19.02/19.16 apply (zenon_or_s _ _ zenon_H187); [ zenon_intro zenon_H150 | zenon_intro zenon_Hcd ]. % 19.02/19.16 exact (zenon_H1fd zenon_H150). % 19.02/19.16 exact (zenon_H12e zenon_Hcd). % 19.02/19.16 apply (zenon_L180_); trivial. % 19.02/19.16 apply (zenon_L176_); trivial. % 19.02/19.16 apply (zenon_L246_); trivial. % 19.02/19.16 apply (zenon_L3_); trivial. % 19.02/19.16 (* end of lemma zenon_L1216_ *) % 19.02/19.16 assert (zenon_L1217_ : (((op (e1) (e0)) = (e2))\/(((op (e1) (e1)) = (e2))\/(((op (e1) (e2)) = (e2))\/((op (e1) (e3)) = (e2))))) -> (~((op (e1) (e0)) = (e2))) -> (~((op (e1) (e1)) = (e2))) -> (~((op (e1) (e2)) = (e2))) -> ((op (e1) (e3)) = (e1)) -> (~((e1) = (e2))) -> False). % 19.02/19.16 do 0 intro. intros zenon_H18c zenon_H177 zenon_H20c zenon_H114 zenon_Hd6 zenon_H7c. % 19.02/19.16 apply (zenon_or_s _ _ zenon_H18c); [ zenon_intro zenon_H86 | zenon_intro zenon_H18d ]. % 19.02/19.16 exact (zenon_H177 zenon_H86). % 19.02/19.16 apply (zenon_or_s _ _ zenon_H18d); [ zenon_intro zenon_H110 | zenon_intro zenon_H18e ]. % 19.02/19.16 exact (zenon_H20c zenon_H110). % 19.02/19.16 apply (zenon_or_s _ _ zenon_H18e); [ zenon_intro zenon_H113 | zenon_intro zenon_Hd7 ]. % 19.02/19.16 exact (zenon_H114 zenon_H113). % 19.02/19.16 apply (zenon_L101_); trivial. % 19.02/19.16 (* end of lemma zenon_L1217_ *) % 19.02/19.16 assert (zenon_L1218_ : (((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 (e2) (e2)) = (e1)) -> (~((op (e1) (e2)) = (op (e2) (e2)))) -> (((op (e1) (e0)) = (e2))\/(((op (e1) (e1)) = (e2))\/(((op (e1) (e2)) = (e2))\/((op (e1) (e3)) = (e2))))) -> (~((op (e1) (e0)) = (e2))) -> (~((op (e1) (e1)) = (e2))) -> (~((op (e1) (e2)) = (e2))) -> (~((e1) = (e2))) -> False). % 19.02/19.16 do 0 intro. intros zenon_H128 zenon_Ha1 zenon_H27 zenon_H10a zenon_Hf1 zenon_H2b zenon_H18c zenon_H177 zenon_H20c zenon_H114 zenon_H7c. % 19.02/19.16 apply (zenon_or_s _ _ zenon_H128); [ zenon_intro zenon_H9d | zenon_intro zenon_H129 ]. % 19.02/19.16 apply (zenon_L262_); trivial. % 19.02/19.16 apply (zenon_or_s _ _ zenon_H129); [ zenon_intro zenon_H10d | zenon_intro zenon_H12a ]. % 19.02/19.16 exact (zenon_H10a zenon_H10d). % 19.02/19.16 apply (zenon_or_s _ _ zenon_H12a); [ zenon_intro zenon_Hf0 | zenon_intro zenon_Hd6 ]. % 19.02/19.16 apply (zenon_L59_); trivial. % 19.02/19.16 apply (zenon_L1217_); trivial. % 19.02/19.16 (* end of lemma zenon_L1218_ *) % 19.02/19.16 assert (zenon_L1219_ : (((op (e3) (e0)) = (e1))\/(((op (e3) (e1)) = (e1))\/(((op (e3) (e2)) = (e1))\/((op (e3) (e3)) = (e1))))) -> ((op (e0) (e0)) = (e2)) -> (~((op (e2) (e0)) = (e2))) -> (~((op (e2) (e0)) = (op (e2) (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) (e1)) = (e1)) -> (~((op (e0) (e1)) = (op (e3) (e1)))) -> ((op (e2) (e2)) = (e1)) -> (~((op (e2) (e2)) = (op (e3) (e2)))) -> ((op (e2) (e3)) = (e0)) -> ((op (e1) (e3)) = (e2)) -> False). % 19.02/19.16 do 0 intro. intros zenon_He8 zenon_H7b zenon_Hef zenon_H52 zenon_H5b zenon_H259 zenon_Ha0 zenon_H210 zenon_Hf1 zenon_H18f zenon_H37 zenon_Hd7. % 19.02/19.16 apply (zenon_or_s _ _ zenon_He8); [ zenon_intro zenon_Hac | zenon_intro zenon_Heb ]. % 19.02/19.16 apply (zenon_L1145_); trivial. % 19.02/19.16 apply (zenon_or_s _ _ zenon_Heb); [ zenon_intro zenon_Hae | zenon_intro zenon_Hec ]. % 19.02/19.16 apply (zenon_L363_); trivial. % 19.02/19.16 apply (zenon_or_s _ _ zenon_Hec); [ zenon_intro zenon_Hba | zenon_intro zenon_Hc4 ]. % 19.02/19.16 apply (zenon_L185_); trivial. % 19.02/19.16 apply (zenon_L72_); trivial. % 19.02/19.16 (* end of lemma zenon_L1219_ *) % 19.02/19.16 assert (zenon_L1220_ : (((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) (e1)) = (op (e1) (e3)))) -> ((op (e1) (e1)) = (e0)) -> ((op (e1) (e3)) = (e2)) -> (~((op (e2) (e2)) = (op (e3) (e2)))) -> ((op (e2) (e2)) = (e1)) -> (~((op (e0) (e1)) = (op (e3) (e1)))) -> ((op (e0) (e1)) = (e1)) -> (((op (e2) (e0)) = (e0))\/(((op (e2) (e0)) = (e1))\/(((op (e2) (e0)) = (e2))\/((op (e2) (e0)) = (e3))))) -> (~((op (e2) (e0)) = (op (e2) (e3)))) -> (~((op (e2) (e0)) = (op (e2) (e2)))) -> (~((op (e2) (e0)) = (e2))) -> ((op (e0) (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)) = (op (e3) (e3)))) -> False). % 19.02/19.16 do 0 intro. intros zenon_H67 zenon_H208 zenon_H48 zenon_H57 zenon_H29 zenon_Hd7 zenon_H18f zenon_Hf1 zenon_H210 zenon_Ha0 zenon_H259 zenon_H5b zenon_H52 zenon_Hef zenon_H7b zenon_He8 zenon_H44 zenon_H71. % 19.02/19.16 apply (zenon_or_s _ _ zenon_H67); [ zenon_intro zenon_H1e | zenon_intro zenon_H68 ]. % 19.02/19.16 apply (zenon_L336_); trivial. % 19.02/19.16 apply (zenon_or_s _ _ zenon_H68); [ zenon_intro zenon_H1f | zenon_intro zenon_H69 ]. % 19.02/19.16 apply (zenon_L13_); trivial. % 19.02/19.16 apply (zenon_or_s _ _ zenon_H69); [ zenon_intro zenon_H37 | zenon_intro zenon_H60 ]. % 19.02/19.16 apply (zenon_L1219_); trivial. % 19.02/19.16 apply (zenon_L21_); trivial. % 19.02/19.16 (* end of lemma zenon_L1220_ *) % 19.02/19.16 assert (zenon_L1221_ : (((op (e1) (e1)) = (e0))\/(((op (e1) (e1)) = (e1))\/(((op (e1) (e1)) = (e2))\/((op (e1) (e1)) = (e3))))) -> (~((op (e1) (e1)) = (op (e1) (e3)))) -> ((op (e1) (e3)) = (e0)) -> (~((op (e1) (e1)) = (e1))) -> (~((op (e1) (e1)) = (e2))) -> (~((op (e0) (e1)) = (op (e1) (e1)))) -> ((op (e0) (e1)) = (e3)) -> False). % 19.02/19.16 do 0 intro. intros zenon_H142 zenon_H57 zenon_H1f zenon_H10a zenon_H20c zenon_H10e zenon_H99. % 19.02/19.16 apply (zenon_or_s _ _ zenon_H142); [ zenon_intro zenon_H29 | zenon_intro zenon_H143 ]. % 19.02/19.16 apply (zenon_L13_); trivial. % 19.02/19.16 apply (zenon_or_s _ _ zenon_H143); [ zenon_intro zenon_H10d | zenon_intro zenon_H144 ]. % 19.02/19.16 exact (zenon_H10a zenon_H10d). % 19.02/19.16 apply (zenon_or_s _ _ zenon_H144); [ zenon_intro zenon_H110 | zenon_intro zenon_H13f ]. % 19.02/19.16 exact (zenon_H20c zenon_H110). % 19.02/19.16 apply (zenon_L108_); trivial. % 19.02/19.16 (* end of lemma zenon_L1221_ *) % 19.02/19.16 assert (zenon_L1222_ : (((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)) = (e0)) -> ((op (e2) (e3)) = (e3)) -> (~((op (e0) (e3)) = (op (e2) (e3)))) -> (~((op (e0) (e3)) = (e2))) -> (~((op (e0) (e1)) = (op (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 (e0) (e1)) = (e2))) -> (((op (e1) (e1)) = (e0))\/(((op (e1) (e1)) = (e1))\/(((op (e1) (e1)) = (e2))\/((op (e1) (e1)) = (e3))))) -> (~((op (e1) (e1)) = (op (e1) (e3)))) -> ((op (e1) (e3)) = (e0)) -> (~((op (e1) (e1)) = (e1))) -> (~((op (e1) (e1)) = (e2))) -> (~((op (e0) (e1)) = (op (e1) (e1)))) -> False). % 19.02/19.16 do 0 intro. intros zenon_H212 zenon_H4a zenon_H48 zenon_Hdd zenon_He2 zenon_H12e zenon_H54 zenon_H1d zenon_He4 zenon_H26d zenon_H142 zenon_H57 zenon_H1f zenon_H10a zenon_H20c zenon_H10e. % 19.02/19.16 apply (zenon_or_s _ _ zenon_H212); [ zenon_intro zenon_H49 | zenon_intro zenon_H213 ]. % 19.02/19.16 apply (zenon_L9_); trivial. % 19.02/19.16 apply (zenon_or_s _ _ zenon_H213); [ zenon_intro zenon_Ha0 | zenon_intro zenon_H214 ]. % 19.02/19.16 apply (zenon_L1147_); trivial. % 19.02/19.16 apply (zenon_or_s _ _ zenon_H214); [ zenon_intro zenon_H10f | zenon_intro zenon_H99 ]. % 19.02/19.16 exact (zenon_H26d zenon_H10f). % 19.02/19.16 apply (zenon_L1221_); trivial. % 19.02/19.16 (* end of lemma zenon_L1222_ *) % 19.02/19.16 assert (zenon_L1223_ : (((op (e0) (e3)) = (e3))\/(((op (e1) (e3)) = (e3))\/(((op (e2) (e3)) = (e3))\/((op (e3) (e3)) = (e3))))) -> (~((e1) = (e3))) -> ((op (e0) (e3)) = (e1)) -> (~((e2) = (e3))) -> ((op (e1) (e3)) = (e2)) -> (~((op (e0) (e1)) = (op (e1) (e1)))) -> (~((op (e1) (e1)) = (e2))) -> (~((op (e1) (e1)) = (e1))) -> ((op (e1) (e3)) = (e0)) -> (~((op (e1) (e1)) = (op (e1) (e3)))) -> (((op (e1) (e1)) = (e0))\/(((op (e1) (e1)) = (e1))\/(((op (e1) (e1)) = (e2))\/((op (e1) (e1)) = (e3))))) -> (~((op (e0) (e1)) = (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)) = (e2))) -> (~((op (e0) (e3)) = (op (e2) (e3)))) -> ((op (e0) (e2)) = (e0)) -> (~((op (e0) (e1)) = (op (e0) (e2)))) -> (((op (e0) (e1)) = (e0))\/(((op (e0) (e1)) = (e1))\/(((op (e0) (e1)) = (e2))\/((op (e0) (e1)) = (e3))))) -> (~((op (e3) (e3)) = (e3))) -> False). % 19.02/19.16 do 0 intro. intros zenon_H136 zenon_H95 zenon_Hc3 zenon_H12b zenon_Hd7 zenon_H10e zenon_H20c zenon_H10a zenon_H1f zenon_H57 zenon_H142 zenon_H26d zenon_He4 zenon_H1d zenon_H54 zenon_H12e zenon_He2 zenon_H48 zenon_H4a zenon_H212 zenon_H102. % 19.02/19.16 apply (zenon_or_s _ _ zenon_H136); [ zenon_intro zenon_He3 | zenon_intro zenon_H137 ]. % 19.02/19.16 apply (zenon_L633_); trivial. % 19.02/19.16 apply (zenon_or_s _ _ zenon_H137); [ zenon_intro zenon_Hdc | zenon_intro zenon_H138 ]. % 19.02/19.16 apply (zenon_L266_); trivial. % 19.02/19.16 apply (zenon_or_s _ _ zenon_H138); [ zenon_intro zenon_Hdd | zenon_intro zenon_H105 ]. % 19.02/19.16 apply (zenon_L1222_); trivial. % 19.02/19.16 exact (zenon_H102 zenon_H105). % 19.02/19.16 (* end of lemma zenon_L1223_ *) % 19.02/19.16 assert (zenon_L1224_ : (((op (e0) (e3)) = (e0))\/(((op (e1) (e3)) = (e0))\/(((op (e2) (e3)) = (e0))\/((op (e3) (e3)) = (e0))))) -> (~((op (e0) (e2)) = (op (e0) (e3)))) -> (~((op (e3) (e3)) = (e3))) -> (((op (e0) (e1)) = (e0))\/(((op (e0) (e1)) = (e1))\/(((op (e0) (e1)) = (e2))\/((op (e0) (e1)) = (e3))))) -> (~((op (e0) (e1)) = (op (e0) (e2)))) -> ((op (e0) (e2)) = (e0)) -> (~((op (e0) (e3)) = (op (e2) (e3)))) -> (~((op (e0) (e3)) = (e2))) -> (~((op (e0) (e1)) = (op (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 (e0) (e1)) = (e2))) -> (((op (e1) (e1)) = (e0))\/(((op (e1) (e1)) = (e1))\/(((op (e1) (e1)) = (e2))\/((op (e1) (e1)) = (e3))))) -> (~((op (e1) (e1)) = (op (e1) (e3)))) -> (~((op (e1) (e1)) = (e1))) -> (~((op (e1) (e1)) = (e2))) -> (~((op (e0) (e1)) = (op (e1) (e1)))) -> ((op (e1) (e3)) = (e2)) -> (~((e2) = (e3))) -> ((op (e0) (e3)) = (e1)) -> (~((e1) = (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) (e0)) = (e0)) -> ((op (e3) (e1)) = (e0)) -> (~((op (e3) (e1)) = (op (e3) (e3)))) -> False). % 19.02/19.16 do 0 intro. intros zenon_H67 zenon_H208 zenon_H102 zenon_H212 zenon_H4a zenon_H48 zenon_He2 zenon_H12e zenon_H54 zenon_H1d zenon_He4 zenon_H26d zenon_H142 zenon_H57 zenon_H10a zenon_H20c zenon_H10e zenon_Hd7 zenon_H12b zenon_Hc3 zenon_H95 zenon_H136 zenon_H5b zenon_H34 zenon_H1b1 zenon_H130. % 19.02/19.16 apply (zenon_or_s _ _ zenon_H67); [ zenon_intro zenon_H1e | zenon_intro zenon_H68 ]. % 19.02/19.16 apply (zenon_L336_); trivial. % 19.02/19.16 apply (zenon_or_s _ _ zenon_H68); [ zenon_intro zenon_H1f | zenon_intro zenon_H69 ]. % 19.02/19.16 apply (zenon_L1223_); trivial. % 19.02/19.16 apply (zenon_or_s _ _ zenon_H69); [ zenon_intro zenon_H37 | zenon_intro zenon_H60 ]. % 19.02/19.16 apply (zenon_L14_); trivial. % 19.02/19.16 apply (zenon_L244_); trivial. % 19.02/19.16 (* end of lemma zenon_L1224_ *) % 19.02/19.16 assert (zenon_L1225_ : (((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)) = (op (e3) (e3)))) -> ((op (e2) (e0)) = (e0)) -> (~((op (e2) (e0)) = (op (e2) (e3)))) -> (((op (e0) (e3)) = (e3))\/(((op (e1) (e3)) = (e3))\/(((op (e2) (e3)) = (e3))\/((op (e3) (e3)) = (e3))))) -> (~((e1) = (e3))) -> (~((e2) = (e3))) -> (~((op (e0) (e1)) = (op (e1) (e1)))) -> (~((op (e1) (e1)) = (e2))) -> (~((op (e1) (e1)) = (e1))) -> (~((op (e1) (e1)) = (op (e1) (e3)))) -> (((op (e1) (e1)) = (e0))\/(((op (e1) (e1)) = (e1))\/(((op (e1) (e1)) = (e2))\/((op (e1) (e1)) = (e3))))) -> (~((op (e0) (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) (e1)) = (op (e0) (e3)))) -> (~((op (e0) (e3)) = (e2))) -> (~((op (e0) (e3)) = (op (e2) (e3)))) -> ((op (e0) (e2)) = (e0)) -> (~((op (e0) (e1)) = (op (e0) (e2)))) -> (((op (e0) (e1)) = (e0))\/(((op (e0) (e1)) = (e1))\/(((op (e0) (e1)) = (e2))\/((op (e0) (e1)) = (e3))))) -> (~((op (e3) (e3)) = (e3))) -> (~((op (e0) (e2)) = (op (e0) (e3)))) -> (((op (e0) (e3)) = (e0))\/(((op (e1) (e3)) = (e0))\/(((op (e2) (e3)) = (e0))\/((op (e3) (e3)) = (e0))))) -> ((op (e2) (e2)) = (e1)) -> ((op (e1) (e2)) = (e3)) -> ((op (e1) (e3)) = (e2)) -> ((op (e0) (e3)) = (e1)) -> False). % 19.02/19.16 do 0 intro. intros zenon_H1ac zenon_H17b zenon_H130 zenon_H34 zenon_H5b zenon_H136 zenon_H95 zenon_H12b zenon_H10e zenon_H20c zenon_H10a zenon_H57 zenon_H142 zenon_H26d zenon_He4 zenon_H1d zenon_H54 zenon_H12e zenon_He2 zenon_H48 zenon_H4a zenon_H212 zenon_H102 zenon_H208 zenon_H67 zenon_Hf1 zenon_H16c zenon_Hd7 zenon_Hc3. % 19.02/19.16 apply (zenon_or_s _ _ zenon_H1ac); [ zenon_intro zenon_H44 | zenon_intro zenon_H1af ]. % 19.02/19.16 apply (zenon_L127_); trivial. % 19.02/19.16 apply (zenon_or_s _ _ zenon_H1af); [ zenon_intro zenon_H1b1 | zenon_intro zenon_H1b0 ]. % 19.02/19.16 apply (zenon_L1224_); trivial. % 19.02/19.16 apply (zenon_or_s _ _ zenon_H1b0); [ zenon_intro zenon_H61 | zenon_intro zenon_H60 ]. % 19.02/19.16 apply (zenon_L156_); trivial. % 19.02/19.16 apply (zenon_L201_); trivial. % 19.02/19.16 (* end of lemma zenon_L1225_ *) % 19.02/19.16 assert (zenon_L1226_ : (((op (e0) (e3)) = (e1))\/(((op (e1) (e3)) = (e1))\/(((op (e2) (e3)) = (e1))\/((op (e3) (e3)) = (e1))))) -> ((op (e1) (e2)) = (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) (e1)) = (e0))\/(((op (e0) (e1)) = (e1))\/(((op (e0) (e1)) = (e2))\/((op (e0) (e1)) = (e3))))) -> (~((op (e0) (e1)) = (op (e0) (e2)))) -> ((op (e0) (e2)) = (e0)) -> (~((op (e0) (e1)) = (e2))) -> (((op (e1) (e1)) = (e0))\/(((op (e1) (e1)) = (e1))\/(((op (e1) (e1)) = (e2))\/((op (e1) (e1)) = (e3))))) -> (~((op (e1) (e1)) = (op (e1) (e3)))) -> (~((op (e1) (e1)) = (e1))) -> (~((op (e1) (e1)) = (e2))) -> (~((op (e0) (e1)) = (op (e1) (e1)))) -> (~((e1) = (e3))) -> (~((op (e2) (e0)) = (op (e2) (e3)))) -> ((op (e2) (e0)) = (e0)) -> (~((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))))) -> (~((e1) = (e2))) -> (~((op (e2) (e2)) = (op (e2) (e3)))) -> ((op (e2) (e2)) = (e1)) -> (((op (e0) (e3)) = (e3))\/(((op (e1) (e3)) = (e3))\/(((op (e2) (e3)) = (e3))\/((op (e3) (e3)) = (e3))))) -> ((op (e2) (e1)) = (e2)) -> (~((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))))) -> (~((e2) = (e3))) -> ((op (e1) (e3)) = (e2)) -> (~((op (e0) (e3)) = (op (e2) (e3)))) -> (~((op (e0) (e3)) = (e2))) -> ((op (e0) (e1)) = (e1)) -> (~((op (e0) (e1)) = (op (e0) (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 (e3) (e3)) = (e3))) -> False). % 19.02/19.16 do 0 intro. intros zenon_H133 zenon_H16c zenon_H67 zenon_H208 zenon_H212 zenon_H4a zenon_H48 zenon_H26d zenon_H142 zenon_H57 zenon_H10a zenon_H20c zenon_H10e zenon_H95 zenon_H5b zenon_H34 zenon_H130 zenon_H17b zenon_H1ac zenon_H7c zenon_H6d zenon_Hf1 zenon_H136 zenon_H1ca zenon_H1c7 zenon_Hf3 zenon_H11f zenon_H12b zenon_Hd7 zenon_He2 zenon_H12e zenon_Ha0 zenon_H54 zenon_H1d zenon_H1f zenon_He4 zenon_H102. % 19.02/19.16 apply (zenon_or_s _ _ zenon_H133); [ zenon_intro zenon_Hc3 | zenon_intro zenon_H134 ]. % 19.02/19.16 apply (zenon_L1225_); trivial. % 19.02/19.16 apply (zenon_or_s _ _ zenon_H134); [ zenon_intro zenon_Hd6 | zenon_intro zenon_H135 ]. % 19.02/19.16 apply (zenon_L101_); trivial. % 19.02/19.16 apply (zenon_or_s _ _ zenon_H135); [ zenon_intro zenon_Hf4 | zenon_intro zenon_Hc4 ]. % 19.02/19.16 apply (zenon_L84_); trivial. % 19.02/19.16 apply (zenon_L1187_); trivial. % 19.02/19.16 (* end of lemma zenon_L1226_ *) % 19.02/19.16 assert (zenon_L1227_ : (~((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) (e1)) = (op (e0) (e3)))) -> (~((op (e0) (e3)) = (e2))) -> (~((op (e0) (e3)) = (op (e2) (e3)))) -> (~((e2) = (e3))) -> (((op (e2) (e3)) = (e0))\/(((op (e2) (e3)) = (e1))\/(((op (e2) (e3)) = (e2))\/((op (e2) (e3)) = (e3))))) -> (~((op (e2) (e3)) = (op (e3) (e3)))) -> (~((op (e2) (e1)) = (op (e2) (e3)))) -> ((op (e2) (e1)) = (e2)) -> (((op (e0) (e3)) = (e3))\/(((op (e1) (e3)) = (e3))\/(((op (e2) (e3)) = (e3))\/((op (e3) (e3)) = (e3))))) -> (~((op (e2) (e2)) = (op (e2) (e3)))) -> (~((e1) = (e2))) -> (((op (e3) (e0)) = (e0))\/(((op (e3) (e1)) = (e0))\/(((op (e3) (e2)) = (e0))\/((op (e3) (e3)) = (e0))))) -> (~((op (e2) (e0)) = (op (e3) (e0)))) -> ((op (e2) (e0)) = (e0)) -> (~((e1) = (e3))) -> (~((op (e0) (e1)) = (op (e1) (e1)))) -> (~((op (e1) (e1)) = (e2))) -> (~((op (e1) (e1)) = (e1))) -> (~((op (e1) (e1)) = (op (e1) (e3)))) -> (((op (e1) (e1)) = (e0))\/(((op (e1) (e1)) = (e1))\/(((op (e1) (e1)) = (e2))\/((op (e1) (e1)) = (e3))))) -> (~((op (e0) (e1)) = (e2))) -> ((op (e0) (e2)) = (e0)) -> (~((op (e0) (e1)) = (op (e0) (e2)))) -> (((op (e0) (e1)) = (e0))\/(((op (e0) (e1)) = (e1))\/(((op (e0) (e1)) = (e2))\/((op (e0) (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) (e2)) = (e3)) -> (((op (e0) (e3)) = (e1))\/(((op (e1) (e3)) = (e1))\/(((op (e2) (e3)) = (e1))\/((op (e3) (e3)) = (e1))))) -> ((op (e1) (e3)) = (e2)) -> (~((op (e2) (e2)) = (op (e3) (e2)))) -> ((op (e2) (e2)) = (e1)) -> (~((op (e0) (e1)) = (op (e3) (e1)))) -> ((op (e0) (e1)) = (e1)) -> (((op (e2) (e0)) = (e0))\/(((op (e2) (e0)) = (e1))\/(((op (e2) (e0)) = (e2))\/((op (e2) (e0)) = (e3))))) -> (~((op (e2) (e0)) = (op (e2) (e3)))) -> (~((op (e2) (e0)) = (op (e2) (e2)))) -> (~((op (e2) (e0)) = (e2))) -> ((op (e0) (e0)) = (e2)) -> (((op (e3) (e0)) = (e1))\/(((op (e3) (e1)) = (e1))\/(((op (e3) (e2)) = (e1))\/((op (e3) (e3)) = (e1))))) -> ((op (e3) (e1)) = (e0)) -> (~((op (e3) (e1)) = (op (e3) (e3)))) -> False). % 19.02/19.16 do 0 intro. intros zenon_H102 zenon_He4 zenon_H1d zenon_H54 zenon_H12e zenon_He2 zenon_H12b zenon_H11f zenon_Hf3 zenon_H1c7 zenon_H1ca zenon_H136 zenon_H6d zenon_H7c zenon_H1ac zenon_H17b zenon_H34 zenon_H95 zenon_H10e zenon_H20c zenon_H10a zenon_H57 zenon_H142 zenon_H26d zenon_H48 zenon_H4a zenon_H212 zenon_H208 zenon_H67 zenon_H16c zenon_H133 zenon_Hd7 zenon_H18f zenon_Hf1 zenon_H210 zenon_Ha0 zenon_H259 zenon_H5b zenon_H52 zenon_Hef zenon_H7b zenon_He8 zenon_H1b1 zenon_H130. % 19.02/19.16 apply (zenon_or_s _ _ zenon_H67); [ zenon_intro zenon_H1e | zenon_intro zenon_H68 ]. % 19.02/19.16 apply (zenon_L336_); trivial. % 19.02/19.16 apply (zenon_or_s _ _ zenon_H68); [ zenon_intro zenon_H1f | zenon_intro zenon_H69 ]. % 19.02/19.16 apply (zenon_L1226_); trivial. % 19.02/19.16 apply (zenon_or_s _ _ zenon_H69); [ zenon_intro zenon_H37 | zenon_intro zenon_H60 ]. % 19.02/19.16 apply (zenon_L1219_); trivial. % 19.02/19.16 apply (zenon_L244_); trivial. % 19.02/19.16 (* end of lemma zenon_L1227_ *) % 19.02/19.16 assert (zenon_L1228_ : (((op (e0) (e3)) = (e1))\/(((op (e1) (e3)) = (e1))\/(((op (e2) (e3)) = (e1))\/((op (e3) (e3)) = (e1))))) -> (~((e1) = (e2))) -> (~((op (e2) (e2)) = (op (e2) (e3)))) -> ((op (e2) (e2)) = (e1)) -> (((op (e0) (e3)) = (e0))\/(((op (e0) (e3)) = (e1))\/(((op (e0) (e3)) = (e2))\/((op (e0) (e3)) = (e3))))) -> (~((op (e0) (e3)) = (op (e3) (e3)))) -> ((op (e3) (e3)) = (e0)) -> (~((op (e0) (e3)) = (e2))) -> (((op (e2) (e3)) = (e0))\/(((op (e2) (e3)) = (e1))\/(((op (e2) (e3)) = (e2))\/((op (e2) (e3)) = (e3))))) -> ((op (e1) (e3)) = (e2)) -> (~((op (e2) (e3)) = (op (e3) (e3)))) -> (~((op (e2) (e1)) = (op (e2) (e3)))) -> ((op (e2) (e1)) = (e2)) -> (~((op (e0) (e3)) = (op (e2) (e3)))) -> False). % 19.02/19.16 do 0 intro. intros zenon_H133 zenon_H7c zenon_H6d zenon_Hf1 zenon_He4 zenon_Hc2 zenon_H60 zenon_H12e zenon_H11f zenon_Hd7 zenon_Hf3 zenon_H1c7 zenon_H1ca zenon_He2. % 19.02/19.16 apply (zenon_or_s _ _ zenon_H133); [ zenon_intro zenon_Hc3 | zenon_intro zenon_H134 ]. % 19.02/19.16 apply (zenon_L201_); trivial. % 19.02/19.16 apply (zenon_or_s _ _ zenon_H134); [ zenon_intro zenon_Hd6 | zenon_intro zenon_H135 ]. % 19.02/19.16 apply (zenon_L101_); trivial. % 19.02/19.16 apply (zenon_or_s _ _ zenon_H135); [ zenon_intro zenon_Hf4 | zenon_intro zenon_Hc4 ]. % 19.02/19.16 apply (zenon_L84_); trivial. % 19.02/19.16 apply (zenon_L1192_); trivial. % 19.02/19.16 (* end of lemma zenon_L1228_ *) % 19.02/19.16 assert (zenon_L1229_ : (((op (e1) (e0)) = (e2))\/(((op (e1) (e1)) = (e2))\/(((op (e1) (e2)) = (e2))\/((op (e1) (e3)) = (e2))))) -> (~((op (e1) (e0)) = (e2))) -> (~((op (e1) (e2)) = (e2))) -> (((op (e0) (e1)) = (e2))\/(((op (e1) (e1)) = (e2))\/(((op (e2) (e1)) = (e2))\/((op (e3) (e1)) = (e2))))) -> (~((op (e3) (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) (e1)) = (op (e0) (e3)))) -> ((op (e0) (e1)) = (e1)) -> (~((op (e0) (e3)) = (e2))) -> (~((op (e0) (e3)) = (op (e2) (e3)))) -> (~((e2) = (e3))) -> (((op (e2) (e3)) = (e0))\/(((op (e2) (e3)) = (e1))\/(((op (e2) (e3)) = (e2))\/((op (e2) (e3)) = (e3))))) -> (~((op (e2) (e3)) = (op (e3) (e3)))) -> (~((op (e2) (e1)) = (op (e2) (e3)))) -> (((op (e0) (e3)) = (e3))\/(((op (e1) (e3)) = (e3))\/(((op (e2) (e3)) = (e3))\/((op (e3) (e3)) = (e3))))) -> ((op (e2) (e2)) = (e1)) -> (~((op (e2) (e2)) = (op (e2) (e3)))) -> (~((e1) = (e2))) -> (((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)) = (op (e3) (e3)))) -> ((op (e2) (e0)) = (e0)) -> (~((op (e2) (e0)) = (op (e2) (e3)))) -> (~((e1) = (e3))) -> (~((op (e0) (e1)) = (op (e1) (e1)))) -> (~((op (e1) (e1)) = (e2))) -> (~((op (e1) (e1)) = (e1))) -> (~((op (e1) (e1)) = (op (e1) (e3)))) -> (((op (e1) (e1)) = (e0))\/(((op (e1) (e1)) = (e1))\/(((op (e1) (e1)) = (e2))\/((op (e1) (e1)) = (e3))))) -> (~((op (e0) (e1)) = (e2))) -> ((op (e0) (e2)) = (e0)) -> (~((op (e0) (e1)) = (op (e0) (e2)))) -> (((op (e0) (e1)) = (e0))\/(((op (e0) (e1)) = (e1))\/(((op (e0) (e1)) = (e2))\/((op (e0) (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) (e2)) = (e3)) -> (((op (e0) (e3)) = (e1))\/(((op (e1) (e3)) = (e1))\/(((op (e2) (e3)) = (e1))\/((op (e3) (e3)) = (e1))))) -> (~((op (e3) (e1)) = (e2))) -> False). % 19.02/19.16 do 0 intro. intros zenon_H18c zenon_H177 zenon_H114 zenon_H1d8 zenon_H102 zenon_He4 zenon_H1f zenon_H1d zenon_H54 zenon_Ha0 zenon_H12e zenon_He2 zenon_H12b zenon_H11f zenon_Hf3 zenon_H1c7 zenon_H136 zenon_Hf1 zenon_H6d zenon_H7c zenon_H1ac zenon_H17b zenon_H130 zenon_H34 zenon_H5b zenon_H95 zenon_H10e zenon_H20c zenon_H10a zenon_H57 zenon_H142 zenon_H26d zenon_H48 zenon_H4a zenon_H212 zenon_H208 zenon_H67 zenon_H16c zenon_H133 zenon_H194. % 19.02/19.16 apply (zenon_or_s _ _ zenon_H18c); [ zenon_intro zenon_H86 | zenon_intro zenon_H18d ]. % 19.02/19.16 exact (zenon_H177 zenon_H86). % 19.02/19.16 apply (zenon_or_s _ _ zenon_H18d); [ zenon_intro zenon_H110 | zenon_intro zenon_H18e ]. % 19.02/19.16 exact (zenon_H20c zenon_H110). % 19.02/19.16 apply (zenon_or_s _ _ zenon_H18e); [ zenon_intro zenon_H113 | zenon_intro zenon_Hd7 ]. % 19.02/19.16 exact (zenon_H114 zenon_H113). % 19.02/19.16 apply (zenon_or_s _ _ zenon_H1d8); [ zenon_intro zenon_H10f | zenon_intro zenon_H1d9 ]. % 19.02/19.16 exact (zenon_H26d zenon_H10f). % 19.02/19.16 apply (zenon_or_s _ _ zenon_H1d9); [ zenon_intro zenon_H110 | zenon_intro zenon_H1da ]. % 19.02/19.16 exact (zenon_H20c zenon_H110). % 19.02/19.16 apply (zenon_or_s _ _ zenon_H1da); [ zenon_intro zenon_H1ca | zenon_intro zenon_H14d ]. % 19.02/19.16 apply (zenon_L1226_); trivial. % 19.02/19.16 exact (zenon_H194 zenon_H14d). % 19.02/19.16 (* end of lemma zenon_L1229_ *) % 19.02/19.16 assert (zenon_L1230_ : (((op (e0) (e3)) = (e2))\/(((op (e1) (e3)) = (e2))\/(((op (e2) (e3)) = (e2))\/((op (e3) (e3)) = (e2))))) -> (~((op (e0) (e3)) = (e2))) -> (~((op (e3) (e3)) = (e3))) -> ((op (e3) (e1)) = (e1)) -> (~((op (e3) (e1)) = (op (e3) (e3)))) -> ((op (e0) (e3)) = (e1)) -> (((op (e3) (e3)) = (e0))\/(((op (e3) (e3)) = (e1))\/(((op (e3) (e3)) = (e2))\/((op (e3) (e3)) = (e3))))) -> (~((op (e2) (e3)) = (e2))) -> ((op (e3) (e2)) = (e2)) -> (~((op (e3) (e2)) = (op (e3) (e3)))) -> False). % 19.02/19.16 do 0 intro. intros zenon_H145 zenon_H12e zenon_H102 zenon_Hae zenon_H130 zenon_Hc3 zenon_H101 zenon_H274 zenon_H151 zenon_H62. % 19.02/19.16 apply (zenon_or_s _ _ zenon_H145); [ zenon_intro zenon_Hcd | zenon_intro zenon_H146 ]. % 19.02/19.16 exact (zenon_H12e zenon_Hcd). % 19.02/19.16 apply (zenon_or_s _ _ zenon_H146); [ zenon_intro zenon_Hd7 | zenon_intro zenon_H147 ]. % 19.02/19.16 apply (zenon_L379_); trivial. % 19.02/19.16 apply (zenon_or_s _ _ zenon_H147); [ zenon_intro zenon_H11d | zenon_intro zenon_Hf6 ]. % 19.02/19.16 exact (zenon_H274 zenon_H11d). % 19.02/19.16 apply (zenon_L119_); trivial. % 19.02/19.16 (* end of lemma zenon_L1230_ *) % 19.02/19.16 assert (zenon_L1231_ : (((op (e3) (e0)) = (e1))\/(((op (e3) (e1)) = (e1))\/(((op (e3) (e2)) = (e1))\/((op (e3) (e3)) = (e1))))) -> (~((e0) = (e1))) -> ((op (e3) (e0)) = (e0)) -> (~((op (e3) (e2)) = (op (e3) (e3)))) -> ((op (e3) (e2)) = (e2)) -> (~((op (e2) (e3)) = (e2))) -> (((op (e3) (e3)) = (e0))\/(((op (e3) (e3)) = (e1))\/(((op (e3) (e3)) = (e2))\/((op (e3) (e3)) = (e3))))) -> (~((op (e3) (e1)) = (op (e3) (e3)))) -> (~((op (e3) (e3)) = (e3))) -> (~((op (e0) (e3)) = (e2))) -> (((op (e0) (e3)) = (e2))\/(((op (e1) (e3)) = (e2))\/(((op (e2) (e3)) = (e2))\/((op (e3) (e3)) = (e2))))) -> ((op (e2) (e2)) = (e1)) -> (~((op (e2) (e2)) = (op (e3) (e2)))) -> (~((op (e0) (e3)) = (op (e3) (e3)))) -> ((op (e0) (e3)) = (e1)) -> False). % 19.02/19.16 do 0 intro. intros zenon_He8 zenon_Ha1 zenon_H44 zenon_H62 zenon_H151 zenon_H274 zenon_H101 zenon_H130 zenon_H102 zenon_H12e zenon_H145 zenon_Hf1 zenon_H18f zenon_Hc2 zenon_Hc3. % 19.02/19.16 apply (zenon_or_s _ _ zenon_He8); [ zenon_intro zenon_Hac | zenon_intro zenon_Heb ]. % 19.02/19.16 apply (zenon_L41_); trivial. % 19.02/19.16 apply (zenon_or_s _ _ zenon_Heb); [ zenon_intro zenon_Hae | zenon_intro zenon_Hec ]. % 19.02/19.16 apply (zenon_L1230_); trivial. % 19.02/19.16 apply (zenon_or_s _ _ zenon_Hec); [ zenon_intro zenon_Hba | zenon_intro zenon_Hc4 ]. % 19.02/19.16 apply (zenon_L185_); trivial. % 19.02/19.16 apply (zenon_L46_); trivial. % 19.02/19.16 (* end of lemma zenon_L1231_ *) % 19.02/19.16 assert (zenon_L1232_ : ((~((op (e1) (e0)) = (e2)))\/((op (e1) (e2)) = (e0))) -> (((op (e1) (e0)) = (e3))\/(((op (e1) (e1)) = (e3))\/(((op (e1) (e2)) = (e3))\/((op (e1) (e3)) = (e3))))) -> (((op (e3) (e0)) = (e2))\/(((op (e3) (e1)) = (e2))\/(((op (e3) (e2)) = (e2))\/((op (e3) (e3)) = (e2))))) -> ((~((op (e3) (e0)) = (e2)))\/((op (e3) (e2)) = (e0))) -> ((~((op (e3) (e2)) = (e2)))\/((op (e3) (e2)) = (e2))) -> (~((op (e0) (e1)) = (e2))) -> (~((op (e3) (e1)) = (op (e3) (e2)))) -> (((op (e0) (e1)) = (e2))\/(((op (e1) (e1)) = (e2))\/(((op (e2) (e1)) = (e2))\/((op (e3) (e1)) = (e2))))) -> (~((op (e0) (e2)) = (e2))) -> (~((op (e2) (e2)) = (e2))) -> (((op (e0) (e2)) = (e2))\/(((op (e1) (e2)) = (e2))\/(((op (e2) (e2)) = (e2))\/((op (e3) (e2)) = (e2))))) -> (~((op (e0) (e0)) = (e0))) -> (((op (e1) (e0)) = (e1))\/(((op (e1) (e1)) = (e1))\/(((op (e1) (e2)) = (e1))\/((op (e1) (e3)) = (e1))))) -> (~((op (e2) (e1)) = (op (e2) (e3)))) -> (~((e1) = (e2))) -> (~((op (e1) (e2)) = (op (e2) (e2)))) -> (~((op (e1) (e1)) = (e1))) -> (~((e0) = (e1))) -> (((op (e2) (e0)) = (e0))\/(((op (e2) (e1)) = (e0))\/(((op (e2) (e2)) = (e0))\/((op (e2) (e3)) = (e0))))) -> (~((op (e2) (e2)) = (op (e2) (e3)))) -> (~((op (e0) (e2)) = (op (e2) (e2)))) -> (~((op (e0) (e2)) = (op (e0) (e3)))) -> ((op (e0) (e2)) = (e0)) -> (~((op (e0) (e1)) = (op (e3) (e1)))) -> (~((op (e0) (e1)) = (op (e0) (e3)))) -> (~((op (e0) (e1)) = (op (e2) (e1)))) -> (((op (e1) (e1)) = (e0))\/(((op (e1) (e1)) = (e1))\/(((op (e1) (e1)) = (e2))\/((op (e1) (e1)) = (e3))))) -> (((op (e0) (e1)) = (e0))\/(((op (e0) (e1)) = (e1))\/(((op (e0) (e1)) = (e2))\/((op (e0) (e1)) = (e3))))) -> (~((op (e3) (e3)) = (e3))) -> (((op (e3) (e3)) = (e0))\/(((op (e3) (e3)) = (e1))\/(((op (e3) (e3)) = (e2))\/((op (e3) (e3)) = (e3))))) -> (~((op (e1) (e0)) = (op (e1) (e3)))) -> (~((op (e2) (e3)) = (op (e3) (e3)))) -> (~((op (e3) (e0)) = (op (e3) (e3)))) -> (((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 (e1) (e1)) = (e1))\/(((op (e2) (e1)) = (e1))\/((op (e3) (e1)) = (e1))))) -> (((op (e2) (e3)) = (e0))\/(((op (e2) (e3)) = (e1))\/(((op (e2) (e3)) = (e2))\/((op (e2) (e3)) = (e3))))) -> (~((op (e0) (e3)) = (op (e2) (e3)))) -> (~((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) (e3)) = (e3))\/(((op (e1) (e3)) = (e3))\/(((op (e2) (e3)) = (e3))\/((op (e3) (e3)) = (e3))))) -> (((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 (e2) (e0)) = (op (e3) (e0)))) -> (~((op (e2) (e0)) = (op (e2) (e3)))) -> (((op (e0) (e1)) = (e0))\/(((op (e1) (e1)) = (e0))\/(((op (e2) (e1)) = (e0))\/((op (e3) (e1)) = (e0))))) -> (~((op (e2) (e0)) = (op (e2) (e1)))) -> (~((op (e1) (e1)) = (op (e1) (e3)))) -> (~((op (e0) (e1)) = (op (e0) (e2)))) -> (~((op (e0) (e3)) = (op (e3) (e3)))) -> (((op (e2) (e0)) = (e2))\/(((op (e2) (e1)) = (e2))\/(((op (e2) (e2)) = (e2))\/((op (e2) (e3)) = (e2))))) -> (~((op (e0) (e2)) = (op (e3) (e2)))) -> (((op (e3) (e0)) = (e0))\/(((op (e3) (e1)) = (e0))\/(((op (e3) (e2)) = (e0))\/((op (e3) (e3)) = (e0))))) -> ((~((op (e1) (e3)) = (e2)))\/((op (e1) (e2)) = (e3))) -> (~((e1) = (e3))) -> ((~((op (e2) (e1)) = (e2)))\/((op (e2) (e2)) = (e1))) -> (((op (e0) (e0)) = (e0))\/(((op (e1) (e0)) = (e0))\/(((op (e2) (e0)) = (e0))\/((op (e3) (e0)) = (e0))))) -> (((op (e2) (e1)) = (e0))\/(((op (e2) (e1)) = (e1))\/(((op (e2) (e1)) = (e2))\/((op (e2) (e1)) = (e3))))) -> (((op (e0) (e0)) = (e1))\/(((op (e1) (e0)) = (e1))\/(((op (e2) (e0)) = (e1))\/((op (e3) (e0)) = (e1))))) -> (~((op (e1) (e2)) = (op (e3) (e2)))) -> (~((op (e0) (e2)) = (op (e1) (e2)))) -> (~((op (e3) (e0)) = (op (e3) (e1)))) -> (((op (e2) (e0)) = (e1))\/(((op (e2) (e1)) = (e1))\/(((op (e2) (e2)) = (e1))\/((op (e2) (e3)) = (e1))))) -> (((op (e1) (e0)) = (e0))\/(((op (e1) (e1)) = (e0))\/(((op (e1) (e2)) = (e0))\/((op (e1) (e3)) = (e0))))) -> (~((op (e1) (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) = (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 (e3) (e0)))) -> (~((op (e1) (e0)) = (op (e2) (e0)))) -> (((op (e1) (e0)) = (e0))\/(((op (e1) (e0)) = (e1))\/(((op (e1) (e0)) = (e2))\/((op (e1) (e0)) = (e3))))) -> (~((op (e1) (e0)) = (op (e1) (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) (e3)) = (e2)))\/((op (e3) (e2)) = (e3))) -> ((~((op (e2) (e3)) = (e2)))\/((op (e2) (e2)) = (e3))) -> ((~((op (e2) (e0)) = (e2)))\/((op (e2) (e2)) = (e0))) -> ((~((op (e1) (e2)) = (e2)))\/((op (e1) (e2)) = (e2))) -> (((op (e0) (e0)) = (e2))\/(((op (e0) (e1)) = (e2))\/(((op (e0) (e2)) = (e2))\/((op (e0) (e3)) = (e2))))) -> (~((op (e0) (e0)) = (op (e0) (e3)))) -> (~((op (e2) (e0)) = (op (e2) (e2)))) -> (~((op (e3) (e0)) = (op (e3) (e2)))) -> (~((e0) = (e3))) -> ((~((op (e3) (e1)) = (e2)))\/((op (e3) (e2)) = (e1))) -> (((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)) = (e2))) -> (~((op (e0) (e1)) = (op (e1) (e1)))) -> (((op (e2) (e0)) = (e0))\/(((op (e2) (e0)) = (e1))\/(((op (e2) (e0)) = (e2))\/((op (e2) (e0)) = (e3))))) -> ((~((op (e1) (e1)) = (e2)))\/((op (e1) (e2)) = (e1))) -> False). % 19.02/19.16 do 0 intro. intros zenon_H27a zenon_H16f zenon_H153 zenon_H270 zenon_H273 zenon_H26d zenon_H1a4 zenon_H1d8 zenon_H1fd zenon_H173 zenon_H172 zenon_H3f zenon_H128 zenon_H1c7 zenon_H7c zenon_H2b zenon_H10a zenon_Ha1 zenon_H2f zenon_H6d zenon_Ha8 zenon_H208 zenon_H48 zenon_H210 zenon_H54 zenon_H17e zenon_H142 zenon_H212 zenon_H102 zenon_H101 zenon_Hd8 zenon_Hf3 zenon_H71 zenon_H133 zenon_H130 zenon_H109 zenon_H11f zenon_He2 zenon_H12b zenon_He4 zenon_H1d zenon_H136 zenon_He8 zenon_H67 zenon_H17b zenon_H5b zenon_H245 zenon_H1f0 zenon_H57 zenon_H4a zenon_Hc2 zenon_H1d5 zenon_H14f zenon_H1ac zenon_H279 zenon_H95 zenon_H271 zenon_H3e zenon_H1cc zenon_H235 zenon_H115 zenon_H195 zenon_H1cf zenon_H106 zenon_H22 zenon_H124 zenon_Hd5 zenon_Hdf zenon_H149 zenon_Hdb zenon_H18c zenon_H1fa zenon_H201 zenon_H25e zenon_H45 zenon_H22d zenon_H18f zenon_H278 zenon_H277 zenon_H276 zenon_H275 zenon_H183 zenon_H189 zenon_H52 zenon_H6f zenon_H9a zenon_H26f zenon_H145 zenon_H62 zenon_H12e zenon_H10e zenon_H259 zenon_H27b. % 19.02/19.16 apply (zenon_or_s _ _ zenon_H27a); [ zenon_intro zenon_H177 | zenon_intro zenon_H2a ]. % 19.02/19.16 apply (zenon_or_s _ _ zenon_H27b); [ zenon_intro zenon_H20c | zenon_intro zenon_Hf0 ]. % 19.02/19.16 apply (zenon_or_s _ _ zenon_H275); [ zenon_intro zenon_H114 | zenon_intro zenon_H113 ]. % 19.02/19.16 apply (zenon_or_s _ _ zenon_H279); [ zenon_intro zenon_H14c | zenon_intro zenon_H16c ]. % 19.02/19.16 apply (zenon_or_s _ _ zenon_H276); [ zenon_intro zenon_Hef | zenon_intro zenon_H2c ]. % 19.02/19.16 apply (zenon_or_s _ _ zenon_H271); [ zenon_intro zenon_H26e | zenon_intro zenon_Hf1 ]. % 19.02/19.16 apply (zenon_L1057_); trivial. % 19.02/19.16 apply (zenon_or_s _ _ zenon_H277); [ zenon_intro zenon_H274 | zenon_intro zenon_Haa ]. % 19.02/19.16 apply (zenon_L1206_); trivial. % 19.02/19.16 apply (zenon_L1203_); trivial. % 19.02/19.16 apply (zenon_L679_); trivial. % 19.02/19.16 apply (zenon_or_s _ _ zenon_H276); [ zenon_intro zenon_Hef | zenon_intro zenon_H2c ]. % 19.02/19.16 apply (zenon_or_s _ _ zenon_H271); [ zenon_intro zenon_H26e | zenon_intro zenon_Hf1 ]. % 19.02/19.16 apply (zenon_L1057_); trivial. % 19.02/19.16 apply (zenon_or_s _ _ zenon_H277); [ zenon_intro zenon_H274 | zenon_intro zenon_Haa ]. % 19.02/19.16 apply (zenon_or_s _ _ zenon_H26f); [ zenon_intro zenon_H194 | zenon_intro zenon_Hba ]. % 19.02/19.16 apply (zenon_or_s _ _ zenon_H273); [ zenon_intro zenon_H272 | zenon_intro zenon_H151 ]. % 19.02/19.16 apply (zenon_L1055_); trivial. % 19.02/19.16 apply (zenon_or_s _ _ zenon_H3e); [ zenon_intro zenon_H42 | zenon_intro zenon_H41 ]. % 19.02/19.16 exact (zenon_H3f zenon_H42). % 19.02/19.16 apply (zenon_or_s _ _ zenon_H41); [ zenon_intro zenon_H27 | zenon_intro zenon_H43 ]. % 19.02/19.16 apply (zenon_L1218_); trivial. % 19.02/19.16 apply (zenon_or_s _ _ zenon_H43); [ zenon_intro zenon_H34 | zenon_intro zenon_H44 ]. % 19.02/19.16 apply (zenon_or_s _ _ zenon_H22d); [ zenon_intro zenon_H7a | zenon_intro zenon_H22e ]. % 19.02/19.16 apply (zenon_L1059_); trivial. % 19.02/19.16 apply (zenon_or_s _ _ zenon_H22e); [ zenon_intro zenon_Ha0 | zenon_intro zenon_H22f ]. % 19.02/19.16 apply (zenon_or_s _ _ zenon_H235); [ zenon_intro zenon_H7a | zenon_intro zenon_H236 ]. % 19.02/19.16 apply (zenon_L1059_); trivial. % 19.02/19.16 apply (zenon_or_s _ _ zenon_H236); [ zenon_intro zenon_H9d | zenon_intro zenon_H237 ]. % 19.02/19.16 apply (zenon_or_s _ _ zenon_H183); [ zenon_intro zenon_H7b | zenon_intro zenon_H186 ]. % 19.02/19.16 apply (zenon_or_s _ _ zenon_H22); [ zenon_intro zenon_H27 | zenon_intro zenon_H26 ]. % 19.02/19.16 apply (zenon_L262_); trivial. % 19.02/19.16 apply (zenon_or_s _ _ zenon_H26); [ zenon_intro zenon_H29 | zenon_intro zenon_H28 ]. % 19.02/19.16 apply (zenon_or_s _ _ zenon_H18c); [ zenon_intro zenon_H86 | zenon_intro zenon_H18d ]. % 19.02/19.16 exact (zenon_H177 zenon_H86). % 19.02/19.16 apply (zenon_or_s _ _ zenon_H18d); [ zenon_intro zenon_H110 | zenon_intro zenon_H18e ]. % 19.02/19.16 exact (zenon_H20c zenon_H110). % 19.02/19.16 apply (zenon_or_s _ _ zenon_H18e); [ zenon_intro zenon_H113 | zenon_intro zenon_Hd7 ]. % 19.02/19.16 exact (zenon_H114 zenon_H113). % 19.02/19.16 apply (zenon_or_s _ _ zenon_H1d8); [ zenon_intro zenon_H10f | zenon_intro zenon_H1d9 ]. % 19.02/19.16 exact (zenon_H26d zenon_H10f). % 19.02/19.16 apply (zenon_or_s _ _ zenon_H1d9); [ zenon_intro zenon_H110 | zenon_intro zenon_H1da ]. % 19.02/19.16 exact (zenon_H20c zenon_H110). % 19.02/19.16 apply (zenon_or_s _ _ zenon_H1da); [ zenon_intro zenon_H1ca | zenon_intro zenon_H14d ]. % 19.02/19.16 apply (zenon_or_s _ _ zenon_H1ac); [ zenon_intro zenon_H44 | zenon_intro zenon_H1af ]. % 19.02/19.16 apply (zenon_L1220_); trivial. % 19.02/19.16 apply (zenon_or_s _ _ zenon_H1af); [ zenon_intro zenon_H1b1 | zenon_intro zenon_H1b0 ]. % 19.02/19.16 apply (zenon_L1227_); trivial. % 19.02/19.16 apply (zenon_or_s _ _ zenon_H1b0); [ zenon_intro zenon_H61 | zenon_intro zenon_H60 ]. % 19.02/19.16 apply (zenon_L342_); trivial. % 19.02/19.16 apply (zenon_L1228_); trivial. % 19.02/19.16 exact (zenon_H194 zenon_H14d). % 19.02/19.16 apply (zenon_or_s _ _ zenon_H28); [ zenon_intro zenon_H2a | zenon_intro zenon_H1f ]. % 19.02/19.16 apply (zenon_L334_); trivial. % 19.02/19.16 apply (zenon_L1229_); trivial. % 19.02/19.16 apply (zenon_or_s _ _ zenon_H186); [ zenon_intro zenon_H10f | zenon_intro zenon_H187 ]. % 19.02/19.16 exact (zenon_H26d zenon_H10f). % 19.02/19.16 apply (zenon_or_s _ _ zenon_H187); [ zenon_intro zenon_H150 | zenon_intro zenon_Hcd ]. % 19.02/19.16 exact (zenon_H1fd zenon_H150). % 19.02/19.16 exact (zenon_H12e zenon_Hcd). % 19.02/19.16 apply (zenon_or_s _ _ zenon_H237); [ zenon_intro zenon_Hed | zenon_intro zenon_Hac ]. % 19.02/19.16 apply (zenon_L93_); trivial. % 19.02/19.16 apply (zenon_or_s _ _ zenon_H183); [ zenon_intro zenon_H7b | zenon_intro zenon_H186 ]. % 19.02/19.16 apply (zenon_or_s _ _ zenon_H18c); [ zenon_intro zenon_H86 | zenon_intro zenon_H18d ]. % 19.02/19.16 exact (zenon_H177 zenon_H86). % 19.02/19.16 apply (zenon_or_s _ _ zenon_H18d); [ zenon_intro zenon_H110 | zenon_intro zenon_H18e ]. % 19.02/19.16 exact (zenon_H20c zenon_H110). % 19.02/19.16 apply (zenon_or_s _ _ zenon_H18e); [ zenon_intro zenon_H113 | zenon_intro zenon_Hd7 ]. % 19.02/19.16 exact (zenon_H114 zenon_H113). % 19.02/19.16 apply (zenon_or_s _ _ zenon_H1d8); [ zenon_intro zenon_H10f | zenon_intro zenon_H1d9 ]. % 19.02/19.16 exact (zenon_H26d zenon_H10f). % 19.02/19.16 apply (zenon_or_s _ _ zenon_H1d9); [ zenon_intro zenon_H110 | zenon_intro zenon_H1da ]. % 19.02/19.16 exact (zenon_H20c zenon_H110). % 19.02/19.16 apply (zenon_or_s _ _ zenon_H1da); [ zenon_intro zenon_H1ca | zenon_intro zenon_H14d ]. % 19.02/19.16 apply (zenon_or_s _ _ zenon_H1ac); [ zenon_intro zenon_H44 | zenon_intro zenon_H1af ]. % 19.02/19.16 apply (zenon_L41_); trivial. % 19.02/19.16 apply (zenon_or_s _ _ zenon_H1af); [ zenon_intro zenon_H1b1 | zenon_intro zenon_H1b0 ]. % 19.02/19.16 apply (zenon_L1227_); trivial. % 19.02/19.16 apply (zenon_or_s _ _ zenon_H1b0); [ zenon_intro zenon_H61 | zenon_intro zenon_H60 ]. % 19.02/19.16 apply (zenon_L156_); trivial. % 19.02/19.16 apply (zenon_L1228_); trivial. % 19.02/19.16 exact (zenon_H194 zenon_H14d). % 19.02/19.16 apply (zenon_or_s _ _ zenon_H186); [ zenon_intro zenon_H10f | zenon_intro zenon_H187 ]. % 19.02/19.16 exact (zenon_H26d zenon_H10f). % 19.02/19.16 apply (zenon_or_s _ _ zenon_H187); [ zenon_intro zenon_H150 | zenon_intro zenon_Hcd ]. % 19.02/19.16 exact (zenon_H1fd zenon_H150). % 19.02/19.16 exact (zenon_H12e zenon_Hcd). % 19.02/19.16 apply (zenon_or_s _ _ zenon_H22f); [ zenon_intro zenon_H122 | zenon_intro zenon_Hc3 ]. % 19.02/19.16 apply (zenon_L355_); trivial. % 19.02/19.16 apply (zenon_or_s _ _ zenon_H18c); [ zenon_intro zenon_H86 | zenon_intro zenon_H18d ]. % 19.02/19.16 exact (zenon_H177 zenon_H86). % 19.02/19.16 apply (zenon_or_s _ _ zenon_H18d); [ zenon_intro zenon_H110 | zenon_intro zenon_H18e ]. % 19.02/19.16 exact (zenon_H20c zenon_H110). % 19.02/19.16 apply (zenon_or_s _ _ zenon_H18e); [ zenon_intro zenon_H113 | zenon_intro zenon_Hd7 ]. % 19.02/19.16 exact (zenon_H114 zenon_H113). % 19.02/19.16 apply (zenon_L1225_); trivial. % 19.02/19.16 apply (zenon_or_s _ _ zenon_H22d); [ zenon_intro zenon_H7a | zenon_intro zenon_H22e ]. % 19.02/19.16 apply (zenon_L1059_); trivial. % 19.02/19.16 apply (zenon_or_s _ _ zenon_H22e); [ zenon_intro zenon_Ha0 | zenon_intro zenon_H22f ]. % 19.02/19.16 apply (zenon_or_s _ _ zenon_H235); [ zenon_intro zenon_H7a | zenon_intro zenon_H236 ]. % 19.02/19.16 apply (zenon_L1059_); trivial. % 19.02/19.16 apply (zenon_or_s _ _ zenon_H236); [ zenon_intro zenon_H9d | zenon_intro zenon_H237 ]. % 19.02/19.16 apply (zenon_or_s _ _ zenon_H183); [ zenon_intro zenon_H7b | zenon_intro zenon_H186 ]. % 19.02/19.16 apply (zenon_or_s _ _ zenon_H22); [ zenon_intro zenon_H27 | zenon_intro zenon_H26 ]. % 19.02/19.16 apply (zenon_L262_); trivial. % 19.02/19.16 apply (zenon_or_s _ _ zenon_H26); [ zenon_intro zenon_H29 | zenon_intro zenon_H28 ]. % 19.02/19.16 apply (zenon_or_s _ _ zenon_H18c); [ zenon_intro zenon_H86 | zenon_intro zenon_H18d ]. % 19.02/19.16 exact (zenon_H177 zenon_H86). % 19.02/19.16 apply (zenon_or_s _ _ zenon_H18d); [ zenon_intro zenon_H110 | zenon_intro zenon_H18e ]. % 19.02/19.16 exact (zenon_H20c zenon_H110). % 19.02/19.16 apply (zenon_or_s _ _ zenon_H18e); [ zenon_intro zenon_H113 | zenon_intro zenon_Hd7 ]. % 19.02/19.16 exact (zenon_H114 zenon_H113). % 19.02/19.16 apply (zenon_L1220_); trivial. % 19.02/19.16 apply (zenon_or_s _ _ zenon_H28); [ zenon_intro zenon_H2a | zenon_intro zenon_H1f ]. % 19.02/19.16 apply (zenon_L334_); trivial. % 19.02/19.16 apply (zenon_or_s _ _ zenon_H18c); [ zenon_intro zenon_H86 | zenon_intro zenon_H18d ]. % 19.02/19.16 exact (zenon_H177 zenon_H86). % 19.02/19.16 apply (zenon_or_s _ _ zenon_H18d); [ zenon_intro zenon_H110 | zenon_intro zenon_H18e ]. % 19.02/19.16 exact (zenon_H20c zenon_H110). % 19.02/19.16 apply (zenon_or_s _ _ zenon_H18e); [ zenon_intro zenon_H113 | zenon_intro zenon_Hd7 ]. % 19.02/19.16 exact (zenon_H114 zenon_H113). % 19.02/19.16 apply (zenon_or_s _ _ zenon_H1d8); [ zenon_intro zenon_H10f | zenon_intro zenon_H1d9 ]. % 19.02/19.16 exact (zenon_H26d zenon_H10f). % 19.02/19.16 apply (zenon_or_s _ _ zenon_H1d9); [ zenon_intro zenon_H110 | zenon_intro zenon_H1da ]. % 19.02/19.16 exact (zenon_H20c zenon_H110). % 19.02/19.16 apply (zenon_or_s _ _ zenon_H1da); [ zenon_intro zenon_H1ca | zenon_intro zenon_H14d ]. % 19.02/19.16 apply (zenon_or_s _ _ zenon_He8); [ zenon_intro zenon_Hac | zenon_intro zenon_Heb ]. % 19.02/19.16 apply (zenon_L41_); trivial. % 19.02/19.16 apply (zenon_or_s _ _ zenon_Heb); [ zenon_intro zenon_Hae | zenon_intro zenon_Hec ]. % 19.02/19.16 apply (zenon_L363_); trivial. % 19.02/19.16 apply (zenon_or_s _ _ zenon_Hec); [ zenon_intro zenon_Hba | zenon_intro zenon_Hc4 ]. % 19.02/19.16 apply (zenon_L419_); trivial. % 19.02/19.16 apply (zenon_L1179_); trivial. % 19.02/19.16 exact (zenon_H194 zenon_H14d). % 19.02/19.16 apply (zenon_or_s _ _ zenon_H186); [ zenon_intro zenon_H10f | zenon_intro zenon_H187 ]. % 19.02/19.16 exact (zenon_H26d zenon_H10f). % 19.02/19.16 apply (zenon_or_s _ _ zenon_H187); [ zenon_intro zenon_H150 | zenon_intro zenon_Hcd ]. % 19.02/19.16 exact (zenon_H1fd zenon_H150). % 19.02/19.16 exact (zenon_H12e zenon_Hcd). % 19.02/19.16 apply (zenon_or_s _ _ zenon_H237); [ zenon_intro zenon_Hed | zenon_intro zenon_Hac ]. % 19.02/19.16 apply (zenon_L93_); trivial. % 19.02/19.16 apply (zenon_L41_); trivial. % 19.02/19.16 apply (zenon_or_s _ _ zenon_H22f); [ zenon_intro zenon_H122 | zenon_intro zenon_Hc3 ]. % 19.02/19.16 apply (zenon_L246_); trivial. % 19.02/19.16 apply (zenon_L1231_); trivial. % 19.02/19.16 apply (zenon_L185_); trivial. % 19.02/19.16 apply (zenon_L1203_); trivial. % 19.02/19.16 apply (zenon_L679_); trivial. % 19.02/19.16 apply (zenon_or_s _ _ zenon_H279); [ zenon_intro zenon_H14c | zenon_intro zenon_H16c ]. % 19.02/19.16 apply (zenon_L1204_); trivial. % 19.02/19.16 apply (zenon_L116_); trivial. % 19.02/19.16 apply (zenon_L1101_); trivial. % 19.02/19.16 apply (zenon_L334_); trivial. % 19.02/19.16 (* end of lemma zenon_L1232_ *) % 19.02/19.17 assert (zenon_L1233_ : ((~((op (e3) (e1)) = (e2)))\/((op (e3) (e2)) = (e1))) -> ((op (e0) (e2)) = (e3)) -> ((op (e2) (e2)) = (e0)) -> (~((op (e0) (e0)) = (e2))) -> (~((op (e1) (e0)) = (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)) = (e2))) -> (~((op (e0) (e1)) = (e2))) -> (~((op (e3) (e0)) = (e2))) -> (((op (e0) (e0)) = (e2))\/(((op (e1) (e0)) = (e2))\/(((op (e2) (e0)) = (e2))\/((op (e3) (e0)) = (e2))))) -> False). % 19.02/19.17 do 0 intro. intros zenon_H26f zenon_Ha9 zenon_H2c zenon_H80 zenon_H177 zenon_H1d8 zenon_H1f0 zenon_H20c zenon_H26d zenon_H14b zenon_H1fe. % 19.02/19.17 apply (zenon_or_s _ _ zenon_H26f); [ zenon_intro zenon_H194 | zenon_intro zenon_Hba ]. % 19.02/19.17 apply (zenon_L1051_); trivial. % 19.02/19.17 apply (zenon_L45_); trivial. % 19.02/19.17 (* end of lemma zenon_L1233_ *) % 19.02/19.17 assert (zenon_L1234_ : ((~((op (e3) (e0)) = (e2)))\/((op (e3) (e2)) = (e0))) -> (~((op (e2) (e2)) = (op (e3) (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) (e0)) = (op (e2) (e1)))) -> (((op (e0) (e1)) = (e2))\/(((op (e1) (e1)) = (e2))\/(((op (e2) (e1)) = (e2))\/((op (e3) (e1)) = (e2))))) -> (~((op (e1) (e0)) = (e2))) -> (~((op (e0) (e0)) = (e2))) -> ((op (e2) (e2)) = (e0)) -> ((op (e0) (e2)) = (e3)) -> ((~((op (e3) (e1)) = (e2)))\/((op (e3) (e2)) = (e1))) -> False). % 19.02/19.17 do 0 intro. intros zenon_H270 zenon_H18f zenon_H1fe zenon_H26d zenon_H20c zenon_H1f0 zenon_H1d8 zenon_H177 zenon_H80 zenon_H2c zenon_Ha9 zenon_H26f. % 19.02/19.17 apply (zenon_or_s _ _ zenon_H270); [ zenon_intro zenon_H14b | zenon_intro zenon_H61 ]. % 19.02/19.17 apply (zenon_L1233_); trivial. % 19.02/19.17 apply (zenon_L146_); trivial. % 19.02/19.17 (* end of lemma zenon_L1234_ *) % 19.02/19.17 assert (zenon_L1235_ : (((op (e1) (e3)) = (e0))\/(((op (e1) (e3)) = (e1))\/(((op (e1) (e3)) = (e2))\/((op (e1) (e3)) = (e3))))) -> ((op (e1) (e0)) = (e0)) -> (~((op (e1) (e0)) = (op (e1) (e3)))) -> ((op (e3) (e3)) = (e1)) -> (~((op (e1) (e3)) = (op (e3) (e3)))) -> (~((op (e1) (e3)) = (e2))) -> (~((op (e1) (e3)) = (op (e2) (e3)))) -> ((op (e2) (e3)) = (e3)) -> False). % 19.02/19.17 do 0 intro. intros zenon_Hdf zenon_H27 zenon_Hd8 zenon_Hc4 zenon_Hd5 zenon_H14c zenon_Hdb zenon_Hdd. % 19.02/19.17 apply (zenon_or_s _ _ zenon_Hdf); [ zenon_intro zenon_H1f | zenon_intro zenon_He0 ]. % 19.02/19.17 apply (zenon_L258_); trivial. % 19.02/19.17 apply (zenon_or_s _ _ zenon_He0); [ zenon_intro zenon_Hd6 | zenon_intro zenon_He1 ]. % 19.02/19.17 apply (zenon_L50_); trivial. % 19.02/19.17 apply (zenon_or_s _ _ zenon_He1); [ zenon_intro zenon_Hd7 | zenon_intro zenon_Hdc ]. % 19.02/19.17 exact (zenon_H14c zenon_Hd7). % 19.02/19.17 apply (zenon_L52_); trivial. % 19.02/19.17 (* end of lemma zenon_L1235_ *) % 19.02/19.17 assert (zenon_L1236_ : (((op (e3) (e3)) = (e0))\/(((op (e3) (e3)) = (e1))\/(((op (e3) (e3)) = (e2))\/((op (e3) (e3)) = (e3))))) -> ((op (e2) (e3)) = (e0)) -> (~((op (e2) (e3)) = (op (e3) (e3)))) -> ((op (e2) (e3)) = (e3)) -> (~((op (e1) (e3)) = (op (e2) (e3)))) -> (~((op (e1) (e3)) = (e2))) -> (~((op (e1) (e3)) = (op (e3) (e3)))) -> (~((op (e1) (e0)) = (op (e1) (e3)))) -> ((op (e1) (e0)) = (e0)) -> (((op (e1) (e3)) = (e0))\/(((op (e1) (e3)) = (e1))\/(((op (e1) (e3)) = (e2))\/((op (e1) (e3)) = (e3))))) -> (~((op (e3) (e0)) = (op (e3) (e3)))) -> ((op (e3) (e0)) = (e2)) -> (~((op (e3) (e3)) = (e3))) -> False). % 19.02/19.17 do 0 intro. intros zenon_H101 zenon_H37 zenon_Hf3 zenon_Hdd zenon_Hdb zenon_H14c zenon_Hd5 zenon_Hd8 zenon_H27 zenon_Hdf zenon_H71 zenon_H148 zenon_H102. % 19.02/19.17 apply (zenon_or_s _ _ zenon_H101); [ zenon_intro zenon_H60 | zenon_intro zenon_H103 ]. % 19.02/19.17 apply (zenon_L219_); trivial. % 19.02/19.17 apply (zenon_or_s _ _ zenon_H103); [ zenon_intro zenon_Hc4 | zenon_intro zenon_H104 ]. % 19.02/19.17 apply (zenon_L1235_); trivial. % 19.02/19.17 apply (zenon_or_s _ _ zenon_H104); [ zenon_intro zenon_Hf6 | zenon_intro zenon_H105 ]. % 19.02/19.17 apply (zenon_L114_); trivial. % 19.02/19.17 exact (zenon_H102 zenon_H105). % 19.02/19.17 (* end of lemma zenon_L1236_ *) % 19.02/19.17 assert (zenon_L1237_ : (((op (e1) (e0)) = (e0))\/(((op (e1) (e0)) = (e1))\/(((op (e1) (e0)) = (e2))\/((op (e1) (e0)) = (e3))))) -> (~((op (e1) (e0)) = (op (e2) (e0)))) -> ((op (e2) (e0)) = (e0)) -> (~((op (e1) (e0)) = (op (e1) (e3)))) -> ((op (e1) (e3)) = (e1)) -> (~((op (e1) (e0)) = (e2))) -> ((op (e3) (e0)) = (e2)) -> ((op (e0) (e0)) = (e1)) -> False). % 19.02/19.17 do 0 intro. intros zenon_H25e zenon_H201 zenon_H34 zenon_Hd8 zenon_Hd6 zenon_H177 zenon_H148 zenon_H7a. % 19.02/19.17 apply (zenon_or_s _ _ zenon_H25e); [ zenon_intro zenon_H27 | zenon_intro zenon_H25f ]. % 19.02/19.17 apply (zenon_L332_); trivial. % 19.02/19.17 apply (zenon_or_s _ _ zenon_H25f); [ zenon_intro zenon_H9d | zenon_intro zenon_H260 ]. % 19.02/19.17 apply (zenon_L360_); trivial. % 19.02/19.17 apply (zenon_or_s _ _ zenon_H260); [ zenon_intro zenon_H86 | zenon_intro zenon_H9e ]. % 19.02/19.17 exact (zenon_H177 zenon_H86). % 19.02/19.17 apply (zenon_L107_); trivial. % 19.02/19.17 (* end of lemma zenon_L1237_ *) % 19.02/19.17 assert (zenon_L1238_ : (((op (e0) (e3)) = (e1))\/(((op (e1) (e3)) = (e1))\/(((op (e2) (e3)) = (e1))\/((op (e3) (e3)) = (e1))))) -> (~((op (e0) (e0)) = (op (e0) (e3)))) -> ((op (e0) (e0)) = (e1)) -> ((op (e3) (e0)) = (e2)) -> (~((op (e1) (e0)) = (e2))) -> (~((op (e1) (e0)) = (op (e1) (e3)))) -> ((op (e2) (e0)) = (e0)) -> (~((op (e1) (e0)) = (op (e2) (e0)))) -> (((op (e1) (e0)) = (e0))\/(((op (e1) (e0)) = (e1))\/(((op (e1) (e0)) = (e2))\/((op (e1) (e0)) = (e3))))) -> (~((op (e2) (e2)) = (op (e2) (e3)))) -> ((op (e2) (e2)) = (e1)) -> ((op (e0) (e3)) = (e2)) -> ((op (e1) (e3)) = (e0)) -> False). % 19.02/19.17 do 0 intro. intros zenon_H133 zenon_H189 zenon_H7a zenon_H148 zenon_H177 zenon_Hd8 zenon_H34 zenon_H201 zenon_H25e zenon_H6d zenon_Hf1 zenon_Hcd zenon_H1f. % 19.02/19.17 apply (zenon_or_s _ _ zenon_H133); [ zenon_intro zenon_Hc3 | zenon_intro zenon_H134 ]. % 19.02/19.17 apply (zenon_L140_); trivial. % 19.02/19.17 apply (zenon_or_s _ _ zenon_H134); [ zenon_intro zenon_Hd6 | zenon_intro zenon_H135 ]. % 19.02/19.17 apply (zenon_L1237_); trivial. % 19.02/19.17 apply (zenon_or_s _ _ zenon_H135); [ zenon_intro zenon_Hf4 | zenon_intro zenon_Hc4 ]. % 19.02/19.17 apply (zenon_L84_); trivial. % 19.02/19.17 apply (zenon_L49_); trivial. % 19.02/19.17 (* end of lemma zenon_L1238_ *) % 19.02/19.17 assert (zenon_L1239_ : ((~((op (e3) (e0)) = (e2)))\/((op (e3) (e2)) = (e0))) -> ((op (e0) (e2)) = (e1)) -> (((op (e0) (e0)) = (e2))\/(((op (e1) (e0)) = (e2))\/(((op (e2) (e0)) = (e2))\/((op (e3) (e0)) = (e2))))) -> (~((op (e0) (e3)) = (e2))) -> (~((op (e1) (e3)) = (e2))) -> (~((op (e2) (e0)) = (op (e2) (e3)))) -> (((op (e0) (e3)) = (e2))\/(((op (e1) (e3)) = (e2))\/(((op (e2) (e3)) = (e2))\/((op (e3) (e3)) = (e2))))) -> (~((op (e1) (e0)) = (e2))) -> (~((op (e0) (e0)) = (e2))) -> (~((op (e2) (e2)) = (op (e3) (e2)))) -> ((op (e2) (e2)) = (e3)) -> ((~((op (e3) (e3)) = (e2)))\/((op (e3) (e2)) = (e3))) -> False). % 19.02/19.17 do 0 intro. intros zenon_H270 zenon_H122 zenon_H1fe zenon_H12e zenon_H14c zenon_H5b zenon_H145 zenon_H177 zenon_H80 zenon_H18f zenon_Haa zenon_H278. % 19.02/19.17 apply (zenon_or_s _ _ zenon_H270); [ zenon_intro zenon_H14b | zenon_intro zenon_H61 ]. % 19.02/19.17 apply (zenon_L1207_); trivial. % 19.02/19.17 apply (zenon_L432_); trivial. % 19.02/19.17 (* end of lemma zenon_L1239_ *) % 19.02/19.17 assert (zenon_L1240_ : (((op (e0) (e0)) = (e2))\/(((op (e1) (e0)) = (e2))\/(((op (e2) (e0)) = (e2))\/((op (e3) (e0)) = (e2))))) -> (~((op (e0) (e0)) = (e2))) -> (~((op (e1) (e0)) = (e2))) -> (~((op (e2) (e0)) = (e2))) -> (~((op (e3) (e0)) = (e2))) -> False). % 19.02/19.17 do 0 intro. intros zenon_H1fe zenon_H80 zenon_H177 zenon_Hef zenon_H14b. % 19.02/19.17 apply (zenon_or_s _ _ zenon_H1fe); [ zenon_intro zenon_H7b | zenon_intro zenon_H1ff ]. % 19.02/19.17 exact (zenon_H80 zenon_H7b). % 19.02/19.17 apply (zenon_or_s _ _ zenon_H1ff); [ zenon_intro zenon_H86 | zenon_intro zenon_H200 ]. % 19.02/19.17 exact (zenon_H177 zenon_H86). % 19.02/19.17 apply (zenon_or_s _ _ zenon_H200); [ zenon_intro zenon_Hee | zenon_intro zenon_H148 ]. % 19.02/19.17 exact (zenon_Hef zenon_Hee). % 19.02/19.17 exact (zenon_H14b zenon_H148). % 19.02/19.17 (* end of lemma zenon_L1240_ *) % 19.02/19.17 assert (zenon_L1241_ : ((~((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 (e1) (e0)) = (e2))) -> (~((op (e0) (e0)) = (e2))) -> ((op (e0) (e2)) = (e1)) -> ((~((op (e3) (e0)) = (e2)))\/((op (e3) (e2)) = (e0))) -> (~((op (e2) (e0)) = (e2))) -> (~((op (e2) (e1)) = (e2))) -> (~((op (e2) (e2)) = (e2))) -> (((op (e2) (e0)) = (e2))\/(((op (e2) (e1)) = (e2))\/(((op (e2) (e2)) = (e2))\/((op (e2) (e3)) = (e2))))) -> False). % 19.02/19.17 do 0 intro. intros zenon_H277 zenon_H1fe zenon_H177 zenon_H80 zenon_H122 zenon_H270 zenon_Hef zenon_H26e zenon_H173 zenon_H1d5. % 19.02/19.17 apply (zenon_or_s _ _ zenon_H277); [ zenon_intro zenon_H274 | zenon_intro zenon_Haa ]. % 19.02/19.17 apply (zenon_L1062_); trivial. % 19.02/19.17 apply (zenon_or_s _ _ zenon_H270); [ zenon_intro zenon_H14b | zenon_intro zenon_H61 ]. % 19.02/19.17 apply (zenon_L1240_); trivial. % 19.02/19.17 apply (zenon_L432_); trivial. % 19.02/19.17 (* end of lemma zenon_L1241_ *) % 19.02/19.17 assert (zenon_L1242_ : ((~((op (e2) (e1)) = (e2)))\/((op (e2) (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 (e2) (e2)) = (e2))) -> (~((op (e2) (e0)) = (e2))) -> ((~((op (e3) (e0)) = (e2)))\/((op (e3) (e2)) = (e0))) -> ((op (e0) (e2)) = (e1)) -> (~((op (e0) (e0)) = (e2))) -> (~((op (e1) (e0)) = (e2))) -> (((op (e0) (e0)) = (e2))\/(((op (e1) (e0)) = (e2))\/(((op (e2) (e0)) = (e2))\/((op (e3) (e0)) = (e2))))) -> ((~((op (e2) (e3)) = (e2)))\/((op (e2) (e2)) = (e3))) -> False). % 19.02/19.17 do 0 intro. intros zenon_H271 zenon_Ha8 zenon_H1d5 zenon_H173 zenon_Hef zenon_H270 zenon_H122 zenon_H80 zenon_H177 zenon_H1fe zenon_H277. % 19.02/19.17 apply (zenon_or_s _ _ zenon_H271); [ zenon_intro zenon_H26e | zenon_intro zenon_Hf1 ]. % 19.02/19.17 apply (zenon_L1241_); trivial. % 19.02/19.17 apply (zenon_L246_); trivial. % 19.02/19.17 (* end of lemma zenon_L1242_ *) % 19.02/19.17 assert (zenon_L1243_ : ((~((op (e2) (e0)) = (e2)))\/((op (e2) (e2)) = (e0))) -> ((op (e1) (e2)) = (e3)) -> ((~((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 (e1) (e0)) = (e2))) -> (~((op (e0) (e0)) = (e2))) -> ((op (e0) (e2)) = (e1)) -> ((~((op (e3) (e0)) = (e2)))\/((op (e3) (e2)) = (e0))) -> (~((op (e2) (e2)) = (e2))) -> (((op (e2) (e0)) = (e2))\/(((op (e2) (e1)) = (e2))\/(((op (e2) (e2)) = (e2))\/((op (e2) (e3)) = (e2))))) -> (~((op (e0) (e2)) = (op (e2) (e2)))) -> ((~((op (e2) (e1)) = (e2)))\/((op (e2) (e2)) = (e1))) -> False). % 19.02/19.17 do 0 intro. intros zenon_H276 zenon_H16c zenon_H277 zenon_H1fe zenon_H177 zenon_H80 zenon_H122 zenon_H270 zenon_H173 zenon_H1d5 zenon_Ha8 zenon_H271. % 19.02/19.17 apply (zenon_or_s _ _ zenon_H276); [ zenon_intro zenon_Hef | zenon_intro zenon_H2c ]. % 19.02/19.17 apply (zenon_L1242_); trivial. % 19.02/19.17 apply (zenon_L603_); trivial. % 19.02/19.17 (* end of lemma zenon_L1243_ *) % 19.02/19.17 assert (zenon_L1244_ : (((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 (e3) (e3)) = (e1)) -> (~((op (e2) (e3)) = (op (e3) (e3)))) -> (~((op (e2) (e3)) = (e2))) -> (~((op (e1) (e3)) = (op (e2) (e3)))) -> ((op (e1) (e3)) = (e3)) -> False). % 19.02/19.17 do 0 intro. intros zenon_H11f zenon_H1e zenon_He2 zenon_Hc4 zenon_Hf3 zenon_H274 zenon_Hdb zenon_Hdc. % 19.02/19.17 apply (zenon_or_s _ _ zenon_H11f); [ zenon_intro zenon_H37 | zenon_intro zenon_H120 ]. % 19.02/19.17 apply (zenon_L367_); trivial. % 19.02/19.17 apply (zenon_or_s _ _ zenon_H120); [ zenon_intro zenon_Hf4 | zenon_intro zenon_H121 ]. % 19.02/19.17 apply (zenon_L60_); trivial. % 19.02/19.17 apply (zenon_or_s _ _ zenon_H121); [ zenon_intro zenon_H11d | zenon_intro zenon_Hdd ]. % 19.02/19.17 exact (zenon_H274 zenon_H11d). % 19.02/19.17 apply (zenon_L52_); trivial. % 19.02/19.17 (* end of lemma zenon_L1244_ *) % 19.02/19.17 assert (zenon_L1245_ : (((op (e1) (e3)) = (e0))\/(((op (e1) (e3)) = (e1))\/(((op (e1) (e3)) = (e2))\/((op (e1) (e3)) = (e3))))) -> (~((op (e1) (e1)) = (op (e1) (e3)))) -> ((op (e1) (e1)) = (e0)) -> ((op (e3) (e3)) = (e1)) -> (~((op (e1) (e3)) = (op (e3) (e3)))) -> (~((op (e1) (e3)) = (e2))) -> (~((op (e1) (e3)) = (op (e2) (e3)))) -> ((op (e2) (e3)) = (e3)) -> False). % 19.02/19.17 do 0 intro. intros zenon_Hdf zenon_H57 zenon_H29 zenon_Hc4 zenon_Hd5 zenon_H14c zenon_Hdb zenon_Hdd. % 19.02/19.17 apply (zenon_or_s _ _ zenon_Hdf); [ zenon_intro zenon_H1f | zenon_intro zenon_He0 ]. % 19.02/19.17 apply (zenon_L13_); trivial. % 19.02/19.17 apply (zenon_or_s _ _ zenon_He0); [ zenon_intro zenon_Hd6 | zenon_intro zenon_He1 ]. % 19.02/19.17 apply (zenon_L50_); trivial. % 19.02/19.17 apply (zenon_or_s _ _ zenon_He1); [ zenon_intro zenon_Hd7 | zenon_intro zenon_Hdc ]. % 19.02/19.17 exact (zenon_H14c zenon_Hd7). % 19.02/19.17 apply (zenon_L52_); trivial. % 19.02/19.17 (* end of lemma zenon_L1245_ *) % 19.02/19.17 assert (zenon_L1246_ : (((op (e2) (e0)) = (e1))\/(((op (e2) (e1)) = (e1))\/(((op (e2) (e2)) = (e1))\/((op (e2) (e3)) = (e1))))) -> (~((e1) = (e2))) -> ((op (e2) (e0)) = (e2)) -> (~((op (e2) (e1)) = (op (e3) (e1)))) -> ((op (e3) (e1)) = (e1)) -> ((op (e0) (e2)) = (e1)) -> (~((op (e0) (e2)) = (op (e2) (e2)))) -> (((op (e2) (e1)) = (e0))\/(((op (e2) (e1)) = (e1))\/(((op (e2) (e1)) = (e2))\/((op (e2) (e1)) = (e3))))) -> (~((op (e2) (e1)) = (op (e2) (e2)))) -> ((op (e2) (e2)) = (e0)) -> (~((op (e2) (e1)) = (op (e2) (e3)))) -> (~((op (e2) (e1)) = (e2))) -> ((op (e0) (e1)) = (e2)) -> ((op (e1) (e1)) = (e0)) -> False). % 19.02/19.17 do 0 intro. intros zenon_H106 zenon_H7c zenon_Hee zenon_Haf zenon_Hae zenon_H122 zenon_Ha8 zenon_H1cc zenon_H24b zenon_H2c zenon_H1c7 zenon_H26e zenon_H10f zenon_H29. % 19.02/19.17 apply (zenon_or_s _ _ zenon_H106); [ zenon_intro zenon_Hed | zenon_intro zenon_H107 ]. % 19.02/19.17 apply (zenon_L58_); trivial. % 19.02/19.17 apply (zenon_or_s _ _ zenon_H107); [ zenon_intro zenon_Ha5 | zenon_intro zenon_H108 ]. % 19.02/19.17 apply (zenon_L42_); trivial. % 19.02/19.17 apply (zenon_or_s _ _ zenon_H108); [ zenon_intro zenon_Hf1 | zenon_intro zenon_Hf4 ]. % 19.02/19.17 apply (zenon_L246_); trivial. % 19.02/19.17 apply (zenon_or_s _ _ zenon_H1cc); [ zenon_intro zenon_H36 | zenon_intro zenon_H1cd ]. % 19.02/19.17 apply (zenon_L645_); trivial. % 19.02/19.17 apply (zenon_or_s _ _ zenon_H1cd); [ zenon_intro zenon_Ha5 | zenon_intro zenon_H1ce ]. % 19.02/19.17 apply (zenon_L188_); trivial. % 19.02/19.17 apply (zenon_or_s _ _ zenon_H1ce); [ zenon_intro zenon_H1ca | zenon_intro zenon_Ha6 ]. % 19.02/19.17 exact (zenon_H26e zenon_H1ca). % 19.02/19.17 apply (zenon_L371_); trivial. % 19.02/19.17 (* end of lemma zenon_L1246_ *) % 19.02/19.17 assert (zenon_L1247_ : (((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) (e3)) = (e3))) -> (((op (e1) (e3)) = (e0))\/(((op (e1) (e3)) = (e1))\/(((op (e1) (e3)) = (e2))\/((op (e1) (e3)) = (e3))))) -> (~((op (e1) (e1)) = (op (e1) (e3)))) -> (~((op (e1) (e3)) = (op (e3) (e3)))) -> (~((op (e1) (e3)) = (e2))) -> (~((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)) = (e0)) -> (~((op (e0) (e3)) = (op (e2) (e3)))) -> (~((op (e2) (e3)) = (op (e3) (e3)))) -> (~((op (e2) (e3)) = (e2))) -> (~((e0) = (e3))) -> (((op (e0) (e3)) = (e3))\/(((op (e1) (e3)) = (e3))\/(((op (e2) (e3)) = (e3))\/((op (e3) (e3)) = (e3))))) -> (~((op (e0) (e2)) = (op (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 (e2) (e0)) = (e1))\/(((op (e2) (e1)) = (e1))\/(((op (e2) (e2)) = (e1))\/((op (e2) (e3)) = (e1))))) -> (~((e1) = (e2))) -> ((op (e2) (e0)) = (e2)) -> (~((op (e2) (e1)) = (op (e3) (e1)))) -> ((op (e0) (e2)) = (e1)) -> (~((op (e0) (e2)) = (op (e2) (e2)))) -> (((op (e2) (e1)) = (e0))\/(((op (e2) (e1)) = (e1))\/(((op (e2) (e1)) = (e2))\/((op (e2) (e1)) = (e3))))) -> (~((op (e2) (e1)) = (op (e2) (e2)))) -> ((op (e2) (e2)) = (e0)) -> (~((op (e2) (e1)) = (op (e2) (e3)))) -> (~((op (e2) (e1)) = (e2))) -> ((op (e0) (e1)) = (e2)) -> ((op (e1) (e1)) = (e0)) -> False). % 19.02/19.17 do 0 intro. intros zenon_H109 zenon_H4a zenon_H10a zenon_H102 zenon_Hdf zenon_H57 zenon_Hd5 zenon_H14c zenon_Hdb zenon_H11f zenon_H1e zenon_He2 zenon_Hf3 zenon_H274 zenon_H9a zenon_H136 zenon_H14f zenon_H44 zenon_Ha1 zenon_He8 zenon_H106 zenon_H7c zenon_Hee zenon_Haf zenon_H122 zenon_Ha8 zenon_H1cc zenon_H24b zenon_H2c zenon_H1c7 zenon_H26e zenon_H10f zenon_H29. % 19.02/19.17 apply (zenon_or_s _ _ zenon_H109); [ zenon_intro zenon_Ha0 | zenon_intro zenon_H10b ]. % 19.02/19.17 apply (zenon_L406_); trivial. % 19.02/19.17 apply (zenon_or_s _ _ zenon_H10b); [ zenon_intro zenon_H10d | zenon_intro zenon_H10c ]. % 19.02/19.17 exact (zenon_H10a zenon_H10d). % 19.02/19.17 apply (zenon_or_s _ _ zenon_H10c); [ zenon_intro zenon_Ha5 | zenon_intro zenon_Hae ]. % 19.02/19.17 apply (zenon_or_s _ _ zenon_He8); [ zenon_intro zenon_Hac | zenon_intro zenon_Heb ]. % 19.02/19.17 apply (zenon_L41_); trivial. % 19.02/19.17 apply (zenon_or_s _ _ zenon_Heb); [ zenon_intro zenon_Hae | zenon_intro zenon_Hec ]. % 19.02/19.17 apply (zenon_L42_); trivial. % 19.02/19.17 apply (zenon_or_s _ _ zenon_Hec); [ zenon_intro zenon_Hba | zenon_intro zenon_Hc4 ]. % 19.02/19.17 apply (zenon_L317_); trivial. % 19.02/19.17 apply (zenon_or_s _ _ zenon_H136); [ zenon_intro zenon_He3 | zenon_intro zenon_H137 ]. % 19.02/19.17 apply (zenon_L515_); trivial. % 19.02/19.17 apply (zenon_or_s _ _ zenon_H137); [ zenon_intro zenon_Hdc | zenon_intro zenon_H138 ]. % 19.02/19.17 apply (zenon_L1244_); trivial. % 19.02/19.17 apply (zenon_or_s _ _ zenon_H138); [ zenon_intro zenon_Hdd | zenon_intro zenon_H105 ]. % 19.02/19.17 apply (zenon_L1245_); trivial. % 19.02/19.17 exact (zenon_H102 zenon_H105). % 19.02/19.17 apply (zenon_L1246_); trivial. % 19.02/19.17 (* end of lemma zenon_L1247_ *) % 19.02/19.17 assert (zenon_L1248_ : ((~((op (e1) (e1)) = (e2)))\/((op (e1) (e2)) = (e1))) -> ((~((op (e1) (e3)) = (e2)))\/((op (e1) (e2)) = (e3))) -> ((~((op (e2) (e1)) = (e2)))\/((op (e2) (e2)) = (e1))) -> ((~((op (e3) (e2)) = (e2)))\/((op (e3) (e2)) = (e2))) -> (~((op (e0) (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 (e0) (e2)) = (e2))) -> (~((op (e2) (e2)) = (e2))) -> (((op (e0) (e2)) = (e2))\/(((op (e1) (e2)) = (e2))\/(((op (e2) (e2)) = (e2))\/((op (e3) (e2)) = (e2))))) -> ((~((op (e3) (e0)) = (e2)))\/((op (e3) (e2)) = (e0))) -> (((op (e0) (e0)) = (e0))\/(((op (e0) (e1)) = (e0))\/(((op (e0) (e2)) = (e0))\/((op (e0) (e3)) = (e0))))) -> (~((op (e0) (e1)) = (op (e0) (e3)))) -> (((op (e0) (e1)) = (e0))\/(((op (e1) (e1)) = (e0))\/(((op (e2) (e1)) = (e0))\/((op (e3) (e1)) = (e0))))) -> (~((e2) = (e3))) -> (~((op (e1) (e0)) = (op (e1) (e2)))) -> ((op (e1) (e2)) = (e0)) -> (((op (e0) (e0)) = (e2))\/(((op (e0) (e1)) = (e2))\/(((op (e0) (e2)) = (e2))\/((op (e0) (e3)) = (e2))))) -> (~((op (e0) (e2)) = (op (e2) (e2)))) -> (((op (e2) (e1)) = (e0))\/(((op (e2) (e1)) = (e1))\/(((op (e2) (e1)) = (e2))\/((op (e2) (e1)) = (e3))))) -> (~((op (e2) (e1)) = (op (e2) (e3)))) -> (((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) (e1)) = (e1))\/(((op (e1) (e1)) = (e1))\/(((op (e2) (e1)) = (e1))\/((op (e3) (e1)) = (e1))))) -> (~((op (e2) (e0)) = (op (e3) (e0)))) -> (((op (e3) (e0)) = (e1))\/(((op (e3) (e1)) = (e1))\/(((op (e3) (e2)) = (e1))\/((op (e3) (e3)) = (e1))))) -> (~((op (e2) (e0)) = (op (e2) (e1)))) -> (((op (e1) (e0)) = (e1))\/(((op (e1) (e1)) = (e1))\/(((op (e1) (e2)) = (e1))\/((op (e1) (e3)) = (e1))))) -> (~((op (e1) (e3)) = (op (e3) (e3)))) -> (~((op (e0) (e2)) = (op (e1) (e2)))) -> (~((op (e1) (e0)) = (op (e2) (e0)))) -> (~((op (e2) (e0)) = (op (e2) (e2)))) -> (((op (e2) (e0)) = (e0))\/(((op (e2) (e0)) = (e1))\/(((op (e2) (e0)) = (e2))\/((op (e2) (e0)) = (e3))))) -> (~((op (e2) (e1)) = (op (e3) (e1)))) -> (~((op (e1) (e2)) = (op (e2) (e2)))) -> (~((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 (e2) (e3)))) -> (((op (e0) (e3)) = (e0))\/(((op (e0) (e3)) = (e1))\/(((op (e0) (e3)) = (e2))\/((op (e0) (e3)) = (e3))))) -> (~((op (e0) (e2)) = (op (e3) (e2)))) -> (~((op (e3) (e0)) = (op (e3) (e3)))) -> (~((op (e3) (e1)) = (op (e3) (e3)))) -> (~((op (e3) (e3)) = (e3))) -> (((op (e3) (e3)) = (e0))\/(((op (e3) (e3)) = (e1))\/(((op (e3) (e3)) = (e2))\/((op (e3) (e3)) = (e3))))) -> (((op (e2) (e0)) = (e0))\/(((op (e2) (e1)) = (e0))\/(((op (e2) (e2)) = (e0))\/((op (e2) (e3)) = (e0))))) -> ((op (e0) (e2)) = (e1)) -> (~((op (e0) (e1)) = (op (e0) (e2)))) -> (~((e0) = (e3))) -> (~((e1) = (e3))) -> (~((op (e0) (e1)) = (op (e2) (e1)))) -> (((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 (e1) (e2)) = (op (e3) (e2)))) -> (~((op (e0) (e0)) = (op (e0) (e2)))) -> (((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 (e1) (e1)) = (e1))) -> (~((e0) = (e1))) -> (~((op (e0) (e0)) = (e2))) -> (((op (e0) (e0)) = (e0))\/(((op (e1) (e0)) = (e0))\/(((op (e2) (e0)) = (e0))\/((op (e3) (e0)) = (e0))))) -> (~((op (e0) (e0)) = (e0))) -> (~((op (e2) (e2)) = (op (e3) (e2)))) -> ((~((op (e3) (e3)) = (e2)))\/((op (e3) (e2)) = (e3))) -> ((~((op (e2) (e3)) = (e2)))\/((op (e2) (e2)) = (e3))) -> ((~((op (e2) (e0)) = (e2)))\/((op (e2) (e2)) = (e0))) -> (~((e0) = (e2))) -> ((~((op (e1) (e2)) = (e2)))\/((op (e1) (e2)) = (e2))) -> False). % 19.02/19.17 do 0 intro. intros zenon_H27b zenon_H279 zenon_H271 zenon_H273 zenon_H12e zenon_H62 zenon_H145 zenon_H1fd zenon_H173 zenon_H172 zenon_H270 zenon_H74 zenon_H54 zenon_H245 zenon_H12b zenon_H24a zenon_H2a zenon_H183 zenon_Ha8 zenon_H1cc zenon_H1c7 zenon_H106 zenon_H1fe zenon_H109 zenon_H17b zenon_He8 zenon_H1f0 zenon_H128 zenon_Hd5 zenon_H195 zenon_H201 zenon_H52 zenon_H259 zenon_Haf zenon_H2b zenon_He2 zenon_Hc2 zenon_Hdf zenon_H1d zenon_Hdb zenon_He4 zenon_H14f zenon_H71 zenon_H130 zenon_H102 zenon_H101 zenon_H2f zenon_H122 zenon_H4a zenon_H9a zenon_H95 zenon_H17e zenon_H168 zenon_H142 zenon_H4f zenon_H115 zenon_H13c zenon_H26a zenon_H1ac zenon_H10a zenon_Ha1 zenon_H80 zenon_H3e zenon_H3f zenon_H18f zenon_H278 zenon_H277 zenon_H276 zenon_H149 zenon_H275. % 19.02/19.17 apply (zenon_or_s _ _ zenon_H27b); [ zenon_intro zenon_H20c | zenon_intro zenon_Hf0 ]. % 19.02/19.17 apply (zenon_or_s _ _ zenon_H275); [ zenon_intro zenon_H114 | zenon_intro zenon_H113 ]. % 19.02/19.17 apply (zenon_or_s _ _ zenon_H279); [ zenon_intro zenon_H14c | zenon_intro zenon_H16c ]. % 19.02/19.17 apply (zenon_L1216_); trivial. % 19.02/19.17 apply (zenon_L521_); trivial. % 19.02/19.17 apply (zenon_L542_); trivial. % 19.02/19.17 apply (zenon_L530_); trivial. % 19.02/19.17 (* end of lemma zenon_L1248_ *) % 19.02/19.17 assert (zenon_L1249_ : (((op (e2) (e0)) = (e1))\/(((op (e2) (e1)) = (e1))\/(((op (e2) (e2)) = (e1))\/((op (e2) (e3)) = (e1))))) -> (~((e1) = (e2))) -> ((op (e2) (e0)) = (e2)) -> (~((op (e2) (e1)) = (op (e3) (e1)))) -> ((op (e3) (e1)) = (e1)) -> ((op (e0) (e2)) = (e1)) -> (~((op (e0) (e2)) = (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) (e0)) = (e0)) -> (~((op (e2) (e3)) = (op (e3) (e3)))) -> ((op (e1) (e3)) = (e0)) -> (~((op (e3) (e3)) = (e3))) -> False). % 19.02/19.17 do 0 intro. intros zenon_H106 zenon_H7c zenon_Hee zenon_Haf zenon_Hae zenon_H122 zenon_Ha8 zenon_H101 zenon_H71 zenon_H44 zenon_Hf3 zenon_H1f zenon_H102. % 19.02/19.17 apply (zenon_or_s _ _ zenon_H106); [ zenon_intro zenon_Hed | zenon_intro zenon_H107 ]. % 19.02/19.17 apply (zenon_L58_); trivial. % 19.02/19.17 apply (zenon_or_s _ _ zenon_H107); [ zenon_intro zenon_Ha5 | zenon_intro zenon_H108 ]. % 19.02/19.17 apply (zenon_L42_); trivial. % 19.02/19.17 apply (zenon_or_s _ _ zenon_H108); [ zenon_intro zenon_Hf1 | zenon_intro zenon_Hf4 ]. % 19.02/19.17 apply (zenon_L246_); trivial. % 19.02/19.17 apply (zenon_L64_); trivial. % 19.02/19.17 (* end of lemma zenon_L1249_ *) % 19.02/19.17 assert (zenon_L1250_ : (((op (e1) (e0)) = (e0))\/(((op (e1) (e1)) = (e0))\/(((op (e1) (e2)) = (e0))\/((op (e1) (e3)) = (e0))))) -> ((op (e1) (e0)) = (e1)) -> ((op (e0) (e1)) = (e2)) -> (~((op (e2) (e1)) = (e2))) -> ((op (e2) (e2)) = (e0)) -> (~((op (e2) (e1)) = (op (e2) (e2)))) -> ((op (e2) (e0)) = (e2)) -> (~((e1) = (e2))) -> ((op (e3) (e0)) = (e0)) -> (((op (e0) (e3)) = (e3))\/(((op (e1) (e3)) = (e3))\/(((op (e2) (e3)) = (e3))\/((op (e3) (e3)) = (e3))))) -> (~((op (e2) (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) (e3)) = (e2))) -> (~((op (e1) (e1)) = (op (e1) (e3)))) -> ((~((op (e1) (e2)) = (e2)))\/((op (e1) (e2)) = (e2))) -> (~((e0) = (e2))) -> ((~((op (e2) (e0)) = (e2)))\/((op (e2) (e2)) = (e0))) -> ((~((op (e2) (e3)) = (e2)))\/((op (e2) (e2)) = (e3))) -> ((~((op (e3) (e3)) = (e2)))\/((op (e3) (e2)) = (e3))) -> (~((op (e2) (e2)) = (op (e3) (e2)))) -> (~((op (e0) (e0)) = (e0))) -> (((op (e0) (e0)) = (e0))\/(((op (e1) (e0)) = (e0))\/(((op (e2) (e0)) = (e0))\/((op (e3) (e0)) = (e0))))) -> (~((op (e0) (e0)) = (e2))) -> (~((e0) = (e1))) -> (~((op (e1) (e1)) = (e1))) -> (((op (e3) (e0)) = (e0))\/(((op (e3) (e1)) = (e0))\/(((op (e3) (e2)) = (e0))\/((op (e3) (e3)) = (e0))))) -> (((op (e0) (e0)) = (e0))\/(((op (e0) (e0)) = (e1))\/(((op (e0) (e0)) = (e2))\/((op (e0) (e0)) = (e3))))) -> (~((op (e0) (e0)) = (op (e0) (e2)))) -> (~((op (e1) (e2)) = (op (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)) = (e3))\/(((op (e0) (e1)) = (e3))\/(((op (e0) (e2)) = (e3))\/((op (e0) (e3)) = (e3))))) -> (~((op (e0) (e1)) = (op (e2) (e1)))) -> (~((e1) = (e3))) -> (~((e0) = (e3))) -> (~((op (e0) (e1)) = (op (e0) (e2)))) -> ((op (e0) (e2)) = (e1)) -> (((op (e2) (e0)) = (e0))\/(((op (e2) (e1)) = (e0))\/(((op (e2) (e2)) = (e0))\/((op (e2) (e3)) = (e0))))) -> (((op (e3) (e3)) = (e0))\/(((op (e3) (e3)) = (e1))\/(((op (e3) (e3)) = (e2))\/((op (e3) (e3)) = (e3))))) -> (~((op (e3) (e3)) = (e3))) -> (~((op (e3) (e1)) = (op (e3) (e3)))) -> (~((op (e3) (e0)) = (op (e3) (e3)))) -> (~((op (e0) (e2)) = (op (e3) (e2)))) -> (((op (e0) (e3)) = (e0))\/(((op (e0) (e3)) = (e1))\/(((op (e0) (e3)) = (e2))\/((op (e0) (e3)) = (e3))))) -> (~((op (e1) (e3)) = (op (e2) (e3)))) -> (((op (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) (e2)) = (op (e2) (e2)))) -> (~((op (e2) (e1)) = (op (e3) (e1)))) -> (((op (e2) (e0)) = (e0))\/(((op (e2) (e0)) = (e1))\/(((op (e2) (e0)) = (e2))\/((op (e2) (e0)) = (e3))))) -> (~((op (e2) (e0)) = (op (e2) (e2)))) -> (~((op (e1) (e0)) = (op (e2) (e0)))) -> (~((op (e0) (e2)) = (op (e1) (e2)))) -> (~((op (e1) (e3)) = (op (e3) (e3)))) -> (((op (e1) (e0)) = (e1))\/(((op (e1) (e1)) = (e1))\/(((op (e1) (e2)) = (e1))\/((op (e1) (e3)) = (e1))))) -> (~((op (e2) (e0)) = (op (e2) (e1)))) -> (((op (e3) (e0)) = (e1))\/(((op (e3) (e1)) = (e1))\/(((op (e3) (e2)) = (e1))\/((op (e3) (e3)) = (e1))))) -> (~((op (e2) (e0)) = (op (e3) (e0)))) -> (((op (e0) (e1)) = (e1))\/(((op (e1) (e1)) = (e1))\/(((op (e2) (e1)) = (e1))\/((op (e3) (e1)) = (e1))))) -> (((op (e0) (e0)) = (e2))\/(((op (e1) (e0)) = (e2))\/(((op (e2) (e0)) = (e2))\/((op (e3) (e0)) = (e2))))) -> (((op (e2) (e0)) = (e1))\/(((op (e2) (e1)) = (e1))\/(((op (e2) (e2)) = (e1))\/((op (e2) (e3)) = (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) (e2)) = (op (e2) (e2)))) -> (((op (e0) (e0)) = (e2))\/(((op (e0) (e1)) = (e2))\/(((op (e0) (e2)) = (e2))\/((op (e0) (e3)) = (e2))))) -> (~((op (e1) (e0)) = (op (e1) (e2)))) -> (~((e2) = (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) (e0)) = (e0))\/(((op (e0) (e1)) = (e0))\/(((op (e0) (e2)) = (e0))\/((op (e0) (e3)) = (e0))))) -> ((~((op (e3) (e0)) = (e2)))\/((op (e3) (e2)) = (e0))) -> (((op (e0) (e2)) = (e2))\/(((op (e1) (e2)) = (e2))\/(((op (e2) (e2)) = (e2))\/((op (e3) (e2)) = (e2))))) -> (~((op (e2) (e2)) = (e2))) -> (~((op (e0) (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 (e0) (e3)) = (e2))) -> ((~((op (e3) (e2)) = (e2)))\/((op (e3) (e2)) = (e2))) -> ((~((op (e2) (e1)) = (e2)))\/((op (e2) (e2)) = (e1))) -> ((~((op (e1) (e3)) = (e2)))\/((op (e1) (e2)) = (e3))) -> ((~((op (e1) (e1)) = (e2)))\/((op (e1) (e2)) = (e1))) -> (~((op (e0) (e3)) = (op (e1) (e3)))) -> ((op (e0) (e3)) = (e0)) -> False). % 19.02/19.17 do 0 intro. intros zenon_H22 zenon_H9d zenon_H10f zenon_H26e zenon_H2c zenon_H24b zenon_Hee zenon_H7c zenon_H44 zenon_H136 zenon_H274 zenon_Hf3 zenon_H11f zenon_H14c zenon_H57 zenon_H275 zenon_H149 zenon_H276 zenon_H277 zenon_H278 zenon_H18f zenon_H3f zenon_H3e zenon_H80 zenon_Ha1 zenon_H10a zenon_H1ac zenon_H26a zenon_H13c zenon_H115 zenon_H4f zenon_H142 zenon_H168 zenon_H17e zenon_H95 zenon_H9a zenon_H4a zenon_H122 zenon_H2f zenon_H101 zenon_H102 zenon_H130 zenon_H71 zenon_H14f zenon_He4 zenon_Hdb zenon_Hdf zenon_Hc2 zenon_He2 zenon_H2b zenon_Haf zenon_H259 zenon_H52 zenon_H201 zenon_H195 zenon_Hd5 zenon_H128 zenon_H1f0 zenon_He8 zenon_H17b zenon_H109 zenon_H1fe zenon_H106 zenon_H1c7 zenon_H1cc zenon_Ha8 zenon_H183 zenon_H24a zenon_H12b zenon_H245 zenon_H54 zenon_H74 zenon_H270 zenon_H172 zenon_H173 zenon_H1fd zenon_H145 zenon_H62 zenon_H12e zenon_H273 zenon_H271 zenon_H279 zenon_H27b zenon_H1d zenon_H1e. % 19.02/19.17 apply (zenon_or_s _ _ zenon_H22); [ zenon_intro zenon_H27 | zenon_intro zenon_H26 ]. % 19.02/19.17 apply (zenon_L262_); trivial. % 19.02/19.17 apply (zenon_or_s _ _ zenon_H26); [ zenon_intro zenon_H29 | zenon_intro zenon_H28 ]. % 19.02/19.17 apply (zenon_L1247_); trivial. % 19.02/19.17 apply (zenon_or_s _ _ zenon_H28); [ zenon_intro zenon_H2a | zenon_intro zenon_H1f ]. % 19.02/19.17 apply (zenon_L1248_); trivial. % 19.02/19.17 apply (zenon_L1_); trivial. % 19.02/19.17 (* end of lemma zenon_L1250_ *) % 19.02/19.17 assert (zenon_L1251_ : (((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)) = (e2))) -> (~((op (e1) (e3)) = (op (e3) (e3)))) -> ((op (e3) (e3)) = (e1)) -> (~((op (e1) (e3)) = (op (e2) (e3)))) -> (((op (e1) (e3)) = (e0))\/(((op (e1) (e3)) = (e1))\/(((op (e1) (e3)) = (e2))\/((op (e1) (e3)) = (e3))))) -> ((op (e3) (e3)) = (e2)) -> ((op (e1) (e3)) = (e0)) -> (~((op (e2) (e3)) = (e2))) -> (~((op (e0) (e3)) = (op (e2) (e3)))) -> ((op (e0) (e3)) = (e3)) -> False). % 19.02/19.17 do 0 intro. intros zenon_H11f zenon_H1d zenon_H14c zenon_Hd5 zenon_Hc4 zenon_Hdb zenon_Hdf zenon_Hf6 zenon_H1f zenon_H274 zenon_He2 zenon_He3. % 19.02/19.17 apply (zenon_or_s _ _ zenon_H11f); [ zenon_intro zenon_H37 | zenon_intro zenon_H120 ]. % 19.02/19.17 apply (zenon_L1088_); trivial. % 19.02/19.17 apply (zenon_or_s _ _ zenon_H120); [ zenon_intro zenon_Hf4 | zenon_intro zenon_H121 ]. % 19.02/19.17 apply (zenon_L63_); trivial. % 19.02/19.17 apply (zenon_or_s _ _ zenon_H121); [ zenon_intro zenon_H11d | zenon_intro zenon_Hdd ]. % 19.02/19.17 exact (zenon_H274 zenon_H11d). % 19.02/19.17 apply (zenon_L54_); trivial. % 19.02/19.17 (* end of lemma zenon_L1251_ *) % 19.02/19.17 assert (zenon_L1252_ : (((op (e0) (e0)) = (e2))\/(((op (e1) (e0)) = (e2))\/(((op (e2) (e0)) = (e2))\/((op (e3) (e0)) = (e2))))) -> (~((op (e0) (e0)) = (e2))) -> (~((op (e1) (e0)) = (e2))) -> (~((e1) = (e2))) -> ((op (e2) (e0)) = (e1)) -> (~((op (e3) (e0)) = (e2))) -> False). % 19.02/19.17 do 0 intro. intros zenon_H1fe zenon_H80 zenon_H177 zenon_H7c zenon_Hed zenon_H14b. % 19.02/19.17 apply (zenon_or_s _ _ zenon_H1fe); [ zenon_intro zenon_H7b | zenon_intro zenon_H1ff ]. % 19.02/19.17 exact (zenon_H80 zenon_H7b). % 19.02/19.17 apply (zenon_or_s _ _ zenon_H1ff); [ zenon_intro zenon_H86 | zenon_intro zenon_H200 ]. % 19.02/19.17 exact (zenon_H177 zenon_H86). % 19.02/19.17 apply (zenon_or_s _ _ zenon_H200); [ zenon_intro zenon_Hee | zenon_intro zenon_H148 ]. % 19.02/19.17 apply (zenon_L58_); trivial. % 19.02/19.17 exact (zenon_H14b zenon_H148). % 19.02/19.17 (* end of lemma zenon_L1252_ *) % 19.02/19.17 assert (zenon_L1253_ : (((op (e0) (e0)) = (e1))\/(((op (e1) (e0)) = (e1))\/(((op (e2) (e0)) = (e1))\/((op (e3) (e0)) = (e1))))) -> (~((op (e0) (e3)) = (e2))) -> (~((op (e0) (e2)) = (e2))) -> (~((op (e0) (e3)) = (op (e2) (e3)))) -> (~((op (e2) (e3)) = (e2))) -> (((op (e1) (e3)) = (e0))\/(((op (e1) (e3)) = (e1))\/(((op (e1) (e3)) = (e2))\/((op (e1) (e3)) = (e3))))) -> (~((op (e1) (e3)) = (op (e2) (e3)))) -> (~((op (e1) (e3)) = (op (e3) (e3)))) -> (~((op (e1) (e3)) = (e2))) -> (~((op (e0) (e3)) = (op (e1) (e3)))) -> (((op (e2) (e3)) = (e0))\/(((op (e2) (e3)) = (e1))\/(((op (e2) (e3)) = (e2))\/((op (e2) (e3)) = (e3))))) -> (~((op (e0) (e3)) = (op (e3) (e3)))) -> (((op (e1) (e0)) = (e0))\/(((op (e1) (e1)) = (e0))\/(((op (e1) (e2)) = (e0))\/((op (e1) (e3)) = (e0))))) -> (~((op (e2) (e1)) = (e2))) -> ((op (e2) (e2)) = (e0)) -> (~((op (e2) (e1)) = (op (e2) (e2)))) -> (((op (e0) (e3)) = (e3))\/(((op (e1) (e3)) = (e3))\/(((op (e2) (e3)) = (e3))\/((op (e3) (e3)) = (e3))))) -> (~((op (e2) (e3)) = (op (e3) (e3)))) -> (~((op (e1) (e1)) = (op (e1) (e3)))) -> ((~((op (e1) (e2)) = (e2)))\/((op (e1) (e2)) = (e2))) -> (~((e0) = (e2))) -> ((~((op (e2) (e0)) = (e2)))\/((op (e2) (e2)) = (e0))) -> ((~((op (e2) (e3)) = (e2)))\/((op (e2) (e2)) = (e3))) -> ((~((op (e3) (e3)) = (e2)))\/((op (e3) (e2)) = (e3))) -> (~((op (e2) (e2)) = (op (e3) (e2)))) -> (~((op (e0) (e0)) = (e0))) -> (((op (e0) (e0)) = (e0))\/(((op (e1) (e0)) = (e0))\/(((op (e2) (e0)) = (e0))\/((op (e3) (e0)) = (e0))))) -> (~((op (e1) (e1)) = (e1))) -> (((op (e3) (e0)) = (e0))\/(((op (e3) (e1)) = (e0))\/(((op (e3) (e2)) = (e0))\/((op (e3) (e3)) = (e0))))) -> (((op (e0) (e0)) = (e0))\/(((op (e0) (e0)) = (e1))\/(((op (e0) (e0)) = (e2))\/((op (e0) (e0)) = (e3))))) -> (~((op (e0) (e0)) = (op (e0) (e2)))) -> (~((op (e1) (e2)) = (op (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)) = (e3))\/(((op (e0) (e1)) = (e3))\/(((op (e0) (e2)) = (e3))\/((op (e0) (e3)) = (e3))))) -> (~((op (e0) (e1)) = (op (e2) (e1)))) -> (~((e1) = (e3))) -> (~((e0) = (e3))) -> (~((op (e0) (e1)) = (op (e0) (e2)))) -> ((op (e0) (e2)) = (e1)) -> (((op (e2) (e0)) = (e0))\/(((op (e2) (e1)) = (e0))\/(((op (e2) (e2)) = (e0))\/((op (e2) (e3)) = (e0))))) -> (((op (e3) (e3)) = (e0))\/(((op (e3) (e3)) = (e1))\/(((op (e3) (e3)) = (e2))\/((op (e3) (e3)) = (e3))))) -> (~((op (e3) (e3)) = (e3))) -> (~((op (e3) (e1)) = (op (e3) (e3)))) -> (~((op (e3) (e0)) = (op (e3) (e3)))) -> (~((op (e0) (e2)) = (op (e3) (e2)))) -> (((op (e0) (e3)) = (e0))\/(((op (e0) (e3)) = (e1))\/(((op (e0) (e3)) = (e2))\/((op (e0) (e3)) = (e3))))) -> (~((op (e1) (e2)) = (op (e2) (e2)))) -> (~((op (e2) (e1)) = (op (e3) (e1)))) -> (((op (e2) (e0)) = (e0))\/(((op (e2) (e0)) = (e1))\/(((op (e2) (e0)) = (e2))\/((op (e2) (e0)) = (e3))))) -> (~((op (e2) (e0)) = (op (e2) (e2)))) -> (~((op (e1) (e0)) = (op (e2) (e0)))) -> (~((op (e0) (e2)) = (op (e1) (e2)))) -> (((op (e1) (e0)) = (e1))\/(((op (e1) (e1)) = (e1))\/(((op (e1) (e2)) = (e1))\/((op (e1) (e3)) = (e1))))) -> (~((op (e2) (e0)) = (op (e2) (e1)))) -> (((op (e3) (e0)) = (e1))\/(((op (e3) (e1)) = (e1))\/(((op (e3) (e2)) = (e1))\/((op (e3) (e3)) = (e1))))) -> (~((op (e2) (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 (e2) (e1)) = (op (e2) (e3)))) -> (((op (e2) (e1)) = (e0))\/(((op (e2) (e1)) = (e1))\/(((op (e2) (e1)) = (e2))\/((op (e2) (e1)) = (e3))))) -> (~((op (e0) (e2)) = (op (e2) (e2)))) -> (((op (e0) (e0)) = (e2))\/(((op (e0) (e1)) = (e2))\/(((op (e0) (e2)) = (e2))\/((op (e0) (e3)) = (e2))))) -> (~((op (e1) (e0)) = (op (e1) (e2)))) -> (~((e2) = (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) (e0)) = (e0))\/(((op (e0) (e1)) = (e0))\/(((op (e0) (e2)) = (e0))\/((op (e0) (e3)) = (e0))))) -> ((~((op (e3) (e0)) = (e2)))\/((op (e3) (e2)) = (e0))) -> (((op (e0) (e2)) = (e2))\/(((op (e1) (e2)) = (e2))\/(((op (e2) (e2)) = (e2))\/((op (e3) (e2)) = (e2))))) -> (~((op (e2) (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 (e3) (e2)) = (e2)))\/((op (e3) (e2)) = (e2))) -> ((~((op (e2) (e1)) = (e2)))\/((op (e2) (e2)) = (e1))) -> ((~((op (e1) (e3)) = (e2)))\/((op (e1) (e2)) = (e3))) -> ((~((op (e1) (e1)) = (e2)))\/((op (e1) (e2)) = (e1))) -> (~((op (e3) (e2)) = (e2))) -> (~((op (e3) (e1)) = (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 (e2) (e2)) = (op (e2) (e3)))) -> (~((op (e1) (e0)) = (op (e3) (e0)))) -> (~((op (e3) (e0)) = (e2))) -> (~((e1) = (e2))) -> (~((op (e1) (e0)) = (e2))) -> (~((op (e0) (e0)) = (e2))) -> (((op (e0) (e0)) = (e2))\/(((op (e1) (e0)) = (e2))\/(((op (e2) (e0)) = (e2))\/((op (e3) (e0)) = (e2))))) -> ((op (e3) (e0)) = (e0)) -> (~((e0) = (e1))) -> False). % 19.02/19.17 do 0 intro. intros zenon_H235 zenon_H12e zenon_H1fd zenon_He2 zenon_H274 zenon_Hdf zenon_Hdb zenon_Hd5 zenon_H14c zenon_H1d zenon_H11f zenon_Hc2 zenon_H22 zenon_H26e zenon_H2c zenon_H24b zenon_H136 zenon_Hf3 zenon_H57 zenon_H275 zenon_H149 zenon_H276 zenon_H277 zenon_H278 zenon_H18f zenon_H3f zenon_H3e zenon_H10a zenon_H1ac zenon_H26a zenon_H13c zenon_H115 zenon_H4f zenon_H142 zenon_H168 zenon_H17e zenon_H95 zenon_H9a zenon_H4a zenon_H122 zenon_H2f zenon_H101 zenon_H102 zenon_H130 zenon_H71 zenon_H14f zenon_He4 zenon_H2b zenon_Haf zenon_H259 zenon_H52 zenon_H201 zenon_H195 zenon_H128 zenon_H1f0 zenon_He8 zenon_H17b zenon_H109 zenon_H106 zenon_H1c7 zenon_H1cc zenon_Ha8 zenon_H183 zenon_H24a zenon_H12b zenon_H245 zenon_H54 zenon_H74 zenon_H270 zenon_H172 zenon_H173 zenon_H145 zenon_H62 zenon_H273 zenon_H271 zenon_H279 zenon_H27b zenon_H272 zenon_H194 zenon_H153 zenon_H67 zenon_H6d zenon_H1fa zenon_H14b zenon_H7c zenon_H177 zenon_H80 zenon_H1fe zenon_H44 zenon_Ha1. % 19.02/19.17 apply (zenon_or_s _ _ zenon_H235); [ zenon_intro zenon_H7a | zenon_intro zenon_H236 ]. % 19.02/19.17 apply (zenon_L92_); trivial. % 19.02/19.17 apply (zenon_or_s _ _ zenon_H236); [ zenon_intro zenon_H9d | zenon_intro zenon_H237 ]. % 19.02/19.17 apply (zenon_or_s _ _ zenon_H183); [ zenon_intro zenon_H7b | zenon_intro zenon_H186 ]. % 19.02/19.17 exact (zenon_H80 zenon_H7b). % 19.02/19.17 apply (zenon_or_s _ _ zenon_H186); [ zenon_intro zenon_H10f | zenon_intro zenon_H187 ]. % 19.02/19.17 apply (zenon_or_s _ _ zenon_H1fe); [ zenon_intro zenon_H7b | zenon_intro zenon_H1ff ]. % 19.02/19.17 exact (zenon_H80 zenon_H7b). % 19.02/19.17 apply (zenon_or_s _ _ zenon_H1ff); [ zenon_intro zenon_H86 | zenon_intro zenon_H200 ]. % 19.02/19.17 exact (zenon_H177 zenon_H86). % 19.02/19.17 apply (zenon_or_s _ _ zenon_H200); [ zenon_intro zenon_Hee | zenon_intro zenon_H148 ]. % 19.02/19.17 apply (zenon_or_s _ _ zenon_H22); [ zenon_intro zenon_H27 | zenon_intro zenon_H26 ]. % 19.02/19.17 apply (zenon_L312_); trivial. % 19.02/19.17 apply (zenon_or_s _ _ zenon_H26); [ zenon_intro zenon_H29 | zenon_intro zenon_H28 ]. % 19.02/19.17 apply (zenon_or_s _ _ zenon_H67); [ zenon_intro zenon_H1e | zenon_intro zenon_H68 ]. % 19.02/19.17 apply (zenon_L1247_); trivial. % 19.02/19.17 apply (zenon_or_s _ _ zenon_H68); [ zenon_intro zenon_H1f | zenon_intro zenon_H69 ]. % 19.02/19.17 apply (zenon_L13_); trivial. % 19.02/19.17 apply (zenon_or_s _ _ zenon_H69); [ zenon_intro zenon_H37 | zenon_intro zenon_H60 ]. % 19.02/19.17 apply (zenon_L18_); trivial. % 19.02/19.17 apply (zenon_L21_); trivial. % 19.02/19.17 apply (zenon_or_s _ _ zenon_H28); [ zenon_intro zenon_H2a | zenon_intro zenon_H1f ]. % 19.02/19.17 apply (zenon_L1248_); trivial. % 19.02/19.17 apply (zenon_or_s _ _ zenon_He8); [ zenon_intro zenon_Hac | zenon_intro zenon_Heb ]. % 19.02/19.17 apply (zenon_L41_); trivial. % 19.02/19.17 apply (zenon_or_s _ _ zenon_Heb); [ zenon_intro zenon_Hae | zenon_intro zenon_Hec ]. % 19.02/19.17 apply (zenon_L1249_); trivial. % 19.02/19.17 apply (zenon_or_s _ _ zenon_Hec); [ zenon_intro zenon_Hba | zenon_intro zenon_Hc4 ]. % 19.02/19.17 apply (zenon_L317_); trivial. % 19.02/19.17 apply (zenon_or_s _ _ zenon_H153); [ zenon_intro zenon_H148 | zenon_intro zenon_H154 ]. % 19.02/19.17 exact (zenon_H14b zenon_H148). % 19.02/19.17 apply (zenon_or_s _ _ zenon_H154); [ zenon_intro zenon_H14d | zenon_intro zenon_H155 ]. % 19.02/19.17 exact (zenon_H194 zenon_H14d). % 19.02/19.17 apply (zenon_or_s _ _ zenon_H155); [ zenon_intro zenon_H151 | zenon_intro zenon_Hf6 ]. % 19.02/19.17 exact (zenon_H272 zenon_H151). % 19.02/19.17 apply (zenon_or_s _ _ zenon_He4); [ zenon_intro zenon_H1e | zenon_intro zenon_He5 ]. % 19.02/19.17 apply (zenon_L1250_); trivial. % 19.02/19.17 apply (zenon_or_s _ _ zenon_He5); [ zenon_intro zenon_Hc3 | zenon_intro zenon_He6 ]. % 19.02/19.17 apply (zenon_L46_); trivial. % 19.02/19.17 apply (zenon_or_s _ _ zenon_He6); [ zenon_intro zenon_Hcd | zenon_intro zenon_He3 ]. % 19.02/19.17 exact (zenon_H12e zenon_Hcd). % 19.02/19.17 apply (zenon_L1251_); trivial. % 19.02/19.17 exact (zenon_H14b zenon_H148). % 19.02/19.17 apply (zenon_or_s _ _ zenon_H187); [ zenon_intro zenon_H150 | zenon_intro zenon_Hcd ]. % 19.02/19.17 exact (zenon_H1fd zenon_H150). % 19.02/19.17 exact (zenon_H12e zenon_Hcd). % 19.02/19.17 apply (zenon_or_s _ _ zenon_H237); [ zenon_intro zenon_Hed | zenon_intro zenon_Hac ]. % 19.02/19.17 apply (zenon_L1252_); trivial. % 19.02/19.17 apply (zenon_L41_); trivial. % 19.02/19.17 (* end of lemma zenon_L1253_ *) % 19.02/19.17 assert (zenon_L1254_ : (((op (e1) (e1)) = (e0))\/(((op (e1) (e1)) = (e1))\/(((op (e1) (e1)) = (e2))\/((op (e1) (e1)) = (e3))))) -> ((op (e1) (e0)) = (e0)) -> (~((op (e1) (e0)) = (op (e1) (e1)))) -> (~((op (e1) (e1)) = (e1))) -> (~((op (e1) (e1)) = (e2))) -> ((op (e0) (e1)) = (e2)) -> ((op (e3) (e1)) = (e0)) -> False). % 19.02/19.17 do 0 intro. intros zenon_H142 zenon_H27 zenon_H45 zenon_H10a zenon_H20c zenon_H10f zenon_H1b1. % 19.02/19.17 apply (zenon_or_s _ _ zenon_H142); [ zenon_intro zenon_H29 | zenon_intro zenon_H143 ]. % 19.02/19.17 apply (zenon_L8_); trivial. % 19.02/19.17 apply (zenon_or_s _ _ zenon_H143); [ zenon_intro zenon_H10d | zenon_intro zenon_H144 ]. % 19.02/19.17 exact (zenon_H10a zenon_H10d). % 19.02/19.17 apply (zenon_or_s _ _ zenon_H144); [ zenon_intro zenon_H110 | zenon_intro zenon_H13f ]. % 19.02/19.17 exact (zenon_H20c zenon_H110). % 19.02/19.17 apply (zenon_L580_); trivial. % 19.02/19.17 (* end of lemma zenon_L1254_ *) % 19.02/19.17 assert (zenon_L1255_ : (((op (e0) (e3)) = (e0))\/(((op (e0) (e3)) = (e1))\/(((op (e0) (e3)) = (e2))\/((op (e0) (e3)) = (e3))))) -> ((op (e3) (e3)) = (e0)) -> (~((op (e0) (e3)) = (op (e3) (e3)))) -> ((op (e1) (e3)) = (e1)) -> (~((op (e0) (e3)) = (op (e1) (e3)))) -> (~((op (e0) (e3)) = (e2))) -> (~((op (e0) (e3)) = (op (e2) (e3)))) -> ((op (e2) (e3)) = (e3)) -> False). % 19.02/19.17 do 0 intro. intros zenon_He4 zenon_H60 zenon_Hc2 zenon_Hd6 zenon_H1d zenon_H12e zenon_He2 zenon_Hdd. % 19.02/19.17 apply (zenon_or_s _ _ zenon_He4); [ zenon_intro zenon_H1e | zenon_intro zenon_He5 ]. % 19.02/19.17 apply (zenon_L440_); trivial. % 19.02/19.17 apply (zenon_or_s _ _ zenon_He5); [ zenon_intro zenon_Hc3 | zenon_intro zenon_He6 ]. % 19.02/19.17 apply (zenon_L79_); trivial. % 19.02/19.17 apply (zenon_or_s _ _ zenon_He6); [ zenon_intro zenon_Hcd | zenon_intro zenon_He3 ]. % 19.02/19.17 exact (zenon_H12e zenon_Hcd). % 19.02/19.17 apply (zenon_L54_); trivial. % 19.02/19.17 (* end of lemma zenon_L1255_ *) % 19.02/19.17 assert (zenon_L1256_ : ((~((op (e0) (e3)) = (e2)))\/((op (e0) (e2)) = (e3))) -> ((~((op (e1) (e3)) = (e2)))\/((op (e1) (e2)) = (e3))) -> ((~((op (e2) (e1)) = (e2)))\/((op (e2) (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 (e2) (e0)) = (e2)))\/((op (e2) (e2)) = (e0))) -> ((~((op (e3) (e2)) = (e2)))\/((op (e3) (e2)) = (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)) = (e2))) -> (~((op (e2) (e2)) = (e2))) -> (((op (e0) (e2)) = (e2))\/(((op (e1) (e2)) = (e2))\/(((op (e2) (e2)) = (e2))\/((op (e3) (e2)) = (e2))))) -> ((~((op (e3) (e0)) = (e2)))\/((op (e3) (e2)) = (e0))) -> ((op (e0) (e2)) = (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)) = (e2))) -> (~((op (e2) (e2)) = (op (e3) (e2)))) -> ((~((op (e3) (e3)) = (e2)))\/((op (e3) (e2)) = (e3))) -> ((~((op (e2) (e3)) = (e2)))\/((op (e2) (e2)) = (e3))) -> (~((op (e0) (e0)) = (e0))) -> (~((e0) = (e1))) -> (~((op (e1) (e1)) = (e1))) -> (~((e1) = (e2))) -> (~((op (e1) (e0)) = (op (e1) (e1)))) -> (~((op (e0) (e0)) = (op (e0) (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 (e1) (e2)) = (e2)))\/((op (e1) (e2)) = (e2))) -> (~((e0) = (e2))) -> (((op (e0) (e0)) = (e0))\/(((op (e1) (e0)) = (e0))\/(((op (e2) (e0)) = (e0))\/((op (e3) (e0)) = (e0))))) -> (((op (e3) (e0)) = (e0))\/(((op (e3) (e1)) = (e0))\/(((op (e3) (e2)) = (e0))\/((op (e3) (e3)) = (e0))))) -> (((op (e0) (e0)) = (e0))\/(((op (e0) (e0)) = (e1))\/(((op (e0) (e0)) = (e2))\/((op (e0) (e0)) = (e3))))) -> (~((op (e1) (e2)) = (op (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)) = (e3))\/(((op (e0) (e1)) = (e3))\/(((op (e0) (e2)) = (e3))\/((op (e0) (e3)) = (e3))))) -> (~((op (e0) (e1)) = (op (e2) (e1)))) -> (~((e1) = (e3))) -> (((op (e2) (e0)) = (e0))\/(((op (e2) (e1)) = (e0))\/(((op (e2) (e2)) = (e0))\/((op (e2) (e3)) = (e0))))) -> (((op (e3) (e3)) = (e0))\/(((op (e3) (e3)) = (e1))\/(((op (e3) (e3)) = (e2))\/((op (e3) (e3)) = (e3))))) -> (~((op (e3) (e1)) = (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 (e0) (e3)) = (op (e3) (e3)))) -> (~((op (e1) (e2)) = (op (e2) (e2)))) -> (((op (e2) (e0)) = (e0))\/(((op (e2) (e0)) = (e1))\/(((op (e2) (e0)) = (e2))\/((op (e2) (e0)) = (e3))))) -> (~((op (e2) (e0)) = (op (e2) (e2)))) -> (~((op (e1) (e0)) = (op (e2) (e0)))) -> (~((op (e0) (e2)) = (op (e1) (e2)))) -> (((op (e1) (e0)) = (e1))\/(((op (e1) (e1)) = (e1))\/(((op (e1) (e2)) = (e1))\/((op (e1) (e3)) = (e1))))) -> (~((op (e2) (e0)) = (op (e2) (e1)))) -> (~((op (e2) (e0)) = (op (e3) (e0)))) -> (((op (e0) (e0)) = (e2))\/(((op (e0) (e1)) = (e2))\/(((op (e0) (e2)) = (e2))\/((op (e0) (e3)) = (e2))))) -> (~((op (e1) (e0)) = (op (e1) (e2)))) -> (~((e2) = (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) (e0)) = (e0))\/(((op (e0) (e1)) = (e0))\/(((op (e0) (e2)) = (e0))\/((op (e0) (e3)) = (e0))))) -> ((~((op (e1) (e1)) = (e2)))\/((op (e1) (e2)) = (e1))) -> (((op (e0) (e1)) = (e1))\/(((op (e1) (e1)) = (e1))\/(((op (e2) (e1)) = (e1))\/((op (e3) (e1)) = (e1))))) -> (((op (e2) (e1)) = (e0))\/(((op (e2) (e1)) = (e1))\/(((op (e2) (e1)) = (e2))\/((op (e2) (e1)) = (e3))))) -> (~((op (e2) (e1)) = (op (e2) (e3)))) -> (~((op (e2) (e1)) = (op (e2) (e2)))) -> (((op (e2) (e0)) = (e1))\/(((op (e2) (e1)) = (e1))\/(((op (e2) (e2)) = (e1))\/((op (e2) (e3)) = (e1))))) -> (~((op (e2) (e1)) = (op (e3) (e1)))) -> (~((op (e0) (e2)) = (op (e3) (e2)))) -> (((op (e0) (e3)) = (e3))\/(((op (e1) (e3)) = (e3))\/(((op (e2) (e3)) = (e3))\/((op (e3) (e3)) = (e3))))) -> (~((op (e3) (e3)) = (e3))) -> (~((op (e1) (e1)) = (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) (e3)) = (op (e2) (e3)))) -> (~((op (e2) (e3)) = (op (e3) (e3)))) -> (~((op (e1) (e3)) = (op (e2) (e3)))) -> (((op (e2) (e3)) = (e0))\/(((op (e2) (e3)) = (e1))\/(((op (e2) (e3)) = (e2))\/((op (e2) (e3)) = (e3))))) -> (~((e0) = (e3))) -> (((op (e3) (e0)) = (e1))\/(((op (e3) (e1)) = (e1))\/(((op (e3) (e2)) = (e1))\/((op (e3) (e3)) = (e1))))) -> (~((op (e0) (e1)) = (op (e0) (e2)))) -> (~((op (e2) (e2)) = (op (e2) (e3)))) -> (~((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)) = (op (e3) (e0)))) -> (((op (e0) (e0)) = (e1))\/(((op (e1) (e0)) = (e1))\/(((op (e2) (e0)) = (e1))\/((op (e3) (e0)) = (e1))))) -> ((~((op (e3) (e1)) = (e2)))\/((op (e3) (e2)) = (e1))) -> ((~((op (e1) (e0)) = (e2)))\/((op (e1) (e2)) = (e0))) -> False). % 19.02/19.17 do 0 intro. intros zenon_H27c zenon_H279 zenon_H271 zenon_Ha8 zenon_H1d5 zenon_H276 zenon_H273 zenon_H62 zenon_H145 zenon_H1fd zenon_H173 zenon_H172 zenon_H270 zenon_H122 zenon_H1fe zenon_H5b zenon_H80 zenon_H18f zenon_H278 zenon_H277 zenon_H3f zenon_Ha1 zenon_H10a zenon_H7c zenon_H45 zenon_H13c zenon_H153 zenon_H22 zenon_H275 zenon_H149 zenon_H3e zenon_H1ac zenon_H26a zenon_H115 zenon_H4f zenon_H142 zenon_H168 zenon_H17e zenon_H95 zenon_H2f zenon_H101 zenon_H130 zenon_He4 zenon_H1d zenon_Hc2 zenon_H2b zenon_H259 zenon_H52 zenon_H201 zenon_H195 zenon_H128 zenon_H1f0 zenon_H17b zenon_H183 zenon_H24a zenon_H12b zenon_H245 zenon_H54 zenon_H74 zenon_H27b zenon_H109 zenon_H1cc zenon_H1c7 zenon_H24b zenon_H106 zenon_Haf zenon_H14f zenon_H136 zenon_H102 zenon_H57 zenon_Hd5 zenon_Hdf zenon_He2 zenon_Hf3 zenon_Hdb zenon_H11f zenon_H9a zenon_He8 zenon_H4a zenon_H6d zenon_H71 zenon_H67 zenon_H1fa zenon_H235 zenon_H26f zenon_H27a. % 19.02/19.17 apply (zenon_or_s _ _ zenon_H27c); [ zenon_intro zenon_H12e | zenon_intro zenon_Ha9 ]. % 19.02/19.17 apply (zenon_or_s _ _ zenon_H27a); [ zenon_intro zenon_H177 | zenon_intro zenon_H2a ]. % 19.02/19.17 apply (zenon_or_s _ _ zenon_H27b); [ zenon_intro zenon_H20c | zenon_intro zenon_Hf0 ]. % 19.02/19.17 apply (zenon_or_s _ _ zenon_H275); [ zenon_intro zenon_H114 | zenon_intro zenon_H113 ]. % 19.02/19.17 apply (zenon_or_s _ _ zenon_H279); [ zenon_intro zenon_H14c | zenon_intro zenon_H16c ]. % 19.02/19.17 apply (zenon_or_s _ _ zenon_H277); [ zenon_intro zenon_H274 | zenon_intro zenon_Haa ]. % 19.02/19.17 apply (zenon_L1206_); trivial. % 19.02/19.17 apply (zenon_L1239_); trivial. % 19.02/19.17 apply (zenon_L1243_); trivial. % 19.02/19.17 apply (zenon_or_s _ _ zenon_H279); [ zenon_intro zenon_H14c | zenon_intro zenon_H16c ]. % 19.02/19.17 apply (zenon_or_s _ _ zenon_H276); [ zenon_intro zenon_Hef | zenon_intro zenon_H2c ]. % 19.02/19.17 apply (zenon_or_s _ _ zenon_H271); [ zenon_intro zenon_H26e | zenon_intro zenon_Hf1 ]. % 19.02/19.17 apply (zenon_or_s _ _ zenon_H277); [ zenon_intro zenon_H274 | zenon_intro zenon_Haa ]. % 19.02/19.17 apply (zenon_L1062_); trivial. % 19.02/19.17 apply (zenon_L1239_); trivial. % 19.02/19.17 apply (zenon_L246_); trivial. % 19.02/19.17 apply (zenon_or_s _ _ zenon_H271); [ zenon_intro zenon_H26e | zenon_intro zenon_Hf1 ]. % 19.02/19.17 apply (zenon_or_s _ _ zenon_H277); [ zenon_intro zenon_H274 | zenon_intro zenon_Haa ]. % 19.02/19.17 apply (zenon_or_s _ _ zenon_H270); [ zenon_intro zenon_H14b | zenon_intro zenon_H61 ]. % 19.02/19.17 apply (zenon_or_s _ _ zenon_H26f); [ zenon_intro zenon_H194 | zenon_intro zenon_Hba ]. % 19.02/19.17 apply (zenon_or_s _ _ zenon_H273); [ zenon_intro zenon_H272 | zenon_intro zenon_H151 ]. % 19.02/19.17 apply (zenon_or_s _ _ zenon_H3e); [ zenon_intro zenon_H42 | zenon_intro zenon_H41 ]. % 19.02/19.17 exact (zenon_H3f zenon_H42). % 19.02/19.17 apply (zenon_or_s _ _ zenon_H41); [ zenon_intro zenon_H27 | zenon_intro zenon_H43 ]. % 19.02/19.17 apply (zenon_or_s _ _ zenon_H183); [ zenon_intro zenon_H7b | zenon_intro zenon_H186 ]. % 19.02/19.17 exact (zenon_H80 zenon_H7b). % 19.02/19.17 apply (zenon_or_s _ _ zenon_H186); [ zenon_intro zenon_H10f | zenon_intro zenon_H187 ]. % 19.02/19.17 apply (zenon_or_s _ _ zenon_H128); [ zenon_intro zenon_H9d | zenon_intro zenon_H129 ]. % 19.02/19.17 apply (zenon_L262_); trivial. % 19.02/19.17 apply (zenon_or_s _ _ zenon_H129); [ zenon_intro zenon_H10d | zenon_intro zenon_H12a ]. % 19.02/19.17 exact (zenon_H10a zenon_H10d). % 19.02/19.17 apply (zenon_or_s _ _ zenon_H12a); [ zenon_intro zenon_Hf0 | zenon_intro zenon_Hd6 ]. % 19.02/19.17 apply (zenon_L68_); trivial. % 19.02/19.17 apply (zenon_or_s _ _ zenon_H1ac); [ zenon_intro zenon_H44 | zenon_intro zenon_H1af ]. % 19.02/19.17 apply (zenon_L1253_); trivial. % 19.02/19.17 apply (zenon_or_s _ _ zenon_H1af); [ zenon_intro zenon_H1b1 | zenon_intro zenon_H1b0 ]. % 19.02/19.17 apply (zenon_L1254_); trivial. % 19.02/19.17 apply (zenon_or_s _ _ zenon_H1b0); [ zenon_intro zenon_H61 | zenon_intro zenon_H60 ]. % 19.02/19.17 apply (zenon_L146_); trivial. % 19.02/19.17 apply (zenon_or_s _ _ zenon_H136); [ zenon_intro zenon_He3 | zenon_intro zenon_H137 ]. % 19.02/19.17 apply (zenon_L1143_); trivial. % 19.02/19.17 apply (zenon_or_s _ _ zenon_H137); [ zenon_intro zenon_Hdc | zenon_intro zenon_H138 ]. % 19.02/19.17 apply (zenon_L83_); trivial. % 19.02/19.17 apply (zenon_or_s _ _ zenon_H138); [ zenon_intro zenon_Hdd | zenon_intro zenon_H105 ]. % 19.02/19.17 apply (zenon_L1255_); trivial. % 19.02/19.17 exact (zenon_H102 zenon_H105). % 19.02/19.17 apply (zenon_or_s _ _ zenon_H187); [ zenon_intro zenon_H150 | zenon_intro zenon_Hcd ]. % 19.02/19.17 exact (zenon_H1fd zenon_H150). % 19.02/19.17 exact (zenon_H12e zenon_Hcd). % 19.02/19.17 apply (zenon_or_s _ _ zenon_H43); [ zenon_intro zenon_H34 | zenon_intro zenon_H44 ]. % 19.02/19.17 apply (zenon_L11_); trivial. % 19.02/19.17 apply (zenon_L1253_); trivial. % 19.02/19.17 apply (zenon_L1174_); trivial. % 19.02/19.17 apply (zenon_L317_); trivial. % 19.02/19.17 apply (zenon_L146_); trivial. % 19.02/19.17 apply (zenon_L1239_); trivial. % 19.02/19.17 apply (zenon_L246_); trivial. % 19.02/19.17 apply (zenon_L116_); trivial. % 19.02/19.17 apply (zenon_L530_); trivial. % 19.02/19.17 apply (zenon_L1248_); trivial. % 19.02/19.17 apply (zenon_L77_); trivial. % 19.02/19.17 (* end of lemma zenon_L1256_ *) % 19.02/19.17 assert (zenon_L1257_ : (((op (e0) (e0)) = (e1))\/(((op (e0) (e1)) = (e1))\/(((op (e0) (e2)) = (e1))\/((op (e0) (e3)) = (e1))))) -> ((op (e3) (e2)) = (e0)) -> ((op (e2) (e0)) = (e0)) -> (((op (e0) (e3)) = (e1))\/(((op (e1) (e3)) = (e1))\/(((op (e2) (e3)) = (e1))\/((op (e3) (e3)) = (e1))))) -> (~((op (e0) (e0)) = (op (e0) (e3)))) -> (~((op (e1) (e0)) = (e2))) -> (~((op (e1) (e0)) = (op (e1) (e3)))) -> (((op (e1) (e0)) = (e0))\/(((op (e1) (e0)) = (e1))\/(((op (e1) (e0)) = (e2))\/((op (e1) (e0)) = (e3))))) -> ((op (e2) (e2)) = (e1)) -> (~((op (e2) (e0)) = (e2))) -> ((op (e0) (e1)) = (e0)) -> ((~((op (e1) (e0)) = (e2)))\/((op (e1) (e2)) = (e0))) -> ((~((op (e3) (e1)) = (e2)))\/((op (e3) (e2)) = (e1))) -> (((op (e0) (e0)) = (e1))\/(((op (e1) (e0)) = (e1))\/(((op (e2) (e0)) = (e1))\/((op (e3) (e0)) = (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)) = (op (e3) (e3)))) -> (~((op (e2) (e2)) = (op (e2) (e3)))) -> (~((op (e0) (e1)) = (op (e0) (e2)))) -> (((op (e3) (e0)) = (e1))\/(((op (e3) (e1)) = (e1))\/(((op (e3) (e2)) = (e1))\/((op (e3) (e3)) = (e1))))) -> (~((e0) = (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) (e3)) = (op (e3) (e3)))) -> (~((op (e0) (e3)) = (op (e2) (e3)))) -> (((op (e1) (e3)) = (e0))\/(((op (e1) (e3)) = (e1))\/(((op (e1) (e3)) = (e2))\/((op (e1) (e3)) = (e3))))) -> (~((op (e1) (e3)) = (op (e3) (e3)))) -> (~((op (e1) (e1)) = (op (e1) (e3)))) -> (~((op (e3) (e3)) = (e3))) -> (((op (e0) (e3)) = (e3))\/(((op (e1) (e3)) = (e3))\/(((op (e2) (e3)) = (e3))\/((op (e3) (e3)) = (e3))))) -> (~((op (e0) (e2)) = (op (e3) (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) (e2)))) -> (~((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)) = (e1))\/(((op (e1) (e1)) = (e1))\/(((op (e2) (e1)) = (e1))\/((op (e3) (e1)) = (e1))))) -> ((~((op (e1) (e1)) = (e2)))\/((op (e1) (e2)) = (e1))) -> (((op (e0) (e0)) = (e0))\/(((op (e0) (e1)) = (e0))\/(((op (e0) (e2)) = (e0))\/((op (e0) (e3)) = (e0))))) -> (~((op (e0) (e1)) = (op (e0) (e3)))) -> (((op (e0) (e1)) = (e0))\/(((op (e1) (e1)) = (e0))\/(((op (e2) (e1)) = (e0))\/((op (e3) (e1)) = (e0))))) -> (~((e2) = (e3))) -> (~((op (e1) (e0)) = (op (e1) (e2)))) -> (~((op (e2) (e0)) = (op (e3) (e0)))) -> (~((op (e2) (e0)) = (op (e2) (e1)))) -> (((op (e1) (e0)) = (e1))\/(((op (e1) (e1)) = (e1))\/(((op (e1) (e2)) = (e1))\/((op (e1) (e3)) = (e1))))) -> (~((op (e0) (e2)) = (op (e1) (e2)))) -> (~((op (e1) (e0)) = (op (e2) (e0)))) -> (~((op (e2) (e0)) = (op (e2) (e2)))) -> (((op (e2) (e0)) = (e0))\/(((op (e2) (e0)) = (e1))\/(((op (e2) (e0)) = (e2))\/((op (e2) (e0)) = (e3))))) -> (~((op (e1) (e2)) = (op (e2) (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 (e3) (e1)) = (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))))) -> (~((e1) = (e3))) -> (~((op (e0) (e1)) = (op (e2) (e1)))) -> (((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 (e1) (e2)) = (op (e3) (e2)))) -> (((op (e0) (e0)) = (e0))\/(((op (e0) (e0)) = (e1))\/(((op (e0) (e0)) = (e2))\/((op (e0) (e0)) = (e3))))) -> (((op (e3) (e0)) = (e0))\/(((op (e3) (e1)) = (e0))\/(((op (e3) (e2)) = (e0))\/((op (e3) (e3)) = (e0))))) -> (((op (e0) (e0)) = (e0))\/(((op (e1) (e0)) = (e0))\/(((op (e2) (e0)) = (e0))\/((op (e3) (e0)) = (e0))))) -> (~((e0) = (e2))) -> ((~((op (e1) (e2)) = (e2)))\/((op (e1) (e2)) = (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 (e0) (e0)) = (op (e0) (e2)))) -> (~((op (e1) (e0)) = (op (e1) (e1)))) -> (~((op (e1) (e1)) = (e1))) -> (~((e0) = (e1))) -> (~((op (e0) (e0)) = (e0))) -> ((~((op (e2) (e3)) = (e2)))\/((op (e2) (e2)) = (e3))) -> ((~((op (e3) (e3)) = (e2)))\/((op (e3) (e2)) = (e3))) -> (~((op (e2) (e2)) = (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)) = (e2)))\/((op (e3) (e2)) = (e0))) -> (((op (e0) (e2)) = (e2))\/(((op (e1) (e2)) = (e2))\/(((op (e2) (e2)) = (e2))\/((op (e3) (e2)) = (e2))))) -> (~((op (e2) (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 (e3) (e2)) = (e2)))\/((op (e3) (e2)) = (e2))) -> ((~((op (e2) (e0)) = (e2)))\/((op (e2) (e2)) = (e0))) -> (((op (e2) (e0)) = (e2))\/(((op (e2) (e1)) = (e2))\/(((op (e2) (e2)) = (e2))\/((op (e2) (e3)) = (e2))))) -> (~((op (e0) (e2)) = (op (e2) (e2)))) -> ((~((op (e2) (e1)) = (e2)))\/((op (e2) (e2)) = (e1))) -> ((~((op (e1) (e3)) = (e2)))\/((op (e1) (e2)) = (e3))) -> ((~((op (e0) (e3)) = (e2)))\/((op (e0) (e2)) = (e3))) -> (((op (e0) (e0)) = (e2))\/(((op (e0) (e1)) = (e2))\/(((op (e0) (e2)) = (e2))\/((op (e0) (e3)) = (e2))))) -> (~((op (e0) (e0)) = (e2))) -> (~((op (e0) (e1)) = (e2))) -> (~((op (e0) (e2)) = (e2))) -> (~((e1) = (e2))) -> False). % 19.02/19.18 do 0 intro. intros zenon_H22d zenon_H61 zenon_H34 zenon_H133 zenon_H189 zenon_H177 zenon_Hd8 zenon_H25e zenon_Hf1 zenon_Hef zenon_H49 zenon_H27a zenon_H26f zenon_H235 zenon_H1fa zenon_H67 zenon_H71 zenon_H6d zenon_H4a zenon_He8 zenon_H9a zenon_H11f zenon_Hdb zenon_Hf3 zenon_He2 zenon_Hdf zenon_Hd5 zenon_H57 zenon_H102 zenon_H136 zenon_H14f zenon_Haf zenon_H106 zenon_H24b zenon_H1c7 zenon_H1cc zenon_H109 zenon_H27b zenon_H74 zenon_H54 zenon_H245 zenon_H12b zenon_H24a zenon_H17b zenon_H1f0 zenon_H128 zenon_H195 zenon_H201 zenon_H52 zenon_H259 zenon_H2b zenon_Hc2 zenon_H1d zenon_He4 zenon_H130 zenon_H101 zenon_H2f zenon_H95 zenon_H17e zenon_H168 zenon_H142 zenon_H4f zenon_H115 zenon_H26a zenon_H1ac zenon_H3e zenon_H149 zenon_H275 zenon_H22 zenon_H153 zenon_H13c zenon_H45 zenon_H10a zenon_Ha1 zenon_H3f zenon_H277 zenon_H278 zenon_H18f zenon_H5b zenon_H1fe zenon_H270 zenon_H172 zenon_H173 zenon_H145 zenon_H62 zenon_H273 zenon_H276 zenon_H1d5 zenon_Ha8 zenon_H271 zenon_H279 zenon_H27c zenon_H183 zenon_H80 zenon_H26d zenon_H1fd zenon_H7c. % 19.02/19.18 apply (zenon_or_s _ _ zenon_H22d); [ zenon_intro zenon_H7a | zenon_intro zenon_H22e ]. % 19.02/19.18 apply (zenon_or_s _ _ zenon_H183); [ zenon_intro zenon_H7b | zenon_intro zenon_H186 ]. % 19.02/19.18 exact (zenon_H80 zenon_H7b). % 19.02/19.18 apply (zenon_or_s _ _ zenon_H186); [ zenon_intro zenon_H10f | zenon_intro zenon_H187 ]. % 19.02/19.18 exact (zenon_H26d zenon_H10f). % 19.02/19.18 apply (zenon_or_s _ _ zenon_H187); [ zenon_intro zenon_H150 | zenon_intro zenon_Hcd ]. % 19.02/19.18 exact (zenon_H1fd zenon_H150). % 19.02/19.18 apply (zenon_or_s _ _ zenon_H1fe); [ zenon_intro zenon_H7b | zenon_intro zenon_H1ff ]. % 19.02/19.18 exact (zenon_H80 zenon_H7b). % 19.02/19.18 apply (zenon_or_s _ _ zenon_H1ff); [ zenon_intro zenon_H86 | zenon_intro zenon_H200 ]. % 19.02/19.18 exact (zenon_H177 zenon_H86). % 19.02/19.18 apply (zenon_or_s _ _ zenon_H200); [ zenon_intro zenon_Hee | zenon_intro zenon_H148 ]. % 19.02/19.18 exact (zenon_Hef zenon_Hee). % 19.02/19.18 apply (zenon_or_s _ _ zenon_H67); [ zenon_intro zenon_H1e | zenon_intro zenon_H68 ]. % 19.02/19.18 apply (zenon_L428_); trivial. % 19.02/19.18 apply (zenon_or_s _ _ zenon_H68); [ zenon_intro zenon_H1f | zenon_intro zenon_H69 ]. % 19.02/19.18 apply (zenon_L1238_); trivial. % 19.02/19.18 apply (zenon_or_s _ _ zenon_H69); [ zenon_intro zenon_H37 | zenon_intro zenon_H60 ]. % 19.02/19.18 apply (zenon_L14_); trivial. % 19.02/19.18 apply (zenon_L15_); trivial. % 19.02/19.18 apply (zenon_or_s _ _ zenon_H22e); [ zenon_intro zenon_Ha0 | zenon_intro zenon_H22f ]. % 19.02/19.18 apply (zenon_L38_); trivial. % 19.02/19.18 apply (zenon_or_s _ _ zenon_H22f); [ zenon_intro zenon_H122 | zenon_intro zenon_Hc3 ]. % 19.02/19.18 apply (zenon_L1256_); trivial. % 19.02/19.18 apply (zenon_L1060_); trivial. % 19.02/19.18 (* end of lemma zenon_L1257_ *) % 19.02/19.18 assert (zenon_L1258_ : ((~((op (e0) (e3)) = (e2)))\/((op (e0) (e2)) = (e3))) -> ((~((op (e1) (e1)) = (e2)))\/((op (e1) (e2)) = (e1))) -> (((op (e2) (e0)) = (e0))\/(((op (e2) (e0)) = (e1))\/(((op (e2) (e0)) = (e2))\/((op (e2) (e0)) = (e3))))) -> (~((op (e0) (e1)) = (op (e1) (e1)))) -> (~((op (e3) (e2)) = (op (e3) (e3)))) -> (((op (e0) (e3)) = (e2))\/(((op (e1) (e3)) = (e2))\/(((op (e2) (e3)) = (e2))\/((op (e3) (e3)) = (e2))))) -> ((~((op (e3) (e1)) = (e2)))\/((op (e3) (e2)) = (e1))) -> (~((e0) = (e3))) -> (~((op (e3) (e0)) = (op (e3) (e2)))) -> (~((op (e2) (e0)) = (op (e2) (e2)))) -> (~((op (e0) (e0)) = (op (e0) (e3)))) -> (((op (e0) (e0)) = (e2))\/(((op (e0) (e1)) = (e2))\/(((op (e0) (e2)) = (e2))\/((op (e0) (e3)) = (e2))))) -> ((~((op (e1) (e2)) = (e2)))\/((op (e1) (e2)) = (e2))) -> ((~((op (e2) (e0)) = (e2)))\/((op (e2) (e2)) = (e0))) -> ((~((op (e2) (e3)) = (e2)))\/((op (e2) (e2)) = (e3))) -> ((~((op (e3) (e3)) = (e2)))\/((op (e3) (e2)) = (e3))) -> (~((op (e2) (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) (e1)))) -> (((op (e1) (e0)) = (e0))\/(((op (e1) (e0)) = (e1))\/(((op (e1) (e0)) = (e2))\/((op (e1) (e0)) = (e3))))) -> (~((op (e1) (e0)) = (op (e2) (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) (e3)) = (op (e2) (e3)))) -> (~((e0) = (e2))) -> (((op (e1) (e3)) = (e0))\/(((op (e1) (e3)) = (e1))\/(((op (e1) (e3)) = (e2))\/((op (e1) (e3)) = (e3))))) -> (~((op (e1) (e3)) = (op (e3) (e3)))) -> (~((op (e1) (e2)) = (op (e1) (e3)))) -> (((op (e1) (e0)) = (e0))\/(((op (e1) (e1)) = (e0))\/(((op (e1) (e2)) = (e0))\/((op (e1) (e3)) = (e0))))) -> (((op (e2) (e0)) = (e1))\/(((op (e2) (e1)) = (e1))\/(((op (e2) (e2)) = (e1))\/((op (e2) (e3)) = (e1))))) -> (~((op (e3) (e0)) = (op (e3) (e1)))) -> (~((op (e0) (e2)) = (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) (e1)) = (e0))\/(((op (e2) (e1)) = (e1))\/(((op (e2) (e1)) = (e2))\/((op (e2) (e1)) = (e3))))) -> (((op (e0) (e0)) = (e0))\/(((op (e1) (e0)) = (e0))\/(((op (e2) (e0)) = (e0))\/((op (e3) (e0)) = (e0))))) -> ((~((op (e2) (e1)) = (e2)))\/((op (e2) (e2)) = (e1))) -> (~((e1) = (e3))) -> ((~((op (e1) (e3)) = (e2)))\/((op (e1) (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 (e2) (e0)) = (e2))\/(((op (e2) (e1)) = (e2))\/(((op (e2) (e2)) = (e2))\/((op (e2) (e3)) = (e2))))) -> (~((op (e0) (e3)) = (op (e3) (e3)))) -> (~((op (e0) (e1)) = (op (e0) (e2)))) -> (~((op (e1) (e1)) = (op (e1) (e3)))) -> (~((op (e2) (e0)) = (op (e2) (e1)))) -> (((op (e0) (e1)) = (e0))\/(((op (e1) (e1)) = (e0))\/(((op (e2) (e1)) = (e0))\/((op (e3) (e1)) = (e0))))) -> (~((op (e2) (e0)) = (op (e2) (e3)))) -> (~((op (e2) (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 (e0) (e3)) = (e3))\/(((op (e1) (e3)) = (e3))\/(((op (e2) (e3)) = (e3))\/((op (e3) (e3)) = (e3))))) -> (~((op (e0) (e3)) = (op (e1) (e3)))) -> (((op (e0) (e3)) = (e0))\/(((op (e0) (e3)) = (e1))\/(((op (e0) (e3)) = (e2))\/((op (e0) (e3)) = (e3))))) -> (~((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)) = (e1))\/(((op (e1) (e1)) = (e1))\/(((op (e2) (e1)) = (e1))\/((op (e3) (e1)) = (e1))))) -> (~((op (e3) (e1)) = (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 (e2) (e3)) = (op (e3) (e3)))) -> (~((op (e1) (e0)) = (op (e1) (e3)))) -> (((op (e3) (e3)) = (e0))\/(((op (e3) (e3)) = (e1))\/(((op (e3) (e3)) = (e2))\/((op (e3) (e3)) = (e3))))) -> (~((op (e3) (e3)) = (e3))) -> (((op (e0) (e1)) = (e0))\/(((op (e0) (e1)) = (e1))\/(((op (e0) (e1)) = (e2))\/((op (e0) (e1)) = (e3))))) -> (((op (e1) (e1)) = (e0))\/(((op (e1) (e1)) = (e1))\/(((op (e1) (e1)) = (e2))\/((op (e1) (e1)) = (e3))))) -> (~((op (e0) (e1)) = (op (e2) (e1)))) -> (~((op (e0) (e1)) = (op (e0) (e3)))) -> (~((op (e0) (e1)) = (op (e3) (e1)))) -> ((op (e0) (e2)) = (e0)) -> (~((op (e0) (e2)) = (op (e0) (e3)))) -> (~((op (e0) (e2)) = (op (e2) (e2)))) -> (~((op (e2) (e2)) = (op (e2) (e3)))) -> (((op (e2) (e0)) = (e0))\/(((op (e2) (e1)) = (e0))\/(((op (e2) (e2)) = (e0))\/((op (e2) (e3)) = (e0))))) -> (~((e0) = (e1))) -> (~((op (e1) (e1)) = (e1))) -> (~((op (e1) (e2)) = (op (e2) (e2)))) -> (~((e1) = (e2))) -> (~((op (e2) (e1)) = (op (e2) (e3)))) -> (((op (e1) (e0)) = (e1))\/(((op (e1) (e1)) = (e1))\/(((op (e1) (e2)) = (e1))\/((op (e1) (e3)) = (e1))))) -> (~((op (e0) (e0)) = (e0))) -> (((op (e0) (e2)) = (e2))\/(((op (e1) (e2)) = (e2))\/(((op (e2) (e2)) = (e2))\/((op (e3) (e2)) = (e2))))) -> (~((op (e2) (e2)) = (e2))) -> (~((op (e0) (e2)) = (e2))) -> (((op (e0) (e1)) = (e2))\/(((op (e1) (e1)) = (e2))\/(((op (e2) (e1)) = (e2))\/((op (e3) (e1)) = (e2))))) -> (~((op (e3) (e1)) = (op (e3) (e2)))) -> (~((op (e0) (e1)) = (e2))) -> ((~((op (e3) (e2)) = (e2)))\/((op (e3) (e2)) = (e2))) -> ((~((op (e3) (e0)) = (e2)))\/((op (e3) (e2)) = (e0))) -> (((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)) = (e2)))\/((op (e1) (e2)) = (e0))) -> False). % 19.02/19.18 do 0 intro. intros zenon_H27c zenon_H27b zenon_H259 zenon_H10e zenon_H62 zenon_H145 zenon_H26f zenon_H9a zenon_H6f zenon_H52 zenon_H189 zenon_H183 zenon_H275 zenon_H276 zenon_H277 zenon_H278 zenon_H18f zenon_H22d zenon_H45 zenon_H25e zenon_H201 zenon_H1fa zenon_H18c zenon_Hdb zenon_H149 zenon_Hdf zenon_Hd5 zenon_H124 zenon_H22 zenon_H106 zenon_H1cf zenon_H195 zenon_H115 zenon_H235 zenon_H1cc zenon_H3e zenon_H271 zenon_H95 zenon_H279 zenon_H1ac zenon_H14f zenon_H1d5 zenon_Hc2 zenon_H4a zenon_H57 zenon_H1f0 zenon_H245 zenon_H5b zenon_H17b zenon_H67 zenon_He8 zenon_H136 zenon_H1d zenon_He4 zenon_H12b zenon_He2 zenon_H11f zenon_H109 zenon_H130 zenon_H133 zenon_H71 zenon_Hf3 zenon_Hd8 zenon_H101 zenon_H102 zenon_H212 zenon_H142 zenon_H17e zenon_H54 zenon_H210 zenon_H48 zenon_H208 zenon_Ha8 zenon_H6d zenon_H2f zenon_Ha1 zenon_H10a zenon_H2b zenon_H7c zenon_H1c7 zenon_H128 zenon_H3f zenon_H172 zenon_H173 zenon_H1fd zenon_H1d8 zenon_H1a4 zenon_H26d zenon_H273 zenon_H270 zenon_H153 zenon_H16f zenon_H27a. % 19.02/19.18 apply (zenon_or_s _ _ zenon_H27c); [ zenon_intro zenon_H12e | zenon_intro zenon_Ha9 ]. % 19.02/19.18 apply (zenon_L1232_); trivial. % 19.02/19.18 apply (zenon_L358_); trivial. % 19.02/19.18 (* end of lemma zenon_L1258_ *) % 19.02/19.18 assert (zenon_L1259_ : (((op (e1) (e0)) = (e2))\/(((op (e1) (e1)) = (e2))\/(((op (e1) (e2)) = (e2))\/((op (e1) (e3)) = (e2))))) -> (~((op (e1) (e0)) = (e2))) -> (~((e0) = (e2))) -> ((op (e1) (e1)) = (e0)) -> (~((op (e1) (e2)) = (e2))) -> (~((op (e1) (e3)) = (e2))) -> False). % 19.02/19.18 do 0 intro. intros zenon_H18c zenon_H177 zenon_H149 zenon_H29 zenon_H114 zenon_H14c. % 19.02/19.18 apply (zenon_or_s _ _ zenon_H18c); [ zenon_intro zenon_H86 | zenon_intro zenon_H18d ]. % 19.02/19.18 exact (zenon_H177 zenon_H86). % 19.02/19.18 apply (zenon_or_s _ _ zenon_H18d); [ zenon_intro zenon_H110 | zenon_intro zenon_H18e ]. % 19.02/19.18 apply (zenon_L354_); trivial. % 19.02/19.18 apply (zenon_or_s _ _ zenon_H18e); [ zenon_intro zenon_H113 | zenon_intro zenon_Hd7 ]. % 19.02/19.18 exact (zenon_H114 zenon_H113). % 19.02/19.18 exact (zenon_H14c zenon_Hd7). % 19.02/19.18 (* end of lemma zenon_L1259_ *) % 19.02/19.18 assert (zenon_L1260_ : (((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) (e1)) = (op (e2) (e3)))) -> ((op (e2) (e3)) = (e1)) -> (~((op (e2) (e1)) = (e2))) -> ((op (e3) (e1)) = (e0)) -> ((op (e1) (e1)) = (e2)) -> False). % 19.02/19.18 do 0 intro. intros zenon_H1cc zenon_H24b zenon_H2c zenon_H1c7 zenon_Hf4 zenon_H26e zenon_H1b1 zenon_H110. % 19.02/19.18 apply (zenon_or_s _ _ zenon_H1cc); [ zenon_intro zenon_H36 | zenon_intro zenon_H1cd ]. % 19.02/19.18 apply (zenon_L645_); trivial. % 19.02/19.18 apply (zenon_or_s _ _ zenon_H1cd); [ zenon_intro zenon_Ha5 | zenon_intro zenon_H1ce ]. % 19.02/19.18 apply (zenon_L188_); trivial. % 19.02/19.18 apply (zenon_or_s _ _ zenon_H1ce); [ zenon_intro zenon_H1ca | zenon_intro zenon_Ha6 ]. % 19.02/19.18 exact (zenon_H26e zenon_H1ca). % 19.02/19.18 apply (zenon_L509_); trivial. % 19.02/19.18 (* end of lemma zenon_L1260_ *) % 19.02/19.18 assert (zenon_L1261_ : (((op (e2) (e0)) = (e1))\/(((op (e2) (e1)) = (e1))\/(((op (e2) (e2)) = (e1))\/((op (e2) (e3)) = (e1))))) -> (~((e1) = (e2))) -> ((op (e2) (e0)) = (e2)) -> ((op (e0) (e1)) = (e1)) -> (~((op (e0) (e1)) = (op (e2) (e1)))) -> ((op (e1) (e2)) = (e1)) -> (~((op (e1) (e2)) = (op (e2) (e2)))) -> (((op (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) (e1)) = (op (e2) (e3)))) -> (~((op (e2) (e1)) = (e2))) -> ((op (e3) (e1)) = (e0)) -> ((op (e1) (e1)) = (e2)) -> False). % 19.02/19.18 do 0 intro. intros zenon_H106 zenon_H7c zenon_Hee zenon_Ha0 zenon_H17e zenon_Hf0 zenon_H2b zenon_H1cc zenon_H24b zenon_H2c zenon_H1c7 zenon_H26e zenon_H1b1 zenon_H110. % 19.02/19.18 apply (zenon_or_s _ _ zenon_H106); [ zenon_intro zenon_Hed | zenon_intro zenon_H107 ]. % 19.02/19.18 apply (zenon_L58_); trivial. % 19.02/19.18 apply (zenon_or_s _ _ zenon_H107); [ zenon_intro zenon_Ha5 | zenon_intro zenon_H108 ]. % 19.02/19.18 apply (zenon_L357_); trivial. % 19.02/19.18 apply (zenon_or_s _ _ zenon_H108); [ zenon_intro zenon_Hf1 | zenon_intro zenon_Hf4 ]. % 19.02/19.18 apply (zenon_L59_); trivial. % 19.02/19.18 apply (zenon_L1260_); trivial. % 19.02/19.18 (* end of lemma zenon_L1261_ *) % 19.02/19.18 assert (zenon_L1262_ : (((op (e0) (e1)) = (e0))\/(((op (e1) (e1)) = (e0))\/(((op (e2) (e1)) = (e0))\/((op (e3) (e1)) = (e0))))) -> (~((e0) = (e1))) -> (~((e0) = (e2))) -> (((op (e1) (e0)) = (e2))\/(((op (e1) (e1)) = (e2))\/(((op (e1) (e2)) = (e2))\/((op (e1) (e3)) = (e2))))) -> (~((op (e1) (e0)) = (e2))) -> (~((op (e2) (e1)) = (e2))) -> (~((op (e2) (e1)) = (op (e2) (e3)))) -> ((op (e2) (e2)) = (e0)) -> (~((op (e2) (e1)) = (op (e2) (e2)))) -> (((op (e2) (e1)) = (e0))\/(((op (e2) (e1)) = (e1))\/(((op (e2) (e1)) = (e2))\/((op (e2) (e1)) = (e3))))) -> (~((op (e1) (e2)) = (op (e2) (e2)))) -> ((op (e1) (e2)) = (e1)) -> (~((op (e0) (e1)) = (op (e2) (e1)))) -> ((op (e0) (e1)) = (e1)) -> ((op (e2) (e0)) = (e2)) -> (~((e1) = (e2))) -> (((op (e2) (e0)) = (e1))\/(((op (e2) (e1)) = (e1))\/(((op (e2) (e2)) = (e1))\/((op (e2) (e3)) = (e1))))) -> (~((op (e1) (e2)) = (e2))) -> (~((op (e1) (e3)) = (e2))) -> False). % 19.02/19.18 do 0 intro. intros zenon_H245 zenon_Ha1 zenon_H149 zenon_H18c zenon_H177 zenon_H26e zenon_H1c7 zenon_H2c zenon_H24b zenon_H1cc zenon_H2b zenon_Hf0 zenon_H17e zenon_Ha0 zenon_Hee zenon_H7c zenon_H106 zenon_H114 zenon_H14c. % 19.02/19.18 apply (zenon_or_s _ _ zenon_H245); [ zenon_intro zenon_H49 | zenon_intro zenon_H246 ]. % 19.02/19.18 apply (zenon_L38_); trivial. % 19.02/19.18 apply (zenon_or_s _ _ zenon_H246); [ zenon_intro zenon_H29 | zenon_intro zenon_H247 ]. % 19.02/19.18 apply (zenon_L1259_); trivial. % 19.02/19.18 apply (zenon_or_s _ _ zenon_H247); [ zenon_intro zenon_H36 | zenon_intro zenon_H1b1 ]. % 19.02/19.18 apply (zenon_L645_); trivial. % 19.02/19.18 apply (zenon_or_s _ _ zenon_H18c); [ zenon_intro zenon_H86 | zenon_intro zenon_H18d ]. % 19.02/19.18 exact (zenon_H177 zenon_H86). % 19.02/19.18 apply (zenon_or_s _ _ zenon_H18d); [ zenon_intro zenon_H110 | zenon_intro zenon_H18e ]. % 19.02/19.18 apply (zenon_L1261_); trivial. % 19.02/19.18 apply (zenon_or_s _ _ zenon_H18e); [ zenon_intro zenon_H113 | zenon_intro zenon_Hd7 ]. % 19.02/19.18 exact (zenon_H114 zenon_H113). % 19.02/19.18 exact (zenon_H14c zenon_Hd7). % 19.02/19.18 (* end of lemma zenon_L1262_ *) % 19.02/19.18 assert (zenon_L1263_ : (((op (e0) (e0)) = (e2))\/(((op (e1) (e0)) = (e2))\/(((op (e2) (e0)) = (e2))\/((op (e3) (e0)) = (e2))))) -> (~((op (e0) (e0)) = (e2))) -> (~((op (e1) (e3)) = (e2))) -> (~((op (e1) (e2)) = (e2))) -> (((op (e2) (e0)) = (e1))\/(((op (e2) (e1)) = (e1))\/(((op (e2) (e2)) = (e1))\/((op (e2) (e3)) = (e1))))) -> (~((e1) = (e2))) -> ((op (e0) (e1)) = (e1)) -> (~((op (e0) (e1)) = (op (e2) (e1)))) -> ((op (e1) (e2)) = (e1)) -> (~((op (e1) (e2)) = (op (e2) (e2)))) -> (((op (e2) (e1)) = (e0))\/(((op (e2) (e1)) = (e1))\/(((op (e2) (e1)) = (e2))\/((op (e2) (e1)) = (e3))))) -> (~((op (e2) (e1)) = (op (e2) (e2)))) -> ((op (e2) (e2)) = (e0)) -> (~((op (e2) (e1)) = (op (e2) (e3)))) -> (~((op (e2) (e1)) = (e2))) -> (~((op (e1) (e0)) = (e2))) -> (((op (e1) (e0)) = (e2))\/(((op (e1) (e1)) = (e2))\/(((op (e1) (e2)) = (e2))\/((op (e1) (e3)) = (e2))))) -> (~((e0) = (e2))) -> (~((e0) = (e1))) -> (((op (e0) (e1)) = (e0))\/(((op (e1) (e1)) = (e0))\/(((op (e2) (e1)) = (e0))\/((op (e3) (e1)) = (e0))))) -> (~((op (e3) (e0)) = (e2))) -> False). % 19.02/19.18 do 0 intro. intros zenon_H1fe zenon_H80 zenon_H14c zenon_H114 zenon_H106 zenon_H7c zenon_Ha0 zenon_H17e zenon_Hf0 zenon_H2b zenon_H1cc zenon_H24b zenon_H2c zenon_H1c7 zenon_H26e zenon_H177 zenon_H18c zenon_H149 zenon_Ha1 zenon_H245 zenon_H14b. % 19.02/19.18 apply (zenon_or_s _ _ zenon_H1fe); [ zenon_intro zenon_H7b | zenon_intro zenon_H1ff ]. % 19.02/19.18 exact (zenon_H80 zenon_H7b). % 19.02/19.18 apply (zenon_or_s _ _ zenon_H1ff); [ zenon_intro zenon_H86 | zenon_intro zenon_H200 ]. % 19.02/19.18 exact (zenon_H177 zenon_H86). % 19.02/19.18 apply (zenon_or_s _ _ zenon_H200); [ zenon_intro zenon_Hee | zenon_intro zenon_H148 ]. % 19.02/19.18 apply (zenon_L1262_); trivial. % 19.02/19.18 exact (zenon_H14b zenon_H148). % 19.02/19.18 (* end of lemma zenon_L1263_ *) % 19.02/19.18 assert (zenon_L1264_ : (((op (e0) (e3)) = (e3))\/(((op (e1) (e3)) = (e3))\/(((op (e2) (e3)) = (e3))\/((op (e3) (e3)) = (e3))))) -> (~((e0) = (e3))) -> (~((op (e2) (e3)) = (e2))) -> (~((op (e2) (e3)) = (op (e3) (e3)))) -> (~((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 (e1) (e3)) = (op (e2) (e3)))) -> (~((op (e1) (e3)) = (e2))) -> (~((op (e1) (e3)) = (op (e3) (e3)))) -> ((op (e3) (e3)) = (e1)) -> (~((op (e1) (e0)) = (op (e1) (e3)))) -> ((op (e1) (e0)) = (e0)) -> (((op (e1) (e3)) = (e0))\/(((op (e1) (e3)) = (e1))\/(((op (e1) (e3)) = (e2))\/((op (e1) (e3)) = (e3))))) -> (~((op (e3) (e3)) = (e3))) -> False). % 19.02/19.18 do 0 intro. intros zenon_H136 zenon_H9a zenon_H274 zenon_Hf3 zenon_He2 zenon_H1e zenon_H11f zenon_Hdb zenon_H14c zenon_Hd5 zenon_Hc4 zenon_Hd8 zenon_H27 zenon_Hdf zenon_H102. % 19.02/19.18 apply (zenon_or_s _ _ zenon_H136); [ zenon_intro zenon_He3 | zenon_intro zenon_H137 ]. % 19.02/19.18 apply (zenon_L515_); trivial. % 19.02/19.18 apply (zenon_or_s _ _ zenon_H137); [ zenon_intro zenon_Hdc | zenon_intro zenon_H138 ]. % 19.02/19.18 apply (zenon_L1244_); trivial. % 19.02/19.18 apply (zenon_or_s _ _ zenon_H138); [ zenon_intro zenon_Hdd | zenon_intro zenon_H105 ]. % 19.02/19.18 apply (zenon_L1235_); trivial. % 19.02/19.18 exact (zenon_H102 zenon_H105). % 19.02/19.18 (* end of lemma zenon_L1264_ *) % 19.02/19.18 assert (zenon_L1265_ : (((op (e2) (e0)) = (e1))\/(((op (e2) (e1)) = (e1))\/(((op (e2) (e2)) = (e1))\/((op (e2) (e3)) = (e1))))) -> (~((e1) = (e2))) -> ((op (e2) (e0)) = (e2)) -> (~((op (e2) (e1)) = (op (e3) (e1)))) -> ((op (e3) (e1)) = (e1)) -> ((op (e1) (e2)) = (e1)) -> (~((op (e1) (e2)) = (op (e2) (e2)))) -> (((op (e2) (e1)) = (e0))\/(((op (e2) (e1)) = (e1))\/(((op (e2) (e1)) = (e2))\/((op (e2) (e1)) = (e3))))) -> (~((op (e2) (e1)) = (op (e2) (e2)))) -> ((op (e2) (e2)) = (e0)) -> (~((op (e2) (e1)) = (op (e2) (e3)))) -> (~((op (e2) (e1)) = (e2))) -> ((op (e3) (e1)) = (e0)) -> ((op (e1) (e1)) = (e2)) -> False). % 19.02/19.18 do 0 intro. intros zenon_H106 zenon_H7c zenon_Hee zenon_Haf zenon_Hae zenon_Hf0 zenon_H2b zenon_H1cc zenon_H24b zenon_H2c zenon_H1c7 zenon_H26e zenon_H1b1 zenon_H110. % 19.02/19.18 apply (zenon_or_s _ _ zenon_H106); [ zenon_intro zenon_Hed | zenon_intro zenon_H107 ]. % 19.02/19.18 apply (zenon_L58_); trivial. % 19.02/19.18 apply (zenon_or_s _ _ zenon_H107); [ zenon_intro zenon_Ha5 | zenon_intro zenon_H108 ]. % 19.02/19.18 apply (zenon_L42_); trivial. % 19.02/19.18 apply (zenon_or_s _ _ zenon_H108); [ zenon_intro zenon_Hf1 | zenon_intro zenon_Hf4 ]. % 19.02/19.18 apply (zenon_L59_); trivial. % 19.02/19.18 apply (zenon_L1260_); trivial. % 19.02/19.18 (* end of lemma zenon_L1265_ *) % 19.02/19.18 assert (zenon_L1266_ : (((op (e1) (e0)) = (e2))\/(((op (e1) (e1)) = (e2))\/(((op (e1) (e2)) = (e2))\/((op (e1) (e3)) = (e2))))) -> (~((op (e1) (e0)) = (e2))) -> ((op (e3) (e1)) = (e0)) -> (~((op (e2) (e1)) = (e2))) -> (~((op (e2) (e1)) = (op (e2) (e3)))) -> ((op (e2) (e2)) = (e0)) -> (~((op (e2) (e1)) = (op (e2) (e2)))) -> (((op (e2) (e1)) = (e0))\/(((op (e2) (e1)) = (e1))\/(((op (e2) (e1)) = (e2))\/((op (e2) (e1)) = (e3))))) -> (~((op (e1) (e2)) = (op (e2) (e2)))) -> ((op (e1) (e2)) = (e1)) -> ((op (e3) (e1)) = (e1)) -> (~((op (e2) (e1)) = (op (e3) (e1)))) -> ((op (e2) (e0)) = (e2)) -> (~((e1) = (e2))) -> (((op (e2) (e0)) = (e1))\/(((op (e2) (e1)) = (e1))\/(((op (e2) (e2)) = (e1))\/((op (e2) (e3)) = (e1))))) -> (~((op (e1) (e2)) = (e2))) -> (~((op (e1) (e3)) = (e2))) -> False). % 19.02/19.18 do 0 intro. intros zenon_H18c zenon_H177 zenon_H1b1 zenon_H26e zenon_H1c7 zenon_H2c zenon_H24b zenon_H1cc zenon_H2b zenon_Hf0 zenon_Hae zenon_Haf zenon_Hee zenon_H7c zenon_H106 zenon_H114 zenon_H14c. % 19.02/19.18 apply (zenon_or_s _ _ zenon_H18c); [ zenon_intro zenon_H86 | zenon_intro zenon_H18d ]. % 19.02/19.18 exact (zenon_H177 zenon_H86). % 19.02/19.18 apply (zenon_or_s _ _ zenon_H18d); [ zenon_intro zenon_H110 | zenon_intro zenon_H18e ]. % 19.02/19.18 apply (zenon_L1265_); trivial. % 19.02/19.18 apply (zenon_or_s _ _ zenon_H18e); [ zenon_intro zenon_H113 | zenon_intro zenon_Hd7 ]. % 19.02/19.18 exact (zenon_H114 zenon_H113). % 19.02/19.18 exact (zenon_H14c zenon_Hd7). % 19.02/19.18 (* end of lemma zenon_L1266_ *) % 19.02/19.18 assert (zenon_L1267_ : (((op (e0) (e1)) = (e1))\/(((op (e1) (e1)) = (e1))\/(((op (e2) (e1)) = (e1))\/((op (e3) (e1)) = (e1))))) -> (~((op (e3) (e0)) = (e2))) -> (((op (e0) (e1)) = (e0))\/(((op (e1) (e1)) = (e0))\/(((op (e2) (e1)) = (e0))\/((op (e3) (e1)) = (e0))))) -> (~((e0) = (e2))) -> (~((op (e0) (e1)) = (op (e2) (e1)))) -> (~((op (e0) (e0)) = (e2))) -> (((op (e0) (e0)) = (e2))\/(((op (e1) (e0)) = (e2))\/(((op (e2) (e0)) = (e2))\/((op (e3) (e0)) = (e2))))) -> (~((op (e1) (e1)) = (e1))) -> (~((op (e3) (e3)) = (e3))) -> (((op (e1) (e3)) = (e0))\/(((op (e1) (e3)) = (e1))\/(((op (e1) (e3)) = (e2))\/((op (e1) (e3)) = (e3))))) -> ((op (e1) (e0)) = (e0)) -> (~((op (e1) (e0)) = (op (e1) (e3)))) -> (~((op (e1) (e3)) = (op (e3) (e3)))) -> (~((op (e1) (e3)) = (op (e2) (e3)))) -> (((op (e2) (e3)) = (e0))\/(((op (e2) (e3)) = (e1))\/(((op (e2) (e3)) = (e2))\/((op (e2) (e3)) = (e3))))) -> ((op (e0) (e3)) = (e0)) -> (~((op (e0) (e3)) = (op (e2) (e3)))) -> (~((op (e2) (e3)) = (op (e3) (e3)))) -> (~((op (e2) (e3)) = (e2))) -> (~((e0) = (e3))) -> (((op (e0) (e3)) = (e3))\/(((op (e1) (e3)) = (e3))\/(((op (e2) (e3)) = (e3))\/((op (e3) (e3)) = (e3))))) -> (~((op (e1) (e2)) = (op (e1) (e3)))) -> (~((e0) = (e1))) -> (((op (e0) (e3)) = (e1))\/(((op (e1) (e3)) = (e1))\/(((op (e2) (e3)) = (e1))\/((op (e3) (e3)) = (e1))))) -> (((op (e1) (e0)) = (e2))\/(((op (e1) (e1)) = (e2))\/(((op (e1) (e2)) = (e2))\/((op (e1) (e3)) = (e2))))) -> (~((op (e1) (e0)) = (e2))) -> ((op (e3) (e1)) = (e0)) -> (~((op (e2) (e1)) = (e2))) -> (~((op (e2) (e1)) = (op (e2) (e3)))) -> ((op (e2) (e2)) = (e0)) -> (~((op (e2) (e1)) = (op (e2) (e2)))) -> (((op (e2) (e1)) = (e0))\/(((op (e2) (e1)) = (e1))\/(((op (e2) (e1)) = (e2))\/((op (e2) (e1)) = (e3))))) -> (~((op (e1) (e2)) = (op (e2) (e2)))) -> ((op (e1) (e2)) = (e1)) -> (~((op (e2) (e1)) = (op (e3) (e1)))) -> ((op (e2) (e0)) = (e2)) -> (~((e1) = (e2))) -> (((op (e2) (e0)) = (e1))\/(((op (e2) (e1)) = (e1))\/(((op (e2) (e2)) = (e1))\/((op (e2) (e3)) = (e1))))) -> (~((op (e1) (e2)) = (e2))) -> (~((op (e1) (e3)) = (e2))) -> False). % 19.02/19.18 do 0 intro. intros zenon_H109 zenon_H14b zenon_H245 zenon_H149 zenon_H17e zenon_H80 zenon_H1fe zenon_H10a zenon_H102 zenon_Hdf zenon_H27 zenon_Hd8 zenon_Hd5 zenon_Hdb zenon_H11f zenon_H1e zenon_He2 zenon_Hf3 zenon_H274 zenon_H9a zenon_H136 zenon_H124 zenon_Ha1 zenon_H133 zenon_H18c zenon_H177 zenon_H1b1 zenon_H26e zenon_H1c7 zenon_H2c zenon_H24b zenon_H1cc zenon_H2b zenon_Hf0 zenon_Haf zenon_Hee zenon_H7c zenon_H106 zenon_H114 zenon_H14c. % 19.02/19.18 apply (zenon_or_s _ _ zenon_H109); [ zenon_intro zenon_Ha0 | zenon_intro zenon_H10b ]. % 19.02/19.18 apply (zenon_L1263_); trivial. % 19.02/19.18 apply (zenon_or_s _ _ zenon_H10b); [ zenon_intro zenon_H10d | zenon_intro zenon_H10c ]. % 19.02/19.18 exact (zenon_H10a zenon_H10d). % 19.02/19.18 apply (zenon_or_s _ _ zenon_H10c); [ zenon_intro zenon_Ha5 | zenon_intro zenon_Hae ]. % 19.02/19.18 apply (zenon_or_s _ _ zenon_H133); [ zenon_intro zenon_Hc3 | zenon_intro zenon_H134 ]. % 19.02/19.18 apply (zenon_L427_); trivial. % 19.02/19.18 apply (zenon_or_s _ _ zenon_H134); [ zenon_intro zenon_Hd6 | zenon_intro zenon_H135 ]. % 19.02/19.18 apply (zenon_L78_); trivial. % 19.02/19.18 apply (zenon_or_s _ _ zenon_H135); [ zenon_intro zenon_Hf4 | zenon_intro zenon_Hc4 ]. % 19.02/19.18 apply (zenon_L188_); trivial. % 19.02/19.18 apply (zenon_L1264_); trivial. % 19.02/19.18 apply (zenon_L1266_); trivial. % 19.02/19.18 (* end of lemma zenon_L1267_ *) % 19.02/19.18 assert (zenon_L1268_ : (((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)) = (op (e3) (e1)))) -> ((op (e2) (e1)) = (e1)) -> ((op (e2) (e2)) = (e0)) -> ((op (e0) (e2)) = (e3)) -> (~((op (e0) (e3)) = (op (e3) (e3)))) -> ((op (e0) (e3)) = (e1)) -> False). % 19.02/19.18 do 0 intro. intros zenon_He8 zenon_Ha1 zenon_H44 zenon_Haf zenon_Ha5 zenon_H2c zenon_Ha9 zenon_Hc2 zenon_Hc3. % 19.02/19.18 apply (zenon_or_s _ _ zenon_He8); [ zenon_intro zenon_Hac | zenon_intro zenon_Heb ]. % 19.02/19.18 apply (zenon_L41_); trivial. % 19.02/19.18 apply (zenon_or_s _ _ zenon_Heb); [ zenon_intro zenon_Hae | zenon_intro zenon_Hec ]. % 19.02/19.18 apply (zenon_L42_); trivial. % 19.02/19.18 apply (zenon_or_s _ _ zenon_Hec); [ zenon_intro zenon_Hba | zenon_intro zenon_Hc4 ]. % 19.02/19.18 apply (zenon_L45_); trivial. % 19.02/19.18 apply (zenon_L46_); trivial. % 19.02/19.18 (* end of lemma zenon_L1268_ *) % 19.02/19.18 assert (zenon_L1269_ : (((op (e0) (e3)) = (e3))\/(((op (e1) (e3)) = (e3))\/(((op (e2) (e3)) = (e3))\/((op (e3) (e3)) = (e3))))) -> (~((op (e0) (e3)) = (op (e2) (e3)))) -> (~((op (e1) (e3)) = (e2))) -> (~((op (e0) (e3)) = (op (e1) (e3)))) -> (~((op (e2) (e3)) = (op (e3) (e3)))) -> (~((op (e2) (e3)) = (e2))) -> ((op (e2) (e1)) = (e1)) -> (~((op (e2) (e1)) = (op (e2) (e3)))) -> ((op (e3) (e3)) = (e2)) -> (((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 (e3) (e3)) = (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))))) -> (~((op (e3) (e3)) = (e3))) -> False). % 19.02/19.18 do 0 intro. intros zenon_H136 zenon_He2 zenon_H14c zenon_H1d zenon_Hf3 zenon_H274 zenon_Ha5 zenon_H1c7 zenon_Hf6 zenon_H11f zenon_Hdb zenon_Hc3 zenon_H60 zenon_Hf0 zenon_H124 zenon_Hd5 zenon_Hdf zenon_H102. % 19.02/19.18 apply (zenon_or_s _ _ zenon_H136); [ zenon_intro zenon_He3 | zenon_intro zenon_H137 ]. % 19.02/19.18 apply (zenon_L1143_); trivial. % 19.02/19.18 apply (zenon_or_s _ _ zenon_H137); [ zenon_intro zenon_Hdc | zenon_intro zenon_H138 ]. % 19.02/19.18 apply (zenon_L1137_); trivial. % 19.02/19.18 apply (zenon_or_s _ _ zenon_H138); [ zenon_intro zenon_Hdd | zenon_intro zenon_H105 ]. % 19.02/19.18 apply (zenon_L202_); trivial. % 19.02/19.18 exact (zenon_H102 zenon_H105). % 19.02/19.18 (* end of lemma zenon_L1269_ *) % 19.02/19.18 assert (zenon_L1270_ : (((op (e3) (e0)) = (e2))\/(((op (e3) (e1)) = (e2))\/(((op (e3) (e2)) = (e2))\/((op (e3) (e3)) = (e2))))) -> (~((op (e3) (e0)) = (e2))) -> (~((op (e3) (e1)) = (e2))) -> (~((op (e3) (e2)) = (e2))) -> (((op (e0) (e3)) = (e3))\/(((op (e1) (e3)) = (e3))\/(((op (e2) (e3)) = (e3))\/((op (e3) (e3)) = (e3))))) -> (~((op (e0) (e3)) = (op (e2) (e3)))) -> (~((op (e1) (e3)) = (e2))) -> (~((op (e0) (e3)) = (op (e1) (e3)))) -> (~((op (e2) (e3)) = (op (e3) (e3)))) -> (~((op (e2) (e3)) = (e2))) -> ((op (e2) (e1)) = (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)) = (op (e2) (e3)))) -> ((op (e0) (e3)) = (e1)) -> ((op (e3) (e3)) = (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))))) -> (~((op (e3) (e3)) = (e3))) -> False). % 19.02/19.18 do 0 intro. intros zenon_H153 zenon_H14b zenon_H194 zenon_H272 zenon_H136 zenon_He2 zenon_H14c zenon_H1d zenon_Hf3 zenon_H274 zenon_Ha5 zenon_H1c7 zenon_H11f zenon_Hdb zenon_Hc3 zenon_H60 zenon_Hf0 zenon_H124 zenon_Hd5 zenon_Hdf zenon_H102. % 19.02/19.18 apply (zenon_or_s _ _ zenon_H153); [ zenon_intro zenon_H148 | zenon_intro zenon_H154 ]. % 19.02/19.18 exact (zenon_H14b zenon_H148). % 19.02/19.18 apply (zenon_or_s _ _ zenon_H154); [ zenon_intro zenon_H14d | zenon_intro zenon_H155 ]. % 19.02/19.18 exact (zenon_H194 zenon_H14d). % 19.02/19.18 apply (zenon_or_s _ _ zenon_H155); [ zenon_intro zenon_H151 | zenon_intro zenon_Hf6 ]. % 19.02/19.18 exact (zenon_H272 zenon_H151). % 19.02/19.18 apply (zenon_L1269_); trivial. % 19.02/19.18 (* end of lemma zenon_L1270_ *) % 19.02/19.18 assert (zenon_L1271_ : (((op (e0) (e3)) = (e0))\/(((op (e1) (e3)) = (e0))\/(((op (e2) (e3)) = (e0))\/((op (e3) (e3)) = (e0))))) -> (~((op (e1) (e2)) = (e2))) -> (((op (e2) (e0)) = (e1))\/(((op (e2) (e1)) = (e1))\/(((op (e2) (e2)) = (e1))\/((op (e2) (e3)) = (e1))))) -> (~((e1) = (e2))) -> ((op (e2) (e0)) = (e2)) -> (~((op (e2) (e1)) = (op (e3) (e1)))) -> (~((op (e1) (e2)) = (op (e2) (e2)))) -> (((op (e2) (e1)) = (e0))\/(((op (e2) (e1)) = (e1))\/(((op (e2) (e1)) = (e2))\/((op (e2) (e1)) = (e3))))) -> (~((op (e2) (e1)) = (op (e2) (e2)))) -> ((op (e2) (e2)) = (e0)) -> (~((op (e2) (e1)) = (e2))) -> ((op (e3) (e1)) = (e0)) -> (~((op (e1) (e0)) = (e2))) -> (((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))) -> (~((e0) = (e3))) -> (~((op (e1) (e1)) = (e1))) -> (((op (e0) (e0)) = (e2))\/(((op (e1) (e0)) = (e2))\/(((op (e2) (e0)) = (e2))\/((op (e3) (e0)) = (e2))))) -> (~((op (e0) (e0)) = (e2))) -> (~((op (e0) (e1)) = (op (e2) (e1)))) -> (~((e0) = (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)) = (e0)) -> (~((op (e1) (e0)) = (op (e1) (e3)))) -> (((op (e3) (e0)) = (e2))\/(((op (e3) (e1)) = (e2))\/(((op (e3) (e2)) = (e2))\/((op (e3) (e3)) = (e2))))) -> (~((op (e3) (e0)) = (e2))) -> (~((op (e3) (e1)) = (e2))) -> (~((op (e3) (e2)) = (e2))) -> (((op (e0) (e3)) = (e3))\/(((op (e1) (e3)) = (e3))\/(((op (e2) (e3)) = (e3))\/((op (e3) (e3)) = (e3))))) -> (~((op (e0) (e3)) = (op (e2) (e3)))) -> (~((op (e1) (e3)) = (e2))) -> (~((op (e0) (e3)) = (op (e1) (e3)))) -> (~((op (e2) (e3)) = (op (e3) (e3)))) -> (~((op (e2) (e3)) = (e2))) -> ((op (e2) (e1)) = (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)) = (op (e2) (e3)))) -> ((op (e0) (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)) = (e3))) -> False). % 19.02/19.18 do 0 intro. intros zenon_H67 zenon_H114 zenon_H106 zenon_H7c zenon_Hee zenon_Haf zenon_H2b zenon_H1cc zenon_H24b zenon_H2c zenon_H26e zenon_H1b1 zenon_H177 zenon_H18c zenon_H133 zenon_Ha1 zenon_H9a zenon_H10a zenon_H1fe zenon_H80 zenon_H17e zenon_H149 zenon_H245 zenon_H109 zenon_H27 zenon_Hd8 zenon_H153 zenon_H14b zenon_H194 zenon_H272 zenon_H136 zenon_He2 zenon_H14c zenon_H1d zenon_Hf3 zenon_H274 zenon_Ha5 zenon_H1c7 zenon_H11f zenon_Hdb zenon_Hc3 zenon_Hf0 zenon_H124 zenon_Hd5 zenon_Hdf zenon_H102. % 19.02/19.18 apply (zenon_or_s _ _ zenon_H67); [ zenon_intro zenon_H1e | zenon_intro zenon_H68 ]. % 19.02/19.18 apply (zenon_L1267_); trivial. % 19.02/19.18 apply (zenon_or_s _ _ zenon_H68); [ zenon_intro zenon_H1f | zenon_intro zenon_H69 ]. % 19.02/19.18 apply (zenon_L258_); trivial. % 19.02/19.18 apply (zenon_or_s _ _ zenon_H69); [ zenon_intro zenon_H37 | zenon_intro zenon_H60 ]. % 19.02/19.18 apply (zenon_L1173_); trivial. % 19.02/19.18 apply (zenon_L1270_); trivial. % 19.02/19.18 (* end of lemma zenon_L1271_ *) % 19.02/19.18 assert (zenon_L1272_ : (((op (e3) (e0)) = (e0))\/(((op (e3) (e1)) = (e0))\/(((op (e3) (e2)) = (e0))\/((op (e3) (e3)) = (e0))))) -> (~((op (e0) (e3)) = (op (e3) (e3)))) -> ((op (e0) (e2)) = (e3)) -> (((op (e3) (e0)) = (e1))\/(((op (e3) (e1)) = (e1))\/(((op (e3) (e2)) = (e1))\/((op (e3) (e3)) = (e1))))) -> (~((op (e1) (e0)) = (op (e1) (e3)))) -> ((op (e1) (e0)) = (e0)) -> (((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))))) -> (~((e0) = (e2))) -> (~((op (e0) (e1)) = (op (e2) (e1)))) -> (~((op (e0) (e0)) = (e2))) -> (((op (e0) (e0)) = (e2))\/(((op (e1) (e0)) = (e2))\/(((op (e2) (e0)) = (e2))\/((op (e3) (e0)) = (e2))))) -> (~((op (e1) (e1)) = (e1))) -> (~((e0) = (e3))) -> (~((e0) = (e1))) -> (((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 (e1) (e0)) = (e2))) -> (~((op (e2) (e1)) = (e2))) -> (~((op (e2) (e1)) = (op (e2) (e2)))) -> (((op (e2) (e1)) = (e0))\/(((op (e2) (e1)) = (e1))\/(((op (e2) (e1)) = (e2))\/((op (e2) (e1)) = (e3))))) -> (~((op (e1) (e2)) = (op (e2) (e2)))) -> (~((op (e2) (e1)) = (op (e3) (e1)))) -> ((op (e2) (e0)) = (e2)) -> (~((e1) = (e2))) -> (((op (e2) (e0)) = (e1))\/(((op (e2) (e1)) = (e1))\/(((op (e2) (e2)) = (e1))\/((op (e2) (e3)) = (e1))))) -> (~((op (e1) (e2)) = (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)) = (e2))\/(((op (e3) (e1)) = (e2))\/(((op (e3) (e2)) = (e2))\/((op (e3) (e3)) = (e2))))) -> (~((op (e3) (e0)) = (e2))) -> (~((op (e3) (e1)) = (e2))) -> (~((op (e3) (e2)) = (e2))) -> (((op (e0) (e3)) = (e3))\/(((op (e1) (e3)) = (e3))\/(((op (e2) (e3)) = (e3))\/((op (e3) (e3)) = (e3))))) -> (~((op (e0) (e3)) = (op (e2) (e3)))) -> (~((op (e1) (e3)) = (e2))) -> (~((op (e0) (e3)) = (op (e1) (e3)))) -> (~((op (e2) (e3)) = (op (e3) (e3)))) -> (~((op (e2) (e3)) = (e2))) -> ((op (e2) (e1)) = (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)) = (op (e2) (e3)))) -> ((op (e0) (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)) = (e3))) -> False). % 19.02/19.18 do 0 intro. intros zenon_H1ac zenon_Hc2 zenon_Ha9 zenon_He8 zenon_Hd8 zenon_H27 zenon_H109 zenon_H245 zenon_H149 zenon_H17e zenon_H80 zenon_H1fe zenon_H10a zenon_H9a zenon_Ha1 zenon_H133 zenon_H18c zenon_H177 zenon_H26e zenon_H24b zenon_H1cc zenon_H2b zenon_Haf zenon_Hee zenon_H7c zenon_H106 zenon_H114 zenon_H67 zenon_H2c zenon_H18f zenon_H153 zenon_H14b zenon_H194 zenon_H272 zenon_H136 zenon_He2 zenon_H14c zenon_H1d zenon_Hf3 zenon_H274 zenon_Ha5 zenon_H1c7 zenon_H11f zenon_Hdb zenon_Hc3 zenon_Hf0 zenon_H124 zenon_Hd5 zenon_Hdf zenon_H102. % 19.02/19.18 apply (zenon_or_s _ _ zenon_H1ac); [ zenon_intro zenon_H44 | zenon_intro zenon_H1af ]. % 19.02/19.18 apply (zenon_L1268_); trivial. % 19.02/19.18 apply (zenon_or_s _ _ zenon_H1af); [ zenon_intro zenon_H1b1 | zenon_intro zenon_H1b0 ]. % 19.02/19.18 apply (zenon_L1271_); trivial. % 19.02/19.18 apply (zenon_or_s _ _ zenon_H1b0); [ zenon_intro zenon_H61 | zenon_intro zenon_H60 ]. % 19.02/19.18 apply (zenon_L146_); trivial. % 19.02/19.18 apply (zenon_L1270_); trivial. % 19.02/19.18 (* end of lemma zenon_L1272_ *) % 19.02/19.18 assert (zenon_L1273_ : (~((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 (e1) (e2)) = (op (e1) (e3)))) -> ((op (e1) (e2)) = (e1)) -> ((op (e0) (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 (e2) (e1)) = (op (e2) (e3)))) -> (~((op (e2) (e3)) = (e2))) -> (~((op (e2) (e3)) = (op (e3) (e3)))) -> (~((op (e0) (e3)) = (op (e1) (e3)))) -> (~((op (e1) (e3)) = (e2))) -> (~((op (e0) (e3)) = (op (e2) (e3)))) -> (((op (e0) (e3)) = (e3))\/(((op (e1) (e3)) = (e3))\/(((op (e2) (e3)) = (e3))\/((op (e3) (e3)) = (e3))))) -> (~((op (e3) (e2)) = (e2))) -> (~((op (e3) (e1)) = (e2))) -> (~((op (e3) (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 (e2) (e2)) = (e0)) -> (((op (e0) (e3)) = (e0))\/(((op (e1) (e3)) = (e0))\/(((op (e2) (e3)) = (e0))\/((op (e3) (e3)) = (e0))))) -> (~((op (e1) (e2)) = (e2))) -> (((op (e2) (e0)) = (e1))\/(((op (e2) (e1)) = (e1))\/(((op (e2) (e2)) = (e1))\/((op (e2) (e3)) = (e1))))) -> (~((e1) = (e2))) -> ((op (e2) (e0)) = (e2)) -> (~((op (e2) (e1)) = (op (e3) (e1)))) -> (~((op (e1) (e2)) = (op (e2) (e2)))) -> (((op (e2) (e1)) = (e0))\/(((op (e2) (e1)) = (e1))\/(((op (e2) (e1)) = (e2))\/((op (e2) (e1)) = (e3))))) -> (~((op (e2) (e1)) = (op (e2) (e2)))) -> (~((op (e2) (e1)) = (e2))) -> (~((op (e1) (e0)) = (e2))) -> (((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))) -> (~((e0) = (e3))) -> (~((op (e1) (e1)) = (e1))) -> (((op (e0) (e0)) = (e2))\/(((op (e1) (e0)) = (e2))\/(((op (e2) (e0)) = (e2))\/((op (e3) (e0)) = (e2))))) -> (~((op (e0) (e0)) = (e2))) -> (~((op (e0) (e1)) = (op (e2) (e1)))) -> (~((e0) = (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)) = (e0)) -> (~((op (e1) (e0)) = (op (e1) (e3)))) -> (((op (e3) (e0)) = (e1))\/(((op (e3) (e1)) = (e1))\/(((op (e3) (e2)) = (e1))\/((op (e3) (e3)) = (e1))))) -> ((op (e0) (e2)) = (e3)) -> (~((op (e0) (e3)) = (op (e3) (e3)))) -> (((op (e3) (e0)) = (e0))\/(((op (e3) (e1)) = (e0))\/(((op (e3) (e2)) = (e0))\/((op (e3) (e3)) = (e0))))) -> (~((op (e3) (e0)) = (op (e3) (e1)))) -> ((op (e3) (e0)) = (e1)) -> False). % 19.02/19.18 do 0 intro. intros zenon_H102 zenon_Hdf zenon_Hd5 zenon_H124 zenon_Hf0 zenon_Hc3 zenon_Hdb zenon_H11f zenon_H1c7 zenon_H274 zenon_Hf3 zenon_H1d zenon_H14c zenon_He2 zenon_H136 zenon_H272 zenon_H194 zenon_H14b zenon_H153 zenon_H18f zenon_H2c zenon_H67 zenon_H114 zenon_H106 zenon_H7c zenon_Hee zenon_Haf zenon_H2b zenon_H1cc zenon_H24b zenon_H26e zenon_H177 zenon_H18c zenon_H133 zenon_Ha1 zenon_H9a zenon_H10a zenon_H1fe zenon_H80 zenon_H17e zenon_H149 zenon_H245 zenon_H109 zenon_H27 zenon_Hd8 zenon_He8 zenon_Ha9 zenon_Hc2 zenon_H1ac zenon_H1cf zenon_Hac. % 19.02/19.18 apply (zenon_or_s _ _ zenon_H109); [ zenon_intro zenon_Ha0 | zenon_intro zenon_H10b ]. % 19.02/19.18 apply (zenon_L1262_); trivial. % 19.02/19.18 apply (zenon_or_s _ _ zenon_H10b); [ zenon_intro zenon_H10d | zenon_intro zenon_H10c ]. % 19.02/19.18 exact (zenon_H10a zenon_H10d). % 19.02/19.18 apply (zenon_or_s _ _ zenon_H10c); [ zenon_intro zenon_Ha5 | zenon_intro zenon_Hae ]. % 19.02/19.18 apply (zenon_L1272_); trivial. % 19.02/19.18 apply (zenon_L242_); trivial. % 19.02/19.18 (* end of lemma zenon_L1273_ *) % 19.02/19.18 assert (zenon_L1274_ : (((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 (e2) (e3)))) -> (((op (e1) (e3)) = (e0))\/(((op (e1) (e3)) = (e1))\/(((op (e1) (e3)) = (e2))\/((op (e1) (e3)) = (e3))))) -> ((op (e3) (e3)) = (e0)) -> (~((op (e1) (e3)) = (op (e3) (e3)))) -> ((op (e2) (e3)) = (e1)) -> (~((op (e1) (e3)) = (op (e2) (e3)))) -> (~((op (e1) (e3)) = (e2))) -> (~((op (e0) (e3)) = (op (e1) (e3)))) -> False). % 19.02/19.18 do 0 intro. intros zenon_He4 zenon_Hc2 zenon_He2 zenon_Hdf zenon_H60 zenon_Hd5 zenon_Hf4 zenon_Hdb zenon_H14c zenon_H1d. % 19.02/19.18 apply (zenon_or_s _ _ zenon_He4); [ zenon_intro zenon_H1e | zenon_intro zenon_He5 ]. % 19.02/19.18 apply (zenon_L440_); trivial. % 19.02/19.18 apply (zenon_or_s _ _ zenon_He5); [ zenon_intro zenon_Hc3 | zenon_intro zenon_He6 ]. % 19.02/19.18 apply (zenon_L272_); trivial. % 19.02/19.18 apply (zenon_or_s _ _ zenon_He6); [ zenon_intro zenon_Hcd | zenon_intro zenon_He3 ]. % 19.02/19.18 apply (zenon_L229_); trivial. % 19.02/19.18 apply (zenon_L1079_); trivial. % 19.02/19.18 (* end of lemma zenon_L1274_ *) % 19.02/19.18 assert (zenon_L1275_ : (((op (e3) (e0)) = (e2))\/(((op (e3) (e1)) = (e2))\/(((op (e3) (e2)) = (e2))\/((op (e3) (e3)) = (e2))))) -> (~((op (e3) (e0)) = (e2))) -> (~((op (e3) (e1)) = (e2))) -> (~((op (e3) (e2)) = (e2))) -> (((op (e0) (e3)) = (e0))\/(((op (e0) (e3)) = (e1))\/(((op (e0) (e3)) = (e2))\/((op (e0) (e3)) = (e3))))) -> ((op (e1) (e0)) = (e0)) -> (~((op (e1) (e0)) = (op (e1) (e3)))) -> (~((e0) = (e3))) -> (~((op (e3) (e3)) = (e3))) -> (~((op (e1) (e2)) = (op (e1) (e3)))) -> ((op (e1) (e2)) = (e1)) -> (~((op (e1) (e3)) = (op (e2) (e3)))) -> (((op (e2) (e3)) = (e0))\/(((op (e2) (e3)) = (e1))\/(((op (e2) (e3)) = (e2))\/((op (e2) (e3)) = (e3))))) -> (~((op (e2) (e1)) = (op (e2) (e3)))) -> ((op (e2) (e1)) = (e1)) -> (~((op (e2) (e3)) = (e2))) -> (~((op (e2) (e3)) = (op (e3) (e3)))) -> (~((op (e0) (e3)) = (op (e2) (e3)))) -> (((op (e0) (e3)) = (e3))\/(((op (e1) (e3)) = (e3))\/(((op (e2) (e3)) = (e3))\/((op (e3) (e3)) = (e3))))) -> (~((op (e0) (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 (e1) (e3)) = (op (e3) (e3)))) -> (~((op (e1) (e3)) = (e2))) -> (~((op (e0) (e3)) = (op (e1) (e3)))) -> False). % 19.02/19.18 do 0 intro. intros zenon_H153 zenon_H14b zenon_H194 zenon_H272 zenon_He4 zenon_H27 zenon_Hd8 zenon_H9a zenon_H102 zenon_H124 zenon_Hf0 zenon_Hdb zenon_H11f zenon_H1c7 zenon_Ha5 zenon_H274 zenon_Hf3 zenon_He2 zenon_H136 zenon_Hc2 zenon_Hdf zenon_H60 zenon_Hc4 zenon_Hd5 zenon_H14c zenon_H1d. % 19.02/19.18 apply (zenon_or_s _ _ zenon_H153); [ zenon_intro zenon_H148 | zenon_intro zenon_H154 ]. % 19.02/19.18 exact (zenon_H14b zenon_H148). % 19.02/19.18 apply (zenon_or_s _ _ zenon_H154); [ zenon_intro zenon_H14d | zenon_intro zenon_H155 ]. % 19.02/19.18 exact (zenon_H194 zenon_H14d). % 19.02/19.18 apply (zenon_or_s _ _ zenon_H155); [ zenon_intro zenon_H151 | zenon_intro zenon_Hf6 ]. % 19.02/19.18 exact (zenon_H272 zenon_H151). % 19.02/19.18 apply (zenon_or_s _ _ zenon_He4); [ zenon_intro zenon_H1e | zenon_intro zenon_He5 ]. % 19.02/19.18 apply (zenon_L1264_); trivial. % 19.02/19.18 apply (zenon_or_s _ _ zenon_He5); [ zenon_intro zenon_Hc3 | zenon_intro zenon_He6 ]. % 19.02/19.18 apply (zenon_L1269_); trivial. % 19.02/19.18 apply (zenon_or_s _ _ zenon_He6); [ zenon_intro zenon_Hcd | zenon_intro zenon_He3 ]. % 19.02/19.18 apply (zenon_L87_); trivial. % 19.02/19.18 apply (zenon_L1092_); trivial. % 19.02/19.18 (* end of lemma zenon_L1275_ *) % 19.02/19.18 assert (zenon_L1276_ : (((op (e0) (e3)) = (e0))\/(((op (e0) (e3)) = (e1))\/(((op (e0) (e3)) = (e2))\/((op (e0) (e3)) = (e3))))) -> (~((op (e2) (e3)) = (op (e3) (e3)))) -> ((op (e1) (e3)) = (e3)) -> ((op (e2) (e1)) = (e1)) -> (~((op (e2) (e1)) = (op (e2) (e3)))) -> (~((op (e0) (e3)) = (op (e3) (e3)))) -> (((op (e2) (e3)) = (e0))\/(((op (e2) (e3)) = (e1))\/(((op (e2) (e3)) = (e2))\/((op (e2) (e3)) = (e3))))) -> (~((op (e0) (e3)) = (op (e1) (e3)))) -> (~((op (e1) (e3)) = (e2))) -> (~((op (e1) (e3)) = (op (e3) (e3)))) -> ((op (e3) (e3)) = (e1)) -> (~((op (e1) (e3)) = (op (e2) (e3)))) -> (((op (e1) (e3)) = (e0))\/(((op (e1) (e3)) = (e1))\/(((op (e1) (e3)) = (e2))\/((op (e1) (e3)) = (e3))))) -> ((op (e3) (e3)) = (e2)) -> ((op (e1) (e3)) = (e0)) -> (~((op (e2) (e3)) = (e2))) -> (~((op (e0) (e3)) = (op (e2) (e3)))) -> False). % 19.02/19.18 do 0 intro. intros zenon_He4 zenon_Hf3 zenon_Hdc zenon_Ha5 zenon_H1c7 zenon_Hc2 zenon_H11f zenon_H1d zenon_H14c zenon_Hd5 zenon_Hc4 zenon_Hdb zenon_Hdf zenon_Hf6 zenon_H1f zenon_H274 zenon_He2. % 19.02/19.18 apply (zenon_or_s _ _ zenon_He4); [ zenon_intro zenon_H1e | zenon_intro zenon_He5 ]. % 19.02/19.18 apply (zenon_L1244_); trivial. % 19.02/19.18 apply (zenon_or_s _ _ zenon_He5); [ zenon_intro zenon_Hc3 | zenon_intro zenon_He6 ]. % 19.02/19.18 apply (zenon_L1137_); trivial. % 19.02/19.18 apply (zenon_or_s _ _ zenon_He6); [ zenon_intro zenon_Hcd | zenon_intro zenon_He3 ]. % 19.02/19.18 apply (zenon_L87_); trivial. % 19.02/19.18 apply (zenon_L1251_); trivial. % 19.02/19.18 (* end of lemma zenon_L1276_ *) % 19.02/19.18 assert (zenon_L1277_ : (((op (e0) (e0)) = (e0))\/(((op (e1) (e0)) = (e0))\/(((op (e2) (e0)) = (e0))\/((op (e3) (e0)) = (e0))))) -> (~((op (e0) (e0)) = (e0))) -> (~((op (e3) (e0)) = (e2))) -> (~((op (e0) (e1)) = (op (e0) (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 (e1) (e1)) = (e0))\/(((op (e2) (e1)) = (e0))\/((op (e3) (e1)) = (e0))))) -> (~((op (e0) (e1)) = (op (e2) (e1)))) -> (~((op (e0) (e0)) = (e2))) -> (((op (e0) (e0)) = (e2))\/(((op (e1) (e0)) = (e2))\/(((op (e2) (e0)) = (e2))\/((op (e3) (e0)) = (e2))))) -> (~((op (e1) (e1)) = (e1))) -> (~((op (e3) (e3)) = (e3))) -> (((op (e1) (e3)) = (e0))\/(((op (e1) (e3)) = (e1))\/(((op (e1) (e3)) = (e2))\/((op (e1) (e3)) = (e3))))) -> (~((op (e1) (e0)) = (op (e1) (e3)))) -> (~((op (e1) (e3)) = (op (e3) (e3)))) -> (~((op (e1) (e3)) = (op (e2) (e3)))) -> (((op (e2) (e3)) = (e0))\/(((op (e2) (e3)) = (e1))\/(((op (e2) (e3)) = (e2))\/((op (e2) (e3)) = (e3))))) -> (~((op (e0) (e3)) = (op (e2) (e3)))) -> (~((op (e2) (e3)) = (op (e3) (e3)))) -> (~((op (e2) (e3)) = (e2))) -> (~((e0) = (e3))) -> (((op (e0) (e3)) = (e3))\/(((op (e1) (e3)) = (e3))\/(((op (e2) (e3)) = (e3))\/((op (e3) (e3)) = (e3))))) -> (~((op (e1) (e2)) = (op (e1) (e3)))) -> (~((e0) = (e1))) -> (((op (e0) (e3)) = (e1))\/(((op (e1) (e3)) = (e1))\/(((op (e2) (e3)) = (e1))\/((op (e3) (e3)) = (e1))))) -> (~((op (e2) (e1)) = (e2))) -> (~((op (e2) (e1)) = (op (e2) (e3)))) -> (~((op (e2) (e1)) = (op (e2) (e2)))) -> (((op (e2) (e1)) = (e0))\/(((op (e2) (e1)) = (e1))\/(((op (e2) (e1)) = (e2))\/((op (e2) (e1)) = (e3))))) -> ((op (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))))) -> (~((op (e2) (e0)) = (op (e2) (e2)))) -> (((op (e1) (e0)) = (e0))\/(((op (e1) (e1)) = (e0))\/(((op (e1) (e2)) = (e0))\/((op (e1) (e3)) = (e0))))) -> (~((op (e1) (e0)) = (op (e3) (e0)))) -> (~((op (e1) (e3)) = (e2))) -> (~((op (e1) (e2)) = (e2))) -> (~((e0) = (e2))) -> (~((op (e1) (e0)) = (e2))) -> (((op (e1) (e0)) = (e2))\/(((op (e1) (e1)) = (e2))\/(((op (e1) (e2)) = (e2))\/((op (e1) (e3)) = (e2))))) -> ((op (e2) (e2)) = (e0)) -> (~((op (e1) (e2)) = (op (e2) (e2)))) -> (~((op (e0) (e3)) = (op (e1) (e3)))) -> ((op (e0) (e3)) = (e0)) -> False). % 19.02/19.18 do 0 intro. intros zenon_H3e zenon_H3f zenon_H14b zenon_H54 zenon_H45 zenon_H109 zenon_H245 zenon_H17e zenon_H80 zenon_H1fe zenon_H10a zenon_H102 zenon_Hdf zenon_Hd8 zenon_Hd5 zenon_Hdb zenon_H11f zenon_He2 zenon_Hf3 zenon_H274 zenon_H9a zenon_H136 zenon_H124 zenon_Ha1 zenon_H133 zenon_H26e zenon_H1c7 zenon_H24b zenon_H1cc zenon_Hf0 zenon_Haf zenon_H7c zenon_H106 zenon_H52 zenon_H22 zenon_H1fa zenon_H14c zenon_H114 zenon_H149 zenon_H177 zenon_H18c zenon_H2c zenon_H2b zenon_H1d zenon_H1e. % 19.02/19.18 apply (zenon_or_s _ _ zenon_H3e); [ zenon_intro zenon_H42 | zenon_intro zenon_H41 ]. % 19.02/19.18 exact (zenon_H3f zenon_H42). % 19.02/19.18 apply (zenon_or_s _ _ zenon_H41); [ zenon_intro zenon_H27 | zenon_intro zenon_H43 ]. % 19.02/19.18 apply (zenon_or_s _ _ zenon_H1fe); [ zenon_intro zenon_H7b | zenon_intro zenon_H1ff ]. % 19.02/19.18 exact (zenon_H80 zenon_H7b). % 19.02/19.18 apply (zenon_or_s _ _ zenon_H1ff); [ zenon_intro zenon_H86 | zenon_intro zenon_H200 ]. % 19.02/19.18 exact (zenon_H177 zenon_H86). % 19.02/19.18 apply (zenon_or_s _ _ zenon_H200); [ zenon_intro zenon_Hee | zenon_intro zenon_H148 ]. % 19.02/19.18 apply (zenon_or_s _ _ zenon_H245); [ zenon_intro zenon_H49 | zenon_intro zenon_H246 ]. % 19.02/19.18 apply (zenon_L12_); trivial. % 19.02/19.18 apply (zenon_or_s _ _ zenon_H246); [ zenon_intro zenon_H29 | zenon_intro zenon_H247 ]. % 19.02/19.18 apply (zenon_L8_); trivial. % 19.02/19.18 apply (zenon_or_s _ _ zenon_H247); [ zenon_intro zenon_H36 | zenon_intro zenon_H1b1 ]. % 19.02/19.18 apply (zenon_L645_); trivial. % 19.02/19.18 apply (zenon_L1267_); trivial. % 19.02/19.18 exact (zenon_H14b zenon_H148). % 19.02/19.18 apply (zenon_or_s _ _ zenon_H43); [ zenon_intro zenon_H34 | zenon_intro zenon_H44 ]. % 19.02/19.18 apply (zenon_L11_); trivial. % 19.02/19.18 apply (zenon_or_s _ _ zenon_H22); [ zenon_intro zenon_H27 | zenon_intro zenon_H26 ]. % 19.02/19.18 apply (zenon_L312_); trivial. % 19.02/19.18 apply (zenon_or_s _ _ zenon_H26); [ zenon_intro zenon_H29 | zenon_intro zenon_H28 ]. % 19.02/19.18 apply (zenon_L1259_); trivial. % 19.02/19.18 apply (zenon_or_s _ _ zenon_H28); [ zenon_intro zenon_H2a | zenon_intro zenon_H1f ]. % 19.02/19.18 apply (zenon_L3_); trivial. % 19.02/19.18 apply (zenon_L1_); trivial. % 19.02/19.18 (* end of lemma zenon_L1277_ *) % 19.02/19.18 assert (zenon_L1278_ : (((op (e3) (e0)) = (e2))\/(((op (e3) (e1)) = (e2))\/(((op (e3) (e2)) = (e2))\/((op (e3) (e3)) = (e2))))) -> (~((op (e3) (e1)) = (e2))) -> (~((op (e3) (e2)) = (e2))) -> ((op (e1) (e3)) = (e0)) -> ((op (e2) (e1)) = (e1)) -> (~((op (e0) (e3)) = (op (e2) (e3)))) -> (~((op (e0) (e3)) = (op (e3) (e3)))) -> ((op (e3) (e3)) = (e1)) -> (((op (e0) (e0)) = (e0))\/(((op (e1) (e0)) = (e0))\/(((op (e2) (e0)) = (e0))\/((op (e3) (e0)) = (e0))))) -> (~((op (e0) (e0)) = (e0))) -> (~((op (e3) (e0)) = (e2))) -> (~((op (e0) (e1)) = (op (e0) (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 (e1) (e1)) = (e0))\/(((op (e2) (e1)) = (e0))\/((op (e3) (e1)) = (e0))))) -> (~((op (e0) (e1)) = (op (e2) (e1)))) -> (~((op (e0) (e0)) = (e2))) -> (((op (e0) (e0)) = (e2))\/(((op (e1) (e0)) = (e2))\/(((op (e2) (e0)) = (e2))\/((op (e3) (e0)) = (e2))))) -> (~((op (e1) (e1)) = (e1))) -> (((op (e1) (e3)) = (e0))\/(((op (e1) (e3)) = (e1))\/(((op (e1) (e3)) = (e2))\/((op (e1) (e3)) = (e3))))) -> (~((op (e1) (e0)) = (op (e1) (e3)))) -> (~((op (e1) (e3)) = (op (e3) (e3)))) -> (~((op (e1) (e3)) = (op (e2) (e3)))) -> (((op (e2) (e3)) = (e0))\/(((op (e2) (e3)) = (e1))\/(((op (e2) (e3)) = (e2))\/((op (e2) (e3)) = (e3))))) -> (~((op (e2) (e3)) = (op (e3) (e3)))) -> (~((op (e2) (e3)) = (e2))) -> (~((e0) = (e3))) -> (((op (e0) (e3)) = (e3))\/(((op (e1) (e3)) = (e3))\/(((op (e2) (e3)) = (e3))\/((op (e3) (e3)) = (e3))))) -> (~((op (e1) (e2)) = (op (e1) (e3)))) -> (~((e0) = (e1))) -> (((op (e0) (e3)) = (e1))\/(((op (e1) (e3)) = (e1))\/(((op (e2) (e3)) = (e1))\/((op (e3) (e3)) = (e1))))) -> (~((op (e2) (e1)) = (e2))) -> (~((op (e2) (e1)) = (op (e2) (e3)))) -> (~((op (e2) (e1)) = (op (e2) (e2)))) -> (((op (e2) (e1)) = (e0))\/(((op (e2) (e1)) = (e1))\/(((op (e2) (e1)) = (e2))\/((op (e2) (e1)) = (e3))))) -> ((op (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))))) -> (~((op (e2) (e0)) = (op (e2) (e2)))) -> (((op (e1) (e0)) = (e0))\/(((op (e1) (e1)) = (e0))\/(((op (e1) (e2)) = (e0))\/((op (e1) (e3)) = (e0))))) -> (~((op (e1) (e0)) = (op (e3) (e0)))) -> (~((op (e1) (e3)) = (e2))) -> (~((op (e1) (e2)) = (e2))) -> (~((e0) = (e2))) -> (~((op (e1) (e0)) = (e2))) -> (((op (e1) (e0)) = (e2))\/(((op (e1) (e1)) = (e2))\/(((op (e1) (e2)) = (e2))\/((op (e1) (e3)) = (e2))))) -> ((op (e2) (e2)) = (e0)) -> (~((op (e1) (e2)) = (op (e2) (e2)))) -> (~((op (e0) (e3)) = (op (e1) (e3)))) -> (((op (e0) (e3)) = (e0))\/(((op (e0) (e3)) = (e1))\/(((op (e0) (e3)) = (e2))\/((op (e0) (e3)) = (e3))))) -> (~((op (e3) (e3)) = (e3))) -> False). % 19.02/19.18 do 0 intro. intros zenon_H153 zenon_H194 zenon_H272 zenon_H1f zenon_Ha5 zenon_He2 zenon_Hc2 zenon_Hc4 zenon_H3e zenon_H3f zenon_H14b zenon_H54 zenon_H45 zenon_H109 zenon_H245 zenon_H17e zenon_H80 zenon_H1fe zenon_H10a zenon_Hdf zenon_Hd8 zenon_Hd5 zenon_Hdb zenon_H11f zenon_Hf3 zenon_H274 zenon_H9a zenon_H136 zenon_H124 zenon_Ha1 zenon_H133 zenon_H26e zenon_H1c7 zenon_H24b zenon_H1cc zenon_Hf0 zenon_Haf zenon_H7c zenon_H106 zenon_H52 zenon_H22 zenon_H1fa zenon_H14c zenon_H114 zenon_H149 zenon_H177 zenon_H18c zenon_H2c zenon_H2b zenon_H1d zenon_He4 zenon_H102. % 19.02/19.18 apply (zenon_or_s _ _ zenon_H153); [ zenon_intro zenon_H148 | zenon_intro zenon_H154 ]. % 19.02/19.18 exact (zenon_H14b zenon_H148). % 19.02/19.18 apply (zenon_or_s _ _ zenon_H154); [ zenon_intro zenon_H14d | zenon_intro zenon_H155 ]. % 19.02/19.18 exact (zenon_H194 zenon_H14d). % 19.02/19.18 apply (zenon_or_s _ _ zenon_H155); [ zenon_intro zenon_H151 | zenon_intro zenon_Hf6 ]. % 19.02/19.18 exact (zenon_H272 zenon_H151). % 19.02/19.18 apply (zenon_or_s _ _ zenon_H136); [ zenon_intro zenon_He3 | zenon_intro zenon_H137 ]. % 19.02/19.18 apply (zenon_L1251_); trivial. % 19.02/19.18 apply (zenon_or_s _ _ zenon_H137); [ zenon_intro zenon_Hdc | zenon_intro zenon_H138 ]. % 19.02/19.18 apply (zenon_L1276_); trivial. % 19.02/19.18 apply (zenon_or_s _ _ zenon_H138); [ zenon_intro zenon_Hdd | zenon_intro zenon_H105 ]. % 19.02/19.18 apply (zenon_or_s _ _ zenon_He4); [ zenon_intro zenon_H1e | zenon_intro zenon_He5 ]. % 19.02/19.18 apply (zenon_L1277_); trivial. % 19.02/19.18 apply (zenon_or_s _ _ zenon_He5); [ zenon_intro zenon_Hc3 | zenon_intro zenon_He6 ]. % 19.02/19.18 apply (zenon_L46_); trivial. % 19.02/19.18 apply (zenon_or_s _ _ zenon_He6); [ zenon_intro zenon_Hcd | zenon_intro zenon_He3 ]. % 19.02/19.18 apply (zenon_L87_); trivial. % 19.02/19.18 apply (zenon_L54_); trivial. % 19.02/19.18 exact (zenon_H102 zenon_H105). % 19.02/19.18 (* end of lemma zenon_L1278_ *) % 19.02/19.18 assert (zenon_L1279_ : (((op (e0) (e3)) = (e0))\/(((op (e0) (e3)) = (e1))\/(((op (e0) (e3)) = (e2))\/((op (e0) (e3)) = (e3))))) -> (~((op (e0) (e3)) = (op (e1) (e3)))) -> ((op (e2) (e2)) = (e0)) -> (((op (e1) (e0)) = (e2))\/(((op (e1) (e1)) = (e2))\/(((op (e1) (e2)) = (e2))\/((op (e1) (e3)) = (e2))))) -> (~((op (e1) (e0)) = (e2))) -> (~((e0) = (e2))) -> (~((op (e1) (e2)) = (e2))) -> (~((op (e1) (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 (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) (e1)) = (op (e2) (e3)))) -> (~((op (e2) (e1)) = (e2))) -> (((op (e0) (e3)) = (e1))\/(((op (e1) (e3)) = (e1))\/(((op (e2) (e3)) = (e1))\/((op (e3) (e3)) = (e1))))) -> (~((e0) = (e1))) -> (~((op (e1) (e2)) = (op (e1) (e3)))) -> (((op (e0) (e3)) = (e3))\/(((op (e1) (e3)) = (e3))\/(((op (e2) (e3)) = (e3))\/((op (e3) (e3)) = (e3))))) -> (~((e0) = (e3))) -> (~((op (e2) (e3)) = (e2))) -> (((op (e2) (e3)) = (e0))\/(((op (e2) (e3)) = (e1))\/(((op (e2) (e3)) = (e2))\/((op (e2) (e3)) = (e3))))) -> (~((op (e1) (e3)) = (op (e2) (e3)))) -> (~((op (e1) (e3)) = (op (e3) (e3)))) -> (~((op (e1) (e0)) = (op (e1) (e3)))) -> (((op (e1) (e3)) = (e0))\/(((op (e1) (e3)) = (e1))\/(((op (e1) (e3)) = (e2))\/((op (e1) (e3)) = (e3))))) -> (~((op (e1) (e1)) = (e1))) -> (((op (e0) (e0)) = (e2))\/(((op (e1) (e0)) = (e2))\/(((op (e2) (e0)) = (e2))\/((op (e3) (e0)) = (e2))))) -> (~((op (e0) (e0)) = (e2))) -> (~((op (e0) (e1)) = (op (e2) (e1)))) -> (((op (e0) (e1)) = (e0))\/(((op (e1) (e1)) = (e0))\/(((op (e2) (e1)) = (e0))\/((op (e3) (e1)) = (e0))))) -> (((op (e0) (e1)) = (e1))\/(((op (e1) (e1)) = (e1))\/(((op (e2) (e1)) = (e1))\/((op (e3) (e1)) = (e1))))) -> (~((op (e1) (e0)) = (op (e1) (e1)))) -> (~((op (e0) (e1)) = (op (e0) (e3)))) -> (~((op (e3) (e0)) = (e2))) -> (~((op (e0) (e0)) = (e0))) -> (((op (e0) (e0)) = (e0))\/(((op (e1) (e0)) = (e0))\/(((op (e2) (e0)) = (e0))\/((op (e3) (e0)) = (e0))))) -> (~((op (e0) (e3)) = (op (e3) (e3)))) -> (~((op (e0) (e3)) = (op (e2) (e3)))) -> (~((op (e3) (e2)) = (e2))) -> (~((op (e3) (e1)) = (e2))) -> (((op (e3) (e0)) = (e2))\/(((op (e3) (e1)) = (e2))\/(((op (e3) (e2)) = (e2))\/((op (e3) (e3)) = (e2))))) -> ((op (e0) (e2)) = (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))))) -> (~((e1) = (e2))) -> ((op (e2) (e0)) = (e2)) -> (~((op (e2) (e1)) = (op (e3) (e1)))) -> ((op (e1) (e2)) = (e1)) -> (~((op (e1) (e2)) = (op (e2) (e2)))) -> (((op (e3) (e3)) = (e0))\/(((op (e3) (e3)) = (e1))\/(((op (e3) (e3)) = (e2))\/((op (e3) (e3)) = (e3))))) -> (~((op (e3) (e0)) = (op (e3) (e3)))) -> ((op (e3) (e0)) = (e0)) -> (~((op (e2) (e3)) = (op (e3) (e3)))) -> (~((op (e3) (e3)) = (e3))) -> False). % 19.02/19.18 do 0 intro. intros zenon_He4 zenon_H1d zenon_H2c zenon_H18c zenon_H177 zenon_H149 zenon_H114 zenon_H14c zenon_H1fa zenon_H22 zenon_H52 zenon_H1cc zenon_H24b zenon_H1c7 zenon_H26e zenon_H133 zenon_Ha1 zenon_H124 zenon_H136 zenon_H9a zenon_H274 zenon_H11f zenon_Hdb zenon_Hd5 zenon_Hd8 zenon_Hdf zenon_H10a zenon_H1fe zenon_H80 zenon_H17e zenon_H245 zenon_H109 zenon_H45 zenon_H54 zenon_H14b zenon_H3f zenon_H3e zenon_Hc2 zenon_He2 zenon_H272 zenon_H194 zenon_H153 zenon_Ha9 zenon_He8 zenon_H106 zenon_H7c zenon_Hee zenon_Haf zenon_Hf0 zenon_H2b zenon_H101 zenon_H71 zenon_H44 zenon_Hf3 zenon_H102. % 19.02/19.18 apply (zenon_or_s _ _ zenon_H22); [ zenon_intro zenon_H27 | zenon_intro zenon_H26 ]. % 19.02/19.18 apply (zenon_L312_); trivial. % 19.02/19.18 apply (zenon_or_s _ _ zenon_H26); [ zenon_intro zenon_H29 | zenon_intro zenon_H28 ]. % 19.02/19.18 apply (zenon_L1259_); trivial. % 19.02/19.18 apply (zenon_or_s _ _ zenon_H28); [ zenon_intro zenon_H2a | zenon_intro zenon_H1f ]. % 19.02/19.18 apply (zenon_L3_); trivial. % 19.02/19.18 apply (zenon_or_s _ _ zenon_H109); [ zenon_intro zenon_Ha0 | zenon_intro zenon_H10b ]. % 19.02/19.18 apply (zenon_L1262_); trivial. % 19.02/19.18 apply (zenon_or_s _ _ zenon_H10b); [ zenon_intro zenon_H10d | zenon_intro zenon_H10c ]. % 19.02/19.18 exact (zenon_H10a zenon_H10d). % 19.02/19.18 apply (zenon_or_s _ _ zenon_H10c); [ zenon_intro zenon_Ha5 | zenon_intro zenon_Hae ]. % 19.02/19.18 apply (zenon_or_s _ _ zenon_He8); [ zenon_intro zenon_Hac | zenon_intro zenon_Heb ]. % 19.02/19.18 apply (zenon_L41_); trivial. % 19.02/19.18 apply (zenon_or_s _ _ zenon_Heb); [ zenon_intro zenon_Hae | zenon_intro zenon_Hec ]. % 19.02/19.18 apply (zenon_L42_); trivial. % 19.02/19.18 apply (zenon_or_s _ _ zenon_Hec); [ zenon_intro zenon_Hba | zenon_intro zenon_Hc4 ]. % 19.02/19.18 apply (zenon_L45_); trivial. % 19.02/19.18 apply (zenon_L1278_); trivial. % 19.02/19.18 apply (zenon_L65_); trivial. % 19.02/19.18 (* end of lemma zenon_L1279_ *) % 19.02/19.18 assert (zenon_L1280_ : ((op (e3) (e1)) = (e1)) -> (((op (e3) (e0)) = (e0))\/(((op (e3) (e1)) = (e0))\/(((op (e3) (e2)) = (e0))\/((op (e3) (e3)) = (e0))))) -> (~((op (e3) (e3)) = (e3))) -> (~((op (e2) (e3)) = (op (e3) (e3)))) -> (~((op (e3) (e0)) = (op (e3) (e3)))) -> (((op (e3) (e3)) = (e0))\/(((op (e3) (e3)) = (e1))\/(((op (e3) (e3)) = (e2))\/((op (e3) (e3)) = (e3))))) -> (~((op (e1) (e2)) = (op (e2) (e2)))) -> ((op (e1) (e2)) = (e1)) -> (~((op (e2) (e1)) = (op (e3) (e1)))) -> ((op (e2) (e0)) = (e2)) -> (~((e1) = (e2))) -> (((op (e2) (e0)) = (e1))\/(((op (e2) (e1)) = (e1))\/(((op (e2) (e2)) = (e1))\/((op (e2) (e3)) = (e1))))) -> (((op (e3) (e0)) = (e1))\/(((op (e3) (e1)) = (e1))\/(((op (e3) (e2)) = (e1))\/((op (e3) (e3)) = (e1))))) -> ((op (e0) (e2)) = (e3)) -> (((op (e3) (e0)) = (e2))\/(((op (e3) (e1)) = (e2))\/(((op (e3) (e2)) = (e2))\/((op (e3) (e3)) = (e2))))) -> (~((op (e3) (e1)) = (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 (e3) (e0)) = (e2))) -> (~((op (e0) (e1)) = (op (e0) (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 (e1) (e1)) = (e0))\/(((op (e2) (e1)) = (e0))\/((op (e3) (e1)) = (e0))))) -> (~((op (e0) (e1)) = (op (e2) (e1)))) -> (~((op (e0) (e0)) = (e2))) -> (((op (e0) (e0)) = (e2))\/(((op (e1) (e0)) = (e2))\/(((op (e2) (e0)) = (e2))\/((op (e3) (e0)) = (e2))))) -> (~((op (e1) (e1)) = (e1))) -> (~((op (e1) (e0)) = (op (e1) (e3)))) -> (((op (e2) (e3)) = (e0))\/(((op (e2) (e3)) = (e1))\/(((op (e2) (e3)) = (e2))\/((op (e2) (e3)) = (e3))))) -> (~((op (e2) (e3)) = (e2))) -> (~((e0) = (e3))) -> (((op (e0) (e3)) = (e3))\/(((op (e1) (e3)) = (e3))\/(((op (e2) (e3)) = (e3))\/((op (e3) (e3)) = (e3))))) -> (~((op (e1) (e2)) = (op (e1) (e3)))) -> (~((e0) = (e1))) -> (((op (e0) (e3)) = (e1))\/(((op (e1) (e3)) = (e1))\/(((op (e2) (e3)) = (e1))\/((op (e3) (e3)) = (e1))))) -> (~((op (e2) (e0)) = (op (e2) (e2)))) -> (((op (e1) (e0)) = (e0))\/(((op (e1) (e1)) = (e0))\/(((op (e1) (e2)) = (e0))\/((op (e1) (e3)) = (e0))))) -> (~((op (e1) (e0)) = (op (e3) (e0)))) -> (~((op (e1) (e2)) = (e2))) -> (~((e0) = (e2))) -> (~((op (e1) (e0)) = (e2))) -> (((op (e1) (e0)) = (e2))\/(((op (e1) (e1)) = (e2))\/(((op (e1) (e2)) = (e2))\/((op (e1) (e3)) = (e2))))) -> ((op (e1) (e1)) = (e2)) -> (~((op (e2) (e1)) = (e2))) -> (~((op (e2) (e1)) = (op (e2) (e3)))) -> (~((op (e2) (e1)) = (op (e2) (e2)))) -> (((op (e2) (e1)) = (e0))\/(((op (e2) (e1)) = (e1))\/(((op (e2) (e1)) = (e2))\/((op (e2) (e1)) = (e3))))) -> ((op (e2) (e2)) = (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 (e3) (e3)))) -> (~((op (e0) (e3)) = (op (e2) (e3)))) -> (((op (e1) (e3)) = (e0))\/(((op (e1) (e3)) = (e1))\/(((op (e1) (e3)) = (e2))\/((op (e1) (e3)) = (e3))))) -> (~((op (e1) (e3)) = (op (e3) (e3)))) -> (~((op (e1) (e3)) = (op (e2) (e3)))) -> (~((op (e1) (e3)) = (e2))) -> (~((op (e0) (e3)) = (op (e1) (e3)))) -> False). % 19.02/19.18 do 0 intro. intros zenon_Hae zenon_H1ac zenon_H102 zenon_Hf3 zenon_H71 zenon_H101 zenon_H2b zenon_Hf0 zenon_Haf zenon_Hee zenon_H7c zenon_H106 zenon_He8 zenon_Ha9 zenon_H153 zenon_H194 zenon_H272 zenon_H3e zenon_H3f zenon_H14b zenon_H54 zenon_H45 zenon_H109 zenon_H245 zenon_H17e zenon_H80 zenon_H1fe zenon_H10a zenon_Hd8 zenon_H11f zenon_H274 zenon_H9a zenon_H136 zenon_H124 zenon_Ha1 zenon_H133 zenon_H52 zenon_H22 zenon_H1fa zenon_H114 zenon_H149 zenon_H177 zenon_H18c zenon_H110 zenon_H26e zenon_H1c7 zenon_H24b zenon_H1cc zenon_H2c zenon_H18f zenon_He4 zenon_Hc2 zenon_He2 zenon_Hdf zenon_Hd5 zenon_Hdb zenon_H14c zenon_H1d. % 19.02/19.18 apply (zenon_or_s _ _ zenon_H106); [ zenon_intro zenon_Hed | zenon_intro zenon_H107 ]. % 19.02/19.18 apply (zenon_L58_); trivial. % 19.02/19.18 apply (zenon_or_s _ _ zenon_H107); [ zenon_intro zenon_Ha5 | zenon_intro zenon_H108 ]. % 19.02/19.18 apply (zenon_L42_); trivial. % 19.02/19.18 apply (zenon_or_s _ _ zenon_H108); [ zenon_intro zenon_Hf1 | zenon_intro zenon_Hf4 ]. % 19.02/19.18 apply (zenon_L59_); trivial. % 19.02/19.18 apply (zenon_or_s _ _ zenon_H1ac); [ zenon_intro zenon_H44 | zenon_intro zenon_H1af ]. % 19.02/19.18 apply (zenon_L1279_); trivial. % 19.02/19.18 apply (zenon_or_s _ _ zenon_H1af); [ zenon_intro zenon_H1b1 | zenon_intro zenon_H1b0 ]. % 19.02/19.18 apply (zenon_L1260_); trivial. % 19.02/19.18 apply (zenon_or_s _ _ zenon_H1b0); [ zenon_intro zenon_H61 | zenon_intro zenon_H60 ]. % 19.02/19.18 apply (zenon_L146_); trivial. % 19.02/19.18 apply (zenon_L1274_); trivial. % 19.02/19.18 (* end of lemma zenon_L1280_ *) % 19.02/19.18 assert (zenon_L1281_ : (~((op (e0) (e3)) = (op (e1) (e3)))) -> (~((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 (e0) (e3)) = (op (e2) (e3)))) -> (~((op (e0) (e3)) = (op (e3) (e3)))) -> (((op (e0) (e3)) = (e0))\/(((op (e0) (e3)) = (e1))\/(((op (e0) (e3)) = (e2))\/((op (e0) (e3)) = (e3))))) -> (~((op (e2) (e2)) = (op (e3) (e2)))) -> ((op (e2) (e2)) = (e0)) -> (((op (e2) (e1)) = (e0))\/(((op (e2) (e1)) = (e1))\/(((op (e2) (e1)) = (e2))\/((op (e2) (e1)) = (e3))))) -> (~((op (e2) (e1)) = (op (e2) (e2)))) -> (~((op (e2) (e1)) = (op (e2) (e3)))) -> (~((op (e2) (e1)) = (e2))) -> (((op (e1) (e0)) = (e2))\/(((op (e1) (e1)) = (e2))\/(((op (e1) (e2)) = (e2))\/((op (e1) (e3)) = (e2))))) -> (~((op (e1) (e0)) = (e2))) -> (~((e0) = (e2))) -> (~((op (e1) (e0)) = (op (e3) (e0)))) -> (((op (e1) (e0)) = (e0))\/(((op (e1) (e1)) = (e0))\/(((op (e1) (e2)) = (e0))\/((op (e1) (e3)) = (e0))))) -> (~((op (e2) (e0)) = (op (e2) (e2)))) -> (((op (e0) (e3)) = (e1))\/(((op (e1) (e3)) = (e1))\/(((op (e2) (e3)) = (e1))\/((op (e3) (e3)) = (e1))))) -> (~((e0) = (e1))) -> (~((op (e1) (e2)) = (op (e1) (e3)))) -> (((op (e0) (e3)) = (e3))\/(((op (e1) (e3)) = (e3))\/(((op (e2) (e3)) = (e3))\/((op (e3) (e3)) = (e3))))) -> (~((e0) = (e3))) -> (~((op (e2) (e3)) = (e2))) -> (((op (e2) (e3)) = (e0))\/(((op (e2) (e3)) = (e1))\/(((op (e2) (e3)) = (e2))\/((op (e2) (e3)) = (e3))))) -> (~((op (e1) (e0)) = (op (e1) (e3)))) -> (~((op (e1) (e1)) = (e1))) -> (((op (e0) (e0)) = (e2))\/(((op (e1) (e0)) = (e2))\/(((op (e2) (e0)) = (e2))\/((op (e3) (e0)) = (e2))))) -> (~((op (e0) (e0)) = (e2))) -> (~((op (e0) (e1)) = (op (e2) (e1)))) -> (((op (e0) (e1)) = (e0))\/(((op (e1) (e1)) = (e0))\/(((op (e2) (e1)) = (e0))\/((op (e3) (e1)) = (e0))))) -> (((op (e0) (e1)) = (e1))\/(((op (e1) (e1)) = (e1))\/(((op (e2) (e1)) = (e1))\/((op (e3) (e1)) = (e1))))) -> (~((op (e1) (e0)) = (op (e1) (e1)))) -> (~((op (e0) (e1)) = (op (e0) (e3)))) -> (~((op (e3) (e0)) = (e2))) -> (~((op (e0) (e0)) = (e0))) -> (((op (e0) (e0)) = (e0))\/(((op (e1) (e0)) = (e0))\/(((op (e2) (e0)) = (e0))\/((op (e3) (e0)) = (e0))))) -> (~((op (e3) (e2)) = (e2))) -> (~((op (e3) (e1)) = (e2))) -> (((op (e3) (e0)) = (e2))\/(((op (e3) (e1)) = (e2))\/(((op (e3) (e2)) = (e2))\/((op (e3) (e3)) = (e2))))) -> ((op (e0) (e2)) = (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))))) -> (~((e1) = (e2))) -> ((op (e2) (e0)) = (e2)) -> (~((op (e2) (e1)) = (op (e3) (e1)))) -> ((op (e1) (e2)) = (e1)) -> (~((op (e1) (e2)) = (op (e2) (e2)))) -> (((op (e3) (e3)) = (e0))\/(((op (e3) (e3)) = (e1))\/(((op (e3) (e3)) = (e2))\/((op (e3) (e3)) = (e3))))) -> (~((op (e3) (e0)) = (op (e3) (e3)))) -> (~((op (e2) (e3)) = (op (e3) (e3)))) -> (~((op (e3) (e3)) = (e3))) -> (((op (e3) (e0)) = (e0))\/(((op (e3) (e1)) = (e0))\/(((op (e3) (e2)) = (e0))\/((op (e3) (e3)) = (e0))))) -> ((op (e3) (e1)) = (e1)) -> (~((op (e1) (e2)) = (e2))) -> (~((op (e1) (e3)) = (e2))) -> False). % 19.02/19.18 do 0 intro. intros zenon_H1d zenon_Hdb zenon_Hd5 zenon_Hdf zenon_He2 zenon_Hc2 zenon_He4 zenon_H18f zenon_H2c zenon_H1cc zenon_H24b zenon_H1c7 zenon_H26e zenon_H18c zenon_H177 zenon_H149 zenon_H1fa zenon_H22 zenon_H52 zenon_H133 zenon_Ha1 zenon_H124 zenon_H136 zenon_H9a zenon_H274 zenon_H11f zenon_Hd8 zenon_H10a zenon_H1fe zenon_H80 zenon_H17e zenon_H245 zenon_H109 zenon_H45 zenon_H54 zenon_H14b zenon_H3f zenon_H3e zenon_H272 zenon_H194 zenon_H153 zenon_Ha9 zenon_He8 zenon_H106 zenon_H7c zenon_Hee zenon_Haf zenon_Hf0 zenon_H2b zenon_H101 zenon_H71 zenon_Hf3 zenon_H102 zenon_H1ac zenon_Hae zenon_H114 zenon_H14c. % 19.02/19.18 apply (zenon_or_s _ _ zenon_H18c); [ zenon_intro zenon_H86 | zenon_intro zenon_H18d ]. % 19.02/19.18 exact (zenon_H177 zenon_H86). % 19.02/19.18 apply (zenon_or_s _ _ zenon_H18d); [ zenon_intro zenon_H110 | zenon_intro zenon_H18e ]. % 19.02/19.18 apply (zenon_L1280_); trivial. % 19.02/19.18 apply (zenon_or_s _ _ zenon_H18e); [ zenon_intro zenon_H113 | zenon_intro zenon_Hd7 ]. % 19.02/19.18 exact (zenon_H114 zenon_H113). % 19.02/19.18 exact (zenon_H14c zenon_Hd7). % 19.02/19.18 (* end of lemma zenon_L1281_ *) % 19.02/19.18 assert (zenon_L1282_ : (((op (e0) (e3)) = (e0))\/(((op (e1) (e3)) = (e0))\/(((op (e2) (e3)) = (e0))\/((op (e3) (e3)) = (e0))))) -> (~((op (e3) (e0)) = (op (e3) (e1)))) -> (~((op (e1) (e2)) = (e2))) -> (((op (e3) (e0)) = (e0))\/(((op (e3) (e1)) = (e0))\/(((op (e3) (e2)) = (e0))\/((op (e3) (e3)) = (e0))))) -> (~((op (e3) (e0)) = (op (e3) (e3)))) -> (((op (e3) (e3)) = (e0))\/(((op (e3) (e3)) = (e1))\/(((op (e3) (e3)) = (e2))\/((op (e3) (e3)) = (e3))))) -> (~((op (e1) (e2)) = (op (e2) (e2)))) -> (~((op (e2) (e1)) = (op (e3) (e1)))) -> ((op (e2) (e0)) = (e2)) -> (~((e1) = (e2))) -> (((op (e2) (e0)) = (e1))\/(((op (e2) (e1)) = (e1))\/(((op (e2) (e2)) = (e1))\/((op (e2) (e3)) = (e1))))) -> (((op (e3) (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)) = (op (e0) (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 (e1) (e1)) = (e0))\/(((op (e2) (e1)) = (e0))\/((op (e3) (e1)) = (e0))))) -> (~((op (e0) (e1)) = (op (e2) (e1)))) -> (~((op (e0) (e0)) = (e2))) -> (((op (e0) (e0)) = (e2))\/(((op (e1) (e0)) = (e2))\/(((op (e2) (e0)) = (e2))\/((op (e3) (e0)) = (e2))))) -> (~((op (e1) (e1)) = (e1))) -> (~((e0) = (e1))) -> (((op (e0) (e3)) = (e1))\/(((op (e1) (e3)) = (e1))\/(((op (e2) (e3)) = (e1))\/((op (e3) (e3)) = (e1))))) -> (~((op (e2) (e0)) = (op (e2) (e2)))) -> (((op (e1) (e0)) = (e0))\/(((op (e1) (e1)) = (e0))\/(((op (e1) (e2)) = (e0))\/((op (e1) (e3)) = (e0))))) -> (~((op (e1) (e0)) = (op (e3) (e0)))) -> (~((e0) = (e2))) -> (~((op (e1) (e0)) = (e2))) -> (((op (e1) (e0)) = (e2))\/(((op (e1) (e1)) = (e2))\/(((op (e1) (e2)) = (e2))\/((op (e1) (e3)) = (e2))))) -> (~((op (e2) (e1)) = (e2))) -> (~((op (e2) (e1)) = (op (e2) (e2)))) -> (((op (e2) (e1)) = (e0))\/(((op (e2) (e1)) = (e1))\/(((op (e2) (e1)) = (e2))\/((op (e2) (e1)) = (e3))))) -> (~((op (e2) (e2)) = (op (e3) (e2)))) -> ((op (e2) (e2)) = (e0)) -> ((op (e0) (e2)) = (e3)) -> (((op (e3) (e0)) = (e2))\/(((op (e3) (e1)) = (e2))\/(((op (e3) (e2)) = (e2))\/((op (e3) (e3)) = (e2))))) -> (~((op (e3) (e0)) = (e2))) -> (~((op (e3) (e1)) = (e2))) -> (~((op (e3) (e2)) = (e2))) -> (((op (e0) (e3)) = (e0))\/(((op (e0) (e3)) = (e1))\/(((op (e0) (e3)) = (e2))\/((op (e0) (e3)) = (e3))))) -> ((op (e1) (e0)) = (e0)) -> (~((op (e1) (e0)) = (op (e1) (e3)))) -> (~((e0) = (e3))) -> (~((op (e3) (e3)) = (e3))) -> (~((op (e1) (e2)) = (op (e1) (e3)))) -> ((op (e1) (e2)) = (e1)) -> (~((op (e1) (e3)) = (op (e2) (e3)))) -> (((op (e2) (e3)) = (e0))\/(((op (e2) (e3)) = (e1))\/(((op (e2) (e3)) = (e2))\/((op (e2) (e3)) = (e3))))) -> (~((op (e2) (e1)) = (op (e2) (e3)))) -> ((op (e2) (e1)) = (e1)) -> (~((op (e2) (e3)) = (e2))) -> (~((op (e2) (e3)) = (op (e3) (e3)))) -> (~((op (e0) (e3)) = (op (e2) (e3)))) -> (((op (e0) (e3)) = (e3))\/(((op (e1) (e3)) = (e3))\/(((op (e2) (e3)) = (e3))\/((op (e3) (e3)) = (e3))))) -> (~((op (e0) (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 (e1) (e3)) = (op (e3) (e3)))) -> (~((op (e1) (e3)) = (e2))) -> (~((op (e0) (e3)) = (op (e1) (e3)))) -> False). % 19.02/19.19 do 0 intro. intros zenon_H67 zenon_H1cf zenon_H114 zenon_H1ac zenon_H71 zenon_H101 zenon_H2b zenon_Haf zenon_Hee zenon_H7c zenon_H106 zenon_He8 zenon_H3e zenon_H3f zenon_H54 zenon_H45 zenon_H109 zenon_H245 zenon_H17e zenon_H80 zenon_H1fe zenon_H10a zenon_Ha1 zenon_H133 zenon_H52 zenon_H22 zenon_H1fa zenon_H149 zenon_H177 zenon_H18c zenon_H26e zenon_H24b zenon_H1cc zenon_H18f zenon_H2c zenon_Ha9 zenon_H153 zenon_H14b zenon_H194 zenon_H272 zenon_He4 zenon_H27 zenon_Hd8 zenon_H9a zenon_H102 zenon_H124 zenon_Hf0 zenon_Hdb zenon_H11f zenon_H1c7 zenon_Ha5 zenon_H274 zenon_Hf3 zenon_He2 zenon_H136 zenon_Hc2 zenon_Hdf zenon_H60 zenon_Hd5 zenon_H14c zenon_H1d. % 19.02/19.19 apply (zenon_or_s _ _ zenon_He8); [ zenon_intro zenon_Hac | zenon_intro zenon_Heb ]. % 19.02/19.19 apply (zenon_or_s _ _ zenon_H133); [ zenon_intro zenon_Hc3 | zenon_intro zenon_H134 ]. % 19.02/19.19 apply (zenon_L1273_); trivial. % 19.02/19.19 apply (zenon_or_s _ _ zenon_H134); [ zenon_intro zenon_Hd6 | zenon_intro zenon_H135 ]. % 19.02/19.19 apply (zenon_L78_); trivial. % 19.02/19.19 apply (zenon_or_s _ _ zenon_H135); [ zenon_intro zenon_Hf4 | zenon_intro zenon_Hc4 ]. % 19.02/19.19 apply (zenon_L1274_); trivial. % 19.02/19.19 apply (zenon_L1275_); trivial. % 19.02/19.19 apply (zenon_or_s _ _ zenon_Heb); [ zenon_intro zenon_Hae | zenon_intro zenon_Hec ]. % 19.02/19.19 apply (zenon_L1281_); trivial. % 19.02/19.19 apply (zenon_or_s _ _ zenon_Hec); [ zenon_intro zenon_Hba | zenon_intro zenon_Hc4 ]. % 19.02/19.19 apply (zenon_L45_); trivial. % 19.02/19.19 apply (zenon_L1275_); trivial. % 19.02/19.19 (* end of lemma zenon_L1282_ *) % 19.02/19.19 assert (zenon_L1283_ : ((op (e1) (e0)) = (e0)) -> (~((op (e3) (e0)) = (op (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) (e3)) = (op (e1) (e3)))) -> (~((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 (e0) (e3)) = (op (e2) (e3)))) -> (~((op (e0) (e3)) = (op (e3) (e3)))) -> (((op (e0) (e3)) = (e0))\/(((op (e0) (e3)) = (e1))\/(((op (e0) (e3)) = (e2))\/((op (e0) (e3)) = (e3))))) -> (~((op (e2) (e2)) = (op (e3) (e2)))) -> ((op (e2) (e2)) = (e0)) -> (((op (e2) (e1)) = (e0))\/(((op (e2) (e1)) = (e1))\/(((op (e2) (e1)) = (e2))\/((op (e2) (e1)) = (e3))))) -> (~((op (e2) (e1)) = (op (e2) (e2)))) -> (~((op (e2) (e1)) = (op (e2) (e3)))) -> (~((op (e2) (e1)) = (e2))) -> (((op (e1) (e0)) = (e2))\/(((op (e1) (e1)) = (e2))\/(((op (e1) (e2)) = (e2))\/((op (e1) (e3)) = (e2))))) -> (~((op (e1) (e0)) = (e2))) -> (~((e0) = (e2))) -> (~((op (e1) (e0)) = (op (e3) (e0)))) -> (((op (e1) (e0)) = (e0))\/(((op (e1) (e1)) = (e0))\/(((op (e1) (e2)) = (e0))\/((op (e1) (e3)) = (e0))))) -> (~((op (e2) (e0)) = (op (e2) (e2)))) -> (((op (e0) (e3)) = (e1))\/(((op (e1) (e3)) = (e1))\/(((op (e2) (e3)) = (e1))\/((op (e3) (e3)) = (e1))))) -> (~((e0) = (e1))) -> (~((op (e1) (e2)) = (op (e1) (e3)))) -> (((op (e0) (e3)) = (e3))\/(((op (e1) (e3)) = (e3))\/(((op (e2) (e3)) = (e3))\/((op (e3) (e3)) = (e3))))) -> (~((e0) = (e3))) -> (~((op (e2) (e3)) = (e2))) -> (((op (e2) (e3)) = (e0))\/(((op (e2) (e3)) = (e1))\/(((op (e2) (e3)) = (e2))\/((op (e2) (e3)) = (e3))))) -> (~((op (e1) (e0)) = (op (e1) (e3)))) -> (~((op (e1) (e1)) = (e1))) -> (((op (e0) (e0)) = (e2))\/(((op (e1) (e0)) = (e2))\/(((op (e2) (e0)) = (e2))\/((op (e3) (e0)) = (e2))))) -> (~((op (e0) (e0)) = (e2))) -> (~((op (e0) (e1)) = (op (e2) (e1)))) -> (((op (e0) (e1)) = (e0))\/(((op (e1) (e1)) = (e0))\/(((op (e2) (e1)) = (e0))\/((op (e3) (e1)) = (e0))))) -> (((op (e0) (e1)) = (e1))\/(((op (e1) (e1)) = (e1))\/(((op (e2) (e1)) = (e1))\/((op (e3) (e1)) = (e1))))) -> (~((op (e1) (e0)) = (op (e1) (e1)))) -> (~((op (e0) (e1)) = (op (e0) (e3)))) -> (~((op (e3) (e0)) = (e2))) -> (~((op (e0) (e0)) = (e0))) -> (((op (e0) (e0)) = (e0))\/(((op (e1) (e0)) = (e0))\/(((op (e2) (e0)) = (e0))\/((op (e3) (e0)) = (e0))))) -> (~((op (e3) (e2)) = (e2))) -> (~((op (e3) (e1)) = (e2))) -> (((op (e3) (e0)) = (e2))\/(((op (e3) (e1)) = (e2))\/(((op (e3) (e2)) = (e2))\/((op (e3) (e3)) = (e2))))) -> ((op (e0) (e2)) = (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))))) -> (~((e1) = (e2))) -> ((op (e2) (e0)) = (e2)) -> (~((op (e2) (e1)) = (op (e3) (e1)))) -> ((op (e1) (e2)) = (e1)) -> (~((op (e1) (e2)) = (op (e2) (e2)))) -> (((op (e3) (e3)) = (e0))\/(((op (e3) (e3)) = (e1))\/(((op (e3) (e3)) = (e2))\/((op (e3) (e3)) = (e3))))) -> (~((op (e3) (e0)) = (op (e3) (e3)))) -> (~((op (e2) (e3)) = (op (e3) (e3)))) -> (~((op (e3) (e3)) = (e3))) -> (((op (e3) (e0)) = (e0))\/(((op (e3) (e1)) = (e0))\/(((op (e3) (e2)) = (e0))\/((op (e3) (e3)) = (e0))))) -> (~((op (e1) (e2)) = (e2))) -> (~((op (e1) (e3)) = (e2))) -> False). % 19.02/19.19 do 0 intro. intros zenon_H27 zenon_H1cf zenon_H67 zenon_H6d zenon_H1d zenon_Hdb zenon_Hd5 zenon_Hdf zenon_He2 zenon_Hc2 zenon_He4 zenon_H18f zenon_H2c zenon_H1cc zenon_H24b zenon_H1c7 zenon_H26e zenon_H18c zenon_H177 zenon_H149 zenon_H1fa zenon_H22 zenon_H52 zenon_H133 zenon_Ha1 zenon_H124 zenon_H136 zenon_H9a zenon_H274 zenon_H11f zenon_Hd8 zenon_H10a zenon_H1fe zenon_H80 zenon_H17e zenon_H245 zenon_H109 zenon_H45 zenon_H54 zenon_H14b zenon_H3f zenon_H3e zenon_H272 zenon_H194 zenon_H153 zenon_Ha9 zenon_He8 zenon_H106 zenon_H7c zenon_Hee zenon_Haf zenon_Hf0 zenon_H2b zenon_H101 zenon_H71 zenon_Hf3 zenon_H102 zenon_H1ac zenon_H114 zenon_H14c. % 19.02/19.19 apply (zenon_or_s _ _ zenon_H109); [ zenon_intro zenon_Ha0 | zenon_intro zenon_H10b ]. % 19.02/19.19 apply (zenon_L1262_); trivial. % 19.02/19.19 apply (zenon_or_s _ _ zenon_H10b); [ zenon_intro zenon_H10d | zenon_intro zenon_H10c ]. % 19.02/19.19 exact (zenon_H10a zenon_H10d). % 19.02/19.19 apply (zenon_or_s _ _ zenon_H10c); [ zenon_intro zenon_Ha5 | zenon_intro zenon_Hae ]. % 19.02/19.19 apply (zenon_or_s _ _ zenon_H1ac); [ zenon_intro zenon_H44 | zenon_intro zenon_H1af ]. % 19.02/19.19 apply (zenon_L312_); trivial. % 19.02/19.19 apply (zenon_or_s _ _ zenon_H1af); [ zenon_intro zenon_H1b1 | zenon_intro zenon_H1b0 ]. % 19.02/19.19 apply (zenon_or_s _ _ zenon_H67); [ zenon_intro zenon_H1e | zenon_intro zenon_H68 ]. % 19.02/19.19 apply (zenon_L1267_); trivial. % 19.02/19.19 apply (zenon_or_s _ _ zenon_H68); [ zenon_intro zenon_H1f | zenon_intro zenon_H69 ]. % 19.02/19.19 apply (zenon_L258_); trivial. % 19.02/19.19 apply (zenon_or_s _ _ zenon_H69); [ zenon_intro zenon_H37 | zenon_intro zenon_H60 ]. % 19.02/19.19 apply (zenon_L18_); trivial. % 19.02/19.19 apply (zenon_L1282_); trivial. % 19.02/19.19 apply (zenon_or_s _ _ zenon_H1b0); [ zenon_intro zenon_H61 | zenon_intro zenon_H60 ]. % 19.02/19.19 apply (zenon_L146_); trivial. % 19.02/19.19 apply (zenon_L1282_); trivial. % 19.02/19.19 apply (zenon_L1281_); trivial. % 19.02/19.19 (* end of lemma zenon_L1283_ *) % 19.02/19.19 assert (zenon_L1284_ : (~((op (e3) (e0)) = (op (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 (e2) (e2)) = (op (e3) (e2)))) -> (((op (e3) (e0)) = (e0))\/(((op (e3) (e1)) = (e0))\/(((op (e3) (e2)) = (e0))\/((op (e3) (e3)) = (e0))))) -> (~((op (e3) (e3)) = (e3))) -> (~((op (e2) (e3)) = (op (e3) (e3)))) -> (~((op (e3) (e0)) = (op (e3) (e3)))) -> (((op (e3) (e3)) = (e0))\/(((op (e3) (e3)) = (e1))\/(((op (e3) (e3)) = (e2))\/((op (e3) (e3)) = (e3))))) -> (~((op (e1) (e2)) = (op (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))))) -> (((op (e3) (e0)) = (e1))\/(((op (e3) (e1)) = (e1))\/(((op (e3) (e2)) = (e1))\/((op (e3) (e3)) = (e1))))) -> ((op (e0) (e2)) = (e3)) -> (((op (e3) (e0)) = (e2))\/(((op (e3) (e1)) = (e2))\/(((op (e3) (e2)) = (e2))\/((op (e3) (e3)) = (e2))))) -> (~((op (e3) (e1)) = (e2))) -> (~((op (e3) (e2)) = (e2))) -> (~((op (e0) (e3)) = (op (e2) (e3)))) -> (~((op (e0) (e3)) = (op (e3) (e3)))) -> (((op (e0) (e0)) = (e0))\/(((op (e1) (e0)) = (e0))\/(((op (e2) (e0)) = (e0))\/((op (e3) (e0)) = (e0))))) -> (~((op (e0) (e0)) = (e0))) -> (~((op (e0) (e1)) = (op (e0) (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 (e1) (e1)) = (e0))\/(((op (e2) (e1)) = (e0))\/((op (e3) (e1)) = (e0))))) -> (~((op (e0) (e1)) = (op (e2) (e1)))) -> (~((op (e0) (e0)) = (e2))) -> (((op (e0) (e0)) = (e2))\/(((op (e1) (e0)) = (e2))\/(((op (e2) (e0)) = (e2))\/((op (e3) (e0)) = (e2))))) -> (~((op (e1) (e1)) = (e1))) -> (((op (e1) (e3)) = (e0))\/(((op (e1) (e3)) = (e1))\/(((op (e1) (e3)) = (e2))\/((op (e1) (e3)) = (e3))))) -> (~((op (e1) (e0)) = (op (e1) (e3)))) -> (~((op (e1) (e3)) = (op (e3) (e3)))) -> (~((op (e1) (e3)) = (op (e2) (e3)))) -> (((op (e2) (e3)) = (e0))\/(((op (e2) (e3)) = (e1))\/(((op (e2) (e3)) = (e2))\/((op (e2) (e3)) = (e3))))) -> (~((op (e2) (e3)) = (e2))) -> (~((e0) = (e3))) -> (((op (e0) (e3)) = (e3))\/(((op (e1) (e3)) = (e3))\/(((op (e2) (e3)) = (e3))\/((op (e3) (e3)) = (e3))))) -> (~((op (e1) (e2)) = (op (e1) (e3)))) -> (~((e0) = (e1))) -> (((op (e0) (e3)) = (e1))\/(((op (e1) (e3)) = (e1))\/(((op (e2) (e3)) = (e1))\/((op (e3) (e3)) = (e1))))) -> (~((op (e2) (e1)) = (e2))) -> (~((op (e2) (e1)) = (op (e2) (e3)))) -> (~((op (e2) (e1)) = (op (e2) (e2)))) -> (((op (e2) (e1)) = (e0))\/(((op (e2) (e1)) = (e1))\/(((op (e2) (e1)) = (e2))\/((op (e2) (e1)) = (e3))))) -> (~((op (e2) (e0)) = (op (e2) (e2)))) -> (((op (e1) (e0)) = (e0))\/(((op (e1) (e1)) = (e0))\/(((op (e1) (e2)) = (e0))\/((op (e1) (e3)) = (e0))))) -> (~((op (e1) (e0)) = (op (e3) (e0)))) -> (~((op (e1) (e3)) = (e2))) -> (~((op (e1) (e2)) = (e2))) -> (~((e0) = (e2))) -> (~((op (e1) (e0)) = (e2))) -> (((op (e1) (e0)) = (e2))\/(((op (e1) (e1)) = (e2))\/(((op (e1) (e2)) = (e2))\/((op (e1) (e3)) = (e2))))) -> ((op (e2) (e2)) = (e0)) -> (~((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)) = (e2))) -> False). % 19.02/19.19 do 0 intro. intros zenon_H1cf zenon_H67 zenon_H6d zenon_H18f zenon_H1ac zenon_H102 zenon_Hf3 zenon_H71 zenon_H101 zenon_H2b zenon_Hf0 zenon_Haf zenon_H7c zenon_H106 zenon_He8 zenon_Ha9 zenon_H153 zenon_H194 zenon_H272 zenon_He2 zenon_Hc2 zenon_H3e zenon_H3f zenon_H54 zenon_H45 zenon_H109 zenon_H245 zenon_H17e zenon_H80 zenon_H1fe zenon_H10a zenon_Hdf zenon_Hd8 zenon_Hd5 zenon_Hdb zenon_H11f zenon_H274 zenon_H9a zenon_H136 zenon_H124 zenon_Ha1 zenon_H133 zenon_H26e zenon_H1c7 zenon_H24b zenon_H1cc zenon_H52 zenon_H22 zenon_H1fa zenon_H14c zenon_H114 zenon_H149 zenon_H177 zenon_H18c zenon_H2c zenon_H1d zenon_He4 zenon_H14b. % 19.02/19.19 apply (zenon_or_s _ _ zenon_H3e); [ zenon_intro zenon_H42 | zenon_intro zenon_H41 ]. % 19.02/19.19 exact (zenon_H3f zenon_H42). % 19.02/19.19 apply (zenon_or_s _ _ zenon_H41); [ zenon_intro zenon_H27 | zenon_intro zenon_H43 ]. % 19.02/19.19 apply (zenon_or_s _ _ zenon_H1fe); [ zenon_intro zenon_H7b | zenon_intro zenon_H1ff ]. % 19.02/19.19 exact (zenon_H80 zenon_H7b). % 19.02/19.19 apply (zenon_or_s _ _ zenon_H1ff); [ zenon_intro zenon_H86 | zenon_intro zenon_H200 ]. % 19.02/19.19 exact (zenon_H177 zenon_H86). % 19.02/19.19 apply (zenon_or_s _ _ zenon_H200); [ zenon_intro zenon_Hee | zenon_intro zenon_H148 ]. % 19.02/19.19 apply (zenon_L1283_); trivial. % 19.02/19.19 exact (zenon_H14b zenon_H148). % 19.02/19.19 apply (zenon_or_s _ _ zenon_H43); [ zenon_intro zenon_H34 | zenon_intro zenon_H44 ]. % 19.02/19.19 apply (zenon_L11_); trivial. % 19.02/19.19 apply (zenon_or_s _ _ zenon_H1fe); [ zenon_intro zenon_H7b | zenon_intro zenon_H1ff ]. % 19.02/19.19 exact (zenon_H80 zenon_H7b). % 19.02/19.19 apply (zenon_or_s _ _ zenon_H1ff); [ zenon_intro zenon_H86 | zenon_intro zenon_H200 ]. % 19.02/19.19 exact (zenon_H177 zenon_H86). % 19.02/19.19 apply (zenon_or_s _ _ zenon_H200); [ zenon_intro zenon_Hee | zenon_intro zenon_H148 ]. % 19.02/19.19 apply (zenon_L1279_); trivial. % 19.02/19.19 exact (zenon_H14b zenon_H148). % 19.02/19.19 (* end of lemma zenon_L1284_ *) % 19.02/19.19 assert (zenon_L1285_ : (((op (e1) (e0)) = (e2))\/(((op (e1) (e1)) = (e2))\/(((op (e1) (e2)) = (e2))\/((op (e1) (e3)) = (e2))))) -> (~((op (e1) (e0)) = (e2))) -> (~((e0) = (e2))) -> ((op (e1) (e1)) = (e0)) -> (~((op (e1) (e2)) = (e2))) -> (((op (e0) (e1)) = (e2))\/(((op (e1) (e1)) = (e2))\/(((op (e2) (e1)) = (e2))\/((op (e3) (e1)) = (e2))))) -> (~((op (e0) (e1)) = (e2))) -> (~((op (e1) (e1)) = (op (e1) (e3)))) -> (~((op (e2) (e1)) = (e2))) -> (~((op (e3) (e1)) = (op (e3) (e2)))) -> ((op (e3) (e2)) = (e2)) -> False). % 19.02/19.19 do 0 intro. intros zenon_H18c zenon_H177 zenon_H149 zenon_H29 zenon_H114 zenon_H1d8 zenon_H26d zenon_H57 zenon_H26e zenon_H1a4 zenon_H151. % 19.02/19.19 apply (zenon_or_s _ _ zenon_H18c); [ zenon_intro zenon_H86 | zenon_intro zenon_H18d ]. % 19.02/19.19 exact (zenon_H177 zenon_H86). % 19.02/19.19 apply (zenon_or_s _ _ zenon_H18d); [ zenon_intro zenon_H110 | zenon_intro zenon_H18e ]. % 19.02/19.19 apply (zenon_L354_); trivial. % 19.02/19.19 apply (zenon_or_s _ _ zenon_H18e); [ zenon_intro zenon_H113 | zenon_intro zenon_Hd7 ]. % 19.02/19.19 exact (zenon_H114 zenon_H113). % 19.02/19.19 apply (zenon_L1083_); trivial. % 19.02/19.19 (* end of lemma zenon_L1285_ *) % 19.02/19.19 assert (zenon_L1286_ : (((op (e1) (e0)) = (e0))\/(((op (e1) (e1)) = (e0))\/(((op (e1) (e2)) = (e0))\/((op (e1) (e3)) = (e0))))) -> (~((op (e1) (e0)) = (op (e3) (e0)))) -> ((op (e3) (e2)) = (e2)) -> (~((op (e3) (e1)) = (op (e3) (e2)))) -> (~((op (e1) (e1)) = (op (e1) (e3)))) -> (~((op (e0) (e1)) = (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 (e1) (e3)) = (e2))) -> (~((op (e1) (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) (e1)) = (op (e2) (e2)))) -> (~((op (e2) (e1)) = (op (e2) (e3)))) -> (~((op (e2) (e1)) = (e2))) -> (~((op (e1) (e0)) = (e2))) -> (((op (e1) (e0)) = (e2))\/(((op (e1) (e1)) = (e2))\/(((op (e1) (e2)) = (e2))\/((op (e1) (e3)) = (e2))))) -> (~((e0) = (e2))) -> (((op (e0) (e1)) = (e0))\/(((op (e1) (e1)) = (e0))\/(((op (e2) (e1)) = (e0))\/((op (e3) (e1)) = (e0))))) -> (~((op (e1) (e1)) = (e1))) -> ((op (e0) (e3)) = (e2)) -> ((op (e0) (e2)) = (e3)) -> ((op (e2) (e2)) = (e0)) -> (~((e0) = (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))))) -> (~((e1) = (e2))) -> ((op (e2) (e0)) = (e2)) -> (~((op (e2) (e1)) = (op (e3) (e1)))) -> ((op (e1) (e2)) = (e1)) -> (~((op (e1) (e2)) = (op (e2) (e2)))) -> (((op (e3) (e3)) = (e0))\/(((op (e3) (e3)) = (e1))\/(((op (e3) (e3)) = (e2))\/((op (e3) (e3)) = (e3))))) -> (~((op (e3) (e0)) = (op (e3) (e3)))) -> ((op (e3) (e0)) = (e0)) -> (~((op (e2) (e3)) = (op (e3) (e3)))) -> (~((op (e3) (e3)) = (e3))) -> False). % 19.02/19.19 do 0 intro. intros zenon_H22 zenon_H1fa zenon_H151 zenon_H1a4 zenon_H57 zenon_H26d zenon_H1d8 zenon_H109 zenon_H14c zenon_H114 zenon_H17e zenon_H1cc zenon_H24b zenon_H1c7 zenon_H26e zenon_H177 zenon_H18c zenon_H149 zenon_H245 zenon_H10a zenon_Hcd zenon_Ha9 zenon_H2c zenon_Ha1 zenon_He8 zenon_H106 zenon_H7c zenon_Hee zenon_Haf zenon_Hf0 zenon_H2b zenon_H101 zenon_H71 zenon_H44 zenon_Hf3 zenon_H102. % 19.02/19.19 apply (zenon_or_s _ _ zenon_H22); [ zenon_intro zenon_H27 | zenon_intro zenon_H26 ]. % 19.02/19.19 apply (zenon_L312_); trivial. % 19.02/19.19 apply (zenon_or_s _ _ zenon_H26); [ zenon_intro zenon_H29 | zenon_intro zenon_H28 ]. % 19.02/19.19 apply (zenon_L1285_); trivial. % 19.02/19.19 apply (zenon_or_s _ _ zenon_H28); [ zenon_intro zenon_H2a | zenon_intro zenon_H1f ]. % 19.02/19.19 apply (zenon_L3_); trivial. % 19.02/19.19 apply (zenon_or_s _ _ zenon_H109); [ zenon_intro zenon_Ha0 | zenon_intro zenon_H10b ]. % 19.02/19.19 apply (zenon_L1262_); trivial. % 19.02/19.19 apply (zenon_or_s _ _ zenon_H10b); [ zenon_intro zenon_H10d | zenon_intro zenon_H10c ]. % 19.02/19.19 exact (zenon_H10a zenon_H10d). % 19.02/19.19 apply (zenon_or_s _ _ zenon_H10c); [ zenon_intro zenon_Ha5 | zenon_intro zenon_Hae ]. % 19.02/19.19 apply (zenon_L129_); trivial. % 19.02/19.19 apply (zenon_L65_); trivial. % 19.02/19.19 (* end of lemma zenon_L1286_ *) % 19.02/19.19 assert (zenon_L1287_ : (((op (e0) (e0)) = (e2))\/(((op (e0) (e1)) = (e2))\/(((op (e0) (e2)) = (e2))\/((op (e0) (e3)) = (e2))))) -> (~((op (e0) (e2)) = (e2))) -> (((op (e0) (e0)) = (e2))\/(((op (e1) (e0)) = (e2))\/(((op (e2) (e0)) = (e2))\/((op (e3) (e0)) = (e2))))) -> (~((op (e0) (e0)) = (e2))) -> (~((op (e3) (e3)) = (e3))) -> (~((op (e2) (e3)) = (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) (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))))) -> (((op (e3) (e0)) = (e1))\/(((op (e3) (e1)) = (e1))\/(((op (e3) (e2)) = (e1))\/((op (e3) (e3)) = (e1))))) -> (~((e0) = (e1))) -> ((op (e2) (e2)) = (e0)) -> ((op (e0) (e2)) = (e3)) -> (~((op (e1) (e1)) = (e1))) -> (((op (e0) (e1)) = (e0))\/(((op (e1) (e1)) = (e0))\/(((op (e2) (e1)) = (e0))\/((op (e3) (e1)) = (e0))))) -> (~((e0) = (e2))) -> (((op (e1) (e0)) = (e2))\/(((op (e1) (e1)) = (e2))\/(((op (e1) (e2)) = (e2))\/((op (e1) (e3)) = (e2))))) -> (~((op (e1) (e0)) = (e2))) -> (~((op (e2) (e1)) = (e2))) -> (~((op (e2) (e1)) = (op (e2) (e3)))) -> (~((op (e2) (e1)) = (op (e2) (e2)))) -> (((op (e2) (e1)) = (e0))\/(((op (e2) (e1)) = (e1))\/(((op (e2) (e1)) = (e2))\/((op (e2) (e1)) = (e3))))) -> (~((op (e0) (e1)) = (op (e2) (e1)))) -> (~((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)) = (e2))\/(((op (e1) (e1)) = (e2))\/(((op (e2) (e1)) = (e2))\/((op (e3) (e1)) = (e2))))) -> (~((op (e0) (e1)) = (e2))) -> (~((op (e1) (e1)) = (op (e1) (e3)))) -> (~((op (e3) (e1)) = (op (e3) (e2)))) -> ((op (e3) (e2)) = (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)) = (e2))) -> False). % 19.02/19.19 do 0 intro. intros zenon_H183 zenon_H1fd zenon_H1fe zenon_H80 zenon_H102 zenon_Hf3 zenon_H44 zenon_H71 zenon_H101 zenon_H2b zenon_Hf0 zenon_Haf zenon_H7c zenon_H106 zenon_He8 zenon_Ha1 zenon_H2c zenon_Ha9 zenon_H10a zenon_H245 zenon_H149 zenon_H18c zenon_H177 zenon_H26e zenon_H1c7 zenon_H24b zenon_H1cc zenon_H17e zenon_H114 zenon_H14c zenon_H109 zenon_H1d8 zenon_H26d zenon_H57 zenon_H1a4 zenon_H151 zenon_H1fa zenon_H22 zenon_H14b. % 19.02/19.19 apply (zenon_or_s _ _ zenon_H183); [ zenon_intro zenon_H7b | zenon_intro zenon_H186 ]. % 19.02/19.19 exact (zenon_H80 zenon_H7b). % 19.02/19.19 apply (zenon_or_s _ _ zenon_H186); [ zenon_intro zenon_H10f | zenon_intro zenon_H187 ]. % 19.02/19.19 exact (zenon_H26d zenon_H10f). % 19.02/19.19 apply (zenon_or_s _ _ zenon_H187); [ zenon_intro zenon_H150 | zenon_intro zenon_Hcd ]. % 19.02/19.19 exact (zenon_H1fd zenon_H150). % 19.02/19.19 apply (zenon_or_s _ _ zenon_H1fe); [ zenon_intro zenon_H7b | zenon_intro zenon_H1ff ]. % 19.02/19.19 exact (zenon_H80 zenon_H7b). % 19.02/19.19 apply (zenon_or_s _ _ zenon_H1ff); [ zenon_intro zenon_H86 | zenon_intro zenon_H200 ]. % 19.02/19.19 exact (zenon_H177 zenon_H86). % 19.02/19.19 apply (zenon_or_s _ _ zenon_H200); [ zenon_intro zenon_Hee | zenon_intro zenon_H148 ]. % 19.02/19.19 apply (zenon_L1286_); trivial. % 19.02/19.19 exact (zenon_H14b zenon_H148). % 19.02/19.19 (* end of lemma zenon_L1287_ *) % 19.02/19.19 assert (zenon_L1288_ : ((op (e3) (e1)) = (e1)) -> (((op (e3) (e0)) = (e0))\/(((op (e3) (e1)) = (e0))\/(((op (e3) (e2)) = (e0))\/((op (e3) (e3)) = (e0))))) -> (~((op (e3) (e3)) = (e3))) -> (~((op (e2) (e3)) = (op (e3) (e3)))) -> (~((op (e3) (e0)) = (op (e3) (e3)))) -> (((op (e3) (e3)) = (e0))\/(((op (e3) (e3)) = (e1))\/(((op (e3) (e3)) = (e2))\/((op (e3) (e3)) = (e3))))) -> (~((op (e1) (e2)) = (op (e2) (e2)))) -> ((op (e1) (e2)) = (e1)) -> (~((op (e2) (e1)) = (op (e3) (e1)))) -> ((op (e2) (e0)) = (e2)) -> (~((e1) = (e2))) -> (((op (e2) (e0)) = (e1))\/(((op (e2) (e1)) = (e1))\/(((op (e2) (e2)) = (e1))\/((op (e2) (e3)) = (e1))))) -> (((op (e3) (e0)) = (e1))\/(((op (e3) (e1)) = (e1))\/(((op (e3) (e2)) = (e1))\/((op (e3) (e3)) = (e1))))) -> (~((e0) = (e1))) -> ((op (e0) (e2)) = (e3)) -> ((op (e0) (e3)) = (e2)) -> (~((op (e1) (e1)) = (e1))) -> (((op (e0) (e1)) = (e0))\/(((op (e1) (e1)) = (e0))\/(((op (e2) (e1)) = (e0))\/((op (e3) (e1)) = (e0))))) -> (~((e0) = (e2))) -> (((op (e1) (e0)) = (e2))\/(((op (e1) (e1)) = (e2))\/(((op (e1) (e2)) = (e2))\/((op (e1) (e3)) = (e2))))) -> (~((op (e1) (e0)) = (e2))) -> (~((op (e0) (e1)) = (op (e2) (e1)))) -> (~((op (e1) (e2)) = (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)) = (e2))) -> (~((op (e1) (e1)) = (op (e1) (e3)))) -> (~((op (e3) (e1)) = (op (e3) (e2)))) -> ((op (e3) (e2)) = (e2)) -> (~((op (e1) (e0)) = (op (e3) (e0)))) -> (((op (e1) (e0)) = (e0))\/(((op (e1) (e1)) = (e0))\/(((op (e1) (e2)) = (e0))\/((op (e1) (e3)) = (e0))))) -> ((op (e1) (e1)) = (e2)) -> (~((op (e2) (e1)) = (e2))) -> (~((op (e2) (e1)) = (op (e2) (e3)))) -> (~((op (e2) (e1)) = (op (e2) (e2)))) -> (((op (e2) (e1)) = (e0))\/(((op (e2) (e1)) = (e1))\/(((op (e2) (e1)) = (e2))\/((op (e2) (e1)) = (e3))))) -> ((op (e2) (e2)) = (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 (e3) (e3)))) -> (~((op (e0) (e3)) = (op (e2) (e3)))) -> (((op (e1) (e3)) = (e0))\/(((op (e1) (e3)) = (e1))\/(((op (e1) (e3)) = (e2))\/((op (e1) (e3)) = (e3))))) -> (~((op (e1) (e3)) = (op (e3) (e3)))) -> (~((op (e1) (e3)) = (op (e2) (e3)))) -> (~((op (e1) (e3)) = (e2))) -> (~((op (e0) (e3)) = (op (e1) (e3)))) -> False). % 19.02/19.19 do 0 intro. intros zenon_Hae zenon_H1ac zenon_H102 zenon_Hf3 zenon_H71 zenon_H101 zenon_H2b zenon_Hf0 zenon_Haf zenon_Hee zenon_H7c zenon_H106 zenon_He8 zenon_Ha1 zenon_Ha9 zenon_Hcd zenon_H10a zenon_H245 zenon_H149 zenon_H18c zenon_H177 zenon_H17e zenon_H114 zenon_H109 zenon_H1d8 zenon_H26d zenon_H57 zenon_H1a4 zenon_H151 zenon_H1fa zenon_H22 zenon_H110 zenon_H26e zenon_H1c7 zenon_H24b zenon_H1cc zenon_H2c zenon_H18f zenon_He4 zenon_Hc2 zenon_He2 zenon_Hdf zenon_Hd5 zenon_Hdb zenon_H14c zenon_H1d. % 19.02/19.19 apply (zenon_or_s _ _ zenon_H106); [ zenon_intro zenon_Hed | zenon_intro zenon_H107 ]. % 19.02/19.19 apply (zenon_L58_); trivial. % 19.02/19.19 apply (zenon_or_s _ _ zenon_H107); [ zenon_intro zenon_Ha5 | zenon_intro zenon_H108 ]. % 19.02/19.19 apply (zenon_L42_); trivial. % 19.02/19.19 apply (zenon_or_s _ _ zenon_H108); [ zenon_intro zenon_Hf1 | zenon_intro zenon_Hf4 ]. % 19.02/19.19 apply (zenon_L59_); trivial. % 19.02/19.19 apply (zenon_or_s _ _ zenon_H1ac); [ zenon_intro zenon_H44 | zenon_intro zenon_H1af ]. % 19.02/19.19 apply (zenon_L1286_); trivial. % 19.02/19.19 apply (zenon_or_s _ _ zenon_H1af); [ zenon_intro zenon_H1b1 | zenon_intro zenon_H1b0 ]. % 19.02/19.19 apply (zenon_L1260_); trivial. % 19.02/19.19 apply (zenon_or_s _ _ zenon_H1b0); [ zenon_intro zenon_H61 | zenon_intro zenon_H60 ]. % 19.02/19.19 apply (zenon_L146_); trivial. % 19.02/19.19 apply (zenon_L1274_); trivial. % 19.02/19.19 (* end of lemma zenon_L1288_ *) % 19.02/19.19 assert (zenon_L1289_ : (((op (e2) (e3)) = (e0))\/(((op (e2) (e3)) = (e1))\/(((op (e2) (e3)) = (e2))\/((op (e2) (e3)) = (e3))))) -> ((op (e3) (e3)) = (e0)) -> (~((op (e2) (e3)) = (op (e3) (e3)))) -> (~((op (e2) (e0)) = (op (e2) (e3)))) -> ((op (e2) (e0)) = (e2)) -> (((op (e1) (e3)) = (e0))\/(((op (e1) (e3)) = (e1))\/(((op (e1) (e3)) = (e2))\/((op (e1) (e3)) = (e3))))) -> ((op (e1) (e0)) = (e0)) -> (~((op (e1) (e0)) = (op (e1) (e3)))) -> ((op (e3) (e3)) = (e1)) -> (~((op (e1) (e3)) = (op (e3) (e3)))) -> (~((op (e1) (e3)) = (e2))) -> (~((op (e1) (e3)) = (op (e2) (e3)))) -> False). % 19.02/19.19 do 0 intro. intros zenon_H11f zenon_H60 zenon_Hf3 zenon_H5b zenon_Hee zenon_Hdf zenon_H27 zenon_Hd8 zenon_Hc4 zenon_Hd5 zenon_H14c zenon_Hdb. % 19.02/19.19 apply (zenon_or_s _ _ zenon_H11f); [ zenon_intro zenon_H37 | zenon_intro zenon_H120 ]. % 19.02/19.19 apply (zenon_L219_); trivial. % 19.02/19.19 apply (zenon_or_s _ _ zenon_H120); [ zenon_intro zenon_Hf4 | zenon_intro zenon_H121 ]. % 19.02/19.19 apply (zenon_L60_); trivial. % 19.02/19.19 apply (zenon_or_s _ _ zenon_H121); [ zenon_intro zenon_H11d | zenon_intro zenon_Hdd ]. % 19.02/19.19 apply (zenon_L73_); trivial. % 19.02/19.19 apply (zenon_L1235_); trivial. % 19.02/19.19 (* end of lemma zenon_L1289_ *) % 19.02/19.19 assert (zenon_L1290_ : (~((op (e1) (e2)) = (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 (e0) (e3)) = (op (e2) (e3)))) -> (~((op (e0) (e3)) = (op (e3) (e3)))) -> (((op (e0) (e3)) = (e0))\/(((op (e0) (e3)) = (e1))\/(((op (e0) (e3)) = (e2))\/((op (e0) (e3)) = (e3))))) -> (~((op (e2) (e2)) = (op (e3) (e2)))) -> ((op (e2) (e2)) = (e0)) -> (((op (e2) (e1)) = (e0))\/(((op (e2) (e1)) = (e1))\/(((op (e2) (e1)) = (e2))\/((op (e2) (e1)) = (e3))))) -> (~((op (e2) (e1)) = (op (e2) (e2)))) -> (~((op (e2) (e1)) = (op (e2) (e3)))) -> (~((op (e2) (e1)) = (e2))) -> ((op (e1) (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 (e3) (e2)) = (e2)) -> (~((op (e3) (e1)) = (op (e3) (e2)))) -> (~((op (e1) (e1)) = (op (e1) (e3)))) -> (~((op (e0) (e1)) = (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 (e1) (e2)) = (e2))) -> (~((op (e0) (e1)) = (op (e2) (e1)))) -> (~((op (e1) (e0)) = (e2))) -> (((op (e1) (e0)) = (e2))\/(((op (e1) (e1)) = (e2))\/(((op (e1) (e2)) = (e2))\/((op (e1) (e3)) = (e2))))) -> (~((e0) = (e2))) -> (((op (e0) (e1)) = (e0))\/(((op (e1) (e1)) = (e0))\/(((op (e2) (e1)) = (e0))\/((op (e3) (e1)) = (e0))))) -> (~((op (e1) (e1)) = (e1))) -> ((op (e0) (e3)) = (e2)) -> ((op (e0) (e2)) = (e3)) -> (~((e0) = (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))))) -> (~((e1) = (e2))) -> (~((op (e2) (e1)) = (op (e3) (e1)))) -> (~((op (e1) (e2)) = (op (e2) (e2)))) -> (((op (e3) (e3)) = (e0))\/(((op (e3) (e3)) = (e1))\/(((op (e3) (e3)) = (e2))\/((op (e3) (e3)) = (e3))))) -> (~((op (e3) (e0)) = (op (e3) (e3)))) -> (~((op (e3) (e3)) = (e3))) -> (((op (e3) (e0)) = (e0))\/(((op (e3) (e1)) = (e0))\/(((op (e3) (e2)) = (e0))\/((op (e3) (e3)) = (e0))))) -> ((op (e1) (e2)) = (e1)) -> (~((op (e1) (e2)) = (op (e3) (e2)))) -> (((op (e2) (e3)) = (e0))\/(((op (e2) (e3)) = (e1))\/(((op (e2) (e3)) = (e2))\/((op (e2) (e3)) = (e3))))) -> ((op (e3) (e3)) = (e0)) -> (~((op (e2) (e3)) = (op (e3) (e3)))) -> (~((op (e2) (e0)) = (op (e2) (e3)))) -> ((op (e2) (e0)) = (e2)) -> (((op (e1) (e3)) = (e0))\/(((op (e1) (e3)) = (e1))\/(((op (e1) (e3)) = (e2))\/((op (e1) (e3)) = (e3))))) -> ((op (e1) (e0)) = (e0)) -> (~((op (e1) (e0)) = (op (e1) (e3)))) -> (~((op (e1) (e3)) = (op (e3) (e3)))) -> (~((op (e1) (e3)) = (e2))) -> (~((op (e1) (e3)) = (op (e2) (e3)))) -> False). % 19.02/19.19 do 0 intro. intros zenon_H124 zenon_H133 zenon_H1d zenon_He2 zenon_Hc2 zenon_He4 zenon_H18f zenon_H2c zenon_H1cc zenon_H24b zenon_H1c7 zenon_H26e zenon_H110 zenon_H22 zenon_H1fa zenon_H151 zenon_H1a4 zenon_H57 zenon_H26d zenon_H1d8 zenon_H109 zenon_H114 zenon_H17e zenon_H177 zenon_H18c zenon_H149 zenon_H245 zenon_H10a zenon_Hcd zenon_Ha9 zenon_Ha1 zenon_He8 zenon_H106 zenon_H7c zenon_Haf zenon_H2b zenon_H101 zenon_H71 zenon_H102 zenon_H1ac zenon_Hf0 zenon_H115 zenon_H11f zenon_H60 zenon_Hf3 zenon_H5b zenon_Hee zenon_Hdf zenon_H27 zenon_Hd8 zenon_Hd5 zenon_H14c zenon_Hdb. % 19.02/19.19 apply (zenon_or_s _ _ zenon_He8); [ zenon_intro zenon_Hac | zenon_intro zenon_Heb ]. % 19.02/19.19 apply (zenon_L230_); trivial. % 19.02/19.19 apply (zenon_or_s _ _ zenon_Heb); [ zenon_intro zenon_Hae | zenon_intro zenon_Hec ]. % 19.02/19.19 apply (zenon_L1288_); trivial. % 19.02/19.19 apply (zenon_or_s _ _ zenon_Hec); [ zenon_intro zenon_Hba | zenon_intro zenon_Hc4 ]. % 19.02/19.19 apply (zenon_L69_); trivial. % 19.02/19.19 apply (zenon_L1289_); trivial. % 19.02/19.19 (* end of lemma zenon_L1290_ *) % 19.02/19.19 assert (zenon_L1291_ : (((op (e2) (e0)) = (e1))\/(((op (e2) (e1)) = (e1))\/(((op (e2) (e2)) = (e1))\/((op (e2) (e3)) = (e1))))) -> ((op (e0) (e0)) = (e1)) -> (~((op (e0) (e0)) = (op (e2) (e0)))) -> (~((op (e2) (e1)) = (op (e3) (e1)))) -> ((op (e1) (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 (e3) (e3)) = (e3))) -> (~((op (e3) (e3)) = (e2))) -> ((op (e3) (e1)) = (e1)) -> (~((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 (e1) (e1)) = (e2)) -> (~((op (e2) (e1)) = (e2))) -> (~((op (e2) (e1)) = (op (e2) (e3)))) -> (~((op (e2) (e1)) = (op (e2) (e2)))) -> (((op (e2) (e1)) = (e0))\/(((op (e2) (e1)) = (e1))\/(((op (e2) (e1)) = (e2))\/((op (e2) (e1)) = (e3))))) -> ((op (e2) (e2)) = (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 (e3) (e3)))) -> (~((op (e0) (e3)) = (op (e2) (e3)))) -> (((op (e1) (e3)) = (e0))\/(((op (e1) (e3)) = (e1))\/(((op (e1) (e3)) = (e2))\/((op (e1) (e3)) = (e3))))) -> (~((op (e1) (e3)) = (op (e3) (e3)))) -> (~((op (e1) (e3)) = (op (e2) (e3)))) -> (~((op (e1) (e3)) = (e2))) -> (~((op (e0) (e3)) = (op (e1) (e3)))) -> False). % 19.02/19.19 do 0 intro. intros zenon_H106 zenon_H7a zenon_H39 zenon_Haf zenon_Hf0 zenon_H2b zenon_H1ac zenon_H102 zenon_Hf7 zenon_Hae zenon_H130 zenon_H71 zenon_H101 zenon_H110 zenon_H26e zenon_H1c7 zenon_H24b zenon_H1cc zenon_H2c zenon_H18f zenon_He4 zenon_Hc2 zenon_He2 zenon_Hdf zenon_Hd5 zenon_Hdb zenon_H14c zenon_H1d. % 19.02/19.19 apply (zenon_or_s _ _ zenon_H106); [ zenon_intro zenon_Hed | zenon_intro zenon_H107 ]. % 19.02/19.19 apply (zenon_L134_); trivial. % 19.02/19.19 apply (zenon_or_s _ _ zenon_H107); [ zenon_intro zenon_Ha5 | zenon_intro zenon_H108 ]. % 19.02/19.19 apply (zenon_L42_); trivial. % 19.02/19.19 apply (zenon_or_s _ _ zenon_H108); [ zenon_intro zenon_Hf1 | zenon_intro zenon_Hf4 ]. % 19.02/19.19 apply (zenon_L59_); trivial. % 19.02/19.19 apply (zenon_or_s _ _ zenon_H1ac); [ zenon_intro zenon_H44 | zenon_intro zenon_H1af ]. % 19.02/19.19 apply (zenon_L1210_); trivial. % 19.02/19.19 apply (zenon_or_s _ _ zenon_H1af); [ zenon_intro zenon_H1b1 | zenon_intro zenon_H1b0 ]. % 19.02/19.19 apply (zenon_L1260_); trivial. % 19.02/19.19 apply (zenon_or_s _ _ zenon_H1b0); [ zenon_intro zenon_H61 | zenon_intro zenon_H60 ]. % 19.02/19.19 apply (zenon_L146_); trivial. % 19.02/19.19 apply (zenon_L1274_); trivial. % 19.02/19.19 (* end of lemma zenon_L1291_ *) % 19.02/19.19 assert (zenon_L1292_ : (((op (e3) (e0)) = (e1))\/(((op (e3) (e1)) = (e1))\/(((op (e3) (e2)) = (e1))\/((op (e3) (e3)) = (e1))))) -> ((op (e0) (e3)) = (e2)) -> (~((op (e1) (e2)) = (op (e1) (e3)))) -> (~((e1) = (e2))) -> (((op (e0) (e3)) = (e1))\/(((op (e1) (e3)) = (e1))\/(((op (e2) (e3)) = (e1))\/((op (e3) (e3)) = (e1))))) -> (~((op (e0) (e3)) = (op (e1) (e3)))) -> (~((op (e0) (e3)) = (op (e2) (e3)))) -> (~((op (e0) (e3)) = (op (e3) (e3)))) -> (((op (e0) (e3)) = (e0))\/(((op (e0) (e3)) = (e1))\/(((op (e0) (e3)) = (e2))\/((op (e0) (e3)) = (e3))))) -> (~((op (e2) (e2)) = (op (e3) (e2)))) -> (((op (e2) (e1)) = (e0))\/(((op (e2) (e1)) = (e1))\/(((op (e2) (e1)) = (e2))\/((op (e2) (e1)) = (e3))))) -> (~((op (e2) (e1)) = (op (e2) (e2)))) -> (~((op (e2) (e1)) = (op (e2) (e3)))) -> (~((op (e2) (e1)) = (e2))) -> ((op (e1) (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 (e3) (e3)) = (e2))) -> (~((op (e3) (e3)) = (e3))) -> (((op (e3) (e0)) = (e0))\/(((op (e3) (e1)) = (e0))\/(((op (e3) (e2)) = (e0))\/((op (e3) (e3)) = (e0))))) -> (~((op (e1) (e2)) = (op (e2) (e2)))) -> ((op (e1) (e2)) = (e1)) -> (~((op (e2) (e1)) = (op (e3) (e1)))) -> (~((op (e0) (e0)) = (op (e2) (e0)))) -> ((op (e0) (e0)) = (e1)) -> (((op (e2) (e0)) = (e1))\/(((op (e2) (e1)) = (e1))\/(((op (e2) (e2)) = (e1))\/((op (e2) (e3)) = (e1))))) -> ((op (e2) (e2)) = (e0)) -> ((op (e0) (e2)) = (e3)) -> (((op (e2) (e3)) = (e0))\/(((op (e2) (e3)) = (e1))\/(((op (e2) (e3)) = (e2))\/((op (e2) (e3)) = (e3))))) -> ((op (e3) (e3)) = (e0)) -> (~((op (e2) (e3)) = (op (e3) (e3)))) -> (~((op (e2) (e0)) = (op (e2) (e3)))) -> ((op (e2) (e0)) = (e2)) -> (((op (e1) (e3)) = (e0))\/(((op (e1) (e3)) = (e1))\/(((op (e1) (e3)) = (e2))\/((op (e1) (e3)) = (e3))))) -> ((op (e1) (e0)) = (e0)) -> (~((op (e1) (e0)) = (op (e1) (e3)))) -> (~((op (e1) (e3)) = (op (e3) (e3)))) -> (~((op (e1) (e3)) = (e2))) -> (~((op (e1) (e3)) = (op (e2) (e3)))) -> False). % 19.02/19.19 do 0 intro. intros zenon_He8 zenon_Hcd zenon_H124 zenon_H7c zenon_H133 zenon_H1d zenon_He2 zenon_Hc2 zenon_He4 zenon_H18f zenon_H1cc zenon_H24b zenon_H1c7 zenon_H26e zenon_H110 zenon_H101 zenon_H71 zenon_H130 zenon_Hf7 zenon_H102 zenon_H1ac zenon_H2b zenon_Hf0 zenon_Haf zenon_H39 zenon_H7a zenon_H106 zenon_H2c zenon_Ha9 zenon_H11f zenon_H60 zenon_Hf3 zenon_H5b zenon_Hee zenon_Hdf zenon_H27 zenon_Hd8 zenon_Hd5 zenon_H14c zenon_Hdb. % 19.02/19.19 apply (zenon_or_s _ _ zenon_He8); [ zenon_intro zenon_Hac | zenon_intro zenon_Heb ]. % 19.02/19.19 apply (zenon_L230_); trivial. % 19.02/19.19 apply (zenon_or_s _ _ zenon_Heb); [ zenon_intro zenon_Hae | zenon_intro zenon_Hec ]. % 19.02/19.19 apply (zenon_L1291_); trivial. % 19.02/19.19 apply (zenon_or_s _ _ zenon_Hec); [ zenon_intro zenon_Hba | zenon_intro zenon_Hc4 ]. % 19.02/19.19 apply (zenon_L45_); trivial. % 19.02/19.19 apply (zenon_L1289_); trivial. % 19.02/19.19 (* end of lemma zenon_L1292_ *) % 19.02/19.19 assert (zenon_L1293_ : ((~((op (e2) (e0)) = (e2)))\/((op (e2) (e2)) = (e0))) -> (~((op (e1) (e2)) = (op (e2) (e2)))) -> (((op (e0) (e0)) = (e2))\/(((op (e0) (e1)) = (e2))\/(((op (e0) (e2)) = (e2))\/((op (e0) (e3)) = (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 (e0) (e2)) = (e2))) -> (~((op (e0) (e1)) = (e2))) -> (~((op (e0) (e0)) = (e2))) -> ((op (e1) (e2)) = (e0)) -> ((op (e0) (e2)) = (e3)) -> ((~((op (e2) (e1)) = (e2)))\/((op (e2) (e2)) = (e1))) -> False). % 19.02/19.19 do 0 intro. intros zenon_H276 zenon_H2b zenon_H183 zenon_H173 zenon_He2 zenon_H1d5 zenon_H1fd zenon_H26d zenon_H80 zenon_H2a zenon_Ha9 zenon_H271. % 19.02/19.19 apply (zenon_or_s _ _ zenon_H276); [ zenon_intro zenon_Hef | zenon_intro zenon_H2c ]. % 19.02/19.19 apply (zenon_or_s _ _ zenon_H271); [ zenon_intro zenon_H26e | zenon_intro zenon_Hf1 ]. % 19.02/19.19 apply (zenon_L1050_); trivial. % 19.02/19.19 apply (zenon_L184_); trivial. % 19.02/19.19 apply (zenon_L3_); trivial. % 19.02/19.19 (* end of lemma zenon_L1293_ *) % 19.02/19.19 assert (zenon_L1294_ : (~((op (e0) (e0)) = (op (e2) (e0)))) -> (~((op (e3) (e1)) = (op (e3) (e3)))) -> ((~((op (e0) (e3)) = (e2)))\/((op (e0) (e2)) = (e3))) -> ((~((op (e1) (e3)) = (e2)))\/((op (e1) (e2)) = (e3))) -> (~((op (e0) (e2)) = (op (e2) (e2)))) -> ((~((op (e2) (e0)) = (e2)))\/((op (e2) (e2)) = (e0))) -> (~((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)) = (e2))\/(((op (e1) (e2)) = (e2))\/(((op (e2) (e2)) = (e2))\/((op (e3) (e2)) = (e2))))) -> ((~((op (e3) (e3)) = (e2)))\/((op (e3) (e2)) = (e3))) -> ((~((op (e2) (e3)) = (e2)))\/((op (e2) (e2)) = (e3))) -> (~((op (e0) (e0)) = (op (e0) (e2)))) -> ((~((op (e1) (e2)) = (e2)))\/((op (e1) (e2)) = (e2))) -> (((op (e0) (e0)) = (e0))\/(((op (e0) (e0)) = (e1))\/(((op (e0) (e0)) = (e2))\/((op (e0) (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)) = (e3))\/(((op (e0) (e1)) = (e3))\/(((op (e0) (e2)) = (e3))\/((op (e0) (e3)) = (e3))))) -> (~((e1) = (e3))) -> (((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 (e1) (e0)) = (op (e2) (e0)))) -> (~((op (e0) (e2)) = (op (e1) (e2)))) -> (((op (e1) (e0)) = (e1))\/(((op (e1) (e1)) = (e1))\/(((op (e1) (e2)) = (e1))\/((op (e1) (e3)) = (e1))))) -> (~((op (e2) (e0)) = (op (e2) (e1)))) -> (~((op (e2) (e0)) = (op (e3) (e0)))) -> (~((op (e1) (e0)) = (op (e1) (e2)))) -> (~((e2) = (e3))) -> (((op (e0) (e0)) = (e0))\/(((op (e0) (e1)) = (e0))\/(((op (e0) (e2)) = (e0))\/((op (e0) (e3)) = (e0))))) -> ((~((op (e1) (e1)) = (e2)))\/((op (e1) (e2)) = (e1))) -> (~((op (e0) (e2)) = (op (e3) (e2)))) -> (~((op (e0) (e1)) = (op (e0) (e2)))) -> (((op (e0) (e0)) = (e1))\/(((op (e1) (e0)) = (e1))\/(((op (e2) (e0)) = (e1))\/((op (e3) (e0)) = (e1))))) -> ((~((op (e1) (e0)) = (e2)))\/((op (e1) (e2)) = (e0))) -> (((op (e0) (e0)) = (e1))\/(((op (e0) (e1)) = (e1))\/(((op (e0) (e2)) = (e1))\/((op (e0) (e3)) = (e1))))) -> ((~((op (e3) (e1)) = (e2)))\/((op (e3) (e2)) = (e1))) -> (~((op (e1) (e0)) = (e2))) -> (~((op (e1) (e0)) = (op (e3) (e0)))) -> (((op (e0) (e3)) = (e0))\/(((op (e0) (e3)) = (e1))\/(((op (e0) (e3)) = (e2))\/((op (e0) (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 (e3) (e0)) = (e2))\/(((op (e3) (e1)) = (e2))\/(((op (e3) (e2)) = (e2))\/((op (e3) (e3)) = (e2))))) -> (~((op (e0) (e3)) = (op (e1) (e3)))) -> (((op (e0) (e3)) = (e0))\/(((op (e1) (e3)) = (e0))\/(((op (e2) (e3)) = (e0))\/((op (e3) (e3)) = (e0))))) -> ((op (e0) (e2)) = (e3)) -> (~((op (e0) (e3)) = (op (e3) (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) (e3)) = (e0))\/(((op (e3) (e3)) = (e1))\/(((op (e3) (e3)) = (e2))\/((op (e3) (e3)) = (e3))))) -> (~((op (e3) (e0)) = (op (e3) (e3)))) -> (~((op (e0) (e1)) = (op (e0) (e3)))) -> (~((op (e1) (e0)) = (op (e1) (e1)))) -> (~((op (e2) (e0)) = (op (e2) (e2)))) -> (((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 (e2) (e2)) = (op (e2) (e3)))) -> (((op (e0) (e0)) = (e2))\/(((op (e1) (e0)) = (e2))\/(((op (e2) (e0)) = (e2))\/((op (e3) (e0)) = (e2))))) -> (((op (e0) (e3)) = (e1))\/(((op (e1) (e3)) = (e1))\/(((op (e2) (e3)) = (e1))\/((op (e3) (e3)) = (e1))))) -> (~((e0) = (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) (e3)) = (op (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) (e0)) = (op (e1) (e3)))) -> (~((op (e3) (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 (e2) (e1)) = (op (e3) (e1)))) -> (((op (e0) (e1)) = (e1))\/(((op (e1) (e1)) = (e1))\/(((op (e2) (e1)) = (e1))\/((op (e3) (e1)) = (e1))))) -> (~((op (e1) (e1)) = (e1))) -> (~((e0) = (e1))) -> (((op (e1) (e0)) = (e2))\/(((op (e1) (e1)) = (e2))\/(((op (e1) (e2)) = (e2))\/((op (e1) (e3)) = (e2))))) -> (~((e0) = (e2))) -> (~((op (e2) (e1)) = (op (e2) (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) (e1)) = (op (e2) (e3)))) -> (((op (e2) (e0)) = (e1))\/(((op (e2) (e1)) = (e1))\/(((op (e2) (e2)) = (e1))\/((op (e2) (e3)) = (e1))))) -> (((op (e0) (e1)) = (e0))\/(((op (e1) (e1)) = (e0))\/(((op (e2) (e1)) = (e0))\/((op (e3) (e1)) = (e0))))) -> (~((op (e0) (e0)) = (e0))) -> (~((op (e2) (e0)) = (op (e2) (e3)))) -> (~((op (e1) (e2)) = (op (e3) (e2)))) -> (~((op (e1) (e1)) = (op (e1) (e3)))) -> (~((op (e3) (e1)) = (op (e3) (e2)))) -> (((op (e0) (e1)) = (e2))\/(((op (e1) (e1)) = (e2))\/(((op (e2) (e1)) = (e2))\/((op (e3) (e1)) = (e2))))) -> ((~((op (e3) (e2)) = (e2)))\/((op (e3) (e2)) = (e2))) -> ((~((op (e3) (e0)) = (e2)))\/((op (e3) (e2)) = (e0))) -> (((op (e0) (e0)) = (e2))\/(((op (e0) (e1)) = (e2))\/(((op (e0) (e2)) = (e2))\/((op (e0) (e3)) = (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 (e0) (e2)) = (e2))) -> (~((op (e0) (e1)) = (e2))) -> (~((op (e0) (e0)) = (e2))) -> (~((op (e1) (e2)) = (op (e2) (e2)))) -> ((op (e1) (e2)) = (e1)) -> ((~((op (e2) (e1)) = (e2)))\/((op (e2) (e2)) = (e1))) -> False). % 19.02/19.19 do 0 intro. intros zenon_H39 zenon_H130 zenon_H27c zenon_H279 zenon_Ha8 zenon_H276 zenon_H62 zenon_H145 zenon_H172 zenon_H278 zenon_H277 zenon_H13c zenon_H275 zenon_H26a zenon_H4f zenon_H142 zenon_H168 zenon_H95 zenon_H2f zenon_H259 zenon_H201 zenon_H195 zenon_H128 zenon_H1f0 zenon_H17b zenon_H24a zenon_H12b zenon_H74 zenon_H27b zenon_H14f zenon_H4a zenon_H235 zenon_H27a zenon_H22d zenon_H26f zenon_H177 zenon_H1fa zenon_He4 zenon_H1ac zenon_H18f zenon_H153 zenon_H1d zenon_H67 zenon_Ha9 zenon_Hc2 zenon_He8 zenon_H1cf zenon_H101 zenon_H71 zenon_H54 zenon_H45 zenon_H52 zenon_H22 zenon_H3e zenon_H6d zenon_H1fe zenon_H133 zenon_H9a zenon_H11f zenon_Hdb zenon_Hf3 zenon_Hdf zenon_Hd5 zenon_Hd8 zenon_H102 zenon_H136 zenon_H124 zenon_Haf zenon_H109 zenon_H10a zenon_Ha1 zenon_H18c zenon_H149 zenon_H24b zenon_H7c zenon_H17e zenon_H1cc zenon_H1c7 zenon_H106 zenon_H245 zenon_H3f zenon_H5b zenon_H115 zenon_H57 zenon_H1a4 zenon_H1d8 zenon_H273 zenon_H270 zenon_H183 zenon_H173 zenon_He2 zenon_H1d5 zenon_H1fd zenon_H26d zenon_H80 zenon_H2b zenon_Hf0 zenon_H271. % 