%------------------------------------------------------------------------------ % File : Zenon---0.7.1 % Problem : ALG150+1 : TPTP v8.1.0. Released v2.7.0. % Transfm : none % Format : tptp:raw % Command : run_zenon %s %d % Computer : n019.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 18:30:33 EDT 2022 % Result : Unsatisfiable 15.09s 15.31s % Output : Proof 15.65s % Verified : % SZS Type : - % Comments : %------------------------------------------------------------------------------ %----WARNING: Could not form TPTP format derivation %------------------------------------------------------------------------------ %----ORIGINAL SYSTEM OUTPUT % 0.07/0.12 % Problem : ALG150+1 : TPTP v8.1.0. Released v2.7.0. % 0.07/0.12 % Command : run_zenon %s %d % 0.12/0.33 % Computer : n019.cluster.edu % 0.12/0.33 % Model : x86_64 x86_64 % 0.12/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz % 0.12/0.33 % Memory : 8042.1875MB % 0.12/0.33 % OS : Linux 3.10.0-693.el7.x86_64 % 0.12/0.33 % CPULimit : 300 % 0.12/0.33 % WCLimit : 600 % 0.12/0.33 % DateTime : Wed Jun 8 08:49:25 EDT 2022 % 0.12/0.33 % CPUTime : % 15.09/15.31 (* PROOF-FOUND *) % 15.09/15.31 % SZS status Unsatisfiable % 15.09/15.31 (* BEGIN-PROOF *) % 15.09/15.31 % SZS output start Proof % 15.09/15.31 Theorem zenon_thm : False. % 15.09/15.31 Proof. % 15.09/15.31 assert (zenon_L1_ : (~((e0) = (e0))) -> False). % 15.09/15.31 do 0 intro. intros zenon_H1d. % 15.09/15.31 apply zenon_H1d. apply refl_equal. % 15.09/15.31 (* end of lemma zenon_L1_ *) % 15.09/15.31 assert (zenon_L2_ : (~((op (e0) (op (e0) (e0))) = (op (e0) (e0)))) -> ((op (e0) (e0)) = (e0)) -> False). % 15.09/15.31 do 0 intro. intros zenon_H1e zenon_H1f. % 15.09/15.31 cut (((op (e0) (e0)) = (e0))); [idtac | apply NNPP; zenon_intro zenon_H20]. % 15.09/15.31 cut (((e0) = (e0))); [idtac | apply NNPP; zenon_intro zenon_H1d]. % 15.09/15.31 congruence. % 15.09/15.31 apply zenon_H1d. apply refl_equal. % 15.09/15.31 exact (zenon_H20 zenon_H1f). % 15.09/15.31 (* end of lemma zenon_L2_ *) % 15.09/15.31 assert (zenon_L3_ : ((op (e1) (e1)) = (e1)) -> ((op (e0) (e1)) = (e1)) -> (~((op (e0) (e1)) = (op (e1) (e1)))) -> False). % 15.09/15.31 do 0 intro. intros zenon_H21 zenon_H22 zenon_H23. % 15.09/15.31 elim (classic ((op (e1) (e1)) = (op (e1) (e1)))); [ zenon_intro zenon_H24 | zenon_intro zenon_H25 ]. % 15.09/15.31 cut (((op (e1) (e1)) = (op (e1) (e1))) = ((op (e0) (e1)) = (op (e1) (e1)))). % 15.09/15.31 intro zenon_D_pnotp. % 15.09/15.31 apply zenon_H23. % 15.09/15.31 rewrite <- zenon_D_pnotp. % 15.09/15.31 exact zenon_H24. % 15.09/15.31 cut (((op (e1) (e1)) = (op (e1) (e1)))); [idtac | apply NNPP; zenon_intro zenon_H25]. % 15.09/15.31 cut (((op (e1) (e1)) = (op (e0) (e1)))); [idtac | apply NNPP; zenon_intro zenon_H26]. % 15.09/15.31 congruence. % 15.09/15.31 cut (((op (e1) (e1)) = (e1)) = ((op (e1) (e1)) = (op (e0) (e1)))). % 15.09/15.31 intro zenon_D_pnotp. % 15.09/15.31 apply zenon_H26. % 15.09/15.31 rewrite <- zenon_D_pnotp. % 15.09/15.31 exact zenon_H21. % 15.09/15.31 cut (((e1) = (op (e0) (e1)))); [idtac | apply NNPP; zenon_intro zenon_H27]. % 15.09/15.31 cut (((op (e1) (e1)) = (op (e1) (e1)))); [idtac | apply NNPP; zenon_intro zenon_H25]. % 15.09/15.31 congruence. % 15.09/15.31 apply zenon_H25. apply refl_equal. % 15.09/15.31 apply zenon_H27. apply sym_equal. exact zenon_H22. % 15.09/15.31 apply zenon_H25. apply refl_equal. % 15.09/15.31 apply zenon_H25. apply refl_equal. % 15.09/15.31 (* end of lemma zenon_L3_ *) % 15.09/15.31 assert (zenon_L4_ : (~((op (e0) (e2)) = (op (e2) (e2)))) -> ((op (e0) (e2)) = (e1)) -> ((op (e2) (e2)) = (e1)) -> False). % 15.09/15.31 do 0 intro. intros zenon_H28 zenon_H29 zenon_H2a. % 15.09/15.31 cut (((op (e0) (e2)) = (e1)) = ((op (e0) (e2)) = (op (e2) (e2)))). % 15.09/15.31 intro zenon_D_pnotp. % 15.09/15.31 apply zenon_H28. % 15.09/15.31 rewrite <- zenon_D_pnotp. % 15.09/15.31 exact zenon_H29. % 15.09/15.31 cut (((e1) = (op (e2) (e2)))); [idtac | apply NNPP; zenon_intro zenon_H2b]. % 15.09/15.31 cut (((op (e0) (e2)) = (op (e0) (e2)))); [idtac | apply NNPP; zenon_intro zenon_H2c]. % 15.09/15.31 congruence. % 15.09/15.31 apply zenon_H2c. apply refl_equal. % 15.09/15.31 apply zenon_H2b. apply sym_equal. exact zenon_H2a. % 15.09/15.31 (* end of lemma zenon_L4_ *) % 15.09/15.31 assert (zenon_L5_ : (((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)) = (e3))) -> False). % 15.09/15.31 do 0 intro. intros zenon_H2d zenon_H2e zenon_H29 zenon_H28 zenon_H2f zenon_H30. % 15.09/15.31 apply (zenon_or_s _ _ zenon_H2d); [ zenon_intro zenon_H32 | zenon_intro zenon_H31 ]. % 15.09/15.31 exact (zenon_H2e zenon_H32). % 15.09/15.31 apply (zenon_or_s _ _ zenon_H31); [ zenon_intro zenon_H2a | zenon_intro zenon_H33 ]. % 15.09/15.31 apply (zenon_L4_); trivial. % 15.09/15.31 apply (zenon_or_s _ _ zenon_H33); [ zenon_intro zenon_H35 | zenon_intro zenon_H34 ]. % 15.09/15.31 exact (zenon_H2f zenon_H35). % 15.09/15.31 exact (zenon_H30 zenon_H34). % 15.09/15.31 (* end of lemma zenon_L5_ *) % 15.09/15.31 assert (zenon_L6_ : (~((op (e0) (e3)) = (op (e3) (e3)))) -> ((op (e0) (e3)) = (e1)) -> ((op (e3) (e3)) = (e1)) -> False). % 15.09/15.31 do 0 intro. intros zenon_H36 zenon_H37 zenon_H38. % 15.09/15.31 cut (((op (e0) (e3)) = (e1)) = ((op (e0) (e3)) = (op (e3) (e3)))). % 15.09/15.31 intro zenon_D_pnotp. % 15.09/15.31 apply zenon_H36. % 15.09/15.31 rewrite <- zenon_D_pnotp. % 15.09/15.31 exact zenon_H37. % 15.09/15.31 cut (((e1) = (op (e3) (e3)))); [idtac | apply NNPP; zenon_intro zenon_H39]. % 15.09/15.31 cut (((op (e0) (e3)) = (op (e0) (e3)))); [idtac | apply NNPP; zenon_intro zenon_H3a]. % 15.09/15.31 congruence. % 15.09/15.31 apply zenon_H3a. apply refl_equal. % 15.09/15.31 apply zenon_H39. apply sym_equal. exact zenon_H38. % 15.09/15.31 (* end of lemma zenon_L6_ *) % 15.09/15.31 assert (zenon_L7_ : (((op (e3) (e3)) = (e0))\/(((op (e3) (e3)) = (e1))\/(((op (e3) (e3)) = (e2))\/((op (e3) (e3)) = (e3))))) -> (~((op (e3) (e3)) = (e0))) -> ((op (e0) (e3)) = (e1)) -> (~((op (e0) (e3)) = (op (e3) (e3)))) -> (~((op (e3) (e3)) = (e2))) -> (~((op (e3) (e3)) = (e3))) -> False). % 15.09/15.31 do 0 intro. intros zenon_H3b zenon_H3c zenon_H37 zenon_H36 zenon_H3d zenon_H3e. % 15.09/15.31 apply (zenon_or_s _ _ zenon_H3b); [ zenon_intro zenon_H40 | zenon_intro zenon_H3f ]. % 15.09/15.31 exact (zenon_H3c zenon_H40). % 15.09/15.31 apply (zenon_or_s _ _ zenon_H3f); [ zenon_intro zenon_H38 | zenon_intro zenon_H41 ]. % 15.09/15.31 apply (zenon_L6_); trivial. % 15.09/15.31 apply (zenon_or_s _ _ zenon_H41); [ zenon_intro zenon_H43 | zenon_intro zenon_H42 ]. % 15.09/15.31 exact (zenon_H3d zenon_H43). % 15.09/15.31 exact (zenon_H3e zenon_H42). % 15.09/15.31 (* end of lemma zenon_L7_ *) % 15.09/15.31 assert (zenon_L8_ : (((op (e0) (e0)) = (e1))\/(((op (e0) (e1)) = (e1))\/(((op (e0) (e2)) = (e1))\/((op (e0) (e3)) = (e1))))) -> (~((op (e0) (e0)) = (e1))) -> (~((op (e0) (e1)) = (op (e1) (e1)))) -> ((op (e1) (e1)) = (e1)) -> (~((op (e2) (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 (e3) (e3)) = (e0))\/(((op (e3) (e3)) = (e1))\/(((op (e3) (e3)) = (e2))\/((op (e3) (e3)) = (e3))))) -> (~((op (e3) (e3)) = (e0))) -> (~((op (e0) (e3)) = (op (e3) (e3)))) -> (~((op (e3) (e3)) = (e2))) -> (~((op (e3) (e3)) = (e3))) -> False). % 15.09/15.32 do 0 intro. intros zenon_H44 zenon_H45 zenon_H23 zenon_H21 zenon_H30 zenon_H2f zenon_H28 zenon_H2e zenon_H2d zenon_H3b zenon_H3c zenon_H36 zenon_H3d zenon_H3e. % 15.09/15.32 apply (zenon_or_s _ _ zenon_H44); [ zenon_intro zenon_H47 | zenon_intro zenon_H46 ]. % 15.09/15.32 exact (zenon_H45 zenon_H47). % 15.09/15.32 apply (zenon_or_s _ _ zenon_H46); [ zenon_intro zenon_H22 | zenon_intro zenon_H48 ]. % 15.09/15.32 apply (zenon_L3_); trivial. % 15.09/15.32 apply (zenon_or_s _ _ zenon_H48); [ zenon_intro zenon_H29 | zenon_intro zenon_H37 ]. % 15.09/15.32 apply (zenon_L5_); trivial. % 15.09/15.32 apply (zenon_L7_); trivial. % 15.09/15.32 (* end of lemma zenon_L8_ *) % 15.09/15.32 assert (zenon_L9_ : ((op (e0) (e1)) = (e0)) -> ((op (e0) (e1)) = (e3)) -> (~((e0) = (e3))) -> False). % 15.09/15.32 do 0 intro. intros zenon_H49 zenon_H4a zenon_H4b. % 15.09/15.32 elim (classic ((e3) = (e3))); [ zenon_intro zenon_H4c | zenon_intro zenon_H4d ]. % 15.09/15.32 cut (((e3) = (e3)) = ((e0) = (e3))). % 15.09/15.32 intro zenon_D_pnotp. % 15.09/15.32 apply zenon_H4b. % 15.09/15.32 rewrite <- zenon_D_pnotp. % 15.09/15.32 exact zenon_H4c. % 15.09/15.32 cut (((e3) = (e3))); [idtac | apply NNPP; zenon_intro zenon_H4d]. % 15.09/15.32 cut (((e3) = (e0))); [idtac | apply NNPP; zenon_intro zenon_H4e]. % 15.09/15.32 congruence. % 15.09/15.32 cut (((op (e0) (e1)) = (e0)) = ((e3) = (e0))). % 15.09/15.32 intro zenon_D_pnotp. % 15.09/15.32 apply zenon_H4e. % 15.09/15.32 rewrite <- zenon_D_pnotp. % 15.09/15.32 exact zenon_H49. % 15.09/15.32 cut (((e0) = (e0))); [idtac | apply NNPP; zenon_intro zenon_H1d]. % 15.09/15.32 cut (((op (e0) (e1)) = (e3))); [idtac | apply NNPP; zenon_intro zenon_H4f]. % 15.09/15.32 congruence. % 15.09/15.32 exact (zenon_H4f zenon_H4a). % 15.09/15.32 apply zenon_H1d. apply refl_equal. % 15.09/15.32 apply zenon_H4d. apply refl_equal. % 15.09/15.32 apply zenon_H4d. apply refl_equal. % 15.09/15.32 (* end of lemma zenon_L9_ *) % 15.09/15.32 assert (zenon_L10_ : (~((op (e0) (e2)) = (op (e2) (e2)))) -> ((op (e0) (e2)) = (e3)) -> ((op (e2) (e2)) = (e3)) -> False). % 15.09/15.32 do 0 intro. intros zenon_H28 zenon_H50 zenon_H34. % 15.09/15.32 cut (((op (e0) (e2)) = (e3)) = ((op (e0) (e2)) = (op (e2) (e2)))). % 15.09/15.32 intro zenon_D_pnotp. % 15.09/15.32 apply zenon_H28. % 15.09/15.32 rewrite <- zenon_D_pnotp. % 15.09/15.32 exact zenon_H50. % 15.09/15.32 cut (((e3) = (op (e2) (e2)))); [idtac | apply NNPP; zenon_intro zenon_H51]. % 15.09/15.32 cut (((op (e0) (e2)) = (op (e0) (e2)))); [idtac | apply NNPP; zenon_intro zenon_H2c]. % 15.09/15.32 congruence. % 15.09/15.32 apply zenon_H2c. apply refl_equal. % 15.09/15.32 apply zenon_H51. apply sym_equal. exact zenon_H34. % 15.09/15.32 (* end of lemma zenon_L10_ *) % 15.09/15.32 assert (zenon_L11_ : (((op (e2) (e2)) = (e0))\/(((op (e2) (e2)) = (e1))\/(((op (e2) (e2)) = (e2))\/((op (e2) (e2)) = (e3))))) -> (~((op (e2) (e2)) = (e0))) -> (~((op (e2) (e2)) = (e1))) -> (~((op (e2) (e2)) = (e2))) -> (~((op (e0) (e2)) = (op (e2) (e2)))) -> ((op (e0) (e2)) = (e3)) -> False). % 15.09/15.32 do 0 intro. intros zenon_H2d zenon_H2e zenon_H52 zenon_H2f zenon_H28 zenon_H50. % 15.09/15.32 apply (zenon_or_s _ _ zenon_H2d); [ zenon_intro zenon_H32 | zenon_intro zenon_H31 ]. % 15.09/15.32 exact (zenon_H2e zenon_H32). % 15.09/15.32 apply (zenon_or_s _ _ zenon_H31); [ zenon_intro zenon_H2a | zenon_intro zenon_H33 ]. % 15.09/15.32 exact (zenon_H52 zenon_H2a). % 15.09/15.32 apply (zenon_or_s _ _ zenon_H33); [ zenon_intro zenon_H35 | zenon_intro zenon_H34 ]. % 15.09/15.32 exact (zenon_H2f zenon_H35). % 15.09/15.32 apply (zenon_L10_); trivial. % 15.09/15.32 (* end of lemma zenon_L11_ *) % 15.09/15.32 assert (zenon_L12_ : ((op (e3) (e3)) = (e3)) -> ((op (e0) (e3)) = (e3)) -> (~((op (e0) (e3)) = (op (e3) (e3)))) -> False). % 15.09/15.32 do 0 intro. intros zenon_H42 zenon_H53 zenon_H36. % 15.09/15.32 elim (classic ((op (e3) (e3)) = (op (e3) (e3)))); [ zenon_intro zenon_H54 | zenon_intro zenon_H55 ]. % 15.09/15.32 cut (((op (e3) (e3)) = (op (e3) (e3))) = ((op (e0) (e3)) = (op (e3) (e3)))). % 15.09/15.32 intro zenon_D_pnotp. % 15.09/15.32 apply zenon_H36. % 15.09/15.32 rewrite <- zenon_D_pnotp. % 15.09/15.32 exact zenon_H54. % 15.09/15.32 cut (((op (e3) (e3)) = (op (e3) (e3)))); [idtac | apply NNPP; zenon_intro zenon_H55]. % 15.09/15.32 cut (((op (e3) (e3)) = (op (e0) (e3)))); [idtac | apply NNPP; zenon_intro zenon_H56]. % 15.09/15.32 congruence. % 15.09/15.32 cut (((op (e3) (e3)) = (e3)) = ((op (e3) (e3)) = (op (e0) (e3)))). % 15.09/15.32 intro zenon_D_pnotp. % 15.09/15.32 apply zenon_H56. % 15.09/15.32 rewrite <- zenon_D_pnotp. % 15.09/15.32 exact zenon_H42. % 15.09/15.32 cut (((e3) = (op (e0) (e3)))); [idtac | apply NNPP; zenon_intro zenon_H57]. % 15.09/15.32 cut (((op (e3) (e3)) = (op (e3) (e3)))); [idtac | apply NNPP; zenon_intro zenon_H55]. % 15.09/15.32 congruence. % 15.09/15.32 apply zenon_H55. apply refl_equal. % 15.09/15.32 apply zenon_H57. apply sym_equal. exact zenon_H53. % 15.09/15.32 apply zenon_H55. apply refl_equal. % 15.09/15.32 apply zenon_H55. apply refl_equal. % 15.09/15.32 (* end of lemma zenon_L12_ *) % 15.09/15.32 assert (zenon_L13_ : (((op (e0) (e0)) = (e3))\/(((op (e0) (e1)) = (e3))\/(((op (e0) (e2)) = (e3))\/((op (e0) (e3)) = (e3))))) -> (~((op (e0) (e0)) = (e3))) -> (~((e0) = (e3))) -> ((op (e0) (e1)) = (e0)) -> (~((op (e0) (e2)) = (op (e2) (e2)))) -> (~((op (e2) (e2)) = (e2))) -> (~((op (e2) (e2)) = (e1))) -> (~((op (e2) (e2)) = (e0))) -> (((op (e2) (e2)) = (e0))\/(((op (e2) (e2)) = (e1))\/(((op (e2) (e2)) = (e2))\/((op (e2) (e2)) = (e3))))) -> ((op (e3) (e3)) = (e3)) -> (~((op (e0) (e3)) = (op (e3) (e3)))) -> False). % 15.09/15.32 do 0 intro. intros zenon_H58 zenon_H59 zenon_H4b zenon_H49 zenon_H28 zenon_H2f zenon_H52 zenon_H2e zenon_H2d zenon_H42 zenon_H36. % 15.09/15.32 apply (zenon_or_s _ _ zenon_H58); [ zenon_intro zenon_H5b | zenon_intro zenon_H5a ]. % 15.09/15.32 exact (zenon_H59 zenon_H5b). % 15.09/15.32 apply (zenon_or_s _ _ zenon_H5a); [ zenon_intro zenon_H4a | zenon_intro zenon_H5c ]. % 15.09/15.32 apply (zenon_L9_); trivial. % 15.09/15.32 apply (zenon_or_s _ _ zenon_H5c); [ zenon_intro zenon_H50 | zenon_intro zenon_H53 ]. % 15.09/15.32 apply (zenon_L11_); trivial. % 15.09/15.32 apply (zenon_L12_); trivial. % 15.09/15.32 (* end of lemma zenon_L13_ *) % 15.09/15.32 assert (zenon_L14_ : ((op (e0) (e1)) = (e0)) -> ((op (e0) (e1)) = (e2)) -> (~((e0) = (e2))) -> False). % 15.09/15.32 do 0 intro. intros zenon_H49 zenon_H5d zenon_H5e. % 15.09/15.32 elim (classic ((e2) = (e2))); [ zenon_intro zenon_H5f | zenon_intro zenon_H60 ]. % 15.09/15.32 cut (((e2) = (e2)) = ((e0) = (e2))). % 15.09/15.32 intro zenon_D_pnotp. % 15.09/15.32 apply zenon_H5e. % 15.09/15.32 rewrite <- zenon_D_pnotp. % 15.09/15.32 exact zenon_H5f. % 15.09/15.32 cut (((e2) = (e2))); [idtac | apply NNPP; zenon_intro zenon_H60]. % 15.09/15.32 cut (((e2) = (e0))); [idtac | apply NNPP; zenon_intro zenon_H61]. % 15.09/15.32 congruence. % 15.09/15.32 cut (((op (e0) (e1)) = (e0)) = ((e2) = (e0))). % 15.09/15.32 intro zenon_D_pnotp. % 15.09/15.32 apply zenon_H61. % 15.09/15.32 rewrite <- zenon_D_pnotp. % 15.09/15.32 exact zenon_H49. % 15.09/15.32 cut (((e0) = (e0))); [idtac | apply NNPP; zenon_intro zenon_H1d]. % 15.09/15.32 cut (((op (e0) (e1)) = (e2))); [idtac | apply NNPP; zenon_intro zenon_H62]. % 15.09/15.32 congruence. % 15.09/15.32 exact (zenon_H62 zenon_H5d). % 15.09/15.32 apply zenon_H1d. apply refl_equal. % 15.09/15.32 apply zenon_H60. apply refl_equal. % 15.09/15.32 apply zenon_H60. apply refl_equal. % 15.09/15.32 (* end of lemma zenon_L14_ *) % 15.09/15.32 assert (zenon_L15_ : ((op (e2) (e2)) = (e2)) -> ((op (e0) (e2)) = (e2)) -> (~((op (e0) (e2)) = (op (e2) (e2)))) -> False). % 15.09/15.32 do 0 intro. intros zenon_H35 zenon_H63 zenon_H28. % 15.09/15.32 elim (classic ((op (e2) (e2)) = (op (e2) (e2)))); [ zenon_intro zenon_H64 | zenon_intro zenon_H65 ]. % 15.09/15.32 cut (((op (e2) (e2)) = (op (e2) (e2))) = ((op (e0) (e2)) = (op (e2) (e2)))). % 15.09/15.32 intro zenon_D_pnotp. % 15.09/15.32 apply zenon_H28. % 15.09/15.32 rewrite <- zenon_D_pnotp. % 15.09/15.32 exact zenon_H64. % 15.09/15.32 cut (((op (e2) (e2)) = (op (e2) (e2)))); [idtac | apply NNPP; zenon_intro zenon_H65]. % 15.09/15.32 cut (((op (e2) (e2)) = (op (e0) (e2)))); [idtac | apply NNPP; zenon_intro zenon_H66]. % 15.09/15.32 congruence. % 15.09/15.32 cut (((op (e2) (e2)) = (e2)) = ((op (e2) (e2)) = (op (e0) (e2)))). % 15.09/15.32 intro zenon_D_pnotp. % 15.09/15.32 apply zenon_H66. % 15.09/15.32 rewrite <- zenon_D_pnotp. % 15.09/15.32 exact zenon_H35. % 15.09/15.32 cut (((e2) = (op (e0) (e2)))); [idtac | apply NNPP; zenon_intro zenon_H67]. % 15.09/15.32 cut (((op (e2) (e2)) = (op (e2) (e2)))); [idtac | apply NNPP; zenon_intro zenon_H65]. % 15.09/15.32 congruence. % 15.09/15.32 apply zenon_H65. apply refl_equal. % 15.09/15.32 apply zenon_H67. apply sym_equal. exact zenon_H63. % 15.09/15.32 apply zenon_H65. apply refl_equal. % 15.09/15.32 apply zenon_H65. apply refl_equal. % 15.09/15.32 (* end of lemma zenon_L15_ *) % 15.09/15.32 assert (zenon_L16_ : (~((e2) = (e2))) -> False). % 15.09/15.32 do 0 intro. intros zenon_H60. % 15.09/15.32 apply zenon_H60. apply refl_equal. % 15.09/15.32 (* end of lemma zenon_L16_ *) % 15.09/15.32 assert (zenon_L17_ : ((op (e1) (e0)) = (e2)) -> ((op (e1) (e0)) = (e3)) -> (~((e2) = (e3))) -> False). % 15.09/15.32 do 0 intro. intros zenon_H68 zenon_H69 zenon_H6a. % 15.09/15.32 elim (classic ((e3) = (e3))); [ zenon_intro zenon_H4c | zenon_intro zenon_H4d ]. % 15.09/15.32 cut (((e3) = (e3)) = ((e2) = (e3))). % 15.09/15.32 intro zenon_D_pnotp. % 15.09/15.32 apply zenon_H6a. % 15.09/15.32 rewrite <- zenon_D_pnotp. % 15.09/15.32 exact zenon_H4c. % 15.09/15.32 cut (((e3) = (e3))); [idtac | apply NNPP; zenon_intro zenon_H4d]. % 15.09/15.32 cut (((e3) = (e2))); [idtac | apply NNPP; zenon_intro zenon_H6b]. % 15.09/15.32 congruence. % 15.09/15.32 cut (((op (e1) (e0)) = (e2)) = ((e3) = (e2))). % 15.09/15.32 intro zenon_D_pnotp. % 15.09/15.32 apply zenon_H6b. % 15.09/15.32 rewrite <- zenon_D_pnotp. % 15.09/15.32 exact zenon_H68. % 15.09/15.32 cut (((e2) = (e2))); [idtac | apply NNPP; zenon_intro zenon_H60]. % 15.09/15.32 cut (((op (e1) (e0)) = (e3))); [idtac | apply NNPP; zenon_intro zenon_H6c]. % 15.09/15.32 congruence. % 15.09/15.32 exact (zenon_H6c zenon_H69). % 15.09/15.32 apply zenon_H60. apply refl_equal. % 15.09/15.32 apply zenon_H4d. apply refl_equal. % 15.09/15.32 apply zenon_H4d. apply refl_equal. % 15.09/15.32 (* end of lemma zenon_L17_ *) % 15.09/15.32 assert (zenon_L18_ : (~((op (op (e0) (e0)) (op (e0) (e0))) = (op (e1) (e1)))) -> ((op (e0) (e0)) = (e1)) -> False). % 15.09/15.32 do 0 intro. intros zenon_H6d zenon_H47. % 15.09/15.32 cut (((op (e0) (e0)) = (e1))); [idtac | apply NNPP; zenon_intro zenon_H45]. % 15.09/15.32 cut (((op (e0) (e0)) = (e1))); [idtac | apply NNPP; zenon_intro zenon_H45]. % 15.09/15.32 congruence. % 15.09/15.32 exact (zenon_H45 zenon_H47). % 15.09/15.32 exact (zenon_H45 zenon_H47). % 15.09/15.32 (* end of lemma zenon_L18_ *) % 15.09/15.32 assert (zenon_L19_ : (~((e3) = (e3))) -> False). % 15.09/15.32 do 0 intro. intros zenon_H4d. % 15.09/15.32 apply zenon_H4d. apply refl_equal. % 15.09/15.32 (* end of lemma zenon_L19_ *) % 15.09/15.32 assert (zenon_L20_ : ((op (e0) (e2)) = (e3)) -> ((op (e1) (e1)) = (e2)) -> ((op (e0) (e0)) = (e1)) -> False). % 15.09/15.32 do 0 intro. intros zenon_H50 zenon_H6e zenon_H47. % 15.09/15.32 apply (zenon_notand_s _ _ ax21); [ zenon_intro zenon_H70 | zenon_intro zenon_H6f ]. % 15.09/15.32 elim (classic ((op (op (e0) (e0)) (op (e0) (e0))) = (op (op (e0) (e0)) (op (e0) (e0))))); [ zenon_intro zenon_H71 | zenon_intro zenon_H72 ]. % 15.09/15.32 cut (((op (op (e0) (e0)) (op (e0) (e0))) = (op (op (e0) (e0)) (op (e0) (e0)))) = ((e2) = (op (op (e0) (e0)) (op (e0) (e0))))). % 15.09/15.32 intro zenon_D_pnotp. % 15.09/15.32 apply zenon_H70. % 15.09/15.32 rewrite <- zenon_D_pnotp. % 15.09/15.32 exact zenon_H71. % 15.09/15.32 cut (((op (op (e0) (e0)) (op (e0) (e0))) = (op (op (e0) (e0)) (op (e0) (e0))))); [idtac | apply NNPP; zenon_intro zenon_H72]. % 15.09/15.32 cut (((op (op (e0) (e0)) (op (e0) (e0))) = (e2))); [idtac | apply NNPP; zenon_intro zenon_H73]. % 15.09/15.32 congruence. % 15.09/15.32 cut (((op (e1) (e1)) = (e2)) = ((op (op (e0) (e0)) (op (e0) (e0))) = (e2))). % 15.09/15.32 intro zenon_D_pnotp. % 15.09/15.32 apply zenon_H73. % 15.09/15.32 rewrite <- zenon_D_pnotp. % 15.09/15.32 exact zenon_H6e. % 15.09/15.32 cut (((e2) = (e2))); [idtac | apply NNPP; zenon_intro zenon_H60]. % 15.09/15.32 cut (((op (e1) (e1)) = (op (op (e0) (e0)) (op (e0) (e0))))); [idtac | apply NNPP; zenon_intro zenon_H74]. % 15.09/15.32 congruence. % 15.09/15.32 elim (classic ((op (op (e0) (e0)) (op (e0) (e0))) = (op (op (e0) (e0)) (op (e0) (e0))))); [ zenon_intro zenon_H71 | zenon_intro zenon_H72 ]. % 15.09/15.32 cut (((op (op (e0) (e0)) (op (e0) (e0))) = (op (op (e0) (e0)) (op (e0) (e0)))) = ((op (e1) (e1)) = (op (op (e0) (e0)) (op (e0) (e0))))). % 15.09/15.32 intro zenon_D_pnotp. % 15.09/15.32 apply zenon_H74. % 15.09/15.32 rewrite <- zenon_D_pnotp. % 15.09/15.32 exact zenon_H71. % 15.09/15.32 cut (((op (op (e0) (e0)) (op (e0) (e0))) = (op (op (e0) (e0)) (op (e0) (e0))))); [idtac | apply NNPP; zenon_intro zenon_H72]. % 15.09/15.32 cut (((op (op (e0) (e0)) (op (e0) (e0))) = (op (e1) (e1)))); [idtac | apply NNPP; zenon_intro zenon_H6d]. % 15.09/15.32 congruence. % 15.09/15.32 apply (zenon_L18_); trivial. % 15.09/15.32 apply zenon_H72. apply refl_equal. % 15.09/15.32 apply zenon_H72. apply refl_equal. % 15.09/15.32 apply zenon_H60. apply refl_equal. % 15.09/15.32 apply zenon_H72. apply refl_equal. % 15.09/15.32 apply zenon_H72. apply refl_equal. % 15.09/15.32 apply (zenon_notand_s _ _ zenon_H6f); [ zenon_intro zenon_H76 | zenon_intro zenon_H75 ]. % 15.09/15.32 apply zenon_H76. apply sym_equal. exact zenon_H47. % 15.09/15.32 elim (classic ((op (e0) (op (op (e0) (e0)) (op (e0) (e0)))) = (op (e0) (op (op (e0) (e0)) (op (e0) (e0)))))); [ zenon_intro zenon_H77 | zenon_intro zenon_H78 ]. % 15.09/15.32 cut (((op (e0) (op (op (e0) (e0)) (op (e0) (e0)))) = (op (e0) (op (op (e0) (e0)) (op (e0) (e0))))) = ((e3) = (op (e0) (op (op (e0) (e0)) (op (e0) (e0)))))). % 15.09/15.32 intro zenon_D_pnotp. % 15.09/15.32 apply zenon_H75. % 15.09/15.32 rewrite <- zenon_D_pnotp. % 15.09/15.32 exact zenon_H77. % 15.09/15.32 cut (((op (e0) (op (op (e0) (e0)) (op (e0) (e0)))) = (op (e0) (op (op (e0) (e0)) (op (e0) (e0)))))); [idtac | apply NNPP; zenon_intro zenon_H78]. % 15.09/15.32 cut (((op (e0) (op (op (e0) (e0)) (op (e0) (e0)))) = (e3))); [idtac | apply NNPP; zenon_intro zenon_H79]. % 15.09/15.32 congruence. % 15.09/15.32 cut (((op (e0) (e2)) = (e3)) = ((op (e0) (op (op (e0) (e0)) (op (e0) (e0)))) = (e3))). % 15.09/15.32 intro zenon_D_pnotp. % 15.09/15.32 apply zenon_H79. % 15.09/15.32 rewrite <- zenon_D_pnotp. % 15.09/15.32 exact zenon_H50. % 15.09/15.32 cut (((e3) = (e3))); [idtac | apply NNPP; zenon_intro zenon_H4d]. % 15.09/15.32 cut (((op (e0) (e2)) = (op (e0) (op (op (e0) (e0)) (op (e0) (e0)))))); [idtac | apply NNPP; zenon_intro zenon_H7a]. % 15.09/15.32 congruence. % 15.09/15.32 elim (classic ((op (e0) (op (op (e0) (e0)) (op (e0) (e0)))) = (op (e0) (op (op (e0) (e0)) (op (e0) (e0)))))); [ zenon_intro zenon_H77 | zenon_intro zenon_H78 ]. % 15.09/15.32 cut (((op (e0) (op (op (e0) (e0)) (op (e0) (e0)))) = (op (e0) (op (op (e0) (e0)) (op (e0) (e0))))) = ((op (e0) (e2)) = (op (e0) (op (op (e0) (e0)) (op (e0) (e0)))))). % 15.09/15.32 intro zenon_D_pnotp. % 15.09/15.32 apply zenon_H7a. % 15.09/15.32 rewrite <- zenon_D_pnotp. % 15.09/15.32 exact zenon_H77. % 15.09/15.32 cut (((op (e0) (op (op (e0) (e0)) (op (e0) (e0)))) = (op (e0) (op (op (e0) (e0)) (op (e0) (e0)))))); [idtac | apply NNPP; zenon_intro zenon_H78]. % 15.09/15.32 cut (((op (e0) (op (op (e0) (e0)) (op (e0) (e0)))) = (op (e0) (e2)))); [idtac | apply NNPP; zenon_intro zenon_H7b]. % 15.09/15.32 congruence. % 15.09/15.32 cut (((op (op (e0) (e0)) (op (e0) (e0))) = (e2))); [idtac | apply NNPP; zenon_intro zenon_H73]. % 15.09/15.32 cut (((e0) = (e0))); [idtac | apply NNPP; zenon_intro zenon_H1d]. % 15.09/15.32 congruence. % 15.09/15.32 apply zenon_H1d. apply refl_equal. % 15.09/15.32 cut (((op (e1) (e1)) = (e2)) = ((op (op (e0) (e0)) (op (e0) (e0))) = (e2))). % 15.09/15.32 intro zenon_D_pnotp. % 15.09/15.32 apply zenon_H73. % 15.09/15.32 rewrite <- zenon_D_pnotp. % 15.09/15.32 exact zenon_H6e. % 15.09/15.32 cut (((e2) = (e2))); [idtac | apply NNPP; zenon_intro zenon_H60]. % 15.09/15.32 cut (((op (e1) (e1)) = (op (op (e0) (e0)) (op (e0) (e0))))); [idtac | apply NNPP; zenon_intro zenon_H74]. % 15.09/15.32 congruence. % 15.09/15.32 elim (classic ((op (op (e0) (e0)) (op (e0) (e0))) = (op (op (e0) (e0)) (op (e0) (e0))))); [ zenon_intro zenon_H71 | zenon_intro zenon_H72 ]. % 15.09/15.32 cut (((op (op (e0) (e0)) (op (e0) (e0))) = (op (op (e0) (e0)) (op (e0) (e0)))) = ((op (e1) (e1)) = (op (op (e0) (e0)) (op (e0) (e0))))). % 15.09/15.32 intro zenon_D_pnotp. % 15.09/15.32 apply zenon_H74. % 15.09/15.32 rewrite <- zenon_D_pnotp. % 15.09/15.32 exact zenon_H71. % 15.09/15.32 cut (((op (op (e0) (e0)) (op (e0) (e0))) = (op (op (e0) (e0)) (op (e0) (e0))))); [idtac | apply NNPP; zenon_intro zenon_H72]. % 15.09/15.32 cut (((op (op (e0) (e0)) (op (e0) (e0))) = (op (e1) (e1)))); [idtac | apply NNPP; zenon_intro zenon_H6d]. % 15.09/15.32 congruence. % 15.09/15.32 apply (zenon_L18_); trivial. % 15.09/15.32 apply zenon_H72. apply refl_equal. % 15.09/15.32 apply zenon_H72. apply refl_equal. % 15.09/15.32 apply zenon_H60. apply refl_equal. % 15.09/15.32 apply zenon_H78. apply refl_equal. % 15.09/15.32 apply zenon_H78. apply refl_equal. % 15.09/15.32 apply zenon_H4d. apply refl_equal. % 15.09/15.32 apply zenon_H78. apply refl_equal. % 15.09/15.32 apply zenon_H78. apply refl_equal. % 15.09/15.32 (* end of lemma zenon_L20_ *) % 15.09/15.32 assert (zenon_L21_ : ((op (e2) (e2)) = (e2)) -> ((op (e1) (e2)) = (e2)) -> (~((op (e1) (e2)) = (op (e2) (e2)))) -> False). % 15.09/15.32 do 0 intro. intros zenon_H35 zenon_H7c zenon_H7d. % 15.09/15.32 elim (classic ((op (e2) (e2)) = (op (e2) (e2)))); [ zenon_intro zenon_H64 | zenon_intro zenon_H65 ]. % 15.09/15.32 cut (((op (e2) (e2)) = (op (e2) (e2))) = ((op (e1) (e2)) = (op (e2) (e2)))). % 15.09/15.32 intro zenon_D_pnotp. % 15.09/15.32 apply zenon_H7d. % 15.09/15.32 rewrite <- zenon_D_pnotp. % 15.09/15.32 exact zenon_H64. % 15.09/15.32 cut (((op (e2) (e2)) = (op (e2) (e2)))); [idtac | apply NNPP; zenon_intro zenon_H65]. % 15.09/15.32 cut (((op (e2) (e2)) = (op (e1) (e2)))); [idtac | apply NNPP; zenon_intro zenon_H7e]. % 15.09/15.32 congruence. % 15.09/15.32 cut (((op (e2) (e2)) = (e2)) = ((op (e2) (e2)) = (op (e1) (e2)))). % 15.09/15.32 intro zenon_D_pnotp. % 15.09/15.32 apply zenon_H7e. % 15.09/15.32 rewrite <- zenon_D_pnotp. % 15.09/15.32 exact zenon_H35. % 15.09/15.32 cut (((e2) = (op (e1) (e2)))); [idtac | apply NNPP; zenon_intro zenon_H7f]. % 15.09/15.32 cut (((op (e2) (e2)) = (op (e2) (e2)))); [idtac | apply NNPP; zenon_intro zenon_H65]. % 15.09/15.32 congruence. % 15.09/15.32 apply zenon_H65. apply refl_equal. % 15.09/15.32 apply zenon_H7f. apply sym_equal. exact zenon_H7c. % 15.09/15.32 apply zenon_H65. apply refl_equal. % 15.09/15.32 apply zenon_H65. apply refl_equal. % 15.09/15.32 (* end of lemma zenon_L21_ *) % 15.09/15.32 assert (zenon_L22_ : (~((op (e0) (e3)) = (op (e1) (e3)))) -> ((op (e0) (e3)) = (e2)) -> ((op (e1) (e3)) = (e2)) -> False). % 15.09/15.32 do 0 intro. intros zenon_H80 zenon_H81 zenon_H82. % 15.09/15.32 cut (((op (e0) (e3)) = (e2)) = ((op (e0) (e3)) = (op (e1) (e3)))). % 15.09/15.32 intro zenon_D_pnotp. % 15.09/15.32 apply zenon_H80. % 15.09/15.32 rewrite <- zenon_D_pnotp. % 15.09/15.32 exact zenon_H81. % 15.09/15.32 cut (((e2) = (op (e1) (e3)))); [idtac | apply NNPP; zenon_intro zenon_H83]. % 15.09/15.32 cut (((op (e0) (e3)) = (op (e0) (e3)))); [idtac | apply NNPP; zenon_intro zenon_H3a]. % 15.09/15.32 congruence. % 15.09/15.32 apply zenon_H3a. apply refl_equal. % 15.09/15.32 apply zenon_H83. apply sym_equal. exact zenon_H82. % 15.09/15.32 (* end of lemma zenon_L22_ *) % 15.09/15.32 assert (zenon_L23_ : (((op (e1) (e0)) = (e2))\/(((op (e1) (e1)) = (e2))\/(((op (e1) (e2)) = (e2))\/((op (e1) (e3)) = (e2))))) -> (~((e2) = (e3))) -> ((op (e1) (e0)) = (e3)) -> ((op (e0) (e0)) = (e1)) -> ((op (e0) (e2)) = (e3)) -> (~((op (e1) (e2)) = (op (e2) (e2)))) -> ((op (e2) (e2)) = (e2)) -> (~((op (e0) (e3)) = (op (e1) (e3)))) -> ((op (e0) (e3)) = (e2)) -> False). % 15.09/15.32 do 0 intro. intros zenon_H84 zenon_H6a zenon_H69 zenon_H47 zenon_H50 zenon_H7d zenon_H35 zenon_H80 zenon_H81. % 15.09/15.32 apply (zenon_or_s _ _ zenon_H84); [ zenon_intro zenon_H68 | zenon_intro zenon_H85 ]. % 15.09/15.32 apply (zenon_L17_); trivial. % 15.09/15.32 apply (zenon_or_s _ _ zenon_H85); [ zenon_intro zenon_H6e | zenon_intro zenon_H86 ]. % 15.09/15.32 apply (zenon_L20_); trivial. % 15.09/15.32 apply (zenon_or_s _ _ zenon_H86); [ zenon_intro zenon_H7c | zenon_intro zenon_H82 ]. % 15.09/15.32 apply (zenon_L21_); trivial. % 15.09/15.32 apply (zenon_L22_); trivial. % 15.09/15.32 (* end of lemma zenon_L23_ *) % 15.09/15.32 assert (zenon_L24_ : (~((op (e0) (e2)) = (op (e1) (e2)))) -> ((op (e0) (e2)) = (e3)) -> ((op (e1) (e2)) = (e3)) -> False). % 15.09/15.32 do 0 intro. intros zenon_H87 zenon_H50 zenon_H88. % 15.09/15.32 cut (((op (e0) (e2)) = (e3)) = ((op (e0) (e2)) = (op (e1) (e2)))). % 15.09/15.32 intro zenon_D_pnotp. % 15.09/15.32 apply zenon_H87. % 15.09/15.32 rewrite <- zenon_D_pnotp. % 15.09/15.32 exact zenon_H50. % 15.09/15.32 cut (((e3) = (op (e1) (e2)))); [idtac | apply NNPP; zenon_intro zenon_H89]. % 15.09/15.32 cut (((op (e0) (e2)) = (op (e0) (e2)))); [idtac | apply NNPP; zenon_intro zenon_H2c]. % 15.09/15.32 congruence. % 15.09/15.32 apply zenon_H2c. apply refl_equal. % 15.09/15.32 apply zenon_H89. apply sym_equal. exact zenon_H88. % 15.09/15.32 (* end of lemma zenon_L24_ *) % 15.09/15.32 assert (zenon_L25_ : ((op (e3) (e3)) = (e3)) -> ((op (e1) (e3)) = (e3)) -> (~((op (e1) (e3)) = (op (e3) (e3)))) -> False). % 15.09/15.32 do 0 intro. intros zenon_H42 zenon_H8a zenon_H8b. % 15.09/15.32 elim (classic ((op (e3) (e3)) = (op (e3) (e3)))); [ zenon_intro zenon_H54 | zenon_intro zenon_H55 ]. % 15.09/15.32 cut (((op (e3) (e3)) = (op (e3) (e3))) = ((op (e1) (e3)) = (op (e3) (e3)))). % 15.09/15.32 intro zenon_D_pnotp. % 15.09/15.32 apply zenon_H8b. % 15.09/15.32 rewrite <- zenon_D_pnotp. % 15.09/15.32 exact zenon_H54. % 15.09/15.32 cut (((op (e3) (e3)) = (op (e3) (e3)))); [idtac | apply NNPP; zenon_intro zenon_H55]. % 15.09/15.32 cut (((op (e3) (e3)) = (op (e1) (e3)))); [idtac | apply NNPP; zenon_intro zenon_H8c]. % 15.09/15.32 congruence. % 15.09/15.32 cut (((op (e3) (e3)) = (e3)) = ((op (e3) (e3)) = (op (e1) (e3)))). % 15.09/15.32 intro zenon_D_pnotp. % 15.09/15.32 apply zenon_H8c. % 15.09/15.32 rewrite <- zenon_D_pnotp. % 15.09/15.32 exact zenon_H42. % 15.09/15.32 cut (((e3) = (op (e1) (e3)))); [idtac | apply NNPP; zenon_intro zenon_H8d]. % 15.09/15.32 cut (((op (e3) (e3)) = (op (e3) (e3)))); [idtac | apply NNPP; zenon_intro zenon_H55]. % 15.09/15.32 congruence. % 15.09/15.32 apply zenon_H55. apply refl_equal. % 15.09/15.32 apply zenon_H8d. apply sym_equal. exact zenon_H8a. % 15.09/15.32 apply zenon_H55. apply refl_equal. % 15.09/15.32 apply zenon_H55. apply refl_equal. % 15.09/15.32 (* end of lemma zenon_L25_ *) % 15.09/15.32 assert (zenon_L26_ : (((op (e0) (e0)) = (e2))\/(((op (e0) (e1)) = (e2))\/(((op (e0) (e2)) = (e2))\/((op (e0) (e3)) = (e2))))) -> (~((op (e0) (e0)) = (e2))) -> (~((e0) = (e2))) -> (~((op (e0) (e2)) = (op (e2) (e2)))) -> (((op (e0) (e0)) = (e3))\/(((op (e0) (e1)) = (e3))\/(((op (e0) (e2)) = (e3))\/((op (e0) (e3)) = (e3))))) -> (~((op (e0) (e0)) = (e3))) -> (~((e0) = (e3))) -> ((op (e0) (e1)) = (e0)) -> (~((op (e1) (e3)) = (op (e3) (e3)))) -> (~((op (e0) (e2)) = (op (e1) (e2)))) -> ((op (e0) (e0)) = (e1)) -> (((op (e1) (e0)) = (e2))\/(((op (e1) (e1)) = (e2))\/(((op (e1) (e2)) = (e2))\/((op (e1) (e3)) = (e2))))) -> (~((e2) = (e3))) -> (~((op (e1) (e2)) = (op (e2) (e2)))) -> ((op (e2) (e2)) = (e2)) -> (~((op (e0) (e3)) = (op (e1) (e3)))) -> (((op (e1) (e0)) = (e3))\/(((op (e1) (e1)) = (e3))\/(((op (e1) (e2)) = (e3))\/((op (e1) (e3)) = (e3))))) -> ((op (e3) (e3)) = (e3)) -> (~((op (e0) (e3)) = (op (e3) (e3)))) -> False). % 15.09/15.32 do 0 intro. intros zenon_H8e zenon_H8f zenon_H5e zenon_H28 zenon_H58 zenon_H59 zenon_H4b zenon_H49 zenon_H8b zenon_H87 zenon_H47 zenon_H84 zenon_H6a zenon_H7d zenon_H35 zenon_H80 zenon_H90 zenon_H42 zenon_H36. % 15.09/15.32 apply (zenon_or_s _ _ zenon_H8e); [ zenon_intro zenon_H92 | zenon_intro zenon_H91 ]. % 15.09/15.32 exact (zenon_H8f zenon_H92). % 15.09/15.32 apply (zenon_or_s _ _ zenon_H91); [ zenon_intro zenon_H5d | zenon_intro zenon_H93 ]. % 15.09/15.32 apply (zenon_L14_); trivial. % 15.09/15.32 apply (zenon_or_s _ _ zenon_H93); [ zenon_intro zenon_H63 | zenon_intro zenon_H81 ]. % 15.09/15.32 apply (zenon_L15_); trivial. % 15.09/15.32 apply (zenon_or_s _ _ zenon_H58); [ zenon_intro zenon_H5b | zenon_intro zenon_H5a ]. % 15.09/15.32 exact (zenon_H59 zenon_H5b). % 15.09/15.32 apply (zenon_or_s _ _ zenon_H5a); [ zenon_intro zenon_H4a | zenon_intro zenon_H5c ]. % 15.09/15.32 apply (zenon_L9_); trivial. % 15.09/15.32 apply (zenon_or_s _ _ zenon_H5c); [ zenon_intro zenon_H50 | zenon_intro zenon_H53 ]. % 15.09/15.32 apply (zenon_or_s _ _ zenon_H90); [ zenon_intro zenon_H69 | zenon_intro zenon_H94 ]. % 15.09/15.32 apply (zenon_L23_); trivial. % 15.09/15.32 apply (zenon_or_s _ _ zenon_H94); [ zenon_intro zenon_H96 | zenon_intro zenon_H95 ]. % 15.09/15.32 apply (zenon_notand_s _ _ ax27); [ zenon_intro zenon_H98 | zenon_intro zenon_H97 ]. % 15.09/15.32 elim (classic ((op (op (e0) (e0)) (op (e0) (e0))) = (op (op (e0) (e0)) (op (e0) (e0))))); [ zenon_intro zenon_H71 | zenon_intro zenon_H72 ]. % 15.09/15.32 cut (((op (op (e0) (e0)) (op (e0) (e0))) = (op (op (e0) (e0)) (op (e0) (e0)))) = ((e3) = (op (op (e0) (e0)) (op (e0) (e0))))). % 15.09/15.32 intro zenon_D_pnotp. % 15.09/15.32 apply zenon_H98. % 15.09/15.32 rewrite <- zenon_D_pnotp. % 15.09/15.32 exact zenon_H71. % 15.09/15.32 cut (((op (op (e0) (e0)) (op (e0) (e0))) = (op (op (e0) (e0)) (op (e0) (e0))))); [idtac | apply NNPP; zenon_intro zenon_H72]. % 15.09/15.32 cut (((op (op (e0) (e0)) (op (e0) (e0))) = (e3))); [idtac | apply NNPP; zenon_intro zenon_H99]. % 15.09/15.32 congruence. % 15.09/15.32 cut (((op (e1) (e1)) = (e3)) = ((op (op (e0) (e0)) (op (e0) (e0))) = (e3))). % 15.09/15.32 intro zenon_D_pnotp. % 15.09/15.32 apply zenon_H99. % 15.09/15.32 rewrite <- zenon_D_pnotp. % 15.09/15.32 exact zenon_H96. % 15.09/15.32 cut (((e3) = (e3))); [idtac | apply NNPP; zenon_intro zenon_H4d]. % 15.09/15.32 cut (((op (e1) (e1)) = (op (op (e0) (e0)) (op (e0) (e0))))); [idtac | apply NNPP; zenon_intro zenon_H74]. % 15.09/15.32 congruence. % 15.09/15.32 elim (classic ((op (op (e0) (e0)) (op (e0) (e0))) = (op (op (e0) (e0)) (op (e0) (e0))))); [ zenon_intro zenon_H71 | zenon_intro zenon_H72 ]. % 15.09/15.32 cut (((op (op (e0) (e0)) (op (e0) (e0))) = (op (op (e0) (e0)) (op (e0) (e0)))) = ((op (e1) (e1)) = (op (op (e0) (e0)) (op (e0) (e0))))). % 15.09/15.32 intro zenon_D_pnotp. % 15.09/15.32 apply zenon_H74. % 15.09/15.32 rewrite <- zenon_D_pnotp. % 15.09/15.32 exact zenon_H71. % 15.09/15.32 cut (((op (op (e0) (e0)) (op (e0) (e0))) = (op (op (e0) (e0)) (op (e0) (e0))))); [idtac | apply NNPP; zenon_intro zenon_H72]. % 15.09/15.32 cut (((op (op (e0) (e0)) (op (e0) (e0))) = (op (e1) (e1)))); [idtac | apply NNPP; zenon_intro zenon_H6d]. % 15.09/15.32 congruence. % 15.09/15.32 apply (zenon_L18_); trivial. % 15.09/15.32 apply zenon_H72. apply refl_equal. % 15.09/15.32 apply zenon_H72. apply refl_equal. % 15.09/15.32 apply zenon_H4d. apply refl_equal. % 15.09/15.32 apply zenon_H72. apply refl_equal. % 15.09/15.32 apply zenon_H72. apply refl_equal. % 15.09/15.32 apply (zenon_notand_s _ _ zenon_H97); [ zenon_intro zenon_H76 | zenon_intro zenon_H9a ]. % 15.09/15.32 apply zenon_H76. apply sym_equal. exact zenon_H47. % 15.09/15.32 elim (classic ((op (e0) (op (op (e0) (e0)) (op (e0) (e0)))) = (op (e0) (op (op (e0) (e0)) (op (e0) (e0)))))); [ zenon_intro zenon_H77 | zenon_intro zenon_H78 ]. % 15.09/15.32 cut (((op (e0) (op (op (e0) (e0)) (op (e0) (e0)))) = (op (e0) (op (op (e0) (e0)) (op (e0) (e0))))) = ((e2) = (op (e0) (op (op (e0) (e0)) (op (e0) (e0)))))). % 15.09/15.32 intro zenon_D_pnotp. % 15.09/15.32 apply zenon_H9a. % 15.09/15.32 rewrite <- zenon_D_pnotp. % 15.09/15.32 exact zenon_H77. % 15.09/15.32 cut (((op (e0) (op (op (e0) (e0)) (op (e0) (e0)))) = (op (e0) (op (op (e0) (e0)) (op (e0) (e0)))))); [idtac | apply NNPP; zenon_intro zenon_H78]. % 15.09/15.32 cut (((op (e0) (op (op (e0) (e0)) (op (e0) (e0)))) = (e2))); [idtac | apply NNPP; zenon_intro zenon_H9b]. % 15.09/15.32 congruence. % 15.09/15.32 cut (((op (e0) (e3)) = (e2)) = ((op (e0) (op (op (e0) (e0)) (op (e0) (e0)))) = (e2))). % 15.09/15.32 intro zenon_D_pnotp. % 15.09/15.32 apply zenon_H9b. % 15.09/15.32 rewrite <- zenon_D_pnotp. % 15.09/15.32 exact zenon_H81. % 15.09/15.32 cut (((e2) = (e2))); [idtac | apply NNPP; zenon_intro zenon_H60]. % 15.09/15.32 cut (((op (e0) (e3)) = (op (e0) (op (op (e0) (e0)) (op (e0) (e0)))))); [idtac | apply NNPP; zenon_intro zenon_H9c]. % 15.09/15.32 congruence. % 15.09/15.32 elim (classic ((op (e0) (op (op (e0) (e0)) (op (e0) (e0)))) = (op (e0) (op (op (e0) (e0)) (op (e0) (e0)))))); [ zenon_intro zenon_H77 | zenon_intro zenon_H78 ]. % 15.09/15.32 cut (((op (e0) (op (op (e0) (e0)) (op (e0) (e0)))) = (op (e0) (op (op (e0) (e0)) (op (e0) (e0))))) = ((op (e0) (e3)) = (op (e0) (op (op (e0) (e0)) (op (e0) (e0)))))). % 15.09/15.32 intro zenon_D_pnotp. % 15.09/15.32 apply zenon_H9c. % 15.09/15.32 rewrite <- zenon_D_pnotp. % 15.09/15.32 exact zenon_H77. % 15.09/15.32 cut (((op (e0) (op (op (e0) (e0)) (op (e0) (e0)))) = (op (e0) (op (op (e0) (e0)) (op (e0) (e0)))))); [idtac | apply NNPP; zenon_intro zenon_H78]. % 15.09/15.32 cut (((op (e0) (op (op (e0) (e0)) (op (e0) (e0)))) = (op (e0) (e3)))); [idtac | apply NNPP; zenon_intro zenon_H9d]. % 15.09/15.32 congruence. % 15.09/15.32 cut (((op (op (e0) (e0)) (op (e0) (e0))) = (e3))); [idtac | apply NNPP; zenon_intro zenon_H99]. % 15.09/15.32 cut (((e0) = (e0))); [idtac | apply NNPP; zenon_intro zenon_H1d]. % 15.09/15.32 congruence. % 15.09/15.32 apply zenon_H1d. apply refl_equal. % 15.09/15.32 cut (((op (e1) (e1)) = (e3)) = ((op (op (e0) (e0)) (op (e0) (e0))) = (e3))). % 15.09/15.32 intro zenon_D_pnotp. % 15.09/15.32 apply zenon_H99. % 15.09/15.32 rewrite <- zenon_D_pnotp. % 15.09/15.32 exact zenon_H96. % 15.09/15.32 cut (((e3) = (e3))); [idtac | apply NNPP; zenon_intro zenon_H4d]. % 15.09/15.32 cut (((op (e1) (e1)) = (op (op (e0) (e0)) (op (e0) (e0))))); [idtac | apply NNPP; zenon_intro zenon_H74]. % 15.09/15.32 congruence. % 15.09/15.32 elim (classic ((op (op (e0) (e0)) (op (e0) (e0))) = (op (op (e0) (e0)) (op (e0) (e0))))); [ zenon_intro zenon_H71 | zenon_intro zenon_H72 ]. % 15.09/15.32 cut (((op (op (e0) (e0)) (op (e0) (e0))) = (op (op (e0) (e0)) (op (e0) (e0)))) = ((op (e1) (e1)) = (op (op (e0) (e0)) (op (e0) (e0))))). % 15.09/15.32 intro zenon_D_pnotp. % 15.09/15.32 apply zenon_H74. % 15.09/15.32 rewrite <- zenon_D_pnotp. % 15.09/15.32 exact zenon_H71. % 15.09/15.32 cut (((op (op (e0) (e0)) (op (e0) (e0))) = (op (op (e0) (e0)) (op (e0) (e0))))); [idtac | apply NNPP; zenon_intro zenon_H72]. % 15.09/15.32 cut (((op (op (e0) (e0)) (op (e0) (e0))) = (op (e1) (e1)))); [idtac | apply NNPP; zenon_intro zenon_H6d]. % 15.09/15.32 congruence. % 15.09/15.32 apply (zenon_L18_); trivial. % 15.09/15.32 apply zenon_H72. apply refl_equal. % 15.09/15.32 apply zenon_H72. apply refl_equal. % 15.09/15.32 apply zenon_H4d. apply refl_equal. % 15.09/15.32 apply zenon_H78. apply refl_equal. % 15.09/15.32 apply zenon_H78. apply refl_equal. % 15.09/15.32 apply zenon_H60. apply refl_equal. % 15.09/15.32 apply zenon_H78. apply refl_equal. % 15.09/15.32 apply zenon_H78. apply refl_equal. % 15.09/15.32 apply (zenon_or_s _ _ zenon_H95); [ zenon_intro zenon_H88 | zenon_intro zenon_H8a ]. % 15.09/15.32 apply (zenon_L24_); trivial. % 15.09/15.32 apply (zenon_L25_); trivial. % 15.09/15.32 apply (zenon_L12_); trivial. % 15.09/15.32 (* end of lemma zenon_L26_ *) % 15.09/15.32 assert (zenon_L27_ : ((op (e0) (e1)) = (e0)) -> ((op (e0) (e1)) = (e1)) -> (~((e0) = (e1))) -> False). % 15.09/15.32 do 0 intro. intros zenon_H49 zenon_H22 zenon_H9e. % 15.09/15.32 elim (classic ((e1) = (e1))); [ zenon_intro zenon_H9f | zenon_intro zenon_Ha0 ]. % 15.09/15.32 cut (((e1) = (e1)) = ((e0) = (e1))). % 15.09/15.32 intro zenon_D_pnotp. % 15.09/15.32 apply zenon_H9e. % 15.09/15.32 rewrite <- zenon_D_pnotp. % 15.09/15.32 exact zenon_H9f. % 15.09/15.32 cut (((e1) = (e1))); [idtac | apply NNPP; zenon_intro zenon_Ha0]. % 15.09/15.32 cut (((e1) = (e0))); [idtac | apply NNPP; zenon_intro zenon_Ha1]. % 15.09/15.32 congruence. % 15.09/15.32 cut (((op (e0) (e1)) = (e0)) = ((e1) = (e0))). % 15.09/15.32 intro zenon_D_pnotp. % 15.09/15.32 apply zenon_Ha1. % 15.09/15.32 rewrite <- zenon_D_pnotp. % 15.09/15.32 exact zenon_H49. % 15.09/15.32 cut (((e0) = (e0))); [idtac | apply NNPP; zenon_intro zenon_H1d]. % 15.09/15.32 cut (((op (e0) (e1)) = (e1))); [idtac | apply NNPP; zenon_intro zenon_Ha2]. % 15.09/15.32 congruence. % 15.09/15.32 exact (zenon_Ha2 zenon_H22). % 15.09/15.32 apply zenon_H1d. apply refl_equal. % 15.09/15.32 apply zenon_Ha0. apply refl_equal. % 15.09/15.32 apply zenon_Ha0. apply refl_equal. % 15.09/15.32 (* end of lemma zenon_L27_ *) % 15.09/15.32 assert (zenon_L28_ : (~((e1) = (e1))) -> False). % 15.09/15.32 do 0 intro. intros zenon_Ha0. % 15.09/15.32 apply zenon_Ha0. apply refl_equal. % 15.09/15.32 (* end of lemma zenon_L28_ *) % 15.09/15.32 assert (zenon_L29_ : ((op (e0) (e2)) = (e1)) -> ((op (e0) (e2)) = (e3)) -> (~((e1) = (e3))) -> False). % 15.09/15.32 do 0 intro. intros zenon_H29 zenon_H50 zenon_Ha3. % 15.09/15.32 elim (classic ((e3) = (e3))); [ zenon_intro zenon_H4c | zenon_intro zenon_H4d ]. % 15.09/15.32 cut (((e3) = (e3)) = ((e1) = (e3))). % 15.09/15.32 intro zenon_D_pnotp. % 15.09/15.32 apply zenon_Ha3. % 15.09/15.32 rewrite <- zenon_D_pnotp. % 15.09/15.32 exact zenon_H4c. % 15.09/15.32 cut (((e3) = (e3))); [idtac | apply NNPP; zenon_intro zenon_H4d]. % 15.09/15.32 cut (((e3) = (e1))); [idtac | apply NNPP; zenon_intro zenon_Ha4]. % 15.09/15.32 congruence. % 15.09/15.32 cut (((op (e0) (e2)) = (e1)) = ((e3) = (e1))). % 15.09/15.32 intro zenon_D_pnotp. % 15.09/15.32 apply zenon_Ha4. % 15.09/15.32 rewrite <- zenon_D_pnotp. % 15.09/15.32 exact zenon_H29. % 15.09/15.32 cut (((e1) = (e1))); [idtac | apply NNPP; zenon_intro zenon_Ha0]. % 15.09/15.32 cut (((op (e0) (e2)) = (e3))); [idtac | apply NNPP; zenon_intro zenon_Ha5]. % 15.09/15.32 congruence. % 15.09/15.32 exact (zenon_Ha5 zenon_H50). % 15.09/15.32 apply zenon_Ha0. apply refl_equal. % 15.09/15.32 apply zenon_H4d. apply refl_equal. % 15.09/15.32 apply zenon_H4d. apply refl_equal. % 15.09/15.32 (* end of lemma zenon_L29_ *) % 15.09/15.32 assert (zenon_L30_ : (((op (e0) (e0)) = (e3))\/(((op (e0) (e1)) = (e3))\/(((op (e0) (e2)) = (e3))\/((op (e0) (e3)) = (e3))))) -> (~((op (e0) (e0)) = (e3))) -> (~((e0) = (e3))) -> ((op (e0) (e1)) = (e0)) -> (~((e1) = (e3))) -> ((op (e0) (e2)) = (e1)) -> ((op (e3) (e3)) = (e3)) -> (~((op (e0) (e3)) = (op (e3) (e3)))) -> False). % 15.09/15.32 do 0 intro. intros zenon_H58 zenon_H59 zenon_H4b zenon_H49 zenon_Ha3 zenon_H29 zenon_H42 zenon_H36. % 15.09/15.32 apply (zenon_or_s _ _ zenon_H58); [ zenon_intro zenon_H5b | zenon_intro zenon_H5a ]. % 15.09/15.32 exact (zenon_H59 zenon_H5b). % 15.09/15.32 apply (zenon_or_s _ _ zenon_H5a); [ zenon_intro zenon_H4a | zenon_intro zenon_H5c ]. % 15.09/15.32 apply (zenon_L9_); trivial. % 15.09/15.32 apply (zenon_or_s _ _ zenon_H5c); [ zenon_intro zenon_H50 | zenon_intro zenon_H53 ]. % 15.09/15.32 apply (zenon_L29_); trivial. % 15.09/15.32 apply (zenon_L12_); trivial. % 15.09/15.32 (* end of lemma zenon_L30_ *) % 15.09/15.32 assert (zenon_L31_ : ((op (e0) (e2)) = (e2)) -> ((op (e0) (e2)) = (e3)) -> (~((e2) = (e3))) -> False). % 15.09/15.32 do 0 intro. intros zenon_H63 zenon_H50 zenon_H6a. % 15.09/15.32 elim (classic ((e3) = (e3))); [ zenon_intro zenon_H4c | zenon_intro zenon_H4d ]. % 15.09/15.32 cut (((e3) = (e3)) = ((e2) = (e3))). % 15.09/15.32 intro zenon_D_pnotp. % 15.09/15.32 apply zenon_H6a. % 15.09/15.32 rewrite <- zenon_D_pnotp. % 15.09/15.32 exact zenon_H4c. % 15.09/15.32 cut (((e3) = (e3))); [idtac | apply NNPP; zenon_intro zenon_H4d]. % 15.09/15.32 cut (((e3) = (e2))); [idtac | apply NNPP; zenon_intro zenon_H6b]. % 15.09/15.32 congruence. % 15.09/15.32 cut (((op (e0) (e2)) = (e2)) = ((e3) = (e2))). % 15.09/15.32 intro zenon_D_pnotp. % 15.09/15.32 apply zenon_H6b. % 15.09/15.32 rewrite <- zenon_D_pnotp. % 15.09/15.32 exact zenon_H63. % 15.09/15.32 cut (((e2) = (e2))); [idtac | apply NNPP; zenon_intro zenon_H60]. % 15.09/15.32 cut (((op (e0) (e2)) = (e3))); [idtac | apply NNPP; zenon_intro zenon_Ha5]. % 15.09/15.32 congruence. % 15.09/15.32 exact (zenon_Ha5 zenon_H50). % 15.09/15.32 apply zenon_H60. apply refl_equal. % 15.09/15.32 apply zenon_H4d. apply refl_equal. % 15.09/15.32 apply zenon_H4d. apply refl_equal. % 15.09/15.32 (* end of lemma zenon_L31_ *) % 15.09/15.32 assert (zenon_L32_ : ((op (e0) (e3)) = (e1)) -> ((op (e0) (e3)) = (e3)) -> (~((e1) = (e3))) -> False). % 15.09/15.32 do 0 intro. intros zenon_H37 zenon_H53 zenon_Ha3. % 15.09/15.32 elim (classic ((e3) = (e3))); [ zenon_intro zenon_H4c | zenon_intro zenon_H4d ]. % 15.09/15.32 cut (((e3) = (e3)) = ((e1) = (e3))). % 15.09/15.32 intro zenon_D_pnotp. % 15.09/15.32 apply zenon_Ha3. % 15.09/15.32 rewrite <- zenon_D_pnotp. % 15.09/15.32 exact zenon_H4c. % 15.09/15.32 cut (((e3) = (e3))); [idtac | apply NNPP; zenon_intro zenon_H4d]. % 15.09/15.32 cut (((e3) = (e1))); [idtac | apply NNPP; zenon_intro zenon_Ha4]. % 15.09/15.32 congruence. % 15.09/15.32 cut (((op (e0) (e3)) = (e1)) = ((e3) = (e1))). % 15.09/15.32 intro zenon_D_pnotp. % 15.09/15.32 apply zenon_Ha4. % 15.09/15.32 rewrite <- zenon_D_pnotp. % 15.09/15.32 exact zenon_H37. % 15.09/15.32 cut (((e1) = (e1))); [idtac | apply NNPP; zenon_intro zenon_Ha0]. % 15.09/15.32 cut (((op (e0) (e3)) = (e3))); [idtac | apply NNPP; zenon_intro zenon_Ha6]. % 15.09/15.32 congruence. % 15.09/15.32 exact (zenon_Ha6 zenon_H53). % 15.09/15.32 apply zenon_Ha0. apply refl_equal. % 15.09/15.32 apply zenon_H4d. apply refl_equal. % 15.09/15.32 apply zenon_H4d. apply refl_equal. % 15.09/15.32 (* end of lemma zenon_L32_ *) % 15.09/15.32 assert (zenon_L33_ : ((op (e0) (e3)) = (e1)) -> ((op (e0) (e3)) = (e2)) -> (~((e1) = (e2))) -> False). % 15.09/15.32 do 0 intro. intros zenon_H37 zenon_H81 zenon_Ha7. % 15.09/15.32 elim (classic ((e2) = (e2))); [ zenon_intro zenon_H5f | zenon_intro zenon_H60 ]. % 15.09/15.32 cut (((e2) = (e2)) = ((e1) = (e2))). % 15.09/15.32 intro zenon_D_pnotp. % 15.09/15.32 apply zenon_Ha7. % 15.09/15.32 rewrite <- zenon_D_pnotp. % 15.09/15.32 exact zenon_H5f. % 15.09/15.32 cut (((e2) = (e2))); [idtac | apply NNPP; zenon_intro zenon_H60]. % 15.09/15.32 cut (((e2) = (e1))); [idtac | apply NNPP; zenon_intro zenon_Ha8]. % 15.09/15.32 congruence. % 15.09/15.32 cut (((op (e0) (e3)) = (e1)) = ((e2) = (e1))). % 15.09/15.32 intro zenon_D_pnotp. % 15.09/15.32 apply zenon_Ha8. % 15.09/15.32 rewrite <- zenon_D_pnotp. % 15.09/15.32 exact zenon_H37. % 15.09/15.32 cut (((e1) = (e1))); [idtac | apply NNPP; zenon_intro zenon_Ha0]. % 15.09/15.32 cut (((op (e0) (e3)) = (e2))); [idtac | apply NNPP; zenon_intro zenon_Ha9]. % 15.09/15.32 congruence. % 15.09/15.32 exact (zenon_Ha9 zenon_H81). % 15.09/15.32 apply zenon_Ha0. apply refl_equal. % 15.09/15.32 apply zenon_H60. apply refl_equal. % 15.09/15.32 apply zenon_H60. apply refl_equal. % 15.09/15.32 (* end of lemma zenon_L33_ *) % 15.09/15.32 assert (zenon_L34_ : (((op (e0) (e0)) = (e2))\/(((op (e0) (e1)) = (e2))\/(((op (e0) (e2)) = (e2))\/((op (e0) (e3)) = (e2))))) -> (~((op (e0) (e0)) = (e2))) -> (~((e0) = (e2))) -> (~((e1) = (e3))) -> (~((e2) = (e3))) -> ((op (e0) (e1)) = (e0)) -> (~((e0) = (e3))) -> (~((op (e0) (e0)) = (e3))) -> (((op (e0) (e0)) = (e3))\/(((op (e0) (e1)) = (e3))\/(((op (e0) (e2)) = (e3))\/((op (e0) (e3)) = (e3))))) -> ((op (e0) (e3)) = (e1)) -> (~((e1) = (e2))) -> False). % 15.09/15.32 do 0 intro. intros zenon_H8e zenon_H8f zenon_H5e zenon_Ha3 zenon_H6a zenon_H49 zenon_H4b zenon_H59 zenon_H58 zenon_H37 zenon_Ha7. % 15.09/15.32 apply (zenon_or_s _ _ zenon_H8e); [ zenon_intro zenon_H92 | zenon_intro zenon_H91 ]. % 15.09/15.32 exact (zenon_H8f zenon_H92). % 15.09/15.32 apply (zenon_or_s _ _ zenon_H91); [ zenon_intro zenon_H5d | zenon_intro zenon_H93 ]. % 15.09/15.32 apply (zenon_L14_); trivial. % 15.09/15.32 apply (zenon_or_s _ _ zenon_H93); [ zenon_intro zenon_H63 | zenon_intro zenon_H81 ]. % 15.09/15.32 apply (zenon_or_s _ _ zenon_H58); [ zenon_intro zenon_H5b | zenon_intro zenon_H5a ]. % 15.09/15.32 exact (zenon_H59 zenon_H5b). % 15.09/15.32 apply (zenon_or_s _ _ zenon_H5a); [ zenon_intro zenon_H4a | zenon_intro zenon_H5c ]. % 15.09/15.32 apply (zenon_L9_); trivial. % 15.09/15.32 apply (zenon_or_s _ _ zenon_H5c); [ zenon_intro zenon_H50 | zenon_intro zenon_H53 ]. % 15.09/15.32 apply (zenon_L31_); trivial. % 15.09/15.32 apply (zenon_L32_); trivial. % 15.09/15.32 apply (zenon_L33_); trivial. % 15.09/15.32 (* end of lemma zenon_L34_ *) % 15.09/15.32 assert (zenon_L35_ : (((op (e0) (e0)) = (e1))\/(((op (e0) (e1)) = (e1))\/(((op (e0) (e2)) = (e1))\/((op (e0) (e3)) = (e1))))) -> (((op (e1) (e0)) = (e3))\/(((op (e1) (e1)) = (e3))\/(((op (e1) (e2)) = (e3))\/((op (e1) (e3)) = (e3))))) -> (~((op (e0) (e3)) = (op (e1) (e3)))) -> ((op (e2) (e2)) = (e2)) -> (~((op (e1) (e2)) = (op (e2) (e2)))) -> (((op (e1) (e0)) = (e2))\/(((op (e1) (e1)) = (e2))\/(((op (e1) (e2)) = (e2))\/((op (e1) (e3)) = (e2))))) -> (~((op (e0) (e2)) = (op (e1) (e2)))) -> (~((op (e1) (e3)) = (op (e3) (e3)))) -> (~((op (e0) (e2)) = (op (e2) (e2)))) -> (~((e0) = (e1))) -> (~((op (e0) (e3)) = (op (e3) (e3)))) -> ((op (e3) (e3)) = (e3)) -> (((op (e0) (e0)) = (e2))\/(((op (e0) (e1)) = (e2))\/(((op (e0) (e2)) = (e2))\/((op (e0) (e3)) = (e2))))) -> (~((op (e0) (e0)) = (e2))) -> (~((e0) = (e2))) -> (~((e1) = (e3))) -> (~((e2) = (e3))) -> ((op (e0) (e1)) = (e0)) -> (~((e0) = (e3))) -> (~((op (e0) (e0)) = (e3))) -> (((op (e0) (e0)) = (e3))\/(((op (e0) (e1)) = (e3))\/(((op (e0) (e2)) = (e3))\/((op (e0) (e3)) = (e3))))) -> (~((e1) = (e2))) -> False). % 15.09/15.32 do 0 intro. intros zenon_H44 zenon_H90 zenon_H80 zenon_H35 zenon_H7d zenon_H84 zenon_H87 zenon_H8b zenon_H28 zenon_H9e zenon_H36 zenon_H42 zenon_H8e zenon_H8f zenon_H5e zenon_Ha3 zenon_H6a zenon_H49 zenon_H4b zenon_H59 zenon_H58 zenon_Ha7. % 15.09/15.32 apply (zenon_or_s _ _ zenon_H44); [ zenon_intro zenon_H47 | zenon_intro zenon_H46 ]. % 15.09/15.32 apply (zenon_L26_); trivial. % 15.09/15.32 apply (zenon_or_s _ _ zenon_H46); [ zenon_intro zenon_H22 | zenon_intro zenon_H48 ]. % 15.09/15.32 apply (zenon_L27_); trivial. % 15.09/15.32 apply (zenon_or_s _ _ zenon_H48); [ zenon_intro zenon_H29 | zenon_intro zenon_H37 ]. % 15.09/15.32 apply (zenon_L30_); trivial. % 15.09/15.32 apply (zenon_L34_); trivial. % 15.09/15.32 (* end of lemma zenon_L35_ *) % 15.09/15.32 assert (zenon_L36_ : ((~((op (e2) (e2)) = (e2)))\/((op (e2) (e2)) = (e2))) -> (((op (e0) (e0)) = (e2))\/(((op (e0) (e1)) = (e2))\/(((op (e0) (e2)) = (e2))\/((op (e0) (e3)) = (e2))))) -> (((op (e1) (e0)) = (e3))\/(((op (e1) (e1)) = (e3))\/(((op (e1) (e2)) = (e3))\/((op (e1) (e3)) = (e3))))) -> (~((op (e1) (e3)) = (op (e3) (e3)))) -> (~((op (e0) (e2)) = (op (e1) (e2)))) -> (~((e2) = (e3))) -> (~((op (e1) (e2)) = (op (e2) (e2)))) -> (~((op (e0) (e3)) = (op (e1) (e3)))) -> (((op (e1) (e0)) = (e2))\/(((op (e1) (e1)) = (e2))\/(((op (e1) (e2)) = (e2))\/((op (e1) (e3)) = (e2))))) -> (~((e0) = (e2))) -> (~((op (e0) (e0)) = (e2))) -> (~((e0) = (e1))) -> (~((e1) = (e3))) -> (~((e1) = (e2))) -> (((op (e0) (e0)) = (e1))\/(((op (e0) (e1)) = (e1))\/(((op (e0) (e2)) = (e1))\/((op (e0) (e3)) = (e1))))) -> (~((op (e0) (e0)) = (e3))) -> (~((e0) = (e3))) -> ((op (e0) (e1)) = (e0)) -> (((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)) = (e1))) -> (~((op (e2) (e2)) = (e0))) -> (~((op (e0) (e3)) = (op (e3) (e3)))) -> ((op (e3) (e3)) = (e3)) -> (((op (e0) (e0)) = (e3))\/(((op (e0) (e1)) = (e3))\/(((op (e0) (e2)) = (e3))\/((op (e0) (e3)) = (e3))))) -> False). % 15.09/15.32 do 0 intro. intros zenon_Haa zenon_H8e zenon_H90 zenon_H8b zenon_H87 zenon_H6a zenon_H7d zenon_H80 zenon_H84 zenon_H5e zenon_H8f zenon_H9e zenon_Ha3 zenon_Ha7 zenon_H44 zenon_H59 zenon_H4b zenon_H49 zenon_H2d zenon_H28 zenon_H52 zenon_H2e zenon_H36 zenon_H42 zenon_H58. % 15.09/15.32 apply (zenon_or_s _ _ zenon_Haa); [ zenon_intro zenon_H2f | zenon_intro zenon_H35 ]. % 15.09/15.32 apply (zenon_L13_); trivial. % 15.09/15.32 apply (zenon_L35_); trivial. % 15.09/15.32 (* end of lemma zenon_L36_ *) % 15.09/15.32 assert (zenon_L37_ : ((op (e0) (e2)) = (e0)) -> ((op (e0) (e2)) = (e1)) -> (~((e0) = (e1))) -> False). % 15.09/15.32 do 0 intro. intros zenon_Hab zenon_H29 zenon_H9e. % 15.09/15.32 elim (classic ((e1) = (e1))); [ zenon_intro zenon_H9f | zenon_intro zenon_Ha0 ]. % 15.09/15.32 cut (((e1) = (e1)) = ((e0) = (e1))). % 15.09/15.32 intro zenon_D_pnotp. % 15.09/15.32 apply zenon_H9e. % 15.09/15.32 rewrite <- zenon_D_pnotp. % 15.09/15.32 exact zenon_H9f. % 15.09/15.32 cut (((e1) = (e1))); [idtac | apply NNPP; zenon_intro zenon_Ha0]. % 15.09/15.32 cut (((e1) = (e0))); [idtac | apply NNPP; zenon_intro zenon_Ha1]. % 15.09/15.32 congruence. % 15.09/15.32 cut (((op (e0) (e2)) = (e0)) = ((e1) = (e0))). % 15.09/15.32 intro zenon_D_pnotp. % 15.09/15.32 apply zenon_Ha1. % 15.09/15.32 rewrite <- zenon_D_pnotp. % 15.09/15.32 exact zenon_Hab. % 15.09/15.32 cut (((e0) = (e0))); [idtac | apply NNPP; zenon_intro zenon_H1d]. % 15.09/15.32 cut (((op (e0) (e2)) = (e1))); [idtac | apply NNPP; zenon_intro zenon_Hac]. % 15.09/15.32 congruence. % 15.09/15.32 exact (zenon_Hac zenon_H29). % 15.09/15.32 apply zenon_H1d. apply refl_equal. % 15.09/15.32 apply zenon_Ha0. apply refl_equal. % 15.09/15.32 apply zenon_Ha0. apply refl_equal. % 15.09/15.32 (* end of lemma zenon_L37_ *) % 15.09/15.32 assert (zenon_L38_ : ((op (e1) (e0)) = (e0)) -> ((op (e1) (e0)) = (e3)) -> (~((e0) = (e3))) -> False). % 15.09/15.32 do 0 intro. intros zenon_Had zenon_H69 zenon_H4b. % 15.09/15.32 elim (classic ((e3) = (e3))); [ zenon_intro zenon_H4c | zenon_intro zenon_H4d ]. % 15.09/15.32 cut (((e3) = (e3)) = ((e0) = (e3))). % 15.09/15.32 intro zenon_D_pnotp. % 15.09/15.32 apply zenon_H4b. % 15.09/15.32 rewrite <- zenon_D_pnotp. % 15.09/15.32 exact zenon_H4c. % 15.09/15.32 cut (((e3) = (e3))); [idtac | apply NNPP; zenon_intro zenon_H4d]. % 15.09/15.32 cut (((e3) = (e0))); [idtac | apply NNPP; zenon_intro zenon_H4e]. % 15.09/15.32 congruence. % 15.09/15.32 cut (((op (e1) (e0)) = (e0)) = ((e3) = (e0))). % 15.09/15.32 intro zenon_D_pnotp. % 15.09/15.32 apply zenon_H4e. % 15.09/15.32 rewrite <- zenon_D_pnotp. % 15.09/15.32 exact zenon_Had. % 15.09/15.32 cut (((e0) = (e0))); [idtac | apply NNPP; zenon_intro zenon_H1d]. % 15.09/15.32 cut (((op (e1) (e0)) = (e3))); [idtac | apply NNPP; zenon_intro zenon_H6c]. % 15.09/15.32 congruence. % 15.09/15.32 exact (zenon_H6c zenon_H69). % 15.09/15.32 apply zenon_H1d. apply refl_equal. % 15.09/15.32 apply zenon_H4d. apply refl_equal. % 15.09/15.32 apply zenon_H4d. apply refl_equal. % 15.09/15.32 (* end of lemma zenon_L38_ *) % 15.09/15.32 assert (zenon_L39_ : ((op (e2) (e0)) = (e1)) -> ((op (e2) (e0)) = (e3)) -> (~((e1) = (e3))) -> False). % 15.09/15.32 do 0 intro. intros zenon_Hae zenon_Haf zenon_Ha3. % 15.09/15.32 elim (classic ((e3) = (e3))); [ zenon_intro zenon_H4c | zenon_intro zenon_H4d ]. % 15.09/15.32 cut (((e3) = (e3)) = ((e1) = (e3))). % 15.09/15.32 intro zenon_D_pnotp. % 15.09/15.32 apply zenon_Ha3. % 15.09/15.32 rewrite <- zenon_D_pnotp. % 15.09/15.32 exact zenon_H4c. % 15.09/15.32 cut (((e3) = (e3))); [idtac | apply NNPP; zenon_intro zenon_H4d]. % 15.09/15.32 cut (((e3) = (e1))); [idtac | apply NNPP; zenon_intro zenon_Ha4]. % 15.09/15.32 congruence. % 15.09/15.32 cut (((op (e2) (e0)) = (e1)) = ((e3) = (e1))). % 15.09/15.32 intro zenon_D_pnotp. % 15.09/15.32 apply zenon_Ha4. % 15.09/15.32 rewrite <- zenon_D_pnotp. % 15.09/15.32 exact zenon_Hae. % 15.09/15.32 cut (((e1) = (e1))); [idtac | apply NNPP; zenon_intro zenon_Ha0]. % 15.09/15.32 cut (((op (e2) (e0)) = (e3))); [idtac | apply NNPP; zenon_intro zenon_Hb0]. % 15.09/15.32 congruence. % 15.09/15.32 exact (zenon_Hb0 zenon_Haf). % 15.09/15.32 apply zenon_Ha0. apply refl_equal. % 15.09/15.32 apply zenon_H4d. apply refl_equal. % 15.09/15.32 apply zenon_H4d. apply refl_equal. % 15.09/15.32 (* end of lemma zenon_L39_ *) % 15.09/15.32 assert (zenon_L40_ : (~((op (e1) (e1)) = (op (e2) (e1)))) -> ((op (e1) (e1)) = (e1)) -> ((op (e2) (e1)) = (e1)) -> False). % 15.09/15.32 do 0 intro. intros zenon_Hb1 zenon_H21 zenon_Hb2. % 15.09/15.32 cut (((op (e1) (e1)) = (e1)) = ((op (e1) (e1)) = (op (e2) (e1)))). % 15.09/15.32 intro zenon_D_pnotp. % 15.09/15.32 apply zenon_Hb1. % 15.09/15.32 rewrite <- zenon_D_pnotp. % 15.09/15.32 exact zenon_H21. % 15.09/15.32 cut (((e1) = (op (e2) (e1)))); [idtac | apply NNPP; zenon_intro zenon_Hb3]. % 15.09/15.32 cut (((op (e1) (e1)) = (op (e1) (e1)))); [idtac | apply NNPP; zenon_intro zenon_H25]. % 15.09/15.32 congruence. % 15.09/15.32 apply zenon_H25. apply refl_equal. % 15.09/15.32 apply zenon_Hb3. apply sym_equal. exact zenon_Hb2. % 15.09/15.32 (* end of lemma zenon_L40_ *) % 15.09/15.32 assert (zenon_L41_ : (~((op (e0) (e3)) = (op (e2) (e3)))) -> ((op (e0) (e3)) = (e1)) -> ((op (e2) (e3)) = (e1)) -> False). % 15.09/15.32 do 0 intro. intros zenon_Hb4 zenon_H37 zenon_Hb5. % 15.09/15.32 cut (((op (e0) (e3)) = (e1)) = ((op (e0) (e3)) = (op (e2) (e3)))). % 15.09/15.32 intro zenon_D_pnotp. % 15.09/15.32 apply zenon_Hb4. % 15.09/15.32 rewrite <- zenon_D_pnotp. % 15.09/15.32 exact zenon_H37. % 15.09/15.32 cut (((e1) = (op (e2) (e3)))); [idtac | apply NNPP; zenon_intro zenon_Hb6]. % 15.09/15.32 cut (((op (e0) (e3)) = (op (e0) (e3)))); [idtac | apply NNPP; zenon_intro zenon_H3a]. % 15.09/15.32 congruence. % 15.09/15.32 apply zenon_H3a. apply refl_equal. % 15.09/15.32 apply zenon_Hb6. apply sym_equal. exact zenon_Hb5. % 15.09/15.32 (* end of lemma zenon_L41_ *) % 15.09/15.32 assert (zenon_L42_ : (((op (e2) (e0)) = (e1))\/(((op (e2) (e1)) = (e1))\/(((op (e2) (e2)) = (e1))\/((op (e2) (e3)) = (e1))))) -> (~((e1) = (e3))) -> ((op (e2) (e0)) = (e3)) -> ((op (e1) (e1)) = (e1)) -> (~((op (e1) (e1)) = (op (e2) (e1)))) -> (~((op (e2) (e2)) = (e1))) -> (~((op (e0) (e3)) = (op (e2) (e3)))) -> ((op (e0) (e3)) = (e1)) -> False). % 15.09/15.32 do 0 intro. intros zenon_Hb7 zenon_Ha3 zenon_Haf zenon_H21 zenon_Hb1 zenon_H52 zenon_Hb4 zenon_H37. % 15.09/15.32 apply (zenon_or_s _ _ zenon_Hb7); [ zenon_intro zenon_Hae | zenon_intro zenon_Hb8 ]. % 15.09/15.32 apply (zenon_L39_); trivial. % 15.09/15.32 apply (zenon_or_s _ _ zenon_Hb8); [ zenon_intro zenon_Hb2 | zenon_intro zenon_Hb9 ]. % 15.09/15.32 apply (zenon_L40_); trivial. % 15.09/15.32 apply (zenon_or_s _ _ zenon_Hb9); [ zenon_intro zenon_H2a | zenon_intro zenon_Hb5 ]. % 15.09/15.32 exact (zenon_H52 zenon_H2a). % 15.09/15.32 apply (zenon_L41_); trivial. % 15.09/15.32 (* end of lemma zenon_L42_ *) % 15.09/15.32 assert (zenon_L43_ : ((op (e3) (e3)) = (e3)) -> ((op (e3) (e0)) = (e3)) -> (~((op (e3) (e0)) = (op (e3) (e3)))) -> False). % 15.09/15.32 do 0 intro. intros zenon_H42 zenon_Hba zenon_Hbb. % 15.09/15.32 elim (classic ((op (e3) (e3)) = (op (e3) (e3)))); [ zenon_intro zenon_H54 | zenon_intro zenon_H55 ]. % 15.09/15.32 cut (((op (e3) (e3)) = (op (e3) (e3))) = ((op (e3) (e0)) = (op (e3) (e3)))). % 15.09/15.32 intro zenon_D_pnotp. % 15.09/15.32 apply zenon_Hbb. % 15.09/15.32 rewrite <- zenon_D_pnotp. % 15.09/15.32 exact zenon_H54. % 15.09/15.32 cut (((op (e3) (e3)) = (op (e3) (e3)))); [idtac | apply NNPP; zenon_intro zenon_H55]. % 15.09/15.32 cut (((op (e3) (e3)) = (op (e3) (e0)))); [idtac | apply NNPP; zenon_intro zenon_Hbc]. % 15.09/15.32 congruence. % 15.09/15.32 cut (((op (e3) (e3)) = (e3)) = ((op (e3) (e3)) = (op (e3) (e0)))). % 15.09/15.32 intro zenon_D_pnotp. % 15.09/15.32 apply zenon_Hbc. % 15.09/15.32 rewrite <- zenon_D_pnotp. % 15.09/15.32 exact zenon_H42. % 15.09/15.32 cut (((e3) = (op (e3) (e0)))); [idtac | apply NNPP; zenon_intro zenon_Hbd]. % 15.09/15.32 cut (((op (e3) (e3)) = (op (e3) (e3)))); [idtac | apply NNPP; zenon_intro zenon_H55]. % 15.09/15.32 congruence. % 15.09/15.32 apply zenon_H55. apply refl_equal. % 15.09/15.32 apply zenon_Hbd. apply sym_equal. exact zenon_Hba. % 15.09/15.32 apply zenon_H55. apply refl_equal. % 15.09/15.32 apply zenon_H55. apply refl_equal. % 15.09/15.32 (* end of lemma zenon_L43_ *) % 15.09/15.32 assert (zenon_L44_ : (((op (e0) (e0)) = (e1))\/(((op (e0) (e1)) = (e1))\/(((op (e0) (e2)) = (e1))\/((op (e0) (e3)) = (e1))))) -> (~((op (e0) (e0)) = (e1))) -> (~((op (e0) (e1)) = (op (e1) (e1)))) -> (~((e0) = (e1))) -> ((op (e0) (e2)) = (e0)) -> (((op (e0) (e0)) = (e3))\/(((op (e1) (e0)) = (e3))\/(((op (e2) (e0)) = (e3))\/((op (e3) (e0)) = (e3))))) -> (~((op (e0) (e0)) = (e3))) -> (~((e0) = (e3))) -> ((op (e1) (e0)) = (e0)) -> (~((op (e0) (e3)) = (op (e2) (e3)))) -> (~((op (e2) (e2)) = (e1))) -> (~((op (e1) (e1)) = (op (e2) (e1)))) -> ((op (e1) (e1)) = (e1)) -> (~((e1) = (e3))) -> (((op (e2) (e0)) = (e1))\/(((op (e2) (e1)) = (e1))\/(((op (e2) (e2)) = (e1))\/((op (e2) (e3)) = (e1))))) -> ((op (e3) (e3)) = (e3)) -> (~((op (e3) (e0)) = (op (e3) (e3)))) -> False). % 15.16/15.32 do 0 intro. intros zenon_H44 zenon_H45 zenon_H23 zenon_H9e zenon_Hab zenon_Hbe zenon_H59 zenon_H4b zenon_Had zenon_Hb4 zenon_H52 zenon_Hb1 zenon_H21 zenon_Ha3 zenon_Hb7 zenon_H42 zenon_Hbb. % 15.16/15.32 apply (zenon_or_s _ _ zenon_H44); [ zenon_intro zenon_H47 | zenon_intro zenon_H46 ]. % 15.16/15.32 exact (zenon_H45 zenon_H47). % 15.16/15.32 apply (zenon_or_s _ _ zenon_H46); [ zenon_intro zenon_H22 | zenon_intro zenon_H48 ]. % 15.16/15.32 apply (zenon_L3_); trivial. % 15.16/15.32 apply (zenon_or_s _ _ zenon_H48); [ zenon_intro zenon_H29 | zenon_intro zenon_H37 ]. % 15.16/15.32 apply (zenon_L37_); trivial. % 15.16/15.32 apply (zenon_or_s _ _ zenon_Hbe); [ zenon_intro zenon_H5b | zenon_intro zenon_Hbf ]. % 15.16/15.32 exact (zenon_H59 zenon_H5b). % 15.16/15.32 apply (zenon_or_s _ _ zenon_Hbf); [ zenon_intro zenon_H69 | zenon_intro zenon_Hc0 ]. % 15.16/15.32 apply (zenon_L38_); trivial. % 15.16/15.32 apply (zenon_or_s _ _ zenon_Hc0); [ zenon_intro zenon_Haf | zenon_intro zenon_Hba ]. % 15.16/15.32 apply (zenon_L42_); trivial. % 15.16/15.32 apply (zenon_L43_); trivial. % 15.16/15.32 (* end of lemma zenon_L44_ *) % 15.16/15.32 assert (zenon_L45_ : (~((op (op (e0) (e0)) (op (e0) (e0))) = (op (e2) (e2)))) -> ((op (e0) (e0)) = (e2)) -> False). % 15.16/15.32 do 0 intro. intros zenon_Hc1 zenon_H92. % 15.16/15.32 cut (((op (e0) (e0)) = (e2))); [idtac | apply NNPP; zenon_intro zenon_H8f]. % 15.16/15.32 cut (((op (e0) (e0)) = (e2))); [idtac | apply NNPP; zenon_intro zenon_H8f]. % 15.16/15.32 congruence. % 15.16/15.32 exact (zenon_H8f zenon_H92). % 15.16/15.32 exact (zenon_H8f zenon_H92). % 15.16/15.32 (* end of lemma zenon_L45_ *) % 15.16/15.32 assert (zenon_L46_ : ((op (e0) (e1)) = (e3)) -> ((op (e2) (e2)) = (e1)) -> ((op (e0) (e0)) = (e2)) -> False). % 15.16/15.32 do 0 intro. intros zenon_H4a zenon_H2a zenon_H92. % 15.16/15.32 apply (zenon_notand_s _ _ ax15); [ zenon_intro zenon_Hc3 | zenon_intro zenon_Hc2 ]. % 15.16/15.32 elim (classic ((op (op (e0) (e0)) (op (e0) (e0))) = (op (op (e0) (e0)) (op (e0) (e0))))); [ zenon_intro zenon_H71 | zenon_intro zenon_H72 ]. % 15.16/15.32 cut (((op (op (e0) (e0)) (op (e0) (e0))) = (op (op (e0) (e0)) (op (e0) (e0)))) = ((e1) = (op (op (e0) (e0)) (op (e0) (e0))))). % 15.16/15.32 intro zenon_D_pnotp. % 15.16/15.32 apply zenon_Hc3. % 15.16/15.32 rewrite <- zenon_D_pnotp. % 15.16/15.32 exact zenon_H71. % 15.16/15.32 cut (((op (op (e0) (e0)) (op (e0) (e0))) = (op (op (e0) (e0)) (op (e0) (e0))))); [idtac | apply NNPP; zenon_intro zenon_H72]. % 15.16/15.32 cut (((op (op (e0) (e0)) (op (e0) (e0))) = (e1))); [idtac | apply NNPP; zenon_intro zenon_Hc4]. % 15.16/15.32 congruence. % 15.16/15.32 cut (((op (e2) (e2)) = (e1)) = ((op (op (e0) (e0)) (op (e0) (e0))) = (e1))). % 15.16/15.32 intro zenon_D_pnotp. % 15.16/15.32 apply zenon_Hc4. % 15.16/15.32 rewrite <- zenon_D_pnotp. % 15.16/15.32 exact zenon_H2a. % 15.16/15.32 cut (((e1) = (e1))); [idtac | apply NNPP; zenon_intro zenon_Ha0]. % 15.16/15.32 cut (((op (e2) (e2)) = (op (op (e0) (e0)) (op (e0) (e0))))); [idtac | apply NNPP; zenon_intro zenon_Hc5]. % 15.16/15.32 congruence. % 15.16/15.32 elim (classic ((op (op (e0) (e0)) (op (e0) (e0))) = (op (op (e0) (e0)) (op (e0) (e0))))); [ zenon_intro zenon_H71 | zenon_intro zenon_H72 ]. % 15.16/15.32 cut (((op (op (e0) (e0)) (op (e0) (e0))) = (op (op (e0) (e0)) (op (e0) (e0)))) = ((op (e2) (e2)) = (op (op (e0) (e0)) (op (e0) (e0))))). % 15.16/15.32 intro zenon_D_pnotp. % 15.16/15.32 apply zenon_Hc5. % 15.16/15.32 rewrite <- zenon_D_pnotp. % 15.16/15.32 exact zenon_H71. % 15.16/15.32 cut (((op (op (e0) (e0)) (op (e0) (e0))) = (op (op (e0) (e0)) (op (e0) (e0))))); [idtac | apply NNPP; zenon_intro zenon_H72]. % 15.16/15.32 cut (((op (op (e0) (e0)) (op (e0) (e0))) = (op (e2) (e2)))); [idtac | apply NNPP; zenon_intro zenon_Hc1]. % 15.16/15.32 congruence. % 15.16/15.32 apply (zenon_L45_); trivial. % 15.16/15.32 apply zenon_H72. apply refl_equal. % 15.16/15.32 apply zenon_H72. apply refl_equal. % 15.16/15.32 apply zenon_Ha0. apply refl_equal. % 15.16/15.32 apply zenon_H72. apply refl_equal. % 15.16/15.32 apply zenon_H72. apply refl_equal. % 15.16/15.32 apply (zenon_notand_s _ _ zenon_Hc2); [ zenon_intro zenon_Hc6 | zenon_intro zenon_H75 ]. % 15.16/15.32 apply zenon_Hc6. apply sym_equal. exact zenon_H92. % 15.16/15.32 elim (classic ((op (e0) (op (op (e0) (e0)) (op (e0) (e0)))) = (op (e0) (op (op (e0) (e0)) (op (e0) (e0)))))); [ zenon_intro zenon_H77 | zenon_intro zenon_H78 ]. % 15.16/15.32 cut (((op (e0) (op (op (e0) (e0)) (op (e0) (e0)))) = (op (e0) (op (op (e0) (e0)) (op (e0) (e0))))) = ((e3) = (op (e0) (op (op (e0) (e0)) (op (e0) (e0)))))). % 15.16/15.32 intro zenon_D_pnotp. % 15.16/15.32 apply zenon_H75. % 15.16/15.32 rewrite <- zenon_D_pnotp. % 15.16/15.32 exact zenon_H77. % 15.16/15.32 cut (((op (e0) (op (op (e0) (e0)) (op (e0) (e0)))) = (op (e0) (op (op (e0) (e0)) (op (e0) (e0)))))); [idtac | apply NNPP; zenon_intro zenon_H78]. % 15.16/15.32 cut (((op (e0) (op (op (e0) (e0)) (op (e0) (e0)))) = (e3))); [idtac | apply NNPP; zenon_intro zenon_H79]. % 15.16/15.32 congruence. % 15.16/15.32 cut (((op (e0) (e1)) = (e3)) = ((op (e0) (op (op (e0) (e0)) (op (e0) (e0)))) = (e3))). % 15.16/15.32 intro zenon_D_pnotp. % 15.16/15.32 apply zenon_H79. % 15.16/15.32 rewrite <- zenon_D_pnotp. % 15.16/15.32 exact zenon_H4a. % 15.16/15.32 cut (((e3) = (e3))); [idtac | apply NNPP; zenon_intro zenon_H4d]. % 15.16/15.32 cut (((op (e0) (e1)) = (op (e0) (op (op (e0) (e0)) (op (e0) (e0)))))); [idtac | apply NNPP; zenon_intro zenon_Hc7]. % 15.16/15.32 congruence. % 15.16/15.32 elim (classic ((op (e0) (op (op (e0) (e0)) (op (e0) (e0)))) = (op (e0) (op (op (e0) (e0)) (op (e0) (e0)))))); [ zenon_intro zenon_H77 | zenon_intro zenon_H78 ]. % 15.16/15.32 cut (((op (e0) (op (op (e0) (e0)) (op (e0) (e0)))) = (op (e0) (op (op (e0) (e0)) (op (e0) (e0))))) = ((op (e0) (e1)) = (op (e0) (op (op (e0) (e0)) (op (e0) (e0)))))). % 15.16/15.32 intro zenon_D_pnotp. % 15.16/15.32 apply zenon_Hc7. % 15.16/15.32 rewrite <- zenon_D_pnotp. % 15.16/15.32 exact zenon_H77. % 15.16/15.32 cut (((op (e0) (op (op (e0) (e0)) (op (e0) (e0)))) = (op (e0) (op (op (e0) (e0)) (op (e0) (e0)))))); [idtac | apply NNPP; zenon_intro zenon_H78]. % 15.16/15.32 cut (((op (e0) (op (op (e0) (e0)) (op (e0) (e0)))) = (op (e0) (e1)))); [idtac | apply NNPP; zenon_intro zenon_Hc8]. % 15.16/15.32 congruence. % 15.16/15.32 cut (((op (op (e0) (e0)) (op (e0) (e0))) = (e1))); [idtac | apply NNPP; zenon_intro zenon_Hc4]. % 15.16/15.32 cut (((e0) = (e0))); [idtac | apply NNPP; zenon_intro zenon_H1d]. % 15.16/15.32 congruence. % 15.16/15.32 apply zenon_H1d. apply refl_equal. % 15.16/15.32 cut (((op (e2) (e2)) = (e1)) = ((op (op (e0) (e0)) (op (e0) (e0))) = (e1))). % 15.16/15.32 intro zenon_D_pnotp. % 15.16/15.32 apply zenon_Hc4. % 15.16/15.32 rewrite <- zenon_D_pnotp. % 15.16/15.32 exact zenon_H2a. % 15.16/15.32 cut (((e1) = (e1))); [idtac | apply NNPP; zenon_intro zenon_Ha0]. % 15.16/15.32 cut (((op (e2) (e2)) = (op (op (e0) (e0)) (op (e0) (e0))))); [idtac | apply NNPP; zenon_intro zenon_Hc5]. % 15.16/15.32 congruence. % 15.16/15.32 elim (classic ((op (op (e0) (e0)) (op (e0) (e0))) = (op (op (e0) (e0)) (op (e0) (e0))))); [ zenon_intro zenon_H71 | zenon_intro zenon_H72 ]. % 15.16/15.32 cut (((op (op (e0) (e0)) (op (e0) (e0))) = (op (op (e0) (e0)) (op (e0) (e0)))) = ((op (e2) (e2)) = (op (op (e0) (e0)) (op (e0) (e0))))). % 15.16/15.32 intro zenon_D_pnotp. % 15.16/15.32 apply zenon_Hc5. % 15.16/15.32 rewrite <- zenon_D_pnotp. % 15.16/15.32 exact zenon_H71. % 15.16/15.32 cut (((op (op (e0) (e0)) (op (e0) (e0))) = (op (op (e0) (e0)) (op (e0) (e0))))); [idtac | apply NNPP; zenon_intro zenon_H72]. % 15.16/15.32 cut (((op (op (e0) (e0)) (op (e0) (e0))) = (op (e2) (e2)))); [idtac | apply NNPP; zenon_intro zenon_Hc1]. % 15.16/15.32 congruence. % 15.16/15.32 apply (zenon_L45_); trivial. % 15.16/15.32 apply zenon_H72. apply refl_equal. % 15.16/15.32 apply zenon_H72. apply refl_equal. % 15.16/15.32 apply zenon_Ha0. apply refl_equal. % 15.16/15.32 apply zenon_H78. apply refl_equal. % 15.16/15.32 apply zenon_H78. apply refl_equal. % 15.16/15.32 apply zenon_H4d. apply refl_equal. % 15.16/15.32 apply zenon_H78. apply refl_equal. % 15.16/15.32 apply zenon_H78. apply refl_equal. % 15.16/15.32 (* end of lemma zenon_L46_ *) % 15.16/15.32 assert (zenon_L47_ : (((op (e2) (e2)) = (e0))\/(((op (e2) (e2)) = (e1))\/(((op (e2) (e2)) = (e2))\/((op (e2) (e2)) = (e3))))) -> (~((op (e2) (e2)) = (e0))) -> ((op (e0) (e0)) = (e2)) -> ((op (e0) (e1)) = (e3)) -> (~((op (e2) (e2)) = (e2))) -> (~((op (e2) (e2)) = (e3))) -> False). % 15.16/15.32 do 0 intro. intros zenon_H2d zenon_H2e zenon_H92 zenon_H4a zenon_H2f zenon_H30. % 15.16/15.32 apply (zenon_or_s _ _ zenon_H2d); [ zenon_intro zenon_H32 | zenon_intro zenon_H31 ]. % 15.16/15.32 exact (zenon_H2e zenon_H32). % 15.16/15.32 apply (zenon_or_s _ _ zenon_H31); [ zenon_intro zenon_H2a | zenon_intro zenon_H33 ]. % 15.16/15.32 apply (zenon_L46_); trivial. % 15.16/15.32 apply (zenon_or_s _ _ zenon_H33); [ zenon_intro zenon_H35 | zenon_intro zenon_H34 ]. % 15.16/15.32 exact (zenon_H2f zenon_H35). % 15.16/15.32 exact (zenon_H30 zenon_H34). % 15.16/15.32 (* end of lemma zenon_L47_ *) % 15.16/15.32 assert (zenon_L48_ : ((op (e0) (e2)) = (e0)) -> ((op (e0) (e2)) = (e3)) -> (~((e0) = (e3))) -> False). % 15.16/15.32 do 0 intro. intros zenon_Hab zenon_H50 zenon_H4b. % 15.16/15.32 elim (classic ((e3) = (e3))); [ zenon_intro zenon_H4c | zenon_intro zenon_H4d ]. % 15.16/15.32 cut (((e3) = (e3)) = ((e0) = (e3))). % 15.16/15.32 intro zenon_D_pnotp. % 15.16/15.32 apply zenon_H4b. % 15.16/15.32 rewrite <- zenon_D_pnotp. % 15.16/15.32 exact zenon_H4c. % 15.16/15.32 cut (((e3) = (e3))); [idtac | apply NNPP; zenon_intro zenon_H4d]. % 15.16/15.32 cut (((e3) = (e0))); [idtac | apply NNPP; zenon_intro zenon_H4e]. % 15.16/15.32 congruence. % 15.16/15.32 cut (((op (e0) (e2)) = (e0)) = ((e3) = (e0))). % 15.16/15.32 intro zenon_D_pnotp. % 15.16/15.32 apply zenon_H4e. % 15.16/15.32 rewrite <- zenon_D_pnotp. % 15.16/15.32 exact zenon_Hab. % 15.16/15.32 cut (((e0) = (e0))); [idtac | apply NNPP; zenon_intro zenon_H1d]. % 15.16/15.32 cut (((op (e0) (e2)) = (e3))); [idtac | apply NNPP; zenon_intro zenon_Ha5]. % 15.16/15.32 congruence. % 15.16/15.32 exact (zenon_Ha5 zenon_H50). % 15.16/15.32 apply zenon_H1d. apply refl_equal. % 15.16/15.32 apply zenon_H4d. apply refl_equal. % 15.16/15.32 apply zenon_H4d. apply refl_equal. % 15.16/15.32 (* end of lemma zenon_L48_ *) % 15.16/15.32 assert (zenon_L49_ : (((op (e0) (e0)) = (e3))\/(((op (e0) (e1)) = (e3))\/(((op (e0) (e2)) = (e3))\/((op (e0) (e3)) = (e3))))) -> (~((op (e0) (e0)) = (e3))) -> (~((op (e2) (e2)) = (e3))) -> (~((op (e2) (e2)) = (e2))) -> ((op (e0) (e0)) = (e2)) -> (~((op (e2) (e2)) = (e0))) -> (((op (e2) (e2)) = (e0))\/(((op (e2) (e2)) = (e1))\/(((op (e2) (e2)) = (e2))\/((op (e2) (e2)) = (e3))))) -> (~((e0) = (e3))) -> ((op (e0) (e2)) = (e0)) -> ((op (e0) (e3)) = (e1)) -> (~((e1) = (e3))) -> False). % 15.16/15.32 do 0 intro. intros zenon_H58 zenon_H59 zenon_H30 zenon_H2f zenon_H92 zenon_H2e zenon_H2d zenon_H4b zenon_Hab zenon_H37 zenon_Ha3. % 15.16/15.32 apply (zenon_or_s _ _ zenon_H58); [ zenon_intro zenon_H5b | zenon_intro zenon_H5a ]. % 15.16/15.32 exact (zenon_H59 zenon_H5b). % 15.16/15.32 apply (zenon_or_s _ _ zenon_H5a); [ zenon_intro zenon_H4a | zenon_intro zenon_H5c ]. % 15.16/15.32 apply (zenon_L47_); trivial. % 15.16/15.32 apply (zenon_or_s _ _ zenon_H5c); [ zenon_intro zenon_H50 | zenon_intro zenon_H53 ]. % 15.16/15.32 apply (zenon_L48_); trivial. % 15.16/15.32 apply (zenon_L32_); trivial. % 15.16/15.32 (* end of lemma zenon_L49_ *) % 15.16/15.32 assert (zenon_L50_ : ((op (e0) (e1)) = (e2)) -> ((op (e0) (e1)) = (e3)) -> (~((e2) = (e3))) -> False). % 15.16/15.32 do 0 intro. intros zenon_H5d zenon_H4a zenon_H6a. % 15.16/15.32 elim (classic ((e3) = (e3))); [ zenon_intro zenon_H4c | zenon_intro zenon_H4d ]. % 15.16/15.32 cut (((e3) = (e3)) = ((e2) = (e3))). % 15.16/15.32 intro zenon_D_pnotp. % 15.16/15.32 apply zenon_H6a. % 15.16/15.32 rewrite <- zenon_D_pnotp. % 15.16/15.32 exact zenon_H4c. % 15.16/15.32 cut (((e3) = (e3))); [idtac | apply NNPP; zenon_intro zenon_H4d]. % 15.16/15.32 cut (((e3) = (e2))); [idtac | apply NNPP; zenon_intro zenon_H6b]. % 15.16/15.32 congruence. % 15.16/15.32 cut (((op (e0) (e1)) = (e2)) = ((e3) = (e2))). % 15.16/15.32 intro zenon_D_pnotp. % 15.16/15.32 apply zenon_H6b. % 15.16/15.32 rewrite <- zenon_D_pnotp. % 15.16/15.32 exact zenon_H5d. % 15.16/15.32 cut (((e2) = (e2))); [idtac | apply NNPP; zenon_intro zenon_H60]. % 15.16/15.32 cut (((op (e0) (e1)) = (e3))); [idtac | apply NNPP; zenon_intro zenon_H4f]. % 15.16/15.32 congruence. % 15.16/15.32 exact (zenon_H4f zenon_H4a). % 15.16/15.32 apply zenon_H60. apply refl_equal. % 15.16/15.32 apply zenon_H4d. apply refl_equal. % 15.16/15.32 apply zenon_H4d. apply refl_equal. % 15.16/15.32 (* end of lemma zenon_L50_ *) % 15.16/15.32 assert (zenon_L51_ : (((op (e0) (e0)) = (e3))\/(((op (e0) (e1)) = (e3))\/(((op (e0) (e2)) = (e3))\/((op (e0) (e3)) = (e3))))) -> (~((op (e0) (e0)) = (e3))) -> (~((e2) = (e3))) -> ((op (e0) (e1)) = (e2)) -> (~((e0) = (e3))) -> ((op (e0) (e2)) = (e0)) -> ((op (e0) (e3)) = (e1)) -> (~((e1) = (e3))) -> False). % 15.16/15.32 do 0 intro. intros zenon_H58 zenon_H59 zenon_H6a zenon_H5d zenon_H4b zenon_Hab zenon_H37 zenon_Ha3. % 15.16/15.32 apply (zenon_or_s _ _ zenon_H58); [ zenon_intro zenon_H5b | zenon_intro zenon_H5a ]. % 15.16/15.32 exact (zenon_H59 zenon_H5b). % 15.16/15.32 apply (zenon_or_s _ _ zenon_H5a); [ zenon_intro zenon_H4a | zenon_intro zenon_H5c ]. % 15.16/15.32 apply (zenon_L50_); trivial. % 15.16/15.32 apply (zenon_or_s _ _ zenon_H5c); [ zenon_intro zenon_H50 | zenon_intro zenon_H53 ]. % 15.16/15.32 apply (zenon_L48_); trivial. % 15.16/15.32 apply (zenon_L32_); trivial. % 15.16/15.32 (* end of lemma zenon_L51_ *) % 15.16/15.32 assert (zenon_L52_ : (~((op (e0) (e2)) = (op (e1) (e2)))) -> ((op (e0) (e2)) = (e2)) -> ((op (e1) (e2)) = (e2)) -> False). % 15.16/15.32 do 0 intro. intros zenon_H87 zenon_H63 zenon_H7c. % 15.16/15.32 cut (((op (e0) (e2)) = (e2)) = ((op (e0) (e2)) = (op (e1) (e2)))). % 15.16/15.32 intro zenon_D_pnotp. % 15.16/15.32 apply zenon_H87. % 15.16/15.32 rewrite <- zenon_D_pnotp. % 15.16/15.32 exact zenon_H63. % 15.16/15.32 cut (((e2) = (op (e1) (e2)))); [idtac | apply NNPP; zenon_intro zenon_H7f]. % 15.16/15.32 cut (((op (e0) (e2)) = (op (e0) (e2)))); [idtac | apply NNPP; zenon_intro zenon_H2c]. % 15.16/15.32 congruence. % 15.16/15.32 apply zenon_H2c. apply refl_equal. % 15.16/15.32 apply zenon_H7f. apply sym_equal. exact zenon_H7c. % 15.16/15.32 (* end of lemma zenon_L52_ *) % 15.16/15.32 assert (zenon_L53_ : (~((op (e0) (e2)) = (op (e0) (e3)))) -> ((op (e0) (e2)) = (e0)) -> ((op (e0) (e3)) = (e0)) -> False). % 15.16/15.32 do 0 intro. intros zenon_Hc9 zenon_Hab zenon_Hca. % 15.16/15.32 cut (((op (e0) (e2)) = (e0)) = ((op (e0) (e2)) = (op (e0) (e3)))). % 15.16/15.32 intro zenon_D_pnotp. % 15.16/15.32 apply zenon_Hc9. % 15.16/15.32 rewrite <- zenon_D_pnotp. % 15.16/15.32 exact zenon_Hab. % 15.16/15.32 cut (((e0) = (op (e0) (e3)))); [idtac | apply NNPP; zenon_intro zenon_Hcb]. % 15.16/15.32 cut (((op (e0) (e2)) = (op (e0) (e2)))); [idtac | apply NNPP; zenon_intro zenon_H2c]. % 15.16/15.32 congruence. % 15.16/15.32 apply zenon_H2c. apply refl_equal. % 15.16/15.32 apply zenon_Hcb. apply sym_equal. exact zenon_Hca. % 15.16/15.32 (* end of lemma zenon_L53_ *) % 15.16/15.32 assert (zenon_L54_ : ((op (e1) (e3)) = (e0)) -> ((op (e1) (e3)) = (e2)) -> (~((e0) = (e2))) -> False). % 15.16/15.32 do 0 intro. intros zenon_Hcc zenon_H82 zenon_H5e. % 15.16/15.32 elim (classic ((e2) = (e2))); [ zenon_intro zenon_H5f | zenon_intro zenon_H60 ]. % 15.16/15.32 cut (((e2) = (e2)) = ((e0) = (e2))). % 15.16/15.32 intro zenon_D_pnotp. % 15.16/15.32 apply zenon_H5e. % 15.16/15.32 rewrite <- zenon_D_pnotp. % 15.16/15.32 exact zenon_H5f. % 15.16/15.32 cut (((e2) = (e2))); [idtac | apply NNPP; zenon_intro zenon_H60]. % 15.16/15.32 cut (((e2) = (e0))); [idtac | apply NNPP; zenon_intro zenon_H61]. % 15.16/15.32 congruence. % 15.16/15.32 cut (((op (e1) (e3)) = (e0)) = ((e2) = (e0))). % 15.16/15.32 intro zenon_D_pnotp. % 15.16/15.32 apply zenon_H61. % 15.16/15.32 rewrite <- zenon_D_pnotp. % 15.16/15.32 exact zenon_Hcc. % 15.16/15.32 cut (((e0) = (e0))); [idtac | apply NNPP; zenon_intro zenon_H1d]. % 15.16/15.32 cut (((op (e1) (e3)) = (e2))); [idtac | apply NNPP; zenon_intro zenon_Hcd]. % 15.16/15.32 congruence. % 15.16/15.32 exact (zenon_Hcd zenon_H82). % 15.16/15.32 apply zenon_H1d. apply refl_equal. % 15.16/15.32 apply zenon_H60. apply refl_equal. % 15.16/15.32 apply zenon_H60. apply refl_equal. % 15.16/15.32 (* end of lemma zenon_L54_ *) % 15.16/15.32 assert (zenon_L55_ : (~((op (e2) (e0)) = (op (e2) (e3)))) -> ((op (e2) (e0)) = (e0)) -> ((op (e2) (e3)) = (e0)) -> False). % 15.16/15.32 do 0 intro. intros zenon_Hce zenon_Hcf zenon_Hd0. % 15.16/15.32 cut (((op (e2) (e0)) = (e0)) = ((op (e2) (e0)) = (op (e2) (e3)))). % 15.16/15.32 intro zenon_D_pnotp. % 15.16/15.32 apply zenon_Hce. % 15.16/15.32 rewrite <- zenon_D_pnotp. % 15.16/15.32 exact zenon_Hcf. % 15.16/15.32 cut (((e0) = (op (e2) (e3)))); [idtac | apply NNPP; zenon_intro zenon_Hd1]. % 15.16/15.32 cut (((op (e2) (e0)) = (op (e2) (e0)))); [idtac | apply NNPP; zenon_intro zenon_Hd2]. % 15.16/15.32 congruence. % 15.16/15.32 apply zenon_Hd2. apply refl_equal. % 15.16/15.32 apply zenon_Hd1. apply sym_equal. exact zenon_Hd0. % 15.16/15.32 (* end of lemma zenon_L55_ *) % 15.16/15.32 assert (zenon_L56_ : (((op (e0) (e3)) = (e0))\/(((op (e1) (e3)) = (e0))\/(((op (e2) (e3)) = (e0))\/((op (e3) (e3)) = (e0))))) -> ((op (e0) (e2)) = (e0)) -> (~((op (e0) (e2)) = (op (e0) (e3)))) -> (~((e0) = (e2))) -> ((op (e1) (e3)) = (e2)) -> ((op (e2) (e0)) = (e0)) -> (~((op (e2) (e0)) = (op (e2) (e3)))) -> (~((op (e3) (e3)) = (e0))) -> False). % 15.16/15.32 do 0 intro. intros zenon_Hd3 zenon_Hab zenon_Hc9 zenon_H5e zenon_H82 zenon_Hcf zenon_Hce zenon_H3c. % 15.16/15.32 apply (zenon_or_s _ _ zenon_Hd3); [ zenon_intro zenon_Hca | zenon_intro zenon_Hd4 ]. % 15.16/15.32 apply (zenon_L53_); trivial. % 15.16/15.32 apply (zenon_or_s _ _ zenon_Hd4); [ zenon_intro zenon_Hcc | zenon_intro zenon_Hd5 ]. % 15.16/15.32 apply (zenon_L54_); trivial. % 15.16/15.32 apply (zenon_or_s _ _ zenon_Hd5); [ zenon_intro zenon_Hd0 | zenon_intro zenon_H40 ]. % 15.16/15.32 apply (zenon_L55_); trivial. % 15.16/15.32 exact (zenon_H3c zenon_H40). % 15.16/15.32 (* end of lemma zenon_L56_ *) % 15.16/15.32 assert (zenon_L57_ : ((op (e2) (e0)) = (e0)) -> ((op (e2) (e0)) = (e3)) -> (~((e0) = (e3))) -> False). % 15.16/15.32 do 0 intro. intros zenon_Hcf zenon_Haf zenon_H4b. % 15.16/15.32 elim (classic ((e3) = (e3))); [ zenon_intro zenon_H4c | zenon_intro zenon_H4d ]. % 15.16/15.32 cut (((e3) = (e3)) = ((e0) = (e3))). % 15.16/15.32 intro zenon_D_pnotp. % 15.16/15.32 apply zenon_H4b. % 15.16/15.32 rewrite <- zenon_D_pnotp. % 15.16/15.32 exact zenon_H4c. % 15.16/15.32 cut (((e3) = (e3))); [idtac | apply NNPP; zenon_intro zenon_H4d]. % 15.16/15.32 cut (((e3) = (e0))); [idtac | apply NNPP; zenon_intro zenon_H4e]. % 15.16/15.32 congruence. % 15.16/15.32 cut (((op (e2) (e0)) = (e0)) = ((e3) = (e0))). % 15.16/15.32 intro zenon_D_pnotp. % 15.16/15.32 apply zenon_H4e. % 15.16/15.32 rewrite <- zenon_D_pnotp. % 15.16/15.32 exact zenon_Hcf. % 15.16/15.32 cut (((e0) = (e0))); [idtac | apply NNPP; zenon_intro zenon_H1d]. % 15.16/15.32 cut (((op (e2) (e0)) = (e3))); [idtac | apply NNPP; zenon_intro zenon_Hb0]. % 15.16/15.32 congruence. % 15.16/15.32 exact (zenon_Hb0 zenon_Haf). % 15.16/15.32 apply zenon_H1d. apply refl_equal. % 15.16/15.32 apply zenon_H4d. apply refl_equal. % 15.16/15.32 apply zenon_H4d. apply refl_equal. % 15.16/15.32 (* end of lemma zenon_L57_ *) % 15.16/15.32 assert (zenon_L58_ : (((op (e0) (e0)) = (e3))\/(((op (e1) (e0)) = (e3))\/(((op (e2) (e0)) = (e3))\/((op (e3) (e0)) = (e3))))) -> (~((op (e0) (e0)) = (e3))) -> (~((op (e3) (e3)) = (e0))) -> (~((op (e2) (e0)) = (op (e2) (e3)))) -> (~((e0) = (e2))) -> (~((op (e0) (e2)) = (op (e0) (e3)))) -> ((op (e0) (e2)) = (e0)) -> (((op (e0) (e3)) = (e0))\/(((op (e1) (e3)) = (e0))\/(((op (e2) (e3)) = (e0))\/((op (e3) (e3)) = (e0))))) -> (~((op (e0) (e2)) = (op (e1) (e2)))) -> ((op (e0) (e2)) = (e2)) -> (~((op (e1) (e1)) = (e2))) -> (~((e2) = (e3))) -> (((op (e1) (e0)) = (e2))\/(((op (e1) (e1)) = (e2))\/(((op (e1) (e2)) = (e2))\/((op (e1) (e3)) = (e2))))) -> (~((e0) = (e3))) -> ((op (e2) (e0)) = (e0)) -> ((op (e3) (e3)) = (e3)) -> (~((op (e3) (e0)) = (op (e3) (e3)))) -> False). % 15.16/15.32 do 0 intro. intros zenon_Hbe zenon_H59 zenon_H3c zenon_Hce zenon_H5e zenon_Hc9 zenon_Hab zenon_Hd3 zenon_H87 zenon_H63 zenon_Hd6 zenon_H6a zenon_H84 zenon_H4b zenon_Hcf zenon_H42 zenon_Hbb. % 15.16/15.32 apply (zenon_or_s _ _ zenon_Hbe); [ zenon_intro zenon_H5b | zenon_intro zenon_Hbf ]. % 15.16/15.32 exact (zenon_H59 zenon_H5b). % 15.16/15.32 apply (zenon_or_s _ _ zenon_Hbf); [ zenon_intro zenon_H69 | zenon_intro zenon_Hc0 ]. % 15.16/15.32 apply (zenon_or_s _ _ zenon_H84); [ zenon_intro zenon_H68 | zenon_intro zenon_H85 ]. % 15.16/15.32 apply (zenon_L17_); trivial. % 15.16/15.32 apply (zenon_or_s _ _ zenon_H85); [ zenon_intro zenon_H6e | zenon_intro zenon_H86 ]. % 15.16/15.32 exact (zenon_Hd6 zenon_H6e). % 15.16/15.32 apply (zenon_or_s _ _ zenon_H86); [ zenon_intro zenon_H7c | zenon_intro zenon_H82 ]. % 15.16/15.32 apply (zenon_L52_); trivial. % 15.16/15.32 apply (zenon_L56_); trivial. % 15.16/15.32 apply (zenon_or_s _ _ zenon_Hc0); [ zenon_intro zenon_Haf | zenon_intro zenon_Hba ]. % 15.16/15.32 apply (zenon_L57_); trivial. % 15.16/15.32 apply (zenon_L43_); trivial. % 15.16/15.32 (* end of lemma zenon_L58_ *) % 15.16/15.32 assert (zenon_L59_ : ((op (e0) (e1)) = (e1)) -> ((op (e0) (e1)) = (e3)) -> (~((e1) = (e3))) -> False). % 15.16/15.32 do 0 intro. intros zenon_H22 zenon_H4a zenon_Ha3. % 15.16/15.32 elim (classic ((e3) = (e3))); [ zenon_intro zenon_H4c | zenon_intro zenon_H4d ]. % 15.16/15.32 cut (((e3) = (e3)) = ((e1) = (e3))). % 15.16/15.32 intro zenon_D_pnotp. % 15.16/15.32 apply zenon_Ha3. % 15.16/15.32 rewrite <- zenon_D_pnotp. % 15.16/15.32 exact zenon_H4c. % 15.16/15.32 cut (((e3) = (e3))); [idtac | apply NNPP; zenon_intro zenon_H4d]. % 15.16/15.32 cut (((e3) = (e1))); [idtac | apply NNPP; zenon_intro zenon_Ha4]. % 15.16/15.32 congruence. % 15.16/15.32 cut (((op (e0) (e1)) = (e1)) = ((e3) = (e1))). % 15.16/15.32 intro zenon_D_pnotp. % 15.16/15.32 apply zenon_Ha4. % 15.16/15.32 rewrite <- zenon_D_pnotp. % 15.16/15.32 exact zenon_H22. % 15.16/15.32 cut (((e1) = (e1))); [idtac | apply NNPP; zenon_intro zenon_Ha0]. % 15.16/15.32 cut (((op (e0) (e1)) = (e3))); [idtac | apply NNPP; zenon_intro zenon_H4f]. % 15.16/15.32 congruence. % 15.16/15.32 exact (zenon_H4f zenon_H4a). % 15.16/15.32 apply zenon_Ha0. apply refl_equal. % 15.16/15.32 apply zenon_H4d. apply refl_equal. % 15.16/15.32 apply zenon_H4d. apply refl_equal. % 15.16/15.32 (* end of lemma zenon_L59_ *) % 15.16/15.32 assert (zenon_L60_ : (((op (e0) (e0)) = (e3))\/(((op (e0) (e1)) = (e3))\/(((op (e0) (e2)) = (e3))\/((op (e0) (e3)) = (e3))))) -> (~((op (e0) (e0)) = (e3))) -> (~((e1) = (e3))) -> ((op (e0) (e1)) = (e1)) -> (~((e0) = (e3))) -> ((op (e0) (e2)) = (e0)) -> ((op (e3) (e3)) = (e3)) -> (~((op (e0) (e3)) = (op (e3) (e3)))) -> False). % 15.16/15.32 do 0 intro. intros zenon_H58 zenon_H59 zenon_Ha3 zenon_H22 zenon_H4b zenon_Hab zenon_H42 zenon_H36. % 15.16/15.32 apply (zenon_or_s _ _ zenon_H58); [ zenon_intro zenon_H5b | zenon_intro zenon_H5a ]. % 15.16/15.32 exact (zenon_H59 zenon_H5b). % 15.16/15.32 apply (zenon_or_s _ _ zenon_H5a); [ zenon_intro zenon_H4a | zenon_intro zenon_H5c ]. % 15.16/15.32 apply (zenon_L59_); trivial. % 15.16/15.32 apply (zenon_or_s _ _ zenon_H5c); [ zenon_intro zenon_H50 | zenon_intro zenon_H53 ]. % 15.16/15.32 apply (zenon_L48_); trivial. % 15.16/15.32 apply (zenon_L12_); trivial. % 15.16/15.32 (* end of lemma zenon_L60_ *) % 15.16/15.32 assert (zenon_L61_ : (~((op (e1) (e0)) = (op (e1) (e1)))) -> ((op (e1) (e0)) = (e1)) -> ((op (e1) (e1)) = (e1)) -> False). % 15.16/15.32 do 0 intro. intros zenon_Hd7 zenon_Hd8 zenon_H21. % 15.16/15.32 cut (((op (e1) (e0)) = (e1)) = ((op (e1) (e0)) = (op (e1) (e1)))). % 15.16/15.32 intro zenon_D_pnotp. % 15.16/15.32 apply zenon_Hd7. % 15.16/15.32 rewrite <- zenon_D_pnotp. % 15.16/15.32 exact zenon_Hd8. % 15.16/15.32 cut (((e1) = (op (e1) (e1)))); [idtac | apply NNPP; zenon_intro zenon_Hd9]. % 15.16/15.32 cut (((op (e1) (e0)) = (op (e1) (e0)))); [idtac | apply NNPP; zenon_intro zenon_Hda]. % 15.16/15.32 congruence. % 15.16/15.32 apply zenon_Hda. apply refl_equal. % 15.16/15.32 apply zenon_Hd9. apply sym_equal. exact zenon_H21. % 15.16/15.32 (* end of lemma zenon_L61_ *) % 15.16/15.32 assert (zenon_L62_ : (~((e0) = (e3))) -> ((op (e3) (e0)) = (e3)) -> ((op (e3) (e0)) = (e0)) -> False). % 15.16/15.32 do 0 intro. intros zenon_H4b zenon_Hba zenon_Hdb. % 15.16/15.32 cut (((op (e3) (e0)) = (e3)) = ((e0) = (e3))). % 15.16/15.32 intro zenon_D_pnotp. % 15.16/15.32 apply zenon_H4b. % 15.16/15.32 rewrite <- zenon_D_pnotp. % 15.16/15.32 exact zenon_Hba. % 15.16/15.32 cut (((e3) = (e3))); [idtac | apply NNPP; zenon_intro zenon_H4d]. % 15.16/15.32 cut (((op (e3) (e0)) = (e0))); [idtac | apply NNPP; zenon_intro zenon_Hdc]. % 15.16/15.32 congruence. % 15.16/15.32 exact (zenon_Hdc zenon_Hdb). % 15.16/15.32 apply zenon_H4d. apply refl_equal. % 15.16/15.32 (* end of lemma zenon_L62_ *) % 15.16/15.32 assert (zenon_L63_ : (((op (e0) (e0)) = (e3))\/(((op (e1) (e0)) = (e3))\/(((op (e2) (e0)) = (e3))\/((op (e3) (e0)) = (e3))))) -> (~((op (e0) (e0)) = (e3))) -> (~((e2) = (e3))) -> ((op (e1) (e0)) = (e2)) -> (~((e1) = (e3))) -> ((op (e2) (e0)) = (e1)) -> (~((e0) = (e3))) -> ((op (e3) (e0)) = (e0)) -> False). % 15.16/15.32 do 0 intro. intros zenon_Hbe zenon_H59 zenon_H6a zenon_H68 zenon_Ha3 zenon_Hae zenon_H4b zenon_Hdb. % 15.16/15.32 apply (zenon_or_s _ _ zenon_Hbe); [ zenon_intro zenon_H5b | zenon_intro zenon_Hbf ]. % 15.16/15.32 exact (zenon_H59 zenon_H5b). % 15.16/15.32 apply (zenon_or_s _ _ zenon_Hbf); [ zenon_intro zenon_H69 | zenon_intro zenon_Hc0 ]. % 15.16/15.32 apply (zenon_L17_); trivial. % 15.16/15.32 apply (zenon_or_s _ _ zenon_Hc0); [ zenon_intro zenon_Haf | zenon_intro zenon_Hba ]. % 15.16/15.32 apply (zenon_L39_); trivial. % 15.16/15.32 apply (zenon_L62_); trivial. % 15.16/15.32 (* end of lemma zenon_L63_ *) % 15.16/15.32 assert (zenon_L64_ : ((op (e2) (e0)) = (e2)) -> ((op (e2) (e0)) = (e3)) -> (~((e2) = (e3))) -> False). % 15.16/15.32 do 0 intro. intros zenon_Hdd zenon_Haf zenon_H6a. % 15.16/15.32 elim (classic ((e3) = (e3))); [ zenon_intro zenon_H4c | zenon_intro zenon_H4d ]. % 15.16/15.32 cut (((e3) = (e3)) = ((e2) = (e3))). % 15.16/15.32 intro zenon_D_pnotp. % 15.16/15.32 apply zenon_H6a. % 15.16/15.32 rewrite <- zenon_D_pnotp. % 15.16/15.32 exact zenon_H4c. % 15.16/15.32 cut (((e3) = (e3))); [idtac | apply NNPP; zenon_intro zenon_H4d]. % 15.16/15.32 cut (((e3) = (e2))); [idtac | apply NNPP; zenon_intro zenon_H6b]. % 15.16/15.32 congruence. % 15.16/15.32 cut (((op (e2) (e0)) = (e2)) = ((e3) = (e2))). % 15.16/15.32 intro zenon_D_pnotp. % 15.16/15.32 apply zenon_H6b. % 15.16/15.32 rewrite <- zenon_D_pnotp. % 15.16/15.32 exact zenon_Hdd. % 15.16/15.32 cut (((e2) = (e2))); [idtac | apply NNPP; zenon_intro zenon_H60]. % 15.16/15.32 cut (((op (e2) (e0)) = (e3))); [idtac | apply NNPP; zenon_intro zenon_Hb0]. % 15.16/15.32 congruence. % 15.16/15.32 exact (zenon_Hb0 zenon_Haf). % 15.16/15.32 apply zenon_H60. apply refl_equal. % 15.16/15.32 apply zenon_H4d. apply refl_equal. % 15.16/15.32 apply zenon_H4d. apply refl_equal. % 15.16/15.32 (* end of lemma zenon_L64_ *) % 15.16/15.32 assert (zenon_L65_ : (~((op (e0) (e1)) = (op (e2) (e1)))) -> ((op (e0) (e1)) = (e3)) -> ((op (e2) (e1)) = (e3)) -> False). % 15.16/15.32 do 0 intro. intros zenon_Hde zenon_H4a zenon_Hdf. % 15.16/15.32 cut (((op (e0) (e1)) = (e3)) = ((op (e0) (e1)) = (op (e2) (e1)))). % 15.16/15.32 intro zenon_D_pnotp. % 15.16/15.32 apply zenon_Hde. % 15.16/15.32 rewrite <- zenon_D_pnotp. % 15.16/15.32 exact zenon_H4a. % 15.16/15.32 cut (((e3) = (op (e2) (e1)))); [idtac | apply NNPP; zenon_intro zenon_He0]. % 15.16/15.32 cut (((op (e0) (e1)) = (op (e0) (e1)))); [idtac | apply NNPP; zenon_intro zenon_He1]. % 15.16/15.32 congruence. % 15.16/15.32 apply zenon_He1. apply refl_equal. % 15.16/15.32 apply zenon_He0. apply sym_equal. exact zenon_Hdf. % 15.16/15.32 (* end of lemma zenon_L65_ *) % 15.16/15.32 assert (zenon_L66_ : ((op (e3) (e3)) = (e3)) -> ((op (e2) (e3)) = (e3)) -> (~((op (e2) (e3)) = (op (e3) (e3)))) -> False). % 15.16/15.32 do 0 intro. intros zenon_H42 zenon_He2 zenon_He3. % 15.16/15.32 elim (classic ((op (e3) (e3)) = (op (e3) (e3)))); [ zenon_intro zenon_H54 | zenon_intro zenon_H55 ]. % 15.16/15.32 cut (((op (e3) (e3)) = (op (e3) (e3))) = ((op (e2) (e3)) = (op (e3) (e3)))). % 15.16/15.32 intro zenon_D_pnotp. % 15.16/15.32 apply zenon_He3. % 15.16/15.32 rewrite <- zenon_D_pnotp. % 15.16/15.32 exact zenon_H54. % 15.16/15.32 cut (((op (e3) (e3)) = (op (e3) (e3)))); [idtac | apply NNPP; zenon_intro zenon_H55]. % 15.16/15.32 cut (((op (e3) (e3)) = (op (e2) (e3)))); [idtac | apply NNPP; zenon_intro zenon_He4]. % 15.16/15.32 congruence. % 15.16/15.32 cut (((op (e3) (e3)) = (e3)) = ((op (e3) (e3)) = (op (e2) (e3)))). % 15.16/15.32 intro zenon_D_pnotp. % 15.16/15.32 apply zenon_He4. % 15.16/15.32 rewrite <- zenon_D_pnotp. % 15.16/15.32 exact zenon_H42. % 15.16/15.32 cut (((e3) = (op (e2) (e3)))); [idtac | apply NNPP; zenon_intro zenon_He5]. % 15.16/15.32 cut (((op (e3) (e3)) = (op (e3) (e3)))); [idtac | apply NNPP; zenon_intro zenon_H55]. % 15.16/15.32 congruence. % 15.16/15.32 apply zenon_H55. apply refl_equal. % 15.16/15.32 apply zenon_He5. apply sym_equal. exact zenon_He2. % 15.16/15.32 apply zenon_H55. apply refl_equal. % 15.16/15.32 apply zenon_H55. apply refl_equal. % 15.16/15.32 (* end of lemma zenon_L66_ *) % 15.16/15.32 assert (zenon_L67_ : (((op (e2) (e0)) = (e3))\/(((op (e2) (e1)) = (e3))\/(((op (e2) (e2)) = (e3))\/((op (e2) (e3)) = (e3))))) -> (~((e2) = (e3))) -> ((op (e2) (e0)) = (e2)) -> ((op (e0) (e1)) = (e3)) -> (~((op (e0) (e1)) = (op (e2) (e1)))) -> (~((op (e2) (e2)) = (e3))) -> ((op (e3) (e3)) = (e3)) -> (~((op (e2) (e3)) = (op (e3) (e3)))) -> False). % 15.16/15.32 do 0 intro. intros zenon_He6 zenon_H6a zenon_Hdd zenon_H4a zenon_Hde zenon_H30 zenon_H42 zenon_He3. % 15.16/15.32 apply (zenon_or_s _ _ zenon_He6); [ zenon_intro zenon_Haf | zenon_intro zenon_He7 ]. % 15.16/15.32 apply (zenon_L64_); trivial. % 15.16/15.32 apply (zenon_or_s _ _ zenon_He7); [ zenon_intro zenon_Hdf | zenon_intro zenon_He8 ]. % 15.16/15.32 apply (zenon_L65_); trivial. % 15.16/15.32 apply (zenon_or_s _ _ zenon_He8); [ zenon_intro zenon_H34 | zenon_intro zenon_He2 ]. % 15.16/15.32 exact (zenon_H30 zenon_H34). % 15.16/15.32 apply (zenon_L66_); trivial. % 15.16/15.32 (* end of lemma zenon_L67_ *) % 15.16/15.32 assert (zenon_L68_ : (((op (e0) (e0)) = (e3))\/(((op (e0) (e1)) = (e3))\/(((op (e0) (e2)) = (e3))\/((op (e0) (e3)) = (e3))))) -> (~((op (e0) (e0)) = (e3))) -> (~((op (e2) (e3)) = (op (e3) (e3)))) -> (~((op (e2) (e2)) = (e3))) -> (~((op (e0) (e1)) = (op (e2) (e1)))) -> ((op (e2) (e0)) = (e2)) -> (~((e2) = (e3))) -> (((op (e2) (e0)) = (e3))\/(((op (e2) (e1)) = (e3))\/(((op (e2) (e2)) = (e3))\/((op (e2) (e3)) = (e3))))) -> (~((e0) = (e3))) -> ((op (e0) (e2)) = (e0)) -> ((op (e3) (e3)) = (e3)) -> (~((op (e0) (e3)) = (op (e3) (e3)))) -> False). % 15.16/15.32 do 0 intro. intros zenon_H58 zenon_H59 zenon_He3 zenon_H30 zenon_Hde zenon_Hdd zenon_H6a zenon_He6 zenon_H4b zenon_Hab zenon_H42 zenon_H36. % 15.16/15.32 apply (zenon_or_s _ _ zenon_H58); [ zenon_intro zenon_H5b | zenon_intro zenon_H5a ]. % 15.16/15.32 exact (zenon_H59 zenon_H5b). % 15.16/15.32 apply (zenon_or_s _ _ zenon_H5a); [ zenon_intro zenon_H4a | zenon_intro zenon_H5c ]. % 15.16/15.32 apply (zenon_L67_); trivial. % 15.16/15.32 apply (zenon_or_s _ _ zenon_H5c); [ zenon_intro zenon_H50 | zenon_intro zenon_H53 ]. % 15.16/15.32 apply (zenon_L48_); trivial. % 15.16/15.32 apply (zenon_L12_); trivial. % 15.16/15.32 (* end of lemma zenon_L68_ *) % 15.16/15.32 assert (zenon_L69_ : ((op (e3) (e0)) = (e0)) -> ((op (e3) (e0)) = (e2)) -> (~((e0) = (e2))) -> False). % 15.16/15.32 do 0 intro. intros zenon_Hdb zenon_He9 zenon_H5e. % 15.16/15.32 elim (classic ((e2) = (e2))); [ zenon_intro zenon_H5f | zenon_intro zenon_H60 ]. % 15.16/15.32 cut (((e2) = (e2)) = ((e0) = (e2))). % 15.16/15.32 intro zenon_D_pnotp. % 15.16/15.32 apply zenon_H5e. % 15.16/15.32 rewrite <- zenon_D_pnotp. % 15.16/15.32 exact zenon_H5f. % 15.16/15.32 cut (((e2) = (e2))); [idtac | apply NNPP; zenon_intro zenon_H60]. % 15.16/15.32 cut (((e2) = (e0))); [idtac | apply NNPP; zenon_intro zenon_H61]. % 15.16/15.32 congruence. % 15.16/15.32 cut (((op (e3) (e0)) = (e0)) = ((e2) = (e0))). % 15.16/15.32 intro zenon_D_pnotp. % 15.16/15.32 apply zenon_H61. % 15.16/15.32 rewrite <- zenon_D_pnotp. % 15.16/15.32 exact zenon_Hdb. % 15.16/15.32 cut (((e0) = (e0))); [idtac | apply NNPP; zenon_intro zenon_H1d]. % 15.16/15.32 cut (((op (e3) (e0)) = (e2))); [idtac | apply NNPP; zenon_intro zenon_Hea]. % 15.16/15.32 congruence. % 15.16/15.32 exact (zenon_Hea zenon_He9). % 15.16/15.32 apply zenon_H1d. apply refl_equal. % 15.16/15.32 apply zenon_H60. apply refl_equal. % 15.16/15.32 apply zenon_H60. apply refl_equal. % 15.16/15.32 (* end of lemma zenon_L69_ *) % 15.16/15.32 assert (zenon_L70_ : (((op (e0) (e0)) = (e2))\/(((op (e1) (e0)) = (e2))\/(((op (e2) (e0)) = (e2))\/((op (e3) (e0)) = (e2))))) -> ((op (e0) (e3)) = (e1)) -> (((op (e2) (e2)) = (e0))\/(((op (e2) (e2)) = (e1))\/(((op (e2) (e2)) = (e2))\/((op (e2) (e2)) = (e3))))) -> (~((op (e2) (e2)) = (e0))) -> (~((op (e2) (e2)) = (e2))) -> ((op (e2) (e0)) = (e1)) -> (~((e1) = (e3))) -> (((op (e0) (e0)) = (e3))\/(((op (e1) (e0)) = (e3))\/(((op (e2) (e0)) = (e3))\/((op (e3) (e0)) = (e3))))) -> (~((op (e0) (e3)) = (op (e3) (e3)))) -> ((op (e3) (e3)) = (e3)) -> ((op (e0) (e2)) = (e0)) -> (~((e0) = (e3))) -> (((op (e2) (e0)) = (e3))\/(((op (e2) (e1)) = (e3))\/(((op (e2) (e2)) = (e3))\/((op (e2) (e3)) = (e3))))) -> (~((e2) = (e3))) -> (~((op (e0) (e1)) = (op (e2) (e1)))) -> (~((op (e2) (e2)) = (e3))) -> (~((op (e2) (e3)) = (op (e3) (e3)))) -> (~((op (e0) (e0)) = (e3))) -> (((op (e0) (e0)) = (e3))\/(((op (e0) (e1)) = (e3))\/(((op (e0) (e2)) = (e3))\/((op (e0) (e3)) = (e3))))) -> ((op (e3) (e0)) = (e0)) -> (~((e0) = (e2))) -> False). % 15.16/15.32 do 0 intro. intros zenon_Heb zenon_H37 zenon_H2d zenon_H2e zenon_H2f zenon_Hae zenon_Ha3 zenon_Hbe zenon_H36 zenon_H42 zenon_Hab zenon_H4b zenon_He6 zenon_H6a zenon_Hde zenon_H30 zenon_He3 zenon_H59 zenon_H58 zenon_Hdb zenon_H5e. % 15.16/15.32 apply (zenon_or_s _ _ zenon_Heb); [ zenon_intro zenon_H92 | zenon_intro zenon_Hec ]. % 15.16/15.32 apply (zenon_L49_); trivial. % 15.16/15.32 apply (zenon_or_s _ _ zenon_Hec); [ zenon_intro zenon_H68 | zenon_intro zenon_Hed ]. % 15.16/15.32 apply (zenon_L63_); trivial. % 15.16/15.32 apply (zenon_or_s _ _ zenon_Hed); [ zenon_intro zenon_Hdd | zenon_intro zenon_He9 ]. % 15.16/15.32 apply (zenon_L68_); trivial. % 15.16/15.32 apply (zenon_L69_); trivial. % 15.16/15.32 (* end of lemma zenon_L70_ *) % 15.16/15.32 assert (zenon_L71_ : ((op (e3) (e0)) = (e0)) -> ((op (e3) (e0)) = (e1)) -> (~((e0) = (e1))) -> False). % 15.16/15.32 do 0 intro. intros zenon_Hdb zenon_Hee zenon_H9e. % 15.16/15.32 elim (classic ((e1) = (e1))); [ zenon_intro zenon_H9f | zenon_intro zenon_Ha0 ]. % 15.16/15.32 cut (((e1) = (e1)) = ((e0) = (e1))). % 15.16/15.32 intro zenon_D_pnotp. % 15.16/15.32 apply zenon_H9e. % 15.16/15.32 rewrite <- zenon_D_pnotp. % 15.16/15.32 exact zenon_H9f. % 15.16/15.32 cut (((e1) = (e1))); [idtac | apply NNPP; zenon_intro zenon_Ha0]. % 15.16/15.32 cut (((e1) = (e0))); [idtac | apply NNPP; zenon_intro zenon_Ha1]. % 15.16/15.32 congruence. % 15.16/15.32 cut (((op (e3) (e0)) = (e0)) = ((e1) = (e0))). % 15.16/15.32 intro zenon_D_pnotp. % 15.16/15.32 apply zenon_Ha1. % 15.16/15.32 rewrite <- zenon_D_pnotp. % 15.16/15.32 exact zenon_Hdb. % 15.16/15.32 cut (((e0) = (e0))); [idtac | apply NNPP; zenon_intro zenon_H1d]. % 15.16/15.32 cut (((op (e3) (e0)) = (e1))); [idtac | apply NNPP; zenon_intro zenon_Hef]. % 15.16/15.32 congruence. % 15.16/15.32 exact (zenon_Hef zenon_Hee). % 15.16/15.32 apply zenon_H1d. apply refl_equal. % 15.16/15.32 apply zenon_Ha0. apply refl_equal. % 15.16/15.32 apply zenon_Ha0. apply refl_equal. % 15.16/15.32 (* end of lemma zenon_L71_ *) % 15.16/15.32 assert (zenon_L72_ : (((op (e0) (e0)) = (e0))\/(((op (e1) (e0)) = (e0))\/(((op (e2) (e0)) = (e0))\/((op (e3) (e0)) = (e0))))) -> (~((op (e0) (e0)) = (e0))) -> (((op (e2) (e0)) = (e1))\/(((op (e2) (e1)) = (e1))\/(((op (e2) (e2)) = (e1))\/((op (e2) (e3)) = (e1))))) -> (~((op (e1) (e1)) = (op (e2) (e1)))) -> (~((op (e2) (e2)) = (e1))) -> (~((op (e0) (e3)) = (op (e2) (e3)))) -> (~((e1) = (e2))) -> (~((op (e3) (e3)) = (e0))) -> (~((op (e2) (e0)) = (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) (e2)) = (op (e1) (e2)))) -> (~((op (e1) (e1)) = (e2))) -> (((op (e1) (e0)) = (e2))\/(((op (e1) (e1)) = (e2))\/(((op (e1) (e2)) = (e2))\/((op (e1) (e3)) = (e2))))) -> (~((op (e3) (e0)) = (op (e3) (e3)))) -> (((op (e0) (e0)) = (e2))\/(((op (e0) (e1)) = (e2))\/(((op (e0) (e2)) = (e2))\/((op (e0) (e3)) = (e2))))) -> (~((op (e0) (e2)) = (op (e2) (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 (e1) (e0)) = (e1))\/(((op (e2) (e0)) = (e1))\/((op (e3) (e0)) = (e1))))) -> (~((op (e0) (e0)) = (e1))) -> ((op (e1) (e1)) = (e1)) -> (~((op (e1) (e0)) = (op (e1) (e1)))) -> (~((e0) = (e2))) -> (((op (e0) (e0)) = (e3))\/(((op (e0) (e1)) = (e3))\/(((op (e0) (e2)) = (e3))\/((op (e0) (e3)) = (e3))))) -> (~((op (e0) (e0)) = (e3))) -> (~((op (e2) (e3)) = (op (e3) (e3)))) -> (~((op (e2) (e2)) = (e3))) -> (~((op (e0) (e1)) = (op (e2) (e1)))) -> (~((e2) = (e3))) -> (((op (e2) (e0)) = (e3))\/(((op (e2) (e1)) = (e3))\/(((op (e2) (e2)) = (e3))\/((op (e2) (e3)) = (e3))))) -> (~((e0) = (e3))) -> ((op (e0) (e2)) = (e0)) -> ((op (e3) (e3)) = (e3)) -> (~((op (e0) (e3)) = (op (e3) (e3)))) -> (((op (e0) (e0)) = (e3))\/(((op (e1) (e0)) = (e3))\/(((op (e2) (e0)) = (e3))\/((op (e3) (e0)) = (e3))))) -> (~((e1) = (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 (e0) (e0)) = (e2))\/(((op (e1) (e0)) = (e2))\/(((op (e2) (e0)) = (e2))\/((op (e3) (e0)) = (e2))))) -> (~((e0) = (e1))) -> False). % 15.16/15.32 do 0 intro. intros zenon_Hf0 zenon_H20 zenon_Hb7 zenon_Hb1 zenon_H52 zenon_Hb4 zenon_Ha7 zenon_H3c zenon_Hce zenon_Hc9 zenon_Hd3 zenon_H87 zenon_Hd6 zenon_H84 zenon_Hbb zenon_H8e zenon_H28 zenon_H23 zenon_H44 zenon_Hf1 zenon_H45 zenon_H21 zenon_Hd7 zenon_H5e zenon_H58 zenon_H59 zenon_He3 zenon_H30 zenon_Hde zenon_H6a zenon_He6 zenon_H4b zenon_Hab zenon_H42 zenon_H36 zenon_Hbe zenon_Ha3 zenon_H2f zenon_H2e zenon_H2d zenon_Heb zenon_H9e. % 15.16/15.32 apply (zenon_or_s _ _ zenon_Hf0); [ zenon_intro zenon_H1f | zenon_intro zenon_Hf2 ]. % 15.16/15.32 exact (zenon_H20 zenon_H1f). % 15.16/15.32 apply (zenon_or_s _ _ zenon_Hf2); [ zenon_intro zenon_Had | zenon_intro zenon_Hf3 ]. % 15.16/15.32 apply (zenon_L44_); trivial. % 15.16/15.32 apply (zenon_or_s _ _ zenon_Hf3); [ zenon_intro zenon_Hcf | zenon_intro zenon_Hdb ]. % 15.16/15.32 apply (zenon_or_s _ _ zenon_H44); [ zenon_intro zenon_H47 | zenon_intro zenon_H46 ]. % 15.16/15.32 exact (zenon_H45 zenon_H47). % 15.16/15.32 apply (zenon_or_s _ _ zenon_H46); [ zenon_intro zenon_H22 | zenon_intro zenon_H48 ]. % 15.16/15.32 apply (zenon_L3_); trivial. % 15.16/15.32 apply (zenon_or_s _ _ zenon_H48); [ zenon_intro zenon_H29 | zenon_intro zenon_H37 ]. % 15.16/15.32 apply (zenon_L5_); trivial. % 15.16/15.32 apply (zenon_or_s _ _ zenon_H8e); [ zenon_intro zenon_H92 | zenon_intro zenon_H91 ]. % 15.16/15.32 apply (zenon_L49_); trivial. % 15.16/15.32 apply (zenon_or_s _ _ zenon_H91); [ zenon_intro zenon_H5d | zenon_intro zenon_H93 ]. % 15.16/15.32 apply (zenon_L51_); trivial. % 15.16/15.32 apply (zenon_or_s _ _ zenon_H93); [ zenon_intro zenon_H63 | zenon_intro zenon_H81 ]. % 15.16/15.32 apply (zenon_L58_); trivial. % 15.16/15.32 apply (zenon_L33_); trivial. % 15.16/15.32 apply (zenon_or_s _ _ zenon_H44); [ zenon_intro zenon_H47 | zenon_intro zenon_H46 ]. % 15.16/15.32 exact (zenon_H45 zenon_H47). % 15.16/15.32 apply (zenon_or_s _ _ zenon_H46); [ zenon_intro zenon_H22 | zenon_intro zenon_H48 ]. % 15.16/15.32 apply (zenon_L60_); trivial. % 15.16/15.32 apply (zenon_or_s _ _ zenon_H48); [ zenon_intro zenon_H29 | zenon_intro zenon_H37 ]. % 15.16/15.32 apply (zenon_L37_); trivial. % 15.16/15.32 apply (zenon_or_s _ _ zenon_Hf1); [ zenon_intro zenon_H47 | zenon_intro zenon_Hf4 ]. % 15.16/15.32 exact (zenon_H45 zenon_H47). % 15.16/15.32 apply (zenon_or_s _ _ zenon_Hf4); [ zenon_intro zenon_Hd8 | zenon_intro zenon_Hf5 ]. % 15.16/15.32 apply (zenon_L61_); trivial. % 15.16/15.32 apply (zenon_or_s _ _ zenon_Hf5); [ zenon_intro zenon_Hae | zenon_intro zenon_Hee ]. % 15.16/15.32 apply (zenon_L70_); trivial. % 15.16/15.32 apply (zenon_L71_); trivial. % 15.16/15.32 (* end of lemma zenon_L72_ *) % 15.16/15.32 assert (zenon_L73_ : ((op (e0) (e3)) = (e0)) -> ((op (e0) (e3)) = (e1)) -> (~((e0) = (e1))) -> False). % 15.16/15.32 do 0 intro. intros zenon_Hca zenon_H37 zenon_H9e. % 15.16/15.32 elim (classic ((e1) = (e1))); [ zenon_intro zenon_H9f | zenon_intro zenon_Ha0 ]. % 15.16/15.32 cut (((e1) = (e1)) = ((e0) = (e1))). % 15.16/15.32 intro zenon_D_pnotp. % 15.16/15.32 apply zenon_H9e. % 15.16/15.32 rewrite <- zenon_D_pnotp. % 15.16/15.32 exact zenon_H9f. % 15.16/15.32 cut (((e1) = (e1))); [idtac | apply NNPP; zenon_intro zenon_Ha0]. % 15.16/15.32 cut (((e1) = (e0))); [idtac | apply NNPP; zenon_intro zenon_Ha1]. % 15.16/15.32 congruence. % 15.16/15.32 cut (((op (e0) (e3)) = (e0)) = ((e1) = (e0))). % 15.16/15.32 intro zenon_D_pnotp. % 15.16/15.32 apply zenon_Ha1. % 15.16/15.32 rewrite <- zenon_D_pnotp. % 15.16/15.32 exact zenon_Hca. % 15.16/15.32 cut (((e0) = (e0))); [idtac | apply NNPP; zenon_intro zenon_H1d]. % 15.16/15.32 cut (((op (e0) (e3)) = (e1))); [idtac | apply NNPP; zenon_intro zenon_Hf6]. % 15.16/15.32 congruence. % 15.16/15.32 exact (zenon_Hf6 zenon_H37). % 15.16/15.32 apply zenon_H1d. apply refl_equal. % 15.16/15.32 apply zenon_Ha0. apply refl_equal. % 15.16/15.32 apply zenon_Ha0. apply refl_equal. % 15.16/15.32 (* end of lemma zenon_L73_ *) % 15.16/15.32 assert (zenon_L74_ : (((op (e0) (e0)) = (e1))\/(((op (e0) (e1)) = (e1))\/(((op (e0) (e2)) = (e1))\/((op (e0) (e3)) = (e1))))) -> (~((op (e0) (e0)) = (e1))) -> (~((op (e0) (e1)) = (op (e1) (e1)))) -> ((op (e1) (e1)) = (e1)) -> (~((op (e2) (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 (e0) (e3)) = (e0)) -> (~((e0) = (e1))) -> False). % 15.16/15.32 do 0 intro. intros zenon_H44 zenon_H45 zenon_H23 zenon_H21 zenon_H30 zenon_H2f zenon_H28 zenon_H2e zenon_H2d zenon_Hca zenon_H9e. % 15.16/15.32 apply (zenon_or_s _ _ zenon_H44); [ zenon_intro zenon_H47 | zenon_intro zenon_H46 ]. % 15.16/15.32 exact (zenon_H45 zenon_H47). % 15.16/15.32 apply (zenon_or_s _ _ zenon_H46); [ zenon_intro zenon_H22 | zenon_intro zenon_H48 ]. % 15.16/15.32 apply (zenon_L3_); trivial. % 15.16/15.32 apply (zenon_or_s _ _ zenon_H48); [ zenon_intro zenon_H29 | zenon_intro zenon_H37 ]. % 15.16/15.32 apply (zenon_L5_); trivial. % 15.16/15.32 apply (zenon_L73_); trivial. % 15.16/15.32 (* end of lemma zenon_L74_ *) % 15.16/15.32 assert (zenon_L75_ : (~((op (op (e2) (e2)) (op (e2) (e2))) = (op (e3) (e3)))) -> ((op (e2) (e2)) = (e3)) -> False). % 15.16/15.32 do 0 intro. intros zenon_Hf7 zenon_H34. % 15.16/15.32 cut (((op (e2) (e2)) = (e3))); [idtac | apply NNPP; zenon_intro zenon_H30]. % 15.16/15.32 cut (((op (e2) (e2)) = (e3))); [idtac | apply NNPP; zenon_intro zenon_H30]. % 15.16/15.32 congruence. % 15.16/15.32 exact (zenon_H30 zenon_H34). % 15.16/15.32 exact (zenon_H30 zenon_H34). % 15.16/15.32 (* end of lemma zenon_L75_ *) % 15.16/15.32 assert (zenon_L76_ : ((op (e2) (e0)) = (e1)) -> ((op (e3) (e3)) = (e0)) -> ((op (e2) (e2)) = (e3)) -> False). % 15.16/15.32 do 0 intro. intros zenon_Hae zenon_H40 zenon_H34. % 15.16/15.32 apply (zenon_notand_s _ _ ax10); [ zenon_intro zenon_Hf9 | zenon_intro zenon_Hf8 ]. % 15.16/15.32 elim (classic ((op (op (e2) (e2)) (op (e2) (e2))) = (op (op (e2) (e2)) (op (e2) (e2))))); [ zenon_intro zenon_Hfa | zenon_intro zenon_Hfb ]. % 15.16/15.32 cut (((op (op (e2) (e2)) (op (e2) (e2))) = (op (op (e2) (e2)) (op (e2) (e2)))) = ((e0) = (op (op (e2) (e2)) (op (e2) (e2))))). % 15.16/15.32 intro zenon_D_pnotp. % 15.16/15.32 apply zenon_Hf9. % 15.16/15.32 rewrite <- zenon_D_pnotp. % 15.16/15.32 exact zenon_Hfa. % 15.16/15.32 cut (((op (op (e2) (e2)) (op (e2) (e2))) = (op (op (e2) (e2)) (op (e2) (e2))))); [idtac | apply NNPP; zenon_intro zenon_Hfb]. % 15.16/15.32 cut (((op (op (e2) (e2)) (op (e2) (e2))) = (e0))); [idtac | apply NNPP; zenon_intro zenon_Hfc]. % 15.16/15.32 congruence. % 15.16/15.32 cut (((op (e3) (e3)) = (e0)) = ((op (op (e2) (e2)) (op (e2) (e2))) = (e0))). % 15.16/15.32 intro zenon_D_pnotp. % 15.16/15.32 apply zenon_Hfc. % 15.16/15.32 rewrite <- zenon_D_pnotp. % 15.16/15.32 exact zenon_H40. % 15.16/15.32 cut (((e0) = (e0))); [idtac | apply NNPP; zenon_intro zenon_H1d]. % 15.16/15.32 cut (((op (e3) (e3)) = (op (op (e2) (e2)) (op (e2) (e2))))); [idtac | apply NNPP; zenon_intro zenon_Hfd]. % 15.16/15.32 congruence. % 15.16/15.32 elim (classic ((op (op (e2) (e2)) (op (e2) (e2))) = (op (op (e2) (e2)) (op (e2) (e2))))); [ zenon_intro zenon_Hfa | zenon_intro zenon_Hfb ]. % 15.16/15.32 cut (((op (op (e2) (e2)) (op (e2) (e2))) = (op (op (e2) (e2)) (op (e2) (e2)))) = ((op (e3) (e3)) = (op (op (e2) (e2)) (op (e2) (e2))))). % 15.16/15.32 intro zenon_D_pnotp. % 15.16/15.32 apply zenon_Hfd. % 15.16/15.32 rewrite <- zenon_D_pnotp. % 15.16/15.32 exact zenon_Hfa. % 15.16/15.32 cut (((op (op (e2) (e2)) (op (e2) (e2))) = (op (op (e2) (e2)) (op (e2) (e2))))); [idtac | apply NNPP; zenon_intro zenon_Hfb]. % 15.16/15.32 cut (((op (op (e2) (e2)) (op (e2) (e2))) = (op (e3) (e3)))); [idtac | apply NNPP; zenon_intro zenon_Hf7]. % 15.16/15.32 congruence. % 15.16/15.32 apply (zenon_L75_); trivial. % 15.16/15.32 apply zenon_Hfb. apply refl_equal. % 15.16/15.32 apply zenon_Hfb. apply refl_equal. % 15.16/15.32 apply zenon_H1d. apply refl_equal. % 15.16/15.32 apply zenon_Hfb. apply refl_equal. % 15.16/15.32 apply zenon_Hfb. apply refl_equal. % 15.16/15.32 apply (zenon_notand_s _ _ zenon_Hf8); [ zenon_intro zenon_H51 | zenon_intro zenon_Hfe ]. % 15.16/15.32 apply zenon_H51. apply sym_equal. exact zenon_H34. % 15.16/15.32 elim (classic ((op (e2) (op (op (e2) (e2)) (op (e2) (e2)))) = (op (e2) (op (op (e2) (e2)) (op (e2) (e2)))))); [ zenon_intro zenon_Hff | zenon_intro zenon_H100 ]. % 15.16/15.32 cut (((op (e2) (op (op (e2) (e2)) (op (e2) (e2)))) = (op (e2) (op (op (e2) (e2)) (op (e2) (e2))))) = ((e1) = (op (e2) (op (op (e2) (e2)) (op (e2) (e2)))))). % 15.16/15.32 intro zenon_D_pnotp. % 15.16/15.32 apply zenon_Hfe. % 15.16/15.32 rewrite <- zenon_D_pnotp. % 15.16/15.32 exact zenon_Hff. % 15.16/15.32 cut (((op (e2) (op (op (e2) (e2)) (op (e2) (e2)))) = (op (e2) (op (op (e2) (e2)) (op (e2) (e2)))))); [idtac | apply NNPP; zenon_intro zenon_H100]. % 15.16/15.32 cut (((op (e2) (op (op (e2) (e2)) (op (e2) (e2)))) = (e1))); [idtac | apply NNPP; zenon_intro zenon_H101]. % 15.16/15.32 congruence. % 15.16/15.32 cut (((op (e2) (e0)) = (e1)) = ((op (e2) (op (op (e2) (e2)) (op (e2) (e2)))) = (e1))). % 15.16/15.32 intro zenon_D_pnotp. % 15.16/15.32 apply zenon_H101. % 15.16/15.32 rewrite <- zenon_D_pnotp. % 15.16/15.32 exact zenon_Hae. % 15.16/15.32 cut (((e1) = (e1))); [idtac | apply NNPP; zenon_intro zenon_Ha0]. % 15.16/15.32 cut (((op (e2) (e0)) = (op (e2) (op (op (e2) (e2)) (op (e2) (e2)))))); [idtac | apply NNPP; zenon_intro zenon_H102]. % 15.16/15.32 congruence. % 15.16/15.32 elim (classic ((op (e2) (op (op (e2) (e2)) (op (e2) (e2)))) = (op (e2) (op (op (e2) (e2)) (op (e2) (e2)))))); [ zenon_intro zenon_Hff | zenon_intro zenon_H100 ]. % 15.16/15.32 cut (((op (e2) (op (op (e2) (e2)) (op (e2) (e2)))) = (op (e2) (op (op (e2) (e2)) (op (e2) (e2))))) = ((op (e2) (e0)) = (op (e2) (op (op (e2) (e2)) (op (e2) (e2)))))). % 15.16/15.32 intro zenon_D_pnotp. % 15.16/15.32 apply zenon_H102. % 15.16/15.32 rewrite <- zenon_D_pnotp. % 15.16/15.32 exact zenon_Hff. % 15.16/15.32 cut (((op (e2) (op (op (e2) (e2)) (op (e2) (e2)))) = (op (e2) (op (op (e2) (e2)) (op (e2) (e2)))))); [idtac | apply NNPP; zenon_intro zenon_H100]. % 15.16/15.32 cut (((op (e2) (op (op (e2) (e2)) (op (e2) (e2)))) = (op (e2) (e0)))); [idtac | apply NNPP; zenon_intro zenon_H103]. % 15.16/15.32 congruence. % 15.16/15.32 cut (((op (op (e2) (e2)) (op (e2) (e2))) = (e0))); [idtac | apply NNPP; zenon_intro zenon_Hfc]. % 15.16/15.32 cut (((e2) = (e2))); [idtac | apply NNPP; zenon_intro zenon_H60]. % 15.16/15.32 congruence. % 15.16/15.32 apply zenon_H60. apply refl_equal. % 15.16/15.32 cut (((op (e3) (e3)) = (e0)) = ((op (op (e2) (e2)) (op (e2) (e2))) = (e0))). % 15.16/15.32 intro zenon_D_pnotp. % 15.16/15.32 apply zenon_Hfc. % 15.16/15.32 rewrite <- zenon_D_pnotp. % 15.16/15.32 exact zenon_H40. % 15.16/15.32 cut (((e0) = (e0))); [idtac | apply NNPP; zenon_intro zenon_H1d]. % 15.16/15.32 cut (((op (e3) (e3)) = (op (op (e2) (e2)) (op (e2) (e2))))); [idtac | apply NNPP; zenon_intro zenon_Hfd]. % 15.16/15.32 congruence. % 15.16/15.32 elim (classic ((op (op (e2) (e2)) (op (e2) (e2))) = (op (op (e2) (e2)) (op (e2) (e2))))); [ zenon_intro zenon_Hfa | zenon_intro zenon_Hfb ]. % 15.16/15.32 cut (((op (op (e2) (e2)) (op (e2) (e2))) = (op (op (e2) (e2)) (op (e2) (e2)))) = ((op (e3) (e3)) = (op (op (e2) (e2)) (op (e2) (e2))))). % 15.16/15.32 intro zenon_D_pnotp. % 15.16/15.32 apply zenon_Hfd. % 15.16/15.32 rewrite <- zenon_D_pnotp. % 15.16/15.32 exact zenon_Hfa. % 15.16/15.32 cut (((op (op (e2) (e2)) (op (e2) (e2))) = (op (op (e2) (e2)) (op (e2) (e2))))); [idtac | apply NNPP; zenon_intro zenon_Hfb]. % 15.16/15.32 cut (((op (op (e2) (e2)) (op (e2) (e2))) = (op (e3) (e3)))); [idtac | apply NNPP; zenon_intro zenon_Hf7]. % 15.16/15.32 congruence. % 15.16/15.32 apply (zenon_L75_); trivial. % 15.16/15.32 apply zenon_Hfb. apply refl_equal. % 15.16/15.32 apply zenon_Hfb. apply refl_equal. % 15.16/15.32 apply zenon_H1d. apply refl_equal. % 15.16/15.32 apply zenon_H100. apply refl_equal. % 15.16/15.32 apply zenon_H100. apply refl_equal. % 15.16/15.32 apply zenon_Ha0. apply refl_equal. % 15.16/15.32 apply zenon_H100. apply refl_equal. % 15.16/15.32 apply zenon_H100. apply refl_equal. % 15.16/15.32 (* end of lemma zenon_L76_ *) % 15.16/15.32 assert (zenon_L77_ : (((op (e3) (e3)) = (e0))\/(((op (e3) (e3)) = (e1))\/(((op (e3) (e3)) = (e2))\/((op (e3) (e3)) = (e3))))) -> ((op (e2) (e2)) = (e3)) -> ((op (e2) (e0)) = (e1)) -> (~((op (e3) (e3)) = (e1))) -> (~((op (e3) (e3)) = (e2))) -> (~((op (e3) (e3)) = (e3))) -> False). % 15.16/15.32 do 0 intro. intros zenon_H3b zenon_H34 zenon_Hae zenon_H104 zenon_H3d zenon_H3e. % 15.16/15.32 apply (zenon_or_s _ _ zenon_H3b); [ zenon_intro zenon_H40 | zenon_intro zenon_H3f ]. % 15.16/15.32 apply (zenon_L76_); trivial. % 15.16/15.32 apply (zenon_or_s _ _ zenon_H3f); [ zenon_intro zenon_H38 | zenon_intro zenon_H41 ]. % 15.16/15.32 exact (zenon_H104 zenon_H38). % 15.16/15.32 apply (zenon_or_s _ _ zenon_H41); [ zenon_intro zenon_H43 | zenon_intro zenon_H42 ]. % 15.16/15.32 exact (zenon_H3d zenon_H43). % 15.16/15.32 exact (zenon_H3e zenon_H42). % 15.16/15.32 (* end of lemma zenon_L77_ *) % 15.16/15.32 assert (zenon_L78_ : (((op (e2) (e2)) = (e0))\/(((op (e2) (e2)) = (e1))\/(((op (e2) (e2)) = (e2))\/((op (e2) (e2)) = (e3))))) -> (~((op (e2) (e2)) = (e0))) -> (~((op (e2) (e2)) = (e1))) -> (~((op (e2) (e2)) = (e2))) -> (((op (e3) (e3)) = (e0))\/(((op (e3) (e3)) = (e1))\/(((op (e3) (e3)) = (e2))\/((op (e3) (e3)) = (e3))))) -> ((op (e2) (e0)) = (e1)) -> (~((op (e3) (e3)) = (e1))) -> (~((op (e3) (e3)) = (e2))) -> (~((op (e3) (e3)) = (e3))) -> False). % 15.16/15.32 do 0 intro. intros zenon_H2d zenon_H2e zenon_H52 zenon_H2f zenon_H3b zenon_Hae zenon_H104 zenon_H3d zenon_H3e. % 15.16/15.32 apply (zenon_or_s _ _ zenon_H2d); [ zenon_intro zenon_H32 | zenon_intro zenon_H31 ]. % 15.16/15.32 exact (zenon_H2e zenon_H32). % 15.16/15.32 apply (zenon_or_s _ _ zenon_H31); [ zenon_intro zenon_H2a | zenon_intro zenon_H33 ]. % 15.16/15.32 exact (zenon_H52 zenon_H2a). % 15.16/15.32 apply (zenon_or_s _ _ zenon_H33); [ zenon_intro zenon_H35 | zenon_intro zenon_H34 ]. % 15.16/15.32 exact (zenon_H2f zenon_H35). % 15.16/15.32 apply (zenon_L77_); trivial. % 15.16/15.32 (* end of lemma zenon_L78_ *) % 15.16/15.32 assert (zenon_L79_ : (~((e1) = (e3))) -> ((op (e3) (e0)) = (e3)) -> ((op (e3) (e0)) = (e1)) -> False). % 15.16/15.32 do 0 intro. intros zenon_Ha3 zenon_Hba zenon_Hee. % 15.16/15.32 cut (((op (e3) (e0)) = (e3)) = ((e1) = (e3))). % 15.16/15.32 intro zenon_D_pnotp. % 15.16/15.32 apply zenon_Ha3. % 15.16/15.32 rewrite <- zenon_D_pnotp. % 15.16/15.32 exact zenon_Hba. % 15.16/15.32 cut (((e3) = (e3))); [idtac | apply NNPP; zenon_intro zenon_H4d]. % 15.16/15.32 cut (((op (e3) (e0)) = (e1))); [idtac | apply NNPP; zenon_intro zenon_Hef]. % 15.16/15.32 congruence. % 15.16/15.32 exact (zenon_Hef zenon_Hee). % 15.16/15.32 apply zenon_H4d. apply refl_equal. % 15.16/15.32 (* end of lemma zenon_L79_ *) % 15.16/15.32 assert (zenon_L80_ : (((op (e0) (e0)) = (e1))\/(((op (e1) (e0)) = (e1))\/(((op (e2) (e0)) = (e1))\/((op (e3) (e0)) = (e1))))) -> (~((op (e0) (e0)) = (e1))) -> ((op (e1) (e1)) = (e1)) -> (~((op (e1) (e0)) = (op (e1) (e1)))) -> (~((op (e3) (e3)) = (e3))) -> (~((op (e3) (e3)) = (e2))) -> (~((op (e3) (e3)) = (e1))) -> (((op (e3) (e3)) = (e0))\/(((op (e3) (e3)) = (e1))\/(((op (e3) (e3)) = (e2))\/((op (e3) (e3)) = (e3))))) -> (~((op (e2) (e2)) = (e2))) -> (~((op (e2) (e2)) = (e1))) -> (~((op (e2) (e2)) = (e0))) -> (((op (e2) (e2)) = (e0))\/(((op (e2) (e2)) = (e1))\/(((op (e2) (e2)) = (e2))\/((op (e2) (e2)) = (e3))))) -> (~((e1) = (e3))) -> ((op (e3) (e0)) = (e3)) -> False). % 15.16/15.32 do 0 intro. intros zenon_Hf1 zenon_H45 zenon_H21 zenon_Hd7 zenon_H3e zenon_H3d zenon_H104 zenon_H3b zenon_H2f zenon_H52 zenon_H2e zenon_H2d zenon_Ha3 zenon_Hba. % 15.16/15.32 apply (zenon_or_s _ _ zenon_Hf1); [ zenon_intro zenon_H47 | zenon_intro zenon_Hf4 ]. % 15.16/15.32 exact (zenon_H45 zenon_H47). % 15.16/15.32 apply (zenon_or_s _ _ zenon_Hf4); [ zenon_intro zenon_Hd8 | zenon_intro zenon_Hf5 ]. % 15.16/15.32 apply (zenon_L61_); trivial. % 15.16/15.32 apply (zenon_or_s _ _ zenon_Hf5); [ zenon_intro zenon_Hae | zenon_intro zenon_Hee ]. % 15.16/15.32 apply (zenon_L78_); trivial. % 15.16/15.32 apply (zenon_L79_); trivial. % 15.16/15.32 (* end of lemma zenon_L80_ *) % 15.16/15.32 assert (zenon_L81_ : (~((op (e3) (e0)) = (op (e3) (e2)))) -> ((op (e3) (e0)) = (e3)) -> ((op (e3) (e2)) = (e3)) -> False). % 15.16/15.32 do 0 intro. intros zenon_H105 zenon_Hba zenon_H106. % 15.16/15.32 cut (((op (e3) (e0)) = (e3)) = ((op (e3) (e0)) = (op (e3) (e2)))). % 15.16/15.32 intro zenon_D_pnotp. % 15.16/15.32 apply zenon_H105. % 15.16/15.32 rewrite <- zenon_D_pnotp. % 15.16/15.32 exact zenon_Hba. % 15.16/15.32 cut (((e3) = (op (e3) (e2)))); [idtac | apply NNPP; zenon_intro zenon_H107]. % 15.16/15.32 cut (((op (e3) (e0)) = (op (e3) (e0)))); [idtac | apply NNPP; zenon_intro zenon_H108]. % 15.16/15.32 congruence. % 15.16/15.32 apply zenon_H108. apply refl_equal. % 15.16/15.32 apply zenon_H107. apply sym_equal. exact zenon_H106. % 15.16/15.32 (* end of lemma zenon_L81_ *) % 15.16/15.32 assert (zenon_L82_ : (~((op (e3) (e0)) = (op (e3) (e1)))) -> ((op (e3) (e0)) = (e3)) -> ((op (e3) (e1)) = (e3)) -> False). % 15.16/15.32 do 0 intro. intros zenon_H109 zenon_Hba zenon_H10a. % 15.16/15.32 cut (((op (e3) (e0)) = (e3)) = ((op (e3) (e0)) = (op (e3) (e1)))). % 15.16/15.32 intro zenon_D_pnotp. % 15.16/15.32 apply zenon_H109. % 15.16/15.32 rewrite <- zenon_D_pnotp. % 15.16/15.32 exact zenon_Hba. % 15.16/15.32 cut (((e3) = (op (e3) (e1)))); [idtac | apply NNPP; zenon_intro zenon_H10b]. % 15.16/15.32 cut (((op (e3) (e0)) = (op (e3) (e0)))); [idtac | apply NNPP; zenon_intro zenon_H108]. % 15.16/15.32 congruence. % 15.16/15.32 apply zenon_H108. apply refl_equal. % 15.16/15.32 apply zenon_H10b. apply sym_equal. exact zenon_H10a. % 15.16/15.32 (* end of lemma zenon_L82_ *) % 15.16/15.32 assert (zenon_L83_ : ((~((op (e3) (e3)) = (e1)))\/((op (e3) (e1)) = (e3))) -> (~((op (e3) (e0)) = (op (e3) (e1)))) -> ((~((op (e3) (e3)) = (e3)))\/((op (e3) (e3)) = (e3))) -> (~((op (e3) (e0)) = (op (e3) (e3)))) -> (~((op (e0) (e0)) = (e1))) -> (~((op (e1) (e0)) = (op (e1) (e1)))) -> ((op (e1) (e1)) = (e1)) -> (((op (e2) (e2)) = (e0))\/(((op (e2) (e2)) = (e1))\/(((op (e2) (e2)) = (e2))\/((op (e2) (e2)) = (e3))))) -> (((op (e3) (e3)) = (e0))\/(((op (e3) (e3)) = (e1))\/(((op (e3) (e3)) = (e2))\/((op (e3) (e3)) = (e3))))) -> (~((op (e2) (e2)) = (e2))) -> (~((op (e2) (e2)) = (e1))) -> (~((op (e2) (e2)) = (e0))) -> (~((e1) = (e3))) -> ((op (e3) (e0)) = (e3)) -> (((op (e0) (e0)) = (e1))\/(((op (e1) (e0)) = (e1))\/(((op (e2) (e0)) = (e1))\/((op (e3) (e0)) = (e1))))) -> (~((op (e3) (e0)) = (op (e3) (e2)))) -> ((~((op (e3) (e3)) = (e2)))\/((op (e3) (e2)) = (e3))) -> False). % 15.16/15.32 do 0 intro. intros zenon_H10c zenon_H109 zenon_H10d zenon_Hbb zenon_H45 zenon_Hd7 zenon_H21 zenon_H2d zenon_H3b zenon_H2f zenon_H52 zenon_H2e zenon_Ha3 zenon_Hba zenon_Hf1 zenon_H105 zenon_H10e. % 15.16/15.32 apply (zenon_or_s _ _ zenon_H10c); [ zenon_intro zenon_H104 | zenon_intro zenon_H10a ]. % 15.16/15.32 apply (zenon_or_s _ _ zenon_H10e); [ zenon_intro zenon_H3d | zenon_intro zenon_H106 ]. % 15.16/15.32 apply (zenon_or_s _ _ zenon_H10d); [ zenon_intro zenon_H3e | zenon_intro zenon_H42 ]. % 15.16/15.32 apply (zenon_L80_); trivial. % 15.16/15.32 apply (zenon_L43_); trivial. % 15.16/15.32 apply (zenon_L81_); trivial. % 15.16/15.32 apply (zenon_L82_); trivial. % 15.16/15.32 (* end of lemma zenon_L83_ *) % 15.16/15.32 assert (zenon_L84_ : ((~((op (e3) (e3)) = (e0)))\/((op (e3) (e0)) = (e3))) -> ((~((op (e3) (e3)) = (e2)))\/((op (e3) (e2)) = (e3))) -> (~((op (e3) (e0)) = (op (e3) (e2)))) -> (((op (e3) (e3)) = (e0))\/(((op (e3) (e3)) = (e1))\/(((op (e3) (e3)) = (e2))\/((op (e3) (e3)) = (e3))))) -> ((~((op (e3) (e3)) = (e3)))\/((op (e3) (e3)) = (e3))) -> (~((op (e3) (e0)) = (op (e3) (e1)))) -> ((~((op (e3) (e3)) = (e1)))\/((op (e3) (e1)) = (e3))) -> (~((op (e0) (e0)) = (e0))) -> ((~((op (e2) (e2)) = (e2)))\/((op (e2) (e2)) = (e2))) -> (((op (e0) (e0)) = (e2))\/(((op (e0) (e1)) = (e2))\/(((op (e0) (e2)) = (e2))\/((op (e0) (e3)) = (e2))))) -> (((op (e1) (e0)) = (e3))\/(((op (e1) (e1)) = (e3))\/(((op (e1) (e2)) = (e3))\/((op (e1) (e3)) = (e3))))) -> (~((op (e1) (e3)) = (op (e3) (e3)))) -> (~((op (e0) (e2)) = (op (e1) (e2)))) -> (~((e2) = (e3))) -> (~((op (e1) (e2)) = (op (e2) (e2)))) -> (~((op (e0) (e3)) = (op (e1) (e3)))) -> (((op (e1) (e0)) = (e2))\/(((op (e1) (e1)) = (e2))\/(((op (e1) (e2)) = (e2))\/((op (e1) (e3)) = (e2))))) -> (~((e0) = (e2))) -> (~((op (e0) (e0)) = (e2))) -> (~((e0) = (e1))) -> (~((e1) = (e3))) -> (~((e1) = (e2))) -> (((op (e0) (e0)) = (e1))\/(((op (e0) (e1)) = (e1))\/(((op (e0) (e2)) = (e1))\/((op (e0) (e3)) = (e1))))) -> (~((op (e0) (e0)) = (e3))) -> (~((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) (e2)) = (e1))) -> (~((op (e2) (e2)) = (e0))) -> (~((op (e0) (e3)) = (op (e3) (e3)))) -> ((op (e3) (e3)) = (e3)) -> (((op (e0) (e0)) = (e3))\/(((op (e0) (e1)) = (e3))\/(((op (e0) (e2)) = (e3))\/((op (e0) (e3)) = (e3))))) -> (((op (e0) (e0)) = (e0))\/(((op (e1) (e0)) = (e0))\/(((op (e2) (e0)) = (e0))\/((op (e3) (e0)) = (e0))))) -> (((op (e0) (e0)) = (e1))\/(((op (e1) (e0)) = (e1))\/(((op (e2) (e0)) = (e1))\/((op (e3) (e0)) = (e1))))) -> (~((op (e0) (e1)) = (op (e2) (e1)))) -> (~((op (e2) (e3)) = (op (e3) (e3)))) -> (((op (e2) (e0)) = (e3))\/(((op (e2) (e1)) = (e3))\/(((op (e2) (e2)) = (e3))\/((op (e2) (e3)) = (e3))))) -> (((op (e0) (e0)) = (e2))\/(((op (e1) (e0)) = (e2))\/(((op (e2) (e0)) = (e2))\/((op (e3) (e0)) = (e2))))) -> (~((op (e1) (e0)) = (op (e1) (e1)))) -> (~((op (e2) (e2)) = (e3))) -> (~((op (e2) (e2)) = (e2))) -> (~((op (e0) (e2)) = (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 (e1) (e1)) = (e2))) -> (~((op (e0) (e0)) = (e1))) -> (~((op (e0) (e1)) = (op (e1) (e1)))) -> ((op (e1) (e1)) = (e1)) -> (((op (e0) (e0)) = (e3))\/(((op (e1) (e0)) = (e3))\/(((op (e2) (e0)) = (e3))\/((op (e3) (e0)) = (e3))))) -> (~((op (e3) (e0)) = (op (e3) (e3)))) -> (~((op (e1) (e1)) = (op (e2) (e1)))) -> (~((op (e0) (e3)) = (op (e2) (e3)))) -> (((op (e2) (e0)) = (e1))\/(((op (e2) (e1)) = (e1))\/(((op (e2) (e2)) = (e1))\/((op (e2) (e3)) = (e1))))) -> (((op (e0) (e0)) = (e0))\/(((op (e0) (e1)) = (e0))\/(((op (e0) (e2)) = (e0))\/((op (e0) (e3)) = (e0))))) -> False). % 15.16/15.32 do 0 intro. intros zenon_H10f zenon_H10e zenon_H105 zenon_H3b zenon_H10d zenon_H109 zenon_H10c zenon_H20 zenon_Haa zenon_H8e zenon_H90 zenon_H8b zenon_H87 zenon_H6a zenon_H7d zenon_H80 zenon_H84 zenon_H5e zenon_H8f zenon_H9e zenon_Ha3 zenon_Ha7 zenon_H44 zenon_H59 zenon_H4b zenon_H2d zenon_H28 zenon_H52 zenon_H2e zenon_H36 zenon_H42 zenon_H58 zenon_Hf0 zenon_Hf1 zenon_Hde zenon_He3 zenon_He6 zenon_Heb zenon_Hd7 zenon_H30 zenon_H2f zenon_Hc9 zenon_Hce zenon_Hd3 zenon_Hd6 zenon_H45 zenon_H23 zenon_H21 zenon_Hbe zenon_Hbb zenon_Hb1 zenon_Hb4 zenon_Hb7 zenon_H110. % 15.16/15.32 apply (zenon_or_s _ _ zenon_H10f); [ zenon_intro zenon_H3c | zenon_intro zenon_Hba ]. % 15.16/15.32 apply (zenon_or_s _ _ zenon_H110); [ zenon_intro zenon_H1f | zenon_intro zenon_H111 ]. % 15.16/15.32 exact (zenon_H20 zenon_H1f). % 15.16/15.32 apply (zenon_or_s _ _ zenon_H111); [ zenon_intro zenon_H49 | zenon_intro zenon_H112 ]. % 15.16/15.32 apply (zenon_L36_); trivial. % 15.16/15.32 apply (zenon_or_s _ _ zenon_H112); [ zenon_intro zenon_Hab | zenon_intro zenon_Hca ]. % 15.16/15.32 apply (zenon_L72_); trivial. % 15.16/15.32 apply (zenon_L74_); trivial. % 15.16/15.32 apply (zenon_L83_); trivial. % 15.16/15.32 (* end of lemma zenon_L84_ *) % 15.16/15.32 assert (zenon_L85_ : ((op (e0) (e3)) = (e1)) -> ((op (e0) (e2)) = (e1)) -> (~((op (e0) (e2)) = (op (e0) (e3)))) -> False). % 15.16/15.32 do 0 intro. intros zenon_H37 zenon_H29 zenon_Hc9. % 15.16/15.32 elim (classic ((op (e0) (e3)) = (op (e0) (e3)))); [ zenon_intro zenon_H113 | zenon_intro zenon_H3a ]. % 15.16/15.32 cut (((op (e0) (e3)) = (op (e0) (e3))) = ((op (e0) (e2)) = (op (e0) (e3)))). % 15.16/15.32 intro zenon_D_pnotp. % 15.16/15.32 apply zenon_Hc9. % 15.16/15.32 rewrite <- zenon_D_pnotp. % 15.16/15.32 exact zenon_H113. % 15.16/15.32 cut (((op (e0) (e3)) = (op (e0) (e3)))); [idtac | apply NNPP; zenon_intro zenon_H3a]. % 15.16/15.32 cut (((op (e0) (e3)) = (op (e0) (e2)))); [idtac | apply NNPP; zenon_intro zenon_H114]. % 15.16/15.32 congruence. % 15.16/15.32 cut (((op (e0) (e3)) = (e1)) = ((op (e0) (e3)) = (op (e0) (e2)))). % 15.16/15.32 intro zenon_D_pnotp. % 15.16/15.32 apply zenon_H114. % 15.16/15.32 rewrite <- zenon_D_pnotp. % 15.16/15.32 exact zenon_H37. % 15.16/15.32 cut (((e1) = (op (e0) (e2)))); [idtac | apply NNPP; zenon_intro zenon_H115]. % 15.16/15.32 cut (((op (e0) (e3)) = (op (e0) (e3)))); [idtac | apply NNPP; zenon_intro zenon_H3a]. % 15.16/15.32 congruence. % 15.16/15.32 apply zenon_H3a. apply refl_equal. % 15.16/15.32 apply zenon_H115. apply sym_equal. exact zenon_H29. % 15.16/15.32 apply zenon_H3a. apply refl_equal. % 15.16/15.32 apply zenon_H3a. apply refl_equal. % 15.16/15.32 (* end of lemma zenon_L85_ *) % 15.16/15.32 assert (zenon_L86_ : (~((op (e1) (e1)) = (op (e1) (e2)))) -> ((op (e1) (e1)) = (e1)) -> ((op (e1) (e2)) = (e1)) -> False). % 15.16/15.32 do 0 intro. intros zenon_H116 zenon_H21 zenon_H117. % 15.16/15.32 cut (((op (e1) (e1)) = (e1)) = ((op (e1) (e1)) = (op (e1) (e2)))). % 15.16/15.32 intro zenon_D_pnotp. % 15.16/15.32 apply zenon_H116. % 15.16/15.32 rewrite <- zenon_D_pnotp. % 15.16/15.32 exact zenon_H21. % 15.16/15.32 cut (((e1) = (op (e1) (e2)))); [idtac | apply NNPP; zenon_intro zenon_H118]. % 15.16/15.32 cut (((op (e1) (e1)) = (op (e1) (e1)))); [idtac | apply NNPP; zenon_intro zenon_H25]. % 15.16/15.32 congruence. % 15.16/15.32 apply zenon_H25. apply refl_equal. % 15.16/15.32 apply zenon_H118. apply sym_equal. exact zenon_H117. % 15.16/15.32 (* end of lemma zenon_L86_ *) % 15.16/15.32 assert (zenon_L87_ : (~((e1) = (e3))) -> ((op (e3) (e2)) = (e3)) -> ((op (e3) (e2)) = (e1)) -> False). % 15.16/15.32 do 0 intro. intros zenon_Ha3 zenon_H106 zenon_H119. % 15.16/15.32 cut (((op (e3) (e2)) = (e3)) = ((e1) = (e3))). % 15.16/15.32 intro zenon_D_pnotp. % 15.16/15.32 apply zenon_Ha3. % 15.16/15.32 rewrite <- zenon_D_pnotp. % 15.16/15.32 exact zenon_H106. % 15.16/15.32 cut (((e3) = (e3))); [idtac | apply NNPP; zenon_intro zenon_H4d]. % 15.16/15.32 cut (((op (e3) (e2)) = (e1))); [idtac | apply NNPP; zenon_intro zenon_H11a]. % 15.16/15.32 congruence. % 15.16/15.32 exact (zenon_H11a zenon_H119). % 15.16/15.32 apply zenon_H4d. apply refl_equal. % 15.16/15.32 (* end of lemma zenon_L87_ *) % 15.16/15.32 assert (zenon_L88_ : (((op (e0) (e2)) = (e1))\/(((op (e1) (e2)) = (e1))\/(((op (e2) (e2)) = (e1))\/((op (e3) (e2)) = (e1))))) -> (~((op (e0) (e2)) = (op (e0) (e3)))) -> ((op (e0) (e3)) = (e1)) -> ((op (e1) (e1)) = (e1)) -> (~((op (e1) (e1)) = (op (e1) (e2)))) -> (~((op (e2) (e2)) = (e1))) -> (~((e1) = (e3))) -> ((op (e3) (e2)) = (e3)) -> False). % 15.16/15.32 do 0 intro. intros zenon_H11b zenon_Hc9 zenon_H37 zenon_H21 zenon_H116 zenon_H52 zenon_Ha3 zenon_H106. % 15.16/15.32 apply (zenon_or_s _ _ zenon_H11b); [ zenon_intro zenon_H29 | zenon_intro zenon_H11c ]. % 15.16/15.32 apply (zenon_L85_); trivial. % 15.16/15.32 apply (zenon_or_s _ _ zenon_H11c); [ zenon_intro zenon_H117 | zenon_intro zenon_H11d ]. % 15.16/15.32 apply (zenon_L86_); trivial. % 15.16/15.32 apply (zenon_or_s _ _ zenon_H11d); [ zenon_intro zenon_H2a | zenon_intro zenon_H119 ]. % 15.16/15.32 exact (zenon_H52 zenon_H2a). % 15.16/15.32 apply (zenon_L87_); trivial. % 15.16/15.32 (* end of lemma zenon_L88_ *) % 15.16/15.32 assert (zenon_L89_ : (((op (e0) (e0)) = (e1))\/(((op (e0) (e1)) = (e1))\/(((op (e0) (e2)) = (e1))\/((op (e0) (e3)) = (e1))))) -> (~((op (e0) (e0)) = (e1))) -> (~((op (e0) (e1)) = (op (e1) (e1)))) -> (~((op (e2) (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 (e0) (e2)) = (e1))\/(((op (e1) (e2)) = (e1))\/(((op (e2) (e2)) = (e1))\/((op (e3) (e2)) = (e1))))) -> (~((op (e0) (e2)) = (op (e0) (e3)))) -> ((op (e1) (e1)) = (e1)) -> (~((op (e1) (e1)) = (op (e1) (e2)))) -> (~((op (e2) (e2)) = (e1))) -> (~((e1) = (e3))) -> ((op (e3) (e2)) = (e3)) -> False). % 15.16/15.32 do 0 intro. intros zenon_H44 zenon_H45 zenon_H23 zenon_H30 zenon_H2f zenon_H28 zenon_H2e zenon_H2d zenon_H11b zenon_Hc9 zenon_H21 zenon_H116 zenon_H52 zenon_Ha3 zenon_H106. % 15.16/15.32 apply (zenon_or_s _ _ zenon_H44); [ zenon_intro zenon_H47 | zenon_intro zenon_H46 ]. % 15.16/15.32 exact (zenon_H45 zenon_H47). % 15.16/15.32 apply (zenon_or_s _ _ zenon_H46); [ zenon_intro zenon_H22 | zenon_intro zenon_H48 ]. % 15.16/15.32 apply (zenon_L3_); trivial. % 15.16/15.32 apply (zenon_or_s _ _ zenon_H48); [ zenon_intro zenon_H29 | zenon_intro zenon_H37 ]. % 15.16/15.32 apply (zenon_L5_); trivial. % 15.16/15.32 apply (zenon_L88_); trivial. % 15.16/15.32 (* end of lemma zenon_L89_ *) % 15.16/15.32 assert (zenon_L90_ : (~((op (e1) (e1)) = (op (e1) (e3)))) -> ((op (e1) (e1)) = (e1)) -> ((op (e1) (e3)) = (e1)) -> False). % 15.16/15.32 do 0 intro. intros zenon_H11e zenon_H21 zenon_H11f. % 15.16/15.32 cut (((op (e1) (e1)) = (e1)) = ((op (e1) (e1)) = (op (e1) (e3)))). % 15.16/15.32 intro zenon_D_pnotp. % 15.16/15.32 apply zenon_H11e. % 15.16/15.32 rewrite <- zenon_D_pnotp. % 15.16/15.32 exact zenon_H21. % 15.16/15.32 cut (((e1) = (op (e1) (e3)))); [idtac | apply NNPP; zenon_intro zenon_H120]. % 15.16/15.32 cut (((op (e1) (e1)) = (op (e1) (e1)))); [idtac | apply NNPP; zenon_intro zenon_H25]. % 15.16/15.32 congruence. % 15.16/15.32 apply zenon_H25. apply refl_equal. % 15.16/15.32 apply zenon_H120. apply sym_equal. exact zenon_H11f. % 15.16/15.32 (* end of lemma zenon_L90_ *) % 15.16/15.32 assert (zenon_L91_ : (~((op (e2) (e0)) = (op (e2) (e3)))) -> ((op (e2) (e0)) = (e1)) -> ((op (e2) (e3)) = (e1)) -> False). % 15.16/15.32 do 0 intro. intros zenon_Hce zenon_Hae zenon_Hb5. % 15.16/15.32 cut (((op (e2) (e0)) = (e1)) = ((op (e2) (e0)) = (op (e2) (e3)))). % 15.16/15.32 intro zenon_D_pnotp. % 15.16/15.32 apply zenon_Hce. % 15.16/15.32 rewrite <- zenon_D_pnotp. % 15.16/15.32 exact zenon_Hae. % 15.16/15.32 cut (((e1) = (op (e2) (e3)))); [idtac | apply NNPP; zenon_intro zenon_Hb6]. % 15.16/15.32 cut (((op (e2) (e0)) = (op (e2) (e0)))); [idtac | apply NNPP; zenon_intro zenon_Hd2]. % 15.16/15.32 congruence. % 15.16/15.32 apply zenon_Hd2. apply refl_equal. % 15.16/15.32 apply zenon_Hb6. apply sym_equal. exact zenon_Hb5. % 15.16/15.32 (* end of lemma zenon_L91_ *) % 15.16/15.32 assert (zenon_L92_ : (((op (e0) (e3)) = (e1))\/(((op (e1) (e3)) = (e1))\/(((op (e2) (e3)) = (e1))\/((op (e3) (e3)) = (e1))))) -> (~((op (e0) (e2)) = (op (e0) (e3)))) -> ((op (e0) (e2)) = (e1)) -> ((op (e1) (e1)) = (e1)) -> (~((op (e1) (e1)) = (op (e1) (e3)))) -> ((op (e2) (e0)) = (e1)) -> (~((op (e2) (e0)) = (op (e2) (e3)))) -> (~((op (e3) (e3)) = (e1))) -> False). % 15.16/15.32 do 0 intro. intros zenon_H121 zenon_Hc9 zenon_H29 zenon_H21 zenon_H11e zenon_Hae zenon_Hce zenon_H104. % 15.16/15.32 apply (zenon_or_s _ _ zenon_H121); [ zenon_intro zenon_H37 | zenon_intro zenon_H122 ]. % 15.16/15.32 apply (zenon_L85_); trivial. % 15.16/15.32 apply (zenon_or_s _ _ zenon_H122); [ zenon_intro zenon_H11f | zenon_intro zenon_H123 ]. % 15.16/15.32 apply (zenon_L90_); trivial. % 15.16/15.32 apply (zenon_or_s _ _ zenon_H123); [ zenon_intro zenon_Hb5 | zenon_intro zenon_H38 ]. % 15.16/15.32 apply (zenon_L91_); trivial. % 15.16/15.32 exact (zenon_H104 zenon_H38). % 15.16/15.32 (* end of lemma zenon_L92_ *) % 15.16/15.32 assert (zenon_L93_ : (~((e1) = (e2))) -> ((op (e2) (e3)) = (e2)) -> ((op (e2) (e3)) = (e1)) -> False). % 15.16/15.32 do 0 intro. intros zenon_Ha7 zenon_H124 zenon_Hb5. % 15.16/15.32 cut (((op (e2) (e3)) = (e2)) = ((e1) = (e2))). % 15.16/15.32 intro zenon_D_pnotp. % 15.16/15.32 apply zenon_Ha7. % 15.16/15.32 rewrite <- zenon_D_pnotp. % 15.16/15.32 exact zenon_H124. % 15.16/15.32 cut (((e2) = (e2))); [idtac | apply NNPP; zenon_intro zenon_H60]. % 15.16/15.32 cut (((op (e2) (e3)) = (e1))); [idtac | apply NNPP; zenon_intro zenon_H125]. % 15.16/15.32 congruence. % 15.16/15.32 exact (zenon_H125 zenon_Hb5). % 15.16/15.32 apply zenon_H60. apply refl_equal. % 15.16/15.32 (* end of lemma zenon_L93_ *) % 15.16/15.32 assert (zenon_L94_ : (((op (e2) (e0)) = (e1))\/(((op (e2) (e1)) = (e1))\/(((op (e2) (e2)) = (e1))\/((op (e2) (e3)) = (e1))))) -> (~((op (e3) (e3)) = (e1))) -> (~((op (e2) (e0)) = (op (e2) (e3)))) -> (~((op (e1) (e1)) = (op (e1) (e3)))) -> ((op (e0) (e2)) = (e1)) -> (~((op (e0) (e2)) = (op (e0) (e3)))) -> (((op (e0) (e3)) = (e1))\/(((op (e1) (e3)) = (e1))\/(((op (e2) (e3)) = (e1))\/((op (e3) (e3)) = (e1))))) -> ((op (e1) (e1)) = (e1)) -> (~((op (e1) (e1)) = (op (e2) (e1)))) -> (~((op (e2) (e2)) = (e1))) -> (~((e1) = (e2))) -> ((op (e2) (e3)) = (e2)) -> False). % 15.16/15.32 do 0 intro. intros zenon_Hb7 zenon_H104 zenon_Hce zenon_H11e zenon_H29 zenon_Hc9 zenon_H121 zenon_H21 zenon_Hb1 zenon_H52 zenon_Ha7 zenon_H124. % 15.16/15.32 apply (zenon_or_s _ _ zenon_Hb7); [ zenon_intro zenon_Hae | zenon_intro zenon_Hb8 ]. % 15.16/15.32 apply (zenon_L92_); trivial. % 15.16/15.32 apply (zenon_or_s _ _ zenon_Hb8); [ zenon_intro zenon_Hb2 | zenon_intro zenon_Hb9 ]. % 15.16/15.32 apply (zenon_L40_); trivial. % 15.16/15.32 apply (zenon_or_s _ _ zenon_Hb9); [ zenon_intro zenon_H2a | zenon_intro zenon_Hb5 ]. % 15.16/15.32 exact (zenon_H52 zenon_H2a). % 15.16/15.32 apply (zenon_L93_); trivial. % 15.16/15.32 (* end of lemma zenon_L94_ *) % 15.16/15.32 assert (zenon_L95_ : (((op (e0) (e0)) = (e1))\/(((op (e0) (e1)) = (e1))\/(((op (e0) (e2)) = (e1))\/((op (e0) (e3)) = (e1))))) -> (~((op (e0) (e0)) = (e1))) -> (~((op (e0) (e1)) = (op (e1) (e1)))) -> ((op (e2) (e3)) = (e2)) -> (~((e1) = (e2))) -> (~((op (e2) (e2)) = (e1))) -> (~((op (e1) (e1)) = (op (e2) (e1)))) -> ((op (e1) (e1)) = (e1)) -> (((op (e0) (e3)) = (e1))\/(((op (e1) (e3)) = (e1))\/(((op (e2) (e3)) = (e1))\/((op (e3) (e3)) = (e1))))) -> (~((op (e0) (e2)) = (op (e0) (e3)))) -> (~((op (e1) (e1)) = (op (e1) (e3)))) -> (~((op (e2) (e0)) = (op (e2) (e3)))) -> (~((op (e3) (e3)) = (e1))) -> (((op (e2) (e0)) = (e1))\/(((op (e2) (e1)) = (e1))\/(((op (e2) (e2)) = (e1))\/((op (e2) (e3)) = (e1))))) -> (((op (e3) (e3)) = (e0))\/(((op (e3) (e3)) = (e1))\/(((op (e3) (e3)) = (e2))\/((op (e3) (e3)) = (e3))))) -> (~((op (e3) (e3)) = (e0))) -> (~((op (e0) (e3)) = (op (e3) (e3)))) -> (~((op (e3) (e3)) = (e2))) -> (~((op (e3) (e3)) = (e3))) -> False). % 15.16/15.32 do 0 intro. intros zenon_H44 zenon_H45 zenon_H23 zenon_H124 zenon_Ha7 zenon_H52 zenon_Hb1 zenon_H21 zenon_H121 zenon_Hc9 zenon_H11e zenon_Hce zenon_H104 zenon_Hb7 zenon_H3b zenon_H3c zenon_H36 zenon_H3d zenon_H3e. % 15.16/15.32 apply (zenon_or_s _ _ zenon_H44); [ zenon_intro zenon_H47 | zenon_intro zenon_H46 ]. % 15.16/15.32 exact (zenon_H45 zenon_H47). % 15.16/15.32 apply (zenon_or_s _ _ zenon_H46); [ zenon_intro zenon_H22 | zenon_intro zenon_H48 ]. % 15.16/15.32 apply (zenon_L3_); trivial. % 15.16/15.32 apply (zenon_or_s _ _ zenon_H48); [ zenon_intro zenon_H29 | zenon_intro zenon_H37 ]. % 15.16/15.32 apply (zenon_L94_); trivial. % 15.16/15.32 apply (zenon_L7_); trivial. % 15.16/15.32 (* end of lemma zenon_L95_ *) % 15.16/15.32 assert (zenon_L96_ : (((op (e2) (e0)) = (e1))\/(((op (e2) (e1)) = (e1))\/(((op (e2) (e2)) = (e1))\/((op (e2) (e3)) = (e1))))) -> (~((e1) = (e3))) -> ((op (e2) (e0)) = (e3)) -> ((op (e1) (e1)) = (e1)) -> (~((op (e1) (e1)) = (op (e2) (e1)))) -> (~((op (e2) (e2)) = (e1))) -> (~((e1) = (e2))) -> ((op (e2) (e3)) = (e2)) -> False). % 15.16/15.32 do 0 intro. intros zenon_Hb7 zenon_Ha3 zenon_Haf zenon_H21 zenon_Hb1 zenon_H52 zenon_Ha7 zenon_H124. % 15.16/15.32 apply (zenon_or_s _ _ zenon_Hb7); [ zenon_intro zenon_Hae | zenon_intro zenon_Hb8 ]. % 15.16/15.32 apply (zenon_L39_); trivial. % 15.16/15.32 apply (zenon_or_s _ _ zenon_Hb8); [ zenon_intro zenon_Hb2 | zenon_intro zenon_Hb9 ]. % 15.16/15.32 apply (zenon_L40_); trivial. % 15.16/15.32 apply (zenon_or_s _ _ zenon_Hb9); [ zenon_intro zenon_H2a | zenon_intro zenon_Hb5 ]. % 15.16/15.32 exact (zenon_H52 zenon_H2a). % 15.16/15.32 apply (zenon_L93_); trivial. % 15.16/15.32 (* end of lemma zenon_L96_ *) % 15.16/15.32 assert (zenon_L97_ : ((op (e0) (e3)) = (e1)) -> ((op (e2) (e2)) = (e3)) -> ((op (e0) (e0)) = (e2)) -> False). % 15.16/15.32 do 0 intro. intros zenon_H37 zenon_H34 zenon_H92. % 15.16/15.32 apply (zenon_notand_s _ _ ax29); [ zenon_intro zenon_H98 | zenon_intro zenon_H126 ]. % 15.16/15.32 elim (classic ((op (op (e0) (e0)) (op (e0) (e0))) = (op (op (e0) (e0)) (op (e0) (e0))))); [ zenon_intro zenon_H71 | zenon_intro zenon_H72 ]. % 15.16/15.32 cut (((op (op (e0) (e0)) (op (e0) (e0))) = (op (op (e0) (e0)) (op (e0) (e0)))) = ((e3) = (op (op (e0) (e0)) (op (e0) (e0))))). % 15.16/15.32 intro zenon_D_pnotp. % 15.16/15.32 apply zenon_H98. % 15.16/15.32 rewrite <- zenon_D_pnotp. % 15.16/15.32 exact zenon_H71. % 15.16/15.32 cut (((op (op (e0) (e0)) (op (e0) (e0))) = (op (op (e0) (e0)) (op (e0) (e0))))); [idtac | apply NNPP; zenon_intro zenon_H72]. % 15.16/15.32 cut (((op (op (e0) (e0)) (op (e0) (e0))) = (e3))); [idtac | apply NNPP; zenon_intro zenon_H99]. % 15.16/15.32 congruence. % 15.16/15.32 cut (((op (e2) (e2)) = (e3)) = ((op (op (e0) (e0)) (op (e0) (e0))) = (e3))). % 15.16/15.32 intro zenon_D_pnotp. % 15.16/15.32 apply zenon_H99. % 15.16/15.32 rewrite <- zenon_D_pnotp. % 15.16/15.32 exact zenon_H34. % 15.16/15.32 cut (((e3) = (e3))); [idtac | apply NNPP; zenon_intro zenon_H4d]. % 15.16/15.32 cut (((op (e2) (e2)) = (op (op (e0) (e0)) (op (e0) (e0))))); [idtac | apply NNPP; zenon_intro zenon_Hc5]. % 15.16/15.32 congruence. % 15.16/15.32 elim (classic ((op (op (e0) (e0)) (op (e0) (e0))) = (op (op (e0) (e0)) (op (e0) (e0))))); [ zenon_intro zenon_H71 | zenon_intro zenon_H72 ]. % 15.16/15.32 cut (((op (op (e0) (e0)) (op (e0) (e0))) = (op (op (e0) (e0)) (op (e0) (e0)))) = ((op (e2) (e2)) = (op (op (e0) (e0)) (op (e0) (e0))))). % 15.16/15.32 intro zenon_D_pnotp. % 15.16/15.32 apply zenon_Hc5. % 15.16/15.32 rewrite <- zenon_D_pnotp. % 15.16/15.32 exact zenon_H71. % 15.16/15.32 cut (((op (op (e0) (e0)) (op (e0) (e0))) = (op (op (e0) (e0)) (op (e0) (e0))))); [idtac | apply NNPP; zenon_intro zenon_H72]. % 15.16/15.32 cut (((op (op (e0) (e0)) (op (e0) (e0))) = (op (e2) (e2)))); [idtac | apply NNPP; zenon_intro zenon_Hc1]. % 15.16/15.32 congruence. % 15.16/15.32 apply (zenon_L45_); trivial. % 15.16/15.32 apply zenon_H72. apply refl_equal. % 15.16/15.32 apply zenon_H72. apply refl_equal. % 15.16/15.32 apply zenon_H4d. apply refl_equal. % 15.16/15.32 apply zenon_H72. apply refl_equal. % 15.16/15.32 apply zenon_H72. apply refl_equal. % 15.16/15.32 apply (zenon_notand_s _ _ zenon_H126); [ zenon_intro zenon_Hc6 | zenon_intro zenon_H127 ]. % 15.16/15.32 apply zenon_Hc6. apply sym_equal. exact zenon_H92. % 15.16/15.32 elim (classic ((op (e0) (op (op (e0) (e0)) (op (e0) (e0)))) = (op (e0) (op (op (e0) (e0)) (op (e0) (e0)))))); [ zenon_intro zenon_H77 | zenon_intro zenon_H78 ]. % 15.16/15.32 cut (((op (e0) (op (op (e0) (e0)) (op (e0) (e0)))) = (op (e0) (op (op (e0) (e0)) (op (e0) (e0))))) = ((e1) = (op (e0) (op (op (e0) (e0)) (op (e0) (e0)))))). % 15.16/15.32 intro zenon_D_pnotp. % 15.16/15.32 apply zenon_H127. % 15.16/15.32 rewrite <- zenon_D_pnotp. % 15.16/15.32 exact zenon_H77. % 15.16/15.32 cut (((op (e0) (op (op (e0) (e0)) (op (e0) (e0)))) = (op (e0) (op (op (e0) (e0)) (op (e0) (e0)))))); [idtac | apply NNPP; zenon_intro zenon_H78]. % 15.16/15.32 cut (((op (e0) (op (op (e0) (e0)) (op (e0) (e0)))) = (e1))); [idtac | apply NNPP; zenon_intro zenon_H128]. % 15.16/15.32 congruence. % 15.16/15.32 cut (((op (e0) (e3)) = (e1)) = ((op (e0) (op (op (e0) (e0)) (op (e0) (e0)))) = (e1))). % 15.16/15.32 intro zenon_D_pnotp. % 15.16/15.32 apply zenon_H128. % 15.16/15.32 rewrite <- zenon_D_pnotp. % 15.16/15.32 exact zenon_H37. % 15.16/15.32 cut (((e1) = (e1))); [idtac | apply NNPP; zenon_intro zenon_Ha0]. % 15.16/15.32 cut (((op (e0) (e3)) = (op (e0) (op (op (e0) (e0)) (op (e0) (e0)))))); [idtac | apply NNPP; zenon_intro zenon_H9c]. % 15.16/15.32 congruence. % 15.16/15.32 elim (classic ((op (e0) (op (op (e0) (e0)) (op (e0) (e0)))) = (op (e0) (op (op (e0) (e0)) (op (e0) (e0)))))); [ zenon_intro zenon_H77 | zenon_intro zenon_H78 ]. % 15.16/15.32 cut (((op (e0) (op (op (e0) (e0)) (op (e0) (e0)))) = (op (e0) (op (op (e0) (e0)) (op (e0) (e0))))) = ((op (e0) (e3)) = (op (e0) (op (op (e0) (e0)) (op (e0) (e0)))))). % 15.16/15.32 intro zenon_D_pnotp. % 15.16/15.32 apply zenon_H9c. % 15.16/15.32 rewrite <- zenon_D_pnotp. % 15.16/15.32 exact zenon_H77. % 15.16/15.32 cut (((op (e0) (op (op (e0) (e0)) (op (e0) (e0)))) = (op (e0) (op (op (e0) (e0)) (op (e0) (e0)))))); [idtac | apply NNPP; zenon_intro zenon_H78]. % 15.16/15.32 cut (((op (e0) (op (op (e0) (e0)) (op (e0) (e0)))) = (op (e0) (e3)))); [idtac | apply NNPP; zenon_intro zenon_H9d]. % 15.16/15.32 congruence. % 15.16/15.32 cut (((op (op (e0) (e0)) (op (e0) (e0))) = (e3))); [idtac | apply NNPP; zenon_intro zenon_H99]. % 15.16/15.32 cut (((e0) = (e0))); [idtac | apply NNPP; zenon_intro zenon_H1d]. % 15.16/15.32 congruence. % 15.16/15.32 apply zenon_H1d. apply refl_equal. % 15.16/15.32 cut (((op (e2) (e2)) = (e3)) = ((op (op (e0) (e0)) (op (e0) (e0))) = (e3))). % 15.16/15.32 intro zenon_D_pnotp. % 15.16/15.32 apply zenon_H99. % 15.16/15.32 rewrite <- zenon_D_pnotp. % 15.16/15.32 exact zenon_H34. % 15.16/15.32 cut (((e3) = (e3))); [idtac | apply NNPP; zenon_intro zenon_H4d]. % 15.16/15.32 cut (((op (e2) (e2)) = (op (op (e0) (e0)) (op (e0) (e0))))); [idtac | apply NNPP; zenon_intro zenon_Hc5]. % 15.16/15.32 congruence. % 15.16/15.32 elim (classic ((op (op (e0) (e0)) (op (e0) (e0))) = (op (op (e0) (e0)) (op (e0) (e0))))); [ zenon_intro zenon_H71 | zenon_intro zenon_H72 ]. % 15.16/15.32 cut (((op (op (e0) (e0)) (op (e0) (e0))) = (op (op (e0) (e0)) (op (e0) (e0)))) = ((op (e2) (e2)) = (op (op (e0) (e0)) (op (e0) (e0))))). % 15.16/15.32 intro zenon_D_pnotp. % 15.16/15.32 apply zenon_Hc5. % 15.16/15.32 rewrite <- zenon_D_pnotp. % 15.16/15.32 exact zenon_H71. % 15.16/15.32 cut (((op (op (e0) (e0)) (op (e0) (e0))) = (op (op (e0) (e0)) (op (e0) (e0))))); [idtac | apply NNPP; zenon_intro zenon_H72]. % 15.16/15.32 cut (((op (op (e0) (e0)) (op (e0) (e0))) = (op (e2) (e2)))); [idtac | apply NNPP; zenon_intro zenon_Hc1]. % 15.16/15.32 congruence. % 15.16/15.32 apply (zenon_L45_); trivial. % 15.16/15.32 apply zenon_H72. apply refl_equal. % 15.16/15.32 apply zenon_H72. apply refl_equal. % 15.16/15.32 apply zenon_H4d. apply refl_equal. % 15.16/15.32 apply zenon_H78. apply refl_equal. % 15.16/15.32 apply zenon_H78. apply refl_equal. % 15.16/15.32 apply zenon_Ha0. apply refl_equal. % 15.16/15.32 apply zenon_H78. apply refl_equal. % 15.16/15.32 apply zenon_H78. apply refl_equal. % 15.16/15.32 (* end of lemma zenon_L97_ *) % 15.16/15.32 assert (zenon_L98_ : ((op (e2) (e3)) = (e2)) -> ((op (e2) (e3)) = (e3)) -> (~((e2) = (e3))) -> False). % 15.16/15.32 do 0 intro. intros zenon_H124 zenon_He2 zenon_H6a. % 15.16/15.32 elim (classic ((e3) = (e3))); [ zenon_intro zenon_H4c | zenon_intro zenon_H4d ]. % 15.16/15.32 cut (((e3) = (e3)) = ((e2) = (e3))). % 15.16/15.32 intro zenon_D_pnotp. % 15.16/15.32 apply zenon_H6a. % 15.16/15.32 rewrite <- zenon_D_pnotp. % 15.16/15.32 exact zenon_H4c. % 15.16/15.32 cut (((e3) = (e3))); [idtac | apply NNPP; zenon_intro zenon_H4d]. % 15.16/15.32 cut (((e3) = (e2))); [idtac | apply NNPP; zenon_intro zenon_H6b]. % 15.16/15.32 congruence. % 15.16/15.32 cut (((op (e2) (e3)) = (e2)) = ((e3) = (e2))). % 15.16/15.32 intro zenon_D_pnotp. % 15.16/15.32 apply zenon_H6b. % 15.16/15.32 rewrite <- zenon_D_pnotp. % 15.16/15.32 exact zenon_H124. % 15.16/15.32 cut (((e2) = (e2))); [idtac | apply NNPP; zenon_intro zenon_H60]. % 15.16/15.32 cut (((op (e2) (e3)) = (e3))); [idtac | apply NNPP; zenon_intro zenon_H129]. % 15.16/15.32 congruence. % 15.16/15.32 exact (zenon_H129 zenon_He2). % 15.16/15.32 apply zenon_H60. apply refl_equal. % 15.16/15.32 apply zenon_H4d. apply refl_equal. % 15.16/15.32 apply zenon_H4d. apply refl_equal. % 15.16/15.32 (* end of lemma zenon_L98_ *) % 15.16/15.32 assert (zenon_L99_ : (((op (e0) (e0)) = (e1))\/(((op (e0) (e1)) = (e1))\/(((op (e0) (e2)) = (e1))\/((op (e0) (e3)) = (e1))))) -> (~((op (e0) (e1)) = (op (e1) (e1)))) -> (~((e0) = (e1))) -> ((op (e0) (e2)) = (e0)) -> (((op (e0) (e0)) = (e3))\/(((op (e0) (e1)) = (e3))\/(((op (e0) (e2)) = (e3))\/((op (e0) (e3)) = (e3))))) -> (~((e2) = (e3))) -> ((op (e2) (e3)) = (e2)) -> (((op (e0) (e0)) = (e0))\/(((op (e0) (e0)) = (e1))\/(((op (e0) (e0)) = (e2))\/((op (e0) (e0)) = (e3))))) -> (~((op (e0) (e0)) = (e0))) -> (~((op (e0) (e0)) = (e1))) -> (~((op (e0) (e0)) = (e3))) -> (~((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)) = (e1)) -> (~((op (e1) (e1)) = (op (e2) (e1)))) -> (~((e1) = (e2))) -> (((op (e2) (e0)) = (e3))\/(((op (e2) (e1)) = (e3))\/(((op (e2) (e2)) = (e3))\/((op (e2) (e3)) = (e3))))) -> (~((op (e0) (e2)) = (op (e2) (e2)))) -> (~((op (e2) (e2)) = (e2))) -> (~((op (e2) (e2)) = (e1))) -> (~((op (e2) (e2)) = (e0))) -> (((op (e2) (e2)) = (e0))\/(((op (e2) (e2)) = (e1))\/(((op (e2) (e2)) = (e2))\/((op (e2) (e2)) = (e3))))) -> (~((e1) = (e3))) -> False). % 15.16/15.32 do 0 intro. intros zenon_H44 zenon_H23 zenon_H9e zenon_Hab zenon_H58 zenon_H6a zenon_H124 zenon_H12a zenon_H20 zenon_H45 zenon_H59 zenon_Hde zenon_Hb7 zenon_H21 zenon_Hb1 zenon_Ha7 zenon_He6 zenon_H28 zenon_H2f zenon_H52 zenon_H2e zenon_H2d zenon_Ha3. % 15.16/15.32 apply (zenon_or_s _ _ zenon_H44); [ zenon_intro zenon_H47 | zenon_intro zenon_H46 ]. % 15.16/15.32 exact (zenon_H45 zenon_H47). % 15.16/15.32 apply (zenon_or_s _ _ zenon_H46); [ zenon_intro zenon_H22 | zenon_intro zenon_H48 ]. % 15.16/15.32 apply (zenon_L3_); trivial. % 15.16/15.32 apply (zenon_or_s _ _ zenon_H48); [ zenon_intro zenon_H29 | zenon_intro zenon_H37 ]. % 15.16/15.32 apply (zenon_L37_); trivial. % 15.16/15.32 apply (zenon_or_s _ _ zenon_H58); [ zenon_intro zenon_H5b | zenon_intro zenon_H5a ]. % 15.16/15.32 exact (zenon_H59 zenon_H5b). % 15.16/15.32 apply (zenon_or_s _ _ zenon_H5a); [ zenon_intro zenon_H4a | zenon_intro zenon_H5c ]. % 15.16/15.32 apply (zenon_or_s _ _ zenon_He6); [ zenon_intro zenon_Haf | zenon_intro zenon_He7 ]. % 15.16/15.32 apply (zenon_L96_); trivial. % 15.16/15.32 apply (zenon_or_s _ _ zenon_He7); [ zenon_intro zenon_Hdf | zenon_intro zenon_He8 ]. % 15.16/15.32 apply (zenon_L65_); trivial. % 15.16/15.32 apply (zenon_or_s _ _ zenon_He8); [ zenon_intro zenon_H34 | zenon_intro zenon_He2 ]. % 15.16/15.32 apply (zenon_or_s _ _ zenon_H12a); [ zenon_intro zenon_H1f | zenon_intro zenon_H12b ]. % 15.16/15.32 exact (zenon_H20 zenon_H1f). % 15.16/15.32 apply (zenon_or_s _ _ zenon_H12b); [ zenon_intro zenon_H47 | zenon_intro zenon_H12c ]. % 15.16/15.32 exact (zenon_H45 zenon_H47). % 15.16/15.32 apply (zenon_or_s _ _ zenon_H12c); [ zenon_intro zenon_H92 | zenon_intro zenon_H5b ]. % 15.16/15.32 apply (zenon_L97_); trivial. % 15.16/15.32 exact (zenon_H59 zenon_H5b). % 15.16/15.32 apply (zenon_L98_); trivial. % 15.16/15.32 apply (zenon_or_s _ _ zenon_H5c); [ zenon_intro zenon_H50 | zenon_intro zenon_H53 ]. % 15.16/15.32 apply (zenon_L11_); trivial. % 15.16/15.32 apply (zenon_L32_); trivial. % 15.16/15.32 (* end of lemma zenon_L99_ *) % 15.16/15.32 assert (zenon_L100_ : (((op (e0) (e0)) = (e1))\/(((op (e0) (e1)) = (e1))\/(((op (e0) (e2)) = (e1))\/((op (e0) (e3)) = (e1))))) -> (~((op (e0) (e0)) = (e1))) -> (~((op (e0) (e1)) = (op (e1) (e1)))) -> ((op (e2) (e3)) = (e2)) -> (~((e1) = (e2))) -> (~((op (e2) (e2)) = (e1))) -> (~((op (e1) (e1)) = (op (e2) (e1)))) -> ((op (e1) (e1)) = (e1)) -> (((op (e0) (e3)) = (e1))\/(((op (e1) (e3)) = (e1))\/(((op (e2) (e3)) = (e1))\/((op (e3) (e3)) = (e1))))) -> (~((op (e0) (e2)) = (op (e0) (e3)))) -> (~((op (e1) (e1)) = (op (e1) (e3)))) -> (~((op (e2) (e0)) = (op (e2) (e3)))) -> (~((op (e3) (e3)) = (e1))) -> (((op (e2) (e0)) = (e1))\/(((op (e2) (e1)) = (e1))\/(((op (e2) (e2)) = (e1))\/((op (e2) (e3)) = (e1))))) -> ((op (e0) (e3)) = (e0)) -> (~((e0) = (e1))) -> False). % 15.16/15.32 do 0 intro. intros zenon_H44 zenon_H45 zenon_H23 zenon_H124 zenon_Ha7 zenon_H52 zenon_Hb1 zenon_H21 zenon_H121 zenon_Hc9 zenon_H11e zenon_Hce zenon_H104 zenon_Hb7 zenon_Hca zenon_H9e. % 15.16/15.32 apply (zenon_or_s _ _ zenon_H44); [ zenon_intro zenon_H47 | zenon_intro zenon_H46 ]. % 15.16/15.32 exact (zenon_H45 zenon_H47). % 15.16/15.32 apply (zenon_or_s _ _ zenon_H46); [ zenon_intro zenon_H22 | zenon_intro zenon_H48 ]. % 15.16/15.32 apply (zenon_L3_); trivial. % 15.16/15.32 apply (zenon_or_s _ _ zenon_H48); [ zenon_intro zenon_H29 | zenon_intro zenon_H37 ]. % 15.16/15.32 apply (zenon_L94_); trivial. % 15.16/15.32 apply (zenon_L73_); trivial. % 15.16/15.32 (* end of lemma zenon_L100_ *) % 15.16/15.32 assert (zenon_L101_ : (((op (e0) (e0)) = (e0))\/(((op (e0) (e1)) = (e0))\/(((op (e0) (e2)) = (e0))\/((op (e0) (e3)) = (e0))))) -> (~((op (e0) (e3)) = (op (e3) (e3)))) -> ((op (e3) (e3)) = (e3)) -> (~((e0) = (e3))) -> (~((e1) = (e3))) -> (((op (e2) (e2)) = (e0))\/(((op (e2) (e2)) = (e1))\/(((op (e2) (e2)) = (e2))\/((op (e2) (e2)) = (e3))))) -> (~((op (e2) (e2)) = (e0))) -> (~((op (e2) (e2)) = (e2))) -> (~((op (e0) (e2)) = (op (e2) (e2)))) -> (((op (e2) (e0)) = (e3))\/(((op (e2) (e1)) = (e3))\/(((op (e2) (e2)) = (e3))\/((op (e2) (e3)) = (e3))))) -> (~((op (e0) (e1)) = (op (e2) (e1)))) -> (~((op (e0) (e0)) = (e3))) -> (~((op (e0) (e0)) = (e0))) -> (((op (e0) (e0)) = (e0))\/(((op (e0) (e0)) = (e1))\/(((op (e0) (e0)) = (e2))\/((op (e0) (e0)) = (e3))))) -> (~((e2) = (e3))) -> (((op (e0) (e0)) = (e3))\/(((op (e0) (e1)) = (e3))\/(((op (e0) (e2)) = (e3))\/((op (e0) (e3)) = (e3))))) -> (((op (e0) (e0)) = (e1))\/(((op (e0) (e1)) = (e1))\/(((op (e0) (e2)) = (e1))\/((op (e0) (e3)) = (e1))))) -> (~((op (e0) (e0)) = (e1))) -> (~((op (e0) (e1)) = (op (e1) (e1)))) -> ((op (e2) (e3)) = (e2)) -> (~((e1) = (e2))) -> (~((op (e2) (e2)) = (e1))) -> (~((op (e1) (e1)) = (op (e2) (e1)))) -> ((op (e1) (e1)) = (e1)) -> (((op (e0) (e3)) = (e1))\/(((op (e1) (e3)) = (e1))\/(((op (e2) (e3)) = (e1))\/((op (e3) (e3)) = (e1))))) -> (~((op (e0) (e2)) = (op (e0) (e3)))) -> (~((op (e1) (e1)) = (op (e1) (e3)))) -> (~((op (e2) (e0)) = (op (e2) (e3)))) -> (~((op (e3) (e3)) = (e1))) -> (((op (e2) (e0)) = (e1))\/(((op (e2) (e1)) = (e1))\/(((op (e2) (e2)) = (e1))\/((op (e2) (e3)) = (e1))))) -> (~((e0) = (e1))) -> False). % 15.16/15.32 do 0 intro. intros zenon_H110 zenon_H36 zenon_H42 zenon_H4b zenon_Ha3 zenon_H2d zenon_H2e zenon_H2f zenon_H28 zenon_He6 zenon_Hde zenon_H59 zenon_H20 zenon_H12a zenon_H6a zenon_H58 zenon_H44 zenon_H45 zenon_H23 zenon_H124 zenon_Ha7 zenon_H52 zenon_Hb1 zenon_H21 zenon_H121 zenon_Hc9 zenon_H11e zenon_Hce zenon_H104 zenon_Hb7 zenon_H9e. % 15.16/15.32 apply (zenon_or_s _ _ zenon_H110); [ zenon_intro zenon_H1f | zenon_intro zenon_H111 ]. % 15.16/15.32 exact (zenon_H20 zenon_H1f). % 15.16/15.32 apply (zenon_or_s _ _ zenon_H111); [ zenon_intro zenon_H49 | zenon_intro zenon_H112 ]. % 15.16/15.32 apply (zenon_L13_); trivial. % 15.16/15.32 apply (zenon_or_s _ _ zenon_H112); [ zenon_intro zenon_Hab | zenon_intro zenon_Hca ]. % 15.16/15.32 apply (zenon_L99_); trivial. % 15.16/15.32 apply (zenon_L100_); trivial. % 15.16/15.32 (* end of lemma zenon_L101_ *) % 15.16/15.32 assert (zenon_L102_ : ((op (e3) (e3)) = (e3)) -> ((op (e3) (e1)) = (e3)) -> (~((op (e3) (e1)) = (op (e3) (e3)))) -> False). % 15.16/15.32 do 0 intro. intros zenon_H42 zenon_H10a zenon_H12d. % 15.16/15.32 elim (classic ((op (e3) (e3)) = (op (e3) (e3)))); [ zenon_intro zenon_H54 | zenon_intro zenon_H55 ]. % 15.16/15.32 cut (((op (e3) (e3)) = (op (e3) (e3))) = ((op (e3) (e1)) = (op (e3) (e3)))). % 15.16/15.32 intro zenon_D_pnotp. % 15.16/15.32 apply zenon_H12d. % 15.16/15.32 rewrite <- zenon_D_pnotp. % 15.16/15.32 exact zenon_H54. % 15.16/15.32 cut (((op (e3) (e3)) = (op (e3) (e3)))); [idtac | apply NNPP; zenon_intro zenon_H55]. % 15.16/15.32 cut (((op (e3) (e3)) = (op (e3) (e1)))); [idtac | apply NNPP; zenon_intro zenon_H12e]. % 15.16/15.32 congruence. % 15.16/15.32 cut (((op (e3) (e3)) = (e3)) = ((op (e3) (e3)) = (op (e3) (e1)))). % 15.16/15.32 intro zenon_D_pnotp. % 15.16/15.32 apply zenon_H12e. % 15.16/15.32 rewrite <- zenon_D_pnotp. % 15.16/15.32 exact zenon_H42. % 15.16/15.32 cut (((e3) = (op (e3) (e1)))); [idtac | apply NNPP; zenon_intro zenon_H10b]. % 15.16/15.32 cut (((op (e3) (e3)) = (op (e3) (e3)))); [idtac | apply NNPP; zenon_intro zenon_H55]. % 15.16/15.32 congruence. % 15.16/15.32 apply zenon_H55. apply refl_equal. % 15.16/15.32 apply zenon_H10b. apply sym_equal. exact zenon_H10a. % 15.16/15.32 apply zenon_H55. apply refl_equal. % 15.16/15.32 apply zenon_H55. apply refl_equal. % 15.16/15.32 (* end of lemma zenon_L102_ *) % 15.16/15.32 assert (zenon_L103_ : ((~((op (e3) (e3)) = (e1)))\/((op (e3) (e1)) = (e3))) -> (~((op (e3) (e1)) = (op (e3) (e3)))) -> (~((op (e0) (e0)) = (e0))) -> (((op (e0) (e0)) = (e3))\/(((op (e0) (e1)) = (e3))\/(((op (e0) (e2)) = (e3))\/((op (e0) (e3)) = (e3))))) -> ((op (e3) (e3)) = (e3)) -> (~((op (e0) (e3)) = (op (e3) (e3)))) -> (~((op (e2) (e2)) = (e0))) -> (~((op (e2) (e2)) = (e1))) -> (~((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))))) -> (~((e0) = (e3))) -> (~((op (e0) (e0)) = (e3))) -> (((op (e0) (e0)) = (e1))\/(((op (e0) (e1)) = (e1))\/(((op (e0) (e2)) = (e1))\/((op (e0) (e3)) = (e1))))) -> (((op (e2) (e0)) = (e3))\/(((op (e2) (e1)) = (e3))\/(((op (e2) (e2)) = (e3))\/((op (e2) (e3)) = (e3))))) -> (~((e2) = (e3))) -> (((op (e0) (e0)) = (e0))\/(((op (e0) (e0)) = (e1))\/(((op (e0) (e0)) = (e2))\/((op (e0) (e0)) = (e3))))) -> (~((op (e0) (e1)) = (op (e2) (e1)))) -> (~((e1) = (e3))) -> (~((op (e1) (e1)) = (op (e2) (e1)))) -> (~((e1) = (e2))) -> ((op (e2) (e3)) = (e2)) -> (((op (e2) (e0)) = (e1))\/(((op (e2) (e1)) = (e1))\/(((op (e2) (e2)) = (e1))\/((op (e2) (e3)) = (e1))))) -> (~((e0) = (e1))) -> ((op (e1) (e1)) = (e1)) -> (~((op (e0) (e1)) = (op (e1) (e1)))) -> (~((op (e0) (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 (e1) (e1)) = (op (e1) (e3)))) -> (~((op (e0) (e2)) = (op (e0) (e3)))) -> (((op (e0) (e0)) = (e0))\/(((op (e0) (e1)) = (e0))\/(((op (e0) (e2)) = (e0))\/((op (e0) (e3)) = (e0))))) -> False). % 15.16/15.32 do 0 intro. intros zenon_H10c zenon_H12d zenon_H20 zenon_H58 zenon_H42 zenon_H36 zenon_H2e zenon_H52 zenon_H2f zenon_H28 zenon_H2d zenon_H4b zenon_H59 zenon_H44 zenon_He6 zenon_H6a zenon_H12a zenon_Hde zenon_Ha3 zenon_Hb1 zenon_Ha7 zenon_H124 zenon_Hb7 zenon_H9e zenon_H21 zenon_H23 zenon_H45 zenon_H121 zenon_Hce zenon_H11e zenon_Hc9 zenon_H110. % 15.16/15.32 apply (zenon_or_s _ _ zenon_H10c); [ zenon_intro zenon_H104 | zenon_intro zenon_H10a ]. % 15.16/15.32 apply (zenon_L101_); trivial. % 15.16/15.32 apply (zenon_L102_); trivial. % 15.16/15.32 (* end of lemma zenon_L103_ *) % 15.16/15.32 assert (zenon_L104_ : ((op (e0) (e2)) = (e1)) -> ((op (e0) (e2)) = (e2)) -> (~((e1) = (e2))) -> False). % 15.16/15.32 do 0 intro. intros zenon_H29 zenon_H63 zenon_Ha7. % 15.16/15.33 elim (classic ((e2) = (e2))); [ zenon_intro zenon_H5f | zenon_intro zenon_H60 ]. % 15.16/15.33 cut (((e2) = (e2)) = ((e1) = (e2))). % 15.16/15.33 intro zenon_D_pnotp. % 15.16/15.33 apply zenon_Ha7. % 15.16/15.33 rewrite <- zenon_D_pnotp. % 15.16/15.33 exact zenon_H5f. % 15.16/15.33 cut (((e2) = (e2))); [idtac | apply NNPP; zenon_intro zenon_H60]. % 15.16/15.33 cut (((e2) = (e1))); [idtac | apply NNPP; zenon_intro zenon_Ha8]. % 15.16/15.33 congruence. % 15.16/15.33 cut (((op (e0) (e2)) = (e1)) = ((e2) = (e1))). % 15.16/15.33 intro zenon_D_pnotp. % 15.16/15.33 apply zenon_Ha8. % 15.16/15.33 rewrite <- zenon_D_pnotp. % 15.16/15.33 exact zenon_H29. % 15.16/15.33 cut (((e1) = (e1))); [idtac | apply NNPP; zenon_intro zenon_Ha0]. % 15.16/15.33 cut (((op (e0) (e2)) = (e2))); [idtac | apply NNPP; zenon_intro zenon_H12f]. % 15.16/15.33 congruence. % 15.16/15.33 exact (zenon_H12f zenon_H63). % 15.16/15.33 apply zenon_Ha0. apply refl_equal. % 15.16/15.33 apply zenon_H60. apply refl_equal. % 15.16/15.33 apply zenon_H60. apply refl_equal. % 15.16/15.33 (* end of lemma zenon_L104_ *) % 15.16/15.33 assert (zenon_L105_ : (((op (e0) (e2)) = (e1))\/(((op (e1) (e2)) = (e1))\/(((op (e2) (e2)) = (e1))\/((op (e3) (e2)) = (e1))))) -> (~((e1) = (e2))) -> ((op (e0) (e2)) = (e2)) -> ((op (e1) (e1)) = (e1)) -> (~((op (e1) (e1)) = (op (e1) (e2)))) -> (~((op (e2) (e2)) = (e1))) -> (~((e1) = (e3))) -> ((op (e3) (e2)) = (e3)) -> False). % 15.16/15.33 do 0 intro. intros zenon_H11b zenon_Ha7 zenon_H63 zenon_H21 zenon_H116 zenon_H52 zenon_Ha3 zenon_H106. % 15.16/15.33 apply (zenon_or_s _ _ zenon_H11b); [ zenon_intro zenon_H29 | zenon_intro zenon_H11c ]. % 15.16/15.33 apply (zenon_L104_); trivial. % 15.16/15.33 apply (zenon_or_s _ _ zenon_H11c); [ zenon_intro zenon_H117 | zenon_intro zenon_H11d ]. % 15.16/15.33 apply (zenon_L86_); trivial. % 15.16/15.33 apply (zenon_or_s _ _ zenon_H11d); [ zenon_intro zenon_H2a | zenon_intro zenon_H119 ]. % 15.16/15.33 exact (zenon_H52 zenon_H2a). % 15.16/15.33 apply (zenon_L87_); trivial. % 15.16/15.33 (* end of lemma zenon_L105_ *) % 15.16/15.33 assert (zenon_L106_ : (~((op (e0) (e3)) = (op (e3) (e3)))) -> ((op (e0) (e3)) = (e2)) -> ((op (e3) (e3)) = (e2)) -> False). % 15.16/15.33 do 0 intro. intros zenon_H36 zenon_H81 zenon_H43. % 15.16/15.33 cut (((op (e0) (e3)) = (e2)) = ((op (e0) (e3)) = (op (e3) (e3)))). % 15.16/15.33 intro zenon_D_pnotp. % 15.16/15.33 apply zenon_H36. % 15.16/15.33 rewrite <- zenon_D_pnotp. % 15.16/15.33 exact zenon_H81. % 15.16/15.33 cut (((e2) = (op (e3) (e3)))); [idtac | apply NNPP; zenon_intro zenon_H130]. % 15.16/15.33 cut (((op (e0) (e3)) = (op (e0) (e3)))); [idtac | apply NNPP; zenon_intro zenon_H3a]. % 15.16/15.33 congruence. % 15.16/15.33 apply zenon_H3a. apply refl_equal. % 15.16/15.33 apply zenon_H130. apply sym_equal. exact zenon_H43. % 15.16/15.33 (* end of lemma zenon_L106_ *) % 15.16/15.33 assert (zenon_L107_ : (((op (e3) (e3)) = (e0))\/(((op (e3) (e3)) = (e1))\/(((op (e3) (e3)) = (e2))\/((op (e3) (e3)) = (e3))))) -> (~((op (e3) (e3)) = (e0))) -> (~((op (e3) (e3)) = (e1))) -> ((op (e0) (e3)) = (e2)) -> (~((op (e0) (e3)) = (op (e3) (e3)))) -> (~((op (e3) (e3)) = (e3))) -> False). % 15.16/15.33 do 0 intro. intros zenon_H3b zenon_H3c zenon_H104 zenon_H81 zenon_H36 zenon_H3e. % 15.16/15.33 apply (zenon_or_s _ _ zenon_H3b); [ zenon_intro zenon_H40 | zenon_intro zenon_H3f ]. % 15.16/15.33 exact (zenon_H3c zenon_H40). % 15.16/15.33 apply (zenon_or_s _ _ zenon_H3f); [ zenon_intro zenon_H38 | zenon_intro zenon_H41 ]. % 15.16/15.33 exact (zenon_H104 zenon_H38). % 15.16/15.33 apply (zenon_or_s _ _ zenon_H41); [ zenon_intro zenon_H43 | zenon_intro zenon_H42 ]. % 15.16/15.33 apply (zenon_L106_); trivial. % 15.16/15.33 exact (zenon_H3e zenon_H42). % 15.16/15.33 (* end of lemma zenon_L107_ *) % 15.16/15.33 assert (zenon_L108_ : (((op (e0) (e0)) = (e2))\/(((op (e0) (e1)) = (e2))\/(((op (e0) (e2)) = (e2))\/((op (e0) (e3)) = (e2))))) -> (~((op (e0) (e0)) = (e2))) -> (~((e0) = (e2))) -> ((op (e0) (e1)) = (e0)) -> ((op (e3) (e2)) = (e3)) -> (~((e1) = (e3))) -> (~((op (e2) (e2)) = (e1))) -> (~((op (e1) (e1)) = (op (e1) (e2)))) -> ((op (e1) (e1)) = (e1)) -> (~((e1) = (e2))) -> (((op (e0) (e2)) = (e1))\/(((op (e1) (e2)) = (e1))\/(((op (e2) (e2)) = (e1))\/((op (e3) (e2)) = (e1))))) -> (((op (e3) (e3)) = (e0))\/(((op (e3) (e3)) = (e1))\/(((op (e3) (e3)) = (e2))\/((op (e3) (e3)) = (e3))))) -> (~((op (e3) (e3)) = (e0))) -> (~((op (e3) (e3)) = (e1))) -> (~((op (e0) (e3)) = (op (e3) (e3)))) -> (~((op (e3) (e3)) = (e3))) -> False). % 15.16/15.33 do 0 intro. intros zenon_H8e zenon_H8f zenon_H5e zenon_H49 zenon_H106 zenon_Ha3 zenon_H52 zenon_H116 zenon_H21 zenon_Ha7 zenon_H11b zenon_H3b zenon_H3c zenon_H104 zenon_H36 zenon_H3e. % 15.16/15.33 apply (zenon_or_s _ _ zenon_H8e); [ zenon_intro zenon_H92 | zenon_intro zenon_H91 ]. % 15.16/15.33 exact (zenon_H8f zenon_H92). % 15.16/15.33 apply (zenon_or_s _ _ zenon_H91); [ zenon_intro zenon_H5d | zenon_intro zenon_H93 ]. % 15.16/15.33 apply (zenon_L14_); trivial. % 15.16/15.33 apply (zenon_or_s _ _ zenon_H93); [ zenon_intro zenon_H63 | zenon_intro zenon_H81 ]. % 15.16/15.33 apply (zenon_L105_); trivial. % 15.16/15.33 apply (zenon_L107_); trivial. % 15.16/15.33 (* end of lemma zenon_L108_ *) % 15.16/15.33 assert (zenon_L109_ : (((op (e0) (e0)) = (e1))\/(((op (e0) (e1)) = (e1))\/(((op (e0) (e2)) = (e1))\/((op (e0) (e3)) = (e1))))) -> (~((op (e0) (e0)) = (e1))) -> (~((op (e0) (e1)) = (op (e1) (e1)))) -> (~((e0) = (e1))) -> ((op (e0) (e2)) = (e0)) -> (((op (e0) (e2)) = (e1))\/(((op (e1) (e2)) = (e1))\/(((op (e2) (e2)) = (e1))\/((op (e3) (e2)) = (e1))))) -> (~((op (e0) (e2)) = (op (e0) (e3)))) -> ((op (e1) (e1)) = (e1)) -> (~((op (e1) (e1)) = (op (e1) (e2)))) -> (~((op (e2) (e2)) = (e1))) -> (~((e1) = (e3))) -> ((op (e3) (e2)) = (e3)) -> False). % 15.16/15.33 do 0 intro. intros zenon_H44 zenon_H45 zenon_H23 zenon_H9e zenon_Hab zenon_H11b zenon_Hc9 zenon_H21 zenon_H116 zenon_H52 zenon_Ha3 zenon_H106. % 15.16/15.33 apply (zenon_or_s _ _ zenon_H44); [ zenon_intro zenon_H47 | zenon_intro zenon_H46 ]. % 15.16/15.33 exact (zenon_H45 zenon_H47). % 15.16/15.33 apply (zenon_or_s _ _ zenon_H46); [ zenon_intro zenon_H22 | zenon_intro zenon_H48 ]. % 15.16/15.33 apply (zenon_L3_); trivial. % 15.16/15.33 apply (zenon_or_s _ _ zenon_H48); [ zenon_intro zenon_H29 | zenon_intro zenon_H37 ]. % 15.16/15.33 apply (zenon_L37_); trivial. % 15.16/15.33 apply (zenon_L88_); trivial. % 15.16/15.33 (* end of lemma zenon_L109_ *) % 15.16/15.33 assert (zenon_L110_ : (~((op (op (e0) (e0)) (op (e0) (e0))) = (op (e3) (e3)))) -> ((op (e0) (e0)) = (e3)) -> False). % 15.16/15.33 do 0 intro. intros zenon_H131 zenon_H5b. % 15.16/15.33 cut (((op (e0) (e0)) = (e3))); [idtac | apply NNPP; zenon_intro zenon_H59]. % 15.16/15.33 cut (((op (e0) (e0)) = (e3))); [idtac | apply NNPP; zenon_intro zenon_H59]. % 15.16/15.33 congruence. % 15.16/15.33 exact (zenon_H59 zenon_H5b). % 15.16/15.33 exact (zenon_H59 zenon_H5b). % 15.16/15.33 (* end of lemma zenon_L110_ *) % 15.16/15.33 assert (zenon_L111_ : ((op (e0) (e1)) = (e2)) -> ((op (e3) (e3)) = (e1)) -> ((op (e0) (e0)) = (e3)) -> False). % 15.16/15.33 do 0 intro. intros zenon_H5d zenon_H38 zenon_H5b. % 15.16/15.33 apply (zenon_notand_s _ _ ax17); [ zenon_intro zenon_Hc3 | zenon_intro zenon_H132 ]. % 15.16/15.33 elim (classic ((op (op (e0) (e0)) (op (e0) (e0))) = (op (op (e0) (e0)) (op (e0) (e0))))); [ zenon_intro zenon_H71 | zenon_intro zenon_H72 ]. % 15.16/15.33 cut (((op (op (e0) (e0)) (op (e0) (e0))) = (op (op (e0) (e0)) (op (e0) (e0)))) = ((e1) = (op (op (e0) (e0)) (op (e0) (e0))))). % 15.16/15.33 intro zenon_D_pnotp. % 15.16/15.33 apply zenon_Hc3. % 15.16/15.33 rewrite <- zenon_D_pnotp. % 15.16/15.33 exact zenon_H71. % 15.16/15.33 cut (((op (op (e0) (e0)) (op (e0) (e0))) = (op (op (e0) (e0)) (op (e0) (e0))))); [idtac | apply NNPP; zenon_intro zenon_H72]. % 15.16/15.33 cut (((op (op (e0) (e0)) (op (e0) (e0))) = (e1))); [idtac | apply NNPP; zenon_intro zenon_Hc4]. % 15.16/15.33 congruence. % 15.16/15.33 cut (((op (e3) (e3)) = (e1)) = ((op (op (e0) (e0)) (op (e0) (e0))) = (e1))). % 15.16/15.33 intro zenon_D_pnotp. % 15.16/15.33 apply zenon_Hc4. % 15.16/15.33 rewrite <- zenon_D_pnotp. % 15.16/15.33 exact zenon_H38. % 15.16/15.33 cut (((e1) = (e1))); [idtac | apply NNPP; zenon_intro zenon_Ha0]. % 15.16/15.33 cut (((op (e3) (e3)) = (op (op (e0) (e0)) (op (e0) (e0))))); [idtac | apply NNPP; zenon_intro zenon_H133]. % 15.16/15.33 congruence. % 15.16/15.33 elim (classic ((op (op (e0) (e0)) (op (e0) (e0))) = (op (op (e0) (e0)) (op (e0) (e0))))); [ zenon_intro zenon_H71 | zenon_intro zenon_H72 ]. % 15.16/15.33 cut (((op (op (e0) (e0)) (op (e0) (e0))) = (op (op (e0) (e0)) (op (e0) (e0)))) = ((op (e3) (e3)) = (op (op (e0) (e0)) (op (e0) (e0))))). % 15.16/15.33 intro zenon_D_pnotp. % 15.16/15.33 apply zenon_H133. % 15.16/15.33 rewrite <- zenon_D_pnotp. % 15.16/15.33 exact zenon_H71. % 15.16/15.33 cut (((op (op (e0) (e0)) (op (e0) (e0))) = (op (op (e0) (e0)) (op (e0) (e0))))); [idtac | apply NNPP; zenon_intro zenon_H72]. % 15.16/15.33 cut (((op (op (e0) (e0)) (op (e0) (e0))) = (op (e3) (e3)))); [idtac | apply NNPP; zenon_intro zenon_H131]. % 15.16/15.33 congruence. % 15.16/15.33 apply (zenon_L110_); trivial. % 15.16/15.33 apply zenon_H72. apply refl_equal. % 15.16/15.33 apply zenon_H72. apply refl_equal. % 15.16/15.33 apply zenon_Ha0. apply refl_equal. % 15.16/15.33 apply zenon_H72. apply refl_equal. % 15.16/15.33 apply zenon_H72. apply refl_equal. % 15.16/15.33 apply (zenon_notand_s _ _ zenon_H132); [ zenon_intro zenon_H134 | zenon_intro zenon_H9a ]. % 15.16/15.33 apply zenon_H134. apply sym_equal. exact zenon_H5b. % 15.16/15.33 elim (classic ((op (e0) (op (op (e0) (e0)) (op (e0) (e0)))) = (op (e0) (op (op (e0) (e0)) (op (e0) (e0)))))); [ zenon_intro zenon_H77 | zenon_intro zenon_H78 ]. % 15.16/15.33 cut (((op (e0) (op (op (e0) (e0)) (op (e0) (e0)))) = (op (e0) (op (op (e0) (e0)) (op (e0) (e0))))) = ((e2) = (op (e0) (op (op (e0) (e0)) (op (e0) (e0)))))). % 15.16/15.33 intro zenon_D_pnotp. % 15.16/15.33 apply zenon_H9a. % 15.16/15.33 rewrite <- zenon_D_pnotp. % 15.16/15.33 exact zenon_H77. % 15.16/15.33 cut (((op (e0) (op (op (e0) (e0)) (op (e0) (e0)))) = (op (e0) (op (op (e0) (e0)) (op (e0) (e0)))))); [idtac | apply NNPP; zenon_intro zenon_H78]. % 15.16/15.33 cut (((op (e0) (op (op (e0) (e0)) (op (e0) (e0)))) = (e2))); [idtac | apply NNPP; zenon_intro zenon_H9b]. % 15.16/15.33 congruence. % 15.16/15.33 cut (((op (e0) (e1)) = (e2)) = ((op (e0) (op (op (e0) (e0)) (op (e0) (e0)))) = (e2))). % 15.16/15.33 intro zenon_D_pnotp. % 15.16/15.33 apply zenon_H9b. % 15.16/15.33 rewrite <- zenon_D_pnotp. % 15.16/15.33 exact zenon_H5d. % 15.16/15.33 cut (((e2) = (e2))); [idtac | apply NNPP; zenon_intro zenon_H60]. % 15.16/15.33 cut (((op (e0) (e1)) = (op (e0) (op (op (e0) (e0)) (op (e0) (e0)))))); [idtac | apply NNPP; zenon_intro zenon_Hc7]. % 15.16/15.33 congruence. % 15.16/15.33 elim (classic ((op (e0) (op (op (e0) (e0)) (op (e0) (e0)))) = (op (e0) (op (op (e0) (e0)) (op (e0) (e0)))))); [ zenon_intro zenon_H77 | zenon_intro zenon_H78 ]. % 15.16/15.33 cut (((op (e0) (op (op (e0) (e0)) (op (e0) (e0)))) = (op (e0) (op (op (e0) (e0)) (op (e0) (e0))))) = ((op (e0) (e1)) = (op (e0) (op (op (e0) (e0)) (op (e0) (e0)))))). % 15.16/15.33 intro zenon_D_pnotp. % 15.16/15.33 apply zenon_Hc7. % 15.16/15.33 rewrite <- zenon_D_pnotp. % 15.16/15.33 exact zenon_H77. % 15.16/15.33 cut (((op (e0) (op (op (e0) (e0)) (op (e0) (e0)))) = (op (e0) (op (op (e0) (e0)) (op (e0) (e0)))))); [idtac | apply NNPP; zenon_intro zenon_H78]. % 15.16/15.33 cut (((op (e0) (op (op (e0) (e0)) (op (e0) (e0)))) = (op (e0) (e1)))); [idtac | apply NNPP; zenon_intro zenon_Hc8]. % 15.16/15.33 congruence. % 15.16/15.33 cut (((op (op (e0) (e0)) (op (e0) (e0))) = (e1))); [idtac | apply NNPP; zenon_intro zenon_Hc4]. % 15.16/15.33 cut (((e0) = (e0))); [idtac | apply NNPP; zenon_intro zenon_H1d]. % 15.16/15.33 congruence. % 15.16/15.33 apply zenon_H1d. apply refl_equal. % 15.16/15.33 cut (((op (e3) (e3)) = (e1)) = ((op (op (e0) (e0)) (op (e0) (e0))) = (e1))). % 15.16/15.33 intro zenon_D_pnotp. % 15.16/15.33 apply zenon_Hc4. % 15.16/15.33 rewrite <- zenon_D_pnotp. % 15.16/15.33 exact zenon_H38. % 15.16/15.33 cut (((e1) = (e1))); [idtac | apply NNPP; zenon_intro zenon_Ha0]. % 15.16/15.33 cut (((op (e3) (e3)) = (op (op (e0) (e0)) (op (e0) (e0))))); [idtac | apply NNPP; zenon_intro zenon_H133]. % 15.16/15.33 congruence. % 15.16/15.33 elim (classic ((op (op (e0) (e0)) (op (e0) (e0))) = (op (op (e0) (e0)) (op (e0) (e0))))); [ zenon_intro zenon_H71 | zenon_intro zenon_H72 ]. % 15.16/15.33 cut (((op (op (e0) (e0)) (op (e0) (e0))) = (op (op (e0) (e0)) (op (e0) (e0)))) = ((op (e3) (e3)) = (op (op (e0) (e0)) (op (e0) (e0))))). % 15.16/15.33 intro zenon_D_pnotp. % 15.16/15.33 apply zenon_H133. % 15.16/15.33 rewrite <- zenon_D_pnotp. % 15.16/15.33 exact zenon_H71. % 15.16/15.33 cut (((op (op (e0) (e0)) (op (e0) (e0))) = (op (op (e0) (e0)) (op (e0) (e0))))); [idtac | apply NNPP; zenon_intro zenon_H72]. % 15.16/15.33 cut (((op (op (e0) (e0)) (op (e0) (e0))) = (op (e3) (e3)))); [idtac | apply NNPP; zenon_intro zenon_H131]. % 15.16/15.33 congruence. % 15.16/15.33 apply (zenon_L110_); trivial. % 15.16/15.33 apply zenon_H72. apply refl_equal. % 15.16/15.33 apply zenon_H72. apply refl_equal. % 15.16/15.33 apply zenon_Ha0. apply refl_equal. % 15.16/15.33 apply zenon_H78. apply refl_equal. % 15.16/15.33 apply zenon_H78. apply refl_equal. % 15.16/15.33 apply zenon_H60. apply refl_equal. % 15.16/15.33 apply zenon_H78. apply refl_equal. % 15.16/15.33 apply zenon_H78. apply refl_equal. % 15.16/15.33 (* end of lemma zenon_L111_ *) % 15.16/15.33 assert (zenon_L112_ : (((op (e0) (e0)) = (e0))\/(((op (e0) (e0)) = (e1))\/(((op (e0) (e0)) = (e2))\/((op (e0) (e0)) = (e3))))) -> (~((op (e0) (e0)) = (e0))) -> (~((op (e0) (e0)) = (e1))) -> (~((op (e0) (e0)) = (e2))) -> (((op (e3) (e3)) = (e0))\/(((op (e3) (e3)) = (e1))\/(((op (e3) (e3)) = (e2))\/((op (e3) (e3)) = (e3))))) -> (~((op (e3) (e3)) = (e0))) -> ((op (e0) (e1)) = (e2)) -> (~((op (e3) (e3)) = (e2))) -> (~((op (e3) (e3)) = (e3))) -> False). % 15.16/15.33 do 0 intro. intros zenon_H12a zenon_H20 zenon_H45 zenon_H8f zenon_H3b zenon_H3c zenon_H5d zenon_H3d zenon_H3e. % 15.16/15.33 apply (zenon_or_s _ _ zenon_H12a); [ zenon_intro zenon_H1f | zenon_intro zenon_H12b ]. % 15.16/15.33 exact (zenon_H20 zenon_H1f). % 15.16/15.33 apply (zenon_or_s _ _ zenon_H12b); [ zenon_intro zenon_H47 | zenon_intro zenon_H12c ]. % 15.16/15.33 exact (zenon_H45 zenon_H47). % 15.16/15.33 apply (zenon_or_s _ _ zenon_H12c); [ zenon_intro zenon_H92 | zenon_intro zenon_H5b ]. % 15.16/15.33 exact (zenon_H8f zenon_H92). % 15.16/15.33 apply (zenon_or_s _ _ zenon_H3b); [ zenon_intro zenon_H40 | zenon_intro zenon_H3f ]. % 15.16/15.33 exact (zenon_H3c zenon_H40). % 15.16/15.33 apply (zenon_or_s _ _ zenon_H3f); [ zenon_intro zenon_H38 | zenon_intro zenon_H41 ]. % 15.16/15.33 apply (zenon_L111_); trivial. % 15.16/15.33 apply (zenon_or_s _ _ zenon_H41); [ zenon_intro zenon_H43 | zenon_intro zenon_H42 ]. % 15.16/15.33 exact (zenon_H3d zenon_H43). % 15.16/15.33 exact (zenon_H3e zenon_H42). % 15.16/15.33 (* end of lemma zenon_L112_ *) % 15.16/15.33 assert (zenon_L113_ : ((op (e0) (e3)) = (e0)) -> ((op (e0) (e3)) = (e2)) -> (~((e0) = (e2))) -> False). % 15.16/15.33 do 0 intro. intros zenon_Hca zenon_H81 zenon_H5e. % 15.16/15.33 elim (classic ((e2) = (e2))); [ zenon_intro zenon_H5f | zenon_intro zenon_H60 ]. % 15.16/15.33 cut (((e2) = (e2)) = ((e0) = (e2))). % 15.16/15.33 intro zenon_D_pnotp. % 15.16/15.33 apply zenon_H5e. % 15.16/15.33 rewrite <- zenon_D_pnotp. % 15.16/15.33 exact zenon_H5f. % 15.16/15.33 cut (((e2) = (e2))); [idtac | apply NNPP; zenon_intro zenon_H60]. % 15.16/15.33 cut (((e2) = (e0))); [idtac | apply NNPP; zenon_intro zenon_H61]. % 15.16/15.33 congruence. % 15.16/15.33 cut (((op (e0) (e3)) = (e0)) = ((e2) = (e0))). % 15.16/15.33 intro zenon_D_pnotp. % 15.16/15.33 apply zenon_H61. % 15.16/15.33 rewrite <- zenon_D_pnotp. % 15.16/15.33 exact zenon_Hca. % 15.16/15.33 cut (((e0) = (e0))); [idtac | apply NNPP; zenon_intro zenon_H1d]. % 15.16/15.33 cut (((op (e0) (e3)) = (e2))); [idtac | apply NNPP; zenon_intro zenon_Ha9]. % 15.16/15.33 congruence. % 15.16/15.33 exact (zenon_Ha9 zenon_H81). % 15.16/15.33 apply zenon_H1d. apply refl_equal. % 15.16/15.33 apply zenon_H60. apply refl_equal. % 15.16/15.33 apply zenon_H60. apply refl_equal. % 15.16/15.33 (* end of lemma zenon_L113_ *) % 15.16/15.33 assert (zenon_L114_ : (((op (e0) (e0)) = (e1))\/(((op (e0) (e1)) = (e1))\/(((op (e0) (e2)) = (e1))\/((op (e0) (e3)) = (e1))))) -> (~((op (e0) (e1)) = (op (e1) (e1)))) -> ((op (e1) (e1)) = (e1)) -> (~((e0) = (e2))) -> ((op (e0) (e3)) = (e0)) -> (~((e1) = (e2))) -> (((op (e0) (e0)) = (e0))\/(((op (e0) (e0)) = (e1))\/(((op (e0) (e0)) = (e2))\/((op (e0) (e0)) = (e3))))) -> (~((op (e0) (e0)) = (e0))) -> (~((op (e0) (e0)) = (e1))) -> (~((op (e0) (e0)) = (e2))) -> (((op (e0) (e0)) = (e2))\/(((op (e0) (e1)) = (e2))\/(((op (e0) (e2)) = (e2))\/((op (e0) (e3)) = (e2))))) -> (((op (e3) (e3)) = (e0))\/(((op (e3) (e3)) = (e1))\/(((op (e3) (e3)) = (e2))\/((op (e3) (e3)) = (e3))))) -> (~((op (e3) (e3)) = (e0))) -> (~((op (e0) (e3)) = (op (e3) (e3)))) -> (~((op (e3) (e3)) = (e2))) -> (~((op (e3) (e3)) = (e3))) -> False). % 15.16/15.33 do 0 intro. intros zenon_H44 zenon_H23 zenon_H21 zenon_H5e zenon_Hca zenon_Ha7 zenon_H12a zenon_H20 zenon_H45 zenon_H8f zenon_H8e zenon_H3b zenon_H3c zenon_H36 zenon_H3d zenon_H3e. % 15.16/15.33 apply (zenon_or_s _ _ zenon_H44); [ zenon_intro zenon_H47 | zenon_intro zenon_H46 ]. % 15.16/15.33 exact (zenon_H45 zenon_H47). % 15.16/15.33 apply (zenon_or_s _ _ zenon_H46); [ zenon_intro zenon_H22 | zenon_intro zenon_H48 ]. % 15.16/15.33 apply (zenon_L3_); trivial. % 15.16/15.33 apply (zenon_or_s _ _ zenon_H48); [ zenon_intro zenon_H29 | zenon_intro zenon_H37 ]. % 15.16/15.33 apply (zenon_or_s _ _ zenon_H8e); [ zenon_intro zenon_H92 | zenon_intro zenon_H91 ]. % 15.16/15.33 exact (zenon_H8f zenon_H92). % 15.16/15.33 apply (zenon_or_s _ _ zenon_H91); [ zenon_intro zenon_H5d | zenon_intro zenon_H93 ]. % 15.16/15.33 apply (zenon_L112_); trivial. % 15.16/15.33 apply (zenon_or_s _ _ zenon_H93); [ zenon_intro zenon_H63 | zenon_intro zenon_H81 ]. % 15.16/15.33 apply (zenon_L104_); trivial. % 15.16/15.33 apply (zenon_L113_); trivial. % 15.16/15.33 apply (zenon_L7_); trivial. % 15.16/15.33 (* end of lemma zenon_L114_ *) % 15.16/15.33 assert (zenon_L115_ : (~((op (e3) (e1)) = (op (e3) (e2)))) -> ((op (e3) (e1)) = (e3)) -> ((op (e3) (e2)) = (e3)) -> False). % 15.16/15.33 do 0 intro. intros zenon_H135 zenon_H10a zenon_H106. % 15.16/15.33 cut (((op (e3) (e1)) = (e3)) = ((op (e3) (e1)) = (op (e3) (e2)))). % 15.16/15.33 intro zenon_D_pnotp. % 15.16/15.33 apply zenon_H135. % 15.16/15.33 rewrite <- zenon_D_pnotp. % 15.16/15.33 exact zenon_H10a. % 15.16/15.33 cut (((e3) = (op (e3) (e2)))); [idtac | apply NNPP; zenon_intro zenon_H107]. % 15.16/15.33 cut (((op (e3) (e1)) = (op (e3) (e1)))); [idtac | apply NNPP; zenon_intro zenon_H136]. % 15.16/15.33 congruence. % 15.16/15.33 apply zenon_H136. apply refl_equal. % 15.16/15.33 apply zenon_H107. apply sym_equal. exact zenon_H106. % 15.16/15.33 (* end of lemma zenon_L115_ *) % 15.16/15.33 assert (zenon_L116_ : ((~((op (e3) (e3)) = (e2)))\/((op (e3) (e2)) = (e3))) -> (~((op (e3) (e1)) = (op (e3) (e2)))) -> (((op (e0) (e0)) = (e1))\/(((op (e0) (e1)) = (e1))\/(((op (e0) (e2)) = (e1))\/((op (e0) (e3)) = (e1))))) -> (~((op (e0) (e3)) = (op (e3) (e3)))) -> (~((op (e0) (e0)) = (e2))) -> (((op (e0) (e0)) = (e0))\/(((op (e0) (e0)) = (e1))\/(((op (e0) (e0)) = (e2))\/((op (e0) (e0)) = (e3))))) -> (~((op (e3) (e3)) = (e0))) -> (((op (e3) (e3)) = (e0))\/(((op (e3) (e3)) = (e1))\/(((op (e3) (e3)) = (e2))\/((op (e3) (e3)) = (e3))))) -> (~((op (e0) (e0)) = (e0))) -> (~((e1) = (e2))) -> (~((e0) = (e2))) -> ((op (e0) (e3)) = (e0)) -> (((op (e0) (e0)) = (e2))\/(((op (e0) (e1)) = (e2))\/(((op (e0) (e2)) = (e2))\/((op (e0) (e3)) = (e2))))) -> ((op (e1) (e1)) = (e1)) -> (~((op (e0) (e1)) = (op (e1) (e1)))) -> (~((op (e0) (e0)) = (e1))) -> (~((op (e3) (e1)) = (op (e3) (e3)))) -> ((op (e3) (e1)) = (e3)) -> ((~((op (e3) (e3)) = (e3)))\/((op (e3) (e3)) = (e3))) -> False). % 15.16/15.33 do 0 intro. intros zenon_H10e zenon_H135 zenon_H44 zenon_H36 zenon_H8f zenon_H12a zenon_H3c zenon_H3b zenon_H20 zenon_Ha7 zenon_H5e zenon_Hca zenon_H8e zenon_H21 zenon_H23 zenon_H45 zenon_H12d zenon_H10a zenon_H10d. % 15.16/15.33 apply (zenon_or_s _ _ zenon_H10e); [ zenon_intro zenon_H3d | zenon_intro zenon_H106 ]. % 15.16/15.33 apply (zenon_or_s _ _ zenon_H10d); [ zenon_intro zenon_H3e | zenon_intro zenon_H42 ]. % 15.16/15.33 apply (zenon_L114_); trivial. % 15.16/15.33 apply (zenon_L102_); trivial. % 15.16/15.33 apply (zenon_L115_); trivial. % 15.16/15.33 (* end of lemma zenon_L116_ *) % 15.16/15.33 assert (zenon_L117_ : ((~((op (e3) (e3)) = (e0)))\/((op (e3) (e0)) = (e3))) -> (~((op (e3) (e0)) = (op (e3) (e2)))) -> (((op (e0) (e0)) = (e1))\/(((op (e1) (e0)) = (e1))\/(((op (e2) (e0)) = (e1))\/((op (e3) (e0)) = (e1))))) -> (~((e1) = (e3))) -> (~((op (e2) (e2)) = (e0))) -> (~((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 (e3) (e0)) = (op (e3) (e3)))) -> (~((op (e3) (e0)) = (op (e3) (e1)))) -> (((op (e0) (e0)) = (e1))\/(((op (e0) (e1)) = (e1))\/(((op (e0) (e2)) = (e1))\/((op (e0) (e3)) = (e1))))) -> ((op (e0) (e3)) = (e0)) -> (~((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 (e1) (e1)) = (op (e1) (e3)))) -> (~((op (e0) (e2)) = (op (e0) (e3)))) -> (~((op (e1) (e1)) = (op (e2) (e1)))) -> (~((op (e2) (e2)) = (e1))) -> (~((e1) = (e2))) -> ((op (e2) (e3)) = (e2)) -> (((op (e2) (e0)) = (e1))\/(((op (e2) (e1)) = (e1))\/(((op (e2) (e2)) = (e1))\/((op (e2) (e3)) = (e1))))) -> ((op (e1) (e1)) = (e1)) -> (~((op (e0) (e1)) = (op (e1) (e1)))) -> (~((op (e0) (e0)) = (e1))) -> ((~((op (e3) (e3)) = (e2)))\/((op (e3) (e2)) = (e3))) -> (~((op (e3) (e1)) = (op (e3) (e2)))) -> (~((op (e0) (e3)) = (op (e3) (e3)))) -> (~((op (e0) (e0)) = (e2))) -> (((op (e0) (e0)) = (e0))\/(((op (e0) (e0)) = (e1))\/(((op (e0) (e0)) = (e2))\/((op (e0) (e0)) = (e3))))) -> (((op (e3) (e3)) = (e0))\/(((op (e3) (e3)) = (e1))\/(((op (e3) (e3)) = (e2))\/((op (e3) (e3)) = (e3))))) -> (~((op (e0) (e0)) = (e0))) -> (~((e0) = (e2))) -> (((op (e0) (e0)) = (e2))\/(((op (e0) (e1)) = (e2))\/(((op (e0) (e2)) = (e2))\/((op (e0) (e3)) = (e2))))) -> (~((op (e3) (e1)) = (op (e3) (e3)))) -> ((~((op (e3) (e3)) = (e3)))\/((op (e3) (e3)) = (e3))) -> ((~((op (e3) (e3)) = (e1)))\/((op (e3) (e1)) = (e3))) -> False). % 15.16/15.33 do 0 intro. intros zenon_H10f zenon_H105 zenon_Hf1 zenon_Ha3 zenon_H2e zenon_H2f zenon_H2d zenon_Hd7 zenon_Hbb zenon_H109 zenon_H44 zenon_Hca zenon_H9e zenon_H121 zenon_Hce zenon_H11e zenon_Hc9 zenon_Hb1 zenon_H52 zenon_Ha7 zenon_H124 zenon_Hb7 zenon_H21 zenon_H23 zenon_H45 zenon_H10e zenon_H135 zenon_H36 zenon_H8f zenon_H12a zenon_H3b zenon_H20 zenon_H5e zenon_H8e zenon_H12d zenon_H10d zenon_H10c. % 15.16/15.33 apply (zenon_or_s _ _ zenon_H10f); [ zenon_intro zenon_H3c | zenon_intro zenon_Hba ]. % 15.16/15.33 apply (zenon_or_s _ _ zenon_H10c); [ zenon_intro zenon_H104 | zenon_intro zenon_H10a ]. % 15.16/15.33 apply (zenon_L100_); trivial. % 15.16/15.33 apply (zenon_L116_); trivial. % 15.16/15.33 apply (zenon_L83_); trivial. % 15.16/15.33 (* end of lemma zenon_L117_ *) % 15.16/15.33 assert (zenon_L118_ : (((op (e0) (e0)) = (e3))\/(((op (e0) (e1)) = (e3))\/(((op (e0) (e2)) = (e3))\/((op (e0) (e3)) = (e3))))) -> (~((op (e0) (e2)) = (op (e2) (e2)))) -> (~((e0) = (e3))) -> (~((op (e0) (e0)) = (e3))) -> (((op (e2) (e0)) = (e3))\/(((op (e2) (e1)) = (e3))\/(((op (e2) (e2)) = (e3))\/((op (e2) (e3)) = (e3))))) -> (~((e2) = (e3))) -> (~((op (e0) (e1)) = (op (e2) (e1)))) -> (~((op (e0) (e0)) = (e0))) -> (((op (e0) (e0)) = (e2))\/(((op (e0) (e1)) = (e2))\/(((op (e0) (e2)) = (e2))\/((op (e0) (e3)) = (e2))))) -> (~((op (e3) (e3)) = (e0))) -> (~((op (e3) (e3)) = (e1))) -> (~((op (e0) (e3)) = (op (e3) (e3)))) -> (((op (e3) (e3)) = (e0))\/(((op (e3) (e3)) = (e1))\/(((op (e3) (e3)) = (e2))\/((op (e3) (e3)) = (e3))))) -> (~((e1) = (e2))) -> (~((op (e1) (e1)) = (op (e1) (e2)))) -> ((op (e1) (e1)) = (e1)) -> (~((op (e2) (e2)) = (e1))) -> (~((e1) = (e3))) -> ((op (e3) (e2)) = (e3)) -> (((op (e0) (e2)) = (e1))\/(((op (e1) (e2)) = (e1))\/(((op (e2) (e2)) = (e1))\/((op (e3) (e2)) = (e1))))) -> (~((e0) = (e2))) -> (~((op (e0) (e0)) = (e2))) -> (((op (e0) (e0)) = (e1))\/(((op (e0) (e1)) = (e1))\/(((op (e0) (e2)) = (e1))\/((op (e0) (e3)) = (e1))))) -> (~((op (e0) (e2)) = (op (e0) (e3)))) -> (~((e0) = (e1))) -> (~((op (e0) (e1)) = (op (e1) (e1)))) -> (~((op (e0) (e0)) = (e1))) -> ((~((op (e3) (e3)) = (e0)))\/((op (e3) (e0)) = (e3))) -> (~((op (e3) (e0)) = (op (e3) (e2)))) -> (((op (e0) (e0)) = (e1))\/(((op (e1) (e0)) = (e1))\/(((op (e2) (e0)) = (e1))\/((op (e3) (e0)) = (e1))))) -> (~((op (e2) (e2)) = (e0))) -> (~((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 (e3) (e0)) = (op (e3) (e3)))) -> (~((op (e3) (e0)) = (op (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 (e1) (e1)) = (op (e1) (e3)))) -> (~((op (e1) (e1)) = (op (e2) (e1)))) -> ((op (e2) (e3)) = (e2)) -> (((op (e2) (e0)) = (e1))\/(((op (e2) (e1)) = (e1))\/(((op (e2) (e2)) = (e1))\/((op (e2) (e3)) = (e1))))) -> ((~((op (e3) (e3)) = (e2)))\/((op (e3) (e2)) = (e3))) -> (~((op (e3) (e1)) = (op (e3) (e2)))) -> (((op (e0) (e0)) = (e0))\/(((op (e0) (e0)) = (e1))\/(((op (e0) (e0)) = (e2))\/((op (e0) (e0)) = (e3))))) -> (~((op (e3) (e1)) = (op (e3) (e3)))) -> ((~((op (e3) (e3)) = (e3)))\/((op (e3) (e3)) = (e3))) -> ((~((op (e3) (e3)) = (e1)))\/((op (e3) (e1)) = (e3))) -> (((op (e0) (e0)) = (e0))\/(((op (e0) (e1)) = (e0))\/(((op (e0) (e2)) = (e0))\/((op (e0) (e3)) = (e0))))) -> False). % 15.16/15.33 do 0 intro. intros zenon_H58 zenon_H28 zenon_H4b zenon_H59 zenon_He6 zenon_H6a zenon_Hde zenon_H20 zenon_H8e zenon_H3c zenon_H104 zenon_H36 zenon_H3b zenon_Ha7 zenon_H116 zenon_H21 zenon_H52 zenon_Ha3 zenon_H106 zenon_H11b zenon_H5e zenon_H8f zenon_H44 zenon_Hc9 zenon_H9e zenon_H23 zenon_H45 zenon_H10f zenon_H105 zenon_Hf1 zenon_H2e zenon_H2f zenon_H2d zenon_Hd7 zenon_Hbb zenon_H109 zenon_H121 zenon_Hce zenon_H11e zenon_Hb1 zenon_H124 zenon_Hb7 zenon_H10e zenon_H135 zenon_H12a zenon_H12d zenon_H10d zenon_H10c zenon_H110. % 15.16/15.33 apply (zenon_or_s _ _ zenon_H10d); [ zenon_intro zenon_H3e | zenon_intro zenon_H42 ]. % 15.16/15.33 apply (zenon_or_s _ _ zenon_H110); [ zenon_intro zenon_H1f | zenon_intro zenon_H111 ]. % 15.16/15.33 exact (zenon_H20 zenon_H1f). % 15.16/15.33 apply (zenon_or_s _ _ zenon_H111); [ zenon_intro zenon_H49 | zenon_intro zenon_H112 ]. % 15.16/15.33 apply (zenon_L108_); trivial. % 15.16/15.33 apply (zenon_or_s _ _ zenon_H112); [ zenon_intro zenon_Hab | zenon_intro zenon_Hca ]. % 15.16/15.33 apply (zenon_L109_); trivial. % 15.16/15.33 apply (zenon_L117_); trivial. % 15.16/15.33 apply (zenon_L101_); trivial. % 15.16/15.33 (* end of lemma zenon_L118_ *) % 15.16/15.33 assert (zenon_L119_ : (~((op (e2) (e0)) = (op (e2) (e3)))) -> ((op (e2) (e0)) = (e2)) -> ((op (e2) (e3)) = (e2)) -> False). % 15.16/15.33 do 0 intro. intros zenon_Hce zenon_Hdd zenon_H124. % 15.16/15.33 cut (((op (e2) (e0)) = (e2)) = ((op (e2) (e0)) = (op (e2) (e3)))). % 15.16/15.33 intro zenon_D_pnotp. % 15.16/15.33 apply zenon_Hce. % 15.16/15.33 rewrite <- zenon_D_pnotp. % 15.16/15.33 exact zenon_Hdd. % 15.16/15.33 cut (((e2) = (op (e2) (e3)))); [idtac | apply NNPP; zenon_intro zenon_H137]. % 15.16/15.33 cut (((op (e2) (e0)) = (op (e2) (e0)))); [idtac | apply NNPP; zenon_intro zenon_Hd2]. % 15.16/15.33 congruence. % 15.16/15.33 apply zenon_Hd2. apply refl_equal. % 15.16/15.33 apply zenon_H137. apply sym_equal. exact zenon_H124. % 15.16/15.33 (* end of lemma zenon_L119_ *) % 15.16/15.33 assert (zenon_L120_ : ((op (e3) (e1)) = (e3)) -> ((op (e0) (e1)) = (e3)) -> (~((op (e0) (e1)) = (op (e3) (e1)))) -> False). % 15.16/15.33 do 0 intro. intros zenon_H10a zenon_H4a zenon_H138. % 15.16/15.33 elim (classic ((op (e3) (e1)) = (op (e3) (e1)))); [ zenon_intro zenon_H139 | zenon_intro zenon_H136 ]. % 15.16/15.33 cut (((op (e3) (e1)) = (op (e3) (e1))) = ((op (e0) (e1)) = (op (e3) (e1)))). % 15.16/15.33 intro zenon_D_pnotp. % 15.16/15.33 apply zenon_H138. % 15.16/15.33 rewrite <- zenon_D_pnotp. % 15.16/15.33 exact zenon_H139. % 15.16/15.33 cut (((op (e3) (e1)) = (op (e3) (e1)))); [idtac | apply NNPP; zenon_intro zenon_H136]. % 15.16/15.33 cut (((op (e3) (e1)) = (op (e0) (e1)))); [idtac | apply NNPP; zenon_intro zenon_H13a]. % 15.16/15.33 congruence. % 15.16/15.33 cut (((op (e3) (e1)) = (e3)) = ((op (e3) (e1)) = (op (e0) (e1)))). % 15.16/15.33 intro zenon_D_pnotp. % 15.16/15.33 apply zenon_H13a. % 15.16/15.33 rewrite <- zenon_D_pnotp. % 15.16/15.33 exact zenon_H10a. % 15.16/15.33 cut (((e3) = (op (e0) (e1)))); [idtac | apply NNPP; zenon_intro zenon_H13b]. % 15.16/15.33 cut (((op (e3) (e1)) = (op (e3) (e1)))); [idtac | apply NNPP; zenon_intro zenon_H136]. % 15.16/15.33 congruence. % 15.16/15.33 apply zenon_H136. apply refl_equal. % 15.16/15.33 apply zenon_H13b. apply sym_equal. exact zenon_H4a. % 15.16/15.33 apply zenon_H136. apply refl_equal. % 15.16/15.33 apply zenon_H136. apply refl_equal. % 15.16/15.33 (* end of lemma zenon_L120_ *) % 15.16/15.33 assert (zenon_L121_ : ((op (e3) (e1)) = (e3)) -> ((op (e2) (e1)) = (e3)) -> (~((op (e2) (e1)) = (op (e3) (e1)))) -> False). % 15.16/15.33 do 0 intro. intros zenon_H10a zenon_Hdf zenon_H13c. % 15.16/15.33 elim (classic ((op (e3) (e1)) = (op (e3) (e1)))); [ zenon_intro zenon_H139 | zenon_intro zenon_H136 ]. % 15.16/15.33 cut (((op (e3) (e1)) = (op (e3) (e1))) = ((op (e2) (e1)) = (op (e3) (e1)))). % 15.16/15.33 intro zenon_D_pnotp. % 15.16/15.33 apply zenon_H13c. % 15.16/15.33 rewrite <- zenon_D_pnotp. % 15.16/15.33 exact zenon_H139. % 15.16/15.33 cut (((op (e3) (e1)) = (op (e3) (e1)))); [idtac | apply NNPP; zenon_intro zenon_H136]. % 15.16/15.33 cut (((op (e3) (e1)) = (op (e2) (e1)))); [idtac | apply NNPP; zenon_intro zenon_H13d]. % 15.16/15.33 congruence. % 15.16/15.33 cut (((op (e3) (e1)) = (e3)) = ((op (e3) (e1)) = (op (e2) (e1)))). % 15.16/15.33 intro zenon_D_pnotp. % 15.16/15.33 apply zenon_H13d. % 15.16/15.33 rewrite <- zenon_D_pnotp. % 15.16/15.33 exact zenon_H10a. % 15.16/15.33 cut (((e3) = (op (e2) (e1)))); [idtac | apply NNPP; zenon_intro zenon_He0]. % 15.16/15.33 cut (((op (e3) (e1)) = (op (e3) (e1)))); [idtac | apply NNPP; zenon_intro zenon_H136]. % 15.16/15.33 congruence. % 15.16/15.33 apply zenon_H136. apply refl_equal. % 15.16/15.33 apply zenon_He0. apply sym_equal. exact zenon_Hdf. % 15.16/15.33 apply zenon_H136. apply refl_equal. % 15.16/15.33 apply zenon_H136. apply refl_equal. % 15.16/15.33 (* end of lemma zenon_L121_ *) % 15.16/15.33 assert (zenon_L122_ : ((op (e3) (e0)) = (e1)) -> ((op (e3) (e0)) = (e2)) -> (~((e1) = (e2))) -> False). % 15.16/15.33 do 0 intro. intros zenon_Hee zenon_He9 zenon_Ha7. % 15.16/15.33 elim (classic ((e2) = (e2))); [ zenon_intro zenon_H5f | zenon_intro zenon_H60 ]. % 15.16/15.33 cut (((e2) = (e2)) = ((e1) = (e2))). % 15.16/15.33 intro zenon_D_pnotp. % 15.16/15.33 apply zenon_Ha7. % 15.16/15.33 rewrite <- zenon_D_pnotp. % 15.16/15.33 exact zenon_H5f. % 15.16/15.33 cut (((e2) = (e2))); [idtac | apply NNPP; zenon_intro zenon_H60]. % 15.16/15.33 cut (((e2) = (e1))); [idtac | apply NNPP; zenon_intro zenon_Ha8]. % 15.16/15.33 congruence. % 15.16/15.33 cut (((op (e3) (e0)) = (e1)) = ((e2) = (e1))). % 15.16/15.33 intro zenon_D_pnotp. % 15.16/15.33 apply zenon_Ha8. % 15.16/15.33 rewrite <- zenon_D_pnotp. % 15.16/15.33 exact zenon_Hee. % 15.16/15.33 cut (((e1) = (e1))); [idtac | apply NNPP; zenon_intro zenon_Ha0]. % 15.16/15.33 cut (((op (e3) (e0)) = (e2))); [idtac | apply NNPP; zenon_intro zenon_Hea]. % 15.16/15.33 congruence. % 15.16/15.33 exact (zenon_Hea zenon_He9). % 15.16/15.33 apply zenon_Ha0. apply refl_equal. % 15.16/15.33 apply zenon_H60. apply refl_equal. % 15.16/15.33 apply zenon_H60. apply refl_equal. % 15.16/15.33 (* end of lemma zenon_L122_ *) % 15.16/15.33 assert (zenon_L123_ : (~((e1) = (e3))) -> ((op (e3) (e1)) = (e3)) -> ((op (e3) (e1)) = (e1)) -> False). % 15.16/15.33 do 0 intro. intros zenon_Ha3 zenon_H10a zenon_H13e. % 15.16/15.33 cut (((op (e3) (e1)) = (e3)) = ((e1) = (e3))). % 15.16/15.33 intro zenon_D_pnotp. % 15.16/15.33 apply zenon_Ha3. % 15.16/15.33 rewrite <- zenon_D_pnotp. % 15.16/15.33 exact zenon_H10a. % 15.16/15.33 cut (((e3) = (e3))); [idtac | apply NNPP; zenon_intro zenon_H4d]. % 15.16/15.33 cut (((op (e3) (e1)) = (e1))); [idtac | apply NNPP; zenon_intro zenon_H13f]. % 15.16/15.33 congruence. % 15.16/15.33 exact (zenon_H13f zenon_H13e). % 15.16/15.33 apply zenon_H4d. apply refl_equal. % 15.16/15.33 (* end of lemma zenon_L123_ *) % 15.16/15.33 assert (zenon_L124_ : (~((op (e0) (e2)) = (op (e3) (e2)))) -> ((op (e0) (e2)) = (e1)) -> ((op (e3) (e2)) = (e1)) -> False). % 15.16/15.33 do 0 intro. intros zenon_H140 zenon_H29 zenon_H119. % 15.16/15.33 cut (((op (e0) (e2)) = (e1)) = ((op (e0) (e2)) = (op (e3) (e2)))). % 15.16/15.33 intro zenon_D_pnotp. % 15.16/15.33 apply zenon_H140. % 15.16/15.33 rewrite <- zenon_D_pnotp. % 15.16/15.33 exact zenon_H29. % 15.16/15.33 cut (((e1) = (op (e3) (e2)))); [idtac | apply NNPP; zenon_intro zenon_H141]. % 15.16/15.33 cut (((op (e0) (e2)) = (op (e0) (e2)))); [idtac | apply NNPP; zenon_intro zenon_H2c]. % 15.16/15.33 congruence. % 15.16/15.33 apply zenon_H2c. apply refl_equal. % 15.16/15.33 apply zenon_H141. apply sym_equal. exact zenon_H119. % 15.16/15.33 (* end of lemma zenon_L124_ *) % 15.16/15.33 assert (zenon_L125_ : (~((op (e0) (e3)) = (op (e2) (e3)))) -> ((op (e0) (e3)) = (e3)) -> ((op (e2) (e3)) = (e3)) -> False). % 15.16/15.33 do 0 intro. intros zenon_Hb4 zenon_H53 zenon_He2. % 15.16/15.33 cut (((op (e0) (e3)) = (e3)) = ((op (e0) (e3)) = (op (e2) (e3)))). % 15.16/15.33 intro zenon_D_pnotp. % 15.16/15.33 apply zenon_Hb4. % 15.16/15.33 rewrite <- zenon_D_pnotp. % 15.16/15.33 exact zenon_H53. % 15.16/15.33 cut (((e3) = (op (e2) (e3)))); [idtac | apply NNPP; zenon_intro zenon_He5]. % 15.16/15.33 cut (((op (e0) (e3)) = (op (e0) (e3)))); [idtac | apply NNPP; zenon_intro zenon_H3a]. % 15.16/15.33 congruence. % 15.16/15.33 apply zenon_H3a. apply refl_equal. % 15.16/15.33 apply zenon_He5. apply sym_equal. exact zenon_He2. % 15.16/15.33 (* end of lemma zenon_L125_ *) % 15.16/15.33 assert (zenon_L126_ : (~((e0) = (e3))) -> ((op (e3) (e1)) = (e3)) -> ((op (e3) (e1)) = (e0)) -> False). % 15.16/15.33 do 0 intro. intros zenon_H4b zenon_H10a zenon_H142. % 15.16/15.33 cut (((op (e3) (e1)) = (e3)) = ((e0) = (e3))). % 15.16/15.33 intro zenon_D_pnotp. % 15.16/15.33 apply zenon_H4b. % 15.16/15.33 rewrite <- zenon_D_pnotp. % 15.16/15.33 exact zenon_H10a. % 15.16/15.33 cut (((e3) = (e3))); [idtac | apply NNPP; zenon_intro zenon_H4d]. % 15.16/15.33 cut (((op (e3) (e1)) = (e0))); [idtac | apply NNPP; zenon_intro zenon_H143]. % 15.16/15.33 congruence. % 15.16/15.33 exact (zenon_H143 zenon_H142). % 15.16/15.33 apply zenon_H4d. apply refl_equal. % 15.16/15.33 (* end of lemma zenon_L126_ *) % 15.16/15.33 assert (zenon_L127_ : (((op (e0) (e0)) = (e3))\/(((op (e0) (e1)) = (e3))\/(((op (e0) (e2)) = (e3))\/((op (e0) (e3)) = (e3))))) -> (~((op (e0) (e0)) = (e3))) -> (~((op (e0) (e1)) = (op (e3) (e1)))) -> (((op (e0) (e1)) = (e0))\/(((op (e1) (e1)) = (e0))\/(((op (e2) (e1)) = (e0))\/((op (e3) (e1)) = (e0))))) -> (~((e0) = (e2))) -> ((op (e0) (e1)) = (e2)) -> (~((op (e1) (e1)) = (e0))) -> (~((op (e0) (e3)) = (op (e2) (e3)))) -> (((op (e3) (e0)) = (e1))\/(((op (e3) (e1)) = (e1))\/(((op (e3) (e2)) = (e1))\/((op (e3) (e3)) = (e1))))) -> (~((e1) = (e2))) -> ((op (e3) (e0)) = (e2)) -> (~((e1) = (e3))) -> ((op (e0) (e2)) = (e1)) -> (~((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 (e1) (e1)) = (e1)) -> (~((op (e1) (e1)) = (op (e2) (e1)))) -> (~((op (e2) (e2)) = (e1))) -> ((op (e2) (e3)) = (e2)) -> (((op (e2) (e0)) = (e3))\/(((op (e2) (e1)) = (e3))\/(((op (e2) (e2)) = (e3))\/((op (e2) (e3)) = (e3))))) -> (~((e0) = (e3))) -> ((op (e3) (e1)) = (e3)) -> False). % 15.16/15.33 do 0 intro. intros zenon_H58 zenon_H59 zenon_H138 zenon_H144 zenon_H5e zenon_H5d zenon_H145 zenon_Hb4 zenon_H146 zenon_Ha7 zenon_He9 zenon_Ha3 zenon_H29 zenon_H140 zenon_H13c zenon_Hb7 zenon_H21 zenon_Hb1 zenon_H52 zenon_H124 zenon_He6 zenon_H4b zenon_H10a. % 15.16/15.33 apply (zenon_or_s _ _ zenon_H58); [ zenon_intro zenon_H5b | zenon_intro zenon_H5a ]. % 15.16/15.33 exact (zenon_H59 zenon_H5b). % 15.16/15.33 apply (zenon_or_s _ _ zenon_H5a); [ zenon_intro zenon_H4a | zenon_intro zenon_H5c ]. % 15.16/15.33 apply (zenon_L120_); trivial. % 15.16/15.33 apply (zenon_or_s _ _ zenon_H5c); [ zenon_intro zenon_H50 | zenon_intro zenon_H53 ]. % 15.16/15.33 apply (zenon_L29_); trivial. % 15.16/15.33 apply (zenon_or_s _ _ zenon_H144); [ zenon_intro zenon_H49 | zenon_intro zenon_H147 ]. % 15.16/15.33 apply (zenon_L14_); trivial. % 15.16/15.33 apply (zenon_or_s _ _ zenon_H147); [ zenon_intro zenon_H149 | zenon_intro zenon_H148 ]. % 15.16/15.33 exact (zenon_H145 zenon_H149). % 15.16/15.33 apply (zenon_or_s _ _ zenon_H148); [ zenon_intro zenon_H14a | zenon_intro zenon_H142 ]. % 15.16/15.33 apply (zenon_or_s _ _ zenon_He6); [ zenon_intro zenon_Haf | zenon_intro zenon_He7 ]. % 15.16/15.33 apply (zenon_L96_); trivial. % 15.16/15.33 apply (zenon_or_s _ _ zenon_He7); [ zenon_intro zenon_Hdf | zenon_intro zenon_He8 ]. % 15.16/15.33 apply (zenon_L121_); trivial. % 15.16/15.33 apply (zenon_or_s _ _ zenon_He8); [ zenon_intro zenon_H34 | zenon_intro zenon_He2 ]. % 15.16/15.33 apply (zenon_or_s _ _ zenon_H146); [ zenon_intro zenon_Hee | zenon_intro zenon_H14b ]. % 15.16/15.33 apply (zenon_L122_); trivial. % 15.16/15.33 apply (zenon_or_s _ _ zenon_H14b); [ zenon_intro zenon_H13e | zenon_intro zenon_H14c ]. % 15.16/15.33 apply (zenon_L123_); trivial. % 15.16/15.33 apply (zenon_or_s _ _ zenon_H14c); [ zenon_intro zenon_H119 | zenon_intro zenon_H38 ]. % 15.16/15.33 apply (zenon_L124_); trivial. % 15.16/15.33 apply (zenon_notand_s _ _ ax16); [ zenon_intro zenon_H14e | zenon_intro zenon_H14d ]. % 15.16/15.33 elim (classic ((op (op (e2) (e2)) (op (e2) (e2))) = (op (op (e2) (e2)) (op (e2) (e2))))); [ zenon_intro zenon_Hfa | zenon_intro zenon_Hfb ]. % 15.16/15.33 cut (((op (op (e2) (e2)) (op (e2) (e2))) = (op (op (e2) (e2)) (op (e2) (e2)))) = ((e1) = (op (op (e2) (e2)) (op (e2) (e2))))). % 15.16/15.33 intro zenon_D_pnotp. % 15.16/15.33 apply zenon_H14e. % 15.16/15.33 rewrite <- zenon_D_pnotp. % 15.16/15.33 exact zenon_Hfa. % 15.16/15.33 cut (((op (op (e2) (e2)) (op (e2) (e2))) = (op (op (e2) (e2)) (op (e2) (e2))))); [idtac | apply NNPP; zenon_intro zenon_Hfb]. % 15.16/15.33 cut (((op (op (e2) (e2)) (op (e2) (e2))) = (e1))); [idtac | apply NNPP; zenon_intro zenon_H14f]. % 15.16/15.33 congruence. % 15.16/15.33 cut (((op (e3) (e3)) = (e1)) = ((op (op (e2) (e2)) (op (e2) (e2))) = (e1))). % 15.16/15.33 intro zenon_D_pnotp. % 15.16/15.33 apply zenon_H14f. % 15.16/15.33 rewrite <- zenon_D_pnotp. % 15.16/15.33 exact zenon_H38. % 15.16/15.33 cut (((e1) = (e1))); [idtac | apply NNPP; zenon_intro zenon_Ha0]. % 15.16/15.33 cut (((op (e3) (e3)) = (op (op (e2) (e2)) (op (e2) (e2))))); [idtac | apply NNPP; zenon_intro zenon_Hfd]. % 15.16/15.33 congruence. % 15.16/15.33 elim (classic ((op (op (e2) (e2)) (op (e2) (e2))) = (op (op (e2) (e2)) (op (e2) (e2))))); [ zenon_intro zenon_Hfa | zenon_intro zenon_Hfb ]. % 15.16/15.33 cut (((op (op (e2) (e2)) (op (e2) (e2))) = (op (op (e2) (e2)) (op (e2) (e2)))) = ((op (e3) (e3)) = (op (op (e2) (e2)) (op (e2) (e2))))). % 15.16/15.33 intro zenon_D_pnotp. % 15.16/15.33 apply zenon_Hfd. % 15.16/15.33 rewrite <- zenon_D_pnotp. % 15.16/15.33 exact zenon_Hfa. % 15.16/15.33 cut (((op (op (e2) (e2)) (op (e2) (e2))) = (op (op (e2) (e2)) (op (e2) (e2))))); [idtac | apply NNPP; zenon_intro zenon_Hfb]. % 15.16/15.33 cut (((op (op (e2) (e2)) (op (e2) (e2))) = (op (e3) (e3)))); [idtac | apply NNPP; zenon_intro zenon_Hf7]. % 15.16/15.33 congruence. % 15.16/15.33 apply (zenon_L75_); trivial. % 15.16/15.33 apply zenon_Hfb. apply refl_equal. % 15.16/15.33 apply zenon_Hfb. apply refl_equal. % 15.16/15.33 apply zenon_Ha0. apply refl_equal. % 15.16/15.33 apply zenon_Hfb. apply refl_equal. % 15.16/15.33 apply zenon_Hfb. apply refl_equal. % 15.16/15.33 apply (zenon_notand_s _ _ zenon_H14d); [ zenon_intro zenon_H51 | zenon_intro zenon_H150 ]. % 15.16/15.33 apply zenon_H51. apply sym_equal. exact zenon_H34. % 15.16/15.33 elim (classic ((op (e2) (op (op (e2) (e2)) (op (e2) (e2)))) = (op (e2) (op (op (e2) (e2)) (op (e2) (e2)))))); [ zenon_intro zenon_Hff | zenon_intro zenon_H100 ]. % 15.16/15.33 cut (((op (e2) (op (op (e2) (e2)) (op (e2) (e2)))) = (op (e2) (op (op (e2) (e2)) (op (e2) (e2))))) = ((e0) = (op (e2) (op (op (e2) (e2)) (op (e2) (e2)))))). % 15.16/15.33 intro zenon_D_pnotp. % 15.16/15.33 apply zenon_H150. % 15.16/15.33 rewrite <- zenon_D_pnotp. % 15.16/15.33 exact zenon_Hff. % 15.16/15.33 cut (((op (e2) (op (op (e2) (e2)) (op (e2) (e2)))) = (op (e2) (op (op (e2) (e2)) (op (e2) (e2)))))); [idtac | apply NNPP; zenon_intro zenon_H100]. % 15.16/15.33 cut (((op (e2) (op (op (e2) (e2)) (op (e2) (e2)))) = (e0))); [idtac | apply NNPP; zenon_intro zenon_H151]. % 15.16/15.33 congruence. % 15.16/15.33 cut (((op (e2) (e1)) = (e0)) = ((op (e2) (op (op (e2) (e2)) (op (e2) (e2)))) = (e0))). % 15.16/15.33 intro zenon_D_pnotp. % 15.16/15.33 apply zenon_H151. % 15.16/15.33 rewrite <- zenon_D_pnotp. % 15.16/15.33 exact zenon_H14a. % 15.16/15.33 cut (((e0) = (e0))); [idtac | apply NNPP; zenon_intro zenon_H1d]. % 15.16/15.33 cut (((op (e2) (e1)) = (op (e2) (op (op (e2) (e2)) (op (e2) (e2)))))); [idtac | apply NNPP; zenon_intro zenon_H152]. % 15.16/15.33 congruence. % 15.16/15.33 elim (classic ((op (e2) (op (op (e2) (e2)) (op (e2) (e2)))) = (op (e2) (op (op (e2) (e2)) (op (e2) (e2)))))); [ zenon_intro zenon_Hff | zenon_intro zenon_H100 ]. % 15.16/15.33 cut (((op (e2) (op (op (e2) (e2)) (op (e2) (e2)))) = (op (e2) (op (op (e2) (e2)) (op (e2) (e2))))) = ((op (e2) (e1)) = (op (e2) (op (op (e2) (e2)) (op (e2) (e2)))))). % 15.16/15.33 intro zenon_D_pnotp. % 15.16/15.33 apply zenon_H152. % 15.16/15.33 rewrite <- zenon_D_pnotp. % 15.16/15.33 exact zenon_Hff. % 15.16/15.33 cut (((op (e2) (op (op (e2) (e2)) (op (e2) (e2)))) = (op (e2) (op (op (e2) (e2)) (op (e2) (e2)))))); [idtac | apply NNPP; zenon_intro zenon_H100]. % 15.16/15.33 cut (((op (e2) (op (op (e2) (e2)) (op (e2) (e2)))) = (op (e2) (e1)))); [idtac | apply NNPP; zenon_intro zenon_H153]. % 15.16/15.33 congruence. % 15.16/15.33 cut (((op (op (e2) (e2)) (op (e2) (e2))) = (e1))); [idtac | apply NNPP; zenon_intro zenon_H14f]. % 15.16/15.33 cut (((e2) = (e2))); [idtac | apply NNPP; zenon_intro zenon_H60]. % 15.16/15.33 congruence. % 15.16/15.33 apply zenon_H60. apply refl_equal. % 15.16/15.33 cut (((op (e3) (e3)) = (e1)) = ((op (op (e2) (e2)) (op (e2) (e2))) = (e1))). % 15.16/15.33 intro zenon_D_pnotp. % 15.16/15.33 apply zenon_H14f. % 15.16/15.33 rewrite <- zenon_D_pnotp. % 15.16/15.33 exact zenon_H38. % 15.16/15.33 cut (((e1) = (e1))); [idtac | apply NNPP; zenon_intro zenon_Ha0]. % 15.16/15.33 cut (((op (e3) (e3)) = (op (op (e2) (e2)) (op (e2) (e2))))); [idtac | apply NNPP; zenon_intro zenon_Hfd]. % 15.16/15.33 congruence. % 15.16/15.33 elim (classic ((op (op (e2) (e2)) (op (e2) (e2))) = (op (op (e2) (e2)) (op (e2) (e2))))); [ zenon_intro zenon_Hfa | zenon_intro zenon_Hfb ]. % 15.16/15.33 cut (((op (op (e2) (e2)) (op (e2) (e2))) = (op (op (e2) (e2)) (op (e2) (e2)))) = ((op (e3) (e3)) = (op (op (e2) (e2)) (op (e2) (e2))))). % 15.16/15.33 intro zenon_D_pnotp. % 15.16/15.33 apply zenon_Hfd. % 15.16/15.33 rewrite <- zenon_D_pnotp. % 15.16/15.33 exact zenon_Hfa. % 15.16/15.33 cut (((op (op (e2) (e2)) (op (e2) (e2))) = (op (op (e2) (e2)) (op (e2) (e2))))); [idtac | apply NNPP; zenon_intro zenon_Hfb]. % 15.16/15.33 cut (((op (op (e2) (e2)) (op (e2) (e2))) = (op (e3) (e3)))); [idtac | apply NNPP; zenon_intro zenon_Hf7]. % 15.16/15.33 congruence. % 15.16/15.33 apply (zenon_L75_); trivial. % 15.16/15.33 apply zenon_Hfb. apply refl_equal. % 15.16/15.33 apply zenon_Hfb. apply refl_equal. % 15.16/15.33 apply zenon_Ha0. apply refl_equal. % 15.16/15.33 apply zenon_H100. apply refl_equal. % 15.16/15.33 apply zenon_H100. apply refl_equal. % 15.16/15.33 apply zenon_H1d. apply refl_equal. % 15.16/15.33 apply zenon_H100. apply refl_equal. % 15.16/15.33 apply zenon_H100. apply refl_equal. % 15.16/15.33 apply (zenon_L125_); trivial. % 15.16/15.33 apply (zenon_L126_); trivial. % 15.16/15.33 (* end of lemma zenon_L127_ *) % 15.16/15.33 assert (zenon_L128_ : ((op (e0) (e3)) = (e2)) -> ((op (e0) (e3)) = (e3)) -> (~((e2) = (e3))) -> False). % 15.16/15.33 do 0 intro. intros zenon_H81 zenon_H53 zenon_H6a. % 15.16/15.33 elim (classic ((e3) = (e3))); [ zenon_intro zenon_H4c | zenon_intro zenon_H4d ]. % 15.16/15.33 cut (((e3) = (e3)) = ((e2) = (e3))). % 15.16/15.33 intro zenon_D_pnotp. % 15.16/15.33 apply zenon_H6a. % 15.16/15.33 rewrite <- zenon_D_pnotp. % 15.16/15.33 exact zenon_H4c. % 15.16/15.33 cut (((e3) = (e3))); [idtac | apply NNPP; zenon_intro zenon_H4d]. % 15.16/15.33 cut (((e3) = (e2))); [idtac | apply NNPP; zenon_intro zenon_H6b]. % 15.16/15.33 congruence. % 15.16/15.33 cut (((op (e0) (e3)) = (e2)) = ((e3) = (e2))). % 15.16/15.33 intro zenon_D_pnotp. % 15.16/15.33 apply zenon_H6b. % 15.16/15.33 rewrite <- zenon_D_pnotp. % 15.16/15.33 exact zenon_H81. % 15.16/15.33 cut (((e2) = (e2))); [idtac | apply NNPP; zenon_intro zenon_H60]. % 15.16/15.33 cut (((op (e0) (e3)) = (e3))); [idtac | apply NNPP; zenon_intro zenon_Ha6]. % 15.16/15.33 congruence. % 15.16/15.33 exact (zenon_Ha6 zenon_H53). % 15.16/15.33 apply zenon_H60. apply refl_equal. % 15.16/15.33 apply zenon_H4d. apply refl_equal. % 15.16/15.33 apply zenon_H4d. apply refl_equal. % 15.16/15.33 (* end of lemma zenon_L128_ *) % 15.16/15.33 assert (zenon_L129_ : (((op (e0) (e0)) = (e3))\/(((op (e0) (e1)) = (e3))\/(((op (e0) (e2)) = (e3))\/((op (e0) (e3)) = (e3))))) -> (~((op (e0) (e0)) = (e3))) -> (~((op (e0) (e1)) = (op (e3) (e1)))) -> ((op (e3) (e1)) = (e3)) -> (~((e1) = (e3))) -> ((op (e0) (e2)) = (e1)) -> ((op (e0) (e3)) = (e2)) -> (~((e2) = (e3))) -> False). % 15.16/15.33 do 0 intro. intros zenon_H58 zenon_H59 zenon_H138 zenon_H10a zenon_Ha3 zenon_H29 zenon_H81 zenon_H6a. % 15.16/15.33 apply (zenon_or_s _ _ zenon_H58); [ zenon_intro zenon_H5b | zenon_intro zenon_H5a ]. % 15.16/15.33 exact (zenon_H59 zenon_H5b). % 15.16/15.33 apply (zenon_or_s _ _ zenon_H5a); [ zenon_intro zenon_H4a | zenon_intro zenon_H5c ]. % 15.16/15.33 apply (zenon_L120_); trivial. % 15.16/15.33 apply (zenon_or_s _ _ zenon_H5c); [ zenon_intro zenon_H50 | zenon_intro zenon_H53 ]. % 15.16/15.33 apply (zenon_L29_); trivial. % 15.16/15.33 apply (zenon_L128_); trivial. % 15.16/15.33 (* end of lemma zenon_L129_ *) % 15.16/15.33 assert (zenon_L130_ : ((~((op (e3) (e3)) = (e2)))\/((op (e3) (e2)) = (e3))) -> (~((op (e3) (e1)) = (op (e3) (e2)))) -> (((op (e0) (e0)) = (e1))\/(((op (e0) (e1)) = (e1))\/(((op (e0) (e2)) = (e1))\/((op (e0) (e3)) = (e1))))) -> (~((op (e3) (e3)) = (e0))) -> (~((op (e0) (e3)) = (op (e3) (e3)))) -> (((op (e3) (e3)) = (e0))\/(((op (e3) (e3)) = (e1))\/(((op (e3) (e3)) = (e2))\/((op (e3) (e3)) = (e3))))) -> (~((op (e0) (e0)) = (e2))) -> (((op (e0) (e0)) = (e2))\/(((op (e1) (e0)) = (e2))\/(((op (e2) (e0)) = (e2))\/((op (e3) (e0)) = (e2))))) -> (~((op (e0) (e1)) = (op (e3) (e1)))) -> (((op (e0) (e1)) = (e0))\/(((op (e1) (e1)) = (e0))\/(((op (e2) (e1)) = (e0))\/((op (e3) (e1)) = (e0))))) -> (~((e0) = (e3))) -> (~((op (e2) (e1)) = (op (e3) (e1)))) -> (((op (e3) (e0)) = (e1))\/(((op (e3) (e1)) = (e1))\/(((op (e3) (e2)) = (e1))\/((op (e3) (e3)) = (e1))))) -> (~((op (e0) (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 (e1) (e1)) = (e0))) -> (~((e0) = (e2))) -> (((op (e0) (e0)) = (e3))\/(((op (e0) (e1)) = (e3))\/(((op (e0) (e2)) = (e3))\/((op (e0) (e3)) = (e3))))) -> (~((op (e2) (e0)) = (op (e2) (e3)))) -> (~((op (e0) (e0)) = (e3))) -> (~((e2) = (e3))) -> (((op (e2) (e0)) = (e1))\/(((op (e2) (e1)) = (e1))\/(((op (e2) (e2)) = (e1))\/((op (e2) (e3)) = (e1))))) -> ((op (e2) (e3)) = (e2)) -> (~((e1) = (e2))) -> (~((op (e2) (e2)) = (e1))) -> (~((op (e1) (e1)) = (op (e2) (e1)))) -> (~((e1) = (e3))) -> (~((op (e3) (e0)) = (op (e3) (e1)))) -> ((op (e3) (e1)) = (e3)) -> (((op (e0) (e0)) = (e3))\/(((op (e1) (e0)) = (e3))\/(((op (e2) (e0)) = (e3))\/((op (e3) (e0)) = (e3))))) -> (((op (e0) (e0)) = (e2))\/(((op (e0) (e1)) = (e2))\/(((op (e0) (e2)) = (e2))\/((op (e0) (e3)) = (e2))))) -> ((op (e1) (e1)) = (e1)) -> (~((op (e0) (e1)) = (op (e1) (e1)))) -> (~((op (e0) (e0)) = (e1))) -> (~((op (e3) (e1)) = (op (e3) (e3)))) -> ((~((op (e3) (e3)) = (e3)))\/((op (e3) (e3)) = (e3))) -> False). % 15.16/15.33 do 0 intro. intros zenon_H10e zenon_H135 zenon_H44 zenon_H3c zenon_H36 zenon_H3b zenon_H8f zenon_Heb zenon_H138 zenon_H144 zenon_H4b zenon_H13c zenon_H146 zenon_H140 zenon_Hb4 zenon_He6 zenon_H145 zenon_H5e zenon_H58 zenon_Hce zenon_H59 zenon_H6a zenon_Hb7 zenon_H124 zenon_Ha7 zenon_H52 zenon_Hb1 zenon_Ha3 zenon_H109 zenon_H10a zenon_Hbe zenon_H8e zenon_H21 zenon_H23 zenon_H45 zenon_H12d zenon_H10d. % 15.16/15.33 apply (zenon_or_s _ _ zenon_H10e); [ zenon_intro zenon_H3d | zenon_intro zenon_H106 ]. % 15.16/15.33 apply (zenon_or_s _ _ zenon_H10d); [ zenon_intro zenon_H3e | zenon_intro zenon_H42 ]. % 15.16/15.33 apply (zenon_or_s _ _ zenon_H44); [ zenon_intro zenon_H47 | zenon_intro zenon_H46 ]. % 15.16/15.33 exact (zenon_H45 zenon_H47). % 15.16/15.33 apply (zenon_or_s _ _ zenon_H46); [ zenon_intro zenon_H22 | zenon_intro zenon_H48 ]. % 15.16/15.33 apply (zenon_L3_); trivial. % 15.16/15.33 apply (zenon_or_s _ _ zenon_H48); [ zenon_intro zenon_H29 | zenon_intro zenon_H37 ]. % 15.16/15.33 apply (zenon_or_s _ _ zenon_H8e); [ zenon_intro zenon_H92 | zenon_intro zenon_H91 ]. % 15.16/15.33 exact (zenon_H8f zenon_H92). % 15.16/15.33 apply (zenon_or_s _ _ zenon_H91); [ zenon_intro zenon_H5d | zenon_intro zenon_H93 ]. % 15.16/15.33 apply (zenon_or_s _ _ zenon_Heb); [ zenon_intro zenon_H92 | zenon_intro zenon_Hec ]. % 15.16/15.33 exact (zenon_H8f zenon_H92). % 15.16/15.33 apply (zenon_or_s _ _ zenon_Hec); [ zenon_intro zenon_H68 | zenon_intro zenon_Hed ]. % 15.16/15.33 apply (zenon_or_s _ _ zenon_Hbe); [ zenon_intro zenon_H5b | zenon_intro zenon_Hbf ]. % 15.16/15.33 exact (zenon_H59 zenon_H5b). % 15.16/15.33 apply (zenon_or_s _ _ zenon_Hbf); [ zenon_intro zenon_H69 | zenon_intro zenon_Hc0 ]. % 15.16/15.33 apply (zenon_L17_); trivial. % 15.16/15.33 apply (zenon_or_s _ _ zenon_Hc0); [ zenon_intro zenon_Haf | zenon_intro zenon_Hba ]. % 15.16/15.33 apply (zenon_L96_); trivial. % 15.16/15.33 apply (zenon_L82_); trivial. % 15.16/15.33 apply (zenon_or_s _ _ zenon_Hed); [ zenon_intro zenon_Hdd | zenon_intro zenon_He9 ]. % 15.16/15.33 apply (zenon_L119_); trivial. % 15.16/15.33 apply (zenon_L127_); trivial. % 15.16/15.33 apply (zenon_or_s _ _ zenon_H93); [ zenon_intro zenon_H63 | zenon_intro zenon_H81 ]. % 15.16/15.33 apply (zenon_L104_); trivial. % 15.16/15.33 apply (zenon_L129_); trivial. % 15.16/15.33 apply (zenon_L7_); trivial. % 15.16/15.33 apply (zenon_L102_); trivial. % 15.16/15.33 apply (zenon_L115_); trivial. % 15.16/15.33 (* end of lemma zenon_L130_ *) % 15.16/15.33 assert (zenon_L131_ : (((op (e0) (e0)) = (e2))\/(((op (e0) (e1)) = (e2))\/(((op (e0) (e2)) = (e2))\/((op (e0) (e3)) = (e2))))) -> (~((op (e0) (e0)) = (e2))) -> (~((e0) = (e2))) -> ((op (e0) (e1)) = (e0)) -> (~((op (e0) (e2)) = (op (e2) (e2)))) -> ((op (e2) (e2)) = (e2)) -> (((op (e3) (e3)) = (e0))\/(((op (e3) (e3)) = (e1))\/(((op (e3) (e3)) = (e2))\/((op (e3) (e3)) = (e3))))) -> (~((op (e3) (e3)) = (e0))) -> (~((op (e3) (e3)) = (e1))) -> (~((op (e0) (e3)) = (op (e3) (e3)))) -> (~((op (e3) (e3)) = (e3))) -> False). % 15.16/15.33 do 0 intro. intros zenon_H8e zenon_H8f zenon_H5e zenon_H49 zenon_H28 zenon_H35 zenon_H3b zenon_H3c zenon_H104 zenon_H36 zenon_H3e. % 15.16/15.33 apply (zenon_or_s _ _ zenon_H8e); [ zenon_intro zenon_H92 | zenon_intro zenon_H91 ]. % 15.16/15.33 exact (zenon_H8f zenon_H92). % 15.16/15.33 apply (zenon_or_s _ _ zenon_H91); [ zenon_intro zenon_H5d | zenon_intro zenon_H93 ]. % 15.16/15.33 apply (zenon_L14_); trivial. % 15.16/15.33 apply (zenon_or_s _ _ zenon_H93); [ zenon_intro zenon_H63 | zenon_intro zenon_H81 ]. % 15.16/15.33 apply (zenon_L15_); trivial. % 15.16/15.33 apply (zenon_L107_); trivial. % 15.16/15.33 (* end of lemma zenon_L131_ *) % 15.16/15.33 assert (zenon_L132_ : (((op (e0) (e0)) = (e1))\/(((op (e0) (e1)) = (e1))\/(((op (e0) (e2)) = (e1))\/((op (e0) (e3)) = (e1))))) -> (~((op (e0) (e0)) = (e1))) -> (~((op (e0) (e1)) = (op (e1) (e1)))) -> ((op (e1) (e1)) = (e1)) -> (~((e0) = (e1))) -> ((op (e0) (e2)) = (e0)) -> (((op (e3) (e3)) = (e0))\/(((op (e3) (e3)) = (e1))\/(((op (e3) (e3)) = (e2))\/((op (e3) (e3)) = (e3))))) -> (~((op (e3) (e3)) = (e0))) -> (~((op (e0) (e3)) = (op (e3) (e3)))) -> (~((op (e3) (e3)) = (e2))) -> (~((op (e3) (e3)) = (e3))) -> False). % 15.16/15.33 do 0 intro. intros zenon_H44 zenon_H45 zenon_H23 zenon_H21 zenon_H9e zenon_Hab zenon_H3b zenon_H3c zenon_H36 zenon_H3d zenon_H3e. % 15.16/15.33 apply (zenon_or_s _ _ zenon_H44); [ zenon_intro zenon_H47 | zenon_intro zenon_H46 ]. % 15.16/15.33 exact (zenon_H45 zenon_H47). % 15.16/15.33 apply (zenon_or_s _ _ zenon_H46); [ zenon_intro zenon_H22 | zenon_intro zenon_H48 ]. % 15.16/15.33 apply (zenon_L3_); trivial. % 15.16/15.33 apply (zenon_or_s _ _ zenon_H48); [ zenon_intro zenon_H29 | zenon_intro zenon_H37 ]. % 15.16/15.33 apply (zenon_L37_); trivial. % 15.16/15.33 apply (zenon_L7_); trivial. % 15.16/15.33 (* end of lemma zenon_L132_ *) % 15.16/15.33 assert (zenon_L133_ : (~((op (e2) (e0)) = (op (e2) (e1)))) -> ((op (e2) (e0)) = (e0)) -> ((op (e2) (e1)) = (e0)) -> False). % 15.16/15.33 do 0 intro. intros zenon_H154 zenon_Hcf zenon_H14a. % 15.16/15.33 cut (((op (e2) (e0)) = (e0)) = ((op (e2) (e0)) = (op (e2) (e1)))). % 15.16/15.33 intro zenon_D_pnotp. % 15.16/15.33 apply zenon_H154. % 15.16/15.33 rewrite <- zenon_D_pnotp. % 15.16/15.33 exact zenon_Hcf. % 15.16/15.33 cut (((e0) = (op (e2) (e1)))); [idtac | apply NNPP; zenon_intro zenon_H155]. % 15.16/15.33 cut (((op (e2) (e0)) = (op (e2) (e0)))); [idtac | apply NNPP; zenon_intro zenon_Hd2]. % 15.16/15.33 congruence. % 15.16/15.33 apply zenon_Hd2. apply refl_equal. % 15.16/15.33 apply zenon_H155. apply sym_equal. exact zenon_H14a. % 15.16/15.33 (* end of lemma zenon_L133_ *) % 15.16/15.33 assert (zenon_L134_ : ((op (e2) (e2)) = (e2)) -> ((op (e2) (e1)) = (e2)) -> (~((op (e2) (e1)) = (op (e2) (e2)))) -> False). % 15.16/15.33 do 0 intro. intros zenon_H35 zenon_H156 zenon_H157. % 15.16/15.33 elim (classic ((op (e2) (e2)) = (op (e2) (e2)))); [ zenon_intro zenon_H64 | zenon_intro zenon_H65 ]. % 15.16/15.33 cut (((op (e2) (e2)) = (op (e2) (e2))) = ((op (e2) (e1)) = (op (e2) (e2)))). % 15.16/15.33 intro zenon_D_pnotp. % 15.16/15.33 apply zenon_H157. % 15.16/15.33 rewrite <- zenon_D_pnotp. % 15.16/15.33 exact zenon_H64. % 15.16/15.33 cut (((op (e2) (e2)) = (op (e2) (e2)))); [idtac | apply NNPP; zenon_intro zenon_H65]. % 15.16/15.33 cut (((op (e2) (e2)) = (op (e2) (e1)))); [idtac | apply NNPP; zenon_intro zenon_H158]. % 15.16/15.33 congruence. % 15.16/15.33 cut (((op (e2) (e2)) = (e2)) = ((op (e2) (e2)) = (op (e2) (e1)))). % 15.16/15.33 intro zenon_D_pnotp. % 15.16/15.33 apply zenon_H158. % 15.16/15.33 rewrite <- zenon_D_pnotp. % 15.16/15.33 exact zenon_H35. % 15.16/15.33 cut (((e2) = (op (e2) (e1)))); [idtac | apply NNPP; zenon_intro zenon_H159]. % 15.16/15.33 cut (((op (e2) (e2)) = (op (e2) (e2)))); [idtac | apply NNPP; zenon_intro zenon_H65]. % 15.16/15.33 congruence. % 15.16/15.33 apply zenon_H65. apply refl_equal. % 15.16/15.33 apply zenon_H159. apply sym_equal. exact zenon_H156. % 15.16/15.33 apply zenon_H65. apply refl_equal. % 15.16/15.33 apply zenon_H65. apply refl_equal. % 15.16/15.33 (* end of lemma zenon_L134_ *) % 15.16/15.33 assert (zenon_L135_ : (((op (e2) (e1)) = (e0))\/(((op (e2) (e1)) = (e1))\/(((op (e2) (e1)) = (e2))\/((op (e2) (e1)) = (e3))))) -> ((op (e2) (e0)) = (e0)) -> (~((op (e2) (e0)) = (op (e2) (e1)))) -> ((op (e1) (e1)) = (e1)) -> (~((op (e1) (e1)) = (op (e2) (e1)))) -> (~((op (e2) (e1)) = (op (e2) (e2)))) -> ((op (e2) (e2)) = (e2)) -> (~((op (e0) (e1)) = (op (e2) (e1)))) -> ((op (e0) (e1)) = (e3)) -> False). % 15.16/15.33 do 0 intro. intros zenon_H15a zenon_Hcf zenon_H154 zenon_H21 zenon_Hb1 zenon_H157 zenon_H35 zenon_Hde zenon_H4a. % 15.16/15.33 apply (zenon_or_s _ _ zenon_H15a); [ zenon_intro zenon_H14a | zenon_intro zenon_H15b ]. % 15.16/15.33 apply (zenon_L133_); trivial. % 15.16/15.33 apply (zenon_or_s _ _ zenon_H15b); [ zenon_intro zenon_Hb2 | zenon_intro zenon_H15c ]. % 15.16/15.33 apply (zenon_L40_); trivial. % 15.16/15.33 apply (zenon_or_s _ _ zenon_H15c); [ zenon_intro zenon_H156 | zenon_intro zenon_Hdf ]. % 15.16/15.33 apply (zenon_L134_); trivial. % 15.16/15.33 apply (zenon_L65_); trivial. % 15.16/15.33 (* end of lemma zenon_L135_ *) % 15.16/15.33 assert (zenon_L136_ : (~((op (e0) (e2)) = (op (e1) (e2)))) -> ((op (e0) (e2)) = (e0)) -> ((op (e1) (e2)) = (e0)) -> False). % 15.16/15.33 do 0 intro. intros zenon_H87 zenon_Hab zenon_H15d. % 15.16/15.33 cut (((op (e0) (e2)) = (e0)) = ((op (e0) (e2)) = (op (e1) (e2)))). % 15.16/15.33 intro zenon_D_pnotp. % 15.16/15.33 apply zenon_H87. % 15.16/15.33 rewrite <- zenon_D_pnotp. % 15.16/15.33 exact zenon_Hab. % 15.16/15.33 cut (((e0) = (op (e1) (e2)))); [idtac | apply NNPP; zenon_intro zenon_H15e]. % 15.16/15.33 cut (((op (e0) (e2)) = (op (e0) (e2)))); [idtac | apply NNPP; zenon_intro zenon_H2c]. % 15.16/15.33 congruence. % 15.16/15.33 apply zenon_H2c. apply refl_equal. % 15.16/15.33 apply zenon_H15e. apply sym_equal. exact zenon_H15d. % 15.16/15.33 (* end of lemma zenon_L136_ *) % 15.16/15.33 assert (zenon_L137_ : (~((op (e2) (e2)) = (op (e2) (e3)))) -> ((op (e2) (e2)) = (e2)) -> ((op (e2) (e3)) = (e2)) -> False). % 15.16/15.33 do 0 intro. intros zenon_H15f zenon_H35 zenon_H124. % 15.16/15.33 cut (((op (e2) (e2)) = (e2)) = ((op (e2) (e2)) = (op (e2) (e3)))). % 15.16/15.33 intro zenon_D_pnotp. % 15.16/15.33 apply zenon_H15f. % 15.16/15.33 rewrite <- zenon_D_pnotp. % 15.16/15.33 exact zenon_H35. % 15.16/15.33 cut (((e2) = (op (e2) (e3)))); [idtac | apply NNPP; zenon_intro zenon_H137]. % 15.16/15.33 cut (((op (e2) (e2)) = (op (e2) (e2)))); [idtac | apply NNPP; zenon_intro zenon_H65]. % 15.16/15.33 congruence. % 15.16/15.33 apply zenon_H65. apply refl_equal. % 15.16/15.33 apply zenon_H137. apply sym_equal. exact zenon_H124. % 15.16/15.33 (* end of lemma zenon_L137_ *) % 15.16/15.33 assert (zenon_L138_ : (((op (e0) (e3)) = (e2))\/(((op (e1) (e3)) = (e2))\/(((op (e2) (e3)) = (e2))\/((op (e3) (e3)) = (e2))))) -> (~((e1) = (e2))) -> ((op (e0) (e3)) = (e1)) -> (~((e0) = (e2))) -> ((op (e1) (e3)) = (e0)) -> ((op (e2) (e2)) = (e2)) -> (~((op (e2) (e2)) = (op (e2) (e3)))) -> (~((op (e3) (e3)) = (e2))) -> False). % 15.16/15.33 do 0 intro. intros zenon_H160 zenon_Ha7 zenon_H37 zenon_H5e zenon_Hcc zenon_H35 zenon_H15f zenon_H3d. % 15.16/15.33 apply (zenon_or_s _ _ zenon_H160); [ zenon_intro zenon_H81 | zenon_intro zenon_H161 ]. % 15.16/15.33 apply (zenon_L33_); trivial. % 15.16/15.33 apply (zenon_or_s _ _ zenon_H161); [ zenon_intro zenon_H82 | zenon_intro zenon_H162 ]. % 15.16/15.33 apply (zenon_L54_); trivial. % 15.16/15.33 apply (zenon_or_s _ _ zenon_H162); [ zenon_intro zenon_H124 | zenon_intro zenon_H43 ]. % 15.16/15.33 apply (zenon_L137_); trivial. % 15.16/15.33 exact (zenon_H3d zenon_H43). % 15.16/15.33 (* end of lemma zenon_L138_ *) % 15.16/15.33 assert (zenon_L139_ : (((op (e1) (e0)) = (e0))\/(((op (e1) (e1)) = (e0))\/(((op (e1) (e2)) = (e0))\/((op (e1) (e3)) = (e0))))) -> (~((e0) = (e3))) -> ((op (e1) (e0)) = (e3)) -> (~((op (e1) (e1)) = (e0))) -> ((op (e0) (e2)) = (e0)) -> (~((op (e0) (e2)) = (op (e1) (e2)))) -> (((op (e0) (e3)) = (e2))\/(((op (e1) (e3)) = (e2))\/(((op (e2) (e3)) = (e2))\/((op (e3) (e3)) = (e2))))) -> (~((e1) = (e2))) -> ((op (e0) (e3)) = (e1)) -> (~((e0) = (e2))) -> ((op (e2) (e2)) = (e2)) -> (~((op (e2) (e2)) = (op (e2) (e3)))) -> (~((op (e3) (e3)) = (e2))) -> False). % 15.16/15.33 do 0 intro. intros zenon_H163 zenon_H4b zenon_H69 zenon_H145 zenon_Hab zenon_H87 zenon_H160 zenon_Ha7 zenon_H37 zenon_H5e zenon_H35 zenon_H15f zenon_H3d. % 15.16/15.33 apply (zenon_or_s _ _ zenon_H163); [ zenon_intro zenon_Had | zenon_intro zenon_H164 ]. % 15.16/15.33 apply (zenon_L38_); trivial. % 15.16/15.33 apply (zenon_or_s _ _ zenon_H164); [ zenon_intro zenon_H149 | zenon_intro zenon_H165 ]. % 15.16/15.33 exact (zenon_H145 zenon_H149). % 15.16/15.33 apply (zenon_or_s _ _ zenon_H165); [ zenon_intro zenon_H15d | zenon_intro zenon_Hcc ]. % 15.16/15.33 apply (zenon_L136_); trivial. % 15.16/15.33 apply (zenon_L138_); trivial. % 15.16/15.33 (* end of lemma zenon_L139_ *) % 15.16/15.33 assert (zenon_L140_ : (((op (e0) (e0)) = (e3))\/(((op (e1) (e0)) = (e3))\/(((op (e2) (e0)) = (e3))\/((op (e3) (e0)) = (e3))))) -> (~((op (e0) (e0)) = (e3))) -> (~((op (e3) (e3)) = (e2))) -> (~((op (e2) (e2)) = (op (e2) (e3)))) -> ((op (e2) (e2)) = (e2)) -> (~((e0) = (e2))) -> (~((e1) = (e2))) -> (((op (e0) (e3)) = (e2))\/(((op (e1) (e3)) = (e2))\/(((op (e2) (e3)) = (e2))\/((op (e3) (e3)) = (e2))))) -> (~((op (e0) (e2)) = (op (e1) (e2)))) -> ((op (e0) (e2)) = (e0)) -> (~((op (e1) (e1)) = (e0))) -> (((op (e1) (e0)) = (e0))\/(((op (e1) (e1)) = (e0))\/(((op (e1) (e2)) = (e0))\/((op (e1) (e3)) = (e0))))) -> ((op (e0) (e3)) = (e1)) -> (~((op (e0) (e3)) = (op (e2) (e3)))) -> (~((op (e2) (e2)) = (e1))) -> (~((op (e1) (e1)) = (op (e2) (e1)))) -> ((op (e1) (e1)) = (e1)) -> (~((e1) = (e3))) -> (((op (e2) (e0)) = (e1))\/(((op (e2) (e1)) = (e1))\/(((op (e2) (e2)) = (e1))\/((op (e2) (e3)) = (e1))))) -> (~((e0) = (e3))) -> ((op (e3) (e0)) = (e0)) -> False). % 15.16/15.33 do 0 intro. intros zenon_Hbe zenon_H59 zenon_H3d zenon_H15f zenon_H35 zenon_H5e zenon_Ha7 zenon_H160 zenon_H87 zenon_Hab zenon_H145 zenon_H163 zenon_H37 zenon_Hb4 zenon_H52 zenon_Hb1 zenon_H21 zenon_Ha3 zenon_Hb7 zenon_H4b zenon_Hdb. % 15.16/15.33 apply (zenon_or_s _ _ zenon_Hbe); [ zenon_intro zenon_H5b | zenon_intro zenon_Hbf ]. % 15.16/15.33 exact (zenon_H59 zenon_H5b). % 15.16/15.33 apply (zenon_or_s _ _ zenon_Hbf); [ zenon_intro zenon_H69 | zenon_intro zenon_Hc0 ]. % 15.16/15.33 apply (zenon_L139_); trivial. % 15.16/15.33 apply (zenon_or_s _ _ zenon_Hc0); [ zenon_intro zenon_Haf | zenon_intro zenon_Hba ]. % 15.16/15.33 apply (zenon_L42_); trivial. % 15.16/15.33 apply (zenon_L62_); trivial. % 15.16/15.33 (* end of lemma zenon_L140_ *) % 15.16/15.33 assert (zenon_L141_ : (((op (e0) (e0)) = (e1))\/(((op (e0) (e1)) = (e1))\/(((op (e0) (e2)) = (e1))\/((op (e0) (e3)) = (e1))))) -> (~((op (e0) (e0)) = (e1))) -> (~((op (e0) (e1)) = (op (e1) (e1)))) -> (~((e0) = (e1))) -> (((op (e0) (e0)) = (e3))\/(((op (e1) (e0)) = (e3))\/(((op (e2) (e0)) = (e3))\/((op (e3) (e0)) = (e3))))) -> (~((op (e0) (e0)) = (e3))) -> (~((op (e3) (e3)) = (e2))) -> (~((op (e2) (e2)) = (op (e2) (e3)))) -> ((op (e2) (e2)) = (e2)) -> (~((e0) = (e2))) -> (~((e1) = (e2))) -> (((op (e0) (e3)) = (e2))\/(((op (e1) (e3)) = (e2))\/(((op (e2) (e3)) = (e2))\/((op (e3) (e3)) = (e2))))) -> (~((op (e0) (e2)) = (op (e1) (e2)))) -> ((op (e0) (e2)) = (e0)) -> (~((op (e1) (e1)) = (e0))) -> (((op (e1) (e0)) = (e0))\/(((op (e1) (e1)) = (e0))\/(((op (e1) (e2)) = (e0))\/((op (e1) (e3)) = (e0))))) -> (~((op (e0) (e3)) = (op (e2) (e3)))) -> (~((op (e2) (e2)) = (e1))) -> (~((op (e1) (e1)) = (op (e2) (e1)))) -> ((op (e1) (e1)) = (e1)) -> (~((e1) = (e3))) -> (((op (e2) (e0)) = (e1))\/(((op (e2) (e1)) = (e1))\/(((op (e2) (e2)) = (e1))\/((op (e2) (e3)) = (e1))))) -> (~((e0) = (e3))) -> ((op (e3) (e0)) = (e0)) -> False). % 15.16/15.33 do 0 intro. intros zenon_H44 zenon_H45 zenon_H23 zenon_H9e zenon_Hbe zenon_H59 zenon_H3d zenon_H15f zenon_H35 zenon_H5e zenon_Ha7 zenon_H160 zenon_H87 zenon_Hab zenon_H145 zenon_H163 zenon_Hb4 zenon_H52 zenon_Hb1 zenon_H21 zenon_Ha3 zenon_Hb7 zenon_H4b zenon_Hdb. % 15.16/15.33 apply (zenon_or_s _ _ zenon_H44); [ zenon_intro zenon_H47 | zenon_intro zenon_H46 ]. % 15.16/15.33 exact (zenon_H45 zenon_H47). % 15.16/15.33 apply (zenon_or_s _ _ zenon_H46); [ zenon_intro zenon_H22 | zenon_intro zenon_H48 ]. % 15.16/15.33 apply (zenon_L3_); trivial. % 15.16/15.33 apply (zenon_or_s _ _ zenon_H48); [ zenon_intro zenon_H29 | zenon_intro zenon_H37 ]. % 15.16/15.33 apply (zenon_L37_); trivial. % 15.16/15.33 apply (zenon_L140_); trivial. % 15.16/15.33 (* end of lemma zenon_L141_ *) % 15.16/15.33 assert (zenon_L142_ : (((op (e0) (e0)) = (e0))\/(((op (e1) (e0)) = (e0))\/(((op (e2) (e0)) = (e0))\/((op (e3) (e0)) = (e0))))) -> (~((op (e0) (e0)) = (e0))) -> (~((op (e3) (e0)) = (op (e3) (e3)))) -> (((op (e2) (e1)) = (e0))\/(((op (e2) (e1)) = (e1))\/(((op (e2) (e1)) = (e2))\/((op (e2) (e1)) = (e3))))) -> (~((op (e2) (e0)) = (op (e2) (e1)))) -> (~((op (e2) (e1)) = (op (e2) (e2)))) -> (~((op (e0) (e1)) = (op (e2) (e1)))) -> (((op (e0) (e0)) = (e3))\/(((op (e0) (e1)) = (e3))\/(((op (e0) (e2)) = (e3))\/((op (e0) (e3)) = (e3))))) -> ((op (e3) (e3)) = (e3)) -> (~((op (e0) (e3)) = (op (e3) (e3)))) -> (((op (e0) (e0)) = (e1))\/(((op (e0) (e1)) = (e1))\/(((op (e0) (e2)) = (e1))\/((op (e0) (e3)) = (e1))))) -> (~((op (e0) (e0)) = (e1))) -> (~((op (e0) (e1)) = (op (e1) (e1)))) -> (~((e0) = (e1))) -> (((op (e0) (e0)) = (e3))\/(((op (e1) (e0)) = (e3))\/(((op (e2) (e0)) = (e3))\/((op (e3) (e0)) = (e3))))) -> (~((op (e0) (e0)) = (e3))) -> (~((op (e3) (e3)) = (e2))) -> (~((op (e2) (e2)) = (op (e2) (e3)))) -> ((op (e2) (e2)) = (e2)) -> (~((e0) = (e2))) -> (~((e1) = (e2))) -> (((op (e0) (e3)) = (e2))\/(((op (e1) (e3)) = (e2))\/(((op (e2) (e3)) = (e2))\/((op (e3) (e3)) = (e2))))) -> (~((op (e0) (e2)) = (op (e1) (e2)))) -> ((op (e0) (e2)) = (e0)) -> (~((op (e1) (e1)) = (e0))) -> (((op (e1) (e0)) = (e0))\/(((op (e1) (e1)) = (e0))\/(((op (e1) (e2)) = (e0))\/((op (e1) (e3)) = (e0))))) -> (~((op (e0) (e3)) = (op (e2) (e3)))) -> (~((op (e2) (e2)) = (e1))) -> (~((op (e1) (e1)) = (op (e2) (e1)))) -> ((op (e1) (e1)) = (e1)) -> (~((e1) = (e3))) -> (((op (e2) (e0)) = (e1))\/(((op (e2) (e1)) = (e1))\/(((op (e2) (e2)) = (e1))\/((op (e2) (e3)) = (e1))))) -> (~((e0) = (e3))) -> False). % 15.16/15.33 do 0 intro. intros zenon_Hf0 zenon_H20 zenon_Hbb zenon_H15a zenon_H154 zenon_H157 zenon_Hde zenon_H58 zenon_H42 zenon_H36 zenon_H44 zenon_H45 zenon_H23 zenon_H9e zenon_Hbe zenon_H59 zenon_H3d zenon_H15f zenon_H35 zenon_H5e zenon_Ha7 zenon_H160 zenon_H87 zenon_Hab zenon_H145 zenon_H163 zenon_Hb4 zenon_H52 zenon_Hb1 zenon_H21 zenon_Ha3 zenon_Hb7 zenon_H4b. % 15.16/15.33 apply (zenon_or_s _ _ zenon_Hf0); [ zenon_intro zenon_H1f | zenon_intro zenon_Hf2 ]. % 15.16/15.33 exact (zenon_H20 zenon_H1f). % 15.16/15.33 apply (zenon_or_s _ _ zenon_Hf2); [ zenon_intro zenon_Had | zenon_intro zenon_Hf3 ]. % 15.16/15.33 apply (zenon_L44_); trivial. % 15.16/15.33 apply (zenon_or_s _ _ zenon_Hf3); [ zenon_intro zenon_Hcf | zenon_intro zenon_Hdb ]. % 15.16/15.33 apply (zenon_or_s _ _ zenon_H44); [ zenon_intro zenon_H47 | zenon_intro zenon_H46 ]. % 15.16/15.33 exact (zenon_H45 zenon_H47). % 15.16/15.33 apply (zenon_or_s _ _ zenon_H46); [ zenon_intro zenon_H22 | zenon_intro zenon_H48 ]. % 15.16/15.33 apply (zenon_L60_); trivial. % 15.16/15.33 apply (zenon_or_s _ _ zenon_H48); [ zenon_intro zenon_H29 | zenon_intro zenon_H37 ]. % 15.16/15.33 apply (zenon_L37_); trivial. % 15.16/15.33 apply (zenon_or_s _ _ zenon_H58); [ zenon_intro zenon_H5b | zenon_intro zenon_H5a ]. % 15.16/15.33 exact (zenon_H59 zenon_H5b). % 15.16/15.33 apply (zenon_or_s _ _ zenon_H5a); [ zenon_intro zenon_H4a | zenon_intro zenon_H5c ]. % 15.16/15.33 apply (zenon_L135_); trivial. % 15.16/15.33 apply (zenon_or_s _ _ zenon_H5c); [ zenon_intro zenon_H50 | zenon_intro zenon_H53 ]. % 15.16/15.33 apply (zenon_L48_); trivial. % 15.16/15.33 apply (zenon_L32_); trivial. % 15.16/15.33 apply (zenon_L141_); trivial. % 15.16/15.33 (* end of lemma zenon_L142_ *) % 15.16/15.33 assert (zenon_L143_ : (~((op (e1) (e0)) = (op (e1) (e2)))) -> ((op (e1) (e0)) = (e0)) -> ((op (e1) (e2)) = (e0)) -> False). % 15.16/15.33 do 0 intro. intros zenon_H166 zenon_Had zenon_H15d. % 15.16/15.33 cut (((op (e1) (e0)) = (e0)) = ((op (e1) (e0)) = (op (e1) (e2)))). % 15.16/15.33 intro zenon_D_pnotp. % 15.16/15.33 apply zenon_H166. % 15.16/15.33 rewrite <- zenon_D_pnotp. % 15.16/15.33 exact zenon_Had. % 15.16/15.33 cut (((e0) = (op (e1) (e2)))); [idtac | apply NNPP; zenon_intro zenon_H15e]. % 15.16/15.33 cut (((op (e1) (e0)) = (op (e1) (e0)))); [idtac | apply NNPP; zenon_intro zenon_Hda]. % 15.16/15.33 congruence. % 15.16/15.33 apply zenon_Hda. apply refl_equal. % 15.16/15.33 apply zenon_H15e. apply sym_equal. exact zenon_H15d. % 15.16/15.33 (* end of lemma zenon_L143_ *) % 15.16/15.33 assert (zenon_L144_ : (~((op (e3) (e1)) = (op (e3) (e2)))) -> ((op (e3) (e1)) = (e0)) -> ((op (e3) (e2)) = (e0)) -> False). % 15.16/15.33 do 0 intro. intros zenon_H135 zenon_H142 zenon_H167. % 15.16/15.33 cut (((op (e3) (e1)) = (e0)) = ((op (e3) (e1)) = (op (e3) (e2)))). % 15.16/15.33 intro zenon_D_pnotp. % 15.16/15.33 apply zenon_H135. % 15.16/15.33 rewrite <- zenon_D_pnotp. % 15.16/15.33 exact zenon_H142. % 15.16/15.33 cut (((e0) = (op (e3) (e2)))); [idtac | apply NNPP; zenon_intro zenon_H168]. % 15.16/15.33 cut (((op (e3) (e1)) = (op (e3) (e1)))); [idtac | apply NNPP; zenon_intro zenon_H136]. % 15.16/15.33 congruence. % 15.16/15.33 apply zenon_H136. apply refl_equal. % 15.16/15.33 apply zenon_H168. apply sym_equal. exact zenon_H167. % 15.16/15.33 (* end of lemma zenon_L144_ *) % 15.16/15.33 assert (zenon_L145_ : (~((op (e3) (e0)) = (op (e3) (e1)))) -> ((op (e3) (e0)) = (e1)) -> ((op (e3) (e1)) = (e1)) -> False). % 15.16/15.33 do 0 intro. intros zenon_H109 zenon_Hee zenon_H13e. % 15.16/15.33 cut (((op (e3) (e0)) = (e1)) = ((op (e3) (e0)) = (op (e3) (e1)))). % 15.16/15.33 intro zenon_D_pnotp. % 15.16/15.33 apply zenon_H109. % 15.16/15.33 rewrite <- zenon_D_pnotp. % 15.16/15.33 exact zenon_Hee. % 15.16/15.33 cut (((e1) = (op (e3) (e1)))); [idtac | apply NNPP; zenon_intro zenon_H169]. % 15.16/15.33 cut (((op (e3) (e0)) = (op (e3) (e0)))); [idtac | apply NNPP; zenon_intro zenon_H108]. % 15.16/15.33 congruence. % 15.16/15.33 apply zenon_H108. apply refl_equal. % 15.16/15.33 apply zenon_H169. apply sym_equal. exact zenon_H13e. % 15.16/15.33 (* end of lemma zenon_L145_ *) % 15.16/15.33 assert (zenon_L146_ : (~((op (e0) (e1)) = (op (e3) (e1)))) -> ((op (e0) (e1)) = (e2)) -> ((op (e3) (e1)) = (e2)) -> False). % 15.16/15.33 do 0 intro. intros zenon_H138 zenon_H5d zenon_H16a. % 15.16/15.33 cut (((op (e0) (e1)) = (e2)) = ((op (e0) (e1)) = (op (e3) (e1)))). % 15.16/15.33 intro zenon_D_pnotp. % 15.16/15.33 apply zenon_H138. % 15.16/15.33 rewrite <- zenon_D_pnotp. % 15.16/15.33 exact zenon_H5d. % 15.16/15.33 cut (((e2) = (op (e3) (e1)))); [idtac | apply NNPP; zenon_intro zenon_H16b]. % 15.16/15.33 cut (((op (e0) (e1)) = (op (e0) (e1)))); [idtac | apply NNPP; zenon_intro zenon_He1]. % 15.16/15.33 congruence. % 15.16/15.33 apply zenon_He1. apply refl_equal. % 15.16/15.33 apply zenon_H16b. apply sym_equal. exact zenon_H16a. % 15.16/15.33 (* end of lemma zenon_L146_ *) % 15.16/15.33 assert (zenon_L147_ : (((op (e3) (e1)) = (e0))\/(((op (e3) (e1)) = (e1))\/(((op (e3) (e1)) = (e2))\/((op (e3) (e1)) = (e3))))) -> ((op (e3) (e2)) = (e0)) -> (~((op (e3) (e1)) = (op (e3) (e2)))) -> ((op (e3) (e0)) = (e1)) -> (~((op (e3) (e0)) = (op (e3) (e1)))) -> ((op (e0) (e1)) = (e2)) -> (~((op (e0) (e1)) = (op (e3) (e1)))) -> ((op (e3) (e3)) = (e3)) -> (~((op (e3) (e1)) = (op (e3) (e3)))) -> False). % 15.16/15.33 do 0 intro. intros zenon_H16c zenon_H167 zenon_H135 zenon_Hee zenon_H109 zenon_H5d zenon_H138 zenon_H42 zenon_H12d. % 15.16/15.33 apply (zenon_or_s _ _ zenon_H16c); [ zenon_intro zenon_H142 | zenon_intro zenon_H16d ]. % 15.16/15.33 apply (zenon_L144_); trivial. % 15.16/15.33 apply (zenon_or_s _ _ zenon_H16d); [ zenon_intro zenon_H13e | zenon_intro zenon_H16e ]. % 15.16/15.33 apply (zenon_L145_); trivial. % 15.16/15.33 apply (zenon_or_s _ _ zenon_H16e); [ zenon_intro zenon_H16a | zenon_intro zenon_H10a ]. % 15.16/15.33 apply (zenon_L146_); trivial. % 15.16/15.33 apply (zenon_L102_); trivial. % 15.16/15.33 (* end of lemma zenon_L147_ *) % 15.16/15.33 assert (zenon_L148_ : (((op (e0) (e2)) = (e0))\/(((op (e1) (e2)) = (e0))\/(((op (e2) (e2)) = (e0))\/((op (e3) (e2)) = (e0))))) -> (~((e0) = (e1))) -> ((op (e0) (e2)) = (e1)) -> ((op (e1) (e0)) = (e0)) -> (~((op (e1) (e0)) = (op (e1) (e2)))) -> (~((op (e2) (e2)) = (e0))) -> (((op (e3) (e1)) = (e0))\/(((op (e3) (e1)) = (e1))\/(((op (e3) (e1)) = (e2))\/((op (e3) (e1)) = (e3))))) -> (~((op (e3) (e1)) = (op (e3) (e2)))) -> ((op (e3) (e0)) = (e1)) -> (~((op (e3) (e0)) = (op (e3) (e1)))) -> ((op (e0) (e1)) = (e2)) -> (~((op (e0) (e1)) = (op (e3) (e1)))) -> ((op (e3) (e3)) = (e3)) -> (~((op (e3) (e1)) = (op (e3) (e3)))) -> False). % 15.16/15.33 do 0 intro. intros zenon_H16f zenon_H9e zenon_H29 zenon_Had zenon_H166 zenon_H2e zenon_H16c zenon_H135 zenon_Hee zenon_H109 zenon_H5d zenon_H138 zenon_H42 zenon_H12d. % 15.16/15.33 apply (zenon_or_s _ _ zenon_H16f); [ zenon_intro zenon_Hab | zenon_intro zenon_H170 ]. % 15.16/15.33 apply (zenon_L37_); trivial. % 15.16/15.33 apply (zenon_or_s _ _ zenon_H170); [ zenon_intro zenon_H15d | zenon_intro zenon_H171 ]. % 15.16/15.33 apply (zenon_L143_); trivial. % 15.16/15.33 apply (zenon_or_s _ _ zenon_H171); [ zenon_intro zenon_H32 | zenon_intro zenon_H167 ]. % 15.16/15.33 exact (zenon_H2e zenon_H32). % 15.16/15.33 apply (zenon_L147_); trivial. % 15.16/15.33 (* end of lemma zenon_L148_ *) % 15.16/15.33 assert (zenon_L149_ : (((op (e0) (e0)) = (e2))\/(((op (e0) (e1)) = (e2))\/(((op (e0) (e2)) = (e2))\/((op (e0) (e3)) = (e2))))) -> (~((op (e0) (e0)) = (e2))) -> (~((op (e3) (e1)) = (op (e3) (e3)))) -> ((op (e3) (e3)) = (e3)) -> (~((op (e0) (e1)) = (op (e3) (e1)))) -> (~((op (e3) (e0)) = (op (e3) (e1)))) -> ((op (e3) (e0)) = (e1)) -> (~((op (e3) (e1)) = (op (e3) (e2)))) -> (((op (e3) (e1)) = (e0))\/(((op (e3) (e1)) = (e1))\/(((op (e3) (e1)) = (e2))\/((op (e3) (e1)) = (e3))))) -> (~((op (e2) (e2)) = (e0))) -> (~((op (e1) (e0)) = (op (e1) (e2)))) -> ((op (e1) (e0)) = (e0)) -> (~((e0) = (e1))) -> (((op (e0) (e2)) = (e0))\/(((op (e1) (e2)) = (e0))\/(((op (e2) (e2)) = (e0))\/((op (e3) (e2)) = (e0))))) -> (~((e1) = (e2))) -> ((op (e0) (e2)) = (e1)) -> ((op (e0) (e3)) = (e0)) -> (~((e0) = (e2))) -> False). % 15.16/15.33 do 0 intro. intros zenon_H8e zenon_H8f zenon_H12d zenon_H42 zenon_H138 zenon_H109 zenon_Hee zenon_H135 zenon_H16c zenon_H2e zenon_H166 zenon_Had zenon_H9e zenon_H16f zenon_Ha7 zenon_H29 zenon_Hca zenon_H5e. % 15.16/15.33 apply (zenon_or_s _ _ zenon_H8e); [ zenon_intro zenon_H92 | zenon_intro zenon_H91 ]. % 15.16/15.33 exact (zenon_H8f zenon_H92). % 15.16/15.33 apply (zenon_or_s _ _ zenon_H91); [ zenon_intro zenon_H5d | zenon_intro zenon_H93 ]. % 15.16/15.33 apply (zenon_L148_); trivial. % 15.16/15.33 apply (zenon_or_s _ _ zenon_H93); [ zenon_intro zenon_H63 | zenon_intro zenon_H81 ]. % 15.16/15.33 apply (zenon_L104_); trivial. % 15.16/15.33 apply (zenon_L113_); trivial. % 15.16/15.33 (* end of lemma zenon_L149_ *) % 15.16/15.33 assert (zenon_L150_ : (((op (e0) (e2)) = (e0))\/(((op (e1) (e2)) = (e0))\/(((op (e2) (e2)) = (e0))\/((op (e3) (e2)) = (e0))))) -> ((op (e0) (e3)) = (e0)) -> (~((op (e0) (e2)) = (op (e0) (e3)))) -> ((op (e1) (e0)) = (e0)) -> (~((op (e1) (e0)) = (op (e1) (e2)))) -> (~((op (e2) (e2)) = (e0))) -> (~((op (e3) (e1)) = (op (e3) (e2)))) -> ((op (e3) (e1)) = (e0)) -> False). % 15.16/15.33 do 0 intro. intros zenon_H16f zenon_Hca zenon_Hc9 zenon_Had zenon_H166 zenon_H2e zenon_H135 zenon_H142. % 15.16/15.33 apply (zenon_or_s _ _ zenon_H16f); [ zenon_intro zenon_Hab | zenon_intro zenon_H170 ]. % 15.16/15.33 apply (zenon_L53_); trivial. % 15.16/15.33 apply (zenon_or_s _ _ zenon_H170); [ zenon_intro zenon_H15d | zenon_intro zenon_H171 ]. % 15.16/15.33 apply (zenon_L143_); trivial. % 15.16/15.33 apply (zenon_or_s _ _ zenon_H171); [ zenon_intro zenon_H32 | zenon_intro zenon_H167 ]. % 15.16/15.33 exact (zenon_H2e zenon_H32). % 15.16/15.33 apply (zenon_L144_); trivial. % 15.16/15.33 (* end of lemma zenon_L150_ *) % 15.16/15.33 assert (zenon_L151_ : (((op (e0) (e1)) = (e0))\/(((op (e1) (e1)) = (e0))\/(((op (e2) (e1)) = (e0))\/((op (e3) (e1)) = (e0))))) -> (~((e0) = (e2))) -> ((op (e0) (e1)) = (e2)) -> (~((op (e1) (e1)) = (e0))) -> ((op (e2) (e0)) = (e0)) -> (~((op (e2) (e0)) = (op (e2) (e1)))) -> (((op (e0) (e2)) = (e0))\/(((op (e1) (e2)) = (e0))\/(((op (e2) (e2)) = (e0))\/((op (e3) (e2)) = (e0))))) -> ((op (e0) (e3)) = (e0)) -> (~((op (e0) (e2)) = (op (e0) (e3)))) -> ((op (e1) (e0)) = (e0)) -> (~((op (e1) (e0)) = (op (e1) (e2)))) -> (~((op (e2) (e2)) = (e0))) -> (~((op (e3) (e1)) = (op (e3) (e2)))) -> False). % 15.16/15.33 do 0 intro. intros zenon_H144 zenon_H5e zenon_H5d zenon_H145 zenon_Hcf zenon_H154 zenon_H16f zenon_Hca zenon_Hc9 zenon_Had zenon_H166 zenon_H2e zenon_H135. % 15.16/15.33 apply (zenon_or_s _ _ zenon_H144); [ zenon_intro zenon_H49 | zenon_intro zenon_H147 ]. % 15.16/15.33 apply (zenon_L14_); trivial. % 15.16/15.33 apply (zenon_or_s _ _ zenon_H147); [ zenon_intro zenon_H149 | zenon_intro zenon_H148 ]. % 15.16/15.33 exact (zenon_H145 zenon_H149). % 15.16/15.33 apply (zenon_or_s _ _ zenon_H148); [ zenon_intro zenon_H14a | zenon_intro zenon_H142 ]. % 15.16/15.33 apply (zenon_L133_); trivial. % 15.16/15.33 apply (zenon_L150_); trivial. % 15.16/15.33 (* end of lemma zenon_L151_ *) % 15.16/15.33 assert (zenon_L152_ : ((op (e1) (e2)) = (e0)) -> ((op (e1) (e2)) = (e3)) -> (~((e0) = (e3))) -> False). % 15.16/15.33 do 0 intro. intros zenon_H15d zenon_H88 zenon_H4b. % 15.16/15.33 elim (classic ((e3) = (e3))); [ zenon_intro zenon_H4c | zenon_intro zenon_H4d ]. % 15.16/15.33 cut (((e3) = (e3)) = ((e0) = (e3))). % 15.16/15.33 intro zenon_D_pnotp. % 15.16/15.33 apply zenon_H4b. % 15.16/15.33 rewrite <- zenon_D_pnotp. % 15.16/15.33 exact zenon_H4c. % 15.16/15.33 cut (((e3) = (e3))); [idtac | apply NNPP; zenon_intro zenon_H4d]. % 15.16/15.33 cut (((e3) = (e0))); [idtac | apply NNPP; zenon_intro zenon_H4e]. % 15.16/15.33 congruence. % 15.16/15.33 cut (((op (e1) (e2)) = (e0)) = ((e3) = (e0))). % 15.16/15.33 intro zenon_D_pnotp. % 15.16/15.33 apply zenon_H4e. % 15.16/15.33 rewrite <- zenon_D_pnotp. % 15.16/15.33 exact zenon_H15d. % 15.16/15.33 cut (((e0) = (e0))); [idtac | apply NNPP; zenon_intro zenon_H1d]. % 15.16/15.33 cut (((op (e1) (e2)) = (e3))); [idtac | apply NNPP; zenon_intro zenon_H172]. % 15.16/15.33 congruence. % 15.16/15.33 exact (zenon_H172 zenon_H88). % 15.16/15.33 apply zenon_H1d. apply refl_equal. % 15.16/15.33 apply zenon_H4d. apply refl_equal. % 15.16/15.33 apply zenon_H4d. apply refl_equal. % 15.16/15.33 (* end of lemma zenon_L152_ *) % 15.16/15.33 assert (zenon_L153_ : ((op (e3) (e3)) = (e3)) -> ((op (e3) (e2)) = (e3)) -> (~((op (e3) (e2)) = (op (e3) (e3)))) -> False). % 15.16/15.33 do 0 intro. intros zenon_H42 zenon_H106 zenon_H173. % 15.16/15.33 elim (classic ((op (e3) (e3)) = (op (e3) (e3)))); [ zenon_intro zenon_H54 | zenon_intro zenon_H55 ]. % 15.16/15.33 cut (((op (e3) (e3)) = (op (e3) (e3))) = ((op (e3) (e2)) = (op (e3) (e3)))). % 15.16/15.33 intro zenon_D_pnotp. % 15.16/15.33 apply zenon_H173. % 15.16/15.33 rewrite <- zenon_D_pnotp. % 15.16/15.33 exact zenon_H54. % 15.16/15.33 cut (((op (e3) (e3)) = (op (e3) (e3)))); [idtac | apply NNPP; zenon_intro zenon_H55]. % 15.16/15.33 cut (((op (e3) (e3)) = (op (e3) (e2)))); [idtac | apply NNPP; zenon_intro zenon_H174]. % 15.16/15.33 congruence. % 15.16/15.33 cut (((op (e3) (e3)) = (e3)) = ((op (e3) (e3)) = (op (e3) (e2)))). % 15.16/15.33 intro zenon_D_pnotp. % 15.16/15.33 apply zenon_H174. % 15.16/15.33 rewrite <- zenon_D_pnotp. % 15.16/15.33 exact zenon_H42. % 15.16/15.33 cut (((e3) = (op (e3) (e2)))); [idtac | apply NNPP; zenon_intro zenon_H107]. % 15.16/15.33 cut (((op (e3) (e3)) = (op (e3) (e3)))); [idtac | apply NNPP; zenon_intro zenon_H55]. % 15.16/15.33 congruence. % 15.16/15.33 apply zenon_H55. apply refl_equal. % 15.16/15.33 apply zenon_H107. apply sym_equal. exact zenon_H106. % 15.16/15.33 apply zenon_H55. apply refl_equal. % 15.16/15.33 apply zenon_H55. apply refl_equal. % 15.16/15.33 (* end of lemma zenon_L153_ *) % 15.16/15.33 assert (zenon_L154_ : (((op (e0) (e2)) = (e3))\/(((op (e1) (e2)) = (e3))\/(((op (e2) (e2)) = (e3))\/((op (e3) (e2)) = (e3))))) -> (~((e1) = (e3))) -> ((op (e0) (e2)) = (e1)) -> (~((e0) = (e3))) -> ((op (e1) (e2)) = (e0)) -> (~((op (e2) (e2)) = (e3))) -> ((op (e3) (e3)) = (e3)) -> (~((op (e3) (e2)) = (op (e3) (e3)))) -> False). % 15.16/15.33 do 0 intro. intros zenon_H175 zenon_Ha3 zenon_H29 zenon_H4b zenon_H15d zenon_H30 zenon_H42 zenon_H173. % 15.16/15.33 apply (zenon_or_s _ _ zenon_H175); [ zenon_intro zenon_H50 | zenon_intro zenon_H176 ]. % 15.16/15.33 apply (zenon_L29_); trivial. % 15.16/15.33 apply (zenon_or_s _ _ zenon_H176); [ zenon_intro zenon_H88 | zenon_intro zenon_H177 ]. % 15.16/15.33 apply (zenon_L152_); trivial. % 15.16/15.33 apply (zenon_or_s _ _ zenon_H177); [ zenon_intro zenon_H34 | zenon_intro zenon_H106 ]. % 15.16/15.33 exact (zenon_H30 zenon_H34). % 15.16/15.33 apply (zenon_L153_); trivial. % 15.16/15.33 (* end of lemma zenon_L154_ *) % 15.16/15.33 assert (zenon_L155_ : (~((op (e0) (e3)) = (op (e1) (e3)))) -> ((op (e0) (e3)) = (e0)) -> ((op (e1) (e3)) = (e0)) -> False). % 15.16/15.33 do 0 intro. intros zenon_H80 zenon_Hca zenon_Hcc. % 15.16/15.33 cut (((op (e0) (e3)) = (e0)) = ((op (e0) (e3)) = (op (e1) (e3)))). % 15.16/15.33 intro zenon_D_pnotp. % 15.16/15.33 apply zenon_H80. % 15.16/15.33 rewrite <- zenon_D_pnotp. % 15.16/15.33 exact zenon_Hca. % 15.16/15.33 cut (((e0) = (op (e1) (e3)))); [idtac | apply NNPP; zenon_intro zenon_H178]. % 15.16/15.33 cut (((op (e0) (e3)) = (op (e0) (e3)))); [idtac | apply NNPP; zenon_intro zenon_H3a]. % 15.16/15.33 congruence. % 15.16/15.33 apply zenon_H3a. apply refl_equal. % 15.16/15.33 apply zenon_H178. apply sym_equal. exact zenon_Hcc. % 15.16/15.34 (* end of lemma zenon_L155_ *) % 15.16/15.34 assert (zenon_L156_ : (~((op (e3) (e0)) = (op (e3) (e2)))) -> ((op (e3) (e0)) = (e0)) -> ((op (e3) (e2)) = (e0)) -> False). % 15.16/15.34 do 0 intro. intros zenon_H105 zenon_Hdb zenon_H167. % 15.16/15.34 cut (((op (e3) (e0)) = (e0)) = ((op (e3) (e0)) = (op (e3) (e2)))). % 15.16/15.34 intro zenon_D_pnotp. % 15.16/15.34 apply zenon_H105. % 15.16/15.34 rewrite <- zenon_D_pnotp. % 15.16/15.34 exact zenon_Hdb. % 15.16/15.34 cut (((e0) = (op (e3) (e2)))); [idtac | apply NNPP; zenon_intro zenon_H168]. % 15.16/15.34 cut (((op (e3) (e0)) = (op (e3) (e0)))); [idtac | apply NNPP; zenon_intro zenon_H108]. % 15.16/15.34 congruence. % 15.16/15.34 apply zenon_H108. apply refl_equal. % 15.16/15.34 apply zenon_H168. apply sym_equal. exact zenon_H167. % 15.16/15.34 (* end of lemma zenon_L156_ *) % 15.16/15.34 assert (zenon_L157_ : (((op (e0) (e2)) = (e0))\/(((op (e1) (e2)) = (e0))\/(((op (e2) (e2)) = (e0))\/((op (e3) (e2)) = (e0))))) -> ((op (e0) (e3)) = (e0)) -> (~((op (e0) (e2)) = (op (e0) (e3)))) -> (~((op (e3) (e2)) = (op (e3) (e3)))) -> ((op (e3) (e3)) = (e3)) -> (~((op (e2) (e2)) = (e3))) -> (~((e0) = (e3))) -> ((op (e0) (e2)) = (e1)) -> (~((e1) = (e3))) -> (((op (e0) (e2)) = (e3))\/(((op (e1) (e2)) = (e3))\/(((op (e2) (e2)) = (e3))\/((op (e3) (e2)) = (e3))))) -> (~((op (e2) (e2)) = (e0))) -> (~((op (e3) (e0)) = (op (e3) (e2)))) -> ((op (e3) (e0)) = (e0)) -> False). % 15.16/15.34 do 0 intro. intros zenon_H16f zenon_Hca zenon_Hc9 zenon_H173 zenon_H42 zenon_H30 zenon_H4b zenon_H29 zenon_Ha3 zenon_H175 zenon_H2e zenon_H105 zenon_Hdb. % 15.16/15.34 apply (zenon_or_s _ _ zenon_H16f); [ zenon_intro zenon_Hab | zenon_intro zenon_H170 ]. % 15.16/15.34 apply (zenon_L53_); trivial. % 15.16/15.34 apply (zenon_or_s _ _ zenon_H170); [ zenon_intro zenon_H15d | zenon_intro zenon_H171 ]. % 15.16/15.34 apply (zenon_L154_); trivial. % 15.16/15.34 apply (zenon_or_s _ _ zenon_H171); [ zenon_intro zenon_H32 | zenon_intro zenon_H167 ]. % 15.16/15.34 exact (zenon_H2e zenon_H32). % 15.16/15.34 apply (zenon_L156_); trivial. % 15.16/15.34 (* end of lemma zenon_L157_ *) % 15.16/15.34 assert (zenon_L158_ : (((op (e0) (e0)) = (e0))\/(((op (e1) (e0)) = (e0))\/(((op (e2) (e0)) = (e0))\/((op (e3) (e0)) = (e0))))) -> (~((op (e0) (e0)) = (e0))) -> (((op (e0) (e0)) = (e1))\/(((op (e1) (e0)) = (e1))\/(((op (e2) (e0)) = (e1))\/((op (e3) (e0)) = (e1))))) -> (~((op (e1) (e0)) = (op (e1) (e1)))) -> (~((op (e3) (e3)) = (e1))) -> (~((op (e2) (e0)) = (op (e2) (e3)))) -> (~((op (e1) (e1)) = (op (e1) (e3)))) -> (((op (e0) (e3)) = (e1))\/(((op (e1) (e3)) = (e1))\/(((op (e2) (e3)) = (e1))\/((op (e3) (e3)) = (e1))))) -> (~((op (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))))) -> (~((e1) = (e2))) -> (((op (e0) (e0)) = (e2))\/(((op (e0) (e1)) = (e2))\/(((op (e0) (e2)) = (e2))\/((op (e0) (e3)) = (e2))))) -> (~((op (e0) (e0)) = (e2))) -> (~((op (e0) (e3)) = (op (e1) (e3)))) -> (~((op (e1) (e1)) = (e0))) -> (((op (e0) (e1)) = (e0))\/(((op (e1) (e1)) = (e0))\/(((op (e2) (e1)) = (e0))\/((op (e3) (e1)) = (e0))))) -> (~((op (e2) (e0)) = (op (e2) (e1)))) -> (~((op (e1) (e0)) = (op (e1) (e2)))) -> (~((op (e3) (e1)) = (op (e3) (e2)))) -> (((op (e1) (e0)) = (e0))\/(((op (e1) (e1)) = (e0))\/(((op (e1) (e2)) = (e0))\/((op (e1) (e3)) = (e0))))) -> (~((op (e0) (e2)) = (op (e2) (e2)))) -> ((op (e2) (e2)) = (e2)) -> (~((e0) = (e2))) -> (((op (e0) (e0)) = (e1))\/(((op (e0) (e1)) = (e1))\/(((op (e0) (e2)) = (e1))\/((op (e0) (e3)) = (e1))))) -> (~((op (e0) (e0)) = (e1))) -> (~((op (e0) (e1)) = (op (e1) (e1)))) -> ((op (e1) (e1)) = (e1)) -> (~((op (e3) (e0)) = (op (e3) (e2)))) -> (~((op (e2) (e2)) = (e0))) -> (((op (e0) (e2)) = (e3))\/(((op (e1) (e2)) = (e3))\/(((op (e2) (e2)) = (e3))\/((op (e3) (e2)) = (e3))))) -> (~((e1) = (e3))) -> (~((e0) = (e3))) -> (~((op (e2) (e2)) = (e3))) -> ((op (e3) (e3)) = (e3)) -> (~((op (e3) (e2)) = (op (e3) (e3)))) -> (~((op (e0) (e2)) = (op (e0) (e3)))) -> (((op (e0) (e2)) = (e0))\/(((op (e1) (e2)) = (e0))\/(((op (e2) (e2)) = (e0))\/((op (e3) (e2)) = (e0))))) -> ((op (e0) (e3)) = (e0)) -> (~((e0) = (e1))) -> False). % 15.16/15.34 do 0 intro. intros zenon_Hf0 zenon_H20 zenon_Hf1 zenon_Hd7 zenon_H104 zenon_Hce zenon_H11e zenon_H121 zenon_H12d zenon_H138 zenon_H109 zenon_H16c zenon_Ha7 zenon_H8e zenon_H8f zenon_H80 zenon_H145 zenon_H144 zenon_H154 zenon_H166 zenon_H135 zenon_H163 zenon_H28 zenon_H35 zenon_H5e zenon_H44 zenon_H45 zenon_H23 zenon_H21 zenon_H105 zenon_H2e zenon_H175 zenon_Ha3 zenon_H4b zenon_H30 zenon_H42 zenon_H173 zenon_Hc9 zenon_H16f zenon_Hca zenon_H9e. % 15.16/15.34 apply (zenon_or_s _ _ zenon_Hf0); [ zenon_intro zenon_H1f | zenon_intro zenon_Hf2 ]. % 15.16/15.34 exact (zenon_H20 zenon_H1f). % 15.16/15.34 apply (zenon_or_s _ _ zenon_Hf2); [ zenon_intro zenon_Had | zenon_intro zenon_Hf3 ]. % 15.16/15.34 apply (zenon_or_s _ _ zenon_H44); [ zenon_intro zenon_H47 | zenon_intro zenon_H46 ]. % 15.16/15.34 exact (zenon_H45 zenon_H47). % 15.16/15.34 apply (zenon_or_s _ _ zenon_H46); [ zenon_intro zenon_H22 | zenon_intro zenon_H48 ]. % 15.16/15.34 apply (zenon_L3_); trivial. % 15.16/15.34 apply (zenon_or_s _ _ zenon_H48); [ zenon_intro zenon_H29 | zenon_intro zenon_H37 ]. % 15.16/15.34 apply (zenon_or_s _ _ zenon_Hf1); [ zenon_intro zenon_H47 | zenon_intro zenon_Hf4 ]. % 15.16/15.34 exact (zenon_H45 zenon_H47). % 15.16/15.34 apply (zenon_or_s _ _ zenon_Hf4); [ zenon_intro zenon_Hd8 | zenon_intro zenon_Hf5 ]. % 15.16/15.34 apply (zenon_L61_); trivial. % 15.16/15.34 apply (zenon_or_s _ _ zenon_Hf5); [ zenon_intro zenon_Hae | zenon_intro zenon_Hee ]. % 15.16/15.34 apply (zenon_L92_); trivial. % 15.16/15.34 apply (zenon_L149_); trivial. % 15.16/15.34 apply (zenon_L73_); trivial. % 15.16/15.34 apply (zenon_or_s _ _ zenon_Hf3); [ zenon_intro zenon_Hcf | zenon_intro zenon_Hdb ]. % 15.16/15.34 apply (zenon_or_s _ _ zenon_H44); [ zenon_intro zenon_H47 | zenon_intro zenon_H46 ]. % 15.16/15.34 exact (zenon_H45 zenon_H47). % 15.16/15.34 apply (zenon_or_s _ _ zenon_H46); [ zenon_intro zenon_H22 | zenon_intro zenon_H48 ]. % 15.16/15.34 apply (zenon_L3_); trivial. % 15.16/15.34 apply (zenon_or_s _ _ zenon_H48); [ zenon_intro zenon_H29 | zenon_intro zenon_H37 ]. % 15.16/15.34 apply (zenon_or_s _ _ zenon_H8e); [ zenon_intro zenon_H92 | zenon_intro zenon_H91 ]. % 15.16/15.34 exact (zenon_H8f zenon_H92). % 15.16/15.34 apply (zenon_or_s _ _ zenon_H91); [ zenon_intro zenon_H5d | zenon_intro zenon_H93 ]. % 15.16/15.34 apply (zenon_or_s _ _ zenon_H163); [ zenon_intro zenon_Had | zenon_intro zenon_H164 ]. % 15.16/15.34 apply (zenon_L151_); trivial. % 15.16/15.34 apply (zenon_or_s _ _ zenon_H164); [ zenon_intro zenon_H149 | zenon_intro zenon_H165 ]. % 15.16/15.34 exact (zenon_H145 zenon_H149). % 15.16/15.34 apply (zenon_or_s _ _ zenon_H165); [ zenon_intro zenon_H15d | zenon_intro zenon_Hcc ]. % 15.16/15.34 apply (zenon_L154_); trivial. % 15.16/15.34 apply (zenon_L155_); trivial. % 15.16/15.34 apply (zenon_or_s _ _ zenon_H93); [ zenon_intro zenon_H63 | zenon_intro zenon_H81 ]. % 15.16/15.34 apply (zenon_L15_); trivial. % 15.16/15.34 apply (zenon_L113_); trivial. % 15.16/15.34 apply (zenon_L73_); trivial. % 15.16/15.34 apply (zenon_or_s _ _ zenon_H44); [ zenon_intro zenon_H47 | zenon_intro zenon_H46 ]. % 15.16/15.34 exact (zenon_H45 zenon_H47). % 15.16/15.34 apply (zenon_or_s _ _ zenon_H46); [ zenon_intro zenon_H22 | zenon_intro zenon_H48 ]. % 15.16/15.34 apply (zenon_L3_); trivial. % 15.16/15.34 apply (zenon_or_s _ _ zenon_H48); [ zenon_intro zenon_H29 | zenon_intro zenon_H37 ]. % 15.16/15.34 apply (zenon_L157_); trivial. % 15.16/15.34 apply (zenon_L73_); trivial. % 15.16/15.34 (* end of lemma zenon_L158_ *) % 15.16/15.34 assert (zenon_L159_ : (((op (e0) (e0)) = (e0))\/(((op (e0) (e1)) = (e0))\/(((op (e0) (e2)) = (e0))\/((op (e0) (e3)) = (e0))))) -> (~((e2) = (e3))) -> (~((op (e1) (e3)) = (op (e3) (e3)))) -> (((op (e1) (e0)) = (e2))\/(((op (e1) (e1)) = (e2))\/(((op (e1) (e2)) = (e2))\/((op (e1) (e3)) = (e2))))) -> (~((op (e1) (e2)) = (op (e2) (e2)))) -> (((op (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 (e1) (e1)) = (op (e2) (e1)))) -> (~((op (e2) (e2)) = (e1))) -> (~((op (e0) (e3)) = (op (e2) (e3)))) -> (~((op (e0) (e2)) = (op (e1) (e2)))) -> (((op (e0) (e3)) = (e2))\/(((op (e1) (e3)) = (e2))\/(((op (e2) (e3)) = (e2))\/((op (e3) (e3)) = (e2))))) -> (~((op (e2) (e2)) = (op (e2) (e3)))) -> (~((op (e3) (e3)) = (e2))) -> (~((op (e0) (e0)) = (e3))) -> (((op (e0) (e0)) = (e3))\/(((op (e1) (e0)) = (e3))\/(((op (e2) (e0)) = (e3))\/((op (e3) (e0)) = (e3))))) -> (~((op (e0) (e3)) = (op (e3) (e3)))) -> (((op (e0) (e0)) = (e3))\/(((op (e0) (e1)) = (e3))\/(((op (e0) (e2)) = (e3))\/((op (e0) (e3)) = (e3))))) -> (~((op (e0) (e1)) = (op (e2) (e1)))) -> (~((op (e2) (e1)) = (op (e2) (e2)))) -> (((op (e2) (e1)) = (e0))\/(((op (e2) (e1)) = (e1))\/(((op (e2) (e1)) = (e2))\/((op (e2) (e1)) = (e3))))) -> (~((op (e3) (e0)) = (op (e3) (e3)))) -> (((op (e0) (e0)) = (e0))\/(((op (e1) (e0)) = (e0))\/(((op (e2) (e0)) = (e0))\/((op (e3) (e0)) = (e0))))) -> (~((op (e0) (e0)) = (e0))) -> (((op (e0) (e0)) = (e1))\/(((op (e1) (e0)) = (e1))\/(((op (e2) (e0)) = (e1))\/((op (e3) (e0)) = (e1))))) -> (~((op (e1) (e0)) = (op (e1) (e1)))) -> (~((op (e3) (e3)) = (e1))) -> (~((op (e2) (e0)) = (op (e2) (e3)))) -> (~((op (e1) (e1)) = (op (e1) (e3)))) -> (((op (e0) (e3)) = (e1))\/(((op (e1) (e3)) = (e1))\/(((op (e2) (e3)) = (e1))\/((op (e3) (e3)) = (e1))))) -> (~((op (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))))) -> (~((e1) = (e2))) -> (((op (e0) (e0)) = (e2))\/(((op (e0) (e1)) = (e2))\/(((op (e0) (e2)) = (e2))\/((op (e0) (e3)) = (e2))))) -> (~((op (e0) (e0)) = (e2))) -> (~((op (e0) (e3)) = (op (e1) (e3)))) -> (~((op (e1) (e1)) = (e0))) -> (((op (e0) (e1)) = (e0))\/(((op (e1) (e1)) = (e0))\/(((op (e2) (e1)) = (e0))\/((op (e3) (e1)) = (e0))))) -> (~((op (e2) (e0)) = (op (e2) (e1)))) -> (~((op (e1) (e0)) = (op (e1) (e2)))) -> (~((op (e3) (e1)) = (op (e3) (e2)))) -> (((op (e1) (e0)) = (e0))\/(((op (e1) (e1)) = (e0))\/(((op (e1) (e2)) = (e0))\/((op (e1) (e3)) = (e0))))) -> (~((op (e0) (e2)) = (op (e2) (e2)))) -> ((op (e2) (e2)) = (e2)) -> (~((e0) = (e2))) -> (((op (e0) (e0)) = (e1))\/(((op (e0) (e1)) = (e1))\/(((op (e0) (e2)) = (e1))\/((op (e0) (e3)) = (e1))))) -> (~((op (e0) (e0)) = (e1))) -> (~((op (e0) (e1)) = (op (e1) (e1)))) -> ((op (e1) (e1)) = (e1)) -> (~((op (e3) (e0)) = (op (e3) (e2)))) -> (~((op (e2) (e2)) = (e0))) -> (((op (e0) (e2)) = (e3))\/(((op (e1) (e2)) = (e3))\/(((op (e2) (e2)) = (e3))\/((op (e3) (e2)) = (e3))))) -> (~((e1) = (e3))) -> (~((e0) = (e3))) -> (~((op (e2) (e2)) = (e3))) -> ((op (e3) (e3)) = (e3)) -> (~((op (e3) (e2)) = (op (e3) (e3)))) -> (~((op (e0) (e2)) = (op (e0) (e3)))) -> (((op (e0) (e2)) = (e0))\/(((op (e1) (e2)) = (e0))\/(((op (e2) (e2)) = (e0))\/((op (e3) (e2)) = (e0))))) -> (~((e0) = (e1))) -> False). % 15.16/15.34 do 0 intro. intros zenon_H110 zenon_H6a zenon_H8b zenon_H84 zenon_H7d zenon_H90 zenon_Hb7 zenon_Hb1 zenon_H52 zenon_Hb4 zenon_H87 zenon_H160 zenon_H15f zenon_H3d zenon_H59 zenon_Hbe zenon_H36 zenon_H58 zenon_Hde zenon_H157 zenon_H15a zenon_Hbb zenon_Hf0 zenon_H20 zenon_Hf1 zenon_Hd7 zenon_H104 zenon_Hce zenon_H11e zenon_H121 zenon_H12d zenon_H138 zenon_H109 zenon_H16c zenon_Ha7 zenon_H8e zenon_H8f zenon_H80 zenon_H145 zenon_H144 zenon_H154 zenon_H166 zenon_H135 zenon_H163 zenon_H28 zenon_H35 zenon_H5e zenon_H44 zenon_H45 zenon_H23 zenon_H21 zenon_H105 zenon_H2e zenon_H175 zenon_Ha3 zenon_H4b zenon_H30 zenon_H42 zenon_H173 zenon_Hc9 zenon_H16f zenon_H9e. % 15.16/15.34 apply (zenon_or_s _ _ zenon_H110); [ zenon_intro zenon_H1f | zenon_intro zenon_H111 ]. % 15.16/15.34 exact (zenon_H20 zenon_H1f). % 15.16/15.34 apply (zenon_or_s _ _ zenon_H111); [ zenon_intro zenon_H49 | zenon_intro zenon_H112 ]. % 15.16/15.34 apply (zenon_L35_); trivial. % 15.16/15.34 apply (zenon_or_s _ _ zenon_H112); [ zenon_intro zenon_Hab | zenon_intro zenon_Hca ]. % 15.16/15.34 apply (zenon_L142_); trivial. % 15.16/15.34 apply (zenon_L158_); trivial. % 15.16/15.34 (* end of lemma zenon_L159_ *) % 15.16/15.34 assert (zenon_L160_ : ((op (e1) (e0)) = (e0)) -> ((op (e1) (e0)) = (e2)) -> (~((e0) = (e2))) -> False). % 15.16/15.34 do 0 intro. intros zenon_Had zenon_H68 zenon_H5e. % 15.16/15.34 elim (classic ((e2) = (e2))); [ zenon_intro zenon_H5f | zenon_intro zenon_H60 ]. % 15.16/15.34 cut (((e2) = (e2)) = ((e0) = (e2))). % 15.16/15.34 intro zenon_D_pnotp. % 15.16/15.34 apply zenon_H5e. % 15.16/15.34 rewrite <- zenon_D_pnotp. % 15.16/15.34 exact zenon_H5f. % 15.16/15.34 cut (((e2) = (e2))); [idtac | apply NNPP; zenon_intro zenon_H60]. % 15.16/15.34 cut (((e2) = (e0))); [idtac | apply NNPP; zenon_intro zenon_H61]. % 15.16/15.34 congruence. % 15.16/15.34 cut (((op (e1) (e0)) = (e0)) = ((e2) = (e0))). % 15.16/15.34 intro zenon_D_pnotp. % 15.16/15.34 apply zenon_H61. % 15.16/15.34 rewrite <- zenon_D_pnotp. % 15.16/15.34 exact zenon_Had. % 15.16/15.34 cut (((e0) = (e0))); [idtac | apply NNPP; zenon_intro zenon_H1d]. % 15.16/15.34 cut (((op (e1) (e0)) = (e2))); [idtac | apply NNPP; zenon_intro zenon_H179]. % 15.16/15.34 congruence. % 15.16/15.34 exact (zenon_H179 zenon_H68). % 15.16/15.34 apply zenon_H1d. apply refl_equal. % 15.16/15.34 apply zenon_H60. apply refl_equal. % 15.16/15.34 apply zenon_H60. apply refl_equal. % 15.16/15.34 (* end of lemma zenon_L160_ *) % 15.16/15.34 assert (zenon_L161_ : ((op (e2) (e2)) = (e2)) -> ((op (e2) (e0)) = (e2)) -> (~((op (e2) (e0)) = (op (e2) (e2)))) -> False). % 15.16/15.34 do 0 intro. intros zenon_H35 zenon_Hdd zenon_H17a. % 15.16/15.34 elim (classic ((op (e2) (e2)) = (op (e2) (e2)))); [ zenon_intro zenon_H64 | zenon_intro zenon_H65 ]. % 15.16/15.34 cut (((op (e2) (e2)) = (op (e2) (e2))) = ((op (e2) (e0)) = (op (e2) (e2)))). % 15.16/15.34 intro zenon_D_pnotp. % 15.16/15.34 apply zenon_H17a. % 15.16/15.34 rewrite <- zenon_D_pnotp. % 15.16/15.34 exact zenon_H64. % 15.16/15.34 cut (((op (e2) (e2)) = (op (e2) (e2)))); [idtac | apply NNPP; zenon_intro zenon_H65]. % 15.16/15.34 cut (((op (e2) (e2)) = (op (e2) (e0)))); [idtac | apply NNPP; zenon_intro zenon_H17b]. % 15.16/15.34 congruence. % 15.16/15.34 cut (((op (e2) (e2)) = (e2)) = ((op (e2) (e2)) = (op (e2) (e0)))). % 15.16/15.34 intro zenon_D_pnotp. % 15.16/15.34 apply zenon_H17b. % 15.16/15.34 rewrite <- zenon_D_pnotp. % 15.16/15.34 exact zenon_H35. % 15.16/15.34 cut (((e2) = (op (e2) (e0)))); [idtac | apply NNPP; zenon_intro zenon_H17c]. % 15.16/15.34 cut (((op (e2) (e2)) = (op (e2) (e2)))); [idtac | apply NNPP; zenon_intro zenon_H65]. % 15.16/15.34 congruence. % 15.16/15.34 apply zenon_H65. apply refl_equal. % 15.16/15.34 apply zenon_H17c. apply sym_equal. exact zenon_Hdd. % 15.16/15.34 apply zenon_H65. apply refl_equal. % 15.16/15.34 apply zenon_H65. apply refl_equal. % 15.16/15.34 (* end of lemma zenon_L161_ *) % 15.16/15.34 assert (zenon_L162_ : ((op (e1) (e0)) = (e1)) -> ((op (e1) (e0)) = (e2)) -> (~((e1) = (e2))) -> False). % 15.16/15.34 do 0 intro. intros zenon_Hd8 zenon_H68 zenon_Ha7. % 15.16/15.34 elim (classic ((e2) = (e2))); [ zenon_intro zenon_H5f | zenon_intro zenon_H60 ]. % 15.16/15.34 cut (((e2) = (e2)) = ((e1) = (e2))). % 15.16/15.34 intro zenon_D_pnotp. % 15.16/15.34 apply zenon_Ha7. % 15.16/15.34 rewrite <- zenon_D_pnotp. % 15.16/15.34 exact zenon_H5f. % 15.16/15.34 cut (((e2) = (e2))); [idtac | apply NNPP; zenon_intro zenon_H60]. % 15.16/15.34 cut (((e2) = (e1))); [idtac | apply NNPP; zenon_intro zenon_Ha8]. % 15.16/15.34 congruence. % 15.16/15.34 cut (((op (e1) (e0)) = (e1)) = ((e2) = (e1))). % 15.16/15.34 intro zenon_D_pnotp. % 15.16/15.34 apply zenon_Ha8. % 15.16/15.34 rewrite <- zenon_D_pnotp. % 15.16/15.34 exact zenon_Hd8. % 15.16/15.34 cut (((e1) = (e1))); [idtac | apply NNPP; zenon_intro zenon_Ha0]. % 15.16/15.34 cut (((op (e1) (e0)) = (e2))); [idtac | apply NNPP; zenon_intro zenon_H179]. % 15.16/15.34 congruence. % 15.16/15.34 exact (zenon_H179 zenon_H68). % 15.16/15.34 apply zenon_Ha0. apply refl_equal. % 15.16/15.34 apply zenon_H60. apply refl_equal. % 15.16/15.34 apply zenon_H60. apply refl_equal. % 15.16/15.34 (* end of lemma zenon_L162_ *) % 15.16/15.34 assert (zenon_L163_ : ((op (e1) (e0)) = (e1)) -> ((op (e1) (e0)) = (e3)) -> (~((e1) = (e3))) -> False). % 15.16/15.34 do 0 intro. intros zenon_Hd8 zenon_H69 zenon_Ha3. % 15.16/15.34 elim (classic ((e3) = (e3))); [ zenon_intro zenon_H4c | zenon_intro zenon_H4d ]. % 15.16/15.34 cut (((e3) = (e3)) = ((e1) = (e3))). % 15.16/15.34 intro zenon_D_pnotp. % 15.16/15.34 apply zenon_Ha3. % 15.16/15.34 rewrite <- zenon_D_pnotp. % 15.16/15.34 exact zenon_H4c. % 15.16/15.34 cut (((e3) = (e3))); [idtac | apply NNPP; zenon_intro zenon_H4d]. % 15.16/15.34 cut (((e3) = (e1))); [idtac | apply NNPP; zenon_intro zenon_Ha4]. % 15.16/15.34 congruence. % 15.16/15.34 cut (((op (e1) (e0)) = (e1)) = ((e3) = (e1))). % 15.16/15.34 intro zenon_D_pnotp. % 15.16/15.34 apply zenon_Ha4. % 15.16/15.34 rewrite <- zenon_D_pnotp. % 15.16/15.34 exact zenon_Hd8. % 15.16/15.34 cut (((e1) = (e1))); [idtac | apply NNPP; zenon_intro zenon_Ha0]. % 15.16/15.34 cut (((op (e1) (e0)) = (e3))); [idtac | apply NNPP; zenon_intro zenon_H6c]. % 15.16/15.34 congruence. % 15.16/15.34 exact (zenon_H6c zenon_H69). % 15.16/15.34 apply zenon_Ha0. apply refl_equal. % 15.16/15.34 apply zenon_H4d. apply refl_equal. % 15.16/15.34 apply zenon_H4d. apply refl_equal. % 15.16/15.34 (* end of lemma zenon_L163_ *) % 15.16/15.34 assert (zenon_L164_ : ((op (e3) (e2)) = (e3)) -> ((op (e1) (e2)) = (e3)) -> (~((op (e1) (e2)) = (op (e3) (e2)))) -> False). % 15.16/15.34 do 0 intro. intros zenon_H106 zenon_H88 zenon_H17d. % 15.16/15.34 elim (classic ((op (e3) (e2)) = (op (e3) (e2)))); [ zenon_intro zenon_H17e | zenon_intro zenon_H17f ]. % 15.16/15.34 cut (((op (e3) (e2)) = (op (e3) (e2))) = ((op (e1) (e2)) = (op (e3) (e2)))). % 15.16/15.34 intro zenon_D_pnotp. % 15.16/15.34 apply zenon_H17d. % 15.16/15.34 rewrite <- zenon_D_pnotp. % 15.16/15.34 exact zenon_H17e. % 15.16/15.34 cut (((op (e3) (e2)) = (op (e3) (e2)))); [idtac | apply NNPP; zenon_intro zenon_H17f]. % 15.16/15.34 cut (((op (e3) (e2)) = (op (e1) (e2)))); [idtac | apply NNPP; zenon_intro zenon_H180]. % 15.16/15.34 congruence. % 15.16/15.34 cut (((op (e3) (e2)) = (e3)) = ((op (e3) (e2)) = (op (e1) (e2)))). % 15.16/15.34 intro zenon_D_pnotp. % 15.16/15.34 apply zenon_H180. % 15.16/15.34 rewrite <- zenon_D_pnotp. % 15.16/15.34 exact zenon_H106. % 15.16/15.34 cut (((e3) = (op (e1) (e2)))); [idtac | apply NNPP; zenon_intro zenon_H89]. % 15.16/15.34 cut (((op (e3) (e2)) = (op (e3) (e2)))); [idtac | apply NNPP; zenon_intro zenon_H17f]. % 15.16/15.34 congruence. % 15.16/15.34 apply zenon_H17f. apply refl_equal. % 15.16/15.34 apply zenon_H89. apply sym_equal. exact zenon_H88. % 15.16/15.34 apply zenon_H17f. apply refl_equal. % 15.16/15.34 apply zenon_H17f. apply refl_equal. % 15.16/15.34 (* end of lemma zenon_L164_ *) % 15.16/15.34 assert (zenon_L165_ : ((op (e1) (e3)) = (e2)) -> ((op (e1) (e3)) = (e3)) -> (~((e2) = (e3))) -> False). % 15.16/15.34 do 0 intro. intros zenon_H82 zenon_H8a zenon_H6a. % 15.16/15.34 elim (classic ((e3) = (e3))); [ zenon_intro zenon_H4c | zenon_intro zenon_H4d ]. % 15.16/15.34 cut (((e3) = (e3)) = ((e2) = (e3))). % 15.16/15.34 intro zenon_D_pnotp. % 15.16/15.34 apply zenon_H6a. % 15.16/15.34 rewrite <- zenon_D_pnotp. % 15.16/15.34 exact zenon_H4c. % 15.16/15.34 cut (((e3) = (e3))); [idtac | apply NNPP; zenon_intro zenon_H4d]. % 15.16/15.34 cut (((e3) = (e2))); [idtac | apply NNPP; zenon_intro zenon_H6b]. % 15.16/15.34 congruence. % 15.16/15.34 cut (((op (e1) (e3)) = (e2)) = ((e3) = (e2))). % 15.16/15.34 intro zenon_D_pnotp. % 15.16/15.34 apply zenon_H6b. % 15.16/15.34 rewrite <- zenon_D_pnotp. % 15.16/15.34 exact zenon_H82. % 15.16/15.34 cut (((e2) = (e2))); [idtac | apply NNPP; zenon_intro zenon_H60]. % 15.16/15.34 cut (((op (e1) (e3)) = (e3))); [idtac | apply NNPP; zenon_intro zenon_H181]. % 15.16/15.34 congruence. % 15.16/15.34 exact (zenon_H181 zenon_H8a). % 15.16/15.34 apply zenon_H60. apply refl_equal. % 15.16/15.34 apply zenon_H4d. apply refl_equal. % 15.16/15.34 apply zenon_H4d. apply refl_equal. % 15.16/15.34 (* end of lemma zenon_L165_ *) % 15.16/15.34 assert (zenon_L166_ : (((op (e1) (e0)) = (e3))\/(((op (e1) (e1)) = (e3))\/(((op (e1) (e2)) = (e3))\/((op (e1) (e3)) = (e3))))) -> (~((e1) = (e3))) -> ((op (e1) (e0)) = (e1)) -> (~((op (e1) (e1)) = (e3))) -> (~((op (e1) (e2)) = (op (e3) (e2)))) -> ((op (e3) (e2)) = (e3)) -> ((op (e1) (e3)) = (e2)) -> (~((e2) = (e3))) -> False). % 15.16/15.34 do 0 intro. intros zenon_H90 zenon_Ha3 zenon_Hd8 zenon_H182 zenon_H17d zenon_H106 zenon_H82 zenon_H6a. % 15.16/15.34 apply (zenon_or_s _ _ zenon_H90); [ zenon_intro zenon_H69 | zenon_intro zenon_H94 ]. % 15.16/15.34 apply (zenon_L163_); trivial. % 15.16/15.34 apply (zenon_or_s _ _ zenon_H94); [ zenon_intro zenon_H96 | zenon_intro zenon_H95 ]. % 15.16/15.34 exact (zenon_H182 zenon_H96). % 15.16/15.34 apply (zenon_or_s _ _ zenon_H95); [ zenon_intro zenon_H88 | zenon_intro zenon_H8a ]. % 15.16/15.34 apply (zenon_L164_); trivial. % 15.16/15.34 apply (zenon_L165_); trivial. % 15.16/15.34 (* end of lemma zenon_L166_ *) % 15.16/15.34 assert (zenon_L167_ : (((op (e1) (e0)) = (e2))\/(((op (e1) (e1)) = (e2))\/(((op (e1) (e2)) = (e2))\/((op (e1) (e3)) = (e2))))) -> (~((e1) = (e2))) -> (~((op (e1) (e1)) = (e2))) -> (~((op (e1) (e2)) = (op (e2) (e2)))) -> ((op (e2) (e2)) = (e2)) -> (((op (e1) (e0)) = (e3))\/(((op (e1) (e1)) = (e3))\/(((op (e1) (e2)) = (e3))\/((op (e1) (e3)) = (e3))))) -> (~((e1) = (e3))) -> ((op (e1) (e0)) = (e1)) -> (~((op (e1) (e1)) = (e3))) -> (~((op (e1) (e2)) = (op (e3) (e2)))) -> ((op (e3) (e2)) = (e3)) -> (~((e2) = (e3))) -> False). % 15.16/15.34 do 0 intro. intros zenon_H84 zenon_Ha7 zenon_Hd6 zenon_H7d zenon_H35 zenon_H90 zenon_Ha3 zenon_Hd8 zenon_H182 zenon_H17d zenon_H106 zenon_H6a. % 15.16/15.34 apply (zenon_or_s _ _ zenon_H84); [ zenon_intro zenon_H68 | zenon_intro zenon_H85 ]. % 15.16/15.34 apply (zenon_L162_); trivial. % 15.16/15.34 apply (zenon_or_s _ _ zenon_H85); [ zenon_intro zenon_H6e | zenon_intro zenon_H86 ]. % 15.16/15.34 exact (zenon_Hd6 zenon_H6e). % 15.16/15.34 apply (zenon_or_s _ _ zenon_H86); [ zenon_intro zenon_H7c | zenon_intro zenon_H82 ]. % 15.16/15.34 apply (zenon_L21_); trivial. % 15.16/15.34 apply (zenon_L166_); trivial. % 15.16/15.34 (* end of lemma zenon_L167_ *) % 15.16/15.34 assert (zenon_L168_ : (((op (e0) (e0)) = (e2))\/(((op (e0) (e1)) = (e2))\/(((op (e0) (e2)) = (e2))\/((op (e0) (e3)) = (e2))))) -> (~((op (e0) (e0)) = (e2))) -> (~((e0) = (e2))) -> ((op (e0) (e1)) = (e0)) -> (~((e1) = (e2))) -> ((op (e0) (e2)) = (e1)) -> (((op (e3) (e3)) = (e0))\/(((op (e3) (e3)) = (e1))\/(((op (e3) (e3)) = (e2))\/((op (e3) (e3)) = (e3))))) -> (~((op (e3) (e3)) = (e0))) -> (~((op (e3) (e3)) = (e1))) -> (~((op (e0) (e3)) = (op (e3) (e3)))) -> (~((op (e3) (e3)) = (e3))) -> False). % 15.16/15.34 do 0 intro. intros zenon_H8e zenon_H8f zenon_H5e zenon_H49 zenon_Ha7 zenon_H29 zenon_H3b zenon_H3c zenon_H104 zenon_H36 zenon_H3e. % 15.16/15.34 apply (zenon_or_s _ _ zenon_H8e); [ zenon_intro zenon_H92 | zenon_intro zenon_H91 ]. % 15.16/15.34 exact (zenon_H8f zenon_H92). % 15.16/15.34 apply (zenon_or_s _ _ zenon_H91); [ zenon_intro zenon_H5d | zenon_intro zenon_H93 ]. % 15.16/15.34 apply (zenon_L14_); trivial. % 15.16/15.34 apply (zenon_or_s _ _ zenon_H93); [ zenon_intro zenon_H63 | zenon_intro zenon_H81 ]. % 15.16/15.34 apply (zenon_L104_); trivial. % 15.16/15.34 apply (zenon_L107_); trivial. % 15.16/15.34 (* end of lemma zenon_L168_ *) % 15.16/15.34 assert (zenon_L169_ : (((op (e0) (e2)) = (e0))\/(((op (e1) (e2)) = (e0))\/(((op (e2) (e2)) = (e0))\/((op (e3) (e2)) = (e0))))) -> ((op (e0) (e3)) = (e0)) -> (~((op (e0) (e2)) = (op (e0) (e3)))) -> (~((e0) = (e3))) -> ((op (e1) (e2)) = (e3)) -> (~((op (e2) (e2)) = (e0))) -> (~((op (e3) (e1)) = (op (e3) (e2)))) -> ((op (e3) (e1)) = (e0)) -> False). % 15.16/15.34 do 0 intro. intros zenon_H16f zenon_Hca zenon_Hc9 zenon_H4b zenon_H88 zenon_H2e zenon_H135 zenon_H142. % 15.16/15.34 apply (zenon_or_s _ _ zenon_H16f); [ zenon_intro zenon_Hab | zenon_intro zenon_H170 ]. % 15.16/15.34 apply (zenon_L53_); trivial. % 15.16/15.34 apply (zenon_or_s _ _ zenon_H170); [ zenon_intro zenon_H15d | zenon_intro zenon_H171 ]. % 15.16/15.34 apply (zenon_L152_); trivial. % 15.16/15.34 apply (zenon_or_s _ _ zenon_H171); [ zenon_intro zenon_H32 | zenon_intro zenon_H167 ]. % 15.16/15.34 exact (zenon_H2e zenon_H32). % 15.16/15.34 apply (zenon_L144_); trivial. % 15.16/15.34 (* end of lemma zenon_L169_ *) % 15.16/15.34 assert (zenon_L170_ : (~((op (op (e3) (e3)) (op (e3) (e3))) = (op (e2) (e2)))) -> ((op (e3) (e3)) = (e2)) -> False). % 15.16/15.34 do 0 intro. intros zenon_H183 zenon_H43. % 15.16/15.34 cut (((op (e3) (e3)) = (e2))); [idtac | apply NNPP; zenon_intro zenon_H3d]. % 15.16/15.34 cut (((op (e3) (e3)) = (e2))); [idtac | apply NNPP; zenon_intro zenon_H3d]. % 15.16/15.34 congruence. % 15.16/15.34 exact (zenon_H3d zenon_H43). % 15.16/15.34 exact (zenon_H3d zenon_H43). % 15.16/15.34 (* end of lemma zenon_L170_ *) % 15.16/15.34 assert (zenon_L171_ : ((op (e3) (e1)) = (e0)) -> ((op (e2) (e2)) = (e1)) -> ((op (e3) (e3)) = (e2)) -> False). % 15.16/15.34 do 0 intro. intros zenon_H142 zenon_H2a zenon_H43. % 15.16/15.34 apply (zenon_notand_s _ _ ax14); [ zenon_intro zenon_H185 | zenon_intro zenon_H184 ]. % 15.16/15.34 elim (classic ((op (op (e3) (e3)) (op (e3) (e3))) = (op (op (e3) (e3)) (op (e3) (e3))))); [ zenon_intro zenon_H186 | zenon_intro zenon_H187 ]. % 15.16/15.34 cut (((op (op (e3) (e3)) (op (e3) (e3))) = (op (op (e3) (e3)) (op (e3) (e3)))) = ((e1) = (op (op (e3) (e3)) (op (e3) (e3))))). % 15.16/15.34 intro zenon_D_pnotp. % 15.16/15.34 apply zenon_H185. % 15.16/15.34 rewrite <- zenon_D_pnotp. % 15.16/15.34 exact zenon_H186. % 15.16/15.34 cut (((op (op (e3) (e3)) (op (e3) (e3))) = (op (op (e3) (e3)) (op (e3) (e3))))); [idtac | apply NNPP; zenon_intro zenon_H187]. % 15.16/15.34 cut (((op (op (e3) (e3)) (op (e3) (e3))) = (e1))); [idtac | apply NNPP; zenon_intro zenon_H188]. % 15.16/15.34 congruence. % 15.16/15.34 cut (((op (e2) (e2)) = (e1)) = ((op (op (e3) (e3)) (op (e3) (e3))) = (e1))). % 15.16/15.34 intro zenon_D_pnotp. % 15.16/15.34 apply zenon_H188. % 15.16/15.34 rewrite <- zenon_D_pnotp. % 15.16/15.34 exact zenon_H2a. % 15.16/15.34 cut (((e1) = (e1))); [idtac | apply NNPP; zenon_intro zenon_Ha0]. % 15.16/15.34 cut (((op (e2) (e2)) = (op (op (e3) (e3)) (op (e3) (e3))))); [idtac | apply NNPP; zenon_intro zenon_H189]. % 15.16/15.34 congruence. % 15.16/15.34 elim (classic ((op (op (e3) (e3)) (op (e3) (e3))) = (op (op (e3) (e3)) (op (e3) (e3))))); [ zenon_intro zenon_H186 | zenon_intro zenon_H187 ]. % 15.16/15.34 cut (((op (op (e3) (e3)) (op (e3) (e3))) = (op (op (e3) (e3)) (op (e3) (e3)))) = ((op (e2) (e2)) = (op (op (e3) (e3)) (op (e3) (e3))))). % 15.16/15.34 intro zenon_D_pnotp. % 15.16/15.34 apply zenon_H189. % 15.16/15.34 rewrite <- zenon_D_pnotp. % 15.16/15.34 exact zenon_H186. % 15.16/15.34 cut (((op (op (e3) (e3)) (op (e3) (e3))) = (op (op (e3) (e3)) (op (e3) (e3))))); [idtac | apply NNPP; zenon_intro zenon_H187]. % 15.16/15.34 cut (((op (op (e3) (e3)) (op (e3) (e3))) = (op (e2) (e2)))); [idtac | apply NNPP; zenon_intro zenon_H183]. % 15.16/15.34 congruence. % 15.16/15.34 apply (zenon_L170_); trivial. % 15.16/15.34 apply zenon_H187. apply refl_equal. % 15.16/15.34 apply zenon_H187. apply refl_equal. % 15.16/15.34 apply zenon_Ha0. apply refl_equal. % 15.16/15.34 apply zenon_H187. apply refl_equal. % 15.16/15.34 apply zenon_H187. apply refl_equal. % 15.16/15.34 apply (zenon_notand_s _ _ zenon_H184); [ zenon_intro zenon_H130 | zenon_intro zenon_H18a ]. % 15.16/15.34 apply zenon_H130. apply sym_equal. exact zenon_H43. % 15.16/15.34 elim (classic ((op (e3) (op (op (e3) (e3)) (op (e3) (e3)))) = (op (e3) (op (op (e3) (e3)) (op (e3) (e3)))))); [ zenon_intro zenon_H18b | zenon_intro zenon_H18c ]. % 15.16/15.34 cut (((op (e3) (op (op (e3) (e3)) (op (e3) (e3)))) = (op (e3) (op (op (e3) (e3)) (op (e3) (e3))))) = ((e0) = (op (e3) (op (op (e3) (e3)) (op (e3) (e3)))))). % 15.16/15.34 intro zenon_D_pnotp. % 15.16/15.34 apply zenon_H18a. % 15.16/15.34 rewrite <- zenon_D_pnotp. % 15.16/15.34 exact zenon_H18b. % 15.16/15.34 cut (((op (e3) (op (op (e3) (e3)) (op (e3) (e3)))) = (op (e3) (op (op (e3) (e3)) (op (e3) (e3)))))); [idtac | apply NNPP; zenon_intro zenon_H18c]. % 15.16/15.34 cut (((op (e3) (op (op (e3) (e3)) (op (e3) (e3)))) = (e0))); [idtac | apply NNPP; zenon_intro zenon_H18d]. % 15.16/15.34 congruence. % 15.16/15.34 cut (((op (e3) (e1)) = (e0)) = ((op (e3) (op (op (e3) (e3)) (op (e3) (e3)))) = (e0))). % 15.16/15.34 intro zenon_D_pnotp. % 15.16/15.34 apply zenon_H18d. % 15.16/15.34 rewrite <- zenon_D_pnotp. % 15.16/15.34 exact zenon_H142. % 15.16/15.34 cut (((e0) = (e0))); [idtac | apply NNPP; zenon_intro zenon_H1d]. % 15.16/15.34 cut (((op (e3) (e1)) = (op (e3) (op (op (e3) (e3)) (op (e3) (e3)))))); [idtac | apply NNPP; zenon_intro zenon_H18e]. % 15.16/15.34 congruence. % 15.16/15.34 elim (classic ((op (e3) (op (op (e3) (e3)) (op (e3) (e3)))) = (op (e3) (op (op (e3) (e3)) (op (e3) (e3)))))); [ zenon_intro zenon_H18b | zenon_intro zenon_H18c ]. % 15.16/15.34 cut (((op (e3) (op (op (e3) (e3)) (op (e3) (e3)))) = (op (e3) (op (op (e3) (e3)) (op (e3) (e3))))) = ((op (e3) (e1)) = (op (e3) (op (op (e3) (e3)) (op (e3) (e3)))))). % 15.16/15.34 intro zenon_D_pnotp. % 15.16/15.34 apply zenon_H18e. % 15.16/15.34 rewrite <- zenon_D_pnotp. % 15.16/15.34 exact zenon_H18b. % 15.16/15.34 cut (((op (e3) (op (op (e3) (e3)) (op (e3) (e3)))) = (op (e3) (op (op (e3) (e3)) (op (e3) (e3)))))); [idtac | apply NNPP; zenon_intro zenon_H18c]. % 15.16/15.34 cut (((op (e3) (op (op (e3) (e3)) (op (e3) (e3)))) = (op (e3) (e1)))); [idtac | apply NNPP; zenon_intro zenon_H18f]. % 15.16/15.34 congruence. % 15.16/15.34 cut (((op (op (e3) (e3)) (op (e3) (e3))) = (e1))); [idtac | apply NNPP; zenon_intro zenon_H188]. % 15.16/15.34 cut (((e3) = (e3))); [idtac | apply NNPP; zenon_intro zenon_H4d]. % 15.16/15.34 congruence. % 15.16/15.34 apply zenon_H4d. apply refl_equal. % 15.16/15.34 cut (((op (e2) (e2)) = (e1)) = ((op (op (e3) (e3)) (op (e3) (e3))) = (e1))). % 15.16/15.34 intro zenon_D_pnotp. % 15.16/15.34 apply zenon_H188. % 15.16/15.34 rewrite <- zenon_D_pnotp. % 15.16/15.34 exact zenon_H2a. % 15.16/15.34 cut (((e1) = (e1))); [idtac | apply NNPP; zenon_intro zenon_Ha0]. % 15.16/15.34 cut (((op (e2) (e2)) = (op (op (e3) (e3)) (op (e3) (e3))))); [idtac | apply NNPP; zenon_intro zenon_H189]. % 15.16/15.34 congruence. % 15.16/15.34 elim (classic ((op (op (e3) (e3)) (op (e3) (e3))) = (op (op (e3) (e3)) (op (e3) (e3))))); [ zenon_intro zenon_H186 | zenon_intro zenon_H187 ]. % 15.16/15.34 cut (((op (op (e3) (e3)) (op (e3) (e3))) = (op (op (e3) (e3)) (op (e3) (e3)))) = ((op (e2) (e2)) = (op (op (e3) (e3)) (op (e3) (e3))))). % 15.16/15.34 intro zenon_D_pnotp. % 15.16/15.34 apply zenon_H189. % 15.16/15.34 rewrite <- zenon_D_pnotp. % 15.16/15.34 exact zenon_H186. % 15.16/15.34 cut (((op (op (e3) (e3)) (op (e3) (e3))) = (op (op (e3) (e3)) (op (e3) (e3))))); [idtac | apply NNPP; zenon_intro zenon_H187]. % 15.16/15.34 cut (((op (op (e3) (e3)) (op (e3) (e3))) = (op (e2) (e2)))); [idtac | apply NNPP; zenon_intro zenon_H183]. % 15.16/15.34 congruence. % 15.16/15.34 apply (zenon_L170_); trivial. % 15.16/15.34 apply zenon_H187. apply refl_equal. % 15.16/15.34 apply zenon_H187. apply refl_equal. % 15.16/15.34 apply zenon_Ha0. apply refl_equal. % 15.16/15.34 apply zenon_H18c. apply refl_equal. % 15.16/15.34 apply zenon_H18c. apply refl_equal. % 15.16/15.34 apply zenon_H1d. apply refl_equal. % 15.16/15.34 apply zenon_H18c. apply refl_equal. % 15.16/15.34 apply zenon_H18c. apply refl_equal. % 15.16/15.34 (* end of lemma zenon_L171_ *) % 15.16/15.34 assert (zenon_L172_ : (((op (e3) (e3)) = (e0))\/(((op (e3) (e3)) = (e1))\/(((op (e3) (e3)) = (e2))\/((op (e3) (e3)) = (e3))))) -> (~((op (e3) (e3)) = (e0))) -> (~((op (e3) (e3)) = (e1))) -> ((op (e2) (e2)) = (e1)) -> ((op (e3) (e1)) = (e0)) -> (~((op (e3) (e3)) = (e3))) -> False). % 15.16/15.34 do 0 intro. intros zenon_H3b zenon_H3c zenon_H104 zenon_H2a zenon_H142 zenon_H3e. % 15.16/15.34 apply (zenon_or_s _ _ zenon_H3b); [ zenon_intro zenon_H40 | zenon_intro zenon_H3f ]. % 15.16/15.34 exact (zenon_H3c zenon_H40). % 15.16/15.34 apply (zenon_or_s _ _ zenon_H3f); [ zenon_intro zenon_H38 | zenon_intro zenon_H41 ]. % 15.16/15.34 exact (zenon_H104 zenon_H38). % 15.16/15.34 apply (zenon_or_s _ _ zenon_H41); [ zenon_intro zenon_H43 | zenon_intro zenon_H42 ]. % 15.16/15.34 apply (zenon_L171_); trivial. % 15.16/15.34 exact (zenon_H3e zenon_H42). % 15.16/15.34 (* end of lemma zenon_L172_ *) % 15.16/15.34 assert (zenon_L173_ : (((op (e0) (e2)) = (e1))\/(((op (e1) (e2)) = (e1))\/(((op (e2) (e2)) = (e1))\/((op (e3) (e2)) = (e1))))) -> (~((op (e2) (e0)) = (op (e2) (e3)))) -> ((op (e2) (e0)) = (e1)) -> (~((op (e1) (e1)) = (op (e1) (e3)))) -> (~((op (e0) (e2)) = (op (e0) (e3)))) -> (((op (e0) (e3)) = (e1))\/(((op (e1) (e3)) = (e1))\/(((op (e2) (e3)) = (e1))\/((op (e3) (e3)) = (e1))))) -> ((op (e1) (e1)) = (e1)) -> (~((op (e1) (e1)) = (op (e1) (e2)))) -> (~((op (e3) (e3)) = (e3))) -> ((op (e3) (e1)) = (e0)) -> (~((op (e3) (e3)) = (e1))) -> (~((op (e3) (e3)) = (e0))) -> (((op (e3) (e3)) = (e0))\/(((op (e3) (e3)) = (e1))\/(((op (e3) (e3)) = (e2))\/((op (e3) (e3)) = (e3))))) -> (~((e1) = (e3))) -> ((op (e3) (e2)) = (e3)) -> False). % 15.16/15.34 do 0 intro. intros zenon_H11b zenon_Hce zenon_Hae zenon_H11e zenon_Hc9 zenon_H121 zenon_H21 zenon_H116 zenon_H3e zenon_H142 zenon_H104 zenon_H3c zenon_H3b zenon_Ha3 zenon_H106. % 15.16/15.34 apply (zenon_or_s _ _ zenon_H11b); [ zenon_intro zenon_H29 | zenon_intro zenon_H11c ]. % 15.16/15.34 apply (zenon_L92_); trivial. % 15.16/15.34 apply (zenon_or_s _ _ zenon_H11c); [ zenon_intro zenon_H117 | zenon_intro zenon_H11d ]. % 15.16/15.34 apply (zenon_L86_); trivial. % 15.16/15.34 apply (zenon_or_s _ _ zenon_H11d); [ zenon_intro zenon_H2a | zenon_intro zenon_H119 ]. % 15.16/15.34 apply (zenon_L172_); trivial. % 15.16/15.34 apply (zenon_L87_); trivial. % 15.16/15.34 (* end of lemma zenon_L173_ *) % 15.16/15.34 assert (zenon_L174_ : ((op (e0) (e2)) = (e1)) -> ((op (e3) (e3)) = (e2)) -> ((op (e0) (e0)) = (e3)) -> False). % 15.16/15.34 do 0 intro. intros zenon_H29 zenon_H43 zenon_H5b. % 15.16/15.34 apply (zenon_notand_s _ _ ax23); [ zenon_intro zenon_H70 | zenon_intro zenon_H190 ]. % 15.16/15.34 elim (classic ((op (op (e0) (e0)) (op (e0) (e0))) = (op (op (e0) (e0)) (op (e0) (e0))))); [ zenon_intro zenon_H71 | zenon_intro zenon_H72 ]. % 15.16/15.34 cut (((op (op (e0) (e0)) (op (e0) (e0))) = (op (op (e0) (e0)) (op (e0) (e0)))) = ((e2) = (op (op (e0) (e0)) (op (e0) (e0))))). % 15.16/15.34 intro zenon_D_pnotp. % 15.16/15.34 apply zenon_H70. % 15.16/15.34 rewrite <- zenon_D_pnotp. % 15.16/15.34 exact zenon_H71. % 15.16/15.34 cut (((op (op (e0) (e0)) (op (e0) (e0))) = (op (op (e0) (e0)) (op (e0) (e0))))); [idtac | apply NNPP; zenon_intro zenon_H72]. % 15.16/15.34 cut (((op (op (e0) (e0)) (op (e0) (e0))) = (e2))); [idtac | apply NNPP; zenon_intro zenon_H73]. % 15.16/15.34 congruence. % 15.16/15.34 cut (((op (e3) (e3)) = (e2)) = ((op (op (e0) (e0)) (op (e0) (e0))) = (e2))). % 15.16/15.34 intro zenon_D_pnotp. % 15.16/15.34 apply zenon_H73. % 15.16/15.34 rewrite <- zenon_D_pnotp. % 15.16/15.34 exact zenon_H43. % 15.16/15.34 cut (((e2) = (e2))); [idtac | apply NNPP; zenon_intro zenon_H60]. % 15.16/15.34 cut (((op (e3) (e3)) = (op (op (e0) (e0)) (op (e0) (e0))))); [idtac | apply NNPP; zenon_intro zenon_H133]. % 15.16/15.34 congruence. % 15.16/15.34 elim (classic ((op (op (e0) (e0)) (op (e0) (e0))) = (op (op (e0) (e0)) (op (e0) (e0))))); [ zenon_intro zenon_H71 | zenon_intro zenon_H72 ]. % 15.16/15.34 cut (((op (op (e0) (e0)) (op (e0) (e0))) = (op (op (e0) (e0)) (op (e0) (e0)))) = ((op (e3) (e3)) = (op (op (e0) (e0)) (op (e0) (e0))))). % 15.16/15.34 intro zenon_D_pnotp. % 15.16/15.34 apply zenon_H133. % 15.16/15.34 rewrite <- zenon_D_pnotp. % 15.16/15.34 exact zenon_H71. % 15.16/15.34 cut (((op (op (e0) (e0)) (op (e0) (e0))) = (op (op (e0) (e0)) (op (e0) (e0))))); [idtac | apply NNPP; zenon_intro zenon_H72]. % 15.16/15.34 cut (((op (op (e0) (e0)) (op (e0) (e0))) = (op (e3) (e3)))); [idtac | apply NNPP; zenon_intro zenon_H131]. % 15.16/15.34 congruence. % 15.16/15.34 apply (zenon_L110_); trivial. % 15.16/15.34 apply zenon_H72. apply refl_equal. % 15.16/15.34 apply zenon_H72. apply refl_equal. % 15.16/15.34 apply zenon_H60. apply refl_equal. % 15.16/15.34 apply zenon_H72. apply refl_equal. % 15.16/15.34 apply zenon_H72. apply refl_equal. % 15.16/15.34 apply (zenon_notand_s _ _ zenon_H190); [ zenon_intro zenon_H134 | zenon_intro zenon_H127 ]. % 15.16/15.34 apply zenon_H134. apply sym_equal. exact zenon_H5b. % 15.16/15.34 elim (classic ((op (e0) (op (op (e0) (e0)) (op (e0) (e0)))) = (op (e0) (op (op (e0) (e0)) (op (e0) (e0)))))); [ zenon_intro zenon_H77 | zenon_intro zenon_H78 ]. % 15.16/15.34 cut (((op (e0) (op (op (e0) (e0)) (op (e0) (e0)))) = (op (e0) (op (op (e0) (e0)) (op (e0) (e0))))) = ((e1) = (op (e0) (op (op (e0) (e0)) (op (e0) (e0)))))). % 15.16/15.34 intro zenon_D_pnotp. % 15.16/15.34 apply zenon_H127. % 15.16/15.34 rewrite <- zenon_D_pnotp. % 15.16/15.34 exact zenon_H77. % 15.16/15.34 cut (((op (e0) (op (op (e0) (e0)) (op (e0) (e0)))) = (op (e0) (op (op (e0) (e0)) (op (e0) (e0)))))); [idtac | apply NNPP; zenon_intro zenon_H78]. % 15.16/15.34 cut (((op (e0) (op (op (e0) (e0)) (op (e0) (e0)))) = (e1))); [idtac | apply NNPP; zenon_intro zenon_H128]. % 15.16/15.34 congruence. % 15.16/15.34 cut (((op (e0) (e2)) = (e1)) = ((op (e0) (op (op (e0) (e0)) (op (e0) (e0)))) = (e1))). % 15.16/15.34 intro zenon_D_pnotp. % 15.16/15.34 apply zenon_H128. % 15.16/15.34 rewrite <- zenon_D_pnotp. % 15.16/15.34 exact zenon_H29. % 15.16/15.34 cut (((e1) = (e1))); [idtac | apply NNPP; zenon_intro zenon_Ha0]. % 15.16/15.34 cut (((op (e0) (e2)) = (op (e0) (op (op (e0) (e0)) (op (e0) (e0)))))); [idtac | apply NNPP; zenon_intro zenon_H7a]. % 15.16/15.34 congruence. % 15.16/15.34 elim (classic ((op (e0) (op (op (e0) (e0)) (op (e0) (e0)))) = (op (e0) (op (op (e0) (e0)) (op (e0) (e0)))))); [ zenon_intro zenon_H77 | zenon_intro zenon_H78 ]. % 15.16/15.34 cut (((op (e0) (op (op (e0) (e0)) (op (e0) (e0)))) = (op (e0) (op (op (e0) (e0)) (op (e0) (e0))))) = ((op (e0) (e2)) = (op (e0) (op (op (e0) (e0)) (op (e0) (e0)))))). % 15.16/15.34 intro zenon_D_pnotp. % 15.16/15.34 apply zenon_H7a. % 15.16/15.34 rewrite <- zenon_D_pnotp. % 15.16/15.34 exact zenon_H77. % 15.16/15.34 cut (((op (e0) (op (op (e0) (e0)) (op (e0) (e0)))) = (op (e0) (op (op (e0) (e0)) (op (e0) (e0)))))); [idtac | apply NNPP; zenon_intro zenon_H78]. % 15.16/15.34 cut (((op (e0) (op (op (e0) (e0)) (op (e0) (e0)))) = (op (e0) (e2)))); [idtac | apply NNPP; zenon_intro zenon_H7b]. % 15.16/15.34 congruence. % 15.16/15.34 cut (((op (op (e0) (e0)) (op (e0) (e0))) = (e2))); [idtac | apply NNPP; zenon_intro zenon_H73]. % 15.16/15.34 cut (((e0) = (e0))); [idtac | apply NNPP; zenon_intro zenon_H1d]. % 15.16/15.34 congruence. % 15.16/15.34 apply zenon_H1d. apply refl_equal. % 15.16/15.34 cut (((op (e3) (e3)) = (e2)) = ((op (op (e0) (e0)) (op (e0) (e0))) = (e2))). % 15.16/15.34 intro zenon_D_pnotp. % 15.16/15.34 apply zenon_H73. % 15.16/15.34 rewrite <- zenon_D_pnotp. % 15.16/15.34 exact zenon_H43. % 15.16/15.34 cut (((e2) = (e2))); [idtac | apply NNPP; zenon_intro zenon_H60]. % 15.16/15.34 cut (((op (e3) (e3)) = (op (op (e0) (e0)) (op (e0) (e0))))); [idtac | apply NNPP; zenon_intro zenon_H133]. % 15.16/15.34 congruence. % 15.16/15.34 elim (classic ((op (op (e0) (e0)) (op (e0) (e0))) = (op (op (e0) (e0)) (op (e0) (e0))))); [ zenon_intro zenon_H71 | zenon_intro zenon_H72 ]. % 15.16/15.34 cut (((op (op (e0) (e0)) (op (e0) (e0))) = (op (op (e0) (e0)) (op (e0) (e0)))) = ((op (e3) (e3)) = (op (op (e0) (e0)) (op (e0) (e0))))). % 15.16/15.34 intro zenon_D_pnotp. % 15.16/15.34 apply zenon_H133. % 15.16/15.34 rewrite <- zenon_D_pnotp. % 15.16/15.34 exact zenon_H71. % 15.16/15.34 cut (((op (op (e0) (e0)) (op (e0) (e0))) = (op (op (e0) (e0)) (op (e0) (e0))))); [idtac | apply NNPP; zenon_intro zenon_H72]. % 15.16/15.34 cut (((op (op (e0) (e0)) (op (e0) (e0))) = (op (e3) (e3)))); [idtac | apply NNPP; zenon_intro zenon_H131]. % 15.16/15.34 congruence. % 15.16/15.34 apply (zenon_L110_); trivial. % 15.16/15.34 apply zenon_H72. apply refl_equal. % 15.16/15.34 apply zenon_H72. apply refl_equal. % 15.16/15.34 apply zenon_H60. apply refl_equal. % 15.16/15.34 apply zenon_H78. apply refl_equal. % 15.16/15.34 apply zenon_H78. apply refl_equal. % 15.16/15.34 apply zenon_Ha0. apply refl_equal. % 15.16/15.34 apply zenon_H78. apply refl_equal. % 15.16/15.34 apply zenon_H78. apply refl_equal. % 15.16/15.34 (* end of lemma zenon_L174_ *) % 15.16/15.34 assert (zenon_L175_ : (((op (e0) (e0)) = (e0))\/(((op (e0) (e0)) = (e1))\/(((op (e0) (e0)) = (e2))\/((op (e0) (e0)) = (e3))))) -> (~((op (e0) (e0)) = (e0))) -> (~((op (e0) (e0)) = (e1))) -> (~((op (e0) (e0)) = (e2))) -> ((op (e0) (e2)) = (e1)) -> ((op (e3) (e3)) = (e2)) -> False). % 15.16/15.34 do 0 intro. intros zenon_H12a zenon_H20 zenon_H45 zenon_H8f zenon_H29 zenon_H43. % 15.16/15.34 apply (zenon_or_s _ _ zenon_H12a); [ zenon_intro zenon_H1f | zenon_intro zenon_H12b ]. % 15.16/15.34 exact (zenon_H20 zenon_H1f). % 15.16/15.34 apply (zenon_or_s _ _ zenon_H12b); [ zenon_intro zenon_H47 | zenon_intro zenon_H12c ]. % 15.16/15.34 exact (zenon_H45 zenon_H47). % 15.16/15.34 apply (zenon_or_s _ _ zenon_H12c); [ zenon_intro zenon_H92 | zenon_intro zenon_H5b ]. % 15.16/15.34 exact (zenon_H8f zenon_H92). % 15.16/15.34 apply (zenon_L174_); trivial. % 15.16/15.34 (* end of lemma zenon_L175_ *) % 15.16/15.34 assert (zenon_L176_ : (((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 (e3) (e3)) = (e1))) -> (~((op (e3) (e3)) = (e0))) -> (((op (e3) (e3)) = (e0))\/(((op (e3) (e3)) = (e1))\/(((op (e3) (e3)) = (e2))\/((op (e3) (e3)) = (e3))))) -> (~((e2) = (e3))) -> ((op (e1) (e3)) = (e3)) -> ((op (e2) (e3)) = (e1)) -> (~((e1) = (e2))) -> (((op (e0) (e0)) = (e0))\/(((op (e0) (e0)) = (e1))\/(((op (e0) (e0)) = (e2))\/((op (e0) (e0)) = (e3))))) -> (~((op (e0) (e0)) = (e0))) -> (~((op (e0) (e0)) = (e1))) -> (~((op (e0) (e0)) = (e2))) -> ((op (e0) (e2)) = (e1)) -> False). % 15.16/15.34 do 0 intro. intros zenon_H160 zenon_H3e zenon_H36 zenon_H104 zenon_H3c zenon_H3b zenon_H6a zenon_H8a zenon_Hb5 zenon_Ha7 zenon_H12a zenon_H20 zenon_H45 zenon_H8f zenon_H29. % 15.16/15.34 apply (zenon_or_s _ _ zenon_H160); [ zenon_intro zenon_H81 | zenon_intro zenon_H161 ]. % 15.16/15.34 apply (zenon_L107_); trivial. % 15.16/15.34 apply (zenon_or_s _ _ zenon_H161); [ zenon_intro zenon_H82 | zenon_intro zenon_H162 ]. % 15.16/15.34 apply (zenon_L165_); trivial. % 15.16/15.34 apply (zenon_or_s _ _ zenon_H162); [ zenon_intro zenon_H124 | zenon_intro zenon_H43 ]. % 15.16/15.34 apply (zenon_L93_); trivial. % 15.16/15.34 apply (zenon_L175_); trivial. % 15.16/15.34 (* end of lemma zenon_L176_ *) % 15.16/15.34 assert (zenon_L177_ : (~((e0) = (e2))) -> ((op (e2) (e0)) = (e2)) -> ((op (e2) (e0)) = (e0)) -> False). % 15.16/15.34 do 0 intro. intros zenon_H5e zenon_Hdd zenon_Hcf. % 15.16/15.34 cut (((op (e2) (e0)) = (e2)) = ((e0) = (e2))). % 15.16/15.34 intro zenon_D_pnotp. % 15.16/15.34 apply zenon_H5e. % 15.16/15.34 rewrite <- zenon_D_pnotp. % 15.16/15.34 exact zenon_Hdd. % 15.16/15.34 cut (((e2) = (e2))); [idtac | apply NNPP; zenon_intro zenon_H60]. % 15.16/15.34 cut (((op (e2) (e0)) = (e0))); [idtac | apply NNPP; zenon_intro zenon_H191]. % 15.16/15.34 congruence. % 15.16/15.34 exact (zenon_H191 zenon_Hcf). % 15.16/15.34 apply zenon_H60. apply refl_equal. % 15.16/15.34 (* end of lemma zenon_L177_ *) % 15.16/15.34 assert (zenon_L178_ : (~((op (e3) (op (e0) (e3))) = (op (e0) (e3)))) -> ((op (e3) (e0)) = (e0)) -> ((op (e0) (e3)) = (e0)) -> False). % 15.16/15.34 do 0 intro. intros zenon_H192 zenon_Hdb zenon_Hca. % 15.16/15.34 cut (((op (e3) (e0)) = (e0)) = ((op (e3) (op (e0) (e3))) = (op (e0) (e3)))). % 15.16/15.34 intro zenon_D_pnotp. % 15.16/15.34 apply zenon_H192. % 15.16/15.34 rewrite <- zenon_D_pnotp. % 15.16/15.34 exact zenon_Hdb. % 15.16/15.34 cut (((e0) = (op (e0) (e3)))); [idtac | apply NNPP; zenon_intro zenon_Hcb]. % 15.16/15.34 cut (((op (e3) (e0)) = (op (e3) (op (e0) (e3))))); [idtac | apply NNPP; zenon_intro zenon_H193]. % 15.16/15.34 congruence. % 15.16/15.34 elim (classic ((op (e3) (op (e0) (e3))) = (op (e3) (op (e0) (e3))))); [ zenon_intro zenon_H194 | zenon_intro zenon_H195 ]. % 15.16/15.34 cut (((op (e3) (op (e0) (e3))) = (op (e3) (op (e0) (e3)))) = ((op (e3) (e0)) = (op (e3) (op (e0) (e3))))). % 15.16/15.34 intro zenon_D_pnotp. % 15.16/15.34 apply zenon_H193. % 15.16/15.34 rewrite <- zenon_D_pnotp. % 15.16/15.34 exact zenon_H194. % 15.16/15.34 cut (((op (e3) (op (e0) (e3))) = (op (e3) (op (e0) (e3))))); [idtac | apply NNPP; zenon_intro zenon_H195]. % 15.16/15.34 cut (((op (e3) (op (e0) (e3))) = (op (e3) (e0)))); [idtac | apply NNPP; zenon_intro zenon_H196]. % 15.16/15.34 congruence. % 15.16/15.34 cut (((op (e0) (e3)) = (e0))); [idtac | apply NNPP; zenon_intro zenon_H197]. % 15.16/15.34 cut (((e3) = (e3))); [idtac | apply NNPP; zenon_intro zenon_H4d]. % 15.16/15.34 congruence. % 15.16/15.34 apply zenon_H4d. apply refl_equal. % 15.16/15.34 exact (zenon_H197 zenon_Hca). % 15.16/15.34 apply zenon_H195. apply refl_equal. % 15.16/15.34 apply zenon_H195. apply refl_equal. % 15.16/15.34 apply zenon_Hcb. apply sym_equal. exact zenon_Hca. % 15.16/15.34 (* end of lemma zenon_L178_ *) % 15.16/15.34 assert (zenon_L179_ : (((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 (e2) (e0)) = (op (e2) (e2)))) -> ((op (e3) (e2)) = (e3)) -> (~((e1) = (e3))) -> (~((op (e2) (e2)) = (e1))) -> (~((op (e1) (e1)) = (op (e1) (e2)))) -> ((op (e1) (e1)) = (e1)) -> (~((op (e0) (e2)) = (op (e0) (e3)))) -> (((op (e0) (e2)) = (e1))\/(((op (e1) (e2)) = (e1))\/(((op (e2) (e2)) = (e1))\/((op (e3) (e2)) = (e1))))) -> (((op (e0) (e0)) = (e1))\/(((op (e1) (e0)) = (e1))\/(((op (e2) (e0)) = (e1))\/((op (e3) (e0)) = (e1))))) -> (~((op (e1) (e2)) = (op (e3) (e2)))) -> ((op (e2) (e2)) = (e2)) -> (~((op (e1) (e2)) = (op (e2) (e2)))) -> (~((op (e1) (e1)) = (e2))) -> (((op (e1) (e0)) = (e2))\/(((op (e1) (e1)) = (e2))\/(((op (e1) (e2)) = (e2))\/((op (e1) (e3)) = (e2))))) -> (((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) (e0)) = (e0))) -> (((op (e0) (e0)) = (e0))\/(((op (e0) (e0)) = (e1))\/(((op (e0) (e0)) = (e2))\/((op (e0) (e0)) = (e3))))) -> (~((e2) = (e3))) -> (((op (e3) (e3)) = (e0))\/(((op (e3) (e3)) = (e1))\/(((op (e3) (e3)) = (e2))\/((op (e3) (e3)) = (e3))))) -> (~((op (e3) (e3)) = (e0))) -> (~((op (e3) (e3)) = (e1))) -> (~((op (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 (e1) (e1)) = (op (e2) (e1)))) -> (~((op (e2) (e0)) = (op (e2) (e3)))) -> (~((op (e1) (e1)) = (op (e1) (e3)))) -> (((op (e0) (e3)) = (e1))\/(((op (e1) (e3)) = (e1))\/(((op (e2) (e3)) = (e1))\/((op (e3) (e3)) = (e1))))) -> (((op (e2) (e0)) = (e1))\/(((op (e2) (e1)) = (e1))\/(((op (e2) (e2)) = (e1))\/((op (e2) (e3)) = (e1))))) -> (((op (e0) (e2)) = (e0))\/(((op (e1) (e2)) = (e0))\/(((op (e2) (e2)) = (e0))\/((op (e3) (e2)) = (e0))))) -> (~((e0) = (e3))) -> (~((op (e2) (e2)) = (e0))) -> (~((op (e3) (e1)) = (op (e3) (e2)))) -> (~((op (e1) (e1)) = (e3))) -> (((op (e1) (e0)) = (e3))\/(((op (e1) (e1)) = (e3))\/(((op (e1) (e2)) = (e3))\/((op (e1) (e3)) = (e3))))) -> (~((op (e2) (e0)) = (op (e2) (e1)))) -> (~((op (e1) (e1)) = (e0))) -> (((op (e0) (e0)) = (e2))\/(((op (e0) (e1)) = (e2))\/(((op (e0) (e2)) = (e2))\/((op (e0) (e3)) = (e2))))) -> (((op (e0) (e1)) = (e0))\/(((op (e1) (e1)) = (e0))\/(((op (e2) (e1)) = (e0))\/((op (e3) (e1)) = (e0))))) -> (~((e0) = (e2))) -> (~((e1) = (e2))) -> (~((op (e0) (e1)) = (op (e1) (e1)))) -> (((op (e0) (e0)) = (e1))\/(((op (e0) (e1)) = (e1))\/(((op (e0) (e2)) = (e1))\/((op (e0) (e3)) = (e1))))) -> (~((op (e3) (op (e0) (e3))) = (op (e0) (e3)))) -> ((op (e0) (e3)) = (e0)) -> False). % 15.16/15.34 do 0 intro. intros zenon_Hf0 zenon_H9e zenon_Hd7 zenon_H17a zenon_H106 zenon_Ha3 zenon_H52 zenon_H116 zenon_H21 zenon_Hc9 zenon_H11b zenon_Hf1 zenon_H17d zenon_H35 zenon_H7d zenon_Hd6 zenon_H84 zenon_Heb zenon_H8f zenon_H45 zenon_H20 zenon_H12a zenon_H6a zenon_H3b zenon_H3c zenon_H104 zenon_H36 zenon_H3e zenon_H160 zenon_Hb1 zenon_Hce zenon_H11e zenon_H121 zenon_Hb7 zenon_H16f zenon_H4b zenon_H2e zenon_H135 zenon_H182 zenon_H90 zenon_H154 zenon_H145 zenon_H8e zenon_H144 zenon_H5e zenon_Ha7 zenon_H23 zenon_H44 zenon_H192 zenon_Hca. % 15.16/15.34 apply (zenon_or_s _ _ zenon_Hf0); [ zenon_intro zenon_H1f | zenon_intro zenon_Hf2 ]. % 15.16/15.34 exact (zenon_H20 zenon_H1f). % 15.16/15.34 apply (zenon_or_s _ _ zenon_Hf2); [ zenon_intro zenon_Had | zenon_intro zenon_Hf3 ]. % 15.16/15.34 apply (zenon_or_s _ _ zenon_H44); [ zenon_intro zenon_H47 | zenon_intro zenon_H46 ]. % 15.16/15.34 exact (zenon_H45 zenon_H47). % 15.16/15.34 apply (zenon_or_s _ _ zenon_H46); [ zenon_intro zenon_H22 | zenon_intro zenon_H48 ]. % 15.16/15.34 apply (zenon_L3_); trivial. % 15.16/15.34 apply (zenon_or_s _ _ zenon_H48); [ zenon_intro zenon_H29 | zenon_intro zenon_H37 ]. % 15.16/15.34 apply (zenon_or_s _ _ zenon_Hf1); [ zenon_intro zenon_H47 | zenon_intro zenon_Hf4 ]. % 15.16/15.34 exact (zenon_H45 zenon_H47). % 15.16/15.34 apply (zenon_or_s _ _ zenon_Hf4); [ zenon_intro zenon_Hd8 | zenon_intro zenon_Hf5 ]. % 15.16/15.34 apply (zenon_L61_); trivial. % 15.16/15.34 apply (zenon_or_s _ _ zenon_Hf5); [ zenon_intro zenon_Hae | zenon_intro zenon_Hee ]. % 15.16/15.34 apply (zenon_L92_); trivial. % 15.16/15.34 apply (zenon_or_s _ _ zenon_Heb); [ zenon_intro zenon_H92 | zenon_intro zenon_Hec ]. % 15.16/15.34 exact (zenon_H8f zenon_H92). % 15.16/15.34 apply (zenon_or_s _ _ zenon_Hec); [ zenon_intro zenon_H68 | zenon_intro zenon_Hed ]. % 15.16/15.34 apply (zenon_L160_); trivial. % 15.16/15.34 apply (zenon_or_s _ _ zenon_Hed); [ zenon_intro zenon_Hdd | zenon_intro zenon_He9 ]. % 15.16/15.34 apply (zenon_L161_); trivial. % 15.16/15.34 apply (zenon_L122_); trivial. % 15.16/15.34 apply (zenon_L73_); trivial. % 15.16/15.34 apply (zenon_or_s _ _ zenon_Hf3); [ zenon_intro zenon_Hcf | zenon_intro zenon_Hdb ]. % 15.16/15.34 apply (zenon_or_s _ _ zenon_H44); [ zenon_intro zenon_H47 | zenon_intro zenon_H46 ]. % 15.16/15.34 exact (zenon_H45 zenon_H47). % 15.16/15.34 apply (zenon_or_s _ _ zenon_H46); [ zenon_intro zenon_H22 | zenon_intro zenon_H48 ]. % 15.16/15.34 apply (zenon_L3_); trivial. % 15.16/15.34 apply (zenon_or_s _ _ zenon_H48); [ zenon_intro zenon_H29 | zenon_intro zenon_H37 ]. % 15.16/15.34 apply (zenon_or_s _ _ zenon_Hf1); [ zenon_intro zenon_H47 | zenon_intro zenon_Hf4 ]. % 15.16/15.34 exact (zenon_H45 zenon_H47). % 15.16/15.34 apply (zenon_or_s _ _ zenon_Hf4); [ zenon_intro zenon_Hd8 | zenon_intro zenon_Hf5 ]. % 15.16/15.34 apply (zenon_L167_); trivial. % 15.16/15.34 apply (zenon_or_s _ _ zenon_Hf5); [ zenon_intro zenon_Hae | zenon_intro zenon_Hee ]. % 15.16/15.34 apply (zenon_L92_); trivial. % 15.16/15.34 apply (zenon_or_s _ _ zenon_Heb); [ zenon_intro zenon_H92 | zenon_intro zenon_Hec ]. % 15.16/15.34 exact (zenon_H8f zenon_H92). % 15.16/15.34 apply (zenon_or_s _ _ zenon_Hec); [ zenon_intro zenon_H68 | zenon_intro zenon_Hed ]. % 15.16/15.34 apply (zenon_or_s _ _ zenon_H144); [ zenon_intro zenon_H49 | zenon_intro zenon_H147 ]. % 15.16/15.34 apply (zenon_L168_); trivial. % 15.16/15.34 apply (zenon_or_s _ _ zenon_H147); [ zenon_intro zenon_H149 | zenon_intro zenon_H148 ]. % 15.16/15.34 exact (zenon_H145 zenon_H149). % 15.16/15.34 apply (zenon_or_s _ _ zenon_H148); [ zenon_intro zenon_H14a | zenon_intro zenon_H142 ]. % 15.16/15.34 apply (zenon_L133_); trivial. % 15.16/15.34 apply (zenon_or_s _ _ zenon_H90); [ zenon_intro zenon_H69 | zenon_intro zenon_H94 ]. % 15.16/15.34 apply (zenon_L17_); trivial. % 15.16/15.34 apply (zenon_or_s _ _ zenon_H94); [ zenon_intro zenon_H96 | zenon_intro zenon_H95 ]. % 15.16/15.34 exact (zenon_H182 zenon_H96). % 15.16/15.34 apply (zenon_or_s _ _ zenon_H95); [ zenon_intro zenon_H88 | zenon_intro zenon_H8a ]. % 15.16/15.34 apply (zenon_L169_); trivial. % 15.16/15.34 apply (zenon_or_s _ _ zenon_Hb7); [ zenon_intro zenon_Hae | zenon_intro zenon_Hb8 ]. % 15.16/15.34 apply (zenon_L173_); trivial. % 15.16/15.34 apply (zenon_or_s _ _ zenon_Hb8); [ zenon_intro zenon_Hb2 | zenon_intro zenon_Hb9 ]. % 15.16/15.34 apply (zenon_L40_); trivial. % 15.16/15.34 apply (zenon_or_s _ _ zenon_Hb9); [ zenon_intro zenon_H2a | zenon_intro zenon_Hb5 ]. % 15.16/15.34 exact (zenon_H52 zenon_H2a). % 15.16/15.34 apply (zenon_L176_); trivial. % 15.16/15.34 apply (zenon_or_s _ _ zenon_Hed); [ zenon_intro zenon_Hdd | zenon_intro zenon_He9 ]. % 15.16/15.34 apply (zenon_L177_); trivial. % 15.16/15.34 apply (zenon_L122_); trivial. % 15.16/15.34 apply (zenon_L88_); trivial. % 15.16/15.34 apply (zenon_L178_); trivial. % 15.16/15.34 (* end of lemma zenon_L179_ *) % 15.16/15.34 assert (zenon_L180_ : (~((op (e0) (e1)) = (op (e2) (e1)))) -> ((op (e0) (e1)) = (e0)) -> ((op (e2) (e1)) = (e0)) -> False). % 15.16/15.34 do 0 intro. intros zenon_Hde zenon_H49 zenon_H14a. % 15.16/15.34 cut (((op (e0) (e1)) = (e0)) = ((op (e0) (e1)) = (op (e2) (e1)))). % 15.16/15.34 intro zenon_D_pnotp. % 15.16/15.34 apply zenon_Hde. % 15.16/15.34 rewrite <- zenon_D_pnotp. % 15.16/15.34 exact zenon_H49. % 15.16/15.34 cut (((e0) = (op (e2) (e1)))); [idtac | apply NNPP; zenon_intro zenon_H155]. % 15.16/15.34 cut (((op (e0) (e1)) = (op (e0) (e1)))); [idtac | apply NNPP; zenon_intro zenon_He1]. % 15.16/15.34 congruence. % 15.16/15.34 apply zenon_He1. apply refl_equal. % 15.16/15.34 apply zenon_H155. apply sym_equal. exact zenon_H14a. % 15.16/15.34 (* end of lemma zenon_L180_ *) % 15.16/15.34 assert (zenon_L181_ : (((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 (e1) (e1)) = (e1)) -> (~((op (e1) (e1)) = (op (e2) (e1)))) -> (~((op (e2) (e1)) = (op (e2) (e2)))) -> ((op (e2) (e2)) = (e2)) -> ((op (e3) (e1)) = (e3)) -> (~((op (e2) (e1)) = (op (e3) (e1)))) -> False). % 15.16/15.34 do 0 intro. intros zenon_H15a zenon_H49 zenon_Hde zenon_H21 zenon_Hb1 zenon_H157 zenon_H35 zenon_H10a zenon_H13c. % 15.16/15.34 apply (zenon_or_s _ _ zenon_H15a); [ zenon_intro zenon_H14a | zenon_intro zenon_H15b ]. % 15.16/15.34 apply (zenon_L180_); trivial. % 15.16/15.34 apply (zenon_or_s _ _ zenon_H15b); [ zenon_intro zenon_Hb2 | zenon_intro zenon_H15c ]. % 15.16/15.34 apply (zenon_L40_); trivial. % 15.16/15.34 apply (zenon_or_s _ _ zenon_H15c); [ zenon_intro zenon_H156 | zenon_intro zenon_Hdf ]. % 15.16/15.34 apply (zenon_L134_); trivial. % 15.16/15.34 apply (zenon_L121_); trivial. % 15.16/15.34 (* end of lemma zenon_L181_ *) % 15.16/15.34 assert (zenon_L182_ : (((op (e0) (e0)) = (e2))\/(((op (e0) (e1)) = (e2))\/(((op (e0) (e2)) = (e2))\/((op (e0) (e3)) = (e2))))) -> (~((op (e3) (e3)) = (e3))) -> (~((op (e3) (e3)) = (e2))) -> (~((op (e3) (e3)) = (e0))) -> (((op (e3) (e3)) = (e0))\/(((op (e3) (e3)) = (e1))\/(((op (e3) (e3)) = (e2))\/((op (e3) (e3)) = (e3))))) -> (~((op (e0) (e0)) = (e2))) -> (~((op (e0) (e0)) = (e1))) -> (~((op (e0) (e0)) = (e0))) -> (((op (e0) (e0)) = (e0))\/(((op (e0) (e0)) = (e1))\/(((op (e0) (e0)) = (e2))\/((op (e0) (e0)) = (e3))))) -> (~((op (e0) (e2)) = (op (e2) (e2)))) -> ((op (e2) (e2)) = (e2)) -> ((op (e0) (e3)) = (e0)) -> (~((e0) = (e2))) -> False). % 15.16/15.34 do 0 intro. intros zenon_H8e zenon_H3e zenon_H3d zenon_H3c zenon_H3b zenon_H8f zenon_H45 zenon_H20 zenon_H12a zenon_H28 zenon_H35 zenon_Hca zenon_H5e. % 15.16/15.34 apply (zenon_or_s _ _ zenon_H8e); [ zenon_intro zenon_H92 | zenon_intro zenon_H91 ]. % 15.16/15.34 exact (zenon_H8f zenon_H92). % 15.16/15.34 apply (zenon_or_s _ _ zenon_H91); [ zenon_intro zenon_H5d | zenon_intro zenon_H93 ]. % 15.16/15.34 apply (zenon_L112_); trivial. % 15.16/15.34 apply (zenon_or_s _ _ zenon_H93); [ zenon_intro zenon_H63 | zenon_intro zenon_H81 ]. % 15.16/15.34 apply (zenon_L15_); trivial. % 15.16/15.34 apply (zenon_L113_); trivial. % 15.16/15.34 (* end of lemma zenon_L182_ *) % 15.16/15.34 assert (zenon_L183_ : ((op (e2) (e1)) = (e2)) -> ((op (e2) (e1)) = (e3)) -> (~((e2) = (e3))) -> False). % 15.16/15.34 do 0 intro. intros zenon_H156 zenon_Hdf zenon_H6a. % 15.16/15.34 elim (classic ((e3) = (e3))); [ zenon_intro zenon_H4c | zenon_intro zenon_H4d ]. % 15.16/15.34 cut (((e3) = (e3)) = ((e2) = (e3))). % 15.16/15.34 intro zenon_D_pnotp. % 15.16/15.34 apply zenon_H6a. % 15.16/15.34 rewrite <- zenon_D_pnotp. % 15.16/15.34 exact zenon_H4c. % 15.16/15.34 cut (((e3) = (e3))); [idtac | apply NNPP; zenon_intro zenon_H4d]. % 15.16/15.34 cut (((e3) = (e2))); [idtac | apply NNPP; zenon_intro zenon_H6b]. % 15.16/15.34 congruence. % 15.16/15.34 cut (((op (e2) (e1)) = (e2)) = ((e3) = (e2))). % 15.16/15.34 intro zenon_D_pnotp. % 15.16/15.34 apply zenon_H6b. % 15.16/15.34 rewrite <- zenon_D_pnotp. % 15.16/15.34 exact zenon_H156. % 15.16/15.34 cut (((e2) = (e2))); [idtac | apply NNPP; zenon_intro zenon_H60]. % 15.16/15.34 cut (((op (e2) (e1)) = (e3))); [idtac | apply NNPP; zenon_intro zenon_H198]. % 15.16/15.34 congruence. % 15.16/15.34 exact (zenon_H198 zenon_Hdf). % 15.16/15.34 apply zenon_H60. apply refl_equal. % 15.16/15.34 apply zenon_H4d. apply refl_equal. % 15.16/15.34 apply zenon_H4d. apply refl_equal. % 15.16/15.34 (* end of lemma zenon_L183_ *) % 15.16/15.34 assert (zenon_L184_ : (((op (e0) (e1)) = (e3))\/(((op (e1) (e1)) = (e3))\/(((op (e2) (e1)) = (e3))\/((op (e3) (e1)) = (e3))))) -> (~((e0) = (e3))) -> ((op (e0) (e1)) = (e0)) -> (~((op (e1) (e1)) = (e3))) -> (~((e2) = (e3))) -> ((op (e2) (e1)) = (e2)) -> (~((op (e3) (e0)) = (op (e3) (e1)))) -> ((op (e3) (e0)) = (e3)) -> False). % 15.16/15.34 do 0 intro. intros zenon_H199 zenon_H4b zenon_H49 zenon_H182 zenon_H6a zenon_H156 zenon_H109 zenon_Hba. % 15.16/15.34 apply (zenon_or_s _ _ zenon_H199); [ zenon_intro zenon_H4a | zenon_intro zenon_H19a ]. % 15.16/15.34 apply (zenon_L9_); trivial. % 15.16/15.34 apply (zenon_or_s _ _ zenon_H19a); [ zenon_intro zenon_H96 | zenon_intro zenon_H19b ]. % 15.16/15.34 exact (zenon_H182 zenon_H96). % 15.16/15.34 apply (zenon_or_s _ _ zenon_H19b); [ zenon_intro zenon_Hdf | zenon_intro zenon_H10a ]. % 15.16/15.34 apply (zenon_L183_); trivial. % 15.16/15.34 apply (zenon_L82_); trivial. % 15.16/15.34 (* end of lemma zenon_L184_ *) % 15.16/15.34 assert (zenon_L185_ : (~((op (op (e3) (e3)) (op (e3) (e3))) = (op (e0) (e0)))) -> ((op (e3) (e3)) = (e0)) -> False). % 15.16/15.34 do 0 intro. intros zenon_H19c zenon_H40. % 15.16/15.34 cut (((op (e3) (e3)) = (e0))); [idtac | apply NNPP; zenon_intro zenon_H3c]. % 15.16/15.34 cut (((op (e3) (e3)) = (e0))); [idtac | apply NNPP; zenon_intro zenon_H3c]. % 15.16/15.34 congruence. % 15.16/15.34 exact (zenon_H3c zenon_H40). % 15.16/15.34 exact (zenon_H3c zenon_H40). % 15.16/15.34 (* end of lemma zenon_L185_ *) % 15.16/15.34 assert (zenon_L186_ : ((op (e3) (e1)) = (e2)) -> ((op (e0) (e0)) = (e1)) -> ((op (e3) (e3)) = (e0)) -> False). % 15.16/15.34 do 0 intro. intros zenon_H16a zenon_H47 zenon_H40. % 15.16/15.34 apply (zenon_notand_s _ _ ax12); [ zenon_intro zenon_H185 | zenon_intro zenon_H19d ]. % 15.16/15.34 elim (classic ((op (op (e3) (e3)) (op (e3) (e3))) = (op (op (e3) (e3)) (op (e3) (e3))))); [ zenon_intro zenon_H186 | zenon_intro zenon_H187 ]. % 15.16/15.34 cut (((op (op (e3) (e3)) (op (e3) (e3))) = (op (op (e3) (e3)) (op (e3) (e3)))) = ((e1) = (op (op (e3) (e3)) (op (e3) (e3))))). % 15.16/15.34 intro zenon_D_pnotp. % 15.16/15.34 apply zenon_H185. % 15.16/15.34 rewrite <- zenon_D_pnotp. % 15.16/15.34 exact zenon_H186. % 15.16/15.34 cut (((op (op (e3) (e3)) (op (e3) (e3))) = (op (op (e3) (e3)) (op (e3) (e3))))); [idtac | apply NNPP; zenon_intro zenon_H187]. % 15.16/15.34 cut (((op (op (e3) (e3)) (op (e3) (e3))) = (e1))); [idtac | apply NNPP; zenon_intro zenon_H188]. % 15.16/15.34 congruence. % 15.16/15.34 cut (((op (e0) (e0)) = (e1)) = ((op (op (e3) (e3)) (op (e3) (e3))) = (e1))). % 15.16/15.34 intro zenon_D_pnotp. % 15.16/15.34 apply zenon_H188. % 15.16/15.34 rewrite <- zenon_D_pnotp. % 15.16/15.34 exact zenon_H47. % 15.16/15.34 cut (((e1) = (e1))); [idtac | apply NNPP; zenon_intro zenon_Ha0]. % 15.16/15.34 cut (((op (e0) (e0)) = (op (op (e3) (e3)) (op (e3) (e3))))); [idtac | apply NNPP; zenon_intro zenon_H19e]. % 15.16/15.34 congruence. % 15.16/15.34 elim (classic ((op (op (e3) (e3)) (op (e3) (e3))) = (op (op (e3) (e3)) (op (e3) (e3))))); [ zenon_intro zenon_H186 | zenon_intro zenon_H187 ]. % 15.16/15.34 cut (((op (op (e3) (e3)) (op (e3) (e3))) = (op (op (e3) (e3)) (op (e3) (e3)))) = ((op (e0) (e0)) = (op (op (e3) (e3)) (op (e3) (e3))))). % 15.16/15.34 intro zenon_D_pnotp. % 15.16/15.34 apply zenon_H19e. % 15.16/15.34 rewrite <- zenon_D_pnotp. % 15.16/15.34 exact zenon_H186. % 15.16/15.34 cut (((op (op (e3) (e3)) (op (e3) (e3))) = (op (op (e3) (e3)) (op (e3) (e3))))); [idtac | apply NNPP; zenon_intro zenon_H187]. % 15.16/15.34 cut (((op (op (e3) (e3)) (op (e3) (e3))) = (op (e0) (e0)))); [idtac | apply NNPP; zenon_intro zenon_H19c]. % 15.16/15.34 congruence. % 15.16/15.34 apply (zenon_L185_); trivial. % 15.16/15.34 apply zenon_H187. apply refl_equal. % 15.16/15.34 apply zenon_H187. apply refl_equal. % 15.16/15.34 apply zenon_Ha0. apply refl_equal. % 15.16/15.34 apply zenon_H187. apply refl_equal. % 15.16/15.34 apply zenon_H187. apply refl_equal. % 15.16/15.34 apply (zenon_notand_s _ _ zenon_H19d); [ zenon_intro zenon_H1a0 | zenon_intro zenon_H19f ]. % 15.16/15.34 apply zenon_H1a0. apply sym_equal. exact zenon_H40. % 15.16/15.34 elim (classic ((op (e3) (op (op (e3) (e3)) (op (e3) (e3)))) = (op (e3) (op (op (e3) (e3)) (op (e3) (e3)))))); [ zenon_intro zenon_H18b | zenon_intro zenon_H18c ]. % 15.16/15.34 cut (((op (e3) (op (op (e3) (e3)) (op (e3) (e3)))) = (op (e3) (op (op (e3) (e3)) (op (e3) (e3))))) = ((e2) = (op (e3) (op (op (e3) (e3)) (op (e3) (e3)))))). % 15.16/15.34 intro zenon_D_pnotp. % 15.16/15.34 apply zenon_H19f. % 15.16/15.34 rewrite <- zenon_D_pnotp. % 15.16/15.34 exact zenon_H18b. % 15.16/15.34 cut (((op (e3) (op (op (e3) (e3)) (op (e3) (e3)))) = (op (e3) (op (op (e3) (e3)) (op (e3) (e3)))))); [idtac | apply NNPP; zenon_intro zenon_H18c]. % 15.16/15.34 cut (((op (e3) (op (op (e3) (e3)) (op (e3) (e3)))) = (e2))); [idtac | apply NNPP; zenon_intro zenon_H1a1]. % 15.16/15.34 congruence. % 15.16/15.34 cut (((op (e3) (e1)) = (e2)) = ((op (e3) (op (op (e3) (e3)) (op (e3) (e3)))) = (e2))). % 15.16/15.34 intro zenon_D_pnotp. % 15.16/15.34 apply zenon_H1a1. % 15.16/15.34 rewrite <- zenon_D_pnotp. % 15.16/15.34 exact zenon_H16a. % 15.16/15.34 cut (((e2) = (e2))); [idtac | apply NNPP; zenon_intro zenon_H60]. % 15.16/15.34 cut (((op (e3) (e1)) = (op (e3) (op (op (e3) (e3)) (op (e3) (e3)))))); [idtac | apply NNPP; zenon_intro zenon_H18e]. % 15.16/15.34 congruence. % 15.16/15.34 elim (classic ((op (e3) (op (op (e3) (e3)) (op (e3) (e3)))) = (op (e3) (op (op (e3) (e3)) (op (e3) (e3)))))); [ zenon_intro zenon_H18b | zenon_intro zenon_H18c ]. % 15.16/15.34 cut (((op (e3) (op (op (e3) (e3)) (op (e3) (e3)))) = (op (e3) (op (op (e3) (e3)) (op (e3) (e3))))) = ((op (e3) (e1)) = (op (e3) (op (op (e3) (e3)) (op (e3) (e3)))))). % 15.16/15.34 intro zenon_D_pnotp. % 15.16/15.34 apply zenon_H18e. % 15.16/15.34 rewrite <- zenon_D_pnotp. % 15.16/15.34 exact zenon_H18b. % 15.16/15.34 cut (((op (e3) (op (op (e3) (e3)) (op (e3) (e3)))) = (op (e3) (op (op (e3) (e3)) (op (e3) (e3)))))); [idtac | apply NNPP; zenon_intro zenon_H18c]. % 15.16/15.34 cut (((op (e3) (op (op (e3) (e3)) (op (e3) (e3)))) = (op (e3) (e1)))); [idtac | apply NNPP; zenon_intro zenon_H18f]. % 15.16/15.34 congruence. % 15.16/15.34 cut (((op (op (e3) (e3)) (op (e3) (e3))) = (e1))); [idtac | apply NNPP; zenon_intro zenon_H188]. % 15.16/15.34 cut (((e3) = (e3))); [idtac | apply NNPP; zenon_intro zenon_H4d]. % 15.16/15.34 congruence. % 15.16/15.34 apply zenon_H4d. apply refl_equal. % 15.16/15.34 cut (((op (e0) (e0)) = (e1)) = ((op (op (e3) (e3)) (op (e3) (e3))) = (e1))). % 15.16/15.34 intro zenon_D_pnotp. % 15.16/15.34 apply zenon_H188. % 15.16/15.34 rewrite <- zenon_D_pnotp. % 15.16/15.34 exact zenon_H47. % 15.16/15.34 cut (((e1) = (e1))); [idtac | apply NNPP; zenon_intro zenon_Ha0]. % 15.16/15.34 cut (((op (e0) (e0)) = (op (op (e3) (e3)) (op (e3) (e3))))); [idtac | apply NNPP; zenon_intro zenon_H19e]. % 15.16/15.34 congruence. % 15.16/15.34 elim (classic ((op (op (e3) (e3)) (op (e3) (e3))) = (op (op (e3) (e3)) (op (e3) (e3))))); [ zenon_intro zenon_H186 | zenon_intro zenon_H187 ]. % 15.16/15.34 cut (((op (op (e3) (e3)) (op (e3) (e3))) = (op (op (e3) (e3)) (op (e3) (e3)))) = ((op (e0) (e0)) = (op (op (e3) (e3)) (op (e3) (e3))))). % 15.16/15.34 intro zenon_D_pnotp. % 15.16/15.34 apply zenon_H19e. % 15.16/15.34 rewrite <- zenon_D_pnotp. % 15.16/15.34 exact zenon_H186. % 15.16/15.34 cut (((op (op (e3) (e3)) (op (e3) (e3))) = (op (op (e3) (e3)) (op (e3) (e3))))); [idtac | apply NNPP; zenon_intro zenon_H187]. % 15.16/15.34 cut (((op (op (e3) (e3)) (op (e3) (e3))) = (op (e0) (e0)))); [idtac | apply NNPP; zenon_intro zenon_H19c]. % 15.16/15.34 congruence. % 15.16/15.34 apply (zenon_L185_); trivial. % 15.16/15.34 apply zenon_H187. apply refl_equal. % 15.16/15.34 apply zenon_H187. apply refl_equal. % 15.16/15.34 apply zenon_Ha0. apply refl_equal. % 15.16/15.34 apply zenon_H18c. apply refl_equal. % 15.16/15.34 apply zenon_H18c. apply refl_equal. % 15.16/15.34 apply zenon_H60. apply refl_equal. % 15.16/15.34 apply zenon_H18c. apply refl_equal. % 15.16/15.34 apply zenon_H18c. apply refl_equal. % 15.16/15.34 (* end of lemma zenon_L186_ *) % 15.16/15.34 assert (zenon_L187_ : (((op (e0) (e0)) = (e0))\/(((op (e0) (e0)) = (e1))\/(((op (e0) (e0)) = (e2))\/((op (e0) (e0)) = (e3))))) -> (~((op (e0) (e0)) = (e0))) -> ((op (e3) (e3)) = (e0)) -> ((op (e3) (e1)) = (e2)) -> (~((op (e0) (e0)) = (e2))) -> (~((op (e0) (e0)) = (e3))) -> False). % 15.16/15.34 do 0 intro. intros zenon_H12a zenon_H20 zenon_H40 zenon_H16a zenon_H8f zenon_H59. % 15.16/15.34 apply (zenon_or_s _ _ zenon_H12a); [ zenon_intro zenon_H1f | zenon_intro zenon_H12b ]. % 15.16/15.34 exact (zenon_H20 zenon_H1f). % 15.16/15.34 apply (zenon_or_s _ _ zenon_H12b); [ zenon_intro zenon_H47 | zenon_intro zenon_H12c ]. % 15.16/15.34 apply (zenon_L186_); trivial. % 15.16/15.34 apply (zenon_or_s _ _ zenon_H12c); [ zenon_intro zenon_H92 | zenon_intro zenon_H5b ]. % 15.16/15.34 exact (zenon_H8f zenon_H92). % 15.16/15.34 exact (zenon_H59 zenon_H5b). % 15.16/15.34 (* end of lemma zenon_L187_ *) % 15.16/15.34 assert (zenon_L188_ : (((op (e3) (e3)) = (e0))\/(((op (e3) (e3)) = (e1))\/(((op (e3) (e3)) = (e2))\/((op (e3) (e3)) = (e3))))) -> (~((op (e0) (e0)) = (e3))) -> (~((op (e0) (e0)) = (e2))) -> ((op (e3) (e1)) = (e2)) -> (~((op (e0) (e0)) = (e0))) -> (((op (e0) (e0)) = (e0))\/(((op (e0) (e0)) = (e1))\/(((op (e0) (e0)) = (e2))\/((op (e0) (e0)) = (e3))))) -> (~((op (e3) (e3)) = (e1))) -> (~((op (e3) (e3)) = (e2))) -> (~((op (e3) (e3)) = (e3))) -> False). % 15.16/15.34 do 0 intro. intros zenon_H3b zenon_H59 zenon_H8f zenon_H16a zenon_H20 zenon_H12a zenon_H104 zenon_H3d zenon_H3e. % 15.16/15.34 apply (zenon_or_s _ _ zenon_H3b); [ zenon_intro zenon_H40 | zenon_intro zenon_H3f ]. % 15.16/15.34 apply (zenon_L187_); trivial. % 15.16/15.34 apply (zenon_or_s _ _ zenon_H3f); [ zenon_intro zenon_H38 | zenon_intro zenon_H41 ]. % 15.16/15.34 exact (zenon_H104 zenon_H38). % 15.16/15.34 apply (zenon_or_s _ _ zenon_H41); [ zenon_intro zenon_H43 | zenon_intro zenon_H42 ]. % 15.16/15.34 exact (zenon_H3d zenon_H43). % 15.16/15.34 exact (zenon_H3e zenon_H42). % 15.16/15.34 (* end of lemma zenon_L188_ *) % 15.16/15.34 assert (zenon_L189_ : (((op (e0) (e1)) = (e2))\/(((op (e1) (e1)) = (e2))\/(((op (e2) (e1)) = (e2))\/((op (e3) (e1)) = (e2))))) -> (~((e0) = (e2))) -> (~((op (e1) (e1)) = (e2))) -> ((op (e3) (e0)) = (e3)) -> (~((op (e3) (e0)) = (op (e3) (e1)))) -> (~((e2) = (e3))) -> (~((op (e1) (e1)) = (e3))) -> ((op (e0) (e1)) = (e0)) -> (~((e0) = (e3))) -> (((op (e0) (e1)) = (e3))\/(((op (e1) (e1)) = (e3))\/(((op (e2) (e1)) = (e3))\/((op (e3) (e1)) = (e3))))) -> (((op (e3) (e3)) = (e0))\/(((op (e3) (e3)) = (e1))\/(((op (e3) (e3)) = (e2))\/((op (e3) (e3)) = (e3))))) -> (~((op (e0) (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 (e3) (e3)) = (e1))) -> (~((op (e3) (e3)) = (e2))) -> (~((op (e3) (e3)) = (e3))) -> False). % 15.16/15.34 do 0 intro. intros zenon_H1a2 zenon_H5e zenon_Hd6 zenon_Hba zenon_H109 zenon_H6a zenon_H182 zenon_H49 zenon_H4b zenon_H199 zenon_H3b zenon_H59 zenon_H8f zenon_H20 zenon_H12a zenon_H104 zenon_H3d zenon_H3e. % 15.16/15.34 apply (zenon_or_s _ _ zenon_H1a2); [ zenon_intro zenon_H5d | zenon_intro zenon_H1a3 ]. % 15.16/15.34 apply (zenon_L14_); trivial. % 15.16/15.34 apply (zenon_or_s _ _ zenon_H1a3); [ zenon_intro zenon_H6e | zenon_intro zenon_H1a4 ]. % 15.16/15.34 exact (zenon_Hd6 zenon_H6e). % 15.16/15.34 apply (zenon_or_s _ _ zenon_H1a4); [ zenon_intro zenon_H156 | zenon_intro zenon_H16a ]. % 15.16/15.34 apply (zenon_L184_); trivial. % 15.16/15.34 apply (zenon_L188_); trivial. % 15.16/15.34 (* end of lemma zenon_L189_ *) % 15.16/15.34 assert (zenon_L190_ : ((~((op (e3) (e3)) = (e3)))\/((op (e3) (e3)) = (e3))) -> (~((op (e3) (e0)) = (op (e3) (e3)))) -> (~((e0) = (e2))) -> ((op (e0) (e1)) = (e0)) -> (~((op (e1) (e1)) = (e2))) -> (((op (e0) (e1)) = (e3))\/(((op (e1) (e1)) = (e3))\/(((op (e2) (e1)) = (e3))\/((op (e3) (e1)) = (e3))))) -> ((op (e3) (e0)) = (e3)) -> (~((op (e3) (e0)) = (op (e3) (e1)))) -> (~((e2) = (e3))) -> (~((op (e1) (e1)) = (e3))) -> (~((e0) = (e3))) -> (((op (e3) (e3)) = (e0))\/(((op (e3) (e3)) = (e1))\/(((op (e3) (e3)) = (e2))\/((op (e3) (e3)) = (e3))))) -> (~((op (e3) (e3)) = (e2))) -> (~((op (e3) (e3)) = (e1))) -> (~((op (e0) (e0)) = (e0))) -> (~((op (e0) (e0)) = (e2))) -> (~((op (e0) (e0)) = (e3))) -> (((op (e0) (e0)) = (e0))\/(((op (e0) (e0)) = (e1))\/(((op (e0) (e0)) = (e2))\/((op (e0) (e0)) = (e3))))) -> (((op (e0) (e1)) = (e2))\/(((op (e1) (e1)) = (e2))\/(((op (e2) (e1)) = (e2))\/((op (e3) (e1)) = (e2))))) -> False). % 15.16/15.34 do 0 intro. intros zenon_H10d zenon_Hbb zenon_H5e zenon_H49 zenon_Hd6 zenon_H199 zenon_Hba zenon_H109 zenon_H6a zenon_H182 zenon_H4b zenon_H3b zenon_H3d zenon_H104 zenon_H20 zenon_H8f zenon_H59 zenon_H12a zenon_H1a2. % 15.16/15.34 apply (zenon_or_s _ _ zenon_H10d); [ zenon_intro zenon_H3e | zenon_intro zenon_H42 ]. % 15.16/15.34 apply (zenon_L189_); trivial. % 15.16/15.34 apply (zenon_L43_); trivial. % 15.16/15.34 (* end of lemma zenon_L190_ *) % 15.16/15.34 assert (zenon_L191_ : ((~((op (e3) (e3)) = (e2)))\/((op (e3) (e2)) = (e3))) -> (~((op (e3) (e0)) = (op (e3) (e2)))) -> (((op (e0) (e1)) = (e2))\/(((op (e1) (e1)) = (e2))\/(((op (e2) (e1)) = (e2))\/((op (e3) (e1)) = (e2))))) -> (((op (e0) (e0)) = (e0))\/(((op (e0) (e0)) = (e1))\/(((op (e0) (e0)) = (e2))\/((op (e0) (e0)) = (e3))))) -> (~((op (e0) (e0)) = (e3))) -> (~((op (e0) (e0)) = (e2))) -> (~((op (e0) (e0)) = (e0))) -> (~((op (e3) (e3)) = (e1))) -> (((op (e3) (e3)) = (e0))\/(((op (e3) (e3)) = (e1))\/(((op (e3) (e3)) = (e2))\/((op (e3) (e3)) = (e3))))) -> (~((e0) = (e3))) -> (~((op (e1) (e1)) = (e3))) -> (~((e2) = (e3))) -> (~((op (e3) (e0)) = (op (e3) (e1)))) -> ((op (e3) (e0)) = (e3)) -> (((op (e0) (e1)) = (e3))\/(((op (e1) (e1)) = (e3))\/(((op (e2) (e1)) = (e3))\/((op (e3) (e1)) = (e3))))) -> (~((op (e1) (e1)) = (e2))) -> ((op (e0) (e1)) = (e0)) -> (~((e0) = (e2))) -> (~((op (e3) (e0)) = (op (e3) (e3)))) -> ((~((op (e3) (e3)) = (e3)))\/((op (e3) (e3)) = (e3))) -> False). % 15.16/15.34 do 0 intro. intros zenon_H10e zenon_H105 zenon_H1a2 zenon_H12a zenon_H59 zenon_H8f zenon_H20 zenon_H104 zenon_H3b zenon_H4b zenon_H182 zenon_H6a zenon_H109 zenon_Hba zenon_H199 zenon_Hd6 zenon_H49 zenon_H5e zenon_Hbb zenon_H10d. % 15.16/15.34 apply (zenon_or_s _ _ zenon_H10e); [ zenon_intro zenon_H3d | zenon_intro zenon_H106 ]. % 15.16/15.34 apply (zenon_L190_); trivial. % 15.16/15.34 apply (zenon_L81_); trivial. % 15.16/15.34 (* end of lemma zenon_L191_ *) % 15.16/15.34 assert (zenon_L192_ : (~((op (op (e1) (e1)) (op (e1) (e1))) = (op (e0) (e0)))) -> ((op (e1) (e1)) = (e0)) -> False). % 15.16/15.34 do 0 intro. intros zenon_H1a5 zenon_H149. % 15.16/15.34 cut (((op (e1) (e1)) = (e0))); [idtac | apply NNPP; zenon_intro zenon_H145]. % 15.16/15.34 cut (((op (e1) (e1)) = (e0))); [idtac | apply NNPP; zenon_intro zenon_H145]. % 15.16/15.34 congruence. % 15.16/15.34 exact (zenon_H145 zenon_H149). % 15.16/15.34 exact (zenon_H145 zenon_H149). % 15.16/15.34 (* end of lemma zenon_L192_ *) % 15.16/15.34 assert (zenon_L193_ : ((op (e1) (e2)) = (e3)) -> ((op (e0) (e0)) = (e2)) -> ((op (e1) (e1)) = (e0)) -> False). % 15.16/15.34 do 0 intro. intros zenon_H88 zenon_H92 zenon_H149. % 15.16/15.34 apply (zenon_notand_s _ _ ax19); [ zenon_intro zenon_H1a7 | zenon_intro zenon_H1a6 ]. % 15.16/15.34 elim (classic ((op (op (e1) (e1)) (op (e1) (e1))) = (op (op (e1) (e1)) (op (e1) (e1))))); [ zenon_intro zenon_H1a8 | zenon_intro zenon_H1a9 ]. % 15.16/15.34 cut (((op (op (e1) (e1)) (op (e1) (e1))) = (op (op (e1) (e1)) (op (e1) (e1)))) = ((e2) = (op (op (e1) (e1)) (op (e1) (e1))))). % 15.16/15.34 intro zenon_D_pnotp. % 15.16/15.34 apply zenon_H1a7. % 15.16/15.34 rewrite <- zenon_D_pnotp. % 15.16/15.34 exact zenon_H1a8. % 15.16/15.34 cut (((op (op (e1) (e1)) (op (e1) (e1))) = (op (op (e1) (e1)) (op (e1) (e1))))); [idtac | apply NNPP; zenon_intro zenon_H1a9]. % 15.16/15.34 cut (((op (op (e1) (e1)) (op (e1) (e1))) = (e2))); [idtac | apply NNPP; zenon_intro zenon_H1aa]. % 15.16/15.34 congruence. % 15.16/15.34 cut (((op (e0) (e0)) = (e2)) = ((op (op (e1) (e1)) (op (e1) (e1))) = (e2))). % 15.16/15.34 intro zenon_D_pnotp. % 15.16/15.34 apply zenon_H1aa. % 15.16/15.34 rewrite <- zenon_D_pnotp. % 15.16/15.34 exact zenon_H92. % 15.16/15.34 cut (((e2) = (e2))); [idtac | apply NNPP; zenon_intro zenon_H60]. % 15.16/15.34 cut (((op (e0) (e0)) = (op (op (e1) (e1)) (op (e1) (e1))))); [idtac | apply NNPP; zenon_intro zenon_H1ab]. % 15.16/15.34 congruence. % 15.16/15.34 elim (classic ((op (op (e1) (e1)) (op (e1) (e1))) = (op (op (e1) (e1)) (op (e1) (e1))))); [ zenon_intro zenon_H1a8 | zenon_intro zenon_H1a9 ]. % 15.16/15.34 cut (((op (op (e1) (e1)) (op (e1) (e1))) = (op (op (e1) (e1)) (op (e1) (e1)))) = ((op (e0) (e0)) = (op (op (e1) (e1)) (op (e1) (e1))))). % 15.16/15.34 intro zenon_D_pnotp. % 15.16/15.34 apply zenon_H1ab. % 15.16/15.34 rewrite <- zenon_D_pnotp. % 15.16/15.34 exact zenon_H1a8. % 15.16/15.34 cut (((op (op (e1) (e1)) (op (e1) (e1))) = (op (op (e1) (e1)) (op (e1) (e1))))); [idtac | apply NNPP; zenon_intro zenon_H1a9]. % 15.16/15.34 cut (((op (op (e1) (e1)) (op (e1) (e1))) = (op (e0) (e0)))); [idtac | apply NNPP; zenon_intro zenon_H1a5]. % 15.16/15.34 congruence. % 15.16/15.34 apply (zenon_L192_); trivial. % 15.16/15.34 apply zenon_H1a9. apply refl_equal. % 15.16/15.34 apply zenon_H1a9. apply refl_equal. % 15.16/15.34 apply zenon_H60. apply refl_equal. % 15.16/15.34 apply zenon_H1a9. apply refl_equal. % 15.16/15.34 apply zenon_H1a9. apply refl_equal. % 15.16/15.34 apply (zenon_notand_s _ _ zenon_H1a6); [ zenon_intro zenon_H1ad | zenon_intro zenon_H1ac ]. % 15.16/15.34 apply zenon_H1ad. apply sym_equal. exact zenon_H149. % 15.16/15.34 elim (classic ((op (e1) (op (op (e1) (e1)) (op (e1) (e1)))) = (op (e1) (op (op (e1) (e1)) (op (e1) (e1)))))); [ zenon_intro zenon_H1ae | zenon_intro zenon_H1af ]. % 15.16/15.34 cut (((op (e1) (op (op (e1) (e1)) (op (e1) (e1)))) = (op (e1) (op (op (e1) (e1)) (op (e1) (e1))))) = ((e3) = (op (e1) (op (op (e1) (e1)) (op (e1) (e1)))))). % 15.16/15.34 intro zenon_D_pnotp. % 15.16/15.34 apply zenon_H1ac. % 15.16/15.34 rewrite <- zenon_D_pnotp. % 15.16/15.34 exact zenon_H1ae. % 15.16/15.34 cut (((op (e1) (op (op (e1) (e1)) (op (e1) (e1)))) = (op (e1) (op (op (e1) (e1)) (op (e1) (e1)))))); [idtac | apply NNPP; zenon_intro zenon_H1af]. % 15.16/15.34 cut (((op (e1) (op (op (e1) (e1)) (op (e1) (e1)))) = (e3))); [idtac | apply NNPP; zenon_intro zenon_H1b0]. % 15.16/15.34 congruence. % 15.16/15.34 cut (((op (e1) (e2)) = (e3)) = ((op (e1) (op (op (e1) (e1)) (op (e1) (e1)))) = (e3))). % 15.16/15.34 intro zenon_D_pnotp. % 15.16/15.34 apply zenon_H1b0. % 15.16/15.34 rewrite <- zenon_D_pnotp. % 15.16/15.34 exact zenon_H88. % 15.16/15.34 cut (((e3) = (e3))); [idtac | apply NNPP; zenon_intro zenon_H4d]. % 15.16/15.34 cut (((op (e1) (e2)) = (op (e1) (op (op (e1) (e1)) (op (e1) (e1)))))); [idtac | apply NNPP; zenon_intro zenon_H1b1]. % 15.16/15.34 congruence. % 15.16/15.34 elim (classic ((op (e1) (op (op (e1) (e1)) (op (e1) (e1)))) = (op (e1) (op (op (e1) (e1)) (op (e1) (e1)))))); [ zenon_intro zenon_H1ae | zenon_intro zenon_H1af ]. % 15.16/15.34 cut (((op (e1) (op (op (e1) (e1)) (op (e1) (e1)))) = (op (e1) (op (op (e1) (e1)) (op (e1) (e1))))) = ((op (e1) (e2)) = (op (e1) (op (op (e1) (e1)) (op (e1) (e1)))))). % 15.16/15.34 intro zenon_D_pnotp. % 15.16/15.34 apply zenon_H1b1. % 15.16/15.34 rewrite <- zenon_D_pnotp. % 15.16/15.34 exact zenon_H1ae. % 15.16/15.34 cut (((op (e1) (op (op (e1) (e1)) (op (e1) (e1)))) = (op (e1) (op (op (e1) (e1)) (op (e1) (e1)))))); [idtac | apply NNPP; zenon_intro zenon_H1af]. % 15.16/15.34 cut (((op (e1) (op (op (e1) (e1)) (op (e1) (e1)))) = (op (e1) (e2)))); [idtac | apply NNPP; zenon_intro zenon_H1b2]. % 15.16/15.34 congruence. % 15.16/15.34 cut (((op (op (e1) (e1)) (op (e1) (e1))) = (e2))); [idtac | apply NNPP; zenon_intro zenon_H1aa]. % 15.16/15.34 cut (((e1) = (e1))); [idtac | apply NNPP; zenon_intro zenon_Ha0]. % 15.16/15.34 congruence. % 15.16/15.34 apply zenon_Ha0. apply refl_equal. % 15.16/15.34 cut (((op (e0) (e0)) = (e2)) = ((op (op (e1) (e1)) (op (e1) (e1))) = (e2))). % 15.16/15.34 intro zenon_D_pnotp. % 15.16/15.34 apply zenon_H1aa. % 15.16/15.34 rewrite <- zenon_D_pnotp. % 15.16/15.34 exact zenon_H92. % 15.16/15.34 cut (((e2) = (e2))); [idtac | apply NNPP; zenon_intro zenon_H60]. % 15.16/15.34 cut (((op (e0) (e0)) = (op (op (e1) (e1)) (op (e1) (e1))))); [idtac | apply NNPP; zenon_intro zenon_H1ab]. % 15.16/15.34 congruence. % 15.16/15.34 elim (classic ((op (op (e1) (e1)) (op (e1) (e1))) = (op (op (e1) (e1)) (op (e1) (e1))))); [ zenon_intro zenon_H1a8 | zenon_intro zenon_H1a9 ]. % 15.16/15.34 cut (((op (op (e1) (e1)) (op (e1) (e1))) = (op (op (e1) (e1)) (op (e1) (e1)))) = ((op (e0) (e0)) = (op (op (e1) (e1)) (op (e1) (e1))))). % 15.16/15.34 intro zenon_D_pnotp. % 15.16/15.34 apply zenon_H1ab. % 15.16/15.34 rewrite <- zenon_D_pnotp. % 15.16/15.34 exact zenon_H1a8. % 15.16/15.34 cut (((op (op (e1) (e1)) (op (e1) (e1))) = (op (op (e1) (e1)) (op (e1) (e1))))); [idtac | apply NNPP; zenon_intro zenon_H1a9]. % 15.16/15.34 cut (((op (op (e1) (e1)) (op (e1) (e1))) = (op (e0) (e0)))); [idtac | apply NNPP; zenon_intro zenon_H1a5]. % 15.16/15.34 congruence. % 15.16/15.34 apply (zenon_L192_); trivial. % 15.16/15.34 apply zenon_H1a9. apply refl_equal. % 15.16/15.34 apply zenon_H1a9. apply refl_equal. % 15.16/15.34 apply zenon_H60. apply refl_equal. % 15.16/15.34 apply zenon_H1af. apply refl_equal. % 15.16/15.34 apply zenon_H1af. apply refl_equal. % 15.16/15.34 apply zenon_H4d. apply refl_equal. % 15.16/15.34 apply zenon_H1af. apply refl_equal. % 15.16/15.34 apply zenon_H1af. apply refl_equal. % 15.16/15.34 (* end of lemma zenon_L193_ *) % 15.16/15.34 assert (zenon_L194_ : (((op (e1) (e1)) = (e0))\/(((op (e1) (e1)) = (e1))\/(((op (e1) (e1)) = (e2))\/((op (e1) (e1)) = (e3))))) -> ((op (e0) (e0)) = (e2)) -> ((op (e1) (e2)) = (e3)) -> (~((op (e1) (e1)) = (e1))) -> (~((op (e1) (e1)) = (e2))) -> (~((op (e1) (e1)) = (e3))) -> False). % 15.16/15.34 do 0 intro. intros zenon_H1b3 zenon_H92 zenon_H88 zenon_H1b4 zenon_Hd6 zenon_H182. % 15.16/15.34 apply (zenon_or_s _ _ zenon_H1b3); [ zenon_intro zenon_H149 | zenon_intro zenon_H1b5 ]. % 15.16/15.34 apply (zenon_L193_); trivial. % 15.16/15.34 apply (zenon_or_s _ _ zenon_H1b5); [ zenon_intro zenon_H21 | zenon_intro zenon_H1b6 ]. % 15.16/15.34 exact (zenon_H1b4 zenon_H21). % 15.16/15.34 apply (zenon_or_s _ _ zenon_H1b6); [ zenon_intro zenon_H6e | zenon_intro zenon_H96 ]. % 15.16/15.34 exact (zenon_Hd6 zenon_H6e). % 15.16/15.34 exact (zenon_H182 zenon_H96). % 15.16/15.34 (* end of lemma zenon_L194_ *) % 15.16/15.34 assert (zenon_L195_ : (((op (e1) (e0)) = (e3))\/(((op (e1) (e1)) = (e3))\/(((op (e1) (e2)) = (e3))\/((op (e1) (e3)) = (e3))))) -> (~((e1) = (e3))) -> ((op (e1) (e0)) = (e1)) -> (~((op (e1) (e1)) = (e3))) -> (~((op (e1) (e1)) = (e2))) -> (~((op (e1) (e1)) = (e1))) -> ((op (e0) (e0)) = (e2)) -> (((op (e1) (e1)) = (e0))\/(((op (e1) (e1)) = (e1))\/(((op (e1) (e1)) = (e2))\/((op (e1) (e1)) = (e3))))) -> ((op (e3) (e3)) = (e3)) -> (~((op (e1) (e3)) = (op (e3) (e3)))) -> False). % 15.16/15.34 do 0 intro. intros zenon_H90 zenon_Ha3 zenon_Hd8 zenon_H182 zenon_Hd6 zenon_H1b4 zenon_H92 zenon_H1b3 zenon_H42 zenon_H8b. % 15.16/15.34 apply (zenon_or_s _ _ zenon_H90); [ zenon_intro zenon_H69 | zenon_intro zenon_H94 ]. % 15.16/15.34 apply (zenon_L163_); trivial. % 15.16/15.34 apply (zenon_or_s _ _ zenon_H94); [ zenon_intro zenon_H96 | zenon_intro zenon_H95 ]. % 15.16/15.34 exact (zenon_H182 zenon_H96). % 15.16/15.34 apply (zenon_or_s _ _ zenon_H95); [ zenon_intro zenon_H88 | zenon_intro zenon_H8a ]. % 15.16/15.34 apply (zenon_L194_); trivial. % 15.16/15.34 apply (zenon_L25_); trivial. % 15.16/15.34 (* end of lemma zenon_L195_ *) % 15.16/15.34 assert (zenon_L196_ : ((op (e1) (e2)) = (e1)) -> ((op (e1) (e2)) = (e3)) -> (~((e1) = (e3))) -> False). % 15.16/15.34 do 0 intro. intros zenon_H117 zenon_H88 zenon_Ha3. % 15.16/15.34 elim (classic ((e3) = (e3))); [ zenon_intro zenon_H4c | zenon_intro zenon_H4d ]. % 15.16/15.34 cut (((e3) = (e3)) = ((e1) = (e3))). % 15.16/15.34 intro zenon_D_pnotp. % 15.16/15.34 apply zenon_Ha3. % 15.16/15.34 rewrite <- zenon_D_pnotp. % 15.16/15.34 exact zenon_H4c. % 15.16/15.34 cut (((e3) = (e3))); [idtac | apply NNPP; zenon_intro zenon_H4d]. % 15.16/15.34 cut (((e3) = (e1))); [idtac | apply NNPP; zenon_intro zenon_Ha4]. % 15.16/15.34 congruence. % 15.16/15.34 cut (((op (e1) (e2)) = (e1)) = ((e3) = (e1))). % 15.16/15.34 intro zenon_D_pnotp. % 15.16/15.34 apply zenon_Ha4. % 15.16/15.34 rewrite <- zenon_D_pnotp. % 15.16/15.34 exact zenon_H117. % 15.16/15.34 cut (((e1) = (e1))); [idtac | apply NNPP; zenon_intro zenon_Ha0]. % 15.16/15.34 cut (((op (e1) (e2)) = (e3))); [idtac | apply NNPP; zenon_intro zenon_H172]. % 15.16/15.34 congruence. % 15.16/15.34 exact (zenon_H172 zenon_H88). % 15.16/15.34 apply zenon_Ha0. apply refl_equal. % 15.16/15.34 apply zenon_H4d. apply refl_equal. % 15.16/15.34 apply zenon_H4d. apply refl_equal. % 15.16/15.34 (* end of lemma zenon_L196_ *) % 15.16/15.34 assert (zenon_L197_ : (((op (e0) (e2)) = (e3))\/(((op (e1) (e2)) = (e3))\/(((op (e2) (e2)) = (e3))\/((op (e3) (e2)) = (e3))))) -> (~((e0) = (e3))) -> ((op (e0) (e2)) = (e0)) -> (~((e1) = (e3))) -> ((op (e1) (e2)) = (e1)) -> (~((op (e2) (e2)) = (e3))) -> ((op (e3) (e3)) = (e3)) -> (~((op (e3) (e2)) = (op (e3) (e3)))) -> False). % 15.16/15.34 do 0 intro. intros zenon_H175 zenon_H4b zenon_Hab zenon_Ha3 zenon_H117 zenon_H30 zenon_H42 zenon_H173. % 15.16/15.34 apply (zenon_or_s _ _ zenon_H175); [ zenon_intro zenon_H50 | zenon_intro zenon_H176 ]. % 15.16/15.34 apply (zenon_L48_); trivial. % 15.16/15.34 apply (zenon_or_s _ _ zenon_H176); [ zenon_intro zenon_H88 | zenon_intro zenon_H177 ]. % 15.16/15.34 apply (zenon_L196_); trivial. % 15.16/15.34 apply (zenon_or_s _ _ zenon_H177); [ zenon_intro zenon_H34 | zenon_intro zenon_H106 ]. % 15.16/15.34 exact (zenon_H30 zenon_H34). % 15.16/15.34 apply (zenon_L153_); trivial. % 15.16/15.34 (* end of lemma zenon_L197_ *) % 15.16/15.34 assert (zenon_L198_ : (((op (e1) (e0)) = (e3))\/(((op (e1) (e1)) = (e3))\/(((op (e1) (e2)) = (e3))\/((op (e1) (e3)) = (e3))))) -> (~((e2) = (e3))) -> ((op (e1) (e0)) = (e2)) -> (~((op (e1) (e1)) = (e3))) -> (~((e1) = (e3))) -> ((op (e1) (e2)) = (e1)) -> ((op (e3) (e3)) = (e3)) -> (~((op (e1) (e3)) = (op (e3) (e3)))) -> False). % 15.16/15.34 do 0 intro. intros zenon_H90 zenon_H6a zenon_H68 zenon_H182 zenon_Ha3 zenon_H117 zenon_H42 zenon_H8b. % 15.16/15.34 apply (zenon_or_s _ _ zenon_H90); [ zenon_intro zenon_H69 | zenon_intro zenon_H94 ]. % 15.16/15.34 apply (zenon_L17_); trivial. % 15.16/15.34 apply (zenon_or_s _ _ zenon_H94); [ zenon_intro zenon_H96 | zenon_intro zenon_H95 ]. % 15.16/15.34 exact (zenon_H182 zenon_H96). % 15.16/15.34 apply (zenon_or_s _ _ zenon_H95); [ zenon_intro zenon_H88 | zenon_intro zenon_H8a ]. % 15.16/15.34 apply (zenon_L196_); trivial. % 15.16/15.34 apply (zenon_L25_); trivial. % 15.16/15.34 (* end of lemma zenon_L198_ *) % 15.16/15.34 assert (zenon_L199_ : (~((op (op (e1) (e1)) (op (e1) (e1))) = (op (e2) (e2)))) -> ((op (e1) (e1)) = (e2)) -> False). % 15.16/15.34 do 0 intro. intros zenon_H1b7 zenon_H6e. % 15.16/15.34 cut (((op (e1) (e1)) = (e2))); [idtac | apply NNPP; zenon_intro zenon_Hd6]. % 15.16/15.34 cut (((op (e1) (e1)) = (e2))); [idtac | apply NNPP; zenon_intro zenon_Hd6]. % 15.16/15.34 congruence. % 15.16/15.34 exact (zenon_Hd6 zenon_H6e). % 15.16/15.34 exact (zenon_Hd6 zenon_H6e). % 15.16/15.34 (* end of lemma zenon_L199_ *) % 15.16/15.34 assert (zenon_L200_ : ((op (e1) (e3)) = (e0)) -> ((op (e2) (e2)) = (e3)) -> ((op (e1) (e1)) = (e2)) -> False). % 15.16/15.34 do 0 intro. intros zenon_Hcc zenon_H34 zenon_H6e. % 15.16/15.34 apply (zenon_notand_s _ _ ax28); [ zenon_intro zenon_H1b9 | zenon_intro zenon_H1b8 ]. % 15.16/15.34 elim (classic ((op (op (e1) (e1)) (op (e1) (e1))) = (op (op (e1) (e1)) (op (e1) (e1))))); [ zenon_intro zenon_H1a8 | zenon_intro zenon_H1a9 ]. % 15.16/15.34 cut (((op (op (e1) (e1)) (op (e1) (e1))) = (op (op (e1) (e1)) (op (e1) (e1)))) = ((e3) = (op (op (e1) (e1)) (op (e1) (e1))))). % 15.16/15.34 intro zenon_D_pnotp. % 15.16/15.34 apply zenon_H1b9. % 15.16/15.34 rewrite <- zenon_D_pnotp. % 15.16/15.34 exact zenon_H1a8. % 15.16/15.34 cut (((op (op (e1) (e1)) (op (e1) (e1))) = (op (op (e1) (e1)) (op (e1) (e1))))); [idtac | apply NNPP; zenon_intro zenon_H1a9]. % 15.16/15.34 cut (((op (op (e1) (e1)) (op (e1) (e1))) = (e3))); [idtac | apply NNPP; zenon_intro zenon_H1ba]. % 15.16/15.34 congruence. % 15.16/15.34 cut (((op (e2) (e2)) = (e3)) = ((op (op (e1) (e1)) (op (e1) (e1))) = (e3))). % 15.16/15.34 intro zenon_D_pnotp. % 15.16/15.34 apply zenon_H1ba. % 15.16/15.34 rewrite <- zenon_D_pnotp. % 15.16/15.34 exact zenon_H34. % 15.16/15.34 cut (((e3) = (e3))); [idtac | apply NNPP; zenon_intro zenon_H4d]. % 15.16/15.34 cut (((op (e2) (e2)) = (op (op (e1) (e1)) (op (e1) (e1))))); [idtac | apply NNPP; zenon_intro zenon_H1bb]. % 15.16/15.34 congruence. % 15.16/15.34 elim (classic ((op (op (e1) (e1)) (op (e1) (e1))) = (op (op (e1) (e1)) (op (e1) (e1))))); [ zenon_intro zenon_H1a8 | zenon_intro zenon_H1a9 ]. % 15.16/15.34 cut (((op (op (e1) (e1)) (op (e1) (e1))) = (op (op (e1) (e1)) (op (e1) (e1)))) = ((op (e2) (e2)) = (op (op (e1) (e1)) (op (e1) (e1))))). % 15.16/15.34 intro zenon_D_pnotp. % 15.16/15.34 apply zenon_H1bb. % 15.16/15.34 rewrite <- zenon_D_pnotp. % 15.16/15.34 exact zenon_H1a8. % 15.16/15.34 cut (((op (op (e1) (e1)) (op (e1) (e1))) = (op (op (e1) (e1)) (op (e1) (e1))))); [idtac | apply NNPP; zenon_intro zenon_H1a9]. % 15.16/15.34 cut (((op (op (e1) (e1)) (op (e1) (e1))) = (op (e2) (e2)))); [idtac | apply NNPP; zenon_intro zenon_H1b7]. % 15.16/15.34 congruence. % 15.16/15.34 apply (zenon_L199_); trivial. % 15.16/15.34 apply zenon_H1a9. apply refl_equal. % 15.16/15.34 apply zenon_H1a9. apply refl_equal. % 15.16/15.34 apply zenon_H4d. apply refl_equal. % 15.16/15.34 apply zenon_H1a9. apply refl_equal. % 15.16/15.34 apply zenon_H1a9. apply refl_equal. % 15.16/15.34 apply (zenon_notand_s _ _ zenon_H1b8); [ zenon_intro zenon_H1bd | zenon_intro zenon_H1bc ]. % 15.16/15.34 apply zenon_H1bd. apply sym_equal. exact zenon_H6e. % 15.16/15.34 elim (classic ((op (e1) (op (op (e1) (e1)) (op (e1) (e1)))) = (op (e1) (op (op (e1) (e1)) (op (e1) (e1)))))); [ zenon_intro zenon_H1ae | zenon_intro zenon_H1af ]. % 15.16/15.34 cut (((op (e1) (op (op (e1) (e1)) (op (e1) (e1)))) = (op (e1) (op (op (e1) (e1)) (op (e1) (e1))))) = ((e0) = (op (e1) (op (op (e1) (e1)) (op (e1) (e1)))))). % 15.16/15.34 intro zenon_D_pnotp. % 15.16/15.34 apply zenon_H1bc. % 15.16/15.34 rewrite <- zenon_D_pnotp. % 15.16/15.34 exact zenon_H1ae. % 15.16/15.34 cut (((op (e1) (op (op (e1) (e1)) (op (e1) (e1)))) = (op (e1) (op (op (e1) (e1)) (op (e1) (e1)))))); [idtac | apply NNPP; zenon_intro zenon_H1af]. % 15.16/15.34 cut (((op (e1) (op (op (e1) (e1)) (op (e1) (e1)))) = (e0))); [idtac | apply NNPP; zenon_intro zenon_H1be]. % 15.16/15.34 congruence. % 15.16/15.34 cut (((op (e1) (e3)) = (e0)) = ((op (e1) (op (op (e1) (e1)) (op (e1) (e1)))) = (e0))). % 15.16/15.34 intro zenon_D_pnotp. % 15.16/15.34 apply zenon_H1be. % 15.16/15.34 rewrite <- zenon_D_pnotp. % 15.16/15.34 exact zenon_Hcc. % 15.16/15.34 cut (((e0) = (e0))); [idtac | apply NNPP; zenon_intro zenon_H1d]. % 15.16/15.34 cut (((op (e1) (e3)) = (op (e1) (op (op (e1) (e1)) (op (e1) (e1)))))); [idtac | apply NNPP; zenon_intro zenon_H1bf]. % 15.16/15.34 congruence. % 15.16/15.34 elim (classic ((op (e1) (op (op (e1) (e1)) (op (e1) (e1)))) = (op (e1) (op (op (e1) (e1)) (op (e1) (e1)))))); [ zenon_intro zenon_H1ae | zenon_intro zenon_H1af ]. % 15.16/15.34 cut (((op (e1) (op (op (e1) (e1)) (op (e1) (e1)))) = (op (e1) (op (op (e1) (e1)) (op (e1) (e1))))) = ((op (e1) (e3)) = (op (e1) (op (op (e1) (e1)) (op (e1) (e1)))))). % 15.16/15.34 intro zenon_D_pnotp. % 15.16/15.34 apply zenon_H1bf. % 15.16/15.34 rewrite <- zenon_D_pnotp. % 15.16/15.34 exact zenon_H1ae. % 15.16/15.34 cut (((op (e1) (op (op (e1) (e1)) (op (e1) (e1)))) = (op (e1) (op (op (e1) (e1)) (op (e1) (e1)))))); [idtac | apply NNPP; zenon_intro zenon_H1af]. % 15.16/15.35 cut (((op (e1) (op (op (e1) (e1)) (op (e1) (e1)))) = (op (e1) (e3)))); [idtac | apply NNPP; zenon_intro zenon_H1c0]. % 15.16/15.35 congruence. % 15.16/15.35 cut (((op (op (e1) (e1)) (op (e1) (e1))) = (e3))); [idtac | apply NNPP; zenon_intro zenon_H1ba]. % 15.16/15.35 cut (((e1) = (e1))); [idtac | apply NNPP; zenon_intro zenon_Ha0]. % 15.16/15.35 congruence. % 15.16/15.35 apply zenon_Ha0. apply refl_equal. % 15.16/15.35 cut (((op (e2) (e2)) = (e3)) = ((op (op (e1) (e1)) (op (e1) (e1))) = (e3))). % 15.16/15.35 intro zenon_D_pnotp. % 15.16/15.35 apply zenon_H1ba. % 15.16/15.35 rewrite <- zenon_D_pnotp. % 15.16/15.35 exact zenon_H34. % 15.16/15.35 cut (((e3) = (e3))); [idtac | apply NNPP; zenon_intro zenon_H4d]. % 15.16/15.35 cut (((op (e2) (e2)) = (op (op (e1) (e1)) (op (e1) (e1))))); [idtac | apply NNPP; zenon_intro zenon_H1bb]. % 15.16/15.35 congruence. % 15.16/15.35 elim (classic ((op (op (e1) (e1)) (op (e1) (e1))) = (op (op (e1) (e1)) (op (e1) (e1))))); [ zenon_intro zenon_H1a8 | zenon_intro zenon_H1a9 ]. % 15.16/15.35 cut (((op (op (e1) (e1)) (op (e1) (e1))) = (op (op (e1) (e1)) (op (e1) (e1)))) = ((op (e2) (e2)) = (op (op (e1) (e1)) (op (e1) (e1))))). % 15.16/15.35 intro zenon_D_pnotp. % 15.16/15.35 apply zenon_H1bb. % 15.16/15.35 rewrite <- zenon_D_pnotp. % 15.16/15.35 exact zenon_H1a8. % 15.16/15.35 cut (((op (op (e1) (e1)) (op (e1) (e1))) = (op (op (e1) (e1)) (op (e1) (e1))))); [idtac | apply NNPP; zenon_intro zenon_H1a9]. % 15.16/15.35 cut (((op (op (e1) (e1)) (op (e1) (e1))) = (op (e2) (e2)))); [idtac | apply NNPP; zenon_intro zenon_H1b7]. % 15.16/15.35 congruence. % 15.16/15.35 apply (zenon_L199_); trivial. % 15.16/15.35 apply zenon_H1a9. apply refl_equal. % 15.16/15.35 apply zenon_H1a9. apply refl_equal. % 15.16/15.35 apply zenon_H4d. apply refl_equal. % 15.16/15.35 apply zenon_H1af. apply refl_equal. % 15.16/15.35 apply zenon_H1af. apply refl_equal. % 15.16/15.35 apply zenon_H1d. apply refl_equal. % 15.16/15.35 apply zenon_H1af. apply refl_equal. % 15.16/15.35 apply zenon_H1af. apply refl_equal. % 15.16/15.35 (* end of lemma zenon_L200_ *) % 15.16/15.35 assert (zenon_L201_ : (~((e0) = (e2))) -> ((op (e2) (e3)) = (e2)) -> ((op (e2) (e3)) = (e0)) -> False). % 15.16/15.35 do 0 intro. intros zenon_H5e zenon_H124 zenon_Hd0. % 15.16/15.35 cut (((op (e2) (e3)) = (e2)) = ((e0) = (e2))). % 15.16/15.35 intro zenon_D_pnotp. % 15.16/15.35 apply zenon_H5e. % 15.16/15.35 rewrite <- zenon_D_pnotp. % 15.16/15.35 exact zenon_H124. % 15.16/15.35 cut (((e2) = (e2))); [idtac | apply NNPP; zenon_intro zenon_H60]. % 15.16/15.35 cut (((op (e2) (e3)) = (e0))); [idtac | apply NNPP; zenon_intro zenon_H1c1]. % 15.16/15.35 congruence. % 15.16/15.35 exact (zenon_H1c1 zenon_Hd0). % 15.16/15.35 apply zenon_H60. apply refl_equal. % 15.16/15.35 (* end of lemma zenon_L201_ *) % 15.16/15.35 assert (zenon_L202_ : (((op (e0) (e3)) = (e0))\/(((op (e1) (e3)) = (e0))\/(((op (e2) (e3)) = (e0))\/((op (e3) (e3)) = (e0))))) -> ((op (e0) (e2)) = (e0)) -> (~((op (e0) (e2)) = (op (e0) (e3)))) -> ((op (e1) (e1)) = (e2)) -> ((op (e2) (e2)) = (e3)) -> ((op (e2) (e3)) = (e2)) -> (~((e0) = (e2))) -> (~((op (e3) (e3)) = (e0))) -> False). % 15.16/15.35 do 0 intro. intros zenon_Hd3 zenon_Hab zenon_Hc9 zenon_H6e zenon_H34 zenon_H124 zenon_H5e zenon_H3c. % 15.16/15.35 apply (zenon_or_s _ _ zenon_Hd3); [ zenon_intro zenon_Hca | zenon_intro zenon_Hd4 ]. % 15.16/15.35 apply (zenon_L53_); trivial. % 15.16/15.35 apply (zenon_or_s _ _ zenon_Hd4); [ zenon_intro zenon_Hcc | zenon_intro zenon_Hd5 ]. % 15.16/15.35 apply (zenon_L200_); trivial. % 15.16/15.35 apply (zenon_or_s _ _ zenon_Hd5); [ zenon_intro zenon_Hd0 | zenon_intro zenon_H40 ]. % 15.16/15.35 apply (zenon_L201_); trivial. % 15.16/15.35 exact (zenon_H3c zenon_H40). % 15.16/15.35 (* end of lemma zenon_L202_ *) % 15.16/15.35 assert (zenon_L203_ : (((op (e0) (e2)) = (e3))\/(((op (e1) (e2)) = (e3))\/(((op (e2) (e2)) = (e3))\/((op (e3) (e2)) = (e3))))) -> (~((e0) = (e3))) -> (~((e1) = (e3))) -> ((op (e1) (e2)) = (e1)) -> (~((op (e3) (e3)) = (e0))) -> (~((e0) = (e2))) -> ((op (e2) (e3)) = (e2)) -> ((op (e1) (e1)) = (e2)) -> (~((op (e0) (e2)) = (op (e0) (e3)))) -> ((op (e0) (e2)) = (e0)) -> (((op (e0) (e3)) = (e0))\/(((op (e1) (e3)) = (e0))\/(((op (e2) (e3)) = (e0))\/((op (e3) (e3)) = (e0))))) -> ((op (e3) (e3)) = (e3)) -> (~((op (e3) (e2)) = (op (e3) (e3)))) -> False). % 15.16/15.35 do 0 intro. intros zenon_H175 zenon_H4b zenon_Ha3 zenon_H117 zenon_H3c zenon_H5e zenon_H124 zenon_H6e zenon_Hc9 zenon_Hab zenon_Hd3 zenon_H42 zenon_H173. % 15.16/15.35 apply (zenon_or_s _ _ zenon_H175); [ zenon_intro zenon_H50 | zenon_intro zenon_H176 ]. % 15.16/15.35 apply (zenon_L48_); trivial. % 15.16/15.35 apply (zenon_or_s _ _ zenon_H176); [ zenon_intro zenon_H88 | zenon_intro zenon_H177 ]. % 15.16/15.35 apply (zenon_L196_); trivial. % 15.16/15.35 apply (zenon_or_s _ _ zenon_H177); [ zenon_intro zenon_H34 | zenon_intro zenon_H106 ]. % 15.16/15.35 apply (zenon_L202_); trivial. % 15.16/15.35 apply (zenon_L153_); trivial. % 15.16/15.35 (* end of lemma zenon_L203_ *) % 15.16/15.35 assert (zenon_L204_ : ((op (e1) (e2)) = (e1)) -> ((op (e1) (e2)) = (e2)) -> (~((e1) = (e2))) -> False). % 15.16/15.35 do 0 intro. intros zenon_H117 zenon_H7c zenon_Ha7. % 15.16/15.35 elim (classic ((e2) = (e2))); [ zenon_intro zenon_H5f | zenon_intro zenon_H60 ]. % 15.16/15.35 cut (((e2) = (e2)) = ((e1) = (e2))). % 15.16/15.35 intro zenon_D_pnotp. % 15.16/15.35 apply zenon_Ha7. % 15.16/15.35 rewrite <- zenon_D_pnotp. % 15.16/15.35 exact zenon_H5f. % 15.16/15.35 cut (((e2) = (e2))); [idtac | apply NNPP; zenon_intro zenon_H60]. % 15.16/15.35 cut (((e2) = (e1))); [idtac | apply NNPP; zenon_intro zenon_Ha8]. % 15.16/15.35 congruence. % 15.16/15.35 cut (((op (e1) (e2)) = (e1)) = ((e2) = (e1))). % 15.16/15.35 intro zenon_D_pnotp. % 15.16/15.35 apply zenon_Ha8. % 15.16/15.35 rewrite <- zenon_D_pnotp. % 15.16/15.35 exact zenon_H117. % 15.16/15.35 cut (((e1) = (e1))); [idtac | apply NNPP; zenon_intro zenon_Ha0]. % 15.16/15.35 cut (((op (e1) (e2)) = (e2))); [idtac | apply NNPP; zenon_intro zenon_H1c2]. % 15.16/15.35 congruence. % 15.16/15.35 exact (zenon_H1c2 zenon_H7c). % 15.16/15.35 apply zenon_Ha0. apply refl_equal. % 15.16/15.35 apply zenon_H60. apply refl_equal. % 15.16/15.35 apply zenon_H60. apply refl_equal. % 15.16/15.35 (* end of lemma zenon_L204_ *) % 15.16/15.35 assert (zenon_L205_ : (((op (e0) (e3)) = (e0))\/(((op (e1) (e3)) = (e0))\/(((op (e2) (e3)) = (e0))\/((op (e3) (e3)) = (e0))))) -> ((op (e0) (e2)) = (e0)) -> (~((op (e0) (e2)) = (op (e0) (e3)))) -> ((op (e1) (e3)) = (e2)) -> ((op (e2) (e3)) = (e2)) -> (~((e0) = (e2))) -> (~((op (e3) (e3)) = (e0))) -> False). % 15.16/15.35 do 0 intro. intros zenon_Hd3 zenon_Hab zenon_Hc9 zenon_H82 zenon_H124 zenon_H5e zenon_H3c. % 15.16/15.35 apply (zenon_or_s _ _ zenon_Hd3); [ zenon_intro zenon_Hca | zenon_intro zenon_Hd4 ]. % 15.16/15.35 apply (zenon_L53_); trivial. % 15.16/15.35 apply (zenon_or_s _ _ zenon_Hd4); [ zenon_intro zenon_Hcc | zenon_intro zenon_Hd5 ]. % 15.16/15.35 apply (zenon_L54_); trivial. % 15.16/15.35 apply (zenon_or_s _ _ zenon_Hd5); [ zenon_intro zenon_Hd0 | zenon_intro zenon_H40 ]. % 15.16/15.35 apply (zenon_L201_); trivial. % 15.16/15.35 exact (zenon_H3c zenon_H40). % 15.16/15.35 (* end of lemma zenon_L205_ *) % 15.16/15.35 assert (zenon_L206_ : (((op (e1) (e0)) = (e2))\/(((op (e1) (e1)) = (e2))\/(((op (e1) (e2)) = (e2))\/((op (e1) (e3)) = (e2))))) -> (~((op (e1) (e3)) = (op (e3) (e3)))) -> (~((op (e1) (e1)) = (e3))) -> (~((e2) = (e3))) -> (((op (e1) (e0)) = (e3))\/(((op (e1) (e1)) = (e3))\/(((op (e1) (e2)) = (e3))\/((op (e1) (e3)) = (e3))))) -> (~((op (e3) (e2)) = (op (e3) (e3)))) -> ((op (e3) (e3)) = (e3)) -> (~((e1) = (e3))) -> (~((e0) = (e3))) -> (((op (e0) (e2)) = (e3))\/(((op (e1) (e2)) = (e3))\/(((op (e2) (e2)) = (e3))\/((op (e3) (e2)) = (e3))))) -> (~((e1) = (e2))) -> ((op (e1) (e2)) = (e1)) -> (((op (e0) (e3)) = (e0))\/(((op (e1) (e3)) = (e0))\/(((op (e2) (e3)) = (e0))\/((op (e3) (e3)) = (e0))))) -> ((op (e0) (e2)) = (e0)) -> (~((op (e0) (e2)) = (op (e0) (e3)))) -> ((op (e2) (e3)) = (e2)) -> (~((e0) = (e2))) -> (~((op (e3) (e3)) = (e0))) -> False). % 15.16/15.35 do 0 intro. intros zenon_H84 zenon_H8b zenon_H182 zenon_H6a zenon_H90 zenon_H173 zenon_H42 zenon_Ha3 zenon_H4b zenon_H175 zenon_Ha7 zenon_H117 zenon_Hd3 zenon_Hab zenon_Hc9 zenon_H124 zenon_H5e zenon_H3c. % 15.16/15.35 apply (zenon_or_s _ _ zenon_H84); [ zenon_intro zenon_H68 | zenon_intro zenon_H85 ]. % 15.16/15.35 apply (zenon_L198_); trivial. % 15.16/15.35 apply (zenon_or_s _ _ zenon_H85); [ zenon_intro zenon_H6e | zenon_intro zenon_H86 ]. % 15.16/15.35 apply (zenon_L203_); trivial. % 15.16/15.35 apply (zenon_or_s _ _ zenon_H86); [ zenon_intro zenon_H7c | zenon_intro zenon_H82 ]. % 15.16/15.35 apply (zenon_L204_); trivial. % 15.16/15.35 apply (zenon_L205_); trivial. % 15.16/15.35 (* end of lemma zenon_L206_ *) % 15.16/15.35 assert (zenon_L207_ : ((~((op (e2) (e2)) = (e3)))\/((op (e2) (e3)) = (e2))) -> (((op (e1) (e0)) = (e2))\/(((op (e1) (e1)) = (e2))\/(((op (e1) (e2)) = (e2))\/((op (e1) (e3)) = (e2))))) -> (~((e1) = (e2))) -> (((op (e0) (e3)) = (e0))\/(((op (e1) (e3)) = (e0))\/(((op (e2) (e3)) = (e0))\/((op (e3) (e3)) = (e0))))) -> (~((e0) = (e2))) -> (~((op (e0) (e2)) = (op (e0) (e3)))) -> (~((e2) = (e3))) -> (~((op (e1) (e1)) = (e3))) -> (~((op (e1) (e3)) = (op (e3) (e3)))) -> (((op (e1) (e0)) = (e3))\/(((op (e1) (e1)) = (e3))\/(((op (e1) (e2)) = (e3))\/((op (e1) (e3)) = (e3))))) -> (~((op (e3) (e0)) = (op (e3) (e3)))) -> ((~((op (e3) (e3)) = (e0)))\/((op (e3) (e0)) = (e3))) -> (~((e0) = (e3))) -> ((op (e0) (e2)) = (e0)) -> (~((e1) = (e3))) -> ((op (e1) (e2)) = (e1)) -> (~((op (e3) (e2)) = (op (e3) (e3)))) -> ((op (e3) (e3)) = (e3)) -> (((op (e0) (e2)) = (e3))\/(((op (e1) (e2)) = (e3))\/(((op (e2) (e2)) = (e3))\/((op (e3) (e2)) = (e3))))) -> False). % 15.16/15.35 do 0 intro. intros zenon_H1c3 zenon_H84 zenon_Ha7 zenon_Hd3 zenon_H5e zenon_Hc9 zenon_H6a zenon_H182 zenon_H8b zenon_H90 zenon_Hbb zenon_H10f zenon_H4b zenon_Hab zenon_Ha3 zenon_H117 zenon_H173 zenon_H42 zenon_H175. % 15.16/15.35 apply (zenon_or_s _ _ zenon_H1c3); [ zenon_intro zenon_H30 | zenon_intro zenon_H124 ]. % 15.16/15.35 apply (zenon_L197_); trivial. % 15.16/15.35 apply (zenon_or_s _ _ zenon_H10f); [ zenon_intro zenon_H3c | zenon_intro zenon_Hba ]. % 15.16/15.35 apply (zenon_L206_); trivial. % 15.16/15.35 apply (zenon_L43_); trivial. % 15.16/15.35 (* end of lemma zenon_L207_ *) % 15.16/15.35 assert (zenon_L208_ : (~((e0) = (e1))) -> ((op (e1) (e3)) = (e1)) -> ((op (e1) (e3)) = (e0)) -> False). % 15.16/15.35 do 0 intro. intros zenon_H9e zenon_H11f zenon_Hcc. % 15.16/15.35 cut (((op (e1) (e3)) = (e1)) = ((e0) = (e1))). % 15.16/15.35 intro zenon_D_pnotp. % 15.16/15.35 apply zenon_H9e. % 15.16/15.35 rewrite <- zenon_D_pnotp. % 15.16/15.35 exact zenon_H11f. % 15.16/15.35 cut (((e1) = (e1))); [idtac | apply NNPP; zenon_intro zenon_Ha0]. % 15.16/15.35 cut (((op (e1) (e3)) = (e0))); [idtac | apply NNPP; zenon_intro zenon_H1c4]. % 15.16/15.35 congruence. % 15.16/15.35 exact (zenon_H1c4 zenon_Hcc). % 15.16/15.35 apply zenon_Ha0. apply refl_equal. % 15.16/15.35 (* end of lemma zenon_L208_ *) % 15.16/15.35 assert (zenon_L209_ : ((op (e1) (e3)) = (e1)) -> ((op (e1) (e3)) = (e2)) -> (~((e1) = (e2))) -> False). % 15.16/15.35 do 0 intro. intros zenon_H11f zenon_H82 zenon_Ha7. % 15.16/15.35 elim (classic ((e2) = (e2))); [ zenon_intro zenon_H5f | zenon_intro zenon_H60 ]. % 15.16/15.35 cut (((e2) = (e2)) = ((e1) = (e2))). % 15.16/15.35 intro zenon_D_pnotp. % 15.16/15.35 apply zenon_Ha7. % 15.16/15.35 rewrite <- zenon_D_pnotp. % 15.16/15.35 exact zenon_H5f. % 15.16/15.35 cut (((e2) = (e2))); [idtac | apply NNPP; zenon_intro zenon_H60]. % 15.16/15.35 cut (((e2) = (e1))); [idtac | apply NNPP; zenon_intro zenon_Ha8]. % 15.16/15.35 congruence. % 15.16/15.35 cut (((op (e1) (e3)) = (e1)) = ((e2) = (e1))). % 15.16/15.35 intro zenon_D_pnotp. % 15.16/15.35 apply zenon_Ha8. % 15.16/15.35 rewrite <- zenon_D_pnotp. % 15.16/15.35 exact zenon_H11f. % 15.16/15.35 cut (((e1) = (e1))); [idtac | apply NNPP; zenon_intro zenon_Ha0]. % 15.16/15.35 cut (((op (e1) (e3)) = (e2))); [idtac | apply NNPP; zenon_intro zenon_Hcd]. % 15.16/15.35 congruence. % 15.16/15.35 exact (zenon_Hcd zenon_H82). % 15.16/15.35 apply zenon_Ha0. apply refl_equal. % 15.16/15.35 apply zenon_H60. apply refl_equal. % 15.16/15.35 apply zenon_H60. apply refl_equal. % 15.16/15.35 (* end of lemma zenon_L209_ *) % 15.16/15.35 assert (zenon_L210_ : (((op (e0) (e3)) = (e2))\/(((op (e1) (e3)) = (e2))\/(((op (e2) (e3)) = (e2))\/((op (e3) (e3)) = (e2))))) -> ((op (e0) (e3)) = (e1)) -> (~((e1) = (e2))) -> ((op (e1) (e3)) = (e1)) -> ((op (e2) (e3)) = (e0)) -> (~((e0) = (e2))) -> (~((op (e3) (e3)) = (e2))) -> False). % 15.16/15.35 do 0 intro. intros zenon_H160 zenon_H37 zenon_Ha7 zenon_H11f zenon_Hd0 zenon_H5e zenon_H3d. % 15.16/15.35 apply (zenon_or_s _ _ zenon_H160); [ zenon_intro zenon_H81 | zenon_intro zenon_H161 ]. % 15.16/15.35 apply (zenon_L33_); trivial. % 15.16/15.35 apply (zenon_or_s _ _ zenon_H161); [ zenon_intro zenon_H82 | zenon_intro zenon_H162 ]. % 15.16/15.35 apply (zenon_L209_); trivial. % 15.16/15.35 apply (zenon_or_s _ _ zenon_H162); [ zenon_intro zenon_H124 | zenon_intro zenon_H43 ]. % 15.16/15.35 apply (zenon_L201_); trivial. % 15.16/15.35 exact (zenon_H3d zenon_H43). % 15.16/15.35 (* end of lemma zenon_L210_ *) % 15.16/15.35 assert (zenon_L211_ : (((op (e0) (e3)) = (e0))\/(((op (e1) (e3)) = (e0))\/(((op (e2) (e3)) = (e0))\/((op (e3) (e3)) = (e0))))) -> (~((e0) = (e1))) -> (~((op (e3) (e3)) = (e2))) -> (~((e0) = (e2))) -> ((op (e1) (e3)) = (e1)) -> (~((e1) = (e2))) -> ((op (e0) (e3)) = (e1)) -> (((op (e0) (e3)) = (e2))\/(((op (e1) (e3)) = (e2))\/(((op (e2) (e3)) = (e2))\/((op (e3) (e3)) = (e2))))) -> (~((op (e3) (e3)) = (e0))) -> False). % 15.16/15.35 do 0 intro. intros zenon_Hd3 zenon_H9e zenon_H3d zenon_H5e zenon_H11f zenon_Ha7 zenon_H37 zenon_H160 zenon_H3c. % 15.16/15.35 apply (zenon_or_s _ _ zenon_Hd3); [ zenon_intro zenon_Hca | zenon_intro zenon_Hd4 ]. % 15.16/15.35 apply (zenon_L73_); trivial. % 15.16/15.35 apply (zenon_or_s _ _ zenon_Hd4); [ zenon_intro zenon_Hcc | zenon_intro zenon_Hd5 ]. % 15.16/15.35 apply (zenon_L208_); trivial. % 15.16/15.35 apply (zenon_or_s _ _ zenon_Hd5); [ zenon_intro zenon_Hd0 | zenon_intro zenon_H40 ]. % 15.16/15.35 apply (zenon_L210_); trivial. % 15.16/15.35 exact (zenon_H3c zenon_H40). % 15.16/15.35 (* end of lemma zenon_L211_ *) % 15.16/15.35 assert (zenon_L212_ : (((op (e1) (e0)) = (e1))\/(((op (e1) (e1)) = (e1))\/(((op (e1) (e2)) = (e1))\/((op (e1) (e3)) = (e1))))) -> (((op (e1) (e1)) = (e0))\/(((op (e1) (e1)) = (e1))\/(((op (e1) (e1)) = (e2))\/((op (e1) (e1)) = (e3))))) -> ((op (e0) (e0)) = (e2)) -> (~((op (e1) (e1)) = (e2))) -> (~((op (e1) (e1)) = (e1))) -> (((op (e0) (e2)) = (e3))\/(((op (e1) (e2)) = (e3))\/(((op (e2) (e2)) = (e3))\/((op (e3) (e2)) = (e3))))) -> ((op (e3) (e3)) = (e3)) -> (~((op (e3) (e2)) = (op (e3) (e3)))) -> (~((e1) = (e3))) -> ((op (e0) (e2)) = (e0)) -> (~((e0) = (e3))) -> ((~((op (e3) (e3)) = (e0)))\/((op (e3) (e0)) = (e3))) -> (~((op (e3) (e0)) = (op (e3) (e3)))) -> (((op (e1) (e0)) = (e3))\/(((op (e1) (e1)) = (e3))\/(((op (e1) (e2)) = (e3))\/((op (e1) (e3)) = (e3))))) -> (~((op (e1) (e3)) = (op (e3) (e3)))) -> (~((op (e1) (e1)) = (e3))) -> (~((e2) = (e3))) -> (~((op (e0) (e2)) = (op (e0) (e3)))) -> (((op (e1) (e0)) = (e2))\/(((op (e1) (e1)) = (e2))\/(((op (e1) (e2)) = (e2))\/((op (e1) (e3)) = (e2))))) -> ((~((op (e2) (e2)) = (e3)))\/((op (e2) (e3)) = (e2))) -> (((op (e0) (e3)) = (e0))\/(((op (e1) (e3)) = (e0))\/(((op (e2) (e3)) = (e0))\/((op (e3) (e3)) = (e0))))) -> (~((e0) = (e1))) -> (~((op (e3) (e3)) = (e2))) -> (~((e0) = (e2))) -> (~((e1) = (e2))) -> ((op (e0) (e3)) = (e1)) -> (((op (e0) (e3)) = (e2))\/(((op (e1) (e3)) = (e2))\/(((op (e2) (e3)) = (e2))\/((op (e3) (e3)) = (e2))))) -> (~((op (e3) (e3)) = (e0))) -> False). % 15.16/15.35 do 0 intro. intros zenon_H1c5 zenon_H1b3 zenon_H92 zenon_Hd6 zenon_H1b4 zenon_H175 zenon_H42 zenon_H173 zenon_Ha3 zenon_Hab zenon_H4b zenon_H10f zenon_Hbb zenon_H90 zenon_H8b zenon_H182 zenon_H6a zenon_Hc9 zenon_H84 zenon_H1c3 zenon_Hd3 zenon_H9e zenon_H3d zenon_H5e zenon_Ha7 zenon_H37 zenon_H160 zenon_H3c. % 15.16/15.35 apply (zenon_or_s _ _ zenon_H1c5); [ zenon_intro zenon_Hd8 | zenon_intro zenon_H1c6 ]. % 15.16/15.35 apply (zenon_L195_); trivial. % 15.16/15.35 apply (zenon_or_s _ _ zenon_H1c6); [ zenon_intro zenon_H21 | zenon_intro zenon_H1c7 ]. % 15.16/15.35 exact (zenon_H1b4 zenon_H21). % 15.16/15.35 apply (zenon_or_s _ _ zenon_H1c7); [ zenon_intro zenon_H117 | zenon_intro zenon_H11f ]. % 15.16/15.35 apply (zenon_L207_); trivial. % 15.16/15.35 apply (zenon_L211_); trivial. % 15.16/15.35 (* end of lemma zenon_L212_ *) % 15.16/15.35 assert (zenon_L213_ : (~((op (e0) (e1)) = (op (e1) (e1)))) -> ((op (e0) (e1)) = (e2)) -> ((op (e1) (e1)) = (e2)) -> False). % 15.16/15.35 do 0 intro. intros zenon_H23 zenon_H5d zenon_H6e. % 15.16/15.35 cut (((op (e0) (e1)) = (e2)) = ((op (e0) (e1)) = (op (e1) (e1)))). % 15.16/15.35 intro zenon_D_pnotp. % 15.16/15.35 apply zenon_H23. % 15.16/15.35 rewrite <- zenon_D_pnotp. % 15.16/15.35 exact zenon_H5d. % 15.16/15.35 cut (((e2) = (op (e1) (e1)))); [idtac | apply NNPP; zenon_intro zenon_H1bd]. % 15.16/15.35 cut (((op (e0) (e1)) = (op (e0) (e1)))); [idtac | apply NNPP; zenon_intro zenon_He1]. % 15.16/15.35 congruence. % 15.16/15.35 apply zenon_He1. apply refl_equal. % 15.16/15.35 apply zenon_H1bd. apply sym_equal. exact zenon_H6e. % 15.16/15.35 (* end of lemma zenon_L213_ *) % 15.16/15.35 assert (zenon_L214_ : (((op (e1) (e1)) = (e0))\/(((op (e1) (e1)) = (e1))\/(((op (e1) (e1)) = (e2))\/((op (e1) (e1)) = (e3))))) -> (~((op (e1) (e1)) = (e0))) -> (~((op (e1) (e1)) = (e1))) -> ((op (e0) (e1)) = (e2)) -> (~((op (e0) (e1)) = (op (e1) (e1)))) -> (~((op (e1) (e1)) = (e3))) -> False). % 15.16/15.35 do 0 intro. intros zenon_H1b3 zenon_H145 zenon_H1b4 zenon_H5d zenon_H23 zenon_H182. % 15.16/15.35 apply (zenon_or_s _ _ zenon_H1b3); [ zenon_intro zenon_H149 | zenon_intro zenon_H1b5 ]. % 15.16/15.35 exact (zenon_H145 zenon_H149). % 15.16/15.35 apply (zenon_or_s _ _ zenon_H1b5); [ zenon_intro zenon_H21 | zenon_intro zenon_H1b6 ]. % 15.16/15.35 exact (zenon_H1b4 zenon_H21). % 15.16/15.35 apply (zenon_or_s _ _ zenon_H1b6); [ zenon_intro zenon_H6e | zenon_intro zenon_H96 ]. % 15.16/15.35 apply (zenon_L213_); trivial. % 15.16/15.35 exact (zenon_H182 zenon_H96). % 15.16/15.35 (* end of lemma zenon_L214_ *) % 15.16/15.35 assert (zenon_L215_ : (((op (e1) (e0)) = (e1))\/(((op (e1) (e1)) = (e1))\/(((op (e1) (e2)) = (e1))\/((op (e1) (e3)) = (e1))))) -> (~((op (e1) (e1)) = (e1))) -> (~((op (e1) (e3)) = (op (e3) (e3)))) -> ((op (e3) (e3)) = (e3)) -> (~((e1) = (e3))) -> (~((op (e1) (e1)) = (e3))) -> ((op (e1) (e0)) = (e2)) -> (~((e2) = (e3))) -> (((op (e1) (e0)) = (e3))\/(((op (e1) (e1)) = (e3))\/(((op (e1) (e2)) = (e3))\/((op (e1) (e3)) = (e3))))) -> (((op (e0) (e3)) = (e0))\/(((op (e1) (e3)) = (e0))\/(((op (e2) (e3)) = (e0))\/((op (e3) (e3)) = (e0))))) -> (~((e0) = (e1))) -> (~((op (e3) (e3)) = (e2))) -> (~((e0) = (e2))) -> (~((e1) = (e2))) -> ((op (e0) (e3)) = (e1)) -> (((op (e0) (e3)) = (e2))\/(((op (e1) (e3)) = (e2))\/(((op (e2) (e3)) = (e2))\/((op (e3) (e3)) = (e2))))) -> (~((op (e3) (e3)) = (e0))) -> False). % 15.16/15.35 do 0 intro. intros zenon_H1c5 zenon_H1b4 zenon_H8b zenon_H42 zenon_Ha3 zenon_H182 zenon_H68 zenon_H6a zenon_H90 zenon_Hd3 zenon_H9e zenon_H3d zenon_H5e zenon_Ha7 zenon_H37 zenon_H160 zenon_H3c. % 15.16/15.35 apply (zenon_or_s _ _ zenon_H1c5); [ zenon_intro zenon_Hd8 | zenon_intro zenon_H1c6 ]. % 15.16/15.35 apply (zenon_L162_); trivial. % 15.16/15.35 apply (zenon_or_s _ _ zenon_H1c6); [ zenon_intro zenon_H21 | zenon_intro zenon_H1c7 ]. % 15.16/15.35 exact (zenon_H1b4 zenon_H21). % 15.16/15.35 apply (zenon_or_s _ _ zenon_H1c7); [ zenon_intro zenon_H117 | zenon_intro zenon_H11f ]. % 15.16/15.35 apply (zenon_L198_); trivial. % 15.16/15.35 apply (zenon_L211_); trivial. % 15.16/15.35 (* end of lemma zenon_L215_ *) % 15.16/15.35 assert (zenon_L216_ : (((op (e1) (e0)) = (e2))\/(((op (e1) (e1)) = (e2))\/(((op (e1) (e2)) = (e2))\/((op (e1) (e3)) = (e2))))) -> (~((e2) = (e3))) -> ((op (e1) (e0)) = (e3)) -> (~((op (e1) (e1)) = (e2))) -> ((op (e0) (e2)) = (e2)) -> (~((op (e0) (e2)) = (op (e1) (e2)))) -> ((op (e1) (e3)) = (e1)) -> (~((e1) = (e2))) -> False). % 15.16/15.35 do 0 intro. intros zenon_H84 zenon_H6a zenon_H69 zenon_Hd6 zenon_H63 zenon_H87 zenon_H11f zenon_Ha7. % 15.16/15.35 apply (zenon_or_s _ _ zenon_H84); [ zenon_intro zenon_H68 | zenon_intro zenon_H85 ]. % 15.16/15.35 apply (zenon_L17_); trivial. % 15.16/15.35 apply (zenon_or_s _ _ zenon_H85); [ zenon_intro zenon_H6e | zenon_intro zenon_H86 ]. % 15.16/15.35 exact (zenon_Hd6 zenon_H6e). % 15.16/15.35 apply (zenon_or_s _ _ zenon_H86); [ zenon_intro zenon_H7c | zenon_intro zenon_H82 ]. % 15.16/15.35 apply (zenon_L52_); trivial. % 15.16/15.35 apply (zenon_L209_); trivial. % 15.16/15.35 (* end of lemma zenon_L216_ *) % 15.16/15.35 assert (zenon_L217_ : (~((op (op (e2) (e2)) (op (e2) (e2))) = (op (e1) (e1)))) -> ((op (e2) (e2)) = (e1)) -> False). % 15.16/15.35 do 0 intro. intros zenon_H1c8 zenon_H2a. % 15.16/15.35 cut (((op (e2) (e2)) = (e1))); [idtac | apply NNPP; zenon_intro zenon_H52]. % 15.16/15.35 cut (((op (e2) (e2)) = (e1))); [idtac | apply NNPP; zenon_intro zenon_H52]. % 15.16/15.35 congruence. % 15.16/15.35 exact (zenon_H52 zenon_H2a). % 15.16/15.35 exact (zenon_H52 zenon_H2a). % 15.16/15.35 (* end of lemma zenon_L217_ *) % 15.16/15.35 assert (zenon_L218_ : ((op (e2) (e0)) = (e3)) -> ((op (e1) (e1)) = (e0)) -> ((op (e2) (e2)) = (e1)) -> False). % 15.16/15.35 do 0 intro. intros zenon_Haf zenon_H149 zenon_H2a. % 15.16/15.35 apply (zenon_notand_s _ _ ax7); [ zenon_intro zenon_Hf9 | zenon_intro zenon_H1c9 ]. % 15.16/15.35 elim (classic ((op (op (e2) (e2)) (op (e2) (e2))) = (op (op (e2) (e2)) (op (e2) (e2))))); [ zenon_intro zenon_Hfa | zenon_intro zenon_Hfb ]. % 15.16/15.35 cut (((op (op (e2) (e2)) (op (e2) (e2))) = (op (op (e2) (e2)) (op (e2) (e2)))) = ((e0) = (op (op (e2) (e2)) (op (e2) (e2))))). % 15.16/15.35 intro zenon_D_pnotp. % 15.16/15.35 apply zenon_Hf9. % 15.16/15.35 rewrite <- zenon_D_pnotp. % 15.16/15.35 exact zenon_Hfa. % 15.16/15.35 cut (((op (op (e2) (e2)) (op (e2) (e2))) = (op (op (e2) (e2)) (op (e2) (e2))))); [idtac | apply NNPP; zenon_intro zenon_Hfb]. % 15.16/15.35 cut (((op (op (e2) (e2)) (op (e2) (e2))) = (e0))); [idtac | apply NNPP; zenon_intro zenon_Hfc]. % 15.16/15.35 congruence. % 15.16/15.35 cut (((op (e1) (e1)) = (e0)) = ((op (op (e2) (e2)) (op (e2) (e2))) = (e0))). % 15.16/15.35 intro zenon_D_pnotp. % 15.16/15.35 apply zenon_Hfc. % 15.16/15.35 rewrite <- zenon_D_pnotp. % 15.16/15.35 exact zenon_H149. % 15.16/15.35 cut (((e0) = (e0))); [idtac | apply NNPP; zenon_intro zenon_H1d]. % 15.16/15.35 cut (((op (e1) (e1)) = (op (op (e2) (e2)) (op (e2) (e2))))); [idtac | apply NNPP; zenon_intro zenon_H1ca]. % 15.16/15.35 congruence. % 15.16/15.35 elim (classic ((op (op (e2) (e2)) (op (e2) (e2))) = (op (op (e2) (e2)) (op (e2) (e2))))); [ zenon_intro zenon_Hfa | zenon_intro zenon_Hfb ]. % 15.16/15.35 cut (((op (op (e2) (e2)) (op (e2) (e2))) = (op (op (e2) (e2)) (op (e2) (e2)))) = ((op (e1) (e1)) = (op (op (e2) (e2)) (op (e2) (e2))))). % 15.16/15.35 intro zenon_D_pnotp. % 15.16/15.35 apply zenon_H1ca. % 15.16/15.35 rewrite <- zenon_D_pnotp. % 15.16/15.35 exact zenon_Hfa. % 15.16/15.35 cut (((op (op (e2) (e2)) (op (e2) (e2))) = (op (op (e2) (e2)) (op (e2) (e2))))); [idtac | apply NNPP; zenon_intro zenon_Hfb]. % 15.16/15.35 cut (((op (op (e2) (e2)) (op (e2) (e2))) = (op (e1) (e1)))); [idtac | apply NNPP; zenon_intro zenon_H1c8]. % 15.16/15.35 congruence. % 15.16/15.35 apply (zenon_L217_); trivial. % 15.16/15.35 apply zenon_Hfb. apply refl_equal. % 15.16/15.35 apply zenon_Hfb. apply refl_equal. % 15.16/15.35 apply zenon_H1d. apply refl_equal. % 15.16/15.35 apply zenon_Hfb. apply refl_equal. % 15.16/15.35 apply zenon_Hfb. apply refl_equal. % 15.16/15.35 apply (zenon_notand_s _ _ zenon_H1c9); [ zenon_intro zenon_H2b | zenon_intro zenon_H1cb ]. % 15.16/15.35 apply zenon_H2b. apply sym_equal. exact zenon_H2a. % 15.16/15.35 elim (classic ((op (e2) (op (op (e2) (e2)) (op (e2) (e2)))) = (op (e2) (op (op (e2) (e2)) (op (e2) (e2)))))); [ zenon_intro zenon_Hff | zenon_intro zenon_H100 ]. % 15.16/15.35 cut (((op (e2) (op (op (e2) (e2)) (op (e2) (e2)))) = (op (e2) (op (op (e2) (e2)) (op (e2) (e2))))) = ((e3) = (op (e2) (op (op (e2) (e2)) (op (e2) (e2)))))). % 15.16/15.35 intro zenon_D_pnotp. % 15.16/15.35 apply zenon_H1cb. % 15.16/15.35 rewrite <- zenon_D_pnotp. % 15.16/15.35 exact zenon_Hff. % 15.16/15.35 cut (((op (e2) (op (op (e2) (e2)) (op (e2) (e2)))) = (op (e2) (op (op (e2) (e2)) (op (e2) (e2)))))); [idtac | apply NNPP; zenon_intro zenon_H100]. % 15.16/15.35 cut (((op (e2) (op (op (e2) (e2)) (op (e2) (e2)))) = (e3))); [idtac | apply NNPP; zenon_intro zenon_H1cc]. % 15.16/15.35 congruence. % 15.16/15.35 cut (((op (e2) (e0)) = (e3)) = ((op (e2) (op (op (e2) (e2)) (op (e2) (e2)))) = (e3))). % 15.16/15.35 intro zenon_D_pnotp. % 15.16/15.35 apply zenon_H1cc. % 15.16/15.35 rewrite <- zenon_D_pnotp. % 15.16/15.35 exact zenon_Haf. % 15.16/15.35 cut (((e3) = (e3))); [idtac | apply NNPP; zenon_intro zenon_H4d]. % 15.16/15.35 cut (((op (e2) (e0)) = (op (e2) (op (op (e2) (e2)) (op (e2) (e2)))))); [idtac | apply NNPP; zenon_intro zenon_H102]. % 15.16/15.35 congruence. % 15.16/15.35 elim (classic ((op (e2) (op (op (e2) (e2)) (op (e2) (e2)))) = (op (e2) (op (op (e2) (e2)) (op (e2) (e2)))))); [ zenon_intro zenon_Hff | zenon_intro zenon_H100 ]. % 15.16/15.35 cut (((op (e2) (op (op (e2) (e2)) (op (e2) (e2)))) = (op (e2) (op (op (e2) (e2)) (op (e2) (e2))))) = ((op (e2) (e0)) = (op (e2) (op (op (e2) (e2)) (op (e2) (e2)))))). % 15.16/15.35 intro zenon_D_pnotp. % 15.16/15.35 apply zenon_H102. % 15.16/15.35 rewrite <- zenon_D_pnotp. % 15.16/15.35 exact zenon_Hff. % 15.16/15.35 cut (((op (e2) (op (op (e2) (e2)) (op (e2) (e2)))) = (op (e2) (op (op (e2) (e2)) (op (e2) (e2)))))); [idtac | apply NNPP; zenon_intro zenon_H100]. % 15.16/15.35 cut (((op (e2) (op (op (e2) (e2)) (op (e2) (e2)))) = (op (e2) (e0)))); [idtac | apply NNPP; zenon_intro zenon_H103]. % 15.16/15.35 congruence. % 15.16/15.35 cut (((op (op (e2) (e2)) (op (e2) (e2))) = (e0))); [idtac | apply NNPP; zenon_intro zenon_Hfc]. % 15.16/15.35 cut (((e2) = (e2))); [idtac | apply NNPP; zenon_intro zenon_H60]. % 15.16/15.35 congruence. % 15.16/15.35 apply zenon_H60. apply refl_equal. % 15.16/15.35 cut (((op (e1) (e1)) = (e0)) = ((op (op (e2) (e2)) (op (e2) (e2))) = (e0))). % 15.16/15.35 intro zenon_D_pnotp. % 15.16/15.35 apply zenon_Hfc. % 15.16/15.35 rewrite <- zenon_D_pnotp. % 15.16/15.35 exact zenon_H149. % 15.16/15.35 cut (((e0) = (e0))); [idtac | apply NNPP; zenon_intro zenon_H1d]. % 15.16/15.35 cut (((op (e1) (e1)) = (op (op (e2) (e2)) (op (e2) (e2))))); [idtac | apply NNPP; zenon_intro zenon_H1ca]. % 15.16/15.35 congruence. % 15.16/15.35 elim (classic ((op (op (e2) (e2)) (op (e2) (e2))) = (op (op (e2) (e2)) (op (e2) (e2))))); [ zenon_intro zenon_Hfa | zenon_intro zenon_Hfb ]. % 15.16/15.35 cut (((op (op (e2) (e2)) (op (e2) (e2))) = (op (op (e2) (e2)) (op (e2) (e2)))) = ((op (e1) (e1)) = (op (op (e2) (e2)) (op (e2) (e2))))). % 15.16/15.35 intro zenon_D_pnotp. % 15.16/15.35 apply zenon_H1ca. % 15.16/15.35 rewrite <- zenon_D_pnotp. % 15.16/15.35 exact zenon_Hfa. % 15.16/15.35 cut (((op (op (e2) (e2)) (op (e2) (e2))) = (op (op (e2) (e2)) (op (e2) (e2))))); [idtac | apply NNPP; zenon_intro zenon_Hfb]. % 15.16/15.35 cut (((op (op (e2) (e2)) (op (e2) (e2))) = (op (e1) (e1)))); [idtac | apply NNPP; zenon_intro zenon_H1c8]. % 15.16/15.35 congruence. % 15.16/15.35 apply (zenon_L217_); trivial. % 15.16/15.35 apply zenon_Hfb. apply refl_equal. % 15.16/15.35 apply zenon_Hfb. apply refl_equal. % 15.16/15.35 apply zenon_H1d. apply refl_equal. % 15.16/15.35 apply zenon_H100. apply refl_equal. % 15.16/15.35 apply zenon_H100. apply refl_equal. % 15.16/15.35 apply zenon_H4d. apply refl_equal. % 15.16/15.35 apply zenon_H100. apply refl_equal. % 15.16/15.35 apply zenon_H100. apply refl_equal. % 15.16/15.35 (* end of lemma zenon_L218_ *) % 15.16/15.35 assert (zenon_L219_ : (((op (e1) (e1)) = (e0))\/(((op (e1) (e1)) = (e1))\/(((op (e1) (e1)) = (e2))\/((op (e1) (e1)) = (e3))))) -> (~((op (e2) (e2)) = (e3))) -> (~((op (e2) (e2)) = (e2))) -> ((op (e2) (e0)) = (e3)) -> (~((op (e2) (e2)) = (e0))) -> (((op (e2) (e2)) = (e0))\/(((op (e2) (e2)) = (e1))\/(((op (e2) (e2)) = (e2))\/((op (e2) (e2)) = (e3))))) -> (~((op (e1) (e1)) = (e1))) -> (~((op (e1) (e1)) = (e2))) -> (~((op (e1) (e1)) = (e3))) -> False). % 15.16/15.35 do 0 intro. intros zenon_H1b3 zenon_H30 zenon_H2f zenon_Haf zenon_H2e zenon_H2d zenon_H1b4 zenon_Hd6 zenon_H182. % 15.16/15.35 apply (zenon_or_s _ _ zenon_H1b3); [ zenon_intro zenon_H149 | zenon_intro zenon_H1b5 ]. % 15.16/15.35 apply (zenon_or_s _ _ zenon_H2d); [ zenon_intro zenon_H32 | zenon_intro zenon_H31 ]. % 15.16/15.35 exact (zenon_H2e zenon_H32). % 15.16/15.35 apply (zenon_or_s _ _ zenon_H31); [ zenon_intro zenon_H2a | zenon_intro zenon_H33 ]. % 15.16/15.35 apply (zenon_L218_); trivial. % 15.16/15.35 apply (zenon_or_s _ _ zenon_H33); [ zenon_intro zenon_H35 | zenon_intro zenon_H34 ]. % 15.16/15.35 exact (zenon_H2f zenon_H35). % 15.16/15.35 exact (zenon_H30 zenon_H34). % 15.16/15.35 apply (zenon_or_s _ _ zenon_H1b5); [ zenon_intro zenon_H21 | zenon_intro zenon_H1b6 ]. % 15.16/15.35 exact (zenon_H1b4 zenon_H21). % 15.16/15.35 apply (zenon_or_s _ _ zenon_H1b6); [ zenon_intro zenon_H6e | zenon_intro zenon_H96 ]. % 15.16/15.35 exact (zenon_Hd6 zenon_H6e). % 15.16/15.35 exact (zenon_H182 zenon_H96). % 15.16/15.35 (* end of lemma zenon_L219_ *) % 15.16/15.35 assert (zenon_L220_ : (~((e2) = (e3))) -> ((op (e3) (e0)) = (e3)) -> ((op (e3) (e0)) = (e2)) -> False). % 15.16/15.35 do 0 intro. intros zenon_H6a zenon_Hba zenon_He9. % 15.16/15.35 cut (((op (e3) (e0)) = (e3)) = ((e2) = (e3))). % 15.16/15.35 intro zenon_D_pnotp. % 15.16/15.35 apply zenon_H6a. % 15.16/15.35 rewrite <- zenon_D_pnotp. % 15.16/15.35 exact zenon_Hba. % 15.16/15.35 cut (((e3) = (e3))); [idtac | apply NNPP; zenon_intro zenon_H4d]. % 15.16/15.35 cut (((op (e3) (e0)) = (e2))); [idtac | apply NNPP; zenon_intro zenon_Hea]. % 15.16/15.35 congruence. % 15.16/15.35 exact (zenon_Hea zenon_He9). % 15.16/15.35 apply zenon_H4d. apply refl_equal. % 15.16/15.35 (* end of lemma zenon_L220_ *) % 15.16/15.35 assert (zenon_L221_ : (((op (e0) (e0)) = (e1))\/(((op (e0) (e1)) = (e1))\/(((op (e0) (e2)) = (e1))\/((op (e0) (e3)) = (e1))))) -> (~((op (e0) (e0)) = (e1))) -> (~((op (e0) (e2)) = (op (e2) (e2)))) -> (((op (e0) (e0)) = (e2))\/(((op (e0) (e1)) = (e2))\/(((op (e0) (e2)) = (e2))\/((op (e0) (e3)) = (e2))))) -> (~((op (e0) (e1)) = (op (e1) (e1)))) -> (~((op (e1) (e1)) = (e0))) -> (~((e2) = (e3))) -> (((op (e1) (e1)) = (e0))\/(((op (e1) (e1)) = (e1))\/(((op (e1) (e1)) = (e2))\/((op (e1) (e1)) = (e3))))) -> (~((op (e2) (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) (e1)) = (e1))) -> (~((op (e1) (e1)) = (e2))) -> (~((op (e1) (e1)) = (e3))) -> (((op (e1) (e0)) = (e1))\/(((op (e1) (e1)) = (e1))\/(((op (e1) (e2)) = (e1))\/((op (e1) (e3)) = (e1))))) -> (~((op (e3) (e2)) = (op (e3) (e3)))) -> ((op (e3) (e3)) = (e3)) -> (~((e1) = (e3))) -> ((op (e0) (e2)) = (e0)) -> (~((e0) = (e3))) -> (((op (e0) (e2)) = (e3))\/(((op (e1) (e2)) = (e3))\/(((op (e2) (e2)) = (e3))\/((op (e3) (e2)) = (e3))))) -> (((op (e1) (e0)) = (e2))\/(((op (e1) (e1)) = (e2))\/(((op (e1) (e2)) = (e2))\/((op (e1) (e3)) = (e2))))) -> (~((op (e0) (e2)) = (op (e1) (e2)))) -> (~((op (e0) (e0)) = (e3))) -> (((op (e0) (e0)) = (e3))\/(((op (e1) (e0)) = (e3))\/(((op (e2) (e0)) = (e3))\/((op (e3) (e0)) = (e3))))) -> (((op (e0) (e0)) = (e3))\/(((op (e0) (e1)) = (e3))\/(((op (e0) (e2)) = (e3))\/((op (e0) (e3)) = (e3))))) -> (~((op (e2) (e3)) = (op (e3) (e3)))) -> (~((op (e0) (e1)) = (op (e2) (e1)))) -> (((op (e2) (e0)) = (e3))\/(((op (e2) (e1)) = (e3))\/(((op (e2) (e2)) = (e3))\/((op (e2) (e3)) = (e3))))) -> (~((op (e0) (e3)) = (op (e3) (e3)))) -> (~((op (e1) (e3)) = (op (e3) (e3)))) -> (((op (e1) (e0)) = (e3))\/(((op (e1) (e1)) = (e3))\/(((op (e1) (e2)) = (e3))\/((op (e1) (e3)) = (e3))))) -> (((op (e0) (e3)) = (e0))\/(((op (e1) (e3)) = (e0))\/(((op (e2) (e3)) = (e0))\/((op (e3) (e3)) = (e0))))) -> (~((e0) = (e1))) -> (~((op (e3) (e3)) = (e2))) -> (~((e0) = (e2))) -> (((op (e0) (e3)) = (e2))\/(((op (e1) (e3)) = (e2))\/(((op (e2) (e3)) = (e2))\/((op (e3) (e3)) = (e2))))) -> (~((op (e3) (e3)) = (e0))) -> ((~((op (e3) (e3)) = (e0)))\/((op (e3) (e0)) = (e3))) -> (~((op (e3) (e0)) = (op (e3) (e3)))) -> (~((op (e0) (e2)) = (op (e0) (e3)))) -> ((~((op (e2) (e2)) = (e3)))\/((op (e2) (e3)) = (e2))) -> (((op (e0) (e0)) = (e2))\/(((op (e1) (e0)) = (e2))\/(((op (e2) (e0)) = (e2))\/((op (e3) (e0)) = (e2))))) -> (~((e1) = (e2))) -> False). % 15.16/15.35 do 0 intro. intros zenon_H44 zenon_H45 zenon_H28 zenon_H8e zenon_H23 zenon_H145 zenon_H6a zenon_H1b3 zenon_H30 zenon_H2f zenon_H2e zenon_H2d zenon_H1b4 zenon_Hd6 zenon_H182 zenon_H1c5 zenon_H173 zenon_H42 zenon_Ha3 zenon_Hab zenon_H4b zenon_H175 zenon_H84 zenon_H87 zenon_H59 zenon_Hbe zenon_H58 zenon_He3 zenon_Hde zenon_He6 zenon_H36 zenon_H8b zenon_H90 zenon_Hd3 zenon_H9e zenon_H3d zenon_H5e zenon_H160 zenon_H3c zenon_H10f zenon_Hbb zenon_Hc9 zenon_H1c3 zenon_Heb zenon_Ha7. % 15.16/15.35 apply (zenon_or_s _ _ zenon_H44); [ zenon_intro zenon_H47 | zenon_intro zenon_H46 ]. % 15.16/15.35 exact (zenon_H45 zenon_H47). % 15.16/15.35 apply (zenon_or_s _ _ zenon_H46); [ zenon_intro zenon_H22 | zenon_intro zenon_H48 ]. % 15.16/15.35 apply (zenon_L60_); trivial. % 15.16/15.35 apply (zenon_or_s _ _ zenon_H48); [ zenon_intro zenon_H29 | zenon_intro zenon_H37 ]. % 15.16/15.35 apply (zenon_L5_); trivial. % 15.16/15.35 apply (zenon_or_s _ _ zenon_H8e); [ zenon_intro zenon_H92 | zenon_intro zenon_H91 ]. % 15.16/15.35 apply (zenon_L212_); trivial. % 15.16/15.35 apply (zenon_or_s _ _ zenon_H91); [ zenon_intro zenon_H5d | zenon_intro zenon_H93 ]. % 15.16/15.35 apply (zenon_L214_); trivial. % 15.16/15.35 apply (zenon_or_s _ _ zenon_H93); [ zenon_intro zenon_H63 | zenon_intro zenon_H81 ]. % 15.16/15.35 apply (zenon_or_s _ _ zenon_Heb); [ zenon_intro zenon_H92 | zenon_intro zenon_Hec ]. % 15.16/15.35 apply (zenon_L212_); trivial. % 15.16/15.35 apply (zenon_or_s _ _ zenon_Hec); [ zenon_intro zenon_H68 | zenon_intro zenon_Hed ]. % 15.16/15.35 apply (zenon_L215_); trivial. % 15.16/15.35 apply (zenon_or_s _ _ zenon_Hed); [ zenon_intro zenon_Hdd | zenon_intro zenon_He9 ]. % 15.16/15.35 apply (zenon_L68_); trivial. % 15.16/15.35 apply (zenon_or_s _ _ zenon_Hbe); [ zenon_intro zenon_H5b | zenon_intro zenon_Hbf ]. % 15.16/15.35 exact (zenon_H59 zenon_H5b). % 15.16/15.35 apply (zenon_or_s _ _ zenon_Hbf); [ zenon_intro zenon_H69 | zenon_intro zenon_Hc0 ]. % 15.16/15.35 apply (zenon_or_s _ _ zenon_H1c5); [ zenon_intro zenon_Hd8 | zenon_intro zenon_H1c6 ]. % 15.16/15.35 apply (zenon_L163_); trivial. % 15.16/15.35 apply (zenon_or_s _ _ zenon_H1c6); [ zenon_intro zenon_H21 | zenon_intro zenon_H1c7 ]. % 15.16/15.35 exact (zenon_H1b4 zenon_H21). % 15.16/15.35 apply (zenon_or_s _ _ zenon_H1c7); [ zenon_intro zenon_H117 | zenon_intro zenon_H11f ]. % 15.16/15.35 apply (zenon_L197_); trivial. % 15.16/15.35 apply (zenon_L216_); trivial. % 15.16/15.35 apply (zenon_or_s _ _ zenon_Hc0); [ zenon_intro zenon_Haf | zenon_intro zenon_Hba ]. % 15.16/15.35 apply (zenon_L219_); trivial. % 15.16/15.35 apply (zenon_L220_); trivial. % 15.16/15.35 apply (zenon_L33_); trivial. % 15.16/15.35 (* end of lemma zenon_L221_ *) % 15.16/15.35 assert (zenon_L222_ : ((~((op (e3) (e3)) = (e2)))\/((op (e3) (e2)) = (e3))) -> (~((op (e0) (e0)) = (e1))) -> (((op (e0) (e0)) = (e3))\/(((op (e0) (e1)) = (e3))\/(((op (e0) (e2)) = (e3))\/((op (e0) (e3)) = (e3))))) -> ((op (e3) (e3)) = (e3)) -> (~((op (e0) (e3)) = (op (e3) (e3)))) -> ((op (e0) (e2)) = (e0)) -> (~((e0) = (e3))) -> (~((e1) = (e3))) -> (~((op (e0) (e0)) = (e3))) -> (((op (e2) (e2)) = (e0))\/(((op (e2) (e2)) = (e1))\/(((op (e2) (e2)) = (e2))\/((op (e2) (e2)) = (e3))))) -> (~((op (e2) (e2)) = (e3))) -> (~((op (e2) (e2)) = (e2))) -> (~((op (e0) (e2)) = (op (e2) (e2)))) -> (~((op (e2) (e2)) = (e0))) -> (((op (e0) (e0)) = (e2))\/(((op (e0) (e1)) = (e2))\/(((op (e0) (e2)) = (e2))\/((op (e0) (e3)) = (e2))))) -> (~((op (e0) (e1)) = (op (e2) (e1)))) -> (~((op (e2) (e3)) = (op (e3) (e3)))) -> (((op (e2) (e0)) = (e3))\/(((op (e2) (e1)) = (e3))\/(((op (e2) (e2)) = (e3))\/((op (e2) (e3)) = (e3))))) -> (((op (e0) (e0)) = (e3))\/(((op (e1) (e0)) = (e3))\/(((op (e2) (e0)) = (e3))\/((op (e3) (e0)) = (e3))))) -> (~((op (e0) (e2)) = (op (e1) (e2)))) -> (((op (e0) (e0)) = (e2))\/(((op (e1) (e0)) = (e2))\/(((op (e2) (e0)) = (e2))\/((op (e3) (e0)) = (e2))))) -> (~((op (e1) (e1)) = (e0))) -> (~((op (e0) (e1)) = (op (e1) (e1)))) -> (((op (e1) (e0)) = (e3))\/(((op (e1) (e1)) = (e3))\/(((op (e1) (e2)) = (e3))\/((op (e1) (e3)) = (e3))))) -> (~((op (e1) (e3)) = (op (e3) (e3)))) -> (~((op (e1) (e1)) = (e1))) -> (~((op (e1) (e1)) = (e2))) -> (((op (e1) (e1)) = (e0))\/(((op (e1) (e1)) = (e1))\/(((op (e1) (e1)) = (e2))\/((op (e1) (e1)) = (e3))))) -> (~((op (e1) (e1)) = (e3))) -> ((~((op (e2) (e2)) = (e3)))\/((op (e2) (e3)) = (e2))) -> (((op (e1) (e0)) = (e2))\/(((op (e1) (e1)) = (e2))\/(((op (e1) (e2)) = (e2))\/((op (e1) (e3)) = (e2))))) -> (~((e1) = (e2))) -> (((op (e0) (e3)) = (e0))\/(((op (e1) (e3)) = (e0))\/(((op (e2) (e3)) = (e0))\/((op (e3) (e3)) = (e0))))) -> (~((e0) = (e2))) -> (~((op (e0) (e2)) = (op (e0) (e3)))) -> (~((e2) = (e3))) -> (~((op (e3) (e0)) = (op (e3) (e3)))) -> ((~((op (e3) (e3)) = (e0)))\/((op (e3) (e0)) = (e3))) -> (~((op (e3) (e2)) = (op (e3) (e3)))) -> (((op (e0) (e2)) = (e3))\/(((op (e1) (e2)) = (e3))\/(((op (e2) (e2)) = (e3))\/((op (e3) (e2)) = (e3))))) -> (~((op (e3) (e3)) = (e0))) -> (((op (e0) (e3)) = (e2))\/(((op (e1) (e3)) = (e2))\/(((op (e2) (e3)) = (e2))\/((op (e3) (e3)) = (e2))))) -> (~((e0) = (e1))) -> (((op (e1) (e0)) = (e1))\/(((op (e1) (e1)) = (e1))\/(((op (e1) (e2)) = (e1))\/((op (e1) (e3)) = (e1))))) -> (((op (e0) (e0)) = (e1))\/(((op (e0) (e1)) = (e1))\/(((op (e0) (e2)) = (e1))\/((op (e0) (e3)) = (e1))))) -> False). % 15.16/15.35 do 0 intro. intros zenon_H10e zenon_H45 zenon_H58 zenon_H42 zenon_H36 zenon_Hab zenon_H4b zenon_Ha3 zenon_H59 zenon_H2d zenon_H30 zenon_H2f zenon_H28 zenon_H2e zenon_H8e zenon_Hde zenon_He3 zenon_He6 zenon_Hbe zenon_H87 zenon_Heb zenon_H145 zenon_H23 zenon_H90 zenon_H8b zenon_H1b4 zenon_Hd6 zenon_H1b3 zenon_H182 zenon_H1c3 zenon_H84 zenon_Ha7 zenon_Hd3 zenon_H5e zenon_Hc9 zenon_H6a zenon_Hbb zenon_H10f zenon_H173 zenon_H175 zenon_H3c zenon_H160 zenon_H9e zenon_H1c5 zenon_H44. % 15.16/15.35 apply (zenon_or_s _ _ zenon_H10e); [ zenon_intro zenon_H3d | zenon_intro zenon_H106 ]. % 15.16/15.35 apply (zenon_L221_); trivial. % 15.16/15.35 apply (zenon_L153_); trivial. % 15.16/15.35 (* end of lemma zenon_L222_ *) % 15.16/15.35 assert (zenon_L223_ : ((op (e0) (e3)) = (e1)) -> ((op (e0) (e1)) = (e1)) -> (~((op (e0) (e1)) = (op (e0) (e3)))) -> False). % 15.16/15.35 do 0 intro. intros zenon_H37 zenon_H22 zenon_H1cd. % 15.16/15.35 elim (classic ((op (e0) (e3)) = (op (e0) (e3)))); [ zenon_intro zenon_H113 | zenon_intro zenon_H3a ]. % 15.16/15.35 cut (((op (e0) (e3)) = (op (e0) (e3))) = ((op (e0) (e1)) = (op (e0) (e3)))). % 15.16/15.35 intro zenon_D_pnotp. % 15.16/15.35 apply zenon_H1cd. % 15.16/15.35 rewrite <- zenon_D_pnotp. % 15.16/15.35 exact zenon_H113. % 15.16/15.35 cut (((op (e0) (e3)) = (op (e0) (e3)))); [idtac | apply NNPP; zenon_intro zenon_H3a]. % 15.16/15.35 cut (((op (e0) (e3)) = (op (e0) (e1)))); [idtac | apply NNPP; zenon_intro zenon_H1ce]. % 15.16/15.35 congruence. % 15.16/15.35 cut (((op (e0) (e3)) = (e1)) = ((op (e0) (e3)) = (op (e0) (e1)))). % 15.16/15.35 intro zenon_D_pnotp. % 15.16/15.35 apply zenon_H1ce. % 15.16/15.35 rewrite <- zenon_D_pnotp. % 15.16/15.35 exact zenon_H37. % 15.16/15.35 cut (((e1) = (op (e0) (e1)))); [idtac | apply NNPP; zenon_intro zenon_H27]. % 15.16/15.35 cut (((op (e0) (e3)) = (op (e0) (e3)))); [idtac | apply NNPP; zenon_intro zenon_H3a]. % 15.16/15.35 congruence. % 15.16/15.35 apply zenon_H3a. apply refl_equal. % 15.16/15.35 apply zenon_H27. apply sym_equal. exact zenon_H22. % 15.16/15.35 apply zenon_H3a. apply refl_equal. % 15.16/15.35 apply zenon_H3a. apply refl_equal. % 15.16/15.35 (* end of lemma zenon_L223_ *) % 15.16/15.35 assert (zenon_L224_ : (~((op (e1) (e0)) = (op (e1) (e3)))) -> ((op (e1) (e0)) = (e1)) -> ((op (e1) (e3)) = (e1)) -> False). % 15.16/15.35 do 0 intro. intros zenon_H1cf zenon_Hd8 zenon_H11f. % 15.16/15.35 cut (((op (e1) (e0)) = (e1)) = ((op (e1) (e0)) = (op (e1) (e3)))). % 15.16/15.35 intro zenon_D_pnotp. % 15.16/15.35 apply zenon_H1cf. % 15.16/15.35 rewrite <- zenon_D_pnotp. % 15.16/15.35 exact zenon_Hd8. % 15.16/15.35 cut (((e1) = (op (e1) (e3)))); [idtac | apply NNPP; zenon_intro zenon_H120]. % 15.16/15.35 cut (((op (e1) (e0)) = (op (e1) (e0)))); [idtac | apply NNPP; zenon_intro zenon_Hda]. % 15.16/15.35 congruence. % 15.16/15.35 apply zenon_Hda. apply refl_equal. % 15.16/15.35 apply zenon_H120. apply sym_equal. exact zenon_H11f. % 15.16/15.35 (* end of lemma zenon_L224_ *) % 15.16/15.35 assert (zenon_L225_ : (((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)) = (e1)) -> (~((op (e1) (e0)) = (op (e1) (e3)))) -> ((op (e2) (e3)) = (e2)) -> (~((e1) = (e2))) -> (~((op (e3) (e3)) = (e1))) -> False). % 15.16/15.35 do 0 intro. intros zenon_H121 zenon_H1cd zenon_H22 zenon_Hd8 zenon_H1cf zenon_H124 zenon_Ha7 zenon_H104. % 15.16/15.35 apply (zenon_or_s _ _ zenon_H121); [ zenon_intro zenon_H37 | zenon_intro zenon_H122 ]. % 15.16/15.35 apply (zenon_L223_); trivial. % 15.16/15.35 apply (zenon_or_s _ _ zenon_H122); [ zenon_intro zenon_H11f | zenon_intro zenon_H123 ]. % 15.16/15.35 apply (zenon_L224_); trivial. % 15.16/15.35 apply (zenon_or_s _ _ zenon_H123); [ zenon_intro zenon_Hb5 | zenon_intro zenon_H38 ]. % 15.16/15.35 apply (zenon_L93_); trivial. % 15.16/15.35 exact (zenon_H104 zenon_H38). % 15.16/15.35 (* end of lemma zenon_L225_ *) % 15.16/15.35 assert (zenon_L226_ : (((op (e1) (e0)) = (e3))\/(((op (e1) (e1)) = (e3))\/(((op (e1) (e2)) = (e3))\/((op (e1) (e3)) = (e3))))) -> (~((e1) = (e3))) -> ((op (e1) (e0)) = (e1)) -> (~((op (e1) (e1)) = (e3))) -> ((op (e0) (e2)) = (e3)) -> (~((op (e0) (e2)) = (op (e1) (e2)))) -> ((op (e3) (e3)) = (e3)) -> (~((op (e1) (e3)) = (op (e3) (e3)))) -> False). % 15.16/15.35 do 0 intro. intros zenon_H90 zenon_Ha3 zenon_Hd8 zenon_H182 zenon_H50 zenon_H87 zenon_H42 zenon_H8b. % 15.16/15.35 apply (zenon_or_s _ _ zenon_H90); [ zenon_intro zenon_H69 | zenon_intro zenon_H94 ]. % 15.16/15.35 apply (zenon_L163_); trivial. % 15.16/15.35 apply (zenon_or_s _ _ zenon_H94); [ zenon_intro zenon_H96 | zenon_intro zenon_H95 ]. % 15.16/15.35 exact (zenon_H182 zenon_H96). % 15.16/15.35 apply (zenon_or_s _ _ zenon_H95); [ zenon_intro zenon_H88 | zenon_intro zenon_H8a ]. % 15.16/15.35 apply (zenon_L24_); trivial. % 15.16/15.35 apply (zenon_L25_); trivial. % 15.16/15.35 (* end of lemma zenon_L226_ *) % 15.16/15.35 assert (zenon_L227_ : (((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) (e3)) = (op (e3) (e3)))) -> (~((op (e0) (e2)) = (op (e1) (e2)))) -> (~((op (e1) (e1)) = (e3))) -> ((op (e1) (e0)) = (e1)) -> (~((e1) = (e3))) -> (((op (e1) (e0)) = (e3))\/(((op (e1) (e1)) = (e3))\/(((op (e1) (e2)) = (e3))\/((op (e1) (e3)) = (e3))))) -> ((op (e3) (e3)) = (e3)) -> (~((op (e0) (e3)) = (op (e3) (e3)))) -> False). % 15.16/15.35 do 0 intro. intros zenon_H58 zenon_H59 zenon_H6a zenon_H5d zenon_H8b zenon_H87 zenon_H182 zenon_Hd8 zenon_Ha3 zenon_H90 zenon_H42 zenon_H36. % 15.16/15.35 apply (zenon_or_s _ _ zenon_H58); [ zenon_intro zenon_H5b | zenon_intro zenon_H5a ]. % 15.16/15.35 exact (zenon_H59 zenon_H5b). % 15.16/15.35 apply (zenon_or_s _ _ zenon_H5a); [ zenon_intro zenon_H4a | zenon_intro zenon_H5c ]. % 15.16/15.35 apply (zenon_L50_); trivial. % 15.16/15.35 apply (zenon_or_s _ _ zenon_H5c); [ zenon_intro zenon_H50 | zenon_intro zenon_H53 ]. % 15.16/15.35 apply (zenon_L226_); trivial. % 15.16/15.35 apply (zenon_L12_); trivial. % 15.16/15.35 (* end of lemma zenon_L227_ *) % 15.16/15.35 assert (zenon_L228_ : (((op (e0) (e0)) = (e1))\/(((op (e0) (e1)) = (e1))\/(((op (e0) (e2)) = (e1))\/((op (e0) (e3)) = (e1))))) -> (~((op (e0) (e0)) = (e1))) -> (~((op (e3) (e3)) = (e1))) -> (~((op (e1) (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))))) -> (~((e0) = (e1))) -> (((op (e0) (e0)) = (e2))\/(((op (e0) (e1)) = (e2))\/(((op (e0) (e2)) = (e2))\/((op (e0) (e3)) = (e2))))) -> (((op (e1) (e1)) = (e0))\/(((op (e1) (e1)) = (e1))\/(((op (e1) (e1)) = (e2))\/((op (e1) (e1)) = (e3))))) -> (~((op (e1) (e1)) = (e1))) -> (~((op (e0) (e3)) = (op (e3) (e3)))) -> ((op (e3) (e3)) = (e3)) -> (((op (e1) (e0)) = (e3))\/(((op (e1) (e1)) = (e3))\/(((op (e1) (e2)) = (e3))\/((op (e1) (e3)) = (e3))))) -> (~((e1) = (e3))) -> (~((op (e1) (e1)) = (e3))) -> (~((op (e1) (e3)) = (op (e3) (e3)))) -> (~((e2) = (e3))) -> (~((op (e0) (e0)) = (e3))) -> (((op (e0) (e0)) = (e3))\/(((op (e0) (e1)) = (e3))\/(((op (e0) (e2)) = (e3))\/((op (e0) (e3)) = (e3))))) -> (~((op (e3) (e3)) = (e0))) -> (~((e0) = (e2))) -> ((op (e2) (e3)) = (e2)) -> (~((op (e0) (e2)) = (op (e0) (e3)))) -> ((op (e0) (e2)) = (e0)) -> (((op (e0) (e3)) = (e0))\/(((op (e1) (e3)) = (e0))\/(((op (e2) (e3)) = (e0))\/((op (e3) (e3)) = (e0))))) -> (~((op (e0) (e2)) = (op (e1) (e2)))) -> (~((op (e1) (e1)) = (e2))) -> ((op (e1) (e0)) = (e1)) -> (((op (e1) (e0)) = (e2))\/(((op (e1) (e1)) = (e2))\/(((op (e1) (e2)) = (e2))\/((op (e1) (e3)) = (e2))))) -> (~((e1) = (e2))) -> False). % 15.16/15.35 do 0 intro. intros zenon_H44 zenon_H45 zenon_H104 zenon_H1cf zenon_H1cd zenon_H121 zenon_H9e zenon_H8e zenon_H1b3 zenon_H1b4 zenon_H36 zenon_H42 zenon_H90 zenon_Ha3 zenon_H182 zenon_H8b zenon_H6a zenon_H59 zenon_H58 zenon_H3c zenon_H5e zenon_H124 zenon_Hc9 zenon_Hab zenon_Hd3 zenon_H87 zenon_Hd6 zenon_Hd8 zenon_H84 zenon_Ha7. % 15.16/15.35 apply (zenon_or_s _ _ zenon_H44); [ zenon_intro zenon_H47 | zenon_intro zenon_H46 ]. % 15.16/15.35 exact (zenon_H45 zenon_H47). % 15.16/15.35 apply (zenon_or_s _ _ zenon_H46); [ zenon_intro zenon_H22 | zenon_intro zenon_H48 ]. % 15.16/15.35 apply (zenon_L225_); trivial. % 15.16/15.35 apply (zenon_or_s _ _ zenon_H48); [ zenon_intro zenon_H29 | zenon_intro zenon_H37 ]. % 15.16/15.35 apply (zenon_L37_); trivial. % 15.16/15.35 apply (zenon_or_s _ _ zenon_H8e); [ zenon_intro zenon_H92 | zenon_intro zenon_H91 ]. % 15.16/15.35 apply (zenon_L195_); trivial. % 15.16/15.35 apply (zenon_or_s _ _ zenon_H91); [ zenon_intro zenon_H5d | zenon_intro zenon_H93 ]. % 15.16/15.35 apply (zenon_L227_); trivial. % 15.16/15.35 apply (zenon_or_s _ _ zenon_H93); [ zenon_intro zenon_H63 | zenon_intro zenon_H81 ]. % 15.16/15.35 apply (zenon_or_s _ _ zenon_H84); [ zenon_intro zenon_H68 | zenon_intro zenon_H85 ]. % 15.16/15.35 apply (zenon_L162_); trivial. % 15.16/15.35 apply (zenon_or_s _ _ zenon_H85); [ zenon_intro zenon_H6e | zenon_intro zenon_H86 ]. % 15.16/15.35 exact (zenon_Hd6 zenon_H6e). % 15.16/15.35 apply (zenon_or_s _ _ zenon_H86); [ zenon_intro zenon_H7c | zenon_intro zenon_H82 ]. % 15.16/15.35 apply (zenon_L52_); trivial. % 15.16/15.35 apply (zenon_L205_); trivial. % 15.16/15.35 apply (zenon_L33_); trivial. % 15.16/15.35 (* end of lemma zenon_L228_ *) % 15.16/15.35 assert (zenon_L229_ : (((op (e2) (e0)) = (e3))\/(((op (e2) (e1)) = (e3))\/(((op (e2) (e2)) = (e3))\/((op (e2) (e3)) = (e3))))) -> (~((e1) = (e3))) -> ((op (e2) (e0)) = (e1)) -> ((op (e0) (e1)) = (e3)) -> (~((op (e0) (e1)) = (op (e2) (e1)))) -> (~((op (e3) (e3)) = (e0))) -> (~((e0) = (e2))) -> ((op (e1) (e1)) = (e2)) -> (~((op (e0) (e2)) = (op (e0) (e3)))) -> ((op (e0) (e2)) = (e0)) -> (((op (e0) (e3)) = (e0))\/(((op (e1) (e3)) = (e0))\/(((op (e2) (e3)) = (e0))\/((op (e3) (e3)) = (e0))))) -> ((op (e2) (e3)) = (e2)) -> (~((e2) = (e3))) -> False). % 15.16/15.35 do 0 intro. intros zenon_He6 zenon_Ha3 zenon_Hae zenon_H4a zenon_Hde zenon_H3c zenon_H5e zenon_H6e zenon_Hc9 zenon_Hab zenon_Hd3 zenon_H124 zenon_H6a. % 15.16/15.35 apply (zenon_or_s _ _ zenon_He6); [ zenon_intro zenon_Haf | zenon_intro zenon_He7 ]. % 15.16/15.35 apply (zenon_L39_); trivial. % 15.16/15.35 apply (zenon_or_s _ _ zenon_He7); [ zenon_intro zenon_Hdf | zenon_intro zenon_He8 ]. % 15.16/15.35 apply (zenon_L65_); trivial. % 15.16/15.35 apply (zenon_or_s _ _ zenon_He8); [ zenon_intro zenon_H34 | zenon_intro zenon_He2 ]. % 15.16/15.35 apply (zenon_L202_); trivial. % 15.16/15.35 apply (zenon_L98_); trivial. % 15.16/15.35 (* end of lemma zenon_L229_ *) % 15.16/15.35 assert (zenon_L230_ : (((op (e0) (e0)) = (e3))\/(((op (e0) (e1)) = (e3))\/(((op (e0) (e2)) = (e3))\/((op (e0) (e3)) = (e3))))) -> (~((op (e3) (e0)) = (op (e3) (e3)))) -> ((op (e2) (e0)) = (e1)) -> (~((e1) = (e3))) -> (((op (e1) (e0)) = (e2))\/(((op (e1) (e1)) = (e2))\/(((op (e1) (e2)) = (e2))\/((op (e1) (e3)) = (e2))))) -> (~((op (e0) (e1)) = (op (e2) (e1)))) -> (((op (e2) (e0)) = (e3))\/(((op (e2) (e1)) = (e3))\/(((op (e2) (e2)) = (e3))\/((op (e2) (e3)) = (e3))))) -> (~((op (e0) (e2)) = (op (e1) (e2)))) -> (((op (e0) (e3)) = (e0))\/(((op (e1) (e3)) = (e0))\/(((op (e2) (e3)) = (e0))\/((op (e3) (e3)) = (e0))))) -> ((op (e0) (e2)) = (e0)) -> (~((op (e0) (e2)) = (op (e0) (e3)))) -> ((op (e2) (e3)) = (e2)) -> (~((e0) = (e2))) -> (~((op (e3) (e3)) = (e0))) -> (~((op (e0) (e0)) = (e3))) -> (((op (e0) (e0)) = (e3))\/(((op (e1) (e0)) = (e3))\/(((op (e2) (e0)) = (e3))\/((op (e3) (e0)) = (e3))))) -> (~((e2) = (e3))) -> ((op (e0) (e2)) = (e2)) -> ((op (e3) (e3)) = (e3)) -> (~((op (e0) (e3)) = (op (e3) (e3)))) -> False). % 15.16/15.35 do 0 intro. intros zenon_H58 zenon_Hbb zenon_Hae zenon_Ha3 zenon_H84 zenon_Hde zenon_He6 zenon_H87 zenon_Hd3 zenon_Hab zenon_Hc9 zenon_H124 zenon_H5e zenon_H3c zenon_H59 zenon_Hbe zenon_H6a zenon_H63 zenon_H42 zenon_H36. % 15.16/15.35 apply (zenon_or_s _ _ zenon_H58); [ zenon_intro zenon_H5b | zenon_intro zenon_H5a ]. % 15.16/15.35 exact (zenon_H59 zenon_H5b). % 15.16/15.35 apply (zenon_or_s _ _ zenon_H5a); [ zenon_intro zenon_H4a | zenon_intro zenon_H5c ]. % 15.16/15.35 apply (zenon_or_s _ _ zenon_Hbe); [ zenon_intro zenon_H5b | zenon_intro zenon_Hbf ]. % 15.16/15.35 exact (zenon_H59 zenon_H5b). % 15.16/15.35 apply (zenon_or_s _ _ zenon_Hbf); [ zenon_intro zenon_H69 | zenon_intro zenon_Hc0 ]. % 15.16/15.35 apply (zenon_or_s _ _ zenon_H84); [ zenon_intro zenon_H68 | zenon_intro zenon_H85 ]. % 15.16/15.35 apply (zenon_L17_); trivial. % 15.16/15.35 apply (zenon_or_s _ _ zenon_H85); [ zenon_intro zenon_H6e | zenon_intro zenon_H86 ]. % 15.16/15.35 apply (zenon_L229_); trivial. % 15.16/15.35 apply (zenon_or_s _ _ zenon_H86); [ zenon_intro zenon_H7c | zenon_intro zenon_H82 ]. % 15.16/15.35 apply (zenon_L52_); trivial. % 15.16/15.35 apply (zenon_L205_); trivial. % 15.16/15.35 apply (zenon_or_s _ _ zenon_Hc0); [ zenon_intro zenon_Haf | zenon_intro zenon_Hba ]. % 15.16/15.35 apply (zenon_L39_); trivial. % 15.16/15.35 apply (zenon_L43_); trivial. % 15.16/15.35 apply (zenon_or_s _ _ zenon_H5c); [ zenon_intro zenon_H50 | zenon_intro zenon_H53 ]. % 15.16/15.35 apply (zenon_L31_); trivial. % 15.16/15.35 apply (zenon_L12_); trivial. % 15.16/15.35 (* end of lemma zenon_L230_ *) % 15.16/15.35 assert (zenon_L231_ : (((op (e0) (e0)) = (e1))\/(((op (e1) (e0)) = (e1))\/(((op (e2) (e0)) = (e1))\/((op (e3) (e0)) = (e1))))) -> (((op (e0) (e3)) = (e1))\/(((op (e1) (e3)) = (e1))\/(((op (e2) (e3)) = (e1))\/((op (e3) (e3)) = (e1))))) -> (~((op (e0) (e1)) = (op (e0) (e3)))) -> (~((op (e1) (e0)) = (op (e1) (e3)))) -> (~((op (e3) (e3)) = (e1))) -> (~((op (e0) (e0)) = (e1))) -> (((op (e0) (e0)) = (e1))\/(((op (e0) (e1)) = (e1))\/(((op (e0) (e2)) = (e1))\/((op (e0) (e3)) = (e1))))) -> (((op (e0) (e0)) = (e3))\/(((op (e0) (e1)) = (e3))\/(((op (e0) (e2)) = (e3))\/((op (e0) (e3)) = (e3))))) -> (~((op (e0) (e1)) = (op (e2) (e1)))) -> (((op (e2) (e0)) = (e3))\/(((op (e2) (e1)) = (e3))\/(((op (e2) (e2)) = (e3))\/((op (e2) (e3)) = (e3))))) -> (~((op (e0) (e2)) = (op (e1) (e2)))) -> (~((op (e0) (e0)) = (e3))) -> (((op (e0) (e0)) = (e3))\/(((op (e1) (e0)) = (e3))\/(((op (e2) (e0)) = (e3))\/((op (e3) (e0)) = (e3))))) -> (~((op (e0) (e3)) = (op (e3) (e3)))) -> (~((op (e1) (e1)) = (e0))) -> (~((op (e0) (e1)) = (op (e1) (e1)))) -> (((op (e0) (e0)) = (e2))\/(((op (e0) (e1)) = (e2))\/(((op (e0) (e2)) = (e2))\/((op (e0) (e3)) = (e2))))) -> (((op (e0) (e0)) = (e2))\/(((op (e1) (e0)) = (e2))\/(((op (e2) (e0)) = (e2))\/((op (e3) (e0)) = (e2))))) -> ((~((op (e2) (e2)) = (e3)))\/((op (e2) (e3)) = (e2))) -> (((op (e1) (e0)) = (e2))\/(((op (e1) (e1)) = (e2))\/(((op (e1) (e2)) = (e2))\/((op (e1) (e3)) = (e2))))) -> (~((op (e0) (e2)) = (op (e0) (e3)))) -> (~((op (e3) (e0)) = (op (e3) (e3)))) -> ((~((op (e3) (e3)) = (e0)))\/((op (e3) (e0)) = (e3))) -> (~((e0) = (e3))) -> ((op (e0) (e2)) = (e0)) -> (~((op (e3) (e2)) = (op (e3) (e3)))) -> (((op (e0) (e2)) = (e3))\/(((op (e1) (e2)) = (e3))\/(((op (e2) (e2)) = (e3))\/((op (e3) (e2)) = (e3))))) -> (~((op (e1) (e1)) = (e2))) -> (((op (e1) (e1)) = (e0))\/(((op (e1) (e1)) = (e1))\/(((op (e1) (e1)) = (e2))\/((op (e1) (e1)) = (e3))))) -> (~((op (e3) (e3)) = (e0))) -> (((op (e0) (e3)) = (e2))\/(((op (e1) (e3)) = (e2))\/(((op (e2) (e3)) = (e2))\/((op (e3) (e3)) = (e2))))) -> (~((e0) = (e2))) -> (~((op (e3) (e3)) = (e2))) -> (~((e0) = (e1))) -> (((op (e0) (e3)) = (e0))\/(((op (e1) (e3)) = (e0))\/(((op (e2) (e3)) = (e0))\/((op (e3) (e3)) = (e0))))) -> (((op (e1) (e0)) = (e3))\/(((op (e1) (e1)) = (e3))\/(((op (e1) (e2)) = (e3))\/((op (e1) (e3)) = (e3))))) -> (~((e2) = (e3))) -> (~((op (e1) (e1)) = (e3))) -> (~((e1) = (e3))) -> ((op (e3) (e3)) = (e3)) -> (~((op (e1) (e3)) = (op (e3) (e3)))) -> (~((op (e1) (e1)) = (e1))) -> (((op (e1) (e0)) = (e1))\/(((op (e1) (e1)) = (e1))\/(((op (e1) (e2)) = (e1))\/((op (e1) (e3)) = (e1))))) -> ((op (e2) (e3)) = (e2)) -> (~((op (e2) (e0)) = (op (e2) (e3)))) -> (~((e1) = (e2))) -> False). % 15.16/15.35 do 0 intro. intros zenon_Hf1 zenon_H121 zenon_H1cd zenon_H1cf zenon_H104 zenon_H45 zenon_H44 zenon_H58 zenon_Hde zenon_He6 zenon_H87 zenon_H59 zenon_Hbe zenon_H36 zenon_H145 zenon_H23 zenon_H8e zenon_Heb zenon_H1c3 zenon_H84 zenon_Hc9 zenon_Hbb zenon_H10f zenon_H4b zenon_Hab zenon_H173 zenon_H175 zenon_Hd6 zenon_H1b3 zenon_H3c zenon_H160 zenon_H5e zenon_H3d zenon_H9e zenon_Hd3 zenon_H90 zenon_H6a zenon_H182 zenon_Ha3 zenon_H42 zenon_H8b zenon_H1b4 zenon_H1c5 zenon_H124 zenon_Hce zenon_Ha7. % 15.16/15.35 apply (zenon_or_s _ _ zenon_H44); [ zenon_intro zenon_H47 | zenon_intro zenon_H46 ]. % 15.16/15.35 exact (zenon_H45 zenon_H47). % 15.16/15.35 apply (zenon_or_s _ _ zenon_H46); [ zenon_intro zenon_H22 | zenon_intro zenon_H48 ]. % 15.16/15.35 apply (zenon_L60_); trivial. % 15.16/15.35 apply (zenon_or_s _ _ zenon_H48); [ zenon_intro zenon_H29 | zenon_intro zenon_H37 ]. % 15.16/15.35 apply (zenon_L37_); trivial. % 15.16/15.35 apply (zenon_or_s _ _ zenon_Hf1); [ zenon_intro zenon_H47 | zenon_intro zenon_Hf4 ]. % 15.16/15.35 exact (zenon_H45 zenon_H47). % 15.16/15.35 apply (zenon_or_s _ _ zenon_Hf4); [ zenon_intro zenon_Hd8 | zenon_intro zenon_Hf5 ]. % 15.16/15.35 apply (zenon_L228_); trivial. % 15.16/15.35 apply (zenon_or_s _ _ zenon_Hf5); [ zenon_intro zenon_Hae | zenon_intro zenon_Hee ]. % 15.16/15.35 apply (zenon_or_s _ _ zenon_H8e); [ zenon_intro zenon_H92 | zenon_intro zenon_H91 ]. % 15.16/15.35 apply (zenon_L212_); trivial. % 15.16/15.35 apply (zenon_or_s _ _ zenon_H91); [ zenon_intro zenon_H5d | zenon_intro zenon_H93 ]. % 15.16/15.35 apply (zenon_L214_); trivial. % 15.16/15.35 apply (zenon_or_s _ _ zenon_H93); [ zenon_intro zenon_H63 | zenon_intro zenon_H81 ]. % 15.16/15.35 apply (zenon_L230_); trivial. % 15.16/15.35 apply (zenon_L33_); trivial. % 15.16/15.35 apply (zenon_or_s _ _ zenon_Heb); [ zenon_intro zenon_H92 | zenon_intro zenon_Hec ]. % 15.16/15.35 apply (zenon_L212_); trivial. % 15.16/15.35 apply (zenon_or_s _ _ zenon_Hec); [ zenon_intro zenon_H68 | zenon_intro zenon_Hed ]. % 15.16/15.35 apply (zenon_L215_); trivial. % 15.16/15.35 apply (zenon_or_s _ _ zenon_Hed); [ zenon_intro zenon_Hdd | zenon_intro zenon_He9 ]. % 15.16/15.35 apply (zenon_L119_); trivial. % 15.16/15.35 apply (zenon_L122_); trivial. % 15.16/15.35 (* end of lemma zenon_L231_ *) % 15.16/15.35 assert (zenon_L232_ : (((op (e0) (e0)) = (e1))\/(((op (e0) (e1)) = (e1))\/(((op (e0) (e2)) = (e1))\/((op (e0) (e3)) = (e1))))) -> (~((op (e0) (e0)) = (e1))) -> (~((op (e0) (e3)) = (op (e3) (e3)))) -> (~((op (e0) (e0)) = (e3))) -> (((op (e0) (e0)) = (e3))\/(((op (e0) (e1)) = (e3))\/(((op (e0) (e2)) = (e3))\/((op (e0) (e3)) = (e3))))) -> (((op (e0) (e0)) = (e2))\/(((op (e0) (e1)) = (e2))\/(((op (e0) (e2)) = (e2))\/((op (e0) (e3)) = (e2))))) -> (~((op (e3) (e3)) = (e0))) -> (((op (e0) (e3)) = (e2))\/(((op (e1) (e3)) = (e2))\/(((op (e2) (e3)) = (e2))\/((op (e3) (e3)) = (e2))))) -> (~((e0) = (e2))) -> (~((op (e3) (e3)) = (e2))) -> (~((e0) = (e1))) -> (((op (e0) (e3)) = (e0))\/(((op (e1) (e3)) = (e0))\/(((op (e2) (e3)) = (e0))\/((op (e3) (e3)) = (e0))))) -> ((~((op (e2) (e2)) = (e3)))\/((op (e2) (e3)) = (e2))) -> (((op (e1) (e0)) = (e2))\/(((op (e1) (e1)) = (e2))\/(((op (e1) (e2)) = (e2))\/((op (e1) (e3)) = (e2))))) -> (~((op (e0) (e2)) = (op (e0) (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))))) -> (~((op (e3) (e0)) = (op (e3) (e3)))) -> ((~((op (e3) (e3)) = (e0)))\/((op (e3) (e0)) = (e3))) -> (~((e0) = (e3))) -> ((op (e0) (e2)) = (e0)) -> (~((e1) = (e3))) -> (~((op (e3) (e2)) = (op (e3) (e3)))) -> ((op (e3) (e3)) = (e3)) -> (((op (e0) (e2)) = (e3))\/(((op (e1) (e2)) = (e3))\/(((op (e2) (e2)) = (e3))\/((op (e3) (e2)) = (e3))))) -> (~((op (e1) (e1)) = (e2))) -> (((op (e1) (e0)) = (e1))\/(((op (e1) (e1)) = (e1))\/(((op (e1) (e2)) = (e1))\/((op (e1) (e3)) = (e1))))) -> (~((op (e1) (e1)) = (e3))) -> (~((op (e0) (e1)) = (op (e1) (e1)))) -> (~((op (e1) (e1)) = (e1))) -> (~((op (e1) (e1)) = (e0))) -> (((op (e1) (e1)) = (e0))\/(((op (e1) (e1)) = (e1))\/(((op (e1) (e1)) = (e2))\/((op (e1) (e1)) = (e3))))) -> (~((op (e0) (e2)) = (op (e2) (e2)))) -> ((op (e2) (e2)) = (e2)) -> (~((e1) = (e2))) -> False). % 15.16/15.35 do 0 intro. intros zenon_H44 zenon_H45 zenon_H36 zenon_H59 zenon_H58 zenon_H8e zenon_H3c zenon_H160 zenon_H5e zenon_H3d zenon_H9e zenon_Hd3 zenon_H1c3 zenon_H84 zenon_Hc9 zenon_H6a zenon_H8b zenon_H90 zenon_Hbb zenon_H10f zenon_H4b zenon_Hab zenon_Ha3 zenon_H173 zenon_H42 zenon_H175 zenon_Hd6 zenon_H1c5 zenon_H182 zenon_H23 zenon_H1b4 zenon_H145 zenon_H1b3 zenon_H28 zenon_H35 zenon_Ha7. % 15.16/15.35 apply (zenon_or_s _ _ zenon_H44); [ zenon_intro zenon_H47 | zenon_intro zenon_H46 ]. % 15.16/15.35 exact (zenon_H45 zenon_H47). % 15.16/15.35 apply (zenon_or_s _ _ zenon_H46); [ zenon_intro zenon_H22 | zenon_intro zenon_H48 ]. % 15.16/15.35 apply (zenon_L60_); trivial. % 15.16/15.35 apply (zenon_or_s _ _ zenon_H48); [ zenon_intro zenon_H29 | zenon_intro zenon_H37 ]. % 15.16/15.35 apply (zenon_L37_); trivial. % 15.16/15.35 apply (zenon_or_s _ _ zenon_H8e); [ zenon_intro zenon_H92 | zenon_intro zenon_H91 ]. % 15.16/15.35 apply (zenon_L212_); trivial. % 15.16/15.35 apply (zenon_or_s _ _ zenon_H91); [ zenon_intro zenon_H5d | zenon_intro zenon_H93 ]. % 15.16/15.35 apply (zenon_L214_); trivial. % 15.16/15.35 apply (zenon_or_s _ _ zenon_H93); [ zenon_intro zenon_H63 | zenon_intro zenon_H81 ]. % 15.16/15.35 apply (zenon_L15_); trivial. % 15.16/15.35 apply (zenon_L33_); trivial. % 15.16/15.35 (* end of lemma zenon_L232_ *) % 15.16/15.35 assert (zenon_L233_ : ((~((op (e2) (e2)) = (e2)))\/((op (e2) (e2)) = (e2))) -> (((op (e0) (e0)) = (e1))\/(((op (e0) (e1)) = (e1))\/(((op (e0) (e2)) = (e1))\/((op (e0) (e3)) = (e1))))) -> (((op (e1) (e0)) = (e1))\/(((op (e1) (e1)) = (e1))\/(((op (e1) (e2)) = (e1))\/((op (e1) (e3)) = (e1))))) -> (~((e0) = (e1))) -> (((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) (e2)) = (op (e3) (e3)))) -> ((~((op (e3) (e3)) = (e0)))\/((op (e3) (e0)) = (e3))) -> (~((op (e3) (e0)) = (op (e3) (e3)))) -> (~((e2) = (e3))) -> (~((op (e0) (e2)) = (op (e0) (e3)))) -> (~((e0) = (e2))) -> (((op (e0) (e3)) = (e0))\/(((op (e1) (e3)) = (e0))\/(((op (e2) (e3)) = (e0))\/((op (e3) (e3)) = (e0))))) -> (~((e1) = (e2))) -> (((op (e1) (e0)) = (e2))\/(((op (e1) (e1)) = (e2))\/(((op (e1) (e2)) = (e2))\/((op (e1) (e3)) = (e2))))) -> ((~((op (e2) (e2)) = (e3)))\/((op (e2) (e3)) = (e2))) -> (~((op (e1) (e1)) = (e3))) -> (((op (e1) (e1)) = (e0))\/(((op (e1) (e1)) = (e1))\/(((op (e1) (e1)) = (e2))\/((op (e1) (e1)) = (e3))))) -> (~((op (e1) (e1)) = (e2))) -> (~((op (e1) (e1)) = (e1))) -> (~((op (e1) (e3)) = (op (e3) (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) (e1)) = (e0))) -> (((op (e0) (e0)) = (e2))\/(((op (e1) (e0)) = (e2))\/(((op (e2) (e0)) = (e2))\/((op (e3) (e0)) = (e2))))) -> (~((op (e0) (e2)) = (op (e1) (e2)))) -> (((op (e0) (e0)) = (e3))\/(((op (e1) (e0)) = (e3))\/(((op (e2) (e0)) = (e3))\/((op (e3) (e0)) = (e3))))) -> (((op (e2) (e0)) = (e3))\/(((op (e2) (e1)) = (e3))\/(((op (e2) (e2)) = (e3))\/((op (e2) (e3)) = (e3))))) -> (~((op (e2) (e3)) = (op (e3) (e3)))) -> (~((op (e0) (e1)) = (op (e2) (e1)))) -> (((op (e0) (e0)) = (e2))\/(((op (e0) (e1)) = (e2))\/(((op (e0) (e2)) = (e2))\/((op (e0) (e3)) = (e2))))) -> (~((op (e2) (e2)) = (e0))) -> (~((op (e0) (e2)) = (op (e2) (e2)))) -> (((op (e2) (e2)) = (e0))\/(((op (e2) (e2)) = (e1))\/(((op (e2) (e2)) = (e2))\/((op (e2) (e2)) = (e3))))) -> (~((op (e0) (e0)) = (e3))) -> (~((e1) = (e3))) -> (~((e0) = (e3))) -> ((op (e0) (e2)) = (e0)) -> (~((op (e0) (e3)) = (op (e3) (e3)))) -> ((op (e3) (e3)) = (e3)) -> (((op (e0) (e0)) = (e3))\/(((op (e0) (e1)) = (e3))\/(((op (e0) (e2)) = (e3))\/((op (e0) (e3)) = (e3))))) -> (~((op (e0) (e0)) = (e1))) -> ((~((op (e3) (e3)) = (e2)))\/((op (e3) (e2)) = (e3))) -> (((op (e0) (e0)) = (e1))\/(((op (e1) (e0)) = (e1))\/(((op (e2) (e0)) = (e1))\/((op (e3) (e0)) = (e1))))) -> (~((op (e2) (e0)) = (op (e2) (e3)))) -> (((op (e0) (e3)) = (e1))\/(((op (e1) (e3)) = (e1))\/(((op (e2) (e3)) = (e1))\/((op (e3) (e3)) = (e1))))) -> (~((op (e1) (e0)) = (op (e1) (e3)))) -> (~((op (e0) (e1)) = (op (e0) (e3)))) -> (~((op (e3) (e1)) = (op (e3) (e3)))) -> ((~((op (e3) (e3)) = (e1)))\/((op (e3) (e1)) = (e3))) -> False). % 15.16/15.35 do 0 intro. intros zenon_Haa zenon_H44 zenon_H1c5 zenon_H9e zenon_H160 zenon_H175 zenon_H173 zenon_H10f zenon_Hbb zenon_H6a zenon_Hc9 zenon_H5e zenon_Hd3 zenon_Ha7 zenon_H84 zenon_H1c3 zenon_H182 zenon_H1b3 zenon_Hd6 zenon_H1b4 zenon_H8b zenon_H90 zenon_H23 zenon_H145 zenon_Heb zenon_H87 zenon_Hbe zenon_He6 zenon_He3 zenon_Hde zenon_H8e zenon_H2e zenon_H28 zenon_H2d zenon_H59 zenon_Ha3 zenon_H4b zenon_Hab zenon_H36 zenon_H42 zenon_H58 zenon_H45 zenon_H10e zenon_Hf1 zenon_Hce zenon_H121 zenon_H1cf zenon_H1cd zenon_H12d zenon_H10c. % 15.16/15.35 apply (zenon_or_s _ _ zenon_Haa); [ zenon_intro zenon_H2f | zenon_intro zenon_H35 ]. % 15.16/15.35 apply (zenon_or_s _ _ zenon_H1c3); [ zenon_intro zenon_H30 | zenon_intro zenon_H124 ]. % 15.16/15.35 apply (zenon_or_s _ _ zenon_H10f); [ zenon_intro zenon_H3c | zenon_intro zenon_Hba ]. % 15.16/15.35 apply (zenon_L222_); trivial. % 15.16/15.35 apply (zenon_L43_); trivial. % 15.16/15.35 apply (zenon_or_s _ _ zenon_H10f); [ zenon_intro zenon_H3c | zenon_intro zenon_Hba ]. % 15.16/15.35 apply (zenon_or_s _ _ zenon_H10c); [ zenon_intro zenon_H104 | zenon_intro zenon_H10a ]. % 15.16/15.35 apply (zenon_or_s _ _ zenon_H10e); [ zenon_intro zenon_H3d | zenon_intro zenon_H106 ]. % 15.16/15.35 apply (zenon_L231_); trivial. % 15.16/15.35 apply (zenon_L153_); trivial. % 15.16/15.35 apply (zenon_L102_); trivial. % 15.16/15.35 apply (zenon_L43_); trivial. % 15.16/15.35 apply (zenon_or_s _ _ zenon_H10f); [ zenon_intro zenon_H3c | zenon_intro zenon_Hba ]. % 15.16/15.35 apply (zenon_or_s _ _ zenon_H10e); [ zenon_intro zenon_H3d | zenon_intro zenon_H106 ]. % 15.16/15.35 apply (zenon_L232_); trivial. % 15.16/15.35 apply (zenon_L153_); trivial. % 15.16/15.35 apply (zenon_L43_); trivial. % 15.16/15.35 (* end of lemma zenon_L233_ *) % 15.16/15.35 assert (zenon_L234_ : ((~((op (e2) (e2)) = (e3)))\/((op (e2) (e3)) = (e2))) -> (~((op (e2) (e0)) = (op (e2) (e3)))) -> (~((op (e0) (e0)) = (e3))) -> (((op (e2) (e0)) = (e3))\/(((op (e2) (e1)) = (e3))\/(((op (e2) (e2)) = (e3))\/((op (e2) (e3)) = (e3))))) -> ((op (e3) (e3)) = (e3)) -> (~((op (e2) (e3)) = (op (e3) (e3)))) -> (~((op (e0) (e1)) = (op (e2) (e1)))) -> ((op (e2) (e0)) = (e2)) -> (~((e2) = (e3))) -> (~((e0) = (e3))) -> ((op (e0) (e2)) = (e0)) -> (~((op (e0) (e3)) = (op (e3) (e3)))) -> (((op (e0) (e0)) = (e3))\/(((op (e0) (e1)) = (e3))\/(((op (e0) (e2)) = (e3))\/((op (e0) (e3)) = (e3))))) -> False). % 15.16/15.35 do 0 intro. intros zenon_H1c3 zenon_Hce zenon_H59 zenon_He6 zenon_H42 zenon_He3 zenon_Hde zenon_Hdd zenon_H6a zenon_H4b zenon_Hab zenon_H36 zenon_H58. % 15.16/15.35 apply (zenon_or_s _ _ zenon_H1c3); [ zenon_intro zenon_H30 | zenon_intro zenon_H124 ]. % 15.16/15.35 apply (zenon_L68_); trivial. % 15.16/15.35 apply (zenon_L119_); trivial. % 15.16/15.35 (* end of lemma zenon_L234_ *) % 15.16/15.35 assert (zenon_L235_ : (((op (e0) (e0)) = (e1))\/(((op (e0) (e1)) = (e1))\/(((op (e0) (e2)) = (e1))\/((op (e0) (e3)) = (e1))))) -> (~((op (e0) (e0)) = (e1))) -> (~((op (e0) (e3)) = (op (e3) (e3)))) -> ((op (e3) (e3)) = (e3)) -> (~((e0) = (e3))) -> (~((e1) = (e3))) -> (~((op (e0) (e0)) = (e3))) -> (((op (e0) (e0)) = (e3))\/(((op (e0) (e1)) = (e3))\/(((op (e0) (e2)) = (e3))\/((op (e0) (e3)) = (e3))))) -> ((op (e0) (e2)) = (e0)) -> (((op (e0) (e3)) = (e0))\/(((op (e1) (e3)) = (e0))\/(((op (e2) (e3)) = (e0))\/((op (e3) (e3)) = (e0))))) -> (~((e0) = (e1))) -> (~((op (e3) (e3)) = (e2))) -> (~((e0) = (e2))) -> ((op (e1) (e3)) = (e1)) -> (~((e1) = (e2))) -> (((op (e0) (e3)) = (e2))\/(((op (e1) (e3)) = (e2))\/(((op (e2) (e3)) = (e2))\/((op (e3) (e3)) = (e2))))) -> (~((op (e3) (e3)) = (e0))) -> False). % 15.16/15.35 do 0 intro. intros zenon_H44 zenon_H45 zenon_H36 zenon_H42 zenon_H4b zenon_Ha3 zenon_H59 zenon_H58 zenon_Hab zenon_Hd3 zenon_H9e zenon_H3d zenon_H5e zenon_H11f zenon_Ha7 zenon_H160 zenon_H3c. % 15.16/15.35 apply (zenon_or_s _ _ zenon_H44); [ zenon_intro zenon_H47 | zenon_intro zenon_H46 ]. % 15.16/15.35 exact (zenon_H45 zenon_H47). % 15.16/15.35 apply (zenon_or_s _ _ zenon_H46); [ zenon_intro zenon_H22 | zenon_intro zenon_H48 ]. % 15.16/15.35 apply (zenon_L60_); trivial. % 15.16/15.35 apply (zenon_or_s _ _ zenon_H48); [ zenon_intro zenon_H29 | zenon_intro zenon_H37 ]. % 15.16/15.35 apply (zenon_L37_); trivial. % 15.16/15.35 apply (zenon_L211_); trivial. % 15.16/15.35 (* end of lemma zenon_L235_ *) % 15.16/15.35 assert (zenon_L236_ : ((~((op (e3) (e3)) = (e0)))\/((op (e3) (e0)) = (e3))) -> (~((op (e3) (e0)) = (op (e3) (e3)))) -> (((op (e0) (e0)) = (e1))\/(((op (e0) (e1)) = (e1))\/(((op (e0) (e2)) = (e1))\/((op (e0) (e3)) = (e1))))) -> ((op (e1) (e3)) = (e1)) -> (((op (e0) (e3)) = (e2))\/(((op (e1) (e3)) = (e2))\/(((op (e2) (e3)) = (e2))\/((op (e3) (e3)) = (e2))))) -> (~((e0) = (e2))) -> (~((e1) = (e2))) -> (((op (e0) (e3)) = (e0))\/(((op (e1) (e3)) = (e0))\/(((op (e2) (e3)) = (e0))\/((op (e3) (e3)) = (e0))))) -> (~((e0) = (e1))) -> (~((op (e0) (e0)) = (e3))) -> (~((e1) = (e3))) -> (~((e0) = (e3))) -> ((op (e0) (e2)) = (e0)) -> (~((op (e0) (e3)) = (op (e3) (e3)))) -> ((op (e3) (e3)) = (e3)) -> (((op (e0) (e0)) = (e3))\/(((op (e0) (e1)) = (e3))\/(((op (e0) (e2)) = (e3))\/((op (e0) (e3)) = (e3))))) -> (~((op (e0) (e0)) = (e1))) -> (~((op (e3) (e2)) = (op (e3) (e3)))) -> ((~((op (e3) (e3)) = (e2)))\/((op (e3) (e2)) = (e3))) -> False). % 15.16/15.35 do 0 intro. intros zenon_H10f zenon_Hbb zenon_H44 zenon_H11f zenon_H160 zenon_H5e zenon_Ha7 zenon_Hd3 zenon_H9e zenon_H59 zenon_Ha3 zenon_H4b zenon_Hab zenon_H36 zenon_H42 zenon_H58 zenon_H45 zenon_H173 zenon_H10e. % 15.16/15.35 apply (zenon_or_s _ _ zenon_H10f); [ zenon_intro zenon_H3c | zenon_intro zenon_Hba ]. % 15.16/15.35 apply (zenon_or_s _ _ zenon_H10e); [ zenon_intro zenon_H3d | zenon_intro zenon_H106 ]. % 15.16/15.35 apply (zenon_L235_); trivial. % 15.16/15.35 apply (zenon_L153_); trivial. % 15.16/15.35 apply (zenon_L43_); trivial. % 15.16/15.35 (* end of lemma zenon_L236_ *) % 15.16/15.35 assert (zenon_L237_ : (~((op (e1) (e2)) = (op (e1) (e3)))) -> ((op (e1) (e2)) = (e1)) -> ((op (e1) (e3)) = (e1)) -> False). % 15.16/15.35 do 0 intro. intros zenon_H1d0 zenon_H117 zenon_H11f. % 15.16/15.35 cut (((op (e1) (e2)) = (e1)) = ((op (e1) (e2)) = (op (e1) (e3)))). % 15.16/15.35 intro zenon_D_pnotp. % 15.16/15.35 apply zenon_H1d0. % 15.16/15.35 rewrite <- zenon_D_pnotp. % 15.16/15.35 exact zenon_H117. % 15.16/15.35 cut (((e1) = (op (e1) (e3)))); [idtac | apply NNPP; zenon_intro zenon_H120]. % 15.16/15.35 cut (((op (e1) (e2)) = (op (e1) (e2)))); [idtac | apply NNPP; zenon_intro zenon_H1d1]. % 15.16/15.35 congruence. % 15.16/15.35 apply zenon_H1d1. apply refl_equal. % 15.16/15.35 apply zenon_H120. apply sym_equal. exact zenon_H11f. % 15.16/15.35 (* end of lemma zenon_L237_ *) % 15.16/15.35 assert (zenon_L238_ : ((~((op (e1) (e1)) = (e3)))\/((op (e1) (e3)) = (e1))) -> (~((op (e1) (e2)) = (op (e1) (e3)))) -> (((op (e0) (e2)) = (e3))\/(((op (e1) (e2)) = (e3))\/(((op (e2) (e2)) = (e3))\/((op (e3) (e2)) = (e3))))) -> ((op (e3) (e3)) = (e3)) -> (~((op (e3) (e2)) = (op (e3) (e3)))) -> ((op (e1) (e2)) = (e1)) -> (~((e1) = (e3))) -> ((op (e0) (e2)) = (e0)) -> (~((e0) = (e3))) -> ((~((op (e3) (e3)) = (e0)))\/((op (e3) (e0)) = (e3))) -> (~((op (e3) (e0)) = (op (e3) (e3)))) -> (((op (e1) (e0)) = (e3))\/(((op (e1) (e1)) = (e3))\/(((op (e1) (e2)) = (e3))\/((op (e1) (e3)) = (e3))))) -> (~((op (e1) (e3)) = (op (e3) (e3)))) -> (~((e2) = (e3))) -> (~((op (e0) (e2)) = (op (e0) (e3)))) -> (~((e0) = (e2))) -> (((op (e0) (e3)) = (e0))\/(((op (e1) (e3)) = (e0))\/(((op (e2) (e3)) = (e0))\/((op (e3) (e3)) = (e0))))) -> (~((e1) = (e2))) -> (((op (e1) (e0)) = (e2))\/(((op (e1) (e1)) = (e2))\/(((op (e1) (e2)) = (e2))\/((op (e1) (e3)) = (e2))))) -> ((~((op (e2) (e2)) = (e3)))\/((op (e2) (e3)) = (e2))) -> False). % 15.16/15.35 do 0 intro. intros zenon_H1d2 zenon_H1d0 zenon_H175 zenon_H42 zenon_H173 zenon_H117 zenon_Ha3 zenon_Hab zenon_H4b zenon_H10f zenon_Hbb zenon_H90 zenon_H8b zenon_H6a zenon_Hc9 zenon_H5e zenon_Hd3 zenon_Ha7 zenon_H84 zenon_H1c3. % 15.16/15.35 apply (zenon_or_s _ _ zenon_H1d2); [ zenon_intro zenon_H182 | zenon_intro zenon_H11f ]. % 15.16/15.35 apply (zenon_L207_); trivial. % 15.16/15.35 apply (zenon_L237_); trivial. % 15.16/15.35 (* end of lemma zenon_L238_ *) % 15.16/15.35 assert (zenon_L239_ : ((~((op (e1) (e1)) = (e2)))\/((op (e1) (e2)) = (e1))) -> (~((op (e1) (e2)) = (op (e1) (e3)))) -> ((~((op (e2) (e2)) = (e0)))\/((op (e2) (e0)) = (e2))) -> ((~((op (e3) (e3)) = (e1)))\/((op (e3) (e1)) = (e3))) -> (~((op (e3) (e1)) = (op (e3) (e3)))) -> (~((op (e0) (e1)) = (op (e0) (e3)))) -> (~((op (e1) (e0)) = (op (e1) (e3)))) -> (((op (e0) (e3)) = (e1))\/(((op (e1) (e3)) = (e1))\/(((op (e2) (e3)) = (e1))\/((op (e3) (e3)) = (e1))))) -> (~((op (e2) (e0)) = (op (e2) (e3)))) -> (((op (e0) (e0)) = (e1))\/(((op (e1) (e0)) = (e1))\/(((op (e2) (e0)) = (e1))\/((op (e3) (e0)) = (e1))))) -> ((~((op (e3) (e3)) = (e2)))\/((op (e3) (e2)) = (e3))) -> (~((op (e0) (e0)) = (e1))) -> (((op (e0) (e0)) = (e3))\/(((op (e0) (e1)) = (e3))\/(((op (e0) (e2)) = (e3))\/((op (e0) (e3)) = (e3))))) -> ((op (e3) (e3)) = (e3)) -> (~((op (e0) (e3)) = (op (e3) (e3)))) -> ((op (e0) (e2)) = (e0)) -> (~((e0) = (e3))) -> (~((e1) = (e3))) -> (~((op (e0) (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 (e0) (e0)) = (e2))\/(((op (e0) (e1)) = (e2))\/(((op (e0) (e2)) = (e2))\/((op (e0) (e3)) = (e2))))) -> (~((op (e0) (e1)) = (op (e2) (e1)))) -> (~((op (e2) (e3)) = (op (e3) (e3)))) -> (((op (e2) (e0)) = (e3))\/(((op (e2) (e1)) = (e3))\/(((op (e2) (e2)) = (e3))\/((op (e2) (e3)) = (e3))))) -> (((op (e0) (e0)) = (e3))\/(((op (e1) (e0)) = (e3))\/(((op (e2) (e0)) = (e3))\/((op (e3) (e0)) = (e3))))) -> (~((op (e0) (e2)) = (op (e1) (e2)))) -> (((op (e0) (e0)) = (e2))\/(((op (e1) (e0)) = (e2))\/(((op (e2) (e0)) = (e2))\/((op (e3) (e0)) = (e2))))) -> (~((op (e1) (e1)) = (e0))) -> (~((op (e0) (e1)) = (op (e1) (e1)))) -> (((op (e1) (e0)) = (e3))\/(((op (e1) (e1)) = (e3))\/(((op (e1) (e2)) = (e3))\/((op (e1) (e3)) = (e3))))) -> (~((op (e1) (e3)) = (op (e3) (e3)))) -> (~((op (e1) (e1)) = (e1))) -> (((op (e1) (e1)) = (e0))\/(((op (e1) (e1)) = (e1))\/(((op (e1) (e1)) = (e2))\/((op (e1) (e1)) = (e3))))) -> ((~((op (e2) (e2)) = (e3)))\/((op (e2) (e3)) = (e2))) -> (((op (e1) (e0)) = (e2))\/(((op (e1) (e1)) = (e2))\/(((op (e1) (e2)) = (e2))\/((op (e1) (e3)) = (e2))))) -> (~((e1) = (e2))) -> (((op (e0) (e3)) = (e0))\/(((op (e1) (e3)) = (e0))\/(((op (e2) (e3)) = (e0))\/((op (e3) (e3)) = (e0))))) -> (~((e0) = (e2))) -> (~((op (e0) (e2)) = (op (e0) (e3)))) -> (~((e2) = (e3))) -> (~((op (e3) (e0)) = (op (e3) (e3)))) -> ((~((op (e3) (e3)) = (e0)))\/((op (e3) (e0)) = (e3))) -> (~((op (e3) (e2)) = (op (e3) (e3)))) -> (((op (e0) (e2)) = (e3))\/(((op (e1) (e2)) = (e3))\/(((op (e2) (e2)) = (e3))\/((op (e3) (e2)) = (e3))))) -> (((op (e0) (e3)) = (e2))\/(((op (e1) (e3)) = (e2))\/(((op (e2) (e3)) = (e2))\/((op (e3) (e3)) = (e2))))) -> (~((e0) = (e1))) -> (((op (e1) (e0)) = (e1))\/(((op (e1) (e1)) = (e1))\/(((op (e1) (e2)) = (e1))\/((op (e1) (e3)) = (e1))))) -> (((op (e0) (e0)) = (e1))\/(((op (e0) (e1)) = (e1))\/(((op (e0) (e2)) = (e1))\/((op (e0) (e3)) = (e1))))) -> ((~((op (e2) (e2)) = (e2)))\/((op (e2) (e2)) = (e2))) -> ((~((op (e1) (e1)) = (e3)))\/((op (e1) (e3)) = (e1))) -> False). % 15.16/15.35 do 0 intro. intros zenon_H1d3 zenon_H1d0 zenon_H1d4 zenon_H10c zenon_H12d zenon_H1cd zenon_H1cf zenon_H121 zenon_Hce zenon_Hf1 zenon_H10e zenon_H45 zenon_H58 zenon_H42 zenon_H36 zenon_Hab zenon_H4b zenon_Ha3 zenon_H59 zenon_H2d zenon_H28 zenon_H8e zenon_Hde zenon_He3 zenon_He6 zenon_Hbe zenon_H87 zenon_Heb zenon_H145 zenon_H23 zenon_H90 zenon_H8b zenon_H1b4 zenon_H1b3 zenon_H1c3 zenon_H84 zenon_Ha7 zenon_Hd3 zenon_H5e zenon_Hc9 zenon_H6a zenon_Hbb zenon_H10f zenon_H173 zenon_H175 zenon_H160 zenon_H9e zenon_H1c5 zenon_H44 zenon_Haa zenon_H1d2. % 15.16/15.35 apply (zenon_or_s _ _ zenon_H1d3); [ zenon_intro zenon_Hd6 | zenon_intro zenon_H117 ]. % 15.16/15.35 apply (zenon_or_s _ _ zenon_H1d2); [ zenon_intro zenon_H182 | zenon_intro zenon_H11f ]. % 15.16/15.35 apply (zenon_or_s _ _ zenon_H1d4); [ zenon_intro zenon_H2e | zenon_intro zenon_Hdd ]. % 15.16/15.35 apply (zenon_L233_); trivial. % 15.16/15.35 apply (zenon_L234_); trivial. % 15.16/15.35 apply (zenon_L236_); trivial. % 15.16/15.35 apply (zenon_L238_); trivial. % 15.16/15.35 (* end of lemma zenon_L239_ *) % 15.16/15.35 assert (zenon_L240_ : (((op (e1) (e2)) = (e0))\/(((op (e1) (e2)) = (e1))\/(((op (e1) (e2)) = (e2))\/((op (e1) (e2)) = (e3))))) -> ((op (e0) (e2)) = (e0)) -> (~((op (e0) (e2)) = (op (e1) (e2)))) -> ((op (e1) (e1)) = (e1)) -> (~((op (e1) (e1)) = (op (e1) (e2)))) -> (~((op (e1) (e2)) = (op (e2) (e2)))) -> ((op (e2) (e2)) = (e2)) -> ((op (e3) (e2)) = (e3)) -> (~((op (e1) (e2)) = (op (e3) (e2)))) -> False). % 15.16/15.35 do 0 intro. intros zenon_H1d5 zenon_Hab zenon_H87 zenon_H21 zenon_H116 zenon_H7d zenon_H35 zenon_H106 zenon_H17d. % 15.16/15.35 apply (zenon_or_s _ _ zenon_H1d5); [ zenon_intro zenon_H15d | zenon_intro zenon_H1d6 ]. % 15.16/15.35 apply (zenon_L136_); trivial. % 15.16/15.35 apply (zenon_or_s _ _ zenon_H1d6); [ zenon_intro zenon_H117 | zenon_intro zenon_H1d7 ]. % 15.16/15.35 apply (zenon_L86_); trivial. % 15.16/15.35 apply (zenon_or_s _ _ zenon_H1d7); [ zenon_intro zenon_H7c | zenon_intro zenon_H88 ]. % 15.16/15.35 apply (zenon_L21_); trivial. % 15.16/15.35 apply (zenon_L164_); trivial. % 15.16/15.35 (* end of lemma zenon_L240_ *) % 15.16/15.35 assert (zenon_L241_ : (((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 (e1) (e1)) = (e3))) -> (~((op (e1) (e1)) = (e2))) -> (~((op (e1) (e1)) = (e1))) -> (((op (e2) (e2)) = (e0))\/(((op (e2) (e2)) = (e1))\/(((op (e2) (e2)) = (e2))\/((op (e2) (e2)) = (e3))))) -> (~((op (e2) (e2)) = (e0))) -> (~((op (e2) (e2)) = (e2))) -> (~((op (e2) (e2)) = (e3))) -> (((op (e1) (e1)) = (e0))\/(((op (e1) (e1)) = (e1))\/(((op (e1) (e1)) = (e2))\/((op (e1) (e1)) = (e3))))) -> ((op (e3) (e3)) = (e3)) -> (~((op (e3) (e0)) = (op (e3) (e3)))) -> False). % 15.16/15.35 do 0 intro. intros zenon_Hbe zenon_H59 zenon_Ha3 zenon_Hd8 zenon_H182 zenon_Hd6 zenon_H1b4 zenon_H2d zenon_H2e zenon_H2f zenon_H30 zenon_H1b3 zenon_H42 zenon_Hbb. % 15.16/15.35 apply (zenon_or_s _ _ zenon_Hbe); [ zenon_intro zenon_H5b | zenon_intro zenon_Hbf ]. % 15.16/15.35 exact (zenon_H59 zenon_H5b). % 15.16/15.35 apply (zenon_or_s _ _ zenon_Hbf); [ zenon_intro zenon_H69 | zenon_intro zenon_Hc0 ]. % 15.16/15.35 apply (zenon_L163_); trivial. % 15.16/15.35 apply (zenon_or_s _ _ zenon_Hc0); [ zenon_intro zenon_Haf | zenon_intro zenon_Hba ]. % 15.16/15.35 apply (zenon_L219_); trivial. % 15.16/15.35 apply (zenon_L43_); trivial. % 15.16/15.35 (* end of lemma zenon_L241_ *) % 15.16/15.35 assert (zenon_L242_ : (((op (e0) (e0)) = (e3))\/(((op (e0) (e1)) = (e3))\/(((op (e0) (e2)) = (e3))\/((op (e0) (e3)) = (e3))))) -> (~((op (e0) (e0)) = (e3))) -> (~((e1) = (e3))) -> ((op (e0) (e1)) = (e1)) -> (~((e2) = (e3))) -> ((op (e0) (e2)) = (e2)) -> ((op (e3) (e3)) = (e3)) -> (~((op (e0) (e3)) = (op (e3) (e3)))) -> False). % 15.16/15.35 do 0 intro. intros zenon_H58 zenon_H59 zenon_Ha3 zenon_H22 zenon_H6a zenon_H63 zenon_H42 zenon_H36. % 15.16/15.35 apply (zenon_or_s _ _ zenon_H58); [ zenon_intro zenon_H5b | zenon_intro zenon_H5a ]. % 15.16/15.35 exact (zenon_H59 zenon_H5b). % 15.16/15.35 apply (zenon_or_s _ _ zenon_H5a); [ zenon_intro zenon_H4a | zenon_intro zenon_H5c ]. % 15.16/15.35 apply (zenon_L59_); trivial. % 15.16/15.35 apply (zenon_or_s _ _ zenon_H5c); [ zenon_intro zenon_H50 | zenon_intro zenon_H53 ]. % 15.16/15.35 apply (zenon_L31_); trivial. % 15.16/15.35 apply (zenon_L12_); trivial. % 15.16/15.35 (* end of lemma zenon_L242_ *) % 15.16/15.35 assert (zenon_L243_ : (((op (e1) (e0)) = (e2))\/(((op (e1) (e1)) = (e2))\/(((op (e1) (e2)) = (e2))\/((op (e1) (e3)) = (e2))))) -> (~((e1) = (e2))) -> ((op (e1) (e0)) = (e1)) -> (~((op (e1) (e1)) = (e2))) -> (~((op (e1) (e2)) = (op (e2) (e2)))) -> ((op (e2) (e2)) = (e2)) -> (~((op (e0) (e3)) = (op (e1) (e3)))) -> ((op (e0) (e3)) = (e2)) -> False). % 15.16/15.35 do 0 intro. intros zenon_H84 zenon_Ha7 zenon_Hd8 zenon_Hd6 zenon_H7d zenon_H35 zenon_H80 zenon_H81. % 15.16/15.35 apply (zenon_or_s _ _ zenon_H84); [ zenon_intro zenon_H68 | zenon_intro zenon_H85 ]. % 15.16/15.35 apply (zenon_L162_); trivial. % 15.16/15.35 apply (zenon_or_s _ _ zenon_H85); [ zenon_intro zenon_H6e | zenon_intro zenon_H86 ]. % 15.16/15.35 exact (zenon_Hd6 zenon_H6e). % 15.16/15.35 apply (zenon_or_s _ _ zenon_H86); [ zenon_intro zenon_H7c | zenon_intro zenon_H82 ]. % 15.16/15.35 apply (zenon_L21_); trivial. % 15.16/15.35 apply (zenon_L22_); trivial. % 15.16/15.35 (* end of lemma zenon_L243_ *) % 15.16/15.35 assert (zenon_L244_ : (((op (e0) (e0)) = (e2))\/(((op (e0) (e1)) = (e2))\/(((op (e0) (e2)) = (e2))\/((op (e0) (e3)) = (e2))))) -> (((op (e1) (e1)) = (e0))\/(((op (e1) (e1)) = (e1))\/(((op (e1) (e1)) = (e2))\/((op (e1) (e1)) = (e3))))) -> (~((op (e1) (e1)) = (e1))) -> (~((op (e1) (e1)) = (e2))) -> (~((op (e0) (e3)) = (op (e3) (e3)))) -> ((op (e3) (e3)) = (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)) = (e3))) -> (~((op (e0) (e2)) = (op (e1) (e2)))) -> (~((op (e1) (e3)) = (op (e3) (e3)))) -> (~((e2) = (e3))) -> (~((op (e0) (e0)) = (e3))) -> (((op (e0) (e0)) = (e3))\/(((op (e0) (e1)) = (e3))\/(((op (e0) (e2)) = (e3))\/((op (e0) (e3)) = (e3))))) -> (~((op (e0) (e2)) = (op (e2) (e2)))) -> ((op (e2) (e2)) = (e2)) -> ((op (e0) (e3)) = (e1)) -> (~((e1) = (e2))) -> False). % 15.16/15.35 do 0 intro. intros zenon_H8e zenon_H1b3 zenon_H1b4 zenon_Hd6 zenon_H36 zenon_H42 zenon_H90 zenon_Ha3 zenon_Hd8 zenon_H182 zenon_H87 zenon_H8b zenon_H6a zenon_H59 zenon_H58 zenon_H28 zenon_H35 zenon_H37 zenon_Ha7. % 15.16/15.35 apply (zenon_or_s _ _ zenon_H8e); [ zenon_intro zenon_H92 | zenon_intro zenon_H91 ]. % 15.16/15.35 apply (zenon_L195_); trivial. % 15.16/15.35 apply (zenon_or_s _ _ zenon_H91); [ zenon_intro zenon_H5d | zenon_intro zenon_H93 ]. % 15.16/15.35 apply (zenon_L227_); trivial. % 15.16/15.35 apply (zenon_or_s _ _ zenon_H93); [ zenon_intro zenon_H63 | zenon_intro zenon_H81 ]. % 15.16/15.35 apply (zenon_L15_); trivial. % 15.16/15.35 apply (zenon_L33_); trivial. % 15.16/15.35 (* end of lemma zenon_L244_ *) % 15.16/15.35 assert (zenon_L245_ : (((op (e0) (e0)) = (e1))\/(((op (e0) (e1)) = (e1))\/(((op (e0) (e2)) = (e1))\/((op (e0) (e3)) = (e1))))) -> (~((op (e0) (e0)) = (e1))) -> (~((op (e0) (e3)) = (op (e1) (e3)))) -> (~((op (e1) (e2)) = (op (e2) (e2)))) -> (((op (e1) (e0)) = (e2))\/(((op (e1) (e1)) = (e2))\/(((op (e1) (e2)) = (e2))\/((op (e1) (e3)) = (e2))))) -> (~((e0) = (e1))) -> ((op (e0) (e2)) = (e0)) -> (((op (e0) (e0)) = (e2))\/(((op (e0) (e1)) = (e2))\/(((op (e0) (e2)) = (e2))\/((op (e0) (e3)) = (e2))))) -> (((op (e1) (e1)) = (e0))\/(((op (e1) (e1)) = (e1))\/(((op (e1) (e1)) = (e2))\/((op (e1) (e1)) = (e3))))) -> (~((op (e1) (e1)) = (e1))) -> (~((op (e1) (e1)) = (e2))) -> (~((op (e0) (e3)) = (op (e3) (e3)))) -> ((op (e3) (e3)) = (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)) = (e3))) -> (~((op (e0) (e2)) = (op (e1) (e2)))) -> (~((op (e1) (e3)) = (op (e3) (e3)))) -> (~((e2) = (e3))) -> (~((op (e0) (e0)) = (e3))) -> (((op (e0) (e0)) = (e3))\/(((op (e0) (e1)) = (e3))\/(((op (e0) (e2)) = (e3))\/((op (e0) (e3)) = (e3))))) -> (~((op (e0) (e2)) = (op (e2) (e2)))) -> ((op (e2) (e2)) = (e2)) -> (~((e1) = (e2))) -> False). % 15.16/15.35 do 0 intro. intros zenon_H44 zenon_H45 zenon_H80 zenon_H7d zenon_H84 zenon_H9e zenon_Hab zenon_H8e zenon_H1b3 zenon_H1b4 zenon_Hd6 zenon_H36 zenon_H42 zenon_H90 zenon_Ha3 zenon_Hd8 zenon_H182 zenon_H87 zenon_H8b zenon_H6a zenon_H59 zenon_H58 zenon_H28 zenon_H35 zenon_Ha7. % 15.16/15.35 apply (zenon_or_s _ _ zenon_H44); [ zenon_intro zenon_H47 | zenon_intro zenon_H46 ]. % 15.16/15.35 exact (zenon_H45 zenon_H47). % 15.16/15.35 apply (zenon_or_s _ _ zenon_H46); [ zenon_intro zenon_H22 | zenon_intro zenon_H48 ]. % 15.16/15.35 apply (zenon_or_s _ _ zenon_H8e); [ zenon_intro zenon_H92 | zenon_intro zenon_H91 ]. % 15.16/15.35 apply (zenon_L195_); trivial. % 15.16/15.35 apply (zenon_or_s _ _ zenon_H91); [ zenon_intro zenon_H5d | zenon_intro zenon_H93 ]. % 15.16/15.35 apply (zenon_L227_); trivial. % 15.16/15.35 apply (zenon_or_s _ _ zenon_H93); [ zenon_intro zenon_H63 | zenon_intro zenon_H81 ]. % 15.16/15.35 apply (zenon_L242_); trivial. % 15.16/15.35 apply (zenon_L243_); trivial. % 15.16/15.35 apply (zenon_or_s _ _ zenon_H48); [ zenon_intro zenon_H29 | zenon_intro zenon_H37 ]. % 15.16/15.35 apply (zenon_L37_); trivial. % 15.16/15.35 apply (zenon_L244_); trivial. % 15.16/15.35 (* end of lemma zenon_L245_ *) % 15.16/15.35 assert (zenon_L246_ : (((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)) -> (~((e2) = (e3))) -> ((op (e2) (e0)) = (e2)) -> ((op (e3) (e3)) = (e3)) -> (~((op (e3) (e0)) = (op (e3) (e3)))) -> False). % 15.16/15.35 do 0 intro. intros zenon_Hbe zenon_H59 zenon_Ha3 zenon_Hd8 zenon_H6a zenon_Hdd zenon_H42 zenon_Hbb. % 15.16/15.35 apply (zenon_or_s _ _ zenon_Hbe); [ zenon_intro zenon_H5b | zenon_intro zenon_Hbf ]. % 15.16/15.35 exact (zenon_H59 zenon_H5b). % 15.16/15.35 apply (zenon_or_s _ _ zenon_Hbf); [ zenon_intro zenon_H69 | zenon_intro zenon_Hc0 ]. % 15.16/15.35 apply (zenon_L163_); trivial. % 15.16/15.35 apply (zenon_or_s _ _ zenon_Hc0); [ zenon_intro zenon_Haf | zenon_intro zenon_Hba ]. % 15.16/15.35 apply (zenon_L64_); trivial. % 15.16/15.35 apply (zenon_L43_); trivial. % 15.16/15.35 (* end of lemma zenon_L246_ *) % 15.16/15.35 assert (zenon_L247_ : ((~((op (e2) (e2)) = (e0)))\/((op (e2) (e0)) = (e2))) -> ((~((op (e2) (e2)) = (e3)))\/((op (e2) (e3)) = (e2))) -> ((~((op (e3) (e3)) = (e1)))\/((op (e3) (e1)) = (e3))) -> (~((op (e3) (e1)) = (op (e3) (e3)))) -> (~((op (e0) (e0)) = (e1))) -> (((op (e0) (e3)) = (e1))\/(((op (e1) (e3)) = (e1))\/(((op (e2) (e3)) = (e1))\/((op (e3) (e3)) = (e1))))) -> (~((e1) = (e2))) -> (~((op (e1) (e0)) = (op (e1) (e3)))) -> (~((op (e0) (e1)) = (op (e0) (e3)))) -> (~((e0) = (e1))) -> ((op (e0) (e2)) = (e0)) -> (((op (e0) (e0)) = (e2))\/(((op (e0) (e1)) = (e2))\/(((op (e0) (e2)) = (e2))\/((op (e0) (e3)) = (e2))))) -> (((op (e0) (e3)) = (e0))\/(((op (e1) (e3)) = (e0))\/(((op (e2) (e3)) = (e0))\/((op (e3) (e3)) = (e0))))) -> (~((e0) = (e2))) -> (~((op (e0) (e2)) = (op (e0) (e3)))) -> (((op (e1) (e0)) = (e2))\/(((op (e1) (e1)) = (e2))\/(((op (e1) (e2)) = (e2))\/((op (e1) (e3)) = (e2))))) -> (~((e2) = (e3))) -> (~((op (e0) (e2)) = (op (e1) (e2)))) -> (~((op (e0) (e3)) = (op (e3) (e3)))) -> (((op (e0) (e0)) = (e3))\/(((op (e0) (e1)) = (e3))\/(((op (e0) (e2)) = (e3))\/((op (e0) (e3)) = (e3))))) -> (~((op (e1) (e3)) = (op (e3) (e3)))) -> (((op (e1) (e0)) = (e3))\/(((op (e1) (e1)) = (e3))\/(((op (e1) (e2)) = (e3))\/((op (e1) (e3)) = (e3))))) -> (((op (e0) (e0)) = (e1))\/(((op (e0) (e1)) = (e1))\/(((op (e0) (e2)) = (e1))\/((op (e0) (e3)) = (e1))))) -> ((~((op (e3) (e3)) = (e0)))\/((op (e3) (e0)) = (e3))) -> (~((op (e0) (e0)) = (e3))) -> (~((e1) = (e3))) -> ((op (e1) (e0)) = (e1)) -> (((op (e1) (e1)) = (e0))\/(((op (e1) (e1)) = (e1))\/(((op (e1) (e1)) = (e2))\/((op (e1) (e1)) = (e3))))) -> (~((op (e1) (e1)) = (e3))) -> (~((op (e1) (e1)) = (e2))) -> (~((op (e1) (e1)) = (e1))) -> (((op (e2) (e2)) = (e0))\/(((op (e2) (e2)) = (e1))\/(((op (e2) (e2)) = (e2))\/((op (e2) (e2)) = (e3))))) -> (~((op (e3) (e0)) = (op (e3) (e3)))) -> ((op (e3) (e3)) = (e3)) -> (((op (e0) (e0)) = (e3))\/(((op (e1) (e0)) = (e3))\/(((op (e2) (e0)) = (e3))\/((op (e3) (e0)) = (e3))))) -> (~((op (e0) (e2)) = (op (e2) (e2)))) -> (~((op (e0) (e3)) = (op (e1) (e3)))) -> (~((op (e1) (e2)) = (op (e2) (e2)))) -> ((~((op (e2) (e2)) = (e2)))\/((op (e2) (e2)) = (e2))) -> False). % 15.16/15.35 do 0 intro. intros zenon_H1d4 zenon_H1c3 zenon_H10c zenon_H12d zenon_H45 zenon_H121 zenon_Ha7 zenon_H1cf zenon_H1cd zenon_H9e zenon_Hab zenon_H8e zenon_Hd3 zenon_H5e zenon_Hc9 zenon_H84 zenon_H6a zenon_H87 zenon_H36 zenon_H58 zenon_H8b zenon_H90 zenon_H44 zenon_H10f zenon_H59 zenon_Ha3 zenon_Hd8 zenon_H1b3 zenon_H182 zenon_Hd6 zenon_H1b4 zenon_H2d zenon_Hbb zenon_H42 zenon_Hbe zenon_H28 zenon_H80 zenon_H7d zenon_Haa. % 15.16/15.35 apply (zenon_or_s _ _ zenon_H1d4); [ zenon_intro zenon_H2e | zenon_intro zenon_Hdd ]. % 15.16/15.35 apply (zenon_or_s _ _ zenon_Haa); [ zenon_intro zenon_H2f | zenon_intro zenon_H35 ]. % 15.16/15.35 apply (zenon_or_s _ _ zenon_H1c3); [ zenon_intro zenon_H30 | zenon_intro zenon_H124 ]. % 15.16/15.35 apply (zenon_L241_); trivial. % 15.16/15.35 apply (zenon_or_s _ _ zenon_H10f); [ zenon_intro zenon_H3c | zenon_intro zenon_Hba ]. % 15.16/15.35 apply (zenon_or_s _ _ zenon_H10c); [ zenon_intro zenon_H104 | zenon_intro zenon_H10a ]. % 15.16/15.35 apply (zenon_L228_); trivial. % 15.16/15.35 apply (zenon_L102_); trivial. % 15.16/15.35 apply (zenon_L43_); trivial. % 15.16/15.35 apply (zenon_L245_); trivial. % 15.16/15.35 apply (zenon_L246_); trivial. % 15.16/15.35 (* end of lemma zenon_L247_ *) % 15.16/15.35 assert (zenon_L248_ : (~((op (e1) (e0)) = (op (e1) (e2)))) -> ((op (e1) (e0)) = (e1)) -> ((op (e1) (e2)) = (e1)) -> False). % 15.16/15.35 do 0 intro. intros zenon_H166 zenon_Hd8 zenon_H117. % 15.16/15.35 cut (((op (e1) (e0)) = (e1)) = ((op (e1) (e0)) = (op (e1) (e2)))). % 15.16/15.35 intro zenon_D_pnotp. % 15.16/15.35 apply zenon_H166. % 15.16/15.35 rewrite <- zenon_D_pnotp. % 15.16/15.35 exact zenon_Hd8. % 15.16/15.35 cut (((e1) = (op (e1) (e2)))); [idtac | apply NNPP; zenon_intro zenon_H118]. % 15.16/15.35 cut (((op (e1) (e0)) = (op (e1) (e0)))); [idtac | apply NNPP; zenon_intro zenon_Hda]. % 15.16/15.35 congruence. % 15.16/15.35 apply zenon_Hda. apply refl_equal. % 15.16/15.35 apply zenon_H118. apply sym_equal. exact zenon_H117. % 15.16/15.35 (* end of lemma zenon_L248_ *) % 15.16/15.35 assert (zenon_L249_ : ((~((op (e1) (e1)) = (e1)))\/((op (e1) (e1)) = (e1))) -> (~((op (e1) (e0)) = (op (e1) (e1)))) -> ((~((op (e1) (e1)) = (e3)))\/((op (e1) (e3)) = (e1))) -> ((~((op (e2) (e2)) = (e2)))\/((op (e2) (e2)) = (e2))) -> (~((op (e1) (e2)) = (op (e2) (e2)))) -> (~((op (e0) (e3)) = (op (e1) (e3)))) -> (~((op (e0) (e2)) = (op (e2) (e2)))) -> (((op (e0) (e0)) = (e3))\/(((op (e1) (e0)) = (e3))\/(((op (e2) (e0)) = (e3))\/((op (e3) (e0)) = (e3))))) -> ((op (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 (e1) (e1)) = (e0))\/(((op (e1) (e1)) = (e1))\/(((op (e1) (e1)) = (e2))\/((op (e1) (e1)) = (e3))))) -> ((op (e1) (e0)) = (e1)) -> (~((e1) = (e3))) -> (~((op (e0) (e0)) = (e3))) -> ((~((op (e3) (e3)) = (e0)))\/((op (e3) (e0)) = (e3))) -> (((op (e0) (e0)) = (e1))\/(((op (e0) (e1)) = (e1))\/(((op (e0) (e2)) = (e1))\/((op (e0) (e3)) = (e1))))) -> (((op (e1) (e0)) = (e3))\/(((op (e1) (e1)) = (e3))\/(((op (e1) (e2)) = (e3))\/((op (e1) (e3)) = (e3))))) -> (~((op (e1) (e3)) = (op (e3) (e3)))) -> (((op (e0) (e0)) = (e3))\/(((op (e0) (e1)) = (e3))\/(((op (e0) (e2)) = (e3))\/((op (e0) (e3)) = (e3))))) -> (~((op (e0) (e3)) = (op (e3) (e3)))) -> (~((op (e0) (e2)) = (op (e1) (e2)))) -> (~((e2) = (e3))) -> (((op (e1) (e0)) = (e2))\/(((op (e1) (e1)) = (e2))\/(((op (e1) (e2)) = (e2))\/((op (e1) (e3)) = (e2))))) -> (~((op (e0) (e2)) = (op (e0) (e3)))) -> (~((e0) = (e2))) -> (((op (e0) (e3)) = (e0))\/(((op (e1) (e3)) = (e0))\/(((op (e2) (e3)) = (e0))\/((op (e3) (e3)) = (e0))))) -> (((op (e0) (e0)) = (e2))\/(((op (e0) (e1)) = (e2))\/(((op (e0) (e2)) = (e2))\/((op (e0) (e3)) = (e2))))) -> ((op (e0) (e2)) = (e0)) -> (~((e0) = (e1))) -> (~((op (e0) (e1)) = (op (e0) (e3)))) -> (~((op (e1) (e0)) = (op (e1) (e3)))) -> (~((e1) = (e2))) -> (((op (e0) (e3)) = (e1))\/(((op (e1) (e3)) = (e1))\/(((op (e2) (e3)) = (e1))\/((op (e3) (e3)) = (e1))))) -> (~((op (e0) (e0)) = (e1))) -> (~((op (e3) (e1)) = (op (e3) (e3)))) -> ((~((op (e3) (e3)) = (e1)))\/((op (e3) (e1)) = (e3))) -> ((~((op (e2) (e2)) = (e3)))\/((op (e2) (e3)) = (e2))) -> ((~((op (e2) (e2)) = (e0)))\/((op (e2) (e0)) = (e2))) -> (~((op (e1) (e0)) = (op (e1) (e2)))) -> ((~((op (e1) (e1)) = (e2)))\/((op (e1) (e2)) = (e1))) -> False). % 15.16/15.35 do 0 intro. intros zenon_H1d8 zenon_Hd7 zenon_H1d2 zenon_Haa zenon_H7d zenon_H80 zenon_H28 zenon_Hbe zenon_H42 zenon_Hbb zenon_H2d zenon_H1b3 zenon_Hd8 zenon_Ha3 zenon_H59 zenon_H10f zenon_H44 zenon_H90 zenon_H8b zenon_H58 zenon_H36 zenon_H87 zenon_H6a zenon_H84 zenon_Hc9 zenon_H5e zenon_Hd3 zenon_H8e zenon_Hab zenon_H9e zenon_H1cd zenon_H1cf zenon_Ha7 zenon_H121 zenon_H45 zenon_H12d zenon_H10c zenon_H1c3 zenon_H1d4 zenon_H166 zenon_H1d3. % 15.16/15.35 apply (zenon_or_s _ _ zenon_H1d8); [ zenon_intro zenon_H1b4 | zenon_intro zenon_H21 ]. % 15.16/15.35 apply (zenon_or_s _ _ zenon_H1d3); [ zenon_intro zenon_Hd6 | zenon_intro zenon_H117 ]. % 15.16/15.35 apply (zenon_or_s _ _ zenon_H1d2); [ zenon_intro zenon_H182 | zenon_intro zenon_H11f ]. % 15.16/15.35 apply (zenon_L247_); trivial. % 15.16/15.35 apply (zenon_L224_); trivial. % 15.16/15.35 apply (zenon_L248_); trivial. % 15.16/15.35 apply (zenon_L61_); trivial. % 15.16/15.35 (* end of lemma zenon_L249_ *) % 15.16/15.35 assert (zenon_L250_ : (((op (e2) (e0)) = (e3))\/(((op (e2) (e1)) = (e3))\/(((op (e2) (e2)) = (e3))\/((op (e2) (e3)) = (e3))))) -> (~((e1) = (e3))) -> ((op (e2) (e0)) = (e1)) -> (~((e2) = (e3))) -> ((op (e2) (e1)) = (e2)) -> (~((op (e2) (e2)) = (e3))) -> ((op (e3) (e3)) = (e3)) -> (~((op (e2) (e3)) = (op (e3) (e3)))) -> False). % 15.16/15.35 do 0 intro. intros zenon_He6 zenon_Ha3 zenon_Hae zenon_H6a zenon_H156 zenon_H30 zenon_H42 zenon_He3. % 15.16/15.35 apply (zenon_or_s _ _ zenon_He6); [ zenon_intro zenon_Haf | zenon_intro zenon_He7 ]. % 15.16/15.35 apply (zenon_L39_); trivial. % 15.16/15.35 apply (zenon_or_s _ _ zenon_He7); [ zenon_intro zenon_Hdf | zenon_intro zenon_He8 ]. % 15.16/15.35 apply (zenon_L183_); trivial. % 15.16/15.35 apply (zenon_or_s _ _ zenon_He8); [ zenon_intro zenon_H34 | zenon_intro zenon_He2 ]. % 15.16/15.35 exact (zenon_H30 zenon_H34). % 15.16/15.35 apply (zenon_L66_); trivial. % 15.16/15.35 (* end of lemma zenon_L250_ *) % 15.16/15.35 assert (zenon_L251_ : ((op (e2) (e1)) = (e2)) -> ((op (e0) (e1)) = (e2)) -> (~((op (e0) (e1)) = (op (e2) (e1)))) -> False). % 15.16/15.35 do 0 intro. intros zenon_H156 zenon_H5d zenon_Hde. % 15.16/15.35 elim (classic ((op (e2) (e1)) = (op (e2) (e1)))); [ zenon_intro zenon_H1d9 | zenon_intro zenon_H1da ]. % 15.16/15.35 cut (((op (e2) (e1)) = (op (e2) (e1))) = ((op (e0) (e1)) = (op (e2) (e1)))). % 15.16/15.35 intro zenon_D_pnotp. % 15.16/15.35 apply zenon_Hde. % 15.16/15.35 rewrite <- zenon_D_pnotp. % 15.16/15.35 exact zenon_H1d9. % 15.16/15.35 cut (((op (e2) (e1)) = (op (e2) (e1)))); [idtac | apply NNPP; zenon_intro zenon_H1da]. % 15.16/15.35 cut (((op (e2) (e1)) = (op (e0) (e1)))); [idtac | apply NNPP; zenon_intro zenon_H1db]. % 15.16/15.35 congruence. % 15.16/15.35 cut (((op (e2) (e1)) = (e2)) = ((op (e2) (e1)) = (op (e0) (e1)))). % 15.16/15.35 intro zenon_D_pnotp. % 15.16/15.35 apply zenon_H1db. % 15.16/15.35 rewrite <- zenon_D_pnotp. % 15.16/15.35 exact zenon_H156. % 15.16/15.35 cut (((e2) = (op (e0) (e1)))); [idtac | apply NNPP; zenon_intro zenon_H1dc]. % 15.16/15.35 cut (((op (e2) (e1)) = (op (e2) (e1)))); [idtac | apply NNPP; zenon_intro zenon_H1da]. % 15.16/15.35 congruence. % 15.16/15.35 apply zenon_H1da. apply refl_equal. % 15.16/15.35 apply zenon_H1dc. apply sym_equal. exact zenon_H5d. % 15.16/15.35 apply zenon_H1da. apply refl_equal. % 15.16/15.35 apply zenon_H1da. apply refl_equal. % 15.16/15.35 (* end of lemma zenon_L251_ *) % 15.16/15.35 assert (zenon_L252_ : (~((op (e2) (e1)) = (op (e3) (e1)))) -> ((op (e2) (e1)) = (e2)) -> ((op (e3) (e1)) = (e2)) -> False). % 15.16/15.35 do 0 intro. intros zenon_H13c zenon_H156 zenon_H16a. % 15.16/15.35 cut (((op (e2) (e1)) = (e2)) = ((op (e2) (e1)) = (op (e3) (e1)))). % 15.16/15.35 intro zenon_D_pnotp. % 15.16/15.35 apply zenon_H13c. % 15.16/15.35 rewrite <- zenon_D_pnotp. % 15.16/15.35 exact zenon_H156. % 15.16/15.35 cut (((e2) = (op (e3) (e1)))); [idtac | apply NNPP; zenon_intro zenon_H16b]. % 15.16/15.35 cut (((op (e2) (e1)) = (op (e2) (e1)))); [idtac | apply NNPP; zenon_intro zenon_H1da]. % 15.16/15.35 congruence. % 15.16/15.35 apply zenon_H1da. apply refl_equal. % 15.16/15.35 apply zenon_H16b. apply sym_equal. exact zenon_H16a. % 15.16/15.35 (* end of lemma zenon_L252_ *) % 15.16/15.35 assert (zenon_L253_ : (~((op (e0) (e2)) = (op (e3) (e2)))) -> ((op (e0) (e2)) = (e2)) -> ((op (e3) (e2)) = (e2)) -> False). % 15.16/15.35 do 0 intro. intros zenon_H140 zenon_H63 zenon_H1dd. % 15.16/15.35 cut (((op (e0) (e2)) = (e2)) = ((op (e0) (e2)) = (op (e3) (e2)))). % 15.16/15.35 intro zenon_D_pnotp. % 15.16/15.35 apply zenon_H140. % 15.16/15.35 rewrite <- zenon_D_pnotp. % 15.16/15.35 exact zenon_H63. % 15.16/15.35 cut (((e2) = (op (e3) (e2)))); [idtac | apply NNPP; zenon_intro zenon_H1de]. % 15.16/15.35 cut (((op (e0) (e2)) = (op (e0) (e2)))); [idtac | apply NNPP; zenon_intro zenon_H2c]. % 15.16/15.35 congruence. % 15.16/15.35 apply zenon_H2c. apply refl_equal. % 15.16/15.35 apply zenon_H1de. apply sym_equal. exact zenon_H1dd. % 15.16/15.35 (* end of lemma zenon_L253_ *) % 15.16/15.35 assert (zenon_L254_ : (((op (e3) (e0)) = (e2))\/(((op (e3) (e1)) = (e2))\/(((op (e3) (e2)) = (e2))\/((op (e3) (e3)) = (e2))))) -> (~((e1) = (e2))) -> ((op (e3) (e0)) = (e1)) -> ((op (e2) (e1)) = (e2)) -> (~((op (e2) (e1)) = (op (e3) (e1)))) -> ((op (e0) (e2)) = (e2)) -> (~((op (e0) (e2)) = (op (e3) (e2)))) -> (~((op (e3) (e3)) = (e2))) -> False). % 15.16/15.35 do 0 intro. intros zenon_H1df zenon_Ha7 zenon_Hee zenon_H156 zenon_H13c zenon_H63 zenon_H140 zenon_H3d. % 15.16/15.35 apply (zenon_or_s _ _ zenon_H1df); [ zenon_intro zenon_He9 | zenon_intro zenon_H1e0 ]. % 15.16/15.35 apply (zenon_L122_); trivial. % 15.16/15.35 apply (zenon_or_s _ _ zenon_H1e0); [ zenon_intro zenon_H16a | zenon_intro zenon_H1e1 ]. % 15.16/15.35 apply (zenon_L252_); trivial. % 15.16/15.35 apply (zenon_or_s _ _ zenon_H1e1); [ zenon_intro zenon_H1dd | zenon_intro zenon_H43 ]. % 15.16/15.35 apply (zenon_L253_); trivial. % 15.16/15.35 exact (zenon_H3d zenon_H43). % 15.16/15.35 (* end of lemma zenon_L254_ *) % 15.16/15.35 assert (zenon_L255_ : (((op (e0) (e0)) = (e2))\/(((op (e0) (e1)) = (e2))\/(((op (e0) (e2)) = (e2))\/((op (e0) (e3)) = (e2))))) -> (~((e1) = (e3))) -> ((op (e0) (e2)) = (e0)) -> (~((e0) = (e3))) -> (((op (e2) (e2)) = (e0))\/(((op (e2) (e2)) = (e1))\/(((op (e2) (e2)) = (e2))\/((op (e2) (e2)) = (e3))))) -> (~((op (e2) (e2)) = (e0))) -> (~((op (e2) (e2)) = (e2))) -> (~((op (e2) (e2)) = (e3))) -> (~((op (e0) (e0)) = (e3))) -> (((op (e0) (e0)) = (e3))\/(((op (e0) (e1)) = (e3))\/(((op (e0) (e2)) = (e3))\/((op (e0) (e3)) = (e3))))) -> (~((op (e0) (e1)) = (op (e2) (e1)))) -> (~((op (e3) (e3)) = (e2))) -> (~((op (e0) (e2)) = (op (e3) (e2)))) -> (~((op (e2) (e1)) = (op (e3) (e1)))) -> ((op (e2) (e1)) = (e2)) -> ((op (e3) (e0)) = (e1)) -> (((op (e3) (e0)) = (e2))\/(((op (e3) (e1)) = (e2))\/(((op (e3) (e2)) = (e2))\/((op (e3) (e3)) = (e2))))) -> ((op (e0) (e3)) = (e1)) -> (~((e1) = (e2))) -> False). % 15.16/15.35 do 0 intro. intros zenon_H8e zenon_Ha3 zenon_Hab zenon_H4b zenon_H2d zenon_H2e zenon_H2f zenon_H30 zenon_H59 zenon_H58 zenon_Hde zenon_H3d zenon_H140 zenon_H13c zenon_H156 zenon_Hee zenon_H1df zenon_H37 zenon_Ha7. % 15.16/15.35 apply (zenon_or_s _ _ zenon_H8e); [ zenon_intro zenon_H92 | zenon_intro zenon_H91 ]. % 15.16/15.35 apply (zenon_L49_); trivial. % 15.16/15.35 apply (zenon_or_s _ _ zenon_H91); [ zenon_intro zenon_H5d | zenon_intro zenon_H93 ]. % 15.16/15.35 apply (zenon_L251_); trivial. % 15.16/15.35 apply (zenon_or_s _ _ zenon_H93); [ zenon_intro zenon_H63 | zenon_intro zenon_H81 ]. % 15.16/15.35 apply (zenon_L254_); trivial. % 15.16/15.35 apply (zenon_L33_); trivial. % 15.16/15.35 (* end of lemma zenon_L255_ *) % 15.16/15.35 assert (zenon_L256_ : (~((op (e2) (e1)) = (op (e2) (e3)))) -> ((op (e2) (e1)) = (e2)) -> ((op (e2) (e3)) = (e2)) -> False). % 15.16/15.35 do 0 intro. intros zenon_H1e2 zenon_H156 zenon_H124. % 15.16/15.35 cut (((op (e2) (e1)) = (e2)) = ((op (e2) (e1)) = (op (e2) (e3)))). % 15.16/15.35 intro zenon_D_pnotp. % 15.16/15.35 apply zenon_H1e2. % 15.16/15.35 rewrite <- zenon_D_pnotp. % 15.16/15.35 exact zenon_H156. % 15.16/15.35 cut (((e2) = (op (e2) (e3)))); [idtac | apply NNPP; zenon_intro zenon_H137]. % 15.16/15.35 cut (((op (e2) (e1)) = (op (e2) (e1)))); [idtac | apply NNPP; zenon_intro zenon_H1da]. % 15.16/15.35 congruence. % 15.16/15.35 apply zenon_H1da. apply refl_equal. % 15.16/15.35 apply zenon_H137. apply sym_equal. exact zenon_H124. % 15.16/15.35 (* end of lemma zenon_L256_ *) % 15.16/15.35 assert (zenon_L257_ : (~((op (e2) (e1)) = (op (e2) (e2)))) -> ((~((op (e3) (e3)) = (e2)))\/((op (e3) (e2)) = (e3))) -> (~((op (e3) (e2)) = (op (e3) (e3)))) -> (~((op (e0) (e0)) = (e1))) -> (((op (e0) (e0)) = (e3))\/(((op (e0) (e1)) = (e3))\/(((op (e0) (e2)) = (e3))\/((op (e0) (e3)) = (e3))))) -> ((op (e3) (e3)) = (e3)) -> (~((op (e0) (e3)) = (op (e3) (e3)))) -> ((op (e0) (e2)) = (e0)) -> (~((e0) = (e3))) -> (~((e1) = (e3))) -> (~((op (e0) (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) (e2)) = (e0))) -> (((op (e0) (e0)) = (e1))\/(((op (e1) (e0)) = (e1))\/(((op (e2) (e0)) = (e1))\/((op (e3) (e0)) = (e1))))) -> (~((op (e0) (e1)) = (op (e2) (e1)))) -> (((op (e3) (e0)) = (e2))\/(((op (e3) (e1)) = (e2))\/(((op (e3) (e2)) = (e2))\/((op (e3) (e3)) = (e2))))) -> (~((op (e0) (e2)) = (op (e3) (e2)))) -> (~((op (e2) (e1)) = (op (e3) (e1)))) -> ((op (e2) (e1)) = (e2)) -> (~((op (e2) (e3)) = (op (e3) (e3)))) -> (((op (e2) (e0)) = (e3))\/(((op (e2) (e1)) = (e3))\/(((op (e2) (e2)) = (e3))\/((op (e2) (e3)) = (e3))))) -> ((~((op (e1) (e1)) = (e2)))\/((op (e1) (e2)) = (e1))) -> (~((op (e1) (e0)) = (op (e1) (e2)))) -> ((~((op (e2) (e2)) = (e0)))\/((op (e2) (e0)) = (e2))) -> ((~((op (e2) (e2)) = (e3)))\/((op (e2) (e3)) = (e2))) -> ((~((op (e3) (e3)) = (e1)))\/((op (e3) (e1)) = (e3))) -> (~((op (e3) (e1)) = (op (e3) (e3)))) -> (((op (e0) (e3)) = (e1))\/(((op (e1) (e3)) = (e1))\/(((op (e2) (e3)) = (e1))\/((op (e3) (e3)) = (e1))))) -> (~((e1) = (e2))) -> (~((op (e1) (e0)) = (op (e1) (e3)))) -> (~((op (e0) (e1)) = (op (e0) (e3)))) -> (~((e0) = (e1))) -> (((op (e0) (e0)) = (e2))\/(((op (e0) (e1)) = (e2))\/(((op (e0) (e2)) = (e2))\/((op (e0) (e3)) = (e2))))) -> (((op (e0) (e3)) = (e0))\/(((op (e1) (e3)) = (e0))\/(((op (e2) (e3)) = (e0))\/((op (e3) (e3)) = (e0))))) -> (~((e0) = (e2))) -> (~((op (e0) (e2)) = (op (e0) (e3)))) -> (((op (e1) (e0)) = (e2))\/(((op (e1) (e1)) = (e2))\/(((op (e1) (e2)) = (e2))\/((op (e1) (e3)) = (e2))))) -> (~((e2) = (e3))) -> (~((op (e0) (e2)) = (op (e1) (e2)))) -> (~((op (e1) (e3)) = (op (e3) (e3)))) -> (((op (e1) (e0)) = (e3))\/(((op (e1) (e1)) = (e3))\/(((op (e1) (e2)) = (e3))\/((op (e1) (e3)) = (e3))))) -> (((op (e0) (e0)) = (e1))\/(((op (e0) (e1)) = (e1))\/(((op (e0) (e2)) = (e1))\/((op (e0) (e3)) = (e1))))) -> ((~((op (e3) (e3)) = (e0)))\/((op (e3) (e0)) = (e3))) -> (((op (e1) (e1)) = (e0))\/(((op (e1) (e1)) = (e1))\/(((op (e1) (e1)) = (e2))\/((op (e1) (e1)) = (e3))))) -> (~((op (e3) (e0)) = (op (e3) (e3)))) -> (((op (e0) (e0)) = (e3))\/(((op (e1) (e0)) = (e3))\/(((op (e2) (e0)) = (e3))\/((op (e3) (e0)) = (e3))))) -> (~((op (e0) (e3)) = (op (e1) (e3)))) -> (~((op (e1) (e2)) = (op (e2) (e2)))) -> ((~((op (e2) (e2)) = (e2)))\/((op (e2) (e2)) = (e2))) -> ((~((op (e1) (e1)) = (e3)))\/((op (e1) (e3)) = (e1))) -> (~((op (e1) (e0)) = (op (e1) (e1)))) -> ((~((op (e1) (e1)) = (e1)))\/((op (e1) (e1)) = (e1))) -> (~((op (e2) (e1)) = (op (e2) (e3)))) -> False). % 15.16/15.35 do 0 intro. intros zenon_H157 zenon_H10e zenon_H173 zenon_H45 zenon_H58 zenon_H42 zenon_H36 zenon_Hab zenon_H4b zenon_Ha3 zenon_H59 zenon_H2d zenon_H28 zenon_H2e zenon_Hf1 zenon_Hde zenon_H1df zenon_H140 zenon_H13c zenon_H156 zenon_He3 zenon_He6 zenon_H1d3 zenon_H166 zenon_H1d4 zenon_H1c3 zenon_H10c zenon_H12d zenon_H121 zenon_Ha7 zenon_H1cf zenon_H1cd zenon_H9e zenon_H8e zenon_Hd3 zenon_H5e zenon_Hc9 zenon_H84 zenon_H6a zenon_H87 zenon_H8b zenon_H90 zenon_H44 zenon_H10f zenon_H1b3 zenon_Hbb zenon_Hbe zenon_H80 zenon_H7d zenon_Haa zenon_H1d2 zenon_Hd7 zenon_H1d8 zenon_H1e2. % 15.16/15.35 apply (zenon_or_s _ _ zenon_Haa); [ zenon_intro zenon_H2f | zenon_intro zenon_H35 ]. % 15.16/15.35 apply (zenon_or_s _ _ zenon_H1c3); [ zenon_intro zenon_H30 | zenon_intro zenon_H124 ]. % 15.16/15.35 apply (zenon_or_s _ _ zenon_H10e); [ zenon_intro zenon_H3d | zenon_intro zenon_H106 ]. % 15.16/15.35 apply (zenon_or_s _ _ zenon_H44); [ zenon_intro zenon_H47 | zenon_intro zenon_H46 ]. % 15.16/15.35 exact (zenon_H45 zenon_H47). % 15.16/15.35 apply (zenon_or_s _ _ zenon_H46); [ zenon_intro zenon_H22 | zenon_intro zenon_H48 ]. % 15.16/15.35 apply (zenon_L60_); trivial. % 15.16/15.35 apply (zenon_or_s _ _ zenon_H48); [ zenon_intro zenon_H29 | zenon_intro zenon_H37 ]. % 15.16/15.35 apply (zenon_L5_); trivial. % 15.16/15.35 apply (zenon_or_s _ _ zenon_Hf1); [ zenon_intro zenon_H47 | zenon_intro zenon_Hf4 ]. % 15.16/15.35 exact (zenon_H45 zenon_H47). % 15.16/15.35 apply (zenon_or_s _ _ zenon_Hf4); [ zenon_intro zenon_Hd8 | zenon_intro zenon_Hf5 ]. % 15.16/15.35 apply (zenon_L249_); trivial. % 15.16/15.35 apply (zenon_or_s _ _ zenon_Hf5); [ zenon_intro zenon_Hae | zenon_intro zenon_Hee ]. % 15.16/15.35 apply (zenon_L250_); trivial. % 15.16/15.35 apply (zenon_L255_); trivial. % 15.16/15.35 apply (zenon_L153_); trivial. % 15.16/15.35 apply (zenon_L256_); trivial. % 15.16/15.35 apply (zenon_L134_); trivial. % 15.16/15.35 (* end of lemma zenon_L257_ *) % 15.16/15.35 assert (zenon_L258_ : ((~((op (e2) (e2)) = (e2)))\/((op (e2) (e2)) = (e2))) -> (~((op (e1) (e1)) = (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)) = (e0))\/(((op (e1) (e1)) = (e0))\/(((op (e1) (e2)) = (e0))\/((op (e1) (e3)) = (e0))))) -> (~((op (e2) (e0)) = (op (e2) (e1)))) -> (~((op (e2) (e1)) = (op (e2) (e2)))) -> (((op (e2) (e1)) = (e0))\/(((op (e2) (e1)) = (e1))\/(((op (e2) (e1)) = (e2))\/((op (e2) (e1)) = (e3))))) -> (((op (e1) (e2)) = (e0))\/(((op (e1) (e2)) = (e1))\/(((op (e1) (e2)) = (e2))\/((op (e1) (e2)) = (e3))))) -> (~((op (e1) (e2)) = (op (e3) (e2)))) -> (~((op (e1) (e2)) = (op (e2) (e2)))) -> (~((op (e1) (e1)) = (op (e1) (e2)))) -> ((~((op (e3) (e3)) = (e2)))\/((op (e3) (e2)) = (e3))) -> ((~((op (e3) (e3)) = (e0)))\/((op (e3) (e0)) = (e3))) -> (~((op (e0) (e0)) = (e0))) -> (((op (e0) (e0)) = (e1))\/(((op (e0) (e1)) = (e1))\/(((op (e0) (e2)) = (e1))\/((op (e0) (e3)) = (e1))))) -> (~((op (e0) (e0)) = (e3))) -> (~((e0) = (e3))) -> (((op (e2) (e0)) = (e1))\/(((op (e2) (e1)) = (e1))\/(((op (e2) (e2)) = (e1))\/((op (e2) (e3)) = (e1))))) -> (~((op (e0) (e3)) = (op (e2) (e3)))) -> (~((op (e1) (e1)) = (op (e2) (e1)))) -> (~((e1) = (e3))) -> (~((op (e3) (e0)) = (op (e3) (e3)))) -> ((op (e3) (e3)) = (e3)) -> (((op (e0) (e0)) = (e3))\/(((op (e1) (e0)) = (e3))\/(((op (e2) (e0)) = (e3))\/((op (e3) (e0)) = (e3))))) -> ((op (e0) (e2)) = (e0)) -> (~((e0) = (e1))) -> ((op (e1) (e1)) = (e1)) -> (~((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))))) -> (~((e2) = (e3))) -> (~((op (e1) (e1)) = (e2))) -> (~((op (e0) (e2)) = (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)))) -> (~((e0) = (e2))) -> (~((op (e0) (e2)) = (op (e0) (e3)))) -> (((op (e1) (e0)) = (e2))\/(((op (e1) (e1)) = (e2))\/(((op (e1) (e2)) = (e2))\/((op (e1) (e3)) = (e2))))) -> (~((e1) = (e2))) -> (((op (e0) (e0)) = (e2))\/(((op (e0) (e1)) = (e2))\/(((op (e0) (e2)) = (e2))\/((op (e0) (e3)) = (e2))))) -> (~((op (e0) (e2)) = (op (e2) (e2)))) -> (((op (e2) (e2)) = (e0))\/(((op (e2) (e2)) = (e1))\/(((op (e2) (e2)) = (e2))\/((op (e2) (e2)) = (e3))))) -> (~((op (e1) (e0)) = (op (e1) (e1)))) -> (((op (e0) (e0)) = (e2))\/(((op (e1) (e0)) = (e2))\/(((op (e2) (e0)) = (e2))\/((op (e3) (e0)) = (e2))))) -> (((op (e2) (e0)) = (e3))\/(((op (e2) (e1)) = (e3))\/(((op (e2) (e2)) = (e3))\/((op (e2) (e3)) = (e3))))) -> (~((op (e2) (e3)) = (op (e3) (e3)))) -> (~((op (e0) (e1)) = (op (e2) (e1)))) -> (((op (e0) (e0)) = (e1))\/(((op (e1) (e0)) = (e1))\/(((op (e2) (e0)) = (e1))\/((op (e3) (e0)) = (e1))))) -> (~((op (e0) (e3)) = (op (e3) (e3)))) -> (((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 (e3) (e1)) = (op (e3) (e3)))) -> (((op (e0) (e0)) = (e0))\/(((op (e0) (e0)) = (e1))\/(((op (e0) (e0)) = (e2))\/((op (e0) (e0)) = (e3))))) -> (((op (e0) (e3)) = (e1))\/(((op (e1) (e3)) = (e1))\/(((op (e2) (e3)) = (e1))\/((op (e3) (e3)) = (e1))))) -> (~((op (e1) (e1)) = (op (e1) (e3)))) -> (((op (e0) (e0)) = (e0))\/(((op (e0) (e1)) = (e0))\/(((op (e0) (e2)) = (e0))\/((op (e0) (e3)) = (e0))))) -> ((~((op (e2) (e2)) = (e3)))\/((op (e2) (e3)) = (e2))) -> (~((op (e3) (e2)) = (op (e3) (e3)))) -> (((op (e3) (e0)) = (e2))\/(((op (e3) (e1)) = (e2))\/(((op (e3) (e2)) = (e2))\/((op (e3) (e3)) = (e2))))) -> (~((op (e0) (e2)) = (op (e3) (e2)))) -> (~((op (e2) (e1)) = (op (e3) (e1)))) -> ((~((op (e1) (e1)) = (e2)))\/((op (e1) (e2)) = (e1))) -> (~((op (e1) (e0)) = (op (e1) (e2)))) -> ((~((op (e2) (e2)) = (e0)))\/((op (e2) (e0)) = (e2))) -> (~((op (e1) (e0)) = (op (e1) (e3)))) -> (~((op (e0) (e1)) = (op (e0) (e3)))) -> (~((op (e1) (e3)) = (op (e3) (e3)))) -> (((op (e1) (e0)) = (e3))\/(((op (e1) (e1)) = (e3))\/(((op (e1) (e2)) = (e3))\/((op (e1) (e3)) = (e3))))) -> (((op (e1) (e1)) = (e0))\/(((op (e1) (e1)) = (e1))\/(((op (e1) (e1)) = (e2))\/((op (e1) (e1)) = (e3))))) -> (~((op (e0) (e3)) = (op (e1) (e3)))) -> ((~((op (e1) (e1)) = (e3)))\/((op (e1) (e3)) = (e1))) -> ((~((op (e1) (e1)) = (e1)))\/((op (e1) (e1)) = (e1))) -> (~((op (e2) (e1)) = (op (e2) (e3)))) -> ((~((op (e2) (e2)) = (e1)))\/((op (e2) (e1)) = (e2))) -> False). % 15.16/15.35 do 0 intro. intros zenon_Haa zenon_H145 zenon_H160 zenon_H15f zenon_H163 zenon_H154 zenon_H157 zenon_H15a zenon_H1d5 zenon_H17d zenon_H7d zenon_H116 zenon_H10e zenon_H10f zenon_H20 zenon_H44 zenon_H59 zenon_H4b zenon_Hb7 zenon_Hb4 zenon_Hb1 zenon_Ha3 zenon_Hbb zenon_H42 zenon_Hbe zenon_Hab zenon_H9e zenon_H21 zenon_H23 zenon_H45 zenon_H58 zenon_H6a zenon_Hd6 zenon_H87 zenon_Hd3 zenon_Hce zenon_H5e zenon_Hc9 zenon_H84 zenon_Ha7 zenon_H8e zenon_H28 zenon_H2d zenon_Hd7 zenon_Heb zenon_He6 zenon_He3 zenon_Hde zenon_Hf1 zenon_H36 zenon_Hf0 zenon_H10c zenon_H12d zenon_H12a zenon_H121 zenon_H11e zenon_H110 zenon_H1c3 zenon_H173 zenon_H1df zenon_H140 zenon_H13c zenon_H1d3 zenon_H166 zenon_H1d4 zenon_H1cf zenon_H1cd zenon_H8b zenon_H90 zenon_H1b3 zenon_H80 zenon_H1d2 zenon_H1d8 zenon_H1e2 zenon_H1e3. % 15.16/15.35 apply (zenon_or_s _ _ zenon_H1d4); [ zenon_intro zenon_H2e | zenon_intro zenon_Hdd ]. % 15.16/15.35 apply (zenon_or_s _ _ zenon_H1e3); [ zenon_intro zenon_H52 | zenon_intro zenon_H156 ]. % 15.16/15.35 apply (zenon_or_s _ _ zenon_Haa); [ zenon_intro zenon_H2f | zenon_intro zenon_H35 ]. % 15.16/15.35 apply (zenon_or_s _ _ zenon_H1c3); [ zenon_intro zenon_H30 | zenon_intro zenon_H124 ]. % 15.16/15.35 apply (zenon_or_s _ _ zenon_H10f); [ zenon_intro zenon_H3c | zenon_intro zenon_Hba ]. % 15.16/15.35 apply (zenon_L72_); trivial. % 15.16/15.35 apply (zenon_L43_); trivial. % 15.16/15.35 apply (zenon_L103_); trivial. % 15.16/15.35 apply (zenon_or_s _ _ zenon_H10e); [ zenon_intro zenon_H3d | zenon_intro zenon_H106 ]. % 15.16/15.35 apply (zenon_L142_); trivial. % 15.16/15.35 apply (zenon_L240_); trivial. % 15.16/15.35 apply (zenon_L257_); trivial. % 15.16/15.35 apply (zenon_L234_); trivial. % 15.16/15.35 (* end of lemma zenon_L258_ *) % 15.16/15.35 assert (zenon_L259_ : ((~((op (e1) (e1)) = (e0)))\/((op (e1) (e0)) = (e1))) -> ((~((op (e1) (e1)) = (e2)))\/((op (e1) (e2)) = (e1))) -> (~((op (e1) (e2)) = (op (e1) (e3)))) -> ((~((op (e2) (e2)) = (e0)))\/((op (e2) (e0)) = (e2))) -> ((~((op (e3) (e3)) = (e1)))\/((op (e3) (e1)) = (e3))) -> (~((op (e3) (e1)) = (op (e3) (e3)))) -> (~((op (e0) (e1)) = (op (e0) (e3)))) -> (~((op (e1) (e0)) = (op (e1) (e3)))) -> (((op (e0) (e3)) = (e1))\/(((op (e1) (e3)) = (e1))\/(((op (e2) (e3)) = (e1))\/((op (e3) (e3)) = (e1))))) -> (~((op (e2) (e0)) = (op (e2) (e3)))) -> (((op (e0) (e0)) = (e1))\/(((op (e1) (e0)) = (e1))\/(((op (e2) (e0)) = (e1))\/((op (e3) (e0)) = (e1))))) -> ((~((op (e3) (e3)) = (e2)))\/((op (e3) (e2)) = (e3))) -> (~((op (e0) (e0)) = (e1))) -> (((op (e0) (e0)) = (e3))\/(((op (e0) (e1)) = (e3))\/(((op (e0) (e2)) = (e3))\/((op (e0) (e3)) = (e3))))) -> ((op (e3) (e3)) = (e3)) -> (~((op (e0) (e3)) = (op (e3) (e3)))) -> ((op (e0) (e2)) = (e0)) -> (~((e0) = (e3))) -> (~((e1) = (e3))) -> (~((op (e0) (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 (e0) (e0)) = (e2))\/(((op (e0) (e1)) = (e2))\/(((op (e0) (e2)) = (e2))\/((op (e0) (e3)) = (e2))))) -> (~((op (e0) (e1)) = (op (e2) (e1)))) -> (~((op (e2) (e3)) = (op (e3) (e3)))) -> (((op (e2) (e0)) = (e3))\/(((op (e2) (e1)) = (e3))\/(((op (e2) (e2)) = (e3))\/((op (e2) (e3)) = (e3))))) -> (((op (e0) (e0)) = (e3))\/(((op (e1) (e0)) = (e3))\/(((op (e2) (e0)) = (e3))\/((op (e3) (e0)) = (e3))))) -> (~((op (e0) (e2)) = (op (e1) (e2)))) -> (((op (e0) (e0)) = (e2))\/(((op (e1) (e0)) = (e2))\/(((op (e2) (e0)) = (e2))\/((op (e3) (e0)) = (e2))))) -> (~((op (e0) (e1)) = (op (e1) (e1)))) -> (((op (e1) (e0)) = (e3))\/(((op (e1) (e1)) = (e3))\/(((op (e1) (e2)) = (e3))\/((op (e1) (e3)) = (e3))))) -> (~((op (e1) (e3)) = (op (e3) (e3)))) -> (((op (e1) (e1)) = (e0))\/(((op (e1) (e1)) = (e1))\/(((op (e1) (e1)) = (e2))\/((op (e1) (e1)) = (e3))))) -> ((~((op (e2) (e2)) = (e3)))\/((op (e2) (e3)) = (e2))) -> (((op (e1) (e0)) = (e2))\/(((op (e1) (e1)) = (e2))\/(((op (e1) (e2)) = (e2))\/((op (e1) (e3)) = (e2))))) -> (~((e1) = (e2))) -> (((op (e0) (e3)) = (e0))\/(((op (e1) (e3)) = (e0))\/(((op (e2) (e3)) = (e0))\/((op (e3) (e3)) = (e0))))) -> (~((e0) = (e2))) -> (~((op (e0) (e2)) = (op (e0) (e3)))) -> (~((e2) = (e3))) -> (~((op (e3) (e0)) = (op (e3) (e3)))) -> ((~((op (e3) (e3)) = (e0)))\/((op (e3) (e0)) = (e3))) -> (~((op (e3) (e2)) = (op (e3) (e3)))) -> (((op (e0) (e2)) = (e3))\/(((op (e1) (e2)) = (e3))\/(((op (e2) (e2)) = (e3))\/((op (e3) (e2)) = (e3))))) -> (((op (e0) (e3)) = (e2))\/(((op (e1) (e3)) = (e2))\/(((op (e2) (e3)) = (e2))\/((op (e3) (e3)) = (e2))))) -> (~((e0) = (e1))) -> (((op (e1) (e0)) = (e1))\/(((op (e1) (e1)) = (e1))\/(((op (e1) (e2)) = (e1))\/((op (e1) (e3)) = (e1))))) -> (((op (e0) (e0)) = (e1))\/(((op (e0) (e1)) = (e1))\/(((op (e0) (e2)) = (e1))\/((op (e0) (e3)) = (e1))))) -> ((~((op (e2) (e2)) = (e2)))\/((op (e2) (e2)) = (e2))) -> ((~((op (e1) (e1)) = (e3)))\/((op (e1) (e3)) = (e1))) -> ((~((op (e2) (e2)) = (e1)))\/((op (e2) (e1)) = (e2))) -> (~((op (e2) (e1)) = (op (e2) (e3)))) -> ((~((op (e1) (e1)) = (e1)))\/((op (e1) (e1)) = (e1))) -> (~((op (e0) (e3)) = (op (e1) (e3)))) -> (~((op (e1) (e0)) = (op (e1) (e2)))) -> (~((op (e2) (e1)) = (op (e3) (e1)))) -> (~((op (e0) (e2)) = (op (e3) (e2)))) -> (((op (e3) (e0)) = (e2))\/(((op (e3) (e1)) = (e2))\/(((op (e3) (e2)) = (e2))\/((op (e3) (e3)) = (e2))))) -> (((op (e0) (e0)) = (e0))\/(((op (e0) (e1)) = (e0))\/(((op (e0) (e2)) = (e0))\/((op (e0) (e3)) = (e0))))) -> (~((op (e1) (e1)) = (op (e1) (e3)))) -> (((op (e0) (e0)) = (e0))\/(((op (e0) (e0)) = (e1))\/(((op (e0) (e0)) = (e2))\/((op (e0) (e0)) = (e3))))) -> (((op (e0) (e0)) = (e0))\/(((op (e1) (e0)) = (e0))\/(((op (e2) (e0)) = (e0))\/((op (e3) (e0)) = (e0))))) -> (~((op (e1) (e0)) = (op (e1) (e1)))) -> (~((op (e1) (e1)) = (op (e2) (e1)))) -> (~((op (e0) (e3)) = (op (e2) (e3)))) -> (((op (e2) (e0)) = (e1))\/(((op (e2) (e1)) = (e1))\/(((op (e2) (e2)) = (e1))\/((op (e2) (e3)) = (e1))))) -> (~((op (e0) (e0)) = (e0))) -> (~((op (e1) (e1)) = (op (e1) (e2)))) -> (~((op (e1) (e2)) = (op (e2) (e2)))) -> (~((op (e1) (e2)) = (op (e3) (e2)))) -> (((op (e1) (e2)) = (e0))\/(((op (e1) (e2)) = (e1))\/(((op (e1) (e2)) = (e2))\/((op (e1) (e2)) = (e3))))) -> (((op (e2) (e1)) = (e0))\/(((op (e2) (e1)) = (e1))\/(((op (e2) (e1)) = (e2))\/((op (e2) (e1)) = (e3))))) -> (~((op (e2) (e1)) = (op (e2) (e2)))) -> (~((op (e2) (e0)) = (op (e2) (e1)))) -> (((op (e1) (e0)) = (e0))\/(((op (e1) (e1)) = (e0))\/(((op (e1) (e2)) = (e0))\/((op (e1) (e3)) = (e0))))) -> (~((op (e2) (e2)) = (op (e2) (e3)))) -> False). % 15.16/15.35 do 0 intro. intros zenon_H1e4 zenon_H1d3 zenon_H1d0 zenon_H1d4 zenon_H10c zenon_H12d zenon_H1cd zenon_H1cf zenon_H121 zenon_Hce zenon_Hf1 zenon_H10e zenon_H45 zenon_H58 zenon_H42 zenon_H36 zenon_Hab zenon_H4b zenon_Ha3 zenon_H59 zenon_H2d zenon_H28 zenon_H8e zenon_Hde zenon_He3 zenon_He6 zenon_Hbe zenon_H87 zenon_Heb zenon_H23 zenon_H90 zenon_H8b zenon_H1b3 zenon_H1c3 zenon_H84 zenon_Ha7 zenon_Hd3 zenon_H5e zenon_Hc9 zenon_H6a zenon_Hbb zenon_H10f zenon_H173 zenon_H175 zenon_H160 zenon_H9e zenon_H1c5 zenon_H44 zenon_Haa zenon_H1d2 