19.02/19.19 apply (zenon_or_s _ _ zenon_H275); [ zenon_intro zenon_H114 | zenon_intro zenon_H113 ]. % 19.02/19.19 apply (zenon_or_s _ _ zenon_H279); [ zenon_intro zenon_H14c | zenon_intro zenon_H16c ]. % 19.02/19.19 apply (zenon_or_s _ _ zenon_H276); [ zenon_intro zenon_Hef | zenon_intro zenon_H2c ]. % 19.02/19.19 apply (zenon_L1205_); trivial. % 19.02/19.19 apply (zenon_or_s _ _ zenon_H271); [ zenon_intro zenon_H26e | zenon_intro zenon_Hf1 ]. % 19.02/19.19 apply (zenon_or_s _ _ zenon_H277); [ zenon_intro zenon_H274 | zenon_intro zenon_Haa ]. % 19.02/19.19 apply (zenon_or_s _ _ zenon_H270); [ zenon_intro zenon_H14b | zenon_intro zenon_H61 ]. % 19.02/19.19 apply (zenon_or_s _ _ zenon_H26f); [ zenon_intro zenon_H194 | zenon_intro zenon_Hba ]. % 19.02/19.19 apply (zenon_or_s _ _ zenon_H273); [ zenon_intro zenon_H272 | zenon_intro zenon_H151 ]. % 19.02/19.19 apply (zenon_L1284_); trivial. % 19.02/19.19 apply (zenon_or_s _ _ zenon_H3e); [ zenon_intro zenon_H42 | zenon_intro zenon_H41 ]. % 19.02/19.19 exact (zenon_H3f zenon_H42). % 19.02/19.19 apply (zenon_or_s _ _ zenon_H41); [ zenon_intro zenon_H27 | zenon_intro zenon_H43 ]. % 19.02/19.19 apply (zenon_or_s _ _ zenon_H183); [ zenon_intro zenon_H7b | zenon_intro zenon_H186 ]. % 19.02/19.19 exact (zenon_H80 zenon_H7b). % 19.02/19.19 apply (zenon_or_s _ _ zenon_H186); [ zenon_intro zenon_H10f | zenon_intro zenon_H187 ]. % 19.02/19.19 exact (zenon_H26d zenon_H10f). % 19.02/19.19 apply (zenon_or_s _ _ zenon_H187); [ zenon_intro zenon_H150 | zenon_intro zenon_Hcd ]. % 19.02/19.19 exact (zenon_H1fd zenon_H150). % 19.02/19.19 apply (zenon_or_s _ _ zenon_H1fe); [ zenon_intro zenon_H7b | zenon_intro zenon_H1ff ]. % 19.02/19.19 exact (zenon_H80 zenon_H7b). % 19.02/19.19 apply (zenon_or_s _ _ zenon_H1ff); [ zenon_intro zenon_H86 | zenon_intro zenon_H200 ]. % 19.02/19.19 exact (zenon_H177 zenon_H86). % 19.02/19.19 apply (zenon_or_s _ _ zenon_H200); [ zenon_intro zenon_Hee | zenon_intro zenon_H148 ]. % 19.02/19.19 apply (zenon_or_s _ _ zenon_H18c); [ zenon_intro zenon_H86 | zenon_intro zenon_H18d ]. % 19.02/19.19 exact (zenon_H177 zenon_H86). % 19.02/19.19 apply (zenon_or_s _ _ zenon_H18d); [ zenon_intro zenon_H110 | zenon_intro zenon_H18e ]. % 19.02/19.19 apply (zenon_or_s _ _ zenon_H1ac); [ zenon_intro zenon_H44 | zenon_intro zenon_H1af ]. % 19.02/19.19 apply (zenon_L1287_); trivial. % 19.02/19.19 apply (zenon_or_s _ _ zenon_H1af); [ zenon_intro zenon_H1b1 | zenon_intro zenon_H1b0 ]. % 19.02/19.19 apply (zenon_or_s _ _ zenon_H67); [ zenon_intro zenon_H1e | zenon_intro zenon_H68 ]. % 19.02/19.19 apply (zenon_L1267_); trivial. % 19.02/19.19 apply (zenon_or_s _ _ zenon_H68); [ zenon_intro zenon_H1f | zenon_intro zenon_H69 ]. % 19.02/19.19 apply (zenon_L258_); trivial. % 19.02/19.19 apply (zenon_or_s _ _ zenon_H69); [ zenon_intro zenon_H37 | zenon_intro zenon_H60 ]. % 19.02/19.19 apply (zenon_L18_); trivial. % 19.02/19.19 apply (zenon_L1290_); trivial. % 19.02/19.19 apply (zenon_or_s _ _ zenon_H1b0); [ zenon_intro zenon_H61 | zenon_intro zenon_H60 ]. % 19.02/19.19 apply (zenon_L146_); trivial. % 19.02/19.19 apply (zenon_L1290_); trivial. % 19.02/19.19 apply (zenon_or_s _ _ zenon_H18e); [ zenon_intro zenon_H113 | zenon_intro zenon_Hd7 ]. % 19.02/19.19 exact (zenon_H114 zenon_H113). % 19.02/19.19 exact (zenon_H14c zenon_Hd7). % 19.02/19.19 exact (zenon_H14b zenon_H148). % 19.02/19.19 apply (zenon_or_s _ _ zenon_H43); [ zenon_intro zenon_H34 | zenon_intro zenon_H44 ]. % 19.02/19.19 apply (zenon_L11_); trivial. % 19.02/19.19 apply (zenon_L1287_); trivial. % 19.02/19.19 apply (zenon_L69_); trivial. % 19.02/19.19 apply (zenon_L146_); trivial. % 19.02/19.19 apply (zenon_or_s _ _ zenon_H270); [ zenon_intro zenon_H14b | zenon_intro zenon_H61 ]. % 19.02/19.19 apply (zenon_or_s _ _ zenon_H278); [ zenon_intro zenon_Hf7 | zenon_intro zenon_H163 ]. % 19.02/19.19 apply (zenon_or_s _ _ zenon_H74); [ zenon_intro zenon_H42 | zenon_intro zenon_H77 ]. % 19.02/19.19 exact (zenon_H3f zenon_H42). % 19.02/19.19 apply (zenon_or_s _ _ zenon_H77); [ zenon_intro zenon_H49 | zenon_intro zenon_H78 ]. % 19.02/19.19 apply (zenon_or_s _ _ zenon_H3e); [ zenon_intro zenon_H42 | zenon_intro zenon_H41 ]. % 19.02/19.19 exact (zenon_H3f zenon_H42). % 19.02/19.19 apply (zenon_or_s _ _ zenon_H41); [ zenon_intro zenon_H27 | zenon_intro zenon_H43 ]. % 19.02/19.19 apply (zenon_or_s _ _ zenon_H22d); [ zenon_intro zenon_H7a | zenon_intro zenon_H22e ]. % 19.02/19.19 apply (zenon_or_s _ _ zenon_H183); [ zenon_intro zenon_H7b | zenon_intro zenon_H186 ]. % 19.02/19.19 exact (zenon_H80 zenon_H7b). % 19.02/19.19 apply (zenon_or_s _ _ zenon_H186); [ zenon_intro zenon_H10f | zenon_intro zenon_H187 ]. % 19.02/19.19 exact (zenon_H26d zenon_H10f). % 19.02/19.19 apply (zenon_or_s _ _ zenon_H187); [ zenon_intro zenon_H150 | zenon_intro zenon_Hcd ]. % 19.02/19.19 exact (zenon_H1fd zenon_H150). % 19.02/19.19 apply (zenon_or_s _ _ zenon_H1fe); [ zenon_intro zenon_H7b | zenon_intro zenon_H1ff ]. % 19.02/19.19 exact (zenon_H80 zenon_H7b). % 19.02/19.19 apply (zenon_or_s _ _ zenon_H1ff); [ zenon_intro zenon_H86 | zenon_intro zenon_H200 ]. % 19.02/19.19 exact (zenon_H177 zenon_H86). % 19.02/19.19 apply (zenon_or_s _ _ zenon_H200); [ zenon_intro zenon_Hee | zenon_intro zenon_H148 ]. % 19.02/19.19 apply (zenon_or_s _ _ zenon_H18c); [ zenon_intro zenon_H86 | zenon_intro zenon_H18d ]. % 19.02/19.19 exact (zenon_H177 zenon_H86). % 19.02/19.19 apply (zenon_or_s _ _ zenon_H18d); [ zenon_intro zenon_H110 | zenon_intro zenon_H18e ]. % 19.02/19.19 apply (zenon_or_s _ _ zenon_H67); [ zenon_intro zenon_H1e | zenon_intro zenon_H68 ]. % 19.02/19.19 apply (zenon_L1061_); trivial. % 19.02/19.19 apply (zenon_or_s _ _ zenon_H68); [ zenon_intro zenon_H1f | zenon_intro zenon_H69 ]. % 19.02/19.19 apply (zenon_L258_); trivial. % 19.02/19.19 apply (zenon_or_s _ _ zenon_H69); [ zenon_intro zenon_H37 | zenon_intro zenon_H60 ]. % 19.02/19.19 apply (zenon_L18_); trivial. % 19.02/19.19 apply (zenon_L1292_); trivial. % 19.02/19.19 apply (zenon_or_s _ _ zenon_H18e); [ zenon_intro zenon_H113 | zenon_intro zenon_Hd7 ]. % 19.02/19.19 exact (zenon_H114 zenon_H113). % 19.02/19.19 exact (zenon_H14c zenon_Hd7). % 19.02/19.19 exact (zenon_H14b zenon_H148). % 19.02/19.19 apply (zenon_or_s _ _ zenon_H22e); [ zenon_intro zenon_Ha0 | zenon_intro zenon_H22f ]. % 19.02/19.19 apply (zenon_L38_); trivial. % 19.02/19.19 apply (zenon_or_s _ _ zenon_H22f); [ zenon_intro zenon_H122 | zenon_intro zenon_Hc3 ]. % 19.02/19.19 apply (zenon_L1256_); trivial. % 19.02/19.19 apply (zenon_L1060_); trivial. % 19.02/19.19 apply (zenon_or_s _ _ zenon_H43); [ zenon_intro zenon_H34 | zenon_intro zenon_H44 ]. % 19.02/19.19 apply (zenon_L11_); trivial. % 19.02/19.19 apply (zenon_or_s _ _ zenon_H183); [ zenon_intro zenon_H7b | zenon_intro zenon_H186 ]. % 19.02/19.19 exact (zenon_H80 zenon_H7b). % 19.02/19.19 apply (zenon_or_s _ _ zenon_H186); [ zenon_intro zenon_H10f | zenon_intro zenon_H187 ]. % 19.02/19.19 exact (zenon_H26d zenon_H10f). % 19.02/19.19 apply (zenon_or_s _ _ zenon_H187); [ zenon_intro zenon_H150 | zenon_intro zenon_Hcd ]. % 19.02/19.19 exact (zenon_H1fd zenon_H150). % 19.02/19.19 apply (zenon_or_s _ _ zenon_H22); [ zenon_intro zenon_H27 | zenon_intro zenon_H26 ]. % 19.02/19.19 apply (zenon_L312_); trivial. % 19.02/19.19 apply (zenon_or_s _ _ zenon_H26); [ zenon_intro zenon_H29 | zenon_intro zenon_H28 ]. % 19.02/19.19 apply (zenon_L1259_); trivial. % 19.02/19.19 apply (zenon_or_s _ _ zenon_H28); [ zenon_intro zenon_H2a | zenon_intro zenon_H1f ]. % 19.02/19.19 apply (zenon_L1293_); trivial. % 19.02/19.19 apply (zenon_or_s _ _ zenon_He8); [ zenon_intro zenon_Hac | zenon_intro zenon_Heb ]. % 19.02/19.19 apply (zenon_L41_); trivial. % 19.02/19.19 apply (zenon_or_s _ _ zenon_Heb); [ zenon_intro zenon_Hae | zenon_intro zenon_Hec ]. % 19.02/19.19 apply (zenon_L1210_); trivial. % 19.02/19.19 apply (zenon_or_s _ _ zenon_Hec); [ zenon_intro zenon_Hba | zenon_intro zenon_Hc4 ]. % 19.02/19.19 apply (zenon_L45_); trivial. % 19.02/19.19 apply (zenon_L49_); trivial. % 19.02/19.19 apply (zenon_or_s _ _ zenon_H78); [ zenon_intro zenon_H48 | zenon_intro zenon_H1e ]. % 19.02/19.19 apply (zenon_L679_); trivial. % 19.02/19.19 apply (zenon_L1061_); trivial. % 19.02/19.19 apply (zenon_L180_); trivial. % 19.02/19.19 apply (zenon_L146_); trivial. % 19.02/19.19 apply (zenon_L59_); trivial. % 19.02/19.19 apply (zenon_L167_); trivial. % 19.02/19.19 apply (zenon_L68_); trivial. % 19.02/19.19 (* end of lemma zenon_L1294_ *) % 19.02/19.19 assert (zenon_L1295_ : (((op (e0) (e0)) = (e2))\/(((op (e1) (e0)) = (e2))\/(((op (e2) (e0)) = (e2))\/((op (e3) (e0)) = (e2))))) -> (~((op (e0) (e0)) = (e2))) -> (~((op (e1) (e0)) = (e2))) -> (~((op (e2) (e0)) = (e2))) -> (((op (e0) (e0)) = (e3))\/(((op (e1) (e0)) = (e3))\/(((op (e2) (e0)) = (e3))\/((op (e3) (e0)) = (e3))))) -> (~((e1) = (e3))) -> ((op (e0) (e0)) = (e1)) -> (~((op (e2) (e0)) = (op (e2) (e2)))) -> ((op (e2) (e2)) = (e3)) -> (~((e2) = (e3))) -> False). % 19.02/19.19 do 0 intro. intros zenon_H1fe zenon_H80 zenon_H177 zenon_Hef zenon_H1e0 zenon_H95 zenon_H7a zenon_H52 zenon_Haa zenon_H12b. % 19.02/19.19 apply (zenon_or_s _ _ zenon_H1fe); [ zenon_intro zenon_H7b | zenon_intro zenon_H1ff ]. % 19.02/19.19 exact (zenon_H80 zenon_H7b). % 19.02/19.19 apply (zenon_or_s _ _ zenon_H1ff); [ zenon_intro zenon_H86 | zenon_intro zenon_H200 ]. % 19.02/19.19 exact (zenon_H177 zenon_H86). % 19.02/19.19 apply (zenon_or_s _ _ zenon_H200); [ zenon_intro zenon_Hee | zenon_intro zenon_H148 ]. % 19.02/19.19 exact (zenon_Hef zenon_Hee). % 19.02/19.19 apply (zenon_L861_); trivial. % 19.02/19.19 (* end of lemma zenon_L1295_ *) % 19.02/19.19 assert (zenon_L1296_ : (((op (e2) (e0)) = (e0))\/(((op (e2) (e0)) = (e1))\/(((op (e2) (e0)) = (e2))\/((op (e2) (e0)) = (e3))))) -> ((op (e2) (e1)) = (e0)) -> (~((op (e2) (e0)) = (op (e2) (e1)))) -> ((op (e0) (e0)) = (e3)) -> ((op (e3) (e0)) = (e2)) -> (~((op (e2) (e0)) = (e2))) -> ((op (e2) (e2)) = (e3)) -> (~((op (e2) (e0)) = (op (e2) (e2)))) -> False). % 19.02/19.19 do 0 intro. intros zenon_H259 zenon_H36 zenon_H1f0 zenon_H3a zenon_H148 zenon_Hef zenon_Haa zenon_H52. % 19.02/19.19 apply (zenon_or_s _ _ zenon_H259); [ zenon_intro zenon_H34 | zenon_intro zenon_H25a ]. % 19.02/19.19 apply (zenon_L642_); trivial. % 19.02/19.19 apply (zenon_or_s _ _ zenon_H25a); [ zenon_intro zenon_Hed | zenon_intro zenon_H25b ]. % 19.02/19.19 apply (zenon_L423_); trivial. % 19.02/19.19 apply (zenon_or_s _ _ zenon_H25b); [ zenon_intro zenon_Hee | zenon_intro zenon_H3b ]. % 19.02/19.19 exact (zenon_Hef zenon_Hee). % 19.02/19.19 apply (zenon_L168_); trivial. % 19.02/19.19 (* end of lemma zenon_L1296_ *) % 19.02/19.19 assert (zenon_L1297_ : (((op (e0) (e0)) = (e0))\/(((op (e0) (e0)) = (e1))\/(((op (e0) (e0)) = (e2))\/((op (e0) (e0)) = (e3))))) -> (~((op (e0) (e0)) = (e0))) -> (~((e2) = (e3))) -> (~((e1) = (e3))) -> (((op (e0) (e0)) = (e3))\/(((op (e1) (e0)) = (e3))\/(((op (e2) (e0)) = (e3))\/((op (e3) (e0)) = (e3))))) -> (~((op (e0) (e0)) = (e2))) -> (((op (e2) (e0)) = (e0))\/(((op (e2) (e0)) = (e1))\/(((op (e2) (e0)) = (e2))\/((op (e2) (e0)) = (e3))))) -> ((op (e2) (e1)) = (e0)) -> (~((op (e2) (e0)) = (op (e2) (e1)))) -> ((op (e3) (e0)) = (e2)) -> (~((op (e2) (e0)) = (e2))) -> ((op (e2) (e2)) = (e3)) -> (~((op (e2) (e0)) = (op (e2) (e2)))) -> False). % 19.02/19.19 do 0 intro. intros zenon_H26a zenon_H3f zenon_H12b zenon_H95 zenon_H1e0 zenon_H80 zenon_H259 zenon_H36 zenon_H1f0 zenon_H148 zenon_Hef zenon_Haa zenon_H52. % 19.02/19.19 apply (zenon_or_s _ _ zenon_H26a); [ zenon_intro zenon_H42 | zenon_intro zenon_H26b ]. % 19.02/19.19 exact (zenon_H3f zenon_H42). % 19.02/19.19 apply (zenon_or_s _ _ zenon_H26b); [ zenon_intro zenon_H7a | zenon_intro zenon_H26c ]. % 19.02/19.19 apply (zenon_L861_); trivial. % 19.02/19.19 apply (zenon_or_s _ _ zenon_H26c); [ zenon_intro zenon_H7b | zenon_intro zenon_H3a ]. % 19.02/19.19 exact (zenon_H80 zenon_H7b). % 19.02/19.19 apply (zenon_L1296_); trivial. % 19.02/19.19 (* end of lemma zenon_L1297_ *) % 19.02/19.19 assert (zenon_L1298_ : (((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))))) -> (~((e0) = (e1))) -> ((op (e0) (e1)) = (e1)) -> (~((op (e1) (e3)) = (op (e2) (e3)))) -> (~((op (e2) (e2)) = (e2))) -> (~((op (e2) (e1)) = (e2))) -> (((op (e2) (e0)) = (e2))\/(((op (e2) (e1)) = (e2))\/(((op (e2) (e2)) = (e2))\/((op (e2) (e3)) = (e2))))) -> (~((op (e1) (e2)) = (e2))) -> (~((e0) = (e2))) -> (~((op (e1) (e0)) = (e2))) -> (((op (e1) (e0)) = (e2))\/(((op (e1) (e1)) = (e2))\/(((op (e1) (e2)) = (e2))\/((op (e1) (e3)) = (e2))))) -> (~((op (e2) (e0)) = (op (e2) (e2)))) -> ((op (e2) (e2)) = (e3)) -> (~((op (e2) (e0)) = (e2))) -> (~((op (e2) (e0)) = (op (e2) (e1)))) -> (((op (e2) (e0)) = (e0))\/(((op (e2) (e0)) = (e1))\/(((op (e2) (e0)) = (e2))\/((op (e2) (e0)) = (e3))))) -> (~((op (e0) (e0)) = (e2))) -> (((op (e0) (e0)) = (e3))\/(((op (e1) (e0)) = (e3))\/(((op (e2) (e0)) = (e3))\/((op (e3) (e0)) = (e3))))) -> (~((e1) = (e3))) -> (~((e2) = (e3))) -> (~((op (e0) (e0)) = (e0))) -> (((op (e0) (e0)) = (e0))\/(((op (e0) (e0)) = (e1))\/(((op (e0) (e0)) = (e2))\/((op (e0) (e0)) = (e3))))) -> (~((op (e3) (e1)) = (op (e3) (e2)))) -> ((op (e3) (e2)) = (e0)) -> False). % 19.02/19.19 do 0 intro. intros zenon_H1fe zenon_H245 zenon_Ha1 zenon_Ha0 zenon_Hdb zenon_H173 zenon_H26e zenon_H1d5 zenon_H114 zenon_H149 zenon_H177 zenon_H18c zenon_H52 zenon_Haa zenon_Hef zenon_H1f0 zenon_H259 zenon_H80 zenon_H1e0 zenon_H95 zenon_H12b zenon_H3f zenon_H26a zenon_H1a4 zenon_H61. % 19.02/19.19 apply (zenon_or_s _ _ zenon_H1fe); [ zenon_intro zenon_H7b | zenon_intro zenon_H1ff ]. % 19.02/19.19 exact (zenon_H80 zenon_H7b). % 19.02/19.19 apply (zenon_or_s _ _ zenon_H1ff); [ zenon_intro zenon_H86 | zenon_intro zenon_H200 ]. % 19.02/19.19 exact (zenon_H177 zenon_H86). % 19.02/19.19 apply (zenon_or_s _ _ zenon_H200); [ zenon_intro zenon_Hee | zenon_intro zenon_H148 ]. % 19.02/19.19 exact (zenon_Hef zenon_Hee). % 19.02/19.19 apply (zenon_or_s _ _ zenon_H245); [ zenon_intro zenon_H49 | zenon_intro zenon_H246 ]. % 19.02/19.19 apply (zenon_L38_); trivial. % 19.02/19.19 apply (zenon_or_s _ _ zenon_H246); [ zenon_intro zenon_H29 | zenon_intro zenon_H247 ]. % 19.02/19.19 apply (zenon_L1066_); trivial. % 19.02/19.19 apply (zenon_or_s _ _ zenon_H247); [ zenon_intro zenon_H36 | zenon_intro zenon_H1b1 ]. % 19.02/19.19 apply (zenon_L1297_); trivial. % 19.02/19.19 apply (zenon_L247_); trivial. % 19.02/19.19 (* end of lemma zenon_L1298_ *) % 19.02/19.19 assert (zenon_L1299_ : (((op (e3) (e0)) = (e2))\/(((op (e3) (e1)) = (e2))\/(((op (e3) (e2)) = (e2))\/((op (e3) (e3)) = (e2))))) -> (~((op (e3) (e0)) = (e2))) -> (~((op (e3) (e1)) = (e2))) -> (~((op (e3) (e2)) = (e2))) -> (~((op (e3) (e3)) = (e2))) -> False). % 19.02/19.19 do 0 intro. intros zenon_H153 zenon_H14b zenon_H194 zenon_H272 zenon_Hf7. % 19.02/19.19 apply (zenon_or_s _ _ zenon_H153); [ zenon_intro zenon_H148 | zenon_intro zenon_H154 ]. % 19.02/19.19 exact (zenon_H14b zenon_H148). % 19.02/19.19 apply (zenon_or_s _ _ zenon_H154); [ zenon_intro zenon_H14d | zenon_intro zenon_H155 ]. % 19.02/19.19 exact (zenon_H194 zenon_H14d). % 19.02/19.19 apply (zenon_or_s _ _ zenon_H155); [ zenon_intro zenon_H151 | zenon_intro zenon_Hf6 ]. % 19.02/19.19 exact (zenon_H272 zenon_H151). % 19.02/19.19 exact (zenon_Hf7 zenon_Hf6). % 19.02/19.19 (* end of lemma zenon_L1299_ *) % 19.02/19.19 assert (zenon_L1300_ : ((~((op (e3) (e2)) = (e2)))\/((op (e3) (e2)) = (e2))) -> ((op (e0) (e2)) = (e2)) -> (~((op (e0) (e2)) = (op (e3) (e2)))) -> (((op (e3) (e0)) = (e2))\/(((op (e3) (e1)) = (e2))\/(((op (e3) (e2)) = (e2))\/((op (e3) (e3)) = (e2))))) -> (~((op (e3) (e1)) = (e2))) -> (~((op (e3) (e0)) = (e2))) -> (~((op (e2) (e2)) = (op (e3) (e2)))) -> ((op (e2) (e2)) = (e3)) -> ((~((op (e3) (e3)) = (e2)))\/((op (e3) (e2)) = (e3))) -> False). % 19.02/19.19 do 0 intro. intros zenon_H273 zenon_H150 zenon_H14f zenon_H153 zenon_H194 zenon_H14b zenon_H18f zenon_Haa zenon_H278. % 19.02/19.19 apply (zenon_or_s _ _ zenon_H273); [ zenon_intro zenon_H272 | zenon_intro zenon_H151 ]. % 19.02/19.19 apply (zenon_or_s _ _ zenon_H278); [ zenon_intro zenon_Hf7 | zenon_intro zenon_H163 ]. % 19.02/19.19 apply (zenon_L1299_); trivial. % 19.02/19.19 apply (zenon_L180_); trivial. % 19.02/19.19 apply (zenon_L104_); trivial. % 19.02/19.19 (* end of lemma zenon_L1300_ *) % 19.02/19.19 assert (zenon_L1301_ : ((~((op (e3) (e0)) = (e2)))\/((op (e3) (e2)) = (e0))) -> (~((op (e1) (e2)) = (op (e3) (e2)))) -> ((~((op (e3) (e2)) = (e2)))\/((op (e3) (e2)) = (e2))) -> ((op (e0) (e2)) = (e2)) -> (~((op (e0) (e2)) = (op (e3) (e2)))) -> (((op (e3) (e0)) = (e2))\/(((op (e3) (e1)) = (e2))\/(((op (e3) (e2)) = (e2))\/((op (e3) (e3)) = (e2))))) -> (~((op (e2) (e2)) = (op (e3) (e2)))) -> ((op (e2) (e2)) = (e3)) -> ((~((op (e3) (e3)) = (e2)))\/((op (e3) (e2)) = (e3))) -> ((op (e1) (e2)) = (e0)) -> ((~((op (e3) (e1)) = (e2)))\/((op (e3) (e2)) = (e1))) -> False). % 19.02/19.19 do 0 intro. intros zenon_H270 zenon_H115 zenon_H273 zenon_H150 zenon_H14f zenon_H153 zenon_H18f zenon_Haa zenon_H278 zenon_H2a zenon_H26f. % 19.02/19.19 apply (zenon_or_s _ _ zenon_H270); [ zenon_intro zenon_H14b | zenon_intro zenon_H61 ]. % 19.02/19.19 apply (zenon_or_s _ _ zenon_H26f); [ zenon_intro zenon_H194 | zenon_intro zenon_Hba ]. % 19.02/19.19 apply (zenon_L1300_); trivial. % 19.02/19.19 apply (zenon_L179_); trivial. % 19.02/19.19 apply (zenon_L176_); trivial. % 19.02/19.19 (* end of lemma zenon_L1301_ *) % 19.02/19.19 assert (zenon_L1302_ : ((~((op (e2) (e3)) = (e2)))\/((op (e2) (e2)) = (e3))) -> ((~((op (e3) (e1)) = (e2)))\/((op (e3) (e2)) = (e1))) -> ((op (e1) (e2)) = (e0)) -> ((~((op (e3) (e3)) = (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 (e0) (e2)) = (op (e3) (e2)))) -> ((op (e0) (e2)) = (e2)) -> ((~((op (e3) (e2)) = (e2)))\/((op (e3) (e2)) = (e2))) -> (~((op (e1) (e2)) = (op (e3) (e2)))) -> ((~((op (e3) (e0)) = (e2)))\/((op (e3) (e2)) = (e0))) -> (~((op (e2) (e0)) = (e2))) -> (~((op (e2) (e1)) = (e2))) -> (~((op (e2) (e2)) = (e2))) -> (((op (e2) (e0)) = (e2))\/(((op (e2) (e1)) = (e2))\/(((op (e2) (e2)) = (e2))\/((op (e2) (e3)) = (e2))))) -> False). % 19.02/19.19 do 0 intro. intros zenon_H277 zenon_H26f zenon_H2a zenon_H278 zenon_H18f zenon_H153 zenon_H14f zenon_H150 zenon_H273 zenon_H115 zenon_H270 zenon_Hef zenon_H26e zenon_H173 zenon_H1d5. % 19.02/19.19 apply (zenon_or_s _ _ zenon_H277); [ zenon_intro zenon_H274 | zenon_intro zenon_Haa ]. % 19.02/19.19 apply (zenon_L1062_); trivial. % 19.02/19.19 apply (zenon_L1301_); trivial. % 19.02/19.19 (* end of lemma zenon_L1302_ *) % 19.02/19.19 assert (zenon_L1303_ : (((op (e3) (e3)) = (e0))\/(((op (e3) (e3)) = (e1))\/(((op (e3) (e3)) = (e2))\/((op (e3) (e3)) = (e3))))) -> ((op (e1) (e3)) = (e0)) -> (~((op (e1) (e3)) = (op (e3) (e3)))) -> ((op (e0) (e3)) = (e1)) -> (~((op (e0) (e3)) = (op (e3) (e3)))) -> (~((op (e3) (e3)) = (e2))) -> (~((op (e3) (e3)) = (e3))) -> False). % 19.02/19.19 do 0 intro. intros zenon_H101 zenon_H1f zenon_Hd5 zenon_Hc3 zenon_Hc2 zenon_Hf7 zenon_H102. % 19.02/19.19 apply (zenon_or_s _ _ zenon_H101); [ zenon_intro zenon_H60 | zenon_intro zenon_H103 ]. % 19.02/19.19 apply (zenon_L136_); trivial. % 19.02/19.19 apply (zenon_or_s _ _ zenon_H103); [ zenon_intro zenon_Hc4 | zenon_intro zenon_H104 ]. % 19.02/19.19 apply (zenon_L46_); trivial. % 19.02/19.19 apply (zenon_or_s _ _ zenon_H104); [ zenon_intro zenon_Hf6 | zenon_intro zenon_H105 ]. % 19.02/19.19 exact (zenon_Hf7 zenon_Hf6). % 19.02/19.19 exact (zenon_H102 zenon_H105). % 19.02/19.19 (* end of lemma zenon_L1303_ *) % 19.02/19.19 assert (zenon_L1304_ : (((op (e2) (e0)) = (e2))\/(((op (e2) (e1)) = (e2))\/(((op (e2) (e2)) = (e2))\/((op (e2) (e3)) = (e2))))) -> (~((op (e2) (e2)) = (e2))) -> (~((op (e2) (e0)) = (e2))) -> (((op (e0) (e1)) = (e2))\/(((op (e1) (e1)) = (e2))\/(((op (e2) (e1)) = (e2))\/((op (e3) (e1)) = (e2))))) -> (~((op (e1) (e1)) = (e2))) -> (~((op (e0) (e1)) = (e2))) -> (~((e1) = (e3))) -> (~((op (e2) (e0)) = (op (e2) (e2)))) -> (~((e2) = (e3))) -> (((op (e0) (e0)) = (e3))\/(((op (e1) (e0)) = (e3))\/(((op (e2) (e0)) = (e3))\/((op (e3) (e0)) = (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 (e1) (e2)) = (e2))) -> (~((e0) = (e2))) -> (((op (e0) (e0)) = (e0))\/(((op (e0) (e0)) = (e1))\/(((op (e0) (e0)) = (e2))\/((op (e0) (e0)) = (e3))))) -> (~((op (e2) (e0)) = (op (e2) (e1)))) -> (((op (e2) (e0)) = (e0))\/(((op (e2) (e0)) = (e1))\/(((op (e2) (e0)) = (e2))\/((op (e2) (e0)) = (e3))))) -> (~((op (e0) (e0)) = (e0))) -> (~((op (e3) (e1)) = (op (e3) (e2)))) -> (((op (e0) (e1)) = (e0))\/(((op (e1) (e1)) = (e0))\/(((op (e2) (e1)) = (e0))\/((op (e3) (e1)) = (e0))))) -> ((~((op (e2) (e0)) = (e2)))\/((op (e2) (e2)) = (e0))) -> ((op (e1) (e2)) = (e3)) -> ((~((op (e2) (e3)) = (e2)))\/((op (e2) (e2)) = (e3))) -> ((~((op (e3) (e0)) = (e2)))\/((op (e3) (e2)) = (e0))) -> (~((op (e0) (e2)) = (op (e2) (e2)))) -> ((~((op (e2) (e1)) = (e2)))\/((op (e2) (e2)) = (e1))) -> (((op (e0) (e0)) = (e1))\/(((op (e1) (e0)) = (e1))\/(((op (e2) (e0)) = (e1))\/((op (e3) (e0)) = (e1))))) -> (~((op (e3) (e0)) = (op (e3) (e2)))) -> (~((op (e1) (e0)) = (op (e2) (e0)))) -> (~((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 (e3) (e1)) = (e2)))\/((op (e3) (e2)) = (e1))) -> ((~((op (e3) (e3)) = (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 (e0) (e2)) = (op (e3) (e2)))) -> ((op (e0) (e2)) = (e2)) -> ((~((op (e3) (e2)) = (e2)))\/((op (e3) (e2)) = (e2))) -> (~((op (e1) (e2)) = (op (e3) (e2)))) -> (((op (e3) (e3)) = (e0))\/(((op (e3) (e3)) = (e1))\/(((op (e3) (e3)) = (e2))\/((op (e3) (e3)) = (e3))))) -> (~((op (e3) (e3)) = (e3))) -> (~((op (e0) (e3)) = (op (e3) (e3)))) -> (~((op (e1) (e3)) = (op (e3) (e3)))) -> (((op (e1) (e0)) = (e0))\/(((op (e1) (e1)) = (e0))\/(((op (e1) (e2)) = (e0))\/((op (e1) (e3)) = (e0))))) -> (~((op (e0) (e0)) = (op (e0) (e3)))) -> (((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 (e0) (e0)) = (e2))\/(((op (e1) (e0)) = (e2))\/(((op (e2) (e0)) = (e2))\/((op (e3) (e0)) = (e2))))) -> False). % 19.02/19.19 do 0 intro. intros zenon_H1d5 zenon_H173 zenon_Hef zenon_H1d8 zenon_H20c zenon_H26d zenon_H95 zenon_H52 zenon_H12b zenon_H1e0 zenon_Ha1 zenon_H18c zenon_Hdb zenon_H114 zenon_H149 zenon_H26a zenon_H1f0 zenon_H259 zenon_H3f zenon_H1a4 zenon_H245 zenon_H276 zenon_H16c zenon_H277 zenon_H270 zenon_Ha8 zenon_H271 zenon_H235 zenon_H6f zenon_H201 zenon_H10a zenon_H1d zenon_H128 zenon_H26f zenon_H278 zenon_H18f zenon_H153 zenon_H14f zenon_H150 zenon_H273 zenon_H115 zenon_H101 zenon_H102 zenon_Hc2 zenon_Hd5 zenon_H22 zenon_H189 zenon_H22d zenon_H80 zenon_H177 zenon_H1fe. % 19.02/19.19 apply (zenon_or_s _ _ zenon_H271); [ zenon_intro zenon_H26e | zenon_intro zenon_Hf1 ]. % 19.02/19.19 apply (zenon_or_s _ _ zenon_H277); [ zenon_intro zenon_H274 | zenon_intro zenon_Haa ]. % 19.02/19.19 apply (zenon_L1062_); trivial. % 19.02/19.19 apply (zenon_or_s _ _ zenon_H270); [ zenon_intro zenon_H14b | zenon_intro zenon_H61 ]. % 19.02/19.19 apply (zenon_L1240_); trivial. % 19.02/19.19 apply (zenon_or_s _ _ zenon_H26f); [ zenon_intro zenon_H194 | zenon_intro zenon_Hba ]. % 19.02/19.19 apply (zenon_L1063_); trivial. % 19.02/19.19 apply (zenon_or_s _ _ zenon_H278); [ zenon_intro zenon_Hf7 | zenon_intro zenon_H163 ]. % 19.02/19.19 apply (zenon_or_s _ _ zenon_H22d); [ zenon_intro zenon_H7a | zenon_intro zenon_H22e ]. % 19.02/19.19 apply (zenon_L1295_); trivial. % 19.02/19.19 apply (zenon_or_s _ _ zenon_H22e); [ zenon_intro zenon_Ha0 | zenon_intro zenon_H22f ]. % 19.02/19.19 apply (zenon_L1298_); trivial. % 19.02/19.19 apply (zenon_or_s _ _ zenon_H22f); [ zenon_intro zenon_H122 | zenon_intro zenon_Hc3 ]. % 19.02/19.19 apply (zenon_L1243_); trivial. % 19.02/19.19 apply (zenon_or_s _ _ zenon_H235); [ zenon_intro zenon_H7a | zenon_intro zenon_H236 ]. % 19.02/19.19 apply (zenon_L140_); trivial. % 19.02/19.19 apply (zenon_or_s _ _ zenon_H236); [ zenon_intro zenon_H9d | zenon_intro zenon_H237 ]. % 19.02/19.19 apply (zenon_or_s _ _ zenon_H22); [ zenon_intro zenon_H27 | zenon_intro zenon_H26 ]. % 19.02/19.19 apply (zenon_L262_); trivial. % 19.02/19.19 apply (zenon_or_s _ _ zenon_H26); [ zenon_intro zenon_H29 | zenon_intro zenon_H28 ]. % 19.02/19.19 apply (zenon_L1066_); trivial. % 19.02/19.19 apply (zenon_or_s _ _ zenon_H28); [ zenon_intro zenon_H2a | zenon_intro zenon_H1f ]. % 19.02/19.19 apply (zenon_L1302_); trivial. % 19.02/19.19 apply (zenon_L1303_); trivial. % 19.02/19.19 apply (zenon_or_s _ _ zenon_H237); [ zenon_intro zenon_Hed | zenon_intro zenon_Hac ]. % 19.02/19.19 apply (zenon_L651_); trivial. % 19.02/19.19 apply (zenon_L249_); trivial. % 19.02/19.19 apply (zenon_L180_); trivial. % 19.02/19.19 apply (zenon_L1053_); trivial. % 19.02/19.19 (* end of lemma zenon_L1304_ *) % 19.02/19.19 assert (zenon_L1305_ : (((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 (e3) (e2)) = (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) (e0)) = (e2))) -> (~((op (e1) (e1)) = (e2))) -> (~((op (e1) (e2)) = (e2))) -> (~((e1) = (e2))) -> False). % 19.02/19.19 do 0 intro. intros zenon_H128 zenon_Ha1 zenon_H27 zenon_H10a zenon_Hba zenon_H115 zenon_H18c zenon_H177 zenon_H20c zenon_H114 zenon_H7c. % 19.02/19.19 apply (zenon_or_s _ _ zenon_H128); [ zenon_intro zenon_H9d | zenon_intro zenon_H129 ]. % 19.02/19.19 apply (zenon_L262_); trivial. % 19.02/19.19 apply (zenon_or_s _ _ zenon_H129); [ zenon_intro zenon_H10d | zenon_intro zenon_H12a ]. % 19.02/19.19 exact (zenon_H10a zenon_H10d). % 19.02/19.19 apply (zenon_or_s _ _ zenon_H12a); [ zenon_intro zenon_Hf0 | zenon_intro zenon_Hd6 ]. % 19.02/19.19 apply (zenon_L69_); trivial. % 19.02/19.19 apply (zenon_L1217_); trivial. % 19.02/19.19 (* end of lemma zenon_L1305_ *) % 19.02/19.19 assert (zenon_L1306_ : (((op (e1) (e0)) = (e0))\/(((op (e1) (e1)) = (e0))\/(((op (e1) (e2)) = (e0))\/((op (e1) (e3)) = (e0))))) -> (~((op (e1) (e0)) = (op (e2) (e0)))) -> (~((e0) = (e2))) -> ((~((op (e3) (e1)) = (e2)))\/((op (e3) (e2)) = (e1))) -> ((~((op (e3) (e3)) = (e2)))\/((op (e3) (e2)) = (e3))) -> ((op (e2) (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 (e0) (e2)) = (op (e3) (e2)))) -> ((op (e0) (e2)) = (e2)) -> ((~((op (e3) (e2)) = (e2)))\/((op (e3) (e2)) = (e2))) -> (~((op (e1) (e2)) = (op (e3) (e2)))) -> ((~((op (e3) (e0)) = (e2)))\/((op (e3) (e2)) = (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) (e0)) = (e2))\/(((op (e1) (e1)) = (e2))\/(((op (e1) (e2)) = (e2))\/((op (e1) (e3)) = (e2))))) -> (~((op (e1) (e0)) = (e2))) -> (~((op (e2) (e1)) = (op (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))))) -> (~((op (e1) (e2)) = (op (e2) (e2)))) -> ((op (e1) (e2)) = (e1)) -> (~((op (e0) (e1)) = (op (e2) (e1)))) -> ((op (e0) (e1)) = (e1)) -> (~((e0) = (e1))) -> (((op (e2) (e0)) = (e1))\/(((op (e2) (e1)) = (e1))\/(((op (e2) (e2)) = (e1))\/((op (e2) (e3)) = (e1))))) -> (~((op (e1) (e2)) = (e2))) -> (((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 (e1) (e3)) = (op (e2) (e3)))) -> False). % 19.02/19.20 do 0 intro. intros zenon_H22 zenon_H201 zenon_H149 zenon_H26f zenon_H278 zenon_Haa zenon_H18f zenon_H153 zenon_H14f zenon_H150 zenon_H273 zenon_H115 zenon_H270 zenon_H245 zenon_H57 zenon_H18c zenon_H177 zenon_H1c7 zenon_H1f0 zenon_H34 zenon_H1cc zenon_H2b zenon_Hf0 zenon_H17e zenon_Ha0 zenon_Ha1 zenon_H106 zenon_H114 zenon_H1d5 zenon_Hef zenon_H26e zenon_H173 zenon_Hdb. % 19.02/19.20 apply (zenon_or_s _ _ zenon_H22); [ zenon_intro zenon_H27 | zenon_intro zenon_H26 ]. % 19.02/19.20 apply (zenon_L332_); trivial. % 19.02/19.20 apply (zenon_or_s _ _ zenon_H26); [ zenon_intro zenon_H29 | zenon_intro zenon_H28 ]. % 19.02/19.20 apply (zenon_L1066_); trivial. % 19.02/19.20 apply (zenon_or_s _ _ zenon_H28); [ zenon_intro zenon_H2a | zenon_intro zenon_H1f ]. % 19.02/19.20 apply (zenon_L1301_); trivial. % 19.02/19.20 apply (zenon_L1096_); trivial. % 19.02/19.20 (* end of lemma zenon_L1306_ *) % 19.02/19.20 assert (zenon_L1307_ : ((~((op (e2) (e0)) = (e2)))\/((op (e2) (e2)) = (e0))) -> ((~((op (e2) (e3)) = (e2)))\/((op (e2) (e2)) = (e3))) -> ((~((op (e3) (e1)) = (e2)))\/((op (e3) (e2)) = (e1))) -> ((op (e1) (e2)) = (e0)) -> ((~((op (e3) (e3)) = (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 (e0) (e2)) = (op (e3) (e2)))) -> ((op (e0) (e2)) = (e2)) -> ((~((op (e3) (e2)) = (e2)))\/((op (e3) (e2)) = (e2))) -> (~((op (e1) (e2)) = (op (e3) (e2)))) -> ((~((op (e3) (e0)) = (e2)))\/((op (e3) (e2)) = (e0))) -> (~((op (e2) (e2)) = (e2))) -> (((op (e2) (e0)) = (e2))\/(((op (e2) (e1)) = (e2))\/(((op (e2) (e2)) = (e2))\/((op (e2) (e3)) = (e2))))) -> (~((op (e1) (e2)) = (op (e2) (e2)))) -> ((op (e1) (e2)) = (e1)) -> ((~((op (e2) (e1)) = (e2)))\/((op (e2) (e2)) = (e1))) -> False). % 19.02/19.20 do 0 intro. intros zenon_H276 zenon_H277 zenon_H26f zenon_H2a zenon_H278 zenon_H18f zenon_H153 zenon_H14f zenon_H150 zenon_H273 zenon_H115 zenon_H270 zenon_H173 zenon_H1d5 zenon_H2b zenon_Hf0 zenon_H271. % 19.02/19.20 apply (zenon_or_s _ _ zenon_H276); [ zenon_intro zenon_Hef | zenon_intro zenon_H2c ]. % 19.02/19.20 apply (zenon_or_s _ _ zenon_H271); [ zenon_intro zenon_H26e | zenon_intro zenon_Hf1 ]. % 19.02/19.20 apply (zenon_L1302_); trivial. % 19.02/19.20 apply (zenon_L59_); trivial. % 19.02/19.20 apply (zenon_L3_); trivial. % 19.02/19.20 (* end of lemma zenon_L1307_ *) % 19.02/19.20 assert (zenon_L1308_ : (((op (e1) (e0)) = (e0))\/(((op (e1) (e1)) = (e0))\/(((op (e1) (e2)) = (e0))\/((op (e1) (e3)) = (e0))))) -> (~((op (e1) (e0)) = (op (e2) (e0)))) -> ((op (e2) (e0)) = (e0)) -> (~((op (e1) (e3)) = (e2))) -> (~((op (e1) (e2)) = (e2))) -> (~((e0) = (e2))) -> (~((op (e1) (e0)) = (e2))) -> (((op (e1) (e0)) = (e2))\/(((op (e1) (e1)) = (e2))\/(((op (e1) (e2)) = (e2))\/((op (e1) (e3)) = (e2))))) -> ((~((op (e2) (e1)) = (e2)))\/((op (e2) (e2)) = (e1))) -> ((op (e1) (e2)) = (e1)) -> (~((op (e1) (e2)) = (op (e2) (e2)))) -> (((op (e2) (e0)) = (e2))\/(((op (e2) (e1)) = (e2))\/(((op (e2) (e2)) = (e2))\/((op (e2) (e3)) = (e2))))) -> (~((op (e2) (e2)) = (e2))) -> ((~((op (e3) (e0)) = (e2)))\/((op (e3) (e2)) = (e0))) -> (~((op (e1) (e2)) = (op (e3) (e2)))) -> ((~((op (e3) (e2)) = (e2)))\/((op (e3) (e2)) = (e2))) -> ((op (e0) (e2)) = (e2)) -> (~((op (e0) (e2)) = (op (e3) (e2)))) -> (((op (e3) (e0)) = (e2))\/(((op (e3) (e1)) = (e2))\/(((op (e3) (e2)) = (e2))\/((op (e3) (e3)) = (e2))))) -> (~((op (e2) (e2)) = (op (e3) (e2)))) -> ((~((op (e3) (e3)) = (e2)))\/((op (e3) (e2)) = (e3))) -> ((~((op (e3) (e1)) = (e2)))\/((op (e3) (e2)) = (e1))) -> ((~((op (e2) (e3)) = (e2)))\/((op (e2) (e2)) = (e3))) -> ((~((op (e2) (e0)) = (e2)))\/((op (e2) (e2)) = (e0))) -> (((op (e3) (e3)) = (e0))\/(((op (e3) (e3)) = (e1))\/(((op (e3) (e3)) = (e2))\/((op (e3) (e3)) = (e3))))) -> (~((op (e1) (e3)) = (op (e3) (e3)))) -> ((op (e0) (e3)) = (e1)) -> (~((op (e0) (e3)) = (op (e3) (e3)))) -> (~((op (e3) (e3)) = (e2))) -> (~((op (e3) (e3)) = (e3))) -> False). % 19.02/19.20 do 0 intro. intros zenon_H22 zenon_H201 zenon_H34 zenon_H14c zenon_H114 zenon_H149 zenon_H177 zenon_H18c zenon_H271 zenon_Hf0 zenon_H2b zenon_H1d5 zenon_H173 zenon_H270 zenon_H115 zenon_H273 zenon_H150 zenon_H14f zenon_H153 zenon_H18f zenon_H278 zenon_H26f zenon_H277 zenon_H276 zenon_H101 zenon_Hd5 zenon_Hc3 zenon_Hc2 zenon_Hf7 zenon_H102. % 19.02/19.20 apply (zenon_or_s _ _ zenon_H22); [ zenon_intro zenon_H27 | zenon_intro zenon_H26 ]. % 19.02/19.20 apply (zenon_L332_); trivial. % 19.02/19.20 apply (zenon_or_s _ _ zenon_H26); [ zenon_intro zenon_H29 | zenon_intro zenon_H28 ]. % 19.02/19.20 apply (zenon_L1259_); trivial. % 19.02/19.20 apply (zenon_or_s _ _ zenon_H28); [ zenon_intro zenon_H2a | zenon_intro zenon_H1f ]. % 19.02/19.20 apply (zenon_L1307_); trivial. % 19.02/19.20 apply (zenon_L1303_); trivial. % 19.02/19.20 (* end of lemma zenon_L1308_ *) % 19.02/19.20 assert (zenon_L1309_ : (((op (e0) (e0)) = (e1))\/(((op (e0) (e1)) = (e1))\/(((op (e0) (e2)) = (e1))\/((op (e0) (e3)) = (e1))))) -> (~((e2) = (e3))) -> (~((op (e2) (e0)) = (op (e2) (e2)))) -> (~((e1) = (e3))) -> (((op (e0) (e0)) = (e3))\/(((op (e1) (e0)) = (e3))\/(((op (e2) (e0)) = (e3))\/((op (e3) (e0)) = (e3))))) -> (~((op (e0) (e0)) = (e2))) -> (((op (e0) (e0)) = (e2))\/(((op (e1) (e0)) = (e2))\/(((op (e2) (e0)) = (e2))\/((op (e3) (e0)) = (e2))))) -> (~((op (e1) (e3)) = (op (e2) (e3)))) -> (~((op (e2) (e1)) = (e2))) -> (~((op (e2) (e0)) = (e2))) -> (((op (e2) (e0)) = (e1))\/(((op (e2) (e1)) = (e1))\/(((op (e2) (e2)) = (e1))\/((op (e2) (e3)) = (e1))))) -> (~((e0) = (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) (e1)))) -> (~((op (e2) (e1)) = (op (e2) (e3)))) -> (~((op (e1) (e1)) = (op (e1) (e3)))) -> (((op (e0) (e1)) = (e0))\/(((op (e1) (e1)) = (e0))\/(((op (e2) (e1)) = (e0))\/((op (e3) (e1)) = (e0))))) -> ((op (e2) (e2)) = (e3)) -> ((op (e3) (e2)) = (e0)) -> (((op (e1) (e0)) = (e0))\/(((op (e1) (e1)) = (e0))\/(((op (e1) (e2)) = (e0))\/((op (e1) (e3)) = (e0))))) -> (~((op (e1) (e0)) = (op (e2) (e0)))) -> ((op (e2) (e0)) = (e0)) -> (~((op (e1) (e3)) = (e2))) -> (~((op (e1) (e2)) = (e2))) -> (~((e0) = (e2))) -> (~((op (e1) (e0)) = (e2))) -> (((op (e1) (e0)) = (e2))\/(((op (e1) (e1)) = (e2))\/(((op (e1) (e2)) = (e2))\/((op (e1) (e3)) = (e2))))) -> ((~((op (e2) (e1)) = (e2)))\/((op (e2) (e2)) = (e1))) -> ((op (e1) (e2)) = (e1)) -> (~((op (e1) (e2)) = (op (e2) (e2)))) -> (((op (e2) (e0)) = (e2))\/(((op (e2) (e1)) = (e2))\/(((op (e2) (e2)) = (e2))\/((op (e2) (e3)) = (e2))))) -> (~((op (e2) (e2)) = (e2))) -> ((~((op (e3) (e0)) = (e2)))\/((op (e3) (e2)) = (e0))) -> (~((op (e1) (e2)) = (op (e3) (e2)))) -> ((~((op (e3) (e2)) = (e2)))\/((op (e3) (e2)) = (e2))) -> ((op (e0) (e2)) = (e2)) -> (~((op (e0) (e2)) = (op (e3) (e2)))) -> (((op (e3) (e0)) = (e2))\/(((op (e3) (e1)) = (e2))\/(((op (e3) (e2)) = (e2))\/((op (e3) (e3)) = (e2))))) -> (~((op (e2) (e2)) = (op (e3) (e2)))) -> ((~((op (e3) (e3)) = (e2)))\/((op (e3) (e2)) = (e3))) -> ((~((op (e3) (e1)) = (e2)))\/((op (e3) (e2)) = (e1))) -> ((~((op (e2) (e3)) = (e2)))\/((op (e2) (e2)) = (e3))) -> ((~((op (e2) (e0)) = (e2)))\/((op (e2) (e2)) = (e0))) -> (((op (e3) (e3)) = (e0))\/(((op (e3) (e3)) = (e1))\/(((op (e3) (e3)) = (e2))\/((op (e3) (e3)) = (e3))))) -> (~((op (e1) (e3)) = (op (e3) (e3)))) -> (~((op (e0) (e3)) = (op (e3) (e3)))) -> (~((op (e3) (e3)) = (e2))) -> (~((op (e3) (e3)) = (e3))) -> False). % 19.02/19.20 do 0 intro. intros zenon_H22d zenon_H12b zenon_H52 zenon_H95 zenon_H1e0 zenon_H80 zenon_H1fe zenon_Hdb zenon_H26e zenon_Hef zenon_H106 zenon_Ha1 zenon_H17e zenon_H1cc zenon_H1f0 zenon_H1c7 zenon_H57 zenon_H245 zenon_Haa zenon_H61 zenon_H22 zenon_H201 zenon_H34 zenon_H14c zenon_H114 zenon_H149 zenon_H177 zenon_H18c zenon_H271 zenon_Hf0 zenon_H2b zenon_H1d5 zenon_H173 zenon_H270 zenon_H115 zenon_H273 zenon_H150 zenon_H14f zenon_H153 zenon_H18f zenon_H278 zenon_H26f zenon_H277 zenon_H276 zenon_H101 zenon_Hd5 zenon_Hc2 zenon_Hf7 zenon_H102. % 19.02/19.20 apply (zenon_or_s _ _ zenon_H22d); [ zenon_intro zenon_H7a | zenon_intro zenon_H22e ]. % 19.02/19.20 apply (zenon_L1295_); trivial. % 19.02/19.20 apply (zenon_or_s _ _ zenon_H22e); [ zenon_intro zenon_Ha0 | zenon_intro zenon_H22f ]. % 19.02/19.20 apply (zenon_L1306_); trivial. % 19.02/19.20 apply (zenon_or_s _ _ zenon_H22f); [ zenon_intro zenon_H122 | zenon_intro zenon_Hc3 ]. % 19.02/19.20 apply (zenon_L432_); trivial. % 19.02/19.20 apply (zenon_L1308_); trivial. % 19.02/19.20 (* end of lemma zenon_L1309_ *) % 19.02/19.20 assert (zenon_L1310_ : ((~((op (e3) (e0)) = (e2)))\/((op (e3) (e2)) = (e0))) -> ((~((op (e3) (e2)) = (e2)))\/((op (e3) (e2)) = (e2))) -> ((op (e0) (e2)) = (e2)) -> (~((op (e0) (e2)) = (op (e3) (e2)))) -> (((op (e3) (e0)) = (e2))\/(((op (e3) (e1)) = (e2))\/(((op (e3) (e2)) = (e2))\/((op (e3) (e3)) = (e2))))) -> (~((op (e2) (e2)) = (op (e3) (e2)))) -> ((op (e2) (e2)) = (e3)) -> ((~((op (e3) (e3)) = (e2)))\/((op (e3) (e2)) = (e3))) -> ((op (e2) (e2)) = (e0)) -> ((op (e0) (e2)) = (e3)) -> ((~((op (e3) (e1)) = (e2)))\/((op (e3) (e2)) = (e1))) -> False). % 19.02/19.20 do 0 intro. intros zenon_H270 zenon_H273 zenon_H150 zenon_H14f zenon_H153 zenon_H18f zenon_Haa zenon_H278 zenon_H2c zenon_Ha9 zenon_H26f. % 19.02/19.20 apply (zenon_or_s _ _ zenon_H270); [ zenon_intro zenon_H14b | zenon_intro zenon_H61 ]. % 19.02/19.20 apply (zenon_or_s _ _ zenon_H26f); [ zenon_intro zenon_H194 | zenon_intro zenon_Hba ]. % 19.02/19.20 apply (zenon_L1300_); trivial. % 19.02/19.20 apply (zenon_L45_); trivial. % 19.02/19.20 apply (zenon_L146_); trivial. % 19.02/19.20 (* end of lemma zenon_L1310_ *) % 19.02/19.20 assert (zenon_L1311_ : ((~((op (e2) (e1)) = (e2)))\/((op (e2) (e2)) = (e1))) -> ((~((op (e3) (e0)) = (e2)))\/((op (e3) (e2)) = (e0))) -> ((~((op (e3) (e2)) = (e2)))\/((op (e3) (e2)) = (e2))) -> ((op (e0) (e2)) = (e2)) -> (~((op (e0) (e2)) = (op (e3) (e2)))) -> (~((op (e0) (e0)) = (e0))) -> (((op (e0) (e1)) = (e0))\/(((op (e1) (e1)) = (e0))\/(((op (e2) (e1)) = (e0))\/((op (e3) (e1)) = (e0))))) -> (((op (e2) (e0)) = (e1))\/(((op (e2) (e1)) = (e1))\/(((op (e2) (e2)) = (e1))\/((op (e2) (e3)) = (e1))))) -> (~((op (e2) (e1)) = (op (e2) (e3)))) -> (((op (e2) (e1)) = (e0))\/(((op (e2) (e1)) = (e1))\/(((op (e2) (e1)) = (e2))\/((op (e2) (e1)) = (e3))))) -> ((op (e1) (e2)) = (e1)) -> (~((op (e1) (e2)) = (op (e2) (e2)))) -> (~((op (e0) (e1)) = (op (e2) (e1)))) -> (~((e1) = (e2))) -> ((op (e2) (e2)) = (e0)) -> (~((op (e2) (e1)) = (op (e2) (e2)))) -> (~((e0) = (e2))) -> (~((op (e1) (e2)) = (e2))) -> (~((op (e1) (e3)) = (e2))) -> (((op (e1) (e0)) = (e2))\/(((op (e1) (e1)) = (e2))\/(((op (e1) (e2)) = (e2))\/((op (e1) (e3)) = (e2))))) -> (~((e0) = (e1))) -> (~((op (e1) (e1)) = (e1))) -> (((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 (e1) (e3)))) -> (((op (e0) (e3)) = (e3))\/(((op (e1) (e3)) = (e3))\/(((op (e2) (e3)) = (e3))\/((op (e3) (e3)) = (e3))))) -> (~((op (e3) (e3)) = (e3))) -> (~((op (e1) (e0)) = (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) (e3)) = (op (e2) (e3)))) -> (~((op (e2) (e3)) = (op (e3) (e3)))) -> (~((op (e1) (e3)) = (op (e2) (e3)))) -> (((op (e2) (e3)) = (e0))\/(((op (e2) (e3)) = (e1))\/(((op (e2) (e3)) = (e2))\/((op (e2) (e3)) = (e3))))) -> (~((e0) = (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 (e2) (e2)) = (op (e2) (e3)))) -> (((op (e0) (e0)) = (e0))\/(((op (e1) (e0)) = (e0))\/(((op (e2) (e0)) = (e0))\/((op (e3) (e0)) = (e0))))) -> (((op (e1) (e0)) = (e0))\/(((op (e1) (e1)) = (e0))\/(((op (e1) (e2)) = (e0))\/((op (e1) (e3)) = (e0))))) -> (~((op (e2) (e0)) = (op (e2) (e2)))) -> (~((op (e1) (e0)) = (op (e1) (e1)))) -> (~((op (e0) (e1)) = (op (e0) (e3)))) -> (~((op (e3) (e0)) = (op (e3) (e3)))) -> (((op (e3) (e3)) = (e0))\/(((op (e3) (e3)) = (e1))\/(((op (e3) (e3)) = (e2))\/((op (e3) (e3)) = (e3))))) -> (~((op (e3) (e0)) = (op (e3) (e1)))) -> (((op (e3) (e0)) = (e1))\/(((op (e3) (e1)) = (e1))\/(((op (e3) (e2)) = (e1))\/((op (e3) (e3)) = (e1))))) -> (~((op (e0) (e3)) = (op (e3) (e3)))) -> ((op (e0) (e2)) = (e3)) -> (((op (e0) (e3)) = (e0))\/(((op (e1) (e3)) = (e0))\/(((op (e2) (e3)) = (e0))\/((op (e3) (e3)) = (e0))))) -> (~((op (e0) (e3)) = (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 (e3) (e0)) = (e0))\/(((op (e3) (e1)) = (e0))\/(((op (e3) (e2)) = (e0))\/((op (e3) (e3)) = (e0))))) -> (((op (e0) (e3)) = (e0))\/(((op (e0) (e3)) = (e1))\/(((op (e0) (e3)) = (e2))\/((op (e0) (e3)) = (e3))))) -> (~((op (e1) (e0)) = (op (e3) (e0)))) -> (~((op (e1) (e0)) = (e2))) -> (~((op (e0) (e0)) = (e2))) -> (~((op (e1) (e2)) = (op (e3) (e2)))) -> ((~((op (e3) (e1)) = (e2)))\/((op (e3) (e2)) = (e1))) -> ((~((op (e3) (e3)) = (e2)))\/((op (e3) (e2)) = (e3))) -> ((~((op (e2) (e3)) = (e2)))\/((op (e2) (e2)) = (e3))) -> False). % 19.02/19.20 do 0 intro. intros zenon_H271 zenon_H270 zenon_H273 zenon_H150 zenon_H14f zenon_H3f zenon_H245 zenon_H106 zenon_H1c7 zenon_H1cc zenon_Hf0 zenon_H2b zenon_H17e zenon_H7c zenon_H2c zenon_H24b zenon_H149 zenon_H114 zenon_H14c zenon_H18c zenon_Ha1 zenon_H10a zenon_H109 zenon_Haf zenon_H124 zenon_H136 zenon_H102 zenon_Hd8 zenon_Hd5 zenon_Hdf zenon_He2 zenon_Hf3 zenon_Hdb zenon_H11f zenon_H9a zenon_H133 zenon_H1fe zenon_H6d zenon_H3e zenon_H22 zenon_H52 zenon_H45 zenon_H54 zenon_H71 zenon_H101 zenon_H1cf zenon_He8 zenon_Hc2 zenon_Ha9 zenon_H67 zenon_H1d zenon_H153 zenon_H18f zenon_H1ac zenon_He4 zenon_H1fa zenon_H177 zenon_H80 zenon_H115 zenon_H26f zenon_H278 zenon_H277. % 19.02/19.20 apply (zenon_or_s _ _ zenon_H271); [ zenon_intro zenon_H26e | zenon_intro zenon_Hf1 ]. % 19.02/19.20 apply (zenon_or_s _ _ zenon_H277); [ zenon_intro zenon_H274 | zenon_intro zenon_Haa ]. % 19.02/19.20 apply (zenon_or_s _ _ zenon_H270); [ zenon_intro zenon_H14b | zenon_intro zenon_H61 ]. % 19.02/19.20 apply (zenon_or_s _ _ zenon_H26f); [ zenon_intro zenon_H194 | zenon_intro zenon_Hba ]. % 19.02/19.20 apply (zenon_or_s _ _ zenon_H273); [ zenon_intro zenon_H272 | zenon_intro zenon_H151 ]. % 19.02/19.20 apply (zenon_L1284_); trivial. % 19.02/19.20 apply (zenon_L104_); trivial. % 19.02/19.20 apply (zenon_L69_); trivial. % 19.02/19.20 apply (zenon_L146_); trivial. % 19.02/19.20 apply (zenon_L1310_); trivial. % 19.02/19.20 apply (zenon_L59_); trivial. % 19.02/19.20 (* end of lemma zenon_L1311_ *) % 19.02/19.20 assert (zenon_L1312_ : (((op (e2) (e0)) = (e0))\/(((op (e2) (e0)) = (e1))\/(((op (e2) (e0)) = (e2))\/((op (e2) (e0)) = (e3))))) -> (~((op (e2) (e0)) = (op (e2) (e3)))) -> ((op (e2) (e3)) = (e0)) -> ((op (e0) (e0)) = (e3)) -> ((op (e3) (e0)) = (e2)) -> (~((op (e2) (e0)) = (e2))) -> ((op (e2) (e2)) = (e3)) -> (~((op (e2) (e0)) = (op (e2) (e2)))) -> False). % 19.02/19.20 do 0 intro. intros zenon_H259 zenon_H5b zenon_H37 zenon_H3a zenon_H148 zenon_Hef zenon_Haa zenon_H52. % 19.02/19.20 apply (zenon_or_s _ _ zenon_H259); [ zenon_intro zenon_H34 | zenon_intro zenon_H25a ]. % 19.02/19.20 apply (zenon_L14_); trivial. % 19.02/19.20 apply (zenon_or_s _ _ zenon_H25a); [ zenon_intro zenon_Hed | zenon_intro zenon_H25b ]. % 19.02/19.20 apply (zenon_L423_); trivial. % 19.02/19.20 apply (zenon_or_s _ _ zenon_H25b); [ zenon_intro zenon_Hee | zenon_intro zenon_H3b ]. % 19.02/19.20 exact (zenon_Hef zenon_Hee). % 19.02/19.20 apply (zenon_L168_); trivial. % 19.02/19.20 (* end of lemma zenon_L1312_ *) % 19.02/19.20 assert (zenon_L1313_ : (((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 (e2) (e1)) = (op (e2) (e3)))) -> (((op (e2) (e1)) = (e0))\/(((op (e2) (e1)) = (e1))\/(((op (e2) (e1)) = (e2))\/((op (e2) (e1)) = (e3))))) -> (~((op (e0) (e1)) = (op (e2) (e1)))) -> (~((e1) = (e2))) -> (~((op (e2) (e1)) = (op (e2) (e2)))) -> (~((e0) = (e1))) -> (~((op (e1) (e1)) = (e1))) -> (((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 (e1) (e3)))) -> (((op (e0) (e3)) = (e3))\/(((op (e1) (e3)) = (e3))\/(((op (e2) (e3)) = (e3))\/((op (e3) (e3)) = (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) (e3)) = (op (e2) (e3)))) -> (~((op (e2) (e3)) = (op (e3) (e3)))) -> (~((op (e1) (e3)) = (op (e2) (e3)))) -> (((op (e2) (e3)) = (e0))\/(((op (e2) (e3)) = (e1))\/(((op (e2) (e3)) = (e2))\/((op (e2) (e3)) = (e3))))) -> (~((e0) = (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 (e2) (e2)) = (op (e2) (e3)))) -> (((op (e0) (e0)) = (e0))\/(((op (e1) (e0)) = (e0))\/(((op (e2) (e0)) = (e0))\/((op (e3) (e0)) = (e0))))) -> (~((op (e1) (e0)) = (op (e1) (e1)))) -> (~((op (e0) (e1)) = (op (e0) (e3)))) -> (~((op (e3) (e0)) = (op (e3) (e3)))) -> (~((op (e3) (e0)) = (op (e3) (e1)))) -> (((op (e3) (e0)) = (e1))\/(((op (e3) (e1)) = (e1))\/(((op (e3) (e2)) = (e1))\/((op (e3) (e3)) = (e1))))) -> ((op (e0) (e2)) = (e3)) -> (((op (e0) (e3)) = (e0))\/(((op (e1) (e3)) = (e0))\/(((op (e2) (e3)) = (e0))\/((op (e3) (e3)) = (e0))))) -> (~((op (e0) (e3)) = (op (e1) (e3)))) -> (((op (e3) (e0)) = (e0))\/(((op (e3) (e1)) = (e0))\/(((op (e3) (e2)) = (e0))\/((op (e3) (e3)) = (e0))))) -> (((op (e0) (e3)) = (e0))\/(((op (e0) (e3)) = (e1))\/(((op (e0) (e3)) = (e2))\/((op (e0) (e3)) = (e3))))) -> (~((op (e1) (e0)) = (op (e3) (e0)))) -> (((op (e0) (e0)) = (e1))\/(((op (e0) (e1)) = (e1))\/(((op (e0) (e2)) = (e1))\/((op (e0) (e3)) = (e1))))) -> (~((op (e2) (e1)) = (e2))) -> (~((op (e1) (e1)) = (op (e1) (e3)))) -> (~((op (e2) (e0)) = (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) (e0)) = (e2))) -> (~((op (e0) (e0)) = (e0))) -> (((op (e0) (e0)) = (e0))\/(((op (e0) (e0)) = (e1))\/(((op (e0) (e0)) = (e2))\/((op (e0) (e0)) = (e3))))) -> (~((op (e2) (e2)) = (op (e3) (e2)))) -> ((op (e3) (e2)) = (e0)) -> (~((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 (e1) (e0)) = (e0))\/(((op (e1) (e1)) = (e0))\/(((op (e1) (e2)) = (e0))\/((op (e1) (e3)) = (e0))))) -> (~((op (e1) (e0)) = (op (e2) (e0)))) -> (~((op (e1) (e3)) = (e2))) -> (~((op (e1) (e2)) = (e2))) -> (~((e0) = (e2))) -> (~((op (e1) (e0)) = (e2))) -> (((op (e1) (e0)) = (e2))\/(((op (e1) (e1)) = (e2))\/(((op (e1) (e2)) = (e2))\/((op (e1) (e3)) = (e2))))) -> ((~((op (e2) (e1)) = (e2)))\/((op (e2) (e2)) = (e1))) -> ((op (e1) (e2)) = (e1)) -> (~((op (e1) (e2)) = (op (e2) (e2)))) -> (((op (e2) (e0)) = (e2))\/(((op (e2) (e1)) = (e2))\/(((op (e2) (e2)) = (e2))\/((op (e2) (e3)) = (e2))))) -> (~((op (e2) (e2)) = (e2))) -> ((~((op (e3) (e0)) = (e2)))\/((op (e3) (e2)) = (e0))) -> (~((op (e1) (e2)) = (op (e3) (e2)))) -> ((~((op (e3) (e2)) = (e2)))\/((op (e3) (e2)) = (e2))) -> ((op (e0) (e2)) = (e2)) -> (~((op (e0) (e2)) = (op (e3) (e2)))) -> (((op (e3) (e0)) = (e2))\/(((op (e3) (e1)) = (e2))\/(((op (e3) (e2)) = (e2))\/((op (e3) (e3)) = (e2))))) -> ((~((op (e3) (e3)) = (e2)))\/((op (e3) (e2)) = (e3))) -> ((~((op (e3) (e1)) = (e2)))\/((op (e3) (e2)) = (e1))) -> ((~((op (e2) (e3)) = (e2)))\/((op (e2) (e2)) = (e3))) -> ((~((op (e2) (e0)) = (e2)))\/((op (e2) (e2)) = (e0))) -> (((op (e3) (e3)) = (e0))\/(((op (e3) (e3)) = (e1))\/(((op (e3) (e3)) = (e2))\/((op (e3) (e3)) = (e3))))) -> (~((op (e1) (e3)) = (op (e3) (e3)))) -> ((op (e0) (e3)) = (e1)) -> (~((op (e0) (e3)) = (op (e3) (e3)))) -> (~((op (e3) (e3)) = (e2))) -> (~((op (e3) (e3)) = (e3))) -> (((op (e2) (e0)) = (e0))\/(((op (e2) (e1)) = (e0))\/(((op (e2) (e2)) = (e0))\/((op (e2) (e3)) = (e0))))) -> (~((op (e2) (e0)) = (op (e2) (e2)))) -> ((op (e2) (e2)) = (e3)) -> ((op (e3) (e0)) = (e2)) -> (~((e2) = (e3))) -> False). % 19.02/19.20 do 0 intro. intros zenon_H245 zenon_H106 zenon_H1c7 zenon_H1cc zenon_H17e zenon_H7c zenon_H24b zenon_Ha1 zenon_H10a zenon_H109 zenon_Haf zenon_H124 zenon_H136 zenon_Hd8 zenon_Hdf zenon_He2 zenon_Hf3 zenon_Hdb zenon_H11f zenon_H9a zenon_H133 zenon_H1fe zenon_H6d zenon_H3e zenon_H45 zenon_H54 zenon_H71 zenon_H1cf zenon_He8 zenon_Ha9 zenon_H67 zenon_H1d zenon_H1ac zenon_He4 zenon_H1fa zenon_H22d zenon_H26e zenon_H57 zenon_Hef zenon_H5b zenon_H259 zenon_H80 zenon_H3f zenon_H26a zenon_H18f zenon_H61 zenon_H95 zenon_H1e0 zenon_H1f0 zenon_H22 zenon_H201 zenon_H14c zenon_H114 zenon_H149 zenon_H177 zenon_H18c zenon_H271 zenon_Hf0 zenon_H2b zenon_H1d5 zenon_H173 zenon_H270 zenon_H115 zenon_H273 zenon_H150 zenon_H14f zenon_H153 zenon_H278 zenon_H26f zenon_H277 zenon_H276 zenon_H101 zenon_Hd5 zenon_Hc3 zenon_Hc2 zenon_Hf7 zenon_H102 zenon_H2f zenon_H52 zenon_Haa zenon_H148 zenon_H12b. % 19.02/19.20 apply (zenon_or_s _ _ zenon_H1e0); [ zenon_intro zenon_H3a | zenon_intro zenon_H1e1 ]. % 19.02/19.20 apply (zenon_or_s _ _ zenon_H2f); [ zenon_intro zenon_H34 | zenon_intro zenon_H33 ]. % 19.02/19.20 apply (zenon_L1309_); trivial. % 19.02/19.20 apply (zenon_or_s _ _ zenon_H33); [ zenon_intro zenon_H36 | zenon_intro zenon_H35 ]. % 19.02/19.20 apply (zenon_L1296_); trivial. % 19.02/19.20 apply (zenon_or_s _ _ zenon_H35); [ zenon_intro zenon_H2c | zenon_intro zenon_H37 ]. % 19.02/19.20 apply (zenon_L1311_); trivial. % 19.02/19.20 apply (zenon_L1312_); trivial. % 19.02/19.20 apply (zenon_or_s _ _ zenon_H1e1); [ zenon_intro zenon_H9e | zenon_intro zenon_H1e2 ]. % 19.02/19.20 apply (zenon_or_s _ _ zenon_H2f); [ zenon_intro zenon_H34 | zenon_intro zenon_H33 ]. % 19.02/19.20 apply (zenon_L1308_); trivial. % 19.02/19.20 apply (zenon_or_s _ _ zenon_H33); [ zenon_intro zenon_H36 | zenon_intro zenon_H35 ]. % 19.02/19.20 apply (zenon_L1297_); trivial. % 19.02/19.20 apply (zenon_or_s _ _ zenon_H35); [ zenon_intro zenon_H2c | zenon_intro zenon_H37 ]. % 19.02/19.20 apply (zenon_L146_); trivial. % 19.02/19.20 apply (zenon_or_s _ _ zenon_H26a); [ zenon_intro zenon_H42 | zenon_intro zenon_H26b ]. % 19.02/19.20 exact (zenon_H3f zenon_H42). % 19.02/19.20 apply (zenon_or_s _ _ zenon_H26b); [ zenon_intro zenon_H7a | zenon_intro zenon_H26c ]. % 19.02/19.20 apply (zenon_L107_); trivial. % 19.02/19.20 apply (zenon_or_s _ _ zenon_H26c); [ zenon_intro zenon_H7b | zenon_intro zenon_H3a ]. % 19.02/19.20 exact (zenon_H80 zenon_H7b). % 19.02/19.20 apply (zenon_L1312_); trivial. % 19.02/19.20 apply (zenon_or_s _ _ zenon_H1e2); [ zenon_intro zenon_H3b | zenon_intro zenon_H15e ]. % 19.02/19.20 apply (zenon_L168_); trivial. % 19.02/19.20 apply (zenon_L109_); trivial. % 19.02/19.20 (* end of lemma zenon_L1313_ *) % 19.02/19.20 assert (zenon_L1314_ : (((op (e2) (e0)) = (e2))\/(((op (e2) (e1)) = (e2))\/(((op (e2) (e2)) = (e2))\/((op (e2) (e3)) = (e2))))) -> (~((op (e2) (e2)) = (e2))) -> (~((op (e2) (e0)) = (e2))) -> (((op (e0) (e0)) = (e1))\/(((op (e0) (e1)) = (e1))\/(((op (e0) (e2)) = (e1))\/((op (e0) (e3)) = (e1))))) -> (~((op (e1) (e3)) = (e2))) -> ((~((op (e2) (e0)) = (e2)))\/((op (e2) (e2)) = (e0))) -> ((~((op (e2) (e3)) = (e2)))\/((op (e2) (e2)) = (e3))) -> ((~((op (e2) (e1)) = (e2)))\/((op (e2) (e2)) = (e1))) -> (((op (e3) (e3)) = (e0))\/(((op (e3) (e3)) = (e1))\/(((op (e3) (e3)) = (e2))\/((op (e3) (e3)) = (e3))))) -> (~((op (e3) (e3)) = (e3))) -> (~((op (e0) (e3)) = (op (e3) (e3)))) -> (~((op (e1) (e3)) = (op (e3) (e3)))) -> (~((op (e1) (e0)) = (op (e2) (e0)))) -> ((~((op (e3) (e0)) = (e2)))\/((op (e3) (e2)) = (e0))) -> (~((op (e1) (e2)) = (op (e3) (e2)))) -> ((~((op (e3) (e2)) = (e2)))\/((op (e3) (e2)) = (e2))) -> ((op (e0) (e2)) = (e2)) -> (~((op (e0) (e2)) = (op (e3) (e2)))) -> (((op (e3) (e0)) = (e2))\/(((op (e3) (e1)) = (e2))\/(((op (e3) (e2)) = (e2))\/((op (e3) (e3)) = (e2))))) -> (~((op (e2) (e2)) = (op (e3) (e2)))) -> ((~((op (e3) (e3)) = (e2)))\/((op (e3) (e2)) = (e3))) -> ((~((op (e3) (e1)) = (e2)))\/((op (e3) (e2)) = (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) (e1)) = (e0))\/(((op (e2) (e1)) = (e1))\/(((op (e2) (e1)) = (e2))\/((op (e2) (e1)) = (e3))))) -> (~((op (e1) (e2)) = (op (e2) (e2)))) -> (~((op (e0) (e1)) = (op (e2) (e1)))) -> (~((op (e1) (e1)) = (op (e1) (e3)))) -> (((op (e1) (e0)) = (e0))\/(((op (e1) (e1)) = (e0))\/(((op (e1) (e2)) = (e0))\/((op (e1) (e3)) = (e0))))) -> (~((e1) = (e2))) -> (~((op (e2) (e1)) = (op (e2) (e2)))) -> (~((op (e1) (e1)) = (e1))) -> (((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 (e1) (e3)))) -> (((op (e0) (e3)) = (e3))\/(((op (e1) (e3)) = (e3))\/(((op (e2) (e3)) = (e3))\/((op (e3) (e3)) = (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) (e3)) = (op (e2) (e3)))) -> (~((op (e2) (e3)) = (op (e3) (e3)))) -> (((op (e2) (e3)) = (e0))\/(((op (e2) (e3)) = (e1))\/(((op (e2) (e3)) = (e2))\/((op (e2) (e3)) = (e3))))) -> (~((e0) = (e3))) -> (((op (e0) (e3)) = (e1))\/(((op (e1) (e3)) = (e1))\/(((op (e2) (e3)) = (e1))\/((op (e3) (e3)) = (e1))))) -> (~((op (e2) (e2)) = (op (e2) (e3)))) -> (((op (e0) (e0)) = (e0))\/(((op (e1) (e0)) = (e0))\/(((op (e2) (e0)) = (e0))\/((op (e3) (e0)) = (e0))))) -> (~((op (e1) (e0)) = (op (e1) (e1)))) -> (~((op (e0) (e1)) = (op (e0) (e3)))) -> (~((op (e3) (e0)) = (op (e3) (e3)))) -> (~((op (e3) (e0)) = (op (e3) (e1)))) -> (((op (e3) (e0)) = (e1))\/(((op (e3) (e1)) = (e1))\/(((op (e3) (e2)) = (e1))\/((op (e3) (e3)) = (e1))))) -> ((op (e0) (e2)) = (e3)) -> (((op (e0) (e3)) = (e0))\/(((op (e1) (e3)) = (e0))\/(((op (e2) (e3)) = (e0))\/((op (e3) (e3)) = (e0))))) -> (~((op (e0) (e3)) = (op (e1) (e3)))) -> (((op (e3) (e0)) = (e0))\/(((op (e3) (e1)) = (e0))\/(((op (e3) (e2)) = (e0))\/((op (e3) (e3)) = (e0))))) -> (((op (e0) (e3)) = (e0))\/(((op (e0) (e3)) = (e1))\/(((op (e0) (e3)) = (e2))\/((op (e0) (e3)) = (e3))))) -> (~((op (e1) (e0)) = (op (e3) (e0)))) -> (~((op (e2) (e0)) = (op (e2) (e3)))) -> (((op (e2) (e0)) = (e0))\/(((op (e2) (e1)) = (e0))\/(((op (e2) (e2)) = (e0))\/((op (e2) (e3)) = (e0))))) -> ((op (e1) (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 (e3) (e1)) = (op (e3) (e2)))) -> (~((op (e0) (e0)) = (e0))) -> (((op (e2) (e0)) = (e0))\/(((op (e2) (e0)) = (e1))\/(((op (e2) (e0)) = (e2))\/((op (e2) (e0)) = (e3))))) -> (~((op (e2) (e0)) = (op (e2) (e1)))) -> (((op (e0) (e0)) = (e0))\/(((op (e0) (e0)) = (e1))\/(((op (e0) (e0)) = (e2))\/((op (e0) (e0)) = (e3))))) -> (~((e0) = (e2))) -> (~((op (e1) (e2)) = (e2))) -> (~((op (e1) (e3)) = (op (e2) (e3)))) -> (((op (e1) (e0)) = (e2))\/(((op (e1) (e1)) = (e2))\/(((op (e1) (e2)) = (e2))\/((op (e1) (e3)) = (e2))))) -> (~((e0) = (e1))) -> (((op (e0) (e0)) = (e3))\/(((op (e1) (e0)) = (e3))\/(((op (e2) (e0)) = (e3))\/((op (e3) (e0)) = (e3))))) -> (~((e2) = (e3))) -> (~((op (e2) (e0)) = (op (e2) (e2)))) -> (~((e1) = (e3))) -> (~((op (e0) (e0)) = (e2))) -> (~((op (e1) (e0)) = (e2))) -> (((op (e0) (e0)) = (e2))\/(((op (e1) (e0)) = (e2))\/(((op (e2) (e0)) = (e2))\/((op (e3) (e0)) = (e2))))) -> False). % 19.02/19.20 do 0 intro. intros zenon_H1d5 zenon_H173 zenon_Hef zenon_H22d zenon_H14c zenon_H276 zenon_H277 zenon_H271 zenon_H101 zenon_H102 zenon_Hc2 zenon_Hd5 zenon_H201 zenon_H270 zenon_H115 zenon_H273 zenon_H150 zenon_H14f zenon_H153 zenon_H18f zenon_H278 zenon_H26f zenon_H106 zenon_H1c7 zenon_H1cc zenon_H2b zenon_H17e zenon_H57 zenon_H22 zenon_H7c zenon_H24b zenon_H10a zenon_H109 zenon_Haf zenon_H124 zenon_H136 zenon_Hd8 zenon_Hdf zenon_He2 zenon_Hf3 zenon_H11f zenon_H9a zenon_H133 zenon_H6d zenon_H3e zenon_H45 zenon_H54 zenon_H71 zenon_H1cf zenon_He8 zenon_Ha9 zenon_H67 zenon_H1d zenon_H1ac zenon_He4 zenon_H1fa zenon_H5b zenon_H2f zenon_Hf0 zenon_H195 zenon_H245 zenon_H1a4 zenon_H3f zenon_H259 zenon_H1f0 zenon_H26a zenon_H149 zenon_H114 zenon_Hdb zenon_H18c zenon_Ha1 zenon_H1e0 zenon_H12b zenon_H52 zenon_H95 zenon_H80 zenon_H177 zenon_H1fe. % 19.02/19.20 apply (zenon_or_s _ _ zenon_H271); [ zenon_intro zenon_H26e | zenon_intro zenon_Hf1 ]. % 19.02/19.20 apply (zenon_or_s _ _ zenon_H277); [ zenon_intro zenon_H274 | zenon_intro zenon_Haa ]. % 19.02/19.20 apply (zenon_L1062_); trivial. % 19.02/19.20 apply (zenon_or_s _ _ zenon_H270); [ zenon_intro zenon_H14b | zenon_intro zenon_H61 ]. % 19.02/19.20 apply (zenon_L1240_); trivial. % 19.02/19.20 apply (zenon_or_s _ _ zenon_H278); [ zenon_intro zenon_Hf7 | zenon_intro zenon_H163 ]. % 19.02/19.20 apply (zenon_or_s _ _ zenon_H22d); [ zenon_intro zenon_H7a | zenon_intro zenon_H22e ]. % 19.02/19.20 apply (zenon_L1295_); trivial. % 19.02/19.20 apply (zenon_or_s _ _ zenon_H22e); [ zenon_intro zenon_Ha0 | zenon_intro zenon_H22f ]. % 19.02/19.20 apply (zenon_L1298_); trivial. % 19.02/19.20 apply (zenon_or_s _ _ zenon_H22f); [ zenon_intro zenon_H122 | zenon_intro zenon_Hc3 ]. % 19.02/19.20 apply (zenon_L530_); trivial. % 19.02/19.20 apply (zenon_or_s _ _ zenon_H1fe); [ zenon_intro zenon_H7b | zenon_intro zenon_H1ff ]. % 19.02/19.20 exact (zenon_H80 zenon_H7b). % 19.02/19.20 apply (zenon_or_s _ _ zenon_H1ff); [ zenon_intro zenon_H86 | zenon_intro zenon_H200 ]. % 19.02/19.20 exact (zenon_H177 zenon_H86). % 19.02/19.20 apply (zenon_or_s _ _ zenon_H200); [ zenon_intro zenon_Hee | zenon_intro zenon_H148 ]. % 19.02/19.20 exact (zenon_Hef zenon_Hee). % 19.02/19.20 apply (zenon_L1313_); trivial. % 19.02/19.20 apply (zenon_L180_); trivial. % 19.02/19.20 apply (zenon_L59_); trivial. % 19.02/19.20 (* end of lemma zenon_L1314_ *) % 19.02/19.20 assert (zenon_L1315_ : ((~((op (e2) (e0)) = (e2)))\/((op (e2) (e2)) = (e0))) -> (~((op (e1) (e2)) = (op (e2) (e2)))) -> ((~((op (e2) (e3)) = (e2)))\/((op (e2) (e2)) = (e3))) -> ((~((op (e3) (e1)) = (e2)))\/((op (e3) (e2)) = (e1))) -> ((op (e1) (e2)) = (e0)) -> ((~((op (e3) (e3)) = (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 (e0) (e2)) = (op (e3) (e2)))) -> ((op (e0) (e2)) = (e2)) -> ((~((op (e3) (e2)) = (e2)))\/((op (e3) (e2)) = (e2))) -> (~((op (e1) (e2)) = (op (e3) (e2)))) -> ((~((op (e3) (e0)) = (e2)))\/((op (e3) (e2)) = (e0))) -> (~((op (e2) (e2)) = (e2))) -> (((op (e2) (e0)) = (e2))\/(((op (e2) (e1)) = (e2))\/(((op (e2) (e2)) = (e2))\/((op (e2) (e3)) = (e2))))) -> ((op (e0) (e2)) = (e3)) -> ((~((op (e2) (e1)) = (e2)))\/((op (e2) (e2)) = (e1))) -> False). % 19.02/19.20 do 0 intro. intros zenon_H276 zenon_H2b zenon_H277 zenon_H26f zenon_H2a zenon_H278 zenon_H18f zenon_H153 zenon_H14f zenon_H150 zenon_H273 zenon_H115 zenon_H270 zenon_H173 zenon_H1d5 zenon_Ha9 zenon_H271. % 19.02/19.20 apply (zenon_or_s _ _ zenon_H276); [ zenon_intro zenon_Hef | zenon_intro zenon_H2c ]. % 19.02/19.20 apply (zenon_or_s _ _ zenon_H271); [ zenon_intro zenon_H26e | zenon_intro zenon_Hf1 ]. % 19.02/19.20 apply (zenon_L1302_); trivial. % 19.02/19.20 apply (zenon_L184_); trivial. % 19.02/19.20 apply (zenon_L3_); trivial. % 19.02/19.20 (* end of lemma zenon_L1315_ *) % 19.02/19.20 assert (zenon_L1316_ : ((~((op (e1) (e0)) = (e2)))\/((op (e1) (e2)) = (e0))) -> ((~((op (e1) (e2)) = (e2)))\/((op (e1) (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) (e2)) = (e3)) -> (((op (e0) (e0)) = (e2))\/(((op (e1) (e0)) = (e2))\/(((op (e2) (e0)) = (e2))\/((op (e3) (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 (e0) (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)) = (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) (e2)) = (op (e3) (e2)))) -> ((~((op (e3) (e2)) = (e2)))\/((op (e3) (e2)) = (e2))) -> ((op (e0) (e2)) = (e2)) -> (~((op (e0) (e2)) = (op (e3) (e2)))) -> (((op (e3) (e0)) = (e2))\/(((op (e3) (e1)) = (e2))\/(((op (e3) (e2)) = (e2))\/((op (e3) (e3)) = (e2))))) -> (~((op (e2) (e2)) = (op (e3) (e2)))) -> ((~((op (e3) (e3)) = (e2)))\/((op (e3) (e2)) = (e3))) -> ((~((op (e3) (e1)) = (e2)))\/((op (e3) (e2)) = (e1))) -> (((op (e1) (e0)) = (e1))\/(((op (e1) (e1)) = (e1))\/(((op (e1) (e2)) = (e1))\/((op (e1) (e3)) = (e1))))) -> (~((op (e0) (e3)) = (op (e1) (e3)))) -> (~((op (e1) (e1)) = (e1))) -> (~((op (e1) (e0)) = (op (e2) (e0)))) -> (~((op (e3) (e0)) = (op (e3) (e2)))) -> (((op (e0) (e0)) = (e1))\/(((op (e1) (e0)) = (e1))\/(((op (e2) (e0)) = (e1))\/((op (e3) (e0)) = (e1))))) -> ((~((op (e2) (e1)) = (e2)))\/((op (e2) (e2)) = (e1))) -> (~((op (e0) (e2)) = (op (e2) (e2)))) -> ((~((op (e3) (e0)) = (e2)))\/((op (e3) (e2)) = (e0))) -> ((~((op (e2) (e3)) = (e2)))\/((op (e2) (e2)) = (e3))) -> ((~((op (e2) (e0)) = (e2)))\/((op (e2) (e2)) = (e0))) -> (((op (e0) (e1)) = (e0))\/(((op (e1) (e1)) = (e0))\/(((op (e2) (e1)) = (e0))\/((op (e3) (e1)) = (e0))))) -> (~((op (e3) (e1)) = (op (e3) (e2)))) -> (~((op (e0) (e0)) = (e0))) -> (((op (e2) (e0)) = (e0))\/(((op (e2) (e0)) = (e1))\/(((op (e2) (e0)) = (e2))\/((op (e2) (e0)) = (e3))))) -> (~((op (e2) (e0)) = (op (e2) (e1)))) -> (((op (e0) (e0)) = (e0))\/(((op (e0) (e0)) = (e1))\/(((op (e0) (e0)) = (e2))\/((op (e0) (e0)) = (e3))))) -> (~((e0) = (e2))) -> (~((op (e1) (e3)) = (op (e2) (e3)))) -> (~((e0) = (e1))) -> (((op (e0) (e0)) = (e3))\/(((op (e1) (e0)) = (e3))\/(((op (e2) (e0)) = (e3))\/((op (e3) (e0)) = (e3))))) -> (~((e2) = (e3))) -> (~((op (e2) (e0)) = (op (e2) (e2)))) -> (~((e1) = (e3))) -> (~((op (e0) (e1)) = (e2))) -> (((op (e0) (e1)) = (e2))\/(((op (e1) (e1)) = (e2))\/(((op (e2) (e1)) = (e2))\/((op (e3) (e1)) = (e2))))) -> (~((op (e2) (e2)) = (e2))) -> (((op (e2) (e0)) = (e2))\/(((op (e2) (e1)) = (e2))\/(((op (e2) (e2)) = (e2))\/((op (e2) (e3)) = (e2))))) -> ((~((op (e1) (e3)) = (e2)))\/((op (e1) (e2)) = (e3))) -> (((op (e2) (e0)) = (e0))\/(((op (e2) (e1)) = (e0))\/(((op (e2) (e2)) = (e0))\/((op (e2) (e3)) = (e0))))) -> (~((op (e2) (e0)) = (op (e2) (e3)))) -> (~((op (e1) (e0)) = (op (e3) (e0)))) -> (((op (e0) (e3)) = (e0))\/(((op (e0) (e3)) = (e1))\/(((op (e0) (e3)) = (e2))\/((op (e0) (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 (e3) (e0)) = (e1))\/(((op (e3) (e1)) = (e1))\/(((op (e3) (e2)) = (e1))\/((op (e3) (e3)) = (e1))))) -> (~((op (e3) (e0)) = (op (e3) (e1)))) -> (~((op (e3) (e0)) = (op (e3) (e3)))) -> (~((op (e0) (e1)) = (op (e0) (e3)))) -> (~((op (e1) (e0)) = (op (e1) (e1)))) -> (((op (e0) (e0)) = (e0))\/(((op (e1) (e0)) = (e0))\/(((op (e2) (e0)) = (e0))\/((op (e3) (e0)) = (e0))))) -> (~((op (e2) (e2)) = (op (e2) (e3)))) -> (((op (e0) (e3)) = (e1))\/(((op (e1) (e3)) = (e1))\/(((op (e2) (e3)) = (e1))\/((op (e3) (e3)) = (e1))))) -> (~((e0) = (e3))) -> (((op (e2) (e3)) = (e0))\/(((op (e2) (e3)) = (e1))\/(((op (e2) (e3)) = (e2))\/((op (e2) (e3)) = (e3))))) -> (~((op (e2) (e3)) = (op (e3) (e3)))) -> (~((op (e0) (e3)) = (op (e2) (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) (e3)) = (e3))\/(((op (e1) (e3)) = (e3))\/(((op (e2) (e3)) = (e3))\/((op (e3) (e3)) = (e3))))) -> (~((op (e1) (e2)) = (op (e1) (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) (e1)) = (op (e2) (e2)))) -> (~((e1) = (e2))) -> (~((op (e1) (e1)) = (op (e1) (e3)))) -> (~((op (e0) (e1)) = (op (e2) (e1)))) -> (~((op (e1) (e2)) = (op (e2) (e2)))) -> (((op (e2) (e1)) = (e0))\/(((op (e2) (e1)) = (e1))\/(((op (e2) (e1)) = (e2))\/((op (e2) (e1)) = (e3))))) -> (~((op (e2) (e1)) = (op (e2) (e3)))) -> (((op (e2) (e0)) = (e1))\/(((op (e2) (e1)) = (e1))\/(((op (e2) (e2)) = (e1))\/((op (e2) (e3)) = (e1))))) -> ((~((op (e1) (e1)) = (e2)))\/((op (e1) (e2)) = (e1))) -> False). % 19.02/19.20 do 0 intro. intros zenon_H27a zenon_H275 zenon_H195 zenon_H18c zenon_Ha9 zenon_H1fe zenon_H80 zenon_H22d zenon_H189 zenon_H22 zenon_Hd5 zenon_Hc2 zenon_H102 zenon_H101 zenon_H115 zenon_H273 zenon_H150 zenon_H14f zenon_H153 zenon_H18f zenon_H278 zenon_H26f zenon_H128 zenon_H1d zenon_H10a zenon_H201 zenon_H6f zenon_H235 zenon_H271 zenon_Ha8 zenon_H270 zenon_H277 zenon_H276 zenon_H245 zenon_H1a4 zenon_H3f zenon_H259 zenon_H1f0 zenon_H26a zenon_H149 zenon_Hdb zenon_Ha1 zenon_H1e0 zenon_H12b zenon_H52 zenon_H95 zenon_H26d zenon_H1d8 zenon_H173 zenon_H1d5 zenon_H279 zenon_H2f zenon_H5b zenon_H1fa zenon_He4 zenon_H1ac zenon_H67 zenon_He8 zenon_H1cf zenon_H71 zenon_H54 zenon_H45 zenon_H3e zenon_H6d zenon_H133 zenon_H9a zenon_H11f zenon_Hf3 zenon_He2 zenon_Hdf zenon_Hd8 zenon_H136 zenon_H124 zenon_Haf zenon_H109 zenon_H24b zenon_H7c zenon_H57 zenon_H17e zenon_H2b zenon_H1cc zenon_H1c7 zenon_H106 zenon_H27b. % 19.02/19.20 apply (zenon_or_s _ _ zenon_H27a); [ zenon_intro zenon_H177 | zenon_intro zenon_H2a ]. % 19.02/19.20 apply (zenon_or_s _ _ zenon_H27b); [ zenon_intro zenon_H20c | zenon_intro zenon_Hf0 ]. % 19.02/19.20 apply (zenon_or_s _ _ zenon_H275); [ zenon_intro zenon_H114 | zenon_intro zenon_H113 ]. % 19.02/19.20 apply (zenon_or_s _ _ zenon_H279); [ zenon_intro zenon_H14c | zenon_intro zenon_H16c ]. % 19.02/19.20 apply (zenon_L1049_); trivial. % 19.02/19.20 apply (zenon_or_s _ _ zenon_H276); [ zenon_intro zenon_Hef | zenon_intro zenon_H2c ]. % 19.02/19.20 apply (zenon_L1304_); trivial. % 19.02/19.20 apply (zenon_L1234_); trivial. % 19.02/19.20 apply (zenon_L153_); trivial. % 19.02/19.20 apply (zenon_or_s _ _ zenon_H275); [ zenon_intro zenon_H114 | zenon_intro zenon_H113 ]. % 19.02/19.20 apply (zenon_or_s _ _ zenon_H279); [ zenon_intro zenon_H14c | zenon_intro zenon_H16c ]. % 19.02/19.20 apply (zenon_or_s _ _ zenon_H276); [ zenon_intro zenon_Hef | zenon_intro zenon_H2c ]. % 19.02/19.20 apply (zenon_L1314_); trivial. % 19.02/19.20 apply (zenon_L1311_); trivial. % 19.02/19.20 apply (zenon_L167_); trivial. % 19.02/19.20 apply (zenon_L68_); trivial. % 19.02/19.20 apply (zenon_L1315_); trivial. % 19.02/19.20 (* end of lemma zenon_L1316_ *) % 19.02/19.20 assert (zenon_L1317_ : (((op (e0) (e1)) = (e2))\/(((op (e1) (e1)) = (e2))\/(((op (e2) (e1)) = (e2))\/((op (e3) (e1)) = (e2))))) -> (~((op (e0) (e1)) = (e2))) -> (~((op (e1) (e1)) = (e2))) -> (~((op (e2) (e1)) = (e2))) -> ((op (e0) (e1)) = (e3)) -> ((op (e1) (e1)) = (e0)) -> False). % 19.02/19.20 do 0 intro. intros zenon_H1d8 zenon_H26d zenon_H20c zenon_H26e zenon_H99 zenon_H29. % 19.02/19.20 apply (zenon_or_s _ _ zenon_H1d8); [ zenon_intro zenon_H10f | zenon_intro zenon_H1d9 ]. % 19.02/19.20 exact (zenon_H26d zenon_H10f). % 19.02/19.20 apply (zenon_or_s _ _ zenon_H1d9); [ zenon_intro zenon_H110 | zenon_intro zenon_H1da ]. % 19.02/19.20 exact (zenon_H20c zenon_H110). % 19.02/19.20 apply (zenon_or_s _ _ zenon_H1da); [ zenon_intro zenon_H1ca | zenon_intro zenon_H14d ]. % 19.02/19.20 exact (zenon_H26e zenon_H1ca). % 19.02/19.20 apply (zenon_L385_); trivial. % 19.02/19.20 (* end of lemma zenon_L1317_ *) % 19.02/19.20 assert (zenon_L1318_ : (((op (e1) (e1)) = (e0))\/(((op (e1) (e1)) = (e1))\/(((op (e1) (e1)) = (e2))\/((op (e1) (e1)) = (e3))))) -> (~((op (e1) (e1)) = (op (e1) (e2)))) -> ((op (e1) (e2)) = (e0)) -> (~((op (e1) (e1)) = (e1))) -> (~((op (e1) (e1)) = (e2))) -> (~((op (e0) (e1)) = (op (e1) (e1)))) -> ((op (e0) (e1)) = (e3)) -> False). % 19.02/19.20 do 0 intro. intros zenon_H142 zenon_H4f zenon_H2a zenon_H10a zenon_H20c zenon_H10e zenon_H99. % 19.02/19.20 apply (zenon_or_s _ _ zenon_H142); [ zenon_intro zenon_H29 | zenon_intro zenon_H143 ]. % 19.02/19.20 apply (zenon_L10_); trivial. % 19.02/19.20 apply (zenon_or_s _ _ zenon_H143); [ zenon_intro zenon_H10d | zenon_intro zenon_H144 ]. % 19.02/19.20 exact (zenon_H10a zenon_H10d). % 19.02/19.20 apply (zenon_or_s _ _ zenon_H144); [ zenon_intro zenon_H110 | zenon_intro zenon_H13f ]. % 19.02/19.20 exact (zenon_H20c zenon_H110). % 19.02/19.20 apply (zenon_L108_); trivial. % 19.02/19.20 (* end of lemma zenon_L1318_ *) % 19.02/19.20 assert (zenon_L1319_ : (((op (e1) (e0)) = (e0))\/(((op (e1) (e1)) = (e0))\/(((op (e1) (e2)) = (e0))\/((op (e1) (e3)) = (e0))))) -> (~((op (e1) (e0)) = (op (e3) (e0)))) -> ((op (e3) (e0)) = (e0)) -> (~((op (e2) (e1)) = (e2))) -> (~((op (e0) (e1)) = (e2))) -> (((op (e0) (e1)) = (e2))\/(((op (e1) (e1)) = (e2))\/(((op (e2) (e1)) = (e2))\/((op (e3) (e1)) = (e2))))) -> (~((op (e1) (e1)) = (op (e1) (e2)))) -> (((op (e1) (e1)) = (e0))\/(((op (e1) (e1)) = (e1))\/(((op (e1) (e1)) = (e2))\/((op (e1) (e1)) = (e3))))) -> (~((op (e1) (e1)) = (op (e1) (e3)))) -> (~((op (e1) (e1)) = (e1))) -> (~((op (e1) (e1)) = (e2))) -> (~((op (e0) (e1)) = (op (e1) (e1)))) -> ((op (e0) (e1)) = (e3)) -> False). % 19.02/19.20 do 0 intro. intros zenon_H22 zenon_H1fa zenon_H44 zenon_H26e zenon_H26d zenon_H1d8 zenon_H4f zenon_H142 zenon_H57 zenon_H10a zenon_H20c zenon_H10e zenon_H99. % 19.02/19.20 apply (zenon_or_s _ _ zenon_H22); [ zenon_intro zenon_H27 | zenon_intro zenon_H26 ]. % 19.02/19.20 apply (zenon_L312_); trivial. % 19.02/19.20 apply (zenon_or_s _ _ zenon_H26); [ zenon_intro zenon_H29 | zenon_intro zenon_H28 ]. % 19.02/19.20 apply (zenon_L1317_); trivial. % 19.02/19.20 apply (zenon_or_s _ _ zenon_H28); [ zenon_intro zenon_H2a | zenon_intro zenon_H1f ]. % 19.02/19.20 apply (zenon_L1318_); trivial. % 19.02/19.20 apply (zenon_L1221_); trivial. % 19.02/19.20 (* end of lemma zenon_L1319_ *) % 19.02/19.20 assert (zenon_L1320_ : (((op (e0) (e0)) = (e3))\/(((op (e0) (e1)) = (e3))\/(((op (e0) (e2)) = (e3))\/((op (e0) (e3)) = (e3))))) -> ((op (e0) (e0)) = (e1)) -> (~((op (e0) (e1)) = (op (e1) (e1)))) -> (~((op (e1) (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 (e2) (e1)) = (e2))) -> ((op (e3) (e0)) = (e0)) -> ((~((op (e1) (e1)) = (e2)))\/((op (e1) (e2)) = (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) (e1)) = (e0))\/(((op (e2) (e1)) = (e1))\/(((op (e2) (e1)) = (e2))\/((op (e2) (e1)) = (e3))))) -> (~((op (e1) (e2)) = (op (e2) (e2)))) -> (~((op (e0) (e1)) = (op (e2) (e1)))) -> (~((op (e1) (e1)) = (op (e1) (e3)))) -> (~((e1) = (e2))) -> (~((op (e2) (e1)) = (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 (e1) (e2)) = (op (e1) (e3)))) -> (((op (e0) (e3)) = (e3))\/(((op (e1) (e3)) = (e3))\/(((op (e2) (e3)) = (e3))\/((op (e3) (e3)) = (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) (e3)) = (op (e2) (e3)))) -> (~((op (e2) (e3)) = (op (e3) (e3)))) -> (((op (e2) (e3)) = (e0))\/(((op (e2) (e3)) = (e1))\/(((op (e2) (e3)) = (e2))\/((op (e2) (e3)) = (e3))))) -> (((op (e0) (e3)) = (e1))\/(((op (e1) (e3)) = (e1))\/(((op (e2) (e3)) = (e1))\/((op (e3) (e3)) = (e1))))) -> (~((op (e2) (e2)) = (op (e2) (e3)))) -> (((op (e0) (e0)) = (e0))\/(((op (e1) (e0)) = (e0))\/(((op (e2) (e0)) = (e0))\/((op (e3) (e0)) = (e0))))) -> (~((op (e1) (e0)) = (op (e1) (e1)))) -> (~((op (e0) (e1)) = (op (e0) (e3)))) -> (~((op (e3) (e0)) = (op (e3) (e3)))) -> (~((op (e3) (e0)) = (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 (e3) (e0)) = (e0))\/(((op (e3) (e1)) = (e0))\/(((op (e3) (e2)) = (e0))\/((op (e3) (e3)) = (e0))))) -> (((op (e0) (e3)) = (e0))\/(((op (e0) (e3)) = (e1))\/(((op (e0) (e3)) = (e2))\/((op (e0) (e3)) = (e3))))) -> (~((op (e1) (e0)) = (op (e3) (e0)))) -> (~((op (e2) (e0)) = (op (e2) (e3)))) -> (((op (e2) (e0)) = (e0))\/(((op (e2) (e1)) = (e0))\/(((op (e2) (e2)) = (e0))\/((op (e2) (e3)) = (e0))))) -> ((~((op (e1) (e3)) = (e2)))\/((op (e1) (e2)) = (e3))) -> (((op (e2) (e0)) = (e2))\/(((op (e2) (e1)) = (e2))\/(((op (e2) (e2)) = (e2))\/((op (e2) (e3)) = (e2))))) -> (~((op (e2) (e2)) = (e2))) -> (((op (e0) (e1)) = (e2))\/(((op (e1) (e1)) = (e2))\/(((op (e2) (e1)) = (e2))\/((op (e3) (e1)) = (e2))))) -> (~((op (e0) (e1)) = (e2))) -> (~((e1) = (e3))) -> (~((op (e2) (e0)) = (op (e2) (e2)))) -> (~((e2) = (e3))) -> (((op (e0) (e0)) = (e3))\/(((op (e1) (e0)) = (e3))\/(((op (e2) (e0)) = (e3))\/((op (e3) (e0)) = (e3))))) -> (~((e0) = (e1))) -> (~((op (e1) (e3)) = (op (e2) (e3)))) -> (~((e0) = (e2))) -> (((op (e0) (e0)) = (e0))\/(((op (e0) (e0)) = (e1))\/(((op (e0) (e0)) = (e2))\/((op (e0) (e0)) = (e3))))) -> (~((op (e2) (e0)) = (op (e2) (e1)))) -> (((op (e2) (e0)) = (e0))\/(((op (e2) (e0)) = (e1))\/(((op (e2) (e0)) = (e2))\/((op (e2) (e0)) = (e3))))) -> (~((op (e0) (e0)) = (e0))) -> (~((op (e3) (e1)) = (op (e3) (e2)))) -> (((op (e0) (e1)) = (e0))\/(((op (e1) (e1)) = (e0))\/(((op (e2) (e1)) = (e0))\/((op (e3) (e1)) = (e0))))) -> ((~((op (e2) (e0)) = (e2)))\/((op (e2) (e2)) = (e0))) -> ((~((op (e2) (e3)) = (e2)))\/((op (e2) (e2)) = (e3))) -> ((~((op (e3) (e0)) = (e2)))\/((op (e3) (e2)) = (e0))) -> (~((op (e0) (e2)) = (op (e2) (e2)))) -> ((~((op (e2) (e1)) = (e2)))\/((op (e2) (e2)) = (e1))) -> (((op (e0) (e0)) = (e1))\/(((op (e1) (e0)) = (e1))\/(((op (e2) (e0)) = (e1))\/((op (e3) (e0)) = (e1))))) -> (~((op (e3) (e0)) = (op (e3) (e2)))) -> (~((op (e1) (e0)) = (op (e2) (e0)))) -> (~((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 (e3) (e1)) = (e2)))\/((op (e3) (e2)) = (e1))) -> ((~((op (e3) (e3)) = (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 (e0) (e2)) = (op (e3) (e2)))) -> ((op (e0) (e2)) = (e2)) -> ((~((op (e3) (e2)) = (e2)))\/((op (e3) (e2)) = (e2))) -> (~((op (e1) (e2)) = (op (e3) (e2)))) -> (((op (e3) (e3)) = (e0))\/(((op (e3) (e3)) = (e1))\/(((op (e3) (e3)) = (e2))\/((op (e3) (e3)) = (e3))))) -> (~((op (e3) (e3)) = (e3))) -> (~((op (e0) (e3)) = (op (e3) (e3)))) -> (~((op (e1) (e3)) = (op (e3) (e3)))) -> (((op (e1) (e0)) = (e0))\/(((op (e1) (e1)) = (e0))\/(((op (e1) (e2)) = (e0))\/((op (e1) (e3)) = (e0))))) -> (~((op (e0) (e0)) = (op (e0) (e3)))) -> (((op (e0) (e0)) = (e1))\/(((op (e0) (e1)) = (e1))\/(((op (e0) (e2)) = (e1))\/((op (e0) (e3)) = (e1))))) -> (~((op (e0) (e0)) = (e2))) -> (((op (e0) (e0)) = (e2))\/(((op (e1) (e0)) = (e2))\/(((op (e2) (e0)) = (e2))\/((op (e3) (e0)) = (e2))))) -> (((op (e1) (e0)) = (e2))\/(((op (e1) (e1)) = (e2))\/(((op (e1) (e2)) = (e2))\/((op (e1) (e3)) = (e2))))) -> (~((op (e0) (e2)) = (op (e1) (e2)))) -> ((~((op (e1) (e2)) = (e2)))\/((op (e1) (e2)) = (e2))) -> ((~((op (e1) (e0)) = (e2)))\/((op (e1) (e2)) = (e0))) -> ((op (e0) (e3)) = (e0)) -> (~((e0) = (e3))) -> False). % 19.02/19.20 do 0 intro. intros zenon_H168 zenon_H7a zenon_H10e zenon_H20c zenon_H142 zenon_H4f zenon_H26e zenon_H44 zenon_H27b zenon_H106 zenon_H1c7 zenon_H1cc zenon_H2b zenon_H17e zenon_H57 zenon_H7c zenon_H24b zenon_H109 zenon_Haf zenon_H124 zenon_H136 zenon_Hd8 zenon_Hdf zenon_He2 zenon_Hf3 zenon_H11f zenon_H133 zenon_H6d zenon_H3e zenon_H45 zenon_H54 zenon_H71 zenon_H1cf zenon_He8 zenon_H67 zenon_H1ac zenon_He4 zenon_H1fa zenon_H5b zenon_H2f zenon_H279 zenon_H1d5 zenon_H173 zenon_H1d8 zenon_H26d zenon_H95 zenon_H52 zenon_H12b zenon_H1e0 zenon_Ha1 zenon_Hdb zenon_H149 zenon_H26a zenon_H1f0 zenon_H259 zenon_H3f zenon_H1a4 zenon_H245 zenon_H276 zenon_H277 zenon_H270 zenon_Ha8 zenon_H271 zenon_H235 zenon_H6f zenon_H201 zenon_H10a zenon_H1d zenon_H128 zenon_H26f zenon_H278 zenon_H18f zenon_H153 zenon_H14f zenon_H150 zenon_H273 zenon_H115 zenon_H101 zenon_H102 zenon_Hc2 zenon_Hd5 zenon_H22 zenon_H189 zenon_H22d zenon_H80 zenon_H1fe zenon_H18c zenon_H195 zenon_H275 zenon_H27a zenon_H1e zenon_H9a. % 19.02/19.20 apply (zenon_or_s _ _ zenon_H168); [ zenon_intro zenon_H3a | zenon_intro zenon_H169 ]. % 19.02/19.20 apply (zenon_L35_); trivial. % 19.02/19.20 apply (zenon_or_s _ _ zenon_H169); [ zenon_intro zenon_H99 | zenon_intro zenon_H16a ]. % 19.02/19.20 apply (zenon_L1319_); trivial. % 19.02/19.20 apply (zenon_or_s _ _ zenon_H16a); [ zenon_intro zenon_Ha9 | zenon_intro zenon_He3 ]. % 19.02/19.20 apply (zenon_L1316_); trivial. % 19.02/19.20 apply (zenon_L515_); trivial. % 19.02/19.20 (* end of lemma zenon_L1320_ *) % 19.02/19.20 assert (zenon_L1321_ : ((op (e3) (e0)) = (e0)) -> (((op (e0) (e0)) = (e2))\/(((op (e1) (e0)) = (e2))\/(((op (e2) (e0)) = (e2))\/((op (e3) (e0)) = (e2))))) -> (~((op (e0) (e0)) = (e2))) -> (~((op (e1) (e0)) = (e2))) -> (~((op (e3) (e0)) = (e2))) -> (~((op (e3) (e3)) = (e3))) -> (~((op (e3) (e1)) = (op (e3) (e3)))) -> (~((op (e2) (e3)) = (op (e3) (e3)))) -> (~((op (e3) (e0)) = (op (e3) (e3)))) -> (((op (e3) (e3)) = (e0))\/(((op (e3) (e3)) = (e1))\/(((op (e3) (e3)) = (e2))\/((op (e3) (e3)) = (e3))))) -> (((op (e0) (e3)) = (e1))\/(((op (e1) (e3)) = (e1))\/(((op (e2) (e3)) = (e1))\/((op (e3) (e3)) = (e1))))) -> (~((op (e0) (e1)) = (op (e0) (e3)))) -> (~((op (e1) (e0)) = (op (e1) (e3)))) -> (~((op (e2) (e2)) = (op (e2) (e3)))) -> ((op (e3) (e2)) = (e1)) -> (~((op (e3) (e2)) = (op (e3) (e3)))) -> (~((op (e0) (e1)) = (op (e2) (e1)))) -> (((op (e2) (e0)) = (e1))\/(((op (e2) (e1)) = (e1))\/(((op (e2) (e2)) = (e1))\/((op (e2) (e3)) = (e1))))) -> (~((op (e2) (e1)) = (e2))) -> (~((op (e1) (e1)) = (e2))) -> (~((op (e0) (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 (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) (e1)) = (e2)))\/((op (e1) (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 (e1) (e2)) = (op (e2) (e2)))) -> (~((op (e1) (e1)) = (op (e1) (e3)))) -> (~((op (e2) (e1)) = (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 (e1) (e2)) = (op (e1) (e3)))) -> (((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) (e3)) = (op (e2) (e3)))) -> (((op (e2) (e3)) = (e0))\/(((op (e2) (e3)) = (e1))\/(((op (e2) (e3)) = (e2))\/((op (e2) (e3)) = (e3))))) -> (((op (e0) (e0)) = (e0))\/(((op (e1) (e0)) = (e0))\/(((op (e2) (e0)) = (e0))\/((op (e3) (e0)) = (e0))))) -> (~((op (e1) (e0)) = (op (e1) (e1)))) -> (~((op (e3) (e0)) = (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 (e3) (e0)) = (e0))\/(((op (e3) (e1)) = (e0))\/(((op (e3) (e2)) = (e0))\/((op (e3) (e3)) = (e0))))) -> (((op (e0) (e3)) = (e0))\/(((op (e0) (e3)) = (e1))\/(((op (e0) (e3)) = (e2))\/((op (e0) (e3)) = (e3))))) -> (~((op (e1) (e0)) = (op (e3) (e0)))) -> (~((op (e2) (e0)) = (op (e2) (e3)))) -> (((op (e2) (e0)) = (e0))\/(((op (e2) (e1)) = (e0))\/(((op (e2) (e2)) = (e0))\/((op (e2) (e3)) = (e0))))) -> ((~((op (e1) (e3)) = (e2)))\/((op (e1) (e2)) = (e3))) -> (((op (e2) (e0)) = (e2))\/(((op (e2) (e1)) = (e2))\/(((op (e2) (e2)) = (e2))\/((op (e2) (e3)) = (e2))))) -> (~((op (e2) (e2)) = (e2))) -> (~((e1) = (e3))) -> (~((op (e2) (e0)) = (op (e2) (e2)))) -> (~((e2) = (e3))) -> (((op (e0) (e0)) = (e3))\/(((op (e1) (e0)) = (e3))\/(((op (e2) (e0)) = (e3))\/((op (e3) (e0)) = (e3))))) -> (~((op (e1) (e3)) = (op (e2) (e3)))) -> (~((e0) = (e2))) -> (((op (e0) (e0)) = (e0))\/(((op (e0) (e0)) = (e1))\/(((op (e0) (e0)) = (e2))\/((op (e0) (e0)) = (e3))))) -> (~((op (e2) (e0)) = (op (e2) (e1)))) -> (((op (e2) (e0)) = (e0))\/(((op (e2) (e0)) = (e1))\/(((op (e2) (e0)) = (e2))\/((op (e2) (e0)) = (e3))))) -> (~((op (e0) (e0)) = (e0))) -> (~((op (e3) (e1)) = (op (e3) (e2)))) -> (((op (e0) (e1)) = (e0))\/(((op (e1) (e1)) = (e0))\/(((op (e2) (e1)) = (e0))\/((op (e3) (e1)) = (e0))))) -> ((~((op (e2) (e0)) = (e2)))\/((op (e2) (e2)) = (e0))) -> ((~((op (e2) (e3)) = (e2)))\/((op (e2) (e2)) = (e3))) -> ((~((op (e3) (e0)) = (e2)))\/((op (e3) (e2)) = (e0))) -> (~((op (e0) (e2)) = (op (e2) (e2)))) -> ((~((op (e2) (e1)) = (e2)))\/((op (e2) (e2)) = (e1))) -> (((op (e0) (e0)) = (e1))\/(((op (e1) (e0)) = (e1))\/(((op (e2) (e0)) = (e1))\/((op (e3) (e0)) = (e1))))) -> (~((op (e3) (e0)) = (op (e3) (e2)))) -> (~((op (e1) (e0)) = (op (e2) (e0)))) -> (~((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 (e3) (e1)) = (e2)))\/((op (e3) (e2)) = (e1))) -> ((~((op (e3) (e3)) = (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 (e0) (e2)) = (op (e3) (e2)))) -> ((~((op (e3) (e2)) = (e2)))\/((op (e3) (e2)) = (e2))) -> (~((op (e1) (e2)) = (op (e3) (e2)))) -> (~((op (e0) (e3)) = (op (e3) (e3)))) -> (~((op (e1) (e3)) = (op (e3) (e3)))) -> (((op (e1) (e0)) = (e0))\/(((op (e1) (e1)) = (e0))\/(((op (e1) (e2)) = (e0))\/((op (e1) (e3)) = (e0))))) -> (~((op (e0) (e0)) = (op (e0) (e3)))) -> (((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) (e2)) = (op (e1) (e2)))) -> ((~((op (e1) (e2)) = (e2)))\/((op (e1) (e2)) = (e2))) -> ((~((op (e1) (e0)) = (e2)))\/((op (e1) (e2)) = (e0))) -> (~((e0) = (e3))) -> (~((e1) = (e2))) -> ((op (e0) (e2)) = (e2)) -> ((op (e0) (e3)) = (e0)) -> (~((e0) = (e1))) -> False). % 19.02/19.20 do 0 intro. intros zenon_H44 zenon_H1fe zenon_H80 zenon_H177 zenon_H14b zenon_H102 zenon_H130 zenon_Hf3 zenon_H71 zenon_H101 zenon_H133 zenon_H54 zenon_Hd8 zenon_H6d zenon_Hba zenon_H62 zenon_H17e zenon_H106 zenon_H26e zenon_H20c zenon_H26d zenon_H1d8 zenon_H168 zenon_H10e zenon_H142 zenon_H4f zenon_H27b zenon_H1c7 zenon_H1cc zenon_H2b zenon_H57 zenon_H24b zenon_H109 zenon_Haf zenon_H124 zenon_H136 zenon_Hdf zenon_He2 zenon_H11f zenon_H3e zenon_H45 zenon_H1cf zenon_He8 zenon_H67 zenon_H1ac zenon_He4 zenon_H1fa zenon_H5b zenon_H2f zenon_H279 zenon_H1d5 zenon_H173 zenon_H95 zenon_H52 zenon_H12b zenon_H1e0 zenon_Hdb zenon_H149 zenon_H26a zenon_H1f0 zenon_H259 zenon_H3f zenon_H1a4 zenon_H245 zenon_H276 zenon_H277 zenon_H270 zenon_Ha8 zenon_H271 zenon_H235 zenon_H6f zenon_H201 zenon_H10a zenon_H1d zenon_H128 zenon_H26f zenon_H278 zenon_H18f zenon_H153 zenon_H14f zenon_H273 zenon_H115 zenon_Hc2 zenon_Hd5 zenon_H22 zenon_H189 zenon_H22d zenon_H18c zenon_H195 zenon_H275 zenon_H27a zenon_H9a zenon_H7c zenon_H150 zenon_H1e zenon_Ha1. % 19.02/19.20 apply (zenon_or_s _ _ zenon_H22d); [ zenon_intro zenon_H7a | zenon_intro zenon_H22e ]. % 19.02/19.20 apply (zenon_L1320_); trivial. % 19.02/19.20 apply (zenon_or_s _ _ zenon_H22e); [ zenon_intro zenon_Ha0 | zenon_intro zenon_H22f ]. % 19.02/19.20 apply (zenon_or_s _ _ zenon_H235); [ zenon_intro zenon_H7a | zenon_intro zenon_H236 ]. % 19.02/19.20 apply (zenon_L1320_); trivial. % 19.02/19.20 apply (zenon_or_s _ _ zenon_H236); [ zenon_intro zenon_H9d | zenon_intro zenon_H237 ]. % 19.02/19.20 apply (zenon_or_s _ _ zenon_H1fe); [ zenon_intro zenon_H7b | zenon_intro zenon_H1ff ]. % 19.02/19.20 exact (zenon_H80 zenon_H7b). % 19.02/19.20 apply (zenon_or_s _ _ zenon_H1ff); [ zenon_intro zenon_H86 | zenon_intro zenon_H200 ]. % 19.02/19.20 exact (zenon_H177 zenon_H86). % 19.02/19.20 apply (zenon_or_s _ _ zenon_H200); [ zenon_intro zenon_Hee | zenon_intro zenon_H148 ]. % 19.02/19.20 apply (zenon_or_s _ _ zenon_H1d8); [ zenon_intro zenon_H10f | zenon_intro zenon_H1d9 ]. % 19.02/19.20 exact (zenon_H26d zenon_H10f). % 19.02/19.20 apply (zenon_or_s _ _ zenon_H1d9); [ zenon_intro zenon_H110 | zenon_intro zenon_H1da ]. % 19.02/19.20 exact (zenon_H20c zenon_H110). % 19.02/19.20 apply (zenon_or_s _ _ zenon_H1da); [ zenon_intro zenon_H1ca | zenon_intro zenon_H14d ]. % 19.02/19.20 exact (zenon_H26e zenon_H1ca). % 19.02/19.20 apply (zenon_or_s _ _ zenon_H106); [ zenon_intro zenon_Hed | zenon_intro zenon_H107 ]. % 19.02/19.20 apply (zenon_L58_); trivial. % 19.02/19.20 apply (zenon_or_s _ _ zenon_H107); [ zenon_intro zenon_Ha5 | zenon_intro zenon_H108 ]. % 19.02/19.20 apply (zenon_L357_); trivial. % 19.02/19.20 apply (zenon_or_s _ _ zenon_H108); [ zenon_intro zenon_Hf1 | zenon_intro zenon_Hf4 ]. % 19.02/19.20 apply (zenon_L419_); trivial. % 19.02/19.20 apply (zenon_L414_); trivial. % 19.02/19.20 exact (zenon_H14b zenon_H148). % 19.02/19.20 apply (zenon_or_s _ _ zenon_H237); [ zenon_intro zenon_Hed | zenon_intro zenon_Hac ]. % 19.02/19.20 apply (zenon_L1252_); trivial. % 19.02/19.20 apply (zenon_L41_); trivial. % 19.02/19.20 apply (zenon_or_s _ _ zenon_H22f); [ zenon_intro zenon_H122 | zenon_intro zenon_Hc3 ]. % 19.02/19.20 apply (zenon_L328_); trivial. % 19.02/19.20 apply (zenon_L427_); trivial. % 19.02/19.20 (* end of lemma zenon_L1321_ *) % 19.02/19.20 assert (zenon_L1322_ : (((op (e0) (e3)) = (e1))\/(((op (e1) (e3)) = (e1))\/(((op (e2) (e3)) = (e1))\/((op (e3) (e3)) = (e1))))) -> (~((e1) = (e3))) -> ((op (e0) (e3)) = (e3)) -> (~((op (e1) (e0)) = (op (e1) (e3)))) -> ((op (e1) (e0)) = (e1)) -> (~((op (e3) (e3)) = (e3))) -> ((op (e1) (e3)) = (e0)) -> (~((op (e2) (e3)) = (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)) = (e1)) -> (~((op (e3) (e2)) = (op (e3) (e3)))) -> False). % 19.02/19.20 do 0 intro. intros zenon_H133 zenon_H95 zenon_He3 zenon_Hd8 zenon_H9d zenon_H102 zenon_H1f zenon_Hf3 zenon_H44 zenon_H71 zenon_H101 zenon_Hba zenon_H62. % 19.02/19.20 apply (zenon_or_s _ _ zenon_H133); [ zenon_intro zenon_Hc3 | zenon_intro zenon_H134 ]. % 19.02/19.20 apply (zenon_L633_); trivial. % 19.02/19.20 apply (zenon_or_s _ _ zenon_H134); [ zenon_intro zenon_Hd6 | zenon_intro zenon_H135 ]. % 19.02/19.20 apply (zenon_L360_); trivial. % 19.02/19.20 apply (zenon_or_s _ _ zenon_H135); [ zenon_intro zenon_Hf4 | zenon_intro zenon_Hc4 ]. % 19.02/19.20 apply (zenon_L64_); trivial. % 19.02/19.20 apply (zenon_L147_); trivial. % 19.02/19.20 (* end of lemma zenon_L1322_ *) % 19.02/19.20 assert (zenon_L1323_ : ((~((op (e0) (e1)) = (e2)))\/((op (e0) (e2)) = (e1))) -> ((~((op (e0) (e3)) = (e2)))\/((op (e0) (e2)) = (e3))) -> ((~((op (e1) (e1)) = (e2)))\/((op (e1) (e2)) = (e1))) -> (((op (e2) (e0)) = (e0))\/(((op (e2) (e0)) = (e1))\/(((op (e2) (e0)) = (e2))\/((op (e2) (e0)) = (e3))))) -> (~((op (e0) (e1)) = (op (e1) (e1)))) -> (~((op (e3) (e2)) = (op (e3) (e3)))) -> (((op (e0) (e3)) = (e2))\/(((op (e1) (e3)) = (e2))\/(((op (e2) (e3)) = (e2))\/((op (e3) (e3)) = (e2))))) -> ((~((op (e3) (e1)) = (e2)))\/((op (e3) (e2)) = (e1))) -> (~((e0) = (e3))) -> (~((op (e3) (e0)) = (op (e3) (e2)))) -> (~((op (e2) (e0)) = (op (e2) (e2)))) -> (~((op (e0) (e0)) = (op (e0) (e3)))) -> (((op (e0) (e0)) = (e2))\/(((op (e0) (e1)) = (e2))\/(((op (e0) (e2)) = (e2))\/((op (e0) (e3)) = (e2))))) -> ((~((op (e1) (e2)) = (e2)))\/((op (e1) (e2)) = (e2))) -> ((~((op (e2) (e0)) = (e2)))\/((op (e2) (e2)) = (e0))) -> ((~((op (e2) (e3)) = (e2)))\/((op (e2) (e2)) = (e3))) -> ((~((op (e3) (e3)) = (e2)))\/((op (e3) (e2)) = (e3))) -> (~((op (e2) (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) (e1)))) -> (((op (e1) (e0)) = (e0))\/(((op (e1) (e0)) = (e1))\/(((op (e1) (e0)) = (e2))\/((op (e1) (e0)) = (e3))))) -> (~((op (e1) (e0)) = (op (e2) (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) (e3)) = (op (e2) (e3)))) -> (~((e0) = (e2))) -> (((op (e1) (e3)) = (e0))\/(((op (e1) (e3)) = (e1))\/(((op (e1) (e3)) = (e2))\/((op (e1) (e3)) = (e3))))) -> (~((op (e1) (e3)) = (op (e3) (e3)))) -> (~((op (e1) (e2)) = (op (e1) (e3)))) -> (((op (e1) (e0)) = (e0))\/(((op (e1) (e1)) = (e0))\/(((op (e1) (e2)) = (e0))\/((op (e1) (e3)) = (e0))))) -> (((op (e2) (e0)) = (e1))\/(((op (e2) (e1)) = (e1))\/(((op (e2) (e2)) = (e1))\/((op (e2) (e3)) = (e1))))) -> (~((op (e3) (e0)) = (op (e3) (e1)))) -> (~((op (e0) (e2)) = (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) (e1)) = (e0))\/(((op (e2) (e1)) = (e1))\/(((op (e2) (e1)) = (e2))\/((op (e2) (e1)) = (e3))))) -> (((op (e0) (e0)) = (e0))\/(((op (e1) (e0)) = (e0))\/(((op (e2) (e0)) = (e0))\/((op (e3) (e0)) = (e0))))) -> ((~((op (e2) (e1)) = (e2)))\/((op (e2) (e2)) = (e1))) -> (~((e1) = (e3))) -> ((~((op (e1) (e3)) = (e2)))\/((op (e1) (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 (e2) (e0)) = (e2))\/(((op (e2) (e1)) = (e2))\/(((op (e2) (e2)) = (e2))\/((op (e2) (e3)) = (e2))))) -> (~((op (e0) (e3)) = (op (e3) (e3)))) -> (~((op (e0) (e1)) = (op (e0) (e2)))) -> (~((op (e1) (e1)) = (op (e1) (e3)))) -> (~((op (e2) (e0)) = (op (e2) (e1)))) -> (((op (e0) (e1)) = (e0))\/(((op (e1) (e1)) = (e0))\/(((op (e2) (e1)) = (e0))\/((op (e3) (e1)) = (e0))))) -> (~((op (e2) (e0)) = (op (e2) (e3)))) -> (~((op (e2) (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 (e0) (e3)) = (e3))\/(((op (e1) (e3)) = (e3))\/(((op (e2) (e3)) = (e3))\/((op (e3) (e3)) = (e3))))) -> (~((op (e0) (e3)) = (op (e1) (e3)))) -> (((op (e0) (e3)) = (e0))\/(((op (e0) (e3)) = (e1))\/(((op (e0) (e3)) = (e2))\/((op (e0) (e3)) = (e3))))) -> (~((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)) = (e1))\/(((op (e1) (e1)) = (e1))\/(((op (e2) (e1)) = (e1))\/((op (e3) (e1)) = (e1))))) -> (~((op (e3) (e1)) = (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 (e2) (e3)) = (op (e3) (e3)))) -> (~((op (e1) (e0)) = (op (e1) (e3)))) -> (((op (e3) (e3)) = (e0))\/(((op (e3) (e3)) = (e1))\/(((op (e3) (e3)) = (e2))\/((op (e3) (e3)) = (e3))))) -> (~((op (e3) (e3)) = (e3))) -> (((op (e0) (e1)) = (e0))\/(((op (e0) (e1)) = (e1))\/(((op (e0) (e1)) = (e2))\/((op (e0) (e1)) = (e3))))) -> (((op (e1) (e1)) = (e0))\/(((op (e1) (e1)) = (e1))\/(((op (e1) (e1)) = (e2))\/((op (e1) (e1)) = (e3))))) -> (~((op (e0) (e1)) = (op (e2) (e1)))) -> (~((op (e0) (e1)) = (op (e0) (e3)))) -> (~((op (e0) (e1)) = (op (e3) (e1)))) -> ((op (e0) (e2)) = (e0)) -> (~((op (e0) (e2)) = (op (e0) (e3)))) -> (~((op (e0) (e2)) = (op (e2) (e2)))) -> (~((op (e2) (e2)) = (op (e2) (e3)))) -> (((op (e2) (e0)) = (e0))\/(((op (e2) (e1)) = (e0))\/(((op (e2) (e2)) = (e0))\/((op (e2) (e3)) = (e0))))) -> (~((e0) = (e1))) -> (~((op (e1) (e1)) = (e1))) -> (~((op (e1) (e2)) = (op (e2) (e2)))) -> (~((e1) = (e2))) -> (~((op (e2) (e1)) = (op (e2) (e3)))) -> (((op (e1) (e0)) = (e1))\/(((op (e1) (e1)) = (e1))\/(((op (e1) (e2)) = (e1))\/((op (e1) (e3)) = (e1))))) -> (~((op (e0) (e0)) = (e0))) -> (((op (e0) (e2)) = (e2))\/(((op (e1) (e2)) = (e2))\/(((op (e2) (e2)) = (e2))\/((op (e3) (e2)) = (e2))))) -> (~((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 (e3) (e2)) = (e2)))\/((op (e3) (e2)) = (e2))) -> ((~((op (e3) (e0)) = (e2)))\/((op (e3) (e2)) = (e0))) -> (((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)) = (e2)))\/((op (e1) (e2)) = (e0))) -> ((~((op (e0) (e2)) = (e2)))\/((op (e0) (e2)) = (e2))) -> False). % 19.02/19.20 do 0 intro. intros zenon_H27d zenon_H27c zenon_H27b zenon_H259 zenon_H10e zenon_H62 zenon_H145 zenon_H26f zenon_H9a zenon_H6f zenon_H52 zenon_H189 zenon_H183 zenon_H275 zenon_H276 zenon_H277 zenon_H278 zenon_H18f zenon_H22d zenon_H45 zenon_H25e zenon_H201 zenon_H1fa zenon_H18c zenon_Hdb zenon_H149 zenon_Hdf zenon_Hd5 zenon_H124 zenon_H22 zenon_H106 zenon_H1cf zenon_H195 zenon_H115 zenon_H235 zenon_H1cc zenon_H3e zenon_H271 zenon_H95 zenon_H279 zenon_H1ac zenon_H14f zenon_H1d5 zenon_Hc2 zenon_H4a zenon_H57 zenon_H1f0 zenon_H245 zenon_H5b zenon_H17b zenon_H67 zenon_He8 zenon_H136 zenon_H1d zenon_He4 zenon_H12b zenon_He2 zenon_H11f zenon_H109 zenon_H130 zenon_H133 zenon_H71 zenon_Hf3 zenon_Hd8 zenon_H101 zenon_H102 zenon_H212 zenon_H142 zenon_H17e zenon_H54 zenon_H210 zenon_H48 zenon_H208 zenon_Ha8 zenon_H6d zenon_H2f zenon_Ha1 zenon_H10a zenon_H2b zenon_H7c zenon_H1c7 zenon_H128 zenon_H3f zenon_H172 zenon_H173 zenon_H1d8 zenon_H1a4 zenon_H273 zenon_H270 zenon_H153 zenon_H16f zenon_H27a zenon_H27e. % 19.02/19.20 apply (zenon_or_s _ _ zenon_H27d); [ zenon_intro zenon_H26d | zenon_intro zenon_H122 ]. % 19.02/19.20 apply (zenon_or_s _ _ zenon_H27e); [ zenon_intro zenon_H1fd | zenon_intro zenon_H150 ]. % 19.02/19.20 apply (zenon_L1258_); trivial. % 19.02/19.20 apply (zenon_L378_); trivial. % 19.02/19.20 apply (zenon_L355_); trivial. % 19.02/19.20 (* end of lemma zenon_L1323_ *) % 19.02/19.20 assert (zenon_L1324_ : (((op (e0) (e0)) = (e1))\/(((op (e0) (e1)) = (e1))\/(((op (e0) (e2)) = (e1))\/((op (e0) (e3)) = (e1))))) -> ((op (e3) (e2)) = (e0)) -> (~((op (e3) (e1)) = (op (e3) (e2)))) -> (((op (e0) (e0)) = (e0))\/(((op (e0) (e0)) = (e1))\/(((op (e0) (e0)) = (e2))\/((op (e0) (e0)) = (e3))))) -> (~((op (e0) (e0)) = (e0))) -> (~((e2) = (e3))) -> (~((e1) = (e3))) -> (((op (e0) (e0)) = (e3))\/(((op (e1) (e0)) = (e3))\/(((op (e2) (e0)) = (e3))\/((op (e3) (e0)) = (e3))))) -> (~((op (e0) (e0)) = (e2))) -> (((op (e2) (e0)) = (e0))\/(((op (e2) (e0)) = (e1))\/(((op (e2) (e0)) = (e2))\/((op (e2) (e0)) = (e3))))) -> (~((op (e2) (e0)) = (op (e2) (e1)))) -> (~((op (e2) (e0)) = (e2))) -> ((op (e2) (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 (e1) (e0)) = (e2))) -> (~((e0) = (e2))) -> (~((op (e1) (e2)) = (e2))) -> (((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 (e1) (e3)) = (op (e2) (e3)))) -> (((op (e0) (e1)) = (e0))\/(((op (e1) (e1)) = (e0))\/(((op (e2) (e1)) = (e0))\/((op (e3) (e1)) = (e0))))) -> (((op (e0) (e0)) = (e2))\/(((op (e1) (e0)) = (e2))\/(((op (e2) (e0)) = (e2))\/((op (e3) (e0)) = (e2))))) -> ((op (e1) (e2)) = (e1)) -> (~((op (e0) (e2)) = (op (e1) (e2)))) -> ((op (e0) (e3)) = (e0)) -> (~((e0) = (e1))) -> False). % 19.02/19.21 do 0 intro. intros zenon_H22d zenon_H61 zenon_H1a4 zenon_H26a zenon_H3f zenon_H12b zenon_H95 zenon_H1e0 zenon_H80 zenon_H259 zenon_H1f0 zenon_Hef zenon_Haa zenon_H52 zenon_H18c zenon_H177 zenon_H149 zenon_H114 zenon_H1d5 zenon_H26e zenon_H173 zenon_Hdb zenon_H245 zenon_H1fe zenon_Hf0 zenon_H195 zenon_H1e zenon_Ha1. % 19.02/19.21 apply (zenon_or_s _ _ zenon_H22d); [ zenon_intro zenon_H7a | zenon_intro zenon_H22e ]. % 19.02/19.21 apply (zenon_L1295_); trivial. % 19.02/19.21 apply (zenon_or_s _ _ zenon_H22e); [ zenon_intro zenon_Ha0 | zenon_intro zenon_H22f ]. % 19.02/19.21 apply (zenon_L1298_); trivial. % 19.02/19.21 apply (zenon_or_s _ _ zenon_H22f); [ zenon_intro zenon_H122 | zenon_intro zenon_Hc3 ]. % 19.02/19.21 apply (zenon_L530_); trivial. % 19.02/19.21 apply (zenon_L427_); trivial. % 19.02/19.21 (* end of lemma zenon_L1324_ *) % 19.02/19.21 assert (zenon_L1325_ : (((op (e2) (e0)) = (e0))\/(((op (e2) (e0)) = (e1))\/(((op (e2) (e0)) = (e2))\/((op (e2) (e0)) = (e3))))) -> (~((op (e2) (e0)) = (op (e2) (e3)))) -> ((op (e2) (e3)) = (e0)) -> (~((op (e0) (e0)) = (op (e2) (e0)))) -> (~((op (e2) (e0)) = (e2))) -> ((op (e1) (e0)) = (e2)) -> ((op (e0) (e0)) = (e1)) -> False). % 19.02/19.21 do 0 intro. intros zenon_H259 zenon_H5b zenon_H37 zenon_H39 zenon_Hef zenon_H86 zenon_H7a. % 19.02/19.21 apply (zenon_or_s _ _ zenon_H259); [ zenon_intro zenon_H34 | zenon_intro zenon_H25a ]. % 19.02/19.21 apply (zenon_L14_); trivial. % 19.02/19.21 apply (zenon_or_s _ _ zenon_H25a); [ zenon_intro zenon_Hed | zenon_intro zenon_H25b ]. % 19.02/19.21 apply (zenon_L134_); trivial. % 19.02/19.21 apply (zenon_or_s _ _ zenon_H25b); [ zenon_intro zenon_Hee | zenon_intro zenon_H3b ]. % 19.02/19.21 exact (zenon_Hef zenon_Hee). % 19.02/19.21 apply (zenon_L33_); trivial. % 19.02/19.21 (* end of lemma zenon_L1325_ *) % 19.02/19.21 assert (zenon_L1326_ : (((op (e0) (e0)) = (e2))\/(((op (e1) (e0)) = (e2))\/(((op (e2) (e0)) = (e2))\/((op (e3) (e0)) = (e2))))) -> (~((op (e0) (e0)) = (e2))) -> (~((op (e3) (e0)) = (op (e3) (e2)))) -> ((op (e3) (e2)) = (e3)) -> ((op (e0) (e0)) = (e1)) -> (((op (e1) (e0)) = (e1))\/(((op (e1) (e1)) = (e1))\/(((op (e1) (e2)) = (e1))\/((op (e1) (e3)) = (e1))))) -> (~((e1) = (e3))) -> (~((op (e1) (e1)) = (e1))) -> ((~((op (e2) (e1)) = (e2)))\/((op (e2) (e2)) = (e1))) -> (((op (e2) (e0)) = (e2))\/(((op (e2) (e1)) = (e2))\/(((op (e2) (e2)) = (e2))\/((op (e2) (e3)) = (e2))))) -> (~((op (e2) (e2)) = (e2))) -> ((~((op (e3) (e0)) = (e2)))\/((op (e3) (e2)) = (e0))) -> (~((op (e1) (e2)) = (op (e3) (e2)))) -> ((~((op (e3) (e2)) = (e2)))\/((op (e3) (e2)) = (e2))) -> ((op (e0) (e2)) = (e2)) -> (~((op (e0) (e2)) = (op (e3) (e2)))) -> (((op (e3) (e0)) = (e2))\/(((op (e3) (e1)) = (e2))\/(((op (e3) (e2)) = (e2))\/((op (e3) (e3)) = (e2))))) -> (~((op (e2) (e2)) = (op (e3) (e2)))) -> ((~((op (e3) (e3)) = (e2)))\/((op (e3) (e2)) = (e3))) -> ((~((op (e3) (e1)) = (e2)))\/((op (e3) (e2)) = (e1))) -> ((~((op (e2) (e3)) = (e2)))\/((op (e2) (e2)) = (e3))) -> ((~((op (e2) (e0)) = (e2)))\/((op (e2) (e2)) = (e0))) -> (((op (e2) (e0)) = (e0))\/(((op (e2) (e1)) = (e0))\/(((op (e2) (e2)) = (e0))\/((op (e2) (e3)) = (e0))))) -> (~((op (e0) (e3)) = (op (e2) (e3)))) -> (~((op (e2) (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 (e1) (e3)) = (e2))) -> (~((op (e0) (e3)) = (op (e1) (e3)))) -> (~((op (e2) (e3)) = (op (e3) (e3)))) -> (((op (e2) (e3)) = (e0))\/(((op (e2) (e3)) = (e1))\/(((op (e2) (e3)) = (e2))\/((op (e2) (e3)) = (e3))))) -> (~((e0) = (e3))) -> (((op (e0) (e3)) = (e0))\/(((op (e1) (e3)) = (e0))\/(((op (e2) (e3)) = (e0))\/((op (e3) (e3)) = (e0))))) -> ((op (e0) (e1)) = (e0)) -> (~((op (e0) (e1)) = (op (e2) (e1)))) -> ((op (e1) (e2)) = (e0)) -> (~((op (e1) (e2)) = (op (e2) (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) (e0)) = (op (e2) (e0)))) -> (((op (e0) (e0)) = (e3))\/(((op (e1) (e0)) = (e3))\/(((op (e2) (e0)) = (e3))\/((op (e3) (e0)) = (e3))))) -> ((op (e2) (e2)) = (e1)) -> (((op (e0) (e0)) = (e3))\/(((op (e0) (e1)) = (e3))\/(((op (e0) (e2)) = (e3))\/((op (e0) (e3)) = (e3))))) -> (~((op (e2) (e0)) = (e2))) -> (~((op (e3) (e0)) = (e2))) -> False). % 19.02/19.21 do 0 intro. intros zenon_H1fe zenon_H80 zenon_H6f zenon_H163 zenon_H7a zenon_H128 zenon_H95 zenon_H10a zenon_H271 zenon_H1d5 zenon_H173 zenon_H270 zenon_H115 zenon_H273 zenon_H150 zenon_H14f zenon_H153 zenon_H18f zenon_H278 zenon_H26f zenon_H277 zenon_H276 zenon_H2f zenon_He2 zenon_H274 zenon_Hdf zenon_Hd5 zenon_Hdb zenon_H14c zenon_H1d zenon_Hf3 zenon_H11f zenon_H9a zenon_H67 zenon_H49 zenon_H17e zenon_H2a zenon_H2b zenon_H259 zenon_H5b zenon_H39 zenon_H1e0 zenon_Hf1 zenon_H168 zenon_Hef zenon_H14b. % 19.02/19.21 apply (zenon_or_s _ _ zenon_H1fe); [ zenon_intro zenon_H7b | zenon_intro zenon_H1ff ]. % 19.02/19.21 exact (zenon_H80 zenon_H7b). % 19.02/19.21 apply (zenon_or_s _ _ zenon_H1ff); [ zenon_intro zenon_H86 | zenon_intro zenon_H200 ]. % 19.02/19.21 apply (zenon_or_s _ _ zenon_H168); [ zenon_intro zenon_H3a | zenon_intro zenon_H169 ]. % 19.02/19.21 apply (zenon_L35_); trivial. % 19.02/19.21 apply (zenon_or_s _ _ zenon_H169); [ zenon_intro zenon_H99 | zenon_intro zenon_H16a ]. % 19.02/19.21 apply (zenon_L36_); trivial. % 19.02/19.21 apply (zenon_or_s _ _ zenon_H16a); [ zenon_intro zenon_Ha9 | zenon_intro zenon_He3 ]. % 19.02/19.21 apply (zenon_L184_); trivial. % 19.02/19.21 apply (zenon_or_s _ _ zenon_H1e0); [ zenon_intro zenon_H3a | zenon_intro zenon_H1e1 ]. % 19.02/19.21 apply (zenon_L35_); trivial. % 19.02/19.21 apply (zenon_or_s _ _ zenon_H1e1); [ zenon_intro zenon_H9e | zenon_intro zenon_H1e2 ]. % 19.02/19.21 apply (zenon_or_s _ _ zenon_H128); [ zenon_intro zenon_H9d | zenon_intro zenon_H129 ]. % 19.02/19.21 apply (zenon_L37_); trivial. % 19.02/19.21 apply (zenon_or_s _ _ zenon_H129); [ zenon_intro zenon_H10d | zenon_intro zenon_H12a ]. % 19.02/19.21 exact (zenon_H10a zenon_H10d). % 19.02/19.21 apply (zenon_or_s _ _ zenon_H12a); [ zenon_intro zenon_Hf0 | zenon_intro zenon_Hd6 ]. % 19.02/19.21 apply (zenon_L1307_); trivial. % 19.02/19.21 apply (zenon_or_s _ _ zenon_H2f); [ zenon_intro zenon_H34 | zenon_intro zenon_H33 ]. % 19.02/19.21 apply (zenon_L1160_); trivial. % 19.02/19.21 apply (zenon_or_s _ _ zenon_H33); [ zenon_intro zenon_H36 | zenon_intro zenon_H35 ]. % 19.02/19.21 apply (zenon_L128_); trivial. % 19.02/19.21 apply (zenon_or_s _ _ zenon_H35); [ zenon_intro zenon_H2c | zenon_intro zenon_H37 ]. % 19.02/19.21 apply (zenon_L3_); trivial. % 19.02/19.21 apply (zenon_L1325_); trivial. % 19.02/19.21 apply (zenon_or_s _ _ zenon_H1e2); [ zenon_intro zenon_H3b | zenon_intro zenon_H15e ]. % 19.02/19.21 apply (zenon_L33_); trivial. % 19.02/19.21 apply (zenon_L286_); trivial. % 19.02/19.21 apply (zenon_or_s _ _ zenon_H200); [ zenon_intro zenon_Hee | zenon_intro zenon_H148 ]. % 19.02/19.21 exact (zenon_Hef zenon_Hee). % 19.02/19.21 exact (zenon_H14b zenon_H148). % 19.02/19.21 (* end of lemma zenon_L1326_ *) % 19.02/19.21 assert (zenon_L1327_ : ((~((op (e0) (e2)) = (e2)))\/((op (e0) (e2)) = (e2))) -> ((~((op (e1) (e0)) = (e2)))\/((op (e1) (e2)) = (e0))) -> ((~((op (e3) (e1)) = (e2)))\/((op (e3) (e2)) = (e1))) -> (((op (e0) (e0)) = (e1))\/(((op (e1) (e0)) = (e1))\/(((op (e2) (e0)) = (e1))\/((op (e3) (e0)) = (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)) = (op (e3) (e3)))) -> (~((op (e2) (e2)) = (op (e2) (e3)))) -> (~((op (e0) (e1)) = (op (e0) (e2)))) -> (((op (e3) (e0)) = (e1))\/(((op (e3) (e1)) = (e1))\/(((op (e3) (e2)) = (e1))\/((op (e3) (e3)) = (e1))))) -> (~((e0) = (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) (e3)) = (op (e3) (e3)))) -> (~((op (e0) (e3)) = (op (e2) (e3)))) -> (((op (e1) (e3)) = (e0))\/(((op (e1) (e3)) = (e1))\/(((op (e1) (e3)) = (e2))\/((op (e1) (e3)) = (e3))))) -> (~((op (e1) (e3)) = (op (e3) (e3)))) -> (~((op (e1) (e1)) = (op (e1) (e3)))) -> (~((op (e3) (e3)) = (e3))) -> (((op (e0) (e3)) = (e3))\/(((op (e1) (e3)) = (e3))\/(((op (e2) (e3)) = (e3))\/((op (e3) (e3)) = (e3))))) -> (~((op (e0) (e2)) = (op (e3) (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) (e2)))) -> (~((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)) = (e1))\/(((op (e1) (e1)) = (e1))\/(((op (e2) (e1)) = (e1))\/((op (e3) (e1)) = (e1))))) -> ((~((op (e1) (e1)) = (e2)))\/((op (e1) (e2)) = (e1))) -> (((op (e0) (e0)) = (e0))\/(((op (e0) (e1)) = (e0))\/(((op (e0) (e2)) = (e0))\/((op (e0) (e3)) = (e0))))) -> (~((op (e0) (e1)) = (op (e0) (e3)))) -> (((op (e0) (e1)) = (e0))\/(((op (e1) (e1)) = (e0))\/(((op (e2) (e1)) = (e0))\/((op (e3) (e1)) = (e0))))) -> (~((e2) = (e3))) -> (~((op (e1) (e0)) = (op (e1) (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)) = (op (e2) (e1)))) -> (((op (e1) (e0)) = (e1))\/(((op (e1) (e1)) = (e1))\/(((op (e1) (e2)) = (e1))\/((op (e1) (e3)) = (e1))))) -> (~((op (e0) (e2)) = (op (e1) (e2)))) -> (~((op (e1) (e0)) = (op (e2) (e0)))) -> (~((op (e2) (e0)) = (op (e2) (e2)))) -> (((op (e2) (e0)) = (e0))\/(((op (e2) (e0)) = (e1))\/(((op (e2) (e0)) = (e2))\/((op (e2) (e0)) = (e3))))) -> (~((op (e1) (e2)) = (op (e2) (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 (e3) (e1)) = (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))))) -> (~((e1) = (e3))) -> (~((op (e0) (e1)) = (op (e2) (e1)))) -> (((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 (e1) (e2)) = (op (e3) (e2)))) -> (((op (e0) (e0)) = (e0))\/(((op (e0) (e0)) = (e1))\/(((op (e0) (e0)) = (e2))\/((op (e0) (e0)) = (e3))))) -> (((op (e3) (e0)) = (e0))\/(((op (e3) (e1)) = (e0))\/(((op (e3) (e2)) = (e0))\/((op (e3) (e3)) = (e0))))) -> (((op (e0) (e0)) = (e0))\/(((op (e1) (e0)) = (e0))\/(((op (e2) (e0)) = (e0))\/((op (e3) (e0)) = (e0))))) -> (~((e0) = (e2))) -> ((~((op (e1) (e2)) = (e2)))\/((op (e1) (e2)) = (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 (e0) (e0)) = (op (e0) (e2)))) -> (~((op (e1) (e0)) = (op (e1) (e1)))) -> (~((e1) = (e2))) -> (~((op (e1) (e1)) = (e1))) -> (~((e0) = (e1))) -> (~((op (e0) (e0)) = (e0))) -> ((~((op (e2) (e3)) = (e2)))\/((op (e2) (e2)) = (e3))) -> ((~((op (e3) (e3)) = (e2)))\/((op (e3) (e2)) = (e3))) -> (~((op (e2) (e2)) = (op (e3) (e2)))) -> (~((op (e0) (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 (e0) (e2)) = (e1)) -> ((~((op (e3) (e0)) = (e2)))\/((op (e3) (e2)) = (e0))) -> (((op (e0) (e2)) = (e2))\/(((op (e1) (e2)) = (e2))\/(((op (e2) (e2)) = (e2))\/((op (e3) (e2)) = (e2))))) -> (~((op (e2) (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 (e3) (e2)) = (e2)))\/((op (e3) (e2)) = (e2))) -> ((~((op (e2) (e0)) = (e2)))\/((op (e2) (e2)) = (e0))) -> (((op (e2) (e0)) = (e2))\/(((op (e2) (e1)) = (e2))\/(((op (e2) (e2)) = (e2))\/((op (e2) (e3)) = (e2))))) -> (~((op (e0) (e2)) = (op (e2) (e2)))) -> ((~((op (e2) (e1)) = (e2)))\/((op (e2) (e2)) = (e1))) -> ((~((op (e1) (e3)) = (e2)))\/((op (e1) (e2)) = (e3))) -> ((~((op (e0) (e3)) = (e2)))\/((op (e0) (e2)) = (e3))) -> False). % 19.02/19.21 do 0 intro. intros zenon_H27e zenon_H27a zenon_H26f zenon_H235 zenon_H1fa zenon_H67 zenon_H71 zenon_H6d zenon_H4a zenon_He8 zenon_H9a zenon_H11f zenon_Hdb zenon_Hf3 zenon_He2 zenon_Hdf zenon_Hd5 zenon_H57 zenon_H102 zenon_H136 zenon_H14f zenon_Haf zenon_H106 zenon_H24b zenon_H1c7 zenon_H1cc zenon_H109 zenon_H27b zenon_H74 zenon_H54 zenon_H245 zenon_H12b zenon_H24a zenon_H183 zenon_H17b zenon_H1f0 zenon_H128 zenon_H195 zenon_H201 zenon_H52 zenon_H259 zenon_H2b zenon_Hc2 zenon_H1d zenon_He4 zenon_H130 zenon_H101 zenon_H2f zenon_H95 zenon_H17e zenon_H168 zenon_H142 zenon_H4f zenon_H115 zenon_H26a zenon_H1ac zenon_H3e zenon_H149 zenon_H275 zenon_H22 zenon_H153 zenon_H13c zenon_H45 zenon_H7c zenon_H10a zenon_Ha1 zenon_H3f zenon_H277 zenon_H278 zenon_H18f zenon_H80 zenon_H5b zenon_H1fe zenon_H122 zenon_H270 zenon_H172 zenon_H173 zenon_H145 zenon_H62 zenon_H273 zenon_H276 zenon_H1d5 zenon_Ha8 zenon_H271 zenon_H279 zenon_H27c. % 19.02/19.21 apply (zenon_or_s _ _ zenon_H27e); [ zenon_intro zenon_H1fd | zenon_intro zenon_H150 ]. % 19.02/19.21 apply (zenon_L1256_); trivial. % 19.02/19.21 apply (zenon_L328_); trivial. % 19.02/19.21 (* end of lemma zenon_L1327_ *) % 19.02/19.21 assert (zenon_L1328_ : (((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 (e0) (e1)) = (e0)) -> (~((op (e0) (e1)) = (op (e2) (e1)))) -> ((op (e1) (e2)) = (e0)) -> (~((op (e1) (e2)) = (op (e2) (e2)))) -> (((op (e3) (e0)) = (e2))\/(((op (e3) (e1)) = (e2))\/(((op (e3) (e2)) = (e2))\/((op (e3) (e3)) = (e2))))) -> (~((op (e3) (e0)) = (e2))) -> (~((op (e3) (e1)) = (e2))) -> (~((op (e3) (e2)) = (e2))) -> ((op (e0) (e3)) = (e1)) -> False). % 19.02/19.21 do 0 intro. intros zenon_H2f zenon_H17b zenon_H44 zenon_H49 zenon_H17e zenon_H2a zenon_H2b zenon_H153 zenon_H14b zenon_H194 zenon_H272 zenon_Hc3. % 19.02/19.21 apply (zenon_or_s _ _ zenon_H2f); [ zenon_intro zenon_H34 | zenon_intro zenon_H33 ]. % 19.02/19.21 apply (zenon_L127_); trivial. % 19.02/19.21 apply (zenon_or_s _ _ zenon_H33); [ zenon_intro zenon_H36 | zenon_intro zenon_H35 ]. % 19.02/19.21 apply (zenon_L128_); trivial. % 19.02/19.21 apply (zenon_or_s _ _ zenon_H35); [ zenon_intro zenon_H2c | zenon_intro zenon_H37 ]. % 19.02/19.21 apply (zenon_L3_); trivial. % 19.02/19.21 apply (zenon_L1173_); trivial. % 19.02/19.21 (* end of lemma zenon_L1328_ *) % 19.02/19.21 assert (zenon_L1329_ : (((op (e0) (e0)) = (e3))\/(((op (e0) (e1)) = (e3))\/(((op (e0) (e2)) = (e3))\/((op (e0) (e3)) = (e3))))) -> ((op (e3) (e0)) = (e1)) -> ((op (e1) (e0)) = (e2)) -> (~((op (e0) (e1)) = (op (e1) (e1)))) -> (~((op (e1) (e1)) = (e2))) -> ((op (e1) (e2)) = (e0)) -> (~((op (e1) (e1)) = (op (e1) (e2)))) -> (((op (e1) (e1)) = (e0))\/(((op (e1) (e1)) = (e1))\/(((op (e1) (e1)) = (e2))\/((op (e1) (e1)) = (e3))))) -> ((~((op (e1) (e1)) = (e2)))\/((op (e1) (e2)) = (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) (e1)) = (e0))\/(((op (e2) (e1)) = (e1))\/(((op (e2) (e1)) = (e2))\/((op (e2) (e1)) = (e3))))) -> (~((op (e1) (e2)) = (op (e2) (e2)))) -> (~((op (e0) (e1)) = (op (e2) (e1)))) -> (~((op (e1) (e1)) = (op (e1) (e3)))) -> (~((e1) = (e2))) -> (~((op (e2) (e1)) = (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 (e1) (e2)) = (op (e1) (e3)))) -> (((op (e0) (e3)) = (e3))\/(((op (e1) (e3)) = (e3))\/(((op (e2) (e3)) = (e3))\/((op (e3) (e3)) = (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) (e3)) = (op (e2) (e3)))) -> (~((op (e2) (e3)) = (op (e3) (e3)))) -> (((op (e2) (e3)) = (e0))\/(((op (e2) (e3)) = (e1))\/(((op (e2) (e3)) = (e2))\/((op (e2) (e3)) = (e3))))) -> (~((e0) = (e3))) -> (((op (e0) (e3)) = (e1))\/(((op (e1) (e3)) = (e1))\/(((op (e2) (e3)) = (e1))\/((op (e3) (e3)) = (e1))))) -> (~((op (e2) (e2)) = (op (e2) (e3)))) -> (((op (e0) (e0)) = (e0))\/(((op (e1) (e0)) = (e0))\/(((op (e2) (e0)) = (e0))\/((op (e3) (e0)) = (e0))))) -> (~((op (e1) (e0)) = (op (e1) (e1)))) -> (~((op (e0) (e1)) = (op (e0) (e3)))) -> (~((op (e3) (e0)) = (op (e3) (e3)))) -> (~((op (e3) (e0)) = (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 (e3) (e0)) = (e0))\/(((op (e3) (e1)) = (e0))\/(((op (e3) (e2)) = (e0))\/((op (e3) (e3)) = (e0))))) -> (((op (e0) (e3)) = (e0))\/(((op (e0) (e3)) = (e1))\/(((op (e0) (e3)) = (e2))\/((op (e0) (e3)) = (e3))))) -> (~((op (e1) (e0)) = (op (e3) (e0)))) -> (~((op (e2) (e0)) = (op (e2) (e3)))) -> (((op (e2) (e0)) = (e0))\/(((op (e2) (e1)) = (e0))\/(((op (e2) (e2)) = (e0))\/((op (e2) (e3)) = (e0))))) -> ((~((op (e1) (e3)) = (e2)))\/((op (e1) (e2)) = (e3))) -> (((op (e2) (e0)) = (e2))\/(((op (e2) (e1)) = (e2))\/(((op (e2) (e2)) = (e2))\/((op (e2) (e3)) = (e2))))) -> (~((op (e2) (e2)) = (e2))) -> (((op (e0) (e1)) = (e2))\/(((op (e1) (e1)) = (e2))\/(((op (e2) (e1)) = (e2))\/((op (e3) (e1)) = (e2))))) -> (~((op (e0) (e1)) = (e2))) -> (~((op (e2) (e0)) = (op (e2) (e2)))) -> (~((e2) = (e3))) -> (((op (e0) (e0)) = (e3))\/(((op (e1) (e0)) = (e3))\/(((op (e2) (e0)) = (e3))\/((op (e3) (e0)) = (e3))))) -> (~((e0) = (e1))) -> (~((op (e1) (e3)) = (op (e2) (e3)))) -> (~((e0) = (e2))) -> (((op (e0) (e0)) = (e0))\/(((op (e0) (e0)) = (e1))\/(((op (e0) (e0)) = (e2))\/((op (e0) (e0)) = (e3))))) -> (~((op (e2) (e0)) = (op (e2) (e1)))) -> (((op (e2) (e0)) = (e0))\/(((op (e2) (e0)) = (e1))\/(((op (e2) (e0)) = (e2))\/((op (e2) (e0)) = (e3))))) -> (~((op (e0) (e0)) = (e0))) -> (~((op (e3) (e1)) = (op (e3) (e2)))) -> (((op (e0) (e1)) = (e0))\/(((op (e1) (e1)) = (e0))\/(((op (e2) (e1)) = (e0))\/((op (e3) (e1)) = (e0))))) -> ((~((op (e2) (e0)) = (e2)))\/((op (e2) (e2)) = (e0))) -> ((~((op (e2) (e3)) = (e2)))\/((op (e2) (e2)) = (e3))) -> ((~((op (e3) (e0)) = (e2)))\/((op (e3) (e2)) = (e0))) -> (~((op (e0) (e2)) = (op (e2) (e2)))) -> ((~((op (e2) (e1)) = (e2)))\/((op (e2) (e2)) = (e1))) -> (((op (e0) (e0)) = (e1))\/(((op (e1) (e0)) = (e1))\/(((op (e2) (e0)) = (e1))\/((op (e3) (e0)) = (e1))))) -> (~((op (e3) (e0)) = (op (e3) (e2)))) -> (~((op (e1) (e0)) = (op (e2) (e0)))) -> (~((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 (e3) (e1)) = (e2)))\/((op (e3) (e2)) = (e1))) -> ((~((op (e3) (e3)) = (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 (e0) (e2)) = (op (e3) (e2)))) -> ((op (e0) (e2)) = (e2)) -> ((~((op (e3) (e2)) = (e2)))\/((op (e3) (e2)) = (e2))) -> (~((op (e1) (e2)) = (op (e3) (e2)))) -> (((op (e3) (e3)) = (e0))\/(((op (e3) (e3)) = (e1))\/(((op (e3) (e3)) = (e2))\/((op (e3) (e3)) = (e3))))) -> (~((op (e3) (e3)) = (e3))) -> (~((op (e0) (e3)) = (op (e3) (e3)))) -> (~((op (e1) (e3)) = (op (e3) (e3)))) -> (((op (e1) (e0)) = (e0))\/(((op (e1) (e1)) = (e0))\/(((op (e1) (e2)) = (e0))\/((op (e1) (e3)) = (e0))))) -> (~((op (e0) (e0)) = (op (e0) (e3)))) -> (((op (e0) (e0)) = (e1))\/(((op (e0) (e1)) = (e1))\/(((op (e0) (e2)) = (e1))\/((op (e0) (e3)) = (e1))))) -> (~((op (e0) (e0)) = (e2))) -> (((op (e0) (e0)) = (e2))\/(((op (e1) (e0)) = (e2))\/(((op (e2) (e0)) = (e2))\/((op (e3) (e0)) = (e2))))) -> (((op (e1) (e0)) = (e2))\/(((op (e1) (e1)) = (e2))\/(((op (e1) (e2)) = (e2))\/((op (e1) (e3)) = (e2))))) -> (~((op (e0) (e2)) = (op (e1) (e2)))) -> ((~((op (e1) (e2)) = (e2)))\/((op (e1) (e2)) = (e2))) -> ((~((op (e1) (e0)) = (e2)))\/((op (e1) (e2)) = (e0))) -> ((op (e0) (e3)) = (e1)) -> (~((e1) = (e3))) -> False). % 19.02/19.21 do 0 intro. intros zenon_H168 zenon_Hac zenon_H86 zenon_H10e zenon_H20c zenon_H2a zenon_H4f zenon_H142 zenon_H27b zenon_H106 zenon_H1c7 zenon_H1cc zenon_H2b zenon_H17e zenon_H57 zenon_H7c zenon_H24b zenon_H109 zenon_Haf zenon_H124 zenon_H136 zenon_Hd8 zenon_Hdf zenon_He2 zenon_Hf3 zenon_H11f zenon_H9a zenon_H133 zenon_H6d zenon_H3e zenon_H45 zenon_H54 zenon_H71 zenon_H1cf zenon_He8 zenon_H67 zenon_H1ac zenon_He4 zenon_H1fa zenon_H5b zenon_H2f zenon_H279 zenon_H1d5 zenon_H173 zenon_H1d8 zenon_H26d zenon_H52 zenon_H12b zenon_H1e0 zenon_Ha1 zenon_Hdb zenon_H149 zenon_H26a zenon_H1f0 zenon_H259 zenon_H3f zenon_H1a4 zenon_H245 zenon_H276 zenon_H277 zenon_H270 zenon_Ha8 zenon_H271 zenon_H235 zenon_H6f zenon_H201 zenon_H10a zenon_H1d zenon_H128 zenon_H26f zenon_H278 zenon_H18f zenon_H153 zenon_H14f zenon_H150 zenon_H273 zenon_H115 zenon_H101 zenon_H102 zenon_Hc2 zenon_Hd5 zenon_H22 zenon_H189 zenon_H22d zenon_H80 zenon_H1fe zenon_H18c zenon_H195 zenon_H275 zenon_H27a zenon_Hc3 zenon_H95. % 19.02/19.21 apply (zenon_or_s _ _ zenon_H168); [ zenon_intro zenon_H3a | zenon_intro zenon_H169 ]. % 19.02/19.21 apply (zenon_L241_); trivial. % 19.02/19.21 apply (zenon_or_s _ _ zenon_H169); [ zenon_intro zenon_H99 | zenon_intro zenon_H16a ]. % 19.02/19.21 apply (zenon_L1318_); trivial. % 19.02/19.21 apply (zenon_or_s _ _ zenon_H16a); [ zenon_intro zenon_Ha9 | zenon_intro zenon_He3 ]. % 19.02/19.21 apply (zenon_L1316_); trivial. % 19.02/19.21 apply (zenon_L633_); trivial. % 19.02/19.21 (* end of lemma zenon_L1329_ *) % 19.02/19.21 assert (zenon_L1330_ : (((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)) = (e2))) -> ((op (e3) (e2)) = (e3)) -> (~((op (e3) (e0)) = (op (e3) (e2)))) -> False). % 19.02/19.21 do 0 intro. intros zenon_H267 zenon_H1b1 zenon_Hae zenon_H1cf zenon_H14b zenon_H163 zenon_H6f. % 19.02/19.21 apply (zenon_or_s _ _ zenon_H267); [ zenon_intro zenon_H44 | zenon_intro zenon_H268 ]. % 19.02/19.21 apply (zenon_L346_); trivial. % 19.02/19.21 apply (zenon_or_s _ _ zenon_H268); [ zenon_intro zenon_Hac | zenon_intro zenon_H269 ]. % 19.02/19.21 apply (zenon_L242_); trivial. % 19.02/19.21 apply (zenon_or_s _ _ zenon_H269); [ zenon_intro zenon_H148 | zenon_intro zenon_H15e ]. % 19.02/19.21 exact (zenon_H14b zenon_H148). % 19.02/19.21 apply (zenon_L286_); trivial. % 19.02/19.21 (* end of lemma zenon_L1330_ *) % 19.02/19.21 assert (zenon_L1331_ : (((op (e1) (e3)) = (e0))\/(((op (e1) (e3)) = (e1))\/(((op (e1) (e3)) = (e2))\/((op (e1) (e3)) = (e3))))) -> (~((op (e1) (e3)) = (op (e3) (e3)))) -> (~((op (e0) (e3)) = (op (e2) (e3)))) -> (~((op (e0) (e3)) = (e2))) -> (~((op (e0) (e3)) = (op (e1) (e3)))) -> (~((op (e0) (e3)) = (op (e3) (e3)))) -> ((op (e3) (e3)) = (e0)) -> (((op (e0) (e3)) = (e0))\/(((op (e0) (e3)) = (e1))\/(((op (e0) (e3)) = (e2))\/((op (e0) (e3)) = (e3))))) -> (~((op (e1) (e3)) = (e2))) -> (~((op (e1) (e3)) = (op (e2) (e3)))) -> ((op (e2) (e3)) = (e3)) -> False). % 19.02/19.21 do 0 intro. intros zenon_Hdf zenon_Hd5 zenon_He2 zenon_H12e zenon_H1d zenon_Hc2 zenon_H60 zenon_He4 zenon_H14c zenon_Hdb zenon_Hdd. % 19.02/19.21 apply (zenon_or_s _ _ zenon_Hdf); [ zenon_intro zenon_H1f | zenon_intro zenon_He0 ]. % 19.02/19.21 apply (zenon_L136_); trivial. % 19.02/19.21 apply (zenon_or_s _ _ zenon_He0); [ zenon_intro zenon_Hd6 | zenon_intro zenon_He1 ]. % 19.02/19.21 apply (zenon_L1255_); trivial. % 19.02/19.21 apply (zenon_or_s _ _ zenon_He1); [ zenon_intro zenon_Hd7 | zenon_intro zenon_Hdc ]. % 19.02/19.21 exact (zenon_H14c zenon_Hd7). % 19.02/19.21 apply (zenon_L52_); trivial. % 19.02/19.21 (* end of lemma zenon_L1331_ *) % 19.02/19.21 assert (zenon_L1332_ : (((op (e0) (e3)) = (e3))\/(((op (e1) (e3)) = (e3))\/(((op (e2) (e3)) = (e3))\/((op (e3) (e3)) = (e3))))) -> (~((op (e2) (e3)) = (e2))) -> ((op (e2) (e2)) = (e1)) -> (~((op (e2) (e2)) = (op (e2) (e3)))) -> (~((op (e2) (e3)) = (op (e3) (e3)))) -> (((op (e2) (e3)) = (e0))\/(((op (e2) (e3)) = (e1))\/(((op (e2) (e3)) = (e2))\/((op (e2) (e3)) = (e3))))) -> (~((op (e1) (e3)) = (op (e2) (e3)))) -> (~((op (e1) (e3)) = (e2))) -> (((op (e0) (e3)) = (e0))\/(((op (e0) (e3)) = (e1))\/(((op (e0) (e3)) = (e2))\/((op (e0) (e3)) = (e3))))) -> ((op (e3) (e3)) = (e0)) -> (~((op (e0) (e3)) = (op (e3) (e3)))) -> (~((op (e0) (e3)) = (op (e1) (e3)))) -> (~((op (e0) (e3)) = (e2))) -> (~((op (e0) (e3)) = (op (e2) (e3)))) -> (~((op (e1) (e3)) = (op (e3) (e3)))) -> (((op (e1) (e3)) = (e0))\/(((op (e1) (e3)) = (e1))\/(((op (e1) (e3)) = (e2))\/((op (e1) (e3)) = (e3))))) -> (~((op (e3) (e3)) = (e3))) -> False). % 19.02/19.21 do 0 intro. intros zenon_H136 zenon_H274 zenon_Hf1 zenon_H6d zenon_Hf3 zenon_H11f zenon_Hdb zenon_H14c zenon_He4 zenon_H60 zenon_Hc2 zenon_H1d zenon_H12e zenon_He2 zenon_Hd5 zenon_Hdf zenon_H102. % 19.02/19.21 apply (zenon_or_s _ _ zenon_H136); [ zenon_intro zenon_He3 | zenon_intro zenon_H137 ]. % 19.02/19.21 apply (zenon_L1143_); trivial. % 19.02/19.21 apply (zenon_or_s _ _ zenon_H137); [ zenon_intro zenon_Hdc | zenon_intro zenon_H138 ]. % 19.02/19.21 apply (zenon_L1164_); trivial. % 19.02/19.21 apply (zenon_or_s _ _ zenon_H138); [ zenon_intro zenon_Hdd | zenon_intro zenon_H105 ]. % 19.02/19.21 apply (zenon_L1331_); trivial. % 19.02/19.21 exact (zenon_H102 zenon_H105). % 19.02/19.21 (* end of lemma zenon_L1332_ *) % 19.02/19.21 assert (zenon_L1333_ : (((op (e0) (e0)) = (e3))\/(((op (e0) (e1)) = (e3))\/(((op (e0) (e2)) = (e3))\/((op (e0) (e3)) = (e3))))) -> (~((e1) = (e3))) -> ((op (e0) (e0)) = (e1)) -> (~((op (e0) (e1)) = (op (e1) (e1)))) -> (~((op (e1) (e1)) = (e2))) -> (~((op (e1) (e1)) = (e1))) -> (~((op (e1) (e1)) = (op (e1) (e2)))) -> (((op (e1) (e1)) = (e0))\/(((op (e1) (e1)) = (e1))\/(((op (e1) (e1)) = (e2))\/((op (e1) (e1)) = (e3))))) -> ((op (e2) (e2)) = (e1)) -> ((op (e1) (e2)) = (e0)) -> ((op (e0) (e3)) = (e0)) -> (~((e0) = (e3))) -> False). % 19.02/19.21 do 0 intro. intros zenon_H168 zenon_H95 zenon_H7a zenon_H10e zenon_H20c zenon_H10a zenon_H4f zenon_H142 zenon_Hf1 zenon_H2a zenon_H1e zenon_H9a. % 19.02/19.21 apply (zenon_or_s _ _ zenon_H168); [ zenon_intro zenon_H3a | zenon_intro zenon_H169 ]. % 19.02/19.21 apply (zenon_L35_); trivial. % 19.02/19.21 apply (zenon_or_s _ _ zenon_H169); [ zenon_intro zenon_H99 | zenon_intro zenon_H16a ]. % 19.02/19.21 apply (zenon_L1318_); trivial. % 19.02/19.21 apply (zenon_or_s _ _ zenon_H16a); [ zenon_intro zenon_Ha9 | zenon_intro zenon_He3 ]. % 19.02/19.21 apply (zenon_L184_); trivial. % 19.02/19.21 apply (zenon_L515_); trivial. % 19.02/19.21 (* end of lemma zenon_L1333_ *) % 19.02/19.21 assert (zenon_L1334_ : (((op (e1) (e3)) = (e0))\/(((op (e1) (e3)) = (e1))\/(((op (e1) (e3)) = (e2))\/((op (e1) (e3)) = (e3))))) -> ((op (e2) (e3)) = (e3)) -> (~((op (e0) (e3)) = (e2))) -> ((op (e0) (e1)) = (e1)) -> (~((op (e0) (e1)) = (op (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 (e1) (e3)) = (op (e3) (e3)))) -> (~((op (e1) (e3)) = (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 (e3) (e3)) = (e1)) -> (~((op (e2) (e3)) = (op (e3) (e3)))) -> (~((op (e2) (e3)) = (e2))) -> (~((op (e1) (e3)) = (op (e2) (e3)))) -> False). % 19.02/19.21 do 0 intro. intros zenon_Hdf zenon_Hdd zenon_H12e zenon_Ha0 zenon_H54 zenon_H1d zenon_He4 zenon_Hd5 zenon_H14c zenon_H11f zenon_H1e zenon_He2 zenon_Hc4 zenon_Hf3 zenon_H274 zenon_Hdb. % 19.02/19.21 apply (zenon_or_s _ _ zenon_Hdf); [ zenon_intro zenon_H1f | zenon_intro zenon_He0 ]. % 19.02/19.21 apply (zenon_L1147_); trivial. % 19.02/19.21 apply (zenon_or_s _ _ zenon_He0); [ zenon_intro zenon_Hd6 | zenon_intro zenon_He1 ]. % 19.02/19.21 apply (zenon_L50_); trivial. % 19.02/19.21 apply (zenon_or_s _ _ zenon_He1); [ zenon_intro zenon_Hd7 | zenon_intro zenon_Hdc ]. % 19.02/19.21 exact (zenon_H14c zenon_Hd7). % 19.02/19.21 apply (zenon_L1244_); trivial. % 19.02/19.21 (* end of lemma zenon_L1334_ *) % 19.02/19.21 assert (zenon_L1335_ : (((op (e3) (e0)) = (e1))\/(((op (e3) (e1)) = (e1))\/(((op (e3) (e2)) = (e1))\/((op (e3) (e3)) = (e1))))) -> ((op (e0) (e0)) = (e3)) -> ((op (e1) (e0)) = (e2)) -> (~((op (e0) (e1)) = (op (e3) (e1)))) -> (~((op (e3) (e2)) = (op (e3) (e3)))) -> ((op (e2) (e2)) = (e1)) -> (~((op (e2) (e2)) = (op (e2) (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) (e3)) = (e3))\/(((op (e1) (e3)) = (e3))\/(((op (e2) (e3)) = (e3))\/((op (e3) (e3)) = (e3))))) -> (~((e0) = (e3))) -> (~((op (e1) (e3)) = (op (e2) (e3)))) -> (~((op (e2) (e3)) = (e2))) -> (~((op (e2) (e3)) = (op (e3) (e3)))) -> (~((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 (e1) (e3)) = (e2))) -> (~((op (e1) (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 (e0) (e1)) = (op (e0) (e3)))) -> ((op (e0) (e1)) = (e1)) -> (~((op (e0) (e3)) = (e2))) -> (((op (e1) (e3)) = (e0))\/(((op (e1) (e3)) = (e1))\/(((op (e1) (e3)) = (e2))\/((op (e1) (e3)) = (e3))))) -> (~((op (e3) (e3)) = (e3))) -> False). % 19.02/19.21 do 0 intro. intros zenon_He8 zenon_H3a zenon_H86 zenon_H210 zenon_H62 zenon_Hf1 zenon_H6d zenon_H9d zenon_Hd8 zenon_H133 zenon_H136 zenon_H9a zenon_Hdb zenon_H274 zenon_Hf3 zenon_He2 zenon_H1e zenon_H11f zenon_H14c zenon_Hd5 zenon_He4 zenon_H1d zenon_H54 zenon_Ha0 zenon_H12e zenon_Hdf zenon_H102. % 19.02/19.21 apply (zenon_or_s _ _ zenon_He8); [ zenon_intro zenon_Hac | zenon_intro zenon_Heb ]. % 19.02/19.21 apply (zenon_L241_); trivial. % 19.02/19.21 apply (zenon_or_s _ _ zenon_Heb); [ zenon_intro zenon_Hae | zenon_intro zenon_Hec ]. % 19.02/19.21 apply (zenon_L363_); trivial. % 19.02/19.21 apply (zenon_or_s _ _ zenon_Hec); [ zenon_intro zenon_Hba | zenon_intro zenon_Hc4 ]. % 19.02/19.21 apply (zenon_L419_); trivial. % 19.02/19.21 apply (zenon_or_s _ _ zenon_H136); [ zenon_intro zenon_He3 | zenon_intro zenon_H137 ]. % 19.02/19.21 apply (zenon_L515_); trivial. % 19.02/19.21 apply (zenon_or_s _ _ zenon_H137); [ zenon_intro zenon_Hdc | zenon_intro zenon_H138 ]. % 19.02/19.21 apply (zenon_L1244_); trivial. % 19.02/19.21 apply (zenon_or_s _ _ zenon_H138); [ zenon_intro zenon_Hdd | zenon_intro zenon_H105 ]. % 19.02/19.21 apply (zenon_L1334_); trivial. % 19.02/19.21 exact (zenon_H102 zenon_H105). % 19.02/19.21 (* end of lemma zenon_L1335_ *) % 19.02/19.21 assert (zenon_L1336_ : (~((op (e3) (e0)) = (e2))) -> (~((op (e2) (e0)) = (e2))) -> (~((op (e0) (e1)) = (op (e1) (e1)))) -> (~((op (e1) (e1)) = (e2))) -> ((op (e1) (e2)) = (e0)) -> (~((op (e1) (e2)) = (op (e1) (e3)))) -> (~((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)) = (op (e3) (e1)))) -> (((op (e0) (e1)) = (e2))\/(((op (e1) (e1)) = (e2))\/(((op (e2) (e1)) = (e2))\/((op (e3) (e1)) = (e2))))) -> (~((op (e0) (e1)) = (e2))) -> (((op (e0) (e0)) = (e3))\/(((op (e1) (e0)) = (e3))\/(((op (e2) (e0)) = (e3))\/((op (e3) (e0)) = (e3))))) -> (~((op (e3) (e1)) = (op (e3) (e2)))) -> (~((op (e3) (e0)) = (op (e3) (e2)))) -> ((op (e0) (e2)) = (e2)) -> (~((op (e0) (e0)) = (op (e0) (e3)))) -> (((op (e0) (e0)) = (e1))\/(((op (e0) (e1)) = (e1))\/(((op (e0) (e2)) = (e1))\/((op (e0) (e3)) = (e1))))) -> (((op (e1) (e0)) = (e2))\/(((op (e1) (e1)) = (e2))\/(((op (e1) (e2)) = (e2))\/((op (e1) (e3)) = (e2))))) -> ((op (e2) (e0)) = (e0)) -> ((op (e2) (e2)) = (e1)) -> (~((op (e0) (e1)) = (op (e3) (e1)))) -> (~((op (e2) (e3)) = (e2))) -> (~((op (e1) (e3)) = (e2))) -> (~((op (e0) (e3)) = (e2))) -> ((~((op (e0) (e3)) = (e2)))\/((op (e0) (e2)) = (e3))) -> ((~((op (e1) (e3)) = (e2)))\/((op (e1) (e2)) = (e3))) -> ((~((op (e2) (e1)) = (e2)))\/((op (e2) (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 (e2) (e0)) = (e2)))\/((op (e2) (e2)) = (e0))) -> ((~((op (e3) (e2)) = (e2)))\/((op (e3) (e2)) = (e2))) -> (~((op (e3) (e2)) = (op (e3) (e3)))) -> (((op (e0) (e3)) = (e2))\/(((op (e1) (e3)) = (e2))\/(((op (e2) (e3)) = (e2))\/((op (e3) (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)) = (e2)))\/((op (e3) (e2)) = (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)) = (e2))) -> (~((op (e2) (e2)) = (op (e3) (e2)))) -> ((~((op (e3) (e3)) = (e2)))\/((op (e3) (e2)) = (e3))) -> ((~((op (e2) (e3)) = (e2)))\/((op (e2) (e2)) = (e3))) -> (~((op (e0) (e0)) = (e0))) -> (~((op (e1) (e1)) = (e1))) -> (~((e1) = (e2))) -> (~((op (e1) (e0)) = (op (e1) (e1)))) -> (~((op (e0) (e0)) = (op (e0) (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 (e1) (e2)) = (e2)))\/((op (e1) (e2)) = (e2))) -> (~((e0) = (e2))) -> (((op (e0) (e0)) = (e0))\/(((op (e1) (e0)) = (e0))\/(((op (e2) (e0)) = (e0))\/((op (e3) (e0)) = (e0))))) -> (((op (e3) (e0)) = (e0))\/(((op (e3) (e1)) = (e0))\/(((op (e3) (e2)) = (e0))\/((op (e3) (e3)) = (e0))))) -> (((op (e0) (e0)) = (e0))\/(((op (e0) (e0)) = (e1))\/(((op (e0) (e0)) = (e2))\/((op (e0) (e0)) = (e3))))) -> (~((op (e1) (e2)) = (op (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)) = (e3))\/(((op (e0) (e1)) = (e3))\/(((op (e0) (e2)) = (e3))\/((op (e0) (e3)) = (e3))))) -> (~((op (e0) (e1)) = (op (e2) (e1)))) -> (~((e1) = (e3))) -> (((op (e2) (e0)) = (e0))\/(((op (e2) (e1)) = (e0))\/(((op (e2) (e2)) = (e0))\/((op (e2) (e3)) = (e0))))) -> (((op (e3) (e3)) = (e0))\/(((op (e3) (e3)) = (e1))\/(((op (e3) (e3)) = (e2))\/((op (e3) (e3)) = (e3))))) -> (~((op (e3) (e1)) = (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 (e0) (e3)) = (op (e3) (e3)))) -> (~((op (e1) (e2)) = (op (e2) (e2)))) -> (((op (e2) (e0)) = (e0))\/(((op (e2) (e0)) = (e1))\/(((op (e2) (e0)) = (e2))\/((op (e2) (e0)) = (e3))))) -> (~((op (e2) (e0)) = (op (e2) (e2)))) -> (~((op (e1) (e0)) = (op (e2) (e0)))) -> (~((op (e0) (e2)) = (op (e1) (e2)))) -> (((op (e1) (e0)) = (e1))\/(((op (e1) (e1)) = (e1))\/(((op (e1) (e2)) = (e1))\/((op (e1) (e3)) = (e1))))) -> (~((op (e2) (e0)) = (op (e2) (e1)))) -> (~((op (e2) (e0)) = (op (e3) (e0)))) -> (((op (e0) (e0)) = (e2))\/(((op (e0) (e1)) = (e2))\/(((op (e0) (e2)) = (e2))\/((op (e0) (e3)) = (e2))))) -> (~((op (e1) (e0)) = (op (e1) (e2)))) -> (~((e2) = (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) (e0)) = (e0))\/(((op (e0) (e1)) = (e0))\/(((op (e0) (e2)) = (e0))\/((op (e0) (e3)) = (e0))))) -> ((~((op (e1) (e1)) = (e2)))\/((op (e1) (e2)) = (e1))) -> (((op (e0) (e1)) = (e1))\/(((op (e1) (e1)) = (e1))\/(((op (e2) (e1)) = (e1))\/((op (e3) (e1)) = (e1))))) -> (((op (e2) (e1)) = (e0))\/(((op (e2) (e1)) = (e1))\/(((op (e2) (e1)) = (e2))\/((op (e2) (e1)) = (e3))))) -> (~((op (e2) (e1)) = (op (e2) (e3)))) -> (~((op (e2) (e1)) = (op (e2) (e2)))) -> (((op (e2) (e0)) = (e1))\/(((op (e2) (e1)) = (e1))\/(((op (e2) (e2)) = (e1))\/((op (e2) (e3)) = (e1))))) -> (~((op (e2) (e1)) = (op (e3) (e1)))) -> (~((op (e0) (e2)) = (op (e3) (e2)))) -> (((op (e0) (e3)) = (e3))\/(((op (e1) (e3)) = (e3))\/(((op (e2) (e3)) = (e3))\/((op (e3) (e3)) = (e3))))) -> (~((op (e3) (e3)) = (e3))) -> (~((op (e1) (e1)) = (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) (e3)) = (op (e2) (e3)))) -> (~((op (e2) (e3)) = (op (e3) (e3)))) -> (~((op (e1) (e3)) = (op (e2) (e3)))) -> (((op (e2) (e3)) = (e0))\/(((op (e2) (e3)) = (e1))\/(((op (e2) (e3)) = (e2))\/((op (e2) (e3)) = (e3))))) -> (~((e0) = (e3))) -> (((op (e3) (e0)) = (e1))\/(((op (e3) (e1)) = (e1))\/(((op (e3) (e2)) = (e1))\/((op (e3) (e3)) = (e1))))) -> (~((op (e0) (e1)) = (op (e0) (e2)))) -> (~((op (e2) (e2)) = (op (e2) (e3)))) -> (~((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)) = (op (e3) (e0)))) -> (((op (e0) (e0)) = (e1))\/(((op (e1) (e0)) = (e1))\/(((op (e2) (e0)) = (e1))\/((op (e3) (e0)) = (e1))))) -> ((~((op (e3) (e1)) = (e2)))\/((op (e3) (e2)) = (e1))) -> ((~((op (e1) (e0)) = (e2)))\/((op (e1) (e2)) = (e0))) -> ((~((op (e0) (e2)) = (e2)))\/((op (e0) (e2)) = (e2))) -> ((op (e0) (e3)) = (e0)) -> (~((e0) = (e1))) -> False). % 19.02/19.21 do 0 intro. intros zenon_H14b zenon_Hef zenon_H10e zenon_H20c zenon_H2a zenon_H124 zenon_Hd8 zenon_H133 zenon_H1cf zenon_H1d8 zenon_H26d zenon_H1e0 zenon_H1a4 zenon_H6f zenon_H150 zenon_H189 zenon_H22d zenon_H18c zenon_H34 zenon_Hf1 zenon_H210 zenon_H274 zenon_H14c zenon_H12e zenon_H27c zenon_H279 zenon_H271 zenon_Ha8 zenon_H1d5 zenon_H276 zenon_H273 zenon_H62 zenon_H145 zenon_H173 zenon_H172 zenon_H270 zenon_H1fe zenon_H5b zenon_H80 zenon_H18f zenon_H278 zenon_H277 zenon_H3f zenon_H10a zenon_H7c zenon_H45 zenon_H13c zenon_H153 zenon_H22 zenon_H275 zenon_H149 zenon_H3e zenon_H1ac zenon_H26a zenon_H115 zenon_H4f zenon_H142 zenon_H168 zenon_H17e zenon_H95 zenon_H2f zenon_H101 zenon_H130 zenon_He4 zenon_H1d zenon_Hc2 zenon_H2b zenon_H259 zenon_H52 zenon_H201 zenon_H195 zenon_H128 zenon_H1f0 zenon_H17b zenon_H183 zenon_H24a zenon_H12b zenon_H245 zenon_H54 zenon_H74 zenon_H27b zenon_H109 zenon_H1cc zenon_H1c7 zenon_H24b zenon_H106 zenon_Haf zenon_H14f zenon_H136 zenon_H102 zenon_H57 zenon_Hd5 zenon_Hdf zenon_He2 zenon_Hf3 zenon_Hdb zenon_H11f zenon_H9a zenon_He8 zenon_H4a zenon_H6d zenon_H71 zenon_H67 zenon_H1fa zenon_H235 zenon_H26f zenon_H27a zenon_H27e zenon_H1e zenon_Ha1. % 19.02/19.21 apply (zenon_or_s _ _ zenon_H22d); [ zenon_intro zenon_H7a | zenon_intro zenon_H22e ]. % 19.02/19.21 apply (zenon_L1333_); trivial. % 19.02/19.21 apply (zenon_or_s _ _ zenon_H22e); [ zenon_intro zenon_Ha0 | zenon_intro zenon_H22f ]. % 19.02/19.21 apply (zenon_or_s _ _ zenon_H235); [ zenon_intro zenon_H7a | zenon_intro zenon_H236 ]. % 19.02/19.21 apply (zenon_L1333_); trivial. % 19.02/19.21 apply (zenon_or_s _ _ zenon_H236); [ zenon_intro zenon_H9d | zenon_intro zenon_H237 ]. % 19.02/19.21 apply (zenon_or_s _ _ zenon_H1fe); [ zenon_intro zenon_H7b | zenon_intro zenon_H1ff ]. % 19.02/19.21 exact (zenon_H80 zenon_H7b). % 19.02/19.21 apply (zenon_or_s _ _ zenon_H1ff); [ zenon_intro zenon_H86 | zenon_intro zenon_H200 ]. % 19.02/19.21 apply (zenon_or_s _ _ zenon_H168); [ zenon_intro zenon_H3a | zenon_intro zenon_H169 ]. % 19.02/19.21 apply (zenon_L1335_); trivial. % 19.02/19.21 apply (zenon_or_s _ _ zenon_H169); [ zenon_intro zenon_H99 | zenon_intro zenon_H16a ]. % 19.02/19.21 apply (zenon_L1318_); trivial. % 19.02/19.21 apply (zenon_or_s _ _ zenon_H16a); [ zenon_intro zenon_Ha9 | zenon_intro zenon_He3 ]. % 19.02/19.21 apply (zenon_L184_); trivial. % 19.02/19.21 apply (zenon_L515_); trivial. % 19.02/19.21 apply (zenon_or_s _ _ zenon_H200); [ zenon_intro zenon_Hee | zenon_intro zenon_H148 ]. % 19.02/19.21 exact (zenon_Hef zenon_Hee). % 19.02/19.21 exact (zenon_H14b zenon_H148). % 19.02/19.21 apply (zenon_or_s _ _ zenon_H237); [ zenon_intro zenon_Hed | zenon_intro zenon_Hac ]. % 19.02/19.21 apply (zenon_L214_); trivial. % 19.02/19.21 apply (zenon_or_s _ _ zenon_H1fe); [ zenon_intro zenon_H7b | zenon_intro zenon_H1ff ]. % 19.02/19.21 exact (zenon_H80 zenon_H7b). % 19.02/19.21 apply (zenon_or_s _ _ zenon_H1ff); [ zenon_intro zenon_H86 | zenon_intro zenon_H200 ]. % 19.02/19.21 apply (zenon_or_s _ _ zenon_H168); [ zenon_intro zenon_H3a | zenon_intro zenon_H169 ]. % 19.02/19.21 apply (zenon_L241_); trivial. % 19.02/19.21 apply (zenon_or_s _ _ zenon_H169); [ zenon_intro zenon_H99 | zenon_intro zenon_H16a ]. % 19.02/19.21 apply (zenon_L1318_); trivial. % 19.02/19.21 apply (zenon_or_s _ _ zenon_H16a); [ zenon_intro zenon_Ha9 | zenon_intro zenon_He3 ]. % 19.02/19.21 apply (zenon_L1316_); trivial. % 19.02/19.21 apply (zenon_L515_); trivial. % 19.02/19.21 apply (zenon_or_s _ _ zenon_H200); [ zenon_intro zenon_Hee | zenon_intro zenon_H148 ]. % 19.02/19.21 exact (zenon_Hef zenon_Hee). % 19.02/19.21 exact (zenon_H14b zenon_H148). % 19.02/19.21 apply (zenon_or_s _ _ zenon_H22f); [ zenon_intro zenon_H122 | zenon_intro zenon_Hc3 ]. % 19.02/19.21 apply (zenon_L1327_); trivial. % 19.02/19.21 apply (zenon_L427_); trivial. % 19.02/19.21 (* end of lemma zenon_L1336_ *) % 19.02/19.21 assert (zenon_L1337_ : (((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)) = (op (e3) (e1)))) -> (~((op (e3) (e2)) = (op (e3) (e3)))) -> ((op (e2) (e2)) = (e1)) -> (~((op (e2) (e2)) = (op (e2) (e3)))) -> ((op (e1) (e0)) = (e1)) -> (~((op (e1) (e0)) = (op (e1) (e3)))) -> ((op (e0) (e1)) = (e1)) -> (~((op (e0) (e1)) = (op (e0) (e3)))) -> (((op (e0) (e3)) = (e1))\/(((op (e1) (e3)) = (e1))\/(((op (e2) (e3)) = (e1))\/((op (e3) (e3)) = (e1))))) -> (((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 (e2) (e3)) = (op (e3) (e3)))) -> (~((op (e2) (e3)) = (e2))) -> (~((op (e1) (e3)) = (op (e2) (e3)))) -> ((op (e1) (e3)) = (e3)) -> False). % 19.02/19.21 do 0 intro. intros zenon_He8 zenon_Ha1 zenon_H44 zenon_H210 zenon_H62 zenon_Hf1 zenon_H6d zenon_H9d zenon_Hd8 zenon_Ha0 zenon_H54 zenon_H133 zenon_H11f zenon_H1e zenon_He2 zenon_Hf3 zenon_H274 zenon_Hdb zenon_Hdc. % 19.02/19.21 apply (zenon_or_s _ _ zenon_He8); [ zenon_intro zenon_Hac | zenon_intro zenon_Heb ]. % 19.02/19.21 apply (zenon_L41_); trivial. % 19.02/19.21 apply (zenon_or_s _ _ zenon_Heb); [ zenon_intro zenon_Hae | zenon_intro zenon_Hec ]. % 19.02/19.21 apply (zenon_L363_); trivial. % 19.02/19.21 apply (zenon_or_s _ _ zenon_Hec); [ zenon_intro zenon_Hba | zenon_intro zenon_Hc4 ]. % 19.02/19.21 apply (zenon_L419_); trivial. % 19.02/19.21 apply (zenon_L1244_); trivial. % 19.02/19.21 (* end of lemma zenon_L1337_ *) % 19.02/19.21 assert (zenon_L1338_ : (~((op (e0) (e1)) = (op (e3) (e1)))) -> (((op (e1) (e0)) = (e3))\/(((op (e1) (e1)) = (e3))\/(((op (e1) (e2)) = (e3))\/((op (e1) (e3)) = (e3))))) -> (((op (e0) (e0)) = (e2))\/(((op (e1) (e0)) = (e2))\/(((op (e2) (e0)) = (e2))\/((op (e3) (e0)) = (e2))))) -> (~((e1) = (e3))) -> (~((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 (e1) (e1)) = (e1))) -> ((~((op (e2) (e0)) = (e2)))\/((op (e2) (e2)) = (e0))) -> (~((op (e1) (e2)) = (op (e2) (e2)))) -> ((~((op (e2) (e1)) = (e2)))\/((op (e2) (e2)) = (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)) = (e0))\/(((op (e2) (e0)) = (e1))\/(((op (e2) (e0)) = (e2))\/((op (e2) (e0)) = (e3))))) -> (~((op (e0) (e1)) = (op (e2) (e1)))) -> (((op (e2) (e3)) = (e0))\/(((op (e2) (e3)) = (e1))\/(((op (e2) (e3)) = (e2))\/((op (e2) (e3)) = (e3))))) -> (~((op (e0) (e3)) = (op (e2) (e3)))) -> (~((op (e1) (e3)) = (op (e2) (e3)))) -> (~((op (e2) (e0)) = (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 (e2) (e3)) = (op (e3) (e3)))) -> (((op (e0) (e3)) = (e0))\/(((op (e1) (e3)) = (e0))\/(((op (e2) (e3)) = (e0))\/((op (e3) (e3)) = (e0))))) -> (((op (e1) (e0)) = (e1))\/(((op (e1) (e1)) = (e1))\/(((op (e1) (e2)) = (e1))\/((op (e1) (e3)) = (e1))))) -> (((op (e0) (e0)) = (e3))\/(((op (e0) (e1)) = (e3))\/(((op (e0) (e2)) = (e3))\/((op (e0) (e3)) = (e3))))) -> (~((op (e0) (e0)) = (e2))) -> (~((e0) = (e1))) -> ((~((op (e0) (e2)) = (e2)))\/((op (e0) (e2)) = (e2))) -> ((~((op (e1) (e0)) = (e2)))\/((op (e1) (e2)) = (e0))) -> (((op (e0) (e0)) = (e1))\/(((op (e1) (e0)) = (e1))\/(((op (e2) (e0)) = (e1))\/((op (e3) (e0)) = (e1))))) -> (~((op (e1) (e0)) = (op (e3) (e0)))) -> (~((op (e3) (e0)) = (op (e3) (e3)))) -> (~((op (e2) (e2)) = (op (e2) (e3)))) -> (~((op (e0) (e1)) = (op (e0) (e2)))) -> (((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 (e0) (e3)) = (e3))\/(((op (e1) (e3)) = (e3))\/(((op (e2) (e3)) = (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 (e2) (e1)) = (op (e2) (e2)))) -> (~((op (e2) (e1)) = (op (e2) (e3)))) -> (((op (e2) (e1)) = (e0))\/(((op (e2) (e1)) = (e1))\/(((op (e2) (e1)) = (e2))\/((op (e2) (e1)) = (e3))))) -> (((op (e0) (e1)) = (e1))\/(((op (e1) (e1)) = (e1))\/(((op (e2) (e1)) = (e1))\/((op (e3) (e1)) = (e1))))) -> ((~((op (e1) (e1)) = (e2)))\/((op (e1) (e2)) = (e1))) -> (((op (e0) (e0)) = (e0))\/(((op (e0) (e1)) = (e0))\/(((op (e0) (e2)) = (e0))\/((op (e0) (e3)) = (e0))))) -> (~((op (e0) (e1)) = (op (e0) (e3)))) -> (((op (e0) (e1)) = (e0))\/(((op (e1) (e1)) = (e0))\/(((op (e2) (e1)) = (e0))\/((op (e3) (e1)) = (e0))))) -> (~((e2) = (e3))) -> (~((op (e1) (e0)) = (op (e1) (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)) = (op (e2) (e1)))) -> (~((op (e0) (e2)) = (op (e1) (e2)))) -> (~((op (e1) (e0)) = (op (e2) (e0)))) -> (~((op (e2) (e0)) = (op (e2) (e2)))) -> (~((op (e0) (e3)) = (op (e3) (e3)))) -> (((op (e0) (e3)) = (e0))\/(((op (e0) (e3)) = (e1))\/(((op (e0) (e3)) = (e2))\/((op (e0) (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 (e1) (e1)) = (e0))\/(((op (e1) (e1)) = (e1))\/(((op (e1) (e1)) = (e2))\/((op (e1) (e1)) = (e3))))) -> (~((op (e1) (e1)) = (op (e1) (e2)))) -> (((op (e0) (e0)) = (e0))\/(((op (e0) (e0)) = (e1))\/(((op (e0) (e0)) = (e2))\/((op (e0) (e0)) = (e3))))) -> (((op (e3) (e0)) = (e0))\/(((op (e3) (e1)) = (e0))\/(((op (e3) (e2)) = (e0))\/((op (e3) (e3)) = (e0))))) -> (((op (e0) (e0)) = (e0))\/(((op (e1) (e0)) = (e0))\/(((op (e2) (e0)) = (e0))\/((op (e3) (e0)) = (e0))))) -> (~((e0) = (e2))) -> ((~((op (e1) (e2)) = (e2)))\/((op (e1) (e2)) = (e2))) -> (((op (e1) (e0)) = (e0))\/(((op (e1) (e1)) = (e0))\/(((op (e1) (e2)) = (e0))\/((op (e1) (e3)) = (e0))))) -> (~((op (e0) (e0)) = (op (e0) (e2)))) -> (~((op (e1) (e0)) = (op (e1) (e1)))) -> (~((e1) = (e2))) -> (((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 (e0) (e2)) = (op (e2) (e2)))) -> ((~((op (e1) (e3)) = (e2)))\/((op (e1) (e2)) = (e3))) -> ((~((op (e0) (e3)) = (e2)))\/((op (e0) (e2)) = (e3))) -> (((op (e3) (e0)) = (e0))\/(((op (e3) (e0)) = (e1))\/(((op (e3) (e0)) = (e2))\/((op (e3) (e0)) = (e3))))) -> (~((op (e0) (e1)) = (op (e1) (e1)))) -> (~((op (e1) (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))))) -> (~((op (e0) (e0)) = (op (e0) (e3)))) -> (~((op (e3) (e1)) = (op (e3) (e2)))) -> (~((op (e0) (e1)) = (e2))) -> (((op (e0) (e1)) = (e2))\/(((op (e1) (e1)) = (e2))\/(((op (e2) (e1)) = (e2))\/((op (e3) (e1)) = (e2))))) -> (~((op (e3) (e0)) = (op (e3) (e1)))) -> (((op (e0) (e3)) = (e1))\/(((op (e1) (e3)) = (e1))\/(((op (e2) (e3)) = (e1))\/((op (e3) (e3)) = (e1))))) -> (~((op (e1) (e0)) = (op (e1) (e3)))) -> (~((op (e1) (e2)) = (op (e1) (e3)))) -> (~((op (e0) (e3)) = (e2))) -> (~((op (e0) (e0)) = (e0))) -> (((op (e2) (e0)) = (e2))\/(((op (e2) (e1)) = (e2))\/(((op (e2) (e2)) = (e2))\/((op (e2) (e3)) = (e2))))) -> (~((op (e2) (e2)) = (e2))) -> ((~((op (e3) (e0)) = (e2)))\/((op (e3) (e2)) = (e0))) -> (~((op (e1) (e2)) = (op (e3) (e2)))) -> ((~((op (e3) (e2)) = (e2)))\/((op (e3) (e2)) = (e2))) -> ((op (e0) (e2)) = (e2)) -> (~((op (e0) (e2)) = (op (e3) (e2)))) -> (((op (e3) (e0)) = (e2))\/(((op (e3) (e1)) = (e2))\/(((op (e3) (e2)) = (e2))\/((op (e3) (e3)) = (e2))))) -> (~((op (e2) (e2)) = (op (e3) (e2)))) -> ((~((op (e3) (e3)) = (e2)))\/((op (e3) (e2)) = (e3))) -> ((op (e1) (e2)) = (e0)) -> ((~((op (e3) (e1)) = (e2)))\/((op (e3) (e2)) = (e1))) -> ((~((op (e2) (e3)) = (e2)))\/((op (e2) (e2)) = (e3))) -> False). % 19.02/19.21 do 0 intro. intros zenon_H210 zenon_H16f zenon_H1fe zenon_H95 zenon_H9a zenon_H1e0 zenon_H6f zenon_H10a zenon_H276 zenon_H2b zenon_H271 zenon_H2f zenon_H39 zenon_H259 zenon_H17e zenon_H11f zenon_He2 zenon_Hdb zenon_H5b zenon_Hd5 zenon_H1d zenon_Hdf zenon_Hf3 zenon_H67 zenon_H128 zenon_H168 zenon_H80 zenon_Ha1 zenon_H27e zenon_H27a zenon_H235 zenon_H1fa zenon_H71 zenon_H6d zenon_H4a zenon_He8 zenon_H57 zenon_H102 zenon_H136 zenon_Haf zenon_H106 zenon_H24b zenon_H1c7 zenon_H1cc zenon_H109 zenon_H27b zenon_H74 zenon_H54 zenon_H245 zenon_H12b zenon_H24a zenon_H183 zenon_H17b zenon_H1f0 zenon_H195 zenon_H201 zenon_H52 zenon_Hc2 zenon_He4 zenon_H130 zenon_H101 zenon_H142 zenon_H4f zenon_H26a zenon_H1ac zenon_H3e zenon_H149 zenon_H275 zenon_H22 zenon_H13c zenon_H45 zenon_H7c zenon_H172 zenon_H145 zenon_H62 zenon_Ha8 zenon_H279 zenon_H27c zenon_H267 zenon_H10e zenon_H20c zenon_H18c zenon_H22d zenon_H189 zenon_H1a4 zenon_H26d zenon_H1d8 zenon_H1cf zenon_H133 zenon_Hd8 zenon_H124 zenon_H12e zenon_H3f zenon_H1d5 zenon_H173 zenon_H270 zenon_H115 zenon_H273 zenon_H150 zenon_H14f zenon_H153 zenon_H18f zenon_H278 zenon_H2a zenon_H26f zenon_H277. % 19.02/19.21 apply (zenon_or_s _ _ zenon_H279); [ zenon_intro zenon_H14c | zenon_intro zenon_H16c ]. % 19.02/19.21 apply (zenon_or_s _ _ zenon_H276); [ zenon_intro zenon_Hef | zenon_intro zenon_H2c ]. % 19.02/19.21 apply (zenon_or_s _ _ zenon_H271); [ zenon_intro zenon_H26e | zenon_intro zenon_Hf1 ]. % 19.02/19.21 apply (zenon_L1302_); trivial. % 19.02/19.21 apply (zenon_or_s _ _ zenon_H277); [ zenon_intro zenon_H274 | zenon_intro zenon_Haa ]. % 19.02/19.21 apply (zenon_or_s _ _ zenon_H270); [ zenon_intro zenon_H14b | zenon_intro zenon_H61 ]. % 19.02/19.21 apply (zenon_or_s _ _ zenon_H26f); [ zenon_intro zenon_H194 | zenon_intro zenon_Hba ]. % 19.02/19.21 apply (zenon_or_s _ _ zenon_H273); [ zenon_intro zenon_H272 | zenon_intro zenon_H151 ]. % 19.02/19.21 apply (zenon_or_s _ _ zenon_H278); [ zenon_intro zenon_Hf7 | zenon_intro zenon_H163 ]. % 19.02/19.21 apply (zenon_L1299_); trivial. % 19.02/19.21 apply (zenon_or_s _ _ zenon_H74); [ zenon_intro zenon_H42 | zenon_intro zenon_H77 ]. % 19.02/19.21 exact (zenon_H3f zenon_H42). % 19.02/19.21 apply (zenon_or_s _ _ zenon_H77); [ zenon_intro zenon_H49 | zenon_intro zenon_H78 ]. % 19.02/19.21 apply (zenon_or_s _ _ zenon_H22d); [ zenon_intro zenon_H7a | zenon_intro zenon_H22e ]. % 19.02/19.21 apply (zenon_L1326_); trivial. % 19.02/19.21 apply (zenon_or_s _ _ zenon_H22e); [ zenon_intro zenon_Ha0 | zenon_intro zenon_H22f ]. % 19.02/19.21 apply (zenon_L38_); trivial. % 19.02/19.21 apply (zenon_or_s _ _ zenon_H22f); [ zenon_intro zenon_H122 | zenon_intro zenon_Hc3 ]. % 19.02/19.21 apply (zenon_L1327_); trivial. % 19.02/19.21 apply (zenon_or_s _ _ zenon_H1fe); [ zenon_intro zenon_H7b | zenon_intro zenon_H1ff ]. % 19.02/19.21 exact (zenon_H80 zenon_H7b). % 19.02/19.21 apply (zenon_or_s _ _ zenon_H1ff); [ zenon_intro zenon_H86 | zenon_intro zenon_H200 ]. % 19.02/19.21 apply (zenon_or_s _ _ zenon_H1ac); [ zenon_intro zenon_H44 | zenon_intro zenon_H1af ]. % 19.02/19.21 apply (zenon_L1328_); trivial. % 19.02/19.21 apply (zenon_or_s _ _ zenon_H1af); [ zenon_intro zenon_H1b1 | zenon_intro zenon_H1b0 ]. % 19.02/19.21 apply (zenon_or_s _ _ zenon_He8); [ zenon_intro zenon_Hac | zenon_intro zenon_Heb ]. % 19.02/19.21 apply (zenon_L1329_); trivial. % 19.02/19.21 apply (zenon_or_s _ _ zenon_Heb); [ zenon_intro zenon_Hae | zenon_intro zenon_Hec ]. % 19.02/19.21 apply (zenon_L1330_); trivial. % 19.02/19.21 apply (zenon_or_s _ _ zenon_Hec); [ zenon_intro zenon_Hba | zenon_intro zenon_Hc4 ]. % 19.02/19.21 apply (zenon_L185_); trivial. % 19.02/19.21 apply (zenon_L46_); trivial. % 19.02/19.21 apply (zenon_or_s _ _ zenon_H1b0); [ zenon_intro zenon_H61 | zenon_intro zenon_H60 ]. % 19.02/19.21 apply (zenon_L176_); trivial. % 19.02/19.21 apply (zenon_L1332_); trivial. % 19.02/19.21 apply (zenon_or_s _ _ zenon_H200); [ zenon_intro zenon_Hee | zenon_intro zenon_H148 ]. % 19.02/19.21 exact (zenon_Hef zenon_Hee). % 19.02/19.21 exact (zenon_H14b zenon_H148). % 19.02/19.21 apply (zenon_or_s _ _ zenon_H78); [ zenon_intro zenon_H48 | zenon_intro zenon_H1e ]. % 19.02/19.21 apply (zenon_L334_); trivial. % 19.02/19.21 apply (zenon_or_s _ _ zenon_H3e); [ zenon_intro zenon_H42 | zenon_intro zenon_H41 ]. % 19.02/19.21 exact (zenon_H3f zenon_H42). % 19.02/19.21 apply (zenon_or_s _ _ zenon_H41); [ zenon_intro zenon_H27 | zenon_intro zenon_H43 ]. % 19.02/19.21 apply (zenon_L644_); trivial. % 19.02/19.21 apply (zenon_or_s _ _ zenon_H43); [ zenon_intro zenon_H34 | zenon_intro zenon_H44 ]. % 19.02/19.21 apply (zenon_L1336_); trivial. % 19.02/19.21 apply (zenon_or_s _ _ zenon_H22d); [ zenon_intro zenon_H7a | zenon_intro zenon_H22e ]. % 19.02/19.21 apply (zenon_L1333_); trivial. % 19.02/19.21 apply (zenon_or_s _ _ zenon_H22e); [ zenon_intro zenon_Ha0 | zenon_intro zenon_H22f ]. % 19.02/19.21 apply (zenon_or_s _ _ zenon_H235); [ zenon_intro zenon_H7a | zenon_intro zenon_H236 ]. % 19.02/19.21 apply (zenon_or_s _ _ zenon_H1fe); [ zenon_intro zenon_H7b | zenon_intro zenon_H1ff ]. % 19.02/19.21 exact (zenon_H80 zenon_H7b). % 19.02/19.21 apply (zenon_or_s _ _ zenon_H1ff); [ zenon_intro zenon_H86 | zenon_intro zenon_H200 ]. % 19.02/19.21 apply (zenon_or_s _ _ zenon_H1e0); [ zenon_intro zenon_H3a | zenon_intro zenon_H1e1 ]. % 19.02/19.21 apply (zenon_L35_); trivial. % 19.02/19.21 apply (zenon_or_s _ _ zenon_H1e1); [ zenon_intro zenon_H9e | zenon_intro zenon_H1e2 ]. % 19.02/19.21 apply (zenon_or_s _ _ zenon_H128); [ zenon_intro zenon_H9d | zenon_intro zenon_H129 ]. % 19.02/19.21 apply (zenon_L37_); trivial. % 19.02/19.21 apply (zenon_or_s _ _ zenon_H129); [ zenon_intro zenon_H10d | zenon_intro zenon_H12a ]. % 19.02/19.21 exact (zenon_H10a zenon_H10d). % 19.02/19.21 apply (zenon_or_s _ _ zenon_H12a); [ zenon_intro zenon_Hf0 | zenon_intro zenon_Hd6 ]. % 19.02/19.21 apply (zenon_L59_); trivial. % 19.02/19.21 apply (zenon_L365_); trivial. % 19.02/19.21 apply (zenon_or_s _ _ zenon_H1e2); [ zenon_intro zenon_H3b | zenon_intro zenon_H15e ]. % 19.02/19.21 apply (zenon_L33_); trivial. % 19.02/19.21 apply (zenon_L286_); trivial. % 19.02/19.21 apply (zenon_or_s _ _ zenon_H200); [ zenon_intro zenon_Hee | zenon_intro zenon_H148 ]. % 19.02/19.21 exact (zenon_Hef zenon_Hee). % 19.02/19.21 exact (zenon_H14b zenon_H148). % 19.02/19.21 apply (zenon_or_s _ _ zenon_H236); [ zenon_intro zenon_H9d | zenon_intro zenon_H237 ]. % 19.02/19.21 apply (zenon_or_s _ _ zenon_H1fe); [ zenon_intro zenon_H7b | zenon_intro zenon_H1ff ]. % 19.02/19.21 exact (zenon_H80 zenon_H7b). % 19.02/19.21 apply (zenon_or_s _ _ zenon_H1ff); [ zenon_intro zenon_H86 | zenon_intro zenon_H200 ]. % 19.02/19.21 apply (zenon_or_s _ _ zenon_H168); [ zenon_intro zenon_H3a | zenon_intro zenon_H169 ]. % 19.02/19.21 apply (zenon_L1335_); trivial. % 19.02/19.21 apply (zenon_or_s _ _ zenon_H169); [ zenon_intro zenon_H99 | zenon_intro zenon_H16a ]. % 19.02/19.21 apply (zenon_or_s _ _ zenon_H16f); [ zenon_intro zenon_H9e | zenon_intro zenon_H170 ]. % 19.02/19.21 apply (zenon_L37_); trivial. % 19.02/19.21 apply (zenon_or_s _ _ zenon_H170); [ zenon_intro zenon_H13f | zenon_intro zenon_H171 ]. % 19.02/19.21 apply (zenon_L108_); trivial. % 19.02/19.21 apply (zenon_or_s _ _ zenon_H171); [ zenon_intro zenon_H16c | zenon_intro zenon_Hdc ]. % 19.02/19.21 apply (zenon_L521_); trivial. % 19.02/19.21 apply (zenon_L1337_); trivial. % 19.02/19.21 apply (zenon_or_s _ _ zenon_H16a); [ zenon_intro zenon_Ha9 | zenon_intro zenon_He3 ]. % 19.02/19.21 apply (zenon_L184_); trivial. % 19.02/19.21 apply (zenon_L515_); trivial. % 19.02/19.21 apply (zenon_or_s _ _ zenon_H200); [ zenon_intro zenon_Hee | zenon_intro zenon_H148 ]. % 19.02/19.21 exact (zenon_Hef zenon_Hee). % 19.02/19.21 exact (zenon_H14b zenon_H148). % 19.02/19.21 apply (zenon_or_s _ _ zenon_H237); [ zenon_intro zenon_Hed | zenon_intro zenon_Hac ]. % 19.02/19.21 apply (zenon_L93_); trivial. % 19.02/19.21 apply (zenon_L41_); trivial. % 19.02/19.21 apply (zenon_or_s _ _ zenon_H22f); [ zenon_intro zenon_H122 | zenon_intro zenon_Hc3 ]. % 19.02/19.21 apply (zenon_L246_); trivial. % 19.02/19.21 apply (zenon_L427_); trivial. % 19.02/19.21 apply (zenon_L1174_); trivial. % 19.02/19.21 apply (zenon_L185_); trivial. % 19.02/19.21 apply (zenon_L176_); trivial. % 19.02/19.21 apply (zenon_L1301_); trivial. % 19.02/19.21 apply (zenon_L3_); trivial. % 19.02/19.21 apply (zenon_L521_); trivial. % 19.02/19.21 (* end of lemma zenon_L1338_ *) % 19.02/19.21 assert (zenon_L1339_ : ((~((op (e2) (e3)) = (e2)))\/((op (e2) (e2)) = (e3))) -> ((~((op (e3) (e1)) = (e2)))\/((op (e3) (e2)) = (e1))) -> ((op (e1) (e2)) = (e0)) -> ((~((op (e3) (e3)) = (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 (e0) (e2)) = (op (e3) (e2)))) -> ((op (e0) (e2)) = (e2)) -> ((~((op (e3) (e2)) = (e2)))\/((op (e3) (e2)) = (e2))) -> (~((op (e1) (e2)) = (op (e3) (e2)))) -> ((~((op (e3) (e0)) = (e2)))\/((op (e3) (e2)) = (e0))) -> (~((op (e2) (e2)) = (e2))) -> (((op (e2) (e0)) = (e2))\/(((op (e2) (e1)) = (e2))\/(((op (e2) (e2)) = (e2))\/((op (e2) (e3)) = (e2))))) -> (~((op (e0) (e0)) = (e0))) -> (~((op (e0) (e3)) = (e2))) -> (~((op (e1) (e2)) = (op (e1) (e3)))) -> (~((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)) = (op (e3) (e1)))) -> (((op (e0) (e1)) = (e2))\/(((op (e1) (e1)) = (e2))\/(((op (e2) (e1)) = (e2))\/((op (e3) (e1)) = (e2))))) -> (~((op (e0) (e1)) = (e2))) -> (~((op (e3) (e1)) = (op (e3) (e2)))) -> (~((op (e0) (e0)) = (op (e0) (e3)))) -> (((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 (e3) (e0)) = (e0))\/(((op (e3) (e0)) = (e1))\/(((op (e3) (e0)) = (e2))\/((op (e3) (e0)) = (e3))))) -> ((~((op (e0) (e3)) = (e2)))\/((op (e0) (e2)) = (e3))) -> ((~((op (e1) (e3)) = (e2)))\/((op (e1) (e2)) = (e3))) -> (~((op (e0) (e2)) = (op (e2) (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)) = (e2))\/(((op (e1) (e2)) = (e2))\/(((op (e2) (e2)) = (e2))\/((op (e3) (e2)) = (e2))))) -> (~((e1) = (e2))) -> (~((op (e1) (e0)) = (op (e1) (e1)))) -> (~((op (e0) (e0)) = (op (e0) (e2)))) -> (((op (e1) (e0)) = (e0))\/(((op (e1) (e1)) = (e0))\/(((op (e1) (e2)) = (e0))\/((op (e1) (e3)) = (e0))))) -> ((~((op (e1) (e2)) = (e2)))\/((op (e1) (e2)) = (e2))) -> (~((e0) = (e2))) -> (((op (e0) (e0)) = (e0))\/(((op (e1) (e0)) = (e0))\/(((op (e2) (e0)) = (e0))\/((op (e3) (e0)) = (e0))))) -> (((op (e3) (e0)) = (e0))\/(((op (e3) (e1)) = (e0))\/(((op (e3) (e2)) = (e0))\/((op (e3) (e3)) = (e0))))) -> (((op (e0) (e0)) = (e0))\/(((op (e0) (e0)) = (e1))\/(((op (e0) (e0)) = (e2))\/((op (e0) (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 (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 (e0) (e3)) = (e1))\/(((op (e0) (e3)) = (e2))\/((op (e0) (e3)) = (e3))))) -> (~((op (e0) (e3)) = (op (e3) (e3)))) -> (~((op (e2) (e0)) = (op (e2) (e2)))) -> (~((op (e1) (e0)) = (op (e2) (e0)))) -> (~((op (e0) (e2)) = (op (e1) (e2)))) -> (~((op (e2) (e0)) = (op (e2) (e1)))) -> (~((op (e2) (e0)) = (op (e3) (e0)))) -> (((op (e0) (e0)) = (e2))\/(((op (e0) (e1)) = (e2))\/(((op (e0) (e2)) = (e2))\/((op (e0) (e3)) = (e2))))) -> (~((op (e1) (e0)) = (op (e1) (e2)))) -> (~((e2) = (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) (e0)) = (e0))\/(((op (e0) (e1)) = (e0))\/(((op (e0) (e2)) = (e0))\/((op (e0) (e3)) = (e0))))) -> ((~((op (e1) (e1)) = (e2)))\/((op (e1) (e2)) = (e1))) -> (((op (e0) (e1)) = (e1))\/(((op (e1) (e1)) = (e1))\/(((op (e2) (e1)) = (e1))\/((op (e3) (e1)) = (e1))))) -> (((op (e2) (e1)) = (e0))\/(((op (e2) (e1)) = (e1))\/(((op (e2) (e1)) = (e2))\/((op (e2) (e1)) = (e3))))) -> (~((op (e2) (e1)) = (op (e2) (e3)))) -> (~((op (e2) (e1)) = (op (e2) (e2)))) -> (((op (e2) (e0)) = (e1))\/(((op (e2) (e1)) = (e1))\/(((op (e2) (e2)) = (e1))\/((op (e2) (e3)) = (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) (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 (e0) (e2)))) -> (~((op (e2) (e2)) = (op (e2) (e3)))) -> (~((op (e3) (e0)) = (op (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 (e1) (e0)) = (e2)))\/((op (e1) (e2)) = (e0))) -> ((~((op (e0) (e2)) = (e2)))\/((op (e0) (e2)) = (e2))) -> (~((e0) = (e1))) -> (~((op (e0) (e0)) = (e2))) -> (((op (e0) (e0)) = (e3))\/(((op (e0) (e1)) = (e3))\/(((op (e0) (e2)) = (e3))\/((op (e0) (e3)) = (e3))))) -> (((op (e1) (e0)) = (e1))\/(((op (e1) (e1)) = (e1))\/(((op (e1) (e2)) = (e1))\/((op (e1) (e3)) = (e1))))) -> (((op (e0) (e3)) = (e0))\/(((op (e1) (e3)) = (e0))\/(((op (e2) (e3)) = (e0))\/((op (e3) (e3)) = (e0))))) -> (~((op (e2) (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 (e2) (e0)) = (op (e2) (e3)))) -> (~((op (e1) (e3)) = (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)) = (op (e2) (e1)))) -> (((op (e2) (e0)) = (e0))\/(((op (e2) (e0)) = (e1))\/(((op (e2) (e0)) = (e2))\/((op (e2) (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 (e2) (e1)) = (e2)))\/((op (e2) (e2)) = (e1))) -> (~((op (e1) (e2)) = (op (e2) (e2)))) -> ((~((op (e2) (e0)) = (e2)))\/((op (e2) (e2)) = (e0))) -> (~((op (e1) (e1)) = (e1))) -> (~((op (e3) (e0)) = (op (e3) (e2)))) -> (((op (e0) (e0)) = (e3))\/(((op (e1) (e0)) = (e3))\/(((op (e2) (e0)) = (e3))\/((op (e3) (e0)) = (e3))))) -> (~((e0) = (e3))) -> (~((e1) = (e3))) -> (((op (e0) (e0)) = (e2))\/(((op (e1) (e0)) = (e2))\/(((op (e2) (e0)) = (e2))\/((op (e3) (e0)) = (e2))))) -> (((op (e1) (e0)) = (e3))\/(((op (e1) (e1)) = (e3))\/(((op (e1) (e2)) = (e3))\/((op (e1) (e3)) = (e3))))) -> (~((op (e0) (e1)) = (op (e3) (e1)))) -> False). % 19.02/19.21 do 0 intro. intros zenon_H277 zenon_H26f zenon_H2a zenon_H278 zenon_H18f zenon_H153 zenon_H14f zenon_H150 zenon_H273 zenon_H115 zenon_H270 zenon_H173 zenon_H1d5 zenon_H3f zenon_H12e zenon_H124 zenon_Hd8 zenon_H133 zenon_H1cf zenon_H1d8 zenon_H26d zenon_H1a4 zenon_H189 zenon_H22d zenon_H18c zenon_H10e zenon_H267 zenon_H27c zenon_H279 zenon_Ha8 zenon_H62 zenon_H145 zenon_H172 zenon_H7c zenon_H45 zenon_H13c zenon_H22 zenon_H275 zenon_H149 zenon_H3e zenon_H1ac zenon_H26a zenon_H4f zenon_H142 zenon_H101 zenon_H130 zenon_He4 zenon_Hc2 zenon_H52 zenon_H201 zenon_H195 zenon_H1f0 zenon_H17b zenon_H183 zenon_H24a zenon_H12b zenon_H245 zenon_H54 zenon_H74 zenon_H27b zenon_H109 zenon_H1cc zenon_H1c7 zenon_H24b zenon_H106 zenon_Haf zenon_H136 zenon_H102 zenon_H57 zenon_He8 zenon_H4a zenon_H6d zenon_H71 zenon_H1fa zenon_H235 zenon_H27a zenon_H27e zenon_Ha1 zenon_H80 zenon_H168 zenon_H128 zenon_H67 zenon_Hf3 zenon_Hdf zenon_H1d zenon_Hd5 zenon_H5b zenon_Hdb zenon_He2 zenon_H11f zenon_H17e zenon_H259 zenon_H39 zenon_H2f zenon_H271 zenon_H2b zenon_H276 zenon_H10a zenon_H6f zenon_H1e0 zenon_H9a zenon_H95 zenon_H1fe zenon_H16f zenon_H210. % 19.02/19.21 apply (zenon_or_s _ _ zenon_H27b); [ zenon_intro zenon_H20c | zenon_intro zenon_Hf0 ]. % 19.02/19.21 apply (zenon_L1338_); trivial. % 19.02/19.21 apply (zenon_L1307_); trivial. % 19.02/19.21 (* end of lemma zenon_L1339_ *) % 19.02/19.21 assert (zenon_L1340_ : (((op (e0) (e3)) = (e0))\/(((op (e0) (e3)) = (e1))\/(((op (e0) (e3)) = (e2))\/((op (e0) (e3)) = (e3))))) -> (~((op (e0) (e3)) = (op (e1) (e3)))) -> ((op (e2) (e2)) = (e0)) -> (((op (e1) (e0)) = (e2))\/(((op (e1) (e1)) = (e2))\/(((op (e1) (e2)) = (e2))\/((op (e1) (e3)) = (e2))))) -> (~((op (e1) (e0)) = (e2))) -> (~((e0) = (e2))) -> (~((op (e1) (e2)) = (e2))) -> (~((op (e1) (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 (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) (e1)) = (op (e2) (e3)))) -> (~((op (e2) (e1)) = (e2))) -> (((op (e0) (e3)) = (e1))\/(((op (e1) (e3)) = (e1))\/(((op (e2) (e3)) = (e1))\/((op (e3) (e3)) = (e1))))) -> (~((e0) = (e1))) -> (~((op (e1) (e2)) = (op (e1) (e3)))) -> (((op (e0) (e3)) = (e3))\/(((op (e1) (e3)) = (e3))\/(((op (e2) (e3)) = (e3))\/((op (e3) (e3)) = (e3))))) -> (~((e0) = (e3))) -> (~((op (e2) (e3)) = (e2))) -> (((op (e2) (e3)) = (e0))\/(((op (e2) (e3)) = (e1))\/(((op (e2) (e3)) = (e2))\/((op (e2) (e3)) = (e3))))) -> (~((op (e1) (e3)) = (op (e2) (e3)))) -> (~((op (e1) (e3)) = (op (e3) (e3)))) -> (~((op (e1) (e0)) = (op (e1) (e3)))) -> (((op (e1) (e3)) = (e0))\/(((op (e1) (e3)) = (e1))\/(((op (e1) (e3)) = (e2))\/((op (e1) (e3)) = (e3))))) -> (~((op (e1) (e1)) = (e1))) -> (((op (e0) (e0)) = (e2))\/(((op (e1) (e0)) = (e2))\/(((op (e2) (e0)) = (e2))\/((op (e3) (e0)) = (e2))))) -> (~((op (e0) (e0)) = (e2))) -> (~((op (e0) (e1)) = (op (e2) (e1)))) -> (((op (e0) (e1)) = (e0))\/(((op (e1) (e1)) = (e0))\/(((op (e2) (e1)) = (e0))\/((op (e3) (e1)) = (e0))))) -> (((op (e0) (e1)) = (e1))\/(((op (e1) (e1)) = (e1))\/(((op (e2) (e1)) = (e1))\/((op (e3) (e1)) = (e1))))) -> (~((op (e1) (e0)) = (op (e1) (e1)))) -> (~((op (e0) (e1)) = (op (e0) (e3)))) -> (~((op (e3) (e0)) = (e2))) -> (~((op (e0) (e0)) = (e0))) -> (((op (e0) (e0)) = (e0))\/(((op (e1) (e0)) = (e0))\/(((op (e2) (e0)) = (e0))\/((op (e3) (e0)) = (e0))))) -> (~((op (e0) (e3)) = (op (e3) (e3)))) -> (~((op (e0) (e3)) = (op (e2) (e3)))) -> (~((op (e3) (e2)) = (e2))) -> (~((op (e3) (e1)) = (e2))) -> (((op (e3) (e0)) = (e2))\/(((op (e3) (e1)) = (e2))\/(((op (e3) (e2)) = (e2))\/((op (e3) (e3)) = (e2))))) -> (~((op (e1) (e2)) = (op (e3) (e2)))) -> (((op (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))))) -> (~((e1) = (e2))) -> ((op (e2) (e0)) = (e2)) -> (~((op (e2) (e1)) = (op (e3) (e1)))) -> ((op (e1) (e2)) = (e1)) -> (~((op (e1) (e2)) = (op (e2) (e2)))) -> (((op (e3) (e3)) = (e0))\/(((op (e3) (e3)) = (e1))\/(((op (e3) (e3)) = (e2))\/((op (e3) (e3)) = (e3))))) -> (~((op (e3) (e0)) = (op (e3) (e3)))) -> ((op (e3) (e0)) = (e0)) -> (~((op (e2) (e3)) = (op (e3) (e3)))) -> ((op (e1) (e3)) = (e0)) -> (~((op (e3) (e3)) = (e3))) -> False). % 19.02/19.22 do 0 intro. intros zenon_He4 zenon_H1d zenon_H2c zenon_H18c zenon_H177 zenon_H149 zenon_H114 zenon_H14c zenon_H1fa zenon_H22 zenon_H52 zenon_H1cc zenon_H24b zenon_H1c7 zenon_H26e zenon_H133 zenon_Ha1 zenon_H124 zenon_H136 zenon_H9a zenon_H274 zenon_H11f zenon_Hdb zenon_Hd5 zenon_Hd8 zenon_Hdf zenon_H10a zenon_H1fe zenon_H80 zenon_H17e zenon_H245 zenon_H109 zenon_H45 zenon_H54 zenon_H14b zenon_H3f zenon_H3e zenon_Hc2 zenon_He2 zenon_H272 zenon_H194 zenon_H153 zenon_H115 zenon_He8 zenon_H106 zenon_H7c zenon_Hee zenon_Haf zenon_Hf0 zenon_H2b zenon_H101 zenon_H71 zenon_H44 zenon_Hf3 zenon_H1f zenon_H102. % 19.02/19.22 apply (zenon_or_s _ _ zenon_H109); [ zenon_intro zenon_Ha0 | zenon_intro zenon_H10b ]. % 19.02/19.22 apply (zenon_L1262_); trivial. % 19.02/19.22 apply (zenon_or_s _ _ zenon_H10b); [ zenon_intro zenon_H10d | zenon_intro zenon_H10c ]. % 19.02/19.22 exact (zenon_H10a zenon_H10d). % 19.02/19.22 apply (zenon_or_s _ _ zenon_H10c); [ zenon_intro zenon_Ha5 | zenon_intro zenon_Hae ]. % 19.02/19.22 apply (zenon_or_s _ _ zenon_He8); [ zenon_intro zenon_Hac | zenon_intro zenon_Heb ]. % 19.02/19.22 apply (zenon_L41_); trivial. % 19.02/19.22 apply (zenon_or_s _ _ zenon_Heb); [ zenon_intro zenon_Hae | zenon_intro zenon_Hec ]. % 19.02/19.22 apply (zenon_L65_); trivial. % 19.02/19.22 apply (zenon_or_s _ _ zenon_Hec); [ zenon_intro zenon_Hba | zenon_intro zenon_Hc4 ]. % 19.02/19.22 apply (zenon_L69_); trivial. % 19.02/19.22 apply (zenon_L1278_); trivial. % 19.02/19.22 apply (zenon_L65_); trivial. % 19.02/19.22 (* end of lemma zenon_L1340_ *) % 19.02/19.22 assert (zenon_L1341_ : (~((op (e0) (e1)) = (op (e3) (e1)))) -> (((op (e1) (e0)) = (e3))\/(((op (e1) (e1)) = (e3))\/(((op (e1) (e2)) = (e3))\/((op (e1) (e3)) = (e3))))) -> (~((e1) = (e3))) -> (((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)) = (e2)))\/((op (e2) (e2)) = (e0))) -> ((~((op (e2) (e1)) = (e2)))\/((op (e2) (e2)) = (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)) = (e0))\/(((op (e2) (e0)) = (e1))\/(((op (e2) (e0)) = (e2))\/((op (e2) (e0)) = (e3))))) -> (~((op (e2) (e0)) = (op (e2) (e3)))) -> (((op (e0) (e3)) = (e0))\/(((op (e1) (e3)) = (e0))\/(((op (e2) (e3)) = (e0))\/((op (e3) (e3)) = (e0))))) -> (((op (e1) (e0)) = (e1))\/(((op (e1) (e1)) = (e1))\/(((op (e1) (e2)) = (e1))\/((op (e1) (e3)) = (e1))))) -> (((op (e0) (e0)) = (e3))\/(((op (e0) (e1)) = (e3))\/(((op (e0) (e2)) = (e3))\/((op (e0) (e3)) = (e3))))) -> ((~((op (e0) (e2)) = (e2)))\/((op (e0) (e2)) = (e2))) -> ((~((op (e1) (e0)) = (e2)))\/((op (e1) (e2)) = (e0))) -> (((op (e0) (e0)) = (e1))\/(((op (e1) (e0)) = (e1))\/(((op (e2) (e0)) = (e1))\/((op (e3) (e0)) = (e1))))) -> (~((op (e2) (e2)) = (op (e2) (e3)))) -> (~((op (e0) (e1)) = (op (e0) (e2)))) -> (~((op (e1) (e1)) = (op (e1) (e3)))) -> ((~((op (e1) (e1)) = (e2)))\/((op (e1) (e2)) = (e1))) -> (((op (e0) (e0)) = (e0))\/(((op (e0) (e1)) = (e0))\/(((op (e0) (e2)) = (e0))\/((op (e0) (e3)) = (e0))))) -> (~((e2) = (e3))) -> (~((op (e1) (e0)) = (op (e1) (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)) = (op (e2) (e1)))) -> (~((op (e0) (e2)) = (op (e1) (e2)))) -> (~((op (e1) (e0)) = (op (e2) (e0)))) -> (~((op (e3) (e1)) = (op (e3) (e3)))) -> (((op (e1) (e1)) = (e0))\/(((op (e1) (e1)) = (e1))\/(((op (e1) (e1)) = (e2))\/((op (e1) (e1)) = (e3))))) -> (~((op (e1) (e1)) = (op (e1) (e2)))) -> (((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 (e1) (e2)) = (e2)))\/((op (e1) (e2)) = (e2))) -> (~((op (e0) (e0)) = (op (e0) (e2)))) -> (((op (e0) (e2)) = (e2))\/(((op (e1) (e2)) = (e2))\/(((op (e2) (e2)) = (e2))\/((op (e3) (e2)) = (e2))))) -> (((op (e0) (e3)) = (e2))\/(((op (e1) (e3)) = (e2))\/(((op (e2) (e3)) = (e2))\/((op (e3) (e3)) = (e2))))) -> (~((op (e3) (e2)) = (op (e3) (e3)))) -> (~((op (e0) (e2)) = (op (e2) (e2)))) -> ((~((op (e1) (e3)) = (e2)))\/((op (e1) (e2)) = (e3))) -> ((~((op (e0) (e3)) = (e2)))\/((op (e0) (e2)) = (e3))) -> (((op (e3) (e0)) = (e0))\/(((op (e3) (e0)) = (e1))\/(((op (e3) (e0)) = (e2))\/((op (e3) (e0)) = (e3))))) -> (~((op (e0) (e1)) = (op (e1) (e1)))) -> (((op (e0) (e0)) = (e1))\/(((op (e0) (e1)) = (e1))\/(((op (e0) (e2)) = (e1))\/((op (e0) (e3)) = (e1))))) -> (~((op (e0) (e0)) = (op (e0) (e3)))) -> (~((op (e3) (e1)) = (op (e3) (e2)))) -> (~((op (e0) (e1)) = (e2))) -> (((op (e0) (e1)) = (e2))\/(((op (e1) (e1)) = (e2))\/(((op (e2) (e1)) = (e2))\/((op (e3) (e1)) = (e2))))) -> (~((op (e3) (e0)) = (op (e3) (e1)))) -> (~((op (e0) (e3)) = (e2))) -> (((op (e2) (e0)) = (e2))\/(((op (e2) (e1)) = (e2))\/(((op (e2) (e2)) = (e2))\/((op (e2) (e3)) = (e2))))) -> (~((op (e2) (e2)) = (e2))) -> ((~((op (e3) (e0)) = (e2)))\/((op (e3) (e2)) = (e0))) -> ((~((op (e3) (e2)) = (e2)))\/((op (e3) (e2)) = (e2))) -> ((op (e0) (e2)) = (e2)) -> (~((op (e0) (e2)) = (op (e3) (e2)))) -> (~((op (e2) (e2)) = (op (e3) (e2)))) -> ((~((op (e3) (e3)) = (e2)))\/((op (e3) (e2)) = (e3))) -> ((~((op (e3) (e1)) = (e2)))\/((op (e3) (e2)) = (e1))) -> ((~((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 (e2) (e2)) = (e0)) -> (((op (e1) (e0)) = (e2))\/(((op (e1) (e1)) = (e2))\/(((op (e1) (e2)) = (e2))\/((op (e1) (e3)) = (e2))))) -> (~((op (e1) (e0)) = (e2))) -> (~((e0) = (e2))) -> (~((op (e1) (e2)) = (e2))) -> (~((op (e1) (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 (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) (e1)) = (op (e2) (e3)))) -> (~((op (e2) (e1)) = (e2))) -> (((op (e0) (e3)) = (e1))\/(((op (e1) (e3)) = (e1))\/(((op (e2) (e3)) = (e1))\/((op (e3) (e3)) = (e1))))) -> (~((e0) = (e1))) -> (~((op (e1) (e2)) = (op (e1) (e3)))) -> (((op (e0) (e3)) = (e3))\/(((op (e1) (e3)) = (e3))\/(((op (e2) (e3)) = (e3))\/((op (e3) (e3)) = (e3))))) -> (~((e0) = (e3))) -> (~((op (e2) (e3)) = (e2))) -> (((op (e2) (e3)) = (e0))\/(((op (e2) (e3)) = (e1))\/(((op (e2) (e3)) = (e2))\/((op (e2) (e3)) = (e3))))) -> (~((op (e1) (e3)) = (op (e2) (e3)))) -> (~((op (e1) (e3)) = (op (e3) (e3)))) -> (~((op (e1) (e0)) = (op (e1) (e3)))) -> (((op (e1) (e3)) = (e0))\/(((op (e1) (e3)) = (e1))\/(((op (e1) (e3)) = (e2))\/((op (e1) (e3)) = (e3))))) -> (~((op (e1) (e1)) = (e1))) -> (((op (e0) (e0)) = (e2))\/(((op (e1) (e0)) = (e2))\/(((op (e2) (e0)) = (e2))\/((op (e3) (e0)) = (e2))))) -> (~((op (e0) (e0)) = (e2))) -> (~((op (e0) (e1)) = (op (e2) (e1)))) -> (((op (e0) (e1)) = (e0))\/(((op (e1) (e1)) = (e0))\/(((op (e2) (e1)) = (e0))\/((op (e3) (e1)) = (e0))))) -> (((op (e0) (e1)) = (e1))\/(((op (e1) (e1)) = (e1))\/(((op (e2) (e1)) = (e1))\/((op (e3) (e1)) = (e1))))) -> (~((op (e1) (e0)) = (op (e1) (e1)))) -> (~((op (e0) (e1)) = (op (e0) (e3)))) -> (~((op (e3) (e0)) = (e2))) -> (~((op (e0) (e0)) = (e0))) -> (((op (e0) (e0)) = (e0))\/(((op (e1) (e0)) = (e0))\/(((op (e2) (e0)) = (e0))\/((op (e3) (e0)) = (e0))))) -> (~((op (e0) (e3)) = (op (e3) (e3)))) -> (~((op (e0) (e3)) = (op (e2) (e3)))) -> (~((op (e3) (e2)) = (e2))) -> (~((op (e3) (e1)) = (e2))) -> (((op (e3) (e0)) = (e2))\/(((op (e3) (e1)) = (e2))\/(((op (e3) (e2)) = (e2))\/((op (e3) (e3)) = (e2))))) -> (~((op (e1) (e2)) = (op (e3) (e2)))) -> (((op (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))))) -> (~((e1) = (e2))) -> ((op (e2) (e0)) = (e2)) -> (~((op (e2) (e1)) = (op (e3) (e1)))) -> ((op (e1) (e2)) = (e1)) -> (~((op (e1) (e2)) = (op (e2) (e2)))) -> (((op (e3) (e3)) = (e0))\/(((op (e3) (e3)) = (e1))\/(((op (e3) (e3)) = (e2))\/((op (e3) (e3)) = (e3))))) -> (~((op (e3) (e0)) = (op (e3) (e3)))) -> ((op (e3) (e0)) = (e0)) -> (~((op (e2) (e3)) = (op (e3) (e3)))) -> (~((op (e3) (e3)) = (e3))) -> False). % 19.02/19.22 do 0 intro. intros zenon_H210 zenon_H16f zenon_H95 zenon_H1e0 zenon_H6f zenon_H276 zenon_H271 zenon_H2f zenon_H39 zenon_H259 zenon_H5b zenon_H67 zenon_H128 zenon_H168 zenon_H27e zenon_H27a zenon_H235 zenon_H6d zenon_H4a zenon_H57 zenon_H27b zenon_H74 zenon_H12b zenon_H24a zenon_H183 zenon_H17b zenon_H1f0 zenon_H195 zenon_H201 zenon_H130 zenon_H142 zenon_H4f zenon_H26a zenon_H1ac zenon_H275 zenon_H13c zenon_H172 zenon_H145 zenon_H62 zenon_Ha8 zenon_H279 zenon_H27c zenon_H267 zenon_H10e zenon_H22d zenon_H189 zenon_H1a4 zenon_H26d zenon_H1d8 zenon_H1cf zenon_H12e zenon_H1d5 zenon_H173 zenon_H270 zenon_H273 zenon_H150 zenon_H14f zenon_H18f zenon_H278 zenon_H26f zenon_H277 zenon_He4 zenon_H1d zenon_H2c zenon_H18c zenon_H177 zenon_H149 zenon_H114 zenon_H14c zenon_H1fa zenon_H22 zenon_H52 zenon_H1cc zenon_H24b zenon_H1c7 zenon_H26e zenon_H133 zenon_Ha1 zenon_H124 zenon_H136 zenon_H9a zenon_H274 zenon_H11f zenon_Hdb zenon_Hd5 zenon_Hd8 zenon_Hdf zenon_H10a zenon_H1fe zenon_H80 zenon_H17e zenon_H245 zenon_H109 zenon_H45 zenon_H54 zenon_H14b zenon_H3f zenon_H3e zenon_Hc2 zenon_He2 zenon_H272 zenon_H194 zenon_H153 zenon_H115 zenon_He8 zenon_H106 zenon_H7c zenon_Hee zenon_Haf zenon_Hf0 zenon_H2b zenon_H101 zenon_H71 zenon_H44 zenon_Hf3 zenon_H102. % 19.02/19.22 apply (zenon_or_s _ _ zenon_H22); [ zenon_intro zenon_H27 | zenon_intro zenon_H26 ]. % 19.02/19.22 apply (zenon_L312_); trivial. % 19.02/19.22 apply (zenon_or_s _ _ zenon_H26); [ zenon_intro zenon_H29 | zenon_intro zenon_H28 ]. % 19.02/19.22 apply (zenon_L1259_); trivial. % 19.02/19.22 apply (zenon_or_s _ _ zenon_H28); [ zenon_intro zenon_H2a | zenon_intro zenon_H1f ]. % 19.02/19.22 apply (zenon_L1339_); trivial. % 19.02/19.22 apply (zenon_L1340_); trivial. % 19.02/19.22 (* end of lemma zenon_L1341_ *) % 19.02/19.22 assert (zenon_L1342_ : (~((op (e3) (e3)) = (e3))) -> (~((op (e2) (e3)) = (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) (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))))) -> (((op (e3) (e0)) = (e1))\/(((op (e3) (e1)) = (e1))\/(((op (e3) (e2)) = (e1))\/((op (e3) (e3)) = (e1))))) -> (~((op (e1) (e2)) = (op (e3) (e2)))) -> (((op (e3) (e0)) = (e2))\/(((op (e3) (e1)) = (e2))\/(((op (e3) (e2)) = (e2))\/((op (e3) (e3)) = (e2))))) -> (~((op (e3) (e1)) = (e2))) -> (~((op (e3) (e2)) = (e2))) -> (~((op (e0) (e3)) = (op (e2) (e3)))) -> (~((op (e0) (e3)) = (op (e3) (e3)))) -> (((op (e0) (e0)) = (e0))\/(((op (e1) (e0)) = (e0))\/(((op (e2) (e0)) = (e0))\/((op (e3) (e0)) = (e0))))) -> (~((op (e0) (e0)) = (e0))) -> (~((op (e0) (e1)) = (op (e0) (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 (e1) (e1)) = (e0))\/(((op (e2) (e1)) = (e0))\/((op (e3) (e1)) = (e0))))) -> (~((op (e0) (e1)) = (op (e2) (e1)))) -> (~((op (e0) (e0)) = (e2))) -> (((op (e0) (e0)) = (e2))\/(((op (e1) (e0)) = (e2))\/(((op (e2) (e0)) = (e2))\/((op (e3) (e0)) = (e2))))) -> (~((op (e1) (e1)) = (e1))) -> (((op (e1) (e3)) = (e0))\/(((op (e1) (e3)) = (e1))\/(((op (e1) (e3)) = (e2))\/((op (e1) (e3)) = (e3))))) -> (~((op (e1) (e0)) = (op (e1) (e3)))) -> (~((op (e1) (e3)) = (op (e3) (e3)))) -> (~((op (e1) (e3)) = (op (e2) (e3)))) -> (((op (e2) (e3)) = (e0))\/(((op (e2) (e3)) = (e1))\/(((op (e2) (e3)) = (e2))\/((op (e2) (e3)) = (e3))))) -> (~((op (e2) (e3)) = (e2))) -> (~((e0) = (e3))) -> (((op (e0) (e3)) = (e3))\/(((op (e1) (e3)) = (e3))\/(((op (e2) (e3)) = (e3))\/((op (e3) (e3)) = (e3))))) -> (~((op (e1) (e2)) = (op (e1) (e3)))) -> (~((e0) = (e1))) -> (((op (e0) (e3)) = (e1))\/(((op (e1) (e3)) = (e1))\/(((op (e2) (e3)) = (e1))\/((op (e3) (e3)) = (e1))))) -> (~((op (e2) (e1)) = (e2))) -> (~((op (e2) (e1)) = (op (e2) (e3)))) -> (~((op (e2) (e1)) = (op (e2) (e2)))) -> (((op (e2) (e1)) = (e0))\/(((op (e2) (e1)) = (e1))\/(((op (e2) (e1)) = (e2))\/((op (e2) (e1)) = (e3))))) -> (~((op (e2) (e0)) = (op (e2) (e2)))) -> (((op (e1) (e0)) = (e0))\/(((op (e1) (e1)) = (e0))\/(((op (e1) (e2)) = (e0))\/((op (e1) (e3)) = (e0))))) -> (~((op (e1) (e0)) = (op (e3) (e0)))) -> (~((op (e1) (e3)) = (e2))) -> (~((op (e1) (e2)) = (e2))) -> (~((e0) = (e2))) -> (~((op (e1) (e0)) = (e2))) -> (((op (e1) (e0)) = (e2))\/(((op (e1) (e1)) = (e2))\/(((op (e1) (e2)) = (e2))\/((op (e1) (e3)) = (e2))))) -> ((op (e2) (e2)) = (e0)) -> (~((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)) = (e2)))\/((op (e2) (e2)) = (e3))) -> ((~((op (e3) (e1)) = (e2)))\/((op (e3) (e2)) = (e1))) -> ((~((op (e3) (e3)) = (e2)))\/((op (e3) (e2)) = (e3))) -> (~((op (e2) (e2)) = (op (e3) (e2)))) -> (~((op (e0) (e2)) = (op (e3) (e2)))) -> ((op (e0) (e2)) = (e2)) -> ((~((op (e3) (e2)) = (e2)))\/((op (e3) (e2)) = (e2))) -> ((~((op (e3) (e0)) = (e2)))\/((op (e3) (e2)) = (e0))) -> (~((op (e2) (e2)) = (e2))) -> (((op (e2) (e0)) = (e2))\/(((op (e2) (e1)) = (e2))\/(((op (e2) (e2)) = (e2))\/((op (e2) (e3)) = (e2))))) -> (~((op (e0) (e3)) = (e2))) -> (~((op (e3) (e0)) = (op (e3) (e1)))) -> (((op (e0) (e1)) = (e2))\/(((op (e1) (e1)) = (e2))\/(((op (e2) (e1)) = (e2))\/((op (e3) (e1)) = (e2))))) -> (~((op (e0) (e1)) = (e2))) -> (~((op (e3) (e1)) = (op (e3) (e2)))) -> (~((op (e0) (e0)) = (op (e0) (e3)))) -> (((op (e0) (e0)) = (e1))\/(((op (e0) (e1)) = (e1))\/(((op (e0) (e2)) = (e1))\/((op (e0) (e3)) = (e1))))) -> (~((op (e0) (e1)) = (op (e1) (e1)))) -> (((op (e3) (e0)) = (e0))\/(((op (e3) (e0)) = (e1))\/(((op (e3) (e0)) = (e2))\/((op (e3) (e0)) = (e3))))) -> ((~((op (e0) (e3)) = (e2)))\/((op (e0) (e2)) = (e3))) -> ((~((op (e1) (e3)) = (e2)))\/((op (e1) (e2)) = (e3))) -> (~((op (e0) (e2)) = (op (e2) (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)) = (e2))\/(((op (e1) (e2)) = (e2))\/(((op (e2) (e2)) = (e2))\/((op (e3) (e2)) = (e2))))) -> (~((op (e0) (e0)) = (op (e0) (e2)))) -> ((~((op (e1) (e2)) = (e2)))\/((op (e1) (e2)) = (e2))) -> (((op (e3) (e0)) = (e0))\/(((op (e3) (e1)) = (e0))\/(((op (e3) (e2)) = (e0))\/((op (e3) (e3)) = (e0))))) -> (((op (e0) (e0)) = (e0))\/(((op (e0) (e0)) = (e1))\/(((op (e0) (e0)) = (e2))\/((op (e0) (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 (e3) (e1)) = (op (e3) (e3)))) -> (~((op (e1) (e0)) = (op (e2) (e0)))) -> (~((op (e0) (e2)) = (op (e1) (e2)))) -> (~((op (e2) (e0)) = (op (e2) (e1)))) -> (~((op (e2) (e0)) = (op (e3) (e0)))) -> (((op (e0) (e0)) = (e2))\/(((op (e0) (e1)) = (e2))\/(((op (e0) (e2)) = (e2))\/((op (e0) (e3)) = (e2))))) -> (~((op (e1) (e0)) = (op (e1) (e2)))) -> (~((e2) = (e3))) -> (((op (e0) (e0)) = (e0))\/(((op (e0) (e1)) = (e0))\/(((op (e0) (e2)) = (e0))\/((op (e0) (e3)) = (e0))))) -> ((~((op (e1) (e1)) = (e2)))\/((op (e1) (e2)) = (e1))) -> (~((op (e1) (e1)) = (op (e1) (e3)))) -> (~((op (e0) (e1)) = (op (e0) (e2)))) -> (~((op (e2) (e2)) = (op (e2) (e3)))) -> (((op (e0) (e0)) = (e1))\/(((op (e1) (e0)) = (e1))\/(((op (e2) (e0)) = (e1))\/((op (e3) (e0)) = (e1))))) -> ((~((op (e1) (e0)) = (e2)))\/((op (e1) (e2)) = (e0))) -> ((~((op (e0) (e2)) = (e2)))\/((op (e0) (e2)) = (e2))) -> (((op (e0) (e0)) = (e3))\/(((op (e0) (e1)) = (e3))\/(((op (e0) (e2)) = (e3))\/((op (e0) (e3)) = (e3))))) -> (((op (e1) (e0)) = (e1))\/(((op (e1) (e1)) = (e1))\/(((op (e1) (e2)) = (e1))\/((op (e1) (e3)) = (e1))))) -> (((op (e0) (e3)) = (e0))\/(((op (e1) (e3)) = (e0))\/(((op (e2) (e3)) = (e0))\/((op (e3) (e3)) = (e0))))) -> (~((op (e2) (e0)) = (op (e2) (e3)))) -> (((op (e2) (e0)) = (e0))\/(((op (e2) (e0)) = (e1))\/(((op (e2) (e0)) = (e2))\/((op (e2) (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 (e2) (e1)) = (e2)))\/((op (e2) (e2)) = (e1))) -> ((~((op (e2) (e0)) = (e2)))\/((op (e2) (e2)) = (e0))) -> (~((op (e3) (e0)) = (op (e3) (e2)))) -> (((op (e0) (e0)) = (e3))\/(((op (e1) (e0)) = (e3))\/(((op (e2) (e0)) = (e3))\/((op (e3) (e0)) = (e3))))) -> (~((e1) = (e3))) -> (((op (e1) (e0)) = (e3))\/(((op (e1) (e1)) = (e3))\/(((op (e1) (e2)) = (e3))\/((op (e1) (e3)) = (e3))))) -> (~((op (e0) (e1)) = (op (e3) (e1)))) -> (~((op (e3) (e0)) = (e2))) -> False). % 19.02/19.22 do 0 intro. intros zenon_H102 zenon_Hf3 zenon_H44 zenon_H71 zenon_H101 zenon_H2b zenon_Hf0 zenon_Haf zenon_H7c zenon_H106 zenon_He8 zenon_H115 zenon_H153 zenon_H194 zenon_H272 zenon_He2 zenon_Hc2 zenon_H3e zenon_H3f zenon_H54 zenon_H45 zenon_H109 zenon_H245 zenon_H17e zenon_H80 zenon_H1fe zenon_H10a zenon_Hdf zenon_Hd8 zenon_Hd5 zenon_Hdb zenon_H11f zenon_H274 zenon_H9a zenon_H136 zenon_H124 zenon_Ha1 zenon_H133 zenon_H26e zenon_H1c7 zenon_H24b zenon_H1cc zenon_H52 zenon_H22 zenon_H1fa zenon_H14c zenon_H114 zenon_H149 zenon_H177 zenon_H18c zenon_H2c zenon_H1d zenon_He4 zenon_H277 zenon_H26f zenon_H278 zenon_H18f zenon_H14f zenon_H150 zenon_H273 zenon_H270 zenon_H173 zenon_H1d5 zenon_H12e zenon_H1cf zenon_H1d8 zenon_H26d zenon_H1a4 zenon_H189 zenon_H22d zenon_H10e zenon_H267 zenon_H27c zenon_H279 zenon_Ha8 zenon_H62 zenon_H145 zenon_H172 zenon_H13c zenon_H275 zenon_H1ac zenon_H26a zenon_H4f zenon_H142 zenon_H130 zenon_H201 zenon_H195 zenon_H1f0 zenon_H17b zenon_H183 zenon_H24a zenon_H12b zenon_H74 zenon_H27b zenon_H57 zenon_H4a zenon_H6d zenon_H235 zenon_H27a zenon_H27e zenon_H168 zenon_H128 zenon_H67 zenon_H5b zenon_H259 zenon_H39 zenon_H2f zenon_H271 zenon_H276 zenon_H6f zenon_H1e0 zenon_H95 zenon_H16f zenon_H210 zenon_H14b. % 19.02/19.22 apply (zenon_or_s _ _ zenon_H1fe); [ zenon_intro zenon_H7b | zenon_intro zenon_H1ff ]. % 19.02/19.22 exact (zenon_H80 zenon_H7b). % 19.02/19.22 apply (zenon_or_s _ _ zenon_H1ff); [ zenon_intro zenon_H86 | zenon_intro zenon_H200 ]. % 19.02/19.22 exact (zenon_H177 zenon_H86). % 19.02/19.22 apply (zenon_or_s _ _ zenon_H200); [ zenon_intro zenon_Hee | zenon_intro zenon_H148 ]. % 19.02/19.22 apply (zenon_L1341_); trivial. % 19.02/19.22 exact (zenon_H14b zenon_H148). % 19.02/19.22 (* end of lemma zenon_L1342_ *) % 19.02/19.22 assert (zenon_L1343_ : (((op (e1) (e0)) = (e3))\/(((op (e1) (e1)) = (e3))\/(((op (e1) (e2)) = (e3))\/((op (e1) (e3)) = (e3))))) -> (~((op (e1) (e0)) = (e3))) -> (~((op (e1) (e1)) = (e3))) -> (~((op (e1) (e2)) = (e3))) -> (~((op (e1) (e3)) = (e3))) -> False). % 19.02/19.22 do 0 intro. intros zenon_H16f zenon_H9f zenon_H1a1 zenon_H16d zenon_H12f. % 19.02/19.22 apply (zenon_or_s _ _ zenon_H16f); [ zenon_intro zenon_H9e | zenon_intro zenon_H170 ]. % 19.02/19.22 exact (zenon_H9f zenon_H9e). % 19.02/19.22 apply (zenon_or_s _ _ zenon_H170); [ zenon_intro zenon_H13f | zenon_intro zenon_H171 ]. % 19.02/19.22 exact (zenon_H1a1 zenon_H13f). % 19.02/19.22 apply (zenon_or_s _ _ zenon_H171); [ zenon_intro zenon_H16c | zenon_intro zenon_Hdc ]. % 19.02/19.22 exact (zenon_H16d zenon_H16c). % 19.02/19.22 exact (zenon_H12f zenon_Hdc). % 19.02/19.22 (* end of lemma zenon_L1343_ *) % 19.02/19.22 assert (zenon_L1344_ : (((op (e2) (e0)) = (e3))\/(((op (e2) (e1)) = (e3))\/(((op (e2) (e2)) = (e3))\/((op (e2) (e3)) = (e3))))) -> (~((op (e2) (e0)) = (e3))) -> (~((op (e2) (e1)) = (e3))) -> (~((op (e2) (e2)) = (e3))) -> (~((op (e2) (e3)) = (e3))) -> False). % 19.02/19.22 do 0 intro. intros zenon_He7 zenon_H27f zenon_Ha7 zenon_H1b3 zenon_H280. % 19.02/19.22 apply (zenon_or_s _ _ zenon_He7); [ zenon_intro zenon_H3b | zenon_intro zenon_He9 ]. % 19.02/19.22 exact (zenon_H27f zenon_H3b). % 19.02/19.22 apply (zenon_or_s _ _ zenon_He9); [ zenon_intro zenon_Ha6 | zenon_intro zenon_Hea ]. % 19.02/19.22 exact (zenon_Ha7 zenon_Ha6). % 19.02/19.22 apply (zenon_or_s _ _ zenon_Hea); [ zenon_intro zenon_Haa | zenon_intro zenon_Hdd ]. % 19.02/19.22 exact (zenon_H1b3 zenon_Haa). % 19.02/19.22 exact (zenon_H280 zenon_Hdd). % 19.02/19.22 (* end of lemma zenon_L1344_ *) % 19.02/19.22 assert (zenon_L1345_ : ((~((op (e2) (e3)) = (e3)))\/((op (e2) (e3)) = (e3))) -> ((op (e1) (e3)) = (e3)) -> (~((op (e1) (e3)) = (op (e2) (e3)))) -> (~((op (e2) (e0)) = (e3))) -> (~((op (e2) (e1)) = (e3))) -> (~((op (e2) (e2)) = (e3))) -> (((op (e2) (e0)) = (e3))\/(((op (e2) (e1)) = (e3))\/(((op (e2) (e2)) = (e3))\/((op (e2) (e3)) = (e3))))) -> False). % 19.02/19.22 do 0 intro. intros zenon_H281 zenon_Hdc zenon_Hdb zenon_H27f zenon_Ha7 zenon_H1b3 zenon_He7. % 19.02/19.22 apply (zenon_or_s _ _ zenon_H281); [ zenon_intro zenon_H280 | zenon_intro zenon_Hdd ]. % 19.02/19.22 apply (zenon_L1344_); trivial. % 19.02/19.22 apply (zenon_L52_); trivial. % 19.02/19.22 (* end of lemma zenon_L1345_ *) % 19.02/19.22 assert (zenon_L1346_ : (((op (e3) (e0)) = (e3))\/(((op (e3) (e1)) = (e3))\/(((op (e3) (e2)) = (e3))\/((op (e3) (e3)) = (e3))))) -> (~((op (e3) (e0)) = (e3))) -> (~((op (e3) (e1)) = (e3))) -> (~((op (e3) (e2)) = (e3))) -> (~((op (e3) (e3)) = (e3))) -> False). % 19.02/19.22 do 0 intro. intros zenon_H165 zenon_H15f zenon_H282 zenon_H283 zenon_H102. % 19.02/19.22 apply (zenon_or_s _ _ zenon_H165); [ zenon_intro zenon_H15e | zenon_intro zenon_H166 ]. % 19.02/19.22 exact (zenon_H15f zenon_H15e). % 19.02/19.22 apply (zenon_or_s _ _ zenon_H166); [ zenon_intro zenon_H161 | zenon_intro zenon_H167 ]. % 19.02/19.22 exact (zenon_H282 zenon_H161). % 19.02/19.22 apply (zenon_or_s _ _ zenon_H167); [ zenon_intro zenon_H163 | zenon_intro zenon_H105 ]. % 19.02/19.22 exact (zenon_H283 zenon_H163). % 19.02/19.22 exact (zenon_H102 zenon_H105). % 19.02/19.22 (* end of lemma zenon_L1346_ *) % 19.02/19.22 assert (zenon_L1347_ : ((~((op (e3) (e2)) = (e3)))\/((op (e3) (e3)) = (e2))) -> ((op (e2) (e3)) = (e2)) -> (~((op (e2) (e3)) = (op (e3) (e3)))) -> (~((op (e3) (e0)) = (e3))) -> (~((op (e3) (e1)) = (e3))) -> (~((op (e3) (e3)) = (e3))) -> (((op (e3) (e0)) = (e3))\/(((op (e3) (e1)) = (e3))\/(((op (e3) (e2)) = (e3))\/((op (e3) (e3)) = (e3))))) -> False). % 19.02/19.22 do 0 intro. intros zenon_H284 zenon_H11d zenon_Hf3 zenon_H15f zenon_H282 zenon_H102 zenon_H165. % 19.02/19.22 apply (zenon_or_s _ _ zenon_H284); [ zenon_intro zenon_H283 | zenon_intro zenon_Hf6 ]. % 19.02/19.22 apply (zenon_L1346_); trivial. % 19.02/19.22 apply (zenon_L97_); trivial. % 19.02/19.22 (* end of lemma zenon_L1347_ *) % 19.02/19.22 assert (zenon_L1348_ : (((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)) = (e3))) -> (~((op (e0) (e3)) = (e3))) -> False). % 19.02/19.22 do 0 intro. intros zenon_H168 zenon_H98 zenon_H9a zenon_H49 zenon_H123 zenon_H12d. % 19.02/19.22 apply (zenon_or_s _ _ zenon_H168); [ zenon_intro zenon_H3a | zenon_intro zenon_H169 ]. % 19.02/19.22 exact (zenon_H98 zenon_H3a). % 19.02/19.22 apply (zenon_or_s _ _ zenon_H169); [ zenon_intro zenon_H99 | zenon_intro zenon_H16a ]. % 19.02/19.22 apply (zenon_L36_); trivial. % 19.02/19.22 apply (zenon_or_s _ _ zenon_H16a); [ zenon_intro zenon_Ha9 | zenon_intro zenon_He3 ]. % 19.02/19.22 exact (zenon_H123 zenon_Ha9). % 19.02/19.22 exact (zenon_H12d zenon_He3). % 19.02/19.22 (* end of lemma zenon_L1348_ *) % 19.02/19.22 assert (zenon_L1349_ : (((op (e0) (e0)) = (e3))\/(((op (e0) (e1)) = (e3))\/(((op (e0) (e2)) = (e3))\/((op (e0) (e3)) = (e3))))) -> (~((op (e0) (e0)) = (e3))) -> (~((op (e0) (e1)) = (e3))) -> (~((e0) = (e3))) -> ((op (e0) (e2)) = (e0)) -> (~((op (e0) (e3)) = (e3))) -> False). % 19.02/19.22 do 0 intro. intros zenon_H168 zenon_H98 zenon_H9c zenon_H9a zenon_H48 zenon_H12d. % 19.02/19.22 apply (zenon_or_s _ _ zenon_H168); [ zenon_intro zenon_H3a | zenon_intro zenon_H169 ]. % 19.02/19.22 exact (zenon_H98 zenon_H3a). % 19.02/19.22 apply (zenon_or_s _ _ zenon_H169); [ zenon_intro zenon_H99 | zenon_intro zenon_H16a ]. % 19.02/19.22 exact (zenon_H9c zenon_H99). % 19.02/19.22 apply (zenon_or_s _ _ zenon_H16a); [ zenon_intro zenon_Ha9 | zenon_intro zenon_He3 ]. % 19.02/19.22 apply (zenon_L358_); trivial. % 19.02/19.22 exact (zenon_H12d zenon_He3). % 19.02/19.22 (* end of lemma zenon_L1349_ *) % 19.02/19.22 assert (zenon_L1350_ : (((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)) = (e3))) -> (~((op (e0) (e2)) = (e3))) -> (~((op (e0) (e3)) = (e3))) -> False). % 19.02/19.22 do 0 intro. intros zenon_H168 zenon_H95 zenon_H7a zenon_H9c zenon_H123 zenon_H12d. % 19.02/19.22 apply (zenon_or_s _ _ zenon_H168); [ zenon_intro zenon_H3a | zenon_intro zenon_H169 ]. % 19.02/19.22 apply (zenon_L35_); trivial. % 19.02/19.22 apply (zenon_or_s _ _ zenon_H169); [ zenon_intro zenon_H99 | zenon_intro zenon_H16a ]. % 19.02/19.22 exact (zenon_H9c zenon_H99). % 19.02/19.22 apply (zenon_or_s _ _ zenon_H16a); [ zenon_intro zenon_Ha9 | zenon_intro zenon_He3 ]. % 19.02/19.22 exact (zenon_H123 zenon_Ha9). % 19.02/19.22 exact (zenon_H12d zenon_He3). % 19.02/19.22 (* end of lemma zenon_L1350_ *) % 19.02/19.22 assert (zenon_L1351_ : (((op (e3) (e2)) = (e0))\/(((op (e3) (e2)) = (e1))\/(((op (e3) (e2)) = (e2))\/((op (e3) (e2)) = (e3))))) -> ((op (e3) (e0)) = (e0)) -> (~((op (e3) (e0)) = (op (e3) (e2)))) -> (~((op (e3) (e2)) = (op (e3) (e3)))) -> ((op (e3) (e3)) = (e1)) -> ((op (e0) (e2)) = (e2)) -> (~((op (e0) (e2)) = (op (e3) (e2)))) -> (~((op (e3) (e2)) = (e3))) -> False). % 19.02/19.22 do 0 intro. intros zenon_H191 zenon_H44 zenon_H6f zenon_H62 zenon_Hc4 zenon_H150 zenon_H14f zenon_H283. % 19.02/19.22 apply (zenon_or_s _ _ zenon_H191); [ zenon_intro zenon_H61 | zenon_intro zenon_H192 ]. % 19.02/19.22 apply (zenon_L19_); trivial. % 19.02/19.22 apply (zenon_or_s _ _ zenon_H192); [ zenon_intro zenon_Hba | zenon_intro zenon_H193 ]. % 19.02/19.22 apply (zenon_L147_); trivial. % 19.02/19.22 apply (zenon_or_s _ _ zenon_H193); [ zenon_intro zenon_H151 | zenon_intro zenon_H163 ]. % 19.02/19.22 apply (zenon_L104_); trivial. % 19.02/19.22 exact (zenon_H283 zenon_H163). % 19.02/19.22 (* end of lemma zenon_L1351_ *) % 19.02/19.22 assert (zenon_L1352_ : (((op (e0) (e2)) = (e0))\/(((op (e0) (e2)) = (e1))\/(((op (e0) (e2)) = (e2))\/((op (e0) (e2)) = (e3))))) -> (~((op (e0) (e2)) = (op (e0) (e3)))) -> ((op (e0) (e3)) = (e0)) -> ((op (e1) (e2)) = (e1)) -> (~((op (e0) (e2)) = (op (e1) (e2)))) -> ((op (e3) (e2)) = (e2)) -> (~((op (e0) (e2)) = (op (e3) (e2)))) -> (~((op (e0) (e2)) = (e3))) -> False). % 19.02/19.22 do 0 intro. intros zenon_H1ba zenon_H208 zenon_H1e zenon_Hf0 zenon_H195 zenon_H151 zenon_H14f zenon_H123. % 19.02/19.22 apply (zenon_or_s _ _ zenon_H1ba); [ zenon_intro zenon_H48 | zenon_intro zenon_H1bb ]. % 19.02/19.22 apply (zenon_L336_); trivial. % 19.02/19.22 apply (zenon_or_s _ _ zenon_H1bb); [ zenon_intro zenon_H122 | zenon_intro zenon_H1bc ]. % 19.02/19.22 apply (zenon_L530_); trivial. % 19.02/19.22 apply (zenon_or_s _ _ zenon_H1bc); [ zenon_intro zenon_H150 | zenon_intro zenon_Ha9 ]. % 19.02/19.22 apply (zenon_L104_); trivial. % 19.02/19.22 exact (zenon_H123 zenon_Ha9). % 19.02/19.22 (* end of lemma zenon_L1352_ *) % 19.02/19.22 assert (zenon_L1353_ : (((op (e3) (e2)) = (e0))\/(((op (e3) (e2)) = (e1))\/(((op (e3) (e2)) = (e2))\/((op (e3) (e2)) = (e3))))) -> ((op (e3) (e1)) = (e0)) -> (~((op (e3) (e1)) = (op (e3) (e2)))) -> (~((op (e3) (e2)) = (op (e3) (e3)))) -> ((op (e3) (e3)) = (e1)) -> (~((op (e0) (e2)) = (e3))) -> (~((op (e0) (e2)) = (op (e3) (e2)))) -> (~((op (e0) (e2)) = (op (e1) (e2)))) -> ((op (e1) (e2)) = (e1)) -> ((op (e0) (e3)) = (e0)) -> (~((op (e0) (e2)) = (op (e0) (e3)))) -> (((op (e0) (e2)) = (e0))\/(((op (e0) (e2)) = (e1))\/(((op (e0) (e2)) = (e2))\/((op (e0) (e2)) = (e3))))) -> (~((op (e3) (e2)) = (e3))) -> False). % 19.02/19.22 do 0 intro. intros zenon_H191 zenon_H1b1 zenon_H1a4 zenon_H62 zenon_Hc4 zenon_H123 zenon_H14f zenon_H195 zenon_Hf0 zenon_H1e zenon_H208 zenon_H1ba zenon_H283. % 19.02/19.22 apply (zenon_or_s _ _ zenon_H191); [ zenon_intro zenon_H61 | zenon_intro zenon_H192 ]. % 19.02/19.22 apply (zenon_L247_); trivial. % 19.02/19.22 apply (zenon_or_s _ _ zenon_H192); [ zenon_intro zenon_Hba | zenon_intro zenon_H193 ]. % 19.02/19.22 apply (zenon_L147_); trivial. % 19.02/19.22 apply (zenon_or_s _ _ zenon_H193); [ zenon_intro zenon_H151 | zenon_intro zenon_H163 ]. % 19.02/19.22 apply (zenon_L1352_); trivial. % 19.02/19.22 exact (zenon_H283 zenon_H163). % 19.02/19.22 (* end of lemma zenon_L1353_ *) % 19.02/19.22 assert (zenon_L1354_ : (((op (e3) (e0)) = (e0))\/(((op (e3) (e0)) = (e1))\/(((op (e3) (e0)) = (e2))\/((op (e3) (e0)) = (e3))))) -> ((op (e3) (e2)) = (e0)) -> (~((op (e3) (e0)) = (op (e3) (e2)))) -> (~((op (e3) (e0)) = (op (e3) (e3)))) -> ((op (e3) (e3)) = (e1)) -> ((op (e3) (e1)) = (e2)) -> (~((op (e3) (e0)) = (op (e3) (e1)))) -> (~((op (e3) (e0)) = (e3))) -> False). % 19.02/19.22 do 0 intro. intros zenon_H267 zenon_H61 zenon_H6f zenon_H71 zenon_Hc4 zenon_H14d zenon_H1cf zenon_H15f. % 19.02/19.22 apply (zenon_or_s _ _ zenon_H267); [ zenon_intro zenon_H44 | zenon_intro zenon_H268 ]. % 19.02/19.22 apply (zenon_L19_); trivial. % 19.02/19.22 apply (zenon_or_s _ _ zenon_H268); [ zenon_intro zenon_Hac | zenon_intro zenon_H269 ]. % 19.02/19.22 apply (zenon_L189_); trivial. % 19.02/19.22 apply (zenon_or_s _ _ zenon_H269); [ zenon_intro zenon_H148 | zenon_intro zenon_H15e ]. % 19.02/19.22 apply (zenon_L436_); trivial. % 19.02/19.22 exact (zenon_H15f zenon_H15e). % 19.02/19.22 (* end of lemma zenon_L1354_ *) % 19.02/19.22 assert (zenon_L1355_ : (((op (e3) (e0)) = (e2))\/(((op (e3) (e1)) = (e2))\/(((op (e3) (e2)) = (e2))\/((op (e3) (e3)) = (e2))))) -> ((op (e0) (e0)) = (e3)) -> ((op (e2) (e0)) = (e1)) -> (~((op (e3) (e0)) = (e3))) -> (~((op (e3) (e0)) = (op (e3) (e1)))) -> ((op (e3) (e3)) = (e1)) -> (~((op (e3) (e0)) = (op (e3) (e3)))) -> (~((op (e3) (e0)) = (op (e3) (e2)))) -> ((op (e3) (e2)) = (e0)) -> (((op (e3) (e0)) = (e0))\/(((op (e3) (e0)) = (e1))\/(((op (e3) (e0)) = (e2))\/((op (e3) (e0)) = (e3))))) -> (~((op (e0) (e2)) = (e3))) -> (~((op (e0) (e2)) = (op (e3) (e2)))) -> (~((op (e0) (e2)) = (op (e1) (e2)))) -> ((op (e1) (e2)) = (e1)) -> ((op (e0) (e3)) = (e0)) -> (~((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)) = (op (e3) (e3)))) -> ((op (e2) (e3)) = (e2)) -> False). % 19.02/19.22 do 0 intro. intros zenon_H153 zenon_H3a zenon_Hed zenon_H15f zenon_H1cf zenon_Hc4 zenon_H71 zenon_H6f zenon_H61 zenon_H267 zenon_H123 zenon_H14f zenon_H195 zenon_Hf0 zenon_H1e zenon_H208 zenon_H1ba zenon_Hf3 zenon_H11d. % 19.02/19.22 apply (zenon_or_s _ _ zenon_H153); [ zenon_intro zenon_H148 | zenon_intro zenon_H154 ]. % 19.02/19.22 apply (zenon_L423_); trivial. % 19.02/19.22 apply (zenon_or_s _ _ zenon_H154); [ zenon_intro zenon_H14d | zenon_intro zenon_H155 ]. % 19.02/19.22 apply (zenon_L1354_); trivial. % 19.02/19.22 apply (zenon_or_s _ _ zenon_H155); [ zenon_intro zenon_H151 | zenon_intro zenon_Hf6 ]. % 19.02/19.22 apply (zenon_L1352_); trivial. % 19.02/19.22 apply (zenon_L97_); trivial. % 19.02/19.22 (* end of lemma zenon_L1355_ *) % 19.02/19.22 assert (zenon_L1356_ : (((op (e3) (e0)) = (e0))\/(((op (e3) (e1)) = (e0))\/(((op (e3) (e2)) = (e0))\/((op (e3) (e3)) = (e0))))) -> ((op (e0) (e2)) = (e2)) -> (~((op (e3) (e2)) = (e3))) -> (~((op (e3) (e2)) = (op (e3) (e3)))) -> (~((op (e3) (e1)) = (op (e3) (e2)))) -> (((op (e3) (e2)) = (e0))\/(((op (e3) (e2)) = (e1))\/(((op (e3) (e2)) = (e2))\/((op (e3) (e2)) = (e3))))) -> ((op (e2) (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 (e0) (e2)) = (op (e0) (e3)))) -> ((op (e1) (e2)) = (e1)) -> (~((op (e0) (e2)) = (op (e1) (e2)))) -> (~((op (e0) (e2)) = (op (e3) (e2)))) -> (~((op (e0) (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) (e3)))) -> ((op (e3) (e3)) = (e1)) -> (~((op (e3) (e0)) = (op (e3) (e1)))) -> (~((op (e3) (e0)) = (e3))) -> ((op (e2) (e0)) = (e1)) -> ((op (e0) (e0)) = (e3)) -> (((op (e3) (e0)) = (e2))\/(((op (e3) (e1)) = (e2))\/(((op (e3) (e2)) = (e2))\/((op (e3) (e3)) = (e2))))) -> (~((op (e0) (e3)) = (op (e3) (e3)))) -> ((op (e0) (e3)) = (e0)) -> False). % 19.02/19.22 do 0 intro. intros zenon_H1ac zenon_H150 zenon_H283 zenon_H62 zenon_H1a4 zenon_H191 zenon_H11d zenon_Hf3 zenon_H1ba zenon_H208 zenon_Hf0 zenon_H195 zenon_H14f zenon_H123 zenon_H267 zenon_H6f zenon_H71 zenon_Hc4 zenon_H1cf zenon_H15f zenon_Hed zenon_H3a zenon_H153 zenon_Hc2 zenon_H1e. % 19.02/19.22 apply (zenon_or_s _ _ zenon_H1ac); [ zenon_intro zenon_H44 | zenon_intro zenon_H1af ]. % 19.02/19.22 apply (zenon_L1351_); trivial. % 19.02/19.22 apply (zenon_or_s _ _ zenon_H1af); [ zenon_intro zenon_H1b1 | zenon_intro zenon_H1b0 ]. % 19.02/19.22 apply (zenon_L1353_); trivial. % 19.02/19.22 apply (zenon_or_s _ _ zenon_H1b0); [ zenon_intro zenon_H61 | zenon_intro zenon_H60 ]. % 19.02/19.22 apply (zenon_L1355_); trivial. % 19.02/19.22 apply (zenon_L440_); trivial. % 19.02/19.22 (* end of lemma zenon_L1356_ *) % 19.02/19.22 assert (zenon_L1357_ : (((op (e0) (e2)) = (e0))\/(((op (e0) (e2)) = (e1))\/(((op (e0) (e2)) = (e2))\/((op (e0) (e2)) = (e3))))) -> (~((op (e0) (e2)) = (op (e0) (e3)))) -> ((op (e0) (e3)) = (e0)) -> (~((op (e0) (e1)) = (op (e0) (e2)))) -> ((op (e0) (e1)) = (e1)) -> ((op (e1) (e2)) = (e2)) -> (~((op (e0) (e2)) = (op (e1) (e2)))) -> (~((op (e0) (e2)) = (e3))) -> False). % 19.02/19.22 do 0 intro. intros zenon_H1ba zenon_H208 zenon_H1e zenon_H4a zenon_Ha0 zenon_H113 zenon_H195 zenon_H123. % 19.02/19.22 apply (zenon_or_s _ _ zenon_H1ba); [ zenon_intro zenon_H48 | zenon_intro zenon_H1bb ]. % 19.02/19.22 apply (zenon_L336_); trivial. % 19.02/19.22 apply (zenon_or_s _ _ zenon_H1bb); [ zenon_intro zenon_H122 | zenon_intro zenon_H1bc ]. % 19.02/19.22 apply (zenon_L406_); trivial. % 19.02/19.22 apply (zenon_or_s _ _ zenon_H1bc); [ zenon_intro zenon_H150 | zenon_intro zenon_Ha9 ]. % 19.02/19.22 apply (zenon_L153_); trivial. % 19.02/19.22 exact (zenon_H123 zenon_Ha9). % 19.02/19.22 (* end of lemma zenon_L1357_ *) % 19.02/19.22 assert (zenon_L1358_ : (((op (e1) (e1)) = (e0))\/(((op (e1) (e1)) = (e1))\/(((op (e1) (e1)) = (e2))\/((op (e1) (e1)) = (e3))))) -> ((op (e1) (e0)) = (e0)) -> (~((op (e1) (e0)) = (op (e1) (e1)))) -> (~((op (e1) (e1)) = (e1))) -> ((op (e0) (e1)) = (e2)) -> (~((op (e0) (e1)) = (op (e1) (e1)))) -> (~((op (e1) (e1)) = (e3))) -> False). % 19.02/19.22 do 0 intro. intros zenon_H142 zenon_H27 zenon_H45 zenon_H10a zenon_H10f zenon_H10e zenon_H1a1. % 19.02/19.22 apply (zenon_or_s _ _ zenon_H142); [ zenon_intro zenon_H29 | zenon_intro zenon_H143 ]. % 19.02/19.22 apply (zenon_L8_); trivial. % 19.02/19.22 apply (zenon_or_s _ _ zenon_H143); [ zenon_intro zenon_H10d | zenon_intro zenon_H144 ]. % 19.02/19.22 exact (zenon_H10a zenon_H10d). % 19.02/19.22 apply (zenon_or_s _ _ zenon_H144); [ zenon_intro zenon_H110 | zenon_intro zenon_H13f ]. % 19.02/19.22 apply (zenon_L67_); trivial. % 19.02/19.22 exact (zenon_H1a1 zenon_H13f). % 19.02/19.22 (* end of lemma zenon_L1358_ *) % 19.02/19.22 assert (zenon_L1359_ : (((op (e0) (e1)) = (e0))\/(((op (e0) (e1)) = (e1))\/(((op (e0) (e1)) = (e2))\/((op (e0) (e1)) = (e3))))) -> (~((op (e0) (e1)) = (op (e0) (e3)))) -> (~((op (e0) (e2)) = (e3))) -> (~((op (e0) (e2)) = (op (e1) (e2)))) -> ((op (e1) (e2)) = (e2)) -> (~((op (e0) (e1)) = (op (e0) (e2)))) -> ((op (e0) (e3)) = (e0)) -> (~((op (e0) (e2)) = (op (e0) (e3)))) -> (((op (e0) (e2)) = (e0))\/(((op (e0) (e2)) = (e1))\/(((op (e0) (e2)) = (e2))\/((op (e0) (e2)) = (e3))))) -> (~((op (e1) (e1)) = (e3))) -> (~((op (e0) (e1)) = (op (e1) (e1)))) -> (~((op (e1) (e1)) = (e1))) -> (~((op (e1) (e0)) = (op (e1) (e1)))) -> ((op (e1) (e0)) = (e0)) -> (((op (e1) (e1)) = (e0))\/(((op (e1) (e1)) = (e1))\/(((op (e1) (e1)) = (e2))\/((op (e1) (e1)) = (e3))))) -> (~((op (e0) (e1)) = (e3))) -> False). % 19.02/19.22 do 0 intro. intros zenon_H212 zenon_H54 zenon_H123 zenon_H195 zenon_H113 zenon_H4a zenon_H1e zenon_H208 zenon_H1ba zenon_H1a1 zenon_H10e zenon_H10a zenon_H45 zenon_H27 zenon_H142 zenon_H9c. % 19.02/19.22 apply (zenon_or_s _ _ zenon_H212); [ zenon_intro zenon_H49 | zenon_intro zenon_H213 ]. % 19.02/19.22 apply (zenon_L12_); trivial. % 19.02/19.22 apply (zenon_or_s _ _ zenon_H213); [ zenon_intro zenon_Ha0 | zenon_intro zenon_H214 ]. % 19.02/19.22 apply (zenon_L1357_); trivial. % 19.02/19.22 apply (zenon_or_s _ _ zenon_H214); [ zenon_intro zenon_H10f | zenon_intro zenon_H99 ]. % 19.02/19.22 apply (zenon_L1358_); trivial. % 19.02/19.22 exact (zenon_H9c zenon_H99). % 19.02/19.22 (* end of lemma zenon_L1359_ *) % 19.02/19.22 assert (zenon_L1360_ : (((op (e0) (e1)) = (e0))\/(((op (e0) (e1)) = (e1))\/(((op (e0) (e1)) = (e2))\/((op (e0) (e1)) = (e3))))) -> (~((op (e0) (e1)) = (op (e0) (e3)))) -> ((op (e0) (e3)) = (e0)) -> (~((op (e0) (e1)) = (op (e0) (e2)))) -> ((op (e0) (e2)) = (e1)) -> ((op (e2) (e1)) = (e2)) -> (~((op (e0) (e1)) = (op (e2) (e1)))) -> (~((op (e0) (e1)) = (e3))) -> False). % 19.02/19.22 do 0 intro. intros zenon_H212 zenon_H54 zenon_H1e zenon_H4a zenon_H122 zenon_H1ca zenon_H17e zenon_H9c. % 19.02/19.22 apply (zenon_or_s _ _ zenon_H212); [ zenon_intro zenon_H49 | zenon_intro zenon_H213 ]. % 19.02/19.22 apply (zenon_L12_); trivial. % 19.02/19.22 apply (zenon_or_s _ _ zenon_H213); [ zenon_intro zenon_Ha0 | zenon_intro zenon_H214 ]. % 19.02/19.22 apply (zenon_L406_); trivial. % 19.02/19.22 apply (zenon_or_s _ _ zenon_H214); [ zenon_intro zenon_H10f | zenon_intro zenon_H99 ]. % 19.02/19.22 apply (zenon_L191_); trivial. % 19.02/19.22 exact (zenon_H9c zenon_H99). % 19.02/19.22 (* end of lemma zenon_L1360_ *) % 19.02/19.22 assert (zenon_L1361_ : (((op (e2) (e0)) = (e2))\/(((op (e2) (e1)) = (e2))\/(((op (e2) (e2)) = (e2))\/((op (e2) (e3)) = (e2))))) -> (~((e1) = (e2))) -> ((op (e2) (e0)) = (e1)) -> (~((op (e0) (e1)) = (e3))) -> (~((op (e0) (e1)) = (op (e2) (e1)))) -> ((op (e0) (e2)) = (e1)) -> (~((op (e0) (e1)) = (op (e0) (e2)))) -> ((op (e0) (e3)) = (e0)) -> (~((op (e0) (e1)) = (op (e0) (e3)))) -> (((op (e0) (e1)) = (e0))\/(((op (e0) (e1)) = (e1))\/(((op (e0) (e1)) = (e2))\/((op (e0) (e1)) = (e3))))) -> (~((op (e2) (e2)) = (e2))) -> (~((op (e2) (e3)) = (op (e3) (e3)))) -> ((op (e3) (e3)) = (e2)) -> False). % 19.02/19.22 do 0 intro. intros zenon_H1d5 zenon_H7c zenon_Hed zenon_H9c zenon_H17e zenon_H122 zenon_H4a zenon_H1e zenon_H54 zenon_H212 zenon_H173 zenon_Hf3 zenon_Hf6. % 19.02/19.22 apply (zenon_or_s _ _ zenon_H1d5); [ zenon_intro zenon_Hee | zenon_intro zenon_H1d6 ]. % 19.02/19.22 apply (zenon_L58_); trivial. % 19.02/19.22 apply (zenon_or_s _ _ zenon_H1d6); [ zenon_intro zenon_H1ca | zenon_intro zenon_H1d7 ]. % 19.02/19.22 apply (zenon_L1360_); trivial. % 19.02/19.22 apply (zenon_or_s _ _ zenon_H1d7); [ zenon_intro zenon_H176 | zenon_intro zenon_H11d ]. % 19.02/19.22 exact (zenon_H173 zenon_H176). % 19.02/19.22 apply (zenon_L97_); trivial. % 19.02/19.22 (* end of lemma zenon_L1361_ *) % 19.02/19.22 assert (zenon_L1362_ : (((op (e3) (e1)) = (e0))\/(((op (e3) (e1)) = (e1))\/(((op (e3) (e1)) = (e2))\/((op (e3) (e1)) = (e3))))) -> ((op (e1) (e1)) = (e3)) -> ((op (e0) (e1)) = (e2)) -> ((op (e3) (e0)) = (e1)) -> (~((op (e3) (e0)) = (op (e3) (e1)))) -> (~((op (e3) (e1)) = (op (e3) (e3)))) -> ((op (e3) (e3)) = (e2)) -> (~((op (e3) (e1)) = (e3))) -> False). % 19.02/19.22 do 0 intro. intros zenon_H22a zenon_H13f zenon_H10f zenon_Hac zenon_H1cf zenon_H130 zenon_Hf6 zenon_H282. % 19.02/19.22 apply (zenon_or_s _ _ zenon_H22a); [ zenon_intro zenon_H1b1 | zenon_intro zenon_H22b ]. % 19.02/19.22 apply (zenon_L580_); trivial. % 19.02/19.22 apply (zenon_or_s _ _ zenon_H22b); [ zenon_intro zenon_Hae | zenon_intro zenon_H22c ]. % 19.02/19.22 apply (zenon_L242_); trivial. % 19.02/19.22 apply (zenon_or_s _ _ zenon_H22c); [ zenon_intro zenon_H14d | zenon_intro zenon_H161 ]. % 19.02/19.22 apply (zenon_L102_); trivial. % 19.02/19.22 exact (zenon_H282 zenon_H161). % 19.02/19.22 (* end of lemma zenon_L1362_ *) % 19.02/19.22 assert (zenon_L1363_ : (((op (e0) (e0)) = (e1))\/(((op (e1) (e0)) = (e1))\/(((op (e2) (e0)) = (e1))\/((op (e3) (e0)) = (e1))))) -> (~((op (e0) (e0)) = (op (e0) (e2)))) -> (~((op (e1) (e0)) = (op (e1) (e3)))) -> ((op (e1) (e3)) = (e1)) -> (~((op (e2) (e3)) = (op (e3) (e3)))) -> (~((op (e2) (e2)) = (e2))) -> (~((op (e0) (e1)) = (op (e2) (e1)))) -> (~((e1) = (e2))) -> (((op (e2) (e0)) = (e2))\/(((op (e2) (e1)) = (e2))\/(((op (e2) (e2)) = (e2))\/((op (e2) (e3)) = (e2))))) -> (((op (e1) (e0)) = (e3))\/(((op (e1) (e1)) = (e3))\/(((op (e1) (e2)) = (e3))\/((op (e1) (e3)) = (e3))))) -> (~((op (e1) (e0)) = (e3))) -> (~((op (e0) (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 (e3) (e3)) = (e2)) -> (~((op (e3) (e1)) = (e3))) -> ((op (e0) (e2)) = (e1)) -> (~((op (e0) (e1)) = (op (e0) (e2)))) -> ((op (e0) (e3)) = (e0)) -> (~((op (e0) (e1)) = (op (e0) (e3)))) -> (((op (e0) (e1)) = (e0))\/(((op (e0) (e1)) = (e1))\/(((op (e0) (e1)) = (e2))\/((op (e0) (e1)) = (e3))))) -> (~((op (e1) (e2)) = (e3))) -> (~((op (e1) (e3)) = (e3))) -> False). % 19.02/19.22 do 0 intro. intros zenon_H235 zenon_H13c zenon_Hd8 zenon_Hd6 zenon_Hf3 zenon_H173 zenon_H17e zenon_H7c zenon_H1d5 zenon_H16f zenon_H9f zenon_H9c zenon_H22a zenon_H1cf zenon_H130 zenon_Hf6 zenon_H282 zenon_H122 zenon_H4a zenon_H1e zenon_H54 zenon_H212 zenon_H16d zenon_H12f. % 19.02/19.22 apply (zenon_or_s _ _ zenon_H235); [ zenon_intro zenon_H7a | zenon_intro zenon_H236 ]. % 19.02/19.22 apply (zenon_L92_); trivial. % 19.02/19.22 apply (zenon_or_s _ _ zenon_H236); [ zenon_intro zenon_H9d | zenon_intro zenon_H237 ]. % 19.02/19.22 apply (zenon_L360_); trivial. % 19.02/19.22 apply (zenon_or_s _ _ zenon_H237); [ zenon_intro zenon_Hed | zenon_intro zenon_Hac ]. % 19.02/19.22 apply (zenon_L1361_); trivial. % 19.02/19.22 apply (zenon_or_s _ _ zenon_H16f); [ zenon_intro zenon_H9e | zenon_intro zenon_H170 ]. % 19.02/19.22 exact (zenon_H9f zenon_H9e). % 19.02/19.22 apply (zenon_or_s _ _ zenon_H170); [ zenon_intro zenon_H13f | zenon_intro zenon_H171 ]. % 19.02/19.22 apply (zenon_or_s _ _ zenon_H212); [ zenon_intro zenon_H49 | zenon_intro zenon_H213 ]. % 19.02/19.22 apply (zenon_L12_); trivial. % 19.02/19.22 apply (zenon_or_s _ _ zenon_H213); [ zenon_intro zenon_Ha0 | zenon_intro zenon_H214 ]. % 19.02/19.22 apply (zenon_L406_); trivial. % 19.02/19.22 apply (zenon_or_s _ _ zenon_H214); [ zenon_intro zenon_H10f | zenon_intro zenon_H99 ]. % 19.02/19.22 apply (zenon_L1362_); trivial. % 19.02/19.22 exact (zenon_H9c zenon_H99). % 19.02/19.22 apply (zenon_or_s _ _ zenon_H171); [ zenon_intro zenon_H16c | zenon_intro zenon_Hdc ]. % 19.02/19.22 exact (zenon_H16d zenon_H16c). % 19.02/19.22 exact (zenon_H12f zenon_Hdc). % 19.02/19.22 (* end of lemma zenon_L1363_ *) % 19.02/19.22 assert (zenon_L1364_ : (((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 (e0) (e2)) = (e2)) -> (~((op (e0) (e2)) = (op (e1) (e2)))) -> (~((op (e1) (e2)) = (e3))) -> False). % 19.02/19.22 do 0 intro. intros zenon_H19d zenon_H27 zenon_H24a zenon_H124 zenon_Hd6 zenon_H150 zenon_H195 zenon_H16d. % 19.02/19.22 apply (zenon_or_s _ _ zenon_H19d); [ zenon_intro zenon_H2a | zenon_intro zenon_H19e ]. % 19.02/19.22 apply (zenon_L644_); trivial. % 19.02/19.22 apply (zenon_or_s _ _ zenon_H19e); [ zenon_intro zenon_Hf0 | zenon_intro zenon_H19f ]. % 19.02/19.22 apply (zenon_L78_); trivial. % 19.02/19.22 apply (zenon_or_s _ _ zenon_H19f); [ zenon_intro zenon_H113 | zenon_intro zenon_H16c ]. % 19.02/19.22 apply (zenon_L153_); trivial. % 19.02/19.22 exact (zenon_H16d zenon_H16c). % 19.02/19.22 (* end of lemma zenon_L1364_ *) % 19.02/19.22 assert (zenon_L1365_ : (((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 (e0) (e1)) = (e1)) -> (~((op (e0) (e1)) = (op (e3) (e1)))) -> (~((op (e3) (e1)) = (op (e3) (e3)))) -> ((op (e3) (e3)) = (e2)) -> (~((op (e3) (e1)) = (e3))) -> False). % 19.02/19.22 do 0 intro. intros zenon_H22a zenon_H44 zenon_H1cf zenon_Ha0 zenon_H210 zenon_H130 zenon_Hf6 zenon_H282. % 19.02/19.22 apply (zenon_or_s _ _ zenon_H22a); [ zenon_intro zenon_H1b1 | zenon_intro zenon_H22b ]. % 19.02/19.22 apply (zenon_L346_); trivial. % 19.02/19.22 apply (zenon_or_s _ _ zenon_H22b); [ zenon_intro zenon_Hae | zenon_intro zenon_H22c ]. % 19.02/19.22 apply (zenon_L363_); trivial. % 19.02/19.22 apply (zenon_or_s _ _ zenon_H22c); [ zenon_intro zenon_H14d | zenon_intro zenon_H161 ]. % 19.02/19.22 apply (zenon_L102_); trivial. % 19.02/19.22 exact (zenon_H282 zenon_H161). % 19.02/19.22 (* end of lemma zenon_L1365_ *) % 19.02/19.22 assert (zenon_L1366_ : (((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) (e3)))) -> (~((op (e0) (e1)) = (op (e3) (e1)))) -> ((op (e0) (e1)) = (e1)) -> (~((op (e3) (e0)) = (op (e3) (e1)))) -> (((op (e3) (e1)) = (e0))\/(((op (e3) (e1)) = (e1))\/(((op (e3) (e1)) = (e2))\/((op (e3) (e1)) = (e3))))) -> ((op (e0) (e0)) = (e3)) -> ((op (e1) (e0)) = (e2)) -> (~((op (e3) (e0)) = (op (e3) (e3)))) -> ((op (e3) (e3)) = (e2)) -> (~((op (e3) (e0)) = (e3))) -> False). % 19.02/19.22 do 0 intro. intros zenon_H267 zenon_H282 zenon_H130 zenon_H210 zenon_Ha0 zenon_H1cf zenon_H22a zenon_H3a zenon_H86 zenon_H71 zenon_Hf6 zenon_H15f. % 19.02/19.22 apply (zenon_or_s _ _ zenon_H267); [ zenon_intro zenon_H44 | zenon_intro zenon_H268 ]. % 19.02/19.22 apply (zenon_L1365_); trivial. % 19.02/19.22 apply (zenon_or_s _ _ zenon_H268); [ zenon_intro zenon_Hac | zenon_intro zenon_H269 ]. % 19.02/19.22 apply (zenon_L241_); trivial. % 19.02/19.22 apply (zenon_or_s _ _ zenon_H269); [ zenon_intro zenon_H148 | zenon_intro zenon_H15e ]. % 19.02/19.22 apply (zenon_L114_); trivial. % 19.02/19.22 exact (zenon_H15f zenon_H15e). % 19.02/19.22 (* end of lemma zenon_L1366_ *) % 19.02/19.22 assert (zenon_L1367_ : (((op (e2) (e2)) = (e0))\/(((op (e2) (e2)) = (e1))\/(((op (e2) (e2)) = (e2))\/((op (e2) (e2)) = (e3))))) -> ((op (e2) (e0)) = (e0)) -> (~((op (e2) (e0)) = (op (e2) (e2)))) -> ((op (e0) (e2)) = (e1)) -> (~((op (e0) (e2)) = (op (e2) (e2)))) -> (~((op (e2) (e2)) = (e2))) -> (~((op (e2) (e2)) = (e3))) -> False). % 19.02/19.22 do 0 intro. intros zenon_H1c4 zenon_H34 zenon_H52 zenon_H122 zenon_Ha8 zenon_H173 zenon_H1b3. % 19.02/19.22 apply (zenon_or_s _ _ zenon_H1c4); [ zenon_intro zenon_H2c | zenon_intro zenon_H1c5 ]. % 19.02/19.22 apply (zenon_L11_); trivial. % 19.02/19.22 apply (zenon_or_s _ _ zenon_H1c5); [ zenon_intro zenon_Hf1 | zenon_intro zenon_H1c6 ]. % 19.02/19.22 apply (zenon_L246_); trivial. % 19.02/19.22 apply (zenon_or_s _ _ zenon_H1c6); [ zenon_intro zenon_H176 | zenon_intro zenon_Haa ]. % 19.02/19.22 exact (zenon_H173 zenon_H176). % 19.02/19.22 exact (zenon_H1b3 zenon_Haa). % 19.02/19.22 (* end of lemma zenon_L1367_ *) % 19.02/19.22 assert (zenon_L1368_ : (((op (e0) (e0)) = (e0))\/(((op (e1) (e0)) = (e0))\/(((op (e2) (e0)) = (e0))\/((op (e3) (e0)) = (e0))))) -> (~((op (e0) (e0)) = (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)) = (op (e1) (e3)))) -> (~((op (e0) (e2)) = (op (e1) (e2)))) -> (~((op (e1) (e2)) = (e3))) -> (((op (e1) (e0)) = (e3))\/(((op (e1) (e1)) = (e3))\/(((op (e1) (e2)) = (e3))\/((op (e1) (e3)) = (e3))))) -> (~((op (e1) (e3)) = (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) (e2)) = (e0))\/(((op (e2) (e2)) = (e1))\/(((op (e2) (e2)) = (e2))\/((op (e2) (e2)) = (e3))))) -> (~((op (e2) (e0)) = (op (e2) (e2)))) -> (~((op (e0) (e2)) = (op (e2) (e2)))) -> (~((op (e2) (e2)) = (e3))) -> (~((op (e1) (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)) = (e3))) -> (~((op (e1) (e0)) = (op (e2) (e0)))) -> (((op (e1) (e0)) = (e0))\/(((op (e1) (e0)) = (e1))\/(((op (e1) (e0)) = (e2))\/((op (e1) (e0)) = (e3))))) -> (((op (e0) (e0)) = (e1))\/(((op (e0) (e1)) = (e1))\/(((op (e0) (e2)) = (e1))\/((op (e0) (e3)) = (e1))))) -> (~((op (e0) (e3)) = (e3))) -> (~((op (e0) (e2)) = (e3))) -> (~((e1) = (e3))) -> (((op (e0) (e0)) = (e3))\/(((op (e0) (e1)) = (e3))\/(((op (e0) (e2)) = (e3))\/((op (e0) (e3)) = (e3))))) -> (~((op (e3) (e1)) = (e3))) -> (~((op (e3) (e1)) = (op (e3) (e3)))) -> (~((op (e0) (e1)) = (op (e3) (e1)))) -> (~((op (e3) (e0)) = (op (e3) (e1)))) -> (((op (e3) (e1)) = (e0))\/(((op (e3) (e1)) = (e1))\/(((op (e3) (e1)) = (e2))\/((op (e3) (e1)) = (e3))))) -> (((op (e2) (e0)) = (e2))\/(((op (e2) (e1)) = (e2))\/(((op (e2) (e2)) = (e2))\/((op (e2) (e3)) = (e2))))) -> (~((e1) = (e2))) -> (~((op (e0) (e1)) = (e3))) -> (~((op (e0) (e1)) = (op (e2) (e1)))) -> (~((op (e0) (e1)) = (op (e0) (e2)))) -> (~((op (e0) (e1)) = (op (e0) (e3)))) -> (((op (e0) (e1)) = (e0))\/(((op (e0) (e1)) = (e1))\/(((op (e0) (e1)) = (e2))\/((op (e0) (e1)) = (e3))))) -> (~((op (e2) (e2)) = (e2))) -> (~((op (e2) (e3)) = (op (e3) (e3)))) -> ((op (e3) (e3)) = (e2)) -> ((op (e1) (e3)) = (e1)) -> (~((op (e1) (e0)) = (op (e1) (e3)))) -> (~((op (e0) (e0)) = (op (e0) (e2)))) -> (((op (e0) (e0)) = (e1))\/(((op (e1) (e0)) = (e1))\/(((op (e2) (e0)) = (e1))\/((op (e3) (e0)) = (e1))))) -> ((op (e0) (e3)) = (e0)) -> (~((e0) = (e1))) -> False). % 19.02/19.22 do 0 intro. intros zenon_H3e zenon_H3f zenon_H19d zenon_H24a zenon_H124 zenon_H195 zenon_H16d zenon_H16f zenon_H12f zenon_H208 zenon_H1ba zenon_H1c4 zenon_H52 zenon_Ha8 zenon_H1b3 zenon_H9f zenon_H267 zenon_H71 zenon_H15f zenon_H201 zenon_H25e zenon_H22d zenon_H12d zenon_H123 zenon_H95 zenon_H168 zenon_H282 zenon_H130 zenon_H210 zenon_H1cf zenon_H22a zenon_H1d5 zenon_H7c zenon_H9c zenon_H17e zenon_H4a zenon_H54 zenon_H212 zenon_H173 zenon_Hf3 zenon_Hf6 zenon_Hd6 zenon_Hd8 zenon_H13c zenon_H235 zenon_H1e zenon_Ha1. % 19.02/19.22 apply (zenon_or_s _ _ zenon_H3e); [ zenon_intro zenon_H42 | zenon_intro zenon_H41 ]. % 19.02/19.22 exact (zenon_H3f zenon_H42). % 19.02/19.22 apply (zenon_or_s _ _ zenon_H41); [ zenon_intro zenon_H27 | zenon_intro zenon_H43 ]. % 19.02/19.22 apply (zenon_or_s _ _ zenon_H1ba); [ zenon_intro zenon_H48 | zenon_intro zenon_H1bb ]. % 19.02/19.22 apply (zenon_L336_); trivial. % 19.02/19.22 apply (zenon_or_s _ _ zenon_H1bb); [ zenon_intro zenon_H122 | zenon_intro zenon_H1bc ]. % 19.02/19.22 apply (zenon_L1363_); trivial. % 19.02/19.22 apply (zenon_or_s _ _ zenon_H1bc); [ zenon_intro zenon_H150 | zenon_intro zenon_Ha9 ]. % 19.02/19.22 apply (zenon_L1364_); trivial. % 19.02/19.22 exact (zenon_H123 zenon_Ha9). % 19.02/19.22 apply (zenon_or_s _ _ zenon_H43); [ zenon_intro zenon_H34 | zenon_intro zenon_H44 ]. % 19.02/19.22 apply (zenon_or_s _ _ zenon_H22d); [ zenon_intro zenon_H7a | zenon_intro zenon_H22e ]. % 19.02/19.22 apply (zenon_L1350_); trivial. % 19.02/19.22 apply (zenon_or_s _ _ zenon_H22e); [ zenon_intro zenon_Ha0 | zenon_intro zenon_H22f ]. % 19.02/19.22 apply (zenon_or_s _ _ zenon_H168); [ zenon_intro zenon_H3a | zenon_intro zenon_H169 ]. % 19.02/19.22 apply (zenon_or_s _ _ zenon_H25e); [ zenon_intro zenon_H27 | zenon_intro zenon_H25f ]. % 19.02/19.22 apply (zenon_L332_); trivial. % 19.02/19.22 apply (zenon_or_s _ _ zenon_H25f); [ zenon_intro zenon_H9d | zenon_intro zenon_H260 ]. % 19.02/19.22 apply (zenon_L360_); trivial. % 19.02/19.22 apply (zenon_or_s _ _ zenon_H260); [ zenon_intro zenon_H86 | zenon_intro zenon_H9e ]. % 19.02/19.22 apply (zenon_L1366_); trivial. % 19.02/19.22 exact (zenon_H9f zenon_H9e). % 19.02/19.22 apply (zenon_or_s _ _ zenon_H169); [ zenon_intro zenon_H99 | zenon_intro zenon_H16a ]. % 19.02/19.22 exact (zenon_H9c zenon_H99). % 19.02/19.22 apply (zenon_or_s _ _ zenon_H16a); [ zenon_intro zenon_Ha9 | zenon_intro zenon_He3 ]. % 19.02/19.22 exact (zenon_H123 zenon_Ha9). % 19.02/19.22 exact (zenon_H12d zenon_He3). % 19.02/19.22 apply (zenon_or_s _ _ zenon_H22f); [ zenon_intro zenon_H122 | zenon_intro zenon_Hc3 ]. % 19.02/19.22 apply (zenon_L1367_); trivial. % 19.02/19.22 apply (zenon_L427_); trivial. % 19.02/19.22 apply (zenon_or_s _ _ zenon_H22d); [ zenon_intro zenon_H7a | zenon_intro zenon_H22e ]. % 19.02/19.22 apply (zenon_L1350_); trivial. % 19.02/19.22 apply (zenon_or_s _ _ zenon_H22e); [ zenon_intro zenon_Ha0 | zenon_intro zenon_H22f ]. % 19.02/19.22 apply (zenon_L1365_); trivial. % 19.02/19.22 apply (zenon_or_s _ _ zenon_H22f); [ zenon_intro zenon_H122 | zenon_intro zenon_Hc3 ]. % 19.02/19.22 apply (zenon_or_s _ _ zenon_H235); [ zenon_intro zenon_H7a | zenon_intro zenon_H236 ]. % 19.02/19.22 apply (zenon_L92_); trivial. % 19.02/19.22 apply (zenon_or_s _ _ zenon_H236); [ zenon_intro zenon_H9d | zenon_intro zenon_H237 ]. % 19.02/19.22 apply (zenon_L360_); trivial. % 19.02/19.22 apply (zenon_or_s _ _ zenon_H237); [ zenon_intro zenon_Hed | zenon_intro zenon_Hac ]. % 19.02/19.22 apply (zenon_L1361_); trivial. % 19.02/19.22 apply (zenon_L41_); trivial. % 19.02/19.22 apply (zenon_L427_); trivial. % 19.02/19.22 (* end of lemma zenon_L1368_ *) % 19.02/19.22 assert (zenon_L1369_ : ((~((op (e3) (e1)) = (e3)))\/((op (e3) (e3)) = (e1))) -> ((op (e1) (e3)) = (e1)) -> (~((op (e1) (e3)) = (op (e3) (e3)))) -> (((op (e3) (e0)) = (e3))\/(((op (e3) (e1)) = (e3))\/(((op (e3) (e2)) = (e3))\/((op (e3) (e3)) = (e3))))) -> (~((op (e3) (e3)) = (e3))) -> (~((op (e3) (e0)) = (e3))) -> (~((op (e2) (e3)) = (op (e3) (e3)))) -> ((op (e2) (e3)) = (e2)) -> ((~((op (e3) (e2)) = (e3)))\/((op (e3) (e3)) = (e2))) -> False). % 19.02/19.22 do 0 intro. intros zenon_H285 zenon_Hd6 zenon_Hd5 zenon_H165 zenon_H102 zenon_H15f zenon_Hf3 zenon_H11d zenon_H284. % 19.13/19.22 apply (zenon_or_s _ _ zenon_H285); [ zenon_intro zenon_H282 | zenon_intro zenon_Hc4 ]. % 19.13/19.22 apply (zenon_L1347_); trivial. % 19.13/19.22 apply (zenon_L50_); trivial. % 19.13/19.22 (* end of lemma zenon_L1369_ *) % 19.13/19.22 assert (zenon_L1370_ : ((~((op (e3) (e0)) = (e3)))\/((op (e3) (e3)) = (e0))) -> ((op (e0) (e3)) = (e0)) -> (~((op (e0) (e3)) = (op (e3) (e3)))) -> ((~((op (e3) (e2)) = (e3)))\/((op (e3) (e3)) = (e2))) -> ((op (e2) (e3)) = (e2)) -> (~((op (e2) (e3)) = (op (e3) (e3)))) -> (~((op (e3) (e3)) = (e3))) -> (((op (e3) (e0)) = (e3))\/(((op (e3) (e1)) = (e3))\/(((op (e3) (e2)) = (e3))\/((op (e3) (e3)) = (e3))))) -> (~((op (e1) (e3)) = (op (e3) (e3)))) -> ((op (e1) (e3)) = (e1)) -> ((~((op (e3) (e1)) = (e3)))\/((op (e3) (e3)) = (e1))) -> False). % 19.13/19.22 do 0 intro. intros zenon_H286 zenon_H1e zenon_Hc2 zenon_H284 zenon_H11d zenon_Hf3 zenon_H102 zenon_H165 zenon_Hd5 zenon_Hd6 zenon_H285. % 19.13/19.22 apply (zenon_or_s _ _ zenon_H286); [ zenon_intro zenon_H15f | zenon_intro zenon_H60 ]. % 19.13/19.22 apply (zenon_L1369_); trivial. % 19.13/19.22 apply (zenon_L440_); trivial. % 19.13/19.22 (* end of lemma zenon_L1370_ *) % 19.13/19.22 assert (zenon_L1371_ : ((~((op (e1) (e2)) = (e3)))\/((op (e1) (e3)) = (e2))) -> ((~((op (e2) (e2)) = (e3)))\/((op (e2) (e3)) = (e2))) -> ((~((op (e3) (e1)) = (e3)))\/((op (e3) (e3)) = (e1))) -> (~((op (e1) (e3)) = (op (e3) (e3)))) -> (((op (e3) (e0)) = (e3))\/(((op (e3) (e1)) = (e3))\/(((op (e3) (e2)) = (e3))\/((op (e3) (e3)) = (e3))))) -> (~((op (e3) (e3)) = (e3))) -> (((op (e0) (e0)) = (e0))\/(((op (e1) (e0)) = (e0))\/(((op (e2) (e0)) = (e0))\/((op (e3) (e0)) = (e0))))) -> (((op (e0) (e0)) = (e3))\/(((op (e0) (e1)) = (e3))\/(((op (e0) (e2)) = (e3))\/((op (e0) (e3)) = (e3))))) -> (~((op (e0) (e3)) = (e3))) -> (~((e1) = (e3))) -> (~((op (e1) (e0)) = (op (e2) (e0)))) -> (((op (e3) (e0)) = (e0))\/(((op (e3) (e0)) = (e1))\/(((op (e3) (e0)) = (e2))\/((op (e3) (e0)) = (e3))))) -> (~((op (e3) (e0)) = (op (e3) (e3)))) -> (~((op (e0) (e1)) = (op (e3) (e1)))) -> (((op (e1) (e0)) = (e0))\/(((op (e1) (e0)) = (e1))\/(((op (e1) (e0)) = (e2))\/((op (e1) (e0)) = (e3))))) -> (((op (e2) (e2)) = (e0))\/(((op (e2) (e2)) = (e1))\/(((op (e2) (e2)) = (e2))\/((op (e2) (e2)) = (e3))))) -> (~((op (e0) (e2)) = (op (e2) (e2)))) -> (~((op (e2) (e0)) = (op (e2) (e2)))) -> (~((e0) = (e1))) -> (((op (e0) (e0)) = (e1))\/(((op (e0) (e1)) = (e1))\/(((op (e0) (e2)) = (e1))\/((op (e0) (e3)) = (e1))))) -> (~((op (e0) (e2)) = (op (e0) (e3)))) -> ((op (e0) (e3)) = (e0)) -> (((op (e0) (e0)) = (e1))\/(((op (e1) (e0)) = (e1))\/(((op (e2) (e0)) = (e1))\/((op (e3) (e0)) = (e1))))) -> (~((op (e1) (e0)) = (e3))) -> (~((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 (e1) (e0)) = (e3))\/(((op (e1) (e1)) = (e3))\/(((op (e1) (e2)) = (e3))\/((op (e1) (e3)) = (e3))))) -> (~((e1) = (e2))) -> (((op (e0) (e1)) = (e0))\/(((op (e0) (e1)) = (e1))\/(((op (e0) (e1)) = (e2))\/((op (e0) (e1)) = (e3))))) -> (~((op (e0) (e1)) = (e3))) -> (~((op (e0) (e1)) = (op (e2) (e1)))) -> (~((op (e0) (e1)) = (op (e0) (e2)))) -> (~((op (e0) (e1)) = (op (e0) (e3)))) -> (~((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) (e3)) = (e1)) -> (~((op (e1) (e0)) = (op (e1) (e3)))) -> (~((op (e0) (e0)) = (op (e0) (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 (e1) (e3)))) -> (~((op (e1) (e0)) = (op (e1) (e2)))) -> (~((op (e0) (e2)) = (e3))) -> (((op (e0) (e2)) = (e0))\/(((op (e0) (e2)) = (e1))\/(((op (e0) (e2)) = (e2))\/((op (e0) (e2)) = (e3))))) -> (~((op (e0) (e0)) = (e0))) -> ((~((op (e3) (e2)) = (e3)))\/((op (e3) (e3)) = (e2))) -> (~((op (e0) (e3)) = (op (e3) (e3)))) -> ((~((op (e3) (e0)) = (e3)))\/((op (e3) (e3)) = (e0))) -> ((~((op (e1) (e3)) = (e3)))\/((op (e1) (e3)) = (e3))) -> False). % 19.13/19.22 do 0 intro. intros zenon_H287 zenon_H288 zenon_H285 zenon_Hd5 zenon_H165 zenon_H102 zenon_H3e zenon_H168 zenon_H12d zenon_H95 zenon_H201 zenon_H267 zenon_H71 zenon_H210 zenon_H25e zenon_H1c4 zenon_Ha8 zenon_H52 zenon_Ha1 zenon_H22d zenon_H208 zenon_H1e zenon_H235 zenon_H9f zenon_H1cf zenon_H130 zenon_H22a zenon_H16f zenon_H7c zenon_H212 zenon_H9c zenon_H17e zenon_H4a zenon_H54 zenon_H173 zenon_Hf3 zenon_H1d5 zenon_Hd6 zenon_Hd8 zenon_H13c zenon_H19d zenon_H195 zenon_H124 zenon_H24a zenon_H123 zenon_H1ba zenon_H3f zenon_H284 zenon_Hc2 zenon_H286 zenon_H289. % 19.13/19.22 apply (zenon_or_s _ _ zenon_H287); [ zenon_intro zenon_H16d | zenon_intro zenon_Hd7 ]. % 19.13/19.22 apply (zenon_or_s _ _ zenon_H289); [ zenon_intro zenon_H12f | zenon_intro zenon_Hdc ]. % 19.13/19.22 apply (zenon_or_s _ _ zenon_H288); [ zenon_intro zenon_H1b3 | zenon_intro zenon_H11d ]. % 19.13/19.22 apply (zenon_or_s _ _ zenon_H286); [ zenon_intro zenon_H15f | zenon_intro zenon_H60 ]. % 19.13/19.22 apply (zenon_or_s _ _ zenon_H285); [ zenon_intro zenon_H282 | zenon_intro zenon_Hc4 ]. % 19.13/19.22 apply (zenon_or_s _ _ zenon_H284); [ zenon_intro zenon_H283 | zenon_intro zenon_Hf6 ]. % 19.13/19.22 apply (zenon_L1346_); trivial. % 19.13/19.22 apply (zenon_L1368_); trivial. % 19.13/19.22 apply (zenon_L50_); trivial. % 19.13/19.22 apply (zenon_L440_); trivial. % 19.13/19.22 apply (zenon_L1370_); trivial. % 19.13/19.22 apply (zenon_L83_); trivial. % 19.13/19.22 apply (zenon_L101_); trivial. % 19.13/19.22 (* end of lemma zenon_L1371_ *) % 19.13/19.22 assert (zenon_L1372_ : (((op (e1) (e0)) = (e1))\/(((op (e1) (e1)) = (e1))\/(((op (e1) (e2)) = (e1))\/((op (e1) (e3)) = (e1))))) -> (~((op (e0) (e2)) = (op (e3) (e2)))) -> (~((op (e1) (e1)) = (e3))) -> (~((op (e0) (e1)) = (op (e1) (e1)))) -> (~((op (e1) (e1)) = (e1))) -> (~((op (e1) (e0)) = (op (e1) (e1)))) -> ((op (e1) (e0)) = (e0)) -> (((op (e1) (e1)) = (e0))\/(((op (e1) (e1)) = (e1))\/(((op (e1) (e1)) = (e2))\/((op (e1) (e1)) = (e3))))) -> (((op (e3) (e0)) = (e0))\/(((op (e3) (e1)) = (e0))\/(((op (e3) (e2)) = (e0))\/((op (e3) (e3)) = (e0))))) -> (~((op (e3) (e2)) = (e3))) -> (~((op (e3) (e2)) = (op (e3) (e3)))) -> (~((op (e3) (e1)) = (op (e3) (e2)))) -> (((op (e3) (e2)) = (e0))\/(((op (e3) (e2)) = (e1))\/(((op (e3) (e2)) = (e2))\/((op (e3) (e2)) = (e3))))) -> ((op (e2) (e3)) = (e2)) -> (~((op (e3) (e0)) = (op (e3) (e2)))) -> ((op (e3) (e3)) = (e1)) -> (~((op (e3) (e0)) = (e3))) -> ((op (e2) (e0)) = (e1)) -> ((op (e0) (e0)) = (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 (e1) (e2)) = (e3)))\/((op (e1) (e3)) = (e2))) -> ((~((op (e2) (e2)) = (e3)))\/((op (e2) (e3)) = (e2))) -> ((~((op (e3) (e1)) = (e3)))\/((op (e3) (e3)) = (e1))) -> (~((op (e1) (e3)) = (op (e3) (e3)))) -> (((op (e3) (e0)) = (e3))\/(((op (e3) (e1)) = (e3))\/(((op (e3) (e2)) = (e3))\/((op (e3) (e3)) = (e3))))) -> (~((op (e3) (e3)) = (e3))) -> (((op (e0) (e0)) = (e0))\/(((op (e1) (e0)) = (e0))\/(((op (e2) (e0)) = (e0))\/((op (e3) (e0)) = (e0))))) -> (((op (e0) (e0)) = (e3))\/(((op (e0) (e1)) = (e3))\/(((op (e0) (e2)) = (e3))\/((op (e0) (e3)) = (e3))))) -> (~((op (e0) (e3)) = (e3))) -> (~((e1) = (e3))) -> (~((op (e1) (e0)) = (op (e2) (e0)))) -> (((op (e3) (e0)) = (e0))\/(((op (e3) (e0)) = (e1))\/(((op (e3) (e0)) = (e2))\/((op (e3) (e0)) = (e3))))) -> (~((op (e3) (e0)) = (op (e3) (e3)))) -> (~((op (e0) (e1)) = (op (e3) (e1)))) -> (((op (e1) (e0)) = (e0))\/(((op (e1) (e0)) = (e1))\/(((op (e1) (e0)) = (e2))\/((op (e1) (e0)) = (e3))))) -> (((op (e2) (e2)) = (e0))\/(((op (e2) (e2)) = (e1))\/(((op (e2) (e2)) = (e2))\/((op (e2) (e2)) = (e3))))) -> (~((op (e0) (e2)) = (op (e2) (e2)))) -> (~((op (e2) (e0)) = (op (e2) (e2)))) -> (~((e0) = (e1))) -> (((op (e0) (e0)) = (e1))\/(((op (e0) (e1)) = (e1))\/(((op (e0) (e2)) = (e1))\/((op (e0) (e3)) = (e1))))) -> (~((op (e0) (e2)) = (op (e0) (e3)))) -> ((op (e0) (e3)) = (e0)) -> (((op (e0) (e0)) = (e1))\/(((op (e1) (e0)) = (e1))\/(((op (e2) (e0)) = (e1))\/((op (e3) (e0)) = (e1))))) -> (~((op (e1) (e0)) = (e3))) -> (~((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 (e1) (e0)) = (e3))\/(((op (e1) (e1)) = (e3))\/(((op (e1) (e2)) = (e3))\/((op (e1) (e3)) = (e3))))) -> (~((e1) = (e2))) -> (((op (e0) (e1)) = (e0))\/(((op (e0) (e1)) = (e1))\/(((op (e0) (e1)) = (e2))\/((op (e0) (e1)) = (e3))))) -> (~((op (e0) (e1)) = (e3))) -> (~((op (e0) (e1)) = (op (e2) (e1)))) -> (~((op (e0) (e1)) = (op (e0) (e2)))) -> (~((op (e0) (e1)) = (op (e0) (e3)))) -> (~((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) (e0)) = (op (e1) (e3)))) -> (~((op (e0) (e0)) = (op (e0) (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 (e1) (e3)))) -> (~((op (e1) (e0)) = (op (e1) (e2)))) -> (~((op (e0) (e2)) = (e3))) -> (((op (e0) (e2)) = (e0))\/(((op (e0) (e2)) = (e1))\/(((op (e0) (e2)) = (e2))\/((op (e0) (e2)) = (e3))))) -> (~((op (e0) (e0)) = (e0))) -> ((~((op (e3) (e2)) = (e3)))\/((op (e3) (e3)) = (e2))) -> (~((op (e0) (e3)) = (op (e3) (e3)))) -> ((~((op (e3) (e0)) = (e3)))\/((op (e3) (e3)) = (e0))) -> ((~((op (e1) (e3)) = (e3)))\/((op (e1) (e3)) = (e3))) -> False). % 19.13/19.22 do 0 intro. intros zenon_H128 zenon_H14f zenon_H1a1 zenon_H10e zenon_H10a zenon_H45 zenon_H27 zenon_H142 zenon_H1ac zenon_H283 zenon_H62 zenon_H1a4 zenon_H191 zenon_H11d zenon_H6f zenon_Hc4 zenon_H15f zenon_Hed zenon_H3a zenon_H153 zenon_H172 zenon_H287 zenon_H288 zenon_H285 zenon_Hd5 zenon_H165 zenon_H102 zenon_H3e zenon_H168 zenon_H12d zenon_H95 zenon_H201 zenon_H267 zenon_H71 zenon_H210 zenon_H25e zenon_H1c4 zenon_Ha8 zenon_H52 zenon_Ha1 zenon_H22d zenon_H208 zenon_H1e zenon_H235 zenon_H9f zenon_H1cf zenon_H130 zenon_H22a zenon_H16f zenon_H7c zenon_H212 zenon_H9c zenon_H17e zenon_H4a zenon_H54 zenon_H173 zenon_Hf3 zenon_H1d5 zenon_Hd8 zenon_H13c zenon_H19d zenon_H195 zenon_H124 zenon_H24a zenon_H123 zenon_H1ba zenon_H3f zenon_H284 zenon_Hc2 zenon_H286 zenon_H289. % 19.13/19.22 apply (zenon_or_s _ _ zenon_H128); [ zenon_intro zenon_H9d | zenon_intro zenon_H129 ]. % 19.13/19.22 apply (zenon_L413_); trivial. % 19.13/19.22 apply (zenon_or_s _ _ zenon_H129); [ zenon_intro zenon_H10d | zenon_intro zenon_H12a ]. % 19.13/19.22 exact (zenon_H10a zenon_H10d). % 19.13/19.22 apply (zenon_or_s _ _ zenon_H12a); [ zenon_intro zenon_Hf0 | zenon_intro zenon_Hd6 ]. % 19.13/19.22 apply (zenon_or_s _ _ zenon_H172); [ zenon_intro zenon_H150 | zenon_intro zenon_H174 ]. % 19.13/19.22 apply (zenon_L1356_); trivial. % 19.13/19.22 apply (zenon_or_s _ _ zenon_H174); [ zenon_intro zenon_H113 | zenon_intro zenon_H175 ]. % 19.13/19.22 apply (zenon_L1359_); trivial. % 19.13/19.22 apply (zenon_or_s _ _ zenon_H175); [ zenon_intro zenon_H176 | zenon_intro zenon_H151 ]. % 19.13/19.22 exact (zenon_H173 zenon_H176). % 19.13/19.22 apply (zenon_L1352_); trivial. % 19.13/19.22 apply (zenon_L1371_); trivial. % 19.13/19.22 (* end of lemma zenon_L1372_ *) % 19.13/19.22 assert (zenon_L1373_ : (((op (e2) (e0)) = (e0))\/(((op (e2) (e0)) = (e1))\/(((op (e2) (e0)) = (e2))\/((op (e2) (e0)) = (e3))))) -> (~((op (e2) (e0)) = (op (e3) (e0)))) -> ((op (e3) (e0)) = (e0)) -> (~((op (e1) (e0)) = (op (e2) (e0)))) -> ((op (e1) (e0)) = (e1)) -> (~((op (e2) (e0)) = (op (e2) (e3)))) -> ((op (e2) (e3)) = (e2)) -> (~((op (e2) (e0)) = (e3))) -> False). % 19.13/19.22 do 0 intro. intros zenon_H259 zenon_H17b zenon_H44 zenon_H201 zenon_H9d zenon_H5b zenon_H11d zenon_H27f. % 19.13/19.22 apply (zenon_or_s _ _ zenon_H259); [ zenon_intro zenon_H34 | zenon_intro zenon_H25a ]. % 19.13/19.22 apply (zenon_L127_); trivial. % 19.13/19.22 apply (zenon_or_s _ _ zenon_H25a); [ zenon_intro zenon_Hed | zenon_intro zenon_H25b ]. % 19.13/19.22 apply (zenon_L413_); trivial. % 19.13/19.22 apply (zenon_or_s _ _ zenon_H25b); [ zenon_intro zenon_Hee | zenon_intro zenon_H3b ]. % 19.13/19.22 apply (zenon_L73_); trivial. % 19.13/19.22 exact (zenon_H27f zenon_H3b). % 19.13/19.22 (* end of lemma zenon_L1373_ *) % 19.13/19.22 assert (zenon_L1374_ : (((op (e0) (e2)) = (e0))\/(((op (e0) (e2)) = (e1))\/(((op (e0) (e2)) = (e2))\/((op (e0) (e2)) = (e3))))) -> (~((op (e0) (e2)) = (op (e0) (e3)))) -> ((op (e0) (e3)) = (e0)) -> ((op (e2) (e2)) = (e1)) -> (~((op (e0) (e2)) = (op (e2) (e2)))) -> ((op (e1) (e2)) = (e2)) -> (~((op (e0) (e2)) = (op (e1) (e2)))) -> (~((op (e0) (e2)) = (e3))) -> False). % 19.13/19.22 do 0 intro. intros zenon_H1ba zenon_H208 zenon_H1e zenon_Hf1 zenon_Ha8 zenon_H113 zenon_H195 zenon_H123. % 19.13/19.22 apply (zenon_or_s _ _ zenon_H1ba); [ zenon_intro zenon_H48 | zenon_intro zenon_H1bb ]. % 19.13/19.22 apply (zenon_L336_); trivial. % 19.13/19.22 apply (zenon_or_s _ _ zenon_H1bb); [ zenon_intro zenon_H122 | zenon_intro zenon_H1bc ]. % 19.13/19.22 apply (zenon_L246_); trivial. % 19.13/19.22 apply (zenon_or_s _ _ zenon_H1bc); [ zenon_intro zenon_H150 | zenon_intro zenon_Ha9 ]. % 19.13/19.22 apply (zenon_L153_); trivial. % 19.13/19.22 exact (zenon_H123 zenon_Ha9). % 19.13/19.22 (* end of lemma zenon_L1374_ *) % 19.13/19.22 assert (zenon_L1375_ : (((op (e1) (e2)) = (e0))\/(((op (e1) (e2)) = (e1))\/(((op (e1) (e2)) = (e2))\/((op (e1) (e2)) = (e3))))) -> ((op (e2) (e2)) = (e0)) -> (~((op (e1) (e2)) = (op (e2) (e2)))) -> (~((op (e3) (e2)) = (e3))) -> (~((op (e0) (e2)) = (op (e3) (e2)))) -> ((op (e3) (e3)) = (e1)) -> (~((op (e3) (e2)) = (op (e3) (e3)))) -> (~((op (e3) (e1)) = (op (e3) (e2)))) -> ((op (e3) (e1)) = (e0)) -> (((op (e3) (e2)) = (e0))\/(((op (e3) (e2)) = (e1))\/(((op (e3) (e2)) = (e2))\/((op (e3) (e2)) = (e3))))) -> (~((op (e0) (e2)) = (e3))) -> (~((op (e0) (e2)) = (op (e1) (e2)))) -> (~((op (e0) (e2)) = (op (e2) (e2)))) -> ((op (e2) (e2)) = (e1)) -> ((op (e0) (e3)) = (e0)) -> (~((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)) = (e3))) -> False). % 19.13/19.22 do 0 intro. intros zenon_H19d zenon_H2c zenon_H2b zenon_H283 zenon_H14f zenon_Hc4 zenon_H62 zenon_H1a4 zenon_H1b1 zenon_H191 zenon_H123 zenon_H195 zenon_Ha8 zenon_Hf1 zenon_H1e zenon_H208 zenon_H1ba zenon_H16d. % 19.13/19.22 apply (zenon_or_s _ _ zenon_H19d); [ zenon_intro zenon_H2a | zenon_intro zenon_H19e ]. % 19.13/19.22 apply (zenon_L3_); trivial. % 19.13/19.22 apply (zenon_or_s _ _ zenon_H19e); [ zenon_intro zenon_Hf0 | zenon_intro zenon_H19f ]. % 19.13/19.22 apply (zenon_L1353_); trivial. % 19.13/19.22 apply (zenon_or_s _ _ zenon_H19f); [ zenon_intro zenon_H113 | zenon_intro zenon_H16c ]. % 19.13/19.22 apply (zenon_L1374_); trivial. % 19.13/19.22 exact (zenon_H16d zenon_H16c). % 19.13/19.22 (* end of lemma zenon_L1375_ *) % 19.13/19.22 assert (zenon_L1376_ : (((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)) = (e1)) -> (~((op (e0) (e1)) = (op (e2) (e1)))) -> (~((op (e2) (e1)) = (op (e2) (e3)))) -> ((op (e2) (e3)) = (e2)) -> (~((op (e2) (e1)) = (e3))) -> False). % 19.13/19.23 do 0 intro. intros zenon_H1cc zenon_H34 zenon_H1f0 zenon_Ha0 zenon_H17e zenon_H1c7 zenon_H11d zenon_Ha7. % 19.13/19.23 apply (zenon_or_s _ _ zenon_H1cc); [ zenon_intro zenon_H36 | zenon_intro zenon_H1cd ]. % 19.13/19.23 apply (zenon_L642_); trivial. % 19.13/19.23 apply (zenon_or_s _ _ zenon_H1cd); [ zenon_intro zenon_Ha5 | zenon_intro zenon_H1ce ]. % 19.13/19.23 apply (zenon_L357_); trivial. % 19.13/19.23 apply (zenon_or_s _ _ zenon_H1ce); [ zenon_intro zenon_H1ca | zenon_intro zenon_Ha6 ]. % 19.13/19.23 apply (zenon_L224_); trivial. % 19.13/19.23 exact (zenon_Ha7 zenon_Ha6). % 19.13/19.23 (* end of lemma zenon_L1376_ *) % 19.13/19.23 assert (zenon_L1377_ : (((op (e1) (e2)) = (e0))\/(((op (e1) (e2)) = (e1))\/(((op (e1) (e2)) = (e2))\/((op (e1) (e2)) = (e3))))) -> ((op (e3) (e2)) = (e0)) -> (~((op (e1) (e2)) = (op (e3) (e2)))) -> (~((op (e2) (e0)) = (e3))) -> ((op (e2) (e3)) = (e2)) -> (~((op (e2) (e0)) = (op (e2) (e3)))) -> (((op (e3) (e0)) = (e0))\/(((op (e3) (e1)) = (e0))\/(((op (e3) (e2)) = (e0))\/((op (e3) (e3)) = (e0))))) -> ((op (e0) (e2)) = (e2)) -> (~((op (e3) (e2)) = (e3))) -> (~((op (e3) (e2)) = (op (e3) (e3)))) -> (~((op (e3) (e1)) = (op (e3) (e2)))) -> (((op (e3) (e2)) = (e0))\/(((op (e3) (e2)) = (e1))\/(((op (e3) (e2)) = (e2))\/((op (e3) (e2)) = (e3))))) -> (~((op (e2) (e3)) = (op (e3) (e3)))) -> (~((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)) = (op (e3) (e2)))) -> (~((op (e3) (e0)) = (op (e3) (e3)))) -> ((op (e3) (e3)) = (e1)) -> (~((op (e3) (e0)) = (op (e3) (e1)))) -> (~((op (e3) (e0)) = (e3))) -> ((op (e0) (e0)) = (e3)) -> (((op (e3) (e0)) = (e2))\/(((op (e3) (e1)) = (e2))\/(((op (e3) (e2)) = (e2))\/((op (e3) (e3)) = (e2))))) -> (~((op (e0) (e3)) = (op (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 (e0) (e1)) = (e1)) -> (~((op (e0) (e1)) = (op (e2) (e1)))) -> (~((op (e2) (e1)) = (op (e2) (e3)))) -> (~((op (e2) (e1)) = (e3))) -> (((op (e2) (e0)) = (e0))\/(((op (e2) (e0)) = (e1))\/(((op (e2) (e0)) = (e2))\/((op (e2) (e0)) = (e3))))) -> (~((op (e0) (e2)) = (e3))) -> (~((op (e0) (e2)) = (op (e1) (e2)))) -> (~((op (e0) (e2)) = (op (e2) (e2)))) -> ((op (e2) (e2)) = (e1)) -> ((op (e0) (e3)) = (e0)) -> (~((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)) = (e3))) -> False). % 19.13/19.23 do 0 intro. intros zenon_H19d zenon_H61 zenon_H115 zenon_H27f zenon_H11d zenon_H5b zenon_H1ac zenon_H150 zenon_H283 zenon_H62 zenon_H1a4 zenon_H191 zenon_Hf3 zenon_H14f zenon_H267 zenon_H6f zenon_H71 zenon_Hc4 zenon_H1cf zenon_H15f zenon_H3a zenon_H153 zenon_Hc2 zenon_H1cc zenon_H1f0 zenon_Ha0 zenon_H17e zenon_H1c7 zenon_Ha7 zenon_H259 zenon_H123 zenon_H195 zenon_Ha8 zenon_Hf1 zenon_H1e zenon_H208 zenon_H1ba zenon_H16d. % 19.13/19.23 apply (zenon_or_s _ _ zenon_H19d); [ zenon_intro zenon_H2a | zenon_intro zenon_H19e ]. % 19.13/19.23 apply (zenon_L176_); trivial. % 19.13/19.23 apply (zenon_or_s _ _ zenon_H19e); [ zenon_intro zenon_Hf0 | zenon_intro zenon_H19f ]. % 19.13/19.23 apply (zenon_or_s _ _ zenon_H259); [ zenon_intro zenon_H34 | zenon_intro zenon_H25a ]. % 19.13/19.23 apply (zenon_L1376_); trivial. % 19.13/19.23 apply (zenon_or_s _ _ zenon_H25a); [ zenon_intro zenon_Hed | zenon_intro zenon_H25b ]. % 19.13/19.23 apply (zenon_L1356_); trivial. % 19.13/19.23 apply (zenon_or_s _ _ zenon_H25b); [ zenon_intro zenon_Hee | zenon_intro zenon_H3b ]. % 19.13/19.23 apply (zenon_L73_); trivial. % 19.13/19.23 exact (zenon_H27f zenon_H3b). % 19.13/19.23 apply (zenon_or_s _ _ zenon_H19f); [ zenon_intro zenon_H113 | zenon_intro zenon_H16c ]. % 19.13/19.23 apply (zenon_L1374_); trivial. % 19.13/19.23 exact (zenon_H16d zenon_H16c). % 19.13/19.23 (* end of lemma zenon_L1377_ *) % 19.13/19.23 assert (zenon_L1378_ : ((op (e1) (e0)) = (e1)) -> (~((op (e1) (e0)) = (op (e2) (e0)))) -> (~((op (e2) (e0)) = (op (e3) (e0)))) -> (~((op (e1) (e2)) = (op (e2) (e2)))) -> ((op (e2) (e2)) = (e0)) -> (~((op (e1) (e2)) = (e3))) -> (((op (e0) (e2)) = (e0))\/(((op (e0) (e2)) = (e1))\/(((op (e0) (e2)) = (e2))\/((op (e0) (e2)) = (e3))))) -> (~((op (e0) (e2)) = (op (e0) (e3)))) -> ((op (e2) (e2)) = (e1)) -> (~((op (e0) (e2)) = (op (e2) (e2)))) -> (~((op (e0) (e2)) = (op (e1) (e2)))) -> (~((op (e0) (e2)) = (e3))) -> (((op (e2) (e0)) = (e0))\/(((op (e2) (e0)) = (e1))\/(((op (e2) (e0)) = (e2))\/((op (e2) (e0)) = (e3))))) -> (~((op (e2) (e1)) = (e3))) -> (~((op (e2) (e1)) = (op (e2) (e3)))) -> (~((op (e0) (e1)) = (op (e2) (e1)))) -> ((op (e0) (e1)) = (e1)) -> (~((op (e2) (e0)) = (op (e2) (e1)))) -> (((op (e2) (e1)) = (e0))\/(((op (e2) (e1)) = (e1))\/(((op (e2) (e1)) = (e2))\/((op (e2) (e1)) = (e3))))) -> (((op (e3) (e0)) = (e2))\/(((op (e3) (e1)) = (e2))\/(((op (e3) (e2)) = (e2))\/((op (e3) (e3)) = (e2))))) -> ((op (e0) (e0)) = (e3)) -> (~((op (e3) (e0)) = (e3))) -> (~((op (e3) (e0)) = (op (e3) (e1)))) -> ((op (e3) (e3)) = (e1)) -> (~((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) (e2)) = (op (e3) (e2)))) -> (~((op (e2) (e3)) = (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) (e2)) = (op (e3) (e3)))) -> (~((op (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)) = (op (e2) (e3)))) -> ((op (e2) (e3)) = (e2)) -> (~((op (e2) (e0)) = (e3))) -> (~((op (e1) (e2)) = (op (e3) (e2)))) -> (((op (e1) (e2)) = (e0))\/(((op (e1) (e2)) = (e1))\/(((op (e1) (e2)) = (e2))\/((op (e1) (e2)) = (e3))))) -> (~((op (e0) (e3)) = (op (e3) (e3)))) -> ((op (e0) (e3)) = (e0)) -> False). % 19.13/19.23 do 0 intro. intros zenon_H9d zenon_H201 zenon_H17b zenon_H2b zenon_H2c zenon_H16d zenon_H1ba zenon_H208 zenon_Hf1 zenon_Ha8 zenon_H195 zenon_H123 zenon_H259 zenon_Ha7 zenon_H1c7 zenon_H17e zenon_Ha0 zenon_H1f0 zenon_H1cc zenon_H153 zenon_H3a zenon_H15f zenon_H1cf zenon_Hc4 zenon_H71 zenon_H6f zenon_H267 zenon_H14f zenon_Hf3 zenon_H191 zenon_H1a4 zenon_H62 zenon_H283 zenon_H150 zenon_H1ac zenon_H5b zenon_H11d zenon_H27f zenon_H115 zenon_H19d zenon_Hc2 zenon_H1e. % 19.13/19.23 apply (zenon_or_s _ _ zenon_H1ac); [ zenon_intro zenon_H44 | zenon_intro zenon_H1af ]. % 19.13/19.23 apply (zenon_L1373_); trivial. % 19.13/19.23 apply (zenon_or_s _ _ zenon_H1af); [ zenon_intro zenon_H1b1 | zenon_intro zenon_H1b0 ]. % 19.13/19.23 apply (zenon_L1375_); trivial. % 19.13/19.23 apply (zenon_or_s _ _ zenon_H1b0); [ zenon_intro zenon_H61 | zenon_intro zenon_H60 ]. % 19.13/19.23 apply (zenon_L1377_); trivial. % 19.13/19.23 apply (zenon_L440_); trivial. % 19.13/19.23 (* end of lemma zenon_L1378_ *) % 19.13/19.23 assert (zenon_L1379_ : (((op (e0) (e2)) = (e0))\/(((op (e0) (e2)) = (e1))\/(((op (e0) (e2)) = (e2))\/((op (e0) (e2)) = (e3))))) -> (~((op (e0) (e2)) = (op (e0) (e3)))) -> ((op (e0) (e3)) = (e0)) -> ((op (e2) (e2)) = (e1)) -> (~((op (e0) (e2)) = (op (e2) (e2)))) -> ((op (e3) (e2)) = (e2)) -> (~((op (e0) (e2)) = (op (e3) (e2)))) -> (~((op (e0) (e2)) = (e3))) -> False). % 19.13/19.23 do 0 intro. intros zenon_H1ba zenon_H208 zenon_H1e zenon_Hf1 zenon_Ha8 zenon_H151 zenon_H14f zenon_H123. % 19.13/19.23 apply (zenon_or_s _ _ zenon_H1ba); [ zenon_intro zenon_H48 | zenon_intro zenon_H1bb ]. % 19.13/19.23 apply (zenon_L336_); trivial. % 19.13/19.23 apply (zenon_or_s _ _ zenon_H1bb); [ zenon_intro zenon_H122 | zenon_intro zenon_H1bc ]. % 19.13/19.23 apply (zenon_L246_); trivial. % 19.13/19.23 apply (zenon_or_s _ _ zenon_H1bc); [ zenon_intro zenon_H150 | zenon_intro zenon_Ha9 ]. % 19.13/19.23 apply (zenon_L104_); trivial. % 19.13/19.23 exact (zenon_H123 zenon_Ha9). % 19.13/19.23 (* end of lemma zenon_L1379_ *) % 19.13/19.23 assert (zenon_L1380_ : (((op (e3) (e1)) = (e0))\/(((op (e3) (e1)) = (e1))\/(((op (e3) (e1)) = (e2))\/((op (e3) (e1)) = (e3))))) -> ((op (e1) (e1)) = (e2)) -> ((op (e2) (e1)) = (e3)) -> ((op (e3) (e0)) = (e1)) -> (~((op (e3) (e0)) = (op (e3) (e1)))) -> (~((op (e3) (e1)) = (op (e3) (e3)))) -> ((op (e3) (e3)) = (e2)) -> (~((op (e3) (e1)) = (e3))) -> False). % 19.13/19.23 do 0 intro. intros zenon_H22a zenon_H110 zenon_Ha6 zenon_Hac zenon_H1cf zenon_H130 zenon_Hf6 zenon_H282. % 19.13/19.23 apply (zenon_or_s _ _ zenon_H22a); [ zenon_intro zenon_H1b1 | zenon_intro zenon_H22b ]. % 19.13/19.23 apply (zenon_L509_); trivial. % 19.13/19.23 apply (zenon_or_s _ _ zenon_H22b); [ zenon_intro zenon_Hae | zenon_intro zenon_H22c ]. % 19.13/19.23 apply (zenon_L242_); trivial. % 19.13/19.23 apply (zenon_or_s _ _ zenon_H22c); [ zenon_intro zenon_H14d | zenon_intro zenon_H161 ]. % 19.13/19.23 apply (zenon_L102_); trivial. % 19.13/19.23 exact (zenon_H282 zenon_H161). % 19.13/19.23 (* end of lemma zenon_L1380_ *) % 19.13/19.23 assert (zenon_L1381_ : (((op (e3) (e0)) = (e0))\/(((op (e3) (e0)) = (e1))\/(((op (e3) (e0)) = (e2))\/((op (e3) (e0)) = (e3))))) -> ((op (e3) (e2)) = (e0)) -> (~((op (e3) (e0)) = (op (e3) (e2)))) -> (~((op (e3) (e1)) = (e3))) -> (~((op (e3) (e1)) = (op (e3) (e3)))) -> (~((op (e3) (e0)) = (op (e3) (e1)))) -> ((op (e2) (e1)) = (e3)) -> ((op (e1) (e1)) = (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) (e3)) = (e2)) -> (~((op (e3) (e0)) = (e3))) -> False). % 19.13/19.23 do 0 intro. intros zenon_H267 zenon_H61 zenon_H6f zenon_H282 zenon_H130 zenon_H1cf zenon_Ha6 zenon_H110 zenon_H22a zenon_H71 zenon_Hf6 zenon_H15f. % 19.13/19.23 apply (zenon_or_s _ _ zenon_H267); [ zenon_intro zenon_H44 | zenon_intro zenon_H268 ]. % 19.13/19.23 apply (zenon_L19_); trivial. % 19.13/19.23 apply (zenon_or_s _ _ zenon_H268); [ zenon_intro zenon_Hac | zenon_intro zenon_H269 ]. % 19.13/19.23 apply (zenon_L1380_); trivial. % 19.13/19.23 apply (zenon_or_s _ _ zenon_H269); [ zenon_intro zenon_H148 | zenon_intro zenon_H15e ]. % 19.13/19.23 apply (zenon_L114_); trivial. % 19.13/19.23 exact (zenon_H15f zenon_H15e). % 19.13/19.23 (* end of lemma zenon_L1381_ *) % 19.13/19.23 assert (zenon_L1382_ : (((op (e0) (e1)) = (e3))\/(((op (e1) (e1)) = (e3))\/(((op (e2) (e1)) = (e3))\/((op (e3) (e1)) = (e3))))) -> (~((op (e0) (e1)) = (e3))) -> (~((op (e1) (e1)) = (e3))) -> ((op (e0) (e3)) = (e0)) -> (~((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) (e2)))) -> (~((op (e3) (e1)) = (op (e3) (e3)))) -> (~((op (e3) (e0)) = (op (e3) (e1)))) -> ((op (e1) (e1)) = (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) (e3)) = (e2)) -> (~((op (e3) (e0)) = (e3))) -> ((op (e1) (e0)) = (e0)) -> (~((op (e1) (e0)) = (op (e3) (e0)))) -> (((op (e3) (e0)) = (e0))\/(((op (e3) (e1)) = (e0))\/(((op (e3) (e2)) = (e0))\/((op (e3) (e3)) = (e0))))) -> (~((op (e3) (e1)) = (e3))) -> False). % 19.13/19.23 do 0 intro. intros zenon_H1a5 zenon_H9c zenon_H1a1 zenon_H1e zenon_Hc2 zenon_H267 zenon_H6f zenon_H130 zenon_H1cf zenon_H110 zenon_H22a zenon_H71 zenon_Hf6 zenon_H15f zenon_H27 zenon_H1fa zenon_H1ac zenon_H282. % 19.13/19.23 apply (zenon_or_s _ _ zenon_H1a5); [ zenon_intro zenon_H99 | zenon_intro zenon_H1a8 ]. % 19.13/19.23 exact (zenon_H9c zenon_H99). % 19.13/19.23 apply (zenon_or_s _ _ zenon_H1a8); [ zenon_intro zenon_H13f | zenon_intro zenon_H1a9 ]. % 19.13/19.23 exact (zenon_H1a1 zenon_H13f). % 19.13/19.23 apply (zenon_or_s _ _ zenon_H1a9); [ zenon_intro zenon_Ha6 | zenon_intro zenon_H161 ]. % 19.13/19.23 apply (zenon_or_s _ _ zenon_H1ac); [ zenon_intro zenon_H44 | zenon_intro zenon_H1af ]. % 19.13/19.23 apply (zenon_L312_); trivial. % 19.13/19.23 apply (zenon_or_s _ _ zenon_H1af); [ zenon_intro zenon_H1b1 | zenon_intro zenon_H1b0 ]. % 19.13/19.23 apply (zenon_L509_); trivial. % 19.13/19.23 apply (zenon_or_s _ _ zenon_H1b0); [ zenon_intro zenon_H61 | zenon_intro zenon_H60 ]. % 19.13/19.23 apply (zenon_L1381_); trivial. % 19.13/19.23 apply (zenon_L440_); trivial. % 19.13/19.23 exact (zenon_H282 zenon_H161). % 19.13/19.23 (* end of lemma zenon_L1382_ *) % 19.13/19.23 assert (zenon_L1383_ : (((op (e2) (e2)) = (e0))\/(((op (e2) (e2)) = (e1))\/(((op (e2) (e2)) = (e2))\/((op (e2) (e2)) = (e3))))) -> ((op (e1) (e2)) = (e0)) -> (~((op (e1) (e2)) = (op (e2) (e2)))) -> ((op (e0) (e2)) = (e1)) -> (~((op (e0) (e2)) = (op (e2) (e2)))) -> (~((op (e2) (e2)) = (e2))) -> (~((op (e2) (e2)) = (e3))) -> False). % 19.13/19.23 do 0 intro. intros zenon_H1c4 zenon_H2a zenon_H2b zenon_H122 zenon_Ha8 zenon_H173 zenon_H1b3. % 19.13/19.23 apply (zenon_or_s _ _ zenon_H1c4); [ zenon_intro zenon_H2c | zenon_intro zenon_H1c5 ]. % 19.13/19.23 apply (zenon_L3_); trivial. % 19.13/19.23 apply (zenon_or_s _ _ zenon_H1c5); [ zenon_intro zenon_Hf1 | zenon_intro zenon_H1c6 ]. % 19.13/19.23 apply (zenon_L246_); trivial. % 19.13/19.23 apply (zenon_or_s _ _ zenon_H1c6); [ zenon_intro zenon_H176 | zenon_intro zenon_Haa ]. % 19.13/19.23 exact (zenon_H173 zenon_H176). % 19.13/19.23 exact (zenon_H1b3 zenon_Haa). % 19.13/19.23 (* end of lemma zenon_L1383_ *) % 19.13/19.23 assert (zenon_L1384_ : (((op (e1) (e0)) = (e0))\/(((op (e1) (e1)) = (e0))\/(((op (e1) (e2)) = (e0))\/((op (e1) (e3)) = (e0))))) -> (~((op (e1) (e0)) = (op (e3) (e0)))) -> ((op (e3) (e0)) = (e0)) -> (~((op (e3) (e1)) = (e3))) -> ((op (e0) (e1)) = (e2)) -> (~((op (e1) (e1)) = (e3))) -> (~((op (e0) (e1)) = (e3))) -> (((op (e0) (e1)) = (e3))\/(((op (e1) (e1)) = (e3))\/(((op (e2) (e1)) = (e3))\/((op (e3) (e1)) = (e3))))) -> (~((op (e2) (e2)) = (e3))) -> (~((op (e2) (e2)) = (e2))) -> (~((op (e0) (e2)) = (op (e2) (e2)))) -> ((op (e0) (e2)) = (e1)) -> (~((op (e1) (e2)) = (op (e2) (e2)))) -> (((op (e2) (e2)) = (e0))\/(((op (e2) (e2)) = (e1))\/(((op (e2) (e2)) = (e2))\/((op (e2) (e2)) = (e3))))) -> (~((op (e0) (e3)) = (op (e1) (e3)))) -> ((op (e0) (e3)) = (e0)) -> False). % 19.13/19.23 do 0 intro. intros zenon_H22 zenon_H1fa zenon_H44 zenon_H282 zenon_H10f zenon_H1a1 zenon_H9c zenon_H1a5 zenon_H1b3 zenon_H173 zenon_Ha8 zenon_H122 zenon_H2b zenon_H1c4 zenon_H1d zenon_H1e. % 19.13/19.23 apply (zenon_or_s _ _ zenon_H22); [ zenon_intro zenon_H27 | zenon_intro zenon_H26 ]. % 19.13/19.23 apply (zenon_L312_); trivial. % 19.13/19.23 apply (zenon_or_s _ _ zenon_H26); [ zenon_intro zenon_H29 | zenon_intro zenon_H28 ]. % 19.13/19.23 apply (zenon_or_s _ _ zenon_H1a5); [ zenon_intro zenon_H99 | zenon_intro zenon_H1a8 ]. % 19.13/19.23 exact (zenon_H9c zenon_H99). % 19.13/19.23 apply (zenon_or_s _ _ zenon_H1a8); [ zenon_intro zenon_H13f | zenon_intro zenon_H1a9 ]. % 19.13/19.23 exact (zenon_H1a1 zenon_H13f). % 19.13/19.23 apply (zenon_or_s _ _ zenon_H1a9); [ zenon_intro zenon_Ha6 | zenon_intro zenon_H161 ]. % 19.13/19.23 apply (zenon_L371_); trivial. % 19.13/19.23 exact (zenon_H282 zenon_H161). % 19.13/19.23 apply (zenon_or_s _ _ zenon_H28); [ zenon_intro zenon_H2a | zenon_intro zenon_H1f ]. % 19.13/19.23 apply (zenon_L1383_); trivial. % 19.13/19.23 apply (zenon_L1_); trivial. % 19.13/19.23 (* end of lemma zenon_L1384_ *) % 19.13/19.23 assert (zenon_L1385_ : (((op (e3) (e0)) = (e0))\/(((op (e3) (e0)) = (e1))\/(((op (e3) (e0)) = (e2))\/((op (e3) (e0)) = (e3))))) -> ((op (e0) (e3)) = (e0)) -> (~((op (e0) (e3)) = (op (e1) (e3)))) -> (((op (e2) (e2)) = (e0))\/(((op (e2) (e2)) = (e1))\/(((op (e2) (e2)) = (e2))\/((op (e2) (e2)) = (e3))))) -> (~((op (e1) (e2)) = (op (e2) (e2)))) -> ((op (e0) (e2)) = (e1)) -> (~((op (e0) (e2)) = (op (e2) (e2)))) -> (~((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)) = (e3))) -> (~((op (e1) (e1)) = (e3))) -> ((op (e0) (e1)) = (e2)) -> (~((op (e3) (e1)) = (e3))) -> (~((op (e1) (e0)) = (op (e3) (e0)))) -> (((op (e1) (e0)) = (e0))\/(((op (e1) (e1)) = (e0))\/(((op (e1) (e2)) = (e0))\/((op (e1) (e3)) = (e0))))) -> ((op (e3) (e1)) = (e1)) -> (~((op (e3) (e0)) = (op (e3) (e1)))) -> (~((op (e3) (e0)) = (op (e3) (e3)))) -> ((op (e3) (e3)) = (e2)) -> (~((op (e3) (e0)) = (e3))) -> False). % 19.13/19.23 do 0 intro. intros zenon_H267 zenon_H1e zenon_H1d zenon_H1c4 zenon_H2b zenon_H122 zenon_Ha8 zenon_H173 zenon_H1b3 zenon_H1a5 zenon_H9c zenon_H1a1 zenon_H10f zenon_H282 zenon_H1fa zenon_H22 zenon_Hae zenon_H1cf zenon_H71 zenon_Hf6 zenon_H15f. % 19.13/19.23 apply (zenon_or_s _ _ zenon_H267); [ zenon_intro zenon_H44 | zenon_intro zenon_H268 ]. % 19.13/19.23 apply (zenon_L1384_); trivial. % 19.13/19.23 apply (zenon_or_s _ _ zenon_H268); [ zenon_intro zenon_Hac | zenon_intro zenon_H269 ]. % 19.13/19.23 apply (zenon_L242_); trivial. % 19.13/19.23 apply (zenon_or_s _ _ zenon_H269); [ zenon_intro zenon_H148 | zenon_intro zenon_H15e ]. % 19.13/19.23 apply (zenon_L114_); trivial. % 19.13/19.23 exact (zenon_H15f zenon_H15e). % 19.13/19.23 (* end of lemma zenon_L1385_ *) % 19.13/19.23 assert (zenon_L1386_ : (((op (e0) (e1)) = (e0))\/(((op (e0) (e1)) = (e1))\/(((op (e0) (e1)) = (e2))\/((op (e0) (e1)) = (e3))))) -> (~((op (e0) (e1)) = (op (e0) (e3)))) -> (~((op (e0) (e2)) = (e3))) -> (~((op (e0) (e2)) = (op (e1) (e2)))) -> ((op (e1) (e2)) = (e2)) -> (~((op (e0) (e1)) = (op (e0) (e2)))) -> (~((op (e0) (e2)) = (op (e0) (e3)))) -> (((op (e0) (e2)) = (e0))\/(((op (e0) (e2)) = (e1))\/(((op (e0) (e2)) = (e2))\/((op (e0) (e2)) = (e3))))) -> (~((op (e3) (e0)) = (e3))) -> ((op (e3) (e3)) = (e2)) -> (~((op (e3) (e0)) = (op (e3) (e3)))) -> (~((op (e3) (e0)) = (op (e3) (e1)))) -> ((op (e3) (e1)) = (e1)) -> (((op (e1) (e0)) = (e0))\/(((op (e1) (e1)) = (e0))\/(((op (e1) (e2)) = (e0))\/((op (e1) (e3)) = (e0))))) -> (~((op (e1) (e0)) = (op (e3) (e0)))) -> (~((op (e3) (e1)) = (e3))) -> (~((op (e1) (e1)) = (e3))) -> (((op (e0) (e1)) = (e3))\/(((op (e1) (e1)) = (e3))\/(((op (e2) (e1)) = (e3))\/((op (e3) (e1)) = (e3))))) -> (~((op (e2) (e2)) = (e3))) -> (~((op (e2) (e2)) = (e2))) -> (~((op (e0) (e2)) = (op (e2) (e2)))) -> ((op (e0) (e2)) = (e1)) -> (~((op (e1) (e2)) = (op (e2) (e2)))) -> (((op (e2) (e2)) = (e0))\/(((op (e2) (e2)) = (e1))\/(((op (e2) (e2)) = (e2))\/((op (e2) (e2)) = (e3))))) -> (~((op (e0) (e3)) = (op (e1) (e3)))) -> ((op (e0) (e3)) = (e0)) -> (((op (e3) (e0)) = (e0))\/(((op (e3) (e0)) = (e1))\/(((op (e3) (e0)) = (e2))\/((op (e3) (e0)) = (e3))))) -> (~((op (e0) (e1)) = (e3))) -> False). % 19.13/19.23 do 0 intro. intros zenon_H212 zenon_H54 zenon_H123 zenon_H195 zenon_H113 zenon_H4a zenon_H208 zenon_H1ba zenon_H15f zenon_Hf6 zenon_H71 zenon_H1cf zenon_Hae zenon_H22 zenon_H1fa zenon_H282 zenon_H1a1 zenon_H1a5 zenon_H1b3 zenon_H173 zenon_Ha8 zenon_H122 zenon_H2b zenon_H1c4 zenon_H1d zenon_H1e zenon_H267 zenon_H9c. % 19.13/19.23 apply (zenon_or_s _ _ zenon_H212); [ zenon_intro zenon_H49 | zenon_intro zenon_H213 ]. % 19.13/19.23 apply (zenon_L12_); trivial. % 19.13/19.23 apply (zenon_or_s _ _ zenon_H213); [ zenon_intro zenon_Ha0 | zenon_intro zenon_H214 ]. % 19.13/19.23 apply (zenon_L1357_); trivial. % 19.13/19.23 apply (zenon_or_s _ _ zenon_H214); [ zenon_intro zenon_H10f | zenon_intro zenon_H99 ]. % 19.13/19.23 apply (zenon_L1385_); trivial. % 19.13/19.23 exact (zenon_H9c zenon_H99). % 19.13/19.23 (* end of lemma zenon_L1386_ *) % 19.13/19.23 assert (zenon_L1387_ : (((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)) = (op (e2) (e3)))) -> ((op (e2) (e3)) = (e1)) -> (~((op (e2) (e2)) = (e2))) -> (~((op (e2) (e2)) = (e3))) -> False). % 19.13/19.23 do 0 intro. intros zenon_H1c4 zenon_H34 zenon_H52 zenon_H6d zenon_Hf4 zenon_H173 zenon_H1b3. % 19.13/19.23 apply (zenon_or_s _ _ zenon_H1c4); [ zenon_intro zenon_H2c | zenon_intro zenon_H1c5 ]. % 19.13/19.23 apply (zenon_L11_); trivial. % 19.13/19.23 apply (zenon_or_s _ _ zenon_H1c5); [ zenon_intro zenon_Hf1 | zenon_intro zenon_H1c6 ]. % 19.13/19.23 apply (zenon_L84_); trivial. % 19.13/19.23 apply (zenon_or_s _ _ zenon_H1c6); [ zenon_intro zenon_H176 | zenon_intro zenon_Haa ]. % 19.13/19.23 exact (zenon_H173 zenon_H176). % 19.13/19.23 exact (zenon_H1b3 zenon_Haa). % 19.13/19.23 (* end of lemma zenon_L1387_ *) % 19.13/19.23 assert (zenon_L1388_ : (((op (e0) (e1)) = (e0))\/(((op (e0) (e1)) = (e1))\/(((op (e0) (e1)) = (e2))\/((op (e0) (e1)) = (e3))))) -> (~((op (e0) (e1)) = (op (e0) (e3)))) -> (~((op (e0) (e2)) = (e3))) -> (~((op (e0) (e2)) = (op (e1) (e2)))) -> ((op (e1) (e2)) = (e2)) -> (~((op (e0) (e1)) = (op (e0) (e2)))) -> ((op (e0) (e3)) = (e0)) -> (~((op (e0) (e2)) = (op (e0) (e3)))) -> (((op (e0) (e2)) = (e0))\/(((op (e0) (e2)) = (e1))\/(((op (e0) (e2)) = (e2))\/((op (e0) (e2)) = (e3))))) -> ((op (e1) (e1)) = (e0)) -> ((op (e2) (e1)) = (e3)) -> (~((op (e0) (e1)) = (e3))) -> False). % 19.13/19.23 do 0 intro. intros zenon_H212 zenon_H54 zenon_H123 zenon_H195 zenon_H113 zenon_H4a zenon_H1e zenon_H208 zenon_H1ba zenon_H29 zenon_Ha6 zenon_H9c. % 19.13/19.23 apply (zenon_or_s _ _ zenon_H212); [ zenon_intro zenon_H49 | zenon_intro zenon_H213 ]. % 19.13/19.23 apply (zenon_L12_); trivial. % 19.13/19.23 apply (zenon_or_s _ _ zenon_H213); [ zenon_intro zenon_Ha0 | zenon_intro zenon_H214 ]. % 19.13/19.23 apply (zenon_L1357_); trivial. % 19.13/19.23 apply (zenon_or_s _ _ zenon_H214); [ zenon_intro zenon_H10f | zenon_intro zenon_H99 ]. % 19.13/19.23 apply (zenon_L371_); trivial. % 19.13/19.23 exact (zenon_H9c zenon_H99). % 19.13/19.23 (* end of lemma zenon_L1388_ *) % 19.13/19.23 assert (zenon_L1389_ : ((~((op (e3) (e2)) = (e3)))\/((op (e3) (e3)) = (e2))) -> (~((op (e0) (e0)) = (e0))) -> (((op (e0) (e0)) = (e1))\/(((op (e0) (e1)) = (e1))\/(((op (e0) (e2)) = (e1))\/((op (e0) (e3)) = (e1))))) -> (~((e0) = (e1))) -> (~((op (e1) (e1)) = (e1))) -> (~((op (e2) (e1)) = (op (e2) (e3)))) -> ((op (e2) (e3)) = (e1)) -> (((op (e0) (e2)) = (e2))\/(((op (e1) (e2)) = (e2))\/(((op (e2) (e2)) = (e2))\/((op (e3) (e2)) = (e2))))) -> (~((op (e3) (e2)) = (op (e3) (e3)))) -> (~((op (e0) (e1)) = (op (e0) (e3)))) -> (((op (e2) (e2)) = (e0))\/(((op (e2) (e2)) = (e1))\/(((op (e2) (e2)) = (e2))\/((op (e2) (e2)) = (e3))))) -> (~((op (e2) (e2)) = (e3))) -> (~((op (e2) (e2)) = (e2))) -> (~((op (e0) (e2)) = (op (e2) (e2)))) -> (~((op (e1) (e2)) = (op (e2) (e2)))) -> (~((op (e0) (e3)) = (op (e1) (e3)))) -> (((op (e1) (e0)) = (e0))\/(((op (e1) (e1)) = (e0))\/(((op (e1) (e2)) = (e0))\/((op (e1) (e3)) = (e0))))) -> (((op (e0) (e1)) = (e0))\/(((op (e0) (e1)) = (e1))\/(((op (e0) (e1)) = (e2))\/((op (e0) (e1)) = (e3))))) -> (~((e1) = (e2))) -> (((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) (e3)) = (op (e3) (e3)))) -> (~((op (e0) (e2)) = (op (e0) (e3)))) -> (~((op (e0) (e1)) = (op (e0) (e2)))) -> (~((op (e0) (e2)) = (op (e1) (e2)))) -> (((op (e0) (e2)) = (e0))\/(((op (e0) (e2)) = (e1))\/(((op (e0) (e2)) = (e2))\/((op (e0) (e2)) = (e3))))) -> (~((op (e1) (e1)) = (e3))) -> (((op (e3) (e0)) = (e0))\/(((op (e3) (e1)) = (e0))\/(((op (e3) (e2)) = (e0))\/((op (e3) (e3)) = (e0))))) -> ((op (e0) (e3)) = (e0)) -> (~((op (e0) (e3)) = (op (e3) (e3)))) -> (~((op (e3) (e0)) = (op (e3) (e2)))) -> (~((op (e1) (e0)) = (op (e3) (e0)))) -> (((op (e0) (e1)) = (e3))\/(((op (e1) (e1)) = (e3))\/(((op (e2) (e1)) = (e3))\/((op (e3) (e1)) = (e3))))) -> (((op (e3) (e1)) = (e0))\/(((op (e3) (e1)) = (e1))\/(((op (e3) (e1)) = (e2))\/((op (e3) (e1)) = (e3))))) -> (~((op (e3) (e1)) = (op (e3) (e3)))) -> (~((op (e0) (e1)) = (op (e3) (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))))) -> (~((e1) = (e3))) -> (~((op (e0) (e1)) = (e3))) -> (~((op (e0) (e2)) = (e3))) -> (~((op (e0) (e3)) = (e3))) -> (((op (e0) (e0)) = (e3))\/(((op (e0) (e1)) = (e3))\/(((op (e0) (e2)) = (e3))\/((op (e0) (e3)) = (e3))))) -> (~((op (e2) (e2)) = (op (e2) (e3)))) -> (~((op (e2) (e0)) = (op (e2) (e2)))) -> (((op (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) (e3)) = (e3))) -> (((op (e3) (e0)) = (e3))\/(((op (e3) (e1)) = (e3))\/(((op (e3) (e2)) = (e3))\/((op (e3) (e3)) = (e3))))) -> False). % 19.13/19.23 do 0 intro. intros zenon_H284 zenon_H3f zenon_H22d zenon_Ha1 zenon_H10a zenon_H1c7 zenon_Hf4 zenon_H172 zenon_H62 zenon_H54 zenon_H1c4 zenon_H1b3 zenon_H173 zenon_Ha8 zenon_H2b zenon_H1d zenon_H22 zenon_H212 zenon_H7c zenon_H109 zenon_H18c zenon_Hd5 zenon_H208 zenon_H4a zenon_H195 zenon_H1ba zenon_H1a1 zenon_H1ac zenon_H1e zenon_Hc2 zenon_H6f zenon_H1fa zenon_H1a5 zenon_H22a zenon_H130 zenon_H210 zenon_H1cf zenon_H71 zenon_H267 zenon_H95 zenon_H9c zenon_H123 zenon_H12d zenon_H168 zenon_H6d zenon_H52 zenon_H3e zenon_H15f zenon_H282 zenon_H102 zenon_H165. % 19.13/19.23 apply (zenon_or_s _ _ zenon_H284); [ zenon_intro zenon_H283 | zenon_intro zenon_Hf6 ]. % 19.13/19.23 apply (zenon_L1346_); trivial. % 19.13/19.23 apply (zenon_or_s _ _ zenon_H3e); [ zenon_intro zenon_H42 | zenon_intro zenon_H41 ]. % 19.13/19.23 exact (zenon_H3f zenon_H42). % 19.13/19.23 apply (zenon_or_s _ _ zenon_H41); [ zenon_intro zenon_H27 | zenon_intro zenon_H43 ]. % 19.13/19.23 apply (zenon_or_s _ _ zenon_H22d); [ zenon_intro zenon_H7a | zenon_intro zenon_H22e ]. % 19.13/19.23 apply (zenon_L1350_); trivial. % 19.13/19.23 apply (zenon_or_s _ _ zenon_H22e); [ zenon_intro zenon_Ha0 | zenon_intro zenon_H22f ]. % 19.13/19.23 apply (zenon_or_s _ _ zenon_H168); [ zenon_intro zenon_H3a | zenon_intro zenon_H169 ]. % 19.13/19.23 apply (zenon_or_s _ _ zenon_H18c); [ zenon_intro zenon_H86 | zenon_intro zenon_H18d ]. % 19.13/19.23 apply (zenon_L1366_); trivial. % 19.13/19.23 apply (zenon_or_s _ _ zenon_H18d); [ zenon_intro zenon_H110 | zenon_intro zenon_H18e ]. % 19.13/19.23 apply (zenon_L1382_); trivial. % 19.13/19.23 apply (zenon_or_s _ _ zenon_H18e); [ zenon_intro zenon_H113 | zenon_intro zenon_Hd7 ]. % 19.13/19.23 apply (zenon_L1357_); trivial. % 19.13/19.23 apply (zenon_L402_); trivial. % 19.13/19.23 apply (zenon_or_s _ _ zenon_H169); [ zenon_intro zenon_H99 | zenon_intro zenon_H16a ]. % 19.13/19.23 exact (zenon_H9c zenon_H99). % 19.13/19.23 apply (zenon_or_s _ _ zenon_H16a); [ zenon_intro zenon_Ha9 | zenon_intro zenon_He3 ]. % 19.13/19.23 exact (zenon_H123 zenon_Ha9). % 19.13/19.23 exact (zenon_H12d zenon_He3). % 19.13/19.23 apply (zenon_or_s _ _ zenon_H22f); [ zenon_intro zenon_H122 | zenon_intro zenon_Hc3 ]. % 19.13/19.23 apply (zenon_or_s _ _ zenon_H109); [ zenon_intro zenon_Ha0 | zenon_intro zenon_H10b ]. % 19.13/19.23 apply (zenon_L406_); trivial. % 19.13/19.23 apply (zenon_or_s _ _ zenon_H10b); [ zenon_intro zenon_H10d | zenon_intro zenon_H10c ]. % 19.13/19.23 exact (zenon_H10a zenon_H10d). % 19.13/19.23 apply (zenon_or_s _ _ zenon_H10c); [ zenon_intro zenon_Ha5 | zenon_intro zenon_Hae ]. % 19.13/19.23 apply (zenon_L188_); trivial. % 19.13/19.23 apply (zenon_or_s _ _ zenon_H172); [ zenon_intro zenon_H150 | zenon_intro zenon_H174 ]. % 19.13/19.23 apply (zenon_L328_); trivial. % 19.13/19.23 apply (zenon_or_s _ _ zenon_H174); [ zenon_intro zenon_H113 | zenon_intro zenon_H175 ]. % 19.13/19.23 apply (zenon_L1386_); trivial. % 19.13/19.23 apply (zenon_or_s _ _ zenon_H175); [ zenon_intro zenon_H176 | zenon_intro zenon_H151 ]. % 19.13/19.23 exact (zenon_H173 zenon_H176). % 19.13/19.23 apply (zenon_L119_); trivial. % 19.13/19.23 apply (zenon_L427_); trivial. % 19.13/19.23 apply (zenon_or_s _ _ zenon_H43); [ zenon_intro zenon_H34 | zenon_intro zenon_H44 ]. % 19.13/19.23 apply (zenon_L1387_); trivial. % 19.13/19.23 apply (zenon_or_s _ _ zenon_H22d); [ zenon_intro zenon_H7a | zenon_intro zenon_H22e ]. % 19.13/19.23 apply (zenon_L1350_); trivial. % 19.13/19.23 apply (zenon_or_s _ _ zenon_H22e); [ zenon_intro zenon_Ha0 | zenon_intro zenon_H22f ]. % 19.13/19.23 apply (zenon_L1365_); trivial. % 19.13/19.23 apply (zenon_or_s _ _ zenon_H22f); [ zenon_intro zenon_H122 | zenon_intro zenon_Hc3 ]. % 19.13/19.23 apply (zenon_or_s _ _ zenon_H22); [ zenon_intro zenon_H27 | zenon_intro zenon_H26 ]. % 19.13/19.23 apply (zenon_L312_); trivial. % 19.13/19.23 apply (zenon_or_s _ _ zenon_H26); [ zenon_intro zenon_H29 | zenon_intro zenon_H28 ]. % 19.13/19.23 apply (zenon_or_s _ _ zenon_H1a5); [ zenon_intro zenon_H99 | zenon_intro zenon_H1a8 ]. % 19.13/19.23 exact (zenon_H9c zenon_H99). % 19.13/19.23 apply (zenon_or_s _ _ zenon_H1a8); [ zenon_intro zenon_H13f | zenon_intro zenon_H1a9 ]. % 19.13/19.23 exact (zenon_H1a1 zenon_H13f). % 19.13/19.23 apply (zenon_or_s _ _ zenon_H1a9); [ zenon_intro zenon_Ha6 | zenon_intro zenon_H161 ]. % 19.13/19.23 apply (zenon_or_s _ _ zenon_H172); [ zenon_intro zenon_H150 | zenon_intro zenon_H174 ]. % 19.13/19.23 apply (zenon_L328_); trivial. % 19.13/19.23 apply (zenon_or_s _ _ zenon_H174); [ zenon_intro zenon_H113 | zenon_intro zenon_H175 ]. % 19.13/19.23 apply (zenon_L1388_); trivial. % 19.13/19.23 apply (zenon_or_s _ _ zenon_H175); [ zenon_intro zenon_H176 | zenon_intro zenon_H151 ]. % 19.13/19.23 exact (zenon_H173 zenon_H176). % 19.13/19.23 apply (zenon_L119_); trivial. % 19.13/19.23 exact (zenon_H282 zenon_H161). % 19.13/19.23 apply (zenon_or_s _ _ zenon_H28); [ zenon_intro zenon_H2a | zenon_intro zenon_H1f ]. % 19.13/19.23 apply (zenon_L1383_); trivial. % 19.13/19.23 apply (zenon_L1_); trivial. % 19.13/19.23 apply (zenon_L427_); trivial. % 19.13/19.23 (* end of lemma zenon_L1389_ *) % 19.13/19.23 assert (zenon_L1390_ : ((~((op (e3) (e1)) = (e3)))\/((op (e3) (e3)) = (e1))) -> ((op (e2) (e3)) = (e1)) -> (((op (e3) (e0)) = (e3))\/(((op (e3) (e1)) = (e3))\/(((op (e3) (e2)) = (e3))\/((op (e3) (e3)) = (e3))))) -> (~((op (e3) (e3)) = (e3))) -> (~((op (e3) (e0)) = (e3))) -> (~((op (e2) (e3)) = (op (e3) (e3)))) -> ((op (e2) (e3)) = (e2)) -> ((~((op (e3) (e2)) = (e3)))\/((op (e3) (e3)) = (e2))) -> False). % 19.13/19.23 do 0 intro. intros zenon_H285 zenon_Hf4 zenon_H165 zenon_H102 zenon_H15f zenon_Hf3 zenon_H11d zenon_H284. % 19.13/19.23 apply (zenon_or_s _ _ zenon_H285); [ zenon_intro zenon_H282 | zenon_intro zenon_Hc4 ]. % 19.13/19.23 apply (zenon_L1347_); trivial. % 19.13/19.23 apply (zenon_L60_); trivial. % 19.13/19.23 (* end of lemma zenon_L1390_ *) % 19.13/19.23 assert (zenon_L1391_ : ((~((op (e3) (e0)) = (e3)))\/((op (e3) (e3)) = (e0))) -> ((op (e0) (e3)) = (e0)) -> (~((op (e0) (e3)) = (op (e3) (e3)))) -> ((~((op (e3) (e2)) = (e3)))\/((op (e3) (e3)) = (e2))) -> ((op (e2) (e3)) = (e2)) -> (~((op (e2) (e3)) = (op (e3) (e3)))) -> (~((op (e3) (e3)) = (e3))) -> (((op (e3) (e0)) = (e3))\/(((op (e3) (e1)) = (e3))\/(((op (e3) (e2)) = (e3))\/((op (e3) (e3)) = (e3))))) -> ((op (e2) (e3)) = (e1)) -> ((~((op (e3) (e1)) = (e3)))\/((op (e3) (e3)) = (e1))) -> False). % 19.13/19.23 do 0 intro. intros zenon_H286 zenon_H1e zenon_Hc2 zenon_H284 zenon_H11d zenon_Hf3 zenon_H102 zenon_H165 zenon_Hf4 zenon_H285. % 19.13/19.23 apply (zenon_or_s _ _ zenon_H286); [ zenon_intro zenon_H15f | zenon_intro zenon_H60 ]. % 19.13/19.23 apply (zenon_L1390_); trivial. % 19.13/19.23 apply (zenon_L440_); trivial. % 19.13/19.23 (* end of lemma zenon_L1391_ *) % 19.13/19.23 assert (zenon_L1392_ : ((~((op (e2) (e2)) = (e3)))\/((op (e2) (e3)) = (e2))) -> ((~((op (e3) (e1)) = (e3)))\/((op (e3) (e3)) = (e1))) -> (~((op (e2) (e3)) = (op (e3) (e3)))) -> (((op (e3) (e0)) = (e3))\/(((op (e3) (e1)) = (e3))\/(((op (e3) (e2)) = (e3))\/((op (e3) (e3)) = (e3))))) -> (~((op (e3) (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 (e2) (e2)) = (op (e2) (e3)))) -> (((op (e0) (e0)) = (e3))\/(((op (e0) (e1)) = (e3))\/(((op (e0) (e2)) = (e3))\/((op (e0) (e3)) = (e3))))) -> (~((op (e0) (e3)) = (e3))) -> (~((op (e0) (e2)) = (e3))) -> (~((op (e0) (e1)) = (e3))) -> (~((e1) = (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) (e1)) = (op (e3) (e1)))) -> (~((op (e3) (e1)) = (op (e3) (e3)))) -> (((op (e3) (e1)) = (e0))\/(((op (e3) (e1)) = (e1))\/(((op (e3) (e1)) = (e2))\/((op (e3) (e1)) = (e3))))) -> (((op (e0) (e1)) = (e3))\/(((op (e1) (e1)) = (e3))\/(((op (e2) (e1)) = (e3))\/((op (e3) (e1)) = (e3))))) -> (~((op (e1) (e0)) = (op (e3) (e0)))) -> (~((op (e3) (e0)) = (op (e3) (e2)))) -> (~((op (e0) (e3)) = (op (e3) (e3)))) -> ((op (e0) (e3)) = (e0)) -> (((op (e3) (e0)) = (e0))\/(((op (e3) (e1)) = (e0))\/(((op (e3) (e2)) = (e0))\/((op (e3) (e3)) = (e0))))) -> (~((op (e1) (e1)) = (e3))) -> (((op (e0) (e2)) = (e0))\/(((op (e0) (e2)) = (e1))\/(((op (e0) (e2)) = (e2))\/((op (e0) (e2)) = (e3))))) -> (~((op (e0) (e2)) = (op (e1) (e2)))) -> (~((op (e0) (e1)) = (op (e0) (e2)))) -> (~((op (e0) (e2)) = (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)) = (e1))\/(((op (e1) (e1)) = (e1))\/(((op (e2) (e1)) = (e1))\/((op (e3) (e1)) = (e1))))) -> (~((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 (e0) (e3)) = (op (e1) (e3)))) -> (~((op (e1) (e2)) = (op (e2) (e2)))) -> (~((op (e0) (e2)) = (op (e2) (e2)))) -> (~((op (e2) (e2)) = (e2))) -> (((op (e2) (e2)) = (e0))\/(((op (e2) (e2)) = (e1))\/(((op (e2) (e2)) = (e2))\/((op (e2) (e2)) = (e3))))) -> (~((op (e0) (e1)) = (op (e0) (e3)))) -> (~((op (e3) (e2)) = (op (e3) (e3)))) -> (((op (e0) (e2)) = (e2))\/(((op (e1) (e2)) = (e2))\/(((op (e2) (e2)) = (e2))\/((op (e3) (e2)) = (e2))))) -> ((op (e2) (e3)) = (e1)) -> (~((op (e2) (e1)) = (op (e2) (e3)))) -> (~((op (e1) (e1)) = (e1))) -> (~((e0) = (e1))) -> (((op (e0) (e0)) = (e1))\/(((op (e0) (e1)) = (e1))\/(((op (e0) (e2)) = (e1))\/((op (e0) (e3)) = (e1))))) -> (~((op (e0) (e0)) = (e0))) -> ((~((op (e3) (e2)) = (e3)))\/((op (e3) (e3)) = (e2))) -> ((~((op (e3) (e0)) = (e3)))\/((op (e3) (e3)) = (e0))) -> False). % 19.13/19.23 do 0 intro. intros zenon_H288 zenon_H285 zenon_Hf3 zenon_H165 zenon_H102 zenon_H3e zenon_H52 zenon_H6d zenon_H168 zenon_H12d zenon_H123 zenon_H9c zenon_H95 zenon_H267 zenon_H71 zenon_H1cf zenon_H210 zenon_H130 zenon_H22a zenon_H1a5 zenon_H1fa zenon_H6f zenon_Hc2 zenon_H1e zenon_H1ac zenon_H1a1 zenon_H1ba zenon_H195 zenon_H4a zenon_H208 zenon_Hd5 zenon_H18c zenon_H109 zenon_H7c zenon_H212 zenon_H22 zenon_H1d zenon_H2b zenon_Ha8 zenon_H173 zenon_H1c4 zenon_H54 zenon_H62 zenon_H172 zenon_Hf4 zenon_H1c7 zenon_H10a zenon_Ha1 zenon_H22d zenon_H3f zenon_H284 zenon_H286. % 19.13/19.23 apply (zenon_or_s _ _ zenon_H288); [ zenon_intro zenon_H1b3 | zenon_intro zenon_H11d ]. % 19.13/19.23 apply (zenon_or_s _ _ zenon_H286); [ zenon_intro zenon_H15f | zenon_intro zenon_H60 ]. % 19.13/19.23 apply (zenon_or_s _ _ zenon_H285); [ zenon_intro zenon_H282 | zenon_intro zenon_Hc4 ]. % 19.13/19.23 apply (zenon_L1389_); trivial. % 19.13/19.23 apply (zenon_L60_); trivial. % 19.13/19.23 apply (zenon_L440_); trivial. % 19.13/19.23 apply (zenon_L1391_); trivial. % 19.13/19.23 (* end of lemma zenon_L1392_ *) % 19.13/19.23 assert (zenon_L1393_ : ((~((op (e1) (e3)) = (e3)))\/((op (e1) (e3)) = (e3))) -> ((~((op (e3) (e0)) = (e3)))\/((op (e3) (e3)) = (e0))) -> (~((op (e0) (e3)) = (op (e3) (e3)))) -> ((~((op (e3) (e2)) = (e3)))\/((op (e3) (e3)) = (e2))) -> (~((op (e0) (e0)) = (e0))) -> (((op (e0) (e2)) = (e0))\/(((op (e0) (e2)) = (e1))\/(((op (e0) (e2)) = (e2))\/((op (e0) (e2)) = (e3))))) -> (~((op (e1) (e0)) = (op (e1) (e2)))) -> (~((op (e1) (e2)) = (op (e1) (e3)))) -> (~((op (e0) (e2)) = (op (e1) (e2)))) -> (((op (e1) (e2)) = (e0))\/(((op (e1) (e2)) = (e1))\/(((op (e1) (e2)) = (e2))\/((op (e1) (e2)) = (e3))))) -> (~((op (e0) (e0)) = (op (e0) (e2)))) -> (~((op (e1) (e0)) = (op (e1) (e3)))) -> (((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) (e1)) = (op (e0) (e3)))) -> (~((op (e0) (e1)) = (op (e0) (e2)))) -> (~((op (e0) (e1)) = (op (e2) (e1)))) -> (((op (e0) (e1)) = (e0))\/(((op (e0) (e1)) = (e1))\/(((op (e0) (e1)) = (e2))\/((op (e0) (e1)) = (e3))))) -> (~((e1) = (e2))) -> (((op (e1) (e0)) = (e3))\/(((op (e1) (e1)) = (e3))\/(((op (e1) (e2)) = (e3))\/((op (e1) (e3)) = (e3))))) -> (((op (e3) (e1)) = (e0))\/(((op (e3) (e1)) = (e1))\/(((op (e3) (e1)) = (e2))\/((op (e3) (e1)) = (e3))))) -> (~((op (e3) (e1)) = (op (e3) (e3)))) -> (~((op (e3) (e0)) = (op (e3) (e1)))) -> (~((op (e1) (e0)) = (e3))) -> (((op (e0) (e0)) = (e1))\/(((op (e1) (e0)) = (e1))\/(((op (e2) (e0)) = (e1))\/((op (e3) (e0)) = (e1))))) -> ((op (e0) (e3)) = (e0)) -> (~((op (e0) (e2)) = (op (e0) (e3)))) -> (((op (e0) (e0)) = (e1))\/(((op (e0) (e1)) = (e1))\/(((op (e0) (e2)) = (e1))\/((op (e0) (e3)) = (e1))))) -> (~((e0) = (e1))) -> (~((op (e2) (e0)) = (op (e2) (e2)))) -> (~((op (e0) (e2)) = (op (e2) (e2)))) -> (((op (e2) (e2)) = (e0))\/(((op (e2) (e2)) = (e1))\/(((op (e2) (e2)) = (e2))\/((op (e2) (e2)) = (e3))))) -> (((op (e1) (e0)) = (e0))\/(((op (e1) (e0)) = (e1))\/(((op (e1) (e0)) = (e2))\/((op (e1) (e0)) = (e3))))) -> (~((op (e0) (e1)) = (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 (e1) (e0)) = (op (e2) (e0)))) -> (~((e1) = (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 (e3) (e3)) = (e3))) -> (((op (e3) (e0)) = (e3))\/(((op (e3) (e1)) = (e3))\/(((op (e3) (e2)) = (e3))\/((op (e3) (e3)) = (e3))))) -> (~((op (e1) (e3)) = (op (e3) (e3)))) -> ((~((op (e3) (e1)) = (e3)))\/((op (e3) (e3)) = (e1))) -> ((~((op (e2) (e2)) = (e3)))\/((op (e2) (e3)) = (e2))) -> ((~((op (e1) (e2)) = (e3)))\/((op (e1) (e3)) = (e2))) -> (((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 (e2) (e0)) = (e1)) -> (~((op (e3) (e0)) = (e3))) -> ((op (e3) (e3)) = (e1)) -> (~((op (e3) (e0)) = (op (e3) (e2)))) -> ((op (e2) (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 (e3) (e0)) = (e0))\/(((op (e3) (e1)) = (e0))\/(((op (e3) (e2)) = (e0))\/((op (e3) (e3)) = (e0))))) -> (((op (e1) (e1)) = (e0))\/(((op (e1) (e1)) = (e1))\/(((op (e1) (e1)) = (e2))\/((op (e1) (e1)) = (e3))))) -> ((op (e1) (e0)) = (e0)) -> (~((op (e1) (e0)) = (op (e1) (e1)))) -> (~((op (e1) (e1)) = (e1))) -> (~((op (e0) (e1)) = (op (e1) (e1)))) -> (~((op (e1) (e1)) = (e3))) -> (~((op (e0) (e2)) = (op (e3) (e2)))) -> (((op (e1) (e0)) = (e1))\/(((op (e1) (e1)) = (e1))\/(((op (e1) (e2)) = (e1))\/((op (e1) (e3)) = (e1))))) -> (~((op (e0) (e1)) = (e3))) -> (~((op (e0) (e2)) = (e3))) -> (~((op (e0) (e3)) = (e3))) -> False). % 19.13/19.23 do 0 intro. intros zenon_H289 zenon_H286 zenon_Hc2 zenon_H284 zenon_H3f zenon_H1ba zenon_H24a zenon_H124 zenon_H195 zenon_H19d zenon_H13c zenon_Hd8 zenon_H1d5 zenon_Hf3 zenon_H173 zenon_H54 zenon_H4a zenon_H17e zenon_H212 zenon_H7c zenon_H16f zenon_H22a zenon_H130 zenon_H1cf zenon_H9f zenon_H235 zenon_H1e zenon_H208 zenon_H22d zenon_Ha1 zenon_H52 zenon_Ha8 zenon_H1c4 zenon_H25e zenon_H210 zenon_H71 zenon_H267 zenon_H201 zenon_H95 zenon_H168 zenon_H3e zenon_H102 zenon_H165 zenon_Hd5 zenon_H285 zenon_H288 zenon_H287 zenon_H172 zenon_H153 zenon_Hed zenon_H15f zenon_Hc4 zenon_H6f zenon_H11d zenon_H191 zenon_H1a4 zenon_H62 zenon_H283 zenon_H1ac zenon_H142 zenon_H27 zenon_H45 zenon_H10a zenon_H10e zenon_H1a1 zenon_H14f zenon_H128 zenon_H9c zenon_H123 zenon_H12d. % 19.13/19.23 apply (zenon_or_s _ _ zenon_H168); [ zenon_intro zenon_H3a | zenon_intro zenon_H169 ]. % 19.13/19.23 apply (zenon_L1372_); trivial. % 19.13/19.23 apply (zenon_or_s _ _ zenon_H169); [ zenon_intro zenon_H99 | zenon_intro zenon_H16a ]. % 19.13/19.23 exact (zenon_H9c zenon_H99). % 19.13/19.23 apply (zenon_or_s _ _ zenon_H16a); [ zenon_intro zenon_Ha9 | zenon_intro zenon_He3 ]. % 19.13/19.23 exact (zenon_H123 zenon_Ha9). % 19.13/19.23 exact (zenon_H12d zenon_He3). % 19.13/19.23 (* end of lemma zenon_L1393_ *) % 19.13/19.23 assert (zenon_L1394_ : (((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)) = (e1)) -> ((op (e3) (e2)) = (e2)) -> (~((op (e3) (e0)) = (op (e3) (e2)))) -> (~((op (e3) (e0)) = (e3))) -> False). % 19.13/19.23 do 0 intro. intros zenon_H267 zenon_H1b1 zenon_H1cf zenon_H71 zenon_Hc4 zenon_H151 zenon_H6f zenon_H15f. % 19.13/19.23 apply (zenon_or_s _ _ zenon_H267); [ zenon_intro zenon_H44 | zenon_intro zenon_H268 ]. % 19.13/19.23 apply (zenon_L346_); trivial. % 19.13/19.23 apply (zenon_or_s _ _ zenon_H268); [ zenon_intro zenon_Hac | zenon_intro zenon_H269 ]. % 19.13/19.23 apply (zenon_L189_); trivial. % 19.13/19.23 apply (zenon_or_s _ _ zenon_H269); [ zenon_intro zenon_H148 | zenon_intro zenon_H15e ]. % 19.13/19.23 apply (zenon_L420_); trivial. % 19.13/19.23 exact (zenon_H15f zenon_H15e). % 19.13/19.23 (* end of lemma zenon_L1394_ *) % 19.13/19.23 assert (zenon_L1395_ : (((op (e3) (e2)) = (e0))\/(((op (e3) (e2)) = (e1))\/(((op (e3) (e2)) = (e2))\/((op (e3) (e2)) = (e3))))) -> ((op (e1) (e2)) = (e0)) -> (~((op (e1) (e2)) = (op (e3) (e2)))) -> (~((op (e3) (e2)) = (op (e3) (e3)))) -> ((op (e3) (e3)) = (e1)) -> ((op (e3) (e0)) = (e2)) -> (~((op (e3) (e0)) = (op (e3) (e2)))) -> (~((op (e3) (e2)) = (e3))) -> False). % 19.13/19.23 do 0 intro. intros zenon_H191 zenon_H2a zenon_H115 zenon_H62 zenon_Hc4 zenon_H148 zenon_H6f zenon_H283. % 19.13/19.23 apply (zenon_or_s _ _ zenon_H191); [ zenon_intro zenon_H61 | zenon_intro zenon_H192 ]. % 19.13/19.23 apply (zenon_L176_); trivial. % 19.13/19.23 apply (zenon_or_s _ _ zenon_H192); [ zenon_intro zenon_Hba | zenon_intro zenon_H193 ]. % 19.13/19.23 apply (zenon_L147_); trivial. % 19.13/19.23 apply (zenon_or_s _ _ zenon_H193); [ zenon_intro zenon_H151 | zenon_intro zenon_H163 ]. % 19.13/19.23 apply (zenon_L420_); trivial. % 19.13/19.23 exact (zenon_H283 zenon_H163). % 19.13/19.23 (* end of lemma zenon_L1395_ *) % 19.13/19.23 assert (zenon_L1396_ : (((op (e3) (e0)) = (e0))\/(((op (e3) (e0)) = (e1))\/(((op (e3) (e0)) = (e2))\/((op (e3) (e0)) = (e3))))) -> (~((op (e2) (e0)) = (op (e3) (e0)))) -> ((op (e2) (e0)) = (e0)) -> (~((op (e3) (e0)) = (op (e3) (e3)))) -> ((op (e3) (e3)) = (e1)) -> ((op (e3) (e1)) = (e2)) -> (~((op (e3) (e0)) = (op (e3) (e1)))) -> (~((op (e3) (e0)) = (e3))) -> False). % 19.13/19.23 do 0 intro. intros zenon_H267 zenon_H17b zenon_H34 zenon_H71 zenon_Hc4 zenon_H14d zenon_H1cf zenon_H15f. % 19.13/19.23 apply (zenon_or_s _ _ zenon_H267); [ zenon_intro zenon_H44 | zenon_intro zenon_H268 ]. % 19.13/19.23 apply (zenon_L127_); trivial. % 19.13/19.23 apply (zenon_or_s _ _ zenon_H268); [ zenon_intro zenon_Hac | zenon_intro zenon_H269 ]. % 19.13/19.23 apply (zenon_L189_); trivial. % 19.13/19.23 apply (zenon_or_s _ _ zenon_H269); [ zenon_intro zenon_H148 | zenon_intro zenon_H15e ]. % 19.13/19.23 apply (zenon_L436_); trivial. % 19.13/19.23 exact (zenon_H15f zenon_H15e). % 19.13/19.23 (* end of lemma zenon_L1396_ *) % 19.13/19.23 assert (zenon_L1397_ : (((op (e3) (e0)) = (e2))\/(((op (e3) (e1)) = (e2))\/(((op (e3) (e2)) = (e2))\/((op (e3) (e3)) = (e2))))) -> (~((op (e3) (e2)) = (e3))) -> (~((op (e3) (e2)) = (op (e3) (e3)))) -> (~((op (e1) (e2)) = (op (e3) (e2)))) -> ((op (e1) (e2)) = (e0)) -> (((op (e3) (e2)) = (e0))\/(((op (e3) (e2)) = (e1))\/(((op (e3) (e2)) = (e2))\/((op (e3) (e2)) = (e3))))) -> ((op (e2) (e0)) = (e0)) -> (~((op (e2) (e0)) = (op (e3) (e0)))) -> (~((op (e3) (e0)) = (e3))) -> (~((op (e3) (e0)) = (op (e3) (e2)))) -> ((op (e3) (e3)) = (e1)) -> (~((op (e3) (e0)) = (op (e3) (e3)))) -> (~((op (e3) (e0)) = (op (e3) (e1)))) -> ((op (e3) (e1)) = (e0)) -> (((op (e3) (e0)) = (e0))\/(((op (e3) (e0)) = (e1))\/(((op (e3) (e0)) = (e2))\/((op (e3) (e0)) = (e3))))) -> (~((op (e2) (e3)) = (op (e3) (e3)))) -> ((op (e2) (e3)) = (e2)) -> False). % 19.13/19.23 do 0 intro. intros zenon_H153 zenon_H283 zenon_H62 zenon_H115 zenon_H2a zenon_H191 zenon_H34 zenon_H17b zenon_H15f zenon_H6f zenon_Hc4 zenon_H71 zenon_H1cf zenon_H1b1 zenon_H267 zenon_Hf3 zenon_H11d. % 19.13/19.23 apply (zenon_or_s _ _ zenon_H153); [ zenon_intro zenon_H148 | zenon_intro zenon_H154 ]. % 19.13/19.23 apply (zenon_L1395_); trivial. % 19.13/19.23 apply (zenon_or_s _ _ zenon_H154); [ zenon_intro zenon_H14d | zenon_intro zenon_H155 ]. % 19.13/19.23 apply (zenon_L1396_); trivial. % 19.13/19.23 apply (zenon_or_s _ _ zenon_H155); [ zenon_intro zenon_H151 | zenon_intro zenon_Hf6 ]. % 19.13/19.23 apply (zenon_L1394_); trivial. % 19.13/19.23 apply (zenon_L97_); trivial. % 19.13/19.23 (* end of lemma zenon_L1397_ *) % 19.13/19.23 assert (zenon_L1398_ : (((op (e2) (e0)) = (e3))\/(((op (e2) (e1)) = (e3))\/(((op (e2) (e2)) = (e3))\/((op (e2) (e3)) = (e3))))) -> (~((op (e2) (e0)) = (e3))) -> (~((op (e2) (e1)) = (e3))) -> ((op (e0) (e3)) = (e0)) -> (~((op (e0) (e3)) = (op (e3) (e3)))) -> ((op (e0) (e2)) = (e1)) -> (((op (e3) (e0)) = (e2))\/(((op (e3) (e1)) = (e2))\/(((op (e3) (e2)) = (e2))\/((op (e3) (e3)) = (e2))))) -> (~((op (e3) (e2)) = (e3))) -> (~((op (e3) (e2)) = (op (e3) (e3)))) -> (~((op (e1) (e2)) = (op (e3) (e2)))) -> ((op (e1) (e2)) = (e0)) -> (((op (e3) (e2)) = (e0))\/(((op (e3) (e2)) = (e1))\/(((op (e3) (e2)) = (e2))\/((op (e3) (e2)) = (e3))))) -> ((op (e2) (e0)) = (e0)) -> (~((op (e2) (e0)) = (op (e3) (e0)))) -> (~((op (e3) (e0)) = (e3))) -> (~((op (e3) (e0)) = (op (e3) (e2)))) -> ((op (e3) (e3)) = (e1)) -> (~((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 (e2) (e3)) = (e2)) -> (((op (e3) (e0)) = (e0))\/(((op (e3) (e1)) = (e0))\/(((op (e3) (e2)) = (e0))\/((op (e3) (e3)) = (e0))))) -> (~((op (e2) (e3)) = (e3))) -> False). % 19.13/19.23 do 0 intro. intros zenon_He7 zenon_H27f zenon_Ha7 zenon_H1e zenon_Hc2 zenon_H122 zenon_H153 zenon_H283 zenon_H62 zenon_H115 zenon_H2a zenon_H191 zenon_H34 zenon_H17b zenon_H15f zenon_H6f zenon_Hc4 zenon_H71 zenon_H1cf zenon_H267 zenon_Hf3 zenon_H11d zenon_H1ac zenon_H280. % 19.13/19.23 apply (zenon_or_s _ _ zenon_He7); [ zenon_intro zenon_H3b | zenon_intro zenon_He9 ]. % 19.13/19.23 exact (zenon_H27f zenon_H3b). % 19.13/19.23 apply (zenon_or_s _ _ zenon_He9); [ zenon_intro zenon_Ha6 | zenon_intro zenon_Hea ]. % 19.13/19.23 exact (zenon_Ha7 zenon_Ha6). % 19.13/19.23 apply (zenon_or_s _ _ zenon_Hea); [ zenon_intro zenon_Haa | zenon_intro zenon_Hdd ]. % 19.13/19.23 apply (zenon_or_s _ _ zenon_H1ac); [ zenon_intro zenon_H44 | zenon_intro zenon_H1af ]. % 19.13/19.23 apply (zenon_L127_); trivial. % 19.13/19.23 apply (zenon_or_s _ _ zenon_H1af); [ zenon_intro zenon_H1b1 | zenon_intro zenon_H1b0 ]. % 19.13/19.23 apply (zenon_L1397_); trivial. % 19.13/19.23 apply (zenon_or_s _ _ zenon_H1b0); [ zenon_intro zenon_H61 | zenon_intro zenon_H60 ]. % 19.13/19.23 apply (zenon_L432_); trivial. % 19.13/19.23 apply (zenon_L440_); trivial. % 19.13/19.23 exact (zenon_H280 zenon_Hdd). % 19.13/19.23 (* end of lemma zenon_L1398_ *) % 19.13/19.23 assert (zenon_L1399_ : (((op (e2) (e0)) = (e3))\/(((op (e2) (e1)) = (e3))\/(((op (e2) (e2)) = (e3))\/((op (e2) (e3)) = (e3))))) -> (~((op (e2) (e0)) = (e3))) -> (~((op (e2) (e1)) = (e3))) -> ((op (e3) (e2)) = (e0)) -> ((op (e0) (e2)) = (e1)) -> (~((op (e2) (e3)) = (e3))) -> False). % 19.13/19.23 do 0 intro. intros zenon_He7 zenon_H27f zenon_Ha7 zenon_H61 zenon_H122 zenon_H280. % 19.13/19.23 apply (zenon_or_s _ _ zenon_He7); [ zenon_intro zenon_H3b | zenon_intro zenon_He9 ]. % 19.13/19.23 exact (zenon_H27f zenon_H3b). % 19.13/19.23 apply (zenon_or_s _ _ zenon_He9); [ zenon_intro zenon_Ha6 | zenon_intro zenon_Hea ]. % 19.13/19.23 exact (zenon_Ha7 zenon_Ha6). % 19.13/19.23 apply (zenon_or_s _ _ zenon_Hea); [ zenon_intro zenon_Haa | zenon_intro zenon_Hdd ]. % 19.13/19.23 apply (zenon_L432_); trivial. % 19.13/19.23 exact (zenon_H280 zenon_Hdd). % 19.13/19.23 (* end of lemma zenon_L1399_ *) % 19.13/19.23 assert (zenon_L1400_ : (((op (e0) (e2)) = (e2))\/(((op (e1) (e2)) = (e2))\/(((op (e2) (e2)) = (e2))\/((op (e3) (e2)) = (e2))))) -> (~((op (e3) (e2)) = (e3))) -> ((op (e3) (e3)) = (e1)) -> (~((op (e3) (e2)) = (op (e3) (e3)))) -> (~((op (e3) (e0)) = (op (e3) (e2)))) -> ((op (e3) (e0)) = (e0)) -> (((op (e3) (e2)) = (e0))\/(((op (e3) (e2)) = (e1))\/(((op (e3) (e2)) = (e2))\/((op (e3) (e2)) = (e3))))) -> ((op (e0) (e1)) = (e1)) -> (~((op (e0) (e1)) = (op (e0) (e2)))) -> (~((op (e2) (e2)) = (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) (e3)) = (e0)) -> ((op (e1) (e2)) = (e1)) -> (~((op (e0) (e2)) = (op (e1) (e2)))) -> (~((op (e0) (e2)) = (op (e3) (e2)))) -> (~((op (e0) (e2)) = (e3))) -> False). % 19.13/19.23 do 0 intro. intros zenon_H172 zenon_H283 zenon_Hc4 zenon_H62 zenon_H6f zenon_H44 zenon_H191 zenon_Ha0 zenon_H4a zenon_H173 zenon_H1ba zenon_H208 zenon_H1e zenon_Hf0 zenon_H195 zenon_H14f zenon_H123. % 19.13/19.23 apply (zenon_or_s _ _ zenon_H172); [ zenon_intro zenon_H150 | zenon_intro zenon_H174 ]. % 19.13/19.23 apply (zenon_L1351_); trivial. % 19.13/19.23 apply (zenon_or_s _ _ zenon_H174); [ zenon_intro zenon_H113 | zenon_intro zenon_H175 ]. % 19.13/19.23 apply (zenon_L1357_); trivial. % 19.13/19.23 apply (zenon_or_s _ _ zenon_H175); [ zenon_intro zenon_H176 | zenon_intro zenon_H151 ]. % 19.13/19.23 exact (zenon_H173 zenon_H176). % 19.13/19.23 apply (zenon_L1352_); trivial. % 19.13/19.23 (* end of lemma zenon_L1400_ *) % 19.13/19.23 assert (zenon_L1401_ : (((op (e0) (e0)) = (e1))\/(((op (e1) (e0)) = (e1))\/(((op (e2) (e0)) = (e1))\/((op (e3) (e0)) = (e1))))) -> (~((op (e0) (e0)) = (op (e0) (e2)))) -> (~((op (e2) (e0)) = (e3))) -> ((op (e2) (e3)) = (e2)) -> (~((op (e2) (e0)) = (op (e2) (e3)))) -> ((op (e3) (e0)) = (e0)) -> (~((op (e2) (e0)) = (op (e3) (e0)))) -> (((op (e2) (e0)) = (e0))\/(((op (e2) (e0)) = (e1))\/(((op (e2) (e0)) = (e2))\/((op (e2) (e0)) = (e3))))) -> (~((op (e1) (e3)) = (op (e3) (e3)))) -> (~((op (e0) (e2)) = (op (e1) (e2)))) -> ((op (e0) (e2)) = (e1)) -> (~((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))))) -> ((op (e3) (e3)) = (e1)) -> (~((op (e3) (e0)) = (op (e3) (e3)))) -> False). % 19.13/19.23 do 0 intro. intros zenon_H235 zenon_H13c zenon_H27f zenon_H11d zenon_H5b zenon_H44 zenon_H17b zenon_H259 zenon_Hd5 zenon_H195 zenon_H122 zenon_H10a zenon_H201 zenon_H128 zenon_Hc4 zenon_H71. % 19.13/19.23 apply (zenon_or_s _ _ zenon_H235); [ zenon_intro zenon_H7a | zenon_intro zenon_H236 ]. % 19.13/19.23 apply (zenon_L92_); trivial. % 19.13/19.23 apply (zenon_or_s _ _ zenon_H236); [ zenon_intro zenon_H9d | zenon_intro zenon_H237 ]. % 19.13/19.23 apply (zenon_L1373_); trivial. % 19.13/19.23 apply (zenon_or_s _ _ zenon_H237); [ zenon_intro zenon_Hed | zenon_intro zenon_Hac ]. % 19.13/19.23 apply (zenon_L531_); trivial. % 19.13/19.23 apply (zenon_L189_); trivial. % 19.13/19.23 (* end of lemma zenon_L1401_ *) % 19.13/19.23 assert (zenon_L1402_ : (((op (e0) (e0)) = (e1))\/(((op (e0) (e1)) = (e1))\/(((op (e0) (e2)) = (e1))\/((op (e0) (e3)) = (e1))))) -> (~((op (e0) (e3)) = (e3))) -> (~((op (e0) (e1)) = (e3))) -> (~((e1) = (e3))) -> (((op (e0) (e0)) = (e3))\/(((op (e0) (e1)) = (e3))\/(((op (e0) (e2)) = (e3))\/((op (e0) (e3)) = (e3))))) -> (((op (e0) (e2)) = (e2))\/(((op (e1) (e2)) = (e2))\/(((op (e2) (e2)) = (e2))\/((op (e3) (e2)) = (e2))))) -> (~((op (e3) (e2)) = (e3))) -> (~((op (e3) (e2)) = (op (e3) (e3)))) -> (~((op (e3) (e0)) = (op (e3) (e2)))) -> (((op (e3) (e2)) = (e0))\/(((op (e3) (e2)) = (e1))\/(((op (e3) (e2)) = (e2))\/((op (e3) (e2)) = (e3))))) -> (~((op (e0) (e1)) = (op (e0) (e2)))) -> (~((op (e2) (e2)) = (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 (e0) (e2)) = (e3))) -> (~((op (e3) (e0)) = (op (e3) (e3)))) -> ((op (e3) (e3)) = (e1)) -> (((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 (e0) (e2)) = (op (e1) (e2)))) -> (~((op (e1) (e3)) = (op (e3) (e3)))) -> (((op (e2) (e0)) = (e0))\/(((op (e2) (e0)) = (e1))\/(((op (e2) (e0)) = (e2))\/((op (e2) (e0)) = (e3))))) -> (~((op (e2) (e0)) = (op (e3) (e0)))) -> ((op (e3) (e0)) = (e0)) -> (~((op (e2) (e0)) = (op (e2) (e3)))) -> ((op (e2) (e3)) = (e2)) -> (~((op (e2) (e0)) = (e3))) -> (~((op (e0) (e0)) = (op (e0) (e2)))) -> (((op (e0) (e0)) = (e1))\/(((op (e1) (e0)) = (e1))\/(((op (e2) (e0)) = (e1))\/((op (e3) (e0)) = (e1))))) -> ((op (e0) (e3)) = (e0)) -> (~((e0) = (e1))) -> False). % 19.13/19.23 do 0 intro. intros zenon_H22d zenon_H12d zenon_H9c zenon_H95 zenon_H168 zenon_H172 zenon_H283 zenon_H62 zenon_H6f zenon_H191 zenon_H4a zenon_H173 zenon_H1ba zenon_H208 zenon_H14f zenon_H123 zenon_H71 zenon_Hc4 zenon_H128 zenon_H201 zenon_H10a zenon_H195 zenon_Hd5 zenon_H259 zenon_H17b zenon_H44 zenon_H5b zenon_H11d zenon_H27f zenon_H13c zenon_H235 zenon_H1e zenon_Ha1. % 19.13/19.23 apply (zenon_or_s _ _ zenon_H22d); [ zenon_intro zenon_H7a | zenon_intro zenon_H22e ]. % 19.13/19.23 apply (zenon_L1350_); trivial. % 19.13/19.23 apply (zenon_or_s _ _ zenon_H22e); [ zenon_intro zenon_Ha0 | zenon_intro zenon_H22f ]. % 19.13/19.23 apply (zenon_or_s _ _ zenon_H128); [ zenon_intro zenon_H9d | zenon_intro zenon_H129 ]. % 19.13/19.23 apply (zenon_L1373_); trivial. % 19.13/19.23 apply (zenon_or_s _ _ zenon_H129); [ zenon_intro zenon_H10d | zenon_intro zenon_H12a ]. % 19.13/19.23 exact (zenon_H10a zenon_H10d). % 19.13/19.23 apply (zenon_or_s _ _ zenon_H12a); [ zenon_intro zenon_Hf0 | zenon_intro zenon_Hd6 ]. % 19.13/19.23 apply (zenon_L1400_); trivial. % 19.13/19.23 apply (zenon_L50_); trivial. % 19.13/19.23 apply (zenon_or_s _ _ zenon_H22f); [ zenon_intro zenon_H122 | zenon_intro zenon_Hc3 ]. % 19.13/19.23 apply (zenon_L1401_); trivial. % 19.13/19.23 apply (zenon_L427_); trivial. % 19.13/19.23 (* end of lemma zenon_L1402_ *) % 19.13/19.23 assert (zenon_L1403_ : (~((op (e0) (e0)) = (e0))) -> (((op (e2) (e0)) = (e3))\/(((op (e2) (e1)) = (e3))\/(((op (e2) (e2)) = (e3))\/((op (e2) (e3)) = (e3))))) -> (~((op (e2) (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))))) -> (~((op (e1) (e2)) = (op (e3) (e2)))) -> (~((op (e2) (e0)) = (op (e2) (e1)))) -> (~((op (e2) (e1)) = (op (e2) (e3)))) -> (~((op (e2) (e1)) = (e3))) -> (((op (e2) (e1)) = (e0))\/(((op (e2) (e1)) = (e1))\/(((op (e2) (e1)) = (e2))\/((op (e2) (e1)) = (e3))))) -> (~((op (e1) (e2)) = (op (e2) (e2)))) -> (~((op (e1) (e2)) = (e3))) -> (~((op (e2) (e0)) = (op (e3) (e0)))) -> (~((op (e2) (e0)) = (op (e2) (e3)))) -> (~((op (e2) (e0)) = (e3))) -> (((op (e2) (e0)) = (e0))\/(((op (e2) (e0)) = (e1))\/(((op (e2) (e0)) = (e2))\/((op (e2) (e0)) = (e3))))) -> (~((op (e1) (e0)) = (op (e2) (e0)))) -> (~((op (e1) (e1)) = (e1))) -> (((op (e0) (e2)) = (e2))\/(((op (e1) (e2)) = (e2))\/(((op (e2) (e2)) = (e2))\/((op (e3) (e2)) = (e2))))) -> (~((op (e2) (e2)) = (e2))) -> (~((op (e0) (e1)) = (op (e0) (e3)))) -> (~((op (e0) (e1)) = (op (e0) (e2)))) -> (((op (e1) (e1)) = (e0))\/(((op (e1) (e1)) = (e1))\/(((op (e1) (e1)) = (e2))\/((op (e1) (e1)) = (e3))))) -> (~((op (e1) (e1)) = (e3))) -> (~((op (e0) (e1)) = (op (e1) (e1)))) -> (~((op (e1) (e0)) = (op (e1) (e1)))) -> (((op (e0) (e1)) = (e0))\/(((op (e0) (e1)) = (e1))\/(((op (e0) (e1)) = (e2))\/((op (e0) (e1)) = (e3))))) -> (((op (e3) (e2)) = (e0))\/(((op (e3) (e2)) = (e1))\/(((op (e3) (e2)) = (e2))\/((op (e3) (e2)) = (e3))))) -> (~((op (e0) (e2)) = (op (e3) (e2)))) -> ((op (e3) (e3)) = (e1)) -> (~((op (e3) (e2)) = (op (e3) (e3)))) -> (~((op (e3) (e0)) = (op (e3) (e2)))) -> (~((op (e0) (e2)) = (op (e1) (e2)))) -> (((op (e0) (e2)) = (e0))\/(((op (e0) (e2)) = (e1))\/(((op (e0) (e2)) = (e2))\/((op (e0) (e2)) = (e3))))) -> (~((op (e3) (e1)) = (op (e3) (e2)))) -> (((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 (e3) (e0)) = (op (e3) (e3)))) -> (~((op (e3) (e0)) = (op (e3) (e1)))) -> (~((op (e3) (e0)) = (e3))) -> (((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 (e1) (e2)) = (e3)))\/((op (e1) (e3)) = (e2))) -> ((~((op (e2) (e2)) = (e3)))\/((op (e2) (e3)) = (e2))) -> ((~((op (e3) (e1)) = (e3)))\/((op (e3) (e3)) = (e1))) -> (~((op (e1) (e3)) = (op (e3) (e3)))) -> (((op (e3) (e0)) = (e3))\/(((op (e3) (e1)) = (e3))\/(((op (e3) (e2)) = (e3))\/((op (e3) (e3)) = (e3))))) -> (~((op (e3) (e3)) = (e3))) -> (((op (e0) (e0)) = (e0))\/(((op (e1) (e0)) = (e0))\/(((op (e2) (e0)) = (e0))\/((op (e3) (e0)) = (e0))))) -> (~((op (e0) (e1)) = (op (e3) (e1)))) -> (((op (e1) (e0)) = (e0))\/(((op (e1) (e0)) = (e1))\/(((op (e1) (e0)) = (e2))\/((op (e1) (e0)) = (e3))))) -> (((op (e2) (e2)) = (e0))\/(((op (e2) (e2)) = (e1))\/(((op (e2) (e2)) = (e2))\/((op (e2) (e2)) = (e3))))) -> (~((op (e0) (e2)) = (op (e2) (e2)))) -> (~((op (e2) (e0)) = (op (e2) (e2)))) -> (~((e0) = (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))))) -> (~((op (e1) (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 (e1) (e0)) = (e3))\/(((op (e1) (e1)) = (e3))\/(((op (e1) (e2)) = (e3))\/((op (e1) (e3)) = (e3))))) -> (~((e1) = (e2))) -> (~((op (e0) (e1)) = (op (e2) (e1)))) -> (((op (e2) (e0)) = (e2))\/(((op (e2) (e1)) = (e2))\/(((op (e2) (e2)) = (e2))\/((op (e2) (e3)) = (e2))))) -> (~((op (e1) (e0)) = (op (e1) (e3)))) -> (~((op (e0) (e0)) = (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 (e3) (e2)) = (e3)))\/((op (e3) (e3)) = (e2))) -> ((~((op (e3) (e0)) = (e3)))\/((op (e3) (e3)) = (e0))) -> ((~((op (e1) (e3)) = (e3)))\/((op (e1) (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)) = (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 (e1) (e0)) = (e2))\/(((op (e1) (e1)) = (e2))\/(((op (e1) (e2)) = (e2))\/((op (e1) (e3)) = (e2))))) -> (~((op (e1) (e0)) = (op (e3) (e0)))) -> (((op (e0) (e1)) = (e3))\/(((op (e1) (e1)) = (e3))\/(((op (e2) (e1)) = (e3))\/((op (e3) (e1)) = (e3))))) -> (~((op (e2) (e2)) = (op (e2) (e3)))) -> (((op (e0) (e2)) = (e0))\/(((op (e1) (e2)) = (e0))\/(((op (e2) (e2)) = (e0))\/((op (e3) (e2)) = (e0))))) -> (~((e1) = (e3))) -> (~((op (e0) (e1)) = (e3))) -> (~((op (e0) (e2)) = (e3))) -> (~((op (e0) (e3)) = (e3))) -> (((op (e0) (e0)) = (e3))\/(((op (e0) (e1)) = (e3))\/(((op (e0) (e2)) = (e3))\/((op (e0) (e3)) = (e3))))) -> False). % 19.13/19.23 do 0 intro. intros zenon_H3f zenon_He7 zenon_H280 zenon_H208 zenon_H1e zenon_H24a zenon_H106 zenon_H115 zenon_H1f0 zenon_H1c7 zenon_Ha7 zenon_H1cc zenon_H2b zenon_H16d zenon_H17b zenon_H5b zenon_H27f zenon_H259 zenon_H201 zenon_H10a zenon_H172 zenon_H173 zenon_H54 zenon_H4a zenon_H142 zenon_H1a1 zenon_H10e zenon_H45 zenon_H212 zenon_H191 zenon_H14f zenon_Hc4 zenon_H62 zenon_H6f zenon_H195 zenon_H1ba zenon_H1a4 zenon_H153 zenon_H11d zenon_Hf3 zenon_H71 zenon_H1cf zenon_H15f zenon_H267 zenon_Hc2 zenon_H1ac zenon_H287 zenon_H288 zenon_H285 zenon_Hd5 zenon_H165 zenon_H102 zenon_H3e zenon_H210 zenon_H25e zenon_H1c4 zenon_Ha8 zenon_H52 zenon_Ha1 zenon_H22d zenon_H235 zenon_H9f zenon_H130 zenon_H22a zenon_H16f zenon_H7c zenon_H17e zenon_H1d5 zenon_Hd8 zenon_H13c zenon_H19d zenon_H124 zenon_H284 zenon_H286 zenon_H289 zenon_H128 zenon_H1d zenon_H22 zenon_H109 zenon_H18c zenon_H1fa zenon_H1a5 zenon_H6d zenon_H6a zenon_H95 zenon_H9c zenon_H123 zenon_H12d zenon_H168. % 19.13/19.23 apply (zenon_or_s _ _ zenon_H284); [ zenon_intro zenon_H283 | zenon_intro zenon_Hf6 ]. % 19.13/19.23 apply (zenon_or_s _ _ zenon_H3e); [ zenon_intro zenon_H42 | zenon_intro zenon_H41 ]. % 19.13/19.23 exact (zenon_H3f zenon_H42). % 19.13/19.23 apply (zenon_or_s _ _ zenon_H41); [ zenon_intro zenon_H27 | zenon_intro zenon_H43 ]. % 19.13/19.23 apply (zenon_or_s _ _ zenon_H22d); [ zenon_intro zenon_H7a | zenon_intro zenon_H22e ]. % 19.13/19.23 apply (zenon_L1350_); trivial. % 19.13/19.23 apply (zenon_or_s _ _ zenon_H22e); [ zenon_intro zenon_Ha0 | zenon_intro zenon_H22f ]. % 19.13/19.23 apply (zenon_or_s _ _ zenon_H235); [ zenon_intro zenon_H7a | zenon_intro zenon_H236 ]. % 19.13/19.23 apply (zenon_L1350_); trivial. % 19.13/19.23 apply (zenon_or_s _ _ zenon_H236); [ zenon_intro zenon_H9d | zenon_intro zenon_H237 ]. % 19.13/19.23 apply (zenon_or_s _ _ zenon_H168); [ zenon_intro zenon_H3a | zenon_intro zenon_H169 ]. % 19.13/19.23 apply (zenon_or_s _ _ zenon_H6a); [ zenon_intro zenon_H48 | zenon_intro zenon_H6b ]. % 19.13/19.23 apply (zenon_L336_); trivial. % 19.13/19.23 apply (zenon_or_s _ _ zenon_H6b); [ zenon_intro zenon_H2a | zenon_intro zenon_H6c ]. % 19.13/19.23 apply (zenon_L644_); trivial. % 19.13/19.23 apply (zenon_or_s _ _ zenon_H6c); [ zenon_intro zenon_H2c | zenon_intro zenon_H61 ]. % 19.13/19.23 apply (zenon_or_s _ _ zenon_H106); [ zenon_intro zenon_Hed | zenon_intro zenon_H107 ]. % 19.13/19.23 apply (zenon_L1372_); trivial. % 19.13/19.23 apply (zenon_or_s _ _ zenon_H107); [ zenon_intro zenon_Ha5 | zenon_intro zenon_H108 ]. % 19.13/19.23 apply (zenon_L357_); trivial. % 19.13/19.23 apply (zenon_or_s _ _ zenon_H108); [ zenon_intro zenon_Hf1 | zenon_intro zenon_Hf4 ]. % 19.13/19.23 apply (zenon_or_s _ _ zenon_H172); [ zenon_intro zenon_H150 | zenon_intro zenon_H174 ]. % 19.13/19.23 apply (zenon_L1378_); trivial. % 19.13/19.23 apply (zenon_or_s _ _ zenon_H174); [ zenon_intro zenon_H113 | zenon_intro zenon_H175 ]. % 19.13/19.23 apply (zenon_L1359_); trivial. % 19.13/19.23 apply (zenon_or_s _ _ zenon_H175); [ zenon_intro zenon_H176 | zenon_intro zenon_H151 ]. % 19.13/19.23 exact (zenon_H173 zenon_H176). % 19.13/19.23 apply (zenon_L1379_); trivial. % 19.13/19.23 apply (zenon_L60_); trivial. % 19.13/19.23 apply (zenon_or_s _ _ zenon_H106); [ zenon_intro zenon_Hed | zenon_intro zenon_H107 ]. % 19.13/19.23 apply (zenon_L413_); trivial. % 19.13/19.23 apply (zenon_or_s _ _ zenon_H107); [ zenon_intro zenon_Ha5 | zenon_intro zenon_H108 ]. % 19.13/19.23 apply (zenon_L357_); trivial. % 19.13/19.23 apply (zenon_or_s _ _ zenon_H108); [ zenon_intro zenon_Hf1 | zenon_intro zenon_Hf4 ]. % 19.13/19.23 apply (zenon_or_s _ _ zenon_H172); [ zenon_intro zenon_H150 | zenon_intro zenon_H174 ]. % 19.13/19.23 apply (zenon_L1377_); trivial. % 19.13/19.23 apply (zenon_or_s _ _ zenon_H174); [ zenon_intro zenon_H113 | zenon_intro zenon_H175 ]. % 19.13/19.23 apply (zenon_L1374_); trivial. % 19.13/19.23 apply (zenon_or_s _ _ zenon_H175); [ zenon_intro zenon_H176 | zenon_intro zenon_H151 ]. % 19.13/19.23 exact (zenon_H173 zenon_H176). % 19.13/19.23 apply (zenon_L1379_); trivial. % 19.13/19.23 apply (zenon_L1392_); trivial. % 19.13/19.23 apply (zenon_or_s _ _ zenon_H169); [ zenon_intro zenon_H99 | zenon_intro zenon_H16a ]. % 19.13/19.23 exact (zenon_H9c zenon_H99). % 19.13/19.23 apply (zenon_or_s _ _ zenon_H16a); [ zenon_intro zenon_Ha9 | zenon_intro zenon_He3 ]. % 19.13/19.23 exact (zenon_H123 zenon_Ha9). % 19.13/19.23 exact (zenon_H12d zenon_He3). % 19.13/19.23 apply (zenon_or_s _ _ zenon_H237); [ zenon_intro zenon_Hed | zenon_intro zenon_Hac ]. % 19.13/19.23 apply (zenon_L1393_); trivial. % 19.13/19.23 apply (zenon_L189_); trivial. % 19.13/19.23 apply (zenon_or_s _ _ zenon_H22f); [ zenon_intro zenon_H122 | zenon_intro zenon_Hc3 ]. % 19.13/19.23 apply (zenon_or_s _ _ zenon_H172); [ zenon_intro zenon_H150 | zenon_intro zenon_H174 ]. % 19.13/19.23 apply (zenon_L328_); trivial. % 19.13/19.23 apply (zenon_or_s _ _ zenon_H174); [ zenon_intro zenon_H113 | zenon_intro zenon_H175 ]. % 19.13/19.23 apply (zenon_L1359_); trivial. % 19.13/19.23 apply (zenon_or_s _ _ zenon_H175); [ zenon_intro zenon_H176 | zenon_intro zenon_H151 ]. % 19.13/19.23 exact (zenon_H173 zenon_H176). % 19.13/19.23 apply (zenon_or_s _ _ zenon_He7); [ zenon_intro zenon_H3b | zenon_intro zenon_He9 ]. % 19.13/19.23 exact (zenon_H27f zenon_H3b). % 19.13/19.23 apply (zenon_or_s _ _ zenon_He9); [ zenon_intro zenon_Ha6 | zenon_intro zenon_Hea ]. % 19.13/19.23 exact (zenon_Ha7 zenon_Ha6). % 19.13/19.23 apply (zenon_or_s _ _ zenon_Hea); [ zenon_intro zenon_Haa | zenon_intro zenon_Hdd ]. % 19.13/19.23 apply (zenon_or_s _ _ zenon_H1ac); [ zenon_intro zenon_H44 | zenon_intro zenon_H1af ]. % 19.13/19.23 apply (zenon_L312_); trivial. % 19.13/19.23 apply (zenon_or_s _ _ zenon_H1af); [ zenon_intro zenon_H1b1 | zenon_intro zenon_H1b0 ]. % 19.13/19.23 apply (zenon_L1394_); trivial. % 19.13/19.23 apply (zenon_or_s _ _ zenon_H1b0); [ zenon_intro zenon_H61 | zenon_intro zenon_H60 ]. % 19.13/19.23 apply (zenon_L432_); trivial. % 19.13/19.23 apply (zenon_L440_); trivial. % 19.13/19.23 exact (zenon_H280 zenon_Hdd). % 19.13/19.23 apply (zenon_L427_); trivial. % 19.13/19.23 apply (zenon_or_s _ _ zenon_H43); [ zenon_intro zenon_H34 | zenon_intro zenon_H44 ]. % 19.13/19.23 apply (zenon_or_s _ _ zenon_H22d); [ zenon_intro zenon_H7a | zenon_intro zenon_H22e ]. % 19.13/19.23 apply (zenon_L1350_); trivial. % 19.13/19.23 apply (zenon_or_s _ _ zenon_H22e); [ zenon_intro zenon_Ha0 | zenon_intro zenon_H22f ]. % 19.13/19.23 apply (zenon_L1376_); trivial. % 19.13/19.23 apply (zenon_or_s _ _ zenon_H22f); [ zenon_intro zenon_H122 | zenon_intro zenon_Hc3 ]. % 19.13/19.23 apply (zenon_or_s _ _ zenon_H6a); [ zenon_intro zenon_H48 | zenon_intro zenon_H6b ]. % 19.13/19.23 apply (zenon_L336_); trivial. % 19.13/19.23 apply (zenon_or_s _ _ zenon_H6b); [ zenon_intro zenon_H2a | zenon_intro zenon_H6c ]. % 19.13/19.23 apply (zenon_L1398_); trivial. % 19.13/19.23 apply (zenon_or_s _ _ zenon_H6c); [ zenon_intro zenon_H2c | zenon_intro zenon_H61 ]. % 19.13/19.23 apply (zenon_L11_); trivial. % 19.13/19.23 apply (zenon_L1399_); trivial. % 19.13/19.23 apply (zenon_L427_); trivial. % 19.13/19.23 apply (zenon_L1402_); trivial. % 19.13/19.23 apply (zenon_L97_); trivial. % 19.13/19.23 (* end of lemma zenon_L1403_ *) % 19.13/19.23 assert (zenon_L1404_ : (((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)) = (e3))) -> (~((op (e0) (e3)) = (e3))) -> False). % 19.13/19.23 do 0 intro. intros zenon_H168 zenon_H98 zenon_H12b zenon_H10f zenon_H123 zenon_H12d. % 19.13/19.23 apply (zenon_or_s _ _ zenon_H168); [ zenon_intro zenon_H3a | zenon_intro zenon_H169 ]. % 19.13/19.23 exact (zenon_H98 zenon_H3a). % 19.13/19.23 apply (zenon_or_s _ _ zenon_H169); [ zenon_intro zenon_H99 | zenon_intro zenon_H16a ]. % 19.13/19.23 apply (zenon_L175_); trivial. % 19.13/19.23 apply (zenon_or_s _ _ zenon_H16a); [ zenon_intro zenon_Ha9 | zenon_intro zenon_He3 ]. % 19.13/19.23 exact (zenon_H123 zenon_Ha9). % 19.13/19.23 exact (zenon_H12d zenon_He3). % 19.13/19.23 (* end of lemma zenon_L1404_ *) % 19.13/19.23 assert (zenon_L1405_ : (((op (e0) (e1)) = (e2))\/(((op (e1) (e1)) = (e2))\/(((op (e2) (e1)) = (e2))\/((op (e3) (e1)) = (e2))))) -> (~((op (e0) (e3)) = (e3))) -> (~((op (e0) (e2)) = (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 (e2) (e1)) = (op (e2) (e3)))) -> ((op (e2) (e3)) = (e2)) -> ((op (e0) (e1)) = (e3)) -> ((op (e1) (e1)) = (e0)) -> False). % 19.13/19.23 do 0 intro. intros zenon_H1d8 zenon_H12d zenon_H123 zenon_H12b zenon_H98 zenon_H168 zenon_H149 zenon_H1c7 zenon_H11d zenon_H99 zenon_H29. % 19.13/19.23 apply (zenon_or_s _ _ zenon_H1d8); [ zenon_intro zenon_H10f | zenon_intro zenon_H1d9 ]. % 19.13/19.23 apply (zenon_L1404_); trivial. % 19.13/19.23 apply (zenon_or_s _ _ zenon_H1d9); [ zenon_intro zenon_H110 | zenon_intro zenon_H1da ]. % 19.13/19.23 apply (zenon_L354_); trivial. % 19.13/19.23 apply (zenon_or_s _ _ zenon_H1da); [ zenon_intro zenon_H1ca | zenon_intro zenon_H14d ]. % 19.13/19.23 apply (zenon_L224_); trivial. % 19.13/19.23 apply (zenon_L385_); trivial. % 19.13/19.23 (* end of lemma zenon_L1405_ *) % 19.13/19.23 assert (zenon_L1406_ : (~((op (e3) (e1)) = (op (e3) (e3)))) -> ((op (e3) (e3)) = (e0)) -> (((op (e1) (e1)) = (e0))\/(((op (e1) (e1)) = (e1))\/(((op (e1) (e1)) = (e2))\/((op (e1) (e1)) = (e3))))) -> ((op (e2) (e3)) = (e2)) -> (~((op (e2) (e1)) = (op (e2) (e3)))) -> (~((e0) = (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) (e1)) = (e2))\/(((op (e1) (e1)) = (e2))\/(((op (e2) (e1)) = (e2))\/((op (e3) (e1)) = (e2))))) -> (~((op (e1) (e1)) = (e1))) -> (~((op (e1) (e1)) = (e3))) -> (~((e0) = (e3))) -> (((op (e0) (e1)) = (e0))\/(((op (e1) (e1)) = (e0))\/(((op (e2) (e1)) = (e0))\/((op (e3) (e1)) = (e0))))) -> (~((op (e0) (e2)) = (e3))) -> (~((op (e0) (e3)) = (e3))) -> False). % 19.13/19.23 do 0 intro. intros zenon_H130 zenon_H60 zenon_H142 zenon_H11d zenon_H1c7 zenon_H149 zenon_H168 zenon_H98 zenon_H12b zenon_H1d8 zenon_H10a zenon_H1a1 zenon_H9a zenon_H245 zenon_H123 zenon_H12d. % 19.13/19.23 apply (zenon_or_s _ _ zenon_H168); [ zenon_intro zenon_H3a | zenon_intro zenon_H169 ]. % 19.13/19.23 exact (zenon_H98 zenon_H3a). % 19.13/19.23 apply (zenon_or_s _ _ zenon_H169); [ zenon_intro zenon_H99 | zenon_intro zenon_H16a ]. % 19.13/19.23 apply (zenon_or_s _ _ zenon_H245); [ zenon_intro zenon_H49 | zenon_intro zenon_H246 ]. % 19.13/19.23 apply (zenon_L36_); trivial. % 19.13/19.23 apply (zenon_or_s _ _ zenon_H246); [ zenon_intro zenon_H29 | zenon_intro zenon_H247 ]. % 19.13/19.23 apply (zenon_L1405_); trivial. % 19.13/19.23 apply (zenon_or_s _ _ zenon_H247); [ zenon_intro zenon_H36 | zenon_intro zenon_H1b1 ]. % 19.13/19.23 apply (zenon_or_s _ _ zenon_H142); [ zenon_intro zenon_H29 | zenon_intro zenon_H143 ]. % 19.13/19.23 apply (zenon_L1405_); trivial. % 19.13/19.23 apply (zenon_or_s _ _ zenon_H143); [ zenon_intro zenon_H10d | zenon_intro zenon_H144 ]. % 19.13/19.23 exact (zenon_H10a zenon_H10d). % 19.13/19.23 apply (zenon_or_s _ _ zenon_H144); [ zenon_intro zenon_H110 | zenon_intro zenon_H13f ]. % 19.13/19.23 apply (zenon_L552_); trivial. % 19.13/19.23 exact (zenon_H1a1 zenon_H13f). % 19.13/19.23 apply (zenon_L244_); trivial. % 19.13/19.23 apply (zenon_or_s _ _ zenon_H16a); [ zenon_intro zenon_Ha9 | zenon_intro zenon_He3 ]. % 19.13/19.23 exact (zenon_H123 zenon_Ha9). % 19.13/19.23 exact (zenon_H12d zenon_He3). % 19.13/19.23 (* end of lemma zenon_L1406_ *) % 19.13/19.23 assert (zenon_L1407_ : (((op (e2) (e2)) = (e0))\/(((op (e2) (e2)) = (e1))\/(((op (e2) (e2)) = (e2))\/((op (e2) (e2)) = (e3))))) -> ((op (e0) (e2)) = (e0)) -> (~((op (e0) (e2)) = (op (e2) (e2)))) -> ((op (e1) (e2)) = (e1)) -> (~((op (e1) (e2)) = (op (e2) (e2)))) -> (~((op (e2) (e2)) = (e2))) -> (~((op (e2) (e2)) = (e3))) -> False). % 19.13/19.23 do 0 intro. intros zenon_H1c4 zenon_H48 zenon_Ha8 zenon_Hf0 zenon_H2b zenon_H173 zenon_H1b3. % 19.13/19.23 apply (zenon_or_s _ _ zenon_H1c4); [ zenon_intro zenon_H2c | zenon_intro zenon_H1c5 ]. % 19.13/19.23 apply (zenon_L679_); trivial. % 19.13/19.23 apply (zenon_or_s _ _ zenon_H1c5); [ zenon_intro zenon_Hf1 | zenon_intro zenon_H1c6 ]. % 19.13/19.23 apply (zenon_L59_); trivial. % 19.13/19.23 apply (zenon_or_s _ _ zenon_H1c6); [ zenon_intro zenon_H176 | zenon_intro zenon_Haa ]. % 19.13/19.23 exact (zenon_H173 zenon_H176). % 19.13/19.23 exact (zenon_H1b3 zenon_Haa). % 19.13/19.23 (* end of lemma zenon_L1407_ *) % 19.13/19.23 assert (zenon_L1408_ : (((op (e0) (e0)) = (e3))\/(((op (e1) (e0)) = (e3))\/(((op (e2) (e0)) = (e3))\/((op (e3) (e0)) = (e3))))) -> (~((op (e0) (e0)) = (e3))) -> ((op (e2) (e3)) = (e1)) -> (~((op (e1) (e3)) = (op (e2) (e3)))) -> (((op (e2) (e2)) = (e0))\/(((op (e2) (e2)) = (e1))\/(((op (e2) (e2)) = (e2))\/((op (e2) (e2)) = (e3))))) -> ((op (e0) (e2)) = (e0)) -> (~((op (e0) (e2)) = (op (e2) (e2)))) -> (~((op (e1) (e2)) = (op (e2) (e2)))) -> (~((op (e2) (e2)) = (e2))) -> (~((op (e2) (e2)) = (e3))) -> (~((op (e1) (e1)) = (e1))) -> (~((e1) = (e3))) -> (((op (e1) (e0)) = (e1))\/(((op (e1) (e1)) = (e1))\/(((op (e1) (e2)) = (e1))\/((op (e1) (e3)) = (e1))))) -> (~((op (e2) (e0)) = (e3))) -> (~((op (e3) (e0)) = (e3))) -> False). % 19.13/19.23 do 0 intro. intros zenon_H1e0 zenon_H98 zenon_Hf4 zenon_Hdb zenon_H1c4 zenon_H48 zenon_Ha8 zenon_H2b zenon_H173 zenon_H1b3 zenon_H10a zenon_H95 zenon_H128 zenon_H27f zenon_H15f. % 19.13/19.23 apply (zenon_or_s _ _ zenon_H1e0); [ zenon_intro zenon_H3a | zenon_intro zenon_H1e1 ]. % 19.13/19.23 exact (zenon_H98 zenon_H3a). % 19.13/19.23 apply (zenon_or_s _ _ zenon_H1e1); [ zenon_intro zenon_H9e | zenon_intro zenon_H1e2 ]. % 19.13/19.23 apply (zenon_or_s _ _ zenon_H128); [ zenon_intro zenon_H9d | zenon_intro zenon_H129 ]. % 19.13/19.23 apply (zenon_L37_); trivial. % 19.13/19.23 apply (zenon_or_s _ _ zenon_H129); [ zenon_intro zenon_H10d | zenon_intro zenon_H12a ]. % 19.13/19.23 exact (zenon_H10a zenon_H10d). % 19.13/19.23 apply (zenon_or_s _ _ zenon_H12a); [ zenon_intro zenon_Hf0 | zenon_intro zenon_Hd6 ]. % 19.13/19.23 apply (zenon_L1407_); trivial. % 19.13/19.23 apply (zenon_L126_); trivial. % 19.13/19.23 apply (zenon_or_s _ _ zenon_H1e2); [ zenon_intro zenon_H3b | zenon_intro zenon_H15e ]. % 19.13/19.23 exact (zenon_H27f zenon_H3b). % 19.13/19.23 exact (zenon_H15f zenon_H15e). % 19.13/19.23 (* end of lemma zenon_L1408_ *) % 19.13/19.23 assert (zenon_L1409_ : (((op (e0) (e0)) = (e0))\/(((op (e0) (e1)) = (e0))\/(((op (e0) (e2)) = (e0))\/((op (e0) (e3)) = (e0))))) -> (~((op (e0) (e0)) = (e0))) -> (~((op (e0) (e2)) = (e3))) -> (~((op (e0) (e3)) = (e3))) -> (~((e0) = (e3))) -> (~((op (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) (e3)) = (op (e3) (e3)))) -> ((op (e3) (e3)) = (e0)) -> False). % 19.13/19.23 do 0 intro. intros zenon_H74 zenon_H3f zenon_H123 zenon_H12d zenon_H9a zenon_H9c zenon_H98 zenon_H168 zenon_Hc2 zenon_H60. % 19.13/19.23 apply (zenon_or_s _ _ zenon_H74); [ zenon_intro zenon_H42 | zenon_intro zenon_H77 ]. % 19.13/19.23 exact (zenon_H3f zenon_H42). % 19.13/19.23 apply (zenon_or_s _ _ zenon_H77); [ zenon_intro zenon_H49 | zenon_intro zenon_H78 ]. % 19.13/19.24 apply (zenon_L1348_); trivial. % 19.13/19.24 apply (zenon_or_s _ _ zenon_H78); [ zenon_intro zenon_H48 | zenon_intro zenon_H1e ]. % 19.13/19.24 apply (zenon_L1349_); trivial. % 19.13/19.24 apply (zenon_L440_); trivial. % 19.13/19.24 (* end of lemma zenon_L1409_ *) % 19.13/19.24 assert (zenon_L1410_ : ((~((op (e3) (e0)) = (e3)))\/((op (e3) (e3)) = (e0))) -> (~((op (e0) (e0)) = (e3))) -> (((op (e0) (e1)) = (e0))\/(((op (e1) (e1)) = (e0))\/(((op (e2) (e1)) = (e0))\/((op (e3) (e1)) = (e0))))) -> (~((op (e3) (e1)) = (op (e3) (e3)))) -> (~((op (e1) (e1)) = (e1))) -> (~((op (e1) (e1)) = (e3))) -> (((op (e1) (e1)) = (e0))\/(((op (e1) (e1)) = (e1))\/(((op (e1) (e1)) = (e2))\/((op (e1) (e1)) = (e3))))) -> (((op (e0) (e0)) = (e3))\/(((op (e0) (e1)) = (e3))\/(((op (e0) (e2)) = (e3))\/((op (e0) (e3)) = (e3))))) -> (~((op (e0) (e3)) = (e3))) -> (~((op (e0) (e2)) = (e3))) -> (~((e2) = (e3))) -> (~((e0) = (e2))) -> (~((op (e2) (e1)) = (op (e2) (e3)))) -> (((op (e0) (e1)) = (e2))\/(((op (e1) (e1)) = (e2))\/(((op (e2) (e1)) = (e2))\/((op (e3) (e1)) = (e2))))) -> (~((e0) = (e3))) -> ((~((op (e3) (e2)) = (e3)))\/((op (e3) (e3)) = (e2))) -> ((op (e2) (e3)) = (e2)) -> (~((op (e2) (e3)) = (op (e3) (e3)))) -> (~((op (e3) (e3)) = (e3))) -> (((op (e3) (e0)) = (e3))\/(((op (e3) (e1)) = (e3))\/(((op (e3) (e2)) = (e3))\/((op (e3) (e3)) = (e3))))) -> ((op (e2) (e3)) = (e1)) -> ((~((op (e3) (e1)) = (e3)))\/((op (e3) (e3)) = (e1))) -> False). % 19.13/19.24 do 0 intro. intros zenon_H286 zenon_H98 zenon_H245 zenon_H130 zenon_H10a zenon_H1a1 zenon_H142 zenon_H168 zenon_H12d zenon_H123 zenon_H12b zenon_H149 zenon_H1c7 zenon_H1d8 zenon_H9a zenon_H284 zenon_H11d zenon_Hf3 zenon_H102 zenon_H165 zenon_Hf4 zenon_H285. % 19.13/19.24 apply (zenon_or_s _ _ zenon_H286); [ zenon_intro zenon_H15f | zenon_intro zenon_H60 ]. % 19.13/19.24 apply (zenon_L1390_); trivial. % 19.13/19.24 apply (zenon_L1406_); trivial. % 19.13/19.24 (* end of lemma zenon_L1410_ *) % 19.13/19.24 assert (zenon_L1411_ : ((~((op (e3) (e2)) = (e3)))\/((op (e3) (e3)) = (e2))) -> ((op (e1) (e3)) = (e2)) -> (~((op (e1) (e3)) = (op (e3) (e3)))) -> (~((op (e3) (e0)) = (e3))) -> (~((op (e3) (e1)) = (e3))) -> (~((op (e3) (e3)) = (e3))) -> (((op (e3) (e0)) = (e3))\/(((op (e3) (e1)) = (e3))\/(((op (e3) (e2)) = (e3))\/((op (e3) (e3)) = (e3))))) -> False). % 19.13/19.24 do 0 intro. intros zenon_H284 zenon_Hd7 zenon_Hd5 zenon_H15f zenon_H282 zenon_H102 zenon_H165. % 19.13/19.24 apply (zenon_or_s _ _ zenon_H284); [ zenon_intro zenon_H283 | zenon_intro zenon_Hf6 ]. % 19.13/19.24 apply (zenon_L1346_); trivial. % 19.13/19.24 apply (zenon_L402_); trivial. % 19.13/19.24 (* end of lemma zenon_L1411_ *) % 19.13/19.24 assert (zenon_L1412_ : (((op (e1) (e1)) = (e0))\/(((op (e1) (e1)) = (e1))\/(((op (e1) (e1)) = (e2))\/((op (e1) (e1)) = (e3))))) -> ((op (e1) (e0)) = (e0)) -> (~((op (e1) (e0)) = (op (e1) (e1)))) -> (~((op (e1) (e1)) = (e1))) -> (~((op (e1) (e1)) = (op (e1) (e3)))) -> ((op (e1) (e3)) = (e2)) -> (~((op (e1) (e1)) = (e3))) -> False). % 19.13/19.24 do 0 intro. intros zenon_H142 zenon_H27 zenon_H45 zenon_H10a zenon_H57 zenon_Hd7 zenon_H1a1. % 19.13/19.24 apply (zenon_or_s _ _ zenon_H142); [ zenon_intro zenon_H29 | zenon_intro zenon_H143 ]. % 19.13/19.24 apply (zenon_L8_); trivial. % 19.13/19.24 apply (zenon_or_s _ _ zenon_H143); [ zenon_intro zenon_H10d | zenon_intro zenon_H144 ]. % 19.13/19.24 exact (zenon_H10a zenon_H10d). % 19.13/19.24 apply (zenon_or_s _ _ zenon_H144); [ zenon_intro zenon_H110 | zenon_intro zenon_H13f ]. % 19.13/19.24 apply (zenon_L283_); trivial. % 19.13/19.24 exact (zenon_H1a1 zenon_H13f). % 19.13/19.24 (* end of lemma zenon_L1412_ *) % 19.13/19.24 assert (zenon_L1413_ : (((op (e3) (e2)) = (e0))\/(((op (e3) (e2)) = (e1))\/(((op (e3) (e2)) = (e2))\/((op (e3) (e2)) = (e3))))) -> ((op (e1) (e2)) = (e0)) -> (~((op (e1) (e2)) = (op (e3) (e2)))) -> (~((op (e3) (e2)) = (op (e3) (e3)))) -> ((op (e3) (e3)) = (e1)) -> ((op (e0) (e2)) = (e2)) -> (~((op (e0) (e2)) = (op (e3) (e2)))) -> (~((op (e3) (e2)) = (e3))) -> False). % 19.13/19.24 do 0 intro. intros zenon_H191 zenon_H2a zenon_H115 zenon_H62 zenon_Hc4 zenon_H150 zenon_H14f zenon_H283. % 19.13/19.24 apply (zenon_or_s _ _ zenon_H191); [ zenon_intro zenon_H61 | zenon_intro zenon_H192 ]. % 19.13/19.24 apply (zenon_L176_); trivial. % 19.13/19.24 apply (zenon_or_s _ _ zenon_H192); [ zenon_intro zenon_Hba | zenon_intro zenon_H193 ]. % 19.13/19.24 apply (zenon_L147_); trivial. % 19.13/19.24 apply (zenon_or_s _ _ zenon_H193); [ zenon_intro zenon_H151 | zenon_intro zenon_H163 ]. % 19.13/19.24 apply (zenon_L104_); trivial. % 19.13/19.24 exact (zenon_H283 zenon_H163). % 19.13/19.24 (* end of lemma zenon_L1413_ *) % 19.13/19.24 assert (zenon_L1414_ : (((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) (e2)) = (e3))) -> (~((op (e0) (e2)) = (op (e3) (e2)))) -> ((op (e0) (e2)) = (e2)) -> ((op (e3) (e3)) = (e1)) -> (~((op (e3) (e2)) = (op (e3) (e3)))) -> (~((op (e1) (e2)) = (op (e3) (e2)))) -> (((op (e3) (e2)) = (e0))\/(((op (e3) (e2)) = (e1))\/(((op (e3) (e2)) = (e2))\/((op (e3) (e2)) = (e3))))) -> (((op (e2) (e2)) = (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)) = (e3)) -> (~((op (e2) (e2)) = (e2))) -> (~((op (e2) (e2)) = (e3))) -> False). % 19.13/19.24 do 0 intro. intros zenon_H6a zenon_H208 zenon_H1e zenon_H283 zenon_H14f zenon_H150 zenon_Hc4 zenon_H62 zenon_H115 zenon_H191 zenon_H1c4 zenon_H34 zenon_H52 zenon_H16c zenon_H173 zenon_H1b3. % 19.13/19.24 apply (zenon_or_s _ _ zenon_H6a); [ zenon_intro zenon_H48 | zenon_intro zenon_H6b ]. % 19.13/19.24 apply (zenon_L336_); trivial. % 19.13/19.24 apply (zenon_or_s _ _ zenon_H6b); [ zenon_intro zenon_H2a | zenon_intro zenon_H6c ]. % 19.13/19.24 apply (zenon_L1413_); trivial. % 19.13/19.24 apply (zenon_or_s _ _ zenon_H6c); [ zenon_intro zenon_H2c | zenon_intro zenon_H61 ]. % 19.13/19.24 apply (zenon_L11_); trivial. % 19.13/19.24 apply (zenon_or_s _ _ zenon_H1c4); [ zenon_intro zenon_H2c | zenon_intro zenon_H1c5 ]. % 19.13/19.24 apply (zenon_L11_); trivial. % 19.13/19.24 apply (zenon_or_s _ _ zenon_H1c5); [ zenon_intro zenon_Hf1 | zenon_intro zenon_H1c6 ]. % 19.13/19.24 apply (zenon_L156_); trivial. % 19.13/19.24 apply (zenon_or_s _ _ zenon_H1c6); [ zenon_intro zenon_H176 | zenon_intro zenon_Haa ]. % 19.13/19.24 exact (zenon_H173 zenon_H176). % 19.13/19.24 exact (zenon_H1b3 zenon_Haa). % 19.13/19.24 (* end of lemma zenon_L1414_ *) % 19.13/19.24 assert (zenon_L1415_ : (((op (e1) (e0)) = (e3))\/(((op (e1) (e1)) = (e3))\/(((op (e1) (e2)) = (e3))\/((op (e1) (e3)) = (e3))))) -> (~((op (e1) (e0)) = (e3))) -> (~((op (e1) (e1)) = (e3))) -> (~((op (e2) (e2)) = (e3))) -> (~((op (e2) (e2)) = (e2))) -> (~((op (e2) (e0)) = (op (e2) (e2)))) -> ((op (e2) (e0)) = (e0)) -> (((op (e2) (e2)) = (e0))\/(((op (e2) (e2)) = (e1))\/(((op (e2) (e2)) = (e2))\/((op (e2) (e2)) = (e3))))) -> (((op (e3) (e2)) = (e0))\/(((op (e3) (e2)) = (e1))\/(((op (e3) (e2)) = (e2))\/((op (e3) (e2)) = (e3))))) -> (~((op (e1) (e2)) = (op (e3) (e2)))) -> (~((op (e3) (e2)) = (op (e3) (e3)))) -> ((op (e3) (e3)) = (e1)) -> ((op (e0) (e2)) = (e2)) -> (~((op (e0) (e2)) = (op (e3) (e2)))) -> (~((op (e3) (e2)) = (e3))) -> ((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))))) -> (~((op (e1) (e3)) = (e3))) -> False). % 19.13/19.24 do 0 intro. intros zenon_H16f zenon_H9f zenon_H1a1 zenon_H1b3 zenon_H173 zenon_H52 zenon_H34 zenon_H1c4 zenon_H191 zenon_H115 zenon_H62 zenon_Hc4 zenon_H150 zenon_H14f zenon_H283 zenon_H1e zenon_H208 zenon_H6a zenon_H12f. % 19.13/19.24 apply (zenon_or_s _ _ zenon_H16f); [ zenon_intro zenon_H9e | zenon_intro zenon_H170 ]. % 19.13/19.24 exact (zenon_H9f zenon_H9e). % 19.13/19.24 apply (zenon_or_s _ _ zenon_H170); [ zenon_intro zenon_H13f | zenon_intro zenon_H171 ]. % 19.13/19.24 exact (zenon_H1a1 zenon_H13f). % 19.13/19.24 apply (zenon_or_s _ _ zenon_H171); [ zenon_intro zenon_H16c | zenon_intro zenon_Hdc ]. % 19.13/19.24 apply (zenon_L1414_); trivial. % 19.13/19.24 exact (zenon_H12f zenon_Hdc). % 19.13/19.24 (* end of lemma zenon_L1415_ *) % 19.13/19.24 assert (zenon_L1416_ : (((op (e2) (e2)) = (e0))\/(((op (e2) (e2)) = (e1))\/(((op (e2) (e2)) = (e2))\/((op (e2) (e2)) = (e3))))) -> ((op (e1) (e2)) = (e3)) -> ((op (e0) (e2)) = (e1)) -> (~((op (e0) (e2)) = (op (e2) (e2)))) -> (~((op (e2) (e2)) = (e2))) -> (~((op (e2) (e2)) = (e3))) -> False). % 19.13/19.24 do 0 intro. intros zenon_H1c4 zenon_H16c zenon_H122 zenon_Ha8 zenon_H173 zenon_H1b3. % 19.13/19.24 apply (zenon_or_s _ _ zenon_H1c4); [ zenon_intro zenon_H2c | zenon_intro zenon_H1c5 ]. % 19.13/19.24 apply (zenon_L603_); trivial. % 19.13/19.24 apply (zenon_or_s _ _ zenon_H1c5); [ zenon_intro zenon_Hf1 | zenon_intro zenon_H1c6 ]. % 19.13/19.24 apply (zenon_L246_); trivial. % 19.13/19.24 apply (zenon_or_s _ _ zenon_H1c6); [ zenon_intro zenon_H176 | zenon_intro zenon_Haa ]. % 19.13/19.24 exact (zenon_H173 zenon_H176). % 19.13/19.24 exact (zenon_H1b3 zenon_Haa). % 19.13/19.24 (* end of lemma zenon_L1416_ *) % 19.13/19.24 assert (zenon_L1417_ : (((op (e0) (e2)) = (e0))\/(((op (e0) (e2)) = (e1))\/(((op (e0) (e2)) = (e2))\/((op (e0) (e2)) = (e3))))) -> (~((op (e0) (e2)) = (op (e0) (e3)))) -> ((op (e0) (e3)) = (e0)) -> (~((op (e2) (e2)) = (e3))) -> (~((op (e2) (e2)) = (e2))) -> (~((op (e0) (e2)) = (op (e2) (e2)))) -> ((op (e1) (e2)) = (e3)) -> (((op (e2) (e2)) = (e0))\/(((op (e2) (e2)) = (e1))\/(((op (e2) (e2)) = (e2))\/((op (e2) (e2)) = (e3))))) -> ((op (e3) (e2)) = (e2)) -> (~((op (e0) (e2)) = (op (e3) (e2)))) -> (~((op (e0) (e2)) = (e3))) -> False). % 19.13/19.24 do 0 intro. intros zenon_H1ba zenon_H208 zenon_H1e zenon_H1b3 zenon_H173 zenon_Ha8 zenon_H16c zenon_H1c4 zenon_H151 zenon_H14f zenon_H123. % 19.13/19.24 apply (zenon_or_s _ _ zenon_H1ba); [ zenon_intro zenon_H48 | zenon_intro zenon_H1bb ]. % 19.13/19.24 apply (zenon_L336_); trivial. % 19.13/19.24 apply (zenon_or_s _ _ zenon_H1bb); [ zenon_intro zenon_H122 | zenon_intro zenon_H1bc ]. % 19.13/19.24 apply (zenon_L1416_); trivial. % 19.13/19.24 apply (zenon_or_s _ _ zenon_H1bc); [ zenon_intro zenon_H150 | zenon_intro zenon_Ha9 ]. % 19.13/19.24 apply (zenon_L104_); trivial. % 19.13/19.24 exact (zenon_H123 zenon_Ha9). % 19.13/19.24 (* end of lemma zenon_L1417_ *) % 19.13/19.24 assert (zenon_L1418_ : (((op (e1) (e0)) = (e3))\/(((op (e1) (e1)) = (e3))\/(((op (e1) (e2)) = (e3))\/((op (e1) (e3)) = (e3))))) -> (~((op (e1) (e0)) = (e3))) -> (~((op (e1) (e1)) = (e3))) -> (~((op (e2) (e2)) = (e3))) -> (~((op (e2) (e2)) = (e2))) -> (~((op (e0) (e2)) = (op (e2) (e2)))) -> ((op (e0) (e2)) = (e1)) -> (((op (e2) (e2)) = (e0))\/(((op (e2) (e2)) = (e1))\/(((op (e2) (e2)) = (e2))\/((op (e2) (e2)) = (e3))))) -> (~((op (e1) (e3)) = (e3))) -> False). % 19.13/19.24 do 0 intro. intros zenon_H16f zenon_H9f zenon_H1a1 zenon_H1b3 zenon_H173 zenon_Ha8 zenon_H122 zenon_H1c4 zenon_H12f. % 19.13/19.24 apply (zenon_or_s _ _ zenon_H16f); [ zenon_intro zenon_H9e | zenon_intro zenon_H170 ]. % 19.13/19.24 exact (zenon_H9f zenon_H9e). % 19.13/19.24 apply (zenon_or_s _ _ zenon_H170); [ zenon_intro zenon_H13f | zenon_intro zenon_H171 ]. % 19.13/19.24 exact (zenon_H1a1 zenon_H13f). % 19.13/19.24 apply (zenon_or_s _ _ zenon_H171); [ zenon_intro zenon_H16c | zenon_intro zenon_Hdc ]. % 19.13/19.24 apply (zenon_L1416_); trivial. % 19.13/19.24 exact (zenon_H12f zenon_Hdc). % 19.13/19.24 (* end of lemma zenon_L1418_ *) % 19.13/19.24 assert (zenon_L1419_ : ((~((op (e3) (e2)) = (e3)))\/((op (e3) (e3)) = (e2))) -> (~((op (e1) (e3)) = (op (e3) (e3)))) -> (~((op (e0) (e0)) = (e0))) -> (((op (e1) (e1)) = (e0))\/(((op (e1) (e1)) = (e1))\/(((op (e1) (e1)) = (e2))\/((op (e1) (e1)) = (e3))))) -> (~((op (e1) (e1)) = (e3))) -> ((op (e1) (e3)) = (e2)) -> (~((op (e1) (e1)) = (op (e1) (e3)))) -> (~((op (e1) (e1)) = (e1))) -> (~((op (e1) (e0)) = (op (e1) (e1)))) -> (((op (e0) (e0)) = (e1))\/(((op (e0) (e1)) = (e1))\/(((op (e0) (e2)) = (e1))\/((op (e0) (e3)) = (e1))))) -> (~((e0) = (e1))) -> (~((op (e1) (e0)) = (e3))) -> (((op (e0) (e2)) = (e2))\/(((op (e1) (e2)) = (e2))\/(((op (e2) (e2)) = (e2))\/((op (e3) (e2)) = (e2))))) -> (~((op (e0) (e2)) = (op (e2) (e2)))) -> (~((op (e0) (e1)) = (op (e0) (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) (e2)) = (e0))\/(((op (e1) (e2)) = (e0))\/(((op (e2) (e2)) = (e0))\/((op (e3) (e2)) = (e0))))) -> (~((op (e2) (e2)) = (e2))) -> (~((op (e2) (e2)) = (e3))) -> (((op (e2) (e2)) = (e0))\/(((op (e2) (e2)) = (e1))\/(((op (e2) (e2)) = (e2))\/((op (e2) (e2)) = (e3))))) -> (~((op (e2) (e0)) = (op (e2) (e2)))) -> (~((op (e1) (e2)) = (op (e3) (e2)))) -> (~((op (e3) (e2)) = (op (e3) (e3)))) -> ((op (e3) (e3)) = (e1)) -> (~((op (e0) (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 (e0) (e2)) = (op (e0) (e3)))) -> (~((op (e1) (e3)) = (e3))) -> (((op (e1) (e0)) = (e3))\/(((op (e1) (e1)) = (e3))\/(((op (e1) (e2)) = (e3))\/((op (e1) (e3)) = (e3))))) -> (~((e1) = (e3))) -> (~((op (e0) (e1)) = (e3))) -> (~((op (e0) (e2)) = (e3))) -> (~((op (e0) (e3)) = (e3))) -> (((op (e0) (e0)) = (e3))\/(((op (e0) (e1)) = (e3))\/(((op (e0) (e2)) = (e3))\/((op (e0) (e3)) = (e3))))) -> (~((op (e3) (e0)) = (op (e3) (e2)))) -> (((op (e0) (e0)) = (e0))\/(((op (e1) (e0)) = (e0))\/(((op (e2) (e0)) = (e0))\/((op (e3) (e0)) = (e0))))) -> False). % 19.13/19.24 do 0 intro. intros zenon_H284 zenon_Hd5 zenon_H3f zenon_H142 zenon_H1a1 zenon_Hd7 zenon_H57 zenon_H10a zenon_H45 zenon_H22d zenon_Ha1 zenon_H9f zenon_H172 zenon_Ha8 zenon_H4a zenon_H195 zenon_H1ba zenon_H6a zenon_H173 zenon_H1b3 zenon_H1c4 zenon_H52 zenon_H115 zenon_H62 zenon_Hc4 zenon_H14f zenon_H191 zenon_H1e zenon_H208 zenon_H12f zenon_H16f zenon_H95 zenon_H9c zenon_H123 zenon_H12d zenon_H168 zenon_H6f zenon_H3e. % 19.13/19.24 apply (zenon_or_s _ _ zenon_H284); [ zenon_intro zenon_H283 | zenon_intro zenon_Hf6 ]. % 19.13/19.24 apply (zenon_or_s _ _ zenon_H3e); [ zenon_intro zenon_H42 | zenon_intro zenon_H41 ]. % 19.13/19.24 exact (zenon_H3f zenon_H42). % 19.13/19.24 apply (zenon_or_s _ _ zenon_H41); [ zenon_intro zenon_H27 | zenon_intro zenon_H43 ]. % 19.13/19.24 apply (zenon_L1412_); trivial. % 19.13/19.24 apply (zenon_or_s _ _ zenon_H43); [ zenon_intro zenon_H34 | zenon_intro zenon_H44 ]. % 19.13/19.24 apply (zenon_or_s _ _ zenon_H22d); [ zenon_intro zenon_H7a | zenon_intro zenon_H22e ]. % 19.13/19.24 apply (zenon_L1350_); trivial. % 19.13/19.24 apply (zenon_or_s _ _ zenon_H22e); [ zenon_intro zenon_Ha0 | zenon_intro zenon_H22f ]. % 19.13/19.24 apply (zenon_or_s _ _ zenon_H16f); [ zenon_intro zenon_H9e | zenon_intro zenon_H170 ]. % 19.13/19.24 exact (zenon_H9f zenon_H9e). % 19.13/19.24 apply (zenon_or_s _ _ zenon_H170); [ zenon_intro zenon_H13f | zenon_intro zenon_H171 ]. % 19.13/19.24 exact (zenon_H1a1 zenon_H13f). % 19.13/19.24 apply (zenon_or_s _ _ zenon_H171); [ zenon_intro zenon_H16c | zenon_intro zenon_Hdc ]. % 19.13/19.24 apply (zenon_or_s _ _ zenon_H172); [ zenon_intro zenon_H150 | zenon_intro zenon_H174 ]. % 19.13/19.24 apply (zenon_L1415_); trivial. % 19.13/19.24 apply (zenon_or_s _ _ zenon_H174); [ zenon_intro zenon_H113 | zenon_intro zenon_H175 ]. % 19.13/19.24 apply (zenon_L1357_); trivial. % 19.13/19.24 apply (zenon_or_s _ _ zenon_H175); [ zenon_intro zenon_H176 | zenon_intro zenon_H151 ]. % 19.13/19.24 exact (zenon_H173 zenon_H176). % 19.13/19.24 apply (zenon_L1417_); trivial. % 19.13/19.24 exact (zenon_H12f zenon_Hdc). % 19.13/19.24 apply (zenon_or_s _ _ zenon_H22f); [ zenon_intro zenon_H122 | zenon_intro zenon_Hc3 ]. % 19.13/19.24 apply (zenon_L1367_); trivial. % 19.13/19.24 apply (zenon_L427_); trivial. % 19.13/19.24 apply (zenon_or_s _ _ zenon_H22d); [ zenon_intro zenon_H7a | zenon_intro zenon_H22e ]. % 19.13/19.24 apply (zenon_L1350_); trivial. % 19.13/19.24 apply (zenon_or_s _ _ zenon_H22e); [ zenon_intro zenon_Ha0 | zenon_intro zenon_H22f ]. % 19.13/19.24 apply (zenon_or_s _ _ zenon_H16f); [ zenon_intro zenon_H9e | zenon_intro zenon_H170 ]. % 19.13/19.24 exact (zenon_H9f zenon_H9e). % 19.13/19.24 apply (zenon_or_s _ _ zenon_H170); [ zenon_intro zenon_H13f | zenon_intro zenon_H171 ]. % 19.13/19.24 exact (zenon_H1a1 zenon_H13f). % 19.13/19.24 apply (zenon_or_s _ _ zenon_H171); [ zenon_intro zenon_H16c | zenon_intro zenon_Hdc ]. % 19.13/19.24 apply (zenon_or_s _ _ zenon_H172); [ zenon_intro zenon_H150 | zenon_intro zenon_H174 ]. % 19.13/19.24 apply (zenon_L1351_); trivial. % 19.13/19.24 apply (zenon_or_s _ _ zenon_H174); [ zenon_intro zenon_H113 | zenon_intro zenon_H175 ]. % 19.13/19.24 apply (zenon_L1357_); trivial. % 19.13/19.24 apply (zenon_or_s _ _ zenon_H175); [ zenon_intro zenon_H176 | zenon_intro zenon_H151 ]. % 19.13/19.24 exact (zenon_H173 zenon_H176). % 19.13/19.24 apply (zenon_L1417_); trivial. % 19.13/19.24 exact (zenon_H12f zenon_Hdc). % 19.13/19.24 apply (zenon_or_s _ _ zenon_H22f); [ zenon_intro zenon_H122 | zenon_intro zenon_Hc3 ]. % 19.13/19.24 apply (zenon_L1418_); trivial. % 19.13/19.24 apply (zenon_L427_); trivial. % 19.13/19.24 apply (zenon_L402_); trivial. % 19.13/19.24 (* end of lemma zenon_L1419_ *) % 19.13/19.24 assert (zenon_L1420_ : ((~((op (e3) (e1)) = (e3)))\/((op (e3) (e3)) = (e1))) -> (~((op (e1) (e3)) = (op (e3) (e3)))) -> (((op (e3) (e0)) = (e3))\/(((op (e3) (e1)) = (e3))\/(((op (e3) (e2)) = (e3))\/((op (e3) (e3)) = (e3))))) -> (~((op (e3) (e3)) = (e3))) -> (~((op (e3) (e0)) = (e3))) -> (((op (e0) (e0)) = (e0))\/(((op (e0) (e1)) = (e0))\/(((op (e0) (e2)) = (e0))\/((op (e0) (e3)) = (e0))))) -> (((op (e0) (e2)) = (e0))\/(((op (e0) (e2)) = (e1))\/(((op (e0) (e2)) = (e2))\/((op (e0) (e2)) = (e3))))) -> (~((op (e1) (e0)) = (op (e1) (e2)))) -> (~((op (e1) (e2)) = (op (e1) (e3)))) -> (~((op (e0) (e2)) = (op (e1) (e2)))) -> (((op (e1) (e2)) = (e0))\/(((op (e1) (e2)) = (e1))\/(((op (e1) (e2)) = (e2))\/((op (e1) (e2)) = (e3))))) -> (~((op (e0) (e0)) = (op (e0) (e2)))) -> (~((op (e1) (e0)) = (op (e1) (e3)))) -> ((op (e1) (e3)) = (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) (e1)) = (op (e0) (e3)))) -> (~((op (e0) (e1)) = (op (e0) (e2)))) -> (~((op (e0) (e1)) = (op (e2) (e1)))) -> (((op (e0) (e1)) = (e0))\/(((op (e0) (e1)) = (e1))\/(((op (e0) (e1)) = (e2))\/((op (e0) (e1)) = (e3))))) -> (~((e1) = (e2))) -> (((op (e1) (e0)) = (e3))\/(((op (e1) (e1)) = (e3))\/(((op (e1) (e2)) = (e3))\/((op (e1) (e3)) = (e3))))) -> (~((op (e1) (e3)) = (e3))) -> (~((op (e1) (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) (e0)) = (op (e3) (e1)))) -> (~((op (e1) (e0)) = (e3))) -> (((op (e0) (e0)) = (e1))\/(((op (e1) (e0)) = (e1))\/(((op (e2) (e0)) = (e1))\/((op (e3) (e0)) = (e1))))) -> (~((op (e0) (e2)) = (op (e0) (e3)))) -> (((op (e0) (e0)) = (e1))\/(((op (e0) (e1)) = (e1))\/(((op (e0) (e2)) = (e1))\/((op (e0) (e3)) = (e1))))) -> (~((e0) = (e1))) -> (~((op (e2) (e0)) = (op (e2) (e2)))) -> (~((op (e0) (e2)) = (op (e2) (e2)))) -> (~((op (e2) (e2)) = (e3))) -> (((op (e2) (e2)) = (e0))\/(((op (e2) (e2)) = (e1))\/(((op (e2) (e2)) = (e2))\/((op (e2) (e2)) = (e3))))) -> (((op (e1) (e0)) = (e0))\/(((op (e1) (e0)) = (e1))\/(((op (e1) (e0)) = (e2))\/((op (e1) (e0)) = (e3))))) -> (~((op (e0) (e1)) = (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 (e1) (e0)) = (op (e2) (e0)))) -> (~((e1) = (e3))) -> (((op (e0) (e0)) = (e0))\/(((op (e1) (e0)) = (e0))\/(((op (e2) (e0)) = (e0))\/((op (e3) (e0)) = (e0))))) -> (~((op (e0) (e1)) = (e3))) -> (~((op (e0) (e0)) = (e3))) -> (~((e0) = (e3))) -> (~((op (e0) (e2)) = (e3))) -> (~((op (e0) (e3)) = (e3))) -> (((op (e0) (e0)) = (e3))\/(((op (e0) (e1)) = (e3))\/(((op (e0) (e2)) = (e3))\/((op (e0) (e3)) = (e3))))) -> (~((op (e0) (e0)) = (e0))) -> ((~((op (e3) (e2)) = (e3)))\/((op (e3) (e3)) = (e2))) -> False). % 19.13/19.24 do 0 intro. intros zenon_H285 zenon_Hd5 zenon_H165 zenon_H102 zenon_H15f zenon_H74 zenon_H1ba zenon_H24a zenon_H124 zenon_H195 zenon_H19d zenon_H13c zenon_Hd8 zenon_Hd6 zenon_H1d5 zenon_Hf3 zenon_H173 zenon_H54 zenon_H4a zenon_H17e zenon_H212 zenon_H7c zenon_H16f zenon_H12f zenon_H16d zenon_H22a zenon_H130 zenon_H1cf zenon_H9f zenon_H235 zenon_H208 zenon_H22d zenon_Ha1 zenon_H52 zenon_Ha8 zenon_H1b3 zenon_H1c4 zenon_H25e zenon_H210 zenon_H71 zenon_H267 zenon_H201 zenon_H95 zenon_H3e zenon_H9c zenon_H98 zenon_H9a zenon_H123 zenon_H12d zenon_H168 zenon_H3f zenon_H284. % 19.13/19.24 apply (zenon_or_s _ _ zenon_H285); [ zenon_intro zenon_H282 | zenon_intro