zenon_H1e3 zenon_H1e2 zenon_H1d8 zenon_H80 zenon_H166 zenon_H13c zenon_H140 zenon_H1df zenon_H110 zenon_H11e zenon_H12a zenon_Hf0 zenon_Hd7 zenon_Hb1 zenon_Hb4 zenon_Hb7 zenon_H20 zenon_H116 zenon_H7d zenon_H17d zenon_H1d5 zenon_H15a zenon_H157 zenon_H154 zenon_H163 zenon_H15f. % 15.16/15.35 apply (zenon_or_s _ _ zenon_H1e4); [ zenon_intro zenon_H145 | zenon_intro zenon_Hd8 ]. % 15.16/15.35 apply (zenon_or_s _ _ zenon_H1d8); [ zenon_intro zenon_H1b4 | zenon_intro zenon_H21 ]. % 15.16/15.35 apply (zenon_L239_); trivial. % 15.16/15.35 apply (zenon_or_s _ _ zenon_H1d3); [ zenon_intro zenon_Hd6 | zenon_intro zenon_H117 ]. % 15.16/15.35 apply (zenon_L258_); trivial. % 15.16/15.35 apply (zenon_L238_); trivial. % 15.16/15.35 apply (zenon_L249_); trivial. % 15.16/15.35 (* end of lemma zenon_L259_ *) % 15.16/15.35 assert (zenon_L260_ : ((~((op (e3) (e3)) = (e3)))\/((op (e3) (e3)) = (e3))) -> (~((op (e2) (e2)) = (op (e2) (e3)))) -> (((op (e1) (e0)) = (e0))\/(((op (e1) (e1)) = (e0))\/(((op (e1) (e2)) = (e0))\/((op (e1) (e3)) = (e0))))) -> (~((op (e2) (e0)) = (op (e2) (e1)))) -> (~((op (e2) (e1)) = (op (e2) (e2)))) -> (((op (e2) (e1)) = (e0))\/(((op (e2) (e1)) = (e1))\/(((op (e2) (e1)) = (e2))\/((op (e2) (e1)) = (e3))))) -> (((op (e1) (e2)) = (e0))\/(((op (e1) (e2)) = (e1))\/(((op (e1) (e2)) = (e2))\/((op (e1) (e2)) = (e3))))) -> (~((op (e1) (e2)) = (op (e3) (e2)))) -> (~((op (e1) (e2)) = (op (e2) (e2)))) -> (~((op (e1) (e1)) = (op (e1) (e2)))) -> (~((op (e0) (e0)) = (e0))) -> (((op (e2) (e0)) = (e1))\/(((op (e2) (e1)) = (e1))\/(((op (e2) (e2)) = (e1))\/((op (e2) (e3)) = (e1))))) -> (~((op (e0) (e3)) = (op (e2) (e3)))) -> (~((op (e1) (e1)) = (op (e2) (e1)))) -> (~((op (e1) (e0)) = (op (e1) (e1)))) -> (((op (e0) (e0)) = (e0))\/(((op (e1) (e0)) = (e0))\/(((op (e2) (e0)) = (e0))\/((op (e3) (e0)) = (e0))))) -> (((op (e0) (e0)) = (e0))\/(((op (e0) (e0)) = (e1))\/(((op (e0) (e0)) = (e2))\/((op (e0) (e0)) = (e3))))) -> (~((op (e1) (e1)) = (op (e1) (e3)))) -> (((op (e0) (e0)) = (e0))\/(((op (e0) (e1)) = (e0))\/(((op (e0) (e2)) = (e0))\/((op (e0) (e3)) = (e0))))) -> (((op (e3) (e0)) = (e2))\/(((op (e3) (e1)) = (e2))\/(((op (e3) (e2)) = (e2))\/((op (e3) (e3)) = (e2))))) -> (~((op (e0) (e2)) = (op (e3) (e2)))) -> (~((op (e2) (e1)) = (op (e3) (e1)))) -> (~((op (e1) (e0)) = (op (e1) (e2)))) -> (~((op (e0) (e3)) = (op (e1) (e3)))) -> ((~((op (e1) (e1)) = (e1)))\/((op (e1) (e1)) = (e1))) -> (~((op (e2) (e1)) = (op (e2) (e3)))) -> ((~((op (e2) (e2)) = (e1)))\/((op (e2) (e1)) = (e2))) -> ((~((op (e1) (e1)) = (e3)))\/((op (e1) (e3)) = (e1))) -> ((~((op (e2) (e2)) = (e2)))\/((op (e2) (e2)) = (e2))) -> (((op (e1) (e0)) = (e1))\/(((op (e1) (e1)) = (e1))\/(((op (e1) (e2)) = (e1))\/((op (e1) (e3)) = (e1))))) -> (((op (e0) (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) (e2)) = (op (e3) (e3)))) -> ((~((op (e3) (e3)) = (e0)))\/((op (e3) (e0)) = (e3))) -> (~((op (e3) (e0)) = (op (e3) (e3)))) -> (~((e2) = (e3))) -> (~((op (e0) (e2)) = (op (e0) (e3)))) -> (~((e0) = (e2))) -> (((op (e0) (e3)) = (e0))\/(((op (e1) (e3)) = (e0))\/(((op (e2) (e3)) = (e0))\/((op (e3) (e3)) = (e0))))) -> (~((e1) = (e2))) -> (((op (e1) (e0)) = (e2))\/(((op (e1) (e1)) = (e2))\/(((op (e1) (e2)) = (e2))\/((op (e1) (e3)) = (e2))))) -> ((~((op (e2) (e2)) = (e3)))\/((op (e2) (e3)) = (e2))) -> (((op (e1) (e1)) = (e0))\/(((op (e1) (e1)) = (e1))\/(((op (e1) (e1)) = (e2))\/((op (e1) (e1)) = (e3))))) -> (~((op (e1) (e3)) = (op (e3) (e3)))) -> (((op (e1) (e0)) = (e3))\/(((op (e1) (e1)) = (e3))\/(((op (e1) (e2)) = (e3))\/((op (e1) (e3)) = (e3))))) -> (((op (e0) (e0)) = (e2))\/(((op (e1) (e0)) = (e2))\/(((op (e2) (e0)) = (e2))\/((op (e3) (e0)) = (e2))))) -> (~((op (e0) (e2)) = (op (e1) (e2)))) -> (((op (e0) (e0)) = (e3))\/(((op (e1) (e0)) = (e3))\/(((op (e2) (e0)) = (e3))\/((op (e3) (e0)) = (e3))))) -> (((op (e2) (e0)) = (e3))\/(((op (e2) (e1)) = (e3))\/(((op (e2) (e2)) = (e3))\/((op (e2) (e3)) = (e3))))) -> (~((op (e2) (e3)) = (op (e3) (e3)))) -> (~((op (e0) (e1)) = (op (e2) (e1)))) -> (((op (e0) (e0)) = (e2))\/(((op (e0) (e1)) = (e2))\/(((op (e0) (e2)) = (e2))\/((op (e0) (e3)) = (e2))))) -> (~((op (e0) (e2)) = (op (e2) (e2)))) -> (((op (e2) (e2)) = (e0))\/(((op (e2) (e2)) = (e1))\/(((op (e2) (e2)) = (e2))\/((op (e2) (e2)) = (e3))))) -> (~((op (e0) (e0)) = (e3))) -> (~((e1) = (e3))) -> (~((e0) = (e3))) -> (((op (e0) (e0)) = (e3))\/(((op (e0) (e1)) = (e3))\/(((op (e0) (e2)) = (e3))\/((op (e0) (e3)) = (e3))))) -> ((~((op (e3) (e3)) = (e2)))\/((op (e3) (e2)) = (e3))) -> (((op (e0) (e0)) = (e1))\/(((op (e1) (e0)) = (e1))\/(((op (e2) (e0)) = (e1))\/((op (e3) (e0)) = (e1))))) -> (~((op (e2) (e0)) = (op (e2) (e3)))) -> (((op (e0) (e3)) = (e1))\/(((op (e1) (e3)) = (e1))\/(((op (e2) (e3)) = (e1))\/((op (e3) (e3)) = (e1))))) -> (~((op (e1) (e0)) = (op (e1) (e3)))) -> (~((op (e0) (e1)) = (op (e0) (e3)))) -> (~((op (e3) (e1)) = (op (e3) (e3)))) -> ((~((op (e3) (e3)) = (e1)))\/((op (e3) (e1)) = (e3))) -> ((~((op (e2) (e2)) = (e0)))\/((op (e2) (e0)) = (e2))) -> (~((op (e1) (e2)) = (op (e1) (e3)))) -> ((~((op (e1) (e1)) = (e2)))\/((op (e1) (e2)) = (e1))) -> ((~((op (e1) (e1)) = (e0)))\/((op (e1) (e0)) = (e1))) -> (~((op (e0) (e0)) = (e1))) -> (~((op (e0) (e1)) = (op (e1) (e1)))) -> ((op (e1) (e1)) = (e1)) -> (~((e0) = (e1))) -> ((op (e0) (e2)) = (e0)) -> (((op (e3) (e3)) = (e0))\/(((op (e3) (e3)) = (e1))\/(((op (e3) (e3)) = (e2))\/((op (e3) (e3)) = (e3))))) -> (~((op (e3) (e3)) = (e2))) -> (~((op (e0) (e3)) = (op (e3) (e3)))) -> (~((op (e3) (e3)) = (e0))) -> (((op (e0) (e0)) = (e1))\/(((op (e0) (e1)) = (e1))\/(((op (e0) (e2)) = (e1))\/((op (e0) (e3)) = (e1))))) -> False). % 15.16/15.35 do 0 intro. intros zenon_H10d zenon_H15f zenon_H163 zenon_H154 zenon_H157 zenon_H15a zenon_H1d5 zenon_H17d zenon_H7d zenon_H116 zenon_H20 zenon_Hb7 zenon_Hb4 zenon_Hb1 zenon_Hd7 zenon_Hf0 zenon_H12a zenon_H11e zenon_H110 zenon_H1df zenon_H140 zenon_H13c zenon_H166 zenon_H80 zenon_H1d8 zenon_H1e2 zenon_H1e3 zenon_H1d2 zenon_Haa zenon_H1c5 zenon_H160 zenon_H175 zenon_H173 zenon_H10f zenon_Hbb zenon_H6a zenon_Hc9 zenon_H5e zenon_Hd3 zenon_Ha7 zenon_H84 zenon_H1c3 zenon_H1b3 zenon_H8b zenon_H90 zenon_Heb zenon_H87 zenon_Hbe zenon_He6 zenon_He3 zenon_Hde zenon_H8e zenon_H28 zenon_H2d zenon_H59 zenon_Ha3 zenon_H4b zenon_H58 zenon_H10e zenon_Hf1 zenon_Hce zenon_H121 zenon_H1cf zenon_H1cd zenon_H12d zenon_H10c zenon_H1d4 zenon_H1d0 zenon_H1d3 zenon_H1e4 zenon_H45 zenon_H23 zenon_H21 zenon_H9e zenon_Hab zenon_H3b zenon_H3d zenon_H36 zenon_H3c zenon_H44. % 15.16/15.35 apply (zenon_or_s _ _ zenon_H10d); [ zenon_intro zenon_H3e | zenon_intro zenon_H42 ]. % 15.16/15.35 apply (zenon_L132_); trivial. % 15.16/15.35 apply (zenon_L259_); trivial. % 15.16/15.35 (* end of lemma zenon_L260_ *) % 15.16/15.35 assert (zenon_L261_ : ((op (e3) (e0)) = (e3)) -> ((op (e2) (e0)) = (e3)) -> (~((op (e2) (e0)) = (op (e3) (e0)))) -> False). % 15.16/15.35 do 0 intro. intros zenon_Hba zenon_Haf zenon_H1e5. % 15.16/15.35 elim (classic ((op (e3) (e0)) = (op (e3) (e0)))); [ zenon_intro zenon_H1e6 | zenon_intro zenon_H108 ]. % 15.16/15.35 cut (((op (e3) (e0)) = (op (e3) (e0))) = ((op (e2) (e0)) = (op (e3) (e0)))). % 15.16/15.35 intro zenon_D_pnotp. % 15.16/15.35 apply zenon_H1e5. % 15.16/15.35 rewrite <- zenon_D_pnotp. % 15.16/15.35 exact zenon_H1e6. % 15.16/15.35 cut (((op (e3) (e0)) = (op (e3) (e0)))); [idtac | apply NNPP; zenon_intro zenon_H108]. % 15.16/15.35 cut (((op (e3) (e0)) = (op (e2) (e0)))); [idtac | apply NNPP; zenon_intro zenon_H1e7]. % 15.16/15.35 congruence. % 15.16/15.35 cut (((op (e3) (e0)) = (e3)) = ((op (e3) (e0)) = (op (e2) (e0)))). % 15.16/15.35 intro zenon_D_pnotp. % 15.16/15.35 apply zenon_H1e7. % 15.16/15.35 rewrite <- zenon_D_pnotp. % 15.16/15.35 exact zenon_Hba. % 15.16/15.35 cut (((e3) = (op (e2) (e0)))); [idtac | apply NNPP; zenon_intro zenon_H1e8]. % 15.16/15.35 cut (((op (e3) (e0)) = (op (e3) (e0)))); [idtac | apply NNPP; zenon_intro zenon_H108]. % 15.16/15.35 congruence. % 15.16/15.35 apply zenon_H108. apply refl_equal. % 15.16/15.35 apply zenon_H1e8. apply sym_equal. exact zenon_Haf. % 15.16/15.35 apply zenon_H108. apply refl_equal. % 15.16/15.35 apply zenon_H108. apply refl_equal. % 15.16/15.35 (* end of lemma zenon_L261_ *) % 15.16/15.35 assert (zenon_L262_ : (((op (e0) (e1)) = (e0))\/(((op (e0) (e1)) = (e1))\/(((op (e0) (e1)) = (e2))\/((op (e0) (e1)) = (e3))))) -> ((op (e2) (e1)) = (e0)) -> (~((op (e0) (e1)) = (op (e1) (e1)))) -> ((op (e1) (e1)) = (e1)) -> ((op (e3) (e1)) = (e2)) -> (~((op (e0) (e1)) = (op (e3) (e1)))) -> (~((op (e0) (e1)) = (op (e2) (e1)))) -> ((op (e2) (e1)) = (e3)) -> False). % 15.16/15.35 do 0 intro. intros zenon_H1e9 zenon_H14a zenon_H23 zenon_H21 zenon_H16a zenon_H138 zenon_Hde zenon_Hdf. % 15.16/15.35 apply (zenon_or_s _ _ zenon_H1e9); [ zenon_intro zenon_H49 | zenon_intro zenon_H1ea ]. % 15.16/15.35 apply (zenon_L180_); trivial. % 15.16/15.35 apply (zenon_or_s _ _ zenon_H1ea); [ zenon_intro zenon_H22 | zenon_intro zenon_H1eb ]. % 15.16/15.35 apply (zenon_L3_); trivial. % 15.16/15.35 apply (zenon_or_s _ _ zenon_H1eb); [ zenon_intro zenon_H5d | zenon_intro zenon_H4a ]. % 15.16/15.35 apply (zenon_L146_); trivial. % 15.16/15.35 apply (zenon_L65_); trivial. % 15.16/15.35 (* end of lemma zenon_L262_ *) % 15.16/15.35 assert (zenon_L263_ : (((op (e0) (e3)) = (e2))\/(((op (e1) (e3)) = (e2))\/(((op (e2) (e3)) = (e2))\/((op (e3) (e3)) = (e2))))) -> (~((e1) = (e2))) -> ((op (e0) (e3)) = (e1)) -> (~((e0) = (e2))) -> ((op (e1) (e3)) = (e0)) -> (~((e2) = (e3))) -> ((op (e2) (e3)) = (e3)) -> (~((op (e3) (e3)) = (e2))) -> False). % 15.16/15.35 do 0 intro. intros zenon_H160 zenon_Ha7 zenon_H37 zenon_H5e zenon_Hcc zenon_H6a zenon_He2 zenon_H3d. % 15.16/15.35 apply (zenon_or_s _ _ zenon_H160); [ zenon_intro zenon_H81 | zenon_intro zenon_H161 ]. % 15.16/15.35 apply (zenon_L33_); trivial. % 15.16/15.35 apply (zenon_or_s _ _ zenon_H161); [ zenon_intro zenon_H82 | zenon_intro zenon_H162 ]. % 15.16/15.35 apply (zenon_L54_); trivial. % 15.16/15.35 apply (zenon_or_s _ _ zenon_H162); [ zenon_intro zenon_H124 | zenon_intro zenon_H43 ]. % 15.16/15.35 apply (zenon_L98_); trivial. % 15.16/15.35 exact (zenon_H3d zenon_H43). % 15.16/15.35 (* end of lemma zenon_L263_ *) % 15.16/15.35 assert (zenon_L264_ : (((op (e3) (e3)) = (e0))\/(((op (e3) (e3)) = (e1))\/(((op (e3) (e3)) = (e2))\/((op (e3) (e3)) = (e3))))) -> ((op (e2) (e3)) = (e0)) -> (~((op (e2) (e3)) = (op (e3) (e3)))) -> (~((op (e3) (e3)) = (e1))) -> (~((op (e3) (e3)) = (e2))) -> (~((op (e3) (e3)) = (e3))) -> False). % 15.16/15.35 do 0 intro. intros zenon_H3b zenon_Hd0 zenon_He3 zenon_H104 zenon_H3d zenon_H3e. % 15.16/15.35 apply (zenon_or_s _ _ zenon_H3b); [ zenon_intro zenon_H40 | zenon_intro zenon_H3f ]. % 15.16/15.35 cut (((op (e2) (e3)) = (e0)) = ((op (e2) (e3)) = (op (e3) (e3)))). % 15.16/15.35 intro zenon_D_pnotp. % 15.16/15.35 apply zenon_He3. % 15.16/15.35 rewrite <- zenon_D_pnotp. % 15.16/15.35 exact zenon_Hd0. % 15.16/15.35 cut (((e0) = (op (e3) (e3)))); [idtac | apply NNPP; zenon_intro zenon_H1a0]. % 15.16/15.35 cut (((op (e2) (e3)) = (op (e2) (e3)))); [idtac | apply NNPP; zenon_intro zenon_H1ec]. % 15.16/15.35 congruence. % 15.16/15.35 apply zenon_H1ec. apply refl_equal. % 15.16/15.35 apply zenon_H1a0. apply sym_equal. exact zenon_H40. % 15.16/15.35 apply (zenon_or_s _ _ zenon_H3f); [ zenon_intro zenon_H38 | zenon_intro zenon_H41 ]. % 15.16/15.35 exact (zenon_H104 zenon_H38). % 15.16/15.35 apply (zenon_or_s _ _ zenon_H41); [ zenon_intro zenon_H43 | zenon_intro zenon_H42 ]. % 15.16/15.35 exact (zenon_H3d zenon_H43). % 15.16/15.35 exact (zenon_H3e zenon_H42). % 15.16/15.35 (* end of lemma zenon_L264_ *) % 15.16/15.35 assert (zenon_L265_ : ((op (e3) (e2)) = (e1)) -> ((op (e0) (e0)) = (e2)) -> ((op (e3) (e3)) = (e0)) -> False). % 15.16/15.35 do 0 intro. intros zenon_H119 zenon_H92 zenon_H40. % 15.16/15.35 apply (zenon_notand_s _ _ ax18); [ zenon_intro zenon_H1ee | zenon_intro zenon_H1ed ]. % 15.16/15.35 elim (classic ((op (op (e3) (e3)) (op (e3) (e3))) = (op (op (e3) (e3)) (op (e3) (e3))))); [ zenon_intro zenon_H186 | zenon_intro zenon_H187 ]. % 15.16/15.35 cut (((op (op (e3) (e3)) (op (e3) (e3))) = (op (op (e3) (e3)) (op (e3) (e3)))) = ((e2) = (op (op (e3) (e3)) (op (e3) (e3))))). % 15.16/15.35 intro zenon_D_pnotp. % 15.16/15.35 apply zenon_H1ee. % 15.16/15.35 rewrite <- zenon_D_pnotp. % 15.16/15.35 exact zenon_H186. % 15.16/15.35 cut (((op (op (e3) (e3)) (op (e3) (e3))) = (op (op (e3) (e3)) (op (e3) (e3))))); [idtac | apply NNPP; zenon_intro zenon_H187]. % 15.16/15.35 cut (((op (op (e3) (e3)) (op (e3) (e3))) = (e2))); [idtac | apply NNPP; zenon_intro zenon_H1ef]. % 15.16/15.35 congruence. % 15.16/15.35 cut (((op (e0) (e0)) = (e2)) = ((op (op (e3) (e3)) (op (e3) (e3))) = (e2))). % 15.16/15.35 intro zenon_D_pnotp. % 15.16/15.35 apply zenon_H1ef. % 15.16/15.35 rewrite <- zenon_D_pnotp. % 15.16/15.35 exact zenon_H92. % 15.16/15.35 cut (((e2) = (e2))); [idtac | apply NNPP; zenon_intro zenon_H60]. % 15.16/15.35 cut (((op (e0) (e0)) = (op (op (e3) (e3)) (op (e3) (e3))))); [idtac | apply NNPP; zenon_intro zenon_H19e]. % 15.16/15.35 congruence. % 15.16/15.35 elim (classic ((op (op (e3) (e3)) (op (e3) (e3))) = (op (op (e3) (e3)) (op (e3) (e3))))); [ zenon_intro zenon_H186 | zenon_intro zenon_H187 ]. % 15.16/15.35 cut (((op (op (e3) (e3)) (op (e3) (e3))) = (op (op (e3) (e3)) (op (e3) (e3)))) = ((op (e0) (e0)) = (op (op (e3) (e3)) (op (e3) (e3))))). % 15.16/15.35 intro zenon_D_pnotp. % 15.16/15.35 apply zenon_H19e. % 15.16/15.35 rewrite <- zenon_D_pnotp. % 15.16/15.35 exact zenon_H186. % 15.16/15.35 cut (((op (op (e3) (e3)) (op (e3) (e3))) = (op (op (e3) (e3)) (op (e3) (e3))))); [idtac | apply NNPP; zenon_intro zenon_H187]. % 15.16/15.36 cut (((op (op (e3) (e3)) (op (e3) (e3))) = (op (e0) (e0)))); [idtac | apply NNPP; zenon_intro zenon_H19c]. % 15.16/15.36 congruence. % 15.16/15.36 apply (zenon_L185_); trivial. % 15.16/15.36 apply zenon_H187. apply refl_equal. % 15.16/15.36 apply zenon_H187. apply refl_equal. % 15.16/15.36 apply zenon_H60. apply refl_equal. % 15.16/15.36 apply zenon_H187. apply refl_equal. % 15.16/15.36 apply zenon_H187. apply refl_equal. % 15.16/15.36 apply (zenon_notand_s _ _ zenon_H1ed); [ zenon_intro zenon_H1a0 | zenon_intro zenon_H1f0 ]. % 15.16/15.36 apply zenon_H1a0. apply sym_equal. exact zenon_H40. % 15.16/15.36 elim (classic ((op (e3) (op (op (e3) (e3)) (op (e3) (e3)))) = (op (e3) (op (op (e3) (e3)) (op (e3) (e3)))))); [ zenon_intro zenon_H18b | zenon_intro zenon_H18c ]. % 15.16/15.36 cut (((op (e3) (op (op (e3) (e3)) (op (e3) (e3)))) = (op (e3) (op (op (e3) (e3)) (op (e3) (e3))))) = ((e1) = (op (e3) (op (op (e3) (e3)) (op (e3) (e3)))))). % 15.16/15.36 intro zenon_D_pnotp. % 15.16/15.36 apply zenon_H1f0. % 15.16/15.36 rewrite <- zenon_D_pnotp. % 15.16/15.36 exact zenon_H18b. % 15.16/15.36 cut (((op (e3) (op (op (e3) (e3)) (op (e3) (e3)))) = (op (e3) (op (op (e3) (e3)) (op (e3) (e3)))))); [idtac | apply NNPP; zenon_intro zenon_H18c]. % 15.16/15.36 cut (((op (e3) (op (op (e3) (e3)) (op (e3) (e3)))) = (e1))); [idtac | apply NNPP; zenon_intro zenon_H1f1]. % 15.16/15.36 congruence. % 15.16/15.36 cut (((op (e3) (e2)) = (e1)) = ((op (e3) (op (op (e3) (e3)) (op (e3) (e3)))) = (e1))). % 15.16/15.36 intro zenon_D_pnotp. % 15.16/15.36 apply zenon_H1f1. % 15.16/15.36 rewrite <- zenon_D_pnotp. % 15.16/15.36 exact zenon_H119. % 15.16/15.36 cut (((e1) = (e1))); [idtac | apply NNPP; zenon_intro zenon_Ha0]. % 15.16/15.36 cut (((op (e3) (e2)) = (op (e3) (op (op (e3) (e3)) (op (e3) (e3)))))); [idtac | apply NNPP; zenon_intro zenon_H1f2]. % 15.16/15.36 congruence. % 15.16/15.36 elim (classic ((op (e3) (op (op (e3) (e3)) (op (e3) (e3)))) = (op (e3) (op (op (e3) (e3)) (op (e3) (e3)))))); [ zenon_intro zenon_H18b | zenon_intro zenon_H18c ]. % 15.16/15.36 cut (((op (e3) (op (op (e3) (e3)) (op (e3) (e3)))) = (op (e3) (op (op (e3) (e3)) (op (e3) (e3))))) = ((op (e3) (e2)) = (op (e3) (op (op (e3) (e3)) (op (e3) (e3)))))). % 15.16/15.36 intro zenon_D_pnotp. % 15.16/15.36 apply zenon_H1f2. % 15.16/15.36 rewrite <- zenon_D_pnotp. % 15.16/15.36 exact zenon_H18b. % 15.16/15.36 cut (((op (e3) (op (op (e3) (e3)) (op (e3) (e3)))) = (op (e3) (op (op (e3) (e3)) (op (e3) (e3)))))); [idtac | apply NNPP; zenon_intro zenon_H18c]. % 15.16/15.36 cut (((op (e3) (op (op (e3) (e3)) (op (e3) (e3)))) = (op (e3) (e2)))); [idtac | apply NNPP; zenon_intro zenon_H1f3]. % 15.16/15.36 congruence. % 15.16/15.36 cut (((op (op (e3) (e3)) (op (e3) (e3))) = (e2))); [idtac | apply NNPP; zenon_intro zenon_H1ef]. % 15.16/15.36 cut (((e3) = (e3))); [idtac | apply NNPP; zenon_intro zenon_H4d]. % 15.16/15.36 congruence. % 15.16/15.36 apply zenon_H4d. apply refl_equal. % 15.16/15.36 cut (((op (e0) (e0)) = (e2)) = ((op (op (e3) (e3)) (op (e3) (e3))) = (e2))). % 15.16/15.36 intro zenon_D_pnotp. % 15.16/15.36 apply zenon_H1ef. % 15.16/15.36 rewrite <- zenon_D_pnotp. % 15.16/15.36 exact zenon_H92. % 15.16/15.36 cut (((e2) = (e2))); [idtac | apply NNPP; zenon_intro zenon_H60]. % 15.16/15.36 cut (((op (e0) (e0)) = (op (op (e3) (e3)) (op (e3) (e3))))); [idtac | apply NNPP; zenon_intro zenon_H19e]. % 15.16/15.36 congruence. % 15.16/15.36 elim (classic ((op (op (e3) (e3)) (op (e3) (e3))) = (op (op (e3) (e3)) (op (e3) (e3))))); [ zenon_intro zenon_H186 | zenon_intro zenon_H187 ]. % 15.16/15.36 cut (((op (op (e3) (e3)) (op (e3) (e3))) = (op (op (e3) (e3)) (op (e3) (e3)))) = ((op (e0) (e0)) = (op (op (e3) (e3)) (op (e3) (e3))))). % 15.16/15.36 intro zenon_D_pnotp. % 15.16/15.36 apply zenon_H19e. % 15.16/15.36 rewrite <- zenon_D_pnotp. % 15.16/15.36 exact zenon_H186. % 15.16/15.36 cut (((op (op (e3) (e3)) (op (e3) (e3))) = (op (op (e3) (e3)) (op (e3) (e3))))); [idtac | apply NNPP; zenon_intro zenon_H187]. % 15.16/15.36 cut (((op (op (e3) (e3)) (op (e3) (e3))) = (op (e0) (e0)))); [idtac | apply NNPP; zenon_intro zenon_H19c]. % 15.16/15.36 congruence. % 15.16/15.36 apply (zenon_L185_); trivial. % 15.16/15.36 apply zenon_H187. apply refl_equal. % 15.16/15.36 apply zenon_H187. apply refl_equal. % 15.16/15.36 apply zenon_H60. apply refl_equal. % 15.16/15.36 apply zenon_H18c. apply refl_equal. % 15.16/15.36 apply zenon_H18c. apply refl_equal. % 15.16/15.36 apply zenon_Ha0. apply refl_equal. % 15.16/15.36 apply zenon_H18c. apply refl_equal. % 15.16/15.36 apply zenon_H18c. apply refl_equal. % 15.16/15.36 (* end of lemma zenon_L265_ *) % 15.16/15.36 assert (zenon_L266_ : (((op (e0) (e3)) = (e0))\/(((op (e1) (e3)) = (e0))\/(((op (e2) (e3)) = (e0))\/((op (e3) (e3)) = (e0))))) -> ((op (e3) (e1)) = (e0)) -> (~((op (e3) (e1)) = (op (e3) (e2)))) -> (~((op (e2) (e2)) = (e0))) -> ((op (e1) (e2)) = (e3)) -> (~((e0) = (e3))) -> (~((op (e0) (e2)) = (op (e0) (e3)))) -> (((op (e0) (e2)) = (e0))\/(((op (e1) (e2)) = (e0))\/(((op (e2) (e2)) = (e0))\/((op (e3) (e2)) = (e0))))) -> ((op (e2) (e3)) = (e3)) -> (~((e2) = (e3))) -> (~((e0) = (e2))) -> ((op (e0) (e3)) = (e1)) -> (~((e1) = (e2))) -> (((op (e0) (e3)) = (e2))\/(((op (e1) (e3)) = (e2))\/(((op (e2) (e3)) = (e2))\/((op (e3) (e3)) = (e2))))) -> (~((op (e3) (e3)) = (e3))) -> (~((op (e3) (e3)) = (e2))) -> (~((op (e3) (e3)) = (e1))) -> (~((op (e2) (e3)) = (op (e3) (e3)))) -> (((op (e3) (e3)) = (e0))\/(((op (e3) (e3)) = (e1))\/(((op (e3) (e3)) = (e2))\/((op (e3) (e3)) = (e3))))) -> ((op (e3) (e2)) = (e1)) -> ((op (e0) (e0)) = (e2)) -> False). % 15.16/15.36 do 0 intro. intros zenon_Hd3 zenon_H142 zenon_H135 zenon_H2e zenon_H88 zenon_H4b zenon_Hc9 zenon_H16f zenon_He2 zenon_H6a zenon_H5e zenon_H37 zenon_Ha7 zenon_H160 zenon_H3e zenon_H3d zenon_H104 zenon_He3 zenon_H3b zenon_H119 zenon_H92. % 15.16/15.36 apply (zenon_or_s _ _ zenon_Hd3); [ zenon_intro zenon_Hca | zenon_intro zenon_Hd4 ]. % 15.16/15.36 apply (zenon_L169_); trivial. % 15.16/15.36 apply (zenon_or_s _ _ zenon_Hd4); [ zenon_intro zenon_Hcc | zenon_intro zenon_Hd5 ]. % 15.16/15.36 apply (zenon_L263_); trivial. % 15.16/15.36 apply (zenon_or_s _ _ zenon_Hd5); [ zenon_intro zenon_Hd0 | zenon_intro zenon_H40 ]. % 15.16/15.36 apply (zenon_L264_); trivial. % 15.16/15.36 apply (zenon_L265_); trivial. % 15.16/15.36 (* end of lemma zenon_L266_ *) % 15.16/15.36 assert (zenon_L267_ : (~((op (e0) (e2)) = (op (e3) (e2)))) -> ((op (e0) (e2)) = (e0)) -> ((op (e3) (e2)) = (e0)) -> False). % 15.16/15.36 do 0 intro. intros zenon_H140 zenon_Hab zenon_H167. % 15.16/15.36 cut (((op (e0) (e2)) = (e0)) = ((op (e0) (e2)) = (op (e3) (e2)))). % 15.16/15.36 intro zenon_D_pnotp. % 15.16/15.36 apply zenon_H140. % 15.16/15.36 rewrite <- zenon_D_pnotp. % 15.16/15.36 exact zenon_Hab. % 15.16/15.36 cut (((e0) = (op (e3) (e2)))); [idtac | apply NNPP; zenon_intro zenon_H168]. % 15.16/15.36 cut (((op (e0) (e2)) = (op (e0) (e2)))); [idtac | apply NNPP; zenon_intro zenon_H2c]. % 15.16/15.36 congruence. % 15.16/15.36 apply zenon_H2c. apply refl_equal. % 15.16/15.36 apply zenon_H168. apply sym_equal. exact zenon_H167. % 15.16/15.36 (* end of lemma zenon_L267_ *) % 15.16/15.36 assert (zenon_L268_ : (((op (e0) (e2)) = (e0))\/(((op (e1) (e2)) = (e0))\/(((op (e2) (e2)) = (e0))\/((op (e3) (e2)) = (e0))))) -> (~((e0) = (e1))) -> ((op (e0) (e2)) = (e1)) -> (~((e0) = (e3))) -> ((op (e1) (e2)) = (e3)) -> (~((op (e2) (e2)) = (e0))) -> (~((op (e3) (e1)) = (op (e3) (e2)))) -> ((op (e3) (e1)) = (e0)) -> False). % 15.16/15.36 do 0 intro. intros zenon_H16f zenon_H9e zenon_H29 zenon_H4b zenon_H88 zenon_H2e zenon_H135 zenon_H142. % 15.16/15.36 apply (zenon_or_s _ _ zenon_H16f); [ zenon_intro zenon_Hab | zenon_intro zenon_H170 ]. % 15.16/15.36 apply (zenon_L37_); trivial. % 15.16/15.36 apply (zenon_or_s _ _ zenon_H170); [ zenon_intro zenon_H15d | zenon_intro zenon_H171 ]. % 15.16/15.36 apply (zenon_L152_); trivial. % 15.16/15.36 apply (zenon_or_s _ _ zenon_H171); [ zenon_intro zenon_H32 | zenon_intro zenon_H167 ]. % 15.16/15.36 exact (zenon_H2e zenon_H32). % 15.16/15.36 apply (zenon_L144_); trivial. % 15.16/15.36 (* end of lemma zenon_L268_ *) % 15.16/15.36 assert (zenon_L269_ : ((op (e2) (e0)) = (e0)) -> ((op (e2) (e0)) = (e1)) -> (~((e0) = (e1))) -> False). % 15.16/15.36 do 0 intro. intros zenon_Hcf zenon_Hae zenon_H9e. % 15.16/15.36 elim (classic ((e1) = (e1))); [ zenon_intro zenon_H9f | zenon_intro zenon_Ha0 ]. % 15.16/15.36 cut (((e1) = (e1)) = ((e0) = (e1))). % 15.16/15.36 intro zenon_D_pnotp. % 15.16/15.36 apply zenon_H9e. % 15.16/15.36 rewrite <- zenon_D_pnotp. % 15.16/15.36 exact zenon_H9f. % 15.16/15.36 cut (((e1) = (e1))); [idtac | apply NNPP; zenon_intro zenon_Ha0]. % 15.16/15.36 cut (((e1) = (e0))); [idtac | apply NNPP; zenon_intro zenon_Ha1]. % 15.16/15.36 congruence. % 15.16/15.36 cut (((op (e2) (e0)) = (e0)) = ((e1) = (e0))). % 15.16/15.36 intro zenon_D_pnotp. % 15.16/15.36 apply zenon_Ha1. % 15.16/15.36 rewrite <- zenon_D_pnotp. % 15.16/15.36 exact zenon_Hcf. % 15.16/15.36 cut (((e0) = (e0))); [idtac | apply NNPP; zenon_intro zenon_H1d]. % 15.16/15.36 cut (((op (e2) (e0)) = (e1))); [idtac | apply NNPP; zenon_intro zenon_H1f4]. % 15.16/15.36 congruence. % 15.16/15.36 exact (zenon_H1f4 zenon_Hae). % 15.16/15.36 apply zenon_H1d. apply refl_equal. % 15.16/15.36 apply zenon_Ha0. apply refl_equal. % 15.16/15.36 apply zenon_Ha0. apply refl_equal. % 15.16/15.36 (* end of lemma zenon_L269_ *) % 15.16/15.36 assert (zenon_L270_ : (((op (e0) (e0)) = (e1))\/(((op (e1) (e0)) = (e1))\/(((op (e2) (e0)) = (e1))\/((op (e3) (e0)) = (e1))))) -> (~((op (e0) (e0)) = (e1))) -> ((op (e1) (e1)) = (e1)) -> (~((op (e1) (e0)) = (op (e1) (e1)))) -> (~((e0) = (e1))) -> ((op (e2) (e0)) = (e0)) -> (~((e1) = (e3))) -> ((op (e3) (e0)) = (e3)) -> False). % 15.16/15.36 do 0 intro. intros zenon_Hf1 zenon_H45 zenon_H21 zenon_Hd7 zenon_H9e zenon_Hcf zenon_Ha3 zenon_Hba. % 15.16/15.36 apply (zenon_or_s _ _ zenon_Hf1); [ zenon_intro zenon_H47 | zenon_intro zenon_Hf4 ]. % 15.16/15.36 exact (zenon_H45 zenon_H47). % 15.16/15.36 apply (zenon_or_s _ _ zenon_Hf4); [ zenon_intro zenon_Hd8 | zenon_intro zenon_Hf5 ]. % 15.16/15.36 apply (zenon_L61_); trivial. % 15.16/15.36 apply (zenon_or_s _ _ zenon_Hf5); [ zenon_intro zenon_Hae | zenon_intro zenon_Hee ]. % 15.16/15.36 apply (zenon_L269_); trivial. % 15.16/15.36 apply (zenon_L79_); trivial. % 15.16/15.36 (* end of lemma zenon_L270_ *) % 15.16/15.36 assert (zenon_L271_ : ((op (e2) (e2)) = (e2)) -> (((op (e0) (e0)) = (e1))\/(((op (e0) (e1)) = (e1))\/(((op (e0) (e2)) = (e1))\/((op (e0) (e3)) = (e1))))) -> (~((op (e0) (e3)) = (op (e3) (e3)))) -> (((op (e3) (e3)) = (e0))\/(((op (e3) (e3)) = (e1))\/(((op (e3) (e3)) = (e2))\/((op (e3) (e3)) = (e3))))) -> ((op (e0) (e2)) = (e0)) -> (~((e0) = (e1))) -> ((op (e1) (e1)) = (e1)) -> (~((op (e0) (e1)) = (op (e1) (e1)))) -> (~((op (e0) (e0)) = (e1))) -> ((~((op (e1) (e1)) = (e0)))\/((op (e1) (e0)) = (e1))) -> ((~((op (e1) (e1)) = (e2)))\/((op (e1) (e2)) = (e1))) -> (~((op (e1) (e2)) = (op (e1) (e3)))) -> ((~((op (e2) (e2)) = (e0)))\/((op (e2) (e0)) = (e2))) -> ((~((op (e3) (e3)) = (e1)))\/((op (e3) (e1)) = (e3))) -> (~((op (e3) (e1)) = (op (e3) (e3)))) -> (~((op (e0) (e1)) = (op (e0) (e3)))) -> (~((op (e1) (e0)) = (op (e1) (e3)))) -> (((op (e0) (e3)) = (e1))\/(((op (e1) (e3)) = (e1))\/(((op (e2) (e3)) = (e1))\/((op (e3) (e3)) = (e1))))) -> (~((op (e2) (e0)) = (op (e2) (e3)))) -> (((op (e0) (e0)) = (e1))\/(((op (e1) (e0)) = (e1))\/(((op (e2) (e0)) = (e1))\/((op (e3) (e0)) = (e1))))) -> ((~((op (e3) (e3)) = (e2)))\/((op (e3) (e2)) = (e3))) -> (((op (e0) (e0)) = (e3))\/(((op (e0) (e1)) = (e3))\/(((op (e0) (e2)) = (e3))\/((op (e0) (e3)) = (e3))))) -> (~((e0) = (e3))) -> (~((e1) = (e3))) -> (~((op (e0) (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 (e0) (e0)) = (e2))\/(((op (e0) (e1)) = (e2))\/(((op (e0) (e2)) = (e2))\/((op (e0) (e3)) = (e2))))) -> (~((op (e0) (e1)) = (op (e2) (e1)))) -> (~((op (e2) (e3)) = (op (e3) (e3)))) -> (((op (e2) (e0)) = (e3))\/(((op (e2) (e1)) = (e3))\/(((op (e2) (e2)) = (e3))\/((op (e2) (e3)) = (e3))))) -> (((op (e0) (e0)) = (e3))\/(((op (e1) (e0)) = (e3))\/(((op (e2) (e0)) = (e3))\/((op (e3) (e0)) = (e3))))) -> (~((op (e0) (e2)) = (op (e1) (e2)))) -> (((op (e0) (e0)) = (e2))\/(((op (e1) (e0)) = (e2))\/(((op (e2) (e0)) = (e2))\/((op (e3) (e0)) = (e2))))) -> (((op (e1) (e0)) = (e3))\/(((op (e1) (e1)) = (e3))\/(((op (e1) (e2)) = (e3))\/((op (e1) (e3)) = (e3))))) -> (~((op (e1) (e3)) = (op (e3) (e3)))) -> (((op (e1) (e1)) = (e0))\/(((op (e1) (e1)) = (e1))\/(((op (e1) (e1)) = (e2))\/((op (e1) (e1)) = (e3))))) -> ((~((op (e2) (e2)) = (e3)))\/((op (e2) (e3)) = (e2))) -> (((op (e1) (e0)) = (e2))\/(((op (e1) (e1)) = (e2))\/(((op (e1) (e2)) = (e2))\/((op (e1) (e3)) = (e2))))) -> (~((e1) = (e2))) -> (((op (e0) (e3)) = (e0))\/(((op (e1) (e3)) = (e0))\/(((op (e2) (e3)) = (e0))\/((op (e3) (e3)) = (e0))))) -> (~((e0) = (e2))) -> (~((op (e0) (e2)) = (op (e0) (e3)))) -> (~((e2) = (e3))) -> (~((op (e3) (e0)) = (op (e3) (e3)))) -> ((~((op (e3) (e3)) = (e0)))\/((op (e3) (e0)) = (e3))) -> (~((op (e3) (e2)) = (op (e3) (e3)))) -> (((op (e0) (e2)) = (e3))\/(((op (e1) (e2)) = (e3))\/(((op (e2) (e2)) = (e3))\/((op (e3) (e2)) = (e3))))) -> (((op (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 (e2) (e2)) = (e2)))\/((op (e2) (e2)) = (e2))) -> ((~((op (e1) (e1)) = (e3)))\/((op (e1) (e3)) = (e1))) -> ((~((op (e2) (e2)) = (e1)))\/((op (e2) (e1)) = (e2))) -> (~((op (e2) (e1)) = (op (e2) (e3)))) -> ((~((op (e1) (e1)) = (e1)))\/((op (e1) (e1)) = (e1))) -> (~((op (e0) (e3)) = (op (e1) (e3)))) -> (~((op (e1) (e0)) = (op (e1) (e2)))) -> (~((op (e2) (e1)) = (op (e3) (e1)))) -> (~((op (e0) (e2)) = (op (e3) (e2)))) -> (((op (e3) (e0)) = (e2))\/(((op (e3) (e1)) = (e2))\/(((op (e3) (e2)) = (e2))\/((op (e3) (e3)) = (e2))))) -> (((op (e0) (e0)) = (e0))\/(((op (e0) (e1)) = (e0))\/(((op (e0) (e2)) = (e0))\/((op (e0) (e3)) = (e0))))) -> (~((op (e1) (e1)) = (op (e1) (e3)))) -> (((op (e0) (e0)) = (e0))\/(((op (e0) (e0)) = (e1))\/(((op (e0) (e0)) = (e2))\/((op (e0) (e0)) = (e3))))) -> (((op (e0) (e0)) = (e0))\/(((op (e1) (e0)) = (e0))\/(((op (e2) (e0)) = (e0))\/((op (e3) (e0)) = (e0))))) -> (~((op (e1) (e0)) = (op (e1) (e1)))) -> (~((op (e1) (e1)) = (op (e2) (e1)))) -> (~((op (e0) (e3)) = (op (e2) (e3)))) -> (((op (e2) (e0)) = (e1))\/(((op (e2) (e1)) = (e1))\/(((op (e2) (e2)) = (e1))\/((op (e2) (e3)) = (e1))))) -> (~((op (e0) (e0)) = (e0))) -> (~((op (e1) (e1)) = (op (e1) (e2)))) -> (~((op (e1) (e2)) = (op (e2) (e2)))) -> (~((op (e1) (e2)) = (op (e3) (e2)))) -> (((op (e1) (e2)) = (e0))\/(((op (e1) (e2)) = (e1))\/(((op (e1) (e2)) = (e2))\/((op (e1) (e2)) = (e3))))) -> (((op (e2) (e1)) = (e0))\/(((op (e2) (e1)) = (e1))\/(((op (e2) (e1)) = (e2))\/((op (e2) (e1)) = (e3))))) -> (~((op (e2) (e1)) = (op (e2) (e2)))) -> (~((op (e2) (e0)) = (op (e2) (e1)))) -> (((op (e1) (e0)) = (e0))\/(((op (e1) (e1)) = (e0))\/(((op (e1) (e2)) = (e0))\/((op (e1) (e3)) = (e0))))) -> (~((op (e2) (e2)) = (op (e2) (e3)))) -> ((~((op (e3) (e3)) = (e3)))\/((op (e3) (e3)) = (e3))) -> (~((op (e3) (e0)) = (op (e3) (e1)))) -> (((op (e0) (e1)) = (e0))\/(((op (e1) (e1)) = (e0))\/(((op (e2) (e1)) = (e0))\/((op (e3) (e1)) = (e0))))) -> (((op (e2) (e0)) = (e0))\/(((op (e2) (e1)) = (e0))\/(((op (e2) (e2)) = (e0))\/((op (e2) (e3)) = (e0))))) -> (~((op (e1) (e1)) = (e2))) -> (((op (e0) (e1)) = (e2))\/(((op (e1) (e1)) = (e2))\/(((op (e2) (e1)) = (e2))\/((op (e3) (e1)) = (e2))))) -> (~((op (e1) (e1)) = (e3))) -> (((op (e0) (e2)) = (e1))\/(((op (e1) (e2)) = (e1))\/(((op (e2) (e2)) = (e1))\/((op (e3) (e2)) = (e1))))) -> (~((op (e2) (e0)) = (op (e3) (e0)))) -> (((op (e0) (e1)) = (e0))\/(((op (e0) (e1)) = (e1))\/(((op (e0) (e1)) = (e2))\/((op (e0) (e1)) = (e3))))) -> (~((op (e0) (e1)) = (op (e3) (e1)))) -> (((op (e3) (e0)) = (e0))\/(((op (e3) (e1)) = (e0))\/(((op (e3) (e2)) = (e0))\/((op (e3) (e3)) = (e0))))) -> (((op (e0) (e2)) = (e0))\/(((op (e1) (e2)) = (e0))\/(((op (e2) (e2)) = (e0))\/((op (e3) (e2)) = (e0))))) -> (~((op (e3) (e1)) = (op (e3) (e2)))) -> (~((op (e2) (e2)) = (e0))) -> (~((op (e2) (e2)) = (e1))) -> (~((op (e1) (e1)) = (e0))) -> (~((op (e3) (e0)) = (op (e3) (e2)))) -> False). % 15.16/15.36 do 0 intro. intros zenon_H35 zenon_H44 zenon_H36 zenon_H3b zenon_Hab zenon_H9e zenon_H21 zenon_H23 zenon_H45 zenon_H1e4 zenon_H1d3 zenon_H1d0 zenon_H1d4 zenon_H10c zenon_H12d zenon_H1cd zenon_H1cf zenon_H121 zenon_Hce zenon_Hf1 zenon_H10e zenon_H58 zenon_H4b zenon_Ha3 zenon_H59 zenon_H2d zenon_H28 zenon_H8e zenon_Hde zenon_He3 zenon_He6 zenon_Hbe zenon_H87 zenon_Heb zenon_H90 zenon_H8b zenon_H1b3 zenon_H1c3 zenon_H84 zenon_Ha7 zenon_Hd3 zenon_H5e zenon_Hc9 zenon_H6a zenon_Hbb zenon_H10f zenon_H173 zenon_H175 zenon_H160 zenon_H1c5 zenon_Haa zenon_H1d2 zenon_H1e3 zenon_H1e2 zenon_H1d8 zenon_H80 zenon_H166 zenon_H13c zenon_H140 zenon_H1df zenon_H110 zenon_H11e zenon_H12a zenon_Hf0 zenon_Hd7 zenon_Hb1 zenon_Hb4 zenon_Hb7 zenon_H20 zenon_H116 zenon_H7d zenon_H17d zenon_H1d5 zenon_H15a zenon_H157 zenon_H154 zenon_H163 zenon_H15f zenon_H10d zenon_H109 zenon_H144 zenon_H1f5 zenon_Hd6 zenon_H1a2 zenon_H182 zenon_H11b zenon_H1e5 zenon_H1e9 zenon_H138 zenon_H1f6 zenon_H16f zenon_H135 zenon_H2e zenon_H52 zenon_H145 zenon_H105. % 15.16/15.36 apply (zenon_or_s _ _ zenon_H1c3); [ zenon_intro zenon_H30 | zenon_intro zenon_H124 ]. % 15.16/15.36 apply (zenon_or_s _ _ zenon_H10f); [ zenon_intro zenon_H3c | zenon_intro zenon_Hba ]. % 15.16/15.36 apply (zenon_or_s _ _ zenon_H10e); [ zenon_intro zenon_H3d | zenon_intro zenon_H106 ]. % 15.16/15.36 apply (zenon_L260_); trivial. % 15.16/15.36 apply (zenon_L240_); trivial. % 15.16/15.36 apply (zenon_or_s _ _ zenon_H10c); [ zenon_intro zenon_H104 | zenon_intro zenon_H10a ]. % 15.16/15.36 apply (zenon_or_s _ _ zenon_H10e); [ zenon_intro zenon_H3d | zenon_intro zenon_H106 ]. % 15.16/15.36 apply (zenon_or_s _ _ zenon_H10d); [ zenon_intro zenon_H3e | zenon_intro zenon_H42 ]. % 15.16/15.36 apply (zenon_or_s _ _ zenon_Hf0); [ zenon_intro zenon_H1f | zenon_intro zenon_Hf2 ]. % 15.16/15.36 exact (zenon_H20 zenon_H1f). % 15.16/15.36 apply (zenon_or_s _ _ zenon_Hf2); [ zenon_intro zenon_Had | zenon_intro zenon_Hf3 ]. % 15.16/15.36 apply (zenon_or_s _ _ zenon_H44); [ zenon_intro zenon_H47 | zenon_intro zenon_H46 ]. % 15.16/15.36 exact (zenon_H45 zenon_H47). % 15.16/15.36 apply (zenon_or_s _ _ zenon_H46); [ zenon_intro zenon_H22 | zenon_intro zenon_H48 ]. % 15.16/15.36 apply (zenon_L3_); trivial. % 15.16/15.36 apply (zenon_or_s _ _ zenon_H48); [ zenon_intro zenon_H29 | zenon_intro zenon_H37 ]. % 15.16/15.36 apply (zenon_L37_); trivial. % 15.16/15.36 apply (zenon_or_s _ _ zenon_Hf1); [ zenon_intro zenon_H47 | zenon_intro zenon_Hf4 ]. % 15.16/15.36 exact (zenon_H45 zenon_H47). % 15.16/15.36 apply (zenon_or_s _ _ zenon_Hf4); [ zenon_intro zenon_Hd8 | zenon_intro zenon_Hf5 ]. % 15.16/15.36 apply (zenon_L61_); trivial. % 15.16/15.36 apply (zenon_or_s _ _ zenon_Hf5); [ zenon_intro zenon_Hae | zenon_intro zenon_Hee ]. % 15.16/15.36 apply (zenon_or_s _ _ zenon_H8e); [ zenon_intro zenon_H92 | zenon_intro zenon_H91 ]. % 15.16/15.36 apply (zenon_or_s _ _ zenon_H58); [ zenon_intro zenon_H5b | zenon_intro zenon_H5a ]. % 15.16/15.36 exact (zenon_H59 zenon_H5b). % 15.16/15.36 apply (zenon_or_s _ _ zenon_H5a); [ zenon_intro zenon_H4a | zenon_intro zenon_H5c ]. % 15.16/15.36 apply (zenon_or_s _ _ zenon_H144); [ zenon_intro zenon_H49 | zenon_intro zenon_H147 ]. % 15.16/15.36 apply (zenon_L9_); trivial. % 15.16/15.36 apply (zenon_or_s _ _ zenon_H147); [ zenon_intro zenon_H149 | zenon_intro zenon_H148 ]. % 15.16/15.36 exact (zenon_H145 zenon_H149). % 15.16/15.36 apply (zenon_or_s _ _ zenon_H148); [ zenon_intro zenon_H14a | zenon_intro zenon_H142 ]. % 15.16/15.36 apply (zenon_or_s _ _ zenon_H84); [ zenon_intro zenon_H68 | zenon_intro zenon_H85 ]. % 15.16/15.36 apply (zenon_L160_); trivial. % 15.16/15.36 apply (zenon_or_s _ _ zenon_H85); [ zenon_intro zenon_H6e | zenon_intro zenon_H86 ]. % 15.16/15.36 exact (zenon_Hd6 zenon_H6e). % 15.16/15.36 apply (zenon_or_s _ _ zenon_H86); [ zenon_intro zenon_H7c | zenon_intro zenon_H82 ]. % 15.16/15.36 apply (zenon_L21_); trivial. % 15.16/15.36 apply (zenon_or_s _ _ zenon_H1a2); [ zenon_intro zenon_H5d | zenon_intro zenon_H1a3 ]. % 15.16/15.36 apply (zenon_L51_); trivial. % 15.16/15.36 apply (zenon_or_s _ _ zenon_H1a3); [ zenon_intro zenon_H6e | zenon_intro zenon_H1a4 ]. % 15.16/15.36 exact (zenon_Hd6 zenon_H6e). % 15.16/15.36 apply (zenon_or_s _ _ zenon_H1a4); [ zenon_intro zenon_H156 | zenon_intro zenon_H16a ]. % 15.16/15.36 apply (zenon_L134_); trivial. % 15.16/15.36 apply (zenon_or_s _ _ zenon_H90); [ zenon_intro zenon_H69 | zenon_intro zenon_H94 ]. % 15.16/15.36 apply (zenon_L38_); trivial. % 15.16/15.36 apply (zenon_or_s _ _ zenon_H94); [ zenon_intro zenon_H96 | zenon_intro zenon_H95 ]. % 15.16/15.36 exact (zenon_H182 zenon_H96). % 15.16/15.36 apply (zenon_or_s _ _ zenon_H95); [ zenon_intro zenon_H88 | zenon_intro zenon_H8a ]. % 15.16/15.36 apply (zenon_or_s _ _ zenon_H11b); [ zenon_intro zenon_H29 | zenon_intro zenon_H11c ]. % 15.16/15.36 apply (zenon_L92_); trivial. % 15.16/15.36 apply (zenon_or_s _ _ zenon_H11c); [ zenon_intro zenon_H117 | zenon_intro zenon_H11d ]. % 15.16/15.36 apply (zenon_L196_); trivial. % 15.16/15.36 apply (zenon_or_s _ _ zenon_H11d); [ zenon_intro zenon_H2a | zenon_intro zenon_H119 ]. % 15.16/15.36 exact (zenon_H52 zenon_H2a). % 15.16/15.36 apply (zenon_or_s _ _ zenon_He6); [ zenon_intro zenon_Haf | zenon_intro zenon_He7 ]. % 15.16/15.36 apply (zenon_L261_); trivial. % 15.16/15.36 apply (zenon_or_s _ _ zenon_He7); [ zenon_intro zenon_Hdf | zenon_intro zenon_He8 ]. % 15.16/15.36 apply (zenon_L262_); trivial. % 15.16/15.36 apply (zenon_or_s _ _ zenon_He8); [ zenon_intro zenon_H34 | zenon_intro zenon_He2 ]. % 15.16/15.36 exact (zenon_H30 zenon_H34). % 15.16/15.36 apply (zenon_or_s _ _ zenon_H1f6); [ zenon_intro zenon_Hdb | zenon_intro zenon_H1f7 ]. % 15.16/15.36 apply (zenon_L140_); trivial. % 15.16/15.36 apply (zenon_or_s _ _ zenon_H1f7); [ zenon_intro zenon_H142 | zenon_intro zenon_H1f8 ]. % 15.16/15.36 apply (zenon_L266_); trivial. % 15.16/15.36 apply (zenon_or_s _ _ zenon_H1f8); [ zenon_intro zenon_H167 | zenon_intro zenon_H40 ]. % 15.16/15.36 apply (zenon_L267_); trivial. % 15.16/15.36 apply (zenon_L265_); trivial. % 15.16/15.36 apply (zenon_L165_); trivial. % 15.16/15.36 apply (zenon_or_s _ _ zenon_H84); [ zenon_intro zenon_H68 | zenon_intro zenon_H85 ]. % 15.16/15.36 apply (zenon_L160_); trivial. % 15.16/15.36 apply (zenon_or_s _ _ zenon_H85); [ zenon_intro zenon_H6e | zenon_intro zenon_H86 ]. % 15.16/15.36 exact (zenon_Hd6 zenon_H6e). % 15.16/15.36 apply (zenon_or_s _ _ zenon_H86); [ zenon_intro zenon_H7c | zenon_intro zenon_H82 ]. % 15.16/15.36 apply (zenon_L21_); trivial. % 15.16/15.36 apply (zenon_or_s _ _ zenon_H1a2); [ zenon_intro zenon_H5d | zenon_intro zenon_H1a3 ]. % 15.16/15.36 apply (zenon_L50_); trivial. % 15.16/15.36 apply (zenon_or_s _ _ zenon_H1a3); [ zenon_intro zenon_H6e | zenon_intro zenon_H1a4 ]. % 15.16/15.36 exact (zenon_Hd6 zenon_H6e). % 15.16/15.36 apply (zenon_or_s _ _ zenon_H1a4); [ zenon_intro zenon_H156 | zenon_intro zenon_H16a ]. % 15.16/15.36 apply (zenon_L134_); trivial. % 15.16/15.36 apply (zenon_or_s _ _ zenon_H90); [ zenon_intro zenon_H69 | zenon_intro zenon_H94 ]. % 15.16/15.36 apply (zenon_L139_); trivial. % 15.16/15.36 apply (zenon_or_s _ _ zenon_H94); [ zenon_intro zenon_H96 | zenon_intro zenon_H95 ]. % 15.16/15.36 exact (zenon_H182 zenon_H96). % 15.16/15.36 apply (zenon_or_s _ _ zenon_H95); [ zenon_intro zenon_H88 | zenon_intro zenon_H8a ]. % 15.16/15.36 apply (zenon_or_s _ _ zenon_H1f5); [ zenon_intro zenon_Hcf | zenon_intro zenon_H1f9 ]. % 15.16/15.36 apply (zenon_L135_); trivial. % 15.16/15.36 apply (zenon_or_s _ _ zenon_H1f9); [ zenon_intro zenon_H14a | zenon_intro zenon_H1fa ]. % 15.16/15.36 apply (zenon_or_s _ _ zenon_H11b); [ zenon_intro zenon_H29 | zenon_intro zenon_H11c ]. % 15.16/15.36 apply (zenon_L268_); trivial. % 15.16/15.36 apply (zenon_or_s _ _ zenon_H11c); [ zenon_intro zenon_H117 | zenon_intro zenon_H11d ]. % 15.16/15.36 apply (zenon_L196_); trivial. % 15.16/15.36 apply (zenon_or_s _ _ zenon_H11d); [ zenon_intro zenon_H2a | zenon_intro zenon_H119 ]. % 15.16/15.36 exact (zenon_H52 zenon_H2a). % 15.16/15.36 apply (zenon_or_s _ _ zenon_He6); [ zenon_intro zenon_Haf | zenon_intro zenon_He7 ]. % 15.16/15.36 apply (zenon_L39_); trivial. % 15.16/15.36 apply (zenon_or_s _ _ zenon_He7); [ zenon_intro zenon_Hdf | zenon_intro zenon_He8 ]. % 15.16/15.36 apply (zenon_L262_); trivial. % 15.16/15.36 apply (zenon_or_s _ _ zenon_He8); [ zenon_intro zenon_H34 | zenon_intro zenon_He2 ]. % 15.16/15.36 exact (zenon_H30 zenon_H34). % 15.16/15.36 apply (zenon_L266_); trivial. % 15.16/15.36 apply (zenon_or_s _ _ zenon_H1fa); [ zenon_intro zenon_H32 | zenon_intro zenon_Hd0 ]. % 15.16/15.36 exact (zenon_H2e zenon_H32). % 15.16/15.36 apply (zenon_L264_); trivial. % 15.16/15.36 apply (zenon_L165_); trivial. % 15.16/15.36 apply (zenon_or_s _ _ zenon_H5c); [ zenon_intro zenon_H50 | zenon_intro zenon_H53 ]. % 15.16/15.36 apply (zenon_L48_); trivial. % 15.16/15.36 apply (zenon_L32_); trivial. % 15.16/15.36 apply (zenon_or_s _ _ zenon_H91); [ zenon_intro zenon_H5d | zenon_intro zenon_H93 ]. % 15.16/15.36 apply (zenon_L51_); trivial. % 15.16/15.36 apply (zenon_or_s _ _ zenon_H93); [ zenon_intro zenon_H63 | zenon_intro zenon_H81 ]. % 15.16/15.36 apply (zenon_L15_); trivial. % 15.16/15.36 apply (zenon_L33_); trivial. % 15.16/15.36 apply (zenon_L79_); trivial. % 15.16/15.36 apply (zenon_or_s _ _ zenon_Hf3); [ zenon_intro zenon_Hcf | zenon_intro zenon_Hdb ]. % 15.16/15.36 apply (zenon_L270_); trivial. % 15.16/15.36 apply (zenon_L141_); trivial. % 15.16/15.36 apply (zenon_L43_); trivial. % 15.16/15.36 apply (zenon_L81_); trivial. % 15.16/15.36 apply (zenon_L82_); trivial. % 15.16/15.36 apply (zenon_L137_); trivial. % 15.16/15.36 (* end of lemma zenon_L271_ *) % 15.16/15.36 assert (zenon_L272_ : (~((op (e2) (e0)) = (op (e2) (e2)))) -> ((op (e2) (e2)) = (e2)) -> (((op (e0) (e0)) = (e1))\/(((op (e0) (e1)) = (e1))\/(((op (e0) (e2)) = (e1))\/((op (e0) (e3)) = (e1))))) -> (~((op (e0) (e3)) = (op (e3) (e3)))) -> (((op (e3) (e3)) = (e0))\/(((op (e3) (e3)) = (e1))\/(((op (e3) (e3)) = (e2))\/((op (e3) (e3)) = (e3))))) -> ((op (e0) (e2)) = (e0)) -> (~((e0) = (e1))) -> ((op (e1) (e1)) = (e1)) -> (~((op (e0) (e1)) = (op (e1) (e1)))) -> (~((op (e0) (e0)) = (e1))) -> ((~((op (e1) (e1)) = (e0)))\/((op (e1) (e0)) = (e1))) -> ((~((op (e1) (e1)) = (e2)))\/((op (e1) (e2)) = (e1))) -> (~((op (e1) (e2)) = (op (e1) (e3)))) -> ((~((op (e2) (e2)) = (e0)))\/((op (e2) (e0)) = (e2))) -> ((~((op (e3) (e3)) = (e1)))\/((op (e3) (e1)) = (e3))) -> (~((op (e3) (e1)) = (op (e3) (e3)))) -> (~((op (e0) (e1)) = (op (e0) (e3)))) -> (~((op (e1) (e0)) = (op (e1) (e3)))) -> (((op (e0) (e3)) = (e1))\/(((op (e1) (e3)) = (e1))\/(((op (e2) (e3)) = (e1))\/((op (e3) (e3)) = (e1))))) -> (~((op (e2) (e0)) = (op (e2) (e3)))) -> (((op (e0) (e0)) = (e1))\/(((op (e1) (e0)) = (e1))\/(((op (e2) (e0)) = (e1))\/((op (e3) (e0)) = (e1))))) -> ((~((op (e3) (e3)) = (e2)))\/((op (e3) (e2)) = (e3))) -> (((op (e0) (e0)) = (e3))\/(((op (e0) (e1)) = (e3))\/(((op (e0) (e2)) = (e3))\/((op (e0) (e3)) = (e3))))) -> (~((e0) = (e3))) -> (~((e1) = (e3))) -> (~((op (e0) (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 (e0) (e0)) = (e2))\/(((op (e0) (e1)) = (e2))\/(((op (e0) (e2)) = (e2))\/((op (e0) (e3)) = (e2))))) -> (~((op (e0) (e1)) = (op (e2) (e1)))) -> (~((op (e2) (e3)) = (op (e3) (e3)))) -> (((op (e2) (e0)) = (e3))\/(((op (e2) (e1)) = (e3))\/(((op (e2) (e2)) = (e3))\/((op (e2) (e3)) = (e3))))) -> (((op (e0) (e0)) = (e3))\/(((op (e1) (e0)) = (e3))\/(((op (e2) (e0)) = (e3))\/((op (e3) (e0)) = (e3))))) -> (~((op (e0) (e2)) = (op (e1) (e2)))) -> (((op (e0) (e0)) = (e2))\/(((op (e1) (e0)) = (e2))\/(((op (e2) (e0)) = (e2))\/((op (e3) (e0)) = (e2))))) -> (((op (e1) (e0)) = (e3))\/(((op (e1) (e1)) = (e3))\/(((op (e1) (e2)) = (e3))\/((op (e1) (e3)) = (e3))))) -> (~((op (e1) (e3)) = (op (e3) (e3)))) -> (((op (e1) (e1)) = (e0))\/(((op (e1) (e1)) = (e1))\/(((op (e1) (e1)) = (e2))\/((op (e1) (e1)) = (e3))))) -> ((~((op (e2) (e2)) = (e3)))\/((op (e2) (e3)) = (e2))) -> (((op (e1) (e0)) = (e2))\/(((op (e1) (e1)) = (e2))\/(((op (e1) (e2)) = (e2))\/((op (e1) (e3)) = (e2))))) -> (~((e1) = (e2))) -> (((op (e0) (e3)) = (e0))\/(((op (e1) (e3)) = (e0))\/(((op (e2) (e3)) = (e0))\/((op (e3) (e3)) = (e0))))) -> (~((e0) = (e2))) -> (~((op (e0) (e2)) = (op (e0) (e3)))) -> (~((e2) = (e3))) -> (~((op (e3) (e0)) = (op (e3) (e3)))) -> ((~((op (e3) (e3)) = (e0)))\/((op (e3) (e0)) = (e3))) -> (~((op (e3) (e2)) = (op (e3) (e3)))) -> (((op (e0) (e2)) = (e3))\/(((op (e1) (e2)) = (e3))\/(((op (e2) (e2)) = (e3))\/((op (e3) (e2)) = (e3))))) -> (((op (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 (e2) (e2)) = (e2)))\/((op (e2) (e2)) = (e2))) -> ((~((op (e1) (e1)) = (e3)))\/((op (e1) (e3)) = (e1))) -> ((~((op (e2) (e2)) = (e1)))\/((op (e2) (e1)) = (e2))) -> (~((op (e2) (e1)) = (op (e2) (e3)))) -> ((~((op (e1) (e1)) = (e1)))\/((op (e1) (e1)) = (e1))) -> (~((op (e0) (e3)) = (op (e1) (e3)))) -> (~((op (e1) (e0)) = (op (e1) (e2)))) -> (~((op (e2) (e1)) = (op (e3) (e1)))) -> (~((op (e0) (e2)) = (op (e3) (e2)))) -> (((op (e3) (e0)) = (e2))\/(((op (e3) (e1)) = (e2))\/(((op (e3) (e2)) = (e2))\/((op (e3) (e3)) = (e2))))) -> (((op (e0) (e0)) = (e0))\/(((op (e0) (e1)) = (e0))\/(((op (e0) (e2)) = (e0))\/((op (e0) (e3)) = (e0))))) -> (~((op (e1) (e1)) = (op (e1) (e3)))) -> (((op (e0) (e0)) = (e0))\/(((op (e0) (e0)) = (e1))\/(((op (e0) (e0)) = (e2))\/((op (e0) (e0)) = (e3))))) -> (((op (e0) (e0)) = (e0))\/(((op (e1) (e0)) = (e0))\/(((op (e2) (e0)) = (e0))\/((op (e3) (e0)) = (e0))))) -> (~((op (e1) (e0)) = (op (e1) (e1)))) -> (~((op (e1) (e1)) = (op (e2) (e1)))) -> (~((op (e0) (e3)) = (op (e2) (e3)))) -> (((op (e2) (e0)) = (e1))\/(((op (e2) (e1)) = (e1))\/(((op (e2) (e2)) = (e1))\/((op (e2) (e3)) = (e1))))) -> (~((op (e0) (e0)) = (e0))) -> (~((op (e1) (e1)) = (op (e1) (e2)))) -> (~((op (e1) (e2)) = (op (e2) (e2)))) -> (~((op (e1) (e2)) = (op (e3) (e2)))) -> (((op (e1) (e2)) = (e0))\/(((op (e1) (e2)) = (e1))\/(((op (e1) (e2)) = (e2))\/((op (e1) (e2)) = (e3))))) -> (((op (e2) (e1)) = (e0))\/(((op (e2) (e1)) = (e1))\/(((op (e2) (e1)) = (e2))\/((op (e2) (e1)) = (e3))))) -> (~((op (e2) (e1)) = (op (e2) (e2)))) -> (~((op (e2) (e0)) = (op (e2) (e1)))) -> (((op (e1) (e0)) = (e0))\/(((op (e1) (e1)) = (e0))\/(((op (e1) (e2)) = (e0))\/((op (e1) (e3)) = (e0))))) -> (~((op (e2) (e2)) = (op (e2) (e3)))) -> ((~((op (e3) (e3)) = (e3)))\/((op (e3) (e3)) = (e3))) -> (~((op (e3) (e0)) = (op (e3) (e1)))) -> (((op (e0) (e1)) = (e0))\/(((op (e1) (e1)) = (e0))\/(((op (e2) (e1)) = (e0))\/((op (e3) (e1)) = (e0))))) -> (((op (e2) (e0)) = (e0))\/(((op (e2) (e1)) = (e0))\/(((op (e2) (e2)) = (e0))\/((op (e2) (e3)) = (e0))))) -> (~((op (e1) (e1)) = (e2))) -> (((op (e0) (e1)) = (e2))\/(((op (e1) (e1)) = (e2))\/(((op (e2) (e1)) = (e2))\/((op (e3) (e1)) = (e2))))) -> (~((op (e1) (e1)) = (e3))) -> (((op (e0) (e2)) = (e1))\/(((op (e1) (e2)) = (e1))\/(((op (e2) (e2)) = (e1))\/((op (e3) (e2)) = (e1))))) -> (~((op (e2) (e0)) = (op (e3) (e0)))) -> (((op (e0) (e1)) = (e0))\/(((op (e0) (e1)) = (e1))\/(((op (e0) (e1)) = (e2))\/((op (e0) (e1)) = (e3))))) -> (~((op (e0) (e1)) = (op (e3) (e1)))) -> (((op (e3) (e0)) = (e0))\/(((op (e3) (e1)) = (e0))\/(((op (e3) (e2)) = (e0))\/((op (e3) (e3)) = (e0))))) -> (((op (e0) (e2)) = (e0))\/(((op (e1) (e2)) = (e0))\/(((op (e2) (e2)) = (e0))\/((op (e3) (e2)) = (e0))))) -> (~((op (e3) (e1)) = (op (e3) (e2)))) -> (~((op (e1) (e1)) = (e0))) -> (~((op (e3) (e0)) = (op (e3) (e2)))) -> False). % 15.16/15.36 do 0 intro. intros zenon_H17a zenon_H35 zenon_H44 zenon_H36 zenon_H3b zenon_Hab zenon_H9e zenon_H21 zenon_H23 zenon_H45 zenon_H1e4 zenon_H1d3 zenon_H1d0 zenon_H1d4 zenon_H10c zenon_H12d zenon_H1cd zenon_H1cf zenon_H121 zenon_Hce zenon_Hf1 zenon_H10e zenon_H58 zenon_H4b zenon_Ha3 zenon_H59 zenon_H2d zenon_H28 zenon_H8e zenon_Hde zenon_He3 zenon_He6 zenon_Hbe zenon_H87 zenon_Heb zenon_H90 zenon_H8b zenon_H1b3 zenon_H1c3 zenon_H84 zenon_Ha7 zenon_Hd3 zenon_H5e zenon_Hc9 zenon_H6a zenon_Hbb zenon_H10f zenon_H173 zenon_H175 zenon_H160 zenon_H1c5 zenon_Haa zenon_H1d2 zenon_H1e3 zenon_H1e2 zenon_H1d8 zenon_H80 zenon_H166 zenon_H13c zenon_H140 zenon_H1df zenon_H110 zenon_H11e zenon_H12a zenon_Hf0 zenon_Hd7 zenon_Hb1 zenon_Hb4 zenon_Hb7 zenon_H20 zenon_H116 zenon_H7d zenon_H17d zenon_H1d5 zenon_H15a zenon_H157 zenon_H154 zenon_H163 zenon_H15f zenon_H10d zenon_H109 zenon_H144 zenon_H1f5 zenon_Hd6 zenon_H1a2 zenon_H182 zenon_H11b zenon_H1e5 zenon_H1e9 zenon_H138 zenon_H1f6 zenon_H16f zenon_H135 zenon_H145 zenon_H105. % 15.16/15.36 apply (zenon_or_s _ _ zenon_H1d4); [ zenon_intro zenon_H2e | zenon_intro zenon_Hdd ]. % 15.16/15.36 apply (zenon_or_s _ _ zenon_H1e3); [ zenon_intro zenon_H52 | zenon_intro zenon_H156 ]. % 15.16/15.36 apply (zenon_L271_); trivial. % 15.16/15.36 apply (zenon_L134_); trivial. % 15.16/15.36 apply (zenon_L161_); trivial. % 15.16/15.36 (* end of lemma zenon_L272_ *) % 15.16/15.36 assert (zenon_L273_ : (~((op (e2) (e0)) = (op (e2) (e2)))) -> ((op (e2) (e2)) = (e2)) -> (((op (e0) (e0)) = (e1))\/(((op (e0) (e1)) = (e1))\/(((op (e0) (e2)) = (e1))\/((op (e0) (e3)) = (e1))))) -> (~((op (e0) (e3)) = (op (e3) (e3)))) -> (((op (e3) (e3)) = (e0))\/(((op (e3) (e3)) = (e1))\/(((op (e3) (e3)) = (e2))\/((op (e3) (e3)) = (e3))))) -> ((op (e0) (e2)) = (e0)) -> (~((e0) = (e1))) -> ((op (e1) (e1)) = (e1)) -> (~((op (e0) (e1)) = (op (e1) (e1)))) -> (~((op (e0) (e0)) = (e1))) -> ((~((op (e1) (e1)) = (e0)))\/((op (e1) (e0)) = (e1))) -> ((~((op (e1) (e1)) = (e2)))\/((op (e1) (e2)) = (e1))) -> (~((op (e1) (e2)) = (op (e1) (e3)))) -> ((~((op (e2) (e2)) = (e0)))\/((op (e2) (e0)) = (e2))) -> ((~((op (e3) (e3)) = (e1)))\/((op (e3) (e1)) = (e3))) -> (~((op (e3) (e1)) = (op (e3) (e3)))) -> (~((op (e0) (e1)) = (op (e0) (e3)))) -> (~((op (e1) (e0)) = (op (e1) (e3)))) -> (((op (e0) (e3)) = (e1))\/(((op (e1) (e3)) = (e1))\/(((op (e2) (e3)) = (e1))\/((op (e3) (e3)) = (e1))))) -> (~((op (e2) (e0)) = (op (e2) (e3)))) -> (((op (e0) (e0)) = (e1))\/(((op (e1) (e0)) = (e1))\/(((op (e2) (e0)) = (e1))\/((op (e3) (e0)) = (e1))))) -> ((~((op (e3) (e3)) = (e2)))\/((op (e3) (e2)) = (e3))) -> (((op (e0) (e0)) = (e3))\/(((op (e0) (e1)) = (e3))\/(((op (e0) (e2)) = (e3))\/((op (e0) (e3)) = (e3))))) -> (~((e0) = (e3))) -> (~((e1) = (e3))) -> (~((op (e0) (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 (e0) (e0)) = (e2))\/(((op (e0) (e1)) = (e2))\/(((op (e0) (e2)) = (e2))\/((op (e0) (e3)) = (e2))))) -> (~((op (e0) (e1)) = (op (e2) (e1)))) -> (~((op (e2) (e3)) = (op (e3) (e3)))) -> (((op (e2) (e0)) = (e3))\/(((op (e2) (e1)) = (e3))\/(((op (e2) (e2)) = (e3))\/((op (e2) (e3)) = (e3))))) -> (((op (e0) (e0)) = (e3))\/(((op (e1) (e0)) = (e3))\/(((op (e2) (e0)) = (e3))\/((op (e3) (e0)) = (e3))))) -> (~((op (e0) (e2)) = (op (e1) (e2)))) -> (((op (e0) (e0)) = (e2))\/(((op (e1) (e0)) = (e2))\/(((op (e2) (e0)) = (e2))\/((op (e3) (e0)) = (e2))))) -> (((op (e1) (e0)) = (e3))\/(((op (e1) (e1)) = (e3))\/(((op (e1) (e2)) = (e3))\/((op (e1) (e3)) = (e3))))) -> (~((op (e1) (e3)) = (op (e3) (e3)))) -> (((op (e1) (e1)) = (e0))\/(((op (e1) (e1)) = (e1))\/(((op (e1) (e1)) = (e2))\/((op (e1) (e1)) = (e3))))) -> ((~((op (e2) (e2)) = (e3)))\/((op (e2) (e3)) = (e2))) -> (((op (e1) (e0)) = (e2))\/(((op (e1) (e1)) = (e2))\/(((op (e1) (e2)) = (e2))\/((op (e1) (e3)) = (e2))))) -> (~((e1) = (e2))) -> (((op (e0) (e3)) = (e0))\/(((op (e1) (e3)) = (e0))\/(((op (e2) (e3)) = (e0))\/((op (e3) (e3)) = (e0))))) -> (~((e0) = (e2))) -> (~((op (e0) (e2)) = (op (e0) (e3)))) -> (~((e2) = (e3))) -> (~((op (e3) (e0)) = (op (e3) (e3)))) -> ((~((op (e3) (e3)) = (e0)))\/((op (e3) (e0)) = (e3))) -> (~((op (e3) (e2)) = (op (e3) (e3)))) -> (((op (e0) (e2)) = (e3))\/(((op (e1) (e2)) = (e3))\/(((op (e2) (e2)) = (e3))\/((op (e3) (e2)) = (e3))))) -> (((op (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 (e2) (e2)) = (e2)))\/((op (e2) (e2)) = (e2))) -> ((~((op (e1) (e1)) = (e3)))\/((op (e1) (e3)) = (e1))) -> ((~((op (e2) (e2)) = (e1)))\/((op (e2) (e1)) = (e2))) -> (~((op (e2) (e1)) = (op (e2) (e3)))) -> ((~((op (e1) (e1)) = (e1)))\/((op (e1) (e1)) = (e1))) -> (~((op (e0) (e3)) = (op (e1) (e3)))) -> (~((op (e1) (e0)) = (op (e1) (e2)))) -> (~((op (e2) (e1)) = (op (e3) (e1)))) -> (~((op (e0) (e2)) = (op (e3) (e2)))) -> (((op (e3) (e0)) = (e2))\/(((op (e3) (e1)) = (e2))\/(((op (e3) (e2)) = (e2))\/((op (e3) (e3)) = (e2))))) -> (((op (e0) (e0)) = (e0))\/(((op (e0) (e1)) = (e0))\/(((op (e0) (e2)) = (e0))\/((op (e0) (e3)) = (e0))))) -> (~((op (e1) (e1)) = (op (e1) (e3)))) -> (((op (e0) (e0)) = (e0))\/(((op (e0) (e0)) = (e1))\/(((op (e0) (e0)) = (e2))\/((op (e0) (e0)) = (e3))))) -> (((op (e0) (e0)) = (e0))\/(((op (e1) (e0)) = (e0))\/(((op (e2) (e0)) = (e0))\/((op (e3) (e0)) = (e0))))) -> (~((op (e1) (e0)) = (op (e1) (e1)))) -> (~((op (e1) (e1)) = (op (e2) (e1)))) -> (~((op (e0) (e3)) = (op (e2) (e3)))) -> (((op (e2) (e0)) = (e1))\/(((op (e2) (e1)) = (e1))\/(((op (e2) (e2)) = (e1))\/((op (e2) (e3)) = (e1))))) -> (~((op (e0) (e0)) = (e0))) -> (~((op (e1) (e1)) = (op (e1) (e2)))) -> (~((op (e1) (e2)) = (op (e2) (e2)))) -> (~((op (e1) (e2)) = (op (e3) (e2)))) -> (((op (e1) (e2)) = (e0))\/(((op (e1) (e2)) = (e1))\/(((op (e1) (e2)) = (e2))\/((op (e1) (e2)) = (e3))))) -> (((op (e2) (e1)) = (e0))\/(((op (e2) (e1)) = (e1))\/(((op (e2) (e1)) = (e2))\/((op (e2) (e1)) = (e3))))) -> (~((op (e2) (e1)) = (op (e2) (e2)))) -> (~((op (e2) (e0)) = (op (e2) (e1)))) -> (((op (e1) (e0)) = (e0))\/(((op (e1) (e1)) = (e0))\/(((op (e1) (e2)) = (e0))\/((op (e1) (e3)) = (e0))))) -> (~((op (e2) (e2)) = (op (e2) (e3)))) -> ((~((op (e3) (e3)) = (e3)))\/((op (e3) (e3)) = (e3))) -> (~((op (e3) (e0)) = (op (e3) (e1)))) -> (((op (e0) (e1)) = (e0))\/(((op (e1) (e1)) = (e0))\/(((op (e2) (e1)) = (e0))\/((op (e3) (e1)) = (e0))))) -> (((op (e2) (e0)) = (e0))\/(((op (e2) (e1)) = (e0))\/(((op (e2) (e2)) = (e0))\/((op (e2) (e3)) = (e0))))) -> (((op (e0) (e1)) = (e2))\/(((op (e1) (e1)) = (e2))\/(((op (e2) (e1)) = (e2))\/((op (e3) (e1)) = (e2))))) -> (((op (e0) (e2)) = (e1))\/(((op (e1) (e2)) = (e1))\/(((op (e2) (e2)) = (e1))\/((op (e3) (e2)) = (e1))))) -> (~((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)) = (op (e3) (e1)))) -> (((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 (e3) (e1)) = (op (e3) (e2)))) -> (~((op (e1) (e1)) = (e0))) -> (~((op (e3) (e0)) = (op (e3) (e2)))) -> False). % 15.16/15.36 do 0 intro. intros zenon_H17a zenon_H35 zenon_H44 zenon_H36 zenon_H3b zenon_Hab zenon_H9e zenon_H21 zenon_H23 zenon_H45 zenon_H1e4 zenon_H1d3 zenon_H1d0 zenon_H1d4 zenon_H10c zenon_H12d zenon_H1cd zenon_H1cf zenon_H121 zenon_Hce zenon_Hf1 zenon_H10e zenon_H58 zenon_H4b zenon_Ha3 zenon_H59 zenon_H2d zenon_H28 zenon_H8e zenon_Hde zenon_He3 zenon_He6 zenon_Hbe zenon_H87 zenon_Heb zenon_H90 zenon_H8b zenon_H1b3 zenon_H1c3 zenon_H84 zenon_Ha7 zenon_Hd3 zenon_H5e zenon_Hc9 zenon_H6a zenon_Hbb zenon_H10f zenon_H173 zenon_H175 zenon_H160 zenon_H1c5 zenon_Haa zenon_H1d2 zenon_H1e3 zenon_H1e2 zenon_H1d8 zenon_H80 zenon_H166 zenon_H13c zenon_H140 zenon_H1df zenon_H110 zenon_H11e zenon_H12a zenon_Hf0 zenon_Hd7 zenon_Hb1 zenon_Hb4 zenon_Hb7 zenon_H20 zenon_H116 zenon_H7d zenon_H17d zenon_H1d5 zenon_H15a zenon_H157 zenon_H154 zenon_H163 zenon_H15f zenon_H10d zenon_H109 zenon_H144 zenon_H1f5 zenon_H1a2 zenon_H11b zenon_H1e5 zenon_H1e9 zenon_H138 zenon_H1f6 zenon_H16f zenon_H135 zenon_H145 zenon_H105. % 15.16/15.36 apply (zenon_or_s _ _ zenon_H1d3); [ zenon_intro zenon_Hd6 | zenon_intro zenon_H117 ]. % 15.16/15.36 apply (zenon_or_s _ _ zenon_H1d2); [ zenon_intro zenon_H182 | zenon_intro zenon_H11f ]. % 15.16/15.36 apply (zenon_L272_); trivial. % 15.16/15.36 apply (zenon_L90_); trivial. % 15.16/15.36 apply (zenon_L86_); trivial. % 15.16/15.36 (* end of lemma zenon_L273_ *) % 15.16/15.36 assert (zenon_L274_ : (((op (e0) (e0)) = (e1))\/(((op (e1) (e0)) = (e1))\/(((op (e2) (e0)) = (e1))\/((op (e3) (e0)) = (e1))))) -> (~((op (e0) (e0)) = (e1))) -> (~((op (e1) (e0)) = (op (e1) (e1)))) -> (~((op (e3) (e3)) = (e1))) -> (~((op (e2) (e0)) = (op (e2) (e3)))) -> (~((op (e1) (e1)) = (op (e1) (e3)))) -> ((op (e1) (e1)) = (e1)) -> ((op (e0) (e2)) = (e1)) -> (~((op (e0) (e2)) = (op (e0) (e3)))) -> (((op (e0) (e3)) = (e1))\/(((op (e1) (e3)) = (e1))\/(((op (e2) (e3)) = (e1))\/((op (e3) (e3)) = (e1))))) -> (~((e1) = (e3))) -> ((op (e3) (e0)) = (e3)) -> False). % 15.16/15.36 do 0 intro. intros zenon_Hf1 zenon_H45 zenon_Hd7 zenon_H104 zenon_Hce zenon_H11e zenon_H21 zenon_H29 zenon_Hc9 zenon_H121 zenon_Ha3 zenon_Hba. % 15.16/15.36 apply (zenon_or_s _ _ zenon_Hf1); [ zenon_intro zenon_H47 | zenon_intro zenon_Hf4 ]. % 15.16/15.36 exact (zenon_H45 zenon_H47). % 15.16/15.36 apply (zenon_or_s _ _ zenon_Hf4); [ zenon_intro zenon_Hd8 | zenon_intro zenon_Hf5 ]. % 15.16/15.36 apply (zenon_L61_); trivial. % 15.16/15.36 apply (zenon_or_s _ _ zenon_Hf5); [ zenon_intro zenon_Hae | zenon_intro zenon_Hee ]. % 15.16/15.36 apply (zenon_L92_); trivial. % 15.16/15.36 apply (zenon_L79_); trivial. % 15.16/15.36 (* end of lemma zenon_L274_ *) % 15.16/15.36 assert (zenon_L275_ : ((~((op (e3) (e3)) = (e1)))\/((op (e3) (e1)) = (e3))) -> (~((op (e3) (e0)) = (op (e3) (e1)))) -> (~((op (e0) (e0)) = (e1))) -> (~((op (e0) (e1)) = (op (e1) (e1)))) -> ((op (e1) (e1)) = (e1)) -> (((op (e0) (e0)) = (e1))\/(((op (e1) (e0)) = (e1))\/(((op (e2) (e0)) = (e1))\/((op (e3) (e0)) = (e1))))) -> ((op (e3) (e0)) = (e3)) -> (~((e1) = (e3))) -> (~((op (e0) (e2)) = (op (e0) (e3)))) -> (~((op (e1) (e1)) = (op (e1) (e3)))) -> (~((op (e2) (e0)) = (op (e2) (e3)))) -> (((op (e0) (e3)) = (e1))\/(((op (e1) (e3)) = (e1))\/(((op (e2) (e3)) = (e1))\/((op (e3) (e3)) = (e1))))) -> (~((op (e1) (e0)) = (op (e1) (e1)))) -> (~((e0) = (e1))) -> ((op (e0) (e3)) = (e0)) -> (((op (e0) (e0)) = (e1))\/(((op (e0) (e1)) = (e1))\/(((op (e0) (e2)) = (e1))\/((op (e0) (e3)) = (e1))))) -> False). % 15.16/15.36 do 0 intro. intros zenon_H10c zenon_H109 zenon_H45 zenon_H23 zenon_H21 zenon_Hf1 zenon_Hba zenon_Ha3 zenon_Hc9 zenon_H11e zenon_Hce zenon_H121 zenon_Hd7 zenon_H9e zenon_Hca zenon_H44. % 15.16/15.36 apply (zenon_or_s _ _ zenon_H10c); [ zenon_intro zenon_H104 | zenon_intro zenon_H10a ]. % 15.16/15.36 apply (zenon_or_s _ _ zenon_H44); [ zenon_intro zenon_H47 | zenon_intro zenon_H46 ]. % 15.16/15.36 exact (zenon_H45 zenon_H47). % 15.16/15.36 apply (zenon_or_s _ _ zenon_H46); [ zenon_intro zenon_H22 | zenon_intro zenon_H48 ]. % 15.16/15.36 apply (zenon_L3_); trivial. % 15.16/15.36 apply (zenon_or_s _ _ zenon_H48); [ zenon_intro zenon_H29 | zenon_intro zenon_H37 ]. % 15.16/15.36 apply (zenon_L274_); trivial. % 15.16/15.36 apply (zenon_L73_); trivial. % 15.16/15.36 apply (zenon_L82_); trivial. % 15.16/15.36 (* end of lemma zenon_L275_ *) % 15.16/15.36 assert (zenon_L276_ : ((~((op (e3) (e3)) = (e0)))\/((op (e3) (e0)) = (e3))) -> ((~((op (e3) (e3)) = (e2)))\/((op (e3) (e2)) = (e3))) -> (~((op (e3) (op (e0) (e3))) = (op (e0) (e3)))) -> (((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) (e2)) = (e1))) -> (~((op (e1) (e1)) = (op (e2) (e1)))) -> (~((op (e1) (e1)) = (op (e1) (e2)))) -> (((op (e0) (e2)) = (e1))\/(((op (e1) (e2)) = (e1))\/(((op (e2) (e2)) = (e1))\/((op (e3) (e2)) = (e1))))) -> (~((op (e1) (e1)) = (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))) -> (~((op (e1) (e2)) = (op (e3) (e2)))) -> (~((op (e1) (e1)) = (e3))) -> (((op (e1) (e0)) = (e2))\/(((op (e1) (e1)) = (e2))\/(((op (e1) (e2)) = (e2))\/((op (e1) (e3)) = (e2))))) -> (~((op (e2) (e0)) = (op (e2) (e2)))) -> (((op (e0) (e0)) = (e2))\/(((op (e1) (e0)) = (e2))\/(((op (e2) (e0)) = (e2))\/((op (e3) (e0)) = (e2))))) -> (((op (e0) (e0)) = (e1))\/(((op (e0) (e1)) = (e1))\/(((op (e0) (e2)) = (e1))\/((op (e0) (e3)) = (e1))))) -> (~((op (e0) (e3)) = (op (e3) (e3)))) -> (~((op (e0) (e0)) = (e2))) -> (((op (e0) (e0)) = (e0))\/(((op (e0) (e0)) = (e1))\/(((op (e0) (e0)) = (e2))\/((op (e0) (e0)) = (e3))))) -> (((op (e3) (e3)) = (e0))\/(((op (e3) (e3)) = (e1))\/(((op (e3) (e3)) = (e2))\/((op (e3) (e3)) = (e3))))) -> (~((op (e0) (e0)) = (e0))) -> (~((e1) = (e2))) -> (~((e0) = (e2))) -> ((op (e0) (e3)) = (e0)) -> (((op (e0) (e0)) = (e2))\/(((op (e0) (e1)) = (e2))\/(((op (e0) (e2)) = (e2))\/((op (e0) (e3)) = (e2))))) -> ((op (e1) (e1)) = (e1)) -> (~((op (e0) (e1)) = (op (e1) (e1)))) -> (~((op (e0) (e0)) = (e1))) -> (((op (e0) (e0)) = (e0))\/(((op (e1) (e0)) = (e0))\/(((op (e2) (e0)) = (e0))\/((op (e3) (e0)) = (e0))))) -> (~((op (e3) (e0)) = (op (e3) (e2)))) -> ((op (e2) (e2)) = (e2)) -> (~((op (e0) (e2)) = (op (e2) (e2)))) -> (((op (e0) (e1)) = (e0))\/(((op (e1) (e1)) = (e0))\/(((op (e2) (e1)) = (e0))\/((op (e3) (e1)) = (e0))))) -> (~((op (e2) (e0)) = (op (e2) (e1)))) -> (~((op (e1) (e1)) = (e0))) -> (((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)) = (e3))) -> (~((e0) = (e3))) -> (~((e1) = (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) (e0)) = (e1))\/(((op (e1) (e0)) = (e1))\/(((op (e2) (e0)) = (e1))\/((op (e3) (e0)) = (e1))))) -> (((op (e0) (e2)) = (e0))\/(((op (e1) (e2)) = (e0))\/(((op (e2) (e2)) = (e0))\/((op (e3) (e2)) = (e0))))) -> (~((op (e3) (e1)) = (op (e3) (e2)))) -> (~((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 (e2) (e2)) = (e0))) -> (~((op (e1) (e0)) = (op (e1) (e2)))) -> (~((e0) = (e1))) -> (~((op (e0) (e2)) = (op (e0) (e3)))) -> (~((op (e1) (e1)) = (op (e1) (e3)))) -> (~((op (e2) (e0)) = (op (e2) (e3)))) -> (((op (e0) (e3)) = (e1))\/(((op (e1) (e3)) = (e1))\/(((op (e2) (e3)) = (e1))\/((op (e3) (e3)) = (e1))))) -> (~((op (e1) (e0)) = (op (e1) (e1)))) -> ((~((op (e3) (e3)) = (e3)))\/((op (e3) (e3)) = (e3))) -> ((~((op (e3) (e3)) = (e1)))\/((op (e3) (e1)) = (e3))) -> False). % 15.16/15.36 do 0 intro. intros zenon_H10f zenon_H10e zenon_H192 zenon_Hb7 zenon_H160 zenon_H52 zenon_Hb1 zenon_H116 zenon_H11b zenon_Hd6 zenon_H7d zenon_H90 zenon_H6a zenon_H17d zenon_H182 zenon_H84 zenon_H17a zenon_Heb zenon_H44 zenon_H36 zenon_H8f zenon_H12a zenon_H3b zenon_H20 zenon_Ha7 zenon_H5e zenon_Hca zenon_H8e zenon_H21 zenon_H23 zenon_H45 zenon_Hf0 zenon_H105 zenon_H35 zenon_H28 zenon_H144 zenon_H154 zenon_H145 zenon_H175 zenon_H173 zenon_H30 zenon_H4b zenon_Ha3 zenon_H80 zenon_H163 zenon_Hf1 zenon_H16f zenon_H135 zenon_H109 zenon_H138 zenon_H12d zenon_H16c zenon_H2e zenon_H166 zenon_H9e zenon_Hc9 zenon_H11e zenon_Hce zenon_H121 zenon_Hd7 zenon_H10d zenon_H10c. % 15.16/15.36 apply (zenon_or_s _ _ zenon_H10f); [ zenon_intro zenon_H3c | zenon_intro zenon_Hba ]. % 15.16/15.36 apply (zenon_or_s _ _ zenon_H10c); [ zenon_intro zenon_H104 | zenon_intro zenon_H10a ]. % 15.16/15.36 apply (zenon_or_s _ _ zenon_H10e); [ zenon_intro zenon_H3d | zenon_intro zenon_H106 ]. % 15.16/15.36 apply (zenon_or_s _ _ zenon_H10d); [ zenon_intro zenon_H3e | zenon_intro zenon_H42 ]. % 15.16/15.36 apply (zenon_L114_); trivial. % 15.16/15.36 apply (zenon_L158_); trivial. % 15.16/15.36 apply (zenon_or_s _ _ zenon_H10d); [ zenon_intro zenon_H3e | zenon_intro zenon_H42 ]. % 15.16/15.36 apply (zenon_L179_); trivial. % 15.16/15.36 apply (zenon_L153_); trivial. % 15.16/15.36 apply (zenon_L116_); trivial. % 15.16/15.36 apply (zenon_L275_); trivial. % 15.16/15.36 (* end of lemma zenon_L276_ *) % 15.16/15.36 assert (zenon_L277_ : ((~((op (e3) (e3)) = (e1)))\/((op (e3) (e1)) = (e3))) -> (~((op (e2) (e1)) = (op (e3) (e1)))) -> ((~((op (e3) (e3)) = (e3)))\/((op (e3) (e3)) = (e3))) -> (~((e1) = (e3))) -> (((op (e0) (e0)) = (e3))\/(((op (e0) (e1)) = (e3))\/(((op (e0) (e2)) = (e3))\/((op (e0) (e3)) = (e3))))) -> (((op (e1) (e0)) = (e2))\/(((op (e1) (e1)) = (e2))\/(((op (e1) (e2)) = (e2))\/((op (e1) (e3)) = (e2))))) -> (~((op (e0) (e3)) = (op (e1) (e3)))) -> (~((op (e1) (e2)) = (op (e2) (e2)))) -> (~((e2) = (e3))) -> (~((op (e0) (e2)) = (op (e1) (e2)))) -> (~((op (e1) (e3)) = (op (e3) (e3)))) -> (((op (e1) (e0)) = (e3))\/(((op (e1) (e1)) = (e3))\/(((op (e1) (e2)) = (e3))\/((op (e1) (e3)) = (e3))))) -> (~((e0) = (e3))) -> (~((op (e0) (e0)) = (e3))) -> (((op (e0) (e0)) = (e0))\/(((op (e1) (e0)) = (e0))\/(((op (e2) (e0)) = (e0))\/((op (e3) (e0)) = (e0))))) -> (~((op (e1) (e1)) = (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)) = (e0))\/(((op (e1) (e1)) = (e0))\/(((op (e1) (e2)) = (e0))\/((op (e1) (e3)) = (e0))))) -> (~((op (e2) (e0)) = (op (e2) (e1)))) -> (~((op (e2) (e1)) = (op (e2) (e2)))) -> (~((op (e0) (e1)) = (op (e2) (e1)))) -> (((op (e2) (e1)) = (e0))\/(((op (e2) (e1)) = (e1))\/(((op (e2) (e1)) = (e2))\/((op (e2) (e1)) = (e3))))) -> (((op (e0) (e0)) = (e3))\/(((op (e1) (e0)) = (e3))\/(((op (e2) (e0)) = (e3))\/((op (e3) (e0)) = (e3))))) -> (~((op (e3) (e0)) = (op (e3) (e3)))) -> (~((op (e1) (e1)) = (op (e2) (e1)))) -> (~((op (e2) (e2)) = (e1))) -> (~((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) (e2)))) -> (((op (e0) (e1)) = (e0))\/(((op (e1) (e1)) = (e0))\/(((op (e2) (e1)) = (e0))\/((op (e3) (e1)) = (e0))))) -> (((op (e0) (e2)) = (e3))\/(((op (e1) (e2)) = (e3))\/(((op (e2) (e2)) = (e3))\/((op (e3) (e2)) = (e3))))) -> (~((op (e3) (e2)) = (op (e3) (e3)))) -> (((op (e0) (e0)) = (e1))\/(((op (e1) (e0)) = (e1))\/(((op (e2) (e0)) = (e1))\/((op (e3) (e0)) = (e1))))) -> (((op (e0) (e2)) = (e0))\/(((op (e1) (e2)) = (e0))\/(((op (e2) (e2)) = (e0))\/((op (e3) (e2)) = (e0))))) -> (~((op (e3) (e1)) = (op (e3) (e2)))) -> (~((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 (e2) (e2)) = (e0))) -> (~((op (e1) (e0)) = (op (e1) (e2)))) -> (~((op (e0) (e2)) = (op (e0) (e3)))) -> (~((op (e1) (e1)) = (op (e1) (e3)))) -> (~((op (e2) (e0)) = (op (e2) (e3)))) -> (((op (e0) (e3)) = (e1))\/(((op (e1) (e3)) = (e1))\/(((op (e2) (e3)) = (e1))\/((op (e3) (e3)) = (e1))))) -> (~((op (e1) (e0)) = (op (e1) (e1)))) -> (~((op (e0) (e0)) = (e0))) -> (((op (e0) (e0)) = (e2))\/(((op (e0) (e1)) = (e2))\/(((op (e0) (e2)) = (e2))\/((op (e0) (e3)) = (e2))))) -> (~((op (e0) (e3)) = (op (e3) (e3)))) -> (((op (e3) (e3)) = (e0))\/(((op (e3) (e3)) = (e1))\/(((op (e3) (e3)) = (e2))\/((op (e3) (e3)) = (e3))))) -> ((op (e2) (e2)) = (e2)) -> (~((op (e0) (e2)) = (op (e2) (e2)))) -> (~((e0) = (e2))) -> (~((op (e0) (e0)) = (e2))) -> (((op (e0) (e0)) = (e1))\/(((op (e0) (e1)) = (e1))\/(((op (e0) (e2)) = (e1))\/((op (e0) (e3)) = (e1))))) -> (~((e0) = (e1))) -> ((op (e1) (e1)) = (e1)) -> (~((op (e0) (e1)) = (op (e1) (e1)))) -> (~((op (e0) (e0)) = (e1))) -> (((op (e0) (e0)) = (e0))\/(((op (e0) (e0)) = (e1))\/(((op (e0) (e0)) = (e2))\/((op (e0) (e0)) = (e3))))) -> (~((e1) = (e2))) -> (((op (e0) (e0)) = (e0))\/(((op (e0) (e1)) = (e0))\/(((op (e0) (e2)) = (e0))\/((op (e0) (e3)) = (e0))))) -> (~((op (e1) (e1)) = (op (e1) (e2)))) -> (((op (e0) (e2)) = (e1))\/(((op (e1) (e2)) = (e1))\/(((op (e2) (e2)) = (e1))\/((op (e3) (e2)) = (e1))))) -> (~((op (e3) (op (e0) (e3))) = (op (e0) (e3)))) -> (~((op (e1) (e1)) = (e2))) -> (~((op (e1) (e2)) = (op (e3) (e2)))) -> (~((op (e1) (e1)) = (e3))) -> (~((op (e2) (e0)) = (op (e2) (e2)))) -> (((op (e0) (e0)) = (e2))\/(((op (e1) (e0)) = (e2))\/(((op (e2) (e0)) = (e2))\/((op (e3) (e0)) = (e2))))) -> ((~((op (e3) (e3)) = (e2)))\/((op (e3) (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 (e1) (e1)) = (e0)))\/((op (e1) (e0)) = (e1))) -> ((~((op (e1) (e1)) = (e2)))\/((op (e1) (e2)) = (e1))) -> (~((op (e1) (e2)) = (op (e1) (e3)))) -> ((~((op (e2) (e2)) = (e0)))\/((op (e2) (e0)) = (e2))) -> (~((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 (e2) (e3)) = (op (e3) (e3)))) -> (((op (e2) (e0)) = (e3))\/(((op (e2) (e1)) = (e3))\/(((op (e2) (e2)) = (e3))\/((op (e2) (e3)) = (e3))))) -> (((op (e1) (e1)) = (e0))\/(((op (e1) (e1)) = (e1))\/(((op (e1) (e1)) = (e2))\/((op (e1) (e1)) = (e3))))) -> ((~((op (e2) (e2)) = (e3)))\/((op (e2) (e3)) = (e2))) -> (((op (e0) (e3)) = (e0))\/(((op (e1) (e3)) = (e0))\/(((op (e2) (e3)) = (e0))\/((op (e3) (e3)) = (e0))))) -> ((~((op (e3) (e3)) = (e0)))\/((op (e3) (e0)) = (e3))) -> (((op (e1) (e0)) = (e1))\/(((op (e1) (e1)) = (e1))\/(((op (e1) (e2)) = (e1))\/((op (e1) (e3)) = (e1))))) -> ((~((op (e2) (e2)) = (e2)))\/((op (e2) (e2)) = (e2))) -> ((~((op (e1) (e1)) = (e3)))\/((op (e1) (e3)) = (e1))) -> ((~((op (e2) (e2)) = (e1)))\/((op (e2) (e1)) = (e2))) -> (~((op (e2) (e1)) = (op (e2) (e3)))) -> ((~((op (e1) (e1)) = (e1)))\/((op (e1) (e1)) = (e1))) -> (~((op (e0) (e2)) = (op (e3) (e2)))) -> (((op (e3) (e0)) = (e2))\/(((op (e3) (e1)) = (e2))\/(((op (e3) (e2)) = (e2))\/((op (e3) (e3)) = (e2))))) -> (((op (e1) (e2)) = (e0))\/(((op (e1) (e2)) = (e1))\/(((op (e1) (e2)) = (e2))\/((op (e1) (e2)) = (e3))))) -> (((op (e2) (e0)) = (e0))\/(((op (e2) (e1)) = (e0))\/(((op (e2) (e2)) = (e0))\/((op (e2) (e3)) = (e0))))) -> (~((op (e2) (e0)) = (op (e3) (e0)))) -> (((op (e0) (e1)) = (e0))\/(((op (e0) (e1)) = (e1))\/(((op (e0) (e1)) = (e2))\/((op (e0) (e1)) = (e3))))) -> (((op (e3) (e0)) = (e0))\/(((op (e3) (e1)) = (e0))\/(((op (e3) (e2)) = (e0))\/((op (e3) (e3)) = (e0))))) -> False). % 15.16/15.36 do 0 intro. intros zenon_H10c zenon_H13c zenon_H10d zenon_Ha3 zenon_H58 zenon_H84 zenon_H80 zenon_H7d zenon_H6a zenon_H87 zenon_H8b zenon_H90 zenon_H4b zenon_H59 zenon_Hf0 zenon_H145 zenon_H160 zenon_H15f zenon_H163 zenon_H154 zenon_H157 zenon_Hde zenon_H15a zenon_Hbe zenon_Hbb zenon_Hb1 zenon_H52 zenon_Hb4 zenon_Hb7 zenon_H105 zenon_H144 zenon_H175 zenon_H173 zenon_Hf1 zenon_H16f zenon_H135 zenon_H109 zenon_H138 zenon_H12d zenon_H16c zenon_H2e zenon_H166 zenon_Hc9 zenon_H11e zenon_Hce zenon_H121 zenon_Hd7 zenon_H20 zenon_H8e zenon_H36 zenon_H3b zenon_H35 zenon_H28 zenon_H5e zenon_H8f zenon_H44 zenon_H9e zenon_H21 zenon_H23 zenon_H45 zenon_H12a zenon_Ha7 zenon_H110 zenon_H116 zenon_H11b zenon_H192 zenon_Hd6 zenon_H17d zenon_H182 zenon_H17a zenon_Heb zenon_H10e zenon_H1a2 zenon_H199 zenon_H1e4 zenon_H1d3 zenon_H1d0 zenon_H1d4 zenon_H1cd zenon_H1cf zenon_H2d zenon_He3 zenon_He6 zenon_H1b3 zenon_H1c3 zenon_Hd3 zenon_H10f zenon_H1c5 zenon_Haa zenon_H1d2 zenon_H1e3 zenon_H1e2 zenon_H1d8 zenon_H140 zenon_H1df zenon_H1d5 zenon_H1f5 zenon_H1e5 zenon_H1e9 zenon_H1f6. % 15.16/15.36 apply (zenon_or_s _ _ zenon_H1c3); [ zenon_intro zenon_H30 | zenon_intro zenon_H124 ]. % 15.16/15.36 apply (zenon_or_s _ _ zenon_H10f); [ zenon_intro zenon_H3c | zenon_intro zenon_Hba ]. % 15.16/15.36 apply (zenon_or_s _ _ zenon_H10c); [ zenon_intro zenon_H104 | zenon_intro zenon_H10a ]. % 15.16/15.36 apply (zenon_or_s _ _ zenon_H10e); [ zenon_intro zenon_H3d | zenon_intro zenon_H106 ]. % 15.16/15.36 apply (zenon_or_s _ _ zenon_H10d); [ zenon_intro zenon_H3e | zenon_intro zenon_H42 ]. % 15.16/15.36 apply (zenon_or_s _ _ zenon_H110); [ zenon_intro zenon_H1f | zenon_intro zenon_H111 ]. % 15.16/15.36 exact (zenon_H20 zenon_H1f). % 15.16/15.36 apply (zenon_or_s _ _ zenon_H111); [ zenon_intro zenon_H49 | zenon_intro zenon_H112 ]. % 15.16/15.36 apply (zenon_L131_); trivial. % 15.16/15.36 apply (zenon_or_s _ _ zenon_H112); [ zenon_intro zenon_Hab | zenon_intro zenon_Hca ]. % 15.16/15.36 apply (zenon_L132_); trivial. % 15.16/15.36 apply (zenon_L114_); trivial. % 15.16/15.36 apply (zenon_L159_); trivial. % 15.16/15.36 apply (zenon_or_s _ _ zenon_H10d); [ zenon_intro zenon_H3e | zenon_intro zenon_H42 ]. % 15.16/15.36 apply (zenon_or_s _ _ zenon_H110); [ zenon_intro zenon_H1f | zenon_intro zenon_H111 ]. % 15.16/15.36 exact (zenon_H20 zenon_H1f). % 15.16/15.36 apply (zenon_or_s _ _ zenon_H111); [ zenon_intro zenon_H49 | zenon_intro zenon_H112 ]. % 15.16/15.36 apply (zenon_L108_); trivial. % 15.16/15.36 apply (zenon_or_s _ _ zenon_H112); [ zenon_intro zenon_Hab | zenon_intro zenon_Hca ]. % 15.16/15.36 apply (zenon_L109_); trivial. % 15.16/15.36 apply (zenon_L179_); trivial. % 15.16/15.36 apply (zenon_L153_); trivial. % 15.16/15.36 apply (zenon_or_s _ _ zenon_H10e); [ zenon_intro zenon_H3d | zenon_intro zenon_H106 ]. % 15.16/15.36 apply (zenon_or_s _ _ zenon_H10d); [ zenon_intro zenon_H3e | zenon_intro zenon_H42 ]. % 15.16/15.36 apply (zenon_or_s _ _ zenon_H110); [ zenon_intro zenon_H1f | zenon_intro zenon_H111 ]. % 15.16/15.36 exact (zenon_H20 zenon_H1f). % 15.16/15.36 apply (zenon_or_s _ _ zenon_H111); [ zenon_intro zenon_H49 | zenon_intro zenon_H112 ]. % 15.16/15.36 apply (zenon_L181_); trivial. % 15.16/15.36 apply (zenon_or_s _ _ zenon_H112); [ zenon_intro zenon_Hab | zenon_intro zenon_Hca ]. % 15.16/15.36 apply (zenon_L132_); trivial. % 15.16/15.36 apply (zenon_L182_); trivial. % 15.16/15.36 apply (zenon_L102_); trivial. % 15.16/15.36 apply (zenon_L115_); trivial. % 15.16/15.36 apply (zenon_or_s _ _ zenon_H10c); [ zenon_intro zenon_H104 | zenon_intro zenon_H10a ]. % 15.16/15.36 apply (zenon_or_s _ _ zenon_H110); [ zenon_intro zenon_H1f | zenon_intro zenon_H111 ]. % 15.16/15.36 exact (zenon_H20 zenon_H1f). % 15.16/15.36 apply (zenon_or_s _ _ zenon_H111); [ zenon_intro zenon_H49 | zenon_intro zenon_H112 ]. % 15.16/15.36 apply (zenon_L191_); trivial. % 15.16/15.36 apply (zenon_or_s _ _ zenon_H112); [ zenon_intro zenon_Hab | zenon_intro zenon_Hca ]. % 15.16/15.36 apply (zenon_L273_); trivial. % 15.16/15.36 apply (zenon_L276_); trivial. % 15.16/15.36 apply (zenon_L82_); trivial. % 15.16/15.36 apply (zenon_L137_); trivial. % 15.16/15.36 (* end of lemma zenon_L277_ *) % 15.16/15.36 assert (zenon_L278_ : (((op (e0) (e1)) = (e3))\/(((op (e1) (e1)) = (e3))\/(((op (e2) (e1)) = (e3))\/((op (e3) (e1)) = (e3))))) -> (~((e0) = (e3))) -> ((op (e0) (e1)) = (e0)) -> (~((op (e1) (e1)) = (e3))) -> (~((e2) = (e3))) -> ((op (e2) (e1)) = (e2)) -> ((op (e3) (e3)) = (e3)) -> (~((op (e3) (e1)) = (op (e3) (e3)))) -> False). % 15.16/15.36 do 0 intro. intros zenon_H199 zenon_H4b zenon_H49 zenon_H182 zenon_H6a zenon_H156 zenon_H42 zenon_H12d. % 15.16/15.36 apply (zenon_or_s _ _ zenon_H199); [ zenon_intro zenon_H4a | zenon_intro zenon_H19a ]. % 15.16/15.36 apply (zenon_L9_); trivial. % 15.16/15.36 apply (zenon_or_s _ _ zenon_H19a); [ zenon_intro zenon_H96 | zenon_intro zenon_H19b ]. % 15.16/15.36 exact (zenon_H182 zenon_H96). % 15.16/15.36 apply (zenon_or_s _ _ zenon_H19b); [ zenon_intro zenon_Hdf | zenon_intro zenon_H10a ]. % 15.16/15.36 apply (zenon_L183_); trivial. % 15.16/15.36 apply (zenon_L102_); trivial. % 15.16/15.36 (* end of lemma zenon_L278_ *) % 15.16/15.36 assert (zenon_L279_ : ((~((op (e2) (e2)) = (e1)))\/((op (e2) (e1)) = (e2))) -> (~((op (e1) (e1)) = (e3))) -> (~((op (e3) (e1)) = (op (e3) (e3)))) -> (((op (e0) (e1)) = (e3))\/(((op (e1) (e1)) = (e3))\/(((op (e2) (e1)) = (e3))\/((op (e3) (e1)) = (e3))))) -> (((op (e0) (e0)) = (e3))\/(((op (e0) (e1)) = (e3))\/(((op (e0) (e2)) = (e3))\/((op (e0) (e3)) = (e3))))) -> ((op (e3) (e3)) = (e3)) -> (~((op (e0) (e3)) = (op (e3) (e3)))) -> (~((op (e2) (e2)) = (e0))) -> (~((op (e0) (e2)) = (op (e2) (e2)))) -> (((op (e2) (e2)) = (e0))\/(((op (e2) (e2)) = (e1))\/(((op (e2) (e2)) = (e2))\/((op (e2) (e2)) = (e3))))) -> ((op (e0) (e1)) = (e0)) -> (~((e0) = (e3))) -> (~((op (e0) (e0)) = (e3))) -> (((op (e0) (e0)) = (e1))\/(((op (e0) (e1)) = (e1))\/(((op (e0) (e2)) = (e1))\/((op (e0) (e3)) = (e1))))) -> (~((e1) = (e2))) -> (~((e1) = (e3))) -> (~((e0) = (e1))) -> (~((op (e0) (e0)) = (e2))) -> (~((e0) = (e2))) -> (((op (e1) (e0)) = (e2))\/(((op (e1) (e1)) = (e2))\/(((op (e1) (e2)) = (e2))\/((op (e1) (e3)) = (e2))))) -> (~((op (e0) (e3)) = (op (e1) (e3)))) -> (~((op (e1) (e2)) = (op (e2) (e2)))) -> (~((e2) = (e3))) -> (~((op (e0) (e2)) = (op (e1) (e2)))) -> (~((op (e1) (e3)) = (op (e3) (e3)))) -> (((op (e1) (e0)) = (e3))\/(((op (e1) (e1)) = (e3))\/(((op (e1) (e2)) = (e3))\/((op (e1) (e3)) = (e3))))) -> (((op (e0) (e0)) = (e2))\/(((op (e0) (e1)) = (e2))\/(((op (e0) (e2)) = (e2))\/((op (e0) (e3)) = (e2))))) -> ((~((op (e2) (e2)) = (e2)))\/((op (e2) (e2)) = (e2))) -> False). % 15.16/15.36 do 0 intro. intros zenon_H1e3 zenon_H182 zenon_H12d zenon_H199 zenon_H58 zenon_H42 zenon_H36 zenon_H2e zenon_H28 zenon_H2d zenon_H49 zenon_H4b zenon_H59 zenon_H44 zenon_Ha7 zenon_Ha3 zenon_H9e zenon_H8f zenon_H5e zenon_H84 zenon_H80 zenon_H7d zenon_H6a zenon_H87 zenon_H8b zenon_H90 zenon_H8e zenon_Haa. % 15.16/15.36 apply (zenon_or_s _ _ zenon_H1e3); [ zenon_intro zenon_H52 | zenon_intro zenon_H156 ]. % 15.16/15.36 apply (zenon_L36_); trivial. % 15.16/15.36 apply (zenon_L278_); trivial. % 15.16/15.36 (* end of lemma zenon_L279_ *) % 15.16/15.36 assert (zenon_L280_ : (~((op (op (e2) (e2)) (op (e2) (e2))) = (op (e0) (e0)))) -> ((op (e2) (e2)) = (e0)) -> False). % 15.16/15.36 do 0 intro. intros zenon_H1fb zenon_H32. % 15.16/15.36 cut (((op (e2) (e2)) = (e0))); [idtac | apply NNPP; zenon_intro zenon_H2e]. % 15.16/15.36 cut (((op (e2) (e2)) = (e0))); [idtac | apply NNPP; zenon_intro zenon_H2e]. % 15.16/15.36 congruence. % 15.16/15.36 exact (zenon_H2e zenon_H32). % 15.16/15.36 exact (zenon_H2e zenon_H32). % 15.16/15.36 (* end of lemma zenon_L280_ *) % 15.16/15.36 assert (zenon_L281_ : ((op (e2) (e1)) = (e3)) -> ((op (e0) (e0)) = (e1)) -> ((op (e2) (e2)) = (e0)) -> False). % 15.16/15.36 do 0 intro. intros zenon_Hdf zenon_H47 zenon_H32. % 15.16/15.36 apply (zenon_notand_s _ _ ax13); [ zenon_intro zenon_H14e | zenon_intro zenon_H1fc ]. % 15.16/15.36 elim (classic ((op (op (e2) (e2)) (op (e2) (e2))) = (op (op (e2) (e2)) (op (e2) (e2))))); [ zenon_intro zenon_Hfa | zenon_intro zenon_Hfb ]. % 15.16/15.36 cut (((op (op (e2) (e2)) (op (e2) (e2))) = (op (op (e2) (e2)) (op (e2) (e2)))) = ((e1) = (op (op (e2) (e2)) (op (e2) (e2))))). % 15.16/15.36 intro zenon_D_pnotp. % 15.16/15.36 apply zenon_H14e. % 15.16/15.36 rewrite <- zenon_D_pnotp. % 15.16/15.36 exact zenon_Hfa. % 15.16/15.36 cut (((op (op (e2) (e2)) (op (e2) (e2))) = (op (op (e2) (e2)) (op (e2) (e2))))); [idtac | apply NNPP; zenon_intro zenon_Hfb]. % 15.16/15.36 cut (((op (op (e2) (e2)) (op (e2) (e2))) = (e1))); [idtac | apply NNPP; zenon_intro zenon_H14f]. % 15.16/15.36 congruence. % 15.16/15.36 cut (((op (e0) (e0)) = (e1)) = ((op (op (e2) (e2)) (op (e2) (e2))) = (e1))). % 15.16/15.36 intro zenon_D_pnotp. % 15.16/15.36 apply zenon_H14f. % 15.16/15.36 rewrite <- zenon_D_pnotp. % 15.16/15.36 exact zenon_H47. % 15.16/15.36 cut (((e1) = (e1))); [idtac | apply NNPP; zenon_intro zenon_Ha0]. % 15.16/15.36 cut (((op (e0) (e0)) = (op (op (e2) (e2)) (op (e2) (e2))))); [idtac | apply NNPP; zenon_intro zenon_H1fd]. % 15.16/15.36 congruence. % 15.16/15.36 elim (classic ((op (op (e2) (e2)) (op (e2) (e2))) = (op (op (e2) (e2)) (op (e2) (e2))))); [ zenon_intro zenon_Hfa | zenon_intro zenon_Hfb ]. % 15.16/15.36 cut (((op (op (e2) (e2)) (op (e2) (e2))) = (op (op (e2) (e2)) (op (e2) (e2)))) = ((op (e0) (e0)) = (op (op (e2) (e2)) (op (e2) (e2))))). % 15.16/15.36 intro zenon_D_pnotp. % 15.16/15.36 apply zenon_H1fd. % 15.16/15.36 rewrite <- zenon_D_pnotp. % 15.16/15.36 exact zenon_Hfa. % 15.16/15.36 cut (((op (op (e2) (e2)) (op (e2) (e2))) = (op (op (e2) (e2)) (op (e2) (e2))))); [idtac | apply NNPP; zenon_intro zenon_Hfb]. % 15.16/15.36 cut (((op (op (e2) (e2)) (op (e2) (e2))) = (op (e0) (e0)))); [idtac | apply NNPP; zenon_intro zenon_H1fb]. % 15.16/15.36 congruence. % 15.16/15.36 apply (zenon_L280_); trivial. % 15.16/15.36 apply zenon_Hfb. apply refl_equal. % 15.16/15.36 apply zenon_Hfb. apply refl_equal. % 15.16/15.36 apply zenon_Ha0. apply refl_equal. % 15.16/15.36 apply zenon_Hfb. apply refl_equal. % 15.16/15.36 apply zenon_Hfb. apply refl_equal. % 15.16/15.36 apply (zenon_notand_s _ _ zenon_H1fc); [ zenon_intro zenon_H1fe | zenon_intro zenon_H1cb ]. % 15.16/15.36 apply zenon_H1fe. apply sym_equal. exact zenon_H32. % 15.16/15.36 elim (classic ((op (e2) (op (op (e2) (e2)) (op (e2) (e2)))) = (op (e2) (op (op (e2) (e2)) (op (e2) (e2)))))); [ zenon_intro zenon_Hff | zenon_intro zenon_H100 ]. % 15.16/15.36 cut (((op (e2) (op (op (e2) (e2)) (op (e2) (e2)))) = (op (e2) (op (op (e2) (e2)) (op (e2) (e2))))) = ((e3) = (op (e2) (op (op (e2) (e2)) (op (e2) (e2)))))). % 15.16/15.36 intro zenon_D_pnotp. % 15.16/15.36 apply zenon_H1cb. % 15.16/15.36 rewrite <- zenon_D_pnotp. % 15.16/15.36 exact zenon_Hff. % 15.16/15.36 cut (((op (e2) (op (op (e2) (e2)) (op (e2) (e2)))) = (op (e2) (op (op (e2) (e2)) (op (e2) (e2)))))); [idtac | apply NNPP; zenon_intro zenon_H100]. % 15.16/15.36 cut (((op (e2) (op (op (e2) (e2)) (op (e2) (e2)))) = (e3))); [idtac | apply NNPP; zenon_intro zenon_H1cc]. % 15.16/15.36 congruence. % 15.16/15.36 cut (((op (e2) (e1)) = (e3)) = ((op (e2) (op (op (e2) (e2)) (op (e2) (e2)))) = (e3))). % 15.16/15.36 intro zenon_D_pnotp. % 15.16/15.36 apply zenon_H1cc. % 15.16/15.36 rewrite <- zenon_D_pnotp. % 15.16/15.36 exact zenon_Hdf. % 15.16/15.36 cut (((e3) = (e3))); [idtac | apply NNPP; zenon_intro zenon_H4d]. % 15.16/15.36 cut (((op (e2) (e1)) = (op (e2) (op (op (e2) (e2)) (op (e2) (e2)))))); [idtac | apply NNPP; zenon_intro zenon_H152]. % 15.16/15.36 congruence. % 15.16/15.36 elim (classic ((op (e2) (op (op (e2) (e2)) (op (e2) (e2)))) = (op (e2) (op (op (e2) (e2)) (op (e2) (e2)))))); [ zenon_intro zenon_Hff | zenon_intro zenon_H100 ]. % 15.16/15.36 cut (((op (e2) (op (op (e2) (e2)) (op (e2) (e2)))) = (op (e2) (op (op (e2) (e2)) (op (e2) (e2))))) = ((op (e2) (e1)) = (op (e2) (op (op (e2) (e2)) (op (e2) (e2)))))). % 15.16/15.36 intro zenon_D_pnotp. % 15.16/15.36 apply zenon_H152. % 15.16/15.36 rewrite <- zenon_D_pnotp. % 15.16/15.36 exact zenon_Hff. % 15.16/15.36 cut (((op (e2) (op (op (e2) (e2)) (op (e2) (e2)))) = (op (e2) (op (op (e2) (e2)) (op (e2) (e2)))))); [idtac | apply NNPP; zenon_intro zenon_H100]. % 15.16/15.36 cut (((op (e2) (op (op (e2) (e2)) (op (e2) (e2)))) = (op (e2) (e1)))); [idtac | apply NNPP; zenon_intro zenon_H153]. % 15.16/15.36 congruence. % 15.16/15.36 cut (((op (op (e2) (e2)) (op (e2) (e2))) = (e1))); [idtac | apply NNPP; zenon_intro zenon_H14f]. % 15.16/15.36 cut (((e2) = (e2))); [idtac | apply NNPP; zenon_intro zenon_H60]. % 15.16/15.36 congruence. % 15.16/15.36 apply zenon_H60. apply refl_equal. % 15.16/15.36 cut (((op (e0) (e0)) = (e1)) = ((op (op (e2) (e2)) (op (e2) (e2))) = (e1))). % 15.16/15.36 intro zenon_D_pnotp. % 15.16/15.36 apply zenon_H14f. % 15.16/15.36 rewrite <- zenon_D_pnotp. % 15.16/15.36 exact zenon_H47. % 15.16/15.36 cut (((e1) = (e1))); [idtac | apply NNPP; zenon_intro zenon_Ha0]. % 15.16/15.36 cut (((op (e0) (e0)) = (op (op (e2) (e2)) (op (e2) (e2))))); [idtac | apply NNPP; zenon_intro zenon_H1fd]. % 15.16/15.36 congruence. % 15.16/15.36 elim (classic ((op (op (e2) (e2)) (op (e2) (e2))) = (op (op (e2) (e2)) (op (e2) (e2))))); [ zenon_intro zenon_Hfa | zenon_intro zenon_Hfb ]. % 15.16/15.36 cut (((op (op (e2) (e2)) (op (e2) (e2))) = (op (op (e2) (e2)) (op (e2) (e2)))) = ((op (e0) (e0)) = (op (op (e2) (e2)) (op (e2) (e2))))). % 15.16/15.36 intro zenon_D_pnotp. % 15.16/15.36 apply zenon_H1fd. % 15.16/15.36 rewrite <- zenon_D_pnotp. % 15.16/15.36 exact zenon_Hfa. % 15.16/15.36 cut (((op (op (e2) (e2)) (op (e2) (e2))) = (op (op (e2) (e2)) (op (e2) (e2))))); [idtac | apply NNPP; zenon_intro zenon_Hfb]. % 15.16/15.36 cut (((op (op (e2) (e2)) (op (e2) (e2))) = (op (e0) (e0)))); [idtac | apply NNPP; zenon_intro zenon_H1fb]. % 15.16/15.36 congruence. % 15.16/15.36 apply (zenon_L280_); trivial. % 15.16/15.36 apply zenon_Hfb. apply refl_equal. % 15.16/15.36 apply zenon_Hfb. apply refl_equal. % 15.16/15.36 apply zenon_Ha0. apply refl_equal. % 15.16/15.36 apply zenon_H100. apply refl_equal. % 15.16/15.36 apply zenon_H100. apply refl_equal. % 15.16/15.36 apply zenon_H4d. apply refl_equal. % 15.16/15.36 apply zenon_H100. apply refl_equal. % 15.16/15.36 apply zenon_H100. apply refl_equal. % 15.16/15.36 (* end of lemma zenon_L281_ *) % 15.16/15.36 assert (zenon_L282_ : (((op (e2) (e2)) = (e0))\/(((op (e2) (e2)) = (e1))\/(((op (e2) (e2)) = (e2))\/((op (e2) (e2)) = (e3))))) -> ((op (e0) (e0)) = (e1)) -> ((op (e2) (e1)) = (e3)) -> (~((op (e2) (e2)) = (e1))) -> (~((op (e2) (e2)) = (e2))) -> (~((op (e2) (e2)) = (e3))) -> False). % 15.16/15.36 do 0 intro. intros zenon_H2d zenon_H47 zenon_Hdf zenon_H52 zenon_H2f zenon_H30. % 15.16/15.36 apply (zenon_or_s _ _ zenon_H2d); [ zenon_intro zenon_H32 | zenon_intro zenon_H31 ]. % 15.16/15.36 apply (zenon_L281_); trivial. % 15.16/15.36 apply (zenon_or_s _ _ zenon_H31); [ zenon_intro zenon_H2a | zenon_intro zenon_H33 ]. % 15.16/15.36 exact (zenon_H52 zenon_H2a). % 15.16/15.36 apply (zenon_or_s _ _ zenon_H33); [ zenon_intro zenon_H35 | zenon_intro zenon_H34 ]. % 15.16/15.36 exact (zenon_H2f zenon_H35). % 15.16/15.36 exact (zenon_H30 zenon_H34). % 15.16/15.36 (* end of lemma zenon_L282_ *) % 15.16/15.36 assert (zenon_L283_ : (((op (e0) (e0)) = (e1))\/(((op (e0) (e1)) = (e1))\/(((op (e0) (e2)) = (e1))\/((op (e0) (e3)) = (e1))))) -> (~((op (e2) (e3)) = (op (e3) (e3)))) -> (~((op (e2) (e2)) = (e3))) -> (((op (e2) (e2)) = (e0))\/(((op (e2) (e2)) = (e1))\/(((op (e2) (e2)) = (e2))\/((op (e2) (e2)) = (e3))))) -> (~((op (e2) (e2)) = (e1))) -> (~((op (e2) (e2)) = (e2))) -> ((op (e2) (e0)) = (e2)) -> (((op (e2) (e0)) = (e3))\/(((op (e2) (e1)) = (e3))\/(((op (e2) (e2)) = (e3))\/((op (e2) (e3)) = (e3))))) -> (~((e0) = (e1))) -> (~((op (e0) (e3)) = (op (e3) (e3)))) -> ((op (e3) (e3)) = (e3)) -> (((op (e0) (e0)) = (e2))\/(((op (e0) (e1)) = (e2))\/(((op (e0) (e2)) = (e2))\/((op (e0) (e3)) = (e2))))) -> (~((op (e0) (e0)) = (e2))) -> (~((e0) = (e2))) -> (~((e1) = (e3))) -> (~((e2) = (e3))) -> ((op (e0) (e1)) = (e0)) -> (~((e0) = (e3))) -> (~((op (e0) (e0)) = (e3))) -> (((op (e0) (e0)) = (e3))\/(((op (e0) (e1)) = (e3))\/(((op (e0) (e2)) = (e3))\/((op (e0) (e3)) = (e3))))) -> (~((e1) = (e2))) -> False). % 15.16/15.36 do 0 intro. intros zenon_H44 zenon_He3 zenon_H30 zenon_H2d zenon_H52 zenon_H2f zenon_Hdd zenon_He6 zenon_H9e zenon_H36 zenon_H42 zenon_H8e zenon_H8f zenon_H5e zenon_Ha3 zenon_H6a zenon_H49 zenon_H4b zenon_H59 zenon_H58 zenon_Ha7. % 15.16/15.36 apply (zenon_or_s _ _ zenon_H44); [ zenon_intro zenon_H47 | zenon_intro zenon_H46 ]. % 15.16/15.36 apply (zenon_or_s _ _ zenon_He6); [ zenon_intro zenon_Haf | zenon_intro zenon_He7 ]. % 15.16/15.36 apply (zenon_L64_); trivial. % 15.16/15.36 apply (zenon_or_s _ _ zenon_He7); [ zenon_intro zenon_Hdf | zenon_intro zenon_He8 ]. % 15.16/15.36 apply (zenon_L282_); trivial. % 15.16/15.36 apply (zenon_or_s _ _ zenon_He8); [ zenon_intro zenon_H34 | zenon_intro zenon_He2 ]. % 15.16/15.36 exact (zenon_H30 zenon_H34). % 15.16/15.36 apply (zenon_L66_); trivial. % 15.16/15.37 apply (zenon_or_s _ _ zenon_H46); [ zenon_intro zenon_H22 | zenon_intro zenon_H48 ]. % 15.16/15.37 apply (zenon_L27_); trivial. % 15.16/15.37 apply (zenon_or_s _ _ zenon_H48); [ zenon_intro zenon_H29 | zenon_intro zenon_H37 ]. % 15.16/15.37 apply (zenon_L30_); trivial. % 15.16/15.37 apply (zenon_L34_); trivial. % 15.16/15.37 (* end of lemma zenon_L283_ *) % 15.16/15.37 assert (zenon_L284_ : (~((op (e2) (e0)) = (op (e2) (e1)))) -> ((op (e2) (e0)) = (e2)) -> ((op (e2) (e1)) = (e2)) -> False). % 15.16/15.37 do 0 intro. intros zenon_H154 zenon_Hdd zenon_H156. % 15.16/15.37 cut (((op (e2) (e0)) = (e2)) = ((op (e2) (e0)) = (op (e2) (e1)))). % 15.16/15.37 intro zenon_D_pnotp. % 15.16/15.37 apply zenon_H154. % 15.16/15.37 rewrite <- zenon_D_pnotp. % 15.16/15.37 exact zenon_Hdd. % 15.16/15.37 cut (((e2) = (op (e2) (e1)))); [idtac | apply NNPP; zenon_intro zenon_H159]. % 15.16/15.37 cut (((op (e2) (e0)) = (op (e2) (e0)))); [idtac | apply NNPP; zenon_intro zenon_Hd2]. % 15.16/15.37 congruence. % 15.16/15.37 apply zenon_Hd2. apply refl_equal. % 15.16/15.37 apply zenon_H159. apply sym_equal. exact zenon_H156. % 15.16/15.37 (* end of lemma zenon_L284_ *) % 15.16/15.37 assert (zenon_L285_ : ((~((op (e2) (e2)) = (e1)))\/((op (e2) (e1)) = (e2))) -> (~((op (e2) (e0)) = (op (e2) (e1)))) -> ((~((op (e2) (e2)) = (e3)))\/((op (e2) (e3)) = (e2))) -> (~((op (e2) (e0)) = (op (e2) (e3)))) -> (((op (e2) (e0)) = (e3))\/(((op (e2) (e1)) = (e3))\/(((op (e2) (e2)) = (e3))\/((op (e2) (e3)) = (e3))))) -> ((op (e3) (e3)) = (e3)) -> (~((op (e2) (e3)) = (op (e3) (e3)))) -> (((op (e2) (e2)) = (e0))\/(((op (e2) (e2)) = (e1))\/(((op (e2) (e2)) = (e2))\/((op (e2) (e2)) = (e3))))) -> ((op (e2) (e0)) = (e2)) -> (~((e2) = (e3))) -> (~((e0) = (e1))) -> ((op (e0) (e1)) = (e0)) -> (((op (e0) (e0)) = (e3))\/(((op (e0) (e1)) = (e3))\/(((op (e0) (e2)) = (e3))\/((op (e0) (e3)) = (e3))))) -> (~((op (e0) (e3)) = (op (e3) (e3)))) -> (~((e1) = (e3))) -> (~((e0) = (e3))) -> (~((op (e0) (e0)) = (e3))) -> (((op (e0) (e0)) = (e2))\/(((op (e0) (e1)) = (e2))\/(((op (e0) (e2)) = (e2))\/((op (e0) (e3)) = (e2))))) -> (~((e1) = (e2))) -> (~((e0) = (e2))) -> (~((op (e0) (e0)) = (e2))) -> (((op (e0) (e0)) = (e1))\/(((op (e0) (e1)) = (e1))\/(((op (e0) (e2)) = (e1))\/((op (e0) (e3)) = (e1))))) -> (~((op (e2) (e0)) = (op (e2) (e2)))) -> ((~((op (e2) (e2)) = (e2)))\/((op (e2) (e2)) = (e2))) -> False). % 15.16/15.37 do 0 intro. intros zenon_H1e3 zenon_H154 zenon_H1c3 zenon_Hce zenon_He6 zenon_H42 zenon_He3 zenon_H2d zenon_Hdd zenon_H6a zenon_H9e zenon_H49 zenon_H58 zenon_H36 zenon_Ha3 zenon_H4b zenon_H59 zenon_H8e zenon_Ha7 zenon_H5e zenon_H8f zenon_H44 zenon_H17a zenon_Haa. % 15.16/15.37 apply (zenon_or_s _ _ zenon_H1e3); [ zenon_intro zenon_H52 | zenon_intro zenon_H156 ]. % 15.16/15.37 apply (zenon_or_s _ _ zenon_Haa); [ zenon_intro zenon_H2f | zenon_intro zenon_H35 ]. % 15.16/15.37 apply (zenon_or_s _ _ zenon_H1c3); [ zenon_intro zenon_H30 | zenon_intro zenon_H124 ]. % 15.16/15.37 apply (zenon_L283_); trivial. % 15.16/15.37 apply (zenon_L119_); trivial. % 15.16/15.37 apply (zenon_L161_); trivial. % 15.16/15.37 apply (zenon_L284_); trivial. % 15.16/15.37 (* end of lemma zenon_L285_ *) % 15.16/15.37 assert (zenon_L286_ : ((~((op (e2) (e2)) = (e0)))\/((op (e2) (e0)) = (e2))) -> (~((op (e2) (e0)) = (op (e2) (e2)))) -> (~((op (e2) (e3)) = (op (e3) (e3)))) -> (((op (e2) (e0)) = (e3))\/(((op (e2) (e1)) = (e3))\/(((op (e2) (e2)) = (e3))\/((op (e2) (e3)) = (e3))))) -> (~((op (e2) (e0)) = (op (e2) (e3)))) -> ((~((op (e2) (e2)) = (e3)))\/((op (e2) (e3)) = (e2))) -> (~((op (e2) (e0)) = (op (e2) (e1)))) -> ((~((op (e2) (e2)) = (e2)))\/((op (e2) (e2)) = (e2))) -> (((op (e0) (e0)) = (e2))\/(((op (e0) (e1)) = (e2))\/(((op (e0) (e2)) = (e2))\/((op (e0) (e3)) = (e2))))) -> (((op (e1) (e0)) = (e3))\/(((op (e1) (e1)) = (e3))\/(((op (e1) (e2)) = (e3))\/((op (e1) (e3)) = (e3))))) -> (~((op (e1) (e3)) = (op (e3) (e3)))) -> (~((op (e0) (e2)) = (op (e1) (e2)))) -> (~((e2) = (e3))) -> (~((op (e1) (e2)) = (op (e2) (e2)))) -> (~((op (e0) (e3)) = (op (e1) (e3)))) -> (((op (e1) (e0)) = (e2))\/(((op (e1) (e1)) = (e2))\/(((op (e1) (e2)) = (e2))\/((op (e1) (e3)) = (e2))))) -> (~((e0) = (e2))) -> (~((op (e0) (e0)) = (e2))) -> (~((e0) = (e1))) -> (~((e1) = (e3))) -> (~((e1) = (e2))) -> (((op (e0) (e0)) = (e1))\/(((op (e0) (e1)) = (e1))\/(((op (e0) (e2)) = (e1))\/((op (e0) (e3)) = (e1))))) -> (~((op (e0) (e0)) = (e3))) -> (~((e0) = (e3))) -> ((op (e0) (e1)) = (e0)) -> (((op (e2) (e2)) = (e0))\/(((op (e2) (e2)) = (e1))\/(((op (e2) (e2)) = (e2))\/((op (e2) (e2)) = (e3))))) -> (~((op (e0) (e2)) = (op (e2) (e2)))) -> (~((op (e0) (e3)) = (op (e3) (e3)))) -> ((op (e3) (e3)) = (e3)) -> (((op (e0) (e0)) = (e3))\/(((op (e0) (e1)) = (e3))\/(((op (e0) (e2)) = (e3))\/((op (e0) (e3)) = (e3))))) -> (((op (e0) (e1)) = (e3))\/(((op (e1) (e1)) = (e3))\/(((op (e2) (e1)) = (e3))\/((op (e3) (e1)) = (e3))))) -> (~((op (e3) (e1)) = (op (e3) (e3)))) -> (~((op (e1) (e1)) = (e3))) -> ((~((op (e2) (e2)) = (e1)))\/((op (e2) (e1)) = (e2))) -> False). % 15.16/15.37 do 0 intro. intros zenon_H1d4 zenon_H17a zenon_He3 zenon_He6 zenon_Hce zenon_H1c3 zenon_H154 zenon_Haa zenon_H8e zenon_H90 zenon_H8b zenon_H87 zenon_H6a zenon_H7d zenon_H80 zenon_H84 zenon_H5e zenon_H8f zenon_H9e zenon_Ha3 zenon_Ha7 zenon_H44 zenon_H59 zenon_H4b zenon_H49 zenon_H2d zenon_H28 zenon_H36 zenon_H42 zenon_H58 zenon_H199 zenon_H12d zenon_H182 zenon_H1e3. % 15.16/15.37 apply (zenon_or_s _ _ zenon_H1d4); [ zenon_intro zenon_H2e | zenon_intro zenon_Hdd ]. % 15.16/15.37 apply (zenon_L279_); trivial. % 15.16/15.37 apply (zenon_L285_); trivial. % 15.16/15.37 (* end of lemma zenon_L286_ *) % 15.16/15.37 assert (zenon_L287_ : ((~((op (e2) (e2)) = (e3)))\/((op (e2) (e3)) = (e2))) -> ((op (e2) (e1)) = (e2)) -> (~((op (e2) (e1)) = (op (e2) (e3)))) -> (~((op (e0) (e0)) = (e1))) -> (~((op (e0) (e1)) = (op (e1) (e1)))) -> ((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 (e0) (e2)) = (op (e2) (e2)))) -> (~((op (e2) (e2)) = (e0))) -> (~((e0) = (e1))) -> ((op (e0) (e3)) = (e0)) -> (((op (e0) (e0)) = (e1))\/(((op (e0) (e1)) = (e1))\/(((op (e0) (e2)) = (e1))\/((op (e0) (e3)) = (e1))))) -> False). % 15.16/15.37 do 0 intro. intros zenon_H1c3 zenon_H156 zenon_H1e2 zenon_H45 zenon_H23 zenon_H21 zenon_H2d zenon_H2f zenon_H28 zenon_H2e zenon_H9e zenon_Hca zenon_H44. % 15.16/15.37 apply (zenon_or_s _ _ zenon_H1c3); [ zenon_intro zenon_H30 | zenon_intro zenon_H124 ]. % 15.16/15.37 apply (zenon_L74_); trivial. % 15.16/15.37 apply (zenon_L256_); trivial. % 15.16/15.37 (* end of lemma zenon_L287_ *) % 15.16/15.37 assert (zenon_L288_ : (~((op (e1) (e1)) = (e3))) -> (((op (e0) (e1)) = (e3))\/(((op (e1) (e1)) = (e3))\/(((op (e2) (e1)) = (e3))\/((op (e3) (e1)) = (e3))))) -> (~((op (e0) (e0)) = (e2))) -> (~((op (e2) (e0)) = (op (e2) (e2)))) -> ((~((op (e2) (e2)) = (e1)))\/((op (e2) (e1)) = (e2))) -> ((~((op (e1) (e1)) = (e1)))\/((op (e1) (e1)) = (e1))) -> ((~((op (e1) (e1)) = (e3)))\/((op (e1) (e3)) = (e1))) -> (~((op (e0) (e3)) = (op (e1) (e3)))) -> (((op (e1) (e1)) = (e0))\/(((op (e1) (e1)) = (e1))\/(((op (e1) (e1)) = (e2))\/((op (e1) (e1)) = (e3))))) -> (((op (e1) (e0)) = (e3))\/(((op (e1) (e1)) = (e3))\/(((op (e1) (e2)) = (e3))\/((op (e1) (e3)) = (e3))))) -> (~((op (e1) (e3)) = (op (e3) (e3)))) -> (~((op (e0) (e1)) = (op (e0) (e3)))) -> (~((op (e1) (e0)) = (op (e1) (e3)))) -> ((~((op (e2) (e2)) = (e0)))\/((op (e2) (e0)) = (e2))) -> (~((op (e1) (e0)) = (op (e1) (e2)))) -> ((~((op (e1) (e1)) = (e2)))\/((op (e1) (e2)) = (e1))) -> (~((op (e2) (e1)) = (op (e3) (e1)))) -> (~((op (e0) (e2)) = (op (e3) (e2)))) -> (((op (e3) (e0)) = (e2))\/(((op (e3) (e1)) = (e2))\/(((op (e3) (e2)) = (e2))\/((op (e3) (e3)) = (e2))))) -> (~((op (e3) (e2)) = (op (e3) (e3)))) -> (((op (e0) (e0)) = (e0))\/(((op (e0) (e1)) = (e0))\/(((op (e0) (e2)) = (e0))\/((op (e0) (e3)) = (e0))))) -> (~((op (e1) (e1)) = (op (e1) (e3)))) -> (((op (e0) (e3)) = (e1))\/(((op (e1) (e3)) = (e1))\/(((op (e2) (e3)) = (e1))\/((op (e3) (e3)) = (e1))))) -> (((op (e0) (e0)) = (e0))\/(((op (e0) (e0)) = (e1))\/(((op (e0) (e0)) = (e2))\/((op (e0) (e0)) = (e3))))) -> (~((op (e3) (e1)) = (op (e3) (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 (e0) (e3)) = (op (e3) (e3)))) -> (((op (e0) (e0)) = (e1))\/(((op (e1) (e0)) = (e1))\/(((op (e2) (e0)) = (e1))\/((op (e3) (e0)) = (e1))))) -> (~((op (e0) (e1)) = (op (e2) (e1)))) -> (~((op (e2) (e3)) = (op (e3) (e3)))) -> (((op (e2) (e0)) = (e3))\/(((op (e2) (e1)) = (e3))\/(((op (e2) (e2)) = (e3))\/((op (e2) (e3)) = (e3))))) -> (((op (e0) (e0)) = (e2))\/(((op (e1) (e0)) = (e2))\/(((op (e2) (e0)) = (e2))\/((op (e3) (e0)) = (e2))))) -> (~((op (e1) (e0)) = (op (e1) (e1)))) -> (((op (e0) (e0)) = (e2))\/(((op (e0) (e1)) = (e2))\/(((op (e0) (e2)) = (e2))\/((op (e0) (e3)) = (e2))))) -> (~((e1) = (e2))) -> (((op (e1) (e0)) = (e2))\/(((op (e1) (e1)) = (e2))\/(((op (e1) (e2)) = (e2))\/((op (e1) (e3)) = (e2))))) -> (~((op (e0) (e2)) = (op (e0) (e3)))) -> (~((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 (e0) (e2)) = (op (e1) (e2)))) -> (~((op (e1) (e1)) = (e2))) -> (~((e2) = (e3))) -> (((op (e0) (e0)) = (e3))\/(((op (e0) (e1)) = (e3))\/(((op (e0) (e2)) = (e3))\/((op (e0) (e3)) = (e3))))) -> (((op (e0) (e0)) = (e3))\/(((op (e1) (e0)) = (e3))\/(((op (e2) (e0)) = (e3))\/((op (e3) (e0)) = (e3))))) -> ((op (e3) (e3)) = (e3)) -> (~((op (e3) (e0)) = (op (e3) (e3)))) -> (~((e1) = (e3))) -> (~((op (e1) (e1)) = (op (e2) (e1)))) -> (~((op (e0) (e3)) = (op (e2) (e3)))) -> (((op (e2) (e0)) = (e1))\/(((op (e2) (e1)) = (e1))\/(((op (e2) (e2)) = (e1))\/((op (e2) (e3)) = (e1))))) -> (~((e0) = (e3))) -> (~((op (e0) (e0)) = (e3))) -> (~((op (e0) (e0)) = (e0))) -> ((~((op (e3) (e3)) = (e0)))\/((op (e3) (e0)) = (e3))) -> ((~((op (e3) (e3)) = (e2)))\/((op (e3) (e2)) = (e3))) -> (~((op (e1) (e1)) = (op (e1) (e2)))) -> (~((op (e1) (e2)) = (op (e2) (e2)))) -> (~((op (e1) (e2)) = (op (e3) (e2)))) -> (((op (e1) (e2)) = (e0))\/(((op (e1) (e2)) = (e1))\/(((op (e1) (e2)) = (e2))\/((op (e1) (e2)) = (e3))))) -> (((op (e2) (e1)) = (e0))\/(((op (e2) (e1)) = (e1))\/(((op (e2) (e1)) = (e2))\/((op (e2) (e1)) = (e3))))) -> (~((op (e2) (e1)) = (op (e2) (e2)))) -> (~((op (e2) (e0)) = (op (e2) (e1)))) -> (((op (e1) (e0)) = (e0))\/(((op (e1) (e1)) = (e0))\/(((op (e1) (e2)) = (e0))\/((op (e1) (e3)) = (e0))))) -> (~((op (e2) (e2)) = (op (e2) (e3)))) -> (((op (e0) (e3)) = (e2))\/(((op (e1) (e3)) = (e2))\/(((op (e2) (e3)) = (e2))\/((op (e3) (e3)) = (e2))))) -> (~((op (e1) (e1)) = (e0))) -> ((~((op (e2) (e2)) = (e2)))\/((op (e2) (e2)) = (e2))) -> ((~((op (e2) (e2)) = (e3)))\/((op (e2) (e3)) = (e2))) -> ((op (e2) (e1)) = (e2)) -> (~((op (e2) (e1)) = (op (e2) (e3)))) -> (~((op (e0) (e0)) = (e1))) -> (~((op (e0) (e1)) = (op (e1) (e1)))) -> ((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 (e0) (e2)) = (op (e2) (e2)))) -> (~((op (e2) (e2)) = (e0))) -> (~((e0) = (e1))) -> (((op (e0) (e0)) = (e1))\/(((op (e0) (e1)) = (e1))\/(((op (e0) (e2)) = (e1))\/((op (e0) (e3)) = (e1))))) -> False). % 15.16/15.37 do 0 intro. intros zenon_H182 zenon_H199 zenon_H8f zenon_H17a zenon_H1e3 zenon_H1d8 zenon_H1d2 zenon_H80 zenon_H1b3 zenon_H90 zenon_H8b zenon_H1cd zenon_H1cf zenon_H1d4 zenon_H166 zenon_H1d3 zenon_H13c zenon_H140 zenon_H1df zenon_H173 zenon_H110 zenon_H11e zenon_H121 zenon_H12a zenon_H12d zenon_H10c zenon_Hf0 zenon_H36 zenon_Hf1 zenon_Hde zenon_He3 zenon_He6 zenon_Heb zenon_Hd7 zenon_H8e zenon_Ha7 zenon_H84 zenon_Hc9 zenon_H5e zenon_Hce zenon_Hd3 zenon_H87 zenon_Hd6 zenon_H6a zenon_H58 zenon_Hbe zenon_H42 zenon_Hbb zenon_Ha3 zenon_Hb1 zenon_Hb4 zenon_Hb7 zenon_H4b zenon_H59 zenon_H20 zenon_H10f zenon_H10e zenon_H116 zenon_H7d zenon_H17d zenon_H1d5 zenon_H15a zenon_H157 zenon_H154 zenon_H163 zenon_H15f zenon_H160 zenon_H145 zenon_Haa zenon_H1c3 zenon_H156 zenon_H1e2 zenon_H45 zenon_H23 zenon_H21 zenon_H2d zenon_H2f zenon_H28 zenon_H2e zenon_H9e zenon_H44. % 15.16/15.37 apply (zenon_or_s _ _ zenon_H110); [ zenon_intro zenon_H1f | zenon_intro zenon_H111 ]. % 15.16/15.37 exact (zenon_H20 zenon_H1f). % 15.16/15.37 apply (zenon_or_s _ _ zenon_H111); [ zenon_intro zenon_H49 | zenon_intro zenon_H112 ]. % 15.16/15.37 apply (zenon_L286_); trivial. % 15.16/15.37 apply (zenon_or_s _ _ zenon_H112); [ zenon_intro zenon_Hab | zenon_intro zenon_Hca ]. % 15.16/15.37 apply (zenon_L258_); trivial. % 15.16/15.37 apply (zenon_L287_); trivial. % 15.16/15.37 (* end of lemma zenon_L288_ *) % 15.16/15.37 assert (zenon_L289_ : (~((op (e1) (op (e0) (e1))) = (op (e0) (e1)))) -> ((op (e1) (e0)) = (e0)) -> ((op (e0) (e1)) = (e0)) -> False). % 15.16/15.37 do 0 intro. intros zenon_H1ff zenon_Had zenon_H49. % 15.16/15.37 cut (((op (e1) (e0)) = (e0)) = ((op (e1) (op (e0) (e1))) = (op (e0) (e1)))). % 15.16/15.37 intro zenon_D_pnotp. % 15.16/15.37 apply zenon_H1ff. % 15.16/15.37 rewrite <- zenon_D_pnotp. % 15.16/15.37 exact zenon_Had. % 15.16/15.37 cut (((e0) = (op (e0) (e1)))); [idtac | apply NNPP; zenon_intro zenon_H200]. % 15.16/15.37 cut (((op (e1) (e0)) = (op (e1) (op (e0) (e1))))); [idtac | apply NNPP; zenon_intro zenon_H201]. % 15.16/15.37 congruence. % 15.16/15.37 elim (classic ((op (e1) (op (e0) (e1))) = (op (e1) (op (e0) (e1))))); [ zenon_intro zenon_H202 | zenon_intro zenon_H203 ]. % 15.16/15.37 cut (((op (e1) (op (e0) (e1))) = (op (e1) (op (e0) (e1)))) = ((op (e1) (e0)) = (op (e1) (op (e0) (e1))))). % 15.16/15.37 intro zenon_D_pnotp. % 15.16/15.37 apply zenon_H201. % 15.16/15.37 rewrite <- zenon_D_pnotp. % 15.16/15.37 exact zenon_H202. % 15.16/15.37 cut (((op (e1) (op (e0) (e1))) = (op (e1) (op (e0) (e1))))); [idtac | apply NNPP; zenon_intro zenon_H203]. % 15.16/15.37 cut (((op (e1) (op (e0) (e1))) = (op (e1) (e0)))); [idtac | apply NNPP; zenon_intro zenon_H204]. % 15.16/15.37 congruence. % 15.16/15.37 cut (((op (e0) (e1)) = (e0))); [idtac | apply NNPP; zenon_intro zenon_H205]. % 15.16/15.37 cut (((e1) = (e1))); [idtac | apply NNPP; zenon_intro zenon_Ha0]. % 15.16/15.37 congruence. % 15.16/15.37 apply zenon_Ha0. apply refl_equal. % 15.16/15.37 exact (zenon_H205 zenon_H49). % 15.16/15.37 apply zenon_H203. apply refl_equal. % 15.16/15.37 apply zenon_H203. apply refl_equal. % 15.16/15.37 apply zenon_H200. apply sym_equal. exact zenon_H49. % 15.16/15.37 (* end of lemma zenon_L289_ *) % 15.16/15.37 assert (zenon_L290_ : (((op (e2) (e0)) = (e3))\/(((op (e2) (e1)) = (e3))\/(((op (e2) (e2)) = (e3))\/((op (e2) (e3)) = (e3))))) -> (~((e0) = (e3))) -> ((op (e2) (e0)) = (e0)) -> (~((e2) = (e3))) -> ((op (e2) (e1)) = (e2)) -> (~((op (e2) (e2)) = (e3))) -> (~((op (e0) (e3)) = (op (e2) (e3)))) -> ((op (e0) (e3)) = (e3)) -> False). % 15.16/15.37 do 0 intro. intros zenon_He6 zenon_H4b zenon_Hcf zenon_H6a zenon_H156 zenon_H30 zenon_Hb4 zenon_H53. % 15.16/15.37 apply (zenon_or_s _ _ zenon_He6); [ zenon_intro zenon_Haf | zenon_intro zenon_He7 ]. % 15.16/15.37 apply (zenon_L57_); trivial. % 15.16/15.37 apply (zenon_or_s _ _ zenon_He7); [ zenon_intro zenon_Hdf | zenon_intro zenon_He8 ]. % 15.16/15.37 apply (zenon_L183_); trivial. % 15.16/15.37 apply (zenon_or_s _ _ zenon_He8); [ zenon_intro zenon_H34 | zenon_intro zenon_He2 ]. % 15.16/15.37 exact (zenon_H30 zenon_H34). % 15.16/15.37 apply (zenon_L125_); trivial. % 15.16/15.37 (* end of lemma zenon_L290_ *) % 15.16/15.37 assert (zenon_L291_ : (((op (e0) (e0)) = (e3))\/(((op (e0) (e1)) = (e3))\/(((op (e0) (e2)) = (e3))\/((op (e0) (e3)) = (e3))))) -> (~((op (e0) (e0)) = (e3))) -> ((op (e0) (e1)) = (e0)) -> ((op (e0) (e2)) = (e2)) -> (((op (e2) (e0)) = (e3))\/(((op (e2) (e1)) = (e3))\/(((op (e2) (e2)) = (e3))\/((op (e2) (e3)) = (e3))))) -> (~((e0) = (e3))) -> ((op (e2) (e0)) = (e0)) -> (~((e2) = (e3))) -> ((op (e2) (e1)) = (e2)) -> (~((op (e2) (e2)) = (e3))) -> (~((op (e0) (e3)) = (op (e2) (e3)))) -> False). % 15.16/15.37 do 0 intro. intros zenon_H58 zenon_H59 zenon_H49 zenon_H63 zenon_He6 zenon_H4b zenon_Hcf zenon_H6a zenon_H156 zenon_H30 zenon_Hb4. % 15.16/15.37 apply (zenon_or_s _ _ zenon_H58); [ zenon_intro zenon_H5b | zenon_intro zenon_H5a ]. % 15.16/15.37 exact (zenon_H59 zenon_H5b). % 15.16/15.37 apply (zenon_or_s _ _ zenon_H5a); [ zenon_intro zenon_H4a | zenon_intro zenon_H5c ]. % 15.16/15.37 apply (zenon_L9_); trivial. % 15.16/15.37 apply (zenon_or_s _ _ zenon_H5c); [ zenon_intro zenon_H50 | zenon_intro zenon_H53 ]. % 15.16/15.37 apply (zenon_L31_); trivial. % 15.16/15.37 apply (zenon_L290_); trivial. % 15.16/15.37 (* end of lemma zenon_L291_ *) % 15.16/15.37 assert (zenon_L292_ : (((op (e0) (e0)) = (e2))\/(((op (e0) (e1)) = (e2))\/(((op (e0) (e2)) = (e2))\/((op (e0) (e3)) = (e2))))) -> (~((op (e0) (e0)) = (e2))) -> (~((e0) = (e2))) -> (~((op (e0) (e3)) = (op (e2) (e3)))) -> (~((op (e2) (e2)) = (e3))) -> ((op (e2) (e1)) = (e2)) -> (~((e2) = (e3))) -> ((op (e2) (e0)) = (e0)) -> (~((e0) = (e3))) -> (((op (e2) (e0)) = (e3))\/(((op (e2) (e1)) = (e3))\/(((op (e2) (e2)) = (e3))\/((op (e2) (e3)) = (e3))))) -> ((op (e0) (e1)) = (e0)) -> (~((op (e0) (e0)) = (e3))) -> (((op (e0) (e0)) = (e3))\/(((op (e0) (e1)) = (e3))\/(((op (e0) (e2)) = (e3))\/((op (e0) (e3)) = (e3))))) -> (((op (e3) (e3)) = (e0))\/(((op (e3) (e3)) = (e1))\/(((op (e3) (e3)) = (e2))\/((op (e3) (e3)) = (e3))))) -> (~((op (e3) (e3)) = (e0))) -> (~((op (e3) (e3)) = (e1))) -> (~((op (e0) (e3)) = (op (e3) (e3)))) -> (~((op (e3) (e3)) = (e3))) -> False). % 15.16/15.37 do 0 intro. intros zenon_H8e zenon_H8f zenon_H5e zenon_Hb4 zenon_H30 zenon_H156 zenon_H6a zenon_Hcf zenon_H4b zenon_He6 zenon_H49 zenon_H59 zenon_H58 zenon_H3b zenon_H3c zenon_H104 zenon_H36 zenon_H3e. % 15.16/15.37 apply (zenon_or_s _ _ zenon_H8e); [ zenon_intro zenon_H92 | zenon_intro zenon_H91 ]. % 15.16/15.37 exact (zenon_H8f zenon_H92). % 15.16/15.37 apply (zenon_or_s _ _ zenon_H91); [ zenon_intro zenon_H5d | zenon_intro zenon_H93 ]. % 15.16/15.37 apply (zenon_L14_); trivial. % 15.16/15.37 apply (zenon_or_s _ _ zenon_H93); [ zenon_intro zenon_H63 | zenon_intro zenon_H81 ]. % 15.16/15.37 apply (zenon_L291_); trivial. % 15.16/15.37 apply (zenon_L107_); trivial. % 15.16/15.37 (* end of lemma zenon_L292_ *) % 15.16/15.37 assert (zenon_L293_ : (~((op (e0) (e3)) = (op (e1) (e3)))) -> ((op (e0) (e3)) = (e3)) -> ((op (e1) (e3)) = (e3)) -> False). % 15.16/15.37 do 0 intro. intros zenon_H80 zenon_H53 zenon_H8a. % 15.16/15.37 cut (((op (e0) (e3)) = (e3)) = ((op (e0) (e3)) = (op (e1) (e3)))). % 15.16/15.37 intro zenon_D_pnotp. % 15.16/15.37 apply zenon_H80. % 15.16/15.37 rewrite <- zenon_D_pnotp. % 15.16/15.37 exact zenon_H53. % 15.16/15.37 cut (((e3) = (op (e1) (e3)))); [idtac | apply NNPP; zenon_intro zenon_H8d]. % 15.16/15.37 cut (((op (e0) (e3)) = (op (e0) (e3)))); [idtac | apply NNPP; zenon_intro zenon_H3a]. % 15.16/15.37 congruence. % 15.16/15.37 apply zenon_H3a. apply refl_equal. % 15.16/15.37 apply zenon_H8d. apply sym_equal. exact zenon_H8a. % 15.16/15.37 (* end of lemma zenon_L293_ *) % 15.16/15.37 assert (zenon_L294_ : (((op (e1) (e0)) = (e3))\/(((op (e1) (e1)) = (e3))\/(((op (e1) (e2)) = (e3))\/((op (e1) (e3)) = (e3))))) -> (~((e2) = (e3))) -> ((op (e1) (e0)) = (e2)) -> (~((op (e1) (e1)) = (e3))) -> (~((op (e1) (e2)) = (op (e3) (e2)))) -> ((op (e3) (e2)) = (e3)) -> (~((op (e0) (e3)) = (op (e1) (e3)))) -> ((op (e0) (e3)) = (e3)) -> False). % 15.16/15.37 do 0 intro. intros zenon_H90 zenon_H6a zenon_H68 zenon_H182 zenon_H17d zenon_H106 zenon_H80 zenon_H53. % 15.16/15.37 apply (zenon_or_s _ _ zenon_H90); [ zenon_intro zenon_H69 | zenon_intro zenon_H94 ]. % 15.16/15.37 apply (zenon_L17_); trivial. % 15.16/15.37 apply (zenon_or_s _ _ zenon_H94); [ zenon_intro zenon_H96 | zenon_intro zenon_H95 ]. % 15.16/15.37 exact (zenon_H182 zenon_H96). % 15.16/15.37 apply (zenon_or_s _ _ zenon_H95); [ zenon_intro zenon_H88 | zenon_intro zenon_H8a ]. % 15.16/15.37 apply (zenon_L164_); trivial. % 15.16/15.37 apply (zenon_L293_); trivial. % 15.16/15.37 (* end of lemma zenon_L294_ *) % 15.16/15.37 assert (zenon_L295_ : (((op (e0) (e1)) = (e2))\/(((op (e1) (e1)) = (e2))\/(((op (e2) (e1)) = (e2))\/((op (e3) (e1)) = (e2))))) -> (~((e0) = (e2))) -> ((op (e0) (e1)) = (e0)) -> (~((op (e1) (e1)) = (e2))) -> ((op (e2) (e0)) = (e2)) -> (~((op (e2) (e0)) = (op (e2) (e1)))) -> (((op (e3) (e3)) = (e0))\/(((op (e3) (e3)) = (e1))\/(((op (e3) (e3)) = (e2))\/((op (e3) (e3)) = (e3))))) -> (~((op (e0) (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 (e3) (e3)) = (e1))) -> (~((op (e3) (e3)) = (e2))) -> (~((op (e3) (e3)) = (e3))) -> False). % 15.16/15.37 do 0 intro. intros zenon_H1a2 zenon_H5e zenon_H49 zenon_Hd6 zenon_Hdd zenon_H154 zenon_H3b zenon_H59 zenon_H8f zenon_H20 zenon_H12a zenon_H104 zenon_H3d zenon_H3e. % 15.16/15.37 apply (zenon_or_s _ _ zenon_H1a2); [ zenon_intro zenon_H5d | zenon_intro zenon_H1a3 ]. % 15.16/15.37 apply (zenon_L14_); trivial. % 15.16/15.37 apply (zenon_or_s _ _ zenon_H1a3); [ zenon_intro zenon_H6e | zenon_intro zenon_H1a4 ]. % 15.16/15.37 exact (zenon_Hd6 zenon_H6e). % 15.16/15.37 apply (zenon_or_s _ _ zenon_H1a4); [ zenon_intro zenon_H156 | zenon_intro zenon_H16a ]. % 15.16/15.37 apply (zenon_L284_); trivial. % 15.16/15.37 apply (zenon_L188_); trivial. % 15.16/15.37 (* end of lemma zenon_L295_ *) % 15.16/15.37 assert (zenon_L296_ : ((~((op (e3) (e3)) = (e3)))\/((op (e3) (e3)) = (e3))) -> (~((op (e3) (e2)) = (op (e3) (e3)))) -> (~((op (e0) (e0)) = (e2))) -> (~((e0) = (e2))) -> ((op (e0) (e1)) = (e0)) -> (((op (e0) (e2)) = (e1))\/(((op (e1) (e2)) = (e1))\/(((op (e2) (e2)) = (e1))\/((op (e3) (e2)) = (e1))))) -> ((op (e3) (e2)) = (e3)) -> (~((e1) = (e3))) -> (~((op (e2) (e2)) = (e1))) -> ((op (e1) (e1)) = (e1)) -> (~((op (e1) (e1)) = (op (e1) (e2)))) -> (~((e1) = (e2))) -> (((op (e3) (e3)) = (e0))\/(((op (e3) (e3)) = (e1))\/(((op (e3) (e3)) = (e2))\/((op (e3) (e3)) = (e3))))) -> (~((op (e0) (e3)) = (op (e3) (e3)))) -> (~((op (e3) (e3)) = (e1))) -> (~((op (e3) (e3)) = (e0))) -> (((op (e0) (e0)) = (e2))\/(((op (e0) (e1)) = (e2))\/(((op (e0) (e2)) = (e2))\/((op (e0) (e3)) = (e2))))) -> False). % 15.16/15.37 do 0 intro. intros zenon_H10d zenon_H173 zenon_H8f zenon_H5e zenon_H49 zenon_H11b zenon_H106 zenon_Ha3 zenon_H52 zenon_H21 zenon_H116 zenon_Ha7 zenon_H3b zenon_H36 zenon_H104 zenon_H3c zenon_H8e. % 15.16/15.37 apply (zenon_or_s _ _ zenon_H10d); [ zenon_intro zenon_H3e | zenon_intro zenon_H42 ]. % 15.16/15.37 apply (zenon_L108_); trivial. % 15.16/15.37 apply (zenon_L153_); trivial. % 15.16/15.37 (* end of lemma zenon_L296_ *) % 15.16/15.37 assert (zenon_L297_ : (~((e2) = (e3))) -> ((op (e3) (e1)) = (e3)) -> ((op (e3) (e1)) = (e2)) -> False). % 15.16/15.37 do 0 intro. intros zenon_H6a zenon_H10a zenon_H16a. % 15.16/15.37 cut (((op (e3) (e1)) = (e3)) = ((e2) = (e3))). % 15.16/15.37 intro zenon_D_pnotp. % 15.16/15.37 apply zenon_H6a. % 15.16/15.37 rewrite <- zenon_D_pnotp. % 15.16/15.37 exact zenon_H10a. % 15.16/15.37 cut (((e3) = (e3))); [idtac | apply NNPP; zenon_intro zenon_H4d]. % 15.16/15.37 cut (((op (e3) (e1)) = (e2))); [idtac | apply NNPP; zenon_intro zenon_H206]. % 15.16/15.37 congruence. % 15.16/15.37 exact (zenon_H206 zenon_H16a). % 15.16/15.37 apply zenon_H4d. apply refl_equal. % 15.16/15.37 (* end of lemma zenon_L297_ *) % 15.16/15.37 assert (zenon_L298_ : (((op (e0) (e1)) = (e2))\/(((op (e1) (e1)) = (e2))\/(((op (e2) (e1)) = (e2))\/((op (e3) (e1)) = (e2))))) -> (~((e0) = (e2))) -> ((op (e0) (e1)) = (e0)) -> (~((op (e1) (e1)) = (e2))) -> ((op (e2) (e0)) = (e2)) -> (~((op (e2) (e0)) = (op (e2) (e1)))) -> (~((e2) = (e3))) -> ((op (e3) (e1)) = (e3)) -> False). % 15.16/15.37 do 0 intro. intros zenon_H1a2 zenon_H5e zenon_H49 zenon_Hd6 zenon_Hdd zenon_H154 zenon_H6a zenon_H10a. % 15.16/15.37 apply (zenon_or_s _ _ zenon_H1a2); [ zenon_intro zenon_H5d | zenon_intro zenon_H1a3 ]. % 15.16/15.37 apply (zenon_L14_); trivial. % 15.16/15.37 apply (zenon_or_s _ _ zenon_H1a3); [ zenon_intro zenon_H6e | zenon_intro zenon_H1a4 ]. % 15.16/15.37 exact (zenon_Hd6 zenon_H6e). % 15.16/15.37 apply (zenon_or_s _ _ zenon_H1a4); [ zenon_intro zenon_H156 | zenon_intro zenon_H16a ]. % 15.16/15.37 apply (zenon_L284_); trivial. % 15.16/15.37 apply (zenon_L297_); trivial. % 15.16/15.37 (* end of lemma zenon_L298_ *) % 15.16/15.37 assert (zenon_L299_ : ((~((op (e3) (e3)) = (e1)))\/((op (e3) (e1)) = (e3))) -> ((~((op (e3) (e3)) = (e3)))\/((op (e3) (e3)) = (e3))) -> (((op (e2) (e0)) = (e3))\/(((op (e2) (e1)) = (e3))\/(((op (e2) (e2)) = (e3))\/((op (e2) (e3)) = (e3))))) -> (~((op (e2) (e3)) = (op (e3) (e3)))) -> (~((op (e2) (e2)) = (e1))) -> (~((op (e2) (e2)) = (e2))) -> (~((op (e2) (e2)) = (e3))) -> (((op (e2) (e2)) = (e0))\/(((op (e2) (e2)) = (e1))\/(((op (e2) (e2)) = (e2))\/((op (e2) (e2)) = (e3))))) -> (~((e2) = (e3))) -> (~((e0) = (e1))) -> (((op (e0) (e0)) = (e3))\/(((op (e0) (e1)) = (e3))\/(((op (e0) (e2)) = (e3))\/((op (e0) (e3)) = (e3))))) -> (~((op (e0) (e3)) = (op (e3) (e3)))) -> (~((e1) = (e3))) -> (~((e0) = (e3))) -> (((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)) = (e1))\/(((op (e0) (e2)) = (e1))\/((op (e0) (e3)) = (e1))))) -> (~((e0) = (e2))) -> ((op (e0) (e1)) = (e0)) -> (~((op (e1) (e1)) = (e2))) -> (~((op (e2) (e0)) = (op (e2) (e1)))) -> ((op (e2) (e0)) = (e2)) -> (((op (e3) (e3)) = (e0))\/(((op (e3) (e3)) = (e1))\/(((op (e3) (e3)) = (e2))\/((op (e3) (e3)) = (e3))))) -> (~((op (e0) (e0)) = (e0))) -> (~((op (e0) (e0)) = (e2))) -> (~((op (e0) (e0)) = (e3))) -> (((op (e0) (e0)) = (e0))\/(((op (e0) (e0)) = (e1))\/(((op (e0) (e0)) = (e2))\/((op (e0) (e0)) = (e3))))) -> (((op (e0) (e1)) = (e2))\/(((op (e1) (e1)) = (e2))\/(((op (e2) (e1)) = (e2))\/((op (e3) (e1)) = (e2))))) -> (~((op (e3) (e2)) = (op (e3) (e3)))) -> (((op (e0) (e2)) = (e1))\/(((op (e1) (e2)) = (e1))\/(((op (e2) (e2)) = (e1))\/((op (e3) (e2)) = (e1))))) -> ((op (e1) (e1)) = (e1)) -> (~((op (e1) (e1)) = (op (e1) (e2)))) -> (~((op (e3) (e3)) = (e0))) -> ((~((op (e3) (e3)) = (e2)))\/((op (e3) (e2)) = (e3))) -> False). % 15.16/15.37 do 0 intro. intros zenon_H10c zenon_H10d zenon_He6 zenon_He3 zenon_H52 zenon_H2f zenon_H30 zenon_H2d zenon_H6a zenon_H9e zenon_H58 zenon_H36 zenon_Ha3 zenon_H4b zenon_H8e zenon_Ha7 zenon_H44 zenon_H5e zenon_H49 zenon_Hd6 zenon_H154 zenon_Hdd zenon_H3b zenon_H20 zenon_H8f zenon_H59 zenon_H12a zenon_H1a2 zenon_H173 zenon_H11b zenon_H21 zenon_H116 zenon_H3c zenon_H10e. % 15.16/15.37 apply (zenon_or_s _ _ zenon_H10c); [ zenon_intro zenon_H104 | zenon_intro zenon_H10a ]. % 15.16/15.37 apply (zenon_or_s _ _ zenon_H10e); [ zenon_intro zenon_H3d | zenon_intro zenon_H106 ]. % 15.16/15.37 apply (zenon_or_s _ _ zenon_H10d); [ zenon_intro zenon_H3e | zenon_intro zenon_H42 ]. % 15.16/15.37 apply (zenon_L295_); trivial. % 15.16/15.37 apply (zenon_L283_); trivial. % 15.16/15.37 apply (zenon_L296_); trivial. % 15.16/15.37 apply (zenon_L298_); trivial. % 15.16/15.37 (* end of lemma zenon_L299_ *) % 15.16/15.37 assert (zenon_L300_ : ((~((op (e3) (e3)) = (e3)))\/((op (e3) (e3)) = (e3))) -> ((op (e3) (e0)) = (e3)) -> (~((op (e3) (e0)) = (op (e3) (e3)))) -> (~((e0) = (e2))) -> ((op (e0) (e1)) = (e0)) -> (~((op (e1) (e1)) = (e2))) -> (~((op (e2) (e0)) = (op (e2) (e1)))) -> ((op (e2) (e0)) = (e2)) -> (((op (e3) (e3)) = (e0))\/(((op (e3) (e3)) = (e1))\/(((op (e3) (e3)) = (e2))\/((op (e3) (e3)) = (e3))))) -> (~((op (e3) (e3)) = (e2))) -> (~((op (e3) (e3)) = (e1))) -> (~((op (e0) (e0)) = (e0))) -> (~((op (e0) (e0)) = (e2))) -> (~((op (e0) (e0)) = (e3))) -> (((op (e0) (e0)) = (e0))\/(((op (e0) (e0)) = (e1))\/(((op (e0) (e0)) = (e2))\/((op (e0) (e0)) = (e3))))) -> (((op (e0) (e1)) = (e2))\/(((op (e1) (e1)) = (e2))\/(((op (e2) (e1)) = (e2))\/((op (e3) (e1)) = (e2))))) -> False). % 15.16/15.37 do 0 intro. intros zenon_H10d zenon_Hba zenon_Hbb zenon_H5e zenon_H49 zenon_Hd6 zenon_H154 zenon_Hdd zenon_H3b zenon_H3d zenon_H104 zenon_H20 zenon_H8f zenon_H59 zenon_H12a zenon_H1a2. % 15.16/15.37 apply (zenon_or_s _ _ zenon_H10d); [ zenon_intro zenon_H3e | zenon_intro zenon_H42 ]. % 15.16/15.37 apply (zenon_L295_); trivial. % 15.16/15.37 apply (zenon_L43_); trivial. % 15.16/15.37 (* end of lemma zenon_L300_ *) % 15.16/15.37 assert (zenon_L301_ : ((~((op (e3) (e3)) = (e1)))\/((op (e3) (e1)) = (e3))) -> (~((op (e3) (e0)) = (op (e3) (e1)))) -> ((~((op (e3) (e3)) = (e3)))\/((op (e3) (e3)) = (e3))) -> ((op (e3) (e0)) = (e3)) -> (~((op (e3) (e0)) = (op (e3) (e3)))) -> (~((e0) = (e2))) -> ((op (e0) (e1)) = (e0)) -> (~((op (e1) (e1)) = (e2))) -> (~((op (e2) (e0)) = (op (e2) (e1)))) -> ((op (e2) (e0)) = (e2)) -> (((op (e3) (e3)) = (e0))\/(((op (e3) (e3)) = (e1))\/(((op (e3) (e3)) = (e2))\/((op (e3) (e3)) = (e3))))) -> (~((op (e0) (e0)) = (e0))) -> (~((op (e0) (e0)) = (e2))) -> (~((op (e0) (e0)) = (e3))) -> (((op (e0) (e0)) = (e0))\/(((op (e0) (e0)) = (e1))\/(((op (e0) (e0)) = (e2))\/((op (e0) (e0)) = (e3))))) -> (((op (e0) (e1)) = (e2))\/(((op (e1) (e1)) = (e2))\/(((op (e2) (e1)) = (e2))\/((op (e3) (e1)) = (e2))))) -> (~((op (e3) (e0)) = (op (e3) (e2)))) -> ((~((op (e3) (e3)) = (e2)))\/((op (e3) (e2)) = (e3))) -> False). % 15.16/15.37 do 0 intro. intros zenon_H10c zenon_H109 zenon_H10d zenon_Hba zenon_Hbb zenon_H5e zenon_H49 zenon_Hd6 zenon_H154 zenon_Hdd zenon_H3b zenon_H20 zenon_H8f zenon_H59 zenon_H12a zenon_H1a2 zenon_H105 zenon_H10e. % 15.16/15.37 apply (zenon_or_s _ _ zenon_H10c); [ zenon_intro zenon_H104 | zenon_intro zenon_H10a ]. % 15.16/15.37 apply (zenon_or_s _ _ zenon_H10e); [ zenon_intro zenon_H3d | zenon_intro zenon_H106 ]. % 15.16/15.37 apply (zenon_L300_); trivial. % 15.16/15.37 apply (zenon_L81_); trivial. % 15.16/15.37 apply (zenon_L82_); trivial. % 15.16/15.37 (* end of lemma zenon_L301_ *) % 15.16/15.37 assert (zenon_L302_ : ((~((op (e2) (e2)) = (e1)))\/((op (e2) (e1)) = (e2))) -> ((~((op (e2) (e2)) = (e3)))\/((op (e2) (e3)) = (e2))) -> (~((op (e2) (e0)) = (op (e2) (e3)))) -> ((~((op (e3) (e3)) = (e1)))\/((op (e3) (e1)) = (e3))) -> ((~((op (e3) (e3)) = (e3)))\/((op (e3) (e3)) = (e3))) -> (((op (e2) (e0)) = (e3))\/(((op (e2) (e1)) = (e3))\/(((op (e2) (e2)) = (e3))\/((op (e2) (e3)) = (e3))))) -> (~((op (e2) (e3)) = (op (e3) (e3)))) -> (((op (e2) (e2)) = (e0))\/(((op (e2) (e2)) = (e1))\/(((op (e2) (e2)) = (e2))\/((op (e2) (e2)) = (e3))))) -> (~((e2) = (e3))) -> (~((e0) = (e1))) -> (((op (e0) (e0)) = (e3))\/(((op (e0) (e1)) = (e3))\/(((op (e0) (e2)) = (e3))\/((op (e0) (e3)) = (e3))))) -> (~((op (e0) (e3)) = (op (e3) (e3)))) -> (~((e1) = (e3))) -> (~((e0) = (e3))) -> (((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)) = (e1))\/(((op (e0) (e2)) = (e1))\/((op (e0) (e3)) = (e1))))) -> (~((e0) = (e2))) -> ((op (e0) (e1)) = (e0)) -> (~((op (e1) (e1)) = (e2))) -> (~((op (e2) (e0)) = (op (e2) (e1)))) -> ((op (e2) (e0)) = (e2)) -> (((op (e3) (e3)) = (e0))\/(((op (e3) (e3)) = (e1))\/(((op (e3) (e3)) = (e2))\/((op (e3) (e3)) = (e3))))) -> (~((op (e0) (e0)) = (e0))) -> (~((op (e0) (e0)) = (e2))) -> (~((op (e0) (e0)) = (e3))) -> (((op (e0) (e0)) = (e0))\/(((op (e0) (e0)) = (e1))\/(((op (e0) (e0)) = (e2))\/((op (e0) (e0)) = (e3))))) -> (((op (e0) (e1)) = (e2))\/(((op (e1) (e1)) = (e2))\/(((op (e2) (e1)) = (e2))\/((op (e3) (e1)) = (e2))))) -> (~((op (e3) (e2)) = (op (e3) (e3)))) -> (((op (e0) (e2)) = (e1))\/(((op (e1) (e2)) = (e1))\/(((op (e2) (e2)) = (e1))\/((op (e3) (e2)) = (e1))))) -> ((op (e1) (e1)) = (e1)) -> (~((op (e1) (e1)) = (op (e1) (e2)))) -> ((~((op (e3) (e3)) = (e2)))\/((op (e3) (e2)) = (e3))) -> (~((op (e3) (e0)) = (op (e3) (e1)))) -> (~((op (e3) (e0)) = (op (e3) (e3)))) -> (~((op (e3) (e0)) = (op (e3) (e2)))) -> ((~((op (e3) (e3)) = (e0)))\/((op (e3) (e0)) = (e3))) -> (~((op (e2) (e0)) = (op (e2) (e2)))) -> ((~((op (e2) (e2)) = (e2)))\/((op (e2) (e2)) = (e2))) -> False). % 15.16/15.37 do 0 intro. intros zenon_H1e3 zenon_H1c3 zenon_Hce zenon_H10c zenon_H10d zenon_He6 zenon_He3 zenon_H2d zenon_H6a zenon_H9e zenon_H58 zenon_H36 zenon_Ha3 zenon_H4b zenon_H8e zenon_Ha7 zenon_H44 zenon_H5e zenon_H49 zenon_Hd6 zenon_H154 zenon_Hdd zenon_H3b zenon_H20 zenon_H8f zenon_H59 zenon_H12a zenon_H1a2 zenon_H173 zenon_H11b zenon_H21 zenon_H116 zenon_H10e zenon_H109 zenon_Hbb zenon_H105 zenon_H10f zenon_H17a zenon_Haa. % 15.16/15.37 apply (zenon_or_s _ _ zenon_H1e3); [ zenon_intro zenon_H52 | zenon_intro zenon_H156 ]. % 15.16/15.37 apply (zenon_or_s _ _ zenon_Haa); [ zenon_intro zenon_H2f | zenon_intro zenon_H35 ]. % 15.16/15.37 apply (zenon_or_s _ _ zenon_H1c3); [ zenon_intro zenon_H30 | zenon_intro zenon_H124 ]. % 15.16/15.37 apply (zenon_or_s _ _ zenon_H10f); [ zenon_intro zenon_H3c | zenon_intro zenon_Hba ]. % 15.16/15.37 apply (zenon_L299_); trivial. % 15.16/15.37 apply (zenon_L301_); trivial. % 15.16/15.37 apply (zenon_L119_); trivial. % 15.16/15.37 apply (zenon_L161_); trivial. % 15.16/15.37 apply (zenon_L284_); trivial. % 15.16/15.37 (* end of lemma zenon_L302_ *) % 15.16/15.37 assert (zenon_L303_ : (~((op (e0) (e0)) = (e0))) -> (~((op (e1) (op (e0) (e1))) = (op (e0) (e1)))) -> ((op (e0) (e1)) = (e0)) -> (((op (e0) (e0)) = (e2))\/(((op (e0) (e1)) = (e2))\/(((op (e0) (e2)) = (e2))\/((op (e0) (e3)) = (e2))))) -> (~((op (e3) (e3)) = (e0))) -> (~((op (e3) (e3)) = (e1))) -> (~((op (e0) (e3)) = (op (e3) (e3)))) -> (((op (e3) (e3)) = (e0))\/(((op (e3) (e3)) = (e1))\/(((op (e3) (e3)) = (e2))\/((op (e3) (e3)) = (e3))))) -> (~((op (e0) (e0)) = (e3))) -> (~((e0) = (e3))) -> (~((e2) = (e3))) -> (((op (e2) (e0)) = (e3))\/(((op (e2) (e1)) = (e3))\/(((op (e2) (e2)) = (e3))\/((op (e2) (e3)) = (e3))))) -> (~((op (e0) (e3)) = (op (e2) (e3)))) -> (~((op (e2) (e2)) = (e3))) -> ((op (e2) (e1)) = (e2)) -> (((op (e0) (e0)) = (e3))\/(((op (e0) (e1)) = (e3))\/(((op (e0) (e2)) = (e3))\/((op (e0) (e3)) = (e3))))) -> (~((e0) = (e2))) -> (~((op (e0) (e0)) = (e2))) -> (~((op (e1) (e1)) = (e3))) -> (~((op (e1) (e2)) = (op (e3) (e2)))) -> ((op (e3) (e2)) = (e3)) -> (~((op (e0) (e3)) = (op (e1) (e3)))) -> (((op (e1) (e0)) = (e3))\/(((op (e1) (e1)) = (e3))\/(((op (e1) (e2)) = (e3))\/((op (e1) (e3)) = (e3))))) -> ((~((op (e2) (e2)) = (e1)))\/((op (e2) (e1)) = (e2))) -> ((~((op (e2) (e2)) = (e3)))\/((op (e2) (e3)) = (e2))) -> (~((op (e2) (e0)) = (op (e2) (e3)))) -> ((~((op (e3) (e3)) = (e1)))\/((op (e3) (e1)) = (e3))) -> ((~((op (e3) (e3)) = (e3)))\/((op (e3) (e3)) = (e3))) -> (~((op (e2) (e3)) = (op (e3) (e3)))) -> (((op (e2) (e2)) = (e0))\/(((op (e2) (e2)) = (e1))\/(((op (e2) (e2)) = (e2))\/((op (e2) (e2)) = (e3))))) -> (~((e0) = (e1))) -> (~((e1) = (e3))) -> (~((e1) = (e2))) -> (((op (e0) (e0)) = (e1))\/(((op (e0) (e1)) = (e1))\/(((op (e0) (e2)) = (e1))\/((op (e0) (e3)) = (e1))))) -> (~((op (e1) (e1)) = (e2))) -> (~((op (e2) (e0)) = (op (e2) (e1)))) -> (((op (e0) (e0)) = (e0))\/(((op (e0) (e0)) = (e1))\/(((op (e0) (e0)) = (e2))\/((op (e0) (e0)) = (e3))))) -> (((op (e0) (e1)) = (e2))\/(((op (e1) (e1)) = (e2))\/(((op (e2) (e1)) = (e2))\/((op (e3) (e1)) = (e2))))) -> (~((op (e3) (e2)) = (op (e3) (e3)))) -> (((op (e0) (e2)) = (e1))\/(((op (e1) (e2)) = (e1))\/(((op (e2) (e2)) = (e1))\/((op (e3) (e2)) = (e1))))) -> ((op (e1) (e1)) = (e1)) -> (~((op (e1) (e1)) = (op (e1) (e2)))) -> ((~((op (e3) (e3)) = (e2)))\/((op (e3) (e2)) = (e3))) -> (~((op (e3) (e0)) = (op (e3) (e1)))) -> (~((op (e3) (e0)) = (op (e3) (e3)))) -> (~((op (e3) (e0)) = (op (e3) (e2)))) -> ((~((op (e3) (e3)) = (e0)))\/((op (e3) (e0)) = (e3))) -> (~((op (e2) (e0)) = (op (e2) (e2)))) -> ((~((op (e2) (e2)) = (e2)))\/((op (e2) (e2)) = (e2))) -> (((op (e0) (e0)) = (e2))\/(((op (e1) (e0)) = (e2))\/(((op (e2) (e0)) = (e2))\/((op (e3) (e0)) = (e2))))) -> (~((op (e0) (e1)) = (op (e2) (e1)))) -> (((op (e0) (e0)) = (e0))\/(((op (e1) (e0)) = (e0))\/(((op (e2) (e0)) = (e0))\/((op (e3) (e0)) = (e0))))) -> False). % 15.16/15.37 do 0 intro. intros zenon_H20 zenon_H1ff zenon_H49 zenon_H8e zenon_H3c zenon_H104 zenon_H36 zenon_H3b zenon_H59 zenon_H4b zenon_H6a zenon_He6 zenon_Hb4 zenon_H30 zenon_H156 zenon_H58 zenon_H5e zenon_H8f zenon_H182 zenon_H17d zenon_H106 zenon_H80 zenon_H90 zenon_H1e3 zenon_H1c3 zenon_Hce zenon_H10c zenon_H10d zenon_He3 zenon_H2d zenon_H9e zenon_Ha3 zenon_Ha7 zenon_H44 zenon_Hd6 zenon_H154 zenon_H12a zenon_H1a2 zenon_H173 zenon_H11b zenon_H21 zenon_H116 zenon_H10e zenon_H109 zenon_Hbb zenon_H105 zenon_H10f zenon_H17a zenon_Haa zenon_Heb zenon_Hde zenon_Hf0. % 15.16/15.37 apply (zenon_or_s _ _ zenon_H10d); [ zenon_intro zenon_H3e | zenon_intro zenon_H42 ]. % 15.16/15.37 apply (zenon_or_s _ _ zenon_Hf0); [ zenon_intro zenon_H1f | zenon_intro zenon_Hf2 ]. % 15.16/15.37 exact (zenon_H20 zenon_H1f). % 15.16/15.37 apply (zenon_or_s _ _ zenon_Hf2); [ zenon_intro zenon_Had | zenon_intro zenon_Hf3 ]. % 15.16/15.37 apply (zenon_L289_); trivial. % 15.16/15.37 apply (zenon_or_s _ _ zenon_Hf3); [ zenon_intro zenon_Hcf | zenon_intro zenon_Hdb ]. % 15.16/15.37 apply (zenon_L292_); trivial. % 15.16/15.37 apply (zenon_or_s _ _ zenon_H8e); [ zenon_intro zenon_H92 | zenon_intro zenon_H91 ]. % 15.16/15.37 exact (zenon_H8f zenon_H92). % 15.16/15.37 apply (zenon_or_s _ _ zenon_H91); [ zenon_intro zenon_H5d | zenon_intro zenon_H93 ]. % 15.16/15.37 apply (zenon_L251_); trivial. % 15.16/15.37 apply (zenon_or_s _ _ zenon_H93); [ zenon_intro zenon_H63 | zenon_intro zenon_H81 ]. % 15.16/15.37 apply (zenon_or_s _ _ zenon_Heb); [ zenon_intro zenon_H92 | zenon_intro zenon_Hec ]. % 15.16/15.37 exact (zenon_H8f zenon_H92). % 15.16/15.37 apply (zenon_or_s _ _ zenon_Hec); [ zenon_intro zenon_H68 | zenon_intro zenon_Hed ]. % 15.16/15.37 apply (zenon_or_s _ _ zenon_H58); [ zenon_intro zenon_H5b | zenon_intro zenon_H5a ]. % 15.16/15.37 exact (zenon_H59 zenon_H5b). % 15.16/15.37 apply (zenon_or_s _ _ zenon_H5a); [ zenon_intro zenon_H4a | zenon_intro zenon_H5c ]. % 15.16/15.37 apply (zenon_L9_); trivial. % 15.16/15.37 apply (zenon_or_s _ _ zenon_H5c); [ zenon_intro zenon_H50 | zenon_intro zenon_H53 ]. % 15.16/15.37 apply (zenon_L31_); trivial. % 15.16/15.37 apply (zenon_L294_); trivial. % 15.16/15.37 apply (zenon_or_s _ _ zenon_Hed); [ zenon_intro zenon_Hdd | zenon_intro zenon_He9 ]. % 15.16/15.37 apply (zenon_L302_); trivial. % 15.16/15.37 apply (zenon_L69_); trivial. % 15.16/15.37 apply (zenon_L107_); trivial. % 15.16/15.37 apply (zenon_L153_); trivial. % 15.16/15.37 (* end of lemma zenon_L303_ *) % 15.16/15.37 assert (zenon_L304_ : (~((e1) = (e2))) -> ((op (e2) (e0)) = (e2)) -> ((op (e2) (e0)) = (e1)) -> False). % 15.16/15.37 do 0 intro. intros zenon_Ha7 zenon_Hdd zenon_Hae. % 15.16/15.37 cut (((op (e2) (e0)) = (e2)) = ((e1) = (e2))). % 15.16/15.37 intro zenon_D_pnotp. % 15.16/15.37 apply zenon_Ha7. % 15.16/15.37 rewrite <- zenon_D_pnotp. % 15.16/15.37 exact zenon_Hdd. % 15.16/15.37 cut (((e2) = (e2))); [idtac | apply NNPP; zenon_intro zenon_H60]. % 15.16/15.37 cut (((op (e2) (e0)) = (e1))); [idtac | apply NNPP; zenon_intro zenon_H1f4]. % 15.16/15.37 congruence. % 15.16/15.37 exact (zenon_H1f4 zenon_Hae). % 15.16/15.37 apply zenon_H60. apply refl_equal. % 15.16/15.37 (* end of lemma zenon_L304_ *) % 15.16/15.37 assert (zenon_L305_ : ((op (e3) (e0)) = (e1)) -> ((op (e2) (e2)) = (e0)) -> ((op (e3) (e3)) = (e2)) -> False). % 15.16/15.37 do 0 intro. intros zenon_Hee zenon_H32 zenon_H43. % 15.16/15.37 apply (zenon_notand_s _ _ ax8); [ zenon_intro zenon_H208 | zenon_intro zenon_H207 ]. % 15.16/15.37 elim (classic ((op (op (e3) (e3)) (op (e3) (e3))) = (op (op (e3) (e3)) (op (e3) (e3))))); [ zenon_intro zenon_H186 | zenon_intro zenon_H187 ]. % 15.16/15.37 cut (((op (op (e3) (e3)) (op (e3) (e3))) = (op (op (e3) (e3)) (op (e3) (e3)))) = ((e0) = (op (op (e3) (e3)) (op (e3) (e3))))). % 15.16/15.37 intro zenon_D_pnotp. % 15.16/15.37 apply zenon_H208. % 15.16/15.37 rewrite <- zenon_D_pnotp. % 15.16/15.37 exact zenon_H186. % 15.16/15.37 cut (((op (op (e3) (e3)) (op (e3) (e3))) = (op (op (e3) (e3)) (op (e3) (e3))))); [idtac | apply NNPP; zenon_intro zenon_H187]. % 15.16/15.37 cut (((op (op (e3) (e3)) (op (e3) (e3))) = (e0))); [idtac | apply NNPP; zenon_intro zenon_H209]. % 15.16/15.37 congruence. % 15.16/15.37 cut (((op (e2) (e2)) = (e0)) = ((op (op (e3) (e3)) (op (e3) (e3))) = (e0))). % 15.16/15.37 intro zenon_D_pnotp. % 15.16/15.37 apply zenon_H209. % 15.16/15.37 rewrite <- zenon_D_pnotp. % 15.16/15.37 exact zenon_H32. % 15.16/15.37 cut (((e0) = (e0))); [idtac | apply NNPP; zenon_intro zenon_H1d]. % 15.16/15.37 cut (((op (e2) (e2)) = (op (op (e3) (e3)) (op (e3) (e3))))); [idtac | apply NNPP; zenon_intro zenon_H189]. % 15.16/15.37 congruence. % 15.16/15.37 elim (classic ((op (op (e3) (e3)) (op (e3) (e3))) = (op (op (e3) (e3)) (op (e3) (e3))))); [ zenon_intro zenon_H186 | zenon_intro zenon_H187 ]. % 15.16/15.37 cut (((op (op (e3) (e3)) (op (e3) (e3))) = (op (op (e3) (e3)) (op (e3) (e3)))) = ((op (e2) (e2)) = (op (op (e3) (e3)) (op (e3) (e3))))). % 15.16/15.37 intro zenon_D_pnotp. % 15.16/15.37 apply zenon_H189. % 15.16/15.37 rewrite <- zenon_D_pnotp. % 15.16/15.37 exact zenon_H186. % 15.16/15.37 cut (((op (op (e3) (e3)) (op (e3) (e3))) = (op (op (e3) (e3)) (op (e3) (e3))))); [idtac | apply NNPP; zenon_intro zenon_H187]. % 15.16/15.37 cut (((op (op (e3) (e3)) (op (e3) (e3))) = (op (e2) (e2)))); [idtac | apply NNPP; zenon_intro zenon_H183]. % 15.16/15.37 congruence. % 15.16/15.37 apply (zenon_L170_); trivial. % 15.16/15.37 apply zenon_H187. apply refl_equal. % 15.16/15.37 apply zenon_H187. apply refl_equal. % 15.16/15.37 apply zenon_H1d. apply refl_equal. % 15.16/15.37 apply zenon_H187. apply refl_equal. % 15.16/15.37 apply zenon_H187. apply refl_equal. % 15.16/15.37 apply (zenon_notand_s _ _ zenon_H207); [ zenon_intro zenon_H130 | zenon_intro zenon_H1f0 ]. % 15.16/15.37 apply zenon_H130. apply sym_equal. exact zenon_H43. % 15.16/15.37 elim (classic ((op (e3) (op (op (e3) (e3)) (op (e3) (e3)))) = (op (e3) (op (op (e3) (e3)) (op (e3) (e3)))))); [ zenon_intro zenon_H18b | zenon_intro zenon_H18c ]. % 15.16/15.37 cut (((op (e3) (op (op (e3) (e3)) (op (e3) (e3)))) = (op (e3) (op (op (e3) (e3)) (op (e3) (e3))))) = ((e1) = (op (e3) (op (op (e3) (e3)) (op (e3) (e3)))))). % 15.16/15.37 intro zenon_D_pnotp. % 15.16/15.37 apply zenon_H1f0. % 15.16/15.37 rewrite <- zenon_D_pnotp. % 15.16/15.37 exact zenon_H18b. % 15.16/15.37 cut (((op (e3) (op (op (e3) (e3)) (op (e3) (e3)))) = (op (e3) (op (op (e3) (e3)) (op (e3) (e3)))))); [idtac | apply NNPP; zenon_intro zenon_H18c]. % 15.16/15.37 cut (((op (e3) (op (op (e3) (e3)) (op (e3) (e3)))) = (e1))); [idtac | apply NNPP; zenon_intro zenon_H1f1]. % 15.16/15.37 congruence. % 15.16/15.37 cut (((op (e3) (e0)) = (e1)) = ((op (e3) (op (op (e3) (e3)) (op (e3) (e3)))) = (e1))). % 15.16/15.37 intro zenon_D_pnotp. % 15.16/15.37 apply zenon_H1f1. % 15.16/15.37 rewrite <- zenon_D_pnotp. % 15.16/15.37 exact zenon_Hee. % 15.16/15.37 cut (((e1) = (e1))); [idtac | apply NNPP; zenon_intro zenon_Ha0]. % 15.16/15.37 cut (((op (e3) (e0)) = (op (e3) (op (op (e3) (e3)) (op (e3) (e3)))))); [idtac | apply NNPP; zenon_intro zenon_H20a]. % 15.16/15.37 congruence. % 15.16/15.37 elim (classic ((op (e3) (op (op (e3) (e3)) (op (e3) (e3)))) = (op (e3) (op (op (e3) (e3)) (op (e3) (e3)))))); [ zenon_intro zenon_H18b | zenon_intro zenon_H18c ]. % 15.16/15.37 cut (((op (e3) (op (op (e3) (e3)) (op (e3) (e3)))) = (op (e3) (op (op (e3) (e3)) (op (e3) (e3))))) = ((op (e3) (e0)) = (op (e3) (op (op (e3) (e3)) (op (e3) (e3)))))). % 15.16/15.37 intro zenon_D_pnotp. % 15.16/15.37 apply zenon_H20a. % 15.16/15.37 rewrite <- zenon_D_pnotp. % 15.16/15.37 exact zenon_H18b. % 15.16/15.37 cut (((op (e3) (op (op (e3) (e3)) (op (e3) (e3)))) = (op (e3) (op (op (e3) (e3)) (op (e3) (e3)))))); [idtac | apply NNPP; zenon_intro zenon_H18c]. % 15.16/15.37 cut (((op (e3) (op (op (e3) (e3)) (op (e3) (e3)))) = (op (e3) (e0)))); [idtac | apply NNPP; zenon_intro zenon_H20b]. % 15.16/15.37 congruence. % 15.16/15.37 cut (((op (op (e3) (e3)) (op (e3) (e3))) = (e0))); [idtac | apply NNPP; zenon_intro zenon_H209]. % 15.16/15.37 cut (((e3) = (e3))); [idtac | apply NNPP; zenon_intro zenon_H4d]. % 15.16/15.37 congruence. % 15.16/15.37 apply zenon_H4d. apply refl_equal. % 15.16/15.37 cut (((op (e2) (e2)) = (e0)) = ((op (op (e3) (e3)) (op (e3) (e3))) = (e0))). % 15.16/15.37 intro zenon_D_pnotp. % 15.16/15.37 apply zenon_H209. % 15.16/15.37 rewrite <- zenon_D_pnotp. % 15.16/15.37 exact zenon_H32. % 15.16/15.37 cut (((e0) = (e0))); [idtac | apply NNPP; zenon_intro zenon_H1d]. % 15.16/15.37 cut (((op (e2) (e2)) = (op (op (e3) (e3)) (op (e3) (e3))))); [idtac | apply NNPP; zenon_intro zenon_H189]. % 15.16/15.37 congruence. % 15.16/15.37 elim (classic ((op (op (e3) (e3)) (op (e3) (e3))) = (op (op (e3) (e3)) (op (e3) (e3))))); [ zenon_intro zenon_H186 | zenon_intro zenon_H187 ]. % 15.16/15.37 cut (((op (op (e3) (e3)) (op (e3) (e3))) = (op (op (e3) (e3)) (op (e3) (e3)))) = ((op (e2) (e2)) = (op (op (e3) (e3)) (op (e3) (e3))))). % 15.16/15.37 intro zenon_D_pnotp. % 15.16/15.37 apply zenon_H189. % 15.16/15.37 rewrite <- zenon_D_pnotp. % 15.16/15.37 exact zenon_H186. % 15.16/15.37 cut (((op (op (e3) (e3)) (op (e3) (e3))) = (op (op (e3) (e3)) (op (e3) (e3))))); [idtac | apply NNPP; zenon_intro zenon_H187]. % 15.16/15.37 cut (((op (op (e3) (e3)) (op (e3) (e3))) = (op (e2) (e2)))); [idtac | apply NNPP; zenon_intro zenon_H183]. % 15.16/15.37 congruence. % 15.16/15.37 apply (zenon_L170_); trivial. % 15.16/15.37 apply zenon_H187. apply refl_equal. % 15.16/15.37 apply zenon_H187. apply refl_equal. % 15.16/15.37 apply zenon_H1d. apply refl_equal. % 15.16/15.37 apply zenon_H18c. apply refl_equal. % 15.16/15.37 apply zenon_H18c. apply refl_equal. % 15.16/15.37 apply zenon_Ha0. apply refl_equal. % 15.16/15.37 apply zenon_H18c. apply refl_equal. % 15.16/15.37 apply zenon_H18c. apply refl_equal. % 15.16/15.37 (* end of lemma zenon_L305_ *) % 15.16/15.37 assert (zenon_L306_ : (((op (e2) (e2)) = (e0))\/(((op (e2) (e2)) = (e1))\/(((op (e2) (e2)) = (e2))\/((op (e2) (e2)) = (e3))))) -> (~((op (e3) (e3)) = (e3))) -> ((op (e3) (e0)) = (e1)) -> (~((op (e3) (e3)) = (e1))) -> (~((op (e3) (e3)) = (e0))) -> (((op (e3) (e3)) = (e0))\/(((op (e3) (e3)) = (e1))\/(((op (e3) (e3)) = (e2))\/((op (e3) (e3)) = (e3))))) -> (~((op (e2) (e2)) = (e1))) -> (~((op (e2) (e2)) = (e2))) -> (~((op (e2) (e2)) = (e3))) -> False). % 15.16/15.37 do 0 intro. intros zenon_H2d zenon_H3e zenon_Hee zenon_H104 zenon_H3c zenon_H3b zenon_H52 zenon_H2f zenon_H30. % 15.16/15.37 apply (zenon_or_s _ _ zenon_H2d); [ zenon_intro zenon_H32 | zenon_intro zenon_H31 ]. % 15.16/15.37 apply (zenon_or_s _ _ zenon_H3b); [ zenon_intro zenon_H40 | zenon_intro zenon_H3f ]. % 15.16/15.37 exact (zenon_H3c zenon_H40). % 15.16/15.37 apply (zenon_or_s _ _ zenon_H3f); [ zenon_intro zenon_H38 | zenon_intro zenon_H41 ]. % 15.16/15.37 exact (zenon_H104 zenon_H38). % 15.16/15.37 apply (zenon_or_s _ _ zenon_H41); [ zenon_intro zenon_H43 | zenon_intro zenon_H42 ]. % 15.16/15.37 apply (zenon_L305_); trivial. % 15.16/15.37 exact (zenon_H3e zenon_H42). % 15.16/15.37 apply (zenon_or_s _ _ zenon_H31); [ zenon_intro zenon_H2a | zenon_intro zenon_H33 ]. % 15.16/15.37 exact (zenon_H52 zenon_H2a). % 15.16/15.37 apply (zenon_or_s _ _ zenon_H33); [ zenon_intro zenon_H35 | zenon_intro zenon_H34 ]. % 15.16/15.37 exact (zenon_H2f zenon_H35). % 15.16/15.37 exact (zenon_H30 zenon_H34). % 15.16/15.37 (* end of lemma zenon_L306_ *) % 15.16/15.37 assert (zenon_L307_ : (((op (e0) (e0)) = (e1))\/(((op (e1) (e0)) = (e1))\/(((op (e2) (e0)) = (e1))\/((op (e3) (e0)) = (e1))))) -> (~((op (e0) (e0)) = (e1))) -> ((op (e1) (e1)) = (e1)) -> (~((op (e1) (e0)) = (op (e1) (e1)))) -> ((op (e2) (e0)) = (e2)) -> (~((e1) = (e2))) -> (((op (e2) (e2)) = (e0))\/(((op (e2) (e2)) = (e1))\/(((op (e2) (e2)) = (e2))\/((op (e2) (e2)) = (e3))))) -> (~((op (e3) (e3)) = (e3))) -> (~((op (e3) (e3)) = (e1))) -> (~((op (e3) (e3)) = (e0))) -> (((op (e3) (e3)) = (e0))\/(((op (e3) (e3)) = (e1))\/(((op (e3) (e3)) = (e2))\/((op (e3) (e3)) = (e3))))) -> (~((op (e2) (e2)) = (e1))) -> (~((op (e2) (e2)) = (e2))) -> (~((op (e2) (e2)) = (e3))) -> False). % 15.16/15.37 do 0 intro. intros zenon_Hf1 zenon_H45 zenon_H21 zenon_Hd7 zenon_Hdd zenon_Ha7 zenon_H2d zenon_H3e zenon_H104 zenon_H3c zenon_H3b zenon_H52 zenon_H2f zenon_H30. % 15.16/15.37 apply (zenon_or_s _ _ zenon_Hf1); [ zenon_intro zenon_H47 | zenon_intro zenon_Hf4 ]. % 15.16/15.37 exact (zenon_H45 zenon_H47). % 15.16/15.37 apply (zenon_or_s _ _ zenon_Hf4); [ zenon_intro zenon_Hd8 | zenon_intro zenon_Hf5 ]. % 15.16/15.37 apply (zenon_L61_); trivial. % 15.16/15.37 apply (zenon_or_s _ _ zenon_Hf5); [ zenon_intro zenon_Hae | zenon_intro zenon_Hee ]. % 15.16/15.37 apply (zenon_L304_); trivial. % 15.16/15.37 apply (zenon_L306_); trivial. % 15.16/15.37 (* end of lemma zenon_L307_ *) % 15.16/15.37 assert (zenon_L308_ : ((~((op (e3) (e3)) = (e3)))\/((op (e3) (e3)) = (e3))) -> ((op (e3) (e2)) = (e3)) -> (~((op (e3) (e2)) = (op (e3) (e3)))) -> (~((op (e0) (e0)) = (e1))) -> (~((op (e1) (e0)) = (op (e1) (e1)))) -> ((op (e1) (e1)) = (e1)) -> (~((e1) = (e2))) -> ((op (e2) (e0)) = (e2)) -> (((op (e2) (e2)) = (e0))\/(((op (e2) (e2)) = (e1))\/(((op (e2) (e2)) = (e2))\/((op (e2) (e2)) = (e3))))) -> (~((op (e2) (e2)) = (e3))) -> (~((op (e2) (e2)) = (e2))) -> (~((op (e2) (e2)) = (e1))) -> (~((op (e3) (e3)) = (e0))) -> (~((op (e3) (e3)) = (e1))) -> (((op (e3) (e3)) = (e0))\/(((op (e3) (e3)) = (e1))\/(((op (e3) (e3)) = (e2))\/((op (e3) (e3)) = (e3))))) -> (((op (e0) (e0)) = (e1))\/(((op (e1) (e0)) = (e1))\/(((op (e2) (e0)) = (e1))\/((op (e3) (e0)) = (e1))))) -> False). % 15.16/15.37 do 0 intro. intros zenon_H10d zenon_H106 zenon_H173 zenon_H45 zenon_Hd7 zenon_H21 zenon_Ha7 zenon_Hdd zenon_H2d zenon_H30 zenon_H2f zenon_H52 zenon_H3c zenon_H104 zenon_H3b zenon_Hf1. % 15.16/15.37 apply (zenon_or_s _ _ zenon_H10d); [ zenon_intro zenon_H3e | zenon_intro zenon_H42 ]. % 15.16/15.37 apply (zenon_L307_); trivial. % 15.16/15.37 apply (zenon_L153_); trivial. % 15.16/15.37 (* end of lemma zenon_L308_ *) % 15.16/15.37 assert (zenon_L309_ : ((~((op (e3) (e3)) = (e2)))\/((op (e3) (e2)) = (e3))) -> (~((op (e3) (e1)) = (op (e3) (e2)))) -> (((op (e0) (e0)) = (e1))\/(((op (e0) (e1)) = (e1))\/(((op (e0) (e2)) = (e1))\/((op (e0) (e3)) = (e1))))) -> (~((op (e3) (e3)) = (e0))) -> (~((op (e0) (e3)) = (op (e3) (e3)))) -> (((op (e3) (e3)) = (e0))\/(((op (e3) (e3)) = (e1))\/(((op (e3) (e3)) = (e2))\/((op (e3) (e3)) = (e3))))) -> ((op (e0) (e2)) = (e0)) -> (~((e0) = (e1))) -> ((op (e1) (e1)) = (e1)) -> (~((op (e0) (e1)) = (op (e1) (e1)))) -> (~((op (e0) (e0)) = (e1))) -> (~((op (e3) (e1)) = (op (e3) (e3)))) -> ((op (e3) (e1)) = (e3)) -> ((~((op (e3) (e3)) = (e3)))\/((op (e3) (e3)) = (e3))) -> False). % 15.16/15.37 do 0 intro. intros zenon_H10e zenon_H135 zenon_H44 zenon_H3c zenon_H36 zenon_H3b zenon_Hab zenon_H9e zenon_H21 zenon_H23 zenon_H45 zenon_H12d zenon_H10a zenon_H10d. % 15.16/15.37 apply (zenon_or_s _ _ zenon_H10e); [ zenon_intro zenon_H3d | zenon_intro zenon_H106 ]. % 15.16/15.37 apply (zenon_or_s _ _ zenon_H10d); [ zenon_intro zenon_H3e | zenon_intro zenon_H42 ]. % 15.16/15.37 apply (zenon_L132_); trivial. % 15.16/15.37 apply (zenon_L102_); trivial. % 15.16/15.37 apply (zenon_L115_); trivial. % 15.16/15.37 (* end of lemma zenon_L309_ *) % 15.16/15.37 assert (zenon_L310_ : (((op (e0) (e0)) = (e1))\/(((op (e1) (e0)) = (e1))\/(((op (e2) (e0)) = (e1))\/((op (e3) (e0)) = (e1))))) -> (~((op (e0) (e0)) = (e1))) -> ((op (e1) (e1)) = (e1)) -> (~((op (e1) (e0)) = (op (e1) (e1)))) -> ((op (e2) (e0)) = (e2)) -> (~((e1) = (e2))) -> (~((e1) = (e3))) -> ((op (e3) (e0)) = (e3)) -> False). % 15.16/15.37 do 0 intro. intros zenon_Hf1 zenon_H45 zenon_H21 zenon_Hd7 zenon_Hdd zenon_Ha7 zenon_Ha3 zenon_Hba. % 15.16/15.37 apply (zenon_or_s _ _ zenon_Hf1); [ zenon_intro zenon_H47 | zenon_intro zenon_Hf4 ]. % 15.16/15.37 exact (zenon_H45 zenon_H47). % 15.16/15.37 apply (zenon_or_s _ _ zenon_Hf4); [ zenon_intro zenon_Hd8 | zenon_intro zenon_Hf5 ]. % 15.16/15.37 apply (zenon_L61_); trivial. % 15.16/15.37 apply (zenon_or_s _ _ zenon_Hf5); [ zenon_intro zenon_Hae | zenon_intro zenon_Hee ]. % 15.16/15.37 apply (zenon_L304_); trivial. % 15.16/15.37 apply (zenon_L79_); trivial. % 15.16/15.37 (* end of lemma zenon_L310_ *) % 15.16/15.37 assert (zenon_L311_ : (~((op (e3) (e1)) = (op (e3) (e2)))) -> ((~((op (e3) (e3)) = (e3)))\/((op (e3) (e3)) = (e3))) -> (~((op (e2) (e2)) = (op (e2) (e3)))) -> (((op (e1) (e0)) = (e0))\/(((op (e1) (e1)) = (e0))\/(((op (e1) (e2)) = (e0))\/((op (e1) (e3)) = (e0))))) -> (~((op (e2) (e0)) = (op (e2) (e1)))) -> (~((op (e2) (e1)) = (op (e2) (e2)))) -> (((op (e2) (e1)) = (e0))\/(((op (e2) (e1)) = (e1))\/(((op (e2) (e1)) = (e2))\/((op (e2) (e1)) = (e3))))) -> (((op (e1) (e2)) = (e0))\/(((op (e1) (e2)) = (e1))\/(((op (e1) (e2)) = (e2))\/((op (e1) (e2)) = (e3))))) -> (~((op (e1) (e2)) = (op (e3) (e2)))) -> (~((op (e1) (e2)) = (op (e2) (e2)))) -> (~((op (e1) (e1)) = (op (e1) (e2)))) -> (~((op (e0) (e0)) = (e0))) -> (((op (e2) (e0)) = (e1))\/(((op (e2) (e1)) = (e1))\/(((op (e2) (e2)) = (e1))\/((op (e2) (e3)) = (e1))))) -> (~((op (e0) (e3)) = (op (e2) (e3)))) -> (~((op (e1) (e1)) = (op (e2) (e1)))) -> (~((op (e1) (e0)) = (op (e1) (e1)))) -> (((op (e0) (e0)) = (e0))\/(((op (e1) (e0)) = (e0))\/(((op (e2) (e0)) = (e0))\/((op (e3) (e0)) = (e0))))) -> (((op (e0) (e0)) = (e0))\/(((op (e0) (e0)) = (e1))\/(((op (e0) (e0)) = (e2))\/((op (e0) (e0)) = (e3))))) -> (~((op (e1) (e1)) = (op (e1) (e3)))) -> (((op (e0) (e0)) = (e0))\/(((op (e0) (e1)) = (e0))\/(((op (e0) (e2)) = (e0))\/((op (e0) (e3)) = (e0))))) -> (((op (e3) (e0)) = (e2))\/(((op (e3) (e1)) = (e2))\/(((op (e3) (e2)) = (e2))\/((op (e3) (e3)) = (e2))))) -> (~((op (e0) (e2)) = (op (e3) (e2)))) -> (~((op (e2) (e1)) = (op (e3) (e1)))) -> (~((op (e1) (e0)) = (op (e1) (e2)))) -> (~((op (e0) (e3)) = (op (e1) (e3)))) -> ((~((op (e1) (e1)) = (e1)))\/((op (e1) (e1)) = (e1))) -> (~((op (e2) (e1)) = (op (e2) (e3)))) -> ((~((op (e2) (e2)) = (e1)))\/((op (e2) (e1)) = (e2))) -> ((~((op (e1) (e1)) = (e3)))\/((op (e1) (e3)) = (e1))) -> ((~((op (e2) (e2)) = (e2)))\/((op (e2) (e2)) = (e2))) -> (((op (e1) (e0)) = (e1))\/(((op (e1) (e1)) = (e1))\/(((op (e1) (e2)) = (e1))\/((op (e1) (e3)) = (e1))))) -> (((op (e0) (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) (e2)) = (op (e3) (e3)))) -> ((~((op (e3) (e3)) = (e0)))\/((op (e3) (e0)) = (e3))) -> (~((op (e3) (e0)) = (op (e3) (e3)))) -> (~((e2) = (e3))) -> (~((op (e0) (e2)) = (op (e0) (e3)))) -> (~((e0) = (e2))) -> (((op (e0) (e3)) = (e0))\/(((op (e1) (e3)) = (e0))\/(((op (e2) (e3)) = (e0))\/((op (e3) (e3)) = (e0))))) -> (~((e1) = (e2))) -> (((op (e1) (e0)) = (e2))\/(((op (e1) (e1)) = (e2))\/(((op (e1) (e2)) = (e2))\/((op (e1) (e3)) = (e2))))) -> ((~((op (e2) (e2)) = (e3)))\/((op (e2) (e3)) = (e2))) -> (((op (e1) (e1)) = (e0))\/(((op (e1) (e1)) = (e1))\/(((op (e1) (e1)) = (e2))\/((op (e1) (e1)) = (e3))))) -> (~((op (e1) (e3)) = (op (e3) (e3)))) -> (((op (e1) (e0)) = (e3))\/(((op (e1) (e1)) = (e3))\/(((op (e1) (e2)) = (e3))\/((op (e1) (e3)) = (e3))))) -> (((op (e0) (e0)) = (e2))\/(((op (e1) (e0)) = (e2))\/(((op (e2) (e0)) = (e2))\/((op (e3) (e0)) = (e2))))) -> (~((op (e0) (e2)) = (op (e1) (e2)))) -> (((op (e0) (e0)) = (e3))\/(((op (e1) (e0)) = (e3))\/(((op (e2) (e0)) = (e3))\/((op (e3) (e0)) = (e3))))) -> (((op (e2) (e0)) = (e3))\/(((op (e2) (e1)) = (e3))\/(((op (e2) (e2)) = (e3))\/((op (e2) (e3)) = (e3))))) -> (~((op (e2) (e3)) = (op (e3) (e3)))) -> (~((op (e0) (e1)) = (op (e2) (e1)))) -> (((op (e0) (e0)) = (e2))\/(((op (e0) (e1)) = (e2))\/(((op (e0) (e2)) = (e2))\/((op (e0) (e3)) = (e2))))) -> (~((op (e0) (e2)) = (op (e2) (e2)))) -> (((op (e2) (e2)) = (e0))\/(((op (e2) (e2)) = (e1))\/(((op (e2) (e2)) = (e2))\/((op (e2) (e2)) = (e3))))) -> (~((op (e0) (e0)) = (e3))) -> (~((e1) = (e3))) -> (~((e0) = (e3))) -> (((op (e0) (e0)) = (e3))\/(((op (e0) (e1)) = (e3))\/(((op (e0) (e2)) = (e3))\/((op (e0) (e3)) = (e3))))) -> ((~((op (e3) (e3)) = (e2)))\/((op (e3) (e2)) = (e3))) -> (((op (e0) (e0)) = (e1))\/(((op (e1) (e0)) = (e1))\/(((op (e2) (e0)) = (e1))\/((op (e3) (e0)) = (e1))))) -> (~((op (e2) (e0)) = (op (e2) (e3)))) -> (((op (e0) (e3)) = (e1))\/(((op (e1) (e3)) = (e1))\/(((op (e2) (e3)) = (e1))\/((op (e3) (e3)) = (e1))))) -> (~((op (e1) (e0)) = (op (e1) (e3)))) -> (~((op (e0) (e1)) = (op (e0) (e3)))) -> (~((op (e3) (e1)) = (op (e3) (e3)))) -> ((~((op (e3) (e3)) = (e1)))\/((op (e3) (e1)) = (e3))) -> ((~((op (e2) (e2)) = (e0)))\/((op (e2) (e0)) = (e2))) -> (~((op (e1) (e2)) = (op (e1) (e3)))) -> ((~((op (e1) (e1)) = (e2)))\/((op (e1) (e2)) = (e1))) -> ((~((op (e1) (e1)) = (e0)))\/((op (e1) (e0)) = (e1))) -> (~((op (e0) (e0)) = (e1))) -> (~((op (e0) (e1)) = (op (e1) (e1)))) -> ((op (e1) (e1)) = (e1)) -> (~((e0) = (e1))) -> ((op (e0) (e2)) = (e0)) -> (((op (e3) (e3)) = (e0))\/(((op (e3) (e3)) = (e1))\/(((op (e3) (e3)) = (e2))\/((op (e3) (e3)) = (e3))))) -> (~((op (e0) (e3)) = (op (e3) (e3)))) -> (((op (e0) (e0)) = (e1))\/(((op (e0) (e1)) = (e1))\/(((op (e0) (e2)) = (e1))\/((op (e0) (e3)) = (e1))))) -> ((op (e2) (e0)) = (e2)) -> (~((op (e2) (e0)) = (op (e2) (e2)))) -> (~((op (e3) (e0)) = (op (e3) (e1)))) -> (((op (e0) (e1)) = (e0))\/(((op (e1) (e1)) = (e0))\/(((op (e2) (e1)) = (e0))\/((op (e3) (e1)) = (e0))))) -> (((op (e2) (e0)) = (e0))\/(((op (e2) (e1)) = (e0))\/(((op (e2) (e2)) = (e0))\/((op (e2) (e3)) = (e0))))) -> (~((op (e1) (e1)) = (e2))) -> (((op (e0) (e1)) = (e2))\/(((op (e1) (e1)) = (e2))\/(((op (e2) (e1)) = (e2))\/((op (e3) (e1)) = (e2))))) -> (~((op (e1) (e1)) = (e3))) -> (((op (e0) (e2)) = (e1))\/(((op (e1) (e2)) = (e1))\/(((op (e2) (e2)) = (e1))\/((op (e3) (e2)) = (e1))))) -> (~((op (e2) (e0)) = (op (e3) (e0)))) -> (((op (e0) (e1)) = (e0))\/(((op (e0) (e1)) = (e1))\/(((op (e0) (e1)) = (e2))\/((op (e0) (e1)) = (e3))))) -> (~((op (e0) (e1)) = (op (e3) (e1)))) -> (((op (e3) (e0)) = (e0))\/(((op (e3) (e1)) = (e0))\/(((op (e3) (e2)) = (e0))\/((op (e3) (e3)) = (e0))))) -> (((op (e0) (e2)) = (e0))\/(((op (e1) (e2)) = (e0))\/(((op (e2) (e2)) = (e0))\/((op (e3) (e2)) = (e0))))) -> (~((op (e1) (e1)) = (e0))) -> (~((op (e3) (e0)) = (op (e3) (e2)))) -> False). % 15.16/15.37 do 0 intro. intros zenon_H135 zenon_H10d zenon_H15f zenon_H163 zenon_H154 zenon_H157 zenon_H15a zenon_H1d5 zenon_H17d zenon_H7d zenon_H116 zenon_H20 zenon_Hb7 zenon_Hb4 zenon_Hb1 zenon_Hd7 zenon_Hf0 zenon_H12a zenon_H11e zenon_H110 zenon_H1df zenon_H140 zenon_H13c zenon_H166 zenon_H80 zenon_H1d8 zenon_H1e2 zenon_H1e3 zenon_H1d2 zenon_Haa zenon_H1c5 zenon_H160 zenon_H175 zenon_H173 zenon_H10f zenon_Hbb zenon_H6a zenon_Hc9 zenon_H5e zenon_Hd3 zenon_Ha7 zenon_H84 zenon_H1c3 zenon_H1b3 zenon_H8b zenon_H90 zenon_Heb zenon_H87 zenon_Hbe zenon_He6 zenon_He3 zenon_Hde zenon_H8e zenon_H28 zenon_H2d zenon_H59 zenon_Ha3 zenon_H4b zenon_H58 zenon_H10e zenon_Hf1 zenon_Hce zenon_H121 zenon_H1cf zenon_H1cd zenon_H12d zenon_H10c zenon_H1d4 zenon_H1d0 zenon_H1d3 zenon_H1e4 zenon_H45 zenon_H23 zenon_H21 zenon_H9e zenon_Hab zenon_H3b zenon_H36 zenon_H44 zenon_Hdd zenon_H17a zenon_H109 zenon_H144 zenon_H1f5 zenon_Hd6 zenon_H1a2 zenon_H182 zenon_H11b zenon_H1e5 zenon_H1e9 zenon_H138 zenon_H1f6 zenon_H16f zenon_H145 zenon_H105. % 15.16/15.37 apply (zenon_or_s _ _ zenon_H1e3); [ zenon_intro zenon_H52 | zenon_intro zenon_H156 ]. % 15.16/15.37 apply (zenon_or_s _ _ zenon_Haa); [ zenon_intro zenon_H2f | zenon_intro zenon_H35 ]. % 15.16/15.37 apply (zenon_or_s _ _ zenon_H1c3); [ zenon_intro zenon_H30 | zenon_intro zenon_H124 ]. % 15.16/15.37 apply (zenon_or_s _ _ zenon_H10f); [ zenon_intro zenon_H3c | zenon_intro zenon_Hba ]. % 15.16/15.37 apply (zenon_or_s _ _ zenon_H10c); [ zenon_intro zenon_H104 | zenon_intro zenon_H10a ]. % 15.16/15.37 apply (zenon_or_s _ _ zenon_H10e); [ zenon_intro zenon_H3d | zenon_intro zenon_H106 ]. % 15.16/15.37 apply (zenon_L260_); trivial. % 15.16/15.37 apply (zenon_L308_); trivial. % 15.16/15.37 apply (zenon_L309_); trivial. % 15.16/15.37 apply (zenon_L310_); trivial. % 15.16/15.37 apply (zenon_L119_); trivial. % 15.16/15.37 apply (zenon_L272_); trivial. % 15.16/15.37 apply (zenon_L284_); trivial. % 15.16/15.37 (* end of lemma zenon_L311_ *) % 15.16/15.37 assert (zenon_L312_ : (~((op (e2) (op (e0) (e2))) = (op (e0) (e2)))) -> ((op (e2) (e0)) = (e0)) -> ((op (e0) (e2)) = (e0)) -> False). % 15.16/15.37 do 0 intro. intros zenon_H20c zenon_Hcf zenon_Hab. % 15.16/15.37 cut (((op (e2) (e0)) = (e0)) = ((op (e2) (op (e0) (e2))) = (op (e0) (e2)))). % 15.16/15.37 intro zenon_D_pnotp. % 15.16/15.37 apply zenon_H20c. % 15.16/15.37 rewrite <- zenon_D_pnotp. % 15.16/15.37 exact zenon_Hcf. % 15.16/15.37 cut (((e0) = (op (e0) (e2)))); [idtac | apply NNPP; zenon_intro zenon_H20d]. % 15.16/15.37 cut (((op (e2) (e0)) = (op (e2) (op (e0) (e2))))); [idtac | apply NNPP; zenon_intro zenon_H20e]. % 15.16/15.37 congruence. % 15.16/15.37 elim (classic ((op (e2) (op (e0) (e2))) = (op (e2) (op (e0) (e2))))); [ zenon_intro zenon_H20f | zenon_intro zenon_H210 ]. % 15.16/15.37 cut (((op (e2) (op (e0) (e2))) = (op (e2) (op (e0) (e2)))) = ((op (e2) (e0)) = (op (e2) (op (e0) (e2))))). % 15.16/15.37 intro zenon_D_pnotp. % 15.16/15.37 apply zenon_H20e. % 15.16/15.37 rewrite <- zenon_D_pnotp. % 15.16/15.37 exact zenon_H20f. % 15.16/15.37 cut (((op (e2) (op (e0) (e2))) = (op (e2) (op (e0) (e2))))); [idtac | apply NNPP; zenon_intro zenon_H210]. % 15.16/15.37 cut (((op (e2) (op (e0) (e2))) = (op (e2) (e0)))); [idtac | apply NNPP; zenon_intro zenon_H211]. % 15.16/15.37 congruence. % 15.16/15.37 cut (((op (e0) (e2)) = (e0))); [idtac | apply NNPP; zenon_intro zenon_H212]. % 15.16/15.37 cut (((e2) = (e2))); [idtac | apply NNPP; zenon_intro zenon_H60]. % 15.16/15.37 congruence. % 15.16/15.37 apply zenon_H60. apply refl_equal. % 15.16/15.37 exact (zenon_H212 zenon_Hab). % 15.16/15.37 apply zenon_H210. apply refl_equal. % 15.16/15.37 apply zenon_H210. apply refl_equal. % 15.16/15.37 apply zenon_H20d. apply sym_equal. exact zenon_Hab. % 15.16/15.37 (* end of lemma zenon_L312_ *) % 15.16/15.37 assert (zenon_L313_ : (~((op (e3) (op (e0) (e3))) = (op (e0) (e3)))) -> ((op (e3) (e1)) = (e1)) -> ((op (e0) (e3)) = (e1)) -> False). % 15.16/15.37 do 0 intro. intros zenon_H192 zenon_H13e zenon_H37. % 15.16/15.37 cut (((op (e3) (e1)) = (e1)) = ((op (e3) (op (e0) (e3))) = (op (e0) (e3)))). % 15.16/15.37 intro zenon_D_pnotp. % 15.16/15.37 apply zenon_H192. % 15.16/15.37 rewrite <- zenon_D_pnotp. % 15.16/15.37 exact zenon_H13e. % 15.16/15.37 cut (((e1) = (op (e0) (e3)))); [idtac | apply NNPP; zenon_intro zenon_H213]. % 15.16/15.37 cut (((op (e3) (e1)) = (op (e3) (op (e0) (e3))))); [idtac | apply NNPP; zenon_intro zenon_H214]. % 15.16/15.37 congruence. % 15.16/15.37 elim (classic ((op (e3) (op (e0) (e3))) = (op (e3) (op (e0) (e3))))); [ zenon_intro zenon_H194 | zenon_intro zenon_H195 ]. % 15.16/15.37 cut (((op (e3) (op (e0) (e3))) = (op (e3) (op (e0) (e3)))) = ((op (e3) (e1)) = (op (e3) (op (e0) (e3))))). % 15.16/15.37 intro zenon_D_pnotp. % 15.16/15.37 apply zenon_H214. % 15.16/15.37 rewrite <- zenon_D_pnotp. % 15.16/15.37 exact zenon_H194. % 15.16/15.37 cut (((op (e3) (op (e0) (e3))) = (op (e3) (op (e0) (e3))))); [idtac | apply NNPP; zenon_intro zenon_H195]. % 15.16/15.37 cut (((op (e3) (op (e0) (e3))) = (op (e3) (e1)))); [idtac | apply NNPP; zenon_intro zenon_H215]. % 15.16/15.37 congruence. % 15.16/15.37 cut (((op (e0) (e3)) = (e1))); [idtac | apply NNPP; zenon_intro zenon_Hf6]. % 15.16/15.37 cut (((e3) = (e3))); [idtac | apply NNPP; zenon_intro zenon_H4d]. % 15.16/15.37 congruence. % 15.16/15.37 apply zenon_H4d. apply refl_equal. % 15.16/15.37 exact (zenon_Hf6 zenon_H37). % 15.16/15.37 apply zenon_H195. apply refl_equal. % 15.16/15.37 apply zenon_H195. apply refl_equal. % 15.16/15.37 apply zenon_H213. apply sym_equal. exact zenon_H37. % 15.16/15.37 (* end of lemma zenon_L313_ *) % 15.16/15.37 assert (zenon_L314_ : (((op (e3) (e0)) = (e1))\/(((op (e3) (e1)) = (e1))\/(((op (e3) (e2)) = (e1))\/((op (e3) (e3)) = (e1))))) -> (~((e0) = (e1))) -> ((op (e3) (e0)) = (e0)) -> ((op (e0) (e3)) = (e1)) -> (~((op (e3) (op (e0) (e3))) = (op (e0) (e3)))) -> ((op (e3) (e2)) = (e3)) -> (~((e1) = (e3))) -> (~((op (e3) (e3)) = (e1))) -> False). % 15.16/15.37 do 0 intro. intros zenon_H146 zenon_H9e zenon_Hdb zenon_H37 zenon_H192 zenon_H106 zenon_Ha3 zenon_H104. % 15.16/15.37 apply (zenon_or_s _ _ zenon_H146); [ zenon_intro zenon_Hee | zenon_intro zenon_H14b ]. % 15.16/15.37 apply (zenon_L71_); trivial. % 15.16/15.37 apply (zenon_or_s _ _ zenon_H14b); [ zenon_intro zenon_H13e | zenon_intro zenon_H14c ]. % 15.16/15.37 apply (zenon_L313_); trivial. % 15.16/15.37 apply (zenon_or_s _ _ zenon_H14c); [ zenon_intro zenon_H119 | zenon_intro zenon_H38 ]. % 15.16/15.37 apply (zenon_L87_); trivial. % 15.16/15.37 exact (zenon_H104 zenon_H38). % 15.16/15.37 (* end of lemma zenon_L314_ *) % 15.16/15.37 assert (zenon_L315_ : (~((e1) = (e2))) -> (~((op (e2) (e0)) = (op (e2) (e1)))) -> ((op (e2) (e1)) = (e2)) -> (~((e0) = (e2))) -> (((op (e0) (e0)) = (e3))\/(((op (e0) (e1)) = (e3))\/(((op (e0) (e2)) = (e3))\/((op (e0) (e3)) = (e3))))) -> (~((op (e0) (e0)) = (e3))) -> (~((e0) = (e3))) -> (((op (e0) (e0)) = (e2))\/(((op (e1) (e0)) = (e2))\/(((op (e2) (e0)) = (e2))\/((op (e3) (e0)) = (e2))))) -> (~((op (e3) (e0)) = (op (e3) (e2)))) -> (~((op (e1) (e1)) = (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 (e0) (e1)) = (op (e3) (e1)))) -> (((op (e0) (e1)) = (e0))\/(((op (e0) (e1)) = (e1))\/(((op (e0) (e1)) = (e2))\/((op (e0) (e1)) = (e3))))) -> (~((op (e2) (e0)) = (op (e3) (e0)))) -> (((op (e0) (e2)) = (e1))\/(((op (e1) (e2)) = (e1))\/(((op (e2) (e2)) = (e1))\/((op (e3) (e2)) = (e1))))) -> (~((op (e1) (e1)) = (e3))) -> (((op (e0) (e1)) = (e2))\/(((op (e1) (e1)) = (e2))\/(((op (e2) (e1)) = (e2))\/((op (e3) (e1)) = (e2))))) -> (~((op (e1) (e1)) = (e2))) -> (((op (e2) (e0)) = (e0))\/(((op (e2) (e1)) = (e0))\/(((op (e2) (e2)) = (e0))\/((op (e2) (e3)) = (e0))))) -> (((op (e0) (e1)) = (e0))\/(((op (e1) (e1)) = (e0))\/(((op (e2) (e1)) = (e0))\/((op (e3) (e1)) = (e0))))) -> (~((op (e3) (e0)) = (op (e3) (e1)))) -> (~((op (e2) (e0)) = (op (e2) (e2)))) -> (~((op (e0) (e3)) = (op (e3) (e3)))) -> (((op (e3) (e3)) = (e0))\/(((op (e3) (e3)) = (e1))\/(((op (e3) (e3)) = (e2))\/((op (e3) (e3)) = (e3))))) -> ((~((op (e1) (e1)) = (e0)))\/((op (e1) (e0)) = (e1))) -> ((~((op (e1) (e1)) = (e2)))\/((op (e1) (e2)) = (e1))) -> (~((op (e1) (e2)) = (op (e1) (e3)))) -> ((~((op (e2) (e2)) = (e0)))\/((op (e2) (e0)) = (e2))) -> ((~((op (e3) (e3)) = (e1)))\/((op (e3) (e1)) = (e3))) -> (~((op (e3) (e1)) = (op (e3) (e3)))) -> (~((op (e0) (e1)) = (op (e0) (e3)))) -> (~((op (e1) (e0)) = (op (e1) (e3)))) -> (((op (e0) (e3)) = (e1))\/(((op (e1) (e3)) = (e1))\/(((op (e2) (e3)) = (e1))\/((op (e3) (e3)) = (e1))))) -> (~((op (e2) (e0)) = (op (e2) (e3)))) -> (((op (e0) (e0)) = (e1))\/(((op (e1) (e0)) = (e1))\/(((op (e2) (e0)) = (e1))\/((op (e3) (e0)) = (e1))))) -> ((~((op (e3) (e3)) = (e2)))\/((op (e3) (e2)) = (e3))) -> (((op (e0) (e0)) = (e2))\/(((op (e0) (e1)) = (e2))\/(((op (e0) (e2)) = (e2))\/((op (e0) (e3)) = (e2))))) -> (~((op (e0) (e1)) = (op (e2) (e1)))) -> (~((op (e2) (e3)) = (op (e3) (e3)))) -> (((op (e2) (e0)) = (e3))\/(((op (e2) (e1)) = (e3))\/(((op (e2) (e2)) = (e3))\/((op (e2) (e3)) = (e3))))) -> (~((op (e0) (e2)) = (op (e1) (e2)))) -> (((op (e1) (e0)) = (e3))\/(((op (e1) (e1)) = (e3))\/(((op (e1) (e2)) = (e3))\/((op (e1) (e3)) = (e3))))) -> (~((op (e1) (e3)) = (op (e3) (e3)))) -> (((op (e1) (e1)) = (e0))\/(((op (e1) (e1)) = (e1))\/(((op (e1) (e1)) = (e2))\/((op (e1) (e1)) = (e3))))) -> ((~((op (e2) (e2)) = (e3)))\/((op (e2) (e3)) = (e2))) -> (((op (e1) (e0)) = (e2))\/(((op (e1) (e1)) = (e2))\/(((op (e1) (e2)) = (e2))\/((op (e1) (e3)) = (e2))))) -> (((op (e0) (e3)) = (e0))\/(((op (e1) (e3)) = (e0))\/(((op (e2) (e3)) = (e0))\/((op (e3) (e3)) = (e0))))) -> (~((op (e0) (e2)) = (op (e0) (e3)))) -> (~((op (e3) (e0)) = (op (e3) (e3)))) -> ((~((op (e3) (e3)) = (e0)))\/((op (e3) (e0)) = (e3))) -> (~((op (e3) (e2)) = (op (e3) (e3)))) -> (((op (e0) (e2)) = (e3))\/(((op (e1) (e2)) = (e3))\/(((op (e2) (e2)) = (e3))\/((op (e3) (e2)) = (e3))))) -> (((op (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 (e2) (e2)) = (e2)))\/((op (e2) (e2)) = (e2))) -> ((~((op (e1) (e1)) = (e3)))\/((op (e1) (e3)) = (e1))) -> ((~((op (e2) (e2)) = (e1)))\/((op (e2) (e1)) = (e2))) -> (~((op (e2) (e1)) = (op (e2) (e3)))) -> ((~((op (e1) (e1)) = (e1)))\/((op (e1) (e1)) = (e1))) -> (~((op (e0) (e3)) = (op (e1) (e3)))) -> (~((op (e1) (e0)) = (op (e1) (e2)))) -> (~((op (e2) (e1)) = (op (e3) (e1)))) -> (~((op (e0) (e2)) = (op (e3) (e2)))) -> (((op (e3) (e0)) = (e2))\/(((op (e3) (e1)) = (e2))\/(((op (e3) (e2)) = (e2))\/((op (e3) (e3)) = (e2))))) -> (((op (e0) (e0)) = (e0))\/(((op (e0) (e1)) = (e0))\/(((op (e0) (e2)) = (e0))\/((op (e0) (e3)) = (e0))))) -> (~((op (e1) (e1)) = (op (e1) (e3)))) -> (((op (e0) (e0)) = (e0))\/(((op (e0) (e0)) = (e1))\/(((op (e0) (e0)) = (e2))\/((op (e0) (e0)) = (e3))))) -> (((op (e0) (e0)) = (e0))\/(((op (e1) (e0)) = (e0))\/(((op (e2) (e0)) = (e0))\/((op (e3) (e0)) = (e0))))) -> (~((op (e1) (e0)) = (op (e1) (e1)))) -> (~((op (e1) (e1)) = (op (e2) (e1)))) -> (~((op (e0) (e3)) = (op (e2) (e3)))) -> (((op (e2) (e0)) = (e1))\/(((op (e2) (e1)) = (e1))\/(((op (e2) (e2)) = (e1))\/((op (e2) (e3)) = (e1))))) -> (~((op (e0) (e0)) = (e0))) -> (~((op (e1) (e1)) = (op (e1) (e2)))) -> (~((op (e1) (e2)) = (op (e2) (e2)))) -> (~((op (e1) (e2)) = (op (e3) (e2)))) -> (((op (e1) (e2)) = (e0))\/(((op (e1) (e2)) = (e1))\/(((op (e1) (e2)) = (e2))\/((op (e1) (e2)) = (e3))))) -> (((op (e2) (e1)) = (e0))\/(((op (e2) (e1)) = (e1))\/(((op (e2) (e1)) = (e2))\/((op (e2) (e1)) = (e3))))) -> (~((op (e2) (e1)) = (op (e2) (e2)))) -> (((op (e1) (e0)) = (e0))\/(((op (e1) (e1)) = (e0))\/(((op (e1) (e2)) = (e0))\/((op (e1) (e3)) = (e0))))) -> (~((op (e2) (e2)) = (op (e2) (e3)))) -> ((~((op (e3) (e3)) = (e3)))\/((op (e3) (e3)) = (e3))) -> (~((op (e3) (e1)) = (op (e3) (e2)))) -> (((op (e0) (e0)) = (e3))\/(((op (e1) (e0)) = (e3))\/(((op (e2) (e0)) = (e3))\/((op (e3) (e0)) = (e3))))) -> (~((e2) = (e3))) -> ((op (e0) (e2)) = (e0)) -> (~((op (e2) (op (e0) (e2))) = (op (e0) (e2)))) -> (((op (e0) (e0)) = (e1))\/(((op (e0) (e1)) = (e1))\/(((op (e0) (e2)) = (e1))\/((op (e0) (e3)) = (e1))))) -> (~((op (e0) (e0)) = (e1))) -> (~((op (e0) (e1)) = (op (e1) (e1)))) -> ((op (e1) (e1)) = (e1)) -> (~((op (e2) (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 (e3) (e0)) = (e1))\/(((op (e3) (e1)) = (e1))\/(((op (e3) (e2)) = (e1))\/((op (e3) (e3)) = (e1))))) -> (~((e0) = (e1))) -> (~((op (e3) (op (e0) (e3))) = (op (e0) (e3)))) -> ((op (e3) (e2)) = (e3)) -> (~((e1) = (e3))) -> (~((op (e3) (e3)) = (e1))) -> False). % 15.16/15.37 do 0 intro. intros zenon_Ha7 zenon_H154 zenon_H156 zenon_H5e zenon_H58 zenon_H59 zenon_H4b zenon_Heb zenon_H105 zenon_H145 zenon_H16f zenon_H1f6 zenon_H138 zenon_H1e9 zenon_H1e5 zenon_H11b zenon_H182 zenon_H1a2 zenon_Hd6 zenon_H1f5 zenon_H144 zenon_H109 zenon_H17a zenon_H36 zenon_H3b zenon_H1e4 zenon_H1d3 zenon_H1d0 zenon_H1d4 zenon_H10c zenon_H12d zenon_H1cd zenon_H1cf zenon_H121 zenon_Hce zenon_Hf1 zenon_H10e zenon_H8e zenon_Hde zenon_He3 zenon_He6 zenon_H87 zenon_H90 zenon_H8b zenon_H1b3 zenon_H1c3 zenon_H84 zenon_Hd3 zenon_Hc9 zenon_Hbb zenon_H10f zenon_H173 zenon_H175 zenon_H160 zenon_H1c5 zenon_Haa zenon_H1d2 zenon_H1e3 zenon_H1e2 zenon_H1d8 zenon_H80 zenon_H166 zenon_H13c zenon_H140 zenon_H1df zenon_H110 zenon_H11e zenon_H12a zenon_Hf0 zenon_Hd7 zenon_Hb1 zenon_Hb4 zenon_Hb7 zenon_H20 zenon_H116 zenon_H7d zenon_H17d zenon_H1d5 zenon_H15a zenon_H157 zenon_H163 zenon_H15f zenon_H10d zenon_H135 zenon_Hbe zenon_H6a zenon_Hab zenon_H20c zenon_H44 zenon_H45 zenon_H23 zenon_H21 zenon_H30 zenon_H2f zenon_H28 zenon_H2e zenon_H2d zenon_H146 zenon_H9e zenon_H192 zenon_H106 zenon_Ha3 zenon_H104. % 15.22/15.38 apply (zenon_or_s _ _ zenon_Hf0); [ zenon_intro zenon_H1f | zenon_intro zenon_Hf2 ]. % 15.22/15.38 exact (zenon_H20 zenon_H1f). % 15.22/15.38 apply (zenon_or_s _ _ zenon_Hf2); [ zenon_intro zenon_Had | zenon_intro zenon_Hf3 ]. % 15.22/15.38 apply (zenon_or_s _ _ zenon_H44); [ zenon_intro zenon_H47 | zenon_intro zenon_H46 ]. % 15.22/15.38 exact (zenon_H45 zenon_H47). % 15.22/15.38 apply (zenon_or_s _ _ zenon_H46); [ zenon_intro zenon_H22 | zenon_intro zenon_H48 ]. % 15.22/15.38 apply (zenon_L3_); trivial. % 15.22/15.38 apply (zenon_or_s _ _ zenon_H48); [ zenon_intro zenon_H29 | zenon_intro zenon_H37 ]. % 15.22/15.38 apply (zenon_L37_); trivial. % 15.22/15.38 apply (zenon_or_s _ _ zenon_Hf1); [ zenon_intro zenon_H47 | zenon_intro zenon_Hf4 ]. % 15.22/15.38 exact (zenon_H45 zenon_H47). % 15.22/15.38 apply (zenon_or_s _ _ zenon_Hf4); [ zenon_intro zenon_Hd8 | zenon_intro zenon_Hf5 ]. % 15.22/15.38 apply (zenon_L61_); trivial. % 15.22/15.38 apply (zenon_or_s _ _ zenon_Hf5); [ zenon_intro zenon_Hae | zenon_intro zenon_Hee ]. % 15.22/15.38 apply (zenon_or_s _ _ zenon_Heb); [ zenon_intro zenon_H92 | zenon_intro zenon_Hec ]. % 15.22/15.38 apply (zenon_L49_); trivial. % 15.22/15.38 apply (zenon_or_s _ _ zenon_Hec); [ zenon_intro zenon_H68 | zenon_intro zenon_Hed ]. % 15.22/15.38 apply (zenon_L160_); trivial. % 15.22/15.38 apply (zenon_or_s _ _ zenon_Hed); [ zenon_intro zenon_Hdd | zenon_intro zenon_He9 ]. % 15.22/15.38 apply (zenon_L311_); trivial. % 15.22/15.38 apply (zenon_or_s _ _ zenon_Hbe); [ zenon_intro zenon_H5b | zenon_intro zenon_Hbf ]. % 15.22/15.38 exact (zenon_H59 zenon_H5b). % 15.22/15.38 apply (zenon_or_s _ _ zenon_Hbf); [ zenon_intro zenon_H69 | zenon_intro zenon_Hc0 ]. % 15.22/15.38 apply (zenon_L38_); trivial. % 15.22/15.38 apply (zenon_or_s _ _ zenon_Hc0); [ zenon_intro zenon_Haf | zenon_intro zenon_Hba ]. % 15.22/15.38 apply (zenon_L39_); trivial. % 15.22/15.38 apply (zenon_L220_); trivial. % 15.22/15.38 apply (zenon_or_s _ _ zenon_Heb); [ zenon_intro zenon_H92 | zenon_intro zenon_Hec ]. % 15.22/15.38 apply (zenon_L49_); trivial. % 15.22/15.38 apply (zenon_or_s _ _ zenon_Hec); [ zenon_intro zenon_H68 | zenon_intro zenon_Hed ]. % 15.22/15.38 apply (zenon_L160_); trivial. % 15.22/15.38 apply (zenon_or_s _ _ zenon_Hed); [ zenon_intro zenon_Hdd | zenon_intro zenon_He9 ]. % 15.22/15.38 apply (zenon_L284_); trivial. % 15.22/15.38 apply (zenon_L122_); trivial. % 15.22/15.38 apply (zenon_or_s _ _ zenon_Hf3); [ zenon_intro zenon_Hcf | zenon_intro zenon_Hdb ]. % 15.22/15.38 apply (zenon_L312_); trivial. % 15.22/15.38 apply (zenon_or_s _ _ zenon_H44); [ zenon_intro zenon_H47 | zenon_intro zenon_H46 ]. % 15.22/15.38 exact (zenon_H45 zenon_H47). % 15.22/15.38 apply (zenon_or_s _ _ zenon_H46); [ zenon_intro zenon_H22 | zenon_intro zenon_H48 ]. % 15.22/15.38 apply (zenon_L3_); trivial. % 15.22/15.38 apply (zenon_or_s _ _ zenon_H48); [ zenon_intro zenon_H29 | zenon_intro zenon_H37 ]. % 15.22/15.38 apply (zenon_L5_); trivial. % 15.22/15.38 apply (zenon_L314_); trivial. % 15.22/15.38 (* end of lemma zenon_L315_ *) % 15.22/15.38 assert (zenon_L316_ : ((~((op (e2) (e2)) = (e3)))\/((op (e2) (e3)) = (e2))) -> ((~((op (e3) (e3)) = (e1)))\/((op (e3) (e1)) = (e3))) -> ((~((op (e3) (e3)) = (e3)))\/((op (e3) (e3)) = (e3))) -> (~((op (e3) (e1)) = (op (e3) (e3)))) -> (((op (e0) (e0)) = (e2))\/(((op (e0) (e1)) = (e2))\/(((op (e0) (e2)) = (e2))\/((op (e0) (e3)) = (e2))))) -> (~((e0) = (e2))) -> (~((op (e0) (e0)) = (e0))) -> (((op (e3) (e3)) = (e0))\/(((op (e3) (e3)) = (e1))\/(((op (e3) (e3)) = (e2))\/((op (e3) (e3)) = (e3))))) -> (((op (e0) (e0)) = (e0))\/(((op (e0) (e0)) = (e1))\/(((op (e0) (e0)) = (e2))\/((op (e0) (e0)) = (e3))))) -> (~((op (e0) (e0)) = (e2))) -> (~((op (e0) (e3)) = (op (e3) (e3)))) -> (~((op (e3) (e1)) = (op (e3) (e2)))) -> ((~((op (e3) (e3)) = (e2)))\/((op (e3) (e2)) = (e3))) -> (((op (e2) (e0)) = (e1))\/(((op (e2) (e1)) = (e1))\/(((op (e2) (e2)) = (e1))\/((op (e2) (e3)) = (e1))))) -> (~((e1) = (e2))) -> (~((op (e2) (e2)) = (e1))) -> (~((op (e1) (e1)) = (op (e2) (e1)))) -> (~((op (e0) (e2)) = (op (e0) (e3)))) -> (~((op (e1) (e1)) = (op (e1) (e3)))) -> (~((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 (e3) (e0)) = (op (e3) (e3)))) -> (~((op (e1) (e0)) = (op (e1) (e1)))) -> (~((e1) = (e3))) -> (((op (e0) (e0)) = (e1))\/(((op (e1) (e0)) = (e1))\/(((op (e2) (e0)) = (e1))\/((op (e3) (e0)) = (e1))))) -> (~((op (e3) (e0)) = (op (e3) (e2)))) -> ((~((op (e3) (e3)) = (e0)))\/((op (e3) (e0)) = (e3))) -> (~((op (e0) (e0)) = (e1))) -> (~((op (e0) (e1)) = (op (e1) (e1)))) -> ((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 (e0) (e2)) = (op (e2) (e2)))) -> (~((op (e2) (e2)) = (e0))) -> (~((e0) = (e1))) -> ((op (e0) (e3)) = (e0)) -> (((op (e0) (e0)) = (e1))\/(((op (e0) (e1)) = (e1))\/(((op (e0) (e2)) = (e1))\/((op (e0) (e3)) = (e1))))) -> False). % 15.22/15.38 do 0 intro. intros zenon_H1c3 zenon_H10c zenon_H10d zenon_H12d zenon_H8e zenon_H5e zenon_H20 zenon_H3b zenon_H12a zenon_H8f zenon_H36 zenon_H135 zenon_H10e zenon_Hb7 zenon_Ha7 zenon_H52 zenon_Hb1 zenon_Hc9 zenon_H11e zenon_Hce zenon_H121 zenon_H109 zenon_Hbb zenon_Hd7 zenon_Ha3 zenon_Hf1 zenon_H105 zenon_H10f zenon_H45 zenon_H23 zenon_H21 zenon_H2d zenon_H2f zenon_H28 zenon_H2e zenon_H9e zenon_Hca zenon_H44. % 15.22/15.38 apply (zenon_or_s _ _ zenon_H1c3); [ zenon_intro zenon_H30 | zenon_intro zenon_H124 ]. % 15.22/15.38 apply (zenon_L74_); trivial. % 15.22/15.38 apply (zenon_L117_); trivial. % 15.22/15.38 (* end of lemma zenon_L316_ *) % 15.22/15.38 assert (zenon_L317_ : ((~((op (e2) (e2)) = (e3)))\/((op (e2) (e3)) = (e2))) -> (~((op (e2) (e2)) = (op (e2) (e3)))) -> ((~((op (e3) (e3)) = (e1)))\/((op (e3) (e1)) = (e3))) -> ((~((op (e3) (e3)) = (e3)))\/((op (e3) (e3)) = (e3))) -> (~((op (e1) (e0)) = (op (e1) (e1)))) -> (((op (e0) (e3)) = (e1))\/(((op (e1) (e3)) = (e1))\/(((op (e2) (e3)) = (e1))\/((op (e3) (e3)) = (e1))))) -> (~((op (e2) (e0)) = (op (e2) (e3)))) -> (~((op (e1) (e1)) = (op (e1) (e3)))) -> (~((op (e0) (e2)) = (op (e0) (e3)))) -> (~((e0) = (e1))) -> (~((op (e1) (e0)) = (op (e1) (e2)))) -> (~((op (e2) (e2)) = (e0))) -> (((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) (e1)) = (op (e3) (e2)))) -> (((op (e0) (e2)) = (e0))\/(((op (e1) (e2)) = (e0))\/(((op (e2) (e2)) = (e0))\/((op (e3) (e2)) = (e0))))) -> (((op (e0) (e0)) = (e1))\/(((op (e1) (e0)) = (e1))\/(((op (e2) (e0)) = (e1))\/((op (e3) (e0)) = (e1))))) -> (((op (e1) (e0)) = (e0))\/(((op (e1) (e1)) = (e0))\/(((op (e1) (e2)) = (e0))\/((op (e1) (e3)) = (e0))))) -> (~((op (e0) (e3)) = (op (e1) (e3)))) -> (~((e1) = (e3))) -> (~((e0) = (e3))) -> (~((op (e3) (e2)) = (op (e3) (e3)))) -> (((op (e0) (e2)) = (e3))\/(((op (e1) (e2)) = (e3))\/(((op (e2) (e2)) = (e3))\/((op (e3) (e2)) = (e3))))) -> (~((op (e1) (e1)) = (e0))) -> (~((op (e2) (e0)) = (op (e2) (e1)))) -> (((op (e0) (e1)) = (e0))\/(((op (e1) (e1)) = (e0))\/(((op (e2) (e1)) = (e0))\/((op (e3) (e1)) = (e0))))) -> (~((op (e0) (e2)) = (op (e2) (e2)))) -> ((op (e2) (e2)) = (e2)) -> (~((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)) = (e1))) -> (~((op (e0) (e1)) = (op (e1) (e1)))) -> ((op (e1) (e1)) = (e1)) -> (((op (e0) (e0)) = (e2))\/(((op (e0) (e1)) = (e2))\/(((op (e0) (e2)) = (e2))\/((op (e0) (e3)) = (e2))))) -> ((op (e0) (e3)) = (e0)) -> (~((e0) = (e2))) -> (~((e1) = (e2))) -> (~((op (e0) (e0)) = (e0))) -> (((op (e3) (e3)) = (e0))\/(((op (e3) (e3)) = (e1))\/(((op (e3) (e3)) = (e2))\/((op (e3) (e3)) = (e3))))) -> (((op (e0) (e0)) = (e0))\/(((op (e0) (e0)) = (e1))\/(((op (e0) (e0)) = (e2))\/((op (e0) (e0)) = (e3))))) -> (~((op (e0) (e0)) = (e2))) -> (~((op (e0) (e3)) = (op (e3) (e3)))) -> (((op (e0) (e0)) = (e1))\/(((op (e0) (e1)) = (e1))\/(((op (e0) (e2)) = (e1))\/((op (e0) (e3)) = (e1))))) -> (((op (e0) (e0)) = (e2))\/(((op (e1) (e0)) = (e2))\/(((op (e2) (e0)) = (e2))\/((op (e3) (e0)) = (e2))))) -> (~((op (e2) (e0)) = (op (e2) (e2)))) -> (((op (e1) (e0)) = (e2))\/(((op (e1) (e1)) = (e2))\/(((op (e1) (e2)) = (e2))\/((op (e1) (e3)) = (e2))))) -> (~((op (e1) (e1)) = (e3))) -> (~((op (e1) (e2)) = (op (e3) (e2)))) -> (~((e2) = (e3))) -> (((op (e1) (e0)) = (e3))\/(((op (e1) (e1)) = (e3))\/(((op (e1) (e2)) = (e3))\/((op (e1) (e3)) = (e3))))) -> (~((op (e1) (e2)) = (op (e2) (e2)))) -> (~((op (e1) (e1)) = (e2))) -> (((op (e0) (e2)) = (e1))\/(((op (e1) (e2)) = (e1))\/(((op (e2) (e2)) = (e1))\/((op (e3) (e2)) = (e1))))) -> (~((op (e1) (e1)) = (op (e1) (e2)))) -> (~((op (e1) (e1)) = (op (e2) (e1)))) -> (~((op (e2) (e2)) = (e1))) -> (((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 (e3) (op (e0) (e3))) = (op (e0) (e3)))) -> ((~((op (e3) (e3)) = (e2)))\/((op (e3) (e2)) = (e3))) -> ((~((op (e3) (e3)) = (e0)))\/((op (e3) (e0)) = (e3))) -> False). % 15.22/15.38 do 0 intro. intros zenon_H1c3 zenon_H15f zenon_H10c zenon_H10d zenon_Hd7 zenon_H121 zenon_Hce zenon_H11e zenon_Hc9 zenon_H9e zenon_H166 zenon_H2e zenon_H16c zenon_H12d zenon_H138 zenon_H109 zenon_H135 zenon_H16f zenon_Hf1 zenon_H163 zenon_H80 zenon_Ha3 zenon_H4b zenon_H173 zenon_H175 zenon_H145 zenon_H154 zenon_H144 zenon_H28 zenon_H35 zenon_H105 zenon_Hf0 zenon_H45 zenon_H23 zenon_H21 zenon_H8e zenon_Hca zenon_H5e zenon_Ha7 zenon_H20 zenon_H3b zenon_H12a zenon_H8f zenon_H36 zenon_H44 zenon_Heb zenon_H17a zenon_H84 zenon_H182 zenon_H17d zenon_H6a zenon_H90 zenon_H7d zenon_Hd6 zenon_H11b zenon_H116 zenon_Hb1 zenon_H52 zenon_H160 zenon_Hb7 zenon_H192 zenon_H10e zenon_H10f. % 15.22/15.38 apply (zenon_or_s _ _ zenon_H1c3); [ zenon_intro zenon_H30 | zenon_intro zenon_H124 ]. % 15.22/15.38 apply (zenon_L276_); trivial. % 15.22/15.38 apply (zenon_L137_); trivial. % 15.22/15.38 (* end of lemma zenon_L317_ *) % 15.22/15.38 assert (zenon_L318_ : ((~((op (e2) (e2)) = (e2)))\/((op (e2) (e2)) = (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) (e3)) = (e0)) -> (~((e0) = (e1))) -> (~((op (e2) (e2)) = (e0))) -> (~((op (e0) (e2)) = (op (e2) (e2)))) -> (((op (e2) (e2)) = (e0))\/(((op (e2) (e2)) = (e1))\/(((op (e2) (e2)) = (e2))\/((op (e2) (e2)) = (e3))))) -> ((op (e1) (e1)) = (e1)) -> (~((op (e0) (e1)) = (op (e1) (e1)))) -> (~((op (e0) (e0)) = (e1))) -> (~((op (e2) (e1)) = (op (e2) (e3)))) -> ((op (e2) (e1)) = (e2)) -> ((~((op (e2) (e2)) = (e3)))\/((op (e2) (e3)) = (e2))) -> False). % 15.22/15.38 do 0 intro. intros zenon_Haa zenon_H157 zenon_H44 zenon_Hca zenon_H9e zenon_H2e zenon_H28 zenon_H2d zenon_H21 zenon_H23 zenon_H45 zenon_H1e2 zenon_H156 zenon_H1c3. % 15.22/15.38 apply (zenon_or_s _ _ zenon_Haa); [ zenon_intro zenon_H2f | zenon_intro zenon_H35 ]. % 15.22/15.38 apply (zenon_L287_); trivial. % 15.22/15.38 apply (zenon_L134_); trivial. % 15.22/15.38 (* end of lemma zenon_L318_ *) % 15.22/15.38 assert (zenon_L319_ : ((op (e2) (e3)) = (e1)) -> ((op (e0) (e0)) = (e3)) -> ((op (e2) (e2)) = (e0)) -> False). % 15.22/15.38 do 0 intro. intros zenon_Hb5 zenon_H5b zenon_H32. % 15.22/15.38 apply (zenon_notand_s _ _ ax24); [ zenon_intro zenon_H217 | zenon_intro zenon_H216 ]. % 15.22/15.38 elim (classic ((op (op (e2) (e2)) (op (e2) (e2))) = (op (op (e2) (e2)) (op (e2) (e2))))); [ zenon_intro zenon_Hfa | zenon_intro zenon_Hfb ]. % 15.22/15.38 cut (((op (op (e2) (e2)) (op (e2) (e2))) = (op (op (e2) (e2)) (op (e2) (e2)))) = ((e3) = (op (op (e2) (e2)) (op (e2) (e2))))). % 15.22/15.38 intro zenon_D_pnotp. % 15.22/15.38 apply zenon_H217. % 15.22/15.38 rewrite <- zenon_D_pnotp. % 15.22/15.38 exact zenon_Hfa. % 15.22/15.38 cut (((op (op (e2) (e2)) (op (e2) (e2))) = (op (op (e2) (e2)) (op (e2) (e2))))); [idtac | apply NNPP; zenon_intro zenon_Hfb]. % 15.22/15.38 cut (((op (op (e2) (e2)) (op (e2) (e2))) = (e3))); [idtac | apply NNPP; zenon_intro zenon_H218]. % 15.22/15.38 congruence. % 15.22/15.38 cut (((op (e0) (e0)) = (e3)) = ((op (op (e2) (e2)) (op (e2) (e2))) = (e3))). % 15.22/15.38 intro zenon_D_pnotp. % 15.22/15.38 apply zenon_H218. % 15.22/15.38 rewrite <- zenon_D_pnotp. % 15.22/15.38 exact zenon_H5b. % 15.22/15.38 cut (((e3) = (e3))); [idtac | apply NNPP; zenon_intro zenon_H4d]. % 15.22/15.38 cut (((op (e0) (e0)) = (op (op (e2) (e2)) (op (e2) (e2))))); [idtac | apply NNPP; zenon_intro zenon_H1fd]. % 15.22/15.38 congruence. % 15.22/15.38 elim (classic ((op (op (e2) (e2)) (op (e2) (e2))) = (op (op (e2) (e2)) (op (e2) (e2))))); [ zenon_intro zenon_Hfa | zenon_intro zenon_Hfb ]. % 15.22/15.38 cut (((op (op (e2) (e2)) (op (e2) (e2))) = (op (op (e2) (e2)) (op (e2) (e2)))) = ((op (e0) (e0)) = (op (op (e2) (e2)) (op (e2) (e2))))). % 15.22/15.38 intro zenon_D_pnotp. % 15.22/15.38 apply zenon_H1fd. % 15.22/15.38 rewrite <- zenon_D_pnotp. % 15.22/15.38 exact zenon_Hfa. % 15.22/15.38 cut (((op (op (e2) (e2)) (op (e2) (e2))) = (op (op (e2) (e2)) (op (e2) (e2))))); [idtac | apply NNPP; zenon_intro zenon_Hfb]. % 15.22/15.38 cut (((op (op (e2) (e2)) (op (e2) (e2))) = (op (e0) (e0)))); [idtac | apply NNPP; zenon_intro zenon_H1fb]. % 15.22/15.38 congruence. % 15.22/15.38 apply (zenon_L280_); trivial. % 15.22/15.38 apply zenon_Hfb. apply refl_equal. % 15.22/15.38 apply zenon_Hfb. apply refl_equal. % 15.22/15.38 apply zenon_H4d. apply refl_equal. % 15.22/15.38 apply zenon_Hfb. apply refl_equal. % 15.22/15.38 apply zenon_Hfb. apply refl_equal. % 15.22/15.38 apply (zenon_notand_s _ _ zenon_H216); [ zenon_intro zenon_H1fe | zenon_intro zenon_Hfe ]. % 15.22/15.38 apply zenon_H1fe. apply sym_equal. exact zenon_H32. % 15.22/15.38 elim (classic ((op (e2) (op (op (e2) (e2)) (op (e2) (e2)))) = (op (e2) (op (op (e2) (e2)) (op (e2) (e2)))))); [ zenon_intro zenon_Hff | zenon_intro zenon_H100 ]. % 15.22/15.38 cut (((op (e2) (op (op (e2) (e2)) (op (e2) (e2)))) = (op (e2) (op (op (e2) (e2)) (op (e2) (e2))))) = ((e1) = (op (e2) (op (op (e2) (e2)) (op (e2) (e2)))))). % 15.22/15.38 intro zenon_D_pnotp. % 15.22/15.38 apply zenon_Hfe. % 15.22/15.38 rewrite <- zenon_D_pnotp. % 15.22/15.38 exact zenon_Hff. % 15.22/15.38 cut (((op (e2) (op (op (e2) (e2)) (op (e2) (e2)))) = (op (e2) (op (op (e2) (e2)) (op (e2) (e2)))))); [idtac | apply NNPP; zenon_intro zenon_H100]. % 15.22/15.38 cut (((op (e2) (op (op (e2) (e2)) (op (e2) (e2)))) = (e1))); [idtac | apply NNPP; zenon_intro zenon_H101]. % 15.22/15.38 congruence. % 15.22/15.38 cut (((op (e2) (e3)) = (e1)) = ((op (e2) (op (op (e2) (e2)) (op (e2) (e2)))) = (e1))). % 15.22/15.38 intro zenon_D_pnotp. % 15.22/15.38 apply zenon_H101. % 15.22/15.38 rewrite <- zenon_D_pnotp. % 15.22/15.38 exact zenon_Hb5. % 15.22/15.38 cut (((e1) = (e1))); [idtac | apply NNPP; zenon_intro zenon_Ha0]. % 15.22/15.38 cut (((op (e2) (e3)) = (op (e2) (op (op (e2) (e2)) (op (e2) (e2)))))); [idtac | apply NNPP; zenon_intro zenon_H219]. % 15.22/15.38 congruence. % 15.22/15.38 elim (classic ((op (e2) (op (op (e2) (e2)) (op (e2) (e2)))) = (op (e2) (op (op (e2) (e2)) (op (e2) (e2)))))); [ zenon_intro zenon_Hff | zenon_intro zenon_H100 ]. % 15.22/15.38 cut (((op (e2) (op (op (e2) (e2)) (op (e2) (e2)))) = (op (e2) (op (op (e2) (e2)) (op (e2) (e2))))) = ((op (e2) (e3)) = (op (e2) (op (op (e2) (e2)) (op (e2) (e2)))))). % 15.22/15.38 intro zenon_D_pnotp. % 15.22/15.38 apply zenon_H219. % 15.22/15.38 rewrite <- zenon_D_pnotp. % 15.22/15.38 exact zenon_Hff. % 15.22/15.38 cut (((op (e2) (op (op (e2) (e2)) (op (e2) (e2)))) = (op (e2) (op (op (e2) (e2)) (op (e2) (e2)))))); [idtac | apply NNPP; zenon_intro zenon_H100]. % 15.22/15.38 cut (((op (e2) (op (op (e2) (e2)) (op (e2) (e2)))) = (op (e2) (e3)))); [idtac | apply NNPP; zenon_intro zenon_H21a]. % 15.22/15.38 congruence. % 15.22/15.38 cut (((op (op (e2) (e2)) (op (e2) (e2))) = (e3))); [idtac | apply NNPP; zenon_intro zenon_H218]. % 15.22/15.38 cut (((e2) = (e2))); [idtac | apply NNPP; zenon_intro zenon_H60]. % 15.22/15.38 congruence. % 15.22/15.38 apply zenon_H60. apply refl_equal. % 15.22/15.38 cut (((op (e0) (e0)) = (e3)) = ((op (op (e2) (e2)) (op (e2) (e2))) = (e3))). % 15.22/15.38 intro zenon_D_pnotp. % 15.22/15.38 apply zenon_H218. % 15.22/15.38 rewrite <- zenon_D_pnotp. % 15.22/15.38 exact zenon_H5b. % 15.22/15.38 cut (((e3) = (e3))); [idtac | apply NNPP; zenon_intro zenon_H4d]. % 15.22/15.38 cut (((op (e0) (e0)) = (op (op (e2) (e2)) (op (e2) (e2))))); [idtac | apply NNPP; zenon_intro zenon_H1fd]. % 15.22/15.38 congruence. % 15.22/15.38 elim (classic ((op (op (e2) (e2)) (op (e2) (e2))) = (op (op (e2) (e2)) (op (e2) (e2))))); [ zenon_intro zenon_Hfa | zenon_intro zenon_Hfb ]. % 15.22/15.38 cut (((op (op (e2) (e2)) (op (e2) (e2))) = (op (op (e2) (e2)) (op (e2) (e2)))) = ((op (e0) (e0)) = (op (op (e2) (e2)) (op (e2) (e2))))). % 15.22/15.38 intro zenon_D_pnotp. % 15.22/15.38 apply zenon_H1fd. % 15.22/15.38 rewrite <- zenon_D_pnotp. % 15.22/15.38 exact zenon_Hfa. % 15.22/15.38 cut (((op (op (e2) (e2)) (op (e2) (e2))) = (op (op (e2) (e2)) (op (e2) (e2))))); [idtac | apply NNPP; zenon_intro zenon_Hfb]. % 15.22/15.38 cut (((op (op (e2) (e2)) (op (e2) (e2))) = (op (e0) (e0)))); [idtac | apply NNPP; zenon_intro zenon_H1fb]. % 15.22/15.38 congruence. % 15.22/15.38 apply (zenon_L280_); trivial. % 15.22/15.38 apply zenon_Hfb. apply refl_equal. % 15.22/15.38 apply zenon_Hfb. apply refl_equal. % 15.22/15.38 apply zenon_H4d. apply refl_equal. % 15.22/15.38 apply zenon_H100. apply refl_equal. % 15.22/15.38 apply zenon_H100. apply refl_equal. % 15.22/15.38 apply zenon_Ha0. apply refl_equal. % 15.22/15.38 apply zenon_H100. apply refl_equal. % 15.22/15.38 apply zenon_H100. apply refl_equal. % 15.22/15.38 (* end of lemma zenon_L319_ *) % 15.22/15.38 assert (zenon_L320_ : (((op (e2) (e2)) = (e0))\/(((op (e2) (e2)) = (e1))\/(((op (e2) (e2)) = (e2))\/((op (e2) (e2)) = (e3))))) -> ((op (e0) (e0)) = (e3)) -> ((op (e2) (e3)) = (e1)) -> (~((op (e2) (e2)) = (e1))) -> (~((op (e2) (e2)) = (e2))) -> (~((op (e2) (e2)) = (e3))) -> False). % 15.22/15.38 do 0 intro. intros zenon_H2d zenon_H5b zenon_Hb5 zenon_H52 zenon_H2f zenon_H30. % 15.22/15.38 apply (zenon_or_s _ _ zenon_H2d); [ zenon_intro zenon_H32 | zenon_intro zenon_H31 ]. % 15.22/15.38 apply (zenon_L319_); trivial. % 15.22/15.38 apply (zenon_or_s _ _ zenon_H31); [ zenon_intro zenon_H2a | zenon_intro zenon_H33 ]. % 15.22/15.38 exact (zenon_H52 zenon_H2a). % 15.22/15.38 apply (zenon_or_s _ _ zenon_H33); [ zenon_intro zenon_H35 | zenon_intro zenon_H34 ]. % 15.22/15.38 exact (zenon_H2f zenon_H35). % 15.22/15.38 exact (zenon_H30 zenon_H34). % 15.22/15.38 (* end of lemma zenon_L320_ *) % 15.22/15.38 assert (zenon_L321_ : (((op (e2) (e0)) = (e1))\/(((op (e2) (e1)) = (e1))\/(((op (e2) (e2)) = (e1))\/((op (e2) (e3)) = (e1))))) -> ((op (e2) (e0)) = (e2)) -> (~((e1) = (e2))) -> ((op (e1) (e1)) = (e1)) -> (~((op (e1) (e1)) = (op (e2) (e1)))) -> (((op (e2) (e2)) = (e0))\/(((op (e2) (e2)) = (e1))\/(((op (e2) (e2)) = (e2))\/((op (e2) (e2)) = (e3))))) -> ((op (e0) (e0)) = (e3)) -> (~((op (e2) (e2)) = (e1))) -> (~((op (e2) (e2)) = (e2))) -> (~((op (e2) (e2)) = (e3))) -> False). % 15.22/15.38 do 0 intro. intros zenon_Hb7 zenon_Hdd zenon_Ha7 zenon_H21 zenon_Hb1 zenon_H2d zenon_H5b zenon_H52 zenon_H2f zenon_H30. % 15.22/15.38 apply (zenon_or_s _ _ zenon_Hb7); [ zenon_intro zenon_Hae | zenon_intro zenon_Hb8 ]. % 15.22/15.38 apply (zenon_L304_); trivial. % 15.22/15.38 apply (zenon_or_s _ _ zenon_Hb8); [ zenon_intro zenon_Hb2 | zenon_intro zenon_Hb9 ]. % 15.22/15.38 apply (zenon_L40_); trivial. % 15.22/15.38 apply (zenon_or_s _ _ zenon_Hb9); [ zenon_intro zenon_H2a | zenon_intro zenon_Hb5 ]. % 15.22/15.38 exact (zenon_H52 zenon_H2a). % 15.22/15.38 apply (zenon_L320_); trivial. % 15.22/15.38 (* end of lemma zenon_L321_ *) % 15.22/15.38 assert (zenon_L322_ : (((op (e2) (e0)) = (e1))\/(((op (e2) (e1)) = (e1))\/(((op (e2) (e2)) = (e1))\/((op (e2) (e3)) = (e1))))) -> ((op (e2) (e0)) = (e2)) -> (~((e1) = (e2))) -> ((op (e1) (e1)) = (e1)) -> (~((op (e1) (e1)) = (op (e2) (e1)))) -> (~((op (e2) (e2)) = (e1))) -> (~((op (e0) (e3)) = (op (e2) (e3)))) -> ((op (e0) (e3)) = (e1)) -> False). % 15.22/15.38 do 0 intro. intros zenon_Hb7 zenon_Hdd zenon_Ha7 zenon_H21 zenon_Hb1 zenon_H52 zenon_Hb4 zenon_H37. % 15.22/15.38 apply (zenon_or_s _ _ zenon_Hb7); [ zenon_intro zenon_Hae | zenon_intro zenon_Hb8 ]. % 15.22/15.38 apply (zenon_L304_); trivial. % 15.22/15.38 apply (zenon_or_s _ _ zenon_Hb8); [ zenon_intro zenon_Hb2 | zenon_intro zenon_Hb9 ]. % 15.22/15.38 apply (zenon_L40_); trivial. % 15.22/15.38 apply (zenon_or_s _ _ zenon_Hb9); [ zenon_intro zenon_H2a | zenon_intro zenon_Hb5 ]. % 15.22/15.38 exact (zenon_H52 zenon_H2a). % 15.22/15.38 apply (zenon_L41_); trivial. % 15.22/15.38 (* end of lemma zenon_L322_ *) % 15.22/15.38 assert (zenon_L323_ : ((~((op (e2) (e2)) = (e2)))\/((op (e2) (e2)) = (e2))) -> (~((op (e2) (e0)) = (op (e2) (e2)))) -> (((op (e0) (e0)) = (e1))\/(((op (e0) (e1)) = (e1))\/(((op (e0) (e2)) = (e1))\/((op (e0) (e3)) = (e1))))) -> (~((op (e0) (e3)) = (op (e2) (e3)))) -> (((op (e2) (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)) = (e1))) -> (~((op (e1) (e1)) = (op (e2) (e1)))) -> ((op (e2) (e0)) = (e2)) -> (~((e1) = (e2))) -> (((op (e2) (e0)) = (e3))\/(((op (e2) (e1)) = (e3))\/(((op (e2) (e2)) = (e3))\/((op (e2) (e3)) = (e3))))) -> ((op (e3) (e3)) = (e3)) -> (~((op (e2) (e3)) = (op (e3) (e3)))) -> (~((op (e0) (e1)) = (op (e2) (e1)))) -> (~((e2) = (e3))) -> (~((e1) = (e3))) -> (~((op (e0) (e3)) = (op (e3) (e3)))) -> (((op (e0) (e0)) = (e3))\/(((op (e0) (e1)) = (e3))\/(((op (e0) (e2)) = (e3))\/((op (e0) (e3)) = (e3))))) -> ((op (e1) (e1)) = (e1)) -> (~((op (e0) (e1)) = (op (e1) (e1)))) -> (~((op (e0) (e0)) = (e1))) -> (~((op (e2) (e0)) = (op (e2) (e3)))) -> ((~((op (e2) (e2)) = (e3)))\/((op (e2) (e3)) = (e2))) -> False). % 15.22/15.38 do 0 intro. intros zenon_Haa zenon_H17a zenon_H44 zenon_Hb4 zenon_Hb7 zenon_H2d zenon_H52 zenon_Hb1 zenon_Hdd zenon_Ha7 zenon_He6 zenon_H42 zenon_He3 zenon_Hde zenon_H6a zenon_Ha3 zenon_H36 zenon_H58 zenon_H21 zenon_H23 zenon_H45 zenon_Hce zenon_H1c3. % 15.22/15.38 apply (zenon_or_s _ _ zenon_Haa); [ zenon_intro zenon_H2f | zenon_intro zenon_H35 ]. % 15.22/15.38 apply (zenon_or_s _ _ zenon_H1c3); [ zenon_intro zenon_H30 | zenon_intro zenon_H124 ]. % 15.22/15.38 apply (zenon_or_s _ _ zenon_H44); [ zenon_intro zenon_H47 | zenon_intro zenon_H46 ]. % 15.22/15.38 exact (zenon_H45 zenon_H47). % 15.22/15.38 apply (zenon_or_s _ _ zenon_H46); [ zenon_intro zenon_H22 | zenon_intro zenon_H48 ]. % 15.22/15.38 apply (zenon_L3_); trivial. % 15.22/15.38 apply (zenon_or_s _ _ zenon_H48); [ zenon_intro zenon_H29 | zenon_intro zenon_H37 ]. % 15.22/15.38 apply (zenon_or_s _ _ zenon_H58); [ zenon_intro zenon_H5b | zenon_intro zenon_H5a ]. % 15.22/15.38 apply (zenon_L321_); trivial. % 15.22/15.38 apply (zenon_or_s _ _ zenon_H5a); [ zenon_intro zenon_H4a | zenon_intro zenon_H5c ]. % 15.22/15.38 apply (zenon_L67_); trivial. % 15.22/15.38 apply (zenon_or_s _ _ zenon_H5c); [ zenon_intro zenon_H50 | zenon_intro zenon_H53 ]. % 15.22/15.38 apply (zenon_L29_); trivial. % 15.22/15.38 apply (zenon_L12_); trivial. % 15.22/15.38 apply (zenon_L322_); trivial. % 15.22/15.38 apply (zenon_L119_); trivial. % 15.22/15.38 apply (zenon_L161_); trivial. % 15.22/15.38 (* end of lemma zenon_L323_ *) % 15.22/15.38 assert (zenon_L324_ : ((~((op (e2) (e2)) = (e0)))\/((op (e2) (e0)) = (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)) = (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 (e2) (e2)) = (e2)))\/((op (e2) (e2)) = (e2))) -> (~((op (e3) (op (e0) (e3))) = (op (e0) (e3)))) -> (((op (e0) (e3)) = (e2))\/(((op (e1) (e3)) = (e2))\/(((op (e2) (e3)) = (e2))\/((op (e3) (e3)) = (e2))))) -> (~((op (e1) (e1)) = (op (e1) (e2)))) -> (((op (e0) (e2)) = (e1))\/(((op (e1) (e2)) = (e1))\/(((op (e2) (e2)) = (e1))\/((op (e3) (e2)) = (e1))))) -> (~((op (e1) (e1)) = (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))) -> (~((op (e1) (e2)) = (op (e3) (e2)))) -> (~((op (e1) (e1)) = (e3))) -> (((op (e1) (e0)) = (e2))\/(((op (e1) (e1)) = (e2))\/(((op (e1) (e2)) = (e2))\/((op (e1) (e3)) = (e2))))) -> (~((op (e2) (e0)) = (op (e2) (e2)))) -> (((op (e0) (e0)) = (e2))\/(((op (e1) (e0)) = (e2))\/(((op (e2) (e0)) = (e2))\/((op (e3) (e0)) = (e2))))) -> (((op (e0) (e0)) = (e0))\/(((op (e1) (e0)) = (e0))\/(((op (e2) (e0)) = (e0))\/((op (e3) (e0)) = (e0))))) -> (((op (e0) (e1)) = (e0))\/(((op (e1) (e1)) = (e0))\/(((op (e2) (e1)) = (e0))\/((op (e3) (e1)) = (e0))))) -> (~((op (e2) (e0)) = (op (e2) (e1)))) -> (~((op (e1) (e1)) = (e0))) -> (((op (e0) (e2)) = (e3))\/(((op (e1) (e2)) = (e3))\/(((op (e2) (e2)) = (e3))\/((op (e3) (e2)) = (e3))))) -> (~((op (e3) (e2)) = (op (e3) (e3)))) -> (~((e0) = (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) (e2)) = (e0))\/(((op (e1) (e2)) = (e0))\/(((op (e2) (e2)) = (e0))\/((op (e3) (e2)) = (e0))))) -> (~((op (e0) (e1)) = (op (e3) (e1)))) -> (((op (e3) (e1)) = (e0))\/(((op (e3) (e1)) = (e1))\/(((op (e3) (e1)) = (e2))\/((op (e3) (e1)) = (e3))))) -> (~((op (e1) (e0)) = (op (e1) (e2)))) -> (~((op (e2) (e2)) = (op (e2) (e3)))) -> (((op (e0) (e0)) = (e1))\/(((op (e0) (e1)) = (e1))\/(((op (e0) (e2)) = (e1))\/((op (e0) (e3)) = (e1))))) -> ((op (e0) (e3)) = (e0)) -> (~((e0) = (e1))) -> (~((op (e0) (e2)) = (op (e2) (e2)))) -> (((op (e2) (e2)) = (e0))\/(((op (e2) (e2)) = (e1))\/(((op (e2) (e2)) = (e2))\/((op (e2) (e2)) = (e3))))) -> ((op (e1) (e1)) = (e1)) -> (~((op (e0) (e1)) = (op (e1) (e1)))) -> (~((op (e0) (e0)) = (e1))) -> ((~((op (e3) (e3)) = (e0)))\/((op (e3) (e0)) = (e3))) -> (~((op (e3) (e0)) = (op (e3) (e2)))) -> (((op (e0) (e0)) = (e1))\/(((op (e1) (e0)) = (e1))\/(((op (e2) (e0)) = (e1))\/((op (e3) (e0)) = (e1))))) -> (~((e1) = (e3))) -> (~((op (e1) (e0)) = (op (e1) (e1)))) -> (~((op (e3) (e0)) = (op (e3) (e3)))) -> (~((op (e3) (e0)) = (op (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 (e1) (e1)) = (op (e1) (e3)))) -> (~((op (e0) (e2)) = (op (e0) (e3)))) -> (~((op (e1) (e1)) = (op (e2) (e1)))) -> (~((e1) = (e2))) -> (((op (e2) (e0)) = (e1))\/(((op (e2) (e1)) = (e1))\/(((op (e2) (e2)) = (e1))\/((op (e2) (e3)) = (e1))))) -> ((~((op (e3) (e3)) = (e2)))\/((op (e3) (e2)) = (e3))) -> (~((op (e3) (e1)) = (op (e3) (e2)))) -> (~((op (e0) (e3)) = (op (e3) (e3)))) -> (~((op (e0) (e0)) = (e2))) -> (((op (e0) (e0)) = (e0))\/(((op (e0) (e0)) = (e1))\/(((op (e0) (e0)) = (e2))\/((op (e0) (e0)) = (e3))))) -> (((op (e3) (e3)) = (e0))\/(((op (e3) (e3)) = (e1))\/(((op (e3) (e3)) = (e2))\/((op (e3) (e3)) = (e3))))) -> (~((op (e0) (e0)) = (e0))) -> (~((e0) = (e2))) -> (((op (e0) (e0)) = (e2))\/(((op (e0) (e1)) = (e2))\/(((op (e0) (e2)) = (e2))\/((op (e0) (e3)) = (e2))))) -> (~((op (e3) (e1)) = (op (e3) (e3)))) -> ((~((op (e3) (e3)) = (e3)))\/((op (e3) (e3)) = (e3))) -> ((~((op (e3) (e3)) = (e1)))\/((op (e3) (e1)) = (e3))) -> ((~((op (e2) (e2)) = (e3)))\/((op (e2) (e3)) = (e2))) -> (~((op (e2) (e1)) = (op (e2) (e2)))) -> (~((op (e2) (e1)) = (op (e2) (e3)))) -> ((~((op (e2) (e2)) = (e1)))\/((op (e2) (e1)) = (e2))) -> False). % 15.22/15.38 do 0 intro. intros zenon_H1d4 zenon_Hb4 zenon_He6 zenon_He3 zenon_Hde zenon_H58 zenon_Haa zenon_H192 zenon_H160 zenon_H116 zenon_H11b zenon_Hd6 zenon_H7d zenon_H90 zenon_H6a zenon_H17d zenon_H182 zenon_H84 zenon_H17a zenon_Heb zenon_Hf0 zenon_H144 zenon_H154 zenon_H145 zenon_H175 zenon_H173 zenon_H4b zenon_H80 zenon_H163 zenon_H16f zenon_H138 zenon_H16c zenon_H166 zenon_H15f zenon_H44 zenon_Hca zenon_H9e zenon_H28 zenon_H2d zenon_H21 zenon_H23 zenon_H45 zenon_H10f zenon_H105 zenon_Hf1 zenon_Ha3 zenon_Hd7 zenon_Hbb zenon_H109 zenon_H121 zenon_Hce zenon_H11e zenon_Hc9 zenon_Hb1 zenon_Ha7 zenon_Hb7 zenon_H10e zenon_H135 zenon_H36 zenon_H8f zenon_H12a zenon_H3b zenon_H20 zenon_H5e zenon_H8e zenon_H12d zenon_H10d zenon_H10c zenon_H1c3 zenon_H157 zenon_H1e2 zenon_H1e3. % 15.22/15.38 apply (zenon_or_s _ _ zenon_H1d4); [ zenon_intro zenon_H2e | zenon_intro zenon_Hdd ]. % 15.22/15.38 apply (zenon_or_s _ _ zenon_H1e3); [ zenon_intro zenon_H52 | zenon_intro zenon_H156 ]. % 15.22/15.38 apply (zenon_or_s _ _ zenon_Haa); [ zenon_intro zenon_H2f | zenon_intro zenon_H35 ]. % 15.22/15.38 apply (zenon_L316_); trivial. % 15.22/15.38 apply (zenon_L317_); trivial. % 15.22/15.38 apply (zenon_L318_); trivial. % 15.22/15.38 apply (zenon_or_s _ _ zenon_H1e3); [ zenon_intro zenon_H52 | zenon_intro zenon_H156 ]. % 15.22/15.38 apply (zenon_or_s _ _ zenon_Haa); [ zenon_intro zenon_H2f | zenon_intro zenon_H35 ]. % 15.22/15.38 apply (zenon_or_s _ _ zenon_H1c3); [ zenon_intro zenon_H30 | zenon_intro zenon_H124 ]. % 15.22/15.38 apply (zenon_or_s _ _ zenon_H10f); [ zenon_intro zenon_H3c | zenon_intro zenon_Hba ]. % 15.22/15.38 apply (zenon_or_s _ _ zenon_H10c); [ zenon_intro zenon_H104 | zenon_intro zenon_H10a ]. % 15.22/15.38 apply (zenon_or_s _ _ zenon_H10e); [ zenon_intro zenon_H3d | zenon_intro zenon_H106 ]. % 15.22/15.38 apply (zenon_or_s _ _ zenon_H10d); [ zenon_intro zenon_H3e | zenon_intro zenon_H42 ]. % 15.22/15.38 apply (zenon_L114_); trivial. % 15.22/15.38 apply (zenon_L323_); trivial. % 15.22/15.38 apply (zenon_L308_); trivial. % 15.22/15.38 apply (zenon_L116_); trivial. % 15.22/15.38 apply (zenon_L310_); trivial. % 15.22/15.38 apply (zenon_L119_); trivial. % 15.22/15.38 apply (zenon_L161_); trivial. % 15.22/15.38 apply (zenon_L284_); trivial. % 15.22/15.38 (* end of lemma zenon_L324_ *) % 15.22/15.38 assert (zenon_L325_ : ((~((op (e3) (e3)) = (e2)))\/((op (e3) (e2)) = (e3))) -> (~((op (e3) (e1)) = (op (e3) (e2)))) -> (((op (e0) (e0)) = (e1))\/(((op (e0) (e1)) = (e1))\/(((op (e0) (e2)) = (e1))\/((op (e0) (e3)) = (e1))))) -> (~((op (e3) (e3)) = (e0))) -> (~((op (e0) (e3)) = (op (e3) (e3)))) -> (((op (e3) (e3)) = (e0))\/(((op (e3) (e3)) = (e1))\/(((op (e3) (e3)) = (e2))\/((op (e3) (e3)) = (e3))))) -> (~((op (e2) (e2)) = (e0))) -> (~((op (e0) (e2)) = (op (e2) (e2)))) -> (~((op (e2) (e2)) = (e2))) -> (~((op (e2) (e2)) = (e3))) -> (((op (e2) (e2)) = (e0))\/(((op (e2) (e2)) = (e1))\/(((op (e2) (e2)) = (e2))\/((op (e2) (e2)) = (e3))))) -> ((op (e1) (e1)) = (e1)) -> (~((op (e0) (e1)) = (op (e1) (e1)))) -> (~((op (e0) (e0)) = (e1))) -> (~((op (e3) (e1)) = (op (e3) (e3)))) -> ((op (e3) (e1)) = (e3)) -> ((~((op (e3) (e3)) = (e3)))\/((op (e3) (e3)) = (e3))) -> False). % 15.22/15.38 do 0 intro. intros zenon_H10e zenon_H135 zenon_H44 zenon_H3c zenon_H36 zenon_H3b zenon_H2e zenon_H28 zenon_H2f zenon_H30 zenon_H2d zenon_H21 zenon_H23 zenon_H45 zenon_H12d zenon_H10a zenon_H10d. % 15.22/15.38 apply (zenon_or_s _ _ zenon_H10e); [ zenon_intro zenon_H3d | zenon_intro zenon_H106 ]. % 15.22/15.38 apply (zenon_or_s _ _ zenon_H10d); [ zenon_intro zenon_H3e | zenon_intro zenon_H42 ]. % 15.22/15.38 apply (zenon_L8_); trivial. % 15.22/15.38 apply (zenon_L102_); trivial. % 15.22/15.38 apply (zenon_L115_); trivial. % 15.22/15.38 (* end of lemma zenon_L325_ *) % 15.22/15.38 assert (zenon_L326_ : (((op (e3) (e0)) = (e2))\/(((op (e3) (e1)) = (e2))\/(((op (e3) (e2)) = (e2))\/((op (e3) (e3)) = (e2))))) -> ((op (e3) (e0)) = (e3)) -> (~((e2) = (e3))) -> ((op (e2) (e1)) = (e2)) -> (~((op (e2) (e1)) = (op (e3) (e1)))) -> ((op (e0) (e2)) = (e2)) -> (~((op (e0) (e2)) = (op (e3) (e2)))) -> (~((op (e3) (e3)) = (e2))) -> False). % 15.22/15.38 do 0 intro. intros zenon_H1df zenon_Hba zenon_H6a zenon_H156 zenon_H13c zenon_H63 zenon_H140 zenon_H3d. % 15.22/15.38 apply (zenon_or_s _ _ zenon_H1df); [ zenon_intro zenon_He9 | zenon_intro zenon_H1e0 ]. % 15.22/15.38 apply (zenon_L220_); trivial. % 15.22/15.38 apply (zenon_or_s _ _ zenon_H1e0); [ zenon_intro zenon_H16a | zenon_intro zenon_H1e1 ]. % 15.22/15.38 apply (zenon_L252_); trivial. % 15.22/15.38 apply (zenon_or_s _ _ zenon_H1e1); [ zenon_intro zenon_H1dd | zenon_intro zenon_H43 ]. % 15.22/15.38 apply (zenon_L253_); trivial. % 15.22/15.38 exact (zenon_H3d zenon_H43). % 15.22/15.38 (* end of lemma zenon_L326_ *) % 15.22/15.38 assert (zenon_L327_ : (((op (e0) (e0)) = (e1))\/(((op (e0) (e1)) = (e1))\/(((op (e0) (e2)) = (e1))\/((op (e0) (e3)) = (e1))))) -> (~((op (e0) (e1)) = (op (e1) (e1)))) -> (((op (e0) (e3)) = (e1))\/(((op (e1) (e3)) = (e1))\/(((op (e2) (e3)) = (e1))\/((op (e3) (e3)) = (e1))))) -> (~((op (e0) (e2)) = (op (e0) (e3)))) -> ((op (e1) (e1)) = (e1)) -> (~((op (e1) (e1)) = (op (e1) (e3)))) -> (~((op (e2) (e0)) = (op (e2) (e3)))) -> (~((op (e3) (e3)) = (e1))) -> (~((op (e1) (e0)) = (op (e1) (e1)))) -> (~((op (e0) (e0)) = (e1))) -> (((op (e0) (e0)) = (e1))\/(((op (e1) (e0)) = (e1))\/(((op (e2) (e0)) = (e1))\/((op (e3) (e0)) = (e1))))) -> (((op (e0) (e0)) = (e2))\/(((op (e0) (e1)) = (e2))\/(((op (e0) (e2)) = (e2))\/((op (e0) (e3)) = (e2))))) -> (~((e1) = (e3))) -> ((op (e0) (e2)) = (e0)) -> (~((e0) = (e3))) -> (((op (e2) (e2)) = (e0))\/(((op (e2) (e2)) = (e1))\/(((op (e2) (e2)) = (e2))\/((op (e2) (e2)) = (e3))))) -> (~((op (e2) (e2)) = (e0))) -> (~((op (e2) (e2)) = (e2))) -> (~((op (e2) (e2)) = (e3))) -> (~((op (e0) (e0)) = (e3))) -> (((op (e0) (e0)) = (e3))\/(((op (e0) (e1)) = (e3))\/(((op (e0) (e2)) = (e3))\/((op (e0) (e3)) = (e3))))) -> (~((op (e0) (e1)) = (op (e2) (e1)))) -> (~((op (e3) (e3)) = (e2))) -> (~((op (e0) (e2)) = (op (e3) (e2)))) -> (~((op (e2) (e1)) = (op (e3) (e1)))) -> ((op (e2) (e1)) = (e2)) -> (~((e2) = (e3))) -> ((op (e3) (e0)) = (e3)) -> (((op (e3) (e0)) = (e2))\/(((op (e3) (e1)) = (e2))\/(((op (e3) (e2)) = (e2))\/((op (e3) (e3)) = (e2))))) -> (~((e1) = (e2))) -> False). % 15.22/15.38 do 0 intro. intros zenon_H44 zenon_H23 zenon_H121 zenon_Hc9 zenon_H21 zenon_H11e zenon_Hce zenon_H104 zenon_Hd7 zenon_H45 zenon_Hf1 zenon_H8e zenon_Ha3 zenon_Hab zenon_H4b zenon_H2d zenon_H2e zenon_H2f zenon_H30 zenon_H59 zenon_H58 zenon_Hde zenon_H3d zenon_H140 zenon_H13c zenon_H156 zenon_H6a zenon_Hba zenon_H1df zenon_Ha7. % 15.22/15.38 apply (zenon_or_s _ _ zenon_H44); [ zenon_intro zenon_H47 | zenon_intro zenon_H46 ]. % 15.22/15.38 exact (zenon_H45 zenon_H47). % 15.22/15.38 apply (zenon_or_s _ _ zenon_H46); [ zenon_intro zenon_H22 | zenon_intro zenon_H48 ]. % 15.22/15.38 apply (zenon_L3_); trivial. % 15.22/15.38 apply (zenon_or_s _ _ zenon_H48); [ zenon_intro zenon_H29 | zenon_intro zenon_H37 ]. % 15.22/15.38 apply (zenon_L274_); trivial. % 15.22/15.38 apply (zenon_or_s _ _ zenon_H8e); [ zenon_intro zenon_H92 | zenon_intro zenon_H91 ]. % 15.22/15.38 apply (zenon_L49_); trivial. % 15.22/15.38 apply (zenon_or_s _ _ zenon_H91); [ zenon_intro zenon_H5d | zenon_intro zenon_H93 ]. % 15.22/15.38 apply (zenon_L251_); trivial. % 15.22/15.38 apply (zenon_or_s _ _ zenon_H93); [ zenon_intro zenon_H63 | zenon_intro zenon_H81 ]. % 15.22/15.38 apply (zenon_L326_); trivial. % 15.22/15.38 apply (zenon_L33_); trivial. % 15.22/15.38 (* end of lemma zenon_L327_ *) % 15.22/15.38 assert (zenon_L328_ : (((op (e3) (e0)) = (e1))\/(((op (e3) (e1)) = (e1))\/(((op (e3) (e2)) = (e1))\/((op (e3) (e3)) = (e1))))) -> (~((op (e3) (op (e0) (e3))) = (op (e0) (e3)))) -> (~((op (e2) (op (e0) (e2))) = (op (e0) (e2)))) -> (~((op (e2) (e0)) = (op (e2) (e2)))) -> (~((op (e3) (e0)) = (op (e3) (e2)))) -> (~((op (e3) (e0)) = (op (e3) (e1)))) -> ((~((op (e3) (e3)) = (e3)))\/((op (e3) (e3)) = (e3))) -> (~((op (e2) (e2)) = (op (e2) (e3)))) -> (((op (e1) (e0)) = (e0))\/(((op (e1) (e1)) = (e0))\/(((op (e1) (e2)) = (e0))\/((op (e1) (e3)) = (e0))))) -> (~((op (e2) (e0)) = (op (e2) (e1)))) -> (~((op (e2) (e1)) = (op (e2) (e2)))) -> (((op (e2) (e1)) = (e0))\/(((op (e2) (e1)) = (e1))\/(((op (e2) (e1)) = (e2))\/((op (e2) (e1)) = (e3))))) -> (((op (e1) (e2)) = (e0))\/(((op (e1) (e2)) = (e1))\/(((op (e1) (e2)) = (e2))\/((op (e1) (e2)) = (e3))))) -> (~((op (e1) (e2)) = (op (e3) (e2)))) -> (~((op (e1) (e2)) = (op (e2) (e2)))) -> (~((op (e1) (e1)) = (op (e1) (e2)))) -> (~((op (e0) (e0)) = (e0))) -> (((op (e2) (e0)) = (e1))\/(((op (e2) (e1)) = (e1))\/(((op (e2) (e2)) = (e1))\/((op (e2) (e3)) = (e1))))) -> (~((op (e0) (e3)) = (op (e2) (e3)))) -> (~((op (e1) (e1)) = (op (e2) (e1)))) -> (~((op (e1) (e0)) = (op (e1) (e1)))) -> (((op (e0) (e0)) = (e0))\/(((op (e1) (e0)) = (e0))\/(((op (e2) (e0)) = (e0))\/((op (e3) (e0)) = (e0))))) -> (((op (e0) (e0)) = (e0))\/(((op (e0) (e0)) = (e1))\/(((op (e0) (e0)) = (e2))\/((op (e0) (e0)) = (e3))))) -> (~((op (e1) (e1)) = (op (e1) (e3)))) -> (((op (e0) (e0)) = (e0))\/(((op (e0) (e1)) = (e0))\/(((op (e0) (e2)) = (e0))\/((op (e0) (e3)) = (e0))))) -> (((op (e3) (e0)) = (e2))\/(((op (e3) (e1)) = (e2))\/(((op (e3) (e2)) = (e2))\/((op (e3) (e3)) = (e2))))) -> (~((op (e0) (e2)) = (op (e3) (e2)))) -> (~((op (e2) (e1)) = (op (e3) (e1)))) -> (~((op (e1) (e0)) = (op (e1) (e2)))) -> (~((op (e0) (e3)) = (op (e1) (e3)))) -> ((~((op (e1) (e1)) = (e1)))\/((op (e1) (e1)) = (e1))) -> (~((op (e2) (e1)) = (op (e2) (e3)))) -> ((~((op (e2) (e2)) = (e1)))\/((op (e2) (e1)) = (e2))) -> ((~((op (e1) (e1)) = (e3)))\/((op (e1) (e3)) = (e1))) -> ((~((op (e2) (e2)) = (e2)))\/((op (e2) (e2)) = (e2))) -> (((op (e1) (e0)) = (e1))\/(((op (e1) (e1)) = (e1))\/(((op (e1) (e2)) = (e1))\/((op (e1) (e3)) = (e1))))) -> (((op (e0) (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) (e2)) = (op (e3) (e3)))) -> ((~((op (e3) (e3)) = (e0)))\/((op (e3) (e0)) = (e3))) -> (~((op (e3) (e0)) = (op (e3) (e3)))) -> (~((e2) = (e3))) -> (~((op (e0) (e2)) = (op (e0) (e3)))) -> (~((e0) = (e2))) -> (((op (e0) (e3)) = (e0))\/(((op (e1) (e3)) = (e0))\/(((op (e2) (e3)) = (e0))\/((op (e3) (e3)) = (e0))))) -> (~((e1) = (e2))) -> (((op (e1) (e0)) = (e2))\/(((op (e1) (e1)) = (e2))\/(((op (e1) (e2)) = (e2))\/((op (e1) (e3)) = (e2))))) -> ((~((op (e2) (e2)) = (e3)))\/((op (e2) (e3)) = (e2))) -> (((op (e1) (e1)) = (e0))\/(((op (e1) (e1)) = (e1))\/(((op (e1) (e1)) = (e2))\/((op (e1) (e1)) = (e3))))) -> (~((op (e1) (e3)) = (op (e3) (e3)))) -> (((op (e1) (e0)) = (e3))\/(((op (e1) (e1)) = (e3))\/(((op (e1) (e2)) = (e3))\/((op (e1) (e3)) = (e3))))) -> (((op (e0) (e0)) = (e2))\/(((op (e1) (e0)) = (e2))\/(((op (e2) (e0)) = (e2))\/((op (e3) (e0)) = (e2))))) -> (~((op (e0) (e2)) = (op (e1) (e2)))) -> (((op (e0) (e0)) = (e3))\/(((op (e1) (e0)) = (e3))\/(((op (e2) (e0)) = (e3))\/((op (e3) (e0)) = (e3))))) -> (((op (e2) (e0)) = (e3))\/(((op (e2) (e1)) = (e3))\/(((op (e2) (e2)) = (e3))\/((op (e2) (e3)) = (e3))))) -> (~((op (e2) (e3)) = (op (e3) (e3)))) -> (~((op (e0) (e1)) = (op (e2) (e1)))) -> (((op (e0) (e0)) = (e2))\/(((op (e0) (e1)) = (e2))\/(((op (e0) (e2)) = (e2))\/((op (e0) (e3)) = (e2))))) -> (~((op (e0) (e2)) = (op (e2) (e2)))) -> (((op (e2) (e2)) = (e0))\/(((op (e2) (e2)) = (e1))\/(((op (e2) (e2)) = (e2))\/((op (e2) (e2)) = (e3))))) -> (~((op (e0) (e0)) = (e3))) -> (~((e1) = (e3))) -> (~((e0) = (e3))) -> (((op (e0) (e0)) = (e3))\/(((op (e0) (e1)) = (e3))\/(((op (e0) (e2)) = (e3))\/((op (e0) (e3)) = (e3))))) -> ((~((op (e3) (e3)) = (e2)))\/((op (e3) (e2)) = (e3))) -> (((op (e0) (e0)) = (e1))\/(((op (e1) (e0)) = (e1))\/(((op (e2) (e0)) = (e1))\/((op (e3) (e0)) = (e1))))) -> (~((op (e2) (e0)) = (op (e2) (e3)))) -> (((op (e0) (e3)) = (e1))\/(((op (e1) (e3)) = (e1))\/(((op (e2) (e3)) = (e1))\/((op (e3) (e3)) = (e1))))) -> (~((op (e1) (e0)) = (op (e1) (e3)))) -> (~((op (e0) (e1)) = (op (e0) (e3)))) -> (~((op (e3) (e1)) = (op (e3) (e3)))) -> ((~((op (e3) (e3)) = (e1)))\/((op (e3) (e1)) = (e3))) -> ((~((op (e2) (e2)) = (e0)))\/((op (e2) (e0)) = (e2))) -> (~((op (e1) (e2)) = (op (e1) (e3)))) -> ((~((op (e1) (e1)) = (e2)))\/((op (e1) (e2)) = (e1))) -> ((~((op (e1) (e1)) = (e0)))\/((op (e1) (e0)) = (e1))) -> (~((op (e0) (e0)) = (e1))) -> (~((op (e0) (e1)) = (op (e1) (e1)))) -> ((op (e1) (e1)) = (e1)) -> (~((e0) = (e1))) -> ((op (e0) (e2)) = (e0)) -> (((op (e3) (e3)) = (e0))\/(((op (e3) (e3)) = (e1))\/(((op (e3) (e3)) = (e2))\/((op (e3) (e3)) = (e3))))) -> (~((op (e0) (e3)) = (op (e3) (e3)))) -> (((op (e0) (e0)) = (e1))\/(((op (e0) (e1)) = (e1))\/(((op (e0) (e2)) = (e1))\/((op (e0) (e3)) = (e1))))) -> (((op (e0) (e2)) = (e1))\/(((op (e1) (e2)) = (e1))\/(((op (e2) (e2)) = (e1))\/((op (e3) (e2)) = (e1))))) -> (((op (e0) (e1)) = (e0))\/(((op (e1) (e1)) = (e0))\/(((op (e2) (e1)) = (e0))\/((op (e3) (e1)) = (e0))))) -> (((op (e2) (e0)) = (e0))\/(((op (e2) (e1)) = (e0))\/(((op (e2) (e2)) = (e0))\/((op (e2) (e3)) = (e0))))) -> (((op (e0) (e1)) = (e2))\/(((op (e1) (e1)) = (e2))\/(((op (e2) (e1)) = (e2))\/((op (e3) (e1)) = (e2))))) -> (~((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)) = (op (e3) (e1)))) -> (((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 (e3) (e1)) = (op (e3) (e2)))) -> False). % 15.22/15.38 do 0 intro. intros zenon_H146 zenon_H192 zenon_H20c zenon_H17a zenon_H105 zenon_H109 zenon_H10d zenon_H15f zenon_H163 zenon_H154 zenon_H157 zenon_H15a zenon_H1d5 zenon_H17d zenon_H7d zenon_H116 zenon_H20 zenon_Hb7 zenon_Hb4 zenon_Hb1 zenon_Hd7 zenon_Hf0 zenon_H12a zenon_H11e zenon_H110 zenon_H1df zenon_H140 zenon_H13c zenon_H166 zenon_H80 zenon_H1d8 zenon_H1e2 zenon_H1e3 zenon_H1d2 zenon_Haa zenon_H1c5 zenon_H160 zenon_H175 zenon_H173 zenon_H10f zenon_Hbb zenon_H6a zenon_Hc9 zenon_H5e zenon_Hd3 zenon_Ha7 zenon_H84 zenon_H1c3 zenon_H1b3 zenon_H8b zenon_H90 zenon_Heb zenon_H87 zenon_Hbe zenon_He6 zenon_He3 zenon_Hde zenon_H8e zenon_H28 zenon_H2d zenon_H59 zenon_Ha3 zenon_H4b zenon_H58 zenon_H10e zenon_Hf1 zenon_Hce zenon_H121 zenon_H1cf zenon_H1cd zenon_H12d zenon_H10c zenon_H1d4 zenon_H1d0 zenon_H1d3 zenon_H1e4 zenon_H45 zenon_H23 zenon_H21 zenon_H9e zenon_Hab zenon_H3b zenon_H36 zenon_H44 zenon_H11b zenon_H144 zenon_H1f5 zenon_H1a2 zenon_H1e5 zenon_H1e9 zenon_H138 zenon_H1f6 zenon_H16f zenon_H135. % 15.22/15.38 apply (zenon_or_s _ _ zenon_H1e4); [ zenon_intro zenon_H145 | zenon_intro zenon_Hd8 ]. % 15.22/15.38 apply (zenon_or_s _ _ zenon_H1d3); [ zenon_intro zenon_Hd6 | zenon_intro zenon_H117 ]. % 15.22/15.38 apply (zenon_or_s _ _ zenon_H1d2); [ zenon_intro zenon_H182 | zenon_intro zenon_H11f ]. % 15.22/15.38 apply (zenon_or_s _ _ zenon_H1d4); [ zenon_intro zenon_H2e | zenon_intro zenon_Hdd ]. % 15.22/15.38 apply (zenon_or_s _ _ zenon_H1e3); [ zenon_intro zenon_H52 | zenon_intro zenon_H156 ]. % 15.22/15.38 apply (zenon_or_s _ _ zenon_Haa); [ zenon_intro zenon_H2f | zenon_intro zenon_H35 ]. % 15.22/15.38 apply (zenon_or_s _ _ zenon_H10f); [ zenon_intro zenon_H3c | zenon_intro zenon_Hba ]. % 15.22/15.38 apply (zenon_or_s _ _ zenon_H10e); [ zenon_intro zenon_H3d | zenon_intro zenon_H106 ]. % 15.22/15.38 apply (zenon_L260_); trivial. % 15.22/15.38 apply (zenon_L109_); trivial. % 15.22/15.38 apply (zenon_L83_); trivial. % 15.22/15.38 apply (zenon_L271_); trivial. % 15.22/15.38 apply (zenon_or_s _ _ zenon_Haa); [ zenon_intro zenon_H2f | zenon_intro zenon_H35 ]. % 15.22/15.38 apply (zenon_or_s _ _ zenon_H1c3); [ zenon_intro zenon_H30 | zenon_intro zenon_H124 ]. % 15.22/15.38 apply (zenon_or_s _ _ zenon_H10f); [ zenon_intro zenon_H3c | zenon_intro zenon_Hba ]. % 15.22/15.38 apply (zenon_or_s _ _ zenon_H10c); [ zenon_intro zenon_H104 | zenon_intro zenon_H10a ]. % 15.22/15.38 apply (zenon_or_s _ _ zenon_H10e); [ zenon_intro zenon_H3d | zenon_intro zenon_H106 ]. % 15.22/15.38 apply (zenon_L260_); trivial. % 15.22/15.38 apply (zenon_L315_); trivial. % 15.22/15.38 apply (zenon_L325_); trivial. % 15.22/15.38 apply (zenon_or_s _ _ zenon_H10c); [ zenon_intro zenon_H104 | zenon_intro zenon_H10a ]. % 15.22/15.38 apply (zenon_or_s _ _ zenon_H10e); [ zenon_intro zenon_H3d | zenon_intro zenon_H106 ]. % 15.22/15.38 apply (zenon_L327_); trivial. % 15.22/15.38 apply (zenon_L81_); trivial. % 15.22/15.38 apply (zenon_L82_); trivial. % 15.22/15.38 apply (zenon_L256_); trivial. % 15.22/15.38 apply (zenon_L134_); trivial. % 15.22/15.38 apply (zenon_L311_); trivial. % 15.22/15.38 apply (zenon_L90_); trivial. % 15.22/15.38 apply (zenon_L86_); trivial. % 15.22/15.38 apply (zenon_L61_); trivial. % 15.22/15.38 (* end of lemma zenon_L328_ *) % 15.22/15.38 assert (zenon_L329_ : ((op (e2) (e0)) = (e2)) -> (~((op (e1) (e1)) = (e2))) -> (~((op (e2) (e2)) = (e3))) -> (~((op (e2) (e2)) = (e2))) -> (~((op (e2) (e2)) = (e1))) -> (~((op (e3) (e1)) = (op (e3) (e2)))) -> (((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 (e0) (e1)) = (op (e3) (e1)))) -> (((op (e0) (e1)) = (e0))\/(((op (e0) (e1)) = (e1))\/(((op (e0) (e1)) = (e2))\/((op (e0) (e1)) = (e3))))) -> (~((op (e2) (e0)) = (op (e3) (e0)))) -> (((op (e0) (e1)) = (e2))\/(((op (e1) (e1)) = (e2))\/(((op (e2) (e1)) = (e2))\/((op (e3) (e1)) = (e2))))) -> (((op (e2) (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)) = (e1))\/(((op (e1) (e2)) = (e1))\/(((op (e2) (e2)) = (e1))\/((op (e3) (e2)) = (e1))))) -> (~((e0) = (e1))) -> ((~((op (e1) (e1)) = (e0)))\/((op (e1) (e0)) = (e1))) -> ((~((op (e1) (e1)) = (e2)))\/((op (e1) (e2)) = (e1))) -> (~((op (e1) (e2)) = (op (e1) (e3)))) -> ((~((op (e2) (e2)) = (e0)))\/((op (e2) (e0)) = (e2))) -> ((~((op (e3) (e3)) = (e1)))\/((op (e3) (e1)) = (e3))) -> (~((op (e3) (e1)) = (op (e3) (e3)))) -> (~((op (e0) (e1)) = (op (e0) (e3)))) -> (~((op (e1) (e0)) = (op (e1) (e3)))) -> (((op (e0) (e3)) = (e1))\/(((op (e1) (e3)) = (e1))\/(((op (e2) (e3)) = (e1))\/((op (e3) (e3)) = (e1))))) -> (~((op (e2) (e0)) = (op (e2) (e3)))) -> (((op (e0) (e0)) = (e1))\/(((op (e1) (e0)) = (e1))\/(((op (e2) (e0)) = (e1))\/((op (e3) (e0)) = (e1))))) -> ((~((op (e3) (e3)) = (e2)))\/((op (e3) (e2)) = (e3))) -> (((op (e0) (e0)) = (e3))\/(((op (e0) (e1)) = (e3))\/(((op (e0) (e2)) = (e3))\/((op (e0) (e3)) = (e3))))) -> (~((e0) = (e3))) -> (~((e1) = (e3))) -> (~((op (e0) (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 (e0) (e1)) = (op (e2) (e1)))) -> (~((op (e2) (e3)) = (op (e3) (e3)))) -> (((op (e2) (e0)) = (e3))\/(((op (e2) (e1)) = (e3))\/(((op (e2) (e2)) = (e3))\/((op (e2) (e3)) = (e3))))) -> (((op (e0) (e0)) = (e3))\/(((op (e1) (e0)) = (e3))\/(((op (e2) (e0)) = (e3))\/((op (e3) (e0)) = (e3))))) -> (~((op (e0) (e2)) = (op (e1) (e2)))) -> (((op (e0) (e0)) = (e2))\/(((op (e1) (e0)) = (e2))\/(((op (e2) (e0)) = (e2))\/((op (e3) (e0)) = (e2))))) -> (((op (e1) (e0)) = (e3))\/(((op (e1) (e1)) = (e3))\/(((op (e1) (e2)) = (e3))\/((op (e1) (e3)) = (e3))))) -> (~((op (e1) (e3)) = (op (e3) (e3)))) -> (((op (e1) (e1)) = (e0))\/(((op (e1) (e1)) = (e1))\/(((op (e1) (e1)) = (e2))\/((op (e1) (e1)) = (e3))))) -> ((~((op (e2) (e2)) = (e3)))\/((op (e2) (e3)) = (e2))) -> (((op (e1) (e0)) = (e2))\/(((op (e1) (e1)) = (e2))\/(((op (e1) (e2)) = (e2))\/((op (e1) (e3)) = (e2))))) -> (((op (e0) (e3)) = (e0))\/(((op (e1) (e3)) = (e0))\/(((op (e2) (e3)) = (e0))\/((op (e3) (e3)) = (e0))))) -> (~((op (e0) (e2)) = (op (e0) (e3)))) -> (~((e2) = (e3))) -> (~((op (e3) (e0)) = (op (e3) (e3)))) -> ((~((op (e3) (e3)) = (e0)))\/((op (e3) (e0)) = (e3))) -> (~((op (e3) (e2)) = (op (e3) (e3)))) -> (((op (e0) (e2)) = (e3))\/(((op (e1) (e2)) = (e3))\/(((op (e2) (e2)) = (e3))\/((op (e3) (e2)) = (e3))))) -> (((op (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 (e2) (e2)) = (e2)))\/((op (e2) (e2)) = (e2))) -> ((~((op (e1) (e1)) = (e3)))\/((op (e1) (e3)) = (e1))) -> ((~((op (e2) (e2)) = (e1)))\/((op (e2) (e1)) = (e2))) -> (~((op (e2) (e1)) = (op (e2) (e3)))) -> ((~((op (e1) (e1)) = (e1)))\/((op (e1) (e1)) = (e1))) -> (~((op (e0) (e3)) = (op (e1) (e3)))) -> (~((op (e1) (e0)) = (op (e1) (e2)))) -> (~((op (e2) (e1)) = (op (e3) (e1)))) -> (~((op (e0) (e2)) = (op (e3) (e2)))) -> (((op (e3) (e0)) = (e2))\/(((op (e3) (e1)) = (e2))\/(((op (e3) (e2)) = (e2))\/((op (e3) (e3)) = (e2))))) -> (((op (e0) (e0)) = (e0))\/(((op (e0) (e1)) = (e0))\/(((op (e0) (e2)) = (e0))\/((op (e0) (e3)) = (e0))))) -> (~((op (e1) (e1)) = (op (e1) (e3)))) -> (((op (e0) (e0)) = (e0))\/(((op (e1) (e0)) = (e0))\/(((op (e2) (e0)) = (e0))\/((op (e3) (e0)) = (e0))))) -> (~((op (e1) (e0)) = (op (e1) (e1)))) -> (~((op (e1) (e1)) = (op (e2) (e1)))) -> (~((op (e0) (e3)) = (op (e2) (e3)))) -> (((op (e2) (e0)) = (e1))\/(((op (e2) (e1)) = (e1))\/(((op (e2) (e2)) = (e1))\/((op (e2) (e3)) = (e1))))) -> (~((op (e1) (e1)) = (op (e1) (e2)))) -> (~((op (e1) (e2)) = (op (e2) (e2)))) -> (~((op (e1) (e2)) = (op (e3) (e2)))) -> (((op (e1) (e2)) = (e0))\/(((op (e1) (e2)) = (e1))\/(((op (e1) (e2)) = (e2))\/((op (e1) (e2)) = (e3))))) -> (((op (e2) (e1)) = (e0))\/(((op (e2) (e1)) = (e1))\/(((op (e2) (e1)) = (e2))\/((op (e2) (e1)) = (e3))))) -> (~((op (e2) (e1)) = (op (e2) (e2)))) -> (~((op (e2) (e0)) = (op (e2) (e1)))) -> (((op (e1) (e0)) = (e0))\/(((op (e1) (e1)) = (e0))\/(((op (e1) (e2)) = (e0))\/((op (e1) (e3)) = (e0))))) -> (~((op (e2) (e2)) = (op (e2) (e3)))) -> ((~((op (e3) (e3)) = (e3)))\/((op (e3) (e3)) = (e3))) -> (~((op (e3) (e0)) = (op (e3) (e1)))) -> (~((op (e3) (e0)) = (op (e3) (e2)))) -> (~((op (e2) (e0)) = (op (e2) (e2)))) -> (~((op (e2) (op (e0) (e2))) = (op (e0) (e2)))) -> (~((op (e3) (op (e0) (e3))) = (op (e0) (e3)))) -> (((op (e3) (e0)) = (e1))\/(((op (e3) (e1)) = (e1))\/(((op (e3) (e2)) = (e1))\/((op (e3) (e3)) = (e1))))) -> (((op (e0) (e0)) = (e1))\/(((op (e0) (e1)) = (e1))\/(((op (e0) (e2)) = (e1))\/((op (e0) (e3)) = (e1))))) -> (~((op (e0) (e1)) = (op (e1) (e1)))) -> ((op (e1) (e1)) = (e1)) -> (~((e0) = (e2))) -> (~((e1) = (e2))) -> (((op (e0) (e0)) = (e0))\/(((op (e0) (e0)) = (e1))\/(((op (e0) (e0)) = (e2))\/((op (e0) (e0)) = (e3))))) -> (~((op (e0) (e0)) = (e0))) -> (~((op (e0) (e0)) = (e1))) -> (~((op (e0) (e0)) = (e2))) -> (((op (e0) (e0)) = (e2))\/(((op (e0) (e1)) = (e2))\/(((op (e0) (e2)) = (e2))\/((op (e0) (e3)) = (e2))))) -> (((op (e3) (e3)) = (e0))\/(((op (e3) (e3)) = (e1))\/(((op (e3) (e3)) = (e2))\/((op (e3) (e3)) = (e3))))) -> (~((op (e3) (e3)) = (e0))) -> (~((op (e0) (e3)) = (op (e3) (e3)))) -> (~((op (e3) (e3)) = (e2))) -> (~((op (e3) (e3)) = (e3))) -> False). % 15.22/15.38 do 0 intro. intros zenon_Hdd zenon_Hd6 zenon_H30 zenon_H2f zenon_H52 zenon_H135 zenon_H16f zenon_H1f6 zenon_H138 zenon_H1e9 zenon_H1e5 zenon_H1a2 zenon_H1f5 zenon_H144 zenon_H11b zenon_H9e zenon_H1e4 zenon_H1d3 zenon_H1d0 zenon_H1d4 zenon_H10c zenon_H12d zenon_H1cd zenon_H1cf zenon_H121 zenon_Hce zenon_Hf1 zenon_H10e zenon_H58 zenon_H4b zenon_Ha3 zenon_H59 zenon_H2d zenon_H28 zenon_Hde zenon_He3 zenon_He6 zenon_Hbe zenon_H87 zenon_Heb zenon_H90 zenon_H8b zenon_H1b3 zenon_H1c3 zenon_H84 zenon_Hd3 zenon_Hc9 zenon_H6a zenon_Hbb zenon_H10f zenon_H173 zenon_H175 zenon_H160 zenon_H1c5 zenon_Haa zenon_H1d2 zenon_H1e3 zenon_H1e2 zenon_H1d8 zenon_H80 zenon_H166 zenon_H13c zenon_H140 zenon_H1df zenon_H110 zenon_H11e zenon_Hf0 zenon_Hd7 zenon_Hb1 zenon_Hb4 zenon_Hb7 zenon_H116 zenon_H7d zenon_H17d zenon_H1d5 zenon_H15a zenon_H157 zenon_H154 zenon_H163 zenon_H15f zenon_H10d zenon_H109 zenon_H105 zenon_H17a zenon_H20c zenon_H192 zenon_H146 zenon_H44 zenon_H23 zenon_H21 zenon_H5e zenon_Ha7 zenon_H12a zenon_H20 zenon_H45 zenon_H8f zenon_H8e zenon_H3b zenon_H3c zenon_H36 zenon_H3d zenon_H3e. % 15.22/15.38 apply (zenon_or_s _ _ zenon_H110); [ zenon_intro zenon_H1f | zenon_intro zenon_H111 ]. % 15.22/15.38 exact (zenon_H20 zenon_H1f). % 15.22/15.38 apply (zenon_or_s _ _ zenon_H111); [ zenon_intro zenon_H49 | zenon_intro zenon_H112 ]. % 15.22/15.38 apply (zenon_L299_); trivial. % 15.22/15.38 apply (zenon_or_s _ _ zenon_H112); [ zenon_intro zenon_Hab | zenon_intro zenon_Hca ]. % 15.22/15.38 apply (zenon_L328_); trivial. % 15.22/15.38 apply (zenon_L114_); trivial. % 15.22/15.38 (* end of lemma zenon_L329_ *) % 15.22/15.38 assert (zenon_L330_ : (((op (e0) (e3)) = (e1))\/(((op (e1) (e3)) = (e1))\/(((op (e2) (e3)) = (e1))\/((op (e3) (e3)) = (e1))))) -> (~((e0) = (e1))) -> ((op (e0) (e3)) = (e0)) -> ((op (e1) (e0)) = (e1)) -> (~((op (e1) (e0)) = (op (e1) (e3)))) -> (~((op (e2) (e2)) = (e3))) -> (~((op (e2) (e2)) = (e2))) -> (~((op (e2) (e2)) = (e1))) -> ((op (e0) (e0)) = (e3)) -> (((op (e2) (e2)) = (e0))\/(((op (e2) (e2)) = (e1))\/(((op (e2) (e2)) = (e2))\/((op (e2) (e2)) = (e3))))) -> (~((op (e3) (e3)) = (e1))) -> False). % 15.22/15.38 do 0 intro. intros zenon_H121 zenon_H9e zenon_Hca zenon_Hd8 zenon_H1cf zenon_H30 zenon_H2f zenon_H52 zenon_H5b zenon_H2d zenon_H104. % 15.22/15.38 apply (zenon_or_s _ _ zenon_H121); [ zenon_intro zenon_H37 | zenon_intro zenon_H122 ]. % 15.22/15.38 apply (zenon_L73_); trivial. % 15.22/15.38 apply (zenon_or_s _ _ zenon_H122); [ zenon_intro zenon_H11f | zenon_intro zenon_H123 ]. % 15.22/15.38 apply (zenon_L224_); trivial. % 15.22/15.38 apply (zenon_or_s _ _ zenon_H123); [ zenon_intro zenon_Hb5 | zenon_intro zenon_H38 ]. % 15.22/15.38 apply (zenon_L320_); trivial. % 15.22/15.38 exact (zenon_H104 zenon_H38). % 15.22/15.38 (* end of lemma zenon_L330_ *) % 15.22/15.38 assert (zenon_L331_ : (((op (e0) (e0)) = (e3))\/(((op (e0) (e1)) = (e3))\/(((op (e0) (e2)) = (e3))\/((op (e0) (e3)) = (e3))))) -> (~((op (e3) (e3)) = (e1))) -> (~((op (e2) (e2)) = (e3))) -> (~((op (e1) (e0)) = (op (e1) (e3)))) -> ((op (e1) (e0)) = (e1)) -> ((op (e0) (e3)) = (e0)) -> (~((e0) = (e1))) -> (((op (e0) (e3)) = (e1))\/(((op (e1) (e3)) = (e1))\/(((op (e2) (e3)) = (e1))\/((op (e3) (e3)) = (e1))))) -> (~((e1) = (e3))) -> ((op (e0) (e1)) = (e1)) -> (~((op (e0) (e2)) = (op (e2) (e2)))) -> (~((op (e2) (e2)) = (e2))) -> (~((op (e2) (e2)) = (e1))) -> (~((op (e2) (e2)) = (e0))) -> (((op (e2) (e2)) = (e0))\/(((op (e2) (e2)) = (e1))\/(((op (e2) (e2)) = (e2))\/((op (e2) (e2)) = (e3))))) -> ((op (e3) (e3)) = (e3)) -> (~((op (e0) (e3)) = (op (e3) (e3)))) -> False). % 15.22/15.38 do 0 intro. intros zenon_H58 zenon_H104 zenon_H30 zenon_H1cf zenon_Hd8 zenon_Hca zenon_H9e zenon_H121 zenon_Ha3 zenon_H22 zenon_H28 zenon_H2f zenon_H52 zenon_H2e zenon_H2d zenon_H42 zenon_H36. % 15.22/15.38 apply (zenon_or_s _ _ zenon_H58); [ zenon_intro zenon_H5b | zenon_intro zenon_H5a ]. % 15.22/15.38 apply (zenon_L330_); trivial. % 15.22/15.38 apply (zenon_or_s _ _ zenon_H5a); [ zenon_intro zenon_H4a | zenon_intro zenon_H5c ]. % 15.22/15.38 apply (zenon_L59_); trivial. % 15.22/15.38 apply (zenon_or_s _ _ zenon_H5c); [ zenon_intro zenon_H50 | zenon_intro zenon_H53 ]. % 15.22/15.38 apply (zenon_L11_); trivial. % 15.22/15.38 apply (zenon_L12_); trivial. % 15.22/15.38 (* end of lemma zenon_L331_ *) % 15.22/15.38 assert (zenon_L332_ : (((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)) -> (~((e1) = (e2))) -> ((op (e1) (e3)) = (e2)) -> ((op (e2) (e0)) = (e1)) -> (~((op (e2) (e0)) = (op (e2) (e3)))) -> (~((op (e3) (e3)) = (e1))) -> False). % 15.22/15.38 do 0 intro. intros zenon_H121 zenon_H1cd zenon_H22 zenon_Ha7 zenon_H82 zenon_Hae zenon_Hce zenon_H104. % 15.22/15.38 apply (zenon_or_s _ _ zenon_H121); [ zenon_intro zenon_H37 | zenon_intro zenon_H122 ]. % 15.22/15.38 apply (zenon_L223_); trivial. % 15.22/15.38 apply (zenon_or_s _ _ zenon_H122); [ zenon_intro zenon_H11f | zenon_intro zenon_H123 ]. % 15.22/15.38 apply (zenon_L209_); trivial. % 15.22/15.38 apply (zenon_or_s _ _ zenon_H123); [ zenon_intro zenon_Hb5 | zenon_intro zenon_H38 ]. % 15.22/15.38 apply (zenon_L91_); trivial. % 15.22/15.38 exact (zenon_H104 zenon_H38). % 15.22/15.38 (* end of lemma zenon_L332_ *) % 15.22/15.38 assert (zenon_L333_ : (((op (e1) (e0)) = (e2))\/(((op (e1) (e1)) = (e2))\/(((op (e1) (e2)) = (e2))\/((op (e1) (e3)) = (e2))))) -> (~((e0) = (e2))) -> ((op (e1) (e0)) = (e0)) -> (~((op (e1) (e1)) = (e2))) -> ((op (e0) (e2)) = (e2)) -> (~((op (e0) (e2)) = (op (e1) (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)) -> (~((e1) = (e2))) -> ((op (e2) (e0)) = (e1)) -> (~((op (e2) (e0)) = (op (e2) (e3)))) -> (~((op (e3) (e3)) = (e1))) -> False). % 15.22/15.38 do 0 intro. intros zenon_H84 zenon_H5e zenon_Had zenon_Hd6 zenon_H63 zenon_H87 zenon_H121 zenon_H1cd zenon_H22 zenon_Ha7 zenon_Hae zenon_Hce zenon_H104. % 15.22/15.38 apply (zenon_or_s _ _ zenon_H84); [ zenon_intro zenon_H68 | zenon_intro zenon_H85 ]. % 15.22/15.38 apply (zenon_L160_); trivial. % 15.22/15.38 apply (zenon_or_s _ _ zenon_H85); [ zenon_intro zenon_H6e | zenon_intro zenon_H86 ]. % 15.22/15.38 exact (zenon_Hd6 zenon_H6e). % 15.22/15.38 apply (zenon_or_s _ _ zenon_H86); [ zenon_intro zenon_H7c | zenon_intro zenon_H82 ]. % 15.22/15.38 apply (zenon_L52_); trivial. % 15.22/15.38 apply (zenon_L332_); trivial. % 15.22/15.38 (* end of lemma zenon_L333_ *) % 15.22/15.38 assert (zenon_L334_ : (((op (e0) (e0)) = (e2))\/(((op (e0) (e1)) = (e2))\/(((op (e0) (e2)) = (e2))\/((op (e0) (e3)) = (e2))))) -> (~((op (e0) (e0)) = (e2))) -> (~((op (e1) (e1)) = (e3))) -> (~((op (e0) (e1)) = (op (e1) (e1)))) -> (~((op (e1) (e1)) = (e1))) -> (~((op (e1) (e1)) = (e0))) -> (((op (e1) (e1)) = (e0))\/(((op (e1) (e1)) = (e1))\/(((op (e1) (e1)) = (e2))\/((op (e1) (e1)) = (e3))))) -> (~((op (e3) (e3)) = (e1))) -> (~((op (e2) (e0)) = (op (e2) (e3)))) -> ((op (e2) (e0)) = (e1)) -> (~((e1) = (e2))) -> ((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) (e2)) = (op (e1) (e2)))) -> (~((op (e1) (e1)) = (e2))) -> ((op (e1) (e0)) = (e0)) -> (((op (e1) (e0)) = (e2))\/(((op (e1) (e1)) = (e2))\/(((op (e1) (e2)) = (e2))\/((op (e1) (e3)) = (e2))))) -> ((op (e0) (e3)) = (e0)) -> (~((e0) = (e2))) -> False). % 15.22/15.38 do 0 intro. intros zenon_H8e zenon_H8f zenon_H182 zenon_H23 zenon_H1b4 zenon_H145 zenon_H1b3 zenon_H104 zenon_Hce zenon_Hae zenon_Ha7 zenon_H22 zenon_H1cd zenon_H121 zenon_H87 zenon_Hd6 zenon_Had zenon_H84 zenon_Hca zenon_H5e. % 15.22/15.38 apply (zenon_or_s _ _ zenon_H8e); [ zenon_intro zenon_H92 | zenon_intro zenon_H91 ]. % 15.22/15.38 exact (zenon_H8f zenon_H92). % 15.22/15.38 apply (zenon_or_s _ _ zenon_H91); [ zenon_intro zenon_H5d | zenon_intro zenon_H93 ]. % 15.22/15.38 apply (zenon_L214_); trivial. % 15.22/15.38 apply (zenon_or_s _ _ zenon_H93); [ zenon_intro zenon_H63 | zenon_intro zenon_H81 ]. % 15.22/15.38 apply (zenon_L333_); trivial. % 15.22/15.38 apply (zenon_L113_); trivial. % 15.22/15.38 (* end of lemma zenon_L334_ *) % 15.22/15.38 assert (zenon_L335_ : (((op (e2) (e2)) = (e0))\/(((op (e2) (e2)) = (e1))\/(((op (e2) (e2)) = (e2))\/((op (e2) (e2)) = (e3))))) -> ((op (e1) (e2)) = (e0)) -> (~((op (e1) (e2)) = (op (e2) (e2)))) -> (~((op (e2) (e2)) = (e1))) -> (~((op (e2) (e2)) = (e2))) -> (~((op (e2) (e2)) = (e3))) -> False). % 15.22/15.38 do 0 intro. intros zenon_H2d zenon_H15d zenon_H7d zenon_H52 zenon_H2f zenon_H30. % 15.22/15.38 apply (zenon_or_s _ _ zenon_H2d); [ zenon_intro zenon_H32 | zenon_intro zenon_H31 ]. % 15.22/15.38 cut (((op (e1) (e2)) = (e0)) = ((op (e1) (e2)) = (op (e2) (e2)))). % 15.22/15.38 intro zenon_D_pnotp. % 15.22/15.38 apply zenon_H7d. % 15.22/15.38 rewrite <- zenon_D_pnotp. % 15.22/15.38 exact zenon_H15d. % 15.22/15.38 cut (((e0) = (op (e2) (e2)))); [idtac | apply NNPP; zenon_intro zenon_H1fe]. % 15.22/15.38 cut (((op (e1) (e2)) = (op (e1) (e2)))); [idtac | apply NNPP; zenon_intro zenon_H1d1]. % 15.22/15.38 congruence. % 15.22/15.38 apply zenon_H1d1. apply refl_equal. % 15.22/15.38 apply zenon_H1fe. apply sym_equal. exact zenon_H32. % 15.22/15.38 apply (zenon_or_s _ _ zenon_H31); [ zenon_intro zenon_H2a | zenon_intro zenon_H33 ]. % 15.22/15.38 exact (zenon_H52 zenon_H2a). % 15.22/15.38 apply (zenon_or_s _ _ zenon_H33); [ zenon_intro zenon_H35 | zenon_intro zenon_H34 ]. % 15.22/15.38 exact (zenon_H2f zenon_H35). % 15.22/15.38 exact (zenon_H30 zenon_H34). % 15.22/15.38 (* end of lemma zenon_L335_ *) % 15.22/15.38 assert (zenon_L336_ : (~((op (e0) (e1)) = (op (e2) (e1)))) -> ((op (e0) (e1)) = (e1)) -> ((op (e2) (e1)) = (e1)) -> False). % 15.22/15.38 do 0 intro. intros zenon_Hde zenon_H22 zenon_Hb2. % 15.22/15.38 cut (((op (e0) (e1)) = (e1)) = ((op (e0) (e1)) = (op (e2) (e1)))). % 15.22/15.38 intro zenon_D_pnotp. % 15.22/15.38 apply zenon_Hde. % 15.22/15.38 rewrite <- zenon_D_pnotp. % 15.22/15.38 exact zenon_H22. % 15.22/15.38 cut (((e1) = (op (e2) (e1)))); [idtac | apply NNPP; zenon_intro zenon_Hb3]. % 15.22/15.38 cut (((op (e0) (e1)) = (op (e0) (e1)))); [idtac | apply NNPP; zenon_intro zenon_He1]. % 15.22/15.38 congruence. % 15.22/15.38 apply zenon_He1. apply refl_equal. % 15.22/15.38 apply zenon_Hb3. apply sym_equal. exact zenon_Hb2. % 15.22/15.38 (* end of lemma zenon_L336_ *) % 15.22/15.38 assert (zenon_L337_ : (((op (e0) (e0)) = (e3))\/(((op (e0) (e1)) = (e3))\/(((op (e0) (e2)) = (e3))\/((op (e0) (e3)) = (e3))))) -> (~((op (e2) (e2)) = (e3))) -> (~((op (e2) (e2)) = (e2))) -> (~((op (e2) (e2)) = (e1))) -> (((op (e2) (e2)) = (e0))\/(((op (e2) (e2)) = (e1))\/(((op (e2) (e2)) = (e2))\/((op (e2) (e2)) = (e3))))) -> (~((op (e0) (e1)) = (op (e2) (e1)))) -> (~((e1) = (e2))) -> ((op (e2) (e0)) = (e2)) -> (((op (e2) (e0)) = (e1))\/(((op (e2) (e1)) = (e1))\/(((op (e2) (e2)) = (e1))\/((op (e2) (e3)) = (e1))))) -> (~((e1) = (e3))) -> ((op (e0) (e1)) = (e1)) -> (~((e2) = (e3))) -> ((op (e0) (e2)) = (e2)) -> ((op (e3) (e3)) = (e3)) -> (~((op (e0) (e3)) = (op (e3) (e3)))) -> False). % 15.22/15.38 do 0 intro. intros zenon_H58 zenon_H30 zenon_H2f zenon_H52 zenon_H2d zenon_Hde zenon_Ha7 zenon_Hdd zenon_Hb7 zenon_Ha3 zenon_H22 zenon_H6a zenon_H63 zenon_H42 zenon_H36. % 15.22/15.38 apply (zenon_or_s _ _ zenon_H58); [ zenon_intro zenon_H5b | zenon_intro zenon_H5a ]. % 15.22/15.38 apply (zenon_or_s _ _ zenon_Hb7); [ zenon_intro zenon_Hae | zenon_intro zenon_Hb8 ]. % 15.22/15.38 apply (zenon_L304_); trivial. % 15.22/15.38 apply (zenon_or_s _ _ zenon_Hb8); [ zenon_intro zenon_Hb2 | zenon_intro zenon_Hb9 ]. % 15.22/15.38 apply (zenon_L336_); trivial. % 15.22/15.38 apply (zenon_or_s _ _ zenon_Hb9); [ zenon_intro zenon_H2a | zenon_intro zenon_Hb5 ]. % 15.22/15.38 exact (zenon_H52 zenon_H2a). % 15.22/15.38 apply (zenon_L320_); trivial. % 15.22/15.38 apply (zenon_or_s _ _ zenon_H5a); [ zenon_intro zenon_H4a | zenon_intro zenon_H5c ]. % 15.22/15.38 apply (zenon_L59_); trivial. % 15.22/15.38 apply (zenon_or_s _ _ zenon_H5c); [ zenon_intro zenon_H50 | zenon_intro zenon_H53 ]. % 15.22/15.38 apply (zenon_L31_); trivial. % 15.22/15.38 apply (zenon_L12_); trivial. % 15.22/15.38 (* end of lemma zenon_L337_ *) % 15.22/15.38 assert (zenon_L338_ : (((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)) = (e0))\/(((op (e1) (e1)) = (e1))\/(((op (e1) (e1)) = (e2))\/((op (e1) (e1)) = (e3))))) -> (~((e1) = (e2))) -> ((op (e3) (e0)) = (e1)) -> (((op (e0) (e0)) = (e3))\/(((op (e0) (e1)) = (e3))\/(((op (e0) (e2)) = (e3))\/((op (e0) (e3)) = (e3))))) -> (~((op (e2) (e2)) = (e3))) -> (~((op (e2) (e2)) = (e2))) -> (~((op (e2) (e2)) = (e1))) -> (((op (e2) (e2)) = (e0))\/(((op (e2) (e2)) = (e1))\/(((op (e2) (e2)) = (e2))\/((op (e2) (e2)) = (e3))))) -> (~((op (e0) (e1)) = (op (e2) (e1)))) -> (((op (e2) (e0)) = (e1))\/(((op (e2) (e1)) = (e1))\/(((op (e2) (e2)) = (e1))\/((op (e2) (e3)) = (e1))))) -> (~((e1) = (e3))) -> ((op (e0) (e1)) = (e1)) -> (~((e2) = (e3))) -> ((op (e3) (e3)) = (e3)) -> (~((op (e0) (e3)) = (op (e3) (e3)))) -> (((op (e1) (e0)) = (e0))\/(((op (e1) (e1)) = (e0))\/(((op (e1) (e2)) = (e0))\/((op (e1) (e3)) = (e0))))) -> (~((op (e1) (e1)) = (e0))) -> (~((op (e1) (e2)) = (op (e2) (e2)))) -> (~((op (e0) (e3)) = (op (e1) (e3)))) -> (~((op (e0) (e0)) = (e2))) -> (((op (e0) (e0)) = (e2))\/(((op (e1) (e0)) = (e2))\/(((op (e2) (e0)) = (e2))\/((op (e3) (e0)) = (e2))))) -> ((op (e0) (e3)) = (e0)) -> (~((e0) = (e2))) -> False). % 15.22/15.38 do 0 intro. intros zenon_H8e zenon_H182 zenon_H23 zenon_H1b4 zenon_H1b3 zenon_Ha7 zenon_Hee zenon_H58 zenon_H30 zenon_H2f zenon_H52 zenon_H2d zenon_Hde zenon_Hb7 zenon_Ha3 zenon_H22 zenon_H6a zenon_H42 zenon_H36 zenon_H163 zenon_H145 zenon_H7d zenon_H80 zenon_H8f zenon_Heb zenon_Hca zenon_H5e. % 15.22/15.38 apply (zenon_or_s _ _ zenon_H8e); [ zenon_intro zenon_H92 | zenon_intro zenon_H91 ]. % 15.22/15.38 exact (zenon_H8f zenon_H92). % 15.22/15.38 apply (zenon_or_s _ _ zenon_H91); [ zenon_intro zenon_H5d | zenon_intro zenon_H93 ]. % 15.22/15.38 apply (zenon_L214_); trivial. % 15.22/15.38 apply (zenon_or_s _ _ zenon_H93); [ zenon_intro zenon_H63 | zenon_intro zenon_H81 ]. % 15.22/15.38 apply (zenon_or_s _ _ zenon_Heb); [ zenon_intro zenon_H92 | zenon_intro zenon_Hec ]. % 15.22/15.38 exact (zenon_H8f zenon_H92). % 15.22/15.38 apply (zenon_or_s _ _ zenon_Hec); [ zenon_intro zenon_H68 | zenon_intro zenon_Hed ]. % 15.22/15.38 apply (zenon_or_s _ _ zenon_H163); [ zenon_intro zenon_Had | zenon_intro zenon_H164 ]. % 15.22/15.38 apply (zenon_L160_); trivial. % 15.22/15.38 apply (zenon_or_s _ _ zenon_H164); [ zenon_intro zenon_H149 | zenon_intro zenon_H165 ]. % 15.22/15.38 exact (zenon_H145 zenon_H149). % 15.22/15.38 apply (zenon_or_s _ _ zenon_H165); [ zenon_intro zenon_H15d | zenon_intro zenon_Hcc ]. % 15.22/15.38 apply (zenon_L335_); trivial. % 15.22/15.38 apply (zenon_L155_); trivial. % 15.22/15.38 apply (zenon_or_s _ _ zenon_Hed); [ zenon_intro zenon_Hdd | zenon_intro zenon_He9 ]. % 15.22/15.38 apply (zenon_L337_); trivial. % 15.22/15.38 apply (zenon_L122_); trivial. % 15.22/15.38 apply (zenon_L113_); trivial. % 15.22/15.38 (* end of lemma zenon_L338_ *) % 15.22/15.38 assert (zenon_L339_ : (((op (e0) (e0)) = (e2))\/(((op (e0) (e1)) = (e2))\/(((op (e0) (e2)) = (e2))\/((op (e0) (e3)) = (e2))))) -> (~((op (e0) (e0)) = (e2))) -> (~((op (e1) (e1)) = (e3))) -> (~((op (e0) (e1)) = (op (e1) (e1)))) -> (~((op (e1) (e1)) = (e1))) -> (~((op (e1) (e1)) = (e0))) -> (((op (e1) (e1)) = (e0))\/(((op (e1) (e1)) = (e1))\/(((op (e1) (e1)) = (e2))\/((op (e1) (e1)) = (e3))))) -> (~((e1) = (e2))) -> ((op (e0) (e2)) = (e1)) -> ((op (e0) (e3)) = (e0)) -> (~((e0) = (e2))) -> False). % 15.22/15.38 do 0 intro. intros zenon_H8e zenon_H8f zenon_H182 zenon_H23 zenon_H1b4 zenon_H145 zenon_H1b3 zenon_Ha7 zenon_H29 zenon_Hca zenon_H5e. % 15.22/15.38 apply (zenon_or_s _ _ zenon_H8e); [ zenon_intro zenon_H92 | zenon_intro zenon_H91 ]. % 15.22/15.38 exact (zenon_H8f zenon_H92). % 15.22/15.38 apply (zenon_or_s _ _ zenon_H91); [ zenon_intro zenon_H5d | zenon_intro zenon_H93 ]. % 15.22/15.38 apply (zenon_L214_); trivial. % 15.22/15.38 apply (zenon_or_s _ _ zenon_H93); [ zenon_intro zenon_H63 | zenon_intro zenon_H81 ]. % 15.22/15.38 apply (zenon_L104_); trivial. % 15.22/15.38 apply (zenon_L113_); trivial. % 15.22/15.38 (* end of lemma zenon_L339_ *) % 15.22/15.38 assert (zenon_L340_ : (((op (e2) (e0)) = (e1))\/(((op (e2) (e1)) = (e1))\/(((op (e2) (e2)) = (e1))\/((op (e2) (e3)) = (e1))))) -> (~((e0) = (e1))) -> ((op (e2) (e0)) = (e0)) -> ((op (e0) (e1)) = (e1)) -> (~((op (e0) (e1)) = (op (e2) (e1)))) -> (~((op (e2) (e2)) = (e1))) -> (~((e1) = (e2))) -> ((op (e2) (e3)) = (e2)) -> False). % 