zenon_Hc4 ]. % 19.13/19.24 apply (zenon_or_s _ _ zenon_H284); [ zenon_intro zenon_H283 | zenon_intro zenon_Hf6 ]. % 19.13/19.24 apply (zenon_L1346_); trivial. % 19.13/19.24 apply (zenon_or_s _ _ zenon_H74); [ zenon_intro zenon_H42 | zenon_intro zenon_H77 ]. % 19.13/19.24 exact (zenon_H3f zenon_H42). % 19.13/19.24 apply (zenon_or_s _ _ zenon_H77); [ zenon_intro zenon_H49 | zenon_intro zenon_H78 ]. % 19.13/19.24 apply (zenon_L1348_); trivial. % 19.13/19.24 apply (zenon_or_s _ _ zenon_H78); [ zenon_intro zenon_H48 | zenon_intro zenon_H1e ]. % 19.13/19.24 apply (zenon_L1349_); trivial. % 19.13/19.24 apply (zenon_L1368_); trivial. % 19.13/19.24 apply (zenon_L50_); trivial. % 19.13/19.24 (* end of lemma zenon_L1420_ *) % 19.13/19.24 assert (zenon_L1421_ : ((~((op (e2) (e3)) = (e3)))\/((op (e2) (e3)) = (e3))) -> ((op (e0) (e3)) = (e3)) -> (~((op (e0) (e3)) = (op (e2) (e3)))) -> (~((op (e2) (e0)) = (e3))) -> (~((op (e2) (e1)) = (e3))) -> (~((op (e2) (e2)) = (e3))) -> (((op (e2) (e0)) = (e3))\/(((op (e2) (e1)) = (e3))\/(((op (e2) (e2)) = (e3))\/((op (e2) (e3)) = (e3))))) -> False). % 19.13/19.24 do 0 intro. intros zenon_H281 zenon_He3 zenon_He2 zenon_H27f zenon_Ha7 zenon_H1b3 zenon_He7. % 19.13/19.24 apply (zenon_or_s _ _ zenon_H281); [ zenon_intro zenon_H280 | zenon_intro zenon_Hdd ]. % 19.13/19.24 apply (zenon_L1344_); trivial. % 19.13/19.24 apply (zenon_L54_); trivial. % 19.13/19.24 (* end of lemma zenon_L1421_ *) % 19.13/19.24 assert (zenon_L1422_ : ((~((op (e3) (e1)) = (e3)))\/((op (e3) (e3)) = (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 (e3) (e3)) = (e3))) -> (~((op (e3) (e0)) = (e3))) -> (~((op (e1) (e3)) = (op (e3) (e3)))) -> ((op (e1) (e3)) = (e2)) -> ((~((op (e3) (e2)) = (e3)))\/((op (e3) (e3)) = (e2))) -> False). % 19.13/19.24 do 0 intro. intros zenon_H285 zenon_Hf4 zenon_Hf3 zenon_H165 zenon_H102 zenon_H15f zenon_Hd5 zenon_Hd7 zenon_H284. % 19.13/19.24 apply (zenon_or_s _ _ zenon_H285); [ zenon_intro zenon_H282 | zenon_intro zenon_Hc4 ]. % 19.13/19.24 apply (zenon_L1411_); trivial. % 19.13/19.24 apply (zenon_L60_); trivial. % 19.13/19.24 (* end of lemma zenon_L1422_ *) % 19.13/19.24 assert (zenon_L1423_ : ((~((op (e2) (e2)) = (e3)))\/((op (e2) (e3)) = (e2))) -> (~((op (e1) (e3)) = (op (e2) (e3)))) -> ((~((op (e3) (e1)) = (e3)))\/((op (e3) (e3)) = (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 (e3) (e3)) = (e3))) -> (~((op (e1) (e3)) = (op (e3) (e3)))) -> ((op (e1) (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) (e0)) = (op (e3) (e3)))) -> (~((op (e2) (e0)) = (op (e2) (e2)))) -> (~((op (e2) (e2)) = (op (e2) (e3)))) -> (~((op (e2) (e2)) = (e2))) -> (((op (e2) (e2)) = (e0))\/(((op (e2) (e2)) = (e1))\/(((op (e2) (e2)) = (e2))\/((op (e2) (e2)) = (e3))))) -> (~((op (e1) (e0)) = (op (e1) (e1)))) -> (~((op (e1) (e1)) = (e1))) -> (~((op (e1) (e1)) = (op (e1) (e3)))) -> (~((op (e1) (e1)) = (e3))) -> (((op (e1) (e1)) = (e0))\/(((op (e1) (e1)) = (e1))\/(((op (e1) (e1)) = (e2))\/((op (e1) (e1)) = (e3))))) -> (~((op (e0) (e0)) = (e0))) -> ((~((op (e3) (e0)) = (e3)))\/((op (e3) (e3)) = (e0))) -> False). % 19.13/19.24 do 0 intro. intros zenon_H288 zenon_Hdb zenon_H285 zenon_Hf4 zenon_Hf3 zenon_H165 zenon_H102 zenon_Hd5 zenon_Hd7 zenon_H284 zenon_H3e zenon_H71 zenon_H52 zenon_H6d zenon_H173 zenon_H1c4 zenon_H45 zenon_H10a zenon_H57 zenon_H1a1 zenon_H142 zenon_H3f zenon_H286. % 19.13/19.24 apply (zenon_or_s _ _ zenon_H288); [ zenon_intro zenon_H1b3 | zenon_intro zenon_H11d ]. % 19.13/19.24 apply (zenon_or_s _ _ zenon_H286); [ zenon_intro zenon_H15f | zenon_intro zenon_H60 ]. % 19.13/19.24 apply (zenon_L1422_); trivial. % 19.13/19.24 apply (zenon_or_s _ _ zenon_H3e); [ zenon_intro zenon_H42 | zenon_intro zenon_H41 ]. % 19.13/19.24 exact (zenon_H3f zenon_H42). % 19.13/19.24 apply (zenon_or_s _ _ zenon_H41); [ zenon_intro zenon_H27 | zenon_intro zenon_H43 ]. % 19.13/19.24 apply (zenon_L1412_); trivial. % 19.13/19.24 apply (zenon_or_s _ _ zenon_H43); [ zenon_intro zenon_H34 | zenon_intro zenon_H44 ]. % 19.13/19.24 apply (zenon_L1387_); trivial. % 19.13/19.24 apply (zenon_L21_); trivial. % 19.13/19.24 apply (zenon_L366_); trivial. % 19.13/19.24 (* end of lemma zenon_L1423_ *) % 19.13/19.24 assert (zenon_L1424_ : ((~((op (e3) (e0)) = (e3)))\/((op (e3) (e3)) = (e0))) -> (~((op (e2) (e3)) = (op (e3) (e3)))) -> ((~((op (e3) (e2)) = (e3)))\/((op (e3) (e3)) = (e2))) -> ((op (e1) (e3)) = (e2)) -> (~((op (e1) (e3)) = (op (e3) (e3)))) -> (~((op (e3) (e3)) = (e3))) -> (((op (e3) (e0)) = (e3))\/(((op (e3) (e1)) = (e3))\/(((op (e3) (e2)) = (e3))\/((op (e3) (e3)) = (e3))))) -> ((op (e2) (e3)) = (e0)) -> ((~((op (e3) (e1)) = (e3)))\/((op (e3) (e3)) = (e1))) -> False). % 19.13/19.24 do 0 intro. intros zenon_H286 zenon_Hf3 zenon_H284 zenon_Hd7 zenon_Hd5 zenon_H102 zenon_H165 zenon_H37 zenon_H285. % 19.13/19.24 apply (zenon_or_s _ _ zenon_H286); [ zenon_intro zenon_H15f | zenon_intro zenon_H60 ]. % 19.13/19.24 apply (zenon_or_s _ _ zenon_H285); [ zenon_intro zenon_H282 | zenon_intro zenon_Hc4 ]. % 19.13/19.24 apply (zenon_L1411_); trivial. % 19.13/19.24 apply (zenon_L72_); trivial. % 19.13/19.24 apply (zenon_L219_); trivial. % 19.13/19.24 (* end of lemma zenon_L1424_ *) % 19.13/19.24 assert (zenon_L1425_ : (((op (e0) (e0)) = (e3))\/(((op (e1) (e0)) = (e3))\/(((op (e2) (e0)) = (e3))\/((op (e3) (e0)) = (e3))))) -> (~((op (e0) (e0)) = (e3))) -> (~((op (e1) (e0)) = (e3))) -> (~((op (e2) (e0)) = (e3))) -> ((op (e3) (e0)) = (e1)) -> (~((e1) = (e3))) -> False). % 19.13/19.24 do 0 intro. intros zenon_H1e0 zenon_H98 zenon_H9f zenon_H27f zenon_Hac zenon_H95. % 19.13/19.24 apply (zenon_or_s _ _ zenon_H1e0); [ zenon_intro zenon_H3a | zenon_intro zenon_H1e1 ]. % 19.13/19.24 exact (zenon_H98 zenon_H3a). % 19.13/19.24 apply (zenon_or_s _ _ zenon_H1e1); [ zenon_intro zenon_H9e | zenon_intro zenon_H1e2 ]. % 19.13/19.24 exact (zenon_H9f zenon_H9e). % 19.13/19.24 apply (zenon_or_s _ _ zenon_H1e2); [ zenon_intro zenon_H3b | zenon_intro zenon_H15e ]. % 19.13/19.24 exact (zenon_H27f zenon_H3b). % 19.13/19.24 apply (zenon_L252_); trivial. % 19.13/19.24 (* end of lemma zenon_L1425_ *) % 19.13/19.24 assert (zenon_L1426_ : (((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)) = (e0)) -> ((op (e2) (e1)) = (e1)) -> (~((op (e0) (e1)) = (op (e2) (e1)))) -> ((op (e3) (e1)) = (e2)) -> (~((op (e0) (e1)) = (op (e3) (e1)))) -> (~((op (e0) (e1)) = (e3))) -> False). % 19.13/19.24 do 0 intro. intros zenon_H212 zenon_H4a zenon_H48 zenon_Ha5 zenon_H17e zenon_H14d zenon_H210 zenon_H9c. % 19.13/19.24 apply (zenon_or_s _ _ zenon_H212); [ zenon_intro zenon_H49 | zenon_intro zenon_H213 ]. % 19.13/19.24 apply (zenon_L9_); trivial. % 19.13/19.24 apply (zenon_or_s _ _ zenon_H213); [ zenon_intro zenon_Ha0 | zenon_intro zenon_H214 ]. % 19.13/19.24 apply (zenon_L357_); trivial. % 19.13/19.24 apply (zenon_or_s _ _ zenon_H214); [ zenon_intro zenon_H10f | zenon_intro zenon_H99 ]. % 19.13/19.24 apply (zenon_L389_); trivial. % 19.13/19.24 exact (zenon_H9c zenon_H99). % 19.13/19.24 (* end of lemma zenon_L1426_ *) % 19.13/19.24 assert (zenon_L1427_ : (((op (e0) (e2)) = (e0))\/(((op (e0) (e2)) = (e1))\/(((op (e0) (e2)) = (e2))\/((op (e0) (e2)) = (e3))))) -> (~((op (e0) (e1)) = (e3))) -> (~((op (e0) (e1)) = (op (e3) (e1)))) -> ((op (e3) (e1)) = (e2)) -> (~((op (e0) (e1)) = (op (e2) (e1)))) -> ((op (e2) (e1)) = (e1)) -> (~((op (e0) (e1)) = (op (e0) (e2)))) -> (((op (e0) (e1)) = (e0))\/(((op (e0) (e1)) = (e1))\/(((op (e0) (e1)) = (e2))\/((op (e0) (e1)) = (e3))))) -> ((op (e3) (e2)) = (e1)) -> (~((op (e0) (e2)) = (op (e3) (e2)))) -> ((op (e1) (e2)) = (e2)) -> (~((op (e0) (e2)) = (op (e1) (e2)))) -> (~((op (e0) (e2)) = (e3))) -> False). % 19.13/19.24 do 0 intro. intros zenon_H1ba zenon_H9c zenon_H210 zenon_H14d zenon_H17e zenon_Ha5 zenon_H4a zenon_H212 zenon_Hba zenon_H14f zenon_H113 zenon_H195 zenon_H123. % 19.13/19.24 apply (zenon_or_s _ _ zenon_H1ba); [ zenon_intro zenon_H48 | zenon_intro zenon_H1bb ]. % 19.13/19.24 apply (zenon_L1426_); trivial. % 19.13/19.24 apply (zenon_or_s _ _ zenon_H1bb); [ zenon_intro zenon_H122 | zenon_intro zenon_H1bc ]. % 19.13/19.24 apply (zenon_L317_); trivial. % 19.13/19.24 apply (zenon_or_s _ _ zenon_H1bc); [ zenon_intro zenon_H150 | zenon_intro zenon_Ha9 ]. % 19.13/19.24 apply (zenon_L153_); trivial. % 19.13/19.24 exact (zenon_H123 zenon_Ha9). % 19.13/19.24 (* end of lemma zenon_L1427_ *) % 19.13/19.24 assert (zenon_L1428_ : (((op (e3) (e1)) = (e0))\/(((op (e3) (e1)) = (e1))\/(((op (e3) (e1)) = (e2))\/((op (e3) (e1)) = (e3))))) -> (~((op (e3) (e1)) = (op (e3) (e3)))) -> ((op (e3) (e3)) = (e0)) -> ((op (e0) (e1)) = (e1)) -> (~((op (e0) (e1)) = (op (e3) (e1)))) -> ((op (e1) (e1)) = (e3)) -> ((op (e2) (e1)) = (e0)) -> (~((op (e3) (e1)) = (e3))) -> False). % 19.13/19.24 do 0 intro. intros zenon_H22a zenon_H130 zenon_H60 zenon_Ha0 zenon_H210 zenon_H13f zenon_H36 zenon_H282. % 19.13/19.24 apply (zenon_or_s _ _ zenon_H22a); [ zenon_intro zenon_H1b1 | zenon_intro zenon_H22b ]. % 19.13/19.24 apply (zenon_L244_); trivial. % 19.13/19.24 apply (zenon_or_s _ _ zenon_H22b); [ zenon_intro zenon_Hae | zenon_intro zenon_H22c ]. % 19.13/19.24 apply (zenon_L363_); trivial. % 19.13/19.24 apply (zenon_or_s _ _ zenon_H22c); [ zenon_intro zenon_H14d | zenon_intro zenon_H161 ]. % 19.13/19.24 apply (zenon_L514_); trivial. % 19.13/19.24 exact (zenon_H282 zenon_H161). % 19.13/19.24 (* end of lemma zenon_L1428_ *) % 19.13/19.24 assert (zenon_L1429_ : (((op (e1) (e0)) = (e3))\/(((op (e1) (e1)) = (e3))\/(((op (e1) (e2)) = (e3))\/((op (e1) (e3)) = (e3))))) -> (~((op (e1) (e0)) = (e3))) -> (~((op (e3) (e1)) = (e3))) -> ((op (e2) (e1)) = (e0)) -> (~((op (e0) (e1)) = (op (e3) (e1)))) -> ((op (e0) (e1)) = (e1)) -> ((op (e3) (e3)) = (e0)) -> (~((op (e3) (e1)) = (op (e3) (e3)))) -> (((op (e3) (e1)) = (e0))\/(((op (e3) (e1)) = (e1))\/(((op (e3) (e1)) = (e2))\/((op (e3) (e1)) = (e3))))) -> (~((op (e1) (e2)) = (e3))) -> (~((op (e1) (e3)) = (e3))) -> False). % 19.13/19.24 do 0 intro. intros zenon_H16f zenon_H9f zenon_H282 zenon_H36 zenon_H210 zenon_Ha0 zenon_H60 zenon_H130 zenon_H22a zenon_H16d zenon_H12f. % 19.13/19.24 apply (zenon_or_s _ _ zenon_H16f); [ zenon_intro zenon_H9e | zenon_intro zenon_H170 ]. % 19.13/19.24 exact (zenon_H9f zenon_H9e). % 19.13/19.24 apply (zenon_or_s _ _ zenon_H170); [ zenon_intro zenon_H13f | zenon_intro zenon_H171 ]. % 19.13/19.24 apply (zenon_L1428_); trivial. % 19.13/19.24 apply (zenon_or_s _ _ zenon_H171); [ zenon_intro zenon_H16c | zenon_intro zenon_Hdc ]. % 19.13/19.24 exact (zenon_H16d zenon_H16c). % 19.13/19.24 exact (zenon_H12f zenon_Hdc). % 19.13/19.24 (* end of lemma zenon_L1429_ *) % 19.13/19.24 assert (zenon_L1430_ : (((op (e1) (e0)) = (e3))\/(((op (e1) (e1)) = (e3))\/(((op (e1) (e2)) = (e3))\/((op (e1) (e3)) = (e3))))) -> (~((op (e1) (e0)) = (e3))) -> (~((op (e3) (e1)) = (e3))) -> (~((op (e0) (e1)) = (op (e3) (e1)))) -> ((op (e0) (e1)) = (e2)) -> ((op (e0) (e1)) = (e1)) -> (((op (e3) (e1)) = (e0))\/(((op (e3) (e1)) = (e1))\/(((op (e3) (e1)) = (e2))\/((op (e3) (e1)) = (e3))))) -> (~((op (e1) (e2)) = (e3))) -> (~((op (e1) (e3)) = (e3))) -> False). % 19.13/19.24 do 0 intro. intros zenon_H16f zenon_H9f zenon_H282 zenon_H210 zenon_H10f zenon_Ha0 zenon_H22a zenon_H16d zenon_H12f. % 19.13/19.24 apply (zenon_or_s _ _ zenon_H16f); [ zenon_intro zenon_H9e | zenon_intro zenon_H170 ]. % 19.13/19.24 exact (zenon_H9f zenon_H9e). % 19.13/19.24 apply (zenon_or_s _ _ zenon_H170); [ zenon_intro zenon_H13f | zenon_intro zenon_H171 ]. % 19.13/19.24 apply (zenon_or_s _ _ zenon_H22a); [ zenon_intro zenon_H1b1 | zenon_intro zenon_H22b ]. % 19.13/19.24 apply (zenon_L580_); trivial. % 19.13/19.24 apply (zenon_or_s _ _ zenon_H22b); [ zenon_intro zenon_Hae | zenon_intro zenon_H22c ]. % 19.13/19.24 apply (zenon_L363_); trivial. % 19.13/19.24 apply (zenon_or_s _ _ zenon_H22c); [ zenon_intro zenon_H14d | zenon_intro zenon_H161 ]. % 19.13/19.24 apply (zenon_L389_); trivial. % 19.13/19.24 exact (zenon_H282 zenon_H161). % 19.13/19.24 apply (zenon_or_s _ _ zenon_H171); [ zenon_intro zenon_H16c | zenon_intro zenon_Hdc ]. % 19.13/19.24 exact (zenon_H16d zenon_H16c). % 19.13/19.24 exact (zenon_H12f zenon_Hdc). % 19.13/19.24 (* end of lemma zenon_L1430_ *) % 19.13/19.24 assert (zenon_L1431_ : (((op (e3) (e1)) = (e0))\/(((op (e3) (e1)) = (e1))\/(((op (e3) (e1)) = (e2))\/((op (e3) (e1)) = (e3))))) -> (~((op (e3) (e1)) = (op (e3) (e3)))) -> ((op (e3) (e3)) = (e0)) -> (~((op (e2) (e1)) = (op (e3) (e1)))) -> ((op (e2) (e1)) = (e1)) -> ((op (e0) (e1)) = (e2)) -> (~((op (e0) (e1)) = (op (e3) (e1)))) -> (~((op (e3) (e1)) = (e3))) -> False). % 19.13/19.24 do 0 intro. intros zenon_H22a zenon_H130 zenon_H60 zenon_Haf zenon_Ha5 zenon_H10f zenon_H210 zenon_H282. % 19.13/19.24 apply (zenon_or_s _ _ zenon_H22a); [ zenon_intro zenon_H1b1 | zenon_intro zenon_H22b ]. % 19.13/19.24 apply (zenon_L244_); trivial. % 19.13/19.24 apply (zenon_or_s _ _ zenon_H22b); [ zenon_intro zenon_Hae | zenon_intro zenon_H22c ]. % 19.13/19.24 apply (zenon_L42_); trivial. % 19.13/19.24 apply (zenon_or_s _ _ zenon_H22c); [ zenon_intro zenon_H14d | zenon_intro zenon_H161 ]. % 19.13/19.24 apply (zenon_L389_); trivial. % 19.13/19.24 exact (zenon_H282 zenon_H161). % 19.13/19.24 (* end of lemma zenon_L1431_ *) % 19.13/19.24 assert (zenon_L1432_ : (((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 (e3) (e1)) = (e1)) -> ((op (e0) (e1)) = (e2)) -> (~((op (e0) (e1)) = (op (e2) (e1)))) -> (~((op (e2) (e1)) = (e3))) -> False). % 19.13/19.24 do 0 intro. intros zenon_H1cc zenon_H34 zenon_H1f0 zenon_Haf zenon_Hae zenon_H10f zenon_H17e zenon_Ha7. % 19.13/19.24 apply (zenon_or_s _ _ zenon_H1cc); [ zenon_intro zenon_H36 | zenon_intro zenon_H1cd ]. % 19.13/19.24 apply (zenon_L642_); trivial. % 19.13/19.24 apply (zenon_or_s _ _ zenon_H1cd); [ zenon_intro zenon_Ha5 | zenon_intro zenon_H1ce ]. % 19.13/19.24 apply (zenon_L42_); trivial. % 19.13/19.24 apply (zenon_or_s _ _ zenon_H1ce); [ zenon_intro zenon_H1ca | zenon_intro zenon_Ha6 ]. % 19.13/19.24 apply (zenon_L191_); trivial. % 19.13/19.24 exact (zenon_Ha7 zenon_Ha6). % 19.13/19.24 (* end of lemma zenon_L1432_ *) % 19.13/19.24 assert (zenon_L1433_ : (((op (e2) (e0)) = (e0))\/(((op (e2) (e0)) = (e1))\/(((op (e2) (e0)) = (e2))\/((op (e2) (e0)) = (e3))))) -> (~((op (e2) (e1)) = (e3))) -> (~((op (e0) (e1)) = (op (e2) (e1)))) -> ((op (e0) (e1)) = (e2)) -> ((op (e3) (e1)) = (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 (e2) (e2)) = (e1)) -> (~((op (e2) (e0)) = (op (e2) (e2)))) -> (~((op (e2) (e0)) = (op (e2) (e3)))) -> ((op (e2) (e3)) = (e2)) -> (~((op (e2) (e0)) = (e3))) -> False). % 19.13/19.24 do 0 intro. intros zenon_H259 zenon_Ha7 zenon_H17e zenon_H10f zenon_Hae zenon_Haf zenon_H1f0 zenon_H1cc zenon_Hf1 zenon_H52 zenon_H5b zenon_H11d zenon_H27f. % 19.13/19.24 apply (zenon_or_s _ _ zenon_H259); [ zenon_intro zenon_H34 | zenon_intro zenon_H25a ]. % 19.13/19.24 apply (zenon_L1432_); trivial. % 19.13/19.24 apply (zenon_or_s _ _ zenon_H25a); [ zenon_intro zenon_Hed | zenon_intro zenon_H25b ]. % 19.13/19.24 apply (zenon_L93_); trivial. % 19.13/19.24 apply (zenon_or_s _ _ zenon_H25b); [ zenon_intro zenon_Hee | zenon_intro zenon_H3b ]. % 19.13/19.24 apply (zenon_L73_); trivial. % 19.13/19.24 exact (zenon_H27f zenon_H3b). % 19.13/19.24 (* end of lemma zenon_L1433_ *) % 19.13/19.24 assert (zenon_L1434_ : (((op (e0) (e1)) = (e1))\/(((op (e1) (e1)) = (e1))\/(((op (e2) (e1)) = (e1))\/((op (e3) (e1)) = (e1))))) -> (~((op (e1) (e3)) = (e3))) -> (~((op (e1) (e2)) = (e3))) -> (~((op (e1) (e0)) = (e3))) -> (((op (e1) (e0)) = (e3))\/(((op (e1) (e1)) = (e3))\/(((op (e1) (e2)) = (e3))\/((op (e1) (e3)) = (e3))))) -> (~((op (e1) (e1)) = (e1))) -> (((op (e2) (e0)) = (e1))\/(((op (e2) (e1)) = (e1))\/(((op (e2) (e2)) = (e1))\/((op (e2) (e3)) = (e1))))) -> ((op (e0) (e0)) = (e1)) -> (~((op (e0) (e0)) = (op (e2) (e0)))) -> (~((op (e3) (e1)) = (e3))) -> (~((op (e0) (e1)) = (op (e3) (e1)))) -> ((op (e3) (e3)) = (e0)) -> (~((op (e3) (e1)) = (op (e3) (e3)))) -> (((op (e3) (e1)) = (e0))\/(((op (e3) (e1)) = (e1))\/(((op (e3) (e1)) = (e2))\/((op (e3) (e1)) = (e3))))) -> (~((op (e2) (e0)) = (e3))) -> ((op (e2) (e3)) = (e2)) -> (~((op (e2) (e0)) = (op (e2) (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) (e0)) = (op (e2) (e1)))) -> (~((op (e2) (e1)) = (op (e3) (e1)))) -> ((op (e0) (e1)) = (e2)) -> (~((op (e0) (e1)) = (op (e2) (e1)))) -> (~((op (e2) (e1)) = (e3))) -> (((op (e2) (e0)) = (e0))\/(((op (e2) (e0)) = (e1))\/(((op (e2) (e0)) = (e2))\/((op (e2) (e0)) = (e3))))) -> (~((op (e1) (e3)) = (op (e2) (e3)))) -> ((op (e1) (e3)) = (e1)) -> False). % 19.13/19.24 do 0 intro. intros zenon_H109 zenon_H12f zenon_H16d zenon_H9f zenon_H16f zenon_H10a zenon_H106 zenon_H7a zenon_H39 zenon_H282 zenon_H210 zenon_H60 zenon_H130 zenon_H22a zenon_H27f zenon_H11d zenon_H5b zenon_H52 zenon_H1cc zenon_H1f0 zenon_Haf zenon_H10f zenon_H17e zenon_Ha7 zenon_H259 zenon_Hdb zenon_Hd6. % 19.13/19.24 apply (zenon_or_s _ _ zenon_H109); [ zenon_intro zenon_Ha0 | zenon_intro zenon_H10b ]. % 19.13/19.24 apply (zenon_L1430_); trivial. % 19.13/19.24 apply (zenon_or_s _ _ zenon_H10b); [ zenon_intro zenon_H10d | zenon_intro zenon_H10c ]. % 19.13/19.24 exact (zenon_H10a zenon_H10d). % 19.13/19.24 apply (zenon_or_s _ _ zenon_H10c); [ zenon_intro zenon_Ha5 | zenon_intro zenon_Hae ]. % 19.13/19.24 apply (zenon_L1431_); trivial. % 19.13/19.24 apply (zenon_or_s _ _ zenon_H106); [ zenon_intro zenon_Hed | zenon_intro zenon_H107 ]. % 19.13/19.24 apply (zenon_L134_); trivial. % 19.13/19.24 apply (zenon_or_s _ _ zenon_H107); [ zenon_intro zenon_Ha5 | zenon_intro zenon_H108 ]. % 19.13/19.24 apply (zenon_L1431_); trivial. % 19.13/19.24 apply (zenon_or_s _ _ zenon_H108); [ zenon_intro zenon_Hf1 | zenon_intro zenon_Hf4 ]. % 19.13/19.24 apply (zenon_L1433_); trivial. % 19.13/19.24 apply (zenon_L126_); trivial. % 19.13/19.24 (* end of lemma zenon_L1434_ *) % 19.13/19.24 assert (zenon_L1435_ : (((op (e0) (e1)) = (e0))\/(((op (e1) (e1)) = (e0))\/(((op (e2) (e1)) = (e0))\/((op (e3) (e1)) = (e0))))) -> ((op (e1) (e0)) = (e0)) -> (~((op (e1) (e0)) = (op (e1) (e1)))) -> (~((op (e1) (e3)) = (e3))) -> (~((op (e1) (e2)) = (e3))) -> (((op (e2) (e0)) = (e1))\/(((op (e2) (e1)) = (e1))\/(((op (e2) (e2)) = (e1))\/((op (e2) (e3)) = (e1))))) -> ((op (e0) (e0)) = (e1)) -> (~((op (e0) (e0)) = (op (e2) (e0)))) -> (~((op (e0) (e1)) = (e3))) -> (((op (e2) (e0)) = (e0))\/(((op (e2) (e0)) = (e1))\/(((op (e2) (e0)) = (e2))\/((op (e2) (e0)) = (e3))))) -> (~((op (e2) (e1)) = (e3))) -> (~((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 (e2) (e0)) = (op (e2) (e2)))) -> (~((op (e2) (e0)) = (op (e2) (e3)))) -> ((op (e2) (e3)) = (e2)) -> (~((op (e2) (e0)) = (e3))) -> (((op (e3) (e1)) = (e0))\/(((op (e3) (e1)) = (e1))\/(((op (e3) (e1)) = (e2))\/((op (e3) (e1)) = (e3))))) -> (~((op (e0) (e1)) = (op (e3) (e1)))) -> (~((op (e3) (e1)) = (e3))) -> (((op (e0) (e1)) = (e0))\/(((op (e0) (e1)) = (e1))\/(((op (e0) (e1)) = (e2))\/((op (e0) (e1)) = (e3))))) -> (~((op (e1) (e3)) = (op (e2) (e3)))) -> ((op (e1) (e3)) = (e1)) -> (~((op (e1) (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 (e1) (e1)) = (e1))) -> (((op (e0) (e1)) = (e1))\/(((op (e1) (e1)) = (e1))\/(((op (e2) (e1)) = (e1))\/((op (e3) (e1)) = (e1))))) -> (~((op (e0) (e1)) = (op (e1) (e1)))) -> (~((op (e2) (e1)) = (op (e2) (e3)))) -> (~((op (e0) (e1)) = (op (e0) (e2)))) -> ((op (e0) (e2)) = (e0)) -> ((op (e3) (e3)) = (e0)) -> (~((op (e3) (e1)) = (op (e3) (e3)))) -> False). % 19.13/19.24 do 0 intro. intros zenon_H245 zenon_H27 zenon_H45 zenon_H12f zenon_H16d zenon_H106 zenon_H7a zenon_H39 zenon_H9c zenon_H259 zenon_Ha7 zenon_H17e zenon_Haf zenon_H1f0 zenon_H1cc zenon_H52 zenon_H5b zenon_H11d zenon_H27f zenon_H22a zenon_H210 zenon_H282 zenon_H212 zenon_Hdb zenon_Hd6 zenon_H9f zenon_H16f zenon_H1d8 zenon_H10a zenon_H109 zenon_H10e zenon_H1c7 zenon_H4a zenon_H48 zenon_H60 zenon_H130. % 19.13/19.24 apply (zenon_or_s _ _ zenon_H245); [ zenon_intro zenon_H49 | zenon_intro zenon_H246 ]. % 19.13/19.24 apply (zenon_L9_); trivial. % 19.13/19.24 apply (zenon_or_s _ _ zenon_H246); [ zenon_intro zenon_H29 | zenon_intro zenon_H247 ]. % 19.13/19.24 apply (zenon_L8_); trivial. % 19.13/19.24 apply (zenon_or_s _ _ zenon_H247); [ zenon_intro zenon_H36 | zenon_intro zenon_H1b1 ]. % 19.13/19.24 apply (zenon_or_s _ _ zenon_H109); [ zenon_intro zenon_Ha0 | zenon_intro zenon_H10b ]. % 19.13/19.24 apply (zenon_L1429_); trivial. % 19.13/19.24 apply (zenon_or_s _ _ zenon_H10b); [ zenon_intro zenon_H10d | zenon_intro zenon_H10c ]. % 19.13/19.24 exact (zenon_H10a zenon_H10d). % 19.13/19.24 apply (zenon_or_s _ _ zenon_H10c); [ zenon_intro zenon_Ha5 | zenon_intro zenon_Hae ]. % 19.13/19.24 apply (zenon_or_s _ _ zenon_H1d8); [ zenon_intro zenon_H10f | zenon_intro zenon_H1d9 ]. % 19.13/19.24 apply (zenon_L1434_); trivial. % 19.13/19.24 apply (zenon_or_s _ _ zenon_H1d9); [ zenon_intro zenon_H110 | zenon_intro zenon_H1da ]. % 19.13/19.24 apply (zenon_or_s _ _ zenon_H16f); [ zenon_intro zenon_H9e | zenon_intro zenon_H170 ]. % 19.13/19.24 exact (zenon_H9f zenon_H9e). % 19.13/19.24 apply (zenon_or_s _ _ zenon_H170); [ zenon_intro zenon_H13f | zenon_intro zenon_H171 ]. % 19.13/19.24 apply (zenon_or_s _ _ zenon_H212); [ zenon_intro zenon_H49 | zenon_intro zenon_H213 ]. % 19.13/19.24 apply (zenon_L9_); trivial. % 19.13/19.24 apply (zenon_or_s _ _ zenon_H213); [ zenon_intro zenon_Ha0 | zenon_intro zenon_H214 ]. % 19.13/19.24 apply (zenon_L1428_); trivial. % 19.13/19.24 apply (zenon_or_s _ _ zenon_H214); [ zenon_intro zenon_H10f | zenon_intro zenon_H99 ]. % 19.13/19.24 apply (zenon_L67_); trivial. % 19.13/19.24 exact (zenon_H9c zenon_H99). % 19.13/19.24 apply (zenon_or_s _ _ zenon_H171); [ zenon_intro zenon_H16c | zenon_intro zenon_Hdc ]. % 19.13/19.24 exact (zenon_H16d zenon_H16c). % 19.13/19.24 exact (zenon_H12f zenon_Hdc). % 19.13/19.24 apply (zenon_or_s _ _ zenon_H1da); [ zenon_intro zenon_H1ca | zenon_intro zenon_H14d ]. % 19.13/19.24 apply (zenon_L224_); trivial. % 19.13/19.24 apply (zenon_L1426_); trivial. % 19.13/19.24 apply (zenon_or_s _ _ zenon_H16f); [ zenon_intro zenon_H9e | zenon_intro zenon_H170 ]. % 19.13/19.24 exact (zenon_H9f zenon_H9e). % 19.13/19.24 apply (zenon_or_s _ _ zenon_H170); [ zenon_intro zenon_H13f | zenon_intro zenon_H171 ]. % 19.13/19.24 apply (zenon_or_s _ _ zenon_H106); [ zenon_intro zenon_Hed | zenon_intro zenon_H107 ]. % 19.13/19.24 apply (zenon_L134_); trivial. % 19.13/19.24 apply (zenon_or_s _ _ zenon_H107); [ zenon_intro zenon_Ha5 | zenon_intro zenon_H108 ]. % 19.13/19.24 apply (zenon_L42_); trivial. % 19.13/19.24 apply (zenon_or_s _ _ zenon_H108); [ zenon_intro zenon_Hf1 | zenon_intro zenon_Hf4 ]. % 19.13/19.24 apply (zenon_or_s _ _ zenon_H212); [ zenon_intro zenon_H49 | zenon_intro zenon_H213 ]. % 19.13/19.24 apply (zenon_L128_); trivial. % 19.13/19.24 apply (zenon_or_s _ _ zenon_H213); [ zenon_intro zenon_Ha0 | zenon_intro zenon_H214 ]. % 19.13/19.24 apply (zenon_L1428_); trivial. % 19.13/19.24 apply (zenon_or_s _ _ zenon_H214); [ zenon_intro zenon_H10f | zenon_intro zenon_H99 ]. % 19.13/19.24 apply (zenon_L1433_); trivial. % 19.13/19.24 exact (zenon_H9c zenon_H99). % 19.13/19.24 apply (zenon_L126_); trivial. % 19.13/19.24 apply (zenon_or_s _ _ zenon_H171); [ zenon_intro zenon_H16c | zenon_intro zenon_Hdc ]. % 19.13/19.24 exact (zenon_H16d zenon_H16c). % 19.13/19.24 exact (zenon_H12f zenon_Hdc). % 19.13/19.24 apply (zenon_L244_); trivial. % 19.13/19.24 (* end of lemma zenon_L1435_ *) % 19.13/19.24 assert (zenon_L1436_ : (((op (e0) (e2)) = (e0))\/(((op (e0) (e2)) = (e1))\/(((op (e0) (e2)) = (e2))\/((op (e0) (e2)) = (e3))))) -> (~((op (e3) (e1)) = (op (e3) (e3)))) -> ((op (e3) (e3)) = (e0)) -> (~((op (e0) (e1)) = (op (e0) (e2)))) -> (~((op (e2) (e1)) = (op (e2) (e3)))) -> (~((op (e0) (e1)) = (op (e1) (e1)))) -> (((op (e0) (e1)) = (e1))\/(((op (e1) (e1)) = (e1))\/(((op (e2) (e1)) = (e1))\/((op (e3) (e1)) = (e1))))) -> (~((op (e1) (e1)) = (e1))) -> (((op (e0) (e1)) = (e2))\/(((op (e1) (e1)) = (e2))\/(((op (e2) (e1)) = (e2))\/((op (e3) (e1)) = (e2))))) -> (((op (e1) (e0)) = (e3))\/(((op (e1) (e1)) = (e3))\/(((op (e1) (e2)) = (e3))\/((op (e1) (e3)) = (e3))))) -> (~((op (e1) (e0)) = (e3))) -> ((op (e1) (e3)) = (e1)) -> (~((op (e1) (e3)) = (op (e2) (e3)))) -> (((op (e0) (e1)) = (e0))\/(((op (e0) (e1)) = (e1))\/(((op (e0) (e1)) = (e2))\/((op (e0) (e1)) = (e3))))) -> (~((op (e3) (e1)) = (e3))) -> (~((op (e0) (e1)) = (op (e3) (e1)))) -> (((op (e3) (e1)) = (e0))\/(((op (e3) (e1)) = (e1))\/(((op (e3) (e1)) = (e2))\/((op (e3) (e1)) = (e3))))) -> (~((op (e2) (e0)) = (e3))) -> ((op (e2) (e3)) = (e2)) -> (~((op (e2) (e0)) = (op (e2) (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) (e0)) = (op (e2) (e1)))) -> (~((op (e2) (e1)) = (op (e3) (e1)))) -> (~((op (e0) (e1)) = (op (e2) (e1)))) -> (~((op (e2) (e1)) = (e3))) -> (((op (e2) (e0)) = (e0))\/(((op (e2) (e0)) = (e1))\/(((op (e2) (e0)) = (e2))\/((op (e2) (e0)) = (e3))))) -> (~((op (e0) (e1)) = (e3))) -> (~((op (e0) (e0)) = (op (e2) (e0)))) -> ((op (e0) (e0)) = (e1)) -> (((op (e2) (e0)) = (e1))\/(((op (e2) (e1)) = (e1))\/(((op (e2) (e2)) = (e1))\/((op (e2) (e3)) = (e1))))) -> (~((op (e1) (e2)) = (e3))) -> (~((op (e1) (e3)) = (e3))) -> (~((op (e1) (e0)) = (op (e1) (e1)))) -> ((op (e1) (e0)) = (e0)) -> (((op (e0) (e1)) = (e0))\/(((op (e1) (e1)) = (e0))\/(((op (e2) (e1)) = (e0))\/((op (e3) (e1)) = (e0))))) -> ((op (e3) (e2)) = (e1)) -> ((op (e3) (e2)) = (e2)) -> (~((op (e0) (e2)) = (op (e3) (e2)))) -> (~((op (e0) (e2)) = (e3))) -> False). % 19.13/19.24 do 0 intro. intros zenon_H1ba zenon_H130 zenon_H60 zenon_H4a zenon_H1c7 zenon_H10e zenon_H109 zenon_H10a zenon_H1d8 zenon_H16f zenon_H9f zenon_Hd6 zenon_Hdb zenon_H212 zenon_H282 zenon_H210 zenon_H22a zenon_H27f zenon_H11d zenon_H5b zenon_H52 zenon_H1cc zenon_H1f0 zenon_Haf zenon_H17e zenon_Ha7 zenon_H259 zenon_H9c zenon_H39 zenon_H7a zenon_H106 zenon_H16d zenon_H12f zenon_H45 zenon_H27 zenon_H245 zenon_Hba zenon_H151 zenon_H14f zenon_H123. % 19.13/19.24 apply (zenon_or_s _ _ zenon_H1ba); [ zenon_intro zenon_H48 | zenon_intro zenon_H1bb ]. % 19.13/19.24 apply (zenon_L1435_); trivial. % 19.13/19.24 apply (zenon_or_s _ _ zenon_H1bb); [ zenon_intro zenon_H122 | zenon_intro zenon_H1bc ]. % 19.13/19.24 apply (zenon_L317_); trivial. % 19.13/19.24 apply (zenon_or_s _ _ zenon_H1bc); [ zenon_intro zenon_H150 | zenon_intro zenon_Ha9 ]. % 19.13/19.24 apply (zenon_L104_); trivial. % 19.13/19.24 exact (zenon_H123 zenon_Ha9). % 19.13/19.24 (* end of lemma zenon_L1436_ *) % 19.13/19.24 assert (zenon_L1437_ : (((op (e3) (e0)) = (e2))\/(((op (e3) (e1)) = (e2))\/(((op (e3) (e2)) = (e2))\/((op (e3) (e3)) = (e2))))) -> (~((e2) = (e3))) -> ((op (e3) (e0)) = (e3)) -> (~((op (e0) (e2)) = (op (e1) (e2)))) -> ((op (e1) (e2)) = (e2)) -> ((op (e2) (e1)) = (e1)) -> (~((op (e0) (e2)) = (e3))) -> (~((op (e0) (e2)) = (op (e3) (e2)))) -> ((op (e3) (e2)) = (e1)) -> (((op (e0) (e1)) = (e0))\/(((op (e1) (e1)) = (e0))\/(((op (e2) (e1)) = (e0))\/((op (e3) (e1)) = (e0))))) -> ((op (e1) (e0)) = (e0)) -> (~((op (e1) (e0)) = (op (e1) (e1)))) -> (~((op (e1) (e3)) = (e3))) -> (~((op (e1) (e2)) = (e3))) -> (((op (e2) (e0)) = (e1))\/(((op (e2) (e1)) = (e1))\/(((op (e2) (e2)) = (e1))\/((op (e2) (e3)) = (e1))))) -> ((op (e0) (e0)) = (e1)) -> (~((op (e0) (e0)) = (op (e2) (e0)))) -> (~((op (e0) (e1)) = (e3))) -> (((op (e2) (e0)) = (e0))\/(((op (e2) (e0)) = (e1))\/(((op (e2) (e0)) = (e2))\/((op (e2) (e0)) = (e3))))) -> (~((op (e2) (e1)) = (e3))) -> (~((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 (e2) (e0)) = (op (e2) (e2)))) -> (~((op (e2) (e0)) = (op (e2) (e3)))) -> (~((op (e2) (e0)) = (e3))) -> (((op (e3) (e1)) = (e0))\/(((op (e3) (e1)) = (e1))\/(((op (e3) (e1)) = (e2))\/((op (e3) (e1)) = (e3))))) -> (~((op (e0) (e1)) = (op (e3) (e1)))) -> (~((op (e3) (e1)) = (e3))) -> (((op (e0) (e1)) = (e0))\/(((op (e0) (e1)) = (e1))\/(((op (e0) (e1)) = (e2))\/((op (e0) (e1)) = (e3))))) -> (~((op (e1) (e3)) = (op (e2) (e3)))) -> ((op (e1) (e3)) = (e1)) -> (~((op (e1) (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 (e1) (e1)) = (e1))) -> (((op (e0) (e1)) = (e1))\/(((op (e1) (e1)) = (e1))\/(((op (e2) (e1)) = (e1))\/((op (e3) (e1)) = (e1))))) -> (~((op (e0) (e1)) = (op (e1) (e1)))) -> (~((op (e2) (e1)) = (op (e2) (e3)))) -> (~((op (e0) (e1)) = (op (e0) (e2)))) -> ((op (e3) (e3)) = (e0)) -> (~((op (e3) (e1)) = (op (e3) (e3)))) -> (((op (e0) (e2)) = (e0))\/(((op (e0) (e2)) = (e1))\/(((op (e0) (e2)) = (e2))\/((op (e0) (e2)) = (e3))))) -> (~((op (e2) (e3)) = (op (e3) (e3)))) -> ((op (e2) (e3)) = (e2)) -> False). % 19.13/19.24 do 0 intro. intros zenon_H153 zenon_H12b zenon_H15e zenon_H195 zenon_H113 zenon_Ha5 zenon_H123 zenon_H14f zenon_Hba zenon_H245 zenon_H27 zenon_H45 zenon_H12f zenon_H16d zenon_H106 zenon_H7a zenon_H39 zenon_H9c zenon_H259 zenon_Ha7 zenon_H17e zenon_Haf zenon_H1f0 zenon_H1cc zenon_H52 zenon_H5b zenon_H27f zenon_H22a zenon_H210 zenon_H282 zenon_H212 zenon_Hdb zenon_Hd6 zenon_H9f zenon_H16f zenon_H1d8 zenon_H10a zenon_H109 zenon_H10e zenon_H1c7 zenon_H4a zenon_H60 zenon_H130 zenon_H1ba zenon_Hf3 zenon_H11d. % 19.13/19.24 apply (zenon_or_s _ _ zenon_H153); [ zenon_intro zenon_H148 | zenon_intro zenon_H154 ]. % 19.13/19.24 apply (zenon_L109_); trivial. % 19.13/19.24 apply (zenon_or_s _ _ zenon_H154); [ zenon_intro zenon_H14d | zenon_intro zenon_H155 ]. % 19.13/19.24 apply (zenon_L1427_); trivial. % 19.13/19.24 apply (zenon_or_s _ _ zenon_H155); [ zenon_intro zenon_H151 | zenon_intro zenon_Hf6 ]. % 19.13/19.24 apply (zenon_L1436_); trivial. % 19.13/19.24 apply (zenon_L97_); trivial. % 19.13/19.24 (* end of lemma zenon_L1437_ *) % 19.13/19.24 assert (zenon_L1438_ : (((op (e3) (e0)) = (e1))\/(((op (e3) (e1)) = (e1))\/(((op (e3) (e2)) = (e1))\/((op (e3) (e3)) = (e1))))) -> (~((e1) = (e3))) -> (~((op (e0) (e0)) = (e3))) -> (((op (e0) (e0)) = (e3))\/(((op (e1) (e0)) = (e3))\/(((op (e2) (e0)) = (e3))\/((op (e3) (e0)) = (e3))))) -> ((op (e2) (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) (e1)) = (op (e3) (e3)))) -> ((op (e3) (e3)) = (e0)) -> (~((op (e0) (e1)) = (op (e0) (e2)))) -> (~((op (e2) (e1)) = (op (e2) (e3)))) -> (~((op (e0) (e1)) = (op (e1) (e1)))) -> (((op (e0) (e1)) = (e1))\/(((op (e1) (e1)) = (e1))\/(((op (e2) (e1)) = (e1))\/((op (e3) (e1)) = (e1))))) -> (~((op (e1) (e1)) = (e1))) -> (((op (e0) (e1)) = (e2))\/(((op (e1) (e1)) = (e2))\/(((op (e2) (e1)) = (e2))\/((op (e3) (e1)) = (e2))))) -> (((op (e1) (e0)) = (e3))\/(((op (e1) (e1)) = (e3))\/(((op (e1) (e2)) = (e3))\/((op (e1) (e3)) = (e3))))) -> (~((op (e1) (e0)) = (e3))) -> (~((op (e1) (e3)) = (op (e2) (e3)))) -> (((op (e0) (e1)) = (e0))\/(((op (e0) (e1)) = (e1))\/(((op (e0) (e1)) = (e2))\/((op (e0) (e1)) = (e3))))) -> (~((op (e3) (e1)) = (e3))) -> (~((op (e0) (e1)) = (op (e3) (e1)))) -> (((op (e3) (e1)) = (e0))\/(((op (e3) (e1)) = (e1))\/(((op (e3) (e1)) = (e2))\/((op (e3) (e1)) = (e3))))) -> (~((op (e2) (e0)) = (e3))) -> (~((op (e2) (e0)) = (op (e2) (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) (e0)) = (op (e2) (e1)))) -> (~((op (e2) (e1)) = (op (e3) (e1)))) -> (~((op (e0) (e1)) = (op (e2) (e1)))) -> (~((op (e2) (e1)) = (e3))) -> (((op (e2) (e0)) = (e0))\/(((op (e2) (e0)) = (e1))\/(((op (e2) (e0)) = (e2))\/((op (e2) (e0)) = (e3))))) -> (~((op (e0) (e1)) = (e3))) -> (~((op (e0) (e0)) = (op (e2) (e0)))) -> ((op (e0) (e0)) = (e1)) -> (((op (e2) (e0)) = (e1))\/(((op (e2) (e1)) = (e1))\/(((op (e2) (e2)) = (e1))\/((op (e2) (e3)) = (e1))))) -> (~((op (e1) (e2)) = (e3))) -> (~((op (e1) (e3)) = (e3))) -> (~((op (e1) (e0)) = (op (e1) (e1)))) -> ((op (e1) (e0)) = (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) (e2)) = (e3))) -> ((op (e2) (e1)) = (e1)) -> ((op (e1) (e2)) = (e2)) -> (~((op (e0) (e2)) = (op (e1) (e2)))) -> ((op (e3) (e0)) = (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 (e1) (e3)) = (e1)) -> False). % 19.13/19.24 do 0 intro. intros zenon_He8 zenon_H95 zenon_H98 zenon_H1e0 zenon_H11d zenon_Hf3 zenon_H1ba zenon_H130 zenon_H60 zenon_H4a zenon_H1c7 zenon_H10e zenon_H109 zenon_H10a zenon_H1d8 zenon_H16f zenon_H9f zenon_Hdb zenon_H212 zenon_H282 zenon_H210 zenon_H22a zenon_H27f zenon_H5b zenon_H52 zenon_H1cc zenon_H1f0 zenon_Haf zenon_H17e zenon_Ha7 zenon_H259 zenon_H9c zenon_H39 zenon_H7a zenon_H106 zenon_H16d zenon_H12f zenon_H45 zenon_H27 zenon_H245 zenon_H14f zenon_H123 zenon_Ha5 zenon_H113 zenon_H195 zenon_H15e zenon_H12b zenon_H153 zenon_Hd5 zenon_Hd6. % 19.13/19.24 apply (zenon_or_s _ _ zenon_He8); [ zenon_intro zenon_Hac | zenon_intro zenon_Heb ]. % 19.13/19.24 apply (zenon_L1425_); trivial. % 19.13/19.24 apply (zenon_or_s _ _ zenon_Heb); [ zenon_intro zenon_Hae | zenon_intro zenon_Hec ]. % 19.13/19.24 apply (zenon_L42_); trivial. % 19.13/19.24 apply (zenon_or_s _ _ zenon_Hec); [ zenon_intro zenon_Hba | zenon_intro zenon_Hc4 ]. % 19.13/19.24 apply (zenon_L1437_); trivial. % 19.13/19.24 apply (zenon_L50_); trivial. % 19.13/19.24 (* end of lemma zenon_L1438_ *) % 19.13/19.24 assert (zenon_L1439_ : (((op (e2) (e1)) = (e0))\/(((op (e2) (e1)) = (e1))\/(((op (e2) (e1)) = (e2))\/((op (e2) (e1)) = (e3))))) -> ((op (e0) (e1)) = (e0)) -> (~((op (e0) (e1)) = (op (e2) (e1)))) -> (~((op (e2) (e1)) = (op (e3) (e1)))) -> ((op (e3) (e1)) = (e1)) -> (~((op (e2) (e1)) = (op (e2) (e3)))) -> ((op (e2) (e3)) = (e2)) -> (~((op (e2) (e1)) = (e3))) -> False). % 19.13/19.24 do 0 intro. intros zenon_H1cc zenon_H49 zenon_H17e zenon_Haf zenon_Hae zenon_H1c7 zenon_H11d zenon_Ha7. % 19.13/19.24 apply (zenon_or_s _ _ zenon_H1cc); [ zenon_intro zenon_H36 | zenon_intro zenon_H1cd ]. % 19.13/19.24 apply (zenon_L128_); trivial. % 19.13/19.24 apply (zenon_or_s _ _ zenon_H1cd); [ zenon_intro zenon_Ha5 | zenon_intro zenon_H1ce ]. % 19.13/19.24 apply (zenon_L42_); trivial. % 19.13/19.24 apply (zenon_or_s _ _ zenon_H1ce); [ zenon_intro zenon_H1ca | zenon_intro zenon_Ha6 ]. % 19.13/19.24 apply (zenon_L224_); trivial. % 19.13/19.24 exact (zenon_Ha7 zenon_Ha6). % 19.13/19.24 (* end of lemma zenon_L1439_ *) % 19.13/19.24 assert (zenon_L1440_ : (((op (e0) (e1)) = (e0))\/(((op (e1) (e1)) = (e0))\/(((op (e2) (e1)) = (e0))\/((op (e3) (e1)) = (e0))))) -> (~((e0) = (e1))) -> ((op (e1) (e0)) = (e0)) -> (~((op (e1) (e0)) = (op (e1) (e1)))) -> (~((op (e1) (e3)) = (e3))) -> (~((op (e1) (e2)) = (e3))) -> (((op (e3) (e1)) = (e0))\/(((op (e3) (e1)) = (e1))\/(((op (e3) (e1)) = (e2))\/((op (e3) (e1)) = (e3))))) -> ((op (e0) (e1)) = (e1)) -> (~((op (e0) (e1)) = (op (e3) (e1)))) -> (~((op (e3) (e1)) = (e3))) -> (~((op (e1) (e0)) = (e3))) -> (((op (e1) (e0)) = (e3))\/(((op (e1) (e1)) = (e3))\/(((op (e1) (e2)) = (e3))\/((op (e1) (e3)) = (e3))))) -> ((op (e3) (e3)) = (e0)) -> (~((op (e3) (e1)) = (op (e3) (e3)))) -> False). % 19.13/19.24 do 0 intro. intros zenon_H245 zenon_Ha1 zenon_H27 zenon_H45 zenon_H12f zenon_H16d zenon_H22a zenon_Ha0 zenon_H210 zenon_H282 zenon_H9f zenon_H16f zenon_H60 zenon_H130. % 19.13/19.24 apply (zenon_or_s _ _ zenon_H245); [ zenon_intro zenon_H49 | zenon_intro zenon_H246 ]. % 19.13/19.24 apply (zenon_L38_); trivial. % 19.13/19.24 apply (zenon_or_s _ _ zenon_H246); [ zenon_intro zenon_H29 | zenon_intro zenon_H247 ]. % 19.13/19.24 apply (zenon_L8_); trivial. % 19.13/19.24 apply (zenon_or_s _ _ zenon_H247); [ zenon_intro zenon_H36 | zenon_intro zenon_H1b1 ]. % 19.13/19.24 apply (zenon_L1429_); trivial. % 19.13/19.24 apply (zenon_L244_); trivial. % 19.13/19.24 (* end of lemma zenon_L1440_ *) % 19.13/19.24 assert (zenon_L1441_ : (((op (e0) (e1)) = (e1))\/(((op (e1) (e1)) = (e1))\/(((op (e2) (e1)) = (e1))\/((op (e3) (e1)) = (e1))))) -> ((op (e2) (e3)) = (e2)) -> (~((op (e2) (e1)) = (op (e2) (e3)))) -> (~((op (e1) (e1)) = (e1))) -> (~((op (e3) (e1)) = (e3))) -> (~((op (e0) (e1)) = (op (e3) (e1)))) -> ((op (e3) (e3)) = (e0)) -> (~((op (e3) (e1)) = (op (e3) (e3)))) -> (((op (e3) (e1)) = (e0))\/(((op (e3) (e1)) = (e1))\/(((op (e3) (e1)) = (e2))\/((op (e3) (e1)) = (e3))))) -> (((op (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 (e0) (e1)) = (e2)) -> (~((op (e0) (e1)) = (op (e2) (e1)))) -> (~((op (e2) (e1)) = (e3))) -> False). % 19.13/19.24 do 0 intro. intros zenon_H109 zenon_H11d zenon_H1c7 zenon_H10a zenon_H282 zenon_H210 zenon_H60 zenon_H130 zenon_H22a zenon_H1cc zenon_H34 zenon_H1f0 zenon_Haf zenon_H10f zenon_H17e zenon_Ha7. % 19.13/19.24 apply (zenon_or_s _ _ zenon_H109); [ zenon_intro zenon_Ha0 | zenon_intro zenon_H10b ]. % 19.13/19.24 apply (zenon_L1376_); trivial. % 19.13/19.24 apply (zenon_or_s _ _ zenon_H10b); [ zenon_intro zenon_H10d | zenon_intro zenon_H10c ]. % 19.13/19.24 exact (zenon_H10a zenon_H10d). % 19.13/19.24 apply (zenon_or_s _ _ zenon_H10c); [ zenon_intro zenon_Ha5 | zenon_intro zenon_Hae ]. % 19.13/19.24 apply (zenon_L1431_); trivial. % 19.13/19.24 apply (zenon_L1432_); trivial. % 19.13/19.24 (* end of lemma zenon_L1441_ *) % 19.13/19.24 assert (zenon_L1442_ : (((op (e0) (e1)) = (e2))\/(((op (e1) (e1)) = (e2))\/(((op (e2) (e1)) = (e2))\/((op (e3) (e1)) = (e2))))) -> (~((op (e2) (e1)) = (e3))) -> (~((op (e0) (e1)) = (op (e2) (e1)))) -> (~((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))))) -> (~((e0) = (e2))) -> ((op (e1) (e1)) = (e0)) -> (~((op (e2) (e1)) = (op (e2) (e3)))) -> ((op (e2) (e3)) = (e2)) -> ((op (e3) (e1)) = (e1)) -> (~((e1) = (e2))) -> False). % 19.13/19.24 do 0 intro. intros zenon_H1d8 zenon_Ha7 zenon_H17e zenon_Haf zenon_H1f0 zenon_H34 zenon_H1cc zenon_H149 zenon_H29 zenon_H1c7 zenon_H11d zenon_Hae zenon_H7c. % 19.13/19.24 apply (zenon_or_s _ _ zenon_H1d8); [ zenon_intro zenon_H10f | zenon_intro zenon_H1d9 ]. % 19.13/19.24 apply (zenon_L1432_); trivial. % 19.13/19.24 apply (zenon_or_s _ _ zenon_H1d9); [ zenon_intro zenon_H110 | zenon_intro zenon_H1da ]. % 19.13/19.24 apply (zenon_L354_); trivial. % 19.13/19.24 apply (zenon_or_s _ _ zenon_H1da); [ zenon_intro zenon_H1ca | zenon_intro zenon_H14d ]. % 19.13/19.24 apply (zenon_L224_); trivial. % 19.13/19.24 apply (zenon_L152_); trivial. % 19.13/19.24 (* end of lemma zenon_L1442_ *) % 19.13/19.24 assert (zenon_L1443_ : (~((op (e0) (e1)) = (e3))) -> (~((op (e0) (e1)) = (op (e3) (e1)))) -> ((op (e0) (e2)) = (e0)) -> (~((op (e0) (e1)) = (op (e0) (e2)))) -> (((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) (e1)) = (e1))) -> (~((op (e3) (e1)) = (e3))) -> ((op (e3) (e3)) = (e0)) -> (~((op (e3) (e1)) = (op (e3) (e3)))) -> (((op (e3) (e1)) = (e0))\/(((op (e3) (e1)) = (e1))\/(((op (e3) (e1)) = (e2))\/((op (e3) (e1)) = (e3))))) -> (((op (e0) (e1)) = (e2))\/(((op (e1) (e1)) = (e2))\/(((op (e2) (e1)) = (e2))\/((op (e3) (e1)) = (e2))))) -> (~((op (e2) (e1)) = (e3))) -> (~((op (e0) (e1)) = (op (e2) (e1)))) -> (~((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))))) -> (~((e0) = (e2))) -> ((op (e1) (e1)) = (e0)) -> (~((op (e2) (e1)) = (op (e2) (e3)))) -> ((op (e2) (e3)) = (e2)) -> (~((e1) = (e2))) -> False). % 19.13/19.24 do 0 intro. intros zenon_H9c zenon_H210 zenon_H48 zenon_H4a zenon_H212 zenon_H109 zenon_H10a zenon_H282 zenon_H60 zenon_H130 zenon_H22a zenon_H1d8 zenon_Ha7 zenon_H17e zenon_Haf zenon_H1f0 zenon_H34 zenon_H1cc zenon_H149 zenon_H29 zenon_H1c7 zenon_H11d zenon_H7c. % 19.13/19.24 apply (zenon_or_s _ _ zenon_H109); [ zenon_intro zenon_Ha0 | zenon_intro zenon_H10b ]. % 19.13/19.24 apply (zenon_L1376_); trivial. % 19.13/19.24 apply (zenon_or_s _ _ zenon_H10b); [ zenon_intro zenon_H10d | zenon_intro zenon_H10c ]. % 19.13/19.24 exact (zenon_H10a zenon_H10d). % 19.13/19.24 apply (zenon_or_s _ _ zenon_H10c); [ zenon_intro zenon_Ha5 | zenon_intro zenon_Hae ]. % 19.13/19.24 apply (zenon_or_s _ _ zenon_H1d8); [ zenon_intro zenon_H10f | zenon_intro zenon_H1d9 ]. % 19.13/19.24 apply (zenon_L1441_); trivial. % 19.13/19.24 apply (zenon_or_s _ _ zenon_H1d9); [ zenon_intro zenon_H110 | zenon_intro zenon_H1da ]. % 19.13/19.24 apply (zenon_L354_); trivial. % 19.13/19.24 apply (zenon_or_s _ _ zenon_H1da); [ zenon_intro zenon_H1ca | zenon_intro zenon_H14d ]. % 19.13/19.24 apply (zenon_L224_); trivial. % 19.13/19.24 apply (zenon_L1426_); trivial. % 19.13/19.24 apply (zenon_L1442_); trivial. % 19.13/19.24 (* end of lemma zenon_L1443_ *) % 19.13/19.24 assert (zenon_L1444_ : (((op (e1) (e1)) = (e0))\/(((op (e1) (e1)) = (e1))\/(((op (e1) (e1)) = (e2))\/((op (e1) (e1)) = (e3))))) -> (~((op (e1) (e1)) = (op (e1) (e3)))) -> ((op (e1) (e3)) = (e0)) -> (~((op (e1) (e1)) = (e1))) -> ((op (e0) (e1)) = (e2)) -> (~((op (e0) (e1)) = (op (e1) (e1)))) -> (~((op (e1) (e1)) = (e3))) -> False). % 19.13/19.24 do 0 intro. intros zenon_H142 zenon_H57 zenon_H1f zenon_H10a zenon_H10f zenon_H10e zenon_H1a1. % 19.13/19.24 apply (zenon_or_s _ _ zenon_H142); [ zenon_intro zenon_H29 | zenon_intro zenon_H143 ]. % 19.13/19.24 apply (zenon_L13_); trivial. % 19.13/19.24 apply (zenon_or_s _ _ zenon_H143); [ zenon_intro zenon_H10d | zenon_intro zenon_H144 ]. % 19.13/19.24 exact (zenon_H10a zenon_H10d). % 19.13/19.24 apply (zenon_or_s _ _ zenon_H144); [ zenon_intro zenon_H110 | zenon_intro zenon_H13f ]. % 19.13/19.24 apply (zenon_L67_); trivial. % 19.13/19.24 exact (zenon_H1a1 zenon_H13f). % 19.13/19.24 (* end of lemma zenon_L1444_ *) % 19.13/19.24 assert (zenon_L1445_ : (((op (e0) (e1)) = (e0))\/(((op (e0) (e1)) = (e1))\/(((op (e0) (e1)) = (e2))\/((op (e0) (e1)) = (e3))))) -> ((op (e2) (e1)) = (e0)) -> ((op (e3) (e3)) = (e1)) -> (~((op (e2) (e3)) = (op (e3) (e3)))) -> (~((op (e1) (e2)) = (op (e2) (e2)))) -> ((op (e1) (e2)) = (e1)) -> (~((op (e0) (e1)) = (op (e2) (e1)))) -> ((op (e1) (e0)) = (e3)) -> ((op (e0) (e0)) = (e2)) -> (((op (e2) (e0)) = (e1))\/(((op (e2) (e1)) = (e1))\/(((op (e2) (e2)) = (e1))\/((op (e2) (e3)) = (e1))))) -> ((op (e1) (e1)) = (e2)) -> (~((op (e0) (e1)) = (op (e1) (e1)))) -> (~((op (e0) (e1)) = (e3))) -> False). % 19.13/19.24 do 0 intro. intros zenon_H212 zenon_H36 zenon_Hc4 zenon_Hf3 zenon_H2b zenon_Hf0 zenon_H17e zenon_H9e zenon_H7b zenon_H106 zenon_H110 zenon_H10e zenon_H9c. % 19.13/19.24 apply (zenon_or_s _ _ zenon_H212); [ zenon_intro zenon_H49 | zenon_intro zenon_H213 ]. % 19.13/19.24 apply (zenon_L128_); trivial. % 19.13/19.24 apply (zenon_or_s _ _ zenon_H213); [ zenon_intro zenon_Ha0 | zenon_intro zenon_H214 ]. % 19.13/19.24 apply (zenon_L1002_); trivial. % 19.13/19.24 apply (zenon_or_s _ _ zenon_H214); [ zenon_intro zenon_H10f | zenon_intro zenon_H99 ]. % 19.13/19.24 apply (zenon_L67_); trivial. % 19.13/19.24 exact (zenon_H9c zenon_H99). % 19.13/19.24 (* end of lemma zenon_L1445_ *) % 19.13/19.24 assert (zenon_L1446_ : (((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 (e0) (e1)) = (e3))) -> (~((op (e0) (e1)) = (op (e1) (e1)))) -> ((op (e1) (e1)) = (e2)) -> (((op (e2) (e0)) = (e1))\/(((op (e2) (e1)) = (e1))\/(((op (e2) (e2)) = (e1))\/((op (e2) (e3)) = (e1))))) -> ((op (e0) (e0)) = (e2)) -> ((op (e1) (e0)) = (e3)) -> (~((op (e0) (e1)) = (op (e2) (e1)))) -> ((op (e1) (e2)) = (e1)) -> (~((op (e1) (e2)) = (op (e2) (e2)))) -> (~((op (e2) (e3)) = (op (e3) (e3)))) -> ((op (e3) (e3)) = (e1)) -> (((op (e0) (e1)) = (e0))\/(((op (e0) (e1)) = (e1))\/(((op (e0) (e1)) = (e2))\/((op (e0) (e1)) = (e3))))) -> ((op (e0) (e2)) = (e0)) -> (~((op (e0) (e2)) = (op (e2) (e2)))) -> (~((op (e1) (e3)) = (op (e2) (e3)))) -> ((op (e1) (e3)) = (e0)) -> False). % 19.13/19.24 do 0 intro. intros zenon_H2f zenon_H17b zenon_H44 zenon_H9c zenon_H10e zenon_H110 zenon_H106 zenon_H7b zenon_H9e zenon_H17e zenon_Hf0 zenon_H2b zenon_Hf3 zenon_Hc4 zenon_H212 zenon_H48 zenon_Ha8 zenon_Hdb zenon_H1f. % 19.13/19.24 apply (zenon_or_s _ _ zenon_H2f); [ zenon_intro zenon_H34 | zenon_intro zenon_H33 ]. % 19.13/19.24 apply (zenon_L127_); trivial. % 19.13/19.24 apply (zenon_or_s _ _ zenon_H33); [ zenon_intro zenon_H36 | zenon_intro zenon_H35 ]. % 19.13/19.24 apply (zenon_L1445_); trivial. % 19.13/19.24 apply (zenon_or_s _ _ zenon_H35); [ zenon_intro zenon_H2c | zenon_intro zenon_H37 ]. % 19.13/19.24 apply (zenon_L679_); trivial. % 19.13/19.24 apply (zenon_L130_); trivial. % 19.13/19.24 (* end of lemma zenon_L1446_ *) % 19.13/19.24 assert (zenon_L1447_ : ((~((op (e3) (e0)) = (e3)))\/((op (e3) (e3)) = (e0))) -> ((op (e1) (e3)) = (e0)) -> ((~((op (e3) (e2)) = (e3)))\/((op (e3) (e3)) = (e2))) -> ((op (e2) (e3)) = (e2)) -> (~((op (e2) (e3)) = (op (e3) (e3)))) -> (~((op (e3) (e3)) = (e3))) -> (((op (e3) (e0)) = (e3))\/(((op (e3) (e1)) = (e3))\/(((op (e3) (e2)) = (e3))\/((op (e3) (e3)) = (e3))))) -> (~((op (e1) (e3)) = (op (e3) (e3)))) -> ((op (e1) (e3)) = (e1)) -> ((~((op (e3) (e1)) = (e3)))\/((op (e3) (e3)) = (e1))) -> False). % 19.13/19.25 do 0 intro. intros zenon_H286 zenon_H1f zenon_H284 zenon_H11d zenon_Hf3 zenon_H102 zenon_H165 zenon_Hd5 zenon_Hd6 zenon_H285. % 19.13/19.25 apply (zenon_or_s _ _ zenon_H286); [ zenon_intro zenon_H15f | zenon_intro zenon_H60 ]. % 19.13/19.25 apply (zenon_L1369_); trivial. % 19.13/19.25 apply (zenon_L136_); trivial. % 19.13/19.25 (* end of lemma zenon_L1447_ *) % 19.13/19.25 assert (zenon_L1448_ : ((~((op (e2) (e0)) = (e3)))\/((op (e2) (e3)) = (e0))) -> ((~((op (e2) (e2)) = (e3)))\/((op (e2) (e3)) = (e2))) -> ((~((op (e3) (e1)) = (e3)))\/((op (e3) (e3)) = (e1))) -> ((op (e1) (e3)) = (e1)) -> (~((op (e1) (e3)) = (op (e3) (e3)))) -> (((op (e3) (e0)) = (e3))\/(((op (e3) (e1)) = (e3))\/(((op (e3) (e2)) = (e3))\/((op (e3) (e3)) = (e3))))) -> (~((op (e3) (e3)) = (e3))) -> (~((op (e2) (e3)) = (op (e3) (e3)))) -> ((~((op (e3) (e2)) = (e3)))\/((op (e3) (e3)) = (e2))) -> ((op (e1) (e3)) = (e0)) -> ((~((op (e3) (e0)) = (e3)))\/((op (e3) (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)) = (e3)) -> ((~((op (e2) (e3)) = (e3)))\/((op (e2) (e3)) = (e3))) -> (~((op (e1) (e3)) = (op (e2) (e3)))) -> ((~((op (e2) (e1)) = (e3)))\/((op (e2) (e3)) = (e1))) -> False). % 19.13/19.25 do 0 intro. intros zenon_H28a zenon_H288 zenon_H285 zenon_Hd6 zenon_Hd5 zenon_H165 zenon_H102 zenon_Hf3 zenon_H284 zenon_H1f zenon_H286 zenon_He7 zenon_He2 zenon_He3 zenon_H281 zenon_Hdb zenon_H28b. % 19.13/19.25 apply (zenon_or_s _ _ zenon_H28a); [ zenon_intro zenon_H27f | zenon_intro zenon_H37 ]. % 19.13/19.25 apply (zenon_or_s _ _ zenon_H28b); [ zenon_intro zenon_Ha7 | zenon_intro zenon_Hf4 ]. % 19.13/19.25 apply (zenon_or_s _ _ zenon_H288); [ zenon_intro zenon_H1b3 | zenon_intro zenon_H11d ]. % 19.13/19.25 apply (zenon_L1421_); trivial. % 19.13/19.25 apply (zenon_L1447_); trivial. % 19.13/19.25 apply (zenon_L126_); trivial. % 19.13/19.25 apply (zenon_L130_); trivial. % 19.13/19.25 (* end of lemma zenon_L1448_ *) % 19.13/19.25 assert (zenon_L1449_ : ((~((op (e3) (e2)) = (e3)))\/((op (e3) (e3)) = (e2))) -> ((op (e0) (e3)) = (e2)) -> (~((op (e0) (e3)) = (op (e3) (e3)))) -> (~((op (e3) (e0)) = (e3))) -> (~((op (e3) (e1)) = (e3))) -> (~((op (e3) (e3)) = (e3))) -> (((op (e3) (e0)) = (e3))\/(((op (e3) (e1)) = (e3))\/(((op (e3) (e2)) = (e3))\/((op (e3) (e3)) = (e3))))) -> False). % 19.13/19.25 do 0 intro. intros zenon_H284 zenon_Hcd zenon_Hc2 zenon_H15f zenon_H282 zenon_H102 zenon_H165. % 19.13/19.25 apply (zenon_or_s _ _ zenon_H284); [ zenon_intro zenon_H283 | zenon_intro zenon_Hf6 ]. % 19.13/19.25 apply (zenon_L1346_); trivial. % 19.13/19.25 apply (zenon_L87_); trivial. % 19.13/19.25 (* end of lemma zenon_L1449_ *) % 19.13/19.25 assert (zenon_L1450_ : ((~((op (e3) (e1)) = (e3)))\/((op (e3) (e3)) = (e1))) -> ((op (e1) (e3)) = (e0)) -> (((op (e3) (e0)) = (e3))\/(((op (e3) (e1)) = (e3))\/(((op (e3) (e2)) = (e3))\/((op (e3) (e3)) = (e3))))) -> (~((op (e3) (e3)) = (e3))) -> (~((op (e3) (e0)) = (e3))) -> (~((op (e0) (e3)) = (op (e3) (e3)))) -> ((op (e0) (e3)) = (e2)) -> ((~((op (e3) (e2)) = (e3)))\/((op (e3) (e3)) = (e2))) -> False). % 19.13/19.25 do 0 intro. intros zenon_H285 zenon_H1f zenon_H165 zenon_H102 zenon_H15f zenon_Hc2 zenon_Hcd zenon_H284. % 19.13/19.25 apply (zenon_or_s _ _ zenon_H285); [ zenon_intro zenon_H282 | zenon_intro zenon_Hc4 ]. % 19.13/19.25 apply (zenon_L1449_); trivial. % 19.13/19.25 apply (zenon_L49_); trivial. % 19.13/19.25 (* end of lemma zenon_L1450_ *) % 19.13/19.25 assert (zenon_L1451_ : (((op (e0) (e0)) = (e2))\/(((op (e0) (e1)) = (e2))\/(((op (e0) (e2)) = (e2))\/((op (e0) (e3)) = (e2))))) -> (~((op (e2) (e0)) = (e3))) -> (((op (e1) (e0)) = (e1))\/(((op (e1) (e1)) = (e1))\/(((op (e1) (e2)) = (e1))\/((op (e1) (e3)) = (e1))))) -> (~((e1) = (e3))) -> (~((op (e1) (e2)) = (op (e2) (e2)))) -> (~((op (e0) (e1)) = (op (e2) (e1)))) -> ((op (e0) (e1)) = (e1)) -> (((op (e2) (e0)) = (e1))\/(((op (e2) (e1)) = (e1))\/(((op (e2) (e2)) = (e1))\/((op (e2) (e3)) = (e1))))) -> ((~((op (e2) (e0)) = (e3)))\/((op (e2) (e3)) = (e0))) -> ((~((op (e2) (e2)) = (e3)))\/((op (e2) (e3)) = (e2))) -> (~((op (e1) (e3)) = (op (e3) (e3)))) -> (~((op (e2) (e3)) = (op (e3) (e3)))) -> ((~((op (e3) (e0)) = (e3)))\/((op (e3) (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)) = (e3)) -> ((~((op (e2) (e3)) = (e3)))\/((op (e2) (e3)) = (e3))) -> (~((op (e1) (e3)) = (op (e2) (e3)))) -> ((~((op (e2) (e1)) = (e3)))\/((op (e2) (e3)) = (e1))) -> (~((op (e0) (e0)) = (e3))) -> (((op (e0) (e0)) = (e3))\/(((op (e1) (e0)) = (e3))\/(((op (e2) (e0)) = (e3))\/((op (e3) (e0)) = (e3))))) -> (~((op (e1) (e1)) = (e3))) -> (~((op (e0) (e1)) = (op (e1) (e1)))) -> (~((op (e1) (e1)) = (e1))) -> (~((op (e1) (e1)) = (op (e1) (e3)))) -> (((op (e1) (e1)) = (e0))\/(((op (e1) (e1)) = (e1))\/(((op (e1) (e1)) = (e2))\/((op (e1) (e1)) = (e3))))) -> (~((op (e3) (e2)) = (e3))) -> (~((op (e0) (e2)) = (op (e3) (e2)))) -> ((op (e3) (e3)) = (e1)) -> (~((op (e3) (e2)) = (op (e3) (e3)))) -> (~((op (e3) (e0)) = (op (e3) (e2)))) -> ((op (e3) (e0)) = (e0)) -> (((op (e3) (e2)) = (e0))\/(((op (e3) (e2)) = (e1))\/(((op (e3) (e2)) = (e2))\/((op (e3) (e2)) = (e3))))) -> ((~((op (e3) (e1)) = (e3)))\/((op (e3) (e3)) = (e1))) -> ((op (e1) (e3)) = (e0)) -> (((op (e3) (e0)) = (e3))\/(((op (e3) (e1)) = (e3))\/(((op (e3) (e2)) = (e3))\/((op (e3) (e3)) = (e3))))) -> (~((op (e3) (e3)) = (e3))) -> (~((op (e3) (e0)) = (e3))) -> (~((op (e0) (e3)) = (op (e3) (e3)))) -> ((~((op (e3) (e2)) = (e3)))\/((op (e3) (e3)) = (e2))) -> False). % 19.13/19.25 do 0 intro. intros zenon_H183 zenon_H27f zenon_H128 zenon_H95 zenon_H2b zenon_H17e zenon_Ha0 zenon_H106 zenon_H28a zenon_H288 zenon_Hd5 zenon_Hf3 zenon_H286 zenon_He7 zenon_He2 zenon_He3 zenon_H281 zenon_Hdb zenon_H28b zenon_H98 zenon_H1e0 zenon_H1a1 zenon_H10e zenon_H10a zenon_H57 zenon_H142 zenon_H283 zenon_H14f zenon_Hc4 zenon_H62 zenon_H6f zenon_H44 zenon_H191 zenon_H285 zenon_H1f zenon_H165 zenon_H102 zenon_H15f zenon_Hc2 zenon_H284. % 19.13/19.25 apply (zenon_or_s _ _ zenon_H183); [ zenon_intro zenon_H7b | zenon_intro zenon_H186 ]. % 19.13/19.25 apply (zenon_or_s _ _ zenon_H1e0); [ zenon_intro zenon_H3a | zenon_intro zenon_H1e1 ]. % 19.13/19.25 exact (zenon_H98 zenon_H3a). % 19.13/19.25 apply (zenon_or_s _ _ zenon_H1e1); [ zenon_intro zenon_H9e | zenon_intro zenon_H1e2 ]. % 19.13/19.25 apply (zenon_or_s _ _ zenon_H128); [ zenon_intro zenon_H9d | zenon_intro zenon_H129 ]. % 19.13/19.25 apply (zenon_L37_); trivial. % 19.13/19.25 apply (zenon_or_s _ _ zenon_H129); [ zenon_intro zenon_H10d | zenon_intro zenon_H12a ]. % 19.13/19.25 exact (zenon_H10a zenon_H10d). % 19.13/19.25 apply (zenon_or_s _ _ zenon_H12a); [ zenon_intro zenon_Hf0 | zenon_intro zenon_Hd6 ]. % 19.13/19.25 apply (zenon_L1002_); trivial. % 19.13/19.25 apply (zenon_L1448_); trivial. % 19.13/19.25 apply (zenon_or_s _ _ zenon_H1e2); [ zenon_intro zenon_H3b | zenon_intro zenon_H15e ]. % 19.13/19.25 exact (zenon_H27f zenon_H3b). % 19.13/19.25 exact (zenon_H15f zenon_H15e). % 19.13/19.25 apply (zenon_or_s _ _ zenon_H186); [ zenon_intro zenon_H10f | zenon_intro zenon_H187 ]. % 19.13/19.25 apply (zenon_L1444_); trivial. % 19.13/19.25 apply (zenon_or_s _ _ zenon_H187); [ zenon_intro zenon_H150 | zenon_intro zenon_Hcd ]. % 19.13/19.25 apply (zenon_L1351_); trivial. % 19.13/19.25 apply (zenon_L1450_); trivial. % 19.13/19.25 (* end of lemma zenon_L1451_ *) % 19.13/19.25 assert (zenon_L1452_ : (((op (e0) (e1)) = (e0))\/(((op (e0) (e1)) = (e1))\/(((op (e0) (e1)) = (e2))\/((op (e0) (e1)) = (e3))))) -> ((op (e2) (e1)) = (e0)) -> ((~((op (e3) (e2)) = (e3)))\/((op (e3) (e3)) = (e2))) -> (~((op (e0) (e3)) = (op (e3) (e3)))) -> (~((op (e3) (e0)) = (e3))) -> (~((op (e3) (e3)) = (e3))) -> (((op (e3) (e0)) = (e3))\/(((op (e3) (e1)) = (e3))\/(((op (e3) (e2)) = (e3))\/((op (e3) (e3)) = (e3))))) -> ((~((op (e3) (e1)) = (e3)))\/((op (e3) (e3)) = (e1))) -> (((op (e3) (e2)) = (e0))\/(((op (e3) (e2)) = (e1))\/(((op (e3) (e2)) = (e2))\/((op (e3) (e2)) = (e3))))) -> ((op (e3) (e0)) = (e0)) -> (~((op (e3) (e0)) = (op (e3) (e2)))) -> (~((op (e3) (e2)) = (op (e3) (e3)))) -> ((op (e3) (e3)) = (e1)) -> (~((op (e0) (e2)) = (op (e3) (e2)))) -> (~((op (e3) (e2)) = (e3))) -> (((op (e0) (e0)) = (e3))\/(((op (e1) (e0)) = (e3))\/(((op (e2) (e0)) = (e3))\/((op (e3) (e0)) = (e3))))) -> (~((op (e0) (e0)) = (e3))) -> ((~((op (e2) (e1)) = (e3)))\/((op (e2) (e3)) = (e1))) -> (~((op (e1) (e3)) = (op (e2) (e3)))) -> ((~((op (e2) (e3)) = (e3)))\/((op (e2) (e3)) = (e3))) -> ((op (e0) (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 (e3) (e0)) = (e3)))\/((op (e3) (e3)) = (e0))) -> (~((op (e2) (e3)) = (op (e3) (e3)))) -> (~((op (e1) (e3)) = (op (e3) (e3)))) -> ((~((op (e2) (e2)) = (e3)))\/((op (e2) (e3)) = (e2))) -> ((~((op (e2) (e0)) = (e3)))\/((op (e2) (e3)) = (e0))) -> (((op (e2) (e0)) = (e1))\/(((op (e2) (e1)) = (e1))\/(((op (e2) (e2)) = (e1))\/((op (e2) (e3)) = (e1))))) -> (~((op (e0) (e1)) = (op (e2) (e1)))) -> (~((op (e1) (e2)) = (op (e2) (e2)))) -> (~((e1) = (e3))) -> (((op (e1) (e0)) = (e1))\/(((op (e1) (e1)) = (e1))\/(((op (e1) (e2)) = (e1))\/((op (e1) (e3)) = (e1))))) -> (~((op (e2) (e0)) = (e3))) -> (((op (e0) (e0)) = (e2))\/(((op (e0) (e1)) = (e2))\/(((op (e0) (e2)) = (e2))\/((op (e0) (e3)) = (e2))))) -> (~((op (e1) (e1)) = (e3))) -> (~((op (e0) (e1)) = (op (e1) (e1)))) -> (~((op (e1) (e1)) = (e1))) -> ((op (e1) (e3)) = (e0)) -> (~((op (e1) (e1)) = (op (e1) (e3)))) -> (((op (e1) (e1)) = (e0))\/(((op (e1) (e1)) = (e1))\/(((op (e1) (e1)) = (e2))\/((op (e1) (e1)) = (e3))))) -> (~((op (e0) (e1)) = (e3))) -> False). % 19.13/19.25 do 0 intro. intros zenon_H212 zenon_H36 zenon_H284 zenon_Hc2 zenon_H15f zenon_H102 zenon_H165 zenon_H285 zenon_H191 zenon_H44 zenon_H6f zenon_H62 zenon_Hc4 zenon_H14f zenon_H283 zenon_H1e0 zenon_H98 zenon_H28b zenon_Hdb zenon_H281 zenon_He3 zenon_He2 zenon_He7 zenon_H286 zenon_Hf3 zenon_Hd5 zenon_H288 zenon_H28a zenon_H106 zenon_H17e zenon_H2b zenon_H95 zenon_H128 zenon_H27f zenon_H183 zenon_H1a1 zenon_H10e zenon_H10a zenon_H1f zenon_H57 zenon_H142 zenon_H9c. % 19.13/19.25 apply (zenon_or_s _ _ zenon_H212); [ zenon_intro zenon_H49 | zenon_intro zenon_H213 ]. % 19.13/19.25 apply (zenon_L128_); trivial. % 19.13/19.25 apply (zenon_or_s _ _ zenon_H213); [ zenon_intro zenon_Ha0 | zenon_intro zenon_H214 ]. % 19.13/19.25 apply (zenon_L1451_); trivial. % 19.13/19.25 apply (zenon_or_s _ _ zenon_H214); [ zenon_intro zenon_H10f | zenon_intro zenon_H99 ]. % 19.13/19.25 apply (zenon_L1444_); trivial. % 19.13/19.25 exact (zenon_H9c zenon_H99). % 19.13/19.25 (* end of lemma zenon_L1452_ *) % 19.13/19.25 assert (zenon_L1453_ : (~((op (e0) (e2)) = (op (e2) (e2)))) -> ((op (e0) (e2)) = (e0)) -> (((op (e0) (e1)) = (e0))\/(((op (e0) (e1)) = (e1))\/(((op (e0) (e1)) = (e2))\/((op (e0) (e1)) = (e3))))) -> (~((op (e0) (e3)) = (op (e3) (e3)))) -> (~((op (e3) (e0)) = (e3))) -> (((op (e3) (e2)) = (e0))\/(((op (e3) (e2)) = (e1))\/(((op (e3) (e2)) = (e2))\/((op (e3) (e2)) = (e3))))) -> ((op (e3) (e0)) = (e0)) -> (~((op (e3) (e0)) = (op (e3) (e2)))) -> (~((op (e3) (e2)) = (op (e3) (e3)))) -> ((op (e3) (e3)) = (e1)) -> (~((op (e0) (e2)) = (op (e3) (e2)))) -> (~((op (e3) (e2)) = (e3))) -> (((op (e0) (e0)) = (e3))\/(((op (e1) (e0)) = (e3))\/(((op (e2) (e0)) = (e3))\/((op (e3) (e0)) = (e3))))) -> (~((op (e0) (e0)) = (e3))) -> (((op (e2) (e0)) = (e1))\/(((op (e2) (e1)) = (e1))\/(((op (e2) (e2)) = (e1))\/((op (e2) (e3)) = (e1))))) -> (~((op (e0) (e1)) = (op (e2) (e1)))) -> (~((op (e1) (e2)) = (op (e2) (e2)))) -> (~((e1) = (e3))) -> (((op (e1) (e0)) = (e1))\/(((op (e1) (e1)) = (e1))\/(((op (e1) (e2)) = (e1))\/((op (e1) (e3)) = (e1))))) -> (~((op (e2) (e0)) = (e3))) -> (((op (e0) (e0)) = (e2))\/(((op (e0) (e1)) = (e2))\/(((op (e0) (e2)) = (e2))\/((op (e0) (e3)) = (e2))))) -> (~((op (e1) (e1)) = (e3))) -> (~((op (e0) (e1)) = (op (e1) (e1)))) -> (~((op (e1) (e1)) = (e1))) -> (~((op (e1) (e1)) = (op (e1) (e3)))) -> (((op (e1) (e1)) = (e0))\/(((op (e1) (e1)) = (e1))\/(((op (e1) (e1)) = (e2))\/((op (e1) (e1)) = (e3))))) -> (~((op (e0) (e1)) = (e3))) -> (((op (e3) (e0)) = (e0))\/(((op (e3) (e0)) = (e1))\/(((op (e3) (e0)) = (e2))\/((op (e3) (e0)) = (e3))))) -> (~((op (e2) (e0)) = (op (e3) (e0)))) -> (~((op (e3) (e0)) = (op (e3) (e3)))) -> (~((op (e3) (e0)) = (op (e3) (e1)))) -> (((op (e2) (e0)) = (e0))\/(((op (e2) (e1)) = (e0))\/(((op (e2) (e2)) = (e0))\/((op (e2) (e3)) = (e0))))) -> ((op (e2) (e3)) = (e2)) -> (~((op (e2) (e1)) = (op (e2) (e3)))) -> ((op (e0) (e0)) = (e2)) -> ((op (e1) (e0)) = (e3)) -> (((op (e0) (e1)) = (e2))\/(((op (e1) (e1)) = (e2))\/(((op (e2) (e1)) = (e2))\/((op (e3) (e1)) = (e2))))) -> ((~((op (e2) (e0)) = (e3)))\/((op (e2) (e3)) = (e0))) -> ((~((op (e2) (e2)) = (e3)))\/((op (e2) (e3)) = (e2))) -> ((~((op (e3) (e1)) = (e3)))\/((op (e3) (e3)) = (e1))) -> (~((op (e1) (e3)) = (op (e3) (e3)))) -> (((op (e3) (e0)) = (e3))\/(((op (e3) (e1)) = (e3))\/(((op (e3) (e2)) = (e3))\/((op (e3) (e3)) = (e3))))) -> (~((op (e3) (e3)) = (e3))) -> (~((op (e2) (e3)) = (op (e3) (e3)))) -> ((~((op (e3) (e2)) = (e3)))\/((op (e3) (e3)) = (e2))) -> ((op (e1) (e3)) = (e0)) -> ((~((op (e3) (e0)) = (e3)))\/((op (e3) (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)) = (e3)) -> ((~((op (e2) (e3)) = (e3)))\/((op (e2) (e3)) = (e3))) -> (~((op (e1) (e3)) = (op (e2) (e3)))) -> ((~((op (e2) (e1)) = (e3)))\/((op (e2) (e3)) = (e1))) -> False). % 19.13/19.25 do 0 intro. intros zenon_Ha8 zenon_H48 zenon_H212 zenon_Hc2 zenon_H15f zenon_H191 zenon_H44 zenon_H6f zenon_H62 zenon_Hc4 zenon_H14f zenon_H283 zenon_H1e0 zenon_H98 zenon_H106 zenon_H17e zenon_H2b zenon_H95 zenon_H128 zenon_H27f zenon_H183 zenon_H1a1 zenon_H10e zenon_H10a zenon_H57 zenon_H142 zenon_H9c zenon_H267 zenon_H17b zenon_H71 zenon_H1cf zenon_H2f zenon_H11d zenon_H1c7 zenon_H7b zenon_H9e zenon_H1d8 zenon_H28a zenon_H288 zenon_H285 zenon_Hd5 zenon_H165 zenon_H102 zenon_Hf3 zenon_H284 zenon_H1f zenon_H286 zenon_He7 zenon_He2 zenon_He3 zenon_H281 zenon_Hdb zenon_H28b. % 19.13/19.25 apply (zenon_or_s _ _ zenon_H128); [ zenon_intro zenon_H9d | zenon_intro zenon_H129 ]. % 19.13/19.25 apply (zenon_L37_); trivial. % 19.13/19.25 apply (zenon_or_s _ _ zenon_H129); [ zenon_intro zenon_H10d | zenon_intro zenon_H12a ]. % 19.13/19.25 exact (zenon_H10a zenon_H10d). % 19.13/19.25 apply (zenon_or_s _ _ zenon_H12a); [ zenon_intro zenon_Hf0 | zenon_intro zenon_Hd6 ]. % 19.13/19.25 apply (zenon_or_s _ _ zenon_H1d8); [ zenon_intro zenon_H10f | zenon_intro zenon_H1d9 ]. % 19.13/19.25 apply (zenon_L1444_); trivial. % 19.13/19.25 apply (zenon_or_s _ _ zenon_H1d9); [ zenon_intro zenon_H110 | zenon_intro zenon_H1da ]. % 19.13/19.25 apply (zenon_L1446_); trivial. % 19.13/19.25 apply (zenon_or_s _ _ zenon_H1da); [ zenon_intro zenon_H1ca | zenon_intro zenon_H14d ]. % 19.13/19.25 apply (zenon_L224_); trivial. % 19.13/19.25 apply (zenon_or_s _ _ zenon_H2f); [ zenon_intro zenon_H34 | zenon_intro zenon_H33 ]. % 19.13/19.25 apply (zenon_L1396_); trivial. % 19.13/19.25 apply (zenon_or_s _ _ zenon_H33); [ zenon_intro zenon_H36 | zenon_intro zenon_H35 ]. % 19.13/19.25 apply (zenon_L1452_); trivial. % 19.13/19.25 apply (zenon_or_s _ _ zenon_H35); [ zenon_intro zenon_H2c | zenon_intro zenon_H37 ]. % 19.13/19.25 apply (zenon_L679_); trivial. % 19.13/19.25 apply (zenon_L130_); trivial. % 19.13/19.25 apply (zenon_L1448_); trivial. % 19.13/19.25 (* end of lemma zenon_L1453_ *) % 19.13/19.25 assert (zenon_L1454_ : (((op (e3) (e0)) = (e0))\/(((op (e3) (e0)) = (e1))\/(((op (e3) (e0)) = (e2))\/((op (e3) (e0)) = (e3))))) -> ((op (e3) (e2)) = (e0)) -> (~((op (e3) (e0)) = (op (e3) (e3)))) -> ((op (e3) (e3)) = (e1)) -> ((op (e3) (e2)) = (e2)) -> (~((op (e3) (e0)) = (op (e3) (e2)))) -> (~((op (e3) (e0)) = (e3))) -> False). % 19.13/19.25 do 0 intro. intros zenon_H267 zenon_H61 zenon_H71 zenon_Hc4 zenon_H151 zenon_H6f zenon_H15f. % 19.13/19.25 apply (zenon_or_s _ _ zenon_H267); [ zenon_intro zenon_H44 | zenon_intro zenon_H268 ]. % 19.13/19.25 apply (zenon_L19_); trivial. % 19.13/19.25 apply (zenon_or_s _ _ zenon_H268); [ zenon_intro zenon_Hac | zenon_intro zenon_H269 ]. % 19.13/19.25 apply (zenon_L189_); trivial. % 19.13/19.25 apply (zenon_or_s _ _ zenon_H269); [ zenon_intro zenon_H148 | zenon_intro zenon_H15e ]. % 19.13/19.25 apply (zenon_L420_); trivial. % 19.13/19.25 exact (zenon_H15f zenon_H15e). % 19.13/19.25 (* end of lemma zenon_L1454_ *) % 19.13/19.25 assert (zenon_L1455_ : (((op (e3) (e0)) = (e0))\/(((op (e3) (e1)) = (e0))\/(((op (e3) (e2)) = (e0))\/((op (e3) (e3)) = (e0))))) -> ((~((op (e2) (e1)) = (e3)))\/((op (e2) (e3)) = (e1))) -> (~((op (e1) (e3)) = (op (e2) (e3)))) -> ((~((op (e2) (e3)) = (e3)))\/((op (e2) (e3)) = (e3))) -> ((op (e0) (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 (e3) (e0)) = (e3)))\/((op (e3) (e3)) = (e0))) -> ((~((op (e3) (e2)) = (e3)))\/((op (e3) (e3)) = (e2))) -> (~((op (e2) (e3)) = (op (e3) (e3)))) -> (~((op (e3) (e3)) = (e3))) -> (((op (e3) (e0)) = (e3))\/(((op (e3) (e1)) = (e3))\/(((op (e3) (e2)) = (e3))\/((op (e3) (e3)) = (e3))))) -> ((~((op (e3) (e1)) = (e3)))\/((op (e3) (e3)) = (e1))) -> ((~((op (e2) (e2)) = (e3)))\/((op (e2) (e3)) = (e2))) -> ((~((op (e2) (e0)) = (e3)))\/((op (e2) (e3)) = (e0))) -> (((op (e0) (e1)) = (e2))\/(((op (e1) (e1)) = (e2))\/(((op (e2) (e1)) = (e2))\/((op (e3) (e1)) = (e2))))) -> ((op (e1) (e0)) = (e3)) -> ((op (e0) (e0)) = (e2)) -> (~((op (e2) (e1)) = (op (e2) (e3)))) -> ((op (e2) (e3)) = (e2)) -> (((op (e2) (e0)) = (e0))\/(((op (e2) (e1)) = (e0))\/(((op (e2) (e2)) = (e0))\/((op (e2) (e3)) = (e0))))) -> (~((op (e2) (e0)) = (op (e3) (e0)))) -> (~((op (e0) (e1)) = (e3))) -> (((op (e1) (e1)) = (e0))\/(((op (e1) (e1)) = (e1))\/(((op (e1) (e1)) = (e2))\/((op (e1) (e1)) = (e3))))) -> (~((op (e1) (e1)) = (op (e1) (e3)))) -> (~((op (e1) (e1)) = (e1))) -> (~((op (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 (e2) (e0)) = (e3))) -> (((op (e1) (e0)) = (e1))\/(((op (e1) (e1)) = (e1))\/(((op (e1) (e2)) = (e1))\/((op (e1) (e3)) = (e1))))) -> (~((e1) = (e3))) -> (~((op (e1) (e2)) = (op (e2) (e2)))) -> (~((op (e0) (e1)) = (op (e2) (e1)))) -> (((op (e2) (e0)) = (e1))\/(((op (e2) (e1)) = (e1))\/(((op (e2) (e2)) = (e1))\/((op (e2) (e3)) = (e1))))) -> (~((op (e0) (e0)) = (e3))) -> (((op (e0) (e0)) = (e3))\/(((op (e1) (e0)) = (e3))\/(((op (e2) (e0)) = (e3))\/((op (e3) (e0)) = (e3))))) -> (~((op (e3) (e2)) = (e3))) -> (~((op (e0) (e2)) = (op (e3) (e2)))) -> (~((op (e3) (e2)) = (op (e3) (e3)))) -> (((op (e3) (e2)) = (e0))\/(((op (e3) (e2)) = (e1))\/(((op (e3) (e2)) = (e2))\/((op (e3) (e2)) = (e3))))) -> (~((op (e0) (e3)) = (op (e3) (e3)))) -> (((op (e0) (e1)) = (e0))\/(((op (e0) (e1)) = (e1))\/(((op (e0) (e1)) = (e2))\/((op (e0) (e1)) = (e3))))) -> ((op (e0) (e2)) = (e0)) -> (~((op (e0) (e2)) = (op (e2) (e2)))) -> (~((op (e3) (e0)) = (op (e3) (e1)))) -> (~((op (e3) (e0)) = (e3))) -> (~((op (e3) (e0)) = (op (e3) (e2)))) -> ((op (e3) (e2)) = (e2)) -> ((op (e3) (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 (e1) (e3)) = (op (e3) (e3)))) -> ((op (e1) (e3)) = (e0)) -> False). % 19.13/19.25 do 0 intro. intros zenon_H1ac zenon_H28b zenon_Hdb zenon_H281 zenon_He3 zenon_He2 zenon_He7 zenon_H286 zenon_H284 zenon_Hf3 zenon_H102 zenon_H165 zenon_H285 zenon_H288 zenon_H28a zenon_H1d8 zenon_H9e zenon_H7b zenon_H1c7 zenon_H11d zenon_H2f zenon_H17b zenon_H9c zenon_H142 zenon_H57 zenon_H10a zenon_H10e zenon_H1a1 zenon_H183 zenon_H27f zenon_H128 zenon_H95 zenon_H2b zenon_H17e zenon_H106 zenon_H98 zenon_H1e0 zenon_H283 zenon_H14f zenon_H62 zenon_H191 zenon_Hc2 zenon_H212 zenon_H48 zenon_Ha8 zenon_H1cf zenon_H15f zenon_H6f zenon_H151 zenon_Hc4 zenon_H71 zenon_H267 zenon_Hd5 zenon_H1f. % 19.13/19.25 apply (zenon_or_s _ _ zenon_H1ac); [ zenon_intro zenon_H44 | zenon_intro zenon_H1af ]. % 19.13/19.25 apply (zenon_L1453_); trivial. % 19.13/19.25 apply (zenon_or_s _ _ zenon_H1af); [ zenon_intro zenon_H1b1 | zenon_intro zenon_H1b0 ]. % 19.13/19.25 apply (zenon_L1394_); trivial. % 19.13/19.25 apply (zenon_or_s _ _ zenon_H1b0); [ zenon_intro zenon_H61 | zenon_intro zenon_H60 ]. % 19.13/19.25 apply (zenon_L1454_); trivial. % 19.13/19.25 apply (zenon_L136_); trivial. % 19.13/19.25 (* end of lemma zenon_L1455_ *) % 19.13/19.25 assert (zenon_L1456_ : (((op (e0) (e2)) = (e0))\/(((op (e0) (e2)) = (e1))\/(((op (e0) (e2)) = (e2))\/((op (e0) (e2)) = (e3))))) -> ((op (e1) (e3)) = (e0)) -> (~((op (e1) (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) (e3)) = (e1)) -> (~((op (e3) (e0)) = (op (e3) (e2)))) -> (~((op (e3) (e0)) = (e3))) -> (~((op (e3) (e0)) = (op (e3) (e1)))) -> (~((op (e0) (e2)) = (op (e2) (e2)))) -> (((op (e0) (e1)) = (e0))\/(((op (e0) (e1)) = (e1))\/(((op (e0) (e1)) = (e2))\/((op (e0) (e1)) = (e3))))) -> (~((op (e0) (e3)) = (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) (e2)) = (e3))) -> (((op (e0) (e0)) = (e3))\/(((op (e1) (e0)) = (e3))\/(((op (e2) (e0)) = (e3))\/((op (e3) (e0)) = (e3))))) -> (~((op (e0) (e0)) = (e3))) -> (((op (e2) (e0)) = (e1))\/(((op (e2) (e1)) = (e1))\/(((op (e2) (e2)) = (e1))\/((op (e2) (e3)) = (e1))))) -> (~((op (e0) (e1)) = (op (e2) (e1)))) -> (~((op (e1) (e2)) = (op (e2) (e2)))) -> (~((e1) = (e3))) -> (((op (e1) (e0)) = (e1))\/(((op (e1) (e1)) = (e1))\/(((op (e1) (e2)) = (e1))\/((op (e1) (e3)) = (e1))))) -> (~((op (e2) (e0)) = (e3))) -> (((op (e0) (e0)) = (e2))\/(((op (e0) (e1)) = (e2))\/(((op (e0) (e2)) = (e2))\/((op (e0) (e3)) = (e2))))) -> (~((op (e1) (e1)) = (e3))) -> (~((op (e0) (e1)) = (op (e1) (e1)))) -> (~((op (e1) (e1)) = (e1))) -> (~((op (e1) (e1)) = (op (e1) (e3)))) -> (((op (e1) (e1)) = (e0))\/(((op (e1) (e1)) = (e1))\/(((op (e1) (e1)) = (e2))\/((op (e1) (e1)) = (e3))))) -> (~((op (e0) (e1)) = (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)) = (e2)) -> (~((op (e2) (e1)) = (op (e2) (e3)))) -> ((op (e0) (e0)) = (e2)) -> ((op (e1) (e0)) = (e3)) -> (((op (e0) (e1)) = (e2))\/(((op (e1) (e1)) = (e2))\/(((op (e2) (e1)) = (e2))\/((op (e3) (e1)) = (e2))))) -> ((~((op (e2) (e0)) = (e3)))\/((op (e2) (e3)) = (e0))) -> ((~((op (e2) (e2)) = (e3)))\/((op (e2) (e3)) = (e2))) -> ((~((op (e3) (e1)) = (e3)))\/((op (e3) (e3)) = (e1))) -> (((op (e3) (e0)) = (e3))\/(((op (e3) (e1)) = (e3))\/(((op (e3) (e2)) = (e3))\/((op (e3) (e3)) = (e3))))) -> (~((op (e3) (e3)) = (e3))) -> (~((op (e2) (e3)) = (op (e3) (e3)))) -> ((~((op (e3) (e2)) = (e3)))\/((op (e3) (e3)) = (e2))) -> ((~((op (e3) (e0)) = (e3)))\/((op (e3) (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)) = (e3)) -> ((~((op (e2) (e3)) = (e3)))\/((op (e2) (e3)) = (e3))) -> (~((op (e1) (e3)) = (op (e2) (e3)))) -> ((~((op (e2) (e1)) = (e3)))\/((op (e2) (e3)) = (e1))) -> (((op (e3) (e0)) = (e0))\/(((op (e3) (e1)) = (e0))\/(((op (e3) (e2)) = (e0))\/((op (e3) (e3)) = (e0))))) -> ((op (e1) (e2)) = (e1)) -> (~((op (e0) (e2)) = (op (e1) (e2)))) -> ((op (e3) (e2)) = (e2)) -> (~((op (e0) (e2)) = (op (e3) (e2)))) -> (~((op (e0) (e2)) = (e3))) -> False). % 19.13/19.25 do 0 intro. intros zenon_H1ba zenon_H1f zenon_Hd5 zenon_H267 zenon_H71 zenon_Hc4 zenon_H6f zenon_H15f zenon_H1cf zenon_Ha8 zenon_H212 zenon_Hc2 zenon_H191 zenon_H62 zenon_H283 zenon_H1e0 zenon_H98 zenon_H106 zenon_H17e zenon_H2b zenon_H95 zenon_H128 zenon_H27f zenon_H183 zenon_H1a1 zenon_H10e zenon_H10a zenon_H57 zenon_H142 zenon_H9c zenon_H17b zenon_H2f zenon_H11d zenon_H1c7 zenon_H7b zenon_H9e zenon_H1d8 zenon_H28a zenon_H288 zenon_H285 zenon_H165 zenon_H102 zenon_Hf3 zenon_H284 zenon_H286 zenon_He7 zenon_He2 zenon_He3 zenon_H281 zenon_Hdb zenon_H28b zenon_H1ac zenon_Hf0 zenon_H195 zenon_H151 zenon_H14f zenon_H123. % 19.13/19.25 apply (zenon_or_s _ _ zenon_H1ba); [ zenon_intro zenon_H48 | zenon_intro zenon_H1bb ]. % 19.13/19.25 apply (zenon_L1455_); trivial. % 19.13/19.25 apply (zenon_or_s _ _ zenon_H1bb); [ zenon_intro zenon_H122 | zenon_intro zenon_H1bc ]. % 19.13/19.25 apply (zenon_L530_); trivial. % 19.13/19.25 apply (zenon_or_s _ _ zenon_H1bc); [ zenon_intro zenon_H150 | zenon_intro zenon_Ha9 ]. % 19.13/19.25 apply (zenon_L104_); trivial. % 19.13/19.25 exact (zenon_H123 zenon_Ha9). % 19.13/19.25 (* end of lemma zenon_L1456_ *) % 19.13/19.25 assert (zenon_L1457_ : (~((op (e3) (e0)) = (e3))) -> (~((op (e2) (e0)) = (e3))) -> (~((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) (e1)) = (e3)))\/((op (e2) (e3)) = (e1))) -> (~((op (e1) (e3)) = (op (e2) (e3)))) -> ((~((op (e2) (e3)) = (e3)))\/((op (e2) (e3)) = (e3))) -> ((op (e0) (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 (e3) (e0)) = (e3)))\/((op (e3) (e3)) = (e0))) -> ((~((op (e3) (e2)) = (e3)))\/((op (e3) (e3)) = (e2))) -> (~((op (e2) (e3)) = (op (e3) (e3)))) -> (~((op (e3) (e3)) = (e3))) -> (((op (e3) (e0)) = (e3))\/(((op (e3) (e1)) = (e3))\/(((op (e3) (e2)) = (e3))\/((op (e3) (e3)) = (e3))))) -> ((~((op (e3) (e1)) = (e3)))\/((op (e3) (e3)) = (e1))) -> ((~((op (e2) (e2)) = (e3)))\/((op (e2) (e3)) = (e2))) -> ((~((op (e2) (e0)) = (e3)))\/((op (e2) (e3)) = (e0))) -> (((op (e0) (e1)) = (e2))\/(((op (e1) (e1)) = (e2))\/(((op (e2) (e1)) = (e2))\/((op (e3) (e1)) = (e2))))) -> (~((op (e2) (e1)) = (op (e2) (e3)))) -> ((op (e2) (e3)) = (e2)) -> (((op (e2) (e0)) = (e0))\/(((op (e2) (e1)) = (e0))\/(((op (e2) (e2)) = (e0))\/((op (e2) (e3)) = (e0))))) -> (~((op (e2) (e0)) = (op (e3) (e0)))) -> (~((op (e0) (e1)) = (e3))) -> (((op (e0) (e0)) = (e2))\/(((op (e0) (e1)) = (e2))\/(((op (e0) (e2)) = (e2))\/((op (e0) (e3)) = (e2))))) -> (((op (e1) (e0)) = (e1))\/(((op (e1) (e1)) = (e1))\/(((op (e1) (e2)) = (e1))\/((op (e1) (e3)) = (e1))))) -> (~((e1) = (e3))) -> (~((op (e1) (e2)) = (op (e2) (e2)))) -> (~((op (e0) (e1)) = (op (e2) (e1)))) -> (((op (e2) (e0)) = (e1))\/(((op (e2) (e1)) = (e1))\/(((op (e2) (e2)) = (e1))\/((op (e2) (e3)) = (e1))))) -> (~((op (e0) (e0)) = (e3))) -> (((op (e0) (e0)) = (e3))\/(((op (e1) (e0)) = (e3))\/(((op (e2) (e0)) = (e3))\/((op (e3) (e0)) = (e3))))) -> (~((op (e0) (e3)) = (op (e3) (e3)))) -> (((op (e0) (e1)) = (e0))\/(((op (e0) (e1)) = (e1))\/(((op (e0) (e1)) = (e2))\/((op (e0) (e1)) = (e3))))) -> (~((op (e0) (e2)) = (op (e2) (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) (e2)) = (e0))\/(((op (e0) (e2)) = (e1))\/(((op (e0) (e2)) = (e2))\/((op (e0) (e2)) = (e3))))) -> (~((op (e2) (e2)) = (e2))) -> (~((e1) = (e2))) -> (((op (e0) (e2)) = (e2))\/(((op (e1) (e2)) = (e2))\/(((op (e2) (e2)) = (e2))\/((op (e3) (e2)) = (e2))))) -> (~((op (e1) (e3)) = (op (e3) (e3)))) -> (~((op (e1) (e1)) = (e3))) -> (~((op (e0) (e1)) = (op (e1) (e1)))) -> (~((op (e1) (e1)) = (e1))) -> (~((op (e1) (e1)) = (op (e1) (e3)))) -> (((op (e1) (e1)) = (e0))\/(((op (e1) (e1)) = (e1))\/(((op (e1) (e1)) = (e2))\/((op (e1) (e1)) = (e3))))) -> (~((op (e3) (e2)) = (e3))) -> (~((op (e0) (e2)) = (op (e3) (e2)))) -> (~((op (e3) (e2)) = (op (e3) (e3)))) -> (~((op (e3) (e0)) = (op (e3) (e2)))) -> ((op (e3) (e0)) = (e0)) -> (((op (e3) (e2)) = (e0))\/(((op (e3) (e2)) = (e1))\/(((op (e3) (e2)) = (e2))\/((op (e3) (e2)) = (e3))))) -> ((op (e1) (e3)) = (e0)) -> ((op (e3) (e3)) = (e1)) -> False). % 19.13/19.25 do 0 intro. intros zenon_H15f zenon_H27f zenon_H123 zenon_H195 zenon_H1ac zenon_H28b zenon_Hdb zenon_H281 zenon_He3 zenon_He2 zenon_He7 zenon_H286 zenon_H284 zenon_Hf3 zenon_H102 zenon_H165 zenon_H285 zenon_H288 zenon_H28a zenon_H1d8 zenon_H1c7 zenon_H11d zenon_H2f zenon_H17b zenon_H9c zenon_H183 zenon_H128 zenon_H95 zenon_H2b zenon_H17e zenon_H106 zenon_H98 zenon_H1e0 zenon_Hc2 zenon_H212 zenon_Ha8 zenon_H1cf zenon_H71 zenon_H267 zenon_H1ba zenon_H173 zenon_H7c zenon_H172 zenon_Hd5 zenon_H1a1 zenon_H10e zenon_H10a zenon_H57 zenon_H142 zenon_H283 zenon_H14f zenon_H62 zenon_H6f zenon_H44 zenon_H191 zenon_H1f zenon_Hc4. % 19.13/19.25 apply (zenon_or_s _ _ zenon_H183); [ zenon_intro zenon_H7b | zenon_intro zenon_H186 ]. % 19.13/19.25 apply (zenon_or_s _ _ zenon_H1e0); [ zenon_intro zenon_H3a | zenon_intro zenon_H1e1 ]. % 19.13/19.25 exact (zenon_H98 zenon_H3a). % 19.13/19.25 apply (zenon_or_s _ _ zenon_H1e1); [ zenon_intro zenon_H9e | zenon_intro zenon_H1e2 ]. % 19.13/19.25 apply (zenon_or_s _ _ zenon_H128); [ zenon_intro zenon_H9d | zenon_intro zenon_H129 ]. % 19.13/19.25 apply (zenon_L37_); trivial. % 19.13/19.25 apply (zenon_or_s _ _ zenon_H129); [ zenon_intro zenon_H10d | zenon_intro zenon_H12a ]. % 19.13/19.25 exact (zenon_H10a zenon_H10d). % 19.13/19.25 apply (zenon_or_s _ _ zenon_H12a); [ zenon_intro zenon_Hf0 | zenon_intro zenon_Hd6 ]. % 19.13/19.25 apply (zenon_or_s _ _ zenon_H172); [ zenon_intro zenon_H150 | zenon_intro zenon_H174 ]. % 19.13/19.25 apply (zenon_L1351_); trivial. % 19.13/19.25 apply (zenon_or_s _ _ zenon_H174); [ zenon_intro zenon_H113 | zenon_intro zenon_H175 ]. % 19.13/19.25 apply (zenon_L68_); trivial. % 19.13/19.25 apply (zenon_or_s _ _ zenon_H175); [ zenon_intro zenon_H176 | zenon_intro zenon_H151 ]. % 19.13/19.25 exact (zenon_H173 zenon_H176). % 19.13/19.25 apply (zenon_L1456_); trivial. % 19.13/19.25 apply (zenon_L50_); trivial. % 19.13/19.25 apply (zenon_or_s _ _ zenon_H1e2); [ zenon_intro zenon_H3b | zenon_intro zenon_H15e ]. % 19.13/19.25 exact (zenon_H27f zenon_H3b). % 19.13/19.25 exact (zenon_H15f zenon_H15e). % 19.13/19.25 apply (zenon_or_s _ _ zenon_H186); [ zenon_intro zenon_H10f | zenon_intro zenon_H187 ]. % 19.13/19.25 apply (zenon_L1444_); trivial. % 19.13/19.25 apply (zenon_or_s _ _ zenon_H187); [ zenon_intro zenon_H150 | zenon_intro zenon_Hcd ]. % 19.13/19.25 apply (zenon_L1351_); trivial. % 19.13/19.25 apply (zenon_L49_); trivial. % 19.13/19.25 (* end of lemma zenon_L1457_ *) % 19.13/19.25 assert (zenon_L1458_ : (((op (e0) (e0)) = (e3))\/(((op (e1) (e0)) = (e3))\/(((op (e2) (e0)) = (e3))\/((op (e3) (e0)) = (e3))))) -> (~((op (e0) (e0)) = (e3))) -> ((op (e0) (e0)) = (e1)) -> ((op (e3) (e0)) = (e2)) -> (~((op (e2) (e0)) = (e3))) -> (~((op (e3) (e0)) = (e3))) -> False). % 19.13/19.25 do 0 intro. intros zenon_H1e0 zenon_H98 zenon_H7a zenon_H148 zenon_H27f zenon_H15f. % 19.13/19.25 apply (zenon_or_s _ _ zenon_H1e0); [ zenon_intro zenon_H3a | zenon_intro zenon_H1e1 ]. % 19.13/19.25 exact (zenon_H98 zenon_H3a). % 19.13/19.25 apply (zenon_or_s _ _ zenon_H1e1); [ zenon_intro zenon_H9e | zenon_intro zenon_H1e2 ]. % 19.13/19.25 apply (zenon_L107_); trivial. % 19.13/19.25 apply (zenon_or_s _ _ zenon_H1e2); [ zenon_intro zenon_H3b | zenon_intro zenon_H15e ]. % 19.13/19.25 exact (zenon_H27f zenon_H3b). % 19.13/19.25 exact (zenon_H15f zenon_H15e). % 19.13/19.25 (* end of lemma zenon_L1458_ *) % 19.13/19.25 assert (zenon_L1459_ : (((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) (e3)))) -> ((op (e3) (e3)) = (e1)) -> ((op (e3) (e1)) = (e2)) -> (~((op (e3) (e0)) = (op (e3) (e1)))) -> (~((op (e3) (e0)) = (e3))) -> False). % 19.13/19.25 do 0 intro. intros zenon_H267 zenon_H1b1 zenon_H71 zenon_Hc4 zenon_H14d zenon_H1cf zenon_H15f. % 19.13/19.25 apply (zenon_or_s _ _ zenon_H267); [ zenon_intro zenon_H44 | zenon_intro zenon_H268 ]. % 19.13/19.25 apply (zenon_L346_); trivial. % 19.13/19.25 apply (zenon_or_s _ _ zenon_H268); [ zenon_intro zenon_Hac | zenon_intro zenon_H269 ]. % 19.13/19.25 apply (zenon_L189_); trivial. % 19.13/19.25 apply (zenon_or_s _ _ zenon_H269); [ zenon_intro zenon_H148 | zenon_intro zenon_H15e ]. % 19.13/19.25 apply (zenon_L436_); trivial. % 19.13/19.25 exact (zenon_H15f zenon_H15e). % 19.13/19.25 (* end of lemma zenon_L1459_ *) % 19.13/19.25 assert (zenon_L1460_ : (((op (e3) (e0)) = (e2))\/(((op (e3) (e1)) = (e2))\/(((op (e3) (e2)) = (e2))\/((op (e3) (e3)) = (e2))))) -> ((op (e0) (e0)) = (e1)) -> ((op (e1) (e0)) = (e3)) -> (~((op (e3) (e0)) = (op (e3) (e1)))) -> (~((op (e3) (e0)) = (e3))) -> (~((op (e3) (e0)) = (op (e3) (e2)))) -> ((op (e3) (e3)) = (e1)) -> (~((op (e3) (e0)) = (op (e3) (e3)))) -> ((op (e3) (e2)) = (e0)) -> (((op (e3) (e0)) = (e0))\/(((op (e3) (e0)) = (e1))\/(((op (e3) (e0)) = (e2))\/((op (e3) (e0)) = (e3))))) -> (~((op (e2) (e3)) = (op (e3) (e3)))) -> ((op (e2) (e3)) = (e2)) -> False). % 19.13/19.25 do 0 intro. intros zenon_H153 zenon_H7a zenon_H9e zenon_H1cf zenon_H15f zenon_H6f zenon_Hc4 zenon_H71 zenon_H61 zenon_H267 zenon_Hf3 zenon_H11d. % 19.13/19.25 apply (zenon_or_s _ _ zenon_H153); [ zenon_intro zenon_H148 | zenon_intro zenon_H154 ]. % 19.13/19.25 apply (zenon_L107_); trivial. % 19.13/19.25 apply (zenon_or_s _ _ zenon_H154); [ zenon_intro zenon_H14d | zenon_intro zenon_H155 ]. % 19.13/19.25 apply (zenon_L1354_); trivial. % 19.13/19.25 apply (zenon_or_s _ _ zenon_H155); [ zenon_intro zenon_H151 | zenon_intro zenon_Hf6 ]. % 19.13/19.25 apply (zenon_L1454_); trivial. % 19.13/19.25 apply (zenon_L97_); trivial. % 19.13/19.25 (* end of lemma zenon_L1460_ *) % 19.13/19.25 assert (zenon_L1461_ : (((op (e0) (e0)) = (e3))\/(((op (e1) (e0)) = (e3))\/(((op (e2) (e0)) = (e3))\/((op (e3) (e0)) = (e3))))) -> (~((op (e0) (e0)) = (e3))) -> ((~((op (e2) (e1)) = (e3)))\/((op (e2) (e3)) = (e1))) -> (~((op (e1) (e3)) = (op (e2) (e3)))) -> ((~((op (e2) (e3)) = (e3)))\/((op (e2) (e3)) = (e3))) -> ((op (e0) (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 (e3) (e0)) = (e3)))\/((op (e3) (e3)) = (e0))) -> ((op (e1) (e3)) = (e0)) -> ((~((op (e3) (e2)) = (e3)))\/((op (e3) (e3)) = (e2))) -> (~((op (e2) (e3)) = (op (e3) (e3)))) -> (~((op (e3) (e3)) = (e3))) -> (((op (e3) (e0)) = (e3))\/(((op (e3) (e1)) = (e3))\/(((op (e3) (e2)) = (e3))\/((op (e3) (e3)) = (e3))))) -> (~((op (e1) (e3)) = (op (e3) (e3)))) -> ((~((op (e3) (e1)) = (e3)))\/((op (e3) (e3)) = (e1))) -> ((~((op (e2) (e2)) = (e3)))\/((op (e2) (e3)) = (e2))) -> ((~((op (e2) (e0)) = (e3)))\/((op (e2) (e3)) = (e0))) -> (~((op (e0) (e2)) = (op (e1) (e2)))) -> ((op (e0) (e2)) = (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) (e0)) = (e3))) -> (~((op (e3) (e0)) = (e3))) -> False). % 19.13/19.25 do 0 intro. intros zenon_H1e0 zenon_H98 zenon_H28b zenon_Hdb zenon_H281 zenon_He3 zenon_He2 zenon_He7 zenon_H286 zenon_H1f zenon_H284 zenon_Hf3 zenon_H102 zenon_H165 zenon_Hd5 zenon_H285 zenon_H288 zenon_H28a zenon_H195 zenon_H122 zenon_H10a zenon_H95 zenon_H128 zenon_H27f zenon_H15f. % 19.13/19.25 apply (zenon_or_s _ _ zenon_H1e0); [ zenon_intro zenon_H3a | zenon_intro zenon_H1e1 ]. % 19.13/19.25 exact (zenon_H98 zenon_H3a). % 19.13/19.25 apply (zenon_or_s _ _ zenon_H1e1); [ zenon_intro zenon_H9e | zenon_intro zenon_H1e2 ]. % 19.13/19.25 apply (zenon_or_s _ _ zenon_H128); [ zenon_intro zenon_H9d | zenon_intro zenon_H129 ]. % 19.13/19.25 apply (zenon_L37_); trivial. % 19.13/19.25 apply (zenon_or_s _ _ zenon_H129); [ zenon_intro zenon_H10d | zenon_intro zenon_H12a ]. % 19.13/19.25 exact (zenon_H10a zenon_H10d). % 19.13/19.25 apply (zenon_or_s _ _ zenon_H12a); [ zenon_intro zenon_Hf0 | zenon_intro zenon_Hd6 ]. % 19.13/19.25 apply (zenon_L530_); trivial. % 19.13/19.25 apply (zenon_L1448_); trivial. % 19.13/19.25 apply (zenon_or_s _ _ zenon_H1e2); [ zenon_intro zenon_H3b | zenon_intro zenon_H15e ]. % 19.13/19.25 exact (zenon_H27f zenon_H3b). % 19.13/19.25 exact (zenon_H15f zenon_H15e). % 19.13/19.25 (* end of lemma zenon_L1461_ *) % 19.13/19.25 assert (zenon_L1462_ : (((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)) = (e3))) -> (~((op (e3) (e0)) = (e3))) -> False). % 19.13/19.25 do 0 intro. intros zenon_H1e0 zenon_H98 zenon_H95 zenon_H9d zenon_H27f zenon_H15f. % 19.13/19.25 apply (zenon_or_s _ _ zenon_H1e0); [ zenon_intro zenon_H3a | zenon_intro zenon_H1e1 ]. % 19.13/19.25 exact (zenon_H98 zenon_H3a). % 19.13/19.25 apply (zenon_or_s _ _ zenon_H1e1); [ zenon_intro zenon_H9e | zenon_intro zenon_H1e2 ]. % 19.13/19.25 apply (zenon_L37_); trivial. % 19.13/19.25 apply (zenon_or_s _ _ zenon_H1e2); [ zenon_intro zenon_H3b | zenon_intro zenon_H15e ]. % 19.13/19.25 exact (zenon_H27f zenon_H3b). % 19.13/19.25 exact (zenon_H15f zenon_H15e). % 19.13/19.25 (* end of lemma zenon_L1462_ *) % 19.13/19.25 assert (zenon_L1463_ : (~((op (e2) (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) (e3)) = (e1)) -> (~((op (e3) (e0)) = (op (e3) (e2)))) -> (~((op (e3) (e0)) = (op (e3) (e1)))) -> (~((op (e0) (e2)) = (op (e2) (e2)))) -> (((op (e0) (e1)) = (e0))\/(((op (e0) (e1)) = (e1))\/(((op (e0) (e1)) = (e2))\/((op (e0) (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 (e0) (e2)) = (op (e3) (e2)))) -> (~((op (e3) (e2)) = (e3))) -> (((op (e0) (e0)) = (e3))\/(((op (e1) (e0)) = (e3))\/(((op (e2) (e0)) = (e3))\/((op (e3) (e0)) = (e3))))) -> (~((op (e0) (e0)) = (e3))) -> (((op (e2) (e0)) = (e1))\/(((op (e2) (e1)) = (e1))\/(((op (e2) (e2)) = (e1))\/((op (e2) (e3)) = (e1))))) -> (~((op (e0) (e1)) = (op (e2) (e1)))) -> (~((op (e1) (e2)) = (op (e2) (e2)))) -> (~((e1) = (e3))) -> (((op (e1) (e0)) = (e1))\/(((op (e1) (e1)) = (e1))\/(((op (e1) (e2)) = (e1))\/((op (e1) (e3)) = (e1))))) -> (((op (e0) (e0)) = (e2))\/(((op (e0) (e1)) = (e2))\/(((op (e0) (e2)) = (e2))\/((op (e0) (e3)) = (e2))))) -> (~((op (e0) (e1)) = (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)) = (e2)) -> (~((op (e2) (e1)) = (op (e2) (e3)))) -> (((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) (e2)) = (e2))) -> (~((e1) = (e2))) -> (((op (e0) (e2)) = (e2))\/(((op (e1) (e2)) = (e2))\/(((op (e2) (e2)) = (e2))\/((op (e3) (e2)) = (e2))))) -> ((~((op (e2) (e0)) = (e3)))\/((op (e2) (e3)) = (e0))) -> ((~((op (e2) (e2)) = (e3)))\/((op (e2) (e3)) = (e2))) -> (~((op (e1) (e3)) = (op (e3) (e3)))) -> (~((op (e2) (e3)) = (op (e3) (e3)))) -> ((~((op (e3) (e0)) = (e3)))\/((op (e3) (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)) = (e3)) -> ((~((op (e2) (e3)) = (e3)))\/((op (e2) (e3)) = (e3))) -> (~((op (e1) (e3)) = (op (e2) (e3)))) -> ((~((op (e2) (e1)) = (e3)))\/((op (e2) (e3)) = (e1))) -> (~((op (e1) (e1)) = (e3))) -> (~((op (e0) (e1)) = (op (e1) (e1)))) -> (~((op (e1) (e1)) = (e1))) -> (~((op (e1) (e1)) = (op (e1) (e3)))) -> (((op (e1) (e1)) = (e0))\/(((op (e1) (e1)) = (e1))\/(((op (e1) (e1)) = (e2))\/((op (e1) (e1)) = (e3))))) -> (~((e0) = (e2))) -> ((op (e0) (e2)) = (e0)) -> ((~((op (e3) (e1)) = (e3)))\/((op (e3) (e3)) = (e1))) -> ((op (e1) (e3)) = (e0)) -> (((op (e3) (e0)) = (e3))\/(((op (e3) (e1)) = (e3))\/(((op (e3) (e2)) = (e3))\/((op (e3) (e3)) = (e3))))) -> (~((op (e3) (e3)) = (e3))) -> (~((op (e3) (e0)) = (e3))) -> (~((op (e0) (e3)) = (op (e3) (e3)))) -> ((~((op (e3) (e2)) = (e3)))\/((op (e3) (e3)) = (e2))) -> False). % 19.13/19.25 do 0 intro. intros zenon_H27f zenon_H267 zenon_H71 zenon_Hc4 zenon_H6f zenon_H1cf zenon_Ha8 zenon_H212 zenon_H191 zenon_H62 zenon_H14f zenon_H283 zenon_H1e0 zenon_H98 zenon_H106 zenon_H17e zenon_H2b zenon_H95 zenon_H128 zenon_H183 zenon_H9c zenon_H17b zenon_H2f zenon_H11d zenon_H1c7 zenon_H1d8 zenon_H1ac zenon_H173 zenon_H7c zenon_H172 zenon_H28a zenon_H288 zenon_Hd5 zenon_Hf3 zenon_H286 zenon_He7 zenon_He2 zenon_He3 zenon_H281 zenon_Hdb zenon_H28b zenon_H1a1 zenon_H10e zenon_H10a zenon_H57 zenon_H142 zenon_H149 zenon_H48 zenon_H285 zenon_H1f zenon_H165 zenon_H102 zenon_H15f zenon_Hc2 zenon_H284. % 19.13/19.25 apply (zenon_or_s _ _ zenon_H183); [ zenon_intro zenon_H7b | zenon_intro zenon_H186 ]. % 19.13/19.25 apply (zenon_or_s _ _ zenon_H1e0); [ zenon_intro zenon_H3a | zenon_intro zenon_H1e1 ]. % 19.13/19.25 exact (zenon_H98 zenon_H3a). % 19.13/19.25 apply (zenon_or_s _ _ zenon_H1e1); [ zenon_intro zenon_H9e | zenon_intro zenon_H1e2 ]. % 19.13/19.25 apply (zenon_or_s _ _ zenon_H128); [ zenon_intro zenon_H9d | zenon_intro zenon_H129 ]. % 19.13/19.25 apply (zenon_L1462_); trivial. % 19.13/19.25 apply (zenon_or_s _ _ zenon_H129); [ zenon_intro zenon_H10d | zenon_intro zenon_H12a ]. % 19.13/19.25 exact (zenon_H10a zenon_H10d). % 19.13/19.25 apply (zenon_or_s _ _ zenon_H12a); [ zenon_intro zenon_Hf0 | zenon_intro zenon_Hd6 ]. % 19.13/19.25 apply (zenon_or_s _ _ zenon_H172); [ zenon_intro zenon_H150 | zenon_intro zenon_H174 ]. % 19.13/19.25 apply (zenon_L378_); trivial. % 19.13/19.25 apply (zenon_or_s _ _ zenon_H174); [ zenon_intro zenon_H113 | zenon_intro zenon_H175 ]. % 19.13/19.25 apply (zenon_L68_); trivial. % 19.13/19.25 apply (zenon_or_s _ _ zenon_H175); [ zenon_intro zenon_H176 | zenon_intro zenon_H151 ]. % 19.13/19.25 exact (zenon_H173 zenon_H176). % 19.13/19.25 apply (zenon_L1455_); trivial. % 19.13/19.25 apply (zenon_L1448_); trivial. % 19.13/19.25 apply (zenon_or_s _ _ zenon_H1e2); [ zenon_intro zenon_H3b | zenon_intro zenon_H15e ]. % 19.13/19.25 exact (zenon_H27f zenon_H3b). % 19.13/19.25 exact (zenon_H15f zenon_H15e). % 19.13/19.25 apply (zenon_or_s _ _ zenon_H186); [ zenon_intro zenon_H10f | zenon_intro zenon_H187 ]. % 19.13/19.25 apply (zenon_L1444_); trivial. % 19.13/19.25 apply (zenon_or_s _ _ zenon_H187); [ zenon_intro zenon_H150 | zenon_intro zenon_Hcd ]. % 19.13/19.25 apply (zenon_L378_); trivial. % 19.13/19.25 apply (zenon_L1450_); trivial. % 19.13/19.25 (* end of lemma zenon_L1463_ *) % 19.13/19.25 assert (zenon_L1464_ : ((~((op (e1) (e3)) = (e3)))\/((op (e1) (e3)) = (e3))) -> (~((e2) = (e3))) -> ((~((op (e3) (e0)) = (e3)))\/((op (e3) (e3)) = (e0))) -> (~((op (e0) (e3)) = (op (e3) (e3)))) -> ((~((op (e3) (e2)) = (e3)))\/((op (e3) (e3)) = (e2))) -> ((op (e1) (e3)) = (e2)) -> (~((op (e1) (e3)) = (op (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)) = (e0))) -> (((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) (e3)))) -> (~((op (e1) (e1)) = (e1))) -> (~((op (e1) (e0)) = (op (e1) (e1)))) -> (((op (e0) (e0)) = (e1))\/(((op (e0) (e1)) = (e1))\/(((op (e0) (e2)) = (e1))\/((op (e0) (e3)) = (e1))))) -> (~((e0) = (e1))) -> (~((op (e1) (e0)) = (e3))) -> (((op (e0) (e2)) = (e2))\/(((op (e1) (e2)) = (e2))\/(((op (e2) (e2)) = (e2))\/((op (e3) (e2)) = (e2))))) -> (~((op (e0) (e2)) = (op (e2) (e2)))) -> (~((op (e0) (e1)) = (op (e0) (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) (e2)) = (e0))\/(((op (e1) (e2)) = (e0))\/(((op (e2) (e2)) = (e0))\/((op (e3) (e2)) = (e0))))) -> (~((op (e2) (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 (e1) (e2)) = (op (e3) (e2)))) -> (~((op (e3) (e2)) = (op (e3) (e3)))) -> (~((op (e0) (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 (e0) (e2)) = (op (e0) (e3)))) -> (((op (e1) (e0)) = (e3))\/(((op (e1) (e1)) = (e3))\/(((op (e1) (e2)) = (e3))\/((op (e1) (e3)) = (e3))))) -> (~((e1) = (e3))) -> (~((op (e0) (e1)) = (e3))) -> (~((op (e0) (e2)) = (e3))) -> (~((op (e0) (e3)) = (e3))) -> (((op (e0) (e0)) = (e3))\/(((op (e0) (e1)) = (e3))\/(((op (e0) (e2)) = (e3))\/((op (e0) (e3)) = (e3))))) -> (~((op (e3) (e0)) = (op (e3) (e2)))) -> (((op (e0) (e0)) = (e0))\/(((op (e1) (e0)) = (e0))\/(((op (e2) (e0)) = (e0))\/((op (e3) (e0)) = (e0))))) -> ((~((op (e3) (e1)) = (e3)))\/((op (e3) (e3)) = (e1))) -> (~((op (e1) (e3)) = (op (e2) (e3)))) -> ((~((op (e2) (e2)) = (e3)))\/((op (e2) (e3)) = (e2))) -> False). % 19.13/19.25 do 0 intro. intros zenon_H289 zenon_H12b zenon_H286 zenon_Hc2 zenon_H284 zenon_Hd7 zenon_Hd5 zenon_H102 zenon_H165 zenon_H3f zenon_H142 zenon_H1a1 zenon_H57 zenon_H10a zenon_H45 zenon_H22d zenon_Ha1 zenon_H9f zenon_H172 zenon_Ha8 zenon_H4a zenon_H195 zenon_H1ba zenon_H6a zenon_H173 zenon_H1c4 zenon_H52 zenon_H115 zenon_H62 zenon_H14f zenon_H191 zenon_H1e zenon_H208 zenon_H16f zenon_H95 zenon_H9c zenon_H123 zenon_H12d zenon_H168 zenon_H6f zenon_H3e zenon_H285 zenon_Hdb zenon_H288. % 19.13/19.25 apply (zenon_or_s _ _ zenon_H289); [ zenon_intro zenon_H12f | zenon_intro zenon_Hdc ]. % 19.13/19.25 apply (zenon_or_s _ _ zenon_H288); [ zenon_intro zenon_H1b3 | zenon_intro zenon_H11d ]. % 19.13/19.25 apply (zenon_or_s _ _ zenon_H286); [ zenon_intro zenon_H15f | zenon_intro zenon_H60 ]. % 19.13/19.25 apply (zenon_or_s _ _ zenon_H285); [ zenon_intro zenon_H282 | zenon_intro zenon_Hc4 ]. % 19.13/19.25 apply (zenon_L1411_); trivial. % 19.13/19.25 apply (zenon_L1419_); trivial. % 19.13/19.25 apply (zenon_L440_); trivial. % 19.13/19.25 apply (zenon_L366_); trivial. % 19.13/19.25 apply (zenon_L266_); trivial. % 19.13/19.25 (* end of lemma zenon_L1464_ *) % 19.13/19.25 assert (zenon_L1465_ : ((~((op (e0) (e2)) = (e3)))\/((op (e0) (e3)) = (e2))) -> (~((e0) = (e2))) -> ((~((op (e1) (e0)) = (e3)))\/((op (e1) (e3)) = (e0))) -> (~((op (e1) (e1)) = (op (e1) (e3)))) -> (~((e2) = (e3))) -> (((op (e1) (e0)) = (e3))\/(((op (e1) (e1)) = (e3))\/(((op (e1) (e2)) = (e3))\/((op (e1) (e3)) = (e3))))) -> ((~((op (e2) (e0)) = (e3)))\/((op (e2) (e3)) = (e0))) -> (~((op (e0) (e3)) = (op (e2) (e3)))) -> ((~((op (e3) (e2)) = (e3)))\/((op (e3) (e3)) = (e2))) -> (~((op (e2) (e3)) = (op (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)) = (e0))) -> (~((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))))) -> (~((op (e1) (e2)) = (op (e3) (e2)))) -> (~((op (e2) (e0)) = (op (e2) (e1)))) -> (~((op (e2) (e1)) = (op (e2) (e3)))) -> (((op (e2) (e1)) = (e0))\/(((op (e2) (e1)) = (e1))\/(((op (e2) (e1)) = (e2))\/((op (e2) (e1)) = (e3))))) -> (~((op (e1) (e2)) = (op (e2) (e2)))) -> (~((op (e2) (e0)) = (op (e3) (e0)))) -> (~((op (e2) (e0)) = (op (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 (e1) (e1)) = (e1))) -> (((op (e0) (e2)) = (e2))\/(((op (e1) (e2)) = (e2))\/(((op (e2) (e2)) = (e2))\/((op (e3) (e2)) = (e2))))) -> (~((op (e2) (e2)) = (e2))) -> (~((op (e0) (e1)) = (op (e0) (e3)))) -> (~((op (e0) (e1)) = (op (e0) (e2)))) -> (((op (e1) (e1)) = (e0))\/(((op (e1) (e1)) = (e1))\/(((op (e1) (e1)) = (e2))\/((op (e1) (e1)) = (e3))))) -> (~((op (e0) (e1)) = (op (e1) (e1)))) -> (~((op (e1) (e0)) = (op (e1) (e1)))) -> (((op (e0) (e1)) = (e0))\/(((op (e0) (e1)) = (e1))\/(((op (e0) (e1)) = (e2))\/((op (e0) (e1)) = (e3))))) -> (((op (e3) (e2)) = (e0))\/(((op (e3) (e2)) = (e1))\/(((op (e3) (e2)) = (e2))\/((op (e3) (e2)) = (e3))))) -> (~((op (e0) (e2)) = (op (e3) (e2)))) -> (~((op (e3) (e2)) = (op (e3) (e3)))) -> (~((op (e3) (e0)) = (op (e3) (e2)))) -> (~((op (e0) (e2)) = (op (e1) (e2)))) -> (((op (e0) (e2)) = (e0))\/(((op (e0) (e2)) = (e1))\/(((op (e0) (e2)) = (e2))\/((op (e0) (e2)) = (e3))))) -> (~((op (e3) (e1)) = (op (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 (e3) (e0)) = (op (e3) (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 (e1) (e2)) = (e3)))\/((op (e1) (e3)) = (e2))) -> ((~((op (e2) (e2)) = (e3)))\/((op (e2) (e3)) = (e2))) -> ((~((op (e3) (e1)) = (e3)))\/((op (e3) (e3)) = (e1))) -> (~((op (e1) (e3)) = (op (e3) (e3)))) -> (((op (e0) (e0)) = (e0))\/(((op (e1) (e0)) = (e0))\/(((op (e2) (e0)) = (e0))\/((op (e3) (e0)) = (e0))))) -> (~((op (e0) (e1)) = (op (e3) (e1)))) -> (((op (e1) (e0)) = (e0))\/(((op (e1) (e0)) = (e1))\/(((op (e1) (e0)) = (e2))\/((op (e1) (e0)) = (e3))))) -> (((op (e2) (e2)) = (e0))\/(((op (e2) (e2)) = (e1))\/(((op (e2) (e2)) = (e2))\/((op (e2) (e2)) = (e3))))) -> (~((op (e0) (e2)) = (op (e2) (e2)))) -> (~((op (e2) (e0)) = (op (e2) (e2)))) -> (~((e0) = (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))))) -> (~((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 (e0) (e1)) = (op (e2) (e1)))) -> (((op (e2) (e0)) = (e2))\/(((op (e2) (e1)) = (e2))\/(((op (e2) (e2)) = (e2))\/((op (e2) (e3)) = (e2))))) -> (~((op (e1) (e0)) = (op (e1) (e3)))) -> (~((op (e0) (e0)) = (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 (e3) (e0)) = (e3)))\/((op (e3) (e3)) = (e0))) -> ((~((op (e1) (e3)) = (e3)))\/((op (e1) (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)) = (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 (e1) (e0)) = (e2))\/(((op (e1) (e1)) = (e2))\/(((op (e1) (e2)) = (e2))\/((op (e1) (e3)) = (e2))))) -> (~((op (e1) (e0)) = (op (e3) (e0)))) -> (((op (e0) (e1)) = (e3))\/(((op (e1) (e1)) = (e3))\/(((op (e2) (e1)) = (e3))\/((op (e3) (e1)) = (e3))))) -> (~((op (e2) (e2)) = (op (e2) (e3)))) -> (((op (e0) (e2)) = (e0))\/(((op (e1) (e2)) = (e0))\/(((op (e2) (e2)) = (e0))\/((op (e3) (e2)) = (e0))))) -> (~((e1) = (e3))) -> (~((op (e0) (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))))) -> (~((op (e1) (e3)) = (op (e2) (e3)))) -> ((~((op (e2) (e3)) = (e3)))\/((op (e2) (e3)) = (e3))) -> ((~((op (e2) (e1)) = (e3)))\/((op (e2) (e3)) = (e1))) -> ((~((op (e1) (e1)) = (e3)))\/((op (e1) (e3)) = (e1))) -> (~((e0) = (e3))) -> ((~((op (e0) (e3)) = (e3)))\/((op (e0) (e3)) = (e3))) -> False). % 19.13/19.25 do 0 intro. intros zenon_H28c zenon_H149 zenon_H28d zenon_H57 zenon_H12b zenon_H16f zenon_H28a zenon_He2 zenon_H284 zenon_Hf3 zenon_H102 zenon_H165 zenon_H3f zenon_H208 zenon_H1e zenon_H24a zenon_H106 zenon_H115 zenon_H1f0 zenon_H1c7 zenon_H1cc zenon_H2b zenon_H17b zenon_H5b zenon_H259 zenon_H201 zenon_H10a zenon_H172 zenon_H173 zenon_H54 zenon_H4a zenon_H142 zenon_H10e zenon_H45 zenon_H212 zenon_H191 zenon_H14f zenon_H62 zenon_H6f zenon_H195 zenon_H1ba zenon_H1a4 zenon_H153 zenon_H71 zenon_H1cf zenon_H267 zenon_Hc2 zenon_H1ac zenon_H287 zenon_H288 zenon_H285 zenon_Hd5 zenon_H3e zenon_H210 zenon_H25e zenon_H1c4 zenon_Ha8 zenon_H52 zenon_Ha1 zenon_H22d zenon_H235 zenon_H130 zenon_H22a zenon_H7c zenon_H17e zenon_H1d5 zenon_Hd8 zenon_H13c zenon_H19d zenon_H124 zenon_H286 zenon_H289 zenon_H128 zenon_H1d zenon_H22 zenon_H109 zenon_H18c zenon_H1fa zenon_H1a5 zenon_H6d zenon_H6a zenon_H95 zenon_H9c zenon_H168 zenon_He7 zenon_Hdb zenon_H281 zenon_H28b zenon_H28e zenon_H9a zenon_H28f. % 19.13/19.25 apply (zenon_or_s _ _ zenon_H28c); [ zenon_intro zenon_H123 | zenon_intro zenon_Hcd ]. % 19.13/19.25 apply (zenon_or_s _ _ zenon_H28f); [ zenon_intro zenon_H12d | zenon_intro zenon_He3 ]. % 19.13/19.25 apply (zenon_or_s _ _ zenon_H28d); [ zenon_intro zenon_H9f | zenon_intro zenon_H1f ]. % 19.13/19.25 apply (zenon_or_s _ _ zenon_H28e); [ zenon_intro zenon_H1a1 | zenon_intro zenon_Hd6 ]. % 19.13/19.25 apply (zenon_or_s _ _ zenon_H287); [ zenon_intro zenon_H16d | zenon_intro zenon_Hd7 ]. % 19.13/19.25 apply (zenon_or_s _ _ zenon_H289); [ zenon_intro zenon_H12f | zenon_intro zenon_Hdc ]. % 19.13/19.25 apply (zenon_L1343_); trivial. % 19.13/19.25 apply (zenon_or_s _ _ zenon_H28a); [ zenon_intro zenon_H27f | zenon_intro zenon_H37 ]. % 19.13/19.25 apply (zenon_or_s _ _ zenon_H28b); [ zenon_intro zenon_Ha7 | zenon_intro zenon_Hf4 ]. % 19.13/19.25 apply (zenon_or_s _ _ zenon_H288); [ zenon_intro zenon_H1b3 | zenon_intro zenon_H11d ]. % 19.13/19.25 apply (zenon_L1345_); trivial. % 19.13/19.25 apply (zenon_or_s _ _ zenon_H281); [ zenon_intro zenon_H280 | zenon_intro zenon_Hdd ]. % 19.13/19.25 apply (zenon_or_s _ _ zenon_H286); [ zenon_intro zenon_H15f | zenon_intro zenon_H60 ]. % 19.13/19.25 apply (zenon_or_s _ _ zenon_H285); [ zenon_intro zenon_H282 | zenon_intro zenon_Hc4 ]. % 19.13/19.25 apply (zenon_L1347_); trivial. % 19.13/19.25 apply (zenon_L1403_); trivial. % 19.13/19.25 apply (zenon_L440_); trivial. % 19.13/19.25 apply (zenon_L52_); trivial. % 19.13/19.25 apply (zenon_L1392_); trivial. % 19.13/19.25 apply (zenon_L367_); trivial. % 19.13/19.25 apply (zenon_L1464_); trivial. % 19.13/19.25 apply (zenon_L1371_); trivial. % 19.13/19.25 apply (zenon_L1_); trivial. % 19.13/19.25 apply (zenon_L515_); trivial. % 19.13/19.25 apply (zenon_L428_); trivial. % 19.13/19.25 (* end of lemma zenon_L1465_ *) % 19.13/19.25 assert (zenon_L1466_ : ((~((op (e2) (e3)) = (e3)))\/((op (e2) (e3)) = (e3))) -> ((op (e0) (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 (e3) (e2)) = (e3)))\/((op (e3) (e3)) = (e2))) -> (~((op (e2) (e3)) = (op (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)) = (e0))) -> (((op (e0) (e0)) = (e1))\/(((op (e0) (e1)) = (e1))\/(((op (e0) (e2)) = (e1))\/((op (e0) (e3)) = (e1))))) -> (~((e0) = (e1))) -> (~((op (e0) (e0)) = (e3))) -> (((op (e3) (e0)) = (e2))\/(((op (e3) (e1)) = (e2))\/(((op (e3) (e2)) = (e2))\/((op (e3) (e3)) = (e2))))) -> (~((e1) = (e3))) -> (~((op (e1) (e1)) = (e1))) -> (((op (e0) (e2)) = (e2))\/(((op (e1) (e2)) = (e2))\/(((op (e2) (e2)) = (e2))\/((op (e3) (e2)) = (e2))))) -> (((op (e3) (e0)) = (e0))\/(((op (e3) (e1)) = (e0))\/(((op (e3) (e2)) = (e0))\/((op (e3) (e3)) = (e0))))) -> (((op (e0) (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)) = (op (e3) (e1)))) -> (~((op (e3) (e0)) = (op (e3) (e3)))) -> (((op (e0) (e0)) = (e3))\/(((op (e1) (e0)) = (e3))\/(((op (e2) (e0)) = (e3))\/((op (e3) (e0)) = (e3))))) -> ((~((op (e2) (e0)) = (e3)))\/((op (e2) (e3)) = (e0))) -> ((~((op (e2) (e2)) = (e3)))\/((op (e2) (e3)) = (e2))) -> ((~((op (e3) (e1)) = (e3)))\/((op (e3) (e3)) = (e1))) -> (~((op (e1) (e3)) = (op (e3) (e3)))) -> ((~((op (e3) (e0)) = (e3)))\/((op (e3) (e3)) = (e0))) -> ((~((op (e2) (e1)) = (e3)))\/((op (e2) (e3)) = (e1))) -> (((op (e1) (e0)) = (e1))\/(((op (e1) (e1)) = (e1))\/(((op (e1) (e2)) = (e1))\/((op (e1) (e3)) = (e1))))) -> (~((op (e0) (e3)) = (op (e3) (e3)))) -> (((op (e0) (e0)) = (e2))\/(((op (e0) (e1)) = (e2))\/(((op (e0) (e2)) = (e2))\/((op (e0) (e3)) = (e2))))) -> (~((op (e2) (e1)) = (op (e2) (e3)))) -> (~((op (e2) (e0)) = (op (e3) (e0)))) -> (((op (e0) (e1)) = (e0))\/(((op (e0) (e1)) = (e1))\/(((op (e0) (e1)) = (e2))\/((op (e0) (e1)) = (e3))))) -> (~((op (e0) (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 (e0) (e1)) = (op (e2) (e1)))) -> (~((op (e0) (e2)) = (op (e2) (e2)))) -> (~((op (e1) (e3)) = (op (e2) (e3)))) -> (((op (e2) (e0)) = (e0))\/(((op (e2) (e1)) = (e0))\/(((op (e2) (e2)) = (e0))\/((op (e2) (e3)) = (e0))))) -> (~((op (e1) (e1)) = (op (e1) (e3)))) -> ((op (e1) (e3)) = (e0)) -> (~((op (e0) (e1)) = (op (e1) (e1)))) -> (((op (e1) (e1)) = (e0))\/(((op (e1) (e1)) = (e1))\/(((op (e1) (e1)) = (e2))\/((op (e1) (e1)) = (e3))))) -> (~((op (e0) (e2)) = (op (e1) (e2)))) -> (~((op (e0) (e2)) = (e3))) -> (((op (e0) (e2)) = (e0))\/(((op (e0) (e2)) = (e1))\/(((op (e0) (e2)) = (e2))\/((op (e0) (e2)) = (e3))))) -> (~((op (e2) (e2)) = (e2))) -> (~((e1) = (e2))) -> (~((op (e3) (e0)) = (op (e3) (e2)))) -> (~((op (e3) (e2)) = (op (e3) (e3)))) -> (~((op (e0) (e2)) = (op (e3) (e2)))) -> (((op (e3) (e2)) = (e0))\/(((op (e3) (e2)) = (e1))\/(((op (e3) (e2)) = (e2))\/((op (e3) (e2)) = (e3))))) -> (~((e0) = (e2))) -> ((~((op (e0) (e2)) = (e3)))\/((op (e0) (e3)) = (e2))) -> ((~((op (e1) (e0)) = (e3)))\/((op (e1) (e3)) = (e0))) -> (~((e2) = (e3))) -> (((op (e1) (e0)) = (e3))\/(((op (e1) (e1)) = (e3))\/(((op (e1) (e2)) = (e3))\/((op (e1) (e3)) = (e3))))) -> (~((op (e0) (e2)) = (op (e0) (e3)))) -> (~((op (e1) (e0)) = (op (e1) (e2)))) -> (~((op (e1) (e2)) = (op (e3) (e2)))) -> (~((op (e2) (e0)) = (op (e2) (e1)))) -> (((op (e2) (e1)) = (e0))\/(((op (e2) (e1)) = (e1))\/(((op (e2) (e1)) = (e2))\/((op (e2) (e1)) = (e3))))) -> (~((op (e2) (e0)) = (op (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)) = (op (e0) (e3)))) -> (~((op (e0) (e1)) = (op (e0) (e2)))) -> (~((op (e1) (e0)) = (op (e1) (e1)))) -> (~((op (e3) (e1)) = (op (e3) (e2)))) -> ((~((op (e1) (e2)) = (e3)))\/((op (e1) (e3)) = (e2))) -> (((op (e0) (e0)) = (e0))\/(((op (e1) (e0)) = (e0))\/(((op (e2) (e0)) = (e0))\/((op (e3) (e0)) = (e0))))) -> (~((op (e0) (e1)) = (op (e3) (e1)))) -> (((op (e1) (e0)) = (e0))\/(((op (e1) (e0)) = (e1))\/(((op (e1) (e0)) = (e2))\/((op (e1) (e0)) = (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) (e0)) = (e1))\/(((op (e1) (e0)) = (e1))\/(((op (e2) (e0)) = (e1))\/((op (e3) (e0)) = (e1))))) -> (~((op (e3) (e1)) = (op (e3) (e3)))) -> (((op (e3) (e1)) = (e0))\/(((op (e3) (e1)) = (e1))\/(((op (e3) (e1)) = (e2))\/((op (e3) (e1)) = (e3))))) -> (((op (e2) (e0)) = (e2))\/(((op (e2) (e1)) = (e2))\/(((op (e2) (e2)) = (e2))\/((op (e2) (e3)) = (e2))))) -> (~((op (e1) (e0)) = (op (e1) (e3)))) -> (~((op (e0) (e0)) = (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) (e3)) = (e3)))\/((op (e1) (e3)) = (e3))) -> (~((op (e0) (e3)) = (op (e1) (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 (e1) (e0)) = (e2))\/(((op (e1) (e1)) = (e2))\/(((op (e1) (e2)) = (e2))\/((op (e1) (e3)) = (e2))))) -> (~((op (e1) (e0)) = (op (e3) (e0)))) -> (((op (e0) (e1)) = (e3))\/(((op (e1) (e1)) = (e3))\/(((op (e2) (e1)) = (e3))\/((op (e3) (e1)) = (e3))))) -> (~((op (e2) (e2)) = (op (e2) (e3)))) -> (((op (e0) (e2)) = (e0))\/(((op (e1) (e2)) = (e0))\/(((op (e2) (e2)) = (e0))\/((op (e3) (e2)) = (e0))))) -> (((op (e0) (e0)) = (e3))\/(((op (e0) (e1)) = (e3))\/(((op (e0) (e2)) = (e3))\/((op (e0) (e3)) = (e3))))) -> ((~((op (e1) (e1)) = (e3)))\/((op (e1) (e3)) = (e1))) -> (~((e0) = (e3))) -> ((~((op (e0) (e3)) = (e3)))\/((op (e0) (e3)) = (e3))) -> (((op (e0) (e0)) = (e0))\/(((op (e0) (e1)) = (e0))\/(((op (e0) (e2)) = (e0))\/((op (e0) (e3)) = (e0))))) -> False). % 19.13/19.25 do 0 intro. intros zenon_H281 zenon_He3 zenon_He2 zenon_He7 zenon_H284 zenon_Hf3 zenon_H102 zenon_H165 zenon_H3f zenon_H22d zenon_Ha1 zenon_H98 zenon_H153 zenon_H95 zenon_H10a zenon_H172 zenon_H1ac zenon_H1d8 zenon_H267 zenon_H1cf zenon_H71 zenon_H1e0 zenon_H28a zenon_H288 zenon_H285 zenon_Hd5 zenon_H286 zenon_H28b zenon_H128 zenon_Hc2 zenon_H183 zenon_H1c7 zenon_H17b zenon_H212 zenon_H9c zenon_H2b zenon_H106 zenon_H17e zenon_Ha8 zenon_Hdb zenon_H2f zenon_H57 zenon_H1f zenon_H10e zenon_H142 zenon_H195 zenon_H123 zenon_H1ba zenon_H173 zenon_H7c zenon_H6f zenon_H62 zenon_H14f zenon_H191 zenon_H149 zenon_H28c zenon_H28d zenon_H12b zenon_H16f zenon_H208 zenon_H24a zenon_H115 zenon_H1f0 zenon_H1cc zenon_H5b zenon_H259 zenon_H201 zenon_H54 zenon_H4a zenon_H45 zenon_H1a4 zenon_H287 zenon_H3e zenon_H210 zenon_H25e zenon_H1c4 zenon_H52 zenon_H235 zenon_H130 zenon_H22a zenon_H1d5 zenon_Hd8 zenon_H13c zenon_H19d zenon_H124 zenon_H289 zenon_H1d zenon_H22 zenon_H109 zenon_H18c zenon_H1fa zenon_H1a5 zenon_H6d zenon_H6a zenon_H168 zenon_H28e zenon_H9a zenon_H28f zenon_H74. % 19.13/19.25 apply (zenon_or_s _ _ zenon_H28e); [ zenon_intro zenon_H1a1 | zenon_intro zenon_Hd6 ]. % 19.13/19.25 apply (zenon_or_s _ _ zenon_H28a); [ zenon_intro zenon_H27f | zenon_intro zenon_H37 ]. % 19.13/19.25 apply (zenon_or_s _ _ zenon_H28b); [ zenon_intro zenon_Ha7 | zenon_intro zenon_Hf4 ]. % 19.13/19.25 apply (zenon_or_s _ _ zenon_H288); [ zenon_intro zenon_H1b3 | zenon_intro zenon_H11d ]. % 19.13/19.25 apply (zenon_L1421_); trivial. % 19.13/19.25 apply (zenon_or_s _ _ zenon_H286); [ zenon_intro zenon_H15f | zenon_intro zenon_H60 ]. % 19.13/19.25 apply (zenon_or_s _ _ zenon_H285); [ zenon_intro zenon_H282 | zenon_intro zenon_Hc4 ]. % 19.13/19.25 apply (zenon_L1347_); trivial. % 19.13/19.25 apply (zenon_or_s _ _ zenon_H284); [ zenon_intro zenon_H283 | zenon_intro zenon_Hf6 ]. % 19.13/19.25 apply (zenon_or_s _ _ zenon_H74); [ zenon_intro zenon_H42 | zenon_intro zenon_H77 ]. % 19.13/19.25 exact (zenon_H3f zenon_H42). % 19.13/19.25 apply (zenon_or_s _ _ zenon_H77); [ zenon_intro zenon_H49 | zenon_intro zenon_H78 ]. % 19.13/19.25 apply (zenon_or_s _ _ zenon_H22d); [ zenon_intro zenon_H7a | zenon_intro zenon_H22e ]. % 19.13/19.25 apply (zenon_or_s _ _ zenon_H1e0); [ zenon_intro zenon_H3a | zenon_intro zenon_H1e1 ]. % 19.13/19.25 exact (zenon_H98 zenon_H3a). % 19.13/19.25 apply (zenon_or_s _ _ zenon_H1e1); [ zenon_intro zenon_H9e | zenon_intro zenon_H1e2 ]. % 19.13/19.25 apply (zenon_or_s _ _ zenon_H1ac); [ zenon_intro zenon_H44 | zenon_intro zenon_H1af ]. % 19.13/19.25 apply (zenon_L1457_); trivial. % 19.13/19.25 apply (zenon_or_s _ _ zenon_H1af); [ zenon_intro zenon_H1b1 | zenon_intro zenon_H1b0 ]. % 19.13/19.25 apply (zenon_or_s _ _ zenon_H153); [ zenon_intro zenon_H148 | zenon_intro zenon_H154 ]. % 19.13/19.25 apply (zenon_L1458_); trivial. % 19.13/19.25 apply (zenon_or_s _ _ zenon_H154); [ zenon_intro zenon_H14d | zenon_intro zenon_H155 ]. % 19.13/19.25 apply (zenon_L1459_); trivial. % 19.13/19.25 apply (zenon_or_s _ _ zenon_H155); [ zenon_intro zenon_H151 | zenon_intro zenon_Hf6 ]. % 19.13/19.25 apply (zenon_L1394_); trivial. % 19.13/19.25 apply (zenon_L97_); trivial. % 19.13/19.25 apply (zenon_or_s _ _ zenon_H1b0); [ zenon_intro zenon_H61 | zenon_intro zenon_H60 ]. % 19.13/19.25 apply (zenon_L1460_); trivial. % 19.13/19.25 apply (zenon_L136_); trivial. % 19.13/19.25 apply (zenon_or_s _ _ zenon_H1e2); [ zenon_intro zenon_H3b | zenon_intro zenon_H15e ]. % 19.13/19.25 exact (zenon_H27f zenon_H3b). % 19.13/19.25 exact (zenon_H15f zenon_H15e). % 19.13/19.25 apply (zenon_or_s _ _ zenon_H22e); [ zenon_intro zenon_Ha0 | zenon_intro zenon_H22f ]. % 19.13/19.25 apply (zenon_L38_); trivial. % 19.13/19.25 apply (zenon_or_s _ _ zenon_H22f); [ zenon_intro zenon_H122 | zenon_intro zenon_Hc3 ]. % 19.13/19.25 apply (zenon_L1461_); trivial. % 19.13/19.25 apply (zenon_L46_); trivial. % 19.13/19.25 apply (zenon_or_s _ _ zenon_H78); [ zenon_intro zenon_H48 | zenon_intro zenon_H1e ]. % 19.13/19.25 apply (zenon_L1463_); trivial. % 19.13/19.25 apply (zenon_L1465_); trivial. % 19.13/19.25 apply (zenon_L97_); trivial. % 19.13/19.25 apply (zenon_L136_); trivial. % 19.13/19.25 apply (zenon_or_s _ _ zenon_H286); [ zenon_intro zenon_H15f | zenon_intro zenon_H60 ]. % 19.13/19.25 apply (zenon_or_s _ _ zenon_H285); [ zenon_intro zenon_H282 | zenon_intro zenon_Hc4 ]. % 19.13/19.25 apply (zenon_or_s _ _ zenon_H284); [ zenon_intro zenon_H283 | zenon_intro zenon_Hf6 ]. % 19.13/19.25 apply (zenon_L1346_); trivial. % 19.13/19.25 apply (zenon_L63_); trivial. % 19.13/19.25 apply (zenon_L60_); trivial. % 19.13/19.25 apply (zenon_L136_); trivial. % 19.13/19.25 apply (zenon_L130_); trivial. % 19.13/19.25 apply (zenon_L1448_); trivial. % 19.13/19.25 (* end of lemma zenon_L1466_ *) % 19.13/19.25 assert (zenon_L1467_ : ((op (e2) (e3)) = (e2)) -> ((op (e2) (e0)) = (e0)) -> (~((op (e2) (e1)) = (op (e3) (e1)))) -> (~((op (e2) (e1)) = (e3))) -> ((op (e3) (e3)) = (e0)) -> (~((op (e3) (e1)) = (e3))) -> ((op (e0) (e2)) = (e0)) -> ((~((op (e2) (e3)) = (e3)))\/((op (e2) (e3)) = (e3))) -> ((op (e0) (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 (e3) (e2)) = (e3)))\/((op (e3) (e3)) = (e2))) -> (~((op (e2) (e3)) = (op (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)) = (e0))) -> (((op (e0) (e0)) = (e1))\/(((op (e0) (e1)) = (e1))\/(((op (e0) (e2)) = (e1))\/((op (e0) (e3)) = (e1))))) -> (~((e0) = (e1))) -> (~((op (e0) (e0)) = (e3))) -> (((op (e3) (e0)) = (e2))\/(((op (e3) (e1)) = (e2))\/(((op (e3) (e2)) = (e2))\/((op (e3) (e3)) = (e2))))) -> (~((e1) = (e3))) -> (~((op (e1) (e1)) = (e1))) -> (((op (e0) (e2)) = (e2))\/(((op (e1) (e2)) = (e2))\/(((op (e2) (e2)) = (e2))\/((op (e3) (e2)) = (e2))))) -> (((op (e3) (e0)) = (e0))\/(((op (e3) (e1)) = (e0))\/(((op (e3) (e2)) = (e0))\/((op (e3) (e3)) = (e0))))) -> (((op (e0) (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)) = (op (e3) (e1)))) -> (~((op (e3) (e0)) = (op (e3) (e3)))) -> (((op (e0) (e0)) = (e3))\/(((op (e1) (e0)) = (e3))\/(((op (e2) (e0)) = (e3))\/((op (e3) (e0)) = (e3))))) -> ((~((op (e2) (e0)) = (e3)))\/((op (e2) (e3)) = (e0))) -> ((~((op (e2) (e2)) = (e3)))\/((op (e2) (e3)) = (e2))) -> ((~((op (e3) (e1)) = (e3)))\/((op (e3) (e3)) = (e1))) -> (~((op (e1) (e3)) = (op (e3) (e3)))) -> ((~((op (e3) (e0)) = (e3)))\/((op (e3) (e3)) = (e0))) -> ((~((op (e2) (e1)) = (e3)))\/((op (e2) (e3)) = (e1))) -> (((op (e1) (e0)) = (e1))\/(((op (e1) (e1)) = (e1))\/(((op (e1) (e2)) = (e1))\/((op (e1) (e3)) = (e1))))) -> (~((op (e0) (e3)) = (op (e3) (e3)))) -> (((op (e0) (e0)) = (e2))\/(((op (e0) (e1)) = (e2))\/(((op (e0) (e2)) = (e2))\/((op (e0) (e3)) = (e2))))) -> (~((op (e2) (e1)) = (op (e2) (e3)))) -> (~((op (e2) (e0)) = (op (e3) (e0)))) -> (((op (e0) (e1)) = (e0))\/(((op (e0) (e1)) = (e1))\/(((op (e0) (e1)) = (e2))\/((op (e0) (e1)) = (e3))))) -> (~((op (e0) (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 (e0) (e1)) = (op (e2) (e1)))) -> (~((op (e0) (e2)) = (op (e2) (e2)))) -> (~((op (e1) (e3)) = (op (e2) (e3)))) -> (((op (e2) (e0)) = (e0))\/(((op (e2) (e1)) = (e0))\/(((op (e2) (e2)) = (e0))\/((op (e2) (e3)) = (e0))))) -> (~((op (e1) (e1)) = (op (e1) (e3)))) -> (~((op (e0) (e1)) = (op (e1) (e1)))) -> (((op (e1) (e1)) = (e0))\/(((op (e1) (e1)) = (e1))\/(((op (e1) (e1)) = (e2))\/((op (e1) (e1)) = (e3))))) -> (~((op (e0) (e2)) = (op (e1) (e2)))) -> (~((op (e0) (e2)) = (e3))) -> (((op (e0) (e2)) = (e0))\/(((op (e0) (e2)) = (e1))\/(((op (e0) (e2)) = (e2))\/((op (e0) (e2)) = (e3))))) -> (~((op (e2) (e2)) = (e2))) -> (~((e1) = (e2))) -> (~((op (e3) (e0)) = (op (e3) (e2)))) -> (~((op (e3) (e2)) = (op (e3) (e3)))) -> (~((op (e0) (e2)) = (op (e3) (e2)))) -> (((op (e3) (e2)) = (e0))\/(((op (e3) (e2)) = (e1))\/(((op (e3) (e2)) = (e2))\/((op (e3) (e2)) = (e3))))) -> (~((e0) = (e2))) -> ((~((op (e0) (e2)) = (e3)))\/((op (e0) (e3)) = (e2))) -> ((~((op (e1) (e0)) = (e3)))\/((op (e1) (e3)) = (e0))) -> (~((e2) = (e3))) -> (((op (e1) (e0)) = (e3))\/(((op (e1) (e1)) = (e3))\/(((op (e1) (e2)) = (e3))\/((op (e1) (e3)) = (e3))))) -> (~((op (e0) (e2)) = (op (e0) (e3)))) -> (~((op (e1) (e0)) = (op (e1) (e2)))) -> (~((op (e1) (e2)) = (op (e3) (e2)))) -> (~((op (e2) (e0)) = (op (e2) (e1)))) -> (((op (e2) (e1)) = (e0))\/(((op (e2) (e1)) = (e1))\/(((op (e2) (e1)) = (e2))\/((op (e2) (e1)) = (e3))))) -> (~((op (e2) (e0)) = (op (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)) = (op (e0) (e3)))) -> (~((op (e0) (e1)) = (op (e0) (e2)))) -> (~((op (e1) (e0)) = (op (e1) (e1)))) -> (~((op (e3) (e1)) = (op (e3) (e2)))) -> ((~((op (e1) (e2)) = (e3)))\/((op (e1) (e3)) = (e2))) -> (((op (e0) (e0)) = (e0))\/(((op (e1) (e0)) = (e0))\/(((op (e2) (e0)) = (e0))\/((op (e3) (e0)) = (e0))))) -> (~((op (e0) (e1)) = (op (e3) (e1)))) -> (((op (e1) (e0)) = (e0))\/(((op (e1) (e0)) = (e1))\/(((op (e1) (e0)) = (e2))\/((op (e1) (e0)) = (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) (e0)) = (e1))\/(((op (e1) (e0)) = (e1))\/(((op (e2) (e0)) = (e1))\/((op (e3) (e0)) = (e1))))) -> (~((op (e3) (e1)) = (op (e3) (e3)))) -> (((op (e3) (e1)) = (e0))\/(((op (e3) (e1)) = (e1))\/(((op (e3) (e1)) = (e2))\/((op (e3) (e1)) = (e3))))) -> (((op (e2) (e0)) = (e2))\/(((op (e2) (e1)) = (e2))\/(((op (e2) (e2)) = (e2))\/((op (e2) (e3)) = (e2))))) -> (~((op (e1) (e0)) = (op (e1) (e3)))) -> (~((op (e0) (e0)) = (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) (e3)) = (e3)))\/((op (e1) (e3)) = (e3))) -> (~((op (e0) (e3)) = (op (e1) (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 (e1) (e0)) = (e2))\/(((op (e1) (e1)) = (e2))\/(((op (e1) (e2)) = (e2))\/((op (e1) (e3)) = (e2))))) -> (~((op (e1) (e0)) = (op (e3) (e0)))) -> (((op (e0) (e1)) = (e3))\/(((op (e1) (e1)) = (e3))\/(((op (e2) (e1)) = (e3))\/((op (e3) (e1)) = (e3))))) -> (~((op (e2) (e2)) = (op (e2) (e3)))) -> (((op (e0) (e2)) = (e0))\/(((op (e1) (e2)) = (e0))\/(((op (e2) (e2)) = (e0))\/((op (e3) (e2)) = (e0))))) -> (((op (e0) (e0)) = (e3))\/(((op (e0) (e1)) = (e3))\/(((op (e0) (e2)) = (e3))\/((op (e0) (e3)) = (e3))))) -> ((~((op (e1) (e1)) = (e3)))\/((op (e1) (e3)) = (e1))) -> (~((e0) = (e3))) -> ((~((op (e0) (e3)) = (e3)))\/((op (e0) (e3)) = (e3))) -> (((op (e0) (e0)) = (e0))\/(((op (e0) (e1)) = (e0))\/(((op (e0) (e2)) = (e0))\/((op (e0) (e3)) = (e0))))) -> False). % 19.13/19.26 do 0 intro. intros zenon_H11d zenon_H34 zenon_Haf zenon_Ha7 zenon_H60 zenon_H282 zenon_H48 zenon_H281 zenon_He3 zenon_He2 zenon_He7 zenon_H284 zenon_Hf3 zenon_H102 zenon_H165 zenon_H3f zenon_H22d zenon_Ha1 zenon_H98 zenon_H153 zenon_H95 zenon_H10a zenon_H172 zenon_H1ac zenon_H1d8 zenon_H267 zenon_H1cf zenon_H71 zenon_H1e0 zenon_H28a zenon_H288 zenon_H285 zenon_Hd5 zenon_H286 zenon_H28b zenon_H128 zenon_Hc2 zenon_H183 zenon_H1c7 zenon_H17b zenon_H212 zenon_H9c zenon_H2b zenon_H106 zenon_H17e zenon_Ha8 zenon_Hdb zenon_H2f zenon_H57 zenon_H10e zenon_H142 zenon_H195 zenon_H123 zenon_H1ba zenon_H173 zenon_H7c zenon_H6f zenon_H62 zenon_H14f zenon_H191 zenon_H149 zenon_H28c zenon_H28d zenon_H12b zenon_H16f zenon_H208 zenon_H24a zenon_H115 zenon_H1f0 zenon_H1cc zenon_H5b zenon_H259 zenon_H201 zenon_H54 zenon_H4a zenon_H45 zenon_H1a4 zenon_H287 zenon_H3e zenon_H210 zenon_H25e zenon_H1c4 zenon_H52 zenon_H235 zenon_H130 zenon_H22a zenon_H1d5 zenon_Hd8 zenon_H13c zenon_H19d zenon_H124 zenon_H289 zenon_H1d zenon_H22 zenon_H109 zenon_H18c zenon_H1fa zenon_H1a5 zenon_H6d zenon_H6a zenon_H168 zenon_H28e zenon_H9a zenon_H28f zenon_H74. % 19.13/19.26 apply (zenon_or_s _ _ zenon_H22); [ zenon_intro zenon_H27 | zenon_intro zenon_H26 ]. % 19.13/19.26 apply (zenon_L332_); trivial. % 19.13/19.26 apply (zenon_or_s _ _ zenon_H26); [ zenon_intro zenon_H29 | zenon_intro zenon_H28 ]. % 19.13/19.26 apply (zenon_L1443_); trivial. % 19.13/19.26 apply (zenon_or_s _ _ zenon_H28); [ zenon_intro zenon_H2a | zenon_intro zenon_H1f ]. % 19.13/19.26 apply (zenon_L334_); trivial. % 19.13/19.26 apply (zenon_L1466_); trivial. % 19.13/19.26 (* end of lemma zenon_L1467_ *) % 19.13/19.26 assert (zenon_L1468_ : (((op (e2) (e0)) = (e3))\/(((op (e2) (e1)) = (e3))\/(((op (e2) (e2)) = (e3))\/((op (e2) (e3)) = (e3))))) -> (~((op (e2) (e1)) = (e3))) -> ((op (e1) (e3)) = (e1)) -> (~((op (e1) (e3)) = (op (e3) (e3)))) -> ((op (e1) (e2)) = (e0)) -> ((op (e2) (e1)) = (e1)) -> (~((op (e2) (e1)) = (op (e3) (e1)))) -> (((op (e0) (e0)) = (e3))\/(((op (e1) (e0)) = (e3))\/(((op (e2) (e0)) = (e3))\/((op (e3) (e0)) = (e3))))) -> (~((op (e0) (e0)) = (e3))) -> (~((op (e1) (e0)) = (e3))) -> (~((op (e2) (e0)) = (e3))) -> (~((e1) = (e3))) -> (((op (e3) (e0)) = (e1))\/(((op (e3) (e1)) = (e1))\/(((op (e3) (e2)) = (e1))\/((op (e3) (e3)) = (e1))))) -> (~((op (e2) (e3)) = (e3))) -> False). % 19.13/19.26 do 0 intro. intros zenon_He7 zenon_Ha7 zenon_Hd6 zenon_Hd5 zenon_H2a zenon_Ha5 zenon_Haf zenon_H1e0 zenon_H98 zenon_H9f zenon_H27f zenon_H95 zenon_He8 zenon_H280. % 19.13/19.26 apply (zenon_or_s _ _ zenon_He7); [ zenon_intro zenon_H3b | zenon_intro zenon_He9 ]. % 19.13/19.26 exact (zenon_H27f zenon_H3b). % 19.13/19.26 apply (zenon_or_s _ _ zenon_He9); [ zenon_intro zenon_Ha6 | zenon_intro zenon_Hea ]. % 19.13/19.26 exact (zenon_Ha7 zenon_Ha6). % 19.13/19.26 apply (zenon_or_s _ _ zenon_Hea); [ zenon_intro zenon_Haa | zenon_intro zenon_Hdd ]. % 19.13/19.26 apply (zenon_or_s _ _ zenon_He8); [ zenon_intro zenon_Hac | zenon_intro zenon_Heb ]. % 19.13/19.26 apply (zenon_L1425_); trivial. % 19.13/19.26 apply (zenon_or_s _ _ zenon_Heb); [ zenon_intro zenon_Hae | zenon_intro zenon_Hec ]. % 19.13/19.26 apply (zenon_L42_); trivial. % 19.13/19.26 apply (zenon_or_s _ _ zenon_Hec); [ zenon_intro zenon_Hba | zenon_intro zenon_Hc4 ]. % 19.13/19.26 apply (zenon_L179_); trivial. % 19.13/19.26 apply (zenon_L50_); trivial. % 19.13/19.26 exact (zenon_H280 zenon_Hdd). % 19.13/19.26 (* end of lemma zenon_L1468_ *) % 19.13/19.26 assert (zenon_L1469_ : (((op (e0) (e0)) = (e3))\/(((op (e1) (e0)) = (e3))\/(((op (e2) (e0)) = (e3))\/((op (e3) (e0)) = (e3))))) -> (~((op (e0) (e0)) = (e3))) -> (~((op (e1) (e0)) = (e3))) -> (~((op (e2) (e0)) = (e3))) -> ((op (e3) (e0)) = (e2)) -> (~((e2) = (e3))) -> False). % 19.13/19.26 do 0 intro. intros zenon_H1e0 zenon_H98 zenon_H9f zenon_H27f zenon_H148 zenon_H12b. % 19.13/19.26 apply (zenon_or_s _ _ zenon_H1e0); [ zenon_intro zenon_H3a | zenon_intro zenon_H1e1 ]. % 19.13/19.26 exact (zenon_H98 zenon_H3a). % 19.13/19.26 apply (zenon_or_s _ _ zenon_H1e1); [ zenon_intro zenon_H9e | zenon_intro zenon_H1e2 ]. % 19.13/19.26 exact (zenon_H9f zenon_H9e). % 19.13/19.26 apply (zenon_or_s _ _ zenon_H1e2); [ zenon_intro zenon_H3b | zenon_intro zenon_H15e ]. % 19.13/19.26 exact (zenon_H27f zenon_H3b). % 19.13/19.26 apply (zenon_L109_); trivial. % 19.13/19.26 (* end of lemma zenon_L1469_ *) % 19.13/19.26 assert (zenon_L1470_ : (((op (e2) (e2)) = (e0))\/(((op (e2) (e2)) = (e1))\/(((op (e2) (e2)) = (e2))\/((op (e2) (e2)) = (e3))))) -> (~((op (e2) (e2)) = (op (e2) (e3)))) -> ((op (e2) (e3)) = (e0)) -> ((op (e1) (e2)) = (e1)) -> (~((op (e1) (e2)) = (op (e2) (e2)))) -> (~((op (e2) (e2)) = (e2))) -> (~((op (e2) (e2)) = (e3))) -> False). % 19.13/19.26 do 0 intro. intros zenon_H1c4 zenon_H6d zenon_H37 zenon_Hf0 zenon_H2b zenon_H173 zenon_H1b3. % 19.13/19.26 apply (zenon_or_s _ _ zenon_H1c4); [ zenon_intro zenon_H2c | zenon_intro zenon_H1c5 ]. % 19.13/19.26 apply (zenon_L18_); trivial. % 19.13/19.26 apply (zenon_or_s _ _ zenon_H1c5); [ zenon_intro zenon_Hf1 | zenon_intro zenon_H1c6 ]. % 19.13/19.26 apply (zenon_L59_); trivial. % 19.13/19.26 apply (zenon_or_s _ _ zenon_H1c6); [ zenon_intro zenon_H176 | zenon_intro zenon_Haa ]. % 19.13/19.26 exact (zenon_H173 zenon_H176). % 19.13/19.26 exact (zenon_H1b3 zenon_Haa). % 19.13/19.26 (* end of lemma zenon_L1470_ *) % 19.13/19.26 assert (zenon_L1471_ : (((op (e2) (e1)) = (e0))\/(((op (e2) (e1)) = (e1))\/(((op (e2) (e1)) = (e2))\/((op (e2) (e1)) = (e3))))) -> (~((op (e2) (e1)) = (op (e2) (e3)))) -> ((op (e2) (e3)) = (e0)) -> (~((op (e2) (e1)) = (op (e3) (e1)))) -> ((op (e3) (e1)) = (e1)) -> ((op (e2) (e0)) = (e2)) -> (~((op (e2) (e0)) = (op (e2) (e1)))) -> (~((op (e2) (e1)) = (e3))) -> False). % 19.13/19.26 do 0 intro. intros zenon_H1cc zenon_H1c7 zenon_H37 zenon_Haf zenon_Hae zenon_Hee zenon_H1f0 zenon_Ha7. % 19.13/19.26 apply (zenon_or_s _ _ zenon_H1cc); [ zenon_intro zenon_H36 | zenon_intro zenon_H1cd ]. % 19.13/19.26 apply (zenon_L640_); trivial. % 19.13/19.26 apply (zenon_or_s _ _ zenon_H1cd); [ zenon_intro zenon_Ha5 | zenon_intro zenon_H1ce ]. % 19.13/19.26 apply (zenon_L42_); trivial. % 19.13/19.26 apply (zenon_or_s _ _ zenon_H1ce); [ zenon_intro zenon_H1ca | zenon_intro zenon_Ha6 ]. % 19.13/19.26 apply (zenon_L277_); trivial. % 19.13/19.26 exact (zenon_Ha7 zenon_Ha6). % 19.13/19.26 (* end of lemma zenon_L1471_ *) % 19.13/19.26 assert (zenon_L1472_ : (((op (e3) (e1)) = (e0))\/(((op (e3) (e1)) = (e1))\/(((op (e3) (e1)) = (e2))\/((op (e3) (e1)) = (e3))))) -> ((op (e1) (e1)) = (e3)) -> ((op (e0) (e1)) = (e2)) -> (~((op (e2) (e1)) = (e3))) -> (~((op (e2) (e0)) = (op (e2) (e1)))) -> ((op (e2) (e0)) = (e2)) -> (~((op (e2) (e1)) = (op (e3) (e1)))) -> ((op (e2) (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 (e3) (e1)) = (op (e3) (e3)))) -> ((op (e3) (e3)) = (e2)) -> (~((op (e3) (e1)) = (e3))) -> False). % 19.13/19.26 do 0 intro. intros zenon_H22a zenon_H13f zenon_H10f zenon_Ha7 zenon_H1f0 zenon_Hee zenon_Haf zenon_H37 zenon_H1c7 zenon_H1cc zenon_H130 zenon_Hf6 zenon_H282. % 19.13/19.26 apply (zenon_or_s _ _ zenon_H22a); [ zenon_intro zenon_H1b1 | zenon_intro zenon_H22b ]. % 19.13/19.26 apply (zenon_L580_); trivial. % 19.13/19.26 apply (zenon_or_s _ _ zenon_H22b); [ zenon_intro zenon_Hae | zenon_intro zenon_H22c ]. % 19.13/19.26 apply (zenon_L1471_); trivial. % 19.13/19.26 apply (zenon_or_s _ _ zenon_H22c); [ zenon_intro zenon_H14d | zenon_intro zenon_H161 ]. % 19.13/19.26 apply (zenon_L102_); trivial. % 19.13/19.26 exact (zenon_H282 zenon_H161). % 19.13/19.26 (* end of lemma zenon_L1472_ *) % 19.13/19.26 assert (zenon_L1473_ : ((~((op (e3) (e0)) = (e3)))\/((op (e3) (e3)) = (e0))) -> ((op (e2) (e3)) = (e0)) -> ((~((op (e3) (e2)) = (e3)))\/((op (e3) (e3)) = (e2))) -> ((op (e2) (e3)) = (e2)) -> (~((op (e2) (e3)) = (op (e3) (e3)))) -> (~((op (e3) (e3)) = (e3))) -> (((op (e3) (e0)) = (e3))\/(((op (e3) (e1)) = (e3))\/(((op (e3) (e2)) = (e3))\/((op (e3) (e3)) = (e3))))) -> (~((op (e1) (e3)) = (op (e3) (e3)))) -> ((op (e1) (e3)) = (e1)) -> ((~((op (e3) (e1)) = (e3)))\/((op (e3) (e3)) = (e1))) -> False). % 19.13/19.26 do 0 intro. intros zenon_H286 zenon_H37 zenon_H284 zenon_H11d zenon_Hf3 zenon_H102 zenon_H165 zenon_Hd5 zenon_Hd6 zenon_H285. % 19.13/19.26 apply (zenon_or_s _ _ zenon_H286); [ zenon_intro zenon_H15f | zenon_intro zenon_H60 ]. % 19.13/19.26 apply (zenon_L1369_); trivial. % 19.13/19.26 apply (zenon_L219_); trivial. % 19.13/19.26 (* end of lemma zenon_L1473_ *) % 19.13/19.26 assert (zenon_L1474_ : (((op (e2) (e0)) = (e2))\/(((op (e2) (e1)) = (e2))\/(((op (e2) (e2)) = (e2))\/((op (e2) (e3)) = (e2))))) -> (~((op (e3) (e1)) = (e3))) -> ((op (e3) (e3)) = (e2)) -> (~((op (e3) (e1)) = (op (e3) (e3)))) -> (((op (e2) (e1)) = (e0))\/(((op (e2) (e1)) = (e1))\/(((op (e2) (e1)) = (e2))\/((op (e2) (e1)) = (e3))))) -> (~((op (e2) (e1)) = (op (e2) (e3)))) -> (~((op (e2) (e1)) = (op (e3) (e1)))) -> (~((op (e2) (e0)) = (op (e2) (e1)))) -> (~((op (e2) (e1)) = (e3))) -> ((op (e1) (e1)) = (e3)) -> (((op (e3) (e1)) = (e0))\/(((op (e3) (e1)) = (e1))\/(((op (e3) (e1)) = (e2))\/((op (e3) (e1)) = (e3))))) -> ((op (e0) (e1)) = (e2)) -> (~((op (e0) (e1)) = (op (e2) (e1)))) -> (~((op (e2) (e2)) = (e2))) -> ((~((op (e3) (e0)) = (e3)))\/((op (e3) (e3)) = (e0))) -> ((op (e2) (e3)) = (e0)) -> ((~((op (e3) (e2)) = (e3)))\/((op (e3) (e3)) = (e2))) -> (~((op (e2) (e3)) = (op (e3) (e3)))) -> (~((op (e3) (e3)) = (e3))) -> (((op (e3) (e0)) = (e3))\/(((op (e3) (e1)) = (e3))\/(((op (e3) (e2)) = (e3))\/((op (e3) (e3)) = (e3))))) -> (~((op (e1) (e3)) = (op (e3) (e3)))) -> ((op (e1) (e3)) = (e1)) -> ((~((op (e3) (e1)) = (e3)))\/((op (e3) (e3)) = (e1))) -> False). % 19.13/19.26 do 0 intro. intros zenon_H1d5 zenon_H282 zenon_Hf6 zenon_H130 zenon_H1cc zenon_H1c7 zenon_Haf zenon_H1f0 zenon_Ha7 zenon_H13f zenon_H22a zenon_H10f zenon_H17e zenon_H173 zenon_H286 zenon_H37 zenon_H284 zenon_Hf3 zenon_H102 zenon_H165 zenon_Hd5 zenon_Hd6 zenon_H285. % 19.13/19.26 apply (zenon_or_s _ _ zenon_H1d5); [ zenon_intro zenon_Hee | zenon_intro zenon_H1d6 ]. % 19.13/19.26 apply (zenon_L1472_); trivial. % 19.13/19.26 apply (zenon_or_s _ _ zenon_H1d6); [ zenon_intro zenon_H1ca | zenon_intro zenon_H1d7 ]. % 19.13/19.26 apply (zenon_L191_); trivial. % 19.13/19.26 apply (zenon_or_s _ _ zenon_H1d7); [ zenon_intro zenon_H176 | zenon_intro zenon_H11d ]. % 19.13/19.26 exact (zenon_H173 zenon_H176). % 19.13/19.26 apply (zenon_L1473_); trivial. % 19.13/19.26 (* end of lemma zenon_L1474_ *) % 19.13/19.26 assert (zenon_L1475_ : (((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)) = (e0)) -> ((op (e3) (e1)) = (e1)) -> (~((op (e0) (e1)) = (op (e3) (e1)))) -> ((~((op (e3) (e1)) = (e3)))\/((op (e3) (e3)) = (e1))) -> ((op (e1) (e3)) = (e1)) -> (~((op (e1) (e3)) = (op (e3) (e3)))) -> (((op (e3) (e0)) = (e3))\/(((op (e3) (e1)) = (e3))\/(((op (e3) (e2)) = (e3))\/((op (e3) (e3)) = (e3))))) -> (~((op (e3) (e3)) = (e3))) -> (~((op (e2) (e3)) = (op (e3) (e3)))) -> ((~((op (e3) (e2)) = (e3)))\/((op (e3) (e3)) = (e2))) -> ((op (e2) (e3)) = (e0)) -> ((~((op (e3) (e0)) = (e3)))\/((op (e3) (e3)) = (e0))) -> (~((op (e2) (e2)) = (e2))) -> (~((op (e0) (e1)) = (op (e2) (e1)))) -> (((op (e3) (e1)) = (e0))\/(((op (e3) (e1)) = (e1))\/(((op (e3) (e1)) = (e2))\/((op (e3) (e1)) = (e3))))) -> ((op (e1) (e1)) = (e3)) -> (~((op (e2) (e1)) = (e3))) -> (~((op (e2) (e0)) = (op (e2) (e1)))) -> (~((op (e2) (e1)) = (op (e3) (e1)))) -> (~((op (e2) (e1)) = (op (e2) (e3)))) -> (((op (e2) (e1)) = (e0))\/(((op (e2) (e1)) = (e1))\/(((op (e2) (e1)) = (e2))\/((op (e2) (e1)) = (e3))))) -> (~((op (e3) (e1)) = (op (e3) (e3)))) -> ((op (e3) (e3)) = (e2)) -> (~((op (e3) (e1)) = (e3))) -> (((op (e2) (e0)) = (e2))\/(((op (e2) (e1)) = (e2))\/(((op (e2) (e2)) = (e2))\/((op (e2) (e3)) = (e2))))) -> (~((op (e0) (e1)) = (e3))) -> False). % 19.13/19.26 do 0 intro. intros zenon_H212 zenon_H4a zenon_H48 zenon_Hae zenon_H210 zenon_H285 zenon_Hd6 zenon_Hd5 zenon_H165 zenon_H102 zenon_Hf3 zenon_H284 zenon_H37 zenon_H286 zenon_H173 zenon_H17e zenon_H22a zenon_H13f zenon_Ha7 zenon_H1f0 zenon_Haf zenon_H1c7 zenon_H1cc zenon_H130 zenon_Hf6 zenon_H282 zenon_H1d5 zenon_H9c. % 19.13/19.26 apply (zenon_or_s _ _ zenon_H212); [ zenon_intro zenon_H49 | zenon_intro zenon_H213 ]. % 19.13/19.26 apply (zenon_L9_); trivial. % 19.13/19.26 apply (zenon_or_s _ _ zenon_H213); [ zenon_intro zenon_Ha0 | zenon_intro zenon_H214 ]. % 19.13/19.26 apply (zenon_L363_); trivial. % 19.13/19.26 apply (zenon_or_s _ _ zenon_H214); [ zenon_intro zenon_H10f | zenon_intro zenon_H99 ]. % 19.13/19.26 apply (zenon_L1474_); trivial. % 19.13/19.26 exact (zenon_H9c zenon_H99). % 19.13/19.26 (* end of lemma zenon_L1475_ *) % 19.13/19.26 assert (zenon_L1476_ : (((op (e1) (e0)) = (e3))\/(((op (e1) (e1)) = (e3))\/(((op (e1) (e2)) = (e3))\/((op (e1) (e3)) = (e3))))) -> (~((op (e1) (e0)) = (e3))) -> (~((op (e0) (e1)) = (e3))) -> (((op (e2) (e0)) = (e2))\/(((op (e2) (e1)) = (e2))\/(((op (e2) (e2)) = (e2))\/((op (e2) (e3)) = (e2))))) -> (~((op (e3) (e1)) = (e3))) -> ((op (e3) (e3)) = (e2)) -> (~((op (e3) (e1)) = (op (e3) (e3)))) -> (((op (e2) (e1)) = (e0))\/(((op (e2) (e1)) = (e1))\/(((op (e2) (e1)) = (e2))\/((op (e2) (e1)) = (e3))))) -> (~((op (e2) (e1)) = (op (e2) (e3)))) -> (~((op (e2) (e1)) = (op (e3) (e1)))) -> (~((op (e2) (e0)) = (op (e2) (e1)))) -> (~((op (e2) (e1)) = (e3))) -> (((op (e3) (e1)) = (e0))\/(((op (e3) (e1)) = (e1))\/(((op (e3) (e1)) = (e2))\/((op (e3) (e1)) = (e3))))) -> (~((op (e0) (e1)) = (op (e2) (e1)))) -> (~((op (e2) (e2)) = (e2))) -> ((~((op (e3) (e0)) = (e3)))\/((op (e3) (e3)) = (e0))) -> ((op (e2) (e3)) = (e0)) -> ((~((op (e3) (e2)) = (e3)))\/((op (e3) (e3)) = (e2))) -> (~((op (e2) (e3)) = (op (e3) (e3)))) -> (~((op (e3) (e3)) = (e3))) -> (((op (e3) (e0)) = (e3))\/(((op (e3) (e1)) = (e3))\/(((op (e3) (e2)) = (e3))\/((op (e3) (e3)) = (e3))))) -> (~((op (e1) (e3)) = (op (e3) (e3)))) -> ((op (e1) (e3)) = (e1)) -> ((~((op (e3) (e1)) = (e3)))\/((op (e3) (e3)) = (e1))) -> (~((op (e0) (e1)) = (op (e3) (e1)))) -> ((op (e3) (e1)) = (e1)) -> ((op (e0) (e2)) = (e0)) -> (~((op (e0) (e1)) = (op (e0) (e2)))) -> (((op (e0) (e1)) = (e0))\/(((op (e0) (e1)) = (e1))\/(((op (e0) (e1)) = (e2))\/((op (e0) (e1)) = (e3))))) -> (~((op (e1) (e2)) = (e3))) -> (~((op (e1) (e3)) = (e3))) -> False). % 19.13/19.26 do 0 intro. intros zenon_H16f zenon_H9f zenon_H9c zenon_H1d5 zenon_H282 zenon_Hf6 zenon_H130 zenon_H1cc zenon_H1c7 zenon_Haf zenon_H1f0 zenon_Ha7 zenon_H22a zenon_H17e zenon_H173 zenon_H286 zenon_H37 zenon_H284 zenon_Hf3 zenon_H102 zenon_H165 zenon_Hd5 zenon_Hd6 zenon_H285 zenon_H210 zenon_Hae zenon_H48 zenon_H4a zenon_H212 zenon_H16d zenon_H12f. % 19.13/19.26 apply (zenon_or_s _ _ zenon_H16f); [ zenon_intro zenon_H9e | zenon_intro zenon_H170 ]. % 19.13/19.26 exact (zenon_H9f zenon_H9e). % 19.13/19.26 apply (zenon_or_s _ _ zenon_H170); [ zenon_intro zenon_H13f | zenon_intro zenon_H171 ]. % 19.13/19.26 apply (zenon_L1475_); trivial. % 19.13/19.26 apply (zenon_or_s _ _ zenon_H171); [ zenon_intro zenon_H16c | zenon_intro zenon_Hdc ]. % 19.13/19.26 exact (zenon_H16d zenon_H16c). % 19.13/19.26 exact (zenon_H12f zenon_Hdc). % 19.13/19.26 (* end of lemma zenon_L1476_ *) % 19.13/19.26 assert (zenon_L1477_ : (((op (e0) (e2)) = (e0))\/(((op (e0) (e2)) = (e1))\/(((op (e0) (e2)) = (e2))\/((op (e0) (e2)) = (e3))))) -> (~((op (e1) (e3)) = (e3))) -> (~((op (e1) (e2)) = (e3))) -> (((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)) = (e1)) -> (~((op (e0) (e1)) = (op (e3) (e1)))) -> ((~((op (e3) (e1)) = (e3)))\/((op (e3) (e3)) = (e1))) -> ((op (e1) (e3)) = (e1)) -> (~((op (e1) (e3)) = (op (e3) (e3)))) -> (((op (e3) (e0)) = (e3))\/(((op (e3) (e1)) = (e3))\/(((op (e3) (e2)) = (e3))\/((op (e3) (e3)) = (e3))))) -> (~((op (e3) (e3)) = (e3))) -> (~((op (e2) (e3)) = (op (e3) (e3)))) -> ((~((op (e3) (e2)) = (e3)))\/((op (e3) (e3)) = (e2))) -> ((op (e2) (e3)) = (e0)) -> ((~((op (e3) (e0)) = (e3)))\/((op (e3) (e3)) = (e0))) -> (~((op (e2) (e2)) = (e2))) -> (~((op (e0) (e1)) = (op (e2) (e1)))) -> (((op (e3) (e1)) = (e0))\/(((op (e3) (e1)) = (e1))\/(((op (e3) (e1)) = (e2))\/((op (e3) (e1)) = (e3))))) -> (~((op (e2) (e1)) = (e3))) -> (~((op (e2) (e0)) = (op (e2) (e1)))) -> (~((op (e2) (e1)) = (op (e3) (e1)))) -> (~((op (e2) (e1)) = (op (e2) (e3)))) -> (((op (e2) (e1)) = (e0))\/(((op (e2) (e1)) = (e1))\/(((op (e2) (e1)) = (e2))\/((op (e2) (e1)) = (e3))))) -> (~((op (e3) (e1)) = (op (e3) (e3)))) -> ((op (e3) (e3)) = (e2)) -> (~((op (e3) (e1)) = (e3))) -> (((op (e2) (e0)) = (e2))\/(((op (e2) (e1)) = (e2))\/(((op (e2) (e2)) = (e2))\/((op (e2) (e3)) = (e2))))) -> (~((op (e0) (e1)) = (e3))) -> (~((op (e1) (e0)) = (e3))) -> (((op (e1) (e0)) = (e3))\/(((op (e1) (e1)) = (e3))\/(((op (e1) (e2)) = (e3))\/((op (e1) (e3)) = (e3))))) -> ((op (e2) (e2)) = (e1)) -> (~((op (e0) (e2)) = (op (e2) (e2)))) -> ((op (e1) (e2)) = (e2)) -> (~((op (e0) (e2)) = (op (e1) (e2)))) -> (~((op (e0) (e2)) = (e3))) -> False). % 19.13/19.26 do 0 intro. intros zenon_H1ba zenon_H12f zenon_H16d zenon_H212 zenon_H4a zenon_Hae zenon_H210 zenon_H285 zenon_Hd6 zenon_Hd5 zenon_H165 zenon_H102 zenon_Hf3 zenon_H284 zenon_H37 zenon_H286 zenon_H173 zenon_H17e zenon_H22a zenon_Ha7 zenon_H1f0 zenon_Haf zenon_H1c7 zenon_H1cc zenon_H130 zenon_Hf6 zenon_H282 zenon_H1d5 zenon_H9c zenon_H9f zenon_H16f zenon_Hf1 zenon_Ha8 zenon_H113 zenon_H195 zenon_H123. % 19.13/19.26 apply (zenon_or_s _ _ zenon_H1ba); [ zenon_intro zenon_H48 | zenon_intro zenon_H1bb ]. % 19.13/19.26 apply (zenon_L1476_); trivial. % 19.13/19.26 apply (zenon_or_s _ _ zenon_H1bb); [ zenon_intro zenon_H122 | zenon_intro zenon_H1bc ]. % 19.13/19.26 apply (zenon_L246_); trivial. % 19.13/19.26 apply (zenon_or_s _ _ zenon_H1bc); [ zenon_intro zenon_H150 | zenon_intro zenon_Ha9 ]. % 19.13/19.26 apply (zenon_L153_); trivial. % 19.13/19.26 exact (zenon_H123 zenon_Ha9). % 19.13/19.26 (* end of lemma zenon_L1477_ *) % 19.13/19.26 assert (zenon_L1478_ : (((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) (e2)) = (e1)) -> (~((op (e3) (e0)) = (op (e3) (e2)))) -> (~((op (e3) (e0)) = (op (e3) (e3)))) -> ((op (e3) (e3)) = (e2)) -> (~((op (e3) (e0)) = (e3))) -> False). % 19.13/19.26 do 0 intro. intros zenon_H267 zenon_H1b1 zenon_H1cf zenon_Hba zenon_H6f zenon_H71 zenon_Hf6 zenon_H15f. % 19.13/19.26 apply (zenon_or_s _ _ zenon_H267); [ zenon_intro zenon_H44 | zenon_intro zenon_H268 ]. % 19.13/19.26 apply (zenon_L346_); trivial. % 19.13/19.26 apply (zenon_or_s _ _ zenon_H268); [ zenon_intro zenon_Hac | zenon_intro zenon_H269 ]. % 19.13/19.26 apply (zenon_L249_); trivial. % 19.13/19.26 apply (zenon_or_s _ _ zenon_H269); [ zenon_intro zenon_H148 | zenon_intro zenon_H15e ]. % 19.13/19.26 apply (zenon_L114_); trivial. % 19.13/19.26 exact (zenon_H15f zenon_H15e). % 19.13/19.26 (* end of lemma zenon_L1478_ *) % 19.13/19.26 assert (zenon_L1479_ : (((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) (e3)))) -> (~((op (e3) (e0)) = (op (e3) (e2)))) -> ((op (e3) (e2)) = (e1)) -> (~((op (e3) (e0)) = (op (e3) (e1)))) -> (((op (e3) (e0)) = (e0))\/(((op (e3) (e0)) = (e1))\/(((op (e3) (e0)) = (e2))\/((op (e3) (e0)) = (e3))))) -> (~((op (e2) (e1)) = (op (e3) (e1)))) -> ((op (e2) (e1)) = (e1)) -> (~((op (e3) (e1)) = (op (e3) (e3)))) -> ((op (e3) (e3)) = (e2)) -> (~((op (e3) (e1)) = (e3))) -> False). % 19.13/19.26 do 0 intro. intros zenon_H22a zenon_H15f zenon_H71 zenon_H6f zenon_Hba zenon_H1cf zenon_H267 zenon_Haf zenon_Ha5 zenon_H130 zenon_Hf6 zenon_H282. % 19.13/19.26 apply (zenon_or_s _ _ zenon_H22a); [ zenon_intro zenon_H1b1 | zenon_intro zenon_H22b ]. % 19.13/19.26 apply (zenon_L1478_); trivial. % 19.13/19.26 apply (zenon_or_s _ _ zenon_H22b); [ zenon_intro zenon_Hae | zenon_intro zenon_H22c ]. % 19.13/19.26 apply (zenon_L42_); trivial. % 19.13/19.26 apply (zenon_or_s _ _ zenon_H22c); [ zenon_intro zenon_H14d | zenon_intro zenon_H161 ]. % 19.13/19.26 apply (zenon_L102_); trivial. % 19.13/19.26 exact (zenon_H282 zenon_H161). % 19.13/19.26 (* end of lemma zenon_L1479_ *) % 19.13/19.26 assert (zenon_L1480_ : (((op (e3) (e0)) = (e1))\/(((op (e3) (e1)) = (e1))\/(((op (e3) (e2)) = (e1))\/((op (e3) (e3)) = (e1))))) -> ((op (e0) (e0)) = (e2)) -> ((op (e2) (e0)) = (e3)) -> (~((op (e0) (e2)) = (e3))) -> (~((op (e0) (e2)) = (op (e1) (e2)))) -> ((op (e1) (e2)) = (e2)) -> (~((op (e0) (e2)) = (op (e2) (e2)))) -> ((op (e2) (e2)) = (e1)) -> (((op (e1) (e0)) = (e3))\/(((op (e1) (e1)) = (e3))\/(((op (e1) (e2)) = (e3))\/((op (e1) (e3)) = (e3))))) -> (~((op (e1) (e0)) = (e3))) -> (~((op (e0) (e1)) = (e3))) -> (((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) (e1)) = (op (e2) (e3)))) -> (~((op (e2) (e0)) = (op (e2) (e1)))) -> (~((op (e2) (e1)) = (e3))) -> (~((op (e0) (e1)) = (op (e2) (e1)))) -> (~((op (e2) (e2)) = (e2))) -> ((~((op (e3) (e0)) = (e3)))\/((op (e3) (e3)) = (e0))) -> ((op (e2) (e3)) = (e0)) -> ((~((op (e3) (e2)) = (e3)))\/((op (e3) (e3)) = (e2))) -> (~((op (e2) (e3)) = (op (e3) (e3)))) -> (~((op (e3) (e3)) = (e3))) -> (((op (e3) (e0)) = (e3))\/(((op (e3) (e1)) = (e3))\/(((op (e3) (e2)) = (e3))\/((op (e3) (e3)) = (e3))))) -> ((~((op (e3) (e1)) = (e3)))\/((op (e3) (e3)) = (e1))) -> (~((op (e0) (e1)) = (op (e3) (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) (e2)) = (e3))) -> (~((op (e1) (e3)) = (e3))) -> (((op (e0) (e2)) = (e0))\/(((op (e0) (e2)) = (e1))\/(((op (e0) (e2)) = (e2))\/((op (e0) (e2)) = (e3))))) -> (~((op (e3) (e1)) = (e3))) -> ((op (e3) (e3)) = (e2)) -> (~((op (e3) (e1)) = (op (e3) (e3)))) -> ((op (e2) (e1)) = (e1)) -> (~((op (e2) (e1)) = (op (e3) (e1)))) -> (((op (e3) (e0)) = (e0))\/(((op (e3) (e0)) = (e1))\/(((op (e3) (e0)) = (e2))\/((op (e3) (e0)) = (e3))))) -> (~((op (e3) (e0)) = (op (e3) (e1)))) -> (~((op (e3) (e0)) = (op (e3) (e2)))) -> (~((op (e3) (e0)) = (op (e3) (e3)))) -> (~((op (e3) (e0)) = (e3))) -> (((op (e3) (e1)) = (e0))\/(((op (e3) (e1)) = (e1))\/(((op (e3) (e1)) = (e2))\/((op (e3) (e1)) = (e3))))) -> (~((op (e1) (e3)) = (op (e3) (e3)))) -> ((op (e1) (e3)) = (e1)) -> False). % 19.13/19.26 do 0 intro. intros zenon_He8 zenon_H7b zenon_H3b zenon_H123 zenon_H195 zenon_H113 zenon_Ha8 zenon_Hf1 zenon_H16f zenon_H9f zenon_H9c zenon_H1d5 zenon_H1cc zenon_H1c7 zenon_H1f0 zenon_Ha7 zenon_H17e zenon_H173 zenon_H286 zenon_H37 zenon_H284 zenon_Hf3 zenon_H102 zenon_H165 zenon_H285 zenon_H210 zenon_H4a zenon_H212 zenon_H16d zenon_H12f zenon_H1ba zenon_H282 zenon_Hf6 zenon_H130 zenon_Ha5 zenon_Haf zenon_H267 zenon_H1cf zenon_H6f zenon_H71 zenon_H15f zenon_H22a zenon_Hd5 zenon_Hd6. % 19.13/19.26 apply (zenon_or_s _ _ zenon_He8); [ zenon_intro zenon_Hac | zenon_intro zenon_Heb ]. % 19.13/19.26 apply (zenon_L308_); trivial. % 19.13/19.26 apply (zenon_or_s _ _ zenon_Heb); [ zenon_intro zenon_Hae | zenon_intro zenon_Hec ]. % 19.13/19.26 apply (zenon_L1477_); trivial. % 19.13/19.26 apply (zenon_or_s _ _ zenon_Hec); [ zenon_intro zenon_Hba | zenon_intro zenon_Hc4 ]. % 19.13/19.26 apply (zenon_L1479_); trivial. % 19.13/19.26 apply (zenon_L50_); trivial. % 19.13/19.26 (* end of lemma zenon_L1480_ *) % 19.13/19.26 assert (zenon_L1481_ : (((op (e2) (e2)) = (e0))\/(((op (e2) (e2)) = (e1))\/(((op (e2) (e2)) = (e2))\/((op (e2) (e2)) = (e3))))) -> (~((op (e2) (e2)) = (op (e2) (e3)))) -> ((op (e2) (e3)) = (e0)) -> ((op (e2) (e0)) = (e1)) -> (~((op (e2) (e0)) = (op (e2) (e2)))) -> (~((op (e2) (e2)) = (e2))) -> (~((op (e2) (e2)) = (e3))) -> False). % 19.13/19.26 do 0 intro. intros zenon_H1c4 zenon_H6d zenon_H37 zenon_Hed zenon_H52 zenon_H173 zenon_H1b3. % 19.13/19.26 apply (zenon_or_s _ _ zenon_H1c4); [ zenon_intro zenon_H2c | zenon_intro zenon_H1c5 ]. % 19.13/19.26 apply (zenon_L18_); trivial. % 19.13/19.26 apply (zenon_or_s _ _ zenon_H1c5); [ zenon_intro zenon_Hf1 | zenon_intro zenon_H1c6 ]. % 19.13/19.26 apply (zenon_L93_); trivial. % 19.13/19.26 apply (zenon_or_s _ _ zenon_H1c6); [ zenon_intro zenon_H176 | zenon_intro zenon_Haa ]. % 19.13/19.26 exact (zenon_H173 zenon_H176). % 19.13/19.26 exact (zenon_H1b3 zenon_Haa). % 19.13/19.26 (* end of lemma zenon_L1481_ *) % 19.13/19.26 assert (zenon_L1482_ : (((op (e1) (e0)) = (e3))\/(((op (e1) (e1)) = (e3))\/(((op (e1) (e2)) = (e3))\/((op (e1) (e3)) = (e3))))) -> (~((op (e1) (e0)) = (e3))) -> ((~((op (e3) (e1)) = (e3)))\/((op (e3) (e3)) = (e1))) -> ((op (e1) (e3)) = (e1)) -> (~((op (e1) (e3)) = (op (e3) (e3)))) -> (((op (e3) (e0)) = (e3))\/(((op (e3) (e1)) = (e3))\/(((op (e3) (e2)) = (e3))\/((op (e3) (e3)) = (e3))))) -> (~((op (e3) (e3)) = (e3))) -> (~((op (e2) (e3)) = (op (e3) (e3)))) -> ((~((op (e3) (e2)) = (e3)))\/((op (e3) (e3)) = (e2))) -> ((op (e2) (e3)) = (e0)) -> ((~((op (e3) (e0)) = (e3)))\/((op (e3) (e3)) = (e0))) -> (~((op (e2) (e2)) = (e2))) -> (~((op (e0) (e1)) = (op (e2) (e1)))) -> ((op (e0) (e1)) = (e2)) -> (((op (e3) (e1)) = (e0))\/(((op (e3) (e1)) = (e1))\/(((op (e3) (e1)) = (e2))\/((op (e3) (e1)) = (e3))))) -> (~((op (e2) (e1)) = (e3))) -> (~((op (e2) (e0)) = (op (e2) (e1)))) -> (~((op (e2) (e1)) = (op (e3) (e1)))) -> (~((op (e2) (e1)) = (op (e2) (e3)))) -> (((op (e2) (e1)) = (e0))\/(((op (e2) (e1)) = (e1))\/(((op (e2) (e1)) = (e2))\/((op (e2) (e1)) = (e3))))) -> (~((op (e3) (e1)) = (op (e3) (e3)))) -> ((op (e3) (e3)) = (e2)) -> (~((op (e3) (e1)) = (e3))) -> (((op (e2) (e0)) = (e2))\/(((op (e2) (e1)) = (e2))\/(((op (e2) (e2)) = (e2))\/((op (e2) (e3)) = (e2))))) -> (~((op (e1) (e2)) = (e3))) -> (~((op (e1) (e3)) = (e3))) -> False). % 19.13/19.26 do 0 intro. intros zenon_H16f zenon_H9f zenon_H285 zenon_Hd6 zenon_Hd5 zenon_H165 zenon_H102 zenon_Hf3 zenon_H284 zenon_H37 zenon_H286 zenon_H173 zenon_H17e zenon_H10f zenon_H22a zenon_Ha7 zenon_H1f0 zenon_Haf zenon_H1c7 zenon_H1cc zenon_H130 zenon_Hf6 zenon_H282 zenon_H1d5 zenon_H16d zenon_H12f. % 19.13/19.26 apply (zenon_or_s _ _ zenon_H16f); [ zenon_intro zenon_H9e | zenon_intro zenon_H170 ]. % 19.13/19.26 exact (zenon_H9f zenon_H9e). % 19.13/19.26 apply (zenon_or_s _ _ zenon_H170); [ zenon_intro zenon_H13f | zenon_intro zenon_H171 ]. % 19.13/19.26 apply (zenon_L1474_); trivial. % 19.13/19.26 apply (zenon_or_s _ _ zenon_H171); [ zenon_intro zenon_H16c | zenon_intro zenon_Hdc ]. % 19.13/19.26 exact (zenon_H16d zenon_H16c). % 19.13/19.26 exact (zenon_H12f zenon_Hdc). % 19.13/19.26 (* end of lemma zenon_L1482_ *) % 19.13/19.26 assert (zenon_L1483_ : ((~((op (e2) (e2)) = (e3)))\/((op (e2) (e3)) = (e2))) -> ((op (e0) (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 (e2) (e1)) = (e3))) -> (~((op (e2) (e0)) = (e3))) -> (~((op (e1) (e3)) = (op (e2) (e3)))) -> ((op (e1) (e3)) = (e3)) -> ((~((op (e2) (e3)) = (e3)))\/((op (e2) (e3)) = (e3))) -> False). % 19.13/19.26 do 0 intro. intros zenon_H288 zenon_Hcd zenon_He2 zenon_He7 zenon_Ha7 zenon_H27f zenon_Hdb zenon_Hdc zenon_H281. % 19.13/19.26 apply (zenon_or_s _ _ zenon_H288); [ zenon_intro zenon_H1b3 | zenon_intro zenon_H11d ]. % 19.13/19.26 apply (zenon_L1345_); trivial. % 19.13/19.26 apply (zenon_L234_); trivial. % 19.13/19.26 (* end of lemma zenon_L1483_ *) % 19.13/19.26 assert (zenon_L1484_ : ((~((op (e3) (e1)) = (e3)))\/((op (e3) (e3)) = (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 (e3) (e3)) = (e3))) -> (~((op (e3) (e0)) = (e3))) -> (~((op (e0) (e3)) = (op (e3) (e3)))) -> ((op (e0) (e3)) = (e2)) -> ((~((op (e3) (e2)) = (e3)))\/((op (e3) (e3)) = (e2))) -> False). % 19.13/19.26 do 0 intro. intros zenon_H285 zenon_Hf4 zenon_Hf3 zenon_H165 zenon_H102 zenon_H15f zenon_Hc2 zenon_Hcd zenon_H284. % 19.13/19.26 apply (zenon_or_s _ _ zenon_H285); [ zenon_intro zenon_H282 | zenon_intro zenon_Hc4 ]. % 19.13/19.26 apply (zenon_L1449_); trivial. % 19.13/19.26 apply (zenon_L60_); trivial. % 19.13/19.26 (* end of lemma zenon_L1484_ *) % 19.13/19.26 assert (zenon_L1485_ : ((~((op (e2) (e1)) = (e3)))\/((op (e2) (e3)) = (e1))) -> ((~((op (e3) (e1)) = (e3)))\/((op (e3) (e3)) = (e1))) -> (~((op (e2) (e3)) = (op (e3) (e3)))) -> (((op (e3) (e0)) = (e3))\/(((op (e3) (e1)) = (e3))\/(((op (e3) (e2)) = (e3))\/((op (e3) (e3)) = (e3))))) -> (~((op (e3) (e3)) = (e3))) -> (~((op (e0) (e3)) = (op (e3) (e3)))) -> ((~((op (e3) (e2)) = (e3)))\/((op (e3) (e3)) = (e2))) -> ((~((op (e3) (e0)) = (e3)))\/((op (e3) (e3)) = (e0))) -> ((~((op (e2) (e3)) = (e3)))\/((op (e2) (e3)) = (e3))) -> ((op (e1) (e3)) = (e3)) -> (~((op (e1) (e3)) = (op (e2) (e3)))) -> (~((op (e2) (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)) = (e2)) -> ((~((op (e2) (e2)) = (e3)))\/((op (e2) (e3)) = (e2))) -> False). % 19.13/19.26 do 0 intro. intros zenon_H28b zenon_H285 zenon_Hf3 zenon_H165 zenon_H102 zenon_Hc2 zenon_H284 zenon_H286 zenon_H281 zenon_Hdc zenon_Hdb zenon_H27f zenon_He7 zenon_He2 zenon_Hcd zenon_H288. % 19.13/19.26 apply (zenon_or_s _ _ zenon_H28b); [ zenon_intro zenon_Ha7 | zenon_intro zenon_Hf4 ]. % 19.13/19.26 apply (zenon_L1483_); trivial. % 19.13/19.26 apply (zenon_or_s _ _ zenon_H286); [ zenon_intro zenon_H15f | zenon_intro zenon_H60 ]. % 19.13/19.26 apply (zenon_L1484_); trivial. % 19.13/19.26 apply (zenon_L229_); trivial. % 19.13/19.26 (* end of lemma zenon_L1485_ *) % 19.13/19.26 assert (zenon_L1486_ : (((op (e2) (e2)) = (e0))\/(((op (e2) (e2)) = (e1))\/(((op (e2) (e2)) = (e2))\/((op (e2) (e2)) = (e3))))) -> (~((op (e1) (e2)) = (op (e2) (e2)))) -> ((op (e1) (e2)) = (e0)) -> ((op (e0) (e2)) = (e3)) -> (~((op (e2) (e2)) = (e2))) -> (~((op (e2) (e2)) = (e3))) -> False). % 19.13/19.26 do 0 intro. intros zenon_H1c4 zenon_H2b zenon_H2a zenon_Ha9 zenon_H173 zenon_H1b3. % 19.13/19.26 apply (zenon_or_s _ _ zenon_H1c4); [ zenon_intro zenon_H2c | zenon_intro zenon_H1c5 ]. % 19.13/19.26 apply (zenon_L3_); trivial. % 19.13/19.26 apply (zenon_or_s _ _ zenon_H1c5); [ zenon_intro zenon_Hf1 | zenon_intro zenon_H1c6 ]. % 19.13/19.26 apply (zenon_L184_); trivial. % 19.13/19.26 apply (zenon_or_s _ _ zenon_H1c6); [ zenon_intro zenon_H176 | zenon_intro zenon_Haa ]. % 19.13/19.26 exact (zenon_H173 zenon_H176). % 19.13/19.26 exact (zenon_H1b3 zenon_Haa). % 19.13/19.26 (* end of lemma zenon_L1486_ *) % 19.13/19.26 assert (zenon_L1487_ : (((op (e0) (e0)) = (e0))\/(((op (e1) (e0)) = (e0))\/(((op (e2) (e0)) = (e0))\/((op (e3) (e0)) = (e0))))) -> (~((op (e0) (e0)) = (e0))) -> (~((e1) = (e3))) -> ((op (e1) (e3)) = (e3)) -> (~((op (e1) (e1)) = (e1))) -> (~((e0) = (e1))) -> (((op (e1) (e0)) = (e1))\/(((op (e1) (e1)) = (e1))\/(((op (e1) (e2)) = (e1))\/((op (e1) (e3)) = (e1))))) -> (~((op (e2) (e0)) = (op (e2) (e3)))) -> (((op (e0) (e0)) = (e3))\/(((op (e0) (e1)) = (e3))\/(((op (e0) (e2)) = (e3))\/((op (e0) (e3)) = (e3))))) -> (~((op (e0) (e0)) = (e3))) -> (~((op (e0) (e1)) = (e3))) -> (~((op (e3) (e0)) = (op (e3) (e2)))) -> ((op (e2) (e3)) = (e0)) -> (~((op (e2) (e2)) = (op (e2) (e3)))) -> (((op (e2) (e2)) = (e0))\/(((op (e2) (e2)) = (e1))\/(((op (e2) (e2)) = (e2))\/((op (e2) (e2)) = (e3))))) -> (~((op (e1) (e2)) = (op (e2) (e2)))) -> (~((op (e2) (e2)) = (e2))) -> (~((op (e2) (e2)) = (e3))) -> (~((e0) = (e3))) -> (((op (e0) (e2)) = (e0))\/(((op (e1) (e2)) = (e0))\/(((op (e2) (e2)) = (e0))\/((op (e3) (e2)) = (e0))))) -> (~((op (e0) (e3)) = (e3))) -> False). % 19.13/19.26 do 0 intro. intros zenon_H3e zenon_H3f zenon_H95 zenon_Hdc zenon_H10a zenon_Ha1 zenon_H128 zenon_H5b zenon_H168 zenon_H98 zenon_H9c zenon_H6f zenon_H37 zenon_H6d zenon_H1c4 zenon_H2b zenon_H173 zenon_H1b3 zenon_H9a zenon_H6a zenon_H12d. % 19.13/19.26 apply (zenon_or_s _ _ zenon_H3e); [ zenon_intro zenon_H42 | zenon_intro zenon_H41 ]. % 19.13/19.26 exact (zenon_H3f zenon_H42). % 19.13/19.26 apply (zenon_or_s _ _ zenon_H41); [ zenon_intro zenon_H27 | zenon_intro zenon_H43 ]. % 19.13/19.26 apply (zenon_or_s _ _ zenon_H128); [ zenon_intro zenon_H9d | zenon_intro zenon_H129 ]. % 19.13/19.26 apply (zenon_L262_); trivial. % 19.13/19.26 apply (zenon_or_s _ _ zenon_H129); [ zenon_intro zenon_H10d | zenon_intro zenon_H12a ]. % 19.13/19.26 exact (zenon_H10a zenon_H10d). % 19.13/19.26 apply (zenon_or_s _ _ zenon_H12a); [ zenon_intro zenon_Hf0 | zenon_intro zenon_Hd6 ]. % 19.13/19.26 apply (zenon_L1470_); trivial. % 19.13/19.26 apply (zenon_L83_); trivial. % 19.13/19.26 apply (zenon_or_s _ _ zenon_H43); [ zenon_intro zenon_H34 | zenon_intro zenon_H44 ]. % 19.13/19.26 apply (zenon_L14_); trivial. % 19.13/19.26 apply (zenon_or_s _ _ zenon_H168); [ zenon_intro zenon_H3a | zenon_intro zenon_H169 ]. % 19.13/19.26 exact (zenon_H98 zenon_H3a). % 19.13/19.26 apply (zenon_or_s _ _ zenon_H169); [ zenon_intro zenon_H99 | zenon_intro zenon_H16a ]. % 19.13/19.26 exact (zenon_H9c zenon_H99). % 19.13/19.26 apply (zenon_or_s _ _ zenon_H16a); [ zenon_intro zenon_Ha9 | zenon_intro zenon_He3 ]. % 19.13/19.26 apply (zenon_or_s _ _ zenon_H6a); [ zenon_intro zenon_H48 | zenon_intro zenon_H6b ]. % 19.13/19.26 apply (zenon_L358_); trivial. % 19.13/19.26 apply (zenon_or_s _ _ zenon_H6b); [ zenon_intro zenon_H2a | zenon_intro zenon_H6c ]. % 19.13/19.26 apply (zenon_L1486_); trivial. % 19.13/19.26 apply (zenon_or_s _ _ zenon_H6c); [ zenon_intro zenon_H2c | zenon_intro zenon_H61 ]. % 19.13/19.26 apply (zenon_L18_); trivial. % 19.13/19.26 apply (zenon_L19_); trivial. % 19.13/19.26 exact (zenon_H12d zenon_He3). % 19.13/19.26 (* end of lemma zenon_L1487_ *) % 19.13/19.26 assert (zenon_L1488_ : ((~((op (e3) (e1)) = (e3)))\/((op (e3) (e3)) = (e1))) -> ((op (e1) (e3)) = (e1)) -> (~((op (e1) (e3)) = (op (e3) (e3)))) -> (((op (e3) (e0)) = (e3))\/(((op (e3) (e1)) = (e3))\/(((op (e3) (e2)) = (e3))\/((op (e3) (e3)) = (e3))))) -> (~((op (e3) (e3)) = (e3))) -> (~((op (e3) (e0)) = (e3))) -> (~((op (e0) (e3)) = (op (e3) (e3)))) -> ((op (e0) (e3)) = (e2)) -> ((~((op (e3) (e2)) = (e3)))\/((op (e3) (e3)) = (e2))) -> False). % 19.13/19.26 do 0 intro. intros zenon_H285 zenon_Hd6 zenon_Hd5 zenon_H165 zenon_H102 zenon_H15f zenon_Hc2 zenon_Hcd zenon_H284. % 19.13/19.26 apply (zenon_or_s _ _ zenon_H285); [ zenon_intro zenon_H282 | zenon_intro zenon_Hc4 ]. % 19.13/19.26 apply (zenon_L1449_); trivial. % 19.13/19.26 apply (zenon_L50_); trivial. % 19.13/19.26 (* end of lemma zenon_L1488_ *) % 19.13/19.26 assert (zenon_L1489_ : (((op (e0) (e2)) = (e0))\/(((op (e1) (e2)) = (e0))\/(((op (e2) (e2)) = (e0))\/((op (e3) (e2)) = (e0))))) -> (~((e0) = (e3))) -> (~((op (e2) (e2)) = (e3))) -> (~((op (e2) (e2)) = (e2))) -> ((op (e0) (e2)) = (e3)) -> (~((op (e1) (e2)) = (op (e2) (e2)))) -> (((op (e2) (e2)) = (e0))\/(((op (e2) (e2)) = (e1))\/(((op (e2) (e2)) = (e2))\/((op (e2) (e2)) = (e3))))) -> ((op (e2) (e0)) = (e0)) -> (~((op (e2) (e0)) = (op (e2) (e2)))) -> ((op (e3) (e3)) = (e0)) -> (~((op (e3) (e2)) = (op (e3) (e3)))) -> False). % 19.13/19.26 do 0 intro. intros zenon_H6a zenon_H9a zenon_H1b3 zenon_H173 zenon_Ha9 zenon_H2b zenon_H1c4 zenon_H34 zenon_H52 zenon_H60 zenon_H62. % 19.13/19.26 apply (zenon_or_s _ _ zenon_H6a); [ zenon_intro zenon_H48 | zenon_intro zenon_H6b ]. % 19.13/19.26 apply (zenon_L358_); trivial. % 19.13/19.26 apply (zenon_or_s _ _ zenon_H6b); [ zenon_intro zenon_H2a | zenon_intro zenon_H6c ]. % 19.13/19.26 apply (zenon_L1486_); trivial. % 19.13/19.26 apply (zenon_or_s _ _ zenon_H6c); [ zenon_intro zenon_H2c | zenon_intro zenon_H61 ]. % 19.13/19.26 apply (zenon_L11_); trivial. % 19.13/19.26 apply (zenon_L15_); trivial. % 19.13/19.26 (* end of lemma zenon_L1489_ *) % 19.13/19.26 assert (zenon_L1490_ : (((op (e3) (e0)) = (e1))\/(((op (e3) (e1)) = (e1))\/(((op (e3) (e2)) = (e1))\/((op (e3) (e3)) = (e1))))) -> (~((e1) = (e3))) -> (~((op (e2) (e0)) = (e3))) -> (~((op (e1) (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 (e3) (e1)))) -> ((op (e2) (e1)) = (e1)) -> ((op (e2) (e2)) = (e0)) -> ((op (e0) (e2)) = (e3)) -> (~((op (e1) (e3)) = (op (e3) (e3)))) -> ((op (e1) (e3)) = (e1)) -> False). % 19.13/19.26 do 0 intro. intros zenon_He8 zenon_H95 zenon_H27f zenon_H9f zenon_H98 zenon_H1e0 zenon_Haf zenon_Ha5 zenon_H2c zenon_Ha9 zenon_Hd5 zenon_Hd6. % 19.13/19.26 apply (zenon_or_s _ _ zenon_He8); [ zenon_intro zenon_Hac | zenon_intro zenon_Heb ]. % 19.13/19.26 apply (zenon_L1425_); trivial. % 19.13/19.26 apply (zenon_or_s _ _ zenon_Heb); [ zenon_intro zenon_Hae | zenon_intro zenon_Hec ]. % 19.13/19.26 apply (zenon_L42_); trivial. % 19.13/19.26 apply (zenon_or_s _ _ zenon_Hec); [ zenon_intro zenon_Hba | zenon_intro zenon_Hc4 ]. % 19.13/19.26 apply (zenon_L45_); trivial. % 19.13/19.26 apply (zenon_L50_); trivial. % 19.13/19.26 (* end of lemma zenon_L1490_ *) % 19.13/19.26 assert (zenon_L1491_ : (((op (e2) (e0)) = (e0))\/(((op (e2) (e1)) = (e0))\/(((op (e2) (e2)) = (e0))\/((op (e2) (e3)) = (e0))))) -> (~((op (e1) (e0)) = (op (e2) (e0)))) -> ((op (e1) (e0)) = (e0)) -> ((op (e0) (e1)) = (e0)) -> (~((op (e0) (e1)) = (op (e2) (e1)))) -> ((op (e1) (e3)) = (e1)) -> (~((op (e1) (e3)) = (op (e3) (e3)))) -> ((op (e0) (e2)) = (e3)) -> ((op (e2) (e1)) = (e1)) -> (~((op (e2) (e1)) = (op (e3) (e1)))) -> (((op (e0) (e0)) = (e3))\/(((op (e1) (e0)) = (e3))\/(((op (e2) (e0)) = (e3))\/((op (e3) (e0)) = (e3))))) -> (~((op (e0) (e0)) = (e3))) -> (~((op (e1) (e0)) = (e3))) -> (~((op (e2) (e0)) = (e3))) -> (~((e1) = (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) (e3)) = (e0)) -> False). % 19.13/19.26 do 0 intro. intros zenon_H2f zenon_H201 zenon_H27 zenon_H49 zenon_H17e zenon_Hd6 zenon_Hd5 zenon_Ha9 zenon_Ha5 zenon_Haf zenon_H1e0 zenon_H98 zenon_H9f zenon_H27f zenon_H95 zenon_He8 zenon_Hf3 zenon_H60. % 19.13/19.26 apply (zenon_or_s _ _ zenon_H2f); [ zenon_intro zenon_H34 | zenon_intro zenon_H33 ]. % 19.13/19.26 apply (zenon_L332_); trivial. % 19.13/19.26 apply (zenon_or_s _ _ zenon_H33); [ zenon_intro zenon_H36 | zenon_intro zenon_H35 ]. % 19.13/19.26 apply (zenon_L128_); trivial. % 19.13/19.26 apply (zenon_or_s _ _ zenon_H35); [ zenon_intro zenon_H2c | zenon_intro zenon_H37 ]. % 19.13/19.26 apply (zenon_L1490_); trivial. % 19.13/19.26 apply (zenon_L219_); trivial. % 19.13/19.26 (* end of lemma zenon_L1491_ *) % 19.13/19.26 assert (zenon_L1492_ : (((op (e2) (e1)) = (e0))\/(((op (e2) (e1)) = (e1))\/(((op (e2) (e1)) = (e2))\/((op (e2) (e1)) = (e3))))) -> ((op (e0) (e1)) = (e0)) -> (~((op (e0) (e1)) = (op (e2) (e1)))) -> (~((op (e2) (e1)) = (op (e3) (e1)))) -> ((op (e3) (e1)) = (e1)) -> ((op (e2) (e0)) = (e2)) -> (~((op (e2) (e0)) = (op (e2) (e1)))) -> (~((op (e2) (e1)) = (e3))) -> False). % 19.13/19.26 do 0 intro. intros zenon_H1cc zenon_H49 zenon_H17e zenon_Haf zenon_Hae zenon_Hee zenon_H1f0 zenon_Ha7. % 19.13/19.26 apply (zenon_or_s _ _ zenon_H1cc); [ zenon_intro zenon_H36 | zenon_intro zenon_H1cd ]. % 19.13/19.26 apply (zenon_L128_); trivial. % 19.13/19.26 apply (zenon_or_s _ _ zenon_H1cd); [ zenon_intro zenon_Ha5 | zenon_intro zenon_H1ce ]. % 19.13/19.26 apply (zenon_L42_); trivial. % 19.13/19.26 apply (zenon_or_s _ _ zenon_H1ce); [ zenon_intro zenon_H1ca | zenon_intro zenon_Ha6 ]. % 19.13/19.26 apply (zenon_L277_); trivial. % 19.13/19.26 exact (zenon_Ha7 zenon_Ha6). % 19.13/19.26 (* end of lemma zenon_L1492_ *) % 19.13/19.26 assert (zenon_L1493_ : (((op (e0) (e0)) = (e3))\/(((op (e0) (e1)) = (e3))\/(((op (e0) (e2)) = (e3))\/((op (e0) (e3)) = (e3))))) -> (~((op (e0) (e1)) = (e3))) -> (~((op (e2) (e1)) = (e3))) -> (~((op (e2) (e0)) = (op (e2) (e1)))) -> ((op (e2) (e0)) = (e2)) -> (~((op (e2) (e1)) = (op (e3) (e1)))) -> (~((op (e0) (e1)) = (op (e2) (e1)))) -> ((op (e0) (e1)) = (e0)) -> (((op (e2) (e1)) = (e0))\/(((op (e2) (e1)) = (e1))\/(((op (e2) (e1)) = (e2))\/((op (e2) (e1)) = (e3))))) -> (((op (e2) (e0)) = (e0))\/(((op (e2) (e1)) = (e0))\/(((op (e2) (e2)) = (e0))\/((op (e2) (e3)) = (e0))))) -> (~((op (e1) (e0)) = (op (e2) (e0)))) -> ((op (e1) (e0)) = (e0)) -> ((op (e1) (e3)) = (e1)) -> (~((op (e1) (e3)) = (op (e3) (e3)))) -> (((op (e0) (e0)) = (e3))\/(((op (e1) (e0)) = (e3))\/(((op (e2) (e0)) = (e3))\/((op (e3) (e0)) = (e3))))) -> (~((op (e0) (e0)) = (e3))) -> (~((op (e1) (e0)) = (e3))) -> (~((op (e2) (e0)) = (e3))) -> (~((e1) = (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) (e3)) = (e0)) -> (~((op (e1) (e1)) = (e1))) -> (~((e0) = (e1))) -> (((op (e0) (e1)) = (e1))\/(((op (e1) (e1)) = (e1))\/(((op (e2) (e1)) = (e1))\/((op (e3) (e1)) = (e1))))) -> (~((op (e0) (e3)) = (e3))) -> False). % 19.13/19.26 do 0 intro. intros zenon_H168 zenon_H9c zenon_Ha7 zenon_H1f0 zenon_Hee zenon_Haf zenon_H17e zenon_H49 zenon_H1cc zenon_H2f zenon_H201 zenon_H27 zenon_Hd6 zenon_Hd5 zenon_H1e0 zenon_H98 zenon_H9f zenon_H27f zenon_H95 zenon_He8 zenon_Hf3 zenon_H60 zenon_H10a zenon_Ha1 zenon_H109 zenon_H12d. % 19.13/19.26 apply (zenon_or_s _ _ zenon_H168); [ zenon_intro zenon_H3a | zenon_intro zenon_H169 ]. % 19.13/19.26 exact (zenon_H98 zenon_H3a). % 19.13/19.26 apply (zenon_or_s _ _ zenon_H169); [ zenon_intro zenon_H99 | zenon_intro zenon_H16a ]. % 19.13/19.26 exact (zenon_H9c zenon_H99). % 19.13/19.26 apply (zenon_or_s _ _ zenon_H16a); [ zenon_intro zenon_Ha9 | zenon_intro zenon_He3 ]. % 19.13/19.26 apply (zenon_or_s _ _ zenon_H109); [ zenon_intro zenon_Ha0 | zenon_intro zenon_H10b ]. % 19.13/19.26 apply (zenon_L38_); trivial. % 19.13/19.26 apply (zenon_or_s _ _ zenon_H10b); [ zenon_intro zenon_H10d | zenon_intro zenon_H10c ]. % 19.13/19.26 exact (zenon_H10a zenon_H10d). % 19.13/19.26 apply (zenon_or_s _ _ zenon_H10c); [ zenon_intro zenon_Ha5 | zenon_intro zenon_Hae ]. % 19.13/19.26 apply (zenon_L1491_); trivial. % 19.13/19.26 apply (zenon_L1492_); trivial. % 19.13/19.26 exact (zenon_H12d zenon_He3). % 19.13/19.26 (* end of lemma zenon_L1493_ *) % 19.13/19.26 assert (zenon_L1494_ : (((op (e2) (e0)) = (e0))\/(((op (e2) (e0)) = (e1))\/(((op (e2) (e0)) = (e2))\/((op (e2) (e0)) = (e3))))) -> ((op (e2) (e2)) = (e0)) -> ((op (e2) (e2)) = (e1)) -> (~((op (e2) (e0)) = (op (e2) (e2)))) -> ((op (e2) (e1)) = (e2)) -> (~((op (e2) (e0)) = (op (e2) (e1)))) -> (~((op (e2) (e0)) = (e3))) -> False). % 19.13/19.26 do 0 intro. intros zenon_H259 zenon_H2c zenon_Hf1 zenon_H52 zenon_H1ca zenon_H1f0 zenon_H27f. % 19.13/19.26 apply (zenon_or_s _ _ zenon_H259); [ zenon_intro zenon_H34 | zenon_intro zenon_H25a ]. % 19.13/19.26 apply (zenon_L11_); trivial. % 19.13/19.26 apply (zenon_or_s _ _ zenon_H25a); [ zenon_intro zenon_Hed | zenon_intro zenon_H25b ]. % 19.13/19.26 apply (zenon_L93_); trivial. % 19.13/19.26 apply (zenon_or_s _ _ zenon_H25b); [ zenon_intro zenon_Hee | zenon_intro zenon_H3b ]. % 19.13/19.26 apply (zenon_L277_); trivial. % 19.13/19.26 exact (zenon_H27f zenon_H3b). % 19.13/19.26 (* end of lemma zenon_L1494_ *) % 19.13/19.26 assert (zenon_L1495_ : (((op (e0) (e0)) = (e0))\/(((op (e0) (e0)) = (e1))\/(((op (e0) (e0)) = (e2))\/((op (e0) (e0)) = (e3))))) -> (~((op (e0) (e0)) = (e0))) -> (~((op (e0) (e0)) = (op (e0) (e2)))) -> ((op (e0) (e2)) = (e1)) -> (~((op (e0) (e0)) = (op (e0) (e3)))) -> ((op (e0) (e3)) = (e2)) -> (~((op (e0) (e0)) = (e3))) -> False). % 19.13/19.26 do 0 intro. intros zenon_H26a zenon_H3f zenon_H13c zenon_H122 zenon_H189 zenon_Hcd zenon_H98. % 19.13/19.26 apply (zenon_or_s _ _ zenon_H26a); [ zenon_intro zenon_H42 | zenon_intro zenon_H26b ]. % 19.13/19.26 exact (zenon_H3f zenon_H42). % 19.13/19.26 apply (zenon_or_s _ _ zenon_H26b); [ zenon_intro zenon_H7a | zenon_intro zenon_H26c ]. % 19.13/19.26 apply (zenon_L92_); trivial. % 19.13/19.26 apply (zenon_or_s _ _ zenon_H26c); [ zenon_intro zenon_H7b | zenon_intro zenon_H3a ]. % 19.13/19.26 apply (zenon_L375_); trivial. % 19.13/19.26 exact (zenon_H98 zenon_H3a). % 19.13/19.26 (* end of lemma zenon_L1495_ *) % 19.13/19.26 assert (zenon_L1496_ : (((op (e0) (e0)) = (e3))\/(((op (e0) (e1)) = (e3))\/(((op (e0) (e2)) = (e3))\/((op (e0) (e3)) = (e3))))) -> (~((op (e0) (e0)) = (e3))) -> (~((op (e0) (e1)) = (e3))) -> (~((op (e3) (e2)) = (op (e3) (e3)))) -> ((op (e3) (e3)) = (e0)) -> (~((op (e2) (e0)) = (op (e2) (e2)))) -> ((op (e2) (e0)) = (e0)) -> (((op (e2) (e2)) = (e0))\/(((op (e2) (e2)) = (e1))\/(((op (e2) (e2)) = (e2))\/((op (e2) (e2)) = (e3))))) -> (~((op (e1) (e2)) = (op (e2) (e2)))) -> (~((op (e2) (e2)) = (e2))) -> (~((op (e2) (e2)) = (e3))) -> (~((e0) = (e3))) -> (((op (e0) (e2)) = (e0))\/(((op (e1) (e2)) = (e0))\/(((op (e2) (e2)) = (e0))\/((op (e3) (e2)) = (e0))))) -> (~((op (e0) (e3)) = (e3))) -> False). % 19.13/19.26 do 0 intro. intros zenon_H168 zenon_H98 zenon_H9c zenon_H62 zenon_H60 zenon_H52 zenon_H34 zenon_H1c4 zenon_H2b zenon_H173 zenon_H1b3 zenon_H9a zenon_H6a zenon_H12d. % 19.13/19.26 apply (zenon_or_s _ _ zenon_H168); [ zenon_intro zenon_H3a | zenon_intro zenon_H169 ]. % 19.13/19.26 exact (zenon_H98 zenon_H3a). % 19.13/19.26 apply (zenon_or_s _ _ zenon_H169); [ zenon_intro zenon_H99 | zenon_intro zenon_H16a ]. % 19.13/19.26 exact (zenon_H9c zenon_H99). % 19.13/19.26 apply (zenon_or_s _ _ zenon_H16a); [ zenon_intro zenon_Ha9 | zenon_intro zenon_He3 ]. % 19.13/19.26 apply (zenon_L1489_); trivial. % 19.13/19.26 exact (zenon_H12d zenon_He3). % 19.13/19.26 (* end of lemma zenon_L1496_ *) % 19.13/19.26 assert (zenon_L1497_ : ((~((op (e3) (e0)) = (e3)))\/((op (e3) (e3)) = (e0))) -> ((op (e2) (e3)) = (e0)) -> (~((op (e2) (e3)) = (op (e3) (e3)))) -> ((~((op (e3) (e2)) = (e3)))\/((op (e3) (e3)) = (e2))) -> ((op (e0) (e3)) = (e2)) -> (~((op (e0) (e3)) = (op (e3) (e3)))) -> (~((op (e3) (e3)) = (e3))) -> (((op (e3) (e0)) = (e3))\/(((op (e3) (e1)) = (e3))\/(((op (e3) (e2)) = (e3))\/((op (e3) (e3)) = (e3))))) -> (~((op (e1) (e3)) = (op (e3) (e3)))) -> ((op (e1) (e3)) = (e1)) -> ((~((op (e3) (e1)) = (e3)))\/((op (e3) (e3)) = (e1))) -> False). % 19.13/19.26 do 0 intro. intros zenon_H286 zenon_H37 zenon_Hf3 zenon_H284 zenon_Hcd zenon_Hc2 zenon_H102 zenon_H165 zenon_Hd5 zenon_Hd6 zenon_H285. % 19.13/19.26 apply (zenon_or_s _ _ zenon_H286); [ zenon_intro zenon_H15f | zenon_intro zenon_H60 ]. % 19.13/19.26 apply (zenon_L1488_); trivial. % 19.13/19.26 apply (zenon_L219_); trivial. % 19.13/19.26 (* end of lemma zenon_L1497_ *) % 19.13/19.26 assert (zenon_L1498_ : ((~((op (e3) (e0)) = (e3)))\/((op (e3) (e3)) = (e0))) -> (~((op (e1) (e3)) = (op (e3) (e3)))) -> ((~((op (e3) (e2)) = (e3)))\/((op (e3) (e3)) = (e2))) -> ((op (e0) (e3)) = (e2)) -> (~((op (e0) (e3)) = (op (e3) (e3)))) -> (~((op (e3) (e3)) = (e3))) -> (((op (e3) (e0)) = (e3))\/(((op (e3) (e1)) = (e3))\/(((op (e3) (e2)) = (e3))\/((op (e3) (e3)) = (e3))))) -> ((op (e1) (e3)) = (e0)) -> ((~((op (e3) (e1)) = (e3)))\/((op (e3) (e3)) = (e1))) -> False). % 19.13/19.26 do 0 intro. intros zenon_H286 zenon_Hd5 zenon_H284 zenon_Hcd zenon_Hc2 zenon_H102 zenon_H165 zenon_H1f zenon_H285. % 19.13/19.26 apply (zenon_or_s _ _ zenon_H286); [ zenon_intro zenon_H15f | zenon_intro zenon_H60 ]. % 19.13/19.26 apply (zenon_L1450_); trivial. % 19.13/19.26 apply (zenon_L136_); trivial. % 19.13/19.26 (* end of lemma zenon_L1498_ *) % 19.13/19.26 assert (zenon_L1499_ : ((~((op (e0) (e3)) = (e3)))\/((op (e0) (e3)) = (e3))) -> (~((e2) = (e3))) -> ((~((op (e1) (e1)) = (e3)))\/((op (e1) (e3)) = (e1))) -> (~((op (e3) (e0)) = (op (e3) (e3)))) -> (~((op (e3) (e2)) = (op (e3) (e3)))) -> (~((op (e2) (e0)) = (op (e2) (e2)))) -> (~((op (e0) (e1)) = (op (e2) (e1)))) -> (((op (e2) (e0)) = (e1))\/(((op (e2) (e1)) = (e1))\/(((op (e2) (e2)) = (e1))\/((op (e2) (e3)) = (e1))))) -> (((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)) = (e1))\/(((op (e1) (e1)) = (e1))\/(((op (e2) (e1)) = (e1))\/((op (e3) (e1)) = (e1))))) -> (((op (e2) (e0)) = (e0))\/(((op (e2) (e0)) = (e1))\/(((op (e2) (e0)) = (e2))\/((op (e2) (e0)) = (e3))))) -> (((op (e2) (e0)) = (e2))\/(((op (e2) (e1)) = (e2))\/(((op (e2) (e2)) = (e2))\/((op (e2) (e3)) = (e2))))) -> (~((op (e1) (e0)) = (op (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 (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 (e0) (e0)) = (op (e0) (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)) = (e0))\/(((op (e0) (e0)) = (e1))\/(((op (e0) (e0)) = (e2))\/((op (e0) (e0)) = (e3))))) -> (~((op (e0) (e0)) = (op (e0) (e3)))) -> (((op (e0) (e0)) = (e1))\/(((op (e0) (e1)) = (e1))\/(((op (e0) (e2)) = (e1))\/((op (e0) (e3)) = (e1))))) -> (((op (e0) (e0)) = (e0))\/(((op (e0) (e1)) = (e0))\/(((op (e0) (e2)) = (e0))\/((op (e0) (e3)) = (e0))))) -> (~((op (e1) (e3)) = (op (e3) (e3)))) -> ((~((op (e1) (e3)) = (e3)))\/((op (e1) (e3)) = (e3))) -> ((~((op (e2) (e1)) = (e3)))\/((op (e2) (e3)) = (e1))) -> ((~((op (e3) (e1)) = (e3)))\/((op (e3) (e3)) = (e1))) -> (~((op (e2) (e3)) = (op (e3) (e3)))) -> (((op (e3) (e0)) = (e3))\/(((op (e3) (e1)) = (e3))\/(((op (e3) (e2)) = (e3))\/((op (e3) (e3)) = (e3))))) -> (~((op (e3) (e3)) = (e3))) -> (~((op (e0) (e3)) = (op (e3) (e3)))) -> ((~((op (e3) (e2)) = (e3)))\/((op (e3) (e3)) = (e2))) -> ((~((op (e3) (e0)) = (e3)))\/((op (e3) (e3)) = (e0))) -> ((~((op (e2) (e3)) = (e3)))\/((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 (e0) (e3)) = (op (e2) (e3)))) -> ((op (e0) (e3)) = (e2)) -> ((~((op (e2) (e2)) = (e3)))\/((op (e2) (e3)) = (e2))) -> (~((op (e0) (e0)) = (e0))) -> (((op (e1) (e0)) = (e1))\/(((op (e1) (e1)) = (e1))\/(((op (e1) (e2)) = (e1))\/((op (e1) (e3)) = (e1))))) -> (~((e1) = (e3))) -> (~((op (e2) (e2)) = (op (e2) (e3)))) -> (~((op (e1) (e2)) = (op (e2) (e2)))) -> (~((op (e2) (e2)) = (e2))) -> (((op (e2) (e2)) = (e0))\/(((op (e2) (e2)) = (e1))\/(((op (e2) (e2)) = (e2))\/((op (e2) (e2)) = (e3))))) -> (~((op (e1) (e1)) = (e1))) -> (~((e0) = (e1))) -> (~((op (e2) (e0)) = (op (e2) (e3)))) -> (((op (e0) (e0)) = (e3))\/(((op (e0) (e1)) = (e3))\/(((op (e0) (e2)) = (e3))\/((op (e0) (e3)) = (e3))))) -> (~((e0) = (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) (e1)) = (e3))) -> (~((op (e0) (e0)) = (e3))) -> (((op (e0) (e0)) = (e0))\/(((op (e1) (e0)) = (e0))\/(((op (e2) (e0)) = (e0))\/((op (e3) (e0)) = (e0))))) -> ((~((op (e2) (e0)) = (e3)))\/((op (e2) (e3)) = (e0))) -> (((op (e1) (e0)) = (e3))\/(((op (e1) (e1)) = (e3))\/(((op (e1) (e2)) = (e3))\/((op (e1) (e3)) = (e3))))) -> (~((op (e0) (e3)) = (op (e1) (e3)))) -> ((~((op (e1) (e2)) = (e3)))\/((op (e1) (e3)) = (e2))) -> ((~((op (e1) (e0)) = (e3)))\/((op (e1) (e3)) = (e0))) -> False). % 19.13/19.26 do 0 intro. intros zenon_H28f zenon_H12b zenon_H28e zenon_H71 zenon_H62 zenon_H52 zenon_H17e zenon_H106 zenon_H1cc zenon_H1f0 zenon_H109 zenon_H259 zenon_H1d5 zenon_H201 zenon_He8 zenon_Haf zenon_H1e0 zenon_H2f zenon_H13c zenon_H124 zenon_H139 zenon_H26a zenon_H189 zenon_H22d zenon_H74 zenon_Hd5 zenon_H289 zenon_H28b zenon_H285 zenon_Hf3 zenon_H165 zenon_H102 zenon_Hc2 zenon_H284 zenon_H286 zenon_H281 zenon_Hdb zenon_He7 zenon_He2 zenon_Hcd zenon_H288 zenon_H3f zenon_H128 zenon_H95 zenon_H6d zenon_H2b zenon_H173 zenon_H1c4 zenon_H10a zenon_Ha1 zenon_H5b zenon_H168 zenon_H9a zenon_H6f zenon_H6a zenon_H9c zenon_H98 zenon_H3e zenon_H28a zenon_H16f zenon_H1d zenon_H287 zenon_H28d. % 19.13/19.26 apply (zenon_or_s _ _ zenon_H28f); [ zenon_intro zenon_H12d | zenon_intro zenon_He3 ]. % 19.13/19.26 apply (zenon_or_s _ _ zenon_H28d); [ zenon_intro zenon_H9f | zenon_intro zenon_H1f ]. % 19.13/19.26 apply (zenon_or_s _ _ zenon_H28e); [ zenon_intro zenon_H1a1 | zenon_intro zenon_Hd6 ]. % 19.13/19.26 apply (zenon_or_s _ _ zenon_H287); [ zenon_intro zenon_H16d | zenon_intro zenon_Hd7 ]. % 19.13/19.26 apply (zenon_or_s _ _ zenon_H289); [ zenon_intro zenon_H12f | zenon_intro zenon_Hdc ]. % 19.13/19.26 apply (zenon_L1343_); trivial. % 19.13/19.26 apply (zenon_or_s _ _ zenon_H28a); [ zenon_intro zenon_H27f | zenon_intro zenon_H37 ]. % 19.13/19.26 apply (zenon_L1485_); trivial. % 19.13/19.26 apply (zenon_or_s _ _ zenon_H288); [ zenon_intro zenon_H1b3 | zenon_intro zenon_H11d ]. % 19.13/19.26 apply (zenon_L1487_); trivial. % 19.13/19.26 apply (zenon_L234_); trivial. % 19.13/19.26 apply (zenon_L70_); trivial. % 19.13/19.26 apply (zenon_or_s _ _ zenon_H28a); [ zenon_intro zenon_H27f | zenon_intro zenon_H37 ]. % 19.13/19.26 apply (zenon_or_s _ _ zenon_H28b); [ zenon_intro zenon_Ha7 | zenon_intro zenon_Hf4 ]. % 19.13/19.26 apply (zenon_or_s _ _ zenon_H288); [ zenon_intro zenon_H1b3 | zenon_intro zenon_H11d ]. % 19.13/19.26 apply (zenon_or_s _ _ zenon_H286); [ zenon_intro zenon_H15f | zenon_intro zenon_H60 ]. % 19.13/19.26 apply (zenon_L1488_); trivial. % 19.13/19.26 apply (zenon_or_s _ _ zenon_H74); [ zenon_intro zenon_H42 | zenon_intro zenon_H77 ]. % 19.13/19.26 exact (zenon_H3f zenon_H42). % 19.13/19.26 apply (zenon_or_s _ _ zenon_H77); [ zenon_intro zenon_H49 | zenon_intro zenon_H78 ]. % 19.13/19.26 apply (zenon_or_s _ _ zenon_H3e); [ zenon_intro zenon_H42 | zenon_intro zenon_H41 ]. % 19.13/19.26 exact (zenon_H3f zenon_H42). % 19.13/19.26 apply (zenon_or_s _ _ zenon_H41); [ zenon_intro zenon_H27 | zenon_intro zenon_H43 ]. % 19.13/19.26 apply (zenon_or_s _ _ zenon_H22d); [ zenon_intro zenon_H7a | zenon_intro zenon_H22e ]. % 19.13/19.26 apply (zenon_or_s _ _ zenon_H168); [ zenon_intro zenon_H3a | zenon_intro zenon_H169 ]. % 19.13/19.26 exact (zenon_H98 zenon_H3a). % 19.13/19.26 apply (zenon_or_s _ _ zenon_H169); [ zenon_intro zenon_H99 | zenon_intro zenon_H16a ]. % 19.13/19.26 exact (zenon_H9c zenon_H99). % 19.13/19.26 apply (zenon_or_s _ _ zenon_H16a); [ zenon_intro zenon_Ha9 | zenon_intro zenon_He3 ]. % 19.13/19.26 apply (zenon_or_s _ _ zenon_H2f); [ zenon_intro zenon_H34 | zenon_intro zenon_H33 ]. % 19.13/19.26 apply (zenon_L1489_); trivial. % 19.13/19.26 apply (zenon_or_s _ _ zenon_H33); [ zenon_intro zenon_H36 | zenon_intro zenon_H35 ]. % 19.13/19.26 apply (zenon_L128_); trivial. % 19.13/19.26 apply (zenon_or_s _ _ zenon_H35); [ zenon_intro zenon_H2c | zenon_intro zenon_H37 ]. % 19.13/19.26 apply (zenon_or_s _ _ zenon_H106); [ zenon_intro zenon_Hed | zenon_intro zenon_H107 ]. % 19.13/19.26 apply (zenon_L94_); trivial. % 19.13/19.26 apply (zenon_or_s _ _ zenon_H107); [ zenon_intro zenon_Ha5 | zenon_intro zenon_H108 ]. % 19.13/19.26 apply (zenon_L1491_); trivial. % 19.13/19.26 apply (zenon_or_s _ _ zenon_H108); [ zenon_intro zenon_Hf1 | zenon_intro zenon_Hf4 ]. % 19.13/19.26 apply (zenon_or_s _ _ zenon_H1d5); [ zenon_intro zenon_Hee | zenon_intro zenon_H1d6 ]. % 19.13/19.26 apply (zenon_L1493_); trivial. % 19.13/19.26 apply (zenon_or_s _ _ zenon_H1d6); [ zenon_intro zenon_H1ca | zenon_intro zenon_H1d7 ]. % 19.13/19.26 apply (zenon_L1494_); trivial. % 19.13/19.26 apply (zenon_or_s _ _ zenon_H1d7); [ zenon_intro zenon_H176 | zenon_intro zenon_H11d ]. % 19.13/19.26 exact (zenon_H173 zenon_H176). % 19.13/19.26 apply (zenon_L234_); trivial. % 19.13/19.26 apply (zenon_L126_); trivial. % 19.13/19.26 apply (zenon_L219_); trivial. % 19.13/19.26 exact (zenon_H12d zenon_He3). % 19.13/19.26 apply (zenon_or_s _ _ zenon_H22e); [ zenon_intro zenon_Ha0 | zenon_intro zenon_H22f ]. % 19.13/19.26 apply (zenon_L38_); trivial. % 19.13/19.26 apply (zenon_or_s _ _ zenon_H22f); [ zenon_intro zenon_H122 | zenon_intro zenon_Hc3 ]. % 19.13/19.26 apply (zenon_L1495_); trivial. % 19.13/19.26 apply (zenon_L79_); trivial. % 19.13/19.26 apply (zenon_or_s _ _ zenon_H43); [ zenon_intro zenon_H34 | zenon_intro zenon_H44 ]. % 19.13/19.26 apply (zenon_L1496_); trivial. % 19.13/19.26 apply (zenon_L21_); trivial. % 19.13/19.26 apply (zenon_or_s _ _ zenon_H78); [ zenon_intro zenon_H48 | zenon_intro zenon_H1e ]. % 19.13/19.26 apply (zenon_L1349_); trivial. % 19.13/19.26 apply (zenon_L440_); trivial. % 19.13/19.26 apply (zenon_L234_); trivial. % 19.13/19.26 apply (zenon_L126_); trivial. % 19.13/19.26 apply (zenon_L1497_); trivial. % 19.13/19.26 apply (zenon_L1498_); trivial. % 19.13/19.26 apply (zenon_L81_); trivial. % 19.13/19.26 (* end of lemma zenon_L1499_ *) % 19.13/19.26 assert (zenon_L1500_ : (((op (e0) (e0)) = (e3))\/(((op (e1) (e0)) = (e3))\/(((op (e2) (e0)) = (e3))\/((op (e3) (e0)) = (e3))))) -> (~((op (e0) (e0)) = (e3))) -> (~((op (e1) (e0)) = (e3))) -> ((op (e0) (e0)) = (e2)) -> ((op (e3) (e0)) = (e1)) -> (~((op (e3) (e0)) = (e3))) -> False). % 19.13/19.26 do 0 intro. intros zenon_H1e0 zenon_H98 zenon_H9f zenon_H7b zenon_Hac zenon_H15f. % 19.13/19.26 apply (zenon_or_s _ _ zenon_H1e0); [ zenon_intro zenon_H3a | zenon_intro zenon_H1e1 ]. % 19.13/19.26 exact (zenon_H98 zenon_H3a). % 19.13/19.26 apply (zenon_or_s _ _ zenon_H1e1); [ zenon_intro zenon_H9e | zenon_intro zenon_H1e2 ]. % 19.13/19.26 exact (zenon_H9f zenon_H9e). % 19.13/19.26 apply (zenon_or_s _ _ zenon_H1e2); [ zenon_intro zenon_H3b | zenon_intro zenon_H15e ]. % 19.13/19.26 apply (zenon_L308_); trivial. % 19.13/19.26 exact (zenon_H15f zenon_H15e). % 19.13/19.26 (* end of lemma zenon_L1500_ *) % 19.13/19.26 assert (zenon_L1501_ : (((op (e1) (e0)) = (e3))\/(((op (e1) (e1)) = (e3))\/(((op (e1) (e2)) = (e3))\/((op (e1) (e3)) = (e3))))) -> (~((op (e1) (e0)) = (e3))) -> (~((op (e3) (e1)) = (e3))) -> ((op (e3) (e3)) = (e2)) -> (~((op (e3) (e1)) = (op (e3) (e3)))) -> (~((op (e3) (e0)) = (op (e3) (e1)))) -> ((op (e3) (e0)) = (e1)) -> ((op (e0) (e1)) = (e2)) -> (((op (e3) (e1)) = (e0))\/(((op (e3) (e1)) = (e1))\/(((op (e3) (e1)) = (e2))\/((op (e3) (e1)) = (e3))))) -> (~((op (e1) (e2)) = (e3))) -> (~((op (e1) (e3)) = (e3))) -> False). % 19.13/19.26 do 0 intro. intros zenon_H16f zenon_H9f zenon_H282 zenon_Hf6 zenon_H130 zenon_H1cf zenon_Hac zenon_H10f zenon_H22a zenon_H16d zenon_H12f. % 19.13/19.26 apply (zenon_or_s _ _ zenon_H16f); [ zenon_intro zenon_H9e | zenon_intro zenon_H170 ]. % 19.13/19.26 exact (zenon_H9f zenon_H9e). % 19.13/19.26 apply (zenon_or_s _ _ zenon_H170); [ zenon_intro zenon_H13f | zenon_intro zenon_H171 ]. % 19.13/19.26 apply (zenon_L1362_); trivial. % 19.13/19.26 apply (zenon_or_s _ _ zenon_H171); [ zenon_intro zenon_H16c | zenon_intro zenon_Hdc ]. % 19.13/19.26 exact (zenon_H16d zenon_H16c). % 19.13/19.26 exact (zenon_H12f zenon_Hdc). % 19.13/19.26 (* end of lemma zenon_L1501_ *) % 19.13/19.26 assert (zenon_L1502_ : (((op (e0) (e0)) = (e1))\/(((op (e1) (e0)) = (e1))\/(((op (e2) (e0)) = (e1))\/((op (e3) (e0)) = (e1))))) -> (~((op (e1) (e0)) = (op (e1) (e3)))) -> ((op (e1) (e3)) = (e1)) -> (~((op (e2) (e2)) = (e3))) -> (~((op (e2) (e2)) = (e2))) -> (~((op (e2) (e0)) = (op (e2) (e2)))) -> ((op (e2) (e3)) = (e0)) -> (~((op (e2) (e2)) = (op (e2) (e3)))) -> (((op (e2) (e2)) = (e0))\/(((op (e2) (e2)) = (e1))\/(((op (e2) (e2)) = (e2))\/((op (e2) (e2)) = (e3))))) -> (((op (e0) (e0)) = (e2))\/(((op (e0) (e1)) = (e2))\/(((op (e0) (e2)) = (e2))\/((op (e0) (e3)) = (e2))))) -> (~((op (e3) (e0)) = (e3))) -> (((op (e0) (e0)) = (e3))\/(((op (e1) (e0)) = (e3))\/(((op (e2) (e0)) = (e3))\/((op (e3) (e0)) = (e3))))) -> (~((op (e1) (e3)) = (e3))) -> (~((op (e1) (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) (e3)))) -> ((op (e3) (e3)) = (e2)) -> (~((op (e3) (e1)) = (e3))) -> (~((op (e1) (e0)) = (e3))) -> (((op (e1) (e0)) = (e3))\/(((op (e1) (e1)) = (e3))\/(((op (e1) (e2)) = (e3))\/((op (e1) (e3)) = (e3))))) -> (~((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)) = (op (e0) (e2)))) -> ((op (e0) (e2)) = (e1)) -> (~((op (e0) (e0)) = (op (e0) (e3)))) -> (~((op (e0) (e0)) = (e3))) -> False). % 19.13/19.26 do 0 intro. intros zenon_H235 zenon_Hd8 zenon_Hd6 zenon_H1b3 zenon_H173 zenon_H52 zenon_H37 zenon_H6d zenon_H1c4 zenon_H183 zenon_H15f zenon_H1e0 zenon_H12f zenon_H16d zenon_H22a zenon_H1cf zenon_H130 zenon_Hf6 zenon_H282 zenon_H9f zenon_H16f zenon_H7c zenon_H26a zenon_H3f zenon_H13c zenon_H122 zenon_H189 zenon_H98. % 19.13/19.26 apply (zenon_or_s _ _ zenon_H235); [ zenon_intro zenon_H7a | zenon_intro zenon_H236 ]. % 19.13/19.26 apply (zenon_L92_); trivial. % 19.13/19.26 apply (zenon_or_s _ _ zenon_H236); [ zenon_intro zenon_H9d | zenon_intro zenon_H237 ]. % 19.13/19.26 apply (zenon_L360_); trivial. % 19.13/19.26 apply (zenon_or_s _ _ zenon_H237); [ zenon_intro zenon_Hed | zenon_intro zenon_Hac ]. % 19.13/19.26 apply (zenon_L1481_); trivial. % 19.13/19.26 apply (zenon_or_s _ _ zenon_H183); [ zenon_intro zenon_H7b | zenon_intro zenon_H186 ]. % 19.13/19.26 apply (zenon_L1500_); trivial. % 19.13/19.26 apply (zenon_or_s _ _ zenon_H186); [ zenon_intro zenon_H10f | zenon_intro zenon_H187 ]. % 19.13/19.26 apply (zenon_L1501_); trivial. % 19.13/19.26 apply (zenon_or_s _ _ zenon_H187); [ zenon_intro zenon_H150 | zenon_intro zenon_Hcd ]. % 19.13/19.26 apply (zenon_L328_); trivial. % 19.13/19.26 apply (zenon_L1495_); trivial. % 19.13/19.26 (* end of lemma zenon_L1502_ *) % 19.13/19.26 assert (zenon_L1503_ : (((op (e1) (e0)) = (e3))\/(((op (e1) (e1)) = (e3))\/(((op (e1) (e2)) = (e3))\/((op (e1) (e3)) = (e3))))) -> (~((op (e1) (e0)) = (e3))) -> ((op (e1) (e3)) = (e1)) -> (~((op (e1) (e3)) = (op (e3) (e3)))) -> (((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) (e2)))) -> (~((op (e3) (e0)) = (op (e3) (e3)))) -> ((op (e3) (e3)) = (e2)) -> (~((op (e3) (e0)) = (e3))) -> (((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)) = (e0)) -> (~((op (e0) (e1)) = (op (e3) (e1)))) -> ((~((op (e3) (e1)) = (e3)))\/((op (e3) (e3)) = (e1))) -> (((op (e3) (e0)) = (e3))\/(((op (e3) (e1)) = (e3))\/(((op (e3) (e2)) = (e3))\/((op (e3) (e3)) = (e3))))) -> (~((op (e3) (e3)) = (e3))) -> (~((op (e2) (e3)) = (op (e3) (e3)))) -> ((~((op (e3) (e2)) = (e3)))\/((op (e3) (e3)) = (e2))) -> ((op (e2) (e3)) = (e0)) -> ((~((op (e3) (e0)) = (e3)))\/((op (e3) (e3)) = (e0))) -> (~((op (e2) (e2)) = (e2))) -> (~((op (e0) (e1)) = (op (e2) (e1)))) -> (((op (e3) (e1)) = (e0))\/(((op (e3) (e1)) = (e1))\/(((op (e3) (e1)) = (e2))\/((op (e3) (e1)) = (e3))))) -> (~((op (e2) (e1)) = (e3))) -> (~((op (e2) (e0)) = (op (e2) (e1)))) -> (~((op (e2) (e1)) = (op (e3) (e1)))) -> (~((op (e2) (e1)) = (op (e2) (e3)))) -> (((op (e2) (e1)) = (e0))\/(((op (e2) (e1)) = (e1))\/(((op (e2) (e1)) = (e2))\/((op (e2) (e1)) = (e3))))) -> (~((op (e3) (e1)) = (op (e3) (e3)))) -> (~((op (e3) (e1)) = (e3))) -> (((op (e2) (e0)) = (e2))\/(((op (e2) (e1)) = (e2))\/(((op (e2) (e2)) = (e2))\/((op (e2) (e3)) = (e2))))) -> (~((op (e0) (e1)) = (e3))) -> ((op (e2) (e0)) = (e3)) -> ((op (e0) (e0)) = (e2)) -> (((op (e3) (e0)) = (e1))\/(((op (e3) (e1)) = (e1))\/(((op (e3) (e2)) = (e1))\/((op (e3) (e3)) = (e1))))) -> (~((op (e1) (e2)) = (e3))) -> (~((op (e1) (e3)) = (e3))) -> False). % 19.13/19.26 do 0 intro. intros zenon_H16f zenon_H9f zenon_Hd6 zenon_Hd5 zenon_H267 zenon_H1b1 zenon_H1cf zenon_H6f zenon_H71 zenon_Hf6 zenon_H15f zenon_H212 zenon_H4a zenon_H48 zenon_H210 zenon_H285 zenon_H165 zenon_H102 zenon_Hf3 zenon_H284 zenon_H37 zenon_H286 zenon_H173 zenon_H17e zenon_H22a zenon_Ha7 zenon_H1f0 zenon_Haf zenon_H1c7 zenon_H1cc zenon_H130 zenon_H282 zenon_H1d5 zenon_H9c zenon_H3b zenon_H7b zenon_He8 zenon_H16d zenon_H12f. % 19.13/19.26 apply (zenon_or_s _ _ zenon_H16f); [ zenon_intro zenon_H9e | zenon_intro zenon_H170 ]. % 19.13/19.26 exact (zenon_H9f zenon_H9e). % 19.13/19.26 apply (zenon_or_s _ _ zenon_H170); [ zenon_intro zenon_H13f | zenon_intro zenon_H171 ]. % 19.13/19.26 apply (zenon_or_s _ _ zenon_He8); [ zenon_intro zenon_Hac | zenon_intro zenon_Heb ]. % 19.13/19.26 apply (zenon_L308_); trivial. % 19.13/19.26 apply (zenon_or_s _ _ zenon_Heb); [ zenon_intro zenon_Hae | zenon_intro zenon_Hec ]. % 19.13/19.26 apply (zenon_L1475_); trivial. % 19.13/19.26 apply (zenon_or_s _ _ zenon_Hec); [ zenon_intro zenon_Hba | zenon_intro zenon_Hc4 ]. % 19.13/19.26 apply (zenon_L1478_); trivial. % 19.13/19.26 apply (zenon_L50_); trivial. % 19.13/19.26 apply (zenon_or_s _ _ zenon_H171); [ zenon_intro zenon_H16c | zenon_intro zenon_Hdc ]. % 19.13/19.26 exact (zenon_H16d zenon_H16c). % 19.13/19.26 exact (zenon_H12f zenon_Hdc). % 19.13/19.26 (* end of lemma zenon_L1503_ *) % 19.13/19.26 assert (zenon_L1504_ : (((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)) = (e0)) -> ((op (e2) (e1)) = (e1)) -> (~((op (e1) (e3)) = (e3))) -> (~((op (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) (e3)) = (e2)) -> (~((op (e3) (e1)) = (op (e3) (e3)))) -> (((op (e2) (e1)) = (e0))\/(((op (e2) (e1)) = (e1))\/(((op (e2) (e1)) = (e2))\/((op (e2) (e1)) = (e3))))) -> (~((op (e2) (e1)) = (op (e2) (e3)))) -> (~((op (e2) (e1)) = (op (e3) (e1)))) -> (~((op (e2) (e0)) = (op (e2) (e1)))) -> (~((op (e2) (e1)) = (e3))) -> (((op (e3) (e1)) = (e0))\/(((op (e3) (e1)) = (e1))\/(((op (e3) (e1)) = (e2))\/((op (e3) (e1)) = (e3))))) -> (~((op (e0) (e1)) = (op (e2) (e1)))) -> (~((op (e2) (e2)) = (e2))) -> ((~((op (e3) (e0)) = (e3)))\/((op (e3) (e3)) = (e0))) -> ((op (e2) (e3)) = (e0)) -> ((~((op (e3) (e2)) = (e3)))\/((op (e3) (e3)) = (e2))) -> (~((op (e2) (e3)) = (op (e3) (e3)))) -> (~((op (e3) (e3)) = (e3))) -> (((op (e3) (e0)) = (e3))\/(((op (e3) (e1)) = (e3))\/(((op (e3) (e2)) = (e3))\/((op (e3) (e3)) = (e3))))) -> (~((op (e1) (e3)) = (op (e3) (e3)))) -> ((op (e1) (e3)) = (e1)) -> ((~((op (e3) (e1)) = (e3)))\/((op (e3) (e3)) = (e1))) -> (~((op (e1) (e0)) = (e3))) -> (((op (e1) (e0)) = (e3))\/(((op (e1) (e1)) = (e3))\/(((op (e1) (e2)) = (e3))\/((op (e1) (e3)) = (e3))))) -> (~((op (e0) (e1)) = (e3))) -> False). % 19.13/19.26 do 0 intro. intros zenon_H212 zenon_H4a zenon_H48 zenon_Ha5 zenon_H12f zenon_H16d zenon_H1d5 zenon_H282 zenon_Hf6 zenon_H130 zenon_H1cc zenon_H1c7 zenon_Haf zenon_H1f0 zenon_Ha7 zenon_H22a zenon_H17e zenon_H173 zenon_H286 zenon_H37 zenon_H284 zenon_Hf3 zenon_H102 zenon_H165 zenon_Hd5 zenon_Hd6 zenon_H285 zenon_H9f zenon_H16f zenon_H9c. % 19.13/19.26 apply (zenon_or_s _ _ zenon_H212); [ zenon_intro zenon_H49 | zenon_intro zenon_H213 ]. % 19.13/19.26 apply (zenon_L9_); trivial. % 19.13/19.26 apply (zenon_or_s _ _ zenon_H213); [ zenon_intro zenon_Ha0 | zenon_intro zenon_H214 ]. % 19.13/19.26 apply (zenon_L357_); trivial. % 19.13/19.26 apply (zenon_or_s _ _ zenon_H214); [ zenon_intro zenon_H10f | zenon_intro zenon_H99 ]. % 19.13/19.26 apply (zenon_L1482_); trivial. % 19.13/19.26 exact (zenon_H9c zenon_H99). % 19.13/19.26 (* end of lemma zenon_L1504_ *) % 19.13/19.26 assert (zenon_L1505_ : (((op (e0) (e0)) = (e0))\/(((op (e1) (e0)) = (e0))\/(((op (e2) (e0)) = (e0))\/((op (e3) (e0)) = (e0))))) -> (~((op (e0) (e0)) = (e0))) -> (~((op (e3) (e0)) = (e3))) -> (~((op (e0) (e3)) = (op (e3) (e3)))) -> (~((e0) = (e2))) -> (((op (e0) (e0)) = (e3))\/(((op (e1) (e0)) = (e3))\/(((op (e2) (e0)) = (e3))\/((op (e3) (e0)) = (e3))))) -> (~((op (e0) (e0)) = (e3))) -> (((op (e3) (e0)) = (e1))\/(((op (e3) (e1)) = (e1))\/(((op (e3) (e2)) = (e1))\/((op (e3) (e3)) = (e1))))) -> (~((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 (e1) (e0)) = (op (e1) (e1)))) -> (((op (e0) (e1)) = (e0))\/(((op (e1) (e1)) = (e0))\/(((op (e2) (e1)) = (e0))\/((op (e3) (e1)) = (e0))))) -> (((op (e0) (e0)) = (e2))\/(((op (e0) (e1)) = (e2))\/(((op (e0) (e2)) = (e2))\/((op (e0) (e3)) = (e2))))) -> (~((op (e2) (e0)) = (op (e2) (e3)))) -> (((op (e0) (e1)) = (e1))\/(((op (e1) (e1)) = (e1))\/(((op (e2) (e1)) = (e1))\/((op (e3) (e1)) = (e1))))) -> (~((op (e3) (e0)) = (op (e3) (e1)))) -> (~((op (e1) (e1)) = (e1))) -> (((op (e1) (e0)) = (e3))\/(((op (e1) (e1)) = (e3))\/(((op (e1) (e2)) = (e3))\/((op (e1) (e3)) = (e3))))) -> (~((op (e1) (e0)) = (e3))) -> (~((op (e0) (e1)) = (e3))) -> (((op (e2) (e0)) = (e2))\/(((op (e2) (e1)) = (e2))\/(((op (e2) (e2)) = (e2))\/((op (e2) (e3)) = (e2))))) -> (~((op (e3) (e1)) = (e3))) -> ((op (e3) (e3)) = (e2)) -> (~((op (e3) (e1)) = (op (e3) (e3)))) -> (((op (e2) (e1)) = (e0))\/(((op (e2) (e1)) = (e1))\/(((op (e2) (e1)) = (e2))\/((op (e2) (e1)) = (e3))))) -> (~((op (e2) (e1)) = (op (e2) (e3)))) -> (~((op (e2) (e1)) = (op (e3) (e1)))) -> (~((op (e2) (e0)) = (op (e2) (e1)))) -> (~((op (e2) (e1)) = (e3))) -> (((op (e3) (e1)) = (e0))\/(((op (e3) (e1)) = (e1))\/(((op (e3) (e1)) = (e2))\/((op (e3) (e1)) = (e3))))) -> (~((op (e0) (e1)) = (op (e2) (e1)))) -> (~((op (e2) (e2)) = (e2))) -> ((~((op (e3) (e0)) = (e3)))\/((op (e3) (e3)) = (e0))) -> ((op (e2) (e3)) = (e0)) -> ((~((op (e3) (e2)) = (e3)))\/((op (e3) (e3)) = (e2))) -> (~((op (e2) (e3)) = (op (e3) (e3)))) -> (~((op (e3) (e3)) = (e3))) -> (((op (e3) (e0)) = (e3))\/(((op (e3) (e1)) = (e3))\/(((op (e3) (e2)) = (e3))\/((op (e3) (e3)) = (e3))))) -> (~((op (e1) (e3)) = (op (e3) (e3)))) -> ((op (e1) (e3)) = (e1)) -> ((~((op (e3) (e1)) = (e3)))\/((op (e3) (e3)) = (e1))) -> (~((op (e0) (e1)) = (op (e3) (e1)))) -> ((op (e0) (e2)) = (e0)) -> (~((op (e0) (e1)) = (op (e0) (e2)))) -> (((op (e0) (e1)) = (e0))\/(((op (e0) (e1)) = (e1))\/(((op (e0) (e1)) = (e2))\/((op (e0) (e1)) = (e3))))) -> (~((op (e1) (e2)) = (e3))) -> (~((op (e1) (e3)) = (e3))) -> False). % 19.13/19.26 do 0 intro. intros zenon_H3e zenon_H3f zenon_H15f zenon_Hc2 zenon_H149 zenon_H1e0 zenon_H98 zenon_He8 zenon_H71 zenon_H6f zenon_H267 zenon_H45 zenon_H245 zenon_H183 zenon_H5b zenon_H109 zenon_H1cf zenon_H10a zenon_H16f zenon_H9f zenon_H9c zenon_H1d5 zenon_H282 zenon_Hf6 zenon_H130 zenon_H1cc zenon_H1c7 zenon_Haf zenon_H1f0 zenon_Ha7 zenon_H22a zenon_H17e zenon_H173 zenon_H286 zenon_H37 zenon_H284 zenon_Hf3 zenon_H102 zenon_H165 zenon_Hd5 zenon_Hd6 zenon_H285 zenon_H210 zenon_H48 zenon_H4a zenon_H212 zenon_H16d zenon_H12f. % 19.13/19.26 apply (zenon_or_s _ _ zenon_H3e); [ zenon_intro zenon_H42 | zenon_intro zenon_H41 ]. % 19.13/19.26 exact (zenon_H3f zenon_H42). % 19.13/19.26 apply (zenon_or_s _ _ zenon_H41); [ zenon_intro zenon_H27 | zenon_intro zenon_H43 ]. % 19.13/19.26 apply (zenon_or_s _ _ zenon_H183); [ zenon_intro zenon_H7b | zenon_intro zenon_H186 ]. % 19.13/19.26 apply (zenon_or_s _ _ zenon_H1e0); [ zenon_intro zenon_H3a | zenon_intro zenon_H1e1 ]. % 19.13/19.26 exact (zenon_H98 zenon_H3a). % 19.13/19.26 apply (zenon_or_s _ _ zenon_H1e1); [ zenon_intro zenon_H9e | zenon_intro zenon_H1e2 ]. % 19.13/19.26 exact (zenon_H9f zenon_H9e). % 19.13/19.26 apply (zenon_or_s _ _ zenon_H1e2); [ zenon_intro zenon_H3b | zenon_intro zenon_H15e ]. % 19.13/19.26 apply (zenon_or_s _ _ zenon_H245); [ zenon_intro zenon_H49 | zenon_intro zenon_H246 ]. % 19.13/19.26 apply (zenon_L9_); trivial. % 19.13/19.26 apply (zenon_or_s _ _ zenon_H246); [ zenon_intro zenon_H29 | zenon_intro zenon_H247 ]. % 19.13/19.26 apply (zenon_L8_); trivial. % 19.13/19.26 apply (zenon_or_s _ _ zenon_H247); [ zenon_intro zenon_H36 | zenon_intro zenon_H1b1 ]. % 19.13/19.26 apply (zenon_L640_); trivial. % 19.13/19.26 apply (zenon_L1503_); trivial. % 19.13/19.26 exact (zenon_H15f zenon_H15e). % 19.13/19.26 apply (zenon_or_s _ _ zenon_H186); [ zenon_intro zenon_H10f | zenon_intro zenon_H187 ]. % 19.13/19.26 apply (zenon_L1482_); trivial. % 19.13/19.26 apply (zenon_or_s _ _ zenon_H187); [ zenon_intro zenon_H150 | zenon_intro zenon_Hcd ]. % 19.13/19.26 apply (zenon_L378_); trivial. % 19.13/19.26 apply (zenon_L1449_); trivial. % 19.13/19.26 apply (zenon_or_s _ _ zenon_H43); [ zenon_intro zenon_H34 | zenon_intro zenon_H44 ]. % 19.13/19.26 apply (zenon_L14_); trivial. % 19.13/19.26 apply (zenon_or_s _ _ zenon_H109); [ zenon_intro zenon_Ha0 | zenon_intro zenon_H10b ]. % 19.13/19.26 apply (zenon_L1365_); trivial. % 19.13/19.26 apply (zenon_or_s _ _ zenon_H10b); [ zenon_intro zenon_H10d | zenon_intro zenon_H10c ]. % 19.13/19.26 exact (zenon_H10a zenon_H10d). % 19.13/19.26 apply (zenon_or_s _ _ zenon_H10c); [ zenon_intro zenon_Ha5 | zenon_intro zenon_Hae ]. % 19.13/19.27 apply (zenon_L1504_); trivial. % 19.13/19.27 apply (zenon_L1476_); trivial. % 19.13/19.27 (* end of lemma zenon_L1505_ *) % 19.13/19.27 assert (zenon_L1506_ : (((op (e1) (e0)) = (e0))\/(((op (e1) (e0)) = (e1))\/(((op (e1) (e0)) = (e2))\/((op (e1) (e0)) = (e3))))) -> ((op (e1) (e2)) = (e0)) -> (~((op (e1) (e0)) = (op (e1) (e2)))) -> (~((op (e1) (e0)) = (op (e1) (e3)))) -> ((op (e1) (e3)) = (e1)) -> ((op (e0) (e0)) = (e1)) -> ((op (e2) (e0)) = (e3)) -> (~((op (e1) (e0)) = (e3))) -> False). % 19.13/19.27 do 0 intro. intros zenon_H25e zenon_H2a zenon_H24a zenon_Hd8 zenon_Hd6 zenon_H7a zenon_H3b zenon_H9f. % 19.13/19.27 apply (zenon_or_s _ _ zenon_H25e); [ zenon_intro zenon_H27 | zenon_intro zenon_H25f ]. % 19.13/19.27 apply (zenon_L644_); trivial. % 19.13/19.27 apply (zenon_or_s _ _ zenon_H25f); [ zenon_intro zenon_H9d | zenon_intro zenon_H260 ]. % 19.13/19.27 apply (zenon_L360_); trivial. % 19.13/19.27 apply (zenon_or_s _ _ zenon_H260); [ zenon_intro zenon_H86 | zenon_intro zenon_H9e ]. % 19.13/19.27 apply (zenon_L33_); trivial. % 19.13/19.27 exact (zenon_H9f zenon_H9e). % 19.13/19.27 (* end of lemma zenon_L1506_ *) % 19.13/19.27 assert (zenon_L1507_ : (((op (e2) (e2)) = (e0))\/(((op (e2) (e2)) = (e1))\/(((op (e2) (e2)) = (e2))\/((op (e2) (e2)) = (e3))))) -> ((op (e1) (e2)) = (e0)) -> (~((op (e1) (e2)) = (op (e2) (e2)))) -> ((op (e2) (e0)) = (e1)) -> (~((op (e2) (e0)) = (op (e2) (e2)))) -> (~((op (e2) (e2)) = (e2))) -> (~((op (e2) (e2)) = (e3))) -> False). % 19.13/19.27 do 0 intro. intros zenon_H1c4 zenon_H2a zenon_H2b zenon_Hed zenon_H52 zenon_H173 zenon_H1b3. % 19.13/19.27 apply (zenon_or_s _ _ zenon_H1c4); [ zenon_intro zenon_H2c | zenon_intro zenon_H1c5 ]. % 19.13/19.27 apply (zenon_L3_); trivial. % 19.13/19.27 apply (zenon_or_s _ _ zenon_H1c5); [ zenon_intro zenon_Hf1 | zenon_intro zenon_H1c6 ]. % 19.13/19.27 apply (zenon_L93_); trivial. % 19.13/19.27 apply (zenon_or_s _ _ zenon_H1c6); [ zenon_intro zenon_H176 | zenon_intro zenon_Haa ]. % 19.13/19.27 exact (zenon_H173 zenon_H176). % 19.13/19.27 exact (zenon_H1b3 zenon_Haa). % 19.13/19.27 (* end of lemma zenon_L1507_ *) % 19.13/19.27 assert (zenon_L1508_ : ((~((op (e3) (e2)) = (e3)))\/((op (e3) (e3)) = (e2))) -> ((op (e0) (e3)) = (e1)) -> ((op (e2) (e3)) = (e0)) -> (~((op (e3) (e0)) = (e3))) -> (~((op (e3) (e1)) = (e3))) -> (~((op (e3) (e3)) = (e3))) -> (((op (e3) (e0)) = (e3))\/(((op (e3) (e1)) = (e3))\/(((op (e3) (e2)) = (e3))\/((op (e3) (e3)) = (e3))))) -> False). % 19.13/19.27 do 0 intro. intros zenon_H284 zenon_Hc3 zenon_H37 zenon_H15f zenon_H282 zenon_H102 zenon_H165. % 19.13/19.27 apply (zenon_or_s _ _ zenon_H284); [ zenon_intro zenon_H283 | zenon_intro zenon_Hf6 ]. % 19.13/19.27 apply (zenon_L1346_); trivial. % 19.13/19.27 apply (zenon_L387_); trivial. % 19.13/19.27 (* end of lemma zenon_L1508_ *) % 19.13/19.27 assert (zenon_L1509_ : (~((op (e0) (e0)) = (e0))) -> (~((op (e1) (e0)) = (op (e1) (e1)))) -> (((op (e0) (e1)) = (e0))\/(((op (e1) (e1)) = (e0))\/(((op (e2) (e1)) = (e0))\/((op (e3) (e1)) = (e0))))) -> (~((e0) = (e2))) -> (((op (e1) (e0)) = (e0))\/(((op (e1) (e0)) = (e1))\/(((op (e1) (e0)) = (e2))\/((op (e1) (e0)) = (e3))))) -> (((op (e0) (e0)) = (e2))\/(((op (e0) (e1)) = (e2))\/(((op (e0) (e2)) = (e2))\/((op (e0) (e3)) = (e2))))) -> ((~((op (e1) (e0)) = (e3)))\/((op (e1) (e3)) = (e0))) -> ((~((op (e1) (e2)) = (e3)))\/((op (e1) (e3)) = (e2))) -> (~((op (e0) (e3)) = (op (e1) (e3)))) -> ((~((op (e2) (e0)) = (e3)))\/((op (e2) (e3)) = (e0))) -> (((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))))) -> (~((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) = (e3))) -> (((op (e1) (e0)) = (e1))\/(((op (e1) (e1)) = (e1))\/(((op (e1) (e2)) = (e1))\/((op (e1) (e3)) = (e1))))) -> ((~((op (e2) (e2)) = (e3)))\/((op (e2) (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 (e2) (e3)) = (e3)))\/((op (e2) (e3)) = (e3))) -> (~((op (e0) (e3)) = (op (e3) (e3)))) -> ((~((op (e2) (e1)) = (e3)))\/((op (e2) (e3)) = (e1))) -> ((~((op (e1) (e3)) = (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)) = (op (e0) (e3)))) -> (((op (e0) (e0)) = (e0))\/(((op (e0) (e0)) = (e1))\/(((op (e0) (e0)) = (e2))\/((op (e0) (e0)) = (e3))))) -> (((op (e2) (e0)) = (e0))\/(((op (e2) (e1)) = (e0))\/(((op (e2) (e2)) = (e0))\/((op (e2) (e3)) = (e0))))) -> (~((op (e1) (e0)) = (op (e2) (e0)))) -> (((op (e2) (e0)) = (e0))\/(((op (e2) (e0)) = (e1))\/(((op (e2) (e0)) = (e2))\/((op (e2) (e0)) = (e3))))) -> ((~((op (e1) (e1)) = (e3)))\/((op (e1) (e3)) = (e1))) -> (~((e2) = (e3))) -> ((~((op (e0) (e3)) = (e3)))\/((op (e0) (e3)) = (e3))) -> (~((op (e0) (e0)) = (e3))) -> (~((op (e1) (e0)) = (e3))) -> (((op (e0) (e1)) = (e1))\/(((op (e1) (e1)) = (e1))\/(((op (e2) (e1)) = (e1))\/((op (e3) (e1)) = (e1))))) -> (~((op (e2) (e0)) = (op (e2) (e2)))) -> (~((op (e1) (e3)) = (op (e2) (e3)))) -> (((op (e2) (e0)) = (e1))\/(((op (e2) (e1)) = (e1))\/(((op (e2) (e2)) = (e1))\/((op (e2) (e3)) = (e1))))) -> (~((op (e0) (e0)) = (op (e0) (e2)))) -> (((op (e2) (e2)) = (e0))\/(((op (e2) (e2)) = (e1))\/(((op (e2) (e2)) = (e2))\/((op (e2) (e2)) = (e3))))) -> (~((op (e2) (e2)) = (e2))) -> (~((op (e1) (e2)) = (op (e2) (e2)))) -> ((op (e2) (e3)) = (e0)) -> (~((op (e2) (e2)) = (op (e2) (e3)))) -> (((op (e0) (e2)) = (e2))\/(((op (e1) (e2)) = (e2))\/(((op (e2) (e2)) = (e2))\/((op (e3) (e2)) = (e2))))) -> (~((op (e3) (e2)) = (op (e3) (e3)))) -> (((op (e0) (e2)) = (e0))\/(((op (e0) (e2)) = (e1))\/(((op (e0) (e2)) = (e2))\/((op (e0) (e2)) = (e3))))) -> (~((op (e0) (e2)) = (e3))) -> (~((op (e0) (e2)) = (op (e2) (e2)))) -> (((op (e0) (e1)) = (e0))\/(((op (e0) (e1)) = (e1))\/(((op (e0) (e1)) = (e2))\/((op (e0) (e1)) = (e3))))) -> (~((op (e0) (e1)) = (e3))) -> (((op (e3) (e1)) = (e0))\/(((op (e3) (e1)) = (e1))\/(((op (e3) (e1)) = (e2))\/((op (e3) (e1)) = (e3))))) -> (~((op (e3) (e1)) = (op (e3) (e3)))) -> (~((op (e2) (e1)) = (op (e2) (e3)))) -> (~((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)) = (op (e2) (e1)))) -> ((~((op (e3) (e0)) = (e3)))\/((op (e3) (e3)) = (e0))) -> ((~((op (e3) (e2)) = (e3)))\/((op (e3) (e3)) = (e2))) -> (~((op (e2) (e3)) = (op (e3) (e3)))) -> (~((op (e1) (e3)) = (op (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) (e1)) = (op (e3) (e1)))) -> (~((op (e0) (e1)) = (op (e0) (e2)))) -> (~((op (e1) (e3)) = (e3))) -> (((op (e1) (e0)) = (e3))\/(((op (e1) (e1)) = (e3))\/(((op (e1) (e2)) = (e3))\/((op (e1) (e3)) = (e3))))) -> (~((op (e3) (e0)) = (op (e3) (e1)))) -> (~((op (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))))) -> (((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) (e3)) = (e1)) -> (~((op (e0) (e2)) = (op (e1) (e2)))) -> (~((op (e1) (e2)) = (e3))) -> (((op (e1) (e2)) = (e0))\/(((op (e1) (e2)) = (e1))\/(((op (e1) (e2)) = (e2))\/((op (e1) (e2)) = (e3))))) -> (((op (e0) (e2)) = (e1))\/(((op (e1) (e2)) = (e1))\/(((op (e2) (e2)) = (e1))\/((op (e3) (e2)) = (e1))))) -> (~((op (e1) (e1)) = (e1))) -> (~((e0) = (e1))) -> (((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))))) -> (~((e1) = (e2))) -> (~((op (e1) (e0)) = (op (e1) (e3)))) -> ((op (e0) (e3)) = (e3)) -> (~((op (e3) (e3)) = (e3))) -> (((op (e3) (e0)) = (e3))\/(((op (e3) (e1)) = (e3))\/(((op (e3) (e2)) = (e3))\/((op (e3) (e3)) = (e3))))) -> False). % 19.13/19.27 do 0 intro. intros zenon_H3f zenon_H45 zenon_H245 zenon_H149 zenon_H25e zenon_H183 zenon_H28d zenon_H287 zenon_H1d zenon_H28a zenon_H3e zenon_H6a zenon_H9a zenon_H168 zenon_H5b zenon_H95 zenon_H128 zenon_H288 zenon_He2 zenon_He7 zenon_H281 zenon_Hc2 zenon_H28b zenon_H289 zenon_H74 zenon_H22d zenon_H189 zenon_H26a zenon_H2f zenon_H201 zenon_H259 zenon_H28e zenon_H12b zenon_H28f zenon_H98 zenon_H9f zenon_H109 zenon_H52 zenon_Hdb zenon_H106 zenon_H13c zenon_H1c4 zenon_H173 zenon_H2b zenon_H37 zenon_H6d zenon_H172 zenon_H62 zenon_H1ba zenon_H123 zenon_Ha8 zenon_H212 zenon_H9c zenon_H22a zenon_H130 zenon_H1c7 zenon_Haf zenon_H1f0 zenon_H1cc zenon_H17e zenon_H286 zenon_H284 zenon_Hf3 zenon_Hd5 zenon_H285 zenon_H1d5 zenon_H210 zenon_H4a zenon_H12f zenon_H16f zenon_H1cf zenon_H6f zenon_H71 zenon_H267 zenon_He8 zenon_H24a zenon_H124 zenon_Hd6 zenon_H195 zenon_H16d zenon_H19d zenon_H139 zenon_H10a zenon_Ha1 zenon_H1e0 zenon_H235 zenon_H7c zenon_Hd8 zenon_He3 zenon_H102 zenon_H165. % 19.13/19.27 apply (zenon_or_s _ _ zenon_H28b); [ zenon_intro zenon_Ha7 | zenon_intro zenon_Hf4 ]. % 19.13/19.27 apply (zenon_or_s _ _ zenon_H288); [ zenon_intro zenon_H1b3 | zenon_intro zenon_H11d ]. % 19.13/19.27 apply (zenon_or_s _ _ zenon_H286); [ zenon_intro zenon_H15f | zenon_intro zenon_H60 ]. % 19.13/19.27 apply (zenon_or_s _ _ zenon_H285); [ zenon_intro zenon_H282 | zenon_intro zenon_Hc4 ]. % 19.13/19.27 apply (zenon_or_s _ _ zenon_H284); [ zenon_intro zenon_H283 | zenon_intro zenon_Hf6 ]. % 19.13/19.27 apply (zenon_L1346_); trivial. % 19.13/19.27 apply (zenon_or_s _ _ zenon_H74); [ zenon_intro zenon_H42 | zenon_intro zenon_H77 ]. % 19.13/19.27 exact (zenon_H3f zenon_H42). % 19.13/19.27 apply (zenon_or_s _ _ zenon_H77); [ zenon_intro zenon_H49 | zenon_intro zenon_H78 ]. % 19.13/19.27 apply (zenon_or_s _ _ zenon_H3e); [ zenon_intro zenon_H42 | zenon_intro zenon_H41 ]. % 19.13/19.27 exact (zenon_H3f zenon_H42). % 19.13/19.27 apply (zenon_or_s _ _ zenon_H41); [ zenon_intro zenon_H27 | zenon_intro zenon_H43 ]. % 19.13/19.27 apply (zenon_or_s _ _ zenon_H22d); [ zenon_intro zenon_H7a | zenon_intro zenon_H22e ]. % 19.13/19.27 apply (zenon_or_s _ _ zenon_H183); [ zenon_intro zenon_H7b | zenon_intro zenon_H186 ]. % 19.13/19.27 apply (zenon_or_s _ _ zenon_H1e0); [ zenon_intro zenon_H3a | zenon_intro zenon_H1e1 ]. % 19.13/19.27 exact (zenon_H98 zenon_H3a). % 19.13/19.27 apply (zenon_or_s _ _ zenon_H1e1); [ zenon_intro zenon_H9e | zenon_intro zenon_H1e2 ]. % 19.13/19.27 exact (zenon_H9f zenon_H9e). % 19.13/19.27 apply (zenon_or_s _ _ zenon_H1e2); [ zenon_intro zenon_H3b | zenon_intro zenon_H15e ]. % 19.13/19.27 apply (zenon_or_s _ _ zenon_H109); [ zenon_intro zenon_Ha0 | zenon_intro zenon_H10b ]. % 19.13/19.27 apply (zenon_L38_); trivial. % 19.13/19.27 apply (zenon_or_s _ _ zenon_H10b); [ zenon_intro zenon_H10d | zenon_intro zenon_H10c ]. % 19.13/19.27 exact (zenon_H10a zenon_H10d). % 19.13/19.27 apply (zenon_or_s _ _ zenon_H10c); [ zenon_intro zenon_Ha5 | zenon_intro zenon_Hae ]. % 19.13/19.27 apply (zenon_or_s _ _ zenon_H139); [ zenon_intro zenon_H122 | zenon_intro zenon_H13a ]. % 19.13/19.27 apply (zenon_L92_); trivial. % 19.13/19.27 apply (zenon_or_s _ _ zenon_H13a); [ zenon_intro zenon_Hf0 | zenon_intro zenon_H13b ]. % 19.13/19.27 apply (zenon_L1470_); trivial. % 19.13/19.27 apply (zenon_or_s _ _ zenon_H13b); [ zenon_intro zenon_Hf1 | zenon_intro zenon_Hba ]. % 19.13/19.27 apply (zenon_or_s _ _ zenon_H172); [ zenon_intro zenon_H150 | zenon_intro zenon_H174 ]. % 19.13/19.27 apply (zenon_L1364_); trivial. % 19.13/19.27 apply (zenon_or_s _ _ zenon_H174); [ zenon_intro zenon_H113 | zenon_intro zenon_H175 ]. % 19.13/19.27 apply (zenon_L1480_); trivial. % 19.13/19.27 apply (zenon_or_s _ _ zenon_H175); [ zenon_intro zenon_H176 | zenon_intro zenon_H151 ]. % 19.13/19.27 exact (zenon_H173 zenon_H176). % 19.13/19.27 apply (zenon_L119_); trivial. % 19.13/19.27 apply (zenon_L1479_); trivial. % 19.13/19.27 apply (zenon_or_s _ _ zenon_H106); [ zenon_intro zenon_Hed | zenon_intro zenon_H107 ]. % 19.13/19.27 apply (zenon_L1481_); trivial. % 19.13/19.27 apply (zenon_or_s _ _ zenon_H107); [ zenon_intro zenon_Ha5 | zenon_intro zenon_H108 ]. % 19.13/19.27 apply (zenon_L42_); trivial. % 19.13/19.27 apply (zenon_or_s _ _ zenon_H108); [ zenon_intro zenon_Hf1 | zenon_intro zenon_Hf4 ]. % 19.13/19.27 apply (zenon_or_s _ _ zenon_H172); [ zenon_intro zenon_H150 | zenon_intro zenon_H174 ]. % 19.13/19.27 apply (zenon_L1364_); trivial. % 19.13/19.27 apply (zenon_or_s _ _ zenon_H174); [ zenon_intro zenon_H113 | zenon_intro zenon_H175 ]. % 19.13/19.27 apply (zenon_L1477_); trivial. % 19.13/19.27 apply (zenon_or_s _ _ zenon_H175); [ zenon_intro zenon_H176 | zenon_intro zenon_H151 ]. % 19.13/19.27 exact (zenon_H173 zenon_H176). % 19.13/19.27 apply (zenon_L119_); trivial. % 19.13/19.27 apply (zenon_L126_); trivial. % 19.13/19.27 exact (zenon_H15f zenon_H15e). % 19.13/19.27 apply (zenon_or_s _ _ zenon_H186); [ zenon_intro zenon_H10f | zenon_intro zenon_H187 ]. % 19.13/19.27 apply (zenon_L1482_); trivial. % 19.13/19.27 apply (zenon_or_s _ _ zenon_H187); [ zenon_intro zenon_H150 | zenon_intro zenon_Hcd ]. % 19.13/19.27 apply (zenon_L1364_); trivial. % 19.13/19.27 apply (zenon_L1499_); trivial. % 19.13/19.27 apply (zenon_or_s _ _ zenon_H22e); [ zenon_intro zenon_Ha0 | zenon_intro zenon_H22f ]. % 19.13/19.27 apply (zenon_L38_); trivial. % 19.13/19.27 apply (zenon_or_s _ _ zenon_H22f); [ zenon_intro zenon_H122 | zenon_intro zenon_Hc3 ]. % 19.13/19.27 apply (zenon_L1502_); trivial. % 19.13/19.27 apply (zenon_L633_); trivial. % 19.13/19.27 apply (zenon_or_s _ _ zenon_H43); [ zenon_intro zenon_H34 | zenon_intro zenon_H44 ]. % 19.13/19.27 apply (zenon_L14_); trivial. % 19.13/19.27 apply (zenon_or_s _ _ zenon_H22d); [ zenon_intro zenon_H7a | zenon_intro zenon_H22e ]. % 19.13/19.27 apply (zenon_or_s _ _ zenon_H1e0); [ zenon_intro zenon_H3a | zenon_intro zenon_H1e1 ]. % 19.13/19.27 exact (zenon_H98 zenon_H3a). % 19.13/19.27 apply (zenon_or_s _ _ zenon_H1e1); [ zenon_intro zenon_H9e | zenon_intro zenon_H1e2 ]. % 19.13/19.27 exact (zenon_H9f zenon_H9e). % 19.13/19.27 apply (zenon_or_s _ _ zenon_H1e2); [ zenon_intro zenon_H3b | zenon_intro zenon_H15e ]. % 19.13/19.27 apply (zenon_or_s _ _ zenon_H6a); [ zenon_intro zenon_H48 | zenon_intro zenon_H6b ]. % 19.13/19.27 apply (zenon_L1505_); trivial. % 19.13/19.27 apply (zenon_or_s _ _ zenon_H6b); [ zenon_intro zenon_H2a | zenon_intro zenon_H6c ]. % 19.13/19.27 apply (zenon_L1506_); trivial. % 19.13/19.27 apply (zenon_or_s _ _ zenon_H6c); [ zenon_intro zenon_H2c | zenon_intro zenon_H61 ]. % 19.13/19.27 apply (zenon_L18_); trivial. % 19.13/19.27 apply (zenon_L19_); trivial. % 19.13/19.27 exact (zenon_H15f zenon_H15e). % 19.13/19.27 apply (zenon_or_s _ _ zenon_H22e); [ zenon_intro zenon_Ha0 | zenon_intro zenon_H22f ]. % 19.13/19.27 apply (zenon_L1365_); trivial. % 19.13/19.27 apply (zenon_or_s _ _ zenon_H22f); [ zenon_intro zenon_H122 | zenon_intro zenon_Hc3 ]. % 19.13/19.27 apply (zenon_or_s _ _ zenon_H235); [ zenon_intro zenon_H7a | zenon_intro zenon_H236 ]. % 19.13/19.27 apply (zenon_L92_); trivial. % 19.13/19.27 apply (zenon_or_s _ _ zenon_H236); [ zenon_intro zenon_H9d | zenon_intro zenon_H237 ]. % 19.13/19.27 apply (zenon_L360_); trivial. % 19.13/19.27 apply (zenon_or_s _ _ zenon_H237); [ zenon_intro zenon_Hed | zenon_intro zenon_Hac ]. % 19.13/19.27 apply (zenon_or_s _ _ zenon_H6a); [ zenon_intro zenon_H48 | zenon_intro zenon_H6b ]. % 19.13/19.27 apply (zenon_L1505_); trivial. % 19.13/19.27 apply (zenon_or_s _ _ zenon_H6b); [ zenon_intro zenon_H2a | zenon_intro zenon_H6c ]. % 19.13/19.27 apply (zenon_L1507_); trivial. % 19.13/19.27 apply (zenon_or_s _ _ zenon_H6c); [ zenon_intro zenon_H2c | zenon_intro zenon_H61 ]. % 19.13/19.27 apply (zenon_L18_); trivial. % 19.13/19.27 apply (zenon_L19_); trivial. % 19.13/19.27 apply (zenon_L41_); trivial. % 19.13/19.27 apply (zenon_L1508_); trivial. % 19.13/19.27 apply (zenon_or_s _ _ zenon_H78); [ zenon_intro zenon_H48 | zenon_intro zenon_H1e ]. % 19.13/19.27 apply (zenon_L1505_); trivial. % 19.13/19.27 apply (zenon_L367_); trivial. % 19.13/19.27 apply (zenon_L50_); trivial. % 19.13/19.27 apply (zenon_L219_); trivial. % 19.13/19.27 apply (zenon_L1473_); trivial. % 19.13/19.27 apply (zenon_L126_); trivial. % 19.13/19.27 (* end of lemma zenon_L1509_ *) % 19.13/19.27 assert (zenon_L1510_ : ((~((op (e3) (e1)) = (e3)))\/((op (e3) (e3)) = (e1))) -> ((op (e0) (e3)) = (e1)) -> (~((op (e0) (e3)) = (op (e3) (e3)))) -> (((op (e3) (e0)) = (e3))\/(((op (e3) (e1)) = (e3))\/(((op (e3) (e2)) = (e3))\/((op (e3) (e3)) = (e3))))) -> (~((op (e3) (e3)) = (e3))) -> (~((op (e3) (e0)) = (e3))) -> (~((op (e2) (e3)) = (op (e3) (e3)))) -> ((op (e2) (e3)) = (e2)) -> ((~((op (e3) (e2)) = (e3)))\/((op (e3) (e3)) = (e2))) -> False). % 19.13/19.27 do 0 intro. intros zenon_H285 zenon_Hc3 zenon_Hc2 zenon_H165 zenon_H102 zenon_H15f zenon_Hf3 zenon_H11d zenon_H284. % 19.13/19.27 apply (zenon_or_s _ _ zenon_H285); [ zenon_intro zenon_H282 | zenon_intro zenon_Hc4 ]. % 19.13/19.27 apply (zenon_L1347_); trivial. % 19.13/19.27 apply (zenon_L46_); trivial. % 19.13/19.27 (* end of lemma zenon_L1510_ *) % 19.13/19.27 assert (zenon_L1511_ : ((~((op (e3) (e1)) = (e3)))\/((op (e3) (e3)) = (e1))) -> (~((op (e0) (e3)) = (op (e3) (e3)))) -> (((op (e3) (e0)) = (e3))\/(((op (e3) (e1)) = (e3))\/(((op (e3) (e2)) = (e3))\/((op (e3) (e3)) = (e3))))) -> (~((op (e3) (e3)) = (e3))) -> (~((op (e3) (e0)) = (e3))) -> ((op (e2) (e3)) = (e0)) -> ((op (e0) (e3)) = (e1)) -> ((~((op (e3) (e2)) = (e3)))\/((op (e3) (e3)) = (e2))) -> False). % 19.13/19.27 do 0 intro. intros zenon_H285 zenon_Hc2 zenon_H165 zenon_H102 zenon_H15f zenon_H37 zenon_Hc3 zenon_H284. % 19.13/19.27 apply (zenon_or_s _ _ zenon_H285); [ zenon_intro zenon_H282 | zenon_intro zenon_Hc4 ]. % 19.13/19.27 apply (zenon_L1508_); trivial. % 19.13/19.27 apply (zenon_L46_); trivial. % 19.13/19.27 (* end of lemma zenon_L1511_ *) % 19.13/19.27 assert (zenon_L1512_ : ((~((op (e3) (e1)) = (e3)))\/((op (e3) (e3)) = (e1))) -> ((op (e0) (e3)) = (e1)) -> (~((op (e0) (e3)) = (op (e3) (e3)))) -> (((op (e3) (e0)) = (e3))\/(((op (e3) (e1)) = (e3))\/(((op (e3) (e2)) = (e3))\/((op (e3) (e3)) = (e3))))) -> (~((op (e3) (e3)) = (e3))) -> (~((op (e3) (e0)) = (e3))) -> (~((op (e1) (e3)) = (op (e3) (e3)))) -> ((op (e1) (e3)) = (e2)) -> ((~((op (e3) (e2)) = (e3)))\/((op (e3) (e3)) = (e2))) -> False). % 19.13/19.27 do 0 intro. intros zenon_H285 zenon_Hc3 zenon_Hc2 zenon_H165 zenon_H102 zenon_H15f zenon_Hd5 zenon_Hd7 zenon_H284. % 19.13/19.27 apply (zenon_or_s _ _ zenon_H285); [ zenon_intro zenon_H282 | zenon_intro zenon_Hc4 ]. % 19.13/19.27 apply (zenon_L1411_); trivial. % 19.13/19.27 apply (zenon_L46_); trivial. % 19.13/19.27 (* end of lemma zenon_L1512_ *) % 19.13/19.27 assert (zenon_L1513_ : ((~((op (e3) (e0)) = (e3)))\/((op (e3) (e3)) = (e0))) -> ((~((op (e3) (e2)) = (e3)))\/((op (e3) (e3)) = (e2))) -> ((op (e1) (e3)) = (e2)) -> (~((op (e1) (e3)) = (op (e3) (e3)))) -> (~((op (e3) (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 (e0) (e3)) = (e1)) -> ((~((op (e3) (e1)) = (e3)))\/((op (e3) (e3)) = (e1))) -> False). % 19.13/19.27 do 0 intro. intros zenon_H286 zenon_H284 zenon_Hd7 zenon_Hd5 zenon_H102 zenon_H165 zenon_Hc2 zenon_Hc3 zenon_H285. % 19.13/19.27 apply (zenon_or_s _ _ zenon_H286); [ zenon_intro zenon_H15f | zenon_intro zenon_H60 ]. % 19.13/19.27 apply (zenon_L1512_); trivial. % 19.13/19.27 apply (zenon_L201_); trivial. % 19.13/19.27 (* end of lemma zenon_L1513_ *) % 19.13/19.27 assert (zenon_L1514_ : (((op (e0) (e0)) = (e3))\/(((op (e1) (e0)) = (e3))\/(((op (e2) (e0)) = (e3))\/((op (e3) (e0)) = (e3))))) -> (~((op (e0) (e0)) = (e3))) -> ((op (e0) (e3)) = (e1)) -> (~((op (e0) (e3)) = (op (e1) (e3)))) -> (((op (e2) (e2)) = (e0))\/(((op (e2) (e2)) = (e1))\/(((op (e2) (e2)) = (e2))\/((op (e2) (e2)) = (e3))))) -> ((op (e0) (e2)) = (e0)) -> (~((op (e0) (e2)) = (op (e2) (e2)))) -> (~((op (e1) (e2)) = (op (e2) (e2)))) -> (~((op (e2) (e2)) = (e2))) -> (~((op (e2) (e2)) = (e3))) -> (~((op (e1) (e1)) = (e1))) -> (~((e1) = (e3))) -> (((op (e1) (e0)) = (e1))\/(((op (e1) (e1)) = (e1))\/(((op (e1) (e2)) = (e1))\/((op (e1) (e3)) = (e1))))) -> (~((op (e2) (e0)) = (e3))) -> (~((op (e3) (e0)) = (e3))) -> False). % 19.13/19.27 do 0 intro. intros zenon_H1e0 zenon_H98 zenon_Hc3 zenon_H1d zenon_H1c4 zenon_H48 zenon_Ha8 zenon_H2b zenon_H173 zenon_H1b3 zenon_H10a zenon_H95 zenon_H128 zenon_H27f zenon_H15f. % 19.13/19.27 apply (zenon_or_s _ _ zenon_H1e0); [ zenon_intro zenon_H3a | zenon_intro zenon_H1e1 ]. % 19.13/19.27 exact (zenon_H98 zenon_H3a). % 19.13/19.27 apply (zenon_or_s _ _ zenon_H1e1); [ zenon_intro zenon_H9e | zenon_intro zenon_H1e2 ]. % 19.13/19.27 apply (zenon_or_s _ _ zenon_H128); [ zenon_intro zenon_H9d | zenon_intro zenon_H129 ]. % 19.13/19.27 apply (zenon_L37_); trivial. % 19.13/19.27 apply (zenon_or_s _ _ zenon_H129); [ zenon_intro zenon_H10d | zenon_intro zenon_H12a ]. % 19.13/19.27 exact (zenon_H10a zenon_H10d). % 19.13/19.27 apply (zenon_or_s _ _ zenon_H12a); [ zenon_intro zenon_Hf0 | zenon_intro zenon_Hd6 ]. % 19.13/19.27 apply (zenon_L1407_); trivial. % 19.13/19.27 apply (zenon_L79_); trivial. % 19.13/19.27 apply (zenon_or_s _ _ zenon_H1e2); [ zenon_intro zenon_H3b | zenon_intro zenon_H15e ]. % 19.13/19.27 exact (zenon_H27f zenon_H3b). % 19.13/19.27 exact (zenon_H15f zenon_H15e). % 19.13/19.27 (* end of lemma zenon_L1514_ *) % 19.13/19.27 assert (zenon_L1515_ : ((~((op (e0) (e1)) = (e3)))\/((op (e0) (e3)) = (e1))) -> ((~((op (e0) (e3)) = (e3)))\/((op (e0) (e3)) = (e3))) -> (~((e0) = (e3))) -> ((~((op (e1) (e1)) = (e3)))\/((op (e1) (e3)) = (e1))) -> ((~((op (e2) (e1)) = (e3)))\/((op (e2) (e3)) = (e1))) -> ((~((op (e2) (e3)) = (e3)))\/((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 (e0) (e0)) = (e3))\/(((op (e0) (e1)) = (e3))\/(((op (e0) (e2)) = (e3))\/((op (e0) (e3)) = (e3))))) -> (~((e1) = (e3))) -> (((op (e0) (e2)) = (e0))\/(((op (e1) (e2)) = (e0))\/(((op (e2) (e2)) = (e0))\/((op (e3) (e2)) = (e0))))) -> (~((op (e2) (e2)) = (op (e2) (e3)))) -> (((op (e0) (e1)) = (e3))\/(((op (e1) (e1)) = (e3))\/(((op (e2) (e1)) = (e3))\/((op (e3) (e1)) = (e3))))) -> (~((op (e1) (e0)) = (op (e3) (e0)))) -> (((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 (e1) (e0)) = (e0))\/(((op (e1) (e1)) = (e0))\/(((op (e1) (e2)) = (e0))\/((op (e1) (e3)) = (e0))))) -> (~((op (e0) (e3)) = (op (e1) (e3)))) -> (((op (e1) (e0)) = (e1))\/(((op (e1) (e1)) = (e1))\/(((op (e1) (e2)) = (e1))\/((op (e1) (e3)) = (e1))))) -> ((~((op (e1) (e3)) = (e3)))\/((op (e1) (e3)) = (e3))) -> ((~((op (e3) (e0)) = (e3)))\/((op (e3) (e3)) = (e0))) -> (~((op (e1) (e2)) = (op (e1) (e3)))) -> (((op (e1) (e2)) = (e0))\/(((op (e1) (e2)) = (e1))\/(((op (e1) (e2)) = (e2))\/((op (e1) (e2)) = (e3))))) -> (~((op (e0) (e0)) = (op (e0) (e2)))) -> (~((op (e1) (e0)) = (op (e1) (e3)))) -> (((op (e2) (e0)) = (e2))\/(((op (e2) (e1)) = (e2))\/(((op (e2) (e2)) = (e2))\/((op (e2) (e3)) = (e2))))) -> (~((op (e0) (e1)) = (op (e2) (e1)))) -> (~((e1) = (e2))) -> (((op (e3) (e1)) = (e0))\/(((op (e3) (e1)) = (e1))\/(((op (e3) (e1)) = (e2))\/((op (e3) (e1)) = (e3))))) -> (~((op (e3) (e1)) = (op (e3) (e3)))) -> (((op (e0) (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))))) -> (~((e0) = (e1))) -> (~((op (e2) (e0)) = (op (e2) (e2)))) -> (~((op (e0) (e2)) = (op (e2) (e2)))) -> (((op (e2) (e2)) = (e0))\/(((op (e2) (e2)) = (e1))\/(((op (e2) (e2)) = (e2))\/((op (e2) (e2)) = (e3))))) -> (((op (e1) (e0)) = (e0))\/(((op (e1) (e0)) = (e1))\/(((op (e1) (e0)) = (e2))\/((op (e1) (e0)) = (e3))))) -> (~((op (e0) (e1)) = (op (e3) (e1)))) -> (((op (e0) (e0)) = (e0))\/(((op (e1) (e0)) = (e0))\/(((op (e2) (e0)) = (e0))\/((op (e3) (e0)) = (e0))))) -> (~((op (e1) (e3)) = (op (e3) (e3)))) -> ((~((op (e3) (e1)) = (e3)))\/((op (e3) (e3)) = (e1))) -> ((~((op (e2) (e2)) = (e3)))\/((op (e2) (e3)) = (e2))) -> ((~((op (e1) (e2)) = (e3)))\/((op (e1) (e3)) = (e2))) -> (((op (e3) (e0)) = (e0))\/(((op (e3) (e1)) = (e0))\/(((op (e3) (e2)) = (e0))\/((op (e3) (e3)) = (e0))))) -> (~((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) (e1)))) -> (~((op (e3) (e0)) = (op (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)) = (e0))\/(((op (e0) (e2)) = (e1))\/(((op (e0) (e2)) = (e2))\/((op (e0) (e2)) = (e3))))) -> (~((op (e0) (e2)) = (op (e1) (e2)))) -> (~((op (e3) (e0)) = (op (e3) (e2)))) -> (~((op (e3) (e2)) = (op (e3) (e3)))) -> (~((op (e0) (e2)) = (op (e3) (e2)))) -> (((op (e3) (e2)) = (e0))\/(((op (e3) (e2)) = (e1))\/(((op (e3) (e2)) = (e2))\/((op (e3) (e2)) = (e3))))) -> (((op (e0) (e1)) = (e0))\/(((op (e0) (e1)) = (e1))\/(((op (e0) (e1)) = (e2))\/((op (e0) (e1)) = (e3))))) -> (~((op (e1) (e0)) = (op (e1) (e1)))) -> (~((op (e0) (e1)) = (op (e1) (e1)))) -> (((op (e1) (e1)) = (e0))\/(((op (e1) (e1)) = (e1))\/(((op (e1) (e1)) = (e2))\/((op (e1) (e1)) = (e3))))) -> (~((op (e0) (e1)) = (op (e0) (e2)))) -> (~((op (e0) (e1)) = (op (e0) (e3)))) -> (~((op (e2) (e2)) = (e2))) -> (((op (e0) (e2)) = (e2))\/(((op (e1) (e2)) = (e2))\/(((op (e2) (e2)) = (e2))\/((op (e3) (e2)) = (e2))))) -> (~((op (e1) (e1)) = (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) (e0)) = (op (e2) (e3)))) -> (~((op (e2) (e0)) = (op (e3) (e0)))) -> (~((op (e1) (e2)) = (op (e2) (e2)))) -> (((op (e2) (e1)) = (e0))\/(((op (e2) (e1)) = (e1))\/(((op (e2) (e1)) = (e2))\/((op (e2) (e1)) = (e3))))) -> (~((op (e2) (e1)) = (op (e2) (e3)))) -> (~((op (e2) (e0)) = (op (e2) (e1)))) -> (~((op (e1) (e2)) = (op (e3) (e2)))) -> (((op (e2) (e0)) = (e1))\/(((op (e2) (e1)) = (e1))\/(((op (e2) (e2)) = (e1))\/((op (e2) (e3)) = (e1))))) -> (~((op (e1) (e0)) = (op (e1) (e2)))) -> ((op (e0) (e3)) = (e0)) -> (~((op (e0) (e2)) = (op (e0) (e3)))) -> (~((op (e0) (e0)) = (e0))) -> (((op (e3) (e0)) = (e3))\/(((op (e3) (e1)) = (e3))\/(((op (e3) (e2)) = (e3))\/((op (e3) (e3)) = (e3))))) -> (~((op (e3) (e3)) = (e3))) -> (~((op (e2) (e3)) = (op (e3) (e3)))) -> ((~((op (e3) (e2)) = (e3)))\/((op (e3) (e3)) = (e2))) -> (~((op (e0) (e3)) = (op (e2) (e3)))) -> ((~((op (e2) (e0)) = (e3)))\/((op (e2) (e3)) = (e0))) -> (((op (e1) (e0)) = (e3))\/(((op (e1) (e1)) = (e3))\/(((op (e1) (e2)) = (e3))\/((op (e1) (e3)) = (e3))))) -> (~((e2) = (e3))) -> (~((op (e1) (e1)) = (op (e1) (e3)))) -> ((~((op (e1) (e0)) = (e3)))\/((op (e1) (e3)) = (e0))) -> (~((e0) = (e2))) -> ((~((op (e0) (e2)) = (e3)))\/((op (e0) (e3)) = (e2))) -> False). % 19.13/19.27 do 0 intro. intros zenon_H290 zenon_H28f zenon_H9a zenon_H28e zenon_H28b zenon_H281 zenon_Hdb zenon_He7 zenon_H168 zenon_H95 zenon_H6a zenon_H6d zenon_H1a5 zenon_H1fa zenon_H18c zenon_H109 zenon_H22 zenon_H1d zenon_H128 zenon_H289 zenon_H286 zenon_H124 zenon_H19d zenon_H13c zenon_Hd8 zenon_H1d5 zenon_H17e zenon_H7c zenon_H22a zenon_H130 zenon_H235 zenon_H22d zenon_Ha1 zenon_H52 zenon_Ha8 zenon_H1c4 zenon_H25e zenon_H210 zenon_H3e zenon_Hd5 zenon_H285 zenon_H288 zenon_H287 zenon_H1ac zenon_Hc2 zenon_H267 zenon_H1cf zenon_H71 zenon_H153 zenon_H1a4 zenon_H1ba zenon_H195 zenon_H6f zenon_H62 zenon_H14f zenon_H191 zenon_H212 zenon_H45 zenon_H10e zenon_H142 zenon_H4a zenon_H54 zenon_H173 zenon_H172 zenon_H10a zenon_H201 zenon_H259 zenon_H5b zenon_H17b zenon_H2b zenon_H1cc zenon_H1c7 zenon_H1f0 zenon_H115 zenon_H106 zenon_H24a zenon_H1e zenon_H208 zenon_H3f zenon_H165 zenon_H102 zenon_Hf3 zenon_H284 zenon_He2 zenon_H28a zenon_H16f zenon_H12b zenon_H57 zenon_H28d zenon_H149 zenon_H28c. % 19.13/19.27 apply (zenon_or_s _ _ zenon_H290); [ zenon_intro zenon_H9c | zenon_intro zenon_Hc3 ]. % 19.13/19.27 apply (zenon_L1465_); trivial. % 19.13/19.27 apply (zenon_L427_); trivial. % 19.13/19.27 (* end of lemma zenon_L1515_ *) % 19.13/19.27 assert (zenon_L1516_ : ((op (e1) (e3)) = (e0)) -> (~((op (e0) (e0)) = (e0))) -> (((op (e0) (e0)) = (e3))\/(((op (e0) (e1)) = (e3))\/(((op (e0) (e2)) = (e3))\/((op (e0) (e3)) = (e3))))) -> (~((op (e0) (e3)) = (e3))) -> (~((op (e0) (e2)) = (e3))) -> (~((e0) = (e3))) -> (~((op (e0) (e0)) = (e3))) -> (((op (e0) (e0)) = (e3))\/(((op (e1) (e0)) = (e3))\/(((op (e2) (e0)) = (e3))\/((op (e3) (e0)) = (e3))))) -> (~((op (e2) (e0)) = (e3))) -> (~((e1) = (e3))) -> (~((op (e1) (e1)) = (e1))) -> (((op (e2) (e2)) = (e0))\/(((op (e2) (e2)) = (e1))\/(((op (e2) (e2)) = (e2))\/((op (e2) (e2)) = (e3))))) -> (~((op (e2) (e2)) = (e3))) -> (~((op (e2) (e2)) = (e2))) -> (~((op (e1) (e2)) = (op (e2) (e2)))) -> (~((op (e0) (e2)) = (op (e2) (e2)))) -> (~((op (e0) (e3)) = (op (e1) (e3)))) -> ((op (e0) (e3)) = (e1)) -> (((op (e1) (e0)) = (e1))\/(((op (e1) (e1)) = (e1))\/(((op (e1) (e2)) = (e1))\/((op (e1) (e3)) = (e1))))) -> ((~((op (e0) (e1)) = (e3)))\/((op (e0) (e3)) = (e1))) -> ((~((op (e0) (e3)) = (e3)))\/((op (e0) (e3)) = (e3))) -> ((~((op (e1) (e1)) = (e3)))\/((op (e1) (e3)) = (e1))) -> ((~((op (e2) (e1)) = (e3)))\/((op (e2) (e3)) = (e1))) -> ((~((op (e2) (e3)) = (e3)))\/((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 (e0) (e2)) = (e0))\/(((op (e1) (e2)) = (e0))\/(((op (e2) (e2)) = (e0))\/((op (e3) (e2)) = (e0))))) -> (~((op (e2) (e2)) = (op (e2) (e3)))) -> (((op (e0) (e1)) = (e3))\/(((op (e1) (e1)) = (e3))\/(((op (e2) (e1)) = (e3))\/((op (e3) (e1)) = (e3))))) -> (~((op (e1) (e0)) = (op (e3) (e0)))) -> (((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 (e1) (e0)) = (e0))\/(((op (e1) (e1)) = (e0))\/(((op (e1) (e2)) = (e0))\/((op (e1) (e3)) = (e0))))) -> ((~((op (e1) (e3)) = (e3)))\/((op (e1) (e3)) = (e3))) -> ((~((op (e3) (e0)) = (e3)))\/((op (e3) (e3)) = (e0))) -> (~((op (e1) (e2)) = (op (e1) (e3)))) -> (((op (e1) (e2)) = (e0))\/(((op (e1) (e2)) = (e1))\/(((op (e1) (e2)) = (e2))\/((op (e1) (e2)) = (e3))))) -> (~((op (e0) (e0)) = (op (e0) (e2)))) -> (~((op (e1) (e0)) = (op (e1) (e3)))) -> (((op (e2) (e0)) = (e2))\/(((op (e2) (e1)) = (e2))\/(((op (e2) (e2)) = (e2))\/((op (e2) (e3)) = (e2))))) -> (~((op (e0) (e1)) = (op (e2) (e1)))) -> (~((e1) = (e2))) -> (((op (e3) (e1)) = (e0))\/(((op (e3) (e1)) = (e1))\/(((op (e3) (e1)) = (e2))\/((op (e3) (e1)) = (e3))))) -> (~((op (e3) (e1)) = (op (e3) (e3)))) -> (((op (e0) (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))))) -> (~((e0) = (e1))) -> (~((op (e2) (e0)) = (op (e2) (e2)))) -> (((op (e1) (e0)) = (e0))\/(((op (e1) (e0)) = (e1))\/(((op (e1) (e0)) = (e2))\/((op (e1) (e0)) = (e3))))) -> (~((op (e0) (e1)) = (op (e3) (e1)))) -> (((op (e0) (e0)) = (e0))\/(((op (e1) (e0)) = (e0))\/(((op (e2) (e0)) = (e0))\/((op (e3) (e0)) = (e0))))) -> (~((op (e1) (e3)) = (op (e3) (e3)))) -> ((~((op (e3) (e1)) = (e3)))\/((op (e3) (e3)) = (e1))) -> ((~((op (e2) (e2)) = (e3)))\/((op (e2) (e3)) = (e2))) -> ((~((op (e1) (e2)) = (e3)))\/((op (e1) (e3)) = (e2))) -> (((op (e3) (e0)) = (e0))\/(((op (e3) (e1)) = (e0))\/(((op (e3) (e2)) = (e0))\/((op (e3) (e3)) = (e0))))) -> (~((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) (e1)))) -> (~((op (e3) (e0)) = (op (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)) = (e0))\/(((op (e0) (e2)) = (e1))\/(((op (e0) (e2)) = (e2))\/((op (e0) (e2)) = (e3))))) -> (~((op (e0) (e2)) = (op (e1) (e2)))) -> (~((op (e3) (e0)) = (op (e3) (e2)))) -> (~((op (e3) (e2)) = (op (e3) (e3)))) -> (~((op (e0) (e2)) = (op (e3) (e2)))) -> (((op (e3) (e2)) = (e0))\/(((op (e3) (e2)) = (e1))\/(((op (e3) (e2)) = (e2))\/((op (e3) (e2)) = (e3))))) -> (((op (e0) (e1)) = (e0))\/(((op (e0) (e1)) = (e1))\/(((op (e0) (e1)) = (e2))\/((op (e0) (e1)) = (e3))))) -> (~((op (e1) (e0)) = (op (e1) (e1)))) -> (~((op (e0) (e1)) = (op (e1) (e1)))) -> (((op (e1) (e1)) = (e0))\/(((op (e1) (e1)) = (e1))\/(((op (e1) (e1)) = (e2))\/((op (e1) (e1)) = (e3))))) -> (~((op (e0) (e1)) = (op (e0) (e2)))) -> (~((op (e0) (e1)) = (op (e0) (e3)))) -> (((op (e0) (e2)) = (e2))\/(((op (e1) (e2)) = (e2))\/(((op (e2) (e2)) = (e2))\/((op (e3) (e2)) = (e2))))) -> (~((op (e1) (e0)) = (op (e2) (e0)))) -> (((op (e2) (e0)) = (e0))\/(((op (e2) (e0)) = (e1))\/(((op (e2) (e0)) = (e2))\/((op (e2) (e0)) = (e3))))) -> (~((op (e2) (e0)) = (op (e2) (e3)))) -> (~((op (e2) (e0)) = (op (e3) (e0)))) -> (((op (e2) (e1)) = (e0))\/(((op (e2) (e1)) = (e1))\/(((op (e2) (e1)) = (e2))\/((op (e2) (e1)) = (e3))))) -> (~((op (e2) (e1)) = (op (e2) (e3)))) -> (~((op (e2) (e0)) = (op (e2) (e1)))) -> (~((op (e1) (e2)) = (op (e3) (e2)))) -> (((op (e2) (e0)) = (e1))\/(((op (e2) (e1)) = (e1))\/(((op (e2) (e2)) = (e1))\/((op (e2) (e3)) = (e1))))) -> (~((op (e1) (e0)) = (op (e1) (e2)))) -> (~((op (e0) (e2)) = (op (e0) (e3)))) -> (((op (e3) (e0)) = (e3))\/(((op (e3) (e1)) = (e3))\/(((op (e3) (e2)) = (e3))\/((op (e3) (e3)) = (e3))))) -> (~((op (e3) (e3)) = (e3))) -> (~((op (e2) (e3)) = (op (e3) (e3)))) -> ((~((op (e3) (e2)) = (e3)))\/((op (e3) (e3)) = (e2))) -> (~((op (e0) (e3)) = (op (e2) (e3)))) -> ((~((op (e2) (e0)) = (e3)))\/((op (e2) (e3)) = (e0))) -> (((op (e1) (e0)) = (e3))\/(((op (e1) (e1)) = (e3))\/(((op (e1) (e2)) = (e3))\/((op (e1) (e3)) = (e3))))) -> (~((e2) = (e3))) -> (~((op (e1) (e1)) = (op (e1) (e3)))) -> ((~((op (e1) (e0)) = (e3)))\/((op (e1) (e3)) = (e0))) -> (~((e0) = (e2))) -> ((~((op (e0) (e2)) = (e3)))\/((op (e0) (e3)) = (e2))) -> (((op (e0) (e0)) = (e0))\/(((op (e0) (e1)) = (e0))\/(((op (e0) (e2)) = (e0))\/((op (e0) (e3)) = (e0))))) -> False). % 19.13/19.27 do 0 intro. intros zenon_H1f zenon_H3f zenon_H168 zenon_H12d zenon_H123 zenon_H9a zenon_H98 zenon_H1e0 zenon_H27f zenon_H95 zenon_H10a zenon_H1c4 zenon_H1b3 zenon_H173 zenon_H2b zenon_Ha8 zenon_H1d zenon_Hc3 zenon_H128 zenon_H290 zenon_H28f zenon_H28e zenon_H28b zenon_H281 zenon_Hdb zenon_He7 zenon_H6a zenon_H6d zenon_H1a5 zenon_H1fa zenon_H18c zenon_H109 zenon_H22 zenon_H289 zenon_H286 zenon_H124 zenon_H19d zenon_H13c zenon_Hd8 zenon_H1d5 zenon_H17e zenon_H7c zenon_H22a zenon_H130 zenon_H235 zenon_H22d zenon_Ha1 zenon_H52 zenon_H25e zenon_H210 zenon_H3e zenon_Hd5 zenon_H285 zenon_H288 zenon_H287 zenon_H1ac zenon_Hc2 zenon_H267 zenon_H1cf zenon_H71 zenon_H153 zenon_H1a4 zenon_H1ba zenon_H195 zenon_H6f zenon_H62 zenon_H14f zenon_H191 zenon_H212 zenon_H45 zenon_H10e zenon_H142 zenon_H4a zenon_H54 zenon_H172 zenon_H201 zenon_H259 zenon_H5b zenon_H17b zenon_H1cc zenon_H1c7 zenon_H1f0 zenon_H115 zenon_H106 zenon_H24a zenon_H208 zenon_H165 zenon_H102 zenon_Hf3 zenon_H284 zenon_He2 zenon_H28a zenon_H16f zenon_H12b zenon_H57 zenon_H28d zenon_H149 zenon_H28c zenon_H74. % 19.13/19.27 apply (zenon_or_s _ _ zenon_H286); [ zenon_intro zenon_H15f | zenon_intro zenon_H60 ]. % 19.13/19.27 apply (zenon_or_s _ _ zenon_H74); [ zenon_intro zenon_H42 | zenon_intro zenon_H77 ]. % 19.13/19.27 exact (zenon_H3f zenon_H42). % 19.13/19.27 apply (zenon_or_s _ _ zenon_H77); [ zenon_intro zenon_H49 | zenon_intro zenon_H78 ]. % 19.13/19.27 apply (zenon_L1348_); trivial. % 19.13/19.27 apply (zenon_or_s _ _ zenon_H78); [ zenon_intro zenon_H48 | zenon_intro zenon_H1e ]. % 19.13/19.27 apply (zenon_L1514_); trivial. % 19.13/19.27 apply (zenon_L1515_); trivial. % 19.13/19.27 apply (zenon_L136_); trivial. % 19.13/19.27 (* end of lemma zenon_L1516_ *) % 19.13/19.27 assert (zenon_L1517_ : ((~((op (e3) (e0)) = (e3)))\/((op (e3) (e3)) = (e0))) -> ((op (e1) (e3)) = (e0)) -> (~((op (e1) (e3)) = (op (e3) (e3)))) -> ((~((op (e3) (e2)) = (e3)))\/((op (e3) (e3)) = (e2))) -> ((op (e2) (e3)) = (e2)) -> (~((op (e2) (e3)) = (op (e3) (e3)))) -> (~((op (e3) (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 (e0) (e3)) = (e1)) -> ((~((op (e3) (e1)) = (e3)))\/((op (e3) (e3)) = (e1))) -> False). % 19.13/19.27 do 0 intro. intros zenon_H286 zenon_H1f zenon_Hd5 zenon_H284 zenon_H11d zenon_Hf3 zenon_H102 zenon_H165 zenon_Hc2 zenon_Hc3 zenon_H285. % 19.13/19.27 apply (zenon_or_s _ _ zenon_H286); [ zenon_intro zenon_H15f | zenon_intro zenon_H60 ]. % 19.13/19.27 apply (zenon_L1510_); trivial. % 19.13/19.27 apply (zenon_L136_); trivial. % 19.13/19.27 (* end of lemma zenon_L1517_ *) % 19.13/19.27 assert (zenon_L1518_ : ((op (e1) (e3)) = (e0)) -> (~((op (e0) (e0)) = (e0))) -> (((op (e0) (e0)) = (e3))\/(((op (e0) (e1)) = (e3))\/(((op (e0) (e2)) = (e3))\/((op (e0) (e3)) = (e3))))) -> (~((op (e0) (e3)) = (e3))) -> (~((op (e0) (e2)) = (e3))) -> (~((e0) = (e3))) -> (~((op (e0) (e0)) = (e3))) -> (((op (e0) (e0)) = (e3))\/(((op (e1) (e0)) = (e3))\/(((op (e2) (e0)) = (e3))\/((op (e3) (e0)) = (e3))))) -> (~((e1) = (e3))) -> (~((op (e1) (e1)) = (e1))) -> (((op (e2) (e2)) = (e0))\/(((op (e2) (e2)) = (e1))\/(((op (e2) (e2)) = (e2))\/((op (e2) (e2)) = (e3))))) -> (~((op (e2) (e2)) = (e2))) -> (~((op (e1) (e2)) = (op (e2) (e2)))) -> (~((op (e0) (e2)) = (op (e2) (e2)))) -> (~((op (e0) (e3)) = (op (e1) (e3)))) -> ((op (e0) (e3)) = (e1)) -> (((op (e1) (e0)) = (e1))\/(((op (e1) (e1)) = (e1))\/(((op (e1) (e2)) = (e1))\/((op (e1) (e3)) = (e1))))) -> ((~((op (e0) (e1)) = (e3)))\/((op (e0) (e3)) = (e1))) -> ((~((op (e0) (e3)) = (e3)))\/((op (e0) (e3)) = (e3))) -> ((~((op (e1) (e1)) = (e3)))\/((op (e1) (e3)) = (e1))) -> ((~((op (e2) (e1)) = (e3)))\/((op (e2) (e3)) = (e1))) -> ((~((op (e2) (e3)) = (e3)))\/((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 (e0) (e2)) = (e0))\/(((op (e1) (e2)) = (e0))\/(((op (e2) (e2)) = (e0))\/((op (e3) (e2)) = (e0))))) -> (~((op (e2) (e2)) = (op (e2) (e3)))) -> (((op (e0) (e1)) = (e3))\/(((op (e1) (e1)) = (e3))\/(((op (e2) (e1)) = (e3))\/((op (e3) (e1)) = (e3))))) -> (~((op (e1) (e0)) = (op (e3) (e0)))) -> (((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 (e1) (e0)) = (e0))\/(((op (e1) (e1)) = (e0))\/(((op (e1) (e2)) = (e0))\/((op (e1) (e3)) = (e0))))) -> ((~((op (e1) (e3)) = (e3)))\/((op (e1) (e3)) = (e3))) -> ((~((op (e3) (e0)) = (e3)))\/((op (e3) (e3)) = (e0))) -> (~((op (e1) (e2)) = (op (e1) (e3)))) -> (((op (e1) (e2)) = (e0))\/(((op (e1) (e2)) = (e1))\/(((op (e1) (e2)) = (e2))\/((op (e1) (e2)) = (e3))))) -> (~((op (e0) (e0)) = (op (e0) (e2)))) -> (~((op (e1) (e0)) = (op (e1) (e3)))) -> (((op (e2) (e0)) = (e2))\/(((op (e2) (e1)) = (e2))\/(((op (e2) (e2)) = (e2))\/((op (e2) (e3)) = (e2))))) -> (~((op (e0) (e1)) = (op (e2) (e1)))) -> (~((e1) = (e2))) -> (((op (e3) (e1)) = (e0))\/(((op (e3) (e1)) = (e1))\/(((op (e3) (e1)) = (e2))\/((op (e3) (e1)) = (e3))))) -> (~((op (e3) (e1)) = (op (e3) (e3)))) -> (((op (e0) (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))))) -> (~((e0) = (e1))) -> (~((op (e2) (e0)) = (op (e2) (e2)))) -> (((op (e1) (e0)) = (e0))\/(((op (e1) (e0)) = (e1))\/(((op (e1) (e0)) = (e2))\/((op (e1) (e0)) = (e3))))) -> (~((op (e0) (e1)) = (op (e3) (e1)))) -> (((op (e0) (e0)) = (e0))\/(((op (e1) (e0)) = (e0))\/(((op (e2) (e0)) = (e0))\/((op (e3) (e0)) = (e0))))) -> (~((op (e1) (e3)) = (op (e3) (e3)))) -> ((~((op (e3) (e1)) = (e3)))\/((op (e3) (e3)) = (e1))) -> ((~((op (e2) (e2)) = (e3)))\/((op (e2) (e3)) = (e2))) -> ((~((op (e1) (e2)) = (e3)))\/((op (e1) (e3)) = (e2))) -> (((op (e3) (e0)) = (e0))\/(((op (e3) (e1)) = (e0))\/(((op (e3) (e2)) = (e0))\/((op (e3) (e3)) = (e0))))) -> (~((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) (e1)))) -> (~((op (e3) (e0)) = (op (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)) = (e0))\/(((op (e0) (e2)) = (e1))\/(((op (e0) (e2)) = (e2))\/((op (e0) (e2)) = (e3))))) -> (~((op (e0) (e2)) = (op (e1) (e2)))) -> (~((op (e3) (e0)) = (op (e3) (e2)))) -> (~((op (e3) (e2)) = (op (e3) (e3)))) -> (~((op (e0) (e2)) = (op (e3) (e2)))) -> (((op (e3) (e2)) = (e0))\/(((op (e3) (e2)) = (e1))\/(((op (e3) (e2)) = (e2))\/((op (e3) (e2)) = (e3))))) -> (((op (e0) (e1)) = (e0))\/(((op (e0) (e1)) = (e1))\/(((op (e0) (e1)) = (e2))\/((op (e0) (e1)) = (e3))))) -> (~((op (e1) (e0)) = (op (e1) (e1)))) -> (~((op (e0) (e1)) = (op (e1) (e1)))) -> (((op (e1) (e1)) = (e0))\/(((op (e1) (e1)) = (e1))\/(((op (e1) (e1)) = (e2))\/((op (e1) (e1)) = (e3))))) -> (~((op (e0) (e1)) = (op (e0) (e2)))) -> (~((op (e0) (e1)) = (op (e0) (e3)))) -> (((op (e0) (e2)) = (e2))\/(((op (e1) (e2)) = (e2))\/(((op (e2) (e2)) = (e2))\/((op (e3) (e2)) = (e2))))) -> (~((op (e1) (e0)) = (op (e2) (e0)))) -> (((op (e2) (e0)) = (e0))\/(((op (e2) (e0)) = (e1))\/(((op (e2) (e0)) = (e2))\/((op (e2) (e0)) = (e3))))) -> (~((op (e2) (e0)) = (op (e2) (e3)))) -> (~((op (e2) (e0)) = (op (e3) (e0)))) -> (((op (e2) (e1)) = (e0))\/(((op (e2) (e1)) = (e1))\/(((op (e2) (e1)) = (e2))\/((op (e2) (e1)) = (e3))))) -> (~((op (e2) (e1)) = (op (e2) (e3)))) -> (~((op (e2) (e0)) = (op (e2) (e1)))) -> (~((op (e1) (e2)) = (op (e3) (e2)))) -> (((op (e2) (e0)) = (e1))\/(((op (e2) (e1)) = (e1))\/(((op (e2) (e2)) = (e1))\/((op (e2) (e3)) = (e1))))) -> (~((op (e1) (e0)) = (op (e1) (e2)))) -> (~((op (e0) (e2)) = (op (e0) (e3)))) -> (((op (e3) (e0)) = (e3))\/(((op (e3) (e1)) = (e3))\/(((op (e3) (e2)) = (e3))\/((op (e3) (e3)) = (e3))))) -> (~((op (e3) (e3)) = (e3))) -> (~((op (e2) (e3)) = (op (e3) (e3)))) -> ((~((op (e3) (e2)) = (e3)))\/((op (e3) (e3)) = (e2))) -> (~((op (e0) (e3)) = (op (e2) (e3)))) -> ((~((op (e2) (e0)) = (e3)))\/((op (e2) (e3)) = (e0))) -> (((op (e1) (e0)) = (e3))\/(((op (e1) (e1)) = (e3))\/(((op (e1) (e2)) = (e3))\/((op (e1) (e3)) = (e3))))) -> (~((e2) = (e3))) -> (~((op (e1) (e1)) = (op (e1) (e3)))) -> ((~((op (e1) (e0)) = (e3)))\/((op (e1) (e3)) = (e0))) -> (~((e0) = (e2))) -> ((~((op (e0) (e2)) = (e3)))\/((op (e0) (e3)) = (e2))) -> (((op (e0) (e0)) = (e0))\/(((op (e0) (e1)) = (e0))\/(((op (e0) (e2)) = (e0))\/((op (e0) (e3)) = (e0))))) -> False). % 19.13/19.27 do 0 intro. intros zenon_H1f zenon_H3f zenon_H168 zenon_H12d zenon_H123 zenon_H9a zenon_H98 zenon_H1e0 zenon_H95 zenon_H10a zenon_H1c4 zenon_H173 zenon_H2b zenon_Ha8 zenon_H1d zenon_Hc3 zenon_H128 zenon_H290 zenon_H28f zenon_H28e zenon_H28b zenon_H281 zenon_Hdb zenon_He7 zenon_H6a zenon_H6d zenon_H1a5 zenon_H1fa zenon_H18c zenon_H109 zenon_H22 zenon_H289 zenon_H286 zenon_H124 zenon_H19d zenon_H13c zenon_Hd8 zenon_H1d5 zenon_H17e zenon_H7c zenon_H22a zenon_H130 zenon_H235 zenon_H22d zenon_Ha1 zenon_H52 zenon_H25e zenon_H210 zenon_H3e zenon_Hd5 zenon_H285 zenon_H288 zenon_H287 zenon_H1ac zenon_Hc2 zenon_H267 zenon_H1cf zenon_H71 zenon_H153 zenon_H1a4 zenon_H1ba zenon_H195 zenon_H6f zenon_H62 zenon_H14f zenon_H191 zenon_H212 zenon_H45 zenon_H10e zenon_H142 zenon_H4a zenon_H54 zenon_H172 zenon_H201 zenon_H259 zenon_H5b zenon_H17b zenon_H1cc zenon_H1c7 zenon_H1f0 zenon_H115 zenon_H106 zenon_H24a zenon_H208 zenon_H165 zenon_H102 zenon_Hf3 zenon_H284 zenon_He2 zenon_H28a zenon_H16f zenon_H12b zenon_H57 zenon_H28d zenon_H149 zenon_H28c zenon_H74. % 19.13/19.27 apply (zenon_or_s _ _ zenon_H28a); [ zenon_intro zenon_H27f | zenon_intro zenon_H37 ]. % 19.13/19.27 apply (zenon_or_s _ _ zenon_H288); [ zenon_intro zenon_H1b3 | zenon_intro zenon_H11d ]. % 19.13/19.27 apply (zenon_L1516_); trivial. % 19.13/19.27 apply (zenon_L1517_); trivial. % 19.13/19.27 apply (zenon_L130_); trivial. % 19.13/19.27 (* end of lemma zenon_L1518_ *) % 19.13/19.27 assert (zenon_L1519_ : (((op (e0) (e0)) = (e0))\/(((op (e0) (e1)) = (e0))\/(((op (e0) (e2)) = (e0))\/((op (e0) (e3)) = (e0))))) -> ((~((op (e0) (e2)) = (e3)))\/((op (e0) (e3)) = (e2))) -> ((~((op (e1) (e0)) = (e3)))\/((op (e1) (e3)) = (e0))) -> (~((op (e1) (e1)) = (op (e1) (e3)))) -> (~((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 (e1) (e2)) = (op (e3) (e2)))) -> (~((op (e2) (e0)) = (op (e2) (e1)))) -> (((op (e2) (e1)) = (e0))\/(((op (e2) (e1)) = (e1))\/(((op (e2) (e1)) = (e2))\/((op (e2) (e1)) = (e3))))) -> (~((op (e2) (e0)) = (op (e3) (e0)))) -> (~((op (e2) (e0)) = (op (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) (e2)) = (e2))\/(((op (e1) (e2)) = (e2))\/(((op (e2) (e2)) = (e2))\/((op (e3) (e2)) = (e2))))) -> (~((op (e0) (e1)) = (op (e0) (e3)))) -> (~((op (e0) (e1)) = (op (e0) (e2)))) -> (~((op (e0) (e1)) = (op (e1) (e1)))) -> (~((op (e1) (e0)) = (op (e1) (e1)))) -> (((op (e0) (e1)) = (e0))\/(((op (e0) (e1)) = (e1))\/(((op (e0) (e1)) = (e2))\/((op (e0) (e1)) = (e3))))) -> (((op (e3) (e2)) = (e0))\/(((op (e3) (e2)) = (e1))\/(((op (e3) (e2)) = (e2))\/((op (e3) (e2)) = (e3))))) -> (~((op (e0) (e2)) = (op (e3) (e2)))) -> (~((op (e3) (e2)) = (op (e3) (e3)))) -> (~((op (e3) (e0)) = (op (e3) (e2)))) -> (~((op (e0) (e2)) = (op (e1) (e2)))) -> (((op (e0) (e2)) = (e0))\/(((op (e0) (e2)) = (e1))\/(((op (e0) (e2)) = (e2))\/((op (e0) (e2)) = (e3))))) -> (~((op (e3) (e1)) = (op (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 (e3) (e0)) = (op (e3) (e1)))) -> (((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) (e0)) = (e0))\/(((op (e1) (e0)) = (e0))\/(((op (e2) (e0)) = (e0))\/((op (e3) (e0)) = (e0))))) -> (~((op (e0) (e1)) = (op (e3) (e1)))) -> (((op (e1) (e0)) = (e0))\/(((op (e1) (e0)) = (e1))\/(((op (e1) (e0)) = (e2))\/((op (e1) (e0)) = (e3))))) -> (~((op (e2) (e0)) = (op (e2) (e2)))) -> (~((e0) = (e1))) -> (((op (e0) (e0)) = (e1))\/(((op (e0) (e1)) = (e1))\/(((op (e0) (e2)) = (e1))\/((op (e0) (e3)) = (e1))))) -> (((op (e0) (e0)) = (e1))\/(((op (e1) (e0)) = (e1))\/(((op (e2) (e0)) = (e1))\/((op (e3) (e0)) = (e1))))) -> (((op (e3) (e1)) = (e0))\/(((op (e3) (e1)) = (e1))\/(((op (e3) (e1)) = (e2))\/((op (e3) (e1)) = (e3))))) -> (~((e1) = (e2))) -> (~((op (e0) (e1)) = (op (e2) (e1)))) -> (((op (e2) (e0)) = (e2))\/(((op (e2) (e1)) = (e2))\/(((op (e2) (e2)) = (e2))\/((op (e2) (e3)) = (e2))))) -> (~((op (e1) (e0)) = (op (e1) (e3)))) -> (~((op (e0) (e0)) = (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) (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 (e1) (e0)) = (e2))\/(((op (e1) (e1)) = (e2))\/(((op (e1) (e2)) = (e2))\/((op (e1) (e3)) = (e2))))) -> (~((op (e1) (e0)) = (op (e3) (e0)))) -> (((op (e0) (e1)) = (e3))\/(((op (e1) (e1)) = (e3))\/(((op (e2) (e1)) = (e3))\/((op (e3) (e1)) = (e3))))) -> (~((op (e2) (e2)) = (op (e2) (e3)))) -> (((op (e0) (e2)) = (e0))\/(((op (e1) (e2)) = (e0))\/(((op (e2) (e2)) = (e0))\/((op (e3) (e2)) = (e0))))) -> ((~((op (e0) (e3)) = (e3)))\/((op (e0) (e3)) = (e3))) -> ((~((op (e0) (e1)) = (e3)))\/((op (e0) (e3)) = (e1))) -> (((op (e1) (e0)) = (e1))\/(((op (e1) (e1)) = (e1))\/(((op (e1) (e2)) = (e1))\/((op (e1) (e3)) = (e1))))) -> (~((op (e0) (e2)) = (op (e2) (e2)))) -> (~((op (e1) (e2)) = (op (e2) (e2)))) -> (~((op (e2) (e2)) = (e2))) -> (((op (e2) (e2)) = (e0))\/(((op (e2) (e2)) = (e1))\/(((op (e2) (e2)) = (e2))\/((op (e2) (e2)) = (e3))))) -> (~((e1) = (e3))) -> (((op (e0) (e0)) = (e3))\/(((op (e1) (e0)) = (e3))\/(((op (e2) (e0)) = (e3))\/((op (e3) (e0)) = (e3))))) -> (~((op (e0) (e0)) = (e0))) -> ((~((op (e1) (e2)) = (e3)))\/((op (e1) (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 (e2) (e0)) = (e3)))\/((op (e2) (e3)) = (e0))) -> ((~((op (e2) (e2)) = (e3)))\/((op (e2) (e3)) = (e2))) -> ((~((op (e3) (e1)) = (e3)))\/((op (e3) (e3)) = (e1))) -> ((op (e0) (e3)) = (e1)) -> (~((op (e0) (e3)) = (op (e3) (e3)))) -> (((op (e3) (e0)) = (e3))\/(((op (e3) (e1)) = (e3))\/(((op (e3) (e2)) = (e3))\/((op (e3) (e3)) = (e3))))) -> (~((op (e3) (e3)) = (e3))) -> (~((op (e2) (e3)) = (op (e3) (e3)))) -> ((~((op (e3) (e2)) = (e3)))\/((op (e3) (e3)) = (e2))) -> (~((e0) = (e3))) -> (((op (e0) (e1)) = (e2))\/(((op (e1) (e1)) = (e2))\/(((op (e2) (e1)) = (e2))\/((op (e3) (e1)) = (e2))))) -> (~((op (e2) (e1)) = (op (e2) (e3)))) -> (~((e0) = (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)) = (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)) = (e3))) -> ((~((op (e3) (e0)) = (e3)))\/((op (e3) (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 (e2) (e3)) = (e3)))\/((op (e2) (e3)) = (e3))) -> (~((op (e0) (e3)) = (op (e2) (e3)))) -> ((~((op (e2) (e1)) = (e3)))\/((op (e2) (e3)) = (e1))) -> ((~((op (e1) (e3)) = (e3)))\/((op (e1) (e3)) = (e3))) -> (~((op (e0) (e3)) = (op (e1) (e3)))) -> ((~((op (e1) (e1)) = (e3)))\/((op (e1) (e3)) = (e1))) -> False). % 19.13/19.27 do 0 intro. intros zenon_H74 zenon_H28c zenon_H28d zenon_H57 zenon_H208 zenon_H24a zenon_H106 zenon_H115 zenon_H1f0 zenon_H1cc zenon_H17b zenon_H5b zenon_H259 zenon_H201 zenon_H172 zenon_H54 zenon_H4a zenon_H10e zenon_H45 zenon_H212 zenon_H191 zenon_H14f zenon_H62 zenon_H6f zenon_H195 zenon_H1ba zenon_H1a4 zenon_H153 zenon_H71 zenon_H1cf zenon_H267 zenon_H1ac zenon_H3e zenon_H210 zenon_H25e zenon_H52 zenon_Ha1 zenon_H22d zenon_H235 zenon_H22a zenon_H7c zenon_H17e zenon_H1d5 zenon_Hd8 zenon_H13c zenon_H19d zenon_H124 zenon_H22 zenon_H109 zenon_H18c zenon_H1fa zenon_H1a5 zenon_H6d zenon_H6a zenon_H28f zenon_H290 zenon_H128 zenon_Ha8 zenon_H2b zenon_H173 zenon_H1c4 zenon_H95 zenon_H1e0 zenon_H3f zenon_H287 zenon_Hd5 zenon_H16f zenon_H28a zenon_H288 zenon_H285 zenon_Hc3 zenon_Hc2 zenon_H165 zenon_H102 zenon_Hf3 zenon_H284 zenon_H9a zenon_H1d8 zenon_H1c7 zenon_H149 zenon_H12b zenon_H168 zenon_H142 zenon_H10a zenon_H130 zenon_H245 zenon_H98 zenon_H286 zenon_He7 zenon_Hdb zenon_H281 zenon_He2 zenon_H28b zenon_H289 zenon_H1d zenon_H28e. % 19.13/19.27 apply (zenon_or_s _ _ zenon_H28c); [ zenon_intro zenon_H123 | zenon_intro zenon_Hcd ]. % 19.13/19.27 apply (zenon_or_s _ _ zenon_H28f); [ zenon_intro zenon_H12d | zenon_intro zenon_He3 ]. % 19.13/19.27 apply (zenon_or_s _ _ zenon_H28d); [ zenon_intro zenon_H9f | zenon_intro zenon_H1f ]. % 19.13/19.27 apply (zenon_or_s _ _ zenon_H28e); [ zenon_intro zenon_H1a1 | zenon_intro zenon_Hd6 ]. % 19.13/19.27 apply (zenon_or_s _ _ zenon_H287); [ zenon_intro zenon_H16d | zenon_intro zenon_Hd7 ]. % 19.13/19.27 apply (zenon_or_s _ _ zenon_H289); [ zenon_intro zenon_H12f | zenon_intro zenon_Hdc ]. % 19.13/19.27 apply (zenon_L1343_); trivial. % 19.13/19.27 apply (zenon_or_s _ _ zenon_H28a); [ zenon_intro zenon_H27f | zenon_intro zenon_H37 ]. % 19.13/19.27 apply (zenon_or_s _ _ zenon_H28b); [ zenon_intro zenon_Ha7 | zenon_intro zenon_Hf4 ]. % 19.13/19.27 apply (zenon_or_s _ _ zenon_H288); [ zenon_intro zenon_H1b3 | zenon_intro zenon_H11d ]. % 19.13/19.27 apply (zenon_L1345_); trivial. % 19.13/19.27 apply (zenon_or_s _ _ zenon_H286); [ zenon_intro zenon_H15f | zenon_intro zenon_H60 ]. % 19.13/19.27 apply (zenon_L1510_); trivial. % 19.13/19.27 apply (zenon_L1406_); trivial. % 19.13/19.27 apply (zenon_L272_); trivial. % 19.13/19.27 apply (zenon_or_s _ _ zenon_H286); [ zenon_intro zenon_H15f | zenon_intro zenon_H60 ]. % 19.13/19.27 apply (zenon_L1511_); trivial. % 19.13/19.27 apply (zenon_L219_); trivial. % 19.13/19.27 apply (zenon_L1513_); trivial. % 19.13/19.27 apply (zenon_L79_); trivial. % 19.13/19.27 apply (zenon_L1518_); trivial. % 19.13/19.27 apply (zenon_L633_); trivial. % 19.13/19.27 apply (zenon_L82_); trivial. % 19.13/19.27 (* end of lemma zenon_L1519_ *) % 19.13/19.27 apply (zenon_and_s _ _ ax1). zenon_intro zenon_H26a. zenon_intro zenon_H291. % 19.13/19.27 apply (zenon_and_s _ _ zenon_H291). zenon_intro zenon_H212. zenon_intro zenon_H292. % 19.13/19.27 apply (zenon_and_s _ _ zenon_H292). zenon_intro zenon_H1ba. zenon_intro zenon_H293. % 19.13/19.27 apply (zenon_and_s _ _ zenon_H293). zenon_intro zenon_He4. zenon_intro zenon_H294. % 19.13/19.27 apply (zenon_and_s _ _ zenon_H294). zenon_intro zenon_H25e. zenon_intro zenon_H295. % 19.13/19.27 apply (zenon_and_s _ _ zenon_H295). zenon_intro zenon_H142. zenon_intro zenon_H296. % 19.13/19.27 apply (zenon_and_s _ _ zenon_H296). zenon_intro zenon_H19d. zenon_intro zenon_H297. % 19.13/19.27 apply (zenon_and_s _ _ zenon_H297). zenon_intro zenon_Hdf. zenon_intro zenon_H298. % 19.13/19.27 apply (zenon_and_s _ _ zenon_H298). zenon_intro zenon_H259. zenon_intro zenon_H299. % 19.13/19.27 apply (zenon_and_s _ _ zenon_H299). zenon_intro zenon_H1cc. zenon_intro zenon_H29a. % 19.13/19.27 apply (zenon_and_s _ _ zenon_H29a). zenon_intro zenon_H1c4. zenon_intro zenon_H29b. % 19.13/19.27 apply (zenon_and_s _ _ zenon_H29b). zenon_intro zenon_H11f. zenon_intro zenon_H29c. % 19.13/19.27 apply (zenon_and_s _ _ zenon_H29c). zenon_intro zenon_H267. zenon_intro zenon_H29d. % 19.13/19.27 apply (zenon_and_s _ _ zenon_H29d). zenon_intro zenon_H22a. zenon_intro zenon_H29e. % 19.13/19.27 apply (zenon_and_s _ _ zenon_H29e). zenon_intro zenon_H191. zenon_intro zenon_H101. % 19.13/19.27 apply (zenon_and_s _ _ ax2). zenon_intro zenon_H74. zenon_intro zenon_H29f. % 19.13/19.27 apply (zenon_and_s _ _ zenon_H29f). zenon_intro zenon_H3e. zenon_intro zenon_H2a0. % 19.13/19.27 apply (zenon_and_s _ _ zenon_H2a0). zenon_intro zenon_H22d. zenon_intro zenon_H2a1. % 19.13/19.27 apply (zenon_and_s _ _ zenon_H2a1). zenon_intro zenon_H235. zenon_intro zenon_H2a2. % 19.13/19.27 apply (zenon_and_s _ _ zenon_H2a2). zenon_intro zenon_H183. zenon_intro zenon_H2a3. % 19.13/19.27 apply (zenon_and_s _ _ zenon_H2a3). zenon_intro zenon_H1fe. zenon_intro zenon_H2a4. % 19.13/19.27 apply (zenon_and_s _ _ zenon_H2a4). zenon_intro zenon_H168. zenon_intro zenon_H2a5. % 19.13/19.27 apply (zenon_and_s _ _ zenon_H2a5). zenon_intro zenon_H1e0. zenon_intro zenon_H2a6. % 19.13/19.27 apply (zenon_and_s _ _ zenon_H2a6). zenon_intro zenon_H22. zenon_intro zenon_H2a7. % 19.13/19.27 apply (zenon_and_s _ _ zenon_H2a7). zenon_intro zenon_H245. zenon_intro zenon_H2a8. % 19.13/19.27 apply (zenon_and_s _ _ zenon_H2a8). zenon_intro zenon_H128. zenon_intro zenon_H2a9. % 19.13/19.27 apply (zenon_and_s _ _ zenon_H2a9). zenon_intro zenon_H109. zenon_intro zenon_H2aa. % 19.13/19.27 apply (zenon_and_s _ _ zenon_H2aa). zenon_intro zenon_H18c. zenon_intro zenon_H2ab. % 19.13/19.27 apply (zenon_and_s _ _ zenon_H2ab). zenon_intro zenon_H1d8. zenon_intro zenon_H2ac. % 19.13/19.27 apply (zenon_and_s _ _ zenon_H2ac). zenon_intro zenon_H16f. zenon_intro zenon_H2ad. % 19.13/19.27 apply (zenon_and_s _ _ zenon_H2ad). zenon_intro zenon_H1a5. zenon_intro zenon_H2ae. % 19.13/19.27 apply (zenon_and_s _ _ zenon_H2ae). zenon_intro zenon_H2f. zenon_intro zenon_H2af. % 19.13/19.27 apply (zenon_and_s _ _ zenon_H2af). zenon_intro zenon_H6a. zenon_intro zenon_H2b0. % 19.13/19.27 apply (zenon_and_s _ _ zenon_H2b0). zenon_intro zenon_H106. zenon_intro zenon_H2b1. % 19.13/19.27 apply (zenon_and_s _ _ zenon_H2b1). zenon_intro zenon_H139. zenon_intro zenon_H2b2. % 19.13/19.27 apply (zenon_and_s _ _ zenon_H2b2). zenon_intro zenon_H1d5. zenon_intro zenon_H2b3. % 19.13/19.27 apply (zenon_and_s _ _ zenon_H2b3). zenon_intro zenon_H172. zenon_intro zenon_H2b4. % 19.13/19.27 apply (zenon_and_s _ _ zenon_H2b4). zenon_intro zenon_He7. zenon_intro zenon_H2b5. % 19.13/19.27 apply (zenon_and_s _ _ zenon_H2b5). zenon_intro zenon_H1a6. zenon_intro zenon_H2b6. % 19.13/19.27 apply (zenon_and_s _ _ zenon_H2b6). zenon_intro zenon_H1ac. zenon_intro zenon_H2b7. % 19.13/19.27 apply (zenon_and_s _ _ zenon_H2b7). zenon_intro zenon_H67. zenon_intro zenon_H2b8. % 19.13/19.27 apply (zenon_and_s _ _ zenon_H2b8). zenon_intro zenon_He8. zenon_intro zenon_H2b9. % 19.13/19.27 apply (zenon_and_s _ _ zenon_H2b9). zenon_intro zenon_H133. zenon_intro zenon_H2ba. % 19.13/19.27 apply (zenon_and_s _ _ zenon_H2ba). zenon_intro zenon_H153. zenon_intro zenon_H2bb. % 19.13/19.27 apply (zenon_and_s _ _ zenon_H2bb). zenon_intro zenon_H145. zenon_intro zenon_H2bc. % 19.13/19.27 apply (zenon_and_s _ _ zenon_H2bc). zenon_intro zenon_H165. zenon_intro zenon_H136. % 19.13/19.27 apply (zenon_and_s _ _ ax3). zenon_intro zenon_H2be. zenon_intro zenon_H2bd. % 19.13/19.27 apply (zenon_and_s _ _ zenon_H2bd). zenon_intro zenon_H39. zenon_intro zenon_H2bf. % 19.13/19.27 apply (zenon_and_s _ _ zenon_H2bf). zenon_intro zenon_H2c1. zenon_intro zenon_H2c0. % 19.13/19.27 apply (zenon_and_s _ _ zenon_H2c0). zenon_intro zenon_H201. zenon_intro zenon_H2c2. % 19.13/19.27 apply (zenon_and_s _ _ zenon_H2c2). zenon_intro zenon_H1fa. zenon_intro zenon_H2c3. % 19.13/19.27 apply (zenon_and_s _ _ zenon_H2c3). zenon_intro zenon_H17b. zenon_intro zenon_H2c4. % 19.13/19.27 apply (zenon_and_s _ _ zenon_H2c4). zenon_intro zenon_H10e. zenon_intro zenon_H2c5. % 19.13/19.27 apply (zenon_and_s _ _ zenon_H2c5). zenon_intro zenon_H17e. zenon_intro zenon_H2c6. % 19.13/19.27 apply (zenon_and_s _ _ zenon_H2c6). zenon_intro zenon_H210. zenon_intro zenon_H2c7. % 19.13/19.27 apply (zenon_and_s _ _ zenon_H2c7). zenon_intro zenon_H13e. zenon_intro zenon_H2c8. % 19.13/19.27 apply (zenon_and_s _ _ zenon_H2c8). zenon_intro zenon_H160. zenon_intro zenon_H2c9. % 19.13/19.27 apply (zenon_and_s _ _ zenon_H2c9). zenon_intro zenon_Haf. zenon_intro zenon_H2ca. % 19.13/19.27 apply (zenon_and_s _ _ zenon_H2ca). zenon_intro zenon_H195. zenon_intro zenon_H2cb. % 19.13/19.27 apply (zenon_and_s _ _ zenon_H2cb). zenon_intro zenon_Ha8. zenon_intro zenon_H2cc. % 19.13/19.27 apply (zenon_and_s _ _ zenon_H2cc). zenon_intro zenon_H14f. zenon_intro zenon_H2cd. % 19.13/19.27 apply (zenon_and_s _ _ zenon_H2cd). zenon_intro zenon_H2b. zenon_intro zenon_H2ce. % 19.13/19.27 apply (zenon_and_s _ _ zenon_H2ce). zenon_intro zenon_H115. zenon_intro zenon_H2cf. % 19.13/19.27 apply (zenon_and_s _ _ zenon_H2cf). zenon_intro zenon_H18f. zenon_intro zenon_H2d0. % 19.13/19.27 apply (zenon_and_s _ _ zenon_H2d0). zenon_intro zenon_H1d. zenon_intro zenon_H2d1. % 19.13/19.27 apply (zenon_and_s _ _ zenon_H2d1). zenon_intro zenon_He2. zenon_intro zenon_H2d2. % 19.13/19.27 apply (zenon_and_s _ _ zenon_H2d2). zenon_intro zenon_Hc2. zenon_intro zenon_H2d3. % 19.13/19.27 apply (zenon_and_s _ _ zenon_H2d3). zenon_intro zenon_Hdb. zenon_intro zenon_H2d4. % 19.13/19.27 apply (zenon_and_s _ _ zenon_H2d4). zenon_intro zenon_Hd5. zenon_intro zenon_H2d5. % 19.13/19.27 apply (zenon_and_s _ _ zenon_H2d5). zenon_intro zenon_Hf3. zenon_intro zenon_H2d6. % 19.13/19.27 apply (zenon_and_s _ _ zenon_H2d6). zenon_intro zenon_H2d8. zenon_intro zenon_H2d7. % 19.13/19.27 apply (zenon_and_s _ _ zenon_H2d7). zenon_intro zenon_H13c. zenon_intro zenon_H2d9. % 19.13/19.27 apply (zenon_and_s _ _ zenon_H2d9). zenon_intro zenon_H189. zenon_intro zenon_H2da. % 19.13/19.27 apply (zenon_and_s _ _ zenon_H2da). zenon_intro zenon_H4a. zenon_intro zenon_H2db. % 19.13/19.27 apply (zenon_and_s _ _ zenon_H2db). zenon_intro zenon_H54. zenon_intro zenon_H2dc. % 19.13/19.27 apply (zenon_and_s _ _ zenon_H2dc). zenon_intro zenon_H208. zenon_intro zenon_H2dd. % 19.13/19.27 apply (zenon_and_s _ _ zenon_H2dd). zenon_intro zenon_H45. zenon_intro zenon_H2de. % 19.13/19.27 apply (zenon_and_s _ _ zenon_H2de). zenon_intro zenon_H24a. zenon_intro zenon_H2df. % 19.13/19.27 apply (zenon_and_s _ _ zenon_H2df). zenon_intro zenon_Hd8. zenon_intro zenon_H2e0. % 19.13/19.27 apply (zenon_and_s _ _ zenon_H2e0). zenon_intro zenon_H4f. zenon_intro zenon_H2e1. % 19.13/19.27 apply (zenon_and_s _ _ zenon_H2e1). zenon_intro zenon_H57. zenon_intro zenon_H2e2. % 19.13/19.27 apply (zenon_and_s _ _ zenon_H2e2). zenon_intro zenon_H124. zenon_intro zenon_H2e3. % 19.13/19.27 apply (zenon_and_s _ _ zenon_H2e3). zenon_intro zenon_H1f0. zenon_intro zenon_H2e4. % 19.13/19.27 apply (zenon_and_s _ _ zenon_H2e4). zenon_intro zenon_H52. zenon_intro zenon_H2e5. % 19.13/19.27 apply (zenon_and_s _ _ zenon_H2e5). zenon_intro zenon_H5b. zenon_intro zenon_H2e6. % 19.13/19.27 apply (zenon_and_s _ _ zenon_H2e6). zenon_intro zenon_H24b. zenon_intro zenon_H2e7. % 19.13/19.27 apply (zenon_and_s _ _ zenon_H2e7). zenon_intro zenon_H1c7. zenon_intro zenon_H2e8. % 19.13/19.27 apply (zenon_and_s _ _ zenon_H2e8). zenon_intro zenon_H6d. zenon_intro zenon_H2e9. % 19.13/19.27 apply (zenon_and_s _ _ zenon_H2e9). zenon_intro zenon_H1cf. zenon_intro zenon_H2ea. % 19.13/19.27 apply (zenon_and_s _ _ zenon_H2ea). zenon_intro zenon_H6f. zenon_intro zenon_H2eb. % 19.13/19.27 apply (zenon_and_s _ _ zenon_H2eb). zenon_intro zenon_H71. zenon_intro zenon_H2ec. % 19.13/19.27 apply (zenon_and_s _ _ zenon_H2ec). zenon_intro zenon_H1a4. zenon_intro zenon_H2ed. % 19.13/19.27 apply (zenon_and_s _ _ zenon_H2ed). zenon_intro zenon_H130. zenon_intro zenon_H62. % 19.13/19.27 apply (zenon_and_s _ _ ax4). zenon_intro zenon_Ha1. zenon_intro zenon_H2ee. % 19.13/19.27 apply (zenon_and_s _ _ zenon_H2ee). zenon_intro zenon_H149. zenon_intro zenon_H2ef. % 19.13/19.27 apply (zenon_and_s _ _ zenon_H2ef). zenon_intro zenon_H9a. zenon_intro zenon_H2f0. % 19.13/19.27 apply (zenon_and_s _ _ zenon_H2f0). zenon_intro zenon_H7c. zenon_intro zenon_H2f1. % 19.13/19.27 apply (zenon_and_s _ _ zenon_H2f1). zenon_intro zenon_H95. zenon_intro zenon_H12b. % 19.13/19.27 apply (zenon_and_s _ _ ax5). zenon_intro zenon_H3f. zenon_intro zenon_H2f2. % 19.13/19.27 apply (zenon_and_s _ _ zenon_H2f2). zenon_intro zenon_H10a. zenon_intro zenon_H2f3. % 19.13/19.27 apply (zenon_and_s _ _ zenon_H2f3). zenon_intro zenon_H173. zenon_intro zenon_H2f4. % 19.13/19.27 apply (zenon_and_s _ _ zenon_H2f4). zenon_intro zenon_H102. zenon_intro zenon_H2f5. % 19.13/19.27 apply (zenon_or_s _ _ zenon_H2f5); [ zenon_intro zenon_H2f7 | zenon_intro zenon_H2f6 ]. % 19.13/19.27 apply (zenon_and_s _ _ zenon_H2f7). zenon_intro zenon_H2f9. zenon_intro zenon_H2f8. % 19.13/19.27 apply (zenon_and_s _ _ zenon_H2f8). zenon_intro zenon_H2fb. zenon_intro zenon_H2fa. % 19.13/19.27 apply (zenon_and_s _ _ zenon_H2fa). zenon_intro zenon_H233. zenon_intro zenon_H2fc. % 19.13/19.27 apply (zenon_and_s _ _ zenon_H2fc). zenon_intro zenon_H204. zenon_intro zenon_H2fd. % 19.13/19.27 apply (zenon_and_s _ _ zenon_H2fd). zenon_intro zenon_H206. zenon_intro zenon_H2fe. % 19.13/19.27 apply (zenon_and_s _ _ zenon_H2fe). zenon_intro zenon_H205. zenon_intro zenon_H2ff. % 19.13/19.27 apply (zenon_and_s _ _ zenon_H2ff). zenon_intro zenon_H178. zenon_intro zenon_H300. % 19.13/19.27 apply (zenon_and_s _ _ zenon_H300). zenon_intro zenon_H179. zenon_intro zenon_H301. % 19.13/19.27 apply (zenon_and_s _ _ zenon_H301). zenon_intro zenon_H1ee. zenon_intro zenon_H302. % 19.13/19.27 apply (zenon_and_s _ _ zenon_H302). zenon_intro zenon_H182. zenon_intro zenon_H303. % 19.13/19.27 apply (zenon_and_s _ _ zenon_H303). zenon_intro zenon_H185. zenon_intro zenon_H304. % 19.13/19.27 apply (zenon_and_s _ _ zenon_H304). zenon_intro zenon_H94. zenon_intro zenon_H305. % 19.13/19.27 apply (zenon_and_s _ _ zenon_H305). zenon_intro zenon_H184. zenon_intro zenon_H306. % 19.13/19.27 apply (zenon_and_s _ _ zenon_H306). zenon_intro zenon_H1ed. zenon_intro zenon_H307. % 19.13/19.27 apply (zenon_and_s _ _ zenon_H307). zenon_intro zenon_H1a7. zenon_intro zenon_H1ec. % 19.13/19.27 apply (zenon_or_s _ _ zenon_H2fb); [ zenon_intro zenon_H20b | zenon_intro zenon_H7a ]. % 19.13/19.27 apply (zenon_or_s _ _ zenon_H233); [ zenon_intro zenon_H75 | zenon_intro zenon_H7b ]. % 19.13/19.27 apply (zenon_or_s _ _ zenon_H204); [ zenon_intro zenon_H76 | zenon_intro zenon_H3a ]. % 19.13/19.27 apply (zenon_or_s _ _ zenon_H74); [ zenon_intro zenon_H42 | zenon_intro zenon_H77 ]. % 19.13/19.27 exact (zenon_H3f zenon_H42). % 19.13/19.27 apply (zenon_or_s _ _ zenon_H77); [ zenon_intro zenon_H49 | zenon_intro zenon_H78 ]. % 19.13/19.27 exact (zenon_H20b zenon_H49). % 19.13/19.27 apply (zenon_or_s _ _ zenon_H78); [ zenon_intro zenon_H48 | zenon_intro zenon_H1e ]. % 19.13/19.27 exact (zenon_H75 zenon_H48). % 19.13/19.27 exact (zenon_H76 zenon_H1e). % 19.13/19.27 apply (zenon_or_s _ _ zenon_H206); [ zenon_intro zenon_H23 | zenon_intro zenon_H27 ]. % 19.13/19.27 apply (zenon_or_s _ _ zenon_H205); [ zenon_intro zenon_H24 | zenon_intro zenon_H9d ]. % 19.13/19.27 apply (zenon_or_s _ _ zenon_H178); [ zenon_intro zenon_H25 | zenon_intro zenon_H86 ]. % 19.13/19.27 apply (zenon_or_s _ _ zenon_H74); [ zenon_intro zenon_H42 | zenon_intro zenon_H77 ]. % 19.13/19.27 exact (zenon_H3f zenon_H42). % 19.13/19.27 apply (zenon_or_s _ _ zenon_H77); [ zenon_intro zenon_H49 | zenon_intro zenon_H78 ]. % 19.13/19.27 exact (zenon_H20b zenon_H49). % 19.13/19.27 apply (zenon_or_s _ _ zenon_H78); [ zenon_intro zenon_H48 | zenon_intro zenon_H1e ]. % 19.13/19.27 exact (zenon_H75 zenon_H48). % 19.13/19.27 apply (zenon_L2_); trivial. % 19.13/19.27 apply (zenon_or_s _ _ zenon_H179); [ zenon_intro zenon_H38 | zenon_intro zenon_H9e ]. % 19.13/19.27 apply (zenon_or_s _ _ zenon_H1ee); [ zenon_intro zenon_H30 | zenon_intro zenon_H34 ]. % 19.13/19.27 apply (zenon_or_s _ _ zenon_H182); [ zenon_intro zenon_H31 | zenon_intro zenon_Hed ]. % 19.13/19.27 apply (zenon_or_s _ _ zenon_H94); [ zenon_intro zenon_H32 | zenon_intro zenon_H3b ]. % 19.13/19.27 apply (zenon_L5_); trivial. % 19.13/19.27 apply (zenon_L6_); trivial. % 19.13/19.27 apply (zenon_or_s _ _ zenon_H185); [ zenon_intro zenon_H81 | zenon_intro zenon_Hee ]. % 19.13/19.27 apply (zenon_or_s _ _ zenon_H184); [ zenon_intro zenon_H40 | zenon_intro zenon_H44 ]. % 19.13/19.27 apply (zenon_L7_); trivial. % 19.13/19.27 apply (zenon_or_s _ _ zenon_H1ed); [ zenon_intro zenon_H1ad | zenon_intro zenon_Hac ]. % 19.13/19.27 apply (zenon_or_s _ _ zenon_H1a7); [ zenon_intro zenon_H18b | zenon_intro zenon_H148 ]. % 19.13/19.27 apply (zenon_or_s _ _ zenon_H74); [ zenon_intro zenon_H42 | zenon_intro zenon_H77 ]. % 19.13/19.27 exact (zenon_H3f zenon_H42). % 19.13/19.27 apply (zenon_or_s _ _ zenon_H77); [ zenon_intro zenon_H49 | zenon_intro zenon_H78 ]. % 19.13/19.27 exact (zenon_H20b zenon_H49). % 19.13/19.27 apply (zenon_or_s _ _ zenon_H78); [ zenon_intro zenon_H48 | zenon_intro zenon_H1e ]. % 19.13/19.27 exact (zenon_H75 zenon_H48). % 19.13/19.27 apply (zenon_or_s _ _ zenon_H22d); [ zenon_intro zenon_H7a | zenon_intro zenon_H22e ]. % 19.13/19.27 apply (zenon_L333_); trivial. % 19.13/19.27 apply (zenon_or_s _ _ zenon_H22e); [ zenon_intro zenon_Ha0 | zenon_intro zenon_H22f ]. % 19.13/19.27 apply (zenon_L702_); trivial. % 19.13/19.27 apply (zenon_or_s _ _ zenon_H22f); [ zenon_intro zenon_H122 | zenon_intro zenon_Hc3 ]. % 19.13/19.27 apply (zenon_or_s _ _ zenon_H183); [ zenon_intro zenon_H7b | zenon_intro zenon_H186 ]. % 19.13/19.27 apply (zenon_L566_); trivial. % 19.13/19.27 apply (zenon_or_s _ _ zenon_H186); [ zenon_intro zenon_H10f | zenon_intro zenon_H187 ]. % 19.13/19.27 apply (zenon_L703_); trivial. % 19.13/19.27 apply (zenon_or_s _ _ zenon_H187); [ zenon_intro zenon_H150 | zenon_intro zenon_Hcd ]. % 19.13/19.27 apply (zenon_L328_); trivial. % 19.13/19.27 apply (zenon_L428_); trivial. % 19.13/19.27 apply (zenon_L427_); trivial. % 19.13/19.27 apply (zenon_L423_); trivial. % 19.13/19.27 apply (zenon_L41_); trivial. % 19.13/19.27 apply (zenon_L58_); trivial. % 19.13/19.27 apply (zenon_L704_); trivial. % 19.13/19.27 apply (zenon_or_s _ _ zenon_H1ee); [ zenon_intro zenon_H30 | zenon_intro zenon_H34 ]. % 19.13/19.27 apply (zenon_or_s _ _ zenon_H184); [ zenon_intro zenon_H40 | zenon_intro zenon_H44 ]. % 19.13/19.27 apply (zenon_L7_); trivial. % 19.13/19.27 apply (zenon_or_s _ _ zenon_H235); [ zenon_intro zenon_H7a | zenon_intro zenon_H236 ]. % 19.13/19.27 apply (zenon_L333_); trivial. % 19.13/19.27 apply (zenon_or_s _ _ zenon_H236); [ zenon_intro zenon_H9d | zenon_intro zenon_H237 ]. % 19.13/19.27 apply (zenon_L695_); trivial. % 19.13/19.27 apply (zenon_or_s _ _ zenon_H237); [ zenon_intro zenon_Hed | zenon_intro zenon_Hac ]. % 19.13/19.27 apply (zenon_L706_); trivial. % 19.13/19.27 apply (zenon_L41_); trivial. % 19.13/19.27 apply (zenon_L704_); trivial. % 19.13/19.27 apply (zenon_L695_); trivial. % 19.13/19.27 apply (zenon_or_s _ _ zenon_H205); [ zenon_intro zenon_H24 | zenon_intro zenon_H9d ]. % 19.13/19.27 apply (zenon_or_s _ _ zenon_H178); [ zenon_intro zenon_H25 | zenon_intro zenon_H86 ]. % 19.13/19.27 apply (zenon_or_s _ _ zenon_H1ee); [ zenon_intro zenon_H30 | zenon_intro zenon_H34 ]. % 19.13/19.27 apply (zenon_or_s _ _ zenon_H182); [ zenon_intro zenon_H31 | zenon_intro zenon_Hed ]. % 19.13/19.27 apply (zenon_or_s _ _ zenon_H185); [ zenon_intro zenon_H81 | zenon_intro zenon_Hee ]. % 19.13/19.27 apply (zenon_or_s _ _ zenon_H1a7); [ zenon_intro zenon_H18b | zenon_intro zenon_H148 ]. % 19.13/19.27 apply (zenon_L694_); trivial. % 19.13/19.27 apply (zenon_or_s _ _ zenon_H74); [ zenon_intro zenon_H42 | zenon_intro zenon_H77 ]. % 19.13/19.27 exact (zenon_H3f zenon_H42). % 19.13/19.27 apply (zenon_or_s _ _ zenon_H77); [ zenon_intro zenon_H49 | zenon_intro zenon_H78 ]. % 19.13/19.27 exact (zenon_H20b zenon_H49). % 19.13/19.27 apply (zenon_or_s _ _ zenon_H78); [ zenon_intro zenon_H48 | zenon_intro zenon_H1e ]. % 19.13/19.27 exact (zenon_H75 zenon_H48). % 19.13/19.27 apply (zenon_or_s _ _ zenon_H235); [ zenon_intro zenon_H7a | zenon_intro zenon_H236 ]. % 19.13/19.27 apply (zenon_L35_); trivial. % 19.13/19.27 apply (zenon_or_s _ _ zenon_H236); [ zenon_intro zenon_H9d | zenon_intro zenon_H237 ]. % 19.13/19.27 apply (zenon_L262_); trivial. % 19.13/19.27 apply (zenon_or_s _ _ zenon_H237); [ zenon_intro zenon_Hed | zenon_intro zenon_Hac ]. % 19.13/19.27 apply (zenon_L423_); trivial. % 19.13/19.27 apply (zenon_L707_); trivial. % 19.13/19.27 apply (zenon_or_s _ _ zenon_H235); [ zenon_intro zenon_H7a | zenon_intro zenon_H236 ]. % 19.13/19.27 apply (zenon_L333_); trivial. % 19.13/19.27 apply (zenon_or_s _ _ zenon_H236); [ zenon_intro zenon_H9d | zenon_intro zenon_H237 ]. % 19.13/19.27 apply (zenon_L262_); trivial. % 19.13/19.27 apply (zenon_or_s _ _ zenon_H237); [ zenon_intro zenon_Hed | zenon_intro zenon_Hac ]. % 19.13/19.27 apply (zenon_L708_); trivial. % 19.13/19.27 apply (zenon_L712_); trivial. % 19.13/19.27 apply (zenon_L708_); trivial. % 19.13/19.27 apply (zenon_L332_); trivial. % 19.13/19.27 apply (zenon_L257_); trivial. % 19.13/19.27 apply (zenon_L262_); trivial. % 19.13/19.27 apply (zenon_L687_); trivial. % 19.13/19.27 apply (zenon_L456_); trivial. % 19.13/19.27 apply (zenon_or_s _ _ zenon_H2f6); [ zenon_intro zenon_H309 | zenon_intro zenon_H308 ]. % 19.13/19.27 apply (zenon_and_s _ _ zenon_H309). zenon_intro zenon_H30b. zenon_intro zenon_H30a. % 19.13/19.27 apply (zenon_and_s _ _ zenon_H30a). zenon_intro zenon_H265. zenon_intro zenon_H30c. % 19.13/19.27 apply (zenon_and_s _ _ zenon_H30c). zenon_intro zenon_H266. zenon_intro zenon_H30d. % 19.13/19.27 apply (zenon_and_s _ _ zenon_H30d). zenon_intro zenon_H25c. zenon_intro zenon_H30e. % 19.13/19.27 apply (zenon_and_s _ _ zenon_H30e). zenon_intro zenon_H25d. zenon_intro zenon_H30f. % 19.13/19.27 apply (zenon_and_s _ _ zenon_H30f). zenon_intro zenon_H311. zenon_intro zenon_H310. % 19.13/19.27 apply (zenon_and_s _ _ zenon_H310). zenon_intro zenon_H256. zenon_intro zenon_H312. % 19.13/19.27 apply (zenon_and_s _ _ zenon_H312). zenon_intro zenon_H258. zenon_intro zenon_H313. % 19.13/19.27 apply (zenon_and_s _ _ zenon_H313). zenon_intro zenon_H257. zenon_intro zenon_H314. % 19.13/19.27 apply (zenon_and_s _ _ zenon_H314). zenon_intro zenon_H262. zenon_intro zenon_H315. % 19.13/19.27 apply (zenon_and_s _ _ zenon_H315). zenon_intro zenon_H253. zenon_intro zenon_H316. % 19.13/19.27 apply (zenon_and_s _ _ zenon_H316). zenon_intro zenon_H263. zenon_intro zenon_H317. % 19.13/19.27 apply (zenon_and_s _ _ zenon_H317). zenon_intro zenon_H254. zenon_intro zenon_H318. % 19.13/19.27 apply (zenon_and_s _ _ zenon_H318). zenon_intro zenon_H261. zenon_intro zenon_H319. % 19.13/19.27 apply (zenon_and_s _ _ zenon_H319). zenon_intro zenon_H252. zenon_intro zenon_H264. % 19.13/19.27 apply (zenon_or_s _ _ zenon_H30b); [ zenon_intro zenon_H84 | zenon_intro zenon_H49 ]. % 19.13/19.27 apply (zenon_or_s _ _ zenon_H265); [ zenon_intro zenon_Ha4 | zenon_intro zenon_Ha0 ]. % 19.13/19.27 apply (zenon_or_s _ _ zenon_H266); [ zenon_intro zenon_H20d | zenon_intro zenon_H10f ]. % 19.13/19.27 apply (zenon_or_s _ _ zenon_H25c); [ zenon_intro zenon_H231 | zenon_intro zenon_H99 ]. % 19.13/19.27 apply (zenon_or_s _ _ zenon_H25d); [ zenon_intro zenon_H1ef | zenon_intro zenon_H29 ]. % 19.13/19.27 apply (zenon_or_s _ _ zenon_H74); [ zenon_intro zenon_H42 | zenon_intro zenon_H77 ]. % 19.13/19.27 exact (zenon_H3f zenon_H42). % 19.13/19.27 apply (zenon_or_s _ _ zenon_H77); [ zenon_intro zenon_H49 | zenon_intro zenon_H78 ]. % 19.13/19.27 apply (zenon_L945_); trivial. % 19.13/19.27 apply (zenon_or_s _ _ zenon_H78); [ zenon_intro zenon_H48 | zenon_intro zenon_H1e ]. % 19.13/19.27 apply (zenon_L946_); trivial. % 19.13/19.27 apply (zenon_L947_); trivial. % 19.13/19.27 apply (zenon_or_s _ _ zenon_H74); [ zenon_intro zenon_H42 | zenon_intro zenon_H77 ]. % 19.13/19.27 exact (zenon_H3f zenon_H42). % 19.13/19.27 apply (zenon_or_s _ _ zenon_H77); [ zenon_intro zenon_H49 | zenon_intro zenon_H78 ]. % 19.13/19.27 apply (zenon_L23_); trivial. % 19.13/19.27 apply (zenon_or_s _ _ zenon_H78); [ zenon_intro zenon_H48 | zenon_intro zenon_H1e ]. % 19.13/19.27 apply (zenon_L946_); trivial. % 19.13/19.27 apply (zenon_L947_); trivial. % 19.13/19.27 apply (zenon_or_s _ _ zenon_H25d); [ zenon_intro zenon_H1ef | zenon_intro zenon_H29 ]. % 19.13/19.27 apply (zenon_or_s _ _ zenon_H256); [ zenon_intro zenon_H24d | zenon_intro zenon_H110 ]. % 19.13/19.27 apply (zenon_or_s _ _ zenon_H258); [ zenon_intro zenon_H24e | zenon_intro zenon_H13f ]. % 19.13/19.27 apply (zenon_L713_); trivial. % 19.13/19.27 apply (zenon_L108_); trivial. % 19.13/19.27 apply (zenon_or_s _ _ zenon_H258); [ zenon_intro zenon_H24e | zenon_intro zenon_H13f ]. % 19.13/19.27 apply (zenon_or_s _ _ zenon_H257); [ zenon_intro zenon_H1db | zenon_intro zenon_H36 ]. % 19.13/19.27 apply (zenon_or_s _ _ zenon_H254); [ zenon_intro zenon_Had | zenon_intro zenon_H1b1 ]. % 19.13/19.27 apply (zenon_L948_); trivial. % 19.13/19.27 apply (zenon_L950_); trivial. % 19.13/19.27 apply (zenon_L552_); trivial. % 19.13/19.27 apply (zenon_L166_); trivial. % 19.13/19.27 apply (zenon_or_s _ _ zenon_H256); [ zenon_intro zenon_H24d | zenon_intro zenon_H110 ]. % 19.13/19.27 apply (zenon_or_s _ _ zenon_H258); [ zenon_intro zenon_H24e | zenon_intro zenon_H13f ]. % 19.13/19.27 apply (zenon_or_s _ _ zenon_H257); [ zenon_intro zenon_H1db | zenon_intro zenon_H36 ]. % 19.13/19.27 apply (zenon_or_s _ _ zenon_H1d8); [ zenon_intro zenon_H10f | zenon_intro zenon_H1d9 ]. % 19.13/19.27 apply (zenon_L975_); trivial. % 19.13/19.27 apply (zenon_or_s _ _ zenon_H1d9); [ zenon_intro zenon_H110 | zenon_intro zenon_H1da ]. % 19.13/19.27 apply (zenon_L354_); trivial. % 19.13/19.27 apply (zenon_or_s _ _ zenon_H1da); [ zenon_intro zenon_H1ca | zenon_intro zenon_H14d ]. % 19.13/19.27 apply (zenon_L982_); trivial. % 19.13/19.27 apply (zenon_L385_); trivial. % 19.13/19.27 apply (zenon_L965_); trivial. % 19.13/19.27 apply (zenon_L108_); trivial. % 19.13/19.27 apply (zenon_L354_); trivial. % 19.13/19.27 apply (zenon_L975_); trivial. % 19.13/19.27 apply (zenon_or_s _ _ zenon_H266); [ zenon_intro zenon_H20d | zenon_intro zenon_H10f ]. % 19.13/19.27 apply (zenon_or_s _ _ zenon_H25c); [ zenon_intro zenon_H231 | zenon_intro zenon_H99 ]. % 19.13/19.27 apply (zenon_or_s _ _ zenon_H25d); [ zenon_intro zenon_H1ef | zenon_intro zenon_H29 ]. % 19.13/19.27 apply (zenon_or_s _ _ zenon_H256); [ zenon_intro zenon_H24d | zenon_intro zenon_H110 ]. % 19.13/19.27 apply (zenon_or_s _ _ zenon_H258); [ zenon_intro zenon_H24e | zenon_intro zenon_H13f ]. % 19.13/19.27 apply (zenon_L713_); trivial. % 19.13/19.27 apply (zenon_or_s _ _ zenon_H257); [ zenon_intro zenon_H1db | zenon_intro zenon_H36 ]. % 19.13/19.27 apply (zenon_or_s _ _ zenon_H262); [ zenon_intro zenon_H24f | zenon_intro zenon_Ha5 ]. % 19.13/19.27 apply (zenon_or_s _ _ zenon_H253); [ zenon_intro zenon_H198 | zenon_intro zenon_H1ca ]. % 19.13/19.27 apply (zenon_L951_); trivial. % 19.13/19.27 apply (zenon_or_s _ _ zenon_H254); [ zenon_intro zenon_Had | zenon_intro zenon_H1b1 ]. % 19.13/19.27 apply (zenon_L983_); trivial. % 19.13/19.27 apply (zenon_or_s _ _ zenon_H264); [ zenon_intro zenon_Hc7 | zenon_intro zenon_H161 ]. % 19.13/19.27 apply (zenon_or_s _ _ zenon_H74); [ zenon_intro zenon_H42 | zenon_intro zenon_H77 ]. % 19.13/19.27 exact (zenon_H3f zenon_H42). % 19.13/19.27 apply (zenon_or_s _ _ zenon_H77); [ zenon_intro zenon_H49 | zenon_intro zenon_H78 ]. % 19.13/19.27 apply (zenon_L984_); trivial. % 19.13/19.27 apply (zenon_or_s _ _ zenon_H78); [ zenon_intro zenon_H48 | zenon_intro zenon_H1e ]. % 19.13/19.27 apply (zenon_or_s _ _ zenon_H3e); [ zenon_intro zenon_H42 | zenon_intro zenon_H41 ]. % 19.13/19.27 exact (zenon_H3f zenon_H42). % 19.13/19.27 apply (zenon_or_s _ _ zenon_H41); [ zenon_intro zenon_H27 | zenon_intro zenon_H43 ]. % 19.13/19.27 apply (zenon_or_s _ _ zenon_H235); [ zenon_intro zenon_H7a | zenon_intro zenon_H236 ]. % 19.13/19.27 exact (zenon_H84 zenon_H7a). % 19.13/19.27 apply (zenon_or_s _ _ zenon_H236); [ zenon_intro zenon_H9d | zenon_intro zenon_H237 ]. % 19.13/19.27 exact (zenon_H1ef zenon_H9d). % 19.13/19.27 apply (zenon_or_s _ _ zenon_H237); [ zenon_intro zenon_Hed | zenon_intro zenon_Hac ]. % 19.13/19.27 exact (zenon_H1db zenon_Hed). % 19.13/19.27 apply (zenon_or_s _ _ zenon_H183); [ zenon_intro zenon_H7b | zenon_intro zenon_H186 ]. % 19.13/19.27 apply (zenon_or_s _ _ zenon_H168); [ zenon_intro zenon_H3a | zenon_intro zenon_H169 ]. % 19.13/19.27 apply (zenon_or_s _ _ zenon_H128); [ zenon_intro zenon_H9d | zenon_intro zenon_H129 ]. % 19.13/19.27 exact (zenon_H1ef zenon_H9d). % 19.13/19.27 apply (zenon_or_s _ _ zenon_H129); [ zenon_intro zenon_H10d | zenon_intro zenon_H12a ]. % 19.13/19.27 exact (zenon_H10a zenon_H10d). % 19.13/19.27 apply (zenon_or_s _ _ zenon_H12a); [ zenon_intro zenon_Hf0 | zenon_intro zenon_Hd6 ]. % 19.13/19.27 exact (zenon_H24d zenon_Hf0). % 19.13/19.27 apply (zenon_or_s _ _ zenon_H18c); [ zenon_intro zenon_H86 | zenon_intro zenon_H18d ]. % 19.13/19.27 apply (zenon_L241_); trivial. % 19.13/19.27 apply (zenon_or_s _ _ zenon_H18d); [ zenon_intro zenon_H110 | zenon_intro zenon_H18e ]. % 19.13/19.27 apply (zenon_L1012_); trivial. % 19.13/19.27 apply (zenon_or_s _ _ zenon_H18e); [ zenon_intro zenon_H113 | zenon_intro zenon_Hd7 ]. % 19.13/19.27 apply (zenon_or_s _ _ zenon_H2f); [ zenon_intro zenon_H34 | zenon_intro zenon_H33 ]. % 19.13/19.27 apply (zenon_L332_); trivial. % 19.13/19.27 apply (zenon_or_s _ _ zenon_H33); [ zenon_intro zenon_H36 | zenon_intro zenon_H35 ]. % 19.13/19.27 apply (zenon_L646_); trivial. % 19.13/19.27 apply (zenon_or_s _ _ zenon_H35); [ zenon_intro zenon_H2c | zenon_intro zenon_H37 ]. % 19.13/19.27 apply (zenon_L1014_); trivial. % 19.13/19.27 apply (zenon_or_s _ _ zenon_H145); [ zenon_intro zenon_Hcd | zenon_intro zenon_H146 ]. % 19.13/19.27 apply (zenon_L375_); trivial. % 19.13/19.27 apply (zenon_or_s _ _ zenon_H146); [ zenon_intro zenon_Hd7 | zenon_intro zenon_H147 ]. % 19.13/19.27 apply (zenon_L101_); trivial. % 19.13/19.27 apply (zenon_or_s _ _ zenon_H147); [ zenon_intro zenon_H11d | zenon_intro zenon_Hf6 ]. % 19.13/19.27 apply (zenon_L224_); trivial. % 19.13/19.27 apply (zenon_L1017_); trivial. % 19.13/19.27 apply (zenon_L101_); trivial. % 19.13/19.27 apply (zenon_or_s _ _ zenon_H169); [ zenon_intro zenon_H99 | zenon_intro zenon_H16a ]. % 19.13/19.27 apply (zenon_L108_); trivial. % 19.13/19.27 apply (zenon_or_s _ _ zenon_H16a); [ zenon_intro zenon_Ha9 | zenon_intro zenon_He3 ]. % 19.13/19.27 apply (zenon_L264_); trivial. % 19.13/19.27 apply (zenon_or_s _ _ zenon_H128); [ zenon_intro zenon_H9d | zenon_intro zenon_H129 ]. % 19.13/19.27 exact (zenon_H1ef zenon_H9d). % 19.13/19.27 apply (zenon_or_s _ _ zenon_H129); [ zenon_intro zenon_H10d | zenon_intro zenon_H12a ]. % 19.13/19.27 exact (zenon_H10a zenon_H10d). % 19.13/19.27 apply (zenon_or_s _ _ zenon_H12a); [ zenon_intro zenon_Hf0 | zenon_intro zenon_Hd6 ]. % 19.13/19.27 exact (zenon_H24d zenon_Hf0). % 19.13/19.27 apply (zenon_or_s _ _ zenon_H18c); [ zenon_intro zenon_H86 | zenon_intro zenon_H18d ]. % 19.13/19.27 apply (zenon_L257_); trivial. % 19.13/19.27 apply (zenon_or_s _ _ zenon_H18d); [ zenon_intro zenon_H110 | zenon_intro zenon_H18e ]. % 19.13/19.27 apply (zenon_L166_); trivial. % 19.13/19.27 apply (zenon_or_s _ _ zenon_H18e); [ zenon_intro zenon_H113 | zenon_intro zenon_Hd7 ]. % 19.13/19.27 apply (zenon_L1016_); trivial. % 19.13/19.27 apply (zenon_L101_); trivial. % 19.13/19.27 apply (zenon_or_s _ _ zenon_H186); [ zenon_intro zenon_H10f | zenon_intro zenon_H187 ]. % 19.13/19.27 apply (zenon_L1018_); trivial. % 19.13/19.27 apply (zenon_or_s _ _ zenon_H187); [ zenon_intro zenon_H150 | zenon_intro zenon_Hcd ]. % 19.13/19.27 apply (zenon_L719_); trivial. % 19.13/19.27 apply (zenon_L1019_); trivial. % 19.13/19.27 apply (zenon_or_s _ _ zenon_H43); [ zenon_intro zenon_H34 | zenon_intro zenon_H44 ]. % 19.13/19.27 apply (zenon_or_s _ _ zenon_H22); [ zenon_intro zenon_H27 | zenon_intro zenon_H26 ]. % 19.13/19.27 apply (zenon_L332_); trivial. % 19.13/19.27 apply (zenon_or_s _ _ zenon_H26); [ zenon_intro zenon_H29 | zenon_intro zenon_H28 ]. % 19.13/19.27 apply (zenon_L348_); trivial. % 19.13/19.27 apply (zenon_or_s _ _ zenon_H28); [ zenon_intro zenon_H2a | zenon_intro zenon_H1f ]. % 19.13/19.27 apply (zenon_L334_); trivial. % 19.13/19.27 apply (zenon_or_s _ _ zenon_H128); [ zenon_intro zenon_H9d | zenon_intro zenon_H129 ]. % 19.13/19.27 exact (zenon_H1ef zenon_H9d). % 19.13/19.27 apply (zenon_or_s _ _ zenon_H129); [ zenon_intro zenon_H10d | zenon_intro zenon_H12a ]. % 19.13/19.27 exact (zenon_H10a zenon_H10d). % 19.13/19.27 apply (zenon_or_s _ _ zenon_H12a); [ zenon_intro zenon_Hf0 | zenon_intro zenon_Hd6 ]. % 19.13/19.27 exact (zenon_H24d zenon_Hf0). % 19.13/19.27 apply (zenon_or_s _ _ zenon_H136); [ zenon_intro zenon_He3 | zenon_intro zenon_H137 ]. % 19.13/19.27 apply (zenon_L571_); trivial. % 19.13/19.27 apply (zenon_or_s _ _ zenon_H137); [ zenon_intro zenon_Hdc | zenon_intro zenon_H138 ]. % 19.13/19.27 apply (zenon_L83_); trivial. % 19.13/19.27 apply (zenon_or_s _ _ zenon_H138); [ zenon_intro zenon_Hdd | zenon_intro zenon_H105 ]. % 19.13/19.27 apply (zenon_L1020_); trivial. % 19.13/19.27 exact (zenon_H102 zenon_H105). % 19.13/19.27 apply (zenon_L346_); trivial. % 19.13/19.27 apply (zenon_or_s _ _ zenon_H3e); [ zenon_intro zenon_H42 | zenon_intro zenon_H41 ]. % 19.13/19.27 exact (zenon_H3f zenon_H42). % 19.13/19.27 apply (zenon_or_s _ _ zenon_H41); [ zenon_intro zenon_H27 | zenon_intro zenon_H43 ]. % 19.13/19.27 apply (zenon_or_s _ _ zenon_H235); [ zenon_intro zenon_H7a | zenon_intro zenon_H236 ]. % 19.13/19.27 exact (zenon_H84 zenon_H7a). % 19.13/19.27 apply (zenon_or_s _ _ zenon_H236); [ zenon_intro zenon_H9d | zenon_intro zenon_H237 ]. % 19.13/19.27 exact (zenon_H1ef zenon_H9d). % 19.13/19.27 apply (zenon_or_s _ _ zenon_H237); [ zenon_intro zenon_Hed | zenon_intro zenon_Hac ]. % 19.13/19.27 exact (zenon_H1db zenon_Hed). % 19.13/19.27 apply (zenon_or_s _ _ zenon_H128); [ zenon_intro zenon_H9d | zenon_intro zenon_H129 ]. % 19.13/19.27 exact (zenon_H1ef zenon_H9d). % 19.13/19.27 apply (zenon_or_s _ _ zenon_H129); [ zenon_intro zenon_H10d | zenon_intro zenon_H12a ]. % 19.13/19.27 exact (zenon_H10a zenon_H10d). % 19.13/19.27 apply (zenon_or_s _ _ zenon_H12a); [ zenon_intro zenon_Hf0 | zenon_intro zenon_Hd6 ]. % 19.13/19.27 exact (zenon_H24d zenon_Hf0). % 19.13/19.27 apply (zenon_or_s _ _ zenon_H18c); [ zenon_intro zenon_H86 | zenon_intro zenon_H18d ]. % 19.13/19.27 apply (zenon_L257_); trivial. % 19.13/19.27 apply (zenon_or_s _ _ zenon_H18d); [ zenon_intro zenon_H110 | zenon_intro zenon_H18e ]. % 19.13/19.27 apply (zenon_L1012_); trivial. % 19.13/19.27 apply (zenon_or_s _ _ zenon_H18e); [ zenon_intro zenon_H113 | zenon_intro zenon_Hd7 ]. % 19.13/19.27 apply (zenon_or_s _ _ zenon_H2f); [ zenon_intro zenon_H34 | zenon_intro zenon_H33 ]. % 19.13/19.27 apply (zenon_L332_); trivial. % 19.13/19.27 apply (zenon_or_s _ _ zenon_H33); [ zenon_intro zenon_H36 | zenon_intro zenon_H35 ]. % 19.13/19.27 apply (zenon_L646_); trivial. % 19.13/19.27 apply (zenon_or_s _ _ zenon_H35); [ zenon_intro zenon_H2c | zenon_intro zenon_H37 ]. % 19.13/19.27 apply (zenon_L1014_); trivial. % 19.13/19.27 apply (zenon_L367_); trivial. % 19.13/19.27 apply (zenon_L101_); trivial. % 19.13/19.27 apply (zenon_or_s _ _ zenon_H43); [ zenon_intro zenon_H34 | zenon_intro zenon_H44 ]. % 19.13/19.27 apply (zenon_or_s _ _ zenon_H235); [ zenon_intro zenon_H7a | zenon_intro zenon_H236 ]. % 19.13/19.27 exact (zenon_H84 zenon_H7a). % 19.13/19.27 apply (zenon_or_s _ _ zenon_H236); [ zenon_intro zenon_H9d | zenon_intro zenon_H237 ]. % 19.13/19.27 exact (zenon_H1ef zenon_H9d). % 19.13/19.27 apply (zenon_or_s _ _ zenon_H237); [ zenon_intro zenon_Hed | zenon_intro zenon_Hac ]. % 19.13/19.27 exact (zenon_H1db zenon_Hed). % 19.13/19.27 apply (zenon_or_s _ _ zenon_H168); [ zenon_intro zenon_H3a | zenon_intro zenon_H169 ]. % 19.13/19.27 apply (zenon_L1024_); trivial. % 19.13/19.27 apply (zenon_or_s _ _ zenon_H169); [ zenon_intro zenon_H99 | zenon_intro zenon_H16a ]. % 19.13/19.27 apply (zenon_L108_); trivial. % 19.13/19.27 apply (zenon_or_s _ _ zenon_H16a); [ zenon_intro zenon_Ha9 | zenon_intro zenon_He3 ]. % 19.13/19.27 apply (zenon_L1025_); trivial. % 19.13/19.27 apply (zenon_L1026_); trivial. % 19.13/19.27 apply (zenon_L346_); trivial. % 19.13/19.27 apply (zenon_L110_); trivial. % 19.13/19.27 apply (zenon_L357_); trivial. % 19.13/19.27 apply (zenon_or_s _ _ zenon_H262); [ zenon_intro zenon_H24f | zenon_intro zenon_Ha5 ]. % 19.13/19.27 apply (zenon_or_s _ _ zenon_H253); [ zenon_intro zenon_H198 | zenon_intro zenon_H1ca ]. % 19.13/19.27 apply (zenon_or_s _ _ zenon_H263); [ zenon_intro zenon_H255 | zenon_intro zenon_Ha6 ]. % 19.13/19.27 apply (zenon_or_s _ _ zenon_H254); [ zenon_intro zenon_Had | zenon_intro zenon_H1b1 ]. % 19.13/19.27 apply (zenon_L1027_); trivial. % 19.13/19.27 apply (zenon_L647_); trivial. % 19.13/19.27 apply (zenon_L95_); trivial. % 19.13/19.27 apply (zenon_or_s _ _ zenon_H254); [ zenon_intro zenon_Had | zenon_intro zenon_H1b1 ]. % 19.13/19.27 apply (zenon_L983_); trivial. % 19.13/19.27 apply (zenon_L647_); trivial. % 19.13/19.27 apply (zenon_L357_); trivial. % 19.13/19.27 apply (zenon_L1012_); trivial. % 19.13/19.27 apply (zenon_L1048_); trivial. % 19.13/19.27 apply (zenon_L403_); trivial. % 19.13/19.27 apply (zenon_L1018_); trivial. % 19.13/19.27 apply (zenon_L984_); trivial. % 19.13/19.27 apply (zenon_or_s _ _ zenon_H308); [ zenon_intro zenon_H31b | zenon_intro zenon_H31a ]. % 19.13/19.27 apply (zenon_and_s _ _ zenon_H31b). zenon_intro zenon_H31d. zenon_intro zenon_H31c. % 19.13/19.27 apply (zenon_and_s _ _ zenon_H31c). zenon_intro zenon_H27d. zenon_intro zenon_H31e. % 19.13/19.27 apply (zenon_and_s _ _ zenon_H31e). zenon_intro zenon_H27e. zenon_intro zenon_H31f. % 19.13/19.27 apply (zenon_and_s _ _ zenon_H31f). zenon_intro zenon_H27c. zenon_intro zenon_H320. % 19.13/19.27 apply (zenon_and_s _ _ zenon_H320). zenon_intro zenon_H27a. zenon_intro zenon_H321. % 19.13/19.27 apply (zenon_and_s _ _ zenon_H321). zenon_intro zenon_H27b. zenon_intro zenon_H322. % 19.13/19.27 apply (zenon_and_s _ _ zenon_H322). zenon_intro zenon_H275. zenon_intro zenon_H323. % 19.13/19.27 apply (zenon_and_s _ _ zenon_H323). zenon_intro zenon_H279. zenon_intro zenon_H324. % 19.13/19.27 apply (zenon_and_s _ _ zenon_H324). zenon_intro zenon_H276. zenon_intro zenon_H325. % 19.13/19.27 apply (zenon_and_s _ _ zenon_H325). zenon_intro zenon_H271. zenon_intro zenon_H326. % 19.13/19.27 apply (zenon_and_s _ _ zenon_H326). zenon_intro zenon_H328. zenon_intro zenon_H327. % 19.13/19.27 apply (zenon_and_s _ _ zenon_H327). zenon_intro zenon_H277. zenon_intro zenon_H329. % 19.13/19.27 apply (zenon_and_s _ _ zenon_H329). zenon_intro zenon_H270. zenon_intro zenon_H32a. % 19.13/19.27 apply (zenon_and_s _ _ zenon_H32a). zenon_intro zenon_H26f. zenon_intro zenon_H32b. % 19.13/19.27 apply (zenon_and_s _ _ zenon_H32b). zenon_intro zenon_H273. zenon_intro zenon_H278. % 19.13/19.27 apply (zenon_or_s _ _ zenon_H31d); [ zenon_intro zenon_H80 | zenon_intro zenon_H48 ]. % 19.13/19.27 apply (zenon_or_s _ _ zenon_H27d); [ zenon_intro zenon_H26d | zenon_intro zenon_H122 ]. % 19.13/19.27 apply (zenon_or_s _ _ zenon_H27e); [ zenon_intro zenon_H1fd | zenon_intro zenon_H150 ]. % 19.13/19.27 apply (zenon_or_s _ _ zenon_H27c); [ zenon_intro zenon_H12e | zenon_intro zenon_Ha9 ]. % 19.13/19.27 apply (zenon_or_s _ _ zenon_H27a); [ zenon_intro zenon_H177 | zenon_intro zenon_H2a ]. % 19.13/19.27 apply (zenon_or_s _ _ zenon_H27b); [ zenon_intro zenon_H20c | zenon_intro zenon_Hf0 ]. % 19.13/19.27 apply (zenon_or_s _ _ zenon_H275); [ zenon_intro zenon_H114 | zenon_intro zenon_H113 ]. % 19.13/19.27 apply (zenon_or_s _ _ zenon_H279); [ zenon_intro zenon_H14c | zenon_intro zenon_H16c ]. % 19.13/19.27 apply (zenon_L1049_); trivial. % 19.13/19.27 apply (zenon_or_s _ _ zenon_H276); [ zenon_intro zenon_Hef | zenon_intro zenon_H2c ]. % 19.13/19.27 apply (zenon_L1054_); trivial. % 19.13/19.27 apply (zenon_or_s _ _ zenon_H271); [ zenon_intro zenon_H26e | zenon_intro zenon_Hf1 ]. % 19.13/19.27 apply (zenon_L1057_); trivial. % 19.13/19.27 apply (zenon_L1058_); trivial. % 19.13/19.27 apply (zenon_or_s _ _ zenon_H279); [ zenon_intro zenon_H14c | zenon_intro zenon_H16c ]. % 19.13/19.27 apply (zenon_or_s _ _ zenon_H276); [ zenon_intro zenon_Hef | zenon_intro zenon_H2c ]. % 19.13/19.27 apply (zenon_or_s _ _ zenon_H271); [ zenon_intro zenon_H26e | zenon_intro zenon_Hf1 ]. % 19.13/19.27 apply (zenon_L1050_); trivial. % 19.13/19.27 apply (zenon_or_s _ _ zenon_H270); [ zenon_intro zenon_H14b | zenon_intro zenon_H61 ]. % 19.13/19.27 apply (zenon_L1052_); trivial. % 19.13/19.27 apply (zenon_or_s _ _ zenon_H74); [ zenon_intro zenon_H42 | zenon_intro zenon_H77 ]. % 19.13/19.27 exact (zenon_H3f zenon_H42). % 19.13/19.27 apply (zenon_or_s _ _ zenon_H77); [ zenon_intro zenon_H49 | zenon_intro zenon_H78 ]. % 19.13/19.27 apply (zenon_or_s _ _ zenon_H22d); [ zenon_intro zenon_H7a | zenon_intro zenon_H22e ]. % 19.13/19.27 apply (zenon_L1059_); trivial. % 19.13/19.27 apply (zenon_or_s _ _ zenon_H22e); [ zenon_intro zenon_Ha0 | zenon_intro zenon_H22f ]. % 19.13/19.27 apply (zenon_L38_); trivial. % 19.13/19.27 apply (zenon_or_s _ _ zenon_H22f); [ zenon_intro zenon_H122 | zenon_intro zenon_Hc3 ]. % 19.13/19.27 apply (zenon_L246_); trivial. % 19.13/19.27 apply (zenon_L1060_); trivial. % 19.13/19.27 apply (zenon_or_s _ _ zenon_H78); [ zenon_intro zenon_H48 | zenon_intro zenon_H1e ]. % 19.13/19.27 apply (zenon_L342_); trivial. % 19.13/19.27 apply (zenon_L1061_); trivial. % 19.13/19.27 apply (zenon_or_s _ _ zenon_H270); [ zenon_intro zenon_H14b | zenon_intro zenon_H61 ]. % 19.13/19.27 apply (zenon_or_s _ _ zenon_H26f); [ zenon_intro zenon_H194 | zenon_intro zenon_Hba ]. % 19.13/19.27 apply (zenon_L1051_); trivial. % 19.13/19.27 apply (zenon_or_s _ _ zenon_H74); [ zenon_intro zenon_H42 | zenon_intro zenon_H77 ]. % 19.13/19.27 exact (zenon_H3f zenon_H42). % 19.13/19.27 apply (zenon_or_s _ _ zenon_H77); [ zenon_intro zenon_H49 | zenon_intro zenon_H78 ]. % 19.13/19.27 apply (zenon_or_s _ _ zenon_H22d); [ zenon_intro zenon_H7a | zenon_intro zenon_H22e ]. % 19.13/19.27 apply (zenon_L1059_); trivial. % 19.13/19.27 apply (zenon_or_s _ _ zenon_H22e); [ zenon_intro zenon_Ha0 | zenon_intro zenon_H22f ]. % 19.13/19.27 apply (zenon_L38_); trivial. % 19.13/19.27 apply (zenon_or_s _ _ zenon_H22f); [ zenon_intro zenon_H122 | zenon_intro zenon_Hc3 ]. % 19.13/19.27 apply (zenon_L317_); trivial. % 19.13/19.27 apply (zenon_L1060_); trivial. % 19.13/19.27 apply (zenon_or_s _ _ zenon_H78); [ zenon_intro zenon_H48 | zenon_intro zenon_H1e ]. % 19.13/19.27 apply (zenon_L1204_); trivial. % 19.13/19.27 apply (zenon_L1061_); trivial. % 19.13/19.27 apply (zenon_L146_); trivial. % 19.13/19.27 apply (zenon_L116_); trivial. % 19.13/19.27 apply (zenon_or_s _ _ zenon_H275); [ zenon_intro zenon_H114 | zenon_intro zenon_H113 ]. % 19.13/19.27 apply (zenon_or_s _ _ zenon_H279); [ zenon_intro zenon_H14c | zenon_intro zenon_H16c ]. % 19.13/19.27 apply (zenon_or_s _ _ zenon_H276); [ zenon_intro zenon_Hef | zenon_intro zenon_H2c ]. % 19.13/19.27 apply (zenon_L1205_); trivial. % 19.13/19.27 apply (zenon_or_s _ _ zenon_H277); [ zenon_intro zenon_H274 | zenon_intro zenon_Haa ]. % 19.13/19.27 apply (zenon_L1206_); trivial. % 19.13/19.27 apply (zenon_L1208_); trivial. % 19.13/19.27 apply (zenon_L167_); trivial. % 19.13/19.27 apply (zenon_L68_); trivial. % 19.13/19.27 apply (zenon_or_s _ _ zenon_H27b); [ zenon_intro zenon_H20c | zenon_intro zenon_Hf0 ]. % 19.13/19.27 apply (zenon_or_s _ _ zenon_H275); [ zenon_intro zenon_H114 | zenon_intro zenon_H113 ]. % 19.13/19.27 apply (zenon_or_s _ _ zenon_H279); [ zenon_intro zenon_H14c | zenon_intro zenon_H16c ]. % 19.13/19.27 apply (zenon_or_s _ _ zenon_H74); [ zenon_intro zenon_H42 | zenon_intro zenon_H77 ]. % 19.13/19.27 exact (zenon_H3f zenon_H42). % 19.13/19.27 apply (zenon_or_s _ _ zenon_H77); [ zenon_intro zenon_H49 | zenon_intro zenon_H78 ]. % 19.13/19.27 apply (zenon_or_s _ _ zenon_H22d); [ zenon_intro zenon_H7a | zenon_intro zenon_H22e ]. % 19.13/19.27 apply (zenon_L1059_); trivial. % 19.13/19.27 apply (zenon_or_s _ _ zenon_H22e); [ zenon_intro zenon_Ha0 | zenon_intro zenon_H22f ]. % 19.13/19.27 apply (zenon_L38_); trivial. % 19.13/19.27 apply (zenon_or_s _ _ zenon_H22f); [ zenon_intro zenon_H122 | zenon_intro zenon_Hc3 ]. % 19.13/19.27 apply (zenon_L1216_); trivial. % 19.13/19.27 apply (zenon_L1060_); trivial. % 19.13/19.27 apply (zenon_or_s _ _ zenon_H78); [ zenon_intro zenon_H48 | zenon_intro zenon_H1e ]. % 19.13/19.27 apply (zenon_L1232_); trivial. % 19.13/19.27 apply (zenon_L1061_); trivial. % 19.13/19.27 apply (zenon_L521_); trivial. % 19.13/19.27 apply (zenon_L542_); trivial. % 19.13/19.27 apply (zenon_or_s _ _ zenon_H276); [ zenon_intro zenon_Hef | zenon_intro zenon_H2c ]. % 19.13/19.27 apply (zenon_L1205_); trivial. % 19.13/19.27 apply (zenon_L3_); trivial. % 19.13/19.27 apply (zenon_or_s _ _ zenon_H27a); [ zenon_intro zenon_H177 | zenon_intro zenon_H2a ]. % 19.13/19.27 apply (zenon_or_s _ _ zenon_H27b); [ zenon_intro zenon_H20c | zenon_intro zenon_Hf0 ]. % 19.13/19.27 apply (zenon_or_s _ _ zenon_H275); [ zenon_intro zenon_H114 | zenon_intro zenon_H113 ]. % 19.13/19.27 apply (zenon_or_s _ _ zenon_H279); [ zenon_intro zenon_H14c | zenon_intro zenon_H16c ]. % 19.13/19.27 apply (zenon_L1049_); trivial. % 19.13/19.27 apply (zenon_or_s _ _ zenon_H276); [ zenon_intro zenon_Hef | zenon_intro zenon_H2c ]. % 19.13/19.27 apply (zenon_L1054_); trivial. % 19.13/19.27 apply (zenon_L1234_); trivial. % 19.13/19.27 apply (zenon_or_s _ _ zenon_H279); [ zenon_intro zenon_H14c | zenon_intro zenon_H16c ]. % 19.13/19.27 apply (zenon_or_s _ _ zenon_H276); [ zenon_intro zenon_Hef | zenon_intro zenon_H2c ]. % 19.13/19.27 apply (zenon_or_s _ _ zenon_H271); [ zenon_intro zenon_H26e | zenon_intro zenon_Hf1 ]. % 19.13/19.27 apply (zenon_L1050_); trivial. % 19.13/19.27 apply (zenon_or_s _ _ zenon_H270); [ zenon_intro zenon_H14b | zenon_intro zenon_H61 ]. % 19.13/19.27 apply (zenon_L1052_); trivial. % 19.13/19.27 apply (zenon_or_s _ _ zenon_H74); [ zenon_intro zenon_H42 | zenon_intro zenon_H77 ]. % 19.13/19.27 exact (zenon_H3f zenon_H42). % 19.13/19.27 apply (zenon_or_s _ _ zenon_H77); [ zenon_intro zenon_H49 | zenon_intro zenon_H78 ]. % 19.13/19.27 apply (zenon_or_s _ _ zenon_H3e); [ zenon_intro zenon_H42 | zenon_intro zenon_H41 ]. % 19.13/19.27 exact (zenon_H3f zenon_H42). % 19.13/19.27 apply (zenon_or_s _ _ zenon_H41); [ zenon_intro zenon_H27 | zenon_intro zenon_H43 ]. % 19.13/19.27 apply (zenon_or_s _ _ zenon_H183); [ zenon_intro zenon_H7b | zenon_intro zenon_H186 ]. % 19.13/19.27 exact (zenon_H80 zenon_H7b). % 19.13/19.27 apply (zenon_or_s _ _ zenon_H186); [ zenon_intro zenon_H10f | zenon_intro zenon_H187 ]. % 19.13/19.27 exact (zenon_H26d zenon_H10f). % 19.13/19.27 apply (zenon_or_s _ _ zenon_H187); [ zenon_intro zenon_H150 | zenon_intro zenon_Hcd ]. % 19.13/19.27 exact (zenon_H1fd zenon_H150). % 19.13/19.27 apply (zenon_or_s _ _ zenon_H1fe); [ zenon_intro zenon_H7b | zenon_intro zenon_H1ff ]. % 19.13/19.27 exact (zenon_H80 zenon_H7b). % 19.13/19.27 apply (zenon_or_s _ _ zenon_H1ff); [ zenon_intro zenon_H86 | zenon_intro zenon_H200 ]. % 19.13/19.27 exact (zenon_H177 zenon_H86). % 19.13/19.27 apply (zenon_or_s _ _ zenon_H200); [ zenon_intro zenon_Hee | zenon_intro zenon_H148 ]. % 19.13/19.27 exact (zenon_Hef zenon_Hee). % 19.13/19.27 apply (zenon_or_s _ _ zenon_H128); [ zenon_intro zenon_H9d | zenon_intro zenon_H129 ]. % 19.13/19.27 apply (zenon_L262_); trivial. % 19.13/19.27 apply (zenon_or_s _ _ zenon_H129); [ zenon_intro zenon_H10d | zenon_intro zenon_H12a ]. % 19.13/19.27 exact (zenon_H10a zenon_H10d). % 19.13/19.27 apply (zenon_or_s _ _ zenon_H12a); [ zenon_intro zenon_Hf0 | zenon_intro zenon_Hd6 ]. % 19.13/19.27 apply (zenon_L68_); trivial. % 19.13/19.27 apply (zenon_or_s _ _ zenon_H2f); [ zenon_intro zenon_H34 | zenon_intro zenon_H33 ]. % 19.13/19.27 apply (zenon_L332_); trivial. % 19.13/19.27 apply (zenon_or_s _ _ zenon_H33); [ zenon_intro zenon_H36 | zenon_intro zenon_H35 ]. % 19.13/19.27 apply (zenon_L128_); trivial. % 19.13/19.27 apply (zenon_or_s _ _ zenon_H35); [ zenon_intro zenon_H2c | zenon_intro zenon_H37 ]. % 19.13/19.27 apply (zenon_L1234_); trivial. % 19.13/19.27 apply (zenon_or_s _ _ zenon_H136); [ zenon_intro zenon_He3 | zenon_intro zenon_H137 ]. % 19.13/19.27 apply (zenon_L81_); trivial. % 19.13/19.27 apply (zenon_or_s _ _ zenon_H137); [ zenon_intro zenon_Hdc | zenon_intro zenon_H138 ]. % 19.13/19.27 apply (zenon_L83_); trivial. % 19.13/19.27 apply (zenon_or_s _ _ zenon_H138); [ zenon_intro zenon_Hdd | zenon_intro zenon_H105 ]. % 19.13/19.27 apply (zenon_L1236_); trivial. % 19.13/19.27 exact (zenon_H102 zenon_H105). % 19.13/19.27 apply (zenon_or_s _ _ zenon_H43); [ zenon_intro zenon_H34 | zenon_intro zenon_H44 ]. % 19.13/19.27 apply (zenon_L1257_); trivial. % 19.13/19.27 apply (zenon_L19_); trivial. % 19.13/19.27 apply (zenon_or_s _ _ zenon_H78); [ zenon_intro zenon_H48 | zenon_intro zenon_H1e ]. % 19.13/19.27 apply (zenon_L1258_); trivial. % 19.13/19.27 apply (zenon_L1061_); trivial. % 19.13/19.27 apply (zenon_L1234_); trivial. % 19.13/19.27 apply (zenon_L116_); trivial. % 19.13/19.27 apply (zenon_L1294_); trivial. % 19.13/19.27 apply (zenon_L1293_); trivial. % 19.13/19.27 apply (zenon_or_s _ _ zenon_H27c); [ zenon_intro zenon_H12e | zenon_intro zenon_Ha9 ]. % 19.13/19.27 apply (zenon_or_s _ _ zenon_H27a); [ zenon_intro zenon_H177 | zenon_intro zenon_H2a ]. % 19.13/19.27 apply (zenon_or_s _ _ zenon_H27b); [ zenon_intro zenon_H20c | zenon_intro zenon_Hf0 ]. % 19.13/19.27 apply (zenon_or_s _ _ zenon_H275); [ zenon_intro zenon_H114 | zenon_intro zenon_H113 ]. % 19.13/19.27 apply (zenon_or_s _ _ zenon_H279); [ zenon_intro zenon_H14c | zenon_intro zenon_H16c ]. % 19.13/19.27 apply (zenon_L1049_); trivial. % 19.13/19.27 apply (zenon_or_s _ _ zenon_H276); [ zenon_intro zenon_Hef | zenon_intro zenon_H2c ]. % 19.13/19.27 apply (zenon_L1304_); trivial. % 19.13/19.27 apply (zenon_or_s _ _ zenon_H271); [ zenon_intro zenon_H26e | zenon_intro zenon_Hf1 ]. % 19.13/19.27 apply (zenon_or_s _ _ zenon_H270); [ zenon_intro zenon_H14b | zenon_intro zenon_H61 ]. % 19.13/19.27 apply (zenon_or_s _ _ zenon_H26f); [ zenon_intro zenon_H194 | zenon_intro zenon_Hba ]. % 19.13/19.27 apply (zenon_L1051_); trivial. % 19.13/19.27 apply (zenon_or_s _ _ zenon_H74); [ zenon_intro zenon_H42 | zenon_intro zenon_H77 ]. % 19.13/19.27 exact (zenon_H3f zenon_H42). % 19.13/19.27 apply (zenon_or_s _ _ zenon_H77); [ zenon_intro zenon_H49 | zenon_intro zenon_H78 ]. % 19.13/19.27 apply (zenon_or_s _ _ zenon_H3e); [ zenon_intro zenon_H42 | zenon_intro zenon_H41 ]. % 19.13/19.27 exact (zenon_H3f zenon_H42). % 19.13/19.27 apply (zenon_or_s _ _ zenon_H41); [ zenon_intro zenon_H27 | zenon_intro zenon_H43 ]. % 19.13/19.27 apply (zenon_L1305_); trivial. % 19.13/19.27 apply (zenon_or_s _ _ zenon_H43); [ zenon_intro zenon_H34 | zenon_intro zenon_H44 ]. % 19.13/19.27 apply (zenon_L11_); trivial. % 19.13/19.27 apply (zenon_or_s _ _ zenon_H22d); [ zenon_intro zenon_H7a | zenon_intro zenon_H22e ]. % 19.13/19.27 apply (zenon_or_s _ _ zenon_H168); [ zenon_intro zenon_H3a | zenon_intro zenon_H169 ]. % 19.13/19.27 apply (zenon_L35_); trivial. % 19.13/19.27 apply (zenon_or_s _ _ zenon_H169); [ zenon_intro zenon_H99 | zenon_intro zenon_H16a ]. % 19.13/19.27 apply (zenon_L36_); trivial. % 19.13/19.27 apply (zenon_or_s _ _ zenon_H16a); [ zenon_intro zenon_Ha9 | zenon_intro zenon_He3 ]. % 19.13/19.27 apply (zenon_L1316_); trivial. % 19.13/19.27 apply (zenon_or_s _ _ zenon_H128); [ zenon_intro zenon_H9d | zenon_intro zenon_H129 ]. % 19.13/19.27 apply (zenon_or_s _ _ zenon_H67); [ zenon_intro zenon_H1e | zenon_intro zenon_H68 ]. % 19.13/19.27 apply (zenon_L1321_); trivial. % 19.13/19.27 apply (zenon_or_s _ _ zenon_H68); [ zenon_intro zenon_H1f | zenon_intro zenon_H69 ]. % 19.13/19.27 apply (zenon_L1322_); trivial. % 19.13/19.27 apply (zenon_or_s _ _ zenon_H69); [ zenon_intro zenon_H37 | zenon_intro zenon_H60 ]. % 19.13/19.27 apply (zenon_L18_); trivial. % 19.13/19.27 apply (zenon_L21_); trivial. % 19.13/19.27 apply (zenon_or_s _ _ zenon_H129); [ zenon_intro zenon_H10d | zenon_intro zenon_H12a ]. % 19.13/19.27 exact (zenon_H10a zenon_H10d). % 19.13/19.27 apply (zenon_or_s _ _ zenon_H12a); [ zenon_intro zenon_Hf0 | zenon_intro zenon_Hd6 ]. % 19.13/19.27 apply (zenon_L167_); trivial. % 19.13/19.27 apply (zenon_L1217_); trivial. % 19.13/19.27 apply (zenon_or_s _ _ zenon_H22e); [ zenon_intro zenon_Ha0 | zenon_intro zenon_H22f ]. % 19.13/19.27 apply (zenon_L38_); trivial. % 19.13/19.27 apply (zenon_or_s _ _ zenon_H22f); [ zenon_intro zenon_H122 | zenon_intro zenon_Hc3 ]. % 19.13/19.27 apply (zenon_L317_); trivial. % 19.13/19.27 apply (zenon_or_s _ _ zenon_H18c); [ zenon_intro zenon_H86 | zenon_intro zenon_H18d ]. % 19.13/19.27 exact (zenon_H177 zenon_H86). % 19.13/19.27 apply (zenon_or_s _ _ zenon_H18d); [ zenon_intro zenon_H110 | zenon_intro zenon_H18e ]. % 19.13/19.27 exact (zenon_H20c zenon_H110). % 19.13/19.27 apply (zenon_or_s _ _ zenon_H18e); [ zenon_intro zenon_H113 | zenon_intro zenon_Hd7 ]. % 19.13/19.27 exact (zenon_H114 zenon_H113). % 19.13/19.27 apply (zenon_or_s _ _ zenon_H1d8); [ zenon_intro zenon_H10f | zenon_intro zenon_H1d9 ]. % 19.13/19.27 exact (zenon_H26d zenon_H10f). % 19.13/19.27 apply (zenon_or_s _ _ zenon_H1d9); [ zenon_intro zenon_H110 | zenon_intro zenon_H1da ]. % 19.13/19.27 exact (zenon_H20c zenon_H110). % 19.13/19.27 apply (zenon_or_s _ _ zenon_H1da); [ zenon_intro zenon_H1ca | zenon_intro zenon_H14d ]. % 19.13/19.27 exact (zenon_H26e zenon_H1ca). % 19.13/19.27 apply (zenon_L500_); trivial. % 19.13/19.27 apply (zenon_or_s _ _ zenon_H78); [ zenon_intro zenon_H48 | zenon_intro zenon_H1e ]. % 19.13/19.27 apply (zenon_L1323_); trivial. % 19.13/19.27 apply (zenon_or_s _ _ zenon_H3e); [ zenon_intro zenon_H42 | zenon_intro zenon_H41 ]. % 19.13/19.27 exact (zenon_H3f zenon_H42). % 19.13/19.27 apply (zenon_or_s _ _ zenon_H41); [ zenon_intro zenon_H27 | zenon_intro zenon_H43 ]. % 19.13/19.27 apply (zenon_L1305_); trivial. % 19.13/19.27 apply (zenon_or_s _ _ zenon_H43); [ zenon_intro zenon_H34 | zenon_intro zenon_H44 ]. % 19.13/19.27 apply (zenon_L11_); trivial. % 19.13/19.27 apply (zenon_L1321_); trivial. % 19.13/19.27 apply (zenon_L146_); trivial. % 19.13/19.27 apply (zenon_L1053_); trivial. % 19.13/19.27 apply (zenon_L153_); trivial. % 19.13/19.27 apply (zenon_or_s _ _ zenon_H275); [ zenon_intro zenon_H114 | zenon_intro zenon_H113 ]. % 19.13/19.27 apply (zenon_or_s _ _ zenon_H279); [ zenon_intro zenon_H14c | zenon_intro zenon_H16c ]. % 19.13/19.27 apply (zenon_or_s _ _ zenon_H276); [ zenon_intro zenon_Hef | zenon_intro zenon_H2c ]. % 19.13/19.27 apply (zenon_or_s _ _ zenon_H271); [ zenon_intro zenon_H26e | zenon_intro zenon_Hf1 ]. % 19.13/19.27 apply (zenon_or_s _ _ zenon_H277); [ zenon_intro zenon_H274 | zenon_intro zenon_Haa ]. % 19.13/19.27 apply (zenon_L1062_); trivial. % 19.13/19.27 apply (zenon_or_s _ _ zenon_H270); [ zenon_intro zenon_H14b | zenon_intro zenon_H61 ]. % 19.13/19.27 apply (zenon_L1207_); trivial. % 19.13/19.27 apply (zenon_or_s _ _ zenon_H278); [ zenon_intro zenon_Hf7 | zenon_intro zenon_H163 ]. % 19.13/19.27 apply (zenon_or_s _ _ zenon_H74); [ zenon_intro zenon_H42 | zenon_intro zenon_H77 ]. % 19.13/19.27 exact (zenon_H3f zenon_H42). % 19.13/19.27 apply (zenon_or_s _ _ zenon_H77); [ zenon_intro zenon_H49 | zenon_intro zenon_H78 ]. % 19.13/19.27 apply (zenon_or_s _ _ zenon_H22d); [ zenon_intro zenon_H7a | zenon_intro zenon_H22e ]. % 19.13/19.27 apply (zenon_L1295_); trivial. % 19.13/19.27 apply (zenon_or_s _ _ zenon_H22e); [ zenon_intro zenon_Ha0 | zenon_intro zenon_H22f ]. % 19.13/19.27 apply (zenon_L1298_); trivial. % 19.13/19.27 apply (zenon_or_s _ _ zenon_H22f); [ zenon_intro zenon_H122 | zenon_intro zenon_Hc3 ]. % 19.13/19.27 apply (zenon_L1239_); trivial. % 19.13/19.27 apply (zenon_or_s _ _ zenon_H1fe); [ zenon_intro zenon_H7b | zenon_intro zenon_H1ff ]. % 19.13/19.27 exact (zenon_H80 zenon_H7b). % 19.13/19.27 apply (zenon_or_s _ _ zenon_H1ff); [ zenon_intro zenon_H86 | zenon_intro zenon_H200 ]. % 19.13/19.27 exact (zenon_H177 zenon_H86). % 19.13/19.27 apply (zenon_or_s _ _ zenon_H200); [ zenon_intro zenon_Hee | zenon_intro zenon_H148 ]. % 19.13/19.27 exact (zenon_Hef zenon_Hee). % 19.13/19.27 apply (zenon_or_s _ _ zenon_H168); [ zenon_intro zenon_H3a | zenon_intro zenon_H169 ]. % 19.13/19.27 apply (zenon_or_s _ _ zenon_H2f); [ zenon_intro zenon_H34 | zenon_intro zenon_H33 ]. % 19.13/19.27 apply (zenon_L1308_); trivial. % 19.13/19.27 apply (zenon_or_s _ _ zenon_H33); [ zenon_intro zenon_H36 | zenon_intro zenon_H35 ]. % 19.13/19.27 apply (zenon_L1296_); trivial. % 19.13/19.27 apply (zenon_or_s _ _ zenon_H35); [ zenon_intro zenon_H2c | zenon_intro zenon_H37 ]. % 19.13/19.27 apply (zenon_L146_); trivial. % 19.13/19.27 apply (zenon_L1312_); trivial. % 19.13/19.27 apply (zenon_or_s _ _ zenon_H169); [ zenon_intro zenon_H99 | zenon_intro zenon_H16a ]. % 19.13/19.27 apply (zenon_L36_); trivial. % 19.13/19.27 apply (zenon_or_s _ _ zenon_H16a); [ zenon_intro zenon_Ha9 | zenon_intro zenon_He3 ]. % 19.13/19.27 apply (zenon_L1313_); trivial. % 19.13/19.27 apply (zenon_L633_); trivial. % 19.13/19.27 apply (zenon_or_s _ _ zenon_H78); [ zenon_intro zenon_H48 | zenon_intro zenon_H1e ]. % 19.13/19.27 apply (zenon_L342_); trivial. % 19.13/19.27 apply (zenon_L1324_); trivial. % 19.13/19.27 apply (zenon_L180_); trivial. % 19.13/19.27 apply (zenon_L59_); trivial. % 19.13/19.27 apply (zenon_or_s _ _ zenon_H271); [ zenon_intro zenon_H26e | zenon_intro zenon_Hf1 ]. % 19.13/19.27 apply (zenon_or_s _ _ zenon_H277); [ zenon_intro zenon_H274 | zenon_intro zenon_Haa ]. % 19.13/19.27 apply (zenon_or_s _ _ zenon_H270); [ zenon_intro zenon_H14b | zenon_intro zenon_H61 ]. % 19.13/19.27 apply (zenon_or_s _ _ zenon_H26f); [ zenon_intro zenon_H194 | zenon_intro zenon_Hba ]. % 19.13/19.27 apply (zenon_or_s _ _ zenon_H273); [ zenon_intro zenon_H272 | zenon_intro zenon_H151 ]. % 19.13/19.27 apply (zenon_or_s _ _ zenon_H74); [ zenon_intro zenon_H42 | zenon_intro zenon_H77 ]. % 19.13/19.27 exact (zenon_H3f zenon_H42). % 19.13/19.27 apply (zenon_or_s _ _ zenon_H77); [ zenon_intro zenon_H49 | zenon_intro zenon_H78 ]. % 19.13/19.27 apply (zenon_or_s _ _ zenon_H3e); [ zenon_intro zenon_H42 | zenon_intro zenon_H41 ]. % 19.13/19.27 exact (zenon_H3f zenon_H42). % 19.13/19.27 apply (zenon_or_s _ _ zenon_H41); [ zenon_intro zenon_H27 | zenon_intro zenon_H43 ]. % 19.13/19.27 apply (zenon_or_s _ _ zenon_H22d); [ zenon_intro zenon_H7a | zenon_intro zenon_H22e ]. % 19.13/19.27 apply (zenon_or_s _ _ zenon_H1fe); [ zenon_intro zenon_H7b | zenon_intro zenon_H1ff ]. % 19.13/19.27 exact (zenon_H80 zenon_H7b). % 19.13/19.27 apply (zenon_or_s _ _ zenon_H1ff); [ zenon_intro zenon_H86 | zenon_intro zenon_H200 ]. % 19.13/19.27 exact (zenon_H177 zenon_H86). % 19.13/19.27 apply (zenon_or_s _ _ zenon_H200); [ zenon_intro zenon_Hee | zenon_intro zenon_H148 ]. % 19.13/19.27 apply (zenon_or_s _ _ zenon_H168); [ zenon_intro zenon_H3a | zenon_intro zenon_H169 ]. % 19.13/19.27 apply (zenon_L35_); trivial. % 19.13/19.27 apply (zenon_or_s _ _ zenon_H169); [ zenon_intro zenon_H99 | zenon_intro zenon_H16a ]. % 19.13/19.27 apply (zenon_L36_); trivial. % 19.13/19.27 apply (zenon_or_s _ _ zenon_H16a); [ zenon_intro zenon_Ha9 | zenon_intro zenon_He3 ]. % 19.13/19.27 apply (zenon_L1284_); trivial. % 19.13/19.27 apply (zenon_or_s _ _ zenon_H1ac); [ zenon_intro zenon_H44 | zenon_intro zenon_H1af ]. % 19.13/19.27 apply (zenon_L1341_); trivial. % 19.13/19.27 apply (zenon_or_s _ _ zenon_H1af); [ zenon_intro zenon_H1b1 | zenon_intro zenon_H1b0 ]. % 19.13/19.27 apply (zenon_or_s _ _ zenon_H67); [ zenon_intro zenon_H1e | zenon_intro zenon_H68 ]. % 19.13/19.27 apply (zenon_L1267_); trivial. % 19.13/19.27 apply (zenon_or_s _ _ zenon_H68); [ zenon_intro zenon_H1f | zenon_intro zenon_H69 ]. % 19.13/19.27 apply (zenon_L258_); trivial. % 19.13/19.27 apply (zenon_or_s _ _ zenon_H69); [ zenon_intro zenon_H37 | zenon_intro zenon_H60 ]. % 19.13/19.27 apply (zenon_L18_); trivial. % 19.13/19.27 apply (zenon_L1143_); trivial. % 19.13/19.27 apply (zenon_or_s _ _ zenon_H1b0); [ zenon_intro zenon_H61 | zenon_intro zenon_H60 ]. % 19.13/19.27 apply (zenon_L146_); trivial. % 19.13/19.27 apply (zenon_L1143_); trivial. % 19.13/19.27 exact (zenon_H14b zenon_H148). % 19.13/19.27 apply (zenon_or_s _ _ zenon_H22e); [ zenon_intro zenon_Ha0 | zenon_intro zenon_H22f ]. % 19.13/19.27 apply (zenon_L1263_); trivial. % 19.13/19.27 apply (zenon_or_s _ _ zenon_H22f); [ zenon_intro zenon_H122 | zenon_intro zenon_Hc3 ]. % 19.13/19.27 apply (zenon_L1327_); trivial. % 19.13/19.27 apply (zenon_or_s _ _ zenon_H235); [ zenon_intro zenon_H7a | zenon_intro zenon_H236 ]. % 19.13/19.27 apply (zenon_L140_); trivial. % 19.13/19.27 apply (zenon_or_s _ _ zenon_H236); [ zenon_intro zenon_H9d | zenon_intro zenon_H237 ]. % 19.13/19.27 apply (zenon_L262_); trivial. % 19.13/19.27 apply (zenon_or_s _ _ zenon_H237); [ zenon_intro zenon_Hed | zenon_intro zenon_Hac ]. % 19.13/19.27 apply (zenon_L1252_); trivial. % 19.13/19.27 apply (zenon_or_s _ _ zenon_H1fe); [ zenon_intro zenon_H7b | zenon_intro zenon_H1ff ]. % 19.13/19.27 exact (zenon_H80 zenon_H7b). % 19.13/19.27 apply (zenon_or_s _ _ zenon_H1ff); [ zenon_intro zenon_H86 | zenon_intro zenon_H200 ]. % 19.13/19.27 exact (zenon_H177 zenon_H86). % 19.13/19.27 apply (zenon_or_s _ _ zenon_H200); [ zenon_intro zenon_Hee | zenon_intro zenon_H148 ]. % 19.13/19.27 apply (zenon_or_s _ _ zenon_H109); [ zenon_intro zenon_Ha0 | zenon_intro zenon_H10b ]. % 19.13/19.27 apply (zenon_L359_); trivial. % 19.13/19.27 apply (zenon_or_s _ _ zenon_H10b); [ zenon_intro zenon_H10d | zenon_intro zenon_H10c ]. % 19.13/19.27 exact (zenon_H10a zenon_H10d). % 19.13/19.27 apply (zenon_or_s _ _ zenon_H10c); [ zenon_intro zenon_Ha5 | zenon_intro zenon_Hae ]. % 19.13/19.27 apply (zenon_or_s _ _ zenon_H1ac); [ zenon_intro zenon_H44 | zenon_intro zenon_H1af ]. % 19.13/19.27 apply (zenon_L1342_); trivial. % 19.13/19.27 apply (zenon_or_s _ _ zenon_H1af); [ zenon_intro zenon_H1b1 | zenon_intro zenon_H1b0 ]. % 19.13/19.27 apply (zenon_L1271_); trivial. % 19.13/19.27 apply (zenon_or_s _ _ zenon_H1b0); [ zenon_intro zenon_H61 | zenon_intro zenon_H60 ]. % 19.13/19.27 apply (zenon_L146_); trivial. % 19.13/19.27 apply (zenon_L1270_); trivial. % 19.13/19.27 apply (zenon_L242_); trivial. % 19.13/19.27 exact (zenon_H14b zenon_H148). % 19.13/19.27 apply (zenon_or_s _ _ zenon_H43); [ zenon_intro zenon_H34 | zenon_intro zenon_H44 ]. % 19.13/19.27 apply (zenon_L11_); trivial. % 19.13/19.27 apply (zenon_L1342_); trivial. % 19.13/19.27 apply (zenon_or_s _ _ zenon_H78); [ zenon_intro zenon_H48 | zenon_intro zenon_H1e ]. % 19.13/19.27 apply (zenon_L679_); trivial. % 19.13/19.27 apply (zenon_L1277_); trivial. % 19.13/19.27 apply (zenon_L104_); trivial. % 19.13/19.27 apply (zenon_L69_); trivial. % 19.13/19.27 apply (zenon_L146_); trivial. % 19.13/19.27 apply (zenon_L1208_); trivial. % 19.13/19.27 apply (zenon_L59_); trivial. % 19.13/19.27 apply (zenon_L167_); trivial. % 19.13/19.27 apply (zenon_L68_); trivial. % 19.13/19.27 apply (zenon_L1339_); trivial. % 19.13/19.27 apply (zenon_L1316_); trivial. % 19.13/19.27 apply (zenon_L1327_); trivial. % 19.13/19.27 apply (zenon_L1323_); trivial. % 19.13/19.27 apply (zenon_and_s _ _ zenon_H31a). zenon_intro zenon_H32d. zenon_intro zenon_H32c. % 19.13/19.27 apply (zenon_and_s _ _ zenon_H32c). zenon_intro zenon_H290. zenon_intro zenon_H32e. % 19.13/19.27 apply (zenon_and_s _ _ zenon_H32e). zenon_intro zenon_H28c. zenon_intro zenon_H32f. % 19.13/19.27 apply (zenon_and_s _ _ zenon_H32f). zenon_intro zenon_H28f. zenon_intro zenon_H330. % 19.13/19.27 apply (zenon_and_s _ _ zenon_H330). zenon_intro zenon_H28d. zenon_intro zenon_H331. % 19.13/19.27 apply (zenon_and_s _ _ zenon_H331). zenon_intro zenon_H28e. zenon_intro zenon_H332. % 19.13/19.27 apply (zenon_and_s _ _ zenon_H332). zenon_intro zenon_H287. zenon_intro zenon_H333. % 19.13/19.27 apply (zenon_and_s _ _ zenon_H333). zenon_intro zenon_H289. zenon_intro zenon_H334. % 19.13/19.27 apply (zenon_and_s _ _ zenon_H334). zenon_intro zenon_H28a. zenon_intro zenon_H335. % 19.13/19.27 apply (zenon_and_s _ _ zenon_H335). zenon_intro zenon_H28b. zenon_intro zenon_H336. % 19.13/19.27 apply (zenon_and_s _ _ zenon_H336). zenon_intro zenon_H288. zenon_intro zenon_H337. % 19.13/19.27 apply (zenon_and_s _ _ zenon_H337). zenon_intro zenon_H281. zenon_intro zenon_H338. % 19.13/19.27 apply (zenon_and_s _ _ zenon_H338). zenon_intro zenon_H286. zenon_intro zenon_H339. % 19.13/19.27 apply (zenon_and_s _ _ zenon_H339). zenon_intro zenon_H285. zenon_intro zenon_H33a. % 19.13/19.27 apply (zenon_and_s _ _ zenon_H33a). zenon_intro zenon_H284. zenon_intro zenon_H33b. % 19.13/19.27 apply (zenon_or_s _ _ zenon_H32d); [ zenon_intro zenon_H98 | zenon_intro zenon_H1e ]. % 19.13/19.27 apply (zenon_or_s _ _ zenon_H290); [ zenon_intro zenon_H9c | zenon_intro zenon_Hc3 ]. % 19.13/19.27 apply (zenon_or_s _ _ zenon_H28c); [ zenon_intro zenon_H123 | zenon_intro zenon_Hcd ]. % 19.13/19.27 apply (zenon_or_s _ _ zenon_H28f); [ zenon_intro zenon_H12d | zenon_intro zenon_He3 ]. % 19.13/19.27 apply (zenon_or_s _ _ zenon_H28d); [ zenon_intro zenon_H9f | zenon_intro zenon_H1f ]. % 19.13/19.27 apply (zenon_or_s _ _ zenon_H28e); [ zenon_intro zenon_H1a1 | zenon_intro zenon_Hd6 ]. % 19.13/19.27 apply (zenon_or_s _ _ zenon_H287); [ zenon_intro zenon_H16d | zenon_intro zenon_Hd7 ]. % 19.13/19.27 apply (zenon_or_s _ _ zenon_H289); [ zenon_intro zenon_H12f | zenon_intro zenon_Hdc ]. % 19.13/19.27 apply (zenon_L1343_); trivial. % 19.13/19.27 apply (zenon_or_s _ _ zenon_H28a); [ zenon_intro zenon_H27f | zenon_intro zenon_H37 ]. % 19.13/19.27 apply (zenon_or_s _ _ zenon_H28b); [ zenon_intro zenon_Ha7 | zenon_intro zenon_Hf4 ]. % 19.13/19.27 apply (zenon_or_s _ _ zenon_H288); [ zenon_intro zenon_H1b3 | zenon_intro zenon_H11d ]. % 19.13/19.27 apply (zenon_L1345_); trivial. % 19.13/19.27 apply (zenon_or_s _ _ zenon_H281); [ zenon_intro zenon_H280 | zenon_intro zenon_Hdd ]. % 19.13/19.27 apply (zenon_or_s _ _ zenon_H286); [ zenon_intro zenon_H15f | zenon_intro zenon_H60 ]. % 19.13/19.27 apply (zenon_or_s _ _ zenon_H285); [ zenon_intro zenon_H282 | zenon_intro zenon_Hc4 ]. % 19.13/19.27 apply (zenon_L1347_); trivial. % 19.13/19.27 apply (zenon_or_s _ _ zenon_H74); [ zenon_intro zenon_H42 | zenon_intro zenon_H77 ]. % 19.13/19.27 exact (zenon_H3f zenon_H42). % 19.13/19.27 apply (zenon_or_s _ _ zenon_H77); [ zenon_intro zenon_H49 | zenon_intro zenon_H78 ]. % 19.13/19.27 apply (zenon_L1348_); trivial. % 19.13/19.27 apply (zenon_or_s _ _ zenon_H78); [ zenon_intro zenon_H48 | zenon_intro zenon_H1e ]. % 19.13/19.27 apply (zenon_L1349_); trivial. % 19.13/19.27 apply (zenon_L1403_); trivial. % 19.13/19.27 apply (zenon_L1406_); trivial. % 19.13/19.27 apply (zenon_L52_); trivial. % 19.13/19.27 apply (zenon_or_s _ _ zenon_H288); [ zenon_intro zenon_H1b3 | zenon_intro zenon_H11d ]. % 19.13/19.27 apply (zenon_or_s _ _ zenon_H286); [ zenon_intro zenon_H15f | zenon_intro zenon_H60 ]. % 19.13/19.27 apply (zenon_or_s _ _ zenon_H285); [ zenon_intro zenon_H282 | zenon_intro zenon_Hc4 ]. % 19.13/19.27 apply (zenon_or_s _ _ zenon_H74); [ zenon_intro zenon_H42 | zenon_intro zenon_H77 ]. % 19.13/19.27 exact (zenon_H3f zenon_H42). % 19.13/19.27 apply (zenon_or_s _ _ zenon_H77); [ zenon_intro zenon_H49 | zenon_intro zenon_H78 ]. % 19.13/19.27 apply (zenon_L1348_); trivial. % 19.13/19.27 apply (zenon_or_s _ _ zenon_H78); [ zenon_intro zenon_H48 | zenon_intro zenon_H1e ]. % 19.13/19.27 apply (zenon_L1408_); trivial. % 19.13/19.27 apply (zenon_L1389_); trivial. % 19.13/19.27 apply (zenon_L60_); trivial. % 19.13/19.27 apply (zenon_L1409_); trivial. % 19.13/19.27 apply (zenon_L1410_); trivial. % 19.13/19.27 apply (zenon_or_s _ _ zenon_H74); [ zenon_intro zenon_H42 | zenon_intro zenon_H77 ]. % 19.13/19.27 exact (zenon_H3f zenon_H42). % 19.13/19.27 apply (zenon_or_s _ _ zenon_H77); [ zenon_intro zenon_H49 | zenon_intro zenon_H78 ]. % 19.13/19.27 apply (zenon_L1348_); trivial. % 19.13/19.27 apply (zenon_or_s _ _ zenon_H78); [ zenon_intro zenon_H48 | zenon_intro zenon_H1e ]. % 19.13/19.27 apply (zenon_L1349_); trivial. % 19.13/19.27 apply (zenon_L367_); trivial. % 19.13/19.27 apply (zenon_or_s _ _ zenon_H289); [ zenon_intro zenon_H12f | zenon_intro zenon_Hdc ]. % 19.13/19.27 apply (zenon_or_s _ _ zenon_H288); [ zenon_intro zenon_H1b3 | zenon_intro zenon_H11d ]. % 19.13/19.27 apply (zenon_or_s _ _ zenon_H286); [ zenon_intro zenon_H15f | zenon_intro zenon_H60 ]. % 19.13/19.27 apply (zenon_or_s _ _ zenon_H285); [ zenon_intro zenon_H282 | zenon_intro zenon_Hc4 ]. % 19.13/19.27 apply (zenon_L1411_); trivial. % 19.13/19.27 apply (zenon_or_s _ _ zenon_H74); [ zenon_intro zenon_H42 | zenon_intro zenon_H77 ]. % 19.13/19.27 exact (zenon_H3f zenon_H42). % 19.13/19.27 apply (zenon_or_s _ _ zenon_H77); [ zenon_intro zenon_H49 | zenon_intro zenon_H78 ]. % 19.13/19.27 apply (zenon_L1348_); trivial. % 19.13/19.27 apply (zenon_or_s _ _ zenon_H78); [ zenon_intro zenon_H48 | zenon_intro zenon_H1e ]. % 19.13/19.27 apply (zenon_L1349_); trivial. % 19.13/19.27 apply (zenon_L1419_); trivial. % 19.13/19.27 apply (zenon_L1409_); trivial. % 19.13/19.27 apply (zenon_L366_); trivial. % 19.13/19.27 apply (zenon_L266_); trivial. % 19.13/19.27 apply (zenon_or_s _ _ zenon_H287); [ zenon_intro zenon_H16d | zenon_intro zenon_Hd7 ]. % 19.13/19.27 apply (zenon_or_s _ _ zenon_H289); [ zenon_intro zenon_H12f | zenon_intro zenon_Hdc ]. % 19.13/19.27 apply (zenon_or_s _ _ zenon_H288); [ zenon_intro zenon_H1b3 | zenon_intro zenon_H11d ]. % 19.13/19.27 apply (zenon_or_s _ _ zenon_H286); [ zenon_intro zenon_H15f | zenon_intro zenon_H60 ]. % 19.13/19.27 apply (zenon_L1420_); trivial. % 19.13/19.27 apply (zenon_L1409_); trivial. % 19.13/19.27 apply (zenon_or_s _ _ zenon_H286); [ zenon_intro zenon_H15f | zenon_intro zenon_H60 ]. % 19.13/19.27 apply (zenon_L1369_); trivial. % 19.13/19.27 apply (zenon_L1409_); trivial. % 19.13/19.27 apply (zenon_L83_); trivial. % 19.13/19.27 apply (zenon_L101_); trivial. % 19.13/19.27 apply (zenon_or_s _ _ zenon_H74); [ zenon_intro zenon_H42 | zenon_intro zenon_H77 ]. % 19.13/19.27 exact (zenon_H3f zenon_H42). % 19.13/19.27 apply (zenon_or_s _ _ zenon_H77); [ zenon_intro zenon_H49 | zenon_intro zenon_H78 ]. % 19.13/19.27 apply (zenon_L1348_); trivial. % 19.13/19.27 apply (zenon_or_s _ _ zenon_H78); [ zenon_intro zenon_H48 | zenon_intro zenon_H1e ]. % 19.13/19.27 apply (zenon_L1349_); trivial. % 19.13/19.27 apply (zenon_L1_); trivial. % 19.13/19.27 apply (zenon_or_s _ _ zenon_H28d); [ zenon_intro zenon_H9f | zenon_intro zenon_H1f ]. % 19.13/19.27 apply (zenon_or_s _ _ zenon_H28e); [ zenon_intro zenon_H1a1 | zenon_intro zenon_Hd6 ]. % 19.13/19.27 apply (zenon_or_s _ _ zenon_H287); [ zenon_intro zenon_H16d | zenon_intro zenon_Hd7 ]. % 19.13/19.27 apply (zenon_or_s _ _ zenon_H289); [ zenon_intro zenon_H12f | zenon_intro zenon_Hdc ]. % 19.13/19.27 apply (zenon_L1343_); trivial. % 19.13/19.27 apply (zenon_L117_); trivial. % 19.13/19.27 apply (zenon_or_s _ _ zenon_H28a); [ zenon_intro zenon_H27f | zenon_intro zenon_H37 ]. % 19.13/19.27 apply (zenon_or_s _ _ zenon_H28b); [ zenon_intro zenon_Ha7 | zenon_intro zenon_Hf4 ]. % 19.13/19.27 apply (zenon_or_s _ _ zenon_H288); [ zenon_intro zenon_H1b3 | zenon_intro zenon_H11d ]. % 19.13/19.27 apply (zenon_L1421_); trivial. % 19.13/19.27 apply (zenon_L366_); trivial. % 19.13/19.27 apply (zenon_L1423_); trivial. % 19.13/19.27 apply (zenon_L1424_); trivial. % 19.13/19.27 apply (zenon_or_s _ _ zenon_H287); [ zenon_intro zenon_H16d | zenon_intro zenon_Hd7 ]. % 19.13/19.27 apply (zenon_or_s _ _ zenon_H289); [ zenon_intro zenon_H12f | zenon_intro zenon_Hdc ]. % 19.13/19.27 apply (zenon_or_s _ _ zenon_H28a); [ zenon_intro zenon_H27f | zenon_intro zenon_H37 ]. % 19.13/19.27 apply (zenon_or_s _ _ zenon_H28b); [ zenon_intro zenon_Ha7 | zenon_intro zenon_Hf4 ]. % 19.13/19.27 apply (zenon_or_s _ _ zenon_H288); [ zenon_intro zenon_H1b3 | zenon_intro zenon_H11d ]. % 19.13/19.27 apply (zenon_L1421_); trivial. % 19.13/19.27 apply (zenon_or_s _ _ zenon_H281); [ zenon_intro zenon_H280 | zenon_intro zenon_Hdd ]. % 19.13/19.27 apply (zenon_or_s _ _ zenon_H286); [ zenon_intro zenon_H15f | zenon_intro zenon_H60 ]. % 19.13/19.27 apply (zenon_L1369_); trivial. % 19.13/19.27 apply (zenon_or_s _ _ zenon_H285); [ zenon_intro zenon_H282 | zenon_intro zenon_Hc4 ]. % 19.13/19.27 apply (zenon_or_s _ _ zenon_H74); [ zenon_intro zenon_H42 | zenon_intro zenon_H77 ]. % 19.13/19.27 exact (zenon_H3f zenon_H42). % 19.13/19.27 apply (zenon_or_s _ _ zenon_H77); [ zenon_intro zenon_H49 | zenon_intro zenon_H78 ]. % 19.13/19.27 apply (zenon_or_s _ _ zenon_H3e); [ zenon_intro zenon_H42 | zenon_intro zenon_H41 ]. % 19.13/19.27 exact (zenon_H3f zenon_H42). % 19.13/19.27 apply (zenon_or_s _ _ zenon_H41); [ zenon_intro zenon_H27 | zenon_intro zenon_H43 ]. % 19.13/19.27 apply (zenon_or_s _ _ zenon_H22d); [ zenon_intro zenon_H7a | zenon_intro zenon_H22e ]. % 19.13/19.27 apply (zenon_or_s _ _ zenon_H1e0); [ zenon_intro zenon_H3a | zenon_intro zenon_H1e1 ]. % 19.13/19.27 exact (zenon_H98 zenon_H3a). % 19.13/19.27 apply (zenon_or_s _ _ zenon_H1e1); [ zenon_intro zenon_H9e | zenon_intro zenon_H1e2 ]. % 19.13/19.27 exact (zenon_H9f zenon_H9e). % 19.13/19.27 apply (zenon_or_s _ _ zenon_H1e2); [ zenon_intro zenon_H3b | zenon_intro zenon_H15e ]. % 19.13/19.27 exact (zenon_H27f zenon_H3b). % 19.13/19.27 apply (zenon_or_s _ _ zenon_H109); [ zenon_intro zenon_Ha0 | zenon_intro zenon_H10b ]. % 19.13/19.27 apply (zenon_L38_); trivial. % 19.13/19.27 apply (zenon_or_s _ _ zenon_H10b); [ zenon_intro zenon_H10d | zenon_intro zenon_H10c ]. % 19.13/19.27 exact (zenon_H10a zenon_H10d). % 19.13/19.27 apply (zenon_or_s _ _ zenon_H10c); [ zenon_intro zenon_Ha5 | zenon_intro zenon_Hae ]. % 19.13/19.27 apply (zenon_or_s _ _ zenon_H172); [ zenon_intro zenon_H150 | zenon_intro zenon_H174 ]. % 19.13/19.27 apply (zenon_L1364_); trivial. % 19.13/19.27 apply (zenon_or_s _ _ zenon_H174); [ zenon_intro zenon_H113 | zenon_intro zenon_H175 ]. % 19.13/19.27 apply (zenon_L1438_); trivial. % 19.13/19.27 apply (zenon_or_s _ _ zenon_H175); [ zenon_intro zenon_H176 | zenon_intro zenon_H151 ]. % 19.13/19.27 exact (zenon_H173 zenon_H176). % 19.13/19.27 apply (zenon_or_s _ _ zenon_He8); [ zenon_intro zenon_Hac | zenon_intro zenon_Heb ]. % 19.13/19.27 apply (zenon_L252_); trivial. % 19.13/19.27 apply (zenon_or_s _ _ zenon_Heb); [ zenon_intro zenon_Hae | zenon_intro zenon_Hec ]. % 19.13/19.27 apply (zenon_L1439_); trivial. % 19.13/19.27 apply (zenon_or_s _ _ zenon_Hec); [ zenon_intro zenon_Hba | zenon_intro zenon_Hc4 ]. % 19.13/19.27 apply (zenon_L1436_); trivial. % 19.13/19.27 apply (zenon_L50_); trivial. % 19.13/19.27 apply (zenon_L1439_); trivial. % 19.13/19.27 apply (zenon_or_s _ _ zenon_H22e); [ zenon_intro zenon_Ha0 | zenon_intro zenon_H22f ]. % 19.13/19.27 apply (zenon_L1440_); trivial. % 19.13/19.27 apply (zenon_or_s _ _ zenon_H22f); [ zenon_intro zenon_H122 | zenon_intro zenon_Hc3 ]. % 19.13/19.27 apply (zenon_or_s _ _ zenon_He8); [ zenon_intro zenon_Hac | zenon_intro zenon_Heb ]. % 19.13/19.27 apply (zenon_L1425_); trivial. % 19.13/19.27 apply (zenon_or_s _ _ zenon_Heb); [ zenon_intro zenon_Hae | zenon_intro zenon_Hec ]. % 19.13/19.27 apply (zenon_L1439_); trivial. % 19.13/19.27 apply (zenon_or_s _ _ zenon_Hec); [ zenon_intro zenon_Hba | zenon_intro zenon_Hc4 ]. % 19.13/19.27 apply (zenon_L317_); trivial. % 19.13/19.27 apply (zenon_L50_); trivial. % 19.13/19.27 apply (zenon_L633_); trivial. % 19.13/19.27 apply (zenon_or_s _ _ zenon_H43); [ zenon_intro zenon_H34 | zenon_intro zenon_H44 ]. % 19.13/19.27 apply (zenon_or_s _ _ zenon_H22); [ zenon_intro zenon_H27 | zenon_intro zenon_H26 ]. % 19.13/19.27 apply (zenon_L332_); trivial. % 19.13/19.27 apply (zenon_or_s _ _ zenon_H26); [ zenon_intro zenon_H29 | zenon_intro zenon_H28 ]. % 19.13/19.27 apply (zenon_or_s _ _ zenon_H109); [ zenon_intro zenon_Ha0 | zenon_intro zenon_H10b ]. % 19.13/19.27 apply (zenon_L1376_); trivial. % 19.13/19.27 apply (zenon_or_s _ _ zenon_H10b); [ zenon_intro zenon_H10d | zenon_intro zenon_H10c ]. % 19.13/19.27 exact (zenon_H10a zenon_H10d). % 19.13/19.27 apply (zenon_or_s _ _ zenon_H10c); [ zenon_intro zenon_Ha5 | zenon_intro zenon_Hae ]. % 19.13/19.27 apply (zenon_or_s _ _ zenon_H6a); [ zenon_intro zenon_H48 | zenon_intro zenon_H6b ]. % 19.13/19.27 apply (zenon_L1467_); trivial. % 19.13/19.27 apply (zenon_or_s _ _ zenon_H6b); [ zenon_intro zenon_H2a | zenon_intro zenon_H6c ]. % 19.13/19.27 apply (zenon_L1468_); trivial. % 19.13/19.27 apply (zenon_or_s _ _ zenon_H6c); [ zenon_intro zenon_H2c | zenon_intro zenon_H61 ]. % 19.13/19.27 apply (zenon_L11_); trivial. % 19.13/19.27 apply (zenon_L15_); trivial. % 19.13/19.27 apply (zenon_L1442_); trivial. % 19.13/19.27 apply (zenon_or_s _ _ zenon_H28); [ zenon_intro zenon_H2a | zenon_intro zenon_H1f ]. % 19.13/19.27 apply (zenon_or_s _ _ zenon_H109); [ zenon_intro zenon_Ha0 | zenon_intro zenon_H10b ]. % 19.13/19.27 apply (zenon_L38_); trivial. % 19.13/19.27 apply (zenon_or_s _ _ zenon_H10b); [ zenon_intro zenon_H10d | zenon_intro zenon_H10c ]. % 19.13/19.27 exact (zenon_H10a zenon_H10d). % 19.13/19.27 apply (zenon_or_s _ _ zenon_H10c); [ zenon_intro zenon_Ha5 | zenon_intro zenon_Hae ]. % 19.13/19.27 apply (zenon_L1468_); trivial. % 19.13/19.27 apply (zenon_or_s _ _ zenon_H106); [ zenon_intro zenon_Hed | zenon_intro zenon_H107 ]. % 19.13/19.27 apply (zenon_L214_); trivial. % 19.13/19.27 apply (zenon_or_s _ _ zenon_H107); [ zenon_intro zenon_Ha5 | zenon_intro zenon_H108 ]. % 19.13/19.27 apply (zenon_L42_); trivial. % 19.13/19.27 apply (zenon_or_s _ _ zenon_H108); [ zenon_intro zenon_Hf1 | zenon_intro zenon_Hf4 ]. % 19.13/19.27 apply (zenon_or_s _ _ zenon_H153); [ zenon_intro zenon_H148 | zenon_intro zenon_H154 ]. % 19.13/19.27 apply (zenon_L1469_); trivial. % 19.13/19.27 apply (zenon_or_s _ _ zenon_H154); [ zenon_intro zenon_H14d | zenon_intro zenon_H155 ]. % 19.13/19.27 apply (zenon_L152_); trivial. % 19.13/19.27 apply (zenon_or_s _ _ zenon_H155); [ zenon_intro zenon_H151 | zenon_intro zenon_Hf6 ]. % 19.13/19.27 apply (zenon_or_s _ _ zenon_H1ba); [ zenon_intro zenon_H48 | zenon_intro zenon_H1bb ]. % 19.13/19.27 apply (zenon_L334_); trivial. % 19.13/19.27 apply (zenon_or_s _ _ zenon_H1bb); [ zenon_intro zenon_H122 | zenon_intro zenon_H1bc ]. % 19.13/19.27 apply (zenon_L246_); trivial. % 19.13/19.27 apply (zenon_or_s _ _ zenon_H1bc); [ zenon_intro zenon_H150 | zenon_intro zenon_Ha9 ]. % 19.13/19.27 apply (zenon_L104_); trivial. % 19.13/19.27 exact (zenon_H123 zenon_Ha9). % 19.13/19.27 apply (zenon_L97_); trivial. % 19.13/19.27 apply (zenon_L126_); trivial. % 19.13/19.27 apply (zenon_L136_); trivial. % 19.13/19.27 apply (zenon_L21_); trivial. % 19.13/19.27 apply (zenon_or_s _ _ zenon_H78); [ zenon_intro zenon_H48 | zenon_intro zenon_H1e ]. % 19.13/19.27 apply (zenon_or_s _ _ zenon_H3e); [ zenon_intro zenon_H42 | zenon_intro zenon_H41 ]. % 19.13/19.27 exact (zenon_H3f zenon_H42). % 19.13/19.27 apply (zenon_or_s _ _ zenon_H41); [ zenon_intro zenon_H27 | zenon_intro zenon_H43 ]. % 19.13/19.27 apply (zenon_or_s _ _ zenon_H22d); [ zenon_intro zenon_H7a | zenon_intro zenon_H22e ]. % 19.13/19.27 apply (zenon_L1435_); trivial. % 19.13/19.27 apply (zenon_or_s _ _ zenon_H22e); [ zenon_intro zenon_Ha0 | zenon_intro zenon_H22f ]. % 19.13/19.27 apply (zenon_L1440_); trivial. % 19.13/19.27 apply (zenon_or_s _ _ zenon_H22f); [ zenon_intro zenon_H122 | zenon_intro zenon_Hc3 ]. % 19.13/19.27 apply (zenon_L355_); trivial. % 19.13/19.27 apply (zenon_L633_); trivial. % 19.13/19.27 apply (zenon_or_s _ _ zenon_H43); [ zenon_intro zenon_H34 | zenon_intro zenon_H44 ]. % 19.13/19.27 apply (zenon_L1467_); trivial. % 19.13/19.27 apply (zenon_L21_); trivial. % 19.13/19.27 apply (zenon_L440_); trivial. % 19.13/19.27 apply (zenon_L50_); trivial. % 19.13/19.27 apply (zenon_L54_); trivial. % 19.13/19.27 apply (zenon_L126_); trivial. % 19.13/19.27 apply (zenon_L1509_); trivial. % 19.13/19.27 apply (zenon_L83_); trivial. % 19.13/19.27 apply (zenon_L101_); trivial. % 19.13/19.27 apply (zenon_L1466_); trivial. % 19.13/19.27 apply (zenon_L1499_); trivial. % 19.13/19.27 apply (zenon_L1519_); trivial. % 19.13/19.27 apply (zenon_L1515_); trivial. % 19.13/19.27 Qed. % 19.13/19.27 % SZS output end Proof % 19.13/19.27 (* END-PROOF *) % 19.13/19.27 nodes searched: 295759 % 19.13/19.27 max branch formulas: 306 % 19.13/19.27 proof nodes created: 17262 % 19.13/19.27 formulas created: 48986 % 19.13/19.27 %------------------------------------------------------------------------------