15.22/15.38 do 0 intro. intros zenon_Hb7 zenon_H9e zenon_Hcf zenon_H22 zenon_Hde zenon_H52 zenon_Ha7 zenon_H124. % 15.22/15.38 apply (zenon_or_s _ _ zenon_Hb7); [ zenon_intro zenon_Hae | zenon_intro zenon_Hb8 ]. % 15.22/15.38 apply (zenon_L269_); trivial. % 15.22/15.38 apply (zenon_or_s _ _ zenon_Hb8); [ zenon_intro zenon_Hb2 | zenon_intro zenon_Hb9 ]. % 15.22/15.38 apply (zenon_L336_); trivial. % 15.22/15.38 apply (zenon_or_s _ _ zenon_Hb9); [ zenon_intro zenon_H2a | zenon_intro zenon_Hb5 ]. % 15.22/15.38 exact (zenon_H52 zenon_H2a). % 15.22/15.38 apply (zenon_L93_); trivial. % 15.22/15.38 (* end of lemma zenon_L340_ *) % 15.22/15.38 assert (zenon_L341_ : (((op (e0) (e0)) = (e1))\/(((op (e0) (e1)) = (e1))\/(((op (e0) (e2)) = (e1))\/((op (e0) (e3)) = (e1))))) -> (~((op (e0) (e0)) = (e1))) -> ((op (e2) (e3)) = (e2)) -> (~((op (e2) (e2)) = (e1))) -> (~((op (e0) (e1)) = (op (e2) (e1)))) -> ((op (e2) (e0)) = (e0)) -> (((op (e2) (e0)) = (e1))\/(((op (e2) (e1)) = (e1))\/(((op (e2) (e2)) = (e1))\/((op (e2) (e3)) = (e1))))) -> (~((e0) = (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 (e0) (e1)) = (op (e1) (e1)))) -> (~((op (e1) (e1)) = (e3))) -> (~((op (e0) (e0)) = (e2))) -> (((op (e0) (e0)) = (e2))\/(((op (e0) (e1)) = (e2))\/(((op (e0) (e2)) = (e2))\/((op (e0) (e3)) = (e2))))) -> ((op (e0) (e3)) = (e0)) -> (~((e0) = (e1))) -> False). % 15.22/15.38 do 0 intro. intros zenon_H44 zenon_H45 zenon_H124 zenon_H52 zenon_Hde zenon_Hcf zenon_Hb7 zenon_H5e zenon_Ha7 zenon_H1b3 zenon_H145 zenon_H1b4 zenon_H23 zenon_H182 zenon_H8f zenon_H8e zenon_Hca zenon_H9e. % 15.22/15.38 apply (zenon_or_s _ _ zenon_H44); [ zenon_intro zenon_H47 | zenon_intro zenon_H46 ]. % 15.22/15.38 exact (zenon_H45 zenon_H47). % 15.22/15.38 apply (zenon_or_s _ _ zenon_H46); [ zenon_intro zenon_H22 | zenon_intro zenon_H48 ]. % 15.22/15.38 apply (zenon_L340_); trivial. % 15.22/15.38 apply (zenon_or_s _ _ zenon_H48); [ zenon_intro zenon_H29 | zenon_intro zenon_H37 ]. % 15.22/15.38 apply (zenon_L339_); trivial. % 15.22/15.38 apply (zenon_L73_); trivial. % 15.22/15.38 (* end of lemma zenon_L341_ *) % 15.22/15.38 assert (zenon_L342_ : ((~((op (e3) (e3)) = (e1)))\/((op (e3) (e1)) = (e3))) -> ((op (e3) (e3)) = (e3)) -> (~((op (e3) (e1)) = (op (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) (e3)) = (e1))\/(((op (e1) (e3)) = (e1))\/(((op (e2) (e3)) = (e1))\/((op (e3) (e3)) = (e1))))) -> ((op (e2) (e3)) = (e2)) -> (~((e1) = (e2))) -> (~((op (e1) (e0)) = (op (e1) (e3)))) -> (~((op (e0) (e1)) = (op (e0) (e3)))) -> (((op (e0) (e0)) = (e2))\/(((op (e0) (e1)) = (e2))\/(((op (e0) (e2)) = (e2))\/((op (e0) (e3)) = (e2))))) -> ((op (e0) (e3)) = (e0)) -> (~((e0) = (e2))) -> (~((op (e1) (e1)) = (e2))) -> (~((op (e0) (e2)) = (op (e1) (e2)))) -> (~((op (e2) (e0)) = (op (e2) (e3)))) -> (((op (e1) (e0)) = (e2))\/(((op (e1) (e1)) = (e2))\/(((op (e1) (e2)) = (e2))\/((op (e1) (e3)) = (e2))))) -> (~((op (e1) (e1)) = (e0))) -> (~((op (e1) (e1)) = (e1))) -> (~((op (e0) (e1)) = (op (e1) (e1)))) -> (~((op (e1) (e1)) = (e3))) -> (((op (e1) (e1)) = (e0))\/(((op (e1) (e1)) = (e1))\/(((op (e1) (e1)) = (e2))\/((op (e1) (e1)) = (e3))))) -> (~((op (e0) (e0)) = (e2))) -> (((op (e0) (e0)) = (e2))\/(((op (e1) (e0)) = (e2))\/(((op (e2) (e0)) = (e2))\/((op (e3) (e0)) = (e2))))) -> (((op (e0) (e0)) = (e1))\/(((op (e1) (e0)) = (e1))\/(((op (e2) (e0)) = (e1))\/((op (e3) (e0)) = (e1))))) -> (~((op (e0) (e0)) = (e1))) -> (~((op (e0) (e1)) = (op (e2) (e1)))) -> (~((op (e2) (e2)) = (e1))) -> (((op (e2) (e0)) = (e1))\/(((op (e2) (e1)) = (e1))\/(((op (e2) (e2)) = (e1))\/((op (e2) (e3)) = (e1))))) -> (~((op (e3) (op (e0) (e3))) = (op (e0) (e3)))) -> (((op (e0) (e0)) = (e0))\/(((op (e1) (e0)) = (e0))\/(((op (e2) (e0)) = (e0))\/((op (e3) (e0)) = (e0))))) -> False). % 15.22/15.39 do 0 intro. intros zenon_H10c zenon_H42 zenon_H12d zenon_H20 zenon_H44 zenon_H9e zenon_H121 zenon_H124 zenon_Ha7 zenon_H1cf zenon_H1cd zenon_H8e zenon_Hca zenon_H5e zenon_Hd6 zenon_H87 zenon_Hce zenon_H84 zenon_H145 zenon_H1b4 zenon_H23 zenon_H182 zenon_H1b3 zenon_H8f zenon_Heb zenon_Hf1 zenon_H45 zenon_Hde zenon_H52 zenon_Hb7 zenon_H192 zenon_Hf0. % 15.22/15.39 apply (zenon_or_s _ _ zenon_H10c); [ zenon_intro zenon_H104 | zenon_intro zenon_H10a ]. % 15.22/15.39 apply (zenon_or_s _ _ zenon_Hf0); [ zenon_intro zenon_H1f | zenon_intro zenon_Hf2 ]. % 15.22/15.39 exact (zenon_H20 zenon_H1f). % 15.22/15.39 apply (zenon_or_s _ _ zenon_Hf2); [ zenon_intro zenon_Had | zenon_intro zenon_Hf3 ]. % 15.22/15.39 apply (zenon_or_s _ _ zenon_H44); [ zenon_intro zenon_H47 | zenon_intro zenon_H46 ]. % 15.22/15.39 exact (zenon_H45 zenon_H47). % 15.22/15.39 apply (zenon_or_s _ _ zenon_H46); [ zenon_intro zenon_H22 | zenon_intro zenon_H48 ]. % 15.22/15.39 apply (zenon_or_s _ _ zenon_Hf1); [ zenon_intro zenon_H47 | zenon_intro zenon_Hf4 ]. % 15.22/15.39 exact (zenon_H45 zenon_H47). % 15.22/15.39 apply (zenon_or_s _ _ zenon_Hf4); [ zenon_intro zenon_Hd8 | zenon_intro zenon_Hf5 ]. % 15.22/15.39 apply (zenon_L225_); trivial. % 15.22/15.39 apply (zenon_or_s _ _ zenon_Hf5); [ zenon_intro zenon_Hae | zenon_intro zenon_Hee ]. % 15.22/15.39 apply (zenon_L334_); trivial. % 15.22/15.39 apply (zenon_or_s _ _ zenon_Heb); [ zenon_intro zenon_H92 | zenon_intro zenon_Hec ]. % 15.22/15.39 exact (zenon_H8f zenon_H92). % 15.22/15.39 apply (zenon_or_s _ _ zenon_Hec); [ zenon_intro zenon_H68 | zenon_intro zenon_Hed ]. % 15.22/15.39 apply (zenon_L160_); trivial. % 15.22/15.39 apply (zenon_or_s _ _ zenon_Hed); [ zenon_intro zenon_Hdd | zenon_intro zenon_He9 ]. % 15.22/15.39 apply (zenon_L119_); trivial. % 15.22/15.39 apply (zenon_L122_); trivial. % 15.22/15.39 apply (zenon_or_s _ _ zenon_H48); [ zenon_intro zenon_H29 | zenon_intro zenon_H37 ]. % 15.22/15.39 apply (zenon_L339_); trivial. % 15.22/15.39 apply (zenon_L73_); trivial. % 15.22/15.39 apply (zenon_or_s _ _ zenon_Hf3); [ zenon_intro zenon_Hcf | zenon_intro zenon_Hdb ]. % 15.22/15.39 apply (zenon_L341_); trivial. % 15.22/15.39 apply (zenon_L178_); trivial. % 15.22/15.39 apply (zenon_L102_); trivial. % 15.22/15.39 (* end of lemma zenon_L342_ *) % 15.22/15.39 assert (zenon_L343_ : (((op (e0) (e0)) = (e2))\/(((op (e0) (e1)) = (e2))\/(((op (e0) (e2)) = (e2))\/((op (e0) (e3)) = (e2))))) -> (~((op (e0) (e0)) = (e2))) -> (~((op (e1) (e1)) = (e3))) -> (~((op (e0) (e1)) = (op (e1) (e1)))) -> (~((op (e1) (e1)) = (e1))) -> (~((op (e1) (e1)) = (e0))) -> (((op (e1) (e1)) = (e0))\/(((op (e1) (e1)) = (e1))\/(((op (e1) (e1)) = (e2))\/((op (e1) (e1)) = (e3))))) -> (~((op (e0) (e2)) = (op (e2) (e2)))) -> ((op (e2) (e2)) = (e2)) -> ((op (e0) (e3)) = (e0)) -> (~((e0) = (e2))) -> False). % 15.22/15.39 do 0 intro. intros zenon_H8e zenon_H8f zenon_H182 zenon_H23 zenon_H1b4 zenon_H145 zenon_H1b3 zenon_H28 zenon_H35 zenon_Hca zenon_H5e. % 15.22/15.39 apply (zenon_or_s _ _ zenon_H8e); [ zenon_intro zenon_H92 | zenon_intro zenon_H91 ]. % 15.22/15.39 exact (zenon_H8f zenon_H92). % 15.22/15.39 apply (zenon_or_s _ _ zenon_H91); [ zenon_intro zenon_H5d | zenon_intro zenon_H93 ]. % 15.22/15.39 apply (zenon_L214_); trivial. % 15.22/15.39 apply (zenon_or_s _ _ zenon_H93); [ zenon_intro zenon_H63 | zenon_intro zenon_H81 ]. % 15.22/15.39 apply (zenon_L15_); trivial. % 15.22/15.39 apply (zenon_L113_); trivial. % 15.22/15.39 (* end of lemma zenon_L343_ *) % 15.22/15.39 assert (zenon_L344_ : ((~((op (e2) (e2)) = (e2)))\/((op (e2) (e2)) = (e2))) -> ((~((op (e3) (e3)) = (e1)))\/((op (e3) (e1)) = (e3))) -> (~((op (e3) (e1)) = (op (e3) (e3)))) -> (~((op (e0) (e0)) = (e0))) -> (((op (e0) (e0)) = (e1))\/(((op (e0) (e1)) = (e1))\/(((op (e0) (e2)) = (e1))\/((op (e0) (e3)) = (e1))))) -> (((op (e0) (e0)) = (e3))\/(((op (e0) (e1)) = (e3))\/(((op (e0) (e2)) = (e3))\/((op (e0) (e3)) = (e3))))) -> ((op (e3) (e3)) = (e3)) -> (~((op (e0) (e3)) = (op (e3) (e3)))) -> (~((op (e2) (e2)) = (e0))) -> (~((op (e0) (e2)) = (op (e2) (e2)))) -> (~((e1) = (e3))) -> (~((e0) = (e1))) -> ((op (e0) (e3)) = (e0)) -> (~((op (e1) (e0)) = (op (e1) (e3)))) -> (((op (e2) (e2)) = (e0))\/(((op (e2) (e2)) = (e1))\/(((op (e2) (e2)) = (e2))\/((op (e2) (e2)) = (e3))))) -> (~((op (e2) (e2)) = (e1))) -> (((op (e0) (e3)) = (e1))\/(((op (e1) (e3)) = (e1))\/(((op (e2) (e3)) = (e1))\/((op (e3) (e3)) = (e1))))) -> (((op (e0) (e0)) = (e2))\/(((op (e0) (e1)) = (e2))\/(((op (e0) (e2)) = (e2))\/((op (e0) (e3)) = (e2))))) -> (~((e0) = (e2))) -> (~((op (e1) (e1)) = (e2))) -> (~((op (e0) (e2)) = (op (e1) (e2)))) -> (~((op (e2) (e0)) = (op (e2) (e3)))) -> (~((e1) = (e2))) -> (~((op (e0) (e1)) = (op (e0) (e3)))) -> (((op (e1) (e0)) = (e2))\/(((op (e1) (e1)) = (e2))\/(((op (e1) (e2)) = (e2))\/((op (e1) (e3)) = (e2))))) -> (~((op (e1) (e1)) = (e0))) -> (~((op (e1) (e1)) = (e1))) -> (~((op (e0) (e1)) = (op (e1) (e1)))) -> (~((op (e1) (e1)) = (e3))) -> (((op (e1) (e1)) = (e0))\/(((op (e1) (e1)) = (e1))\/(((op (e1) (e1)) = (e2))\/((op (e1) (e1)) = (e3))))) -> (~((op (e0) (e0)) = (e2))) -> (((op (e1) (e0)) = (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)))) -> (~((e2) = (e3))) -> (~((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)) = (e2))\/(((op (e1) (e0)) = (e2))\/(((op (e2) (e0)) = (e2))\/((op (e3) (e0)) = (e2))))) -> (((op (e0) (e0)) = (e1))\/(((op (e1) (e0)) = (e1))\/(((op (e2) (e0)) = (e1))\/((op (e3) (e0)) = (e1))))) -> (~((op (e0) (e0)) = (e1))) -> (~((op (e3) (op (e0) (e3))) = (op (e0) (e3)))) -> (((op (e0) (e0)) = (e0))\/(((op (e1) (e0)) = (e0))\/(((op (e2) (e0)) = (e0))\/((op (e3) (e0)) = (e0))))) -> ((~((op (e2) (e2)) = (e3)))\/((op (e2) (e3)) = (e2))) -> False). % 15.22/15.39 do 0 intro. intros zenon_Haa zenon_H10c zenon_H12d zenon_H20 zenon_H44 zenon_H58 zenon_H42 zenon_H36 zenon_H2e zenon_H28 zenon_Ha3 zenon_H9e zenon_Hca zenon_H1cf zenon_H2d zenon_H52 zenon_H121 zenon_H8e zenon_H5e zenon_Hd6 zenon_H87 zenon_Hce zenon_Ha7 zenon_H1cd zenon_H84 zenon_H145 zenon_H1b4 zenon_H23 zenon_H182 zenon_H1b3 zenon_H8f zenon_H163 zenon_H80 zenon_H7d zenon_H6a zenon_Hde zenon_Hb7 zenon_Heb zenon_Hf1 zenon_H45 zenon_H192 zenon_Hf0 zenon_H1c3. % 15.22/15.39 apply (zenon_or_s _ _ zenon_Haa); [ zenon_intro zenon_H2f | zenon_intro zenon_H35 ]. % 15.22/15.39 apply (zenon_or_s _ _ zenon_H1c3); [ zenon_intro zenon_H30 | zenon_intro zenon_H124 ]. % 15.22/15.39 apply (zenon_or_s _ _ zenon_H10c); [ zenon_intro zenon_H104 | zenon_intro zenon_H10a ]. % 15.22/15.39 apply (zenon_or_s _ _ zenon_Hf0); [ zenon_intro zenon_H1f | zenon_intro zenon_Hf2 ]. % 15.22/15.39 exact (zenon_H20 zenon_H1f). % 15.22/15.39 apply (zenon_or_s _ _ zenon_Hf2); [ zenon_intro zenon_Had | zenon_intro zenon_Hf3 ]. % 15.22/15.39 apply (zenon_or_s _ _ zenon_H44); [ zenon_intro zenon_H47 | zenon_intro zenon_H46 ]. % 15.22/15.39 exact (zenon_H45 zenon_H47). % 15.22/15.39 apply (zenon_or_s _ _ zenon_H46); [ zenon_intro zenon_H22 | zenon_intro zenon_H48 ]. % 15.22/15.39 apply (zenon_or_s _ _ zenon_Hf1); [ zenon_intro zenon_H47 | zenon_intro zenon_Hf4 ]. % 15.22/15.39 exact (zenon_H45 zenon_H47). % 15.22/15.39 apply (zenon_or_s _ _ zenon_Hf4); [ zenon_intro zenon_Hd8 | zenon_intro zenon_Hf5 ]. % 15.22/15.39 apply (zenon_L331_); trivial. % 15.22/15.39 apply (zenon_or_s _ _ zenon_Hf5); [ zenon_intro zenon_Hae | zenon_intro zenon_Hee ]. % 15.22/15.39 apply (zenon_L334_); trivial. % 15.22/15.39 apply (zenon_L338_); trivial. % 15.22/15.39 apply (zenon_or_s _ _ zenon_H48); [ zenon_intro zenon_H29 | zenon_intro zenon_H37 ]. % 15.22/15.39 apply (zenon_L339_); trivial. % 15.22/15.39 apply (zenon_L73_); trivial. % 15.22/15.39 apply (zenon_or_s _ _ zenon_Hf3); [ zenon_intro zenon_Hcf | zenon_intro zenon_Hdb ]. % 15.22/15.39 apply (zenon_or_s _ _ zenon_H44); [ zenon_intro zenon_H47 | zenon_intro zenon_H46 ]. % 15.22/15.39 exact (zenon_H45 zenon_H47). % 15.22/15.39 apply (zenon_or_s _ _ zenon_H46); [ zenon_intro zenon_H22 | zenon_intro zenon_H48 ]. % 15.22/15.39 apply (zenon_or_s _ _ zenon_Hf1); [ zenon_intro zenon_H47 | zenon_intro zenon_Hf4 ]. % 15.22/15.39 exact (zenon_H45 zenon_H47). % 15.22/15.39 apply (zenon_or_s _ _ zenon_Hf4); [ zenon_intro zenon_Hd8 | zenon_intro zenon_Hf5 ]. % 15.22/15.39 apply (zenon_L331_); trivial. % 15.22/15.39 apply (zenon_or_s _ _ zenon_Hf5); [ zenon_intro zenon_Hae | zenon_intro zenon_Hee ]. % 15.22/15.39 apply (zenon_L269_); trivial. % 15.22/15.39 apply (zenon_L338_); trivial. % 15.22/15.39 apply (zenon_or_s _ _ zenon_H48); [ zenon_intro zenon_H29 | zenon_intro zenon_H37 ]. % 15.22/15.39 apply (zenon_L5_); trivial. % 15.22/15.39 apply (zenon_L73_); trivial. % 15.22/15.39 apply (zenon_L178_); trivial. % 15.22/15.39 apply (zenon_L102_); trivial. % 15.22/15.39 apply (zenon_L342_); trivial. % 15.22/15.39 apply (zenon_L343_); trivial. % 15.22/15.39 (* end of lemma zenon_L344_ *) % 15.22/15.39 assert (zenon_L345_ : (((op (e0) (e0)) = (e2))\/(((op (e0) (e1)) = (e2))\/(((op (e0) (e2)) = (e2))\/((op (e0) (e3)) = (e2))))) -> (~((op (e0) (e0)) = (e2))) -> (~((op (e1) (e1)) = (e3))) -> (~((op (e0) (e1)) = (op (e1) (e1)))) -> (~((op (e1) (e1)) = (e1))) -> (~((op (e1) (e1)) = (e0))) -> (((op (e1) (e1)) = (e0))\/(((op (e1) (e1)) = (e1))\/(((op (e1) (e1)) = (e2))\/((op (e1) (e1)) = (e3))))) -> (~((op (e0) (e2)) = (op (e2) (e2)))) -> ((op (e2) (e2)) = (e2)) -> (((op (e3) (e3)) = (e0))\/(((op (e3) (e3)) = (e1))\/(((op (e3) (e3)) = (e2))\/((op (e3) (e3)) = (e3))))) -> (~((op (e3) (e3)) = (e0))) -> (~((op (e3) (e3)) = (e1))) -> (~((op (e0) (e3)) = (op (e3) (e3)))) -> (~((op (e3) (e3)) = (e3))) -> False). % 15.22/15.39 do 0 intro. intros zenon_H8e zenon_H8f zenon_H182 zenon_H23 zenon_H1b4 zenon_H145 zenon_H1b3 zenon_H28 zenon_H35 zenon_H3b zenon_H3c zenon_H104 zenon_H36 zenon_H3e. % 15.22/15.39 apply (zenon_or_s _ _ zenon_H8e); [ zenon_intro zenon_H92 | zenon_intro zenon_H91 ]. % 15.22/15.39 exact (zenon_H8f zenon_H92). % 15.22/15.39 apply (zenon_or_s _ _ zenon_H91); [ zenon_intro zenon_H5d | zenon_intro zenon_H93 ]. % 15.22/15.39 apply (zenon_L214_); trivial. % 15.22/15.39 apply (zenon_or_s _ _ zenon_H93); [ zenon_intro zenon_H63 | zenon_intro zenon_H81 ]. % 15.22/15.39 apply (zenon_L15_); trivial. % 15.22/15.39 apply (zenon_L107_); trivial. % 15.22/15.39 (* end of lemma zenon_L345_ *) % 15.22/15.39 assert (zenon_L346_ : (~((op (e0) (e1)) = (op (e1) (e1)))) -> ((op (e0) (e1)) = (e0)) -> ((op (e1) (e1)) = (e0)) -> False). % 15.22/15.39 do 0 intro. intros zenon_H23 zenon_H49 zenon_H149. % 15.22/15.39 cut (((op (e0) (e1)) = (e0)) = ((op (e0) (e1)) = (op (e1) (e1)))). % 15.22/15.39 intro zenon_D_pnotp. % 15.22/15.39 apply zenon_H23. % 15.22/15.39 rewrite <- zenon_D_pnotp. % 15.22/15.39 exact zenon_H49. % 15.22/15.39 cut (((e0) = (op (e1) (e1)))); [idtac | apply NNPP; zenon_intro zenon_H1ad]. % 15.22/15.39 cut (((op (e0) (e1)) = (op (e0) (e1)))); [idtac | apply NNPP; zenon_intro zenon_He1]. % 15.22/15.39 congruence. % 15.22/15.39 apply zenon_He1. apply refl_equal. % 15.22/15.39 apply zenon_H1ad. apply sym_equal. exact zenon_H149. % 15.22/15.39 (* end of lemma zenon_L346_ *) % 15.22/15.39 assert (zenon_L347_ : (((op (e1) (e1)) = (e0))\/(((op (e1) (e1)) = (e1))\/(((op (e1) (e1)) = (e2))\/((op (e1) (e1)) = (e3))))) -> ((op (e0) (e1)) = (e0)) -> (~((op (e0) (e1)) = (op (e1) (e1)))) -> (~((op (e1) (e1)) = (e1))) -> (~((op (e1) (e1)) = (e2))) -> (~((op (e1) (e1)) = (e3))) -> False). % 15.22/15.39 do 0 intro. intros zenon_H1b3 zenon_H49 zenon_H23 zenon_H1b4 zenon_Hd6 zenon_H182. % 15.22/15.39 apply (zenon_or_s _ _ zenon_H1b3); [ zenon_intro zenon_H149 | zenon_intro zenon_H1b5 ]. % 15.22/15.39 apply (zenon_L346_); trivial. % 15.22/15.39 apply (zenon_or_s _ _ zenon_H1b5); [ zenon_intro zenon_H21 | zenon_intro zenon_H1b6 ]. % 15.22/15.39 exact (zenon_H1b4 zenon_H21). % 15.22/15.39 apply (zenon_or_s _ _ zenon_H1b6); [ zenon_intro zenon_H6e | zenon_intro zenon_H96 ]. % 15.22/15.39 exact (zenon_Hd6 zenon_H6e). % 15.22/15.39 exact (zenon_H182 zenon_H96). % 15.22/15.39 (* end of lemma zenon_L347_ *) % 15.22/15.39 assert (zenon_L348_ : ((~((op (e3) (e3)) = (e2)))\/((op (e3) (e2)) = (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)) = (e2))) -> (~((op (e1) (e1)) = (e1))) -> (~((op (e0) (e1)) = (op (e1) (e1)))) -> (((op (e0) (e0)) = (e1))\/(((op (e0) (e1)) = (e1))\/(((op (e0) (e2)) = (e1))\/((op (e0) (e3)) = (e1))))) -> (((op (e1) (e0)) = (e1))\/(((op (e1) (e1)) = (e1))\/(((op (e1) (e2)) = (e1))\/((op (e1) (e3)) = (e1))))) -> (((op (e0) (e3)) = (e2))\/(((op (e1) (e3)) = (e2))\/(((op (e2) (e3)) = (e2))\/((op (e3) (e3)) = (e2))))) -> (~((op (e3) (e3)) = (e0))) -> (((op (e0) (e2)) = (e3))\/(((op (e1) (e2)) = (e3))\/(((op (e2) (e2)) = (e3))\/((op (e3) (e2)) = (e3))))) -> (~((op (e3) (e2)) = (op (e3) (e3)))) -> ((~((op (e3) (e3)) = (e0)))\/((op (e3) (e0)) = (e3))) -> (~((op (e3) (e0)) = (op (e3) (e3)))) -> (~((e2) = (e3))) -> (~((op (e0) (e2)) = (op (e0) (e3)))) -> (~((e0) = (e2))) -> (((op (e0) (e3)) = (e0))\/(((op (e1) (e3)) = (e0))\/(((op (e2) (e3)) = (e0))\/((op (e3) (e3)) = (e0))))) -> (~((e1) = (e2))) -> (((op (e1) (e0)) = (e2))\/(((op (e1) (e1)) = (e2))\/(((op (e1) (e2)) = (e2))\/((op (e1) (e3)) = (e2))))) -> ((~((op (e2) (e2)) = (e3)))\/((op (e2) (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 (e1) (e1)) = (e0))) -> (~((op (e0) (e2)) = (op (e2) (e2)))) -> ((op (e2) (e2)) = (e2)) -> (((op (e0) (e0)) = (e2))\/(((op (e0) (e1)) = (e2))\/(((op (e0) (e2)) = (e2))\/((op (e0) (e3)) = (e2))))) -> (~((e0) = (e1))) -> (~((op (e0) (e0)) = (e3))) -> (~((e1) = (e3))) -> (~((e0) = (e3))) -> (~((op (e0) (e3)) = (op (e3) (e3)))) -> ((op (e3) (e3)) = (e3)) -> (((op (e0) (e0)) = (e3))\/(((op (e0) (e1)) = (e3))\/(((op (e0) (e2)) = (e3))\/((op (e0) (e3)) = (e3))))) -> (~((op (e0) (e0)) = (e1))) -> (~((op (e0) (e0)) = (e2))) -> (((op (e0) (e0)) = (e0))\/(((op (e0) (e1)) = (e0))\/(((op (e0) (e2)) = (e0))\/((op (e0) (e3)) = (e0))))) -> False). % 15.22/15.39 do 0 intro. intros zenon_H10e zenon_H20 zenon_H1b3 zenon_H182 zenon_Hd6 zenon_H1b4 zenon_H23 zenon_H44 zenon_H1c5 zenon_H160 zenon_H3c zenon_H175 zenon_H173 zenon_H10f zenon_Hbb zenon_H6a zenon_Hc9 zenon_H5e zenon_Hd3 zenon_Ha7 zenon_H84 zenon_H1c3 zenon_H8b zenon_H90 zenon_H145 zenon_H28 zenon_H35 zenon_H8e zenon_H9e zenon_H59 zenon_Ha3 zenon_H4b zenon_H36 zenon_H42 zenon_H58 zenon_H45 zenon_H8f zenon_H110. % 15.22/15.39 apply (zenon_or_s _ _ zenon_H10e); [ zenon_intro zenon_H3d | zenon_intro zenon_H106 ]. % 15.22/15.39 apply (zenon_or_s _ _ zenon_H110); [ zenon_intro zenon_H1f | zenon_intro zenon_H111 ]. % 15.22/15.39 exact (zenon_H20 zenon_H1f). % 15.22/15.39 apply (zenon_or_s _ _ zenon_H111); [ zenon_intro zenon_H49 | zenon_intro zenon_H112 ]. % 15.22/15.39 apply (zenon_L347_); trivial. % 15.22/15.39 apply (zenon_or_s _ _ zenon_H112); [ zenon_intro zenon_Hab | zenon_intro zenon_Hca ]. % 15.22/15.39 apply (zenon_L232_); trivial. % 15.22/15.39 apply (zenon_L343_); trivial. % 15.22/15.39 apply (zenon_L153_); trivial. % 15.22/15.39 (* end of lemma zenon_L348_ *) % 15.22/15.39 assert (zenon_L349_ : (((op (e0) (e1)) = (e2))\/(((op (e1) (e1)) = (e2))\/(((op (e2) (e1)) = (e2))\/((op (e3) (e1)) = (e2))))) -> (~((e0) = (e2))) -> ((op (e0) (e1)) = (e0)) -> (~((op (e1) (e1)) = (e2))) -> (~((op (e2) (e1)) = (op (e2) (e2)))) -> ((op (e2) (e2)) = (e2)) -> (~((e2) = (e3))) -> ((op (e3) (e1)) = (e3)) -> False). % 15.22/15.39 do 0 intro. intros zenon_H1a2 zenon_H5e zenon_H49 zenon_Hd6 zenon_H157 zenon_H35 zenon_H6a zenon_H10a. % 15.22/15.39 apply (zenon_or_s _ _ zenon_H1a2); [ zenon_intro zenon_H5d | zenon_intro zenon_H1a3 ]. % 15.22/15.39 apply (zenon_L14_); trivial. % 15.22/15.39 apply (zenon_or_s _ _ zenon_H1a3); [ zenon_intro zenon_H6e | zenon_intro zenon_H1a4 ]. % 15.22/15.39 exact (zenon_Hd6 zenon_H6e). % 15.22/15.39 apply (zenon_or_s _ _ zenon_H1a4); [ zenon_intro zenon_H156 | zenon_intro zenon_H16a ]. % 15.22/15.39 apply (zenon_L134_); trivial. % 15.22/15.39 apply (zenon_L297_); trivial. % 15.22/15.39 (* end of lemma zenon_L349_ *) % 15.22/15.39 assert (zenon_L350_ : ((op (e0) (e3)) = (e2)) -> ((op (e0) (e1)) = (e2)) -> (~((op (e0) (e1)) = (op (e0) (e3)))) -> False). % 15.22/15.39 do 0 intro. intros zenon_H81 zenon_H5d zenon_H1cd. % 15.22/15.39 elim (classic ((op (e0) (e3)) = (op (e0) (e3)))); [ zenon_intro zenon_H113 | zenon_intro zenon_H3a ]. % 15.22/15.39 cut (((op (e0) (e3)) = (op (e0) (e3))) = ((op (e0) (e1)) = (op (e0) (e3)))). % 15.22/15.39 intro zenon_D_pnotp. % 15.22/15.39 apply zenon_H1cd. % 15.22/15.39 rewrite <- zenon_D_pnotp. % 15.22/15.39 exact zenon_H113. % 15.22/15.39 cut (((op (e0) (e3)) = (op (e0) (e3)))); [idtac | apply NNPP; zenon_intro zenon_H3a]. % 15.22/15.39 cut (((op (e0) (e3)) = (op (e0) (e1)))); [idtac | apply NNPP; zenon_intro zenon_H1ce]. % 15.22/15.39 congruence. % 15.22/15.39 cut (((op (e0) (e3)) = (e2)) = ((op (e0) (e3)) = (op (e0) (e1)))). % 15.22/15.39 intro zenon_D_pnotp. % 15.22/15.39 apply zenon_H1ce. % 15.22/15.39 rewrite <- zenon_D_pnotp. % 15.22/15.39 exact zenon_H81. % 15.22/15.39 cut (((e2) = (op (e0) (e1)))); [idtac | apply NNPP; zenon_intro zenon_H1dc]. % 15.22/15.39 cut (((op (e0) (e3)) = (op (e0) (e3)))); [idtac | apply NNPP; zenon_intro zenon_H3a]. % 15.22/15.39 congruence. % 15.22/15.39 apply zenon_H3a. apply refl_equal. % 15.22/15.39 apply zenon_H1dc. apply sym_equal. exact zenon_H5d. % 15.22/15.39 apply zenon_H3a. apply refl_equal. % 15.22/15.39 apply zenon_H3a. apply refl_equal. % 15.22/15.39 (* end of lemma zenon_L350_ *) % 15.22/15.39 assert (zenon_L351_ : (~((e0) = (e2))) -> ((op (e2) (e1)) = (e2)) -> ((op (e2) (e1)) = (e0)) -> False). % 15.22/15.39 do 0 intro. intros zenon_H5e zenon_H156 zenon_H14a. % 15.22/15.39 cut (((op (e2) (e1)) = (e2)) = ((e0) = (e2))). % 15.22/15.39 intro zenon_D_pnotp. % 15.22/15.39 apply zenon_H5e. % 15.22/15.39 rewrite <- zenon_D_pnotp. % 15.22/15.39 exact zenon_H156. % 15.22/15.39 cut (((e2) = (e2))); [idtac | apply NNPP; zenon_intro zenon_H60]. % 15.22/15.39 cut (((op (e2) (e1)) = (e0))); [idtac | apply NNPP; zenon_intro zenon_H21b]. % 15.22/15.39 congruence. % 15.22/15.39 exact (zenon_H21b zenon_H14a). % 15.22/15.39 apply zenon_H60. apply refl_equal. % 15.22/15.39 (* end of lemma zenon_L351_ *) % 15.22/15.39 assert (zenon_L352_ : (((op (e0) (e1)) = (e2))\/(((op (e1) (e1)) = (e2))\/(((op (e2) (e1)) = (e2))\/((op (e3) (e1)) = (e2))))) -> (~((op (e0) (e1)) = (op (e0) (e3)))) -> ((op (e0) (e3)) = (e2)) -> (~((op (e1) (e1)) = (e2))) -> ((op (e2) (e1)) = (e0)) -> (~((e0) = (e2))) -> (~((e2) = (e3))) -> ((op (e3) (e1)) = (e3)) -> False). % 15.22/15.39 do 0 intro. intros zenon_H1a2 zenon_H1cd zenon_H81 zenon_Hd6 zenon_H14a zenon_H5e zenon_H6a zenon_H10a. % 15.22/15.39 apply (zenon_or_s _ _ zenon_H1a2); [ zenon_intro zenon_H5d | zenon_intro zenon_H1a3 ]. % 15.22/15.39 apply (zenon_L350_); trivial. % 15.22/15.39 apply (zenon_or_s _ _ zenon_H1a3); [ zenon_intro zenon_H6e | zenon_intro zenon_H1a4 ]. % 15.22/15.39 exact (zenon_Hd6 zenon_H6e). % 15.22/15.39 apply (zenon_or_s _ _ zenon_H1a4); [ zenon_intro zenon_H156 | zenon_intro zenon_H16a ]. % 15.22/15.39 apply (zenon_L351_); trivial. % 15.22/15.39 apply (zenon_L297_); trivial. % 15.22/15.39 (* end of lemma zenon_L352_ *) % 15.22/15.39 assert (zenon_L353_ : (((op (e0) (e1)) = (e0))\/(((op (e1) (e1)) = (e0))\/(((op (e2) (e1)) = (e0))\/((op (e3) (e1)) = (e0))))) -> ((op (e2) (e2)) = (e2)) -> (~((op (e2) (e1)) = (op (e2) (e2)))) -> (~((op (e1) (e1)) = (e0))) -> (~((e2) = (e3))) -> (~((e0) = (e2))) -> (~((op (e1) (e1)) = (e2))) -> ((op (e0) (e3)) = (e2)) -> (~((op (e0) (e1)) = (op (e0) (e3)))) -> (((op (e0) (e1)) = (e2))\/(((op (e1) (e1)) = (e2))\/(((op (e2) (e1)) = (e2))\/((op (e3) (e1)) = (e2))))) -> (~((e0) = (e3))) -> ((op (e3) (e1)) = (e3)) -> False). % 15.22/15.39 do 0 intro. intros zenon_H144 zenon_H35 zenon_H157 zenon_H145 zenon_H6a zenon_H5e zenon_Hd6 zenon_H81 zenon_H1cd zenon_H1a2 zenon_H4b zenon_H10a. % 15.22/15.39 apply (zenon_or_s _ _ zenon_H144); [ zenon_intro zenon_H49 | zenon_intro zenon_H147 ]. % 15.22/15.39 apply (zenon_L349_); trivial. % 15.22/15.39 apply (zenon_or_s _ _ zenon_H147); [ zenon_intro zenon_H149 | zenon_intro zenon_H148 ]. % 15.22/15.39 exact (zenon_H145 zenon_H149). % 15.22/15.39 apply (zenon_or_s _ _ zenon_H148); [ zenon_intro zenon_H14a | zenon_intro zenon_H142 ]. % 15.22/15.39 apply (zenon_L352_); trivial. % 15.22/15.39 apply (zenon_L126_); trivial. % 15.22/15.39 (* end of lemma zenon_L353_ *) % 15.22/15.39 assert (zenon_L354_ : (((op (e0) (e0)) = (e2))\/(((op (e0) (e1)) = (e2))\/(((op (e0) (e2)) = (e2))\/((op (e0) (e3)) = (e2))))) -> (~((op (e0) (e0)) = (e2))) -> (~((op (e1) (e1)) = (e3))) -> (~((op (e0) (e1)) = (op (e1) (e1)))) -> (~((op (e1) (e1)) = (e1))) -> (((op (e1) (e1)) = (e0))\/(((op (e1) (e1)) = (e1))\/(((op (e1) (e1)) = (e2))\/((op (e1) (e1)) = (e3))))) -> (~((op (e0) (e2)) = (op (e2) (e2)))) -> (((op (e0) (e1)) = (e0))\/(((op (e1) (e1)) = (e0))\/(((op (e2) (e1)) = (e0))\/((op (e3) (e1)) = (e0))))) -> ((op (e2) (e2)) = (e2)) -> (~((op (e2) (e1)) = (op (e2) (e2)))) -> (~((op (e1) (e1)) = (e0))) -> (~((e2) = (e3))) -> (~((e0) = (e2))) -> (~((op (e1) (e1)) = (e2))) -> (~((op (e0) (e1)) = (op (e0) (e3)))) -> (((op (e0) (e1)) = (e2))\/(((op (e1) (e1)) = (e2))\/(((op (e2) (e1)) = (e2))\/((op (e3) (e1)) = (e2))))) -> (~((e0) = (e3))) -> ((op (e3) (e1)) = (e3)) -> False). % 15.22/15.39 do 0 intro. intros zenon_H8e zenon_H8f zenon_H182 zenon_H23 zenon_H1b4 zenon_H1b3 zenon_H28 zenon_H144 zenon_H35 zenon_H157 zenon_H145 zenon_H6a zenon_H5e zenon_Hd6 zenon_H1cd zenon_H1a2 zenon_H4b zenon_H10a. % 15.22/15.39 apply (zenon_or_s _ _ zenon_H8e); [ zenon_intro zenon_H92 | zenon_intro zenon_H91 ]. % 15.22/15.39 exact (zenon_H8f zenon_H92). % 15.22/15.39 apply (zenon_or_s _ _ zenon_H91); [ zenon_intro zenon_H5d | zenon_intro zenon_H93 ]. % 15.22/15.39 apply (zenon_L214_); trivial. % 15.22/15.39 apply (zenon_or_s _ _ zenon_H93); [ zenon_intro zenon_H63 | zenon_intro zenon_H81 ]. % 15.22/15.39 apply (zenon_L15_); trivial. % 15.22/15.39 apply (zenon_L353_); trivial. % 15.22/15.39 (* end of lemma zenon_L354_ *) % 15.22/15.39 assert (zenon_L355_ : (~((op (op (e1) (e1)) (op (e1) (e1))) = (op (e3) (e3)))) -> ((op (e1) (e1)) = (e3)) -> False). % 15.22/15.39 do 0 intro. intros zenon_H21c zenon_H96. % 15.22/15.39 cut (((op (e1) (e1)) = (e3))); [idtac | apply NNPP; zenon_intro zenon_H182]. % 15.22/15.39 cut (((op (e1) (e1)) = (e3))); [idtac | apply NNPP; zenon_intro zenon_H182]. % 15.22/15.39 congruence. % 15.22/15.39 exact (zenon_H182 zenon_H96). % 15.22/15.39 exact (zenon_H182 zenon_H96). % 15.22/15.39 (* end of lemma zenon_L355_ *) % 15.22/15.39 assert (zenon_L356_ : ((op (e1) (e0)) = (e2)) -> ((op (e3) (e3)) = (e0)) -> ((op (e1) (e1)) = (e3)) -> False). % 15.22/15.39 do 0 intro. intros zenon_H68 zenon_H40 zenon_H96. % 15.22/15.39 apply (zenon_notand_s _ _ ax11); [ zenon_intro zenon_H21e | zenon_intro zenon_H21d ]. % 15.22/15.39 elim (classic ((op (op (e1) (e1)) (op (e1) (e1))) = (op (op (e1) (e1)) (op (e1) (e1))))); [ zenon_intro zenon_H1a8 | zenon_intro zenon_H1a9 ]. % 15.22/15.39 cut (((op (op (e1) (e1)) (op (e1) (e1))) = (op (op (e1) (e1)) (op (e1) (e1)))) = ((e0) = (op (op (e1) (e1)) (op (e1) (e1))))). % 15.22/15.39 intro zenon_D_pnotp. % 15.22/15.39 apply zenon_H21e. % 15.22/15.39 rewrite <- zenon_D_pnotp. % 15.22/15.39 exact zenon_H1a8. % 15.22/15.39 cut (((op (op (e1) (e1)) (op (e1) (e1))) = (op (op (e1) (e1)) (op (e1) (e1))))); [idtac | apply NNPP; zenon_intro zenon_H1a9]. % 15.22/15.39 cut (((op (op (e1) (e1)) (op (e1) (e1))) = (e0))); [idtac | apply NNPP; zenon_intro zenon_H21f]. % 15.22/15.39 congruence. % 15.22/15.39 cut (((op (e3) (e3)) = (e0)) = ((op (op (e1) (e1)) (op (e1) (e1))) = (e0))). % 15.22/15.39 intro zenon_D_pnotp. % 15.22/15.39 apply zenon_H21f. % 15.22/15.39 rewrite <- zenon_D_pnotp. % 15.22/15.39 exact zenon_H40. % 15.22/15.39 cut (((e0) = (e0))); [idtac | apply NNPP; zenon_intro zenon_H1d]. % 15.22/15.39 cut (((op (e3) (e3)) = (op (op (e1) (e1)) (op (e1) (e1))))); [idtac | apply NNPP; zenon_intro zenon_H220]. % 15.22/15.39 congruence. % 15.22/15.39 elim (classic ((op (op (e1) (e1)) (op (e1) (e1))) = (op (op (e1) (e1)) (op (e1) (e1))))); [ zenon_intro zenon_H1a8 | zenon_intro zenon_H1a9 ]. % 15.22/15.39 cut (((op (op (e1) (e1)) (op (e1) (e1))) = (op (op (e1) (e1)) (op (e1) (e1)))) = ((op (e3) (e3)) = (op (op (e1) (e1)) (op (e1) (e1))))). % 15.22/15.39 intro zenon_D_pnotp. % 15.22/15.39 apply zenon_H220. % 15.22/15.39 rewrite <- zenon_D_pnotp. % 15.22/15.39 exact zenon_H1a8. % 15.22/15.39 cut (((op (op (e1) (e1)) (op (e1) (e1))) = (op (op (e1) (e1)) (op (e1) (e1))))); [idtac | apply NNPP; zenon_intro zenon_H1a9]. % 15.22/15.39 cut (((op (op (e1) (e1)) (op (e1) (e1))) = (op (e3) (e3)))); [idtac | apply NNPP; zenon_intro zenon_H21c]. % 15.22/15.39 congruence. % 15.22/15.39 apply (zenon_L355_); trivial. % 15.22/15.39 apply zenon_H1a9. apply refl_equal. % 15.22/15.39 apply zenon_H1a9. apply refl_equal. % 15.22/15.39 apply zenon_H1d. apply refl_equal. % 15.22/15.39 apply zenon_H1a9. apply refl_equal. % 15.22/15.39 apply zenon_H1a9. apply refl_equal. % 15.22/15.39 apply (zenon_notand_s _ _ zenon_H21d); [ zenon_intro zenon_H222 | zenon_intro zenon_H221 ]. % 15.22/15.39 apply zenon_H222. apply sym_equal. exact zenon_H96. % 15.22/15.39 elim (classic ((op (e1) (op (op (e1) (e1)) (op (e1) (e1)))) = (op (e1) (op (op (e1) (e1)) (op (e1) (e1)))))); [ zenon_intro zenon_H1ae | zenon_intro zenon_H1af ]. % 15.22/15.39 cut (((op (e1) (op (op (e1) (e1)) (op (e1) (e1)))) = (op (e1) (op (op (e1) (e1)) (op (e1) (e1))))) = ((e2) = (op (e1) (op (op (e1) (e1)) (op (e1) (e1)))))). % 15.22/15.39 intro zenon_D_pnotp. % 15.22/15.39 apply zenon_H221. % 15.22/15.39 rewrite <- zenon_D_pnotp. % 15.22/15.39 exact zenon_H1ae. % 15.22/15.39 cut (((op (e1) (op (op (e1) (e1)) (op (e1) (e1)))) = (op (e1) (op (op (e1) (e1)) (op (e1) (e1)))))); [idtac | apply NNPP; zenon_intro zenon_H1af]. % 15.22/15.39 cut (((op (e1) (op (op (e1) (e1)) (op (e1) (e1)))) = (e2))); [idtac | apply NNPP; zenon_intro zenon_H223]. % 15.22/15.39 congruence. % 15.22/15.39 cut (((op (e1) (e0)) = (e2)) = ((op (e1) (op (op (e1) (e1)) (op (e1) (e1)))) = (e2))). % 15.22/15.39 intro zenon_D_pnotp. % 15.22/15.39 apply zenon_H223. % 15.22/15.39 rewrite <- zenon_D_pnotp. % 15.22/15.39 exact zenon_H68. % 15.22/15.39 cut (((e2) = (e2))); [idtac | apply NNPP; zenon_intro zenon_H60]. % 15.22/15.39 cut (((op (e1) (e0)) = (op (e1) (op (op (e1) (e1)) (op (e1) (e1)))))); [idtac | apply NNPP; zenon_intro zenon_H224]. % 15.22/15.39 congruence. % 15.22/15.39 elim (classic ((op (e1) (op (op (e1) (e1)) (op (e1) (e1)))) = (op (e1) (op (op (e1) (e1)) (op (e1) (e1)))))); [ zenon_intro zenon_H1ae | zenon_intro zenon_H1af ]. % 15.22/15.39 cut (((op (e1) (op (op (e1) (e1)) (op (e1) (e1)))) = (op (e1) (op (op (e1) (e1)) (op (e1) (e1))))) = ((op (e1) (e0)) = (op (e1) (op (op (e1) (e1)) (op (e1) (e1)))))). % 15.22/15.39 intro zenon_D_pnotp. % 15.22/15.39 apply zenon_H224. % 15.22/15.39 rewrite <- zenon_D_pnotp. % 15.22/15.39 exact zenon_H1ae. % 15.22/15.39 cut (((op (e1) (op (op (e1) (e1)) (op (e1) (e1)))) = (op (e1) (op (op (e1) (e1)) (op (e1) (e1)))))); [idtac | apply NNPP; zenon_intro zenon_H1af]. % 15.22/15.39 cut (((op (e1) (op (op (e1) (e1)) (op (e1) (e1)))) = (op (e1) (e0)))); [idtac | apply NNPP; zenon_intro zenon_H225]. % 15.22/15.39 congruence. % 15.22/15.39 cut (((op (op (e1) (e1)) (op (e1) (e1))) = (e0))); [idtac | apply NNPP; zenon_intro zenon_H21f]. % 15.22/15.39 cut (((e1) = (e1))); [idtac | apply NNPP; zenon_intro zenon_Ha0]. % 15.22/15.39 congruence. % 15.22/15.39 apply zenon_Ha0. apply refl_equal. % 15.22/15.39 cut (((op (e3) (e3)) = (e0)) = ((op (op (e1) (e1)) (op (e1) (e1))) = (e0))). % 15.22/15.39 intro zenon_D_pnotp. % 15.22/15.39 apply zenon_H21f. % 15.22/15.39 rewrite <- zenon_D_pnotp. % 15.22/15.39 exact zenon_H40. % 15.22/15.39 cut (((e0) = (e0))); [idtac | apply NNPP; zenon_intro zenon_H1d]. % 15.22/15.39 cut (((op (e3) (e3)) = (op (op (e1) (e1)) (op (e1) (e1))))); [idtac | apply NNPP; zenon_intro zenon_H220]. % 15.22/15.39 congruence. % 15.22/15.39 elim (classic ((op (op (e1) (e1)) (op (e1) (e1))) = (op (op (e1) (e1)) (op (e1) (e1))))); [ zenon_intro zenon_H1a8 | zenon_intro zenon_H1a9 ]. % 15.22/15.39 cut (((op (op (e1) (e1)) (op (e1) (e1))) = (op (op (e1) (e1)) (op (e1) (e1)))) = ((op (e3) (e3)) = (op (op (e1) (e1)) (op (e1) (e1))))). % 15.22/15.39 intro zenon_D_pnotp. % 15.22/15.39 apply zenon_H220. % 15.22/15.39 rewrite <- zenon_D_pnotp. % 15.22/15.39 exact zenon_H1a8. % 15.22/15.39 cut (((op (op (e1) (e1)) (op (e1) (e1))) = (op (op (e1) (e1)) (op (e1) (e1))))); [idtac | apply NNPP; zenon_intro zenon_H1a9]. % 15.22/15.39 cut (((op (op (e1) (e1)) (op (e1) (e1))) = (op (e3) (e3)))); [idtac | apply NNPP; zenon_intro zenon_H21c]. % 15.22/15.39 congruence. % 15.22/15.39 apply (zenon_L355_); trivial. % 15.22/15.39 apply zenon_H1a9. apply refl_equal. % 15.22/15.39 apply zenon_H1a9. apply refl_equal. % 15.22/15.39 apply zenon_H1d. apply refl_equal. % 15.22/15.39 apply zenon_H1af. apply refl_equal. % 15.22/15.39 apply zenon_H1af. apply refl_equal. % 15.22/15.39 apply zenon_H60. apply refl_equal. % 15.22/15.39 apply zenon_H1af. apply refl_equal. % 15.22/15.39 apply zenon_H1af. apply refl_equal. % 15.22/15.39 (* end of lemma zenon_L356_ *) % 15.22/15.39 assert (zenon_L357_ : (((op (e1) (e1)) = (e0))\/(((op (e1) (e1)) = (e1))\/(((op (e1) (e1)) = (e2))\/((op (e1) (e1)) = (e3))))) -> (~((op (e1) (e1)) = (e0))) -> (~((op (e1) (e1)) = (e1))) -> (~((op (e1) (e1)) = (e2))) -> (((op (e3) (e3)) = (e0))\/(((op (e3) (e3)) = (e1))\/(((op (e3) (e3)) = (e2))\/((op (e3) (e3)) = (e3))))) -> ((op (e1) (e0)) = (e2)) -> (~((op (e3) (e3)) = (e1))) -> (~((op (e3) (e3)) = (e2))) -> (~((op (e3) (e3)) = (e3))) -> False). % 15.22/15.39 do 0 intro. intros zenon_H1b3 zenon_H145 zenon_H1b4 zenon_Hd6 zenon_H3b zenon_H68 zenon_H104 zenon_H3d zenon_H3e. % 15.22/15.39 apply (zenon_or_s _ _ zenon_H1b3); [ zenon_intro zenon_H149 | zenon_intro zenon_H1b5 ]. % 15.22/15.39 exact (zenon_H145 zenon_H149). % 15.22/15.39 apply (zenon_or_s _ _ zenon_H1b5); [ zenon_intro zenon_H21 | zenon_intro zenon_H1b6 ]. % 15.22/15.39 exact (zenon_H1b4 zenon_H21). % 15.22/15.39 apply (zenon_or_s _ _ zenon_H1b6); [ zenon_intro zenon_H6e | zenon_intro zenon_H96 ]. % 15.22/15.39 exact (zenon_Hd6 zenon_H6e). % 15.22/15.39 apply (zenon_or_s _ _ zenon_H3b); [ zenon_intro zenon_H40 | zenon_intro zenon_H3f ]. % 15.22/15.39 apply (zenon_L356_); trivial. % 15.22/15.39 apply (zenon_or_s _ _ zenon_H3f); [ zenon_intro zenon_H38 | zenon_intro zenon_H41 ]. % 15.22/15.39 exact (zenon_H104 zenon_H38). % 15.22/15.39 apply (zenon_or_s _ _ zenon_H41); [ zenon_intro zenon_H43 | zenon_intro zenon_H42 ]. % 15.22/15.39 exact (zenon_H3d zenon_H43). % 15.22/15.39 exact (zenon_H3e zenon_H42). % 15.22/15.39 (* end of lemma zenon_L357_ *) % 15.22/15.39 assert (zenon_L358_ : (((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 (e3) (e3)) = (e2))) -> (~((op (e3) (e3)) = (e1))) -> (((op (e3) (e3)) = (e0))\/(((op (e3) (e3)) = (e1))\/(((op (e3) (e3)) = (e2))\/((op (e3) (e3)) = (e3))))) -> (~((op (e1) (e1)) = (e2))) -> (~((op (e1) (e1)) = (e1))) -> (~((op (e1) (e1)) = (e0))) -> (((op (e1) (e1)) = (e0))\/(((op (e1) (e1)) = (e1))\/(((op (e1) (e1)) = (e2))\/((op (e1) (e1)) = (e3))))) -> (~((op (e2) (e0)) = (op (e2) (e2)))) -> ((op (e2) (e2)) = (e2)) -> (~((e2) = (e3))) -> ((op (e3) (e0)) = (e3)) -> False). % 15.22/15.39 do 0 intro. intros zenon_Heb zenon_H8f zenon_H3e zenon_H3d zenon_H104 zenon_H3b zenon_Hd6 zenon_H1b4 zenon_H145 zenon_H1b3 zenon_H17a zenon_H35 zenon_H6a zenon_Hba. % 15.22/15.39 apply (zenon_or_s _ _ zenon_Heb); [ zenon_intro zenon_H92 | zenon_intro zenon_Hec ]. % 15.22/15.39 exact (zenon_H8f zenon_H92). % 15.22/15.39 apply (zenon_or_s _ _ zenon_Hec); [ zenon_intro zenon_H68 | zenon_intro zenon_Hed ]. % 15.22/15.39 apply (zenon_L357_); trivial. % 15.22/15.39 apply (zenon_or_s _ _ zenon_Hed); [ zenon_intro zenon_Hdd | zenon_intro zenon_He9 ]. % 15.22/15.39 apply (zenon_L161_); trivial. % 15.22/15.39 apply (zenon_L220_); trivial. % 15.22/15.39 (* end of lemma zenon_L358_ *) % 15.22/15.39 assert (zenon_L359_ : ((~((op (e3) (e3)) = (e1)))\/((op (e3) (e1)) = (e3))) -> (~((op (e3) (e0)) = (op (e3) (e1)))) -> ((~((op (e3) (e3)) = (e3)))\/((op (e3) (e3)) = (e3))) -> (~((op (e3) (e0)) = (op (e3) (e3)))) -> (~((op (e0) (e0)) = (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 (e1) (e1)) = (e2))) -> (~((op (e1) (e1)) = (e1))) -> (~((op (e1) (e1)) = (e0))) -> (~((op (e2) (e0)) = (op (e2) (e2)))) -> ((op (e2) (e2)) = (e2)) -> (~((e2) = (e3))) -> ((op (e3) (e0)) = (e3)) -> (((op (e0) (e0)) = (e2))\/(((op (e1) (e0)) = (e2))\/(((op (e2) (e0)) = (e2))\/((op (e3) (e0)) = (e2))))) -> (~((op (e3) (e0)) = (op (e3) (e2)))) -> ((~((op (e3) (e3)) = (e2)))\/((op (e3) (e2)) = (e3))) -> False). % 15.22/15.39 do 0 intro. intros zenon_H10c zenon_H109 zenon_H10d zenon_Hbb zenon_H8f zenon_H1b3 zenon_H3b zenon_Hd6 zenon_H1b4 zenon_H145 zenon_H17a zenon_H35 zenon_H6a zenon_Hba zenon_Heb zenon_H105 zenon_H10e. % 15.22/15.39 apply (zenon_or_s _ _ zenon_H10c); [ zenon_intro zenon_H104 | zenon_intro zenon_H10a ]. % 15.22/15.39 apply (zenon_or_s _ _ zenon_H10e); [ zenon_intro zenon_H3d | zenon_intro zenon_H106 ]. % 15.22/15.39 apply (zenon_or_s _ _ zenon_H10d); [ zenon_intro zenon_H3e | zenon_intro zenon_H42 ]. % 15.22/15.39 apply (zenon_L358_); trivial. % 15.22/15.39 apply (zenon_L43_); trivial. % 15.22/15.39 apply (zenon_L81_); trivial. % 15.22/15.39 apply (zenon_L82_); trivial. % 15.22/15.39 (* end of lemma zenon_L359_ *) % 15.22/15.39 assert (zenon_L360_ : (~((op (e3) (e0)) = (op (e3) (e2)))) -> (((op (e0) (e0)) = (e2))\/(((op (e1) (e0)) = (e2))\/(((op (e2) (e0)) = (e2))\/((op (e3) (e0)) = (e2))))) -> (~((op (e2) (e0)) = (op (e2) (e2)))) -> (~((op (e3) (e0)) = (op (e3) (e1)))) -> ((~((op (e3) (e3)) = (e3)))\/((op (e3) (e3)) = (e3))) -> (((op (e0) (e0)) = (e0))\/(((op (e0) (e1)) = (e0))\/(((op (e0) (e2)) = (e0))\/((op (e0) (e3)) = (e0))))) -> (~((op (e0) (e0)) = (e1))) -> (((op (e0) (e0)) = (e3))\/(((op (e0) (e1)) = (e3))\/(((op (e0) (e2)) = (e3))\/((op (e0) (e3)) = (e3))))) -> (~((e0) = (e3))) -> (~((e1) = (e3))) -> (~((op (e0) (e0)) = (e3))) -> (~((e0) = (e1))) -> (((op (e1) (e0)) = (e3))\/(((op (e1) (e1)) = (e3))\/(((op (e1) (e2)) = (e3))\/((op (e1) (e3)) = (e3))))) -> (~((op (e1) (e3)) = (op (e3) (e3)))) -> ((~((op (e2) (e2)) = (e3)))\/((op (e2) (e3)) = (e2))) -> (((op (e1) (e0)) = (e2))\/(((op (e1) (e1)) = (e2))\/(((op (e1) (e2)) = (e2))\/((op (e1) (e3)) = (e2))))) -> (~((e1) = (e2))) -> (((op (e0) (e3)) = (e0))\/(((op (e1) (e3)) = (e0))\/(((op (e2) (e3)) = (e0))\/((op (e3) (e3)) = (e0))))) -> (~((e0) = (e2))) -> (~((op (e0) (e2)) = (op (e0) (e3)))) -> (~((e2) = (e3))) -> (~((op (e3) (e0)) = (op (e3) (e3)))) -> ((~((op (e3) (e3)) = (e0)))\/((op (e3) (e0)) = (e3))) -> (~((op (e3) (e2)) = (op (e3) (e3)))) -> (((op (e0) (e2)) = (e3))\/(((op (e1) (e2)) = (e3))\/(((op (e2) (e2)) = (e3))\/((op (e3) (e2)) = (e3))))) -> (((op (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 (e0) (e0)) = (e1))\/(((op (e0) (e1)) = (e1))\/(((op (e0) (e2)) = (e1))\/((op (e0) (e3)) = (e1))))) -> (~((op (e1) (e1)) = (e2))) -> (~((op (e0) (e0)) = (e0))) -> ((~((op (e3) (e3)) = (e2)))\/((op (e3) (e2)) = (e3))) -> (~((op (e0) (e0)) = (e2))) -> (((op (e1) (e1)) = (e0))\/(((op (e1) (e1)) = (e1))\/(((op (e1) (e1)) = (e2))\/((op (e1) (e1)) = (e3))))) -> (~((op (e1) (e1)) = (e3))) -> (~((op (e0) (e1)) = (op (e1) (e1)))) -> (~((op (e1) (e1)) = (e1))) -> (~((op (e1) (e1)) = (e0))) -> (~((op (e0) (e2)) = (op (e2) (e2)))) -> ((op (e2) (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 (e0) (e0)) = (e2))\/(((op (e0) (e1)) = (e2))\/(((op (e0) (e2)) = (e2))\/((op (e0) (e3)) = (e2))))) -> (((op (e0) (e1)) = (e2))\/(((op (e1) (e1)) = (e2))\/(((op (e2) (e1)) = (e2))\/((op (e3) (e1)) = (e2))))) -> (~((op (e2) (e1)) = (op (e2) (e2)))) -> (~((op (e0) (e1)) = (op (e0) (e3)))) -> (((op (e0) (e1)) = (e0))\/(((op (e1) (e1)) = (e0))\/(((op (e2) (e1)) = (e0))\/((op (e3) (e1)) = (e0))))) -> ((~((op (e3) (e3)) = (e1)))\/((op (e3) (e1)) = (e3))) -> False). % 15.22/15.39 do 0 intro. intros zenon_H105 zenon_Heb zenon_H17a zenon_H109 zenon_H10d zenon_H110 zenon_H45 zenon_H58 zenon_H4b zenon_Ha3 zenon_H59 zenon_H9e zenon_H90 zenon_H8b zenon_H1c3 zenon_H84 zenon_Ha7 zenon_Hd3 zenon_H5e zenon_Hc9 zenon_H6a zenon_Hbb zenon_H10f zenon_H173 zenon_H175 zenon_H160 zenon_H1c5 zenon_H44 zenon_Hd6 zenon_H20 zenon_H10e zenon_H8f zenon_H1b3 zenon_H182 zenon_H23 zenon_H1b4 zenon_H145 zenon_H28 zenon_H35 zenon_H3b zenon_H36 zenon_H8e zenon_H1a2 zenon_H157 zenon_H1cd zenon_H144 zenon_H10c. % 15.22/15.39 apply (zenon_or_s _ _ zenon_H10f); [ zenon_intro zenon_H3c | zenon_intro zenon_Hba ]. % 15.22/15.39 apply (zenon_or_s _ _ zenon_H10c); [ zenon_intro zenon_H104 | zenon_intro zenon_H10a ]. % 15.22/15.39 apply (zenon_or_s _ _ zenon_H10d); [ zenon_intro zenon_H3e | zenon_intro zenon_H42 ]. % 15.22/15.39 apply (zenon_L345_); trivial. % 15.22/15.39 apply (zenon_L348_); trivial. % 15.22/15.39 apply (zenon_L354_); trivial. % 15.22/15.39 apply (zenon_L359_); trivial. % 15.22/15.39 (* end of lemma zenon_L360_ *) % 15.22/15.39 assert (zenon_L361_ : (((op (e0) (e1)) = (e0))\/(((op (e1) (e1)) = (e0))\/(((op (e2) (e1)) = (e0))\/((op (e3) (e1)) = (e0))))) -> (~((op (e3) (e1)) = (op (e3) (e3)))) -> ((op (e3) (e3)) = (e3)) -> (~((op (e1) (e1)) = (e0))) -> (~((e0) = (e2))) -> (((op (e0) (e1)) = (e3))\/(((op (e1) (e1)) = (e3))\/(((op (e2) (e1)) = (e3))\/((op (e3) (e1)) = (e3))))) -> (~((e1) = (e3))) -> ((op (e0) (e1)) = (e1)) -> (~((op (e1) (e1)) = (e3))) -> (~((e2) = (e3))) -> ((op (e2) (e1)) = (e2)) -> (~((e0) = (e3))) -> False). % 15.22/15.39 do 0 intro. intros zenon_H144 zenon_H12d zenon_H42 zenon_H145 zenon_H5e zenon_H199 zenon_Ha3 zenon_H22 zenon_H182 zenon_H6a zenon_H156 zenon_H4b. % 15.22/15.39 apply (zenon_or_s _ _ zenon_H144); [ zenon_intro zenon_H49 | zenon_intro zenon_H147 ]. % 15.22/15.39 apply (zenon_L278_); trivial. % 15.22/15.39 apply (zenon_or_s _ _ zenon_H147); [ zenon_intro zenon_H149 | zenon_intro zenon_H148 ]. % 15.22/15.39 exact (zenon_H145 zenon_H149). % 15.22/15.39 apply (zenon_or_s _ _ zenon_H148); [ zenon_intro zenon_H14a | zenon_intro zenon_H142 ]. % 15.22/15.39 apply (zenon_L351_); trivial. % 15.22/15.39 apply (zenon_or_s _ _ zenon_H199); [ zenon_intro zenon_H4a | zenon_intro zenon_H19a ]. % 15.22/15.39 apply (zenon_L59_); trivial. % 15.22/15.39 apply (zenon_or_s _ _ zenon_H19a); [ zenon_intro zenon_H96 | zenon_intro zenon_H19b ]. % 15.22/15.39 exact (zenon_H182 zenon_H96). % 15.22/15.39 apply (zenon_or_s _ _ zenon_H19b); [ zenon_intro zenon_Hdf | zenon_intro zenon_H10a ]. % 15.22/15.39 apply (zenon_L183_); trivial. % 15.22/15.39 apply (zenon_L126_); trivial. % 15.22/15.39 (* end of lemma zenon_L361_ *) % 15.22/15.39 assert (zenon_L362_ : (((op (e0) (e0)) = (e1))\/(((op (e0) (e1)) = (e1))\/(((op (e0) (e2)) = (e1))\/((op (e0) (e3)) = (e1))))) -> (~((op (e0) (e0)) = (e1))) -> (~((e0) = (e3))) -> ((op (e2) (e1)) = (e2)) -> (~((e2) = (e3))) -> (~((e1) = (e3))) -> (((op (e0) (e1)) = (e3))\/(((op (e1) (e1)) = (e3))\/(((op (e2) (e1)) = (e3))\/((op (e3) (e1)) = (e3))))) -> ((op (e3) (e3)) = (e3)) -> (~((op (e3) (e1)) = (op (e3) (e3)))) -> (((op (e0) (e1)) = (e0))\/(((op (e1) (e1)) = (e0))\/(((op (e2) (e1)) = (e0))\/((op (e3) (e1)) = (e0))))) -> (~((e0) = (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 (e0) (e1)) = (op (e1) (e1)))) -> (~((op (e1) (e1)) = (e3))) -> (~((op (e0) (e0)) = (e2))) -> (((op (e0) (e0)) = (e2))\/(((op (e0) (e1)) = (e2))\/(((op (e0) (e2)) = (e2))\/((op (e0) (e3)) = (e2))))) -> ((op (e0) (e3)) = (e0)) -> (~((e0) = (e1))) -> False). % 15.22/15.39 do 0 intro. intros zenon_H44 zenon_H45 zenon_H4b zenon_H156 zenon_H6a zenon_Ha3 zenon_H199 zenon_H42 zenon_H12d zenon_H144 zenon_H5e zenon_Ha7 zenon_H1b3 zenon_H145 zenon_H1b4 zenon_H23 zenon_H182 zenon_H8f zenon_H8e zenon_Hca zenon_H9e. % 15.22/15.39 apply (zenon_or_s _ _ zenon_H44); [ zenon_intro zenon_H47 | zenon_intro zenon_H46 ]. % 15.22/15.39 exact (zenon_H45 zenon_H47). % 15.22/15.39 apply (zenon_or_s _ _ zenon_H46); [ zenon_intro zenon_H22 | zenon_intro zenon_H48 ]. % 15.22/15.39 apply (zenon_L361_); trivial. % 15.22/15.39 apply (zenon_or_s _ _ zenon_H48); [ zenon_intro zenon_H29 | zenon_intro zenon_H37 ]. % 15.22/15.39 apply (zenon_L339_); trivial. % 15.22/15.39 apply (zenon_L73_); trivial. % 15.22/15.39 (* end of lemma zenon_L362_ *) % 15.22/15.39 assert (zenon_L363_ : (((op (e0) (e0)) = (e2))\/(((op (e0) (e1)) = (e2))\/(((op (e0) (e2)) = (e2))\/((op (e0) (e3)) = (e2))))) -> (~((op (e0) (e0)) = (e2))) -> (~((op (e1) (e1)) = (e3))) -> (~((op (e0) (e1)) = (op (e1) (e1)))) -> (~((op (e1) (e1)) = (e1))) -> (~((op (e1) (e1)) = (e0))) -> (((op (e1) (e1)) = (e0))\/(((op (e1) (e1)) = (e1))\/(((op (e1) (e1)) = (e2))\/((op (e1) (e1)) = (e3))))) -> (~((op (e0) (e3)) = (op (e3) (e3)))) -> ((op (e3) (e3)) = (e3)) -> (~((e2) = (e3))) -> ((op (e0) (e1)) = (e1)) -> (~((e1) = (e3))) -> (((op (e2) (e0)) = (e1))\/(((op (e2) (e1)) = (e1))\/(((op (e2) (e2)) = (e1))\/((op (e2) (e3)) = (e1))))) -> ((op (e2) (e0)) = (e2)) -> (~((e1) = (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 (e2) (e2)) = (e3))) -> (((op (e0) (e0)) = (e3))\/(((op (e0) (e1)) = (e3))\/(((op (e0) (e2)) = (e3))\/((op (e0) (e3)) = (e3))))) -> ((op (e0) (e3)) = (e0)) -> (~((e0) = (e2))) -> False). % 15.22/15.39 do 0 intro. intros zenon_H8e zenon_H8f zenon_H182 zenon_H23 zenon_H1b4 zenon_H145 zenon_H1b3 zenon_H36 zenon_H42 zenon_H6a zenon_H22 zenon_Ha3 zenon_Hb7 zenon_Hdd zenon_Ha7 zenon_Hde zenon_H2d zenon_H52 zenon_H2f zenon_H30 zenon_H58 zenon_Hca zenon_H5e. % 15.22/15.39 apply (zenon_or_s _ _ zenon_H8e); [ zenon_intro zenon_H92 | zenon_intro zenon_H91 ]. % 15.22/15.39 exact (zenon_H8f zenon_H92). % 15.22/15.39 apply (zenon_or_s _ _ zenon_H91); [ zenon_intro zenon_H5d | zenon_intro zenon_H93 ]. % 15.22/15.39 apply (zenon_L214_); trivial. % 15.22/15.39 apply (zenon_or_s _ _ zenon_H93); [ zenon_intro zenon_H63 | zenon_intro zenon_H81 ]. % 15.22/15.39 apply (zenon_L337_); trivial. % 15.22/15.39 apply (zenon_L113_); trivial. % 15.22/15.39 (* end of lemma zenon_L363_ *) % 15.22/15.39 assert (zenon_L364_ : (((op (e0) (e0)) = (e1))\/(((op (e0) (e1)) = (e1))\/(((op (e0) (e2)) = (e1))\/((op (e0) (e3)) = (e1))))) -> (~((op (e0) (e0)) = (e1))) -> (((op (e0) (e0)) = (e3))\/(((op (e0) (e1)) = (e3))\/(((op (e0) (e2)) = (e3))\/((op (e0) (e3)) = (e3))))) -> (~((op (e2) (e2)) = (e3))) -> (~((op (e2) (e2)) = (e2))) -> (~((op (e2) (e2)) = (e1))) -> (((op (e2) (e2)) = (e0))\/(((op (e2) (e2)) = (e1))\/(((op (e2) (e2)) = (e2))\/((op (e2) (e2)) = (e3))))) -> (~((op (e0) (e1)) = (op (e2) (e1)))) -> ((op (e2) (e0)) = (e2)) -> (((op (e2) (e0)) = (e1))\/(((op (e2) (e1)) = (e1))\/(((op (e2) (e2)) = (e1))\/((op (e2) (e3)) = (e1))))) -> (~((e1) = (e3))) -> (~((e2) = (e3))) -> ((op (e3) (e3)) = (e3)) -> (~((op (e0) (e3)) = (op (e3) (e3)))) -> (~((e0) = (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 (e0) (e1)) = (op (e1) (e1)))) -> (~((op (e1) (e1)) = (e3))) -> (~((op (e0) (e0)) = (e2))) -> (((op (e0) (e0)) = (e2))\/(((op (e0) (e1)) = (e2))\/(((op (e0) (e2)) = (e2))\/((op (e0) (e3)) = (e2))))) -> ((op (e0) (e3)) = (e0)) -> (~((e0) = (e1))) -> False). % 15.22/15.39 do 0 intro. intros zenon_H44 zenon_H45 zenon_H58 zenon_H30 zenon_H2f zenon_H52 zenon_H2d zenon_Hde zenon_Hdd zenon_Hb7 zenon_Ha3 zenon_H6a zenon_H42 zenon_H36 zenon_H5e zenon_Ha7 zenon_H1b3 zenon_H145 zenon_H1b4 zenon_H23 zenon_H182 zenon_H8f zenon_H8e zenon_Hca zenon_H9e. % 15.22/15.39 apply (zenon_or_s _ _ zenon_H44); [ zenon_intro zenon_H47 | zenon_intro zenon_H46 ]. % 15.22/15.39 exact (zenon_H45 zenon_H47). % 15.22/15.39 apply (zenon_or_s _ _ zenon_H46); [ zenon_intro zenon_H22 | zenon_intro zenon_H48 ]. % 15.22/15.39 apply (zenon_L363_); trivial. % 15.22/15.39 apply (zenon_or_s _ _ zenon_H48); [ zenon_intro zenon_H29 | zenon_intro zenon_H37 ]. % 15.22/15.39 apply (zenon_L339_); trivial. % 15.22/15.39 apply (zenon_L73_); trivial. % 15.22/15.39 (* end of lemma zenon_L364_ *) % 15.22/15.39 assert (zenon_L365_ : ((~((op (e2) (e2)) = (e1)))\/((op (e2) (e1)) = (e2))) -> (~((op (e2) (e0)) = (op (e2) (e1)))) -> ((~((op (e2) (e2)) = (e3)))\/((op (e2) (e3)) = (e2))) -> (~((op (e2) (e0)) = (op (e2) (e3)))) -> (~((op (e0) (e0)) = (e0))) -> (((op (e0) (e0)) = (e1))\/(((op (e0) (e1)) = (e1))\/(((op (e0) (e2)) = (e1))\/((op (e0) (e3)) = (e1))))) -> (~((op (e0) (e0)) = (e2))) -> (~((e0) = (e2))) -> (~((e1) = (e2))) -> (((op (e0) (e0)) = (e2))\/(((op (e0) (e1)) = (e2))\/(((op (e0) (e2)) = (e2))\/((op (e0) (e3)) = (e2))))) -> (~((op (e0) (e0)) = (e3))) -> (~((e0) = (e3))) -> (~((e1) = (e3))) -> (~((op (e0) (e3)) = (op (e3) (e3)))) -> (((op (e0) (e0)) = (e3))\/(((op (e0) (e1)) = (e3))\/(((op (e0) (e2)) = (e3))\/((op (e0) (e3)) = (e3))))) -> (~((e0) = (e1))) -> (~((e2) = (e3))) -> ((op (e2) (e0)) = (e2)) -> (((op (e2) (e2)) = (e0))\/(((op (e2) (e2)) = (e1))\/(((op (e2) (e2)) = (e2))\/((op (e2) (e2)) = (e3))))) -> (~((op (e2) (e3)) = (op (e3) (e3)))) -> ((op (e3) (e3)) = (e3)) -> (((op (e2) (e0)) = (e3))\/(((op (e2) (e1)) = (e3))\/(((op (e2) (e2)) = (e3))\/((op (e2) (e3)) = (e3))))) -> (~((op (e0) (e1)) = (op (e2) (e1)))) -> (((op (e1) (e1)) = (e0))\/(((op (e1) (e1)) = (e1))\/(((op (e1) (e1)) = (e2))\/((op (e1) (e1)) = (e3))))) -> (~((op (e1) (e1)) = (e3))) -> (~((op (e0) (e1)) = (op (e1) (e1)))) -> (~((op (e1) (e1)) = (e1))) -> (~((op (e1) (e1)) = (e0))) -> (((op (e2) (e0)) = (e1))\/(((op (e2) (e1)) = (e1))\/(((op (e2) (e2)) = (e1))\/((op (e2) (e3)) = (e1))))) -> (~((op (e0) (e0)) = (e1))) -> (((op (e0) (e0)) = (e0))\/(((op (e0) (e1)) = (e0))\/(((op (e0) (e2)) = (e0))\/((op (e0) (e3)) = (e0))))) -> (~((op (e2) (e0)) = (op (e2) (e2)))) -> ((~((op (e2) (e2)) = (e2)))\/((op (e2) (e2)) = (e2))) -> False). % 15.22/15.39 do 0 intro. intros zenon_H1e3 zenon_H154 zenon_H1c3 zenon_Hce zenon_H20 zenon_H44 zenon_H8f zenon_H5e zenon_Ha7 zenon_H8e zenon_H59 zenon_H4b zenon_Ha3 zenon_H36 zenon_H58 zenon_H9e zenon_H6a zenon_Hdd zenon_H2d zenon_He3 zenon_H42 zenon_He6 zenon_Hde zenon_H1b3 zenon_H182 zenon_H23 zenon_H1b4 zenon_H145 zenon_Hb7 zenon_H45 zenon_H110 zenon_H17a zenon_Haa. % 15.22/15.39 apply (zenon_or_s _ _ zenon_H1e3); [ zenon_intro zenon_H52 | zenon_intro zenon_H156 ]. % 15.22/15.39 apply (zenon_or_s _ _ zenon_Haa); [ zenon_intro zenon_H2f | zenon_intro zenon_H35 ]. % 15.22/15.39 apply (zenon_or_s _ _ zenon_H1c3); [ zenon_intro zenon_H30 | zenon_intro zenon_H124 ]. % 15.22/15.39 apply (zenon_or_s _ _ zenon_H110); [ zenon_intro zenon_H1f | zenon_intro zenon_H111 ]. % 15.22/15.39 exact (zenon_H20 zenon_H1f). % 15.22/15.39 apply (zenon_or_s _ _ zenon_H111); [ zenon_intro zenon_H49 | zenon_intro zenon_H112 ]. % 15.22/15.39 apply (zenon_L283_); trivial. % 15.22/15.39 apply (zenon_or_s _ _ zenon_H112); [ zenon_intro zenon_Hab | zenon_intro zenon_Hca ]. % 15.22/15.39 apply (zenon_L68_); trivial. % 15.22/15.39 apply (zenon_L364_); trivial. % 15.22/15.39 apply (zenon_L119_); trivial. % 15.22/15.39 apply (zenon_L161_); trivial. % 15.22/15.39 apply (zenon_L284_); trivial. % 15.22/15.39 (* end of lemma zenon_L365_ *) % 15.22/15.39 assert (zenon_L366_ : (((op (e0) (e3)) = (e2))\/(((op (e1) (e3)) = (e2))\/(((op (e2) (e3)) = (e2))\/((op (e3) (e3)) = (e2))))) -> (~((op (e0) (e1)) = (op (e0) (e3)))) -> ((op (e0) (e1)) = (e2)) -> (~((e1) = (e2))) -> ((op (e1) (e3)) = (e1)) -> ((op (e2) (e3)) = (e0)) -> (~((e0) = (e2))) -> (~((op (e3) (e3)) = (e2))) -> False). % 15.22/15.39 do 0 intro. intros zenon_H160 zenon_H1cd zenon_H5d zenon_Ha7 zenon_H11f zenon_Hd0 zenon_H5e zenon_H3d. % 15.22/15.39 apply (zenon_or_s _ _ zenon_H160); [ zenon_intro zenon_H81 | zenon_intro zenon_H161 ]. % 15.22/15.39 apply (zenon_L350_); trivial. % 15.22/15.39 apply (zenon_or_s _ _ zenon_H161); [ zenon_intro zenon_H82 | zenon_intro zenon_H162 ]. % 15.22/15.39 apply (zenon_L209_); trivial. % 15.22/15.39 apply (zenon_or_s _ _ zenon_H162); [ zenon_intro zenon_H124 | zenon_intro zenon_H43 ]. % 15.22/15.39 apply (zenon_L201_); trivial. % 15.22/15.39 exact (zenon_H3d zenon_H43). % 15.22/15.39 (* end of lemma zenon_L366_ *) % 15.22/15.39 assert (zenon_L367_ : (((op (e0) (e3)) = (e0))\/(((op (e1) (e3)) = (e0))\/(((op (e2) (e3)) = (e0))\/((op (e3) (e3)) = (e0))))) -> ((op (e0) (e3)) = (e1)) -> (~((e0) = (e1))) -> (~((op (e3) (e3)) = (e2))) -> (~((e0) = (e2))) -> ((op (e1) (e3)) = (e1)) -> (~((e1) = (e2))) -> ((op (e0) (e1)) = (e2)) -> (~((op (e0) (e1)) = (op (e0) (e3)))) -> (((op (e0) (e3)) = (e2))\/(((op (e1) (e3)) = (e2))\/(((op (e2) (e3)) = (e2))\/((op (e3) (e3)) = (e2))))) -> (~((op (e3) (e3)) = (e0))) -> False). % 15.22/15.39 do 0 intro. intros zenon_Hd3 zenon_H37 zenon_H9e zenon_H3d zenon_H5e zenon_H11f zenon_Ha7 zenon_H5d zenon_H1cd zenon_H160 zenon_H3c. % 15.22/15.39 apply (zenon_or_s _ _ zenon_Hd3); [ zenon_intro zenon_Hca | zenon_intro zenon_Hd4 ]. % 15.22/15.39 apply (zenon_L73_); trivial. % 15.22/15.39 apply (zenon_or_s _ _ zenon_Hd4); [ zenon_intro zenon_Hcc | zenon_intro zenon_Hd5 ]. % 15.22/15.39 apply (zenon_L208_); trivial. % 15.22/15.39 apply (zenon_or_s _ _ zenon_Hd5); [ zenon_intro zenon_Hd0 | zenon_intro zenon_H40 ]. % 15.22/15.39 apply (zenon_L366_); trivial. % 15.22/15.39 exact (zenon_H3c zenon_H40). % 15.22/15.39 (* end of lemma zenon_L367_ *) % 15.22/15.39 assert (zenon_L368_ : (((op (e0) (e0)) = (e2))\/(((op (e0) (e1)) = (e2))\/(((op (e0) (e2)) = (e2))\/((op (e0) (e3)) = (e2))))) -> (~((op (e0) (e0)) = (e2))) -> (~((op (e3) (e3)) = (e0))) -> (((op (e0) (e3)) = (e2))\/(((op (e1) (e3)) = (e2))\/(((op (e2) (e3)) = (e2))\/((op (e3) (e3)) = (e2))))) -> (~((op (e0) (e1)) = (op (e0) (e3)))) -> ((op (e1) (e3)) = (e1)) -> (~((e0) = (e2))) -> (~((op (e3) (e3)) = (e2))) -> (~((e0) = (e1))) -> (((op (e0) (e3)) = (e0))\/(((op (e1) (e3)) = (e0))\/(((op (e2) (e3)) = (e0))\/((op (e3) (e3)) = (e0))))) -> (~((op (e0) (e2)) = (op (e2) (e2)))) -> ((op (e2) (e2)) = (e2)) -> ((op (e0) (e3)) = (e1)) -> (~((e1) = (e2))) -> False). % 15.22/15.39 do 0 intro. intros zenon_H8e zenon_H8f zenon_H3c zenon_H160 zenon_H1cd zenon_H11f zenon_H5e zenon_H3d zenon_H9e zenon_Hd3 zenon_H28 zenon_H35 zenon_H37 zenon_Ha7. % 15.22/15.39 apply (zenon_or_s _ _ zenon_H8e); [ zenon_intro zenon_H92 | zenon_intro zenon_H91 ]. % 15.22/15.39 exact (zenon_H8f zenon_H92). % 15.22/15.39 apply (zenon_or_s _ _ zenon_H91); [ zenon_intro zenon_H5d | zenon_intro zenon_H93 ]. % 15.22/15.39 apply (zenon_L367_); trivial. % 15.22/15.39 apply (zenon_or_s _ _ zenon_H93); [ zenon_intro zenon_H63 | zenon_intro zenon_H81 ]. % 15.22/15.39 apply (zenon_L15_); trivial. % 15.22/15.39 apply (zenon_L33_); trivial. % 15.22/15.39 (* end of lemma zenon_L368_ *) % 15.22/15.39 assert (zenon_L369_ : (((op (e0) (e0)) = (e1))\/(((op (e0) (e1)) = (e1))\/(((op (e0) (e2)) = (e1))\/((op (e0) (e3)) = (e1))))) -> (((op (e1) (e0)) = (e3))\/(((op (e1) (e1)) = (e3))\/(((op (e1) (e2)) = (e3))\/((op (e1) (e3)) = (e3))))) -> (~((op (e0) (e3)) = (op (e1) (e3)))) -> (~((op (e1) (e2)) = (op (e2) (e2)))) -> (~((e2) = (e3))) -> (((op (e1) (e0)) = (e2))\/(((op (e1) (e1)) = (e2))\/(((op (e1) (e2)) = (e2))\/((op (e1) (e3)) = (e2))))) -> (~((op (e0) (e2)) = (op (e1) (e2)))) -> (~((op (e1) (e3)) = (op (e3) (e3)))) -> (~((op (e0) (e3)) = (op (e3) (e3)))) -> ((op (e3) (e3)) = (e3)) -> (~((e1) = (e3))) -> ((op (e0) (e1)) = (e0)) -> (~((e0) = (e3))) -> (~((op (e0) (e0)) = (e3))) -> (((op (e0) (e0)) = (e3))\/(((op (e0) (e1)) = (e3))\/(((op (e0) (e2)) = (e3))\/((op (e0) (e3)) = (e3))))) -> (((op (e0) (e0)) = (e2))\/(((op (e0) (e1)) = (e2))\/(((op (e0) (e2)) = (e2))\/((op (e0) (e3)) = (e2))))) -> (~((op (e0) (e0)) = (e2))) -> (~((op (e3) (e3)) = (e0))) -> (((op (e0) (e3)) = (e2))\/(((op (e1) (e3)) = (e2))\/(((op (e2) (e3)) = (e2))\/((op (e3) (e3)) = (e2))))) -> (~((op (e0) (e1)) = (op (e0) (e3)))) -> ((op (e1) (e3)) = (e1)) -> (~((e0) = (e2))) -> (~((op (e3) (e3)) = (e2))) -> (~((e0) = (e1))) -> (((op (e0) (e3)) = (e0))\/(((op (e1) (e3)) = (e0))\/(((op (e2) (e3)) = (e0))\/((op (e3) (e3)) = (e0))))) -> (~((op (e0) (e2)) = (op (e2) (e2)))) -> ((op (e2) (e2)) = (e2)) -> (~((e1) = (e2))) -> False). % 15.22/15.39 do 0 intro. intros zenon_H44 zenon_H90 zenon_H80 zenon_H7d zenon_H6a zenon_H84 zenon_H87 zenon_H8b zenon_H36 zenon_H42 zenon_Ha3 zenon_H49 zenon_H4b zenon_H59 zenon_H58 zenon_H8e zenon_H8f zenon_H3c zenon_H160 zenon_H1cd zenon_H11f zenon_H5e zenon_H3d zenon_H9e zenon_Hd3 zenon_H28 zenon_H35 zenon_Ha7. % 15.22/15.39 apply (zenon_or_s _ _ zenon_H44); [ zenon_intro zenon_H47 | zenon_intro zenon_H46 ]. % 15.22/15.39 apply (zenon_L26_); trivial. % 15.22/15.39 apply (zenon_or_s _ _ zenon_H46); [ zenon_intro zenon_H22 | zenon_intro zenon_H48 ]. % 15.22/15.39 apply (zenon_L27_); trivial. % 15.22/15.39 apply (zenon_or_s _ _ zenon_H48); [ zenon_intro zenon_H29 | zenon_intro zenon_H37 ]. % 15.22/15.39 apply (zenon_L30_); trivial. % 15.22/15.39 apply (zenon_L368_); trivial. % 15.22/15.39 (* end of lemma zenon_L369_ *) % 15.22/15.39 assert (zenon_L370_ : ((~((op (e2) (e2)) = (e2)))\/((op (e2) (e2)) = (e2))) -> ((~((op (e3) (e3)) = (e2)))\/((op (e3) (e2)) = (e3))) -> (~((op (e3) (e2)) = (op (e3) (e3)))) -> (((op (e0) (e0)) = (e2))\/(((op (e0) (e1)) = (e2))\/(((op (e0) (e2)) = (e2))\/((op (e0) (e3)) = (e2))))) -> (((op (e1) (e0)) = (e3))\/(((op (e1) (e1)) = (e3))\/(((op (e1) (e2)) = (e3))\/((op (e1) (e3)) = (e3))))) -> (~((op (e1) (e3)) = (op (e3) (e3)))) -> (~((op (e0) (e2)) = (op (e1) (e2)))) -> (~((e2) = (e3))) -> (~((op (e1) (e2)) = (op (e2) (e2)))) -> (~((op (e0) (e3)) = (op (e1) (e3)))) -> (((op (e1) (e0)) = (e2))\/(((op (e1) (e1)) = (e2))\/(((op (e1) (e2)) = (e2))\/((op (e1) (e3)) = (e2))))) -> (~((e0) = (e2))) -> (~((op (e0) (e0)) = (e2))) -> (~((e0) = (e1))) -> (~((e1) = (e3))) -> ((op (e1) (e3)) = (e1)) -> (((op (e0) (e3)) = (e2))\/(((op (e1) (e3)) = (e2))\/(((op (e2) (e3)) = (e2))\/((op (e3) (e3)) = (e2))))) -> (~((e1) = (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)) = (e1))\/(((op (e0) (e1)) = (e1))\/(((op (e0) (e2)) = (e1))\/((op (e0) (e3)) = (e1))))) -> (~((op (e3) (e0)) = (op (e3) (e3)))) -> ((~((op (e3) (e3)) = (e0)))\/((op (e3) (e0)) = (e3))) -> (~((op (e0) (e0)) = (e3))) -> (~((e0) = (e3))) -> ((op (e0) (e1)) = (e0)) -> (((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)) = (e1))) -> (~((op (e2) (e2)) = (e0))) -> (~((op (e0) (e3)) = (op (e3) (e3)))) -> ((op (e3) (e3)) = (e3)) -> (((op (e0) (e0)) = (e3))\/(((op (e0) (e1)) = (e3))\/(((op (e0) (e2)) = (e3))\/((op (e0) (e3)) = (e3))))) -> False). % 15.22/15.39 do 0 intro. intros zenon_Haa zenon_H10e zenon_H173 zenon_H8e zenon_H90 zenon_H8b zenon_H87 zenon_H6a zenon_H7d zenon_H80 zenon_H84 zenon_H5e zenon_H8f zenon_H9e zenon_Ha3 zenon_H11f zenon_H160 zenon_Ha7 zenon_H1cd zenon_Hd3 zenon_H44 zenon_Hbb zenon_H10f zenon_H59 zenon_H4b zenon_H49 zenon_H2d zenon_H28 zenon_H52 zenon_H2e zenon_H36 zenon_H42 zenon_H58. % 15.22/15.39 apply (zenon_or_s _ _ zenon_Haa); [ zenon_intro zenon_H2f | zenon_intro zenon_H35 ]. % 15.22/15.39 apply (zenon_L13_); trivial. % 15.22/15.39 apply (zenon_or_s _ _ zenon_H10f); [ zenon_intro zenon_H3c | zenon_intro zenon_Hba ]. % 15.22/15.39 apply (zenon_or_s _ _ zenon_H10e); [ zenon_intro zenon_H3d | zenon_intro zenon_H106 ]. % 15.22/15.39 apply (zenon_L369_); trivial. % 15.22/15.39 apply (zenon_L153_); trivial. % 15.22/15.39 apply (zenon_L43_); trivial. % 15.22/15.39 (* end of lemma zenon_L370_ *) % 15.22/15.39 assert (zenon_L371_ : (((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)) -> (~((e2) = (e3))) -> ((op (e0) (e2)) = (e2)) -> ((op (e3) (e3)) = (e3)) -> (~((op (e0) (e3)) = (op (e3) (e3)))) -> False). % 15.22/15.39 do 0 intro. intros zenon_H58 zenon_H59 zenon_H4b zenon_H49 zenon_H6a zenon_H63 zenon_H42 zenon_H36. % 15.22/15.39 apply (zenon_or_s _ _ zenon_H58); [ zenon_intro zenon_H5b | zenon_intro zenon_H5a ]. % 15.22/15.39 exact (zenon_H59 zenon_H5b). % 15.22/15.39 apply (zenon_or_s _ _ zenon_H5a); [ zenon_intro zenon_H4a | zenon_intro zenon_H5c ]. % 15.22/15.39 apply (zenon_L9_); trivial. % 15.22/15.39 apply (zenon_or_s _ _ zenon_H5c); [ zenon_intro zenon_H50 | zenon_intro zenon_H53 ]. % 15.22/15.39 apply (zenon_L31_); trivial. % 15.22/15.39 apply (zenon_L12_); trivial. % 15.22/15.39 (* end of lemma zenon_L371_ *) % 15.22/15.39 assert (zenon_L372_ : (~((e1) = (e2))) -> ((op (e2) (e1)) = (e2)) -> ((op (e2) (e1)) = (e1)) -> False). % 15.22/15.39 do 0 intro. intros zenon_Ha7 zenon_H156 zenon_Hb2. % 15.22/15.39 cut (((op (e2) (e1)) = (e2)) = ((e1) = (e2))). % 15.22/15.39 intro zenon_D_pnotp. % 15.22/15.39 apply zenon_Ha7. % 15.22/15.39 rewrite <- zenon_D_pnotp. % 15.22/15.39 exact zenon_H156. % 15.22/15.39 cut (((e2) = (e2))); [idtac | apply NNPP; zenon_intro zenon_H60]. % 15.22/15.39 cut (((op (e2) (e1)) = (e1))); [idtac | apply NNPP; zenon_intro zenon_H226]. % 15.22/15.39 congruence. % 15.22/15.39 exact (zenon_H226 zenon_Hb2). % 15.22/15.39 apply zenon_H60. apply refl_equal. % 15.22/15.39 (* end of lemma zenon_L372_ *) % 15.22/15.39 assert (zenon_L373_ : (((op (e0) (e3)) = (e0))\/(((op (e1) (e3)) = (e0))\/(((op (e2) (e3)) = (e0))\/((op (e3) (e3)) = (e0))))) -> (~((e0) = (e2))) -> ((op (e0) (e3)) = (e2)) -> ((op (e1) (e3)) = (e1)) -> (~((e0) = (e1))) -> ((op (e2) (e0)) = (e0)) -> (~((op (e2) (e0)) = (op (e2) (e3)))) -> (~((op (e3) (e3)) = (e0))) -> False). % 15.22/15.39 do 0 intro. intros zenon_Hd3 zenon_H5e zenon_H81 zenon_H11f zenon_H9e zenon_Hcf zenon_Hce zenon_H3c. % 15.22/15.39 apply (zenon_or_s _ _ zenon_Hd3); [ zenon_intro zenon_Hca | zenon_intro zenon_Hd4 ]. % 15.22/15.39 apply (zenon_L113_); trivial. % 15.22/15.39 apply (zenon_or_s _ _ zenon_Hd4); [ zenon_intro zenon_Hcc | zenon_intro zenon_Hd5 ]. % 15.22/15.39 apply (zenon_L208_); trivial. % 15.22/15.39 apply (zenon_or_s _ _ zenon_Hd5); [ zenon_intro zenon_Hd0 | zenon_intro zenon_H40 ]. % 15.22/15.39 apply (zenon_L55_); trivial. % 15.22/15.39 exact (zenon_H3c zenon_H40). % 15.22/15.39 (* end of lemma zenon_L373_ *) % 15.22/15.39 assert (zenon_L374_ : ((op (e2) (e3)) = (e0)) -> ((op (e1) (e1)) = (e3)) -> ((op (e2) (e2)) = (e1)) -> False). % 15.22/15.39 do 0 intro. intros zenon_Hd0 zenon_H96 zenon_H2a. % 15.22/15.39 apply (zenon_notand_s _ _ ax26); [ zenon_intro zenon_H217 | zenon_intro zenon_H227 ]. % 15.22/15.39 elim (classic ((op (op (e2) (e2)) (op (e2) (e2))) = (op (op (e2) (e2)) (op (e2) (e2))))); [ zenon_intro zenon_Hfa | zenon_intro zenon_Hfb ]. % 15.22/15.39 cut (((op (op (e2) (e2)) (op (e2) (e2))) = (op (op (e2) (e2)) (op (e2) (e2)))) = ((e3) = (op (op (e2) (e2)) (op (e2) (e2))))). % 15.22/15.39 intro zenon_D_pnotp. % 15.22/15.39 apply zenon_H217. % 15.22/15.39 rewrite <- zenon_D_pnotp. % 15.22/15.39 exact zenon_Hfa. % 15.22/15.39 cut (((op (op (e2) (e2)) (op (e2) (e2))) = (op (op (e2) (e2)) (op (e2) (e2))))); [idtac | apply NNPP; zenon_intro zenon_Hfb]. % 15.22/15.39 cut (((op (op (e2) (e2)) (op (e2) (e2))) = (e3))); [idtac | apply NNPP; zenon_intro zenon_H218]. % 15.22/15.39 congruence. % 15.22/15.39 cut (((op (e1) (e1)) = (e3)) = ((op (op (e2) (e2)) (op (e2) (e2))) = (e3))). % 15.22/15.39 intro zenon_D_pnotp. % 15.22/15.39 apply zenon_H218. % 15.22/15.39 rewrite <- zenon_D_pnotp. % 15.22/15.39 exact zenon_H96. % 15.22/15.39 cut (((e3) = (e3))); [idtac | apply NNPP; zenon_intro zenon_H4d]. % 15.22/15.39 cut (((op (e1) (e1)) = (op (op (e2) (e2)) (op (e2) (e2))))); [idtac | apply NNPP; zenon_intro zenon_H1ca]. % 15.22/15.39 congruence. % 15.22/15.39 elim (classic ((op (op (e2) (e2)) (op (e2) (e2))) = (op (op (e2) (e2)) (op (e2) (e2))))); [ zenon_intro zenon_Hfa | zenon_intro zenon_Hfb ]. % 15.22/15.39 cut (((op (op (e2) (e2)) (op (e2) (e2))) = (op (op (e2) (e2)) (op (e2) (e2)))) = ((op (e1) (e1)) = (op (op (e2) (e2)) (op (e2) (e2))))). % 15.22/15.39 intro zenon_D_pnotp. % 15.22/15.39 apply zenon_H1ca. % 15.22/15.39 rewrite <- zenon_D_pnotp. % 15.22/15.39 exact zenon_Hfa. % 15.22/15.39 cut (((op (op (e2) (e2)) (op (e2) (e2))) = (op (op (e2) (e2)) (op (e2) (e2))))); [idtac | apply NNPP; zenon_intro zenon_Hfb]. % 15.22/15.39 cut (((op (op (e2) (e2)) (op (e2) (e2))) = (op (e1) (e1)))); [idtac | apply NNPP; zenon_intro zenon_H1c8]. % 15.22/15.39 congruence. % 15.22/15.39 apply (zenon_L217_); trivial. % 15.22/15.39 apply zenon_Hfb. apply refl_equal. % 15.22/15.39 apply zenon_Hfb. apply refl_equal. % 15.22/15.39 apply zenon_H4d. apply refl_equal. % 15.22/15.39 apply zenon_Hfb. apply refl_equal. % 15.22/15.39 apply zenon_Hfb. apply refl_equal. % 15.22/15.39 apply (zenon_notand_s _ _ zenon_H227); [ zenon_intro zenon_H2b | zenon_intro zenon_H150 ]. % 15.22/15.39 apply zenon_H2b. apply sym_equal. exact zenon_H2a. % 15.22/15.39 elim (classic ((op (e2) (op (op (e2) (e2)) (op (e2) (e2)))) = (op (e2) (op (op (e2) (e2)) (op (e2) (e2)))))); [ zenon_intro zenon_Hff | zenon_intro zenon_H100 ]. % 15.22/15.39 cut (((op (e2) (op (op (e2) (e2)) (op (e2) (e2)))) = (op (e2) (op (op (e2) (e2)) (op (e2) (e2))))) = ((e0) = (op (e2) (op (op (e2) (e2)) (op (e2) (e2)))))). % 15.22/15.39 intro zenon_D_pnotp. % 15.22/15.39 apply zenon_H150. % 15.22/15.39 rewrite <- zenon_D_pnotp. % 15.22/15.39 exact zenon_Hff. % 15.22/15.39 cut (((op (e2) (op (op (e2) (e2)) (op (e2) (e2)))) = (op (e2) (op (op (e2) (e2)) (op (e2) (e2)))))); [idtac | apply NNPP; zenon_intro zenon_H100]. % 15.22/15.39 cut (((op (e2) (op (op (e2) (e2)) (op (e2) (e2)))) = (e0))); [idtac | apply NNPP; zenon_intro zenon_H151]. % 15.22/15.39 congruence. % 15.22/15.39 cut (((op (e2) (e3)) = (e0)) = ((op (e2) (op (op (e2) (e2)) (op (e2) (e2)))) = (e0))). % 15.22/15.39 intro zenon_D_pnotp. % 15.22/15.39 apply zenon_H151. % 15.22/15.39 rewrite <- zenon_D_pnotp. % 15.22/15.39 exact zenon_Hd0. % 15.22/15.39 cut (((e0) = (e0))); [idtac | apply NNPP; zenon_intro zenon_H1d]. % 15.22/15.39 cut (((op (e2) (e3)) = (op (e2) (op (op (e2) (e2)) (op (e2) (e2)))))); [idtac | apply NNPP; zenon_intro zenon_H219]. % 15.22/15.39 congruence. % 15.22/15.39 elim (classic ((op (e2) (op (op (e2) (e2)) (op (e2) (e2)))) = (op (e2) (op (op (e2) (e2)) (op (e2) (e2)))))); [ zenon_intro zenon_Hff | zenon_intro zenon_H100 ]. % 15.22/15.39 cut (((op (e2) (op (op (e2) (e2)) (op (e2) (e2)))) = (op (e2) (op (op (e2) (e2)) (op (e2) (e2))))) = ((op (e2) (e3)) = (op (e2) (op (op (e2) (e2)) (op (e2) (e2)))))). % 15.22/15.39 intro zenon_D_pnotp. % 15.22/15.39 apply zenon_H219. % 15.22/15.39 rewrite <- zenon_D_pnotp. % 15.22/15.39 exact zenon_Hff. % 15.22/15.39 cut (((op (e2) (op (op (e2) (e2)) (op (e2) (e2)))) = (op (e2) (op (op (e2) (e2)) (op (e2) (e2)))))); [idtac | apply NNPP; zenon_intro zenon_H100]. % 15.22/15.39 cut (((op (e2) (op (op (e2) (e2)) (op (e2) (e2)))) = (op (e2) (e3)))); [idtac | apply NNPP; zenon_intro zenon_H21a]. % 15.22/15.39 congruence. % 15.22/15.39 cut (((op (op (e2) (e2)) (op (e2) (e2))) = (e3))); [idtac | apply NNPP; zenon_intro zenon_H218]. % 15.22/15.39 cut (((e2) = (e2))); [idtac | apply NNPP; zenon_intro zenon_H60]. % 15.22/15.39 congruence. % 15.22/15.39 apply zenon_H60. apply refl_equal. % 15.22/15.39 cut (((op (e1) (e1)) = (e3)) = ((op (op (e2) (e2)) (op (e2) (e2))) = (e3))). % 15.22/15.39 intro zenon_D_pnotp. % 15.22/15.39 apply zenon_H218. % 15.22/15.39 rewrite <- zenon_D_pnotp. % 15.22/15.39 exact zenon_H96. % 15.22/15.39 cut (((e3) = (e3))); [idtac | apply NNPP; zenon_intro zenon_H4d]. % 15.22/15.39 cut (((op (e1) (e1)) = (op (op (e2) (e2)) (op (e2) (e2))))); [idtac | apply NNPP; zenon_intro zenon_H1ca]. % 15.22/15.39 congruence. % 15.22/15.39 elim (classic ((op (op (e2) (e2)) (op (e2) (e2))) = (op (op (e2) (e2)) (op (e2) (e2))))); [ zenon_intro zenon_Hfa | zenon_intro zenon_Hfb ]. % 15.22/15.39 cut (((op (op (e2) (e2)) (op (e2) (e2))) = (op (op (e2) (e2)) (op (e2) (e2)))) = ((op (e1) (e1)) = (op (op (e2) (e2)) (op (e2) (e2))))). % 15.22/15.39 intro zenon_D_pnotp. % 15.22/15.39 apply zenon_H1ca. % 15.22/15.39 rewrite <- zenon_D_pnotp. % 15.22/15.39 exact zenon_Hfa. % 15.22/15.39 cut (((op (op (e2) (e2)) (op (e2) (e2))) = (op (op (e2) (e2)) (op (e2) (e2))))); [idtac | apply NNPP; zenon_intro zenon_Hfb]. % 15.22/15.39 cut (((op (op (e2) (e2)) (op (e2) (e2))) = (op (e1) (e1)))); [idtac | apply NNPP; zenon_intro zenon_H1c8]. % 15.22/15.39 congruence. % 15.22/15.39 apply (zenon_L217_); trivial. % 15.22/15.39 apply zenon_Hfb. apply refl_equal. % 15.22/15.39 apply zenon_Hfb. apply refl_equal. % 15.22/15.39 apply zenon_H4d. apply refl_equal. % 15.22/15.39 apply zenon_H100. apply refl_equal. % 15.22/15.39 apply zenon_H100. apply refl_equal. % 15.22/15.39 apply zenon_H1d. apply refl_equal. % 15.22/15.39 apply zenon_H100. apply refl_equal. % 15.22/15.39 apply zenon_H100. apply refl_equal. % 15.22/15.39 (* end of lemma zenon_L374_ *) % 15.22/15.39 assert (zenon_L375_ : (((op (e2) (e2)) = (e0))\/(((op (e2) (e2)) = (e1))\/(((op (e2) (e2)) = (e2))\/((op (e2) (e2)) = (e3))))) -> (~((op (e2) (e2)) = (e0))) -> ((op (e1) (e1)) = (e3)) -> ((op (e2) (e3)) = (e0)) -> (~((op (e2) (e2)) = (e2))) -> (~((op (e2) (e2)) = (e3))) -> False). % 15.22/15.39 do 0 intro. intros zenon_H2d zenon_H2e zenon_H96 zenon_Hd0 zenon_H2f zenon_H30. % 15.22/15.39 apply (zenon_or_s _ _ zenon_H2d); [ zenon_intro zenon_H32 | zenon_intro zenon_H31 ]. % 15.22/15.39 exact (zenon_H2e zenon_H32). % 15.22/15.39 apply (zenon_or_s _ _ zenon_H31); [ zenon_intro zenon_H2a | zenon_intro zenon_H33 ]. % 15.22/15.39 apply (zenon_L374_); trivial. % 15.22/15.39 apply (zenon_or_s _ _ zenon_H33); [ zenon_intro zenon_H35 | zenon_intro zenon_H34 ]. % 15.22/15.39 exact (zenon_H2f zenon_H35). % 15.22/15.39 exact (zenon_H30 zenon_H34). % 15.22/15.39 (* end of lemma zenon_L375_ *) % 15.22/15.39 assert (zenon_L376_ : (((op (e2) (e0)) = (e0))\/(((op (e2) (e1)) = (e0))\/(((op (e2) (e2)) = (e0))\/((op (e2) (e3)) = (e0))))) -> (~((op (e3) (e3)) = (e0))) -> (~((op (e2) (e0)) = (op (e2) (e3)))) -> (~((e0) = (e1))) -> ((op (e1) (e3)) = (e1)) -> ((op (e0) (e3)) = (e2)) -> (((op (e0) (e3)) = (e0))\/(((op (e1) (e3)) = (e0))\/(((op (e2) (e3)) = (e0))\/((op (e3) (e3)) = (e0))))) -> ((op (e2) (e1)) = (e2)) -> (~((e0) = (e2))) -> (((op (e2) (e2)) = (e0))\/(((op (e2) (e2)) = (e1))\/(((op (e2) (e2)) = (e2))\/((op (e2) (e2)) = (e3))))) -> (~((op (e2) (e2)) = (e0))) -> ((op (e1) (e1)) = (e3)) -> (~((op (e2) (e2)) = (e2))) -> (~((op (e2) (e2)) = (e3))) -> False). % 15.22/15.39 do 0 intro. intros zenon_H1f5 zenon_H3c zenon_Hce zenon_H9e zenon_H11f zenon_H81 zenon_Hd3 zenon_H156 zenon_H5e zenon_H2d zenon_H2e zenon_H96 zenon_H2f zenon_H30. % 15.22/15.39 apply (zenon_or_s _ _ zenon_H1f5); [ zenon_intro zenon_Hcf | zenon_intro zenon_H1f9 ]. % 15.22/15.39 apply (zenon_L373_); trivial. % 15.22/15.39 apply (zenon_or_s _ _ zenon_H1f9); [ zenon_intro zenon_H14a | zenon_intro zenon_H1fa ]. % 15.22/15.39 apply (zenon_L351_); trivial. % 15.22/15.39 apply (zenon_or_s _ _ zenon_H1fa); [ zenon_intro zenon_H32 | zenon_intro zenon_Hd0 ]. % 15.22/15.39 exact (zenon_H2e zenon_H32). % 15.22/15.39 apply (zenon_L375_); trivial. % 15.22/15.39 (* end of lemma zenon_L376_ *) % 15.22/15.39 assert (zenon_L377_ : (((op (e0) (e0)) = (e2))\/(((op (e0) (e1)) = (e2))\/(((op (e0) (e2)) = (e2))\/((op (e0) (e3)) = (e2))))) -> (~((op (e0) (e0)) = (e2))) -> (~((op (e0) (e1)) = (op (e2) (e1)))) -> (~((op (e0) (e3)) = (op (e3) (e3)))) -> ((op (e3) (e3)) = (e3)) -> (~((op (e0) (e0)) = (e3))) -> (((op (e0) (e0)) = (e3))\/(((op (e0) (e1)) = (e3))\/(((op (e0) (e2)) = (e3))\/((op (e0) (e3)) = (e3))))) -> (((op (e0) (e1)) = (e1))\/(((op (e1) (e1)) = (e1))\/(((op (e2) (e1)) = (e1))\/((op (e3) (e1)) = (e1))))) -> (~((op (e1) (e1)) = (e1))) -> (~((e1) = (e2))) -> (((op (e0) (e1)) = (e3))\/(((op (e1) (e1)) = (e3))\/(((op (e2) (e1)) = (e3))\/((op (e3) (e1)) = (e3))))) -> (~((e0) = (e3))) -> ((op (e0) (e1)) = (e0)) -> (~((op (e2) (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) = (e2))) -> (((op (e0) (e3)) = (e0))\/(((op (e1) (e3)) = (e0))\/(((op (e2) (e3)) = (e0))\/((op (e3) (e3)) = (e0))))) -> ((op (e1) (e3)) = (e1)) -> (~((e0) = (e1))) -> (~((op (e2) (e0)) = (op (e2) (e3)))) -> (~((op (e3) (e3)) = (e0))) -> (((op (e2) (e0)) = (e0))\/(((op (e2) (e1)) = (e0))\/(((op (e2) (e2)) = (e0))\/((op (e2) (e3)) = (e0))))) -> (~((e2) = (e3))) -> ((op (e2) (e1)) = (e2)) -> (~((e1) = (e3))) -> False). % 15.22/15.39 do 0 intro. intros zenon_H8e zenon_H8f zenon_Hde zenon_H36 zenon_H42 zenon_H59 zenon_H58 zenon_H228 zenon_H1b4 zenon_Ha7 zenon_H199 zenon_H4b zenon_H49 zenon_H30 zenon_H2f zenon_H2e zenon_H2d zenon_H5e zenon_Hd3 zenon_H11f zenon_H9e zenon_Hce zenon_H3c zenon_H1f5 zenon_H6a zenon_H156 zenon_Ha3. % 15.22/15.39 apply (zenon_or_s _ _ zenon_H8e); [ zenon_intro zenon_H92 | zenon_intro zenon_H91 ]. % 15.22/15.39 exact (zenon_H8f zenon_H92). % 15.22/15.39 apply (zenon_or_s _ _ zenon_H91); [ zenon_intro zenon_H5d | zenon_intro zenon_H93 ]. % 15.22/15.39 apply (zenon_L251_); trivial. % 15.22/15.39 apply (zenon_or_s _ _ zenon_H93); [ zenon_intro zenon_H63 | zenon_intro zenon_H81 ]. % 15.22/15.39 apply (zenon_L371_); trivial. % 15.22/15.39 apply (zenon_or_s _ _ zenon_H228); [ zenon_intro zenon_H22 | zenon_intro zenon_H229 ]. % 15.22/15.39 apply (zenon_L27_); trivial. % 15.22/15.39 apply (zenon_or_s _ _ zenon_H229); [ zenon_intro zenon_H21 | zenon_intro zenon_H22a ]. % 15.22/15.39 exact (zenon_H1b4 zenon_H21). % 15.22/15.39 apply (zenon_or_s _ _ zenon_H22a); [ zenon_intro zenon_Hb2 | zenon_intro zenon_H13e ]. % 15.22/15.39 apply (zenon_L372_); trivial. % 15.22/15.39 apply (zenon_or_s _ _ zenon_H199); [ zenon_intro zenon_H4a | zenon_intro zenon_H19a ]. % 15.22/15.39 apply (zenon_L9_); trivial. % 15.22/15.39 apply (zenon_or_s _ _ zenon_H19a); [ zenon_intro zenon_H96 | zenon_intro zenon_H19b ]. % 15.22/15.39 apply (zenon_L376_); trivial. % 15.22/15.39 apply (zenon_or_s _ _ zenon_H19b); [ zenon_intro zenon_Hdf | zenon_intro zenon_H10a ]. % 15.22/15.39 apply (zenon_L183_); trivial. % 15.22/15.39 apply (zenon_L123_); trivial. % 15.22/15.39 (* end of lemma zenon_L377_ *) % 15.22/15.39 assert (zenon_L378_ : ((~((op (e1) (e1)) = (e3)))\/((op (e1) (e3)) = (e1))) -> ((~((op (e2) (e2)) = (e1)))\/((op (e2) (e1)) = (e2))) -> ((~((op (e2) (e2)) = (e3)))\/((op (e2) (e3)) = (e2))) -> (~((op (e2) (e1)) = (op (e2) (e3)))) -> (((op (e0) (e1)) = (e3))\/(((op (e1) (e1)) = (e3))\/(((op (e2) (e1)) = (e3))\/((op (e3) (e1)) = (e3))))) -> (~((op (e2) (e0)) = (op (e2) (e3)))) -> (((op (e2) (e0)) = (e0))\/(((op (e2) (e1)) = (e0))\/(((op (e2) (e2)) = (e0))\/((op (e2) (e3)) = (e0))))) -> (((op (e0) (e1)) = (e1))\/(((op (e1) (e1)) = (e1))\/(((op (e2) (e1)) = (e1))\/((op (e3) (e1)) = (e1))))) -> (~((op (e0) (e1)) = (op (e2) (e1)))) -> (~((op (e2) (e1)) = (op (e2) (e2)))) -> (((op (e0) (e0)) = (e3))\/(((op (e0) (e1)) = (e3))\/(((op (e0) (e2)) = (e3))\/((op (e0) (e3)) = (e3))))) -> ((op (e3) (e3)) = (e3)) -> (~((op (e0) (e3)) = (op (e3) (e3)))) -> (~((op (e0) (e2)) = (op (e2) (e2)))) -> (((op (e2) (e2)) = (e0))\/(((op (e2) (e2)) = (e1))\/(((op (e2) (e2)) = (e2))\/((op (e2) (e2)) = (e3))))) -> (~((e0) = (e3))) -> (~((op (e0) (e0)) = (e3))) -> ((~((op (e3) (e3)) = (e0)))\/((op (e3) (e0)) = (e3))) -> (~((op (e3) (e0)) = (op (e3) (e3)))) -> (((op (e0) (e0)) = (e1))\/(((op (e0) (e1)) = (e1))\/(((op (e0) (e2)) = (e1))\/((op (e0) (e3)) = (e1))))) -> (((op (e0) (e3)) = (e0))\/(((op (e1) (e3)) = (e0))\/(((op (e2) (e3)) = (e0))\/((op (e3) (e3)) = (e0))))) -> (~((op (e0) (e1)) = (op (e0) (e3)))) -> (~((e1) = (e2))) -> (((op (e0) (e3)) = (e2))\/(((op (e1) (e3)) = (e2))\/(((op (e2) (e3)) = (e2))\/((op (e3) (e3)) = (e2))))) -> (~((e1) = (e3))) -> (~((e0) = (e1))) -> (~((op (e0) (e0)) = (e2))) -> (~((e0) = (e2))) -> (((op (e1) (e0)) = (e2))\/(((op (e1) (e1)) = (e2))\/(((op (e1) (e2)) = (e2))\/((op (e1) (e3)) = (e2))))) -> (~((op (e0) (e3)) = (op (e1) (e3)))) -> (~((op (e1) (e2)) = (op (e2) (e2)))) -> (~((e2) = (e3))) -> (~((op (e0) (e2)) = (op (e1) (e2)))) -> (~((op (e1) (e3)) = (op (e3) (e3)))) -> (((op (e1) (e0)) = (e3))\/(((op (e1) (e1)) = (e3))\/(((op (e1) (e2)) = (e3))\/((op (e1) (e3)) = (e3))))) -> (((op (e0) (e0)) = (e2))\/(((op (e0) (e1)) = (e2))\/(((op (e0) (e2)) = (e2))\/((op (e0) (e3)) = (e2))))) -> (~((op (e3) (e2)) = (op (e3) (e3)))) -> ((~((op (e3) (e3)) = (e2)))\/((op (e3) (e2)) = (e3))) -> ((~((op (e2) (e2)) = (e2)))\/((op (e2) (e2)) = (e2))) -> (~((op (e2) (e0)) = (op (e2) (e1)))) -> (((op (e2) (e0)) = (e3))\/(((op (e2) (e1)) = (e3))\/(((op (e2) (e2)) = (e3))\/((op (e2) (e3)) = (e3))))) -> (~((op (e2) (e3)) = (op (e3) (e3)))) -> (~((op (e2) (e0)) = (op (e2) (e2)))) -> ((~((op (e2) (e2)) = (e0)))\/((op (e2) (e0)) = (e2))) -> (~((op (e0) (e1)) = (op (e1) (e1)))) -> ((op (e0) (e1)) = (e0)) -> (~((op (e1) (e1)) = (e1))) -> (~((op (e1) (e1)) = (e2))) -> (((op (e1) (e1)) = (e0))\/(((op (e1) (e1)) = (e1))\/(((op (e1) (e1)) = (e2))\/((op (e1) (e1)) = (e3))))) -> False). % 15.22/15.40 do 0 intro. intros zenon_H1d2 zenon_H1e3 zenon_H1c3 zenon_H1e2 zenon_H199 zenon_Hce zenon_H1f5 zenon_H228 zenon_Hde zenon_H157 zenon_H58 zenon_H42 zenon_H36 zenon_H28 zenon_H2d zenon_H4b zenon_H59 zenon_H10f zenon_Hbb zenon_H44 zenon_Hd3 zenon_H1cd zenon_Ha7 zenon_H160 zenon_Ha3 zenon_H9e zenon_H8f zenon_H5e zenon_H84 zenon_H80 zenon_H7d zenon_H6a zenon_H87 zenon_H8b zenon_H90 zenon_H8e zenon_H173 zenon_H10e zenon_Haa zenon_H154 zenon_He6 zenon_He3 zenon_H17a zenon_H1d4 zenon_H23 zenon_H49 zenon_H1b4 zenon_Hd6 zenon_H1b3. % 15.22/15.40 apply (zenon_or_s _ _ zenon_H1d2); [ zenon_intro zenon_H182 | zenon_intro zenon_H11f ]. % 15.22/15.40 apply (zenon_L347_); trivial. % 15.22/15.40 apply (zenon_or_s _ _ zenon_H1d4); [ zenon_intro zenon_H2e | zenon_intro zenon_Hdd ]. % 15.22/15.40 apply (zenon_or_s _ _ zenon_H1e3); [ zenon_intro zenon_H52 | zenon_intro zenon_H156 ]. % 15.22/15.40 apply (zenon_L370_); trivial. % 15.22/15.40 apply (zenon_or_s _ _ zenon_Haa); [ zenon_intro zenon_H2f | zenon_intro zenon_H35 ]. % 15.22/15.40 apply (zenon_or_s _ _ zenon_H1c3); [ zenon_intro zenon_H30 | zenon_intro zenon_H124 ]. % 15.22/15.40 apply (zenon_or_s _ _ zenon_H10f); [ zenon_intro zenon_H3c | zenon_intro zenon_Hba ]. % 15.22/15.40 apply (zenon_L377_); trivial. % 15.22/15.40 apply (zenon_L43_); trivial. % 15.22/15.40 apply (zenon_L256_); trivial. % 15.22/15.40 apply (zenon_L134_); trivial. % 15.22/15.40 apply (zenon_L285_); trivial. % 15.22/15.40 (* end of lemma zenon_L378_ *) % 15.22/15.40 assert (zenon_L379_ : (((op (e1) (e0)) = (e3))\/(((op (e1) (e1)) = (e3))\/(((op (e1) (e2)) = (e3))\/((op (e1) (e3)) = (e3))))) -> (~((e2) = (e3))) -> ((op (e1) (e0)) = (e2)) -> (~((op (e1) (e1)) = (e3))) -> ((op (e0) (e2)) = (e3)) -> (~((op (e0) (e2)) = (op (e1) (e2)))) -> ((op (e3) (e3)) = (e3)) -> (~((op (e1) (e3)) = (op (e3) (e3)))) -> False). % 15.22/15.40 do 0 intro. intros zenon_H90 zenon_H6a zenon_H68 zenon_H182 zenon_H50 zenon_H87 zenon_H42 zenon_H8b. % 15.22/15.40 apply (zenon_or_s _ _ zenon_H90); [ zenon_intro zenon_H69 | zenon_intro zenon_H94 ]. % 15.22/15.40 apply (zenon_L17_); trivial. % 15.22/15.40 apply (zenon_or_s _ _ zenon_H94); [ zenon_intro zenon_H96 | zenon_intro zenon_H95 ]. % 15.22/15.40 exact (zenon_H182 zenon_H96). % 15.22/15.40 apply (zenon_or_s _ _ zenon_H95); [ zenon_intro zenon_H88 | zenon_intro zenon_H8a ]. % 15.22/15.40 apply (zenon_L24_); trivial. % 15.22/15.40 apply (zenon_L25_); trivial. % 15.22/15.40 (* end of lemma zenon_L379_ *) % 15.22/15.40 assert (zenon_L380_ : (((op (e0) (e0)) = (e2))\/(((op (e0) (e1)) = (e2))\/(((op (e0) (e2)) = (e2))\/((op (e0) (e3)) = (e2))))) -> (~((op (e0) (e0)) = (e2))) -> (~((op (e1) (e1)) = (e3))) -> (~((op (e0) (e1)) = (op (e1) (e1)))) -> (~((op (e1) (e1)) = (e1))) -> (~((op (e1) (e1)) = (e0))) -> (((op (e1) (e1)) = (e0))\/(((op (e1) (e1)) = (e1))\/(((op (e1) (e1)) = (e2))\/((op (e1) (e1)) = (e3))))) -> (~((op (e0) (e2)) = (op (e2) (e2)))) -> ((op (e2) (e2)) = (e2)) -> ((op (e0) (e3)) = (e1)) -> (~((e1) = (e2))) -> False). % 15.22/15.40 do 0 intro. intros zenon_H8e zenon_H8f zenon_H182 zenon_H23 zenon_H1b4 zenon_H145 zenon_H1b3 zenon_H28 zenon_H35 zenon_H37 zenon_Ha7. % 15.22/15.40 apply (zenon_or_s _ _ zenon_H8e); [ zenon_intro zenon_H92 | zenon_intro zenon_H91 ]. % 15.22/15.40 exact (zenon_H8f zenon_H92). % 15.22/15.40 apply (zenon_or_s _ _ zenon_H91); [ zenon_intro zenon_H5d | zenon_intro zenon_H93 ]. % 15.22/15.40 apply (zenon_L214_); trivial. % 15.22/15.40 apply (zenon_or_s _ _ zenon_H93); [ zenon_intro zenon_H63 | zenon_intro zenon_H81 ]. % 15.22/15.40 apply (zenon_L15_); trivial. % 15.22/15.40 apply (zenon_L33_); trivial. % 15.22/15.40 (* end of lemma zenon_L380_ *) % 15.22/15.40 assert (zenon_L381_ : (((op (e0) (e0)) = (e1))\/(((op (e0) (e1)) = (e1))\/(((op (e0) (e2)) = (e1))\/((op (e0) (e3)) = (e1))))) -> (~((e2) = (e3))) -> (((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 (e1) (e2)))) -> (((op (e1) (e0)) = (e3))\/(((op (e1) (e1)) = (e3))\/(((op (e1) (e2)) = (e3))\/((op (e1) (e3)) = (e3))))) -> ((op (e1) (e2)) = (e1)) -> (~((op (e0) (e3)) = (op (e1) (e3)))) -> (~((e0) = (e2))) -> (~((e0) = (e1))) -> (~((op (e0) (e3)) = (op (e3) (e3)))) -> ((op (e3) (e3)) = (e3)) -> (~((e1) = (e3))) -> ((op (e0) (e1)) = (e0)) -> (~((e0) = (e3))) -> (~((op (e0) (e0)) = (e3))) -> (((op (e0) (e0)) = (e3))\/(((op (e0) (e1)) = (e3))\/(((op (e0) (e2)) = (e3))\/((op (e0) (e3)) = (e3))))) -> (((op (e0) (e0)) = (e2))\/(((op (e0) (e1)) = (e2))\/(((op (e0) (e2)) = (e2))\/((op (e0) (e3)) = (e2))))) -> (~((op (e0) (e0)) = (e2))) -> (~((op (e1) (e1)) = (e3))) -> (~((op (e0) (e1)) = (op (e1) (e1)))) -> (~((op (e1) (e1)) = (e1))) -> (~((op (e1) (e1)) = (e0))) -> (((op (e1) (e1)) = (e0))\/(((op (e1) (e1)) = (e1))\/(((op (e1) (e1)) = (e2))\/((op (e1) (e1)) = (e3))))) -> (~((op (e0) (e2)) = (op (e2) (e2)))) -> ((op (e2) (e2)) = (e2)) -> (~((e1) = (e2))) -> False). % 15.22/15.40 do 0 intro. intros zenon_H44 zenon_H6a zenon_H84 zenon_H8b zenon_H87 zenon_H90 zenon_H117 zenon_H80 zenon_H5e zenon_H9e zenon_H36 zenon_H42 zenon_Ha3 zenon_H49 zenon_H4b zenon_H59 zenon_H58 zenon_H8e zenon_H8f zenon_H182 zenon_H23 zenon_H1b4 zenon_H145 zenon_H1b3 zenon_H28 zenon_H35 zenon_Ha7. % 15.22/15.40 apply (zenon_or_s _ _ zenon_H44); [ zenon_intro zenon_H47 | zenon_intro zenon_H46 ]. % 15.22/15.40 apply (zenon_or_s _ _ zenon_H8e); [ zenon_intro zenon_H92 | zenon_intro zenon_H91 ]. % 15.22/15.40 exact (zenon_H8f zenon_H92). % 15.22/15.40 apply (zenon_or_s _ _ zenon_H91); [ zenon_intro zenon_H5d | zenon_intro zenon_H93 ]. % 15.22/15.40 apply (zenon_L14_); trivial. % 15.22/15.40 apply (zenon_or_s _ _ zenon_H93); [ zenon_intro zenon_H63 | zenon_intro zenon_H81 ]. % 15.22/15.40 apply (zenon_L371_); trivial. % 15.22/15.40 apply (zenon_or_s _ _ zenon_H58); [ zenon_intro zenon_H5b | zenon_intro zenon_H5a ]. % 15.22/15.40 exact (zenon_H59 zenon_H5b). % 15.22/15.40 apply (zenon_or_s _ _ zenon_H5a); [ zenon_intro zenon_H4a | zenon_intro zenon_H5c ]. % 15.22/15.40 apply (zenon_L9_); trivial. % 15.22/15.40 apply (zenon_or_s _ _ zenon_H5c); [ zenon_intro zenon_H50 | zenon_intro zenon_H53 ]. % 15.22/15.40 apply (zenon_or_s _ _ zenon_H84); [ zenon_intro zenon_H68 | zenon_intro zenon_H85 ]. % 15.22/15.40 apply (zenon_L379_); trivial. % 15.22/15.40 apply (zenon_or_s _ _ zenon_H85); [ zenon_intro zenon_H6e | zenon_intro zenon_H86 ]. % 15.22/15.40 apply (zenon_L20_); trivial. % 15.22/15.40 apply (zenon_or_s _ _ zenon_H86); [ zenon_intro zenon_H7c | zenon_intro zenon_H82 ]. % 15.22/15.40 apply (zenon_L204_); trivial. % 15.22/15.40 apply (zenon_L22_); trivial. % 15.22/15.40 apply (zenon_L128_); trivial. % 15.22/15.40 apply (zenon_or_s _ _ zenon_H46); [ zenon_intro zenon_H22 | zenon_intro zenon_H48 ]. % 15.22/15.40 apply (zenon_L27_); trivial. % 15.22/15.40 apply (zenon_or_s _ _ zenon_H48); [ zenon_intro zenon_H29 | zenon_intro zenon_H37 ]. % 15.22/15.40 apply (zenon_L30_); trivial. % 15.22/15.40 apply (zenon_L380_); trivial. % 15.22/15.40 (* end of lemma zenon_L381_ *) % 15.22/15.40 assert (zenon_L382_ : ((~((op (e2) (e2)) = (e2)))\/((op (e2) (e2)) = (e2))) -> (((op (e0) (e0)) = (e2))\/(((op (e0) (e1)) = (e2))\/(((op (e0) (e2)) = (e2))\/((op (e0) (e3)) = (e2))))) -> (((op (e1) (e0)) = (e2))\/(((op (e1) (e1)) = (e2))\/(((op (e1) (e2)) = (e2))\/((op (e1) (e3)) = (e2))))) -> (~((op (e0) (e3)) = (op (e1) (e3)))) -> ((op (e1) (e2)) = (e1)) -> (~((e1) = (e2))) -> (~((op (e1) (e1)) = (e3))) -> (~((op (e0) (e2)) = (op (e1) (e2)))) -> (~((op (e1) (e3)) = (op (e3) (e3)))) -> (((op (e1) (e0)) = (e3))\/(((op (e1) (e1)) = (e3))\/(((op (e1) (e2)) = (e3))\/((op (e1) (e3)) = (e3))))) -> (~((e2) = (e3))) -> (~((e0) = (e2))) -> (~((op (e0) (e0)) = (e2))) -> (~((e0) = (e1))) -> (~((e1) = (e3))) -> (~((op (e1) (e1)) = (e0))) -> (~((op (e1) (e1)) = (e1))) -> (~((op (e0) (e1)) = (op (e1) (e1)))) -> (((op (e1) (e1)) = (e0))\/(((op (e1) (e1)) = (e1))\/(((op (e1) (e1)) = (e2))\/((op (e1) (e1)) = (e3))))) -> (((op (e0) (e0)) = (e1))\/(((op (e0) (e1)) = (e1))\/(((op (e0) (e2)) = (e1))\/((op (e0) (e3)) = (e1))))) -> (~((op (e0) (e0)) = (e3))) -> (~((e0) = (e3))) -> ((op (e0) (e1)) = (e0)) -> (((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)) = (e1))) -> (~((op (e2) (e2)) = (e0))) -> (~((op (e0) (e3)) = (op (e3) (e3)))) -> ((op (e3) (e3)) = (e3)) -> (((op (e0) (e0)) = (e3))\/(((op (e0) (e1)) = (e3))\/(((op (e0) (e2)) = (e3))\/((op (e0) (e3)) = (e3))))) -> False). % 15.22/15.40 do 0 intro. intros zenon_Haa zenon_H8e zenon_H84 zenon_H80 zenon_H117 zenon_Ha7 zenon_H182 zenon_H87 zenon_H8b zenon_H90 zenon_H6a zenon_H5e zenon_H8f zenon_H9e zenon_Ha3 zenon_H145 zenon_H1b4 zenon_H23 zenon_H1b3 zenon_H44 zenon_H59 zenon_H4b zenon_H49 zenon_H2d zenon_H28 zenon_H52 zenon_H2e zenon_H36 zenon_H42 zenon_H58. % 15.22/15.40 apply (zenon_or_s _ _ zenon_Haa); [ zenon_intro zenon_H2f | zenon_intro zenon_H35 ]. % 15.22/15.40 apply (zenon_L13_); trivial. % 15.22/15.40 apply (zenon_L381_); trivial. % 15.22/15.40 (* end of lemma zenon_L382_ *) % 15.22/15.40 assert (zenon_L383_ : ((op (e1) (e0)) = (e3)) -> ((op (e2) (e2)) = (e0)) -> ((op (e1) (e1)) = (e2)) -> False). % 15.22/15.40 do 0 intro. intros zenon_H69 zenon_H32 zenon_H6e. % 15.22/15.40 apply (zenon_notand_s _ _ ax9); [ zenon_intro zenon_H21e | zenon_intro zenon_H22b ]. % 15.22/15.40 elim (classic ((op (op (e1) (e1)) (op (e1) (e1))) = (op (op (e1) (e1)) (op (e1) (e1))))); [ zenon_intro zenon_H1a8 | zenon_intro zenon_H1a9 ]. % 15.22/15.40 cut (((op (op (e1) (e1)) (op (e1) (e1))) = (op (op (e1) (e1)) (op (e1) (e1)))) = ((e0) = (op (op (e1) (e1)) (op (e1) (e1))))). % 15.22/15.40 intro zenon_D_pnotp. % 15.22/15.40 apply zenon_H21e. % 15.22/15.40 rewrite <- zenon_D_pnotp. % 15.22/15.40 exact zenon_H1a8. % 15.22/15.40 cut (((op (op (e1) (e1)) (op (e1) (e1))) = (op (op (e1) (e1)) (op (e1) (e1))))); [idtac | apply NNPP; zenon_intro zenon_H1a9]. % 15.22/15.40 cut (((op (op (e1) (e1)) (op (e1) (e1))) = (e0))); [idtac | apply NNPP; zenon_intro zenon_H21f]. % 15.22/15.40 congruence. % 15.22/15.40 cut (((op (e2) (e2)) = (e0)) = ((op (op (e1) (e1)) (op (e1) (e1))) = (e0))). % 15.22/15.40 intro zenon_D_pnotp. % 15.22/15.40 apply zenon_H21f. % 15.22/15.40 rewrite <- zenon_D_pnotp. % 15.22/15.40 exact zenon_H32. % 15.22/15.40 cut (((e0) = (e0))); [idtac | apply NNPP; zenon_intro zenon_H1d]. % 15.22/15.40 cut (((op (e2) (e2)) = (op (op (e1) (e1)) (op (e1) (e1))))); [idtac | apply NNPP; zenon_intro zenon_H1bb]. % 15.22/15.40 congruence. % 15.22/15.40 elim (classic ((op (op (e1) (e1)) (op (e1) (e1))) = (op (op (e1) (e1)) (op (e1) (e1))))); [ zenon_intro zenon_H1a8 | zenon_intro zenon_H1a9 ]. % 15.22/15.40 cut (((op (op (e1) (e1)) (op (e1) (e1))) = (op (op (e1) (e1)) (op (e1) (e1)))) = ((op (e2) (e2)) = (op (op (e1) (e1)) (op (e1) (e1))))). % 15.22/15.40 intro zenon_D_pnotp. % 15.22/15.40 apply zenon_H1bb. % 15.22/15.40 rewrite <- zenon_D_pnotp. % 15.22/15.40 exact zenon_H1a8. % 15.22/15.40 cut (((op (op (e1) (e1)) (op (e1) (e1))) = (op (op (e1) (e1)) (op (e1) (e1))))); [idtac | apply NNPP; zenon_intro zenon_H1a9]. % 15.22/15.40 cut (((op (op (e1) (e1)) (op (e1) (e1))) = (op (e2) (e2)))); [idtac | apply NNPP; zenon_intro zenon_H1b7]. % 15.22/15.40 congruence. % 15.22/15.40 apply (zenon_L199_); trivial. % 15.22/15.40 apply zenon_H1a9. apply refl_equal. % 15.22/15.40 apply zenon_H1a9. apply refl_equal. % 15.22/15.40 apply zenon_H1d. apply refl_equal. % 15.22/15.40 apply zenon_H1a9. apply refl_equal. % 15.22/15.40 apply zenon_H1a9. apply refl_equal. % 15.22/15.40 apply (zenon_notand_s _ _ zenon_H22b); [ zenon_intro zenon_H1bd | zenon_intro zenon_H1ac ]. % 15.22/15.40 apply zenon_H1bd. apply sym_equal. exact zenon_H6e. % 15.22/15.40 elim (classic ((op (e1) (op (op (e1) (e1)) (op (e1) (e1)))) = (op (e1) (op (op (e1) (e1)) (op (e1) (e1)))))); [ zenon_intro zenon_H1ae | zenon_intro zenon_H1af ]. % 15.22/15.40 cut (((op (e1) (op (op (e1) (e1)) (op (e1) (e1)))) = (op (e1) (op (op (e1) (e1)) (op (e1) (e1))))) = ((e3) = (op (e1) (op (op (e1) (e1)) (op (e1) (e1)))))). % 15.22/15.40 intro zenon_D_pnotp. % 15.22/15.40 apply zenon_H1ac. % 15.22/15.40 rewrite <- zenon_D_pnotp. % 15.22/15.40 exact zenon_H1ae. % 15.22/15.40 cut (((op (e1) (op (op (e1) (e1)) (op (e1) (e1)))) = (op (e1) (op (op (e1) (e1)) (op (e1) (e1)))))); [idtac | apply NNPP; zenon_intro zenon_H1af]. % 15.22/15.40 cut (((op (e1) (op (op (e1) (e1)) (op (e1) (e1)))) = (e3))); [idtac | apply NNPP; zenon_intro zenon_H1b0]. % 15.22/15.40 congruence. % 15.22/15.40 cut (((op (e1) (e0)) = (e3)) = ((op (e1) (op (op (e1) (e1)) (op (e1) (e1)))) = (e3))). % 15.22/15.40 intro zenon_D_pnotp. % 15.22/15.40 apply zenon_H1b0. % 15.22/15.40 rewrite <- zenon_D_pnotp. % 15.22/15.40 exact zenon_H69. % 15.22/15.40 cut (((e3) = (e3))); [idtac | apply NNPP; zenon_intro zenon_H4d]. % 15.22/15.40 cut (((op (e1) (e0)) = (op (e1) (op (op (e1) (e1)) (op (e1) (e1)))))); [idtac | apply NNPP; zenon_intro zenon_H224]. % 15.22/15.40 congruence. % 15.22/15.40 elim (classic ((op (e1) (op (op (e1) (e1)) (op (e1) (e1)))) = (op (e1) (op (op (e1) (e1)) (op (e1) (e1)))))); [ zenon_intro zenon_H1ae | zenon_intro zenon_H1af ]. % 15.22/15.40 cut (((op (e1) (op (op (e1) (e1)) (op (e1) (e1)))) = (op (e1) (op (op (e1) (e1)) (op (e1) (e1))))) = ((op (e1) (e0)) = (op (e1) (op (op (e1) (e1)) (op (e1) (e1)))))). % 15.22/15.40 intro zenon_D_pnotp. % 15.22/15.40 apply zenon_H224. % 15.22/15.40 rewrite <- zenon_D_pnotp. % 15.22/15.40 exact zenon_H1ae. % 15.22/15.40 cut (((op (e1) (op (op (e1) (e1)) (op (e1) (e1)))) = (op (e1) (op (op (e1) (e1)) (op (e1) (e1)))))); [idtac | apply NNPP; zenon_intro zenon_H1af]. % 15.22/15.40 cut (((op (e1) (op (op (e1) (e1)) (op (e1) (e1)))) = (op (e1) (e0)))); [idtac | apply NNPP; zenon_intro zenon_H225]. % 15.22/15.40 congruence. % 15.22/15.40 cut (((op (op (e1) (e1)) (op (e1) (e1))) = (e0))); [idtac | apply NNPP; zenon_intro zenon_H21f]. % 15.22/15.40 cut (((e1) = (e1))); [idtac | apply NNPP; zenon_intro zenon_Ha0]. % 15.22/15.40 congruence. % 15.22/15.40 apply zenon_Ha0. apply refl_equal. % 15.22/15.40 cut (((op (e2) (e2)) = (e0)) = ((op (op (e1) (e1)) (op (e1) (e1))) = (e0))). % 15.22/15.40 intro zenon_D_pnotp. % 15.22/15.40 apply zenon_H21f. % 15.22/15.40 rewrite <- zenon_D_pnotp. % 15.22/15.40 exact zenon_H32. % 15.22/15.40 cut (((e0) = (e0))); [idtac | apply NNPP; zenon_intro zenon_H1d]. % 15.22/15.40 cut (((op (e2) (e2)) = (op (op (e1) (e1)) (op (e1) (e1))))); [idtac | apply NNPP; zenon_intro zenon_H1bb]. % 15.22/15.40 congruence. % 15.22/15.40 elim (classic ((op (op (e1) (e1)) (op (e1) (e1))) = (op (op (e1) (e1)) (op (e1) (e1))))); [ zenon_intro zenon_H1a8 | zenon_intro zenon_H1a9 ]. % 15.22/15.40 cut (((op (op (e1) (e1)) (op (e1) (e1))) = (op (op (e1) (e1)) (op (e1) (e1)))) = ((op (e2) (e2)) = (op (op (e1) (e1)) (op (e1) (e1))))). % 15.22/15.40 intro zenon_D_pnotp. % 15.22/15.40 apply zenon_H1bb. % 15.22/15.40 rewrite <- zenon_D_pnotp. % 15.22/15.40 exact zenon_H1a8. % 15.22/15.40 cut (((op (op (e1) (e1)) (op (e1) (e1))) = (op (op (e1) (e1)) (op (e1) (e1))))); [idtac | apply NNPP; zenon_intro zenon_H1a9]. % 15.22/15.40 cut (((op (op (e1) (e1)) (op (e1) (e1))) = (op (e2) (e2)))); [idtac | apply NNPP; zenon_intro zenon_H1b7]. % 15.22/15.40 congruence. % 15.22/15.40 apply (zenon_L199_); trivial. % 15.22/15.40 apply zenon_H1a9. apply refl_equal. % 15.22/15.40 apply zenon_H1a9. apply refl_equal. % 15.22/15.40 apply zenon_H1d. apply refl_equal. % 15.22/15.40 apply zenon_H1af. apply refl_equal. % 15.22/15.40 apply zenon_H1af. apply refl_equal. % 15.22/15.40 apply zenon_H4d. apply refl_equal. % 15.22/15.40 apply zenon_H1af. apply refl_equal. % 15.22/15.40 apply zenon_H1af. apply refl_equal. % 15.22/15.40 (* end of lemma zenon_L383_ *) % 15.22/15.40 assert (zenon_L384_ : (((op (e2) (e2)) = (e0))\/(((op (e2) (e2)) = (e1))\/(((op (e2) (e2)) = (e2))\/((op (e2) (e2)) = (e3))))) -> ((op (e1) (e1)) = (e2)) -> ((op (e1) (e0)) = (e3)) -> (~((op (e2) (e2)) = (e1))) -> (~((op (e2) (e2)) = (e2))) -> (~((op (e2) (e2)) = (e3))) -> False). % 15.22/15.40 do 0 intro. intros zenon_H2d zenon_H6e zenon_H69 zenon_H52 zenon_H2f zenon_H30. % 15.22/15.40 apply (zenon_or_s _ _ zenon_H2d); [ zenon_intro zenon_H32 | zenon_intro zenon_H31 ]. % 15.22/15.40 apply (zenon_L383_); trivial. % 15.22/15.40 apply (zenon_or_s _ _ zenon_H31); [ zenon_intro zenon_H2a | zenon_intro zenon_H33 ]. % 15.22/15.40 exact (zenon_H52 zenon_H2a). % 15.22/15.40 apply (zenon_or_s _ _ zenon_H33); [ zenon_intro zenon_H35 | zenon_intro zenon_H34 ]. % 15.22/15.40 exact (zenon_H2f zenon_H35). % 15.22/15.40 exact (zenon_H30 zenon_H34). % 15.22/15.40 (* end of lemma zenon_L384_ *) % 15.22/15.40 assert (zenon_L385_ : (((op (e1) (e0)) = (e2))\/(((op (e1) (e1)) = (e2))\/(((op (e1) (e2)) = (e2))\/((op (e1) (e3)) = (e2))))) -> (~((e2) = (e3))) -> (~((op (e2) (e2)) = (e3))) -> (~((op (e2) (e2)) = (e2))) -> (~((op (e2) (e2)) = (e1))) -> ((op (e1) (e0)) = (e3)) -> (((op (e2) (e2)) = (e0))\/(((op (e2) (e2)) = (e1))\/(((op (e2) (e2)) = (e2))\/((op (e2) (e2)) = (e3))))) -> (~((e1) = (e2))) -> ((op (e1) (e2)) = (e1)) -> (~((op (e0) (e3)) = (op (e1) (e3)))) -> ((op (e0) (e3)) = (e2)) -> False). % 15.22/15.40 do 0 intro. intros zenon_H84 zenon_H6a zenon_H30 zenon_H2f zenon_H52 zenon_H69 zenon_H2d zenon_Ha7 zenon_H117 zenon_H80 zenon_H81. % 15.22/15.40 apply (zenon_or_s _ _ zenon_H84); [ zenon_intro zenon_H68 | zenon_intro zenon_H85 ]. % 15.22/15.40 apply (zenon_L17_); trivial. % 15.22/15.40 apply (zenon_or_s _ _ zenon_H85); [ zenon_intro zenon_H6e | zenon_intro zenon_H86 ]. % 15.22/15.40 apply (zenon_L384_); trivial. % 15.22/15.40 apply (zenon_or_s _ _ zenon_H86); [ zenon_intro zenon_H7c | zenon_intro zenon_H82 ]. % 15.22/15.40 apply (zenon_L204_); trivial. % 15.22/15.40 apply (zenon_L22_); trivial. % 15.22/15.40 (* end of lemma zenon_L385_ *) % 15.22/15.40 assert (zenon_L386_ : (((op (e0) (e0)) = (e3))\/(((op (e1) (e0)) = (e3))\/(((op (e2) (e0)) = (e3))\/((op (e3) (e0)) = (e3))))) -> (~((op (e0) (e0)) = (e3))) -> ((op (e0) (e3)) = (e2)) -> (~((op (e0) (e3)) = (op (e1) (e3)))) -> ((op (e1) (e2)) = (e1)) -> (~((e1) = (e2))) -> (((op (e2) (e2)) = (e0))\/(((op (e2) (e2)) = (e1))\/(((op (e2) (e2)) = (e2))\/((op (e2) (e2)) = (e3))))) -> (~((op (e2) (e2)) = (e1))) -> (~((op (e2) (e2)) = (e2))) -> (~((op (e2) (e2)) = (e3))) -> (((op (e1) (e0)) = (e2))\/(((op (e1) (e1)) = (e2))\/(((op (e1) (e2)) = (e2))\/((op (e1) (e3)) = (e2))))) -> (~((e2) = (e3))) -> ((op (e2) (e0)) = (e2)) -> ((op (e3) (e3)) = (e3)) -> (~((op (e3) (e0)) = (op (e3) (e3)))) -> False). % 15.22/15.40 do 0 intro. intros zenon_Hbe zenon_H59 zenon_H81 zenon_H80 zenon_H117 zenon_Ha7 zenon_H2d zenon_H52 zenon_H2f zenon_H30 zenon_H84 zenon_H6a zenon_Hdd zenon_H42 zenon_Hbb. % 15.22/15.40 apply (zenon_or_s _ _ zenon_Hbe); [ zenon_intro zenon_H5b | zenon_intro zenon_Hbf ]. % 15.22/15.40 exact (zenon_H59 zenon_H5b). % 15.22/15.40 apply (zenon_or_s _ _ zenon_Hbf); [ zenon_intro zenon_H69 | zenon_intro zenon_Hc0 ]. % 15.22/15.40 apply (zenon_L385_); trivial. % 15.22/15.40 apply (zenon_or_s _ _ zenon_Hc0); [ zenon_intro zenon_Haf | zenon_intro zenon_Hba ]. % 15.22/15.40 apply (zenon_L64_); trivial. % 15.22/15.40 apply (zenon_L43_); trivial. % 15.22/15.40 (* end of lemma zenon_L386_ *) % 15.22/15.40 assert (zenon_L387_ : ((~((op (e1) (e1)) = (e2)))\/((op (e1) (e2)) = (e1))) -> (((op (e0) (e0)) = (e3))\/(((op (e1) (e0)) = (e3))\/(((op (e2) (e0)) = (e3))\/((op (e3) (e0)) = (e3))))) -> (~((op (e1) (e1)) = (e0))) -> (~((op (e3) (e1)) = (op (e3) (e3)))) -> (~((op (e1) (e2)) = (op (e1) (e3)))) -> (((op (e1) (e1)) = (e0))\/(((op (e1) (e1)) = (e1))\/(((op (e1) (e1)) = (e2))\/((op (e1) (e1)) = (e3))))) -> (~((op (e1) (e1)) = (e1))) -> ((op (e0) (e1)) = (e0)) -> (~((op (e0) (e1)) = (op (e1) (e1)))) -> ((~((op (e2) (e2)) = (e0)))\/((op (e2) (e0)) = (e2))) -> (~((op (e2) (e0)) = (op (e2) (e2)))) -> (~((op (e2) (e3)) = (op (e3) (e3)))) -> (((op (e2) (e0)) = (e3))\/(((op (e2) (e1)) = (e3))\/(((op (e2) (e2)) = (e3))\/((op (e2) (e3)) = (e3))))) -> (~((op (e2) (e0)) = (op (e2) (e1)))) -> ((~((op (e2) (e2)) = (e2)))\/((op (e2) (e2)) = (e2))) -> ((~((op (e3) (e3)) = (e2)))\/((op (e3) (e2)) = (e3))) -> (~((op (e3) (e2)) = (op (e3) (e3)))) -> (((op (e0) (e0)) = (e2))\/(((op (e0) (e1)) = (e2))\/(((op (e0) (e2)) = (e2))\/((op (e0) (e3)) = (e2))))) -> (((op (e1) (e0)) = (e3))\/(((op (e1) (e1)) = (e3))\/(((op (e1) (e2)) = (e3))\/((op (e1) (e3)) = (e3))))) -> (~((op (e1) (e3)) = (op (e3) (e3)))) -> (~((op (e0) (e2)) = (op (e1) (e2)))) -> (~((e2) = (e3))) -> (~((op (e1) (e2)) = (op (e2) (e2)))) -> (~((op (e0) (e3)) = (op (e1) (e3)))) -> (((op (e1) (e0)) = (e2))\/(((op (e1) (e1)) = (e2))\/(((op (e1) (e2)) = (e2))\/((op (e1) (e3)) = (e2))))) -> (~((e0) = (e2))) -> (~((op (e0) (e0)) = (e2))) -> (~((e0) = (e1))) -> (~((e1) = (e3))) -> (((op (e0) (e3)) = (e2))\/(((op (e1) (e3)) = (e2))\/(((op (e2) (e3)) = (e2))\/((op (e3) (e3)) = (e2))))) -> (~((e1) = (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)) = (e1))\/(((op (e0) (e1)) = (e1))\/(((op (e0) (e2)) = (e1))\/((op (e0) (e3)) = (e1))))) -> (~((op (e3) (e0)) = (op (e3) (e3)))) -> ((~((op (e3) (e3)) = (e0)))\/((op (e3) (e0)) = (e3))) -> (~((op (e0) (e0)) = (e3))) -> (~((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 (e0) (e3)) = (op (e3) (e3)))) -> ((op (e3) (e3)) = (e3)) -> (((op (e0) (e0)) = (e3))\/(((op (e0) (e1)) = (e3))\/(((op (e0) (e2)) = (e3))\/((op (e0) (e3)) = (e3))))) -> (~((op (e2) (e1)) = (op (e2) (e2)))) -> (~((op (e0) (e1)) = (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) (e1)) = (e0))\/(((op (e2) (e2)) = (e0))\/((op (e2) (e3)) = (e0))))) -> (~((op (e2) (e0)) = (op (e2) (e3)))) -> (((op (e0) (e1)) = (e3))\/(((op (e1) (e1)) = (e3))\/(((op (e2) (e1)) = (e3))\/((op (e3) (e1)) = (e3))))) -> (~((op (e2) (e1)) = (op (e2) (e3)))) -> ((~((op (e2) (e2)) = (e3)))\/((op (e2) (e3)) = (e2))) -> ((~((op (e2) (e2)) = (e1)))\/((op (e2) (e1)) = (e2))) -> ((~((op (e1) (e1)) = (e3)))\/((op (e1) (e3)) = (e1))) -> False). % 15.22/15.40 do 0 intro. intros zenon_H1d3 zenon_Hbe zenon_H145 zenon_H12d zenon_H1d0 zenon_H1b3 zenon_H1b4 zenon_H49 zenon_H23 zenon_H1d4 zenon_H17a zenon_He3 zenon_He6 zenon_H154 zenon_Haa zenon_H10e zenon_H173 zenon_H8e zenon_H90 zenon_H8b zenon_H87 zenon_H6a zenon_H7d zenon_H80 zenon_H84 zenon_H5e zenon_H8f zenon_H9e zenon_Ha3 zenon_H160 zenon_Ha7 zenon_H1cd zenon_Hd3 zenon_H44 zenon_Hbb zenon_H10f zenon_H59 zenon_H4b zenon_H2d zenon_H28 zenon_H36 zenon_H42 zenon_H58 zenon_H157 zenon_Hde zenon_H228 zenon_H1f5 zenon_Hce zenon_H199 zenon_H1e2 zenon_H1c3 zenon_H1e3 zenon_H1d2. % 15.22/15.40 apply (zenon_or_s _ _ zenon_H1d3); [ zenon_intro zenon_Hd6 | zenon_intro zenon_H117 ]. % 15.22/15.40 apply (zenon_L378_); trivial. % 15.22/15.40 apply (zenon_or_s _ _ zenon_H1d2); [ zenon_intro zenon_H182 | zenon_intro zenon_H11f ]. % 15.22/15.40 apply (zenon_or_s _ _ zenon_H1d4); [ zenon_intro zenon_H2e | zenon_intro zenon_Hdd ]. % 15.22/15.40 apply (zenon_or_s _ _ zenon_H1e3); [ zenon_intro zenon_H52 | zenon_intro zenon_H156 ]. % 15.22/15.40 apply (zenon_L382_); trivial. % 15.22/15.40 apply (zenon_L278_); trivial. % 15.22/15.40 apply (zenon_or_s _ _ zenon_H1e3); [ zenon_intro zenon_H52 | zenon_intro zenon_H156 ]. % 15.22/15.40 apply (zenon_or_s _ _ zenon_Haa); [ zenon_intro zenon_H2f | zenon_intro zenon_H35 ]. % 15.22/15.40 apply (zenon_or_s _ _ zenon_H1c3); [ zenon_intro zenon_H30 | zenon_intro zenon_H124 ]. % 15.22/15.40 apply (zenon_or_s _ _ zenon_H8e); [ zenon_intro zenon_H92 | zenon_intro zenon_H91 ]. % 15.22/15.40 exact (zenon_H8f zenon_H92). % 15.22/15.40 apply (zenon_or_s _ _ zenon_H91); [ zenon_intro zenon_H5d | zenon_intro zenon_H93 ]. % 15.22/15.40 apply (zenon_L14_); trivial. % 15.22/15.40 apply (zenon_or_s _ _ zenon_H93); [ zenon_intro zenon_H63 | zenon_intro zenon_H81 ]. % 15.22/15.40 apply (zenon_L371_); trivial. % 15.22/15.40 apply (zenon_L386_); trivial. % 15.22/15.40 apply (zenon_L119_); trivial. % 15.22/15.40 apply (zenon_L161_); trivial. % 15.22/15.40 apply (zenon_L278_); trivial. % 15.22/15.40 apply (zenon_L237_); trivial. % 15.22/15.40 (* end of lemma zenon_L387_ *) % 15.22/15.40 assert (zenon_L388_ : (((op (e1) (e0)) = (e2))\/(((op (e1) (e1)) = (e2))\/(((op (e1) (e2)) = (e2))\/((op (e1) (e3)) = (e2))))) -> (~((e0) = (e2))) -> ((op (e1) (e0)) = (e0)) -> (~((op (e1) (e1)) = (e2))) -> ((op (e0) (e1)) = (e2)) -> (~((op (e1) (op (e0) (e1))) = (op (e0) (e1)))) -> ((op (e1) (e3)) = (e1)) -> (~((e1) = (e2))) -> False). % 15.22/15.40 do 0 intro. intros zenon_H84 zenon_H5e zenon_Had zenon_Hd6 zenon_H5d zenon_H1ff zenon_H11f zenon_Ha7. % 15.22/15.40 apply (zenon_or_s _ _ zenon_H84); [ zenon_intro zenon_H68 | zenon_intro zenon_H85 ]. % 15.22/15.40 apply (zenon_L160_); trivial. % 15.22/15.40 apply (zenon_or_s _ _ zenon_H85); [ zenon_intro zenon_H6e | zenon_intro zenon_H86 ]. % 15.22/15.40 exact (zenon_Hd6 zenon_H6e). % 15.22/15.40 apply (zenon_or_s _ _ zenon_H86); [ zenon_intro zenon_H7c | zenon_intro zenon_H82 ]. % 15.22/15.40 cut (((op (e1) (e2)) = (e2)) = ((op (e1) (op (e0) (e1))) = (op (e0) (e1)))). % 15.22/15.40 intro zenon_D_pnotp. % 15.22/15.40 apply zenon_H1ff. % 15.22/15.40 rewrite <- zenon_D_pnotp. % 15.22/15.40 exact zenon_H7c. % 15.22/15.40 cut (((e2) = (op (e0) (e1)))); [idtac | apply NNPP; zenon_intro zenon_H1dc]. % 15.22/15.40 cut (((op (e1) (e2)) = (op (e1) (op (e0) (e1))))); [idtac | apply NNPP; zenon_intro zenon_H22c]. % 15.22/15.40 congruence. % 15.22/15.40 elim (classic ((op (e1) (op (e0) (e1))) = (op (e1) (op (e0) (e1))))); [ zenon_intro zenon_H202 | zenon_intro zenon_H203 ]. % 15.22/15.40 cut (((op (e1) (op (e0) (e1))) = (op (e1) (op (e0) (e1)))) = ((op (e1) (e2)) = (op (e1) (op (e0) (e1))))). % 15.22/15.40 intro zenon_D_pnotp. % 15.22/15.40 apply zenon_H22c. % 15.22/15.40 rewrite <- zenon_D_pnotp. % 15.22/15.40 exact zenon_H202. % 15.22/15.40 cut (((op (e1) (op (e0) (e1))) = (op (e1) (op (e0) (e1))))); [idtac | apply NNPP; zenon_intro zenon_H203]. % 15.22/15.40 cut (((op (e1) (op (e0) (e1))) = (op (e1) (e2)))); [idtac | apply NNPP; zenon_intro zenon_H22d]. % 15.22/15.40 congruence. % 15.22/15.40 cut (((op (e0) (e1)) = (e2))); [idtac | apply NNPP; zenon_intro zenon_H62]. % 15.22/15.40 cut (((e1) = (e1))); [idtac | apply NNPP; zenon_intro zenon_Ha0]. % 15.22/15.40 congruence. % 15.22/15.40 apply zenon_Ha0. apply refl_equal. % 15.22/15.40 exact (zenon_H62 zenon_H5d). % 15.22/15.40 apply zenon_H203. apply refl_equal. % 15.22/15.40 apply zenon_H203. apply refl_equal. % 15.22/15.40 apply zenon_H1dc. apply sym_equal. exact zenon_H5d. % 15.22/15.40 apply (zenon_L209_); trivial. % 15.22/15.40 (* end of lemma zenon_L388_ *) % 15.22/15.40 assert (zenon_L389_ : (((op (e0) (e3)) = (e2))\/(((op (e1) (e3)) = (e2))\/(((op (e2) (e3)) = (e2))\/((op (e3) (e3)) = (e2))))) -> (~((e0) = (e2))) -> ((op (e0) (e3)) = (e0)) -> (~((e1) = (e2))) -> ((op (e1) (e3)) = (e1)) -> ((op (e2) (e0)) = (e2)) -> (~((op (e2) (e0)) = (op (e2) (e3)))) -> (~((op (e3) (e3)) = (e2))) -> False). % 15.22/15.40 do 0 intro. intros zenon_H160 zenon_H5e zenon_Hca zenon_Ha7 zenon_H11f zenon_Hdd zenon_Hce zenon_H3d. % 15.22/15.40 apply (zenon_or_s _ _ zenon_H160); [ zenon_intro zenon_H81 | zenon_intro zenon_H161 ]. % 15.22/15.40 apply (zenon_L113_); trivial. % 15.22/15.40 apply (zenon_or_s _ _ zenon_H161); [ zenon_intro zenon_H82 | zenon_intro zenon_H162 ]. % 15.22/15.40 apply (zenon_L209_); trivial. % 15.22/15.40 apply (zenon_or_s _ _ zenon_H162); [ zenon_intro zenon_H124 | zenon_intro zenon_H43 ]. % 15.22/15.40 apply (zenon_L119_); trivial. % 15.22/15.40 exact (zenon_H3d zenon_H43). % 15.22/15.40 (* end of lemma zenon_L389_ *) % 15.22/15.40 assert (zenon_L390_ : (((op (e0) (e0)) = (e2))\/(((op (e1) (e0)) = (e2))\/(((op (e2) (e0)) = (e2))\/((op (e3) (e0)) = (e2))))) -> (~((op (e0) (e0)) = (e2))) -> ((op (e1) (e0)) = (e0)) -> (~((op (e3) (e3)) = (e2))) -> (~((op (e2) (e0)) = (op (e2) (e3)))) -> ((op (e1) (e3)) = (e1)) -> ((op (e0) (e3)) = (e0)) -> (~((e0) = (e2))) -> (((op (e0) (e3)) = (e2))\/(((op (e1) (e3)) = (e2))\/(((op (e2) (e3)) = (e2))\/((op (e3) (e3)) = (e2))))) -> ((op (e3) (e0)) = (e1)) -> (~((e1) = (e2))) -> False). % 15.22/15.40 do 0 intro. intros zenon_Heb zenon_H8f zenon_Had zenon_H3d zenon_Hce zenon_H11f zenon_Hca zenon_H5e zenon_H160 zenon_Hee zenon_Ha7. % 15.22/15.40 apply (zenon_or_s _ _ zenon_Heb); [ zenon_intro zenon_H92 | zenon_intro zenon_Hec ]. % 15.22/15.40 exact (zenon_H8f zenon_H92). % 15.22/15.40 apply (zenon_or_s _ _ zenon_Hec); [ zenon_intro zenon_H68 | zenon_intro zenon_Hed ]. % 15.22/15.40 apply (zenon_L160_); trivial. % 15.22/15.40 apply (zenon_or_s _ _ zenon_Hed); [ zenon_intro zenon_Hdd | zenon_intro zenon_He9 ]. % 15.22/15.40 apply (zenon_L389_); trivial. % 15.22/15.40 apply (zenon_L122_); trivial. % 15.22/15.40 (* end of lemma zenon_L390_ *) % 15.22/15.40 assert (zenon_L391_ : ((~((op (e3) (e3)) = (e2)))\/((op (e3) (e2)) = (e3))) -> (~((op (e3) (e2)) = (op (e3) (e3)))) -> (~((op (e0) (e0)) = (e0))) -> (((op (e0) (e0)) = (e1))\/(((op (e0) (e1)) = (e1))\/(((op (e0) (e2)) = (e1))\/((op (e0) (e3)) = (e1))))) -> (~((op (e3) (e3)) = (e0))) -> (((op (e0) (e3)) = (e0))\/(((op (e1) (e3)) = (e0))\/(((op (e2) (e3)) = (e0))\/((op (e3) (e3)) = (e0))))) -> (((op (e0) (e0)) = (e3))\/(((op (e0) (e1)) = (e3))\/(((op (e0) (e2)) = (e3))\/((op (e0) (e3)) = (e3))))) -> ((op (e3) (e3)) = (e3)) -> (~((op (e0) (e3)) = (op (e3) (e3)))) -> (~((op (e2) (e2)) = (e0))) -> (~((op (e0) (e2)) = (op (e2) (e2)))) -> (~((e1) = (e3))) -> (~((e0) = (e1))) -> ((op (e0) (e3)) = (e0)) -> (~((op (e1) (e0)) = (op (e1) (e3)))) -> (((op (e2) (e2)) = (e0))\/(((op (e2) (e2)) = (e1))\/(((op (e2) (e2)) = (e2))\/((op (e2) (e2)) = (e3))))) -> (~((op (e2) (e2)) = (e3))) -> (~((op (e2) (e2)) = (e2))) -> (~((op (e2) (e2)) = (e1))) -> (~((op (e3) (e3)) = (e1))) -> (((op (e0) (e3)) = (e1))\/(((op (e1) (e3)) = (e1))\/(((op (e2) (e3)) = (e1))\/((op (e3) (e3)) = (e1))))) -> (((op (e0) (e0)) = (e2))\/(((op (e0) (e1)) = (e2))\/(((op (e0) (e2)) = (e2))\/((op (e0) (e3)) = (e2))))) -> (~((op (e0) (e2)) = (op (e1) (e2)))) -> (~((op (e2) (e0)) = (op (e2) (e3)))) -> (~((op (e0) (e1)) = (op (e0) (e3)))) -> (~((e0) = (e2))) -> (~((op (e1) (e1)) = (e2))) -> (~((op (e1) (op (e0) (e1))) = (op (e0) (e1)))) -> (~((e1) = (e2))) -> ((op (e1) (e3)) = (e1)) -> (((op (e1) (e0)) = (e2))\/(((op (e1) (e1)) = (e2))\/(((op (e1) (e2)) = (e2))\/((op (e1) (e3)) = (e2))))) -> (~((op (e0) (e0)) = (e2))) -> (((op (e0) (e0)) = (e2))\/(((op (e1) (e0)) = (e2))\/(((op (e2) (e0)) = (e2))\/((op (e3) (e0)) = (e2))))) -> (((op (e0) (e3)) = (e2))\/(((op (e1) (e3)) = (e2))\/(((op (e2) (e3)) = (e2))\/((op (e3) (e3)) = (e2))))) -> (((op (e0) (e0)) = (e1))\/(((op (e1) (e0)) = (e1))\/(((op (e2) (e0)) = (e1))\/((op (e3) (e0)) = (e1))))) -> (~((op (e0) (e0)) = (e1))) -> (((op (e1) (e0)) = (e0))\/(((op (e1) (e1)) = (e0))\/(((op (e1) (e2)) = (e0))\/((op (e1) (e3)) = (e0))))) -> (~((op (e1) (e2)) = (op (e2) (e2)))) -> (~((op (e1) (e1)) = (e0))) -> (~((op (e3) (op (e0) (e3))) = (op (e0) (e3)))) -> (((op (e0) (e0)) = (e0))\/(((op (e1) (e0)) = (e0))\/(((op (e2) (e0)) = (e0))\/((op (e3) (e0)) = (e0))))) -> False). % 15.22/15.40 do 0 intro. intros zenon_H10e zenon_H173 zenon_H20 zenon_H44 zenon_H3c zenon_Hd3 zenon_H58 zenon_H42 zenon_H36 zenon_H2e zenon_H28 zenon_Ha3 zenon_H9e zenon_Hca zenon_H1cf zenon_H2d zenon_H30 zenon_H2f zenon_H52 zenon_H104 zenon_H121 zenon_H8e zenon_H87 zenon_Hce zenon_H1cd zenon_H5e zenon_Hd6 zenon_H1ff zenon_Ha7 zenon_H11f zenon_H84 zenon_H8f zenon_Heb zenon_H160 zenon_Hf1 zenon_H45 zenon_H163 zenon_H7d zenon_H145 zenon_H192 zenon_Hf0. % 15.22/15.40 apply (zenon_or_s _ _ zenon_H10e); [ zenon_intro zenon_H3d | zenon_intro zenon_H106 ]. % 15.22/15.40 apply (zenon_or_s _ _ zenon_Hf0); [ zenon_intro zenon_H1f | zenon_intro zenon_Hf2 ]. % 15.22/15.40 exact (zenon_H20 zenon_H1f). % 15.22/15.40 apply (zenon_or_s _ _ zenon_Hf2); [ zenon_intro zenon_Had | zenon_intro zenon_Hf3 ]. % 15.22/15.40 apply (zenon_or_s _ _ zenon_H44); [ zenon_intro zenon_H47 | zenon_intro zenon_H46 ]. % 15.22/15.40 exact (zenon_H45 zenon_H47). % 15.22/15.40 apply (zenon_or_s _ _ zenon_H46); [ zenon_intro zenon_H22 | zenon_intro zenon_H48 ]. % 15.22/15.40 apply (zenon_or_s _ _ zenon_Hf1); [ zenon_intro zenon_H47 | zenon_intro zenon_Hf4 ]. % 15.22/15.40 exact (zenon_H45 zenon_H47). % 15.22/15.40 apply (zenon_or_s _ _ zenon_Hf4); [ zenon_intro zenon_Hd8 | zenon_intro zenon_Hf5 ]. % 15.22/15.40 apply (zenon_L331_); trivial. % 15.22/15.40 apply (zenon_or_s _ _ zenon_Hf5); [ zenon_intro zenon_Hae | zenon_intro zenon_Hee ]. % 15.22/15.40 apply (zenon_or_s _ _ zenon_H8e); [ zenon_intro zenon_H92 | zenon_intro zenon_H91 ]. % 15.22/15.40 exact (zenon_H8f zenon_H92). % 15.22/15.40 apply (zenon_or_s _ _ zenon_H91); [ zenon_intro zenon_H5d | zenon_intro zenon_H93 ]. % 15.22/15.40 apply (zenon_L388_); trivial. % 15.22/15.40 apply (zenon_or_s _ _ zenon_H93); [ zenon_intro zenon_H63 | zenon_intro zenon_H81 ]. % 15.22/15.40 apply (zenon_L333_); trivial. % 15.22/15.40 apply (zenon_L113_); trivial. % 15.22/15.40 apply (zenon_L390_); trivial. % 15.22/15.40 apply (zenon_or_s _ _ zenon_H48); [ zenon_intro zenon_H29 | zenon_intro zenon_H37 ]. % 15.22/15.40 apply (zenon_L5_); trivial. % 15.22/15.40 apply (zenon_L211_); trivial. % 15.22/15.40 apply (zenon_or_s _ _ zenon_Hf3); [ zenon_intro zenon_Hcf | zenon_intro zenon_Hdb ]. % 15.22/15.40 apply (zenon_or_s _ _ zenon_H44); [ zenon_intro zenon_H47 | zenon_intro zenon_H46 ]. % 15.22/15.40 exact (zenon_H45 zenon_H47). % 15.22/15.40 apply (zenon_or_s _ _ zenon_H46); [ zenon_intro zenon_H22 | zenon_intro zenon_H48 ]. % 15.22/15.40 apply (zenon_or_s _ _ zenon_Hf1); [ zenon_intro zenon_H47 | zenon_intro zenon_Hf4 ]. % 15.22/15.40 exact (zenon_H45 zenon_H47). % 15.22/15.40 apply (zenon_or_s _ _ zenon_Hf4); [ zenon_intro zenon_Hd8 | zenon_intro zenon_Hf5 ]. % 15.22/15.40 apply (zenon_L331_); trivial. % 15.22/15.40 apply (zenon_or_s _ _ zenon_Hf5); [ zenon_intro zenon_Hae | zenon_intro zenon_Hee ]. % 15.22/15.40 apply (zenon_L269_); trivial. % 15.22/15.40 apply (zenon_or_s _ _ zenon_H163); [ zenon_intro zenon_Had | zenon_intro zenon_H164 ]. % 15.22/15.40 apply (zenon_L390_); trivial. % 15.22/15.40 apply (zenon_or_s _ _ zenon_H164); [ zenon_intro zenon_H149 | zenon_intro zenon_H165 ]. % 15.22/15.40 exact (zenon_H145 zenon_H149). % 15.22/15.40 apply (zenon_or_s _ _ zenon_H165); [ zenon_intro zenon_H15d | zenon_intro zenon_Hcc ]. % 15.22/15.40 apply (zenon_L335_); trivial. % 15.22/15.40 apply (zenon_L208_); trivial. % 15.22/15.40 apply (zenon_or_s _ _ zenon_H48); [ zenon_intro zenon_H29 | zenon_intro zenon_H37 ]. % 15.22/15.40 apply (zenon_L5_); trivial. % 15.22/15.40 apply (zenon_L73_); trivial. % 15.22/15.40 apply (zenon_L178_); trivial. % 15.22/15.40 apply (zenon_L153_); trivial. % 15.22/15.40 (* end of lemma zenon_L391_ *) % 15.22/15.40 assert (zenon_L392_ : ((~((op (e3) (e3)) = (e3)))\/((op (e3) (e3)) = (e3))) -> (~((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) (e2)) = (e2))) -> (~((op (e2) (e2)) = (e1))) -> (~((op (e2) (e2)) = (e0))) -> (~((op (e0) (e3)) = (op (e3) (e3)))) -> (((op (e0) (e0)) = (e3))\/(((op (e0) (e1)) = (e3))\/(((op (e0) (e2)) = (e3))\/((op (e0) (e3)) = (e3))))) -> (~((e0) = (e2))) -> ((op (e0) (e1)) = (e0)) -> (~((op (e1) (e1)) = (e2))) -> (~((op (e2) (e1)) = (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) (e3)) = (e2))) -> (~((op (e3) (e3)) = (e1))) -> (~((op (e0) (e0)) = (e0))) -> (~((op (e0) (e0)) = (e2))) -> (~((op (e0) (e0)) = (e3))) -> (((op (e0) (e0)) = (e0))\/(((op (e0) (e0)) = (e1))\/(((op (e0) (e0)) = (e2))\/((op (e0) (e0)) = (e3))))) -> (((op (e0) (e1)) = (e2))\/(((op (e1) (e1)) = (e2))\/(((op (e2) (e1)) = (e2))\/((op (e3) (e1)) = (e2))))) -> False). % 15.22/15.40 do 0 intro. intros zenon_H10d zenon_H4b zenon_H2d zenon_H28 zenon_H2f zenon_H52 zenon_H2e zenon_H36 zenon_H58 zenon_H5e zenon_H49 zenon_Hd6 zenon_H1e2 zenon_H124 zenon_H3b zenon_H3d zenon_H104 zenon_H20 zenon_H8f zenon_H59 zenon_H12a zenon_H1a2. % 15.22/15.40 apply (zenon_or_s _ _ zenon_H10d); [ zenon_intro zenon_H3e | zenon_intro zenon_H42 ]. % 15.22/15.40 apply (zenon_or_s _ _ zenon_H1a2); [ zenon_intro zenon_H5d | zenon_intro zenon_H1a3 ]. % 15.22/15.40 apply (zenon_L14_); trivial. % 15.22/15.40 apply (zenon_or_s _ _ zenon_H1a3); [ zenon_intro zenon_H6e | zenon_intro zenon_H1a4 ]. % 15.22/15.40 exact (zenon_Hd6 zenon_H6e). % 15.22/15.40 apply (zenon_or_s _ _ zenon_H1a4); [ zenon_intro zenon_H156 | zenon_intro zenon_H16a ]. % 15.22/15.40 apply (zenon_L256_); trivial. % 15.22/15.40 apply (zenon_L188_); trivial. % 15.22/15.40 apply (zenon_L13_); trivial. % 15.22/15.40 (* end of lemma zenon_L392_ *) % 15.22/15.40 assert (zenon_L393_ : (~((op (e1) (e0)) = (op (e3) (e0)))) -> ((op (e1) (e0)) = (e1)) -> ((op (e3) (e0)) = (e1)) -> False). % 15.22/15.40 do 0 intro. intros zenon_H22e zenon_Hd8 zenon_Hee. % 15.22/15.40 cut (((op (e1) (e0)) = (e1)) = ((op (e1) (e0)) = (op (e3) (e0)))). % 15.22/15.40 intro zenon_D_pnotp. % 15.22/15.40 apply zenon_H22e. % 15.22/15.40 rewrite <- zenon_D_pnotp. % 15.22/15.40 exact zenon_Hd8. % 15.22/15.40 cut (((e1) = (op (e3) (e0)))); [idtac | apply NNPP; zenon_intro zenon_H22f]. % 15.22/15.40 cut (((op (e1) (e0)) = (op (e1) (e0)))); [idtac | apply NNPP; zenon_intro zenon_Hda]. % 15.22/15.40 congruence. % 15.22/15.40 apply zenon_Hda. apply refl_equal. % 15.22/15.40 apply zenon_H22f. apply sym_equal. exact zenon_Hee. % 15.22/15.40 (* end of lemma zenon_L393_ *) % 15.22/15.40 assert (zenon_L394_ : (~((op (e3) (e1)) = (op (e3) (e2)))) -> ((op (e3) (e1)) = (e1)) -> ((op (e3) (e2)) = (e1)) -> False). % 15.22/15.40 do 0 intro. intros zenon_H135 zenon_H13e zenon_H119. % 15.22/15.40 cut (((op (e3) (e1)) = (e1)) = ((op (e3) (e1)) = (op (e3) (e2)))). % 15.22/15.40 intro zenon_D_pnotp. % 15.22/15.40 apply zenon_H135. % 15.22/15.40 rewrite <- zenon_D_pnotp. % 15.22/15.40 exact zenon_H13e. % 15.22/15.40 cut (((e1) = (op (e3) (e2)))); [idtac | apply NNPP; zenon_intro zenon_H141]. % 15.22/15.40 cut (((op (e3) (e1)) = (op (e3) (e1)))); [idtac | apply NNPP; zenon_intro zenon_H136]. % 15.22/15.40 congruence. % 15.22/15.40 apply zenon_H136. apply refl_equal. % 15.22/15.40 apply zenon_H141. apply sym_equal. exact zenon_H119. % 15.22/15.40 (* end of lemma zenon_L394_ *) % 15.22/15.40 assert (zenon_L395_ : (((op (e0) (e2)) = (e1))\/(((op (e1) (e2)) = (e1))\/(((op (e2) (e2)) = (e1))\/((op (e3) (e2)) = (e1))))) -> (~((op (e0) (e2)) = (op (e0) (e3)))) -> ((op (e0) (e3)) = (e1)) -> (~((e1) = (e3))) -> ((op (e1) (e2)) = (e3)) -> (~((op (e2) (e2)) = (e1))) -> (~((op (e3) (e1)) = (op (e3) (e2)))) -> ((op (e3) (e1)) = (e1)) -> False). % 15.22/15.40 do 0 intro. intros zenon_H11b zenon_Hc9 zenon_H37 zenon_Ha3 zenon_H88 zenon_H52 zenon_H135 zenon_H13e. % 15.22/15.40 apply (zenon_or_s _ _ zenon_H11b); [ zenon_intro zenon_H29 | zenon_intro zenon_H11c ]. % 15.22/15.40 apply (zenon_L85_); trivial. % 15.22/15.40 apply (zenon_or_s _ _ zenon_H11c); [ zenon_intro zenon_H117 | zenon_intro zenon_H11d ]. % 15.22/15.40 apply (zenon_L196_); trivial. % 15.22/15.40 apply (zenon_or_s _ _ zenon_H11d); [ zenon_intro zenon_H2a | zenon_intro zenon_H119 ]. % 15.22/15.40 exact (zenon_H52 zenon_H2a). % 15.22/15.40 apply (zenon_L394_); trivial. % 15.22/15.40 (* end of lemma zenon_L395_ *) % 15.22/15.40 assert (zenon_L396_ : (((op (e0) (e3)) = (e1))\/(((op (e1) (e3)) = (e1))\/(((op (e2) (e3)) = (e1))\/((op (e3) (e3)) = (e1))))) -> ((op (e3) (e1)) = (e1)) -> (~((op (e3) (e1)) = (op (e3) (e2)))) -> (~((op (e2) (e2)) = (e1))) -> ((op (e1) (e2)) = (e3)) -> (~((e1) = (e3))) -> (~((op (e0) (e2)) = (op (e0) (e3)))) -> (((op (e0) (e2)) = (e1))\/(((op (e1) (e2)) = (e1))\/(((op (e2) (e2)) = (e1))\/((op (e3) (e2)) = (e1))))) -> ((op (e1) (e0)) = (e1)) -> (~((op (e1) (e0)) = (op (e1) (e3)))) -> ((op (e2) (e3)) = (e2)) -> (~((e1) = (e2))) -> (~((op (e3) (e3)) = (e1))) -> False). % 15.22/15.40 do 0 intro. intros zenon_H121 zenon_H13e zenon_H135 zenon_H52 zenon_H88 zenon_Ha3 zenon_Hc9 zenon_H11b zenon_Hd8 zenon_H1cf zenon_H124 zenon_Ha7 zenon_H104. % 15.22/15.40 apply (zenon_or_s _ _ zenon_H121); [ zenon_intro zenon_H37 | zenon_intro zenon_H122 ]. % 15.22/15.40 apply (zenon_L395_); trivial. % 15.22/15.40 apply (zenon_or_s _ _ zenon_H122); [ zenon_intro zenon_H11f | zenon_intro zenon_H123 ]. % 15.22/15.40 apply (zenon_L224_); trivial. % 15.22/15.40 apply (zenon_or_s _ _ zenon_H123); [ zenon_intro zenon_Hb5 | zenon_intro zenon_H38 ]. % 15.22/15.40 apply (zenon_L93_); trivial. % 15.22/15.40 exact (zenon_H104 zenon_H38). % 15.22/15.40 (* end of lemma zenon_L396_ *) % 15.22/15.40 assert (zenon_L397_ : (((op (e1) (e0)) = (e3))\/(((op (e1) (e1)) = (e3))\/(((op (e1) (e2)) = (e3))\/((op (e1) (e3)) = (e3))))) -> (~((op (e1) (e1)) = (e3))) -> (~((op (e3) (e3)) = (e1))) -> (~((op (e0) (e2)) = (op (e3) (e2)))) -> ((op (e0) (e2)) = (e1)) -> (((op (e0) (e3)) = (e1))\/(((op (e1) (e3)) = (e1))\/(((op (e2) (e3)) = (e1))\/((op (e3) (e3)) = (e1))))) -> (~((op (e3) (e1)) = (op (e3) (e2)))) -> (~((op (e2) (e2)) = (e1))) -> (~((e1) = (e3))) -> (~((op (e0) (e2)) = (op (e0) (e3)))) -> (((op (e0) (e2)) = (e1))\/(((op (e1) (e2)) = (e1))\/(((op (e2) (e2)) = (e1))\/((op (e3) (e2)) = (e1))))) -> ((op (e1) (e0)) = (e1)) -> (~((op (e1) (e0)) = (op (e1) (e3)))) -> ((op (e2) (e3)) = (e2)) -> (~((e1) = (e2))) -> (~((op (e1) (e0)) = (op (e3) (e0)))) -> (((op (e3) (e0)) = (e1))\/(((op (e3) (e1)) = (e1))\/(((op (e3) (e2)) = (e1))\/((op (e3) (e3)) = (e1))))) -> ((op (e3) (e3)) = (e3)) -> (~((op (e1) (e3)) = (op (e3) (e3)))) -> False). % 15.22/15.40 do 0 intro. intros zenon_H90 zenon_H182 zenon_H104 zenon_H140 zenon_H29 zenon_H121 zenon_H135 zenon_H52 zenon_Ha3 zenon_Hc9 zenon_H11b zenon_Hd8 zenon_H1cf zenon_H124 zenon_Ha7 zenon_H22e zenon_H146 zenon_H42 zenon_H8b. % 15.22/15.40 apply (zenon_or_s _ _ zenon_H90); [ zenon_intro zenon_H69 | zenon_intro zenon_H94 ]. % 15.22/15.40 apply (zenon_L163_); trivial. % 15.22/15.40 apply (zenon_or_s _ _ zenon_H94); [ zenon_intro zenon_H96 | zenon_intro zenon_H95 ]. % 15.22/15.40 exact (zenon_H182 zenon_H96). % 15.22/15.40 apply (zenon_or_s _ _ zenon_H95); [ zenon_intro zenon_H88 | zenon_intro zenon_H8a ]. % 15.22/15.40 apply (zenon_or_s _ _ zenon_H146); [ zenon_intro zenon_Hee | zenon_intro zenon_H14b ]. % 15.22/15.40 apply (zenon_L393_); trivial. % 15.22/15.40 apply (zenon_or_s _ _ zenon_H14b); [ zenon_intro zenon_H13e | zenon_intro zenon_H14c ]. % 15.22/15.40 apply (zenon_L396_); trivial. % 15.22/15.40 apply (zenon_or_s _ _ zenon_H14c); [ zenon_intro zenon_H119 | zenon_intro zenon_H38 ]. % 15.22/15.40 apply (zenon_L124_); trivial. % 15.22/15.40 exact (zenon_H104 zenon_H38). % 15.22/15.40 apply (zenon_L25_); trivial. % 15.22/15.40 (* end of lemma zenon_L397_ *) % 15.22/15.40 assert (zenon_L398_ : (((op (e0) (e0)) = (e1))\/(((op (e0) (e1)) = (e1))\/(((op (e0) (e2)) = (e1))\/((op (e0) (e3)) = (e1))))) -> (~((op (e0) (e0)) = (e1))) -> (~((op (e0) (e1)) = (op (e0) (e3)))) -> (~((op (e1) (e3)) = (op (e3) (e3)))) -> ((op (e3) (e3)) = (e3)) -> (((op (e3) (e0)) = (e1))\/(((op (e3) (e1)) = (e1))\/(((op (e3) (e2)) = (e1))\/((op (e3) (e3)) = (e1))))) -> (~((op (e1) (e0)) = (op (e3) (e0)))) -> (~((e1) = (e2))) -> ((op (e2) (e3)) = (e2)) -> (~((op (e1) (e0)) = (op (e1) (e3)))) -> ((op (e1) (e0)) = (e1)) -> (((op (e0) (e2)) = (e1))\/(((op (e1) (e2)) = (e1))\/(((op (e2) (e2)) = (e1))\/((op (e3) (e2)) = (e1))))) -> (~((op (e0) (e2)) = (op (e0) (e3)))) -> (~((e1) = (e3))) -> (~((op (e2) (e2)) = (e1))) -> (~((op (e3) (e1)) = (op (e3) (e2)))) -> (((op (e0) (e3)) = (e1))\/(((op (e1) (e3)) = (e1))\/(((op (e2) (e3)) = (e1))\/((op (e3) (e3)) = (e1))))) -> (~((op (e0) (e2)) = (op (e3) (e2)))) -> (~((op (e3) (e3)) = (e1))) -> (~((op (e1) (e1)) = (e3))) -> (((op (e1) (e0)) = (e3))\/(((op (e1) (e1)) = (e3))\/(((op (e1) (e2)) = (e3))\/((op (e1) (e3)) = (e3))))) -> ((op (e0) (e3)) = (e0)) -> (~((e0) = (e1))) -> False). % 15.22/15.40 do 0 intro. intros zenon_H44 zenon_H45 zenon_H1cd zenon_H8b zenon_H42 zenon_H146 zenon_H22e zenon_Ha7 zenon_H124 zenon_H1cf zenon_Hd8 zenon_H11b zenon_Hc9 zenon_Ha3 zenon_H52 zenon_H135 zenon_H121 zenon_H140 zenon_H104 zenon_H182 zenon_H90 zenon_Hca zenon_H9e. % 15.22/15.40 apply (zenon_or_s _ _ zenon_H44); [ zenon_intro zenon_H47 | zenon_intro zenon_H46 ]. % 15.22/15.40 exact (zenon_H45 zenon_H47). % 15.22/15.40 apply (zenon_or_s _ _ zenon_H46); [ zenon_intro zenon_H22 | zenon_intro zenon_H48 ]. % 15.22/15.40 apply (zenon_L225_); trivial. % 15.22/15.40 apply (zenon_or_s _ _ zenon_H48); [ zenon_intro zenon_H29 | zenon_intro zenon_H37 ]. % 15.22/15.40 apply (zenon_L397_); trivial. % 15.22/15.40 apply (zenon_L73_); trivial. % 15.22/15.40 (* end of lemma zenon_L398_ *) % 15.22/15.40 assert (zenon_L399_ : ((op (e1) (e3)) = (e2)) -> ((op (e0) (e0)) = (e3)) -> ((op (e1) (e1)) = (e0)) -> False). % 15.22/15.40 do 0 intro. intros zenon_H82 zenon_H5b zenon_H149. % 15.22/15.40 apply (zenon_notand_s _ _ ax25); [ zenon_intro zenon_H1b9 | zenon_intro zenon_H230 ]. % 15.22/15.40 elim (classic ((op (op (e1) (e1)) (op (e1) (e1))) = (op (op (e1) (e1)) (op (e1) (e1))))); [ zenon_intro zenon_H1a8 | zenon_intro zenon_H1a9 ]. % 15.22/15.40 cut (((op (op (e1) (e1)) (op (e1) (e1))) = (op (op (e1) (e1)) (op (e1) (e1)))) = ((e3) = (op (op (e1) (e1)) (op (e1) (e1))))). % 15.22/15.40 intro zenon_D_pnotp. % 15.22/15.40 apply zenon_H1b9. % 15.22/15.40 rewrite <- zenon_D_pnotp. % 15.22/15.40 exact zenon_H1a8. % 15.22/15.40 cut (((op (op (e1) (e1)) (op (e1) (e1))) = (op (op (e1) (e1)) (op (e1) (e1))))); [idtac | apply NNPP; zenon_intro zenon_H1a9]. % 15.22/15.40 cut (((op (op (e1) (e1)) (op (e1) (e1))) = (e3))); [idtac | apply NNPP; zenon_intro zenon_H1ba]. % 15.22/15.40 congruence. % 15.22/15.40 cut (((op (e0) (e0)) = (e3)) = ((op (op (e1) (e1)) (op (e1) (e1))) = (e3))). % 15.22/15.40 intro zenon_D_pnotp. % 15.22/15.40 apply zenon_H1ba. % 15.22/15.40 rewrite <- zenon_D_pnotp. % 15.22/15.40 exact zenon_H5b. % 15.22/15.40 cut (((e3) = (e3))); [idtac | apply NNPP; zenon_intro zenon_H4d]. % 15.22/15.40 cut (((op (e0) (e0)) = (op (op (e1) (e1)) (op (e1) (e1))))); [idtac | apply NNPP; zenon_intro zenon_H1ab]. % 15.22/15.40 congruence. % 15.22/15.40 elim (classic ((op (op (e1) (e1)) (op (e1) (e1))) = (op (op (e1) (e1)) (op (e1) (e1))))); [ zenon_intro zenon_H1a8 | zenon_intro zenon_H1a9 ]. % 15.22/15.40 cut (((op (op (e1) (e1)) (op (e1) (e1))) = (op (op (e1) (e1)) (op (e1) (e1)))) = ((op (e0) (e0)) = (op (op (e1) (e1)) (op (e1) (e1))))). % 15.22/15.40 intro zenon_D_pnotp. % 15.22/15.40 apply zenon_H1ab. % 15.22/15.40 rewrite <- zenon_D_pnotp. % 15.22/15.40 exact zenon_H1a8. % 15.22/15.40 cut (((op (op (e1) (e1)) (op (e1) (e1))) = (op (op (e1) (e1)) (op (e1) (e1))))); [idtac | apply NNPP; zenon_intro zenon_H1a9]. % 15.22/15.40 cut (((op (op (e1) (e1)) (op (e1) (e1))) = (op (e0) (e0)))); [idtac | apply NNPP; zenon_intro zenon_H1a5]. % 15.22/15.40 congruence. % 15.22/15.40 apply (zenon_L192_); trivial. % 15.22/15.40 apply zenon_H1a9. apply refl_equal. % 15.22/15.40 apply zenon_H1a9. apply refl_equal. % 15.22/15.40 apply zenon_H4d. apply refl_equal. % 15.22/15.40 apply zenon_H1a9. apply refl_equal. % 15.22/15.40 apply zenon_H1a9. apply refl_equal. % 15.22/15.40 apply (zenon_notand_s _ _ zenon_H230); [ zenon_intro zenon_H1ad | zenon_intro zenon_H221 ]. % 15.22/15.40 apply zenon_H1ad. apply sym_equal. exact zenon_H149. % 15.22/15.40 elim (classic ((op (e1) (op (op (e1) (e1)) (op (e1) (e1)))) = (op (e1) (op (op (e1) (e1)) (op (e1) (e1)))))); [ zenon_intro zenon_H1ae | zenon_intro zenon_H1af ]. % 15.22/15.40 cut (((op (e1) (op (op (e1) (e1)) (op (e1) (e1)))) = (op (e1) (op (op (e1) (e1)) (op (e1) (e1))))) = ((e2) = (op (e1) (op (op (e1) (e1)) (op (e1) (e1)))))). % 15.22/15.40 intro zenon_D_pnotp. % 15.22/15.40 apply zenon_H221. % 15.22/15.40 rewrite <- zenon_D_pnotp. % 15.22/15.40 exact zenon_H1ae. % 15.22/15.40 cut (((op (e1) (op (op (e1) (e1)) (op (e1) (e1)))) = (op (e1) (op (op (e1) (e1)) (op (e1) (e1)))))); [idtac | apply NNPP; zenon_intro zenon_H1af]. % 15.22/15.40 cut (((op (e1) (op (op (e1) (e1)) (op (e1) (e1)))) = (e2))); [idtac | apply NNPP; zenon_intro zenon_H223]. % 15.22/15.40 congruence. % 15.22/15.40 cut (((op (e1) (e3)) = (e2)) = ((op (e1) (op (op (e1) (e1)) (op (e1) (e1)))) = (e2))). % 15.22/15.40 intro zenon_D_pnotp. % 15.22/15.40 apply zenon_H223. % 15.22/15.40 rewrite <- zenon_D_pnotp. % 15.22/15.40 exact zenon_H82. % 15.22/15.40 cut (((e2) = (e2))); [idtac | apply NNPP; zenon_intro zenon_H60]. % 15.22/15.40 cut (((op (e1) (e3)) = (op (e1) (op (op (e1) (e1)) (op (e1) (e1)))))); [idtac | apply NNPP; zenon_intro zenon_H1bf]. % 15.22/15.40 congruence. % 15.22/15.40 elim (classic ((op (e1) (op (op (e1) (e1)) (op (e1) (e1)))) = (op (e1) (op (op (e1) (e1)) (op (e1) (e1)))))); [ zenon_intro zenon_H1ae | zenon_intro zenon_H1af ]. % 15.22/15.40 cut (((op (e1) (op (op (e1) (e1)) (op (e1) (e1)))) = (op (e1) (op (op (e1) (e1)) (op (e1) (e1))))) = ((op (e1) (e3)) = (op (e1) (op (op (e1) (e1)) (op (e1) (e1)))))). % 15.22/15.40 intro zenon_D_pnotp. % 15.22/15.40 apply zenon_H1bf. % 15.22/15.40 rewrite <- zenon_D_pnotp. % 15.22/15.40 exact zenon_H1ae. % 15.22/15.40 cut (((op (e1) (op (op (e1) (e1)) (op (e1) (e1)))) = (op (e1) (op (op (e1) (e1)) (op (e1) (e1)))))); [idtac | apply NNPP; zenon_intro zenon_H1af]. % 15.22/15.40 cut (((op (e1) (op (op (e1) (e1)) (op (e1) (e1)))) = (op (e1) (e3)))); [idtac | apply NNPP; zenon_intro zenon_H1c0]. % 15.22/15.40 congruence. % 15.22/15.40 cut (((op (op (e1) (e1)) (op (e1) (e1))) = (e3))); [idtac | apply NNPP; zenon_intro zenon_H1ba]. % 15.22/15.40 cut (((e1) = (e1))); [idtac | apply NNPP; zenon_intro zenon_Ha0]. % 15.22/15.40 congruence. % 15.22/15.40 apply zenon_Ha0. apply refl_equal. % 15.22/15.40 cut (((op (e0) (e0)) = (e3)) = ((op (op (e1) (e1)) (op (e1) (e1))) = (e3))). % 15.22/15.40 intro zenon_D_pnotp. % 15.22/15.40 apply zenon_H1ba. % 15.22/15.40 rewrite <- zenon_D_pnotp. % 15.22/15.40 exact zenon_H5b. % 15.22/15.40 cut (((e3) = (e3))); [idtac | apply NNPP; zenon_intro zenon_H4d]. % 15.22/15.40 cut (((op (e0) (e0)) = (op (op (e1) (e1)) (op (e1) (e1))))); [idtac | apply NNPP; zenon_intro zenon_H1ab]. % 15.22/15.40 congruence. % 15.22/15.40 elim (classic ((op (op (e1) (e1)) (op (e1) (e1))) = (op (op (e1) (e1)) (op (e1) (e1))))); [ zenon_intro zenon_H1a8 | zenon_intro zenon_H1a9 ]. % 15.22/15.40 cut (((op (op (e1) (e1)) (op (e1) (e1))) = (op (op (e1) (e1)) (op (e1) (e1)))) = ((op (e0) (e0)) = (op (op (e1) (e1)) (op (e1) (e1))))). % 15.22/15.40 intro zenon_D_pnotp. % 15.22/15.40 apply zenon_H1ab. % 15.22/15.40 rewrite <- zenon_D_pnotp. % 15.22/15.40 exact zenon_H1a8. % 15.22/15.40 cut (((op (op (e1) (e1)) (op (e1) (e1))) = (op (op (e1) (e1)) (op (e1) (e1))))); [idtac | apply NNPP; zenon_intro zenon_H1a9]. % 15.22/15.40 cut (((op (op (e1) (e1)) (op (e1) (e1))) = (op (e0) (e0)))); [idtac | apply NNPP; zenon_intro zenon_H1a5]. % 15.22/15.40 congruence. % 15.22/15.40 apply (zenon_L192_); trivial. % 15.22/15.40 apply zenon_H1a9. apply refl_equal. % 15.22/15.40 apply zenon_H1a9. apply refl_equal. % 15.22/15.40 apply zenon_H4d. apply refl_equal. % 15.22/15.40 apply zenon_H1af. apply refl_equal. % 15.22/15.40 apply zenon_H1af. apply refl_equal. % 15.22/15.40 apply zenon_H60. apply refl_equal. % 15.22/15.40 apply zenon_H1af. apply refl_equal. % 15.22/15.40 apply zenon_H1af. apply refl_equal. % 15.22/15.40 (* end of lemma zenon_L399_ *) % 15.22/15.40 assert (zenon_L400_ : (((op (e1) (e1)) = (e0))\/(((op (e1) (e1)) = (e1))\/(((op (e1) (e1)) = (e2))\/((op (e1) (e1)) = (e3))))) -> ((op (e0) (e0)) = (e3)) -> ((op (e1) (e3)) = (e2)) -> (~((op (e1) (e1)) = (e1))) -> (~((op (e1) (e1)) = (e2))) -> (~((op (e1) (e1)) = (e3))) -> False). % 15.22/15.40 do 0 intro. intros zenon_H1b3 zenon_H5b zenon_H82 zenon_H1b4 zenon_Hd6 zenon_H182. % 15.22/15.40 apply (zenon_or_s _ _ zenon_H1b3); [ zenon_intro zenon_H149 | zenon_intro zenon_H1b5 ]. % 15.22/15.40 apply (zenon_L399_); trivial. % 15.22/15.40 apply (zenon_or_s _ _ zenon_H1b5); [ zenon_intro zenon_H21 | zenon_intro zenon_H1b6 ]. % 15.22/15.40 exact (zenon_H1b4 zenon_H21). % 15.22/15.40 apply (zenon_or_s _ _ zenon_H1b6); [ zenon_intro zenon_H6e | zenon_intro zenon_H96 ]. % 15.22/15.40 exact (zenon_Hd6 zenon_H6e). % 15.22/15.40 exact (zenon_H182 zenon_H96). % 15.22/15.40 (* end of lemma zenon_L400_ *) % 15.22/15.40 assert (zenon_L401_ : (((op (e1) (e0)) = (e2))\/(((op (e1) (e1)) = (e2))\/(((op (e1) (e2)) = (e2))\/((op (e1) (e3)) = (e2))))) -> (~((e1) = (e2))) -> ((op (e1) (e0)) = (e1)) -> (~((op (e1) (e2)) = (op (e2) (e2)))) -> ((op (e2) (e2)) = (e2)) -> (((op (e1) (e1)) = (e0))\/(((op (e1) (e1)) = (e1))\/(((op (e1) (e1)) = (e2))\/((op (e1) (e1)) = (e3))))) -> ((op (e0) (e0)) = (e3)) -> (~((op (e1) (e1)) = (e1))) -> (~((op (e1) (e1)) = (e2))) -> (~((op (e1) (e1)) = (e3))) -> False). % 15.22/15.40 do 0 intro. intros zenon_H84 zenon_Ha7 zenon_Hd8 zenon_H7d zenon_H35 zenon_H1b3 zenon_H5b zenon_H1b4 zenon_Hd6 zenon_H182. % 15.22/15.40 apply (zenon_or_s _ _ zenon_H84); [ zenon_intro zenon_H68 | zenon_intro zenon_H85 ]. % 15.22/15.40 apply (zenon_L162_); trivial. % 15.22/15.40 apply (zenon_or_s _ _ zenon_H85); [ zenon_intro zenon_H6e | zenon_intro zenon_H86 ]. % 15.22/15.40 exact (zenon_Hd6 zenon_H6e). % 15.22/15.40 apply (zenon_or_s _ _ zenon_H86); [ zenon_intro zenon_H7c | zenon_intro zenon_H82 ]. % 15.22/15.40 apply (zenon_L21_); trivial. % 15.22/15.40 apply (zenon_L400_); trivial. % 15.22/15.40 (* end of lemma zenon_L401_ *) % 15.22/15.40 assert (zenon_L402_ : (((op (e0) (e0)) = (e1))\/(((op (e0) (e1)) = (e1))\/(((op (e0) (e2)) = (e1))\/((op (e0) (e3)) = (e1))))) -> (~((op (e0) (e0)) = (e1))) -> (((op (e1) (e0)) = (e3))\/(((op (e1) (e1)) = (e3))\/(((op (e1) (e2)) = (e3))\/((op (e1) (e3)) = (e3))))) -> (~((op (e0) (e2)) = (op (e1) (e2)))) -> (~((op (e1) (e3)) = (op (e3) (e3)))) -> (~((e0) = (e2))) -> (~((e1) = (e2))) -> (((op (e0) (e0)) = (e3))\/(((op (e0) (e1)) = (e3))\/(((op (e0) (e2)) = (e3))\/((op (e0) (e3)) = (e3))))) -> (~((op (e1) (e1)) = (e3))) -> (~((op (e1) (e1)) = (e2))) -> (~((op (e1) (e1)) = (e1))) -> (((op (e1) (e1)) = (e0))\/(((op (e1) (e1)) = (e1))\/(((op (e1) (e1)) = (e2))\/((op (e1) (e1)) = (e3))))) -> ((op (e2) (e2)) = (e2)) -> (~((op (e1) (e2)) = (op (e2) (e2)))) -> ((op (e1) (e0)) = (e1)) -> (((op (e1) (e0)) = (e2))\/(((op (e1) (e1)) = (e2))\/(((op (e1) (e2)) = (e2))\/((op (e1) (e3)) = (e2))))) -> (~((e2) = (e3))) -> (~((e1) = (e3))) -> ((op (e3) (e3)) = (e3)) -> (~((op (e0) (e3)) = (op (e3) (e3)))) -> (~((op (e0) (e0)) = (e2))) -> (((op (e0) (e0)) = (e2))\/(((op (e0) (e1)) = (e2))\/(((op (e0) (e2)) = (e2))\/((op (e0) (e3)) = (e2))))) -> ((op (e0) (e3)) = (e0)) -> (~((e0) = (e1))) -> False). % 15.22/15.40 do 0 intro. intros zenon_H44 zenon_H45 zenon_H90 zenon_H87 zenon_H8b zenon_H5e zenon_Ha7 zenon_H58 zenon_H182 zenon_Hd6 zenon_H1b4 zenon_H1b3 zenon_H35 zenon_H7d zenon_Hd8 zenon_H84 zenon_H6a zenon_Ha3 zenon_H42 zenon_H36 zenon_H8f zenon_H8e zenon_Hca zenon_H9e. % 15.22/15.40 apply (zenon_or_s _ _ zenon_H44); [ zenon_intro zenon_H47 | zenon_intro zenon_H46 ]. % 15.22/15.40 exact (zenon_H45 zenon_H47). % 15.22/15.40 apply (zenon_or_s _ _ zenon_H46); [ zenon_intro zenon_H22 | zenon_intro zenon_H48 ]. % 15.22/15.40 apply (zenon_or_s _ _ zenon_H58); [ zenon_intro zenon_H5b | zenon_intro zenon_H5a ]. % 15.22/15.40 apply (zenon_L401_); trivial. % 15.22/15.40 apply (zenon_or_s _ _ zenon_H5a); [ zenon_intro zenon_H4a | zenon_intro zenon_H5c ]. % 15.22/15.40 apply (zenon_L59_); trivial. % 15.22/15.40 apply (zenon_or_s _ _ zenon_H5c); [ zenon_intro zenon_H50 | zenon_intro zenon_H53 ]. % 15.22/15.40 apply (zenon_L226_); trivial. % 15.22/15.40 apply (zenon_L12_); trivial. % 15.22/15.40 apply (zenon_or_s _ _ zenon_H48); [ zenon_intro zenon_H29 | zenon_intro zenon_H37 ]. % 15.22/15.40 apply (zenon_or_s _ _ zenon_H8e); [ zenon_intro zenon_H92 | zenon_intro zenon_H91 ]. % 15.22/15.40 exact (zenon_H8f zenon_H92). % 15.22/15.40 apply (zenon_or_s _ _ zenon_H91); [ zenon_intro zenon_H5d | zenon_intro zenon_H93 ]. % 15.22/15.40 apply (zenon_or_s _ _ zenon_H58); [ zenon_intro zenon_H5b | zenon_intro zenon_H5a ]. % 15.22/15.40 apply (zenon_L401_); trivial. % 15.22/15.40 apply (zenon_or_s _ _ zenon_H5a); [ zenon_intro zenon_H4a | zenon_intro zenon_H5c ]. % 15.22/15.40 apply (zenon_L50_); trivial. % 15.22/15.40 apply (zenon_or_s _ _ zenon_H5c); [ zenon_intro zenon_H50 | zenon_intro zenon_H53 ]. % 15.22/15.40 apply (zenon_L29_); trivial. % 15.22/15.40 apply (zenon_L12_); trivial. % 15.22/15.40 apply (zenon_or_s _ _ zenon_H93); [ zenon_intro zenon_H63 | zenon_intro zenon_H81 ]. % 15.22/15.40 apply (zenon_L104_); trivial. % 15.22/15.40 apply (zenon_L113_); trivial. % 15.22/15.40 apply (zenon_L73_); trivial. % 15.22/15.40 (* end of lemma zenon_L402_ *) % 15.22/15.40 assert (zenon_L403_ : (~((op (op (e3) (e3)) (op (e3) (e3))) = (op (e1) (e1)))) -> ((op (e3) (e3)) = (e1)) -> False). % 15.22/15.40 do 0 intro. intros zenon_H231 zenon_H38. % 15.22/15.40 cut (((op (e3) (e3)) = (e1))); [idtac | apply NNPP; zenon_intro zenon_H104]. % 15.22/15.40 cut (((op (e3) (e3)) = (e1))); [idtac | apply NNPP; zenon_intro zenon_H104]. % 15.22/15.40 congruence. % 15.22/15.40 exact (zenon_H104 zenon_H38). % 15.22/15.40 exact (zenon_H104 zenon_H38). % 15.22/15.40 (* end of lemma zenon_L403_ *) % 15.22/15.40 assert (zenon_L404_ : ((op (e3) (e0)) = (e2)) -> ((op (e1) (e1)) = (e0)) -> ((op (e3) (e3)) = (e1)) -> False). % 15.22/15.40 do 0 intro. intros zenon_He9 zenon_H149 zenon_H38. % 15.22/15.40 apply (zenon_notand_s _ _ ax6); [ zenon_intro zenon_H208 | zenon_intro zenon_H232 ]. % 15.22/15.40 elim (classic ((op (op (e3) (e3)) (op (e3) (e3))) = (op (op (e3) (e3)) (op (e3) (e3))))); [ zenon_intro zenon_H186 | zenon_intro zenon_H187 ]. % 15.22/15.40 cut (((op (op (e3) (e3)) (op (e3) (e3))) = (op (op (e3) (e3)) (op (e3) (e3)))) = ((e0) = (op (op (e3) (e3)) (op (e3) (e3))))). % 15.22/15.40 intro zenon_D_pnotp. % 15.22/15.40 apply zenon_H208. % 15.22/15.40 rewrite <- zenon_D_pnotp. % 15.22/15.40 exact zenon_H186. % 15.22/15.40 cut (((op (op (e3) (e3)) (op (e3) (e3))) = (op (op (e3) (e3)) (op (e3) (e3))))); [idtac | apply NNPP; zenon_intro zenon_H187]. % 15.22/15.40 cut (((op (op (e3) (e3)) (op (e3) (e3))) = (e0))); [idtac | apply NNPP; zenon_intro zenon_H209]. % 15.22/15.40 congruence. % 15.22/15.40 cut (((op (e1) (e1)) = (e0)) = ((op (op (e3) (e3)) (op (e3) (e3))) = (e0))). % 15.22/15.40 intro zenon_D_pnotp. % 15.22/15.40 apply zenon_H209. % 15.22/15.40 rewrite <- zenon_D_pnotp. % 15.22/15.40 exact zenon_H149. % 15.22/15.40 cut (((e0) = (e0))); [idtac | apply NNPP; zenon_intro zenon_H1d]. % 15.22/15.40 cut (((op (e1) (e1)) = (op (op (e3) (e3)) (op (e3) (e3))))); [idtac | apply NNPP; zenon_intro zenon_H233]. % 15.22/15.40 congruence. % 15.22/15.40 elim (classic ((op (op (e3) (e3)) (op (e3) (e3))) = (op (op (e3) (e3)) (op (e3) (e3))))); [ zenon_intro zenon_H186 | zenon_intro zenon_H187 ]. % 15.22/15.40 cut (((op (op (e3) (e3)) (op (e3) (e3))) = (op (op (e3) (e3)) (op (e3) (e3)))) = ((op (e1) (e1)) = (op (op (e3) (e3)) (op (e3) (e3))))). % 15.22/15.40 intro zenon_D_pnotp. % 15.22/15.40 apply zenon_H233. % 15.22/15.40 rewrite <- zenon_D_pnotp. % 15.22/15.40 exact zenon_H186. % 15.22/15.40 cut (((op (op (e3) (e3)) (op (e3) (e3))) = (op (op (e3) (e3)) (op (e3) (e3))))); [idtac | apply NNPP; zenon_intro zenon_H187]. % 15.22/15.40 cut (((op (op (e3) (e3)) (op (e3) (e3))) = (op (e1) (e1)))); [idtac | apply NNPP; zenon_intro zenon_H231]. % 15.22/15.40 congruence. % 15.22/15.40 apply (zenon_L403_); trivial. % 15.22/15.40 apply zenon_H187. apply refl_equal. % 15.22/15.40 apply zenon_H187. apply refl_equal. % 15.22/15.40 apply zenon_H1d. apply refl_equal. % 15.22/15.40 apply zenon_H187. apply refl_equal. % 15.22/15.40 apply zenon_H187. apply refl_equal. % 15.22/15.40 apply (zenon_notand_s _ _ zenon_H232); [ zenon_intro zenon_H39 | zenon_intro zenon_H19f ]. % 15.22/15.40 apply zenon_H39. apply sym_equal. exact zenon_H38. % 15.22/15.40 elim (classic ((op (e3) (op (op (e3) (e3)) (op (e3) (e3)))) = (op (e3) (op (op (e3) (e3)) (op (e3) (e3)))))); [ zenon_intro zenon_H18b | zenon_intro zenon_H18c ]. % 15.22/15.40 cut (((op (e3) (op (op (e3) (e3)) (op (e3) (e3)))) = (op (e3) (op (op (e3) (e3)) (op (e3) (e3))))) = ((e2) = (op (e3) (op (op (e3) (e3)) (op (e3) (e3)))))). % 15.22/15.40 intro zenon_D_pnotp. % 15.22/15.40 apply zenon_H19f. % 15.22/15.40 rewrite <- zenon_D_pnotp. % 15.22/15.40 exact zenon_H18b. % 15.22/15.40 cut (((op (e3) (op (op (e3) (e3)) (op (e3) (e3)))) = (op (e3) (op (op (e3) (e3)) (op (e3) (e3)))))); [idtac | apply NNPP; zenon_intro zenon_H18c]. % 15.22/15.40 cut (((op (e3) (op (op (e3) (e3)) (op (e3) (e3)))) = (e2))); [idtac | apply NNPP; zenon_intro zenon_H1a1]. % 15.22/15.40 congruence. % 15.22/15.40 cut (((op (e3) (e0)) = (e2)) = ((op (e3) (op (op (e3) (e3)) (op (e3) (e3)))) = (e2))). % 15.22/15.40 intro zenon_D_pnotp. % 15.22/15.40 apply zenon_H1a1. % 15.22/15.40 rewrite <- zenon_D_pnotp. % 15.22/15.40 exact zenon_He9. % 15.22/15.40 cut (((e2) = (e2))); [idtac | apply NNPP; zenon_intro zenon_H60]. % 15.22/15.40 cut (((op (e3) (e0)) = (op (e3) (op (op (e3) (e3)) (op (e3) (e3)))))); [idtac | apply NNPP; zenon_intro zenon_H20a]. % 15.22/15.40 congruence. % 15.22/15.40 elim (classic ((op (e3) (op (op (e3) (e3)) (op (e3) (e3)))) = (op (e3) (op (op (e3) (e3)) (op (e3) (e3)))))); [ zenon_intro zenon_H18b | zenon_intro zenon_H18c ]. % 15.22/15.40 cut (((op (e3) (op (op (e3) (e3)) (op (e3) (e3)))) = (op (e3) (op (op (e3) (e3)) (op (e3) (e3))))) = ((op (e3) (e0)) = (op (e3) (op (op (e3) (e3)) (op (e3) (e3)))))). % 15.22/15.40 intro zenon_D_pnotp. % 15.22/15.40 apply zenon_H20a. % 15.22/15.40 rewrite <- zenon_D_pnotp. % 15.22/15.40 exact zenon_H18b. % 15.22/15.40 cut (((op (e3) (op (op (e3) (e3)) (op (e3) (e3)))) = (op (e3) (op (op (e3) (e3)) (op (e3) (e3)))))); [idtac | apply NNPP; zenon_intro zenon_H18c]. % 15.22/15.40 cut (((op (e3) (op (op (e3) (e3)) (op (e3) (e3)))) = (op (e3) (e0)))); [idtac | apply NNPP; zenon_intro zenon_H20b]. % 15.22/15.40 congruence. % 15.22/15.40 cut (((op (op (e3) (e3)) (op (e3) (e3))) = (e0))); [idtac | apply NNPP; zenon_intro zenon_H209]. % 15.22/15.40 cut (((e3) = (e3))); [idtac | apply NNPP; zenon_intro zenon_H4d]. % 15.22/15.40 congruence. % 15.22/15.40 apply zenon_H4d. apply refl_equal. % 15.22/15.40 cut (((op (e1) (e1)) = (e0)) = ((op (op (e3) (e3)) (op (e3) (e3))) = (e0))). % 15.22/15.40 intro zenon_D_pnotp. % 15.22/15.40 apply zenon_H209. % 15.22/15.40 rewrite <- zenon_D_pnotp. % 15.22/15.40 exact zenon_H149. % 15.22/15.40 cut (((e0) = (e0))); [idtac | apply NNPP; zenon_intro zenon_H1d]. % 15.22/15.40 cut (((op (e1) (e1)) = (op (op (e3) (e3)) (op (e3) (e3))))); [idtac | apply NNPP; zenon_intro zenon_H233]. % 15.22/15.40 congruence. % 15.22/15.40 elim (classic ((op (op (e3) (e3)) (op (e3) (e3))) = (op (op (e3) (e3)) (op (e3) (e3))))); [ zenon_intro zenon_H186 | zenon_intro zenon_H187 ]. % 15.22/15.40 cut (((op (op (e3) (e3)) (op (e3) (e3))) = (op (op (e3) (e3)) (op (e3) (e3)))) = ((op (e1) (e1)) = (op (op (e3) (e3)) (op (e3) (e3))))). % 15.22/15.40 intro zenon_D_pnotp. % 15.22/15.40 apply zenon_H233. % 15.22/15.40 rewrite <- zenon_D_pnotp. % 15.22/15.40 exact zenon_H186. % 15.22/15.40 cut (((op (op (e3) (e3)) (op (e3) (e3))) = (op (op (e3) (e3)) (op (e3) (e3))))); [idtac | apply NNPP; zenon_intro zenon_H187]. % 15.22/15.40 cut (((op (op (e3) (e3)) (op (e3) (e3))) = (op (e1) (e1)))); [idtac | apply NNPP; zenon_intro zenon_H231]. % 15.22/15.40 congruence. % 15.22/15.40 apply (zenon_L403_); trivial. % 15.22/15.40 apply zenon_H187. apply refl_equal. % 15.22/15.40 apply zenon_H187. apply refl_equal. % 15.22/15.40 apply zenon_H1d. apply refl_equal. % 15.22/15.40 apply zenon_H18c. apply refl_equal. % 15.22/15.40 apply zenon_H18c. apply refl_equal. % 15.22/15.40 apply zenon_H60. apply refl_equal. % 15.22/15.40 apply zenon_H18c. apply refl_equal. % 15.22/15.40 apply zenon_H18c. apply refl_equal. % 15.22/15.40 (* end of lemma zenon_L404_ *) % 15.22/15.40 assert (zenon_L405_ : (((op (e3) (e3)) = (e0))\/(((op (e3) (e3)) = (e1))\/(((op (e3) (e3)) = (e2))\/((op (e3) (e3)) = (e3))))) -> (~((op (e3) (e3)) = (e0))) -> ((op (e1) (e1)) = (e0)) -> ((op (e3) (e0)) = (e2)) -> (~((op (e3) (e3)) = (e2))) -> (~((op (e3) (e3)) = (e3))) -> False). % 15.22/15.40 do 0 intro. intros zenon_H3b zenon_H3c zenon_H149 zenon_He9 zenon_H3d zenon_H3e. % 15.22/15.40 apply (zenon_or_s _ _ zenon_H3b); [ zenon_intro zenon_H40 | zenon_intro zenon_H3f ]. % 15.22/15.40 exact (zenon_H3c zenon_H40). % 15.22/15.40 apply (zenon_or_s _ _ zenon_H3f); [ zenon_intro zenon_H38 | zenon_intro zenon_H41 ]. % 15.22/15.40 apply (zenon_L404_); trivial. % 15.22/15.40 apply (zenon_or_s _ _ zenon_H41); [ zenon_intro zenon_H43 | zenon_intro zenon_H42 ]. % 15.22/15.40 exact (zenon_H3d zenon_H43). % 15.22/15.40 exact (zenon_H3e zenon_H42). % 15.22/15.40 (* end of lemma zenon_L405_ *) % 15.22/15.40 assert (zenon_L406_ : (((op (e1) (e1)) = (e0))\/(((op (e1) (e1)) = (e1))\/(((op (e1) (e1)) = (e2))\/((op (e1) (e1)) = (e3))))) -> (~((op (e3) (e3)) = (e3))) -> (~((op (e3) (e3)) = (e2))) -> ((op (e3) (e0)) = (e2)) -> (~((op (e3) (e3)) = (e0))) -> (((op (e3) (e3)) = (e0))\/(((op (e3) (e3)) = (e1))\/(((op (e3) (e3)) = (e2))\/((op (e3) (e3)) = (e3))))) -> (~((op (e1) (e1)) = (e1))) -> (~((op (e1) (e1)) = (e2))) -> (~((op (e1) (e1)) = (e3))) -> False). % 15.22/15.40 do 0 intro. intros zenon_H1b3 zenon_H3e zenon_H3d zenon_He9 zenon_H3c zenon_H3b zenon_H1b4 zenon_Hd6 zenon_H182. % 15.22/15.40 apply (zenon_or_s _ _ zenon_H1b3); [ zenon_intro zenon_H149 | zenon_intro zenon_H1b5 ]. % 15.22/15.40 apply (zenon_L405_); trivial. % 15.22/15.40 apply (zenon_or_s _ _ zenon_H1b5); [ zenon_intro zenon_H21 | zenon_intro zenon_H1b6 ]. % 15.22/15.40 exact (zenon_H1b4 zenon_H21). % 15.22/15.40 apply (zenon_or_s _ _ zenon_H1b6); [ zenon_intro zenon_H6e | zenon_intro zenon_H96 ]. % 15.22/15.40 exact (zenon_Hd6 zenon_H6e). % 15.22/15.40 exact (zenon_H182 zenon_H96). % 15.22/15.40 (* end of lemma zenon_L406_ *) % 15.22/15.40 assert (zenon_L407_ : (((op (e0) (e0)) = (e2))\/(((op (e1) (e0)) = (e2))\/(((op (e2) (e0)) = (e2))\/((op (e3) (e0)) = (e2))))) -> (~((op (e0) (e0)) = (e2))) -> (~((e1) = (e2))) -> ((op (e1) (e0)) = (e1)) -> ((op (e2) (e1)) = (e2)) -> (~((op (e2) (e0)) = (op (e2) (e1)))) -> (((op (e1) (e1)) = (e0))\/(((op (e1) (e1)) = (e1))\/(((op (e1) (e1)) = (e2))\/((op (e1) (e1)) = (e3))))) -> (~((op (e3) (e3)) = (e3))) -> (~((op (e3) (e3)) = (e2))) -> (~((op (e3) (e3)) = (e0))) -> (((op (e3) (e3)) = (e0))\/(((op (e3) (e3)) = (e1))\/(((op (e3) (e3)) = (e2))\/((op (e3) (e3)) = (e3))))) -> (~((op (e1) (e1)) = (e1))) -> (~((op (e1) (e1)) = (e2))) -> (~((op (e1) (e1)) = (e3))) -> False). % 15.22/15.40 do 0 intro. intros zenon_Heb zenon_H8f zenon_Ha7 zenon_Hd8 zenon_H156 zenon_H154 zenon_H1b3 zenon_H3e zenon_H3d zenon_H3c zenon_H3b zenon_H1b4 zenon_Hd6 zenon_H182. % 15.22/15.40 apply (zenon_or_s _ _ zenon_Heb); [ zenon_intro zenon_H92 | zenon_intro zenon_Hec ]. % 15.22/15.40 exact (zenon_H8f zenon_H92). % 15.22/15.40 apply (zenon_or_s _ _ zenon_Hec); [ zenon_intro zenon_H68 | zenon_intro zenon_Hed ]. % 15.22/15.40 apply (zenon_L162_); trivial. % 15.22/15.40 apply (zenon_or_s _ _ zenon_Hed); [ zenon_intro zenon_Hdd | zenon_intro zenon_He9 ]. % 15.22/15.40 apply (zenon_L284_); trivial. % 15.22/15.40 apply (zenon_L406_); trivial. % 15.22/15.40 (* end of lemma zenon_L407_ *) % 15.22/15.40 assert (zenon_L408_ : ((~((op (e3) (e3)) = (e3)))\/((op (e3) (e3)) = (e3))) -> ((op (e3) (e1)) = (e3)) -> (~((op (e3) (e1)) = (op (e3) (e3)))) -> (~((op (e0) (e0)) = (e2))) -> (~((e1) = (e2))) -> ((op (e1) (e0)) = (e1)) -> (~((op (e2) (e0)) = (op (e2) (e1)))) -> ((op (e2) (e1)) = (e2)) -> (((op (e1) (e1)) = (e0))\/(((op (e1) (e1)) = (e1))\/(((op (e1) (e1)) = (e2))\/((op (e1) (e1)) = (e3))))) -> (~((op (e1) (e1)) = (e3))) -> (~((op (e1) (e1)) = (e2))) -> (~((op (e1) (e1)) = (e1))) -> (~((op (e3) (e3)) = (e0))) -> (~((op (e3) (e3)) = (e2))) -> (((op (e3) (e3)) = (e0))\/(((op (e3) (e3)) = (e1))\/(((op (e3) (e3)) = (e2))\/((op (e3) (e3)) = (e3))))) -> (((op (e0) (e0)) = (e2))\/(((op (e1) (e0)) = (e2))\/(((op (e2) (e0)) = (e2))\/((op (e3) (e0)) = (e2))))) -> False). % 15.22/15.40 do 0 intro. intros zenon_H10d zenon_H10a zenon_H12d zenon_H8f zenon_Ha7 zenon_Hd8 zenon_H154 zenon_H156 zenon_H1b3 zenon_H182 zenon_Hd6 zenon_H1b4 zenon_H3c zenon_H3d zenon_H3b zenon_Heb. % 15.22/15.40 apply (zenon_or_s _ _ zenon_H10d); [ zenon_intro zenon_H3e | zenon_intro zenon_H42 ]. % 15.22/15.40 apply (zenon_L407_); trivial. % 15.22/15.40 apply (zenon_L102_); trivial. % 15.22/15.40 (* end of lemma zenon_L408_ *) % 15.22/15.40 assert (zenon_L409_ : ((~((op (e2) (e2)) = (e1)))\/((op (e2) (e1)) = (e2))) -> (~((op (e2) (e1)) = (op (e2) (e3)))) -> ((~((op (e3) (e3)) = (e2)))\/((op (e3) (e2)) = (e3))) -> (~((op (e3) (e2)) = (op (e3) (e3)))) -> (((op (e0) (e1)) = (e3))\/(((op (e1) (e1)) = (e3))\/(((op (e2) (e1)) = (e3))\/((op (e3) (e1)) = (e3))))) -> (((op (e0) (e0)) = (e2))\/(((op (e1) (e0)) = (e2))\/(((op (e2) (e0)) = (e2))\/((op (e3) (e0)) = (e2))))) -> (((op (e3) (e3)) = (e0))\/(((op (e3) (e3)) = (e1))\/(((op (e3) (e3)) = (e2))\/((op (e3) (e3)) = (e3))))) -> (~((op (e2) (e0)) = (op (e2) (e1)))) -> ((~((op (e3) (e3)) = (e3)))\/((op (e3) (e3)) = (e3))) -> (~((op (e3) (e0)) = (op (e3) (e3)))) -> ((~((op (e3) (e3)) = (e0)))\/((op (e3) (e0)) = (e3))) -> (~((op (e2) (e1)) = (op (e2) (e2)))) -> ((~((op (e2) (e2)) = (e3)))\/((op (e2) (e3)) = (e2))) -> (~((op (e1) (e1)) = (e3))) -> (((op (e3) (e0)) = (e1))\/(((op (e3) (e1)) = (e1))\/(((op (e3) (e2)) = (e1))\/((op (e3) (e3)) = (e1))))) -> (~((op (e0) (e2)) = (op (e3) (e2)))) -> (((op (e0) (e2)) = (e1))\/(((op (e1) (e2)) = (e1))\/(((op (e2) (e2)) = (e1))\/((op (e3) (e2)) = (e1))))) -> (~((op (e3) (e1)) = (op (e3) (e2)))) -> (~((op (e0) (e2)) = (op (e0) (e3)))) -> (~((op (e1) (e0)) = (op (e3) (e0)))) -> (~((op (e1) (e3)) = (op (e3) (e3)))) -> (((op (e1) (e0)) = (e3))\/(((op (e1) (e1)) = (e3))\/(((op (e1) (e2)) = (e3))\/((op (e1) (e3)) = (e3))))) -> (~((op (e0) (e1)) = (op (e0) (e3)))) -> (~((e1) = (e2))) -> (((op (e0) (e0)) = (e1))\/(((op (e0) (e1)) = (e1))\/(((op (e0) (e2)) = (e1))\/((op (e0) (e3)) = (e1))))) -> (((op (e0) (e3)) = (e1))\/(((op (e1) (e3)) = (e1))\/(((op (e2) (e3)) = (e1))\/((op (e3) (e3)) = (e1))))) -> (((op (e2) (e2)) = (e0))\/(((op (e2) (e2)) = (e1))\/(((op (e2) (e2)) = (e2))\/((op (e2) (e2)) = (e3))))) -> ((op (e1) (e0)) = (e1)) -> (~((op (e1) (e0)) = (op (e1) (e3)))) -> ((op (e0) (e3)) = (e0)) -> (~((e0) = (e1))) -> (~((e1) = (e3))) -> (~((op (e0) (e2)) = (op (e2) (e2)))) -> (~((op (e2) (e2)) = (e0))) -> (~((op (e0) (e3)) = (op (e3) (e3)))) -> ((op (e3) (e3)) = (e3)) -> (((op (e0) (e0)) = (e3))\/(((op (e0) (e1)) = (e3))\/(((op (e0) (e2)) = (e3))\/((op (e0) (e3)) = (e3))))) -> (~((op (e0) (e0)) = (e1))) -> (~((op (e3) (e1)) = (op (e3) (e3)))) -> ((~((op (e3) (e3)) = (e1)))\/((op (e3) (e1)) = (e3))) -> (~((op (e0) (e0)) = (e2))) -> (~((e2) = (e3))) -> (~((e0) = (e2))) -> (((op (e0) (e0)) = (e2))\/(((op (e0) (e1)) = (e2))\/(((op (e0) (e2)) = (e2))\/((op (e0) (e3)) = (e2))))) -> (((op (e1) (e0)) = (e2))\/(((op (e1) (e1)) = (e2))\/(((op (e1) (e2)) = (e2))\/((op (e1) (e3)) = (e2))))) -> (~((op (e1) (e1)) = (e1))) -> (((op (e1) (e1)) = (e0))\/(((op (e1) (e1)) = (e1))\/(((op (e1) (e1)) = (e2))\/((op (e1) (e1)) = (e3))))) -> (~((op (e1) (e2)) = (op (e2) (e2)))) -> (~((op (e1) (e1)) = (e2))) -> (~((op (e0) (e2)) = (op (e1) (e2)))) -> ((~((op (e2) (e2)) = (e2)))\/((op (e2) (e2)) = (e2))) -> False). % 15.22/15.40 do 0 intro. intros zenon_H1e3 zenon_H1e2 zenon_H10e zenon_H173 zenon_H199 zenon_Heb zenon_H3b zenon_H154 zenon_H10d zenon_Hbb zenon_H10f zenon_H157 zenon_H1c3 zenon_H182 zenon_H146 zenon_H140 zenon_H11b zenon_H135 zenon_Hc9 zenon_H22e zenon_H8b zenon_H90 zenon_H1cd zenon_Ha7 zenon_H44 zenon_H121 zenon_H2d zenon_Hd8 zenon_H1cf zenon_Hca zenon_H9e zenon_Ha3 zenon_H28 zenon_H2e zenon_H36 zenon_H42 zenon_H58 zenon_H45 zenon_H12d zenon_H10c zenon_H8f zenon_H6a zenon_H5e zenon_H8e zenon_H84 zenon_H1b4 zenon_H1b3 zenon_H7d zenon_Hd6 zenon_H87 zenon_Haa. % 15.22/15.40 apply (zenon_or_s _ _ zenon_H1e3); [ zenon_intro zenon_H52 | zenon_intro zenon_H156 ]. % 15.22/15.40 apply (zenon_or_s _ _ zenon_Haa); [ zenon_intro zenon_H2f | zenon_intro zenon_H35 ]. % 15.22/15.40 apply (zenon_or_s _ _ zenon_H1c3); [ zenon_intro zenon_H30 | zenon_intro zenon_H124 ]. % 15.22/15.40 apply (zenon_or_s _ _ zenon_H10c); [ zenon_intro zenon_H104 | zenon_intro zenon_H10a ]. % 15.22/15.40 apply (zenon_or_s _ _ zenon_H44); [ zenon_intro zenon_H47 | zenon_intro zenon_H46 ]. % 15.22/15.40 exact (zenon_H45 zenon_H47). % 15.22/15.40 apply (zenon_or_s _ _ zenon_H46); [ zenon_intro zenon_H22 | zenon_intro zenon_H48 ]. % 15.22/15.40 apply (zenon_L331_); trivial. % 15.22/15.40 apply (zenon_or_s _ _ zenon_H48); [ zenon_intro zenon_H29 | zenon_intro zenon_H37 ]. % 15.22/15.40 apply (zenon_L5_); trivial. % 15.22/15.40 apply (zenon_L73_); trivial. % 15.22/15.40 apply (zenon_L102_); trivial. % 15.22/15.40 apply (zenon_or_s _ _ zenon_H10c); [ zenon_intro zenon_H104 | zenon_intro zenon_H10a ]. % 15.22/15.40 apply (zenon_L398_); trivial. % 15.22/15.40 apply (zenon_L102_); trivial. % 15.22/15.40 apply (zenon_L402_); trivial. % 15.22/15.40 apply (zenon_or_s _ _ zenon_Haa); [ zenon_intro zenon_H2f | zenon_intro zenon_H35 ]. % 15.22/15.40 apply (zenon_or_s _ _ zenon_H1c3); [ zenon_intro zenon_H30 | zenon_intro zenon_H124 ]. % 15.22/15.40 apply (zenon_or_s _ _ zenon_H10f); [ zenon_intro zenon_H3c | zenon_intro zenon_Hba ]. % 15.22/15.40 apply (zenon_or_s _ _ zenon_H10e); [ zenon_intro zenon_H3d | zenon_intro zenon_H106 ]. % 15.22/15.40 apply (zenon_or_s _ _ zenon_H44); [ zenon_intro zenon_H47 | zenon_intro zenon_H46 ]. % 15.22/15.40 exact (zenon_H45 zenon_H47). % 15.22/15.40 apply (zenon_or_s _ _ zenon_H46); [ zenon_intro zenon_H22 | zenon_intro zenon_H48 ]. % 15.22/15.40 apply (zenon_or_s _ _ zenon_H199); [ zenon_intro zenon_H4a | zenon_intro zenon_H19a ]. % 15.22/15.40 apply (zenon_L59_); trivial. % 15.22/15.40 apply (zenon_or_s _ _ zenon_H19a); [ zenon_intro zenon_H96 | zenon_intro zenon_H19b ]. % 15.22/15.40 exact (zenon_H182 zenon_H96). % 15.22/15.40 apply (zenon_or_s _ _ zenon_H19b); [ zenon_intro zenon_Hdf | zenon_intro zenon_H10a ]. % 15.22/15.40 apply (zenon_L183_); trivial. % 15.22/15.40 apply (zenon_L408_); trivial. % 15.22/15.40 apply (zenon_or_s _ _ zenon_H48); [ zenon_intro zenon_H29 | zenon_intro zenon_H37 ]. % 15.22/15.40 apply (zenon_L5_); trivial. % 15.22/15.40 apply (zenon_L73_); trivial. % 15.22/15.40 apply (zenon_L153_); trivial. % 15.22/15.40 apply (zenon_L43_); trivial. % 15.22/15.40 apply (zenon_L256_); trivial. % 15.22/15.40 apply (zenon_L134_); trivial. % 15.22/15.40 (* end of lemma zenon_L409_ *) % 15.22/15.40 assert (zenon_L410_ : (((op (e0) (e3)) = (e2))\/(((op (e1) (e3)) = (e2))\/(((op (e2) (e3)) = (e2))\/((op (e3) (e3)) = (e2))))) -> (~((op (e0) (e1)) = (op (e0) (e3)))) -> ((op (e0) (e1)) = (e2)) -> (~((e2) = (e3))) -> ((op (e1) (e3)) = (e3)) -> ((op (e2) (e0)) = (e2)) -> (~((op (e2) (e0)) = (op (e2) (e3)))) -> (~((op (e3) (e3)) = (e2))) -> False). % 15.22/15.40 do 0 intro. intros zenon_H160 zenon_H1cd zenon_H5d zenon_H6a zenon_H8a zenon_Hdd zenon_Hce zenon_H3d. % 15.22/15.40 apply (zenon_or_s _ _ zenon_H160); [ zenon_intro zenon_H81 | zenon_intro zenon_H161 ]. % 15.22/15.40 apply (zenon_L350_); trivial. % 15.22/15.40 apply (zenon_or_s _ _ zenon_H161); [ zenon_intro zenon_H82 | zenon_intro zenon_H162 ]. % 15.22/15.40 apply (zenon_L165_); trivial. % 15.22/15.40 apply (zenon_or_s _ _ zenon_H162); [ zenon_intro zenon_H124 | zenon_intro zenon_H43 ]. % 15.22/15.40 apply (zenon_L119_); trivial. % 15.22/15.40 exact (zenon_H3d zenon_H43). % 15.22/15.40 (* end of lemma zenon_L410_ *) % 15.22/15.40 assert (zenon_L411_ : (((op (e1) (e0)) = (e3))\/(((op (e1) (e1)) = (e3))\/(((op (e1) (e2)) = (e3))\/((op (e1) (e3)) = (e3))))) -> (~((e1) = (e3))) -> ((op (e1) (e0)) = (e1)) -> (~((op (e1) (e1)) = (e3))) -> ((op (e0) (e2)) = (e3)) -> (~((op (e0) (e2)) = (op (e1) (e2)))) -> (((op (e0) (e3)) = (e2))\/(((op (e1) (e3)) = (e2))\/(((op (e2) (e3)) = (e2))\/((op (e3) (e3)) = (e2))))) -> (~((op (e0) (e1)) = (op (e0) (e3)))) -> ((op (e0) (e1)) = (e2)) -> (~((e2) = (e3))) -> ((op (e2) (e0)) = (e2)) -> (~((op (e2) (e0)) = (op (e2) (e3)))) -> (~((op (e3) (e3)) = (e2))) -> False). % 15.22/15.40 do 0 intro. intros zenon_H90 zenon_Ha3 zenon_Hd8 zenon_H182 zenon_H50 zenon_H87 zenon_H160 zenon_H1cd zenon_H5d zenon_H6a zenon_Hdd zenon_Hce zenon_H3d. % 15.22/15.40 apply (zenon_or_s _ _ zenon_H90); [ zenon_intro zenon_H69 | zenon_intro zenon_H94 ]. % 15.22/15.40 apply (zenon_L163_); trivial. % 15.22/15.40 apply (zenon_or_s _ _ zenon_H94); [ zenon_intro zenon_H96 | zenon_intro zenon_H95 ]. % 15.22/15.40 exact (zenon_H182 zenon_H96). % 15.22/15.40 apply (zenon_or_s _ _ zenon_H95); [ zenon_intro zenon_H88 | zenon_intro zenon_H8a ]. % 15.22/15.40 apply (zenon_L24_); trivial. % 15.22/15.40 apply (zenon_L410_); trivial. % 15.22/15.40 (* end of lemma zenon_L411_ *) % 15.22/15.40 assert (zenon_L412_ : (((op (e0) (e0)) = (e3))\/(((op (e0) (e1)) = (e3))\/(((op (e0) (e2)) = (e3))\/((op (e0) (e3)) = (e3))))) -> (~((op (e3) (e3)) = (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 (e2) (e2)) = (e3))) -> (~((op (e1) (e0)) = (op (e1) (e3)))) -> ((op (e0) (e3)) = (e0)) -> (~((e0) = (e1))) -> (((op (e0) (e3)) = (e1))\/(((op (e1) (e3)) = (e1))\/(((op (e2) (e3)) = (e1))\/((op (e3) (e3)) = (e1))))) -> (~((op (e3) (e3)) = (e2))) -> (~((op (e2) (e0)) = (op (e2) (e3)))) -> ((op (e2) (e0)) = (e2)) -> (~((e2) = (e3))) -> ((op (e0) (e1)) = (e2)) -> (~((op (e0) (e1)) = (op (e0) (e3)))) -> (((op (e0) (e3)) = (e2))\/(((op (e1) (e3)) = (e2))\/(((op (e2) (e3)) = (e2))\/((op (e3) (e3)) = (e2))))) -> (~((op (e0) (e2)) = (op (e1) (e2)))) -> (~((op (e1) (e1)) = (e3))) -> ((op (e1) (e0)) = (e1)) -> (~((e1) = (e3))) -> (((op (e1) (e0)) = (e3))\/(((op (e1) (e1)) = (e3))\/(((op (e1) (e2)) = (e3))\/((op (e1) (e3)) = (e3))))) -> ((op (e3) (e3)) = (e3)) -> (~((op (e0) (e3)) = (op (e3) (e3)))) -> False). % 15.22/15.40 do 0 intro. intros zenon_H58 zenon_H104 zenon_H2d zenon_H52 zenon_H2f zenon_H30 zenon_H1cf zenon_Hca zenon_H9e zenon_H121 zenon_H3d zenon_Hce zenon_Hdd zenon_H6a zenon_H5d zenon_H1cd zenon_H160 zenon_H87 zenon_H182 zenon_Hd8 zenon_Ha3 zenon_H90 zenon_H42 zenon_H36. % 15.22/15.40 apply (zenon_or_s _ _ zenon_H58); [ zenon_intro zenon_H5b | zenon_intro zenon_H5a ]. % 15.22/15.40 apply (zenon_L330_); trivial. % 15.22/15.40 apply (zenon_or_s _ _ zenon_H5a); [ zenon_intro zenon_H4a | zenon_intro zenon_H5c ]. % 15.22/15.40 apply (zenon_L50_); trivial. % 15.22/15.40 apply (zenon_or_s _ _ zenon_H5c); [ zenon_intro zenon_H50 | zenon_intro zenon_H53 ]. % 15.22/15.41 apply (zenon_L411_); trivial. % 15.22/15.41 apply (zenon_L12_); trivial. % 15.22/15.41 (* end of lemma zenon_L412_ *) % 15.22/15.41 assert (zenon_L413_ : (((op (e0) (e0)) = (e3))\/(((op (e0) (e1)) = (e3))\/(((op (e0) (e2)) = (e3))\/((op (e0) (e3)) = (e3))))) -> (~((op (e3) (e3)) = (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 (e2) (e2)) = (e3))) -> (~((op (e1) (e0)) = (op (e1) (e3)))) -> ((op (e1) (e0)) = (e1)) -> ((op (e0) (e3)) = (e0)) -> (~((e0) = (e1))) -> (((op (e0) (e3)) = (e1))\/(((op (e1) (e3)) = (e1))\/(((op (e2) (e3)) = (e1))\/((op (e3) (e3)) = (e1))))) -> (~((e1) = (e3))) -> ((op (e0) (e1)) = (e1)) -> (~((e2) = (e3))) -> ((op (e0) (e2)) = (e2)) -> ((op (e3) (e3)) = (e3)) -> (~((op (e0) (e3)) = (op (e3) (e3)))) -> False). % 15.22/15.41 do 0 intro. intros zenon_H58 zenon_H104 zenon_H2d zenon_H52 zenon_H2f zenon_H30 zenon_H1cf zenon_Hd8 zenon_Hca zenon_H9e zenon_H121 zenon_Ha3 zenon_H22 zenon_H6a zenon_H63 zenon_H42 zenon_H36. % 15.22/15.41 apply (zenon_or_s _ _ zenon_H58); [ zenon_intro zenon_H5b | zenon_intro zenon_H5a ]. % 15.22/15.41 apply (zenon_L330_); trivial. % 15.22/15.41 apply (zenon_or_s _ _ zenon_H5a); [ zenon_intro zenon_H4a | zenon_intro zenon_H5c ]. % 15.22/15.41 apply (zenon_L59_); trivial. % 15.22/15.41 apply (zenon_or_s _ _ zenon_H5c); [ zenon_intro zenon_H50 | zenon_intro zenon_H53 ]. % 15.22/15.41 apply (zenon_L31_); trivial. % 15.22/15.41 apply (zenon_L12_); trivial. % 15.22/15.41 (* end of lemma zenon_L413_ *) % 15.22/15.41 assert (zenon_L414_ : ((op (e3) (e1)) = (e1)) -> ((op (e3) (e1)) = (e2)) -> (~((e1) = (e2))) -> False). % 15.22/15.41 do 0 intro. intros zenon_H13e zenon_H16a zenon_Ha7. % 15.22/15.41 elim (classic ((e2) = (e2))); [ zenon_intro zenon_H5f | zenon_intro zenon_H60 ]. % 15.22/15.41 cut (((e2) = (e2)) = ((e1) = (e2))). % 15.22/15.41 intro zenon_D_pnotp. % 15.22/15.41 apply zenon_Ha7. % 15.22/15.41 rewrite <- zenon_D_pnotp. % 15.22/15.41 exact zenon_H5f. % 15.22/15.41 cut (((e2) = (e2))); [idtac | apply NNPP; zenon_intro zenon_H60]. % 15.22/15.41 cut (((e2) = (e1))); [idtac | apply NNPP; zenon_intro zenon_Ha8]. % 15.22/15.41 congruence. % 15.22/15.41 cut (((op (e3) (e1)) = (e1)) = ((e2) = (e1))). % 15.22/15.41 intro zenon_D_pnotp. % 15.22/15.41 apply zenon_Ha8. % 15.22/15.41 rewrite <- zenon_D_pnotp. % 15.22/15.41 exact zenon_H13e. % 15.22/15.41 cut (((e1) = (e1))); [idtac | apply NNPP; zenon_intro zenon_Ha0]. % 15.22/15.41 cut (((op (e3) (e1)) = (e2))); [idtac | apply NNPP; zenon_intro zenon_H206]. % 15.22/15.41 congruence. % 15.22/15.41 exact (zenon_H206 zenon_H16a). % 15.22/15.41 apply zenon_Ha0. apply refl_equal. % 15.22/15.41 apply zenon_H60. apply refl_equal. % 15.22/15.41 apply zenon_H60. apply refl_equal. % 15.22/15.41 (* end of lemma zenon_L414_ *) % 15.22/15.41 assert (zenon_L415_ : (((op (e0) (e1)) = (e2))\/(((op (e1) (e1)) = (e2))\/(((op (e2) (e1)) = (e2))\/((op (e3) (e1)) = (e2))))) -> (~((op (e0) (e1)) = (op (e0) (e3)))) -> ((op (e0) (e3)) = (e2)) -> (~((op (e1) (e1)) = (e2))) -> ((op (e2) (e0)) = (e2)) -> (~((op (e2) (e0)) = (op (e2) (e1)))) -> ((op (e3) (e1)) = (e1)) -> (~((e1) = (e2))) -> False). % 15.22/15.41 do 0 intro. intros zenon_H1a2 zenon_H1cd zenon_H81 zenon_Hd6 zenon_Hdd zenon_H154 zenon_H13e zenon_Ha7. % 15.22/15.41 apply (zenon_or_s _ _ zenon_H1a2); [ zenon_intro zenon_H5d | zenon_intro zenon_H1a3 ]. % 15.22/15.41 apply (zenon_L350_); trivial. % 15.22/15.41 apply (zenon_or_s _ _ zenon_H1a3); [ zenon_intro zenon_H6e | zenon_intro zenon_H1a4 ]. % 15.22/15.41 exact (zenon_Hd6 zenon_H6e). % 15.22/15.41 apply (zenon_or_s _ _ zenon_H1a4); [ zenon_intro zenon_H156 | zenon_intro zenon_H16a ]. % 15.22/15.41 apply (zenon_L284_); trivial. % 15.22/15.41 apply (zenon_L414_); trivial. % 15.22/15.41 (* end of lemma zenon_L415_ *) % 15.22/15.41 assert (zenon_L416_ : (((op (e3) (e0)) = (e1))\/(((op (e3) (e1)) = (e1))\/(((op (e3) (e2)) = (e1))\/((op (e3) (e3)) = (e1))))) -> ((op (e1) (e0)) = (e1)) -> (~((op (e1) (e0)) = (op (e3) (e0)))) -> (~((e1) = (e2))) -> (~((op (e2) (e0)) = (op (e2) (e1)))) -> ((op (e2) (e0)) = (e2)) -> (~((op (e1) (e1)) = (e2))) -> ((op (e0) (e3)) = (e2)) -> (~((op (e0) (e1)) = (op (e0) (e3)))) -> (((op (e0) (e1)) = (e2))\/(((op (e1) (e1)) = (e2))\/(((op (e2) (e1)) = (e2))\/((op (e3) (e1)) = (e2))))) -> ((op (e0) (e2)) = (e1)) -> (~((op (e0) (e2)) = (op (e3) (e2)))) -> (~((op (e3) (e3)) = (e1))) -> False). % 15.22/15.41 do 0 intro. intros zenon_H146 zenon_Hd8 zenon_H22e zenon_Ha7 zenon_H154 zenon_Hdd zenon_Hd6 zenon_H81 zenon_H1cd zenon_H1a2 zenon_H29 zenon_H140 zenon_H104. % 15.22/15.41 apply (zenon_or_s _ _ zenon_H146); [ zenon_intro zenon_Hee | zenon_intro zenon_H14b ]. % 15.22/15.41 apply (zenon_L393_); trivial. % 15.22/15.41 apply (zenon_or_s _ _ zenon_H14b); [ zenon_intro zenon_H13e | zenon_intro zenon_H14c ]. % 15.22/15.41 apply (zenon_L415_); trivial. % 15.22/15.41 apply (zenon_or_s _ _ zenon_H14c); [ zenon_intro zenon_H119 | zenon_intro zenon_H38 ]. % 15.22/15.41 apply (zenon_L124_); trivial. % 15.22/15.41 exact (zenon_H104 zenon_H38). % 15.22/15.41 (* end of lemma zenon_L416_ *) % 15.22/15.41 assert (zenon_L417_ : (((op (e1) (e0)) = (e3))\/(((op (e1) (e1)) = (e3))\/(((op (e1) (e2)) = (e3))\/((op (e1) (e3)) = (e3))))) -> (~((e1) = (e3))) -> ((op (e1) (e0)) = (e1)) -> (~((op (e1) (e1)) = (e3))) -> (~((op (e1) (e2)) = (op (e3) (e2)))) -> ((op (e3) (e2)) = (e3)) -> ((op (e3) (e3)) = (e3)) -> (~((op (e1) (e3)) = (op (e3) (e3)))) -> False). % 15.22/15.41 do 0 intro. intros zenon_H90 zenon_Ha3 zenon_Hd8 zenon_H182 zenon_H17d zenon_H106 zenon_H42 zenon_H8b. % 15.22/15.41 apply (zenon_or_s _ _ zenon_H90); [ zenon_intro zenon_H69 | zenon_intro zenon_H94 ]. % 15.22/15.41 apply (zenon_L163_); trivial. % 15.22/15.41 apply (zenon_or_s _ _ zenon_H94); [ zenon_intro zenon_H96 | zenon_intro zenon_H95 ]. % 15.22/15.41 exact (zenon_H182 zenon_H96). % 15.22/15.41 apply (zenon_or_s _ _ zenon_H95); [ zenon_intro zenon_H88 | zenon_intro zenon_H8a ]. % 15.22/15.41 apply (zenon_L164_); trivial. % 15.22/15.41 apply (zenon_L25_); trivial. % 15.22/15.41 (* end of lemma zenon_L417_ *) % 15.22/15.41 assert (zenon_L418_ : ((~((op (e3) (e3)) = (e2)))\/((op (e3) (e2)) = (e3))) -> (~((op (e1) (e2)) = (op (e3) (e2)))) -> (~((op (e1) (e3)) = (op (e3) (e3)))) -> (~((op (e0) (e0)) = (e1))) -> (((op (e0) (e0)) = (e2))\/(((op (e0) (e1)) = (e2))\/(((op (e0) (e2)) = (e2))\/((op (e0) (e3)) = (e2))))) -> (~((e0) = (e2))) -> (((op (e0) (e3)) = (e1))\/(((op (e1) (e3)) = (e1))\/(((op (e2) (e3)) = (e1))\/((op (e3) (e3)) = (e1))))) -> (~((op (e3) (e3)) = (e1))) -> (~((op (e2) (e2)) = (e1))) -> (~((op (e2) (e2)) = (e2))) -> (~((op (e2) (e2)) = (e3))) -> (((op (e2) (e2)) = (e0))\/(((op (e2) (e2)) = (e1))\/(((op (e2) (e2)) = (e2))\/((op (e2) (e2)) = (e3))))) -> ((op (e1) (e0)) = (e1)) -> (~((op (e1) (e0)) = (op (e1) (e3)))) -> ((op (e0) (e3)) = (e0)) -> (~((e0) = (e1))) -> (~((e2) = (e3))) -> (((op (e1) (e0)) = (e3))\/(((op (e1) (e1)) = (e3))\/(((op (e1) (e2)) = (e3))\/((op (e1) (e3)) = (e3))))) -> (~((op (e0) (e1)) = (op (e0) (e3)))) -> (~((op (e2) (e0)) = (op (e2) (e3)))) -> ((op (e2) (e0)) = (e2)) -> (((op (e0) (e3)) = (e2))\/(((op (e1) (e3)) = (e2))\/(((op (e2) (e3)) = (e2))\/((op (e3) (e3)) = (e2))))) -> (~((op (e0) (e2)) = (op (e1) (e2)))) -> (~((op (e1) (e1)) = (e3))) -> (~((e1) = (e3))) -> (~((op (e0) (e3)) = (op (e3) (e3)))) -> ((op (e3) (e3)) = (e3)) -> (((op (e0) (e0)) = (e3))\/(((op (e0) (e1)) = (e3))\/(((op (e0) (e2)) = (e3))\/((op (e0) (e3)) = (e3))))) -> (~((op (e0) (e0)) = (e2))) -> (~((op (e1) (e0)) = (op (e3) (e0)))) -> (((op (e0) (e1)) = (e2))\/(((op (e1) (e1)) = (e2))\/(((op (e2) (e1)) = (e2))\/((op (e3) (e1)) = (e2))))) -> (~((op (e2) (e0)) = (op (e2) (e1)))) -> (~((op (e1) (e1)) = (e2))) -> (~((op (e0) (e2)) = (op (e3) (e2)))) -> (((op (e3) (e0)) = (e1))\/(((op (e3) (e1)) = (e1))\/(((op (e3) (e2)) = (e1))\/((op (e3) (e3)) = (e1))))) -> (~((e1) = (e2))) -> (((op (e0) (e0)) = (e1))\/(((op (e0) (e1)) = (e1))\/(((op (e0) (e2)) = (e1))\/((op (e0) (e3)) = (e1))))) -> False). % 15.22/15.41 do 0 intro. intros zenon_H10e zenon_H17d zenon_H8b zenon_H45 zenon_H8e zenon_H5e zenon_H121 zenon_H104 zenon_H52 zenon_H2f zenon_H30 zenon_H2d zenon_Hd8 zenon_H1cf zenon_Hca zenon_H9e zenon_H6a zenon_H90 zenon_H1cd zenon_Hce zenon_Hdd zenon_H160 zenon_H87 zenon_H182 zenon_Ha3 zenon_H36 zenon_H42 zenon_H58 zenon_H8f zenon_H22e zenon_H1a2 zenon_H154 zenon_Hd6 zenon_H140 zenon_H146 zenon_Ha7 zenon_H44. % 15.22/15.41 apply (zenon_or_s _ _ zenon_H10e); [ zenon_intro zenon_H3d | zenon_intro zenon_H106 ]. % 15.22/15.41 apply (zenon_or_s _ _ zenon_H44); [ zenon_intro zenon_H47 | zenon_intro zenon_H46 ]. % 15.22/15.41 exact (zenon_H45 zenon_H47). % 15.22/15.41 apply (zenon_or_s _ _ zenon_H46); [ zenon_intro zenon_H22 | zenon_intro zenon_H48 ]. % 15.22/15.41 apply (zenon_or_s _ _ zenon_H8e); [ zenon_intro zenon_H92 | zenon_intro zenon_H91 ]. % 15.22/15.41 exact (zenon_H8f zenon_H92). % 15.22/15.41 apply (zenon_or_s _ _ zenon_H91); [ zenon_intro zenon_H5d | zenon_intro zenon_H93 ]. % 15.22/15.41 apply (zenon_L412_); trivial. % 15.22/15.41 apply (zenon_or_s _ _ zenon_H93); [ zenon_intro zenon_H63 | zenon_intro zenon_H81 ]. % 15.22/15.41 apply (zenon_L413_); trivial. % 15.22/15.41 apply (zenon_L113_); trivial. % 15.22/15.41 apply (zenon_or_s _ _ zenon_H48); [ zenon_intro zenon_H29 | zenon_intro zenon_H37 ]. % 15.22/15.41 apply (zenon_or_s _ _ zenon_H8e); [ zenon_intro zenon_H92 | zenon_intro zenon_H91 ]. % 15.22/15.41 exact (zenon_H8f zenon_H92). % 15.22/15.41 apply (zenon_or_s _ _ zenon_H91); [ zenon_intro zenon_H5d | zenon_intro zenon_H93 ]. % 15.22/15.41 apply (zenon_L412_); trivial. % 15.22/15.41 apply (zenon_or_s _ _ zenon_H93); [ zenon_intro zenon_H63 | zenon_intro zenon_H81 ]. % 15.22/15.41 apply (zenon_L104_); trivial. % 15.22/15.41 apply (zenon_L416_); trivial. % 15.22/15.41 apply (zenon_L73_); trivial. % 15.22/15.41 apply (zenon_L417_); trivial. % 15.22/15.41 (* end of lemma zenon_L418_ *) % 15.22/15.41 assert (zenon_L419_ : ((~((op (e1) (e1)) = (e3)))\/((op (e1) (e3)) = (e1))) -> ((~((op (e2) (e2)) = (e1)))\/((op (e2) (e1)) = (e2))) -> (~((op (e2) (e1)) = (op (e2) (e3)))) -> ((~((op (e3) (e3)) = (e2)))\/((op (e3) (e2)) = (e3))) -> (~((op (e3) (e2)) = (op (e3) (e3)))) -> (((op (e0) (e1)) = (e3))\/(((op (e1) (e1)) = (e3))\/(((op (e2) (e1)) = (e3))\/((op (e3) (e1)) = (e3))))) -> (((op (e0) (e0)) = (e2))\/(((op (e1) (e0)) = (e2))\/(((op (e2) (e0)) = (e2))\/((op (e3) (e0)) = (e2))))) -> (((op (e3) (e3)) = (e0))\/(((op (e3) (e3)) = (e1))\/(((op (e3) (e3)) = (e2))\/((op (e3) (e3)) = (e3))))) -> (~((op (e2) (e0)) = (op (e2) (e1)))) -> ((~((op (e3) (e3)) = (e3)))\/((op (e3) (e3)) = (e3))) -> (~((op (e3) (e0)) = (op (e3) (e3)))) -> ((~((op (e3) (e3)) = (e0)))\/((op (e3) (e0)) = (e3))) -> (~((op (e2) (e1)) = (op (e2) (e2)))) -> ((~((op (e2) (e2)) = (e3)))\/((op (e2) (e3)) = (e2))) -> (((op (e3) (e0)) = (e1))\/(((op (e3) (e1)) = (e1))\/(((op (e3) (e2)) = (e1))\/((op (e3) (e3)) = (e1))))) -> (~((op (e0) (e2)) = (op (e3) (e2)))) -> (((op (e0) (e2)) = (e1))\/(((op (e1) (e2)) = (e1))\/(((op (e2) (e2)) = (e1))\/((op (e3) (e2)) = (e1))))) -> (~((op (e3) (e1)) = (op (e3) (e2)))) -> (~((op (e0) (e2)) = (op (e0) (e3)))) -> (~((op (e1) (e0)) = (op (e3) (e0)))) -> (~((op (e1) (e3)) = (op (e3) (e3)))) -> (((op (e1) (e0)) = (e3))\/(((op (e1) (e1)) = (e3))\/(((op (e1) (e2)) = (e3))\/((op (e1) (e3)) = (e3))))) -> (~((op (e0) (e1)) = (op (e0) (e3)))) -> (~((e1) = (e2))) -> (((op (e0) (e0)) = (e1))\/(((op (e0) (e1)) = (e1))\/(((op (e0) (e2)) = (e1))\/((op (e0) (e3)) = (e1))))) -> (((op (e0) (e3)) = (e1))\/(((op (e1) (e3)) = (e1))\/(((op (e2) (e3)) = (e1))\/((op (e3) (e3)) = (e1))))) -> (((op (e2) (e2)) = (e0))\/(((op (e2) (e2)) = (e1))\/(((op (e2) (e2)) = (e2))\/((op (e2) (e2)) = (e3))))) -> ((op (e1) (e0)) = (e1)) -> (~((op (e1) (e0)) = (op (e1) (e3)))) -> ((op (e0) (e3)) = (e0)) -> (~((e0) = (e1))) -> (~((e1) = (e3))) -> (~((op (e0) (e2)) = (op (e2) (e2)))) -> (~((op (e0) (e3)) = (op (e3) (e3)))) -> ((op (e3) (e3)) = (e3)) -> (((op (e0) (e0)) = (e3))\/(((op (e0) (e1)) = (e3))\/(((op (e0) (e2)) = (e3))\/((op (e0) (e3)) = (e3))))) -> (~((op (e0) (e0)) = (e1))) -> (~((op (e3) (e1)) = (op (e3) (e3)))) -> ((~((op (e3) (e3)) = (e1)))\/((op (e3) (e1)) = (e3))) -> (~((op (e0) (e0)) = (e2))) -> (~((e2) = (e3))) -> (~((e0) = (e2))) -> (((op (e0) (e0)) = (e2))\/(((op (e0) (e1)) = (e2))\/(((op (e0) (e2)) = (e2))\/((op (e0) (e3)) = (e2))))) -> (((op (e1) (e0)) = (e2))\/(((op (e1) (e1)) = (e2))\/(((op (e1) (e2)) = (e2))\/((op (e1) (e3)) = (e2))))) -> (~((op (e1) (e1)) = (e1))) -> (((op (e1) (e1)) = (e0))\/(((op (e1) (e1)) = (e1))\/(((op (e1) (e1)) = (e2))\/((op (e1) (e1)) = (e3))))) -> (~((op (e1) (e2)) = (op (e2) (e2)))) -> (~((op (e1) (e1)) = (e2))) -> (~((op (e0) (e2)) = (op (e1) (e2)))) -> ((~((op (e2) (e2)) = (e2)))\/((op (e2) (e2)) = (e2))) -> (~((op (e1) (e2)) = (op (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 (e0) (e1)) = (e2))\/(((op (e1) (e1)) = (e2))\/(((op (e2) (e1)) = (e2))\/((op (e3) (e1)) = (e2))))) -> (~((op (e2) (e0)) = (op (e2) (e2)))) -> ((~((op (e2) (e2)) = (e0)))\/((op (e2) (e0)) = (e2))) -> False). % 15.22/15.41 do 0 intro. intros zenon_H1d2 zenon_H1e3 zenon_H1e2 zenon_H10e zenon_H173 zenon_H199 zenon_Heb zenon_H3b zenon_H154 zenon_H10d zenon_Hbb zenon_H10f zenon_H157 zenon_H1c3 zenon_H146 zenon_H140 zenon_H11b zenon_H135 zenon_Hc9 zenon_H22e zenon_H8b zenon_H90 zenon_H1cd zenon_Ha7 zenon_H44 zenon_H121 zenon_H2d zenon_Hd8 zenon_H1cf zenon_Hca zenon_H9e zenon_Ha3 zenon_H28 zenon_H36 zenon_H42 zenon_H58 zenon_H45 zenon_H12d zenon_H10c zenon_H8f zenon_H6a zenon_H5e zenon_H8e zenon_H84 zenon_H1b4 zenon_H1b3 zenon_H7d zenon_Hd6 zenon_H87 zenon_Haa zenon_H17d zenon_Hce zenon_H160 zenon_H1a2 zenon_H17a zenon_H1d4. % 15.22/15.41 apply (zenon_or_s _ _ zenon_H1d2); [ zenon_intro zenon_H182 | zenon_intro zenon_H11f ]. % 15.22/15.41 apply (zenon_or_s _ _ zenon_H1d4); [ zenon_intro zenon_H2e | zenon_intro zenon_Hdd ]. % 15.22/15.41 apply (zenon_L409_); trivial. % 15.22/15.41 apply (zenon_or_s _ _ zenon_H1e3); [ zenon_intro zenon_H52 | zenon_intro zenon_H156 ]. % 15.22/15.41 apply (zenon_or_s _ _ zenon_Haa); [ zenon_intro zenon_H2f | zenon_intro zenon_H35 ]. % 15.22/15.41 apply (zenon_or_s _ _ zenon_H1c3); [ zenon_intro zenon_H30 | zenon_intro zenon_H124 ]. % 15.22/15.41 apply (zenon_or_s _ _ zenon_H10c); [ zenon_intro zenon_H104 | zenon_intro zenon_H10a ]. % 15.22/15.41 apply (zenon_L418_); trivial. % 15.22/15.41 apply (zenon_L102_); trivial. % 15.22/15.41 apply (zenon_L119_); trivial. % 15.22/15.41 apply (zenon_L161_); trivial. % 15.22/15.41 apply (zenon_L284_); trivial. % 15.22/15.41 apply (zenon_L224_); trivial. % 15.22/15.41 (* end of lemma zenon_L419_ *) % 15.22/15.41 assert (zenon_L420_ : ((~((op (e1) (e1)) = (e2)))\/((op (e1) (e2)) = (e1))) -> (~((op (e1) (e0)) = (op (e1) (e2)))) -> ((~((op (e2) (e2)) = (e0)))\/((op (e2) (e0)) = (e2))) -> (~((op (e2) (e0)) = (op (e2) (e2)))) -> (((op (e0) (e1)) = (e2))\/(((op (e1) (e1)) = (e2))\/(((op (e2) (e1)) = (e2))\/((op (e3) (e1)) = (e2))))) -> (((op (e0) (e3)) = (e2))\/(((op (e1) (e3)) = (e2))\/(((op (e2) (e3)) = (e2))\/((op (e3) (e3)) = (e2))))) -> (~((op (e2) (e0)) = (op (e2) (e3)))) -> (~((op (e1) (e2)) = (op (e3) (e2)))) -> ((~((op (e2) (e2)) = (e2)))\/((op (e2) (e2)) = (e2))) -> (~((op (e0) (e2)) = (op (e1) (e2)))) -> (~((op (e1) (e2)) = (op (e2) (e2)))) -> (((op (e1) (e1)) = (e0))\/(((op (e1) (e1)) = (e1))\/(((op (e1) (e1)) = (e2))\/((op (e1) (e1)) = (e3))))) -> (~((op (e1) (e1)) = (e1))) -> (((op (e1) (e0)) = (e2))\/(((op (e1) (e1)) = (e2))\/(((op (e1) (e2)) = (e2))\/((op (e1) (e3)) = (e2))))) -> (((op (e0) (e0)) = (e2))\/(((op (e0) (e1)) = (e2))\/(((op (e0) (e2)) = (e2))\/((op (e0) (e3)) = (e2))))) -> (~((e0) = (e2))) -> (~((e2) = (e3))) -> (~((op (e0) (e0)) = (e2))) -> ((~((op (e3) (e3)) = (e1)))\/((op (e3) (e1)) = (e3))) -> (~((op (e3) (e1)) = (op (e3) (e3)))) -> (~((op (e0) (e0)) = (e1))) -> (((op (e0) (e0)) = (e3))\/(((op (e0) (e1)) = (e3))\/(((op (e0) (e2)) = (e3))\/((op (e0) (e3)) = (e3))))) -> ((op (e3) (e3)) = (e3)) -> (~((op (e0) (e3)) = (op (e3) (e3)))) -> (~((op (e0) (e2)) = (op (e2) (e2)))) -> (~((e1) = (e3))) -> (~((e0) = (e1))) -> ((op (e0) (e3)) = (e0)) -> (~((op (e1) (e0)) = (op (e1) (e3)))) -> ((op (e1) (e0)) = (e1)) -> (((op (e2) (e2)) = (e0))\/(((op (e2) (e2)) = (e1))\/(((op (e2) (e2)) = (e2))\/((op (e2) (e2)) = (e3))))) -> (((op (e0) (e3)) = (e1))\/(((op (e1) (e3)) = (e1))\/(((op (e2) (e3)) = (e1))\/((op (e3) (e3)) = (e1))))) -> (((op (e0) (e0)) = (e1))\/(((op (e0) (e1)) = (e1))\/(((op (e0) (e2)) = (e1))\/((op (e0) (e3)) = (e1))))) -> (~((e1) = (e2))) -> (~((op (e0) (e1)) = (op (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) (e0)) = (op (e3) (e0)))) -> (~((op (e0) (e2)) = (op (e0) (e3)))) -> (~((op (e3) (e1)) = (op (e3) (e2)))) -> (((op (e0) (e2)) = (e1))\/(((op (e1) (e2)) = (e1))\/(((op (e2) (e2)) = (e1))\/((op (e3) (e2)) = (e1))))) -> (~((op (e0) (e2)) = (op (e3) (e2)))) -> (((op (e3) (e0)) = (e1))\/(((op (e3) (e1)) = (e1))\/(((op (e3) (e2)) = (e1))\/((op (e3) (e3)) = (e1))))) -> ((~((op (e2) (e2)) = (e3)))\/((op (e2) (e3)) = (e2))) -> (~((op (e2) (e1)) = (op (e2) (e2)))) -> ((~((op (e3) (e3)) = (e0)))\/((op (e3) (e0)) = (e3))) -> (~((op (e3) (e0)) = (op (e3) (e3)))) -> ((~((op (e3) (e3)) = (e3)))\/((op (e3) (e3)) = (e3))) -> (~((op (e2) (e0)) = (op (e2) (e1)))) -> (((op (e3) (e3)) = (e0))\/(((op (e3) (e3)) = (e1))\/(((op (e3) (e3)) = (e2))\/((op (e3) (e3)) = (e3))))) -> (((op (e0) (e0)) = (e2))\/(((op (e1) (e0)) = (e2))\/(((op (e2) (e0)) = (e2))\/((op (e3) (e0)) = (e2))))) -> (((op (e0) (e1)) = (e3))\/(((op (e1) (e1)) = (e3))\/(((op (e2) (e1)) = (e3))\/((op (e3) (e1)) = (e3))))) -> (~((op (e3) (e2)) = (op (e3) (e3)))) -> ((~((op (e3) (e3)) = (e2)))\/((op (e3) (e2)) = (e3))) -> (~((op (e2) (e1)) = (op (e2) (e3)))) -> ((~((op (e2) (e2)) = (e1)))\/((op (e2) (e1)) = (e2))) -> ((~((op (e1) (e1)) = (e3)))\/((op (e1) (e3)) = (e1))) -> False). % 15.22/15.41 do 0 intro. intros zenon_H1d3 zenon_H166 zenon_H1d4 zenon_H17a zenon_H1a2 zenon_H160 zenon_Hce zenon_H17d zenon_Haa zenon_H87 zenon_H7d zenon_H1b3 zenon_H1b4 zenon_H84 zenon_H8e zenon_H5e zenon_H6a zenon_H8f zenon_H10c zenon_H12d zenon_H45 zenon_H58 zenon_H42 zenon_H36 zenon_H28 zenon_Ha3 zenon_H9e zenon_Hca zenon_H1cf zenon_Hd8 zenon_H2d zenon_H121 zenon_H44 zenon_Ha7 zenon_H1cd zenon_H90 zenon_H8b zenon_H22e zenon_Hc9 zenon_H135 zenon_H11b zenon_H140 zenon_H146 zenon_H1c3 zenon_H157 zenon_H10f zenon_Hbb zenon_H10d zenon_H154 zenon_H3b zenon_Heb zenon_H199 zenon_H173 zenon_H10e zenon_H1e2 zenon_H1e3 zenon_H1d2. % 15.22/15.41 apply (zenon_or_s _ _ zenon_H1d3); [ zenon_intro zenon_Hd6 | zenon_intro zenon_H117 ]. % 15.22/15.41 apply (zenon_L419_); trivial. % 15.22/15.41 apply (zenon_L248_); trivial. % 15.22/15.41 (* end of lemma zenon_L420_ *) % 15.22/15.41 assert (zenon_L421_ : (((op (e0) (e3)) = (e0))\/(((op (e1) (e3)) = (e0))\/(((op (e2) (e3)) = (e0))\/((op (e3) (e3)) = (e0))))) -> ((op (e0) (e3)) = (e2)) -> ((op (e1) (e3)) = (e1)) -> (~((e0) = (e1))) -> ((op (e2) (e3)) = (e2)) -> (~((e0) = (e2))) -> (~((op (e3) (e3)) = (e0))) -> False). % 15.22/15.41 do 0 intro. intros zenon_Hd3 zenon_H81 zenon_H11f zenon_H9e zenon_H124 zenon_H5e zenon_H3c. % 15.22/15.41 apply (zenon_or_s _ _ zenon_Hd3); [ zenon_intro zenon_Hca | zenon_intro zenon_Hd4 ]. % 15.22/15.41 apply (zenon_L113_); trivial. % 15.22/15.41 apply (zenon_or_s _ _ zenon_Hd4); [ zenon_intro zenon_Hcc | zenon_intro zenon_Hd5 ]. % 15.22/15.41 apply (zenon_L208_); trivial. % 15.22/15.41 apply (zenon_or_s _ _ zenon_Hd5); [ zenon_intro zenon_Hd0 | zenon_intro zenon_H40 ]. % 15.22/15.41 apply (zenon_L201_); trivial. % 15.22/15.41 exact (zenon_H3c zenon_H40). % 15.22/15.41 (* end of lemma zenon_L421_ *) % 15.22/15.41 assert (zenon_L422_ : (((op (e0) (e0)) = (e0))\/(((op (e1) (e0)) = (e0))\/(((op (e2) (e0)) = (e0))\/((op (e3) (e0)) = (e0))))) -> (~((op (e0) (e0)) = (e0))) -> (~((op (e3) (e3)) = (e0))) -> (((op (e0) (e3)) = (e2))\/(((op (e1) (e3)) = (e2))\/(((op (e2) (e3)) = (e2))\/((op (e3) (e3)) = (e2))))) -> (~((e0) = (e2))) -> (~((op (e3) (e3)) = (e2))) -> (((op (e0) (e3)) = (e0))\/(((op (e1) (e3)) = (e0))\/(((op (e2) (e3)) = (e0))\/((op (e3) (e3)) = (e0))))) -> (((op (e0) (e0)) = (e2))\/(((op (e0) (e1)) = (e2))\/(((op (e0) (e2)) = (e2))\/((op (e0) (e3)) = (e2))))) -> (~((op (e0) (e0)) = (e2))) -> (~((op (e1) (op (e0) (e1))) = (op (e0) (e1)))) -> (~((op (e1) (e1)) = (e2))) -> (((op (e1) (e0)) = (e2))\/(((op (e1) (e1)) = (e2))\/(((op (e1) (e2)) = (e2))\/((op (e1) (e3)) = (e2))))) -> ((~((op (e1) (e1)) = (e3)))\/((op (e1) (e3)) = (e1))) -> ((~((op (e2) (e2)) = (e1)))\/((op (e2) (e1)) = (e2))) -> (~((op (e2) (e1)) = (op (e2) (e3)))) -> ((~((op (e3) (e3)) = (e2)))\/((op (e3) (e2)) = (e3))) -> (~((op (e3) (e2)) = (op (e3) (e3)))) -> (((op (e0) (e1)) = (e3))\/(((op (e1) (e1)) = (e3))\/(((op (e2) (e1)) = (e3))\/((op (e3) (e1)) = (e3))))) -> (((op (e3) (e3)) = (e0))\/(((op (e3) (e3)) = (e1))\/(((op (e3) (e3)) = (e2))\/((op (e3) (e3)) = (e3))))) -> (~((op (e2) (e0)) = (op (e2) (e1)))) -> ((~((op (e3) (e3)) = (e3)))\/((op (e3) (e3)) = (e3))) -> (~((op (e3) (e0)) = (op (e3) (e3)))) -> ((~((op (e3) (e3)) = (e0)))\/((op (e3) (e0)) = (e3))) -> (~((op (e2) (e1)) = (op (e2) (e2)))) -> ((~((op (e2) (e2)) = (e3)))\/((op (e2) (e3)) = (e2))) -> (((op (e3) (e0)) = (e1))\/(((op (e3) (e1)) = (e1))\/(((op (e3) (e2)) = (e1))\/((op (e3) (e3)) = (e1))))) -> (~((op (e0) (e2)) = (op (e3) (e2)))) -> (((op (e0) (e2)) = (e1))\/(((op (e1) (e2)) = (e1))\/(((op (e2) (e2)) = (e1))\/((op (e3) (e2)) = (e1))))) -> (~((op (e3) (e1)) = (op (e3) (e2)))) -> (~((op (e0) (e2)) = (op (e0) (e3)))) -> (~((op (e1) (e0)) = (op (e3) (e0)))) -> (~((op (e1) (e3)) = (op (e3) (e3)))) -> (((op (e1) (e0)) = (e3))\/(((op (e1) (e1)) = (e3))\/(((op (e1) (e2)) = (e3))\/((op (e1) (e3)) = (e3))))) -> (((op (e2) (e2)) = (e0))\/(((op (e2) (e2)) = (e1))\/(((op (e2) (e2)) = (e2))\/((op (e2) (e2)) = (e3))))) -> (~((e1) = (e3))) -> (~((op (e0) (e2)) = (op (e2) (e2)))) -> (~((op (e0) (e3)) = (op (e3) (e3)))) -> ((op (e3) (e3)) = (e3)) -> (((op (e0) (e0)) = (e3))\/(((op (e0) (e1)) = (e3))\/(((op (e0) (e2)) = (e3))\/((op (e0) (e3)) = (e3))))) -> (~((op (e3) (e1)) = (op (e3) (e3)))) -> ((~((op (e3) (e3)) = (e1)))\/((op (e3) (e1)) = (e3))) -> (~((e2) = (e3))) -> (((op (e1) (e1)) = (e0))\/(((op (e1) (e1)) = (e1))\/(((op (e1) (e1)) = (e2))\/((op (e1) (e1)) = (e3))))) -> (~((op (e1) (e2)) = (op (e2) (e2)))) -> ((~((op (e2) (e2)) = (e2)))\/((op (e2) (e2)) = (e2))) -> (~((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) (e2)))) -> ((~((op (e2) (e2)) = (e0)))\/((op (e2) (e0)) = (e2))) -> (~((op (e1) (e0)) = (op (e1) (e2)))) -> ((~((op (e1) (e1)) = (e2)))\/((op (e1) (e2)) = (e1))) -> (~((op (e0) (e2)) = (op (e1) (e2)))) -> (((op (e0) (e3)) = (e1))\/(((op (e1) (e3)) = (e1))\/(((op (e2) (e3)) = (e1))\/((op (e3) (e3)) = (e1))))) -> (~((op (e0) (e1)) = (op (e0) (e3)))) -> (~((op (e3) (e3)) = (e1))) -> (((op (e0) (e0)) = (e2))\/(((op (e1) (e0)) = (e2))\/(((op (e2) (e0)) = (e2))\/((op (e3) (e0)) = (e2))))) -> (~((op (e2) (e0)) = (op (e2) (e3)))) -> (~((e0) = (e1))) -> (((op (e0) (e0)) = (e1))\/(((op (e1) (e0)) = (e1))\/(((op (e2) (e0)) = (e1))\/((op (e3) (e0)) = (e1))))) -> (~((op (e0) (e0)) = (e1))) -> ((op (e1) (e3)) = (e1)) -> (~((op (e1) (e0)) = (op (e1) (e3)))) -> (((op (e0) (e1)) = (e1))\/(((op (e1) (e1)) = (e1))\/(((op (e2) (e1)) = (e1))\/((op (e3) (e1)) = (e1))))) -> ((op (e2) (e3)) = (e2)) -> (~((e1) = (e2))) -> (~((op (e2) (e2)) = (e1))) -> (~((op (e0) (e1)) = (op (e2) (e1)))) -> (((op (e2) (e0)) = (e1))\/(((op (e2) (e1)) = (e1))\/(((op (e2) (e2)) = (e1))\/((op (e2) (e3)) = (e1))))) -> (~((op (e1) (e1)) = (e1))) -> (~((op (e2) (op (e0) (e2))) = (op (e0) (e2)))) -> (~((op (e3) (e0)) = (op (e3) (e1)))) -> (((op (e0) (e0)) = (e1))\/(((op (e0) (e1)) = (e1))\/(((op (e0) (e2)) = (e1))\/((op (e0) (e3)) = (e1))))) -> (~((op (e3) (op (e0) (e3))) = (op (e0) (e3)))) -> ((op (e0) (e3)) = (e0)) -> False). % 15.22/15.41 do 0 intro. intros zenon_Hf0 zenon_H20 zenon_H3c zenon_H160 zenon_H5e zenon_H3d zenon_Hd3 zenon_H8e zenon_H8f zenon_H1ff zenon_Hd6 zenon_H84 zenon_H1d2 zenon_H1e3 zenon_H1e2 zenon_H10e zenon_H173 zenon_H199 zenon_H3b zenon_H154 zenon_H10d zenon_Hbb zenon_H10f zenon_H157 zenon_H1c3 zenon_H146 zenon_H140 zenon_H11b zenon_H135 zenon_Hc9 zenon_H22e zenon_H8b zenon_H90 zenon_H2d zenon_Ha3 zenon_H28 zenon_H36 zenon_H42 zenon_H58 zenon_H12d zenon_H10c zenon_H6a zenon_H1b3 zenon_H7d zenon_Haa zenon_H17d zenon_H1a2 zenon_H17a zenon_H1d4 zenon_H166 zenon_H1d3 zenon_H87 zenon_H121 zenon_H1cd zenon_H104 zenon_Heb zenon_Hce zenon_H9e zenon_Hf1 zenon_H45 zenon_H11f zenon_H1cf zenon_H228 zenon_H124 zenon_Ha7 zenon_H52 zenon_Hde zenon_Hb7 zenon_H1b4 zenon_H20c zenon_H109 zenon_H44 zenon_H192 zenon_Hca. % 15.22/15.41 apply (zenon_or_s _ _ zenon_Hf0); [ zenon_intro zenon_H1f | zenon_intro zenon_Hf2 ]. % 15.22/15.41 exact (zenon_H20 zenon_H1f). % 15.22/15.41 apply (zenon_or_s _ _ zenon_Hf2); [ zenon_intro zenon_Had | zenon_intro zenon_Hf3 ]. % 15.22/15.41 apply (zenon_or_s _ _ zenon_H44); [ zenon_intro zenon_H47 | zenon_intro zenon_H46 ]. % 15.22/15.41 exact (zenon_H45 zenon_H47). % 15.22/15.41 apply (zenon_or_s _ _ zenon_H46); [ zenon_intro zenon_H22 | zenon_intro zenon_H48 ]. % 15.22/15.41 apply (zenon_or_s _ _ zenon_Hf1); [ zenon_intro zenon_H47 | zenon_intro zenon_Hf4 ]. % 15.22/15.41 exact (zenon_H45 zenon_H47). % 15.22/15.41 apply (zenon_or_s _ _ zenon_Hf4); [ zenon_intro zenon_Hd8 | zenon_intro zenon_Hf5 ]. % 15.22/15.41 apply (zenon_L420_); trivial. % 15.22/15.41 apply (zenon_or_s _ _ zenon_Hf5); [ zenon_intro zenon_Hae | zenon_intro zenon_Hee ]. % 15.22/15.41 apply (zenon_or_s _ _ zenon_H8e); [ zenon_intro zenon_H92 | zenon_intro zenon_H91 ]. % 15.22/15.41 exact (zenon_H8f zenon_H92). % 15.22/15.41 apply (zenon_or_s _ _ zenon_H91); [ zenon_intro zenon_H5d | zenon_intro zenon_H93 ]. % 15.22/15.41 apply (zenon_L388_); trivial. % 15.22/15.41 apply (zenon_or_s _ _ zenon_H93); [ zenon_intro zenon_H63 | zenon_intro zenon_H81 ]. % 15.22/15.41 apply (zenon_L333_); trivial. % 15.22/15.41 apply (zenon_L421_); trivial. % 15.22/15.41 apply (zenon_L390_); trivial. % 15.22/15.41 apply (zenon_or_s _ _ zenon_H48); [ zenon_intro zenon_H29 | zenon_intro zenon_H37 ]. % 15.22/15.41 apply (zenon_or_s _ _ zenon_H8e); [ zenon_intro zenon_H92 | zenon_intro zenon_H91 ]. % 15.22/15.41 exact (zenon_H8f zenon_H92). % 15.22/15.41 apply (zenon_or_s _ _ zenon_H91); [ zenon_intro zenon_H5d | zenon_intro zenon_H93 ]. % 15.22/15.41 apply (zenon_L388_); trivial. % 15.22/15.41 apply (zenon_or_s _ _ zenon_H93); [ zenon_intro zenon_H63 | zenon_intro zenon_H81 ]. % 15.22/15.41 apply (zenon_L104_); trivial. % 15.22/15.41 apply (zenon_L421_); trivial. % 15.22/15.41 apply (zenon_L211_); trivial. % 15.22/15.41 apply (zenon_or_s _ _ zenon_Hf3); [ zenon_intro zenon_Hcf | zenon_intro zenon_Hdb ]. % 15.22/15.41 apply (zenon_or_s _ _ zenon_H44); [ zenon_intro zenon_H47 | zenon_intro zenon_H46 ]. % 15.22/15.41 exact (zenon_H45 zenon_H47). % 15.22/15.41 apply (zenon_or_s _ _ zenon_H46); [ zenon_intro zenon_H22 | zenon_intro zenon_H48 ]. % 15.22/15.41 apply (zenon_L340_); trivial. % 15.22/15.41 apply (zenon_or_s _ _ zenon_H48); [ zenon_intro zenon_H29 | zenon_intro zenon_H37 ]. % 15.22/15.41 apply (zenon_or_s _ _ zenon_Hf1); [ zenon_intro zenon_H47 | zenon_intro zenon_Hf4 ]. % 15.22/15.41 exact (zenon_H45 zenon_H47). % 15.22/15.41 apply (zenon_or_s _ _ zenon_Hf4); [ zenon_intro zenon_Hd8 | zenon_intro zenon_Hf5 ]. % 15.22/15.41 apply (zenon_L224_); trivial. % 15.22/15.41 apply (zenon_or_s _ _ zenon_Hf5); [ zenon_intro zenon_Hae | zenon_intro zenon_Hee ]. % 15.22/15.41 apply (zenon_L269_); trivial. % 15.22/15.41 apply (zenon_or_s _ _ zenon_H228); [ zenon_intro zenon_H22 | zenon_intro zenon_H229 ]. % 15.22/15.41 apply (zenon_L340_); trivial. % 15.22/15.41 apply (zenon_or_s _ _ zenon_H229); [ zenon_intro zenon_H21 | zenon_intro zenon_H22a ]. % 15.22/15.41 exact (zenon_H1b4 zenon_H21). % 15.22/15.41 apply (zenon_or_s _ _ zenon_H22a); [ zenon_intro zenon_Hb2 | zenon_intro zenon_H13e ]. % 15.22/15.41 cut (((op (e2) (e1)) = (e1)) = ((op (e2) (op (e0) (e2))) = (op (e0) (e2)))). % 15.22/15.41 intro zenon_D_pnotp. % 15.22/15.41 apply zenon_H20c. % 15.22/15.41 rewrite <- zenon_D_pnotp. % 15.22/15.41 exact zenon_Hb2. % 15.22/15.41 cut (((e1) = (op (e0) (e2)))); [idtac | apply NNPP; zenon_intro zenon_H115]. % 15.22/15.41 cut (((op (e2) (e1)) = (op (e2) (op (e0) (e2))))); [idtac | apply NNPP; zenon_intro zenon_H234]. % 15.22/15.41 congruence. % 15.22/15.41 elim (classic ((op (e2) (op (e0) (e2))) = (op (e2) (op (e0) (e2))))); [ zenon_intro zenon_H20f | zenon_intro zenon_H210 ]. % 15.22/15.41 cut (((op (e2) (op (e0) (e2))) = (op (e2) (op (e0) (e2)))) = ((op (e2) (e1)) = (op (e2) (op (e0) (e2))))). % 15.22/15.41 intro zenon_D_pnotp. % 15.22/15.41 apply zenon_H234. % 15.22/15.41 rewrite <- zenon_D_pnotp. % 15.22/15.41 exact zenon_H20f. % 15.22/15.41 cut (((op (e2) (op (e0) (e2))) = (op (e2) (op (e0) (e2))))); [idtac | apply NNPP; zenon_intro zenon_H210]. % 15.22/15.41 cut (((op (e2) (op (e0) (e2))) = (op (e2) (e1)))); [idtac | apply NNPP; zenon_intro zenon_H235]. % 15.22/15.41 congruence. % 15.22/15.41 cut (((op (e0) (e2)) = (e1))); [idtac | apply NNPP; zenon_intro zenon_Hac]. % 15.22/15.41 cut (((e2) = (e2))); [idtac | apply NNPP; zenon_intro zenon_H60]. % 15.22/15.41 congruence. % 15.22/15.41 apply zenon_H60. apply refl_equal. % 15.22/15.41 exact (zenon_Hac zenon_H29). % 15.22/15.41 apply zenon_H210. apply refl_equal. % 15.22/15.41 apply zenon_H210. apply refl_equal. % 15.22/15.41 apply zenon_H115. apply sym_equal. exact zenon_H29. % 15.22/15.41 apply (zenon_L145_); trivial. % 15.22/15.41 apply (zenon_L73_); trivial. % 15.22/15.41 apply (zenon_L178_); trivial. % 15.22/15.41 (* end of lemma zenon_L422_ *) % 15.22/15.41 assert (zenon_L423_ : (((op (e0) (e3)) = (e2))\/(((op (e1) (e3)) = (e2))\/(((op (e2) (e3)) = (e2))\/((op (e3) (e3)) = (e2))))) -> (~((op (e0) (e1)) = (op (e0) (e3)))) -> ((op (e0) (e1)) = (e2)) -> (~((e1) = (e2))) -> ((op (e1) (e3)) = (e1)) -> ((op (e2) (e2)) = (e2)) -> (~((op (e2) (e2)) = (op (e2) (e3)))) -> (~((op (e3) (e3)) = (e2))) -> False). % 15.22/15.41 do 0 intro. intros zenon_H160 zenon_H1cd zenon_H5d zenon_Ha7 zenon_H11f zenon_H35 zenon_H15f zenon_H3d. % 15.22/15.41 apply (zenon_or_s _ _ zenon_H160); [ zenon_intro zenon_H81 | zenon_intro zenon_H161 ]. % 15.22/15.41 apply (zenon_L350_); trivial. % 15.22/15.41 apply (zenon_or_s _ _ zenon_H161); [ zenon_intro zenon_H82 | zenon_intro zenon_H162 ]. % 15.22/15.41 apply (zenon_L209_); trivial. % 15.22/15.41 apply (zenon_or_s _ _ zenon_H162); [ zenon_intro zenon_H124 | zenon_intro zenon_H43 ]. % 15.22/15.41 apply (zenon_L137_); trivial. % 15.22/15.41 exact (zenon_H3d zenon_H43). % 15.22/15.41 (* end of lemma zenon_L423_ *) % 15.22/15.41 assert (zenon_L424_ : (((op (e0) (e0)) = (e2))\/(((op (e0) (e1)) = (e2))\/(((op (e0) (e2)) = (e2))\/((op (e0) (e3)) = (e2))))) -> (~((op (e0) (e0)) = (e2))) -> (~((op (e3) (e3)) = (e2))) -> (~((op (e2) (e2)) = (op (e2) (e3)))) -> ((op (e1) (e3)) = (e1)) -> (~((e1) = (e2))) -> (~((op (e0) (e1)) = (op (e0) (e3)))) -> (((op (e0) (e3)) = (e2))\/(((op (e1) (e3)) = (e2))\/(((op (e2) (e3)) = (e2))\/((op (e3) (e3)) = (e2))))) -> (~((op (e0) (e2)) = (op (e2) (e2)))) -> ((op (e2) (e2)) = (e2)) -> ((op (e0) (e3)) = (e0)) -> (~((e0) = (e2))) -> False). % 15.22/15.41 do 0 intro. intros zenon_H8e zenon_H8f zenon_H3d zenon_H15f zenon_H11f zenon_Ha7 zenon_H1cd zenon_H160 zenon_H28 zenon_H35 zenon_Hca zenon_H5e. % 15.22/15.41 apply (zenon_or_s _ _ zenon_H8e); [ zenon_intro zenon_H92 | zenon_intro zenon_H91 ]. % 15.22/15.41 exact (zenon_H8f zenon_H92). % 15.22/15.41 apply (zenon_or_s _ _ zenon_H91); [ zenon_intro zenon_H5d | zenon_intro zenon_H93 ]. % 15.22/15.41 apply (zenon_L423_); trivial. % 15.22/15.41 apply (zenon_or_s _ _ zenon_H93); [ zenon_intro zenon_H63 | zenon_intro zenon_H81 ]. % 15.22/15.41 apply (zenon_L15_); trivial. % 15.22/15.41 apply (zenon_L113_); trivial. % 15.22/15.41 (* end of lemma zenon_L424_ *) % 15.22/15.41 assert (zenon_L425_ : (((op (e0) (e0)) = (e0))\/(((op (e0) (e1)) = (e0))\/(((op (e0) (e2)) = (e0))\/((op (e0) (e3)) = (e0))))) -> (~((op (e0) (e0)) = (e0))) -> (~((op (e1) (e3)) = (op (e3) (e3)))) -> (~((op (e0) (e2)) = (op (e1) (e2)))) -> (((op (e1) (e0)) = (e2))\/(((op (e1) (e1)) = (e2))\/(((op (e1) (e2)) = (e2))\/((op (e1) (e3)) = (e2))))) -> (~((e2) = (e3))) -> (~((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))))) -> (~((op (e3) (e3)) = (e0))) -> (~((e0) = (e1))) -> (((op (e0) (e3)) = (e0))\/(((op (e1) (e3)) = (e0))\/(((op (e2) (e3)) = (e0))\/((op (e3) (e3)) = (e0))))) -> (((op (e0) (e0)) = (e3))\/(((op (e0) (e1)) = (e3))\/(((op (e0) (e2)) = (e3))\/((op (e0) (e3)) = (e3))))) -> (~((op (e0) (e0)) = (e3))) -> (~((e1) = (e3))) -> (~((e0) = (e3))) -> ((op (e3) (e3)) = (e3)) -> (~((op (e0) (e3)) = (op (e3) (e3)))) -> (~((op (e0) (e0)) = (e1))) -> (((op (e0) (e0)) = (e1))\/(((op (e0) (e1)) = (e1))\/(((op (e0) (e2)) = (e1))\/((op (e0) (e3)) = (e1))))) -> (((op (e0) (e0)) = (e2))\/(((op (e0) (e1)) = (e2))\/(((op (e0) (e2)) = (e2))\/((op (e0) (e3)) = (e2))))) -> (~((op (e0) (e0)) = (e2))) -> (~((op (e3) (e3)) = (e2))) -> (~((op (e2) (e2)) = (op (e2) (e3)))) -> ((op (e1) (e3)) = (e1)) -> (~((e1) = (e2))) -> (~((op (e0) (e1)) = (op (e0) (e3)))) -> (((op (e0) (e3)) = (e2))\/(((op (e1) (e3)) = (e2))\/(((op (e2) (e3)) = (e2))\/((op (e3) (e3)) = (e2))))) -> (~((op (e0) (e2)) = (op (e2) (e2)))) -> ((op (e2) (e2)) = (e2)) -> (~((e0) = (e2))) -> False). % 15.22/15.41 do 0 intro. intros zenon_H110 zenon_H20 zenon_H8b zenon_H87 zenon_H84 zenon_H6a zenon_H7d zenon_H80 zenon_H90 zenon_H3c zenon_H9e zenon_Hd3 zenon_H58 zenon_H59 zenon_Ha3 zenon_H4b zenon_H42 zenon_H36 zenon_H45 zenon_H44 zenon_H8e zenon_H8f zenon_H3d zenon_H15f zenon_H11f zenon_Ha7 zenon_H1cd zenon_H160 zenon_H28 zenon_H35 zenon_H5e. % 15.22/15.41 apply (zenon_or_s _ _ zenon_H110); [ zenon_intro zenon_H1f | zenon_intro zenon_H111 ]. % 15.22/15.41 exact (zenon_H20 zenon_H1f). % 15.22/15.41 apply (zenon_or_s _ _ zenon_H111); [ zenon_intro zenon_H49 | zenon_intro zenon_H112 ]. % 15.22/15.41 apply (zenon_L369_); trivial. % 15.22/15.41 apply (zenon_or_s _ _ zenon_H112); [ zenon_intro zenon_Hab | zenon_intro zenon_Hca ]. % 15.22/15.41 apply (zenon_L235_); trivial. % 15.22/15.41 apply (zenon_L424_); trivial. % 15.22/15.41 (* end of lemma zenon_L425_ *) % 15.22/15.41 assert (zenon_L426_ : ((~((op (e3) (e3)) = (e0)))\/((op (e3) (e0)) = (e3))) -> (~((op (e3) (e0)) = (op (e3) (e3)))) -> (((op (e0) (e0)) = (e0))\/(((op (e0) (e1)) = (e0))\/(((op (e0) (e2)) = (e0))\/((op (e0) (e3)) = (e0))))) -> (~((op (e2) (e2)) = (op (e2) (e3)))) -> (~((op (e0) (e0)) = (e1))) -> (((op (e0) (e0)) = (e2))\/(((op (e0) (e1)) = (e2))\/(((op (e0) (e2)) = (e2))\/((op (e0) (e3)) = (e2))))) -> (~((op (e0) (e0)) = (e3))) -> (~((e0) = (e3))) -> (((op (e1) (e0)) = (e3))\/(((op (e1) (e1)) = (e3))\/(((op (e1) (e2)) = (e3))\/((op (e1) (e3)) = (e3))))) -> ((op (e3) (e3)) = (e3)) -> (~((op (e1) (e3)) = (op (e3) (e3)))) -> (~((op (e0) (e2)) = (op (e1) (e2)))) -> (~((e2) = (e3))) -> (~((op (e1) (e2)) = (op (e2) (e2)))) -> (~((op (e0) (e3)) = (op (e1) (e3)))) -> (((op (e1) (e0)) = (e2))\/(((op (e1) (e1)) = (e2))\/(((op (e1) (e2)) = (e2))\/((op (e1) (e3)) = (e2))))) -> (~((op (e0) (e3)) = (op (e3) (e3)))) -> (((op (e0) (e0)) = (e3))\/(((op (e0) (e1)) = (e3))\/(((op (e0) (e2)) = (e3))\/((op (e0) (e3)) = (e3))))) -> ((op (e2) (e2)) = (e2)) -> (~((op (e0) (e2)) = (op (e2) (e2)))) -> (~((e0) = (e2))) -> (~((op (e0) (e0)) = (e2))) -> (~((e0) = (e1))) -> (~((e1) = (e3))) -> ((op (e1) (e3)) = (e1)) -> (((op (e0) (e3)) = (e2))\/(((op (e1) (e3)) = (e2))\/(((op (e2) (e3)) = (e2))\/((op (e3) (e3)) = (e2))))) -> (~((e1) = (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)) = (e1))\/(((op (e0) (e1)) = (e1))\/(((op (e0) (e2)) = (e1))\/((op (e0) (e3)) = (e1))))) -> (~((op (e0) (e0)) = (e0))) -> (~((op (e3) (e2)) = (op (e3) (e3)))) -> ((~((op (e3) (e3)) = (e2)))\/((op (e3) (e2)) = (e3))) -> False). % 15.22/15.41 do 0 intro. intros zenon_H10f zenon_Hbb zenon_H110 zenon_H15f zenon_H45 zenon_H8e zenon_H59 zenon_H4b zenon_H90 zenon_H42 zenon_H8b zenon_H87 zenon_H6a zenon_H7d zenon_H80 zenon_H84 zenon_H36 zenon_H58 zenon_H35 zenon_H28 zenon_H5e zenon_H8f zenon_H9e zenon_Ha3 zenon_H11f zenon_H160 zenon_Ha7 zenon_H1cd zenon_Hd3 zenon_H44 zenon_H20 zenon_H173 zenon_H10e. % 15.22/15.41 apply (zenon_or_s _ _ zenon_H10f); [ zenon_intro zenon_H3c | zenon_intro zenon_Hba ]. % 15.22/15.41 apply (zenon_or_s _ _ zenon_H10e); [ zenon_intro zenon_H3d | zenon_intro zenon_H106 ]. % 15.22/15.41 apply (zenon_L425_); trivial. % 15.22/15.41 apply (zenon_L153_); trivial. % 15.22/15.41 apply (zenon_L43_); trivial. % 15.22/15.41 (* end of lemma zenon_L426_ *) % 15.22/15.41 assert (zenon_L427_ : (((op (e0) (e1)) = (e0))\/(((op (e1) (e1)) = (e0))\/(((op (e2) (e1)) = (e0))\/((op (e3) (e1)) = (e0))))) -> (~((op (e1) (e1)) = (e0))) -> (((op (e0) (e1)) = (e3))\/(((op (e1) (e1)) = (e3))\/(((op (e2) (e1)) = (e3))\/((op (e3) (e1)) = (e3))))) -> (~((e1) = (e3))) -> ((op (e0) (e1)) = (e1)) -> (~((op (e2) (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) = (e2))) -> ((op (e2) (e0)) = (e1)) -> (~((e0) = (e1))) -> (((op (e2) (e0)) = (e0))\/(((op (e2) (e1)) = (e0))\/(((op (e2) (e2)) = (e0))\/((op (e2) (e3)) = (e0))))) -> (~((e2) = (e3))) -> ((op (e2) (e1)) = (e2)) -> (~((e0) = (e3))) -> False). % 15.22/15.41 do 0 intro. intros zenon_H144 zenon_H145 zenon_H199 zenon_Ha3 zenon_H22 zenon_H30 zenon_H2f zenon_H2e zenon_H2d zenon_H5e zenon_Hae zenon_H9e zenon_H1f5 zenon_H6a zenon_H156 zenon_H4b. % 15.22/15.41 apply (zenon_or_s _ _ zenon_H144); [ zenon_intro zenon_H49 | zenon_intro zenon_H147 ]. % 15.22/15.41 apply (zenon_L27_); trivial. % 15.22/15.41 apply (zenon_or_s _ _ zenon_H147); [ zenon_intro zenon_H149 | zenon_intro zenon_H148 ]. % 15.22/15.41 exact (zenon_H145 zenon_H149). % 15.22/15.41 apply (zenon_or_s _ _ zenon_H148); [ zenon_intro zenon_H14a | zenon_intro zenon_H142 ]. % 15.22/15.41 apply (zenon_L351_); trivial. % 15.22/15.41 apply (zenon_or_s _ _ zenon_H199); [ zenon_intro zenon_H4a | zenon_intro zenon_H19a ]. % 15.22/15.41 apply (zenon_L59_); trivial. % 15.22/15.41 apply (zenon_or_s _ _ zenon_H19a); [ zenon_intro zenon_H96 | zenon_intro zenon_H19b ]. % 15.22/15.41 apply (zenon_or_s _ _ zenon_H1f5); [ zenon_intro zenon_Hcf | zenon_intro zenon_H1f9 ]. % 15.22/15.41 apply (zenon_L269_); trivial. % 15.22/15.41 apply (zenon_or_s _ _ zenon_H1f9); [ zenon_intro zenon_H14a | zenon_intro zenon_H1fa ]. % 15.22/15.41 apply (zenon_L351_); trivial. % 15.22/15.41 apply (zenon_or_s _ _ zenon_H1fa); [ zenon_intro zenon_H32 | zenon_intro zenon_Hd0 ]. % 15.22/15.41 exact (zenon_H2e zenon_H32). % 15.22/15.41 apply (zenon_L375_); trivial. % 15.22/15.41 apply (zenon_or_s _ _ zenon_H19b); [ zenon_intro zenon_Hdf | zenon_intro zenon_H10a ]. % 15.22/15.41 apply (zenon_L183_); trivial. % 15.22/15.41 apply (zenon_L126_); trivial. % 15.22/15.41 (* end of lemma zenon_L427_ *) % 15.22/15.41 assert (zenon_L428_ : (((op (e0) (e0)) = (e2))\/(((op (e0) (e1)) = (e2))\/(((op (e0) (e2)) = (e2))\/((op (e0) (e3)) = (e2))))) -> (~((op (e0) (e0)) = (e2))) -> (~((op (e0) (e1)) = (op (e2) (e1)))) -> (~((op (e3) (e3)) = (e2))) -> (~((op (e0) (e2)) = (op (e3) (e2)))) -> (~((op (e2) (e1)) = (op (e3) (e1)))) -> ((op (e2) (e1)) = (e2)) -> ((op (e3) (e0)) = (e1)) -> (~((e1) = (e2))) -> (((op (e3) (e0)) = (e2))\/(((op (e3) (e1)) = (e2))\/(((op (e3) (e2)) = (e2))\/((op (e3) (e3)) = (e2))))) -> ((op (e0) (e3)) = (e0)) -> (~((e0) = (e2))) -> False). % 15.22/15.41 do 0 intro. intros zenon_H8e zenon_H8f zenon_Hde zenon_H3d zenon_H140 zenon_H13c zenon_H156 zenon_Hee zenon_Ha7 zenon_H1df zenon_Hca zenon_H5e. % 15.22/15.41 apply (zenon_or_s _ _ zenon_H8e); [ zenon_intro zenon_H92 | zenon_intro zenon_H91 ]. % 15.22/15.41 exact (zenon_H8f zenon_H92). % 15.22/15.41 apply (zenon_or_s _ _ zenon_H91); [ zenon_intro zenon_H5d | zenon_intro zenon_H93 ]. % 15.22/15.41 apply (zenon_L251_); trivial. % 15.22/15.41 apply (zenon_or_s _ _ zenon_H93); [ zenon_intro zenon_H63 | zenon_intro zenon_H81 ]. % 15.22/15.41 apply (zenon_L254_); trivial. % 15.22/15.41 apply (zenon_L113_); trivial. % 15.22/15.41 (* end of lemma zenon_L428_ *) % 15.22/15.41 assert (zenon_L429_ : ((op (e0) (e3)) = (e0)) -> (((op (e3) (e0)) = (e2))\/(((op (e3) (e1)) = (e2))\/(((op (e3) (e2)) = (e2))\/((op (e3) (e3)) = (e2))))) -> ((op (e2) (e1)) = (e2)) -> (~((op (e2) (e1)) = (op (e3) (e1)))) -> (~((op (e0) (e2)) = (op (e3) (e2)))) -> (~((op (e0) (e1)) = (op (e2) (e1)))) -> (~((op (e0) (e0)) = (e2))) -> (((op (e0) (e0)) = (e2))\/(((op (e0) (e1)) = (e2))\/(((op (e0) (e2)) = (e2))\/((op (e0) (e3)) = (e2))))) -> (((op (e0) (e1)) = (e0))\/(((op (e1) (e1)) = (e0))\/(((op (e2) (e1)) = (e0))\/((op (e3) (e1)) = (e0))))) -> (~((op (e1) (e1)) = (e0))) -> (((op (e0) (e1)) = (e3))\/(((op (e1) (e1)) = (e3))\/(((op (e2) (e1)) = (e3))\/((op (e3) (e1)) = (e3))))) -> (~((e1) = (e3))) -> (((op (e2) (e0)) = (e0))\/(((op (e2) (e1)) = (e0))\/(((op (e2) (e2)) = (e0))\/((op (e2) (e3)) = (e0))))) -> (~((e2) = (e3))) -> (~((e0) = (e3))) -> ((~((op (e1) (e1)) = (e3)))\/((op (e1) (e3)) = (e1))) -> ((~((op (e2) (e2)) = (e1)))\/((op (e2) (e1)) = (e2))) -> (~((op (e2) (e1)) = (op (e2) (e3)))) -> ((~((op (e3) (e3)) = (e2)))\/((op (e3) (e2)) = (e3))) -> (~((op (e3) (e2)) = (op (e3) (e3)))) -> (((op (e0) (e0)) = (e2))\/(((op (e1) (e0)) = (e2))\/(((op (e2) (e0)) = (e2))\/((op (e3) (e0)) = (e2))))) -> (((op (e3) (e3)) = (e0))\/(((op (e3) (e3)) = (e1))\/(((op (e3) (e3)) = (e2))\/((op (e3) (e3)) = (e3))))) -> (~((op (e2) (e0)) = (op (e2) (e1)))) -> ((~((op (e3) (e3)) = (e3)))\/((op (e3) (e3)) = (e3))) -> (~((op (e3) (e0)) = (op (e3) (e3)))) -> ((~((op (e3) (e3)) = (e0)))\/((op (e3) (e0)) = (e3))) -> (~((op (e2) (e1)) = (op (e2) (e2)))) -> ((~((op (e2) (e2)) = (e3)))\/((op (e2) (e3)) = (e2))) -> (((op (e3) (e0)) = (e1))\/(((op (e3) (e1)) = (e1))\/(((op (e3) (e2)) = (e1))\/((op (e3) (e3)) = (e1))))) -> (((op (e0) (e2)) = (e1))\/(((op (e1) (e2)) = (e1))\/(((op (e2) (e2)) = (e1))\/((op (e3) (e2)) = (e1))))) -> (~((op (e3) (e1)) = (op (e3) (e2)))) -> (~((op (e0) (e2)) = (op (e0) (e3)))) -> (~((op (e1) (e0)) = (op (e3) (e0)))) -> (~((op (e1) (e3)) = (op (e3) (e3)))) -> (((op (e1) (e0)) = (e3))\/(((op (e1) (e1)) = (e3))\/(((op (e1) (e2)) = (e3))\/((op (e1) (e3)) = (e3))))) -> (~((op (e0) (e1)) = (op (e0) (e3)))) -> (((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 (e1) (e0)) = (op (e1) (e3)))) -> (~((op (e0) (e3)) = (op (e3) (e3)))) -> ((op (e3) (e3)) = (e3)) -> (((op (e0) (e0)) = (e3))\/(((op (e0) (e1)) = (e3))\/(((op (e0) (e2)) = (e3))\/((op (e0) (e3)) = (e3))))) -> (~((op (e0) (e0)) = (e1))) -> (~((op (e3) (e1)) = (op (e3) (e3)))) -> ((~((op (e3) (e3)) = (e1)))\/((op (e3) (e1)) = (e3))) -> (((op (e1) (e0)) = (e2))\/(((op (e1) (e1)) = (e2))\/(((op (e1) (e2)) = (e2))\/((op (e1) (e3)) = (e2))))) -> (~((op (e1) (e1)) = (e1))) -> (((op (e1) (e1)) = (e0))\/(((op (e1) (e1)) = (e1))\/(((op (e1) (e1)) = (e2))\/((op (e1) (e1)) = (e3))))) -> (~((op (e1) (e2)) = (op (e2) (e2)))) -> (~((op (e1) (e1)) = (e2))) -> (~((op (e0) (e2)) = (op (e1) (e2)))) -> ((~((op (e2) (e2)) = (e2)))\/((op (e2) (e2)) = (e2))) -> (~((op (e1) (e2)) = (op (e3) (e2)))) -> (~((op (e2) (e0)) = (op (e2) (e3)))) -> (((op (e0) (e1)) = (e2))\/(((op (e1) (e1)) = (e2))\/(((op (e2) (e1)) = (e2))\/((op (e3) (e1)) = (e2))))) -> (~((op (e2) (e0)) = (op (e2) (e2)))) -> ((~((op (e2) (e2)) = (e0)))\/((op (e2) (e0)) = (e2))) -> (((op (e0) (e0)) = (e1))\/(((op (e1) (e0)) = (e1))\/(((op (e2) (e0)) = (e1))\/((op (e3) (e0)) = (e1))))) -> (~((op (e2) (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 (e0) (e3)) = (e0))\/(((op (e1) (e3)) = (e0))\/(((op (e2) (e3)) = (e0))\/((op (e3) (e3)) = (e0))))) -> (~((e0) = (e1))) -> (~((op (e3) (e3)) = (e2))) -> (~((e0) = (e2))) -> ((op (e1) (e3)) = (e1)) -> (~((e1) = (e2))) -> (((op (e0) (e3)) = (e2))\/(((op (e1) (e3)) = (e2))\/(((op (e2) (e3)) = (e2))\/((op (e3) (e3)) = (e2))))) -> (~((op (e3) (e3)) = (e0))) -> False). % 15.22/15.41 do 0 intro. intros zenon_Hca zenon_H1df zenon_H156 zenon_H13c zenon_H140 zenon_Hde zenon_H8f zenon_H8e zenon_H144 zenon_H145 zenon_H199 zenon_Ha3 zenon_H1f5 zenon_H6a zenon_H4b zenon_H1d2 zenon_H1e3 zenon_H1e2 zenon_H10e zenon_H173 zenon_Heb zenon_H3b zenon_H154 zenon_H10d zenon_Hbb zenon_H10f zenon_H157 zenon_H1c3 zenon_H146 zenon_H11b zenon_H135 zenon_Hc9 zenon_H22e zenon_H8b zenon_H90 zenon_H1cd zenon_H44 zenon_H121 zenon_H1cf zenon_H36 zenon_H42 zenon_H58 zenon_H45 zenon_H12d zenon_H10c zenon_H84 zenon_H1b4 zenon_H1b3 zenon_H7d zenon_Hd6 zenon_H87 zenon_Haa zenon_H17d zenon_Hce zenon_H1a2 zenon_H17a zenon_H1d4 zenon_Hf1 zenon_H30 zenon_H2f zenon_H28 zenon_H2e zenon_H2d zenon_Hd3 zenon_H9e zenon_H3d zenon_H5e zenon_H11f zenon_Ha7 zenon_H160 zenon_H3c. % 15.22/15.41 apply (zenon_or_s _ _ zenon_H44); [ zenon_intro zenon_H47 | zenon_intro zenon_H46 ]. % 15.22/15.41 exact (zenon_H45 zenon_H47). % 15.22/15.41 apply (zenon_or_s _ _ zenon_H46); [ zenon_intro zenon_H22 | zenon_intro zenon_H48 ]. % 15.22/15.41 apply (zenon_or_s _ _ zenon_Hf1); [ zenon_intro zenon_H47 | zenon_intro zenon_Hf4 ]. % 15.22/15.41 exact (zenon_H45 zenon_H47). % 15.22/15.41 apply (zenon_or_s _ _ zenon_Hf4); [ zenon_intro zenon_Hd8 | zenon_intro zenon_Hf5 ]. % 15.22/15.41 apply (zenon_L419_); trivial. % 15.22/15.41 apply (zenon_or_s _ _ zenon_Hf5); [ zenon_intro zenon_Hae | zenon_intro zenon_Hee ]. % 15.22/15.41 apply (zenon_L427_); trivial. % 15.22/15.41 apply (zenon_L428_); trivial. % 15.22/15.41 apply (zenon_or_s _ _ zenon_H48); [ zenon_intro zenon_H29 | zenon_intro zenon_H37 ]. % 15.22/15.41 apply (zenon_L5_); trivial. % 15.22/15.41 apply (zenon_L211_); trivial. % 15.22/15.41 (* end of lemma zenon_L429_ *) % 15.22/15.41 assert (zenon_L430_ : (((op (e0) (e0)) = (e0))\/(((op (e0) (e1)) = (e0))\/(((op (e0) (e2)) = (e0))\/((op (e0) (e3)) = (e0))))) -> (((op (e0) (e0)) = (e1))\/(((op (e1) (e0)) = (e1))\/(((op (e2) (e0)) = (e1))\/((op (e3) (e0)) = (e1))))) -> (((op (e3) (e0)) = (e2))\/(((op (e3) (e1)) = (e2))\/(((op (e3) (e2)) = (e2))\/((op (e3) (e3)) = (e2))))) -> (~((op (e2) (e1)) = (op (e3) (e1)))) -> (~((op (e1) (e1)) = (e0))) -> (((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 (e2) (e0)) = (op (e2) (e2)))) -> (((op (e0) (e1)) = (e2))\/(((op (e1) (e1)) = (e2))\/(((op (e2) (e1)) = (e2))\/((op (e3) (e1)) = (e2))))) -> (~((op (e1) (e2)) = (op (e3) (e2)))) -> ((~((op (e2) (e2)) = (e2)))\/((op (e2) (e2)) = (e2))) -> (~((op (e0) (e2)) = (op (e1) (e2)))) -> (~((op (e1) (e1)) = (e2))) -> (~((op (e1) (e2)) = (op (e2) (e2)))) -> (((op (e1) (e1)) = (e0))\/(((op (e1) (e1)) = (e1))\/(((op (e1) (e1)) = (e2))\/((op (e1) (e1)) = (e3))))) -> (((op (e1) (e0)) = (e2))\/(((op (e1) (e1)) = (e2))\/(((op (e1) (e2)) = (e2))\/((op (e1) (e3)) = (e2))))) -> ((~((op (e3) (e3)) = (e1)))\/((op (e3) (e1)) = (e3))) -> (~((op (e3) (e1)) = (op (e3) (e3)))) -> (~((op (e0) (e2)) = (op (e2) (e2)))) -> (~((op (e1) (e0)) = (op (e1) (e3)))) -> (((op (e0) (e3)) = (e1))\/(((op (e1) (e3)) = (e1))\/(((op (e2) (e3)) = (e1))\/((op (e3) (e3)) = (e1))))) -> (~((op (e0) (e1)) = (op (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) (e0)) = (op (e3) (e0)))) -> (~((op (e0) (e2)) = (op (e0) (e3)))) -> (~((op (e3) (e1)) = (op (e3) (e2)))) -> (((op (e0) (e2)) = (e1))\/(((op (e1) (e2)) = (e1))\/(((op (e2) (e2)) = (e1))\/((op (e3) (e2)) = (e1))))) -> (~((op (e0) (e2)) = (op (e3) (e2)))) -> (((op (e3) (e0)) = (e1))\/(((op (e3) (e1)) = (e1))\/(((op (e3) (e2)) = (e1))\/((op (e3) (e3)) = (e1))))) -> ((~((op (e2) (e2)) = (e3)))\/((op (e2) (e3)) = (e2))) -> (~((op (e2) (e1)) = (op (e2) (e2)))) -> ((~((op (e3) (e3)) = (e0)))\/((op (e3) (e0)) = (e3))) -> (~((op (e3) (e0)) = (op (e3) (e3)))) -> ((~((op (e3) (e3)) = (e3)))\/((op (e3) (e3)) = (e3))) -> (~((op (e2) (e0)) = (op (e2) (e1)))) -> (((op (e3) (e3)) = (e0))\/(((op (e3) (e3)) = (e1))\/(((op (e3) (e3)) = (e2))\/((op (e3) (e3)) = (e3))))) -> (((op (e0) (e0)) = (e2))\/(((op (e1) (e0)) = (e2))\/(((op (e2) (e0)) = (e2))\/((op (e3) (e0)) = (e2))))) -> (~((op (e3) (e2)) = (op (e3) (e3)))) -> ((~((op (e3) (e3)) = (e2)))\/((op (e3) (e2)) = (e3))) -> (~((op (e2) (e1)) = (op (e2) (e3)))) -> ((~((op (e2) (e2)) = (e1)))\/((op (e2) (e1)) = (e2))) -> ((~((op (e1) (e1)) = (e3)))\/((op (e1) (e3)) = (e1))) -> (~((op (e0) (e0)) = (e1))) -> (((op (e0) (e3)) = (e2))\/(((op (e1) (e3)) = (e2))\/(((op (e2) (e3)) = (e2))\/((op (e3) (e3)) = (e2))))) -> (((op (e0) (e0)) = (e1))\/(((op (e0) (e1)) = (e1))\/(((op (e0) (e2)) = (e1))\/((op (e0) (e3)) = (e1))))) -> (~((op (e0) (e0)) = (e2))) -> (~((op (e0) (e1)) = (op (e2) (e1)))) -> ((op (e2) (e1)) = (e2)) -> (((op (e0) (e0)) = (e3))\/(((op (e0) (e1)) = (e3))\/(((op (e0) (e2)) = (e3))\/((op (e0) (e3)) = (e3))))) -> ((op (e3) (e3)) = (e3)) -> (~((op (e0) (e3)) = (op (e3) (e3)))) -> (~((e2) = (e3))) -> (~((e0) = (e3))) -> (~((op (e0) (e0)) = (e3))) -> (((op (e0) (e1)) = (e1))\/(((op (e1) (e1)) = (e1))\/(((op (e2) (e1)) = (e1))\/((op (e3) (e1)) = (e1))))) -> (((op (e2) (e0)) = (e0))\/(((op (e2) (e1)) = (e0))\/(((op (e2) (e2)) = (e0))\/((op (e2) (e3)) = (e0))))) -> (((op (e2) (e2)) = (e0))\/(((op (e2) (e2)) = (e1))\/(((op (e2) (e2)) = (e2))\/((op (e2) (e2)) = (e3))))) -> (~((op (e2) (e2)) = (e0))) -> (~((e0) = (e2))) -> ((op (e1) (e3)) = (e1)) -> (~((op (e2) (e0)) = (op (e2) (e3)))) -> (((op (e0) (e3)) = (e0))\/(((op (e1) (e3)) = (e0))\/(((op (e2) (e3)) = (e0))\/((op (e3) (e3)) = (e0))))) -> (~((e1) = (e3))) -> (((op (e0) (e1)) = (e3))\/(((op (e1) (e1)) = (e3))\/(((op (e2) (e1)) = (e3))\/((op (e3) (e1)) = (e3))))) -> (~((e1) = (e2))) -> (~((op (e1) (e1)) = (e1))) -> (~((e0) = (e1))) -> (((op (e0) (e0)) = (e2))\/(((op (e0) (e1)) = (e2))\/(((op (e0) (e2)) = (e2))\/((op (e0) (e3)) = (e2))))) -> (~((op (e0) (e0)) = (e0))) -> False). % 15.22/15.41 do 0 intro. intros zenon_H110 zenon_Hf1 zenon_H1df zenon_H13c zenon_H145 zenon_H144 zenon_H1d4 zenon_H17a zenon_H1a2 zenon_H17d zenon_Haa zenon_H87 zenon_Hd6 zenon_H7d zenon_H1b3 zenon_H84 zenon_H10c zenon_H12d zenon_H28 zenon_H1cf zenon_H121 zenon_H1cd zenon_H90 zenon_H8b zenon_H22e zenon_Hc9 zenon_H135 zenon_H11b zenon_H140 zenon_H146 zenon_H1c3 zenon_H157 zenon_H10f zenon_Hbb zenon_H10d zenon_H154 zenon_H3b zenon_Heb zenon_H173 zenon_H10e zenon_H1e2 zenon_H1e3 zenon_H1d2 zenon_H45 zenon_H160 zenon_H44 zenon_H8f zenon_Hde zenon_H156 zenon_H58 zenon_H42 zenon_H36 zenon_H6a zenon_H4b zenon_H59 zenon_H228 zenon_H1f5 zenon_H2d zenon_H2e zenon_H5e zenon_H11f zenon_Hce zenon_Hd3 zenon_Ha3 zenon_H199 zenon_Ha7 zenon_H1b4 zenon_H9e zenon_H8e zenon_H20. % 15.22/15.41 apply (zenon_or_s _ _ zenon_Haa); [ zenon_intro zenon_H2f | zenon_intro zenon_H35 ]. % 15.22/15.41 apply (zenon_or_s _ _ zenon_H1c3); [ zenon_intro zenon_H30 | zenon_intro zenon_H124 ]. % 15.22/15.41 apply (zenon_or_s _ _ zenon_H10f); [ zenon_intro zenon_H3c | zenon_intro zenon_Hba ]. % 15.22/15.41 apply (zenon_or_s _ _ zenon_H10e); [ zenon_intro zenon_H3d | zenon_intro zenon_H106 ]. % 15.22/15.41 apply (zenon_or_s _ _ zenon_H110); [ zenon_intro zenon_H1f | zenon_intro zenon_H111 ]. % 15.22/15.41 exact (zenon_H20 zenon_H1f). % 15.22/15.41 apply (zenon_or_s _ _ zenon_H111); [ zenon_intro zenon_H49 | zenon_intro zenon_H112 ]. % 15.22/15.41 apply (zenon_L377_); trivial. % 15.22/15.41 apply (zenon_or_s _ _ zenon_H112); [ zenon_intro zenon_Hab | zenon_intro zenon_Hca ]. % 15.22/15.41 apply (zenon_L235_); trivial. % 15.22/15.41 apply (zenon_L429_); trivial. % 15.22/15.41 apply (zenon_L153_); trivial. % 15.22/15.41 apply (zenon_L43_); trivial. % 15.22/15.41 apply (zenon_L256_); trivial. % 15.22/15.41 apply (zenon_L134_); trivial. % 15.22/15.41 (* end of lemma zenon_L430_ *) % 15.22/15.41 assert (zenon_L431_ : ((~((op (e3) (e3)) = (e2)))\/((op (e3) (e2)) = (e3))) -> ((op (e3) (e3)) = (e3)) -> (~((op (e3) (e2)) = (op (e3) (e3)))) -> (~((e0) = (e2))) -> ((op (e0) (e3)) = (e0)) -> (~((e1) = (e2))) -> ((op (e1) (e3)) = (e1)) -> (~((op (e2) (e0)) = (op (e2) (e3)))) -> ((op (e2) (e0)) = (e2)) -> (((op (e0) (e3)) = (e2))\/(((op (e1) (e3)) = (e2))\/(((op (e2) (e3)) = (e2))\/((op (e3) (e3)) = (e2))))) -> False). % 15.22/15.41 do 0 intro. intros zenon_H10e zenon_H42 zenon_H173 zenon_H5e zenon_Hca zenon_Ha7 zenon_H11f zenon_Hce zenon_Hdd zenon_H160. % 15.22/15.41 apply (zenon_or_s _ _ zenon_H10e); [ zenon_intro zenon_H3d | zenon_intro zenon_H106 ]. % 15.22/15.41 apply (zenon_L389_); trivial. % 15.22/15.41 apply (zenon_L153_); trivial. % 15.22/15.41 (* end of lemma zenon_L431_ *) % 15.22/15.41 assert (zenon_L432_ : ((~((op (e2) (e2)) = (e1)))\/((op (e2) (e1)) = (e2))) -> (~((op (e2) (e0)) = (op (e2) (e1)))) -> ((~((op (e2) (e2)) = (e3)))\/((op (e2) (e3)) = (e2))) -> (~((op (e0) (e0)) = (e0))) -> (((op (e0) (e0)) = (e1))\/(((op (e0) (e1)) = (e1))\/(((op (e0) (e2)) = (e1))\/((op (e0) (e3)) = (e1))))) -> (~((op (e0) (e0)) = (e2))) -> (~((e0) = (e2))) -> (~((e1) = (e2))) -> (((op (e0) (e0)) = (e2))\/(((op (e0) (e1)) = (e2))\/(((op (e0) (e2)) = (e2))\/((op (e0) (e3)) = (e2))))) -> (~((op (e0) (e0)) = (e3))) -> (~((e0) = (e3))) -> (~((e1) = (e3))) -> (~((op (e0) (e3)) = (op (e3) (e3)))) -> (((op (e0) (e0)) = (e3))\/(((op (e0) (e1)) = (e3))\/(((op (e0) (e2)) = (e3))\/((op (e0) (e3)) = (e3))))) -> (~((e0) = (e1))) -> (~((e2) = (e3))) -> ((op (e2) (e0)) = (e2)) -> (((op (e2) (e2)) = (e0))\/(((op (e2) (e2)) = (e1))\/(((op (e2) (e2)) = (e2))\/((op (e2) (e2)) = (e3))))) -> (~((op (e2) (e3)) = (op (e3) (e3)))) -> ((op (e3) (e3)) = (e3)) -> (((op (e2) (e0)) = (e3))\/(((op (e2) (e1)) = (e3))\/(((op (e2) (e2)) = (e3))\/((op (e2) (e3)) = (e3))))) -> ((op (e1) (e3)) = (e1)) -> (((op (e0) (e3)) = (e2))\/(((op (e1) (e3)) = (e2))\/(((op (e2) (e3)) = (e2))\/((op (e3) (e3)) = (e2))))) -> (((op (e0) (e3)) = (e0))\/(((op (e1) (e3)) = (e0))\/(((op (e2) (e3)) = (e0))\/((op (e3) (e3)) = (e0))))) -> (~((op (e0) (e0)) = (e1))) -> ((~((op (e3) (e3)) = (e2)))\/((op (e3) (e2)) = (e3))) -> (~((op (e3) (e2)) = (op (e3) (e3)))) -> (~((op (e2) (e0)) = (op (e2) (e3)))) -> (((op (e0) (e0)) = (e0))\/(((op (e0) (e1)) = (e0))\/(((op (e0) (e2)) = (e0))\/((op (e0) (e3)) = (e0))))) -> (~((op (e3) (e0)) = (op (e3) (e3)))) -> ((~((op (e3) (e3)) = (e0)))\/((op (e3) (e0)) = (e3))) -> (~((op (e2) (e0)) = (op (e2) (e2)))) -> ((~((op (e2) (e2)) = (e2)))\/((op (e2) (e2)) = (e2))) -> False). % 15.22/15.41 do 0 intro. intros zenon_H1e3 zenon_H154 zenon_H1c3 zenon_H20 zenon_H44 zenon_H8f zenon_H5e zenon_Ha7 zenon_H8e zenon_H59 zenon_H4b zenon_Ha3 zenon_H36 zenon_H58 zenon_H9e zenon_H6a zenon_Hdd zenon_H2d zenon_He3 zenon_H42 zenon_He6 zenon_H11f zenon_H160 zenon_Hd3 zenon_H45 zenon_H10e zenon_H173 zenon_Hce zenon_H110 zenon_Hbb zenon_H10f zenon_H17a zenon_Haa. % 15.22/15.41 apply (zenon_or_s _ _ zenon_H1e3); [ zenon_intro zenon_H52 | zenon_intro zenon_H156 ]. % 15.22/15.41 apply (zenon_or_s _ _ zenon_Haa); [ zenon_intro zenon_H2f | zenon_intro zenon_H35 ]. % 15.22/15.41 apply (zenon_or_s _ _ zenon_H1c3); [ zenon_intro zenon_H30 | zenon_intro zenon_H124 ]. % 15.22/15.41 apply (zenon_or_s _ _ zenon_H10f); [ zenon_intro zenon_H3c | zenon_intro zenon_Hba ]. % 15.22/15.41 apply (zenon_or_s _ _ zenon_H10e); [ zenon_intro zenon_H3d | zenon_intro zenon_H106 ]. % 15.22/15.41 apply (zenon_or_s _ _ zenon_H110); [ zenon_intro zenon_H1f | zenon_intro zenon_H111 ]. % 15.22/15.41 exact (zenon_H20 zenon_H1f). % 15.22/15.41 apply (zenon_or_s _ _ zenon_H111); [ zenon_intro zenon_H49 | zenon_intro zenon_H112 ]. % 15.22/15.41 apply (zenon_L283_); trivial. % 15.22/15.41 apply (zenon_or_s _ _ zenon_H112); [ zenon_intro zenon_Hab | zenon_intro zenon_Hca ]. % 15.22/15.41 apply (zenon_L235_); trivial. % 15.22/15.41 apply (zenon_L431_); trivial. % 15.22/15.41 apply (zenon_L153_); trivial. % 15.22/15.41 apply (zenon_L43_); trivial. % 15.22/15.41 apply (zenon_L119_); trivial. % 15.22/15.41 apply (zenon_L161_); trivial. % 15.22/15.41 apply (zenon_L284_); trivial. % 15.22/15.41 (* end of lemma zenon_L432_ *) % 15.22/15.41 assert (zenon_L433_ : (((op (e1) (e0)) = (e3))\/(((op (e1) (e1)) = (e3))\/(((op (e1) (e2)) = (e3))\/((op (e1) (e3)) = (e3))))) -> (~((op (e2) (e2)) = (e3))) -> (~((op (e2) (e2)) = (e2))) -> (~((op (e2) (e2)) = (e1))) -> ((op (e1) (e1)) = (e2)) -> (((op (e2) (e2)) = (e0))\/(((op (e2) (e2)) = (e1))\/(((op (e2) (e2)) = (e2))\/((op (e2) (e2)) = (e3))))) -> (~((op (e1) (e1)) = (e3))) -> (~((e1) = (e3))) -> ((op (e1) (e2)) = (e1)) -> ((op (e3) (e3)) = (e3)) -> (~((op (e1) (e3)) = (op (e3) (e3)))) -> False). % 15.22/15.41 do 0 intro. intros zenon_H90 zenon_H30 zenon_H2f zenon_H52 zenon_H6e zenon_H2d zenon_H182 zenon_Ha3 zenon_H117 zenon_H42 zenon_H8b. % 15.22/15.41 apply (zenon_or_s _ _ zenon_H90); [ zenon_intro zenon_H69 | zenon_intro zenon_H94 ]. % 15.22/15.41 apply (zenon_L384_); trivial. % 15.22/15.41 apply (zenon_or_s _ _ zenon_H94); [ zenon_intro zenon_H96 | zenon_intro zenon_H95 ]. % 15.22/15.41 exact (zenon_H182 zenon_H96). % 15.22/15.41 apply (zenon_or_s _ _ zenon_H95); [ zenon_intro zenon_H88 | zenon_intro zenon_H8a ]. % 15.22/15.41 apply (zenon_L196_); trivial. % 15.22/15.41 apply (zenon_L25_); trivial. % 15.22/15.41 (* end of lemma zenon_L433_ *) % 15.22/15.41 assert (zenon_L434_ : (((op (e0) (e0)) = (e2))\/(((op (e1) (e0)) = (e2))\/(((op (e2) (e0)) = (e2))\/((op (e3) (e0)) = (e2))))) -> (~((op (e1) (e3)) = (op (e3) (e3)))) -> ((op (e1) (e2)) = (e1)) -> (((op (e1) (e0)) = (e3))\/(((op (e1) (e1)) = (e3))\/(((op (e1) (e2)) = (e3))\/((op (e1) (e3)) = (e3))))) -> (~((e0) = (e2))) -> ((op (e0) (e3)) = (e0)) -> (((op (e0) (e0)) = (e3))\/(((op (e0) (e1)) = (e3))\/(((op (e0) (e2)) = (e3))\/((op (e0) (e3)) = (e3))))) -> (~((op (e2) (e2)) = (e3))) -> (~((op (e2) (e2)) = (e2))) -> (~((op (e2) (e2)) = (e1))) -> (((op (e2) (e2)) = (e0))\/(((op (e2) (e2)) = (e1))\/(((op (e2) (e2)) = (e2))\/((op (e2) (e2)) = (e3))))) -> (~((op (e0) (e1)) = (op (e2) (e1)))) -> (((op (e2) (e0)) = (e1))\/(((op (e2) (e1)) = (e1))\/(((op (e2) (e2)) = (e1))\/((op (e2) (e3)) = (e1))))) -> (~((e1) = (e3))) -> ((op (e0) (e1)) = (e1)) -> (~((e2) = (e3))) -> ((op (e3) (e3)) = (e3)) -> (~((op (e0) (e3)) = (op (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 (e0) (e1)) = (op (e1) (e1)))) -> (~((op (e1) (e1)) = (e3))) -> (~((op (e0) (e0)) = (e2))) -> (((op (e0) (e0)) = (e2))\/(((op (e0) (e1)) = (e2))\/(((op (e0) (e2)) = (e2))\/((op (e0) (e3)) = (e2))))) -> ((op (e3) (e0)) = (e1)) -> (~((e1) = (e2))) -> False). % 15.22/15.41 do 0 intro. intros zenon_Heb zenon_H8b zenon_H117 zenon_H90 zenon_H5e zenon_Hca zenon_H58 zenon_H30 zenon_H2f zenon_H52 zenon_H2d zenon_Hde zenon_Hb7 zenon_Ha3 zenon_H22 zenon_H6a zenon_H42 zenon_H36 zenon_H1b3 zenon_H145 zenon_H1b4 zenon_H23 zenon_H182 zenon_H8f zenon_H8e zenon_Hee zenon_Ha7. % 15.22/15.41 apply (zenon_or_s _ _ zenon_Heb); [ zenon_intro zenon_H92 | zenon_intro zenon_Hec ]. % 15.22/15.41 exact (zenon_H8f zenon_H92). % 15.22/15.41 apply (zenon_or_s _ _ zenon_Hec); [ zenon_intro zenon_H68 | zenon_intro zenon_Hed ]. % 15.22/15.41 apply (zenon_L198_); trivial. % 15.22/15.41 apply (zenon_or_s _ _ zenon_Hed); [ zenon_intro zenon_Hdd | zenon_intro zenon_He9 ]. % 15.22/15.41 apply (zenon_L363_); trivial. % 15.22/15.41 apply (zenon_L122_); trivial. % 15.22/15.41 (* end of lemma zenon_L434_ *) % 15.22/15.41 assert (zenon_L435_ : (((op (e0) (e0)) = (e1))\/(((op (e0) (e1)) = (e1))\/(((op (e0) (e2)) = (e1))\/((op (e0) (e3)) = (e1))))) -> (~((e1) = (e2))) -> (((op (e0) (e0)) = (e2))\/(((op (e0) (e1)) = (e2))\/(((op (e0) (e2)) = (e2))\/((op (e0) (e3)) = (e2))))) -> (~((op (e0) (e0)) = (e2))) -> (~((op (e1) (e1)) = (e3))) -> (~((op (e0) (e1)) = (op (e1) (e1)))) -> (~((op (e1) (e1)) = (e1))) -> (~((op (e1) (e1)) = (e0))) -> (((op (e1) (e1)) = (e0))\/(((op (e1) (e1)) = (e1))\/(((op (e1) (e1)) = (e2))\/((op (e1) (e1)) = (e3))))) -> (~((op (e0) (e3)) = (op (e3) (e3)))) -> ((op (e3) (e3)) = (e3)) -> (~((e2) = (e3))) -> (~((e1) = (e3))) -> (((op (e2) (e0)) = (e1))\/(((op (e2) (e1)) = (e1))\/(((op (e2) (e2)) = (e1))\/((op (e2) (e3)) = (e1))))) -> (~((op (e0) (e1)) = (op (e2) (e1)))) -> (~((op (e2) (e2)) = (e1))) -> (((op (e0) (e0)) = (e3))\/(((op (e0) (e1)) = (e3))\/(((op (e0) (e2)) = (e3))\/((op (e0) (e3)) = (e3))))) -> (~((e0) = (e2))) -> (((op (e1) (e0)) = (e3))\/(((op (e1) (e1)) = (e3))\/(((op (e1) (e2)) = (e3))\/((op (e1) (e3)) = (e3))))) -> ((op (e1) (e2)) = (e1)) -> (~((op (e1) (e3)) = (op (e3) (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) (e3)) = (e1))\/(((op (e1) (e3)) = (e1))\/(((op (e2) (e3)) = (e1))\/((op (e3) (e3)) = (e1))))) -> (~((op (e0) (e1)) = (op (e0) (e3)))) -> (~((op (e2) (e0)) = (op (e2) (e3)))) -> (~((op (e3) (e3)) = (e1))) -> (~((op (e1) (e0)) = (op (e1) (e3)))) -> (~((op (e0) (e0)) = (e1))) -> (((op (e0) (e0)) = (e1))\/(((op (e1) (e0)) = (e1))\/(((op (e2) (e0)) = (e1))\/((op (e3) (e0)) = (e1))))) -> (~((op (e2) (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 (e0) (e3)) = (e0)) -> (~((e0) = (e1))) -> False). % 15.22/15.41 do 0 intro. intros zenon_H44 zenon_Ha7 zenon_H8e zenon_H8f zenon_H182 zenon_H23 zenon_H1b4 zenon_H145 zenon_H1b3 zenon_H36 zenon_H42 zenon_H6a zenon_Ha3 zenon_Hb7 zenon_Hde zenon_H52 zenon_H58 zenon_H5e zenon_H90 zenon_H117 zenon_H8b zenon_Heb zenon_H84 zenon_H121 zenon_H1cd zenon_Hce zenon_H104 zenon_H1cf zenon_H45 zenon_Hf1 zenon_H30 zenon_H2f zenon_H28 zenon_H2e zenon_H2d zenon_Hca zenon_H9e. % 15.22/15.41 apply (zenon_or_s _ _ zenon_H44); [ zenon_intro zenon_H47 | zenon_intro zenon_H46 ]. % 15.22/15.41 exact (zenon_H45 zenon_H47). % 15.22/15.41 apply (zenon_or_s _ _ zenon_H46); [ zenon_intro zenon_H22 | zenon_intro zenon_H48 ]. % 15.22/15.41 apply (zenon_or_s _ _ zenon_Hf1); [ zenon_intro zenon_H47 | zenon_intro zenon_Hf4 ]. % 15.22/15.41 exact (zenon_H45 zenon_H47). % 15.22/15.41 apply (zenon_or_s _ _ zenon_Hf4); [ zenon_intro zenon_Hd8 | zenon_intro zenon_Hf5 ]. % 15.22/15.41 apply (zenon_L331_); trivial. % 15.22/15.41 apply (zenon_or_s _ _ zenon_Hf5); [ zenon_intro zenon_Hae | zenon_intro zenon_Hee ]. % 15.22/15.41 apply (zenon_or_s _ _ zenon_H84); [ zenon_intro zenon_H68 | zenon_intro zenon_H85 ]. % 15.22/15.41 apply (zenon_L198_); trivial. % 15.22/15.41 apply (zenon_or_s _ _ zenon_H85); [ zenon_intro zenon_H6e | zenon_intro zenon_H86 ]. % 15.22/15.41 apply (zenon_L433_); trivial. % 15.22/15.41 apply (zenon_or_s _ _ zenon_H86); [ zenon_intro zenon_H7c | zenon_intro zenon_H82 ]. % 15.22/15.41 apply (zenon_L204_); trivial. % 15.22/15.41 apply (zenon_L332_); trivial. % 15.22/15.41 apply (zenon_L434_); trivial. % 15.22/15.41 apply (zenon_or_s _ _ zenon_H48); [ zenon_intro zenon_H29 | zenon_intro zenon_H37 ]. % 15.22/15.41 apply (zenon_L5_); trivial. % 15.22/15.41 apply (zenon_L73_); trivial. % 15.22/15.41 (* end of lemma zenon_L435_ *) % 15.22/15.41 assert (zenon_L436_ : (((op (e0) (e3)) = (e1))\/(((op (e1) (e3)) = (e1))\/(((op (e2) (e3)) = (e1))\/((op (e3) (e3)) = (e1))))) -> (~((e0) = (e1))) -> ((op (e0) (e3)) = (e0)) -> ((op (e1) (e2)) = (e1)) -> (~((op (e1) (e2)) = (op (e1) (e3)))) -> ((op (e2) (e3)) = (e2)) -> (~((e1) = (e2))) -> (~((op (e3) (e3)) = (e1))) -> False). % 15.22/15.41 do 0 intro. intros zenon_H121 zenon_H9e zenon_Hca zenon_H117 zenon_H1d0 zenon_H124 zenon_Ha7 zenon_H104. % 15.22/15.41 apply (zenon_or_s _ _ zenon_H121); [ zenon_intro zenon_H37 | zenon_intro zenon_H122 ]. % 15.22/15.41 apply (zenon_L73_); trivial. % 15.22/15.41 apply (zenon_or_s _ _ zenon_H122); [ zenon_intro zenon_H11f | zenon_intro zenon_H123 ]. % 15.22/15.41 apply (zenon_L237_); trivial. % 15.22/15.41 apply (zenon_or_s _ _ zenon_H123); [ zenon_intro zenon_Hb5 | zenon_intro zenon_H38 ]. % 15.22/15.41 apply (zenon_L93_); trivial. % 15.22/15.41 exact (zenon_H104 zenon_H38). % 15.22/15.41 (* end of lemma zenon_L436_ *) % 15.22/15.41 assert (zenon_L437_ : ((~((op (e3) (e3)) = (e1)))\/((op (e3) (e1)) = (e3))) -> (~((op (e3) (e0)) = (op (e3) (e1)))) -> ((~((op (e3) (e3)) = (e3)))\/((op (e3) (e3)) = (e3))) -> (~((op (e3) (e0)) = (op (e3) (e3)))) -> (~((op (e0) (e0)) = (e1))) -> (~((op (e1) (e0)) = (op (e1) (e2)))) -> ((op (e1) (e2)) = (e1)) -> (((op (e2) (e2)) = (e0))\/(((op (e2) (e2)) = (e1))\/(((op (e2) (e2)) = (e2))\/((op (e2) (e2)) = (e3))))) -> (((op (e3) (e3)) = (e0))\/(((op (e3) (e3)) = (e1))\/(((op (e3) (e3)) = (e2))\/((op (e3) (e3)) = (e3))))) -> (~((op (e2) (e2)) = (e2))) -> (~((op (e2) (e2)) = (e1))) -> (~((op (e2) (e2)) = (e0))) -> (~((e1) = (e3))) -> ((op (e3) (e0)) = (e3)) -> (((op (e0) (e0)) = (e1))\/(((op (e1) (e0)) = (e1))\/(((op (e2) (e0)) = (e1))\/((op (e3) (e0)) = (e1))))) -> (~((op (e3) (e0)) = (op (e3) (e2)))) -> ((~((op (e3) (e3)) = (e2)))\/((op (e3) (e2)) = (e3))) -> False). % 15.22/15.41 do 0 intro. intros zenon_H10c zenon_H109 zenon_H10d zenon_Hbb zenon_H45 zenon_H166 zenon_H117 zenon_H2d zenon_H3b zenon_H2f zenon_H52 zenon_H2e zenon_Ha3 zenon_Hba zenon_Hf1 zenon_H105 zenon_H10e. % 15.22/15.41 apply (zenon_or_s _ _ zenon_H10c); [ zenon_intro zenon_H104 | zenon_intro zenon_H10a ]. % 15.22/15.41 apply (zenon_or_s _ _ zenon_H10e); [ zenon_intro zenon_H3d | zenon_intro zenon_H106 ]. % 15.22/15.41 apply (zenon_or_s _ _ zenon_H10d); [ zenon_intro zenon_H3e | zenon_intro zenon_H42 ]. % 15.22/15.41 apply (zenon_or_s _ _ zenon_Hf1); [ zenon_intro zenon_H47 | zenon_intro zenon_Hf4 ]. % 15.22/15.41 exact (zenon_H45 zenon_H47). % 15.22/15.41 apply (zenon_or_s _ _ zenon_Hf4); [ zenon_intro zenon_Hd8 | zenon_intro zenon_Hf5 ]. % 15.22/15.41 apply (zenon_L248_); trivial. % 15.22/15.41 apply (zenon_or_s _ _ zenon_Hf5); [ zenon_intro zenon_Hae | zenon_intro zenon_Hee ]. % 15.22/15.41 apply (zenon_L78_); trivial. % 15.22/15.41 apply (zenon_L79_); trivial. % 15.22/15.41 apply (zenon_L43_); trivial. % 15.22/15.41 apply (zenon_L81_); trivial. % 15.22/15.41 apply (zenon_L82_); trivial. % 15.22/15.41 (* end of lemma zenon_L437_ *) % 15.22/15.41 assert (zenon_L438_ : ((~((op (e1) (e1)) = (e3)))\/((op (e1) (e3)) = (e1))) -> ((op (e1) (e2)) = (e1)) -> (~((op (e1) (e2)) = (op (e1) (e3)))) -> (~((op (e0) (e0)) = (e2))) -> (((op (e1) (e1)) = (e0))\/(((op (e1) (e1)) = (e1))\/(((op (e1) (e1)) = (e2))\/((op (e1) (e1)) = (e3))))) -> (~((op (e0) (e1)) = (op (e1) (e1)))) -> (~((op (e1) (e1)) = (e1))) -> (~((op (e1) (e1)) = (e0))) -> (~((op (e0) (e2)) = (op (e2) (e2)))) -> ((op (e2) (e2)) = (e2)) -> (~((e0) = (e2))) -> ((op (e0) (e3)) = (e0)) -> (((op (e0) (e0)) = (e2))\/(((op (e0) (e1)) = (e2))\/(((op (e0) (e2)) = (e2))\/((op (e0) (e3)) = (e2))))) -> False). % 15.22/15.41 do 0 intro. intros zenon_H1d2 zenon_H117 zenon_H1d0 zenon_H8f zenon_H1b3 zenon_H23 zenon_H1b4 zenon_H145 zenon_H28 zenon_H35 zenon_H5e zenon_Hca zenon_H8e. % 15.22/15.41 apply (zenon_or_s _ _ zenon_H1d2); [ zenon_intro zenon_H182 | zenon_intro zenon_H11f ]. % 15.22/15.41 apply (zenon_L343_); trivial. % 15.22/15.41 apply (zenon_L237_); trivial. % 15.22/15.41 (* end of lemma zenon_L438_ *) % 15.22/15.41 assert (zenon_L439_ : (((op (e0) (e0)) = (e0))\/(((op (e0) (e1)) = (e0))\/(((op (e0) (e2)) = (e0))\/((op (e0) (e3)) = (e0))))) -> (~((op (e0) (e0)) = (e0))) -> (~((e1) = (e2))) -> (~((op (e1) (e1)) = (e3))) -> (((op (e0) (e0)) = (e3))\/(((op (e0) (e1)) = (e3))\/(((op (e0) (e2)) = (e3))\/((op (e0) (e3)) = (e3))))) -> (~((op (e0) (e0)) = (e3))) -> (~((op (e0) (e3)) = (op (e3) (e3)))) -> (~((e0) = (e1))) -> (~((op (e0) (e3)) = (op (e1) (e3)))) -> (((op (e1) (e0)) = (e3))\/(((op (e1) (e1)) = (e3))\/(((op (e1) (e2)) = (e3))\/((op (e1) (e3)) = (e3))))) -> (~((op (e0) (e2)) = (op (e1) (e2)))) -> (~((op (e1) (e3)) = (op (e3) (e3)))) -> (((op (e1) (e0)) = (e2))\/(((op (e1) (e1)) = (e2))\/(((op (e1) (e2)) = (e2))\/((op (e1) (e3)) = (e2))))) -> (~((e2) = (e3))) -> (((op (e0) (e0)) = (e1))\/(((op (e0) (e1)) = (e1))\/(((op (e0) (e2)) = (e1))\/((op (e0) (e3)) = (e1))))) -> (~((op (e3) (e2)) = (op (e3) (e3)))) -> ((op (e3) (e3)) = (e3)) -> (~((op (e2) (e2)) = (e3))) -> (~((e1) = (e3))) -> (~((e0) = (e3))) -> (((op (e0) (e2)) = (e3))\/(((op (e1) (e2)) = (e3))\/(((op (e2) (e2)) = (e3))\/((op (e3) (e2)) = (e3))))) -> ((~((op (e1) (e1)) = (e3)))\/((op (e1) (e3)) = (e1))) -> ((op (e1) (e2)) = (e1)) -> (~((op (e1) (e2)) = (op (e1) (e3)))) -> (~((op (e0) (e0)) = (e2))) -> (((op (e1) (e1)) = (e0))\/(((op (e1) (e1)) = (e1))\/(((op (e1) (e1)) = (e2))\/((op (e1) (e1)) = (e3))))) -> (~((op (e0) (e1)) = (op (e1) (e1)))) -> (~((op (e1) (e1)) = (e1))) -> (~((op (e1) (e1)) = (e0))) -> (~((op (e0) (e2)) = (op (e2) (e2)))) -> ((op (e2) (e2)) = (e2)) -> (~((e0) = (e2))) -> (((op (e0) (e0)) = (e2))\/(((op (e0) (e1)) = (e2))\/(((op (e0) (e2)) = (e2))\/((op (e0) (e3)) = (e2))))) -> False). % 15.22/15.41 do 0 intro. intros zenon_H110 zenon_H20 zenon_Ha7 zenon_H182 zenon_H58 zenon_H59 zenon_H36 zenon_H9e zenon_H80 zenon_H90 zenon_H87 zenon_H8b zenon_H84 zenon_H6a zenon_H44 zenon_H173 zenon_H42 zenon_H30 zenon_Ha3 zenon_H4b zenon_H175 zenon_H1d2 zenon_H117 zenon_H1d0 zenon_H8f zenon_H1b3 zenon_H23 zenon_H1b4 zenon_H145 zenon_H28 zenon_H35 zenon_H5e zenon_H8e. % 15.22/15.41 apply (zenon_or_s _ _ zenon_H110); [ zenon_intro zenon_H1f | zenon_intro zenon_H111 ]. % 15.22/15.41 exact (zenon_H20 zenon_H1f). % 15.22/15.41 apply (zenon_or_s _ _ zenon_H111); [ zenon_intro zenon_H49 | zenon_intro zenon_H112 ]. % 15.22/15.41 apply (zenon_L381_); trivial. % 15.22/15.41 apply (zenon_or_s _ _ zenon_H112); [ zenon_intro zenon_Hab | zenon_intro zenon_Hca ]. % 15.22/15.41 apply (zenon_L197_); trivial. % 15.22/15.41 apply (zenon_L438_); trivial. % 15.22/15.41 (* end of lemma zenon_L439_ *) % 15.22/15.41 assert (zenon_L440_ : ((~((op (e2) (e2)) = (e1)))\/((op (e2) (e1)) = (e2))) -> (((op (e0) (e1)) = (e0))\/(((op (e1) (e1)) = (e0))\/(((op (e2) (e1)) = (e0))\/((op (e3) (e1)) = (e0))))) -> (((op (e0) (e1)) = (e3))\/(((op (e1) (e1)) = (e3))\/(((op (e2) (e1)) = (e3))\/((op (e3) (e1)) = (e3))))) -> (~((op (e2) (e1)) = (op (e2) (e3)))) -> ((~((op (e2) (e2)) = (e2)))\/((op (e2) (e2)) = (e2))) -> (~((op (e0) (e3)) = (op (e1) (e3)))) -> (~((op (e0) (e2)) = (op (e1) (e2)))) -> (~((op (e1) (e2)) = (op (e1) (e3)))) -> (~((op (e3) (e0)) = (op (e3) (e1)))) -> ((~((op (e3) (e3)) = (e3)))\/((op (e3) (e3)) = (e3))) -> (~((op (e1) (e0)) = (op (e1) (e2)))) -> (((op (e3) (e3)) = (e0))\/(((op (e3) (e3)) = (e1))\/(((op (e3) (e3)) = (e2))\/((op (e3) (e3)) = (e3))))) -> (~((op (e3) (e0)) = (op (e3) (e2)))) -> ((~((op (e3) (e3)) = (e2)))\/((op (e3) (e2)) = (e3))) -> (((op (e0) (e0)) = (e0))\/(((op (e0) (e1)) = (e0))\/(((op (e0) (e2)) = (e0))\/((op (e0) (e3)) = (e0))))) -> (~((op (e0) (e0)) = (e1))) -> (((op (e0) (e0)) = (e1))\/(((op (e1) (e0)) = (e1))\/(((op (e2) (e0)) = (e1))\/((op (e3) (e0)) = (e1))))) -> (~((op (e0) (e0)) = (e2))) -> (((op (e0) (e0)) = (e2))\/(((op (e0) (e1)) = (e2))\/(((op (e0) (e2)) = (e2))\/((op (e0) (e3)) = (e2))))) -> (((op (e2) (e0)) = (e1))\/(((op (e2) (e1)) = (e1))\/(((op (e2) (e2)) = (e1))\/((op (e2) (e3)) = (e1))))) -> (~((op (e0) (e1)) = (op (e2) (e1)))) -> (~((op (e1) (e1)) = (e0))) -> (~((op (e1) (e1)) = (e1))) -> (~((op (e0) (e1)) = (op (e1) (e1)))) -> (((op (e1) (e1)) = (e0))\/(((op (e1) (e1)) = (e1))\/(((op (e1) (e1)) = (e2))\/((op (e1) (e1)) = (e3))))) -> (((op (e0) (e0)) = (e2))\/(((op (e1) (e0)) = (e2))\/(((op (e2) (e0)) = (e2))\/((op (e3) (e0)) = (e2))))) -> (~((op (e2) (e0)) = (op (e2) (e3)))) -> (~((op (e0) (e1)) = (op (e0) (e3)))) -> (((op (e0) (e3)) = (e1))\/(((op (e1) (e3)) = (e1))\/(((op (e2) (e3)) = (e1))\/((op (e3) (e3)) = (e1))))) -> (~((op (e1) (e0)) = (op (e1) (e3)))) -> (~((e0) = (e1))) -> (((op (e0) (e0)) = (e1))\/(((op (e0) (e1)) = (e1))\/(((op (e0) (e2)) = (e1))\/((op (e0) (e3)) = (e1))))) -> (((op (e0) (e2)) = (e3))\/(((op (e1) (e2)) = (e3))\/(((op (e2) (e2)) = (e3))\/((op (e3) (e2)) = (e3))))) -> (~((op (e3) (e2)) = (op (e3) (e3)))) -> ((op (e1) (e2)) = (e1)) -> (~((e1) = (e3))) -> ((~((op (e3) (e3)) = (e0)))\/((op (e3) (e0)) = (e3))) -> (~((op (e3) (e0)) = (op (e3) (e3)))) -> (((op (e1) (e0)) = (e3))\/(((op (e1) (e1)) = (e3))\/(((op (e1) (e2)) = (e3))\/((op (e1) (e3)) = (e3))))) -> (~((op (e1) (e3)) = (op (e3) (e3)))) -> (~((op (e1) (e1)) = (e3))) -> (~((e2) = (e3))) -> (~((op (e0) (e2)) = (op (e0) (e3)))) -> (~((e0) = (e2))) -> (((op (e0) (e3)) = (e0))\/(((op (e1) (e3)) = (e0))\/(((op (e2) (e3)) = (e0))\/((op (e3) (e3)) = (e0))))) -> (~((e1) = (e2))) -> (((op (e1) (e0)) = (e2))\/(((op (e1) (e1)) = (e2))\/(((op (e1) (e2)) = (e2))\/((op (e1) (e3)) = (e2))))) -> ((~((op (e2) (e2)) = (e3)))\/((op (e2) (e3)) = (e2))) -> (~((op (e0) (e0)) = (e3))) -> (~((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) (e2)) = (e0))) -> (~((op (e0) (e3)) = (op (e3) (e3)))) -> ((op (e3) (e3)) = (e3)) -> (((op (e0) (e0)) = (e3))\/(((op (e0) (e1)) = (e3))\/(((op (e0) (e2)) = (e3))\/((op (e0) (e3)) = (e3))))) -> (~((op (e0) (e0)) = (e0))) -> (~((op (e3) (e1)) = (op (e3) (e3)))) -> ((~((op (e3) (e3)) = (e1)))\/((op (e3) (e1)) = (e3))) -> (~((op (e2) (e2)) = (op (e2) (e3)))) -> ((~((op (e1) (e1)) = (e3)))\/((op (e1) (e3)) = (e1))) -> False). % 15.22/15.41 do 0 intro. intros zenon_H1e3 zenon_H144 zenon_H199 zenon_H1e2 zenon_Haa zenon_H80 zenon_H87 zenon_H1d0 zenon_H109 zenon_H10d zenon_H166 zenon_H3b zenon_H105 zenon_H10e zenon_H110 zenon_H45 zenon_Hf1 zenon_H8f zenon_H8e zenon_Hb7 zenon_Hde zenon_H145 zenon_H1b4 zenon_H23 zenon_H1b3 zenon_Heb zenon_Hce zenon_H1cd zenon_H121 zenon_H1cf zenon_H9e zenon_H44 zenon_H175 zenon_H173 zenon_H117 zenon_Ha3 zenon_H10f zenon_Hbb zenon_H90 zenon_H8b zenon_H182 zenon_H6a zenon_Hc9 zenon_H5e zenon_Hd3 zenon_Ha7 zenon_H84 zenon_H1c3 zenon_H59 zenon_H4b zenon_H2d zenon_H28 zenon_H2e zenon_H36 zenon_H42 zenon_H58 zenon_H20 zenon_H12d zenon_H10c zenon_H15f zenon_H1d2. % 15.22/15.41 apply (zenon_or_s _ _ zenon_H1e3); [ zenon_intro zenon_H52 | zenon_intro zenon_H156 ]. % 15.22/15.41 apply (zenon_or_s _ _ zenon_Haa); [ zenon_intro zenon_H2f | zenon_intro zenon_H35 ]. % 15.22/15.41 apply (zenon_or_s _ _ zenon_H1c3); [ zenon_intro zenon_H30 | zenon_intro zenon_H124 ]. % 15.22/15.41 apply (zenon_or_s _ _ zenon_H10c); [ zenon_intro zenon_H104 | zenon_intro zenon_H10a ]. % 15.22/15.41 apply (zenon_or_s _ _ zenon_H110); [ zenon_intro zenon_H1f | zenon_intro zenon_H111 ]. % 15.22/15.41 exact (zenon_H20 zenon_H1f). % 15.22/15.41 apply (zenon_or_s _ _ zenon_H111); [ zenon_intro zenon_H49 | zenon_intro zenon_H112 ]. % 15.22/15.41 apply (zenon_L13_); trivial. % 15.22/15.41 apply (zenon_or_s _ _ zenon_H112); [ zenon_intro zenon_Hab | zenon_intro zenon_Hca ]. % 15.22/15.41 apply (zenon_L207_); trivial. % 15.22/15.41 apply (zenon_L435_); trivial. % 15.22/15.41 apply (zenon_L102_); trivial. % 15.22/15.41 apply (zenon_or_s _ _ zenon_H10f); [ zenon_intro zenon_H3c | zenon_intro zenon_Hba ]. % 15.22/15.41 apply (zenon_or_s _ _ zenon_H10c); [ zenon_intro zenon_H104 | zenon_intro zenon_H10a ]. % 15.22/15.41 apply (zenon_or_s _ _ zenon_H110); [ zenon_intro zenon_H1f | zenon_intro zenon_H111 ]. % 15.22/15.41 exact (zenon_H20 zenon_H1f). % 15.22/15.41 apply (zenon_or_s _ _ zenon_H111); [ zenon_intro zenon_H49 | zenon_intro zenon_H112 ]. % 15.22/15.41 apply (zenon_L382_); trivial. % 15.22/15.41 apply (zenon_or_s _ _ zenon_H112); [ zenon_intro zenon_Hab | zenon_intro zenon_Hca ]. % 15.22/15.41 apply (zenon_L206_); trivial. % 15.22/15.41 apply (zenon_L436_); trivial. % 15.22/15.41 apply (zenon_L102_); trivial. % 15.22/15.41 apply (zenon_L437_); trivial. % 15.22/15.41 apply (zenon_or_s _ _ zenon_H1c3); [ zenon_intro zenon_H30 | zenon_intro zenon_H124 ]. % 15.22/15.41 apply (zenon_L439_); trivial. % 15.22/15.41 apply (zenon_L137_); trivial. % 15.22/15.41 apply (zenon_or_s _ _ zenon_H1c3); [ zenon_intro zenon_H30 | zenon_intro zenon_H124 ]. % 15.22/15.41 apply (zenon_or_s _ _ zenon_H110); [ zenon_intro zenon_H1f | zenon_intro zenon_H111 ]. % 15.22/15.41 exact (zenon_H20 zenon_H1f). % 15.22/15.41 apply (zenon_or_s _ _ zenon_H111); [ zenon_intro zenon_H49 | zenon_intro zenon_H112 ]. % 15.22/15.41 apply (zenon_L278_); trivial. % 15.22/15.41 apply (zenon_or_s _ _ zenon_H112); [ zenon_intro zenon_Hab | zenon_intro zenon_Hca ]. % 15.22/15.41 apply (zenon_L197_); trivial. % 15.22/15.41 apply (zenon_L362_); trivial. % 15.22/15.41 apply (zenon_L256_); trivial. % 15.22/15.41 (* end of lemma zenon_L440_ *) % 15.22/15.41 assert (zenon_L441_ : ((~((op (e2) (e2)) = (e1)))\/((op (e2) (e1)) = (e2))) -> (((op (e0) (e1)) = (e0))\/(((op (e1) (e1)) = (e0))\/(((op (e2) (e1)) = (e0))\/((op (e3) (e1)) = (e0))))) -> (((op (e0) (e1)) = (e3))\/(((op (e1) (e1)) = (e3))\/(((op (e2) (e1)) = (e3))\/((op (e3) (e1)) = (e3))))) -> (~((op (e2) (e1)) = (op (e2) (e3)))) -> ((~((op (e2) (e2)) = (e2)))\/((op (e2) (e2)) = (e2))) -> (~((op (e0) (e3)) = (op (e1) (e3)))) -> (~((op (e0) (e2)) = (op (e1) (e2)))) -> (~((op (e1) (e2)) = (op (e1) (e3)))) -> (~((op (e3) (e0)) = (op (e3) (e1)))) -> ((~((op (e3) (e3)) = (e3)))\/((op (e3) (e3)) = (e3))) -> (~((op (e1) (e0)) = (op (e1) (e2)))) -> (((op (e3) (e3)) = (e0))\/(((op (e3) (e3)) = (e1))\/(((op (e3) (e3)) = (e2))\/((op (e3) (e3)) = (e3))))) -> (~((op (e3) (e0)) = (op (e3) (e2)))) -> ((~((op (e3) (e3)) = (e2)))\/((op (e3) (e2)) = (e3))) -> (((op (e0) (e0)) = (e0))\/(((op (e0) (e1)) = (e0))\/(((op (e0) (e2)) = (e0))\/((op (e0) (e3)) = (e0))))) -> (~((op (e0) (e0)) = (e1))) -> (((op (e0) (e0)) = (e1))\/(((op (e1) (e0)) = (e1))\/(((op (e2) (e0)) = (e1))\/((op (e3) (e0)) = (e1))))) -> (~((op (e0) (e0)) = (e2))) -> (((op (e0) (e0)) = (e2))\/(((op (e0) (e1)) = (e2))\/(((op (e0) (e2)) = (e2))\/((op (e0) (e3)) = (e2))))) -> (((op (e2) (e0)) = (e1))\/(((op (e2) (e1)) = (e1))\/(((op (e2) (e2)) = (e1))\/((op (e2) (e3)) = (e1))))) -> (~((op (e0) (e1)) = (op (e2) (e1)))) -> (~((op (e1) (e1)) = (e0))) -> (~((op (e1) (e1)) = (e1))) -> (~((op (e0) (e1)) = (op (e1) (e1)))) -> (((op (e1) (e1)) = (e0))\/(((op (e1) (e1)) = (e1))\/(((op (e1) (e1)) = (e2))\/((op (e1) (e1)) = (e3))))) -> (((op (e0) (e0)) = (e2))\/(((op (e1) (e0)) = (e2))\/(((op (e2) (e0)) = (e2))\/((op (e3) (e0)) = (e2))))) -> (~((op (e2) (e0)) = (op (e2) (e3)))) -> (~((op (e0) (e1)) = (op (e0) (e3)))) -> (((op (e0) (e3)) = (e1))\/(((op (e1) (e3)) = (e1))\/(((op (e2) (e3)) = (e1))\/((op (e3) (e3)) = (e1))))) -> (~((op (e1) (e0)) = (op (e1) (e3)))) -> (~((e0) = (e1))) -> (((op (e0) (e0)) = (e1))\/(((op (e0) (e1)) = (e1))\/(((op (e0) (e2)) = (e1))\/((op (e0) (e3)) = (e1))))) -> (((op (e0) (e2)) = (e3))\/(((op (e1) (e2)) = (e3))\/(((op (e2) (e2)) = (e3))\/((op (e3) (e2)) = (e3))))) -> (~((op (e3) (e2)) = (op (e3) (e3)))) -> ((op (e1) (e2)) = (e1)) -> (~((e1) = (e3))) -> ((~((op (e3) (e3)) = (e0)))\/((op (e3) (e0)) = (e3))) -> (~((op (e3) (e0)) = (op (e3) (e3)))) -> (((op (e1) (e0)) = (e3))\/(((op (e1) (e1)) = (e3))\/(((op (e1) (e2)) = (e3))\/((op (e1) (e3)) = (e3))))) -> (~((op (e1) (e3)) = (op (e3) (e3)))) -> (~((e2) = (e3))) -> (~((op (e0) (e2)) = (op (e0) (e3)))) -> (~((e0) = (e2))) -> (((op (e0) (e3)) = (e0))\/(((op (e1) (e3)) = (e0))\/(((op (e2) (e3)) = (e0))\/((op (e3) (e3)) = (e0))))) -> (~((e1) = (e2))) -> (((op (e1) (e0)) = (e2))\/(((op (e1) (e1)) = (e2))\/(((op (e1) (e2)) = (e2))\/((op (e1) (e3)) = (e2))))) -> ((~((op (e2) (e2)) = (e3)))\/((op (e2) (e3)) = (e2))) -> (~((op (e0) (e0)) = (e3))) -> (~((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 (e0) (e3)) = (op (e3) (e3)))) -> ((op (e3) (e3)) = (e3)) -> (((op (e0) (e0)) = (e3))\/(((op (e0) (e1)) = (e3))\/(((op (e0) (e2)) = (e3))\/((op (e0) (e3)) = (e3))))) -> (~((op (e0) (e0)) = (e0))) -> (~((op (e3) (e1)) = (op (e3) (e3)))) -> ((~((op (e3) (e3)) = (e1)))\/((op (e3) (e1)) = (e3))) -> (~((op (e2) (e2)) = (op (e2) (e3)))) -> ((~((op (e1) (e1)) = (e3)))\/((op (e1) (e3)) = (e1))) -> (~((op (e2) (e0)) = (op (e2) (e1)))) -> (~((op (e2) (e3)) = (op (e3) (e3)))) -> (((op (e2) (e0)) = (e3))\/(((op (e2) (e1)) = (e3))\/(((op (e2) (e2)) = (e3))\/((op (e2) (e3)) = (e3))))) -> (~((op (e2) (e0)) = (op (e2) (e2)))) -> ((~((op (e2) (e2)) = (e0)))\/((op (e2) (e0)) = (e2))) -> False). % 15.22/15.41 do 0 intro. intros zenon_H1e3 zenon_H144 zenon_H199 zenon_H1e2 zenon_Haa zenon_H80 zenon_H87 zenon_H1d0 zenon_H109 zenon_H10d zenon_H166 zenon_H3b zenon_H105 zenon_H10e zenon_H110 zenon_H45 zenon_Hf1 zenon_H8f zenon_H8e zenon_Hb7 zenon_Hde zenon_H145 zenon_H1b4 zenon_H23 zenon_H1b3 zenon_Heb zenon_Hce zenon_H1cd zenon_H121 zenon_H1cf zenon_H9e zenon_H44 zenon_H175 zenon_H173 zenon_H117 zenon_Ha3 zenon_H10f zenon_Hbb zenon_H90 zenon_H8b zenon_H6a zenon_Hc9 zenon_H5e zenon_Hd3 zenon_Ha7 zenon_H84 zenon_H1c3 zenon_H59 zenon_H4b zenon_H2d zenon_H28 zenon_H36 zenon_H42 zenon_H58 zenon_H20 zenon_H12d zenon_H10c zenon_H15f zenon_H1d2 zenon_H154 zenon_He3 zenon_He6 zenon_H17a zenon_H1d4. % 15.22/15.41 apply (zenon_or_s _ _ zenon_H1d2); [ zenon_intro zenon_H182 | zenon_intro zenon_H11f ]. % 15.22/15.41 apply (zenon_or_s _ _ zenon_H1d4); [ zenon_intro zenon_H2e | zenon_intro zenon_Hdd ]. % 15.22/15.41 apply (zenon_L440_); trivial. % 15.22/15.41 apply (zenon_L365_); trivial. % 15.22/15.41 apply (zenon_L237_); trivial. % 15.22/15.41 (* end of lemma zenon_L441_ *) % 15.22/15.41 assert (zenon_L442_ : ((~((op (e2) (e2)) = (e1)))\/((op (e2) (e1)) = (e2))) -> (~((op (e2) (e0)) = (op (e2) (e1)))) -> ((~((op (e2) (e2)) = (e3)))\/((op (e2) (e3)) = (e2))) -> (~((op (e2) (e0)) = (op (e2) (e3)))) -> (~((op (e0) (e0)) = (e1))) -> (~((op (e0) (e1)) = (op (e1) (e1)))) -> ((op (e1) (e1)) = (e1)) -> (((op (e0) (e0)) = (e3))\/(((op (e0) (e1)) = (e3))\/(((op (e0) (e2)) = (e3))\/((op (e0) (e3)) = (e3))))) -> (~((op (e0) (e3)) = (op (e3) (e3)))) -> (~((e1) = (e3))) -> (~((e2) = (e3))) -> (~((op (e0) (e1)) = (op (e2) (e1)))) -> (~((op (e2) (e3)) = (op (e3) (e3)))) -> ((op (e3) (e3)) = (e3)) -> (((op (e2) (e0)) = (e3))\/(((op (e2) (e1)) = (e3))\/(((op (e2) (e2)) = (e3))\/((op (e2) (e3)) = (e3))))) -> (~((e1) = (e2))) -> ((op (e2) (e0)) = (e2)) -> (~((op (e1) (e1)) = (op (e2) (e1)))) -> (((op (e2) (e2)) = (e0))\/(((op (e2) (e2)) = (e1))\/(((op (e2) (e2)) = (e2))\/((op (e2) (e2)) = (e3))))) -> (((op (e2) (e0)) = (e1))\/(((op (e2) (e1)) = (e1))\/(((op (e2) (e2)) = (e1))\/((op (e2) (e3)) = (e1))))) -> (~((op (e0) (e3)) = (op (e2) (e3)))) -> (((op (e0) (e0)) = (e1))\/(((op (e0) (e1)) = (e1))\/(((op (e0) (e2)) = (e1))\/((op (e0) (e3)) = (e1))))) -> (~((op (e2) (e0)) = (op (e2) (e2)))) -> ((~((op (e2) (e2)) = (e2)))\/((op (e2) (e2)) = (e2))) -> False). % 15.22/15.41 do 0 intro. intros zenon_H1e3 zenon_H154 zenon_H1c3 zenon_Hce zenon_H45 zenon_H23 zenon_H21 zenon_H58 zenon_H36 zenon_Ha3 zenon_H6a zenon_Hde zenon_He3 zenon_H42 zenon_He6 zenon_Ha7 zenon_Hdd zenon_Hb1 zenon_H2d zenon_Hb7 zenon_Hb4 zenon_H44 zenon_H17a zenon_Haa. % 15.22/15.41 apply (zenon_or_s _ _ zenon_H1e3); [ zenon_intro zenon_H52 | zenon_intro zenon_H156 ]. % 15.22/15.41 apply (zenon_L323_); trivial. % 15.22/15.41 apply (zenon_L284_); trivial. % 15.22/15.41 (* end of lemma zenon_L442_ *) % 15.22/15.41 assert (zenon_L443_ : ((~((op (e1) (e1)) = (e3)))\/((op (e1) (e3)) = (e1))) -> ((op (e1) (e0)) = (e1)) -> (~((op (e1) (e0)) = (op (e1) (e3)))) -> (~((op (e0) (e1)) = (op (e1) (e1)))) -> ((op (e0) (e1)) = (e0)) -> (~((op (e1) (e1)) = (e1))) -> (~((op (e1) (e1)) = (e2))) -> (((op (e1) (e1)) = (e0))\/(((op (e1) (e1)) = (e1))\/(((op (e1) (e1)) = (e2))\/((op (e1) (e1)) = (e3))))) -> False). % 15.22/15.41 do 0 intro. intros zenon_H1d2 zenon_Hd8 zenon_H1cf zenon_H23 zenon_H49 zenon_H1b4 zenon_Hd6 zenon_H1b3. % 15.22/15.41 apply (zenon_or_s _ _ zenon_H1d2); [ zenon_intro zenon_H182 | zenon_intro zenon_H11f ]. % 15.22/15.41 apply (zenon_L347_); trivial. % 15.22/15.41 apply (zenon_L224_); trivial. % 15.22/15.41 (* end of lemma zenon_L443_ *) % 15.22/15.41 assert (zenon_L444_ : ((~((op (e1) (e1)) = (e2)))\/((op (e1) (e2)) = (e1))) -> (~((op (e1) (e0)) = (op (e1) (e2)))) -> (((op (e1) (e1)) = (e0))\/(((op (e1) (e1)) = (e1))\/(((op (e1) (e1)) = (e2))\/((op (e1) (e1)) = (e3))))) -> (~((op (e1) (e1)) = (e1))) -> ((op (e0) (e1)) = (e0)) -> (~((op (e0) (e1)) = (op (e1) (e1)))) -> (~((op (e1) (e0)) = (op (e1) (e3)))) -> ((op (e1) (e0)) = (e1)) -> ((~((op (e1) (e1)) = (e3)))\/((op (e1) (e3)) = (e1))) -> False). % 15.22/15.41 do 0 intro. intros zenon_H1d3 zenon_H166 zenon_H1b3 zenon_H1b4 zenon_H49 zenon_H23 zenon_H1cf zenon_Hd8 zenon_H1d2. % 15.22/15.41 apply (zenon_or_s _ _ zenon_H1d3); [ zenon_intro zenon_Hd6 | zenon_intro zenon_H117 ]. % 15.22/15.41 apply (zenon_L443_); trivial. % 15.22/15.41 apply (zenon_L248_); trivial. % 15.22/15.41 (* end of lemma zenon_L444_ *) % 15.22/15.41 assert (zenon_L445_ : ((~((op (e2) (e2)) = (e1)))\/((op (e2) (e1)) = (e2))) -> (~((op (e2) (e1)) = (op (e2) (e3)))) -> (((op (e0) (e1)) = (e3))\/(((op (e1) (e1)) = (e3))\/(((op (e2) (e1)) = (e3))\/((op (e3) (e1)) = (e3))))) -> (~((op (e2) (e0)) = (op (e2) (e3)))) -> (((op (e2) (e0)) = (e0))\/(((op (e2) (e1)) = (e0))\/(((op (e2) (e2)) = (e0))\/((op (e2) (e3)) = (e0))))) -> (((op (e0) (e1)) = (e1))\/(((op (e1) (e1)) = (e1))\/(((op (e2) (e1)) = (e1))\/((op (e3) (e1)) = (e1))))) -> (~((op (e0) (e1)) = (op (e2) (e1)))) -> (~((op (e2) (e1)) = (op (e2) (e2)))) -> (~((op (e0) (e2)) = (op (e2) (e2)))) -> (~((e0) = (e3))) -> (((op (e0) (e3)) = (e2))\/(((op (e1) (e3)) = (e2))\/(((op (e2) (e3)) = (e2))\/((op (e3) (e3)) = (e2))))) -> (~((op (e0) (e0)) = (e2))) -> (~((op (e0) (e3)) = (op (e1) (e3)))) -> (~((op (e1) (e2)) = (op (e2) (e2)))) -> (~((op (e3) (e2)) = (op (e3) (e3)))) -> ((~((op (e3) (e3)) = (e2)))\/((op (e3) (e2)) = (e3))) -> ((~((op (e2) (e2)) = (e2)))\/((op (e2) (e2)) = (e2))) -> (~((op (e2) (e0)) = (op (e2) (e1)))) -> (((op (e2) (e0)) = (e3))\/(((op (e2) (e1)) = (e3))\/(((op (e2) (e2)) = (e3))\/((op (e2) (e3)) = (e3))))) -> (~((op (e2) (e3)) = (op (e3) (e3)))) -> (~((op (e2) (e0)) = (op (e2) (e2)))) -> ((~((op (e2) (e2)) = (e0)))\/((op (e2) (e0)) = (e2))) -> (((op (e0) (e0)) = (e3))\/(((op (e1) (e0)) = (e3))\/(((op (e2) (e0)) = (e3))\/((op (e3) (e0)) = (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)) = (e0))) -> (~((op (e1) (e1)) = (e1))) -> (~((op (e1) (e1)) = (e2))) -> (~((op (e1) (e1)) = (e3))) -> (((op (e1) (e1)) = (e0))\/(((op (e1) (e1)) = (e1))\/(((op (e1) (e1)) = (e2))\/((op (e1) (e1)) = (e3))))) -> ((op (e1) (e0)) = (e1)) -> (~((e1) = (e3))) -> (~((op (e0) (e0)) = (e3))) -> ((~((op (e3) (e3)) = (e0)))\/((op (e3) (e0)) = (e3))) -> (((op (e0) (e0)) = (e0))\/(((op (e0) (e1)) = (e0))\/(((op (e0) (e2)) = (e0))\/((op (e0) (e3)) = (e0))))) -> (~((op (e1) (e0)) = (op (e3) (e0)))) -> (~((op (e2) (e2)) = (e1))) -> (~((op (e3) (e1)) = (op (e3) (e2)))) -> (((op (e0) (e2)) = (e1))\/(((op (e1) (e2)) = (e1))\/(((op (e2) (e2)) = (e1))\/((op (e3) (e2)) = (e1))))) -> (~((op (e0) (e2)) = (op (e3) (e2)))) -> (((op (e3) (e0)) = (e1))\/(((op (e3) (e1)) = (e1))\/(((op (e3) (e2)) = (e1))\/((op (e3) (e3)) = (e1))))) -> (~((op (e0) (e0)) = (e1))) -> (((op (e0) (e3)) = (e1))\/(((op (e1) (e3)) = (e1))\/(((op (e2) (e3)) = (e1))\/((op (e3) (e3)) = (e1))))) -> (~((e1) = (e2))) -> (~((op (e0) (e1)) = (op (e0) (e3)))) -> (~((e0) = (e1))) -> (((op (e0) (e0)) = (e2))\/(((op (e0) (e1)) = (e2))\/(((op (e0) (e2)) = (e2))\/((op (e0) (e3)) = (e2))))) -> (((op (e0) (e3)) = (e0))\/(((op (e1) (e3)) = (e0))\/(((op (e2) (e3)) = (e0))\/((op (e3) (e3)) = (e0))))) -> (~((e0) = (e2))) -> (~((op (e0) (e2)) = (op (e0) (e3)))) -> (((op (e1) (e0)) = (e2))\/(((op (e1) (e1)) = (e2))\/(((op (e1) (e2)) = (e2))\/((op (e1) (e3)) = (e2))))) -> (~((e2) = (e3))) -> (~((op (e0) (e2)) = (op (e1) (e2)))) -> (~((op (e0) (e3)) = (op (e3) (e3)))) -> (((op (e0) (e0)) = (e3))\/(((op (e0) (e1)) = (e3))\/(((op (e0) (e2)) = (e3))\/((op (e0) (e3)) = (e3))))) -> (~((op (e1) (e3)) = (op (e3) (e3)))) -> (((op (e1) (e0)) = (e3))\/(((op (e1) (e1)) = (e3))\/(((op (e1) (e2)) = (e3))\/((op (e1) (e3)) = (e3))))) -> (((op (e0) (e0)) = (e1))\/(((op (e0) (e1)) = (e1))\/(((op (e0) (e2)) = (e1))\/((op (e0) (e3)) = (e1))))) -> ((~((op (e1) (e1)) = (e3)))\/((op (e1) (e3)) = (e1))) -> (~((op (e1) (e0)) = (op (e1) (e3)))) -> (~((op (e0) (e1)) = (op (e1) (e1)))) -> (~((op (e1) (e0)) = (op (e1) (e2)))) -> ((~((op (e1) (e1)) = (e2)))\/((op (e1) (e2)) = (e1))) -> (~((op (e0) (e0)) = (e0))) -> (~((op (e3) (e1)) = (op (e3) (e3)))) -> ((~((op (e3) (e3)) = (e1)))\/((op (e3) (e1)) = (e3))) -> ((~((op (e2) (e2)) = (e3)))\/((op (e2) (e3)) = (e2))) -> False). % 15.22/15.41 do 0 intro. intros zenon_H1e3 zenon_H1e2 zenon_H199 zenon_Hce zenon_H1f5 zenon_H228 zenon_Hde zenon_H157 zenon_H28 zenon_H4b zenon_H160 zenon_H8f zenon_H80 zenon_H7d zenon_H173 zenon_H10e zenon_Haa zenon_H154 zenon_He6 zenon_He3 zenon_H17a zenon_H1d4 zenon_Hbe zenon_H42 zenon_Hbb zenon_H2d zenon_H2e zenon_H1b4 zenon_Hd6 zenon_H182 zenon_H1b3 zenon_Hd8 zenon_Ha3 zenon_H59 zenon_H10f zenon_H110 zenon_H22e zenon_H52 zenon_H135 zenon_H11b zenon_H140 zenon_H146 zenon_H45 zenon_H121 zenon_Ha7 zenon_H1cd zenon_H9e zenon_H8e zenon_Hd3 zenon_H5e zenon_Hc9 zenon_H84 zenon_H6a zenon_H87 zenon_H36 zenon_H58 zenon_H8b zenon_H90 zenon_H44 zenon_H1d2 zenon_H1cf zenon_H23 zenon_H166 zenon_H1d3 zenon_H20 zenon_H12d zenon_H10c zenon_H1c3. % 15.22/15.41 apply (zenon_or_s _ _ zenon_Haa); [ zenon_intro zenon_H2f | zenon_intro zenon_H35 ]. % 15.22/15.41 apply (zenon_or_s _ _ zenon_H1c3); [ zenon_intro zenon_H30 | zenon_intro zenon_H124 ]. % 15.22/15.41 apply (zenon_L241_); trivial. % 15.22/15.41 apply (zenon_or_s _ _ zenon_H10f); [ zenon_intro zenon_H3c | zenon_intro zenon_Hba ]. % 15.22/15.41 apply (zenon_or_s _ _ zenon_H10c); [ zenon_intro zenon_H104 | zenon_intro zenon_H10a ]. % 15.22/15.41 apply (zenon_or_s _ _ zenon_H110); [ zenon_intro zenon_H1f | zenon_intro zenon_H111 ]. % 15.22/15.41 exact (zenon_H20 zenon_H1f). % 15.22/15.41 apply (zenon_or_s _ _ zenon_H111); [ zenon_intro zenon_H49 | zenon_intro zenon_H112 ]. % 15.22/15.41 apply (zenon_L444_); trivial. % 15.22/15.41 apply (zenon_or_s _ _ zenon_H112); [ zenon_intro zenon_Hab | zenon_intro zenon_Hca ]. % 15.22/15.41 apply (zenon_L228_); trivial. % 15.22/15.41 apply (zenon_L398_); trivial. % 15.22/15.41 apply (zenon_L102_); trivial. % 15.22/15.41 apply (zenon_L43_); trivial. % 15.22/15.41 apply (zenon_or_s _ _ zenon_H110); [ zenon_intro zenon_H1f | zenon_intro zenon_H111 ]. % 15.22/15.41 exact (zenon_H20 zenon_H1f). % 15.22/15.41 apply (zenon_or_s _ _ zenon_H111); [ zenon_intro zenon_H49 | zenon_intro zenon_H112 ]. % 15.22/15.41 apply (zenon_L378_); trivial. % 15.22/15.41 apply (zenon_or_s _ _ zenon_H112); [ zenon_intro zenon_Hab | zenon_intro zenon_Hca ]. % 15.22/15.41 apply (zenon_L245_); trivial. % 15.22/15.41 apply (zenon_L402_); trivial. % 15.22/15.41 (* end of lemma zenon_L445_ *) % 15.22/15.41 assert (zenon_L446_ : ((~((op (e2) (e2)) = (e3)))\/((op (e2) (e3)) = (e2))) -> ((op (e2) (e1)) = (e2)) -> (~((op (e2) (e1)) = (op (e2) (e3)))) -> (~((op (e0) (e0)) = (e3))) -> (~((e1) = (e3))) -> ((op (e1) (e0)) = (e1)) -> (((op (e1) (e1)) = (e0))\/(((op (e1) (e1)) = (e1))\/(((op (e1) (e1)) = (e2))\/((op (e1) (e1)) = (e3))))) -> (~((op (e1) (e1)) = (e3))) -> (~((op (e1) (e1)) = (e2))) -> (~((op (e1) (e1)) = (e1))) -> (~((op (e2) (e2)) = (e0))) -> (~((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 (e3) (e3)) = (e3)) -> (((op (e0) (e0)) = (e3))\/(((op (e1) (e0)) = (e3))\/(((op (e2) (e0)) = (e3))\/((op (e3) (e0)) = (e3))))) -> False). % 15.22/15.41 do 0 intro. intros zenon_H1c3 zenon_H156 zenon_H1e2 zenon_H59 zenon_Ha3 zenon_Hd8 zenon_H1b3 zenon_H182 zenon_Hd6 zenon_H1b4 zenon_H2e zenon_H2f zenon_H2d zenon_Hbb zenon_H42 zenon_Hbe. % 15.22/15.41 apply (zenon_or_s _ _ zenon_H1c3); [ zenon_intro zenon_H30 | zenon_intro zenon_H124 ]. % 15.22/15.41 apply (zenon_L241_); trivial. % 15.22/15.41 apply (zenon_L256_); trivial. % 15.22/15.41 (* end of lemma zenon_L446_ *) % 15.22/15.41 assert (zenon_L447_ : ((~((op (e2) (e2)) = (e2)))\/((op (e2) (e2)) = (e2))) -> (~((op (e2) (e1)) = (op (e2) (e2)))) -> (((op (e0) (e0)) = (e3))\/(((op (e1) (e0)) = (e3))\/(((op (e2) (e0)) = (e3))\/((op (e3) (e0)) = (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)) = (e0))) -> (~((op (e1) (e1)) = (e1))) -> (~((op (e1) (e1)) = (e2))) -> (~((op (e1) (e1)) = (e3))) -> (((op (e1) (e1)) = (e0))\/(((op (e1) (e1)) = (e1))\/(((op (e1) (e1)) = (e2))\/((op (e1) (e1)) = (e3))))) -> ((op (e1) (e0)) = (e1)) -> (~((e1) = (e3))) -> (~((op (e0) (e0)) = (e3))) -> (~((op (e2) (e1)) = (op (e2) (e3)))) -> ((op (e2) (e1)) = (e2)) -> ((~((op (e2) (e2)) = (e3)))\/((op (e2) (e3)) = (e2))) -> False). % 15.22/15.41 do 0 intro. intros zenon_Haa zenon_H157 zenon_Hbe zenon_H42 zenon_Hbb zenon_H2d zenon_H2e zenon_H1b4 zenon_Hd6 zenon_H182 zenon_H1b3 zenon_Hd8 zenon_Ha3 zenon_H59 zenon_H1e2 zenon_H156 zenon_H1c3. % 15.22/15.41 apply (zenon_or_s _ _ zenon_Haa); [ zenon_intro zenon_H2f | zenon_intro zenon_H35 ]. % 15.22/15.41 apply (zenon_L446_); trivial. % 15.22/15.41 apply (zenon_L134_); trivial. % 15.22/15.41 (* end of lemma zenon_L447_ *) % 15.22/15.41 assert (zenon_L448_ : ((~((op (e1) (e1)) = (e1)))\/((op (e1) (e1)) = (e1))) -> (~((op (e1) (e0)) = (op (e1) (e1)))) -> ((~((op (e2) (e2)) = (e3)))\/((op (e2) (e3)) = (e2))) -> ((~((op (e3) (e3)) = (e1)))\/((op (e3) (e1)) = (e3))) -> (~((op (e3) (e1)) = (op (e3) (e3)))) -> (~((op (e0) (e0)) = (e0))) -> ((~((op (e1) (e1)) = (e2)))\/((op (e1) (e2)) = (e1))) -> (~((op (e1) (e0)) = (op (e1) (e2)))) -> (~((op (e0) (e1)) = (op (e1) (e1)))) -> (~((op (e1) (e0)) = (op (e1) (e3)))) -> ((~((op (e1) (e1)) = (e3)))\/((op (e1) (e3)) = (e1))) -> (((op (e0) (e0)) = (e1))\/(((op (e0) (e1)) = (e1))\/(((op (e0) (e2)) = (e1))\/((op (e0) (e3)) = (e1))))) -> (((op (e1) (e0)) = (e3))\/(((op (e1) (e1)) = (e3))\/(((op (e1) (e2)) = (e3))\/((op (e1) (e3)) = (e3))))) -> (~((op (e1) (e3)) = (op (e3) (e3)))) -> (((op (e0) (e0)) = (e3))\/(((op (e0) (e1)) = (e3))\/(((op (e0) (e2)) = (e3))\/((op (e0) (e3)) = (e3))))) -> (~((op (e0) (e3)) = (op (e3) (e3)))) -> (~((op (e0) (e2)) = (op (e1) (e2)))) -> (~((e2) = (e3))) -> (((op (e1) (e0)) = (e2))\/(((op (e1) (e1)) = (e2))\/(((op (e1) (e2)) = (e2))\/((op (e1) (e3)) = (e2))))) -> (~((op (e0) (e2)) = (op (e0) (e3)))) -> (~((e0) = (e2))) -> (((op (e0) (e3)) = (e0))\/(((op (e1) (e3)) = (e0))\/(((op (e2) (e3)) = (e0))\/((op (e3) (e3)) = (e0))))) -> (((op (e0) (e0)) = (e2))\/(((op (e0) (e1)) = (e2))\/(((op (e0) (e2)) = (e2))\/((op (e0) (e3)) = (e2))))) -> (~((e0) = (e1))) -> (~((op (e0) (e1)) = (op (e0) (e3)))) -> (~((e1) = (e2))) -> (((op (e0) (e3)) = (e1))\/(((op (e1) (e3)) = (e1))\/(((op (e2) (e3)) = (e1))\/((op (e3) (e3)) = (e1))))) -> (~((op (e0) (e0)) = (e1))) -> (((op (e3) (e0)) = (e1))\/(((op (e3) (e1)) = (e1))\/(((op (e3) (e2)) = (e1))\/((op (e3) (e3)) = (e1))))) -> (~((op (e0) (e2)) = (op (e3) (e2)))) -> (((op (e0) (e2)) = (e1))\/(((op (e1) (e2)) = (e1))\/(((op (e2) (e2)) = (e1))\/((op (e3) (e2)) = (e1))))) -> (~((op (e3) (e1)) = (op (e3) (e2)))) -> (~((op (e1) (e0)) = (op (e3) (e0)))) -> (((op (e0) (e0)) = (e0))\/(((op (e0) (e1)) = (e0))\/(((op (e0) (e2)) = (e0))\/((op (e0) (e3)) = (e0))))) -> ((~((op (e3) (e3)) = (e0)))\/((op (e3) (e0)) = (e3))) -> (~((op (e0) (e0)) = (e3))) -> (~((e1) = (e3))) -> ((op (e1) (e0)) = (e1)) -> (((op (e1) (e1)) = (e0))\/(((op (e1) (e1)) = (e1))\/(((op (e1) (e1)) = (e2))\/((op (e1) (e1)) = (e3))))) -> (((op (e2) (e2)) = (e0))\/(((op (e2) (e2)) = (e1))\/(((op (e2) (e2)) = (e2))\/((op (e2) (e2)) = (e3))))) -> (~((op (e3) (e0)) = (op (e3) (e3)))) -> ((op (e3) (e3)) = (e3)) -> (((op (e0) (e0)) = (e3))\/(((op (e1) (e0)) = (e3))\/(((op (e2) (e0)) = (e3))\/((op (e3) (e0)) = (e3))))) -> ((~((op (e2) (e2)) = (e0)))\/((op (e2) (e0)) = (e2))) -> (~((op (e2) (e0)) = (op (e2) (e2)))) -> (~((op (e2) (e3)) = (op (e3) (e3)))) -> (((op (e2) (e0)) = (e3))\/(((op (e2) (e1)) = (e3))\/(((op (e2) (e2)) = (e3))\/((op (e2) (e3)) = (e3))))) -> (~((op (e2) (e0)) = (op (e2) (e1)))) -> ((~((op (e2) (e2)) = (e2)))\/((op (e2) (e2)) = (e2))) -> ((~((op (e3) (e3)) = (e2)))\/((op (e3) (e2)) = (e3))) -> (~((op (e3) (e2)) = (op (e3) (e3)))) -> (~((op (e1) (e2)) = (op (e2) (e2)))) -> (~((op (e0) (e3)) = (op (e1) (e3)))) -> (~((op (e0) (e0)) = (e2))) -> (((op (e0) (e3)) = (e2))\/(((op (e1) (e3)) = (e2))\/(((op (e2) (e3)) = (e2))\/((op (e3) (e3)) = (e2))))) -> (~((e0) = (e3))) -> (~((op (e0) (e2)) = (op (e2) (e2)))) -> (~((op (e2) (e1)) = (op (e2) (e2)))) -> (~((op (e0) (e1)) = (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) (e1)) = (e0))\/(((op (e2) (e2)) = (e0))\/((op (e2) (e3)) = (e0))))) -> (~((op (e2) (e0)) = (op (e2) (e3)))) -> (((op (e0) (e1)) = (e3))\/(((op (e1) (e1)) = (e3))\/(((op (e2) (e1)) = (e3))\/((op (e3) (e1)) = (e3))))) -> (~((op (e2) (e1)) = (op (e2) (e3)))) -> ((~((op (e2) (e2)) = (e1)))\/((op (e2) (e1)) = (e2))) -> False). % 15.22/15.41 do 0 intro. intros zenon_H1d8 zenon_Hd7 zenon_H1c3 zenon_H10c zenon_H12d zenon_H20 zenon_H1d3 zenon_H166 zenon_H23 zenon_H1cf zenon_H1d2 zenon_H44 zenon_H90 zenon_H8b zenon_H58 zenon_H36 zenon_H87 zenon_H6a zenon_H84 zenon_Hc9 zenon_H5e zenon_Hd3 zenon_H8e zenon_H9e zenon_H1cd zenon_Ha7 zenon_H121 zenon_H45 zenon_H146 zenon_H140 zenon_H11b zenon_H135 zenon_H22e zenon_H110 zenon_H10f zenon_H59 zenon_Ha3 zenon_Hd8 zenon_H1b3 zenon_H2d zenon_Hbb zenon_H42 zenon_Hbe zenon_H1d4 zenon_H17a zenon_He3 zenon_He6 zenon_H154 zenon_Haa zenon_H10e zenon_H173 zenon_H7d zenon_H80 zenon_H8f zenon_H160 zenon_H4b zenon_H28 zenon_H157 zenon_Hde zenon_H228 zenon_H1f5 zenon_Hce zenon_H199 zenon_H1e2 zenon_H1e3. % 15.22/15.41 apply (zenon_or_s _ _ zenon_H1d8); [ zenon_intro zenon_H1b4 | zenon_intro zenon_H21 ]. % 15.22/15.41 apply (zenon_or_s _ _ zenon_H1d3); [ zenon_intro zenon_Hd6 | zenon_intro zenon_H117 ]. % 15.22/15.41 apply (zenon_or_s _ _ zenon_H1d2); [ zenon_intro zenon_H182 | zenon_intro zenon_H11f ]. % 15.22/15.41 apply (zenon_or_s _ _ zenon_H1d4); [ zenon_intro zenon_H2e | zenon_intro zenon_Hdd ]. % 15.22/15.41 apply (zenon_or_s _ _ zenon_H1e3); [ zenon_intro zenon_H52 | zenon_intro zenon_H156 ]. % 15.22/15.41 apply (zenon_L445_); trivial. % 15.22/15.41 apply (zenon_L447_); trivial. % 15.22/15.41 apply (zenon_L246_); trivial. % 15.22/15.41 apply (zenon_L224_); trivial. % 15.22/15.41 apply (zenon_L248_); trivial. % 15.22/15.41 apply (zenon_L61_); trivial. % 15.22/15.41 (* end of lemma zenon_L448_ *) % 15.22/15.41 assert (zenon_L449_ : ((~((op (e2) (e2)) = (e1)))\/((op (e2) (e1)) = (e2))) -> (~((op (e2) (e0)) = (op (e2) (e1)))) -> ((~((op (e2) (e2)) = (e3)))\/((op (e2) (e3)) = (e2))) -> (~((op (e2) (e0)) = (op (e2) (e3)))) -> (~((op (e0) (e0)) = (e1))) -> (((op (e0) (e0)) = (e2))\/(((op (e0) (e1)) = (e2))\/(((op (e0) (e2)) = (e2))\/((op (e0) (e3)) = (e2))))) -> ((op (e0) (e3)) = (e0)) -> (~((e0) = (e2))) -> (((op (e2) (e0)) = (e1))\/(((op (e2) (e1)) = (e1))\/(((op (e2) (e2)) = (e1))\/((op (e2) (e3)) = (e1))))) -> (((op (e2) (e2)) = (e0))\/(((op (e2) (e2)) = (e1))\/(((op (e2) (e2)) = (e2))\/((op (e2) (e2)) = (e3))))) -> (~((op (e0) (e1)) = (op (e2) (e1)))) -> ((op (e2) (e0)) = (e2)) -> (~((e1) = (e2))) -> (~((e1) = (e3))) -> (~((e2) = (e3))) -> (~((op (e0) (e3)) = (op (e3) (e3)))) -> ((op (e3) (e3)) = (e3)) -> (((op (e0) (e0)) = (e3))\/(((op (e0) (e1)) = (e3))\/(((op (e0) (e2)) = (e3))\/((op (e0) (e3)) = (e3))))) -> (~((op (e1) (e1)) = (e0))) -> (~((op (e1) (e1)) = (e1))) -> (~((op (e0) (e1)) = (op (e1) (e1)))) -> (~((op (e1) (e1)) = (e3))) -> (((op (e1) (e1)) = (e0))\/(((op (e1) (e1)) = (e1))\/(((op (e1) (e1)) = (e2))\/((op (e1) (e1)) = (e3))))) -> (~((op (e0) (e0)) = (e2))) -> (~((e0) = (e1))) -> (((op (e0) (e0)) = (e1))\/(((op (e0) (e1)) = (e1))\/(((op (e0) (e2)) = (e1))\/((op (e0) (e3)) = (e1))))) -> (~((op (e0) (e2)) = (op (e2) (e2)))) -> ((~((op (e2) (e2)) = (e2)))\/((op (e2) (e2)) = (e2))) -> False). % 15.22/15.41 do 0 intro. intros zenon_H1e3 zenon_H154 zenon_H1c3 zenon_Hce zenon_H45 zenon_H8e zenon_Hca zenon_H5e zenon_Hb7 zenon_H2d zenon_Hde zenon_Hdd zenon_Ha7 zenon_Ha3 zenon_H6a zenon_H36 zenon_H42 zenon_H58 zenon_H145 zenon_H1b4 zenon_H23 zenon_H182 zenon_H1b3 zenon_H8f zenon_H9e zenon_H44 zenon_H28 zenon_Haa. % 15.22/15.41 apply (zenon_or_s _ _ zenon_H1e3); [ zenon_intro zenon_H52 | zenon_intro zenon_H156 ]. % 15.22/15.41 apply (zenon_or_s _ _ zenon_Haa); [ zenon_intro zenon_H2f | zenon_intro zenon_H35 ]. % 15.22/15.41 apply (zenon_or_s _ _ zenon_H1c3); [ zenon_intro zenon_H30 | zenon_intro zenon_H124 ]. % 15.22/15.41 apply (zenon_L364_); trivial. % 15.22/15.41 apply (zenon_L119_); trivial. % 15.22/15.41 apply (zenon_L343_); trivial. % 15.22/15.41 apply (zenon_L284_); trivial. % 15.22/15.41 (* end of lemma zenon_L449_ *) % 15.22/15.41 assert (zenon_L450_ : ((~((op (e3) (e3)) = (e2)))\/((op (e3) (e2)) = (e3))) -> ((op (e3) (e3)) = (e3)) -> (~((op (e3) (e2)) = (op (e3) (e3)))) -> (~((op (e0) (e0)) = (e2))) -> (((op (e0) (e3)) = (e2))\/(((op (e1) (e3)) = (e2))\/(((op (e2) (e3)) = (e2))\/((op (e3) (e3)) = (e2))))) -> ((op (e2) (e2)) = (e2)) -> (~((op (e2) (e2)) = (op (e2) (e3)))) -> ((op (e1) (e3)) = (e1)) -> (~((e1) = (e2))) -> (~((op (e0) (e1)) = (op (e0) (e3)))) -> (~((op (e0) (e2)) = (op (e2) (e2)))) -> (~((e0) = (e2))) -> ((op (e0) (e3)) = (e0)) -> (((op (e0) (e0)) = (e2))\/(((op (e0) (e1)) = (e2))\/(((op (e0) (e2)) = (e2))\/((op (e0) (e3)) = (e2))))) -> False). % 15.22/15.41 do 0 intro. intros zenon_H10e zenon_H42 zenon_H173 zenon_H8f zenon_H160 zenon_H35 zenon_H15f zenon_H11f zenon_Ha7 zenon_H1cd zenon_H28 zenon_H5e zenon_Hca zenon_H8e. % 15.22/15.41 apply (zenon_or_s _ _ zenon_H10e); [ zenon_intro zenon_H3d | zenon_intro zenon_H106 ]. % 15.22/15.41 apply (zenon_L424_); trivial. % 15.22/15.41 apply (zenon_L153_); trivial. % 15.22/15.41 (* end of lemma zenon_L450_ *) % 15.22/15.41 assert (zenon_L451_ : ((op (e1) (e3)) = (e1)) -> (((op (e0) (e3)) = (e0))\/(((op (e1) (e3)) = (e0))\/(((op (e2) (e3)) = (e0))\/((op (e3) (e3)) = (e0))))) -> ((~((op (e1) (e1)) = (e3)))\/((op (e1) (e3)) = (e1))) -> ((~((op (e2) (e2)) = (e1)))\/((op (e2) (e1)) = (e2))) -> (~((op (e2) (e1)) = (op (e2) (e3)))) -> ((~((op (e3) (e3)) = (e2)))\/((op (e3) (e2)) = (e3))) -> (~((op (e3) (e2)) = (op (e3) (e3)))) -> (((op (e0) (e1)) = (e3))\/(((op (e1) (e1)) = (e3))\/(((op (e2) (e1)) = (e3))\/((op (e3) (e1)) = (e3))))) -> (((op (e0) (e0)) = (e2))\/(((op (e1) (e0)) = (e2))\/(((op (e2) (e0)) = (e2))\/((op (e3) (e0)) = (e2))))) -> (((op (e3) (e3)) = (e0))\/(((op (e3) (e3)) = (e1))\/(((op (e3) (e3)) = (e2))\/((op (e3) (e3)) = (e3))))) -> (~((op (e2) (e0)) = (op (e2) (e1)))) -> ((~((op (e3) (e3)) = (e3)))\/((op (e3) (e3)) = (e3))) -> (~((op (e3) (e0)) = (op (e3) (e3)))) -> ((~((op (e3) (e3)) = (e0)))\/((op (e3) (e0)) = (e3))) -> (~((op (e2) (e1)) = (op (e2) (e2)))) -> ((~((op (e2) (e2)) = (e3)))\/((op (e2) (e3)) = (e2))) -> (((op (e3) (e0)) = (e1))\/(((op (e3) (e1)) = (e1))\/(((op (e3) (e2)) = (e1))\/((op (e3) (e3)) = (e1))))) -> (~((op (e0) (e2)) = (op (e3) (e2)))) -> (((op (e0) (e2)) = (e1))\/(((op (e1) (e2)) = (e1))\/(((op (e2) (e2)) = (e1))\/((op (e3) (e2)) = (e1))))) -> (~((op (e3) (e1)) = (op (e3) (e2)))) -> (~((op (e0) (e2)) = (op (e0) (e3)))) -> (~((op (e1) (e0)) = (op (e3) (e0)))) -> (~((op (e1) (e3)) = (op (e3) (e3)))) -> (((op (e1) (e0)) = (e3))\/(((op (e1) (e1)) = (e3))\/(((op (e1) (e2)) = (e3))\/((op (e1) (e3)) = (e3))))) -> (~((op (e0) (e1)) = (op (e0) (e3)))) -> (~((e1) = (e2))) -> (((op (e0) (e0)) = (e1))\/(((op (e0) (e1)) = (e1))\/(((op (e0) (e2)) = (e1))\/((op (e0) (e3)) = (e1))))) -> (((op (e0) (e3)) = (e1))\/(((op (e1) (e3)) = (e1))\/(((op (e2) (e3)) = (e1))\/((op (e3) (e3)) = (e1))))) -> (((op (e2) (e2)) = (e0))\/(((op (e2) (e2)) = (e1))\/(((op (e2) (e2)) = (e2))\/((op (e2) (e2)) = (e3))))) -> (~((op (e1) (e0)) = (op (e1) (e3)))) -> ((op (e0) (e3)) = (e0)) -> (~((e0) = (e1))) -> (~((e1) = (e3))) -> (~((op (e0) (e2)) = (op (e2) (e2)))) -> (~((op (e0) (e3)) = (op (e3) (e3)))) -> ((op (e3) (e3)) = (e3)) -> (((op (e0) (e0)) = (e3))\/(((op (e0) (e1)) = (e3))\/(((op (e0) (e2)) = (e3))\/((op (e0) (e3)) = (e3))))) -> (~((op (e3) (e1)) = (op (e3) (e3)))) -> ((~((op (e3) (e3)) = (e1)))\/((op (e3) (e1)) = (e3))) -> (~((op (e0) (e0)) = (e2))) -> (~((e2) = (e3))) -> (~((e0) = (e2))) -> (((op (e0) (e0)) = (e2))\/(((op (e0) (e1)) = (e2))\/(((op (e0) (e2)) = (e2))\/((op (e0) (e3)) = (e2))))) -> (((op (e1) (e0)) = (e2))\/(((op (e1) (e1)) = (e2))\/(((op (e1) (e2)) = (e2))\/((op (e1) (e3)) = (e2))))) -> (~((op (e1) (e1)) = (e1))) -> (((op (e1) (e1)) = (e0))\/(((op (e1) (e1)) = (e1))\/(((op (e1) (e1)) = (e2))\/((op (e1) (e1)) = (e3))))) -> (~((op (e1) (e2)) = (op (e2) (e2)))) -> (~((op (e1) (e1)) = (e2))) -> (~((op (e0) (e2)) = (op (e1) (e2)))) -> ((~((op (e2) (e2)) = (e2)))\/((op (e2) (e2)) = (e2))) -> (~((op (e1) (e2)) = (op (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 (e0) (e1)) = (e2))\/(((op (e1) (e1)) = (e2))\/(((op (e2) (e1)) = (e2))\/((op (e3) (e1)) = (e2))))) -> (~((op (e2) (e0)) = (op (e2) (e2)))) -> ((~((op (e2) (e2)) = (e0)))\/((op (e2) (e0)) = (e2))) -> (((op (e0) (e1)) = (e0))\/(((op (e1) (e1)) = (e0))\/(((op (e2) (e1)) = (e0))\/((op (e3) (e1)) = (e0))))) -> (((op (e2) (e0)) = (e0))\/(((op (e2) (e1)) = (e0))\/(((op (e2) (e2)) = (e0))\/((op (e2) (e3)) = (e0))))) -> (~((op (e2) (e2)) = (e0))) -> (~((e0) = (e3))) -> ((op (e2) (e1)) = (e2)) -> (~((op (e1) (e1)) = (e0))) -> (~((op (e2) (e1)) = (op (e3) (e1)))) -> (((op (e3) (e0)) = (e2))\/(((op (e3) (e1)) = (e2))\/(((op (e3) (e2)) = (e2))\/((op (e3) (e3)) = (e2))))) -> (~((op (e0) (e1)) = (op (e2) (e1)))) -> (((op (e0) (e0)) = (e1))\/(((op (e1) (e0)) = (e1))\/(((op (e2) (e0)) = (e1))\/((op (e3) (e0)) = (e1))))) -> (~((op (e0) (e0)) = (e1))) -> False). % 15.22/15.41 do 0 intro. intros zenon_H11f zenon_Hd3 zenon_H1d2 zenon_H1e3 zenon_H1e2 zenon_H10e zenon_H173 zenon_H199 zenon_Heb zenon_H3b zenon_H154 zenon_H10d zenon_Hbb zenon_H10f zenon_H157 zenon_H1c3 zenon_H146 zenon_H140 zenon_H11b zenon_H135 zenon_Hc9 zenon_H22e zenon_H8b zenon_H90 zenon_H1cd zenon_Ha7 zenon_H44 zenon_H121 zenon_H2d zenon_H1cf zenon_Hca zenon_H9e zenon_Ha3 zenon_H28 zenon_H36 zenon_H42 zenon_H58 zenon_H12d zenon_H10c zenon_H8f zenon_H6a zenon_H5e zenon_H8e zenon_H84 zenon_H1b4 zenon_H1b3 zenon_H7d zenon_Hd6 zenon_H87 zenon_Haa zenon_H17d zenon_Hce zenon_H160 zenon_H1a2 zenon_H17a zenon_H1d4 zenon_H144 zenon_H1f5 zenon_H2e zenon_H4b zenon_H156 zenon_H145 zenon_H13c zenon_H1df zenon_Hde zenon_Hf1 zenon_H45. % 15.22/15.41 apply (zenon_or_s _ _ zenon_Haa); [ zenon_intro zenon_H2f | zenon_intro zenon_H35 ]. % 15.22/15.41 apply (zenon_or_s _ _ zenon_H1c3); [ zenon_intro zenon_H30 | zenon_intro zenon_H124 ]. % 15.22/15.41 apply (zenon_or_s _ _ zenon_H10f); [ zenon_intro zenon_H3c | zenon_intro zenon_Hba ]. % 15.22/15.41 apply (zenon_or_s _ _ zenon_H10e); [ zenon_intro zenon_H3d | zenon_intro zenon_H106 ]. % 15.22/15.41 apply (zenon_L429_); trivial. % 15.22/15.41 apply (zenon_L153_); trivial. % 15.22/15.41 apply (zenon_L43_); trivial. % 15.22/15.41 apply (zenon_L256_); trivial. % 15.22/15.41 apply (zenon_L134_); trivial. % 15.22/15.41 (* end of lemma zenon_L451_ *) % 15.22/15.41 assert (zenon_L452_ : ((~((op (e3) (e3)) = (e1)))\/((op (e3) (e1)) = (e3))) -> ((op (e3) (e3)) = (e3)) -> (~((op (e3) (e1)) = (op (e3) (e3)))) -> (~((e0) = (e1))) -> ((op (e0) (e3)) = (e0)) -> (~((op (e1) (e2)) = (op (e1) (e3)))) -> ((op (e1) (e2)) = (e1)) -> (~((e1) = (e2))) -> ((op (e2) (e3)) = (e2)) -> (((op (e0) (e3)) = (e1))\/(((op (e1) (e3)) = (e1))\/(((op (e2) (e3)) = (e1))\/((op (e3) (e3)) = (e1))))) -> False). % 15.22/15.41 do 0 intro. intros zenon_H10c zenon_H42 zenon_H12d zenon_H9e zenon_Hca zenon_H1d0 zenon_H117 zenon_Ha7 zenon_H124 zenon_H121. % 15.22/15.41 apply (zenon_or_s _ _ zenon_H10c); [ zenon_intro zenon_H104 | zenon_intro zenon_H10a ]. % 15.22/15.41 apply (zenon_L436_); trivial. % 15.22/15.41 apply (zenon_L102_); trivial. % 15.22/15.41 (* end of lemma zenon_L452_ *) % 15.22/15.41 assert (zenon_L453_ : ((~((op (e1) (e1)) = (e3)))\/((op (e1) (e3)) = (e1))) -> ((~((op (e2) (e2)) = (e1)))\/((op (e2) (e1)) = (e2))) -> (((op (e0) (e1)) = (e0))\/(((op (e1) (e1)) = (e0))\/(((op (e2) (e1)) = (e0))\/((op (e3) (e1)) = (e0))))) -> (~((e0) = (e3))) -> (((op (e0) (e1)) = (e3))\/(((op (e1) (e1)) = (e3))\/(((op (e2) (e1)) = (e3))\/((op (e3) (e1)) = (e3))))) -> ((~((op (e2) (e2)) = (e3)))\/((op (e2) (e3)) = (e2))) -> (~((op (e1) (e2)) = (op (e1) (e3)))) -> (((op (e0) (e0)) = (e1))\/(((op (e0) (e1)) = (e1))\/(((op (e0) (e2)) = (e1))\/((op (e0) (e3)) = (e1))))) -> (((op (e0) (e0)) = (e3))\/(((op (e0) (e1)) = (e3))\/(((op (e0) (e2)) = (e3))\/((op (e0) (e3)) = (e3))))) -> ((op (e3) (e3)) = (e3)) -> (~((op (e0) (e3)) = (op (e3) (e3)))) -> (~((op (e0) (e2)) = (op (e2) (e2)))) -> (~((e1) = (e3))) -> (~((e0) = (e1))) -> ((op (e0) (e3)) = (e0)) -> (~((op (e1) (e0)) = (op (e1) (e3)))) -> (((op (e2) (e2)) = (e0))\/(((op (e2) (e2)) = (e1))\/(((op (e2) (e2)) = (e2))\/((op (e2) (e2)) = (e3))))) -> (((op (e0) (e3)) = (e1))\/(((op (e1) (e3)) = (e1))\/(((op (e2) (e3)) = (e1))\/((op (e3) (e3)) = (e1))))) -> (((op (e1) (e0)) = (e2))\/(((op (e1) (e1)) = (e2))\/(((op (e1) (e2)) = (e2))\/((op (e1) (e3)) = (e2))))) -> (~((op (e0) (e1)) = (op (e0) (e3)))) -> (~((op (e2) (e0)) = (op (e2) (e3)))) -> (~((e1) = (e2))) -> (~((e2) = (e3))) -> ((op (e1) (e2)) = (e1)) -> (~((op (e1) (e3)) = (op (e3) (e3)))) -> (((op (e1) (e0)) = (e3))\/(((op (e1) (e1)) = (e3))\/(((op (e1) (e2)) = (e3))\/((op (e1) (e3)) = (e3))))) -> (((op (e0) (e0)) = (e2))\/(((op (e1) (e0)) = (e2))\/(((op (e2) (e0)) = (e2))\/((op (e3) (e0)) = (e2))))) -> (((op (e1) (e1)) = (e0))\/(((op (e1) (e1)) = (e1))\/(((op (e1) (e1)) = (e2))\/((op (e1) (e1)) = (e3))))) -> (~((op (e0) (e1)) = (op (e1) (e1)))) -> (~((op (e1) (e1)) = (e1))) -> (~((op (e1) (e1)) = (e0))) -> (~((op (e0) (e1)) = (op (e2) (e1)))) -> (((op (e2) (e0)) = (e1))\/(((op (e2) (e1)) = (e1))\/(((op (e2) (e2)) = (e1))\/((op (e2) (e3)) = (e1))))) -> (~((e0) = (e2))) -> (((op (e0) (e0)) = (e2))\/(((op (e0) (e1)) = (e2))\/(((op (e0) (e2)) = (e2))\/((op (e0) (e3)) = (e2))))) -> (~((op (e0) (e0)) = (e2))) -> (((op (e0) (e0)) = (e1))\/(((op (e1) (e0)) = (e1))\/(((op (e2) (e0)) = (e1))\/((op (e3) (e0)) = (e1))))) -> (~((op (e0) (e0)) = (e1))) -> (~((op (e3) (e1)) = (op (e3) (e3)))) -> ((~((op (e3) (e3)) = (e1)))\/((op (e3) (e1)) = (e3))) -> ((~((op (e2) (e2)) = (e2)))\/((op (e2) (e2)) = (e2))) -> (~((op (e2) (e0)) = (op (e2) (e1)))) -> ((~((op (e2) (e2)) = (e0)))\/((op (e2) (e0)) = (e2))) -> False). % 15.22/15.41 do 0 intro. intros zenon_H1d2 zenon_H1e3 zenon_H144 zenon_H4b zenon_H199 zenon_H1c3 zenon_H1d0 zenon_H44 zenon_H58 zenon_H42 zenon_H36 zenon_H28 zenon_Ha3 zenon_H9e zenon_Hca zenon_H1cf zenon_H2d zenon_H121 zenon_H84 zenon_H1cd zenon_Hce zenon_Ha7 zenon_H6a zenon_H117 zenon_H8b zenon_H90 zenon_Heb zenon_H1b3 zenon_H23 zenon_H1b4 zenon_H145 zenon_Hde zenon_Hb7 zenon_H5e zenon_H8e zenon_H8f zenon_Hf1 zenon_H45 zenon_H12d zenon_H10c zenon_Haa zenon_H154 zenon_H1d4. % 15.22/15.41 apply (zenon_or_s _ _ zenon_H1d2); [ zenon_intro zenon_H182 | zenon_intro zenon_H11f ]. % 15.22/15.41 apply (zenon_or_s _ _ zenon_H1d4); [ zenon_intro zenon_H2e | zenon_intro zenon_Hdd ]. % 15.22/15.41 apply (zenon_or_s _ _ zenon_H1e3); [ zenon_intro zenon_H52 | zenon_intro zenon_H156 ]. % 15.22/15.41 apply (zenon_or_s _ _ zenon_Haa); [ zenon_intro zenon_H2f | zenon_intro zenon_H35 ]. % 15.22/15.41 apply (zenon_or_s _ _ zenon_H1c3); [ zenon_intro zenon_H30 | zenon_intro zenon_H124 ]. % 15.22/15.41 apply (zenon_or_s _ _ zenon_H10c); [ zenon_intro zenon_H104 | zenon_intro zenon_H10a ]. % 15.22/15.41 apply (zenon_L435_); trivial. % 15.22/15.41 apply (zenon_L102_); trivial. % 15.22/15.41 apply (zenon_L452_); trivial. % 15.22/15.41 apply (zenon_L343_); trivial. % 15.22/15.41 apply (zenon_L362_); trivial. % 15.22/15.41 apply (zenon_L449_); trivial. % 15.22/15.41 apply (zenon_L237_); trivial. % 15.22/15.41 (* end of lemma zenon_L453_ *) % 15.22/15.41 assert (zenon_L454_ : ((~((op (e1) (e1)) = (e1)))\/((op (e1) (e1)) = (e1))) -> (~((op (e1) (e0)) = (op (e1) (e1)))) -> ((~((op (e1) (e1)) = (e3)))\/((op (e1) (e3)) = (e1))) -> ((~((op (e2) (e2)) = (e1)))\/((op (e2) (e1)) = (e2))) -> (~((op (e2) (e1)) = (op (e2) (e3)))) -> ((~((op (e3) (e3)) = (e2)))\/((op (e3) (e2)) = (e3))) -> (~((op (e3) (e2)) = (op (e3) (e3)))) -> (((op (e0) (e1)) = (e3))\/(((op (e1) (e1)) = (e3))\/(((op (e2) (e1)) = (e3))\/((op (e3) (e1)) = (e3))))) -> (((op (e0) (e0)) = (e2))\/(((op (e1) (e0)) = (e2))\/(((op (e2) (e0)) = (e2))\/((op (e3) (e0)) = (e2))))) -> (((op (e3) (e3)) = (e0))\/(((op (e3) (e3)) = (e1))\/(((op (e3) (e3)) = (e2))\/((op (e3) (e3)) = (e3))))) -> (~((op (e2) (e0)) = (op (e2) (e1)))) -> ((~((op (e3) (e3)) = (e3)))\/((op (e3) (e3)) = (e3))) -> (~((op (e3) (e0)) = (op (e3) (e3)))) -> ((~((op (e3) (e3)) = (e0)))\/((op (e3) (e0)) = (e3))) -> (~((op (e2) (e1)) = (op (e2) (e2)))) -> ((~((op (e2) (e2)) = (e3)))\/((op (e2) (e3)) = (e2))) -> (((op (e3) (e0)) = (e1))\/(((op (e3) (e1)) = (e1))\/(((op (e3) (e2)) = (e1))\/((op (e3) (e3)) = (e1))))) -> (~((op (e0) (e2)) = (op (e3) (e2)))) -> (((op (e0) (e2)) = (e1))\/(((op (e1) (e2)) = (e1))\/(((op (e2) (e2)) = (e1))\/((op (e3) (e2)) = (e1))))) -> (~((op (e3) (e1)) = (op (e3) (e2)))) -> (~((op (e0) (e2)) = (op (e0) (e3)))) -> (~((op (e1) (e0)) = (op (e3) (e0)))) -> (~((op (e1) (e3)) = (op (e3) (e3)))) -> (((op (e1) (e0)) = (e3))\/(((op (e1) (e1)) = (e3))\/(((op (e1) (e2)) = (e3))\/((op (e1) (e3)) = (e3))))) -> (~((op (e0) (e1)) = (op (e0) (e3)))) -> (~((e1) = (e2))) -> (((op (e0) (e0)) = (e1))\/(((op (e0) (e1)) = (e1))\/(((op (e0) (e2)) = (e1))\/((op (e0) (e3)) = (e1))))) -> (((op (e0) (e3)) = (e1))\/(((op (e1) (e3)) = (e1))\/(((op (e2) (e3)) = (e1))\/((op (e3) (e3)) = (e1))))) -> (((op (e2) (e2)) = (e0))\/(((op (e2) (e2)) = (e1))\/(((op (e2) (e2)) = (e2))\/((op (e2) (e2)) = (e3))))) -> ((op (e1) (e0)) = (e1)) -> (~((op (e1) (e0)) = (op (e1) (e3)))) -> ((op (e0) (e3)) = (e0)) -> (~((e0) = (e1))) -> (~((e1) = (e3))) -> (~((op (e0) (e2)) = (op (e2) (e2)))) -> (~((op (e0) (e3)) = (op (e3) (e3)))) -> ((op (e3) (e3)) = (e3)) -> (((op (e0) (e0)) = (e3))\/(((op (e0) (e1)) = (e3))\/(((op (e0) (e2)) = (e3))\/((op (e0) (e3)) = (e3))))) -> (~((op (e0) (e0)) = (e1))) -> (~((op (e3) (e1)) = (op (e3) (e3)))) -> ((~((op (e3) (e3)) = (e1)))\/((op (e3) (e1)) = (e3))) -> (~((op (e0) (e0)) = (e2))) -> (~((e2) = (e3))) -> (~((e0) = (e2))) -> (((op (e0) (e0)) = (e2))\/(((op (e0) (e1)) = (e2))\/(((op (e0) (e2)) = (e2))\/((op (e0) (e3)) = (e2))))) -> (((op (e1) (e0)) = (e2))\/(((op (e1) (e1)) = (e2))\/(((op (e1) (e2)) = (e2))\/((op (e1) (e3)) = (e2))))) -> (((op (e1) (e1)) = (e0))\/(((op (e1) (e1)) = (e1))\/(((op (e1) (e1)) = (e2))\/((op (e1) (e1)) = (e3))))) -> (~((op (e1) (e2)) = (op (e2) (e2)))) -> (~((op (e0) (e2)) = (op (e1) (e2)))) -> ((~((op (e2) (e2)) = (e2)))\/((op (e2) (e2)) = (e2))) -> (~((op (e1) (e2)) = (op (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 (e0) (e1)) = (e2))\/(((op (e1) (e1)) = (e2))\/(((op (e2) (e1)) = (e2))\/((op (e3) (e1)) = (e2))))) -> (~((op (e2) (e0)) = (op (e2) (e2)))) -> ((~((op (e2) (e2)) = (e0)))\/((op (e2) (e0)) = (e2))) -> (~((op (e1) (e0)) = (op (e1) (e2)))) -> ((~((op (e1) (e1)) = (e2)))\/((op (e1) (e2)) = (e1))) -> False). % 15.22/15.41 do 0 intro. intros zenon_H1d8 zenon_Hd7 zenon_H1d2 zenon_H1e3 zenon_H1e2 zenon_H10e zenon_H173 zenon_H199 zenon_Heb zenon_H3b zenon_H154 zenon_H10d zenon_Hbb zenon_H10f zenon_H157 zenon_H1c3 zenon_H146 zenon_H140 zenon_H11b zenon_H135 zenon_Hc9 zenon_H22e zenon_H8b zenon_H90 zenon_H1cd zenon_Ha7 zenon_H44 zenon_H121 zenon_H2d zenon_Hd8 zenon_H1cf zenon_Hca zenon_H9e zenon_Ha3 zenon_H28 zenon_H36 zenon_H42 zenon_H58 zenon_H45 zenon_H12d zenon_H10c zenon_H8f zenon_H6a zenon_H5e zenon_H8e zenon_H84 zenon_H1b3 zenon_H7d zenon_H87 zenon_Haa zenon_H17d zenon_Hce zenon_H160 zenon_H1a2 zenon_H17a zenon_H1d4 zenon_H166 zenon_H1d3. % 15.22/15.41 apply (zenon_or_s _ _ zenon_H1d8); [ zenon_intro zenon_H1b4 | zenon_intro zenon_H21 ]. % 15.22/15.41 apply (zenon_L420_); trivial. % 15.22/15.41 apply (zenon_L61_); trivial. % 15.22/15.41 (* end of lemma zenon_L454_ *) % 15.22/15.41 assert (zenon_L455_ : ((~((op (e0) (e0)) = (e3)))\/((op (e0) (e3)) = (e0))) -> ((~((op (e1) (e1)) = (e1)))\/((op (e1) (e1)) = (e1))) -> (~((op (e1) (e1)) = (op (e1) (e2)))) -> (((op (e1) (e2)) = (e0))\/(((op (e1) (e2)) = (e1))\/(((op (e1) (e2)) = (e2))\/((op (e1) (e2)) = (e3))))) -> (~((op (e1) (e1)) = (op (e1) (e3)))) -> (~((op (e0) (e3)) = (op (e2) (e3)))) -> (~((op (e1) (e1)) = (op (e2) (e1)))) -> (~((op (e1) (e0)) = (op (e1) (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 (e0) (e1)) = (op (e3) (e1)))) -> (((op (e3) (e1)) = (e0))\/(((op (e3) (e1)) = (e1))\/(((op (e3) (e1)) = (e2))\/((op (e3) (e1)) = (e3))))) -> (~((op (e2) (e1)) = (op (e3) (e1)))) -> (((op (e3) (e0)) = (e2))\/(((op (e3) (e1)) = (e2))\/(((op (e3) (e2)) = (e2))\/((op (e3) (e3)) = (e2))))) -> (~((op (e1) (e0)) = (op (e1) (e2)))) -> (~((op (e1) (e2)) = (op (e3) (e2)))) -> (~((op (e1) (e0)) = (op (e3) (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) (e2)) = (op (e3) (e2)))) -> (((op (e3) (e0)) = (e1))\/(((op (e3) (e1)) = (e1))\/(((op (e3) (e2)) = (e1))\/((op (e3) (e3)) = (e1))))) -> (~((op (e2) (op (e0) (e2))) = (op (e0) (e2)))) -> (((op (e0) (e0)) = (e0))\/(((op (e0) (e0)) = (e1))\/(((op (e0) (e0)) = (e2))\/((op (e0) (e0)) = (e3))))) -> (~((op (e1) (op (e0) (e1))) = (op (e0) (e1)))) -> ((~((op (e1) (e1)) = (e3)))\/((op (e1) (e3)) = (e1))) -> (((op (e2) (e0)) = (e0))\/(((op (e2) (e1)) = (e0))\/(((op (e2) (e2)) = (e0))\/((op (e2) (e3)) = (e0))))) -> (((op (e0) (e1)) = (e1))\/(((op (e1) (e1)) = (e1))\/(((op (e2) (e1)) = (e1))\/((op (e3) (e1)) = (e1))))) -> (~((op (e1) (e2)) = (op (e1) (e3)))) -> ((~((op (e1) (e1)) = (e2)))\/((op (e1) (e2)) = (e1))) -> (~((op (e2) (e2)) = (op (e2) (e3)))) -> (~((op (e2) (e1)) = (op (e2) (e3)))) -> ((~((op (e2) (e2)) = (e1)))\/((op (e2) (e1)) = (e2))) -> (((op (e0) (e1)) = (e3))\/(((op (e1) (e1)) = (e3))\/(((op (e2) (e1)) = (e3))\/((op (e3) (e1)) = (e3))))) -> (((op (e0) (e0)) = (e0))\/(((op (e0) (e1)) = (e0))\/(((op (e0) (e2)) = (e0))\/((op (e0) (e3)) = (e0))))) -> (((op (e0) (e0)) = (e0))\/(((op (e1) (e0)) = (e0))\/(((op (e2) (e0)) = (e0))\/((op (e3) (e0)) = (e0))))) -> (~((op (e3) (op (e0) (e3))) = (op (e0) (e3)))) -> (((op (e0) (e0)) = (e1))\/(((op (e1) (e0)) = (e1))\/(((op (e2) (e0)) = (e1))\/((op (e3) (e0)) = (e1))))) -> (((op (e2) (e0)) = (e1))\/(((op (e2) (e1)) = (e1))\/(((op (e2) (e2)) = (e1))\/((op (e2) (e3)) = (e1))))) -> (((op (e1) (e0)) = (e0))\/(((op (e1) (e1)) = (e0))\/(((op (e1) (e2)) = (e0))\/((op (e1) (e3)) = (e0))))) -> (~((op (e0) (e1)) = (op (e0) (e3)))) -> (~((op (e2) (e0)) = (op (e2) (e3)))) -> (((op (e0) (e3)) = (e1))\/(((op (e1) (e3)) = (e1))\/(((op (e2) (e3)) = (e1))\/((op (e3) (e3)) = (e1))))) -> (~((op (e1) (e0)) = (op (e1) (e3)))) -> (~((op (e3) (e1)) = (op (e3) (e3)))) -> ((~((op (e3) (e3)) = (e1)))\/((op (e3) (e1)) = (e3))) -> (((op (e1) (e0)) = (e1))\/(((op (e1) (e1)) = (e1))\/(((op (e1) (e2)) = (e1))\/((op (e1) (e3)) = (e1))))) -> (((op (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) (e2)) = (op (e3) (e3)))) -> ((~((op (e3) (e3)) = (e0)))\/((op (e3) (e0)) = (e3))) -> (~((op (e3) (e0)) = (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 (e2) (e2)) = (e3)))\/((op (e2) (e3)) = (e2))) -> (((op (e1) (e1)) = (e0))\/(((op (e1) (e1)) = (e1))\/(((op (e1) (e1)) = (e2))\/((op (e1) (e1)) = (e3))))) -> (~((op (e0) (e1)) = (op (e1) (e1)))) -> (((op (e0) (e0)) = (e2))\/(((op (e1) (e0)) = (e2))\/(((op (e2) (e0)) = (e2))\/((op (e3) (e0)) = (e2))))) -> (((op (e0) (e0)) = (e3))\/(((op (e1) (e0)) = (e3))\/(((op (e2) (e0)) = (e3))\/((op (e3) (e0)) = (e3))))) -> (((op (e2) (e0)) = (e3))\/(((op (e2) (e1)) = (e3))\/(((op (e2) (e2)) = (e3))\/((op (e2) (e3)) = (e3))))) -> (~((op (e2) (e3)) = (op (e3) (e3)))) -> (~((op (e0) (e1)) = (op (e2) (e1)))) -> (~((op (e0) (e0)) = (e1))) -> ((~((op (e3) (e3)) = (e2)))\/((op (e3) (e2)) = (e3))) -> (((op (e0) (e0)) = (e3))\/(((op (e0) (e1)) = (e3))\/(((op (e0) (e2)) = (e3))\/((op (e0) (e3)) = (e3))))) -> ((op (e3) (e3)) = (e3)) -> (~((op (e0) (e3)) = (op (e3) (e3)))) -> (~((op (e0) (e2)) = (op (e2) (e2)))) -> (((op (e2) (e2)) = (e0))\/(((op (e2) (e2)) = (e1))\/(((op (e2) (e2)) = (e2))\/((op (e2) (e2)) = (e3))))) -> (~((e0) = (e3))) -> (((op (e0) (e0)) = (e1))\/(((op (e0) (e1)) = (e1))\/(((op (e0) (e2)) = (e1))\/((op (e0) (e3)) = (e1))))) -> (~((e1) = (e2))) -> (~((e1) = (e3))) -> (~((e0) = (e1))) -> (~((op (e0) (e0)) = (e2))) -> (~((e0) = (e2))) -> (((op (e1) (e0)) = (e2))\/(((op (e1) (e1)) = (e2))\/(((op (e1) (e2)) = (e2))\/((op (e1) (e3)) = (e2))))) -> (~((op (e0) (e3)) = (op (e1) (e3)))) -> (~((op (e1) (e2)) = (op (e2) (e2)))) -> (~((e2) = (e3))) -> (~((op (e0) (e2)) = (op (e1) (e2)))) -> (~((op (e1) (e3)) = (op (e3) (e3)))) -> (((op (e1) (e0)) = (e3))\/(((op (e1) (e1)) = (e3))\/(((op (e1) (e2)) = (e3))\/((op (e1) (e3)) = (e3))))) -> (((op (e0) (e0)) = (e2))\/(((op (e0) (e1)) = (e2))\/(((op (e0) (e2)) = (e2))\/((op (e0) (e3)) = (e2))))) -> ((~((op (e2) (e2)) = (e2)))\/((op (e2) (e2)) = (e2))) -> (~((op (e0) (e0)) = (e0))) -> (~((op (e3) (e0)) = (op (e3) (e2)))) -> (~((op (e2) (e0)) = (op (e2) (e2)))) -> (~((op (e3) (e0)) = (op (e3) (e1)))) -> ((~((op (e3) (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)) = (e2))\/(((op (e1) (e1)) = (e2))\/(((op (e2) (e1)) = (e2))\/((op (e3) (e1)) = (e2))))) -> (~((op (e2) (e1)) = (op (e2) (e2)))) -> (((op (e0) (e1)) = (e0))\/(((op (e1) (e1)) = (e0))\/(((op (e2) (e1)) = (e0))\/((op (e3) (e1)) = (e0))))) -> (~((op (e2) (e0)) = (op (e2) (e1)))) -> ((~((op (e2) (e2)) = (e0)))\/((op (e2) (e0)) = (e2))) -> ((~((op (e1) (e1)) = (e0)))\/((op (e1) (e0)) = (e1))) -> False). % 15.22/15.41 do 0 intro. intros zenon_H236 zenon_H1d8 zenon_H116 zenon_H1d5 zenon_H11e zenon_Hb4 zenon_Hb1 zenon_Hd7 zenon_H15a zenon_H16f zenon_H138 zenon_H16c zenon_H13c zenon_H1df zenon_H166 zenon_H17d zenon_H22e zenon_H135 zenon_H11b zenon_H140 zenon_H146 zenon_H20c zenon_H12a zenon_H1ff zenon_H1d2 zenon_H1f5 zenon_H228 zenon_H1d0 zenon_H1d3 zenon_H15f zenon_H1e2 zenon_H1e3 zenon_H199 zenon_H110 zenon_Hf0 zenon_H192 zenon_Hf1 zenon_Hb7 zenon_H163 zenon_H1cd zenon_Hce zenon_H121 zenon_H1cf zenon_H12d zenon_H10c zenon_H1c5 zenon_H160 zenon_H175 zenon_H173 zenon_H10f zenon_Hbb zenon_Hc9 zenon_Hd3 zenon_H1c3 zenon_H1b3 zenon_H23 zenon_Heb zenon_Hbe zenon_He6 zenon_He3 zenon_Hde zenon_H45 zenon_H10e zenon_H58 zenon_H42 zenon_H36 zenon_H28 zenon_H2d zenon_H4b zenon_H44 zenon_Ha7 zenon_Ha3 zenon_H9e zenon_H8f zenon_H5e zenon_H84 zenon_H80 zenon_H7d zenon_H6a zenon_H87 zenon_H8b zenon_H90 zenon_H8e zenon_Haa zenon_H20 zenon_H105 zenon_H17a zenon_H109 zenon_H10d zenon_H3b zenon_H1a2 zenon_H157 zenon_H144 zenon_H154 zenon_H1d4 zenon_H1e4. % 15.22/15.41 apply (zenon_or_s _ _ zenon_H236); [ zenon_intro zenon_H59 | zenon_intro zenon_Hca ]. % 15.22/15.41 apply (zenon_or_s _ _ zenon_H1e4); [ zenon_intro zenon_H145 | zenon_intro zenon_Hd8 ]. % 15.22/15.41 apply (zenon_or_s _ _ zenon_H1d8); [ zenon_intro zenon_H1b4 | zenon_intro zenon_H21 ]. % 15.22/15.41 apply (zenon_or_s _ _ zenon_H1d3); [ zenon_intro zenon_Hd6 | zenon_intro zenon_H117 ]. % 15.22/15.41 apply (zenon_or_s _ _ zenon_H1d2); [ zenon_intro zenon_H182 | zenon_intro zenon_H11f ]. % 15.22/15.41 apply (zenon_or_s _ _ zenon_H1d4); [ zenon_intro zenon_H2e | zenon_intro zenon_Hdd ]. % 15.22/15.41 apply (zenon_or_s _ _ zenon_H1e3); [ zenon_intro zenon_H52 | zenon_intro zenon_H156 ]. % 15.22/15.41 apply (zenon_or_s _ _ zenon_Haa); [ zenon_intro zenon_H2f | zenon_intro zenon_H35 ]. % 15.22/15.41 apply (zenon_or_s _ _ zenon_H1c3); [ zenon_intro zenon_H30 | zenon_intro zenon_H124 ]. % 15.22/15.41 apply (zenon_or_s _ _ zenon_H10f); [ zenon_intro zenon_H3c | zenon_intro zenon_Hba ]. % 15.22/15.41 apply (zenon_or_s _ _ zenon_H110); [ zenon_intro zenon_H1f | zenon_intro zenon_H111 ]. % 15.22/15.41 exact (zenon_H20 zenon_H1f). % 15.22/15.41 apply (zenon_or_s _ _ zenon_H111); [ zenon_intro zenon_H49 | zenon_intro zenon_H112 ]. % 15.22/15.41 apply (zenon_L36_); trivial. % 15.22/15.41 apply (zenon_or_s _ _ zenon_H112); [ zenon_intro zenon_Hab | zenon_intro zenon_Hca ]. % 15.22/15.41 apply (zenon_L222_); trivial. % 15.22/15.41 apply (zenon_L344_); trivial. % 15.22/15.41 apply (zenon_L43_); trivial. % 15.22/15.41 apply (zenon_or_s _ _ zenon_H10f); [ zenon_intro zenon_H3c | zenon_intro zenon_Hba ]. % 15.22/15.41 apply (zenon_or_s _ _ zenon_H10c); [ zenon_intro zenon_H104 | zenon_intro zenon_H10a ]. % 15.22/15.41 apply (zenon_or_s _ _ zenon_H10e); [ zenon_intro zenon_H3d | zenon_intro zenon_H106 ]. % 15.22/15.42 apply (zenon_or_s _ _ zenon_H110); [ zenon_intro zenon_H1f | zenon_intro zenon_H111 ]. % 15.22/15.42 exact (zenon_H20 zenon_H1f). % 15.22/15.42 apply (zenon_or_s _ _ zenon_H111); [ zenon_intro zenon_H49 | zenon_intro zenon_H112 ]. % 15.22/15.42 apply (zenon_L13_); trivial. % 15.22/15.42 apply (zenon_or_s _ _ zenon_H112); [ zenon_intro zenon_Hab | zenon_intro zenon_Hca ]. % 15.22/15.42 apply (zenon_L231_); trivial. % 15.22/15.42 apply (zenon_L342_); trivial. % 15.22/15.42 apply (zenon_L153_); trivial. % 15.22/15.42 apply (zenon_L102_); trivial. % 15.22/15.42 apply (zenon_L43_); trivial. % 15.22/15.42 apply (zenon_L360_); trivial. % 15.22/15.42 apply (zenon_or_s _ _ zenon_Haa); [ zenon_intro zenon_H2f | zenon_intro zenon_H35 ]. % 15.22/15.42 apply (zenon_or_s _ _ zenon_H1c3); [ zenon_intro zenon_H30 | zenon_intro zenon_H124 ]. % 15.22/15.42 apply (zenon_or_s _ _ zenon_H10f); [ zenon_intro zenon_H3c | zenon_intro zenon_Hba ]. % 15.22/15.42 apply (zenon_or_s _ _ zenon_H10e); [ zenon_intro zenon_H3d | zenon_intro zenon_H106 ]. % 15.22/15.42 apply (zenon_or_s _ _ zenon_H110); [ zenon_intro zenon_H1f | zenon_intro zenon_H111 ]. % 15.22/15.42 exact (zenon_H20 zenon_H1f). % 15.22/15.42 apply (zenon_or_s _ _ zenon_H111); [ zenon_intro zenon_H49 | zenon_intro zenon_H112 ]. % 15.22/15.42 apply (zenon_L279_); trivial. % 15.22/15.42 apply (zenon_or_s _ _ zenon_H112); [ zenon_intro zenon_Hab | zenon_intro zenon_Hca ]. % 15.22/15.42 apply (zenon_L221_); trivial. % 15.22/15.42 apply (zenon_L362_); trivial. % 15.22/15.42 apply (zenon_L153_); trivial. % 15.22/15.42 apply (zenon_L43_); trivial. % 15.22/15.42 apply (zenon_L256_); trivial. % 15.22/15.42 apply (zenon_L134_); trivial. % 15.22/15.42 apply (zenon_L365_); trivial. % 15.22/15.42 apply (zenon_or_s _ _ zenon_H1d4); [ zenon_intro zenon_H2e | zenon_intro zenon_Hdd ]. % 15.22/15.42 apply (zenon_or_s _ _ zenon_H1e3); [ zenon_intro zenon_H52 | zenon_intro zenon_H156 ]. % 15.22/15.42 apply (zenon_or_s _ _ zenon_Haa); [ zenon_intro zenon_H2f | zenon_intro zenon_H35 ]. % 15.22/15.42 apply (zenon_or_s _ _ zenon_H1c3); [ zenon_intro zenon_H30 | zenon_intro zenon_H124 ]. % 15.22/15.42 apply (zenon_or_s _ _ zenon_H10f); [ zenon_intro zenon_H3c | zenon_intro zenon_Hba ]. % 15.22/15.42 apply (zenon_or_s _ _ zenon_H10c); [ zenon_intro zenon_H104 | zenon_intro zenon_H10a ]. % 15.22/15.42 apply (zenon_or_s _ _ zenon_H10e); [ zenon_intro zenon_H3d | zenon_intro zenon_H106 ]. % 15.22/15.42 apply (zenon_or_s _ _ zenon_H110); [ zenon_intro zenon_H1f | zenon_intro zenon_H111 ]. % 15.22/15.42 exact (zenon_H20 zenon_H1f). % 15.22/15.42 apply (zenon_or_s _ _ zenon_H111); [ zenon_intro zenon_H49 | zenon_intro zenon_H112 ]. % 15.22/15.42 apply (zenon_L387_); trivial. % 15.22/15.42 apply (zenon_or_s _ _ zenon_H112); [ zenon_intro zenon_Hab | zenon_intro zenon_Hca ]. % 15.22/15.42 apply (zenon_L235_); trivial. % 15.22/15.42 apply (zenon_L391_); trivial. % 15.22/15.42 apply (zenon_L153_); trivial. % 15.22/15.42 apply (zenon_L102_); trivial. % 15.22/15.42 apply (zenon_L43_); trivial. % 15.22/15.42 apply (zenon_or_s _ _ zenon_H10f); [ zenon_intro zenon_H3c | zenon_intro zenon_Hba ]. % 15.22/15.42 apply (zenon_or_s _ _ zenon_H10c); [ zenon_intro zenon_H104 | zenon_intro zenon_H10a ]. % 15.22/15.42 apply (zenon_or_s _ _ zenon_H10e); [ zenon_intro zenon_H3d | zenon_intro zenon_H106 ]. % 15.22/15.42 apply (zenon_or_s _ _ zenon_H110); [ zenon_intro zenon_H1f | zenon_intro zenon_H111 ]. % 15.22/15.42 exact (zenon_H20 zenon_H1f). % 15.22/15.42 apply (zenon_or_s _ _ zenon_H111); [ zenon_intro zenon_H49 | zenon_intro zenon_H112 ]. % 15.22/15.42 apply (zenon_L392_); trivial. % 15.22/15.42 apply (zenon_or_s _ _ zenon_H112); [ zenon_intro zenon_Hab | zenon_intro zenon_Hca ]. % 15.22/15.42 apply (zenon_L235_); trivial. % 15.22/15.42 apply (zenon_L422_); trivial. % 15.22/15.42 apply (zenon_L153_); trivial. % 15.22/15.42 apply (zenon_L102_); trivial. % 15.22/15.42 apply (zenon_L43_); trivial. % 15.22/15.42 apply (zenon_L426_); trivial. % 15.22/15.42 apply (zenon_L430_); trivial. % 15.22/15.42 apply (zenon_L432_); trivial. % 15.22/15.42 apply (zenon_L441_); trivial. % 15.22/15.42 apply (zenon_or_s _ _ zenon_H1d3); [ zenon_intro zenon_Hd6 | zenon_intro zenon_H117 ]. % 15.22/15.42 apply (zenon_or_s _ _ zenon_H1d2); [ zenon_intro zenon_H182 | zenon_intro zenon_H11f ]. % 15.22/15.42 apply (zenon_or_s _ _ zenon_H1d4); [ zenon_intro zenon_H2e | zenon_intro zenon_Hdd ]. % 15.22/15.42 apply (zenon_or_s _ _ zenon_H1e3); [ zenon_intro zenon_H52 | zenon_intro zenon_H156 ]. % 15.22/15.42 apply (zenon_or_s _ _ zenon_Haa); [ zenon_intro zenon_H2f | zenon_intro zenon_H35 ]. % 15.22/15.42 apply (zenon_or_s _ _ zenon_H1c3); [ zenon_intro zenon_H30 | zenon_intro zenon_H124 ]. % 15.22/15.42 apply (zenon_L84_); trivial. % 15.22/15.42 apply (zenon_L103_); trivial. % 15.22/15.42 apply (zenon_or_s _ _ zenon_H1c3); [ zenon_intro zenon_H30 | zenon_intro zenon_H124 ]. % 15.22/15.42 apply (zenon_or_s _ _ zenon_H10c); [ zenon_intro zenon_H104 | zenon_intro zenon_H10a ]. % 15.22/15.42 apply (zenon_or_s _ _ zenon_H10e); [ zenon_intro zenon_H3d | zenon_intro zenon_H106 ]. % 15.22/15.42 apply (zenon_L159_); trivial. % 15.22/15.42 apply (zenon_L153_); trivial. % 15.22/15.42 apply (zenon_L102_); trivial. % 15.22/15.42 apply (zenon_L137_); trivial. % 15.22/15.42 apply (zenon_or_s _ _ zenon_Haa); [ zenon_intro zenon_H2f | zenon_intro zenon_H35 ]. % 15.22/15.42 apply (zenon_L288_); trivial. % 15.22/15.42 apply (zenon_L134_); trivial. % 15.22/15.42 apply (zenon_L442_); trivial. % 15.22/15.42 apply (zenon_L90_); trivial. % 15.22/15.42 apply (zenon_L86_); trivial. % 15.22/15.42 apply (zenon_L448_); trivial. % 15.22/15.42 apply (zenon_or_s _ _ zenon_H1e4); [ zenon_intro zenon_H145 | zenon_intro zenon_Hd8 ]. % 15.22/15.42 apply (zenon_or_s _ _ zenon_H1d8); [ zenon_intro zenon_H1b4 | zenon_intro zenon_H21 ]. % 15.22/15.42 apply (zenon_or_s _ _ zenon_H1d3); [ zenon_intro zenon_Hd6 | zenon_intro zenon_H117 ]. % 15.22/15.42 apply (zenon_or_s _ _ zenon_H1d2); [ zenon_intro zenon_H182 | zenon_intro zenon_H11f ]. % 15.22/15.42 apply (zenon_or_s _ _ zenon_H1d4); [ zenon_intro zenon_H2e | zenon_intro zenon_Hdd ]. % 15.22/15.42 apply (zenon_or_s _ _ zenon_H1e3); [ zenon_intro zenon_H52 | zenon_intro zenon_H156 ]. % 15.22/15.42 apply (zenon_L344_); trivial. % 15.22/15.42 apply (zenon_L362_); trivial. % 15.22/15.42 apply (zenon_L449_); trivial. % 15.22/15.42 apply (zenon_or_s _ _ zenon_H1d4); [ zenon_intro zenon_H2e | zenon_intro zenon_Hdd ]. % 15.22/15.42 apply (zenon_or_s _ _ zenon_H1e3); [ zenon_intro zenon_H52 | zenon_intro zenon_H156 ]. % 15.22/15.42 apply (zenon_or_s _ _ zenon_Haa); [ zenon_intro zenon_H2f | zenon_intro zenon_H35 ]. % 15.22/15.42 apply (zenon_or_s _ _ zenon_H1c3); [ zenon_intro zenon_H30 | zenon_intro zenon_H124 ]. % 15.22/15.42 apply (zenon_or_s _ _ zenon_H10f); [ zenon_intro zenon_H3c | zenon_intro zenon_Hba ]. % 15.22/15.42 apply (zenon_or_s _ _ zenon_H10c); [ zenon_intro zenon_H104 | zenon_intro zenon_H10a ]. % 15.22/15.42 apply (zenon_L391_); trivial. % 15.22/15.42 apply (zenon_L102_); trivial. % 15.22/15.42 apply (zenon_L43_); trivial. % 15.22/15.42 apply (zenon_or_s _ _ zenon_H10f); [ zenon_intro zenon_H3c | zenon_intro zenon_Hba ]. % 15.22/15.42 apply (zenon_or_s _ _ zenon_H10c); [ zenon_intro zenon_H104 | zenon_intro zenon_H10a ]. % 15.22/15.42 apply (zenon_or_s _ _ zenon_H10e); [ zenon_intro zenon_H3d | zenon_intro zenon_H106 ]. % 15.22/15.42 apply (zenon_L422_); trivial. % 15.22/15.42 apply (zenon_L153_); trivial. % 15.22/15.42 apply (zenon_L102_); trivial. % 15.22/15.42 apply (zenon_L43_); trivial. % 15.22/15.42 apply (zenon_L450_); trivial. % 15.22/15.42 apply (zenon_L451_); trivial. % 15.22/15.42 apply (zenon_L431_); trivial. % 15.22/15.42 apply (zenon_L453_); trivial. % 15.22/15.42 apply (zenon_or_s _ _ zenon_H1d4); [ zenon_intro zenon_H2e | zenon_intro zenon_Hdd ]. % 15.22/15.42 apply (zenon_or_s _ _ zenon_H1e3); [ zenon_intro zenon_H52 | zenon_intro zenon_H156 ]. % 15.22/15.42 apply (zenon_or_s _ _ zenon_Haa); [ zenon_intro zenon_H2f | zenon_intro zenon_H35 ]. % 15.22/15.42 apply (zenon_L316_); trivial. % 15.22/15.42 apply (zenon_or_s _ _ zenon_H1c3); [ zenon_intro zenon_H30 | zenon_intro zenon_H124 ]. % 15.22/15.42 apply (zenon_or_s _ _ zenon_H10c); [ zenon_intro zenon_H104 | zenon_intro zenon_H10a ]. % 15.22/15.42 apply (zenon_L158_); trivial. % 15.22/15.42 apply (zenon_L102_); trivial. % 15.22/15.42 apply (zenon_L137_); trivial. % 15.22/15.42 apply (zenon_L318_); trivial. % 15.22/15.42 apply (zenon_L442_); trivial. % 15.22/15.42 apply (zenon_L454_); trivial. % 15.22/15.42 (* end of lemma zenon_L455_ *) % 15.22/15.42 assert (zenon_L456_ : (((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)) -> (~((e2) = (e3))) -> ((op (e2) (e0)) = (e2)) -> (~((op (e3) (e0)) = (op (e3) (e2)))) -> ((op (e3) (e2)) = (e3)) -> False). % 15.22/15.42 do 0 intro. intros zenon_Hbe zenon_H59 zenon_Ha3 zenon_Hd8 zenon_H6a zenon_Hdd zenon_H105 zenon_H106. % 15.22/15.42 apply (zenon_or_s _ _ zenon_Hbe); [ zenon_intro zenon_H5b | zenon_intro zenon_Hbf ]. % 15.22/15.42 exact (zenon_H59 zenon_H5b). % 15.22/15.42 apply (zenon_or_s _ _ zenon_Hbf); [ zenon_intro zenon_H69 | zenon_intro zenon_Hc0 ]. % 15.22/15.42 apply (zenon_L163_); trivial. % 15.22/15.42 apply (zenon_or_s _ _ zenon_Hc0); [ zenon_intro zenon_Haf | zenon_intro zenon_Hba ]. % 15.22/15.42 apply (zenon_L64_); trivial. % 15.22/15.42 apply (zenon_L81_); trivial. % 15.22/15.42 (* end of lemma zenon_L456_ *) % 15.22/15.42 assert (zenon_L457_ : (((op (e0) (e0)) = (e1))\/(((op (e1) (e0)) = (e1))\/(((op (e2) (e0)) = (e1))\/((op (e3) (e0)) = (e1))))) -> (~((op (e0) (e0)) = (e1))) -> ((op (e3) (e2)) = (e3)) -> (~((op (e3) (e0)) = (op (e3) (e2)))) -> (~((e2) = (e3))) -> (~((e1) = (e3))) -> (~((op (e0) (e0)) = (e3))) -> (((op (e0) (e0)) = (e3))\/(((op (e1) (e0)) = (e3))\/(((op (e2) (e0)) = (e3))\/((op (e3) (e0)) = (e3))))) -> ((op (e2) (e0)) = (e2)) -> (~((e1) = (e2))) -> (((op (e2) (e2)) = (e0))\/(((op (e2) (e2)) = (e1))\/(((op (e2) (e2)) = (e2))\/((op (e2) (e2)) = (e3))))) -> (~((op (e3) (e3)) = (e3))) -> (~((op (e3) (e3)) = (e1))) -> (~((op (e3) (e3)) = (e0))) -> (((op (e3) (e3)) = (e0))\/(((op (e3) (e3)) = (e1))\/(((op (e3) (e3)) = (e2))\/((op (e3) (e3)) = (e3))))) -> (~((op (e2) (e2)) = (e1))) -> (~((op (e2) (e2)) = (e2))) -> (~((op (e2) (e2)) = (e3))) -> False). % 15.22/15.42 do 0 intro. intros zenon_Hf1 zenon_H45 zenon_H106 zenon_H105 zenon_H6a zenon_Ha3 zenon_H59 zenon_Hbe zenon_Hdd zenon_Ha7 zenon_H2d zenon_H3e zenon_H104 zenon_H3c zenon_H3b zenon_H52 zenon_H2f zenon_H30. % 15.22/15.42 apply (zenon_or_s _ _ zenon_Hf1); [ zenon_intro zenon_H47 | zenon_intro zenon_Hf4 ]. % 15.22/15.42 exact (zenon_H45 zenon_H47). % 15.22/15.42 apply (zenon_or_s _ _ zenon_Hf4); [ zenon_intro zenon_Hd8 | zenon_intro zenon_Hf5 ]. % 15.22/15.42 apply (zenon_L456_); trivial. % 15.22/15.42 apply (zenon_or_s _ _ zenon_Hf5); [ zenon_intro zenon_Hae | zenon_intro zenon_Hee ]. % 15.22/15.42 apply (zenon_L304_); trivial. % 15.22/15.42 apply (zenon_L306_); trivial. % 15.22/15.42 (* end of lemma zenon_L457_ *) % 15.22/15.42 assert (zenon_L458_ : ((~((op (e3) (e3)) = (e3)))\/((op (e3) (e3)) = (e3))) -> (~((op (e3) (e2)) = (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) (e2)) = (e3)) -> (~((op (e3) (e0)) = (op (e3) (e2)))) -> ((op (e2) (e0)) = (e2)) -> (~((e2) = (e3))) -> (~((e1) = (e3))) -> (~((op (e0) (e0)) = (e3))) -> (~((e1) = (e2))) -> (((op (e2) (e2)) = (e0))\/(((op (e2) (e2)) = (e1))\/(((op (e2) (e2)) = (e2))\/((op (e2) (e2)) = (e3))))) -> (~((op (e2) (e2)) = (e3))) -> (~((op (e2) (e2)) = (e2))) -> (~((op (e2) (e2)) = (e1))) -> (~((op (e3) (e3)) = (e0))) -> (~((op (e3) (e3)) = (e1))) -> (((op (e3) (e3)) = (e0))\/(((op (e3) (e3)) = (e1))\/(((op (e3) (e3)) = (e2))\/((op (e3) (e3)) = (e3))))) -> (((op (e0) (e0)) = (e1))\/(((op (e1) (e0)) = (e1))\/(((op (e2) (e0)) = (e1))\/((op (e3) (e0)) = (e1))))) -> False). % 15.22/15.42 do 0 intro. intros zenon_H10d zenon_H173 zenon_H45 zenon_Hbe zenon_H106 zenon_H105 zenon_Hdd zenon_H6a zenon_Ha3 zenon_H59 zenon_Ha7 zenon_H2d zenon_H30 zenon_H2f zenon_H52 zenon_H3c zenon_H104 zenon_H3b zenon_Hf1. % 15.22/15.42 apply (zenon_or_s _ _ zenon_H10d); [ zenon_intro zenon_H3e | zenon_intro zenon_H42 ]. % 15.22/15.42 apply (zenon_L457_); trivial. % 15.22/15.42 apply (zenon_L153_); trivial. % 15.22/15.42 (* end of lemma zenon_L458_ *) % 15.22/15.42 assert (zenon_L459_ : (((op (e0) (e3)) = (e2))\/(((op (e1) (e3)) = (e2))\/(((op (e2) (e3)) = (e2))\/((op (e3) (e3)) = (e2))))) -> (~((e2) = (e3))) -> ((op (e0) (e3)) = (e3)) -> (~((e0) = (e2))) -> ((op (e1) (e3)) = (e0)) -> ((op (e2) (e0)) = (e2)) -> (~((op (e2) (e0)) = (op (e2) (e3)))) -> (~((op (e3) (e3)) = (e2))) -> False). % 15.22/15.42 do 0 intro. intros zenon_H160 zenon_H6a zenon_H53 zenon_H5e zenon_Hcc zenon_Hdd zenon_Hce zenon_H3d. % 15.22/15.42 apply (zenon_or_s _ _ zenon_H160); [ zenon_intro zenon_H81 | zenon_intro zenon_H161 ]. % 15.22/15.42 apply (zenon_L128_); trivial. % 15.22/15.42 apply (zenon_or_s _ _ zenon_H161); [ zenon_intro zenon_H82 | zenon_intro zenon_H162 ]. % 15.22/15.42 apply (zenon_L54_); trivial. % 15.22/15.42 apply (zenon_or_s _ _ zenon_H162); [ zenon_intro zenon_H124 | zenon_intro zenon_H43 ]. % 15.22/15.42 apply (zenon_L119_); trivial. % 15.22/15.42 exact (zenon_H3d zenon_H43). % 15.22/15.42 (* end of lemma zenon_L459_ *) % 15.22/15.42 assert (zenon_L460_ : (((op (e0) (e3)) = (e2))\/(((op (e1) (e3)) = (e2))\/(((op (e2) (e3)) = (e2))\/((op (e3) (e3)) = (e2))))) -> (~((e2) = (e3))) -> ((op (e0) (e3)) = (e3)) -> (~((e0) = (e2))) -> ((op (e1) (e3)) = (e0)) -> ((op (e2) (e1)) = (e2)) -> (~((op (e2) (e1)) = (op (e2) (e3)))) -> (~((op (e3) (e3)) = (e2))) -> False). % 15.22/15.42 do 0 intro. intros zenon_H160 zenon_H6a zenon_H53 zenon_H5e zenon_Hcc zenon_H156 zenon_H1e2 zenon_H3d. % 15.22/15.42 apply (zenon_or_s _ _ zenon_H160); [ zenon_intro zenon_H81 | zenon_intro zenon_H161 ]. % 15.22/15.42 apply (zenon_L128_); trivial. % 15.22/15.42 apply (zenon_or_s _ _ zenon_H161); [ zenon_intro zenon_H82 | zenon_intro zenon_H162 ]. % 15.22/15.42 apply (zenon_L54_); trivial. % 15.22/15.42 apply (zenon_or_s _ _ zenon_H162); [ zenon_intro zenon_H124 | zenon_intro zenon_H43 ]. % 15.22/15.42 apply (zenon_L256_); trivial. % 15.22/15.42 exact (zenon_H3d zenon_H43). % 15.22/15.42 (* end of lemma zenon_L460_ *) % 15.22/15.42 assert (zenon_L461_ : (((op (e2) (e0)) = (e1))\/(((op (e2) (e1)) = (e1))\/(((op (e2) (e2)) = (e1))\/((op (e2) (e3)) = (e1))))) -> (~((e1) = (e3))) -> ((op (e2) (e0)) = (e3)) -> ((op (e1) (e1)) = (e1)) -> (~((op (e1) (e1)) = (op (e2) (e1)))) -> (~((op (e2) (e2)) = (e1))) -> (((op (e2) (e0)) = (e2))\/(((op (e2) (e1)) = (e2))\/(((op (e2) (e2)) = (e2))\/((op (e2) (e3)) = (e2))))) -> (~((op (e2) (e0)) = (op (e2) (e3)))) -> (~((op (e3) (e3)) = (e2))) -> (~((op (e2) (e1)) = (op (e2) (e3)))) -> ((op (e1) (e3)) = (e0)) -> (~((e0) = (e2))) -> ((op (e0) (e3)) = (e3)) -> (~((e2) = (e3))) -> (((op (e0) (e3)) = (e2))\/(((op (e1) (e3)) = (e2))\/(((op (e2) (e3)) = (e2))\/((op (e3) (e3)) = (e2))))) -> (~((op (e2) (e2)) = (e2))) -> (~((e1) = (e2))) -> False). % 15.22/15.42 do 0 intro. intros zenon_Hb7 zenon_Ha3 zenon_Haf zenon_H21 zenon_Hb1 zenon_H52 zenon_H237 zenon_Hce zenon_H3d zenon_H1e2 zenon_Hcc zenon_H5e zenon_H53 zenon_H6a zenon_H160 zenon_H2f zenon_Ha7. % 15.22/15.42 apply (zenon_or_s _ _ zenon_Hb7); [ zenon_intro zenon_Hae | zenon_intro zenon_Hb8 ]. % 15.22/15.42 apply (zenon_L39_); trivial. % 15.22/15.42 apply (zenon_or_s _ _ zenon_Hb8); [ zenon_intro zenon_Hb2 | zenon_intro zenon_Hb9 ]. % 15.22/15.42 apply (zenon_L40_); trivial. % 15.22/15.42 apply (zenon_or_s _ _ zenon_Hb9); [ zenon_intro zenon_H2a | zenon_intro zenon_Hb5 ]. % 15.22/15.42 exact (zenon_H52 zenon_H2a). % 15.22/15.42 apply (zenon_or_s _ _ zenon_H237); [ zenon_intro zenon_Hdd | zenon_intro zenon_H238 ]. % 15.22/15.42 apply (zenon_L459_); trivial. % 15.22/15.42 apply (zenon_or_s _ _ zenon_H238); [ zenon_intro zenon_H156 | zenon_intro zenon_H239 ]. % 15.22/15.42 apply (zenon_L460_); trivial. % 15.22/15.42 apply (zenon_or_s _ _ zenon_H239); [ zenon_intro zenon_H35 | zenon_intro zenon_H124 ]. % 15.22/15.42 exact (zenon_H2f zenon_H35). % 15.22/15.42 apply (zenon_L93_); trivial. % 15.22/15.42 (* end of lemma zenon_L461_ *) % 15.22/15.42 assert (zenon_L462_ : (((op (e1) (e0)) = (e0))\/(((op (e1) (e1)) = (e0))\/(((op (e1) (e2)) = (e0))\/((op (e1) (e3)) = (e0))))) -> ((op (e1) (e0)) = (e2)) -> (~((op (e1) (e1)) = (e0))) -> (~((op (e2) (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)) = (e1))\/(((op (e2) (e1)) = (e1))\/(((op (e2) (e2)) = (e1))\/((op (e2) (e3)) = (e1))))) -> (~((e1) = (e3))) -> ((op (e2) (e0)) = (e3)) -> ((op (e1) (e1)) = (e1)) -> (~((op (e1) (e1)) = (op (e2) (e1)))) -> (~((op (e2) (e2)) = (e1))) -> (((op (e2) (e0)) = (e2))\/(((op (e2) (e1)) = (e2))\/(((op (e2) (e2)) = (e2))\/((op (e2) (e3)) = (e2))))) -> (~((op (e2) (e0)) = (op (e2) (e3)))) -> (~((op (e3) (e3)) = (e2))) -> (~((op (e2) (e1)) = (op (e2) (e3)))) -> (~((e0) = (e2))) -> ((op (e0) (e3)) = (e3)) -> (~((e2) = (e3))) -> (((op (e0) (e3)) = (e2))\/(((op (e1) (e3)) = (e2))\/(((op (e2) (e3)) = (e2))\/((op (e3) (e3)) = (e2))))) -> (~((op (e2) (e2)) = (e2))) -> (~((e1) = (e2))) -> False). % 15.22/15.42 do 0 intro. intros zenon_H163 zenon_H68 zenon_H145 zenon_H30 zenon_H7d zenon_H2d zenon_Hb7 zenon_Ha3 zenon_Haf zenon_H21 zenon_Hb1 zenon_H52 zenon_H237 zenon_Hce zenon_H3d zenon_H1e2 zenon_H5e zenon_H53 zenon_H6a zenon_H160 zenon_H2f zenon_Ha7. % 15.22/15.42 apply (zenon_or_s _ _ zenon_H163); [ zenon_intro zenon_Had | zenon_intro zenon_H164 ]. % 15.22/15.42 apply (zenon_L160_); trivial. % 15.22/15.42 apply (zenon_or_s _ _ zenon_H164); [ zenon_intro zenon_H149 | zenon_intro zenon_H165 ]. % 15.22/15.42 exact (zenon_H145 zenon_H149). % 15.22/15.42 apply (zenon_or_s _ _ zenon_H165); [ zenon_intro zenon_H15d | zenon_intro zenon_Hcc ]. % 15.22/15.42 apply (zenon_L335_); trivial. % 15.22/15.42 apply (zenon_L461_); trivial. % 15.22/15.42 (* end of lemma zenon_L462_ *) % 15.22/15.42 assert (zenon_L463_ : (~((op (e0) (e1)) = (op (e0) (e3)))) -> ((op (e0) (e1)) = (e0)) -> ((op (e0) (e3)) = (e0)) -> False). % 15.22/15.42 do 0 intro. intros zenon_H1cd zenon_H49 zenon_Hca. % 15.22/15.42 cut (((op (e0) (e1)) = (e0)) = ((op (e0) (e1)) = (op (e0) (e3)))). % 15.22/15.42 intro zenon_D_pnotp. % 15.22/15.42 apply zenon_H1cd. % 15.22/15.42 rewrite <- zenon_D_pnotp. % 15.22/15.42 exact zenon_H49. % 15.22/15.42 cut (((e0) = (op (e0) (e3)))); [idtac | apply NNPP; zenon_intro zenon_Hcb]. % 15.22/15.42 cut (((op (e0) (e1)) = (op (e0) (e1)))); [idtac | apply NNPP; zenon_intro zenon_He1]. % 15.22/15.42 congruence. % 15.22/15.42 apply zenon_He1. apply refl_equal. % 15.22/15.42 apply zenon_Hcb. apply sym_equal. exact zenon_Hca. % 15.22/15.42 (* end of lemma zenon_L463_ *) % 15.22/15.42 assert (zenon_L464_ : (~((op (e1) (e3)) = (op (e3) (e3)))) -> ((op (e1) (e3)) = (e0)) -> ((op (e3) (e3)) = (e0)) -> False). % 15.22/15.42 do 0 intro. intros zenon_H8b zenon_Hcc zenon_H40. % 15.22/15.42 cut (((op (e1) (e3)) = (e0)) = ((op (e1) (e3)) = (op (e3) (e3)))). % 15.22/15.42 intro zenon_D_pnotp. % 15.22/15.42 apply zenon_H8b. % 15.22/15.42 rewrite <- zenon_D_pnotp. % 15.22/15.42 exact zenon_Hcc. % 15.22/15.42 cut (((e0) = (op (e3) (e3)))); [idtac | apply NNPP; zenon_intro zenon_H1a0]. % 15.22/15.42 cut (((op (e1) (e3)) = (op (e1) (e3)))); [idtac | apply NNPP; zenon_intro zenon_H23a]. % 15.22/15.42 congruence. % 15.22/15.42 apply zenon_H23a. apply refl_equal. % 15.22/15.42 apply zenon_H1a0. apply sym_equal. exact zenon_H40. % 15.22/15.42 (* end of lemma zenon_L464_ *) % 15.22/15.42 assert (zenon_L465_ : (((op (e3) (e3)) = (e0))\/(((op (e3) (e3)) = (e1))\/(((op (e3) (e3)) = (e2))\/((op (e3) (e3)) = (e3))))) -> ((op (e1) (e3)) = (e0)) -> (~((op (e1) (e3)) = (op (e3) (e3)))) -> (~((op (e3) (e3)) = (e1))) -> (~((op (e3) (e3)) = (e2))) -> (~((op (e3) (e3)) = (e3))) -> False). % 15.22/15.42 do 0 intro. intros zenon_H3b zenon_Hcc zenon_H8b zenon_H104 zenon_H3d zenon_H3e. % 15.22/15.42 apply (zenon_or_s _ _ zenon_H3b); [ zenon_intro zenon_H40 | zenon_intro zenon_H3f ]. % 15.22/15.42 apply (zenon_L464_); trivial. % 15.22/15.42 apply (zenon_or_s _ _ zenon_H3f); [ zenon_intro zenon_H38 | zenon_intro zenon_H41 ]. % 15.22/15.42 exact (zenon_H104 zenon_H38). % 15.22/15.42 apply (zenon_or_s _ _ zenon_H41); [ zenon_intro zenon_H43 | zenon_intro zenon_H42 ]. % 15.22/15.42 exact (zenon_H3d zenon_H43). % 15.22/15.42 exact (zenon_H3e zenon_H42). % 15.22/15.42 (* end of lemma zenon_L465_ *) % 15.22/15.42 assert (zenon_L466_ : (((op (e0) (e3)) = (e0))\/(((op (e1) (e3)) = (e0))\/(((op (e2) (e3)) = (e0))\/((op (e3) (e3)) = (e0))))) -> ((op (e0) (e1)) = (e0)) -> (~((op (e0) (e1)) = (op (e0) (e3)))) -> (~((op (e3) (e3)) = (e3))) -> (~((op (e3) (e3)) = (e2))) -> (~((op (e3) (e3)) = (e1))) -> (~((op (e1) (e3)) = (op (e3) (e3)))) -> (((op (e3) (e3)) = (e0))\/(((op (e3) (e3)) = (e1))\/(((op (e3) (e3)) = (e2))\/((op (e3) (e3)) = (e3))))) -> ((op (e2) (e0)) = (e0)) -> (~((op (e2) (e0)) = (op (e2) (e3)))) -> (((op (e0) (e0)) = (e0))\/(((op (e0) (e0)) = (e1))\/(((op (e0) (e0)) = (e2))\/((op (e0) (e0)) = (e3))))) -> (~((op (e0) (e0)) = (e0))) -> ((op (e3) (e1)) = (e2)) -> (~((op (e0) (e0)) = (e2))) -> (~((op (e0) (e0)) = (e3))) -> False). % 15.22/15.42 do 0 intro. intros zenon_Hd3 zenon_H49 zenon_H1cd zenon_H3e zenon_H3d zenon_H104 zenon_H8b zenon_H3b zenon_Hcf zenon_Hce zenon_H12a zenon_H20 zenon_H16a zenon_H8f zenon_H59. % 15.22/15.42 apply (zenon_or_s _ _ zenon_Hd3); [ zenon_intro zenon_Hca | zenon_intro zenon_Hd4 ]. % 15.22/15.42 apply (zenon_L463_); trivial. % 15.22/15.42 apply (zenon_or_s _ _ zenon_Hd4); [ zenon_intro zenon_Hcc | zenon_intro zenon_Hd5 ]. % 15.22/15.42 apply (zenon_L465_); trivial. % 15.22/15.42 apply (zenon_or_s _ _ zenon_Hd5); [ zenon_intro zenon_Hd0 | zenon_intro zenon_H40 ]. % 15.22/15.42 apply (zenon_L55_); trivial. % 15.22/15.42 apply (zenon_L187_); trivial. % 15.22/15.42 (* end of lemma zenon_L466_ *) % 15.22/15.42 assert (zenon_L467_ : (((op (e0) (e1)) = (e2))\/(((op (e1) (e1)) = (e2))\/(((op (e2) (e1)) = (e2))\/((op (e3) (e1)) = (e2))))) -> (~((e0) = (e2))) -> (~((op (e1) (e1)) = (e2))) -> ((op (e2) (e0)) = (e2)) -> (~((op (e2) (e0)) = (op (e2) (e1)))) -> (((op (e0) (e3)) = (e0))\/(((op (e1) (e3)) = (e0))\/(((op (e2) (e3)) = (e0))\/((op (e3) (e3)) = (e0))))) -> ((op (e0) (e1)) = (e0)) -> (~((op (e0) (e1)) = (op (e0) (e3)))) -> (~((op (e3) (e3)) = (e3))) -> (~((op (e3) (e3)) = (e2))) -> (~((op (e3) (e3)) = (e1))) -> (~((op (e1) (e3)) = (op (e3) (e3)))) -> (((op (e3) (e3)) = (e0))\/(((op (e3) (e3)) = (e1))\/(((op (e3) (e3)) = (e2))\/((op (e3) (e3)) = (e3))))) -> ((op (e2) (e0)) = (e0)) -> (~((op (e2) (e0)) = (op (e2) (e3)))) -> (((op (e0) (e0)) = (e0))\/(((op (e0) (e0)) = (e1))\/(((op (e0) (e0)) = (e2))\/((op (e0) (e0)) = (e3))))) -> (~((op (e0) (e0)) = (e0))) -> (~((op (e0) (e0)) = (e2))) -> (~((op (e0) (e0)) = (e3))) -> False). % 15.22/15.42 do 0 intro. intros zenon_H1a2 zenon_H5e zenon_Hd6 zenon_Hdd zenon_H154 zenon_Hd3 zenon_H49 zenon_H1cd zenon_H3e zenon_H3d zenon_H104 zenon_H8b zenon_H3b zenon_Hcf zenon_Hce zenon_H12a zenon_H20 zenon_H8f zenon_H59. % 15.22/15.42 apply (zenon_or_s _ _ zenon_H1a2); [ zenon_intro zenon_H5d | zenon_intro zenon_H1a3 ]. % 15.22/15.42 apply (zenon_L14_); trivial. % 15.22/15.42 apply (zenon_or_s _ _ zenon_H1a3); [ zenon_intro zenon_H6e | zenon_intro zenon_H1a4 ]. % 15.22/15.42 exact (zenon_Hd6 zenon_H6e). % 15.22/15.42 apply (zenon_or_s _ _ zenon_H1a4); [ zenon_intro zenon_H156 | zenon_intro zenon_H16a ]. % 15.22/15.42 apply (zenon_L284_); trivial. % 15.22/15.42 apply (zenon_L466_); trivial. % 15.22/15.42 (* end of lemma zenon_L467_ *) % 15.22/15.42 assert (zenon_L468_ : (((op (e0) (e3)) = (e0))\/(((op (e1) (e3)) = (e0))\/(((op (e2) (e3)) = (e0))\/((op (e3) (e3)) = (e0))))) -> ((op (e0) (e1)) = (e0)) -> (~((op (e0) (e1)) = (op (e0) (e3)))) -> (~((e0) = (e2))) -> ((op (e1) (e3)) = (e2)) -> ((op (e2) (e0)) = (e0)) -> (~((op (e2) (e0)) = (op (e2) (e3)))) -> ((op (e3) (e1)) = (e2)) -> ((op (e0) (e0)) = (e1)) -> False). % 15.22/15.42 do 0 intro. intros zenon_Hd3 zenon_H49 zenon_H1cd zenon_H5e zenon_H82 zenon_Hcf zenon_Hce zenon_H16a zenon_H47. % 15.22/15.42 apply (zenon_or_s _ _ zenon_Hd3); [ zenon_intro zenon_Hca | zenon_intro zenon_Hd4 ]. % 15.22/15.42 apply (zenon_L463_); trivial. % 15.22/15.42 apply (zenon_or_s _ _ zenon_Hd4); [ zenon_intro zenon_Hcc | zenon_intro zenon_Hd5 ]. % 15.22/15.42 apply (zenon_L54_); trivial. % 15.22/15.42 apply (zenon_or_s _ _ zenon_Hd5); [ zenon_intro zenon_Hd0 | zenon_intro zenon_H40 ]. % 15.22/15.42 apply (zenon_L55_); trivial. % 15.22/15.42 apply (zenon_L186_); trivial. % 15.22/15.42 (* end of lemma zenon_L468_ *) % 15.22/15.42 assert (zenon_L469_ : (((op (e0) (e0)) = (e3))\/(((op (e1) (e0)) = (e3))\/(((op (e2) (e0)) = (e3))\/((op (e3) (e0)) = (e3))))) -> ((op (e0) (e0)) = (e1)) -> (~((op (e2) (e0)) = (op (e2) (e3)))) -> (~((e0) = (e2))) -> (~((op (e0) (e1)) = (op (e0) (e3)))) -> ((op (e0) (e1)) = (e0)) -> (((op (e0) (e3)) = (e0))\/(((op (e1) (e3)) = (e0))\/(((op (e2) (e3)) = (e0))\/((op (e3) (e3)) = (e0))))) -> (((op (e0) (e0)) = (e3))\/(((op (e0) (e1)) = (e3))\/(((op (e0) (e2)) = (e3))\/((op (e0) (e3)) = (e3))))) -> (~((op (e0) (e0)) = (e3))) -> ((op (e0) (e2)) = (e2)) -> (((op (e2) (e0)) = (e3))\/(((op (e2) (e1)) = (e3))\/(((op (e2) (e2)) = (e3))\/((op (e2) (e3)) = (e3))))) -> (~((op (e2) (e2)) = (e3))) -> (~((op (e0) (e3)) = (op (e2) (e3)))) -> (~((op (e1) (e1)) = (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)) = (e2))\/(((op (e1) (e1)) = (e2))\/(((op (e1) (e2)) = (e2))\/((op (e1) (e3)) = (e2))))) -> (~((e0) = (e3))) -> ((op (e2) (e0)) = (e0)) -> (~((e2) = (e3))) -> ((op (e3) (e0)) = (e2)) -> False). % 15.22/15.42 do 0 intro. intros zenon_Hbe zenon_H47 zenon_Hce zenon_H5e zenon_H1cd zenon_H49 zenon_Hd3 zenon_H58 zenon_H59 zenon_H63 zenon_He6 zenon_H30 zenon_Hb4 zenon_Hd6 zenon_H1a2 zenon_H87 zenon_H84 zenon_H4b zenon_Hcf zenon_H6a zenon_He9. % 15.22/15.42 apply (zenon_or_s _ _ zenon_Hbe); [ zenon_intro zenon_H5b | zenon_intro zenon_Hbf ]. % 15.22/15.42 exact (zenon_H59 zenon_H5b). % 15.22/15.42 apply (zenon_or_s _ _ zenon_Hbf); [ zenon_intro zenon_H69 | zenon_intro zenon_Hc0 ]. % 15.22/15.42 apply (zenon_or_s _ _ zenon_H84); [ zenon_intro zenon_H68 | zenon_intro zenon_H85 ]. % 15.22/15.42 apply (zenon_L17_); trivial. % 15.22/15.42 apply (zenon_or_s _ _ zenon_H85); [ zenon_intro zenon_H6e | zenon_intro zenon_H86 ]. % 15.22/15.42 exact (zenon_Hd6 zenon_H6e). % 15.22/15.42 apply (zenon_or_s _ _ zenon_H86); [ zenon_intro zenon_H7c | zenon_intro zenon_H82 ]. % 15.22/15.42 apply (zenon_L52_); trivial. % 15.22/15.42 apply (zenon_or_s _ _ zenon_H1a2); [ zenon_intro zenon_H5d | zenon_intro zenon_H1a3 ]. % 15.22/15.42 apply (zenon_L14_); trivial. % 15.22/15.42 apply (zenon_or_s _ _ zenon_H1a3); [ zenon_intro zenon_H6e | zenon_intro zenon_H1a4 ]. % 15.22/15.42 exact (zenon_Hd6 zenon_H6e). % 15.22/15.42 apply (zenon_or_s _ _ zenon_H1a4); [ zenon_intro zenon_H156 | zenon_intro zenon_H16a ]. % 15.22/15.42 apply (zenon_L291_); trivial. % 15.22/15.42 apply (zenon_L468_); trivial. % 15.22/15.42 apply (zenon_or_s _ _ zenon_Hc0); [ zenon_intro zenon_Haf | zenon_intro zenon_Hba ]. % 15.22/15.42 apply (zenon_L57_); trivial. % 15.22/15.42 apply (zenon_L220_); trivial. % 15.22/15.42 (* end of lemma zenon_L469_ *) % 15.22/15.42 assert (zenon_L470_ : (((op (e3) (e0)) = (e2))\/(((op (e3) (e1)) = (e2))\/(((op (e3) (e2)) = (e2))\/((op (e3) (e3)) = (e2))))) -> (~((e0) = (e2))) -> ((op (e3) (e0)) = (e0)) -> ((op (e2) (e1)) = (e2)) -> (~((op (e2) (e1)) = (op (e3) (e1)))) -> ((op (e0) (e2)) = (e2)) -> (~((op (e0) (e2)) = (op (e3) (e2)))) -> (~((op (e3) (e3)) = (e2))) -> False). % 15.22/15.42 do 0 intro. intros zenon_H1df zenon_H5e zenon_Hdb zenon_H156 zenon_H13c zenon_H63 zenon_H140 zenon_H3d. % 15.22/15.42 apply (zenon_or_s _ _ zenon_H1df); [ zenon_intro zenon_He9 | zenon_intro zenon_H1e0 ]. % 15.22/15.42 apply (zenon_L69_); trivial. % 15.22/15.42 apply (zenon_or_s _ _ zenon_H1e0); [ zenon_intro zenon_H16a | zenon_intro zenon_H1e1 ]. % 15.22/15.42 apply (zenon_L252_); trivial. % 15.22/15.42 apply (zenon_or_s _ _ zenon_H1e1); [ zenon_intro zenon_H1dd | zenon_intro zenon_H43 ]. % 15.22/15.42 apply (zenon_L253_); trivial. % 15.22/15.42 exact (zenon_H3d zenon_H43). % 15.22/15.42 (* end of lemma zenon_L470_ *) % 15.22/15.42 assert (zenon_L471_ : (((op (e0) (e0)) = (e2))\/(((op (e0) (e1)) = (e2))\/(((op (e0) (e2)) = (e2))\/((op (e0) (e3)) = (e2))))) -> (~((op (e3) (e3)) = (e2))) -> (((op (e0) (e0)) = (e0))\/(((op (e0) (e0)) = (e1))\/(((op (e0) (e0)) = (e2))\/((op (e0) (e0)) = (e3))))) -> (~((op (e0) (e0)) = (e0))) -> (~((op (e0) (e0)) = (e2))) -> (~((op (e0) (e0)) = (e3))) -> (((op (e3) (e0)) = (e2))\/(((op (e3) (e1)) = (e2))\/(((op (e3) (e2)) = (e2))\/((op (e3) (e3)) = (e2))))) -> (~((e0) = (e2))) -> ((op (e3) (e0)) = (e0)) -> (~((op (e2) (e1)) = (op (e3) (e1)))) -> (~((op (e0) (e2)) = (op (e3) (e2)))) -> (~((op (e1) (e1)) = (e2))) -> ((op (e0) (e1)) = (e0)) -> (((op (e0) (e1)) = (e2))\/(((op (e1) (e1)) = (e2))\/(((op (e2) (e1)) = (e2))\/((op (e3) (e1)) = (e2))))) -> (((op (e3) (e3)) = (e0))\/(((op (e3) (e3)) = (e1))\/(((op (e3) (e3)) = (e2))\/((op (e3) (e3)) = (e3))))) -> (~((op (e3) (e3)) = (e0))) -> (~((op (e3) (e3)) = (e1))) -> (~((op (e0) (e3)) = (op (e3) (e3)))) -> (~((op (e3) (e3)) = (e3))) -> False). % 15.22/15.42 do 0 intro. intros zenon_H8e zenon_H3d zenon_H12a zenon_H20 zenon_H8f zenon_H59 zenon_H1df zenon_H5e zenon_Hdb zenon_H13c zenon_H140 zenon_Hd6 zenon_H49 zenon_H1a2 zenon_H3b zenon_H3c zenon_H104 zenon_H36 zenon_H3e. % 15.22/15.42 apply (zenon_or_s _ _ zenon_H8e); [ zenon_intro zenon_H92 | zenon_intro zenon_H91 ]. % 15.22/15.42 exact (zenon_H8f zenon_H92). % 15.22/15.42 apply (zenon_or_s _ _ zenon_H91); [ zenon_intro zenon_H5d | zenon_intro zenon_H93 ]. % 15.22/15.42 apply (zenon_L14_); trivial. % 15.22/15.42 apply (zenon_or_s _ _ zenon_H93); [ zenon_intro zenon_H63 | zenon_intro zenon_H81 ]. % 15.22/15.42 apply (zenon_or_s _ _ zenon_H1a2); [ zenon_intro zenon_H5d | zenon_intro zenon_H1a3 ]. % 15.22/15.42 apply (zenon_L14_); trivial. % 15.22/15.42 apply (zenon_or_s _ _ zenon_H1a3); [ zenon_intro zenon_H6e | zenon_intro zenon_H1a4 ]. % 15.22/15.42 exact (zenon_Hd6 zenon_H6e). % 15.22/15.42 apply (zenon_or_s _ _ zenon_H1a4); [ zenon_intro zenon_H156 | zenon_intro zenon_H16a ]. % 15.22/15.42 apply (zenon_L470_); trivial. % 15.22/15.42 apply (zenon_L188_); trivial. % 15.22/15.42 apply (zenon_L107_); trivial. % 15.22/15.42 (* end of lemma zenon_L471_ *) % 15.22/15.42 assert (zenon_L472_ : (((op (e0) (e0)) = (e3))\/(((op (e1) (e0)) = (e3))\/(((op (e2) (e0)) = (e3))\/((op (e3) (e0)) = (e3))))) -> (~((op (e0) (e0)) = (e3))) -> (~((e2) = (e3))) -> ((op (e1) (e0)) = (e2)) -> (~((e0) = (e3))) -> ((op (e2) (e0)) = (e0)) -> (~((op (e3) (e0)) = (op (e3) (e1)))) -> ((op (e3) (e1)) = (e3)) -> False). % 15.22/15.42 do 0 intro. intros zenon_Hbe zenon_H59 zenon_H6a zenon_H68 zenon_H4b zenon_Hcf zenon_H109 zenon_H10a. % 15.22/15.42 apply (zenon_or_s _ _ zenon_Hbe); [ zenon_intro zenon_H5b | zenon_intro zenon_Hbf ]. % 15.22/15.42 exact (zenon_H59 zenon_H5b). % 15.22/15.42 apply (zenon_or_s _ _ zenon_Hbf); [ zenon_intro zenon_H69 | zenon_intro zenon_Hc0 ]. % 15.22/15.42 apply (zenon_L17_); trivial. % 15.22/15.42 apply (zenon_or_s _ _ zenon_Hc0); [ zenon_intro zenon_Haf | zenon_intro zenon_Hba ]. % 15.22/15.42 apply (zenon_L57_); trivial. % 15.22/15.42 apply (zenon_L82_); trivial. % 15.22/15.42 (* end of lemma zenon_L472_ *) % 15.22/15.42 assert (zenon_L473_ : (((op (e0) (e0)) = (e3))\/(((op (e0) (e1)) = (e3))\/(((op (e0) (e2)) = (e3))\/((op (e0) (e3)) = (e3))))) -> (~((op (e0) (e0)) = (e3))) -> (~((e0) = (e3))) -> ((op (e0) (e1)) = (e0)) -> (~((op (e0) (e2)) = (op (e2) (e2)))) -> (~((op (e2) (e2)) = (e2))) -> (~((op (e2) (e2)) = (e1))) -> (~((op (e2) (e2)) = (e0))) -> (((op (e2) (e2)) = (e0))\/(((op (e2) (e2)) = (e1))\/(((op (e2) (e2)) = (e2))\/((op (e2) (e2)) = (e3))))) -> ((op (e0) (e3)) = (e2)) -> (~((e2) = (e3))) -> False). % 15.22/15.42 do 0 intro. intros zenon_H58 zenon_H59 zenon_H4b zenon_H49 zenon_H28 zenon_H2f zenon_H52 zenon_H2e zenon_H2d zenon_H81 zenon_H6a. % 15.22/15.42 apply (zenon_or_s _ _ zenon_H58); [ zenon_intro zenon_H5b | zenon_intro zenon_H5a ]. % 15.22/15.42 exact (zenon_H59 zenon_H5b). % 15.22/15.42 apply (zenon_or_s _ _ zenon_H5a); [ zenon_intro zenon_H4a | zenon_intro zenon_H5c ]. % 15.22/15.42 apply (zenon_L9_); trivial. % 15.22/15.42 apply (zenon_or_s _ _ zenon_H5c); [ zenon_intro zenon_H50 | zenon_intro zenon_H53 ]. % 15.22/15.42 apply (zenon_L11_); trivial. % 15.22/15.42 apply (zenon_L128_); trivial. % 15.22/15.42 (* end of lemma zenon_L473_ *) % 15.22/15.42 assert (zenon_L474_ : (((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)) = (e0))) -> ((op (e2) (e0)) = (e0)) -> (~((op (e2) (e0)) = (op (e2) (e1)))) -> (~((e0) = (e3))) -> ((op (e3) (e1)) = (e3)) -> False). % 15.22/15.42 do 0 intro. intros zenon_H144 zenon_H9e zenon_H22 zenon_H145 zenon_Hcf zenon_H154 zenon_H4b zenon_H10a. % 15.22/15.42 apply (zenon_or_s _ _ zenon_H144); [ zenon_intro zenon_H49 | zenon_intro zenon_H147 ]. % 15.22/15.42 apply (zenon_L27_); trivial. % 15.22/15.42 apply (zenon_or_s _ _ zenon_H147); [ zenon_intro zenon_H149 | zenon_intro zenon_H148 ]. % 15.22/15.42 exact (zenon_H145 zenon_H149). % 15.22/15.42 apply (zenon_or_s _ _ zenon_H148); [ zenon_intro zenon_H14a | zenon_intro zenon_H142 ]. % 15.22/15.42 apply (zenon_L133_); trivial. % 15.22/15.42 apply (zenon_L126_); trivial. % 15.22/15.42 (* end of lemma zenon_L474_ *) % 15.22/15.42 assert (zenon_L475_ : ((~((op (e3) (e3)) = (e1)))\/((op (e3) (e1)) = (e3))) -> ((~((op (e3) (e3)) = (e3)))\/((op (e3) (e3)) = (e3))) -> (~((op (e3) (e0)) = (op (e3) (e3)))) -> (~((e0) = (e2))) -> ((op (e0) (e1)) = (e0)) -> (~((op (e1) (e1)) = (e2))) -> (((op (e0) (e1)) = (e3))\/(((op (e1) (e1)) = (e3))\/(((op (e2) (e1)) = (e3))\/((op (e3) (e1)) = (e3))))) -> ((op (e3) (e0)) = (e3)) -> (~((op (e3) (e0)) = (op (e3) (e1)))) -> (~((e2) = (e3))) -> (~((op (e1) (e1)) = (e3))) -> (~((e0) = (e3))) -> (((op (e3) (e3)) = (e0))\/(((op (e3) (e3)) = (e1))\/(((op (e3) (e3)) = (e2))\/((op (e3) (e3)) = (e3))))) -> (~((op (e0) (e0)) = (e0))) -> (~((op (e0) (e0)) = (e2))) -> (~((op (e0) (e0)) = (e3))) -> (((op (e0) (e0)) = (e0))\/(((op (e0) (e0)) = (e1))\/(((op (e0) (e0)) = (e2))\/((op (e0) (e0)) = (e3))))) -> (((op (e0) (e1)) = (e2))\/(((op (e1) (e1)) = (e2))\/(((op (e2) (e1)) = (e2))\/((op (e3) (e1)) = (e2))))) -> (~((op (e3) (e0)) = (op (e3) (e2)))) -> ((~((op (e3) (e3)) = (e2)))\/((op (e3) (e2)) = (e3))) -> False). % 15.22/15.42 do 0 intro. intros zenon_H10c zenon_H10d zenon_Hbb zenon_H5e zenon_H49 zenon_Hd6 zenon_H199 zenon_Hba zenon_H109 zenon_H6a zenon_H182 zenon_H4b zenon_H3b zenon_H20 zenon_H8f zenon_H59 zenon_H12a zenon_H1a2 zenon_H105 zenon_H10e. % 15.22/15.42 apply (zenon_or_s _ _ zenon_H10c); [ zenon_intro zenon_H104 | zenon_intro zenon_H10a ]. % 15.22/15.42 apply (zenon_L191_); trivial. % 15.22/15.42 apply (zenon_L82_); trivial. % 15.22/15.42 (* end of lemma zenon_L475_ *) % 15.22/15.42 assert (zenon_L476_ : ((~((op (e3) (e3)) = (e2)))\/((op (e3) (e2)) = (e3))) -> (((op (e0) (e0)) = (e2))\/(((op (e0) (e1)) = (e2))\/(((op (e0) (e2)) = (e2))\/((op (e0) (e3)) = (e2))))) -> (~((op (e3) (e3)) = (e0))) -> (~((e1) = (e2))) -> (~((op (e1) (e1)) = (op (e1) (e2)))) -> ((op (e1) (e1)) = (e1)) -> (~((e1) = (e3))) -> (((op (e0) (e2)) = (e1))\/(((op (e1) (e2)) = (e1))\/(((op (e2) (e2)) = (e1))\/((op (e3) (e2)) = (e1))))) -> (~((op (e3) (e2)) = (op (e3) (e3)))) -> (((op (e0) (e1)) = (e2))\/(((op (e1) (e1)) = (e2))\/(((op (e2) (e1)) = (e2))\/((op (e3) (e1)) = (e2))))) -> (((op (e0) (e0)) = (e0))\/(((op (e0) (e0)) = (e1))\/(((op (e0) (e0)) = (e2))\/((op (e0) (e0)) = (e3))))) -> (~((op (e0) (e0)) = (e3))) -> (~((op (e0) (e0)) = (e2))) -> (~((op (e0) (e0)) = (e0))) -> (~((op (e3) (e3)) = (e1))) -> (((op (e3) (e3)) = (e0))\/(((op (e3) (e3)) = (e1))\/(((op (e3) (e3)) = (e2))\/((op (e3) (e3)) = (e3))))) -> ((op (e2) (e3)) = (e2)) -> (~((op (e2) (e1)) = (op (e2) (e3)))) -> (~((op (e1) (e1)) = (e2))) -> ((op (e0) (e1)) = (e0)) -> (~((e0) = (e2))) -> (((op (e0) (e0)) = (e3))\/(((op (e0) (e1)) = (e3))\/(((op (e0) (e2)) = (e3))\/((op (e0) (e3)) = (e3))))) -> (~((op (e0) (e3)) = (op (e3) (e3)))) -> (~((op (e2) (e2)) = (e0))) -> (~((op (e2) (e2)) = (e1))) -> (~((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))))) -> (~((e0) = (e3))) -> ((~((op (e3) (e3)) = (e3)))\/((op (e3) (e3)) = (e3))) -> False). % 15.22/15.42 do 0 intro. intros zenon_H10e zenon_H8e zenon_H3c zenon_Ha7 zenon_H116 zenon_H21 zenon_Ha3 zenon_H11b zenon_H173 zenon_H1a2 zenon_H12a zenon_H59 zenon_H8f zenon_H20 zenon_H104 zenon_H3b zenon_H124 zenon_H1e2 zenon_Hd6 zenon_H49 zenon_H5e zenon_H58 zenon_H36 zenon_H2e zenon_H52 zenon_H2f zenon_H28 zenon_H2d zenon_H4b zenon_H10d. % 15.22/15.42 apply (zenon_or_s _ _ zenon_H10e); [ zenon_intro zenon_H3d | zenon_intro zenon_H106 ]. % 15.22/15.42 apply (zenon_L392_); trivial. % 15.22/15.42 apply (zenon_L296_); trivial. % 15.22/15.42 (* end of lemma zenon_L476_ *) % 15.22/15.42 assert (zenon_L477_ : (((op (e2) (e0)) = (e1))\/(((op (e2) (e1)) = (e1))\/(((op (e2) (e2)) = (e1))\/((op (e2) (e3)) = (e1))))) -> (~((e0) = (e1))) -> ((op (e2) (e0)) = (e0)) -> ((op (e1) (e1)) = (e1)) -> (~((op (e1) (e1)) = (op (e2) (e1)))) -> (~((op (e2) (e2)) = (e1))) -> (~((e1) = (e2))) -> ((op (e2) (e3)) = (e2)) -> False). % 15.22/15.42 do 0 intro. intros zenon_Hb7 zenon_H9e zenon_Hcf zenon_H21 zenon_Hb1 zenon_H52 zenon_Ha7 zenon_H124. % 15.22/15.42 apply (zenon_or_s _ _ zenon_Hb7); [ zenon_intro zenon_Hae | zenon_intro zenon_Hb8 ]. % 15.22/15.42 apply (zenon_L269_); trivial. % 15.22/15.42 apply (zenon_or_s _ _ zenon_Hb8); [ zenon_intro zenon_Hb2 | zenon_intro zenon_Hb9 ]. % 15.22/15.42 apply (zenon_L40_); trivial. % 15.22/15.42 apply (zenon_or_s _ _ zenon_Hb9); [ zenon_intro zenon_H2a | zenon_intro zenon_Hb5 ]. % 15.22/15.42 exact (zenon_H52 zenon_H2a). % 15.22/15.42 apply (zenon_L93_); trivial. % 15.22/15.42 (* end of lemma zenon_L477_ *) % 15.22/15.42 assert (zenon_L478_ : (((op (e0) (e0)) = (e3))\/(((op (e1) (e0)) = (e3))\/(((op (e2) (e0)) = (e3))\/((op (e3) (e0)) = (e3))))) -> (~((op (e0) (e0)) = (e3))) -> (~((e2) = (e3))) -> ((op (e1) (e0)) = (e2)) -> ((op (e2) (e3)) = (e2)) -> (~((e1) = (e2))) -> (~((op (e2) (e2)) = (e1))) -> (~((op (e1) (e1)) = (op (e2) (e1)))) -> ((op (e1) (e1)) = (e1)) -> (~((e1) = (e3))) -> (((op (e2) (e0)) = (e1))\/(((op (e2) (e1)) = (e1))\/(((op (e2) (e2)) = (e1))\/((op (e2) (e3)) = (e1))))) -> (~((e0) = (e3))) -> ((op (e3) (e0)) = (e0)) -> False). % 15.22/15.42 do 0 intro. intros zenon_Hbe zenon_H59 zenon_H6a zenon_H68 zenon_H124 zenon_Ha7 zenon_H52 zenon_Hb1 zenon_H21 zenon_Ha3 zenon_Hb7 zenon_H4b zenon_Hdb. % 15.22/15.42 apply (zenon_or_s _ _ zenon_Hbe); [ zenon_intro zenon_H5b | zenon_intro zenon_Hbf ]. % 15.22/15.42 exact (zenon_H59 zenon_H5b). % 15.22/15.42 apply (zenon_or_s _ _ zenon_Hbf); [ zenon_intro zenon_H69 | zenon_intro zenon_Hc0 ]. % 15.22/15.42 apply (zenon_L17_); trivial. % 15.22/15.42 apply (zenon_or_s _ _ zenon_Hc0); [ zenon_intro zenon_Haf | zenon_intro zenon_Hba ]. % 15.22/15.42 apply (zenon_L96_); trivial. % 15.22/15.42 apply (zenon_L62_); trivial. % 15.22/15.42 (* end of lemma zenon_L478_ *) % 15.22/15.42 assert (zenon_L479_ : (((op (e0) (e0)) = (e2))\/(((op (e1) (e0)) = (e2))\/(((op (e2) (e0)) = (e2))\/((op (e3) (e0)) = (e2))))) -> (~((op (e0) (e0)) = (e2))) -> (~((e0) = (e3))) -> (((op (e2) (e0)) = (e1))\/(((op (e2) (e1)) = (e1))\/(((op (e2) (e2)) = (e1))\/((op (e2) (e3)) = (e1))))) -> (~((e1) = (e3))) -> ((op (e1) (e1)) = (e1)) -> (~((op (e1) (e1)) = (op (e2) (e1)))) -> (~((op (e2) (e2)) = (e1))) -> (~((e1) = (e2))) -> ((op (e2) (e3)) = (e2)) -> (~((op (e0) (e0)) = (e3))) -> (((op (e0) (e0)) = (e3))\/(((op (e1) (e0)) = (e3))\/(((op (e2) (e0)) = (e3))\/((op (e3) (e0)) = (e3))))) -> ((op (e3) (e1)) = (e3)) -> (~((e2) = (e3))) -> (~((op (e2) (e0)) = (op (e2) (e1)))) -> (~((op (e1) (e1)) = (e2))) -> ((op (e0) (e1)) = (e0)) -> (((op (e0) (e1)) = (e2))\/(((op (e1) (e1)) = (e2))\/(((op (e2) (e1)) = (e2))\/((op (e3) (e1)) = (e2))))) -> ((op (e3) (e0)) = (e0)) -> (~((e0) = (e2))) -> False). % 15.22/15.42 do 0 intro. intros zenon_Heb zenon_H8f zenon_H4b zenon_Hb7 zenon_Ha3 zenon_H21 zenon_Hb1 zenon_H52 zenon_Ha7 zenon_H124 zenon_H59 zenon_Hbe zenon_H10a zenon_H6a zenon_H154 zenon_Hd6 zenon_H49 zenon_H1a2 zenon_Hdb zenon_H5e. % 15.22/15.42 apply (zenon_or_s _ _ zenon_Heb); [ zenon_intro zenon_H92 | zenon_intro zenon_Hec ]. % 15.22/15.42 exact (zenon_H8f zenon_H92). % 15.22/15.42 apply (zenon_or_s _ _ zenon_Hec); [ zenon_intro zenon_H68 | zenon_intro zenon_Hed ]. % 15.22/15.42 apply (zenon_L478_); trivial. % 15.22/15.42 apply (zenon_or_s _ _ zenon_Hed); [ zenon_intro zenon_Hdd | zenon_intro zenon_He9 ]. % 15.22/15.42 apply (zenon_L298_); trivial. % 15.22/15.42 apply (zenon_L69_); trivial. % 15.22/15.42 (* end of lemma zenon_L479_ *) % 15.22/15.42 assert (zenon_L480_ : ((~((op (e3) (e3)) = (e0)))\/((op (e3) (e0)) = (e3))) -> ((~((op (e3) (e3)) = (e2)))\/((op (e3) (e2)) = (e3))) -> (~((op (e3) (e0)) = (op (e3) (e2)))) -> (((op (e0) (e0)) = (e0))\/(((op (e0) (e0)) = (e1))\/(((op (e0) (e0)) = (e2))\/((op (e0) (e0)) = (e3))))) -> (~((op (e0) (e0)) = (e0))) -> (~((op (e1) (e1)) = (e3))) -> (~((op (e3) (e0)) = (op (e3) (e1)))) -> (((op (e0) (e1)) = (e3))\/(((op (e1) (e1)) = (e3))\/(((op (e2) (e1)) = (e3))\/((op (e3) (e1)) = (e3))))) -> (~((op (e3) (e0)) = (op (e3) (e3)))) -> ((~((op (e3) (e3)) = (e3)))\/((op (e3) (e3)) = (e3))) -> (((op (e0) (e0)) = (e3))\/(((op (e0) (e1)) = (e3))\/(((op (e0) (e2)) = (e3))\/((op (e0) (e3)) = (e3))))) -> (~((op (e2) (e2)) = (e0))) -> (~((op (e2) (e2)) = (e1))) -> (((op (e2) (e2)) = (e0))\/(((op (e2) (e2)) = (e1))\/(((op (e2) (e2)) = (e2))\/((op (e2) (e2)) = (e3))))) -> (~((e0) = (e3))) -> (~((op (e0) (e0)) = (e3))) -> (((op (e0) (e0)) = (e1))\/(((op (e0) (e1)) = (e1))\/(((op (e0) (e2)) = (e1))\/((op (e0) (e3)) = (e1))))) -> (~((e1) = (e2))) -> (~((e1) = (e3))) -> (~((e0) = (e1))) -> (((op (e1) (e0)) = (e2))\/(((op (e1) (e1)) = (e2))\/(((op (e1) (e2)) = (e2))\/((op (e1) (e3)) = (e2))))) -> (~((op (e0) (e3)) = (op (e1) (e3)))) -> (~((op (e1) (e2)) = (op (e2) (e2)))) -> (~((e2) = (e3))) -> (~((op (e0) (e2)) = (op (e1) (e2)))) -> (~((op (e1) (e3)) = (op (e3) (e3)))) -> (((op (e1) (e0)) = (e3))\/(((op (e1) (e1)) = (e3))\/(((op (e1) (e2)) = (e3))\/((op (e1) (e3)) = (e3))))) -> ((~((op (e2) (e2)) = (e2)))\/((op (e2) (e2)) = (e2))) -> (~((op (e0) (e0)) = (e2))) -> (~((e0) = (e2))) -> ((op (e0) (e1)) = (e0)) -> (~((op (e0) (e2)) = (op (e2) (e2)))) -> ((op (e2) (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 (e0) (e0)) = (e2))\/(((op (e0) (e1)) = (e2))\/(((op (e0) (e2)) = (e2))\/((op (e0) (e3)) = (e2))))) -> (((op (e0) (e1)) = (e2))\/(((op (e1) (e1)) = (e2))\/(((op (e2) (e1)) = (e2))\/((op (e3) (e1)) = (e2))))) -> (~((op (e2) (e1)) = (op (e2) (e2)))) -> (~((op (e1) (e1)) = (e2))) -> ((~((op (e3) (e3)) = (e1)))\/((op (e3) (e1)) = (e3))) -> False). % 15.22/15.42 do 0 intro. intros zenon_H10f zenon_H10e zenon_H105 zenon_H12a zenon_H20 zenon_H182 zenon_H109 zenon_H199 zenon_Hbb zenon_H10d zenon_H58 zenon_H2e zenon_H52 zenon_H2d zenon_H4b zenon_H59 zenon_H44 zenon_Ha7 zenon_Ha3 zenon_H9e zenon_H84 zenon_H80 zenon_H7d zenon_H6a zenon_H87 zenon_H8b zenon_H90 zenon_Haa zenon_H8f zenon_H5e zenon_H49 zenon_H28 zenon_H35 zenon_H3b zenon_H36 zenon_H8e zenon_H1a2 zenon_H157 zenon_Hd6 zenon_H10c. % 15.22/15.42 apply (zenon_or_s _ _ zenon_H10f); [ zenon_intro zenon_H3c | zenon_intro zenon_Hba ]. % 15.22/15.42 apply (zenon_or_s _ _ zenon_H10c); [ zenon_intro zenon_H104 | zenon_intro zenon_H10a ]. % 15.22/15.42 apply (zenon_or_s _ _ zenon_H10d); [ zenon_intro zenon_H3e | zenon_intro zenon_H42 ]. % 15.22/15.42 apply (zenon_L131_); trivial. % 15.22/15.42 apply (zenon_L36_); trivial. % 15.22/15.42 apply (zenon_L349_); trivial. % 15.22/15.42 apply (zenon_L475_); trivial. % 15.22/15.42 (* end of lemma zenon_L480_ *) % 15.22/15.42 assert (zenon_L481_ : (((op (e0) (e0)) = (e2))\/(((op (e0) (e1)) = (e2))\/(((op (e0) (e2)) = (e2))\/((op (e0) (e3)) = (e2))))) -> (~((op (e0) (e0)) = (e2))) -> ((op (e0) (e1)) = (e0)) -> (~((op (e3) (e3)) = (e2))) -> (~((op (e0) (e2)) = (op (e3) (e2)))) -> (~((op (e2) (e1)) = (op (e3) (e1)))) -> ((op (e2) (e1)) = (e2)) -> ((op (e3) (e0)) = (e0)) -> (~((e0) = (e2))) -> (((op (e3) (e0)) = (e2))\/(((op (e3) (e1)) = (e2))\/(((op (e3) (e2)) = (e2))\/((op (e3) (e3)) = (e2))))) -> (((op (e3) (e3)) = (e0))\/(((op (e3) (e3)) = (e1))\/(((op (e3) (e3)) = (e2))\/((op (e3) (e3)) = (e3))))) -> (~((op (e3) (e3)) = (e0))) -> (~((op (e3) (e3)) = (e1))) -> (~((op (e0) (e3)) = (op (e3) (e3)))) -> (~((op (e3) (e3)) = (e3))) -> False). % 15.22/15.42 do 0 intro. intros zenon_H8e zenon_H8f zenon_H49 zenon_H3d zenon_H140 zenon_H13c zenon_H156 zenon_Hdb zenon_H5e zenon_H1df zenon_H3b zenon_H3c zenon_H104 zenon_H36 zenon_H3e. % 15.22/15.42 apply (zenon_or_s _ _ zenon_H8e); [ zenon_intro zenon_H92 | zenon_intro zenon_H91 ]. % 15.22/15.42 exact (zenon_H8f zenon_H92). % 15.22/15.42 apply (zenon_or_s _ _ zenon_H91); [ zenon_intro zenon_H5d | zenon_intro zenon_H93 ]. % 15.22/15.42 apply (zenon_L14_); trivial. % 15.22/15.42 apply (zenon_or_s _ _ zenon_H93); [ zenon_intro zenon_H63 | zenon_intro zenon_H81 ]. % 15.22/15.42 apply (zenon_L470_); trivial. % 15.22/15.42 apply (zenon_L107_); trivial. % 15.22/15.42 (* end of lemma zenon_L481_ *) % 15.22/15.42 assert (zenon_L482_ : (((op (e2) (e0)) = (e2))\/(((op (e2) (e1)) = (e2))\/(((op (e2) (e2)) = (e2))\/((op (e2) (e3)) = (e2))))) -> (~((e2) = (e3))) -> ((op (e2) (e0)) = (e3)) -> ((op (e3) (e1)) = (e2)) -> (~((op (e2) (e1)) = (op (e3) (e1)))) -> (~((op (e2) (e2)) = (e2))) -> (~((e0) = (e2))) -> ((op (e2) (e3)) = (e0)) -> False). % 15.22/15.42 do 0 intro. intros zenon_H237 zenon_H6a zenon_Haf zenon_H16a zenon_H13c zenon_H2f zenon_H5e zenon_Hd0. % 15.22/15.42 apply (zenon_or_s _ _ zenon_H237); [ zenon_intro zenon_Hdd | zenon_intro zenon_H238 ]. % 15.22/15.42 apply (zenon_L64_); trivial. % 15.22/15.42 apply (zenon_or_s _ _ zenon_H238); [ zenon_intro zenon_H156 | zenon_intro zenon_H239 ]. % 15.22/15.42 apply (zenon_L252_); trivial. % 15.22/15.42 apply (zenon_or_s _ _ zenon_H239); [ zenon_intro zenon_H35 | zenon_intro zenon_H124 ]. % 15.22/15.42 exact (zenon_H2f zenon_H35). % 15.22/15.42 apply (zenon_L201_); trivial. % 15.22/15.42 (* end of lemma zenon_L482_ *) % 15.22/15.42 assert (zenon_L483_ : (~((op (e3) (op (e0) (e3))) = (op (e0) (e3)))) -> ((op (e3) (e2)) = (e2)) -> ((op (e0) (e3)) = (e2)) -> False). % 15.22/15.42 do 0 intro. intros zenon_H192 zenon_H1dd zenon_H81. % 15.22/15.42 cut (((op (e3) (e2)) = (e2)) = ((op (e3) (op (e0) (e3))) = (op (e0) (e3)))). % 15.22/15.42 intro zenon_D_pnotp. % 15.22/15.42 apply zenon_H192. % 15.22/15.42 rewrite <- zenon_D_pnotp. % 15.22/15.42 exact zenon_H1dd. % 15.22/15.42 cut (((e2) = (op (e0) (e3)))); [idtac | apply NNPP; zenon_intro zenon_H23b]. % 15.22/15.42 cut (((op (e3) (e2)) = (op (e3) (op (e0) (e3))))); [idtac | apply NNPP; zenon_intro zenon_H23c]. % 15.22/15.42 congruence. % 15.22/15.42 elim (classic ((op (e3) (op (e0) (e3))) = (op (e3) (op (e0) (e3))))); [ zenon_intro zenon_H194 | zenon_intro zenon_H195 ]. % 15.22/15.42 cut (((op (e3) (op (e0) (e3))) = (op (e3) (op (e0) (e3)))) = ((op (e3) (e2)) = (op (e3) (op (e0) (e3))))). % 15.22/15.42 intro zenon_D_pnotp. % 15.22/15.42 apply zenon_H23c. % 15.22/15.42 rewrite <- zenon_D_pnotp. % 15.22/15.42 exact zenon_H194. % 15.22/15.42 cut (((op (e3) (op (e0) (e3))) = (op (e3) (op (e0) (e3))))); [idtac | apply NNPP; zenon_intro zenon_H195]. % 15.22/15.42 cut (((op (e3) (op (e0) (e3))) = (op (e3) (e2)))); [idtac | apply NNPP; zenon_intro zenon_H23d]. % 15.22/15.42 congruence. % 15.22/15.42 cut (((op (e0) (e3)) = (e2))); [idtac | apply NNPP; zenon_intro zenon_Ha9]. % 15.22/15.42 cut (((e3) = (e3))); [idtac | apply NNPP; zenon_intro zenon_H4d]. % 15.22/15.42 congruence. % 15.22/15.42 apply zenon_H4d. apply refl_equal. % 15.22/15.42 exact (zenon_Ha9 zenon_H81). % 15.22/15.42 apply zenon_H195. apply refl_equal. % 15.22/15.42 apply zenon_H195. apply refl_equal. % 15.22/15.42 apply zenon_H23b. apply sym_equal. exact zenon_H81. % 15.22/15.42 (* end of lemma zenon_L483_ *) % 15.22/15.42 assert (zenon_L484_ : ((~((op (e1) (e1)) = (e1)))\/((op (e1) (e1)) = (e1))) -> (~((op (e1) (e0)) = (op (e1) (e1)))) -> ((~((op (e1) (e1)) = (e3)))\/((op (e1) (e3)) = (e1))) -> ((op (e1) (e0)) = (e1)) -> (~((op (e1) (e0)) = (op (e1) (e3)))) -> (~((op (e0) (e1)) = (op (e1) (e1)))) -> ((op (e0) (e1)) = (e0)) -> (((op (e1) (e1)) = (e0))\/(((op (e1) (e1)) = (e1))\/(((op (e1) (e1)) = (e2))\/((op (e1) (e1)) = (e3))))) -> (~((op (e1) (e0)) = (op (e1) (e2)))) -> ((~((op (e1) (e1)) = (e2)))\/((op (e1) (e2)) = (e1))) -> False). % 15.22/15.42 do 0 intro. intros zenon_H1d8 zenon_Hd7 zenon_H1d2 zenon_Hd8 zenon_H1cf zenon_H23 zenon_H49 zenon_H1b3 zenon_H166 zenon_H1d3. % 15.22/15.42 apply (zenon_or_s _ _ zenon_H1d8); [ zenon_intro zenon_H1b4 | zenon_intro zenon_H21 ]. % 15.22/15.42 apply (zenon_L444_); trivial. % 15.22/15.42 apply (zenon_L61_); trivial. % 15.22/15.42 (* end of lemma zenon_L484_ *) % 15.22/15.42 assert (zenon_L485_ : (~((op (e0) (e1)) = (op (e0) (e2)))) -> ((op (e0) (e1)) = (e0)) -> ((op (e0) (e2)) = (e0)) -> False). % 15.22/15.42 do 0 intro. intros zenon_H23e zenon_H49 zenon_Hab. % 15.22/15.42 cut (((op (e0) (e1)) = (e0)) = ((op (e0) (e1)) = (op (e0) (e2)))). % 15.22/15.42 intro zenon_D_pnotp. % 15.22/15.42 apply zenon_H23e. % 15.22/15.42 rewrite <- zenon_D_pnotp. % 15.22/15.42 exact zenon_H49. % 15.22/15.42 cut (((e0) = (op (e0) (e2)))); [idtac | apply NNPP; zenon_intro zenon_H20d]. % 15.22/15.42 cut (((op (e0) (e1)) = (op (e0) (e1)))); [idtac | apply NNPP; zenon_intro zenon_He1]. % 15.22/15.42 congruence. % 15.22/15.42 apply zenon_He1. apply refl_equal. % 15.22/15.42 apply zenon_H20d. apply sym_equal. exact zenon_Hab. % 15.22/15.42 (* end of lemma zenon_L485_ *) % 15.22/15.42 assert (zenon_L486_ : (((op (e1) (e0)) = (e2))\/(((op (e1) (e1)) = (e2))\/(((op (e1) (e2)) = (e2))\/((op (e1) (e3)) = (e2))))) -> (~((op (e3) (e3)) = (e3))) -> (~((op (e3) (e3)) = (e2))) -> (~((op (e3) (e3)) = (e1))) -> (((op (e3) (e3)) = (e0))\/(((op (e3) (e3)) = (e1))\/(((op (e3) (e3)) = (e2))\/((op (e3) (e3)) = (e3))))) -> (~((op (e1) (e1)) = (e1))) -> (~((op (e1) (e1)) = (e0))) -> (((op (e1) (e1)) = (e0))\/(((op (e1) (e1)) = (e1))\/(((op (e1) (e1)) = (e2))\/((op (e1) (e1)) = (e3))))) -> (~((op (e1) (e1)) = (e2))) -> (~((op (e1) (e2)) = (op (e2) (e2)))) -> ((op (e2) (e2)) = (e2)) -> ((op (e1) (e3)) = (e1)) -> (~((e1) = (e2))) -> False). % 15.22/15.42 do 0 intro. intros zenon_H84 zenon_H3e zenon_H3d zenon_H104 zenon_H3b zenon_H1b4 zenon_H145 zenon_H1b3 zenon_Hd6 zenon_H7d zenon_H35 zenon_H11f zenon_Ha7. % 15.22/15.42 apply (zenon_or_s _ _ zenon_H84); [ zenon_intro zenon_H68 | zenon_intro zenon_H85 ]. % 15.22/15.42 apply (zenon_L357_); trivial. % 15.22/15.42 apply (zenon_or_s _ _ zenon_H85); [ zenon_intro zenon_H6e | zenon_intro zenon_H86 ]. % 15.22/15.42 exact (zenon_Hd6 zenon_H6e). % 15.22/15.42 apply (zenon_or_s _ _ zenon_H86); [ zenon_intro zenon_H7c | zenon_intro zenon_H82 ]. % 15.22/15.42 apply (zenon_L21_); trivial. % 15.22/15.42 apply (zenon_L209_); trivial. % 15.22/15.42 (* end of lemma zenon_L486_ *) % 15.22/15.42 assert (zenon_L487_ : ((~((op (e3) (e3)) = (e3)))\/((op (e3) (e3)) = (e3))) -> (~((op (e0) (e0)) = (e0))) -> (((op (e0) (e0)) = (e1))\/(((op (e0) (e1)) = (e1))\/(((op (e0) (e2)) = (e1))\/((op (e0) (e3)) = (e1))))) -> (((op (e0) (e3)) = (e0))\/(((op (e1) (e3)) = (e0))\/(((op (e2) (e3)) = (e0))\/((op (e3) (e3)) = (e0))))) -> (~((op (e3) (e3)) = (e0))) -> (~((op (e0) (e1)) = (op (e0) (e3)))) -> (((op (e0) (e3)) = (e2))\/(((op (e1) (e3)) = (e2))\/(((op (e2) (e3)) = (e2))\/((op (e3) (e3)) = (e2))))) -> (~((e1) = (e3))) -> (~((e0) = (e1))) -> (~((op (e0) (e0)) = (e2))) -> (~((e0) = (e2))) -> (~((op (e0) (e2)) = (op (e2) (e2)))) -> (((op (e0) (e0)) = (e3))\/(((op (e0) (e1)) = (e3))\/(((op (e0) (e2)) = (e3))\/((op (e0) (e3)) = (e3))))) -> (~((op (e0) (e3)) = (op (e3) (e3)))) -> (~((op (e0) (e3)) = (op (e1) (e3)))) -> (~((e2) = (e3))) -> (~((op (e0) (e2)) = (op (e1) (e2)))) -> (~((op (e1) (e3)) = (op (e3) (e3)))) -> (((op (e1) (e0)) = (e3))\/(((op (e1) (e1)) = (e3))\/(((op (e1) (e2)) = (e3))\/((op (e1) (e3)) = (e3))))) -> (~((e0) = (e3))) -> (~((op (e0) (e0)) = (e3))) -> (((op (e0) (e0)) = (e2))\/(((op (e0) (e1)) = (e2))\/(((op (e0) (e2)) = (e2))\/((op (e0) (e3)) = (e2))))) -> (~((op (e0) (e0)) = (e1))) -> (~((op (e2) (e2)) = (op (e2) (e3)))) -> (((op (e0) (e0)) = (e0))\/(((op (e0) (e1)) = (e0))\/(((op (e0) (e2)) = (e0))\/((op (e0) (e3)) = (e0))))) -> (((op (e1) (e1)) = (e0))\/(((op (e1) (e1)) = (e1))\/(((op (e1) (e1)) = (e2))\/((op (e1) (e1)) = (e3))))) -> (~((op (e3) (e3)) = (e1))) -> (~((op (e3) (e3)) = (e2))) -> (((op (e3) (e3)) = (e0))\/(((op (e3) (e3)) = (e1))\/(((op (e3) (e3)) = (e2))\/((op (e3) (e3)) = (e3))))) -> (~((op (e1) (e1)) = (e2))) -> (~((op (e1) (e1)) = (e1))) -> (~((op (e1) (e1)) = (e0))) -> (~((op (e1) (e2)) = (op (e2) (e2)))) -> ((op (e2) (e2)) = (e2)) -> (~((e1) = (e2))) -> ((op (e1) (e3)) = (e1)) -> (((op (e1) (e0)) = (e2))\/(((op (e1) (e1)) = (e2))\/(((op (e1) (e2)) = (e2))\/((op (e1) (e3)) = (e2))))) -> False). % 15.22/15.42 do 0 intro. intros zenon_H10d zenon_H20 zenon_H44 zenon_Hd3 zenon_H3c zenon_H1cd zenon_H160 zenon_Ha3 zenon_H9e zenon_H8f zenon_H5e zenon_H28 zenon_H58 zenon_H36 zenon_H80 zenon_H6a zenon_H87 zenon_H8b zenon_H90 zenon_H4b zenon_H59 zenon_H8e zenon_H45 zenon_H15f zenon_H110 zenon_H1b3 zenon_H104 zenon_H3d zenon_H3b zenon_Hd6 zenon_H1b4 zenon_H145 zenon_H7d zenon_H35 zenon_Ha7 zenon_H11f zenon_H84. % 15.22/15.42 apply (zenon_or_s _ _ zenon_H10d); [ zenon_intro zenon_H3e | zenon_intro zenon_H42 ]. % 15.22/15.42 apply (zenon_L486_); trivial. % 15.22/15.42 apply (zenon_L425_); trivial. % 15.22/15.42 (* end of lemma zenon_L487_ *) % 15.22/15.42 assert (zenon_L488_ : ((op (e1) (e2)) = (e0)) -> ((op (e3) (e3)) = (e2)) -> ((op (e1) (e1)) = (e3)) -> False). % 15.22/15.42 do 0 intro. intros zenon_H15d zenon_H43 zenon_H96. % 15.22/15.42 apply (zenon_notand_s _ _ ax22); [ zenon_intro zenon_H1a7 | zenon_intro zenon_H23f ]. % 15.22/15.42 elim (classic ((op (op (e1) (e1)) (op (e1) (e1))) = (op (op (e1) (e1)) (op (e1) (e1))))); [ zenon_intro zenon_H1a8 | zenon_intro zenon_H1a9 ]. % 15.22/15.42 cut (((op (op (e1) (e1)) (op (e1) (e1))) = (op (op (e1) (e1)) (op (e1) (e1)))) = ((e2) = (op (op (e1) (e1)) (op (e1) (e1))))). % 15.22/15.42 intro zenon_D_pnotp. % 15.22/15.42 apply zenon_H1a7. % 15.22/15.42 rewrite <- zenon_D_pnotp. % 15.22/15.42 exact zenon_H1a8. % 15.22/15.42 cut (((op (op (e1) (e1)) (op (e1) (e1))) = (op (op (e1) (e1)) (op (e1) (e1))))); [idtac | apply NNPP; zenon_intro zenon_H1a9]. % 15.22/15.42 cut (((op (op (e1) (e1)) (op (e1) (e1))) = (e2))); [idtac | apply NNPP; zenon_intro zenon_H1aa]. % 15.22/15.42 congruence. % 15.22/15.42 cut (((op (e3) (e3)) = (e2)) = ((op (op (e1) (e1)) (op (e1) (e1))) = (e2))). % 15.22/15.42 intro zenon_D_pnotp. % 15.22/15.42 apply zenon_H1aa. % 15.22/15.42 rewrite <- zenon_D_pnotp. % 15.22/15.42 exact zenon_H43. % 15.22/15.42 cut (((e2) = (e2))); [idtac | apply NNPP; zenon_intro zenon_H60]. % 15.22/15.42 cut (((op (e3) (e3)) = (op (op (e1) (e1)) (op (e1) (e1))))); [idtac | apply NNPP; zenon_intro zenon_H220]. % 15.22/15.42 congruence. % 15.22/15.42 elim (classic ((op (op (e1) (e1)) (op (e1) (e1))) = (op (op (e1) (e1)) (op (e1) (e1))))); [ zenon_intro zenon_H1a8 | zenon_intro zenon_H1a9 ]. % 15.22/15.42 cut (((op (op (e1) (e1)) (op (e1) (e1))) = (op (op (e1) (e1)) (op (e1) (e1)))) = ((op (e3) (e3)) = (op (op (e1) (e1)) (op (e1) (e1))))). % 15.22/15.42 intro zenon_D_pnotp. % 15.22/15.42 apply zenon_H220. % 15.22/15.42 rewrite <- zenon_D_pnotp. % 15.22/15.42 exact zenon_H1a8. % 15.22/15.42 cut (((op (op (e1) (e1)) (op (e1) (e1))) = (op (op (e1) (e1)) (op (e1) (e1))))); [idtac | apply NNPP; zenon_intro zenon_H1a9]. % 15.22/15.42 cut (((op (op (e1) (e1)) (op (e1) (e1))) = (op (e3) (e3)))); [idtac | apply NNPP; zenon_intro zenon_H21c]. % 15.22/15.42 congruence. % 15.22/15.42 apply (zenon_L355_); trivial. % 15.22/15.42 apply zenon_H1a9. apply refl_equal. % 15.22/15.42 apply zenon_H1a9. apply refl_equal. % 15.22/15.42 apply zenon_H60. apply refl_equal. % 15.22/15.42 apply zenon_H1a9. apply refl_equal. % 15.22/15.42 apply zenon_H1a9. apply refl_equal. % 15.22/15.42 apply (zenon_notand_s _ _ zenon_H23f); [ zenon_intro zenon_H222 | zenon_intro zenon_H1bc ]. % 15.22/15.42 apply zenon_H222. apply sym_equal. exact zenon_H96. % 15.22/15.42 elim (classic ((op (e1) (op (op (e1) (e1)) (op (e1) (e1)))) = (op (e1) (op (op (e1) (e1)) (op (e1) (e1)))))); [ zenon_intro zenon_H1ae | zenon_intro zenon_H1af ]. % 15.22/15.42 cut (((op (e1) (op (op (e1) (e1)) (op (e1) (e1)))) = (op (e1) (op (op (e1) (e1)) (op (e1) (e1))))) = ((e0) = (op (e1) (op (op (e1) (e1)) (op (e1) (e1)))))). % 15.22/15.42 intro zenon_D_pnotp. % 15.22/15.42 apply zenon_H1bc. % 15.22/15.42 rewrite <- zenon_D_pnotp. % 15.22/15.42 exact zenon_H1ae. % 15.22/15.42 cut (((op (e1) (op (op (e1) (e1)) (op (e1) (e1)))) = (op (e1) (op (op (e1) (e1)) (op (e1) (e1)))))); [idtac | apply NNPP; zenon_intro zenon_H1af]. % 15.22/15.42 cut (((op (e1) (op (op (e1) (e1)) (op (e1) (e1)))) = (e0))); [idtac | apply NNPP; zenon_intro zenon_H1be]. % 15.22/15.42 congruence. % 15.22/15.42 cut (((op (e1) (e2)) = (e0)) = ((op (e1) (op (op (e1) (e1)) (op (e1) (e1)))) = (e0))). % 15.22/15.42 intro zenon_D_pnotp. % 15.22/15.42 apply zenon_H1be. % 15.22/15.42 rewrite <- zenon_D_pnotp. % 15.22/15.42 exact zenon_H15d. % 15.22/15.42 cut (((e0) = (e0))); [idtac | apply NNPP; zenon_intro zenon_H1d]. % 15.22/15.42 cut (((op (e1) (e2)) = (op (e1) (op (op (e1) (e1)) (op (e1) (e1)))))); [idtac | apply NNPP; zenon_intro zenon_H1b1]. % 15.22/15.42 congruence. % 15.22/15.42 elim (classic ((op (e1) (op (op (e1) (e1)) (op (e1) (e1)))) = (op (e1) (op (op (e1) (e1)) (op (e1) (e1)))))); [ zenon_intro zenon_H1ae | zenon_intro zenon_H1af ]. % 15.22/15.42 cut (((op (e1) (op (op (e1) (e1)) (op (e1) (e1)))) = (op (e1) (op (op (e1) (e1)) (op (e1) (e1))))) = ((op (e1) (e2)) = (op (e1) (op (op (e1) (e1)) (op (e1) (e1)))))). % 15.22/15.42 intro zenon_D_pnotp. % 15.22/15.42 apply zenon_H1b1. % 15.22/15.42 rewrite <- zenon_D_pnotp. % 15.22/15.42 exact zenon_H1ae. % 15.22/15.42 cut (((op (e1) (op (op (e1) (e1)) (op (e1) (e1)))) = (op (e1) (op (op (e1) (e1)) (op (e1) (e1)))))); [idtac | apply NNPP; zenon_intro zenon_H1af]. % 15.22/15.42 cut (((op (e1) (op (op (e1) (e1)) (op (e1) (e1)))) = (op (e1) (e2)))); [idtac | apply NNPP; zenon_intro zenon_H1b2]. % 15.22/15.42 congruence. % 15.22/15.42 cut (((op (op (e1) (e1)) (op (e1) (e1))) = (e2))); [idtac | apply NNPP; zenon_intro zenon_H1aa]. % 15.22/15.42 cut (((e1) = (e1))); [idtac | apply NNPP; zenon_intro zenon_Ha0]. % 15.22/15.42 congruence. % 15.22/15.42 apply zenon_Ha0. apply refl_equal. % 15.22/15.42 cut (((op (e3) (e3)) = (e2)) = ((op (op (e1) (e1)) (op (e1) (e1))) = (e2))). % 15.22/15.42 intro zenon_D_pnotp. % 15.22/15.42 apply zenon_H1aa. % 15.22/15.42 rewrite <- zenon_D_pnotp. % 15.22/15.42 exact zenon_H43. % 15.22/15.42 cut (((e2) = (e2))); [idtac | apply NNPP; zenon_intro zenon_H60]. % 15.22/15.42 cut (((op (e3) (e3)) = (op (op (e1) (e1)) (op (e1) (e1))))); [idtac | apply NNPP; zenon_intro zenon_H220]. % 15.22/15.42 congruence. % 15.22/15.42 elim (classic ((op (op (e1) (e1)) (op (e1) (e1))) = (op (op (e1) (e1)) (op (e1) (e1))))); [ zenon_intro zenon_H1a8 | zenon_intro zenon_H1a9 ]. % 15.22/15.42 cut (((op (op (e1) (e1)) (op (e1) (e1))) = (op (op (e1) (e1)) (op (e1) (e1)))) = ((op (e3) (e3)) = (op (op (e1) (e1)) (op (e1) (e1))))). % 15.22/15.42 intro zenon_D_pnotp. % 15.22/15.42 apply zenon_H220. % 15.22/15.42 rewrite <- zenon_D_pnotp. % 15.22/15.42 exact zenon_H1a8. % 15.22/15.42 cut (((op (op (e1) (e1)) (op (e1) (e1))) = (op (op (e1) (e1)) (op (e1) (e1))))); [idtac | apply NNPP; zenon_intro zenon_H1a9]. % 15.22/15.42 cut (((op (op (e1) (e1)) (op (e1) (e1))) = (op (e3) (e3)))); [idtac | apply NNPP; zenon_intro zenon_H21c]. % 15.22/15.42 congruence. % 15.22/15.42 apply (zenon_L355_); trivial. % 15.22/15.42 apply zenon_H1a9. apply refl_equal. % 15.22/15.42 apply zenon_H1a9. apply refl_equal. % 15.22/15.42 apply zenon_H60. apply refl_equal. % 15.22/15.42 apply zenon_H1af. apply refl_equal. % 15.22/15.42 apply zenon_H1af. apply refl_equal. % 15.22/15.42 apply zenon_H1d. apply refl_equal. % 15.22/15.42 apply zenon_H1af. apply refl_equal. % 15.22/15.42 apply zenon_H1af. apply refl_equal. % 15.22/15.42 (* end of lemma zenon_L488_ *) % 15.22/15.42 assert (zenon_L489_ : (((op (e3) (e3)) = (e0))\/(((op (e3) (e3)) = (e1))\/(((op (e3) (e3)) = (e2))\/((op (e3) (e3)) = (e3))))) -> (~((op (e3) (e3)) = (e0))) -> (~((op (e3) (e3)) = (e1))) -> ((op (e1) (e1)) = (e3)) -> ((op (e1) (e2)) = (e0)) -> (~((op (e3) (e3)) = (e3))) -> False). % 15.22/15.42 do 0 intro. intros zenon_H3b zenon_H3c zenon_H104 zenon_H96 zenon_H15d zenon_H3e. % 15.22/15.42 apply (zenon_or_s _ _ zenon_H3b); [ zenon_intro zenon_H40 | zenon_intro zenon_H3f ]. % 15.22/15.42 exact (zenon_H3c zenon_H40). % 15.22/15.42 apply (zenon_or_s _ _ zenon_H3f); [ zenon_intro zenon_H38 | zenon_intro zenon_H41 ]. % 15.22/15.42 exact (zenon_H104 zenon_H38). % 15.22/15.42 apply (zenon_or_s _ _ zenon_H41); [ zenon_intro zenon_H43 | zenon_intro zenon_H42 ]. % 15.22/15.42 apply (zenon_L488_); trivial. % 15.22/15.42 exact (zenon_H3e zenon_H42). % 15.22/15.42 (* end of lemma zenon_L489_ *) % 15.22/15.42 assert (zenon_L490_ : (((op (e1) (e1)) = (e0))\/(((op (e1) (e1)) = (e1))\/(((op (e1) (e1)) = (e2))\/((op (e1) (e1)) = (e3))))) -> (~((op (e1) (e1)) = (e0))) -> (~((op (e1) (e1)) = (e1))) -> (~((op (e1) (e1)) = (e2))) -> (((op (e3) (e3)) = (e0))\/(((op (e3) (e3)) = (e1))\/(((op (e3) (e3)) = (e2))\/((op (e3) (e3)) = (e3))))) -> (~((op (e3) (e3)) = (e0))) -> (~((op (e3) (e3)) = (e1))) -> ((op (e1) (e2)) = (e0)) -> (~((op (e3) (e3)) = (e3))) -> False). % 15.22/15.42 do 0 intro. intros zenon_H1b3 zenon_H145 zenon_H1b4 zenon_Hd6 zenon_H3b zenon_H3c zenon_H104 zenon_H15d zenon_H3e. % 15.22/15.42 apply (zenon_or_s _ _ zenon_H1b3); [ zenon_intro zenon_H149 | zenon_intro zenon_H1b5 ]. % 15.22/15.42 exact (zenon_H145 zenon_H149). % 15.22/15.42 apply (zenon_or_s _ _ zenon_H1b5); [ zenon_intro zenon_H21 | zenon_intro zenon_H1b6 ]. % 15.22/15.42 exact (zenon_H1b4 zenon_H21). % 15.22/15.42 apply (zenon_or_s _ _ zenon_H1b6); [ zenon_intro zenon_H6e | zenon_intro zenon_H96 ]. % 15.22/15.42 exact (zenon_Hd6 zenon_H6e). % 15.22/15.42 apply (zenon_L489_); trivial. % 15.22/15.42 (* end of lemma zenon_L490_ *) % 15.22/15.42 assert (zenon_L491_ : (((op (e1) (e0)) = (e0))\/(((op (e1) (e1)) = (e0))\/(((op (e1) (e2)) = (e0))\/((op (e1) (e3)) = (e0))))) -> (~((e1) = (e2))) -> (~((op (e1) (op (e0) (e1))) = (op (e0) (e1)))) -> ((op (e0) (e1)) = (e2)) -> (~((e0) = (e2))) -> (((op (e1) (e0)) = (e2))\/(((op (e1) (e1)) = (e2))\/(((op (e1) (e2)) = (e2))\/((op (e1) (e3)) = (e2))))) -> (~((op (e3) (e3)) = (e3))) -> (~((op (e3) (e3)) = (e1))) -> (~((op (e3) (e3)) = (e0))) -> (((op (e3) (e3)) = (e0))\/(((op (e3) (e3)) = (e1))\/(((op (e3) (e3)) = (e2))\/((op (e3) (e3)) = (e3))))) -> (~((op (e1) (e1)) = (e2))) -> (~((op (e1) (e1)) = (e1))) -> (~((op (e1) (e1)) = (e0))) -> (((op (e1) (e1)) = (e0))\/(((op (e1) (e1)) = (e1))\/(((op (e1) (e1)) = (e2))\/((op (e1) (e1)) = (e3))))) -> (~((e0) = (e1))) -> ((op (e1) (e3)) = (e1)) -> False). % 15.22/15.42 do 0 intro. intros zenon_H163 zenon_Ha7 zenon_H1ff zenon_H5d zenon_H5e zenon_H84 zenon_H3e zenon_H104 zenon_H3c zenon_H3b zenon_Hd6 zenon_H1b4 zenon_H145 zenon_H1b3 zenon_H9e zenon_H11f. % 15.22/15.42 apply (zenon_or_s _ _ zenon_H163); [ zenon_intro zenon_Had | zenon_intro zenon_H164 ]. % 15.22/15.42 apply (zenon_L388_); trivial. % 15.22/15.42 apply (zenon_or_s _ _ zenon_H164); [ zenon_intro zenon_H149 | zenon_intro zenon_H165 ]. % 15.22/15.42 exact (zenon_H145 zenon_H149). % 15.22/15.42 apply (zenon_or_s _ _ zenon_H165); [ zenon_intro zenon_H15d | zenon_intro zenon_Hcc ]. % 15.22/15.42 apply (zenon_L490_); trivial. % 15.22/15.42 apply (zenon_L208_); trivial. % 15.22/15.42 (* end of lemma zenon_L491_ *) % 15.22/15.42 assert (zenon_L492_ : ((~((op (e3) (e3)) = (e3)))\/((op (e3) (e3)) = (e3))) -> ((op (e3) (e2)) = (e3)) -> (~((op (e3) (e2)) = (op (e3) (e3)))) -> (~((op (e0) (e0)) = (e2))) -> (((op (e1) (e0)) = (e0))\/(((op (e1) (e1)) = (e0))\/(((op (e1) (e2)) = (e0))\/((op (e1) (e3)) = (e0))))) -> (~((e0) = (e1))) -> (~((op (e1) (e1)) = (e1))) -> (((op (e3) (e3)) = (e0))\/(((op (e3) (e3)) = (e1))\/(((op (e3) (e3)) = (e2))\/((op (e3) (e3)) = (e3))))) -> (~((op (e3) (e3)) = (e1))) -> (~((op (e3) (e3)) = (e0))) -> (((op (e1) (e1)) = (e0))\/(((op (e1) (e1)) = (e1))\/(((op (e1) (e1)) = (e2))\/((op (e1) (e1)) = (e3))))) -> (~((op (e1) (e1)) = (e0))) -> (~((e0) = (e2))) -> (~((op (e1) (e1)) = (e2))) -> (~((op (e1) (op (e0) (e1))) = (op (e0) (e1)))) -> (~((e1) = (e2))) -> ((op (e1) (e3)) = (e1)) -> (((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)) = (e2)) -> (~((op (e0) (e3)) = (op (e3) (e3)))) -> (((op (e0) (e0)) = (e2))\/(((op (e0) (e1)) = (e2))\/(((op (e0) (e2)) = (e2))\/((op (e0) (e3)) = (e2))))) -> False). % 15.22/15.42 do 0 intro. intros zenon_H10d zenon_H106 zenon_H173 zenon_H8f zenon_H163 zenon_H9e zenon_H1b4 zenon_H3b zenon_H104 zenon_H3c zenon_H1b3 zenon_H145 zenon_H5e zenon_Hd6 zenon_H1ff zenon_Ha7 zenon_H11f zenon_H84 zenon_H28 zenon_H35 zenon_H36 zenon_H8e. % 15.22/15.42 apply (zenon_or_s _ _ zenon_H10d); [ zenon_intro zenon_H3e | zenon_intro zenon_H42 ]. % 15.22/15.42 apply (zenon_or_s _ _ zenon_H8e); [ zenon_intro zenon_H92 | zenon_intro zenon_H91 ]. % 15.22/15.42 exact (zenon_H8f zenon_H92). % 15.22/15.42 apply (zenon_or_s _ _ zenon_H91); [ zenon_intro zenon_H5d | zenon_intro zenon_H93 ]. % 15.22/15.42 apply (zenon_L491_); trivial. % 15.22/15.42 apply (zenon_or_s _ _ zenon_H93); [ zenon_intro zenon_H63 | zenon_intro zenon_H81 ]. % 15.22/15.42 apply (zenon_L15_); trivial. % 15.22/15.42 apply (zenon_L107_); trivial. % 15.22/15.42 apply (zenon_L153_); trivial. % 15.22/15.42 (* end of lemma zenon_L492_ *) % 15.22/15.42 assert (zenon_L493_ : (((op (e0) (e1)) = (e2))\/(((op (e1) (e1)) = (e2))\/(((op (e2) (e1)) = (e2))\/((op (e3) (e1)) = (e2))))) -> (~((op (e3) (e3)) = (e2))) -> (~((op (e2) (e2)) = (op (e2) (e3)))) -> ((op (e2) (e2)) = (e2)) -> ((op (e1) (e3)) = (e1)) -> (~((e1) = (e2))) -> (~((op (e0) (e1)) = (op (e0) (e3)))) -> (((op (e0) (e3)) = (e2))\/(((op (e1) (e3)) = (e2))\/(((op (e2) (e3)) = (e2))\/((op (e3) (e3)) = (e2))))) -> (~((op (e1) (e1)) = (e2))) -> ((op (e2) (e1)) = (e0)) -> (~((e0) = (e2))) -> (~((e2) = (e3))) -> ((op (e3) (e1)) = (e3)) -> False). % 15.22/15.42 do 0 intro. intros zenon_H1a2 zenon_H3d zenon_H15f zenon_H35 zenon_H11f zenon_Ha7 zenon_H1cd zenon_H160 zenon_Hd6 zenon_H14a zenon_H5e zenon_H6a zenon_H10a. % 15.22/15.42 apply (zenon_or_s _ _ zenon_H1a2); [ zenon_intro zenon_H5d | zenon_intro zenon_H1a3 ]. % 15.22/15.42 apply (zenon_L423_); trivial. % 15.22/15.42 apply (zenon_or_s _ _ zenon_H1a3); [ zenon_intro zenon_H6e | zenon_intro zenon_H1a4 ]. % 15.22/15.42 exact (zenon_Hd6 zenon_H6e). % 15.22/15.42 apply (zenon_or_s _ _ zenon_H1a4); [ zenon_intro zenon_H156 | zenon_intro zenon_H16a ]. % 15.22/15.42 apply (zenon_L351_); trivial. % 15.22/15.42 apply (zenon_L297_); trivial. % 15.22/15.42 (* end of lemma zenon_L493_ *) % 15.22/15.42 assert (zenon_L494_ : ((~((op (e3) (e3)) = (e2)))\/((op (e3) (e2)) = (e3))) -> (~((op (e3) (e1)) = (op (e3) (e2)))) -> (((op (e0) (e1)) = (e2))\/(((op (e1) (e1)) = (e2))\/(((op (e2) (e1)) = (e2))\/((op (e3) (e1)) = (e2))))) -> ((op (e3) (e1)) = (e3)) -> (~((e2) = (e3))) -> ((op (e2) (e2)) = (e2)) -> (~((op (e2) (e1)) = (op (e2) (e2)))) -> (~((op (e1) (e1)) = (e2))) -> (~((e0) = (e2))) -> (~((op (e1) (e1)) = (e0))) -> (~((op (e0) (e1)) = (op (e0) (e3)))) -> (~((e1) = (e2))) -> ((op (e1) (e3)) = (e1)) -> (~((op (e2) (e2)) = (op (e2) (e3)))) -> (((op (e0) (e3)) = (e2))\/(((op (e1) (e3)) = (e2))\/(((op (e2) (e3)) = (e2))\/((op (e3) (e3)) = (e2))))) -> (~((e0) = (e3))) -> (((op (e0) (e1)) = (e0))\/(((op (e1) (e1)) = (e0))\/(((op (e2) (e1)) = (e0))\/((op (e3) (e1)) = (e0))))) -> False). % 15.22/15.42 do 0 intro. intros zenon_H10e zenon_H135 zenon_H1a2 zenon_H10a zenon_H6a zenon_H35 zenon_H157 zenon_Hd6 zenon_H5e zenon_H145 zenon_H1cd zenon_Ha7 zenon_H11f zenon_H15f zenon_H160 zenon_H4b zenon_H144. % 15.22/15.42 apply (zenon_or_s _ _ zenon_H10e); [ zenon_intro zenon_H3d | zenon_intro zenon_H106 ]. % 15.22/15.42 apply (zenon_or_s _ _ zenon_H144); [ zenon_intro zenon_H49 | zenon_intro zenon_H147 ]. % 15.22/15.42 apply (zenon_L349_); trivial. % 15.22/15.42 apply (zenon_or_s _ _ zenon_H147); [ zenon_intro zenon_H149 | zenon_intro zenon_H148 ]. % 15.22/15.42 exact (zenon_H145 zenon_H149). % 15.22/15.42 apply (zenon_or_s _ _ zenon_H148); [ zenon_intro zenon_H14a | zenon_intro zenon_H142 ]. % 15.22/15.42 apply (zenon_L493_); trivial. % 15.22/15.42 apply (zenon_L126_); trivial. % 15.22/15.42 apply (zenon_L115_); trivial. % 15.22/15.42 (* end of lemma zenon_L494_ *) % 15.22/15.42 assert (zenon_L495_ : ((~((op (e3) (e3)) = (e3)))\/((op (e3) (e3)) = (e3))) -> (~((op (e0) (e0)) = (e0))) -> (((op (e0) (e0)) = (e1))\/(((op (e0) (e1)) = (e1))\/(((op (e0) (e2)) = (e1))\/((op (e0) (e3)) = (e1))))) -> (~((e1) = (e3))) -> (~((e0) = (e1))) -> (~((e0) = (e2))) -> (((op (e0) (e0)) = (e3))\/(((op (e0) (e1)) = (e3))\/(((op (e0) (e2)) = (e3))\/((op (e0) (e3)) = (e3))))) -> (~((e2) = (e3))) -> (~((e0) = (e3))) -> (~((op (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 (e0) (e2)) = (op (e1) (e2)))) -> (~((e1) = (e2))) -> ((op (e1) (e2)) = (e1)) -> (~((op (e0) (e3)) = (op (e1) (e3)))) -> (((op (e1) (e0)) = (e2))\/(((op (e1) (e1)) = (e2))\/(((op (e1) (e2)) = (e2))\/((op (e1) (e3)) = (e2))))) -> (((op (e0) (e2)) = (e3))\/(((op (e1) (e2)) = (e3))\/(((op (e2) (e2)) = (e3))\/((op (e3) (e2)) = (e3))))) -> (~((op (e3) (e2)) = (op (e3) (e3)))) -> (~((op (e2) (e2)) = (e3))) -> ((~((op (e1) (e1)) = (e3)))\/((op (e1) (e3)) = (e1))) -> (~((op (e1) (e2)) = (op (e1) (e3)))) -> (((op (e0) (e0)) = (e0))\/(((op (e0) (e1)) = (e0))\/(((op (e0) (e2)) = (e0))\/((op (e0) (e3)) = (e0))))) -> (~((op (e0) (e0)) = (e2))) -> (((op (e1) (e1)) = (e0))\/(((op (e1) (e1)) = (e1))\/(((op (e1) (e1)) = (e2))\/((op (e1) (e1)) = (e3))))) -> (~((op (e1) (e1)) = (e3))) -> (~((op (e0) (e1)) = (op (e1) (e1)))) -> (~((op (e1) (e1)) = (e1))) -> (~((op (e1) (e1)) = (e0))) -> (~((op (e0) (e2)) = (op (e2) (e2)))) -> ((op (e2) (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)) = (e1))) -> (~((op (e3) (e3)) = (e0))) -> (((op (e0) (e0)) = (e2))\/(((op (e0) (e1)) = (e2))\/(((op (e0) (e2)) = (e2))\/((op (e0) (e3)) = (e2))))) -> False). % 15.22/15.42 do 0 intro. intros zenon_H10d zenon_H20 zenon_H44 zenon_Ha3 zenon_H9e zenon_H5e zenon_H58 zenon_H6a zenon_H4b zenon_H59 zenon_H90 zenon_H8b zenon_H87 zenon_Ha7 zenon_H117 zenon_H80 zenon_H84 zenon_H175 zenon_H173 zenon_H30 zenon_H1d2 zenon_H1d0 zenon_H110 zenon_H8f zenon_H1b3 zenon_H182 zenon_H23 zenon_H1b4 zenon_H145 zenon_H28 zenon_H35 zenon_H3b zenon_H36 zenon_H104 zenon_H3c zenon_H8e. % 15.22/15.42 apply (zenon_or_s _ _ zenon_H10d); [ zenon_intro zenon_H3e | zenon_intro zenon_H42 ]. % 15.22/15.42 apply (zenon_L345_); trivial. % 15.22/15.42 apply (zenon_L439_); trivial. % 15.22/15.42 (* end of lemma zenon_L495_ *) % 15.22/15.42 assert (zenon_L496_ : (~((e0) = (e1))) -> ((op (e1) (e2)) = (e1)) -> ((op (e1) (e2)) = (e0)) -> False). % 15.22/15.42 do 0 intro. intros zenon_H9e zenon_H117 zenon_H15d. % 15.22/15.42 cut (((op (e1) (e2)) = (e1)) = ((e0) = (e1))). % 15.22/15.42 intro zenon_D_pnotp. % 15.22/15.42 apply zenon_H9e. % 15.22/15.42 rewrite <- zenon_D_pnotp. % 15.22/15.42 exact zenon_H117. % 15.22/15.42 cut (((e1) = (e1))); [idtac | apply NNPP; zenon_intro zenon_Ha0]. % 15.22/15.42 cut (((op (e1) (e2)) = (e0))); [idtac | apply NNPP; zenon_intro zenon_H240]. % 15.22/15.42 congruence. % 15.22/15.42 exact (zenon_H240 zenon_H15d). % 15.22/15.42 apply zenon_Ha0. apply refl_equal. % 15.22/15.42 (* end of lemma zenon_L496_ *) % 15.22/15.42 assert (zenon_L497_ : ((op (e3) (e2)) = (e0)) -> ((op (e1) (e1)) = (e2)) -> ((op (e3) (e3)) = (e1)) -> False). % 15.22/15.42 do 0 intro. intros zenon_H167 zenon_H6e zenon_H38. % 15.22/15.42 apply (zenon_notand_s _ _ ax20); [ zenon_intro zenon_H1ee | zenon_intro zenon_H241 ]. % 15.22/15.42 elim (classic ((op (op (e3) (e3)) (op (e3) (e3))) = (op (op (e3) (e3)) (op (e3) (e3))))); [ zenon_intro zenon_H186 | zenon_intro zenon_H187 ]. % 15.22/15.42 cut (((op (op (e3) (e3)) (op (e3) (e3))) = (op (op (e3) (e3)) (op (e3) (e3)))) = ((e2) = (op (op (e3) (e3)) (op (e3) (e3))))). % 15.22/15.42 intro zenon_D_pnotp. % 15.22/15.42 apply zenon_H1ee. % 15.22/15.42 rewrite <- zenon_D_pnotp. % 15.22/15.42 exact zenon_H186. % 15.22/15.42 cut (((op (op (e3) (e3)) (op (e3) (e3))) = (op (op (e3) (e3)) (op (e3) (e3))))); [idtac | apply NNPP; zenon_intro zenon_H187]. % 15.22/15.42 cut (((op (op (e3) (e3)) (op (e3) (e3))) = (e2))); [idtac | apply NNPP; zenon_intro zenon_H1ef]. % 15.22/15.42 congruence. % 15.22/15.42 cut (((op (e1) (e1)) = (e2)) = ((op (op (e3) (e3)) (op (e3) (e3))) = (e2))). % 15.22/15.42 intro zenon_D_pnotp. % 15.22/15.42 apply zenon_H1ef. % 15.22/15.42 rewrite <- zenon_D_pnotp. % 15.22/15.42 exact zenon_H6e. % 15.22/15.42 cut (((e2) = (e2))); [idtac | apply NNPP; zenon_intro zenon_H60]. % 15.22/15.42 cut (((op (e1) (e1)) = (op (op (e3) (e3)) (op (e3) (e3))))); [idtac | apply NNPP; zenon_intro zenon_H233]. % 15.22/15.42 congruence. % 15.22/15.42 elim (classic ((op (op (e3) (e3)) (op (e3) (e3))) = (op (op (e3) (e3)) (op (e3) (e3))))); [ zenon_intro zenon_H186 | zenon_intro zenon_H187 ]. % 15.22/15.42 cut (((op (op (e3) (e3)) (op (e3) (e3))) = (op (op (e3) (e3)) (op (e3) (e3)))) = ((op (e1) (e1)) = (op (op (e3) (e3)) (op (e3) (e3))))). % 15.22/15.42 intro zenon_D_pnotp. % 15.22/15.42 apply zenon_H233. % 15.22/15.42 rewrite <- zenon_D_pnotp. % 15.22/15.42 exact zenon_H186. % 15.22/15.42 cut (((op (op (e3) (e3)) (op (e3) (e3))) = (op (op (e3) (e3)) (op (e3) (e3))))); [idtac | apply NNPP; zenon_intro zenon_H187]. % 15.22/15.42 cut (((op (op (e3) (e3)) (op (e3) (e3))) = (op (e1) (e1)))); [idtac | apply NNPP; zenon_intro zenon_H231]. % 15.22/15.42 congruence. % 15.22/15.42 apply (zenon_L403_); trivial. % 15.22/15.42 apply zenon_H187. apply refl_equal. % 15.22/15.42 apply zenon_H187. apply refl_equal. % 15.22/15.42 apply zenon_H60. apply refl_equal. % 15.22/15.42 apply zenon_H187. apply refl_equal. % 15.22/15.42 apply zenon_H187. apply refl_equal. % 15.22/15.42 apply (zenon_notand_s _ _ zenon_H241); [ zenon_intro zenon_H39 | zenon_intro zenon_H18a ]. % 15.22/15.42 apply zenon_H39. apply sym_equal. exact zenon_H38. % 15.22/15.42 elim (classic ((op (e3) (op (op (e3) (e3)) (op (e3) (e3)))) = (op (e3) (op (op (e3) (e3)) (op (e3) (e3)))))); [ zenon_intro zenon_H18b | zenon_intro zenon_H18c ]. % 15.22/15.42 cut (((op (e3) (op (op (e3) (e3)) (op (e3) (e3)))) = (op (e3) (op (op (e3) (e3)) (op (e3) (e3))))) = ((e0) = (op (e3) (op (op (e3) (e3)) (op (e3) (e3)))))). % 15.22/15.42 intro zenon_D_pnotp. % 15.22/15.42 apply zenon_H18a. % 15.22/15.42 rewrite <- zenon_D_pnotp. % 15.22/15.42 exact zenon_H18b. % 15.22/15.42 cut (((op (e3) (op (op (e3) (e3)) (op (e3) (e3)))) = (op (e3) (op (op (e3) (e3)) (op (e3) (e3)))))); [idtac | apply NNPP; zenon_intro zenon_H18c]. % 15.22/15.42 cut (((op (e3) (op (op (e3) (e3)) (op (e3) (e3)))) = (e0))); [idtac | apply NNPP; zenon_intro zenon_H18d]. % 15.22/15.42 congruence. % 15.22/15.42 cut (((op (e3) (e2)) = (e0)) = ((op (e3) (op (op (e3) (e3)) (op (e3) (e3)))) = (e0))). % 15.22/15.42 intro zenon_D_pnotp. % 15.22/15.42 apply zenon_H18d. % 15.22/15.42 rewrite <- zenon_D_pnotp. % 15.22/15.42 exact zenon_H167. % 15.22/15.42 cut (((e0) = (e0))); [idtac | apply NNPP; zenon_intro zenon_H1d]. % 15.22/15.42 cut (((op (e3) (e2)) = (op (e3) (op (op (e3) (e3)) (op (e3) (e3)))))); [idtac | apply NNPP; zenon_intro zenon_H1f2]. % 15.22/15.42 congruence. % 15.22/15.42 elim (classic ((op (e3) (op (op (e3) (e3)) (op (e3) (e3)))) = (op (e3) (op (op (e3) (e3)) (op (e3) (e3)))))); [ zenon_intro zenon_H18b | zenon_intro zenon_H18c ]. % 15.22/15.42 cut (((op (e3) (op (op (e3) (e3)) (op (e3) (e3)))) = (op (e3) (op (op (e3) (e3)) (op (e3) (e3))))) = ((op (e3) (e2)) = (op (e3) (op (op (e3) (e3)) (op (e3) (e3)))))). % 15.22/15.42 intro zenon_D_pnotp. % 15.22/15.42 apply zenon_H1f2. % 15.22/15.42 rewrite <- zenon_D_pnotp. % 15.22/15.42 exact zenon_H18b. % 15.22/15.42 cut (((op (e3) (op (op (e3) (e3)) (op (e3) (e3)))) = (op (e3) (op (op (e3) (e3)) (op (e3) (e3)))))); [idtac | apply NNPP; zenon_intro zenon_H18c]. % 15.22/15.42 cut (((op (e3) (op (op (e3) (e3)) (op (e3) (e3)))) = (op (e3) (e2)))); [idtac | apply NNPP; zenon_intro zenon_H1f3]. % 15.22/15.42 congruence. % 15.22/15.42 cut (((op (op (e3) (e3)) (op (e3) (e3))) = (e2))); [idtac | apply NNPP; zenon_intro zenon_H1ef]. % 15.22/15.42 cut (((e3) = (e3))); [idtac | apply NNPP; zenon_intro zenon_H4d]. % 15.22/15.42 congruence. % 15.22/15.42 apply zenon_H4d. apply refl_equal. % 15.22/15.42 cut (((op (e1) (e1)) = (e2)) = ((op (op (e3) (e3)) (op (e3) (e3))) = (e2))). % 15.22/15.42 intro zenon_D_pnotp. % 15.22/15.42 apply zenon_H1ef. % 15.22/15.42 rewrite <- zenon_D_pnotp. % 15.22/15.42 exact zenon_H6e. % 15.22/15.42 cut (((e2) = (e2))); [idtac | apply NNPP; zenon_intro zenon_H60]. % 15.22/15.42 cut (((op (e1) (e1)) = (op (op (e3) (e3)) (op (e3) (e3))))); [idtac | apply NNPP; zenon_intro zenon_H233]. % 15.22/15.42 congruence. % 15.22/15.42 elim (classic ((op (op (e3) (e3)) (op (e3) (e3))) = (op (op (e3) (e3)) (op (e3) (e3))))); [ zenon_intro zenon_H186 | zenon_intro zenon_H187 ]. % 15.22/15.42 cut (((op (op (e3) (e3)) (op (e3) (e3))) = (op (op (e3) (e3)) (op (e3) (e3)))) = ((op (e1) (e1)) = (op (op (e3) (e3)) (op (e3) (e3))))). % 15.22/15.42 intro zenon_D_pnotp. % 15.22/15.42 apply zenon_H233. % 15.22/15.42 rewrite <- zenon_D_pnotp. % 15.22/15.42 exact zenon_H186. % 15.22/15.42 cut (((op (op (e3) (e3)) (op (e3) (e3))) = (op (op (e3) (e3)) (op (e3) (e3))))); [idtac | apply NNPP; zenon_intro zenon_H187]. % 15.22/15.42 cut (((op (op (e3) (e3)) (op (e3) (e3))) = (op (e1) (e1)))); [idtac | apply NNPP; zenon_intro zenon_H231]. % 15.22/15.42 congruence. % 15.22/15.42 apply (zenon_L403_); trivial. % 15.22/15.42 apply zenon_H187. apply refl_equal. % 15.22/15.42 apply zenon_H187. apply refl_equal. % 15.22/15.42 apply zenon_H60. apply refl_equal. % 15.22/15.42 apply zenon_H18c. apply refl_equal. % 15.22/15.42 apply zenon_H18c. apply refl_equal. % 15.22/15.42 apply zenon_H1d. apply refl_equal. % 15.22/15.42 apply zenon_H18c. apply refl_equal. % 15.22/15.42 apply zenon_H18c. apply refl_equal. % 15.22/15.42 (* end of lemma zenon_L497_ *) % 15.22/15.42 assert (zenon_L498_ : (((op (e3) (e3)) = (e0))\/(((op (e3) (e3)) = (e1))\/(((op (e3) (e3)) = (e2))\/((op (e3) (e3)) = (e3))))) -> (~((op (e3) (e3)) = (e0))) -> ((op (e1) (e1)) = (e2)) -> ((op (e3) (e2)) = (e0)) -> (~((op (e3) (e3)) = (e2))) -> (~((op (e3) (e3)) = (e3))) -> False). % 15.22/15.42 do 0 intro. intros zenon_H3b zenon_H3c zenon_H6e zenon_H167 zenon_H3d zenon_H3e. % 15.22/15.42 apply (zenon_or_s _ _ zenon_H3b); [ zenon_intro zenon_H40 | zenon_intro zenon_H3f ]. % 15.22/15.42 exact (zenon_H3c zenon_H40). % 15.22/15.42 apply (zenon_or_s _ _ zenon_H3f); [ zenon_intro zenon_H38 | zenon_intro zenon_H41 ]. % 15.22/15.42 apply (zenon_L497_); trivial. % 15.22/15.42 apply (zenon_or_s _ _ zenon_H41); [ zenon_intro zenon_H43 | zenon_intro zenon_H42 ]. % 15.22/15.42 exact (zenon_H3d zenon_H43). % 15.22/15.42 exact (zenon_H3e zenon_H42). % 15.22/15.42 (* end of lemma zenon_L498_ *) % 15.22/15.42 assert (zenon_L499_ : (((op (e0) (e2)) = (e0))\/(((op (e1) (e2)) = (e0))\/(((op (e2) (e2)) = (e0))\/((op (e3) (e2)) = (e0))))) -> (~((e0) = (e3))) -> ((op (e0) (e2)) = (e3)) -> ((op (e1) (e2)) = (e1)) -> (~((e0) = (e1))) -> (~((op (e2) (e2)) = (e0))) -> (((op (e3) (e3)) = (e0))\/(((op (e3) (e3)) = (e1))\/(((op (e3) (e3)) = (e2))\/((op (e3) (e3)) = (e3))))) -> (~((op (e3) (e3)) = (e0))) -> ((op (e1) (e1)) = (e2)) -> (~((op (e3) (e3)) = (e2))) -> (~((op (e3) (e3)) = (e3))) -> False). % 15.22/15.42 do 0 intro. intros zenon_H16f zenon_H4b zenon_H50 zenon_H117 zenon_H9e zenon_H2e zenon_H3b zenon_H3c zenon_H6e zenon_H3d zenon_H3e. % 15.22/15.42 apply (zenon_or_s _ _ zenon_H16f); [ zenon_intro zenon_Hab | zenon_intro zenon_H170 ]. % 15.22/15.42 apply (zenon_L48_); trivial. % 15.22/15.42 apply (zenon_or_s _ _ zenon_H170); [ zenon_intro zenon_H15d | zenon_intro zenon_H171 ]. % 15.22/15.42 apply (zenon_L496_); trivial. % 15.22/15.42 apply (zenon_or_s _ _ zenon_H171); [ zenon_intro zenon_H32 | zenon_intro zenon_H167 ]. % 15.22/15.42 exact (zenon_H2e zenon_H32). % 15.22/15.42 apply (zenon_L498_); trivial. % 15.22/15.42 (* end of lemma zenon_L499_ *) % 15.22/15.42 assert (zenon_L500_ : (((op (e0) (e1)) = (e2))\/(((op (e1) (e1)) = (e2))\/(((op (e2) (e1)) = (e2))\/((op (e3) (e1)) = (e2))))) -> (~((op (e1) (e1)) = (e3))) -> (~((op (e0) (e1)) = (op (e1) (e1)))) -> (~((op (e1) (e1)) = (e1))) -> (~((op (e1) (e1)) = (e0))) -> (((op (e1) (e1)) = (e0))\/(((op (e1) (e1)) = (e1))\/(((op (e1) (e1)) = (e2))\/((op (e1) (e1)) = (e3))))) -> (~((op (e3) (e1)) = (op (e3) (e2)))) -> (~((op (e2) (e2)) = (e3))) -> ((op (e1) (e2)) = (e1)) -> (~((e1) = (e3))) -> (((op (e0) (e2)) = (e0))\/(((op (e1) (e2)) = (e0))\/(((op (e2) (e2)) = (e0))\/((op (e3) (e2)) = (e0))))) -> (~((e0) = (e3))) -> (~((e0) = (e1))) -> (~((op (e2) (e2)) = (e0))) -> (((op (e3) (e3)) = (e0))\/(((op (e3) (e3)) = (e1))\/(((op (e3) (e3)) = (e2))\/((op (e3) (e3)) = (e3))))) -> (~((op (e3) (e3)) = (e0))) -> (~((op (e3) (e3)) = (e2))) -> (~((op (e3) (e3)) = (e3))) -> (((op (e0) (e2)) = (e3))\/(((op (e1) (e2)) = (e3))\/(((op (e2) (e2)) = (e3))\/((op (e3) (e2)) = (e3))))) -> ((op (e2) (e1)) = (e0)) -> (~((e0) = (e2))) -> (~((e2) = (e3))) -> ((op (e3) (e1)) = (e3)) -> False). % 15.22/15.42 do 0 intro. intros zenon_H1a2 zenon_H182 zenon_H23 zenon_H1b4 zenon_H145 zenon_H1b3 zenon_H135 zenon_H30 zenon_H117 zenon_Ha3 zenon_H16f zenon_H4b zenon_H9e zenon_H2e zenon_H3b zenon_H3c zenon_H3d zenon_H3e zenon_H175 zenon_H14a zenon_H5e zenon_H6a zenon_H10a. % 15.22/15.42 apply (zenon_or_s _ _ zenon_H1a2); [ zenon_intro zenon_H5d | zenon_intro zenon_H1a3 ]. % 15.22/15.42 apply (zenon_L214_); trivial. % 15.22/15.42 apply (zenon_or_s _ _ zenon_H1a3); [ zenon_intro zenon_H6e | zenon_intro zenon_H1a4 ]. % 15.22/15.42 apply (zenon_or_s _ _ zenon_H175); [ zenon_intro zenon_H50 | zenon_intro zenon_H176 ]. % 15.22/15.42 apply (zenon_L499_); trivial. % 15.22/15.42 apply (zenon_or_s _ _ zenon_H176); [ zenon_intro zenon_H88 | zenon_intro zenon_H177 ]. % 15.22/15.42 apply (zenon_L196_); trivial. % 15.22/15.42 apply (zenon_or_s _ _ zenon_H177); [ zenon_intro zenon_H34 | zenon_intro zenon_H106 ]. % 15.22/15.42 exact (zenon_H30 zenon_H34). % 15.22/15.42 apply (zenon_L115_); trivial. % 15.22/15.42 apply (zenon_or_s _ _ zenon_H1a4); [ zenon_intro zenon_H156 | zenon_intro zenon_H16a ]. % 15.22/15.42 apply (zenon_L351_); trivial. % 15.22/15.42 apply (zenon_L297_); trivial. % 15.22/15.42 (* end of lemma zenon_L500_ *) % 15.22/15.42 assert (zenon_L501_ : (((op (e0) (e2)) = (e3))\/(((op (e1) (e2)) = (e3))\/(((op (e2) (e2)) = (e3))\/((op (e3) (e2)) = (e3))))) -> ((op (e0) (e2)) = (e1)) -> (~((e1) = (e3))) -> ((op (e1) (e2)) = (e1)) -> (~((op (e2) (e2)) = (e3))) -> (~((op (e3) (e1)) = (op (e3) (e2)))) -> ((op (e3) (e1)) = (e3)) -> False). % 15.22/15.43 do 0 intro. intros zenon_H175 zenon_H29 zenon_Ha3 zenon_H117 zenon_H30 zenon_H135 zenon_H10a. % 15.22/15.43 apply (zenon_or_s _ _ zenon_H175); [ zenon_intro zenon_H50 | zenon_intro zenon_H176 ]. % 15.22/15.43 apply (zenon_L29_); trivial. % 15.22/15.43 apply (zenon_or_s _ _ zenon_H176); [ zenon_intro zenon_H88 | zenon_intro zenon_H177 ]. % 15.22/15.43 apply (zenon_L196_); trivial. % 15.22/15.43 apply (zenon_or_s _ _ zenon_H177); [ zenon_intro zenon_H34 | zenon_intro zenon_H106 ]. % 15.22/15.43 exact (zenon_H30 zenon_H34). % 15.22/15.43 apply (zenon_L115_); trivial. % 15.22/15.43 (* end of lemma zenon_L501_ *) % 15.22/15.43 assert (zenon_L502_ : ((~((op (e3) (e3)) = (e2)))\/((op (e3) (e2)) = (e3))) -> (((op (e0) (e0)) = (e1))\/(((op (e0) (e1)) = (e1))\/(((op (e0) (e2)) = (e1))\/((op (e0) (e3)) = (e1))))) -> (~((op (e0) (e3)) = (op (e3) (e3)))) -> (~((e0) = (e1))) -> (~((op (e1) (e1)) = (e0))) -> (((op (e0) (e1)) = (e2))\/(((op (e1) (e1)) = (e2))\/(((op (e2) (e1)) = (e2))\/((op (e3) (e1)) = (e2))))) -> (~((e2) = (e3))) -> (~((e0) = (e2))) -> (((op (e0) (e2)) = (e0))\/(((op (e1) (e2)) = (e0))\/(((op (e2) (e2)) = (e0))\/((op (e3) (e2)) = (e0))))) -> (~((op (e3) (e3)) = (e0))) -> (((op (e3) (e3)) = (e0))\/(((op (e3) (e3)) = (e1))\/(((op (e3) (e3)) = (e2))\/((op (e3) (e3)) = (e3))))) -> (~((op (e2) (e2)) = (e0))) -> ((op (e1) (e2)) = (e1)) -> (~((e0) = (e3))) -> (~((e1) = (e3))) -> (~((op (e2) (e2)) = (e3))) -> (~((op (e3) (e1)) = (op (e3) (e2)))) -> ((op (e3) (e1)) = (e3)) -> (((op (e0) (e2)) = (e3))\/(((op (e1) (e2)) = (e3))\/(((op (e2) (e2)) = (e3))\/((op (e3) (e2)) = (e3))))) -> (~((op (e1) (e1)) = (e1))) -> (~((op (e0) (e1)) = (op (e1) (e1)))) -> (~((op (e1) (e1)) = (e3))) -> (((op (e1) (e1)) = (e0))\/(((op (e1) (e1)) = (e1))\/(((op (e1) (e1)) = (e2))\/((op (e1) (e1)) = (e3))))) -> (((op (e0) (e1)) = (e0))\/(((op (e1) (e1)) = (e0))\/(((op (e2) (e1)) = (e0))\/((op (e3) (e1)) = (e0))))) -> (~((op (e0) (e0)) = (e1))) -> (~((op (e3) (e1)) = (op (e3) (e3)))) -> ((~((op (e3) (e3)) = (e3)))\/((op (e3) (e3)) = (e3))) -> False). % 15.22/15.43 do 0 intro. intros zenon_H10e zenon_H44 zenon_H36 zenon_H9e zenon_H145 zenon_H1a2 zenon_H6a zenon_H5e zenon_H16f zenon_H3c zenon_H3b zenon_H2e zenon_H117 zenon_H4b zenon_Ha3 zenon_H30 zenon_H135 zenon_H10a zenon_H175 zenon_H1b4 zenon_H23 zenon_H182 zenon_H1b3 zenon_H144 zenon_H45 zenon_H12d zenon_H10d. % 15.22/15.43 apply (zenon_or_s _ _ zenon_H10e); [ zenon_intro zenon_H3d | zenon_intro zenon_H106 ]. % 15.22/15.43 apply (zenon_or_s _ _ zenon_H10d); [ zenon_intro zenon_H3e | zenon_intro zenon_H42 ]. % 15.22/15.43 apply (zenon_or_s _ _ zenon_H44); [ zenon_intro zenon_H47 | zenon_intro zenon_H46 ]. % 15.22/15.43 exact (zenon_H45 zenon_H47). % 15.22/15.43 apply (zenon_or_s _ _ zenon_H46); [ zenon_intro zenon_H22 | zenon_intro zenon_H48 ]. % 15.22/15.43 apply (zenon_or_s _ _ zenon_H144); [ zenon_intro zenon_H49 | zenon_intro zenon_H147 ]. % 15.22/15.43 apply (zenon_L27_); trivial. % 15.22/15.43 apply (zenon_or_s _ _ zenon_H147); [ zenon_intro zenon_H149 | zenon_intro zenon_H148 ]. % 15.22/15.43 exact (zenon_H145 zenon_H149). % 15.22/15.43 apply (zenon_or_s _ _ zenon_H148); [ zenon_intro zenon_H14a | zenon_intro zenon_H142 ]. % 15.22/15.43 apply (zenon_L500_); trivial. % 15.22/15.43 apply (zenon_L126_); trivial. % 15.22/15.43 apply (zenon_or_s _ _ zenon_H48); [ zenon_intro zenon_H29 | zenon_intro zenon_H37 ]. % 15.22/15.43 apply (zenon_L501_); trivial. % 15.22/15.43 apply (zenon_L7_); trivial. % 15.22/15.43 apply (zenon_L102_); trivial. % 15.22/15.43 apply (zenon_L115_); trivial. % 15.22/15.43 (* end of lemma zenon_L502_ *) % 15.22/15.43 assert (zenon_L503_ : ((~((op (e3) (e3)) = (e1)))\/((op (e3) (e1)) = (e3))) -> (~((op (e3) (e1)) = (op (e3) (e3)))) -> (~((op (e0) (e0)) = (e1))) -> (((op (e0) (e1)) = (e0))\/(((op (e1) (e1)) = (e0))\/(((op (e2) (e1)) = (e0))\/((op (e3) (e1)) = (e0))))) -> (~((op (e3) (e1)) = (op (e3) (e2)))) -> (~((op (e2) (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 (e3) (e3)) = (e2)))\/((op (e3) (e2)) = (e3))) -> (((op (e0) (e0)) = (e2))\/(((op (e0) (e1)) = (e2))\/(((op (e0) (e2)) = (e2))\/((op (e0) (e3)) = (e2))))) -> (~((op (e3) (e3)) = (e0))) -> (~((op (e0) (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) (e2)) = (op (e2) (e2)))) -> (~((op (e1) (e1)) = (e0))) -> (~((op (e1) (e1)) = (e1))) -> (~((op (e0) (e1)) = (op (e1) (e1)))) -> (~((op (e1) (e1)) = (e3))) -> (((op (e1) (e1)) = (e0))\/(((op (e1) (e1)) = (e1))\/(((op (e1) (e1)) = (e2))\/((op (e1) (e1)) = (e3))))) -> (~((op (e0) (e0)) = (e2))) -> (((op (e0) (e0)) = (e0))\/(((op (e0) (e1)) = (e0))\/(((op (e0) (e2)) = (e0))\/((op (e0) (e3)) = (e0))))) -> (~((op (e1) (e2)) = (op (e1) (e3)))) -> ((~((op (e1) (e1)) = (e3)))\/((op (e1) (e3)) = (e1))) -> (~((op (e2) (e2)) = (e3))) -> (~((op (e3) (e2)) = (op (e3) (e3)))) -> (((op (e0) (e2)) = (e3))\/(((op (e1) (e2)) = (e3))\/(((op (e2) (e2)) = (e3))\/((op (e3) (e2)) = (e3))))) -> (((op (e1) (e0)) = (e2))\/(((op (e1) (e1)) = (e2))\/(((op (e1) (e2)) = (e2))\/((op (e1) (e3)) = (e2))))) -> (~((op (e0) (e3)) = (op (e1) (e3)))) -> ((op (e1) (e2)) = (e1)) -> (~((e1) = (e2))) -> (~((op (e0) (e2)) = (op (e1) (e2)))) -> (~((op (e1) (e3)) = (op (e3) (e3)))) -> (((op (e1) (e0)) = (e3))\/(((op (e1) (e1)) = (e3))\/(((op (e1) (e2)) = (e3))\/((op (e1) (e3)) = (e3))))) -> (~((op (e0) (e0)) = (e3))) -> (~((e0) = (e3))) -> (~((e2) = (e3))) -> (((op (e0) (e0)) = (e3))\/(((op (e0) (e1)) = (e3))\/(((op (e0) (e2)) = (e3))\/((op (e0) (e3)) = (e3))))) -> (~((e0) = (e2))) -> (~((e0) = (e1))) -> (~((e1) = (e3))) -> (((op (e0) (e0)) = (e1))\/(((op (e0) (e1)) = (e1))\/(((op (e0) (e2)) = (e1))\/((op (e0) (e3)) = (e1))))) -> (~((op (e0) (e0)) = (e0))) -> ((~((op (e3) (e3)) = (e3)))\/((op (e3) (e3)) = (e3))) -> False). % 15.22/15.43 do 0 intro. intros zenon_H10c zenon_H12d zenon_H45 zenon_H144 zenon_H135 zenon_H2e zenon_H16f zenon_H1a2 zenon_H10e zenon_H8e zenon_H3c zenon_H36 zenon_H3b zenon_H35 zenon_H28 zenon_H145 zenon_H1b4 zenon_H23 zenon_H182 zenon_H1b3 zenon_H8f zenon_H110 zenon_H1d0 zenon_H1d2 zenon_H30 zenon_H173 zenon_H175 zenon_H84 zenon_H80 zenon_H117 zenon_Ha7 zenon_H87 zenon_H8b zenon_H90 zenon_H59 zenon_H4b zenon_H6a zenon_H58 zenon_H5e zenon_H9e zenon_Ha3 zenon_H44 zenon_H20 zenon_H10d. % 15.22/15.43 apply (zenon_or_s _ _ zenon_H10c); [ zenon_intro zenon_H104 | zenon_intro zenon_H10a ]. % 15.22/15.43 apply (zenon_L495_); trivial. % 15.22/15.43 apply (zenon_L502_); trivial. % 15.22/15.43 (* end of lemma zenon_L503_ *) % 15.22/15.43 assert (zenon_L504_ : (((op (e0) (e1)) = (e2))\/(((op (e1) (e1)) = (e2))\/(((op (e2) (e1)) = (e2))\/((op (e3) (e1)) = (e2))))) -> (~((op (e0) (e1)) = (op (e0) (e3)))) -> ((op (e0) (e3)) = (e2)) -> ((op (e0) (e0)) = (e1)) -> ((op (e0) (e2)) = (e3)) -> ((op (e3) (e0)) = (e3)) -> (~((op (e3) (e0)) = (op (e3) (e1)))) -> (~((e2) = (e3))) -> (~((op (e1) (e1)) = (e3))) -> ((op (e0) (e1)) = (e0)) -> (~((e0) = (e3))) -> (((op (e0) (e1)) = (e3))\/(((op (e1) (e1)) = (e3))\/(((op (e2) (e1)) = (e3))\/((op (e3) (e1)) = (e3))))) -> ((op (e3) (e1)) = (e1)) -> (~((e1) = (e2))) -> False). % 15.22/15.43 do 0 intro. intros zenon_H1a2 zenon_H1cd zenon_H81 zenon_H47 zenon_H50 zenon_Hba zenon_H109 zenon_H6a zenon_H182 zenon_H49 zenon_H4b zenon_H199 zenon_H13e zenon_Ha7. % 15.22/15.43 apply (zenon_or_s _ _ zenon_H1a2); [ zenon_intro zenon_H5d | zenon_intro zenon_H1a3 ]. % 15.22/15.43 apply (zenon_L350_); trivial. % 15.22/15.43 apply (zenon_or_s _ _ zenon_H1a3); [ zenon_intro zenon_H6e | zenon_intro zenon_H1a4 ]. % 15.22/15.43 apply (zenon_L20_); trivial. % 15.22/15.43 apply (zenon_or_s _ _ zenon_H1a4); [ zenon_intro zenon_H156 | zenon_intro zenon_H16a ]. % 15.22/15.43 apply (zenon_L184_); trivial. % 15.22/15.43 apply (zenon_L414_); trivial. % 15.22/15.43 (* end of lemma zenon_L504_ *) % 15.22/15.43 assert (zenon_L505_ : (((op (e0) (e0)) = (e3))\/(((op (e0) (e1)) = (e3))\/(((op (e0) (e2)) = (e3))\/((op (e0) (e3)) = (e3))))) -> (~((op (e0) (e0)) = (e3))) -> (~((e0) = (e3))) -> ((op (e0) (e1)) = (e0)) -> (~((e1) = (e3))) -> ((op (e0) (e2)) = (e1)) -> ((op (e0) (e3)) = (e2)) -> (~((e2) = (e3))) -> False). % 15.22/15.43 do 0 intro. intros zenon_H58 zenon_H59 zenon_H4b zenon_H49 zenon_Ha3 zenon_H29 zenon_H81 zenon_H6a. % 15.22/15.43 apply (zenon_or_s _ _ zenon_H58); [ zenon_intro zenon_H5b | zenon_intro zenon_H5a ]. % 15.22/15.43 exact (zenon_H59 zenon_H5b). % 15.22/15.43 apply (zenon_or_s _ _ zenon_H5a); [ zenon_intro zenon_H4a | zenon_intro zenon_H5c ]. % 15.22/15.43 apply (zenon_L9_); trivial. % 15.22/15.43 apply (zenon_or_s _ _ zenon_H5c); [ zenon_intro zenon_H50 | zenon_intro zenon_H53 ]. % 15.22/15.43 apply (zenon_L29_); trivial. % 15.22/15.43 apply (zenon_L128_); trivial. % 15.22/15.43 (* end of lemma zenon_L505_ *) % 15.22/15.43 assert (zenon_L506_ : (((op (e0) (e0)) = (e1))\/(((op (e0) (e1)) = (e1))\/(((op (e0) (e2)) = (e1))\/((op (e0) (e3)) = (e1))))) -> (((op (e0) (e1)) = (e1))\/(((op (e1) (e1)) = (e1))\/(((op (e2) (e1)) = (e1))\/((op (e3) (e1)) = (e1))))) -> (~((op (e3) (e3)) = (e3))) -> (~((op (e3) (e3)) = (e2))) -> (~((op (e3) (e3)) = (e1))) -> (((op (e0) (e0)) = (e0))\/(((op (e0) (e0)) = (e1))\/(((op (e0) (e0)) = (e2))\/((op (e0) (e0)) = (e3))))) -> (~((op (e0) (e0)) = (e0))) -> (((op (e3) (e3)) = (e0))\/(((op (e3) (e3)) = (e1))\/(((op (e3) (e3)) = (e2))\/((op (e3) (e3)) = (e3))))) -> (((op (e0) (e1)) = (e2))\/(((op (e1) (e1)) = (e2))\/(((op (e2) (e1)) = (e2))\/((op (e3) (e1)) = (e2))))) -> (~((op (e0) (e1)) = (op (e0) (e3)))) -> ((op (e3) (e0)) = (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))) -> (~((e0) = (e1))) -> (~((e2) = (e3))) -> (~((e1) = (e3))) -> ((op (e0) (e1)) = (e0)) -> (~((e0) = (e3))) -> (~((op (e0) (e0)) = (e3))) -> (((op (e0) (e0)) = (e3))\/(((op (e0) (e1)) = (e3))\/(((op (e0) (e2)) = (e3))\/((op (e0) (e3)) = (e3))))) -> (((op (e0) (e0)) = (e2))\/(((op (e0) (e1)) = (e2))\/(((op (e0) (e2)) = (e2))\/((op (e0) (e3)) = (e2))))) -> (~((op (e0) (e0)) = (e2))) -> (~((op (e1) (e1)) = (e3))) -> (~((op (e0) (e1)) = (op (e1) (e1)))) -> (~((op (e1) (e1)) = (e1))) -> (~((op (e1) (e1)) = (e0))) -> (((op (e1) (e1)) = (e0))\/(((op (e1) (e1)) = (e1))\/(((op (e1) (e1)) = (e2))\/((op (e1) (e1)) = (e3))))) -> (~((op (e0) (e2)) = (op (e2) (e2)))) -> ((op (e2) (e2)) = (e2)) -> (~((e1) = (e2))) -> False). % 15.22/15.43 do 0 intro. intros zenon_H44 zenon_H228 zenon_H3e zenon_H3d zenon_H104 zenon_H12a zenon_H20 zenon_H3b zenon_H1a2 zenon_H1cd zenon_Hba zenon_H109 zenon_H199 zenon_H5e zenon_H9e zenon_H6a zenon_Ha3 zenon_H49 zenon_H4b zenon_H59 zenon_H58 zenon_H8e zenon_H8f zenon_H182 zenon_H23 zenon_H1b4 zenon_H145 zenon_H1b3 zenon_H28 zenon_H35 zenon_Ha7. % 15.22/15.43 apply (zenon_or_s _ _ zenon_H44); [ zenon_intro zenon_H47 | zenon_intro zenon_H46 ]. % 15.22/15.43 apply (zenon_or_s _ _ zenon_H8e); [ zenon_intro zenon_H92 | zenon_intro zenon_H91 ]. % 15.22/15.43 exact (zenon_H8f zenon_H92). % 15.22/15.43 apply (zenon_or_s _ _ zenon_H91); [ zenon_intro zenon_H5d | zenon_intro zenon_H93 ]. % 15.22/15.43 apply (zenon_L14_); trivial. % 15.22/15.43 apply (zenon_or_s _ _ zenon_H93); [ zenon_intro zenon_H63 | zenon_intro zenon_H81 ]. % 15.22/15.43 apply (zenon_L15_); trivial. % 15.22/15.43 apply (zenon_or_s _ _ zenon_H58); [ zenon_intro zenon_H5b | zenon_intro zenon_H5a ]. % 15.22/15.43 exact (zenon_H59 zenon_H5b). % 15.22/15.43 apply (zenon_or_s _ _ zenon_H5a); [ zenon_intro zenon_H4a | zenon_intro zenon_H5c ]. % 15.22/15.43 apply (zenon_L9_); trivial. % 15.22/15.43 apply (zenon_or_s _ _ zenon_H5c); [ zenon_intro zenon_H50 | zenon_intro zenon_H53 ]. % 15.22/15.43 apply (zenon_or_s _ _ zenon_H228); [ zenon_intro zenon_H22 | zenon_intro zenon_H229 ]. % 15.22/15.43 apply (zenon_L27_); trivial. % 15.22/15.43 apply (zenon_or_s _ _ zenon_H229); [ zenon_intro zenon_H21 | zenon_intro zenon_H22a ]. % 15.22/15.43 exact (zenon_H1b4 zenon_H21). % 15.22/15.43 apply (zenon_or_s _ _ zenon_H22a); [ zenon_intro zenon_Hb2 | zenon_intro zenon_H13e ]. % 15.22/15.43 apply (zenon_or_s _ _ zenon_H1a2); [ zenon_intro zenon_H5d | zenon_intro zenon_H1a3 ]. % 15.22/15.43 apply (zenon_L350_); trivial. % 15.22/15.43 apply (zenon_or_s _ _ zenon_H1a3); [ zenon_intro zenon_H6e | zenon_intro zenon_H1a4 ]. % 15.22/15.43 apply (zenon_L20_); trivial. % 15.22/15.43 apply (zenon_or_s _ _ zenon_H1a4); [ zenon_intro zenon_H156 | zenon_intro zenon_H16a ]. % 15.22/15.43 apply (zenon_L372_); trivial. % 15.22/15.43 apply (zenon_L188_); trivial. % 15.22/15.43 apply (zenon_L504_); trivial. % 15.22/15.43 apply (zenon_L128_); trivial. % 15.22/15.43 apply (zenon_or_s _ _ zenon_H46); [ zenon_intro zenon_H22 | zenon_intro zenon_H48 ]. % 15.22/15.43 apply (zenon_L27_); trivial. % 15.22/15.43 apply (zenon_or_s _ _ zenon_H48); [ zenon_intro zenon_H29 | zenon_intro zenon_H37 ]. % 15.22/15.43 apply (zenon_or_s _ _ zenon_H8e); [ zenon_intro zenon_H92 | zenon_intro zenon_H91 ]. % 15.22/15.43 exact (zenon_H8f zenon_H92). % 15.22/15.43 apply (zenon_or_s _ _ zenon_H91); [ zenon_intro zenon_H5d | zenon_intro zenon_H93 ]. % 15.22/15.43 apply (zenon_L214_); trivial. % 15.22/15.43 apply (zenon_or_s _ _ zenon_H93); [ zenon_intro zenon_H63 | zenon_intro zenon_H81 ]. % 15.22/15.43 apply (zenon_L104_); trivial. % 15.22/15.43 apply (zenon_L505_); trivial. % 15.22/15.43 apply (zenon_L380_); trivial. % 15.22/15.43 (* end of lemma zenon_L506_ *) % 15.22/15.43 assert (zenon_L507_ : (((op (e0) (e2)) = (e3))\/(((op (e1) (e2)) = (e3))\/(((op (e2) (e2)) = (e3))\/((op (e3) (e2)) = (e3))))) -> (~((e0) = (e3))) -> ((op (e0) (e2)) = (e0)) -> (~((e1) = (e3))) -> ((op (e1) (e2)) = (e1)) -> (~((op (e2) (e2)) = (e3))) -> (~((op (e3) (e0)) = (op (e3) (e2)))) -> ((op (e3) (e0)) = (e3)) -> False). % 15.22/15.43 do 0 intro. intros zenon_H175 zenon_H4b zenon_Hab zenon_Ha3 zenon_H117 zenon_H30 zenon_H105 zenon_Hba. % 15.22/15.43 apply (zenon_or_s _ _ zenon_H175); [ zenon_intro zenon_H50 | zenon_intro zenon_H176 ]. % 15.22/15.43 apply (zenon_L48_); trivial. % 15.22/15.43 apply (zenon_or_s _ _ zenon_H176); [ zenon_intro zenon_H88 | zenon_intro zenon_H177 ]. % 15.22/15.43 apply (zenon_L196_); trivial. % 15.22/15.43 apply (zenon_or_s _ _ zenon_H177); [ zenon_intro zenon_H34 | zenon_intro zenon_H106 ]. % 15.22/15.43 exact (zenon_H30 zenon_H34). % 15.22/15.43 apply (zenon_L81_); trivial. % 15.22/15.43 (* end of lemma zenon_L507_ *) % 15.22/15.43 assert (zenon_L508_ : (((op (e0) (e0)) = (e2))\/(((op (e1) (e0)) = (e2))\/(((op (e2) (e0)) = (e2))\/((op (e3) (e0)) = (e2))))) -> (~((op (e0) (e0)) = (e2))) -> (~((e1) = (e2))) -> ((op (e1) (e0)) = (e1)) -> (~((op (e2) (e0)) = (op (e2) (e2)))) -> ((op (e2) (e2)) = (e2)) -> (((op (e1) (e1)) = (e0))\/(((op (e1) (e1)) = (e1))\/(((op (e1) (e1)) = (e2))\/((op (e1) (e1)) = (e3))))) -> (~((op (e3) (e3)) = (e3))) -> (~((op (e3) (e3)) = (e2))) -> (~((op (e3) (e3)) = (e0))) -> (((op (e3) (e3)) = (e0))\/(((op (e3) (e3)) = (e1))\/(((op (e3) (e3)) = (e2))\/((op (e3) (e3)) = (e3))))) -> (~((op (e1) (e1)) = (e1))) -> (~((op (e1) (e1)) = (e2))) -> (~((op (e1) (e1)) = (e3))) -> False). % 15.22/15.43 do 0 intro. intros zenon_Heb zenon_H8f zenon_Ha7 zenon_Hd8 zenon_H17a zenon_H35 zenon_H1b3 zenon_H3e zenon_H3d zenon_H3c zenon_H3b zenon_H1b4 zenon_Hd6 zenon_H182. % 15.22/15.43 apply (zenon_or_s _ _ zenon_Heb); [ zenon_intro zenon_H92 | zenon_intro zenon_Hec ]. % 15.22/15.43 exact (zenon_H8f zenon_H92). % 15.22/15.43 apply (zenon_or_s _ _ zenon_Hec); [ zenon_intro zenon_H68 | zenon_intro zenon_Hed ]. % 15.22/15.43 apply (zenon_L162_); trivial. % 15.22/15.43 apply (zenon_or_s _ _ zenon_Hed); [ zenon_intro zenon_Hdd | zenon_intro zenon_He9 ]. % 15.22/15.43 apply (zenon_L161_); trivial. % 15.22/15.43 apply (zenon_L406_); trivial. % 15.22/15.43 (* end of lemma zenon_L508_ *) % 15.22/15.43 assert (zenon_L509_ : (((op (e1) (e0)) = (e2))\/(((op (e1) (e1)) = (e2))\/(((op (e1) (e2)) = (e2))\/((op (e1) (e3)) = (e2))))) -> (~((e1) = (e2))) -> (~((op (e1) (e2)) = (op (e2) (e2)))) -> ((op (e2) (e2)) = (e2)) -> (((op (e1) (e0)) = (e3))\/(((op (e1) (e1)) = (e3))\/(((op (e1) (e2)) = (e3))\/((op (e1) (e3)) = (e3))))) -> (~((e1) = (e3))) -> ((op (e1) (e0)) = (e1)) -> (~((op (e1) (e1)) = (e3))) -> (~((op (e1) (e1)) = (e2))) -> (~((op (e1) (e1)) = (e1))) -> ((op (e0) (e0)) = (e2)) -> (((op (e1) (e1)) = (e0))\/(((op (e1) (e1)) = (e1))\/(((op (e1) (e1)) = (e2))\/((op (e1) (e1)) = (e3))))) -> (~((e2) = (e3))) -> False). % 15.22/15.43 do 0 intro. intros zenon_H84 zenon_Ha7 zenon_H7d zenon_H35 zenon_H90 zenon_Ha3 zenon_Hd8 zenon_H182 zenon_Hd6 zenon_H1b4 zenon_H92 zenon_H1b3 zenon_H6a. % 15.22/15.43 apply (zenon_or_s _ _ zenon_H84); [ zenon_intro zenon_H68 | zenon_intro zenon_H85 ]. % 15.22/15.43 apply (zenon_L162_); trivial. % 15.22/15.43 apply (zenon_or_s _ _ zenon_H85); [ zenon_intro zenon_H6e | zenon_intro zenon_H86 ]. % 15.22/15.43 exact (zenon_Hd6 zenon_H6e). % 15.22/15.43 apply (zenon_or_s _ _ zenon_H86); [ zenon_intro zenon_H7c | zenon_intro zenon_H82 ]. % 15.22/15.43 apply (zenon_L21_); trivial. % 15.22/15.43 apply (zenon_or_s _ _ zenon_H90); [ zenon_intro zenon_H69 | zenon_intro zenon_H94 ]. % 15.22/15.43 apply (zenon_L163_); trivial. % 15.22/15.43 apply (zenon_or_s _ _ zenon_H94); [ zenon_intro zenon_H96 | zenon_intro zenon_H95 ]. % 15.22/15.43 exact (zenon_H182 zenon_H96). % 15.22/15.43 apply (zenon_or_s _ _ zenon_H95); [ zenon_intro zenon_H88 | zenon_intro zenon_H8a ]. % 15.22/15.43 apply (zenon_L194_); trivial. % 15.22/15.43 apply (zenon_L165_); trivial. % 15.22/15.43 (* end of lemma zenon_L509_ *) % 15.22/15.43 assert (zenon_L510_ : (((op (e0) (e0)) = (e2))\/(((op (e1) (e0)) = (e2))\/(((op (e2) (e0)) = (e2))\/((op (e3) (e0)) = (e2))))) -> (((op (e1) (e1)) = (e0))\/(((op (e1) (e1)) = (e1))\/(((op (e1) (e1)) = (e2))\/((op (e1) (e1)) = (e3))))) -> (~((op (e1) (e1)) = (e1))) -> (~((op (e1) (e1)) = (e2))) -> (~((op (e1) (e1)) = (e3))) -> (~((e1) = (e3))) -> (((op (e1) (e0)) = (e3))\/(((op (e1) (e1)) = (e3))\/(((op (e1) (e2)) = (e3))\/((op (e1) (e3)) = (e3))))) -> (~((op (e1) (e2)) = (op (e2) (e2)))) -> (((op (e1) (e0)) = (e2))\/(((op (e1) (e1)) = (e2))\/(((op (e1) (e2)) = (e2))\/((op (e1) (e3)) = (e2))))) -> (~((e1) = (e2))) -> ((op (e1) (e0)) = (e1)) -> (~((op (e2) (e0)) = (op (e2) (e2)))) -> ((op (e2) (e2)) = (e2)) -> (~((e2) = (e3))) -> ((op (e3) (e0)) = (e3)) -> False). % 15.22/15.43 do 0 intro. intros zenon_Heb zenon_H1b3 zenon_H1b4 zenon_Hd6 zenon_H182 zenon_Ha3 zenon_H90 zenon_H7d zenon_H84 zenon_Ha7 zenon_Hd8 zenon_H17a zenon_H35 zenon_H6a zenon_Hba. % 15.22/15.43 apply (zenon_or_s _ _ zenon_Heb); [ zenon_intro zenon_H92 | zenon_intro zenon_Hec ]. % 15.22/15.43 apply (zenon_L509_); trivial. % 15.22/15.43 apply (zenon_or_s _ _ zenon_Hec); [ zenon_intro zenon_H68 | zenon_intro zenon_Hed ]. % 15.22/15.43 apply (zenon_L162_); trivial. % 15.22/15.43 apply (zenon_or_s _ _ zenon_Hed); [ zenon_intro zenon_Hdd | zenon_intro zenon_He9 ]. % 15.22/15.43 apply (zenon_L161_); trivial. % 15.22/15.43 apply (zenon_L220_); trivial. % 15.22/15.43 (* end of lemma zenon_L510_ *) % 15.22/15.43 assert (zenon_L511_ : (((op (e0) (e0)) = (e2))\/(((op (e1) (e0)) = (e2))\/(((op (e2) (e0)) = (e2))\/((op (e3) (e0)) = (e2))))) -> (~((e2) = (e3))) -> (~((e1) = (e3))) -> (((op (e1) (e0)) = (e3))\/(((op (e1) (e1)) = (e3))\/(((op (e1) (e2)) = (e3))\/((op (e1) (e3)) = (e3))))) -> (~((op (e1) (e2)) = (op (e2) (e2)))) -> (((op (e1) (e0)) = (e2))\/(((op (e1) (e1)) = (e2))\/(((op (e1) (e2)) = (e2))\/((op (e1) (e3)) = (e2))))) -> (~((e1) = (e2))) -> ((op (e1) (e0)) = (e1)) -> (~((op (e2) (e0)) = (op (e2) (e2)))) -> ((op (e2) (e2)) = (e2)) -> (((op (e1) (e1)) = (e0))\/(((op (e1) (e1)) = (e1))\/(((op (e1) (e1)) = (e2))\/((op (e1) (e1)) = (e3))))) -> (~((op (e3) (e3)) = (e3))) -> (~((op (e3) (e3)) = (e2))) -> (~((op (e3) (e3)) = (e0))) -> (((op (e3) (e3)) = (e0))\/(((op (e3) (e3)) = (e1))\/(((op (e3) (e3)) = (e2))\/((op (e3) (e3)) = (e3))))) -> (~((op (e1) (e1)) = (e1))) -> (~((op (e1) (e1)) = (e2))) -> (~((op (e1) (e1)) = (e3))) -> False). % 15.22/15.43 do 0 intro. intros zenon_Heb zenon_H6a zenon_Ha3 zenon_H90 zenon_H7d zenon_H84 zenon_Ha7 zenon_Hd8 zenon_H17a zenon_H35 zenon_H1b3 zenon_H3e zenon_H3d zenon_H3c zenon_H3b zenon_H1b4 zenon_Hd6 zenon_H182. % 15.22/15.43 apply (zenon_or_s _ _ zenon_Heb); [ zenon_intro zenon_H92 | zenon_intro zenon_Hec ]. % 15.22/15.43 apply (zenon_L509_); trivial. % 15.22/15.43 apply (zenon_or_s _ _ zenon_Hec); [ zenon_intro zenon_H68 | zenon_intro zenon_Hed ]. % 15.22/15.43 apply (zenon_L162_); trivial. % 15.22/15.43 apply (zenon_or_s _ _ zenon_Hed); [ zenon_intro zenon_Hdd | zenon_intro zenon_He9 ]. % 15.22/15.43 apply (zenon_L161_); trivial. % 15.22/15.43 apply (zenon_L406_); trivial. % 15.22/15.43 (* end of lemma zenon_L511_ *) % 15.22/15.43 assert (zenon_L512_ : (((op (e1) (e0)) = (e3))\/(((op (e1) (e1)) = (e3))\/(((op (e1) (e2)) = (e3))\/((op (e1) (e3)) = (e3))))) -> (~((e0) = (e3))) -> ((op (e1) (e0)) = (e0)) -> (~((op (e1) (e1)) = (e3))) -> (~((e1) = (e3))) -> ((op (e1) (e2)) = (e1)) -> (~((op (e1) (op (e0) (e1))) = (op (e0) (e1)))) -> ((op (e0) (e1)) = (e3)) -> False). % 15.22/15.43 do 0 intro. intros zenon_H90 zenon_H4b zenon_Had zenon_H182 zenon_Ha3 zenon_H117 zenon_H1ff zenon_H4a. % 15.22/15.43 apply (zenon_or_s _ _ zenon_H90); [ zenon_intro zenon_H69 | zenon_intro zenon_H94 ]. % 15.22/15.43 apply (zenon_L38_); trivial. % 15.22/15.43 apply (zenon_or_s _ _ zenon_H94); [ zenon_intro zenon_H96 | zenon_intro zenon_H95 ]. % 15.22/15.43 exact (zenon_H182 zenon_H96). % 15.22/15.43 apply (zenon_or_s _ _ zenon_H95); [ zenon_intro zenon_H88 | zenon_intro zenon_H8a ]. % 15.22/15.43 apply (zenon_L196_); trivial. % 15.22/15.43 cut (((op (e1) (e3)) = (e3)) = ((op (e1) (op (e0) (e1))) = (op (e0) (e1)))). % 15.22/15.43 intro zenon_D_pnotp. % 15.22/15.43 apply zenon_H1ff. % 15.22/15.43 rewrite <- zenon_D_pnotp. % 15.22/15.43 exact zenon_H8a. % 15.22/15.43 cut (((e3) = (op (e0) (e1)))); [idtac | apply NNPP; zenon_intro zenon_H13b]. % 15.22/15.43 cut (((op (e1) (e3)) = (op (e1) (op (e0) (e1))))); [idtac | apply NNPP; zenon_intro zenon_H242]. % 15.22/15.43 congruence. % 15.22/15.43 elim (classic ((op (e1) (op (e0) (e1))) = (op (e1) (op (e0) (e1))))); [ zenon_intro zenon_H202 | zenon_intro zenon_H203 ]. % 15.22/15.43 cut (((op (e1) (op (e0) (e1))) = (op (e1) (op (e0) (e1)))) = ((op (e1) (e3)) = (op (e1) (op (e0) (e1))))). % 15.22/15.43 intro zenon_D_pnotp. % 15.22/15.43 apply zenon_H242. % 15.22/15.43 rewrite <- zenon_D_pnotp. % 15.22/15.43 exact zenon_H202. % 15.22/15.43 cut (((op (e1) (op (e0) (e1))) = (op (e1) (op (e0) (e1))))); [idtac | apply NNPP; zenon_intro zenon_H203]. % 15.22/15.43 cut (((op (e1) (op (e0) (e1))) = (op (e1) (e3)))); [idtac | apply NNPP; zenon_intro zenon_H243]. % 15.22/15.43 congruence. % 15.22/15.43 cut (((op (e0) (e1)) = (e3))); [idtac | apply NNPP; zenon_intro zenon_H4f]. % 15.22/15.43 cut (((e1) = (e1))); [idtac | apply NNPP; zenon_intro zenon_Ha0]. % 15.22/15.43 congruence. % 15.22/15.43 apply zenon_Ha0. apply refl_equal. % 15.22/15.43 exact (zenon_H4f zenon_H4a). % 15.22/15.43 apply zenon_H203. apply refl_equal. % 15.22/15.43 apply zenon_H203. apply refl_equal. % 15.22/15.43 apply zenon_H13b. apply sym_equal. exact zenon_H4a. % 15.22/15.43 (* end of lemma zenon_L512_ *) % 15.22/15.43 assert (zenon_L513_ : (((op (e1) (e0)) = (e2))\/(((op (e1) (e1)) = (e2))\/(((op (e1) (e2)) = (e2))\/((op (e1) (e3)) = (e2))))) -> (~((e0) = (e2))) -> ((op (e1) (e0)) = (e0)) -> (~((op (e1) (e1)) = (e2))) -> (~((op (e1) (e2)) = (op (e2) (e2)))) -> ((op (e2) (e2)) = (e2)) -> ((op (e1) (e3)) = (e1)) -> (~((e1) = (e2))) -> False). % 15.22/15.43 do 0 intro. intros zenon_H84 zenon_H5e zenon_Had zenon_Hd6 zenon_H7d zenon_H35 zenon_H11f zenon_Ha7. % 15.22/15.43 apply (zenon_or_s _ _ zenon_H84); [ zenon_intro zenon_H68 | zenon_intro zenon_H85 ]. % 15.22/15.43 apply (zenon_L160_); trivial. % 15.22/15.43 apply (zenon_or_s _ _ zenon_H85); [ zenon_intro zenon_H6e | zenon_intro zenon_H86 ]. % 15.22/15.43 exact (zenon_Hd6 zenon_H6e). % 15.22/15.43 apply (zenon_or_s _ _ zenon_H86); [ zenon_intro zenon_H7c | zenon_intro zenon_H82 ]. % 15.22/15.43 apply (zenon_L21_); trivial. % 15.22/15.43 apply (zenon_L209_); trivial. % 15.22/15.43 (* end of lemma zenon_L513_ *) % 15.22/15.43 assert (zenon_L514_ : ((~((op (e1) (e1)) = (e3)))\/((op (e1) (e3)) = (e1))) -> ((~((op (e3) (e3)) = (e2)))\/((op (e3) (e2)) = (e3))) -> (~((op (e1) (e2)) = (op (e3) (e2)))) -> (((op (e0) (e0)) = (e2))\/(((op (e1) (e0)) = (e2))\/(((op (e2) (e0)) = (e2))\/((op (e3) (e0)) = (e2))))) -> (((op (e3) (e3)) = (e0))\/(((op (e3) (e3)) = (e1))\/(((op (e3) (e3)) = (e2))\/((op (e3) (e3)) = (e3))))) -> (~((op (e2) (e0)) = (op (e2) (e2)))) -> (~((e1) = (e2))) -> ((op (e1) (e0)) = (e1)) -> (~((op (e1) (e1)) = (e2))) -> (~((op (e1) (e2)) = (op (e2) (e2)))) -> ((op (e2) (e2)) = (e2)) -> (((op (e1) (e0)) = (e3))\/(((op (e1) (e1)) = (e3))\/(((op (e1) (e2)) = (e3))\/((op (e1) (e3)) = (e3))))) -> (~((e2) = (e3))) -> (~((op (e1) (e1)) = (e1))) -> (((op (e1) (e1)) = (e0))\/(((op (e1) (e1)) = (e1))\/(((op (e1) (e1)) = (e2))\/((op (e1) (e1)) = (e3))))) -> (~((e1) = (e3))) -> (((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 (e2) (e2)) = (e3)))\/((op (e2) (e3)) = (e2))) -> ((~((op (e3) (e3)) = (e1)))\/((op (e3) (e1)) = (e3))) -> (~((op (e3) (e1)) = (op (e3) (e3)))) -> (~((op (e0) (e0)) = (e1))) -> (((op (e0) (e3)) = (e1))\/(((op (e1) (e3)) = (e1))\/(((op (e2) (e3)) = (e1))\/((op (e3) (e3)) = (e1))))) -> (~((op (e1) (e0)) = (op (e1) (e3)))) -> (~((op (e0) (e1)) = (op (e0) (e3)))) -> (~((e0) = (e1))) -> ((op (e0) (e2)) = (e0)) -> (((op (e0) (e0)) = (e2))\/(((op (e0) (e1)) = (e2))\/(((op (e0) (e2)) = (e2))\/((op (e0) (e3)) = (e2))))) -> (((op (e0) (e3)) = (e0))\/(((op (e1) (e3)) = (e0))\/(((op (e2) (e3)) = (e0))\/((op (e3) (e3)) = (e0))))) -> (~((e0) = (e2))) -> (~((op (e0) (e2)) = (op (e0) (e3)))) -> (~((op (e0) (e2)) = (op (e1) (e2)))) -> (~((op (e0) (e3)) = (op (e3) (e3)))) -> (((op (e0) (e0)) = (e3))\/(((op (e0) (e1)) = (e3))\/(((op (e0) (e2)) = (e3))\/((op (e0) (e3)) = (e3))))) -> (~((op (e1) (e3)) = (op (e3) (e3)))) -> (((op (e0) (e0)) = (e1))\/(((op (e0) (e1)) = (e1))\/(((op (e0) (e2)) = (e1))\/((op (e0) (e3)) = (e1))))) -> ((~((op (e3) (e3)) = (e0)))\/((op (e3) (e0)) = (e3))) -> (~((op (e0) (e0)) = (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) (e0)) = (e3))\/(((op (e1) (e0)) = (e3))\/(((op (e2) (e0)) = (e3))\/((op (e3) (e0)) = (e3))))) -> (~((op (e0) (e2)) = (op (e2) (e2)))) -> (~((op (e0) (e3)) = (op (e1) (e3)))) -> ((~((op (e2) (e2)) = (e2)))\/((op (e2) (e2)) = (e2))) -> ((~((op (e3) (e3)) = (e3)))\/((op (e3) (e3)) = (e3))) -> False). % 15.22/15.43 do 0 intro. intros zenon_H1d2 zenon_H10e zenon_H17d zenon_Heb zenon_H3b zenon_H17a zenon_Ha7 zenon_Hd8 zenon_Hd6 zenon_H7d zenon_H35 zenon_H90 zenon_H6a zenon_H1b4 zenon_H1b3 zenon_Ha3 zenon_H84 zenon_H1d4 zenon_H1c3 zenon_H10c zenon_H12d zenon_H45 zenon_H121 zenon_H1cf zenon_H1cd zenon_H9e zenon_Hab zenon_H8e zenon_Hd3 zenon_H5e zenon_Hc9 zenon_H87 zenon_H36 zenon_H58 zenon_H8b zenon_H44 zenon_H10f zenon_H59 zenon_H2d zenon_Hbb zenon_Hbe zenon_H28 zenon_H80 zenon_Haa zenon_H10d. % 15.22/15.43 apply (zenon_or_s _ _ zenon_H1d2); [ zenon_intro zenon_H182 | zenon_intro zenon_H11f ]. % 15.22/15.43 apply (zenon_or_s _ _ zenon_H10f); [ zenon_intro zenon_H3c | zenon_intro zenon_Hba ]. % 15.22/15.43 apply (zenon_or_s _ _ zenon_H10e); [ zenon_intro zenon_H3d | zenon_intro zenon_H106 ]. % 15.22/15.43 apply (zenon_or_s _ _ zenon_H10d); [ zenon_intro zenon_H3e | zenon_intro zenon_H42 ]. % 15.22/15.43 apply (zenon_L511_); trivial. % 15.22/15.43 apply (zenon_L247_); trivial. % 15.22/15.43 apply (zenon_L167_); trivial. % 15.22/15.43 apply (zenon_L510_); trivial. % 15.22/15.43 apply (zenon_L224_); trivial. % 15.22/15.43 (* end of lemma zenon_L514_ *) % 15.22/15.43 assert (zenon_L515_ : (((op (e1) (e0)) = (e2))\/(((op (e1) (e1)) = (e2))\/(((op (e1) (e2)) = (e2))\/((op (e1) (e3)) = (e2))))) -> (~((e2) = (e3))) -> ((op (e1) (e0)) = (e3)) -> (~((op (e1) (e1)) = (e2))) -> (~((op (e1) (e2)) = (op (e2) (e2)))) -> ((op (e2) (e2)) = (e2)) -> ((op (e1) (e3)) = (e1)) -> (~((e1) = (e2))) -> False). % 15.22/15.43 do 0 intro. intros zenon_H84 zenon_H6a zenon_H69 zenon_Hd6 zenon_H7d zenon_H35 zenon_H11f zenon_Ha7. % 15.22/15.43 apply (zenon_or_s _ _ zenon_H84); [ zenon_intro zenon_H68 | zenon_intro zenon_H85 ]. % 15.22/15.43 apply (zenon_L17_); trivial. % 15.22/15.43 apply (zenon_or_s _ _ zenon_H85); [ zenon_intro zenon_H6e | zenon_intro zenon_H86 ]. % 15.22/15.43 exact (zenon_Hd6 zenon_H6e). % 15.22/15.43 apply (zenon_or_s _ _ zenon_H86); [ zenon_intro zenon_H7c | zenon_intro zenon_H82 ]. % 15.22/15.43 apply (zenon_L21_); trivial. % 15.22/15.43 apply (zenon_L209_); trivial. % 15.22/15.43 (* end of lemma zenon_L515_ *) % 15.22/15.43 assert (zenon_L516_ : (((op (e0) (e0)) = (e3))\/(((op (e1) (e0)) = (e3))\/(((op (e2) (e0)) = (e3))\/((op (e3) (e0)) = (e3))))) -> (~((op (e0) (e0)) = (e3))) -> (~((e1) = (e2))) -> ((op (e1) (e3)) = (e1)) -> ((op (e2) (e2)) = (e2)) -> (~((op (e1) (e2)) = (op (e2) (e2)))) -> (~((op (e1) (e1)) = (e2))) -> (~((e2) = (e3))) -> (((op (e1) (e0)) = (e2))\/(((op (e1) (e1)) = (e2))\/(((op (e1) (e2)) = (e2))\/((op (e1) (e3)) = (e2))))) -> (~((e0) = (e3))) -> ((op (e2) (e0)) = (e0)) -> (~((e1) = (e3))) -> ((op (e3) (e0)) = (e1)) -> False). % 15.22/15.43 do 0 intro. intros zenon_Hbe zenon_H59 zenon_Ha7 zenon_H11f zenon_H35 zenon_H7d zenon_Hd6 zenon_H6a zenon_H84 zenon_H4b zenon_Hcf zenon_Ha3 zenon_Hee. % 15.22/15.43 apply (zenon_or_s _ _ zenon_Hbe); [ zenon_intro zenon_H5b | zenon_intro zenon_Hbf ]. % 15.22/15.43 exact (zenon_H59 zenon_H5b). % 15.22/15.43 apply (zenon_or_s _ _ zenon_Hbf); [ zenon_intro zenon_H69 | zenon_intro zenon_Hc0 ]. % 15.22/15.43 apply (zenon_L515_); trivial. % 15.22/15.43 apply (zenon_or_s _ _ zenon_Hc0); [ zenon_intro zenon_Haf | zenon_intro zenon_Hba ]. % 15.22/15.43 apply (zenon_L57_); trivial. % 15.22/15.43 apply (zenon_L79_); trivial. % 15.22/15.43 (* end of lemma zenon_L516_ *) % 15.22/15.43 assert (zenon_L517_ : (((op (e0) (e0)) = (e1))\/(((op (e1) (e0)) = (e1))\/(((op (e2) (e0)) = (e1))\/((op (e3) (e0)) = (e1))))) -> ((~((op (e3) (e3)) = (e3)))\/((op (e3) (e3)) = (e3))) -> ((~((op (e2) (e2)) = (e2)))\/((op (e2) (e2)) = (e2))) -> (~((op (e0) (e3)) = (op (e1) (e3)))) -> (~((op (e0) (e2)) = (op (e2) (e2)))) -> (~((op (e3) (e0)) = (op (e3) (e3)))) -> (((op (e2) (e2)) = (e0))\/(((op (e2) (e2)) = (e1))\/(((op (e2) (e2)) = (e2))\/((op (e2) (e2)) = (e3))))) -> ((~((op (e3) (e3)) = (e0)))\/((op (e3) (e0)) = (e3))) -> (((op (e0) (e0)) = (e1))\/(((op (e0) (e1)) = (e1))\/(((op (e0) (e2)) = (e1))\/((op (e0) (e3)) = (e1))))) -> (~((op (e1) (e3)) = (op (e3) (e3)))) -> (((op (e0) (e0)) = (e3))\/(((op (e0) (e1)) = (e3))\/(((op (e0) (e2)) = (e3))\/((op (e0) (e3)) = (e3))))) -> (~((op (e0) (e3)) = (op (e3) (e3)))) -> (~((op (e0) (e2)) = (op (e1) (e2)))) -> (~((op (e0) (e2)) = (op (e0) (e3)))) -> (~((e0) = (e2))) -> (((op (e0) (e3)) = (e0))\/(((op (e1) (e3)) = (e0))\/(((op (e2) (e3)) = (e0))\/((op (e3) (e3)) = (e0))))) -> (((op (e0) (e0)) = (e2))\/(((op (e0) (e1)) = (e2))\/(((op (e0) (e2)) = (e2))\/((op (e0) (e3)) = (e2))))) -> ((op (e0) (e2)) = (e0)) -> (~((op (e0) (e1)) = (op (e0) (e3)))) -> (~((op (e1) (e0)) = (op (e1) (e3)))) -> (((op (e0) (e3)) = (e1))\/(((op (e1) (e3)) = (e1))\/(((op (e2) (e3)) = (e1))\/((op (e3) (e3)) = (e1))))) -> (~((op (e0) (e0)) = (e1))) -> (~((op (e3) (e1)) = (op (e3) (e3)))) -> ((~((op (e3) (e3)) = (e1)))\/((op (e3) (e1)) = (e3))) -> ((~((op (e2) (e2)) = (e3)))\/((op (e2) (e3)) = (e2))) -> ((~((op (e2) (e2)) = (e0)))\/((op (e2) (e0)) = (e2))) -> (((op (e1) (e1)) = (e0))\/(((op (e1) (e1)) = (e1))\/(((op (e1) (e1)) = (e2))\/((op (e1) (e1)) = (e3))))) -> (~((op (e1) (e1)) = (e1))) -> (((op (e1) (e0)) = (e3))\/(((op (e1) (e1)) = (e3))\/(((op (e1) (e2)) = (e3))\/((op (e1) (e3)) = (e3))))) -> (~((op (e2) (e0)) = (op (e2) (e2)))) -> (((op (e3) (e3)) = (e0))\/(((op (e3) (e3)) = (e1))\/(((op (e3) (e3)) = (e2))\/((op (e3) (e3)) = (e3))))) -> (((op (e0) (e0)) = (e2))\/(((op (e1) (e0)) = (e2))\/(((op (e2) (e0)) = (e2))\/((op (e3) (e0)) = (e2))))) -> (~((op (e1) (e2)) = (op (e3) (e2)))) -> ((~((op (e3) (e3)) = (e2)))\/((op (e3) (e2)) = (e3))) -> ((~((op (e1) (e1)) = (e3)))\/((op (e1) (e3)) = (e1))) -> (~((e0) = (e1))) -> (((op (e0) (e0)) = (e3))\/(((op (e1) (e0)) = (e3))\/(((op (e2) (e0)) = (e3))\/((op (e3) (e0)) = (e3))))) -> (~((op (e0) (e0)) = (e3))) -> (~((e1) = (e2))) -> ((op (e1) (e3)) = (e1)) -> ((op (e2) (e2)) = (e2)) -> (~((op (e1) (e2)) = (op (e2) (e2)))) -> (~((op (e1) (e1)) = (e2))) -> (~((e2) = (e3))) -> (((op (e1) (e0)) = (e2))\/(((op (e1) (e1)) = (e2))\/(((op (e1) (e2)) = (e2))\/((op (e1) (e3)) = (e2))))) -> (~((e0) = (e3))) -> ((op (e2) (e0)) = (e0)) -> (~((e1) = (e3))) -> False). % 15.22/15.43 do 0 intro. intros zenon_Hf1 zenon_H10d zenon_Haa zenon_H80 zenon_H28 zenon_Hbb zenon_H2d zenon_H10f zenon_H44 zenon_H8b zenon_H58 zenon_H36 zenon_H87 zenon_Hc9 zenon_H5e zenon_Hd3 zenon_H8e zenon_Hab zenon_H1cd zenon_H1cf zenon_H121 zenon_H45 zenon_H12d zenon_H10c zenon_H1c3 zenon_H1d4 zenon_H1b3 zenon_H1b4 zenon_H90 zenon_H17a zenon_H3b zenon_Heb zenon_H17d zenon_H10e zenon_H1d2 zenon_H9e zenon_Hbe zenon_H59 zenon_Ha7 zenon_H11f zenon_H35 zenon_H7d zenon_Hd6 zenon_H6a zenon_H84 zenon_H4b zenon_Hcf zenon_Ha3. % 15.22/15.43 apply (zenon_or_s _ _ zenon_Hf1); [ zenon_intro zenon_H47 | zenon_intro zenon_Hf4 ]. % 15.22/15.43 exact (zenon_H45 zenon_H47). % 15.22/15.43 apply (zenon_or_s _ _ zenon_Hf4); [ zenon_intro zenon_Hd8 | zenon_intro zenon_Hf5 ]. % 15.22/15.43 apply (zenon_L514_); trivial. % 15.22/15.43 apply (zenon_or_s _ _ zenon_Hf5); [ zenon_intro zenon_Hae | zenon_intro zenon_Hee ]. % 15.22/15.43 apply (zenon_L269_); trivial. % 15.22/15.43 apply (zenon_L516_); trivial. % 15.22/15.43 (* end of lemma zenon_L517_ *) % 15.22/15.43 assert (zenon_L518_ : (((op (e0) (e0)) = (e1))\/(((op (e1) (e0)) = (e1))\/(((op (e2) (e0)) = (e1))\/((op (e3) (e0)) = (e1))))) -> (~((op (e0) (e0)) = (e1))) -> (~((op (e1) (e0)) = (op (e1) (e3)))) -> (~((e0) = (e3))) -> (~((e1) = (e3))) -> (((op (e1) (e0)) = (e2))\/(((op (e1) (e1)) = (e2))\/(((op (e1) (e2)) = (e2))\/((op (e1) (e3)) = (e2))))) -> (~((e2) = (e3))) -> (~((op (e1) (e1)) = (e2))) -> (~((op (e1) (e2)) = (op (e2) (e2)))) -> ((op (e2) (e2)) = (e2)) -> ((op (e1) (e3)) = (e1)) -> (~((e1) = (e2))) -> (~((op (e0) (e0)) = (e3))) -> (((op (e0) (e0)) = (e3))\/(((op (e1) (e0)) = (e3))\/(((op (e2) (e0)) = (e3))\/((op (e3) (e0)) = (e3))))) -> ((op (e3) (e0)) = (e0)) -> (~((e0) = (e1))) -> False). % 15.22/15.43 do 0 intro. intros zenon_Hf1 zenon_H45 zenon_H1cf zenon_H4b zenon_Ha3 zenon_H84 zenon_H6a zenon_Hd6 zenon_H7d zenon_H35 zenon_H11f zenon_Ha7 zenon_H59 zenon_Hbe zenon_Hdb zenon_H9e. % 15.22/15.43 apply (zenon_or_s _ _ zenon_Hf1); [ zenon_intro zenon_H47 | zenon_intro zenon_Hf4 ]. % 15.22/15.43 exact (zenon_H45 zenon_H47). % 15.22/15.43 apply (zenon_or_s _ _ zenon_Hf4); [ zenon_intro zenon_Hd8 | zenon_intro zenon_Hf5 ]. % 15.22/15.43 apply (zenon_L224_); trivial. % 15.22/15.43 apply (zenon_or_s _ _ zenon_Hf5); [ zenon_intro zenon_Hae | zenon_intro zenon_Hee ]. % 15.22/15.43 apply (zenon_or_s _ _ zenon_Hbe); [ zenon_intro zenon_H5b | zenon_intro zenon_Hbf ]. % 15.22/15.43 exact (zenon_H59 zenon_H5b). % 15.22/15.43 apply (zenon_or_s _ _ zenon_Hbf); [ zenon_intro zenon_H69 | zenon_intro zenon_Hc0 ]. % 15.22/15.43 apply (zenon_L515_); trivial. % 15.22/15.43 apply (zenon_or_s _ _ zenon_Hc0); [ zenon_intro zenon_Haf | zenon_intro zenon_Hba ]. % 15.22/15.43 apply (zenon_L39_); trivial. % 15.22/15.43 apply (zenon_L62_); trivial. % 15.22/15.43 apply (zenon_L71_); trivial. % 15.22/15.43 (* end of lemma zenon_L518_ *) % 15.22/15.43 assert (zenon_L519_ : (((op (e0) (e0)) = (e0))\/(((op (e1) (e0)) = (e0))\/(((op (e2) (e0)) = (e0))\/((op (e3) (e0)) = (e0))))) -> (~((op (e0) (e0)) = (e0))) -> ((~((op (e1) (e1)) = (e3)))\/((op (e1) (e3)) = (e1))) -> ((~((op (e3) (e3)) = (e2)))\/((op (e3) (e2)) = (e3))) -> (~((op (e1) (e2)) = (op (e3) (e2)))) -> (((op (e0) (e0)) = (e2))\/(((op (e1) (e0)) = (e2))\/(((op (e2) (e0)) = (e2))\/((op (e3) (e0)) = (e2))))) -> (((op (e3) (e3)) = (e0))\/(((op (e3) (e3)) = (e1))\/(((op (e3) (e3)) = (e2))\/((op (e3) (e3)) = (e3))))) -> (~((op (e2) (e0)) = (op (e2) (e2)))) -> (((op (e1) (e0)) = (e3))\/(((op (e1) (e1)) = (e3))\/(((op (e1) (e2)) = (e3))\/((op (e1) (e3)) = (e3))))) -> (~((op (e1) (e1)) = (e1))) -> (((op (e1) (e1)) = (e0))\/(((op (e1) (e1)) = (e1))\/(((op (e1) (e1)) = (e2))\/((op (e1) (e1)) = (e3))))) -> ((~((op (e2) (e2)) = (e0)))\/((op (e2) (e0)) = (e2))) -> ((~((op (e2) (e2)) = (e3)))\/((op (e2) (e3)) = (e2))) -> ((~((op (e3) (e3)) = (e1)))\/((op (e3) (e1)) = (e3))) -> (~((op (e3) (e1)) = (op (e3) (e3)))) -> (((op (e0) (e3)) = (e1))\/(((op (e1) (e3)) = (e1))\/(((op (e2) (e3)) = (e1))\/((op (e3) (e3)) = (e1))))) -> (~((op (e0) (e1)) = (op (e0) (e3)))) -> ((op (e0) (e2)) = (e0)) -> (((op (e0) (e0)) = (e2))\/(((op (e0) (e1)) = (e2))\/(((op (e0) (e2)) = (e2))\/((op (e0) (e3)) = (e2))))) -> (((op (e0) (e3)) = (e0))\/(((op (e1) (e3)) = (e0))\/(((op (e2) (e3)) = (e0))\/((op (e3) (e3)) = (e0))))) -> (~((e0) = (e2))) -> (~((op (e0) (e2)) = (op (e0) (e3)))) -> (~((op (e0) (e2)) = (op (e1) (e2)))) -> (~((op (e0) (e3)) = (op (e3) (e3)))) -> (((op (e0) (e0)) = (e3))\/(((op (e0) (e1)) = (e3))\/(((op (e0) (e2)) = (e3))\/((op (e0) (e3)) = (e3))))) -> (~((op (e1) (e3)) = (op (e3) (e3)))) -> (((op (e0) (e0)) = (e1))\/(((op (e0) (e1)) = (e1))\/(((op (e0) (e2)) = (e1))\/((op (e0) (e3)) = (e1))))) -> ((~((op (e3) (e3)) = (e0)))\/((op (e3) (e0)) = (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) (e2)) = (op (e2) (e2)))) -> (~((op (e0) (e3)) = (op (e1) (e3)))) -> ((~((op (e2) (e2)) = (e2)))\/((op (e2) (e2)) = (e2))) -> ((~((op (e3) (e3)) = (e3)))\/((op (e3) (e3)) = (e3))) -> (((op (e0) (e0)) = (e1))\/(((op (e1) (e0)) = (e1))\/(((op (e2) (e0)) = (e1))\/((op (e3) (e0)) = (e1))))) -> (~((op (e0) (e0)) = (e1))) -> (~((op (e1) (e0)) = (op (e1) (e3)))) -> (~((e0) = (e3))) -> (~((e1) = (e3))) -> (((op (e1) (e0)) = (e2))\/(((op (e1) (e1)) = (e2))\/(((op (e1) (e2)) = (e2))\/((op (e1) (e3)) = (e2))))) -> (~((e2) = (e3))) -> (~((op (e1) (e1)) = (e2))) -> (~((op (e1) (e2)) = (op (e2) (e2)))) -> ((op (e2) (e2)) = (e2)) -> ((op (e1) (e3)) = (e1)) -> (~((e1) = (e2))) -> (~((op (e0) (e0)) = (e3))) -> (((op (e0) (e0)) = (e3))\/(((op (e1) (e0)) = (e3))\/(((op (e2) (e0)) = (e3))\/((op (e3) (e0)) = (e3))))) -> (~((e0) = (e1))) -> False). % 15.22/15.43 do 0 intro. intros zenon_Hf0 zenon_H20 zenon_H1d2 zenon_H10e zenon_H17d zenon_Heb zenon_H3b zenon_H17a zenon_H90 zenon_H1b4 zenon_H1b3 zenon_H1d4 zenon_H1c3 zenon_H10c zenon_H12d zenon_H121 zenon_H1cd zenon_Hab zenon_H8e zenon_Hd3 zenon_H5e zenon_Hc9 zenon_H87 zenon_H36 zenon_H58 zenon_H8b zenon_H44 zenon_H10f zenon_H2d zenon_Hbb zenon_H28 zenon_H80 zenon_Haa zenon_H10d zenon_Hf1 zenon_H45 zenon_H1cf zenon_H4b zenon_Ha3 zenon_H84 zenon_H6a zenon_Hd6 zenon_H7d zenon_H35 zenon_H11f zenon_Ha7 zenon_H59 zenon_Hbe zenon_H9e. % 15.22/15.43 apply (zenon_or_s _ _ zenon_Hf0); [ zenon_intro zenon_H1f | zenon_intro zenon_Hf2 ]. % 15.22/15.43 exact (zenon_H20 zenon_H1f). % 15.22/15.43 apply (zenon_or_s _ _ zenon_Hf2); [ zenon_intro zenon_Had | zenon_intro zenon_Hf3 ]. % 15.22/15.43 apply (zenon_L513_); trivial. % 15.22/15.43 apply (zenon_or_s _ _ zenon_Hf3); [ zenon_intro zenon_Hcf | zenon_intro zenon_Hdb ]. % 15.22/15.43 apply (zenon_L517_); trivial. % 15.22/15.43 apply (zenon_L518_); trivial. % 15.22/15.43 (* end of lemma zenon_L519_ *) % 15.22/15.43 assert (zenon_L520_ : (((op (e1) (e0)) = (e1))\/(((op (e1) (e1)) = (e1))\/(((op (e1) (e2)) = (e1))\/((op (e1) (e3)) = (e1))))) -> ((op (e0) (e0)) = (e2)) -> ((op (e0) (e1)) = (e3)) -> (~((op (e1) (op (e0) (e1))) = (op (e0) (e1)))) -> (~((op (e1) (e1)) = (e3))) -> ((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 (e1) (e1)) = (e3)))\/((op (e1) (e3)) = (e1))) -> ((~((op (e3) (e3)) = (e2)))\/((op (e3) (e2)) = (e3))) -> (~((op (e1) (e2)) = (op (e3) (e2)))) -> (((op (e0) (e0)) = (e2))\/(((op (e1) (e0)) = (e2))\/(((op (e2) (e0)) = (e2))\/((op (e3) (e0)) = (e2))))) -> (((op (e3) (e3)) = (e0))\/(((op (e3) (e3)) = (e1))\/(((op (e3) (e3)) = (e2))\/((op (e3) (e3)) = (e3))))) -> (~((op (e2) (e0)) = (op (e2) (e2)))) -> (((op (e1) (e0)) = (e3))\/(((op (e1) (e1)) = (e3))\/(((op (e1) (e2)) = (e3))\/((op (e1) (e3)) = (e3))))) -> (~((op (e1) (e1)) = (e1))) -> (((op (e1) (e1)) = (e0))\/(((op (e1) (e1)) = (e1))\/(((op (e1) (e1)) = (e2))\/((op (e1) (e1)) = (e3))))) -> ((~((op (e2) (e2)) = (e0)))\/((op (e2) (e0)) = (e2))) -> ((~((op (e2) (e2)) = (e3)))\/((op (e2) (e3)) = (e2))) -> ((~((op (e3) (e3)) = (e1)))\/((op (e3) (e1)) = (e3))) -> (~((op (e3) (e1)) = (op (e3) (e3)))) -> (((op (e0) (e3)) = (e1))\/(((op (e1) (e3)) = (e1))\/(((op (e2) (e3)) = (e1))\/((op (e3) (e3)) = (e1))))) -> (~((op (e0) (e1)) = (op (e0) (e3)))) -> ((op (e0) (e2)) = (e0)) -> (((op (e0) (e0)) = (e2))\/(((op (e0) (e1)) = (e2))\/(((op (e0) (e2)) = (e2))\/((op (e0) (e3)) = (e2))))) -> (((op (e0) (e3)) = (e0))\/(((op (e1) (e3)) = (e0))\/(((op (e2) (e3)) = (e0))\/((op (e3) (e3)) = (e0))))) -> (~((e0) = (e2))) -> (~((op (e0) (e2)) = (op (e0) (e3)))) -> (~((op (e0) (e2)) = (op (e1) (e2)))) -> (~((op (e0) (e3)) = (op (e3) (e3)))) -> (((op (e0) (e0)) = (e3))\/(((op (e0) (e1)) = (e3))\/(((op (e0) (e2)) = (e3))\/((op (e0) (e3)) = (e3))))) -> (~((op (e1) (e3)) = (op (e3) (e3)))) -> (((op (e0) (e0)) = (e1))\/(((op (e0) (e1)) = (e1))\/(((op (e0) (e2)) = (e1))\/((op (e0) (e3)) = (e1))))) -> ((~((op (e3) (e3)) = (e0)))\/((op (e3) (e0)) = (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) (e2)) = (op (e2) (e2)))) -> (~((op (e0) (e3)) = (op (e1) (e3)))) -> ((~((op (e2) (e2)) = (e2)))\/((op (e2) (e2)) = (e2))) -> ((~((op (e3) (e3)) = (e3)))\/((op (e3) (e3)) = (e3))) -> (((op (e0) (e0)) = (e1))\/(((op (e1) (e0)) = (e1))\/(((op (e2) (e0)) = (e1))\/((op (e3) (e0)) = (e1))))) -> (~((op (e0) (e0)) = (e1))) -> (~((op (e1) (e0)) = (op (e1) (e3)))) -> (~((e0) = (e3))) -> (~((e1) = (e3))) -> (((op (e1) (e0)) = (e2))\/(((op (e1) (e1)) = (e2))\/(((op (e1) (e2)) = (e2))\/((op (e1) (e3)) = (e2))))) -> (~((e2) = (e3))) -> (~((op (e1) (e1)) = (e2))) -> (~((op (e1) (e2)) = (op (e2) (e2)))) -> ((op (e2) (e2)) = (e2)) -> (~((e1) = (e2))) -> (~((op (e0) (e0)) = (e3))) -> (((op (e0) (e0)) = (e3))\/(((op (e1) (e0)) = (e3))\/(((op (e2) (e0)) = (e3))\/((op (e3) (e0)) = (e3))))) -> (~((e0) = (e1))) -> False). % 15.22/15.43 do 0 intro. intros zenon_H1c5 zenon_H92 zenon_H4a zenon_H1ff zenon_H182 zenon_Had zenon_Hf0 zenon_H20 zenon_H1d2 zenon_H10e zenon_H17d zenon_Heb zenon_H3b zenon_H17a zenon_H90 zenon_H1b4 zenon_H1b3 zenon_H1d4 zenon_H1c3 zenon_H10c zenon_H12d zenon_H121 zenon_H1cd zenon_Hab zenon_H8e zenon_Hd3 zenon_H5e zenon_Hc9 zenon_H87 zenon_H36 zenon_H58 zenon_H8b zenon_H44 zenon_H10f zenon_H2d zenon_Hbb zenon_H28 zenon_H80 zenon_Haa zenon_H10d zenon_Hf1 zenon_H45 zenon_H1cf zenon_H4b zenon_Ha3 zenon_H84 zenon_H6a zenon_Hd6 zenon_H7d zenon_H35 zenon_Ha7 zenon_H59 zenon_Hbe zenon_H9e. % 15.22/15.43 apply (zenon_or_s _ _ zenon_H1c5); [ zenon_intro zenon_Hd8 | zenon_intro zenon_H1c6 ]. % 15.22/15.43 apply (zenon_L509_); trivial. % 15.22/15.43 apply (zenon_or_s _ _ zenon_H1c6); [ zenon_intro zenon_H21 | zenon_intro zenon_H1c7 ]. % 15.22/15.43 exact (zenon_H1b4 zenon_H21). % 15.22/15.43 apply (zenon_or_s _ _ zenon_H1c7); [ zenon_intro zenon_H117 | zenon_intro zenon_H11f ]. % 15.22/15.43 apply (zenon_L512_); trivial. % 15.22/15.43 apply (zenon_L519_); trivial. % 15.22/15.43 (* end of lemma zenon_L520_ *) % 15.22/15.43 assert (zenon_L521_ : (((op (e1) (e0)) = (e3))\/(((op (e1) (e1)) = (e3))\/(((op (e1) (e2)) = (e3))\/((op (e1) (e3)) = (e3))))) -> (~((e0) = (e3))) -> ((op (e1) (e0)) = (e0)) -> (~((op (e1) (e1)) = (e3))) -> (~((e1) = (e3))) -> ((op (e1) (e2)) = (e1)) -> (~((op (e0) (e3)) = (op (e1) (e3)))) -> ((op (e0) (e3)) = (e3)) -> False). % 15.22/15.43 do 0 intro. intros zenon_H90 zenon_H4b zenon_Had zenon_H182 zenon_Ha3 zenon_H117 zenon_H80 zenon_H53. % 15.22/15.43 apply (zenon_or_s _ _ zenon_H90); [ zenon_intro zenon_H69 | zenon_intro zenon_H94 ]. % 15.22/15.43 apply (zenon_L38_); trivial. % 15.22/15.43 apply (zenon_or_s _ _ zenon_H94); [ zenon_intro zenon_H96 | zenon_intro zenon_H95 ]. % 15.22/15.43 exact (zenon_H182 zenon_H96). % 15.22/15.43 apply (zenon_or_s _ _ zenon_H95); [ zenon_intro zenon_H88 | zenon_intro zenon_H8a ]. % 15.22/15.43 apply (zenon_L196_); trivial. % 15.22/15.43 apply (zenon_L293_); trivial. % 15.22/15.43 (* end of lemma zenon_L521_ *) % 15.22/15.43 assert (zenon_L522_ : (((op (e1) (e0)) = (e2))\/(((op (e1) (e1)) = (e2))\/(((op (e1) (e2)) = (e2))\/((op (e1) (e3)) = (e2))))) -> (~((op (e3) (e3)) = (e3))) -> (~((op (e3) (e3)) = (e2))) -> (~((op (e3) (e3)) = (e1))) -> (((op (e3) (e3)) = (e0))\/(((op (e3) (e3)) = (e1))\/(((op (e3) (e3)) = (e2))\/((op (e3) (e3)) = (e3))))) -> (~((op (e1) (e1)) = (e1))) -> (~((op (e1) (e1)) = (e0))) -> (((op (e1) (e1)) = (e0))\/(((op (e1) (e1)) = (e1))\/(((op (e1) (e1)) = (e2))\/((op (e1) (e1)) = (e3))))) -> (~((op (e1) (e1)) = (e2))) -> (~((op (e1) (e2)) = (op (e2) (e2)))) -> ((op (e2) (e2)) = (e2)) -> (~((op (e0) (e3)) = (op (e1) (e3)))) -> ((op (e0) (e3)) = (e2)) -> False). % 15.22/15.43 do 0 intro. intros zenon_H84 zenon_H3e zenon_H3d zenon_H104 zenon_H3b zenon_H1b4 zenon_H145 zenon_H1b3 zenon_Hd6 zenon_H7d zenon_H35 zenon_H80 zenon_H81. % 15.22/15.43 apply (zenon_or_s _ _ zenon_H84); [ zenon_intro zenon_H68 | zenon_intro zenon_H85 ]. % 15.22/15.43 apply (zenon_L357_); trivial. % 15.22/15.43 apply (zenon_or_s _ _ zenon_H85); [ zenon_intro zenon_H6e | zenon_intro zenon_H86 ]. % 15.22/15.43 exact (zenon_Hd6 zenon_H6e). % 15.22/15.43 apply (zenon_or_s _ _ zenon_H86); [ zenon_intro zenon_H7c | zenon_intro zenon_H82 ]. % 15.22/15.43 apply (zenon_L21_); trivial. % 15.22/15.43 apply (zenon_L22_); trivial. % 15.22/15.43 (* end of lemma zenon_L522_ *) % 15.22/15.43 assert (zenon_L523_ : (((op (e0) (e0)) = (e2))\/(((op (e1) (e0)) = (e2))\/(((op (e2) (e0)) = (e2))\/((op (e3) (e0)) = (e2))))) -> (~((e2) = (e3))) -> (((op (e1) (e1)) = (e0))\/(((op (e1) (e1)) = (e1))\/(((op (e1) (e1)) = (e2))\/((op (e1) (e1)) = (e3))))) -> (~((op (e1) (e1)) = (e1))) -> (~((op (e1) (e1)) = (e2))) -> (~((op (e1) (e1)) = (e3))) -> (~((e1) = (e3))) -> (((op (e1) (e0)) = (e3))\/(((op (e1) (e1)) = (e3))\/(((op (e1) (e2)) = (e3))\/((op (e1) (e3)) = (e3))))) -> (~((op (e1) (e2)) = (op (e2) (e2)))) -> (((op (e1) (e0)) = (e2))\/(((op (e1) (e1)) = (e2))\/(((op (e1) (e2)) = (e2))\/((op (e1) (e3)) = (e2))))) -> (~((e1) = (e2))) -> ((op (e1) (e0)) = (e1)) -> (~((op (e2) (e0)) = (op (e2) (e2)))) -> ((op (e2) (e2)) = (e2)) -> ((op (e3) (e0)) = (e0)) -> (~((e0) = (e2))) -> False). % 15.22/15.43 do 0 intro. intros zenon_Heb zenon_H6a zenon_H1b3 zenon_H1b4 zenon_Hd6 zenon_H182 zenon_Ha3 zenon_H90 zenon_H7d zenon_H84 zenon_Ha7 zenon_Hd8 zenon_H17a zenon_H35 zenon_Hdb zenon_H5e. % 15.22/15.43 apply (zenon_or_s _ _ zenon_Heb); [ zenon_intro zenon_H92 | zenon_intro zenon_Hec ]. % 15.22/15.43 apply (zenon_L509_); trivial. % 15.22/15.43 apply (zenon_or_s _ _ zenon_Hec); [ zenon_intro zenon_H68 | zenon_intro zenon_Hed ]. % 15.22/15.43 apply (zenon_L162_); trivial. % 15.22/15.43 apply (zenon_or_s _ _ zenon_Hed); [ zenon_intro zenon_Hdd | zenon_intro zenon_He9 ]. % 15.22/15.43 apply (zenon_L161_); trivial. % 15.22/15.43 apply (zenon_L69_); trivial. % 15.22/15.43 (* end of lemma zenon_L523_ *) % 15.22/15.43 assert (zenon_L524_ : (((op (e1) (e0)) = (e2))\/(((op (e1) (e1)) = (e2))\/(((op (e1) (e2)) = (e2))\/((op (e1) (e3)) = (e2))))) -> (~((e2) = (e3))) -> ((op (e1) (e0)) = (e3)) -> (~((op (e1) (e1)) = (e2))) -> (~((op (e1) (e2)) = (op (e2) (e2)))) -> ((op (e2) (e2)) = (e2)) -> ((op (e1) (e3)) = (e0)) -> (~((e0) = (e2))) -> False). % 15.22/15.43 do 0 intro. intros zenon_H84 zenon_H6a zenon_H69 zenon_Hd6 zenon_H7d zenon_H35 zenon_Hcc zenon_H5e. % 15.22/15.43 apply (zenon_or_s _ _ zenon_H84); [ zenon_intro zenon_H68 | zenon_intro zenon_H85 ]. % 15.22/15.43 apply (zenon_L17_); trivial. % 15.22/15.43 apply (zenon_or_s _ _ zenon_H85); [ zenon_intro zenon_H6e | zenon_intro zenon_H86 ]. % 15.22/15.43 exact (zenon_Hd6 zenon_H6e). % 15.22/15.43 apply (zenon_or_s _ _ zenon_H86); [ zenon_intro zenon_H7c | zenon_intro zenon_H82 ]. % 15.22/15.43 apply (zenon_L21_); trivial. % 15.22/15.43 apply (zenon_L54_); trivial. % 15.22/15.43 (* end of lemma zenon_L524_ *) % 15.22/15.43 assert (zenon_L525_ : (((op (e1) (e0)) = (e0))\/(((op (e1) (e1)) = (e0))\/(((op (e1) (e2)) = (e0))\/((op (e1) (e3)) = (e0))))) -> (~((e0) = (e3))) -> (~((op (e3) (e3)) = (e3))) -> (~((op (e3) (e3)) = (e1))) -> (~((op (e3) (e3)) = (e0))) -> (((op (e3) (e3)) = (e0))\/(((op (e3) (e3)) = (e1))\/(((op (e3) (e3)) = (e2))\/((op (e3) (e3)) = (e3))))) -> (~((op (e1) (e1)) = (e1))) -> (~((op (e1) (e1)) = (e0))) -> (((op (e1) (e1)) = (e0))\/(((op (e1) (e1)) = (e1))\/(((op (e1) (e1)) = (e2))\/((op (e1) (e1)) = (e3))))) -> (((op (e1) (e0)) = (e2))\/(((op (e1) (e1)) = (e2))\/(((op (e1) (e2)) = (e2))\/((op (e1) (e3)) = (e2))))) -> (~((e2) = (e3))) -> ((op (e1) (e0)) = (e3)) -> (~((op (e1) (e1)) = (e2))) -> (~((op (e1) (e2)) = (op (e2) (e2)))) -> ((op (e2) (e2)) = (e2)) -> (~((e0) = (e2))) -> False). % 15.22/15.43 do 0 intro. intros zenon_H163 zenon_H4b zenon_H3e zenon_H104 zenon_H3c zenon_H3b zenon_H1b4 zenon_H145 zenon_H1b3 zenon_H84 zenon_H6a zenon_H69 zenon_Hd6 zenon_H7d zenon_H35 zenon_H5e. % 15.22/15.43 apply (zenon_or_s _ _ zenon_H163); [ zenon_intro zenon_Had | zenon_intro zenon_H164 ]. % 15.22/15.43 apply (zenon_L38_); trivial. % 15.22/15.43 apply (zenon_or_s _ _ zenon_H164); [ zenon_intro zenon_H149 | zenon_intro zenon_H165 ]. % 15.22/15.43 exact (zenon_H145 zenon_H149). % 15.22/15.43 apply (zenon_or_s _ _ zenon_H165); [ zenon_intro zenon_H15d | zenon_intro zenon_Hcc ]. % 15.22/15.43 apply (zenon_L490_); trivial. % 15.22/15.43 apply (zenon_L524_); trivial. % 15.22/15.43 (* end of lemma zenon_L525_ *) % 15.22/15.43 assert (zenon_L526_ : (((op (e0) (e0)) = (e1))\/(((op (e1) (e0)) = (e1))\/(((op (e2) (e0)) = (e1))\/((op (e3) (e0)) = (e1))))) -> (~((op (e0) (e0)) = (e1))) -> (~((op (e2) (e0)) = (op (e2) (e2)))) -> (~((e1) = (e2))) -> (((op (e1) (e0)) = (e3))\/(((op (e1) (e1)) = (e3))\/(((op (e1) (e2)) = (e3))\/((op (e1) (e3)) = (e3))))) -> (~((op (e1) (e1)) = (e3))) -> (((op (e0) (e0)) = (e2))\/(((op (e1) (e0)) = (e2))\/(((op (e2) (e0)) = (e2))\/((op (e3) (e0)) = (e2))))) -> (~((e0) = (e3))) -> (~((e1) = (e3))) -> (((op (e1) (e0)) = (e0))\/(((op (e1) (e1)) = (e0))\/(((op (e1) (e2)) = (e0))\/((op (e1) (e3)) = (e0))))) -> (~((op (e3) (e3)) = (e3))) -> (~((op (e3) (e3)) = (e1))) -> (~((op (e3) (e3)) = (e0))) -> (((op (e3) (e3)) = (e0))\/(((op (e3) (e3)) = (e1))\/(((op (e3) (e3)) = (e2))\/((op (e3) (e3)) = (e3))))) -> (~((op (e1) (e1)) = (e1))) -> (~((op (e1) (e1)) = (e0))) -> (((op (e1) (e1)) = (e0))\/(((op (e1) (e1)) = (e1))\/(((op (e1) (e1)) = (e2))\/((op (e1) (e1)) = (e3))))) -> (((op (e1) (e0)) = (e2))\/(((op (e1) (e1)) = (e2))\/(((op (e1) (e2)) = (e2))\/((op (e1) (e3)) = (e2))))) -> (~((e2) = (e3))) -> (~((op (e1) (e1)) = (e2))) -> (~((op (e1) (e2)) = (op (e2) (e2)))) -> ((op (e2) (e2)) = (e2)) -> (~((e0) = (e2))) -> (~((op (e0) (e0)) = (e3))) -> (((op (e0) (e0)) = (e3))\/(((op (e1) (e0)) = (e3))\/(((op (e2) (e0)) = (e3))\/((op (e3) (e0)) = (e3))))) -> ((op (e3) (e0)) = (e0)) -> (~((e0) = (e1))) -> False). % 15.22/15.43 do 0 intro. intros zenon_Hf1 zenon_H45 zenon_H17a zenon_Ha7 zenon_H90 zenon_H182 zenon_Heb zenon_H4b zenon_Ha3 zenon_H163 zenon_H3e zenon_H104 zenon_H3c zenon_H3b zenon_H1b4 zenon_H145 zenon_H1b3 zenon_H84 zenon_H6a zenon_Hd6 zenon_H7d zenon_H35 zenon_H5e zenon_H59 zenon_Hbe zenon_Hdb zenon_H9e. % 15.22/15.43 apply (zenon_or_s _ _ zenon_Hf1); [ zenon_intro zenon_H47 | zenon_intro zenon_Hf4 ]. % 15.22/15.43 exact (zenon_H45 zenon_H47). % 15.22/15.43 apply (zenon_or_s _ _ zenon_Hf4); [ zenon_intro zenon_Hd8 | zenon_intro zenon_Hf5 ]. % 15.22/15.43 apply (zenon_L523_); trivial. % 15.22/15.43 apply (zenon_or_s _ _ zenon_Hf5); [ zenon_intro zenon_Hae | zenon_intro zenon_Hee ]. % 15.22/15.43 apply (zenon_or_s _ _ zenon_Hbe); [ zenon_intro zenon_H5b | zenon_intro zenon_Hbf ]. % 15.22/15.43 exact (zenon_H59 zenon_H5b). % 15.22/15.43 apply (zenon_or_s _ _ zenon_Hbf); [ zenon_intro zenon_H69 | zenon_intro zenon_Hc0 ]. % 15.22/15.43 apply (zenon_L525_); trivial. % 15.22/15.43 apply (zenon_or_s _ _ zenon_Hc0); [ zenon_intro zenon_Haf | zenon_intro zenon_Hba ]. % 15.22/15.43 apply (zenon_L39_); trivial. % 15.22/15.43 apply (zenon_L62_); trivial. % 15.22/15.43 apply (zenon_L71_); trivial. % 15.22/15.43 (* end of lemma zenon_L526_ *) % 15.22/15.43 assert (zenon_L527_ : (((op (e1) (e0)) = (e3))\/(((op (e1) (e1)) = (e3))\/(((op (e1) (e2)) = (e3))\/((op (e1) (e3)) = (e3))))) -> (~((e1) = (e3))) -> ((op (e1) (e0)) = (e1)) -> (~((op (e1) (e1)) = (e3))) -> (~((op (e1) (e2)) = (op (e3) (e2)))) -> ((op (e3) (e2)) = (e3)) -> (~((op (e0) (e3)) = (op (e1) (e3)))) -> ((op (e0) (e3)) = (e3)) -> False). % 15.22/15.43 do 0 intro. intros zenon_H90 zenon_Ha3 zenon_Hd8 zenon_H182 zenon_H17d zenon_H106 zenon_H80 zenon_H53. % 15.22/15.43 apply (zenon_or_s _ _ zenon_H90); [ zenon_intro zenon_H69 | zenon_intro zenon_H94 ]. % 15.22/15.43 apply (zenon_L163_); trivial. % 15.22/15.43 apply (zenon_or_s _ _ zenon_H94); [ zenon_intro zenon_H96 | zenon_intro zenon_H95 ]. % 15.22/15.43 exact (zenon_H182 zenon_H96). % 15.22/15.43 apply (zenon_or_s _ _ zenon_H95); [ zenon_intro zenon_H88 | zenon_intro zenon_H8a ]. % 15.22/15.43 apply (zenon_L164_); trivial. % 15.22/15.43 apply (zenon_L293_); trivial. % 15.22/15.43 (* end of lemma zenon_L527_ *) % 15.22/15.43 assert (zenon_L528_ : (((op (e0) (e0)) = (e3))\/(((op (e1) (e0)) = (e3))\/(((op (e2) (e0)) = (e3))\/((op (e3) (e0)) = (e3))))) -> (~((op (e0) (e0)) = (e3))) -> (~((e2) = (e3))) -> ((op (e1) (e0)) = (e2)) -> (~((e1) = (e3))) -> ((op (e2) (e0)) = (e1)) -> (~((op (e3) (e0)) = (op (e3) (e2)))) -> ((op (e3) (e2)) = (e3)) -> False). % 15.22/15.43 do 0 intro. intros zenon_Hbe zenon_H59 zenon_H6a zenon_H68 zenon_Ha3 zenon_Hae zenon_H105 zenon_H106. % 15.22/15.43 apply (zenon_or_s _ _ zenon_Hbe); [ zenon_intro zenon_H5b | zenon_intro zenon_Hbf ]. % 15.22/15.43 exact (zenon_H59 zenon_H5b). % 15.22/15.43 apply (zenon_or_s _ _ zenon_Hbf); [ zenon_intro zenon_H69 | zenon_intro zenon_Hc0 ]. % 15.22/15.43 apply (zenon_L17_); trivial. % 15.22/15.43 apply (zenon_or_s _ _ zenon_Hc0); [ zenon_intro zenon_Haf | zenon_intro zenon_Hba ]. % 15.22/15.43 apply (zenon_L39_); trivial. % 15.22/15.43 apply (zenon_L81_); trivial. % 15.22/15.43 (* end of lemma zenon_L528_ *) % 15.22/15.43 assert (zenon_L529_ : (~((op (e1) (e3)) = (op (e2) (e3)))) -> ((op (e1) (e3)) = (e1)) -> ((op (e2) (e3)) = (e1)) -> False). % 15.22/15.43 do 0 intro. intros zenon_H244 zenon_H11f zenon_Hb5. % 15.22/15.43 cut (((op (e1) (e3)) = (e1)) = ((op (e1) (e3)) = (op (e2) (e3)))). % 15.22/15.43 intro zenon_D_pnotp. % 15.22/15.43 apply zenon_H244. % 15.22/15.43 rewrite <- zenon_D_pnotp. % 15.22/15.43 exact zenon_H11f. % 15.22/15.43 cut (((e1) = (op (e2) (e3)))); [idtac | apply NNPP; zenon_intro zenon_Hb6]. % 15.22/15.43 cut (((op (e1) (e3)) = (op (e1) (e3)))); [idtac | apply NNPP; zenon_intro zenon_H23a]. % 15.22/15.43 congruence. % 15.22/15.43 apply zenon_H23a. apply refl_equal. % 15.22/15.43 apply zenon_Hb6. apply sym_equal. exact zenon_Hb5. % 15.22/15.43 (* end of lemma zenon_L529_ *) % 15.22/15.43 assert (zenon_L530_ : (((op (e2) (e0)) = (e1))\/(((op (e2) (e1)) = (e1))\/(((op (e2) (e2)) = (e1))\/((op (e2) (e3)) = (e1))))) -> ((op (e3) (e2)) = (e3)) -> (~((op (e3) (e0)) = (op (e3) (e2)))) -> (~((e1) = (e3))) -> ((op (e1) (e0)) = (e2)) -> (~((e2) = (e3))) -> (~((op (e0) (e0)) = (e3))) -> (((op (e0) (e0)) = (e3))\/(((op (e1) (e0)) = (e3))\/(((op (e2) (e0)) = (e3))\/((op (e3) (e0)) = (e3))))) -> ((op (e0) (e1)) = (e1)) -> (~((op (e0) (e1)) = (op (e2) (e1)))) -> (~((op (e2) (e2)) = (e1))) -> (~((op (e1) (e3)) = (op (e2) (e3)))) -> ((op (e1) (e3)) = (e1)) -> False). % 15.22/15.43 do 0 intro. intros zenon_Hb7 zenon_H106 zenon_H105 zenon_Ha3 zenon_H68 zenon_H6a zenon_H59 zenon_Hbe zenon_H22 zenon_Hde zenon_H52 zenon_H244 zenon_H11f. % 15.22/15.43 apply (zenon_or_s _ _ zenon_Hb7); [ zenon_intro zenon_Hae | zenon_intro zenon_Hb8 ]. % 15.22/15.43 apply (zenon_L528_); trivial. % 15.22/15.43 apply (zenon_or_s _ _ zenon_Hb8); [ zenon_intro zenon_Hb2 | zenon_intro zenon_Hb9 ]. % 15.22/15.43 apply (zenon_L336_); trivial. % 15.22/15.43 apply (zenon_or_s _ _ zenon_Hb9); [ zenon_intro zenon_H2a | zenon_intro zenon_Hb5 ]. % 15.22/15.43 exact (zenon_H52 zenon_H2a). % 15.22/15.43 apply (zenon_L529_); trivial. % 15.22/15.43 (* end of lemma zenon_L530_ *) % 15.22/15.43 assert (zenon_L531_ : (((op (e1) (e0)) = (e2))\/(((op (e1) (e1)) = (e2))\/(((op (e1) (e2)) = (e2))\/((op (e1) (e3)) = (e2))))) -> (~((op (e1) (e3)) = (op (e2) (e3)))) -> (~((op (e2) (e2)) = (e1))) -> (~((op (e0) (e1)) = (op (e2) (e1)))) -> ((op (e0) (e1)) = (e1)) -> (((op (e0) (e0)) = (e3))\/(((op (e1) (e0)) = (e3))\/(((op (e2) (e0)) = (e3))\/((op (e3) (e0)) = (e3))))) -> (~((op (e0) (e0)) = (e3))) -> (~((e2) = (e3))) -> (~((e1) = (e3))) -> (~((op (e3) (e0)) = (op (e3) (e2)))) -> ((op (e3) (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)) = (op (e2) (e2)))) -> ((op (e2) (e2)) = (e2)) -> ((op (e1) (e3)) = (e1)) -> (~((e1) = (e2))) -> False). % 15.22/15.43 do 0 intro. intros zenon_H84 zenon_H244 zenon_H52 zenon_Hde zenon_H22 zenon_Hbe zenon_H59 zenon_H6a zenon_Ha3 zenon_H105 zenon_H106 zenon_Hb7 zenon_Hd6 zenon_H7d zenon_H35 zenon_H11f zenon_Ha7. % 15.22/15.43 apply (zenon_or_s _ _ zenon_H84); [ zenon_intro zenon_H68 | zenon_intro zenon_H85 ]. % 15.22/15.43 apply (zenon_L530_); trivial. % 15.22/15.43 apply (zenon_or_s _ _ zenon_H85); [ zenon_intro zenon_H6e | zenon_intro zenon_H86 ]. % 15.22/15.43 exact (zenon_Hd6 zenon_H6e). % 15.22/15.43 apply (zenon_or_s _ _ zenon_H86); [ zenon_intro zenon_H7c | zenon_intro zenon_H82 ]. % 15.22/15.43 apply (zenon_L21_); trivial. % 15.22/15.43 apply (zenon_L209_); trivial. % 15.22/15.43 (* end of lemma zenon_L531_ *) % 15.22/15.43 assert (zenon_L532_ : (((op (e0) (e0)) = (e3))\/(((op (e0) (e1)) = (e3))\/(((op (e0) (e2)) = (e3))\/((op (e0) (e3)) = (e3))))) -> ((op (e0) (e2)) = (e0)) -> (((op (e1) (e0)) = (e1))\/(((op (e1) (e1)) = (e1))\/(((op (e1) (e2)) = (e1))\/((op (e1) (e3)) = (e1))))) -> (~((op (e1) (e2)) = (op (e3) (e2)))) -> (~((op (e1) (e1)) = (e1))) -> (~((op (e0) (e3)) = (op (e1) (e3)))) -> (~((op (e1) (e1)) = (e3))) -> ((op (e1) (e0)) = (e0)) -> (~((e0) = (e3))) -> (((op (e1) (e0)) = (e3))\/(((op (e1) (e1)) = (e3))\/(((op (e1) (e2)) = (e3))\/((op (e1) (e3)) = (e3))))) -> (((op (e1) (e0)) = (e2))\/(((op (e1) (e1)) = (e2))\/(((op (e1) (e2)) = (e2))\/((op (e1) (e3)) = (e2))))) -> (~((op (e1) (e3)) = (op (e2) (e3)))) -> (~((op (e2) (e2)) = (e1))) -> (~((op (e0) (e1)) = (op (e2) (e1)))) -> ((op (e0) (e1)) = (e1)) -> (((op (e0) (e0)) = (e3))\/(((op (e1) (e0)) = (e3))\/(((op (e2) (e0)) = (e3))\/((op (e3) (e0)) = (e3))))) -> (~((op (e0) (e0)) = (e3))) -> (~((e2) = (e3))) -> (~((e1) = (e3))) -> (~((op (e3) (e0)) = (op (e3) (e2)))) -> ((op (e3) (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)) = (op (e2) (e2)))) -> ((op (e2) (e2)) = (e2)) -> (~((e1) = (e2))) -> False). % 15.22/15.43 do 0 intro. intros zenon_H58 zenon_Hab zenon_H1c5 zenon_H17d zenon_H1b4 zenon_H80 zenon_H182 zenon_Had zenon_H4b zenon_H90 zenon_H84 zenon_H244 zenon_H52 zenon_Hde zenon_H22 zenon_Hbe zenon_H59 zenon_H6a zenon_Ha3 zenon_H105 zenon_H106 zenon_Hb7 zenon_Hd6 zenon_H7d zenon_H35 zenon_Ha7. % 15.22/15.43 apply (zenon_or_s _ _ zenon_H58); [ zenon_intro zenon_H5b | zenon_intro zenon_H5a ]. % 15.22/15.43 exact (zenon_H59 zenon_H5b). % 15.22/15.43 apply (zenon_or_s _ _ zenon_H5a); [ zenon_intro zenon_H4a | zenon_intro zenon_H5c ]. % 15.22/15.43 apply (zenon_L59_); trivial. % 15.22/15.43 apply (zenon_or_s _ _ zenon_H5c); [ zenon_intro zenon_H50 | zenon_intro zenon_H53 ]. % 15.22/15.43 apply (zenon_L48_); trivial. % 15.22/15.43 apply (zenon_or_s _ _ zenon_H1c5); [ zenon_intro zenon_Hd8 | zenon_intro zenon_H1c6 ]. % 15.22/15.43 apply (zenon_L527_); trivial. % 15.22/15.43 apply (zenon_or_s _ _ zenon_H1c6); [ zenon_intro zenon_H21 | zenon_intro zenon_H1c7 ]. % 15.22/15.43 exact (zenon_H1b4 zenon_H21). % 15.22/15.43 apply (zenon_or_s _ _ zenon_H1c7); [ zenon_intro zenon_H117 | zenon_intro zenon_H11f ]. % 15.22/15.43 apply (zenon_L521_); trivial. % 15.22/15.43 apply (zenon_L531_); trivial. % 15.22/15.43 (* end of lemma zenon_L532_ *) % 15.22/15.43 assert (zenon_L533_ : ((op (e3) (e2)) = (e3)) -> ((op (e0) (e2)) = (e3)) -> (~((op (e0) (e2)) = (op (e3) (e2)))) -> False). % 15.22/15.43 do 0 intro. intros zenon_H106 zenon_H50 zenon_H140. % 15.22/15.43 elim (classic ((op (e3) (e2)) = (op (e3) (e2)))); [ zenon_intro zenon_H17e | zenon_intro zenon_H17f ]. % 15.22/15.43 cut (((op (e3) (e2)) = (op (e3) (e2))) = ((op (e0) (e2)) = (op (e3) (e2)))). % 15.22/15.43 intro zenon_D_pnotp. % 15.22/15.43 apply zenon_H140. % 15.22/15.43 rewrite <- zenon_D_pnotp. % 15.22/15.43 exact zenon_H17e. % 15.22/15.43 cut (((op (e3) (e2)) = (op (e3) (e2)))); [idtac | apply NNPP; zenon_intro zenon_H17f]. % 15.22/15.43 cut (((op (e3) (e2)) = (op (e0) (e2)))); [idtac | apply NNPP; zenon_intro zenon_H245]. % 15.22/15.43 congruence. % 15.22/15.43 cut (((op (e3) (e2)) = (e3)) = ((op (e3) (e2)) = (op (e0) (e2)))). % 15.22/15.43 intro zenon_D_pnotp. % 15.22/15.43 apply zenon_H245. % 15.22/15.43 rewrite <- zenon_D_pnotp. % 15.22/15.43 exact zenon_H106. % 15.22/15.43 cut (((e3) = (op (e0) (e2)))); [idtac | apply NNPP; zenon_intro zenon_H246]. % 15.22/15.43 cut (((op (e3) (e2)) = (op (e3) (e2)))); [idtac | apply NNPP; zenon_intro zenon_H17f]. % 15.22/15.43 congruence. % 15.22/15.43 apply zenon_H17f. apply refl_equal. % 15.22/15.43 apply zenon_H246. apply sym_equal. exact zenon_H50. % 15.22/15.43 apply zenon_H17f. apply refl_equal. % 15.22/15.43 apply zenon_H17f. apply refl_equal. % 15.22/15.43 (* end of lemma zenon_L533_ *) % 15.22/15.43 assert (zenon_L534_ : (((op (e0) (e0)) = (e3))\/(((op (e0) (e1)) = (e3))\/(((op (e0) (e2)) = (e3))\/((op (e0) (e3)) = (e3))))) -> (~((op (e0) (e0)) = (e3))) -> (~((e2) = (e3))) -> ((op (e0) (e1)) = (e2)) -> (~((op (e0) (e2)) = (op (e3) (e2)))) -> ((op (e3) (e2)) = (e3)) -> ((op (e0) (e3)) = (e1)) -> (~((e1) = (e3))) -> False). % 15.22/15.43 do 0 intro. intros zenon_H58 zenon_H59 zenon_H6a zenon_H5d zenon_H140 zenon_H106 zenon_H37 zenon_Ha3. % 15.22/15.43 apply (zenon_or_s _ _ zenon_H58); [ zenon_intro zenon_H5b | zenon_intro zenon_H5a ]. % 15.22/15.43 exact (zenon_H59 zenon_H5b). % 15.22/15.43 apply (zenon_or_s _ _ zenon_H5a); [ zenon_intro zenon_H4a | zenon_intro zenon_H5c ]. % 15.22/15.43 apply (zenon_L50_); trivial. % 15.22/15.43 apply (zenon_or_s _ _ zenon_H5c); [ zenon_intro zenon_H50 | zenon_intro zenon_H53 ]. % 15.22/15.43 apply (zenon_L533_); trivial. % 15.22/15.43 apply (zenon_L32_); trivial. % 15.22/15.43 (* end of lemma zenon_L534_ *) % 15.22/15.43 assert (zenon_L535_ : ((~((op (e3) (e3)) = (e3)))\/((op (e3) (e3)) = (e3))) -> ((op (e3) (e1)) = (e3)) -> (~((op (e3) (e1)) = (op (e3) (e3)))) -> (((op (e1) (e0)) = (e2))\/(((op (e1) (e1)) = (e2))\/(((op (e1) (e2)) = (e2))\/((op (e1) (e3)) = (e2))))) -> (~((e1) = (e3))) -> (~((op (e1) (e1)) = (e3))) -> (((op (e1) (e1)) = (e0))\/(((op (e1) (e1)) = (e1))\/(((op (e1) (e1)) = (e2))\/((op (e1) (e1)) = (e3))))) -> (~((op (e1) (e1)) = (e1))) -> (~((e2) = (e3))) -> (((op (e1) (e0)) = (e3))\/(((op (e1) (e1)) = (e3))\/(((op (e1) (e2)) = (e3))\/((op (e1) (e3)) = (e3))))) -> ((op (e2) (e2)) = (e2)) -> (~((op (e1) (e2)) = (op (e2) (e2)))) -> (~((op (e1) (e1)) = (e2))) -> ((op (e1) (e0)) = (e1)) -> (~((e1) = (e2))) -> (~((op (e2) (e0)) = (op (e2) (e2)))) -> (~((op (e3) (e3)) = (e0))) -> (~((op (e3) (e3)) = (e2))) -> (((op (e3) (e3)) = (e0))\/(((op (e3) (e3)) = (e1))\/(((op (e3) (e3)) = (e2))\/((op (e3) (e3)) = (e3))))) -> (((op (e0) (e0)) = (e2))\/(((op (e1) (e0)) = (e2))\/(((op (e2) (e0)) = (e2))\/((op (e3) (e0)) = (e2))))) -> False). % 15.22/15.43 do 0 intro. intros zenon_H10d zenon_H10a zenon_H12d zenon_H84 zenon_Ha3 zenon_H182 zenon_H1b3 zenon_H1b4 zenon_H6a zenon_H90 zenon_H35 zenon_H7d zenon_Hd6 zenon_Hd8 zenon_Ha7 zenon_H17a zenon_H3c zenon_H3d zenon_H3b zenon_Heb. % 15.22/15.43 apply (zenon_or_s _ _ zenon_H10d); [ zenon_intro zenon_H3e | zenon_intro zenon_H42 ]. % 15.22/15.43 apply (zenon_L511_); trivial. % 15.22/15.43 apply (zenon_L102_); trivial. % 15.22/15.43 (* end of lemma zenon_L535_ *) % 15.22/15.43 assert (zenon_L536_ : (((op (e2) (e0)) = (e3))\/(((op (e2) (e1)) = (e3))\/(((op (e2) (e2)) = (e3))\/((op (e2) (e3)) = (e3))))) -> (~((e1) = (e3))) -> ((op (e2) (e0)) = (e1)) -> (~((op (e2) (e1)) = (op (e3) (e1)))) -> ((op (e3) (e1)) = (e3)) -> (~((op (e2) (e2)) = (e3))) -> (~((op (e0) (e3)) = (op (e2) (e3)))) -> ((op (e0) (e3)) = (e3)) -> False). % 15.22/15.43 do 0 intro. intros zenon_He6 zenon_Ha3 zenon_Hae zenon_H13c zenon_H10a zenon_H30 zenon_Hb4 zenon_H53. % 15.22/15.43 apply (zenon_or_s _ _ zenon_He6); [ zenon_intro zenon_Haf | zenon_intro zenon_He7 ]. % 15.22/15.43 apply (zenon_L39_); trivial. % 15.22/15.43 apply (zenon_or_s _ _ zenon_He7); [ zenon_intro zenon_Hdf | zenon_intro zenon_He8 ]. % 15.22/15.43 apply (zenon_L121_); trivial. % 15.22/15.43 apply (zenon_or_s _ _ zenon_He8); [ zenon_intro zenon_H34 | zenon_intro zenon_He2 ]. % 15.22/15.43 exact (zenon_H30 zenon_H34). % 15.22/15.43 apply (zenon_L125_); trivial. % 15.22/15.43 (* end of lemma zenon_L536_ *) % 15.22/15.43 assert (zenon_L537_ : (((op (e0) (e0)) = (e3))\/(((op (e0) (e1)) = (e3))\/(((op (e0) (e2)) = (e3))\/((op (e0) (e3)) = (e3))))) -> (~((op (e0) (e0)) = (e3))) -> (~((op (e0) (e1)) = (op (e3) (e1)))) -> (~((e0) = (e3))) -> ((op (e0) (e2)) = (e0)) -> (((op (e2) (e0)) = (e3))\/(((op (e2) (e1)) = (e3))\/(((op (e2) (e2)) = (e3))\/((op (e2) (e3)) = (e3))))) -> (~((e1) = (e3))) -> ((op (e2) (e0)) = (e1)) -> (~((op (e2) (e1)) = (op (e3) (e1)))) -> ((op (e3) (e1)) = (e3)) -> (~((op (e2) (e2)) = (e3))) -> (~((op (e0) (e3)) = (op (e2) (e3)))) -> False). % 15.22/15.43 do 0 intro. intros zenon_H58 zenon_H59 zenon_H138 zenon_H4b zenon_Hab zenon_He6 zenon_Ha3 zenon_Hae zenon_H13c zenon_H10a zenon_H30 zenon_Hb4. % 15.22/15.43 apply (zenon_or_s _ _ zenon_H58); [ zenon_intro zenon_H5b | zenon_intro zenon_H5a ]. % 15.22/15.43 exact (zenon_H59 zenon_H5b). % 15.22/15.43 apply (zenon_or_s _ _ zenon_H5a); [ zenon_intro zenon_H4a | zenon_intro zenon_H5c ]. % 15.22/15.43 apply (zenon_L120_); trivial. % 15.22/15.43 apply (zenon_or_s _ _ zenon_H5c); [ zenon_intro zenon_H50 | zenon_intro zenon_H53 ]. % 15.22/15.43 apply (zenon_L48_); trivial. % 15.22/15.43 apply (zenon_L536_); trivial. % 15.22/15.43 (* end of lemma zenon_L537_ *) % 15.22/15.43 assert (zenon_L538_ : ((~((op (e3) (e3)) = (e2)))\/((op (e3) (e2)) = (e3))) -> (((op (e0) (e0)) = (e1))\/(((op (e1) (e0)) = (e1))\/(((op (e2) (e0)) = (e1))\/((op (e3) (e0)) = (e1))))) -> (((op (e0) (e1)) = (e2))\/(((op (e1) (e1)) = (e2))\/(((op (e2) (e1)) = (e2))\/((op (e3) (e1)) = (e2))))) -> (~((op (e2) (e1)) = (op (e2) (e2)))) -> (~((e0) = (e2))) -> (~((op (e1) (e1)) = (e0))) -> (((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))))) -> (~((op (e2) (e2)) = (op (e2) (e3)))) -> (~((op (e0) (e1)) = (op (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) (e1)) = (op (e3) (e2)))) -> (~((e0) = (e1))) -> (~((op (e2) (e2)) = (e0))) -> (((op (e0) (e2)) = (e0))\/(((op (e1) (e2)) = (e0))\/(((op (e2) (e2)) = (e0))\/((op (e3) (e2)) = (e0))))) -> (~((op (e1) (e0)) = (op (e3) (e0)))) -> (((op (e0) (e1)) = (e0))\/(((op (e1) (e1)) = (e0))\/(((op (e2) (e1)) = (e0))\/((op (e3) (e1)) = (e0))))) -> (~((op (e0) (e0)) = (e3))) -> (~((op (e0) (e1)) = (op (e3) (e1)))) -> (~((e0) = (e3))) -> ((op (e0) (e2)) = (e0)) -> (((op (e2) (e0)) = (e3))\/(((op (e2) (e1)) = (e3))\/(((op (e2) (e2)) = (e3))\/((op (e2) (e3)) = (e3))))) -> (~((op (e0) (e3)) = (op (e2) (e3)))) -> (~((op (e2) (e2)) = (e3))) -> (~((op (e2) (e1)) = (op (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 (e3) (e3)) = (e0))\/(((op (e3) (e3)) = (e1))\/(((op (e3) (e3)) = (e2))\/((op (e3) (e3)) = (e3))))) -> (~((op (e3) (e3)) = (e0))) -> (~((op (e2) (e0)) = (op (e2) (e2)))) -> (~((e1) = (e2))) -> (~((op (e1) (e1)) = (e2))) -> (~((op (e1) (e2)) = (op (e2) (e2)))) -> ((op (e2) (e2)) = (e2)) -> (((op (e1) (e0)) = (e3))\/(((op (e1) (e1)) = (e3))\/(((op (e1) (e2)) = (e3))\/((op (e1) (e3)) = (e3))))) -> (~((e2) = (e3))) -> (~((op (e1) (e1)) = (e1))) -> (((op (e1) (e1)) = (e0))\/(((op (e1) (e1)) = (e1))\/(((op (e1) (e1)) = (e2))\/((op (e1) (e1)) = (e3))))) -> (~((op (e1) (e1)) = (e3))) -> (~((e1) = (e3))) -> (((op (e1) (e0)) = (e2))\/(((op (e1) (e1)) = (e2))\/(((op (e1) (e2)) = (e2))\/((op (e1) (e3)) = (e2))))) -> (~((op (e3) (e1)) = (op (e3) (e3)))) -> ((op (e3) (e1)) = (e3)) -> ((~((op (e3) (e3)) = (e3)))\/((op (e3) (e3)) = (e3))) -> (~((op (e0) (e0)) = (e1))) -> False). % 15.22/15.43 do 0 intro. intros zenon_H10e zenon_Hf1 zenon_H1a2 zenon_H157 zenon_H5e zenon_H145 zenon_H1c5 zenon_H160 zenon_H15f zenon_H1cd zenon_H23 zenon_H175 zenon_H135 zenon_H9e zenon_H2e zenon_H16f zenon_H22e zenon_H144 zenon_H59 zenon_H138 zenon_H4b zenon_Hab zenon_He6 zenon_Hb4 zenon_H30 zenon_H13c zenon_H58 zenon_Heb zenon_H3b zenon_H3c zenon_H17a zenon_Ha7 zenon_Hd6 zenon_H7d zenon_H35 zenon_H90 zenon_H6a zenon_H1b4 zenon_H1b3 zenon_H182 zenon_Ha3 zenon_H84 zenon_H12d zenon_H10a zenon_H10d zenon_H45. % 15.22/15.43 apply (zenon_or_s _ _ zenon_H10e); [ zenon_intro zenon_H3d | zenon_intro zenon_H106 ]. % 15.22/15.43 apply (zenon_or_s _ _ zenon_H10d); [ zenon_intro zenon_H3e | zenon_intro zenon_H42 ]. % 15.22/15.43 apply (zenon_or_s _ _ zenon_Hf1); [ zenon_intro zenon_H47 | zenon_intro zenon_Hf4 ]. % 15.22/15.43 exact (zenon_H45 zenon_H47). % 15.22/15.43 apply (zenon_or_s _ _ zenon_Hf4); [ zenon_intro zenon_Hd8 | zenon_intro zenon_Hf5 ]. % 15.22/15.43 apply (zenon_L535_); trivial. % 15.22/15.43 apply (zenon_or_s _ _ zenon_Hf5); [ zenon_intro zenon_Hae | zenon_intro zenon_Hee ]. % 15.22/15.43 apply (zenon_L537_); trivial. % 15.22/15.43 apply (zenon_or_s _ _ zenon_H144); [ zenon_intro zenon_H49 | zenon_intro zenon_H147 ]. % 15.22/15.43 apply (zenon_L349_); trivial. % 15.22/15.43 apply (zenon_or_s _ _ zenon_H147); [ zenon_intro zenon_H149 | zenon_intro zenon_H148 ]. % 15.22/15.43 exact (zenon_H145 zenon_H149). % 15.22/15.43 apply (zenon_or_s _ _ zenon_H148); [ zenon_intro zenon_H14a | zenon_intro zenon_H142 ]. % 15.22/15.43 apply (zenon_or_s _ _ zenon_H1c5); [ zenon_intro zenon_Hd8 | zenon_intro zenon_H1c6 ]. % 15.22/15.43 apply (zenon_L393_); trivial. % 15.22/15.43 apply (zenon_or_s _ _ zenon_H1c6); [ zenon_intro zenon_H21 | zenon_intro zenon_H1c7 ]. % 15.22/15.43 exact (zenon_H1b4 zenon_H21). % 15.22/15.43 apply (zenon_or_s _ _ zenon_H1c7); [ zenon_intro zenon_H117 | zenon_intro zenon_H11f ]. % 15.22/15.43 apply (zenon_L500_); trivial. % 15.22/15.43 apply (zenon_L493_); trivial. % 15.22/15.43 apply (zenon_L126_); trivial. % 15.22/15.43 apply (zenon_L102_); trivial. % 15.22/15.44 apply (zenon_L115_); trivial. % 15.22/15.44 (* end of lemma zenon_L538_ *) % 15.22/15.44 assert (zenon_L539_ : ((~((op (e1) (e1)) = (e2)))\/((op (e1) (e2)) = (e1))) -> (~((op (e1) (e0)) = (op (e1) (e2)))) -> ((~((op (e3) (e3)) = (e3)))\/((op (e3) (e3)) = (e3))) -> ((~((op (e2) (e2)) = (e2)))\/((op (e2) (e2)) = (e2))) -> (~((op (e0) (e3)) = (op (e1) (e3)))) -> (~((op (e0) (e2)) = (op (e2) (e2)))) -> (((op (e0) (e0)) = (e3))\/(((op (e1) (e0)) = (e3))\/(((op (e2) (e0)) = (e3))\/((op (e3) (e0)) = (e3))))) -> (~((op (e3) (e0)) = (op (e3) (e3)))) -> (((op (e2) (e2)) = (e0))\/(((op (e2) (e2)) = (e1))\/(((op (e2) (e2)) = (e2))\/((op (e2) (e2)) = (e3))))) -> (~((op (e0) (e0)) = (e3))) -> ((~((op (e3) (e3)) = (e0)))\/((op (e3) (e0)) = (e3))) -> (((op (e0) (e0)) = (e1))\/(((op (e0) (e1)) = (e1))\/(((op (e0) (e2)) = (e1))\/((op (e0) (e3)) = (e1))))) -> (~((op (e1) (e3)) = (op (e3) (e3)))) -> (((op (e0) (e0)) = (e3))\/(((op (e0) (e1)) = (e3))\/(((op (e0) (e2)) = (e3))\/((op (e0) (e3)) = (e3))))) -> (~((op (e0) (e3)) = (op (e3) (e3)))) -> (~((op (e0) (e2)) = (op (e1) (e2)))) -> (~((op (e0) (e2)) = (op (e0) (e3)))) -> (~((e0) = (e2))) -> (((op (e0) (e3)) = (e0))\/(((op (e1) (e3)) = (e0))\/(((op (e2) (e3)) = (e0))\/((op (e3) (e3)) = (e0))))) -> (((op (e0) (e0)) = (e2))\/(((op (e0) (e1)) = (e2))\/(((op (e0) (e2)) = (e2))\/((op (e0) (e3)) = (e2))))) -> ((op (e0) (e2)) = (e0)) -> (~((e0) = (e1))) -> (~((op (e0) (e1)) = (op (e0) (e3)))) -> (~((op (e1) (e0)) = (op (e1) (e3)))) -> (((op (e0) (e3)) = (e1))\/(((op (e1) (e3)) = (e1))\/(((op (e2) (e3)) = (e1))\/((op (e3) (e3)) = (e1))))) -> (~((op (e0) (e0)) = (e1))) -> (~((op (e3) (e1)) = (op (e3) (e3)))) -> ((~((op (e3) (e3)) = (e1)))\/((op (e3) (e1)) = (e3))) -> ((~((op (e2) (e2)) = (e3)))\/((op (e2) (e3)) = (e2))) -> ((~((op (e2) (e2)) = (e0)))\/((op (e2) (e0)) = (e2))) -> (((op (e1) (e0)) = (e2))\/(((op (e1) (e1)) = (e2))\/(((op (e1) (e2)) = (e2))\/((op (e1) (e3)) = (e2))))) -> (~((e1) = (e3))) -> (((op (e1) (e1)) = (e0))\/(((op (e1) (e1)) = (e1))\/(((op (e1) (e1)) = (e2))\/((op (e1) (e1)) = (e3))))) -> (~((op (e1) (e1)) = (e1))) -> (~((e2) = (e3))) -> (((op (e1) (e0)) = (e3))\/(((op (e1) (e1)) = (e3))\/(((op (e1) (e2)) = (e3))\/((op (e1) (e3)) = (e3))))) -> ((op (e2) (e2)) = (e2)) -> (~((op (e1) (e2)) = (op (e2) (e2)))) -> ((op (e1) (e0)) = (e1)) -> (~((e1) = (e2))) -> (~((op (e2) (e0)) = (op (e2) (e2)))) -> (((op (e3) (e3)) = (e0))\/(((op (e3) (e3)) = (e1))\/(((op (e3) (e3)) = (e2))\/((op (e3) (e3)) = (e3))))) -> (((op (e0) (e0)) = (e2))\/(((op (e1) (e0)) = (e2))\/(((op (e2) (e0)) = (e2))\/((op (e3) (e0)) = (e2))))) -> (~((op (e1) (e2)) = (op (e3) (e2)))) -> ((~((op (e3) (e3)) = (e2)))\/((op (e3) (e2)) = (e3))) -> ((~((op (e1) (e1)) = (e3)))\/((op (e1) (e3)) = (e1))) -> False). % 15.22/15.44 do 0 intro. intros zenon_H1d3 zenon_H166 zenon_H10d zenon_Haa zenon_H80 zenon_H28 zenon_Hbe zenon_Hbb zenon_H2d zenon_H59 zenon_H10f zenon_H44 zenon_H8b zenon_H58 zenon_H36 zenon_H87 zenon_Hc9 zenon_H5e zenon_Hd3 zenon_H8e zenon_Hab zenon_H9e zenon_H1cd zenon_H1cf zenon_H121 zenon_H45 zenon_H12d zenon_H10c zenon_H1c3 zenon_H1d4 zenon_H84 zenon_Ha3 zenon_H1b3 zenon_H1b4 zenon_H6a zenon_H90 zenon_H35 zenon_H7d zenon_Hd8 zenon_Ha7 zenon_H17a zenon_H3b zenon_Heb zenon_H17d zenon_H10e zenon_H1d2. % 15.22/15.44 apply (zenon_or_s _ _ zenon_H1d3); [ zenon_intro zenon_Hd6 | zenon_intro zenon_H117 ]. % 15.22/15.44 apply (zenon_L514_); trivial. % 15.22/15.44 apply (zenon_L248_); trivial. % 15.22/15.44 (* end of lemma zenon_L539_ *) % 15.22/15.44 assert (zenon_L540_ : (~((op (e1) (e0)) = (op (e2) (e0)))) -> ((op (e1) (e0)) = (e1)) -> ((op (e2) (e0)) = (e1)) -> False). % 15.22/15.44 do 0 intro. intros zenon_H247 zenon_Hd8 zenon_Hae. % 15.22/15.44 cut (((op (e1) (e0)) = (e1)) = ((op (e1) (e0)) = (op (e2) (e0)))). % 15.22/15.44 intro zenon_D_pnotp. % 15.22/15.44 apply zenon_H247. % 15.22/15.44 rewrite <- zenon_D_pnotp. % 15.22/15.44 exact zenon_Hd8. % 15.22/15.44 cut (((e1) = (op (e2) (e0)))); [idtac | apply NNPP; zenon_intro zenon_H248]. % 15.22/15.44 cut (((op (e1) (e0)) = (op (e1) (e0)))); [idtac | apply NNPP; zenon_intro zenon_Hda]. % 15.22/15.44 congruence. % 15.22/15.44 apply zenon_Hda. apply refl_equal. % 15.22/15.44 apply zenon_H248. apply sym_equal. exact zenon_Hae. % 15.22/15.44 (* end of lemma zenon_L540_ *) % 15.22/15.44 assert (zenon_L541_ : (((op (e0) (e0)) = (e3))\/(((op (e1) (e0)) = (e3))\/(((op (e2) (e0)) = (e3))\/((op (e3) (e0)) = (e3))))) -> (~((op (e0) (e0)) = (e3))) -> ((op (e1) (e0)) = (e0)) -> ((op (e2) (e0)) = (e1)) -> (((op (e0) (e2)) = (e3))\/(((op (e1) (e2)) = (e3))\/(((op (e2) (e2)) = (e3))\/((op (e3) (e2)) = (e3))))) -> (~((e0) = (e3))) -> ((op (e0) (e2)) = (e0)) -> (~((e1) = (e3))) -> ((op (e1) (e2)) = (e1)) -> (~((op (e2) (e2)) = (e3))) -> (~((op (e3) (e0)) = (op (e3) (e2)))) -> False). % 15.22/15.44 do 0 intro. intros zenon_Hbe zenon_H59 zenon_Had zenon_Hae zenon_H175 zenon_H4b zenon_Hab zenon_Ha3 zenon_H117 zenon_H30 zenon_H105. % 15.22/15.44 apply (zenon_or_s _ _ zenon_Hbe); [ zenon_intro zenon_H5b | zenon_intro zenon_Hbf ]. % 15.22/15.44 exact (zenon_H59 zenon_H5b). % 15.22/15.44 apply (zenon_or_s _ _ zenon_Hbf); [ zenon_intro zenon_H69 | zenon_intro zenon_Hc0 ]. % 15.22/15.44 apply (zenon_L38_); trivial. % 15.22/15.44 apply (zenon_or_s _ _ zenon_Hc0); [ zenon_intro zenon_Haf | zenon_intro zenon_Hba ]. % 15.22/15.44 apply (zenon_L39_); trivial. % 15.22/15.44 apply (zenon_L507_); trivial. % 15.22/15.44 (* end of lemma zenon_L541_ *) % 15.22/15.44 assert (zenon_L542_ : ((~((op (e3) (e3)) = (e3)))\/((op (e3) (e3)) = (e3))) -> ((~((op (e3) (e3)) = (e2)))\/((op (e3) (e2)) = (e3))) -> (~((op (e3) (e2)) = (op (e3) (e3)))) -> (~((op (e0) (e0)) = (e1))) -> (((op (e0) (e0)) = (e3))\/(((op (e0) (e1)) = (e3))\/(((op (e0) (e2)) = (e3))\/((op (e0) (e3)) = (e3))))) -> (~((op (e0) (e3)) = (op (e3) (e3)))) -> ((op (e0) (e2)) = (e0)) -> (~((e0) = (e3))) -> (~((e1) = (e3))) -> (~((op (e0) (e0)) = (e3))) -> (~((e0) = (e1))) -> (((op (e0) (e3)) = (e0))\/(((op (e1) (e3)) = (e0))\/(((op (e2) (e3)) = (e0))\/((op (e3) (e3)) = (e0))))) -> (~((e0) = (e2))) -> (((op (e0) (e3)) = (e2))\/(((op (e1) (e3)) = (e2))\/(((op (e2) (e3)) = (e2))\/((op (e3) (e3)) = (e2))))) -> (((op (e0) (e0)) = (e1))\/(((op (e0) (e1)) = (e1))\/(((op (e0) (e2)) = (e1))\/((op (e0) (e3)) = (e1))))) -> (~((op (e3) (e0)) = (op (e3) (e3)))) -> ((~((op (e3) (e3)) = (e0)))\/((op (e3) (e0)) = (e3))) -> (((op (e1) (e1)) = (e0))\/(((op (e1) (e1)) = (e1))\/(((op (e1) (e1)) = (e2))\/((op (e1) (e1)) = (e3))))) -> (~((op (e3) (e3)) = (e1))) -> (~((op (e3) (e3)) = (e2))) -> (((op (e3) (e3)) = (e0))\/(((op (e3) (e3)) = (e1))\/(((op (e3) (e3)) = (e2))\/((op (e3) (e3)) = (e3))))) -> (~((op (e1) (e1)) = (e2))) -> (~((op (e1) (e1)) = (e1))) -> (~((op (e1) (e1)) = (e0))) -> (~((op (e1) (e2)) = (op (e2) (e2)))) -> ((op (e2) (e2)) = (e2)) -> (~((e1) = (e2))) -> ((op (e1) (e3)) = (e1)) -> (((op (e1) (e0)) = (e2))\/(((op (e1) (e1)) = (e2))\/(((op (e1) (e2)) = (e2))\/((op (e1) (e3)) = (e2))))) -> False). % 15.22/15.44 do 0 intro. intros zenon_H10d zenon_H10e zenon_H173 zenon_H45 zenon_H58 zenon_H36 zenon_Hab zenon_H4b zenon_Ha3 zenon_H59 zenon_H9e zenon_Hd3 zenon_H5e zenon_H160 zenon_H44 zenon_Hbb zenon_H10f zenon_H1b3 zenon_H104 zenon_H3d zenon_H3b zenon_Hd6 zenon_H1b4 zenon_H145 zenon_H7d zenon_H35 zenon_Ha7 zenon_H11f zenon_H84. % 15.22/15.44 apply (zenon_or_s _ _ zenon_H10d); [ zenon_intro zenon_H3e | zenon_intro zenon_H42 ]. % 15.22/15.44 apply (zenon_L486_); trivial. % 15.22/15.44 apply (zenon_L236_); trivial. % 15.22/15.44 (* end of lemma zenon_L542_ *) % 15.22/15.44 assert (zenon_L543_ : ((~((op (e3) (e3)) = (e1)))\/((op (e3) (e1)) = (e3))) -> (~((op (e3) (e0)) = (op (e3) (e1)))) -> ((~((op (e3) (e3)) = (e3)))\/((op (e3) (e3)) = (e3))) -> ((~((op (e3) (e3)) = (e2)))\/((op (e3) (e2)) = (e3))) -> (~((op (e3) (e2)) = (op (e3) (e3)))) -> (~((op (e0) (e0)) = (e1))) -> (((op (e0) (e0)) = (e3))\/(((op (e0) (e1)) = (e3))\/(((op (e0) (e2)) = (e3))\/((op (e0) (e3)) = (e3))))) -> (~((op (e0) (e3)) = (op (e3) (e3)))) -> ((op (e0) (e2)) = (e0)) -> (~((e0) = (e3))) -> (~((e1) = (e3))) -> (~((op (e0) (e0)) = (e3))) -> (~((e0) = (e1))) -> (((op (e0) (e3)) = (e0))\/(((op (e1) (e3)) = (e0))\/(((op (e2) (e3)) = (e0))\/((op (e3) (e3)) = (e0))))) -> (~((e0) = (e2))) -> (((op (e0) (e3)) = (e2))\/(((op (e1) (e3)) = (e2))\/(((op (e2) (e3)) = (e2))\/((op (e3) (e3)) = (e2))))) -> (((op (e0) (e0)) = (e1))\/(((op (e0) (e1)) = (e1))\/(((op (e0) (e2)) = (e1))\/((op (e0) (e3)) = (e1))))) -> (~((op (e3) (e0)) = (op (e3) (e3)))) -> ((~((op (e3) (e3)) = (e0)))\/((op (e3) (e0)) = (e3))) -> (((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 (e1) (e1)) = (e2))) -> (~((op (e1) (e1)) = (e1))) -> (~((op (e1) (e1)) = (e0))) -> (~((op (e1) (e2)) = (op (e2) (e2)))) -> ((op (e2) (e2)) = (e2)) -> (~((e1) = (e2))) -> ((op (e1) (e3)) = (e1)) -> (((op (e1) (e0)) = (e2))\/(((op (e1) (e1)) = (e2))\/(((op (e1) (e2)) = (e2))\/((op (e1) (e3)) = (e2))))) -> (~((op (e3) (e0)) = (op (e3) (e2)))) -> ((op (e3) (e0)) = (e3)) -> False). % 15.22/15.44 do 0 intro. intros zenon_H10c zenon_H109 zenon_H10d zenon_H10e zenon_H173 zenon_H45 zenon_H58 zenon_H36 zenon_Hab zenon_H4b zenon_Ha3 zenon_H59 zenon_H9e zenon_Hd3 zenon_H5e zenon_H160 zenon_H44 zenon_Hbb zenon_H10f zenon_H1b3 zenon_H3b zenon_Hd6 zenon_H1b4 zenon_H145 zenon_H7d zenon_H35 zenon_Ha7 zenon_H11f zenon_H84 zenon_H105 zenon_Hba. % 15.22/15.44 apply (zenon_or_s _ _ zenon_H10c); [ zenon_intro zenon_H104 | zenon_intro zenon_H10a ]. % 15.22/15.44 apply (zenon_or_s _ _ zenon_H10e); [ zenon_intro zenon_H3d | zenon_intro zenon_H106 ]. % 15.22/15.44 apply (zenon_L542_); trivial. % 15.22/15.44 apply (zenon_L81_); trivial. % 15.22/15.44 apply (zenon_L82_); trivial. % 15.22/15.44 (* end of lemma zenon_L543_ *) % 15.22/15.44 assert (zenon_L544_ : (((op (e0) (e0)) = (e3))\/(((op (e1) (e0)) = (e3))\/(((op (e2) (e0)) = (e3))\/((op (e3) (e0)) = (e3))))) -> (~((e2) = (e3))) -> ((op (e2) (e0)) = (e1)) -> ((~((op (e3) (e3)) = (e1)))\/((op (e3) (e1)) = (e3))) -> (~((op (e3) (e0)) = (op (e3) (e1)))) -> ((~((op (e3) (e3)) = (e3)))\/((op (e3) (e3)) = (e3))) -> ((~((op (e3) (e3)) = (e2)))\/((op (e3) (e2)) = (e3))) -> (~((op (e3) (e2)) = (op (e3) (e3)))) -> (~((op (e0) (e0)) = (e1))) -> (((op (e0) (e0)) = (e3))\/(((op (e0) (e1)) = (e3))\/(((op (e0) (e2)) = (e3))\/((op (e0) (e3)) = (e3))))) -> (~((op (e0) (e3)) = (op (e3) (e3)))) -> ((op (e0) (e2)) = (e0)) -> (~((e0) = (e3))) -> (~((e1) = (e3))) -> (~((op (e0) (e0)) = (e3))) -> (~((e0) = (e1))) -> (((op (e0) (e3)) = (e0))\/(((op (e1) (e3)) = (e0))\/(((op (e2) (e3)) = (e0))\/((op (e3) (e3)) = (e0))))) -> (~((e0) = (e2))) -> (((op (e0) (e3)) = (e2))\/(((op (e1) (e3)) = (e2))\/(((op (e2) (e3)) = (e2))\/((op (e3) (e3)) = (e2))))) -> (((op (e0) (e0)) = (e1))\/(((op (e0) (e1)) = (e1))\/(((op (e0) (e2)) = (e1))\/((op (e0) (e3)) = (e1))))) -> (~((op (e3) (e0)) = (op (e3) (e3)))) -> ((~((op (e3) (e3)) = (e0)))\/((op (e3) (e0)) = (e3))) -> (((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 (e1) (e1)) = (e2))) -> (~((op (e1) (e1)) = (e1))) -> (~((op (e1) (e1)) = (e0))) -> (~((op (e1) (e2)) = (op (e2) (e2)))) -> ((op (e2) (e2)) = (e2)) -> (~((e1) = (e2))) -> ((op (e1) (e3)) = (e1)) -> (((op (e1) (e0)) = (e2))\/(((op (e1) (e1)) = (e2))\/(((op (e1) (e2)) = (e2))\/((op (e1) (e3)) = (e2))))) -> (~((op (e3) (e0)) = (op (e3) (e2)))) -> False). % 15.22/15.44 do 0 intro. intros zenon_Hbe zenon_H6a zenon_Hae zenon_H10c zenon_H109 zenon_H10d zenon_H10e zenon_H173 zenon_H45 zenon_H58 zenon_H36 zenon_Hab zenon_H4b zenon_Ha3 zenon_H59 zenon_H9e zenon_Hd3 zenon_H5e zenon_H160 zenon_H44 zenon_Hbb zenon_H10f zenon_H1b3 zenon_H3b zenon_Hd6 zenon_H1b4 zenon_H145 zenon_H7d zenon_H35 zenon_Ha7 zenon_H11f zenon_H84 zenon_H105. % 15.22/15.44 apply (zenon_or_s _ _ zenon_Hbe); [ zenon_intro zenon_H5b | zenon_intro zenon_Hbf ]. % 15.22/15.44 exact (zenon_H59 zenon_H5b). % 15.22/15.44 apply (zenon_or_s _ _ zenon_Hbf); [ zenon_intro zenon_H69 | zenon_intro zenon_Hc0 ]. % 15.22/15.44 apply (zenon_L515_); trivial. % 15.22/15.44 apply (zenon_or_s _ _ zenon_Hc0); [ zenon_intro zenon_Haf | zenon_intro zenon_Hba ]. % 15.22/15.44 apply (zenon_L39_); trivial. % 15.22/15.44 apply (zenon_L543_); trivial. % 15.22/15.44 (* end of lemma zenon_L544_ *) % 15.22/15.44 assert (zenon_L545_ : (((op (e1) (e0)) = (e1))\/(((op (e1) (e1)) = (e1))\/(((op (e1) (e2)) = (e1))\/((op (e1) (e3)) = (e1))))) -> (~((op (e1) (e0)) = (op (e2) (e0)))) -> (~((op (e2) (e2)) = (e3))) -> (((op (e0) (e2)) = (e3))\/(((op (e1) (e2)) = (e3))\/(((op (e2) (e2)) = (e3))\/((op (e3) (e2)) = (e3))))) -> ((op (e1) (e0)) = (e0)) -> (((op (e0) (e0)) = (e3))\/(((op (e1) (e0)) = (e3))\/(((op (e2) (e0)) = (e3))\/((op (e3) (e0)) = (e3))))) -> (~((e2) = (e3))) -> ((op (e2) (e0)) = (e1)) -> ((~((op (e3) (e3)) = (e1)))\/((op (e3) (e1)) = (e3))) -> (~((op (e3) (e0)) = (op (e3) (e1)))) -> ((~((op (e3) (e3)) = (e3)))\/((op (e3) (e3)) = (e3))) -> ((~((op (e3) (e3)) = (e2)))\/((op (e3) (e2)) = (e3))) -> (~((op (e3) (e2)) = (op (e3) (e3)))) -> (~((op (e0) (e0)) = (e1))) -> (((op (e0) (e0)) = (e3))\/(((op (e0) (e1)) = (e3))\/(((op (e0) (e2)) = (e3))\/((op (e0) (e3)) = (e3))))) -> (~((op (e0) (e3)) = (op (e3) (e3)))) -> ((op (e0) (e2)) = (e0)) -> (~((e0) = (e3))) -> (~((e1) = (e3))) -> (~((op (e0) (e0)) = (e3))) -> (~((e0) = (e1))) -> (((op (e0) (e3)) = (e0))\/(((op (e1) (e3)) = (e0))\/(((op (e2) (e3)) = (e0))\/((op (e3) (e3)) = (e0))))) -> (~((e0) = (e2))) -> (((op (e0) (e3)) = (e2))\/(((op (e1) (e3)) = (e2))\/(((op (e2) (e3)) = (e2))\/((op (e3) (e3)) = (e2))))) -> (((op (e0) (e0)) = (e1))\/(((op (e0) (e1)) = (e1))\/(((op (e0) (e2)) = (e1))\/((op (e0) (e3)) = (e1))))) -> (~((op (e3) (e0)) = (op (e3) (e3)))) -> ((~((op (e3) (e3)) = (e0)))\/((op (e3) (e0)) = (e3))) -> (((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 (e1) (e1)) = (e2))) -> (~((op (e1) (e1)) = (e1))) -> (~((op (e1) (e1)) = (e0))) -> (~((op (e1) (e2)) = (op (e2) (e2)))) -> ((op (e2) (e2)) = (e2)) -> (~((e1) = (e2))) -> (((op (e1) (e0)) = (e2))\/(((op (e1) (e1)) = (e2))\/(((op (e1) (e2)) = (e2))\/((op (e1) (e3)) = (e2))))) -> (~((op (e3) (e0)) = (op (e3) (e2)))) -> False). % 15.22/15.44 do 0 intro. intros zenon_H1c5 zenon_H247 zenon_H30 zenon_H175 zenon_Had zenon_Hbe zenon_H6a zenon_Hae zenon_H10c zenon_H109 zenon_H10d zenon_H10e zenon_H173 zenon_H45 zenon_H58 zenon_H36 zenon_Hab zenon_H4b zenon_Ha3 zenon_H59 zenon_H9e zenon_Hd3 zenon_H5e zenon_H160 zenon_H44 zenon_Hbb zenon_H10f zenon_H1b3 zenon_H3b zenon_Hd6 zenon_H1b4 zenon_H145 zenon_H7d zenon_H35 zenon_Ha7 zenon_H84 zenon_H105. % 15.22/15.44 apply (zenon_or_s _ _ zenon_H1c5); [ zenon_intro zenon_Hd8 | zenon_intro zenon_H1c6 ]. % 15.22/15.44 apply (zenon_L540_); trivial. % 15.22/15.44 apply (zenon_or_s _ _ zenon_H1c6); [ zenon_intro zenon_H21 | zenon_intro zenon_H1c7 ]. % 15.22/15.44 exact (zenon_H1b4 zenon_H21). % 15.22/15.44 apply (zenon_or_s _ _ zenon_H1c7); [ zenon_intro zenon_H117 | zenon_intro zenon_H11f ]. % 15.22/15.44 apply (zenon_L541_); trivial. % 15.22/15.44 apply (zenon_L544_); trivial. % 15.22/15.44 (* end of lemma zenon_L545_ *) % 15.22/15.44 assert (zenon_L546_ : (((op (e0) (e0)) = (e1))\/(((op (e1) (e0)) = (e1))\/(((op (e2) (e0)) = (e1))\/((op (e3) (e0)) = (e1))))) -> ((~((op (e1) (e1)) = (e3)))\/((op (e1) (e3)) = (e1))) -> ((~((op (e3) (e3)) = (e2)))\/((op (e3) (e2)) = (e3))) -> (~((op (e1) (e2)) = (op (e3) (e2)))) -> (((op (e0) (e0)) = (e2))\/(((op (e1) (e0)) = (e2))\/(((op (e2) (e0)) = (e2))\/((op (e3) (e0)) = (e2))))) -> (((op (e3) (e3)) = (e0))\/(((op (e3) (e3)) = (e1))\/(((op (e3) (e3)) = (e2))\/((op (e3) (e3)) = (e3))))) -> (~((op (e2) (e0)) = (op (e2) (e2)))) -> (~((e1) = (e2))) -> (~((op (e1) (e2)) = (op (e2) (e2)))) -> ((op (e2) (e2)) = (e2)) -> (((op (e1) (e0)) = (e3))\/(((op (e1) (e1)) = (e3))\/(((op (e1) (e2)) = (e3))\/((op (e1) (e3)) = (e3))))) -> (~((e2) = (e3))) -> (~((op (e1) (e1)) = (e1))) -> (((op (e1) (e1)) = (e0))\/(((op (e1) (e1)) = (e1))\/(((op (e1) (e1)) = (e2))\/((op (e1) (e1)) = (e3))))) -> (((op (e1) (e0)) = (e2))\/(((op (e1) (e1)) = (e2))\/(((op (e1) (e2)) = (e2))\/((op (e1) (e3)) = (e2))))) -> ((~((op (e2) (e2)) = (e0)))\/((op (e2) (e0)) = (e2))) -> ((~((op (e2) (e2)) = (e3)))\/((op (e2) (e3)) = (e2))) -> ((~((op (e3) (e3)) = (e1)))\/((op (e3) (e1)) = (e3))) -> (~((op (e3) (e1)) = (op (e3) (e3)))) -> (~((op (e0) (e0)) = (e1))) -> (((op (e0) (e3)) = (e1))\/(((op (e1) (e3)) = (e1))\/(((op (e2) (e3)) = (e1))\/((op (e3) (e3)) = (e1))))) -> (~((op (e1) (e0)) = (op (e1) (e3)))) -> (~((op (e0) (e1)) = (op (e0) (e3)))) -> ((op (e0) (e2)) = (e0)) -> (((op (e0) (e0)) = (e2))\/(((op (e0) (e1)) = (e2))\/(((op (e0) (e2)) = (e2))\/((op (e0) (e3)) = (e2))))) -> (((op (e0) (e3)) = (e0))\/(((op (e1) (e3)) = (e0))\/(((op (e2) (e3)) = (e0))\/((op (e3) (e3)) = (e0))))) -> (~((e0) = (e2))) -> (~((op (e0) (e2)) = (op (e0) (e3)))) -> (~((op (e0) (e2)) = (op (e1) (e2)))) -> (~((op (e0) (e3)) = (op (e3) (e3)))) -> (((op (e0) (e0)) = (e3))\/(((op (e0) (e1)) = (e3))\/(((op (e0) (e2)) = (e3))\/((op (e0) (e3)) = (e3))))) -> (~((op (e1) (e3)) = (op (e3) (e3)))) -> (((op (e0) (e0)) = (e1))\/(((op (e0) (e1)) = (e1))\/(((op (e0) (e2)) = (e1))\/((op (e0) (e3)) = (e1))))) -> ((~((op (e3) (e3)) = (e0)))\/((op (e3) (e0)) = (e3))) -> (~((op (e0) (e0)) = (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) (e0)) = (e3))\/(((op (e1) (e0)) = (e3))\/(((op (e2) (e0)) = (e3))\/((op (e3) (e0)) = (e3))))) -> (~((op (e0) (e2)) = (op (e2) (e2)))) -> (~((op (e0) (e3)) = (op (e1) (e3)))) -> ((~((op (e2) (e2)) = (e2)))\/((op (e2) (e2)) = (e2))) -> ((~((op (e3) (e3)) = (e3)))\/((op (e3) (e3)) = (e3))) -> (~((op (e1) (e0)) = (op (e1) (e2)))) -> ((~((op (e1) (e1)) = (e2)))\/((op (e1) (e2)) = (e1))) -> (~((e0) = (e1))) -> ((op (e2) (e0)) = (e0)) -> (~((e1) = (e3))) -> ((op (e3) (e0)) = (e3)) -> False). % 15.22/15.44 do 0 intro. intros zenon_Hf1 zenon_H1d2 zenon_H10e zenon_H17d zenon_Heb zenon_H3b zenon_H17a zenon_Ha7 zenon_H7d zenon_H35 zenon_H90 zenon_H6a zenon_H1b4 zenon_H1b3 zenon_H84 zenon_H1d4 zenon_H1c3 zenon_H10c zenon_H12d zenon_H45 zenon_H121 zenon_H1cf zenon_H1cd zenon_Hab zenon_H8e zenon_Hd3 zenon_H5e zenon_Hc9 zenon_H87 zenon_H36 zenon_H58 zenon_H8b zenon_H44 zenon_H10f zenon_H59 zenon_H2d zenon_Hbb zenon_Hbe zenon_H28 zenon_H80 zenon_Haa zenon_H10d zenon_H166 zenon_H1d3 zenon_H9e zenon_Hcf zenon_Ha3 zenon_Hba. % 15.22/15.44 apply (zenon_or_s _ _ zenon_Hf1); [ zenon_intro zenon_H47 | zenon_intro zenon_Hf4 ]. % 15.22/15.44 exact (zenon_H45 zenon_H47). % 15.22/15.44 apply (zenon_or_s _ _ zenon_Hf4); [ zenon_intro zenon_Hd8 | zenon_intro zenon_Hf5 ]. % 15.22/15.44 apply (zenon_L539_); trivial. % 15.22/15.44 apply (zenon_or_s _ _ zenon_Hf5); [ zenon_intro zenon_Hae | zenon_intro zenon_Hee ]. % 15.22/15.44 apply (zenon_L269_); trivial. % 15.22/15.44 apply (zenon_L79_); trivial. % 15.22/15.44 (* end of lemma zenon_L546_ *) % 15.22/15.44 assert (zenon_L547_ : (((op (e0) (e0)) = (e0))\/(((op (e1) (e0)) = (e0))\/(((op (e2) (e0)) = (e0))\/((op (e3) (e0)) = (e0))))) -> (~((op (e0) (e0)) = (e0))) -> (((op (e1) (e0)) = (e1))\/(((op (e1) (e1)) = (e1))\/(((op (e1) (e2)) = (e1))\/((op (e1) (e3)) = (e1))))) -> (~((op (e1) (e0)) = (op (e2) (e0)))) -> (~((op (e2) (e2)) = (e3))) -> (((op (e0) (e2)) = (e3))\/(((op (e1) (e2)) = (e3))\/(((op (e2) (e2)) = (e3))\/((op (e3) (e2)) = (e3))))) -> (~((op (e3) (e0)) = (op (e3) (e1)))) -> (~((op (e3) (e2)) = (op (e3) (e3)))) -> (((op (e0) (e3)) = (e2))\/(((op (e1) (e3)) = (e2))\/(((op (e2) (e3)) = (e2))\/((op (e3) (e3)) = (e2))))) -> (~((op (e1) (e1)) = (e2))) -> (~((op (e1) (e1)) = (e0))) -> (~((op (e3) (e0)) = (op (e3) (e2)))) -> (~((e1) = (e3))) -> (~((e0) = (e1))) -> ((~((op (e1) (e1)) = (e2)))\/((op (e1) (e2)) = (e1))) -> (~((op (e1) (e0)) = (op (e1) (e2)))) -> ((~((op (e3) (e3)) = (e3)))\/((op (e3) (e3)) = (e3))) -> ((~((op (e2) (e2)) = (e2)))\/((op (e2) (e2)) = (e2))) -> (~((op (e0) (e3)) = (op (e1) (e3)))) -> (~((op (e0) (e2)) = (op (e2) (e2)))) -> (((op (e0) (e0)) = (e3))\/(((op (e1) (e0)) = (e3))\/(((op (e2) (e0)) = (e3))\/((op (e3) (e0)) = (e3))))) -> (~((op (e3) (e0)) = (op (e3) (e3)))) -> (((op (e2) (e2)) = (e0))\/(((op (e2) (e2)) = (e1))\/(((op (e2) (e2)) = (e2))\/((op (e2) (e2)) = (e3))))) -> (~((op (e0) (e0)) = (e3))) -> ((~((op (e3) (e3)) = (e0)))\/((op (e3) (e0)) = (e3))) -> (((op (e0) (e0)) = (e1))\/(((op (e0) (e1)) = (e1))\/(((op (e0) (e2)) = (e1))\/((op (e0) (e3)) = (e1))))) -> (~((op (e1) (e3)) = (op (e3) (e3)))) -> (((op (e0) (e0)) = (e3))\/(((op (e0) (e1)) = (e3))\/(((op (e0) (e2)) = (e3))\/((op (e0) (e3)) = (e3))))) -> (~((op (e0) (e3)) = (op (e3) (e3)))) -> (~((op (e0) (e2)) = (op (e1) (e2)))) -> (~((op (e0) (e2)) = (op (e0) (e3)))) -> (~((e0) = (e2))) -> (((op (e0) (e3)) = (e0))\/(((op (e1) (e3)) = (e0))\/(((op (e2) (e3)) = (e0))\/((op (e3) (e3)) = (e0))))) -> (((op (e0) (e0)) = (e2))\/(((op (e0) (e1)) = (e2))\/(((op (e0) (e2)) = (e2))\/((op (e0) (e3)) = (e2))))) -> ((op (e0) (e2)) = (e0)) -> (~((op (e0) (e1)) = (op (e0) (e3)))) -> (~((op (e1) (e0)) = (op (e1) (e3)))) -> (((op (e0) (e3)) = (e1))\/(((op (e1) (e3)) = (e1))\/(((op (e2) (e3)) = (e1))\/((op (e3) (e3)) = (e1))))) -> (~((op (e0) (e0)) = (e1))) -> (~((op (e3) (e1)) = (op (e3) (e3)))) -> ((~((op (e3) (e3)) = (e1)))\/((op (e3) (e1)) = (e3))) -> ((~((op (e2) (e2)) = (e3)))\/((op (e2) (e3)) = (e2))) -> ((~((op (e2) (e2)) = (e0)))\/((op (e2) (e0)) = (e2))) -> (((op (e1) (e0)) = (e2))\/(((op (e1) (e1)) = (e2))\/(((op (e1) (e2)) = (e2))\/((op (e1) (e3)) = (e2))))) -> (((op (e1) (e1)) = (e0))\/(((op (e1) (e1)) = (e1))\/(((op (e1) (e1)) = (e2))\/((op (e1) (e1)) = (e3))))) -> (~((op (e1) (e1)) = (e1))) -> (~((e2) = (e3))) -> (((op (e1) (e0)) = (e3))\/(((op (e1) (e1)) = (e3))\/(((op (e1) (e2)) = (e3))\/((op (e1) (e3)) = (e3))))) -> ((op (e2) (e2)) = (e2)) -> (~((op (e1) (e2)) = (op (e2) (e2)))) -> (~((e1) = (e2))) -> (~((op (e2) (e0)) = (op (e2) (e2)))) -> (((op (e3) (e3)) = (e0))\/(((op (e3) (e3)) = (e1))\/(((op (e3) (e3)) = (e2))\/((op (e3) (e3)) = (e3))))) -> (((op (e0) (e0)) = (e2))\/(((op (e1) (e0)) = (e2))\/(((op (e2) (e0)) = (e2))\/((op (e3) (e0)) = (e2))))) -> (~((op (e1) (e2)) = (op (e3) (e2)))) -> ((~((op (e3) (e3)) = (e2)))\/((op (e3) (e2)) = (e3))) -> ((~((op (e1) (e1)) = (e3)))\/((op (e1) (e3)) = (e1))) -> (((op (e0) (e0)) = (e1))\/(((op (e1) (e0)) = (e1))\/(((op (e2) (e0)) = (e1))\/((op (e3) (e0)) = (e1))))) -> (~((e0) = (e3))) -> ((op (e3) (e0)) = (e3)) -> False). % 15.22/15.44 do 0 intro. intros zenon_Hf0 zenon_H20 zenon_H1c5 zenon_H247 zenon_H30 zenon_H175 zenon_H109 zenon_H173 zenon_H160 zenon_Hd6 zenon_H145 zenon_H105 zenon_Ha3 zenon_H9e zenon_H1d3 zenon_H166 zenon_H10d zenon_Haa zenon_H80 zenon_H28 zenon_Hbe zenon_Hbb zenon_H2d zenon_H59 zenon_H10f zenon_H44 zenon_H8b zenon_H58 zenon_H36 zenon_H87 zenon_Hc9 zenon_H5e zenon_Hd3 zenon_H8e zenon_Hab zenon_H1cd zenon_H1cf zenon_H121 zenon_H45 zenon_H12d zenon_H10c zenon_H1c3 zenon_H1d4 zenon_H84 zenon_H1b3 zenon_H1b4 zenon_H6a zenon_H90 zenon_H35 zenon_H7d zenon_Ha7 zenon_H17a zenon_H3b zenon_Heb zenon_H17d zenon_H10e zenon_H1d2 zenon_Hf1 zenon_H4b zenon_Hba. % 15.22/15.44 apply (zenon_or_s _ _ zenon_Hf0); [ zenon_intro zenon_H1f | zenon_intro zenon_Hf2 ]. % 15.22/15.44 exact (zenon_H20 zenon_H1f). % 15.22/15.44 apply (zenon_or_s _ _ zenon_Hf2); [ zenon_intro zenon_Had | zenon_intro zenon_Hf3 ]. % 15.22/15.44 apply (zenon_or_s _ _ zenon_Hf1); [ zenon_intro zenon_H47 | zenon_intro zenon_Hf4 ]. % 15.22/15.44 exact (zenon_H45 zenon_H47). % 15.22/15.44 apply (zenon_or_s _ _ zenon_Hf4); [ zenon_intro zenon_Hd8 | zenon_intro zenon_Hf5 ]. % 15.22/15.44 apply (zenon_L539_); trivial. % 15.22/15.44 apply (zenon_or_s _ _ zenon_Hf5); [ zenon_intro zenon_Hae | zenon_intro zenon_Hee ]. % 15.22/15.44 apply (zenon_L545_); trivial. % 15.22/15.44 apply (zenon_L79_); trivial. % 15.22/15.44 apply (zenon_or_s _ _ zenon_Hf3); [ zenon_intro zenon_Hcf | zenon_intro zenon_Hdb ]. % 15.22/15.44 apply (zenon_L546_); trivial. % 15.22/15.44 apply (zenon_L62_); trivial. % 15.22/15.44 (* end of lemma zenon_L547_ *) % 15.22/15.44 assert (zenon_L548_ : (((op (e0) (e0)) = (e3))\/(((op (e0) (e1)) = (e3))\/(((op (e0) (e2)) = (e3))\/((op (e0) (e3)) = (e3))))) -> (~((op (e0) (e0)) = (e3))) -> (~((op (e1) (op (e0) (e1))) = (op (e0) (e1)))) -> ((op (e0) (e2)) = (e0)) -> (((op (e1) (e0)) = (e3))\/(((op (e1) (e1)) = (e3))\/(((op (e1) (e2)) = (e3))\/((op (e1) (e3)) = (e3))))) -> (~((e0) = (e3))) -> ((op (e1) (e0)) = (e0)) -> (~((op (e1) (e1)) = (e3))) -> (~((e1) = (e3))) -> ((op (e1) (e2)) = (e1)) -> (~((op (e0) (e3)) = (op (e1) (e3)))) -> False). % 15.22/15.44 do 0 intro. intros zenon_H58 zenon_H59 zenon_H1ff zenon_Hab zenon_H90 zenon_H4b zenon_Had zenon_H182 zenon_Ha3 zenon_H117 zenon_H80. % 15.22/15.44 apply (zenon_or_s _ _ zenon_H58); [ zenon_intro zenon_H5b | zenon_intro zenon_H5a ]. % 15.22/15.44 exact (zenon_H59 zenon_H5b). % 15.22/15.44 apply (zenon_or_s _ _ zenon_H5a); [ zenon_intro zenon_H4a | zenon_intro zenon_H5c ]. % 15.22/15.44 apply (zenon_L512_); trivial. % 15.22/15.44 apply (zenon_or_s _ _ zenon_H5c); [ zenon_intro zenon_H50 | zenon_intro zenon_H53 ]. % 15.22/15.44 apply (zenon_L48_); trivial. % 15.22/15.44 apply (zenon_L521_); trivial. % 15.22/15.44 (* end of lemma zenon_L548_ *) % 15.22/15.44 assert (zenon_L549_ : (((op (e0) (e3)) = (e1))\/(((op (e1) (e3)) = (e1))\/(((op (e2) (e3)) = (e1))\/((op (e3) (e3)) = (e1))))) -> (~((e1) = (e3))) -> ((op (e0) (e3)) = (e3)) -> ((op (e1) (e2)) = (e1)) -> (~((op (e1) (e2)) = (op (e1) (e3)))) -> ((op (e2) (e0)) = (e1)) -> (~((op (e2) (e0)) = (op (e2) (e3)))) -> (~((op (e3) (e3)) = (e1))) -> False). % 15.22/15.44 do 0 intro. intros zenon_H121 zenon_Ha3 zenon_H53 zenon_H117 zenon_H1d0 zenon_Hae zenon_Hce zenon_H104. % 15.22/15.44 apply (zenon_or_s _ _ zenon_H121); [ zenon_intro zenon_H37 | zenon_intro zenon_H122 ]. % 15.22/15.44 apply (zenon_L32_); trivial. % 15.22/15.44 apply (zenon_or_s _ _ zenon_H122); [ zenon_intro zenon_H11f | zenon_intro zenon_H123 ]. % 15.22/15.44 apply (zenon_L237_); trivial. % 15.22/15.44 apply (zenon_or_s _ _ zenon_H123); [ zenon_intro zenon_Hb5 | zenon_intro zenon_H38 ]. % 15.22/15.44 apply (zenon_L91_); trivial. % 15.22/15.44 exact (zenon_H104 zenon_H38). % 15.22/15.44 (* end of lemma zenon_L549_ *) % 15.22/15.44 assert (zenon_L550_ : (((op (e0) (e0)) = (e1))\/(((op (e1) (e0)) = (e1))\/(((op (e2) (e0)) = (e1))\/((op (e3) (e0)) = (e1))))) -> (~((op (e0) (e0)) = (e1))) -> (~((op (e1) (e0)) = (op (e1) (e2)))) -> (~((op (e3) (e3)) = (e1))) -> (~((op (e2) (e0)) = (op (e2) (e3)))) -> (~((op (e1) (e2)) = (op (e1) (e3)))) -> ((op (e1) (e2)) = (e1)) -> (~((e1) = (e3))) -> (((op (e0) (e3)) = (e1))\/(((op (e1) (e3)) = (e1))\/(((op (e2) (e3)) = (e1))\/((op (e3) (e3)) = (e1))))) -> ((op (e0) (e2)) = (e0)) -> (~((e0) = (e3))) -> ((op (e0) (e1)) = (e1)) -> (~((op (e0) (e0)) = (e3))) -> (((op (e0) (e0)) = (e3))\/(((op (e0) (e1)) = (e3))\/(((op (e0) (e2)) = (e3))\/((op (e0) (e3)) = (e3))))) -> ((op (e3) (e0)) = (e0)) -> (~((e0) = (e1))) -> False). % 15.22/15.44 do 0 intro. intros zenon_Hf1 zenon_H45 zenon_H166 zenon_H104 zenon_Hce zenon_H1d0 zenon_H117 zenon_Ha3 zenon_H121 zenon_Hab zenon_H4b zenon_H22 zenon_H59 zenon_H58 zenon_Hdb zenon_H9e. % 15.22/15.44 apply (zenon_or_s _ _ zenon_Hf1); [ zenon_intro zenon_H47 | zenon_intro zenon_Hf4 ]. % 15.22/15.44 exact (zenon_H45 zenon_H47). % 15.22/15.44 apply (zenon_or_s _ _ zenon_Hf4); [ zenon_intro zenon_Hd8 | zenon_intro zenon_Hf5 ]. % 15.22/15.44 apply (zenon_L248_); trivial. % 15.22/15.44 apply (zenon_or_s _ _ zenon_Hf5); [ zenon_intro zenon_Hae | zenon_intro zenon_Hee ]. % 15.22/15.44 apply (zenon_or_s _ _ zenon_H58); [ zenon_intro zenon_H5b | zenon_intro zenon_H5a ]. % 15.22/15.44 exact (zenon_H59 zenon_H5b). % 15.22/15.44 apply (zenon_or_s _ _ zenon_H5a); [ zenon_intro zenon_H4a | zenon_intro zenon_H5c ]. % 15.22/15.44 apply (zenon_L59_); trivial. % 15.22/15.44 apply (zenon_or_s _ _ zenon_H5c); [ zenon_intro zenon_H50 | zenon_intro zenon_H53 ]. % 15.22/15.44 apply (zenon_L48_); trivial. % 15.22/15.44 apply (zenon_L549_); trivial. % 15.22/15.44 apply (zenon_L71_); trivial. % 15.22/15.44 (* end of lemma zenon_L550_ *) % 15.22/15.44 assert (zenon_L551_ : (((op (e0) (e3)) = (e1))\/(((op (e1) (e3)) = (e1))\/(((op (e2) (e3)) = (e1))\/((op (e3) (e3)) = (e1))))) -> (~((op (e0) (e2)) = (op (e0) (e3)))) -> ((op (e0) (e2)) = (e1)) -> ((op (e1) (e2)) = (e1)) -> (~((op (e1) (e2)) = (op (e1) (e3)))) -> ((op (e2) (e0)) = (e1)) -> (~((op (e2) (e0)) = (op (e2) (e3)))) -> (~((op (e3) (e3)) = (e1))) -> False). % 15.22/15.44 do 0 intro. intros zenon_H121 zenon_Hc9 zenon_H29 zenon_H117 zenon_H1d0 zenon_Hae zenon_Hce zenon_H104. % 15.22/15.44 apply (zenon_or_s _ _ zenon_H121); [ zenon_intro zenon_H37 | zenon_intro zenon_H122 ]. % 15.22/15.44 apply (zenon_L85_); trivial. % 15.22/15.44 apply (zenon_or_s _ _ zenon_H122); [ zenon_intro zenon_H11f | zenon_intro zenon_H123 ]. % 15.22/15.44 apply (zenon_L237_); trivial. % 15.22/15.44 apply (zenon_or_s _ _ zenon_H123); [ zenon_intro zenon_Hb5 | zenon_intro zenon_H38 ]. % 15.22/15.44 apply (zenon_L91_); trivial. % 15.22/15.44 exact (zenon_H104 zenon_H38). % 15.22/15.44 (* end of lemma zenon_L551_ *) % 15.22/15.44 assert (zenon_L552_ : (((op (e0) (e0)) = (e1))\/(((op (e1) (e0)) = (e1))\/(((op (e2) (e0)) = (e1))\/((op (e3) (e0)) = (e1))))) -> (~((op (e0) (e0)) = (e1))) -> (~((op (e1) (e0)) = (op (e1) (e2)))) -> (~((op (e3) (e3)) = (e1))) -> (~((op (e2) (e0)) = (op (e2) (e3)))) -> (~((op (e1) (e2)) = (op (e1) (e3)))) -> ((op (e1) (e2)) = (e1)) -> ((op (e0) (e2)) = (e1)) -> (~((op (e0) (e2)) = (op (e0) (e3)))) -> (((op (e0) (e3)) = (e1))\/(((op (e1) (e3)) = (e1))\/(((op (e2) (e3)) = (e1))\/((op (e3) (e3)) = (e1))))) -> ((op (e3) (e0)) = (e0)) -> (~((e0) = (e1))) -> False). % 15.22/15.44 do 0 intro. intros zenon_Hf1 zenon_H45 zenon_H166 zenon_H104 zenon_Hce zenon_H1d0 zenon_H117 zenon_H29 zenon_Hc9 zenon_H121 zenon_Hdb zenon_H9e. % 15.22/15.44 apply (zenon_or_s _ _ zenon_Hf1); [ zenon_intro zenon_H47 | zenon_intro zenon_Hf4 ]. % 15.22/15.44 exact (zenon_H45 zenon_H47). % 15.22/15.44 apply (zenon_or_s _ _ zenon_Hf4); [ zenon_intro zenon_Hd8 | zenon_intro zenon_Hf5 ]. % 15.22/15.44 apply (zenon_L248_); trivial. % 15.22/15.44 apply (zenon_or_s _ _ zenon_Hf5); [ zenon_intro zenon_Hae | zenon_intro zenon_Hee ]. % 15.22/15.44 apply (zenon_L551_); trivial. % 15.22/15.44 apply (zenon_L71_); trivial. % 15.22/15.44 (* end of lemma zenon_L552_ *) % 15.22/15.44 assert (zenon_L553_ : ((~((op (e1) (e1)) = (e1)))\/((op (e1) (e1)) = (e1))) -> (~((op (e1) (e0)) = (op (e1) (e1)))) -> ((~((op (e1) (e1)) = (e3)))\/((op (e1) (e3)) = (e1))) -> ((~((op (e3) (e3)) = (e2)))\/((op (e3) (e2)) = (e3))) -> (~((op (e1) (e2)) = (op (e3) (e2)))) -> (((op (e0) (e0)) = (e2))\/(((op (e1) (e0)) = (e2))\/(((op (e2) (e0)) = (e2))\/((op (e3) (e0)) = (e2))))) -> (((op (e3) (e3)) = (e0))\/(((op (e3) (e3)) = (e1))\/(((op (e3) (e3)) = (e2))\/((op (e3) (e3)) = (e3))))) -> (~((op (e2) (e0)) = (op (e2) (e2)))) -> (~((e1) = (e2))) -> ((op (e1) (e0)) = (e1)) -> (~((op (e1) (e2)) = (op (e2) (e2)))) -> ((op (e2) (e2)) = (e2)) -> (((op (e1) (e0)) = (e3))\/(((op (e1) (e1)) = (e3))\/(((op (e1) (e2)) = (e3))\/((op (e1) (e3)) = (e3))))) -> (~((e2) = (e3))) -> (((op (e1) (e1)) = (e0))\/(((op (e1) (e1)) = (e1))\/(((op (e1) (e1)) = (e2))\/((op (e1) (e1)) = (e3))))) -> (~((e1) = (e3))) -> (((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 (e2) (e2)) = (e3)))\/((op (e2) (e3)) = (e2))) -> ((~((op (e3) (e3)) = (e1)))\/((op (e3) (e1)) = (e3))) -> (~((op (e3) (e1)) = (op (e3) (e3)))) -> (~((op (e0) (e0)) = (e1))) -> (((op (e0) (e3)) = (e1))\/(((op (e1) (e3)) = (e1))\/(((op (e2) (e3)) = (e1))\/((op (e3) (e3)) = (e1))))) -> (~((op (e1) (e0)) = (op (e1) (e3)))) -> (~((op (e0) (e1)) = (op (e0) (e3)))) -> (~((e0) = (e1))) -> ((op (e0) (e2)) = (e0)) -> (((op (e0) (e0)) = (e2))\/(((op (e0) (e1)) = (e2))\/(((op (e0) (e2)) = (e2))\/((op (e0) (e3)) = (e2))))) -> (((op (e0) (e3)) = (e0))\/(((op (e1) (e3)) = (e0))\/(((op (e2) (e3)) = (e0))\/((op (e3) (e3)) = (e0))))) -> (~((e0) = (e2))) -> (~((op (e0) (e2)) = (op (e0) (e3)))) -> (~((op (e0) (e2)) = (op (e1) (e2)))) -> (~((op (e0) (e3)) = (op (e3) (e3)))) -> (((op (e0) (e0)) = (e3))\/(((op (e0) (e1)) = (e3))\/(((op (e0) (e2)) = (e3))\/((op (e0) (e3)) = (e3))))) -> (~((op (e1) (e3)) = (op (e3) (e3)))) -> (((op (e0) (e0)) = (e1))\/(((op (e0) (e1)) = (e1))\/(((op (e0) (e2)) = (e1))\/((op (e0) (e3)) = (e1))))) -> ((~((op (e3) (e3)) = (e0)))\/((op (e3) (e0)) = (e3))) -> (~((op (e0) (e0)) = (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) (e0)) = (e3))\/(((op (e1) (e0)) = (e3))\/(((op (e2) (e0)) = (e3))\/((op (e3) (e0)) = (e3))))) -> (~((op (e0) (e2)) = (op (e2) (e2)))) -> (~((op (e0) (e3)) = (op (e1) (e3)))) -> ((~((op (e2) (e2)) = (e2)))\/((op (e2) (e2)) = (e2))) -> ((~((op (e3) (e3)) = (e3)))\/((op (e3) (e3)) = (e3))) -> (~((op (e1) (e0)) = (op (e1) (e2)))) -> ((~((op (e1) (e1)) = (e2)))\/((op (e1) (e2)) = (e1))) -> False). % 15.22/15.44 do 0 intro. intros zenon_H1d8 zenon_Hd7 zenon_H1d2 zenon_H10e zenon_H17d zenon_Heb zenon_H3b zenon_H17a zenon_Ha7 zenon_Hd8 zenon_H7d zenon_H35 zenon_H90 zenon_H6a zenon_H1b3 zenon_Ha3 zenon_H84 zenon_H1d4 zenon_H1c3 zenon_H10c zenon_H12d zenon_H45 zenon_H121 zenon_H1cf zenon_H1cd zenon_H9e zenon_Hab zenon_H8e zenon_Hd3 zenon_H5e zenon_Hc9 zenon_H87 zenon_H36 zenon_H58 zenon_H8b zenon_H44 zenon_H10f zenon_H59 zenon_H2d zenon_Hbb zenon_Hbe zenon_H28 zenon_H80 zenon_Haa zenon_H10d zenon_H166 zenon_H1d3. % 15.22/15.44 apply (zenon_or_s _ _ zenon_H1d8); [ zenon_intro zenon_H1b4 | zenon_intro zenon_H21 ]. % 15.22/15.44 apply (zenon_L539_); trivial. % 15.22/15.44 apply (zenon_L61_); trivial. % 15.22/15.44 (* end of lemma zenon_L553_ *) % 15.22/15.44 assert (zenon_L554_ : ((~((op (e3) (e3)) = (e2)))\/((op (e3) (e2)) = (e3))) -> (~((op (e3) (e1)) = (op (e3) (e2)))) -> (~((op (e0) (e0)) = (e2))) -> (((op (e0) (e3)) = (e2))\/(((op (e1) (e3)) = (e2))\/(((op (e2) (e3)) = (e2))\/((op (e3) (e3)) = (e2))))) -> ((op (e2) (e2)) = (e2)) -> (~((op (e2) (e2)) = (op (e2) (e3)))) -> ((op (e1) (e3)) = (e1)) -> (~((e1) = (e2))) -> (~((op (e0) (e1)) = (op (e0) (e3)))) -> (~((op (e0) (e2)) = (op (e2) (e2)))) -> (((op (e0) (e1)) = (e0))\/(((op (e1) (e1)) = (e0))\/(((op (e2) (e1)) = (e0))\/((op (e3) (e1)) = (e0))))) -> (~((e0) = (e3))) -> (~((op (e1) (e1)) = (e0))) -> (~((e0) = (e2))) -> (~((op (e1) (e1)) = (e2))) -> (~((op (e2) (e1)) = (op (e2) (e2)))) -> (~((e2) = (e3))) -> ((op (e3) (e1)) = (e3)) -> (((op (e0) (e1)) = (e2))\/(((op (e1) (e1)) = (e2))\/(((op (e2) (e1)) = (e2))\/((op (e3) (e1)) = (e2))))) -> (((op (e0) (e0)) = (e2))\/(((op (e0) (e1)) = (e2))\/(((op (e0) (e2)) = (e2))\/((op (e0) (e3)) = (e2))))) -> False). % 15.22/15.44 do 0 intro. intros zenon_H10e zenon_H135 zenon_H8f zenon_H160 zenon_H35 zenon_H15f zenon_H11f zenon_Ha7 zenon_H1cd zenon_H28 zenon_H144 zenon_H4b zenon_H145 zenon_H5e zenon_Hd6 zenon_H157 zenon_H6a zenon_H10a zenon_H1a2 zenon_H8e. % 15.22/15.44 apply (zenon_or_s _ _ zenon_H10e); [ zenon_intro zenon_H3d | zenon_intro zenon_H106 ]. % 15.22/15.44 apply (zenon_or_s _ _ zenon_H8e); [ zenon_intro zenon_H92 | zenon_intro zenon_H91 ]. % 15.22/15.44 exact (zenon_H8f zenon_H92). % 15.22/15.44 apply (zenon_or_s _ _ zenon_H91); [ zenon_intro zenon_H5d | zenon_intro zenon_H93 ]. % 15.22/15.44 apply (zenon_L423_); trivial. % 15.22/15.44 apply (zenon_or_s _ _ zenon_H93); [ zenon_intro zenon_H63 | zenon_intro zenon_H81 ]. % 15.22/15.44 apply (zenon_L15_); trivial. % 15.22/15.44 apply (zenon_L353_); trivial. % 15.22/15.44 apply (zenon_L115_); trivial. % 15.22/15.44 (* end of lemma zenon_L554_ *) % 15.22/15.44 assert (zenon_L555_ : (((op (e0) (e0)) = (e2))\/(((op (e0) (e1)) = (e2))\/(((op (e0) (e2)) = (e2))\/((op (e0) (e3)) = (e2))))) -> (~((op (e0) (e0)) = (e2))) -> (~((e0) = (e2))) -> ((op (e0) (e1)) = (e0)) -> (~((e1) = (e2))) -> (((op (e0) (e0)) = (e3))\/(((op (e0) (e1)) = (e3))\/(((op (e0) (e2)) = (e3))\/((op (e0) (e3)) = (e3))))) -> (~((op (e0) (e0)) = (e3))) -> (~((op (e0) (e1)) = (op (e3) (e1)))) -> ((op (e3) (e1)) = (e3)) -> (~((e1) = (e3))) -> ((op (e0) (e2)) = (e1)) -> (~((e2) = (e3))) -> False). % 15.22/15.44 do 0 intro. intros zenon_H8e zenon_H8f zenon_H5e zenon_H49 zenon_Ha7 zenon_H58 zenon_H59 zenon_H138 zenon_H10a zenon_Ha3 zenon_H29 zenon_H6a. % 15.22/15.44 apply (zenon_or_s _ _ zenon_H8e); [ zenon_intro zenon_H92 | zenon_intro zenon_H91 ]. % 15.22/15.44 exact (zenon_H8f zenon_H92). % 15.22/15.44 apply (zenon_or_s _ _ zenon_H91); [ zenon_intro zenon_H5d | zenon_intro zenon_H93 ]. % 15.22/15.44 apply (zenon_L14_); trivial. % 15.22/15.44 apply (zenon_or_s _ _ zenon_H93); [ zenon_intro zenon_H63 | zenon_intro zenon_H81 ]. % 15.22/15.44 apply (zenon_L104_); trivial. % 15.22/15.44 apply (zenon_L129_); trivial. % 15.22/15.44 (* end of lemma zenon_L555_ *) % 15.22/15.44 assert (zenon_L556_ : ((~((op (e3) (e3)) = (e3)))\/((op (e3) (e3)) = (e3))) -> (~((op (e3) (e0)) = (op (e3) (e3)))) -> (((op (e0) (e0)) = (e2))\/(((op (e0) (e1)) = (e2))\/(((op (e0) (e2)) = (e2))\/((op (e0) (e3)) = (e2))))) -> (~((op (e0) (e0)) = (e3))) -> (~((e0) = (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)) = (e3)) -> (~((op (e3) (e0)) = (op (e3) (e1)))) -> (~((e2) = (e3))) -> (~((op (e1) (e1)) = (e3))) -> (~((op (e0) (e1)) = (op (e0) (e3)))) -> (~((e1) = (e2))) -> (((op (e3) (e3)) = (e0))\/(((op (e3) (e3)) = (e1))\/(((op (e3) (e3)) = (e2))\/((op (e3) (e3)) = (e3))))) -> (~((op (e3) (e3)) = (e2))) -> (~((op (e3) (e3)) = (e1))) -> (~((op (e0) (e0)) = (e0))) -> (((op (e0) (e0)) = (e0))\/(((op (e0) (e0)) = (e1))\/(((op (e0) (e0)) = (e2))\/((op (e0) (e0)) = (e3))))) -> (((op (e0) (e1)) = (e2))\/(((op (e1) (e1)) = (e2))\/(((op (e2) (e1)) = (e2))\/((op (e3) (e1)) = (e2))))) -> (~((op (e1) (e1)) = (e1))) -> (~((e0) = (e1))) -> (((op (e0) (e0)) = (e3))\/(((op (e0) (e1)) = (e3))\/(((op (e0) (e2)) = (e3))\/((op (e0) (e3)) = (e3))))) -> ((op (e2) (e2)) = (e2)) -> (~((op (e0) (e2)) = (op (e2) (e2)))) -> ((op (e0) (e1)) = (e0)) -> (~((e0) = (e2))) -> (~((op (e0) (e0)) = (e2))) -> (~((e1) = (e3))) -> (~((op (e1) (e1)) = (e0))) -> (~((op (e0) (e1)) = (op (e1) (e1)))) -> (((op (e1) (e1)) = (e0))\/(((op (e1) (e1)) = (e1))\/(((op (e1) (e1)) = (e2))\/((op (e1) (e1)) = (e3))))) -> (((op (e0) (e0)) = (e1))\/(((op (e0) (e1)) = (e1))\/(((op (e0) (e2)) = (e1))\/((op (e0) (e3)) = (e1))))) -> False). % 15.22/15.44 do 0 intro. intros zenon_H10d zenon_Hbb zenon_H8e zenon_H59 zenon_H4b zenon_H228 zenon_H199 zenon_Hba zenon_H109 zenon_H6a zenon_H182 zenon_H1cd zenon_Ha7 zenon_H3b zenon_H3d zenon_H104 zenon_H20 zenon_H12a zenon_H1a2 zenon_H1b4 zenon_H9e zenon_H58 zenon_H35 zenon_H28 zenon_H49 zenon_H5e zenon_H8f zenon_Ha3 zenon_H145 zenon_H23 zenon_H1b3 zenon_H44. % 15.22/15.44 apply (zenon_or_s _ _ zenon_H10d); [ zenon_intro zenon_H3e | zenon_intro zenon_H42 ]. % 15.22/15.44 apply (zenon_L506_); trivial. % 15.22/15.44 apply (zenon_L43_); trivial. % 15.22/15.44 (* end of lemma zenon_L556_ *) % 15.22/15.44 assert (zenon_L557_ : ((~((op (e1) (e1)) = (e2)))\/((op (e1) (e2)) = (e1))) -> (~((op (e3) (e1)) = (op (e3) (e3)))) -> (~((op (e0) (e1)) = (op (e3) (e1)))) -> (((op (e0) (e0)) = (e0))\/(((op (e0) (e1)) = (e0))\/(((op (e0) (e2)) = (e0))\/((op (e0) (e3)) = (e0))))) -> (~((op (e1) (e2)) = (op (e1) (e3)))) -> (((op (e0) (e2)) = (e3))\/(((op (e1) (e2)) = (e3))\/(((op (e2) (e2)) = (e3))\/((op (e3) (e2)) = (e3))))) -> (~((op (e0) (e0)) = (e0))) -> (((op (e0) (e0)) = (e0))\/(((op (e0) (e0)) = (e1))\/(((op (e0) (e0)) = (e2))\/((op (e0) (e0)) = (e3))))) -> (((op (e1) (e1)) = (e0))\/(((op (e1) (e1)) = (e1))\/(((op (e1) (e1)) = (e2))\/((op (e1) (e1)) = (e3))))) -> (~((op (e1) (e1)) = (e1))) -> ((op (e0) (e1)) = (e0)) -> (~((op (e0) (e1)) = (op (e1) (e1)))) -> (~((op (e3) (e0)) = (op (e3) (e2)))) -> (((op (e0) (e0)) = (e2))\/(((op (e1) (e0)) = (e2))\/(((op (e2) (e0)) = (e2))\/((op (e3) (e0)) = (e2))))) -> (~((op (e3) (e0)) = (op (e3) (e1)))) -> ((~((op (e3) (e3)) = (e3)))\/((op (e3) (e3)) = (e3))) -> ((~((op (e2) (e2)) = (e0)))\/((op (e2) (e0)) = (e2))) -> (~((op (e2) (e0)) = (op (e2) (e2)))) -> (~((op (e2) (e3)) = (op (e3) (e3)))) -> (((op (e2) (e0)) = (e3))\/(((op (e2) (e1)) = (e3))\/(((op (e2) (e2)) = (e3))\/((op (e2) (e3)) = (e3))))) -> (~((op (e2) (e0)) = (op (e2) (e1)))) -> ((~((op (e2) (e2)) = (e2)))\/((op (e2) (e2)) = (e2))) -> ((~((op (e3) (e3)) = (e2)))\/((op (e3) (e2)) = (e3))) -> (~((op (e3) (e2)) = (op (e3) (e3)))) -> (((op (e1) (e0)) = (e3))\/(((op (e1) (e1)) = (e3))\/(((op (e1) (e2)) = (e3))\/((op (e1) (e3)) = (e3))))) -> (~((op (e1) (e3)) = (op (e3) (e3)))) -> (~((op (e0) (e2)) = (op (e1) (e2)))) -> (~((e2) = (e3))) -> (~((op (e1) (e2)) = (op (e2) (e2)))) -> (~((op (e0) (e3)) = (op (e1) (e3)))) -> (((op (e1) (e0)) = (e2))\/(((op (e1) (e1)) = (e2))\/(((op (e1) (e2)) = (e2))\/((op (e1) (e3)) = (e2))))) -> (~((e0) = (e1))) -> (~((e1) = (e3))) -> (((op (e0) (e3)) = (e2))\/(((op (e1) (e3)) = (e2))\/(((op (e2) (e3)) = (e2))\/((op (e3) (e3)) = (e2))))) -> (~((e1) = (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)) = (e1))\/(((op (e0) (e1)) = (e1))\/(((op (e0) (e2)) = (e1))\/((op (e0) (e3)) = (e1))))) -> (~((op (e3) (e0)) = (op (e3) (e3)))) -> ((~((op (e3) (e3)) = (e0)))\/((op (e3) (e0)) = (e3))) -> (~((op (e0) (e0)) = (e3))) -> (~((e0) = (e3))) -> (((op (e2) (e2)) = (e0))\/(((op (e2) (e2)) = (e1))\/(((op (e2) (e2)) = (e2))\/((op (e2) (e2)) = (e3))))) -> (((op (e0) (e0)) = (e3))\/(((op (e0) (e1)) = (e3))\/(((op (e0) (e2)) = (e3))\/((op (e0) (e3)) = (e3))))) -> (~((op (e2) (e1)) = (op (e2) (e2)))) -> (~((op (e0) (e1)) = (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) (e1)) = (e0))\/(((op (e2) (e2)) = (e0))\/((op (e2) (e3)) = (e0))))) -> (~((op (e2) (e0)) = (op (e2) (e3)))) -> (((op (e0) (e1)) = (e3))\/(((op (e1) (e1)) = (e3))\/(((op (e2) (e1)) = (e3))\/((op (e3) (e1)) = (e3))))) -> (~((op (e2) (e1)) = (op (e2) (e3)))) -> ((~((op (e2) (e2)) = (e3)))\/((op (e2) (e3)) = (e2))) -> ((~((op (e2) (e2)) = (e1)))\/((op (e2) (e1)) = (e2))) -> ((~((op (e1) (e1)) = (e3)))\/((op (e1) (e3)) = (e1))) -> (~((op (e0) (e0)) = (e2))) -> (~((e0) = (e2))) -> (~((op (e0) (e2)) = (op (e2) (e2)))) -> ((op (e2) (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 (e0) (e0)) = (e2))\/(((op (e0) (e1)) = (e2))\/(((op (e0) (e2)) = (e2))\/((op (e0) (e3)) = (e2))))) -> (~((op (e3) (e1)) = (op (e3) (e2)))) -> (~((op (e2) (e2)) = (op (e2) (e3)))) -> (((op (e0) (e1)) = (e0))\/(((op (e1) (e1)) = (e0))\/(((op (e2) (e1)) = (e0))\/((op (e3) (e1)) = (e0))))) -> (~((op (e1) (e1)) = (e0))) -> (((op (e0) (e1)) = (e2))\/(((op (e1) (e1)) = (e2))\/(((op (e2) (e1)) = (e2))\/((op (e3) (e1)) = (e2))))) -> ((~((op (e3) (e3)) = (e1)))\/((op (e3) (e1)) = (e3))) -> False). % 15.22/15.44 do 0 intro. intros zenon_H1d3 zenon_H12d zenon_H138 zenon_H110 zenon_H1d0 zenon_H175 zenon_H20 zenon_H12a zenon_H1b3 zenon_H1b4 zenon_H49 zenon_H23 zenon_H105 zenon_Heb zenon_H109 zenon_H10d zenon_H1d4 zenon_H17a zenon_He3 zenon_He6 zenon_H154 zenon_Haa zenon_H10e zenon_H173 zenon_H90 zenon_H8b zenon_H87 zenon_H6a zenon_H7d zenon_H80 zenon_H84 zenon_H9e zenon_Ha3 zenon_H160 zenon_Ha7 zenon_H1cd zenon_Hd3 zenon_H44 zenon_Hbb zenon_H10f zenon_H59 zenon_H4b zenon_H2d zenon_H58 zenon_H157 zenon_Hde zenon_H228 zenon_H1f5 zenon_Hce zenon_H199 zenon_H1e2 zenon_H1c3 zenon_H1e3 zenon_H1d2 zenon_H8f zenon_H5e zenon_H28 zenon_H35 zenon_H3b zenon_H36 zenon_H8e zenon_H135 zenon_H15f zenon_H144 zenon_H145 zenon_H1a2 zenon_H10c. % 15.22/15.44 apply (zenon_or_s _ _ zenon_H1d3); [ zenon_intro zenon_Hd6 | zenon_intro zenon_H117 ]. % 15.22/15.44 apply (zenon_or_s _ _ zenon_H1d2); [ zenon_intro zenon_H182 | zenon_intro zenon_H11f ]. % 15.22/15.44 apply (zenon_L347_); trivial. % 15.22/15.44 apply (zenon_or_s _ _ zenon_H10f); [ zenon_intro zenon_H3c | zenon_intro zenon_Hba ]. % 15.22/15.44 apply (zenon_or_s _ _ zenon_H10c); [ zenon_intro zenon_H104 | zenon_intro zenon_H10a ]. % 15.22/15.44 apply (zenon_or_s _ _ zenon_H10d); [ zenon_intro zenon_H3e | zenon_intro zenon_H42 ]. % 15.22/15.44 apply (zenon_L131_); trivial. % 15.22/15.44 apply (zenon_L378_); trivial. % 15.22/15.44 apply (zenon_L554_); trivial. % 15.22/15.44 apply (zenon_L359_); trivial. % 15.22/15.44 apply (zenon_or_s _ _ zenon_H1d2); [ zenon_intro zenon_H182 | zenon_intro zenon_H11f ]. % 15.22/15.44 apply (zenon_or_s _ _ zenon_H1c3); [ zenon_intro zenon_H30 | zenon_intro zenon_H124 ]. % 15.22/15.44 apply (zenon_or_s _ _ zenon_H10f); [ zenon_intro zenon_H3c | zenon_intro zenon_Hba ]. % 15.22/15.44 apply (zenon_or_s _ _ zenon_H10c); [ zenon_intro zenon_H104 | zenon_intro zenon_H10a ]. % 15.22/15.44 apply (zenon_L495_); trivial. % 15.22/15.44 apply (zenon_or_s _ _ zenon_H10e); [ zenon_intro zenon_H3d | zenon_intro zenon_H106 ]. % 15.22/15.44 apply (zenon_or_s _ _ zenon_H10d); [ zenon_intro zenon_H3e | zenon_intro zenon_H42 ]. % 15.22/15.44 apply (zenon_or_s _ _ zenon_H44); [ zenon_intro zenon_H47 | zenon_intro zenon_H46 ]. % 15.22/15.44 apply (zenon_or_s _ _ zenon_H8e); [ zenon_intro zenon_H92 | zenon_intro zenon_H91 ]. % 15.22/15.44 exact (zenon_H8f zenon_H92). % 15.22/15.44 apply (zenon_or_s _ _ zenon_H91); [ zenon_intro zenon_H5d | zenon_intro zenon_H93 ]. % 15.22/15.44 apply (zenon_L214_); trivial. % 15.22/15.44 apply (zenon_or_s _ _ zenon_H93); [ zenon_intro zenon_H63 | zenon_intro zenon_H81 ]. % 15.22/15.44 apply (zenon_L15_); trivial. % 15.22/15.44 apply (zenon_or_s _ _ zenon_H58); [ zenon_intro zenon_H5b | zenon_intro zenon_H5a ]. % 15.22/15.44 exact (zenon_H59 zenon_H5b). % 15.22/15.44 apply (zenon_or_s _ _ zenon_H5a); [ zenon_intro zenon_H4a | zenon_intro zenon_H5c ]. % 15.22/15.44 apply (zenon_L120_); trivial. % 15.22/15.44 apply (zenon_or_s _ _ zenon_H5c); [ zenon_intro zenon_H50 | zenon_intro zenon_H53 ]. % 15.22/15.44 apply (zenon_or_s _ _ zenon_H228); [ zenon_intro zenon_H22 | zenon_intro zenon_H229 ]. % 15.22/15.44 apply (zenon_L27_); trivial. % 15.22/15.44 apply (zenon_or_s _ _ zenon_H229); [ zenon_intro zenon_H21 | zenon_intro zenon_H22a ]. % 15.22/15.44 exact (zenon_H1b4 zenon_H21). % 15.22/15.44 apply (zenon_or_s _ _ zenon_H22a); [ zenon_intro zenon_Hb2 | zenon_intro zenon_H13e ]. % 15.22/15.44 apply (zenon_or_s _ _ zenon_H1a2); [ zenon_intro zenon_H5d | zenon_intro zenon_H1a3 ]. % 15.22/15.44 apply (zenon_L350_); trivial. % 15.22/15.44 apply (zenon_or_s _ _ zenon_H1a3); [ zenon_intro zenon_H6e | zenon_intro zenon_H1a4 ]. % 15.22/15.44 apply (zenon_L20_); trivial. % 15.22/15.44 apply (zenon_or_s _ _ zenon_H1a4); [ zenon_intro zenon_H156 | zenon_intro zenon_H16a ]. % 15.22/15.44 apply (zenon_L372_); trivial. % 15.22/15.44 apply (zenon_L297_); trivial. % 15.22/15.44 apply (zenon_L123_); trivial. % 15.22/15.44 apply (zenon_L128_); trivial. % 15.22/15.44 apply (zenon_or_s _ _ zenon_H46); [ zenon_intro zenon_H22 | zenon_intro zenon_H48 ]. % 15.22/15.44 apply (zenon_L27_); trivial. % 15.22/15.44 apply (zenon_or_s _ _ zenon_H48); [ zenon_intro zenon_H29 | zenon_intro zenon_H37 ]. % 15.22/15.44 apply (zenon_L555_); trivial. % 15.22/15.44 apply (zenon_L7_); trivial. % 15.22/15.44 apply (zenon_L102_); trivial. % 15.22/15.44 apply (zenon_L115_); trivial. % 15.22/15.44 apply (zenon_or_s _ _ zenon_H10c); [ zenon_intro zenon_H104 | zenon_intro zenon_H10a ]. % 15.22/15.44 apply (zenon_or_s _ _ zenon_H10e); [ zenon_intro zenon_H3d | zenon_intro zenon_H106 ]. % 15.22/15.44 apply (zenon_L556_); trivial. % 15.22/15.44 apply (zenon_L81_); trivial. % 15.22/15.44 apply (zenon_L82_); trivial. % 15.22/15.44 apply (zenon_L137_); trivial. % 15.22/15.44 apply (zenon_L237_); trivial. % 15.22/15.44 (* end of lemma zenon_L557_ *) % 15.22/15.44 assert (zenon_L558_ : ((~((op (e0) (e0)) = (e0)))\/((op (e0) (e0)) = (e0))) -> (~((op (e0) (op (e0) (e0))) = (op (e0) (e0)))) -> ((~((op (e0) (e0)) = (e2)))\/((op (e0) (e2)) = (e0))) -> ((~((op (e1) (e1)) = (e0)))\/((op (e1) (e0)) = (e1))) -> ((~((op (e2) (e2)) = (e0)))\/((op (e2) (e0)) = (e2))) -> (~((op (e2) (e0)) = (op (e2) (e1)))) -> (((op (e0) (e1)) = (e0))\/(((op (e1) (e1)) = (e0))\/(((op (e2) (e1)) = (e0))\/((op (e3) (e1)) = (e0))))) -> (~((op (e2) (e1)) = (op (e2) (e2)))) -> (((op (e0) (e1)) = (e2))\/(((op (e1) (e1)) = (e2))\/(((op (e2) (e1)) = (e2))\/((op (e3) (e1)) = (e2))))) -> (((op (e3) (e3)) = (e0))\/(((op (e3) (e3)) = (e1))\/(((op (e3) (e3)) = (e2))\/((op (e3) (e3)) = (e3))))) -> ((~((op (e3) (e3)) = (e3)))\/((op (e3) (e3)) = (e3))) -> (~((op (e3) (e0)) = (op (e3) (e1)))) -> (~((op (e2) (e0)) = (op (e2) (e2)))) -> (~((op (e3) (e0)) = (op (e3) (e2)))) -> ((~((op (e2) (e2)) = (e2)))\/((op (e2) (e2)) = (e2))) -> (((op (e0) (e0)) = (e2))\/(((op (e0) (e1)) = (e2))\/(((op (e0) (e2)) = (e2))\/((op (e0) (e3)) = (e2))))) -> (((op (e1) (e0)) = (e3))\/(((op (e1) (e1)) = (e3))\/(((op (e1) (e2)) = (e3))\/((op (e1) (e3)) = (e3))))) -> (~((op (e1) (e3)) = (op (e3) (e3)))) -> (~((op (e0) (e2)) = (op (e1) (e2)))) -> (~((e2) = (e3))) -> (~((op (e1) (e2)) = (op (e2) (e2)))) -> (~((op (e0) (e3)) = (op (e1) (e3)))) -> (((op (e1) (e0)) = (e2))\/(((op (e1) (e1)) = (e2))\/(((op (e1) (e2)) = (e2))\/((op (e1) (e3)) = (e2))))) -> (~((e0) = (e2))) -> (~((e0) = (e1))) -> (~((e1) = (e3))) -> (~((e1) = (e2))) -> (((op (e0) (e0)) = (e1))\/(((op (e0) (e1)) = (e1))\/(((op (e0) (e2)) = (e1))\/((op (e0) (e3)) = (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 (e0) (e3)) = (op (e3) (e3)))) -> ((op (e3) (e3)) = (e3)) -> (((op (e0) (e0)) = (e3))\/(((op (e0) (e1)) = (e3))\/(((op (e0) (e2)) = (e3))\/((op (e0) (e3)) = (e3))))) -> ((~((op (e3) (e3)) = (e2)))\/((op (e3) (e2)) = (e3))) -> (~((op (e0) (e1)) = (op (e2) (e1)))) -> (~((op (e2) (e3)) = (op (e3) (e3)))) -> (((op (e2) (e0)) = (e3))\/(((op (e2) (e1)) = (e3))\/(((op (e2) (e2)) = (e3))\/((op (e2) (e3)) = (e3))))) -> (((op (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) (e1)) = (op (e1) (e1)))) -> (((op (e1) (e1)) = (e0))\/(((op (e1) (e1)) = (e1))\/(((op (e1) (e1)) = (e2))\/((op (e1) (e1)) = (e3))))) -> ((~((op (e2) (e2)) = (e3)))\/((op (e2) (e3)) = (e2))) -> (((op (e0) (e3)) = (e0))\/(((op (e1) (e3)) = (e0))\/(((op (e2) (e3)) = (e0))\/((op (e3) (e3)) = (e0))))) -> (~((op (e0) (e2)) = (op (e0) (e3)))) -> (~((op (e3) (e0)) = (op (e3) (e3)))) -> ((~((op (e3) (e3)) = (e0)))\/((op (e3) (e0)) = (e3))) -> (~((op (e3) (e2)) = (op (e3) (e3)))) -> (((op (e0) (e2)) = (e3))\/(((op (e1) (e2)) = (e3))\/(((op (e2) (e2)) = (e3))\/((op (e3) (e2)) = (e3))))) -> (((op (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 (e3) (e3)) = (e1)))\/((op (e3) (e1)) = (e3))) -> (~((op (e3) (e1)) = (op (e3) (e3)))) -> (~((op (e1) (e0)) = (op (e1) (e3)))) -> (((op (e0) (e3)) = (e1))\/(((op (e1) (e3)) = (e1))\/(((op (e2) (e3)) = (e1))\/((op (e3) (e3)) = (e1))))) -> (~((op (e2) (e0)) = (op (e2) (e3)))) -> (~((op (e0) (e1)) = (op (e0) (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 (e0) (e0)) = (e1))\/(((op (e1) (e0)) = (e1))\/(((op (e2) (e0)) = (e1))\/((op (e3) (e0)) = (e1))))) -> (~((op (e3) (op (e0) (e3))) = (op (e0) (e3)))) -> (((op (e0) (e0)) = (e0))\/(((op (e1) (e0)) = (e0))\/(((op (e2) (e0)) = (e0))\/((op (e3) (e0)) = (e0))))) -> (((op (e0) (e0)) = (e0))\/(((op (e0) (e1)) = (e0))\/(((op (e0) (e2)) = (e0))\/((op (e0) (e3)) = (e0))))) -> (((op (e0) (e1)) = (e3))\/(((op (e1) (e1)) = (e3))\/(((op (e2) (e1)) = (e3))\/((op (e3) (e1)) = (e3))))) -> ((~((op (e2) (e2)) = (e1)))\/((op (e2) (e1)) = (e2))) -> (~((op (e2) (e1)) = (op (e2) (e3)))) -> (~((op (e2) (e2)) = (op (e2) (e3)))) -> ((~((op (e1) (e1)) = (e2)))\/((op (e1) (e2)) = (e1))) -> (~((op (e1) (e2)) = (op (e1) (e3)))) -> (((op (e0) (e1)) = (e1))\/(((op (e1) (e1)) = (e1))\/(((op (e2) (e1)) = (e1))\/((op (e3) (e1)) = (e1))))) -> (((op (e2) (e0)) = (e0))\/(((op (e2) (e1)) = (e0))\/(((op (e2) (e2)) = (e0))\/((op (e2) (e3)) = (e0))))) -> ((~((op (e1) (e1)) = (e3)))\/((op (e1) (e3)) = (e1))) -> (~((op (e1) (op (e0) (e1))) = (op (e0) (e1)))) -> (((op (e0) (e0)) = (e0))\/(((op (e0) (e0)) = (e1))\/(((op (e0) (e0)) = (e2))\/((op (e0) (e0)) = (e3))))) -> (~((op (e2) (op (e0) (e2))) = (op (e0) (e2)))) -> (((op (e3) (e0)) = (e1))\/(((op (e3) (e1)) = (e1))\/(((op (e3) (e2)) = (e1))\/((op (e3) (e3)) = (e1))))) -> (~((op (e0) (e2)) = (op (e3) (e2)))) -> (((op (e0) (e2)) = (e1))\/(((op (e1) (e2)) = (e1))\/(((op (e2) (e2)) = (e1))\/((op (e3) (e2)) = (e1))))) -> (~((op (e3) (e1)) = (op (e3) (e2)))) -> (~((op (e1) (e0)) = (op (e3) (e0)))) -> (~((op (e1) (e2)) = (op (e3) (e2)))) -> (~((op (e1) (e0)) = (op (e1) (e2)))) -> (((op (e3) (e0)) = (e2))\/(((op (e3) (e1)) = (e2))\/(((op (e3) (e2)) = (e2))\/((op (e3) (e3)) = (e2))))) -> (~((op (e2) (e1)) = (op (e3) (e1)))) -> (((op (e3) (e1)) = (e0))\/(((op (e3) (e1)) = (e1))\/(((op (e3) (e1)) = (e2))\/((op (e3) (e1)) = (e3))))) -> (~((op (e0) (e1)) = (op (e3) (e1)))) -> (((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) (e0)) = (op (e1) (e1)))) -> (~((op (e1) (e1)) = (op (e2) (e1)))) -> (~((op (e0) (e3)) = (op (e2) (e3)))) -> (~((op (e1) (e1)) = (op (e1) (e3)))) -> (((op (e1) (e2)) = (e0))\/(((op (e1) (e2)) = (e1))\/(((op (e1) (e2)) = (e2))\/((op (e1) (e2)) = (e3))))) -> (~((op (e1) (e1)) = (op (e1) (e2)))) -> ((~((op (e1) (e1)) = (e1)))\/((op (e1) (e1)) = (e1))) -> ((~((op (e0) (e0)) = (e3)))\/((op (e0) (e3)) = (e0))) -> (~((op (e0) (e1)) = (op (e0) (e2)))) -> ((~((op (e0) (e0)) = (e1)))\/((op (e0) (e1)) = (e0))) -> False). % 15.22/15.44 do 0 intro. intros zenon_H249 zenon_H1e zenon_H24a zenon_H1e4 zenon_H1d4 zenon_H154 zenon_H144 zenon_H157 zenon_H1a2 zenon_H3b zenon_H10d zenon_H109 zenon_H17a zenon_H105 zenon_Haa zenon_H8e zenon_H90 zenon_H8b zenon_H87 zenon_H6a zenon_H7d zenon_H80 zenon_H84 zenon_H5e zenon_H9e zenon_Ha3 zenon_Ha7 zenon_H44 zenon_H4b zenon_H2d zenon_H28 zenon_H36 zenon_H42 zenon_H58 zenon_H10e zenon_Hde zenon_He3 zenon_He6 zenon_Hbe zenon_Heb zenon_H23 zenon_H1b3 zenon_H1c3 zenon_Hd3 zenon_Hc9 zenon_Hbb zenon_H10f zenon_H173 zenon_H175 zenon_H160 zenon_H1c5 zenon_H10c zenon_H12d zenon_H1cf zenon_H121 zenon_Hce zenon_H1cd zenon_H163 zenon_Hb7 zenon_Hf1 zenon_H192 zenon_Hf0 zenon_H110 zenon_H199 zenon_H1e3 zenon_H1e2 zenon_H15f zenon_H1d3 zenon_H1d0 zenon_H228 zenon_H1f5 zenon_H1d2 zenon_H1ff zenon_H12a zenon_H20c zenon_H146 zenon_H140 zenon_H11b zenon_H135 zenon_H22e zenon_H17d zenon_H166 zenon_H1df zenon_H13c zenon_H16c zenon_H138 zenon_H16f zenon_H15a zenon_Hd7 zenon_Hb1 zenon_Hb4 zenon_H11e zenon_H1d5 zenon_H116 zenon_H1d8 zenon_H236 zenon_H23e zenon_H24b. % 15.22/15.44 apply (zenon_or_s _ _ zenon_H249); [ zenon_intro zenon_H20 | zenon_intro zenon_H1f ]. % 15.22/15.44 apply (zenon_or_s _ _ zenon_H24b); [ zenon_intro zenon_H45 | zenon_intro zenon_H49 ]. % 15.22/15.44 apply (zenon_or_s _ _ zenon_H24a); [ zenon_intro zenon_H8f | zenon_intro zenon_Hab ]. % 15.22/15.44 apply (zenon_L455_); trivial. % 15.22/15.44 apply (zenon_or_s _ _ zenon_H236); [ zenon_intro zenon_H59 | zenon_intro zenon_Hca ]. % 15.22/15.44 apply (zenon_L259_); trivial. % 15.22/15.44 apply (zenon_L53_); trivial. % 15.22/15.44 apply (zenon_or_s _ _ zenon_H24a); [ zenon_intro zenon_H8f | zenon_intro zenon_Hab ]. % 15.22/15.44 apply (zenon_or_s _ _ zenon_H236); [ zenon_intro zenon_H59 | zenon_intro zenon_Hca ]. % 15.22/15.44 apply (zenon_or_s _ _ zenon_H1e4); [ zenon_intro zenon_H145 | zenon_intro zenon_Hd8 ]. % 15.22/15.44 apply (zenon_or_s _ _ zenon_H1d8); [ zenon_intro zenon_H1b4 | zenon_intro zenon_H21 ]. % 15.22/15.44 apply (zenon_L387_); trivial. % 15.22/15.44 apply (zenon_or_s _ _ zenon_H1d2); [ zenon_intro zenon_H182 | zenon_intro zenon_H11f ]. % 15.22/15.44 apply (zenon_L286_); trivial. % 15.22/15.44 apply (zenon_L90_); trivial. % 15.22/15.44 apply (zenon_L484_); trivial. % 15.22/15.44 apply (zenon_L463_); trivial. % 15.22/15.44 apply (zenon_L485_); trivial. % 15.22/15.44 apply (zenon_L2_); trivial. % 15.22/15.44 (* end of lemma zenon_L558_ *) % 15.22/15.44 assert (zenon_L559_ : (~((op (e0) (e0)) = (op (e1) (e0)))) -> ((op (e0) (e0)) = (e0)) -> ((op (e1) (e0)) = (e0)) -> False). % 15.22/15.44 do 0 intro. intros zenon_H24c zenon_H1f zenon_Had. % 15.22/15.44 cut (((op (e0) (e0)) = (e0)) = ((op (e0) (e0)) = (op (e1) (e0)))). % 15.22/15.44 intro zenon_D_pnotp. % 15.22/15.44 apply zenon_H24c. % 15.22/15.44 rewrite <- zenon_D_pnotp. % 15.22/15.44 exact zenon_H1f. % 15.22/15.44 cut (((e0) = (op (e1) (e0)))); [idtac | apply NNPP; zenon_intro zenon_H24d]. % 15.22/15.44 cut (((op (e0) (e0)) = (op (e0) (e0)))); [idtac | apply NNPP; zenon_intro zenon_H24e]. % 15.22/15.44 congruence. % 15.22/15.44 apply zenon_H24e. apply refl_equal. % 15.22/15.44 apply zenon_H24d. apply sym_equal. exact zenon_Had. % 15.22/15.44 (* end of lemma zenon_L559_ *) % 15.22/15.44 assert (zenon_L560_ : (((op (e1) (e0)) = (e0))\/(((op (e1) (e1)) = (e0))\/(((op (e1) (e2)) = (e0))\/((op (e1) (e3)) = (e0))))) -> ((op (e0) (e0)) = (e0)) -> (~((op (e0) (e0)) = (op (e1) (e0)))) -> (~((op (e3) (e3)) = (e0))) -> (~((op (e1) (e1)) = (e2))) -> (~((op (e1) (e1)) = (e1))) -> (~((op (e1) (e1)) = (e0))) -> (((op (e1) (e1)) = (e0))\/(((op (e1) (e1)) = (e1))\/(((op (e1) (e1)) = (e2))\/((op (e1) (e1)) = (e3))))) -> (((op (e3) (e3)) = (e0))\/(((op (e3) (e3)) = (e1))\/(((op (e3) (e3)) = (e2))\/((op (e3) (e3)) = (e3))))) -> (~((op (e1) (e3)) = (op (e3) (e3)))) -> (~((op (e3) (e3)) = (e1))) -> (~((op (e3) (e3)) = (e2))) -> (~((op (e3) (e3)) = (e3))) -> False). % 15.22/15.44 do 0 intro. intros zenon_H163 zenon_H1f zenon_H24c zenon_H3c zenon_Hd6 zenon_H1b4 zenon_H145 zenon_H1b3 zenon_H3b zenon_H8b zenon_H104 zenon_H3d zenon_H3e. % 15.22/15.44 apply (zenon_or_s _ _ zenon_H163); [ zenon_intro zenon_Had | zenon_intro zenon_H164 ]. % 15.22/15.44 apply (zenon_L559_); trivial. % 15.22/15.44 apply (zenon_or_s _ _ zenon_H164); [ zenon_intro zenon_H149 | zenon_intro zenon_H165 ]. % 15.22/15.44 exact (zenon_H145 zenon_H149). % 15.22/15.44 apply (zenon_or_s _ _ zenon_H165); [ zenon_intro zenon_H15d | zenon_intro zenon_Hcc ]. % 15.22/15.44 apply (zenon_L490_); trivial. % 15.22/15.44 apply (zenon_L465_); trivial. % 15.22/15.44 (* end of lemma zenon_L560_ *) % 15.22/15.44 assert (zenon_L561_ : (((op (e3) (e0)) = (e1))\/(((op (e3) (e1)) = (e1))\/(((op (e3) (e2)) = (e1))\/((op (e3) (e3)) = (e1))))) -> ((op (e3) (e0)) = (e2)) -> (~((e1) = (e2))) -> ((op (e3) (e1)) = (e2)) -> ((op (e0) (e2)) = (e1)) -> (~((op (e0) (e2)) = (op (e3) (e2)))) -> (~((op (e3) (e3)) = (e1))) -> False). % 15.22/15.44 do 0 intro. intros zenon_H146 zenon_He9 zenon_Ha7 zenon_H16a zenon_H29 zenon_H140 zenon_H104. % 15.22/15.44 apply (zenon_or_s _ _ zenon_H146); [ zenon_intro zenon_Hee | zenon_intro zenon_H14b ]. % 15.22/15.44 apply (zenon_L122_); trivial. % 15.22/15.44 apply (zenon_or_s _ _ zenon_H14b); [ zenon_intro zenon_H13e | zenon_intro zenon_H14c ]. % 15.22/15.44 apply (zenon_L414_); trivial. % 15.22/15.44 apply (zenon_or_s _ _ zenon_H14c); [ zenon_intro zenon_H119 | zenon_intro zenon_H38 ]. % 15.22/15.44 apply (zenon_L124_); trivial. % 15.22/15.44 exact (zenon_H104 zenon_H38). % 15.22/15.44 (* end of lemma zenon_L561_ *) % 15.22/15.44 assert (zenon_L562_ : (~((op (e0) (e0)) = (op (e0) (e3)))) -> ((op (e0) (e0)) = (e0)) -> ((op (e0) (e3)) = (e0)) -> False). % 15.22/15.44 do 0 intro. intros zenon_H24f zenon_H1f zenon_Hca. % 15.22/15.44 cut (((op (e0) (e0)) = (e0)) = ((op (e0) (e0)) = (op (e0) (e3)))). % 15.22/15.44 intro zenon_D_pnotp. % 15.22/15.44 apply zenon_H24f. % 15.22/15.44 rewrite <- zenon_D_pnotp. % 15.22/15.44 exact zenon_H1f. % 15.22/15.44 cut (((e0) = (op (e0) (e3)))); [idtac | apply NNPP; zenon_intro zenon_Hcb]. % 15.22/15.44 cut (((op (e0) (e0)) = (op (e0) (e0)))); [idtac | apply NNPP; zenon_intro zenon_H24e]. % 15.22/15.44 congruence. % 15.22/15.44 apply zenon_H24e. apply refl_equal. % 15.22/15.44 apply zenon_Hcb. apply sym_equal. exact zenon_Hca. % 15.22/15.44 (* end of lemma zenon_L562_ *) % 15.22/15.44 assert (zenon_L563_ : (((op (e0) (e3)) = (e0))\/(((op (e1) (e3)) = (e0))\/(((op (e2) (e3)) = (e0))\/((op (e3) (e3)) = (e0))))) -> ((op (e0) (e0)) = (e0)) -> (~((op (e0) (e0)) = (op (e0) (e3)))) -> ((op (e1) (e3)) = (e2)) -> ((op (e2) (e3)) = (e2)) -> (~((e0) = (e2))) -> (~((op (e3) (e3)) = (e0))) -> False). % 15.22/15.44 do 0 intro. intros zenon_Hd3 zenon_H1f zenon_H24f zenon_H82 zenon_H124 zenon_H5e zenon_H3c. % 15.22/15.44 apply (zenon_or_s _ _ zenon_Hd3); [ zenon_intro zenon_Hca | zenon_intro zenon_Hd4 ]. % 15.22/15.44 apply (zenon_L562_); trivial. % 15.22/15.44 apply (zenon_or_s _ _ zenon_Hd4); [ zenon_intro zenon_Hcc | zenon_intro zenon_Hd5 ]. % 15.22/15.44 apply (zenon_L54_); trivial. % 15.22/15.44 apply (zenon_or_s _ _ zenon_Hd5); [ zenon_intro zenon_Hd0 | zenon_intro zenon_H40 ]. % 15.22/15.44 apply (zenon_L201_); trivial. % 15.22/15.44 exact (zenon_H3c zenon_H40). % 15.22/15.44 (* end of lemma zenon_L563_ *) % 15.22/15.44 assert (zenon_L564_ : (((op (e1) (e0)) = (e2))\/(((op (e1) (e1)) = (e2))\/(((op (e1) (e2)) = (e2))\/((op (e1) (e3)) = (e2))))) -> (~((e1) = (e2))) -> ((op (e1) (e0)) = (e1)) -> (~((op (e1) (e1)) = (e2))) -> ((op (e0) (e2)) = (e2)) -> (~((op (e0) (e2)) = (op (e1) (e2)))) -> (((op (e0) (e3)) = (e0))\/(((op (e1) (e3)) = (e0))\/(((op (e2) (e3)) = (e0))\/((op (e3) (e3)) = (e0))))) -> ((op (e0) (e0)) = (e0)) -> (~((op (e0) (e0)) = (op (e0) (e3)))) -> ((op (e2) (e3)) = (e2)) -> (~((e0) = (e2))) -> (~((op (e3) (e3)) = (e0))) -> False). % 15.22/15.44 do 0 intro. intros zenon_H84 zenon_Ha7 zenon_Hd8 zenon_Hd6 zenon_H63 zenon_H87 zenon_Hd3 zenon_H1f zenon_H24f zenon_H124 zenon_H5e zenon_H3c. % 15.22/15.44 apply (zenon_or_s _ _ zenon_H84); [ zenon_intro zenon_H68 | zenon_intro zenon_H85 ]. % 15.22/15.44 apply (zenon_L162_); trivial. % 15.22/15.44 apply (zenon_or_s _ _ zenon_H85); [ zenon_intro zenon_H6e | zenon_intro zenon_H86 ]. % 15.22/15.44 exact (zenon_Hd6 zenon_H6e). % 15.22/15.44 apply (zenon_or_s _ _ zenon_H86); [ zenon_intro zenon_H7c | zenon_intro zenon_H82 ]. % 15.22/15.44 apply (zenon_L52_); trivial. % 15.22/15.44 apply (zenon_L563_); trivial. % 15.22/15.44 (* end of lemma zenon_L564_ *) % 15.22/15.44 assert (zenon_L565_ : ((~((op (e3) (e3)) = (e1)))\/((op (e3) (e1)) = (e3))) -> (~((op (e3) (e1)) = (op (e3) (e3)))) -> (~((op (e0) (e0)) = (e1))) -> (((op (e0) (e3)) = (e1))\/(((op (e1) (e3)) = (e1))\/(((op (e2) (e3)) = (e1))\/((op (e3) (e3)) = (e1))))) -> ((op (e2) (e3)) = (e2)) -> (~((e1) = (e2))) -> ((op (e1) (e0)) = (e1)) -> (~((op (e1) (e0)) = (op (e1) (e3)))) -> (~((op (e0) (e1)) = (op (e0) (e3)))) -> (((op (e0) (e0)) = (e2))\/(((op (e0) (e1)) = (e2))\/(((op (e0) (e2)) = (e2))\/((op (e0) (e3)) = (e2))))) -> (((op (e3) (e0)) = (e1))\/(((op (e3) (e1)) = (e1))\/(((op (e3) (e2)) = (e1))\/((op (e3) (e3)) = (e1))))) -> (~((op (e0) (e2)) = (op (e3) (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)) = (op (e3) (e0)))) -> ((~((op (e2) (e2)) = (e3)))\/((op (e2) (e3)) = (e2))) -> (~((op (e2) (e1)) = (op (e2) (e3)))) -> (((op (e1) (e1)) = (e0))\/(((op (e1) (e1)) = (e1))\/(((op (e1) (e1)) = (e2))\/((op (e1) (e1)) = (e3))))) -> (~((op (e1) (e1)) = (e1))) -> (~((op (e2) (e2)) = (e0))) -> (((op (e2) (e2)) = (e0))\/(((op (e2) (e2)) = (e1))\/(((op (e2) (e2)) = (e2))\/((op (e2) (e2)) = (e3))))) -> (~((op (e3) (e0)) = (op (e3) (e3)))) -> (((op (e0) (e0)) = (e3))\/(((op (e1) (e0)) = (e3))\/(((op (e2) (e0)) = (e3))\/((op (e3) (e0)) = (e3))))) -> (~((op (e2) (e1)) = (op (e2) (e2)))) -> ((~((op (e2) (e2)) = (e2)))\/((op (e2) (e2)) = (e2))) -> (((op (e0) (e0)) = (e2))\/(((op (e1) (e0)) = (e2))\/(((op (e2) (e0)) = (e2))\/((op (e3) (e0)) = (e2))))) -> (~((op (e0) (e0)) = (e3))) -> (~((e2) = (e3))) -> (((op (e1) (e0)) = (e3))\/(((op (e1) (e1)) = (e3))\/(((op (e1) (e2)) = (e3))\/((op (e1) (e3)) = (e3))))) -> ((op (e3) (e3)) = (e3)) -> (~((op (e1) (e3)) = (op (e3) (e3)))) -> (~((op (e0) (e2)) = (op (e1) (e2)))) -> (~((op (e1) (e1)) = (e3))) -> (~((e1) = (e3))) -> (~((op (e0) (e3)) = (op (e3) (e3)))) -> (((op (e0) (e0)) = (e3))\/(((op (e0) (e1)) = (e3))\/(((op (e0) (e2)) = (e3))\/((op (e0) (e3)) = (e3))))) -> (~((op (e0) (e0)) = (e2))) -> (((op (e0) (e3)) = (e0))\/(((op (e1) (e3)) = (e0))\/(((op (e2) (e3)) = (e0))\/((op (e3) (e3)) = (e0))))) -> (~((op (e3) (e3)) = (e0))) -> (~((e0) = (e2))) -> ((op (e0) (e0)) = (e0)) -> (~((op (e0) (e0)) = (op (e0) (e3)))) -> (((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))))) -> False). % 15.22/15.44 do 0 intro. intros zenon_H10c zenon_H12d zenon_H45 zenon_H121 zenon_H124 zenon_Ha7 zenon_Hd8 zenon_H1cf zenon_H1cd zenon_H8e zenon_H146 zenon_H140 zenon_Hd6 zenon_H154 zenon_H1a2 zenon_H22e zenon_H1c3 zenon_H1e2 zenon_H1b3 zenon_H1b4 zenon_H2e zenon_H2d zenon_Hbb zenon_Hbe zenon_H157 zenon_Haa zenon_Heb zenon_H59 zenon_H6a zenon_H90 zenon_H42 zenon_H8b zenon_H87 zenon_H182 zenon_Ha3 zenon_H36 zenon_H58 zenon_H8f zenon_Hd3 zenon_H3c zenon_H5e zenon_H1f zenon_H24f zenon_H84 zenon_H44. % 15.22/15.44 apply (zenon_or_s _ _ zenon_H10c); [ zenon_intro zenon_H104 | zenon_intro zenon_H10a ]. % 15.22/15.44 apply (zenon_or_s _ _ zenon_H44); [ zenon_intro zenon_H47 | zenon_intro zenon_H46 ]. % 15.22/15.44 exact (zenon_H45 zenon_H47). % 15.22/15.44 apply (zenon_or_s _ _ zenon_H46); [ zenon_intro zenon_H22 | zenon_intro zenon_H48 ]. % 15.22/15.44 apply (zenon_L225_); trivial. % 15.22/15.44 apply (zenon_or_s _ _ zenon_H48); [ zenon_intro zenon_H29 | zenon_intro zenon_H37 ]. % 15.22/15.44 apply (zenon_or_s _ _ zenon_H8e); [ zenon_intro zenon_H92 | zenon_intro zenon_H91 ]. % 15.22/15.44 exact (zenon_H8f zenon_H92). % 15.22/15.44 apply (zenon_or_s _ _ zenon_H91); [ zenon_intro zenon_H5d | zenon_intro zenon_H93 ]. % 15.22/15.44 apply (zenon_L227_); trivial. % 15.22/15.44 apply (zenon_or_s _ _ zenon_H93); [ zenon_intro zenon_H63 | zenon_intro zenon_H81 ]. % 15.22/15.44 apply (zenon_L104_); trivial. % 15.22/15.44 apply (zenon_or_s _ _ zenon_Heb); [ zenon_intro zenon_H92 | zenon_intro zenon_Hec ]. % 15.22/15.44 exact (zenon_H8f zenon_H92). % 15.22/15.44 apply (zenon_or_s _ _ zenon_Hec); [ zenon_intro zenon_H68 | zenon_intro zenon_Hed ]. % 15.22/15.44 apply (zenon_L162_); trivial. % 15.22/15.44 apply (zenon_or_s _ _ zenon_Hed); [ zenon_intro zenon_Hdd | zenon_intro zenon_He9 ]. % 15.22/15.44 apply (zenon_L416_); trivial. % 15.22/15.44 apply (zenon_or_s _ _ zenon_H1a2); [ zenon_intro zenon_H5d | zenon_intro zenon_H1a3 ]. % 15.22/15.44 apply (zenon_L227_); trivial. % 15.22/15.44 apply (zenon_or_s _ _ zenon_H1a3); [ zenon_intro zenon_H6e | zenon_intro zenon_H1a4 ]. % 15.22/15.44 exact (zenon_Hd6 zenon_H6e). % 15.22/15.44 apply (zenon_or_s _ _ zenon_H1a4); [ zenon_intro zenon_H156 | zenon_intro zenon_H16a ]. % 15.22/15.44 apply (zenon_L447_); trivial. % 15.22/15.44 apply (zenon_L561_); trivial. % 15.22/15.44 apply (zenon_or_s _ _ zenon_H8e); [ zenon_intro zenon_H92 | zenon_intro zenon_H91 ]. % 15.22/15.44 exact (zenon_H8f zenon_H92). % 15.22/15.44 apply (zenon_or_s _ _ zenon_H91); [ zenon_intro zenon_H5d | zenon_intro zenon_H93 ]. % 15.22/15.44 apply (zenon_L227_); trivial. % 15.22/15.44 apply (zenon_or_s _ _ zenon_H93); [ zenon_intro zenon_H63 | zenon_intro zenon_H81 ]. % 15.22/15.44 apply (zenon_L564_); trivial. % 15.22/15.44 apply (zenon_L33_); trivial. % 15.22/15.44 apply (zenon_L102_); trivial. % 15.22/15.44 (* end of lemma zenon_L565_ *) % 15.22/15.44 assert (zenon_L566_ : ((~((op (e3) (e3)) = (e1)))\/((op (e3) (e1)) = (e3))) -> (~((op (e3) (e1)) = (op (e3) (e3)))) -> (~((op (e0) (e0)) = (e1))) -> (((op (e0) (e3)) = (e1))\/(((op (e1) (e3)) = (e1))\/(((op (e2) (e3)) = (e1))\/((op (e3) (e3)) = (e1))))) -> (~((e1) = (e2))) -> (~((op (e1) (e0)) = (op (e1) (e3)))) -> (~((op (e0) (e1)) = (op (e0) (e3)))) -> (((op (e0) (e0)) = (e2))\/(((op (e0) (e1)) = (e2))\/(((op (e0) (e2)) = (e2))\/((op (e0) (e3)) = (e2))))) -> (((op (e3) (e0)) = (e1))\/(((op (e3) (e1)) = (e1))\/(((op (e3) (e2)) = (e1))\/((op (e3) (e3)) = (e1))))) -> (~((op (e0) (e2)) = (op (e3) (e2)))) -> (~((op (e2) (e0)) = (op (e2) (e1)))) -> (((op (e0) (e1)) = (e2))\/(((op (e1) (e1)) = (e2))\/(((op (e2) (e1)) = (e2))\/((op (e3) (e1)) = (e2))))) -> (~((op (e1) (e0)) = (op (e3) (e0)))) -> ((~((op (e2) (e2)) = (e3)))\/((op (e2) (e3)) = (e2))) -> (~((op (e2) (e1)) = (op (e2) (e3)))) -> (~((op (e2) (e1)) = (op (e2) (e2)))) -> ((~((op (e2) (e2)) = (e2)))\/((op (e2) (e2)) = (e2))) -> (((op (e0) (e0)) = (e2))\/(((op (e1) (e0)) = (e2))\/(((op (e2) (e0)) = (e2))\/((op (e3) (e0)) = (e2))))) -> (~((e2) = (e3))) -> (((op (e1) (e0)) = (e3))\/(((op (e1) (e1)) = (e3))\/(((op (e1) (e2)) = (e3))\/((op (e1) (e3)) = (e3))))) -> (~((op (e1) (e3)) = (op (e3) (e3)))) -> (~((op (e0) (e2)) = (op (e1) (e2)))) -> (~((op (e0) (e3)) = (op (e3) (e3)))) -> (((op (e0) (e0)) = (e3))\/(((op (e0) (e1)) = (e3))\/(((op (e0) (e2)) = (e3))\/((op (e0) (e3)) = (e3))))) -> (~((op (e0) (e0)) = (e2))) -> (((op (e0) (e3)) = (e0))\/(((op (e1) (e3)) = (e0))\/(((op (e2) (e3)) = (e0))\/((op (e3) (e3)) = (e0))))) -> (~((e0) = (e2))) -> ((op (e0) (e0)) = (e0)) -> (~((op (e0) (e0)) = (op (e0) (e3)))) -> (((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 (e3) (e3)) = (e0)))\/((op (e3) (e0)) = (e3))) -> (~((op (e0) (e0)) = (e3))) -> (~((e1) = (e3))) -> ((op (e1) (e0)) = (e1)) -> (((op (e1) (e1)) = (e0))\/(((op (e1) (e1)) = (e1))\/(((op (e1) (e1)) = (e2))\/((op (e1) (e1)) = (e3))))) -> (~((op (e1) (e1)) = (e3))) -> (~((op (e1) (e1)) = (e2))) -> (~((op (e1) (e1)) = (e1))) -> (~((op (e2) (e2)) = (e0))) -> (~((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 (e3) (e3)) = (e3)) -> (((op (e0) (e0)) = (e3))\/(((op (e1) (e0)) = (e3))\/(((op (e2) (e0)) = (e3))\/((op (e3) (e0)) = (e3))))) -> False). % 15.22/15.44 do 0 intro. intros zenon_H10c zenon_H12d zenon_H45 zenon_H121 zenon_Ha7 zenon_H1cf zenon_H1cd zenon_H8e zenon_H146 zenon_H140 zenon_H154 zenon_H1a2 zenon_H22e zenon_H1c3 zenon_H1e2 zenon_H157 zenon_Haa zenon_Heb zenon_H6a zenon_H90 zenon_H8b zenon_H87 zenon_H36 zenon_H58 zenon_H8f zenon_Hd3 zenon_H5e zenon_H1f zenon_H24f zenon_H84 zenon_H44 zenon_H10f zenon_H59 zenon_Ha3 zenon_Hd8 zenon_H1b3 zenon_H182 zenon_Hd6 zenon_H1b4 zenon_H2e zenon_H2f zenon_H2d zenon_Hbb zenon_H42 zenon_Hbe. % 15.22/15.44 apply (zenon_or_s _ _ zenon_H1c3); [ zenon_intro zenon_H30 | zenon_intro zenon_H124 ]. % 15.22/15.44 apply (zenon_L241_); trivial. % 15.22/15.44 apply (zenon_or_s _ _ zenon_H10f); [ zenon_intro zenon_H3c | zenon_intro zenon_Hba ]. % 15.22/15.44 apply (zenon_L565_); trivial. % 15.22/15.44 apply (zenon_L43_); trivial. % 15.22/15.44 (* end of lemma zenon_L566_ *) % 15.22/15.44 assert (zenon_L567_ : (~((op (e0) (e0)) = (op (e0) (e2)))) -> ((op (e0) (e0)) = (e0)) -> ((op (e0) (e2)) = (e0)) -> False). % 15.22/15.44 do 0 intro. intros zenon_H250 zenon_H1f zenon_Hab. % 15.22/15.44 cut (((op (e0) (e0)) = (e0)) = ((op (e0) (e0)) = (op (e0) (e2)))). % 15.22/15.44 intro zenon_D_pnotp. % 15.22/15.44 apply zenon_H250. % 15.22/15.44 rewrite <- zenon_D_pnotp. % 15.22/15.44 exact zenon_H1f. % 15.22/15.44 cut (((e0) = (op (e0) (e2)))); [idtac | apply NNPP; zenon_intro zenon_H20d]. % 15.22/15.44 cut (((op (e0) (e0)) = (op (e0) (e0)))); [idtac | apply NNPP; zenon_intro zenon_H24e]. % 15.22/15.44 congruence. % 15.22/15.44 apply zenon_H24e. apply refl_equal. % 15.22/15.44 apply zenon_H20d. apply sym_equal. exact zenon_Hab. % 15.22/15.44 (* end of lemma zenon_L567_ *) % 15.22/15.44 assert (zenon_L568_ : (((op (e0) (e2)) = (e0))\/(((op (e0) (e2)) = (e1))\/(((op (e0) (e2)) = (e2))\/((op (e0) (e2)) = (e3))))) -> ((op (e0) (e0)) = (e0)) -> (~((op (e0) (e0)) = (op (e0) (e2)))) -> ((op (e3) (e2)) = (e1)) -> (~((op (e0) (e2)) = (op (e3) (e2)))) -> (~((op (e0) (e2)) = (op (e2) (e2)))) -> ((op (e2) (e2)) = (e2)) -> (~((op (e0) (e2)) = (op (e1) (e2)))) -> ((op (e1) (e2)) = (e3)) -> False). % 15.22/15.44 do 0 intro. intros zenon_H251 zenon_H1f zenon_H250 zenon_H119 zenon_H140 zenon_H28 zenon_H35 zenon_H87 zenon_H88. % 15.22/15.44 apply (zenon_or_s _ _ zenon_H251); [ zenon_intro zenon_Hab | zenon_intro zenon_H252 ]. % 15.22/15.44 apply (zenon_L567_); trivial. % 15.22/15.44 apply (zenon_or_s _ _ zenon_H252); [ zenon_intro zenon_H29 | zenon_intro zenon_H253 ]. % 15.22/15.44 apply (zenon_L124_); trivial. % 15.22/15.44 apply (zenon_or_s _ _ zenon_H253); [ zenon_intro zenon_H63 | zenon_intro zenon_H50 ]. % 15.22/15.44 apply (zenon_L15_); trivial. % 15.22/15.44 apply (zenon_L24_); trivial. % 15.22/15.44 (* end of lemma zenon_L568_ *) % 15.22/15.44 assert (zenon_L569_ : (((op (e0) (e2)) = (e1))\/(((op (e1) (e2)) = (e1))\/(((op (e2) (e2)) = (e1))\/((op (e3) (e2)) = (e1))))) -> (~((op (e0) (e2)) = (op (e0) (e3)))) -> ((op (e0) (e3)) = (e1)) -> (~((e1) = (e3))) -> (~((op (e2) (e2)) = (e1))) -> (((op (e0) (e2)) = (e0))\/(((op (e0) (e2)) = (e1))\/(((op (e0) (e2)) = (e2))\/((op (e0) (e2)) = (e3))))) -> ((op (e0) (e0)) = (e0)) -> (~((op (e0) (e0)) = (op (e0) (e2)))) -> (~((op (e0) (e2)) = (op (e3) (e2)))) -> (~((op (e0) (e2)) = (op (e2) (e2)))) -> ((op (e2) (e2)) = (e2)) -> (~((op (e0) (e2)) = (op (e1) (e2)))) -> ((op (e1) (e2)) = (e3)) -> False). % 15.22/15.45 do 0 intro. intros zenon_H11b zenon_Hc9 zenon_H37 zenon_Ha3 zenon_H52 zenon_H251 zenon_H1f zenon_H250 zenon_H140 zenon_H28 zenon_H35 zenon_H87 zenon_H88. % 15.22/15.45 apply (zenon_or_s _ _ zenon_H11b); [ zenon_intro zenon_H29 | zenon_intro zenon_H11c ]. % 15.22/15.45 apply (zenon_L85_); trivial. % 15.22/15.45 apply (zenon_or_s _ _ zenon_H11c); [ zenon_intro zenon_H117 | zenon_intro zenon_H11d ]. % 15.22/15.45 apply (zenon_L196_); trivial. % 15.22/15.45 apply (zenon_or_s _ _ zenon_H11d); [ zenon_intro zenon_H2a | zenon_intro zenon_H119 ]. % 15.22/15.45 exact (zenon_H52 zenon_H2a). % 15.22/15.45 apply (zenon_L568_); trivial. % 15.22/15.45 (* end of lemma zenon_L569_ *) % 15.22/15.45 assert (zenon_L570_ : (((op (e1) (e0)) = (e3))\/(((op (e1) (e1)) = (e3))\/(((op (e1) (e2)) = (e3))\/((op (e1) (e3)) = (e3))))) -> ((op (e1) (e0)) = (e1)) -> (~((op (e1) (e1)) = (e3))) -> (~((op (e0) (e2)) = (op (e1) (e2)))) -> ((op (e2) (e2)) = (e2)) -> (~((op (e0) (e2)) = (op (e2) (e2)))) -> (~((op (e0) (e2)) = (op (e3) (e2)))) -> (~((op (e0) (e0)) = (op (e0) (e2)))) -> ((op (e0) (e0)) = (e0)) -> (((op (e0) (e2)) = (e0))\/(((op (e0) (e2)) = (e1))\/(((op (e0) (e2)) = (e2))\/((op (e0) (e2)) = (e3))))) -> (~((op (e2) (e2)) = (e1))) -> (~((e1) = (e3))) -> ((op (e0) (e3)) = (e1)) -> (~((op (e0) (e2)) = (op (e0) (e3)))) -> (((op (e0) (e2)) = (e1))\/(((op (e1) (e2)) = (e1))\/(((op (e2) (e2)) = (e1))\/((op (e3) (e2)) = (e1))))) -> ((op (e3) (e3)) = (e3)) -> (~((op (e1) (e3)) = (op (e3) (e3)))) -> False). % 15.22/15.45 do 0 intro. intros zenon_H90 zenon_Hd8 zenon_H182 zenon_H87 zenon_H35 zenon_H28 zenon_H140 zenon_H250 zenon_H1f zenon_H251 zenon_H52 zenon_Ha3 zenon_H37 zenon_Hc9 zenon_H11b zenon_H42 zenon_H8b. % 15.22/15.45 apply (zenon_or_s _ _ zenon_H90); [ zenon_intro zenon_H69 | zenon_intro zenon_H94 ]. % 15.22/15.45 apply (zenon_L163_); trivial. % 15.22/15.45 apply (zenon_or_s _ _ zenon_H94); [ zenon_intro zenon_H96 | zenon_intro zenon_H95 ]. % 15.22/15.45 exact (zenon_H182 zenon_H96). % 15.22/15.45 apply (zenon_or_s _ _ zenon_H95); [ zenon_intro zenon_H88 | zenon_intro zenon_H8a ]. % 15.22/15.45 apply (zenon_L569_); trivial. % 15.22/15.45 apply (zenon_L25_); trivial. % 15.22/15.45 (* end of lemma zenon_L570_ *) % 15.22/15.45 assert (zenon_L571_ : (((op (e0) (e3)) = (e0))\/(((op (e0) (e3)) = (e1))\/(((op (e0) (e3)) = (e2))\/((op (e0) (e3)) = (e3))))) -> ((op (e0) (e0)) = (e0)) -> (~((op (e0) (e0)) = (op (e0) (e3)))) -> ((op (e2) (e3)) = (e1)) -> (~((op (e0) (e3)) = (op (e2) (e3)))) -> ((op (e1) (e3)) = (e2)) -> (~((op (e0) (e3)) = (op (e1) (e3)))) -> ((op (e3) (e3)) = (e3)) -> (~((op (e0) (e3)) = (op (e3) (e3)))) -> False). % 15.22/15.45 do 0 intro. intros zenon_H254 zenon_H1f zenon_H24f zenon_Hb5 zenon_Hb4 zenon_H82 zenon_H80 zenon_H42 zenon_H36. % 15.22/15.45 apply (zenon_or_s _ _ zenon_H254); [ zenon_intro zenon_Hca | zenon_intro zenon_H255 ]. % 15.22/15.45 apply (zenon_L562_); trivial. % 15.22/15.45 apply (zenon_or_s _ _ zenon_H255); [ zenon_intro zenon_H37 | zenon_intro zenon_H256 ]. % 15.22/15.45 apply (zenon_L41_); trivial. % 15.22/15.45 apply (zenon_or_s _ _ zenon_H256); [ zenon_intro zenon_H81 | zenon_intro zenon_H53 ]. % 15.22/15.45 apply (zenon_L22_); trivial. % 15.22/15.45 apply (zenon_L12_); trivial. % 15.22/15.45 (* end of lemma zenon_L571_ *) % 15.22/15.45 assert (zenon_L572_ : (((op (e0) (e0)) = (e3))\/(((op (e0) (e1)) = (e3))\/(((op (e0) (e2)) = (e3))\/((op (e0) (e3)) = (e3))))) -> (~((op (e0) (e0)) = (e3))) -> (~((op (e0) (e1)) = (op (e3) (e1)))) -> ((op (e3) (e1)) = (e3)) -> (~((op (e1) (e3)) = (op (e3) (e3)))) -> (~((op (e0) (e2)) = (op (e1) (e2)))) -> (~((op (e1) (e1)) = (e3))) -> ((op (e1) (e0)) = (e1)) -> (~((e1) = (e3))) -> (((op (e1) (e0)) = (e3))\/(((op (e1) (e1)) = (e3))\/(((op (e1) (e2)) = (e3))\/((op (e1) (e3)) = (e3))))) -> ((op (e3) (e3)) = (e3)) -> (~((op (e0) (e3)) = (op (e3) (e3)))) -> False). % 15.22/15.45 do 0 intro. intros zenon_H58 zenon_H59 zenon_H138 zenon_H10a zenon_H8b zenon_H87 zenon_H182 zenon_Hd8 zenon_Ha3 zenon_H90 zenon_H42 zenon_H36. % 15.22/15.45 apply (zenon_or_s _ _ zenon_H58); [ zenon_intro zenon_H5b | zenon_intro zenon_H5a ]. % 15.22/15.45 exact (zenon_H59 zenon_H5b). % 15.22/15.45 apply (zenon_or_s _ _ zenon_H5a); [ zenon_intro zenon_H4a | zenon_intro zenon_H5c ]. % 15.22/15.45 apply (zenon_L120_); trivial. % 15.22/15.45 apply (zenon_or_s _ _ zenon_H5c); [ zenon_intro zenon_H50 | zenon_intro zenon_H53 ]. % 15.22/15.45 apply (zenon_L226_); trivial. % 15.22/15.45 apply (zenon_L12_); trivial. % 15.22/15.45 (* end of lemma zenon_L572_ *) % 15.22/15.45 assert (zenon_L573_ : ((~((op (e3) (e3)) = (e1)))\/((op (e3) (e1)) = (e3))) -> (~((op (e0) (e0)) = (e3))) -> (~((op (e0) (e1)) = (op (e3) (e1)))) -> (((op (e0) (e0)) = (e3))\/(((op (e0) (e1)) = (e3))\/(((op (e0) (e2)) = (e3))\/((op (e0) (e3)) = (e3))))) -> (~((e1) = (e2))) -> ((op (e1) (e0)) = (e1)) -> (~((op (e1) (e1)) = (e2))) -> (~((op (e1) (e2)) = (op (e2) (e2)))) -> ((op (e2) (e2)) = (e2)) -> (((op (e0) (e3)) = (e1))\/(((op (e1) (e3)) = (e1))\/(((op (e2) (e3)) = (e1))\/((op (e3) (e3)) = (e1))))) -> (~((op (e0) (e0)) = (op (e0) (e3)))) -> (~((op (e0) (e3)) = (op (e2) (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 (e1) (e0)) = (op (e1) (e3)))) -> (~((e1) = (e3))) -> (~((op (e1) (e1)) = (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)) = (e0)) -> (~((op (e0) (e2)) = (op (e3) (e2)))) -> (~((op (e0) (e2)) = (op (e2) (e2)))) -> (~((op (e0) (e2)) = (op (e1) (e2)))) -> (((op (e0) (e2)) = (e0))\/(((op (e0) (e2)) = (e1))\/(((op (e0) (e2)) = (e2))\/((op (e0) (e2)) = (e3))))) -> (~((op (e2) (e2)) = (e1))) -> (~((op (e0) (e2)) = (op (e0) (e3)))) -> (~((op (e1) (e3)) = (op (e3) (e3)))) -> ((op (e3) (e3)) = (e3)) -> (((op (e1) (e0)) = (e3))\/(((op (e1) (e1)) = (e3))\/(((op (e1) (e2)) = (e3))\/((op (e1) (e3)) = (e3))))) -> (((op (e1) (e0)) = (e2))\/(((op (e1) (e1)) = (e2))\/(((op (e1) (e2)) = (e2))\/((op (e1) (e3)) = (e2))))) -> False). % 15.22/15.45 do 0 intro. intros zenon_H10c zenon_H59 zenon_H138 zenon_H58 zenon_Ha7 zenon_Hd8 zenon_Hd6 zenon_H7d zenon_H35 zenon_H121 zenon_H24f zenon_Hb4 zenon_H80 zenon_H36 zenon_H254 zenon_H1cf zenon_Ha3 zenon_H182 zenon_H11b zenon_H250 zenon_H1f zenon_H140 zenon_H28 zenon_H87 zenon_H251 zenon_H52 zenon_Hc9 zenon_H8b zenon_H42 zenon_H90 zenon_H84. % 15.22/15.45 apply (zenon_or_s _ _ zenon_H10c); [ zenon_intro zenon_H104 | zenon_intro zenon_H10a ]. % 15.22/15.45 apply (zenon_or_s _ _ zenon_H84); [ zenon_intro zenon_H68 | zenon_intro zenon_H85 ]. % 15.22/15.45 apply (zenon_L162_); trivial. % 15.22/15.45 apply (zenon_or_s _ _ zenon_H85); [ zenon_intro zenon_H6e | zenon_intro zenon_H86 ]. % 15.22/15.45 exact (zenon_Hd6 zenon_H6e). % 15.22/15.45 apply (zenon_or_s _ _ zenon_H86); [ zenon_intro zenon_H7c | zenon_intro zenon_H82 ]. % 15.22/15.45 apply (zenon_L21_); trivial. % 15.22/15.45 apply (zenon_or_s _ _ zenon_H121); [ zenon_intro zenon_H37 | zenon_intro zenon_H122 ]. % 15.22/15.45 apply (zenon_L570_); trivial. % 15.22/15.45 apply (zenon_or_s _ _ zenon_H122); [ zenon_intro zenon_H11f | zenon_intro zenon_H123 ]. % 15.22/15.45 apply (zenon_L224_); trivial. % 15.22/15.45 apply (zenon_or_s _ _ zenon_H123); [ zenon_intro zenon_Hb5 | zenon_intro zenon_H38 ]. % 15.22/15.45 apply (zenon_L571_); trivial. % 15.22/15.45 exact (zenon_H104 zenon_H38). % 15.22/15.45 apply (zenon_L572_); trivial. % 15.22/15.45 (* end of lemma zenon_L573_ *) % 15.22/15.45 assert (zenon_L574_ : (~((op (e0) (e2)) = (op (e0) (e3)))) -> (~((op (e2) (e2)) = (e1))) -> (((op (e0) (e2)) = (e0))\/(((op (e0) (e2)) = (e1))\/(((op (e0) (e2)) = (e2))\/((op (e0) (e2)) = (e3))))) -> (~((op (e0) (e2)) = (op (e2) (e2)))) -> (~((op (e0) (e0)) = (op (e0) (e2)))) -> (((op (e0) (e2)) = (e1))\/(((op (e1) (e2)) = (e1))\/(((op (e2) (e2)) = (e1))\/((op (e3) (e2)) = (e1))))) -> (((op (e0) (e3)) = (e0))\/(((op (e0) (e3)) = (e1))\/(((op (e0) (e3)) = (e2))\/((op (e0) (e3)) = (e3))))) -> (~((op (e0) (e3)) = (op (e1) (e3)))) -> (~((op (e0) (e3)) = (op (e2) (e3)))) -> (~((op (e1) (e2)) = (op (e2) (e2)))) -> (~((op (e0) (e1)) = (op (e3) (e1)))) -> (((op (e0) (e0)) = (e3))\/(((op (e1) (e0)) = (e3))\/(((op (e2) (e0)) = (e3))\/((op (e3) (e0)) = (e3))))) -> ((op (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)) = (e0))) -> (~((op (e1) (e1)) = (e1))) -> (~((op (e1) (e1)) = (e2))) -> (~((op (e1) (e1)) = (e3))) -> (((op (e1) (e1)) = (e0))\/(((op (e1) (e1)) = (e1))\/(((op (e1) (e1)) = (e2))\/((op (e1) (e1)) = (e3))))) -> ((op (e1) (e0)) = (e1)) -> (~((e1) = (e3))) -> (~((op (e0) (e0)) = (e3))) -> ((~((op (e3) (e3)) = (e0)))\/((op (e3) (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) (e0)) = (op (e0) (e3)))) -> ((op (e0) (e0)) = (e0)) -> (~((e0) = (e2))) -> (((op (e0) (e3)) = (e0))\/(((op (e1) (e3)) = (e0))\/(((op (e2) (e3)) = (e0))\/((op (e3) (e3)) = (e0))))) -> (~((op (e0) (e0)) = (e2))) -> (((op (e0) (e0)) = (e3))\/(((op (e0) (e1)) = (e3))\/(((op (e0) (e2)) = (e3))\/((op (e0) (e3)) = (e3))))) -> (~((op (e0) (e3)) = (op (e3) (e3)))) -> (~((op (e0) (e2)) = (op (e1) (e2)))) -> (~((op (e1) (e3)) = (op (e3) (e3)))) -> (((op (e1) (e0)) = (e3))\/(((op (e1) (e1)) = (e3))\/(((op (e1) (e2)) = (e3))\/((op (e1) (e3)) = (e3))))) -> (~((e2) = (e3))) -> (((op (e0) (e0)) = (e2))\/(((op (e1) (e0)) = (e2))\/(((op (e2) (e0)) = (e2))\/((op (e3) (e0)) = (e2))))) -> ((~((op (e2) (e2)) = (e2)))\/((op (e2) (e2)) = (e2))) -> (~((op (e2) (e1)) = (op (e2) (e2)))) -> (~((op (e2) (e1)) = (op (e2) (e3)))) -> ((~((op (e2) (e2)) = (e3)))\/((op (e2) (e3)) = (e2))) -> (~((op (e1) (e0)) = (op (e3) (e0)))) -> (((op (e0) (e1)) = (e2))\/(((op (e1) (e1)) = (e2))\/(((op (e2) (e1)) = (e2))\/((op (e3) (e1)) = (e2))))) -> (~((op (e2) (e0)) = (op (e2) (e1)))) -> (~((op (e0) (e2)) = (op (e3) (e2)))) -> (((op (e3) (e0)) = (e1))\/(((op (e3) (e1)) = (e1))\/(((op (e3) (e2)) = (e1))\/((op (e3) (e3)) = (e1))))) -> (((op (e0) (e0)) = (e2))\/(((op (e0) (e1)) = (e2))\/(((op (e0) (e2)) = (e2))\/((op (e0) (e3)) = (e2))))) -> (~((op (e0) (e1)) = (op (e0) (e3)))) -> (~((op (e1) (e0)) = (op (e1) (e3)))) -> (~((e1) = (e2))) -> (((op (e0) (e3)) = (e1))\/(((op (e1) (e3)) = (e1))\/(((op (e2) (e3)) = (e1))\/((op (e3) (e3)) = (e1))))) -> (~((op (e0) (e0)) = (e1))) -> (~((op (e3) (e1)) = (op (e3) (e3)))) -> ((~((op (e3) (e3)) = (e1)))\/((op (e3) (e1)) = (e3))) -> False). % 15.22/15.45 do 0 intro. intros zenon_Hc9 zenon_H52 zenon_H251 zenon_H28 zenon_H250 zenon_H11b zenon_H254 zenon_H80 zenon_Hb4 zenon_H7d zenon_H138 zenon_Hbe zenon_H42 zenon_Hbb zenon_H2d zenon_H2e zenon_H1b4 zenon_Hd6 zenon_H182 zenon_H1b3 zenon_Hd8 zenon_Ha3 zenon_H59 zenon_H10f zenon_H44 zenon_H84 zenon_H24f zenon_H1f zenon_H5e zenon_Hd3 zenon_H8f zenon_H58 zenon_H36 zenon_H87 zenon_H8b zenon_H90 zenon_H6a zenon_Heb zenon_Haa zenon_H157 zenon_H1e2 zenon_H1c3 zenon_H22e zenon_H1a2 zenon_H154 zenon_H140 zenon_H146 zenon_H8e zenon_H1cd zenon_H1cf zenon_Ha7 zenon_H121 zenon_H45 zenon_H12d zenon_H10c. % 15.22/15.45 apply (zenon_or_s _ _ zenon_Haa); [ zenon_intro zenon_H2f | zenon_intro zenon_H35 ]. % 15.22/15.45 apply (zenon_L566_); trivial. % 15.22/15.45 apply (zenon_L573_); trivial. % 15.22/15.45 (* end of lemma zenon_L574_ *) % 15.22/15.45 assert (zenon_L575_ : ((~((op (e2) (e2)) = (e0)))\/((op (e2) (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 (e0) (e2)) = (op (e2) (e2)))) -> (~((op (e0) (e0)) = (op (e0) (e2)))) -> (((op (e0) (e2)) = (e1))\/(((op (e1) (e2)) = (e1))\/(((op (e2) (e2)) = (e1))\/((op (e3) (e2)) = (e1))))) -> (((op (e0) (e3)) = (e0))\/(((op (e0) (e3)) = (e1))\/(((op (e0) (e3)) = (e2))\/((op (e0) (e3)) = (e3))))) -> (~((op (e0) (e3)) = (op (e1) (e3)))) -> (~((op (e0) (e3)) = (op (e2) (e3)))) -> (~((op (e1) (e2)) = (op (e2) (e2)))) -> (~((op (e0) (e1)) = (op (e3) (e1)))) -> (((op (e0) (e0)) = (e3))\/(((op (e1) (e0)) = (e3))\/(((op (e2) (e0)) = (e3))\/((op (e3) (e0)) = (e3))))) -> ((op (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 (e1) (e1)) = (e1))) -> (~((op (e1) (e1)) = (e2))) -> (~((op (e1) (e1)) = (e3))) -> (((op (e1) (e1)) = (e0))\/(((op (e1) (e1)) = (e1))\/(((op (e1) (e1)) = (e2))\/((op (e1) (e1)) = (e3))))) -> ((op (e1) (e0)) = (e1)) -> (~((e1) = (e3))) -> (~((op (e0) (e0)) = (e3))) -> ((~((op (e3) (e3)) = (e0)))\/((op (e3) (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) (e0)) = (op (e0) (e3)))) -> ((op (e0) (e0)) = (e0)) -> (~((e0) = (e2))) -> (((op (e0) (e3)) = (e0))\/(((op (e1) (e3)) = (e0))\/(((op (e2) (e3)) = (e0))\/((op (e3) (e3)) = (e0))))) -> (~((op (e0) (e0)) = (e2))) -> (((op (e0) (e0)) = (e3))\/(((op (e0) (e1)) = (e3))\/(((op (e0) (e2)) = (e3))\/((op (e0) (e3)) = (e3))))) -> (~((op (e0) (e3)) = (op (e3) (e3)))) -> (~((op (e0) (e2)) = (op (e1) (e2)))) -> (~((op (e1) (e3)) = (op (e3) (e3)))) -> (((op (e1) (e0)) = (e3))\/(((op (e1) (e1)) = (e3))\/(((op (e1) (e2)) = (e3))\/((op (e1) (e3)) = (e3))))) -> (~((e2) = (e3))) -> (((op (e0) (e0)) = (e2))\/(((op (e1) (e0)) = (e2))\/(((op (e2) (e0)) = (e2))\/((op (e3) (e0)) = (e2))))) -> ((~((op (e2) (e2)) = (e2)))\/((op (e2) (e2)) = (e2))) -> (~((op (e2) (e1)) = (op (e2) (e2)))) -> (~((op (e2) (e1)) = (op (e2) (e3)))) -> ((~((op (e2) (e2)) = (e3)))\/((op (e2) (e3)) = (e2))) -> (~((op (e1) (e0)) = (op (e3) (e0)))) -> (((op (e0) (e1)) = (e2))\/(((op (e1) (e1)) = (e2))\/(((op (e2) (e1)) = (e2))\/((op (e3) (e1)) = (e2))))) -> (~((op (e2) (e0)) = (op (e2) (e1)))) -> (~((op (e0) (e2)) = (op (e3) (e2)))) -> (((op (e3) (e0)) = (e1))\/(((op (e3) (e1)) = (e1))\/(((op (e3) (e2)) = (e1))\/((op (e3) (e3)) = (e1))))) -> (((op (e0) (e0)) = (e2))\/(((op (e0) (e1)) = (e2))\/(((op (e0) (e2)) = (e2))\/((op (e0) (e3)) = (e2))))) -> (~((op (e0) (e1)) = (op (e0) (e3)))) -> (~((op (e1) (e0)) = (op (e1) (e3)))) -> (~((e1) = (e2))) -> (((op (e0) (e3)) = (e1))\/(((op (e1) (e3)) = (e1))\/(((op (e2) (e3)) = (e1))\/((op (e3) (e3)) = (e1))))) -> (~((op (e0) (e0)) = (e1))) -> (~((op (e3) (e1)) = (op (e3) (e3)))) -> ((~((op (e3) (e3)) = (e1)))\/((op (e3) (e1)) = (e3))) -> ((~((op (e2) (e2)) = (e1)))\/((op (e2) (e1)) = (e2))) -> False). % 15.22/15.45 do 0 intro. intros zenon_H1d4 zenon_Hc9 zenon_H251 zenon_H28 zenon_H250 zenon_H11b zenon_H254 zenon_H80 zenon_Hb4 zenon_H7d zenon_H138 zenon_Hbe zenon_H42 zenon_Hbb zenon_H2d zenon_H1b4 zenon_Hd6 zenon_H182 zenon_H1b3 zenon_Hd8 zenon_Ha3 zenon_H59 zenon_H10f zenon_H44 zenon_H84 zenon_H24f zenon_H1f zenon_H5e zenon_Hd3 zenon_H8f zenon_H58 zenon_H36 zenon_H87 zenon_H8b zenon_H90 zenon_H6a zenon_Heb zenon_Haa zenon_H157 zenon_H1e2 zenon_H1c3 zenon_H22e zenon_H1a2 zenon_H154 zenon_H140 zenon_H146 zenon_H8e zenon_H1cd zenon_H1cf zenon_Ha7 zenon_H121 zenon_H45 zenon_H12d zenon_H10c zenon_H1e3. % 15.22/15.45 apply (zenon_or_s _ _ zenon_H1d4); [ zenon_intro zenon_H2e | zenon_intro zenon_Hdd ]. % 15.22/15.45 apply (zenon_or_s _ _ zenon_H1e3); [ zenon_intro zenon_H52 | zenon_intro zenon_H156 ]. % 15.22/15.45 apply (zenon_L574_); trivial. % 15.22/15.45 apply (zenon_L447_); trivial. % 15.22/15.45 apply (zenon_L246_); trivial. % 15.22/15.45 (* end of lemma zenon_L575_ *) % 15.22/15.45 assert (zenon_L576_ : ((~((op (e1) (e1)) = (e3)))\/((op (e1) (e3)) = (e1))) -> ((~((op (e2) (e2)) = (e1)))\/((op (e2) (e1)) = (e2))) -> ((~((op (e3) (e3)) = (e1)))\/((op (e3) (e1)) = (e3))) -> (~((op (e3) (e1)) = (op (e3) (e3)))) -> (~((op (e0) (e0)) = (e1))) -> (((op (e0) (e3)) = (e1))\/(((op (e1) (e3)) = (e1))\/(((op (e2) (e3)) = (e1))\/((op (e3) (e3)) = (e1))))) -> (~((e1) = (e2))) -> (~((op (e1) (e0)) = (op (e1) (e3)))) -> (~((op (e0) (e1)) = (op (e0) (e3)))) -> (((op (e0) (e0)) = (e2))\/(((op (e0) (e1)) = (e2))\/(((op (e0) (e2)) = (e2))\/((op (e0) (e3)) = (e2))))) -> (((op (e3) (e0)) = (e1))\/(((op (e3) (e1)) = (e1))\/(((op (e3) (e2)) = (e1))\/((op (e3) (e3)) = (e1))))) -> (~((op (e0) (e2)) = (op (e3) (e2)))) -> (~((op (e2) (e0)) = (op (e2) (e1)))) -> (((op (e0) (e1)) = (e2))\/(((op (e1) (e1)) = (e2))\/(((op (e2) (e1)) = (e2))\/((op (e3) (e1)) = (e2))))) -> (~((op (e1) (e0)) = (op (e3) (e0)))) -> ((~((op (e2) (e2)) = (e3)))\/((op (e2) (e3)) = (e2))) -> (~((op (e2) (e1)) = (op (e2) (e3)))) -> (~((op (e2) (e1)) = (op (e2) (e2)))) -> ((~((op (e2) (e2)) = (e2)))\/((op (e2) (e2)) = (e2))) -> (((op (e0) (e0)) = (e2))\/(((op (e1) (e0)) = (e2))\/(((op (e2) (e0)) = (e2))\/((op (e3) (e0)) = (e2))))) -> (~((e2) = (e3))) -> (((op (e1) (e0)) = (e3))\/(((op (e1) (e1)) = (e3))\/(((op (e1) (e2)) = (e3))\/((op (e1) (e3)) = (e3))))) -> (~((op (e1) (e3)) = (op (e3) (e3)))) -> (~((op (e0) (e2)) = (op (e1) (e2)))) -> (~((op (e0) (e3)) = (op (e3) (e3)))) -> (((op (e0) (e0)) = (e3))\/(((op (e0) (e1)) = (e3))\/(((op (e0) (e2)) = (e3))\/((op (e0) (e3)) = (e3))))) -> (~((op (e0) (e0)) = (e2))) -> (((op (e0) (e3)) = (e0))\/(((op (e1) (e3)) = (e0))\/(((op (e2) (e3)) = (e0))\/((op (e3) (e3)) = (e0))))) -> (~((e0) = (e2))) -> ((op (e0) (e0)) = (e0)) -> (~((op (e0) (e0)) = (op (e0) (e3)))) -> (((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 (e3) (e3)) = (e0)))\/((op (e3) (e0)) = (e3))) -> (~((op (e0) (e0)) = (e3))) -> (~((e1) = (e3))) -> ((op (e1) (e0)) = (e1)) -> (((op (e1) (e1)) = (e0))\/(((op (e1) (e1)) = (e1))\/(((op (e1) (e1)) = (e2))\/((op (e1) (e1)) = (e3))))) -> (~((op (e1) (e1)) = (e2))) -> (~((op (e1) (e1)) = (e1))) -> (((op (e2) (e2)) = (e0))\/(((op (e2) (e2)) = (e1))\/(((op (e2) (e2)) = (e2))\/((op (e2) (e2)) = (e3))))) -> (~((op (e3) (e0)) = (op (e3) (e3)))) -> ((op (e3) (e3)) = (e3)) -> (((op (e0) (e0)) = (e3))\/(((op (e1) (e0)) = (e3))\/(((op (e2) (e0)) = (e3))\/((op (e3) (e0)) = (e3))))) -> (~((op (e0) (e1)) = (op (e3) (e1)))) -> (~((op (e1) (e2)) = (op (e2) (e2)))) -> (~((op (e0) (e3)) = (op (e2) (e3)))) -> (~((op (e0) (e3)) = (op (e1) (e3)))) -> (((op (e0) (e3)) = (e0))\/(((op (e0) (e3)) = (e1))\/(((op (e0) (e3)) = (e2))\/((op (e0) (e3)) = (e3))))) -> (((op (e0) (e2)) = (e1))\/(((op (e1) (e2)) = (e1))\/(((op (e2) (e2)) = (e1))\/((op (e3) (e2)) = (e1))))) -> (~((op (e0) (e0)) = (op (e0) (e2)))) -> (~((op (e0) (e2)) = (op (e2) (e2)))) -> (((op (e0) (e2)) = (e0))\/(((op (e0) (e2)) = (e1))\/(((op (e0) (e2)) = (e2))\/((op (e0) (e2)) = (e3))))) -> (~((op (e0) (e2)) = (op (e0) (e3)))) -> ((~((op (e2) (e2)) = (e0)))\/((op (e2) (e0)) = (e2))) -> False). % 15.22/15.45 do 0 intro. intros zenon_H1d2 zenon_H1e3 zenon_H10c zenon_H12d zenon_H45 zenon_H121 zenon_Ha7 zenon_H1cf zenon_H1cd zenon_H8e zenon_H146 zenon_H140 zenon_H154 zenon_H1a2 zenon_H22e zenon_H1c3 zenon_H1e2 zenon_H157 zenon_Haa zenon_Heb zenon_H6a zenon_H90 zenon_H8b zenon_H87 zenon_H36 zenon_H58 zenon_H8f zenon_Hd3 zenon_H5e zenon_H1f zenon_H24f zenon_H84 zenon_H44 zenon_H10f zenon_H59 zenon_Ha3 zenon_Hd8 zenon_H1b3 zenon_Hd6 zenon_H1b4 zenon_H2d zenon_Hbb zenon_H42 zenon_Hbe zenon_H138 zenon_H7d zenon_Hb4 zenon_H80 zenon_H254 zenon_H11b zenon_H250 zenon_H28 zenon_H251 zenon_Hc9 zenon_H1d4. % 15.22/15.45 apply (zenon_or_s _ _ zenon_H1d2); [ zenon_intro zenon_H182 | zenon_intro zenon_H11f ]. % 15.22/15.45 apply (zenon_L575_); trivial. % 15.22/15.45 apply (zenon_L224_); trivial. % 15.22/15.45 (* end of lemma zenon_L576_ *) % 15.22/15.45 assert (zenon_L577_ : ((~((op (e1) (e1)) = (e2)))\/((op (e1) (e2)) = (e1))) -> (~((op (e1) (e0)) = (op (e1) (e2)))) -> ((~((op (e2) (e2)) = (e0)))\/((op (e2) (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 (e0) (e2)) = (op (e2) (e2)))) -> (~((op (e0) (e0)) = (op (e0) (e2)))) -> (((op (e0) (e2)) = (e1))\/(((op (e1) (e2)) = (e1))\/(((op (e2) (e2)) = (e1))\/((op (e3) (e2)) = (e1))))) -> (((op (e0) (e3)) = (e0))\/(((op (e0) (e3)) = (e1))\/(((op (e0) (e3)) = (e2))\/((op (e0) (e3)) = (e3))))) -> (~((op (e0) (e3)) = (op (e1) (e3)))) -> (~((op (e0) (e3)) = (op (e2) (e3)))) -> (~((op (e1) (e2)) = (op (e2) (e2)))) -> (~((op (e0) (e1)) = (op (e3) (e1)))) -> (((op (e0) (e0)) = (e3))\/(((op (e1) (e0)) = (e3))\/(((op (e2) (e0)) = (e3))\/((op (e3) (e0)) = (e3))))) -> ((op (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 (e1) (e1)) = (e1))) -> (((op (e1) (e1)) = (e0))\/(((op (e1) (e1)) = (e1))\/(((op (e1) (e1)) = (e2))\/((op (e1) (e1)) = (e3))))) -> ((op (e1) (e0)) = (e1)) -> (~((e1) = (e3))) -> (~((op (e0) (e0)) = (e3))) -> ((~((op (e3) (e3)) = (e0)))\/((op (e3) (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) (e0)) = (op (e0) (e3)))) -> ((op (e0) (e0)) = (e0)) -> (~((e0) = (e2))) -> (((op (e0) (e3)) = (e0))\/(((op (e1) (e3)) = (e0))\/(((op (e2) (e3)) = (e0))\/((op (e3) (e3)) = (e0))))) -> (~((op (e0) (e0)) = (e2))) -> (((op (e0) (e0)) = (e3))\/(((op (e0) (e1)) = (e3))\/(((op (e0) (e2)) = (e3))\/((op (e0) (e3)) = (e3))))) -> (~((op (e0) (e3)) = (op (e3) (e3)))) -> (~((op (e0) (e2)) = (op (e1) (e2)))) -> (~((op (e1) (e3)) = (op (e3) (e3)))) -> (((op (e1) (e0)) = (e3))\/(((op (e1) (e1)) = (e3))\/(((op (e1) (e2)) = (e3))\/((op (e1) (e3)) = (e3))))) -> (~((e2) = (e3))) -> (((op (e0) (e0)) = (e2))\/(((op (e1) (e0)) = (e2))\/(((op (e2) (e0)) = (e2))\/((op (e3) (e0)) = (e2))))) -> ((~((op (e2) (e2)) = (e2)))\/((op (e2) (e2)) = (e2))) -> (~((op (e2) (e1)) = (op (e2) (e2)))) -> (~((op (e2) (e1)) = (op (e2) (e3)))) -> ((~((op (e2) (e2)) = (e3)))\/((op (e2) (e3)) = (e2))) -> (~((op (e1) (e0)) = (op (e3) (e0)))) -> (((op (e0) (e1)) = (e2))\/(((op (e1) (e1)) = (e2))\/(((op (e2) (e1)) = (e2))\/((op (e3) (e1)) = (e2))))) -> (~((op (e2) (e0)) = (op (e2) (e1)))) -> (~((op (e0) (e2)) = (op (e3) (e2)))) -> (((op (e3) (e0)) = (e1))\/(((op (e3) (e1)) = (e1))\/(((op (e3) (e2)) = (e1))\/((op (e3) (e3)) = (e1))))) -> (((op (e0) (e0)) = (e2))\/(((op (e0) (e1)) = (e2))\/(((op (e0) (e2)) = (e2))\/((op (e0) (e3)) = (e2))))) -> (~((op (e0) (e1)) = (op (e0) (e3)))) -> (~((op (e1) (e0)) = (op (e1) (e3)))) -> (~((e1) = (e2))) -> (((op (e0) (e3)) = (e1))\/(((op (e1) (e3)) = (e1))\/(((op (e2) (e3)) = (e1))\/((op (e3) (e3)) = (e1))))) -> (~((op (e0) (e0)) = (e1))) -> (~((op (e3) (e1)) = (op (e3) (e3)))) -> ((~((op (e3) (e3)) = (e1)))\/((op (e3) (e1)) = (e3))) -> ((~((op (e2) (e2)) = (e1)))\/((op (e2) (e1)) = (e2))) -> ((~((op (e1) (e1)) = (e3)))\/((op (e1) (e3)) = (e1))) -> False). % 15.22/15.45 do 0 intro. intros zenon_H1d3 zenon_H166 zenon_H1d4 zenon_Hc9 zenon_H251 zenon_H28 zenon_H250 zenon_H11b zenon_H254 zenon_H80 zenon_Hb4 zenon_H7d zenon_H138 zenon_Hbe zenon_H42 zenon_Hbb zenon_H2d zenon_H1b4 zenon_H1b3 zenon_Hd8 zenon_Ha3 zenon_H59 zenon_H10f zenon_H44 zenon_H84 zenon_H24f zenon_H1f zenon_H5e zenon_Hd3 zenon_H8f zenon_H58 zenon_H36 zenon_H87 zenon_H8b zenon_H90 zenon_H6a zenon_Heb zenon_Haa zenon_H157 zenon_H1e2 zenon_H1c3 zenon_H22e zenon_H1a2 zenon_H154 zenon_H140 zenon_H146 zenon_H8e zenon_H1cd zenon_H1cf zenon_Ha7 zenon_H121 zenon_H45 zenon_H12d zenon_H10c zenon_H1e3 zenon_H1d2. % 15.22/15.45 apply (zenon_or_s _ _ zenon_H1d3); [ zenon_intro zenon_Hd6 | zenon_intro zenon_H117 ]. % 15.22/15.45 apply (zenon_L576_); trivial. % 15.22/15.45 apply (zenon_L248_); trivial. % 15.22/15.45 (* end of lemma zenon_L577_ *) % 15.22/15.45 assert (zenon_L578_ : (((op (e0) (e0)) = (e3))\/(((op (e0) (e1)) = (e3))\/(((op (e0) (e2)) = (e3))\/((op (e0) (e3)) = (e3))))) -> (~((op (e0) (e0)) = (e3))) -> ((op (e0) (e1)) = (e1)) -> (~((op (e0) (e2)) = (op (e2) (e2)))) -> (~((op (e2) (e2)) = (e2))) -> (~((op (e2) (e2)) = (e1))) -> (~((op (e2) (e2)) = (e0))) -> (((op (e2) (e2)) = (e0))\/(((op (e2) (e2)) = (e1))\/(((op (e2) (e2)) = (e2))\/((op (e2) (e2)) = (e3))))) -> (((op (e0) (e3)) = (e1))\/(((op (e1) (e3)) = (e1))\/(((op (e2) (e3)) = (e1))\/((op (e3) (e3)) = (e1))))) -> (~((e1) = (e3))) -> ((op (e1) (e2)) = (e1)) -> (~((op (e1) (e2)) = (op (e1) (e3)))) -> ((op (e2) (e0)) = (e1)) -> (~((op (e2) (e0)) = (op (e2) (e3)))) -> (~((op (e3) (e3)) = (e1))) -> False). % 15.22/15.45 do 0 intro. intros zenon_H58 zenon_H59 zenon_H22 zenon_H28 zenon_H2f zenon_H52 zenon_H2e zenon_H2d zenon_H121 zenon_Ha3 zenon_H117 zenon_H1d0 zenon_Hae zenon_Hce zenon_H104. % 15.22/15.45 apply (zenon_or_s _ _ zenon_H58); [ zenon_intro zenon_H5b | zenon_intro zenon_H5a ]. % 15.22/15.45 exact (zenon_H59 zenon_H5b). % 15.22/15.45 apply (zenon_or_s _ _ zenon_H5a); [ zenon_intro zenon_H4a | zenon_intro zenon_H5c ]. % 15.22/15.45 apply (zenon_L59_); trivial. % 15.22/15.45 apply (zenon_or_s _ _ zenon_H5c); [ zenon_intro zenon_H50 | zenon_intro zenon_H53 ]. % 15.22/15.45 apply (zenon_L11_); trivial. % 15.22/15.45 apply (zenon_L549_); trivial. % 15.22/15.45 (* end of lemma zenon_L578_ *) % 15.22/15.45 assert (zenon_L579_ : (((op (e0) (e0)) = (e3))\/(((op (e1) (e0)) = (e3))\/(((op (e2) (e0)) = (e3))\/((op (e3) (e0)) = (e3))))) -> (~((op (e0) (e0)) = (e3))) -> (~((e0) = (e2))) -> (~((op (e0) (e2)) = (op (e1) (e2)))) -> ((op (e0) (e2)) = (e2)) -> (((op (e1) (e0)) = (e3))\/(((op (e1) (e1)) = (e3))\/(((op (e1) (e2)) = (e3))\/((op (e1) (e3)) = (e3))))) -> (~((op (e2) (e2)) = (e3))) -> (~((op (e2) (e2)) = (e2))) -> (~((op (e2) (e2)) = (e1))) -> (((op (e2) (e2)) = (e0))\/(((op (e2) (e2)) = (e1))\/(((op (e2) (e2)) = (e2))\/((op (e2) (e2)) = (e3))))) -> (~((op (e1) (e1)) = (e3))) -> ((op (e1) (e2)) = (e1)) -> ((op (e3) (e3)) = (e3)) -> (~((op (e1) (e3)) = (op (e3) (e3)))) -> (((op (e1) (e0)) = (e2))\/(((op (e1) (e1)) = (e2))\/(((op (e1) (e2)) = (e2))\/((op (e1) (e3)) = (e2))))) -> (~((e0) = (e1))) -> (~((op (e1) (e1)) = (e0))) -> (~((op (e0) (e0)) = (op (e1) (e0)))) -> ((op (e0) (e0)) = (e0)) -> (((op (e1) (e0)) = (e0))\/(((op (e1) (e1)) = (e0))\/(((op (e1) (e2)) = (e0))\/((op (e1) (e3)) = (e0))))) -> (~((e2) = (e3))) -> ((op (e2) (e0)) = (e2)) -> (~((e1) = (e3))) -> ((op (e3) (e0)) = (e1)) -> False). % 15.22/15.45 do 0 intro. intros zenon_Hbe zenon_H59 zenon_H5e zenon_H87 zenon_H63 zenon_H90 zenon_H30 zenon_H2f zenon_H52 zenon_H2d zenon_H182 zenon_H117 zenon_H42 zenon_H8b zenon_H84 zenon_H9e zenon_H145 zenon_H24c zenon_H1f zenon_H163 zenon_H6a zenon_Hdd zenon_Ha3 zenon_Hee. % 15.22/15.45 apply (zenon_or_s _ _ zenon_Hbe); [ zenon_intro zenon_H5b | zenon_intro zenon_Hbf ]. % 15.22/15.45 exact (zenon_H59 zenon_H5b). % 15.22/15.45 apply (zenon_or_s _ _ zenon_Hbf); [ zenon_intro zenon_H69 | zenon_intro zenon_Hc0 ]. % 15.22/15.45 apply (zenon_or_s _ _ zenon_H163); [ zenon_intro zenon_Had | zenon_intro zenon_H164 ]. % 15.22/15.45 apply (zenon_L559_); trivial. % 15.22/15.45 apply (zenon_or_s _ _ zenon_H164); [ zenon_intro zenon_H149 | zenon_intro zenon_H165 ]. % 15.22/15.45 exact (zenon_H145 zenon_H149). % 15.22/15.45 apply (zenon_or_s _ _ zenon_H165); [ zenon_intro zenon_H15d | zenon_intro zenon_Hcc ]. % 15.22/15.45 apply (zenon_L496_); trivial. % 15.22/15.45 apply (zenon_or_s _ _ zenon_H84); [ zenon_intro zenon_H68 | zenon_intro zenon_H85 ]. % 15.22/15.45 apply (zenon_L17_); trivial. % 15.22/15.45 apply (zenon_or_s _ _ zenon_H85); [ zenon_intro zenon_H6e | zenon_intro zenon_H86 ]. % 15.22/15.45 apply (zenon_L433_); trivial. % 15.22/15.45 apply (zenon_or_s _ _ zenon_H86); [ zenon_intro zenon_H7c | zenon_intro zenon_H82 ]. % 15.22/15.45 apply (zenon_L52_); trivial. % 15.22/15.45 apply (zenon_L54_); trivial. % 15.22/15.45 apply (zenon_or_s _ _ zenon_Hc0); [ zenon_intro zenon_Haf | zenon_intro zenon_Hba ]. % 15.22/15.45 apply (zenon_L64_); trivial. % 15.22/15.45 apply (zenon_L79_); trivial. % 15.22/15.45 (* end of lemma zenon_L579_ *) % 15.22/15.45 assert (zenon_L580_ : (((op (e0) (e0)) = (e3))\/(((op (e1) (e0)) = (e3))\/(((op (e2) (e0)) = (e3))\/((op (e3) (e0)) = (e3))))) -> (~((op (e0) (e0)) = (e3))) -> ((op (e0) (e3)) = (e2)) -> (~((op (e0) (e3)) = (op (e1) (e3)))) -> ((op (e1) (e2)) = (e1)) -> (~((e1) = (e2))) -> (((op (e2) (e2)) = (e0))\/(((op (e2) (e2)) = (e1))\/(((op (e2) (e2)) = (e2))\/((op (e2) (e2)) = (e3))))) -> (~((op (e2) (e2)) = (e1))) -> (~((op (e2) (e2)) = (e2))) -> (~((op (e2) (e2)) = (e3))) -> (((op (e1) (e0)) = (e2))\/(((op (e1) (e1)) = (e2))\/(((op (e1) (e2)) = (e2))\/((op (e1) (e3)) = (e2))))) -> (~((e2) = (e3))) -> ((op (e2) (e0)) = (e2)) -> (~((e1) = (e3))) -> ((op (e3) (e0)) = (e1)) -> False). % 15.22/15.45 do 0 intro. intros zenon_Hbe zenon_H59 zenon_H81 zenon_H80 zenon_H117 zenon_Ha7 zenon_H2d zenon_H52 zenon_H2f zenon_H30 zenon_H84 zenon_H6a zenon_Hdd zenon_Ha3 zenon_Hee. % 15.22/15.45 apply (zenon_or_s _ _ zenon_Hbe); [ zenon_intro zenon_H5b | zenon_intro zenon_Hbf ]. % 15.22/15.45 exact (zenon_H59 zenon_H5b). % 15.22/15.45 apply (zenon_or_s _ _ zenon_Hbf); [ zenon_intro zenon_H69 | zenon_intro zenon_Hc0 ]. % 15.22/15.45 apply (zenon_L385_); trivial. % 15.22/15.45 apply (zenon_or_s _ _ zenon_Hc0); [ zenon_intro zenon_Haf | zenon_intro zenon_Hba ]. % 15.22/15.45 apply (zenon_L64_); trivial. % 15.22/15.45 apply (zenon_L79_); trivial. % 15.22/15.45 (* end of lemma zenon_L580_ *) % 15.22/15.45 assert (zenon_L581_ : (((op (e0) (e0)) = (e2))\/(((op (e1) (e0)) = (e2))\/(((op (e2) (e0)) = (e2))\/((op (e3) (e0)) = (e2))))) -> (~((op (e0) (e0)) = (e2))) -> (~((op (e1) (e3)) = (op (e3) (e3)))) -> ((op (e3) (e3)) = (e3)) -> (~((op (e1) (e1)) = (e3))) -> (((op (e1) (e0)) = (e3))\/(((op (e1) (e1)) = (e3))\/(((op (e1) (e2)) = (e3))\/((op (e1) (e3)) = (e3))))) -> (~((e1) = (e3))) -> (~((e2) = (e3))) -> (((op (e1) (e0)) = (e2))\/(((op (e1) (e1)) = (e2))\/(((op (e1) (e2)) = (e2))\/((op (e1) (e3)) = (e2))))) -> (~((op (e2) (e2)) = (e3))) -> (~((op (e2) (e2)) = (e2))) -> (~((op (e2) (e2)) = (e1))) -> (((op (e2) (e2)) = (e0))\/(((op (e2) (e2)) = (e1))\/(((op (e2) (e2)) = (e2))\/((op (e2) (e2)) = (e3))))) -> ((op (e1) (e2)) = (e1)) -> (~((op (e0) (e3)) = (op (e1) (e3)))) -> ((op (e0) (e3)) = (e2)) -> (~((op (e0) (e0)) = (e3))) -> (((op (e0) (e0)) = (e3))\/(((op (e1) (e0)) = (e3))\/(((op (e2) (e0)) = (e3))\/((op (e3) (e0)) = (e3))))) -> ((op (e3) (e0)) = (e1)) -> (~((e1) = (e2))) -> False). % 15.22/15.45 do 0 intro. intros zenon_Heb zenon_H8f zenon_H8b zenon_H42 zenon_H182 zenon_H90 zenon_Ha3 zenon_H6a zenon_H84 zenon_H30 zenon_H2f zenon_H52 zenon_H2d zenon_H117 zenon_H80 zenon_H81 zenon_H59 zenon_Hbe zenon_Hee zenon_Ha7. % 15.22/15.45 apply (zenon_or_s _ _ zenon_Heb); [ zenon_intro zenon_H92 | zenon_intro zenon_Hec ]. % 15.22/15.45 exact (zenon_H8f zenon_H92). % 15.22/15.45 apply (zenon_or_s _ _ zenon_Hec); [ zenon_intro zenon_H68 | zenon_intro zenon_Hed ]. % 15.22/15.45 apply (zenon_L198_); trivial. % 15.22/15.45 apply (zenon_or_s _ _ zenon_Hed); [ zenon_intro zenon_Hdd | zenon_intro zenon_He9 ]. % 15.22/15.45 apply (zenon_L580_); trivial. % 15.22/15.45 apply (zenon_L122_); trivial. % 15.22/15.45 (* end of lemma zenon_L581_ *) % 15.22/15.45 assert (zenon_L582_ : (((op (e0) (e0)) = (e2))\/(((op (e0) (e1)) = (e2))\/(((op (e0) (e2)) = (e2))\/((op (e0) (e3)) = (e2))))) -> (~((op (e0) (e1)) = (op (e1) (e1)))) -> (~((op (e1) (e1)) = (e1))) -> (((op (e1) (e1)) = (e0))\/(((op (e1) (e1)) = (e1))\/(((op (e1) (e1)) = (e2))\/((op (e1) (e1)) = (e3))))) -> (~((e0) = (e2))) -> (~((op (e0) (e2)) = (op (e1) (e2)))) -> (~((e0) = (e1))) -> (~((op (e1) (e1)) = (e0))) -> (~((op (e0) (e0)) = (op (e1) (e0)))) -> ((op (e0) (e0)) = (e0)) -> (((op (e1) (e0)) = (e0))\/(((op (e1) (e1)) = (e0))\/(((op (e1) (e2)) = (e0))\/((op (e1) (e3)) = (e0))))) -> (((op (e0) (e0)) = (e2))\/(((op (e1) (e0)) = (e2))\/(((op (e2) (e0)) = (e2))\/((op (e3) (e0)) = (e2))))) -> (~((op (e0) (e0)) = (e2))) -> (~((op (e1) (e3)) = (op (e3) (e3)))) -> ((op (e3) (e3)) = (e3)) -> (~((op (e1) (e1)) = (e3))) -> (((op (e1) (e0)) = (e3))\/(((op (e1) (e1)) = (e3))\/(((op (e1) (e2)) = (e3))\/((op (e1) (e3)) = (e3))))) -> (~((e1) = (e3))) -> (~((e2) = (e3))) -> (((op (e1) (e0)) = (e2))\/(((op (e1) (e1)) = (e2))\/(((op (e1) (e2)) = (e2))\/((op (e1) (e3)) = (e2))))) -> (~((op (e2) (e2)) = (e3))) -> (~((op (e2) (e2)) = (e2))) -> (~((op (e2) (e2)) = (e1))) -> (((op (e2) (e2)) = (e0))\/(((op (e2) (e2)) = (e1))\/(((op (e2) (e2)) = (e2))\/((op (e2) (e2)) = (e3))))) -> ((op (e1) (e2)) = (e1)) -> (~((op (e0) (e3)) = (op (e1) (e3)))) -> (~((op (e0) (e0)) = (e3))) -> (((op (e0) (e0)) = (e3))\/(((op (e1) (e0)) = (e3))\/(((op (e2) (e0)) = (e3))\/((op (e3) (e0)) = (e3))))) -> ((op (e3) (e0)) = (e1)) -> (~((e1) = (e2))) -> False). % 15.22/15.45 do 0 intro. intros zenon_H8e zenon_H23 zenon_H1b4 zenon_H1b3 zenon_H5e zenon_H87 zenon_H9e zenon_H145 zenon_H24c zenon_H1f zenon_H163 zenon_Heb zenon_H8f zenon_H8b zenon_H42 zenon_H182 zenon_H90 zenon_Ha3 zenon_H6a zenon_H84 zenon_H30 zenon_H2f zenon_H52 zenon_H2d zenon_H117 zenon_H80 zenon_H59 zenon_Hbe zenon_Hee zenon_Ha7. % 15.22/15.45 apply (zenon_or_s _ _ zenon_H8e); [ zenon_intro zenon_H92 | zenon_intro zenon_H91 ]. % 15.22/15.45 exact (zenon_H8f zenon_H92). % 15.22/15.45 apply (zenon_or_s _ _ zenon_H91); [ zenon_intro zenon_H5d | zenon_intro zenon_H93 ]. % 15.22/15.45 apply (zenon_L214_); trivial. % 15.22/15.45 apply (zenon_or_s _ _ zenon_H93); [ zenon_intro zenon_H63 | zenon_intro zenon_H81 ]. % 15.22/15.45 apply (zenon_or_s _ _ zenon_Heb); [ zenon_intro zenon_H92 | zenon_intro zenon_Hec ]. % 15.22/15.45 exact (zenon_H8f zenon_H92). % 15.22/15.45 apply (zenon_or_s _ _ zenon_Hec); [ zenon_intro zenon_H68 | zenon_intro zenon_Hed ]. % 15.22/15.45 apply (zenon_L198_); trivial. % 15.22/15.45 apply (zenon_or_s _ _ zenon_Hed); [ zenon_intro zenon_Hdd | zenon_intro zenon_He9 ]. % 15.22/15.45 apply (zenon_L579_); trivial. % 15.22/15.45 apply (zenon_L122_); trivial. % 15.22/15.45 apply (zenon_L581_); trivial. % 15.22/15.45 (* end of lemma zenon_L582_ *) % 15.22/15.45 assert (zenon_L583_ : ((~((op (e1) (e1)) = (e1)))\/((op (e1) (e1)) = (e1))) -> (~((op (e1) (e0)) = (op (e1) (e1)))) -> ((~((op (e1) (e1)) = (e3)))\/((op (e1) (e3)) = (e1))) -> ((~((op (e2) (e2)) = (e1)))\/((op (e2) (e1)) = (e2))) -> ((~((op (e3) (e3)) = (e1)))\/((op (e3) (e1)) = (e3))) -> (~((op (e3) (e1)) = (op (e3) (e3)))) -> (~((op (e0) (e0)) = (e1))) -> (((op (e0) (e3)) = (e1))\/(((op (e1) (e3)) = (e1))\/(((op (e2) (e3)) = (e1))\/((op (e3) (e3)) = (e1))))) -> (~((e1) = (e2))) -> (~((op (e1) (e0)) = (op (e1) (e3)))) -> (~((op (e0) (e1)) = (op (e0) (e3)))) -> (((op (e0) (e0)) = (e2))\/(((op (e0) (e1)) = (e2))\/(((op (e0) (e2)) = (e2))\/((op (e0) (e3)) = (e2))))) -> (((op (e3) (e0)) = (e1))\/(((op (e3) (e1)) = (e1))\/(((op (e3) (e2)) = (e1))\/((op (e3) (e3)) = (e1))))) -> (~((op (e0) (e2)) = (op (e3) (e2)))) -> (~((op (e2) (e0)) = (op (e2) (e1)))) -> (((op (e0) (e1)) = (e2))\/(((op (e1) (e1)) = (e2))\/(((op (e2) (e1)) = (e2))\/((op (e3) (e1)) = (e2))))) -> (~((op (e1) (e0)) = (op (e3) (e0)))) -> ((~((op (e2) (e2)) = (e3)))\/((op (e2) (e3)) = (e2))) -> (~((op (e2) (e1)) = (op (e2) (e3)))) -> (~((op (e2) (e1)) = (op (e2) (e2)))) -> ((~((op (e2) (e2)) = (e2)))\/((op (e2) (e2)) = (e2))) -> (((op (e0) (e0)) = (e2))\/(((op (e1) (e0)) = (e2))\/(((op (e2) (e0)) = (e2))\/((op (e3) (e0)) = (e2))))) -> (~((e2) = (e3))) -> (((op (e1) (e0)) = (e3))\/(((op (e1) (e1)) = (e3))\/(((op (e1) (e2)) = (e3))\/((op (e1) (e3)) = (e3))))) -> (~((op (e1) (e3)) = (op (e3) (e3)))) -> (~((op (e0) (e2)) = (op (e1) (e2)))) -> (~((op (e0) (e3)) = (op (e3) (e3)))) -> (((op (e0) (e0)) = (e3))\/(((op (e0) (e1)) = (e3))\/(((op (e0) (e2)) = (e3))\/((op (e0) (e3)) = (e3))))) -> (~((op (e0) (e0)) = (e2))) -> (((op (e0) (e3)) = (e0))\/(((op (e1) (e3)) = (e0))\/(((op (e2) (e3)) = (e0))\/((op (e3) (e3)) = (e0))))) -> (~((e0) = (e2))) -> ((op (e0) (e0)) = (e0)) -> (~((op (e0) (e0)) = (op (e0) (e3)))) -> (((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 (e3) (e3)) = (e0)))\/((op (e3) (e0)) = (e3))) -> (~((op (e0) (e0)) = (e3))) -> (~((e1) = (e3))) -> ((op (e1) (e0)) = (e1)) -> (((op (e1) (e1)) = (e0))\/(((op (e1) (e1)) = (e1))\/(((op (e1) (e1)) = (e2))\/((op (e1) (e1)) = (e3))))) -> (((op (e2) (e2)) = (e0))\/(((op (e2) (e2)) = (e1))\/(((op (e2) (e2)) = (e2))\/((op (e2) (e2)) = (e3))))) -> (~((op (e3) (e0)) = (op (e3) (e3)))) -> ((op (e3) (e3)) = (e3)) -> (((op (e0) (e0)) = (e3))\/(((op (e1) (e0)) = (e3))\/(((op (e2) (e0)) = (e3))\/((op (e3) (e0)) = (e3))))) -> (~((op (e0) (e1)) = (op (e3) (e1)))) -> (~((op (e1) (e2)) = (op (e2) (e2)))) -> (~((op (e0) (e3)) = (op (e2) (e3)))) -> (~((op (e0) (e3)) = (op (e1) (e3)))) -> (((op (e0) (e3)) = (e0))\/(((op (e0) (e3)) = (e1))\/(((op (e0) (e3)) = (e2))\/((op (e0) (e3)) = (e3))))) -> (((op (e0) (e2)) = (e1))\/(((op (e1) (e2)) = (e1))\/(((op (e2) (e2)) = (e1))\/((op (e3) (e2)) = (e1))))) -> (~((op (e0) (e0)) = (op (e0) (e2)))) -> (~((op (e0) (e2)) = (op (e2) (e2)))) -> (((op (e0) (e2)) = (e0))\/(((op (e0) (e2)) = (e1))\/(((op (e0) (e2)) = (e2))\/((op (e0) (e2)) = (e3))))) -> (~((op (e0) (e2)) = (op (e0) (e3)))) -> ((~((op (e2) (e2)) = (e0)))\/((op (e2) (e0)) = (e2))) -> (~((op (e1) (e0)) = (op (e1) (e2)))) -> ((~((op (e1) (e1)) = (e2)))\/((op (e1) (e2)) = (e1))) -> False). % 15.22/15.45 do 0 intro. intros zenon_H1d8 zenon_Hd7 zenon_H1d2 zenon_H1e3 zenon_H10c zenon_H12d zenon_H45 zenon_H121 zenon_Ha7 zenon_H1cf zenon_H1cd zenon_H8e zenon_H146 zenon_H140 zenon_H154 zenon_H1a2 zenon_H22e zenon_H1c3 zenon_H1e2 zenon_H157 zenon_Haa zenon_Heb zenon_H6a zenon_H90 zenon_H8b zenon_H87 zenon_H36 zenon_H58 zenon_H8f zenon_Hd3 zenon_H5e zenon_H1f zenon_H24f zenon_H84 zenon_H44 zenon_H10f zenon_H59 zenon_Ha3 zenon_Hd8 zenon_H1b3 zenon_H2d zenon_Hbb zenon_H42 zenon_Hbe zenon_H138 zenon_H7d zenon_Hb4 zenon_H80 zenon_H254 zenon_H11b zenon_H250 zenon_H28 zenon_H251 zenon_Hc9 zenon_H1d4 zenon_H166 zenon_H1d3. % 15.22/15.45 apply (zenon_or_s _ _ zenon_H1d8); [ zenon_intro zenon_H1b4 | zenon_intro zenon_H21 ]. % 15.22/15.45 apply (zenon_L577_); trivial. % 15.22/15.45 apply (zenon_L61_); trivial. % 15.22/15.45 (* end of lemma zenon_L583_ *) % 15.22/15.45 assert (zenon_L584_ : (~((op (e2) (e0)) = (op (e2) (e3)))) -> (~((op (e0) (e0)) = (e1))) -> ((~((op (e1) (e1)) = (e1)))\/((op (e1) (e1)) = (e1))) -> (~((op (e1) (e0)) = (op (e1) (e1)))) -> ((~((op (e1) (e1)) = (e3)))\/((op (e1) (e3)) = (e1))) -> ((~((op (e2) (e2)) = (e1)))\/((op (e2) (e1)) = (e2))) -> ((~((op (e3) (e3)) = (e1)))\/((op (e3) (e1)) = (e3))) -> (~((op (e3) (e1)) = (op (e3) (e3)))) -> (((op (e0) (e3)) = (e1))\/(((op (e1) (e3)) = (e1))\/(((op (e2) (e3)) = (e1))\/((op (e3) (e3)) = (e1))))) -> (~((e1) = (e2))) -> (~((op (e1) (e0)) = (op (e1) (e3)))) -> (~((op (e0) (e1)) = (op (e0) (e3)))) -> (((op (e0) (e0)) = (e2))\/(((op (e0) (e1)) = (e2))\/(((op (e0) (e2)) = (e2))\/((op (e0) (e3)) = (e2))))) -> (((op (e3) (e0)) = (e1))\/(((op (e3) (e1)) = (e1))\/(((op (e3) (e2)) = (e1))\/((op (e3) (e3)) = (e1))))) -> (~((op (e0) (e2)) = (op (e3) (e2)))) -> (~((op (e2) (e0)) = (op (e2) (e1)))) -> (((op (e0) (e1)) = (e2))\/(((op (e1) (e1)) = (e2))\/(((op (e2) (e1)) = (e2))\/((op (e3) (e1)) = (e2))))) -> (~((op (e1) (e0)) = (op (e3) (e0)))) -> ((~((op (e2) (e2)) = (e3)))\/((op (e2) (e3)) = (e2))) -> (~((op (e2) (e1)) = (op (e2) (e3)))) -> (~((op (e2) (e1)) = (op (e2) (e2)))) -> ((~((op (e2) (e2)) = (e2)))\/((op (e2) (e2)) = (e2))) -> (((op (e0) (e0)) = (e2))\/(((op (e1) (e0)) = (e2))\/(((op (e2) (e0)) = (e2))\/((op (e3) (e0)) = (e2))))) -> (~((e2) = (e3))) -> (((op (e1) (e0)) = (e3))\/(((op (e1) (e1)) = (e3))\/(((op (e1) (e2)) = (e3))\/((op (e1) (e3)) = (e3))))) -> (~((op (e1) (e3)) = (op (e3) (e3)))) -> (~((op (e0) (e2)) = (op (e1) (e2)))) -> (~((op (e0) (e3)) = (op (e3) (e3)))) -> (((op (e0) (e0)) = (e3))\/(((op (e0) (e1)) = (e3))\/(((op (e0) (e2)) = (e3))\/((op (e0) (e3)) = (e3))))) -> (~((op (e0) (e0)) = (e2))) -> (((op (e0) (e3)) = (e0))\/(((op (e1) (e3)) = (e0))\/(((op (e2) (e3)) = (e0))\/((op (e3) (e3)) = (e0))))) -> (~((e0) = (e2))) -> ((op (e0) (e0)) = (e0)) -> (~((op (e0) (e0)) = (op (e0) (e3)))) -> (((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 (e3) (e3)) = (e0)))\/((op (e3) (e0)) = (e3))) -> (~((op (e0) (e0)) = (e3))) -> (~((e1) = (e3))) -> (((op (e1) (e1)) = (e0))\/(((op (e1) (e1)) = (e1))\/(((op (e1) (e1)) = (e2))\/((op (e1) (e1)) = (e3))))) -> (((op (e2) (e2)) = (e0))\/(((op (e2) (e2)) = (e1))\/(((op (e2) (e2)) = (e2))\/((op (e2) (e2)) = (e3))))) -> (~((op (e3) (e0)) = (op (e3) (e3)))) -> ((op (e3) (e3)) = (e3)) -> (((op (e0) (e0)) = (e3))\/(((op (e1) (e0)) = (e3))\/(((op (e2) (e0)) = (e3))\/((op (e3) (e0)) = (e3))))) -> (~((op (e0) (e1)) = (op (e3) (e1)))) -> (~((op (e1) (e2)) = (op (e2) (e2)))) -> (~((op (e0) (e3)) = (op (e2) (e3)))) -> (~((op (e0) (e3)) = (op (e1) (e3)))) -> (((op (e0) (e3)) = (e0))\/(((op (e0) (e3)) = (e1))\/(((op (e0) (e3)) = (e2))\/((op (e0) (e3)) = (e3))))) -> (((op (e0) (e2)) = (e1))\/(((op (e1) (e2)) = (e1))\/(((op (e2) (e2)) = (e1))\/((op (e3) (e2)) = (e1))))) -> (~((op (e0) (e0)) = (op (e0) (e2)))) -> (~((op (e0) (e2)) = (op (e2) (e2)))) -> (((op (e0) (e2)) = (e0))\/(((op (e0) (e2)) = (e1))\/(((op (e0) (e2)) = (e2))\/((op (e0) (e2)) = (e3))))) -> (~((op (e0) (e2)) = (op (e0) (e3)))) -> ((~((op (e2) (e2)) = (e0)))\/((op (e2) (e0)) = (e2))) -> (~((op (e1) (e0)) = (op (e1) (e2)))) -> ((~((op (e1) (e1)) = (e2)))\/((op (e1) (e2)) = (e1))) -> ((op (e2) (e0)) = (e2)) -> (((op (e1) (e0)) = (e0))\/(((op (e1) (e1)) = (e0))\/(((op (e1) (e2)) = (e0))\/((op (e1) (e3)) = (e0))))) -> (~((op (e2) (e2)) = (e1))) -> (~((op (e2) (e2)) = (e2))) -> ((op (e1) (e2)) = (e1)) -> (~((e0) = (e1))) -> (~((op (e0) (e0)) = (op (e1) (e0)))) -> (~((op (e1) (e1)) = (e0))) -> (~((op (e1) (e1)) = (e1))) -> (~((op (e0) (e1)) = (op (e1) (e1)))) -> (~((op (e1) (e1)) = (e3))) -> (((op (e0) (e0)) = (e1))\/(((op (e1) (e0)) = (e1))\/(((op (e2) (e0)) = (e1))\/((op (e3) (e0)) = (e1))))) -> False). % 15.22/15.45 do 0 intro. intros zenon_Hce zenon_H45 zenon_H1d8 zenon_Hd7 zenon_H1d2 zenon_H1e3 zenon_H10c zenon_H12d zenon_H121 zenon_Ha7 zenon_H1cf zenon_H1cd zenon_H8e zenon_H146 zenon_H140 zenon_H154 zenon_H1a2 zenon_H22e zenon_H1c3 zenon_H1e2 zenon_H157 zenon_Haa zenon_Heb zenon_H6a zenon_H90 zenon_H8b zenon_H87 zenon_H36 zenon_H58 zenon_H8f zenon_Hd3 zenon_H5e zenon_H1f zenon_H24f zenon_H84 zenon_H44 zenon_H10f zenon_H59 zenon_Ha3 zenon_H1b3 zenon_H2d zenon_Hbb zenon_H42 zenon_Hbe zenon_H138 zenon_H7d zenon_Hb4 zenon_H80 zenon_H254 zenon_H11b zenon_H250 zenon_H28 zenon_H251 zenon_Hc9 zenon_H1d4 zenon_H166 zenon_H1d3 zenon_Hdd zenon_H163 zenon_H52 zenon_H2f zenon_H117 zenon_H9e zenon_H24c zenon_H145 zenon_H1b4 zenon_H23 zenon_H182 zenon_Hf1. % 15.22/15.45 apply (zenon_or_s _ _ zenon_H1c3); [ zenon_intro zenon_H30 | zenon_intro zenon_H124 ]. % 15.22/15.45 apply (zenon_or_s _ _ zenon_Hf1); [ zenon_intro zenon_H47 | zenon_intro zenon_Hf4 ]. % 15.22/15.45 exact (zenon_H45 zenon_H47). % 15.22/15.45 apply (zenon_or_s _ _ zenon_Hf4); [ zenon_intro zenon_Hd8 | zenon_intro zenon_Hf5 ]. % 15.22/15.45 apply (zenon_L583_); trivial. % 15.22/15.45 apply (zenon_or_s _ _ zenon_Hf5); [ zenon_intro zenon_Hae | zenon_intro zenon_Hee ]. % 15.22/15.45 apply (zenon_L304_); trivial. % 15.22/15.45 apply (zenon_or_s _ _ zenon_H8e); [ zenon_intro zenon_H92 | zenon_intro zenon_H91 ]. % 15.22/15.45 exact (zenon_H8f zenon_H92). % 15.22/15.45 apply (zenon_or_s _ _ zenon_H91); [ zenon_intro zenon_H5d | zenon_intro zenon_H93 ]. % 15.22/15.45 apply (zenon_L214_); trivial. % 15.22/15.45 apply (zenon_or_s _ _ zenon_H93); [ zenon_intro zenon_H63 | zenon_intro zenon_H81 ]. % 15.22/15.45 apply (zenon_L579_); trivial. % 15.22/15.45 apply (zenon_L386_); trivial. % 15.22/15.45 apply (zenon_L119_); trivial. % 15.22/15.45 (* end of lemma zenon_L584_ *) % 15.22/15.45 assert (zenon_L585_ : (((op (e1) (e0)) = (e2))\/(((op (e1) (e1)) = (e2))\/(((op (e1) (e2)) = (e2))\/((op (e1) (e3)) = (e2))))) -> ((op (e1) (e0)) = (e3)) -> (~((op (e3) (e3)) = (e2))) -> (~((e2) = (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 (e2) (e1)))) -> ((op (e0) (e1)) = (e3)) -> ((op (e2) (e0)) = (e1)) -> (~((e1) = (e3))) -> (((op (e2) (e0)) = (e3))\/(((op (e2) (e1)) = (e3))\/(((op (e2) (e2)) = (e3))\/((op (e2) (e3)) = (e3))))) -> ((op (e0) (e2)) = (e2)) -> (~((op (e0) (e2)) = (op (e1) (e2)))) -> ((op (e1) (e3)) = (e0)) -> (~((e0) = (e2))) -> False). % 15.22/15.45 do 0 intro. intros zenon_H84 zenon_H69 zenon_H3d zenon_H6a zenon_H37 zenon_Ha7 zenon_H160 zenon_Hde zenon_H4a zenon_Hae zenon_Ha3 zenon_He6 zenon_H63 zenon_H87 zenon_Hcc zenon_H5e. % 15.22/15.45 apply (zenon_or_s _ _ zenon_H84); [ zenon_intro zenon_H68 | zenon_intro zenon_H85 ]. % 15.22/15.45 apply (zenon_L17_); trivial. % 15.22/15.45 apply (zenon_or_s _ _ zenon_H85); [ zenon_intro zenon_H6e | zenon_intro zenon_H86 ]. % 15.22/15.45 apply (zenon_or_s _ _ zenon_He6); [ zenon_intro zenon_Haf | zenon_intro zenon_He7 ]. % 15.22/15.45 apply (zenon_L39_); trivial. % 15.22/15.45 apply (zenon_or_s _ _ zenon_He7); [ zenon_intro zenon_Hdf | zenon_intro zenon_He8 ]. % 15.22/15.45 apply (zenon_L65_); trivial. % 15.22/15.45 apply (zenon_or_s _ _ zenon_He8); [ zenon_intro zenon_H34 | zenon_intro zenon_He2 ]. % 15.22/15.45 apply (zenon_L200_); trivial. % 15.22/15.45 apply (zenon_L263_); trivial. % 15.22/15.45 apply (zenon_or_s _ _ zenon_H86); [ zenon_intro zenon_H7c | zenon_intro zenon_H82 ]. % 15.22/15.45 apply (zenon_L52_); trivial. % 15.22/15.45 apply (zenon_L54_); trivial. % 15.22/15.45 (* end of lemma zenon_L585_ *) % 15.22/15.45 assert (zenon_L586_ : (((op (e1) (e0)) = (e0))\/(((op (e1) (e1)) = (e0))\/(((op (e1) (e2)) = (e0))\/((op (e1) (e3)) = (e0))))) -> ((op (e0) (e0)) = (e0)) -> (~((op (e0) (e0)) = (op (e1) (e0)))) -> (~((op (e1) (e1)) = (e0))) -> ((op (e1) (e2)) = (e1)) -> (~((e0) = (e1))) -> (((op (e1) (e0)) = (e2))\/(((op (e1) (e1)) = (e2))\/(((op (e1) (e2)) = (e2))\/((op (e1) (e3)) = (e2))))) -> ((op (e1) (e0)) = (e3)) -> (~((op (e3) (e3)) = (e2))) -> (~((e2) = (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 (e2) (e1)))) -> ((op (e0) (e1)) = (e3)) -> ((op (e2) (e0)) = (e1)) -> (~((e1) = (e3))) -> (((op (e2) (e0)) = (e3))\/(((op (e2) (e1)) = (e3))\/(((op (e2) (e2)) = (e3))\/((op (e2) (e3)) = (e3))))) -> ((op (e0) (e2)) = (e2)) -> (~((op (e0) (e2)) = (op (e1) (e2)))) -> (~((e0) = (e2))) -> False). % 15.22/15.45 do 0 intro. intros zenon_H163 zenon_H1f zenon_H24c zenon_H145 zenon_H117 zenon_H9e zenon_H84 zenon_H69 zenon_H3d zenon_H6a zenon_H37 zenon_Ha7 zenon_H160 zenon_Hde zenon_H4a zenon_Hae zenon_Ha3 zenon_He6 zenon_H63 zenon_H87 zenon_H5e. % 15.22/15.45 apply (zenon_or_s _ _ zenon_H163); [ zenon_intro zenon_Had | zenon_intro zenon_H164 ]. % 15.22/15.45 apply (zenon_L559_); trivial. % 15.22/15.45 apply (zenon_or_s _ _ zenon_H164); [ zenon_intro zenon_H149 | zenon_intro zenon_H165 ]. % 15.22/15.45 exact (zenon_H145 zenon_H149). % 15.22/15.45 apply (zenon_or_s _ _ zenon_H165); [ zenon_intro zenon_H15d | zenon_intro zenon_Hcc ]. % 15.22/15.45 apply (zenon_L496_); trivial. % 15.22/15.45 apply (zenon_L585_); trivial. % 15.22/15.45 (* end of lemma zenon_L586_ *) % 15.22/15.45 assert (zenon_L587_ : (((op (e0) (e0)) = (e3))\/(((op (e0) (e1)) = (e3))\/(((op (e0) (e2)) = (e3))\/((op (e0) (e3)) = (e3))))) -> ((op (e3) (e0)) = (e2)) -> ((op (e2) (e0)) = (e1)) -> (((op (e1) (e0)) = (e0))\/(((op (e1) (e1)) = (e0))\/(((op (e1) (e2)) = (e0))\/((op (e1) (e3)) = (e0))))) -> ((op (e0) (e0)) = (e0)) -> (~((op (e0) (e0)) = (op (e1) (e0)))) -> (~((op (e1) (e1)) = (e0))) -> ((op (e1) (e2)) = (e1)) -> (~((e0) = (e1))) -> (((op (e1) (e0)) = (e2))\/(((op (e1) (e1)) = (e2))\/(((op (e1) (e2)) = (e2))\/((op (e1) (e3)) = (e2))))) -> (~((op (e3) (e3)) = (e2))) -> (~((e1) = (e2))) -> (((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)) = (e3))\/(((op (e2) (e1)) = (e3))\/(((op (e2) (e2)) = (e3))\/((op (e2) (e3)) = (e3))))) -> (~((op (e0) (e2)) = (op (e1) (e2)))) -> (~((e0) = (e2))) -> (~((op (e0) (e0)) = (e3))) -> (((op (e0) (e0)) = (e3))\/(((op (e1) (e0)) = (e3))\/(((op (e2) (e0)) = (e3))\/((op (e3) (e0)) = (e3))))) -> (~((e2) = (e3))) -> ((op (e0) (e2)) = (e2)) -> ((op (e0) (e3)) = (e1)) -> (~((e1) = (e3))) -> False). % 15.22/15.45 do 0 intro. intros zenon_H58 zenon_He9 zenon_Hae zenon_H163 zenon_H1f zenon_H24c zenon_H145 zenon_H117 zenon_H9e zenon_H84 zenon_H3d zenon_Ha7 zenon_H160 zenon_Hde zenon_He6 zenon_H87 zenon_H5e zenon_H59 zenon_Hbe zenon_H6a zenon_H63 zenon_H37 zenon_Ha3. % 15.22/15.45 apply (zenon_or_s _ _ zenon_H58); [ zenon_intro zenon_H5b | zenon_intro zenon_H5a ]. % 15.22/15.45 exact (zenon_H59 zenon_H5b). % 15.22/15.45 apply (zenon_or_s _ _ zenon_H5a); [ zenon_intro zenon_H4a | zenon_intro zenon_H5c ]. % 15.22/15.45 apply (zenon_or_s _ _ zenon_Hbe); [ zenon_intro zenon_H5b | zenon_intro zenon_Hbf ]. % 15.22/15.45 exact (zenon_H59 zenon_H5b). % 15.22/15.45 apply (zenon_or_s _ _ zenon_Hbf); [ zenon_intro zenon_H69 | zenon_intro zenon_Hc0 ]. % 15.22/15.45 apply (zenon_L586_); trivial. % 15.22/15.45 apply (zenon_or_s _ _ zenon_Hc0); [ zenon_intro zenon_Haf | zenon_intro zenon_Hba ]. % 15.22/15.45 apply (zenon_L39_); trivial. % 15.22/15.45 apply (zenon_L220_); trivial. % 15.22/15.45 apply (zenon_or_s _ _ zenon_H5c); [ zenon_intro zenon_H50 | zenon_intro zenon_H53 ]. % 15.22/15.45 apply (zenon_L31_); trivial. % 15.22/15.45 apply (zenon_L32_); trivial. % 15.22/15.45 (* end of lemma zenon_L587_ *) % 15.22/15.45 assert (zenon_L588_ : (~((op (e1) (e2)) = (op (e1) (e3)))) -> (~((op (e3) (e3)) = (e1))) -> (~((op (e2) (e2)) = (e0))) -> (((op (e0) (e0)) = (e1))\/(((op (e1) (e0)) = (e1))\/(((op (e2) (e0)) = (e1))\/((op (e3) (e0)) = (e1))))) -> ((~((op (e1) (e1)) = (e2)))\/((op (e1) (e2)) = (e1))) -> (~((op (e1) (e0)) = (op (e1) (e2)))) -> ((~((op (e2) (e2)) = (e0)))\/((op (e2) (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 (e0) (e2)) = (op (e2) (e2)))) -> (~((op (e0) (e0)) = (op (e0) (e2)))) -> (((op (e0) (e2)) = (e1))\/(((op (e1) (e2)) = (e1))\/(((op (e2) (e2)) = (e1))\/((op (e3) (e2)) = (e1))))) -> (((op (e0) (e3)) = (e0))\/(((op (e0) (e3)) = (e1))\/(((op (e0) (e3)) = (e2))\/((op (e0) (e3)) = (e3))))) -> (~((op (e0) (e3)) = (op (e2) (e3)))) -> (~((op (e1) (e2)) = (op (e2) (e2)))) -> (~((op (e0) (e1)) = (op (e3) (e1)))) -> (~((op (e3) (e0)) = (op (e3) (e3)))) -> ((~((op (e3) (e3)) = (e0)))\/((op (e3) (e0)) = (e3))) -> (((op (e0) (e0)) = (e1))\/(((op (e0) (e1)) = (e1))\/(((op (e0) (e2)) = (e1))\/((op (e0) (e3)) = (e1))))) -> (~((op (e0) (e0)) = (op (e0) (e3)))) -> (((op (e0) (e3)) = (e0))\/(((op (e1) (e3)) = (e0))\/(((op (e2) (e3)) = (e0))\/((op (e3) (e3)) = (e0))))) -> (~((op (e0) (e3)) = (op (e3) (e3)))) -> ((~((op (e2) (e2)) = (e2)))\/((op (e2) (e2)) = (e2))) -> (~((op (e2) (e1)) = (op (e2) (e2)))) -> (~((op (e2) (e1)) = (op (e2) (e3)))) -> ((~((op (e2) (e2)) = (e3)))\/((op (e2) (e3)) = (e2))) -> (~((op (e1) (e0)) = (op (e3) (e0)))) -> (((op (e0) (e1)) = (e2))\/(((op (e1) (e1)) = (e2))\/(((op (e2) (e1)) = (e2))\/((op (e3) (e1)) = (e2))))) -> (~((op (e2) (e0)) = (op (e2) (e1)))) -> (~((op (e0) (e2)) = (op (e3) (e2)))) -> (((op (e3) (e0)) = (e1))\/(((op (e3) (e1)) = (e1))\/(((op (e3) (e2)) = (e1))\/((op (e3) (e3)) = (e1))))) -> (~((op (e0) (e1)) = (op (e0) (e3)))) -> (~((op (e1) (e0)) = (op (e1) (e3)))) -> (((op (e0) (e3)) = (e1))\/(((op (e1) (e3)) = (e1))\/(((op (e2) (e3)) = (e1))\/((op (e3) (e3)) = (e1))))) -> (~((op (e3) (e1)) = (op (e3) (e3)))) -> ((~((op (e3) (e3)) = (e1)))\/((op (e3) (e1)) = (e3))) -> ((~((op (e2) (e2)) = (e1)))\/((op (e2) (e1)) = (e2))) -> ((~((op (e1) (e1)) = (e3)))\/((op (e1) (e3)) = (e1))) -> (~((op (e1) (e0)) = (op (e1) (e1)))) -> ((~((op (e1) (e1)) = (e1)))\/((op (e1) (e1)) = (e1))) -> (~((op (e0) (e0)) = (e1))) -> (~((op (e2) (e0)) = (op (e2) (e3)))) -> (((op (e0) (e0)) = (e3))\/(((op (e0) (e1)) = (e3))\/(((op (e0) (e2)) = (e3))\/((op (e0) (e3)) = (e3))))) -> (~((op (e3) (e3)) = (e2))) -> (((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)) = (e3))\/(((op (e2) (e1)) = (e3))\/(((op (e2) (e2)) = (e3))\/((op (e2) (e3)) = (e3))))) -> (((op (e0) (e0)) = (e2))\/(((op (e0) (e1)) = (e2))\/(((op (e0) (e2)) = (e2))\/((op (e0) (e3)) = (e2))))) -> (~((op (e0) (e1)) = (op (e1) (e1)))) -> (~((op (e1) (e1)) = (e1))) -> (((op (e1) (e1)) = (e0))\/(((op (e1) (e1)) = (e1))\/(((op (e1) (e1)) = (e2))\/((op (e1) (e1)) = (e3))))) -> (~((e0) = (e2))) -> (~((op (e0) (e2)) = (op (e1) (e2)))) -> (~((e0) = (e1))) -> (~((op (e1) (e1)) = (e0))) -> (~((op (e0) (e0)) = (op (e1) (e0)))) -> ((op (e0) (e0)) = (e0)) -> (((op (e1) (e0)) = (e0))\/(((op (e1) (e1)) = (e0))\/(((op (e1) (e2)) = (e0))\/((op (e1) (e3)) = (e0))))) -> (((op (e0) (e0)) = (e2))\/(((op (e1) (e0)) = (e2))\/(((op (e2) (e0)) = (e2))\/((op (e3) (e0)) = (e2))))) -> (~((op (e0) (e0)) = (e2))) -> (~((op (e1) (e3)) = (op (e3) (e3)))) -> ((op (e3) (e3)) = (e3)) -> (~((op (e1) (e1)) = (e3))) -> (((op (e1) (e0)) = (e3))\/(((op (e1) (e1)) = (e3))\/(((op (e1) (e2)) = (e3))\/((op (e1) (e3)) = (e3))))) -> (~((e1) = (e3))) -> (~((e2) = (e3))) -> (((op (e1) (e0)) = (e2))\/(((op (e1) (e1)) = (e2))\/(((op (e1) (e2)) = (e2))\/((op (e1) (e3)) = (e2))))) -> (~((op (e2) (e2)) = (e3))) -> (~((op (e2) (e2)) = (e2))) -> (~((op (e2) (e2)) = (e1))) -> (((op (e2) (e2)) = (e0))\/(((op (e2) (e2)) = (e1))\/(((op (e2) (e2)) = (e2))\/((op (e2) (e2)) = (e3))))) -> ((op (e1) (e2)) = (e1)) -> (~((op (e0) (e3)) = (op (e1) (e3)))) -> (~((op (e0) (e0)) = (e3))) -> (((op (e0) (e0)) = (e3))\/(((op (e1) (e0)) = (e3))\/(((op (e2) (e0)) = (e3))\/((op (e3) (e0)) = (e3))))) -> (~((e1) = (e2))) -> False). % 15.22/15.45 do 0 intro. intros zenon_H1d0 zenon_H104 zenon_H2e zenon_Hf1 zenon_H1d3 zenon_H166 zenon_H1d4 zenon_Hc9 zenon_H251 zenon_H28 zenon_H250 zenon_H11b zenon_H254 zenon_Hb4 zenon_H7d zenon_H138 zenon_Hbb zenon_H10f zenon_H44 zenon_H24f zenon_Hd3 zenon_H36 zenon_Haa zenon_H157 zenon_H1e2 zenon_H1c3 zenon_H22e zenon_H1a2 zenon_H154 zenon_H140 zenon_H146 zenon_H1cd zenon_H1cf zenon_H121 zenon_H12d zenon_H10c zenon_H1e3 zenon_H1d2 zenon_Hd7 zenon_H1d8 zenon_H45 zenon_Hce zenon_H58 zenon_H3d zenon_H160 zenon_Hde zenon_He6 zenon_H8e zenon_H23 zenon_H1b4 zenon_H1b3 zenon_H5e zenon_H87 zenon_H9e zenon_H145 zenon_H24c zenon_H1f zenon_H163 zenon_Heb zenon_H8f zenon_H8b zenon_H42 zenon_H182 zenon_H90 zenon_Ha3 zenon_H6a zenon_H84 zenon_H30 zenon_H2f zenon_H52 zenon_H2d zenon_H117 zenon_H80 zenon_H59 zenon_Hbe zenon_Ha7. % 15.22/15.45 apply (zenon_or_s _ _ zenon_H44); [ zenon_intro zenon_H47 | zenon_intro zenon_H46 ]. % 15.22/15.45 exact (zenon_H45 zenon_H47). % 15.22/15.45 apply (zenon_or_s _ _ zenon_H46); [ zenon_intro zenon_H22 | zenon_intro zenon_H48 ]. % 15.22/15.45 apply (zenon_or_s _ _ zenon_Hf1); [ zenon_intro zenon_H47 | zenon_intro zenon_Hf4 ]. % 15.22/15.45 exact (zenon_H45 zenon_H47). % 15.22/15.45 apply (zenon_or_s _ _ zenon_Hf4); [ zenon_intro zenon_Hd8 | zenon_intro zenon_Hf5 ]. % 15.22/15.45 apply (zenon_L577_); trivial. % 15.22/15.45 apply (zenon_or_s _ _ zenon_Hf5); [ zenon_intro zenon_Hae | zenon_intro zenon_Hee ]. % 15.22/15.45 apply (zenon_L578_); trivial. % 15.22/15.45 apply (zenon_L582_); trivial. % 15.22/15.45 apply (zenon_or_s _ _ zenon_H48); [ zenon_intro zenon_H29 | zenon_intro zenon_H37 ]. % 15.22/15.45 apply (zenon_L5_); trivial. % 15.22/15.45 apply (zenon_or_s _ _ zenon_Hf1); [ zenon_intro zenon_H47 | zenon_intro zenon_Hf4 ]. % 15.22/15.45 exact (zenon_H45 zenon_H47). % 15.22/15.45 apply (zenon_or_s _ _ zenon_Hf4); [ zenon_intro zenon_Hd8 | zenon_intro zenon_Hf5 ]. % 15.22/15.45 apply (zenon_L583_); trivial. % 15.22/15.45 apply (zenon_or_s _ _ zenon_Hf5); [ zenon_intro zenon_Hae | zenon_intro zenon_Hee ]. % 15.22/15.45 apply (zenon_or_s _ _ zenon_H8e); [ zenon_intro zenon_H92 | zenon_intro zenon_H91 ]. % 15.22/15.45 exact (zenon_H8f zenon_H92). % 15.22/15.45 apply (zenon_or_s _ _ zenon_H91); [ zenon_intro zenon_H5d | zenon_intro zenon_H93 ]. % 15.22/15.45 apply (zenon_L214_); trivial. % 15.22/15.45 apply (zenon_or_s _ _ zenon_H93); [ zenon_intro zenon_H63 | zenon_intro zenon_H81 ]. % 15.22/15.45 apply (zenon_or_s _ _ zenon_Heb); [ zenon_intro zenon_H92 | zenon_intro zenon_Hec ]. % 15.22/15.45 exact (zenon_H8f zenon_H92). % 15.22/15.45 apply (zenon_or_s _ _ zenon_Hec); [ zenon_intro zenon_H68 | zenon_intro zenon_Hed ]. % 15.22/15.45 apply (zenon_L198_); trivial. % 15.22/15.45 apply (zenon_or_s _ _ zenon_Hed); [ zenon_intro zenon_Hdd | zenon_intro zenon_He9 ]. % 15.22/15.45 apply (zenon_L584_); trivial. % 15.22/15.45 apply (zenon_L587_); trivial. % 15.22/15.45 apply (zenon_L33_); trivial. % 15.22/15.45 apply (zenon_L582_); trivial. % 15.22/15.45 (* end of lemma zenon_L588_ *) % 15.22/15.45 assert (zenon_L589_ : (~((e0) = (e3))) -> ((op (e3) (e2)) = (e3)) -> ((op (e3) (e2)) = (e0)) -> False). % 15.22/15.45 do 0 intro. intros zenon_H4b zenon_H106 zenon_H167. % 15.22/15.45 cut (((op (e3) (e2)) = (e3)) = ((e0) = (e3))). % 15.22/15.45 intro zenon_D_pnotp. % 15.22/15.45 apply zenon_H4b. % 15.22/15.45 rewrite <- zenon_D_pnotp. % 15.22/15.45 exact zenon_H106. % 15.22/15.45 cut (((e3) = (e3))); [idtac | apply NNPP; zenon_intro zenon_H4d]. % 15.22/15.45 cut (((op (e3) (e2)) = (e0))); [idtac | apply NNPP; zenon_intro zenon_H257]. % 15.22/15.45 congruence. % 15.22/15.45 exact (zenon_H257 zenon_H167). % 15.22/15.45 apply zenon_H4d. apply refl_equal. % 15.22/15.45 (* end of lemma zenon_L589_ *) % 15.22/15.45 assert (zenon_L590_ : (((op (e0) (e2)) = (e0))\/(((op (e1) (e2)) = (e0))\/(((op (e2) (e2)) = (e0))\/((op (e3) (e2)) = (e0))))) -> ((op (e0) (e0)) = (e0)) -> (~((op (e0) (e0)) = (op (e0) (e2)))) -> ((op (e1) (e2)) = (e1)) -> (~((e0) = (e1))) -> (~((op (e2) (e2)) = (e0))) -> (~((e0) = (e3))) -> ((op (e3) (e2)) = (e3)) -> False). % 15.22/15.45 do 0 intro. intros zenon_H16f zenon_H1f zenon_H250 zenon_H117 zenon_H9e zenon_H2e zenon_H4b zenon_H106. % 15.22/15.45 apply (zenon_or_s _ _ zenon_H16f); [ zenon_intro zenon_Hab | zenon_intro zenon_H170 ]. % 15.22/15.45 apply (zenon_L567_); trivial. % 15.22/15.45 apply (zenon_or_s _ _ zenon_H170); [ zenon_intro zenon_H15d | zenon_intro zenon_H171 ]. % 15.22/15.45 apply (zenon_L496_); trivial. % 15.22/15.45 apply (zenon_or_s _ _ zenon_H171); [ zenon_intro zenon_H32 | zenon_intro zenon_H167 ]. % 15.22/15.45 exact (zenon_H2e zenon_H32). % 15.22/15.45 apply (zenon_L589_); trivial. % 15.22/15.45 (* end of lemma zenon_L590_ *) % 15.22/15.45 assert (zenon_L591_ : (((op (e0) (e0)) = (e2))\/(((op (e1) (e0)) = (e2))\/(((op (e2) (e0)) = (e2))\/((op (e3) (e0)) = (e2))))) -> (~((op (e0) (e0)) = (e2))) -> (~((op (e1) (e3)) = (op (e3) (e3)))) -> ((op (e3) (e3)) = (e3)) -> ((op (e1) (e2)) = (e1)) -> (~((e1) = (e3))) -> (~((op (e1) (e1)) = (e3))) -> (~((e2) = (e3))) -> (((op (e1) (e0)) = (e3))\/(((op (e1) (e1)) = (e3))\/(((op (e1) (e2)) = (e3))\/((op (e1) (e3)) = (e3))))) -> ((op (e2) (e3)) = (e2)) -> (~((op (e2) (e0)) = (op (e2) (e3)))) -> ((op (e3) (e0)) = (e1)) -> (~((e1) = (e2))) -> False). % 15.22/15.45 do 0 intro. intros zenon_Heb zenon_H8f zenon_H8b zenon_H42 zenon_H117 zenon_Ha3 zenon_H182 zenon_H6a zenon_H90 zenon_H124 zenon_Hce zenon_Hee zenon_Ha7. % 15.22/15.45 apply (zenon_or_s _ _ zenon_Heb); [ zenon_intro zenon_H92 | zenon_intro zenon_Hec ]. % 15.22/15.45 exact (zenon_H8f zenon_H92). % 15.22/15.45 apply (zenon_or_s _ _ zenon_Hec); [ zenon_intro zenon_H68 | zenon_intro zenon_Hed ]. % 15.22/15.45 apply (zenon_L198_); trivial. % 15.22/15.45 apply (zenon_or_s _ _ zenon_Hed); [ zenon_intro zenon_Hdd | zenon_intro zenon_He9 ]. % 15.22/15.45 apply (zenon_L119_); trivial. % 15.22/15.45 apply (zenon_L122_); trivial. % 15.22/15.45 (* end of lemma zenon_L591_ *) % 15.22/15.45 assert (zenon_L592_ : (((op (e0) (e0)) = (e3))\/(((op (e1) (e0)) = (e3))\/(((op (e2) (e0)) = (e3))\/((op (e3) (e0)) = (e3))))) -> (~((op (e0) (e0)) = (e3))) -> (~((e2) = (e3))) -> ((op (e1) (e0)) = (e2)) -> (~((e1) = (e3))) -> ((op (e2) (e0)) = (e1)) -> ((op (e3) (e3)) = (e3)) -> (~((op (e3) (e0)) = (op (e3) (e3)))) -> False). % 15.22/15.45 do 0 intro. intros zenon_Hbe zenon_H59 zenon_H6a zenon_H68 zenon_Ha3 zenon_Hae zenon_H42 zenon_Hbb. % 15.22/15.45 apply (zenon_or_s _ _ zenon_Hbe); [ zenon_intro zenon_H5b | zenon_intro zenon_Hbf ]. % 15.22/15.45 exact (zenon_H59 zenon_H5b). % 15.22/15.45 apply (zenon_or_s _ _ zenon_Hbf); [ zenon_intro zenon_H69 | zenon_intro zenon_Hc0 ]. % 15.22/15.45 apply (zenon_L17_); trivial. % 15.22/15.45 apply (zenon_or_s _ _ zenon_Hc0); [ zenon_intro zenon_Haf | zenon_intro zenon_Hba ]. % 15.22/15.45 apply (zenon_L39_); trivial. % 15.22/15.45 apply (zenon_L43_); trivial. % 15.22/15.45 (* end of lemma zenon_L592_ *) % 15.22/15.45 assert (zenon_L593_ : (~((op (e2) (e2)) = (e2))) -> (~((op (e2) (e2)) = (e1))) -> (~((op (e2) (e2)) = (e0))) -> (~((op (e1) (e2)) = (op (e1) (e3)))) -> (~((op (e3) (e3)) = (e1))) -> ((~((op (e1) (e1)) = (e1)))\/((op (e1) (e1)) = (e1))) -> (~((op (e1) (e0)) = (op (e1) (e1)))) -> (((op (e0) (e0)) = (e1))\/(((op (e1) (e0)) = (e1))\/(((op (e2) (e0)) = (e1))\/((op (e3) (e0)) = (e1))))) -> ((~((op (e1) (e1)) = (e3)))\/((op (e1) (e3)) = (e1))) -> ((~((op (e2) (e2)) = (e1)))\/((op (e2) (e1)) = (e2))) -> ((~((op (e3) (e3)) = (e1)))\/((op (e3) (e1)) = (e3))) -> (~((op (e3) (e1)) = (op (e3) (e3)))) -> (~((op (e0) (e0)) = (e1))) -> (((op (e0) (e3)) = (e1))\/(((op (e1) (e3)) = (e1))\/(((op (e2) (e3)) = (e1))\/((op (e3) (e3)) = (e1))))) -> (~((op (e1) (e0)) = (op (e1) (e3)))) -> (~((op (e0) (e1)) = (op (e0) (e3)))) -> (((op (e3) (e0)) = (e1))\/(((op (e3) (e1)) = (e1))\/(((op (e3) (e2)) = (e1))\/((op (e3) (e3)) = (e1))))) -> (~((op (e0) (e2)) = (op (e3) (e2)))) -> (~((op (e2) (e0)) = (op (e2) (e1)))) -> (((op (e0) (e1)) = (e2))\/(((op (e1) (e1)) = (e2))\/(((op (e2) (e1)) = (e2))\/((op (e3) (e1)) = (e2))))) -> (~((op (e1) (e0)) = (op (e3) (e0)))) -> ((~((op (e2) (e2)) = (e3)))\/((op (e2) (e3)) = (e2))) -> (~((op (e2) (e1)) = (op (e2) (e3)))) -> (~((op (e2) (e1)) = (op (e2) (e2)))) -> ((~((op (e2) (e2)) = (e2)))\/((op (e2) (e2)) = (e2))) -> (~((op (e0) (e3)) = (op (e3) (e3)))) -> (((op (e0) (e3)) = (e0))\/(((op (e1) (e3)) = (e0))\/(((op (e2) (e3)) = (e0))\/((op (e3) (e3)) = (e0))))) -> (~((op (e0) (e0)) = (op (e0) (e3)))) -> (((op (e0) (e0)) = (e1))\/(((op (e0) (e1)) = (e1))\/(((op (e0) (e2)) = (e1))\/((op (e0) (e3)) = (e1))))) -> ((~((op (e3) (e3)) = (e0)))\/((op (e3) (e0)) = (e3))) -> (((op (e2) (e2)) = (e0))\/(((op (e2) (e2)) = (e1))\/(((op (e2) (e2)) = (e2))\/((op (e2) (e2)) = (e3))))) -> (~((op (e0) (e1)) = (op (e3) (e1)))) -> (~((op (e1) (e2)) = (op (e2) (e2)))) -> (~((op (e0) (e3)) = (op (e2) (e3)))) -> (~((op (e0) (e3)) = (op (e1) (e3)))) -> (((op (e0) (e3)) = (e0))\/(((op (e0) (e3)) = (e1))\/(((op (e0) (e3)) = (e2))\/((op (e0) (e3)) = (e3))))) -> (((op (e0) (e2)) = (e1))\/(((op (e1) (e2)) = (e1))\/(((op (e2) (e2)) = (e1))\/((op (e3) (e2)) = (e1))))) -> (~((op (e0) (e0)) = (op (e0) (e2)))) -> (~((op (e0) (e2)) = (op (e2) (e2)))) -> (((op (e0) (e2)) = (e0))\/(((op (e0) (e2)) = (e1))\/(((op (e0) (e2)) = (e2))\/((op (e0) (e2)) = (e3))))) -> (~((op (e0) (e2)) = (op (e0) (e3)))) -> ((~((op (e2) (e2)) = (e0)))\/((op (e2) (e0)) = (e2))) -> (~((op (e1) (e0)) = (op (e1) (e2)))) -> ((~((op (e1) (e1)) = (e2)))\/((op (e1) (e2)) = (e1))) -> (~((op (e3) (e0)) = (op (e3) (e3)))) -> (((op (e0) (e0)) = (e3))\/(((op (e0) (e1)) = (e3))\/(((op (e0) (e2)) = (e3))\/((op (e0) (e3)) = (e3))))) -> (((op (e1) (e0)) = (e0))\/(((op (e1) (e1)) = (e0))\/(((op (e1) (e2)) = (e0))\/((op (e1) (e3)) = (e0))))) -> ((op (e0) (e0)) = (e0)) -> (~((op (e0) (e0)) = (op (e1) (e0)))) -> (~((op (e1) (e1)) = (e0))) -> (~((e0) = (e1))) -> (((op (e1) (e0)) = (e2))\/(((op (e1) (e1)) = (e2))\/(((op (e1) (e2)) = (e2))\/((op (e1) (e3)) = (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 (e2) (e1)))) -> (((op (e2) (e0)) = (e3))\/(((op (e2) (e1)) = (e3))\/(((op (e2) (e2)) = (e3))\/((op (e2) (e3)) = (e3))))) -> (~((op (e0) (e2)) = (op (e1) (e2)))) -> (~((e0) = (e2))) -> (~((op (e0) (e0)) = (e3))) -> (((op (e0) (e0)) = (e3))\/(((op (e1) (e0)) = (e3))\/(((op (e2) (e0)) = (e3))\/((op (e3) (e0)) = (e3))))) -> (((op (e1) (e1)) = (e0))\/(((op (e1) (e1)) = (e1))\/(((op (e1) (e1)) = (e2))\/((op (e1) (e1)) = (e3))))) -> (~((op (e1) (e1)) = (e1))) -> (~((op (e0) (e1)) = (op (e1) (e1)))) -> (((op (e0) (e0)) = (e2))\/(((op (e0) (e1)) = (e2))\/(((op (e0) (e2)) = (e2))\/((op (e0) (e3)) = (e2))))) -> (((op (e0) (e0)) = (e2))\/(((op (e1) (e0)) = (e2))\/(((op (e2) (e0)) = (e2))\/((op (e3) (e0)) = (e2))))) -> (~((op (e0) (e0)) = (e2))) -> (~((op (e1) (e3)) = (op (e3) (e3)))) -> ((op (e3) (e3)) = (e3)) -> ((op (e1) (e2)) = (e1)) -> (~((e1) = (e3))) -> (~((op (e1) (e1)) = (e3))) -> (~((e2) = (e3))) -> (((op (e1) (e0)) = (e3))\/(((op (e1) (e1)) = (e3))\/(((op (e1) (e2)) = (e3))\/((op (e1) (e3)) = (e3))))) -> ((op (e2) (e3)) = (e2)) -> (~((op (e2) (e0)) = (op (e2) (e3)))) -> (~((e1) = (e2))) -> False). % 15.22/15.45 do 0 intro. intros zenon_H2f zenon_H52 zenon_H2e zenon_H1d0 zenon_H104 zenon_H1d8 zenon_Hd7 zenon_Hf1 zenon_H1d2 zenon_H1e3 zenon_H10c zenon_H12d zenon_H45 zenon_H121 zenon_H1cf zenon_H1cd zenon_H146 zenon_H140 zenon_H154 zenon_H1a2 zenon_H22e zenon_H1c3 zenon_H1e2 zenon_H157 zenon_Haa zenon_H36 zenon_Hd3 zenon_H24f zenon_H44 zenon_H10f zenon_H2d zenon_H138 zenon_H7d zenon_Hb4 zenon_H80 zenon_H254 zenon_H11b zenon_H250 zenon_H28 zenon_H251 zenon_Hc9 zenon_H1d4 zenon_H166 zenon_H1d3 zenon_Hbb zenon_H58 zenon_H163 zenon_H1f zenon_H24c zenon_H145 zenon_H9e zenon_H84 zenon_H3d zenon_H160 zenon_Hde zenon_He6 zenon_H87 zenon_H5e zenon_H59 zenon_Hbe zenon_H1b3 zenon_H1b4 zenon_H23 zenon_H8e zenon_Heb zenon_H8f zenon_H8b zenon_H42 zenon_H117 zenon_Ha3 zenon_H182 zenon_H6a zenon_H90 zenon_H124 zenon_Hce zenon_Ha7. % 15.22/15.45 apply (zenon_or_s _ _ zenon_H44); [ zenon_intro zenon_H47 | zenon_intro zenon_H46 ]. % 15.22/15.45 exact (zenon_H45 zenon_H47). % 15.22/15.45 apply (zenon_or_s _ _ zenon_H46); [ zenon_intro zenon_H22 | zenon_intro zenon_H48 ]. % 15.22/15.45 apply (zenon_or_s _ _ zenon_Hf1); [ zenon_intro zenon_H47 | zenon_intro zenon_Hf4 ]. % 15.22/15.45 exact (zenon_H45 zenon_H47). % 15.22/15.45 apply (zenon_or_s _ _ zenon_Hf4); [ zenon_intro zenon_Hd8 | zenon_intro zenon_Hf5 ]. % 15.22/15.45 apply (zenon_L577_); trivial. % 15.22/15.45 apply (zenon_or_s _ _ zenon_Hf5); [ zenon_intro zenon_Hae | zenon_intro zenon_Hee ]. % 15.22/15.45 apply (zenon_L578_); trivial. % 15.22/15.45 apply (zenon_L591_); trivial. % 15.22/15.45 apply (zenon_or_s _ _ zenon_H48); [ zenon_intro zenon_H29 | zenon_intro zenon_H37 ]. % 15.22/15.45 apply (zenon_or_s _ _ zenon_Hf1); [ zenon_intro zenon_H47 | zenon_intro zenon_Hf4 ]. % 15.22/15.45 exact (zenon_H45 zenon_H47). % 15.22/15.45 apply (zenon_or_s _ _ zenon_Hf4); [ zenon_intro zenon_Hd8 | zenon_intro zenon_Hf5 ]. % 15.22/15.45 apply (zenon_L583_); trivial. % 15.22/15.45 apply (zenon_or_s _ _ zenon_Hf5); [ zenon_intro zenon_Hae | zenon_intro zenon_Hee ]. % 15.22/15.45 apply (zenon_L551_); trivial. % 15.22/15.45 apply (zenon_L591_); trivial. % 15.22/15.45 apply (zenon_or_s _ _ zenon_Hf1); [ zenon_intro zenon_H47 | zenon_intro zenon_Hf4 ]. % 15.22/15.45 exact (zenon_H45 zenon_H47). % 15.22/15.45 apply (zenon_or_s _ _ zenon_Hf4); [ zenon_intro zenon_Hd8 | zenon_intro zenon_Hf5 ]. % 15.22/15.45 apply (zenon_L577_); trivial. % 15.22/15.45 apply (zenon_or_s _ _ zenon_Hf5); [ zenon_intro zenon_Hae | zenon_intro zenon_Hee ]. % 15.22/15.45 apply (zenon_or_s _ _ zenon_H8e); [ zenon_intro zenon_H92 | zenon_intro zenon_H91 ]. % 15.22/15.45 exact (zenon_H8f zenon_H92). % 15.22/15.45 apply (zenon_or_s _ _ zenon_H91); [ zenon_intro zenon_H5d | zenon_intro zenon_H93 ]. % 15.22/15.45 apply (zenon_L214_); trivial. % 15.22/15.45 apply (zenon_or_s _ _ zenon_H93); [ zenon_intro zenon_H63 | zenon_intro zenon_H81 ]. % 15.22/15.45 apply (zenon_or_s _ _ zenon_Heb); [ zenon_intro zenon_H92 | zenon_intro zenon_Hec ]. % 15.22/15.45 exact (zenon_H8f zenon_H92). % 15.22/15.45 apply (zenon_or_s _ _ zenon_Hec); [ zenon_intro zenon_H68 | zenon_intro zenon_Hed ]. % 15.22/15.45 apply (zenon_L592_); trivial. % 15.22/15.45 apply (zenon_or_s _ _ zenon_Hed); [ zenon_intro zenon_Hdd | zenon_intro zenon_He9 ]. % 15.22/15.45 apply (zenon_L119_); trivial. % 15.22/15.45 apply (zenon_L587_); trivial. % 15.22/15.45 apply (zenon_L33_); trivial. % 15.22/15.45 apply (zenon_L591_); trivial. % 15.22/15.45 (* end of lemma zenon_L593_ *) % 15.22/15.45 assert (zenon_L594_ : (((op (e0) (e3)) = (e1))\/(((op (e1) (e3)) = (e1))\/(((op (e2) (e3)) = (e1))\/((op (e3) (e3)) = (e1))))) -> (~((op (e3) (e3)) = (e2))) -> (~((op (e2) (e2)) = (op (e2) (e3)))) -> ((op (e2) (e2)) = (e2)) -> ((op (e1) (e3)) = (e0)) -> (~((e0) = (e2))) -> (~((e1) = (e2))) -> (((op (e0) (e3)) = (e2))\/(((op (e1) (e3)) = (e2))\/(((op (e2) (e3)) = (e2))\/((op (e3) (e3)) = (e2))))) -> ((op (e1) (e2)) = (e1)) -> (~((op (e1) (e2)) = (op (e1) (e3)))) -> ((op (e2) (e0)) = (e1)) -> (~((op (e2) (e0)) = (op (e2) (e3)))) -> (~((op (e3) (e3)) = (e1))) -> False). % 15.31/15.46 do 0 intro. intros zenon_H121 zenon_H3d zenon_H15f zenon_H35 zenon_Hcc zenon_H5e zenon_Ha7 zenon_H160 zenon_H117 zenon_H1d0 zenon_Hae zenon_Hce zenon_H104. % 15.31/15.46 apply (zenon_or_s _ _ zenon_H121); [ zenon_intro zenon_H37 | zenon_intro zenon_H122 ]. % 15.31/15.46 apply (zenon_L138_); trivial. % 15.31/15.46 apply (zenon_or_s _ _ zenon_H122); [ zenon_intro zenon_H11f | zenon_intro zenon_H123 ]. % 15.31/15.46 apply (zenon_L237_); trivial. % 15.31/15.46 apply (zenon_or_s _ _ zenon_H123); [ zenon_intro zenon_Hb5 | zenon_intro zenon_H38 ]. % 15.31/15.46 apply (zenon_L91_); trivial. % 15.31/15.46 exact (zenon_H104 zenon_H38). % 15.31/15.46 (* end of lemma zenon_L594_ *) % 15.31/15.46 assert (zenon_L595_ : (((op (e1) (e0)) = (e0))\/(((op (e1) (e1)) = (e0))\/(((op (e1) (e2)) = (e0))\/((op (e1) (e3)) = (e0))))) -> ((op (e0) (e0)) = (e0)) -> (~((op (e0) (e0)) = (op (e1) (e0)))) -> (~((op (e1) (e1)) = (e0))) -> (~((e0) = (e1))) -> (((op (e0) (e3)) = (e1))\/(((op (e1) (e3)) = (e1))\/(((op (e2) (e3)) = (e1))\/((op (e3) (e3)) = (e1))))) -> (~((op (e3) (e3)) = (e2))) -> (~((op (e2) (e2)) = (op (e2) (e3)))) -> ((op (e2) (e2)) = (e2)) -> (~((e0) = (e2))) -> (~((e1) = (e2))) -> (((op (e0) (e3)) = (e2))\/(((op (e1) (e3)) = (e2))\/(((op (e2) (e3)) = (e2))\/((op (e3) (e3)) = (e2))))) -> ((op (e1) (e2)) = (e1)) -> (~((op (e1) (e2)) = (op (e1) (e3)))) -> ((op (e2) (e0)) = (e1)) -> (~((op (e2) (e0)) = (op (e2) (e3)))) -> (~((op (e3) (e3)) = (e1))) -> False). % 15.31/15.46 do 0 intro. intros zenon_H163 zenon_H1f zenon_H24c zenon_H145 zenon_H9e zenon_H121 zenon_H3d zenon_H15f zenon_H35 zenon_H5e zenon_Ha7 zenon_H160 zenon_H117 zenon_H1d0 zenon_Hae zenon_Hce zenon_H104. % 15.31/15.46 apply (zenon_or_s _ _ zenon_H163); [ zenon_intro zenon_Had | zenon_intro zenon_H164 ]. % 15.31/15.46 apply (zenon_L559_); trivial. % 15.31/15.46 apply (zenon_or_s _ _ zenon_H164); [ zenon_intro zenon_H149 | zenon_intro zenon_H165 ]. % 15.31/15.46 exact (zenon_H145 zenon_H149). % 15.31/15.46 apply (zenon_or_s _ _ zenon_H165); [ zenon_intro zenon_H15d | zenon_intro zenon_Hcc ]. % 15.31/15.46 apply (zenon_L496_); trivial. % 15.31/15.46 apply (zenon_L594_); trivial. % 15.31/15.46 (* end of lemma zenon_L595_ *) % 15.31/15.46 assert (zenon_L596_ : (((op (e0) (e0)) = (e2))\/(((op (e1) (e0)) = (e2))\/(((op (e2) (e0)) = (e2))\/((op (e3) (e0)) = (e2))))) -> (~((op (e0) (e0)) = (e2))) -> (~((op (e1) (e3)) = (op (e3) (e3)))) -> ((op (e3) (e3)) = (e3)) -> ((op (e1) (e2)) = (e1)) -> (~((e1) = (e3))) -> (~((op (e1) (e1)) = (e3))) -> (~((e2) = (e3))) -> (((op (e1) (e0)) = (e3))\/(((op (e1) (e1)) = (e3))\/(((op (e1) (e2)) = (e3))\/((op (e1) (e3)) = (e3))))) -> (~((op (e2) (e0)) = (op (e2) (e2)))) -> ((op (e2) (e2)) = (e2)) -> ((op (e3) (e0)) = (e1)) -> (~((e1) = (e2))) -> False). % 15.31/15.46 do 0 intro. intros zenon_Heb zenon_H8f zenon_H8b zenon_H42 zenon_H117 zenon_Ha3 zenon_H182 zenon_H6a zenon_H90 zenon_H17a zenon_H35 zenon_Hee zenon_Ha7. % 15.31/15.46 apply (zenon_or_s _ _ zenon_Heb); [ zenon_intro zenon_H92 | zenon_intro zenon_Hec ]. % 15.31/15.46 exact (zenon_H8f zenon_H92). % 15.31/15.46 apply (zenon_or_s _ _ zenon_Hec); [ zenon_intro zenon_H68 | zenon_intro zenon_Hed ]. % 15.31/15.46 apply (zenon_L198_); trivial. % 15.31/15.46 apply (zenon_or_s _ _ zenon_Hed); [ zenon_intro zenon_Hdd | zenon_intro zenon_He9 ]. % 15.31/15.46 apply (zenon_L161_); trivial. % 15.31/15.46 apply (zenon_L122_); trivial. % 15.31/15.46 (* end of lemma zenon_L596_ *) % 15.31/15.46 assert (zenon_L597_ : (((op (e0) (e0)) = (e1))\/(((op (e1) (e0)) = (e1))\/(((op (e2) (e0)) = (e1))\/((op (e3) (e0)) = (e1))))) -> ((~((op (e1) (e1)) = (e2)))\/((op (e1) (e2)) = (e1))) -> (~((op (e1) (e0)) = (op (e1) (e2)))) -> ((~((op (e2) (e2)) = (e0)))\/((op (e2) (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 (e0) (e2)) = (op (e2) (e2)))) -> (~((op (e0) (e0)) = (op (e0) (e2)))) -> (((op (e0) (e2)) = (e1))\/(((op (e1) (e2)) = (e1))\/(((op (e2) (e2)) = (e1))\/((op (e3) (e2)) = (e1))))) -> (((op (e0) (e3)) = (e0))\/(((op (e0) (e3)) = (e1))\/(((op (e0) (e3)) = (e2))\/((op (e0) (e3)) = (e3))))) -> (~((op (e0) (e3)) = (op (e1) (e3)))) -> (~((op (e0) (e3)) = (op (e2) (e3)))) -> (~((op (e1) (e2)) = (op (e2) (e2)))) -> (~((op (e0) (e1)) = (op (e3) (e1)))) -> (((op (e0) (e0)) = (e3))\/(((op (e1) (e0)) = (e3))\/(((op (e2) (e0)) = (e3))\/((op (e3) (e0)) = (e3))))) -> (~((op (e3) (e0)) = (op (e3) (e3)))) -> (((op (e2) (e2)) = (e0))\/(((op (e2) (e2)) = (e1))\/(((op (e2) (e2)) = (e2))\/((op (e2) (e2)) = (e3))))) -> (((op (e1) (e1)) = (e0))\/(((op (e1) (e1)) = (e1))\/(((op (e1) (e1)) = (e2))\/((op (e1) (e1)) = (e3))))) -> (~((op (e0) (e0)) = (e3))) -> ((~((op (e3) (e3)) = (e0)))\/((op (e3) (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) (e0)) = (op (e0) (e3)))) -> (((op (e0) (e3)) = (e0))\/(((op (e1) (e3)) = (e0))\/(((op (e2) (e3)) = (e0))\/((op (e3) (e3)) = (e0))))) -> (((op (e0) (e0)) = (e3))\/(((op (e0) (e1)) = (e3))\/(((op (e0) (e2)) = (e3))\/((op (e0) (e3)) = (e3))))) -> (~((op (e0) (e3)) = (op (e3) (e3)))) -> (~((op (e0) (e2)) = (op (e1) (e2)))) -> ((~((op (e2) (e2)) = (e2)))\/((op (e2) (e2)) = (e2))) -> (~((op (e2) (e1)) = (op (e2) (e2)))) -> (~((op (e2) (e1)) = (op (e2) (e3)))) -> ((~((op (e2) (e2)) = (e3)))\/((op (e2) (e3)) = (e2))) -> (~((op (e1) (e0)) = (op (e3) (e0)))) -> (((op (e0) (e1)) = (e2))\/(((op (e1) (e1)) = (e2))\/(((op (e2) (e1)) = (e2))\/((op (e3) (e1)) = (e2))))) -> (~((op (e2) (e0)) = (op (e2) (e1)))) -> (~((op (e0) (e2)) = (op (e3) (e2)))) -> (((op (e3) (e0)) = (e1))\/(((op (e3) (e1)) = (e1))\/(((op (e3) (e2)) = (e1))\/((op (e3) (e3)) = (e1))))) -> (((op (e0) (e0)) = (e2))\/(((op (e0) (e1)) = (e2))\/(((op (e0) (e2)) = (e2))\/((op (e0) (e3)) = (e2))))) -> (~((op (e0) (e1)) = (op (e0) (e3)))) -> (~((op (e1) (e0)) = (op (e1) (e3)))) -> (~((op (e0) (e0)) = (e1))) -> (~((op (e3) (e1)) = (op (e3) (e3)))) -> ((~((op (e3) (e3)) = (e1)))\/((op (e3) (e1)) = (e3))) -> ((~((op (e2) (e2)) = (e1)))\/((op (e2) (e1)) = (e2))) -> ((~((op (e1) (e1)) = (e3)))\/((op (e1) (e3)) = (e1))) -> (~((op (e1) (e0)) = (op (e1) (e1)))) -> ((~((op (e1) (e1)) = (e1)))\/((op (e1) (e1)) = (e1))) -> (~((op (e3) (e3)) = (e1))) -> (~((op (e2) (e0)) = (op (e2) (e3)))) -> (~((op (e1) (e2)) = (op (e1) (e3)))) -> (((op (e0) (e3)) = (e2))\/(((op (e1) (e3)) = (e2))\/(((op (e2) (e3)) = (e2))\/((op (e3) (e3)) = (e2))))) -> (~((e0) = (e2))) -> (~((op (e2) (e2)) = (op (e2) (e3)))) -> (~((op (e3) (e3)) = (e2))) -> (((op (e0) (e3)) = (e1))\/(((op (e1) (e3)) = (e1))\/(((op (e2) (e3)) = (e1))\/((op (e3) (e3)) = (e1))))) -> (~((e0) = (e1))) -> (~((op (e1) (e1)) = (e0))) -> (~((op (e0) (e0)) = (op (e1) (e0)))) -> ((op (e0) (e0)) = (e0)) -> (((op (e1) (e0)) = (e0))\/(((op (e1) (e1)) = (e0))\/(((op (e1) (e2)) = (e0))\/((op (e1) (e3)) = (e0))))) -> (((op (e0) (e0)) = (e2))\/(((op (e1) (e0)) = (e2))\/(((op (e2) (e0)) = (e2))\/((op (e3) (e0)) = (e2))))) -> (~((op (e0) (e0)) = (e2))) -> (~((op (e1) (e3)) = (op (e3) (e3)))) -> ((op (e3) (e3)) = (e3)) -> ((op (e1) (e2)) = (e1)) -> (~((e1) = (e3))) -> (~((op (e1) (e1)) = (e3))) -> (~((e2) = (e3))) -> (((op (e1) (e0)) = (e3))\/(((op (e1) (e1)) = (e3))\/(((op (e1) (e2)) = (e3))\/((op (e1) (e3)) = (e3))))) -> (~((op (e2) (e0)) = (op (e2) (e2)))) -> ((op (e2) (e2)) = (e2)) -> (~((e1) = (e2))) -> False). % 15.31/15.46 do 0 intro. intros zenon_Hf1 zenon_H1d3 zenon_H166 zenon_H1d4 zenon_Hc9 zenon_H251 zenon_H28 zenon_H250 zenon_H11b zenon_H254 zenon_H80 zenon_Hb4 zenon_H7d zenon_H138 zenon_Hbe zenon_Hbb zenon_H2d zenon_H1b3 zenon_H59 zenon_H10f zenon_H44 zenon_H84 zenon_H24f zenon_Hd3 zenon_H58 zenon_H36 zenon_H87 zenon_Haa zenon_H157 zenon_H1e2 zenon_H1c3 zenon_H22e zenon_H1a2 zenon_H154 zenon_H140 zenon_H146 zenon_H8e zenon_H1cd zenon_H1cf zenon_H45 zenon_H12d zenon_H10c zenon_H1e3 zenon_H1d2 zenon_Hd7 zenon_H1d8 zenon_H104 zenon_Hce zenon_H1d0 zenon_H160 zenon_H5e zenon_H15f zenon_H3d zenon_H121 zenon_H9e zenon_H145 zenon_H24c zenon_H1f zenon_H163 zenon_Heb zenon_H8f zenon_H8b zenon_H42 zenon_H117 zenon_Ha3 zenon_H182 zenon_H6a zenon_H90 zenon_H17a zenon_H35 zenon_Ha7. % 15.31/15.46 apply (zenon_or_s _ _ zenon_Hf1); [ zenon_intro zenon_H47 | zenon_intro zenon_Hf4 ]. % 15.31/15.46 exact (zenon_H45 zenon_H47). % 15.31/15.46 apply (zenon_or_s _ _ zenon_Hf4); [ zenon_intro zenon_Hd8 | zenon_intro zenon_Hf5 ]. % 15.31/15.46 apply (zenon_L583_); trivial. % 15.31/15.46 apply (zenon_or_s _ _ zenon_Hf5); [ zenon_intro zenon_Hae | zenon_intro zenon_Hee ]. % 15.31/15.46 apply (zenon_L595_); trivial. % 15.31/15.46 apply (zenon_L596_); trivial. % 15.31/15.46 (* end of lemma zenon_L597_ *) % 15.31/15.46 assert (zenon_L598_ : (~((op (e0) (e0)) = (op (e2) (e0)))) -> ((op (e0) (e0)) = (e0)) -> ((op (e2) (e0)) = (e0)) -> False). % 15.31/15.46 do 0 intro. intros zenon_H258 zenon_H1f zenon_Hcf. % 15.31/15.46 cut (((op (e0) (e0)) = (e0)) = ((op (e0) (e0)) = (op (e2) (e0)))). % 15.31/15.46 intro zenon_D_pnotp. % 15.31/15.46 apply zenon_H258. % 15.31/15.46 rewrite <- zenon_D_pnotp. % 15.31/15.46 exact zenon_H1f. % 15.31/15.46 cut (((e0) = (op (e2) (e0)))); [idtac | apply NNPP; zenon_intro zenon_H259]. % 15.31/15.46 cut (((op (e0) (e0)) = (op (e0) (e0)))); [idtac | apply NNPP; zenon_intro zenon_H24e]. % 15.31/15.46 congruence. % 15.31/15.46 apply zenon_H24e. apply refl_equal. % 15.31/15.46 apply zenon_H259. apply sym_equal. exact zenon_Hcf. % 15.31/15.46 (* end of lemma zenon_L598_ *) % 15.31/15.46 assert (zenon_L599_ : (~((op (e1) (e3)) = (op (e2) (e3)))) -> ((op (e1) (e3)) = (e0)) -> ((op (e2) (e3)) = (e0)) -> False). % 15.31/15.46 do 0 intro. intros zenon_H244 zenon_Hcc zenon_Hd0. % 15.31/15.46 cut (((op (e1) (e3)) = (e0)) = ((op (e1) (e3)) = (op (e2) (e3)))). % 15.31/15.46 intro zenon_D_pnotp. % 15.31/15.46 apply zenon_H244. % 15.31/15.46 rewrite <- zenon_D_pnotp. % 15.31/15.46 exact zenon_Hcc. % 15.31/15.46 cut (((e0) = (op (e2) (e3)))); [idtac | apply NNPP; zenon_intro zenon_Hd1]. % 15.31/15.46 cut (((op (e1) (e3)) = (op (e1) (e3)))); [idtac | apply NNPP; zenon_intro zenon_H23a]. % 15.31/15.46 congruence. % 15.31/15.46 apply zenon_H23a. apply refl_equal. % 15.31/15.46 apply zenon_Hd1. apply sym_equal. exact zenon_Hd0. % 15.31/15.46 (* end of lemma zenon_L599_ *) % 15.31/15.46 assert (zenon_L600_ : (((op (e2) (e0)) = (e0))\/(((op (e2) (e1)) = (e0))\/(((op (e2) (e2)) = (e0))\/((op (e2) (e3)) = (e0))))) -> ((op (e0) (e0)) = (e0)) -> (~((op (e0) (e0)) = (op (e2) (e0)))) -> ((op (e2) (e1)) = (e2)) -> (~((e0) = (e2))) -> (~((op (e2) (e2)) = (e0))) -> (~((op (e1) (e3)) = (op (e2) (e3)))) -> ((op (e1) (e3)) = (e0)) -> False). % 15.31/15.46 do 0 intro. intros zenon_H1f5 zenon_H1f zenon_H258 zenon_H156 zenon_H5e zenon_H2e zenon_H244 zenon_Hcc. % 15.31/15.46 apply (zenon_or_s _ _ zenon_H1f5); [ zenon_intro zenon_Hcf | zenon_intro zenon_H1f9 ]. % 15.31/15.46 apply (zenon_L598_); trivial. % 15.31/15.46 apply (zenon_or_s _ _ zenon_H1f9); [ zenon_intro zenon_H14a | zenon_intro zenon_H1fa ]. % 15.31/15.46 apply (zenon_L351_); trivial. % 15.31/15.46 apply (zenon_or_s _ _ zenon_H1fa); [ zenon_intro zenon_H32 | zenon_intro zenon_Hd0 ]. % 15.31/15.46 exact (zenon_H2e zenon_H32). % 15.31/15.46 apply (zenon_L599_); trivial. % 15.31/15.46 (* end of lemma zenon_L600_ *) % 15.31/15.46 assert (zenon_L601_ : (((op (e1) (e0)) = (e0))\/(((op (e1) (e1)) = (e0))\/(((op (e1) (e2)) = (e0))\/((op (e1) (e3)) = (e0))))) -> (~((op (e0) (e0)) = (op (e1) (e0)))) -> (~((op (e1) (e1)) = (e0))) -> ((op (e1) (e2)) = (e1)) -> (~((e0) = (e1))) -> (((op (e2) (e0)) = (e0))\/(((op (e2) (e1)) = (e0))\/(((op (e2) (e2)) = (e0))\/((op (e2) (e3)) = (e0))))) -> ((op (e0) (e0)) = (e0)) -> (~((op (e0) (e0)) = (op (e2) (e0)))) -> ((op (e2) (e1)) = (e2)) -> (~((e0) = (e2))) -> (~((op (e2) (e2)) = (e0))) -> (~((op (e1) (e3)) = (op (e2) (e3)))) -> False). % 15.31/15.46 do 0 intro. intros zenon_H163 zenon_H24c zenon_H145 zenon_H117 zenon_H9e zenon_H1f5 zenon_H1f zenon_H258 zenon_H156 zenon_H5e zenon_H2e zenon_H244. % 15.31/15.46 apply (zenon_or_s _ _ zenon_H163); [ zenon_intro zenon_Had | zenon_intro zenon_H164 ]. % 15.31/15.46 apply (zenon_L559_); trivial. % 15.31/15.46 apply (zenon_or_s _ _ zenon_H164); [ zenon_intro zenon_H149 | zenon_intro zenon_H165 ]. % 15.31/15.46 exact (zenon_H145 zenon_H149). % 15.31/15.46 apply (zenon_or_s _ _ zenon_H165); [ zenon_intro zenon_H15d | zenon_intro zenon_Hcc ]. % 15.31/15.46 apply (zenon_L496_); trivial. % 15.31/15.46 apply (zenon_L600_); trivial. % 15.31/15.46 (* end of lemma zenon_L601_ *) % 15.31/15.46 assert (zenon_L602_ : (((op (e2) (e0)) = (e0))\/(((op (e2) (e1)) = (e0))\/(((op (e2) (e2)) = (e0))\/((op (e2) (e3)) = (e0))))) -> (~((op (e1) (e3)) = (op (e2) (e3)))) -> (~((op (e0) (e0)) = (op (e2) (e0)))) -> (~((op (e3) (e2)) = (op (e3) (e3)))) -> ((~((op (e3) (e3)) = (e2)))\/((op (e3) (e2)) = (e3))) -> (~((e0) = (e3))) -> (((op (e0) (e2)) = (e0))\/(((op (e1) (e2)) = (e0))\/(((op (e2) (e2)) = (e0))\/((op (e3) (e2)) = (e0))))) -> (~((op (e0) (e0)) = (e1))) -> (((op (e0) (e0)) = (e1))\/(((op (e1) (e0)) = (e1))\/(((op (e2) (e0)) = (e1))\/((op (e3) (e0)) = (e1))))) -> (~((op (e1) (e1)) = (e3))) -> (~((op (e0) (e1)) = (op (e1) (e1)))) -> (~((op (e1) (e1)) = (e0))) -> (((op (e1) (e0)) = (e0))\/(((op (e1) (e1)) = (e0))\/(((op (e1) (e2)) = (e0))\/((op (e1) (e3)) = (e0))))) -> (~((e0) = (e1))) -> (~((op (e0) (e0)) = (op (e1) (e0)))) -> (~((op (e2) (e2)) = (e0))) -> (~((op (e2) (e0)) = (op (e2) (e3)))) -> ((op (e1) (e2)) = (e1)) -> (~((op (e1) (e2)) = (op (e1) (e3)))) -> ((~((op (e1) (e1)) = (e3)))\/((op (e1) (e3)) = (e1))) -> ((~((op (e2) (e2)) = (e1)))\/((op (e2) (e1)) = (e2))) -> ((~((op (e3) (e3)) = (e1)))\/((op (e3) (e1)) = (e3))) -> (~((op (e3) (e1)) = (op (e3) (e3)))) -> (((op (e0) (e3)) = (e1))\/(((op (e1) (e3)) = (e1))\/(((op (e2) (e3)) = (e1))\/((op (e3) (e3)) = (e1))))) -> (~((e1) = (e2))) -> (~((op (e1) (e0)) = (op (e1) (e3)))) -> (~((op (e0) (e1)) = (op (e0) (e3)))) -> (((op (e0) (e0)) = (e2))\/(((op (e0) (e1)) = (e2))\/(((op (e0) (e2)) = (e2))\/((op (e0) (e3)) = (e2))))) -> (((op (e3) (e0)) = (e1))\/(((op (e3) (e1)) = (e1))\/(((op (e3) (e2)) = (e1))\/((op (e3) (e3)) = (e1))))) -> (~((op (e0) (e2)) = (op (e3) (e2)))) -> (~((op (e2) (e0)) = (op (e2) (e1)))) -> (((op (e0) (e1)) = (e2))\/(((op (e1) (e1)) = (e2))\/(((op (e2) (e1)) = (e2))\/((op (e3) (e1)) = (e2))))) -> (~((op (e1) (e0)) = (op (e3) (e0)))) -> ((~((op (e2) (e2)) = (e3)))\/((op (e2) (e3)) = (e2))) -> (~((op (e2) (e1)) = (op (e2) (e3)))) -> (~((op (e2) (e1)) = (op (e2) (e2)))) -> ((~((op (e2) (e2)) = (e2)))\/((op (e2) (e2)) = (e2))) -> (((op (e0) (e0)) = (e2))\/(((op (e1) (e0)) = (e2))\/(((op (e2) (e0)) = (e2))\/((op (e3) (e0)) = (e2))))) -> (~((e2) = (e3))) -> (((op (e1) (e0)) = (e3))\/(((op (e1) (e1)) = (e3))\/(((op (e1) (e2)) = (e3))\/((op (e1) (e3)) = (e3))))) -> (~((op (e1) (e3)) = (op (e3) (e3)))) -> (~((op (e0) (e2)) = (op (e1) (e2)))) -> (~((op (e0) (e3)) = (op (e3) (e3)))) -> (((op (e0) (e0)) = (e3))\/(((op (e0) (e1)) = (e3))\/(((op (e0) (e2)) = (e3))\/((op (e0) (e3)) = (e3))))) -> (~((op (e0) (e0)) = (e2))) -> (((op (e0) (e3)) = (e0))\/(((op (e1) (e3)) = (e0))\/(((op (e2) (e3)) = (e0))\/((op (e3) (e3)) = (e0))))) -> (~((e0) = (e2))) -> ((op (e0) (e0)) = (e0)) -> (~((op (e0) (e0)) = (op (e0) (e3)))) -> (((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 (e3) (e3)) = (e0)))\/((op (e3) (e0)) = (e3))) -> (~((op (e0) (e0)) = (e3))) -> (~((e1) = (e3))) -> (((op (e1) (e1)) = (e0))\/(((op (e1) (e1)) = (e1))\/(((op (e1) (e1)) = (e2))\/((op (e1) (e1)) = (e3))))) -> (~((op (e1) (e1)) = (e1))) -> (((op (e2) (e2)) = (e0))\/(((op (e2) (e2)) = (e1))\/(((op (e2) (e2)) = (e2))\/((op (e2) (e2)) = (e3))))) -> (~((op (e3) (e0)) = (op (e3) (e3)))) -> ((op (e3) (e3)) = (e3)) -> (((op (e0) (e0)) = (e3))\/(((op (e1) (e0)) = (e3))\/(((op (e2) (e0)) = (e3))\/((op (e3) (e0)) = (e3))))) -> (~((op (e0) (e1)) = (op (e3) (e1)))) -> (~((op (e1) (e2)) = (op (e2) (e2)))) -> (~((op (e0) (e3)) = (op (e2) (e3)))) -> (~((op (e0) (e3)) = (op (e1) (e3)))) -> (((op (e0) (e3)) = (e0))\/(((op (e0) (e3)) = (e1))\/(((op (e0) (e3)) = (e2))\/((op (e0) (e3)) = (e3))))) -> (((op (e0) (e2)) = (e1))\/(((op (e1) (e2)) = (e1))\/(((op (e2) (e2)) = (e1))\/((op (e3) (e2)) = (e1))))) -> (~((op (e0) (e0)) = (op (e0) (e2)))) -> (~((op (e0) (e2)) = (op (e2) (e2)))) -> (((op (e0) (e2)) = (e0))\/(((op (e0) (e2)) = (e1))\/(((op (e0) (e2)) = (e2))\/((op (e0) (e2)) = (e3))))) -> (~((op (e0) (e2)) = (op (e0) (e3)))) -> ((~((op (e2) (e2)) = (e0)))\/((op (e2) (e0)) = (e2))) -> (~((op (e1) (e0)) = (op (e1) (e2)))) -> ((~((op (e1) (e1)) = (e2)))\/((op (e1) (e2)) = (e1))) -> (~((op (e0) (e1)) = (op (e2) (e1)))) -> (((op (e0) (e3)) = (e2))\/(((op (e1) (e3)) = (e2))\/(((op (e2) (e3)) = (e2))\/((op (e3) (e3)) = (e2))))) -> (((op (e2) (e0)) = (e3))\/(((op (e2) (e1)) = (e3))\/(((op (e2) (e2)) = (e3))\/((op (e2) (e3)) = (e3))))) -> (~((op (e1) (e0)) = (op (e1) (e1)))) -> ((~((op (e1) (e1)) = (e1)))\/((op (e1) (e1)) = (e1))) -> (~((op (e2) (e0)) = (op (e2) (e2)))) -> (~((op (e2) (e2)) = (op (e2) (e3)))) -> False). % 15.31/15.46 do 0 intro. intros zenon_H1f5 zenon_H244 zenon_H258 zenon_H173 zenon_H10e zenon_H4b zenon_H16f zenon_H45 zenon_Hf1 zenon_H182 zenon_H23 zenon_H145 zenon_H163 zenon_H9e zenon_H24c zenon_H2e zenon_Hce zenon_H117 zenon_H1d0 zenon_H1d2 zenon_H1e3 zenon_H10c zenon_H12d zenon_H121 zenon_Ha7 zenon_H1cf zenon_H1cd zenon_H8e zenon_H146 zenon_H140 zenon_H154 zenon_H1a2 zenon_H22e zenon_H1c3 zenon_H1e2 zenon_H157 zenon_Haa zenon_Heb zenon_H6a zenon_H90 zenon_H8b zenon_H87 zenon_H36 zenon_H58 zenon_H8f zenon_Hd3 zenon_H5e zenon_H1f zenon_H24f zenon_H84 zenon_H44 zenon_H10f zenon_H59 zenon_Ha3 zenon_H1b3 zenon_H1b4 zenon_H2d zenon_Hbb zenon_H42 zenon_Hbe zenon_H138 zenon_H7d zenon_Hb4 zenon_H80 zenon_H254 zenon_H11b zenon_H250 zenon_H28 zenon_H251 zenon_Hc9 zenon_H1d4 zenon_H166 zenon_H1d3 zenon_Hde zenon_H160 zenon_He6 zenon_Hd7 zenon_H1d8 zenon_H17a zenon_H15f. % 15.31/15.46 apply (zenon_or_s _ _ zenon_H1e3); [ zenon_intro zenon_H52 | zenon_intro zenon_H156 ]. % 15.31/15.46 apply (zenon_or_s _ _ zenon_Haa); [ zenon_intro zenon_H2f | zenon_intro zenon_H35 ]. % 15.31/15.46 apply (zenon_or_s _ _ zenon_H1c3); [ zenon_intro zenon_H30 | zenon_intro zenon_H124 ]. % 15.31/15.46 apply (zenon_or_s _ _ zenon_H10c); [ zenon_intro zenon_H104 | zenon_intro zenon_H10a ]. % 15.31/15.46 apply (zenon_or_s _ _ zenon_H10e); [ zenon_intro zenon_H3d | zenon_intro zenon_H106 ]. % 15.31/15.46 apply (zenon_L588_); trivial. % 15.31/15.46 apply (zenon_L590_); trivial. % 15.31/15.46 apply (zenon_L102_); trivial. % 15.31/15.46 apply (zenon_or_s _ _ zenon_H10c); [ zenon_intro zenon_H104 | zenon_intro zenon_H10a ]. % 15.31/15.46 apply (zenon_or_s _ _ zenon_H10e); [ zenon_intro zenon_H3d | zenon_intro zenon_H106 ]. % 15.31/15.46 apply (zenon_L593_); trivial. % 15.31/15.46 apply (zenon_L153_); trivial. % 15.31/15.46 apply (zenon_L102_); trivial. % 15.31/15.46 apply (zenon_or_s _ _ zenon_H10c); [ zenon_intro zenon_H104 | zenon_intro zenon_H10a ]. % 15.31/15.46 apply (zenon_or_s _ _ zenon_H10e); [ zenon_intro zenon_H3d | zenon_intro zenon_H106 ]. % 15.31/15.46 apply (zenon_L597_); trivial. % 15.31/15.46 apply (zenon_L590_); trivial. % 15.31/15.46 apply (zenon_L102_); trivial. % 15.31/15.46 apply (zenon_L601_); trivial. % 15.31/15.46 (* end of lemma zenon_L602_ *) % 15.31/15.46 assert (zenon_L603_ : (((op (e1) (e0)) = (e0))\/(((op (e1) (e1)) = (e0))\/(((op (e1) (e2)) = (e0))\/((op (e1) (e3)) = (e0))))) -> ((op (e0) (e0)) = (e0)) -> (~((op (e0) (e0)) = (op (e1) (e0)))) -> (~((op (e1) (e1)) = (e0))) -> (~((op (e2) (e2)) = (e3))) -> (~((op (e2) (e2)) = (e2))) -> (~((op (e2) (e2)) = (e1))) -> (~((op (e1) (e2)) = (op (e2) (e2)))) -> (((op (e2) (e2)) = (e0))\/(((op (e2) (e2)) = (e1))\/(((op (e2) (e2)) = (e2))\/((op (e2) (e2)) = (e3))))) -> (~((e0) = (e1))) -> ((op (e1) (e3)) = (e1)) -> False). % 15.31/15.46 do 0 intro. intros zenon_H163 zenon_H1f zenon_H24c zenon_H145 zenon_H30 zenon_H2f zenon_H52 zenon_H7d zenon_H2d zenon_H9e zenon_H11f. % 15.31/15.46 apply (zenon_or_s _ _ zenon_H163); [ zenon_intro zenon_Had | zenon_intro zenon_H164 ]. % 15.31/15.46 apply (zenon_L559_); trivial. % 15.31/15.46 apply (zenon_or_s _ _ zenon_H164); [ zenon_intro zenon_H149 | zenon_intro zenon_H165 ]. % 15.31/15.46 exact (zenon_H145 zenon_H149). % 15.31/15.46 apply (zenon_or_s _ _ zenon_H165); [ zenon_intro zenon_H15d | zenon_intro zenon_Hcc ]. % 15.31/15.46 apply (zenon_L335_); trivial. % 15.31/15.46 apply (zenon_L208_); trivial. % 15.31/15.46 (* end of lemma zenon_L603_ *) % 15.31/15.46 assert (zenon_L604_ : (((op (e0) (e3)) = (e0))\/(((op (e1) (e3)) = (e0))\/(((op (e2) (e3)) = (e0))\/((op (e3) (e3)) = (e0))))) -> ((op (e0) (e0)) = (e0)) -> (~((op (e0) (e0)) = (op (e0) (e3)))) -> ((op (e1) (e3)) = (e1)) -> (~((e0) = (e1))) -> ((op (e2) (e3)) = (e2)) -> (~((e0) = (e2))) -> (~((op (e3) (e3)) = (e0))) -> False). % 15.31/15.46 do 0 intro. intros zenon_Hd3 zenon_H1f zenon_H24f zenon_H11f zenon_H9e zenon_H124 zenon_H5e zenon_H3c. % 15.31/15.46 apply (zenon_or_s _ _ zenon_Hd3); [ zenon_intro zenon_Hca | zenon_intro zenon_Hd4 ]. % 15.31/15.46 apply (zenon_L562_); trivial. % 15.31/15.46 apply (zenon_or_s _ _ zenon_Hd4); [ zenon_intro zenon_Hcc | zenon_intro zenon_Hd5 ]. % 15.31/15.46 apply (zenon_L208_); trivial. % 15.31/15.46 apply (zenon_or_s _ _ zenon_Hd5); [ zenon_intro zenon_Hd0 | zenon_intro zenon_H40 ]. % 15.31/15.46 apply (zenon_L201_); trivial. % 15.31/15.46 exact (zenon_H3c zenon_H40). % 15.31/15.46 (* end of lemma zenon_L604_ *) % 15.31/15.46 assert (zenon_L605_ : ((~((op (e2) (e2)) = (e3)))\/((op (e2) (e3)) = (e2))) -> (((op (e0) (e3)) = (e0))\/(((op (e1) (e3)) = (e0))\/(((op (e2) (e3)) = (e0))\/((op (e3) (e3)) = (e0))))) -> (~((e0) = (e2))) -> (~((op (e0) (e0)) = (op (e0) (e3)))) -> (~((op (e3) (e0)) = (op (e3) (e3)))) -> ((op (e3) (e3)) = (e3)) -> ((~((op (e3) (e3)) = (e0)))\/((op (e3) (e0)) = (e3))) -> (~((op (e0) (e0)) = (op (e1) (e0)))) -> ((op (e0) (e0)) = (e0)) -> (~((op (e1) (e1)) = (e0))) -> (((op (e2) (e2)) = (e0))\/(((op (e2) (e2)) = (e1))\/(((op (e2) (e2)) = (e2))\/((op (e2) (e2)) = (e3))))) -> (~((op (e2) (e2)) = (e2))) -> (~((op (e2) (e2)) = (e1))) -> (~((op (e1) (e2)) = (op (e2) (e2)))) -> (~((e0) = (e1))) -> ((op (e1) (e3)) = (e1)) -> (((op (e1) (e0)) = (e0))\/(((op (e1) (e1)) = (e0))\/(((op (e1) (e2)) = (e0))\/((op (e1) (e3)) = (e0))))) -> False). % 15.31/15.46 do 0 intro. intros zenon_H1c3 zenon_Hd3 zenon_H5e zenon_H24f zenon_Hbb zenon_H42 zenon_H10f zenon_H24c zenon_H1f zenon_H145 zenon_H2d zenon_H2f zenon_H52 zenon_H7d zenon_H9e zenon_H11f zenon_H163. % 15.31/15.46 apply (zenon_or_s _ _ zenon_H1c3); [ zenon_intro zenon_H30 | zenon_intro zenon_H124 ]. % 15.31/15.46 apply (zenon_L603_); trivial. % 15.31/15.46 apply (zenon_or_s _ _ zenon_H10f); [ zenon_intro zenon_H3c | zenon_intro zenon_Hba ]. % 15.31/15.46 apply (zenon_L604_); trivial. % 15.31/15.46 apply (zenon_L43_); trivial. % 15.31/15.46 (* end of lemma zenon_L605_ *) % 15.31/15.46 assert (zenon_L606_ : (((op (e2) (e0)) = (e1))\/(((op (e2) (e1)) = (e1))\/(((op (e2) (e2)) = (e1))\/((op (e2) (e3)) = (e1))))) -> (~((op (e3) (e0)) = (op (e3) (e3)))) -> ((op (e3) (e3)) = (e3)) -> (~((e1) = (e3))) -> ((op (e1) (e0)) = (e2)) -> (~((e2) = (e3))) -> (~((op (e0) (e0)) = (e3))) -> (((op (e0) (e0)) = (e3))\/(((op (e1) (e0)) = (e3))\/(((op (e2) (e0)) = (e3))\/((op (e3) (e0)) = (e3))))) -> ((op (e0) (e1)) = (e1)) -> (~((op (e0) (e1)) = (op (e2) (e1)))) -> (~((op (e2) (e2)) = (e1))) -> (~((op (e1) (e3)) = (op (e2) (e3)))) -> ((op (e1) (e3)) = (e1)) -> False). % 15.31/15.46 do 0 intro. intros zenon_Hb7 zenon_Hbb zenon_H42 zenon_Ha3 zenon_H68 zenon_H6a zenon_H59 zenon_Hbe zenon_H22 zenon_Hde zenon_H52 zenon_H244 zenon_H11f. % 15.31/15.46 apply (zenon_or_s _ _ zenon_Hb7); [ zenon_intro zenon_Hae | zenon_intro zenon_Hb8 ]. % 15.31/15.46 apply (zenon_L592_); trivial. % 15.31/15.46 apply (zenon_or_s _ _ zenon_Hb8); [ zenon_intro zenon_Hb2 | zenon_intro zenon_Hb9 ]. % 15.31/15.46 apply (zenon_L336_); trivial. % 15.31/15.46 apply (zenon_or_s _ _ zenon_Hb9); [ zenon_intro zenon_H2a | zenon_intro zenon_Hb5 ]. % 15.31/15.46 exact (zenon_H52 zenon_H2a). % 15.31/15.46 apply (zenon_L529_); trivial. % 15.31/15.46 (* end of lemma zenon_L606_ *) % 15.31/15.46 assert (zenon_L607_ : (((op (e0) (e0)) = (e1))\/(((op (e0) (e1)) = (e1))\/(((op (e0) (e2)) = (e1))\/((op (e0) (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 (e3) (e0)) = (op (e3) (e3)))) -> (~((e2) = (e3))) -> (~((op (e0) (e0)) = (e3))) -> (((op (e0) (e0)) = (e3))\/(((op (e1) (e0)) = (e3))\/(((op (e2) (e0)) = (e3))\/((op (e3) (e0)) = (e3))))) -> (~((op (e0) (e1)) = (op (e2) (e1)))) -> (~((op (e2) (e2)) = (e1))) -> (~((op (e1) (e3)) = (op (e2) (e3)))) -> (((op (e0) (e0)) = (e2))\/(((op (e1) (e0)) = (e2))\/(((op (e2) (e0)) = (e2))\/((op (e3) (e0)) = (e2))))) -> (~((op (e1) (e2)) = (op (e2) (e2)))) -> (~((op (e1) (e1)) = (e2))) -> (((op (e1) (e0)) = (e2))\/(((op (e1) (e1)) = (e2))\/(((op (e1) (e2)) = (e2))\/((op (e1) (e3)) = (e2))))) -> (~((op (e1) (e0)) = (op (e1) (e3)))) -> (~((op (e0) (e0)) = (e1))) -> (((op (e0) (e0)) = (e1))\/(((op (e1) (e0)) = (e1))\/(((op (e2) (e0)) = (e1))\/((op (e3) (e0)) = (e1))))) -> (((op (e0) (e2)) = (e3))\/(((op (e1) (e2)) = (e3))\/(((op (e2) (e2)) = (e3))\/((op (e3) (e2)) = (e3))))) -> (~((e1) = (e3))) -> (~((e0) = (e3))) -> (~((op (e2) (e2)) = (e3))) -> ((op (e3) (e3)) = (e3)) -> (~((op (e3) (e2)) = (op (e3) (e3)))) -> (~((op (e1) (e1)) = (e0))) -> (~((op (e0) (e0)) = (op (e1) (e0)))) -> ((op (e0) (e0)) = (e0)) -> (((op (e1) (e0)) = (e0))\/(((op (e1) (e1)) = (e0))\/(((op (e1) (e2)) = (e0))\/((op (e1) (e3)) = (e0))))) -> (((op (e0) (e0)) = (e2))\/(((op (e0) (e1)) = (e2))\/(((op (e0) (e2)) = (e2))\/((op (e0) (e3)) = (e2))))) -> (~((op (e0) (e0)) = (e2))) -> (~((op (e3) (e3)) = (e0))) -> (((op (e0) (e3)) = (e2))\/(((op (e1) (e3)) = (e2))\/(((op (e2) (e3)) = (e2))\/((op (e3) (e3)) = (e2))))) -> (~((op (e0) (e1)) = (op (e0) (e3)))) -> ((op (e1) (e3)) = (e1)) -> (~((e0) = (e2))) -> (~((op (e3) (e3)) = (e2))) -> (~((e0) = (e1))) -> (((op (e0) (e3)) = (e0))\/(((op (e1) (e3)) = (e0))\/(((op (e2) (e3)) = (e0))\/((op (e3) (e3)) = (e0))))) -> (~((op (e0) (e2)) = (op (e2) (e2)))) -> ((op (e2) (e2)) = (e2)) -> (~((e1) = (e2))) -> False). % 15.31/15.46 do 0 intro. intros zenon_H44 zenon_H17a zenon_Hb7 zenon_Hbb zenon_H6a zenon_H59 zenon_Hbe zenon_Hde zenon_H52 zenon_H244 zenon_Heb zenon_H7d zenon_Hd6 zenon_H84 zenon_H1cf zenon_H45 zenon_Hf1 zenon_H175 zenon_Ha3 zenon_H4b zenon_H30 zenon_H42 zenon_H173 zenon_H145 zenon_H24c zenon_H1f zenon_H163 zenon_H8e zenon_H8f zenon_H3c zenon_H160 zenon_H1cd zenon_H11f zenon_H5e zenon_H3d zenon_H9e zenon_Hd3 zenon_H28 zenon_H35 zenon_Ha7. % 15.31/15.46 apply (zenon_or_s _ _ zenon_H44); [ zenon_intro zenon_H47 | zenon_intro zenon_H46 ]. % 15.31/15.46 exact (zenon_H45 zenon_H47). % 15.31/15.46 apply (zenon_or_s _ _ zenon_H46); [ zenon_intro zenon_H22 | zenon_intro zenon_H48 ]. % 15.31/15.46 apply (zenon_or_s _ _ zenon_Hf1); [ zenon_intro zenon_H47 | zenon_intro zenon_Hf4 ]. % 15.31/15.46 exact (zenon_H45 zenon_H47). % 15.31/15.46 apply (zenon_or_s _ _ zenon_Hf4); [ zenon_intro zenon_Hd8 | zenon_intro zenon_Hf5 ]. % 15.31/15.46 apply (zenon_L224_); trivial. % 15.31/15.46 apply (zenon_or_s _ _ zenon_Hf5); [ zenon_intro zenon_Hae | zenon_intro zenon_Hee ]. % 15.31/15.46 apply (zenon_or_s _ _ zenon_Heb); [ zenon_intro zenon_H92 | zenon_intro zenon_Hec ]. % 15.31/15.46 exact (zenon_H8f zenon_H92). % 15.31/15.46 apply (zenon_or_s _ _ zenon_Hec); [ zenon_intro zenon_H68 | zenon_intro zenon_Hed ]. % 15.31/15.46 apply (zenon_L606_); trivial. % 15.31/15.46 apply (zenon_or_s _ _ zenon_Hed); [ zenon_intro zenon_Hdd | zenon_intro zenon_He9 ]. % 15.31/15.46 apply (zenon_L161_); trivial. % 15.31/15.46 apply (zenon_or_s _ _ zenon_Hbe); [ zenon_intro zenon_H5b | zenon_intro zenon_Hbf ]. % 15.31/15.46 exact (zenon_H59 zenon_H5b). % 15.31/15.46 apply (zenon_or_s _ _ zenon_Hbf); [ zenon_intro zenon_H69 | zenon_intro zenon_Hc0 ]. % 15.31/15.46 apply (zenon_L515_); trivial. % 15.31/15.46 apply (zenon_or_s _ _ zenon_Hc0); [ zenon_intro zenon_Haf | zenon_intro zenon_Hba ]. % 15.31/15.46 apply (zenon_L39_); trivial. % 15.31/15.46 apply (zenon_L220_); trivial. % 15.31/15.46 apply (zenon_or_s _ _ zenon_Heb); [ zenon_intro zenon_H92 | zenon_intro zenon_Hec ]. % 15.31/15.46 exact (zenon_H8f zenon_H92). % 15.31/15.46 apply (zenon_or_s _ _ zenon_Hec); [ zenon_intro zenon_H68 | zenon_intro zenon_Hed ]. % 15.31/15.46 apply (zenon_L606_); trivial. % 15.31/15.46 apply (zenon_or_s _ _ zenon_Hed); [ zenon_intro zenon_Hdd | zenon_intro zenon_He9 ]. % 15.31/15.46 apply (zenon_L161_); trivial. % 15.31/15.46 apply (zenon_L122_); trivial. % 15.31/15.46 apply (zenon_or_s _ _ zenon_H48); [ zenon_intro zenon_H29 | zenon_intro zenon_H37 ]. % 15.31/15.46 apply (zenon_or_s _ _ zenon_H163); [ zenon_intro zenon_Had | zenon_intro zenon_H164 ]. % 15.31/15.46 apply (zenon_L559_); trivial. % 15.31/15.46 apply (zenon_or_s _ _ zenon_H164); [ zenon_intro zenon_H149 | zenon_intro zenon_H165 ]. % 15.31/15.46 exact (zenon_H145 zenon_H149). % 15.31/15.46 apply (zenon_or_s _ _ zenon_H165); [ zenon_intro zenon_H15d | zenon_intro zenon_Hcc ]. % 15.31/15.46 apply (zenon_L154_); trivial. % 15.31/15.46 apply (zenon_L208_); trivial. % 15.31/15.46 apply (zenon_L368_); trivial. % 15.31/15.46 (* end of lemma zenon_L607_ *) % 15.31/15.46 assert (zenon_L608_ : (((op (e0) (e0)) = (e3))\/(((op (e1) (e0)) = (e3))\/(((op (e2) (e0)) = (e3))\/((op (e3) (e0)) = (e3))))) -> (~((op (e0) (e0)) = (e3))) -> (~((e1) = (e2))) -> ((op (e1) (e3)) = (e1)) -> (~((op (e0) (e2)) = (op (e1) (e2)))) -> ((op (e0) (e2)) = (e2)) -> (~((op (e1) (e1)) = (e2))) -> (((op (e1) (e0)) = (e2))\/(((op (e1) (e1)) = (e2))\/(((op (e1) (e2)) = (e2))\/((op (e1) (e3)) = (e2))))) -> (~((e1) = (e3))) -> ((op (e2) (e0)) = (e1)) -> (~((e2) = (e3))) -> ((op (e3) (e0)) = (e2)) -> False). % 15.31/15.46 do 0 intro. intros zenon_Hbe zenon_H59 zenon_Ha7 zenon_H11f zenon_H87 zenon_H63 zenon_Hd6 zenon_H84 zenon_Ha3 zenon_Hae zenon_H6a zenon_He9. % 15.31/15.46 apply (zenon_or_s _ _ zenon_Hbe); [ zenon_intro zenon_H5b | zenon_intro zenon_Hbf ]. % 15.31/15.46 exact (zenon_H59 zenon_H5b). % 15.31/15.46 apply (zenon_or_s _ _ zenon_Hbf); [ zenon_intro zenon_H69 | zenon_intro zenon_Hc0 ]. % 15.31/15.46 apply (zenon_L216_); trivial. % 15.31/15.46 apply (zenon_or_s _ _ zenon_Hc0); [ zenon_intro zenon_Haf | zenon_intro zenon_Hba ]. % 15.31/15.46 apply (zenon_L39_); trivial. % 15.31/15.46 apply (zenon_L220_); trivial. % 15.31/15.46 (* end of lemma zenon_L608_ *) % 15.31/15.46 assert (zenon_L609_ : (((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) (e3)))) -> ((op (e3) (e3)) = (e3)) -> (((op (e0) (e0)) = (e3))\/(((op (e1) (e0)) = (e3))\/(((op (e2) (e0)) = (e3))\/((op (e3) (e0)) = (e3))))) -> (~((op (e0) (e0)) = (e3))) -> (~((e1) = (e2))) -> ((op (e1) (e3)) = (e1)) -> (~((op (e0) (e2)) = (op (e1) (e2)))) -> ((op (e0) (e2)) = (e2)) -> (~((op (e1) (e1)) = (e2))) -> (((op (e1) (e0)) = (e2))\/(((op (e1) (e1)) = (e2))\/(((op (e1) (e2)) = (e2))\/((op (e1) (e3)) = (e2))))) -> (~((e1) = (e3))) -> ((op (e2) (e0)) = (e1)) -> (~((e2) = (e3))) -> False). % 15.31/15.46 do 0 intro. intros zenon_Heb zenon_H8f zenon_Hbb zenon_H42 zenon_Hbe zenon_H59 zenon_Ha7 zenon_H11f zenon_H87 zenon_H63 zenon_Hd6 zenon_H84 zenon_Ha3 zenon_Hae zenon_H6a. % 15.31/15.46 apply (zenon_or_s _ _ zenon_Heb); [ zenon_intro zenon_H92 | zenon_intro zenon_Hec ]. % 15.31/15.46 exact (zenon_H8f zenon_H92). % 15.31/15.46 apply (zenon_or_s _ _ zenon_Hec); [ zenon_intro zenon_H68 | zenon_intro zenon_Hed ]. % 15.31/15.46 apply (zenon_L592_); trivial. % 15.31/15.46 apply (zenon_or_s _ _ zenon_Hed); [ zenon_intro zenon_Hdd | zenon_intro zenon_He9 ]. % 15.31/15.46 apply (zenon_L304_); trivial. % 15.31/15.46 apply (zenon_L608_); trivial. % 15.31/15.46 (* end of lemma zenon_L609_ *) % 15.31/15.46 assert (zenon_L610_ : (~((op (e0) (e0)) = (op (e0) (e1)))) -> ((op (e0) (e0)) = (e0)) -> ((op (e0) (e1)) = (e0)) -> False). % 15.31/15.46 do 0 intro. intros zenon_H25a zenon_H1f zenon_H49. % 15.31/15.46 cut (((op (e0) (e0)) = (e0)) = ((op (e0) (e0)) = (op (e0) (e1)))). % 15.31/15.46 intro zenon_D_pnotp. % 15.31/15.46 apply zenon_H25a. % 15.31/15.46 rewrite <- zenon_D_pnotp. % 15.31/15.46 exact zenon_H1f. % 15.31/15.46 cut (((e0) = (op (e0) (e1)))); [idtac | apply NNPP; zenon_intro zenon_H200]. % 15.31/15.46 cut (((op (e0) (e0)) = (op (e0) (e0)))); [idtac | apply NNPP; zenon_intro zenon_H24e]. % 15.31/15.46 congruence. % 15.31/15.46 apply zenon_H24e. apply refl_equal. % 15.31/15.46 apply zenon_H200. apply sym_equal. exact zenon_H49. % 15.31/15.46 (* end of lemma zenon_L610_ *) % 15.31/15.46 assert (zenon_L611_ : (((op (e0) (e1)) = (e3))\/(((op (e1) (e1)) = (e3))\/(((op (e2) (e1)) = (e3))\/((op (e3) (e1)) = (e3))))) -> (~((e1) = (e3))) -> ((op (e0) (e1)) = (e1)) -> (~((op (e2) (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) = (e2))) -> (((op (e0) (e3)) = (e0))\/(((op (e1) (e3)) = (e0))\/(((op (e2) (e3)) = (e0))\/((op (e3) (e3)) = (e0))))) -> ((op (e0) (e3)) = (e2)) -> ((op (e1) (e3)) = (e1)) -> (~((e0) = (e1))) -> (~((op (e2) (e0)) = (op (e2) (e3)))) -> (~((op (e3) (e3)) = (e0))) -> (((op (e2) (e0)) = (e0))\/(((op (e2) (e1)) = (e0))\/(((op (e2) (e2)) = (e0))\/((op (e2) (e3)) = (e0))))) -> (~((e2) = (e3))) -> ((op (e2) (e1)) = (e2)) -> (~((e0) = (e3))) -> ((op (e3) (e1)) = (e0)) -> False). % 15.31/15.46 do 0 intro. intros zenon_H199 zenon_Ha3 zenon_H22 zenon_H30 zenon_H2f zenon_H2e zenon_H2d zenon_H5e zenon_Hd3 zenon_H81 zenon_H11f zenon_H9e zenon_Hce zenon_H3c zenon_H1f5 zenon_H6a zenon_H156 zenon_H4b zenon_H142. % 15.31/15.46 apply (zenon_or_s _ _ zenon_H199); [ zenon_intro zenon_H4a | zenon_intro zenon_H19a ]. % 15.31/15.46 apply (zenon_L59_); trivial. % 15.31/15.46 apply (zenon_or_s _ _ zenon_H19a); [ zenon_intro zenon_H96 | zenon_intro zenon_H19b ]. % 15.31/15.46 apply (zenon_L376_); trivial. % 15.31/15.46 apply (zenon_or_s _ _ zenon_H19b); [ zenon_intro zenon_Hdf | zenon_intro zenon_H10a ]. % 15.31/15.46 apply (zenon_L183_); trivial. % 15.31/15.46 apply (zenon_L126_); trivial. % 15.31/15.46 (* end of lemma zenon_L611_ *) % 15.31/15.46 assert (zenon_L612_ : (((op (e0) (e1)) = (e0))\/(((op (e1) (e1)) = (e0))\/(((op (e2) (e1)) = (e0))\/((op (e3) (e1)) = (e0))))) -> ((op (e0) (e0)) = (e0)) -> (~((op (e0) (e0)) = (op (e0) (e1)))) -> (~((op (e1) (e1)) = (e0))) -> (((op (e0) (e1)) = (e3))\/(((op (e1) (e1)) = (e3))\/(((op (e2) (e1)) = (e3))\/((op (e3) (e1)) = (e3))))) -> (~((e1) = (e3))) -> ((op (e0) (e1)) = (e1)) -> (~((op (e2) (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) = (e2))) -> (((op (e0) (e3)) = (e0))\/(((op (e1) (e3)) = (e0))\/(((op (e2) (e3)) = (e0))\/((op (e3) (e3)) = (e0))))) -> ((op (e0) (e3)) = (e2)) -> ((op (e1) (e3)) = (e1)) -> (~((e0) = (e1))) -> (~((op (e2) (e0)) = (op (e2) (e3)))) -> (~((op (e3) (e3)) = (e0))) -> (((op (e2) (e0)) = (e0))\/(((op (e2) (e1)) = (e0))\/(((op (e2) (e2)) = (e0))\/((op (e2) (e3)) = (e0))))) -> (~((e2) = (e3))) -> ((op (e2) (e1)) = (e2)) -> (~((e0) = (e3))) -> False). % 15.31/15.46 do 0 intro. intros zenon_H144 zenon_H1f zenon_H25a zenon_H145 zenon_H199 zenon_Ha3 zenon_H22 zenon_H30 zenon_H2f zenon_H2e zenon_H2d zenon_H5e zenon_Hd3 zenon_H81 zenon_H11f zenon_H9e zenon_Hce zenon_H3c zenon_H1f5 zenon_H6a zenon_H156 zenon_H4b. % 15.31/15.46 apply (zenon_or_s _ _ zenon_H144); [ zenon_intro zenon_H49 | zenon_intro zenon_H147 ]. % 15.31/15.46 apply (zenon_L610_); trivial. % 15.31/15.46 apply (zenon_or_s _ _ zenon_H147); [ zenon_intro zenon_H149 | zenon_intro zenon_H148 ]. % 15.31/15.46 exact (zenon_H145 zenon_H149). % 15.31/15.46 apply (zenon_or_s _ _ zenon_H148); [ zenon_intro zenon_H14a | zenon_intro zenon_H142 ]. % 15.31/15.46 apply (zenon_L351_); trivial. % 15.31/15.46 apply (zenon_L611_); trivial. % 15.31/15.46 (* end of lemma zenon_L612_ *) % 15.31/15.46 assert (zenon_L613_ : (((op (e2) (e0)) = (e1))\/(((op (e2) (e1)) = (e1))\/(((op (e2) (e2)) = (e1))\/((op (e2) (e3)) = (e1))))) -> (~((e1) = (e3))) -> ((op (e2) (e0)) = (e3)) -> ((op (e2) (e1)) = (e2)) -> (~((e1) = (e2))) -> ((op (e1) (e1)) = (e3)) -> ((op (e2) (e3)) = (e0)) -> (~((op (e1) (e3)) = (op (e2) (e3)))) -> ((op (e1) (e3)) = (e1)) -> False). % 15.31/15.46 do 0 intro. intros zenon_Hb7 zenon_Ha3 zenon_Haf zenon_H156 zenon_Ha7 zenon_H96 zenon_Hd0 zenon_H244 zenon_H11f. % 15.31/15.46 apply (zenon_or_s _ _ zenon_Hb7); [ zenon_intro zenon_Hae | zenon_intro zenon_Hb8 ]. % 15.31/15.46 apply (zenon_L39_); trivial. % 15.31/15.46 apply (zenon_or_s _ _ zenon_Hb8); [ zenon_intro zenon_Hb2 | zenon_intro zenon_Hb9 ]. % 15.31/15.46 apply (zenon_L372_); trivial. % 15.31/15.46 apply (zenon_or_s _ _ zenon_Hb9); [ zenon_intro zenon_H2a | zenon_intro zenon_Hb5 ]. % 15.31/15.46 apply (zenon_L374_); trivial. % 15.31/15.46 apply (zenon_L529_); trivial. % 15.31/15.46 (* end of lemma zenon_L613_ *) % 15.31/15.46 assert (zenon_L614_ : (((op (e2) (e0)) = (e0))\/(((op (e2) (e1)) = (e0))\/(((op (e2) (e2)) = (e0))\/((op (e2) (e3)) = (e0))))) -> ((op (e0) (e0)) = (e0)) -> (~((op (e0) (e0)) = (op (e2) (e0)))) -> (~((e0) = (e2))) -> (~((op (e2) (e2)) = (e0))) -> (((op (e2) (e0)) = (e1))\/(((op (e2) (e1)) = (e1))\/(((op (e2) (e2)) = (e1))\/((op (e2) (e3)) = (e1))))) -> (~((e1) = (e3))) -> ((op (e2) (e0)) = (e3)) -> ((op (e2) (e1)) = (e2)) -> (~((e1) = (e2))) -> ((op (e1) (e1)) = (e3)) -> (~((op (e1) (e3)) = (op (e2) (e3)))) -> ((op (e1) (e3)) = (e1)) -> False). % 15.31/15.46 do 0 intro. intros zenon_H1f5 zenon_H1f zenon_H258 zenon_H5e zenon_H2e zenon_Hb7 zenon_Ha3 zenon_Haf zenon_H156 zenon_Ha7 zenon_H96 zenon_H244 zenon_H11f. % 15.31/15.46 apply (zenon_or_s _ _ zenon_H1f5); [ zenon_intro zenon_Hcf | zenon_intro zenon_H1f9 ]. % 15.31/15.46 apply (zenon_L598_); trivial. % 15.31/15.46 apply (zenon_or_s _ _ zenon_H1f9); [ zenon_intro zenon_H14a | zenon_intro zenon_H1fa ]. % 15.31/15.46 apply (zenon_L351_); trivial. % 15.31/15.46 apply (zenon_or_s _ _ zenon_H1fa); [ zenon_intro zenon_H32 | zenon_intro zenon_Hd0 ]. % 15.31/15.46 exact (zenon_H2e zenon_H32). % 15.31/15.46 apply (zenon_L613_); trivial. % 15.31/15.46 (* end of lemma zenon_L614_ *) % 15.31/15.46 assert (zenon_L615_ : (((op (e0) (e2)) = (e0))\/(((op (e0) (e2)) = (e1))\/(((op (e0) (e2)) = (e2))\/((op (e0) (e2)) = (e3))))) -> ((op (e1) (e2)) = (e0)) -> ((op (e2) (e2)) = (e1)) -> (~((op (e0) (e2)) = (op (e2) (e2)))) -> ((op (e3) (e2)) = (e2)) -> (~((op (e0) (e2)) = (op (e3) (e2)))) -> (~((op (e0) (e2)) = (op (e1) (e2)))) -> ((op (e1) (e2)) = (e3)) -> False). % 15.31/15.46 do 0 intro. intros zenon_H251 zenon_H15d zenon_H2a zenon_H28 zenon_H1dd zenon_H140 zenon_H87 zenon_H88. % 15.31/15.46 apply (zenon_or_s _ _ zenon_H251); [ zenon_intro zenon_Hab | zenon_intro zenon_H252 ]. % 15.31/15.46 apply (zenon_L136_); trivial. % 15.31/15.46 apply (zenon_or_s _ _ zenon_H252); [ zenon_intro zenon_H29 | zenon_intro zenon_H253 ]. % 15.31/15.46 apply (zenon_L4_); trivial. % 15.31/15.46 apply (zenon_or_s _ _ zenon_H253); [ zenon_intro zenon_H63 | zenon_intro zenon_H50 ]. % 15.31/15.46 apply (zenon_L253_); trivial. % 15.31/15.46 apply (zenon_L24_); trivial. % 15.31/15.46 (* end of lemma zenon_L615_ *) % 15.31/15.46 assert (zenon_L616_ : (((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 (e0) (e3)) = (op (e3) (e3)))) -> (~((op (e0) (e3)) = (op (e1) (e3)))) -> (~((op (e0) (e3)) = (op (e2) (e3)))) -> ((op (e2) (e3)) = (e1)) -> (~((op (e0) (e0)) = (op (e0) (e3)))) -> ((op (e0) (e0)) = (e0)) -> (((op (e0) (e3)) = (e0))\/(((op (e0) (e3)) = (e1))\/(((op (e0) (e3)) = (e2))\/((op (e0) (e3)) = (e3))))) -> ((op (e3) (e3)) = (e3)) -> (~((op (e1) (e3)) = (op (e3) (e3)))) -> False). % 15.31/15.46 do 0 intro. intros zenon_H25b zenon_Hd0 zenon_H244 zenon_H36 zenon_H80 zenon_Hb4 zenon_Hb5 zenon_H24f zenon_H1f zenon_H254 zenon_H42 zenon_H8b. % 15.31/15.46 apply (zenon_or_s _ _ zenon_H25b); [ zenon_intro zenon_Hcc | zenon_intro zenon_H25c ]. % 15.31/15.46 apply (zenon_L599_); trivial. % 15.31/15.46 apply (zenon_or_s _ _ zenon_H25c); [ zenon_intro zenon_H11f | zenon_intro zenon_H25d ]. % 15.31/15.46 apply (zenon_L529_); trivial. % 15.31/15.46 apply (zenon_or_s _ _ zenon_H25d); [ zenon_intro zenon_H82 | zenon_intro zenon_H8a ]. % 15.31/15.46 apply (zenon_L571_); trivial. % 15.31/15.46 apply (zenon_L25_); trivial. % 15.31/15.46 (* end of lemma zenon_L616_ *) % 15.31/15.46 assert (zenon_L617_ : (((op (e0) (e0)) = (e2))\/(((op (e1) (e0)) = (e2))\/(((op (e2) (e0)) = (e2))\/((op (e3) (e0)) = (e2))))) -> (~((op (e0) (e0)) = (e2))) -> (~((e1) = (e3))) -> (((op (e1) (e0)) = (e0))\/(((op (e1) (e1)) = (e0))\/(((op (e1) (e2)) = (e0))\/((op (e1) (e3)) = (e0))))) -> (~((op (e0) (e0)) = (op (e1) (e0)))) -> (~((op (e1) (e1)) = (e0))) -> (~((op (e1) (e3)) = (op (e3) (e3)))) -> ((op (e3) (e3)) = (e3)) -> (((op (e2) (e0)) = (e0))\/(((op (e2) (e1)) = (e0))\/(((op (e2) (e2)) = (e0))\/((op (e2) (e3)) = (e0))))) -> (~((op (e0) (e0)) = (op (e2) (e0)))) -> (~((e0) = (e2))) -> (~((op (e2) (e2)) = (e0))) -> (((op (e2) (e0)) = (e1))\/(((op (e2) (e1)) = (e1))\/(((op (e2) (e2)) = (e1))\/((op (e2) (e3)) = (e1))))) -> (~((op (e3) (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 (e3) (e2)))) -> (~((op (e0) (e2)) = (op (e1) (e2)))) -> (~((op (e2) (e1)) = (op (e3) (e1)))) -> (((op (e3) (e0)) = (e2))\/(((op (e3) (e1)) = (e2))\/(((op (e3) (e2)) = (e2))\/((op (e3) (e3)) = (e2))))) -> (((op (e1) (e3)) = (e0))\/(((op (e1) (e3)) = (e1))\/(((op (e1) (e3)) = (e2))\/((op (e1) (e3)) = (e3))))) -> (~((op (e1) (e3)) = (op (e2) (e3)))) -> (~((op (e0) (e3)) = (op (e3) (e3)))) -> (~((op (e0) (e3)) = (op (e1) (e3)))) -> (~((op (e0) (e3)) = (op (e2) (e3)))) -> (~((op (e0) (e0)) = (op (e0) (e3)))) -> ((op (e0) (e0)) = (e0)) -> (((op (e0) (e3)) = (e0))\/(((op (e0) (e3)) = (e1))\/(((op (e0) (e3)) = (e2))\/((op (e0) (e3)) = (e3))))) -> (~((e2) = (e3))) -> (((op (e1) (e0)) = (e3))\/(((op (e1) (e1)) = (e3))\/(((op (e1) (e2)) = (e3))\/((op (e1) (e3)) = (e3))))) -> (~((e0) = (e1))) -> ((op (e1) (e3)) = (e1)) -> (~((op (e0) (e0)) = (e3))) -> (((op (e0) (e0)) = (e3))\/(((op (e1) (e0)) = (e3))\/(((op (e2) (e0)) = (e3))\/((op (e3) (e0)) = (e3))))) -> ((op (e2) (e1)) = (e2)) -> (~((op (e2) (e0)) = (op (e2) (e1)))) -> ((op (e3) (e0)) = (e1)) -> (~((e1) = (e2))) -> False). % 15.31/15.46 do 0 intro. intros zenon_Heb zenon_H8f zenon_Ha3 zenon_H163 zenon_H24c zenon_H145 zenon_H8b zenon_H42 zenon_H1f5 zenon_H258 zenon_H5e zenon_H2e zenon_Hb7 zenon_H3d zenon_H251 zenon_H28 zenon_H140 zenon_H87 zenon_H13c zenon_H1df zenon_H25b zenon_H244 zenon_H36 zenon_H80 zenon_Hb4 zenon_H24f zenon_H1f zenon_H254 zenon_H6a zenon_H90 zenon_H9e zenon_H11f zenon_H59 zenon_Hbe zenon_H156 zenon_H154 zenon_Hee zenon_Ha7. % 15.31/15.46 apply (zenon_or_s _ _ zenon_Heb); [ zenon_intro zenon_H92 | zenon_intro zenon_Hec ]. % 15.31/15.46 exact (zenon_H8f zenon_H92). % 15.31/15.46 apply (zenon_or_s _ _ zenon_Hec); [ zenon_intro zenon_H68 | zenon_intro zenon_Hed ]. % 15.31/15.46 apply (zenon_or_s _ _ zenon_Hbe); [ zenon_intro zenon_H5b | zenon_intro zenon_Hbf ]. % 15.31/15.46 exact (zenon_H59 zenon_H5b). % 15.31/15.46 apply (zenon_or_s _ _ zenon_Hbf); [ zenon_intro zenon_H69 | zenon_intro zenon_Hc0 ]. % 15.31/15.46 apply (zenon_L17_); trivial. % 15.31/15.46 apply (zenon_or_s _ _ zenon_Hc0); [ zenon_intro zenon_Haf | zenon_intro zenon_Hba ]. % 15.31/15.46 apply (zenon_or_s _ _ zenon_H163); [ zenon_intro zenon_Had | zenon_intro zenon_H164 ]. % 15.31/15.46 apply (zenon_L559_); trivial. % 15.31/15.46 apply (zenon_or_s _ _ zenon_H164); [ zenon_intro zenon_H149 | zenon_intro zenon_H165 ]. % 15.31/15.46 exact (zenon_H145 zenon_H149). % 15.31/15.46 apply (zenon_or_s _ _ zenon_H165); [ zenon_intro zenon_H15d | zenon_intro zenon_Hcc ]. % 15.31/15.46 apply (zenon_or_s _ _ zenon_H90); [ zenon_intro zenon_H69 | zenon_intro zenon_H94 ]. % 15.31/15.46 apply (zenon_L17_); trivial. % 15.31/15.46 apply (zenon_or_s _ _ zenon_H94); [ zenon_intro zenon_H96 | zenon_intro zenon_H95 ]. % 15.31/15.46 apply (zenon_L614_); trivial. % 15.31/15.46 apply (zenon_or_s _ _ zenon_H95); [ zenon_intro zenon_H88 | zenon_intro zenon_H8a ]. % 15.31/15.46 apply (zenon_or_s _ _ zenon_H1f5); [ zenon_intro zenon_Hcf | zenon_intro zenon_H1f9 ]. % 15.31/15.46 apply (zenon_L598_); trivial. % 15.31/15.46 apply (zenon_or_s _ _ zenon_H1f9); [ zenon_intro zenon_H14a | zenon_intro zenon_H1fa ]. % 15.31/15.46 apply (zenon_L351_); trivial. % 15.31/15.46 apply (zenon_or_s _ _ zenon_H1fa); [ zenon_intro zenon_H32 | zenon_intro zenon_Hd0 ]. % 15.31/15.46 exact (zenon_H2e zenon_H32). % 15.31/15.46 apply (zenon_or_s _ _ zenon_Hb7); [ zenon_intro zenon_Hae | zenon_intro zenon_Hb8 ]. % 15.31/15.46 apply (zenon_L39_); trivial. % 15.31/15.46 apply (zenon_or_s _ _ zenon_Hb8); [ zenon_intro zenon_Hb2 | zenon_intro zenon_Hb9 ]. % 15.31/15.46 apply (zenon_L372_); trivial. % 15.31/15.46 apply (zenon_or_s _ _ zenon_Hb9); [ zenon_intro zenon_H2a | zenon_intro zenon_Hb5 ]. % 15.31/15.46 apply (zenon_or_s _ _ zenon_H1df); [ zenon_intro zenon_He9 | zenon_intro zenon_H1e0 ]. % 15.31/15.46 apply (zenon_L122_); trivial. % 15.31/15.46 apply (zenon_or_s _ _ zenon_H1e0); [ zenon_intro zenon_H16a | zenon_intro zenon_H1e1 ]. % 15.31/15.46 apply (zenon_L252_); trivial. % 15.31/15.46 apply (zenon_or_s _ _ zenon_H1e1); [ zenon_intro zenon_H1dd | zenon_intro zenon_H43 ]. % 15.31/15.46 apply (zenon_L615_); trivial. % 15.31/15.46 exact (zenon_H3d zenon_H43). % 15.31/15.46 apply (zenon_L616_); trivial. % 15.31/15.46 apply (zenon_L25_); trivial. % 15.31/15.46 apply (zenon_L208_); trivial. % 15.31/15.46 apply (zenon_L79_); trivial. % 15.31/15.46 apply (zenon_or_s _ _ zenon_Hed); [ zenon_intro zenon_Hdd | zenon_intro zenon_He9 ]. % 15.31/15.46 apply (zenon_L284_); trivial. % 15.31/15.46 apply (zenon_L122_); trivial. % 15.31/15.46 (* end of lemma zenon_L617_ *) % 15.31/15.46 assert (zenon_L618_ : (((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 (e2) (e1)) = (e2)) -> (~((e1) = (e2))) -> (~((op (e3) (e0)) = (op (e3) (e1)))) -> ((op (e3) (e0)) = (e1)) -> False). % 15.31/15.46 do 0 intro. intros zenon_H228 zenon_H1cd zenon_H37 zenon_H1b4 zenon_H156 zenon_Ha7 zenon_H109 zenon_Hee. % 15.31/15.46 apply (zenon_or_s _ _ zenon_H228); [ zenon_intro zenon_H22 | zenon_intro zenon_H229 ]. % 15.31/15.46 apply (zenon_L223_); trivial. % 15.31/15.46 apply (zenon_or_s _ _ zenon_H229); [ zenon_intro zenon_H21 | zenon_intro zenon_H22a ]. % 15.31/15.46 exact (zenon_H1b4 zenon_H21). % 15.31/15.46 apply (zenon_or_s _ _ zenon_H22a); [ zenon_intro zenon_Hb2 | zenon_intro zenon_H13e ]. % 15.31/15.46 apply (zenon_L372_); trivial. % 15.31/15.46 apply (zenon_L145_); trivial. % 15.31/15.46 (* end of lemma zenon_L618_ *) % 15.31/15.46 assert (zenon_L619_ : (~((op (e2) (e0)) = (op (e2) (e1)))) -> (~((e0) = (e1))) -> (((op (e1) (e0)) = (e3))\/(((op (e1) (e1)) = (e3))\/(((op (e1) (e2)) = (e3))\/((op (e1) (e3)) = (e3))))) -> (((op (e0) (e3)) = (e0))\/(((op (e0) (e3)) = (e1))\/(((op (e0) (e3)) = (e2))\/((op (e0) (e3)) = (e3))))) -> ((op (e0) (e0)) = (e0)) -> (~((op (e0) (e0)) = (op (e0) (e3)))) -> (~((op (e0) (e3)) = (op (e2) (e3)))) -> (~((op (e0) (e3)) = (op (e1) (e3)))) -> (~((op (e0) (e3)) = (op (e3) (e3)))) -> (~((op (e1) (e3)) = (op (e2) (e3)))) -> (((op (e1) (e3)) = (e0))\/(((op (e1) (e3)) = (e1))\/(((op (e1) (e3)) = (e2))\/((op (e1) (e3)) = (e3))))) -> (((op (e3) (e0)) = (e2))\/(((op (e3) (e1)) = (e2))\/(((op (e3) (e2)) = (e2))\/((op (e3) (e3)) = (e2))))) -> (~((op (e2) (e1)) = (op (e3) (e1)))) -> (~((op (e0) (e2)) = (op (e3) (e2)))) -> (((op (e0) (e2)) = (e0))\/(((op (e0) (e2)) = (e1))\/(((op (e0) (e2)) = (e2))\/((op (e0) (e2)) = (e3))))) -> (~((op (e3) (e3)) = (e2))) -> (((op (e2) (e0)) = (e1))\/(((op (e2) (e1)) = (e1))\/(((op (e2) (e2)) = (e1))\/((op (e2) (e3)) = (e1))))) -> (~((e0) = (e2))) -> (~((op (e0) (e0)) = (op (e2) (e0)))) -> (((op (e2) (e0)) = (e0))\/(((op (e2) (e1)) = (e0))\/(((op (e2) (e2)) = (e0))\/((op (e2) (e3)) = (e0))))) -> (~((op (e1) (e3)) = (op (e3) (e3)))) -> (~((op (e1) (e1)) = (e0))) -> (~((op (e0) (e0)) = (op (e1) (e0)))) -> (((op (e1) (e0)) = (e0))\/(((op (e1) (e1)) = (e0))\/(((op (e1) (e2)) = (e0))\/((op (e1) (e3)) = (e0))))) -> (((op (e0) (e1)) = (e0))\/(((op (e1) (e1)) = (e0))\/(((op (e2) (e1)) = (e0))\/((op (e3) (e1)) = (e0))))) -> (~((op (e0) (e0)) = (op (e0) (e1)))) -> (((op (e0) (e1)) = (e3))\/(((op (e1) (e1)) = (e3))\/(((op (e2) (e1)) = (e3))\/((op (e3) (e1)) = (e3))))) -> (((op (e0) (e3)) = (e0))\/(((op (e1) (e3)) = (e0))\/(((op (e2) (e3)) = (e0))\/((op (e3) (e3)) = (e0))))) -> (~((op (e2) (e0)) = (op (e2) (e3)))) -> (~((op (e3) (e3)) = (e0))) -> (~((e0) = (e3))) -> ((~((op (e1) (e1)) = (e3)))\/((op (e1) (e3)) = (e1))) -> ((~((op (e2) (e2)) = (e1)))\/((op (e2) (e1)) = (e2))) -> ((~((op (e3) (e3)) = (e1)))\/((op (e3) (e1)) = (e3))) -> (~((op (e3) (e1)) = (op (e3) (e3)))) -> (((op (e0) (e3)) = (e1))\/(((op (e1) (e3)) = (e1))\/(((op (e2) (e3)) = (e1))\/((op (e3) (e3)) = (e1))))) -> (((op (e3) (e0)) = (e1))\/(((op (e3) (e1)) = (e1))\/(((op (e3) (e2)) = (e1))\/((op (e3) (e3)) = (e1))))) -> (((op (e0) (e1)) = (e2))\/(((op (e1) (e1)) = (e2))\/(((op (e2) (e1)) = (e2))\/((op (e3) (e1)) = (e2))))) -> (~((op (e1) (e0)) = (op (e3) (e0)))) -> ((~((op (e2) (e2)) = (e3)))\/((op (e2) (e3)) = (e2))) -> (~((op (e2) (e1)) = (op (e2) (e3)))) -> (~((op (e2) (e1)) = (op (e2) (e2)))) -> ((~((op (e2) (e2)) = (e2)))\/((op (e2) (e2)) = (e2))) -> (((op (e0) (e0)) = (e3))\/(((op (e0) (e1)) = (e3))\/(((op (e0) (e2)) = (e3))\/((op (e0) (e3)) = (e3))))) -> (((op (e0) (e0)) = (e1))\/(((op (e0) (e1)) = (e1))\/(((op (e0) (e2)) = (e1))\/((op (e0) (e3)) = (e1))))) -> ((~((op (e3) (e3)) = (e0)))\/((op (e3) (e0)) = (e3))) -> (((op (e1) (e1)) = (e0))\/(((op (e1) (e1)) = (e1))\/(((op (e1) (e1)) = (e2))\/((op (e1) (e1)) = (e3))))) -> (~((op (e0) (e1)) = (op (e3) (e1)))) -> (~((op (e1) (e2)) = (op (e2) (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)) = (op (e0) (e3)))) -> ((~((op (e2) (e2)) = (e0)))\/((op (e2) (e0)) = (e2))) -> (~((op (e2) (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 (e0) (e0)) = (e1))\/(((op (e1) (e0)) = (e1))\/(((op (e2) (e0)) = (e1))\/((op (e3) (e0)) = (e1))))) -> (~((op (e0) (e0)) = (e1))) -> (~((op (e1) (e0)) = (op (e1) (e3)))) -> (((op (e0) (e0)) = (e2))\/(((op (e1) (e0)) = (e2))\/(((op (e2) (e0)) = (e2))\/((op (e3) (e0)) = (e2))))) -> (~((op (e0) (e0)) = (e2))) -> (~((op (e3) (e0)) = (op (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)) = (e3))) -> ((op (e1) (e3)) = (e1)) -> (~((op (e0) (e2)) = (op (e1) (e2)))) -> (~((op (e1) (e1)) = (e2))) -> (((op (e1) (e0)) = (e2))\/(((op (e1) (e1)) = (e2))\/(((op (e1) (e2)) = (e2))\/((op (e1) (e3)) = (e2))))) -> (~((e1) = (e3))) -> (~((e2) = (e3))) -> (~((op (e0) (e1)) = (op (e2) (e1)))) -> (((op (e0) (e0)) = (e2))\/(((op (e0) (e1)) = (e2))\/(((op (e0) (e2)) = (e2))\/((op (e0) (e3)) = (e2))))) -> (((op (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) (e1)) = (e2)) -> (~((e1) = (e2))) -> (~((op (e3) (e0)) = (op (e3) (e1)))) -> False). % 15.31/15.46 do 0 intro. intros zenon_H154 zenon_H9e zenon_H90 zenon_H254 zenon_H1f zenon_H24f zenon_Hb4 zenon_H80 zenon_H36 zenon_H244 zenon_H25b zenon_H1df zenon_H13c zenon_H140 zenon_H251 zenon_H3d zenon_Hb7 zenon_H5e zenon_H258 zenon_H1f5 zenon_H8b zenon_H145 zenon_H24c zenon_H163 zenon_H144 zenon_H25a zenon_H199 zenon_Hd3 zenon_Hce zenon_H3c zenon_H4b zenon_H1d2 zenon_H1e3 zenon_H10c zenon_H12d zenon_H121 zenon_H146 zenon_H1a2 zenon_H22e zenon_H1c3 zenon_H1e2 zenon_H157 zenon_Haa zenon_H58 zenon_H44 zenon_H10f zenon_H1b3 zenon_H138 zenon_H7d zenon_H11b zenon_H250 zenon_Hc9 zenon_H1d4 zenon_H30 zenon_H2f zenon_H28 zenon_H2e zenon_H2d zenon_Hf1 zenon_H45 zenon_H1cf zenon_Heb zenon_H8f zenon_Hbb zenon_H42 zenon_Hbe zenon_H59 zenon_H11f zenon_H87 zenon_Hd6 zenon_H84 zenon_Ha3 zenon_H6a zenon_Hde zenon_H8e zenon_H228 zenon_H1cd zenon_H1b4 zenon_H156 zenon_Ha7 zenon_H109. % 15.31/15.46 apply (zenon_or_s _ _ zenon_H44); [ zenon_intro zenon_H47 | zenon_intro zenon_H46 ]. % 15.31/15.46 exact (zenon_H45 zenon_H47). % 15.31/15.46 apply (zenon_or_s _ _ zenon_H46); [ zenon_intro zenon_H22 | zenon_intro zenon_H48 ]. % 15.31/15.46 apply (zenon_or_s _ _ zenon_Hf1); [ zenon_intro zenon_H47 | zenon_intro zenon_Hf4 ]. % 15.31/15.46 exact (zenon_H45 zenon_H47). % 15.31/15.46 apply (zenon_or_s _ _ zenon_Hf4); [ zenon_intro zenon_Hd8 | zenon_intro zenon_Hf5 ]. % 15.31/15.46 apply (zenon_L576_); trivial. % 15.31/15.46 apply (zenon_or_s _ _ zenon_Hf5); [ zenon_intro zenon_Hae | zenon_intro zenon_Hee ]. % 15.31/15.46 apply (zenon_or_s _ _ zenon_H8e); [ zenon_intro zenon_H92 | zenon_intro zenon_H91 ]. % 15.31/15.46 exact (zenon_H8f zenon_H92). % 15.31/15.46 apply (zenon_or_s _ _ zenon_H91); [ zenon_intro zenon_H5d | zenon_intro zenon_H93 ]. % 15.31/15.46 apply (zenon_L251_); trivial. % 15.31/15.46 apply (zenon_or_s _ _ zenon_H93); [ zenon_intro zenon_H63 | zenon_intro zenon_H81 ]. % 15.31/15.46 apply (zenon_L609_); trivial. % 15.31/15.46 apply (zenon_L612_); trivial. % 15.31/15.46 apply (zenon_L617_); trivial. % 15.31/15.46 apply (zenon_or_s _ _ zenon_H48); [ zenon_intro zenon_H29 | zenon_intro zenon_H37 ]. % 15.31/15.46 apply (zenon_L5_); trivial. % 15.31/15.46 apply (zenon_or_s _ _ zenon_Hf1); [ zenon_intro zenon_H47 | zenon_intro zenon_Hf4 ]. % 15.31/15.46 exact (zenon_H45 zenon_H47). % 15.31/15.46 apply (zenon_or_s _ _ zenon_Hf4); [ zenon_intro zenon_Hd8 | zenon_intro zenon_Hf5 ]. % 15.31/15.46 apply (zenon_L224_); trivial. % 15.31/15.46 apply (zenon_or_s _ _ zenon_Hf5); [ zenon_intro zenon_Hae | zenon_intro zenon_Hee ]. % 15.31/15.46 apply (zenon_or_s _ _ zenon_H8e); [ zenon_intro zenon_H92 | zenon_intro zenon_H91 ]. % 15.31/15.46 exact (zenon_H8f zenon_H92). % 15.31/15.46 apply (zenon_or_s _ _ zenon_H91); [ zenon_intro zenon_H5d | zenon_intro zenon_H93 ]. % 15.31/15.46 apply (zenon_L251_); trivial. % 15.31/15.46 apply (zenon_or_s _ _ zenon_H93); [ zenon_intro zenon_H63 | zenon_intro zenon_H81 ]. % 15.31/15.46 apply (zenon_L609_); trivial. % 15.31/15.46 apply (zenon_L33_); trivial. % 15.31/15.46 apply (zenon_L618_); trivial. % 15.31/15.46 (* end of lemma zenon_L619_ *) % 15.31/15.46 assert (zenon_L620_ : (((op (e1) (e3)) = (e0))\/(((op (e1) (e3)) = (e1))\/(((op (e1) (e3)) = (e2))\/((op (e1) (e3)) = (e3))))) -> (~((op (e2) (e1)) = (op (e3) (e1)))) -> (((op (e3) (e0)) = (e2))\/(((op (e3) (e1)) = (e2))\/(((op (e3) (e2)) = (e2))\/((op (e3) (e3)) = (e2))))) -> (~((op (e0) (e0)) = (op (e2) (e0)))) -> (((op (e0) (e1)) = (e0))\/(((op (e1) (e1)) = (e0))\/(((op (e2) (e1)) = (e0))\/((op (e3) (e1)) = (e0))))) -> (((op (e2) (e0)) = (e0))\/(((op (e2) (e1)) = (e0))\/(((op (e2) (e2)) = (e0))\/((op (e2) (e3)) = (e0))))) -> (~((op (e2) (e2)) = (e0))) -> (~((op (e2) (e0)) = (op (e2) (e3)))) -> (((op (e0) (e1)) = (e3))\/(((op (e1) (e1)) = (e3))\/(((op (e2) (e1)) = (e3))\/((op (e3) (e1)) = (e3))))) -> (~((op (e0) (e0)) = (op (e0) (e1)))) -> ((~((op (e2) (e2)) = (e0)))\/((op (e2) (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 (e0) (e0)) = (op (e0) (e2)))) -> (((op (e0) (e2)) = (e1))\/(((op (e1) (e2)) = (e1))\/(((op (e2) (e2)) = (e1))\/((op (e3) (e2)) = (e1))))) -> (((op (e0) (e3)) = (e0))\/(((op (e0) (e3)) = (e1))\/(((op (e0) (e3)) = (e2))\/((op (e0) (e3)) = (e3))))) -> (~((op (e0) (e3)) = (op (e1) (e3)))) -> (~((op (e0) (e3)) = (op (e2) (e3)))) -> (~((op (e0) (e1)) = (op (e3) (e1)))) -> (~((op (e1) (e1)) = (e1))) -> (((op (e1) (e1)) = (e0))\/(((op (e1) (e1)) = (e1))\/(((op (e1) (e1)) = (e2))\/((op (e1) (e1)) = (e3))))) -> (((op (e0) (e0)) = (e3))\/(((op (e0) (e1)) = (e3))\/(((op (e0) (e2)) = (e3))\/((op (e0) (e3)) = (e3))))) -> (~((op (e0) (e3)) = (op (e3) (e3)))) -> (~((op (e0) (e2)) = (op (e1) (e2)))) -> (~((op (e1) (e3)) = (op (e3) (e3)))) -> (((op (e1) (e0)) = (e3))\/(((op (e1) (e1)) = (e3))\/(((op (e1) (e2)) = (e3))\/((op (e1) (e3)) = (e3))))) -> (~((op (e2) (e1)) = (op (e2) (e2)))) -> (~((op (e2) (e1)) = (op (e2) (e3)))) -> (~((op (e1) (e0)) = (op (e3) (e0)))) -> (((op (e0) (e1)) = (e2))\/(((op (e1) (e1)) = (e2))\/(((op (e2) (e1)) = (e2))\/((op (e3) (e1)) = (e2))))) -> (~((op (e2) (e0)) = (op (e2) (e1)))) -> (~((op (e0) (e2)) = (op (e3) (e2)))) -> (((op (e3) (e0)) = (e1))\/(((op (e3) (e1)) = (e1))\/(((op (e3) (e2)) = (e1))\/((op (e3) (e3)) = (e1))))) -> (((op (e0) (e3)) = (e1))\/(((op (e1) (e3)) = (e1))\/(((op (e2) (e3)) = (e1))\/((op (e3) (e3)) = (e1))))) -> (~((op (e3) (e1)) = (op (e3) (e3)))) -> ((~((op (e3) (e3)) = (e1)))\/((op (e3) (e1)) = (e3))) -> ((~((op (e2) (e2)) = (e1)))\/((op (e2) (e1)) = (e2))) -> ((~((op (e1) (e1)) = (e3)))\/((op (e1) (e3)) = (e1))) -> (~((op (e3) (e0)) = (op (e3) (e1)))) -> (((op (e0) (e1)) = (e1))\/(((op (e1) (e1)) = (e1))\/(((op (e2) (e1)) = (e1))\/((op (e3) (e1)) = (e1))))) -> ((~((op (e2) (e2)) = (e3)))\/((op (e2) (e3)) = (e2))) -> (((op (e0) (e3)) = (e0))\/(((op (e1) (e3)) = (e0))\/(((op (e2) (e3)) = (e0))\/((op (e3) (e3)) = (e0))))) -> (~((e0) = (e2))) -> (~((op (e0) (e0)) = (op (e0) (e3)))) -> (~((op (e3) (e0)) = (op (e3) (e3)))) -> ((op (e3) (e3)) = (e3)) -> ((~((op (e3) (e3)) = (e0)))\/((op (e3) (e0)) = (e3))) -> (~((op (e0) (e0)) = (op (e1) (e0)))) -> ((op (e0) (e0)) = (e0)) -> (~((op (e1) (e1)) = (e0))) -> (((op (e2) (e2)) = (e0))\/(((op (e2) (e2)) = (e1))\/(((op (e2) (e2)) = (e2))\/((op (e2) (e2)) = (e3))))) -> (~((op (e1) (e2)) = (op (e2) (e2)))) -> (~((e0) = (e1))) -> ((op (e1) (e3)) = (e1)) -> (((op (e1) (e0)) = (e0))\/(((op (e1) (e1)) = (e0))\/(((op (e1) (e2)) = (e0))\/((op (e1) (e3)) = (e0))))) -> (~((op (e2) (e2)) = (op (e2) (e3)))) -> ((~((op (e3) (e3)) = (e2)))\/((op (e3) (e2)) = (e3))) -> (~((op (e0) (e0)) = (e1))) -> (((op (e0) (e0)) = (e1))\/(((op (e1) (e0)) = (e1))\/(((op (e2) (e0)) = (e1))\/((op (e3) (e0)) = (e1))))) -> (~((op (e0) (e0)) = (e2))) -> (((op (e2) (e0)) = (e1))\/(((op (e2) (e1)) = (e1))\/(((op (e2) (e2)) = (e1))\/((op (e2) (e3)) = (e1))))) -> (~((op (e1) (e3)) = (op (e2) (e3)))) -> (~((op (e0) (e1)) = (op (e2) (e1)))) -> (~((op (e0) (e0)) = (e3))) -> (~((e2) = (e3))) -> (~((e1) = (e3))) -> (((op (e0) (e0)) = (e3))\/(((op (e1) (e0)) = (e3))\/(((op (e2) (e0)) = (e3))\/((op (e3) (e0)) = (e3))))) -> (~((op (e2) (e0)) = (op (e2) (e2)))) -> (~((op (e1) (e1)) = (e2))) -> (~((e1) = (e2))) -> (((op (e1) (e0)) = (e2))\/(((op (e1) (e1)) = (e2))\/(((op (e1) (e2)) = (e2))\/((op (e1) (e3)) = (e2))))) -> (((op (e0) (e0)) = (e2))\/(((op (e1) (e0)) = (e2))\/(((op (e2) (e0)) = (e2))\/((op (e3) (e0)) = (e2))))) -> (~((op (e1) (e0)) = (op (e1) (e3)))) -> (~((e0) = (e3))) -> (~((op (e3) (e2)) = (op (e3) (e3)))) -> (((op (e0) (e2)) = (e3))\/(((op (e1) (e2)) = (e3))\/(((op (e2) (e2)) = (e3))\/((op (e3) (e2)) = (e3))))) -> (((op (e0) (e0)) = (e2))\/(((op (e0) (e1)) = (e2))\/(((op (e0) (e2)) = (e2))\/((op (e0) (e3)) = (e2))))) -> (~((op (e0) (e2)) = (op (e2) (e2)))) -> (((op (e0) (e3)) = (e2))\/(((op (e1) (e3)) = (e2))\/(((op (e2) (e3)) = (e2))\/((op (e3) (e3)) = (e2))))) -> (~((op (e0) (e1)) = (op (e0) (e3)))) -> (((op (e0) (e0)) = (e1))\/(((op (e0) (e1)) = (e1))\/(((op (e0) (e2)) = (e1))\/((op (e0) (e3)) = (e1))))) -> ((~((op (e2) (e2)) = (e2)))\/((op (e2) (e2)) = (e2))) -> False). % 15.31/15.46 do 0 intro. intros zenon_H25b zenon_H13c zenon_H1df zenon_H258 zenon_H144 zenon_H1f5 zenon_H2e zenon_Hce zenon_H199 zenon_H25a zenon_H1d4 zenon_Hc9 zenon_H251 zenon_H250 zenon_H11b zenon_H254 zenon_H80 zenon_Hb4 zenon_H138 zenon_H1b4 zenon_H1b3 zenon_H58 zenon_H36 zenon_H87 zenon_H8b zenon_H90 zenon_H157 zenon_H1e2 zenon_H22e zenon_H1a2 zenon_H154 zenon_H140 zenon_H146 zenon_H121 zenon_H12d zenon_H10c zenon_H1e3 zenon_H1d2 zenon_H109 zenon_H228 zenon_H1c3 zenon_Hd3 zenon_H5e zenon_H24f zenon_Hbb zenon_H42 zenon_H10f zenon_H24c zenon_H1f zenon_H145 zenon_H2d zenon_H7d zenon_H9e zenon_H11f zenon_H163 zenon_H15f zenon_H10e zenon_H45 zenon_Hf1 zenon_H8f zenon_Hb7 zenon_H244 zenon_Hde zenon_H59 zenon_H6a zenon_Ha3 zenon_Hbe zenon_H17a zenon_Hd6 zenon_Ha7 zenon_H84 zenon_Heb zenon_H1cf zenon_H4b zenon_H173 zenon_H175 zenon_H8e zenon_H28 zenon_H160 zenon_H1cd zenon_H44 zenon_Haa. % 15.31/15.46 apply (zenon_or_s _ _ zenon_H1e3); [ zenon_intro zenon_H52 | zenon_intro zenon_H156 ]. % 15.31/15.46 apply (zenon_or_s _ _ zenon_Haa); [ zenon_intro zenon_H2f | zenon_intro zenon_H35 ]. % 15.31/15.46 apply (zenon_L605_); trivial. % 15.31/15.46 apply (zenon_or_s _ _ zenon_H1c3); [ zenon_intro zenon_H30 | zenon_intro zenon_H124 ]. % 15.31/15.46 apply (zenon_or_s _ _ zenon_H10f); [ zenon_intro zenon_H3c | zenon_intro zenon_Hba ]. % 15.31/15.46 apply (zenon_or_s _ _ zenon_H10e); [ zenon_intro zenon_H3d | zenon_intro zenon_H106 ]. % 15.31/15.46 apply (zenon_L607_); trivial. % 15.31/15.46 apply (zenon_L153_); trivial. % 15.31/15.46 apply (zenon_L43_); trivial. % 15.31/15.46 apply (zenon_L137_); trivial. % 15.31/15.46 apply (zenon_or_s _ _ zenon_Haa); [ zenon_intro zenon_H2f | zenon_intro zenon_H35 ]. % 15.31/15.46 apply (zenon_or_s _ _ zenon_H1c3); [ zenon_intro zenon_H30 | zenon_intro zenon_H124 ]. % 15.31/15.46 apply (zenon_or_s _ _ zenon_H10f); [ zenon_intro zenon_H3c | zenon_intro zenon_Hba ]. % 15.31/15.46 apply (zenon_or_s _ _ zenon_H10e); [ zenon_intro zenon_H3d | zenon_intro zenon_H106 ]. % 15.31/15.46 apply (zenon_L619_); trivial. % 15.31/15.46 apply (zenon_L153_); trivial. % 15.31/15.46 apply (zenon_L43_); trivial. % 15.31/15.46 apply (zenon_L256_); trivial. % 15.31/15.46 apply (zenon_L134_); trivial. % 15.31/15.46 (* end of lemma zenon_L620_ *) % 15.31/15.46 assert (zenon_L621_ : (((op (e1) (e0)) = (e1))\/(((op (e1) (e1)) = (e1))\/(((op (e1) (e2)) = (e1))\/((op (e1) (e3)) = (e1))))) -> (~((op (e2) (e2)) = (e1))) -> ((~((op (e1) (e1)) = (e1)))\/((op (e1) (e1)) = (e1))) -> (~((op (e1) (e0)) = (op (e1) (e1)))) -> (((op (e2) (e0)) = (e3))\/(((op (e2) (e1)) = (e3))\/(((op (e2) (e2)) = (e3))\/((op (e2) (e3)) = (e3))))) -> ((~((op (e1) (e1)) = (e2)))\/((op (e1) (e2)) = (e1))) -> (~((op (e1) (e0)) = (op (e1) (e2)))) -> (~((op (e1) (e2)) = (op (e1) (e3)))) -> (~((op (e0) (e1)) = (op (e1) (e1)))) -> (~((op (e1) (e1)) = (e3))) -> (((op (e0) (e2)) = (e0))\/(((op (e1) (e2)) = (e0))\/(((op (e2) (e2)) = (e0))\/((op (e3) (e2)) = (e0))))) -> (((op (e1) (e3)) = (e0))\/(((op (e1) (e3)) = (e1))\/(((op (e1) (e3)) = (e2))\/((op (e1) (e3)) = (e3))))) -> (~((op (e2) (e1)) = (op (e3) (e1)))) -> (((op (e3) (e0)) = (e2))\/(((op (e3) (e1)) = (e2))\/(((op (e3) (e2)) = (e2))\/((op (e3) (e3)) = (e2))))) -> (~((op (e0) (e0)) = (op (e2) (e0)))) -> (((op (e0) (e1)) = (e0))\/(((op (e1) (e1)) = (e0))\/(((op (e2) (e1)) = (e0))\/((op (e3) (e1)) = (e0))))) -> (((op (e2) (e0)) = (e0))\/(((op (e2) (e1)) = (e0))\/(((op (e2) (e2)) = (e0))\/((op (e2) (e3)) = (e0))))) -> (~((op (e2) (e2)) = (e0))) -> (~((op (e2) (e0)) = (op (e2) (e3)))) -> (((op (e0) (e1)) = (e3))\/(((op (e1) (e1)) = (e3))\/(((op (e2) (e1)) = (e3))\/((op (e3) (e1)) = (e3))))) -> (~((op (e0) (e0)) = (op (e0) (e1)))) -> ((~((op (e2) (e2)) = (e0)))\/((op (e2) (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 (e0) (e0)) = (op (e0) (e2)))) -> (((op (e0) (e2)) = (e1))\/(((op (e1) (e2)) = (e1))\/(((op (e2) (e2)) = (e1))\/((op (e3) (e2)) = (e1))))) -> (((op (e0) (e3)) = (e0))\/(((op (e0) (e3)) = (e1))\/(((op (e0) (e3)) = (e2))\/((op (e0) (e3)) = (e3))))) -> (~((op (e0) (e3)) = (op (e1) (e3)))) -> (~((op (e0) (e3)) = (op (e2) (e3)))) -> (~((op (e0) (e1)) = (op (e3) (e1)))) -> (~((op (e1) (e1)) = (e1))) -> (((op (e1) (e1)) = (e0))\/(((op (e1) (e1)) = (e1))\/(((op (e1) (e1)) = (e2))\/((op (e1) (e1)) = (e3))))) -> (((op (e0) (e0)) = (e3))\/(((op (e0) (e1)) = (e3))\/(((op (e0) (e2)) = (e3))\/((op (e0) (e3)) = (e3))))) -> (~((op (e0) (e3)) = (op (e3) (e3)))) -> (~((op (e0) (e2)) = (op (e1) (e2)))) -> (~((op (e1) (e3)) = (op (e3) (e3)))) -> (((op (e1) (e0)) = (e3))\/(((op (e1) (e1)) = (e3))\/(((op (e1) (e2)) = (e3))\/((op (e1) (e3)) = (e3))))) -> (~((op (e2) (e1)) = (op (e2) (e2)))) -> (~((op (e2) (e1)) = (op (e2) (e3)))) -> (~((op (e1) (e0)) = (op (e3) (e0)))) -> (((op (e0) (e1)) = (e2))\/(((op (e1) (e1)) = (e2))\/(((op (e2) (e1)) = (e2))\/((op (e3) (e1)) = (e2))))) -> (~((op (e2) (e0)) = (op (e2) (e1)))) -> (~((op (e0) (e2)) = (op (e3) (e2)))) -> (((op (e3) (e0)) = (e1))\/(((op (e3) (e1)) = (e1))\/(((op (e3) (e2)) = (e1))\/((op (e3) (e3)) = (e1))))) -> (((op (e0) (e3)) = (e1))\/(((op (e1) (e3)) = (e1))\/(((op (e2) (e3)) = (e1))\/((op (e3) (e3)) = (e1))))) -> (~((op (e3) (e1)) = (op (e3) (e3)))) -> ((~((op (e3) (e3)) = (e1)))\/((op (e3) (e1)) = (e3))) -> ((~((op (e2) (e2)) = (e1)))\/((op (e2) (e1)) = (e2))) -> ((~((op (e1) (e1)) = (e3)))\/((op (e1) (e3)) = (e1))) -> (~((op (e3) (e0)) = (op (e3) (e1)))) -> (((op (e0) (e1)) = (e1))\/(((op (e1) (e1)) = (e1))\/(((op (e2) (e1)) = (e1))\/((op (e3) (e1)) = (e1))))) -> ((~((op (e2) (e2)) = (e3)))\/((op (e2) (e3)) = (e2))) -> (((op (e0) (e3)) = (e0))\/(((op (e1) (e3)) = (e0))\/(((op (e2) (e3)) = (e0))\/((op (e3) (e3)) = (e0))))) -> (~((e0) = (e2))) -> (~((op (e0) (e0)) = (op (e0) (e3)))) -> (~((op (e3) (e0)) = (op (e3) (e3)))) -> ((op (e3) (e3)) = (e3)) -> ((~((op (e3) (e3)) = (e0)))\/((op (e3) (e0)) = (e3))) -> (~((op (e0) (e0)) = (op (e1) (e0)))) -> ((op (e0) (e0)) = (e0)) -> (~((op (e1) (e1)) = (e0))) -> (((op (e2) (e2)) = (e0))\/(((op (e2) (e2)) = (e1))\/(((op (e2) (e2)) = (e2))\/((op (e2) (e2)) = (e3))))) -> (~((op (e1) (e2)) = (op (e2) (e2)))) -> (~((e0) = (e1))) -> (((op (e1) (e0)) = (e0))\/(((op (e1) (e1)) = (e0))\/(((op (e1) (e2)) = (e0))\/((op (e1) (e3)) = (e0))))) -> (~((op (e2) (e2)) = (op (e2) (e3)))) -> ((~((op (e3) (e3)) = (e2)))\/((op (e3) (e2)) = (e3))) -> (~((op (e0) (e0)) = (e1))) -> (((op (e0) (e0)) = (e1))\/(((op (e1) (e0)) = (e1))\/(((op (e2) (e0)) = (e1))\/((op (e3) (e0)) = (e1))))) -> (~((op (e0) (e0)) = (e2))) -> (((op (e2) (e0)) = (e1))\/(((op (e2) (e1)) = (e1))\/(((op (e2) (e2)) = (e1))\/((op (e2) (e3)) = (e1))))) -> (~((op (e1) (e3)) = (op (e2) (e3)))) -> (~((op (e0) (e1)) = (op (e2) (e1)))) -> (~((op (e0) (e0)) = (e3))) -> (~((e2) = (e3))) -> (~((e1) = (e3))) -> (((op (e0) (e0)) = (e3))\/(((op (e1) (e0)) = (e3))\/(((op (e2) (e0)) = (e3))\/((op (e3) (e0)) = (e3))))) -> (~((op (e2) (e0)) = (op (e2) (e2)))) -> (~((op (e1) (e1)) = (e2))) -> (~((e1) = (e2))) -> (((op (e1) (e0)) = (e2))\/(((op (e1) (e1)) = (e2))\/(((op (e1) (e2)) = (e2))\/((op (e1) (e3)) = (e2))))) -> (((op (e0) (e0)) = (e2))\/(((op (e1) (e0)) = (e2))\/(((op (e2) (e0)) = (e2))\/((op (e3) (e0)) = (e2))))) -> (~((op (e1) (e0)) = (op (e1) (e3)))) -> (~((e0) = (e3))) -> (~((op (e3) (e2)) = (op (e3) (e3)))) -> (((op (e0) (e2)) = (e3))\/(((op (e1) (e2)) = (e3))\/(((op (e2) (e2)) = (e3))\/((op (e3) (e2)) = (e3))))) -> (((op (e0) (e0)) = (e2))\/(((op (e0) (e1)) = (e2))\/(((op (e0) (e2)) = (e2))\/((op (e0) (e3)) = (e2))))) -> (~((op (e0) (e2)) = (op (e2) (e2)))) -> (((op (e0) (e3)) = (e2))\/(((op (e1) (e3)) = (e2))\/(((op (e2) (e3)) = (e2))\/((op (e3) (e3)) = (e2))))) -> (~((op (e0) (e1)) = (op (e0) (e3)))) -> (((op (e0) (e0)) = (e1))\/(((op (e0) (e1)) = (e1))\/(((op (e0) (e2)) = (e1))\/((op (e0) (e3)) = (e1))))) -> ((~((op (e2) (e2)) = (e2)))\/((op (e2) (e2)) = (e2))) -> False). % 15.31/15.46 do 0 intro. intros zenon_H1c5 zenon_H52 zenon_H1d8 zenon_Hd7 zenon_He6 zenon_H1d3 zenon_H166 zenon_H1d0 zenon_H23 zenon_H182 zenon_H16f zenon_H25b zenon_H13c zenon_H1df zenon_H258 zenon_H144 zenon_H1f5 zenon_H2e zenon_Hce zenon_H199 zenon_H25a zenon_H1d4 zenon_Hc9 zenon_H251 zenon_H250 zenon_H11b zenon_H254 zenon_H80 zenon_Hb4 zenon_H138 zenon_H1b4 zenon_H1b3 zenon_H58 zenon_H36 zenon_H87 zenon_H8b zenon_H90 zenon_H157 zenon_H1e2 zenon_H22e zenon_H1a2 zenon_H154 zenon_H140 zenon_H146 zenon_H121 zenon_H12d zenon_H10c zenon_H1e3 zenon_H1d2 zenon_H109 zenon_H228 zenon_H1c3 zenon_Hd3 zenon_H5e zenon_H24f zenon_Hbb zenon_H42 zenon_H10f zenon_H24c zenon_H1f zenon_H145 zenon_H2d zenon_H7d zenon_H9e zenon_H163 zenon_H15f zenon_H10e zenon_H45 zenon_Hf1 zenon_H8f zenon_Hb7 zenon_H244 zenon_Hde zenon_H59 zenon_H6a zenon_Ha3 zenon_Hbe zenon_H17a zenon_Hd6 zenon_Ha7 zenon_H84 zenon_Heb zenon_H1cf zenon_H4b zenon_H173 zenon_H175 zenon_H8e zenon_H28 zenon_H160 zenon_H1cd zenon_H44 zenon_Haa. % 15.31/15.46 apply (zenon_or_s _ _ zenon_H1c5); [ zenon_intro zenon_Hd8 | zenon_intro zenon_H1c6 ]. % 15.31/15.46 apply (zenon_L574_); trivial. % 15.31/15.46 apply (zenon_or_s _ _ zenon_H1c6); [ zenon_intro zenon_H21 | zenon_intro zenon_H1c7 ]. % 15.31/15.46 exact (zenon_H1b4 zenon_H21). % 15.31/15.46 apply (zenon_or_s _ _ zenon_H1c7); [ zenon_intro zenon_H117 | zenon_intro zenon_H11f ]. % 15.31/15.46 apply (zenon_L602_); trivial. % 15.31/15.46 apply (zenon_L620_); trivial. % 15.31/15.46 (* end of lemma zenon_L621_ *) % 15.31/15.46 assert (zenon_L622_ : (((op (e0) (e2)) = (e0))\/(((op (e1) (e2)) = (e0))\/(((op (e2) (e2)) = (e0))\/((op (e3) (e2)) = (e0))))) -> ((op (e0) (e0)) = (e0)) -> (~((op (e0) (e0)) = (op (e0) (e2)))) -> ((op (e1) (e2)) = (e1)) -> (~((e0) = (e1))) -> (~((op (e2) (e2)) = (e0))) -> (~((op (e3) (e1)) = (op (e3) (e2)))) -> ((op (e3) (e1)) = (e0)) -> False). % 15.31/15.46 do 0 intro. intros zenon_H16f zenon_H1f zenon_H250 zenon_H117 zenon_H9e zenon_H2e zenon_H135 zenon_H142. % 15.31/15.46 apply (zenon_or_s _ _ zenon_H16f); [ zenon_intro zenon_Hab | zenon_intro zenon_H170 ]. % 15.31/15.46 apply (zenon_L567_); trivial. % 15.31/15.46 apply (zenon_or_s _ _ zenon_H170); [ zenon_intro zenon_H15d | zenon_intro zenon_H171 ]. % 15.31/15.46 apply (zenon_L496_); trivial. % 15.31/15.46 apply (zenon_or_s _ _ zenon_H171); [ zenon_intro zenon_H32 | zenon_intro zenon_H167 ]. % 15.31/15.47 exact (zenon_H2e zenon_H32). % 15.31/15.47 apply (zenon_L144_); trivial. % 15.31/15.47 (* end of lemma zenon_L622_ *) % 15.31/15.47 assert (zenon_L623_ : (((op (e0) (e0)) = (e3))\/(((op (e1) (e0)) = (e3))\/(((op (e2) (e0)) = (e3))\/((op (e3) (e0)) = (e3))))) -> (~((op (e0) (e0)) = (e3))) -> (~((e2) = (e3))) -> ((op (e1) (e0)) = (e2)) -> (~((op (e1) (e1)) = (e3))) -> (~((op (e1) (e1)) = (e2))) -> (~((op (e1) (e1)) = (e1))) -> (((op (e2) (e2)) = (e0))\/(((op (e2) (e2)) = (e1))\/(((op (e2) (e2)) = (e2))\/((op (e2) (e2)) = (e3))))) -> (~((op (e2) (e2)) = (e0))) -> (~((op (e2) (e2)) = (e2))) -> (~((op (e2) (e2)) = (e3))) -> (((op (e1) (e1)) = (e0))\/(((op (e1) (e1)) = (e1))\/(((op (e1) (e1)) = (e2))\/((op (e1) (e1)) = (e3))))) -> (~((e1) = (e3))) -> ((op (e3) (e0)) = (e1)) -> False). % 15.31/15.47 do 0 intro. intros zenon_Hbe zenon_H59 zenon_H6a zenon_H68 zenon_H182 zenon_Hd6 zenon_H1b4 zenon_H2d zenon_H2e zenon_H2f zenon_H30 zenon_H1b3 zenon_Ha3 zenon_Hee. % 15.31/15.47 apply (zenon_or_s _ _ zenon_Hbe); [ zenon_intro zenon_H5b | zenon_intro zenon_Hbf ]. % 15.31/15.47 exact (zenon_H59 zenon_H5b). % 15.31/15.47 apply (zenon_or_s _ _ zenon_Hbf); [ zenon_intro zenon_H69 | zenon_intro zenon_Hc0 ]. % 15.31/15.47 apply (zenon_L17_); trivial. % 15.31/15.47 apply (zenon_or_s _ _ zenon_Hc0); [ zenon_intro zenon_Haf | zenon_intro zenon_Hba ]. % 15.31/15.47 apply (zenon_L219_); trivial. % 15.31/15.47 apply (zenon_L79_); trivial. % 15.31/15.47 (* end of lemma zenon_L623_ *) % 15.31/15.47 assert (zenon_L624_ : (((op (e0) (e0)) = (e2))\/(((op (e1) (e0)) = (e2))\/(((op (e2) (e0)) = (e2))\/((op (e3) (e0)) = (e2))))) -> (~((op (e0) (e0)) = (e2))) -> (~((e1) = (e3))) -> (((op (e1) (e1)) = (e0))\/(((op (e1) (e1)) = (e1))\/(((op (e1) (e1)) = (e2))\/((op (e1) (e1)) = (e3))))) -> (~((op (e2) (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) (e1)) = (e1))) -> (~((op (e1) (e1)) = (e2))) -> (~((op (e1) (e1)) = (e3))) -> (~((e2) = (e3))) -> (~((op (e0) (e0)) = (e3))) -> (((op (e0) (e0)) = (e3))\/(((op (e1) (e0)) = (e3))\/(((op (e2) (e0)) = (e3))\/((op (e3) (e0)) = (e3))))) -> ((op (e2) (e1)) = (e2)) -> (~((op (e2) (e0)) = (op (e2) (e1)))) -> ((op (e3) (e0)) = (e1)) -> (~((e1) = (e2))) -> False). % 15.31/15.47 do 0 intro. intros zenon_Heb zenon_H8f zenon_Ha3 zenon_H1b3 zenon_H30 zenon_H2f zenon_H2e zenon_H2d zenon_H1b4 zenon_Hd6 zenon_H182 zenon_H6a zenon_H59 zenon_Hbe zenon_H156 zenon_H154 zenon_Hee zenon_Ha7. % 15.31/15.47 apply (zenon_or_s _ _ zenon_Heb); [ zenon_intro zenon_H92 | zenon_intro zenon_Hec ]. % 15.31/15.47 exact (zenon_H8f zenon_H92). % 15.31/15.47 apply (zenon_or_s _ _ zenon_Hec); [ zenon_intro zenon_H68 | zenon_intro zenon_Hed ]. % 15.31/15.47 apply (zenon_L623_); trivial. % 15.31/15.47 apply (zenon_or_s _ _ zenon_Hed); [ zenon_intro zenon_Hdd | zenon_intro zenon_He9 ]. % 15.31/15.47 apply (zenon_L284_); trivial. % 15.31/15.47 apply (zenon_L122_); trivial. % 15.31/15.47 (* end of lemma zenon_L624_ *) % 15.31/15.47 assert (zenon_L625_ : (((op (e0) (e3)) = (e2))\/(((op (e1) (e3)) = (e2))\/(((op (e2) (e3)) = (e2))\/((op (e3) (e3)) = (e2))))) -> (~((e1) = (e2))) -> ((op (e0) (e3)) = (e1)) -> (~((e0) = (e2))) -> ((op (e1) (e3)) = (e0)) -> ((op (e2) (e1)) = (e2)) -> (~((op (e2) (e1)) = (op (e2) (e3)))) -> (~((op (e3) (e3)) = (e2))) -> False). % 15.31/15.47 do 0 intro. intros zenon_H160 zenon_Ha7 zenon_H37 zenon_H5e zenon_Hcc zenon_H156 zenon_H1e2 zenon_H3d. % 15.31/15.47 apply (zenon_or_s _ _ zenon_H160); [ zenon_intro zenon_H81 | zenon_intro zenon_H161 ]. % 15.31/15.47 apply (zenon_L33_); trivial. % 15.31/15.47 apply (zenon_or_s _ _ zenon_H161); [ zenon_intro zenon_H82 | zenon_intro zenon_H162 ]. % 15.31/15.47 apply (zenon_L54_); trivial. % 15.31/15.47 apply (zenon_or_s _ _ zenon_H162); [ zenon_intro zenon_H124 | zenon_intro zenon_H43 ]. % 15.31/15.47 apply (zenon_L256_); trivial. % 15.31/15.47 exact (zenon_H3d zenon_H43). % 15.31/15.47 (* end of lemma zenon_L625_ *) % 15.31/15.47 assert (zenon_L626_ : (~((op (e1) (e2)) = (op (e3) (e2)))) -> ((op (e1) (e2)) = (e0)) -> ((op (e3) (e2)) = (e0)) -> False). % 15.31/15.47 do 0 intro. intros zenon_H17d zenon_H15d zenon_H167. % 15.31/15.47 cut (((op (e1) (e2)) = (e0)) = ((op (e1) (e2)) = (op (e3) (e2)))). % 15.31/15.47 intro zenon_D_pnotp. % 15.31/15.47 apply zenon_H17d. % 15.31/15.47 rewrite <- zenon_D_pnotp. % 15.31/15.47 exact zenon_H15d. % 15.31/15.47 cut (((e0) = (op (e3) (e2)))); [idtac | apply NNPP; zenon_intro zenon_H168]. % 15.31/15.47 cut (((op (e1) (e2)) = (op (e1) (e2)))); [idtac | apply NNPP; zenon_intro zenon_H1d1]. % 15.31/15.47 congruence. % 15.31/15.47 apply zenon_H1d1. apply refl_equal. % 15.31/15.47 apply zenon_H168. apply sym_equal. exact zenon_H167. % 15.31/15.47 (* end of lemma zenon_L626_ *) % 15.31/15.47 assert (zenon_L627_ : (((op (e3) (e2)) = (e0))\/(((op (e3) (e2)) = (e1))\/(((op (e3) (e2)) = (e2))\/((op (e3) (e2)) = (e3))))) -> ((op (e1) (e2)) = (e0)) -> ((op (e3) (e1)) = (e1)) -> (~((op (e3) (e1)) = (op (e3) (e2)))) -> ((op (e0) (e2)) = (e2)) -> (~((op (e0) (e2)) = (op (e3) (e2)))) -> (((op (e1) (e0)) = (e3))\/(((op (e1) (e1)) = (e3))\/(((op (e1) (e2)) = (e3))\/((op (e1) (e3)) = (e3))))) -> (~((e1) = (e3))) -> ((op (e1) (e0)) = (e1)) -> (~((op (e1) (e1)) = (e3))) -> (~((op (e1) (e2)) = (op (e3) (e2)))) -> ((op (e1) (e3)) = (e2)) -> (~((e2) = (e3))) -> False). % 15.31/15.47 do 0 intro. intros zenon_H25e zenon_H15d zenon_H13e zenon_H135 zenon_H63 zenon_H140 zenon_H90 zenon_Ha3 zenon_Hd8 zenon_H182 zenon_H17d zenon_H82 zenon_H6a. % 15.31/15.47 apply (zenon_or_s _ _ zenon_H25e); [ zenon_intro zenon_H167 | zenon_intro zenon_H25f ]. % 15.31/15.47 apply (zenon_L626_); trivial. % 15.31/15.47 apply (zenon_or_s _ _ zenon_H25f); [ zenon_intro zenon_H119 | zenon_intro zenon_H260 ]. % 15.31/15.47 apply (zenon_L394_); trivial. % 15.31/15.47 apply (zenon_or_s _ _ zenon_H260); [ zenon_intro zenon_H1dd | zenon_intro zenon_H106 ]. % 15.31/15.47 apply (zenon_L253_); trivial. % 15.31/15.47 apply (zenon_L166_); trivial. % 15.31/15.47 (* end of lemma zenon_L627_ *) % 15.31/15.47 assert (zenon_L628_ : (((op (e0) (e3)) = (e2))\/(((op (e1) (e3)) = (e2))\/(((op (e2) (e3)) = (e2))\/((op (e3) (e3)) = (e2))))) -> (~((e1) = (e2))) -> ((op (e0) (e3)) = (e1)) -> (~((e2) = (e3))) -> (~((op (e1) (e2)) = (op (e3) (e2)))) -> (~((op (e1) (e1)) = (e3))) -> ((op (e1) (e0)) = (e1)) -> (~((e1) = (e3))) -> (((op (e1) (e0)) = (e3))\/(((op (e1) (e1)) = (e3))\/(((op (e1) (e2)) = (e3))\/((op (e1) (e3)) = (e3))))) -> (~((op (e0) (e2)) = (op (e3) (e2)))) -> ((op (e0) (e2)) = (e2)) -> (~((op (e3) (e1)) = (op (e3) (e2)))) -> ((op (e3) (e1)) = (e1)) -> ((op (e1) (e2)) = (e0)) -> (((op (e3) (e2)) = (e0))\/(((op (e3) (e2)) = (e1))\/(((op (e3) (e2)) = (e2))\/((op (e3) (e2)) = (e3))))) -> ((op (e2) (e3)) = (e0)) -> (~((e0) = (e2))) -> (~((op (e3) (e3)) = (e2))) -> False). % 15.31/15.47 do 0 intro. intros zenon_H160 zenon_Ha7 zenon_H37 zenon_H6a zenon_H17d zenon_H182 zenon_Hd8 zenon_Ha3 zenon_H90 zenon_H140 zenon_H63 zenon_H135 zenon_H13e zenon_H15d zenon_H25e zenon_Hd0 zenon_H5e zenon_H3d. % 15.31/15.47 apply (zenon_or_s _ _ zenon_H160); [ zenon_intro zenon_H81 | zenon_intro zenon_H161 ]. % 15.31/15.47 apply (zenon_L33_); trivial. % 15.31/15.47 apply (zenon_or_s _ _ zenon_H161); [ zenon_intro zenon_H82 | zenon_intro zenon_H162 ]. % 15.31/15.47 apply (zenon_L627_); trivial. % 15.31/15.47 apply (zenon_or_s _ _ zenon_H162); [ zenon_intro zenon_H124 | zenon_intro zenon_H43 ]. % 15.31/15.47 apply (zenon_L201_); trivial. % 15.31/15.47 exact (zenon_H3d zenon_H43). % 15.31/15.47 (* end of lemma zenon_L628_ *) % 15.31/15.47 assert (zenon_L629_ : (((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) (e3)) = (e0))\/(((op (e1) (e3)) = (e0))\/(((op (e2) (e3)) = (e0))\/((op (e3) (e3)) = (e0))))) -> ((op (e0) (e0)) = (e0)) -> (~((op (e0) (e0)) = (op (e0) (e3)))) -> (~((op (e2) (e1)) = (op (e2) (e3)))) -> ((op (e2) (e1)) = (e2)) -> (~((op (e3) (e3)) = (e2))) -> (~((e0) = (e2))) -> (((op (e3) (e2)) = (e0))\/(((op (e3) (e2)) = (e1))\/(((op (e3) (e2)) = (e2))\/((op (e3) (e2)) = (e3))))) -> ((op (e1) (e2)) = (e0)) -> (~((op (e3) (e1)) = (op (e3) (e2)))) -> ((op (e0) (e2)) = (e2)) -> (~((op (e0) (e2)) = (op (e3) (e2)))) -> (((op (e1) (e0)) = (e3))\/(((op (e1) (e1)) = (e3))\/(((op (e1) (e2)) = (e3))\/((op (e1) (e3)) = (e3))))) -> (~((e1) = (e3))) -> ((op (e1) (e0)) = (e1)) -> (~((op (e1) (e1)) = (e3))) -> (~((op (e1) (e2)) = (op (e3) (e2)))) -> (~((e2) = (e3))) -> ((op (e0) (e3)) = (e1)) -> (~((e1) = (e2))) -> (((op (e0) (e3)) = (e2))\/(((op (e1) (e3)) = (e2))\/(((op (e2) (e3)) = (e2))\/((op (e3) (e3)) = (e2))))) -> (~((op (e3) (e3)) = (e0))) -> False). % 15.31/15.47 do 0 intro. intros zenon_H228 zenon_H1cd zenon_H1b4 zenon_Hd3 zenon_H1f zenon_H24f zenon_H1e2 zenon_H156 zenon_H3d zenon_H5e zenon_H25e zenon_H15d zenon_H135 zenon_H63 zenon_H140 zenon_H90 zenon_Ha3 zenon_Hd8 zenon_H182 zenon_H17d zenon_H6a zenon_H37 zenon_Ha7 zenon_H160 zenon_H3c. % 15.31/15.47 apply (zenon_or_s _ _ zenon_H228); [ zenon_intro zenon_H22 | zenon_intro zenon_H229 ]. % 15.31/15.47 apply (zenon_L223_); trivial. % 15.31/15.47 apply (zenon_or_s _ _ zenon_H229); [ zenon_intro zenon_H21 | zenon_intro zenon_H22a ]. % 15.31/15.47 exact (zenon_H1b4 zenon_H21). % 15.31/15.47 apply (zenon_or_s _ _ zenon_H22a); [ zenon_intro zenon_Hb2 | zenon_intro zenon_H13e ]. % 15.31/15.47 apply (zenon_L372_); trivial. % 15.31/15.47 apply (zenon_or_s _ _ zenon_Hd3); [ zenon_intro zenon_Hca | zenon_intro zenon_Hd4 ]. % 15.31/15.47 apply (zenon_L562_); trivial. % 15.31/15.47 apply (zenon_or_s _ _ zenon_Hd4); [ zenon_intro zenon_Hcc | zenon_intro zenon_Hd5 ]. % 15.31/15.47 apply (zenon_L625_); trivial. % 15.31/15.47 apply (zenon_or_s _ _ zenon_Hd5); [ zenon_intro zenon_Hd0 | zenon_intro zenon_H40 ]. % 15.31/15.47 apply (zenon_L628_); trivial. % 15.31/15.47 exact (zenon_H3c zenon_H40). % 15.31/15.47 (* end of lemma zenon_L629_ *) % 15.31/15.47 assert (zenon_L630_ : (((op (e1) (e0)) = (e2))\/(((op (e1) (e1)) = (e2))\/(((op (e1) (e2)) = (e2))\/((op (e1) (e3)) = (e2))))) -> (~((e2) = (e3))) -> ((op (e1) (e0)) = (e3)) -> (~((op (e1) (e1)) = (e2))) -> ((op (e0) (e2)) = (e2)) -> (~((op (e0) (e2)) = (op (e1) (e2)))) -> ((op (e1) (e3)) = (e0)) -> (~((e0) = (e2))) -> False). % 15.31/15.47 do 0 intro. intros zenon_H84 zenon_H6a zenon_H69 zenon_Hd6 zenon_H63 zenon_H87 zenon_Hcc zenon_H5e. % 15.31/15.47 apply (zenon_or_s _ _ zenon_H84); [ zenon_intro zenon_H68 | zenon_intro zenon_H85 ]. % 15.31/15.47 apply (zenon_L17_); trivial. % 15.31/15.47 apply (zenon_or_s _ _ zenon_H85); [ zenon_intro zenon_H6e | zenon_intro zenon_H86 ]. % 15.31/15.47 exact (zenon_Hd6 zenon_H6e). % 15.31/15.47 apply (zenon_or_s _ _ zenon_H86); [ zenon_intro zenon_H7c | zenon_intro zenon_H82 ]. % 15.31/15.47 apply (zenon_L52_); trivial. % 15.31/15.47 apply (zenon_L54_); trivial. % 15.31/15.47 (* end of lemma zenon_L630_ *) % 15.31/15.47 assert (zenon_L631_ : (((op (e0) (e2)) = (e0))\/(((op (e0) (e2)) = (e1))\/(((op (e0) (e2)) = (e2))\/((op (e0) (e2)) = (e3))))) -> ((op (e1) (e2)) = (e0)) -> (~((op (e0) (e2)) = (op (e0) (e3)))) -> ((op (e0) (e3)) = (e1)) -> ((op (e3) (e2)) = (e2)) -> (~((op (e0) (e2)) = (op (e3) (e2)))) -> (~((op (e0) (e2)) = (op (e1) (e2)))) -> ((op (e1) (e2)) = (e3)) -> False). % 15.31/15.47 do 0 intro. intros zenon_H251 zenon_H15d zenon_Hc9 zenon_H37 zenon_H1dd zenon_H140 zenon_H87 zenon_H88. % 15.31/15.47 apply (zenon_or_s _ _ zenon_H251); [ zenon_intro zenon_Hab | zenon_intro zenon_H252 ]. % 15.31/15.47 apply (zenon_L136_); trivial. % 15.31/15.47 apply (zenon_or_s _ _ zenon_H252); [ zenon_intro zenon_H29 | zenon_intro zenon_H253 ]. % 15.31/15.47 apply (zenon_L85_); trivial. % 15.31/15.47 apply (zenon_or_s _ _ zenon_H253); [ zenon_intro zenon_H63 | zenon_intro zenon_H50 ]. % 15.31/15.47 apply (zenon_L253_); trivial. % 15.31/15.47 apply (zenon_L24_); trivial. % 15.31/15.47 (* end of lemma zenon_L631_ *) % 15.31/15.47 assert (zenon_L632_ : (((op (e3) (e0)) = (e2))\/(((op (e3) (e1)) = (e2))\/(((op (e3) (e2)) = (e2))\/((op (e3) (e3)) = (e2))))) -> (~((e1) = (e2))) -> ((op (e3) (e0)) = (e1)) -> ((op (e2) (e1)) = (e2)) -> (~((op (e2) (e1)) = (op (e3) (e1)))) -> ((op (e1) (e2)) = (e3)) -> (~((op (e0) (e2)) = (op (e1) (e2)))) -> (~((op (e0) (e2)) = (op (e3) (e2)))) -> ((op (e0) (e3)) = (e1)) -> (~((op (e0) (e2)) = (op (e0) (e3)))) -> ((op (e1) (e2)) = (e0)) -> (((op (e0) (e2)) = (e0))\/(((op (e0) (e2)) = (e1))\/(((op (e0) (e2)) = (e2))\/((op (e0) (e2)) = (e3))))) -> (~((op (e3) (e3)) = (e2))) -> False). % 15.31/15.47 do 0 intro. intros zenon_H1df zenon_Ha7 zenon_Hee zenon_H156 zenon_H13c zenon_H88 zenon_H87 zenon_H140 zenon_H37 zenon_Hc9 zenon_H15d zenon_H251 zenon_H3d. % 15.31/15.47 apply (zenon_or_s _ _ zenon_H1df); [ zenon_intro zenon_He9 | zenon_intro zenon_H1e0 ]. % 15.31/15.47 apply (zenon_L122_); trivial. % 15.31/15.47 apply (zenon_or_s _ _ zenon_H1e0); [ zenon_intro zenon_H16a | zenon_intro zenon_H1e1 ]. % 15.31/15.47 apply (zenon_L252_); trivial. % 15.31/15.47 apply (zenon_or_s _ _ zenon_H1e1); [ zenon_intro zenon_H1dd | zenon_intro zenon_H43 ]. % 15.31/15.47 apply (zenon_L631_); trivial. % 15.31/15.47 exact (zenon_H3d zenon_H43). % 15.31/15.47 (* end of lemma zenon_L632_ *) % 15.31/15.47 assert (zenon_L633_ : (((op (e1) (e0)) = (e3))\/(((op (e1) (e1)) = (e3))\/(((op (e1) (e2)) = (e3))\/((op (e1) (e3)) = (e3))))) -> (~((e2) = (e3))) -> ((op (e1) (e0)) = (e2)) -> (~((op (e1) (e1)) = (e3))) -> (~((op (e3) (e3)) = (e2))) -> (((op (e0) (e2)) = (e0))\/(((op (e0) (e2)) = (e1))\/(((op (e0) (e2)) = (e2))\/((op (e0) (e2)) = (e3))))) -> ((op (e1) (e2)) = (e0)) -> (~((op (e0) (e2)) = (op (e0) (e3)))) -> ((op (e0) (e3)) = (e1)) -> (~((op (e0) (e2)) = (op (e3) (e2)))) -> (~((op (e0) (e2)) = (op (e1) (e2)))) -> (~((op (e2) (e1)) = (op (e3) (e1)))) -> ((op (e2) (e1)) = (e2)) -> ((op (e3) (e0)) = (e1)) -> (~((e1) = (e2))) -> (((op (e3) (e0)) = (e2))\/(((op (e3) (e1)) = (e2))\/(((op (e3) (e2)) = (e2))\/((op (e3) (e3)) = (e2))))) -> ((op (e3) (e3)) = (e3)) -> (~((op (e1) (e3)) = (op (e3) (e3)))) -> False). % 15.31/15.47 do 0 intro. intros zenon_H90 zenon_H6a zenon_H68 zenon_H182 zenon_H3d zenon_H251 zenon_H15d zenon_Hc9 zenon_H37 zenon_H140 zenon_H87 zenon_H13c zenon_H156 zenon_Hee zenon_Ha7 zenon_H1df zenon_H42 zenon_H8b. % 15.31/15.47 apply (zenon_or_s _ _ zenon_H90); [ zenon_intro zenon_H69 | zenon_intro zenon_H94 ]. % 15.31/15.47 apply (zenon_L17_); trivial. % 15.31/15.47 apply (zenon_or_s _ _ zenon_H94); [ zenon_intro zenon_H96 | zenon_intro zenon_H95 ]. % 15.31/15.47 exact (zenon_H182 zenon_H96). % 15.31/15.47 apply (zenon_or_s _ _ zenon_H95); [ zenon_intro zenon_H88 | zenon_intro zenon_H8a ]. % 15.31/15.47 apply (zenon_L632_); trivial. % 15.31/15.47 apply (zenon_L25_); trivial. % 15.31/15.47 (* end of lemma zenon_L633_ *) % 15.31/15.47 assert (zenon_L634_ : (((op (e0) (e0)) = (e2))\/(((op (e1) (e0)) = (e2))\/(((op (e2) (e0)) = (e2))\/((op (e3) (e0)) = (e2))))) -> (~((op (e0) (e0)) = (e2))) -> (~((op (e3) (e3)) = (e2))) -> (~((op (e2) (e1)) = (op (e2) (e3)))) -> (~((e0) = (e2))) -> ((op (e0) (e3)) = (e1)) -> (((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))))) -> (~((e2) = (e3))) -> (~((op (e1) (e1)) = (e3))) -> (((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)) = (op (e1) (e2)))) -> (~((op (e2) (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 (e1) (e3)) = (op (e3) (e3)))) -> (~((op (e1) (e1)) = (e0))) -> (~((op (e0) (e0)) = (op (e1) (e0)))) -> ((op (e0) (e0)) = (e0)) -> (((op (e1) (e0)) = (e0))\/(((op (e1) (e1)) = (e0))\/(((op (e1) (e2)) = (e0))\/((op (e1) (e3)) = (e0))))) -> ((op (e2) (e1)) = (e2)) -> (~((op (e2) (e0)) = (op (e2) (e1)))) -> ((op (e3) (e0)) = (e1)) -> (~((e1) = (e2))) -> False). % 15.31/15.47 do 0 intro. intros zenon_Heb zenon_H8f zenon_H3d zenon_H1e2 zenon_H5e zenon_H37 zenon_H160 zenon_H90 zenon_H6a zenon_H182 zenon_H251 zenon_Hc9 zenon_H140 zenon_H87 zenon_H13c zenon_H1df zenon_H42 zenon_H8b zenon_H145 zenon_H24c zenon_H1f zenon_H163 zenon_H156 zenon_H154 zenon_Hee zenon_Ha7. % 15.31/15.47 apply (zenon_or_s _ _ zenon_Heb); [ zenon_intro zenon_H92 | zenon_intro zenon_Hec ]. % 15.31/15.47 exact (zenon_H8f zenon_H92). % 15.31/15.47 apply (zenon_or_s _ _ zenon_Hec); [ zenon_intro zenon_H68 | zenon_intro zenon_Hed ]. % 15.31/15.47 apply (zenon_or_s _ _ zenon_H163); [ zenon_intro zenon_Had | zenon_intro zenon_H164 ]. % 15.31/15.47 apply (zenon_L559_); trivial. % 15.31/15.47 apply (zenon_or_s _ _ zenon_H164); [ zenon_intro zenon_H149 | zenon_intro zenon_H165 ]. % 15.31/15.47 exact (zenon_H145 zenon_H149). % 15.31/15.47 apply (zenon_or_s _ _ zenon_H165); [ zenon_intro zenon_H15d | zenon_intro zenon_Hcc ]. % 15.31/15.47 apply (zenon_L633_); trivial. % 15.31/15.47 apply (zenon_L625_); trivial. % 15.31/15.47 apply (zenon_or_s _ _ zenon_Hed); [ zenon_intro zenon_Hdd | zenon_intro zenon_He9 ]. % 15.31/15.47 apply (zenon_L284_); trivial. % 15.31/15.47 apply (zenon_L122_); trivial. % 15.31/15.47 (* end of lemma zenon_L634_ *) % 15.31/15.47 assert (zenon_L635_ : (((op (e0) (e0)) = (e1))\/(((op (e0) (e1)) = (e1))\/(((op (e0) (e2)) = (e1))\/((op (e0) (e3)) = (e1))))) -> (~((op (e0) (e1)) = (op (e1) (e1)))) -> (~((op (e0) (e3)) = (op (e3) (e3)))) -> (~((e0) = (e3))) -> (((op (e2) (e0)) = (e0))\/(((op (e2) (e1)) = (e0))\/(((op (e2) (e2)) = (e0))\/((op (e2) (e3)) = (e0))))) -> (~((op (e2) (e0)) = (op (e2) (e3)))) -> (((op (e0) (e1)) = (e3))\/(((op (e1) (e1)) = (e3))\/(((op (e2) (e1)) = (e3))\/((op (e3) (e1)) = (e3))))) -> (((op (e0) (e2)) = (e0))\/(((op (e1) (e2)) = (e0))\/(((op (e2) (e2)) = (e0))\/((op (e3) (e2)) = (e0))))) -> (~((op (e0) (e0)) = (op (e0) (e2)))) -> (~((op (e3) (e1)) = (op (e3) (e3)))) -> (((op (e0) (e1)) = (e0))\/(((op (e1) (e1)) = (e0))\/(((op (e2) (e1)) = (e0))\/((op (e3) (e1)) = (e0))))) -> (~((op (e0) (e2)) = (op (e2) (e2)))) -> (((op (e0) (e0)) = (e1))\/(((op (e1) (e0)) = (e1))\/(((op (e2) (e0)) = (e1))\/((op (e3) (e0)) = (e1))))) -> (~((op (e0) (e0)) = (e1))) -> ((~((op (e2) (e2)) = (e3)))\/((op (e2) (e3)) = (e2))) -> (~((op (e3) (e0)) = (op (e3) (e3)))) -> (((op (e0) (e0)) = (e3))\/(((op (e0) (e1)) = (e3))\/(((op (e0) (e2)) = (e3))\/((op (e0) (e3)) = (e3))))) -> (((op (e1) (e1)) = (e0))\/(((op (e1) (e1)) = (e1))\/(((op (e1) (e1)) = (e2))\/((op (e1) (e1)) = (e3))))) -> (~((op (e2) (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) (e1)) = (e1))) -> (~((op (e1) (e1)) = (e2))) -> (~((e0) = (e1))) -> (~((op (e0) (e1)) = (op (e2) (e1)))) -> (((op (e2) (e0)) = (e3))\/(((op (e2) (e1)) = (e3))\/(((op (e2) (e2)) = (e3))\/((op (e2) (e3)) = (e3))))) -> (((op (e0) (e1)) = (e1))\/(((op (e1) (e1)) = (e1))\/(((op (e2) (e1)) = (e1))\/((op (e3) (e1)) = (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) (e0)) = (op (e0) (e3)))) -> (((op (e3) (e2)) = (e0))\/(((op (e3) (e2)) = (e1))\/(((op (e3) (e2)) = (e2))\/((op (e3) (e2)) = (e3))))) -> (~((op (e3) (e1)) = (op (e3) (e2)))) -> (~((op (e1) (e2)) = (op (e3) (e2)))) -> (~((op (e3) (e3)) = (e0))) -> (((op (e1) (e0)) = (e1))\/(((op (e1) (e1)) = (e1))\/(((op (e1) (e2)) = (e1))\/((op (e1) (e3)) = (e1))))) -> (((op (e1) (e0)) = (e2))\/(((op (e1) (e1)) = (e2))\/(((op (e1) (e2)) = (e2))\/((op (e1) (e3)) = (e2))))) -> (~((op (e0) (e0)) = (e3))) -> (((op (e0) (e0)) = (e3))\/(((op (e1) (e0)) = (e3))\/(((op (e2) (e0)) = (e3))\/((op (e3) (e0)) = (e3))))) -> (~((e1) = (e3))) -> (((op (e0) (e0)) = (e2))\/(((op (e0) (e1)) = (e2))\/(((op (e0) (e2)) = (e2))\/((op (e0) (e3)) = (e2))))) -> (((op (e0) (e0)) = (e2))\/(((op (e1) (e0)) = (e2))\/(((op (e2) (e0)) = (e2))\/((op (e3) (e0)) = (e2))))) -> (~((op (e0) (e0)) = (e2))) -> (~((op (e3) (e3)) = (e2))) -> (~((op (e2) (e1)) = (op (e2) (e3)))) -> (~((e0) = (e2))) -> (((op (e0) (e3)) = (e2))\/(((op (e1) (e3)) = (e2))\/(((op (e2) (e3)) = (e2))\/((op (e3) (e3)) = (e2))))) -> (((op (e1) (e0)) = (e3))\/(((op (e1) (e1)) = (e3))\/(((op (e1) (e2)) = (e3))\/((op (e1) (e3)) = (e3))))) -> (~((e2) = (e3))) -> (~((op (e1) (e1)) = (e3))) -> (((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)) = (op (e1) (e2)))) -> (~((op (e2) (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 (e1) (e3)) = (op (e3) (e3)))) -> (~((op (e1) (e1)) = (e0))) -> (~((op (e0) (e0)) = (op (e1) (e0)))) -> ((op (e0) (e0)) = (e0)) -> (((op (e1) (e0)) = (e0))\/(((op (e1) (e1)) = (e0))\/(((op (e1) (e2)) = (e0))\/((op (e1) (e3)) = (e0))))) -> ((op (e2) (e1)) = (e2)) -> (~((op (e2) (e0)) = (op (e2) (e1)))) -> (~((e1) = (e2))) -> False). % 15.31/15.47 do 0 intro. intros zenon_H44 zenon_H23 zenon_H36 zenon_H4b zenon_H1f5 zenon_Hce zenon_H199 zenon_H16f zenon_H250 zenon_H12d zenon_H144 zenon_H28 zenon_Hf1 zenon_H45 zenon_H1c3 zenon_Hbb zenon_H58 zenon_H1b3 zenon_H30 zenon_H2f zenon_H2e zenon_H2d zenon_H1b4 zenon_Hd6 zenon_H9e zenon_Hde zenon_He6 zenon_H228 zenon_H1cd zenon_Hd3 zenon_H24f zenon_H25e zenon_H135 zenon_H17d zenon_H3c zenon_H1c5 zenon_H84 zenon_H59 zenon_Hbe zenon_Ha3 zenon_H8e zenon_Heb zenon_H8f zenon_H3d zenon_H1e2 zenon_H5e zenon_H160 zenon_H90 zenon_H6a zenon_H182 zenon_H251 zenon_Hc9 zenon_H140 zenon_H87 zenon_H13c zenon_H1df zenon_H42 zenon_H8b zenon_H145 zenon_H24c zenon_H1f zenon_H163 zenon_H156 zenon_H154 zenon_Ha7. % 15.31/15.47 apply (zenon_or_s _ _ zenon_H44); [ zenon_intro zenon_H47 | zenon_intro zenon_H46 ]. % 15.31/15.47 exact (zenon_H45 zenon_H47). % 15.31/15.47 apply (zenon_or_s _ _ zenon_H46); [ zenon_intro zenon_H22 | zenon_intro zenon_H48 ]. % 15.31/15.47 apply (zenon_or_s _ _ zenon_Hf1); [ zenon_intro zenon_H47 | zenon_intro zenon_Hf4 ]. % 15.31/15.47 exact (zenon_H45 zenon_H47). % 15.31/15.47 apply (zenon_or_s _ _ zenon_Hf4); [ zenon_intro zenon_Hd8 | zenon_intro zenon_Hf5 ]. % 15.31/15.47 apply (zenon_L446_); trivial. % 15.31/15.47 apply (zenon_or_s _ _ zenon_Hf5); [ zenon_intro zenon_Hae | zenon_intro zenon_Hee ]. % 15.31/15.47 apply (zenon_or_s _ _ zenon_H8e); [ zenon_intro zenon_H92 | zenon_intro zenon_H91 ]. % 15.31/15.47 exact (zenon_H8f zenon_H92). % 15.31/15.47 apply (zenon_or_s _ _ zenon_H91); [ zenon_intro zenon_H5d | zenon_intro zenon_H93 ]. % 15.31/15.47 apply (zenon_L214_); trivial. % 15.31/15.47 apply (zenon_or_s _ _ zenon_H93); [ zenon_intro zenon_H63 | zenon_intro zenon_H81 ]. % 15.31/15.47 apply (zenon_L242_); trivial. % 15.31/15.47 apply (zenon_or_s _ _ zenon_Hbe); [ zenon_intro zenon_H5b | zenon_intro zenon_Hbf ]. % 15.31/15.47 exact (zenon_H59 zenon_H5b). % 15.31/15.47 apply (zenon_or_s _ _ zenon_Hbf); [ zenon_intro zenon_H69 | zenon_intro zenon_Hc0 ]. % 15.31/15.47 apply (zenon_or_s _ _ zenon_H144); [ zenon_intro zenon_H49 | zenon_intro zenon_H147 ]. % 15.31/15.47 apply (zenon_L278_); trivial. % 15.31/15.47 apply (zenon_or_s _ _ zenon_H147); [ zenon_intro zenon_H149 | zenon_intro zenon_H148 ]. % 15.31/15.47 exact (zenon_H145 zenon_H149). % 15.31/15.47 apply (zenon_or_s _ _ zenon_H148); [ zenon_intro zenon_H14a | zenon_intro zenon_H142 ]. % 15.31/15.47 apply (zenon_L351_); trivial. % 15.31/15.47 apply (zenon_or_s _ _ zenon_H1c5); [ zenon_intro zenon_Hd8 | zenon_intro zenon_H1c6 ]. % 15.31/15.47 apply (zenon_L163_); trivial. % 15.31/15.47 apply (zenon_or_s _ _ zenon_H1c6); [ zenon_intro zenon_H21 | zenon_intro zenon_H1c7 ]. % 15.31/15.47 exact (zenon_H1b4 zenon_H21). % 15.31/15.47 apply (zenon_or_s _ _ zenon_H1c7); [ zenon_intro zenon_H117 | zenon_intro zenon_H11f ]. % 15.31/15.47 apply (zenon_L622_); trivial. % 15.31/15.47 apply (zenon_L611_); trivial. % 15.31/15.47 apply (zenon_or_s _ _ zenon_Hc0); [ zenon_intro zenon_Haf | zenon_intro zenon_Hba ]. % 15.31/15.47 apply (zenon_L39_); trivial. % 15.31/15.47 apply (zenon_L43_); trivial. % 15.31/15.47 apply (zenon_L624_); trivial. % 15.31/15.47 apply (zenon_or_s _ _ zenon_H48); [ zenon_intro zenon_H29 | zenon_intro zenon_H37 ]. % 15.31/15.47 apply (zenon_L5_); trivial. % 15.31/15.47 apply (zenon_or_s _ _ zenon_Hf1); [ zenon_intro zenon_H47 | zenon_intro zenon_Hf4 ]. % 15.31/15.47 exact (zenon_H45 zenon_H47). % 15.31/15.47 apply (zenon_or_s _ _ zenon_Hf4); [ zenon_intro zenon_Hd8 | zenon_intro zenon_Hf5 ]. % 15.31/15.47 apply (zenon_L446_); trivial. % 15.31/15.47 apply (zenon_or_s _ _ zenon_Hf5); [ zenon_intro zenon_Hae | zenon_intro zenon_Hee ]. % 15.31/15.47 apply (zenon_or_s _ _ zenon_H8e); [ zenon_intro zenon_H92 | zenon_intro zenon_H91 ]. % 15.31/15.47 exact (zenon_H8f zenon_H92). % 15.31/15.47 apply (zenon_or_s _ _ zenon_H91); [ zenon_intro zenon_H5d | zenon_intro zenon_H93 ]. % 15.31/15.47 apply (zenon_L251_); trivial. % 15.31/15.47 apply (zenon_or_s _ _ zenon_H93); [ zenon_intro zenon_H63 | zenon_intro zenon_H81 ]. % 15.31/15.47 apply (zenon_or_s _ _ zenon_Heb); [ zenon_intro zenon_H92 | zenon_intro zenon_Hec ]. % 15.31/15.47 exact (zenon_H8f zenon_H92). % 15.31/15.47 apply (zenon_or_s _ _ zenon_Hec); [ zenon_intro zenon_H68 | zenon_intro zenon_Hed ]. % 15.31/15.47 apply (zenon_L592_); trivial. % 15.31/15.47 apply (zenon_or_s _ _ zenon_Hed); [ zenon_intro zenon_Hdd | zenon_intro zenon_He9 ]. % 15.31/15.47 apply (zenon_L304_); trivial. % 15.31/15.47 apply (zenon_or_s _ _ zenon_H58); [ zenon_intro zenon_H5b | zenon_intro zenon_H5a ]. % 15.31/15.47 exact (zenon_H59 zenon_H5b). % 15.31/15.47 apply (zenon_or_s _ _ zenon_H5a); [ zenon_intro zenon_H4a | zenon_intro zenon_H5c ]. % 15.31/15.47 apply (zenon_or_s _ _ zenon_Hbe); [ zenon_intro zenon_H5b | zenon_intro zenon_Hbf ]. % 15.31/15.47 exact (zenon_H59 zenon_H5b). % 15.31/15.47 apply (zenon_or_s _ _ zenon_Hbf); [ zenon_intro zenon_H69 | zenon_intro zenon_Hc0 ]. % 15.31/15.47 apply (zenon_or_s _ _ zenon_H163); [ zenon_intro zenon_Had | zenon_intro zenon_H164 ]. % 15.31/15.47 apply (zenon_L559_); trivial. % 15.31/15.47 apply (zenon_or_s _ _ zenon_H164); [ zenon_intro zenon_H149 | zenon_intro zenon_H165 ]. % 15.31/15.47 exact (zenon_H145 zenon_H149). % 15.31/15.47 apply (zenon_or_s _ _ zenon_H165); [ zenon_intro zenon_H15d | zenon_intro zenon_Hcc ]. % 15.31/15.47 apply (zenon_or_s _ _ zenon_H1c5); [ zenon_intro zenon_Hd8 | zenon_intro zenon_H1c6 ]. % 15.31/15.47 apply (zenon_L629_); trivial. % 15.31/15.47 apply (zenon_or_s _ _ zenon_H1c6); [ zenon_intro zenon_H21 | zenon_intro zenon_H1c7 ]. % 15.31/15.47 exact (zenon_H1b4 zenon_H21). % 15.31/15.47 apply (zenon_or_s _ _ zenon_H1c7); [ zenon_intro zenon_H117 | zenon_intro zenon_H11f ]. % 15.31/15.47 apply (zenon_L586_); trivial. % 15.31/15.47 apply (zenon_L216_); trivial. % 15.31/15.47 apply (zenon_L630_); trivial. % 15.31/15.47 apply (zenon_or_s _ _ zenon_Hc0); [ zenon_intro zenon_Haf | zenon_intro zenon_Hba ]. % 15.31/15.47 apply (zenon_L219_); trivial. % 15.31/15.47 apply (zenon_L220_); trivial. % 15.31/15.47 apply (zenon_or_s _ _ zenon_H5c); [ zenon_intro zenon_H50 | zenon_intro zenon_H53 ]. % 15.31/15.47 apply (zenon_L31_); trivial. % 15.31/15.47 apply (zenon_L32_); trivial. % 15.31/15.47 apply (zenon_L33_); trivial. % 15.31/15.47 apply (zenon_L634_); trivial. % 15.31/15.47 (* end of lemma zenon_L635_ *) % 15.31/15.47 assert (zenon_L636_ : (~((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 (e0) (e2)) = (op (e0) (e3)))) -> (((op (e0) (e2)) = (e0))\/(((op (e0) (e2)) = (e1))\/(((op (e0) (e2)) = (e2))\/((op (e0) (e2)) = (e3))))) -> (~((op (e0) (e2)) = (op (e2) (e2)))) -> (~((op (e0) (e0)) = (op (e0) (e2)))) -> (((op (e0) (e2)) = (e1))\/(((op (e1) (e2)) = (e1))\/(((op (e2) (e2)) = (e1))\/((op (e3) (e2)) = (e1))))) -> (((op (e0) (e3)) = (e0))\/(((op (e0) (e3)) = (e1))\/(((op (e0) (e3)) = (e2))\/((op (e0) (e3)) = (e3))))) -> (~((op (e0) (e3)) = (op (e1) (e3)))) -> (~((op (e0) (e3)) = (op (e2) (e3)))) -> (~((op (e1) (e2)) = (op (e2) (e2)))) -> (~((op (e0) (e1)) = (op (e3) (e1)))) -> (((op (e0) (e0)) = (e3))\/(((op (e1) (e0)) = (e3))\/(((op (e2) (e0)) = (e3))\/((op (e3) (e0)) = (e3))))) -> ((op (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)) = (e0))) -> (~((op (e1) (e1)) = (e1))) -> (~((op (e1) (e1)) = (e2))) -> (~((op (e1) (e1)) = (e3))) -> (((op (e1) (e1)) = (e0))\/(((op (e1) (e1)) = (e1))\/(((op (e1) (e1)) = (e2))\/((op (e1) (e1)) = (e3))))) -> (~((e1) = (e3))) -> (~((op (e0) (e0)) = (e3))) -> ((~((op (e3) (e3)) = (e0)))\/((op (e3) (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) (e0)) = (op (e0) (e3)))) -> ((op (e0) (e0)) = (e0)) -> (~((e0) = (e2))) -> (((op (e0) (e3)) = (e0))\/(((op (e1) (e3)) = (e0))\/(((op (e2) (e3)) = (e0))\/((op (e3) (e3)) = (e0))))) -> (~((op (e0) (e0)) = (e2))) -> (((op (e0) (e0)) = (e3))\/(((op (e0) (e1)) = (e3))\/(((op (e0) (e2)) = (e3))\/((op (e0) (e3)) = (e3))))) -> (~((op (e0) (e3)) = (op (e3) (e3)))) -> (~((op (e0) (e2)) = (op (e1) (e2)))) -> (~((op (e1) (e3)) = (op (e3) (e3)))) -> (((op (e1) (e0)) = (e3))\/(((op (e1) (e1)) = (e3))\/(((op (e1) (e2)) = (e3))\/((op (e1) (e3)) = (e3))))) -> (~((e2) = (e3))) -> (((op (e0) (e0)) = (e2))\/(((op (e1) (e0)) = (e2))\/(((op (e2) (e0)) = (e2))\/((op (e3) (e0)) = (e2))))) -> ((~((op (e2) (e2)) = (e2)))\/((op (e2) (e2)) = (e2))) -> (~((op (e2) (e1)) = (op (e2) (e2)))) -> (~((op (e2) (e1)) = (op (e2) (e3)))) -> ((~((op (e2) (e2)) = (e3)))\/((op (e2) (e3)) = (e2))) -> (~((op (e1) (e0)) = (op (e3) (e0)))) -> (((op (e0) (e1)) = (e2))\/(((op (e1) (e1)) = (e2))\/(((op (e2) (e1)) = (e2))\/((op (e3) (e1)) = (e2))))) -> (~((op (e2) (e0)) = (op (e2) (e1)))) -> (~((op (e0) (e2)) = (op (e3) (e2)))) -> (((op (e3) (e0)) = (e1))\/(((op (e3) (e1)) = (e1))\/(((op (e3) (e2)) = (e1))\/((op (e3) (e3)) = (e1))))) -> (((op (e0) (e0)) = (e2))\/(((op (e0) (e1)) = (e2))\/(((op (e0) (e2)) = (e2))\/((op (e0) (e3)) = (e2))))) -> (~((op (e0) (e1)) = (op (e0) (e3)))) -> (~((op (e1) (e0)) = (op (e1) (e3)))) -> (~((e1) = (e2))) -> (((op (e0) (e3)) = (e1))\/(((op (e1) (e3)) = (e1))\/(((op (e2) (e3)) = (e1))\/((op (e3) (e3)) = (e1))))) -> (~((op (e0) (e0)) = (e1))) -> (~((op (e3) (e1)) = (op (e3) (e3)))) -> ((~((op (e3) (e3)) = (e1)))\/((op (e3) (e1)) = (e3))) -> (((op (e2) (e0)) = (e0))\/(((op (e2) (e1)) = (e0))\/(((op (e2) (e2)) = (e0))\/((op (e2) (e3)) = (e0))))) -> (~((op (e1) (e3)) = (op (e2) (e3)))) -> (~((op (e0) (e0)) = (op (e2) (e0)))) -> (~((op (e3) (e2)) = (op (e3) (e3)))) -> ((~((op (e3) (e3)) = (e2)))\/((op (e3) (e2)) = (e3))) -> (~((e0) = (e3))) -> (((op (e0) (e2)) = (e0))\/(((op (e1) (e2)) = (e0))\/(((op (e2) (e2)) = (e0))\/((op (e3) (e2)) = (e0))))) -> (((op (e0) (e0)) = (e1))\/(((op (e1) (e0)) = (e1))\/(((op (e2) (e0)) = (e1))\/((op (e3) (e0)) = (e1))))) -> (~((op (e0) (e1)) = (op (e1) (e1)))) -> (~((op (e1) (e1)) = (e0))) -> (((op (e1) (e0)) = (e0))\/(((op (e1) (e1)) = (e0))\/(((op (e1) (e2)) = (e0))\/((op (e1) (e3)) = (e0))))) -> (~((e0) = (e1))) -> (~((op (e0) (e0)) = (op (e1) (e0)))) -> (~((op (e2) (e0)) = (op (e2) (e3)))) -> (~((op (e1) (e2)) = (op (e1) (e3)))) -> ((~((op (e1) (e1)) = (e3)))\/((op (e1) (e3)) = (e1))) -> ((~((op (e2) (e2)) = (e1)))\/((op (e2) (e1)) = (e2))) -> ((~((op (e2) (e2)) = (e0)))\/((op (e2) (e0)) = (e2))) -> (~((op (e1) (e0)) = (op (e1) (e2)))) -> ((~((op (e1) (e1)) = (e2)))\/((op (e1) (e2)) = (e1))) -> (~((op (e0) (e1)) = (op (e2) (e1)))) -> (((op (e0) (e3)) = (e2))\/(((op (e1) (e3)) = (e2))\/(((op (e2) (e3)) = (e2))\/((op (e3) (e3)) = (e2))))) -> (((op (e2) (e0)) = (e3))\/(((op (e2) (e1)) = (e3))\/(((op (e2) (e2)) = (e3))\/((op (e2) (e3)) = (e3))))) -> (~((op (e1) (e0)) = (op (e1) (e1)))) -> ((~((op (e1) (e1)) = (e1)))\/((op (e1) (e1)) = (e1))) -> (~((op (e2) (e0)) = (op (e2) (e2)))) -> (~((op (e2) (e2)) = (op (e2) (e3)))) -> (((op (e1) (e3)) = (e0))\/(((op (e1) (e3)) = (e1))\/(((op (e1) (e3)) = (e2))\/((op (e1) (e3)) = (e3))))) -> (~((op (e2) (e1)) = (op (e3) (e1)))) -> (((op (e3) (e0)) = (e2))\/(((op (e3) (e1)) = (e2))\/(((op (e3) (e2)) = (e2))\/((op (e3) (e3)) = (e2))))) -> (((op (e0) (e1)) = (e0))\/(((op (e1) (e1)) = (e0))\/(((op (e2) (e1)) = (e0))\/((op (e3) (e1)) = (e0))))) -> (((op (e0) (e1)) = (e3))\/(((op (e1) (e1)) = (e3))\/(((op (e2) (e1)) = (e3))\/((op (e3) (e1)) = (e3))))) -> (~((op (e0) (e0)) = (op (e0) (e1)))) -> (~((op (e3) (e0)) = (op (e3) (e1)))) -> (((op (e0) (e1)) = (e1))\/(((op (e1) (e1)) = (e1))\/(((op (e2) (e1)) = (e1))\/((op (e3) (e1)) = (e1))))) -> (((op (e2) (e0)) = (e1))\/(((op (e2) (e1)) = (e1))\/(((op (e2) (e2)) = (e1))\/((op (e2) (e3)) = (e1))))) -> (((op (e0) (e2)) = (e3))\/(((op (e1) (e2)) = (e3))\/(((op (e2) (e2)) = (e3))\/((op (e3) (e2)) = (e3))))) -> (((op (e1) (e0)) = (e1))\/(((op (e1) (e1)) = (e1))\/(((op (e1) (e2)) = (e1))\/((op (e1) (e3)) = (e1))))) -> False). % 15.31/15.47 do 0 intro. intros zenon_H135 zenon_H25e zenon_H17d zenon_Hc9 zenon_H251 zenon_H28 zenon_H250 zenon_H11b zenon_H254 zenon_H80 zenon_Hb4 zenon_H7d zenon_H138 zenon_Hbe zenon_H42 zenon_Hbb zenon_H2d zenon_H2e zenon_H1b4 zenon_Hd6 zenon_H182 zenon_H1b3 zenon_Ha3 zenon_H59 zenon_H10f zenon_H44 zenon_H84 zenon_H24f zenon_H1f zenon_H5e zenon_Hd3 zenon_H8f zenon_H58 zenon_H36 zenon_H87 zenon_H8b zenon_H90 zenon_H6a zenon_Heb zenon_Haa zenon_H157 zenon_H1e2 zenon_H1c3 zenon_H22e zenon_H1a2 zenon_H154 zenon_H140 zenon_H146 zenon_H8e zenon_H1cd zenon_H1cf zenon_Ha7 zenon_H121 zenon_H45 zenon_H12d zenon_H10c zenon_H1f5 zenon_H244 zenon_H258 zenon_H173 zenon_H10e zenon_H4b zenon_H16f zenon_Hf1 zenon_H23 zenon_H145 zenon_H163 zenon_H9e zenon_H24c zenon_Hce zenon_H1d0 zenon_H1d2 zenon_H1e3 zenon_H1d4 zenon_H166 zenon_H1d3 zenon_Hde zenon_H160 zenon_He6 zenon_Hd7 zenon_H1d8 zenon_H17a zenon_H15f zenon_H25b zenon_H13c zenon_H1df zenon_H144 zenon_H199 zenon_H25a zenon_H109 zenon_H228 zenon_Hb7 zenon_H175 zenon_H1c5. % 15.31/15.47 apply (zenon_or_s _ _ zenon_H1e3); [ zenon_intro zenon_H52 | zenon_intro zenon_H156 ]. % 15.31/15.47 apply (zenon_L621_); trivial. % 15.31/15.47 apply (zenon_or_s _ _ zenon_Haa); [ zenon_intro zenon_H2f | zenon_intro zenon_H35 ]. % 15.31/15.47 apply (zenon_or_s _ _ zenon_H1c3); [ zenon_intro zenon_H30 | zenon_intro zenon_H124 ]. % 15.31/15.47 apply (zenon_or_s _ _ zenon_H10f); [ zenon_intro zenon_H3c | zenon_intro zenon_Hba ]. % 15.31/15.47 apply (zenon_or_s _ _ zenon_H10e); [ zenon_intro zenon_H3d | zenon_intro zenon_H106 ]. % 15.31/15.47 apply (zenon_L635_); trivial. % 15.31/15.47 apply (zenon_L153_); trivial. % 15.31/15.47 apply (zenon_L43_); trivial. % 15.31/15.47 apply (zenon_L256_); trivial. % 15.31/15.47 apply (zenon_L134_); trivial. % 15.31/15.47 (* end of lemma zenon_L636_ *) % 15.31/15.47 assert (zenon_L637_ : ((~((op (e3) (e3)) = (e3)))\/((op (e3) (e3)) = (e3))) -> (((op (e1) (e0)) = (e1))\/(((op (e1) (e1)) = (e1))\/(((op (e1) (e2)) = (e1))\/((op (e1) (e3)) = (e1))))) -> (((op (e0) (e2)) = (e3))\/(((op (e1) (e2)) = (e3))\/(((op (e2) (e2)) = (e3))\/((op (e3) (e2)) = (e3))))) -> (((op (e2) (e0)) = (e1))\/(((op (e2) (e1)) = (e1))\/(((op (e2) (e2)) = (e1))\/((op (e2) (e3)) = (e1))))) -> (((op (e0) (e1)) = (e1))\/(((op (e1) (e1)) = (e1))\/(((op (e2) (e1)) = (e1))\/((op (e3) (e1)) = (e1))))) -> (~((op (e3) (e0)) = (op (e3) (e1)))) -> (~((op (e0) (e0)) = (op (e0) (e1)))) -> (((op (e0) (e1)) = (e3))\/(((op (e1) (e1)) = (e3))\/(((op (e2) (e1)) = (e3))\/((op (e3) (e1)) = (e3))))) -> (((op (e0) (e1)) = (e0))\/(((op (e1) (e1)) = (e0))\/(((op (e2) (e1)) = (e0))\/((op (e3) (e1)) = (e0))))) -> (((op (e3) (e0)) = (e2))\/(((op (e3) (e1)) = (e2))\/(((op (e3) (e2)) = (e2))\/((op (e3) (e3)) = (e2))))) -> (~((op (e2) (e1)) = (op (e3) (e1)))) -> (((op (e1) (e3)) = (e0))\/(((op (e1) (e3)) = (e1))\/(((op (e1) (e3)) = (e2))\/((op (e1) (e3)) = (e3))))) -> (~((op (e2) (e2)) = (op (e2) (e3)))) -> (~((op (e2) (e0)) = (op (e2) (e2)))) -> ((~((op (e1) (e1)) = (e1)))\/((op (e1) (e1)) = (e1))) -> (~((op (e1) (e0)) = (op (e1) (e1)))) -> (((op (e2) (e0)) = (e3))\/(((op (e2) (e1)) = (e3))\/(((op (e2) (e2)) = (e3))\/((op (e2) (e3)) = (e3))))) -> (((op (e0) (e3)) = (e2))\/(((op (e1) (e3)) = (e2))\/(((op (e2) (e3)) = (e2))\/((op (e3) (e3)) = (e2))))) -> (~((op (e0) (e1)) = (op (e2) (e1)))) -> ((~((op (e1) (e1)) = (e2)))\/((op (e1) (e2)) = (e1))) -> (~((op (e1) (e0)) = (op (e1) (e2)))) -> ((~((op (e2) (e2)) = (e0)))\/((op (e2) (e0)) = (e2))) -> ((~((op (e2) (e2)) = (e1)))\/((op (e2) (e1)) = (e2))) -> ((~((op (e1) (e1)) = (e3)))\/((op (e1) (e3)) = (e1))) -> (~((op (e1) (e2)) = (op (e1) (e3)))) -> (~((op (e2) (e0)) = (op (e2) (e3)))) -> (~((e0) = (e1))) -> (~((op (e0) (e1)) = (op (e1) (e1)))) -> (((op (e0) (e0)) = (e1))\/(((op (e1) (e0)) = (e1))\/(((op (e2) (e0)) = (e1))\/((op (e3) (e0)) = (e1))))) -> (((op (e0) (e2)) = (e0))\/(((op (e1) (e2)) = (e0))\/(((op (e2) (e2)) = (e0))\/((op (e3) (e2)) = (e0))))) -> (~((e0) = (e3))) -> ((~((op (e3) (e3)) = (e2)))\/((op (e3) (e2)) = (e3))) -> (~((op (e3) (e2)) = (op (e3) (e3)))) -> (~((op (e0) (e0)) = (op (e2) (e0)))) -> (~((op (e1) (e3)) = (op (e2) (e3)))) -> (((op (e2) (e0)) = (e0))\/(((op (e2) (e1)) = (e0))\/(((op (e2) (e2)) = (e0))\/((op (e2) (e3)) = (e0))))) -> ((~((op (e3) (e3)) = (e1)))\/((op (e3) (e1)) = (e3))) -> (~((op (e3) (e1)) = (op (e3) (e3)))) -> (~((op (e0) (e0)) = (e1))) -> (((op (e0) (e3)) = (e1))\/(((op (e1) (e3)) = (e1))\/(((op (e2) (e3)) = (e1))\/((op (e3) (e3)) = (e1))))) -> (~((e1) = (e2))) -> (~((op (e1) (e0)) = (op (e1) (e3)))) -> (~((op (e0) (e1)) = (op (e0) (e3)))) -> (((op (e0) (e0)) = (e2))\/(((op (e0) (e1)) = (e2))\/(((op (e0) (e2)) = (e2))\/((op (e0) (e3)) = (e2))))) -> (((op (e3) (e0)) = (e1))\/(((op (e3) (e1)) = (e1))\/(((op (e3) (e2)) = (e1))\/((op (e3) (e3)) = (e1))))) -> (~((op (e0) (e2)) = (op (e3) (e2)))) -> (~((op (e2) (e0)) = (op (e2) (e1)))) -> (((op (e0) (e1)) = (e2))\/(((op (e1) (e1)) = (e2))\/(((op (e2) (e1)) = (e2))\/((op (e3) (e1)) = (e2))))) -> (~((op (e1) (e0)) = (op (e3) (e0)))) -> ((~((op (e2) (e2)) = (e3)))\/((op (e2) (e3)) = (e2))) -> (~((op (e2) (e1)) = (op (e2) (e3)))) -> (~((op (e2) (e1)) = (op (e2) (e2)))) -> ((~((op (e2) (e2)) = (e2)))\/((op (e2) (e2)) = (e2))) -> (((op (e0) (e0)) = (e2))\/(((op (e1) (e0)) = (e2))\/(((op (e2) (e0)) = (e2))\/((op (e3) (e0)) = (e2))))) -> (~((e2) = (e3))) -> (((op (e1) (e0)) = (e3))\/(((op (e1) (e1)) = (e3))\/(((op (e1) (e2)) = (e3))\/((op (e1) (e3)) = (e3))))) -> (~((op (e0) (e2)) = (op (e1) (e2)))) -> (~((op (e0) (e3)) = (op (e3) (e3)))) -> (((op (e0) (e0)) = (e3))\/(((op (e0) (e1)) = (e3))\/(((op (e0) (e2)) = (e3))\/((op (e0) (e3)) = (e3))))) -> (~((op (e0) (e0)) = (e2))) -> (((op (e0) (e3)) = (e0))\/(((op (e1) (e3)) = (e0))\/(((op (e2) (e3)) = (e0))\/((op (e3) (e3)) = (e0))))) -> (~((e0) = (e2))) -> (~((op (e0) (e0)) = (op (e0) (e3)))) -> (((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 (e3) (e3)) = (e0)))\/((op (e3) (e0)) = (e3))) -> (~((op (e0) (e0)) = (e3))) -> (~((e1) = (e3))) -> (~((op (e1) (e1)) = (e3))) -> (~((op (e2) (e2)) = (e0))) -> (((op (e2) (e2)) = (e0))\/(((op (e2) (e2)) = (e1))\/(((op (e2) (e2)) = (e2))\/((op (e2) (e2)) = (e3))))) -> (~((op (e3) (e0)) = (op (e3) (e3)))) -> (((op (e0) (e0)) = (e3))\/(((op (e1) (e0)) = (e3))\/(((op (e2) (e0)) = (e3))\/((op (e3) (e0)) = (e3))))) -> (~((op (e0) (e1)) = (op (e3) (e1)))) -> (~((op (e1) (e2)) = (op (e2) (e2)))) -> (~((op (e0) (e3)) = (op (e2) (e3)))) -> (~((op (e0) (e3)) = (op (e1) (e3)))) -> (((op (e0) (e3)) = (e0))\/(((op (e0) (e3)) = (e1))\/(((op (e0) (e3)) = (e2))\/((op (e0) (e3)) = (e3))))) -> (((op (e0) (e2)) = (e1))\/(((op (e1) (e2)) = (e1))\/(((op (e2) (e2)) = (e1))\/((op (e3) (e2)) = (e1))))) -> (~((op (e0) (e0)) = (op (e0) (e2)))) -> (~((op (e0) (e2)) = (op (e2) (e2)))) -> (((op (e0) (e2)) = (e0))\/(((op (e0) (e2)) = (e1))\/(((op (e0) (e2)) = (e2))\/((op (e0) (e2)) = (e3))))) -> (~((op (e0) (e2)) = (op (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 (e3) (e1)) = (op (e3) (e2)))) -> (~((op (e0) (e0)) = (op (e1) (e0)))) -> ((op (e0) (e0)) = (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)) = (e0))\/(((op (e3) (e3)) = (e1))\/(((op (e3) (e3)) = (e2))\/((op (e3) (e3)) = (e3))))) -> (~((op (e1) (e1)) = (e2))) -> (~((op (e1) (e1)) = (e1))) -> (~((op (e3) (e3)) = (e2))) -> (~((op (e1) (e3)) = (op (e3) (e3)))) -> (((op (e1) (e0)) = (e0))\/(((op (e1) (e1)) = (e0))\/(((op (e1) (e2)) = (e0))\/((op (e1) (e3)) = (e0))))) -> False). % 15.31/15.47 do 0 intro. intros zenon_H10d zenon_H1c5 zenon_H175 zenon_Hb7 zenon_H228 zenon_H109 zenon_H25a zenon_H199 zenon_H144 zenon_H1df zenon_H13c zenon_H25b zenon_H15f zenon_H17a zenon_H1d8 zenon_Hd7 zenon_He6 zenon_H160 zenon_Hde zenon_H1d3 zenon_H166 zenon_H1d4 zenon_H1e3 zenon_H1d2 zenon_H1d0 zenon_Hce zenon_H9e zenon_H23 zenon_Hf1 zenon_H16f zenon_H4b zenon_H10e zenon_H173 zenon_H258 zenon_H244 zenon_H1f5 zenon_H10c zenon_H12d zenon_H45 zenon_H121 zenon_Ha7 zenon_H1cf zenon_H1cd zenon_H8e zenon_H146 zenon_H140 zenon_H154 zenon_H1a2 zenon_H22e zenon_H1c3 zenon_H1e2 zenon_H157 zenon_Haa zenon_Heb zenon_H6a zenon_H90 zenon_H87 zenon_H36 zenon_H58 zenon_H8f zenon_Hd3 zenon_H5e zenon_H24f zenon_H84 zenon_H44 zenon_H10f zenon_H59 zenon_Ha3 zenon_H182 zenon_H2e zenon_H2d zenon_Hbb zenon_Hbe zenon_H138 zenon_H7d zenon_Hb4 zenon_H80 zenon_H254 zenon_H11b zenon_H250 zenon_H28 zenon_H251 zenon_Hc9 zenon_H17d zenon_H25e zenon_H135 zenon_H24c zenon_H1f zenon_H145 zenon_H1b3 zenon_H3c zenon_H104 zenon_H3b zenon_Hd6 zenon_H1b4 zenon_H3d zenon_H8b zenon_H163. % 15.31/15.47 apply (zenon_or_s _ _ zenon_H10d); [ zenon_intro zenon_H3e | zenon_intro zenon_H42 ]. % 15.31/15.47 apply (zenon_L560_); trivial. % 15.31/15.47 apply (zenon_L636_); trivial. % 15.31/15.47 (* end of lemma zenon_L637_ *) % 15.31/15.47 assert (zenon_L638_ : (~((op (e0) (op (e1) (e0))) = (op (e1) (e0)))) -> ((op (e0) (e2)) = (e2)) -> ((op (e1) (e0)) = (e2)) -> False). % 15.31/15.47 do 0 intro. intros zenon_H261 zenon_H63 zenon_H68. % 15.31/15.47 cut (((op (e0) (e2)) = (e2)) = ((op (e0) (op (e1) (e0))) = (op (e1) (e0)))). % 15.31/15.47 intro zenon_D_pnotp. % 15.31/15.47 apply zenon_H261. % 15.31/15.47 rewrite <- zenon_D_pnotp. % 15.31/15.47 exact zenon_H63. % 15.31/15.47 cut (((e2) = (op (e1) (e0)))); [idtac | apply NNPP; zenon_intro zenon_H262]. % 15.31/15.47 cut (((op (e0) (e2)) = (op (e0) (op (e1) (e0))))); [idtac | apply NNPP; zenon_intro zenon_H263]. % 15.31/15.47 congruence. % 15.31/15.47 elim (classic ((op (e0) (op (e1) (e0))) = (op (e0) (op (e1) (e0))))); [ zenon_intro zenon_H264 | zenon_intro zenon_H265 ]. % 15.31/15.47 cut (((op (e0) (op (e1) (e0))) = (op (e0) (op (e1) (e0)))) = ((op (e0) (e2)) = (op (e0) (op (e1) (e0))))). % 15.31/15.47 intro zenon_D_pnotp. % 15.31/15.47 apply zenon_H263. % 15.31/15.47 rewrite <- zenon_D_pnotp. % 15.31/15.47 exact zenon_H264. % 15.31/15.47 cut (((op (e0) (op (e1) (e0))) = (op (e0) (op (e1) (e0))))); [idtac | apply NNPP; zenon_intro zenon_H265]. % 15.31/15.47 cut (((op (e0) (op (e1) (e0))) = (op (e0) (e2)))); [idtac | apply NNPP; zenon_intro zenon_H266]. % 15.31/15.47 congruence. % 15.31/15.47 cut (((op (e1) (e0)) = (e2))); [idtac | apply NNPP; zenon_intro zenon_H179]. % 15.31/15.47 cut (((e0) = (e0))); [idtac | apply NNPP; zenon_intro zenon_H1d]. % 15.31/15.47 congruence. % 15.31/15.47 apply zenon_H1d. apply refl_equal. % 15.31/15.47 exact (zenon_H179 zenon_H68). % 15.31/15.47 apply zenon_H265. apply refl_equal. % 15.31/15.47 apply zenon_H265. apply refl_equal. % 15.31/15.47 apply zenon_H262. apply sym_equal. exact zenon_H68. % 15.31/15.47 (* end of lemma zenon_L638_ *) % 15.31/15.47 assert (zenon_L639_ : (((op (e1) (e0)) = (e0))\/(((op (e1) (e1)) = (e0))\/(((op (e1) (e2)) = (e0))\/((op (e1) (e3)) = (e0))))) -> ((op (e0) (e0)) = (e0)) -> (~((op (e0) (e0)) = (op (e1) (e0)))) -> (~((op (e1) (e1)) = (e0))) -> (~((op (e2) (e2)) = (e3))) -> (~((op (e2) (e2)) = (e2))) -> (~((op (e2) (e2)) = (e1))) -> (~((op (e1) (e2)) = (op (e2) (e2)))) -> (((op (e2) (e2)) = (e0))\/(((op (e2) (e2)) = (e1))\/(((op (e2) (e2)) = (e2))\/((op (e2) (e2)) = (e3))))) -> (((op (e1) (e0)) = (e2))\/(((op (e1) (e1)) = (e2))\/(((op (e1) (e2)) = (e2))\/((op (e1) (e3)) = (e2))))) -> (~((e2) = (e3))) -> ((op (e1) (e0)) = (e3)) -> (~((op (e1) (e1)) = (e2))) -> ((op (e0) (e2)) = (e2)) -> (~((op (e0) (e2)) = (op (e1) (e2)))) -> (~((e0) = (e2))) -> False). % 15.31/15.47 do 0 intro. intros zenon_H163 zenon_H1f zenon_H24c zenon_H145 zenon_H30 zenon_H2f zenon_H52 zenon_H7d zenon_H2d zenon_H84 zenon_H6a zenon_H69 zenon_Hd6 zenon_H63 zenon_H87 zenon_H5e. % 15.31/15.47 apply (zenon_or_s _ _ zenon_H163); [ zenon_intro zenon_Had | zenon_intro zenon_H164 ]. % 15.31/15.47 apply (zenon_L559_); trivial. % 15.31/15.47 apply (zenon_or_s _ _ zenon_H164); [ zenon_intro zenon_H149 | zenon_intro zenon_H165 ]. % 15.31/15.47 exact (zenon_H145 zenon_H149). % 15.31/15.47 apply (zenon_or_s _ _ zenon_H165); [ zenon_intro zenon_H15d | zenon_intro zenon_Hcc ]. % 15.31/15.47 apply (zenon_L335_); trivial. % 15.31/15.47 apply (zenon_L630_); trivial. % 15.31/15.47 (* end of lemma zenon_L639_ *) % 15.31/15.47 assert (zenon_L640_ : (((op (e0) (e0)) = (e3))\/(((op (e1) (e0)) = (e3))\/(((op (e2) (e0)) = (e3))\/((op (e3) (e0)) = (e3))))) -> (~((op (e0) (e0)) = (e3))) -> (~((e0) = (e2))) -> (~((op (e0) (e2)) = (op (e1) (e2)))) -> ((op (e0) (e2)) = (e2)) -> (~((op (e1) (e1)) = (e2))) -> (((op (e1) (e0)) = (e2))\/(((op (e1) (e1)) = (e2))\/(((op (e1) (e2)) = (e2))\/((op (e1) (e3)) = (e2))))) -> (((op (e2) (e2)) = (e0))\/(((op (e2) (e2)) = (e1))\/(((op (e2) (e2)) = (e2))\/((op (e2) (e2)) = (e3))))) -> (~((op (e1) (e2)) = (op (e2) (e2)))) -> (~((op (e2) (e2)) = (e1))) -> (~((op (e2) (e2)) = (e2))) -> (~((op (e2) (e2)) = (e3))) -> (~((op (e1) (e1)) = (e0))) -> (~((op (e0) (e0)) = (op (e1) (e0)))) -> ((op (e0) (e0)) = (e0)) -> (((op (e1) (e0)) = (e0))\/(((op (e1) (e1)) = (e0))\/(((op (e1) (e2)) = (e0))\/((op (e1) (e3)) = (e0))))) -> (~((e2) = (e3))) -> ((op (e2) (e0)) = (e2)) -> (~((e1) = (e3))) -> ((op (e3) (e0)) = (e1)) -> False). % 15.31/15.47 do 0 intro. intros zenon_Hbe zenon_H59 zenon_H5e zenon_H87 zenon_H63 zenon_Hd6 zenon_H84 zenon_H2d zenon_H7d zenon_H52 zenon_H2f zenon_H30 zenon_H145 zenon_H24c zenon_H1f zenon_H163 zenon_H6a zenon_Hdd zenon_Ha3 zenon_Hee. % 15.31/15.47 apply (zenon_or_s _ _ zenon_Hbe); [ zenon_intro zenon_H5b | zenon_intro zenon_Hbf ]. % 15.31/15.47 exact (zenon_H59 zenon_H5b). % 15.31/15.47 apply (zenon_or_s _ _ zenon_Hbf); [ zenon_intro zenon_H69 | zenon_intro zenon_Hc0 ]. % 15.31/15.47 apply (zenon_L639_); trivial. % 15.31/15.47 apply (zenon_or_s _ _ zenon_Hc0); [ zenon_intro zenon_Haf | zenon_intro zenon_Hba ]. % 15.31/15.47 apply (zenon_L64_); trivial. % 15.31/15.47 apply (zenon_L79_); trivial. % 15.31/15.47 (* end of lemma zenon_L640_ *) % 15.31/15.47 assert (zenon_L641_ : (((op (e1) (e0)) = (e1))\/(((op (e1) (e1)) = (e1))\/(((op (e1) (e2)) = (e1))\/((op (e1) (e3)) = (e1))))) -> (~((e1) = (e3))) -> (~((op (e1) (e1)) = (e1))) -> ((op (e0) (e3)) = (e2)) -> (~((op (e0) (e3)) = (op (e1) (e3)))) -> (~((e1) = (e2))) -> (((op (e2) (e2)) = (e0))\/(((op (e2) (e2)) = (e1))\/(((op (e2) (e2)) = (e2))\/((op (e2) (e2)) = (e3))))) -> ((op (e1) (e0)) = (e3)) -> (~((op (e2) (e2)) = (e1))) -> (~((op (e2) (e2)) = (e2))) -> (~((op (e2) (e2)) = (e3))) -> (~((e2) = (e3))) -> (((op (e1) (e0)) = (e2))\/(((op (e1) (e1)) = (e2))\/(((op (e1) (e2)) = (e2))\/((op (e1) (e3)) = (e2))))) -> (~((e0) = (e1))) -> ((op (e1) (e3)) = (e0)) -> False). % 15.31/15.47 do 0 intro. intros zenon_H1c5 zenon_Ha3 zenon_H1b4 zenon_H81 zenon_H80 zenon_Ha7 zenon_H2d zenon_H69 zenon_H52 zenon_H2f zenon_H30 zenon_H6a zenon_H84 zenon_H9e zenon_Hcc. % 15.31/15.47 apply (zenon_or_s _ _ zenon_H1c5); [ zenon_intro zenon_Hd8 | zenon_intro zenon_H1c6 ]. % 15.31/15.47 apply (zenon_L163_); trivial. % 15.31/15.47 apply (zenon_or_s _ _ zenon_H1c6); [ zenon_intro zenon_H21 | zenon_intro zenon_H1c7 ]. % 15.31/15.47 exact (zenon_H1b4 zenon_H21). % 15.31/15.47 apply (zenon_or_s _ _ zenon_H1c7); [ zenon_intro zenon_H117 | zenon_intro zenon_H11f ]. % 15.31/15.47 apply (zenon_L385_); trivial. % 15.31/15.47 apply (zenon_L208_); trivial. % 15.31/15.47 (* end of lemma zenon_L641_ *) % 15.31/15.47 assert (zenon_L642_ : (((op (e1) (e0)) = (e0))\/(((op (e1) (e1)) = (e0))\/(((op (e1) (e2)) = (e0))\/((op (e1) (e3)) = (e0))))) -> ((op (e0) (e0)) = (e0)) -> (~((op (e0) (e0)) = (op (e1) (e0)))) -> (~((op (e1) (e1)) = (e0))) -> (~((op (e1) (e2)) = (op (e2) (e2)))) -> (((op (e1) (e0)) = (e1))\/(((op (e1) (e1)) = (e1))\/(((op (e1) (e2)) = (e1))\/((op (e1) (e3)) = (e1))))) -> (~((e1) = (e3))) -> (~((op (e1) (e1)) = (e1))) -> ((op (e0) (e3)) = (e2)) -> (~((op (e0) (e3)) = (op (e1) (e3)))) -> (~((e1) = (e2))) -> (((op (e2) (e2)) = (e0))\/(((op (e2) (e2)) = (e1))\/(((op (e2) (e2)) = (e2))\/((op (e2) (e2)) = (e3))))) -> ((op (e1) (e0)) = (e3)) -> (~((op (e2) (e2)) = (e1))) -> (~((op (e2) (e2)) = (e2))) -> (~((op (e2) (e2)) = (e3))) -> (~((e2) = (e3))) -> (((op (e1) (e0)) = (e2))\/(((op (e1) (e1)) = (e2))\/(((op (e1) (e2)) = (e2))\/((op (e1) (e3)) = (e2))))) -> (~((e0) = (e1))) -> False). % 15.31/15.47 do 0 intro. intros zenon_H163 zenon_H1f zenon_H24c zenon_H145 zenon_H7d zenon_H1c5 zenon_Ha3 zenon_H1b4 zenon_H81 zenon_H80 zenon_Ha7 zenon_H2d zenon_H69 zenon_H52 zenon_H2f zenon_H30 zenon_H6a zenon_H84 zenon_H9e. % 15.31/15.47 apply (zenon_or_s _ _ zenon_H163); [ zenon_intro zenon_Had | zenon_intro zenon_H164 ]. % 15.31/15.47 apply (zenon_L559_); trivial. % 15.31/15.47 apply (zenon_or_s _ _ zenon_H164); [ zenon_intro zenon_H149 | zenon_intro zenon_H165 ]. % 15.31/15.47 exact (zenon_H145 zenon_H149). % 15.31/15.47 apply (zenon_or_s _ _ zenon_H165); [ zenon_intro zenon_H15d | zenon_intro zenon_Hcc ]. % 15.31/15.47 apply (zenon_L335_); trivial. % 15.31/15.47 apply (zenon_L641_); trivial. % 15.31/15.47 (* end of lemma zenon_L642_ *) % 15.31/15.47 assert (zenon_L643_ : (((op (e0) (e0)) = (e1))\/(((op (e1) (e0)) = (e1))\/(((op (e2) (e0)) = (e1))\/((op (e3) (e0)) = (e1))))) -> (~((op (e0) (e0)) = (e1))) -> (((op (e0) (e0)) = (e2))\/(((op (e0) (e1)) = (e2))\/(((op (e0) (e2)) = (e2))\/((op (e0) (e3)) = (e2))))) -> (~((op (e0) (e0)) = (e2))) -> (~((op (e1) (e1)) = (e3))) -> (~((op (e0) (e1)) = (op (e1) (e1)))) -> (((op (e1) (e1)) = (e0))\/(((op (e1) (e1)) = (e1))\/(((op (e1) (e1)) = (e2))\/((op (e1) (e1)) = (e3))))) -> (~((op (e1) (e1)) = (e2))) -> (~((op (e0) (e2)) = (op (e1) (e2)))) -> (~((e0) = (e2))) -> (((op (e0) (e0)) = (e3))\/(((op (e1) (e0)) = (e3))\/(((op (e2) (e0)) = (e3))\/((op (e3) (e0)) = (e3))))) -> (~((op (e0) (e0)) = (e3))) -> (~((e0) = (e1))) -> (((op (e1) (e0)) = (e2))\/(((op (e1) (e1)) = (e2))\/(((op (e1) (e2)) = (e2))\/((op (e1) (e3)) = (e2))))) -> (~((op (e2) (e2)) = (e3))) -> (~((op (e2) (e2)) = (e2))) -> (~((op (e2) (e2)) = (e1))) -> (((op (e2) (e2)) = (e0))\/(((op (e2) (e2)) = (e1))\/(((op (e2) (e2)) = (e2))\/((op (e2) (e2)) = (e3))))) -> (~((e1) = (e2))) -> (~((op (e0) (e3)) = (op (e1) (e3)))) -> (~((op (e1) (e1)) = (e1))) -> (~((e1) = (e3))) -> (((op (e1) (e0)) = (e1))\/(((op (e1) (e1)) = (e1))\/(((op (e1) (e2)) = (e1))\/((op (e1) (e3)) = (e1))))) -> (~((op (e1) (e2)) = (op (e2) (e2)))) -> (~((op (e1) (e1)) = (e0))) -> (~((op (e0) (e0)) = (op (e1) (e0)))) -> ((op (e0) (e0)) = (e0)) -> (((op (e1) (e0)) = (e0))\/(((op (e1) (e1)) = (e0))\/(((op (e1) (e2)) = (e0))\/((op (e1) (e3)) = (e0))))) -> (~((e2) = (e3))) -> ((op (e2) (e0)) = (e2)) -> ((op (e3) (e3)) = (e3)) -> (~((op (e3) (e0)) = (op (e3) (e3)))) -> False). % 15.31/15.47 do 0 intro. intros zenon_Hf1 zenon_H45 zenon_H8e zenon_H8f zenon_H182 zenon_H23 zenon_H1b3 zenon_Hd6 zenon_H87 zenon_H5e zenon_Hbe zenon_H59 zenon_H9e zenon_H84 zenon_H30 zenon_H2f zenon_H52 zenon_H2d zenon_Ha7 zenon_H80 zenon_H1b4 zenon_Ha3 zenon_H1c5 zenon_H7d zenon_H145 zenon_H24c zenon_H1f zenon_H163 zenon_H6a zenon_Hdd zenon_H42 zenon_Hbb. % 15.31/15.47 apply (zenon_or_s _ _ zenon_Hf1); [ zenon_intro zenon_H47 | zenon_intro zenon_Hf4 ]. % 15.31/15.47 exact (zenon_H45 zenon_H47). % 15.31/15.47 apply (zenon_or_s _ _ zenon_Hf4); [ zenon_intro zenon_Hd8 | zenon_intro zenon_Hf5 ]. % 15.31/15.47 apply (zenon_L246_); trivial. % 15.31/15.47 apply (zenon_or_s _ _ zenon_Hf5); [ zenon_intro zenon_Hae | zenon_intro zenon_Hee ]. % 15.31/15.47 apply (zenon_L304_); trivial. % 15.31/15.47 apply (zenon_or_s _ _ zenon_H8e); [ zenon_intro zenon_H92 | zenon_intro zenon_H91 ]. % 15.31/15.47 exact (zenon_H8f zenon_H92). % 15.31/15.47 apply (zenon_or_s _ _ zenon_H91); [ zenon_intro zenon_H5d | zenon_intro zenon_H93 ]. % 15.31/15.47 apply (zenon_L214_); trivial. % 15.31/15.47 apply (zenon_or_s _ _ zenon_H93); [ zenon_intro zenon_H63 | zenon_intro zenon_H81 ]. % 15.31/15.47 apply (zenon_L640_); trivial. % 15.31/15.47 apply (zenon_or_s _ _ zenon_Hbe); [ zenon_intro zenon_H5b | zenon_intro zenon_Hbf ]. % 15.31/15.47 exact (zenon_H59 zenon_H5b). % 15.31/15.47 apply (zenon_or_s _ _ zenon_Hbf); [ zenon_intro zenon_H69 | zenon_intro zenon_Hc0 ]. % 15.31/15.47 apply (zenon_L642_); trivial. % 15.31/15.47 apply (zenon_or_s _ _ zenon_Hc0); [ zenon_intro zenon_Haf | zenon_intro zenon_Hba ]. % 15.31/15.47 apply (zenon_L64_); trivial. % 15.31/15.47 apply (zenon_L43_); trivial. % 15.31/15.47 (* end of lemma zenon_L643_ *) % 15.31/15.47 assert (zenon_L644_ : (~((op (e0) (op (e1) (e0))) = (op (e1) (e0)))) -> ((op (e0) (e1)) = (e1)) -> ((op (e1) (e0)) = (e1)) -> False). % 15.31/15.47 do 0 intro. intros zenon_H261 zenon_H22 zenon_Hd8. % 15.31/15.47 cut (((op (e0) (e1)) = (e1)) = ((op (e0) (op (e1) (e0))) = (op (e1) (e0)))). % 15.31/15.47 intro zenon_D_pnotp. % 15.31/15.47 apply zenon_H261. % 15.31/15.47 rewrite <- zenon_D_pnotp. % 15.31/15.47 exact zenon_H22. % 15.31/15.47 cut (((e1) = (op (e1) (e0)))); [idtac | apply NNPP; zenon_intro zenon_H267]. % 15.31/15.47 cut (((op (e0) (e1)) = (op (e0) (op (e1) (e0))))); [idtac | apply NNPP; zenon_intro zenon_H268]. % 15.31/15.47 congruence. % 15.31/15.47 elim (classic ((op (e0) (op (e1) (e0))) = (op (e0) (op (e1) (e0))))); [ zenon_intro zenon_H264 | zenon_intro zenon_H265 ]. % 15.31/15.47 cut (((op (e0) (op (e1) (e0))) = (op (e0) (op (e1) (e0)))) = ((op (e0) (e1)) = (op (e0) (op (e1) (e0))))). % 15.31/15.47 intro zenon_D_pnotp. % 15.31/15.47 apply zenon_H268. % 15.31/15.47 rewrite <- zenon_D_pnotp. % 15.31/15.47 exact zenon_H264. % 15.31/15.47 cut (((op (e0) (op (e1) (e0))) = (op (e0) (op (e1) (e0))))); [idtac | apply NNPP; zenon_intro zenon_H265]. % 15.31/15.47 cut (((op (e0) (op (e1) (e0))) = (op (e0) (e1)))); [idtac | apply NNPP; zenon_intro zenon_H269]. % 15.31/15.47 congruence. % 15.31/15.47 cut (((op (e1) (e0)) = (e1))); [idtac | apply NNPP; zenon_intro zenon_H26a]. % 15.31/15.47 cut (((e0) = (e0))); [idtac | apply NNPP; zenon_intro zenon_H1d]. % 15.31/15.47 congruence. % 15.31/15.47 apply zenon_H1d. apply refl_equal. % 15.31/15.47 exact (zenon_H26a zenon_Hd8). % 15.31/15.47 apply zenon_H265. apply refl_equal. % 15.31/15.47 apply zenon_H265. apply refl_equal. % 15.31/15.47 apply zenon_H267. apply sym_equal. exact zenon_Hd8. % 15.31/15.47 (* end of lemma zenon_L644_ *) % 15.31/15.47 assert (zenon_L645_ : (((op (e1) (e0)) = (e0))\/(((op (e1) (e1)) = (e0))\/(((op (e1) (e2)) = (e0))\/((op (e1) (e3)) = (e0))))) -> ((op (e0) (e0)) = (e0)) -> (~((op (e0) (e0)) = (op (e1) (e0)))) -> (~((op (e1) (e1)) = (e0))) -> (~((op (e2) (e2)) = (e3))) -> (~((op (e2) (e2)) = (e2))) -> (~((op (e2) (e2)) = (e1))) -> (~((op (e1) (e2)) = (op (e2) (e2)))) -> (((op (e2) (e2)) = (e0))\/(((op (e2) (e2)) = (e1))\/(((op (e2) (e2)) = (e2))\/((op (e2) (e2)) = (e3))))) -> (((op (e0) (e3)) = (e2))\/(((op (e1) (e3)) = (e2))\/(((op (e2) (e3)) = (e2))\/((op (e3) (e3)) = (e2))))) -> (~((e2) = (e3))) -> ((op (e0) (e3)) = (e3)) -> (~((e0) = (e2))) -> ((op (e2) (e0)) = (e2)) -> (~((op (e2) (e0)) = (op (e2) (e3)))) -> (~((op (e3) (e3)) = (e2))) -> False). % 15.31/15.47 do 0 intro. intros zenon_H163 zenon_H1f zenon_H24c zenon_H145 zenon_H30 zenon_H2f zenon_H52 zenon_H7d zenon_H2d zenon_H160 zenon_H6a zenon_H53 zenon_H5e zenon_Hdd zenon_Hce zenon_H3d. % 15.31/15.47 apply (zenon_or_s _ _ zenon_H163); [ zenon_intro zenon_Had | zenon_intro zenon_H164 ]. % 15.31/15.47 apply (zenon_L559_); trivial. % 15.31/15.47 apply (zenon_or_s _ _ zenon_H164); [ zenon_intro zenon_H149 | zenon_intro zenon_H165 ]. % 15.31/15.47 exact (zenon_H145 zenon_H149). % 15.31/15.47 apply (zenon_or_s _ _ zenon_H165); [ zenon_intro zenon_H15d | zenon_intro zenon_Hcc ]. % 15.31/15.47 apply (zenon_L335_); trivial. % 15.31/15.47 apply (zenon_L459_); trivial. % 15.31/15.47 (* end of lemma zenon_L645_ *) % 15.31/15.47 assert (zenon_L646_ : (((op (e0) (e0)) = (e2))\/(((op (e0) (e1)) = (e2))\/(((op (e0) (e2)) = (e2))\/((op (e0) (e3)) = (e2))))) -> (~((op (e0) (e0)) = (e2))) -> (~((op (e3) (e3)) = (e2))) -> (~((op (e2) (e0)) = (op (e2) (e3)))) -> ((op (e2) (e0)) = (e2)) -> (~((e0) = (e2))) -> (((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 (e1) (e2)) = (op (e2) (e2)))) -> (~((op (e2) (e2)) = (e1))) -> (~((op (e2) (e2)) = (e2))) -> (~((op (e2) (e2)) = (e3))) -> (~((op (e1) (e1)) = (e0))) -> (~((op (e0) (e0)) = (op (e1) (e0)))) -> ((op (e0) (e0)) = (e0)) -> (((op (e1) (e0)) = (e0))\/(((op (e1) (e1)) = (e0))\/(((op (e1) (e2)) = (e0))\/((op (e1) (e3)) = (e0))))) -> (~((e1) = (e2))) -> (((op (e0) (e0)) = (e3))\/(((op (e0) (e1)) = (e3))\/(((op (e0) (e2)) = (e3))\/((op (e0) (e3)) = (e3))))) -> (~((op (e0) (e0)) = (e3))) -> (~((op (e0) (e1)) = (op (e3) (e1)))) -> ((op (e3) (e1)) = (e3)) -> (~((e1) = (e3))) -> ((op (e0) (e2)) = (e1)) -> (~((e2) = (e3))) -> False). % 15.31/15.47 do 0 intro. intros zenon_H8e zenon_H8f zenon_H3d zenon_Hce zenon_Hdd zenon_H5e zenon_H160 zenon_H2d zenon_H7d zenon_H52 zenon_H2f zenon_H30 zenon_H145 zenon_H24c zenon_H1f zenon_H163 zenon_Ha7 zenon_H58 zenon_H59 zenon_H138 zenon_H10a zenon_Ha3 zenon_H29 zenon_H6a. % 15.31/15.47 apply (zenon_or_s _ _ zenon_H8e); [ zenon_intro zenon_H92 | zenon_intro zenon_H91 ]. % 15.31/15.47 exact (zenon_H8f zenon_H92). % 15.31/15.47 apply (zenon_or_s _ _ zenon_H91); [ zenon_intro zenon_H5d | zenon_intro zenon_H93 ]. % 15.31/15.47 apply (zenon_or_s _ _ zenon_H58); [ zenon_intro zenon_H5b | zenon_intro zenon_H5a ]. % 15.31/15.47 exact (zenon_H59 zenon_H5b). % 15.31/15.47 apply (zenon_or_s _ _ zenon_H5a); [ zenon_intro zenon_H4a | zenon_intro zenon_H5c ]. % 15.31/15.47 apply (zenon_L50_); trivial. % 15.31/15.47 apply (zenon_or_s _ _ zenon_H5c); [ zenon_intro zenon_H50 | zenon_intro zenon_H53 ]. % 15.31/15.47 apply (zenon_L29_); trivial. % 15.31/15.47 apply (zenon_L645_); trivial. % 15.31/15.47 apply (zenon_or_s _ _ zenon_H93); [ zenon_intro zenon_H63 | zenon_intro zenon_H81 ]. % 15.31/15.47 apply (zenon_L104_); trivial. % 15.31/15.47 apply (zenon_L129_); trivial. % 15.31/15.47 (* end of lemma zenon_L646_ *) % 15.31/15.47 assert (zenon_L647_ : (~((op (e0) (op (e1) (e0))) = (op (e1) (e0)))) -> ((op (e0) (e3)) = (e3)) -> ((op (e1) (e0)) = (e3)) -> False). % 15.31/15.47 do 0 intro. intros zenon_H261 zenon_H53 zenon_H69. % 15.31/15.47 cut (((op (e0) (e3)) = (e3)) = ((op (e0) (op (e1) (e0))) = (op (e1) (e0)))). % 15.31/15.47 intro zenon_D_pnotp. % 15.31/15.47 apply zenon_H261. % 15.31/15.47 rewrite <- zenon_D_pnotp. % 15.31/15.47 exact zenon_H53. % 15.31/15.47 cut (((e3) = (op (e1) (e0)))); [idtac | apply NNPP; zenon_intro zenon_H26b]. % 15.31/15.47 cut (((op (e0) (e3)) = (op (e0) (op (e1) (e0))))); [idtac | apply NNPP; zenon_intro zenon_H26c]. % 15.31/15.47 congruence. % 15.31/15.47 elim (classic ((op (e0) (op (e1) (e0))) = (op (e0) (op (e1) (e0))))); [ zenon_intro zenon_H264 | zenon_intro zenon_H265 ]. % 15.31/15.47 cut (((op (e0) (op (e1) (e0))) = (op (e0) (op (e1) (e0)))) = ((op (e0) (e3)) = (op (e0) (op (e1) (e0))))). % 15.31/15.47 intro zenon_D_pnotp. % 15.31/15.47 apply zenon_H26c. % 15.31/15.47 rewrite <- zenon_D_pnotp. % 15.31/15.47 exact zenon_H264. % 15.31/15.47 cut (((op (e0) (op (e1) (e0))) = (op (e0) (op (e1) (e0))))); [idtac | apply NNPP; zenon_intro zenon_H265]. % 15.31/15.47 cut (((op (e0) (op (e1) (e0))) = (op (e0) (e3)))); [idtac | apply NNPP; zenon_intro zenon_H26d]. % 15.31/15.47 congruence. % 15.31/15.47 cut (((op (e1) (e0)) = (e3))); [idtac | apply NNPP; zenon_intro zenon_H6c]. % 15.31/15.47 cut (((e0) = (e0))); [idtac | apply NNPP; zenon_intro zenon_H1d]. % 15.31/15.47 congruence. % 15.31/15.47 apply zenon_H1d. apply refl_equal. % 15.31/15.47 exact (zenon_H6c zenon_H69). % 15.31/15.47 apply zenon_H265. apply refl_equal. % 15.31/15.47 apply zenon_H265. apply refl_equal. % 15.31/15.47 apply zenon_H26b. apply sym_equal. exact zenon_H69. % 15.31/15.47 (* end of lemma zenon_L647_ *) % 15.31/15.47 assert (zenon_L648_ : (~((op (e3) (op (e1) (e3))) = (op (e1) (e3)))) -> ((op (e3) (e1)) = (e1)) -> ((op (e1) (e3)) = (e1)) -> False). % 15.31/15.47 do 0 intro. intros zenon_H26e zenon_H13e zenon_H11f. % 15.31/15.47 cut (((op (e3) (e1)) = (e1)) = ((op (e3) (op (e1) (e3))) = (op (e1) (e3)))). % 15.31/15.47 intro zenon_D_pnotp. % 15.31/15.47 apply zenon_H26e. % 15.31/15.47 rewrite <- zenon_D_pnotp. % 15.31/15.47 exact zenon_H13e. % 15.31/15.47 cut (((e1) = (op (e1) (e3)))); [idtac | apply NNPP; zenon_intro zenon_H120]. % 15.31/15.47 cut (((op (e3) (e1)) = (op (e3) (op (e1) (e3))))); [idtac | apply NNPP; zenon_intro zenon_H26f]. % 15.31/15.47 congruence. % 15.31/15.47 elim (classic ((op (e3) (op (e1) (e3))) = (op (e3) (op (e1) (e3))))); [ zenon_intro zenon_H270 | zenon_intro zenon_H271 ]. % 15.31/15.47 cut (((op (e3) (op (e1) (e3))) = (op (e3) (op (e1) (e3)))) = ((op (e3) (e1)) = (op (e3) (op (e1) (e3))))). % 15.31/15.47 intro zenon_D_pnotp. % 15.31/15.47 apply zenon_H26f. % 15.31/15.47 rewrite <- zenon_D_pnotp. % 15.31/15.47 exact zenon_H270. % 15.31/15.47 cut (((op (e3) (op (e1) (e3))) = (op (e3) (op (e1) (e3))))); [idtac | apply NNPP; zenon_intro zenon_H271]. % 15.31/15.47 cut (((op (e3) (op (e1) (e3))) = (op (e3) (e1)))); [idtac | apply NNPP; zenon_intro zenon_H272]. % 15.31/15.47 congruence. % 15.31/15.47 cut (((op (e1) (e3)) = (e1))); [idtac | apply NNPP; zenon_intro zenon_H273]. % 15.31/15.47 cut (((e3) = (e3))); [idtac | apply NNPP; zenon_intro zenon_H4d]. % 15.31/15.47 congruence. % 15.31/15.47 apply zenon_H4d. apply refl_equal. % 15.31/15.47 exact (zenon_H273 zenon_H11f). % 15.31/15.47 apply zenon_H271. apply refl_equal. % 15.31/15.47 apply zenon_H271. apply refl_equal. % 15.31/15.47 apply zenon_H120. apply sym_equal. exact zenon_H11f. % 15.31/15.47 (* end of lemma zenon_L648_ *) % 15.31/15.47 assert (zenon_L649_ : (~((op (e3) (op (e1) (e3))) = (op (e3) (e2)))) -> ((op (e1) (e3)) = (e2)) -> False). % 15.31/15.47 do 0 intro. intros zenon_H274 zenon_H82. % 15.31/15.47 cut (((op (e1) (e3)) = (e2))); [idtac | apply NNPP; zenon_intro zenon_Hcd]. % 15.31/15.47 cut (((e3) = (e3))); [idtac | apply NNPP; zenon_intro zenon_H4d]. % 15.31/15.47 congruence. % 15.31/15.47 apply zenon_H4d. apply refl_equal. % 15.31/15.47 exact (zenon_Hcd zenon_H82). % 15.31/15.47 (* end of lemma zenon_L649_ *) % 15.31/15.47 assert (zenon_L650_ : (~((op (e3) (op (e1) (e3))) = (op (e1) (e3)))) -> ((op (e3) (e2)) = (e2)) -> ((op (e1) (e3)) = (e2)) -> False). % 15.31/15.47 do 0 intro. intros zenon_H26e zenon_H1dd zenon_H82. % 15.31/15.47 cut (((op (e3) (e2)) = (e2)) = ((op (e3) (op (e1) (e3))) = (op (e1) (e3)))). % 15.31/15.47 intro zenon_D_pnotp. % 15.31/15.47 apply zenon_H26e. % 15.31/15.47 rewrite <- zenon_D_pnotp. % 15.31/15.47 exact zenon_H1dd. % 15.31/15.47 cut (((e2) = (op (e1) (e3)))); [idtac | apply NNPP; zenon_intro zenon_H83]. % 15.31/15.47 cut (((op (e3) (e2)) = (op (e3) (op (e1) (e3))))); [idtac | apply NNPP; zenon_intro zenon_H275]. % 15.31/15.47 congruence. % 15.31/15.47 elim (classic ((op (e3) (op (e1) (e3))) = (op (e3) (op (e1) (e3))))); [ zenon_intro zenon_H270 | zenon_intro zenon_H271 ]. % 15.31/15.47 cut (((op (e3) (op (e1) (e3))) = (op (e3) (op (e1) (e3)))) = ((op (e3) (e2)) = (op (e3) (op (e1) (e3))))). % 15.31/15.47 intro zenon_D_pnotp. % 15.31/15.47 apply zenon_H275. % 15.31/15.47 rewrite <- zenon_D_pnotp. % 15.31/15.47 exact zenon_H270. % 15.31/15.47 cut (((op (e3) (op (e1) (e3))) = (op (e3) (op (e1) (e3))))); [idtac | apply NNPP; zenon_intro zenon_H271]. % 15.31/15.47 cut (((op (e3) (op (e1) (e3))) = (op (e3) (e2)))); [idtac | apply NNPP; zenon_intro zenon_H274]. % 15.31/15.47 congruence. % 15.31/15.47 apply (zenon_L649_); trivial. % 15.31/15.47 apply zenon_H271. apply refl_equal. % 15.31/15.47 apply zenon_H271. apply refl_equal. % 15.31/15.47 apply zenon_H83. apply sym_equal. exact zenon_H82. % 15.31/15.47 (* end of lemma zenon_L650_ *) % 15.31/15.47 assert (zenon_L651_ : (((op (e3) (e0)) = (e2))\/(((op (e3) (e1)) = (e2))\/(((op (e3) (e2)) = (e2))\/((op (e3) (e3)) = (e2))))) -> ((op (e3) (e0)) = (e3)) -> (~((e2) = (e3))) -> ((op (e0) (e1)) = (e2)) -> (~((op (e0) (e1)) = (op (e3) (e1)))) -> (~((e1) = (e2))) -> ((op (e2) (e3)) = (e1)) -> (~((op (e3) (op (e1) (e3))) = (op (e1) (e3)))) -> (((op (e0) (e1)) = (e2))\/(((op (e1) (e1)) = (e2))\/(((op (e2) (e1)) = (e2))\/((op (e3) (e1)) = (e2))))) -> (~((op (e0) (e1)) = (op (e0) (e3)))) -> (~((op (e1) (e1)) = (e2))) -> ((op (e2) (e0)) = (e2)) -> (~((op (e2) (e0)) = (op (e2) (e1)))) -> ((op (e3) (e1)) = (e1)) -> (((op (e0) (e3)) = (e2))\/(((op (e1) (e3)) = (e2))\/(((op (e2) (e3)) = (e2))\/((op (e3) (e3)) = (e2))))) -> (~((op (e3) (e3)) = (e2))) -> False). % 15.31/15.47 do 0 intro. intros zenon_H1df zenon_Hba zenon_H6a zenon_H5d zenon_H138 zenon_Ha7 zenon_Hb5 zenon_H26e zenon_H1a2 zenon_H1cd zenon_Hd6 zenon_Hdd zenon_H154 zenon_H13e zenon_H160 zenon_H3d. % 15.31/15.47 apply (zenon_or_s _ _ zenon_H1df); [ zenon_intro zenon_He9 | zenon_intro zenon_H1e0 ]. % 15.31/15.47 apply (zenon_L220_); trivial. % 15.31/15.47 apply (zenon_or_s _ _ zenon_H1e0); [ zenon_intro zenon_H16a | zenon_intro zenon_H1e1 ]. % 15.31/15.47 apply (zenon_L146_); trivial. % 15.31/15.47 apply (zenon_or_s _ _ zenon_H1e1); [ zenon_intro zenon_H1dd | zenon_intro zenon_H43 ]. % 15.31/15.47 apply (zenon_or_s _ _ zenon_H160); [ zenon_intro zenon_H81 | zenon_intro zenon_H161 ]. % 15.31/15.47 apply (zenon_L415_); trivial. % 15.31/15.47 apply (zenon_or_s _ _ zenon_H161); [ zenon_intro zenon_H82 | zenon_intro zenon_H162 ]. % 15.31/15.47 apply (zenon_L650_); trivial. % 15.31/15.47 apply (zenon_or_s _ _ zenon_H162); [ zenon_intro zenon_H124 | zenon_intro zenon_H43 ]. % 15.31/15.47 apply (zenon_L93_); trivial. % 15.31/15.47 exact (zenon_H3d zenon_H43). % 15.31/15.47 exact (zenon_H3d zenon_H43). % 15.31/15.47 (* end of lemma zenon_L651_ *) % 15.31/15.47 assert (zenon_L652_ : (((op (e0) (e3)) = (e1))\/(((op (e1) (e3)) = (e1))\/(((op (e2) (e3)) = (e1))\/((op (e3) (e3)) = (e1))))) -> (~((op (e3) (e1)) = (op (e3) (e2)))) -> (~((op (e2) (e2)) = (e1))) -> ((op (e1) (e2)) = (e3)) -> (~((e1) = (e3))) -> (~((op (e0) (e2)) = (op (e0) (e3)))) -> (((op (e0) (e2)) = (e1))\/(((op (e1) (e2)) = (e1))\/(((op (e2) (e2)) = (e1))\/((op (e3) (e2)) = (e1))))) -> (~((op (e3) (e3)) = (e2))) -> (((op (e0) (e3)) = (e2))\/(((op (e1) (e3)) = (e2))\/(((op (e2) (e3)) = (e2))\/((op (e3) (e3)) = (e2))))) -> ((op (e3) (e1)) = (e1)) -> (~((op (e2) (e0)) = (op (e2) (e1)))) -> ((op (e2) (e0)) = (e2)) -> (~((op (e1) (e1)) = (e2))) -> (~((op (e0) (e1)) = (op (e0) (e3)))) -> (((op (e0) (e1)) = (e2))\/(((op (e1) (e1)) = (e2))\/(((op (e2) (e1)) = (e2))\/((op (e3) (e1)) = (e2))))) -> (~((op (e3) (op (e1) (e3))) = (op (e1) (e3)))) -> (~((e1) = (e2))) -> (~((op (e0) (e1)) = (op (e3) (e1)))) -> ((op (e0) (e1)) = (e2)) -> (~((e2) = (e3))) -> ((op (e3) (e0)) = (e3)) -> (((op (e3) (e0)) = (e2))\/(((op (e3) (e1)) = (e2))\/(((op (e3) (e2)) = (e2))\/((op (e3) (e3)) = (e2))))) -> (~((op (e3) (e3)) = (e1))) -> False). % 15.31/15.48 do 0 intro. intros zenon_H121 zenon_H135 zenon_H52 zenon_H88 zenon_Ha3 zenon_Hc9 zenon_H11b zenon_H3d zenon_H160 zenon_H13e zenon_H154 zenon_Hdd zenon_Hd6 zenon_H1cd zenon_H1a2 zenon_H26e zenon_Ha7 zenon_H138 zenon_H5d zenon_H6a zenon_Hba zenon_H1df zenon_H104. % 15.31/15.48 apply (zenon_or_s _ _ zenon_H121); [ zenon_intro zenon_H37 | zenon_intro zenon_H122 ]. % 15.31/15.48 apply (zenon_L395_); trivial. % 15.31/15.48 apply (zenon_or_s _ _ zenon_H122); [ zenon_intro zenon_H11f | zenon_intro zenon_H123 ]. % 15.31/15.48 apply (zenon_L648_); trivial. % 15.31/15.48 apply (zenon_or_s _ _ zenon_H123); [ zenon_intro zenon_Hb5 | zenon_intro zenon_H38 ]. % 15.31/15.48 apply (zenon_L651_); trivial. % 15.31/15.48 exact (zenon_H104 zenon_H38). % 15.31/15.48 (* end of lemma zenon_L652_ *) % 15.31/15.48 assert (zenon_L653_ : (((op (e3) (e0)) = (e1))\/(((op (e3) (e1)) = (e1))\/(((op (e3) (e2)) = (e1))\/((op (e3) (e3)) = (e1))))) -> (((op (e3) (e0)) = (e2))\/(((op (e3) (e1)) = (e2))\/(((op (e3) (e2)) = (e2))\/((op (e3) (e3)) = (e2))))) -> ((op (e3) (e0)) = (e3)) -> (~((e2) = (e3))) -> ((op (e0) (e1)) = (e2)) -> (~((op (e0) (e1)) = (op (e3) (e1)))) -> (~((e1) = (e2))) -> (~((op (e3) (op (e1) (e3))) = (op (e1) (e3)))) -> (((op (e0) (e1)) = (e2))\/(((op (e1) (e1)) = (e2))\/(((op (e2) (e1)) = (e2))\/((op (e3) (e1)) = (e2))))) -> (~((op (e0) (e1)) = (op (e0) (e3)))) -> (~((op (e1) (e1)) = (e2))) -> ((op (e2) (e0)) = (e2)) -> (~((op (e2) (e0)) = (op (e2) (e1)))) -> (((op (e0) (e3)) = (e2))\/(((op (e1) (e3)) = (e2))\/(((op (e2) (e3)) = (e2))\/((op (e3) (e3)) = (e2))))) -> (~((op (e3) (e3)) = (e2))) -> (((op (e0) (e2)) = (e1))\/(((op (e1) (e2)) = (e1))\/(((op (e2) (e2)) = (e1))\/((op (e3) (e2)) = (e1))))) -> (~((op (e0) (e2)) = (op (e0) (e3)))) -> (~((e1) = (e3))) -> ((op (e1) (e2)) = (e3)) -> (~((op (e2) (e2)) = (e1))) -> (~((op (e3) (e1)) = (op (e3) (e2)))) -> (((op (e0) (e3)) = (e1))\/(((op (e1) (e3)) = (e1))\/(((op (e2) (e3)) = (e1))\/((op (e3) (e3)) = (e1))))) -> ((op (e0) (e2)) = (e1)) -> (~((op (e0) (e2)) = (op (e3) (e2)))) -> (~((op (e3) (e3)) = (e1))) -> False). % 15.31/15.48 do 0 intro. intros zenon_H146 zenon_H1df zenon_Hba zenon_H6a zenon_H5d zenon_H138 zenon_Ha7 zenon_H26e zenon_H1a2 zenon_H1cd zenon_Hd6 zenon_Hdd zenon_H154 zenon_H160 zenon_H3d zenon_H11b zenon_Hc9 zenon_Ha3 zenon_H88 zenon_H52 zenon_H135 zenon_H121 zenon_H29 zenon_H140 zenon_H104. % 15.31/15.48 apply (zenon_or_s _ _ zenon_H146); [ zenon_intro zenon_Hee | zenon_intro zenon_H14b ]. % 15.31/15.48 apply (zenon_L79_); trivial. % 15.31/15.48 apply (zenon_or_s _ _ zenon_H14b); [ zenon_intro zenon_H13e | zenon_intro zenon_H14c ]. % 15.31/15.48 apply (zenon_L652_); trivial. % 15.31/15.48 apply (zenon_or_s _ _ zenon_H14c); [ zenon_intro zenon_H119 | zenon_intro zenon_H38 ]. % 15.31/15.48 apply (zenon_L124_); trivial. % 15.31/15.48 exact (zenon_H104 zenon_H38). % 15.31/15.48 (* end of lemma zenon_L653_ *) % 15.31/15.48 assert (zenon_L654_ : (((op (e1) (e0)) = (e3))\/(((op (e1) (e1)) = (e3))\/(((op (e1) (e2)) = (e3))\/((op (e1) (e3)) = (e3))))) -> ((op (e0) (e3)) = (e3)) -> (~((op (e0) (op (e1) (e0))) = (op (e1) (e0)))) -> (~((op (e1) (e1)) = (e3))) -> (~((op (e3) (e3)) = (e1))) -> (~((op (e0) (e2)) = (op (e3) (e2)))) -> ((op (e0) (e2)) = (e1)) -> (((op (e0) (e3)) = (e1))\/(((op (e1) (e3)) = (e1))\/(((op (e2) (e3)) = (e1))\/((op (e3) (e3)) = (e1))))) -> (~((op (e3) (e1)) = (op (e3) (e2)))) -> (~((op (e2) (e2)) = (e1))) -> (~((e1) = (e3))) -> (~((op (e0) (e2)) = (op (e0) (e3)))) -> (((op (e0) (e2)) = (e1))\/(((op (e1) (e2)) = (e1))\/(((op (e2) (e2)) = (e1))\/((op (e3) (e2)) = (e1))))) -> (~((op (e2) (e0)) = (op (e2) (e1)))) -> (~((op (e1) (e1)) = (e2))) -> (((op (e0) (e1)) = (e2))\/(((op (e1) (e1)) = (e2))\/(((op (e2) (e1)) = (e2))\/((op (e3) (e1)) = (e2))))) -> (~((op (e3) (op (e1) (e3))) = (op (e1) (e3)))) -> (~((e1) = (e2))) -> (~((op (e0) (e1)) = (op (e3) (e1)))) -> ((op (e3) (e0)) = (e3)) -> (((op (e3) (e0)) = (e2))\/(((op (e3) (e1)) = (e2))\/(((op (e3) (e2)) = (e2))\/((op (e3) (e3)) = (e2))))) -> (((op (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))))) -> (~((op (e0) (e1)) = (op (e0) (e3)))) -> ((op (e0) (e1)) = (e2)) -> (~((e2) = (e3))) -> ((op (e2) (e0)) = (e2)) -> (~((op (e2) (e0)) = (op (e2) (e3)))) -> (~((op (e3) (e3)) = (e2))) -> False). % 15.31/15.48 do 0 intro. intros zenon_H90 zenon_H53 zenon_H261 zenon_H182 zenon_H104 zenon_H140 zenon_H29 zenon_H121 zenon_H135 zenon_H52 zenon_Ha3 zenon_Hc9 zenon_H11b zenon_H154 zenon_Hd6 zenon_H1a2 zenon_H26e zenon_Ha7 zenon_H138 zenon_Hba zenon_H1df zenon_H146 zenon_H160 zenon_H1cd zenon_H5d zenon_H6a zenon_Hdd zenon_Hce zenon_H3d. % 15.31/15.48 apply (zenon_or_s _ _ zenon_H90); [ zenon_intro zenon_H69 | zenon_intro zenon_H94 ]. % 15.31/15.48 apply (zenon_L647_); trivial. % 15.31/15.48 apply (zenon_or_s _ _ zenon_H94); [ zenon_intro zenon_H96 | zenon_intro zenon_H95 ]. % 15.31/15.48 exact (zenon_H182 zenon_H96). % 15.31/15.48 apply (zenon_or_s _ _ zenon_H95); [ zenon_intro zenon_H88 | zenon_intro zenon_H8a ]. % 15.31/15.48 apply (zenon_L653_); trivial. % 15.31/15.48 apply (zenon_L410_); trivial. % 15.31/15.48 (* end of lemma zenon_L654_ *) % 15.31/15.48 assert (zenon_L655_ : (((op (e0) (e0)) = (e2))\/(((op (e0) (e1)) = (e2))\/(((op (e0) (e2)) = (e2))\/((op (e0) (e3)) = (e2))))) -> (~((op (e0) (e0)) = (e2))) -> (~((op (e3) (e3)) = (e2))) -> (~((op (e2) (e0)) = (op (e2) (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) (e0)) = (e3)) -> (~((op (e0) (e1)) = (op (e3) (e1)))) -> (~((op (e3) (op (e1) (e3))) = (op (e1) (e3)))) -> (((op (e0) (e2)) = (e1))\/(((op (e1) (e2)) = (e1))\/(((op (e2) (e2)) = (e1))\/((op (e3) (e2)) = (e1))))) -> (~((op (e0) (e2)) = (op (e0) (e3)))) -> (~((e1) = (e3))) -> (~((op (e2) (e2)) = (e1))) -> (~((op (e3) (e1)) = (op (e3) (e2)))) -> (((op (e0) (e3)) = (e1))\/(((op (e1) (e3)) = (e1))\/(((op (e2) (e3)) = (e1))\/((op (e3) (e3)) = (e1))))) -> (~((op (e1) (e1)) = (e3))) -> (~((op (e0) (op (e1) (e0))) = (op (e1) (e0)))) -> (((op (e1) (e0)) = (e3))\/(((op (e1) (e1)) = (e3))\/(((op (e1) (e2)) = (e3))\/((op (e1) (e3)) = (e3))))) -> (~((op (e0) (e0)) = (e3))) -> (((op (e0) (e0)) = (e3))\/(((op (e0) (e1)) = (e3))\/(((op (e0) (e2)) = (e3))\/((op (e0) (e3)) = (e3))))) -> (((op (e3) (e0)) = (e1))\/(((op (e3) (e1)) = (e1))\/(((op (e3) (e2)) = (e1))\/((op (e3) (e3)) = (e1))))) -> ((op (e1) (e0)) = (e1)) -> (~((op (e1) (e0)) = (op (e3) (e0)))) -> (~((e1) = (e2))) -> (~((op (e2) (e0)) = (op (e2) (e1)))) -> ((op (e2) (e0)) = (e2)) -> (~((op (e1) (e1)) = (e2))) -> (~((op (e0) (e1)) = (op (e0) (e3)))) -> (((op (e0) (e1)) = (e2))\/(((op (e1) (e1)) = (e2))\/(((op (e2) (e1)) = (e2))\/((op (e3) (e1)) = (e2))))) -> ((op (e0) (e2)) = (e1)) -> (~((op (e0) (e2)) = (op (e3) (e2)))) -> (~((op (e3) (e3)) = (e1))) -> False). % 15.31/15.48 do 0 intro. intros zenon_H8e zenon_H8f zenon_H3d zenon_Hce zenon_H6a zenon_H160 zenon_H1df zenon_Hba zenon_H138 zenon_H26e zenon_H11b zenon_Hc9 zenon_Ha3 zenon_H52 zenon_H135 zenon_H121 zenon_H182 zenon_H261 zenon_H90 zenon_H59 zenon_H58 zenon_H146 zenon_Hd8 zenon_H22e zenon_Ha7 zenon_H154 zenon_Hdd zenon_Hd6 zenon_H1cd zenon_H1a2 zenon_H29 zenon_H140 zenon_H104. % 15.31/15.48 apply (zenon_or_s _ _ zenon_H8e); [ zenon_intro zenon_H92 | zenon_intro zenon_H91 ]. % 15.31/15.48 exact (zenon_H8f zenon_H92). % 15.31/15.48 apply (zenon_or_s _ _ zenon_H91); [ zenon_intro zenon_H5d | zenon_intro zenon_H93 ]. % 15.31/15.48 apply (zenon_or_s _ _ zenon_H58); [ zenon_intro zenon_H5b | zenon_intro zenon_H5a ]. % 15.31/15.48 exact (zenon_H59 zenon_H5b). % 15.31/15.48 apply (zenon_or_s _ _ zenon_H5a); [ zenon_intro zenon_H4a | zenon_intro zenon_H5c ]. % 15.31/15.48 apply (zenon_L50_); trivial. % 15.31/15.48 apply (zenon_or_s _ _ zenon_H5c); [ zenon_intro zenon_H50 | zenon_intro zenon_H53 ]. % 15.31/15.48 apply (zenon_L29_); trivial. % 15.31/15.48 apply (zenon_L654_); trivial. % 15.31/15.48 apply (zenon_or_s _ _ zenon_H93); [ zenon_intro zenon_H63 | zenon_intro zenon_H81 ]. % 15.31/15.48 apply (zenon_L104_); trivial. % 15.31/15.48 apply (zenon_L416_); trivial. % 15.31/15.48 (* end of lemma zenon_L655_ *) % 15.31/15.48 assert (zenon_L656_ : (((op (e0) (e0)) = (e3))\/(((op (e0) (e1)) = (e3))\/(((op (e0) (e2)) = (e3))\/((op (e0) (e3)) = (e3))))) -> (~((op (e0) (e0)) = (e3))) -> (~((op (e3) (e3)) = (e2))) -> (~((op (e2) (e0)) = (op (e2) (e3)))) -> ((op (e2) (e0)) = (e2)) -> (~((e2) = (e3))) -> ((op (e0) (e1)) = (e2)) -> (~((op (e0) (e1)) = (op (e0) (e3)))) -> (((op (e0) (e3)) = (e2))\/(((op (e1) (e3)) = (e2))\/(((op (e2) (e3)) = (e2))\/((op (e3) (e3)) = (e2))))) -> (~((op (e0) (e2)) = (op (e1) (e2)))) -> (~((op (e1) (e1)) = (e3))) -> ((op (e1) (e0)) = (e1)) -> (((op (e1) (e0)) = (e3))\/(((op (e1) (e1)) = (e3))\/(((op (e1) (e2)) = (e3))\/((op (e1) (e3)) = (e3))))) -> ((op (e0) (e3)) = (e1)) -> (~((e1) = (e3))) -> False). % 15.31/15.48 do 0 intro. intros zenon_H58 zenon_H59 zenon_H3d zenon_Hce zenon_Hdd zenon_H6a zenon_H5d zenon_H1cd zenon_H160 zenon_H87 zenon_H182 zenon_Hd8 zenon_H90 zenon_H37 zenon_Ha3. % 15.31/15.48 apply (zenon_or_s _ _ zenon_H58); [ zenon_intro zenon_H5b | zenon_intro zenon_H5a ]. % 15.31/15.48 exact (zenon_H59 zenon_H5b). % 15.31/15.48 apply (zenon_or_s _ _ zenon_H5a); [ zenon_intro zenon_H4a | zenon_intro zenon_H5c ]. % 15.31/15.48 apply (zenon_L50_); trivial. % 15.31/15.48 apply (zenon_or_s _ _ zenon_H5c); [ zenon_intro zenon_H50 | zenon_intro zenon_H53 ]. % 15.31/15.48 apply (zenon_L411_); trivial. % 15.31/15.48 apply (zenon_L32_); trivial. % 15.31/15.48 (* end of lemma zenon_L656_ *) % 15.31/15.48 assert (zenon_L657_ : (~((op (e2) (op (e1) (e2))) = (op (e2) (e3)))) -> ((op (e1) (e2)) = (e3)) -> False). % 15.31/15.48 do 0 intro. intros zenon_H276 zenon_H88. % 15.31/15.48 cut (((op (e1) (e2)) = (e3))); [idtac | apply NNPP; zenon_intro zenon_H172]. % 15.31/15.48 cut (((e2) = (e2))); [idtac | apply NNPP; zenon_intro zenon_H60]. % 15.31/15.48 congruence. % 15.31/15.48 apply zenon_H60. apply refl_equal. % 15.31/15.48 exact (zenon_H172 zenon_H88). % 15.31/15.48 (* end of lemma zenon_L657_ *) % 15.31/15.48 assert (zenon_L658_ : (((op (e0) (e0)) = (e3))\/(((op (e0) (e1)) = (e3))\/(((op (e0) (e2)) = (e3))\/((op (e0) (e3)) = (e3))))) -> (~((op (e0) (e0)) = (e3))) -> (((op (e2) (e0)) = (e3))\/(((op (e2) (e1)) = (e3))\/(((op (e2) (e2)) = (e3))\/((op (e2) (e3)) = (e3))))) -> (~((op (e2) (e0)) = (op (e3) (e0)))) -> ((op (e3) (e0)) = (e3)) -> (~((op (e0) (e1)) = (op (e2) (e1)))) -> (~((op (e2) (e2)) = (e3))) -> (~((op (e2) (op (e1) (e2))) = (op (e1) (e2)))) -> (~((op (e1) (e1)) = (e3))) -> ((op (e1) (e0)) = (e1)) -> (((op (e1) (e0)) = (e3))\/(((op (e1) (e1)) = (e3))\/(((op (e1) (e2)) = (e3))\/((op (e1) (e3)) = (e3))))) -> (~((op (e0) (e2)) = (op (e1) (e2)))) -> (~((op (e1) (e1)) = (e2))) -> (~((op (e0) (op (e1) (e0))) = (op (e1) (e0)))) -> (((op (e1) (e0)) = (e2))\/(((op (e1) (e1)) = (e2))\/(((op (e1) (e2)) = (e2))\/((op (e1) (e3)) = (e2))))) -> (~((e2) = (e3))) -> ((op (e0) (e2)) = (e2)) -> ((op (e0) (e3)) = (e1)) -> (~((e1) = (e3))) -> False). % 15.31/15.48 do 0 intro. intros zenon_H58 zenon_H59 zenon_He6 zenon_H1e5 zenon_Hba zenon_Hde zenon_H30 zenon_H277 zenon_H182 zenon_Hd8 zenon_H90 zenon_H87 zenon_Hd6 zenon_H261 zenon_H84 zenon_H6a zenon_H63 zenon_H37 zenon_Ha3. % 15.31/15.48 apply (zenon_or_s _ _ zenon_H58); [ zenon_intro zenon_H5b | zenon_intro zenon_H5a ]. % 15.31/15.48 exact (zenon_H59 zenon_H5b). % 15.31/15.48 apply (zenon_or_s _ _ zenon_H5a); [ zenon_intro zenon_H4a | zenon_intro zenon_H5c ]. % 15.31/15.48 apply (zenon_or_s _ _ zenon_H84); [ zenon_intro zenon_H68 | zenon_intro zenon_H85 ]. % 15.31/15.48 apply (zenon_L638_); trivial. % 15.31/15.48 apply (zenon_or_s _ _ zenon_H85); [ zenon_intro zenon_H6e | zenon_intro zenon_H86 ]. % 15.31/15.48 exact (zenon_Hd6 zenon_H6e). % 15.31/15.48 apply (zenon_or_s _ _ zenon_H86); [ zenon_intro zenon_H7c | zenon_intro zenon_H82 ]. % 15.31/15.48 apply (zenon_L52_); trivial. % 15.31/15.48 apply (zenon_or_s _ _ zenon_H90); [ zenon_intro zenon_H69 | zenon_intro zenon_H94 ]. % 15.31/15.48 apply (zenon_L163_); trivial. % 15.31/15.48 apply (zenon_or_s _ _ zenon_H94); [ zenon_intro zenon_H96 | zenon_intro zenon_H95 ]. % 15.31/15.48 exact (zenon_H182 zenon_H96). % 15.31/15.48 apply (zenon_or_s _ _ zenon_H95); [ zenon_intro zenon_H88 | zenon_intro zenon_H8a ]. % 15.31/15.48 apply (zenon_or_s _ _ zenon_He6); [ zenon_intro zenon_Haf | zenon_intro zenon_He7 ]. % 15.31/15.48 apply (zenon_L261_); trivial. % 15.31/15.48 apply (zenon_or_s _ _ zenon_He7); [ zenon_intro zenon_Hdf | zenon_intro zenon_He8 ]. % 15.31/15.48 apply (zenon_L65_); trivial. % 15.31/15.48 apply (zenon_or_s _ _ zenon_He8); [ zenon_intro zenon_H34 | zenon_intro zenon_He2 ]. % 15.31/15.48 exact (zenon_H30 zenon_H34). % 15.31/15.48 cut (((op (e2) (e3)) = (e3)) = ((op (e2) (op (e1) (e2))) = (op (e1) (e2)))). % 15.31/15.48 intro zenon_D_pnotp. % 15.31/15.48 apply zenon_H277. % 15.31/15.48 rewrite <- zenon_D_pnotp. % 15.31/15.48 exact zenon_He2. % 15.31/15.48 cut (((e3) = (op (e1) (e2)))); [idtac | apply NNPP; zenon_intro zenon_H89]. % 15.31/15.48 cut (((op (e2) (e3)) = (op (e2) (op (e1) (e2))))); [idtac | apply NNPP; zenon_intro zenon_H278]. % 15.31/15.48 congruence. % 15.31/15.48 elim (classic ((op (e2) (op (e1) (e2))) = (op (e2) (op (e1) (e2))))); [ zenon_intro zenon_H279 | zenon_intro zenon_H27a ]. % 15.31/15.48 cut (((op (e2) (op (e1) (e2))) = (op (e2) (op (e1) (e2)))) = ((op (e2) (e3)) = (op (e2) (op (e1) (e2))))). % 15.31/15.48 intro zenon_D_pnotp. % 15.31/15.48 apply zenon_H278. % 15.31/15.48 rewrite <- zenon_D_pnotp. % 15.31/15.48 exact zenon_H279. % 15.31/15.48 cut (((op (e2) (op (e1) (e2))) = (op (e2) (op (e1) (e2))))); [idtac | apply NNPP; zenon_intro zenon_H27a]. % 15.31/15.48 cut (((op (e2) (op (e1) (e2))) = (op (e2) (e3)))); [idtac | apply NNPP; zenon_intro zenon_H276]. % 15.31/15.48 congruence. % 15.31/15.48 apply (zenon_L657_); trivial. % 15.31/15.48 apply zenon_H27a. apply refl_equal. % 15.31/15.48 apply zenon_H27a. apply refl_equal. % 15.31/15.48 apply zenon_H89. apply sym_equal. exact zenon_H88. % 15.31/15.48 apply (zenon_L165_); trivial. % 15.31/15.48 apply (zenon_or_s _ _ zenon_H5c); [ zenon_intro zenon_H50 | zenon_intro zenon_H53 ]. % 15.31/15.48 apply (zenon_L31_); trivial. % 15.31/15.48 apply (zenon_L32_); trivial. % 15.31/15.48 (* end of lemma zenon_L658_ *) % 15.31/15.48 assert (zenon_L659_ : (((op (e0) (e0)) = (e1))\/(((op (e0) (e1)) = (e1))\/(((op (e0) (e2)) = (e1))\/((op (e0) (e3)) = (e1))))) -> (~((op (e0) (e0)) = (e1))) -> (~((op (e3) (e3)) = (e1))) -> (~((op (e0) (e2)) = (op (e3) (e2)))) -> (((op (e0) (e1)) = (e2))\/(((op (e1) (e1)) = (e2))\/(((op (e2) (e1)) = (e2))\/((op (e3) (e1)) = (e2))))) -> (~((op (e2) (e0)) = (op (e2) (e1)))) -> (~((op (e1) (e0)) = (op (e3) (e0)))) -> (((op (e3) (e0)) = (e1))\/(((op (e3) (e1)) = (e1))\/(((op (e3) (e2)) = (e1))\/((op (e3) (e3)) = (e1))))) -> (((op (e0) (e3)) = (e1))\/(((op (e1) (e3)) = (e1))\/(((op (e2) (e3)) = (e1))\/((op (e3) (e3)) = (e1))))) -> (~((op (e3) (e1)) = (op (e3) (e2)))) -> (~((op (e2) (e2)) = (e1))) -> (~((op (e0) (e2)) = (op (e0) (e3)))) -> (((op (e0) (e2)) = (e1))\/(((op (e1) (e2)) = (e1))\/(((op (e2) (e2)) = (e1))\/((op (e3) (e2)) = (e1))))) -> (~((op (e3) (op (e1) (e3))) = (op (e1) (e3)))) -> (~((op (e0) (e1)) = (op (e3) (e1)))) -> (((op (e3) (e0)) = (e2))\/(((op (e3) (e1)) = (e2))\/(((op (e3) (e2)) = (e2))\/((op (e3) (e3)) = (e2))))) -> (((op (e0) (e0)) = (e2))\/(((op (e0) (e1)) = (e2))\/(((op (e0) (e2)) = (e2))\/((op (e0) (e3)) = (e2))))) -> (~((op (e0) (e0)) = (e2))) -> (((op (e0) (e3)) = (e2))\/(((op (e1) (e3)) = (e2))\/(((op (e2) (e3)) = (e2))\/((op (e3) (e3)) = (e2))))) -> (~((op (e0) (e1)) = (op (e0) (e3)))) -> ((op (e2) (e0)) = (e2)) -> (~((op (e2) (e0)) = (op (e2) (e3)))) -> (~((op (e3) (e3)) = (e2))) -> (~((e1) = (e3))) -> (~((e2) = (e3))) -> (((op (e1) (e0)) = (e2))\/(((op (e1) (e1)) = (e2))\/(((op (e1) (e2)) = (e2))\/((op (e1) (e3)) = (e2))))) -> (~((op (e0) (op (e1) (e0))) = (op (e1) (e0)))) -> (~((op (e1) (e1)) = (e2))) -> (~((op (e0) (e2)) = (op (e1) (e2)))) -> (((op (e1) (e0)) = (e3))\/(((op (e1) (e1)) = (e3))\/(((op (e1) (e2)) = (e3))\/((op (e1) (e3)) = (e3))))) -> ((op (e1) (e0)) = (e1)) -> (~((op (e1) (e1)) = (e3))) -> (~((op (e2) (op (e1) (e2))) = (op (e1) (e2)))) -> (~((op (e2) (e2)) = (e3))) -> (~((op (e0) (e1)) = (op (e2) (e1)))) -> ((op (e3) (e0)) = (e3)) -> (~((op (e2) (e0)) = (op (e3) (e0)))) -> (((op (e2) (e0)) = (e3))\/(((op (e2) (e1)) = (e3))\/(((op (e2) (e2)) = (e3))\/((op (e2) (e3)) = (e3))))) -> (~((op (e0) (e0)) = (e3))) -> (((op (e0) (e0)) = (e3))\/(((op (e0) (e1)) = (e3))\/(((op (e0) (e2)) = (e3))\/((op (e0) (e3)) = (e3))))) -> (~((e1) = (e2))) -> False). % 15.31/15.48 do 0 intro. intros zenon_H44 zenon_H45 zenon_H104 zenon_H140 zenon_H1a2 zenon_H154 zenon_H22e zenon_H146 zenon_H121 zenon_H135 zenon_H52 zenon_Hc9 zenon_H11b zenon_H26e zenon_H138 zenon_H1df zenon_H8e zenon_H8f zenon_H160 zenon_H1cd zenon_Hdd zenon_Hce zenon_H3d zenon_Ha3 zenon_H6a zenon_H84 zenon_H261 zenon_Hd6 zenon_H87 zenon_H90 zenon_Hd8 zenon_H182 zenon_H277 zenon_H30 zenon_Hde zenon_Hba zenon_H1e5 zenon_He6 zenon_H59 zenon_H58 zenon_Ha7. % 15.31/15.48 apply (zenon_or_s _ _ zenon_H44); [ zenon_intro zenon_H47 | zenon_intro zenon_H46 ]. % 15.31/15.48 exact (zenon_H45 zenon_H47). % 15.31/15.48 apply (zenon_or_s _ _ zenon_H46); [ zenon_intro zenon_H22 | zenon_intro zenon_H48 ]. % 15.31/15.48 apply (zenon_L644_); trivial. % 15.31/15.48 apply (zenon_or_s _ _ zenon_H48); [ zenon_intro zenon_H29 | zenon_intro zenon_H37 ]. % 15.31/15.48 apply (zenon_L655_); trivial. % 15.31/15.48 apply (zenon_or_s _ _ zenon_H8e); [ zenon_intro zenon_H92 | zenon_intro zenon_H91 ]. % 15.31/15.48 exact (zenon_H8f zenon_H92). % 15.31/15.48 apply (zenon_or_s _ _ zenon_H91); [ zenon_intro zenon_H5d | zenon_intro zenon_H93 ]. % 15.31/15.48 apply (zenon_L656_); trivial. % 15.31/15.48 apply (zenon_or_s _ _ zenon_H93); [ zenon_intro zenon_H63 | zenon_intro zenon_H81 ]. % 15.31/15.48 apply (zenon_L658_); trivial. % 15.31/15.48 apply (zenon_L33_); trivial. % 15.31/15.48 (* end of lemma zenon_L659_ *) % 15.31/15.48 assert (zenon_L660_ : ((~((op (e2) (e2)) = (e2)))\/((op (e2) (e2)) = (e2))) -> (~((op (e2) (e0)) = (op (e2) (e2)))) -> ((~((op (e3) (e3)) = (e0)))\/((op (e3) (e0)) = (e3))) -> (~((op (e2) (e0)) = (op (e3) (e0)))) -> (~((op (e0) (e1)) = (op (e2) (e1)))) -> (~((op (e2) (op (e1) (e2))) = (op (e1) (e2)))) -> (((op (e2) (e0)) = (e3))\/(((op (e2) (e1)) = (e3))\/(((op (e2) (e2)) = (e3))\/((op (e2) (e3)) = (e3))))) -> (((op (e3) (e0)) = (e1))\/(((op (e3) (e1)) = (e1))\/(((op (e3) (e2)) = (e1))\/((op (e3) (e3)) = (e1))))) -> (~((op (e0) (e2)) = (op (e3) (e2)))) -> (((op (e0) (e2)) = (e1))\/(((op (e1) (e2)) = (e1))\/(((op (e2) (e2)) = (e1))\/((op (e3) (e2)) = (e1))))) -> (~((op (e0) (e2)) = (op (e0) (e3)))) -> (~((op (e3) (op (e1) (e3))) = (op (e1) (e3)))) -> (((op (e3) (e0)) = (e2))\/(((op (e3) (e1)) = (e2))\/(((op (e3) (e2)) = (e2))\/((op (e3) (e3)) = (e2))))) -> (((op (e0) (e1)) = (e2))\/(((op (e1) (e1)) = (e2))\/(((op (e2) (e1)) = (e2))\/((op (e3) (e1)) = (e2))))) -> (~((op (e2) (e0)) = (op (e2) (e1)))) -> (~((op (e0) (e1)) = (op (e0) (e3)))) -> (((op (e0) (e3)) = (e1))\/(((op (e1) (e3)) = (e1))\/(((op (e2) (e3)) = (e1))\/((op (e3) (e3)) = (e1))))) -> (((op (e1) (e0)) = (e3))\/(((op (e1) (e1)) = (e3))\/(((op (e1) (e2)) = (e3))\/((op (e1) (e3)) = (e3))))) -> (~((op (e1) (e0)) = (op (e3) (e0)))) -> ((~((op (e3) (e3)) = (e2)))\/((op (e3) (e2)) = (e3))) -> (~((op (e3) (e0)) = (op (e3) (e2)))) -> (~((op (e3) (e2)) = (op (e3) (e3)))) -> (((op (e1) (e0)) = (e0))\/(((op (e1) (e1)) = (e0))\/(((op (e1) (e2)) = (e0))\/((op (e1) (e3)) = (e0))))) -> (~((op (e1) (e3)) = (op (e3) (e3)))) -> (~((op (e1) (e1)) = (e1))) -> (~((op (e1) (e1)) = (e2))) -> (((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)) = (e0))) -> ((op (e0) (e0)) = (e0)) -> (~((op (e0) (e0)) = (op (e1) (e0)))) -> (((op (e0) (e0)) = (e1))\/(((op (e1) (e0)) = (e1))\/(((op (e2) (e0)) = (e1))\/((op (e3) (e0)) = (e1))))) -> (~((op (e0) (e0)) = (e2))) -> (~((op (e1) (e1)) = (e3))) -> (~((op (e0) (e1)) = (op (e1) (e1)))) -> (((op (e2) (e2)) = (e0))\/(((op (e2) (e2)) = (e1))\/(((op (e2) (e2)) = (e2))\/((op (e2) (e2)) = (e3))))) -> (~((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))))) -> (~((e0) = (e2))) -> (~((op (e0) (e2)) = (op (e1) (e2)))) -> (((op (e1) (e0)) = (e1))\/(((op (e1) (e1)) = (e1))\/(((op (e1) (e2)) = (e1))\/((op (e1) (e3)) = (e1))))) -> (~((e0) = (e1))) -> (~((op (e0) (e3)) = (op (e1) (e3)))) -> (((op (e0) (e0)) = (e2))\/(((op (e0) (e1)) = (e2))\/(((op (e0) (e2)) = (e2))\/((op (e0) (e3)) = (e2))))) -> (~((e1) = (e2))) -> (~((op (e0) (e0)) = (e3))) -> (~((e1) = (e3))) -> (~((e2) = (e3))) -> ((op (e2) (e0)) = (e2)) -> (~((op (e3) (e0)) = (op (e3) (e3)))) -> (((op (e0) (e0)) = (e3))\/(((op (e1) (e0)) = (e3))\/(((op (e2) (e0)) = (e3))\/((op (e3) (e0)) = (e3))))) -> (~((op (e0) (e0)) = (e1))) -> ((~((op (e3) (e3)) = (e3)))\/((op (e3) (e3)) = (e3))) -> (~((op (e3) (e1)) = (op (e3) (e2)))) -> (((op (e0) (e0)) = (e1))\/(((op (e0) (e1)) = (e1))\/(((op (e0) (e2)) = (e1))\/((op (e0) (e3)) = (e1))))) -> (~((op (e0) (e3)) = (op (e3) (e3)))) -> (((op (e0) (e0)) = (e3))\/(((op (e0) (e1)) = (e3))\/(((op (e0) (e2)) = (e3))\/((op (e0) (e3)) = (e3))))) -> (((op (e0) (e3)) = (e2))\/(((op (e1) (e3)) = (e2))\/(((op (e2) (e3)) = (e2))\/((op (e3) (e3)) = (e2))))) -> (~((op (e2) (e0)) = (op (e2) (e3)))) -> (~((op (e0) (e1)) = (op (e3) (e1)))) -> (~((op (e0) (op (e1) (e0))) = (op (e1) (e0)))) -> (~((op (e3) (e0)) = (op (e3) (e1)))) -> (~((op (e3) (e1)) = (op (e3) (e3)))) -> ((~((op (e3) (e3)) = (e1)))\/((op (e3) (e1)) = (e3))) -> ((~((op (e2) (e2)) = (e3)))\/((op (e2) (e3)) = (e2))) -> False). % 15.31/15.48 do 0 intro. intros zenon_Haa zenon_H17a zenon_H10f zenon_H1e5 zenon_Hde zenon_H277 zenon_He6 zenon_H146 zenon_H140 zenon_H11b zenon_Hc9 zenon_H26e zenon_H1df zenon_H1a2 zenon_H154 zenon_H1cd zenon_H121 zenon_H90 zenon_H22e zenon_H10e zenon_H105 zenon_H173 zenon_H163 zenon_H8b zenon_H1b4 zenon_Hd6 zenon_H3b zenon_H1b3 zenon_H145 zenon_H1f zenon_H24c zenon_Hf1 zenon_H8f zenon_H182 zenon_H23 zenon_H2d zenon_H52 zenon_H7d zenon_H84 zenon_H5e zenon_H87 zenon_H1c5 zenon_H9e zenon_H80 zenon_H8e zenon_Ha7 zenon_H59 zenon_Ha3 zenon_H6a zenon_Hdd zenon_Hbb zenon_Hbe zenon_H45 zenon_H10d zenon_H135 zenon_H44 zenon_H36 zenon_H58 zenon_H160 zenon_Hce zenon_H138 zenon_H261 zenon_H109 zenon_H12d zenon_H10c zenon_H1c3. % 15.31/15.48 apply (zenon_or_s _ _ zenon_Haa); [ zenon_intro zenon_H2f | zenon_intro zenon_H35 ]. % 15.31/15.48 apply (zenon_or_s _ _ zenon_H1c3); [ zenon_intro zenon_H30 | zenon_intro zenon_H124 ]. % 15.31/15.48 apply (zenon_or_s _ _ zenon_H10f); [ zenon_intro zenon_H3c | zenon_intro zenon_Hba ]. % 15.31/15.48 apply (zenon_or_s _ _ zenon_H10c); [ zenon_intro zenon_H104 | zenon_intro zenon_H10a ]. % 15.31/15.48 apply (zenon_or_s _ _ zenon_H10e); [ zenon_intro zenon_H3d | zenon_intro zenon_H106 ]. % 15.31/15.48 apply (zenon_or_s _ _ zenon_H10d); [ zenon_intro zenon_H3e | zenon_intro zenon_H42 ]. % 15.31/15.48 apply (zenon_L560_); trivial. % 15.31/15.48 apply (zenon_L643_); trivial. % 15.31/15.48 apply (zenon_L458_); trivial. % 15.31/15.48 apply (zenon_or_s _ _ zenon_H10e); [ zenon_intro zenon_H3d | zenon_intro zenon_H106 ]. % 15.31/15.48 apply (zenon_or_s _ _ zenon_H10d); [ zenon_intro zenon_H3e | zenon_intro zenon_H42 ]. % 15.31/15.48 apply (zenon_or_s _ _ zenon_H44); [ zenon_intro zenon_H47 | zenon_intro zenon_H46 ]. % 15.31/15.48 exact (zenon_H45 zenon_H47). % 15.31/15.48 apply (zenon_or_s _ _ zenon_H46); [ zenon_intro zenon_H22 | zenon_intro zenon_H48 ]. % 15.31/15.48 apply (zenon_or_s _ _ zenon_Hf1); [ zenon_intro zenon_H47 | zenon_intro zenon_Hf4 ]. % 15.31/15.48 exact (zenon_H45 zenon_H47). % 15.31/15.48 apply (zenon_or_s _ _ zenon_Hf4); [ zenon_intro zenon_Hd8 | zenon_intro zenon_Hf5 ]. % 15.31/15.48 apply (zenon_L644_); trivial. % 15.31/15.48 apply (zenon_or_s _ _ zenon_Hf5); [ zenon_intro zenon_Hae | zenon_intro zenon_Hee ]. % 15.31/15.48 apply (zenon_L304_); trivial. % 15.31/15.48 apply (zenon_or_s _ _ zenon_H8e); [ zenon_intro zenon_H92 | zenon_intro zenon_H91 ]. % 15.31/15.48 exact (zenon_H8f zenon_H92). % 15.31/15.48 apply (zenon_or_s _ _ zenon_H91); [ zenon_intro zenon_H5d | zenon_intro zenon_H93 ]. % 15.31/15.48 apply (zenon_L214_); trivial. % 15.31/15.48 apply (zenon_or_s _ _ zenon_H93); [ zenon_intro zenon_H63 | zenon_intro zenon_H81 ]. % 15.31/15.48 apply (zenon_L640_); trivial. % 15.31/15.48 apply (zenon_or_s _ _ zenon_Hbe); [ zenon_intro zenon_H5b | zenon_intro zenon_Hbf ]. % 15.31/15.48 exact (zenon_H59 zenon_H5b). % 15.31/15.48 apply (zenon_or_s _ _ zenon_Hbf); [ zenon_intro zenon_H69 | zenon_intro zenon_Hc0 ]. % 15.31/15.48 apply (zenon_L642_); trivial. % 15.31/15.48 apply (zenon_or_s _ _ zenon_Hc0); [ zenon_intro zenon_Haf | zenon_intro zenon_Hba ]. % 15.31/15.48 apply (zenon_L64_); trivial. % 15.31/15.48 apply (zenon_L82_); trivial. % 15.31/15.48 apply (zenon_or_s _ _ zenon_H48); [ zenon_intro zenon_H29 | zenon_intro zenon_H37 ]. % 15.31/15.48 apply (zenon_L646_); trivial. % 15.31/15.48 apply (zenon_L7_); trivial. % 15.31/15.48 apply (zenon_L102_); trivial. % 15.31/15.48 apply (zenon_L115_); trivial. % 15.31/15.48 apply (zenon_or_s _ _ zenon_H10c); [ zenon_intro zenon_H104 | zenon_intro zenon_H10a ]. % 15.31/15.48 apply (zenon_or_s _ _ zenon_H10e); [ zenon_intro zenon_H3d | zenon_intro zenon_H106 ]. % 15.31/15.48 apply (zenon_or_s _ _ zenon_Hf1); [ zenon_intro zenon_H47 | zenon_intro zenon_Hf4 ]. % 15.31/15.48 exact (zenon_H45 zenon_H47). % 15.31/15.48 apply (zenon_or_s _ _ zenon_Hf4); [ zenon_intro zenon_Hd8 | zenon_intro zenon_Hf5 ]. % 15.31/15.48 apply (zenon_L659_); trivial. % 15.31/15.48 apply (zenon_or_s _ _ zenon_Hf5); [ zenon_intro zenon_Hae | zenon_intro zenon_Hee ]. % 15.31/15.48 apply (zenon_L304_); trivial. % 15.31/15.48 apply (zenon_L79_); trivial. % 15.31/15.48 apply (zenon_L81_); trivial. % 15.31/15.48 apply (zenon_L82_); trivial. % 15.31/15.48 apply (zenon_L119_); trivial. % 15.31/15.48 apply (zenon_L161_); trivial. % 15.31/15.48 (* end of lemma zenon_L660_ *) % 15.31/15.48 assert (zenon_L661_ : (((op (e0) (e0)) = (e3))\/(((op (e1) (e0)) = (e3))\/(((op (e2) (e0)) = (e3))\/((op (e3) (e0)) = (e3))))) -> (~((op (e0) (e0)) = (e3))) -> (~((e0) = (e2))) -> (~((op (e0) (e2)) = (op (e1) (e2)))) -> ((op (e0) (e2)) = (e2)) -> (((op (e1) (e0)) = (e2))\/(((op (e1) (e1)) = (e2))\/(((op (e1) (e2)) = (e2))\/((op (e1) (e3)) = (e2))))) -> (~((op (e1) (e2)) = (op (e2) (e2)))) -> (~((op (e2) (e2)) = (e1))) -> (~((op (e1) (e1)) = (e0))) -> (~((op (e0) (e0)) = (op (e1) (e0)))) -> ((op (e0) (e0)) = (e0)) -> (((op (e1) (e0)) = (e0))\/(((op (e1) (e1)) = (e0))\/(((op (e1) (e2)) = (e0))\/((op (e1) (e3)) = (e0))))) -> (~((op (e1) (e1)) = (e3))) -> (~((op (e1) (e1)) = (e2))) -> (~((op (e1) (e1)) = (e1))) -> (((op (e2) (e2)) = (e0))\/(((op (e2) (e2)) = (e1))\/(((op (e2) (e2)) = (e2))\/((op (e2) (e2)) = (e3))))) -> (~((op (e2) (e2)) = (e0))) -> (~((op (e2) (e2)) = (e2))) -> (~((op (e2) (e2)) = (e3))) -> (((op (e1) (e1)) = (e0))\/(((op (e1) (e1)) = (e1))\/(((op (e1) (e1)) = (e2))\/((op (e1) (e1)) = (e3))))) -> (~((e2) = (e3))) -> ((op (e3) (e0)) = (e2)) -> False). % 15.31/15.48 do 0 intro. intros zenon_Hbe zenon_H59 zenon_H5e zenon_H87 zenon_H63 zenon_H84 zenon_H7d zenon_H52 zenon_H145 zenon_H24c zenon_H1f zenon_H163 zenon_H182 zenon_Hd6 zenon_H1b4 zenon_H2d zenon_H2e zenon_H2f zenon_H30 zenon_H1b3 zenon_H6a zenon_He9. % 15.31/15.48 apply (zenon_or_s _ _ zenon_Hbe); [ zenon_intro zenon_H5b | zenon_intro zenon_Hbf ]. % 15.31/15.48 exact (zenon_H59 zenon_H5b). % 15.31/15.48 apply (zenon_or_s _ _ zenon_Hbf); [ zenon_intro zenon_H69 | zenon_intro zenon_Hc0 ]. % 15.31/15.48 apply (zenon_L639_); trivial. % 15.31/15.48 apply (zenon_or_s _ _ zenon_Hc0); [ zenon_intro zenon_Haf | zenon_intro zenon_Hba ]. % 15.31/15.48 apply (zenon_L219_); trivial. % 15.31/15.48 apply (zenon_L220_); trivial. % 15.31/15.48 (* end of lemma zenon_L661_ *) % 15.31/15.48 assert (zenon_L662_ : (((op (e0) (e0)) = (e2))\/(((op (e1) (e0)) = (e2))\/(((op (e2) (e0)) = (e2))\/((op (e3) (e0)) = (e2))))) -> ((~((op (e2) (e2)) = (e3)))\/((op (e2) (e3)) = (e2))) -> ((~((op (e3) (e3)) = (e1)))\/((op (e3) (e1)) = (e3))) -> (~((op (e3) (e1)) = (op (e3) (e3)))) -> (~((op (e3) (e0)) = (op (e3) (e1)))) -> (~((op (e0) (op (e1) (e0))) = (op (e1) (e0)))) -> (~((op (e0) (e1)) = (op (e3) (e1)))) -> (~((op (e2) (e0)) = (op (e2) (e3)))) -> (((op (e0) (e3)) = (e2))\/(((op (e1) (e3)) = (e2))\/(((op (e2) (e3)) = (e2))\/((op (e3) (e3)) = (e2))))) -> (((op (e0) (e0)) = (e3))\/(((op (e0) (e1)) = (e3))\/(((op (e0) (e2)) = (e3))\/((op (e0) (e3)) = (e3))))) -> (~((op (e0) (e3)) = (op (e3) (e3)))) -> (((op (e0) (e0)) = (e1))\/(((op (e0) (e1)) = (e1))\/(((op (e0) (e2)) = (e1))\/((op (e0) (e3)) = (e1))))) -> (~((op (e3) (e1)) = (op (e3) (e2)))) -> ((~((op (e3) (e3)) = (e3)))\/((op (e3) (e3)) = (e3))) -> (~((op (e0) (e0)) = (e1))) -> (~((op (e3) (e0)) = (op (e3) (e3)))) -> (~((e1) = (e3))) -> (~((e1) = (e2))) -> (((op (e0) (e0)) = (e2))\/(((op (e0) (e1)) = (e2))\/(((op (e0) (e2)) = (e2))\/((op (e0) (e3)) = (e2))))) -> (~((op (e0) (e3)) = (op (e1) (e3)))) -> (~((e0) = (e1))) -> (((op (e1) (e0)) = (e1))\/(((op (e1) (e1)) = (e1))\/(((op (e1) (e2)) = (e1))\/((op (e1) (e3)) = (e1))))) -> (~((op (e0) (e1)) = (op (e1) (e1)))) -> (~((op (e0) (e0)) = (e2))) -> (((op (e0) (e0)) = (e1))\/(((op (e1) (e0)) = (e1))\/(((op (e2) (e0)) = (e1))\/((op (e3) (e0)) = (e1))))) -> (((op (e3) (e3)) = (e0))\/(((op (e3) (e3)) = (e1))\/(((op (e3) (e3)) = (e2))\/((op (e3) (e3)) = (e3))))) -> (~((op (e1) (e3)) = (op (e3) (e3)))) -> (~((op (e3) (e2)) = (op (e3) (e3)))) -> (~((op (e3) (e0)) = (op (e3) (e2)))) -> ((~((op (e3) (e3)) = (e2)))\/((op (e3) (e2)) = (e3))) -> (~((op (e1) (e0)) = (op (e3) (e0)))) -> (((op (e1) (e0)) = (e3))\/(((op (e1) (e1)) = (e3))\/(((op (e1) (e2)) = (e3))\/((op (e1) (e3)) = (e3))))) -> (((op (e0) (e3)) = (e1))\/(((op (e1) (e3)) = (e1))\/(((op (e2) (e3)) = (e1))\/((op (e3) (e3)) = (e1))))) -> (~((op (e0) (e1)) = (op (e0) (e3)))) -> (~((op (e2) (e0)) = (op (e2) (e1)))) -> (((op (e0) (e1)) = (e2))\/(((op (e1) (e1)) = (e2))\/(((op (e2) (e1)) = (e2))\/((op (e3) (e1)) = (e2))))) -> (((op (e3) (e0)) = (e2))\/(((op (e3) (e1)) = (e2))\/(((op (e3) (e2)) = (e2))\/((op (e3) (e3)) = (e2))))) -> (~((op (e3) (op (e1) (e3))) = (op (e1) (e3)))) -> (~((op (e0) (e2)) = (op (e0) (e3)))) -> (((op (e0) (e2)) = (e1))\/(((op (e1) (e2)) = (e1))\/(((op (e2) (e2)) = (e1))\/((op (e3) (e2)) = (e1))))) -> (~((op (e0) (e2)) = (op (e3) (e2)))) -> (((op (e3) (e0)) = (e1))\/(((op (e3) (e1)) = (e1))\/(((op (e3) (e2)) = (e1))\/((op (e3) (e3)) = (e1))))) -> (((op (e2) (e0)) = (e3))\/(((op (e2) (e1)) = (e3))\/(((op (e2) (e2)) = (e3))\/((op (e2) (e3)) = (e3))))) -> (~((op (e2) (op (e1) (e2))) = (op (e1) (e2)))) -> (~((op (e0) (e1)) = (op (e2) (e1)))) -> (~((op (e2) (e0)) = (op (e3) (e0)))) -> ((~((op (e3) (e3)) = (e0)))\/((op (e3) (e0)) = (e3))) -> (~((op (e2) (e0)) = (op (e2) (e2)))) -> ((~((op (e2) (e2)) = (e2)))\/((op (e2) (e2)) = (e2))) -> (((op (e0) (e0)) = (e3))\/(((op (e1) (e0)) = (e3))\/(((op (e2) (e0)) = (e3))\/((op (e3) (e0)) = (e3))))) -> (~((op (e0) (e0)) = (e3))) -> (~((e0) = (e2))) -> (~((op (e0) (e2)) = (op (e1) (e2)))) -> ((op (e0) (e2)) = (e2)) -> (((op (e1) (e0)) = (e2))\/(((op (e1) (e1)) = (e2))\/(((op (e1) (e2)) = (e2))\/((op (e1) (e3)) = (e2))))) -> (~((op (e1) (e2)) = (op (e2) (e2)))) -> (~((op (e2) (e2)) = (e1))) -> (~((op (e1) (e1)) = (e0))) -> (~((op (e0) (e0)) = (op (e1) (e0)))) -> ((op (e0) (e0)) = (e0)) -> (((op (e1) (e0)) = (e0))\/(((op (e1) (e1)) = (e0))\/(((op (e1) (e2)) = (e0))\/((op (e1) (e3)) = (e0))))) -> (~((op (e1) (e1)) = (e3))) -> (~((op (e1) (e1)) = (e2))) -> (~((op (e1) (e1)) = (e1))) -> (((op (e2) (e2)) = (e0))\/(((op (e2) (e2)) = (e1))\/(((op (e2) (e2)) = (e2))\/((op (e2) (e2)) = (e3))))) -> (~((op (e2) (e2)) = (e0))) -> (~((op (e2) (e2)) = (e2))) -> (~((op (e2) (e2)) = (e3))) -> (((op (e1) (e1)) = (e0))\/(((op (e1) (e1)) = (e1))\/(((op (e1) (e1)) = (e2))\/((op (e1) (e1)) = (e3))))) -> (~((e2) = (e3))) -> False). % 15.31/15.48 do 0 intro. intros zenon_Heb zenon_H1c3 zenon_H10c zenon_H12d zenon_H109 zenon_H261 zenon_H138 zenon_Hce zenon_H160 zenon_H58 zenon_H36 zenon_H44 zenon_H135 zenon_H10d zenon_H45 zenon_Hbb zenon_Ha3 zenon_Ha7 zenon_H8e zenon_H80 zenon_H9e zenon_H1c5 zenon_H23 zenon_H8f zenon_Hf1 zenon_H3b zenon_H8b zenon_H173 zenon_H105 zenon_H10e zenon_H22e zenon_H90 zenon_H121 zenon_H1cd zenon_H154 zenon_H1a2 zenon_H1df zenon_H26e zenon_Hc9 zenon_H11b zenon_H140 zenon_H146 zenon_He6 zenon_H277 zenon_Hde zenon_H1e5 zenon_H10f zenon_H17a zenon_Haa zenon_Hbe zenon_H59 zenon_H5e zenon_H87 zenon_H63 zenon_H84 zenon_H7d zenon_H52 zenon_H145 zenon_H24c zenon_H1f zenon_H163 zenon_H182 zenon_Hd6 zenon_H1b4 zenon_H2d zenon_H2e zenon_H2f zenon_H30 zenon_H1b3 zenon_H6a. % 15.31/15.48 apply (zenon_or_s _ _ zenon_Heb); [ zenon_intro zenon_H92 | zenon_intro zenon_Hec ]. % 15.31/15.48 exact (zenon_H8f zenon_H92). % 15.31/15.48 apply (zenon_or_s _ _ zenon_Hec); [ zenon_intro zenon_H68 | zenon_intro zenon_Hed ]. % 15.31/15.48 apply (zenon_L638_); trivial. % 15.31/15.48 apply (zenon_or_s _ _ zenon_Hed); [ zenon_intro zenon_Hdd | zenon_intro zenon_He9 ]. % 15.31/15.48 apply (zenon_L660_); trivial. % 15.31/15.48 apply (zenon_L661_); trivial. % 15.31/15.48 (* end of lemma zenon_L662_ *) % 15.31/15.48 assert (zenon_L663_ : (((op (e0) (e0)) = (e3))\/(((op (e0) (e1)) = (e3))\/(((op (e0) (e2)) = (e3))\/((op (e0) (e3)) = (e3))))) -> (~((op (e0) (e0)) = (e3))) -> (~((e1) = (e3))) -> ((op (e0) (e1)) = (e1)) -> (~((op (e0) (e2)) = (op (e2) (e2)))) -> (~((op (e2) (e2)) = (e2))) -> (~((op (e2) (e2)) = (e1))) -> (~((op (e2) (e2)) = (e0))) -> (((op (e2) (e2)) = (e0))\/(((op (e2) (e2)) = (e1))\/(((op (e2) (e2)) = (e2))\/((op (e2) (e2)) = (e3))))) -> ((op (e0) (e3)) = (e2)) -> (~((e2) = (e3))) -> False). % 15.31/15.48 do 0 intro. intros zenon_H58 zenon_H59 zenon_Ha3 zenon_H22 zenon_H28 zenon_H2f zenon_H52 zenon_H2e zenon_H2d zenon_H81 zenon_H6a. % 15.31/15.48 apply (zenon_or_s _ _ zenon_H58); [ zenon_intro zenon_H5b | zenon_intro zenon_H5a ]. % 15.31/15.48 exact (zenon_H59 zenon_H5b). % 15.31/15.48 apply (zenon_or_s _ _ zenon_H5a); [ zenon_intro zenon_H4a | zenon_intro zenon_H5c ]. % 15.31/15.48 apply (zenon_L59_); trivial. % 15.31/15.48 apply (zenon_or_s _ _ zenon_H5c); [ zenon_intro zenon_H50 | zenon_intro zenon_H53 ]. % 15.31/15.48 apply (zenon_L11_); trivial. % 15.31/15.48 apply (zenon_L128_); trivial. % 15.31/15.48 (* end of lemma zenon_L663_ *) % 15.31/15.48 assert (zenon_L664_ : (((op (e1) (e1)) = (e0))\/(((op (e1) (e1)) = (e1))\/(((op (e1) (e1)) = (e2))\/((op (e1) (e1)) = (e3))))) -> (~((op (e2) (e2)) = (e3))) -> (~((op (e1) (e1)) = (e1))) -> (~((op (e1) (e1)) = (e2))) -> (~((op (e1) (e1)) = (e3))) -> (((op (e1) (e0)) = (e0))\/(((op (e1) (e1)) = (e0))\/(((op (e1) (e2)) = (e0))\/((op (e1) (e3)) = (e0))))) -> ((op (e0) (e0)) = (e0)) -> (~((op (e0) (e0)) = (op (e1) (e0)))) -> (~((op (e1) (e1)) = (e0))) -> (~((op (e1) (e2)) = (op (e2) (e2)))) -> (((op (e1) (e0)) = (e2))\/(((op (e1) (e1)) = (e2))\/(((op (e1) (e2)) = (e2))\/((op (e1) (e3)) = (e2))))) -> (~((op (e0) (e2)) = (op (e1) (e2)))) -> (~((e0) = (e2))) -> (((op (e0) (e0)) = (e3))\/(((op (e1) (e0)) = (e3))\/(((op (e2) (e0)) = (e3))\/((op (e3) (e0)) = (e3))))) -> ((~((op (e2) (e2)) = (e2)))\/((op (e2) (e2)) = (e2))) -> (~((op (e2) (e0)) = (op (e2) (e2)))) -> ((~((op (e3) (e3)) = (e0)))\/((op (e3) (e0)) = (e3))) -> (~((op (e2) (e0)) = (op (e3) (e0)))) -> (~((op (e0) (e1)) = (op (e2) (e1)))) -> (~((op (e2) (op (e1) (e2))) = (op (e1) (e2)))) -> (((op (e2) (e0)) = (e3))\/(((op (e2) (e1)) = (e3))\/(((op (e2) (e2)) = (e3))\/((op (e2) (e3)) = (e3))))) -> (((op (e3) (e0)) = (e1))\/(((op (e3) (e1)) = (e1))\/(((op (e3) (e2)) = (e1))\/((op (e3) (e3)) = (e1))))) -> (~((op (e0) (e2)) = (op (e3) (e2)))) -> (((op (e0) (e2)) = (e1))\/(((op (e1) (e2)) = (e1))\/(((op (e2) (e2)) = (e1))\/((op (e3) (e2)) = (e1))))) -> (~((op (e0) (e2)) = (op (e0) (e3)))) -> (~((op (e3) (op (e1) (e3))) = (op (e1) (e3)))) -> (((op (e3) (e0)) = (e2))\/(((op (e3) (e1)) = (e2))\/(((op (e3) (e2)) = (e2))\/((op (e3) (e3)) = (e2))))) -> (((op (e0) (e1)) = (e2))\/(((op (e1) (e1)) = (e2))\/(((op (e2) (e1)) = (e2))\/((op (e3) (e1)) = (e2))))) -> (~((op (e2) (e0)) = (op (e2) (e1)))) -> (~((op (e0) (e1)) = (op (e0) (e3)))) -> (((op (e0) (e3)) = (e1))\/(((op (e1) (e3)) = (e1))\/(((op (e2) (e3)) = (e1))\/((op (e3) (e3)) = (e1))))) -> (((op (e1) (e0)) = (e3))\/(((op (e1) (e1)) = (e3))\/(((op (e1) (e2)) = (e3))\/((op (e1) (e3)) = (e3))))) -> (~((op (e1) (e0)) = (op (e3) (e0)))) -> ((~((op (e3) (e3)) = (e2)))\/((op (e3) (e2)) = (e3))) -> (~((op (e3) (e0)) = (op (e3) (e2)))) -> (~((op (e3) (e2)) = (op (e3) (e3)))) -> (~((op (e1) (e3)) = (op (e3) (e3)))) -> (((op (e3) (e3)) = (e0))\/(((op (e3) (e3)) = (e1))\/(((op (e3) (e3)) = (e2))\/((op (e3) (e3)) = (e3))))) -> (((op (e0) (e0)) = (e1))\/(((op (e1) (e0)) = (e1))\/(((op (e2) (e0)) = (e1))\/((op (e3) (e0)) = (e1))))) -> (~((op (e0) (e0)) = (e2))) -> (~((op (e0) (e1)) = (op (e1) (e1)))) -> (((op (e1) (e0)) = (e1))\/(((op (e1) (e1)) = (e1))\/(((op (e1) (e2)) = (e1))\/((op (e1) (e3)) = (e1))))) -> (~((e0) = (e1))) -> (~((op (e0) (e3)) = (op (e1) (e3)))) -> (((op (e0) (e0)) = (e2))\/(((op (e0) (e1)) = (e2))\/(((op (e0) (e2)) = (e2))\/((op (e0) (e3)) = (e2))))) -> (~((e1) = (e2))) -> (~((op (e3) (e0)) = (op (e3) (e3)))) -> (~((op (e0) (e0)) = (e1))) -> ((~((op (e3) (e3)) = (e3)))\/((op (e3) (e3)) = (e3))) -> (~((op (e3) (e1)) = (op (e3) (e2)))) -> (((op (e0) (e0)) = (e1))\/(((op (e0) (e1)) = (e1))\/(((op (e0) (e2)) = (e1))\/((op (e0) (e3)) = (e1))))) -> (~((op (e0) (e3)) = (op (e3) (e3)))) -> (((op (e0) (e3)) = (e2))\/(((op (e1) (e3)) = (e2))\/(((op (e2) (e3)) = (e2))\/((op (e3) (e3)) = (e2))))) -> (~((op (e2) (e0)) = (op (e2) (e3)))) -> (~((op (e0) (e1)) = (op (e3) (e1)))) -> (~((op (e0) (op (e1) (e0))) = (op (e1) (e0)))) -> (~((op (e3) (e0)) = (op (e3) (e1)))) -> (~((op (e3) (e1)) = (op (e3) (e3)))) -> ((~((op (e3) (e3)) = (e1)))\/((op (e3) (e1)) = (e3))) -> ((~((op (e2) (e2)) = (e3)))\/((op (e2) (e3)) = (e2))) -> (((op (e0) (e0)) = (e2))\/(((op (e1) (e0)) = (e2))\/(((op (e2) (e0)) = (e2))\/((op (e3) (e0)) = (e2))))) -> (((op (e0) (e0)) = (e3))\/(((op (e0) (e1)) = (e3))\/(((op (e0) (e2)) = (e3))\/((op (e0) (e3)) = (e3))))) -> (~((op (e0) (e0)) = (e3))) -> (~((e1) = (e3))) -> ((op (e0) (e1)) = (e1)) -> (~((op (e0) (e2)) = (op (e2) (e2)))) -> (~((op (e2) (e2)) = (e2))) -> (~((op (e2) (e2)) = (e1))) -> (~((op (e2) (e2)) = (e0))) -> (((op (e2) (e2)) = (e0))\/(((op (e2) (e2)) = (e1))\/(((op (e2) (e2)) = (e2))\/((op (e2) (e2)) = (e3))))) -> (~((e2) = (e3))) -> False). % 15.31/15.48 do 0 intro. intros zenon_H1b3 zenon_H30 zenon_H1b4 zenon_Hd6 zenon_H182 zenon_H163 zenon_H1f zenon_H24c zenon_H145 zenon_H7d zenon_H84 zenon_H87 zenon_H5e zenon_Hbe zenon_Haa zenon_H17a zenon_H10f zenon_H1e5 zenon_Hde zenon_H277 zenon_He6 zenon_H146 zenon_H140 zenon_H11b zenon_Hc9 zenon_H26e zenon_H1df zenon_H1a2 zenon_H154 zenon_H1cd zenon_H121 zenon_H90 zenon_H22e zenon_H10e zenon_H105 zenon_H173 zenon_H8b zenon_H3b zenon_Hf1 zenon_H8f zenon_H23 zenon_H1c5 zenon_H9e zenon_H80 zenon_H8e zenon_Ha7 zenon_Hbb zenon_H45 zenon_H10d zenon_H135 zenon_H44 zenon_H36 zenon_H160 zenon_Hce zenon_H138 zenon_H261 zenon_H109 zenon_H12d zenon_H10c zenon_H1c3 zenon_Heb zenon_H58 zenon_H59 zenon_Ha3 zenon_H22 zenon_H28 zenon_H2f zenon_H52 zenon_H2e zenon_H2d zenon_H6a. % 15.31/15.48 apply (zenon_or_s _ _ zenon_H8e); [ zenon_intro zenon_H92 | zenon_intro zenon_H91 ]. % 15.31/15.48 exact (zenon_H8f zenon_H92). % 15.31/15.48 apply (zenon_or_s _ _ zenon_H91); [ zenon_intro zenon_H5d | zenon_intro zenon_H93 ]. % 15.31/15.48 apply (zenon_L214_); trivial. % 15.31/15.48 apply (zenon_or_s _ _ zenon_H93); [ zenon_intro zenon_H63 | zenon_intro zenon_H81 ]. % 15.31/15.48 apply (zenon_L662_); trivial. % 15.31/15.48 apply (zenon_L663_); trivial. % 15.31/15.48 (* end of lemma zenon_L664_ *) % 15.31/15.48 assert (zenon_L665_ : (((op (e0) (e0)) = (e2))\/(((op (e0) (e1)) = (e2))\/(((op (e0) (e2)) = (e2))\/((op (e0) (e3)) = (e2))))) -> (~((op (e0) (e0)) = (e2))) -> (~((op (e1) (e1)) = (e3))) -> (~((op (e0) (e1)) = (op (e1) (e1)))) -> (~((op (e1) (e1)) = (e1))) -> (~((op (e1) (e1)) = (e0))) -> (((op (e1) (e1)) = (e0))\/(((op (e1) (e1)) = (e1))\/(((op (e1) (e1)) = (e2))\/((op (e1) (e1)) = (e3))))) -> (~((e1) = (e2))) -> ((op (e0) (e2)) = (e1)) -> (((op (e3) (e3)) = (e0))\/(((op (e3) (e3)) = (e1))\/(((op (e3) (e3)) = (e2))\/((op (e3) (e3)) = (e3))))) -> (~((op (e3) (e3)) = (e0))) -> (~((op (e3) (e3)) = (e1))) -> (~((op (e0) (e3)) = (op (e3) (e3)))) -> (~((op (e3) (e3)) = (e3))) -> False). % 15.31/15.48 do 0 intro. intros zenon_H8e zenon_H8f zenon_H182 zenon_H23 zenon_H1b4 zenon_H145 zenon_H1b3 zenon_Ha7 zenon_H29 zenon_H3b zenon_H3c zenon_H104 zenon_H36 zenon_H3e. % 15.31/15.48 apply (zenon_or_s _ _ zenon_H8e); [ zenon_intro zenon_H92 | zenon_intro zenon_H91 ]. % 15.31/15.48 exact (zenon_H8f zenon_H92). % 15.31/15.48 apply (zenon_or_s _ _ zenon_H91); [ zenon_intro zenon_H5d | zenon_intro zenon_H93 ]. % 15.31/15.48 apply (zenon_L214_); trivial. % 15.31/15.48 apply (zenon_or_s _ _ zenon_H93); [ zenon_intro zenon_H63 | zenon_intro zenon_H81 ]. % 15.31/15.48 apply (zenon_L104_); trivial. % 15.31/15.48 apply (zenon_L107_); trivial. % 15.31/15.48 (* end of lemma zenon_L665_ *) % 15.31/15.48 assert (zenon_L666_ : (((op (e0) (e0)) = (e2))\/(((op (e0) (e1)) = (e2))\/(((op (e0) (e2)) = (e2))\/((op (e0) (e3)) = (e2))))) -> (~((op (e0) (e0)) = (e2))) -> (~((op (e1) (e1)) = (e3))) -> (~((op (e0) (e1)) = (op (e1) (e1)))) -> (~((op (e1) (e1)) = (e1))) -> (~((op (e1) (e1)) = (e0))) -> (((op (e1) (e1)) = (e0))\/(((op (e1) (e1)) = (e1))\/(((op (e1) (e1)) = (e2))\/((op (e1) (e1)) = (e3))))) -> (~((e1) = (e2))) -> (((op (e0) (e0)) = (e3))\/(((op (e0) (e1)) = (e3))\/(((op (e0) (e2)) = (e3))\/((op (e0) (e3)) = (e3))))) -> (~((op (e0) (e0)) = (e3))) -> (~((op (e0) (e1)) = (op (e3) (e1)))) -> ((op (e3) (e1)) = (e3)) -> (~((e1) = (e3))) -> ((op (e0) (e2)) = (e1)) -> (~((e2) = (e3))) -> False). % 15.31/15.48 do 0 intro. intros zenon_H8e zenon_H8f zenon_H182 zenon_H23 zenon_H1b4 zenon_H145 zenon_H1b3 zenon_Ha7 zenon_H58 zenon_H59 zenon_H138 zenon_H10a zenon_Ha3 zenon_H29 zenon_H6a. % 15.31/15.48 apply (zenon_or_s _ _ zenon_H8e); [ zenon_intro zenon_H92 | zenon_intro zenon_H91 ]. % 15.31/15.48 exact (zenon_H8f zenon_H92). % 15.31/15.48 apply (zenon_or_s _ _ zenon_H91); [ zenon_intro zenon_H5d | zenon_intro zenon_H93 ]. % 15.31/15.48 apply (zenon_L214_); trivial. % 15.31/15.48 apply (zenon_or_s _ _ zenon_H93); [ zenon_intro zenon_H63 | zenon_intro zenon_H81 ]. % 15.31/15.48 apply (zenon_L104_); trivial. % 15.31/15.48 apply (zenon_L129_); trivial. % 15.31/15.48 (* end of lemma zenon_L666_ *) % 15.31/15.48 assert (zenon_L667_ : (((op (e0) (e0)) = (e3))\/(((op (e0) (e1)) = (e3))\/(((op (e0) (e2)) = (e3))\/((op (e0) (e3)) = (e3))))) -> (~((op (e0) (e2)) = (op (e1) (e2)))) -> ((op (e1) (e0)) = (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 (e1) (e1)) = (e3))\/(((op (e1) (e2)) = (e3))\/((op (e1) (e3)) = (e3))))) -> (~((op (e0) (op (e1) (e0))) = (op (e1) (e0)))) -> (~((op (e1) (e1)) = (e3))) -> (~((op (e3) (e3)) = (e1))) -> (~((op (e0) (e2)) = (op (e3) (e2)))) -> ((op (e0) (e2)) = (e1)) -> (((op (e0) (e3)) = (e1))\/(((op (e1) (e3)) = (e1))\/(((op (e2) (e3)) = (e1))\/((op (e3) (e3)) = (e1))))) -> (~((op (e3) (e1)) = (op (e3) (e2)))) -> (~((op (e2) (e2)) = (e1))) -> (~((e1) = (e3))) -> (~((op (e0) (e2)) = (op (e0) (e3)))) -> (((op (e0) (e2)) = (e1))\/(((op (e1) (e2)) = (e1))\/(((op (e2) (e2)) = (e1))\/((op (e3) (e2)) = (e1))))) -> (~((op (e2) (e0)) = (op (e2) (e1)))) -> (~((op (e1) (e1)) = (e2))) -> (((op (e0) (e1)) = (e2))\/(((op (e1) (e1)) = (e2))\/(((op (e2) (e1)) = (e2))\/((op (e3) (e1)) = (e2))))) -> (~((op (e3) (op (e1) (e3))) = (op (e1) (e3)))) -> (~((e1) = (e2))) -> (~((op (e0) (e1)) = (op (e3) (e1)))) -> (((op (e3) (e0)) = (e2))\/(((op (e3) (e1)) = (e2))\/(((op (e3) (e2)) = (e2))\/((op (e3) (e3)) = (e2))))) -> (((op (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))))) -> (~((op (e0) (e1)) = (op (e0) (e3)))) -> ((op (e0) (e1)) = (e2)) -> (~((e2) = (e3))) -> ((op (e2) (e0)) = (e2)) -> (~((op (e2) (e0)) = (op (e2) (e3)))) -> (~((op (e3) (e3)) = (e2))) -> False). % 15.31/15.48 do 0 intro. intros zenon_H58 zenon_H87 zenon_Hd8 zenon_Hbe zenon_H59 zenon_H90 zenon_H261 zenon_H182 zenon_H104 zenon_H140 zenon_H29 zenon_H121 zenon_H135 zenon_H52 zenon_Ha3 zenon_Hc9 zenon_H11b zenon_H154 zenon_Hd6 zenon_H1a2 zenon_H26e zenon_Ha7 zenon_H138 zenon_H1df zenon_H146 zenon_H160 zenon_H1cd zenon_H5d zenon_H6a zenon_Hdd zenon_Hce zenon_H3d. % 15.31/15.48 apply (zenon_or_s _ _ zenon_H58); [ zenon_intro zenon_H5b | zenon_intro zenon_H5a ]. % 15.31/15.48 exact (zenon_H59 zenon_H5b). % 15.31/15.48 apply (zenon_or_s _ _ zenon_H5a); [ zenon_intro zenon_H4a | zenon_intro zenon_H5c ]. % 15.31/15.48 apply (zenon_L50_); trivial. % 15.31/15.48 apply (zenon_or_s _ _ zenon_H5c); [ zenon_intro zenon_H50 | zenon_intro zenon_H53 ]. % 15.31/15.48 apply (zenon_L411_); trivial. % 15.31/15.48 apply (zenon_or_s _ _ zenon_Hbe); [ zenon_intro zenon_H5b | zenon_intro zenon_Hbf ]. % 15.31/15.48 exact (zenon_H59 zenon_H5b). % 15.31/15.48 apply (zenon_or_s _ _ zenon_Hbf); [ zenon_intro zenon_H69 | zenon_intro zenon_Hc0 ]. % 15.31/15.48 apply (zenon_L647_); trivial. % 15.31/15.48 apply (zenon_or_s _ _ zenon_Hc0); [ zenon_intro zenon_Haf | zenon_intro zenon_Hba ]. % 15.31/15.48 apply (zenon_L64_); trivial. % 15.31/15.48 apply (zenon_L654_); trivial. % 15.31/15.48 (* end of lemma zenon_L667_ *) % 15.31/15.48 assert (zenon_L668_ : (((op (e0) (e0)) = (e2))\/(((op (e0) (e1)) = (e2))\/(((op (e0) (e2)) = (e2))\/((op (e0) (e3)) = (e2))))) -> (((op (e0) (e0)) = (e3))\/(((op (e0) (e1)) = (e3))\/(((op (e0) (e2)) = (e3))\/((op (e0) (e3)) = (e3))))) -> (~((op (e0) (e2)) = (op (e1) (e2)))) -> (((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 (e1) (e1)) = (e3))\/(((op (e1) (e2)) = (e3))\/((op (e1) (e3)) = (e3))))) -> (~((op (e0) (op (e1) (e0))) = (op (e1) (e0)))) -> (~((op (e1) (e1)) = (e3))) -> (((op (e0) (e3)) = (e1))\/(((op (e1) (e3)) = (e1))\/(((op (e2) (e3)) = (e1))\/((op (e3) (e3)) = (e1))))) -> (~((op (e3) (e1)) = (op (e3) (e2)))) -> (~((op (e2) (e2)) = (e1))) -> (~((e1) = (e3))) -> (~((op (e0) (e2)) = (op (e0) (e3)))) -> (((op (e0) (e2)) = (e1))\/(((op (e1) (e2)) = (e1))\/(((op (e2) (e2)) = (e1))\/((op (e3) (e2)) = (e1))))) -> (~((op (e3) (op (e1) (e3))) = (op (e1) (e3)))) -> (~((op (e0) (e1)) = (op (e3) (e1)))) -> (((op (e3) (e0)) = (e2))\/(((op (e3) (e1)) = (e2))\/(((op (e3) (e2)) = (e2))\/((op (e3) (e3)) = (e2))))) -> (((op (e0) (e3)) = (e2))\/(((op (e1) (e3)) = (e2))\/(((op (e2) (e3)) = (e2))\/((op (e3) (e3)) = (e2))))) -> (~((op (e2) (e0)) = (op (e2) (e3)))) -> (~((op (e3) (e3)) = (e2))) -> (((op (e0) (e0)) = (e2))\/(((op (e1) (e0)) = (e2))\/(((op (e2) (e0)) = (e2))\/((op (e3) (e0)) = (e2))))) -> (~((op (e0) (e0)) = (e2))) -> (~((op (e3) (e3)) = (e1))) -> (~((op (e0) (e2)) = (op (e3) (e2)))) -> ((op (e0) (e2)) = (e1)) -> (((op (e0) (e1)) = (e2))\/(((op (e1) (e1)) = (e2))\/(((op (e2) (e1)) = (e2))\/((op (e3) (e1)) = (e2))))) -> (~((op (e0) (e1)) = (op (e0) (e3)))) -> (~((op (e1) (e1)) = (e2))) -> (~((op (e2) (e0)) = (op (e2) (e1)))) -> (~((e1) = (e2))) -> (~((op (e1) (e0)) = (op (e3) (e0)))) -> ((op (e1) (e0)) = (e1)) -> (((op (e3) (e0)) = (e1))\/(((op (e3) (e1)) = (e1))\/(((op (e3) (e2)) = (e1))\/((op (e3) (e3)) = (e1))))) -> (~((e2) = (e3))) -> ((op (e3) (e0)) = (e3)) -> False). % 15.31/15.48 do 0 intro. intros zenon_H8e zenon_H58 zenon_H87 zenon_Hbe zenon_H59 zenon_H90 zenon_H261 zenon_H182 zenon_H121 zenon_H135 zenon_H52 zenon_Ha3 zenon_Hc9 zenon_H11b zenon_H26e zenon_H138 zenon_H1df zenon_H160 zenon_Hce zenon_H3d zenon_Heb zenon_H8f zenon_H104 zenon_H140 zenon_H29 zenon_H1a2 zenon_H1cd zenon_Hd6 zenon_H154 zenon_Ha7 zenon_H22e zenon_Hd8 zenon_H146 zenon_H6a zenon_Hba. % 15.31/15.48 apply (zenon_or_s _ _ zenon_H8e); [ zenon_intro zenon_H92 | zenon_intro zenon_H91 ]. % 15.31/15.48 exact (zenon_H8f zenon_H92). % 15.31/15.48 apply (zenon_or_s _ _ zenon_H91); [ zenon_intro zenon_H5d | zenon_intro zenon_H93 ]. % 15.31/15.48 apply (zenon_or_s _ _ zenon_Heb); [ zenon_intro zenon_H92 | zenon_intro zenon_Hec ]. % 15.31/15.48 exact (zenon_H8f zenon_H92). % 15.31/15.48 apply (zenon_or_s _ _ zenon_Hec); [ zenon_intro zenon_H68 | zenon_intro zenon_Hed ]. % 15.31/15.48 apply (zenon_L162_); trivial. % 15.31/15.48 apply (zenon_or_s _ _ zenon_Hed); [ zenon_intro zenon_Hdd | zenon_intro zenon_He9 ]. % 15.31/15.48 apply (zenon_L667_); trivial. % 15.31/15.48 apply (zenon_L220_); trivial. % 15.31/15.48 apply (zenon_or_s _ _ zenon_H93); [ zenon_intro zenon_H63 | zenon_intro zenon_H81 ]. % 15.31/15.48 apply (zenon_L104_); trivial. % 15.31/15.48 apply (zenon_or_s _ _ zenon_Heb); [ zenon_intro zenon_H92 | zenon_intro zenon_Hec ]. % 15.31/15.48 exact (zenon_H8f zenon_H92). % 15.31/15.48 apply (zenon_or_s _ _ zenon_Hec); [ zenon_intro zenon_H68 | zenon_intro zenon_Hed ]. % 15.31/15.48 apply (zenon_L162_); trivial. % 15.31/15.48 apply (zenon_or_s _ _ zenon_Hed); [ zenon_intro zenon_Hdd | zenon_intro zenon_He9 ]. % 15.31/15.48 apply (zenon_L416_); trivial. % 15.31/15.48 apply (zenon_L220_); trivial. % 15.31/15.48 (* end of lemma zenon_L668_ *) % 15.31/15.48 assert (zenon_L669_ : (((op (e0) (e0)) = (e2))\/(((op (e1) (e0)) = (e2))\/(((op (e2) (e0)) = (e2))\/((op (e3) (e0)) = (e2))))) -> (~((op (e0) (e0)) = (e2))) -> (~((e1) = (e2))) -> (~((e1) = (e3))) -> ((op (e0) (e3)) = (e1)) -> (((op (e1) (e0)) = (e3))\/(((op (e1) (e1)) = (e3))\/(((op (e1) (e2)) = (e3))\/((op (e1) (e3)) = (e3))))) -> ((op (e1) (e0)) = (e1)) -> (~((op (e1) (e1)) = (e3))) -> (~((op (e0) (e2)) = (op (e1) (e2)))) -> (((op (e0) (e3)) = (e2))\/(((op (e1) (e3)) = (e2))\/(((op (e2) (e3)) = (e2))\/((op (e3) (e3)) = (e2))))) -> (~((op (e0) (e1)) = (op (e0) (e3)))) -> ((op (e0) (e1)) = (e2)) -> (~((op (e2) (e0)) = (op (e2) (e3)))) -> (~((op (e3) (e3)) = (e2))) -> (~((op (e0) (e0)) = (e3))) -> (((op (e0) (e0)) = (e3))\/(((op (e0) (e1)) = (e3))\/(((op (e0) (e2)) = (e3))\/((op (e0) (e3)) = (e3))))) -> (~((e2) = (e3))) -> ((op (e3) (e0)) = (e3)) -> False). % 15.31/15.48 do 0 intro. intros zenon_Heb zenon_H8f zenon_Ha7 zenon_Ha3 zenon_H37 zenon_H90 zenon_Hd8 zenon_H182 zenon_H87 zenon_H160 zenon_H1cd zenon_H5d zenon_Hce zenon_H3d zenon_H59 zenon_H58 zenon_H6a zenon_Hba. % 15.31/15.48 apply (zenon_or_s _ _ zenon_Heb); [ zenon_intro zenon_H92 | zenon_intro zenon_Hec ]. % 15.31/15.48 exact (zenon_H8f zenon_H92). % 15.31/15.48 apply (zenon_or_s _ _ zenon_Hec); [ zenon_intro zenon_H68 | zenon_intro zenon_Hed ]. % 15.31/15.48 apply (zenon_L162_); trivial. % 15.31/15.48 apply (zenon_or_s _ _ zenon_Hed); [ zenon_intro zenon_Hdd | zenon_intro zenon_He9 ]. % 15.31/15.48 apply (zenon_L656_); trivial. % 15.31/15.48 apply (zenon_L220_); trivial. % 15.31/15.48 (* end of lemma zenon_L669_ *) % 15.31/15.48 assert (zenon_L670_ : (((op (e0) (e0)) = (e2))\/(((op (e0) (e1)) = (e2))\/(((op (e0) (e2)) = (e2))\/((op (e0) (e3)) = (e2))))) -> (~((op (e3) (e3)) = (e2))) -> (~((op (e2) (e0)) = (op (e2) (e3)))) -> (~((op (e0) (e1)) = (op (e0) (e3)))) -> (((op (e0) (e3)) = (e2))\/(((op (e1) (e3)) = (e2))\/(((op (e2) (e3)) = (e2))\/((op (e3) (e3)) = (e2))))) -> (~((op (e0) (e0)) = (e2))) -> (((op (e0) (e0)) = (e2))\/(((op (e1) (e0)) = (e2))\/(((op (e2) (e0)) = (e2))\/((op (e3) (e0)) = (e2))))) -> (~((e1) = (e3))) -> (~((e2) = (e3))) -> (((op (e1) (e0)) = (e2))\/(((op (e1) (e1)) = (e2))\/(((op (e1) (e2)) = (e2))\/((op (e1) (e3)) = (e2))))) -> (~((op (e0) (op (e1) (e0))) = (op (e1) (e0)))) -> (~((op (e1) (e1)) = (e2))) -> (~((op (e0) (e2)) = (op (e1) (e2)))) -> (((op (e1) (e0)) = (e3))\/(((op (e1) (e1)) = (e3))\/(((op (e1) (e2)) = (e3))\/((op (e1) (e3)) = (e3))))) -> ((op (e1) (e0)) = (e1)) -> (~((op (e1) (e1)) = (e3))) -> (~((op (e2) (op (e1) (e2))) = (op (e1) (e2)))) -> (~((op (e2) (e2)) = (e3))) -> (~((op (e0) (e1)) = (op (e2) (e1)))) -> ((op (e3) (e0)) = (e3)) -> (~((op (e2) (e0)) = (op (e3) (e0)))) -> (((op (e2) (e0)) = (e3))\/(((op (e2) (e1)) = (e3))\/(((op (e2) (e2)) = (e3))\/((op (e2) (e3)) = (e3))))) -> (~((op (e0) (e0)) = (e3))) -> (((op (e0) (e0)) = (e3))\/(((op (e0) (e1)) = (e3))\/(((op (e0) (e2)) = (e3))\/((op (e0) (e3)) = (e3))))) -> ((op (e0) (e3)) = (e1)) -> (~((e1) = (e2))) -> False). % 15.31/15.48 do 0 intro. intros zenon_H8e zenon_H3d zenon_Hce zenon_H1cd zenon_H160 zenon_H8f zenon_Heb zenon_Ha3 zenon_H6a zenon_H84 zenon_H261 zenon_Hd6 zenon_H87 zenon_H90 zenon_Hd8 zenon_H182 zenon_H277 zenon_H30 zenon_Hde zenon_Hba zenon_H1e5 zenon_He6 zenon_H59 zenon_H58 zenon_H37 zenon_Ha7. % 15.31/15.48 apply (zenon_or_s _ _ zenon_H8e); [ zenon_intro zenon_H92 | zenon_intro zenon_H91 ]. % 15.31/15.48 exact (zenon_H8f zenon_H92). % 15.31/15.48 apply (zenon_or_s _ _ zenon_H91); [ zenon_intro zenon_H5d | zenon_intro zenon_H93 ]. % 15.31/15.48 apply (zenon_L669_); trivial. % 15.31/15.48 apply (zenon_or_s _ _ zenon_H93); [ zenon_intro zenon_H63 | zenon_intro zenon_H81 ]. % 15.31/15.48 apply (zenon_L658_); trivial. % 15.31/15.48 apply (zenon_L33_); trivial. % 15.31/15.48 (* end of lemma zenon_L670_ *) % 15.31/15.48 assert (zenon_L671_ : (((op (e0) (e0)) = (e1))\/(((op (e0) (e1)) = (e1))\/(((op (e0) (e2)) = (e1))\/((op (e0) (e3)) = (e1))))) -> (~((op (e0) (e0)) = (e1))) -> (((op (e3) (e0)) = (e1))\/(((op (e3) (e1)) = (e1))\/(((op (e3) (e2)) = (e1))\/((op (e3) (e3)) = (e1))))) -> (~((op (e1) (e0)) = (op (e3) (e0)))) -> (~((op (e2) (e0)) = (op (e2) (e1)))) -> (((op (e0) (e1)) = (e2))\/(((op (e1) (e1)) = (e2))\/(((op (e2) (e1)) = (e2))\/((op (e3) (e1)) = (e2))))) -> (~((op (e0) (e2)) = (op (e3) (e2)))) -> (~((op (e3) (e3)) = (e1))) -> (((op (e3) (e0)) = (e2))\/(((op (e3) (e1)) = (e2))\/(((op (e3) (e2)) = (e2))\/((op (e3) (e3)) = (e2))))) -> (~((op (e0) (e1)) = (op (e3) (e1)))) -> (~((op (e3) (op (e1) (e3))) = (op (e1) (e3)))) -> (((op (e0) (e2)) = (e1))\/(((op (e1) (e2)) = (e1))\/(((op (e2) (e2)) = (e1))\/((op (e3) (e2)) = (e1))))) -> (~((op (e0) (e2)) = (op (e0) (e3)))) -> (~((op (e2) (e2)) = (e1))) -> (~((op (e3) (e1)) = (op (e3) (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 (e0) (e0)) = (e2))\/(((op (e0) (e1)) = (e2))\/(((op (e0) (e2)) = (e2))\/((op (e0) (e3)) = (e2))))) -> (~((op (e3) (e3)) = (e2))) -> (~((op (e2) (e0)) = (op (e2) (e3)))) -> (~((op (e0) (e1)) = (op (e0) (e3)))) -> (((op (e0) (e3)) = (e2))\/(((op (e1) (e3)) = (e2))\/(((op (e2) (e3)) = (e2))\/((op (e3) (e3)) = (e2))))) -> (~((op (e0) (e0)) = (e2))) -> (((op (e0) (e0)) = (e2))\/(((op (e1) (e0)) = (e2))\/(((op (e2) (e0)) = (e2))\/((op (e3) (e0)) = (e2))))) -> (~((e1) = (e3))) -> (~((e2) = (e3))) -> (((op (e1) (e0)) = (e2))\/(((op (e1) (e1)) = (e2))\/(((op (e1) (e2)) = (e2))\/((op (e1) (e3)) = (e2))))) -> (~((op (e0) (op (e1) (e0))) = (op (e1) (e0)))) -> (~((op (e1) (e1)) = (e2))) -> (~((op (e0) (e2)) = (op (e1) (e2)))) -> (((op (e1) (e0)) = (e3))\/(((op (e1) (e1)) = (e3))\/(((op (e1) (e2)) = (e3))\/((op (e1) (e3)) = (e3))))) -> ((op (e1) (e0)) = (e1)) -> (~((op (e1) (e1)) = (e3))) -> (~((op (e2) (op (e1) (e2))) = (op (e1) (e2)))) -> (~((op (e2) (e2)) = (e3))) -> (~((op (e0) (e1)) = (op (e2) (e1)))) -> ((op (e3) (e0)) = (e3)) -> (~((op (e2) (e0)) = (op (e3) (e0)))) -> (((op (e2) (e0)) = (e3))\/(((op (e2) (e1)) = (e3))\/(((op (e2) (e2)) = (e3))\/((op (e2) (e3)) = (e3))))) -> (~((op (e0) (e0)) = (e3))) -> (((op (e0) (e0)) = (e3))\/(((op (e0) (e1)) = (e3))\/(((op (e0) (e2)) = (e3))\/((op (e0) (e3)) = (e3))))) -> (~((e1) = (e2))) -> False). % 15.31/15.48 do 0 intro. intros zenon_H44 zenon_H45 zenon_H146 zenon_H22e zenon_H154 zenon_H1a2 zenon_H140 zenon_H104 zenon_H1df zenon_H138 zenon_H26e zenon_H11b zenon_Hc9 zenon_H52 zenon_H135 zenon_H121 zenon_Hbe zenon_H8e zenon_H3d zenon_Hce zenon_H1cd zenon_H160 zenon_H8f zenon_Heb zenon_Ha3 zenon_H6a zenon_H84 zenon_H261 zenon_Hd6 zenon_H87 zenon_H90 zenon_Hd8 zenon_H182 zenon_H277 zenon_H30 zenon_Hde zenon_Hba zenon_H1e5 zenon_He6 zenon_H59 zenon_H58 zenon_Ha7. % 15.31/15.48 apply (zenon_or_s _ _ zenon_H44); [ zenon_intro zenon_H47 | zenon_intro zenon_H46 ]. % 15.31/15.48 exact (zenon_H45 zenon_H47). % 15.31/15.48 apply (zenon_or_s _ _ zenon_H46); [ zenon_intro zenon_H22 | zenon_intro zenon_H48 ]. % 15.31/15.48 apply (zenon_L644_); trivial. % 15.31/15.48 apply (zenon_or_s _ _ zenon_H48); [ zenon_intro zenon_H29 | zenon_intro zenon_H37 ]. % 15.31/15.48 apply (zenon_L668_); trivial. % 15.31/15.48 apply (zenon_L670_); trivial. % 15.31/15.48 (* end of lemma zenon_L671_ *) % 15.31/15.48 assert (zenon_L672_ : (((op (e0) (e0)) = (e1))\/(((op (e0) (e1)) = (e1))\/(((op (e0) (e2)) = (e1))\/((op (e0) (e3)) = (e1))))) -> (~((op (e0) (e0)) = (e1))) -> (~((op (e3) (e3)) = (e1))) -> (~((op (e0) (e2)) = (op (e3) (e2)))) -> (((op (e0) (e1)) = (e2))\/(((op (e1) (e1)) = (e2))\/(((op (e2) (e1)) = (e2))\/((op (e3) (e1)) = (e2))))) -> (~((op (e0) (e1)) = (op (e0) (e3)))) -> (~((op (e1) (e1)) = (e2))) -> ((op (e2) (e0)) = (e2)) -> (~((op (e2) (e0)) = (op (e2) (e1)))) -> (~((e1) = (e2))) -> (~((op (e1) (e0)) = (op (e3) (e0)))) -> ((op (e1) (e0)) = (e1)) -> (((op (e3) (e0)) = (e1))\/(((op (e3) (e1)) = (e1))\/(((op (e3) (e2)) = (e1))\/((op (e3) (e3)) = (e1))))) -> (((op (e0) (e0)) = (e3))\/(((op (e0) (e1)) = (e3))\/(((op (e0) (e2)) = (e3))\/((op (e0) (e3)) = (e3))))) -> (~((op (e0) (e2)) = (op (e1) (e2)))) -> (((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 (e1) (e1)) = (e3))\/(((op (e1) (e2)) = (e3))\/((op (e1) (e3)) = (e3))))) -> (~((op (e0) (op (e1) (e0))) = (op (e1) (e0)))) -> (~((op (e1) (e1)) = (e3))) -> (((op (e0) (e3)) = (e1))\/(((op (e1) (e3)) = (e1))\/(((op (e2) (e3)) = (e1))\/((op (e3) (e3)) = (e1))))) -> (~((op (e3) (e1)) = (op (e3) (e2)))) -> (~((op (e2) (e2)) = (e1))) -> (~((e1) = (e3))) -> (~((op (e0) (e2)) = (op (e0) (e3)))) -> (((op (e0) (e2)) = (e1))\/(((op (e1) (e2)) = (e1))\/(((op (e2) (e2)) = (e1))\/((op (e3) (e2)) = (e1))))) -> (~((op (e3) (op (e1) (e3))) = (op (e1) (e3)))) -> (~((op (e0) (e1)) = (op (e3) (e1)))) -> (((op (e3) (e0)) = (e2))\/(((op (e3) (e1)) = (e2))\/(((op (e3) (e2)) = (e2))\/((op (e3) (e3)) = (e2))))) -> (((op (e0) (e3)) = (e2))\/(((op (e1) (e3)) = (e2))\/(((op (e2) (e3)) = (e2))\/((op (e3) (e3)) = (e2))))) -> (~((e2) = (e3))) -> (~((op (e2) (e0)) = (op (e2) (e3)))) -> (~((op (e0) (e0)) = (e2))) -> (((op (e0) (e0)) = (e2))\/(((op (e0) (e1)) = (e2))\/(((op (e0) (e2)) = (e2))\/((op (e0) (e3)) = (e2))))) -> (((op (e3) (e3)) = (e0))\/(((op (e3) (e3)) = (e1))\/(((op (e3) (e3)) = (e2))\/((op (e3) (e3)) = (e3))))) -> (~((op (e3) (e3)) = (e0))) -> (~((op (e0) (e3)) = (op (e3) (e3)))) -> (~((op (e3) (e3)) = (e2))) -> (~((op (e3) (e3)) = (e3))) -> False). % 15.31/15.48 do 0 intro. intros zenon_H44 zenon_H45 zenon_H104 zenon_H140 zenon_H1a2 zenon_H1cd zenon_Hd6 zenon_Hdd zenon_H154 zenon_Ha7 zenon_H22e zenon_Hd8 zenon_H146 zenon_H58 zenon_H87 zenon_Hbe zenon_H59 zenon_H90 zenon_H261 zenon_H182 zenon_H121 zenon_H135 zenon_H52 zenon_Ha3 zenon_Hc9 zenon_H11b zenon_H26e zenon_H138 zenon_H1df zenon_H160 zenon_H6a zenon_Hce zenon_H8f zenon_H8e zenon_H3b zenon_H3c zenon_H36 zenon_H3d zenon_H3e. % 15.31/15.48 apply (zenon_or_s _ _ zenon_H44); [ zenon_intro zenon_H47 | zenon_intro zenon_H46 ]. % 15.31/15.48 exact (zenon_H45 zenon_H47). % 15.31/15.48 apply (zenon_or_s _ _ zenon_H46); [ zenon_intro zenon_H22 | zenon_intro zenon_H48 ]. % 15.31/15.48 apply (zenon_L644_); trivial. % 15.31/15.48 apply (zenon_or_s _ _ zenon_H48); [ zenon_intro zenon_H29 | zenon_intro zenon_H37 ]. % 15.31/15.48 apply (zenon_or_s _ _ zenon_H8e); [ zenon_intro zenon_H92 | zenon_intro zenon_H91 ]. % 15.31/15.48 exact (zenon_H8f zenon_H92). % 15.31/15.48 apply (zenon_or_s _ _ zenon_H91); [ zenon_intro zenon_H5d | zenon_intro zenon_H93 ]. % 15.31/15.48 apply (zenon_L667_); trivial. % 15.31/15.48 apply (zenon_or_s _ _ zenon_H93); [ zenon_intro zenon_H63 | zenon_intro zenon_H81 ]. % 15.31/15.48 apply (zenon_L104_); trivial. % 15.31/15.48 apply (zenon_L416_); trivial. % 15.31/15.48 apply (zenon_L7_); trivial. % 15.31/15.48 (* end of lemma zenon_L672_ *) % 15.31/15.48 assert (zenon_L673_ : (((op (e0) (e0)) = (e2))\/(((op (e1) (e0)) = (e2))\/(((op (e2) (e0)) = (e2))\/((op (e3) (e0)) = (e2))))) -> (~((op (e0) (e3)) = (op (e3) (e3)))) -> (((op (e0) (e0)) = (e2))\/(((op (e0) (e1)) = (e2))\/(((op (e0) (e2)) = (e2))\/((op (e0) (e3)) = (e2))))) -> (~((op (e0) (e0)) = (e2))) -> (~((op (e2) (e0)) = (op (e2) (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 (e0) (e1)) = (op (e3) (e1)))) -> (~((op (e3) (op (e1) (e3))) = (op (e1) (e3)))) -> (((op (e0) (e2)) = (e1))\/(((op (e1) (e2)) = (e1))\/(((op (e2) (e2)) = (e1))\/((op (e3) (e2)) = (e1))))) -> (~((op (e0) (e2)) = (op (e0) (e3)))) -> (~((e1) = (e3))) -> (~((op (e2) (e2)) = (e1))) -> (~((op (e3) (e1)) = (op (e3) (e2)))) -> (((op (e0) (e3)) = (e1))\/(((op (e1) (e3)) = (e1))\/(((op (e2) (e3)) = (e1))\/((op (e3) (e3)) = (e1))))) -> (~((op (e0) (op (e1) (e0))) = (op (e1) (e0)))) -> (((op (e1) (e0)) = (e3))\/(((op (e1) (e1)) = (e3))\/(((op (e1) (e2)) = (e3))\/((op (e1) (e3)) = (e3))))) -> (~((op (e0) (e0)) = (e3))) -> (((op (e0) (e0)) = (e3))\/(((op (e1) (e0)) = (e3))\/(((op (e2) (e0)) = (e3))\/((op (e3) (e0)) = (e3))))) -> (~((op (e0) (e2)) = (op (e1) (e2)))) -> (((op (e0) (e0)) = (e3))\/(((op (e0) (e1)) = (e3))\/(((op (e0) (e2)) = (e3))\/((op (e0) (e3)) = (e3))))) -> (((op (e3) (e0)) = (e1))\/(((op (e3) (e1)) = (e1))\/(((op (e3) (e2)) = (e1))\/((op (e3) (e3)) = (e1))))) -> ((op (e1) (e0)) = (e1)) -> (~((op (e1) (e0)) = (op (e3) (e0)))) -> (~((e1) = (e2))) -> (~((op (e2) (e0)) = (op (e2) (e1)))) -> (~((op (e0) (e1)) = (op (e0) (e3)))) -> (((op (e0) (e1)) = (e2))\/(((op (e1) (e1)) = (e2))\/(((op (e2) (e1)) = (e2))\/((op (e3) (e1)) = (e2))))) -> (~((op (e0) (e2)) = (op (e3) (e2)))) -> (~((op (e3) (e3)) = (e1))) -> (~((op (e0) (e0)) = (e1))) -> (((op (e0) (e0)) = (e1))\/(((op (e0) (e1)) = (e1))\/(((op (e0) (e2)) = (e1))\/((op (e0) (e3)) = (e1))))) -> (((op (e1) (e1)) = (e0))\/(((op (e1) (e1)) = (e1))\/(((op (e1) (e1)) = (e2))\/((op (e1) (e1)) = (e3))))) -> (~((op (e3) (e3)) = (e3))) -> (~((op (e3) (e3)) = (e2))) -> (~((op (e3) (e3)) = (e0))) -> (((op (e3) (e3)) = (e0))\/(((op (e3) (e3)) = (e1))\/(((op (e3) (e3)) = (e2))\/((op (e3) (e3)) = (e3))))) -> (~((op (e1) (e1)) = (e1))) -> (~((op (e1) (e1)) = (e2))) -> (~((op (e1) (e1)) = (e3))) -> False). % 15.31/15.48 do 0 intro. intros zenon_Heb zenon_H36 zenon_H8e zenon_H8f zenon_Hce zenon_H6a zenon_H160 zenon_H1df zenon_H138 zenon_H26e zenon_H11b zenon_Hc9 zenon_Ha3 zenon_H52 zenon_H135 zenon_H121 zenon_H261 zenon_H90 zenon_H59 zenon_Hbe zenon_H87 zenon_H58 zenon_H146 zenon_Hd8 zenon_H22e zenon_Ha7 zenon_H154 zenon_H1cd zenon_H1a2 zenon_H140 zenon_H104 zenon_H45 zenon_H44 zenon_H1b3 zenon_H3e zenon_H3d zenon_H3c zenon_H3b zenon_H1b4 zenon_Hd6 zenon_H182. % 15.31/15.48 apply (zenon_or_s _ _ zenon_Heb); [ zenon_intro zenon_H92 | zenon_intro zenon_Hec ]. % 15.31/15.48 exact (zenon_H8f zenon_H92). % 15.31/15.48 apply (zenon_or_s _ _ zenon_Hec); [ zenon_intro zenon_H68 | zenon_intro zenon_Hed ]. % 15.31/15.48 apply (zenon_L162_); trivial. % 15.31/15.48 apply (zenon_or_s _ _ zenon_Hed); [ zenon_intro zenon_Hdd | zenon_intro zenon_He9 ]. % 15.31/15.48 apply (zenon_L672_); trivial. % 15.31/15.48 apply (zenon_L406_); trivial. % 15.31/15.48 (* end of lemma zenon_L673_ *) % 15.31/15.48 assert (zenon_L674_ : (((op (e0) (e0)) = (e2))\/(((op (e0) (e1)) = (e2))\/(((op (e0) (e2)) = (e2))\/((op (e0) (e3)) = (e2))))) -> (~((op (e0) (e0)) = (e2))) -> (~((e1) = (e3))) -> ((op (e3) (e2)) = (e3)) -> (~((op (e0) (e2)) = (op (e3) (e2)))) -> (~((e2) = (e3))) -> (~((op (e0) (e0)) = (e3))) -> (((op (e0) (e0)) = (e3))\/(((op (e0) (e1)) = (e3))\/(((op (e0) (e2)) = (e3))\/((op (e0) (e3)) = (e3))))) -> (~((op (e3) (e3)) = (e0))) -> (~((e0) = (e2))) -> ((op (e2) (e3)) = (e2)) -> (~((op (e0) (e0)) = (op (e0) (e3)))) -> ((op (e0) (e0)) = (e0)) -> (((op (e0) (e3)) = (e0))\/(((op (e1) (e3)) = (e0))\/(((op (e2) (e3)) = (e0))\/((op (e3) (e3)) = (e0))))) -> (~((op (e0) (e2)) = (op (e1) (e2)))) -> (~((op (e1) (e1)) = (e2))) -> ((op (e1) (e0)) = (e1)) -> (((op (e1) (e0)) = (e2))\/(((op (e1) (e1)) = (e2))\/(((op (e1) (e2)) = (e2))\/((op (e1) (e3)) = (e2))))) -> ((op (e0) (e3)) = (e1)) -> (~((e1) = (e2))) -> False). % 15.31/15.48 do 0 intro. intros zenon_H8e zenon_H8f zenon_Ha3 zenon_H106 zenon_H140 zenon_H6a zenon_H59 zenon_H58 zenon_H3c zenon_H5e zenon_H124 zenon_H24f zenon_H1f zenon_Hd3 zenon_H87 zenon_Hd6 zenon_Hd8 zenon_H84 zenon_H37 zenon_Ha7. % 15.31/15.48 apply (zenon_or_s _ _ zenon_H8e); [ zenon_intro zenon_H92 | zenon_intro zenon_H91 ]. % 15.31/15.48 exact (zenon_H8f zenon_H92). % 15.31/15.48 apply (zenon_or_s _ _ zenon_H91); [ zenon_intro zenon_H5d | zenon_intro zenon_H93 ]. % 15.31/15.48 apply (zenon_L534_); trivial. % 15.31/15.48 apply (zenon_or_s _ _ zenon_H93); [ zenon_intro zenon_H63 | zenon_intro zenon_H81 ]. % 15.31/15.48 apply (zenon_L564_); trivial. % 15.31/15.48 apply (zenon_L33_); trivial. % 15.31/15.48 (* end of lemma zenon_L674_ *) % 15.31/15.48 assert (zenon_L675_ : ((~((op (e3) (e3)) = (e2)))\/((op (e3) (e2)) = (e3))) -> (~((op (e1) (e2)) = (op (e3) (e2)))) -> (~((op (e0) (e3)) = (op (e1) (e3)))) -> (((op (e0) (e0)) = (e2))\/(((op (e1) (e0)) = (e2))\/(((op (e2) (e0)) = (e2))\/((op (e3) (e0)) = (e2))))) -> (~((op (e1) (e1)) = (e1))) -> (((op (e1) (e1)) = (e0))\/(((op (e1) (e1)) = (e1))\/(((op (e1) (e1)) = (e2))\/((op (e1) (e1)) = (e3))))) -> (~((op (e0) (e0)) = (e1))) -> (~((op (e0) (op (e1) (e0))) = (op (e1) (e0)))) -> (((op (e0) (e0)) = (e2))\/(((op (e0) (e1)) = (e2))\/(((op (e0) (e2)) = (e2))\/((op (e0) (e3)) = (e2))))) -> (~((op (e1) (e0)) = (op (e3) (e0)))) -> (~((op (e0) (e0)) = (e3))) -> (~((e2) = (e3))) -> (((op (e1) (e0)) = (e3))\/(((op (e1) (e1)) = (e3))\/(((op (e1) (e2)) = (e3))\/((op (e1) (e3)) = (e3))))) -> (~((op (e0) (e1)) = (op (e0) (e3)))) -> (~((op (e2) (e0)) = (op (e2) (e3)))) -> (((op (e0) (e3)) = (e2))\/(((op (e1) (e3)) = (e2))\/(((op (e2) (e3)) = (e2))\/((op (e3) (e3)) = (e2))))) -> (~((op (e0) (e2)) = (op (e1) (e2)))) -> (~((op (e1) (e1)) = (e3))) -> (~((e1) = (e3))) -> (((op (e0) (e0)) = (e3))\/(((op (e1) (e0)) = (e3))\/(((op (e2) (e0)) = (e3))\/((op (e3) (e0)) = (e3))))) -> (((op (e3) (e0)) = (e1))\/(((op (e3) (e1)) = (e1))\/(((op (e3) (e2)) = (e1))\/((op (e3) (e3)) = (e1))))) -> (~((op (e0) (e2)) = (op (e3) (e2)))) -> (((op (e0) (e2)) = (e1))\/(((op (e1) (e2)) = (e1))\/(((op (e2) (e2)) = (e1))\/((op (e3) (e2)) = (e1))))) -> (~((op (e3) (e1)) = (op (e3) (e2)))) -> (~((op (e2) (e2)) = (e1))) -> (~((op (e0) (e2)) = (op (e0) (e3)))) -> (~((op (e3) (op (e1) (e3))) = (op (e1) (e3)))) -> (((op (e3) (e0)) = (e2))\/(((op (e3) (e1)) = (e2))\/(((op (e3) (e2)) = (e2))\/((op (e3) (e3)) = (e2))))) -> (((op (e0) (e1)) = (e2))\/(((op (e1) (e1)) = (e2))\/(((op (e2) (e1)) = (e2))\/((op (e3) (e1)) = (e2))))) -> (~((op (e2) (e0)) = (op (e2) (e1)))) -> (~((op (e1) (e1)) = (e2))) -> (~((op (e0) (e1)) = (op (e3) (e1)))) -> (~((op (e3) (e3)) = (e1))) -> (((op (e0) (e3)) = (e1))\/(((op (e1) (e3)) = (e1))\/(((op (e2) (e3)) = (e1))\/((op (e3) (e3)) = (e1))))) -> (((op (e0) (e0)) = (e3))\/(((op (e0) (e1)) = (e3))\/(((op (e0) (e2)) = (e3))\/((op (e0) (e3)) = (e3))))) -> (((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)) = (e0))) -> (((op (e0) (e0)) = (e1))\/(((op (e0) (e1)) = (e1))\/(((op (e0) (e2)) = (e1))\/((op (e0) (e3)) = (e1))))) -> ((op (e1) (e0)) = (e1)) -> (~((e1) = (e2))) -> (~((op (e0) (e0)) = (e2))) -> ((~((op (e3) (e3)) = (e1)))\/((op (e3) (e1)) = (e3))) -> (~((op (e3) (e1)) = (op (e3) (e3)))) -> ((op (e2) (e3)) = (e2)) -> (~((op (e1) (e0)) = (op (e1) (e3)))) -> ((~((op (e2) (e2)) = (e3)))\/((op (e2) (e3)) = (e2))) -> (~((op (e2) (e1)) = (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)) = (op (e3) (e3)))) -> (~((op (e2) (e1)) = (op (e2) (e2)))) -> ((~((op (e2) (e2)) = (e2)))\/((op (e2) (e2)) = (e2))) -> (~((op (e1) (e3)) = (op (e3) (e3)))) -> (((op (e0) (e3)) = (e0))\/(((op (e1) (e3)) = (e0))\/(((op (e2) (e3)) = (e0))\/((op (e3) (e3)) = (e0))))) -> (~((e0) = (e2))) -> ((op (e0) (e0)) = (e0)) -> (~((op (e0) (e0)) = (op (e0) (e3)))) -> (((op (e1) (e0)) = (e2))\/(((op (e1) (e1)) = (e2))\/(((op (e1) (e2)) = (e2))\/((op (e1) (e3)) = (e2))))) -> ((~((op (e3) (e3)) = (e3)))\/((op (e3) (e3)) = (e3))) -> False). % 15.31/15.48 do 0 intro. intros zenon_H10e zenon_H17d zenon_H80 zenon_Heb zenon_H1b4 zenon_H1b3 zenon_H45 zenon_H261 zenon_H8e zenon_H22e zenon_H59 zenon_H6a zenon_H90 zenon_H1cd zenon_Hce zenon_H160 zenon_H87 zenon_H182 zenon_Ha3 zenon_Hbe zenon_H146 zenon_H140 zenon_H11b zenon_H135 zenon_H52 zenon_Hc9 zenon_H26e zenon_H1df zenon_H1a2 zenon_H154 zenon_Hd6 zenon_H138 zenon_H104 zenon_H121 zenon_H58 zenon_H3b zenon_H36 zenon_H3c zenon_H44 zenon_Hd8 zenon_Ha7 zenon_H8f zenon_H10c zenon_H12d zenon_H124 zenon_H1cf zenon_H1c3 zenon_H1e2 zenon_H2e zenon_H2d zenon_Hbb zenon_H157 zenon_Haa zenon_H8b zenon_Hd3 zenon_H5e zenon_H1f zenon_H24f zenon_H84 zenon_H10d. % 15.31/15.48 apply (zenon_or_s _ _ zenon_H10e); [ zenon_intro zenon_H3d | zenon_intro zenon_H106 ]. % 15.31/15.48 apply (zenon_or_s _ _ zenon_H10d); [ zenon_intro zenon_H3e | zenon_intro zenon_H42 ]. % 15.31/15.48 apply (zenon_L673_); trivial. % 15.31/15.48 apply (zenon_L565_); trivial. % 15.31/15.48 apply (zenon_or_s _ _ zenon_H10d); [ zenon_intro zenon_H3e | zenon_intro zenon_H42 ]. % 15.31/15.48 apply (zenon_or_s _ _ zenon_H44); [ zenon_intro zenon_H47 | zenon_intro zenon_H46 ]. % 15.31/15.48 exact (zenon_H45 zenon_H47). % 15.31/15.48 apply (zenon_or_s _ _ zenon_H46); [ zenon_intro zenon_H22 | zenon_intro zenon_H48 ]. % 15.31/15.48 apply (zenon_L644_); trivial. % 15.31/15.48 apply (zenon_or_s _ _ zenon_H48); [ zenon_intro zenon_H29 | zenon_intro zenon_H37 ]. % 15.31/15.48 apply (zenon_or_s _ _ zenon_H8e); [ zenon_intro zenon_H92 | zenon_intro zenon_H91 ]. % 15.31/15.48 exact (zenon_H8f zenon_H92). % 15.31/15.48 apply (zenon_or_s _ _ zenon_H91); [ zenon_intro zenon_H5d | zenon_intro zenon_H93 ]. % 15.31/15.48 apply (zenon_or_s _ _ zenon_H58); [ zenon_intro zenon_H5b | zenon_intro zenon_H5a ]. % 15.31/15.48 exact (zenon_H59 zenon_H5b). % 15.31/15.48 apply (zenon_or_s _ _ zenon_H5a); [ zenon_intro zenon_H4a | zenon_intro zenon_H5c ]. % 15.31/15.48 apply (zenon_L50_); trivial. % 15.31/15.48 apply (zenon_or_s _ _ zenon_H5c); [ zenon_intro zenon_H50 | zenon_intro zenon_H53 ]. % 15.31/15.48 apply (zenon_L29_); trivial. % 15.31/15.48 apply (zenon_L527_); trivial. % 15.31/15.48 apply (zenon_or_s _ _ zenon_H93); [ zenon_intro zenon_H63 | zenon_intro zenon_H81 ]. % 15.31/15.48 apply (zenon_L564_); trivial. % 15.31/15.48 apply (zenon_L107_); trivial. % 15.31/15.48 apply (zenon_L674_); trivial. % 15.31/15.48 apply (zenon_L417_); trivial. % 15.31/15.48 (* end of lemma zenon_L675_ *) % 15.31/15.48 assert (zenon_L676_ : (((op (e1) (e0)) = (e2))\/(((op (e1) (e1)) = (e2))\/(((op (e1) (e2)) = (e2))\/((op (e1) (e3)) = (e2))))) -> (~((op (e0) (op (e1) (e0))) = (op (e1) (e0)))) -> (~((op (e1) (e1)) = (e2))) -> ((op (e0) (e2)) = (e2)) -> (~((op (e0) (e2)) = (op (e1) (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)) -> (~((e1) = (e2))) -> ((op (e2) (e0)) = (e1)) -> (~((op (e2) (e0)) = (op (e2) (e3)))) -> (~((op (e3) (e3)) = (e1))) -> False). % 15.31/15.48 do 0 intro. intros zenon_H84 zenon_H261 zenon_Hd6 zenon_H63 zenon_H87 zenon_H121 zenon_H1cd zenon_H22 zenon_Ha7 zenon_Hae zenon_Hce zenon_H104. % 15.31/15.48 apply (zenon_or_s _ _ zenon_H84); [ zenon_intro zenon_H68 | zenon_intro zenon_H85 ]. % 15.31/15.48 apply (zenon_L638_); trivial. % 15.31/15.48 apply (zenon_or_s _ _ zenon_H85); [ zenon_intro zenon_H6e | zenon_intro zenon_H86 ]. % 15.31/15.48 exact (zenon_Hd6 zenon_H6e). % 15.31/15.48 apply (zenon_or_s _ _ zenon_H86); [ zenon_intro zenon_H7c | zenon_intro zenon_H82 ]. % 15.31/15.48 apply (zenon_L52_); trivial. % 15.31/15.48 apply (zenon_L332_); trivial. % 15.31/15.48 (* end of lemma zenon_L676_ *) % 15.31/15.48 assert (zenon_L677_ : (((op (e0) (e0)) = (e2))\/(((op (e1) (e0)) = (e2))\/(((op (e2) (e0)) = (e2))\/((op (e3) (e0)) = (e2))))) -> (~((op (e0) (e0)) = (e2))) -> ((op (e0) (e2)) = (e2)) -> (~((op (e0) (op (e1) (e0))) = (op (e1) (e0)))) -> ((op (e2) (e3)) = (e2)) -> (~((op (e2) (e0)) = (op (e2) (e3)))) -> ((op (e3) (e0)) = (e1)) -> (~((e1) = (e2))) -> False). % 15.31/15.48 do 0 intro. intros zenon_Heb zenon_H8f zenon_H63 zenon_H261 zenon_H124 zenon_Hce zenon_Hee zenon_Ha7. % 15.31/15.48 apply (zenon_or_s _ _ zenon_Heb); [ zenon_intro zenon_H92 | zenon_intro zenon_Hec ]. % 15.31/15.48 exact (zenon_H8f zenon_H92). % 15.31/15.48 apply (zenon_or_s _ _ zenon_Hec); [ zenon_intro zenon_H68 | zenon_intro zenon_Hed ]. % 15.31/15.48 apply (zenon_L638_); trivial. % 15.31/15.49 apply (zenon_or_s _ _ zenon_Hed); [ zenon_intro zenon_Hdd | zenon_intro zenon_He9 ]. % 15.31/15.49 apply (zenon_L119_); trivial. % 15.31/15.49 apply (zenon_L122_); trivial. % 15.31/15.49 (* end of lemma zenon_L677_ *) % 15.31/15.49 assert (zenon_L678_ : (((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)) = (e0))) -> (((op (e1) (e1)) = (e0))\/(((op (e1) (e1)) = (e1))\/(((op (e1) (e1)) = (e2))\/((op (e1) (e1)) = (e3))))) -> (~((e1) = (e2))) -> ((op (e3) (e0)) = (e1)) -> (~((op (e2) (e0)) = (op (e2) (e3)))) -> ((op (e2) (e3)) = (e2)) -> (~((op (e0) (op (e1) (e0))) = (op (e1) (e0)))) -> (~((op (e0) (e0)) = (e2))) -> (((op (e0) (e0)) = (e2))\/(((op (e1) (e0)) = (e2))\/(((op (e2) (e0)) = (e2))\/((op (e3) (e0)) = (e2))))) -> (((op (e0) (e0)) = (e3))\/(((op (e0) (e1)) = (e3))\/(((op (e0) (e2)) = (e3))\/((op (e0) (e3)) = (e3))))) -> (~((op (e0) (e0)) = (e3))) -> (~((e1) = (e3))) -> ((op (e0) (e1)) = (e1)) -> (~((op (e0) (e2)) = (op (e2) (e2)))) -> (~((op (e2) (e2)) = (e2))) -> (~((op (e2) (e2)) = (e1))) -> (~((op (e2) (e2)) = (e0))) -> (((op (e2) (e2)) = (e0))\/(((op (e2) (e2)) = (e1))\/(((op (e2) (e2)) = (e2))\/((op (e2) (e2)) = (e3))))) -> (~((e2) = (e3))) -> False). % 15.31/15.49 do 0 intro. intros zenon_H8e zenon_H182 zenon_H23 zenon_H1b4 zenon_H145 zenon_H1b3 zenon_Ha7 zenon_Hee zenon_Hce zenon_H124 zenon_H261 zenon_H8f zenon_Heb zenon_H58 zenon_H59 zenon_Ha3 zenon_H22 zenon_H28 zenon_H2f zenon_H52 zenon_H2e zenon_H2d zenon_H6a. % 15.31/15.49 apply (zenon_or_s _ _ zenon_H8e); [ zenon_intro zenon_H92 | zenon_intro zenon_H91 ]. % 15.31/15.49 exact (zenon_H8f zenon_H92). % 15.31/15.49 apply (zenon_or_s _ _ zenon_H91); [ zenon_intro zenon_H5d | zenon_intro zenon_H93 ]. % 15.31/15.49 apply (zenon_L214_); trivial. % 15.31/15.49 apply (zenon_or_s _ _ zenon_H93); [ zenon_intro zenon_H63 | zenon_intro zenon_H81 ]. % 15.31/15.49 apply (zenon_L677_); trivial. % 15.31/15.49 apply (zenon_L663_); trivial. % 15.31/15.49 (* end of lemma zenon_L678_ *) % 15.31/15.49 assert (zenon_L679_ : (((op (e1) (e0)) = (e2))\/(((op (e1) (e1)) = (e2))\/(((op (e1) (e2)) = (e2))\/((op (e1) (e3)) = (e2))))) -> (~((e2) = (e3))) -> ((op (e1) (e0)) = (e3)) -> (~((op (e1) (e1)) = (e2))) -> ((op (e0) (e2)) = (e2)) -> (~((op (e0) (e2)) = (op (e1) (e2)))) -> (((op (e0) (e3)) = (e0))\/(((op (e1) (e3)) = (e0))\/(((op (e2) (e3)) = (e0))\/((op (e3) (e3)) = (e0))))) -> ((op (e0) (e0)) = (e0)) -> (~((op (e0) (e0)) = (op (e0) (e3)))) -> ((op (e2) (e3)) = (e2)) -> (~((e0) = (e2))) -> (~((op (e3) (e3)) = (e0))) -> False). % 15.31/15.49 do 0 intro. intros zenon_H84 zenon_H6a zenon_H69 zenon_Hd6 zenon_H63 zenon_H87 zenon_Hd3 zenon_H1f zenon_H24f zenon_H124 zenon_H5e zenon_H3c. % 15.31/15.49 apply (zenon_or_s _ _ zenon_H84); [ zenon_intro zenon_H68 | zenon_intro zenon_H85 ]. % 15.31/15.49 apply (zenon_L17_); trivial. % 15.31/15.49 apply (zenon_or_s _ _ zenon_H85); [ zenon_intro zenon_H6e | zenon_intro zenon_H86 ]. % 15.31/15.49 exact (zenon_Hd6 zenon_H6e). % 15.31/15.49 apply (zenon_or_s _ _ zenon_H86); [ zenon_intro zenon_H7c | zenon_intro zenon_H82 ]. % 15.31/15.49 apply (zenon_L52_); trivial. % 15.31/15.49 apply (zenon_L563_); trivial. % 15.31/15.49 (* end of lemma zenon_L679_ *) % 15.31/15.49 assert (zenon_L680_ : (((op (e0) (e0)) = (e3))\/(((op (e1) (e0)) = (e3))\/(((op (e2) (e0)) = (e3))\/((op (e3) (e0)) = (e3))))) -> (~((op (e0) (e0)) = (e3))) -> ((op (e0) (e3)) = (e3)) -> (~((op (e0) (op (e1) (e0))) = (op (e1) (e0)))) -> (~((e1) = (e3))) -> ((op (e2) (e0)) = (e1)) -> (~((e2) = (e3))) -> ((op (e3) (e0)) = (e2)) -> False). % 15.31/15.49 do 0 intro. intros zenon_Hbe zenon_H59 zenon_H53 zenon_H261 zenon_Ha3 zenon_Hae zenon_H6a zenon_He9. % 15.31/15.49 apply (zenon_or_s _ _ zenon_Hbe); [ zenon_intro zenon_H5b | zenon_intro zenon_Hbf ]. % 15.31/15.49 exact (zenon_H59 zenon_H5b). % 15.31/15.49 apply (zenon_or_s _ _ zenon_Hbf); [ zenon_intro zenon_H69 | zenon_intro zenon_Hc0 ]. % 15.31/15.49 apply (zenon_L647_); trivial. % 15.31/15.49 apply (zenon_or_s _ _ zenon_Hc0); [ zenon_intro zenon_Haf | zenon_intro zenon_Hba ]. % 15.31/15.49 apply (zenon_L39_); trivial. % 15.31/15.49 apply (zenon_L220_); trivial. % 15.31/15.49 (* end of lemma zenon_L680_ *) % 15.31/15.49 assert (zenon_L681_ : ((~((op (e3) (e3)) = (e2)))\/((op (e3) (e2)) = (e3))) -> (~((op (e3) (e1)) = (op (e3) (e2)))) -> (((op (e0) (e0)) = (e1))\/(((op (e0) (e1)) = (e1))\/(((op (e0) (e2)) = (e1))\/((op (e0) (e3)) = (e1))))) -> (~((op (e3) (e3)) = (e0))) -> (~((op (e0) (e3)) = (op (e3) (e3)))) -> (((op (e3) (e3)) = (e0))\/(((op (e3) (e3)) = (e1))\/(((op (e3) (e3)) = (e2))\/((op (e3) (e3)) = (e3))))) -> (~((op (e0) (op (e1) (e0))) = (op (e1) (e0)))) -> (((op (e0) (e0)) = (e2))\/(((op (e0) (e1)) = (e2))\/(((op (e0) (e2)) = (e2))\/((op (e0) (e3)) = (e2))))) -> (((op (e2) (e2)) = (e0))\/(((op (e2) (e2)) = (e1))\/(((op (e2) (e2)) = (e2))\/((op (e2) (e2)) = (e3))))) -> (~((op (e0) (e2)) = (op (e2) (e2)))) -> (~((op (e2) (e2)) = (e2))) -> (~((op (e2) (e2)) = (e1))) -> (~((op (e2) (e2)) = (e0))) -> (~((op (e2) (e0)) = (op (e2) (e3)))) -> ((op (e2) (e3)) = (e2)) -> (((op (e0) (e0)) = (e3))\/(((op (e0) (e1)) = (e3))\/(((op (e0) (e2)) = (e3))\/((op (e0) (e3)) = (e3))))) -> (~((e1) = (e3))) -> (((op (e0) (e0)) = (e3))\/(((op (e1) (e0)) = (e3))\/(((op (e2) (e0)) = (e3))\/((op (e3) (e0)) = (e3))))) -> (~((e2) = (e3))) -> ((op (e3) (e1)) = (e3)) -> (~((op (e0) (e1)) = (op (e3) (e1)))) -> (~((op (e0) (e0)) = (e3))) -> (((op (e0) (e0)) = (e2))\/(((op (e1) (e0)) = (e2))\/(((op (e2) (e0)) = (e2))\/((op (e3) (e0)) = (e2))))) -> (~((op (e1) (e1)) = (e0))) -> (~((op (e1) (e1)) = (e1))) -> (~((op (e0) (e1)) = (op (e1) (e1)))) -> (~((op (e1) (e1)) = (e3))) -> (((op (e1) (e1)) = (e0))\/(((op (e1) (e1)) = (e1))\/(((op (e1) (e1)) = (e2))\/((op (e1) (e1)) = (e3))))) -> (~((op (e0) (e0)) = (e2))) -> (~((e1) = (e2))) -> (((op (e0) (e0)) = (e1))\/(((op (e1) (e0)) = (e1))\/(((op (e2) (e0)) = (e1))\/((op (e3) (e0)) = (e1))))) -> (~((op (e0) (e0)) = (e1))) -> (~((op (e3) (e1)) = (op (e3) (e3)))) -> ((~((op (e3) (e3)) = (e3)))\/((op (e3) (e3)) = (e3))) -> False). % 15.31/15.49 do 0 intro. intros zenon_H10e zenon_H135 zenon_H44 zenon_H3c zenon_H36 zenon_H3b zenon_H261 zenon_H8e zenon_H2d zenon_H28 zenon_H2f zenon_H52 zenon_H2e zenon_Hce zenon_H124 zenon_H58 zenon_Ha3 zenon_Hbe zenon_H6a zenon_H10a zenon_H138 zenon_H59 zenon_Heb zenon_H145 zenon_H1b4 zenon_H23 zenon_H182 zenon_H1b3 zenon_H8f zenon_Ha7 zenon_Hf1 zenon_H45 zenon_H12d zenon_H10d. % 15.31/15.49 apply (zenon_or_s _ _ zenon_H10e); [ zenon_intro zenon_H3d | zenon_intro zenon_H106 ]. % 15.31/15.49 apply (zenon_or_s _ _ zenon_H10d); [ zenon_intro zenon_H3e | zenon_intro zenon_H42 ]. % 15.31/15.49 apply (zenon_or_s _ _ zenon_H44); [ zenon_intro zenon_H47 | zenon_intro zenon_H46 ]. % 15.31/15.49 exact (zenon_H45 zenon_H47). % 15.31/15.49 apply (zenon_or_s _ _ zenon_H46); [ zenon_intro zenon_H22 | zenon_intro zenon_H48 ]. % 15.31/15.49 apply (zenon_or_s _ _ zenon_Hf1); [ zenon_intro zenon_H47 | zenon_intro zenon_Hf4 ]. % 15.31/15.49 exact (zenon_H45 zenon_H47). % 15.31/15.49 apply (zenon_or_s _ _ zenon_Hf4); [ zenon_intro zenon_Hd8 | zenon_intro zenon_Hf5 ]. % 15.31/15.49 apply (zenon_L644_); trivial. % 15.31/15.49 apply (zenon_or_s _ _ zenon_Hf5); [ zenon_intro zenon_Hae | zenon_intro zenon_Hee ]. % 15.31/15.49 apply (zenon_or_s _ _ zenon_H8e); [ zenon_intro zenon_H92 | zenon_intro zenon_H91 ]. % 15.31/15.49 exact (zenon_H8f zenon_H92). % 15.31/15.49 apply (zenon_or_s _ _ zenon_H91); [ zenon_intro zenon_H5d | zenon_intro zenon_H93 ]. % 15.31/15.49 apply (zenon_L214_); trivial. % 15.31/15.49 apply (zenon_or_s _ _ zenon_H93); [ zenon_intro zenon_H63 | zenon_intro zenon_H81 ]. % 15.31/15.49 apply (zenon_or_s _ _ zenon_Heb); [ zenon_intro zenon_H92 | zenon_intro zenon_Hec ]. % 15.31/15.49 exact (zenon_H8f zenon_H92). % 15.31/15.49 apply (zenon_or_s _ _ zenon_Hec); [ zenon_intro zenon_H68 | zenon_intro zenon_Hed ]. % 15.31/15.49 apply (zenon_L638_); trivial. % 15.31/15.49 apply (zenon_or_s _ _ zenon_Hed); [ zenon_intro zenon_Hdd | zenon_intro zenon_He9 ]. % 15.31/15.49 apply (zenon_L119_); trivial. % 15.31/15.49 apply (zenon_or_s _ _ zenon_H58); [ zenon_intro zenon_H5b | zenon_intro zenon_H5a ]. % 15.31/15.49 exact (zenon_H59 zenon_H5b). % 15.31/15.49 apply (zenon_or_s _ _ zenon_H5a); [ zenon_intro zenon_H4a | zenon_intro zenon_H5c ]. % 15.31/15.49 apply (zenon_L120_); trivial. % 15.31/15.49 apply (zenon_or_s _ _ zenon_H5c); [ zenon_intro zenon_H50 | zenon_intro zenon_H53 ]. % 15.31/15.49 apply (zenon_L31_); trivial. % 15.31/15.49 apply (zenon_L680_); trivial. % 15.31/15.49 apply (zenon_L663_); trivial. % 15.31/15.49 apply (zenon_L678_); trivial. % 15.31/15.49 apply (zenon_or_s _ _ zenon_H48); [ zenon_intro zenon_H29 | zenon_intro zenon_H37 ]. % 15.31/15.49 apply (zenon_L666_); trivial. % 15.31/15.49 apply (zenon_L7_); trivial. % 15.31/15.49 apply (zenon_L102_); trivial. % 15.31/15.49 apply (zenon_L115_); trivial. % 15.31/15.49 (* end of lemma zenon_L681_ *) % 15.31/15.49 assert (zenon_L682_ : ((~((op (e3) (e3)) = (e2)))\/((op (e3) (e2)) = (e3))) -> (~((op (e3) (e0)) = (op (e3) (e2)))) -> (~((op (e0) (e0)) = (e1))) -> (((op (e0) (e3)) = (e1))\/(((op (e1) (e3)) = (e1))\/(((op (e2) (e3)) = (e1))\/((op (e3) (e3)) = (e1))))) -> (~((op (e3) (e3)) = (e1))) -> ((op (e2) (e3)) = (e2)) -> (~((e1) = (e2))) -> ((op (e1) (e0)) = (e1)) -> (~((op (e1) (e0)) = (op (e1) (e3)))) -> (~((op (e0) (e1)) = (op (e0) (e3)))) -> (((op (e0) (e0)) = (e2))\/(((op (e0) (e1)) = (e2))\/(((op (e0) (e2)) = (e2))\/((op (e0) (e3)) = (e2))))) -> (~((op (e1) (e0)) = (op (e3) (e0)))) -> (((op (e0) (e0)) = (e3))\/(((op (e0) (e1)) = (e3))\/(((op (e0) (e2)) = (e3))\/((op (e0) (e3)) = (e3))))) -> (~((op (e0) (op (e1) (e0))) = (op (e1) (e0)))) -> (~((op (e0) (e1)) = (op (e3) (e1)))) -> (~((op (e1) (e1)) = (e2))) -> (~((op (e2) (e0)) = (op (e2) (e1)))) -> (((op (e0) (e1)) = (e2))\/(((op (e1) (e1)) = (e2))\/(((op (e2) (e1)) = (e2))\/((op (e3) (e1)) = (e2))))) -> (((op (e3) (e0)) = (e2))\/(((op (e3) (e1)) = (e2))\/(((op (e3) (e2)) = (e2))\/((op (e3) (e3)) = (e2))))) -> (~((op (e3) (op (e1) (e3))) = (op (e1) (e3)))) -> (~((op (e0) (e2)) = (op (e0) (e3)))) -> (~((op (e2) (e2)) = (e1))) -> (~((op (e3) (e1)) = (op (e3) (e2)))) -> (((op (e0) (e2)) = (e1))\/(((op (e1) (e2)) = (e1))\/(((op (e2) (e2)) = (e1))\/((op (e3) (e2)) = (e1))))) -> (~((op (e0) (e2)) = (op (e3) (e2)))) -> (((op (e3) (e0)) = (e1))\/(((op (e3) (e1)) = (e1))\/(((op (e3) (e2)) = (e1))\/((op (e3) (e3)) = (e1))))) -> (((op (e0) (e0)) = (e3))\/(((op (e1) (e0)) = (e3))\/(((op (e2) (e0)) = (e3))\/((op (e3) (e0)) = (e3))))) -> (~((e1) = (e3))) -> (~((op (e1) (e1)) = (e3))) -> (~((op (e0) (e2)) = (op (e1) (e2)))) -> (((op (e0) (e3)) = (e2))\/(((op (e1) (e3)) = (e2))\/(((op (e2) (e3)) = (e2))\/((op (e3) (e3)) = (e2))))) -> (~((op (e2) (e0)) = (op (e2) (e3)))) -> (((op (e1) (e0)) = (e3))\/(((op (e1) (e1)) = (e3))\/(((op (e1) (e2)) = (e3))\/((op (e1) (e3)) = (e3))))) -> (~((e2) = (e3))) -> (~((op (e0) (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)) = (e2))) -> (((op (e0) (e0)) = (e1))\/(((op (e0) (e1)) = (e1))\/(((op (e0) (e2)) = (e1))\/((op (e0) (e3)) = (e1))))) -> False). % 15.31/15.49 do 0 intro. intros zenon_H10e zenon_H105 zenon_H45 zenon_H121 zenon_H104 zenon_H124 zenon_Ha7 zenon_Hd8 zenon_H1cf zenon_H1cd zenon_H8e zenon_H22e zenon_H58 zenon_H261 zenon_H138 zenon_Hd6 zenon_H154 zenon_H1a2 zenon_H1df zenon_H26e zenon_Hc9 zenon_H52 zenon_H135 zenon_H11b zenon_H140 zenon_H146 zenon_Hbe zenon_Ha3 zenon_H182 zenon_H87 zenon_H160 zenon_Hce zenon_H90 zenon_H6a zenon_H59 zenon_Hba zenon_Heb zenon_H8f zenon_H44. % 15.31/15.49 apply (zenon_or_s _ _ zenon_H10e); [ zenon_intro zenon_H3d | zenon_intro zenon_H106 ]. % 15.31/15.49 apply (zenon_or_s _ _ zenon_H44); [ zenon_intro zenon_H47 | zenon_intro zenon_H46 ]. % 15.31/15.49 exact (zenon_H45 zenon_H47). % 15.31/15.49 apply (zenon_or_s _ _ zenon_H46); [ zenon_intro zenon_H22 | zenon_intro zenon_H48 ]. % 15.31/15.49 apply (zenon_L225_); trivial. % 15.31/15.49 apply (zenon_or_s _ _ zenon_H48); [ zenon_intro zenon_H29 | zenon_intro zenon_H37 ]. % 15.31/15.49 apply (zenon_L668_); trivial. % 15.31/15.49 apply (zenon_or_s _ _ zenon_H8e); [ zenon_intro zenon_H92 | zenon_intro zenon_H91 ]. % 15.31/15.49 exact (zenon_H8f zenon_H92). % 15.31/15.49 apply (zenon_or_s _ _ zenon_H91); [ zenon_intro zenon_H5d | zenon_intro zenon_H93 ]. % 15.31/15.49 apply (zenon_L669_); trivial. % 15.31/15.49 apply (zenon_or_s _ _ zenon_H93); [ zenon_intro zenon_H63 | zenon_intro zenon_H81 ]. % 15.31/15.49 apply (zenon_or_s _ _ zenon_Heb); [ zenon_intro zenon_H92 | zenon_intro zenon_Hec ]. % 15.31/15.49 exact (zenon_H8f zenon_H92). % 15.31/15.49 apply (zenon_or_s _ _ zenon_Hec); [ zenon_intro zenon_H68 | zenon_intro zenon_Hed ]. % 15.31/15.49 apply (zenon_L638_); trivial. % 15.31/15.49 apply (zenon_or_s _ _ zenon_Hed); [ zenon_intro zenon_Hdd | zenon_intro zenon_He9 ]. % 15.31/15.49 apply (zenon_L119_); trivial. % 15.31/15.49 apply (zenon_L220_); trivial. % 15.31/15.49 apply (zenon_L33_); trivial. % 15.31/15.49 apply (zenon_L81_); trivial. % 15.31/15.49 (* end of lemma zenon_L682_ *) % 15.31/15.49 assert (zenon_L683_ : (((op (e2) (e2)) = (e0))\/(((op (e2) (e2)) = (e1))\/(((op (e2) (e2)) = (e2))\/((op (e2) (e2)) = (e3))))) -> (~((op (e2) (e2)) = (e0))) -> (~((op (e2) (e2)) = (e1))) -> (~((op (e2) (e2)) = (e2))) -> ((op (e2) (e0)) = (e1)) -> ((op (e3) (e3)) = (e0)) -> False). % 15.31/15.49 do 0 intro. intros zenon_H2d zenon_H2e zenon_H52 zenon_H2f zenon_Hae zenon_H40. % 15.31/15.49 apply (zenon_or_s _ _ zenon_H2d); [ zenon_intro zenon_H32 | zenon_intro zenon_H31 ]. % 15.31/15.49 exact (zenon_H2e zenon_H32). % 15.31/15.49 apply (zenon_or_s _ _ zenon_H31); [ zenon_intro zenon_H2a | zenon_intro zenon_H33 ]. % 15.31/15.49 exact (zenon_H52 zenon_H2a). % 15.31/15.49 apply (zenon_or_s _ _ zenon_H33); [ zenon_intro zenon_H35 | zenon_intro zenon_H34 ]. % 15.31/15.49 exact (zenon_H2f zenon_H35). % 15.31/15.49 apply (zenon_L76_); trivial. % 15.31/15.49 (* end of lemma zenon_L683_ *) % 15.31/15.49 assert (zenon_L684_ : (((op (e0) (e3)) = (e0))\/(((op (e1) (e3)) = (e0))\/(((op (e2) (e3)) = (e0))\/((op (e3) (e3)) = (e0))))) -> ((op (e0) (e0)) = (e0)) -> (~((op (e0) (e0)) = (op (e0) (e3)))) -> (~((op (e3) (e3)) = (e3))) -> (~((op (e3) (e3)) = (e2))) -> (~((op (e3) (e3)) = (e1))) -> (~((op (e1) (e3)) = (op (e3) (e3)))) -> (((op (e3) (e3)) = (e0))\/(((op (e3) (e3)) = (e1))\/(((op (e3) (e3)) = (e2))\/((op (e3) (e3)) = (e3))))) -> ((op (e2) (e3)) = (e2)) -> (~((e0) = (e2))) -> (((op (e2) (e2)) = (e0))\/(((op (e2) (e2)) = (e1))\/(((op (e2) (e2)) = (e2))\/((op (e2) (e2)) = (e3))))) -> (~((op (e2) (e2)) = (e0))) -> (~((op (e2) (e2)) = (e1))) -> (~((op (e2) (e2)) = (e2))) -> ((op (e2) (e0)) = (e1)) -> False). % 15.31/15.49 do 0 intro. intros zenon_Hd3 zenon_H1f zenon_H24f zenon_H3e zenon_H3d zenon_H104 zenon_H8b zenon_H3b zenon_H124 zenon_H5e zenon_H2d zenon_H2e zenon_H52 zenon_H2f zenon_Hae. % 15.31/15.49 apply (zenon_or_s _ _ zenon_Hd3); [ zenon_intro zenon_Hca | zenon_intro zenon_Hd4 ]. % 15.31/15.49 apply (zenon_L562_); trivial. % 15.31/15.49 apply (zenon_or_s _ _ zenon_Hd4); [ zenon_intro zenon_Hcc | zenon_intro zenon_Hd5 ]. % 15.31/15.49 apply (zenon_L465_); trivial. % 15.31/15.49 apply (zenon_or_s _ _ zenon_Hd5); [ zenon_intro zenon_Hd0 | zenon_intro zenon_H40 ]. % 15.31/15.49 apply (zenon_L201_); trivial. % 15.31/15.49 apply (zenon_L683_); trivial. % 15.31/15.49 (* end of lemma zenon_L684_ *) % 15.31/15.49 assert (zenon_L685_ : (~((op (e3) (e0)) = (op (e3) (e2)))) -> ((~((op (e3) (e3)) = (e3)))\/((op (e3) (e3)) = (e3))) -> (~((op (e0) (e2)) = (op (e0) (e3)))) -> (~((op (e2) (e2)) = (e1))) -> (((op (e0) (e2)) = (e0))\/(((op (e0) (e2)) = (e1))\/(((op (e0) (e2)) = (e2))\/((op (e0) (e2)) = (e3))))) -> (~((op (e0) (e0)) = (op (e0) (e2)))) -> (((op (e0) (e2)) = (e1))\/(((op (e1) (e2)) = (e1))\/(((op (e2) (e2)) = (e1))\/((op (e3) (e2)) = (e1))))) -> (((op (e0) (e3)) = (e0))\/(((op (e0) (e3)) = (e1))\/(((op (e0) (e3)) = (e2))\/((op (e0) (e3)) = (e3))))) -> (~((op (e0) (e3)) = (op (e1) (e3)))) -> (~((op (e0) (e3)) = (op (e2) (e3)))) -> (~((op (e1) (e2)) = (op (e2) (e2)))) -> (~((op (e0) (e1)) = (op (e3) (e1)))) -> (((op (e0) (e0)) = (e3))\/(((op (e1) (e0)) = (e3))\/(((op (e2) (e0)) = (e3))\/((op (e3) (e0)) = (e3))))) -> (~((op (e3) (e0)) = (op (e3) (e3)))) -> (((op (e2) (e2)) = (e0))\/(((op (e2) (e2)) = (e1))\/(((op (e2) (e2)) = (e2))\/((op (e2) (e2)) = (e3))))) -> (~((op (e2) (e2)) = (e0))) -> (~((op (e1) (e1)) = (e2))) -> (~((e1) = (e3))) -> (~((op (e0) (e0)) = (e3))) -> ((~((op (e3) (e3)) = (e0)))\/((op (e3) (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) (e0)) = (op (e0) (e3)))) -> ((op (e0) (e0)) = (e0)) -> (~((e0) = (e2))) -> (((op (e0) (e3)) = (e0))\/(((op (e1) (e3)) = (e0))\/(((op (e2) (e3)) = (e0))\/((op (e3) (e3)) = (e0))))) -> (((op (e0) (e0)) = (e3))\/(((op (e0) (e1)) = (e3))\/(((op (e0) (e2)) = (e3))\/((op (e0) (e3)) = (e3))))) -> (~((op (e0) (e2)) = (op (e1) (e2)))) -> (~((op (e1) (e3)) = (op (e3) (e3)))) -> (((op (e1) (e0)) = (e3))\/(((op (e1) (e1)) = (e3))\/(((op (e1) (e2)) = (e3))\/((op (e1) (e3)) = (e3))))) -> (~((e2) = (e3))) -> (((op (e0) (e0)) = (e2))\/(((op (e1) (e0)) = (e2))\/(((op (e2) (e0)) = (e2))\/((op (e3) (e0)) = (e2))))) -> ((~((op (e2) (e2)) = (e2)))\/((op (e2) (e2)) = (e2))) -> (~((op (e2) (e1)) = (op (e2) (e2)))) -> (~((op (e2) (e1)) = (op (e2) (e3)))) -> ((~((op (e2) (e2)) = (e3)))\/((op (e2) (e3)) = (e2))) -> (~((op (e1) (e0)) = (op (e3) (e0)))) -> (((op (e0) (e1)) = (e2))\/(((op (e1) (e1)) = (e2))\/(((op (e2) (e1)) = (e2))\/((op (e3) (e1)) = (e2))))) -> (~((op (e2) (e0)) = (op (e2) (e1)))) -> (~((op (e0) (e2)) = (op (e3) (e2)))) -> (((op (e3) (e0)) = (e1))\/(((op (e3) (e1)) = (e1))\/(((op (e3) (e2)) = (e1))\/((op (e3) (e3)) = (e1))))) -> (~((op (e0) (e1)) = (op (e0) (e3)))) -> (~((op (e1) (e0)) = (op (e1) (e3)))) -> (~((e1) = (e2))) -> (((op (e0) (e3)) = (e1))\/(((op (e1) (e3)) = (e1))\/(((op (e2) (e3)) = (e1))\/((op (e3) (e3)) = (e1))))) -> (~((op (e0) (e0)) = (e1))) -> (~((op (e3) (e1)) = (op (e3) (e3)))) -> ((~((op (e3) (e3)) = (e1)))\/((op (e3) (e1)) = (e3))) -> (((op (e2) (e0)) = (e0))\/(((op (e2) (e1)) = (e0))\/(((op (e2) (e2)) = (e0))\/((op (e2) (e3)) = (e0))))) -> (~((op (e1) (e3)) = (op (e2) (e3)))) -> (~((op (e0) (e0)) = (op (e2) (e0)))) -> (~((op (e3) (e2)) = (op (e3) (e3)))) -> ((~((op (e3) (e3)) = (e2)))\/((op (e3) (e2)) = (e3))) -> (~((e0) = (e3))) -> (((op (e0) (e2)) = (e0))\/(((op (e1) (e2)) = (e0))\/(((op (e2) (e2)) = (e0))\/((op (e3) (e2)) = (e0))))) -> (((op (e0) (e0)) = (e1))\/(((op (e1) (e0)) = (e1))\/(((op (e2) (e0)) = (e1))\/((op (e3) (e0)) = (e1))))) -> (((op (e1) (e0)) = (e0))\/(((op (e1) (e1)) = (e0))\/(((op (e1) (e2)) = (e0))\/((op (e1) (e3)) = (e0))))) -> (~((e0) = (e1))) -> (~((op (e0) (e0)) = (op (e1) (e0)))) -> (~((op (e2) (e0)) = (op (e2) (e3)))) -> (~((op (e1) (e2)) = (op (e1) (e3)))) -> ((~((op (e1) (e1)) = (e3)))\/((op (e1) (e3)) = (e1))) -> ((~((op (e2) (e2)) = (e1)))\/((op (e2) (e1)) = (e2))) -> ((~((op (e2) (e2)) = (e0)))\/((op (e2) (e0)) = (e2))) -> (~((op (e1) (e0)) = (op (e1) (e2)))) -> ((~((op (e1) (e1)) = (e2)))\/((op (e1) (e2)) = (e1))) -> (~((op (e0) (e1)) = (op (e2) (e1)))) -> (((op (e0) (e3)) = (e2))\/(((op (e1) (e3)) = (e2))\/(((op (e2) (e3)) = (e2))\/((op (e3) (e3)) = (e2))))) -> (((op (e2) (e0)) = (e3))\/(((op (e2) (e1)) = (e3))\/(((op (e2) (e2)) = (e3))\/((op (e2) (e3)) = (e3))))) -> (~((op (e1) (e0)) = (op (e1) (e1)))) -> ((~((op (e1) (e1)) = (e1)))\/((op (e1) (e1)) = (e1))) -> (~((op (e2) (e0)) = (op (e2) (e2)))) -> (~((op (e2) (e2)) = (op (e2) (e3)))) -> (((op (e1) (e3)) = (e0))\/(((op (e1) (e3)) = (e1))\/(((op (e1) (e3)) = (e2))\/((op (e1) (e3)) = (e3))))) -> (~((op (e2) (e1)) = (op (e3) (e1)))) -> (((op (e3) (e0)) = (e2))\/(((op (e3) (e1)) = (e2))\/(((op (e3) (e2)) = (e2))\/((op (e3) (e3)) = (e2))))) -> (((op (e0) (e1)) = (e0))\/(((op (e1) (e1)) = (e0))\/(((op (e2) (e1)) = (e0))\/((op (e3) (e1)) = (e0))))) -> (((op (e0) (e1)) = (e3))\/(((op (e1) (e1)) = (e3))\/(((op (e2) (e1)) = (e3))\/((op (e3) (e1)) = (e3))))) -> (~((op (e0) (e0)) = (op (e0) (e1)))) -> (~((op (e3) (e0)) = (op (e3) (e1)))) -> (((op (e0) (e1)) = (e1))\/(((op (e1) (e1)) = (e1))\/(((op (e2) (e1)) = (e1))\/((op (e3) (e1)) = (e1))))) -> (((op (e2) (e0)) = (e1))\/(((op (e2) (e1)) = (e1))\/(((op (e2) (e2)) = (e1))\/((op (e2) (e3)) = (e1))))) -> (((op (e0) (e2)) = (e3))\/(((op (e1) (e2)) = (e3))\/(((op (e2) (e2)) = (e3))\/((op (e3) (e2)) = (e3))))) -> (((op (e1) (e0)) = (e1))\/(((op (e1) (e1)) = (e1))\/(((op (e1) (e2)) = (e1))\/((op (e1) (e3)) = (e1))))) -> (~((op (e0) (e0)) = (e2))) -> (((op (e1) (e1)) = (e0))\/(((op (e1) (e1)) = (e1))\/(((op (e1) (e1)) = (e2))\/((op (e1) (e1)) = (e3))))) -> (~((op (e1) (e1)) = (e3))) -> (~((op (e0) (e1)) = (op (e1) (e1)))) -> (~((op (e1) (e1)) = (e1))) -> (~((op (e1) (e1)) = (e0))) -> (~((op (e0) (e2)) = (op (e2) (e2)))) -> ((op (e2) (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 (e0) (e0)) = (e2))\/(((op (e0) (e1)) = (e2))\/(((op (e0) (e2)) = (e2))\/((op (e0) (e3)) = (e2))))) -> False). % 15.31/15.49 do 0 intro. intros zenon_H105 zenon_H10d zenon_Hc9 zenon_H52 zenon_H251 zenon_H250 zenon_H11b zenon_H254 zenon_H80 zenon_Hb4 zenon_H7d zenon_H138 zenon_Hbe zenon_Hbb zenon_H2d zenon_H2e zenon_Hd6 zenon_Ha3 zenon_H59 zenon_H10f zenon_H44 zenon_H84 zenon_H24f zenon_H1f zenon_H5e zenon_Hd3 zenon_H58 zenon_H87 zenon_H8b zenon_H90 zenon_H6a zenon_Heb zenon_Haa zenon_H157 zenon_H1e2 zenon_H1c3 zenon_H22e zenon_H1a2 zenon_H154 zenon_H140 zenon_H146 zenon_H1cd zenon_H1cf zenon_Ha7 zenon_H121 zenon_H45 zenon_H12d zenon_H10c zenon_H1f5 zenon_H244 zenon_H258 zenon_H173 zenon_H10e zenon_H4b zenon_H16f zenon_Hf1 zenon_H163 zenon_H9e zenon_H24c zenon_Hce zenon_H1d0 zenon_H1d2 zenon_H1e3 zenon_H1d4 zenon_H166 zenon_H1d3 zenon_Hde zenon_H160 zenon_He6 zenon_Hd7 zenon_H1d8 zenon_H17a zenon_H15f zenon_H25b zenon_H13c zenon_H1df zenon_H144 zenon_H199 zenon_H25a zenon_H109 zenon_H228 zenon_Hb7 zenon_H175 zenon_H1c5 zenon_H8f zenon_H1b3 zenon_H182 zenon_H23 zenon_H1b4 zenon_H145 zenon_H28 zenon_H35 zenon_H3b zenon_H36 zenon_H8e. % 15.31/15.49 apply (zenon_or_s _ _ zenon_H10f); [ zenon_intro zenon_H3c | zenon_intro zenon_Hba ]. % 15.31/15.49 apply (zenon_or_s _ _ zenon_H10c); [ zenon_intro zenon_H104 | zenon_intro zenon_H10a ]. % 15.31/15.49 apply (zenon_or_s _ _ zenon_H10d); [ zenon_intro zenon_H3e | zenon_intro zenon_H42 ]. % 15.31/15.49 apply (zenon_L345_); trivial. % 15.31/15.49 apply (zenon_L621_); trivial. % 15.31/15.49 apply (zenon_L354_); trivial. % 15.31/15.49 apply (zenon_L359_); trivial. % 15.31/15.49 (* end of lemma zenon_L685_ *) % 15.31/15.49 assert (zenon_L686_ : (((op (e1) (e0)) = (e0))\/(((op (e1) (e1)) = (e0))\/(((op (e1) (e2)) = (e0))\/((op (e1) (e3)) = (e0))))) -> (~((op (e0) (e0)) = (op (e1) (e0)))) -> (~((op (e3) (e3)) = (e3))) -> (~((op (e3) (e3)) = (e1))) -> (~((op (e3) (e3)) = (e0))) -> (((op (e3) (e3)) = (e0))\/(((op (e3) (e3)) = (e1))\/(((op (e3) (e3)) = (e2))\/((op (e3) (e3)) = (e3))))) -> (~((op (e1) (e1)) = (e2))) -> (~((op (e1) (e1)) = (e1))) -> (~((op (e1) (e1)) = (e0))) -> (((op (e1) (e1)) = (e0))\/(((op (e1) (e1)) = (e1))\/(((op (e1) (e1)) = (e2))\/((op (e1) (e1)) = (e3))))) -> (((op (e2) (e0)) = (e0))\/(((op (e2) (e1)) = (e0))\/(((op (e2) (e2)) = (e0))\/((op (e2) (e3)) = (e0))))) -> ((op (e0) (e0)) = (e0)) -> (~((op (e0) (e0)) = (op (e2) (e0)))) -> ((op (e2) (e1)) = (e2)) -> (~((e0) = (e2))) -> (~((op (e2) (e2)) = (e0))) -> (~((op (e1) (e3)) = (op (e2) (e3)))) -> False). % 15.31/15.49 do 0 intro. intros zenon_H163 zenon_H24c zenon_H3e zenon_H104 zenon_H3c zenon_H3b zenon_Hd6 zenon_H1b4 zenon_H145 zenon_H1b3 zenon_H1f5 zenon_H1f zenon_H258 zenon_H156 zenon_H5e zenon_H2e zenon_H244. % 15.31/15.49 apply (zenon_or_s _ _ zenon_H163); [ zenon_intro zenon_Had | zenon_intro zenon_H164 ]. % 15.31/15.49 apply (zenon_L559_); trivial. % 15.31/15.49 apply (zenon_or_s _ _ zenon_H164); [ zenon_intro zenon_H149 | zenon_intro zenon_H165 ]. % 15.31/15.49 exact (zenon_H145 zenon_H149). % 15.31/15.49 apply (zenon_or_s _ _ zenon_H165); [ zenon_intro zenon_H15d | zenon_intro zenon_Hcc ]. % 15.31/15.49 apply (zenon_L490_); trivial. % 15.31/15.49 apply (zenon_L600_); trivial. % 15.31/15.49 (* end of lemma zenon_L686_ *) % 15.31/15.49 assert (zenon_L687_ : (((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 (e3) (e3)) = (e2))) -> (~((op (e3) (e3)) = (e1))) -> (((op (e3) (e3)) = (e0))\/(((op (e3) (e3)) = (e1))\/(((op (e3) (e3)) = (e2))\/((op (e3) (e3)) = (e3))))) -> (~((op (e1) (e1)) = (e2))) -> (~((op (e1) (e1)) = (e1))) -> (~((op (e1) (e1)) = (e0))) -> (((op (e1) (e1)) = (e0))\/(((op (e1) (e1)) = (e1))\/(((op (e1) (e1)) = (e2))\/((op (e1) (e1)) = (e3))))) -> ((op (e2) (e1)) = (e2)) -> (~((op (e2) (e0)) = (op (e2) (e1)))) -> ((op (e3) (e0)) = (e1)) -> (~((e1) = (e2))) -> False). % 15.31/15.49 do 0 intro. intros zenon_Heb zenon_H8f zenon_H3e zenon_H3d zenon_H104 zenon_H3b zenon_Hd6 zenon_H1b4 zenon_H145 zenon_H1b3 zenon_H156 zenon_H154 zenon_Hee zenon_Ha7. % 15.31/15.49 apply (zenon_or_s _ _ zenon_Heb); [ zenon_intro zenon_H92 | zenon_intro zenon_Hec ]. % 15.31/15.49 exact (zenon_H8f zenon_H92). % 15.31/15.49 apply (zenon_or_s _ _ zenon_Hec); [ zenon_intro zenon_H68 | zenon_intro zenon_Hed ]. % 15.31/15.49 apply (zenon_L357_); trivial. % 15.31/15.49 apply (zenon_or_s _ _ zenon_Hed); [ zenon_intro zenon_Hdd | zenon_intro zenon_He9 ]. % 15.31/15.49 apply (zenon_L284_); trivial. % 15.31/15.49 apply (zenon_L122_); trivial. % 15.31/15.49 (* end of lemma zenon_L687_ *) % 15.31/15.49 assert (zenon_L688_ : (((op (e0) (e0)) = (e2))\/(((op (e0) (e1)) = (e2))\/(((op (e0) (e2)) = (e2))\/((op (e0) (e3)) = (e2))))) -> (~((op (e0) (e0)) = (e2))) -> (~((op (e0) (e1)) = (op (e2) (e1)))) -> (~((op (e3) (e3)) = (e2))) -> (~((op (e0) (e2)) = (op (e3) (e2)))) -> (~((op (e2) (e1)) = (op (e3) (e1)))) -> ((op (e2) (e1)) = (e2)) -> (~((e2) = (e3))) -> ((op (e3) (e0)) = (e3)) -> (((op (e3) (e0)) = (e2))\/(((op (e3) (e1)) = (e2))\/(((op (e3) (e2)) = (e2))\/((op (e3) (e3)) = (e2))))) -> ((op (e0) (e3)) = (e1)) -> (~((e1) = (e2))) -> False). % 15.31/15.49 do 0 intro. intros zenon_H8e zenon_H8f zenon_Hde zenon_H3d zenon_H140 zenon_H13c zenon_H156 zenon_H6a zenon_Hba zenon_H1df zenon_H37 zenon_Ha7. % 15.31/15.49 apply (zenon_or_s _ _ zenon_H8e); [ zenon_intro zenon_H92 | zenon_intro zenon_H91 ]. % 15.31/15.49 exact (zenon_H8f zenon_H92). % 15.31/15.49 apply (zenon_or_s _ _ zenon_H91); [ zenon_intro zenon_H5d | zenon_intro zenon_H93 ]. % 15.31/15.49 apply (zenon_L251_); trivial. % 15.31/15.49 apply (zenon_or_s _ _ zenon_H93); [ zenon_intro zenon_H63 | zenon_intro zenon_H81 ]. % 15.31/15.49 apply (zenon_L326_); trivial. % 15.31/15.49 apply (zenon_L33_); trivial. % 15.31/15.49 (* end of lemma zenon_L688_ *) % 15.31/15.49 assert (zenon_L689_ : ((~((op (e3) (e3)) = (e1)))\/((op (e3) (e1)) = (e3))) -> (~((op (e3) (e0)) = (op (e3) (e1)))) -> ((~((op (e3) (e3)) = (e3)))\/((op (e3) (e3)) = (e3))) -> (~((op (e3) (e0)) = (op (e3) (e3)))) -> (~((op (e0) (e0)) = (e1))) -> (((op (e0) (e0)) = (e1))\/(((op (e1) (e0)) = (e1))\/(((op (e2) (e0)) = (e1))\/((op (e3) (e0)) = (e1))))) -> (~((op (e0) (e0)) = (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 (e1) (e1)) = (e2))) -> (~((op (e1) (e1)) = (e1))) -> (~((op (e2) (e0)) = (op (e2) (e1)))) -> (~((e1) = (e2))) -> (((op (e0) (e0)) = (e2))\/(((op (e1) (e0)) = (e2))\/(((op (e2) (e0)) = (e2))\/((op (e3) (e0)) = (e2))))) -> (~((e0) = (e1))) -> (~((op (e1) (e1)) = (e0))) -> (~((e0) = (e2))) -> ((op (e2) (e1)) = (e2)) -> (((op (e0) (e1)) = (e3))\/(((op (e1) (e1)) = (e3))\/(((op (e2) (e1)) = (e3))\/((op (e3) (e1)) = (e3))))) -> (~((e0) = (e3))) -> (~((e2) = (e3))) -> (~((op (e2) (e2)) = (e0))) -> (((op (e2) (e2)) = (e0))\/(((op (e2) (e2)) = (e1))\/(((op (e2) (e2)) = (e2))\/((op (e2) (e2)) = (e3))))) -> (~((op (e2) (e2)) = (e3))) -> (~((op (e2) (e2)) = (e2))) -> (((op (e2) (e0)) = (e0))\/(((op (e2) (e1)) = (e0))\/(((op (e2) (e2)) = (e0))\/((op (e2) (e3)) = (e0))))) -> (~((e1) = (e3))) -> (((op (e0) (e1)) = (e0))\/(((op (e1) (e1)) = (e0))\/(((op (e2) (e1)) = (e0))\/((op (e3) (e1)) = (e0))))) -> (~((op (e0) (op (e1) (e0))) = (op (e1) (e0)))) -> (~((op (e0) (e2)) = (op (e2) (e2)))) -> (((op (e0) (e0)) = (e2))\/(((op (e0) (e1)) = (e2))\/(((op (e0) (e2)) = (e2))\/((op (e0) (e3)) = (e2))))) -> ((op (e3) (e0)) = (e3)) -> (~((op (e2) (e1)) = (op (e3) (e1)))) -> (~((op (e0) (e2)) = (op (e3) (e2)))) -> (((op (e3) (e0)) = (e2))\/(((op (e3) (e1)) = (e2))\/(((op (e3) (e2)) = (e2))\/((op (e3) (e3)) = (e2))))) -> (~((op (e0) (e1)) = (op (e2) (e1)))) -> (((op (e0) (e0)) = (e1))\/(((op (e0) (e1)) = (e1))\/(((op (e0) (e2)) = (e1))\/((op (e0) (e3)) = (e1))))) -> (~((op (e3) (e0)) = (op (e3) (e2)))) -> ((~((op (e3) (e3)) = (e2)))\/((op (e3) (e2)) = (e3))) -> False). % 15.31/15.49 do 0 intro. intros zenon_H10c zenon_H109 zenon_H10d zenon_Hbb zenon_H45 zenon_Hf1 zenon_H8f zenon_H1b3 zenon_H3b zenon_Hd6 zenon_H1b4 zenon_H154 zenon_Ha7 zenon_Heb zenon_H9e zenon_H145 zenon_H5e zenon_H156 zenon_H199 zenon_H4b zenon_H6a zenon_H2e zenon_H2d zenon_H30 zenon_H2f zenon_H1f5 zenon_Ha3 zenon_H144 zenon_H261 zenon_H28 zenon_H8e zenon_Hba zenon_H13c zenon_H140 zenon_H1df zenon_Hde zenon_H44 zenon_H105 zenon_H10e. % 15.31/15.49 apply (zenon_or_s _ _ zenon_H10c); [ zenon_intro zenon_H104 | zenon_intro zenon_H10a ]. % 15.31/15.49 apply (zenon_or_s _ _ zenon_H10e); [ zenon_intro zenon_H3d | zenon_intro zenon_H106 ]. % 15.31/15.49 apply (zenon_or_s _ _ zenon_H10d); [ zenon_intro zenon_H3e | zenon_intro zenon_H42 ]. % 15.31/15.49 apply (zenon_or_s _ _ zenon_H44); [ zenon_intro zenon_H47 | zenon_intro zenon_H46 ]. % 15.31/15.49 exact (zenon_H45 zenon_H47). % 15.31/15.49 apply (zenon_or_s _ _ zenon_H46); [ zenon_intro zenon_H22 | zenon_intro zenon_H48 ]. % 15.31/15.49 apply (zenon_or_s _ _ zenon_Hf1); [ zenon_intro zenon_H47 | zenon_intro zenon_Hf4 ]. % 15.31/15.49 exact (zenon_H45 zenon_H47). % 15.31/15.49 apply (zenon_or_s _ _ zenon_Hf4); [ zenon_intro zenon_Hd8 | zenon_intro zenon_Hf5 ]. % 15.31/15.49 apply (zenon_L644_); trivial. % 15.31/15.49 apply (zenon_or_s _ _ zenon_Hf5); [ zenon_intro zenon_Hae | zenon_intro zenon_Hee ]. % 15.31/15.49 apply (zenon_L427_); trivial. % 15.31/15.49 apply (zenon_L687_); trivial. % 15.31/15.49 apply (zenon_or_s _ _ zenon_H48); [ zenon_intro zenon_H29 | zenon_intro zenon_H37 ]. % 15.31/15.49 apply (zenon_L5_); trivial. % 15.31/15.49 apply (zenon_L688_); trivial. % 15.31/15.49 apply (zenon_L43_); trivial. % 15.31/15.49 apply (zenon_L81_); trivial. % 15.31/15.49 apply (zenon_L82_); trivial. % 15.31/15.49 (* end of lemma zenon_L689_ *) % 15.31/15.49 assert (zenon_L690_ : (((op (e1) (e0)) = (e0))\/(((op (e1) (e1)) = (e0))\/(((op (e1) (e2)) = (e0))\/((op (e1) (e3)) = (e0))))) -> ((op (e0) (e0)) = (e0)) -> (~((op (e0) (e0)) = (op (e1) (e0)))) -> (~((op (e3) (e3)) = (e3))) -> (~((op (e3) (e3)) = (e1))) -> (~((op (e3) (e3)) = (e0))) -> (((op (e3) (e3)) = (e0))\/(((op (e3) (e3)) = (e1))\/(((op (e3) (e3)) = (e2))\/((op (e3) (e3)) = (e3))))) -> (~((op (e1) (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))))) -> (~((e0) = (e1))) -> ((op (e1) (e3)) = (e1)) -> False). % 15.31/15.49 do 0 intro. intros zenon_H163 zenon_H1f zenon_H24c zenon_H3e zenon_H104 zenon_H3c zenon_H3b zenon_Hd6 zenon_H1b4 zenon_H145 zenon_H1b3 zenon_H9e zenon_H11f. % 15.31/15.49 apply (zenon_or_s _ _ zenon_H163); [ zenon_intro zenon_Had | zenon_intro zenon_H164 ]. % 15.31/15.49 apply (zenon_L559_); trivial. % 15.31/15.49 apply (zenon_or_s _ _ zenon_H164); [ zenon_intro zenon_H149 | zenon_intro zenon_H165 ]. % 15.31/15.49 exact (zenon_H145 zenon_H149). % 15.31/15.49 apply (zenon_or_s _ _ zenon_H165); [ zenon_intro zenon_H15d | zenon_intro zenon_Hcc ]. % 15.31/15.49 apply (zenon_L490_); trivial. % 15.31/15.49 apply (zenon_L208_); trivial. % 15.31/15.49 (* end of lemma zenon_L690_ *) % 15.31/15.49 assert (zenon_L691_ : ((~((op (e3) (e3)) = (e3)))\/((op (e3) (e3)) = (e3))) -> ((op (e3) (e2)) = (e3)) -> (~((op (e3) (e2)) = (op (e3) (e3)))) -> (~((op (e0) (e0)) = (op (e1) (e0)))) -> ((op (e0) (e0)) = (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)) = (e0))\/(((op (e3) (e3)) = (e1))\/(((op (e3) (e3)) = (e2))\/((op (e3) (e3)) = (e3))))) -> (~((op (e1) (e1)) = (e2))) -> (~((op (e1) (e1)) = (e1))) -> (~((e0) = (e1))) -> ((op (e1) (e3)) = (e1)) -> (((op (e1) (e0)) = (e0))\/(((op (e1) (e1)) = (e0))\/(((op (e1) (e2)) = (e0))\/((op (e1) (e3)) = (e0))))) -> False). % 15.31/15.49 do 0 intro. intros zenon_H10d zenon_H106 zenon_H173 zenon_H24c zenon_H1f zenon_H145 zenon_H1b3 zenon_H3c zenon_H104 zenon_H3b zenon_Hd6 zenon_H1b4 zenon_H9e zenon_H11f zenon_H163. % 15.31/15.49 apply (zenon_or_s _ _ zenon_H10d); [ zenon_intro zenon_H3e | zenon_intro zenon_H42 ]. % 15.31/15.49 apply (zenon_L690_); trivial. % 15.31/15.49 apply (zenon_L153_); trivial. % 15.31/15.49 (* end of lemma zenon_L691_ *) % 15.31/15.49 assert (zenon_L692_ : ((~((op (e2) (e2)) = (e3)))\/((op (e2) (e3)) = (e2))) -> ((~((op (e3) (e3)) = (e1)))\/((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) (e2)))) -> (((op (e0) (e1)) = (e0))\/(((op (e1) (e1)) = (e0))\/(((op (e2) (e1)) = (e0))\/((op (e3) (e1)) = (e0))))) -> (~((op (e2) (e2)) = (op (e2) (e3)))) -> (~((op (e3) (e1)) = (op (e3) (e2)))) -> ((~((op (e3) (e3)) = (e3)))\/((op (e3) (e3)) = (e3))) -> (~((op (e0) (e0)) = (e1))) -> (((op (e0) (e0)) = (e1))\/(((op (e1) (e0)) = (e1))\/(((op (e2) (e0)) = (e1))\/((op (e3) (e0)) = (e1))))) -> (~((op (e0) (e0)) = (e2))) -> (((op (e2) (e0)) = (e1))\/(((op (e2) (e1)) = (e1))\/(((op (e2) (e2)) = (e1))\/((op (e2) (e3)) = (e1))))) -> (~((op (e1) (e3)) = (op (e2) (e3)))) -> (~((op (e2) (e2)) = (e1))) -> (~((op (e0) (e1)) = (op (e2) (e1)))) -> (~((op (e0) (e0)) = (e3))) -> (~((e2) = (e3))) -> (~((e1) = (e3))) -> (~((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)) = (op (e2) (e2)))) -> ((op (e2) (e2)) = (e2)) -> (~((op (e1) (e2)) = (op (e2) (e2)))) -> (~((e1) = (e2))) -> (((op (e1) (e0)) = (e2))\/(((op (e1) (e1)) = (e2))\/(((op (e1) (e2)) = (e2))\/((op (e1) (e3)) = (e2))))) -> (((op (e0) (e0)) = (e2))\/(((op (e1) (e0)) = (e2))\/(((op (e2) (e0)) = (e2))\/((op (e3) (e0)) = (e2))))) -> (~((op (e1) (e0)) = (op (e1) (e3)))) -> (~((e0) = (e3))) -> (~((op (e3) (e2)) = (op (e3) (e3)))) -> (((op (e0) (e2)) = (e3))\/(((op (e1) (e2)) = (e3))\/(((op (e2) (e2)) = (e3))\/((op (e3) (e2)) = (e3))))) -> (((op (e0) (e0)) = (e2))\/(((op (e0) (e1)) = (e2))\/(((op (e0) (e2)) = (e2))\/((op (e0) (e3)) = (e2))))) -> (~((op (e0) (e2)) = (op (e2) (e2)))) -> (((op (e0) (e3)) = (e2))\/(((op (e1) (e3)) = (e2))\/(((op (e2) (e3)) = (e2))\/((op (e3) (e3)) = (e2))))) -> (~((e0) = (e2))) -> (~((op (e0) (e1)) = (op (e0) (e3)))) -> (((op (e0) (e3)) = (e0))\/(((op (e1) (e3)) = (e0))\/(((op (e2) (e3)) = (e0))\/((op (e3) (e3)) = (e0))))) -> (((op (e0) (e0)) = (e1))\/(((op (e0) (e1)) = (e1))\/(((op (e0) (e2)) = (e1))\/((op (e0) (e3)) = (e1))))) -> (~((op (e0) (e0)) = (op (e1) (e0)))) -> ((op (e0) (e0)) = (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 (e1) (e1)) = (e2))) -> (~((op (e1) (e1)) = (e1))) -> (~((e0) = (e1))) -> ((op (e1) (e3)) = (e1)) -> (((op (e1) (e0)) = (e0))\/(((op (e1) (e1)) = (e0))\/(((op (e1) (e2)) = (e0))\/((op (e1) (e3)) = (e0))))) -> ((~((op (e3) (e3)) = (e2)))\/((op (e3) (e2)) = (e3))) -> (~((op (e3) (e0)) = (op (e3) (e1)))) -> (~((op (e3) (e0)) = (op (e3) (e2)))) -> ((~((op (e3) (e3)) = (e0)))\/((op (e3) (e0)) = (e3))) -> False). % 15.31/15.49 do 0 intro. intros zenon_H1c3 zenon_H10c zenon_H1a2 zenon_H157 zenon_H144 zenon_H15f zenon_H135 zenon_H10d zenon_H45 zenon_Hf1 zenon_H8f zenon_Hb7 zenon_H244 zenon_H52 zenon_Hde zenon_H59 zenon_H6a zenon_Ha3 zenon_Hbb zenon_Hbe zenon_H17a zenon_H35 zenon_H7d zenon_Ha7 zenon_H84 zenon_Heb zenon_H1cf zenon_H4b zenon_H173 zenon_H175 zenon_H8e zenon_H28 zenon_H160 zenon_H5e zenon_H1cd zenon_Hd3 zenon_H44 zenon_H24c zenon_H1f zenon_H145 zenon_H1b3 zenon_H3b zenon_Hd6 zenon_H1b4 zenon_H9e zenon_H11f zenon_H163 zenon_H10e zenon_H109 zenon_H105 zenon_H10f. % 15.31/15.49 apply (zenon_or_s _ _ zenon_H1c3); [ zenon_intro zenon_H30 | zenon_intro zenon_H124 ]. % 15.31/15.49 apply (zenon_or_s _ _ zenon_H10f); [ zenon_intro zenon_H3c | zenon_intro zenon_Hba ]. % 15.31/15.49 apply (zenon_or_s _ _ zenon_H10c); [ zenon_intro zenon_H104 | zenon_intro zenon_H10a ]. % 15.31/15.49 apply (zenon_or_s _ _ zenon_H10e); [ zenon_intro zenon_H3d | zenon_intro zenon_H106 ]. % 15.31/15.49 apply (zenon_or_s _ _ zenon_H10d); [ zenon_intro zenon_H3e | zenon_intro zenon_H42 ]. % 15.31/15.49 apply (zenon_L690_); trivial. % 15.31/15.49 apply (zenon_L607_); trivial. % 15.31/15.49 apply (zenon_L691_); trivial. % 15.31/15.49 apply (zenon_L554_); trivial. % 15.31/15.49 apply (zenon_L359_); trivial. % 15.31/15.49 apply (zenon_L137_); trivial. % 15.31/15.49 (* end of lemma zenon_L692_ *) % 15.31/15.49 assert (zenon_L693_ : ((~((op (e3) (e3)) = (e3)))\/((op (e3) (e3)) = (e3))) -> (~((op (e0) (e0)) = (op (e1) (e0)))) -> (((op (e1) (e3)) = (e0))\/(((op (e1) (e3)) = (e1))\/(((op (e1) (e3)) = (e2))\/((op (e1) (e3)) = (e3))))) -> (~((op (e0) (e0)) = (op (e2) (e0)))) -> (((op (e2) (e0)) = (e1))\/(((op (e2) (e1)) = (e1))\/(((op (e2) (e2)) = (e1))\/((op (e2) (e3)) = (e1))))) -> (~((op (e1) (e3)) = (op (e2) (e3)))) -> (((op (e1) (e0)) = (e0))\/(((op (e1) (e1)) = (e0))\/(((op (e1) (e2)) = (e0))\/((op (e1) (e3)) = (e0))))) -> ((~((op (e2) (e2)) = (e0)))\/((op (e2) (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 (e0) (e0)) = (op (e0) (e2)))) -> (((op (e0) (e2)) = (e1))\/(((op (e1) (e2)) = (e1))\/(((op (e2) (e2)) = (e1))\/((op (e3) (e2)) = (e1))))) -> (((op (e0) (e3)) = (e0))\/(((op (e0) (e3)) = (e1))\/(((op (e0) (e3)) = (e2))\/((op (e0) (e3)) = (e3))))) -> (~((op (e0) (e3)) = (op (e1) (e3)))) -> (~((op (e0) (e3)) = (op (e2) (e3)))) -> (~((op (e1) (e2)) = (op (e2) (e2)))) -> (~((op (e0) (e1)) = (op (e3) (e1)))) -> (((op (e0) (e0)) = (e3))\/(((op (e1) (e0)) = (e3))\/(((op (e2) (e0)) = (e3))\/((op (e3) (e0)) = (e3))))) -> (~((op (e3) (e0)) = (op (e3) (e3)))) -> (~((op (e1) (e1)) = (e1))) -> (~((op (e1) (e1)) = (e2))) -> (((op (e1) (e1)) = (e0))\/(((op (e1) (e1)) = (e1))\/(((op (e1) (e1)) = (e2))\/((op (e1) (e1)) = (e3))))) -> (~((op (e0) (e0)) = (e3))) -> ((~((op (e3) (e3)) = (e0)))\/((op (e3) (e0)) = (e3))) -> (((op (e1) (e0)) = (e2))\/(((op (e1) (e1)) = (e2))\/(((op (e1) (e2)) = (e2))\/((op (e1) (e3)) = (e2))))) -> (~((op (e0) (e0)) = (op (e0) (e3)))) -> (((op (e0) (e0)) = (e3))\/(((op (e0) (e1)) = (e3))\/(((op (e0) (e2)) = (e3))\/((op (e0) (e3)) = (e3))))) -> (~((op (e0) (e2)) = (op (e1) (e2)))) -> (~((op (e1) (e3)) = (op (e3) (e3)))) -> (((op (e1) (e0)) = (e3))\/(((op (e1) (e1)) = (e3))\/(((op (e1) (e2)) = (e3))\/((op (e1) (e3)) = (e3))))) -> (((op (e0) (e0)) = (e2))\/(((op (e1) (e0)) = (e2))\/(((op (e2) (e0)) = (e2))\/((op (e3) (e0)) = (e2))))) -> ((~((op (e2) (e2)) = (e2)))\/((op (e2) (e2)) = (e2))) -> (~((op (e2) (e1)) = (op (e2) (e2)))) -> (~((op (e2) (e1)) = (op (e2) (e3)))) -> ((~((op (e2) (e2)) = (e3)))\/((op (e2) (e3)) = (e2))) -> (~((op (e1) (e0)) = (op (e3) (e0)))) -> (((op (e0) (e1)) = (e2))\/(((op (e1) (e1)) = (e2))\/(((op (e2) (e1)) = (e2))\/((op (e3) (e1)) = (e2))))) -> (~((op (e2) (e0)) = (op (e2) (e1)))) -> (((op (e3) (e0)) = (e1))\/(((op (e3) (e1)) = (e1))\/(((op (e3) (e2)) = (e1))\/((op (e3) (e3)) = (e1))))) -> (~((op (e0) (e1)) = (op (e0) (e3)))) -> (~((op (e1) (e0)) = (op (e1) (e3)))) -> (((op (e0) (e3)) = (e1))\/(((op (e1) (e3)) = (e1))\/(((op (e2) (e3)) = (e1))\/((op (e3) (e3)) = (e1))))) -> (~((op (e3) (e1)) = (op (e3) (e3)))) -> ((~((op (e3) (e3)) = (e1)))\/((op (e3) (e1)) = (e3))) -> ((~((op (e2) (e2)) = (e1)))\/((op (e2) (e1)) = (e2))) -> ((~((op (e1) (e1)) = (e3)))\/((op (e1) (e3)) = (e1))) -> (~((op (e3) (e0)) = (op (e3) (e1)))) -> (((op (e0) (e1)) = (e1))\/(((op (e1) (e1)) = (e1))\/(((op (e2) (e1)) = (e1))\/((op (e3) (e1)) = (e1))))) -> (~((op (e0) (e0)) = (e1))) -> (((op (e0) (e0)) = (e1))\/(((op (e1) (e0)) = (e1))\/(((op (e2) (e0)) = (e1))\/((op (e3) (e0)) = (e1))))) -> (~((op (e0) (e0)) = (e2))) -> (~((op (e0) (e1)) = (op (e2) (e1)))) -> (((op (e3) (e0)) = (e2))\/(((op (e3) (e1)) = (e2))\/(((op (e3) (e2)) = (e2))\/((op (e3) (e3)) = (e2))))) -> (~((op (e3) (e3)) = (e2))) -> (~((op (e0) (e2)) = (op (e3) (e2)))) -> (~((op (e2) (e1)) = (op (e3) (e1)))) -> (~((e1) = (e2))) -> ((op (e1) (e3)) = (e1)) -> (~((op (e2) (e0)) = (op (e2) (e3)))) -> (~((op (e3) (e3)) = (e0))) -> (((op (e0) (e3)) = (e0))\/(((op (e1) (e3)) = (e0))\/(((op (e2) (e3)) = (e0))\/((op (e3) (e3)) = (e0))))) -> ((op (e0) (e0)) = (e0)) -> (~((op (e0) (e0)) = (op (e0) (e1)))) -> (((op (e0) (e0)) = (e2))\/(((op (e0) (e1)) = (e2))\/(((op (e0) (e2)) = (e2))\/((op (e0) (e3)) = (e2))))) -> (~((e0) = (e1))) -> (~((op (e1) (e1)) = (e0))) -> (~((e0) = (e2))) -> ((op (e2) (e1)) = (e2)) -> (((op (e0) (e1)) = (e3))\/(((op (e1) (e1)) = (e3))\/(((op (e2) (e1)) = (e3))\/((op (e3) (e1)) = (e3))))) -> (~((e0) = (e3))) -> (~((e2) = (e3))) -> (~((op (e2) (e2)) = (e0))) -> (((op (e2) (e2)) = (e0))\/(((op (e2) (e2)) = (e1))\/(((op (e2) (e2)) = (e2))\/((op (e2) (e2)) = (e3))))) -> (~((op (e2) (e2)) = (e3))) -> (~((op (e2) (e2)) = (e2))) -> (((op (e2) (e0)) = (e0))\/(((op (e2) (e1)) = (e0))\/(((op (e2) (e2)) = (e0))\/((op (e2) (e3)) = (e0))))) -> (~((e1) = (e3))) -> (((op (e0) (e1)) = (e0))\/(((op (e1) (e1)) = (e0))\/(((op (e2) (e1)) = (e0))\/((op (e3) (e1)) = (e0))))) -> (~((op (e0) (op (e1) (e0))) = (op (e1) (e0)))) -> (~((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 (e3) (e3)))) -> (((op (e0) (e0)) = (e1))\/(((op (e0) (e1)) = (e1))\/(((op (e0) (e2)) = (e1))\/((op (e0) (e3)) = (e1))))) -> False). % 15.31/15.49 do 0 intro. intros zenon_H10d zenon_H24c zenon_H25b zenon_H258 zenon_Hb7 zenon_H244 zenon_H163 zenon_H1d4 zenon_Hc9 zenon_H251 zenon_H250 zenon_H11b zenon_H254 zenon_H80 zenon_Hb4 zenon_H7d zenon_H138 zenon_Hbe zenon_Hbb zenon_H1b4 zenon_Hd6 zenon_H1b3 zenon_H59 zenon_H10f zenon_H84 zenon_H24f zenon_H58 zenon_H87 zenon_H8b zenon_H90 zenon_Heb zenon_Haa zenon_H157 zenon_H1e2 zenon_H1c3 zenon_H22e zenon_H1a2 zenon_H154 zenon_H146 zenon_H1cd zenon_H1cf zenon_H121 zenon_H12d zenon_H10c zenon_H1e3 zenon_H1d2 zenon_H109 zenon_H228 zenon_H45 zenon_Hf1 zenon_H8f zenon_Hde zenon_H1df zenon_H3d zenon_H140 zenon_H13c zenon_Ha7 zenon_H11f zenon_Hce zenon_H3c zenon_Hd3 zenon_H1f zenon_H25a zenon_H8e zenon_H9e zenon_H145 zenon_H5e zenon_H156 zenon_H199 zenon_H4b zenon_H6a zenon_H2e zenon_H2d zenon_H30 zenon_H2f zenon_H1f5 zenon_Ha3 zenon_H144 zenon_H261 zenon_H28 zenon_H3b zenon_H36 zenon_H44. % 15.31/15.49 apply (zenon_or_s _ _ zenon_H10d); [ zenon_intro zenon_H3e | zenon_intro zenon_H42 ]. % 15.31/15.49 apply (zenon_or_s _ _ zenon_H44); [ zenon_intro zenon_H47 | zenon_intro zenon_H46 ]. % 15.31/15.49 exact (zenon_H45 zenon_H47). % 15.31/15.49 apply (zenon_or_s _ _ zenon_H46); [ zenon_intro zenon_H22 | zenon_intro zenon_H48 ]. % 15.31/15.49 apply (zenon_or_s _ _ zenon_Hf1); [ zenon_intro zenon_H47 | zenon_intro zenon_Hf4 ]. % 15.31/15.49 exact (zenon_H45 zenon_H47). % 15.31/15.49 apply (zenon_or_s _ _ zenon_Hf4); [ zenon_intro zenon_Hd8 | zenon_intro zenon_Hf5 ]. % 15.31/15.49 apply (zenon_L644_); trivial. % 15.31/15.49 apply (zenon_or_s _ _ zenon_Hf5); [ zenon_intro zenon_Hae | zenon_intro zenon_Hee ]. % 15.31/15.49 apply (zenon_L427_); trivial. % 15.31/15.49 apply (zenon_or_s _ _ zenon_H8e); [ zenon_intro zenon_H92 | zenon_intro zenon_H91 ]. % 15.31/15.49 exact (zenon_H8f zenon_H92). % 15.31/15.49 apply (zenon_or_s _ _ zenon_H91); [ zenon_intro zenon_H5d | zenon_intro zenon_H93 ]. % 15.31/15.49 apply (zenon_L251_); trivial. % 15.31/15.49 apply (zenon_or_s _ _ zenon_H93); [ zenon_intro zenon_H63 | zenon_intro zenon_H81 ]. % 15.31/15.49 apply (zenon_L254_); trivial. % 15.31/15.49 apply (zenon_L612_); trivial. % 15.31/15.49 apply (zenon_or_s _ _ zenon_H48); [ zenon_intro zenon_H29 | zenon_intro zenon_H37 ]. % 15.31/15.49 apply (zenon_L5_); trivial. % 15.31/15.49 apply (zenon_L7_); trivial. % 15.31/15.49 apply (zenon_L619_); trivial. % 15.31/15.49 (* end of lemma zenon_L693_ *) % 15.31/15.49 assert (zenon_L694_ : ((~((op (e2) (e2)) = (e2)))\/((op (e2) (e2)) = (e2))) -> (~((op (e2) (e0)) = (op (e2) (e2)))) -> (((op (e1) (e0)) = (e0))\/(((op (e1) (e1)) = (e0))\/(((op (e1) (e2)) = (e0))\/((op (e1) (e3)) = (e0))))) -> ((op (e1) (e3)) = (e1)) -> (~((e0) = (e1))) -> (~((op (e1) (e2)) = (op (e2) (e2)))) -> (~((op (e2) (e2)) = (e1))) -> (((op (e2) (e2)) = (e0))\/(((op (e2) (e2)) = (e1))\/(((op (e2) (e2)) = (e2))\/((op (e2) (e2)) = (e3))))) -> (~((op (e1) (e1)) = (e0))) -> ((op (e0) (e0)) = (e0)) -> (~((op (e0) (e0)) = (op (e1) (e0)))) -> (~((op (e2) (e0)) = (op (e2) (e3)))) -> ((op (e2) (e0)) = (e2)) -> ((~((op (e2) (e2)) = (e3)))\/((op (e2) (e3)) = (e2))) -> False). % 15.31/15.49 do 0 intro. intros zenon_Haa zenon_H17a zenon_H163 zenon_H11f zenon_H9e zenon_H7d zenon_H52 zenon_H2d zenon_H145 zenon_H1f zenon_H24c zenon_Hce zenon_Hdd zenon_H1c3. % 15.31/15.49 apply (zenon_or_s _ _ zenon_Haa); [ zenon_intro zenon_H2f | zenon_intro zenon_H35 ]. % 15.31/15.49 apply (zenon_or_s _ _ zenon_H1c3); [ zenon_intro zenon_H30 | zenon_intro zenon_H124 ]. % 15.31/15.49 apply (zenon_L603_); trivial. % 15.31/15.49 apply (zenon_L119_); trivial. % 15.31/15.49 apply (zenon_L161_); trivial. % 15.31/15.49 (* end of lemma zenon_L694_ *) % 15.31/15.49 assert (zenon_L695_ : ((~((op (e2) (e2)) = (e1)))\/((op (e2) (e1)) = (e2))) -> (~((op (e2) (e0)) = (op (e2) (e1)))) -> ((~((op (e2) (e2)) = (e3)))\/((op (e2) (e3)) = (e2))) -> ((op (e2) (e0)) = (e2)) -> (~((op (e2) (e0)) = (op (e2) (e3)))) -> (~((op (e0) (e0)) = (op (e1) (e0)))) -> ((op (e0) (e0)) = (e0)) -> (~((op (e1) (e1)) = (e0))) -> (((op (e2) (e2)) = (e0))\/(((op (e2) (e2)) = (e1))\/(((op (e2) (e2)) = (e2))\/((op (e2) (e2)) = (e3))))) -> (~((op (e1) (e2)) = (op (e2) (e2)))) -> (~((e0) = (e1))) -> ((op (e1) (e3)) = (e1)) -> (((op (e1) (e0)) = (e0))\/(((op (e1) (e1)) = (e0))\/(((op (e1) (e2)) = (e0))\/((op (e1) (e3)) = (e0))))) -> (~((op (e2) (e0)) = (op (e2) (e2)))) -> ((~((op (e2) (e2)) = (e2)))\/((op (e2) (e2)) = (e2))) -> False). % 15.31/15.49 do 0 intro. intros zenon_H1e3 zenon_H154 zenon_H1c3 zenon_Hdd zenon_Hce zenon_H24c zenon_H1f zenon_H145 zenon_H2d zenon_H7d zenon_H9e zenon_H11f zenon_H163 zenon_H17a zenon_Haa. % 15.31/15.49 apply (zenon_or_s _ _ zenon_H1e3); [ zenon_intro zenon_H52 | zenon_intro zenon_H156 ]. % 15.31/15.49 apply (zenon_L694_); trivial. % 15.31/15.49 apply (zenon_L284_); trivial. % 15.31/15.49 (* end of lemma zenon_L695_ *) % 15.31/15.49 assert (zenon_L696_ : (((op (e0) (e0)) = (e2))\/(((op (e0) (e1)) = (e2))\/(((op (e0) (e2)) = (e2))\/((op (e0) (e3)) = (e2))))) -> (~((op (e0) (e0)) = (e2))) -> (~((op (e1) (e1)) = (e3))) -> (~((op (e0) (e1)) = (op (e1) (e1)))) -> (~((op (e1) (e1)) = (e1))) -> (~((op (e1) (e1)) = (e0))) -> (((op (e1) (e1)) = (e0))\/(((op (e1) (e1)) = (e1))\/(((op (e1) (e1)) = (e2))\/((op (e1) (e1)) = (e3))))) -> (~((op (e3) (e3)) = (e1))) -> (~((op (e2) (e0)) = (op (e2) (e3)))) -> ((op (e2) (e0)) = (e1)) -> (~((e1) = (e2))) -> ((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) (e2)) = (op (e1) (e2)))) -> (~((op (e1) (e1)) = (e2))) -> (~((op (e0) (op (e1) (e0))) = (op (e1) (e0)))) -> (((op (e1) (e0)) = (e2))\/(((op (e1) (e1)) = (e2))\/(((op (e1) (e2)) = (e2))\/((op (e1) (e3)) = (e2))))) -> ((op (e0) (e3)) = (e0)) -> (~((e0) = (e2))) -> False). % 15.31/15.49 do 0 intro. intros zenon_H8e zenon_H8f zenon_H182 zenon_H23 zenon_H1b4 zenon_H145 zenon_H1b3 zenon_H104 zenon_Hce zenon_Hae zenon_Ha7 zenon_H22 zenon_H1cd zenon_H121 zenon_H87 zenon_Hd6 zenon_H261 zenon_H84 zenon_Hca zenon_H5e. % 15.31/15.49 apply (zenon_or_s _ _ zenon_H8e); [ zenon_intro zenon_H92 | zenon_intro zenon_H91 ]. % 15.31/15.49 exact (zenon_H8f zenon_H92). % 15.31/15.49 apply (zenon_or_s _ _ zenon_H91); [ zenon_intro zenon_H5d | zenon_intro zenon_H93 ]. % 15.31/15.49 apply (zenon_L214_); trivial. % 15.31/15.49 apply (zenon_or_s _ _ zenon_H93); [ zenon_intro zenon_H63 | zenon_intro zenon_H81 ]. % 15.31/15.49 apply (zenon_L676_); trivial. % 15.31/15.49 apply (zenon_L113_); trivial. % 15.31/15.49 (* end of lemma zenon_L696_ *) % 15.31/15.49 assert (zenon_L697_ : (((op (e0) (e0)) = (e2))\/(((op (e1) (e0)) = (e2))\/(((op (e2) (e0)) = (e2))\/((op (e3) (e0)) = (e2))))) -> (~((op (e0) (e0)) = (e2))) -> (~((op (e0) (op (e1) (e0))) = (op (e1) (e0)))) -> (~((op (e0) (e3)) = (op (e3) (e3)))) -> ((op (e3) (e3)) = (e3)) -> ((op (e0) (e2)) = (e2)) -> (~((e2) = (e3))) -> ((op (e0) (e1)) = (e1)) -> (~((e1) = (e3))) -> (((op (e2) (e0)) = (e1))\/(((op (e2) (e1)) = (e1))\/(((op (e2) (e2)) = (e1))\/((op (e2) (e3)) = (e1))))) -> (~((op (e0) (e1)) = (op (e2) (e1)))) -> (((op (e2) (e2)) = (e0))\/(((op (e2) (e2)) = (e1))\/(((op (e2) (e2)) = (e2))\/((op (e2) (e2)) = (e3))))) -> (~((op (e2) (e2)) = (e1))) -> (~((op (e2) (e2)) = (e2))) -> (~((op (e2) (e2)) = (e3))) -> (((op (e0) (e0)) = (e3))\/(((op (e0) (e1)) = (e3))\/(((op (e0) (e2)) = (e3))\/((op (e0) (e3)) = (e3))))) -> ((op (e3) (e0)) = (e1)) -> (~((e1) = (e2))) -> False). % 15.31/15.49 do 0 intro. intros zenon_Heb zenon_H8f zenon_H261 zenon_H36 zenon_H42 zenon_H63 zenon_H6a zenon_H22 zenon_Ha3 zenon_Hb7 zenon_Hde zenon_H2d zenon_H52 zenon_H2f zenon_H30 zenon_H58 zenon_Hee zenon_Ha7. % 15.31/15.49 apply (zenon_or_s _ _ zenon_Heb); [ zenon_intro zenon_H92 | zenon_intro zenon_Hec ]. % 15.31/15.49 exact (zenon_H8f zenon_H92). % 15.31/15.49 apply (zenon_or_s _ _ zenon_Hec); [ zenon_intro zenon_H68 | zenon_intro zenon_Hed ]. % 15.31/15.49 apply (zenon_L638_); trivial. % 15.31/15.49 apply (zenon_or_s _ _ zenon_Hed); [ zenon_intro zenon_Hdd | zenon_intro zenon_He9 ]. % 15.31/15.49 apply (zenon_L337_); trivial. % 15.31/15.49 apply (zenon_L122_); trivial. % 15.31/15.49 (* end of lemma zenon_L697_ *) % 15.31/15.49 assert (zenon_L698_ : (~((op (e1) (op (e1) (e1))) = (op (e1) (e1)))) -> ((op (e1) (e1)) = (e1)) -> False). % 15.31/15.49 do 0 intro. intros zenon_H27b zenon_H21. % 15.31/15.49 cut (((op (e1) (e1)) = (e1))); [idtac | apply NNPP; zenon_intro zenon_H1b4]. % 15.31/15.49 cut (((e1) = (e1))); [idtac | apply NNPP; zenon_intro zenon_Ha0]. % 15.31/15.49 congruence. % 15.31/15.49 apply zenon_Ha0. apply refl_equal. % 15.31/15.49 exact (zenon_H1b4 zenon_H21). % 15.31/15.49 (* end of lemma zenon_L698_ *) % 15.31/15.49 assert (zenon_L699_ : ((~((op (e1) (e1)) = (e1)))\/((op (e1) (e1)) = (e1))) -> (~((op (e1) (op (e1) (e1))) = (op (e1) (e1)))) -> ((~((op (e1) (e1)) = (e3)))\/((op (e1) (e3)) = (e1))) -> ((~((op (e2) (e2)) = (e2)))\/((op (e2) (e2)) = (e2))) -> (((op (e0) (e0)) = (e1))\/(((op (e0) (e1)) = (e1))\/(((op (e0) (e2)) = (e1))\/((op (e0) (e3)) = (e1))))) -> (((op (e1) (e0)) = (e1))\/(((op (e1) (e1)) = (e1))\/(((op (e1) (e2)) = (e1))\/((op (e1) (e3)) = (e1))))) -> (~((e0) = (e1))) -> (((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) (e2)) = (op (e3) (e3)))) -> ((~((op (e3) (e3)) = (e0)))\/((op (e3) (e0)) = (e3))) -> (~((op (e3) (e0)) = (op (e3) (e3)))) -> (~((e2) = (e3))) -> (~((op (e0) (e2)) = (op (e0) (e3)))) -> (~((e0) = (e2))) -> (((op (e0) (e3)) = (e0))\/(((op (e1) (e3)) = (e0))\/(((op (e2) (e3)) = (e0))\/((op (e3) (e3)) = (e0))))) -> (~((e1) = (e2))) -> (((op (e1) (e0)) = (e2))\/(((op (e1) (e1)) = (e2))\/(((op (e1) (e2)) = (e2))\/((op (e1) (e3)) = (e2))))) -> ((~((op (e2) (e2)) = (e3)))\/((op (e2) (e3)) = (e2))) -> (((op (e1) (e1)) = (e0))\/(((op (e1) (e1)) = (e1))\/(((op (e1) (e1)) = (e2))\/((op (e1) (e1)) = (e3))))) -> (~((op (e1) (e3)) = (op (e3) (e3)))) -> (((op (e1) (e0)) = (e3))\/(((op (e1) (e1)) = (e3))\/(((op (e1) (e2)) = (e3))\/((op (e1) (e3)) = (e3))))) -> (~((op (e0) (e1)) = (op (e1) (e1)))) -> (~((op (e1) (e1)) = (e0))) -> (((op (e0) (e0)) = (e2))\/(((op (e1) (e0)) = (e2))\/(((op (e2) (e0)) = (e2))\/((op (e3) (e0)) = (e2))))) -> (~((op (e0) (e2)) = (op (e1) (e2)))) -> (((op (e0) (e0)) = (e3))\/(((op (e1) (e0)) = (e3))\/(((op (e2) (e0)) = (e3))\/((op (e3) (e0)) = (e3))))) -> (((op (e2) (e0)) = (e3))\/(((op (e2) (e1)) = (e3))\/(((op (e2) (e2)) = (e3))\/((op (e2) (e3)) = (e3))))) -> (~((op (e2) (e3)) = (op (e3) (e3)))) -> (~((op (e0) (e1)) = (op (e2) (e1)))) -> (((op (e0) (e0)) = (e2))\/(((op (e0) (e1)) = (e2))\/(((op (e0) (e2)) = (e2))\/((op (e0) (e3)) = (e2))))) -> (~((op (e0) (e2)) = (op (e2) (e2)))) -> (((op (e2) (e2)) = (e0))\/(((op (e2) (e2)) = (e1))\/(((op (e2) (e2)) = (e2))\/((op (e2) (e2)) = (e3))))) -> (~((op (e0) (e0)) = (e3))) -> (~((e1) = (e3))) -> (~((e0) = (e3))) -> ((op (e0) (e2)) = (e0)) -> (~((op (e0) (e3)) = (op (e3) (e3)))) -> ((op (e3) (e3)) = (e3)) -> (((op (e0) (e0)) = (e3))\/(((op (e0) (e1)) = (e3))\/(((op (e0) (e2)) = (e3))\/((op (e0) (e3)) = (e3))))) -> (~((op (e0) (e0)) = (e1))) -> ((~((op (e3) (e3)) = (e2)))\/((op (e3) (e2)) = (e3))) -> (((op (e0) (e0)) = (e1))\/(((op (e1) (e0)) = (e1))\/(((op (e2) (e0)) = (e1))\/((op (e3) (e0)) = (e1))))) -> (~((op (e2) (e0)) = (op (e2) (e3)))) -> (((op (e0) (e3)) = (e1))\/(((op (e1) (e3)) = (e1))\/(((op (e2) (e3)) = (e1))\/((op (e3) (e3)) = (e1))))) -> (~((op (e1) (e0)) = (op (e1) (e3)))) -> (~((op (e0) (e1)) = (op (e0) (e3)))) -> (~((op (e3) (e1)) = (op (e3) (e3)))) -> ((~((op (e3) (e3)) = (e1)))\/((op (e3) (e1)) = (e3))) -> ((~((op (e2) (e2)) = (e0)))\/((op (e2) (e0)) = (e2))) -> (~((op (e1) (e2)) = (op (e1) (e3)))) -> ((~((op (e1) (e1)) = (e2)))\/((op (e1) (e2)) = (e1))) -> False). % 15.31/15.49 do 0 intro. intros zenon_H1d8 zenon_H27b zenon_H1d2 zenon_Haa zenon_H44 zenon_H1c5 zenon_H9e zenon_H160 zenon_H175 zenon_H173 zenon_H10f zenon_Hbb zenon_H6a zenon_Hc9 zenon_H5e zenon_Hd3 zenon_Ha7 zenon_H84 zenon_H1c3 zenon_H1b3 zenon_H8b zenon_H90 zenon_H23 zenon_H145 zenon_Heb zenon_H87 zenon_Hbe zenon_He6 zenon_He3 zenon_Hde zenon_H8e zenon_H28 zenon_H2d zenon_H59 zenon_Ha3 zenon_H4b zenon_Hab zenon_H36 zenon_H42 zenon_H58 zenon_H45 zenon_H10e zenon_Hf1 zenon_Hce zenon_H121 zenon_H1cf zenon_H1cd zenon_H12d zenon_H10c zenon_H1d4 zenon_H1d0 zenon_H1d3. % 15.31/15.49 apply (zenon_or_s _ _ zenon_H1d8); [ zenon_intro zenon_H1b4 | zenon_intro zenon_H21 ]. % 15.31/15.49 apply (zenon_L239_); trivial. % 15.31/15.49 apply (zenon_L698_); trivial. % 15.31/15.49 (* end of lemma zenon_L699_ *) % 15.31/15.49 assert (zenon_L700_ : ((~((op (e0) (e0)) = (e3)))\/((op (e0) (e3)) = (e0))) -> ((~((op (e1) (e1)) = (e1)))\/((op (e1) (e1)) = (e1))) -> (~((op (e1) (op (e1) (e1))) = (op (e1) (e1)))) -> ((~((op (e1) (e1)) = (e3)))\/((op (e1) (e3)) = (e1))) -> ((~((op (e2) (e2)) = (e2)))\/((op (e2) (e2)) = (e2))) -> (((op (e0) (e0)) = (e1))\/(((op (e0) (e1)) = (e1))\/(((op (e0) (e2)) = (e1))\/((op (e0) (e3)) = (e1))))) -> (((op (e1) (e0)) = (e1))\/(((op (e1) (e1)) = (e1))\/(((op (e1) (e2)) = (e1))\/((op (e1) (e3)) = (e1))))) -> (~((e0) = (e1))) -> (((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) (e2)) = (op (e3) (e3)))) -> ((~((op (e3) (e3)) = (e0)))\/((op (e3) (e0)) = (e3))) -> (~((op (e3) (e0)) = (op (e3) (e3)))) -> (~((e2) = (e3))) -> (~((op (e0) (e2)) = (op (e0) (e3)))) -> (~((e0) = (e2))) -> (((op (e0) (e3)) = (e0))\/(((op (e1) (e3)) = (e0))\/(((op (e2) (e3)) = (e0))\/((op (e3) (e3)) = (e0))))) -> (~((e1) = (e2))) -> (((op (e1) (e0)) = (e2))\/(((op (e1) (e1)) = (e2))\/(((op (e1) (e2)) = (e2))\/((op (e1) (e3)) = (e2))))) -> ((~((op (e2) (e2)) = (e3)))\/((op (e2) (e3)) = (e2))) -> (((op (e1) (e1)) = (e0))\/(((op (e1) (e1)) = (e1))\/(((op (e1) (e1)) = (e2))\/((op (e1) (e1)) = (e3))))) -> (~((op (e1) (e3)) = (op (e3) (e3)))) -> (((op (e1) (e0)) = (e3))\/(((op (e1) (e1)) = (e3))\/(((op (e1) (e2)) = (e3))\/((op (e1) (e3)) = (e3))))) -> (~((op (e0) (e1)) = (op (e1) (e1)))) -> (((op (e0) (e0)) = (e2))\/(((op (e1) (e0)) = (e2))\/(((op (e2) (e0)) = (e2))\/((op (e3) (e0)) = (e2))))) -> (~((op (e0) (e2)) = (op (e1) (e2)))) -> (((op (e0) (e0)) = (e3))\/(((op (e1) (e0)) = (e3))\/(((op (e2) (e0)) = (e3))\/((op (e3) (e0)) = (e3))))) -> (((op (e2) (e0)) = (e3))\/(((op (e2) (e1)) = (e3))\/(((op (e2) (e2)) = (e3))\/((op (e2) (e3)) = (e3))))) -> (~((op (e2) (e3)) = (op (e3) (e3)))) -> (~((op (e0) (e1)) = (op (e2) (e1)))) -> (((op (e0) (e0)) = (e2))\/(((op (e0) (e1)) = (e2))\/(((op (e0) (e2)) = (e2))\/((op (e0) (e3)) = (e2))))) -> (~((op (e0) (e2)) = (op (e2) (e2)))) -> (((op (e2) (e2)) = (e0))\/(((op (e2) (e2)) = (e1))\/(((op (e2) (e2)) = (e2))\/((op (e2) (e2)) = (e3))))) -> (~((e1) = (e3))) -> (~((e0) = (e3))) -> ((op (e0) (e2)) = (e0)) -> (~((op (e0) (e3)) = (op (e3) (e3)))) -> ((op (e3) (e3)) = (e3)) -> (((op (e0) (e0)) = (e3))\/(((op (e0) (e1)) = (e3))\/(((op (e0) (e2)) = (e3))\/((op (e0) (e3)) = (e3))))) -> (~((op (e0) (e0)) = (e1))) -> ((~((op (e3) (e3)) = (e2)))\/((op (e3) (e2)) = (e3))) -> (((op (e0) (e0)) = (e1))\/(((op (e1) (e0)) = (e1))\/(((op (e2) (e0)) = (e1))\/((op (e3) (e0)) = (e1))))) -> (~((op (e2) (e0)) = (op (e2) (e3)))) -> (((op (e0) (e3)) = (e1))\/(((op (e1) (e3)) = (e1))\/(((op (e2) (e3)) = (e1))\/((op (e3) (e3)) = (e1))))) -> (~((op (e1) (e0)) = (op (e1) (e3)))) -> (~((op (e0) (e1)) = (op (e0) (e3)))) -> (~((op (e3) (e1)) = (op (e3) (e3)))) -> ((~((op (e3) (e3)) = (e1)))\/((op (e3) (e1)) = (e3))) -> ((~((op (e2) (e2)) = (e0)))\/((op (e2) (e0)) = (e2))) -> (~((op (e1) (e2)) = (op (e1) (e3)))) -> ((~((op (e1) (e1)) = (e2)))\/((op (e1) (e2)) = (e1))) -> (~((op (e1) (e0)) = (op (e1) (e1)))) -> (~((op (e1) (e2)) = (op (e2) (e2)))) -> (~((op (e0) (e3)) = (op (e1) (e3)))) -> (~((op (e1) (e0)) = (op (e1) (e2)))) -> ((~((op (e1) (e1)) = (e0)))\/((op (e1) (e0)) = (e1))) -> False). % 15.31/15.49 do 0 intro. intros zenon_H236 zenon_H1d8 zenon_H27b zenon_H1d2 zenon_Haa zenon_H44 zenon_H1c5 zenon_H9e zenon_H160 zenon_H175 zenon_H173 zenon_H10f zenon_Hbb zenon_H6a zenon_Hc9 zenon_H5e zenon_Hd3 zenon_Ha7 zenon_H84 zenon_H1c3 zenon_H1b3 zenon_H8b zenon_H90 zenon_H23 zenon_Heb zenon_H87 zenon_Hbe zenon_He6 zenon_He3 zenon_Hde zenon_H8e zenon_H28 zenon_H2d zenon_Ha3 zenon_H4b zenon_Hab zenon_H36 zenon_H42 zenon_H58 zenon_H45 zenon_H10e zenon_Hf1 zenon_Hce zenon_H121 zenon_H1cf zenon_H1cd zenon_H12d zenon_H10c zenon_H1d4 zenon_H1d0 zenon_H1d3 zenon_Hd7 zenon_H7d zenon_H80 zenon_H166 zenon_H1e4. % 15.31/15.49 apply (zenon_or_s _ _ zenon_H236); [ zenon_intro zenon_H59 | zenon_intro zenon_Hca ]. % 15.31/15.49 apply (zenon_or_s _ _ zenon_H1e4); [ zenon_intro zenon_H145 | zenon_intro zenon_Hd8 ]. % 15.31/15.49 apply (zenon_L699_); trivial. % 15.31/15.49 apply (zenon_L249_); trivial. % 15.31/15.49 apply (zenon_L53_); trivial. % 15.31/15.49 (* end of lemma zenon_L700_ *) % 15.31/15.49 assert (zenon_L701_ : (((op (e0) (e2)) = (e0))\/(((op (e1) (e2)) = (e0))\/(((op (e2) (e2)) = (e0))\/((op (e3) (e2)) = (e0))))) -> ((~((op (e1) (e1)) = (e0)))\/((op (e1) (e0)) = (e1))) -> (~((op (e0) (e3)) = (op (e1) (e3)))) -> (~((op (e1) (e2)) = (op (e2) (e2)))) -> (~((op (e1) (e0)) = (op (e1) (e1)))) -> ((~((op (e1) (e1)) = (e2)))\/((op (e1) (e2)) = (e1))) -> (~((op (e1) (e2)) = (op (e1) (e3)))) -> ((~((op (e2) (e2)) = (e0)))\/((op (e2) (e0)) = (e2))) -> ((~((op (e3) (e3)) = (e1)))\/((op (e3) (e1)) = (e3))) -> (~((op (e0) (e1)) = (op (e0) (e3)))) -> (~((op (e1) (e0)) = (op (e1) (e3)))) -> (((op (e0) (e3)) = (e1))\/(((op (e1) (e3)) = (e1))\/(((op (e2) (e3)) = (e1))\/((op (e3) (e3)) = (e1))))) -> (~((op (e2) (e0)) = (op (e2) (e3)))) -> (((op (e0) (e0)) = (e1))\/(((op (e1) (e0)) = (e1))\/(((op (e2) (e0)) = (e1))\/((op (e3) (e0)) = (e1))))) -> ((~((op (e3) (e3)) = (e2)))\/((op (e3) (e2)) = (e3))) -> (~((op (e0) (e0)) = (e1))) -> (((op (e0) (e0)) = (e3))\/(((op (e0) (e1)) = (e3))\/(((op (e0) (e2)) = (e3))\/((op (e0) (e3)) = (e3))))) -> (~((op (e0) (e3)) = (op (e3) (e3)))) -> (~((e0) = (e3))) -> (~((e1) = (e3))) -> (((op (e2) (e2)) = (e0))\/(((op (e2) (e2)) = (e1))\/(((op (e2) (e2)) = (e2))\/((op (e2) (e2)) = (e3))))) -> (~((op (e0) (e2)) = (op (e2) (e2)))) -> (((op (e0) (e0)) = (e2))\/(((op (e0) (e1)) = (e2))\/(((op (e0) (e2)) = (e2))\/((op (e0) (e3)) = (e2))))) -> (~((op (e0) (e1)) = (op (e2) (e1)))) -> (~((op (e2) (e3)) = (op (e3) (e3)))) -> (((op (e2) (e0)) = (e3))\/(((op (e2) (e1)) = (e3))\/(((op (e2) (e2)) = (e3))\/((op (e2) (e3)) = (e3))))) -> (((op (e0) (e0)) = (e3))\/(((op (e1) (e0)) = (e3))\/(((op (e2) (e0)) = (e3))\/((op (e3) (e0)) = (e3))))) -> (~((op (e0) (e2)) = (op (e1) (e2)))) -> (((op (e0) (e0)) = (e2))\/(((op (e1) (e0)) = (e2))\/(((op (e2) (e0)) = (e2))\/((op (e3) (e0)) = (e2))))) -> (~((op (e0) (e1)) = (op (e1) (e1)))) -> (((op (e1) (e0)) = (e3))\/(((op (e1) (e1)) = (e3))\/(((op (e1) (e2)) = (e3))\/((op (e1) (e3)) = (e3))))) -> (~((op (e1) (e3)) = (op (e3) (e3)))) -> (((op (e1) (e1)) = (e0))\/(((op (e1) (e1)) = (e1))\/(((op (e1) (e1)) = (e2))\/((op (e1) (e1)) = (e3))))) -> ((~((op (e2) (e2)) = (e3)))\/((op (e2) (e3)) = (e2))) -> (((op (e1) (e0)) = (e2))\/(((op (e1) (e1)) = (e2))\/(((op (e1) (e2)) = (e2))\/((op (e1) (e3)) = (e2))))) -> (~((e1) = (e2))) -> (((op (e0) (e3)) = (e0))\/(((op (e1) (e3)) = (e0))\/(((op (e2) (e3)) = (e0))\/((op (e3) (e3)) = (e0))))) -> (~((e0) = (e2))) -> (~((op (e0) (e2)) = (op (e0) (e3)))) -> (~((e2) = (e3))) -> (~((op (e3) (e0)) = (op (e3) (e3)))) -> ((~((op (e3) (e3)) = (e0)))\/((op (e3) (e0)) = (e3))) -> (~((op (e3) (e2)) = (op (e3) (e3)))) -> (((op (e0) (e2)) = (e3))\/(((op (e1) (e2)) = (e3))\/(((op (e2) (e2)) = (e3))\/((op (e3) (e2)) = (e3))))) -> (((op (e0) (e3)) = (e2))\/(((op (e1) (e3)) = (e2))\/(((op (e2) (e3)) = (e2))\/((op (e3) (e3)) = (e2))))) -> (~((e0) = (e1))) -> (((op (e1) (e0)) = (e1))\/(((op (e1) (e1)) = (e1))\/(((op (e1) (e2)) = (e1))\/((op (e1) (e3)) = (e1))))) -> (((op (e0) (e0)) = (e1))\/(((op (e0) (e1)) = (e1))\/(((op (e0) (e2)) = (e1))\/((op (e0) (e3)) = (e1))))) -> ((~((op (e2) (e2)) = (e2)))\/((op (e2) (e2)) = (e2))) -> ((~((op (e1) (e1)) = (e3)))\/((op (e1) (e3)) = (e1))) -> (~((op (e1) (op (e1) (e1))) = (op (e1) (e1)))) -> ((~((op (e1) (e1)) = (e1)))\/((op (e1) (e1)) = (e1))) -> ((~((op (e0) (e0)) = (e3)))\/((op (e0) (e3)) = (e0))) -> ((op (e1) (e0)) = (e0)) -> (~((op (e1) (e0)) = (op (e1) (e2)))) -> (~((op (e2) (e2)) = (e0))) -> (((op (e3) (e1)) = (e0))\/(((op (e3) (e1)) = (e1))\/(((op (e3) (e1)) = (e2))\/((op (e3) (e1)) = (e3))))) -> (~((op (e3) (e1)) = (op (e3) (e2)))) -> ((op (e3) (e0)) = (e1)) -> (~((op (e3) (e0)) = (op (e3) (e1)))) -> ((op (e0) (e1)) = (e2)) -> (~((op (e0) (e1)) = (op (e3) (e1)))) -> ((op (e3) (e3)) = (e3)) -> (~((op (e3) (e1)) = (op (e3) (e3)))) -> False). % 15.31/15.49 do 0 intro. intros zenon_H16f zenon_H1e4 zenon_H80 zenon_H7d zenon_Hd7 zenon_H1d3 zenon_H1d0 zenon_H1d4 zenon_H10c zenon_H1cd zenon_H1cf zenon_H121 zenon_Hce zenon_Hf1 zenon_H10e zenon_H45 zenon_H58 zenon_H36 zenon_H4b zenon_Ha3 zenon_H2d zenon_H28 zenon_H8e zenon_Hde zenon_He3 zenon_He6 zenon_Hbe zenon_H87 zenon_Heb zenon_H23 zenon_H90 zenon_H8b zenon_H1b3 zenon_H1c3 zenon_H84 zenon_Ha7 zenon_Hd3 zenon_H5e zenon_Hc9 zenon_H6a zenon_Hbb zenon_H10f zenon_H173 zenon_H175 zenon_H160 zenon_H9e zenon_H1c5 zenon_H44 zenon_Haa zenon_H1d2 zenon_H27b zenon_H1d8 zenon_H236 zenon_Had zenon_H166 zenon_H2e zenon_H16c zenon_H135 zenon_Hee zenon_H109 zenon_H5d zenon_H138 zenon_H42 zenon_H12d. % 15.31/15.49 apply (zenon_or_s _ _ zenon_H16f); [ zenon_intro zenon_Hab | zenon_intro zenon_H170 ]. % 15.31/15.49 apply (zenon_L700_); trivial. % 15.31/15.49 apply (zenon_or_s _ _ zenon_H170); [ zenon_intro zenon_H15d | zenon_intro zenon_H171 ]. % 15.31/15.49 apply (zenon_L143_); trivial. % 15.31/15.49 apply (zenon_or_s _ _ zenon_H171); [ zenon_intro zenon_H32 | zenon_intro zenon_H167 ]. % 15.31/15.49 exact (zenon_H2e zenon_H32). % 15.31/15.49 apply (zenon_L147_); trivial. % 15.31/15.49 (* end of lemma zenon_L701_ *) % 15.31/15.49 assert (zenon_L702_ : (((op (e0) (e0)) = (e2))\/(((op (e1) (e0)) = (e2))\/(((op (e2) (e0)) = (e2))\/((op (e3) (e0)) = (e2))))) -> (~((op (e1) (e3)) = (op (e3) (e3)))) -> ((op (e3) (e3)) = (e3)) -> (((op (e1) (e1)) = (e0))\/(((op (e1) (e1)) = (e1))\/(((op (e1) (e1)) = (e2))\/((op (e1) (e1)) = (e3))))) -> (~((op (e1) (e1)) = (e1))) -> (~((op (e1) (e1)) = (e2))) -> (~((op (e1) (e1)) = (e3))) -> (~((e1) = (e3))) -> (((op (e1) (e0)) = (e3))\/(((op (e1) (e1)) = (e3))\/(((op (e1) (e2)) = (e3))\/((op (e1) (e3)) = (e3))))) -> (~((e1) = (e2))) -> ((op (e1) (e0)) = (e1)) -> ((op (e2) (e3)) = (e2)) -> (~((op (e2) (e0)) = (op (e2) (e3)))) -> ((op (e3) (e0)) = (e0)) -> (~((e0) = (e2))) -> False). % 15.36/15.50 do 0 intro. intros zenon_Heb zenon_H8b zenon_H42 zenon_H1b3 zenon_H1b4 zenon_Hd6 zenon_H182 zenon_Ha3 zenon_H90 zenon_Ha7 zenon_Hd8 zenon_H124 zenon_Hce zenon_Hdb zenon_H5e. % 15.36/15.50 apply (zenon_or_s _ _ zenon_Heb); [ zenon_intro zenon_H92 | zenon_intro zenon_Hec ]. % 15.36/15.50 apply (zenon_L195_); trivial. % 15.36/15.50 apply (zenon_or_s _ _ zenon_Hec); [ zenon_intro zenon_H68 | zenon_intro zenon_Hed ]. % 15.36/15.50 apply (zenon_L162_); trivial. % 15.36/15.50 apply (zenon_or_s _ _ zenon_Hed); [ zenon_intro zenon_Hdd | zenon_intro zenon_He9 ]. % 15.36/15.50 apply (zenon_L119_); trivial. % 15.36/15.50 apply (zenon_L69_); trivial. % 15.36/15.50 (* end of lemma zenon_L702_ *) % 15.36/15.50 assert (zenon_L703_ : (((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 (e0) (e1)) = (op (e3) (e1)))) -> (~((op (e3) (e0)) = (op (e3) (e1)))) -> (~((op (e3) (e1)) = (op (e3) (e2)))) -> (((op (e3) (e1)) = (e0))\/(((op (e3) (e1)) = (e1))\/(((op (e3) (e1)) = (e2))\/((op (e3) (e1)) = (e3))))) -> (~((op (e2) (e2)) = (e0))) -> (~((op (e1) (e0)) = (op (e1) (e2)))) -> ((~((op (e0) (e0)) = (e3)))\/((op (e0) (e3)) = (e0))) -> ((~((op (e1) (e1)) = (e1)))\/((op (e1) (e1)) = (e1))) -> (~((op (e1) (op (e1) (e1))) = (op (e1) (e1)))) -> ((~((op (e1) (e1)) = (e3)))\/((op (e1) (e3)) = (e1))) -> ((~((op (e2) (e2)) = (e2)))\/((op (e2) (e2)) = (e2))) -> (((op (e1) (e0)) = (e1))\/(((op (e1) (e1)) = (e1))\/(((op (e1) (e2)) = (e1))\/((op (e1) (e3)) = (e1))))) -> (((op (e0) (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) (e2)) = (op (e3) (e3)))) -> ((~((op (e3) (e3)) = (e0)))\/((op (e3) (e0)) = (e3))) -> (~((op (e3) (e0)) = (op (e3) (e3)))) -> (~((e2) = (e3))) -> (~((op (e0) (e2)) = (op (e0) (e3)))) -> (((op (e0) (e3)) = (e0))\/(((op (e1) (e3)) = (e0))\/(((op (e2) (e3)) = (e0))\/((op (e3) (e3)) = (e0))))) -> ((~((op (e2) (e2)) = (e3)))\/((op (e2) (e3)) = (e2))) -> (((op (e0) (e0)) = (e3))\/(((op (e1) (e0)) = (e3))\/(((op (e2) (e0)) = (e3))\/((op (e3) (e0)) = (e3))))) -> (((op (e2) (e0)) = (e3))\/(((op (e2) (e1)) = (e3))\/(((op (e2) (e2)) = (e3))\/((op (e2) (e3)) = (e3))))) -> (~((op (e2) (e3)) = (op (e3) (e3)))) -> (~((op (e0) (e2)) = (op (e2) (e2)))) -> (((op (e2) (e2)) = (e0))\/(((op (e2) (e2)) = (e1))\/(((op (e2) (e2)) = (e2))\/((op (e2) (e2)) = (e3))))) -> (~((e0) = (e3))) -> (~((op (e0) (e3)) = (op (e3) (e3)))) -> (((op (e0) (e0)) = (e3))\/(((op (e0) (e1)) = (e3))\/(((op (e0) (e2)) = (e3))\/((op (e0) (e3)) = (e3))))) -> ((~((op (e3) (e3)) = (e2)))\/((op (e3) (e2)) = (e3))) -> (~((op (e1) (e0)) = (op (e1) (e3)))) -> ((~((op (e3) (e3)) = (e1)))\/((op (e3) (e1)) = (e3))) -> ((~((op (e2) (e2)) = (e0)))\/((op (e2) (e0)) = (e2))) -> (~((op (e1) (e2)) = (op (e1) (e3)))) -> ((~((op (e1) (e1)) = (e2)))\/((op (e1) (e2)) = (e1))) -> (~((op (e1) (e0)) = (op (e1) (e1)))) -> (~((op (e1) (e2)) = (op (e2) (e2)))) -> (~((op (e0) (e3)) = (op (e1) (e3)))) -> ((~((op (e1) (e1)) = (e0)))\/((op (e1) (e0)) = (e1))) -> (((op (e0) (e2)) = (e0))\/(((op (e1) (e2)) = (e0))\/(((op (e2) (e2)) = (e0))\/((op (e3) (e2)) = (e0))))) -> (((op (e2) (e0)) = (e1))\/(((op (e2) (e1)) = (e1))\/(((op (e2) (e2)) = (e1))\/((op (e2) (e3)) = (e1))))) -> (~((op (e0) (e1)) = (op (e2) (e1)))) -> (~((op (e2) (e2)) = (e1))) -> (((op (e0) (e0)) = (e1))\/(((op (e0) (e1)) = (e1))\/(((op (e0) (e2)) = (e1))\/((op (e0) (e3)) = (e1))))) -> (~((op (e3) (e3)) = (e1))) -> (~((op (e2) (e0)) = (op (e2) (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) (e2)) = (op (e1) (e2)))) -> (~((op (e1) (e1)) = (e2))) -> (~((op (e0) (op (e1) (e0))) = (op (e1) (e0)))) -> (((op (e1) (e0)) = (e2))\/(((op (e1) (e1)) = (e2))\/(((op (e1) (e2)) = (e2))\/((op (e1) (e3)) = (e2))))) -> (((op (e0) (e0)) = (e2))\/(((op (e1) (e0)) = (e2))\/(((op (e2) (e0)) = (e2))\/((op (e3) (e0)) = (e2))))) -> (~((op (e1) (e3)) = (op (e3) (e3)))) -> ((op (e3) (e3)) = (e3)) -> (~((e1) = (e3))) -> (((op (e1) (e0)) = (e3))\/(((op (e1) (e1)) = (e3))\/(((op (e1) (e2)) = (e3))\/((op (e1) (e3)) = (e3))))) -> ((op (e2) (e3)) = (e2)) -> (~((op (e0) (e0)) = (e1))) -> (((op (e0) (e0)) = (e1))\/(((op (e1) (e0)) = (e1))\/(((op (e2) (e0)) = (e1))\/((op (e3) (e0)) = (e1))))) -> (~((e0) = (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 (e0) (e1)) = (op (e1) (e1)))) -> (~((op (e1) (e1)) = (e3))) -> (~((op (e0) (e0)) = (e2))) -> (((op (e0) (e0)) = (e2))\/(((op (e0) (e1)) = (e2))\/(((op (e0) (e2)) = (e2))\/((op (e0) (e3)) = (e2))))) -> ((op (e0) (e3)) = (e0)) -> (~((e0) = (e1))) -> False). % 15.36/15.50 do 0 intro. intros zenon_Hf0 zenon_H20 zenon_H12d zenon_H138 zenon_H109 zenon_H135 zenon_H16c zenon_H2e zenon_H166 zenon_H236 zenon_H1d8 zenon_H27b zenon_H1d2 zenon_Haa zenon_H1c5 zenon_H160 zenon_H175 zenon_H173 zenon_H10f zenon_Hbb zenon_H6a zenon_Hc9 zenon_Hd3 zenon_H1c3 zenon_Hbe zenon_He6 zenon_He3 zenon_H28 zenon_H2d zenon_H4b zenon_H36 zenon_H58 zenon_H10e zenon_H1cf zenon_H10c zenon_H1d4 zenon_H1d0 zenon_H1d3 zenon_Hd7 zenon_H7d zenon_H80 zenon_H1e4 zenon_H16f zenon_Hb7 zenon_Hde zenon_H52 zenon_H44 zenon_H104 zenon_Hce zenon_H1cd zenon_H121 zenon_H87 zenon_Hd6 zenon_H261 zenon_H84 zenon_Heb zenon_H8b zenon_H42 zenon_Ha3 zenon_H90 zenon_H124 zenon_H45 zenon_Hf1 zenon_H5e zenon_Ha7 zenon_H1b3 zenon_H145 zenon_H1b4 zenon_H23 zenon_H182 zenon_H8f zenon_H8e zenon_Hca zenon_H9e. % 15.36/15.50 apply (zenon_or_s _ _ zenon_Hf0); [ zenon_intro zenon_H1f | zenon_intro zenon_Hf2 ]. % 15.36/15.50 exact (zenon_H20 zenon_H1f). % 15.36/15.50 apply (zenon_or_s _ _ zenon_Hf2); [ zenon_intro zenon_Had | zenon_intro zenon_Hf3 ]. % 15.36/15.50 apply (zenon_or_s _ _ zenon_H44); [ zenon_intro zenon_H47 | zenon_intro zenon_H46 ]. % 15.36/15.50 exact (zenon_H45 zenon_H47). % 15.36/15.50 apply (zenon_or_s _ _ zenon_H46); [ zenon_intro zenon_H22 | zenon_intro zenon_H48 ]. % 15.36/15.50 apply (zenon_or_s _ _ zenon_Hf1); [ zenon_intro zenon_H47 | zenon_intro zenon_Hf4 ]. % 15.36/15.50 exact (zenon_H45 zenon_H47). % 15.36/15.50 apply (zenon_or_s _ _ zenon_Hf4); [ zenon_intro zenon_Hd8 | zenon_intro zenon_Hf5 ]. % 15.36/15.50 apply (zenon_L225_); trivial. % 15.36/15.50 apply (zenon_or_s _ _ zenon_Hf5); [ zenon_intro zenon_Hae | zenon_intro zenon_Hee ]. % 15.36/15.50 apply (zenon_L696_); trivial. % 15.36/15.50 apply (zenon_or_s _ _ zenon_H8e); [ zenon_intro zenon_H92 | zenon_intro zenon_H91 ]. % 15.36/15.50 exact (zenon_H8f zenon_H92). % 15.36/15.50 apply (zenon_or_s _ _ zenon_H91); [ zenon_intro zenon_H5d | zenon_intro zenon_H93 ]. % 15.36/15.50 apply (zenon_L701_); trivial. % 15.36/15.50 apply (zenon_or_s _ _ zenon_H93); [ zenon_intro zenon_H63 | zenon_intro zenon_H81 ]. % 15.36/15.50 apply (zenon_L677_); trivial. % 15.36/15.50 apply (zenon_L113_); trivial. % 15.36/15.50 apply (zenon_or_s _ _ zenon_H48); [ zenon_intro zenon_H29 | zenon_intro zenon_H37 ]. % 15.36/15.50 apply (zenon_L339_); trivial. % 15.36/15.50 apply (zenon_L73_); trivial. % 15.36/15.50 apply (zenon_or_s _ _ zenon_Hf3); [ zenon_intro zenon_Hcf | zenon_intro zenon_Hdb ]. % 15.36/15.50 apply (zenon_L341_); trivial. % 15.36/15.50 apply (zenon_or_s _ _ zenon_H44); [ zenon_intro zenon_H47 | zenon_intro zenon_H46 ]. % 15.36/15.50 exact (zenon_H45 zenon_H47). % 15.36/15.50 apply (zenon_or_s _ _ zenon_H46); [ zenon_intro zenon_H22 | zenon_intro zenon_H48 ]. % 15.36/15.50 apply (zenon_or_s _ _ zenon_Hf1); [ zenon_intro zenon_H47 | zenon_intro zenon_Hf4 ]. % 15.36/15.50 exact (zenon_H45 zenon_H47). % 15.36/15.50 apply (zenon_or_s _ _ zenon_Hf4); [ zenon_intro zenon_Hd8 | zenon_intro zenon_Hf5 ]. % 15.36/15.50 apply (zenon_L702_); trivial. % 15.36/15.50 apply (zenon_or_s _ _ zenon_Hf5); [ zenon_intro zenon_Hae | zenon_intro zenon_Hee ]. % 15.36/15.50 apply (zenon_L696_); trivial. % 15.36/15.50 apply (zenon_L71_); trivial. % 15.36/15.50 apply (zenon_or_s _ _ zenon_H48); [ zenon_intro zenon_H29 | zenon_intro zenon_H37 ]. % 15.36/15.50 apply (zenon_L339_); trivial. % 15.36/15.50 apply (zenon_L73_); trivial. % 15.36/15.50 (* end of lemma zenon_L703_ *) % 15.36/15.50 assert (zenon_L704_ : ((~((op (e2) (e2)) = (e1)))\/((op (e2) (e1)) = (e2))) -> (((op (e0) (e1)) = (e0))\/(((op (e1) (e1)) = (e0))\/(((op (e2) (e1)) = (e0))\/((op (e3) (e1)) = (e0))))) -> (((op (e0) (e1)) = (e3))\/(((op (e1) (e1)) = (e3))\/(((op (e2) (e1)) = (e3))\/((op (e3) (e1)) = (e3))))) -> (((op (e0) (e0)) = (e0))\/(((op (e1) (e0)) = (e0))\/(((op (e2) (e0)) = (e0))\/((op (e3) (e0)) = (e0))))) -> (((op (e0) (e2)) = (e0))\/(((op (e1) (e2)) = (e0))\/(((op (e2) (e2)) = (e0))\/((op (e3) (e2)) = (e0))))) -> (~((op (e3) (e1)) = (op (e3) (e2)))) -> (~((op (e3) (e0)) = (op (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 (e1) (e1)) = (e0)))\/((op (e1) (e0)) = (e1))) -> (~((op (e1) (e0)) = (op (e1) (e2)))) -> (~((op (e0) (e3)) = (op (e1) (e3)))) -> (~((op (e1) (e2)) = (op (e2) (e2)))) -> (~((op (e1) (e0)) = (op (e1) (e1)))) -> ((~((op (e1) (e1)) = (e2)))\/((op (e1) (e2)) = (e1))) -> (~((op (e1) (e2)) = (op (e1) (e3)))) -> ((~((op (e2) (e2)) = (e0)))\/((op (e2) (e0)) = (e2))) -> ((~((op (e3) (e3)) = (e2)))\/((op (e3) (e2)) = (e3))) -> (~((e0) = (e3))) -> (~((op (e2) (e3)) = (op (e3) (e3)))) -> (((op (e2) (e0)) = (e3))\/(((op (e2) (e1)) = (e3))\/(((op (e2) (e2)) = (e3))\/((op (e2) (e3)) = (e3))))) -> (((op (e0) (e0)) = (e3))\/(((op (e1) (e0)) = (e3))\/(((op (e2) (e0)) = (e3))\/((op (e3) (e0)) = (e3))))) -> (((op (e1) (e0)) = (e3))\/(((op (e1) (e1)) = (e3))\/(((op (e1) (e2)) = (e3))\/((op (e1) (e3)) = (e3))))) -> (~((op (e1) (e3)) = (op (e3) (e3)))) -> ((~((op (e2) (e2)) = (e3)))\/((op (e2) (e3)) = (e2))) -> (((op (e0) (e3)) = (e0))\/(((op (e1) (e3)) = (e0))\/(((op (e2) (e3)) = (e0))\/((op (e3) (e3)) = (e0))))) -> (~((op (e0) (e2)) = (op (e0) (e3)))) -> (~((op (e3) (e0)) = (op (e3) (e3)))) -> ((~((op (e3) (e3)) = (e0)))\/((op (e3) (e0)) = (e3))) -> (~((op (e3) (e2)) = (op (e3) (e3)))) -> (((op (e0) (e2)) = (e3))\/(((op (e1) (e2)) = (e3))\/(((op (e2) (e2)) = (e3))\/((op (e3) (e2)) = (e3))))) -> (((op (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 (e2) (e2)) = (e2)))\/((op (e2) (e2)) = (e2))) -> ((~((op (e1) (e1)) = (e3)))\/((op (e1) (e3)) = (e1))) -> (~((op (e1) (op (e1) (e1))) = (op (e1) (e1)))) -> ((~((op (e1) (e1)) = (e1)))\/((op (e1) (e1)) = (e1))) -> ((~((op (e0) (e0)) = (e3)))\/((op (e0) (e3)) = (e0))) -> (~((op (e0) (e0)) = (e0))) -> (((op (e0) (e0)) = (e1))\/(((op (e0) (e1)) = (e1))\/(((op (e0) (e2)) = (e1))\/((op (e0) (e3)) = (e1))))) -> (((op (e0) (e0)) = (e3))\/(((op (e0) (e1)) = (e3))\/(((op (e0) (e2)) = (e3))\/((op (e0) (e3)) = (e3))))) -> ((op (e3) (e3)) = (e3)) -> (~((op (e0) (e3)) = (op (e3) (e3)))) -> (~((op (e2) (e2)) = (e0))) -> (~((op (e0) (e2)) = (op (e2) (e2)))) -> (~((e1) = (e3))) -> (~((e0) = (e1))) -> ((op (e0) (e3)) = (e0)) -> (~((op (e1) (e0)) = (op (e1) (e3)))) -> (((op (e2) (e2)) = (e0))\/(((op (e2) (e2)) = (e1))\/(((op (e2) (e2)) = (e2))\/((op (e2) (e2)) = (e3))))) -> (((op (e0) (e3)) = (e1))\/(((op (e1) (e3)) = (e1))\/(((op (e2) (e3)) = (e1))\/((op (e3) (e3)) = (e1))))) -> (((op (e0) (e0)) = (e2))\/(((op (e0) (e1)) = (e2))\/(((op (e0) (e2)) = (e2))\/((op (e0) (e3)) = (e2))))) -> (~((e0) = (e2))) -> (~((op (e0) (op (e1) (e0))) = (op (e1) (e0)))) -> (~((op (e1) (e1)) = (e2))) -> (~((op (e0) (e2)) = (op (e1) (e2)))) -> (~((op (e2) (e0)) = (op (e2) (e3)))) -> (~((e1) = (e2))) -> (~((op (e0) (e1)) = (op (e0) (e3)))) -> (((op (e1) (e0)) = (e2))\/(((op (e1) (e1)) = (e2))\/(((op (e1) (e2)) = (e2))\/((op (e1) (e3)) = (e2))))) -> (~((op (e1) (e1)) = (e0))) -> (~((op (e1) (e1)) = (e1))) -> (~((op (e0) (e1)) = (op (e1) (e1)))) -> (~((op (e1) (e1)) = (e3))) -> (((op (e1) (e1)) = (e0))\/(((op (e1) (e1)) = (e1))\/(((op (e1) (e1)) = (e2))\/((op (e1) (e1)) = (e3))))) -> (~((op (e0) (e0)) = (e2))) -> (~((e2) = (e3))) -> (~((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)) = (e2))\/(((op (e1) (e0)) = (e2))\/(((op (e2) (e0)) = (e2))\/((op (e3) (e0)) = (e2))))) -> (((op (e0) (e0)) = (e1))\/(((op (e1) (e0)) = (e1))\/(((op (e2) (e0)) = (e1))\/((op (e3) (e0)) = (e1))))) -> (~((op (e0) (e0)) = (e1))) -> (~((op (e3) (e1)) = (op (e3) (e3)))) -> ((~((op (e3) (e3)) = (e1)))\/((op (e3) (e1)) = (e3))) -> False). % 15.36/15.50 do 0 intro. intros zenon_H1e3 zenon_H144 zenon_H199 zenon_Hf0 zenon_H16f zenon_H135 zenon_H109 zenon_H138 zenon_H16c zenon_H1e4 zenon_H166 zenon_H80 zenon_H7d zenon_Hd7 zenon_H1d3 zenon_H1d0 zenon_H1d4 zenon_H10e zenon_H4b zenon_He3 zenon_He6 zenon_Hbe zenon_H90 zenon_H8b zenon_H1c3 zenon_Hd3 zenon_Hc9 zenon_Hbb zenon_H10f zenon_H173 zenon_H175 zenon_H160 zenon_H1c5 zenon_Haa zenon_H1d2 zenon_H27b zenon_H1d8 zenon_H236 zenon_H20 zenon_H44 zenon_H58 zenon_H42 zenon_H36 zenon_H2e zenon_H28 zenon_Ha3 zenon_H9e zenon_Hca zenon_H1cf zenon_H2d zenon_H121 zenon_H8e zenon_H5e zenon_H261 zenon_Hd6 zenon_H87 zenon_Hce zenon_Ha7 zenon_H1cd zenon_H84 zenon_H145 zenon_H1b4 zenon_H23 zenon_H182 zenon_H1b3 zenon_H8f zenon_H6a zenon_Hde zenon_Hb7 zenon_Heb zenon_Hf1 zenon_H45 zenon_H12d zenon_H10c. % 15.36/15.50 apply (zenon_or_s _ _ zenon_H1e3); [ zenon_intro zenon_H52 | zenon_intro zenon_H156 ]. % 15.36/15.50 apply (zenon_or_s _ _ zenon_Haa); [ zenon_intro zenon_H2f | zenon_intro zenon_H35 ]. % 15.36/15.50 apply (zenon_or_s _ _ zenon_H1c3); [ zenon_intro zenon_H30 | zenon_intro zenon_H124 ]. % 15.36/15.50 apply (zenon_or_s _ _ zenon_H10c); [ zenon_intro zenon_H104 | zenon_intro zenon_H10a ]. % 15.36/15.50 apply (zenon_or_s _ _ zenon_H44); [ zenon_intro zenon_H47 | zenon_intro zenon_H46 ]. % 15.36/15.50 exact (zenon_H45 zenon_H47). % 15.36/15.50 apply (zenon_or_s _ _ zenon_H46); [ zenon_intro zenon_H22 | zenon_intro zenon_H48 ]. % 15.36/15.50 apply (zenon_or_s _ _ zenon_Hf1); [ zenon_intro zenon_H47 | zenon_intro zenon_Hf4 ]. % 15.36/15.50 exact (zenon_H45 zenon_H47). % 15.36/15.50 apply (zenon_or_s _ _ zenon_Hf4); [ zenon_intro zenon_Hd8 | zenon_intro zenon_Hf5 ]. % 15.36/15.50 apply (zenon_L331_); trivial. % 15.36/15.50 apply (zenon_or_s _ _ zenon_Hf5); [ zenon_intro zenon_Hae | zenon_intro zenon_Hee ]. % 15.36/15.50 apply (zenon_L696_); trivial. % 15.36/15.50 apply (zenon_or_s _ _ zenon_H8e); [ zenon_intro zenon_H92 | zenon_intro zenon_H91 ]. % 15.36/15.50 exact (zenon_H8f zenon_H92). % 15.36/15.50 apply (zenon_or_s _ _ zenon_H91); [ zenon_intro zenon_H5d | zenon_intro zenon_H93 ]. % 15.36/15.50 apply (zenon_L214_); trivial. % 15.36/15.50 apply (zenon_or_s _ _ zenon_H93); [ zenon_intro zenon_H63 | zenon_intro zenon_H81 ]. % 15.36/15.50 apply (zenon_L697_); trivial. % 15.36/15.50 apply (zenon_L113_); trivial. % 15.36/15.50 apply (zenon_or_s _ _ zenon_H48); [ zenon_intro zenon_H29 | zenon_intro zenon_H37 ]. % 15.36/15.50 apply (zenon_L5_); trivial. % 15.36/15.50 apply (zenon_L73_); trivial. % 15.36/15.50 apply (zenon_L102_); trivial. % 15.36/15.50 apply (zenon_or_s _ _ zenon_H10c); [ zenon_intro zenon_H104 | zenon_intro zenon_H10a ]. % 15.36/15.50 apply (zenon_L703_); trivial. % 15.36/15.50 apply (zenon_L102_); trivial. % 15.36/15.50 apply (zenon_L343_); trivial. % 15.36/15.50 apply (zenon_L362_); trivial. % 15.36/15.50 (* end of lemma zenon_L704_ *) % 15.36/15.50 assert (zenon_L705_ : (~((op (e0) (e0)) = (e0))) -> ((~((op (e1) (e1)) = (e3)))\/((op (e1) (e3)) = (e1))) -> ((~((op (e2) (e2)) = (e1)))\/((op (e2) (e1)) = (e2))) -> ((~((op (e2) (e2)) = (e3)))\/((op (e2) (e3)) = (e2))) -> (~((op (e2) (e1)) = (op (e2) (e3)))) -> (((op (e0) (e1)) = (e3))\/(((op (e1) (e1)) = (e3))\/(((op (e2) (e1)) = (e3))\/((op (e3) (e1)) = (e3))))) -> (~((op (e2) (e0)) = (op (e2) (e3)))) -> (((op (e2) (e0)) = (e0))\/(((op (e2) (e1)) = (e0))\/(((op (e2) (e2)) = (e0))\/((op (e2) (e3)) = (e0))))) -> (((op (e0) (e1)) = (e1))\/(((op (e1) (e1)) = (e1))\/(((op (e2) (e1)) = (e1))\/((op (e3) (e1)) = (e1))))) -> (~((op (e0) (e1)) = (op (e2) (e1)))) -> (~((op (e2) (e1)) = (op (e2) (e2)))) -> (((op (e0) (e0)) = (e3))\/(((op (e0) (e1)) = (e3))\/(((op (e0) (e2)) = (e3))\/((op (e0) (e3)) = (e3))))) -> ((op (e3) (e3)) = (e3)) -> (~((op (e0) (e3)) = (op (e3) (e3)))) -> (~((op (e0) (e2)) = (op (e2) (e2)))) -> (((op (e2) (e2)) = (e0))\/(((op (e2) (e2)) = (e1))\/(((op (e2) (e2)) = (e2))\/((op (e2) (e2)) = (e3))))) -> (~((e0) = (e3))) -> (~((op (e0) (e0)) = (e3))) -> ((~((op (e3) (e3)) = (e0)))\/((op (e3) (e0)) = (e3))) -> (~((op (e3) (e0)) = (op (e3) (e3)))) -> (((op (e0) (e0)) = (e1))\/(((op (e0) (e1)) = (e1))\/(((op (e0) (e2)) = (e1))\/((op (e0) (e3)) = (e1))))) -> (((op (e0) (e3)) = (e0))\/(((op (e1) (e3)) = (e0))\/(((op (e2) (e3)) = (e0))\/((op (e3) (e3)) = (e0))))) -> (~((op (e0) (e1)) = (op (e0) (e3)))) -> (~((e1) = (e2))) -> (((op (e0) (e3)) = (e2))\/(((op (e1) (e3)) = (e2))\/(((op (e2) (e3)) = (e2))\/((op (e3) (e3)) = (e2))))) -> (~((e1) = (e3))) -> (~((e0) = (e1))) -> (~((op (e0) (e0)) = (e2))) -> (~((e0) = (e2))) -> (((op (e1) (e0)) = (e2))\/(((op (e1) (e1)) = (e2))\/(((op (e1) (e2)) = (e2))\/((op (e1) (e3)) = (e2))))) -> (~((op (e0) (e3)) = (op (e1) (e3)))) -> (~((op (e1) (e2)) = (op (e2) (e2)))) -> (~((e2) = (e3))) -> (~((op (e0) (e2)) = (op (e1) (e2)))) -> (~((op (e1) (e3)) = (op (e3) (e3)))) -> (((op (e1) (e0)) = (e3))\/(((op (e1) (e1)) = (e3))\/(((op (e1) (e2)) = (e3))\/((op (e1) (e3)) = (e3))))) -> (((op (e0) (e0)) = (e2))\/(((op (e0) (e1)) = (e2))\/(((op (e0) (e2)) = (e2))\/((op (e0) (e3)) = (e2))))) -> (~((op (e3) (e2)) = (op (e3) (e3)))) -> ((~((op (e3) (e3)) = (e2)))\/((op (e3) (e2)) = (e3))) -> ((~((op (e2) (e2)) = (e2)))\/((op (e2) (e2)) = (e2))) -> (~((op (e2) (e0)) = (op (e2) (e1)))) -> (((op (e2) (e0)) = (e3))\/(((op (e2) (e1)) = (e3))\/(((op (e2) (e2)) = (e3))\/((op (e2) (e3)) = (e3))))) -> (~((op (e2) (e3)) = (op (e3) (e3)))) -> (~((op (e2) (e0)) = (op (e2) (e2)))) -> ((~((op (e2) (e2)) = (e0)))\/((op (e2) (e0)) = (e2))) -> (~((op (e0) (e1)) = (op (e1) (e1)))) -> (~((op (e1) (e1)) = (e1))) -> (~((op (e1) (e1)) = (e2))) -> (((op (e1) (e1)) = (e0))\/(((op (e1) (e1)) = (e1))\/(((op (e1) (e1)) = (e2))\/((op (e1) (e1)) = (e3))))) -> (~((op (e0) (e0)) = (e1))) -> (~((op (e2) (e2)) = (e3))) -> (~((op (e2) (e2)) = (e2))) -> (~((op (e2) (e2)) = (e0))) -> (((op (e0) (e0)) = (e3))\/(((op (e1) (e0)) = (e3))\/(((op (e2) (e0)) = (e3))\/((op (e3) (e0)) = (e3))))) -> (((op (e0) (e0)) = (e2))\/(((op (e1) (e0)) = (e2))\/(((op (e2) (e0)) = (e2))\/((op (e3) (e0)) = (e2))))) -> (~((op (e1) (e1)) = (e0))) -> (~((op (e1) (e1)) = (e3))) -> (~((op (e0) (e2)) = (op (e0) (e3)))) -> (((op (e0) (e2)) = (e3))\/(((op (e1) (e2)) = (e3))\/(((op (e2) (e2)) = (e3))\/((op (e3) (e2)) = (e3))))) -> (((op (e1) (e0)) = (e1))\/(((op (e1) (e1)) = (e1))\/(((op (e1) (e2)) = (e1))\/((op (e1) (e3)) = (e1))))) -> (((op (e0) (e1)) = (e0))\/(((op (e1) (e1)) = (e0))\/(((op (e2) (e1)) = (e0))\/((op (e3) (e1)) = (e0))))) -> (((op (e0) (e0)) = (e0))\/(((op (e1) (e0)) = (e0))\/(((op (e2) (e0)) = (e0))\/((op (e3) (e0)) = (e0))))) -> (((op (e0) (e2)) = (e0))\/(((op (e1) (e2)) = (e0))\/(((op (e2) (e2)) = (e0))\/((op (e3) (e2)) = (e0))))) -> (~((op (e3) (e1)) = (op (e3) (e2)))) -> (~((op (e3) (e0)) = (op (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 (e1) (e1)) = (e0)))\/((op (e1) (e0)) = (e1))) -> (~((op (e1) (e0)) = (op (e1) (e2)))) -> (~((op (e1) (e0)) = (op (e1) (e1)))) -> ((~((op (e1) (e1)) = (e2)))\/((op (e1) (e2)) = (e1))) -> (~((op (e1) (e2)) = (op (e1) (e3)))) -> (~((op (e1) (op (e1) (e1))) = (op (e1) (e1)))) -> ((~((op (e1) (e1)) = (e1)))\/((op (e1) (e1)) = (e1))) -> ((~((op (e0) (e0)) = (e3)))\/((op (e0) (e3)) = (e0))) -> (~((op (e1) (e0)) = (op (e1) (e3)))) -> (((op (e0) (e3)) = (e1))\/(((op (e1) (e3)) = (e1))\/(((op (e2) (e3)) = (e1))\/((op (e3) (e3)) = (e1))))) -> (~((op (e0) (op (e1) (e0))) = (op (e1) (e0)))) -> (((op (e2) (e0)) = (e1))\/(((op (e2) (e1)) = (e1))\/(((op (e2) (e2)) = (e1))\/((op (e2) (e3)) = (e1))))) -> (((op (e0) (e0)) = (e1))\/(((op (e1) (e0)) = (e1))\/(((op (e2) (e0)) = (e1))\/((op (e3) (e0)) = (e1))))) -> (~((op (e3) (e1)) = (op (e3) (e3)))) -> ((~((op (e3) (e3)) = (e1)))\/((op (e3) (e1)) = (e3))) -> (((op (e0) (e0)) = (e0))\/(((op (e0) (e1)) = (e0))\/(((op (e0) (e2)) = (e0))\/((op (e0) (e3)) = (e0))))) -> False). % 15.36/15.50 do 0 intro. intros zenon_H20 zenon_H1d2 zenon_H1e3 zenon_H1c3 zenon_H1e2 zenon_H199 zenon_Hce zenon_H1f5 zenon_H228 zenon_Hde zenon_H157 zenon_H58 zenon_H42 zenon_H36 zenon_H28 zenon_H2d zenon_H4b zenon_H59 zenon_H10f zenon_Hbb zenon_H44 zenon_Hd3 zenon_H1cd zenon_Ha7 zenon_H160 zenon_Ha3 zenon_H9e zenon_H8f zenon_H5e zenon_H84 zenon_H80 zenon_H7d zenon_H6a zenon_H87 zenon_H8b zenon_H90 zenon_H8e zenon_H173 zenon_H10e zenon_Haa zenon_H154 zenon_He6 zenon_He3 zenon_H17a zenon_H1d4 zenon_H23 zenon_H1b4 zenon_Hd6 zenon_H1b3 zenon_H45 zenon_H30 zenon_H2f zenon_H2e zenon_Hbe zenon_Heb zenon_H145 zenon_H182 zenon_Hc9 zenon_H175 zenon_H1c5 zenon_H144 zenon_Hf0 zenon_H16f zenon_H135 zenon_H109 zenon_H138 zenon_H16c zenon_H1e4 zenon_H166 zenon_Hd7 zenon_H1d3 zenon_H1d0 zenon_H27b zenon_H1d8 zenon_H236 zenon_H1cf zenon_H121 zenon_H261 zenon_Hb7 zenon_Hf1 zenon_H12d zenon_H10c zenon_H110. % 15.36/15.50 apply (zenon_or_s _ _ zenon_H10f); [ zenon_intro zenon_H3c | zenon_intro zenon_Hba ]. % 15.36/15.50 apply (zenon_or_s _ _ zenon_H110); [ zenon_intro zenon_H1f | zenon_intro zenon_H111 ]. % 15.36/15.50 exact (zenon_H20 zenon_H1f). % 15.36/15.50 apply (zenon_or_s _ _ zenon_H111); [ zenon_intro zenon_H49 | zenon_intro zenon_H112 ]. % 15.36/15.50 apply (zenon_L378_); trivial. % 15.36/15.50 apply (zenon_or_s _ _ zenon_H112); [ zenon_intro zenon_Hab | zenon_intro zenon_Hca ]. % 15.36/15.50 apply (zenon_L222_); trivial. % 15.36/15.50 apply (zenon_L704_); trivial. % 15.36/15.50 apply (zenon_L43_); trivial. % 15.36/15.50 (* end of lemma zenon_L705_ *) % 15.36/15.50 assert (zenon_L706_ : (((op (e3) (e0)) = (e1))\/(((op (e3) (e1)) = (e1))\/(((op (e3) (e2)) = (e1))\/((op (e3) (e3)) = (e1))))) -> (~((op (e3) (e1)) = (op (e3) (e3)))) -> ((op (e3) (e3)) = (e3)) -> (~((op (e0) (e1)) = (op (e3) (e1)))) -> ((op (e0) (e1)) = (e2)) -> (~((op (e3) (e0)) = (op (e3) (e1)))) -> (~((op (e3) (e1)) = (op (e3) (e2)))) -> (((op (e3) (e1)) = (e0))\/(((op (e3) (e1)) = (e1))\/(((op (e3) (e1)) = (e2))\/((op (e3) (e1)) = (e3))))) -> (~((op (e2) (e2)) = (e0))) -> (~((op (e1) (e0)) = (op (e1) (e2)))) -> ((op (e1) (e0)) = (e0)) -> (~((e0) = (e1))) -> (((op (e0) (e2)) = (e0))\/(((op (e1) (e2)) = (e0))\/(((op (e2) (e2)) = (e0))\/((op (e3) (e2)) = (e0))))) -> ((op (e1) (e3)) = (e1)) -> (~((op (e3) (op (e1) (e3))) = (op (e1) (e3)))) -> ((op (e0) (e2)) = (e1)) -> (~((op (e0) (e2)) = (op (e3) (e2)))) -> (~((op (e3) (e3)) = (e1))) -> False). % 15.36/15.50 do 0 intro. intros zenon_H146 zenon_H12d zenon_H42 zenon_H138 zenon_H5d zenon_H109 zenon_H135 zenon_H16c zenon_H2e zenon_H166 zenon_Had zenon_H9e zenon_H16f zenon_H11f zenon_H26e zenon_H29 zenon_H140 zenon_H104. % 15.36/15.50 apply (zenon_or_s _ _ zenon_H146); [ zenon_intro zenon_Hee | zenon_intro zenon_H14b ]. % 15.36/15.50 apply (zenon_L148_); trivial. % 15.36/15.50 apply (zenon_or_s _ _ zenon_H14b); [ zenon_intro zenon_H13e | zenon_intro zenon_H14c ]. % 15.36/15.50 apply (zenon_L648_); trivial. % 15.36/15.50 apply (zenon_or_s _ _ zenon_H14c); [ zenon_intro zenon_H119 | zenon_intro zenon_H38 ]. % 15.36/15.50 apply (zenon_L124_); trivial. % 15.36/15.50 exact (zenon_H104 zenon_H38). % 15.36/15.50 (* end of lemma zenon_L706_ *) % 15.36/15.50 assert (zenon_L707_ : (((op (e3) (e1)) = (e0))\/(((op (e3) (e1)) = (e1))\/(((op (e3) (e1)) = (e2))\/((op (e3) (e1)) = (e3))))) -> ((op (e3) (e2)) = (e0)) -> ((op (e3) (e2)) = (e1)) -> (~((op (e3) (e1)) = (op (e3) (e2)))) -> ((op (e2) (e1)) = (e2)) -> (~((op (e2) (e1)) = (op (e3) (e1)))) -> ((op (e3) (e3)) = (e3)) -> (~((op (e3) (e1)) = (op (e3) (e3)))) -> False). % 15.36/15.50 do 0 intro. intros zenon_H16c zenon_H167 zenon_H119 zenon_H135 zenon_H156 zenon_H13c zenon_H42 zenon_H12d. % 15.36/15.50 apply (zenon_or_s _ _ zenon_H16c); [ zenon_intro zenon_H142 | zenon_intro zenon_H16d ]. % 15.36/15.50 apply (zenon_L144_); trivial. % 15.36/15.50 apply (zenon_or_s _ _ zenon_H16d); [ zenon_intro zenon_H13e | zenon_intro zenon_H16e ]. % 15.36/15.50 apply (zenon_L394_); trivial. % 15.36/15.50 apply (zenon_or_s _ _ zenon_H16e); [ zenon_intro zenon_H16a | zenon_intro zenon_H10a ]. % 15.36/15.50 apply (zenon_L252_); trivial. % 15.36/15.50 apply (zenon_L102_); trivial. % 15.36/15.50 (* end of lemma zenon_L707_ *) % 15.36/15.50 assert (zenon_L708_ : (((op (e3) (e1)) = (e0))\/(((op (e3) (e1)) = (e1))\/(((op (e3) (e1)) = (e2))\/((op (e3) (e1)) = (e3))))) -> ((op (e3) (e2)) = (e0)) -> (~((op (e3) (e1)) = (op (e3) (e2)))) -> ((op (e1) (e3)) = (e1)) -> (~((op (e3) (op (e1) (e3))) = (op (e1) (e3)))) -> ((op (e0) (e1)) = (e2)) -> (~((op (e0) (e1)) = (op (e3) (e1)))) -> ((op (e2) (e1)) = (e3)) -> (~((op (e2) (e1)) = (op (e3) (e1)))) -> False). % 15.36/15.50 do 0 intro. intros zenon_H16c zenon_H167 zenon_H135 zenon_H11f zenon_H26e zenon_H5d zenon_H138 zenon_Hdf zenon_H13c. % 15.36/15.50 apply (zenon_or_s _ _ zenon_H16c); [ zenon_intro zenon_H142 | zenon_intro zenon_H16d ]. % 15.36/15.50 apply (zenon_L144_); trivial. % 15.36/15.50 apply (zenon_or_s _ _ zenon_H16d); [ zenon_intro zenon_H13e | zenon_intro zenon_H16e ]. % 15.36/15.50 apply (zenon_L648_); trivial. % 15.36/15.50 apply (zenon_or_s _ _ zenon_H16e); [ zenon_intro zenon_H16a | zenon_intro zenon_H10a ]. % 15.36/15.50 apply (zenon_L146_); trivial. % 15.36/15.50 apply (zenon_L121_); trivial. % 15.36/15.50 (* end of lemma zenon_L708_ *) % 15.36/15.50 assert (zenon_L709_ : (((op (e3) (e0)) = (e1))\/(((op (e3) (e1)) = (e1))\/(((op (e3) (e2)) = (e1))\/((op (e3) (e3)) = (e1))))) -> (~((e1) = (e2))) -> ((op (e3) (e0)) = (e2)) -> ((op (e1) (e3)) = (e1)) -> (~((op (e3) (op (e1) (e3))) = (op (e1) (e3)))) -> ((op (e0) (e2)) = (e1)) -> (~((op (e0) (e2)) = (op (e3) (e2)))) -> (~((op (e3) (e3)) = (e1))) -> False). % 15.36/15.50 do 0 intro. intros zenon_H146 zenon_Ha7 zenon_He9 zenon_H11f zenon_H26e zenon_H29 zenon_H140 zenon_H104. % 15.36/15.50 apply (zenon_or_s _ _ zenon_H146); [ zenon_intro zenon_Hee | zenon_intro zenon_H14b ]. % 15.36/15.50 apply (zenon_L122_); trivial. % 15.36/15.50 apply (zenon_or_s _ _ zenon_H14b); [ zenon_intro zenon_H13e | zenon_intro zenon_H14c ]. % 15.36/15.50 apply (zenon_L648_); trivial. % 15.36/15.50 apply (zenon_or_s _ _ zenon_H14c); [ zenon_intro zenon_H119 | zenon_intro zenon_H38 ]. % 15.36/15.50 apply (zenon_L124_); trivial. % 15.36/15.50 exact (zenon_H104 zenon_H38). % 15.36/15.50 (* end of lemma zenon_L709_ *) % 15.36/15.50 assert (zenon_L710_ : (((op (e0) (e2)) = (e0))\/(((op (e0) (e2)) = (e1))\/(((op (e0) (e2)) = (e2))\/((op (e0) (e2)) = (e3))))) -> ((op (e3) (e2)) = (e0)) -> (~((op (e3) (e3)) = (e1))) -> (~((op (e0) (e2)) = (op (e3) (e2)))) -> (~((op (e3) (op (e1) (e3))) = (op (e1) (e3)))) -> ((op (e1) (e3)) = (e1)) -> ((op (e3) (e0)) = (e2)) -> (~((e1) = (e2))) -> (((op (e3) (e0)) = (e1))\/(((op (e3) (e1)) = (e1))\/(((op (e3) (e2)) = (e1))\/((op (e3) (e3)) = (e1))))) -> ((op (e1) (e2)) = (e2)) -> (~((op (e0) (e2)) = (op (e1) (e2)))) -> (~((op (e0) (e2)) = (op (e2) (e2)))) -> ((op (e2) (e2)) = (e3)) -> False). % 15.36/15.50 do 0 intro. intros zenon_H251 zenon_H167 zenon_H104 zenon_H140 zenon_H26e zenon_H11f zenon_He9 zenon_Ha7 zenon_H146 zenon_H7c zenon_H87 zenon_H28 zenon_H34. % 15.36/15.50 apply (zenon_or_s _ _ zenon_H251); [ zenon_intro zenon_Hab | zenon_intro zenon_H252 ]. % 15.36/15.50 apply (zenon_L267_); trivial. % 15.36/15.50 apply (zenon_or_s _ _ zenon_H252); [ zenon_intro zenon_H29 | zenon_intro zenon_H253 ]. % 15.36/15.50 apply (zenon_L709_); trivial. % 15.36/15.50 apply (zenon_or_s _ _ zenon_H253); [ zenon_intro zenon_H63 | zenon_intro zenon_H50 ]. % 15.36/15.50 apply (zenon_L52_); trivial. % 15.36/15.50 apply (zenon_L10_); trivial. % 15.36/15.50 (* end of lemma zenon_L710_ *) % 15.36/15.50 assert (zenon_L711_ : (((op (e0) (e3)) = (e0))\/(((op (e1) (e3)) = (e0))\/(((op (e2) (e3)) = (e0))\/((op (e3) (e3)) = (e0))))) -> ((op (e0) (e2)) = (e0)) -> (~((op (e0) (e2)) = (op (e0) (e3)))) -> ((op (e1) (e3)) = (e1)) -> (~((e0) = (e1))) -> ((op (e2) (e3)) = (e2)) -> (~((e0) = (e2))) -> (~((op (e3) (e3)) = (e0))) -> False). % 15.36/15.50 do 0 intro. intros zenon_Hd3 zenon_Hab zenon_Hc9 zenon_H11f zenon_H9e zenon_H124 zenon_H5e zenon_H3c. % 15.36/15.50 apply (zenon_or_s _ _ zenon_Hd3); [ zenon_intro zenon_Hca | zenon_intro zenon_Hd4 ]. % 15.36/15.50 apply (zenon_L53_); trivial. % 15.36/15.50 apply (zenon_or_s _ _ zenon_Hd4); [ zenon_intro zenon_Hcc | zenon_intro zenon_Hd5 ]. % 15.36/15.50 apply (zenon_L208_); trivial. % 15.36/15.50 apply (zenon_or_s _ _ zenon_Hd5); [ zenon_intro zenon_Hd0 | zenon_intro zenon_H40 ]. % 15.36/15.50 apply (zenon_L201_); trivial. % 15.36/15.50 exact (zenon_H3c zenon_H40). % 15.36/15.50 (* end of lemma zenon_L711_ *) % 15.36/15.50 assert (zenon_L712_ : ((~((op (e3) (e3)) = (e0)))\/((op (e3) (e0)) = (e3))) -> ((op (e3) (e3)) = (e3)) -> (~((op (e3) (e0)) = (op (e3) (e3)))) -> (~((op (e0) (e2)) = (op (e0) (e3)))) -> ((op (e0) (e2)) = (e0)) -> (~((e0) = (e1))) -> ((op (e1) (e3)) = (e1)) -> (~((e0) = (e2))) -> ((op (e2) (e3)) = (e2)) -> (((op (e0) (e3)) = (e0))\/(((op (e1) (e3)) = (e0))\/(((op (e2) (e3)) = (e0))\/((op (e3) (e3)) = (e0))))) -> False). % 15.36/15.50 do 0 intro. intros zenon_H10f zenon_H42 zenon_Hbb zenon_Hc9 zenon_Hab zenon_H9e zenon_H11f zenon_H5e zenon_H124 zenon_Hd3. % 15.36/15.50 apply (zenon_or_s _ _ zenon_H10f); [ zenon_intro zenon_H3c | zenon_intro zenon_Hba ]. % 15.36/15.50 apply (zenon_L711_); trivial. % 15.36/15.50 apply (zenon_L43_); trivial. % 15.36/15.50 (* end of lemma zenon_L712_ *) % 15.36/15.50 assert (zenon_L713_ : (((op (e0) (e2)) = (e0))\/(((op (e0) (e2)) = (e1))\/(((op (e0) (e2)) = (e2))\/((op (e0) (e2)) = (e3))))) -> (((op (e0) (e3)) = (e0))\/(((op (e1) (e3)) = (e0))\/(((op (e2) (e3)) = (e0))\/((op (e3) (e3)) = (e0))))) -> ((op (e2) (e3)) = (e2)) -> (~((e0) = (e2))) -> ((op (e1) (e3)) = (e1)) -> (~((e0) = (e1))) -> (~((op (e0) (e2)) = (op (e0) (e3)))) -> (~((op (e3) (e0)) = (op (e3) (e3)))) -> ((op (e3) (e3)) = (e3)) -> ((~((op (e3) (e3)) = (e0)))\/((op (e3) (e0)) = (e3))) -> ((op (e3) (e2)) = (e1)) -> ((op (e3) (e2)) = (e2)) -> (~((op (e0) (e2)) = (op (e3) (e2)))) -> (~((op (e0) (e2)) = (op (e2) (e2)))) -> ((op (e2) (e2)) = (e3)) -> False). % 15.36/15.50 do 0 intro. intros zenon_H251 zenon_Hd3 zenon_H124 zenon_H5e zenon_H11f zenon_H9e zenon_Hc9 zenon_Hbb zenon_H42 zenon_H10f zenon_H119 zenon_H1dd zenon_H140 zenon_H28 zenon_H34. % 15.36/15.50 apply (zenon_or_s _ _ zenon_H251); [ zenon_intro zenon_Hab | zenon_intro zenon_H252 ]. % 15.36/15.50 apply (zenon_L712_); trivial. % 15.36/15.50 apply (zenon_or_s _ _ zenon_H252); [ zenon_intro zenon_H29 | zenon_intro zenon_H253 ]. % 15.36/15.50 apply (zenon_L124_); trivial. % 15.36/15.50 apply (zenon_or_s _ _ zenon_H253); [ zenon_intro zenon_H63 | zenon_intro zenon_H50 ]. % 15.36/15.50 apply (zenon_L253_); trivial. % 15.36/15.50 apply (zenon_L10_); trivial. % 15.36/15.50 (* end of lemma zenon_L713_ *) % 15.36/15.50 assert (zenon_L714_ : (((op (e2) (e0)) = (e3))\/(((op (e2) (e1)) = (e3))\/(((op (e2) (e2)) = (e3))\/((op (e2) (e3)) = (e3))))) -> (~((e1) = (e3))) -> ((op (e2) (e0)) = (e1)) -> (~((op (e2) (e1)) = (op (e3) (e1)))) -> (~((op (e3) (e3)) = (e1))) -> (((op (e0) (e2)) = (e0))\/(((op (e0) (e2)) = (e1))\/(((op (e0) (e2)) = (e2))\/((op (e0) (e2)) = (e3))))) -> (((op (e0) (e3)) = (e0))\/(((op (e1) (e3)) = (e0))\/(((op (e2) (e3)) = (e0))\/((op (e3) (e3)) = (e0))))) -> ((op (e2) (e3)) = (e2)) -> (~((e0) = (e2))) -> ((op (e1) (e3)) = (e1)) -> (~((e0) = (e1))) -> (~((op (e0) (e2)) = (op (e0) (e3)))) -> (~((op (e3) (e0)) = (op (e3) (e3)))) -> ((~((op (e3) (e3)) = (e0)))\/((op (e3) (e0)) = (e3))) -> ((op (e3) (e2)) = (e2)) -> (~((op (e0) (e2)) = (op (e3) (e2)))) -> (~((op (e0) (e2)) = (op (e2) (e2)))) -> (~((op (e3) (op (e1) (e3))) = (op (e1) (e3)))) -> (((op (e3) (e1)) = (e0))\/(((op (e3) (e1)) = (e1))\/(((op (e3) (e1)) = (e2))\/((op (e3) (e1)) = (e3))))) -> ((op (e3) (e2)) = (e0)) -> (~((op (e3) (e1)) = (op (e3) (e2)))) -> (~((op (e3) (e0)) = (op (e3) (e1)))) -> ((op (e0) (e1)) = (e2)) -> (~((op (e0) (e1)) = (op (e3) (e1)))) -> (~((op (e3) (e1)) = (op (e3) (e3)))) -> (((op (e3) (e0)) = (e1))\/(((op (e3) (e1)) = (e1))\/(((op (e3) (e2)) = (e1))\/((op (e3) (e3)) = (e1))))) -> ((op (e3) (e3)) = (e3)) -> (~((op (e2) (e3)) = (op (e3) (e3)))) -> False). % 15.36/15.50 do 0 intro. intros zenon_He6 zenon_Ha3 zenon_Hae zenon_H13c zenon_H104 zenon_H251 zenon_Hd3 zenon_H124 zenon_H5e zenon_H11f zenon_H9e zenon_Hc9 zenon_Hbb zenon_H10f zenon_H1dd zenon_H140 zenon_H28 zenon_H26e zenon_H16c zenon_H167 zenon_H135 zenon_H109 zenon_H5d zenon_H138 zenon_H12d zenon_H146 zenon_H42 zenon_He3. % 15.36/15.50 apply (zenon_or_s _ _ zenon_He6); [ zenon_intro zenon_Haf | zenon_intro zenon_He7 ]. % 15.36/15.50 apply (zenon_L39_); trivial. % 15.36/15.50 apply (zenon_or_s _ _ zenon_He7); [ zenon_intro zenon_Hdf | zenon_intro zenon_He8 ]. % 15.36/15.50 apply (zenon_L708_); trivial. % 15.36/15.50 apply (zenon_or_s _ _ zenon_He8); [ zenon_intro zenon_H34 | zenon_intro zenon_He2 ]. % 15.36/15.50 apply (zenon_or_s _ _ zenon_H146); [ zenon_intro zenon_Hee | zenon_intro zenon_H14b ]. % 15.36/15.50 apply (zenon_L147_); trivial. % 15.36/15.50 apply (zenon_or_s _ _ zenon_H14b); [ zenon_intro zenon_H13e | zenon_intro zenon_H14c ]. % 15.36/15.50 apply (zenon_L648_); trivial. % 15.36/15.50 apply (zenon_or_s _ _ zenon_H14c); [ zenon_intro zenon_H119 | zenon_intro zenon_H38 ]. % 15.36/15.50 apply (zenon_L713_); trivial. % 15.36/15.50 exact (zenon_H104 zenon_H38). % 15.36/15.50 apply (zenon_L66_); trivial. % 15.36/15.50 (* end of lemma zenon_L714_ *) % 15.36/15.50 assert (zenon_L715_ : (((op (e0) (e2)) = (e2))\/(((op (e1) (e2)) = (e2))\/(((op (e2) (e2)) = (e2))\/((op (e3) (e2)) = (e2))))) -> ((op (e1) (e0)) = (e2)) -> (~((op (e0) (op (e1) (e0))) = (op (e1) (e0)))) -> (~((e2) = (e3))) -> (((op (e3) (e0)) = (e2))\/(((op (e3) (e1)) = (e2))\/(((op (e3) (e2)) = (e2))\/((op (e3) (e3)) = (e2))))) -> (~((op (e0) (e2)) = (op (e1) (e2)))) -> (~((e1) = (e2))) -> ((op (e3) (e2)) = (e1)) -> (~((op (e3) (e3)) = (e2))) -> (~((op (e2) (e2)) = (e2))) -> (((op (e2) (e0)) = (e3))\/(((op (e2) (e1)) = (e3))\/(((op (e2) (e2)) = (e3))\/((op (e2) (e3)) = (e3))))) -> (~((e1) = (e3))) -> ((op (e2) (e0)) = (e1)) -> (~((op (e2) (e1)) = (op (e3) (e1)))) -> (~((op (e3) (e3)) = (e1))) -> (((op (e0) (e2)) = (e0))\/(((op (e0) (e2)) = (e1))\/(((op (e0) (e2)) = (e2))\/((op (e0) (e2)) = (e3))))) -> (((op (e0) (e3)) = (e0))\/(((op (e1) (e3)) = (e0))\/(((op (e2) (e3)) = (e0))\/((op (e3) (e3)) = (e0))))) -> ((op (e2) (e3)) = (e2)) -> (~((e0) = (e2))) -> ((op (e1) (e3)) = (e1)) -> (~((e0) = (e1))) -> (~((op (e0) (e2)) = (op (e0) (e3)))) -> (~((op (e3) (e0)) = (op (e3) (e3)))) -> ((~((op (e3) (e3)) = (e0)))\/((op (e3) (e0)) = (e3))) -> (~((op (e0) (e2)) = (op (e3) (e2)))) -> (~((op (e0) (e2)) = (op (e2) (e2)))) -> (~((op (e3) (op (e1) (e3))) = (op (e1) (e3)))) -> (((op (e3) (e1)) = (e0))\/(((op (e3) (e1)) = (e1))\/(((op (e3) (e1)) = (e2))\/((op (e3) (e1)) = (e3))))) -> ((op (e3) (e2)) = (e0)) -> (~((op (e3) (e1)) = (op (e3) (e2)))) -> (~((op (e3) (e0)) = (op (e3) (e1)))) -> ((op (e0) (e1)) = (e2)) -> (~((op (e0) (e1)) = (op (e3) (e1)))) -> (~((op (e3) (e1)) = (op (e3) (e3)))) -> (((op (e3) (e0)) = (e1))\/(((op (e3) (e1)) = (e1))\/(((op (e3) (e2)) = (e1))\/((op (e3) (e3)) = (e1))))) -> ((op (e3) (e3)) = (e3)) -> (~((op (e2) (e3)) = (op (e3) (e3)))) -> False). % 15.36/15.50 do 0 intro. intros zenon_H27c zenon_H68 zenon_H261 zenon_H6a zenon_H1df zenon_H87 zenon_Ha7 zenon_H119 zenon_H3d zenon_H2f zenon_He6 zenon_Ha3 zenon_Hae zenon_H13c zenon_H104 zenon_H251 zenon_Hd3 zenon_H124 zenon_H5e zenon_H11f zenon_H9e zenon_Hc9 zenon_Hbb zenon_H10f zenon_H140 zenon_H28 zenon_H26e zenon_H16c zenon_H167 zenon_H135 zenon_H109 zenon_H5d zenon_H138 zenon_H12d zenon_H146 zenon_H42 zenon_He3. % 15.36/15.50 apply (zenon_or_s _ _ zenon_H27c); [ zenon_intro zenon_H63 | zenon_intro zenon_H27d ]. % 15.36/15.50 apply (zenon_L638_); trivial. % 15.36/15.50 apply (zenon_or_s _ _ zenon_H27d); [ zenon_intro zenon_H7c | zenon_intro zenon_H27e ]. % 15.36/15.50 apply (zenon_or_s _ _ zenon_He6); [ zenon_intro zenon_Haf | zenon_intro zenon_He7 ]. % 15.36/15.50 apply (zenon_L39_); trivial. % 15.36/15.50 apply (zenon_or_s _ _ zenon_He7); [ zenon_intro zenon_Hdf | zenon_intro zenon_He8 ]. % 15.36/15.50 apply (zenon_L708_); trivial. % 15.36/15.50 apply (zenon_or_s _ _ zenon_He8); [ zenon_intro zenon_H34 | zenon_intro zenon_He2 ]. % 15.36/15.50 apply (zenon_or_s _ _ zenon_H1df); [ zenon_intro zenon_He9 | zenon_intro zenon_H1e0 ]. % 15.36/15.50 apply (zenon_L710_); trivial. % 15.36/15.50 apply (zenon_or_s _ _ zenon_H1e0); [ zenon_intro zenon_H16a | zenon_intro zenon_H1e1 ]. % 15.36/15.50 apply (zenon_L146_); trivial. % 15.36/15.50 apply (zenon_or_s _ _ zenon_H1e1); [ zenon_intro zenon_H1dd | zenon_intro zenon_H43 ]. % 15.36/15.50 apply (zenon_L713_); trivial. % 15.36/15.50 exact (zenon_H3d zenon_H43). % 15.36/15.50 apply (zenon_L98_); trivial. % 15.36/15.50 apply (zenon_or_s _ _ zenon_H27e); [ zenon_intro zenon_H35 | zenon_intro zenon_H1dd ]. % 15.36/15.50 exact (zenon_H2f zenon_H35). % 15.36/15.50 apply (zenon_L714_); trivial. % 15.36/15.50 (* end of lemma zenon_L715_ *) % 15.36/15.50 assert (zenon_L716_ : (((op (e2) (e0)) = (e2))\/(((op (e2) (e1)) = (e2))\/(((op (e2) (e2)) = (e2))\/((op (e2) (e3)) = (e2))))) -> (~((op (e2) (e0)) = (op (e2) (e3)))) -> ((op (e0) (e3)) = (e0)) -> (((op (e0) (e3)) = (e2))\/(((op (e1) (e3)) = (e2))\/(((op (e2) (e3)) = (e2))\/((op (e3) (e3)) = (e2))))) -> (((op (e0) (e2)) = (e2))\/(((op (e1) (e2)) = (e2))\/(((op (e2) (e2)) = (e2))\/((op (e3) (e2)) = (e2))))) -> ((op (e1) (e0)) = (e2)) -> (~((op (e0) (op (e1) (e0))) = (op (e1) (e0)))) -> (~((e2) = (e3))) -> (((op (e3) (e0)) = (e2))\/(((op (e3) (e1)) = (e2))\/(((op (e3) (e2)) = (e2))\/((op (e3) (e3)) = (e2))))) -> (~((op (e0) (e2)) = (op (e1) (e2)))) -> (~((e1) = (e2))) -> ((op (e3) (e2)) = (e1)) -> (~((op (e3) (e3)) = (e2))) -> (~((op (e2) (e2)) = (e2))) -> (((op (e2) (e0)) = (e3))\/(((op (e2) (e1)) = (e3))\/(((op (e2) (e2)) = (e3))\/((op (e2) (e3)) = (e3))))) -> (~((e1) = (e3))) -> ((op (e2) (e0)) = (e1)) -> (~((op (e2) (e1)) = (op (e3) (e1)))) -> (~((op (e3) (e3)) = (e1))) -> (((op (e0) (e2)) = (e0))\/(((op (e0) (e2)) = (e1))\/(((op (e0) (e2)) = (e2))\/((op (e0) (e2)) = (e3))))) -> (((op (e0) (e3)) = (e0))\/(((op (e1) (e3)) = (e0))\/(((op (e2) (e3)) = (e0))\/((op (e3) (e3)) = (e0))))) -> (~((e0) = (e2))) -> ((op (e1) (e3)) = (e1)) -> (~((e0) = (e1))) -> (~((op (e0) (e2)) = (op (e0) (e3)))) -> (~((op (e3) (e0)) = (op (e3) (e3)))) -> ((~((op (e3) (e3)) = (e0)))\/((op (e3) (e0)) = (e3))) -> (~((op (e0) (e2)) = (op (e3) (e2)))) -> (~((op (e0) (e2)) = (op (e2) (e2)))) -> (~((op (e3) (op (e1) (e3))) = (op (e1) (e3)))) -> (((op (e3) (e1)) = (e0))\/(((op (e3) (e1)) = (e1))\/(((op (e3) (e1)) = (e2))\/((op (e3) (e1)) = (e3))))) -> ((op (e3) (e2)) = (e0)) -> (~((op (e3) (e1)) = (op (e3) (e2)))) -> (~((op (e3) (e0)) = (op (e3) (e1)))) -> ((op (e0) (e1)) = (e2)) -> (~((op (e0) (e1)) = (op (e3) (e1)))) -> (~((op (e3) (e1)) = (op (e3) (e3)))) -> (((op (e3) (e0)) = (e1))\/(((op (e3) (e1)) = (e1))\/(((op (e3) (e2)) = (e1))\/((op (e3) (e3)) = (e1))))) -> ((op (e3) (e3)) = (e3)) -> (~((op (e2) (e3)) = (op (e3) (e3)))) -> False). % 15.36/15.50 do 0 intro. intros zenon_H237 zenon_Hce zenon_Hca zenon_H160 zenon_H27c zenon_H68 zenon_H261 zenon_H6a zenon_H1df zenon_H87 zenon_Ha7 zenon_H119 zenon_H3d zenon_H2f zenon_He6 zenon_Ha3 zenon_Hae zenon_H13c zenon_H104 zenon_H251 zenon_Hd3 zenon_H5e zenon_H11f zenon_H9e zenon_Hc9 zenon_Hbb zenon_H10f zenon_H140 zenon_H28 zenon_H26e zenon_H16c zenon_H167 zenon_H135 zenon_H109 zenon_H5d zenon_H138 zenon_H12d zenon_H146 zenon_H42 zenon_He3. % 15.36/15.50 apply (zenon_or_s _ _ zenon_H237); [ zenon_intro zenon_Hdd | zenon_intro zenon_H238 ]. % 15.36/15.50 apply (zenon_L389_); trivial. % 15.36/15.50 apply (zenon_or_s _ _ zenon_H238); [ zenon_intro zenon_H156 | zenon_intro zenon_H239 ]. % 15.36/15.50 apply (zenon_L707_); trivial. % 15.36/15.50 apply (zenon_or_s _ _ zenon_H239); [ zenon_intro zenon_H35 | zenon_intro zenon_H124 ]. % 15.36/15.50 exact (zenon_H2f zenon_H35). % 15.36/15.50 apply (zenon_L715_); trivial. % 15.36/15.50 (* end of lemma zenon_L716_ *) % 15.36/15.50 assert (zenon_L717_ : (((op (e2) (e0)) = (e3))\/(((op (e2) (e1)) = (e3))\/(((op (e2) (e2)) = (e3))\/((op (e2) (e3)) = (e3))))) -> (~((e1) = (e3))) -> ((op (e2) (e0)) = (e1)) -> (~((op (e2) (e1)) = (op (e3) (e1)))) -> (~((op (e0) (e1)) = (op (e3) (e1)))) -> ((op (e0) (e1)) = (e2)) -> (~((op (e3) (e1)) = (op (e3) (e2)))) -> (((op (e3) (e1)) = (e0))\/(((op (e3) (e1)) = (e1))\/(((op (e3) (e1)) = (e2))\/((op (e3) (e1)) = (e3))))) -> (~((op (e0) (e2)) = (op (e2) (e2)))) -> (~((op (e0) (e2)) = (op (e1) (e2)))) -> ((op (e1) (e2)) = (e2)) -> (((op (e3) (e0)) = (e1))\/(((op (e3) (e1)) = (e1))\/(((op (e3) (e2)) = (e1))\/((op (e3) (e3)) = (e1))))) -> (~((e1) = (e2))) -> ((op (e3) (e0)) = (e2)) -> ((op (e1) (e3)) = (e1)) -> (~((op (e3) (op (e1) (e3))) = (op (e1) (e3)))) -> (~((op (e0) (e2)) = (op (e3) (e2)))) -> (~((op (e3) (e3)) = (e1))) -> ((op (e3) (e2)) = (e0)) -> (((op (e0) (e2)) = (e0))\/(((op (e0) (e2)) = (e1))\/(((op (e0) (e2)) = (e2))\/((op (e0) (e2)) = (e3))))) -> ((op (e3) (e3)) = (e3)) -> (~((op (e2) (e3)) = (op (e3) (e3)))) -> False). % 15.36/15.50 do 0 intro. intros zenon_He6 zenon_Ha3 zenon_Hae zenon_H13c zenon_H138 zenon_H5d zenon_H135 zenon_H16c zenon_H28 zenon_H87 zenon_H7c zenon_H146 zenon_Ha7 zenon_He9 zenon_H11f zenon_H26e zenon_H140 zenon_H104 zenon_H167 zenon_H251 zenon_H42 zenon_He3. % 15.36/15.50 apply (zenon_or_s _ _ zenon_He6); [ zenon_intro zenon_Haf | zenon_intro zenon_He7 ]. % 15.36/15.50 apply (zenon_L39_); trivial. % 15.36/15.50 apply (zenon_or_s _ _ zenon_He7); [ zenon_intro zenon_Hdf | zenon_intro zenon_He8 ]. % 15.36/15.50 apply (zenon_L708_); trivial. % 15.36/15.50 apply (zenon_or_s _ _ zenon_He8); [ zenon_intro zenon_H34 | zenon_intro zenon_He2 ]. % 15.36/15.50 apply (zenon_L710_); trivial. % 15.36/15.50 apply (zenon_L66_); trivial. % 15.36/15.50 (* end of lemma zenon_L717_ *) % 15.36/15.50 assert (zenon_L718_ : (((op (e0) (e2)) = (e0))\/(((op (e1) (e2)) = (e0))\/(((op (e2) (e2)) = (e0))\/((op (e3) (e2)) = (e0))))) -> ((op (e0) (e3)) = (e0)) -> (~((op (e0) (e2)) = (op (e0) (e3)))) -> ((op (e1) (e0)) = (e0)) -> (~((op (e1) (e0)) = (op (e1) (e2)))) -> (~((op (e2) (e2)) = (e0))) -> (((op (e2) (e0)) = (e3))\/(((op (e2) (e1)) = (e3))\/(((op (e2) (e2)) = (e3))\/((op (e2) (e3)) = (e3))))) -> (~((e1) = (e3))) -> ((op (e2) (e0)) = (e1)) -> (~((op (e2) (e1)) = (op (e3) (e1)))) -> (~((op (e0) (e1)) = (op (e3) (e1)))) -> ((op (e0) (e1)) = (e2)) -> (~((op (e3) (e1)) = (op (e3) (e2)))) -> (((op (e3) (e1)) = (e0))\/(((op (e3) (e1)) = (e1))\/(((op (e3) (e1)) = (e2))\/((op (e3) (e1)) = (e3))))) -> (~((op (e0) (e2)) = (op (e2) (e2)))) -> (~((op (e0) (e2)) = (op (e1) (e2)))) -> ((op (e1) (e2)) = (e2)) -> (((op (e3) (e0)) = (e1))\/(((op (e3) (e1)) = (e1))\/(((op (e3) (e2)) = (e1))\/((op (e3) (e3)) = (e1))))) -> (~((e1) = (e2))) -> ((op (e3) (e0)) = (e2)) -> ((op (e1) (e3)) = (e1)) -> (~((op (e3) (op (e1) (e3))) = (op (e1) (e3)))) -> (~((op (e0) (e2)) = (op (e3) (e2)))) -> (~((op (e3) (e3)) = (e1))) -> (((op (e0) (e2)) = (e0))\/(((op (e0) (e2)) = (e1))\/(((op (e0) (e2)) = (e2))\/((op (e0) (e2)) = (e3))))) -> ((op (e3) (e3)) = (e3)) -> (~((op (e2) (e3)) = (op (e3) (e3)))) -> False). % 15.36/15.50 do 0 intro. intros zenon_H16f zenon_Hca zenon_Hc9 zenon_Had zenon_H166 zenon_H2e zenon_He6 zenon_Ha3 zenon_Hae zenon_H13c zenon_H138 zenon_H5d zenon_H135 zenon_H16c zenon_H28 zenon_H87 zenon_H7c zenon_H146 zenon_Ha7 zenon_He9 zenon_H11f zenon_H26e zenon_H140 zenon_H104 zenon_H251 zenon_H42 zenon_He3. % 15.36/15.50 apply (zenon_or_s _ _ zenon_H16f); [ zenon_intro zenon_Hab | zenon_intro zenon_H170 ]. % 15.36/15.50 apply (zenon_L53_); trivial. % 15.36/15.50 apply (zenon_or_s _ _ zenon_H170); [ zenon_intro zenon_H15d | zenon_intro zenon_H171 ]. % 15.36/15.50 apply (zenon_L143_); trivial. % 15.36/15.50 apply (zenon_or_s _ _ zenon_H171); [ zenon_intro zenon_H32 | zenon_intro zenon_H167 ]. % 15.36/15.50 exact (zenon_H2e zenon_H32). % 15.36/15.50 apply (zenon_L717_); trivial. % 15.36/15.50 (* end of lemma zenon_L718_ *) % 15.36/15.50 assert (zenon_L719_ : (~((op (e2) (op (e1) (e2))) = (op (e2) (e0)))) -> ((op (e1) (e2)) = (e0)) -> False). % 15.36/15.50 do 0 intro. intros zenon_H27f zenon_H15d. % 15.36/15.50 cut (((op (e1) (e2)) = (e0))); [idtac | apply NNPP; zenon_intro zenon_H240]. % 15.36/15.50 cut (((e2) = (e2))); [idtac | apply NNPP; zenon_intro zenon_H60]. % 15.36/15.50 congruence. % 15.36/15.50 apply zenon_H60. apply refl_equal. % 15.36/15.50 exact (zenon_H240 zenon_H15d). % 15.36/15.50 (* end of lemma zenon_L719_ *) % 15.36/15.50 assert (zenon_L720_ : (~((op (e2) (op (e1) (e2))) = (op (e1) (e2)))) -> ((op (e2) (e0)) = (e0)) -> ((op (e1) (e2)) = (e0)) -> False). % 15.36/15.50 do 0 intro. intros zenon_H277 zenon_Hcf zenon_H15d. % 15.36/15.50 cut (((op (e2) (e0)) = (e0)) = ((op (e2) (op (e1) (e2))) = (op (e1) (e2)))). % 15.36/15.50 intro zenon_D_pnotp. % 15.36/15.50 apply zenon_H277. % 15.36/15.50 rewrite <- zenon_D_pnotp. % 15.36/15.50 exact zenon_Hcf. % 15.36/15.50 cut (((e0) = (op (e1) (e2)))); [idtac | apply NNPP; zenon_intro zenon_H15e]. % 15.36/15.50 cut (((op (e2) (e0)) = (op (e2) (op (e1) (e2))))); [idtac | apply NNPP; zenon_intro zenon_H280]. % 15.36/15.50 congruence. % 15.36/15.50 elim (classic ((op (e2) (op (e1) (e2))) = (op (e2) (op (e1) (e2))))); [ zenon_intro zenon_H279 | zenon_intro zenon_H27a ]. % 15.36/15.50 cut (((op (e2) (op (e1) (e2))) = (op (e2) (op (e1) (e2)))) = ((op (e2) (e0)) = (op (e2) (op (e1) (e2))))). % 15.36/15.50 intro zenon_D_pnotp. % 15.36/15.50 apply zenon_H280. % 15.36/15.50 rewrite <- zenon_D_pnotp. % 15.36/15.50 exact zenon_H279. % 15.36/15.50 cut (((op (e2) (op (e1) (e2))) = (op (e2) (op (e1) (e2))))); [idtac | apply NNPP; zenon_intro zenon_H27a]. % 15.36/15.50 cut (((op (e2) (op (e1) (e2))) = (op (e2) (e0)))); [idtac | apply NNPP; zenon_intro zenon_H27f]. % 15.36/15.50 congruence. % 15.36/15.50 apply (zenon_L719_); trivial. % 15.36/15.50 apply zenon_H27a. apply refl_equal. % 15.36/15.50 apply zenon_H27a. apply refl_equal. % 15.36/15.50 apply zenon_H15e. apply sym_equal. exact zenon_H15d. % 15.36/15.50 (* end of lemma zenon_L720_ *) % 15.36/15.50 assert (zenon_L721_ : (((op (e0) (e1)) = (e0))\/(((op (e1) (e1)) = (e0))\/(((op (e2) (e1)) = (e0))\/((op (e3) (e1)) = (e0))))) -> (~((e0) = (e2))) -> ((op (e0) (e1)) = (e2)) -> (~((op (e1) (e1)) = (e0))) -> (~((op (e2) (e0)) = (op (e2) (e1)))) -> (((op (e0) (e2)) = (e0))\/(((op (e1) (e2)) = (e0))\/(((op (e2) (e2)) = (e0))\/((op (e3) (e2)) = (e0))))) -> (~((e0) = (e1))) -> ((op (e0) (e2)) = (e1)) -> ((op (e2) (e0)) = (e0)) -> (~((op (e2) (op (e1) (e2))) = (op (e1) (e2)))) -> (~((op (e2) (e2)) = (e0))) -> (~((op (e3) (e1)) = (op (e3) (e2)))) -> False). % 15.36/15.50 do 0 intro. intros zenon_H144 zenon_H5e zenon_H5d zenon_H145 zenon_H154 zenon_H16f zenon_H9e zenon_H29 zenon_Hcf zenon_H277 zenon_H2e zenon_H135. % 15.36/15.50 apply (zenon_or_s _ _ zenon_H144); [ zenon_intro zenon_H49 | zenon_intro zenon_H147 ]. % 15.36/15.50 apply (zenon_L14_); trivial. % 15.36/15.50 apply (zenon_or_s _ _ zenon_H147); [ zenon_intro zenon_H149 | zenon_intro zenon_H148 ]. % 15.36/15.50 exact (zenon_H145 zenon_H149). % 15.36/15.50 apply (zenon_or_s _ _ zenon_H148); [ zenon_intro zenon_H14a | zenon_intro zenon_H142 ]. % 15.36/15.50 apply (zenon_L133_); trivial. % 15.36/15.50 apply (zenon_or_s _ _ zenon_H16f); [ zenon_intro zenon_Hab | zenon_intro zenon_H170 ]. % 15.36/15.50 apply (zenon_L37_); trivial. % 15.36/15.50 apply (zenon_or_s _ _ zenon_H170); [ zenon_intro zenon_H15d | zenon_intro zenon_H171 ]. % 15.36/15.50 apply (zenon_L720_); trivial. % 15.36/15.50 apply (zenon_or_s _ _ zenon_H171); [ zenon_intro zenon_H32 | zenon_intro zenon_H167 ]. % 15.36/15.50 exact (zenon_H2e zenon_H32). % 15.36/15.50 apply (zenon_L144_); trivial. % 15.36/15.50 (* end of lemma zenon_L721_ *) % 15.36/15.50 assert (zenon_L722_ : (((op (e0) (e0)) = (e2))\/(((op (e0) (e1)) = (e2))\/(((op (e0) (e2)) = (e2))\/((op (e0) (e3)) = (e2))))) -> (~((op (e0) (e0)) = (e2))) -> (~((op (e3) (e1)) = (op (e3) (e2)))) -> (~((op (e2) (e2)) = (e0))) -> (~((op (e2) (op (e1) (e2))) = (op (e1) (e2)))) -> (((op (e0) (e2)) = (e0))\/(((op (e1) (e2)) = (e0))\/(((op (e2) (e2)) = (e0))\/((op (e3) (e2)) = (e0))))) -> (~((op (e2) (e0)) = (op (e2) (e1)))) -> (~((op (e1) (e1)) = (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))\/(((op (e1) (e3)) = (e0))\/(((op (e2) (e3)) = (e0))\/((op (e3) (e3)) = (e0))))) -> (~((e0) = (e2))) -> ((op (e1) (e3)) = (e1)) -> (~((e0) = (e1))) -> ((op (e2) (e0)) = (e0)) -> (~((op (e2) (e0)) = (op (e2) (e3)))) -> (~((op (e3) (e3)) = (e0))) -> False). % 15.36/15.50 do 0 intro. intros zenon_H8e zenon_H8f zenon_H135 zenon_H2e zenon_H277 zenon_H16f zenon_H154 zenon_H145 zenon_H144 zenon_Ha7 zenon_H29 zenon_Hd3 zenon_H5e zenon_H11f zenon_H9e zenon_Hcf zenon_Hce zenon_H3c. % 15.36/15.50 apply (zenon_or_s _ _ zenon_H8e); [ zenon_intro zenon_H92 | zenon_intro zenon_H91 ]. % 15.36/15.50 exact (zenon_H8f zenon_H92). % 15.36/15.50 apply (zenon_or_s _ _ zenon_H91); [ zenon_intro zenon_H5d | zenon_intro zenon_H93 ]. % 15.36/15.50 apply (zenon_L721_); trivial. % 15.36/15.50 apply (zenon_or_s _ _ zenon_H93); [ zenon_intro zenon_H63 | zenon_intro zenon_H81 ]. % 15.36/15.50 apply (zenon_L104_); trivial. % 15.36/15.50 apply (zenon_L373_); trivial. % 15.36/15.50 (* end of lemma zenon_L722_ *) % 15.36/15.50 assert (zenon_L723_ : (((op (e0) (e2)) = (e0))\/(((op (e1) (e2)) = (e0))\/(((op (e2) (e2)) = (e0))\/((op (e3) (e2)) = (e0))))) -> ((~((op (e1) (e1)) = (e0)))\/((op (e1) (e0)) = (e1))) -> (~((op (e1) (e0)) = (op (e1) (e2)))) -> (~((op (e0) (e3)) = (op (e1) (e3)))) -> (~((op (e1) (e0)) = (op (e1) (e1)))) -> ((~((op (e1) (e1)) = (e2)))\/((op (e1) (e2)) = (e1))) -> (~((op (e1) (e2)) = (op (e1) (e3)))) -> ((~((op (e2) (e2)) = (e0)))\/((op (e2) (e0)) = (e2))) -> ((~((op (e3) (e3)) = (e1)))\/((op (e3) (e1)) = (e3))) -> (~((op (e3) (e1)) = (op (e3) (e3)))) -> (~((op (e0) (e1)) = (op (e0) (e3)))) -> (~((op (e1) (e0)) = (op (e1) (e3)))) -> (((op (e0) (e3)) = (e1))\/(((op (e1) (e3)) = (e1))\/(((op (e2) (e3)) = (e1))\/((op (e3) (e3)) = (e1))))) -> (~((op (e2) (e0)) = (op (e2) (e3)))) -> (((op (e0) (e0)) = (e1))\/(((op (e1) (e0)) = (e1))\/(((op (e2) (e0)) = (e1))\/((op (e3) (e0)) = (e1))))) -> ((~((op (e3) (e3)) = (e2)))\/((op (e3) (e2)) = (e3))) -> (~((op (e0) (e0)) = (e1))) -> (((op (e0) (e0)) = (e3))\/(((op (e0) (e1)) = (e3))\/(((op (e0) (e2)) = (e3))\/((op (e0) (e3)) = (e3))))) -> ((op (e3) (e3)) = (e3)) -> (~((op (e0) (e3)) = (op (e3) (e3)))) -> (~((e0) = (e3))) -> (~((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 (e0) (e1)) = (op (e2) (e1)))) -> (~((op (e2) (e3)) = (op (e3) (e3)))) -> (((op (e2) (e0)) = (e3))\/(((op (e2) (e1)) = (e3))\/(((op (e2) (e2)) = (e3))\/((op (e2) (e3)) = (e3))))) -> (((op (e0) (e0)) = (e3))\/(((op (e1) (e0)) = (e3))\/(((op (e2) (e0)) = (e3))\/((op (e3) (e0)) = (e3))))) -> (~((op (e0) (e2)) = (op (e1) (e2)))) -> (((op (e0) (e0)) = (e2))\/(((op (e1) (e0)) = (e2))\/(((op (e2) (e0)) = (e2))\/((op (e3) (e0)) = (e2))))) -> (~((op (e0) (e1)) = (op (e1) (e1)))) -> (((op (e1) (e0)) = (e3))\/(((op (e1) (e1)) = (e3))\/(((op (e1) (e2)) = (e3))\/((op (e1) (e3)) = (e3))))) -> (~((op (e1) (e3)) = (op (e3) (e3)))) -> (((op (e1) (e1)) = (e0))\/(((op (e1) (e1)) = (e1))\/(((op (e1) (e1)) = (e2))\/((op (e1) (e1)) = (e3))))) -> ((~((op (e2) (e2)) = (e3)))\/((op (e2) (e3)) = (e2))) -> (((op (e1) (e0)) = (e2))\/(((op (e1) (e1)) = (e2))\/(((op (e1) (e2)) = (e2))\/((op (e1) (e3)) = (e2))))) -> (~((e1) = (e2))) -> (((op (e0) (e3)) = (e0))\/(((op (e1) (e3)) = (e0))\/(((op (e2) (e3)) = (e0))\/((op (e3) (e3)) = (e0))))) -> (~((e0) = (e2))) -> (~((op (e0) (e2)) = (op (e0) (e3)))) -> (~((e2) = (e3))) -> (~((op (e3) (e0)) = (op (e3) (e3)))) -> ((~((op (e3) (e3)) = (e0)))\/((op (e3) (e0)) = (e3))) -> (~((op (e3) (e2)) = (op (e3) (e3)))) -> (((op (e0) (e2)) = (e3))\/(((op (e1) (e2)) = (e3))\/(((op (e2) (e2)) = (e3))\/((op (e3) (e2)) = (e3))))) -> (((op (e0) (e3)) = (e2))\/(((op (e1) (e3)) = (e2))\/(((op (e2) (e3)) = (e2))\/((op (e3) (e3)) = (e2))))) -> (~((e0) = (e1))) -> (((op (e1) (e0)) = (e1))\/(((op (e1) (e1)) = (e1))\/(((op (e1) (e2)) = (e1))\/((op (e1) (e3)) = (e1))))) -> (((op (e0) (e0)) = (e1))\/(((op (e0) (e1)) = (e1))\/(((op (e0) (e2)) = (e1))\/((op (e0) (e3)) = (e1))))) -> ((~((op (e2) (e2)) = (e2)))\/((op (e2) (e2)) = (e2))) -> ((~((op (e1) (e1)) = (e3)))\/((op (e1) (e3)) = (e1))) -> (~((op (e1) (op (e1) (e1))) = (op (e1) (e1)))) -> ((~((op (e1) (e1)) = (e1)))\/((op (e1) (e1)) = (e1))) -> ((~((op (e0) (e0)) = (e3)))\/((op (e0) (e3)) = (e0))) -> (~((op (e2) (e2)) = (e3))) -> (~((op (e2) (e2)) = (e2))) -> (~((op (e2) (e2)) = (e1))) -> (~((op (e1) (e2)) = (op (e2) (e2)))) -> (((op (e2) (e2)) = (e0))\/(((op (e2) (e2)) = (e1))\/(((op (e2) (e2)) = (e2))\/((op (e2) (e2)) = (e3))))) -> (~((op (e2) (e2)) = (e0))) -> (~((op (e3) (e0)) = (op (e3) (e2)))) -> ((op (e3) (e0)) = (e0)) -> False). % 15.36/15.50 do 0 intro. intros zenon_H16f zenon_H1e4 zenon_H166 zenon_H80 zenon_Hd7 zenon_H1d3 zenon_H1d0 zenon_H1d4 zenon_H10c zenon_H12d zenon_H1cd zenon_H1cf zenon_H121 zenon_Hce zenon_Hf1 zenon_H10e zenon_H45 zenon_H58 zenon_H42 zenon_H36 zenon_H4b zenon_Ha3 zenon_H28 zenon_H8e zenon_Hde zenon_He3 zenon_He6 zenon_Hbe zenon_H87 zenon_Heb zenon_H23 zenon_H90 zenon_H8b zenon_H1b3 zenon_H1c3 zenon_H84 zenon_Ha7 zenon_Hd3 zenon_H5e zenon_Hc9 zenon_H6a zenon_Hbb zenon_H10f zenon_H173 zenon_H175 zenon_H160 zenon_H9e zenon_H1c5 zenon_H44 zenon_Haa zenon_H1d2 zenon_H27b zenon_H1d8 zenon_H236 zenon_H30 zenon_H2f zenon_H52 zenon_H7d zenon_H2d zenon_H2e zenon_H105 zenon_Hdb. % 15.36/15.50 apply (zenon_or_s _ _ zenon_H16f); [ zenon_intro zenon_Hab | zenon_intro zenon_H170 ]. % 15.36/15.50 apply (zenon_L700_); trivial. % 15.36/15.50 apply (zenon_or_s _ _ zenon_H170); [ zenon_intro zenon_H15d | zenon_intro zenon_H171 ]. % 15.36/15.50 apply (zenon_L335_); trivial. % 15.36/15.50 apply (zenon_or_s _ _ zenon_H171); [ zenon_intro zenon_H32 | zenon_intro zenon_H167 ]. % 15.36/15.50 exact (zenon_H2e zenon_H32). % 15.36/15.50 apply (zenon_L156_); trivial. % 15.36/15.50 (* end of lemma zenon_L723_ *) % 15.36/15.50 assert (zenon_L724_ : (~((op (e0) (e0)) = (e0))) -> (((op (e0) (e0)) = (e3))\/(((op (e0) (e1)) = (e3))\/(((op (e0) (e2)) = (e3))\/((op (e0) (e3)) = (e3))))) -> ((op (e3) (e3)) = (e3)) -> (~((op (e0) (e3)) = (op (e3) (e3)))) -> (~((op (e2) (e2)) = (e0))) -> (~((op (e0) (e2)) = (op (e2) (e2)))) -> (~((e1) = (e3))) -> (~((e0) = (e1))) -> ((op (e0) (e3)) = (e0)) -> (~((op (e1) (e0)) = (op (e1) (e3)))) -> (((op (e2) (e2)) = (e0))\/(((op (e2) (e2)) = (e1))\/(((op (e2) (e2)) = (e2))\/((op (e2) (e2)) = (e3))))) -> (~((op (e2) (e2)) = (e3))) -> (~((op (e2) (e2)) = (e2))) -> (~((op (e2) (e2)) = (e1))) -> (~((op (e3) (e3)) = (e1))) -> (((op (e0) (e3)) = (e1))\/(((op (e1) (e3)) = (e1))\/(((op (e2) (e3)) = (e1))\/((op (e3) (e3)) = (e1))))) -> (((op (e3) (e0)) = (e1))\/(((op (e3) (e1)) = (e1))\/(((op (e3) (e2)) = (e1))\/((op (e3) (e3)) = (e1))))) -> (~((op (e0) (e2)) = (op (e3) (e2)))) -> ((op (e1) (e3)) = (e1)) -> (~((op (e3) (op (e1) (e3))) = (op (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 (e3) (e0)) = (op (e3) (e1)))) -> (~((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)) = (e1)))\/((op (e2) (e1)) = (e2))) -> (((op (e0) (e1)) = (e0))\/(((op (e1) (e1)) = (e0))\/(((op (e2) (e1)) = (e0))\/((op (e3) (e1)) = (e0))))) -> (((op (e0) (e1)) = (e3))\/(((op (e1) (e1)) = (e3))\/(((op (e2) (e1)) = (e3))\/((op (e3) (e1)) = (e3))))) -> (~((op (e1) (e1)) = (e1))) -> (~((op (e1) (e1)) = (e0))) -> (((op (e2) (e0)) = (e1))\/(((op (e2) (e1)) = (e1))\/(((op (e2) (e2)) = (e1))\/((op (e2) (e3)) = (e1))))) -> (~((op (e2) (e0)) = (op (e2) (e1)))) -> (((op (e2) (e0)) = (e2))\/(((op (e2) (e1)) = (e2))\/(((op (e2) (e2)) = (e2))\/((op (e2) (e3)) = (e2))))) -> (~((op (e0) (op (e1) (e0))) = (op (e1) (e0)))) -> (((op (e0) (e2)) = (e0))\/(((op (e0) (e2)) = (e1))\/(((op (e0) (e2)) = (e2))\/((op (e0) (e2)) = (e3))))) -> (((op (e3) (e0)) = (e2))\/(((op (e3) (e1)) = (e2))\/(((op (e3) (e2)) = (e2))\/((op (e3) (e3)) = (e2))))) -> (((op (e0) (e2)) = (e2))\/(((op (e1) (e2)) = (e2))\/(((op (e2) (e2)) = (e2))\/((op (e3) (e2)) = (e2))))) -> (~((op (e2) (e1)) = (op (e3) (e1)))) -> (((op (e0) (e2)) = (e1))\/(((op (e1) (e2)) = (e1))\/(((op (e2) (e2)) = (e1))\/((op (e3) (e2)) = (e1))))) -> ((~((op (e1) (e1)) = (e0)))\/((op (e1) (e0)) = (e1))) -> (~((op (e1) (e0)) = (op (e1) (e2)))) -> (~((op (e0) (e3)) = (op (e1) (e3)))) -> (~((op (e1) (e2)) = (op (e2) (e2)))) -> (~((op (e1) (e0)) = (op (e1) (e1)))) -> ((~((op (e1) (e1)) = (e2)))\/((op (e1) (e2)) = (e1))) -> (~((op (e1) (e2)) = (op (e1) (e3)))) -> ((~((op (e2) (e2)) = (e0)))\/((op (e2) (e0)) = (e2))) -> ((~((op (e3) (e3)) = (e1)))\/((op (e3) (e1)) = (e3))) -> (~((op (e3) (e1)) = (op (e3) (e3)))) -> (~((op (e0) (e1)) = (op (e0) (e3)))) -> (~((op (e2) (e0)) = (op (e2) (e3)))) -> (((op (e0) (e0)) = (e1))\/(((op (e1) (e0)) = (e1))\/(((op (e2) (e0)) = (e1))\/((op (e3) (e0)) = (e1))))) -> ((~((op (e3) (e3)) = (e2)))\/((op (e3) (e2)) = (e3))) -> (~((e0) = (e3))) -> (((op (e0) (e0)) = (e2))\/(((op (e0) (e1)) = (e2))\/(((op (e0) (e2)) = (e2))\/((op (e0) (e3)) = (e2))))) -> (~((op (e0) (e1)) = (op (e2) (e1)))) -> (~((op (e2) (e3)) = (op (e3) (e3)))) -> (((op (e2) (e0)) = (e3))\/(((op (e2) (e1)) = (e3))\/(((op (e2) (e2)) = (e3))\/((op (e2) (e3)) = (e3))))) -> (((op (e0) (e0)) = (e3))\/(((op (e1) (e0)) = (e3))\/(((op (e2) (e0)) = (e3))\/((op (e3) (e0)) = (e3))))) -> (~((op (e0) (e2)) = (op (e1) (e2)))) -> (((op (e0) (e0)) = (e2))\/(((op (e1) (e0)) = (e2))\/(((op (e2) (e0)) = (e2))\/((op (e3) (e0)) = (e2))))) -> (~((op (e0) (e1)) = (op (e1) (e1)))) -> (((op (e1) (e0)) = (e3))\/(((op (e1) (e1)) = (e3))\/(((op (e1) (e2)) = (e3))\/((op (e1) (e3)) = (e3))))) -> (~((op (e1) (e3)) = (op (e3) (e3)))) -> (((op (e1) (e1)) = (e0))\/(((op (e1) (e1)) = (e1))\/(((op (e1) (e1)) = (e2))\/((op (e1) (e1)) = (e3))))) -> ((~((op (e2) (e2)) = (e3)))\/((op (e2) (e3)) = (e2))) -> (((op (e1) (e0)) = (e2))\/(((op (e1) (e1)) = (e2))\/(((op (e1) (e2)) = (e2))\/((op (e1) (e3)) = (e2))))) -> (~((e1) = (e2))) -> (((op (e0) (e3)) = (e0))\/(((op (e1) (e3)) = (e0))\/(((op (e2) (e3)) = (e0))\/((op (e3) (e3)) = (e0))))) -> (~((e0) = (e2))) -> (~((op (e0) (e2)) = (op (e0) (e3)))) -> (~((e2) = (e3))) -> (~((op (e3) (e0)) = (op (e3) (e3)))) -> ((~((op (e3) (e3)) = (e0)))\/((op (e3) (e0)) = (e3))) -> (~((op (e3) (e2)) = (op (e3) (e3)))) -> (((op (e0) (e2)) = (e3))\/(((op (e1) (e2)) = (e3))\/(((op (e2) (e2)) = (e3))\/((op (e3) (e2)) = (e3))))) -> (((op (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 (e0) (e0)) = (e1))\/(((op (e0) (e1)) = (e1))\/(((op (e0) (e2)) = (e1))\/((op (e0) (e3)) = (e1))))) -> ((~((op (e2) (e2)) = (e2)))\/((op (e2) (e2)) = (e2))) -> ((~((op (e1) (e1)) = (e3)))\/((op (e1) (e3)) = (e1))) -> (~((op (e1) (op (e1) (e1))) = (op (e1) (e1)))) -> ((~((op (e1) (e1)) = (e1)))\/((op (e1) (e1)) = (e1))) -> ((~((op (e0) (e0)) = (e3)))\/((op (e0) (e3)) = (e0))) -> (~((op (e1) (e1)) = (e2))) -> (~((op (e0) (e0)) = (e2))) -> (~((op (e0) (e0)) = (e1))) -> (~((op (e2) (op (e1) (e2))) = (op (e1) (e2)))) -> (~((op (e3) (e3)) = (e0))) -> (((op (e1) (e0)) = (e0))\/(((op (e1) (e1)) = (e0))\/(((op (e1) (e2)) = (e0))\/((op (e1) (e3)) = (e0))))) -> (~((op (e3) (e0)) = (op (e3) (e2)))) -> (((op (e0) (e0)) = (e0))\/(((op (e1) (e0)) = (e0))\/(((op (e2) (e0)) = (e0))\/((op (e3) (e0)) = (e0))))) -> False). % 15.36/15.50 do 0 intro. intros zenon_H20 zenon_H58 zenon_H42 zenon_H36 zenon_H2e zenon_H28 zenon_Ha3 zenon_H9e zenon_Hca zenon_H1cf zenon_H2d zenon_H30 zenon_H2f zenon_H52 zenon_H104 zenon_H121 zenon_H146 zenon_H140 zenon_H11f zenon_H26e zenon_H16c zenon_H138 zenon_H109 zenon_H135 zenon_H16f zenon_H1e3 zenon_H144 zenon_H199 zenon_H1b4 zenon_H145 zenon_Hb7 zenon_H154 zenon_H237 zenon_H261 zenon_H251 zenon_H1df zenon_H27c zenon_H13c zenon_H11b zenon_H1e4 zenon_H166 zenon_H80 zenon_H7d zenon_Hd7 zenon_H1d3 zenon_H1d0 zenon_H1d4 zenon_H10c zenon_H12d zenon_H1cd zenon_Hce zenon_Hf1 zenon_H10e zenon_H4b zenon_H8e zenon_Hde zenon_He3 zenon_He6 zenon_Hbe zenon_H87 zenon_Heb zenon_H23 zenon_H90 zenon_H8b zenon_H1b3 zenon_H1c3 zenon_H84 zenon_Ha7 zenon_Hd3 zenon_H5e zenon_Hc9 zenon_H6a zenon_Hbb zenon_H10f zenon_H173 zenon_H175 zenon_H160 zenon_H1c5 zenon_H44 zenon_Haa zenon_H1d2 zenon_H27b zenon_H1d8 zenon_H236 zenon_Hd6 zenon_H8f zenon_H45 zenon_H277 zenon_H3c zenon_H163 zenon_H105 zenon_Hf0. % 15.36/15.50 apply (zenon_or_s _ _ zenon_H10e); [ zenon_intro zenon_H3d | zenon_intro zenon_H106 ]. % 15.36/15.50 apply (zenon_or_s _ _ zenon_Hf0); [ zenon_intro zenon_H1f | zenon_intro zenon_Hf2 ]. % 15.36/15.50 exact (zenon_H20 zenon_H1f). % 15.36/15.50 apply (zenon_or_s _ _ zenon_Hf2); [ zenon_intro zenon_Had | zenon_intro zenon_Hf3 ]. % 15.36/15.50 apply (zenon_or_s _ _ zenon_H44); [ zenon_intro zenon_H47 | zenon_intro zenon_H46 ]. % 15.36/15.50 exact (zenon_H45 zenon_H47). % 15.36/15.50 apply (zenon_or_s _ _ zenon_H46); [ zenon_intro zenon_H22 | zenon_intro zenon_H48 ]. % 15.36/15.50 apply (zenon_or_s _ _ zenon_Hf1); [ zenon_intro zenon_H47 | zenon_intro zenon_Hf4 ]. % 15.36/15.50 exact (zenon_H45 zenon_H47). % 15.36/15.50 apply (zenon_or_s _ _ zenon_Hf4); [ zenon_intro zenon_Hd8 | zenon_intro zenon_Hf5 ]. % 15.36/15.50 apply (zenon_L331_); trivial. % 15.36/15.50 apply (zenon_or_s _ _ zenon_Hf5); [ zenon_intro zenon_Hae | zenon_intro zenon_Hee ]. % 15.36/15.50 apply (zenon_or_s _ _ zenon_H8e); [ zenon_intro zenon_H92 | zenon_intro zenon_H91 ]. % 15.36/15.50 exact (zenon_H8f zenon_H92). % 15.36/15.50 apply (zenon_or_s _ _ zenon_H91); [ zenon_intro zenon_H5d | zenon_intro zenon_H93 ]. % 15.36/15.50 apply (zenon_or_s _ _ zenon_Heb); [ zenon_intro zenon_H92 | zenon_intro zenon_Hec ]. % 15.36/15.50 exact (zenon_H8f zenon_H92). % 15.36/15.50 apply (zenon_or_s _ _ zenon_Hec); [ zenon_intro zenon_H68 | zenon_intro zenon_Hed ]. % 15.36/15.50 apply (zenon_or_s _ _ zenon_H16f); [ zenon_intro zenon_Hab | zenon_intro zenon_H170 ]. % 15.36/15.50 apply (zenon_L700_); trivial. % 15.36/15.50 apply (zenon_or_s _ _ zenon_H170); [ zenon_intro zenon_H15d | zenon_intro zenon_H171 ]. % 15.36/15.50 apply (zenon_L143_); trivial. % 15.36/15.50 apply (zenon_or_s _ _ zenon_H171); [ zenon_intro zenon_H32 | zenon_intro zenon_H167 ]. % 15.36/15.50 exact (zenon_H2e zenon_H32). % 15.36/15.50 apply (zenon_or_s _ _ zenon_H11b); [ zenon_intro zenon_H29 | zenon_intro zenon_H11c ]. % 15.36/15.50 apply (zenon_L706_); trivial. % 15.36/15.50 apply (zenon_or_s _ _ zenon_H11c); [ zenon_intro zenon_H117 | zenon_intro zenon_H11d ]. % 15.36/15.50 apply (zenon_L453_); trivial. % 15.36/15.50 apply (zenon_or_s _ _ zenon_H11d); [ zenon_intro zenon_H2a | zenon_intro zenon_H119 ]. % 15.36/15.50 exact (zenon_H52 zenon_H2a). % 15.36/15.50 apply (zenon_L716_); trivial. % 15.36/15.50 apply (zenon_or_s _ _ zenon_Hed); [ zenon_intro zenon_Hdd | zenon_intro zenon_He9 ]. % 15.36/15.50 apply (zenon_L389_); trivial. % 15.36/15.50 apply (zenon_or_s _ _ zenon_H84); [ zenon_intro zenon_H68 | zenon_intro zenon_H85 ]. % 15.36/15.50 apply (zenon_or_s _ _ zenon_H16f); [ zenon_intro zenon_Hab | zenon_intro zenon_H170 ]. % 15.36/15.50 apply (zenon_L700_); trivial. % 15.36/15.50 apply (zenon_or_s _ _ zenon_H170); [ zenon_intro zenon_H15d | zenon_intro zenon_H171 ]. % 15.36/15.50 apply (zenon_L143_); trivial. % 15.36/15.50 apply (zenon_or_s _ _ zenon_H171); [ zenon_intro zenon_H32 | zenon_intro zenon_H167 ]. % 15.36/15.50 exact (zenon_H2e zenon_H32). % 15.36/15.50 apply (zenon_or_s _ _ zenon_H11b); [ zenon_intro zenon_H29 | zenon_intro zenon_H11c ]. % 15.36/15.50 apply (zenon_L709_); trivial. % 15.36/15.50 apply (zenon_or_s _ _ zenon_H11c); [ zenon_intro zenon_H117 | zenon_intro zenon_H11d ]. % 15.36/15.50 apply (zenon_L453_); trivial. % 15.36/15.50 apply (zenon_or_s _ _ zenon_H11d); [ zenon_intro zenon_H2a | zenon_intro zenon_H119 ]. % 15.36/15.50 exact (zenon_H52 zenon_H2a). % 15.36/15.50 apply (zenon_L716_); trivial. % 15.36/15.50 apply (zenon_or_s _ _ zenon_H85); [ zenon_intro zenon_H6e | zenon_intro zenon_H86 ]. % 15.36/15.50 exact (zenon_Hd6 zenon_H6e). % 15.36/15.50 apply (zenon_or_s _ _ zenon_H86); [ zenon_intro zenon_H7c | zenon_intro zenon_H82 ]. % 15.36/15.50 apply (zenon_L718_); trivial. % 15.36/15.50 apply (zenon_L209_); trivial. % 15.36/15.50 apply (zenon_or_s _ _ zenon_H93); [ zenon_intro zenon_H63 | zenon_intro zenon_H81 ]. % 15.36/15.50 apply (zenon_L676_); trivial. % 15.36/15.50 apply (zenon_L113_); trivial. % 15.36/15.50 apply (zenon_or_s _ _ zenon_H8e); [ zenon_intro zenon_H92 | zenon_intro zenon_H91 ]. % 15.36/15.50 exact (zenon_H8f zenon_H92). % 15.36/15.50 apply (zenon_or_s _ _ zenon_H91); [ zenon_intro zenon_H5d | zenon_intro zenon_H93 ]. % 15.36/15.50 apply (zenon_L701_); trivial. % 15.36/15.50 apply (zenon_or_s _ _ zenon_H93); [ zenon_intro zenon_H63 | zenon_intro zenon_H81 ]. % 15.36/15.50 apply (zenon_L697_); trivial. % 15.36/15.50 apply (zenon_L113_); trivial. % 15.36/15.50 apply (zenon_or_s _ _ zenon_H48); [ zenon_intro zenon_H29 | zenon_intro zenon_H37 ]. % 15.36/15.50 apply (zenon_L5_); trivial. % 15.36/15.50 apply (zenon_L73_); trivial. % 15.36/15.50 apply (zenon_or_s _ _ zenon_Hf3); [ zenon_intro zenon_Hcf | zenon_intro zenon_Hdb ]. % 15.36/15.50 apply (zenon_or_s _ _ zenon_H44); [ zenon_intro zenon_H47 | zenon_intro zenon_H46 ]. % 15.36/15.50 exact (zenon_H45 zenon_H47). % 15.36/15.50 apply (zenon_or_s _ _ zenon_H46); [ zenon_intro zenon_H22 | zenon_intro zenon_H48 ]. % 15.36/15.50 apply (zenon_or_s _ _ zenon_Hf1); [ zenon_intro zenon_H47 | zenon_intro zenon_Hf4 ]. % 15.36/15.50 exact (zenon_H45 zenon_H47). % 15.36/15.50 apply (zenon_or_s _ _ zenon_Hf4); [ zenon_intro zenon_Hd8 | zenon_intro zenon_Hf5 ]. % 15.36/15.50 apply (zenon_L331_); trivial. % 15.36/15.50 apply (zenon_or_s _ _ zenon_Hf5); [ zenon_intro zenon_Hae | zenon_intro zenon_Hee ]. % 15.36/15.50 apply (zenon_L269_); trivial. % 15.36/15.50 apply (zenon_or_s _ _ zenon_H8e); [ zenon_intro zenon_H92 | zenon_intro zenon_H91 ]. % 15.36/15.50 exact (zenon_H8f zenon_H92). % 15.36/15.50 apply (zenon_or_s _ _ zenon_H91); [ zenon_intro zenon_H5d | zenon_intro zenon_H93 ]. % 15.36/15.50 apply (zenon_or_s _ _ zenon_H163); [ zenon_intro zenon_Had | zenon_intro zenon_H164 ]. % 15.36/15.50 apply (zenon_L151_); trivial. % 15.36/15.50 apply (zenon_or_s _ _ zenon_H164); [ zenon_intro zenon_H149 | zenon_intro zenon_H165 ]. % 15.36/15.50 exact (zenon_H145 zenon_H149). % 15.36/15.50 apply (zenon_or_s _ _ zenon_H165); [ zenon_intro zenon_H15d | zenon_intro zenon_Hcc ]. % 15.36/15.50 apply (zenon_L335_); trivial. % 15.36/15.50 apply (zenon_L155_); trivial. % 15.36/15.50 apply (zenon_or_s _ _ zenon_H93); [ zenon_intro zenon_H63 | zenon_intro zenon_H81 ]. % 15.36/15.50 apply (zenon_L697_); trivial. % 15.36/15.50 apply (zenon_L373_); trivial. % 15.36/15.50 apply (zenon_or_s _ _ zenon_H48); [ zenon_intro zenon_H29 | zenon_intro zenon_H37 ]. % 15.36/15.50 apply (zenon_L722_); trivial. % 15.36/15.50 apply (zenon_L211_); trivial. % 15.36/15.50 apply (zenon_L723_); trivial. % 15.36/15.50 apply (zenon_L153_); trivial. % 15.36/15.50 (* end of lemma zenon_L724_ *) % 15.36/15.50 assert (zenon_L725_ : (((op (e0) (e0)) = (e2))\/(((op (e0) (e1)) = (e2))\/(((op (e0) (e2)) = (e2))\/((op (e0) (e3)) = (e2))))) -> (~((op (e0) (e0)) = (e2))) -> (~((op (e3) (e3)) = (e1))) -> (~((op (e0) (e2)) = (op (e3) (e2)))) -> (~((op (e3) (op (e1) (e3))) = (op (e1) (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)) = (e0))) -> (((op (e3) (e1)) = (e0))\/(((op (e3) (e1)) = (e1))\/(((op (e3) (e1)) = (e2))\/((op (e3) (e1)) = (e3))))) -> (~((op (e3) (e1)) = (op (e3) (e2)))) -> (~((op (e3) (e0)) = (op (e3) (e1)))) -> (~((op (e0) (e1)) = (op (e3) (e1)))) -> ((op (e3) (e3)) = (e3)) -> (~((op (e3) (e1)) = (op (e3) (e3)))) -> (((op (e3) (e0)) = (e1))\/(((op (e3) (e1)) = (e1))\/(((op (e3) (e2)) = (e1))\/((op (e3) (e3)) = (e1))))) -> (~((e1) = (e2))) -> ((op (e0) (e2)) = (e1)) -> (((op (e0) (e3)) = (e0))\/(((op (e1) (e3)) = (e0))\/(((op (e2) (e3)) = (e0))\/((op (e3) (e3)) = (e0))))) -> ((op (e1) (e3)) = (e1)) -> (~((e0) = (e1))) -> ((op (e2) (e3)) = (e2)) -> (~((e0) = (e2))) -> (~((op (e3) (e3)) = (e0))) -> False). % 15.36/15.50 do 0 intro. intros zenon_H8e zenon_H8f zenon_H104 zenon_H140 zenon_H26e zenon_H16f zenon_Had zenon_H166 zenon_H2e zenon_H16c zenon_H135 zenon_H109 zenon_H138 zenon_H42 zenon_H12d zenon_H146 zenon_Ha7 zenon_H29 zenon_Hd3 zenon_H11f zenon_H9e zenon_H124 zenon_H5e zenon_H3c. % 15.36/15.50 apply (zenon_or_s _ _ zenon_H8e); [ zenon_intro zenon_H92 | zenon_intro zenon_H91 ]. % 15.36/15.50 exact (zenon_H8f zenon_H92). % 15.36/15.50 apply (zenon_or_s _ _ zenon_H91); [ zenon_intro zenon_H5d | zenon_intro zenon_H93 ]. % 15.36/15.50 apply (zenon_L706_); trivial. % 15.36/15.50 apply (zenon_or_s _ _ zenon_H93); [ zenon_intro zenon_H63 | zenon_intro zenon_H81 ]. % 15.36/15.50 apply (zenon_L104_); trivial. % 15.36/15.50 apply (zenon_L421_); trivial. % 15.36/15.50 (* end of lemma zenon_L725_ *) % 15.36/15.50 assert (zenon_L726_ : (((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)) = (e1)) -> (~((op (e3) (op (e1) (e3))) = (op (e1) (e3)))) -> ((op (e0) (e2)) = (e1)) -> (~((op (e0) (e2)) = (op (e3) (e2)))) -> (~((op (e3) (e3)) = (e1))) -> False). % 15.36/15.50 do 0 intro. intros zenon_H146 zenon_H9e zenon_Hdb zenon_H11f zenon_H26e zenon_H29 zenon_H140 zenon_H104. % 15.36/15.50 apply (zenon_or_s _ _ zenon_H146); [ zenon_intro zenon_Hee | zenon_intro zenon_H14b ]. % 15.36/15.50 apply (zenon_L71_); trivial. % 15.36/15.50 apply (zenon_or_s _ _ zenon_H14b); [ zenon_intro zenon_H13e | zenon_intro zenon_H14c ]. % 15.36/15.50 apply (zenon_L648_); trivial. % 15.36/15.50 apply (zenon_or_s _ _ zenon_H14c); [ zenon_intro zenon_H119 | zenon_intro zenon_H38 ]. % 15.36/15.50 apply (zenon_L124_); trivial. % 15.36/15.50 exact (zenon_H104 zenon_H38). % 15.36/15.50 (* end of lemma zenon_L726_ *) % 15.36/15.50 assert (zenon_L727_ : (((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 (e2) (e2)) = (e3)) -> (~((op (e0) (e2)) = (op (e2) (e2)))) -> (~((op (e0) (e2)) = (op (e3) (e2)))) -> ((op (e3) (e2)) = (e1)) -> ((~((op (e3) (e3)) = (e0)))\/((op (e3) (e0)) = (e3))) -> ((op (e3) (e3)) = (e3)) -> (~((op (e3) (e0)) = (op (e3) (e3)))) -> (~((op (e0) (e2)) = (op (e0) (e3)))) -> (~((e0) = (e1))) -> ((op (e1) (e3)) = (e1)) -> (~((e0) = (e2))) -> ((op (e2) (e3)) = (e2)) -> (((op (e0) (e3)) = (e0))\/(((op (e1) (e3)) = (e0))\/(((op (e2) (e3)) = (e0))\/((op (e3) (e3)) = (e0))))) -> (((op (e0) (e2)) = (e0))\/(((op (e0) (e2)) = (e1))\/(((op (e0) (e2)) = (e2))\/((op (e0) (e2)) = (e3))))) -> (~((op (e3) (e3)) = (e2))) -> False). % 15.36/15.50 do 0 intro. intros zenon_H1df zenon_Hdb zenon_H5d zenon_H138 zenon_H34 zenon_H28 zenon_H140 zenon_H119 zenon_H10f zenon_H42 zenon_Hbb zenon_Hc9 zenon_H9e zenon_H11f zenon_H5e zenon_H124 zenon_Hd3 zenon_H251 zenon_H3d. % 15.36/15.50 apply (zenon_or_s _ _ zenon_H1df); [ zenon_intro zenon_He9 | zenon_intro zenon_H1e0 ]. % 15.36/15.50 apply (zenon_L69_); trivial. % 15.36/15.50 apply (zenon_or_s _ _ zenon_H1e0); [ zenon_intro zenon_H16a | zenon_intro zenon_H1e1 ]. % 15.36/15.50 apply (zenon_L146_); trivial. % 15.36/15.50 apply (zenon_or_s _ _ zenon_H1e1); [ zenon_intro zenon_H1dd | zenon_intro zenon_H43 ]. % 15.36/15.50 apply (zenon_L713_); trivial. % 15.36/15.50 exact (zenon_H3d zenon_H43). % 15.36/15.50 (* end of lemma zenon_L727_ *) % 15.36/15.50 assert (zenon_L728_ : (((op (e0) (e2)) = (e1))\/(((op (e1) (e2)) = (e1))\/(((op (e2) (e2)) = (e1))\/((op (e3) (e2)) = (e1))))) -> (~((op (e3) (e3)) = (e1))) -> (~((op (e3) (op (e1) (e3))) = (op (e1) (e3)))) -> (((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))))) -> (~((op (e2) (e2)) = (e2))) -> (~((op (e2) (e2)) = (e1))) -> (~((op (e2) (e2)) = (e0))) -> (((op (e2) (e2)) = (e0))\/(((op (e2) (e2)) = (e1))\/(((op (e2) (e2)) = (e2))\/((op (e2) (e2)) = (e3))))) -> (~((e0) = (e3))) -> ((op (e1) (e2)) = (e0)) -> (~((op (e3) (e3)) = (e2))) -> (((op (e0) (e2)) = (e0))\/(((op (e0) (e2)) = (e1))\/(((op (e0) (e2)) = (e2))\/((op (e0) (e2)) = (e3))))) -> (((op (e0) (e3)) = (e0))\/(((op (e1) (e3)) = (e0))\/(((op (e2) (e3)) = (e0))\/((op (e3) (e3)) = (e0))))) -> ((op (e2) (e3)) = (e2)) -> (~((e0) = (e2))) -> ((op (e1) (e3)) = (e1)) -> (~((e0) = (e1))) -> (~((op (e0) (e2)) = (op (e0) (e3)))) -> (~((op (e3) (e0)) = (op (e3) (e3)))) -> ((~((op (e3) (e3)) = (e0)))\/((op (e3) (e0)) = (e3))) -> (~((op (e0) (e2)) = (op (e3) (e2)))) -> (~((op (e0) (e2)) = (op (e2) (e2)))) -> (~((op (e0) (e1)) = (op (e3) (e1)))) -> ((op (e0) (e1)) = (e2)) -> ((op (e3) (e0)) = (e0)) -> (((op (e3) (e0)) = (e2))\/(((op (e3) (e1)) = (e2))\/(((op (e3) (e2)) = (e2))\/((op (e3) (e3)) = (e2))))) -> ((op (e3) (e3)) = (e3)) -> (~((op (e3) (e2)) = (op (e3) (e3)))) -> False). % 15.36/15.50 do 0 intro. intros zenon_H11b zenon_H104 zenon_H26e zenon_H146 zenon_H175 zenon_H2f zenon_H52 zenon_H2e zenon_H2d zenon_H4b zenon_H15d zenon_H3d zenon_H251 zenon_Hd3 zenon_H124 zenon_H5e zenon_H11f zenon_H9e zenon_Hc9 zenon_Hbb zenon_H10f zenon_H140 zenon_H28 zenon_H138 zenon_H5d zenon_Hdb zenon_H1df zenon_H42 zenon_H173. % 15.36/15.50 apply (zenon_or_s _ _ zenon_H11b); [ zenon_intro zenon_H29 | zenon_intro zenon_H11c ]. % 15.36/15.50 apply (zenon_L726_); trivial. % 15.36/15.50 apply (zenon_or_s _ _ zenon_H11c); [ zenon_intro zenon_H117 | zenon_intro zenon_H11d ]. % 15.36/15.50 apply (zenon_L496_); trivial. % 15.36/15.50 apply (zenon_or_s _ _ zenon_H11d); [ zenon_intro zenon_H2a | zenon_intro zenon_H119 ]. % 15.36/15.50 exact (zenon_H52 zenon_H2a). % 15.36/15.50 apply (zenon_or_s _ _ zenon_H175); [ zenon_intro zenon_H50 | zenon_intro zenon_H176 ]. % 15.36/15.50 apply (zenon_L11_); trivial. % 15.36/15.50 apply (zenon_or_s _ _ zenon_H176); [ zenon_intro zenon_H88 | zenon_intro zenon_H177 ]. % 15.36/15.50 apply (zenon_L152_); trivial. % 15.36/15.50 apply (zenon_or_s _ _ zenon_H177); [ zenon_intro zenon_H34 | zenon_intro zenon_H106 ]. % 15.36/15.50 apply (zenon_L727_); trivial. % 15.36/15.50 apply (zenon_L153_); trivial. % 15.36/15.50 (* end of lemma zenon_L728_ *) % 15.36/15.50 assert (zenon_L729_ : (((op (e0) (e0)) = (e2))\/(((op (e1) (e0)) = (e2))\/(((op (e2) (e0)) = (e2))\/((op (e3) (e0)) = (e2))))) -> (~((op (e0) (e0)) = (e2))) -> ((op (e0) (e2)) = (e2)) -> (~((op (e0) (op (e1) (e0))) = (op (e1) (e0)))) -> (((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)) = (e1)) -> (~((e1) = (e2))) -> ((op (e0) (e3)) = (e0)) -> (~((op (e3) (e2)) = (op (e3) (e3)))) -> ((op (e3) (e3)) = (e3)) -> ((~((op (e3) (e3)) = (e2)))\/((op (e3) (e2)) = (e3))) -> ((op (e3) (e0)) = (e0)) -> (~((e0) = (e2))) -> False). % 15.36/15.50 do 0 intro. intros zenon_Heb zenon_H8f zenon_H63 zenon_H261 zenon_H160 zenon_Hce zenon_H11f zenon_Ha7 zenon_Hca zenon_H173 zenon_H42 zenon_H10e zenon_Hdb zenon_H5e. % 15.36/15.50 apply (zenon_or_s _ _ zenon_Heb); [ zenon_intro zenon_H92 | zenon_intro zenon_Hec ]. % 15.36/15.50 exact (zenon_H8f zenon_H92). % 15.36/15.50 apply (zenon_or_s _ _ zenon_Hec); [ zenon_intro zenon_H68 | zenon_intro zenon_Hed ]. % 15.36/15.50 apply (zenon_L638_); trivial. % 15.36/15.50 apply (zenon_or_s _ _ zenon_Hed); [ zenon_intro zenon_Hdd | zenon_intro zenon_He9 ]. % 15.36/15.50 apply (zenon_L431_); trivial. % 15.36/15.50 apply (zenon_L69_); trivial. % 15.36/15.50 (* end of lemma zenon_L729_ *) % 15.36/15.50 assert (zenon_L730_ : (((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) (e2)))) -> (((op (e3) (e1)) = (e0))\/(((op (e3) (e1)) = (e1))\/(((op (e3) (e1)) = (e2))\/((op (e3) (e1)) = (e3))))) -> (~((op (e3) (e0)) = (op (e3) (e1)))) -> (~((op (e3) (e1)) = (op (e3) (e3)))) -> (((op (e0) (e0)) = (e1))\/(((op (e1) (e0)) = (e1))\/(((op (e2) (e0)) = (e1))\/((op (e3) (e0)) = (e1))))) -> (~((op (e1) (e0)) = (op (e1) (e3)))) -> (((op (e1) (e0)) = (e2))\/(((op (e1) (e1)) = (e2))\/(((op (e1) (e2)) = (e2))\/((op (e1) (e3)) = (e2))))) -> (~((op (e1) (e1)) = (e2))) -> (~((op (e0) (e2)) = (op (e1) (e2)))) -> (((op (e0) (e3)) = (e1))\/(((op (e1) (e3)) = (e1))\/(((op (e2) (e3)) = (e1))\/((op (e3) (e3)) = (e1))))) -> (~((op (e0) (e1)) = (op (e0) (e3)))) -> (~((e2) = (e3))) -> ((~((op (e3) (e3)) = (e1)))\/((op (e3) (e1)) = (e3))) -> (~((op (e1) (e2)) = (op (e1) (e3)))) -> (((op (e0) (e2)) = (e2))\/(((op (e1) (e2)) = (e2))\/(((op (e2) (e2)) = (e2))\/((op (e3) (e2)) = (e2))))) -> (((op (e2) (e0)) = (e3))\/(((op (e2) (e1)) = (e3))\/(((op (e2) (e2)) = (e3))\/((op (e2) (e3)) = (e3))))) -> (~((e1) = (e3))) -> (~((op (e2) (e1)) = (op (e3) (e1)))) -> (~((op (e2) (e3)) = (op (e3) (e3)))) -> (~((op (e3) (e1)) = (op (e3) (e2)))) -> (~((op (e2) (op (e1) (e2))) = (op (e1) (e2)))) -> (~((op (e2) (e0)) = (op (e2) (e1)))) -> (~((op (e1) (e1)) = (e0))) -> (((op (e0) (e1)) = (e0))\/(((op (e1) (e1)) = (e0))\/(((op (e2) (e1)) = (e0))\/((op (e3) (e1)) = (e0))))) -> (~((op (e3) (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 (e0) (e0)) = (e1))) -> (((op (e0) (e0)) = (e1))\/(((op (e0) (e1)) = (e1))\/(((op (e0) (e2)) = (e1))\/((op (e0) (e3)) = (e1))))) -> (((op (e0) (e0)) = (e2))\/(((op (e0) (e1)) = (e2))\/(((op (e0) (e2)) = (e2))\/((op (e0) (e3)) = (e2))))) -> (~((op (e3) (e0)) = (op (e3) (e2)))) -> (~((op (e2) (e2)) = (e0))) -> (((op (e0) (e2)) = (e1))\/(((op (e1) (e2)) = (e1))\/(((op (e2) (e2)) = (e1))\/((op (e3) (e2)) = (e1))))) -> (~((op (e3) (e3)) = (e1))) -> (~((op (e3) (op (e1) (e3))) = (op (e1) (e3)))) -> (((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))))) -> (~((op (e2) (e2)) = (e2))) -> (~((op (e2) (e2)) = (e1))) -> (((op (e2) (e2)) = (e0))\/(((op (e2) (e2)) = (e1))\/(((op (e2) (e2)) = (e2))\/((op (e2) (e2)) = (e3))))) -> (~((e0) = (e3))) -> (~((op (e3) (e3)) = (e2))) -> (((op (e0) (e2)) = (e0))\/(((op (e0) (e2)) = (e1))\/(((op (e0) (e2)) = (e2))\/((op (e0) (e2)) = (e3))))) -> (((op (e0) (e3)) = (e0))\/(((op (e1) (e3)) = (e0))\/(((op (e2) (e3)) = (e0))\/((op (e3) (e3)) = (e0))))) -> ((op (e2) (e3)) = (e2)) -> (~((e0) = (e1))) -> (~((op (e0) (e2)) = (op (e0) (e3)))) -> (~((op (e3) (e0)) = (op (e3) (e3)))) -> ((~((op (e3) (e3)) = (e0)))\/((op (e3) (e0)) = (e3))) -> (~((op (e0) (e2)) = (op (e3) (e2)))) -> (~((op (e0) (e2)) = (op (e2) (e2)))) -> (~((op (e0) (e1)) = (op (e3) (e1)))) -> (((op (e3) (e0)) = (e2))\/(((op (e3) (e1)) = (e2))\/(((op (e3) (e2)) = (e2))\/((op (e3) (e3)) = (e2))))) -> (((op (e0) (e2)) = (e0))\/(((op (e1) (e2)) = (e0))\/(((op (e2) (e2)) = (e0))\/((op (e3) (e2)) = (e0))))) -> ((~((op (e3) (e3)) = (e2)))\/((op (e3) (e2)) = (e3))) -> ((op (e3) (e3)) = (e3)) -> (~((op (e3) (e2)) = (op (e3) (e3)))) -> (~((e1) = (e2))) -> ((op (e1) (e3)) = (e1)) -> (~((op (e2) (e0)) = (op (e2) (e3)))) -> (((op (e0) (e3)) = (e2))\/(((op (e1) (e3)) = (e2))\/(((op (e2) (e3)) = (e2))\/((op (e3) (e3)) = (e2))))) -> (~((op (e0) (op (e1) (e0))) = (op (e1) (e0)))) -> (~((op (e0) (e0)) = (e2))) -> (((op (e0) (e0)) = (e2))\/(((op (e1) (e0)) = (e2))\/(((op (e2) (e0)) = (e2))\/((op (e3) (e0)) = (e2))))) -> ((op (e0) (e3)) = (e0)) -> (~((e0) = (e2))) -> False). % 15.36/15.50 do 0 intro. intros zenon_Hf0 zenon_H20 zenon_H166 zenon_H16c zenon_H109 zenon_H12d zenon_Hf1 zenon_H1cf zenon_H84 zenon_Hd6 zenon_H87 zenon_H121 zenon_H1cd zenon_H6a zenon_H10c zenon_H1d0 zenon_H27c zenon_He6 zenon_Ha3 zenon_H13c zenon_He3 zenon_H135 zenon_H277 zenon_H154 zenon_H145 zenon_H144 zenon_H3c zenon_Hb7 zenon_Hde zenon_H45 zenon_H44 zenon_H8e zenon_H105 zenon_H2e zenon_H11b zenon_H104 zenon_H26e zenon_H146 zenon_H175 zenon_H2f zenon_H52 zenon_H2d zenon_H4b zenon_H3d zenon_H251 zenon_Hd3 zenon_H124 zenon_H9e zenon_Hc9 zenon_Hbb zenon_H10f zenon_H140 zenon_H28 zenon_H138 zenon_H1df zenon_H16f zenon_H10e zenon_H42 zenon_H173 zenon_Ha7 zenon_H11f zenon_Hce zenon_H160 zenon_H261 zenon_H8f zenon_Heb zenon_Hca zenon_H5e. % 15.36/15.50 apply (zenon_or_s _ _ zenon_Hf0); [ zenon_intro zenon_H1f | zenon_intro zenon_Hf2 ]. % 15.36/15.50 exact (zenon_H20 zenon_H1f). % 15.36/15.50 apply (zenon_or_s _ _ zenon_Hf2); [ zenon_intro zenon_Had | zenon_intro zenon_Hf3 ]. % 15.36/15.50 apply (zenon_or_s _ _ zenon_H44); [ zenon_intro zenon_H47 | zenon_intro zenon_H46 ]. % 15.36/15.50 exact (zenon_H45 zenon_H47). % 15.36/15.50 apply (zenon_or_s _ _ zenon_H46); [ zenon_intro zenon_H22 | zenon_intro zenon_H48 ]. % 15.36/15.50 apply (zenon_or_s _ _ zenon_Hf1); [ zenon_intro zenon_H47 | zenon_intro zenon_Hf4 ]. % 15.36/15.50 exact (zenon_H45 zenon_H47). % 15.36/15.50 apply (zenon_or_s _ _ zenon_Hf4); [ zenon_intro zenon_Hd8 | zenon_intro zenon_Hf5 ]. % 15.36/15.50 apply (zenon_L225_); trivial. % 15.36/15.50 apply (zenon_or_s _ _ zenon_Hf5); [ zenon_intro zenon_Hae | zenon_intro zenon_Hee ]. % 15.36/15.50 apply (zenon_or_s _ _ zenon_H8e); [ zenon_intro zenon_H92 | zenon_intro zenon_H91 ]. % 15.36/15.50 exact (zenon_H8f zenon_H92). % 15.36/15.50 apply (zenon_or_s _ _ zenon_H91); [ zenon_intro zenon_H5d | zenon_intro zenon_H93 ]. % 15.36/15.50 apply (zenon_or_s _ _ zenon_Heb); [ zenon_intro zenon_H92 | zenon_intro zenon_Hec ]. % 15.36/15.50 exact (zenon_H8f zenon_H92). % 15.36/15.50 apply (zenon_or_s _ _ zenon_Hec); [ zenon_intro zenon_H68 | zenon_intro zenon_Hed ]. % 15.36/15.50 apply (zenon_or_s _ _ zenon_H16f); [ zenon_intro zenon_Hab | zenon_intro zenon_H170 ]. % 15.36/15.50 apply (zenon_L53_); trivial. % 15.36/15.50 apply (zenon_or_s _ _ zenon_H170); [ zenon_intro zenon_H15d | zenon_intro zenon_H171 ]. % 15.36/15.50 apply (zenon_L143_); trivial. % 15.36/15.50 apply (zenon_or_s _ _ zenon_H171); [ zenon_intro zenon_H32 | zenon_intro zenon_H167 ]. % 15.36/15.50 exact (zenon_H2e zenon_H32). % 15.36/15.50 apply (zenon_or_s _ _ zenon_H11b); [ zenon_intro zenon_H29 | zenon_intro zenon_H11c ]. % 15.36/15.50 apply (zenon_L706_); trivial. % 15.36/15.50 apply (zenon_or_s _ _ zenon_H11c); [ zenon_intro zenon_H117 | zenon_intro zenon_H11d ]. % 15.36/15.50 apply (zenon_L452_); trivial. % 15.36/15.50 apply (zenon_or_s _ _ zenon_H11d); [ zenon_intro zenon_H2a | zenon_intro zenon_H119 ]. % 15.36/15.50 exact (zenon_H52 zenon_H2a). % 15.36/15.50 apply (zenon_L715_); trivial. % 15.36/15.50 apply (zenon_or_s _ _ zenon_Hed); [ zenon_intro zenon_Hdd | zenon_intro zenon_He9 ]. % 15.36/15.50 apply (zenon_L304_); trivial. % 15.36/15.50 apply (zenon_or_s _ _ zenon_H16f); [ zenon_intro zenon_Hab | zenon_intro zenon_H170 ]. % 15.36/15.50 apply (zenon_L53_); trivial. % 15.36/15.50 apply (zenon_or_s _ _ zenon_H170); [ zenon_intro zenon_H15d | zenon_intro zenon_H171 ]. % 15.36/15.50 apply (zenon_L143_); trivial. % 15.36/15.50 apply (zenon_or_s _ _ zenon_H171); [ zenon_intro zenon_H32 | zenon_intro zenon_H167 ]. % 15.36/15.50 exact (zenon_H2e zenon_H32). % 15.36/15.50 apply (zenon_or_s _ _ zenon_H27c); [ zenon_intro zenon_H63 | zenon_intro zenon_H27d ]. % 15.36/15.50 apply (zenon_L676_); trivial. % 15.36/15.50 apply (zenon_or_s _ _ zenon_H27d); [ zenon_intro zenon_H7c | zenon_intro zenon_H27e ]. % 15.36/15.50 apply (zenon_L717_); trivial. % 15.36/15.50 apply (zenon_or_s _ _ zenon_H27e); [ zenon_intro zenon_H35 | zenon_intro zenon_H1dd ]. % 15.36/15.50 exact (zenon_H2f zenon_H35). % 15.36/15.50 apply (zenon_L714_); trivial. % 15.36/15.50 apply (zenon_or_s _ _ zenon_H93); [ zenon_intro zenon_H63 | zenon_intro zenon_H81 ]. % 15.36/15.50 apply (zenon_L676_); trivial. % 15.36/15.50 apply (zenon_L421_); trivial. % 15.36/15.50 apply (zenon_or_s _ _ zenon_H8e); [ zenon_intro zenon_H92 | zenon_intro zenon_H91 ]. % 15.36/15.50 exact (zenon_H8f zenon_H92). % 15.36/15.50 apply (zenon_or_s _ _ zenon_H91); [ zenon_intro zenon_H5d | zenon_intro zenon_H93 ]. % 15.36/15.50 apply (zenon_or_s _ _ zenon_H16f); [ zenon_intro zenon_Hab | zenon_intro zenon_H170 ]. % 15.36/15.50 apply (zenon_L712_); trivial. % 15.36/15.50 apply (zenon_or_s _ _ zenon_H170); [ zenon_intro zenon_H15d | zenon_intro zenon_H171 ]. % 15.36/15.50 apply (zenon_L143_); trivial. % 15.36/15.50 apply (zenon_or_s _ _ zenon_H171); [ zenon_intro zenon_H32 | zenon_intro zenon_H167 ]. % 15.36/15.50 exact (zenon_H2e zenon_H32). % 15.36/15.50 apply (zenon_L147_); trivial. % 15.36/15.50 apply (zenon_or_s _ _ zenon_H93); [ zenon_intro zenon_H63 | zenon_intro zenon_H81 ]. % 15.36/15.50 apply (zenon_L677_); trivial. % 15.36/15.50 apply (zenon_L113_); trivial. % 15.36/15.50 apply (zenon_or_s _ _ zenon_H48); [ zenon_intro zenon_H29 | zenon_intro zenon_H37 ]. % 15.36/15.50 apply (zenon_L725_); trivial. % 15.36/15.50 apply (zenon_L211_); trivial. % 15.36/15.50 apply (zenon_or_s _ _ zenon_Hf3); [ zenon_intro zenon_Hcf | zenon_intro zenon_Hdb ]. % 15.36/15.50 apply (zenon_or_s _ _ zenon_H44); [ zenon_intro zenon_H47 | zenon_intro zenon_H46 ]. % 15.36/15.50 exact (zenon_H45 zenon_H47). % 15.36/15.50 apply (zenon_or_s _ _ zenon_H46); [ zenon_intro zenon_H22 | zenon_intro zenon_H48 ]. % 15.36/15.50 apply (zenon_L340_); trivial. % 15.36/15.50 apply (zenon_or_s _ _ zenon_H48); [ zenon_intro zenon_H29 | zenon_intro zenon_H37 ]. % 15.36/15.50 apply (zenon_L722_); trivial. % 15.36/15.50 apply (zenon_L73_); trivial. % 15.36/15.50 apply (zenon_or_s _ _ zenon_H8e); [ zenon_intro zenon_H92 | zenon_intro zenon_H91 ]. % 15.36/15.50 exact (zenon_H8f zenon_H92). % 15.36/15.50 apply (zenon_or_s _ _ zenon_H91); [ zenon_intro zenon_H5d | zenon_intro zenon_H93 ]. % 15.36/15.50 apply (zenon_or_s _ _ zenon_H16f); [ zenon_intro zenon_Hab | zenon_intro zenon_H170 ]. % 15.36/15.50 apply (zenon_L712_); trivial. % 15.36/15.50 apply (zenon_or_s _ _ zenon_H170); [ zenon_intro zenon_H15d | zenon_intro zenon_H171 ]. % 15.36/15.50 apply (zenon_L728_); trivial. % 15.36/15.50 apply (zenon_or_s _ _ zenon_H171); [ zenon_intro zenon_H32 | zenon_intro zenon_H167 ]. % 15.36/15.50 exact (zenon_H2e zenon_H32). % 15.36/15.50 apply (zenon_L156_); trivial. % 15.36/15.50 apply (zenon_or_s _ _ zenon_H93); [ zenon_intro zenon_H63 | zenon_intro zenon_H81 ]. % 15.36/15.50 apply (zenon_L729_); trivial. % 15.36/15.50 apply (zenon_L113_); trivial. % 15.36/15.50 (* end of lemma zenon_L730_ *) % 15.36/15.50 assert (zenon_L731_ : ((~((op (e0) (e0)) = (e3)))\/((op (e0) (e3)) = (e0))) -> ((~((op (e1) (e1)) = (e1)))\/((op (e1) (e1)) = (e1))) -> (~((op (e1) (op (e1) (e1))) = (op (e1) (e1)))) -> ((~((op (e1) (e1)) = (e3)))\/((op (e1) (e3)) = (e1))) -> ((~((op (e2) (e2)) = (e1)))\/((op (e2) (e1)) = (e2))) -> ((~((op (e2) (e2)) = (e3)))\/((op (e2) (e3)) = (e2))) -> (~((op (e2) (e1)) = (op (e2) (e3)))) -> (((op (e0) (e1)) = (e3))\/(((op (e1) (e1)) = (e3))\/(((op (e2) (e1)) = (e3))\/((op (e3) (e1)) = (e3))))) -> (~((op (e2) (e0)) = (op (e2) (e3)))) -> (((op (e2) (e0)) = (e0))\/(((op (e2) (e1)) = (e0))\/(((op (e2) (e2)) = (e0))\/((op (e2) (e3)) = (e0))))) -> (((op (e0) (e1)) = (e1))\/(((op (e1) (e1)) = (e1))\/(((op (e2) (e1)) = (e1))\/((op (e3) (e1)) = (e1))))) -> (~((op (e0) (e1)) = (op (e2) (e1)))) -> (~((op (e2) (e1)) = (op (e2) (e2)))) -> (((op (e0) (e0)) = (e3))\/(((op (e0) (e1)) = (e3))\/(((op (e0) (e2)) = (e3))\/((op (e0) (e3)) = (e3))))) -> ((op (e3) (e3)) = (e3)) -> (~((op (e0) (e3)) = (op (e3) (e3)))) -> (~((op (e0) (e2)) = (op (e2) (e2)))) -> (((op (e2) (e2)) = (e0))\/(((op (e2) (e2)) = (e1))\/(((op (e2) (e2)) = (e2))\/((op (e2) (e2)) = (e3))))) -> (~((e0) = (e3))) -> ((~((op (e3) (e3)) = (e0)))\/((op (e3) (e0)) = (e3))) -> (~((op (e3) (e0)) = (op (e3) (e3)))) -> (((op (e0) (e0)) = (e1))\/(((op (e0) (e1)) = (e1))\/(((op (e0) (e2)) = (e1))\/((op (e0) (e3)) = (e1))))) -> (((op (e0) (e3)) = (e0))\/(((op (e1) (e3)) = (e0))\/(((op (e2) (e3)) = (e0))\/((op (e3) (e3)) = (e0))))) -> (~((op (e0) (e1)) = (op (e0) (e3)))) -> (~((e1) = (e2))) -> (((op (e0) (e3)) = (e2))\/(((op (e1) (e3)) = (e2))\/(((op (e2) (e3)) = (e2))\/((op (e3) (e3)) = (e2))))) -> (~((e1) = (e3))) -> (~((e0) = (e1))) -> (~((op (e0) (e0)) = (e2))) -> (~((e0) = (e2))) -> (((op (e1) (e0)) = (e2))\/(((op (e1) (e1)) = (e2))\/(((op (e1) (e2)) = (e2))\/((op (e1) (e3)) = (e2))))) -> (~((op (e0) (e3)) = (op (e1) (e3)))) -> (~((op (e1) (e2)) = (op (e2) (e2)))) -> (~((e2) = (e3))) -> (~((op (e0) (e2)) = (op (e1) (e2)))) -> (~((op (e1) (e3)) = (op (e3) (e3)))) -> (((op (e1) (e0)) = (e3))\/(((op (e1) (e1)) = (e3))\/(((op (e1) (e2)) = (e3))\/((op (e1) (e3)) = (e3))))) -> (((op (e0) (e0)) = (e2))\/(((op (e0) (e1)) = (e2))\/(((op (e0) (e2)) = (e2))\/((op (e0) (e3)) = (e2))))) -> (~((op (e3) (e2)) = (op (e3) (e3)))) -> ((~((op (e3) (e3)) = (e2)))\/((op (e3) (e2)) = (e3))) -> ((~((op (e2) (e2)) = (e2)))\/((op (e2) (e2)) = (e2))) -> (~((op (e2) (e0)) = (op (e2) (e1)))) -> (((op (e2) (e0)) = (e3))\/(((op (e2) (e1)) = (e3))\/(((op (e2) (e2)) = (e3))\/((op (e2) (e3)) = (e3))))) -> (~((op (e2) (e3)) = (op (e3) (e3)))) -> (~((op (e2) (e0)) = (op (e2) (e2)))) -> ((~((op (e2) (e2)) = (e0)))\/((op (e2) (e0)) = (e2))) -> (~((op (e0) (e1)) = (op (e1) (e1)))) -> ((op (e0) (e1)) = (e0)) -> (((op (e1) (e1)) = (e0))\/(((op (e1) (e1)) = (e1))\/(((op (e1) (e1)) = (e2))\/((op (e1) (e1)) = (e3))))) -> (~((op (e1) (e2)) = (op (e1) (e3)))) -> (~((op (e3) (e1)) = (op (e3) (e3)))) -> (((op (e0) (e0)) = (e3))\/(((op (e1) (e0)) = (e3))\/(((op (e2) (e0)) = (e3))\/((op (e3) (e0)) = (e3))))) -> ((~((op (e1) (e1)) = (e2)))\/((op (e1) (e2)) = (e1))) -> (~((op (e1) (e0)) = (op (e1) (e1)))) -> (~((op (e1) (e0)) = (op (e1) (e3)))) -> (~((op (e1) (e0)) = (op (e1) (e2)))) -> ((~((op (e1) (e1)) = (e0)))\/((op (e1) (e0)) = (e1))) -> False). % 15.36/15.50 do 0 intro. intros zenon_H236 zenon_H1d8 zenon_H27b zenon_H1d2 zenon_H1e3 zenon_H1c3 zenon_H1e2 zenon_H199 zenon_Hce zenon_H1f5 zenon_H228 zenon_Hde zenon_H157 zenon_H58 zenon_H42 zenon_H36 zenon_H28 zenon_H2d zenon_H4b zenon_H10f zenon_Hbb zenon_H44 zenon_Hd3 zenon_H1cd zenon_Ha7 zenon_H160 zenon_Ha3 zenon_H9e zenon_H8f zenon_H5e zenon_H84 zenon_H80 zenon_H7d zenon_H6a zenon_H87 zenon_H8b zenon_H90 zenon_H8e zenon_H173 zenon_H10e zenon_Haa zenon_H154 zenon_He6 zenon_He3 zenon_H17a zenon_H1d4 zenon_H23 zenon_H49 zenon_H1b3 zenon_H1d0 zenon_H12d zenon_Hbe zenon_H1d3 zenon_Hd7 zenon_H1cf zenon_H166 zenon_H1e4. % 15.36/15.50 apply (zenon_or_s _ _ zenon_H236); [ zenon_intro zenon_H59 | zenon_intro zenon_Hca ]. % 15.36/15.50 apply (zenon_or_s _ _ zenon_H1e4); [ zenon_intro zenon_H145 | zenon_intro zenon_Hd8 ]. % 15.36/15.50 apply (zenon_or_s _ _ zenon_H1d8); [ zenon_intro zenon_H1b4 | zenon_intro zenon_H21 ]. % 15.36/15.50 apply (zenon_L387_); trivial. % 15.36/15.50 apply (zenon_L698_); trivial. % 15.36/15.50 apply (zenon_L484_); trivial. % 15.36/15.50 apply (zenon_L463_); trivial. % 15.36/15.50 (* end of lemma zenon_L731_ *) % 15.36/15.50 assert (zenon_L732_ : (~((op (e1) (op (e1) (e1))) = (op (e1) (e1)))) -> (~((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 (e0) (e2)) = (op (e0) (e3)))) -> (((op (e0) (e2)) = (e0))\/(((op (e0) (e2)) = (e1))\/(((op (e0) (e2)) = (e2))\/((op (e0) (e2)) = (e3))))) -> (~((op (e0) (e2)) = (op (e2) (e2)))) -> (~((op (e0) (e0)) = (op (e0) (e2)))) -> (((op (e0) (e2)) = (e1))\/(((op (e1) (e2)) = (e1))\/(((op (e2) (e2)) = (e1))\/((op (e3) (e2)) = (e1))))) -> (((op (e0) (e3)) = (e0))\/(((op (e0) (e3)) = (e1))\/(((op (e0) (e3)) = (e2))\/((op (e0) (e3)) = (e3))))) -> (~((op (e0) (e3)) = (op (e1) (e3)))) -> (~((op (e0) (e3)) = (op (e2) (e3)))) -> (~((op (e1) (e2)) = (op (e2) (e2)))) -> (~((op (e0) (e1)) = (op (e3) (e1)))) -> (((op (e0) (e0)) = (e3))\/(((op (e1) (e0)) = (e3))\/(((op (e2) (e0)) = (e3))\/((op (e3) (e0)) = (e3))))) -> ((op (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 (e1) (e1)) = (e0))\/(((op (e1) (e1)) = (e1))\/(((op (e1) (e1)) = (e2))\/((op (e1) (e1)) = (e3))))) -> (~((e1) = (e3))) -> (~((op (e0) (e0)) = (e3))) -> ((~((op (e3) (e3)) = (e0)))\/((op (e3) (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) (e0)) = (op (e0) (e3)))) -> ((op (e0) (e0)) = (e0)) -> (~((e0) = (e2))) -> (((op (e0) (e3)) = (e0))\/(((op (e1) (e3)) = (e0))\/(((op (e2) (e3)) = (e0))\/((op (e3) (e3)) = (e0))))) -> (~((op (e0) (e0)) = (e2))) -> (((op (e0) (e0)) = (e3))\/(((op (e0) (e1)) = (e3))\/(((op (e0) (e2)) = (e3))\/((op (e0) (e3)) = (e3))))) -> (~((op (e0) (e3)) = (op (e3) (e3)))) -> (~((op (e0) (e2)) = (op (e1) (e2)))) -> (~((op (e1) (e3)) = (op (e3) (e3)))) -> (((op (e1) (e0)) = (e3))\/(((op (e1) (e1)) = (e3))\/(((op (e1) (e2)) = (e3))\/((op (e1) (e3)) = (e3))))) -> (~((e2) = (e3))) -> (((op (e0) (e0)) = (e2))\/(((op (e1) (e0)) = (e2))\/(((op (e2) (e0)) = (e2))\/((op (e3) (e0)) = (e2))))) -> ((~((op (e2) (e2)) = (e2)))\/((op (e2) (e2)) = (e2))) -> (~((op (e2) (e1)) = (op (e2) (e2)))) -> (~((op (e2) (e1)) = (op (e2) (e3)))) -> ((~((op (e2) (e2)) = (e3)))\/((op (e2) (e3)) = (e2))) -> (~((op (e1) (e0)) = (op (e3) (e0)))) -> (((op (e0) (e1)) = (e2))\/(((op (e1) (e1)) = (e2))\/(((op (e2) (e1)) = (e2))\/((op (e3) (e1)) = (e2))))) -> (~((op (e2) (e0)) = (op (e2) (e1)))) -> (~((op (e0) (e2)) = (op (e3) (e2)))) -> (((op (e3) (e0)) = (e1))\/(((op (e3) (e1)) = (e1))\/(((op (e3) (e2)) = (e1))\/((op (e3) (e3)) = (e1))))) -> (((op (e0) (e0)) = (e2))\/(((op (e0) (e1)) = (e2))\/(((op (e0) (e2)) = (e2))\/((op (e0) (e3)) = (e2))))) -> (~((op (e0) (e1)) = (op (e0) (e3)))) -> (~((op (e1) (e0)) = (op (e1) (e3)))) -> (~((e1) = (e2))) -> (((op (e0) (e3)) = (e1))\/(((op (e1) (e3)) = (e1))\/(((op (e2) (e3)) = (e1))\/((op (e3) (e3)) = (e1))))) -> (~((op (e0) (e0)) = (e1))) -> (~((op (e3) (e1)) = (op (e3) (e3)))) -> ((~((op (e3) (e3)) = (e1)))\/((op (e3) (e1)) = (e3))) -> (((op (e2) (e0)) = (e0))\/(((op (e2) (e1)) = (e0))\/(((op (e2) (e2)) = (e0))\/((op (e2) (e3)) = (e0))))) -> (~((op (e1) (e3)) = (op (e2) (e3)))) -> (~((op (e0) (e0)) = (op (e2) (e0)))) -> (~((op (e3) (e2)) = (op (e3) (e3)))) -> ((~((op (e3) (e3)) = (e2)))\/((op (e3) (e2)) = (e3))) -> (~((e0) = (e3))) -> (((op (e0) (e2)) = (e0))\/(((op (e1) (e2)) = (e0))\/(((op (e2) (e2)) = (e0))\/((op (e3) (e2)) = (e0))))) -> (((op (e0) (e0)) = (e1))\/(((op (e1) (e0)) = (e1))\/(((op (e2) (e0)) = (e1))\/((op (e3) (e0)) = (e1))))) -> (~((op (e0) (e1)) = (op (e1) (e1)))) -> (~((op (e1) (e1)) = (e0))) -> (((op (e1) (e0)) = (e0))\/(((op (e1) (e1)) = (e0))\/(((op (e1) (e2)) = (e0))\/((op (e1) (e3)) = (e0))))) -> (~((e0) = (e1))) -> (~((op (e0) (e0)) = (op (e1) (e0)))) -> (~((op (e2) (e0)) = (op (e2) (e3)))) -> (~((op (e1) (e2)) = (op (e1) (e3)))) -> ((~((op (e1) (e1)) = (e3)))\/((op (e1) (e3)) = (e1))) -> ((~((op (e2) (e2)) = (e1)))\/((op (e2) (e1)) = (e2))) -> ((~((op (e2) (e2)) = (e0)))\/((op (e2) (e0)) = (e2))) -> (~((op (e1) (e0)) = (op (e1) (e2)))) -> ((~((op (e1) (e1)) = (e2)))\/((op (e1) (e2)) = (e1))) -> (~((op (e0) (e1)) = (op (e2) (e1)))) -> (((op (e0) (e3)) = (e2))\/(((op (e1) (e3)) = (e2))\/(((op (e2) (e3)) = (e2))\/((op (e3) (e3)) = (e2))))) -> (((op (e2) (e0)) = (e3))\/(((op (e2) (e1)) = (e3))\/(((op (e2) (e2)) = (e3))\/((op (e2) (e3)) = (e3))))) -> (~((op (e1) (e0)) = (op (e1) (e1)))) -> ((~((op (e1) (e1)) = (e1)))\/((op (e1) (e1)) = (e1))) -> (~((op (e2) (e0)) = (op (e2) (e2)))) -> (~((op (e2) (e2)) = (op (e2) (e3)))) -> (((op (e1) (e3)) = (e0))\/(((op (e1) (e3)) = (e1))\/(((op (e1) (e3)) = (e2))\/((op (e1) (e3)) = (e3))))) -> (~((op (e2) (e1)) = (op (e3) (e1)))) -> (((op (e3) (e0)) = (e2))\/(((op (e3) (e1)) = (e2))\/(((op (e3) (e2)) = (e2))\/((op (e3) (e3)) = (e2))))) -> (((op (e0) (e1)) = (e0))\/(((op (e1) (e1)) = (e0))\/(((op (e2) (e1)) = (e0))\/((op (e3) (e1)) = (e0))))) -> (((op (e0) (e1)) = (e3))\/(((op (e1) (e1)) = (e3))\/(((op (e2) (e1)) = (e3))\/((op (e3) (e1)) = (e3))))) -> (~((op (e0) (e0)) = (op (e0) (e1)))) -> (~((op (e3) (e0)) = (op (e3) (e1)))) -> (((op (e0) (e1)) = (e1))\/(((op (e1) (e1)) = (e1))\/(((op (e2) (e1)) = (e1))\/((op (e3) (e1)) = (e1))))) -> (((op (e2) (e0)) = (e1))\/(((op (e2) (e1)) = (e1))\/(((op (e2) (e2)) = (e1))\/((op (e2) (e3)) = (e1))))) -> (((op (e0) (e2)) = (e3))\/(((op (e1) (e2)) = (e3))\/(((op (e2) (e2)) = (e3))\/((op (e3) (e2)) = (e3))))) -> (((op (e1) (e0)) = (e1))\/(((op (e1) (e1)) = (e1))\/(((op (e1) (e2)) = (e1))\/((op (e1) (e3)) = (e1))))) -> False). % 15.36/15.50 do 0 intro. intros zenon_H27b zenon_H135 zenon_H25e zenon_H17d zenon_Hc9 zenon_H251 zenon_H28 zenon_H250 zenon_H11b zenon_H254 zenon_H80 zenon_Hb4 zenon_H7d zenon_H138 zenon_Hbe zenon_H42 zenon_Hbb zenon_H2d zenon_H1b3 zenon_Ha3 zenon_H59 zenon_H10f zenon_H44 zenon_H84 zenon_H24f zenon_H1f zenon_H5e zenon_Hd3 zenon_H8f zenon_H58 zenon_H36 zenon_H87 zenon_H8b zenon_H90 zenon_H6a zenon_Heb zenon_Haa zenon_H157 zenon_H1e2 zenon_H1c3 zenon_H22e zenon_H1a2 zenon_H154 zenon_H140 zenon_H146 zenon_H8e zenon_H1cd zenon_H1cf zenon_Ha7 zenon_H121 zenon_H45 zenon_H12d zenon_H10c zenon_H1f5 zenon_H244 zenon_H258 zenon_H173 zenon_H10e zenon_H4b zenon_H16f zenon_Hf1 zenon_H23 zenon_H145 zenon_H163 zenon_H9e zenon_H24c zenon_Hce zenon_H1d0 zenon_H1d2 zenon_H1e3 zenon_H1d4 zenon_H166 zenon_H1d3 zenon_Hde zenon_H160 zenon_He6 zenon_Hd7 zenon_H1d8 zenon_H17a zenon_H15f zenon_H25b zenon_H13c zenon_H1df zenon_H144 zenon_H199 zenon_H25a zenon_H109 zenon_H228 zenon_Hb7 zenon_H175 zenon_H1c5. % 15.36/15.50 apply (zenon_or_s _ _ zenon_H1d8); [ zenon_intro zenon_H1b4 | zenon_intro zenon_H21 ]. % 15.36/15.50 apply (zenon_or_s _ _ zenon_H1d3); [ zenon_intro zenon_Hd6 | zenon_intro zenon_H117 ]. % 15.36/15.50 apply (zenon_or_s _ _ zenon_H1d2); [ zenon_intro zenon_H182 | zenon_intro zenon_H11f ]. % 15.36/15.50 apply (zenon_or_s _ _ zenon_H1d4); [ zenon_intro zenon_H2e | zenon_intro zenon_Hdd ]. % 15.36/15.50 apply (zenon_L636_); trivial. % 15.36/15.50 apply (zenon_or_s _ _ zenon_H1e3); [ zenon_intro zenon_H52 | zenon_intro zenon_H156 ]. % 15.36/15.50 apply (zenon_or_s _ _ zenon_Haa); [ zenon_intro zenon_H2f | zenon_intro zenon_H35 ]. % 15.36/15.50 apply (zenon_or_s _ _ zenon_H1c3); [ zenon_intro zenon_H30 | zenon_intro zenon_H124 ]. % 15.36/15.50 apply (zenon_L643_); trivial. % 15.36/15.50 apply (zenon_L119_); trivial. % 15.36/15.50 apply (zenon_L161_); trivial. % 15.36/15.50 apply (zenon_L284_); trivial. % 15.36/15.50 apply (zenon_or_s _ _ zenon_H1d4); [ zenon_intro zenon_H2e | zenon_intro zenon_Hdd ]. % 15.36/15.50 apply (zenon_L620_); trivial. % 15.36/15.50 apply (zenon_L695_); trivial. % 15.36/15.50 apply (zenon_or_s _ _ zenon_H1d2); [ zenon_intro zenon_H182 | zenon_intro zenon_H11f ]. % 15.36/15.50 apply (zenon_or_s _ _ zenon_H1d4); [ zenon_intro zenon_H2e | zenon_intro zenon_Hdd ]. % 15.36/15.50 apply (zenon_L602_); trivial. % 15.36/15.50 apply (zenon_or_s _ _ zenon_H1e3); [ zenon_intro zenon_H52 | zenon_intro zenon_H156 ]. % 15.36/15.50 apply (zenon_or_s _ _ zenon_Haa); [ zenon_intro zenon_H2f | zenon_intro zenon_H35 ]. % 15.36/15.50 apply (zenon_L584_); trivial. % 15.36/15.50 apply (zenon_L161_); trivial. % 15.36/15.50 apply (zenon_L284_); trivial. % 15.36/15.50 apply (zenon_L237_); trivial. % 15.36/15.50 apply (zenon_L698_); trivial. % 15.36/15.50 (* end of lemma zenon_L732_ *) % 15.36/15.50 assert (zenon_L733_ : ((~((op (e0) (e0)) = (e0)))\/((op (e0) (e0)) = (e0))) -> (~((op (e0) (e0)) = (op (e0) (e1)))) -> (((op (e1) (e3)) = (e0))\/(((op (e1) (e3)) = (e1))\/(((op (e1) (e3)) = (e2))\/((op (e1) (e3)) = (e3))))) -> (~((op (e0) (e0)) = (op (e1) (e0)))) -> (~((op (e0) (e0)) = (op (e2) (e0)))) -> (~((op (e1) (e3)) = (op (e2) (e3)))) -> (~((op (e0) (e0)) = (op (e0) (e3)))) -> (~((op (e0) (e3)) = (op (e2) (e3)))) -> (((op (e0) (e3)) = (e0))\/(((op (e0) (e3)) = (e1))\/(((op (e0) (e3)) = (e2))\/((op (e0) (e3)) = (e3))))) -> (~((op (e0) (e0)) = (op (e0) (e2)))) -> (((op (e3) (e2)) = (e0))\/(((op (e3) (e2)) = (e1))\/(((op (e3) (e2)) = (e2))\/((op (e3) (e2)) = (e3))))) -> ((~((op (e0) (e0)) = (e2)))\/((op (e0) (e2)) = (e0))) -> ((~((op (e1) (e1)) = (e3)))\/((op (e1) (e3)) = (e1))) -> ((~((op (e2) (e2)) = (e1)))\/((op (e2) (e1)) = (e2))) -> ((~((op (e2) (e2)) = (e3)))\/((op (e2) (e3)) = (e2))) -> (~((op (e2) (e1)) = (op (e2) (e3)))) -> (((op (e0) (e1)) = (e3))\/(((op (e1) (e1)) = (e3))\/(((op (e2) (e1)) = (e3))\/((op (e3) (e1)) = (e3))))) -> (~((op (e2) (e0)) = (op (e2) (e3)))) -> (((op (e2) (e0)) = (e0))\/(((op (e2) (e1)) = (e0))\/(((op (e2) (e2)) = (e0))\/((op (e2) (e3)) = (e0))))) -> (((op (e0) (e1)) = (e1))\/(((op (e1) (e1)) = (e1))\/(((op (e2) (e1)) = (e1))\/((op (e3) (e1)) = (e1))))) -> (~((op (e0) (e1)) = (op (e2) (e1)))) -> (~((op (e2) (e1)) = (op (e2) (e2)))) -> (((op (e0) (e0)) = (e3))\/(((op (e0) (e1)) = (e3))\/(((op (e0) (e2)) = (e3))\/((op (e0) (e3)) = (e3))))) -> ((op (e3) (e3)) = (e3)) -> (~((op (e0) (e3)) = (op (e3) (e3)))) -> (~((op (e0) (e2)) = (op (e2) (e2)))) -> (((op (e2) (e2)) = (e0))\/(((op (e2) (e2)) = (e1))\/(((op (e2) (e2)) = (e2))\/((op (e2) (e2)) = (e3))))) -> (~((e0) = (e3))) -> ((~((op (e3) (e3)) = (e0)))\/((op (e3) (e0)) = (e3))) -> (~((op (e3) (e0)) = (op (e3) (e3)))) -> (((op (e0) (e0)) = (e1))\/(((op (e0) (e1)) = (e1))\/(((op (e0) (e2)) = (e1))\/((op (e0) (e3)) = (e1))))) -> (((op (e0) (e3)) = (e0))\/(((op (e1) (e3)) = (e0))\/(((op (e2) (e3)) = (e0))\/((op (e3) (e3)) = (e0))))) -> (~((op (e0) (e1)) = (op (e0) (e3)))) -> (~((e1) = (e2))) -> (((op (e0) (e3)) = (e2))\/(((op (e1) (e3)) = (e2))\/(((op (e2) (e3)) = (e2))\/((op (e3) (e3)) = (e2))))) -> (~((e1) = (e3))) -> (~((e0) = (e1))) -> (~((e0) = (e2))) -> (((op (e1) (e0)) = (e2))\/(((op (e1) (e1)) = (e2))\/(((op (e1) (e2)) = (e2))\/((op (e1) (e3)) = (e2))))) -> (~((op (e0) (e3)) = (op (e1) (e3)))) -> (~((op (e1) (e2)) = (op (e2) (e2)))) -> (~((e2) = (e3))) -> (~((op (e0) (e2)) = (op (e1) (e2)))) -> (~((op (e1) (e3)) = (op (e3) (e3)))) -> (((op (e1) (e0)) = (e3))\/(((op (e1) (e1)) = (e3))\/(((op (e1) (e2)) = (e3))\/((op (e1) (e3)) = (e3))))) -> (((op (e0) (e0)) = (e2))\/(((op (e0) (e1)) = (e2))\/(((op (e0) (e2)) = (e2))\/((op (e0) (e3)) = (e2))))) -> (~((op (e3) (e2)) = (op (e3) (e3)))) -> ((~((op (e3) (e3)) = (e2)))\/((op (e3) (e2)) = (e3))) -> ((~((op (e2) (e2)) = (e2)))\/((op (e2) (e2)) = (e2))) -> (~((op (e2) (e0)) = (op (e2) (e1)))) -> (((op (e2) (e0)) = (e3))\/(((op (e2) (e1)) = (e3))\/(((op (e2) (e2)) = (e3))\/((op (e2) (e3)) = (e3))))) -> (~((op (e2) (e3)) = (op (e3) (e3)))) -> (~((op (e2) (e0)) = (op (e2) (e2)))) -> ((~((op (e2) (e2)) = (e0)))\/((op (e2) (e0)) = (e2))) -> (~((op (e0) (e1)) = (op (e1) (e1)))) -> (((op (e1) (e1)) = (e0))\/(((op (e1) (e1)) = (e1))\/(((op (e1) (e1)) = (e2))\/((op (e1) (e1)) = (e3))))) -> (((op (e0) (e0)) = (e3))\/(((op (e1) (e0)) = (e3))\/(((op (e2) (e0)) = (e3))\/((op (e3) (e0)) = (e3))))) -> (((op (e0) (e0)) = (e2))\/(((op (e1) (e0)) = (e2))\/(((op (e2) (e0)) = (e2))\/((op (e3) (e0)) = (e2))))) -> (~((op (e0) (e2)) = (op (e0) (e3)))) -> (((op (e0) (e2)) = (e3))\/(((op (e1) (e2)) = (e3))\/(((op (e2) (e2)) = (e3))\/((op (e3) (e2)) = (e3))))) -> (((op (e1) (e0)) = (e1))\/(((op (e1) (e1)) = (e1))\/(((op (e1) (e2)) = (e1))\/((op (e1) (e3)) = (e1))))) -> (((op (e0) (e1)) = (e0))\/(((op (e1) (e1)) = (e0))\/(((op (e2) (e1)) = (e0))\/((op (e3) (e1)) = (e0))))) -> (((op (e0) (e0)) = (e0))\/(((op (e1) (e0)) = (e0))\/(((op (e2) (e0)) = (e0))\/((op (e3) (e0)) = (e0))))) -> (((op (e0) (e2)) = (e0))\/(((op (e1) (e2)) = (e0))\/(((op (e2) (e2)) = (e0))\/((op (e3) (e2)) = (e0))))) -> (~((op (e3) (e1)) = (op (e3) (e2)))) -> (~((op (e3) (e0)) = (op (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 (e1) (e1)) = (e0)))\/((op (e1) (e0)) = (e1))) -> (~((op (e1) (e0)) = (op (e1) (e2)))) -> (~((op (e1) (e0)) = (op (e1) (e1)))) -> ((~((op (e1) (e1)) = (e2)))\/((op (e1) (e2)) = (e1))) -> (~((op (e1) (e2)) = (op (e1) (e3)))) -> (~((op (e1) (op (e1) (e1))) = (op (e1) (e1)))) -> ((~((op (e1) (e1)) = (e1)))\/((op (e1) (e1)) = (e1))) -> ((~((op (e0) (e0)) = (e3)))\/((op (e0) (e3)) = (e0))) -> (~((op (e1) (e0)) = (op (e1) (e3)))) -> (((op (e0) (e3)) = (e1))\/(((op (e1) (e3)) = (e1))\/(((op (e2) (e3)) = (e1))\/((op (e3) (e3)) = (e1))))) -> (~((op (e0) (op (e1) (e0))) = (op (e1) (e0)))) -> (((op (e2) (e0)) = (e1))\/(((op (e2) (e1)) = (e1))\/(((op (e2) (e2)) = (e1))\/((op (e2) (e3)) = (e1))))) -> (((op (e0) (e0)) = (e1))\/(((op (e1) (e0)) = (e1))\/(((op (e2) (e0)) = (e1))\/((op (e3) (e0)) = (e1))))) -> (~((op (e3) (e1)) = (op (e3) (e3)))) -> ((~((op (e3) (e3)) = (e1)))\/((op (e3) (e1)) = (e3))) -> (((op (e0) (e0)) = (e0))\/(((op (e0) (e1)) = (e0))\/(((op (e0) (e2)) = (e0))\/((op (e0) (e3)) = (e0))))) -> ((~((op (e3) (e3)) = (e3)))\/((op (e3) (e3)) = (e3))) -> (((op (e3) (e3)) = (e0))\/(((op (e3) (e3)) = (e1))\/(((op (e3) (e3)) = (e2))\/((op (e3) (e3)) = (e3))))) -> (((op (e0) (e0)) = (e0))\/(((op (e0) (e0)) = (e1))\/(((op (e0) (e0)) = (e2))\/((op (e0) (e0)) = (e3))))) -> (((op (e0) (e1)) = (e2))\/(((op (e1) (e1)) = (e2))\/(((op (e2) (e1)) = (e2))\/((op (e3) (e1)) = (e2))))) -> (~((op (e2) (e2)) = (op (e2) (e3)))) -> (((op (e3) (e0)) = (e1))\/(((op (e3) (e1)) = (e1))\/(((op (e3) (e2)) = (e1))\/((op (e3) (e3)) = (e1))))) -> (~((op (e0) (e2)) = (op (e3) (e2)))) -> (~((op (e3) (op (e1) (e3))) = (op (e1) (e3)))) -> (((op (e2) (e0)) = (e2))\/(((op (e2) (e1)) = (e2))\/(((op (e2) (e2)) = (e2))\/((op (e2) (e3)) = (e2))))) -> (((op (e0) (e2)) = (e0))\/(((op (e0) (e2)) = (e1))\/(((op (e0) (e2)) = (e2))\/((op (e0) (e2)) = (e3))))) -> (((op (e3) (e0)) = (e2))\/(((op (e3) (e1)) = (e2))\/(((op (e3) (e2)) = (e2))\/((op (e3) (e3)) = (e2))))) -> (((op (e0) (e2)) = (e2))\/(((op (e1) (e2)) = (e2))\/(((op (e2) (e2)) = (e2))\/((op (e3) (e2)) = (e2))))) -> (~((op (e2) (e1)) = (op (e3) (e1)))) -> (((op (e0) (e2)) = (e1))\/(((op (e1) (e2)) = (e1))\/(((op (e2) (e2)) = (e1))\/((op (e3) (e2)) = (e1))))) -> (~((op (e2) (op (e1) (e2))) = (op (e1) (e2)))) -> (((op (e1) (e0)) = (e0))\/(((op (e1) (e1)) = (e0))\/(((op (e1) (e2)) = (e0))\/((op (e1) (e3)) = (e0))))) -> (~((op (e3) (e0)) = (op (e3) (e2)))) -> (~((op (e1) (e2)) = (op (e3) (e2)))) -> (~((op (e1) (e0)) = (op (e3) (e0)))) -> (~((op (e0) (e1)) = (op (e0) (e2)))) -> ((~((op (e0) (e0)) = (e1)))\/((op (e0) (e1)) = (e0))) -> False). % 15.36/15.50 do 0 intro. intros zenon_H249 zenon_H25a zenon_H25b zenon_H24c zenon_H258 zenon_H244 zenon_H24f zenon_Hb4 zenon_H254 zenon_H250 zenon_H25e zenon_H24a zenon_H1d2 zenon_H1e3 zenon_H1c3 zenon_H1e2 zenon_H199 zenon_Hce zenon_H1f5 zenon_H228 zenon_Hde zenon_H157 zenon_H58 zenon_H42 zenon_H36 zenon_H28 zenon_H2d zenon_H4b zenon_H10f zenon_Hbb zenon_H44 zenon_Hd3 zenon_H1cd zenon_Ha7 zenon_H160 zenon_Ha3 zenon_H9e zenon_H5e zenon_H84 zenon_H80 zenon_H7d zenon_H6a zenon_H87 zenon_H8b zenon_H90 zenon_H8e zenon_H173 zenon_H10e zenon_Haa zenon_H154 zenon_He6 zenon_He3 zenon_H17a zenon_H1d4 zenon_H23 zenon_H1b3 zenon_Hbe zenon_Heb zenon_Hc9 zenon_H175 zenon_H1c5 zenon_H144 zenon_Hf0 zenon_H16f zenon_H135 zenon_H109 zenon_H138 zenon_H16c zenon_H1e4 zenon_H166 zenon_Hd7 zenon_H1d3 zenon_H1d0 zenon_H27b zenon_H1d8 zenon_H236 zenon_H1cf zenon_H121 zenon_H261 zenon_Hb7 zenon_Hf1 zenon_H12d zenon_H10c zenon_H110 zenon_H10d zenon_H3b zenon_H12a zenon_H1a2 zenon_H15f zenon_H146 zenon_H140 zenon_H26e zenon_H237 zenon_H251 zenon_H1df zenon_H27c zenon_H13c zenon_H11b zenon_H277 zenon_H163 zenon_H105 zenon_H17d zenon_H22e zenon_H23e zenon_H24b. % 15.36/15.50 apply (zenon_or_s _ _ zenon_H249); [ zenon_intro zenon_H20 | zenon_intro zenon_H1f ]. % 15.36/15.50 apply (zenon_or_s _ _ zenon_H24b); [ zenon_intro zenon_H45 | zenon_intro zenon_H49 ]. % 15.36/15.50 apply (zenon_or_s _ _ zenon_H24a); [ zenon_intro zenon_H8f | zenon_intro zenon_Hab ]. % 15.36/15.50 apply (zenon_or_s _ _ zenon_H236); [ zenon_intro zenon_H59 | zenon_intro zenon_Hca ]. % 15.36/15.50 apply (zenon_or_s _ _ zenon_H1e4); [ zenon_intro zenon_H145 | zenon_intro zenon_Hd8 ]. % 15.36/15.50 apply (zenon_or_s _ _ zenon_H1d8); [ zenon_intro zenon_H1b4 | zenon_intro zenon_H21 ]. % 15.36/15.50 apply (zenon_or_s _ _ zenon_H1d3); [ zenon_intro zenon_Hd6 | zenon_intro zenon_H117 ]. % 15.36/15.50 apply (zenon_or_s _ _ zenon_H1d2); [ zenon_intro zenon_H182 | zenon_intro zenon_H11f ]. % 15.36/15.50 apply (zenon_or_s _ _ zenon_H1d4); [ zenon_intro zenon_H2e | zenon_intro zenon_Hdd ]. % 15.36/15.50 apply (zenon_or_s _ _ zenon_H1e3); [ zenon_intro zenon_H52 | zenon_intro zenon_H156 ]. % 15.36/15.50 apply (zenon_or_s _ _ zenon_Haa); [ zenon_intro zenon_H2f | zenon_intro zenon_H35 ]. % 15.36/15.50 apply (zenon_or_s _ _ zenon_H1c3); [ zenon_intro zenon_H30 | zenon_intro zenon_H124 ]. % 15.36/15.50 apply (zenon_L705_); trivial. % 15.36/15.50 apply (zenon_or_s _ _ zenon_H10f); [ zenon_intro zenon_H3c | zenon_intro zenon_Hba ]. % 15.36/15.50 apply (zenon_or_s _ _ zenon_H10c); [ zenon_intro zenon_H104 | zenon_intro zenon_H10a ]. % 15.36/15.50 apply (zenon_or_s _ _ zenon_H10e); [ zenon_intro zenon_H3d | zenon_intro zenon_H106 ]. % 15.36/15.50 apply (zenon_or_s _ _ zenon_H110); [ zenon_intro zenon_H1f | zenon_intro zenon_H111 ]. % 15.36/15.50 exact (zenon_H20 zenon_H1f). % 15.36/15.50 apply (zenon_or_s _ _ zenon_H111); [ zenon_intro zenon_H49 | zenon_intro zenon_H112 ]. % 15.36/15.50 apply (zenon_L392_); trivial. % 15.36/15.50 apply (zenon_or_s _ _ zenon_H112); [ zenon_intro zenon_Hab | zenon_intro zenon_Hca ]. % 15.36/15.50 apply (zenon_L231_); trivial. % 15.36/15.50 apply (zenon_L703_); trivial. % 15.36/15.50 apply (zenon_L153_); trivial. % 15.36/15.50 apply (zenon_L102_); trivial. % 15.36/15.50 apply (zenon_L43_); trivial. % 15.36/15.50 apply (zenon_or_s _ _ zenon_H10f); [ zenon_intro zenon_H3c | zenon_intro zenon_Hba ]. % 15.36/15.50 apply (zenon_L348_); trivial. % 15.36/15.50 apply (zenon_L43_); trivial. % 15.36/15.50 apply (zenon_or_s _ _ zenon_Haa); [ zenon_intro zenon_H2f | zenon_intro zenon_H35 ]. % 15.36/15.50 apply (zenon_or_s _ _ zenon_H1c3); [ zenon_intro zenon_H30 | zenon_intro zenon_H124 ]. % 15.36/15.50 apply (zenon_L705_); trivial. % 15.36/15.50 apply (zenon_L256_); trivial. % 15.36/15.50 apply (zenon_L134_); trivial. % 15.36/15.50 apply (zenon_L365_); trivial. % 15.36/15.50 apply (zenon_or_s _ _ zenon_H1d4); [ zenon_intro zenon_H2e | zenon_intro zenon_Hdd ]. % 15.36/15.50 apply (zenon_or_s _ _ zenon_H1e3); [ zenon_intro zenon_H52 | zenon_intro zenon_H156 ]. % 15.36/15.50 apply (zenon_or_s _ _ zenon_Haa); [ zenon_intro zenon_H2f | zenon_intro zenon_H35 ]. % 15.36/15.50 apply (zenon_or_s _ _ zenon_H1c3); [ zenon_intro zenon_H30 | zenon_intro zenon_H124 ]. % 15.36/15.50 apply (zenon_or_s _ _ zenon_H10f); [ zenon_intro zenon_H3c | zenon_intro zenon_Hba ]. % 15.36/15.50 apply (zenon_or_s _ _ zenon_H10c); [ zenon_intro zenon_H104 | zenon_intro zenon_H10a ]. % 15.36/15.50 apply (zenon_or_s _ _ zenon_H10e); [ zenon_intro zenon_H3d | zenon_intro zenon_H106 ]. % 15.36/15.50 apply (zenon_or_s _ _ zenon_H110); [ zenon_intro zenon_H1f | zenon_intro zenon_H111 ]. % 15.36/15.50 exact (zenon_H20 zenon_H1f). % 15.36/15.50 apply (zenon_or_s _ _ zenon_H111); [ zenon_intro zenon_H49 | zenon_intro zenon_H112 ]. % 15.36/15.50 apply (zenon_L13_); trivial. % 15.36/15.50 apply (zenon_or_s _ _ zenon_H112); [ zenon_intro zenon_Hab | zenon_intro zenon_Hca ]. % 15.36/15.50 apply (zenon_L235_); trivial. % 15.36/15.50 apply (zenon_L724_); trivial. % 15.36/15.50 apply (zenon_L153_); trivial. % 15.36/15.50 apply (zenon_L102_); trivial. % 15.36/15.50 apply (zenon_L43_); trivial. % 15.36/15.50 apply (zenon_or_s _ _ zenon_H10f); [ zenon_intro zenon_H3c | zenon_intro zenon_Hba ]. % 15.36/15.50 apply (zenon_or_s _ _ zenon_H10c); [ zenon_intro zenon_H104 | zenon_intro zenon_H10a ]. % 15.36/15.50 apply (zenon_or_s _ _ zenon_H10e); [ zenon_intro zenon_H3d | zenon_intro zenon_H106 ]. % 15.36/15.50 apply (zenon_or_s _ _ zenon_H110); [ zenon_intro zenon_H1f | zenon_intro zenon_H111 ]. % 15.36/15.50 exact (zenon_H20 zenon_H1f). % 15.36/15.50 apply (zenon_or_s _ _ zenon_H111); [ zenon_intro zenon_H49 | zenon_intro zenon_H112 ]. % 15.36/15.50 apply (zenon_L370_); trivial. % 15.36/15.50 apply (zenon_or_s _ _ zenon_H112); [ zenon_intro zenon_Hab | zenon_intro zenon_Hca ]. % 15.36/15.50 apply (zenon_L235_); trivial. % 15.36/15.50 apply (zenon_L730_); trivial. % 15.36/15.50 apply (zenon_L153_); trivial. % 15.36/15.50 apply (zenon_L102_); trivial. % 15.36/15.50 apply (zenon_L43_); trivial. % 15.36/15.50 apply (zenon_L426_); trivial. % 15.36/15.50 apply (zenon_L430_); trivial. % 15.36/15.50 apply (zenon_L432_); trivial. % 15.36/15.50 apply (zenon_L441_); trivial. % 15.36/15.50 apply (zenon_L698_); trivial. % 15.36/15.50 apply (zenon_L448_); trivial. % 15.36/15.50 apply (zenon_or_s _ _ zenon_H1e4); [ zenon_intro zenon_H145 | zenon_intro zenon_Hd8 ]. % 15.36/15.50 apply (zenon_or_s _ _ zenon_H1d8); [ zenon_intro zenon_H1b4 | zenon_intro zenon_H21 ]. % 15.36/15.50 apply (zenon_or_s _ _ zenon_H1d3); [ zenon_intro zenon_Hd6 | zenon_intro zenon_H117 ]. % 15.36/15.51 apply (zenon_or_s _ _ zenon_H1d2); [ zenon_intro zenon_H182 | zenon_intro zenon_H11f ]. % 15.36/15.51 apply (zenon_or_s _ _ zenon_H1d4); [ zenon_intro zenon_H2e | zenon_intro zenon_Hdd ]. % 15.36/15.51 apply (zenon_L704_); trivial. % 15.36/15.51 apply (zenon_L449_); trivial. % 15.36/15.51 apply (zenon_or_s _ _ zenon_H1d4); [ zenon_intro zenon_H2e | zenon_intro zenon_Hdd ]. % 15.36/15.51 apply (zenon_or_s _ _ zenon_H1e3); [ zenon_intro zenon_H52 | zenon_intro zenon_H156 ]. % 15.36/15.51 apply (zenon_or_s _ _ zenon_Haa); [ zenon_intro zenon_H2f | zenon_intro zenon_H35 ]. % 15.36/15.51 apply (zenon_or_s _ _ zenon_H1c3); [ zenon_intro zenon_H30 | zenon_intro zenon_H124 ]. % 15.36/15.51 apply (zenon_or_s _ _ zenon_H10f); [ zenon_intro zenon_H3c | zenon_intro zenon_Hba ]. % 15.36/15.51 apply (zenon_or_s _ _ zenon_H10c); [ zenon_intro zenon_H104 | zenon_intro zenon_H10a ]. % 15.36/15.51 apply (zenon_L724_); trivial. % 15.36/15.51 apply (zenon_L102_); trivial. % 15.36/15.51 apply (zenon_L43_); trivial. % 15.36/15.51 apply (zenon_or_s _ _ zenon_H10f); [ zenon_intro zenon_H3c | zenon_intro zenon_Hba ]. % 15.36/15.51 apply (zenon_or_s _ _ zenon_H10c); [ zenon_intro zenon_H104 | zenon_intro zenon_H10a ]. % 15.36/15.51 apply (zenon_or_s _ _ zenon_H10e); [ zenon_intro zenon_H3d | zenon_intro zenon_H106 ]. % 15.36/15.51 apply (zenon_L730_); trivial. % 15.36/15.51 apply (zenon_L153_); trivial. % 15.36/15.51 apply (zenon_L102_); trivial. % 15.36/15.51 apply (zenon_L43_); trivial. % 15.36/15.51 apply (zenon_L450_); trivial. % 15.36/15.51 apply (zenon_L451_); trivial. % 15.36/15.51 apply (zenon_L431_); trivial. % 15.36/15.51 apply (zenon_L453_); trivial. % 15.36/15.51 apply (zenon_L698_); trivial. % 15.36/15.51 apply (zenon_L454_); trivial. % 15.36/15.51 apply (zenon_L700_); trivial. % 15.36/15.51 apply (zenon_or_s _ _ zenon_H24a); [ zenon_intro zenon_H8f | zenon_intro zenon_Hab ]. % 15.36/15.51 apply (zenon_L731_); trivial. % 15.36/15.51 apply (zenon_L485_); trivial. % 15.36/15.51 apply (zenon_or_s _ _ zenon_H24b); [ zenon_intro zenon_H45 | zenon_intro zenon_H49 ]. % 15.36/15.51 apply (zenon_or_s _ _ zenon_H24a); [ zenon_intro zenon_H8f | zenon_intro zenon_Hab ]. % 15.36/15.51 apply (zenon_or_s _ _ zenon_H236); [ zenon_intro zenon_H59 | zenon_intro zenon_Hca ]. % 15.36/15.51 apply (zenon_or_s _ _ zenon_H1e4); [ zenon_intro zenon_H145 | zenon_intro zenon_Hd8 ]. % 15.36/15.51 apply (zenon_L732_); trivial. % 15.36/15.51 apply (zenon_L583_); trivial. % 15.36/15.51 apply (zenon_L562_); trivial. % 15.36/15.51 apply (zenon_L567_); trivial. % 15.36/15.51 apply (zenon_L610_); trivial. % 15.36/15.51 (* end of lemma zenon_L733_ *) % 15.36/15.51 assert (zenon_L734_ : (((op (e0) (e0)) = (e2))\/(((op (e1) (e0)) = (e2))\/(((op (e2) (e0)) = (e2))\/((op (e3) (e0)) = (e2))))) -> (((op (e3) (e3)) = (e0))\/(((op (e3) (e3)) = (e1))\/(((op (e3) (e3)) = (e2))\/((op (e3) (e3)) = (e3))))) -> (~((op (e3) (e3)) = (e0))) -> (~((op (e1) (e1)) = (e1))) -> (~((op (e1) (e1)) = (e2))) -> (~((op (e1) (e1)) = (e3))) -> (((op (e1) (e1)) = (e0))\/(((op (e1) (e1)) = (e1))\/(((op (e1) (e1)) = (e2))\/((op (e1) (e1)) = (e3))))) -> ((op (e2) (e2)) = (e2)) -> (~((op (e2) (e0)) = (op (e2) (e2)))) -> ((op (e1) (e0)) = (e1)) -> (~((e1) = (e2))) -> (~((op (e0) (e0)) = (e2))) -> ((~((op (e0) (e0)) = (e0)))\/((op (e0) (e0)) = (e0))) -> (~((op (e0) (e0)) = (op (e0) (e1)))) -> (((op (e1) (e3)) = (e0))\/(((op (e1) (e3)) = (e1))\/(((op (e1) (e3)) = (e2))\/((op (e1) (e3)) = (e3))))) -> (~((op (e0) (e0)) = (op (e1) (e0)))) -> (~((op (e0) (e0)) = (op (e2) (e0)))) -> (~((op (e1) (e3)) = (op (e2) (e3)))) -> (~((op (e0) (e0)) = (op (e0) (e3)))) -> (~((op (e0) (e3)) = (op (e2) (e3)))) -> (((op (e0) (e3)) = (e0))\/(((op (e0) (e3)) = (e1))\/(((op (e0) (e3)) = (e2))\/((op (e0) (e3)) = (e3))))) -> (~((op (e0) (e0)) = (op (e0) (e2)))) -> (((op (e3) (e2)) = (e0))\/(((op (e3) (e2)) = (e1))\/(((op (e3) (e2)) = (e2))\/((op (e3) (e2)) = (e3))))) -> ((~((op (e0) (e0)) = (e2)))\/((op (e0) (e2)) = (e0))) -> ((~((op (e1) (e1)) = (e3)))\/((op (e1) (e3)) = (e1))) -> ((~((op (e2) (e2)) = (e1)))\/((op (e2) (e1)) = (e2))) -> ((~((op (e2) (e2)) = (e3)))\/((op (e2) (e3)) = (e2))) -> (~((op (e2) (e1)) = (op (e2) (e3)))) -> (((op (e0) (e1)) = (e3))\/(((op (e1) (e1)) = (e3))\/(((op (e2) (e1)) = (e3))\/((op (e3) (e1)) = (e3))))) -> (~((op (e2) (e0)) = (op (e2) (e3)))) -> (((op (e2) (e0)) = (e0))\/(((op (e2) (e1)) = (e0))\/(((op (e2) (e2)) = (e0))\/((op (e2) (e3)) = (e0))))) -> (((op (e0) (e1)) = (e1))\/(((op (e1) (e1)) = (e1))\/(((op (e2) (e1)) = (e1))\/((op (e3) (e1)) = (e1))))) -> (~((op (e0) (e1)) = (op (e2) (e1)))) -> (~((op (e2) (e1)) = (op (e2) (e2)))) -> (((op (e0) (e0)) = (e3))\/(((op (e0) (e1)) = (e3))\/(((op (e0) (e2)) = (e3))\/((op (e0) (e3)) = (e3))))) -> (~((op (e0) (e3)) = (op (e3) (e3)))) -> (~((op (e0) (e2)) = (op (e2) (e2)))) -> (((op (e2) (e2)) = (e0))\/(((op (e2) (e2)) = (e1))\/(((op (e2) (e2)) = (e2))\/((op (e2) (e2)) = (e3))))) -> (~((e0) = (e3))) -> ((~((op (e3) (e3)) = (e0)))\/((op (e3) (e0)) = (e3))) -> (~((op (e3) (e0)) = (op (e3) (e3)))) -> (((op (e0) (e0)) = (e1))\/(((op (e0) (e1)) = (e1))\/(((op (e0) (e2)) = (e1))\/((op (e0) (e3)) = (e1))))) -> (((op (e0) (e3)) = (e0))\/(((op (e1) (e3)) = (e0))\/(((op (e2) (e3)) = (e0))\/((op (e3) (e3)) = (e0))))) -> (~((op (e0) (e1)) = (op (e0) (e3)))) -> (((op (e0) (e3)) = (e2))\/(((op (e1) (e3)) = (e2))\/(((op (e2) (e3)) = (e2))\/((op (e3) (e3)) = (e2))))) -> (~((e1) = (e3))) -> (~((e0) = (e1))) -> (~((e0) = (e2))) -> (((op (e1) (e0)) = (e2))\/(((op (e1) (e1)) = (e2))\/(((op (e1) (e2)) = (e2))\/((op (e1) (e3)) = (e2))))) -> (~((op (e0) (e3)) = (op (e1) (e3)))) -> (~((op (e1) (e2)) = (op (e2) (e2)))) -> (~((e2) = (e3))) -> (~((op (e0) (e2)) = (op (e1) (e2)))) -> (~((op (e1) (e3)) = (op (e3) (e3)))) -> (((op (e1) (e0)) = (e3))\/(((op (e1) (e1)) = (e3))\/(((op (e1) (e2)) = (e3))\/((op (e1) (e3)) = (e3))))) -> (((op (e0) (e0)) = (e2))\/(((op (e0) (e1)) = (e2))\/(((op (e0) (e2)) = (e2))\/((op (e0) (e3)) = (e2))))) -> (~((op (e3) (e2)) = (op (e3) (e3)))) -> ((~((op (e3) (e3)) = (e2)))\/((op (e3) (e2)) = (e3))) -> ((~((op (e2) (e2)) = (e2)))\/((op (e2) (e2)) = (e2))) -> (~((op (e2) (e0)) = (op (e2) (e1)))) -> (((op (e2) (e0)) = (e3))\/(((op (e2) (e1)) = (e3))\/(((op (e2) (e2)) = (e3))\/((op (e2) (e3)) = (e3))))) -> (~((op (e2) (e3)) = (op (e3) (e3)))) -> ((~((op (e2) (e2)) = (e0)))\/((op (e2) (e0)) = (e2))) -> (~((op (e0) (e1)) = (op (e1) (e1)))) -> (((op (e0) (e0)) = (e3))\/(((op (e1) (e0)) = (e3))\/(((op (e2) (e0)) = (e3))\/((op (e3) (e0)) = (e3))))) -> (~((op (e0) (e2)) = (op (e0) (e3)))) -> (((op (e0) (e2)) = (e3))\/(((op (e1) (e2)) = (e3))\/(((op (e2) (e2)) = (e3))\/((op (e3) (e2)) = (e3))))) -> (((op (e1) (e0)) = (e1))\/(((op (e1) (e1)) = (e1))\/(((op (e1) (e2)) = (e1))\/((op (e1) (e3)) = (e1))))) -> (((op (e0) (e1)) = (e0))\/(((op (e1) (e1)) = (e0))\/(((op (e2) (e1)) = (e0))\/((op (e3) (e1)) = (e0))))) -> (((op (e0) (e0)) = (e0))\/(((op (e1) (e0)) = (e0))\/(((op (e2) (e0)) = (e0))\/((op (e3) (e0)) = (e0))))) -> (((op (e0) (e2)) = (e0))\/(((op (e1) (e2)) = (e0))\/(((op (e2) (e2)) = (e0))\/((op (e3) (e2)) = (e0))))) -> (~((op (e3) (e1)) = (op (e3) (e2)))) -> (~((op (e3) (e0)) = (op (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 (e1) (e1)) = (e0)))\/((op (e1) (e0)) = (e1))) -> (~((op (e1) (e0)) = (op (e1) (e2)))) -> (~((op (e1) (e0)) = (op (e1) (e1)))) -> ((~((op (e1) (e1)) = (e2)))\/((op (e1) (e2)) = (e1))) -> (~((op (e1) (e2)) = (op (e1) (e3)))) -> (~((op (e1) (op (e1) (e1))) = (op (e1) (e1)))) -> ((~((op (e1) (e1)) = (e1)))\/((op (e1) (e1)) = (e1))) -> ((~((op (e0) (e0)) = (e3)))\/((op (e0) (e3)) = (e0))) -> (~((op (e1) (e0)) = (op (e1) (e3)))) -> (((op (e0) (e3)) = (e1))\/(((op (e1) (e3)) = (e1))\/(((op (e2) (e3)) = (e1))\/((op (e3) (e3)) = (e1))))) -> (~((op (e0) (op (e1) (e0))) = (op (e1) (e0)))) -> (((op (e2) (e0)) = (e1))\/(((op (e2) (e1)) = (e1))\/(((op (e2) (e2)) = (e1))\/((op (e2) (e3)) = (e1))))) -> (((op (e0) (e0)) = (e1))\/(((op (e1) (e0)) = (e1))\/(((op (e2) (e0)) = (e1))\/((op (e3) (e0)) = (e1))))) -> (~((op (e3) (e1)) = (op (e3) (e3)))) -> ((~((op (e3) (e3)) = (e1)))\/((op (e3) (e1)) = (e3))) -> (((op (e0) (e0)) = (e0))\/(((op (e0) (e1)) = (e0))\/(((op (e0) (e2)) = (e0))\/((op (e0) (e3)) = (e0))))) -> ((~((op (e3) (e3)) = (e3)))\/((op (e3) (e3)) = (e3))) -> (((op (e0) (e0)) = (e0))\/(((op (e0) (e0)) = (e1))\/(((op (e0) (e0)) = (e2))\/((op (e0) (e0)) = (e3))))) -> (((op (e0) (e1)) = (e2))\/(((op (e1) (e1)) = (e2))\/(((op (e2) (e1)) = (e2))\/((op (e3) (e1)) = (e2))))) -> (~((op (e2) (e2)) = (op (e2) (e3)))) -> (((op (e3) (e0)) = (e1))\/(((op (e3) (e1)) = (e1))\/(((op (e3) (e2)) = (e1))\/((op (e3) (e3)) = (e1))))) -> (~((op (e0) (e2)) = (op (e3) (e2)))) -> (~((op (e3) (op (e1) (e3))) = (op (e1) (e3)))) -> (((op (e2) (e0)) = (e2))\/(((op (e2) (e1)) = (e2))\/(((op (e2) (e2)) = (e2))\/((op (e2) (e3)) = (e2))))) -> (((op (e0) (e2)) = (e0))\/(((op (e0) (e2)) = (e1))\/(((op (e0) (e2)) = (e2))\/((op (e0) (e2)) = (e3))))) -> (((op (e3) (e0)) = (e2))\/(((op (e3) (e1)) = (e2))\/(((op (e3) (e2)) = (e2))\/((op (e3) (e3)) = (e2))))) -> (((op (e0) (e2)) = (e2))\/(((op (e1) (e2)) = (e2))\/(((op (e2) (e2)) = (e2))\/((op (e3) (e2)) = (e2))))) -> (~((op (e2) (e1)) = (op (e3) (e1)))) -> (((op (e0) (e2)) = (e1))\/(((op (e1) (e2)) = (e1))\/(((op (e2) (e2)) = (e1))\/((op (e3) (e2)) = (e1))))) -> (~((op (e2) (op (e1) (e2))) = (op (e1) (e2)))) -> (((op (e1) (e0)) = (e0))\/(((op (e1) (e1)) = (e0))\/(((op (e1) (e2)) = (e0))\/((op (e1) (e3)) = (e0))))) -> (~((op (e3) (e0)) = (op (e3) (e2)))) -> (~((op (e1) (e2)) = (op (e3) (e2)))) -> (~((op (e1) (e0)) = (op (e3) (e0)))) -> (~((op (e0) (e1)) = (op (e0) (e2)))) -> ((~((op (e0) (e0)) = (e1)))\/((op (e0) (e1)) = (e0))) -> False). % 15.36/15.51 do 0 intro. intros zenon_Heb zenon_H3b zenon_H3c zenon_H1b4 zenon_Hd6 zenon_H182 zenon_H1b3 zenon_H35 zenon_H17a zenon_Hd8 zenon_Ha7 zenon_H8f zenon_H249 zenon_H25a zenon_H25b zenon_H24c zenon_H258 zenon_H244 zenon_H24f zenon_Hb4 zenon_H254 zenon_H250 zenon_H25e zenon_H24a zenon_H1d2 zenon_H1e3 zenon_H1c3 zenon_H1e2 zenon_H199 zenon_Hce zenon_H1f5 zenon_H228 zenon_Hde zenon_H157 zenon_H58 zenon_H36 zenon_H28 zenon_H2d zenon_H4b zenon_H10f zenon_Hbb zenon_H44 zenon_Hd3 zenon_H1cd zenon_H160 zenon_Ha3 zenon_H9e zenon_H5e zenon_H84 zenon_H80 zenon_H7d zenon_H6a zenon_H87 zenon_H8b zenon_H90 zenon_H8e zenon_H173 zenon_H10e zenon_Haa zenon_H154 zenon_He6 zenon_He3 zenon_H1d4 zenon_H23 zenon_Hbe zenon_Hc9 zenon_H175 zenon_H1c5 zenon_H144 zenon_Hf0 zenon_H16f zenon_H135 zenon_H109 zenon_H138 zenon_H16c zenon_H1e4 zenon_H166 zenon_Hd7 zenon_H1d3 zenon_H1d0 zenon_H27b zenon_H1d8 zenon_H236 zenon_H1cf zenon_H121 zenon_H261 zenon_Hb7 zenon_Hf1 zenon_H12d zenon_H10c zenon_H110 zenon_H10d zenon_H12a zenon_H1a2 zenon_H15f zenon_H146 zenon_H140 zenon_H26e zenon_H237 zenon_H251 zenon_H1df zenon_H27c zenon_H13c zenon_H11b zenon_H277 zenon_H163 zenon_H105 zenon_H17d zenon_H22e zenon_H23e zenon_H24b. % 15.36/15.51 apply (zenon_or_s _ _ zenon_H10e); [ zenon_intro zenon_H3d | zenon_intro zenon_H106 ]. % 15.36/15.51 apply (zenon_or_s _ _ zenon_H10d); [ zenon_intro zenon_H3e | zenon_intro zenon_H42 ]. % 15.36/15.51 apply (zenon_L508_); trivial. % 15.36/15.51 apply (zenon_L733_); trivial. % 15.36/15.51 apply (zenon_L167_); trivial. % 15.36/15.51 (* end of lemma zenon_L734_ *) % 15.36/15.51 assert (zenon_L735_ : (((op (e2) (e0)) = (e0))\/(((op (e2) (e0)) = (e1))\/(((op (e2) (e0)) = (e2))\/((op (e2) (e0)) = (e3))))) -> ((op (e0) (e0)) = (e0)) -> (~((op (e0) (e0)) = (op (e2) (e0)))) -> ((op (e1) (e0)) = (e1)) -> (~((op (e1) (e0)) = (op (e2) (e0)))) -> (~((op (e2) (e0)) = (op (e2) (e2)))) -> ((op (e2) (e2)) = (e2)) -> ((op (e3) (e0)) = (e3)) -> (~((op (e2) (e0)) = (op (e3) (e0)))) -> False). % 15.36/15.51 do 0 intro. intros zenon_H281 zenon_H1f zenon_H258 zenon_Hd8 zenon_H247 zenon_H17a zenon_H35 zenon_Hba zenon_H1e5. % 15.36/15.51 apply (zenon_or_s _ _ zenon_H281); [ zenon_intro zenon_Hcf | zenon_intro zenon_H282 ]. % 15.36/15.51 apply (zenon_L598_); trivial. % 15.36/15.51 apply (zenon_or_s _ _ zenon_H282); [ zenon_intro zenon_Hae | zenon_intro zenon_H283 ]. % 15.36/15.51 apply (zenon_L540_); trivial. % 15.36/15.51 apply (zenon_or_s _ _ zenon_H283); [ zenon_intro zenon_Hdd | zenon_intro zenon_Haf ]. % 15.36/15.51 apply (zenon_L161_); trivial. % 15.36/15.51 apply (zenon_L261_); trivial. % 15.36/15.51 (* end of lemma zenon_L735_ *) % 15.36/15.51 assert (zenon_L736_ : (((op (e0) (e0)) = (e2))\/(((op (e1) (e0)) = (e2))\/(((op (e2) (e0)) = (e2))\/((op (e3) (e0)) = (e2))))) -> (((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 (e2) (e2)) = (e2)) -> (~((op (e2) (e0)) = (op (e2) (e2)))) -> ((op (e1) (e0)) = (e1)) -> (~((e1) = (e2))) -> (~((op (e0) (e0)) = (e2))) -> ((~((op (e0) (e0)) = (e0)))\/((op (e0) (e0)) = (e0))) -> (~((op (e0) (e0)) = (op (e0) (e1)))) -> (((op (e1) (e3)) = (e0))\/(((op (e1) (e3)) = (e1))\/(((op (e1) (e3)) = (e2))\/((op (e1) (e3)) = (e3))))) -> (~((op (e0) (e0)) = (op (e1) (e0)))) -> (~((op (e0) (e0)) = (op (e2) (e0)))) -> (~((op (e1) (e3)) = (op (e2) (e3)))) -> (~((op (e0) (e0)) = (op (e0) (e3)))) -> (~((op (e0) (e3)) = (op (e2) (e3)))) -> (((op (e0) (e3)) = (e0))\/(((op (e0) (e3)) = (e1))\/(((op (e0) (e3)) = (e2))\/((op (e0) (e3)) = (e3))))) -> (~((op (e0) (e0)) = (op (e0) (e2)))) -> (((op (e3) (e2)) = (e0))\/(((op (e3) (e2)) = (e1))\/(((op (e3) (e2)) = (e2))\/((op (e3) (e2)) = (e3))))) -> ((~((op (e0) (e0)) = (e2)))\/((op (e0) (e2)) = (e0))) -> ((~((op (e1) (e1)) = (e3)))\/((op (e1) (e3)) = (e1))) -> ((~((op (e2) (e2)) = (e1)))\/((op (e2) (e1)) = (e2))) -> ((~((op (e2) (e2)) = (e3)))\/((op (e2) (e3)) = (e2))) -> (~((op (e2) (e1)) = (op (e2) (e3)))) -> (((op (e0) (e1)) = (e3))\/(((op (e1) (e1)) = (e3))\/(((op (e2) (e1)) = (e3))\/((op (e3) (e1)) = (e3))))) -> (~((op (e2) (e0)) = (op (e2) (e3)))) -> (((op (e2) (e0)) = (e0))\/(((op (e2) (e1)) = (e0))\/(((op (e2) (e2)) = (e0))\/((op (e2) (e3)) = (e0))))) -> (((op (e0) (e1)) = (e1))\/(((op (e1) (e1)) = (e1))\/(((op (e2) (e1)) = (e1))\/((op (e3) (e1)) = (e1))))) -> (~((op (e0) (e1)) = (op (e2) (e1)))) -> (~((op (e2) (e1)) = (op (e2) (e2)))) -> (((op (e0) (e0)) = (e3))\/(((op (e0) (e1)) = (e3))\/(((op (e0) (e2)) = (e3))\/((op (e0) (e3)) = (e3))))) -> (~((op (e0) (e3)) = (op (e3) (e3)))) -> (~((op (e0) (e2)) = (op (e2) (e2)))) -> (((op (e2) (e2)) = (e0))\/(((op (e2) (e2)) = (e1))\/(((op (e2) (e2)) = (e2))\/((op (e2) (e2)) = (e3))))) -> (~((e0) = (e3))) -> ((~((op (e3) (e3)) = (e0)))\/((op (e3) (e0)) = (e3))) -> (~((op (e3) (e0)) = (op (e3) (e3)))) -> (((op (e0) (e0)) = (e1))\/(((op (e0) (e1)) = (e1))\/(((op (e0) (e2)) = (e1))\/((op (e0) (e3)) = (e1))))) -> (((op (e0) (e3)) = (e0))\/(((op (e1) (e3)) = (e0))\/(((op (e2) (e3)) = (e0))\/((op (e3) (e3)) = (e0))))) -> (~((op (e0) (e1)) = (op (e0) (e3)))) -> (((op (e0) (e3)) = (e2))\/(((op (e1) (e3)) = (e2))\/(((op (e2) (e3)) = (e2))\/((op (e3) (e3)) = (e2))))) -> (~((e1) = (e3))) -> (~((e0) = (e1))) -> (~((e0) = (e2))) -> (((op (e1) (e0)) = (e2))\/(((op (e1) (e1)) = (e2))\/(((op (e1) (e2)) = (e2))\/((op (e1) (e3)) = (e2))))) -> (~((op (e0) (e3)) = (op (e1) (e3)))) -> (~((op (e1) (e2)) = (op (e2) (e2)))) -> (~((e2) = (e3))) -> (~((op (e0) (e2)) = (op (e1) (e2)))) -> (~((op (e1) (e3)) = (op (e3) (e3)))) -> (((op (e1) (e0)) = (e3))\/(((op (e1) (e1)) = (e3))\/(((op (e1) (e2)) = (e3))\/((op (e1) (e3)) = (e3))))) -> (((op (e0) (e0)) = (e2))\/(((op (e0) (e1)) = (e2))\/(((op (e0) (e2)) = (e2))\/((op (e0) (e3)) = (e2))))) -> (~((op (e3) (e2)) = (op (e3) (e3)))) -> ((~((op (e3) (e3)) = (e2)))\/((op (e3) (e2)) = (e3))) -> ((~((op (e2) (e2)) = (e2)))\/((op (e2) (e2)) = (e2))) -> (~((op (e2) (e0)) = (op (e2) (e1)))) -> (((op (e2) (e0)) = (e3))\/(((op (e2) (e1)) = (e3))\/(((op (e2) (e2)) = (e3))\/((op (e2) (e3)) = (e3))))) -> (~((op (e2) (e3)) = (op (e3) (e3)))) -> ((~((op (e2) (e2)) = (e0)))\/((op (e2) (e0)) = (e2))) -> (~((op (e0) (e1)) = (op (e1) (e1)))) -> (((op (e0) (e0)) = (e3))\/(((op (e1) (e0)) = (e3))\/(((op (e2) (e0)) = (e3))\/((op (e3) (e0)) = (e3))))) -> (~((op (e0) (e2)) = (op (e0) (e3)))) -> (((op (e0) (e2)) = (e3))\/(((op (e1) (e2)) = (e3))\/(((op (e2) (e2)) = (e3))\/((op (e3) (e2)) = (e3))))) -> (((op (e1) (e0)) = (e1))\/(((op (e1) (e1)) = (e1))\/(((op (e1) (e2)) = (e1))\/((op (e1) (e3)) = (e1))))) -> (((op (e0) (e1)) = (e0))\/(((op (e1) (e1)) = (e0))\/(((op (e2) (e1)) = (e0))\/((op (e3) (e1)) = (e0))))) -> (((op (e0) (e0)) = (e0))\/(((op (e1) (e0)) = (e0))\/(((op (e2) (e0)) = (e0))\/((op (e3) (e0)) = (e0))))) -> (((op (e0) (e2)) = (e0))\/(((op (e1) (e2)) = (e0))\/(((op (e2) (e2)) = (e0))\/((op (e3) (e2)) = (e0))))) -> (~((op (e3) (e1)) = (op (e3) (e2)))) -> (~((op (e3) (e0)) = (op (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 (e1) (e1)) = (e0)))\/((op (e1) (e0)) = (e1))) -> (~((op (e1) (e0)) = (op (e1) (e2)))) -> (~((op (e1) (e0)) = (op (e1) (e1)))) -> ((~((op (e1) (e1)) = (e2)))\/((op (e1) (e2)) = (e1))) -> (~((op (e1) (e2)) = (op (e1) (e3)))) -> (~((op (e1) (op (e1) (e1))) = (op (e1) (e1)))) -> ((~((op (e1) (e1)) = (e1)))\/((op (e1) (e1)) = (e1))) -> ((~((op (e0) (e0)) = (e3)))\/((op (e0) (e3)) = (e0))) -> (~((op (e1) (e0)) = (op (e1) (e3)))) -> (((op (e0) (e3)) = (e1))\/(((op (e1) (e3)) = (e1))\/(((op (e2) (e3)) = (e1))\/((op (e3) (e3)) = (e1))))) -> (~((op (e0) (op (e1) (e0))) = (op (e1) (e0)))) -> (((op (e2) (e0)) = (e1))\/(((op (e2) (e1)) = (e1))\/(((op (e2) (e2)) = (e1))\/((op (e2) (e3)) = (e1))))) -> (((op (e0) (e0)) = (e1))\/(((op (e1) (e0)) = (e1))\/(((op (e2) (e0)) = (e1))\/((op (e3) (e0)) = (e1))))) -> (~((op (e3) (e1)) = (op (e3) (e3)))) -> ((~((op (e3) (e3)) = (e1)))\/((op (e3) (e1)) = (e3))) -> (((op (e0) (e0)) = (e0))\/(((op (e0) (e1)) = (e0))\/(((op (e0) (e2)) = (e0))\/((op (e0) (e3)) = (e0))))) -> ((~((op (e3) (e3)) = (e3)))\/((op (e3) (e3)) = (e3))) -> (((op (e0) (e0)) = (e0))\/(((op (e0) (e0)) = (e1))\/(((op (e0) (e0)) = (e2))\/((op (e0) (e0)) = (e3))))) -> (((op (e0) (e1)) = (e2))\/(((op (e1) (e1)) = (e2))\/(((op (e2) (e1)) = (e2))\/((op (e3) (e1)) = (e2))))) -> (~((op (e2) (e2)) = (op (e2) (e3)))) -> (((op (e3) (e0)) = (e1))\/(((op (e3) (e1)) = (e1))\/(((op (e3) (e2)) = (e1))\/((op (e3) (e3)) = (e1))))) -> (~((op (e0) (e2)) = (op (e3) (e2)))) -> (~((op (e3) (op (e1) (e3))) = (op (e1) (e3)))) -> (((op (e2) (e0)) = (e2))\/(((op (e2) (e1)) = (e2))\/(((op (e2) (e2)) = (e2))\/((op (e2) (e3)) = (e2))))) -> (((op (e0) (e2)) = (e0))\/(((op (e0) (e2)) = (e1))\/(((op (e0) (e2)) = (e2))\/((op (e0) (e2)) = (e3))))) -> (((op (e3) (e0)) = (e2))\/(((op (e3) (e1)) = (e2))\/(((op (e3) (e2)) = (e2))\/((op (e3) (e3)) = (e2))))) -> (((op (e0) (e2)) = (e2))\/(((op (e1) (e2)) = (e2))\/(((op (e2) (e2)) = (e2))\/((op (e3) (e2)) = (e2))))) -> (~((op (e2) (e1)) = (op (e3) (e1)))) -> (((op (e0) (e2)) = (e1))\/(((op (e1) (e2)) = (e1))\/(((op (e2) (e2)) = (e1))\/((op (e3) (e2)) = (e1))))) -> (~((op (e2) (op (e1) (e2))) = (op (e1) (e2)))) -> (((op (e1) (e0)) = (e0))\/(((op (e1) (e1)) = (e0))\/(((op (e1) (e2)) = (e0))\/((op (e1) (e3)) = (e0))))) -> (~((op (e3) (e0)) = (op (e3) (e2)))) -> (~((op (e1) (e2)) = (op (e3) (e2)))) -> (~((op (e1) (e0)) = (op (e3) (e0)))) -> (~((op (e0) (e1)) = (op (e0) (e2)))) -> ((~((op (e0) (e0)) = (e1)))\/((op (e0) (e1)) = (e0))) -> (((op (e2) (e0)) = (e0))\/(((op (e2) (e0)) = (e1))\/(((op (e2) (e0)) = (e2))\/((op (e2) (e0)) = (e3))))) -> (~((op (e2) (e0)) = (op (e3) (e0)))) -> (~((op (e1) (e0)) = (op (e2) (e0)))) -> ((op (e0) (e0)) = (e0)) -> False). % 15.36/15.51 do 0 intro. intros zenon_Heb zenon_H3b zenon_H1b3 zenon_H35 zenon_H17a zenon_Hd8 zenon_Ha7 zenon_H8f zenon_H249 zenon_H25a zenon_H25b zenon_H24c zenon_H258 zenon_H244 zenon_H24f zenon_Hb4 zenon_H254 zenon_H250 zenon_H25e zenon_H24a zenon_H1d2 zenon_H1e3 zenon_H1c3 zenon_H1e2 zenon_H199 zenon_Hce zenon_H1f5 zenon_H228 zenon_Hde zenon_H157 zenon_H58 zenon_H36 zenon_H28 zenon_H2d zenon_H4b zenon_H10f zenon_Hbb zenon_H44 zenon_Hd3 zenon_H1cd zenon_H160 zenon_Ha3 zenon_H9e zenon_H5e zenon_H84 zenon_H80 zenon_H7d zenon_H6a zenon_H87 zenon_H8b zenon_H90 zenon_H8e zenon_H173 zenon_H10e zenon_Haa zenon_H154 zenon_He6 zenon_He3 zenon_H1d4 zenon_H23 zenon_Hbe zenon_Hc9 zenon_H175 zenon_H1c5 zenon_H144 zenon_Hf0 zenon_H16f zenon_H135 zenon_H109 zenon_H138 zenon_H16c zenon_H1e4 zenon_H166 zenon_Hd7 zenon_H1d3 zenon_H1d0 zenon_H27b zenon_H1d8 zenon_H236 zenon_H1cf zenon_H121 zenon_H261 zenon_Hb7 zenon_Hf1 zenon_H12d zenon_H10c zenon_H110 zenon_H10d zenon_H12a zenon_H1a2 zenon_H15f zenon_H146 zenon_H140 zenon_H26e zenon_H237 zenon_H251 zenon_H1df zenon_H27c zenon_H13c zenon_H11b zenon_H277 zenon_H163 zenon_H105 zenon_H17d zenon_H22e zenon_H23e zenon_H24b zenon_H281 zenon_H1e5 zenon_H247 zenon_H1f. % 15.36/15.51 apply (zenon_or_s _ _ zenon_H1d8); [ zenon_intro zenon_H1b4 | zenon_intro zenon_H21 ]. % 15.36/15.51 apply (zenon_or_s _ _ zenon_H1d3); [ zenon_intro zenon_Hd6 | zenon_intro zenon_H117 ]. % 15.36/15.51 apply (zenon_or_s _ _ zenon_H1d2); [ zenon_intro zenon_H182 | zenon_intro zenon_H11f ]. % 15.36/15.51 apply (zenon_or_s _ _ zenon_H10f); [ zenon_intro zenon_H3c | zenon_intro zenon_Hba ]. % 15.36/15.51 apply (zenon_L734_); trivial. % 15.36/15.51 apply (zenon_L735_); trivial. % 15.36/15.51 apply (zenon_L224_); trivial. % 15.36/15.51 apply (zenon_L248_); trivial. % 15.36/15.51 apply (zenon_L61_); trivial. % 15.36/15.51 (* end of lemma zenon_L736_ *) % 15.36/15.51 assert (zenon_L737_ : (((op (e0) (e1)) = (e2))\/(((op (e1) (e1)) = (e2))\/(((op (e2) (e1)) = (e2))\/((op (e3) (e1)) = (e2))))) -> (~((op (e0) (e1)) = (op (e0) (e3)))) -> ((op (e0) (e3)) = (e2)) -> (~((op (e3) (e3)) = (e3))) -> (~((op (e3) (e3)) = (e2))) -> (~((op (e3) (e3)) = (e0))) -> (((op (e3) (e3)) = (e0))\/(((op (e3) (e3)) = (e1))\/(((op (e3) (e3)) = (e2))\/((op (e3) (e3)) = (e3))))) -> (~((op (e2) (e2)) = (e0))) -> (~((e0) = (e1))) -> ((op (e1) (e2)) = (e1)) -> ((op (e0) (e2)) = (e3)) -> (~((e0) = (e3))) -> (((op (e0) (e2)) = (e0))\/(((op (e1) (e2)) = (e0))\/(((op (e2) (e2)) = (e0))\/((op (e3) (e2)) = (e0))))) -> ((op (e2) (e1)) = (e0)) -> (~((e0) = (e2))) -> (~((e2) = (e3))) -> ((op (e3) (e1)) = (e3)) -> False). % 15.36/15.51 do 0 intro. intros zenon_H1a2 zenon_H1cd zenon_H81 zenon_H3e zenon_H3d zenon_H3c zenon_H3b zenon_H2e zenon_H9e zenon_H117 zenon_H50 zenon_H4b zenon_H16f zenon_H14a zenon_H5e zenon_H6a zenon_H10a. % 15.36/15.51 apply (zenon_or_s _ _ zenon_H1a2); [ zenon_intro zenon_H5d | zenon_intro zenon_H1a3 ]. % 15.36/15.51 apply (zenon_L350_); trivial. % 15.36/15.51 apply (zenon_or_s _ _ zenon_H1a3); [ zenon_intro zenon_H6e | zenon_intro zenon_H1a4 ]. % 15.36/15.51 apply (zenon_L499_); trivial. % 15.36/15.51 apply (zenon_or_s _ _ zenon_H1a4); [ zenon_intro zenon_H156 | zenon_intro zenon_H16a ]. % 15.36/15.51 apply (zenon_L351_); trivial. % 15.36/15.51 apply (zenon_L297_); trivial. % 15.36/15.51 (* end of lemma zenon_L737_ *) % 15.36/15.51 assert (zenon_L738_ : (((op (e1) (e0)) = (e1))\/(((op (e1) (e1)) = (e1))\/(((op (e1) (e2)) = (e1))\/((op (e1) (e3)) = (e1))))) -> (~((e1) = (e2))) -> ((op (e1) (e0)) = (e2)) -> (~((op (e1) (e1)) = (e1))) -> ((op (e3) (e1)) = (e0)) -> (~((op (e3) (e1)) = (op (e3) (e2)))) -> (~((op (e2) (e2)) = (e0))) -> (~((op (e0) (e0)) = (op (e0) (e2)))) -> ((op (e0) (e0)) = (e0)) -> (((op (e0) (e2)) = (e0))\/(((op (e1) (e2)) = (e0))\/(((op (e2) (e2)) = (e0))\/((op (e3) (e2)) = (e0))))) -> (~((e0) = (e1))) -> ((op (e1) (e3)) = (e0)) -> False). % 15.36/15.51 do 0 intro. intros zenon_H1c5 zenon_Ha7 zenon_H68 zenon_H1b4 zenon_H142 zenon_H135 zenon_H2e zenon_H250 zenon_H1f zenon_H16f zenon_H9e zenon_Hcc. % 15.36/15.51 apply (zenon_or_s _ _ zenon_H1c5); [ zenon_intro zenon_Hd8 | zenon_intro zenon_H1c6 ]. % 15.36/15.51 apply (zenon_L162_); trivial. % 15.36/15.51 apply (zenon_or_s _ _ zenon_H1c6); [ zenon_intro zenon_H21 | zenon_intro zenon_H1c7 ]. % 15.36/15.51 exact (zenon_H1b4 zenon_H21). % 15.36/15.51 apply (zenon_or_s _ _ zenon_H1c7); [ zenon_intro zenon_H117 | zenon_intro zenon_H11f ]. % 15.36/15.51 apply (zenon_L622_); trivial. % 15.36/15.51 apply (zenon_L208_); trivial. % 15.36/15.51 (* end of lemma zenon_L738_ *) % 15.36/15.51 assert (zenon_L739_ : (~((op (e1) (e0)) = (op (e2) (e0)))) -> (~((op (e2) (e0)) = (op (e3) (e0)))) -> (((op (e2) (e0)) = (e0))\/(((op (e2) (e0)) = (e1))\/(((op (e2) (e0)) = (e2))\/((op (e2) (e0)) = (e3))))) -> ((~((op (e0) (e0)) = (e1)))\/((op (e0) (e1)) = (e0))) -> (~((op (e0) (e1)) = (op (e0) (e2)))) -> (~((op (e1) (e2)) = (op (e3) (e2)))) -> (~((op (e3) (e0)) = (op (e3) (e2)))) -> (~((op (e2) (op (e1) (e2))) = (op (e1) (e2)))) -> (~((op (e2) (e1)) = (op (e3) (e1)))) -> (((op (e0) (e2)) = (e2))\/(((op (e1) (e2)) = (e2))\/(((op (e2) (e2)) = (e2))\/((op (e3) (e2)) = (e2))))) -> (((op (e3) (e0)) = (e2))\/(((op (e3) (e1)) = (e2))\/(((op (e3) (e2)) = (e2))\/((op (e3) (e3)) = (e2))))) -> (((op (e2) (e0)) = (e2))\/(((op (e2) (e1)) = (e2))\/(((op (e2) (e2)) = (e2))\/((op (e2) (e3)) = (e2))))) -> (~((op (e3) (op (e1) (e3))) = (op (e1) (e3)))) -> (((op (e0) (e0)) = (e0))\/(((op (e0) (e0)) = (e1))\/(((op (e0) (e0)) = (e2))\/((op (e0) (e0)) = (e3))))) -> (((op (e0) (e0)) = (e0))\/(((op (e0) (e1)) = (e0))\/(((op (e0) (e2)) = (e0))\/((op (e0) (e3)) = (e0))))) -> (((op (e2) (e0)) = (e1))\/(((op (e2) (e1)) = (e1))\/(((op (e2) (e2)) = (e1))\/((op (e2) (e3)) = (e1))))) -> (~((op (e0) (op (e1) (e0))) = (op (e1) (e0)))) -> ((~((op (e0) (e0)) = (e3)))\/((op (e0) (e3)) = (e0))) -> (~((op (e1) (op (e1) (e1))) = (op (e1) (e1)))) -> ((~((op (e1) (e1)) = (e0)))\/((op (e1) (e0)) = (e1))) -> (((op (e3) (e1)) = (e0))\/(((op (e3) (e1)) = (e1))\/(((op (e3) (e1)) = (e2))\/((op (e3) (e1)) = (e3))))) -> (~((op (e3) (e0)) = (op (e3) (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) (e1)) = (e0))\/(((op (e1) (e1)) = (e0))\/(((op (e2) (e1)) = (e0))\/((op (e3) (e1)) = (e0))))) -> (((op (e1) (e0)) = (e1))\/(((op (e1) (e1)) = (e1))\/(((op (e1) (e2)) = (e1))\/((op (e1) (e3)) = (e1))))) -> (((op (e0) (e2)) = (e3))\/(((op (e1) (e2)) = (e3))\/(((op (e2) (e2)) = (e3))\/((op (e3) (e2)) = (e3))))) -> (~((op (e2) (e3)) = (op (e3) (e3)))) -> (((op (e2) (e0)) = (e3))\/(((op (e2) (e1)) = (e3))\/(((op (e2) (e2)) = (e3))\/((op (e2) (e3)) = (e3))))) -> (~((op (e3) (e2)) = (op (e3) (e3)))) -> (~((op (e0) (e1)) = (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) (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) (e0)) = (e2)))\/((op (e0) (e2)) = (e0))) -> (((op (e3) (e2)) = (e0))\/(((op (e3) (e2)) = (e1))\/(((op (e3) (e2)) = (e2))\/((op (e3) (e2)) = (e3))))) -> (~((op (e1) (e3)) = (op (e2) (e3)))) -> (~((op (e0) (e0)) = (op (e2) (e0)))) -> (((op (e1) (e3)) = (e0))\/(((op (e1) (e3)) = (e1))\/(((op (e1) (e3)) = (e2))\/((op (e1) (e3)) = (e3))))) -> (~((op (e0) (e0)) = (op (e0) (e1)))) -> ((~((op (e0) (e0)) = (e0)))\/((op (e0) (e0)) = (e0))) -> ((~((op (e3) (e3)) = (e3)))\/((op (e3) (e3)) = (e3))) -> (~((op (e0) (e0)) = (e1))) -> ((~((op (e1) (e1)) = (e1)))\/((op (e1) (e1)) = (e1))) -> (~((op (e1) (e0)) = (op (e1) (e1)))) -> ((~((op (e1) (e1)) = (e3)))\/((op (e1) (e3)) = (e1))) -> ((~((op (e2) (e2)) = (e1)))\/((op (e2) (e1)) = (e2))) -> ((~((op (e3) (e3)) = (e1)))\/((op (e3) (e1)) = (e3))) -> (~((op (e3) (e1)) = (op (e3) (e3)))) -> (((op (e0) (e3)) = (e1))\/(((op (e1) (e3)) = (e1))\/(((op (e2) (e3)) = (e1))\/((op (e3) (e3)) = (e1))))) -> (~((e1) = (e2))) -> (~((op (e1) (e0)) = (op (e1) (e3)))) -> (~((op (e0) (e1)) = (op (e0) (e3)))) -> (((op (e3) (e0)) = (e1))\/(((op (e3) (e1)) = (e1))\/(((op (e3) (e2)) = (e1))\/((op (e3) (e3)) = (e1))))) -> (~((op (e0) (e2)) = (op (e3) (e2)))) -> (~((op (e2) (e0)) = (op (e2) (e1)))) -> (((op (e0) (e1)) = (e2))\/(((op (e1) (e1)) = (e2))\/(((op (e2) (e1)) = (e2))\/((op (e3) (e1)) = (e2))))) -> (~((op (e1) (e0)) = (op (e3) (e0)))) -> ((~((op (e2) (e2)) = (e3)))\/((op (e2) (e3)) = (e2))) -> (~((op (e2) (e1)) = (op (e2) (e3)))) -> (~((op (e2) (e1)) = (op (e2) (e2)))) -> ((~((op (e2) (e2)) = (e2)))\/((op (e2) (e2)) = (e2))) -> (((op (e0) (e0)) = (e2))\/(((op (e1) (e0)) = (e2))\/(((op (e2) (e0)) = (e2))\/((op (e3) (e0)) = (e2))))) -> (~((e2) = (e3))) -> (((op (e1) (e0)) = (e3))\/(((op (e1) (e1)) = (e3))\/(((op (e1) (e2)) = (e3))\/((op (e1) (e3)) = (e3))))) -> (~((op (e1) (e3)) = (op (e3) (e3)))) -> (~((op (e0) (e2)) = (op (e1) (e2)))) -> (((op (e0) (e0)) = (e3))\/(((op (e0) (e1)) = (e3))\/(((op (e0) (e2)) = (e3))\/((op (e0) (e3)) = (e3))))) -> (((op (e0) (e3)) = (e0))\/(((op (e1) (e3)) = (e0))\/(((op (e2) (e3)) = (e0))\/((op (e3) (e3)) = (e0))))) -> (~((e0) = (e2))) -> ((op (e0) (e0)) = (e0)) -> (~((op (e0) (e0)) = (op (e0) (e3)))) -> (((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 (e3) (e3)) = (e0)))\/((op (e3) (e0)) = (e3))) -> (~((op (e0) (e0)) = (e3))) -> (~((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) (e0)) = (e3))\/(((op (e1) (e0)) = (e3))\/(((op (e2) (e0)) = (e3))\/((op (e3) (e0)) = (e3))))) -> (~((op (e0) (e1)) = (op (e3) (e1)))) -> (~((op (e1) (e2)) = (op (e2) (e2)))) -> (~((op (e0) (e3)) = (op (e2) (e3)))) -> (~((op (e0) (e3)) = (op (e1) (e3)))) -> (((op (e0) (e3)) = (e0))\/(((op (e0) (e3)) = (e1))\/(((op (e0) (e3)) = (e2))\/((op (e0) (e3)) = (e3))))) -> (((op (e0) (e2)) = (e1))\/(((op (e1) (e2)) = (e1))\/(((op (e2) (e2)) = (e1))\/((op (e3) (e2)) = (e1))))) -> (~((op (e0) (e0)) = (op (e0) (e2)))) -> (((op (e0) (e2)) = (e0))\/(((op (e0) (e2)) = (e1))\/(((op (e0) (e2)) = (e2))\/((op (e0) (e2)) = (e3))))) -> (~((op (e0) (e2)) = (op (e0) (e3)))) -> ((~((op (e2) (e2)) = (e0)))\/((op (e2) (e0)) = (e2))) -> (~((op (e1) (e0)) = (op (e1) (e2)))) -> ((~((op (e1) (e1)) = (e2)))\/((op (e1) (e2)) = (e1))) -> (((op (e1) (e0)) = (e0))\/(((op (e1) (e1)) = (e0))\/(((op (e1) (e2)) = (e0))\/((op (e1) (e3)) = (e0))))) -> (((op (e0) (e3)) = (e2))\/(((op (e1) (e3)) = (e2))\/(((op (e2) (e3)) = (e2))\/((op (e3) (e3)) = (e2))))) -> (~((op (e2) (e2)) = (op (e2) (e3)))) -> (~((op (e1) (e2)) = (op (e1) (e3)))) -> (~((op (e2) (e0)) = (op (e2) (e3)))) -> ((op (e1) (e2)) = (e1)) -> (~((e0) = (e1))) -> (~((op (e0) (e0)) = (op (e1) (e0)))) -> (~((op (e2) (e0)) = (op (e2) (e2)))) -> (((op (e0) (e0)) = (e1))\/(((op (e1) (e0)) = (e1))\/(((op (e2) (e0)) = (e1))\/((op (e3) (e0)) = (e1))))) -> (~((op (e0) (e0)) = (e2))) -> (((op (e1) (e1)) = (e0))\/(((op (e1) (e1)) = (e1))\/(((op (e1) (e1)) = (e2))\/((op (e1) (e1)) = (e3))))) -> (~((op (e1) (e1)) = (e3))) -> (~((op (e0) (e1)) = (op (e1) (e1)))) -> (~((op (e1) (e1)) = (e1))) -> (~((op (e1) (e1)) = (e0))) -> (~((op (e0) (e2)) = (op (e2) (e2)))) -> ((op (e2) (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 (e0) (e0)) = (e2))\/(((op (e0) (e1)) = (e2))\/(((op (e0) (e2)) = (e2))\/((op (e0) (e3)) = (e2))))) -> (((op (e0) (e2)) = (e0))\/(((op (e1) (e2)) = (e0))\/(((op (e2) (e2)) = (e0))\/((op (e3) (e2)) = (e0))))) -> (~((e0) = (e3))) -> (~((op (e2) (e2)) = (e0))) -> ((~((op (e3) (e3)) = (e2)))\/((op (e3) (e2)) = (e3))) -> False). % 15.36/15.51 do 0 intro. intros zenon_H247 zenon_H1e5 zenon_H281 zenon_H24b zenon_H23e zenon_H17d zenon_H105 zenon_H277 zenon_H13c zenon_H27c zenon_H1df zenon_H237 zenon_H26e zenon_H12a zenon_H110 zenon_Hb7 zenon_H261 zenon_H236 zenon_H27b zenon_H1e4 zenon_H16c zenon_H109 zenon_H135 zenon_Hf0 zenon_H144 zenon_H1c5 zenon_H175 zenon_He3 zenon_He6 zenon_H173 zenon_Hde zenon_H228 zenon_H1f5 zenon_H199 zenon_H24a zenon_H25e zenon_H244 zenon_H258 zenon_H25b zenon_H25a zenon_H249 zenon_H10d zenon_H45 zenon_H1d8 zenon_Hd7 zenon_H1d2 zenon_H1e3 zenon_H10c zenon_H12d zenon_H121 zenon_Ha7 zenon_H1cf zenon_H1cd zenon_H146 zenon_H140 zenon_H154 zenon_H1a2 zenon_H22e zenon_H1c3 zenon_H1e2 zenon_H157 zenon_Haa zenon_Heb zenon_H6a zenon_H90 zenon_H8b zenon_H87 zenon_H58 zenon_Hd3 zenon_H5e zenon_H1f zenon_H24f zenon_H84 zenon_H44 zenon_H10f zenon_H59 zenon_Ha3 zenon_H2d zenon_Hbb zenon_Hbe zenon_H138 zenon_H7d zenon_Hb4 zenon_H80 zenon_H254 zenon_H11b zenon_H250 zenon_H251 zenon_Hc9 zenon_H1d4 zenon_H166 zenon_H1d3 zenon_H163 zenon_H160 zenon_H15f zenon_H1d0 zenon_Hce zenon_H117 zenon_H9e zenon_H24c zenon_H17a zenon_Hf1 zenon_H8f zenon_H1b3 zenon_H182 zenon_H23 zenon_H1b4 zenon_H145 zenon_H28 zenon_H35 zenon_H3b zenon_H36 zenon_H8e zenon_H16f zenon_H4b zenon_H2e zenon_H10e. % 15.36/15.51 apply (zenon_or_s _ _ zenon_H1c3); [ zenon_intro zenon_H30 | zenon_intro zenon_H124 ]. % 15.36/15.51 apply (zenon_or_s _ _ zenon_H10f); [ zenon_intro zenon_H3c | zenon_intro zenon_Hba ]. % 15.36/15.51 apply (zenon_or_s _ _ zenon_H10c); [ zenon_intro zenon_H104 | zenon_intro zenon_H10a ]. % 15.36/15.51 apply (zenon_or_s _ _ zenon_H10e); [ zenon_intro zenon_H3d | zenon_intro zenon_H106 ]. % 15.36/15.51 apply (zenon_or_s _ _ zenon_H10d); [ zenon_intro zenon_H3e | zenon_intro zenon_H42 ]. % 15.36/15.51 apply (zenon_L345_); trivial. % 15.36/15.51 apply (zenon_L597_); trivial. % 15.36/15.51 apply (zenon_L590_); trivial. % 15.36/15.51 apply (zenon_or_s _ _ zenon_H10e); [ zenon_intro zenon_H3d | zenon_intro zenon_H106 ]. % 15.36/15.51 apply (zenon_or_s _ _ zenon_H10d); [ zenon_intro zenon_H3e | zenon_intro zenon_H42 ]. % 15.36/15.51 apply (zenon_or_s _ _ zenon_H44); [ zenon_intro zenon_H47 | zenon_intro zenon_H46 ]. % 15.36/15.51 exact (zenon_H45 zenon_H47). % 15.36/15.51 apply (zenon_or_s _ _ zenon_H46); [ zenon_intro zenon_H22 | zenon_intro zenon_H48 ]. % 15.36/15.51 apply (zenon_or_s _ _ zenon_Hf1); [ zenon_intro zenon_H47 | zenon_intro zenon_Hf4 ]. % 15.36/15.51 exact (zenon_H45 zenon_H47). % 15.36/15.51 apply (zenon_or_s _ _ zenon_Hf4); [ zenon_intro zenon_Hd8 | zenon_intro zenon_Hf5 ]. % 15.36/15.51 apply (zenon_L736_); trivial. % 15.36/15.51 apply (zenon_or_s _ _ zenon_Hf5); [ zenon_intro zenon_Hae | zenon_intro zenon_Hee ]. % 15.36/15.51 apply (zenon_or_s _ _ zenon_H8e); [ zenon_intro zenon_H92 | zenon_intro zenon_H91 ]. % 15.36/15.51 exact (zenon_H8f zenon_H92). % 15.36/15.51 apply (zenon_or_s _ _ zenon_H91); [ zenon_intro zenon_H5d | zenon_intro zenon_H93 ]. % 15.36/15.51 apply (zenon_L214_); trivial. % 15.36/15.51 apply (zenon_or_s _ _ zenon_H93); [ zenon_intro zenon_H63 | zenon_intro zenon_H81 ]. % 15.36/15.51 apply (zenon_L15_); trivial. % 15.36/15.51 apply (zenon_or_s _ _ zenon_H58); [ zenon_intro zenon_H5b | zenon_intro zenon_H5a ]. % 15.36/15.51 exact (zenon_H59 zenon_H5b). % 15.36/15.51 apply (zenon_or_s _ _ zenon_H5a); [ zenon_intro zenon_H4a | zenon_intro zenon_H5c ]. % 15.36/15.51 apply (zenon_L59_); trivial. % 15.36/15.51 apply (zenon_or_s _ _ zenon_H5c); [ zenon_intro zenon_H50 | zenon_intro zenon_H53 ]. % 15.36/15.51 apply (zenon_or_s _ _ zenon_H144); [ zenon_intro zenon_H49 | zenon_intro zenon_H147 ]. % 15.36/15.51 apply (zenon_L610_); trivial. % 15.36/15.51 apply (zenon_or_s _ _ zenon_H147); [ zenon_intro zenon_H149 | zenon_intro zenon_H148 ]. % 15.36/15.51 exact (zenon_H145 zenon_H149). % 15.36/15.51 apply (zenon_or_s _ _ zenon_H148); [ zenon_intro zenon_H14a | zenon_intro zenon_H142 ]. % 15.36/15.51 apply (zenon_L737_); trivial. % 15.36/15.51 apply (zenon_L126_); trivial. % 15.36/15.51 apply (zenon_L536_); trivial. % 15.36/15.51 apply (zenon_or_s _ _ zenon_H8e); [ zenon_intro zenon_H92 | zenon_intro zenon_H91 ]. % 15.36/15.51 exact (zenon_H8f zenon_H92). % 15.36/15.51 apply (zenon_or_s _ _ zenon_H91); [ zenon_intro zenon_H5d | zenon_intro zenon_H93 ]. % 15.36/15.51 apply (zenon_L214_); trivial. % 15.36/15.51 apply (zenon_or_s _ _ zenon_H93); [ zenon_intro zenon_H63 | zenon_intro zenon_H81 ]. % 15.36/15.51 apply (zenon_L15_); trivial. % 15.36/15.51 apply (zenon_or_s _ _ zenon_Heb); [ zenon_intro zenon_H92 | zenon_intro zenon_Hec ]. % 15.36/15.51 exact (zenon_H8f zenon_H92). % 15.36/15.51 apply (zenon_or_s _ _ zenon_Hec); [ zenon_intro zenon_H68 | zenon_intro zenon_Hed ]. % 15.36/15.51 apply (zenon_or_s _ _ zenon_H58); [ zenon_intro zenon_H5b | zenon_intro zenon_H5a ]. % 15.36/15.51 exact (zenon_H59 zenon_H5b). % 15.36/15.51 apply (zenon_or_s _ _ zenon_H5a); [ zenon_intro zenon_H4a | zenon_intro zenon_H5c ]. % 15.36/15.51 apply (zenon_L120_); trivial. % 15.36/15.51 apply (zenon_or_s _ _ zenon_H5c); [ zenon_intro zenon_H50 | zenon_intro zenon_H53 ]. % 15.36/15.51 apply (zenon_or_s _ _ zenon_H163); [ zenon_intro zenon_Had | zenon_intro zenon_H164 ]. % 15.36/15.51 apply (zenon_L559_); trivial. % 15.36/15.51 apply (zenon_or_s _ _ zenon_H164); [ zenon_intro zenon_H149 | zenon_intro zenon_H165 ]. % 15.36/15.51 exact (zenon_H145 zenon_H149). % 15.36/15.51 apply (zenon_or_s _ _ zenon_H165); [ zenon_intro zenon_H15d | zenon_intro zenon_Hcc ]. % 15.36/15.51 apply (zenon_L496_); trivial. % 15.36/15.51 apply (zenon_or_s _ _ zenon_H144); [ zenon_intro zenon_H49 | zenon_intro zenon_H147 ]. % 15.36/15.51 apply (zenon_L27_); trivial. % 15.36/15.51 apply (zenon_or_s _ _ zenon_H147); [ zenon_intro zenon_H149 | zenon_intro zenon_H148 ]. % 15.36/15.51 exact (zenon_H145 zenon_H149). % 15.36/15.51 apply (zenon_or_s _ _ zenon_H148); [ zenon_intro zenon_H14a | zenon_intro zenon_H142 ]. % 15.36/15.51 apply (zenon_L737_); trivial. % 15.36/15.51 apply (zenon_L738_); trivial. % 15.36/15.51 apply (zenon_L128_); trivial. % 15.36/15.51 apply (zenon_or_s _ _ zenon_Hed); [ zenon_intro zenon_Hdd | zenon_intro zenon_He9 ]. % 15.36/15.51 apply (zenon_L161_); trivial. % 15.36/15.51 apply (zenon_L122_); trivial. % 15.36/15.51 apply (zenon_or_s _ _ zenon_H48); [ zenon_intro zenon_H29 | zenon_intro zenon_H37 ]. % 15.36/15.51 apply (zenon_L666_); trivial. % 15.36/15.51 apply (zenon_L7_); trivial. % 15.36/15.51 apply (zenon_L102_); trivial. % 15.36/15.51 apply (zenon_L115_); trivial. % 15.36/15.51 apply (zenon_or_s _ _ zenon_H10c); [ zenon_intro zenon_H104 | zenon_intro zenon_H10a ]. % 15.36/15.51 apply (zenon_or_s _ _ zenon_H10e); [ zenon_intro zenon_H3d | zenon_intro zenon_H106 ]. % 15.36/15.51 apply (zenon_or_s _ _ zenon_Hf1); [ zenon_intro zenon_H47 | zenon_intro zenon_Hf4 ]. % 15.36/15.51 exact (zenon_H45 zenon_H47). % 15.36/15.51 apply (zenon_or_s _ _ zenon_Hf4); [ zenon_intro zenon_Hd8 | zenon_intro zenon_Hf5 ]. % 15.36/15.51 apply (zenon_L735_); trivial. % 15.36/15.51 apply (zenon_or_s _ _ zenon_Hf5); [ zenon_intro zenon_Hae | zenon_intro zenon_Hee ]. % 15.36/15.51 apply (zenon_L595_); trivial. % 15.36/15.51 apply (zenon_L79_); trivial. % 15.36/15.51 apply (zenon_L81_); trivial. % 15.36/15.51 apply (zenon_L82_); trivial. % 15.36/15.51 apply (zenon_L137_); trivial. % 15.36/15.51 (* end of lemma zenon_L739_ *) % 15.36/15.51 assert (zenon_L740_ : (((op (e0) (e0)) = (e1))\/(((op (e1) (e0)) = (e1))\/(((op (e2) (e0)) = (e1))\/((op (e3) (e0)) = (e1))))) -> (~((op (e0) (e0)) = (e1))) -> (~((op (e1) (e0)) = (op (e1) (e2)))) -> (~((op (e2) (e0)) = (op (e2) (e3)))) -> (~((op (e1) (e2)) = (op (e1) (e3)))) -> ((op (e1) (e2)) = (e1)) -> ((op (e0) (e2)) = (e1)) -> (~((op (e0) (e2)) = (op (e0) (e3)))) -> (((op (e0) (e3)) = (e1))\/(((op (e1) (e3)) = (e1))\/(((op (e2) (e3)) = (e1))\/((op (e3) (e3)) = (e1))))) -> (((op (e2) (e2)) = (e0))\/(((op (e2) (e2)) = (e1))\/(((op (e2) (e2)) = (e2))\/((op (e2) (e2)) = (e3))))) -> (~((op (e3) (e3)) = (e3))) -> (~((op (e3) (e3)) = (e1))) -> (~((op (e3) (e3)) = (e0))) -> (((op (e3) (e3)) = (e0))\/(((op (e3) (e3)) = (e1))\/(((op (e3) (e3)) = (e2))\/((op (e3) (e3)) = (e3))))) -> (~((op (e2) (e2)) = (e1))) -> (~((op (e2) (e2)) = (e2))) -> (~((op (e2) (e2)) = (e3))) -> False). % 15.36/15.51 do 0 intro. intros zenon_Hf1 zenon_H45 zenon_H166 zenon_Hce zenon_H1d0 zenon_H117 zenon_H29 zenon_Hc9 zenon_H121 zenon_H2d zenon_H3e zenon_H104 zenon_H3c zenon_H3b zenon_H52 zenon_H2f zenon_H30. % 15.36/15.51 apply (zenon_or_s _ _ zenon_Hf1); [ zenon_intro zenon_H47 | zenon_intro zenon_Hf4 ]. % 15.36/15.51 exact (zenon_H45 zenon_H47). % 15.36/15.51 apply (zenon_or_s _ _ zenon_Hf4); [ zenon_intro zenon_Hd8 | zenon_intro zenon_Hf5 ]. % 15.36/15.51 apply (zenon_L248_); trivial. % 15.36/15.51 apply (zenon_or_s _ _ zenon_Hf5); [ zenon_intro zenon_Hae | zenon_intro zenon_Hee ]. % 15.36/15.51 apply (zenon_L551_); trivial. % 15.36/15.51 apply (zenon_L306_); trivial. % 15.36/15.51 (* end of lemma zenon_L740_ *) % 15.36/15.51 assert (zenon_L741_ : (~((op (e2) (op (e1) (e2))) = (op (e2) (e1)))) -> ((op (e1) (e2)) = (e1)) -> False). % 15.36/15.51 do 0 intro. intros zenon_H284 zenon_H117. % 15.36/15.51 cut (((op (e1) (e2)) = (e1))); [idtac | apply NNPP; zenon_intro zenon_H285]. % 15.36/15.51 cut (((e2) = (e2))); [idtac | apply NNPP; zenon_intro zenon_H60]. % 15.36/15.51 congruence. % 15.36/15.51 apply zenon_H60. apply refl_equal. % 15.36/15.51 exact (zenon_H285 zenon_H117). % 15.36/15.51 (* end of lemma zenon_L741_ *) % 15.36/15.51 assert (zenon_L742_ : (~((op (e2) (op (e1) (e2))) = (op (e1) (e2)))) -> ((op (e2) (e1)) = (e1)) -> ((op (e1) (e2)) = (e1)) -> False). % 15.36/15.51 do 0 intro. intros zenon_H277 zenon_Hb2 zenon_H117. % 15.36/15.51 cut (((op (e2) (e1)) = (e1)) = ((op (e2) (op (e1) (e2))) = (op (e1) (e2)))). % 15.36/15.51 intro zenon_D_pnotp. % 15.36/15.51 apply zenon_H277. % 15.36/15.51 rewrite <- zenon_D_pnotp. % 15.36/15.51 exact zenon_Hb2. % 15.36/15.51 cut (((e1) = (op (e1) (e2)))); [idtac | apply NNPP; zenon_intro zenon_H118]. % 15.36/15.51 cut (((op (e2) (e1)) = (op (e2) (op (e1) (e2))))); [idtac | apply NNPP; zenon_intro zenon_H286]. % 15.36/15.51 congruence. % 15.36/15.51 elim (classic ((op (e2) (op (e1) (e2))) = (op (e2) (op (e1) (e2))))); [ zenon_intro zenon_H279 | zenon_intro zenon_H27a ]. % 15.36/15.51 cut (((op (e2) (op (e1) (e2))) = (op (e2) (op (e1) (e2)))) = ((op (e2) (e1)) = (op (e2) (op (e1) (e2))))). % 15.36/15.51 intro zenon_D_pnotp. % 15.36/15.51 apply zenon_H286. % 15.36/15.51 rewrite <- zenon_D_pnotp. % 15.36/15.51 exact zenon_H279. % 15.36/15.51 cut (((op (e2) (op (e1) (e2))) = (op (e2) (op (e1) (e2))))); [idtac | apply NNPP; zenon_intro zenon_H27a]. % 15.36/15.51 cut (((op (e2) (op (e1) (e2))) = (op (e2) (e1)))); [idtac | apply NNPP; zenon_intro zenon_H284]. % 15.36/15.51 congruence. % 15.36/15.51 apply (zenon_L741_); trivial. % 15.36/15.51 apply zenon_H27a. apply refl_equal. % 15.36/15.51 apply zenon_H27a. apply refl_equal. % 15.36/15.51 apply zenon_H118. apply sym_equal. exact zenon_H117. % 15.36/15.51 (* end of lemma zenon_L742_ *) % 15.36/15.51 assert (zenon_L743_ : (((op (e0) (e1)) = (e1))\/(((op (e1) (e1)) = (e1))\/(((op (e2) (e1)) = (e1))\/((op (e3) (e1)) = (e1))))) -> (~((e1) = (e3))) -> ((op (e0) (e1)) = (e3)) -> (~((op (e1) (e1)) = (e1))) -> ((op (e1) (e2)) = (e1)) -> (~((op (e2) (op (e1) (e2))) = (op (e1) (e2)))) -> (~((op (e3) (e0)) = (op (e3) (e1)))) -> ((op (e3) (e0)) = (e1)) -> False). % 15.36/15.51 do 0 intro. intros zenon_H228 zenon_Ha3 zenon_H4a zenon_H1b4 zenon_H117 zenon_H277 zenon_H109 zenon_Hee. % 15.36/15.51 apply (zenon_or_s _ _ zenon_H228); [ zenon_intro zenon_H22 | zenon_intro zenon_H229 ]. % 15.36/15.51 apply (zenon_L59_); trivial. % 15.36/15.51 apply (zenon_or_s _ _ zenon_H229); [ zenon_intro zenon_H21 | zenon_intro zenon_H22a ]. % 15.36/15.51 exact (zenon_H1b4 zenon_H21). % 15.36/15.51 apply (zenon_or_s _ _ zenon_H22a); [ zenon_intro zenon_Hb2 | zenon_intro zenon_H13e ]. % 15.36/15.51 apply (zenon_L742_); trivial. % 15.36/15.51 apply (zenon_L145_); trivial. % 15.36/15.51 (* end of lemma zenon_L743_ *) % 15.36/15.51 assert (zenon_L744_ : (((op (e0) (e0)) = (e3))\/(((op (e1) (e0)) = (e3))\/(((op (e2) (e0)) = (e3))\/((op (e3) (e0)) = (e3))))) -> (~((op (e0) (e0)) = (e3))) -> ((op (e0) (e3)) = (e3)) -> (~((op (e0) (op (e1) (e0))) = (op (e1) (e0)))) -> (~((e2) = (e3))) -> ((op (e2) (e0)) = (e2)) -> (~((op (e3) (e0)) = (op (e3) (e1)))) -> ((op (e3) (e1)) = (e3)) -> False). % 15.36/15.51 do 0 intro. intros zenon_Hbe zenon_H59 zenon_H53 zenon_H261 zenon_H6a zenon_Hdd zenon_H109 zenon_H10a. % 15.36/15.51 apply (zenon_or_s _ _ zenon_Hbe); [ zenon_intro zenon_H5b | zenon_intro zenon_Hbf ]. % 15.36/15.51 exact (zenon_H59 zenon_H5b). % 15.36/15.51 apply (zenon_or_s _ _ zenon_Hbf); [ zenon_intro zenon_H69 | zenon_intro zenon_Hc0 ]. % 15.36/15.51 apply (zenon_L647_); trivial. % 15.36/15.51 apply (zenon_or_s _ _ zenon_Hc0); [ zenon_intro zenon_Haf | zenon_intro zenon_Hba ]. % 15.36/15.51 apply (zenon_L64_); trivial. % 15.36/15.51 apply (zenon_L82_); trivial. % 15.36/15.51 (* end of lemma zenon_L744_ *) % 15.36/15.51 assert (zenon_L745_ : ((~((op (e3) (e3)) = (e2)))\/((op (e3) (e2)) = (e3))) -> (~((e0) = (e3))) -> (((op (e0) (e2)) = (e0))\/(((op (e1) (e2)) = (e0))\/(((op (e2) (e2)) = (e0))\/((op (e3) (e2)) = (e0))))) -> (((op (e0) (e0)) = (e2))\/(((op (e0) (e1)) = (e2))\/(((op (e0) (e2)) = (e2))\/((op (e0) (e3)) = (e2))))) -> (~((op (e0) (e3)) = (op (e3) (e3)))) -> (((op (e3) (e3)) = (e0))\/(((op (e3) (e3)) = (e1))\/(((op (e3) (e3)) = (e2))\/((op (e3) (e3)) = (e3))))) -> ((op (e2) (e2)) = (e2)) -> (~((op (e0) (e2)) = (op (e2) (e2)))) -> (~((op (e1) (e1)) = (e0))) -> (~((op (e1) (e1)) = (e1))) -> (~((op (e0) (e1)) = (op (e1) (e1)))) -> (~((op (e1) (e1)) = (e3))) -> (((op (e1) (e1)) = (e0))\/(((op (e1) (e1)) = (e1))\/(((op (e1) (e1)) = (e2))\/((op (e1) (e1)) = (e3))))) -> (~((op (e0) (e0)) = (e2))) -> (((op (e0) (e0)) = (e1))\/(((op (e1) (e0)) = (e1))\/(((op (e2) (e0)) = (e1))\/((op (e3) (e0)) = (e1))))) -> (~((op (e2) (e0)) = (op (e2) (e2)))) -> (~((op (e0) (e0)) = (op (e1) (e0)))) -> (~((e0) = (e1))) -> ((op (e1) (e2)) = (e1)) -> (~((op (e2) (e0)) = (op (e2) (e3)))) -> (~((op (e1) (e2)) = (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 (e1) (e0)) = (e0))\/(((op (e1) (e1)) = (e0))\/(((op (e1) (e2)) = (e0))\/((op (e1) (e3)) = (e0))))) -> ((~((op (e1) (e1)) = (e2)))\/((op (e1) (e2)) = (e1))) -> (~((op (e1) (e0)) = (op (e1) (e2)))) -> ((~((op (e2) (e2)) = (e0)))\/((op (e2) (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 (e0) (e0)) = (op (e0) (e2)))) -> (((op (e0) (e2)) = (e1))\/(((op (e1) (e2)) = (e1))\/(((op (e2) (e2)) = (e1))\/((op (e3) (e2)) = (e1))))) -> (((op (e0) (e3)) = (e0))\/(((op (e0) (e3)) = (e1))\/(((op (e0) (e3)) = (e2))\/((op (e0) (e3)) = (e3))))) -> (~((op (e0) (e3)) = (op (e1) (e3)))) -> (~((op (e0) (e3)) = (op (e2) (e3)))) -> (~((op (e1) (e2)) = (op (e2) (e2)))) -> (~((op (e0) (e1)) = (op (e3) (e1)))) -> (((op (e0) (e0)) = (e3))\/(((op (e1) (e0)) = (e3))\/(((op (e2) (e0)) = (e3))\/((op (e3) (e0)) = (e3))))) -> (~((op (e3) (e0)) = (op (e3) (e3)))) -> (((op (e2) (e2)) = (e0))\/(((op (e2) (e2)) = (e1))\/(((op (e2) (e2)) = (e2))\/((op (e2) (e2)) = (e3))))) -> (~((e1) = (e3))) -> (~((op (e0) (e0)) = (e3))) -> ((~((op (e3) (e3)) = (e0)))\/((op (e3) (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) (e0)) = (op (e0) (e3)))) -> ((op (e0) (e0)) = (e0)) -> (~((e0) = (e2))) -> (((op (e0) (e3)) = (e0))\/(((op (e1) (e3)) = (e0))\/(((op (e2) (e3)) = (e0))\/((op (e3) (e3)) = (e0))))) -> (((op (e0) (e0)) = (e3))\/(((op (e0) (e1)) = (e3))\/(((op (e0) (e2)) = (e3))\/((op (e0) (e3)) = (e3))))) -> (~((op (e0) (e2)) = (op (e1) (e2)))) -> (~((op (e1) (e3)) = (op (e3) (e3)))) -> (((op (e1) (e0)) = (e3))\/(((op (e1) (e1)) = (e3))\/(((op (e1) (e2)) = (e3))\/((op (e1) (e3)) = (e3))))) -> (~((e2) = (e3))) -> (((op (e0) (e0)) = (e2))\/(((op (e1) (e0)) = (e2))\/(((op (e2) (e0)) = (e2))\/((op (e3) (e0)) = (e2))))) -> ((~((op (e2) (e2)) = (e2)))\/((op (e2) (e2)) = (e2))) -> (~((op (e2) (e1)) = (op (e2) (e2)))) -> (~((op (e2) (e1)) = (op (e2) (e3)))) -> ((~((op (e2) (e2)) = (e3)))\/((op (e2) (e3)) = (e2))) -> (~((op (e1) (e0)) = (op (e3) (e0)))) -> (((op (e0) (e1)) = (e2))\/(((op (e1) (e1)) = (e2))\/(((op (e2) (e1)) = (e2))\/((op (e3) (e1)) = (e2))))) -> (~((op (e2) (e0)) = (op (e2) (e1)))) -> (~((op (e0) (e2)) = (op (e3) (e2)))) -> (((op (e3) (e0)) = (e1))\/(((op (e3) (e1)) = (e1))\/(((op (e3) (e2)) = (e1))\/((op (e3) (e3)) = (e1))))) -> (~((op (e0) (e1)) = (op (e0) (e3)))) -> (~((op (e1) (e0)) = (op (e1) (e3)))) -> (~((e1) = (e2))) -> (((op (e0) (e3)) = (e1))\/(((op (e1) (e3)) = (e1))\/(((op (e2) (e3)) = (e1))\/((op (e3) (e3)) = (e1))))) -> (~((op (e3) (e1)) = (op (e3) (e3)))) -> ((~((op (e3) (e3)) = (e1)))\/((op (e3) (e1)) = (e3))) -> ((~((op (e2) (e2)) = (e1)))\/((op (e2) (e1)) = (e2))) -> ((~((op (e1) (e1)) = (e3)))\/((op (e1) (e3)) = (e1))) -> (~((op (e1) (e0)) = (op (e1) (e1)))) -> ((~((op (e1) (e1)) = (e1)))\/((op (e1) (e1)) = (e1))) -> (~((op (e0) (e0)) = (e1))) -> ((~((op (e3) (e3)) = (e3)))\/((op (e3) (e3)) = (e3))) -> ((~((op (e0) (e0)) = (e0)))\/((op (e0) (e0)) = (e0))) -> (~((op (e0) (e0)) = (op (e0) (e1)))) -> (((op (e1) (e3)) = (e0))\/(((op (e1) (e3)) = (e1))\/(((op (e1) (e3)) = (e2))\/((op (e1) (e3)) = (e3))))) -> (~((op (e0) (e0)) = (op (e2) (e0)))) -> (~((op (e1) (e3)) = (op (e2) (e3)))) -> (((op (e3) (e2)) = (e0))\/(((op (e3) (e2)) = (e1))\/(((op (e3) (e2)) = (e2))\/((op (e3) (e2)) = (e3))))) -> ((~((op (e0) (e0)) = (e2)))\/((op (e0) (e2)) = (e0))) -> (((op (e0) (e1)) = (e3))\/(((op (e1) (e1)) = (e3))\/(((op (e2) (e1)) = (e3))\/((op (e3) (e1)) = (e3))))) -> (((op (e2) (e0)) = (e0))\/(((op (e2) (e1)) = (e0))\/(((op (e2) (e2)) = (e0))\/((op (e2) (e3)) = (e0))))) -> (((op (e0) (e1)) = (e1))\/(((op (e1) (e1)) = (e1))\/(((op (e2) (e1)) = (e1))\/((op (e3) (e1)) = (e1))))) -> (~((op (e0) (e1)) = (op (e2) (e1)))) -> (~((op (e3) (e2)) = (op (e3) (e3)))) -> (((op (e2) (e0)) = (e3))\/(((op (e2) (e1)) = (e3))\/(((op (e2) (e2)) = (e3))\/((op (e2) (e3)) = (e3))))) -> (~((op (e2) (e3)) = (op (e3) (e3)))) -> (((op (e0) (e2)) = (e3))\/(((op (e1) (e2)) = (e3))\/(((op (e2) (e2)) = (e3))\/((op (e3) (e2)) = (e3))))) -> (((op (e1) (e0)) = (e1))\/(((op (e1) (e1)) = (e1))\/(((op (e1) (e2)) = (e1))\/((op (e1) (e3)) = (e1))))) -> (((op (e0) (e1)) = (e0))\/(((op (e1) (e1)) = (e0))\/(((op (e2) (e1)) = (e0))\/((op (e3) (e1)) = (e0))))) -> (((op (e0) (e0)) = (e0))\/(((op (e1) (e0)) = (e0))\/(((op (e2) (e0)) = (e0))\/((op (e3) (e0)) = (e0))))) -> (~((op (e3) (e1)) = (op (e3) (e2)))) -> (~((op (e3) (e0)) = (op (e3) (e1)))) -> (((op (e3) (e1)) = (e0))\/(((op (e3) (e1)) = (e1))\/(((op (e3) (e1)) = (e2))\/((op (e3) (e1)) = (e3))))) -> ((~((op (e1) (e1)) = (e0)))\/((op (e1) (e0)) = (e1))) -> (~((op (e1) (op (e1) (e1))) = (op (e1) (e1)))) -> ((~((op (e0) (e0)) = (e3)))\/((op (e0) (e3)) = (e0))) -> (~((op (e0) (op (e1) (e0))) = (op (e1) (e0)))) -> (((op (e2) (e0)) = (e1))\/(((op (e2) (e1)) = (e1))\/(((op (e2) (e2)) = (e1))\/((op (e2) (e3)) = (e1))))) -> (((op (e0) (e0)) = (e0))\/(((op (e0) (e1)) = (e0))\/(((op (e0) (e2)) = (e0))\/((op (e0) (e3)) = (e0))))) -> (((op (e0) (e0)) = (e0))\/(((op (e0) (e0)) = (e1))\/(((op (e0) (e0)) = (e2))\/((op (e0) (e0)) = (e3))))) -> (~((op (e3) (op (e1) (e3))) = (op (e1) (e3)))) -> (((op (e2) (e0)) = (e2))\/(((op (e2) (e1)) = (e2))\/(((op (e2) (e2)) = (e2))\/((op (e2) (e3)) = (e2))))) -> (((op (e3) (e0)) = (e2))\/(((op (e3) (e1)) = (e2))\/(((op (e3) (e2)) = (e2))\/((op (e3) (e3)) = (e2))))) -> (((op (e0) (e2)) = (e2))\/(((op (e1) (e2)) = (e2))\/(((op (e2) (e2)) = (e2))\/((op (e3) (e2)) = (e2))))) -> (~((op (e2) (e1)) = (op (e3) (e1)))) -> (~((op (e2) (op (e1) (e2))) = (op (e1) (e2)))) -> (~((op (e3) (e0)) = (op (e3) (e2)))) -> (~((op (e1) (e2)) = (op (e3) (e2)))) -> (~((op (e0) (e1)) = (op (e0) (e2)))) -> ((~((op (e0) (e0)) = (e1)))\/((op (e0) (e1)) = (e0))) -> (((op (e2) (e0)) = (e0))\/(((op (e2) (e0)) = (e1))\/(((op (e2) (e0)) = (e2))\/((op (e2) (e0)) = (e3))))) -> (~((op (e2) (e0)) = (op (e3) (e0)))) -> (~((op (e1) (e0)) = (op (e2) (e0)))) -> False). % 15.36/15.51 do 0 intro. intros zenon_H10e zenon_H4b zenon_H16f zenon_H8e zenon_H36 zenon_H3b zenon_H35 zenon_H28 zenon_H145 zenon_H1b4 zenon_H23 zenon_H182 zenon_H1b3 zenon_H8f zenon_Hf1 zenon_H17a zenon_H24c zenon_H9e zenon_H117 zenon_Hce zenon_H1d0 zenon_H15f zenon_H160 zenon_H163 zenon_H1d3 zenon_H166 zenon_H1d4 zenon_Hc9 zenon_H251 zenon_H250 zenon_H11b zenon_H254 zenon_H80 zenon_Hb4 zenon_H7d zenon_H138 zenon_Hbe zenon_Hbb zenon_H2d zenon_Ha3 zenon_H59 zenon_H10f zenon_H44 zenon_H84 zenon_H24f zenon_H1f zenon_H5e zenon_Hd3 zenon_H58 zenon_H87 zenon_H8b zenon_H90 zenon_H6a zenon_Heb zenon_Haa zenon_H157 zenon_H1e2 zenon_H1c3 zenon_H22e zenon_H1a2 zenon_H154 zenon_H140 zenon_H146 zenon_H1cd zenon_H1cf zenon_Ha7 zenon_H121 zenon_H12d zenon_H10c zenon_H1e3 zenon_H1d2 zenon_Hd7 zenon_H1d8 zenon_H45 zenon_H10d zenon_H249 zenon_H25a zenon_H25b zenon_H258 zenon_H244 zenon_H25e zenon_H24a zenon_H199 zenon_H1f5 zenon_H228 zenon_Hde zenon_H173 zenon_He6 zenon_He3 zenon_H175 zenon_H1c5 zenon_H144 zenon_Hf0 zenon_H135 zenon_H109 zenon_H16c zenon_H1e4 zenon_H27b zenon_H236 zenon_H261 zenon_Hb7 zenon_H110 zenon_H12a zenon_H26e zenon_H237 zenon_H1df zenon_H27c zenon_H13c zenon_H277 zenon_H105 zenon_H17d zenon_H23e zenon_H24b zenon_H281 zenon_H1e5 zenon_H247. % 15.36/15.51 apply (zenon_or_s _ _ zenon_H1d4); [ zenon_intro zenon_H2e | zenon_intro zenon_Hdd ]. % 15.36/15.51 apply (zenon_L739_); trivial. % 15.36/15.51 apply (zenon_L161_); trivial. % 15.36/15.51 (* end of lemma zenon_L745_ *) % 15.36/15.51 assert (zenon_L746_ : (((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 (e1) (e1)) = (e3))) -> (~((op (e1) (e1)) = (e2))) -> (~((op (e1) (e1)) = (e1))) -> (((op (e2) (e2)) = (e0))\/(((op (e2) (e2)) = (e1))\/(((op (e2) (e2)) = (e2))\/((op (e2) (e2)) = (e3))))) -> (~((op (e2) (e2)) = (e0))) -> (~((op (e2) (e2)) = (e2))) -> (~((op (e2) (e2)) = (e3))) -> (((op (e1) (e1)) = (e0))\/(((op (e1) (e1)) = (e1))\/(((op (e1) (e1)) = (e2))\/((op (e1) (e1)) = (e3))))) -> (~((e2) = (e3))) -> ((op (e3) (e0)) = (e2)) -> False). % 15.36/15.51 do 0 intro. intros zenon_Hbe zenon_H59 zenon_Ha3 zenon_Hd8 zenon_H182 zenon_Hd6 zenon_H1b4 zenon_H2d zenon_H2e zenon_H2f zenon_H30 zenon_H1b3 zenon_H6a zenon_He9. % 15.36/15.51 apply (zenon_or_s _ _ zenon_Hbe); [ zenon_intro zenon_H5b | zenon_intro zenon_Hbf ]. % 15.36/15.51 exact (zenon_H59 zenon_H5b). % 15.36/15.51 apply (zenon_or_s _ _ zenon_Hbf); [ zenon_intro zenon_H69 | zenon_intro zenon_Hc0 ]. % 15.36/15.51 apply (zenon_L163_); trivial. % 15.36/15.51 apply (zenon_or_s _ _ zenon_Hc0); [ zenon_intro zenon_Haf | zenon_intro zenon_Hba ]. % 15.36/15.51 apply (zenon_L219_); trivial. % 15.36/15.51 apply (zenon_L220_); trivial. % 15.36/15.51 (* end of lemma zenon_L746_ *) % 15.36/15.51 assert (zenon_L747_ : (((op (e0) (e0)) = (e2))\/(((op (e1) (e0)) = (e2))\/(((op (e2) (e0)) = (e2))\/((op (e3) (e0)) = (e2))))) -> (~((op (e0) (e0)) = (e2))) -> (~((op (e2) (e2)) = (e1))) -> (((op (e3) (e3)) = (e0))\/(((op (e3) (e3)) = (e1))\/(((op (e3) (e3)) = (e2))\/((op (e3) (e3)) = (e3))))) -> (~((op (e3) (e3)) = (e0))) -> (~((op (e3) (e3)) = (e1))) -> (~((op (e3) (e3)) = (e3))) -> (~((e1) = (e2))) -> (~((op (e3) (e0)) = (op (e3) (e2)))) -> ((op (e3) (e2)) = (e3)) -> (~((op (e0) (e0)) = (e1))) -> (((op (e0) (e0)) = (e1))\/(((op (e1) (e0)) = (e1))\/(((op (e2) (e0)) = (e1))\/((op (e3) (e0)) = (e1))))) -> (((op (e0) (e0)) = (e3))\/(((op (e1) (e0)) = (e3))\/(((op (e2) (e0)) = (e3))\/((op (e3) (e0)) = (e3))))) -> (~((op (e0) (e0)) = (e3))) -> (~((e1) = (e3))) -> ((op (e1) (e0)) = (e1)) -> (~((op (e1) (e1)) = (e3))) -> (~((op (e1) (e1)) = (e2))) -> (~((op (e1) (e1)) = (e1))) -> (((op (e2) (e2)) = (e0))\/(((op (e2) (e2)) = (e1))\/(((op (e2) (e2)) = (e2))\/((op (e2) (e2)) = (e3))))) -> (~((op (e2) (e2)) = (e0))) -> (~((op (e2) (e2)) = (e2))) -> (~((op (e2) (e2)) = (e3))) -> (((op (e1) (e1)) = (e0))\/(((op (e1) (e1)) = (e1))\/(((op (e1) (e1)) = (e2))\/((op (e1) (e1)) = (e3))))) -> (~((e2) = (e3))) -> False). % 15.36/15.51 do 0 intro. intros zenon_Heb zenon_H8f zenon_H52 zenon_H3b zenon_H3c zenon_H104 zenon_H3e zenon_Ha7 zenon_H105 zenon_H106 zenon_H45 zenon_Hf1 zenon_Hbe zenon_H59 zenon_Ha3 zenon_Hd8 zenon_H182 zenon_Hd6 zenon_H1b4 zenon_H2d zenon_H2e zenon_H2f zenon_H30 zenon_H1b3 zenon_H6a. % 15.36/15.51 apply (zenon_or_s _ _ zenon_Heb); [ zenon_intro zenon_H92 | zenon_intro zenon_Hec ]. % 15.36/15.51 exact (zenon_H8f zenon_H92). % 15.36/15.51 apply (zenon_or_s _ _ zenon_Hec); [ zenon_intro zenon_H68 | zenon_intro zenon_Hed ]. % 15.36/15.51 apply (zenon_L162_); trivial. % 15.36/15.51 apply (zenon_or_s _ _ zenon_Hed); [ zenon_intro zenon_Hdd | zenon_intro zenon_He9 ]. % 15.36/15.51 apply (zenon_L457_); trivial. % 15.36/15.51 apply (zenon_L746_); trivial. % 15.36/15.51 (* end of lemma zenon_L747_ *) % 15.36/15.51 assert (zenon_L748_ : ((~((op (e3) (e3)) = (e3)))\/((op (e3) (e3)) = (e3))) -> (~((op (e1) (e2)) = (op (e3) (e2)))) -> (~((op (e1) (e3)) = (op (e3) (e3)))) -> (((op (e1) (e0)) = (e3))\/(((op (e1) (e1)) = (e3))\/(((op (e1) (e2)) = (e3))\/((op (e1) (e3)) = (e3))))) -> (~((op (e0) (e0)) = (e2))) -> (~((e1) = (e2))) -> ((op (e1) (e0)) = (e1)) -> (((op (e0) (e0)) = (e1))\/(((op (e1) (e0)) = (e1))\/(((op (e2) (e0)) = (e1))\/((op (e3) (e0)) = (e1))))) -> (((op (e3) (e3)) = (e0))\/(((op (e3) (e3)) = (e1))\/(((op (e3) (e3)) = (e2))\/((op (e3) (e3)) = (e3))))) -> (~((op (e3) (e3)) = (e1))) -> (~((op (e3) (e3)) = (e0))) -> (~((op (e2) (e2)) = (e1))) -> (~((op (e2) (e2)) = (e2))) -> (~((op (e2) (e2)) = (e3))) -> (((op (e2) (e2)) = (e0))\/(((op (e2) (e2)) = (e1))\/(((op (e2) (e2)) = (e2))\/((op (e2) (e2)) = (e3))))) -> (~((op (e0) (e0)) = (e3))) -> (~((e1) = (e3))) -> (~((e2) = (e3))) -> (~((op (e3) (e0)) = (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)) = (e1))) -> (~((op (e2) (e2)) = (e0))) -> (~((op (e1) (e1)) = (e1))) -> (~((op (e1) (e1)) = (e2))) -> (~((op (e1) (e1)) = (e3))) -> (((op (e1) (e1)) = (e0))\/(((op (e1) (e1)) = (e1))\/(((op (e1) (e1)) = (e2))\/((op (e1) (e1)) = (e3))))) -> (((op (e0) (e0)) = (e2))\/(((op (e1) (e0)) = (e2))\/(((op (e2) (e0)) = (e2))\/((op (e3) (e0)) = (e2))))) -> False). % 15.36/15.51 do 0 intro. intros zenon_H10d zenon_H17d zenon_H8b zenon_H90 zenon_H8f zenon_Ha7 zenon_Hd8 zenon_Hf1 zenon_H3b zenon_H104 zenon_H3c zenon_H52 zenon_H2f zenon_H30 zenon_H2d zenon_H59 zenon_Ha3 zenon_H6a zenon_H105 zenon_H106 zenon_Hbe zenon_H45 zenon_H2e zenon_H1b4 zenon_Hd6 zenon_H182 zenon_H1b3 zenon_Heb. % 15.36/15.51 apply (zenon_or_s _ _ zenon_H10d); [ zenon_intro zenon_H3e | zenon_intro zenon_H42 ]. % 15.36/15.51 apply (zenon_L747_); trivial. % 15.36/15.51 apply (zenon_L417_); trivial. % 15.36/15.51 (* end of lemma zenon_L748_ *) % 15.36/15.51 assert (zenon_L749_ : (((op (e0) (e0)) = (e2))\/(((op (e0) (e1)) = (e2))\/(((op (e0) (e2)) = (e2))\/((op (e0) (e3)) = (e2))))) -> (~((op (e0) (e0)) = (e2))) -> (~((op (e3) (e0)) = (op (e3) (e1)))) -> ((op (e2) (e0)) = (e2)) -> (~((op (e0) (op (e1) (e0))) = (op (e1) (e0)))) -> (((op (e0) (e0)) = (e3))\/(((op (e1) (e0)) = (e3))\/(((op (e2) (e0)) = (e3))\/((op (e3) (e0)) = (e3))))) -> (((op (e1) (e0)) = (e3))\/(((op (e1) (e1)) = (e3))\/(((op (e1) (e2)) = (e3))\/((op (e1) (e3)) = (e3))))) -> ((op (e1) (e0)) = (e1)) -> (~((op (e1) (e1)) = (e3))) -> (~((op (e0) (e2)) = (op (e1) (e2)))) -> (((op (e0) (e3)) = (e2))\/(((op (e1) (e3)) = (e2))\/(((op (e2) (e3)) = (e2))\/((op (e3) (e3)) = (e2))))) -> (~((op (e0) (e1)) = (op (e0) (e3)))) -> (~((op (e2) (e0)) = (op (e2) (e3)))) -> (~((op (e3) (e3)) = (e2))) -> (~((e1) = (e2))) -> (((op (e0) (e0)) = (e3))\/(((op (e0) (e1)) = (e3))\/(((op (e0) (e2)) = (e3))\/((op (e0) (e3)) = (e3))))) -> (~((op (e0) (e0)) = (e3))) -> (~((op (e0) (e1)) = (op (e3) (e1)))) -> ((op (e3) (e1)) = (e3)) -> (~((e1) = (e3))) -> ((op (e0) (e2)) = (e1)) -> (~((e2) = (e3))) -> False). % 15.36/15.51 do 0 intro. intros zenon_H8e zenon_H8f zenon_H109 zenon_Hdd zenon_H261 zenon_Hbe zenon_H90 zenon_Hd8 zenon_H182 zenon_H87 zenon_H160 zenon_H1cd zenon_Hce zenon_H3d zenon_Ha7 zenon_H58 zenon_H59 zenon_H138 zenon_H10a zenon_Ha3 zenon_H29 zenon_H6a. % 15.36/15.51 apply (zenon_or_s _ _ zenon_H8e); [ zenon_intro zenon_H92 | zenon_intro zenon_H91 ]. % 15.36/15.51 exact (zenon_H8f zenon_H92). % 15.36/15.51 apply (zenon_or_s _ _ zenon_H91); [ zenon_intro zenon_H5d | zenon_intro zenon_H93 ]. % 15.36/15.51 apply (zenon_or_s _ _ zenon_H58); [ zenon_intro zenon_H5b | zenon_intro zenon_H5a ]. % 15.36/15.51 exact (zenon_H59 zenon_H5b). % 15.36/15.51 apply (zenon_or_s _ _ zenon_H5a); [ zenon_intro zenon_H4a | zenon_intro zenon_H5c ]. % 15.36/15.51 apply (zenon_L50_); trivial. % 15.36/15.51 apply (zenon_or_s _ _ zenon_H5c); [ zenon_intro zenon_H50 | zenon_intro zenon_H53 ]. % 15.36/15.51 apply (zenon_L411_); trivial. % 15.36/15.51 apply (zenon_L744_); trivial. % 15.36/15.51 apply (zenon_or_s _ _ zenon_H93); [ zenon_intro zenon_H63 | zenon_intro zenon_H81 ]. % 15.36/15.51 apply (zenon_L104_); trivial. % 15.36/15.51 apply (zenon_L129_); trivial. % 15.36/15.51 (* end of lemma zenon_L749_ *) % 15.36/15.51 assert (zenon_L750_ : ((~((op (e3) (e3)) = (e2)))\/((op (e3) (e2)) = (e3))) -> (~((op (e3) (e1)) = (op (e3) (e2)))) -> (((op (e0) (e0)) = (e1))\/(((op (e0) (e1)) = (e1))\/(((op (e0) (e2)) = (e1))\/((op (e0) (e3)) = (e1))))) -> (~((op (e0) (e3)) = (op (e3) (e3)))) -> (~((op (e0) (e0)) = (e2))) -> (~((e1) = (e2))) -> (((op (e0) (e0)) = (e2))\/(((op (e0) (e1)) = (e2))\/(((op (e0) (e2)) = (e2))\/((op (e0) (e3)) = (e2))))) -> (~((op (e0) (e1)) = (op (e3) (e1)))) -> (~((op (e0) (e0)) = (e3))) -> (~((e2) = (e3))) -> (((op (e1) (e0)) = (e3))\/(((op (e1) (e1)) = (e3))\/(((op (e1) (e2)) = (e3))\/((op (e1) (e3)) = (e3))))) -> (~((op (e0) (e1)) = (op (e0) (e3)))) -> (~((op (e2) (e0)) = (op (e2) (e3)))) -> (((op (e0) (e3)) = (e2))\/(((op (e1) (e3)) = (e2))\/(((op (e2) (e3)) = (e2))\/((op (e3) (e3)) = (e2))))) -> (~((op (e0) (e2)) = (op (e1) (e2)))) -> (~((op (e1) (e1)) = (e3))) -> (~((e1) = (e3))) -> (((op (e0) (e0)) = (e3))\/(((op (e1) (e0)) = (e3))\/(((op (e2) (e0)) = (e3))\/((op (e3) (e0)) = (e3))))) -> ((op (e3) (e1)) = (e3)) -> (~((op (e3) (e0)) = (op (e3) (e1)))) -> (((op (e0) (e0)) = (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)) = (e2))) -> (~((op (e1) (e1)) = (e1))) -> (~((op (e3) (e3)) = (e0))) -> (((op (e3) (e3)) = (e0))\/(((op (e3) (e3)) = (e1))\/(((op (e3) (e3)) = (e2))\/((op (e3) (e3)) = (e3))))) -> (((op (e0) (e0)) = (e2))\/(((op (e1) (e0)) = (e2))\/(((op (e2) (e0)) = (e2))\/((op (e3) (e0)) = (e2))))) -> ((op (e1) (e0)) = (e1)) -> (~((op (e0) (op (e1) (e0))) = (op (e1) (e0)))) -> (~((op (e0) (e0)) = (e1))) -> (~((op (e1) (e3)) = (op (e3) (e3)))) -> ((~((op (e3) (e3)) = (e3)))\/((op (e3) (e3)) = (e3))) -> False). % 15.36/15.51 do 0 intro. intros zenon_H10e zenon_H135 zenon_H44 zenon_H36 zenon_H8f zenon_Ha7 zenon_H8e zenon_H138 zenon_H59 zenon_H6a zenon_H90 zenon_H1cd zenon_Hce zenon_H160 zenon_H87 zenon_H182 zenon_Ha3 zenon_Hbe zenon_H10a zenon_H109 zenon_H58 zenon_H1b3 zenon_Hd6 zenon_H1b4 zenon_H3c zenon_H3b zenon_Heb zenon_Hd8 zenon_H261 zenon_H45 zenon_H8b zenon_H10d. % 15.36/15.51 apply (zenon_or_s _ _ zenon_H10e); [ zenon_intro zenon_H3d | zenon_intro zenon_H106 ]. % 15.36/15.51 apply (zenon_or_s _ _ zenon_H10d); [ zenon_intro zenon_H3e | zenon_intro zenon_H42 ]. % 15.36/15.51 apply (zenon_or_s _ _ zenon_H44); [ zenon_intro zenon_H47 | zenon_intro zenon_H46 ]. % 15.36/15.51 exact (zenon_H45 zenon_H47). % 15.36/15.51 apply (zenon_or_s _ _ zenon_H46); [ zenon_intro zenon_H22 | zenon_intro zenon_H48 ]. % 15.36/15.51 apply (zenon_L644_); trivial. % 15.36/15.51 apply (zenon_or_s _ _ zenon_H48); [ zenon_intro zenon_H29 | zenon_intro zenon_H37 ]. % 15.36/15.51 apply (zenon_or_s _ _ zenon_Heb); [ zenon_intro zenon_H92 | zenon_intro zenon_Hec ]. % 15.36/15.51 exact (zenon_H8f zenon_H92). % 15.36/15.51 apply (zenon_or_s _ _ zenon_Hec); [ zenon_intro zenon_H68 | zenon_intro zenon_Hed ]. % 15.36/15.51 apply (zenon_L162_); trivial. % 15.36/15.51 apply (zenon_or_s _ _ zenon_Hed); [ zenon_intro zenon_Hdd | zenon_intro zenon_He9 ]. % 15.36/15.51 apply (zenon_L749_); trivial. % 15.36/15.51 apply (zenon_L406_); trivial. % 15.36/15.51 apply (zenon_L7_); trivial. % 15.36/15.51 apply (zenon_L572_); trivial. % 15.36/15.51 apply (zenon_L115_); trivial. % 15.36/15.51 (* end of lemma zenon_L750_ *) % 15.36/15.51 assert (zenon_L751_ : (((op (e0) (e0)) = (e2))\/(((op (e1) (e0)) = (e2))\/(((op (e2) (e0)) = (e2))\/((op (e3) (e0)) = (e2))))) -> (((op (e3) (e3)) = (e0))\/(((op (e3) (e3)) = (e1))\/(((op (e3) (e3)) = (e2))\/((op (e3) (e3)) = (e3))))) -> (~((op (e1) (e1)) = (e1))) -> (~((op (e1) (e1)) = (e2))) -> (((op (e1) (e1)) = (e0))\/(((op (e1) (e1)) = (e1))\/(((op (e1) (e1)) = (e2))\/((op (e1) (e1)) = (e3))))) -> ((op (e2) (e2)) = (e2)) -> (~((op (e2) (e0)) = (op (e2) (e2)))) -> ((op (e1) (e0)) = (e1)) -> (~((e1) = (e2))) -> (~((op (e0) (e0)) = (e2))) -> ((~((op (e0) (e0)) = (e0)))\/((op (e0) (e0)) = (e0))) -> (~((op (e0) (e0)) = (op (e0) (e1)))) -> (((op (e1) (e3)) = (e0))\/(((op (e1) (e3)) = (e1))\/(((op (e1) (e3)) = (e2))\/((op (e1) (e3)) = (e3))))) -> (~((op (e0) (e0)) = (op (e1) (e0)))) -> (~((op (e0) (e0)) = (op (e2) (e0)))) -> (~((op (e1) (e3)) = (op (e2) (e3)))) -> (~((op (e0) (e0)) = (op (e0) (e3)))) -> (~((op (e0) (e3)) = (op (e2) (e3)))) -> (((op (e0) (e3)) = (e0))\/(((op (e0) (e3)) = (e1))\/(((op (e0) (e3)) = (e2))\/((op (e0) (e3)) = (e3))))) -> (~((op (e0) (e0)) = (op (e0) (e2)))) -> (((op (e3) (e2)) = (e0))\/(((op (e3) (e2)) = (e1))\/(((op (e3) (e2)) = (e2))\/((op (e3) (e2)) = (e3))))) -> ((~((op (e0) (e0)) = (e2)))\/((op (e0) (e2)) = (e0))) -> ((~((op (e1) (e1)) = (e3)))\/((op (e1) (e3)) = (e1))) -> ((~((op (e2) (e2)) = (e1)))\/((op (e2) (e1)) = (e2))) -> ((~((op (e2) (e2)) = (e3)))\/((op (e2) (e3)) = (e2))) -> (~((op (e2) (e1)) = (op (e2) (e3)))) -> (((op (e0) (e1)) = (e3))\/(((op (e1) (e1)) = (e3))\/(((op (e2) (e1)) = (e3))\/((op (e3) (e1)) = (e3))))) -> (~((op (e2) (e0)) = (op (e2) (e3)))) -> (((op (e2) (e0)) = (e0))\/(((op (e2) (e1)) = (e0))\/(((op (e2) (e2)) = (e0))\/((op (e2) (e3)) = (e0))))) -> (((op (e0) (e1)) = (e1))\/(((op (e1) (e1)) = (e1))\/(((op (e2) (e1)) = (e1))\/((op (e3) (e1)) = (e1))))) -> (~((op (e0) (e1)) = (op (e2) (e1)))) -> (~((op (e2) (e1)) = (op (e2) (e2)))) -> (((op (e0) (e0)) = (e3))\/(((op (e0) (e1)) = (e3))\/(((op (e0) (e2)) = (e3))\/((op (e0) (e3)) = (e3))))) -> (~((op (e0) (e3)) = (op (e3) (e3)))) -> (~((op (e0) (e2)) = (op (e2) (e2)))) -> (((op (e2) (e2)) = (e0))\/(((op (e2) (e2)) = (e1))\/(((op (e2) (e2)) = (e2))\/((op (e2) (e2)) = (e3))))) -> (~((e0) = (e3))) -> ((~((op (e3) (e3)) = (e0)))\/((op (e3) (e0)) = (e3))) -> (~((op (e3) (e0)) = (op (e3) (e3)))) -> (((op (e0) (e0)) = (e1))\/(((op (e0) (e1)) = (e1))\/(((op (e0) (e2)) = (e1))\/((op (e0) (e3)) = (e1))))) -> (((op (e0) (e3)) = (e0))\/(((op (e1) (e3)) = (e0))\/(((op (e2) (e3)) = (e0))\/((op (e3) (e3)) = (e0))))) -> (~((op (e0) (e1)) = (op (e0) (e3)))) -> (((op (e0) (e3)) = (e2))\/(((op (e1) (e3)) = (e2))\/(((op (e2) (e3)) = (e2))\/((op (e3) (e3)) = (e2))))) -> (~((e1) = (e3))) -> (~((e0) = (e1))) -> (~((e0) = (e2))) -> (((op (e1) (e0)) = (e2))\/(((op (e1) (e1)) = (e2))\/(((op (e1) (e2)) = (e2))\/((op (e1) (e3)) = (e2))))) -> (~((op (e0) (e3)) = (op (e1) (e3)))) -> (~((op (e1) (e2)) = (op (e2) (e2)))) -> (~((e2) = (e3))) -> (~((op (e0) (e2)) = (op (e1) (e2)))) -> (~((op (e1) (e3)) = (op (e3) (e3)))) -> (((op (e1) (e0)) = (e3))\/(((op (e1) (e1)) = (e3))\/(((op (e1) (e2)) = (e3))\/((op (e1) (e3)) = (e3))))) -> (((op (e0) (e0)) = (e2))\/(((op (e0) (e1)) = (e2))\/(((op (e0) (e2)) = (e2))\/((op (e0) (e3)) = (e2))))) -> (~((op (e3) (e2)) = (op (e3) (e3)))) -> ((~((op (e3) (e3)) = (e2)))\/((op (e3) (e2)) = (e3))) -> ((~((op (e2) (e2)) = (e2)))\/((op (e2) (e2)) = (e2))) -> (~((op (e2) (e0)) = (op (e2) (e1)))) -> (((op (e2) (e0)) = (e3))\/(((op (e2) (e1)) = (e3))\/(((op (e2) (e2)) = (e3))\/((op (e2) (e3)) = (e3))))) -> (~((op (e2) (e3)) = (op (e3) (e3)))) -> ((~((op (e2) (e2)) = (e0)))\/((op (e2) (e0)) = (e2))) -> (~((op (e0) (e1)) = (op (e1) (e1)))) -> (((op (e0) (e0)) = (e3))\/(((op (e1) (e0)) = (e3))\/(((op (e2) (e0)) = (e3))\/((op (e3) (e0)) = (e3))))) -> (~((op (e0) (e2)) = (op (e0) (e3)))) -> (((op (e0) (e2)) = (e3))\/(((op (e1) (e2)) = (e3))\/(((op (e2) (e2)) = (e3))\/((op (e3) (e2)) = (e3))))) -> (((op (e1) (e0)) = (e1))\/(((op (e1) (e1)) = (e1))\/(((op (e1) (e2)) = (e1))\/((op (e1) (e3)) = (e1))))) -> (((op (e0) (e1)) = (e0))\/(((op (e1) (e1)) = (e0))\/(((op (e2) (e1)) = (e0))\/((op (e3) (e1)) = (e0))))) -> (((op (e0) (e0)) = (e0))\/(((op (e1) (e0)) = (e0))\/(((op (e2) (e0)) = (e0))\/((op (e3) (e0)) = (e0))))) -> (((op (e0) (e2)) = (e0))\/(((op (e1) (e2)) = (e0))\/(((op (e2) (e2)) = (e0))\/((op (e3) (e2)) = (e0))))) -> (~((op (e3) (e1)) = (op (e3) (e2)))) -> (~((op (e3) (e0)) = (op (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 (e1) (e1)) = (e0)))\/((op (e1) (e0)) = (e1))) -> (~((op (e1) (e0)) = (op (e1) (e2)))) -> (~((op (e1) (e0)) = (op (e1) (e1)))) -> ((~((op (e1) (e1)) = (e2)))\/((op (e1) (e2)) = (e1))) -> (~((op (e1) (e2)) = (op (e1) (e3)))) -> (~((op (e1) (op (e1) (e1))) = (op (e1) (e1)))) -> ((~((op (e1) (e1)) = (e1)))\/((op (e1) (e1)) = (e1))) -> ((~((op (e0) (e0)) = (e3)))\/((op (e0) (e3)) = (e0))) -> (~((op (e1) (e0)) = (op (e1) (e3)))) -> (((op (e0) (e3)) = (e1))\/(((op (e1) (e3)) = (e1))\/(((op (e2) (e3)) = (e1))\/((op (e3) (e3)) = (e1))))) -> (~((op (e0) (op (e1) (e0))) = (op (e1) (e0)))) -> (((op (e2) (e0)) = (e1))\/(((op (e2) (e1)) = (e1))\/(((op (e2) (e2)) = (e1))\/((op (e2) (e3)) = (e1))))) -> (((op (e0) (e0)) = (e1))\/(((op (e1) (e0)) = (e1))\/(((op (e2) (e0)) = (e1))\/((op (e3) (e0)) = (e1))))) -> (~((op (e3) (e1)) = (op (e3) (e3)))) -> ((~((op (e3) (e3)) = (e1)))\/((op (e3) (e1)) = (e3))) -> (((op (e0) (e0)) = (e0))\/(((op (e0) (e1)) = (e0))\/(((op (e0) (e2)) = (e0))\/((op (e0) (e3)) = (e0))))) -> ((~((op (e3) (e3)) = (e3)))\/((op (e3) (e3)) = (e3))) -> (((op (e0) (e0)) = (e0))\/(((op (e0) (e0)) = (e1))\/(((op (e0) (e0)) = (e2))\/((op (e0) (e0)) = (e3))))) -> (((op (e0) (e1)) = (e2))\/(((op (e1) (e1)) = (e2))\/(((op (e2) (e1)) = (e2))\/((op (e3) (e1)) = (e2))))) -> (~((op (e2) (e2)) = (op (e2) (e3)))) -> (((op (e3) (e0)) = (e1))\/(((op (e3) (e1)) = (e1))\/(((op (e3) (e2)) = (e1))\/((op (e3) (e3)) = (e1))))) -> (~((op (e0) (e2)) = (op (e3) (e2)))) -> (~((op (e3) (op (e1) (e3))) = (op (e1) (e3)))) -> (((op (e2) (e0)) = (e2))\/(((op (e2) (e1)) = (e2))\/(((op (e2) (e2)) = (e2))\/((op (e2) (e3)) = (e2))))) -> (((op (e0) (e2)) = (e0))\/(((op (e0) (e2)) = (e1))\/(((op (e0) (e2)) = (e2))\/((op (e0) (e2)) = (e3))))) -> (((op (e3) (e0)) = (e2))\/(((op (e3) (e1)) = (e2))\/(((op (e3) (e2)) = (e2))\/((op (e3) (e3)) = (e2))))) -> (((op (e0) (e2)) = (e2))\/(((op (e1) (e2)) = (e2))\/(((op (e2) (e2)) = (e2))\/((op (e3) (e2)) = (e2))))) -> (~((op (e2) (e1)) = (op (e3) (e1)))) -> (((op (e0) (e2)) = (e1))\/(((op (e1) (e2)) = (e1))\/(((op (e2) (e2)) = (e1))\/((op (e3) (e2)) = (e1))))) -> (~((op (e2) (op (e1) (e2))) = (op (e1) (e2)))) -> (((op (e1) (e0)) = (e0))\/(((op (e1) (e1)) = (e0))\/(((op (e1) (e2)) = (e0))\/((op (e1) (e3)) = (e0))))) -> (~((op (e3) (e0)) = (op (e3) (e2)))) -> (~((op (e1) (e2)) = (op (e3) (e2)))) -> (~((op (e1) (e0)) = (op (e3) (e0)))) -> (~((op (e0) (e1)) = (op (e0) (e2)))) -> ((~((op (e0) (e0)) = (e1)))\/((op (e0) (e1)) = (e0))) -> False). % 15.36/15.51 do 0 intro. intros zenon_Heb zenon_H3b zenon_H1b4 zenon_Hd6 zenon_H1b3 zenon_H35 zenon_H17a zenon_Hd8 zenon_Ha7 zenon_H8f zenon_H249 zenon_H25a zenon_H25b zenon_H24c zenon_H258 zenon_H244 zenon_H24f zenon_Hb4 zenon_H254 zenon_H250 zenon_H25e zenon_H24a zenon_H1d2 zenon_H1e3 zenon_H1c3 zenon_H1e2 zenon_H199 zenon_Hce zenon_H1f5 zenon_H228 zenon_Hde zenon_H157 zenon_H58 zenon_H36 zenon_H28 zenon_H2d zenon_H4b zenon_H10f zenon_Hbb zenon_H44 zenon_Hd3 zenon_H1cd zenon_H160 zenon_Ha3 zenon_H9e zenon_H5e zenon_H84 zenon_H80 zenon_H7d zenon_H6a zenon_H87 zenon_H8b zenon_H90 zenon_H8e zenon_H173 zenon_H10e zenon_Haa zenon_H154 zenon_He6 zenon_He3 zenon_H1d4 zenon_H23 zenon_Hbe zenon_Hc9 zenon_H175 zenon_H1c5 zenon_H144 zenon_Hf0 zenon_H16f zenon_H135 zenon_H109 zenon_H138 zenon_H16c zenon_H1e4 zenon_H166 zenon_Hd7 zenon_H1d3 zenon_H1d0 zenon_H27b zenon_H1d8 zenon_H236 zenon_H1cf zenon_H121 zenon_H261 zenon_Hb7 zenon_Hf1 zenon_H12d zenon_H10c zenon_H110 zenon_H10d zenon_H12a zenon_H1a2 zenon_H15f zenon_H146 zenon_H140 zenon_H26e zenon_H237 zenon_H251 zenon_H1df zenon_H27c zenon_H13c zenon_H11b zenon_H277 zenon_H163 zenon_H105 zenon_H17d zenon_H22e zenon_H23e zenon_H24b. % 15.36/15.51 apply (zenon_or_s _ _ zenon_H1d2); [ zenon_intro zenon_H182 | zenon_intro zenon_H11f ]. % 15.36/15.51 apply (zenon_or_s _ _ zenon_H10f); [ zenon_intro zenon_H3c | zenon_intro zenon_Hba ]. % 15.36/15.51 apply (zenon_L734_); trivial. % 15.36/15.51 apply (zenon_L510_); trivial. % 15.36/15.51 apply (zenon_L224_); trivial. % 15.36/15.51 (* end of lemma zenon_L751_ *) % 15.36/15.51 assert (zenon_L752_ : (((op (e0) (e0)) = (e3))\/(((op (e0) (e1)) = (e3))\/(((op (e0) (e2)) = (e3))\/((op (e0) (e3)) = (e3))))) -> (~((op (e0) (e0)) = (e3))) -> ((op (e3) (e0)) = (e1)) -> (~((op (e3) (e0)) = (op (e3) (e1)))) -> (((op (e0) (e2)) = (e1))\/(((op (e1) (e2)) = (e1))\/(((op (e2) (e2)) = (e1))\/((op (e3) (e2)) = (e1))))) -> (~((op (e0) (e2)) = (op (e0) (e3)))) -> (~((op (e2) (op (e1) (e2))) = (op (e1) (e2)))) -> (~((op (e2) (e2)) = (e1))) -> ((op (e3) (e2)) = (e3)) -> (~((op (e1) (e1)) = (e1))) -> (((op (e0) (e1)) = (e1))\/(((op (e1) (e1)) = (e1))\/(((op (e2) (e1)) = (e1))\/((op (e3) (e1)) = (e1))))) -> (~((e0) = (e3))) -> ((op (e0) (e2)) = (e0)) -> ((op (e0) (e3)) = (e1)) -> (~((e1) = (e3))) -> False). % 15.36/15.51 do 0 intro. intros zenon_H58 zenon_H59 zenon_Hee zenon_H109 zenon_H11b zenon_Hc9 zenon_H277 zenon_H52 zenon_H106 zenon_H1b4 zenon_H228 zenon_H4b zenon_Hab zenon_H37 zenon_Ha3. % 15.36/15.51 apply (zenon_or_s _ _ zenon_H58); [ zenon_intro zenon_H5b | zenon_intro zenon_H5a ]. % 15.36/15.51 exact (zenon_H59 zenon_H5b). % 15.36/15.51 apply (zenon_or_s _ _ zenon_H5a); [ zenon_intro zenon_H4a | zenon_intro zenon_H5c ]. % 15.36/15.51 apply (zenon_or_s _ _ zenon_H228); [ zenon_intro zenon_H22 | zenon_intro zenon_H229 ]. % 15.36/15.51 apply (zenon_L59_); trivial. % 15.36/15.51 apply (zenon_or_s _ _ zenon_H229); [ zenon_intro zenon_H21 | zenon_intro zenon_H22a ]. % 15.36/15.51 exact (zenon_H1b4 zenon_H21). % 15.36/15.51 apply (zenon_or_s _ _ zenon_H22a); [ zenon_intro zenon_Hb2 | zenon_intro zenon_H13e ]. % 15.36/15.51 apply (zenon_or_s _ _ zenon_H11b); [ zenon_intro zenon_H29 | zenon_intro zenon_H11c ]. % 15.36/15.51 apply (zenon_L85_); trivial. % 15.36/15.51 apply (zenon_or_s _ _ zenon_H11c); [ zenon_intro zenon_H117 | zenon_intro zenon_H11d ]. % 15.36/15.51 apply (zenon_L742_); trivial. % 15.36/15.51 apply (zenon_or_s _ _ zenon_H11d); [ zenon_intro zenon_H2a | zenon_intro zenon_H119 ]. % 15.36/15.51 exact (zenon_H52 zenon_H2a). % 15.36/15.51 apply (zenon_L87_); trivial. % 15.36/15.51 apply (zenon_L145_); trivial. % 15.36/15.51 apply (zenon_or_s _ _ zenon_H5c); [ zenon_intro zenon_H50 | zenon_intro zenon_H53 ]. % 15.36/15.51 apply (zenon_L48_); trivial. % 15.36/15.51 apply (zenon_L32_); trivial. % 15.36/15.51 (* end of lemma zenon_L752_ *) % 15.36/15.51 assert (zenon_L753_ : (((op (e0) (e0)) = (e3))\/(((op (e1) (e0)) = (e3))\/(((op (e2) (e0)) = (e3))\/((op (e3) (e0)) = (e3))))) -> (~((op (e3) (e0)) = (op (e3) (e2)))) -> (~((e2) = (e3))) -> (~((op (e0) (e1)) = (op (e2) (e1)))) -> (~((op (e2) (e2)) = (e1))) -> (~((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)) = (e1))\/(((op (e1) (e0)) = (e1))\/(((op (e2) (e0)) = (e1))\/((op (e3) (e0)) = (e1))))) -> (((op (e0) (e1)) = (e1))\/(((op (e1) (e1)) = (e1))\/(((op (e2) (e1)) = (e1))\/((op (e3) (e1)) = (e1))))) -> (~((op (e0) (e2)) = (op (e0) (e3)))) -> (~((op (e2) (op (e1) (e2))) = (op (e1) (e2)))) -> (((op (e0) (e2)) = (e1))\/(((op (e1) (e2)) = (e1))\/(((op (e2) (e2)) = (e1))\/((op (e3) (e2)) = (e1))))) -> ((~((op (e3) (e3)) = (e1)))\/((op (e3) (e1)) = (e3))) -> (~((op (e3) (e0)) = (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) (e3)) = (e1)) -> (~((e1) = (e2))) -> ((op (e2) (e2)) = (e2)) -> (~((op (e1) (e2)) = (op (e2) (e2)))) -> (~((op (e1) (e1)) = (e0))) -> (~((op (e1) (e1)) = (e1))) -> (~((op (e1) (e1)) = (e2))) -> (((op (e3) (e3)) = (e0))\/(((op (e3) (e3)) = (e1))\/(((op (e3) (e3)) = (e2))\/((op (e3) (e3)) = (e3))))) -> (~((op (e3) (e3)) = (e1))) -> (((op (e1) (e1)) = (e0))\/(((op (e1) (e1)) = (e1))\/(((op (e1) (e1)) = (e2))\/((op (e1) (e1)) = (e3))))) -> ((~((op (e3) (e3)) = (e0)))\/((op (e3) (e0)) = (e3))) -> (~((op (e3) (e0)) = (op (e3) (e3)))) -> (((op (e0) (e0)) = (e1))\/(((op (e0) (e1)) = (e1))\/(((op (e0) (e2)) = (e1))\/((op (e0) (e3)) = (e1))))) -> (((op (e0) (e3)) = (e2))\/(((op (e1) (e3)) = (e2))\/(((op (e2) (e3)) = (e2))\/((op (e3) (e3)) = (e2))))) -> (~((e0) = (e2))) -> (((op (e0) (e3)) = (e0))\/(((op (e1) (e3)) = (e0))\/(((op (e2) (e3)) = (e0))\/((op (e3) (e3)) = (e0))))) -> (~((e0) = (e1))) -> (~((op (e0) (e0)) = (e3))) -> (~((e1) = (e3))) -> (~((e0) = (e3))) -> ((op (e0) (e2)) = (e0)) -> (~((op (e0) (e3)) = (op (e3) (e3)))) -> (((op (e0) (e0)) = (e3))\/(((op (e0) (e1)) = (e3))\/(((op (e0) (e2)) = (e3))\/((op (e0) (e3)) = (e3))))) -> (~((op (e0) (e0)) = (e1))) -> (~((op (e3) (e2)) = (op (e3) (e3)))) -> ((~((op (e3) (e3)) = (e2)))\/((op (e3) (e2)) = (e3))) -> ((~((op (e3) (e3)) = (e3)))\/((op (e3) (e3)) = (e3))) -> False). % 15.36/15.51 do 0 intro. intros zenon_Hbe zenon_H105 zenon_H6a zenon_Hde zenon_H52 zenon_H244 zenon_Hb7 zenon_Hf1 zenon_H228 zenon_Hc9 zenon_H277 zenon_H11b zenon_H10c zenon_H109 zenon_H1cf zenon_H84 zenon_H11f zenon_Ha7 zenon_H35 zenon_H7d zenon_H145 zenon_H1b4 zenon_Hd6 zenon_H3b zenon_H104 zenon_H1b3 zenon_H10f zenon_Hbb zenon_H44 zenon_H160 zenon_H5e zenon_Hd3 zenon_H9e zenon_H59 zenon_Ha3 zenon_H4b zenon_Hab zenon_H36 zenon_H58 zenon_H45 zenon_H173 zenon_H10e zenon_H10d. % 15.36/15.51 apply (zenon_or_s _ _ zenon_H10e); [ zenon_intro zenon_H3d | zenon_intro zenon_H106 ]. % 15.36/15.51 apply (zenon_L542_); trivial. % 15.36/15.51 apply (zenon_or_s _ _ zenon_H44); [ zenon_intro zenon_H47 | zenon_intro zenon_H46 ]. % 15.36/15.51 exact (zenon_H45 zenon_H47). % 15.36/15.51 apply (zenon_or_s _ _ zenon_H46); [ zenon_intro zenon_H22 | zenon_intro zenon_H48 ]. % 15.36/15.51 apply (zenon_L531_); trivial. % 15.36/15.51 apply (zenon_or_s _ _ zenon_H48); [ zenon_intro zenon_H29 | zenon_intro zenon_H37 ]. % 15.36/15.51 apply (zenon_L37_); trivial. % 15.36/15.51 apply (zenon_or_s _ _ zenon_Hf1); [ zenon_intro zenon_H47 | zenon_intro zenon_Hf4 ]. % 15.36/15.51 exact (zenon_H45 zenon_H47). % 15.36/15.51 apply (zenon_or_s _ _ zenon_Hf4); [ zenon_intro zenon_Hd8 | zenon_intro zenon_Hf5 ]. % 15.36/15.51 apply (zenon_L224_); trivial. % 15.36/15.51 apply (zenon_or_s _ _ zenon_Hf5); [ zenon_intro zenon_Hae | zenon_intro zenon_Hee ]. % 15.36/15.51 apply (zenon_L544_); trivial. % 15.36/15.51 apply (zenon_L752_); trivial. % 15.36/15.51 (* end of lemma zenon_L753_ *) % 15.36/15.51 assert (zenon_L754_ : ((~((op (e2) (e2)) = (e1)))\/((op (e2) (e1)) = (e2))) -> (((op (e0) (e0)) = (e3))\/(((op (e1) (e0)) = (e3))\/(((op (e2) (e0)) = (e3))\/((op (e3) (e0)) = (e3))))) -> (~((op (e3) (e0)) = (op (e3) (e2)))) -> (~((e2) = (e3))) -> (~((op (e0) (e1)) = (op (e2) (e1)))) -> (~((op (e1) (e3)) = (op (e2) (e3)))) -> (((op (e2) (e0)) = (e1))\/(((op (e2) (e1)) = (e1))\/(((op (e2) (e2)) = (e1))\/((op (e2) (e3)) = (e1))))) -> (((op (e0) (e0)) = (e1))\/(((op (e1) (e0)) = (e1))\/(((op (e2) (e0)) = (e1))\/((op (e3) (e0)) = (e1))))) -> (((op (e0) (e1)) = (e1))\/(((op (e1) (e1)) = (e1))\/(((op (e2) (e1)) = (e1))\/((op (e3) (e1)) = (e1))))) -> (~((op (e0) (e2)) = (op (e0) (e3)))) -> (~((op (e2) (op (e1) (e2))) = (op (e1) (e2)))) -> (((op (e0) (e2)) = (e1))\/(((op (e1) (e2)) = (e1))\/(((op (e2) (e2)) = (e1))\/((op (e3) (e2)) = (e1))))) -> ((~((op (e3) (e3)) = (e1)))\/((op (e3) (e1)) = (e3))) -> (~((op (e3) (e0)) = (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) (e3)) = (e1)) -> (~((e1) = (e2))) -> ((op (e2) (e2)) = (e2)) -> (~((op (e1) (e2)) = (op (e2) (e2)))) -> (~((op (e1) (e1)) = (e0))) -> (~((op (e1) (e1)) = (e1))) -> (~((op (e1) (e1)) = (e2))) -> (((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 (e3) (e3)) = (e0)))\/((op (e3) (e0)) = (e3))) -> (~((op (e3) (e0)) = (op (e3) (e3)))) -> (((op (e0) (e0)) = (e1))\/(((op (e0) (e1)) = (e1))\/(((op (e0) (e2)) = (e1))\/((op (e0) (e3)) = (e1))))) -> (((op (e0) (e3)) = (e2))\/(((op (e1) (e3)) = (e2))\/(((op (e2) (e3)) = (e2))\/((op (e3) (e3)) = (e2))))) -> (~((e0) = (e2))) -> (((op (e0) (e3)) = (e0))\/(((op (e1) (e3)) = (e0))\/(((op (e2) (e3)) = (e0))\/((op (e3) (e3)) = (e0))))) -> (~((e0) = (e1))) -> (~((op (e0) (e0)) = (e3))) -> (~((e1) = (e3))) -> (~((e0) = (e3))) -> ((op (e0) (e2)) = (e0)) -> (~((op (e0) (e3)) = (op (e3) (e3)))) -> (((op (e0) (e0)) = (e3))\/(((op (e0) (e1)) = (e3))\/(((op (e0) (e2)) = (e3))\/((op (e0) (e3)) = (e3))))) -> (~((op (e0) (e0)) = (e1))) -> (~((op (e3) (e2)) = (op (e3) (e3)))) -> ((~((op (e3) (e3)) = (e2)))\/((op (e3) (e2)) = (e3))) -> ((~((op (e3) (e3)) = (e3)))\/((op (e3) (e3)) = (e3))) -> (~((op (e3) (e1)) = (op (e3) (e2)))) -> (((op (e0) (e1)) = (e2))\/(((op (e1) (e1)) = (e2))\/(((op (e2) (e1)) = (e2))\/((op (e3) (e1)) = (e2))))) -> (~((op (e2) (e1)) = (op (e2) (e2)))) -> (~((op (e0) (e1)) = (op (e0) (e3)))) -> (~((op (e2) (e2)) = (op (e2) (e3)))) -> (((op (e0) (e1)) = (e0))\/(((op (e1) (e1)) = (e0))\/(((op (e2) (e1)) = (e0))\/((op (e3) (e1)) = (e0))))) -> False). % 15.36/15.51 do 0 intro. intros zenon_H1e3 zenon_Hbe zenon_H105 zenon_H6a zenon_Hde zenon_H244 zenon_Hb7 zenon_Hf1 zenon_H228 zenon_Hc9 zenon_H277 zenon_H11b zenon_H10c zenon_H109 zenon_H1cf zenon_H84 zenon_H11f zenon_Ha7 zenon_H35 zenon_H7d zenon_H145 zenon_H1b4 zenon_Hd6 zenon_H3b zenon_H1b3 zenon_H10f zenon_Hbb zenon_H44 zenon_H160 zenon_H5e zenon_Hd3 zenon_H9e zenon_H59 zenon_Ha3 zenon_H4b zenon_Hab zenon_H36 zenon_H58 zenon_H45 zenon_H173 zenon_H10e zenon_H10d zenon_H135 zenon_H1a2 zenon_H157 zenon_H1cd zenon_H15f zenon_H144. % 15.36/15.51 apply (zenon_or_s _ _ zenon_H1e3); [ zenon_intro zenon_H52 | zenon_intro zenon_H156 ]. % 15.36/15.51 apply (zenon_or_s _ _ zenon_H10c); [ zenon_intro zenon_H104 | zenon_intro zenon_H10a ]. % 15.36/15.51 apply (zenon_L753_); trivial. % 15.36/15.51 apply (zenon_L494_); trivial. % 15.36/15.51 apply (zenon_L134_); trivial. % 15.36/15.51 (* end of lemma zenon_L754_ *) % 15.36/15.51 assert (zenon_L755_ : (((op (e0) (e0)) = (e3))\/(((op (e0) (e1)) = (e3))\/(((op (e0) (e2)) = (e3))\/((op (e0) (e3)) = (e3))))) -> (~((op (e0) (e0)) = (e3))) -> (~((e1) = (e3))) -> ((op (e0) (e1)) = (e1)) -> (~((e0) = (e3))) -> ((op (e0) (e2)) = (e0)) -> ((op (e0) (e3)) = (e2)) -> (~((e2) = (e3))) -> False). % 15.36/15.51 do 0 intro. intros zenon_H58 zenon_H59 zenon_Ha3 zenon_H22 zenon_H4b zenon_Hab zenon_H81 zenon_H6a. % 15.36/15.51 apply (zenon_or_s _ _ zenon_H58); [ zenon_intro zenon_H5b | zenon_intro zenon_H5a ]. % 15.36/15.51 exact (zenon_H59 zenon_H5b). % 15.36/15.51 apply (zenon_or_s _ _ zenon_H5a); [ zenon_intro zenon_H4a | zenon_intro zenon_H5c ]. % 15.36/15.51 apply (zenon_L59_); trivial. % 15.36/15.51 apply (zenon_or_s _ _ zenon_H5c); [ zenon_intro zenon_H50 | zenon_intro zenon_H53 ]. % 15.36/15.51 apply (zenon_L48_); trivial. % 15.36/15.51 apply (zenon_L128_); trivial. % 15.36/15.51 (* end of lemma zenon_L755_ *) % 15.36/15.51 assert (zenon_L756_ : ((op (e3) (e0)) = (e0)) -> ((op (e1) (e0)) = (e0)) -> (~((op (e1) (e0)) = (op (e3) (e0)))) -> False). % 15.36/15.51 do 0 intro. intros zenon_Hdb zenon_Had zenon_H22e. % 15.36/15.51 elim (classic ((op (e3) (e0)) = (op (e3) (e0)))); [ zenon_intro zenon_H1e6 | zenon_intro zenon_H108 ]. % 15.36/15.51 cut (((op (e3) (e0)) = (op (e3) (e0))) = ((op (e1) (e0)) = (op (e3) (e0)))). % 15.36/15.51 intro zenon_D_pnotp. % 15.36/15.51 apply zenon_H22e. % 15.36/15.51 rewrite <- zenon_D_pnotp. % 15.36/15.51 exact zenon_H1e6. % 15.36/15.51 cut (((op (e3) (e0)) = (op (e3) (e0)))); [idtac | apply NNPP; zenon_intro zenon_H108]. % 15.36/15.51 cut (((op (e3) (e0)) = (op (e1) (e0)))); [idtac | apply NNPP; zenon_intro zenon_H287]. % 15.36/15.51 congruence. % 15.36/15.51 cut (((op (e3) (e0)) = (e0)) = ((op (e3) (e0)) = (op (e1) (e0)))). % 15.36/15.51 intro zenon_D_pnotp. % 15.36/15.51 apply zenon_H287. % 15.36/15.51 rewrite <- zenon_D_pnotp. % 15.36/15.51 exact zenon_Hdb. % 15.36/15.51 cut (((e0) = (op (e1) (e0)))); [idtac | apply NNPP; zenon_intro zenon_H24d]. % 15.36/15.51 cut (((op (e3) (e0)) = (op (e3) (e0)))); [idtac | apply NNPP; zenon_intro zenon_H108]. % 15.36/15.51 congruence. % 15.36/15.51 apply zenon_H108. apply refl_equal. % 15.36/15.51 apply zenon_H24d. apply sym_equal. exact zenon_Had. % 15.36/15.51 apply zenon_H108. apply refl_equal. % 15.36/15.51 apply zenon_H108. apply refl_equal. % 15.36/15.51 (* end of lemma zenon_L756_ *) % 15.36/15.51 assert (zenon_L757_ : (~((op (e3) (op (e1) (e3))) = (op (e3) (e0)))) -> ((op (e1) (e3)) = (e0)) -> False). % 15.36/15.51 do 0 intro. intros zenon_H288 zenon_Hcc. % 15.36/15.51 cut (((op (e1) (e3)) = (e0))); [idtac | apply NNPP; zenon_intro zenon_H1c4]. % 15.36/15.51 cut (((e3) = (e3))); [idtac | apply NNPP; zenon_intro zenon_H4d]. % 15.36/15.51 congruence. % 15.36/15.51 apply zenon_H4d. apply refl_equal. % 15.36/15.51 exact (zenon_H1c4 zenon_Hcc). % 15.36/15.51 (* end of lemma zenon_L757_ *) % 15.36/15.51 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)) = (e0))) -> ((op (e0) (e2)) = (e0)) -> (~((op (e0) (e2)) = (op (e1) (e2)))) -> (~((op (e3) (op (e1) (e3))) = (op (e1) (e3)))) -> ((op (e3) (e0)) = (e0)) -> False). % 15.36/15.51 do 0 intro. intros zenon_H163 zenon_H22e zenon_H145 zenon_Hab zenon_H87 zenon_H26e zenon_Hdb. % 15.36/15.51 apply (zenon_or_s _ _ zenon_H163); [ zenon_intro zenon_Had | zenon_intro zenon_H164 ]. % 15.36/15.51 apply (zenon_L756_); trivial. % 15.36/15.51 apply (zenon_or_s _ _ zenon_H164); [ zenon_intro zenon_H149 | zenon_intro zenon_H165 ]. % 15.36/15.51 exact (zenon_H145 zenon_H149). % 15.36/15.51 apply (zenon_or_s _ _ zenon_H165); [ zenon_intro zenon_H15d | zenon_intro zenon_Hcc ]. % 15.36/15.51 apply (zenon_L136_); trivial. % 15.36/15.51 cut (((op (e3) (e0)) = (e0)) = ((op (e3) (op (e1) (e3))) = (op (e1) (e3)))). % 15.36/15.51 intro zenon_D_pnotp. % 15.36/15.51 apply zenon_H26e. % 15.36/15.51 rewrite <- zenon_D_pnotp. % 15.36/15.51 exact zenon_Hdb. % 15.36/15.51 cut (((e0) = (op (e1) (e3)))); [idtac | apply NNPP; zenon_intro zenon_H178]. % 15.36/15.51 cut (((op (e3) (e0)) = (op (e3) (op (e1) (e3))))); [idtac | apply NNPP; zenon_intro zenon_H289]. % 15.36/15.51 congruence. % 15.36/15.51 elim (classic ((op (e3) (op (e1) (e3))) = (op (e3) (op (e1) (e3))))); [ zenon_intro zenon_H270 | zenon_intro zenon_H271 ]. % 15.36/15.51 cut (((op (e3) (op (e1) (e3))) = (op (e3) (op (e1) (e3)))) = ((op (e3) (e0)) = (op (e3) (op (e1) (e3))))). % 15.36/15.51 intro zenon_D_pnotp. % 15.36/15.51 apply zenon_H289. % 15.36/15.51 rewrite <- zenon_D_pnotp. % 15.36/15.51 exact zenon_H270. % 15.36/15.51 cut (((op (e3) (op (e1) (e3))) = (op (e3) (op (e1) (e3))))); [idtac | apply NNPP; zenon_intro zenon_H271]. % 15.36/15.51 cut (((op (e3) (op (e1) (e3))) = (op (e3) (e0)))); [idtac | apply NNPP; zenon_intro zenon_H288]. % 15.36/15.51 congruence. % 15.36/15.51 apply (zenon_L757_); trivial. % 15.36/15.51 apply zenon_H271. apply refl_equal. % 15.36/15.51 apply zenon_H271. apply refl_equal. % 15.36/15.51 apply zenon_H178. apply sym_equal. exact zenon_Hcc. % 15.36/15.51 (* end of lemma zenon_L758_ *) % 15.36/15.51 assert (zenon_L759_ : (~((op (e1) (e2)) = (op (e3) (e2)))) -> ((op (e1) (e2)) = (e1)) -> ((op (e3) (e2)) = (e1)) -> False). % 15.36/15.51 do 0 intro. intros zenon_H17d zenon_H117 zenon_H119. % 15.36/15.51 cut (((op (e1) (e2)) = (e1)) = ((op (e1) (e2)) = (op (e3) (e2)))). % 15.36/15.51 intro zenon_D_pnotp. % 15.36/15.51 apply zenon_H17d. % 15.36/15.51 rewrite <- zenon_D_pnotp. % 15.36/15.51 exact zenon_H117. % 15.36/15.51 cut (((e1) = (op (e3) (e2)))); [idtac | apply NNPP; zenon_intro zenon_H141]. % 15.36/15.51 cut (((op (e1) (e2)) = (op (e1) (e2)))); [idtac | apply NNPP; zenon_intro zenon_H1d1]. % 15.36/15.51 congruence. % 15.36/15.51 apply zenon_H1d1. apply refl_equal. % 15.36/15.51 apply zenon_H141. apply sym_equal. exact zenon_H119. % 15.36/15.51 (* end of lemma zenon_L759_ *) % 15.36/15.51 assert (zenon_L760_ : (((op (e1) (e2)) = (e0))\/(((op (e1) (e2)) = (e1))\/(((op (e1) (e2)) = (e2))\/((op (e1) (e2)) = (e3))))) -> ((op (e0) (e2)) = (e0)) -> ((op (e3) (e2)) = (e1)) -> (~((op (e1) (e2)) = (op (e3) (e2)))) -> (~((op (e1) (e2)) = (op (e2) (e2)))) -> ((op (e2) (e2)) = (e2)) -> (~((op (e0) (e2)) = (op (e1) (e2)))) -> ((op (e0) (e2)) = (e3)) -> False). % 15.36/15.51 do 0 intro. intros zenon_H1d5 zenon_Hab zenon_H119 zenon_H17d zenon_H7d zenon_H35 zenon_H87 zenon_H50. % 15.36/15.51 apply (zenon_or_s _ _ zenon_H1d5); [ zenon_intro zenon_H15d | zenon_intro zenon_H1d6 ]. % 15.36/15.51 apply (zenon_L136_); trivial. % 15.36/15.51 apply (zenon_or_s _ _ zenon_H1d6); [ zenon_intro zenon_H117 | zenon_intro zenon_H1d7 ]. % 15.36/15.51 apply (zenon_L759_); trivial. % 15.36/15.51 apply (zenon_or_s _ _ zenon_H1d7); [ zenon_intro zenon_H7c | zenon_intro zenon_H88 ]. % 15.36/15.51 apply (zenon_L21_); trivial. % 15.36/15.51 apply (zenon_L24_); trivial. % 15.36/15.51 (* end of lemma zenon_L760_ *) % 15.36/15.51 assert (zenon_L761_ : (((op (e0) (e2)) = (e1))\/(((op (e1) (e2)) = (e1))\/(((op (e2) (e2)) = (e1))\/((op (e3) (e2)) = (e1))))) -> (~((e1) = (e3))) -> ((op (e1) (e0)) = (e1)) -> (~((op (e1) (e0)) = (op (e1) (e2)))) -> (~((op (e2) (e2)) = (e1))) -> (((op (e1) (e2)) = (e0))\/(((op (e1) (e2)) = (e1))\/(((op (e1) (e2)) = (e2))\/((op (e1) (e2)) = (e3))))) -> ((op (e0) (e2)) = (e0)) -> (~((op (e1) (e2)) = (op (e3) (e2)))) -> (~((op (e1) (e2)) = (op (e2) (e2)))) -> ((op (e2) (e2)) = (e2)) -> (~((op (e0) (e2)) = (op (e1) (e2)))) -> ((op (e0) (e2)) = (e3)) -> False). % 15.36/15.51 do 0 intro. intros zenon_H11b zenon_Ha3 zenon_Hd8 zenon_H166 zenon_H52 zenon_H1d5 zenon_Hab zenon_H17d zenon_H7d zenon_H35 zenon_H87 zenon_H50. % 15.36/15.51 apply (zenon_or_s _ _ zenon_H11b); [ zenon_intro zenon_H29 | zenon_intro zenon_H11c ]. % 15.36/15.51 apply (zenon_L29_); trivial. % 15.36/15.51 apply (zenon_or_s _ _ zenon_H11c); [ zenon_intro zenon_H117 | zenon_intro zenon_H11d ]. % 15.36/15.51 apply (zenon_L248_); trivial. % 15.36/15.51 apply (zenon_or_s _ _ zenon_H11d); [ zenon_intro zenon_H2a | zenon_intro zenon_H119 ]. % 15.36/15.51 exact (zenon_H52 zenon_H2a). % 15.36/15.51 apply (zenon_L760_); trivial. % 15.36/15.51 (* end of lemma zenon_L761_ *) % 15.36/15.51 assert (zenon_L762_ : (((op (e0) (e0)) = (e2))\/(((op (e0) (e1)) = (e2))\/(((op (e0) (e2)) = (e2))\/((op (e0) (e3)) = (e2))))) -> (((op (e1) (e1)) = (e0))\/(((op (e1) (e1)) = (e1))\/(((op (e1) (e1)) = (e2))\/((op (e1) (e1)) = (e3))))) -> (~((op (e1) (e1)) = (e1))) -> (~((op (e1) (e1)) = (e2))) -> (~((op (e1) (e1)) = (e3))) -> (((op (e1) (e0)) = (e3))\/(((op (e1) (e1)) = (e3))\/(((op (e1) (e2)) = (e3))\/((op (e1) (e3)) = (e3))))) -> (((op (e1) (e0)) = (e2))\/(((op (e1) (e1)) = (e2))\/(((op (e1) (e2)) = (e2))\/((op (e1) (e3)) = (e2))))) -> (~((e1) = (e3))) -> (((op (e0) (e2)) = (e1))\/(((op (e1) (e2)) = (e1))\/(((op (e2) (e2)) = (e1))\/((op (e3) (e2)) = (e1))))) -> ((op (e1) (e0)) = (e1)) -> (~((op (e1) (e0)) = (op (e1) (e2)))) -> (~((op (e2) (e2)) = (e1))) -> (((op (e1) (e2)) = (e0))\/(((op (e1) (e2)) = (e1))\/(((op (e1) (e2)) = (e2))\/((op (e1) (e2)) = (e3))))) -> ((op (e0) (e2)) = (e0)) -> (~((op (e1) (e2)) = (op (e3) (e2)))) -> (~((op (e1) (e2)) = (op (e2) (e2)))) -> (~((op (e0) (e2)) = (op (e1) (e2)))) -> (~((e2) = (e3))) -> (~((op (e0) (e0)) = (e3))) -> (((op (e0) (e0)) = (e3))\/(((op (e0) (e1)) = (e3))\/(((op (e0) (e2)) = (e3))\/((op (e0) (e3)) = (e3))))) -> (~((op (e0) (e2)) = (op (e2) (e2)))) -> ((op (e2) (e2)) = (e2)) -> ((op (e0) (e3)) = (e1)) -> (~((e1) = (e2))) -> False). % 15.36/15.51 do 0 intro. intros zenon_H8e zenon_H1b3 zenon_H1b4 zenon_Hd6 zenon_H182 zenon_H90 zenon_H84 zenon_Ha3 zenon_H11b zenon_Hd8 zenon_H166 zenon_H52 zenon_H1d5 zenon_Hab zenon_H17d zenon_H7d zenon_H87 zenon_H6a zenon_H59 zenon_H58 zenon_H28 zenon_H35 zenon_H37 zenon_Ha7. % 15.36/15.51 apply (zenon_or_s _ _ zenon_H8e); [ zenon_intro zenon_H92 | zenon_intro zenon_H91 ]. % 15.36/15.51 apply (zenon_L509_); trivial. % 15.36/15.51 apply (zenon_or_s _ _ zenon_H91); [ zenon_intro zenon_H5d | zenon_intro zenon_H93 ]. % 15.36/15.51 apply (zenon_or_s _ _ zenon_H58); [ zenon_intro zenon_H5b | zenon_intro zenon_H5a ]. % 15.36/15.51 exact (zenon_H59 zenon_H5b). % 15.36/15.51 apply (zenon_or_s _ _ zenon_H5a); [ zenon_intro zenon_H4a | zenon_intro zenon_H5c ]. % 15.36/15.51 apply (zenon_L50_); trivial. % 15.36/15.51 apply (zenon_or_s _ _ zenon_H5c); [ zenon_intro zenon_H50 | zenon_intro zenon_H53 ]. % 15.36/15.51 apply (zenon_L761_); trivial. % 15.36/15.51 apply (zenon_L32_); trivial. % 15.36/15.51 apply (zenon_or_s _ _ zenon_H93); [ zenon_intro zenon_H63 | zenon_intro zenon_H81 ]. % 15.36/15.51 apply (zenon_L15_); trivial. % 15.36/15.51 apply (zenon_L33_); trivial. % 15.36/15.51 (* end of lemma zenon_L762_ *) % 15.36/15.51 assert (zenon_L763_ : (((op (e0) (e3)) = (e1))\/(((op (e1) (e3)) = (e1))\/(((op (e2) (e3)) = (e1))\/((op (e3) (e3)) = (e1))))) -> (~((op (e3) (e3)) = (e3))) -> (~((op (e3) (e3)) = (e2))) -> (~((op (e0) (e3)) = (op (e3) (e3)))) -> (~((op (e3) (e3)) = (e0))) -> (((op (e3) (e3)) = (e0))\/(((op (e3) (e3)) = (e1))\/(((op (e3) (e3)) = (e2))\/((op (e3) (e3)) = (e3))))) -> ((op (e1) (e2)) = (e1)) -> (~((op (e1) (e2)) = (op (e1) (e3)))) -> ((op (e2) (e0)) = (e1)) -> (~((op (e2) (e0)) = (op (e2) (e3)))) -> (~((op (e3) (e3)) = (e1))) -> False). % 15.36/15.51 do 0 intro. intros zenon_H121 zenon_H3e zenon_H3d zenon_H36 zenon_H3c zenon_H3b zenon_H117 zenon_H1d0 zenon_Hae zenon_Hce zenon_H104. % 15.36/15.51 apply (zenon_or_s _ _ zenon_H121); [ zenon_intro zenon_H37 | zenon_intro zenon_H122 ]. % 15.36/15.51 apply (zenon_L7_); trivial. % 15.36/15.51 apply (zenon_or_s _ _ zenon_H122); [ zenon_intro zenon_H11f | zenon_intro zenon_H123 ]. % 15.36/15.51 apply (zenon_L237_); trivial. % 15.36/15.51 apply (zenon_or_s _ _ zenon_H123); [ zenon_intro zenon_Hb5 | zenon_intro zenon_H38 ]. % 15.36/15.51 apply (zenon_L91_); trivial. % 15.36/15.51 exact (zenon_H104 zenon_H38). % 15.36/15.51 (* end of lemma zenon_L763_ *) % 15.36/15.51 assert (zenon_L764_ : (((op (e0) (e0)) = (e1))\/(((op (e1) (e0)) = (e1))\/(((op (e2) (e0)) = (e1))\/((op (e3) (e0)) = (e1))))) -> (~((op (e0) (e0)) = (e1))) -> ((op (e1) (e2)) = (e1)) -> (~((op (e1) (e0)) = (op (e1) (e2)))) -> (~((e0) = (e1))) -> ((op (e2) (e0)) = (e0)) -> (~((e1) = (e3))) -> ((op (e3) (e0)) = (e3)) -> False). % 15.36/15.51 do 0 intro. intros zenon_Hf1 zenon_H45 zenon_H117 zenon_H166 zenon_H9e zenon_Hcf zenon_Ha3 zenon_Hba. % 15.36/15.51 apply (zenon_or_s _ _ zenon_Hf1); [ zenon_intro zenon_H47 | zenon_intro zenon_Hf4 ]. % 15.36/15.51 exact (zenon_H45 zenon_H47). % 15.36/15.51 apply (zenon_or_s _ _ zenon_Hf4); [ zenon_intro zenon_Hd8 | zenon_intro zenon_Hf5 ]. % 15.36/15.51 apply (zenon_L248_); trivial. % 15.36/15.51 apply (zenon_or_s _ _ zenon_Hf5); [ zenon_intro zenon_Hae | zenon_intro zenon_Hee ]. % 15.36/15.51 apply (zenon_L269_); trivial. % 15.36/15.51 apply (zenon_L79_); trivial. % 15.36/15.51 (* end of lemma zenon_L764_ *) % 15.36/15.51 assert (zenon_L765_ : (((op (e0) (e0)) = (e3))\/(((op (e1) (e0)) = (e3))\/(((op (e2) (e0)) = (e3))\/((op (e3) (e0)) = (e3))))) -> (~((op (e0) (e0)) = (e3))) -> ((op (e0) (e3)) = (e3)) -> (~((op (e0) (op (e1) (e0))) = (op (e1) (e0)))) -> (~((e0) = (e3))) -> ((op (e2) (e0)) = (e0)) -> (~((op (e3) (e0)) = (op (e3) (e2)))) -> ((op (e3) (e2)) = (e3)) -> False). % 15.36/15.52 do 0 intro. intros zenon_Hbe zenon_H59 zenon_H53 zenon_H261 zenon_H4b zenon_Hcf zenon_H105 zenon_H106. % 15.36/15.52 apply (zenon_or_s _ _ zenon_Hbe); [ zenon_intro zenon_H5b | zenon_intro zenon_Hbf ]. % 15.36/15.52 exact (zenon_H59 zenon_H5b). % 15.36/15.52 apply (zenon_or_s _ _ zenon_Hbf); [ zenon_intro zenon_H69 | zenon_intro zenon_Hc0 ]. % 15.36/15.52 apply (zenon_L647_); trivial. % 15.36/15.52 apply (zenon_or_s _ _ zenon_Hc0); [ zenon_intro zenon_Haf | zenon_intro zenon_Hba ]. % 15.36/15.52 apply (zenon_L57_); trivial. % 15.36/15.52 apply (zenon_L81_); trivial. % 15.36/15.52 (* end of lemma zenon_L765_ *) % 15.36/15.52 assert (zenon_L766_ : (~((op (e0) (e2)) = (op (e3) (e2)))) -> (~((op (e3) (e0)) = (op (e3) (e2)))) -> (~((op (e2) (e2)) = (e3))) -> (((op (e0) (e0)) = (e0))\/(((op (e1) (e0)) = (e0))\/(((op (e2) (e0)) = (e0))\/((op (e3) (e0)) = (e0))))) -> (~((op (e1) (e0)) = (op (e3) (e0)))) -> (~((op (e1) (e1)) = (e0))) -> (~((op (e3) (op (e1) (e3))) = (op (e1) (e3)))) -> (((op (e1) (e0)) = (e0))\/(((op (e1) (e1)) = (e0))\/(((op (e1) (e2)) = (e0))\/((op (e1) (e3)) = (e0))))) -> (~((op (e0) (op (e1) (e0))) = (op (e1) (e0)))) -> (~((op (e0) (e0)) = (e1))) -> ((~((op (e1) (e1)) = (e1)))\/((op (e1) (e1)) = (e1))) -> (~((op (e1) (e0)) = (op (e1) (e1)))) -> ((~((op (e1) (e1)) = (e3)))\/((op (e1) (e3)) = (e1))) -> ((~((op (e3) (e3)) = (e2)))\/((op (e3) (e2)) = (e3))) -> (~((op (e1) (e2)) = (op (e3) (e2)))) -> (((op (e0) (e0)) = (e2))\/(((op (e1) (e0)) = (e2))\/(((op (e2) (e0)) = (e2))\/((op (e3) (e0)) = (e2))))) -> (((op (e3) (e3)) = (e0))\/(((op (e3) (e3)) = (e1))\/(((op (e3) (e3)) = (e2))\/((op (e3) (e3)) = (e3))))) -> (~((op (e2) (e0)) = (op (e2) (e2)))) -> (~((e1) = (e2))) -> (~((op (e1) (e2)) = (op (e2) (e2)))) -> ((op (e2) (e2)) = (e2)) -> (((op (e1) (e0)) = (e3))\/(((op (e1) (e1)) = (e3))\/(((op (e1) (e2)) = (e3))\/((op (e1) (e3)) = (e3))))) -> (~((e2) = (e3))) -> (((op (e1) (e1)) = (e0))\/(((op (e1) (e1)) = (e1))\/(((op (e1) (e1)) = (e2))\/((op (e1) (e1)) = (e3))))) -> (~((e1) = (e3))) -> (((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 (e2) (e2)) = (e3)))\/((op (e2) (e3)) = (e2))) -> ((~((op (e3) (e3)) = (e1)))\/((op (e3) (e1)) = (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) (e0)) = (op (e1) (e3)))) -> (~((op (e0) (e1)) = (op (e0) (e3)))) -> (~((e0) = (e1))) -> ((op (e0) (e2)) = (e0)) -> (((op (e0) (e0)) = (e2))\/(((op (e0) (e1)) = (e2))\/(((op (e0) (e2)) = (e2))\/((op (e0) (e3)) = (e2))))) -> (((op (e0) (e3)) = (e0))\/(((op (e1) (e3)) = (e0))\/(((op (e2) (e3)) = (e0))\/((op (e3) (e3)) = (e0))))) -> (~((e0) = (e2))) -> (~((op (e0) (e2)) = (op (e0) (e3)))) -> (~((op (e0) (e2)) = (op (e1) (e2)))) -> (~((op (e0) (e3)) = (op (e3) (e3)))) -> (((op (e0) (e0)) = (e3))\/(((op (e0) (e1)) = (e3))\/(((op (e0) (e2)) = (e3))\/((op (e0) (e3)) = (e3))))) -> (~((op (e1) (e3)) = (op (e3) (e3)))) -> (((op (e0) (e0)) = (e1))\/(((op (e0) (e1)) = (e1))\/(((op (e0) (e2)) = (e1))\/((op (e0) (e3)) = (e1))))) -> ((~((op (e3) (e3)) = (e0)))\/((op (e3) (e0)) = (e3))) -> (~((op (e0) (e0)) = (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) (e0)) = (e3))\/(((op (e1) (e0)) = (e3))\/(((op (e2) (e0)) = (e3))\/((op (e3) (e0)) = (e3))))) -> (~((op (e0) (e2)) = (op (e2) (e2)))) -> (~((op (e0) (e3)) = (op (e1) (e3)))) -> ((~((op (e2) (e2)) = (e2)))\/((op (e2) (e2)) = (e2))) -> ((~((op (e3) (e3)) = (e3)))\/((op (e3) (e3)) = (e3))) -> (~((op (e1) (e0)) = (op (e1) (e2)))) -> ((~((op (e1) (e1)) = (e2)))\/((op (e1) (e2)) = (e1))) -> (~((op (e2) (e0)) = (op (e2) (e3)))) -> ((op (e1) (e2)) = (e1)) -> (~((op (e1) (e2)) = (op (e1) (e3)))) -> (~((op (e1) (e1)) = (e3))) -> (~((e0) = (e3))) -> (~((op (e1) (e1)) = (e1))) -> (~((op (e2) (op (e1) (e2))) = (op (e1) (e2)))) -> (~((op (e3) (e0)) = (op (e3) (e1)))) -> (((op (e0) (e1)) = (e1))\/(((op (e1) (e1)) = (e1))\/(((op (e2) (e1)) = (e1))\/((op (e3) (e1)) = (e1))))) -> (((op (e0) (e0)) = (e1))\/(((op (e1) (e0)) = (e1))\/(((op (e2) (e0)) = (e1))\/((op (e3) (e0)) = (e1))))) -> (~((op (e0) (e0)) = (e0))) -> (~((op (e1) (op (e1) (e1))) = (op (e1) (e1)))) -> (((op (e1) (e0)) = (e1))\/(((op (e1) (e1)) = (e1))\/(((op (e1) (e2)) = (e1))\/((op (e1) (e3)) = (e1))))) -> (((op (e0) (e3)) = (e2))\/(((op (e1) (e3)) = (e2))\/(((op (e2) (e3)) = (e2))\/((op (e3) (e3)) = (e2))))) -> (((op (e0) (e2)) = (e3))\/(((op (e1) (e2)) = (e3))\/(((op (e2) (e2)) = (e3))\/((op (e3) (e2)) = (e3))))) -> (~((op (e3) (e2)) = (op (e3) (e3)))) -> (~((op (e0) (e1)) = (op (e1) (e1)))) -> (((op (e2) (e0)) = (e3))\/(((op (e2) (e1)) = (e3))\/(((op (e2) (e2)) = (e3))\/((op (e2) (e3)) = (e3))))) -> (~((op (e2) (e3)) = (op (e3) (e3)))) -> (~((op (e0) (e1)) = (op (e2) (e1)))) -> (((op (e0) (e1)) = (e2))\/(((op (e1) (e1)) = (e2))\/(((op (e2) (e1)) = (e2))\/((op (e3) (e1)) = (e2))))) -> (((op (e0) (e2)) = (e0))\/(((op (e1) (e2)) = (e0))\/(((op (e2) (e2)) = (e0))\/((op (e3) (e2)) = (e0))))) -> (~((op (e2) (e2)) = (e0))) -> (~((op (e3) (e1)) = (op (e3) (e2)))) -> (((op (e0) (e1)) = (e0))\/(((op (e1) (e1)) = (e0))\/(((op (e2) (e1)) = (e0))\/((op (e3) (e1)) = (e0))))) -> False). % 15.36/15.52 do 0 intro. intros zenon_H140 zenon_H105 zenon_H30 zenon_Hf0 zenon_H22e zenon_H145 zenon_H26e zenon_H163 zenon_H261 zenon_H45 zenon_H1d8 zenon_Hd7 zenon_H1d2 zenon_H10e zenon_H17d zenon_Heb zenon_H3b zenon_H17a zenon_Ha7 zenon_H7d zenon_H35 zenon_H90 zenon_H6a zenon_H1b3 zenon_Ha3 zenon_H84 zenon_H1d4 zenon_H1c3 zenon_H10c zenon_H12d zenon_H121 zenon_H1cf zenon_H1cd zenon_H9e zenon_Hab zenon_H8e zenon_Hd3 zenon_H5e zenon_Hc9 zenon_H87 zenon_H36 zenon_H58 zenon_H8b zenon_H44 zenon_H10f zenon_H59 zenon_H2d zenon_Hbb zenon_Hbe zenon_H28 zenon_H80 zenon_Haa zenon_H10d zenon_H166 zenon_H1d3 zenon_Hce zenon_H117 zenon_H1d0 zenon_H182 zenon_H4b zenon_H1b4 zenon_H277 zenon_H109 zenon_H228 zenon_Hf1 zenon_H20 zenon_H27b zenon_H1c5 zenon_H160 zenon_H175 zenon_H173 zenon_H23 zenon_He6 zenon_He3 zenon_Hde zenon_H1a2 zenon_H16f zenon_H2e zenon_H135 zenon_H144. % 15.36/15.52 apply (zenon_or_s _ _ zenon_H10f); [ zenon_intro zenon_H3c | zenon_intro zenon_Hba ]. % 15.36/15.52 apply (zenon_or_s _ _ zenon_H10c); [ zenon_intro zenon_H104 | zenon_intro zenon_H10a ]. % 15.36/15.52 apply (zenon_or_s _ _ zenon_H10e); [ zenon_intro zenon_H3d | zenon_intro zenon_H106 ]. % 15.36/15.52 apply (zenon_or_s _ _ zenon_H10d); [ zenon_intro zenon_H3e | zenon_intro zenon_H42 ]. % 15.36/15.52 apply (zenon_or_s _ _ zenon_Hf0); [ zenon_intro zenon_H1f | zenon_intro zenon_Hf2 ]. % 15.36/15.52 exact (zenon_H20 zenon_H1f). % 15.36/15.52 apply (zenon_or_s _ _ zenon_Hf2); [ zenon_intro zenon_Had | zenon_intro zenon_Hf3 ]. % 15.36/15.52 apply (zenon_or_s _ _ zenon_Hf1); [ zenon_intro zenon_H47 | zenon_intro zenon_Hf4 ]. % 15.36/15.52 exact (zenon_H45 zenon_H47). % 15.36/15.52 apply (zenon_or_s _ _ zenon_Hf4); [ zenon_intro zenon_Hd8 | zenon_intro zenon_Hf5 ]. % 15.36/15.52 apply (zenon_L553_); trivial. % 15.36/15.52 apply (zenon_or_s _ _ zenon_Hf5); [ zenon_intro zenon_Hae | zenon_intro zenon_Hee ]. % 15.36/15.52 apply (zenon_L763_); trivial. % 15.36/15.52 apply (zenon_or_s _ _ zenon_H58); [ zenon_intro zenon_H5b | zenon_intro zenon_H5a ]. % 15.36/15.52 exact (zenon_H59 zenon_H5b). % 15.36/15.52 apply (zenon_or_s _ _ zenon_H5a); [ zenon_intro zenon_H4a | zenon_intro zenon_H5c ]. % 15.36/15.52 apply (zenon_L743_); trivial. % 15.36/15.52 apply (zenon_or_s _ _ zenon_H5c); [ zenon_intro zenon_H50 | zenon_intro zenon_H53 ]. % 15.36/15.52 apply (zenon_L48_); trivial. % 15.36/15.52 apply (zenon_L521_); trivial. % 15.36/15.52 apply (zenon_or_s _ _ zenon_Hf3); [ zenon_intro zenon_Hcf | zenon_intro zenon_Hdb ]. % 15.36/15.52 apply (zenon_or_s _ _ zenon_Hf1); [ zenon_intro zenon_H47 | zenon_intro zenon_Hf4 ]. % 15.36/15.52 exact (zenon_H45 zenon_H47). % 15.36/15.52 apply (zenon_or_s _ _ zenon_Hf4); [ zenon_intro zenon_Hd8 | zenon_intro zenon_Hf5 ]. % 15.36/15.52 apply (zenon_L248_); trivial. % 15.36/15.52 apply (zenon_or_s _ _ zenon_Hf5); [ zenon_intro zenon_Hae | zenon_intro zenon_Hee ]. % 15.36/15.52 apply (zenon_L269_); trivial. % 15.36/15.52 apply (zenon_or_s _ _ zenon_H58); [ zenon_intro zenon_H5b | zenon_intro zenon_H5a ]. % 15.36/15.52 exact (zenon_H59 zenon_H5b). % 15.36/15.52 apply (zenon_or_s _ _ zenon_H5a); [ zenon_intro zenon_H4a | zenon_intro zenon_H5c ]. % 15.36/15.52 apply (zenon_L743_); trivial. % 15.36/15.52 apply (zenon_or_s _ _ zenon_H5c); [ zenon_intro zenon_H50 | zenon_intro zenon_H53 ]. % 15.36/15.52 apply (zenon_L48_); trivial. % 15.36/15.52 apply (zenon_or_s _ _ zenon_Hbe); [ zenon_intro zenon_H5b | zenon_intro zenon_Hbf ]. % 15.36/15.52 exact (zenon_H59 zenon_H5b). % 15.36/15.52 apply (zenon_or_s _ _ zenon_Hbf); [ zenon_intro zenon_H69 | zenon_intro zenon_Hc0 ]. % 15.36/15.52 apply (zenon_L647_); trivial. % 15.36/15.52 apply (zenon_or_s _ _ zenon_Hc0); [ zenon_intro zenon_Haf | zenon_intro zenon_Hba ]. % 15.36/15.52 apply (zenon_L57_); trivial. % 15.36/15.52 apply (zenon_L764_); trivial. % 15.36/15.52 apply (zenon_L758_); trivial. % 15.36/15.52 apply (zenon_L699_); trivial. % 15.36/15.52 apply (zenon_or_s _ _ zenon_Hf0); [ zenon_intro zenon_H1f | zenon_intro zenon_Hf2 ]. % 15.36/15.52 exact (zenon_H20 zenon_H1f). % 15.36/15.52 apply (zenon_or_s _ _ zenon_Hf2); [ zenon_intro zenon_Had | zenon_intro zenon_Hf3 ]. % 15.36/15.52 apply (zenon_or_s _ _ zenon_Hf1); [ zenon_intro zenon_H47 | zenon_intro zenon_Hf4 ]. % 15.36/15.52 exact (zenon_H45 zenon_H47). % 15.36/15.52 apply (zenon_or_s _ _ zenon_Hf4); [ zenon_intro zenon_Hd8 | zenon_intro zenon_Hf5 ]. % 15.36/15.52 apply (zenon_L553_); trivial. % 15.36/15.52 apply (zenon_or_s _ _ zenon_Hf5); [ zenon_intro zenon_Hae | zenon_intro zenon_Hee ]. % 15.36/15.52 apply (zenon_L541_); trivial. % 15.36/15.52 apply (zenon_or_s _ _ zenon_H58); [ zenon_intro zenon_H5b | zenon_intro zenon_H5a ]. % 15.36/15.52 exact (zenon_H59 zenon_H5b). % 15.36/15.52 apply (zenon_or_s _ _ zenon_H5a); [ zenon_intro zenon_H4a | zenon_intro zenon_H5c ]. % 15.36/15.52 apply (zenon_L743_); trivial. % 15.36/15.52 apply (zenon_or_s _ _ zenon_H5c); [ zenon_intro zenon_H50 | zenon_intro zenon_H53 ]. % 15.36/15.52 apply (zenon_L533_); trivial. % 15.36/15.52 apply (zenon_L521_); trivial. % 15.36/15.52 apply (zenon_or_s _ _ zenon_Hf3); [ zenon_intro zenon_Hcf | zenon_intro zenon_Hdb ]. % 15.36/15.52 apply (zenon_or_s _ _ zenon_Hf1); [ zenon_intro zenon_H47 | zenon_intro zenon_Hf4 ]. % 15.36/15.52 exact (zenon_H45 zenon_H47). % 15.36/15.52 apply (zenon_or_s _ _ zenon_Hf4); [ zenon_intro zenon_Hd8 | zenon_intro zenon_Hf5 ]. % 15.36/15.52 apply (zenon_L553_); trivial. % 15.36/15.52 apply (zenon_or_s _ _ zenon_Hf5); [ zenon_intro zenon_Hae | zenon_intro zenon_Hee ]. % 15.36/15.52 apply (zenon_L269_); trivial. % 15.36/15.52 apply (zenon_or_s _ _ zenon_H58); [ zenon_intro zenon_H5b | zenon_intro zenon_H5a ]. % 15.36/15.52 exact (zenon_H59 zenon_H5b). % 15.36/15.52 apply (zenon_or_s _ _ zenon_H5a); [ zenon_intro zenon_H4a | zenon_intro zenon_H5c ]. % 15.36/15.52 apply (zenon_L743_); trivial. % 15.36/15.52 apply (zenon_or_s _ _ zenon_H5c); [ zenon_intro zenon_H50 | zenon_intro zenon_H53 ]. % 15.36/15.52 apply (zenon_L533_); trivial. % 15.36/15.52 apply (zenon_L765_); trivial. % 15.36/15.52 apply (zenon_L758_); trivial. % 15.36/15.52 apply (zenon_L502_); trivial. % 15.36/15.52 apply (zenon_L507_); trivial. % 15.36/15.52 (* end of lemma zenon_L766_ *) % 15.36/15.52 assert (zenon_L767_ : ((op (e0) (e0)) = (e2)) -> (((op (e0) (e1)) = (e0))\/(((op (e1) (e1)) = (e0))\/(((op (e2) (e1)) = (e0))\/((op (e3) (e1)) = (e0))))) -> (~((op (e3) (e1)) = (op (e3) (e2)))) -> (~((op (e2) (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 (e0) (e1)) = (op (e2) (e1)))) -> (~((op (e2) (e3)) = (op (e3) (e3)))) -> (((op (e2) (e0)) = (e3))\/(((op (e2) (e1)) = (e3))\/(((op (e2) (e2)) = (e3))\/((op (e2) (e3)) = (e3))))) -> (~((op (e0) (e1)) = (op (e1) (e1)))) -> (((op (e0) (e2)) = (e3))\/(((op (e1) (e2)) = (e3))\/(((op (e2) (e2)) = (e3))\/((op (e3) (e2)) = (e3))))) -> (((op (e1) (e0)) = (e1))\/(((op (e1) (e1)) = (e1))\/(((op (e1) (e2)) = (e1))\/((op (e1) (e3)) = (e1))))) -> (~((op (e1) (op (e1) (e1))) = (op (e1) (e1)))) -> (~((op (e0) (e0)) = (e0))) -> (((op (e0) (e0)) = (e1))\/(((op (e1) (e0)) = (e1))\/(((op (e2) (e0)) = (e1))\/((op (e3) (e0)) = (e1))))) -> (((op (e0) (e1)) = (e1))\/(((op (e1) (e1)) = (e1))\/(((op (e2) (e1)) = (e1))\/((op (e3) (e1)) = (e1))))) -> (~((op (e2) (op (e1) (e2))) = (op (e1) (e2)))) -> (~((op (e1) (e1)) = (e3))) -> (~((op (e1) (e2)) = (op (e1) (e3)))) -> (~((op (e2) (e0)) = (op (e2) (e3)))) -> ((~((op (e1) (e1)) = (e2)))\/((op (e1) (e2)) = (e1))) -> (~((op (e1) (e0)) = (op (e1) (e2)))) -> ((~((op (e2) (e2)) = (e2)))\/((op (e2) (e2)) = (e2))) -> (~((op (e0) (e3)) = (op (e1) (e3)))) -> (~((op (e0) (e2)) = (op (e2) (e2)))) -> (((op (e2) (e2)) = (e0))\/(((op (e2) (e2)) = (e1))\/(((op (e2) (e2)) = (e2))\/((op (e2) (e2)) = (e3))))) -> (~((op (e1) (e3)) = (op (e3) (e3)))) -> (~((op (e0) (e2)) = (op (e1) (e2)))) -> (~((op (e0) (e2)) = (op (e0) (e3)))) -> (((op (e0) (e0)) = (e2))\/(((op (e0) (e1)) = (e2))\/(((op (e0) (e2)) = (e2))\/((op (e0) (e3)) = (e2))))) -> (~((op (e0) (e1)) = (op (e0) (e3)))) -> (~((op (e1) (e0)) = (op (e1) (e3)))) -> (((op (e0) (e3)) = (e1))\/(((op (e1) (e3)) = (e1))\/(((op (e2) (e3)) = (e1))\/((op (e3) (e3)) = (e1))))) -> (~((op (e3) (e1)) = (op (e3) (e3)))) -> ((~((op (e2) (e2)) = (e3)))\/((op (e2) (e3)) = (e2))) -> ((~((op (e2) (e2)) = (e0)))\/((op (e2) (e0)) = (e2))) -> (((op (e1) (e0)) = (e3))\/(((op (e1) (e1)) = (e3))\/(((op (e1) (e2)) = (e3))\/((op (e1) (e3)) = (e3))))) -> (~((op (e2) (e0)) = (op (e2) (e2)))) -> (((op (e0) (e0)) = (e2))\/(((op (e1) (e0)) = (e2))\/(((op (e2) (e0)) = (e2))\/((op (e3) (e0)) = (e2))))) -> (~((op (e1) (e2)) = (op (e3) (e2)))) -> ((~((op (e1) (e1)) = (e3)))\/((op (e1) (e3)) = (e1))) -> (~((op (e1) (e0)) = (op (e1) (e1)))) -> ((~((op (e1) (e1)) = (e1)))\/((op (e1) (e1)) = (e1))) -> (~((op (e0) (op (e1) (e0))) = (op (e1) (e0)))) -> (((op (e1) (e0)) = (e0))\/(((op (e1) (e1)) = (e0))\/(((op (e1) (e2)) = (e0))\/((op (e1) (e3)) = (e0))))) -> (~((op (e3) (op (e1) (e3))) = (op (e1) (e3)))) -> (~((op (e1) (e0)) = (op (e3) (e0)))) -> (((op (e0) (e0)) = (e0))\/(((op (e1) (e0)) = (e0))\/(((op (e2) (e0)) = (e0))\/((op (e3) (e0)) = (e0))))) -> (~((op (e2) (e2)) = (e3))) -> (~((op (e0) (e2)) = (op (e3) (e2)))) -> (((op (e0) (e0)) = (e3))\/(((op (e1) (e0)) = (e3))\/(((op (e2) (e0)) = (e3))\/((op (e3) (e0)) = (e3))))) -> (~((e2) = (e3))) -> ((op (e2) (e0)) = (e1)) -> ((~((op (e3) (e3)) = (e1)))\/((op (e3) (e1)) = (e3))) -> (~((op (e3) (e0)) = (op (e3) (e1)))) -> ((~((op (e3) (e3)) = (e3)))\/((op (e3) (e3)) = (e3))) -> ((~((op (e3) (e3)) = (e2)))\/((op (e3) (e2)) = (e3))) -> (~((op (e3) (e2)) = (op (e3) (e3)))) -> (~((op (e0) (e0)) = (e1))) -> (((op (e0) (e0)) = (e3))\/(((op (e0) (e1)) = (e3))\/(((op (e0) (e2)) = (e3))\/((op (e0) (e3)) = (e3))))) -> (~((op (e0) (e3)) = (op (e3) (e3)))) -> ((op (e0) (e2)) = (e0)) -> (~((e0) = (e3))) -> (~((e1) = (e3))) -> (~((op (e0) (e0)) = (e3))) -> (~((e0) = (e1))) -> (((op (e0) (e3)) = (e0))\/(((op (e1) (e3)) = (e0))\/(((op (e2) (e3)) = (e0))\/((op (e3) (e3)) = (e0))))) -> (~((e0) = (e2))) -> (((op (e0) (e3)) = (e2))\/(((op (e1) (e3)) = (e2))\/(((op (e2) (e3)) = (e2))\/((op (e3) (e3)) = (e2))))) -> (((op (e0) (e0)) = (e1))\/(((op (e0) (e1)) = (e1))\/(((op (e0) (e2)) = (e1))\/((op (e0) (e3)) = (e1))))) -> (~((op (e3) (e0)) = (op (e3) (e3)))) -> ((~((op (e3) (e3)) = (e0)))\/((op (e3) (e0)) = (e3))) -> (((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 (e1) (e1)) = (e2))) -> (~((op (e1) (e1)) = (e1))) -> (~((op (e1) (e1)) = (e0))) -> (~((op (e1) (e2)) = (op (e2) (e2)))) -> ((op (e2) (e2)) = (e2)) -> (~((e1) = (e2))) -> (((op (e1) (e0)) = (e2))\/(((op (e1) (e1)) = (e2))\/(((op (e1) (e2)) = (e2))\/((op (e1) (e3)) = (e2))))) -> (~((op (e3) (e0)) = (op (e3) (e2)))) -> False). % 15.36/15.52 do 0 intro. intros zenon_H92 zenon_H144 zenon_H135 zenon_H2e zenon_H16f zenon_H1a2 zenon_Hde zenon_He3 zenon_He6 zenon_H23 zenon_H175 zenon_H1c5 zenon_H27b zenon_H20 zenon_Hf1 zenon_H228 zenon_H277 zenon_H182 zenon_H1d0 zenon_Hce zenon_H1d3 zenon_H166 zenon_Haa zenon_H80 zenon_H28 zenon_H2d zenon_H8b zenon_H87 zenon_Hc9 zenon_H8e zenon_H1cd zenon_H1cf zenon_H121 zenon_H12d zenon_H1c3 zenon_H1d4 zenon_H90 zenon_H17a zenon_Heb zenon_H17d zenon_H1d2 zenon_Hd7 zenon_H1d8 zenon_H261 zenon_H163 zenon_H26e zenon_H22e zenon_Hf0 zenon_H30 zenon_H140 zenon_Hbe zenon_H6a zenon_Hae zenon_H10c zenon_H109 zenon_H10d zenon_H10e zenon_H173 zenon_H45 zenon_H58 zenon_H36 zenon_Hab zenon_H4b zenon_Ha3 zenon_H59 zenon_H9e zenon_Hd3 zenon_H5e zenon_H160 zenon_H44 zenon_Hbb zenon_H10f zenon_H1b3 zenon_H3b zenon_Hd6 zenon_H1b4 zenon_H145 zenon_H7d zenon_H35 zenon_Ha7 zenon_H84 zenon_H105. % 15.36/15.52 apply (zenon_or_s _ _ zenon_H1c5); [ zenon_intro zenon_Hd8 | zenon_intro zenon_H1c6 ]. % 15.36/15.52 apply (zenon_L509_); trivial. % 15.36/15.52 apply (zenon_or_s _ _ zenon_H1c6); [ zenon_intro zenon_H21 | zenon_intro zenon_H1c7 ]. % 15.36/15.52 exact (zenon_H1b4 zenon_H21). % 15.36/15.52 apply (zenon_or_s _ _ zenon_H1c7); [ zenon_intro zenon_H117 | zenon_intro zenon_H11f ]. % 15.36/15.52 apply (zenon_L766_); trivial. % 15.36/15.52 apply (zenon_L544_); trivial. % 15.36/15.52 (* end of lemma zenon_L767_ *) % 15.36/15.52 assert (zenon_L768_ : (~((op (e3) (e0)) = (op (e3) (e2)))) -> (((op (e1) (e0)) = (e2))\/(((op (e1) (e1)) = (e2))\/(((op (e1) (e2)) = (e2))\/((op (e1) (e3)) = (e2))))) -> (~((op (e1) (e2)) = (op (e2) (e2)))) -> (~((op (e1) (e1)) = (e2))) -> (((op (e3) (e3)) = (e0))\/(((op (e3) (e3)) = (e1))\/(((op (e3) (e3)) = (e2))\/((op (e3) (e3)) = (e3))))) -> ((~((op (e3) (e3)) = (e0)))\/((op (e3) (e0)) = (e3))) -> (~((op (e3) (e0)) = (op (e3) (e3)))) -> (((op (e0) (e0)) = (e1))\/(((op (e0) (e1)) = (e1))\/(((op (e0) (e2)) = (e1))\/((op (e0) (e3)) = (e1))))) -> (((op (e0) (e3)) = (e2))\/(((op (e1) (e3)) = (e2))\/(((op (e2) (e3)) = (e2))\/((op (e3) (e3)) = (e2))))) -> (~((e0) = (e2))) -> (((op (e0) (e3)) = (e0))\/(((op (e1) (e3)) = (e0))\/(((op (e2) (e3)) = (e0))\/((op (e3) (e3)) = (e0))))) -> (~((e0) = (e1))) -> (~((op (e0) (e0)) = (e3))) -> (~((e1) = (e3))) -> (~((e0) = (e3))) -> ((op (e0) (e2)) = (e0)) -> (~((op (e0) (e3)) = (op (e3) (e3)))) -> (((op (e0) (e0)) = (e3))\/(((op (e0) (e1)) = (e3))\/(((op (e0) (e2)) = (e3))\/((op (e0) (e3)) = (e3))))) -> (~((op (e0) (e0)) = (e1))) -> (~((op (e3) (e2)) = (op (e3) (e3)))) -> ((~((op (e3) (e3)) = (e2)))\/((op (e3) (e2)) = (e3))) -> ((~((op (e3) (e3)) = (e3)))\/((op (e3) (e3)) = (e3))) -> (~((op (e3) (e0)) = (op (e3) (e1)))) -> ((~((op (e3) (e3)) = (e1)))\/((op (e3) (e1)) = (e3))) -> ((op (e2) (e0)) = (e1)) -> (~((e2) = (e3))) -> (((op (e0) (e0)) = (e3))\/(((op (e1) (e0)) = (e3))\/(((op (e2) (e0)) = (e3))\/((op (e3) (e0)) = (e3))))) -> (~((op (e0) (e2)) = (op (e3) (e2)))) -> (~((op (e2) (e2)) = (e3))) -> (((op (e0) (e0)) = (e0))\/(((op (e1) (e0)) = (e0))\/(((op (e2) (e0)) = (e0))\/((op (e3) (e0)) = (e0))))) -> (~((op (e1) (e0)) = (op (e3) (e0)))) -> (~((op (e3) (op (e1) (e3))) = (op (e1) (e3)))) -> (((op (e1) (e0)) = (e0))\/(((op (e1) (e1)) = (e0))\/(((op (e1) (e2)) = (e0))\/((op (e1) (e3)) = (e0))))) -> (~((op (e0) (op (e1) (e0))) = (op (e1) (e0)))) -> ((~((op (e1) (e1)) = (e1)))\/((op (e1) (e1)) = (e1))) -> (~((op (e1) (e0)) = (op (e1) (e1)))) -> ((~((op (e1) (e1)) = (e3)))\/((op (e1) (e3)) = (e1))) -> (~((op (e1) (e2)) = (op (e3) (e2)))) -> (((op (e0) (e0)) = (e2))\/(((op (e1) (e0)) = (e2))\/(((op (e2) (e0)) = (e2))\/((op (e3) (e0)) = (e2))))) -> (~((op (e2) (e0)) = (op (e2) (e2)))) -> (((op (e1) (e0)) = (e3))\/(((op (e1) (e1)) = (e3))\/(((op (e1) (e2)) = (e3))\/((op (e1) (e3)) = (e3))))) -> ((~((op (e2) (e2)) = (e0)))\/((op (e2) (e0)) = (e2))) -> ((~((op (e2) (e2)) = (e3)))\/((op (e2) (e3)) = (e2))) -> (~((op (e3) (e1)) = (op (e3) (e3)))) -> (((op (e0) (e3)) = (e1))\/(((op (e1) (e3)) = (e1))\/(((op (e2) (e3)) = (e1))\/((op (e3) (e3)) = (e1))))) -> (~((op (e1) (e0)) = (op (e1) (e3)))) -> (~((op (e0) (e1)) = (op (e0) (e3)))) -> (((op (e0) (e0)) = (e2))\/(((op (e0) (e1)) = (e2))\/(((op (e0) (e2)) = (e2))\/((op (e0) (e3)) = (e2))))) -> (~((op (e0) (e2)) = (op (e0) (e3)))) -> (~((op (e0) (e2)) = (op (e1) (e2)))) -> (~((op (e1) (e3)) = (op (e3) (e3)))) -> (((op (e2) (e2)) = (e0))\/(((op (e2) (e2)) = (e1))\/(((op (e2) (e2)) = (e2))\/((op (e2) (e2)) = (e3))))) -> (~((op (e0) (e3)) = (op (e1) (e3)))) -> ((~((op (e2) (e2)) = (e2)))\/((op (e2) (e2)) = (e2))) -> (~((op (e1) (e0)) = (op (e1) (e2)))) -> ((~((op (e1) (e1)) = (e2)))\/((op (e1) (e2)) = (e1))) -> (~((op (e2) (e0)) = (op (e2) (e3)))) -> (~((op (e1) (e2)) = (op (e1) (e3)))) -> (~((op (e2) (op (e1) (e2))) = (op (e1) (e2)))) -> (((op (e0) (e1)) = (e1))\/(((op (e1) (e1)) = (e1))\/(((op (e2) (e1)) = (e1))\/((op (e3) (e1)) = (e1))))) -> (((op (e0) (e0)) = (e1))\/(((op (e1) (e0)) = (e1))\/(((op (e2) (e0)) = (e1))\/((op (e3) (e0)) = (e1))))) -> (~((op (e0) (e0)) = (e0))) -> (~((op (e1) (op (e1) (e1))) = (op (e1) (e1)))) -> (((op (e1) (e0)) = (e1))\/(((op (e1) (e1)) = (e1))\/(((op (e1) (e2)) = (e1))\/((op (e1) (e3)) = (e1))))) -> (((op (e0) (e2)) = (e3))\/(((op (e1) (e2)) = (e3))\/(((op (e2) (e2)) = (e3))\/((op (e3) (e2)) = (e3))))) -> (((op (e2) (e0)) = (e3))\/(((op (e2) (e1)) = (e3))\/(((op (e2) (e2)) = (e3))\/((op (e2) (e3)) = (e3))))) -> (~((op (e2) (e3)) = (op (e3) (e3)))) -> (~((op (e0) (e1)) = (op (e2) (e1)))) -> (((op (e0) (e1)) = (e2))\/(((op (e1) (e1)) = (e2))\/(((op (e2) (e1)) = (e2))\/((op (e3) (e1)) = (e2))))) -> (((op (e0) (e2)) = (e0))\/(((op (e1) (e2)) = (e0))\/(((op (e2) (e2)) = (e0))\/((op (e3) (e2)) = (e0))))) -> (~((op (e2) (e2)) = (e0))) -> (~((op (e3) (e1)) = (op (e3) (e2)))) -> (((op (e0) (e1)) = (e0))\/(((op (e1) (e1)) = (e0))\/(((op (e2) (e1)) = (e0))\/((op (e3) (e1)) = (e0))))) -> (~((op (e1) (e1)) = (e3))) -> (~((op (e0) (e1)) = (op (e1) (e1)))) -> (~((op (e1) (e1)) = (e1))) -> (~((op (e1) (e1)) = (e0))) -> (((op (e1) (e1)) = (e0))\/(((op (e1) (e1)) = (e1))\/(((op (e1) (e1)) = (e2))\/((op (e1) (e1)) = (e3))))) -> (~((op (e0) (e2)) = (op (e2) (e2)))) -> ((op (e2) (e2)) = (e2)) -> ((op (e0) (e3)) = (e1)) -> (~((e1) = (e2))) -> False). % 15.36/15.52 do 0 intro. intros zenon_H105 zenon_H84 zenon_H7d zenon_Hd6 zenon_H3b zenon_H10f zenon_Hbb zenon_H44 zenon_H160 zenon_H5e zenon_Hd3 zenon_H9e zenon_H59 zenon_Ha3 zenon_H4b zenon_Hab zenon_H36 zenon_H58 zenon_H45 zenon_H173 zenon_H10e zenon_H10d zenon_H109 zenon_H10c zenon_Hae zenon_H6a zenon_Hbe zenon_H140 zenon_H30 zenon_Hf0 zenon_H22e zenon_H26e zenon_H163 zenon_H261 zenon_H1d8 zenon_Hd7 zenon_H1d2 zenon_H17d zenon_Heb zenon_H17a zenon_H90 zenon_H1d4 zenon_H1c3 zenon_H12d zenon_H121 zenon_H1cf zenon_H1cd zenon_H8e zenon_Hc9 zenon_H87 zenon_H8b zenon_H2d zenon_H80 zenon_Haa zenon_H166 zenon_H1d3 zenon_Hce zenon_H1d0 zenon_H277 zenon_H228 zenon_Hf1 zenon_H20 zenon_H27b zenon_H1c5 zenon_H175 zenon_He6 zenon_He3 zenon_Hde zenon_H1a2 zenon_H16f zenon_H2e zenon_H135 zenon_H144 zenon_H182 zenon_H23 zenon_H1b4 zenon_H145 zenon_H1b3 zenon_H28 zenon_H35 zenon_H37 zenon_Ha7. % 15.36/15.52 apply (zenon_or_s _ _ zenon_H8e); [ zenon_intro zenon_H92 | zenon_intro zenon_H91 ]. % 15.36/15.52 apply (zenon_L767_); trivial. % 15.36/15.52 apply (zenon_or_s _ _ zenon_H91); [ zenon_intro zenon_H5d | zenon_intro zenon_H93 ]. % 15.36/15.52 apply (zenon_L214_); trivial. % 15.36/15.52 apply (zenon_or_s _ _ zenon_H93); [ zenon_intro zenon_H63 | zenon_intro zenon_H81 ]. % 15.36/15.52 apply (zenon_L15_); trivial. % 15.36/15.52 apply (zenon_L33_); trivial. % 15.36/15.52 (* end of lemma zenon_L768_ *) % 15.36/15.52 assert (zenon_L769_ : (((op (e1) (e2)) = (e0))\/(((op (e1) (e2)) = (e1))\/(((op (e1) (e2)) = (e2))\/((op (e1) (e2)) = (e3))))) -> (~((e1) = (e2))) -> ((op (e2) (e2)) = (e2)) -> (~((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 (e0) (e1)) = (op (e1) (e1)))) -> (~((op (e1) (e1)) = (e3))) -> (((op (e0) (e1)) = (e0))\/(((op (e1) (e1)) = (e0))\/(((op (e2) (e1)) = (e0))\/((op (e3) (e1)) = (e0))))) -> (~((op (e3) (e1)) = (op (e3) (e2)))) -> (~((op (e2) (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 (e0) (e1)) = (op (e2) (e1)))) -> (~((op (e2) (e3)) = (op (e3) (e3)))) -> (((op (e2) (e0)) = (e3))\/(((op (e2) (e1)) = (e3))\/(((op (e2) (e2)) = (e3))\/((op (e2) (e3)) = (e3))))) -> (((op (e0) (e2)) = (e3))\/(((op (e1) (e2)) = (e3))\/(((op (e2) (e2)) = (e3))\/((op (e3) (e2)) = (e3))))) -> (((op (e1) (e0)) = (e1))\/(((op (e1) (e1)) = (e1))\/(((op (e1) (e2)) = (e1))\/((op (e1) (e3)) = (e1))))) -> (~((op (e1) (op (e1) (e1))) = (op (e1) (e1)))) -> (~((op (e0) (e0)) = (e0))) -> (((op (e0) (e0)) = (e1))\/(((op (e1) (e0)) = (e1))\/(((op (e2) (e0)) = (e1))\/((op (e3) (e0)) = (e1))))) -> (~((op (e1) (e2)) = (op (e1) (e3)))) -> (~((op (e2) (e0)) = (op (e2) (e3)))) -> ((~((op (e1) (e1)) = (e2)))\/((op (e1) (e2)) = (e1))) -> (~((op (e1) (e0)) = (op (e1) (e2)))) -> ((~((op (e2) (e2)) = (e2)))\/((op (e2) (e2)) = (e2))) -> (~((op (e0) (e3)) = (op (e1) (e3)))) -> (((op (e2) (e2)) = (e0))\/(((op (e2) (e2)) = (e1))\/(((op (e2) (e2)) = (e2))\/((op (e2) (e2)) = (e3))))) -> (~((op (e1) (e3)) = (op (e3) (e3)))) -> (~((op (e0) (e2)) = (op (e1) (e2)))) -> (((op (e0) (e0)) = (e2))\/(((op (e0) (e1)) = (e2))\/(((op (e0) (e2)) = (e2))\/((op (e0) (e3)) = (e2))))) -> (~((op (e0) (e1)) = (op (e0) (e3)))) -> (~((op (e1) (e0)) = (op (e1) (e3)))) -> (((op (e0) (e3)) = (e1))\/(((op (e1) (e3)) = (e1))\/(((op (e2) (e3)) = (e1))\/((op (e3) (e3)) = (e1))))) -> (~((op (e3) (e1)) = (op (e3) (e3)))) -> ((~((op (e2) (e2)) = (e3)))\/((op (e2) (e3)) = (e2))) -> ((~((op (e2) (e2)) = (e0)))\/((op (e2) (e0)) = (e2))) -> (((op (e1) (e0)) = (e3))\/(((op (e1) (e1)) = (e3))\/(((op (e1) (e2)) = (e3))\/((op (e1) (e3)) = (e3))))) -> (~((op (e2) (e0)) = (op (e2) (e2)))) -> (((op (e0) (e0)) = (e2))\/(((op (e1) (e0)) = (e2))\/(((op (e2) (e0)) = (e2))\/((op (e3) (e0)) = (e2))))) -> (~((op (e1) (e2)) = (op (e3) (e2)))) -> ((~((op (e1) (e1)) = (e3)))\/((op (e1) (e3)) = (e1))) -> (~((op (e1) (e0)) = (op (e1) (e1)))) -> ((~((op (e1) (e1)) = (e1)))\/((op (e1) (e1)) = (e1))) -> (~((op (e0) (op (e1) (e0))) = (op (e1) (e0)))) -> (((op (e1) (e0)) = (e0))\/(((op (e1) (e1)) = (e0))\/(((op (e1) (e2)) = (e0))\/((op (e1) (e3)) = (e0))))) -> (~((op (e3) (op (e1) (e3))) = (op (e1) (e3)))) -> (~((op (e1) (e0)) = (op (e3) (e0)))) -> (((op (e0) (e0)) = (e0))\/(((op (e1) (e0)) = (e0))\/(((op (e2) (e0)) = (e0))\/((op (e3) (e0)) = (e0))))) -> (~((op (e2) (e2)) = (e3))) -> (~((op (e0) (e2)) = (op (e3) (e2)))) -> (((op (e0) (e0)) = (e3))\/(((op (e1) (e0)) = (e3))\/(((op (e2) (e0)) = (e3))\/((op (e3) (e0)) = (e3))))) -> (~((e2) = (e3))) -> ((~((op (e3) (e3)) = (e1)))\/((op (e3) (e1)) = (e3))) -> ((~((op (e3) (e3)) = (e3)))\/((op (e3) (e3)) = (e3))) -> ((~((op (e3) (e3)) = (e2)))\/((op (e3) (e2)) = (e3))) -> (~((op (e3) (e2)) = (op (e3) (e3)))) -> (~((op (e0) (e0)) = (e1))) -> (~((op (e0) (e3)) = (op (e3) (e3)))) -> (~((e0) = (e1))) -> (((op (e0) (e3)) = (e0))\/(((op (e1) (e3)) = (e0))\/(((op (e2) (e3)) = (e0))\/((op (e3) (e3)) = (e0))))) -> (~((e0) = (e2))) -> (((op (e0) (e3)) = (e2))\/(((op (e1) (e3)) = (e2))\/(((op (e2) (e3)) = (e2))\/((op (e3) (e3)) = (e2))))) -> (((op (e0) (e0)) = (e1))\/(((op (e0) (e1)) = (e1))\/(((op (e0) (e2)) = (e1))\/((op (e0) (e3)) = (e1))))) -> (~((op (e3) (e0)) = (op (e3) (e3)))) -> ((~((op (e3) (e3)) = (e0)))\/((op (e3) (e0)) = (e3))) -> (((op (e3) (e3)) = (e0))\/(((op (e3) (e3)) = (e1))\/(((op (e3) (e3)) = (e2))\/((op (e3) (e3)) = (e3))))) -> (~((op (e1) (e1)) = (e2))) -> (~((op (e1) (e2)) = (op (e2) (e2)))) -> (((op (e1) (e0)) = (e2))\/(((op (e1) (e1)) = (e2))\/(((op (e1) (e2)) = (e2))\/((op (e1) (e3)) = (e2))))) -> (~((op (e3) (e0)) = (op (e3) (e2)))) -> (((op (e0) (e0)) = (e3))\/(((op (e0) (e1)) = (e3))\/(((op (e0) (e2)) = (e3))\/((op (e0) (e3)) = (e3))))) -> (~((op (e0) (e0)) = (e3))) -> (~((op (e3) (e0)) = (op (e3) (e1)))) -> (((op (e0) (e2)) = (e1))\/(((op (e1) (e2)) = (e1))\/(((op (e2) (e2)) = (e1))\/((op (e3) (e2)) = (e1))))) -> (~((op (e0) (e2)) = (op (e0) (e3)))) -> (~((op (e2) (op (e1) (e2))) = (op (e1) (e2)))) -> (~((op (e2) (e2)) = (e1))) -> ((op (e3) (e2)) = (e3)) -> (~((op (e1) (e1)) = (e1))) -> (((op (e0) (e1)) = (e1))\/(((op (e1) (e1)) = (e1))\/(((op (e2) (e1)) = (e1))\/((op (e3) (e1)) = (e1))))) -> (~((e0) = (e3))) -> ((op (e0) (e2)) = (e0)) -> ((op (e0) (e3)) = (e1)) -> (~((e1) = (e3))) -> False). % 15.36/15.52 do 0 intro. intros zenon_H1d5 zenon_Ha7 zenon_H35 zenon_H28 zenon_H1b3 zenon_H145 zenon_H23 zenon_H182 zenon_H144 zenon_H135 zenon_H2e zenon_H16f zenon_H1a2 zenon_Hde zenon_He3 zenon_He6 zenon_H175 zenon_H1c5 zenon_H27b zenon_H20 zenon_Hf1 zenon_H1d0 zenon_Hce zenon_H1d3 zenon_H166 zenon_Haa zenon_H80 zenon_H2d zenon_H8b zenon_H87 zenon_H8e zenon_H1cd zenon_H1cf zenon_H121 zenon_H12d zenon_H1c3 zenon_H1d4 zenon_H90 zenon_H17a zenon_Heb zenon_H17d zenon_H1d2 zenon_Hd7 zenon_H1d8 zenon_H261 zenon_H163 zenon_H26e zenon_H22e zenon_Hf0 zenon_H30 zenon_H140 zenon_Hbe zenon_H6a zenon_H10c zenon_H10d zenon_H10e zenon_H173 zenon_H45 zenon_H36 zenon_H9e zenon_Hd3 zenon_H5e zenon_H160 zenon_H44 zenon_Hbb zenon_H10f zenon_H3b zenon_Hd6 zenon_H7d zenon_H84 zenon_H105 zenon_H58 zenon_H59 zenon_H109 zenon_H11b zenon_Hc9 zenon_H277 zenon_H52 zenon_H106 zenon_H1b4 zenon_H228 zenon_H4b zenon_Hab zenon_H37 zenon_Ha3. % 15.36/15.52 apply (zenon_or_s _ _ zenon_Hf1); [ zenon_intro zenon_H47 | zenon_intro zenon_Hf4 ]. % 15.36/15.52 exact (zenon_H45 zenon_H47). % 15.36/15.52 apply (zenon_or_s _ _ zenon_Hf4); [ zenon_intro zenon_Hd8 | zenon_intro zenon_Hf5 ]. % 15.36/15.52 apply (zenon_L762_); trivial. % 15.36/15.52 apply (zenon_or_s _ _ zenon_Hf5); [ zenon_intro zenon_Hae | zenon_intro zenon_Hee ]. % 15.36/15.52 apply (zenon_L768_); trivial. % 15.36/15.52 apply (zenon_L752_); trivial. % 15.36/15.52 (* end of lemma zenon_L769_ *) % 15.36/15.52 assert (zenon_L770_ : ((~((op (e0) (e0)) = (e3)))\/((op (e0) (e3)) = (e0))) -> (((op (e0) (e2)) = (e3))\/(((op (e1) (e2)) = (e3))\/(((op (e2) (e2)) = (e3))\/((op (e3) (e2)) = (e3))))) -> (~((op (e0) (e0)) = (e0))) -> (((op (e1) (e0)) = (e2))\/(((op (e1) (e1)) = (e2))\/(((op (e1) (e2)) = (e2))\/((op (e1) (e3)) = (e2))))) -> (((op (e1) (e1)) = (e0))\/(((op (e1) (e1)) = (e1))\/(((op (e1) (e1)) = (e2))\/((op (e1) (e1)) = (e3))))) -> (~((e2) = (e3))) -> (((op (e1) (e0)) = (e3))\/(((op (e1) (e1)) = (e3))\/(((op (e1) (e2)) = (e3))\/((op (e1) (e3)) = (e3))))) -> ((op (e2) (e2)) = (e2)) -> (~((op (e1) (e2)) = (op (e2) (e2)))) -> (~((e1) = (e2))) -> (~((op (e0) (e3)) = (op (e1) (e3)))) -> ((~((op (e2) (e2)) = (e1)))\/((op (e2) (e1)) = (e2))) -> (((op (e0) (e0)) = (e3))\/(((op (e1) (e0)) = (e3))\/(((op (e2) (e0)) = (e3))\/((op (e3) (e0)) = (e3))))) -> (~((op (e3) (e0)) = (op (e3) (e2)))) -> (~((op (e0) (e1)) = (op (e2) (e1)))) -> (~((op (e1) (e3)) = (op (e2) (e3)))) -> (((op (e2) (e0)) = (e1))\/(((op (e2) (e1)) = (e1))\/(((op (e2) (e2)) = (e1))\/((op (e2) (e3)) = (e1))))) -> (((op (e0) (e0)) = (e1))\/(((op (e1) (e0)) = (e1))\/(((op (e2) (e0)) = (e1))\/((op (e3) (e0)) = (e1))))) -> (((op (e0) (e1)) = (e1))\/(((op (e1) (e1)) = (e1))\/(((op (e2) (e1)) = (e1))\/((op (e3) (e1)) = (e1))))) -> (~((op (e0) (e2)) = (op (e0) (e3)))) -> (~((op (e2) (op (e1) (e2))) = (op (e1) (e2)))) -> (((op (e0) (e2)) = (e1))\/(((op (e1) (e2)) = (e1))\/(((op (e2) (e2)) = (e1))\/((op (e3) (e2)) = (e1))))) -> ((~((op (e3) (e3)) = (e1)))\/((op (e3) (e1)) = (e3))) -> (~((op (e3) (e0)) = (op (e3) (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) (e3)) = (e0)))\/((op (e3) (e0)) = (e3))) -> (~((op (e3) (e0)) = (op (e3) (e3)))) -> (((op (e0) (e0)) = (e1))\/(((op (e0) (e1)) = (e1))\/(((op (e0) (e2)) = (e1))\/((op (e0) (e3)) = (e1))))) -> (((op (e0) (e3)) = (e2))\/(((op (e1) (e3)) = (e2))\/(((op (e2) (e3)) = (e2))\/((op (e3) (e3)) = (e2))))) -> (~((e0) = (e2))) -> (((op (e0) (e3)) = (e0))\/(((op (e1) (e3)) = (e0))\/(((op (e2) (e3)) = (e0))\/((op (e3) (e3)) = (e0))))) -> (~((e0) = (e1))) -> (~((op (e0) (e3)) = (op (e3) (e3)))) -> (((op (e0) (e0)) = (e3))\/(((op (e0) (e1)) = (e3))\/(((op (e0) (e2)) = (e3))\/((op (e0) (e3)) = (e3))))) -> (~((op (e3) (e2)) = (op (e3) (e3)))) -> ((~((op (e3) (e3)) = (e2)))\/((op (e3) (e2)) = (e3))) -> ((~((op (e3) (e3)) = (e3)))\/((op (e3) (e3)) = (e3))) -> (~((op (e3) (e1)) = (op (e3) (e2)))) -> (((op (e0) (e1)) = (e2))\/(((op (e1) (e1)) = (e2))\/(((op (e2) (e1)) = (e2))\/((op (e3) (e1)) = (e2))))) -> (~((op (e2) (e1)) = (op (e2) (e2)))) -> (~((op (e0) (e1)) = (op (e0) (e3)))) -> (~((op (e2) (e2)) = (op (e2) (e3)))) -> (((op (e0) (e1)) = (e0))\/(((op (e1) (e1)) = (e0))\/(((op (e2) (e1)) = (e0))\/((op (e3) (e1)) = (e0))))) -> (((op (e1) (e0)) = (e1))\/(((op (e1) (e1)) = (e1))\/(((op (e1) (e2)) = (e1))\/((op (e1) (e3)) = (e1))))) -> ((op (e0) (e2)) = (e0)) -> (~((e0) = (e3))) -> (~((e1) = (e3))) -> (~((op (e0) (e1)) = (op (e1) (e1)))) -> (~((op (e0) (e2)) = (op (e2) (e2)))) -> (((op (e0) (e0)) = (e2))\/(((op (e0) (e1)) = (e2))\/(((op (e0) (e2)) = (e2))\/((op (e0) (e3)) = (e2))))) -> (~((op (e0) (e0)) = (e1))) -> ((~((op (e1) (e1)) = (e2)))\/((op (e1) (e2)) = (e1))) -> (~((op (e1) (e0)) = (op (e1) (e2)))) -> ((~((op (e2) (e2)) = (e2)))\/((op (e2) (e2)) = (e2))) -> (((op (e2) (e2)) = (e0))\/(((op (e2) (e2)) = (e1))\/(((op (e2) (e2)) = (e2))\/((op (e2) (e2)) = (e3))))) -> (~((op (e1) (e3)) = (op (e3) (e3)))) -> (~((op (e0) (e2)) = (op (e1) (e2)))) -> (((op (e0) (e3)) = (e1))\/(((op (e1) (e3)) = (e1))\/(((op (e2) (e3)) = (e1))\/((op (e3) (e3)) = (e1))))) -> (~((op (e3) (e1)) = (op (e3) (e3)))) -> ((~((op (e2) (e2)) = (e3)))\/((op (e2) (e3)) = (e2))) -> ((~((op (e2) (e2)) = (e0)))\/((op (e2) (e0)) = (e2))) -> (~((op (e2) (e0)) = (op (e2) (e2)))) -> (((op (e0) (e0)) = (e2))\/(((op (e1) (e0)) = (e2))\/(((op (e2) (e0)) = (e2))\/((op (e3) (e0)) = (e2))))) -> (~((op (e1) (e2)) = (op (e3) (e2)))) -> ((~((op (e1) (e1)) = (e3)))\/((op (e1) (e3)) = (e1))) -> (~((op (e0) (op (e1) (e0))) = (op (e1) (e0)))) -> (((op (e1) (e0)) = (e0))\/(((op (e1) (e1)) = (e0))\/(((op (e1) (e2)) = (e0))\/((op (e1) (e3)) = (e0))))) -> (~((op (e3) (op (e1) (e3))) = (op (e1) (e3)))) -> (~((op (e1) (e0)) = (op (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))))) -> (~((op (e2) (e3)) = (op (e3) (e3)))) -> (((op (e2) (e0)) = (e3))\/(((op (e2) (e1)) = (e3))\/(((op (e2) (e2)) = (e3))\/((op (e2) (e3)) = (e3))))) -> (~((op (e1) (op (e1) (e1))) = (op (e1) (e1)))) -> (~((op (e1) (e2)) = (op (e1) (e3)))) -> (~((op (e2) (e0)) = (op (e2) (e3)))) -> (~((op (e1) (e0)) = (op (e1) (e1)))) -> ((~((op (e1) (e1)) = (e1)))\/((op (e1) (e1)) = (e1))) -> (~((op (e0) (e2)) = (op (e3) (e2)))) -> (((op (e1) (e2)) = (e0))\/(((op (e1) (e2)) = (e1))\/(((op (e1) (e2)) = (e2))\/((op (e1) (e2)) = (e3))))) -> ((~((op (e1) (e1)) = (e0)))\/((op (e1) (e0)) = (e1))) -> False). % 15.36/15.52 do 0 intro. intros zenon_H236 zenon_H175 zenon_H20 zenon_H84 zenon_H1b3 zenon_H6a zenon_H90 zenon_H35 zenon_H7d zenon_Ha7 zenon_H80 zenon_H1e3 zenon_Hbe zenon_H105 zenon_Hde zenon_H244 zenon_Hb7 zenon_Hf1 zenon_H228 zenon_Hc9 zenon_H277 zenon_H11b zenon_H10c zenon_H109 zenon_H1cf zenon_H3b zenon_H10f zenon_Hbb zenon_H44 zenon_H160 zenon_H5e zenon_Hd3 zenon_H9e zenon_H36 zenon_H58 zenon_H173 zenon_H10e zenon_H10d zenon_H135 zenon_H1a2 zenon_H157 zenon_H1cd zenon_H15f zenon_H144 zenon_H1c5 zenon_Hab zenon_H4b zenon_Ha3 zenon_H23 zenon_H28 zenon_H8e zenon_H45 zenon_H1d3 zenon_H166 zenon_Haa zenon_H2d zenon_H8b zenon_H87 zenon_H121 zenon_H12d zenon_H1c3 zenon_H1d4 zenon_H17a zenon_Heb zenon_H17d zenon_H1d2 zenon_H261 zenon_H163 zenon_H26e zenon_H22e zenon_Hf0 zenon_H16f zenon_He3 zenon_He6 zenon_H27b zenon_H1d0 zenon_Hce zenon_Hd7 zenon_H1d8 zenon_H140 zenon_H1d5 zenon_H1e4. % 15.36/15.52 apply (zenon_or_s _ _ zenon_H236); [ zenon_intro zenon_H59 | zenon_intro zenon_Hca ]. % 15.36/15.52 apply (zenon_or_s _ _ zenon_H1e4); [ zenon_intro zenon_H145 | zenon_intro zenon_Hd8 ]. % 15.36/15.52 apply (zenon_or_s _ _ zenon_H1d8); [ zenon_intro zenon_H1b4 | zenon_intro zenon_H21 ]. % 15.36/15.52 apply (zenon_or_s _ _ zenon_H1d3); [ zenon_intro zenon_Hd6 | zenon_intro zenon_H117 ]. % 15.36/15.52 apply (zenon_or_s _ _ zenon_H1d2); [ zenon_intro zenon_H182 | zenon_intro zenon_H11f ]. % 15.36/15.52 apply (zenon_or_s _ _ zenon_H1d4); [ zenon_intro zenon_H2e | zenon_intro zenon_Hdd ]. % 15.36/15.52 apply (zenon_or_s _ _ zenon_H1e3); [ zenon_intro zenon_H52 | zenon_intro zenon_H156 ]. % 15.36/15.52 apply (zenon_or_s _ _ zenon_H1c3); [ zenon_intro zenon_H30 | zenon_intro zenon_H124 ]. % 15.36/15.52 apply (zenon_or_s _ _ zenon_H10f); [ zenon_intro zenon_H3c | zenon_intro zenon_Hba ]. % 15.36/15.52 apply (zenon_or_s _ _ zenon_H10e); [ zenon_intro zenon_H3d | zenon_intro zenon_H106 ]. % 15.36/15.52 apply (zenon_or_s _ _ zenon_H10d); [ zenon_intro zenon_H3e | zenon_intro zenon_H42 ]. % 15.36/15.52 apply (zenon_or_s _ _ zenon_Hf0); [ zenon_intro zenon_H1f | zenon_intro zenon_Hf2 ]. % 15.36/15.52 exact (zenon_H20 zenon_H1f). % 15.36/15.52 apply (zenon_or_s _ _ zenon_Hf2); [ zenon_intro zenon_Had | zenon_intro zenon_Hf3 ]. % 15.36/15.52 apply (zenon_or_s _ _ zenon_H44); [ zenon_intro zenon_H47 | zenon_intro zenon_H46 ]. % 15.36/15.52 exact (zenon_H45 zenon_H47). % 15.36/15.52 apply (zenon_or_s _ _ zenon_H46); [ zenon_intro zenon_H22 | zenon_intro zenon_H48 ]. % 15.36/15.52 apply (zenon_or_s _ _ zenon_H8e); [ zenon_intro zenon_H92 | zenon_intro zenon_H91 ]. % 15.36/15.52 apply (zenon_or_s _ _ zenon_H58); [ zenon_intro zenon_H5b | zenon_intro zenon_H5a ]. % 15.36/15.52 exact (zenon_H59 zenon_H5b). % 15.36/15.52 apply (zenon_or_s _ _ zenon_H5a); [ zenon_intro zenon_H4a | zenon_intro zenon_H5c ]. % 15.36/15.52 apply (zenon_L59_); trivial. % 15.36/15.52 apply (zenon_or_s _ _ zenon_H5c); [ zenon_intro zenon_H50 | zenon_intro zenon_H53 ]. % 15.36/15.52 apply (zenon_L48_); trivial. % 15.36/15.52 apply (zenon_or_s _ _ zenon_H1c5); [ zenon_intro zenon_Hd8 | zenon_intro zenon_H1c6 ]. % 15.36/15.52 apply (zenon_L509_); trivial. % 15.36/15.52 apply (zenon_or_s _ _ zenon_H1c6); [ zenon_intro zenon_H21 | zenon_intro zenon_H1c7 ]. % 15.36/15.52 exact (zenon_H1b4 zenon_H21). % 15.36/15.52 apply (zenon_or_s _ _ zenon_H1c7); [ zenon_intro zenon_H117 | zenon_intro zenon_H11f ]. % 15.36/15.52 apply (zenon_L521_); trivial. % 15.36/15.52 apply (zenon_L754_); trivial. % 15.36/15.52 apply (zenon_or_s _ _ zenon_H91); [ zenon_intro zenon_H5d | zenon_intro zenon_H93 ]. % 15.36/15.52 apply (zenon_L214_); trivial. % 15.36/15.52 apply (zenon_or_s _ _ zenon_H93); [ zenon_intro zenon_H63 | zenon_intro zenon_H81 ]. % 15.36/15.52 apply (zenon_L15_); trivial. % 15.36/15.52 apply (zenon_L755_); trivial. % 15.36/15.52 apply (zenon_or_s _ _ zenon_H48); [ zenon_intro zenon_H29 | zenon_intro zenon_H37 ]. % 15.36/15.52 apply (zenon_L37_); trivial. % 15.36/15.52 apply (zenon_L7_); trivial. % 15.36/15.52 apply (zenon_or_s _ _ zenon_Hf3); [ zenon_intro zenon_Hcf | zenon_intro zenon_Hdb ]. % 15.36/15.52 apply (zenon_or_s _ _ zenon_H44); [ zenon_intro zenon_H47 | zenon_intro zenon_H46 ]. % 15.36/15.52 exact (zenon_H45 zenon_H47). % 15.36/15.52 apply (zenon_or_s _ _ zenon_H46); [ zenon_intro zenon_H22 | zenon_intro zenon_H48 ]. % 15.36/15.52 apply (zenon_or_s _ _ zenon_H58); [ zenon_intro zenon_H5b | zenon_intro zenon_H5a ]. % 15.36/15.52 exact (zenon_H59 zenon_H5b). % 15.36/15.52 apply (zenon_or_s _ _ zenon_H5a); [ zenon_intro zenon_H4a | zenon_intro zenon_H5c ]. % 15.36/15.52 apply (zenon_L59_); trivial. % 15.36/15.52 apply (zenon_or_s _ _ zenon_H5c); [ zenon_intro zenon_H50 | zenon_intro zenon_H53 ]. % 15.36/15.52 apply (zenon_L48_); trivial. % 15.36/15.52 apply (zenon_or_s _ _ zenon_Hbe); [ zenon_intro zenon_H5b | zenon_intro zenon_Hbf ]. % 15.36/15.52 exact (zenon_H59 zenon_H5b). % 15.36/15.52 apply (zenon_or_s _ _ zenon_Hbf); [ zenon_intro zenon_H69 | zenon_intro zenon_Hc0 ]. % 15.36/15.52 apply (zenon_L647_); trivial. % 15.36/15.52 apply (zenon_or_s _ _ zenon_Hc0); [ zenon_intro zenon_Haf | zenon_intro zenon_Hba ]. % 15.36/15.52 apply (zenon_L57_); trivial. % 15.36/15.52 apply (zenon_L546_); trivial. % 15.36/15.52 apply (zenon_or_s _ _ zenon_H48); [ zenon_intro zenon_H29 | zenon_intro zenon_H37 ]. % 15.36/15.52 apply (zenon_L37_); trivial. % 15.36/15.52 apply (zenon_L7_); trivial. % 15.36/15.52 apply (zenon_L758_); trivial. % 15.36/15.52 apply (zenon_L232_); trivial. % 15.36/15.52 apply (zenon_or_s _ _ zenon_Hf0); [ zenon_intro zenon_H1f | zenon_intro zenon_Hf2 ]. % 15.36/15.52 exact (zenon_H20 zenon_H1f). % 15.36/15.52 apply (zenon_or_s _ _ zenon_Hf2); [ zenon_intro zenon_Had | zenon_intro zenon_Hf3 ]. % 15.36/15.52 apply (zenon_or_s _ _ zenon_H44); [ zenon_intro zenon_H47 | zenon_intro zenon_H46 ]. % 15.36/15.52 exact (zenon_H45 zenon_H47). % 15.36/15.52 apply (zenon_or_s _ _ zenon_H46); [ zenon_intro zenon_H22 | zenon_intro zenon_H48 ]. % 15.36/15.52 apply (zenon_L532_); trivial. % 15.36/15.52 apply (zenon_or_s _ _ zenon_H48); [ zenon_intro zenon_H29 | zenon_intro zenon_H37 ]. % 15.36/15.52 apply (zenon_L37_); trivial. % 15.36/15.52 apply (zenon_L769_); trivial. % 15.36/15.52 apply (zenon_or_s _ _ zenon_Hf3); [ zenon_intro zenon_Hcf | zenon_intro zenon_Hdb ]. % 15.36/15.52 apply (zenon_or_s _ _ zenon_H44); [ zenon_intro zenon_H47 | zenon_intro zenon_H46 ]. % 15.36/15.52 exact (zenon_H45 zenon_H47). % 15.36/15.52 apply (zenon_or_s _ _ zenon_H46); [ zenon_intro zenon_H22 | zenon_intro zenon_H48 ]. % 15.36/15.52 apply (zenon_or_s _ _ zenon_H58); [ zenon_intro zenon_H5b | zenon_intro zenon_H5a ]. % 15.36/15.52 exact (zenon_H59 zenon_H5b). % 15.36/15.52 apply (zenon_or_s _ _ zenon_H5a); [ zenon_intro zenon_H4a | zenon_intro zenon_H5c ]. % 15.36/15.52 apply (zenon_L59_); trivial. % 15.36/15.52 apply (zenon_or_s _ _ zenon_H5c); [ zenon_intro zenon_H50 | zenon_intro zenon_H53 ]. % 15.36/15.52 apply (zenon_L533_); trivial. % 15.36/15.52 apply (zenon_L765_); trivial. % 15.36/15.52 apply (zenon_or_s _ _ zenon_H48); [ zenon_intro zenon_H29 | zenon_intro zenon_H37 ]. % 15.36/15.52 apply (zenon_L37_); trivial. % 15.36/15.52 apply (zenon_L769_); trivial. % 15.36/15.52 apply (zenon_L758_); trivial. % 15.36/15.52 apply (zenon_or_s _ _ zenon_H10c); [ zenon_intro zenon_H104 | zenon_intro zenon_H10a ]. % 15.36/15.52 apply (zenon_or_s _ _ zenon_H44); [ zenon_intro zenon_H47 | zenon_intro zenon_H46 ]. % 15.36/15.52 exact (zenon_H45 zenon_H47). % 15.36/15.52 apply (zenon_or_s _ _ zenon_H46); [ zenon_intro zenon_H22 | zenon_intro zenon_H48 ]. % 15.36/15.52 apply (zenon_or_s _ _ zenon_Hf1); [ zenon_intro zenon_H47 | zenon_intro zenon_Hf4 ]. % 15.36/15.52 exact (zenon_H45 zenon_H47). % 15.36/15.52 apply (zenon_or_s _ _ zenon_Hf4); [ zenon_intro zenon_Hd8 | zenon_intro zenon_Hf5 ]. % 15.36/15.52 apply (zenon_L539_); trivial. % 15.36/15.52 apply (zenon_or_s _ _ zenon_Hf5); [ zenon_intro zenon_Hae | zenon_intro zenon_Hee ]. % 15.36/15.52 apply (zenon_or_s _ _ zenon_H8e); [ zenon_intro zenon_H92 | zenon_intro zenon_H91 ]. % 15.36/15.52 apply (zenon_L767_); trivial. % 15.36/15.52 apply (zenon_or_s _ _ zenon_H91); [ zenon_intro zenon_H5d | zenon_intro zenon_H93 ]. % 15.36/15.52 apply (zenon_L214_); trivial. % 15.36/15.52 apply (zenon_or_s _ _ zenon_H93); [ zenon_intro zenon_H63 | zenon_intro zenon_H81 ]. % 15.36/15.52 apply (zenon_L676_); trivial. % 15.36/15.52 apply (zenon_L755_); trivial. % 15.36/15.52 apply (zenon_L79_); trivial. % 15.36/15.52 apply (zenon_or_s _ _ zenon_H48); [ zenon_intro zenon_H29 | zenon_intro zenon_H37 ]. % 15.36/15.52 apply (zenon_L37_); trivial. % 15.36/15.52 apply (zenon_or_s _ _ zenon_Hf1); [ zenon_intro zenon_H47 | zenon_intro zenon_Hf4 ]. % 15.36/15.52 exact (zenon_H45 zenon_H47). % 15.36/15.52 apply (zenon_or_s _ _ zenon_Hf4); [ zenon_intro zenon_Hd8 | zenon_intro zenon_Hf5 ]. % 15.36/15.52 apply (zenon_L762_); trivial. % 15.36/15.52 apply (zenon_or_s _ _ zenon_Hf5); [ zenon_intro zenon_Hae | zenon_intro zenon_Hee ]. % 15.36/15.52 apply (zenon_L768_); trivial. % 15.36/15.52 apply (zenon_L79_); trivial. % 15.36/15.52 apply (zenon_L82_); trivial. % 15.36/15.52 apply (zenon_L137_); trivial. % 15.36/15.52 apply (zenon_L134_); trivial. % 15.36/15.52 apply (zenon_L161_); trivial. % 15.36/15.52 apply (zenon_L754_); trivial. % 15.36/15.52 apply (zenon_or_s _ _ zenon_H1d2); [ zenon_intro zenon_H182 | zenon_intro zenon_H11f ]. % 15.36/15.52 apply (zenon_or_s _ _ zenon_H1d4); [ zenon_intro zenon_H2e | zenon_intro zenon_Hdd ]. % 15.36/15.52 apply (zenon_or_s _ _ zenon_H1c3); [ zenon_intro zenon_H30 | zenon_intro zenon_H124 ]. % 15.36/15.52 apply (zenon_L766_); trivial. % 15.36/15.52 apply (zenon_L137_); trivial. % 15.36/15.52 apply (zenon_L161_); trivial. % 15.36/15.52 apply (zenon_L237_); trivial. % 15.36/15.52 apply (zenon_L698_); trivial. % 15.36/15.52 apply (zenon_L553_); trivial. % 15.36/15.52 apply (zenon_L53_); trivial. % 15.36/15.52 (* end of lemma zenon_L770_ *) % 15.36/15.52 assert (zenon_L771_ : ((~((op (e1) (e1)) = (e0)))\/((op (e1) (e0)) = (e1))) -> (((op (e1) (e2)) = (e0))\/(((op (e1) (e2)) = (e1))\/(((op (e1) (e2)) = (e2))\/((op (e1) (e2)) = (e3))))) -> (~((op (e0) (e2)) = (op (e3) (e2)))) -> ((~((op (e1) (e1)) = (e1)))\/((op (e1) (e1)) = (e1))) -> (~((op (e1) (e0)) = (op (e1) (e1)))) -> (~((op (e2) (e0)) = (op (e2) (e3)))) -> (~((op (e1) (e2)) = (op (e1) (e3)))) -> (~((op (e1) (op (e1) (e1))) = (op (e1) (e1)))) -> (((op (e2) (e0)) = (e3))\/(((op (e2) (e1)) = (e3))\/(((op (e2) (e2)) = (e3))\/((op (e2) (e3)) = (e3))))) -> (~((op (e2) (e3)) = (op (e3) (e3)))) -> (((op (e0) (e2)) = (e0))\/(((op (e1) (e2)) = (e0))\/(((op (e2) (e2)) = (e0))\/((op (e3) (e2)) = (e0))))) -> (((op (e0) (e0)) = (e0))\/(((op (e1) (e0)) = (e0))\/(((op (e2) (e0)) = (e0))\/((op (e3) (e0)) = (e0))))) -> (~((op (e1) (e0)) = (op (e3) (e0)))) -> (~((op (e3) (op (e1) (e3))) = (op (e1) (e3)))) -> (((op (e1) (e0)) = (e0))\/(((op (e1) (e1)) = (e0))\/(((op (e1) (e2)) = (e0))\/((op (e1) (e3)) = (e0))))) -> (~((op (e0) (op (e1) (e0))) = (op (e1) (e0)))) -> ((~((op (e1) (e1)) = (e3)))\/((op (e1) (e3)) = (e1))) -> (~((op (e1) (e2)) = (op (e3) (e2)))) -> (((op (e0) (e0)) = (e2))\/(((op (e1) (e0)) = (e2))\/(((op (e2) (e0)) = (e2))\/((op (e3) (e0)) = (e2))))) -> (~((op (e2) (e0)) = (op (e2) (e2)))) -> ((~((op (e2) (e2)) = (e0)))\/((op (e2) (e0)) = (e2))) -> ((~((op (e2) (e2)) = (e3)))\/((op (e2) (e3)) = (e2))) -> (~((op (e3) (e1)) = (op (e3) (e3)))) -> (((op (e0) (e3)) = (e1))\/(((op (e1) (e3)) = (e1))\/(((op (e2) (e3)) = (e1))\/((op (e3) (e3)) = (e1))))) -> (~((op (e0) (e2)) = (op (e1) (e2)))) -> (~((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)) = (e2)))\/((op (e2) (e2)) = (e2))) -> (~((op (e1) (e0)) = (op (e1) (e2)))) -> ((~((op (e1) (e1)) = (e2)))\/((op (e1) (e2)) = (e1))) -> (~((op (e0) (e0)) = (e1))) -> (((op (e0) (e0)) = (e2))\/(((op (e0) (e1)) = (e2))\/(((op (e0) (e2)) = (e2))\/((op (e0) (e3)) = (e2))))) -> (~((op (e0) (e2)) = (op (e2) (e2)))) -> (~((op (e0) (e1)) = (op (e1) (e1)))) -> (~((e1) = (e3))) -> (((op (e1) (e0)) = (e1))\/(((op (e1) (e1)) = (e1))\/(((op (e1) (e2)) = (e1))\/((op (e1) (e3)) = (e1))))) -> (((op (e0) (e1)) = (e0))\/(((op (e1) (e1)) = (e0))\/(((op (e2) (e1)) = (e0))\/((op (e3) (e1)) = (e0))))) -> (~((op (e2) (e2)) = (op (e2) (e3)))) -> (~((op (e0) (e1)) = (op (e0) (e3)))) -> (~((op (e2) (e1)) = (op (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) (e3)) = (e3)))\/((op (e3) (e3)) = (e3))) -> ((~((op (e3) (e3)) = (e2)))\/((op (e3) (e2)) = (e3))) -> (~((op (e3) (e2)) = (op (e3) (e3)))) -> (((op (e0) (e0)) = (e3))\/(((op (e0) (e1)) = (e3))\/(((op (e0) (e2)) = (e3))\/((op (e0) (e3)) = (e3))))) -> (~((op (e0) (e3)) = (op (e3) (e3)))) -> (~((e0) = (e1))) -> (((op (e0) (e3)) = (e0))\/(((op (e1) (e3)) = (e0))\/(((op (e2) (e3)) = (e0))\/((op (e3) (e3)) = (e0))))) -> (~((e0) = (e2))) -> (((op (e0) (e3)) = (e2))\/(((op (e1) (e3)) = (e2))\/(((op (e2) (e3)) = (e2))\/((op (e3) (e3)) = (e2))))) -> (((op (e0) (e0)) = (e1))\/(((op (e0) (e1)) = (e1))\/(((op (e0) (e2)) = (e1))\/((op (e0) (e3)) = (e1))))) -> (~((op (e3) (e0)) = (op (e3) (e3)))) -> ((~((op (e3) (e3)) = (e0)))\/((op (e3) (e0)) = (e3))) -> (~((op (e1) (e0)) = (op (e1) (e3)))) -> (~((op (e3) (e0)) = (op (e3) (e1)))) -> ((~((op (e3) (e3)) = (e1)))\/((op (e3) (e1)) = (e3))) -> (((op (e0) (e2)) = (e1))\/(((op (e1) (e2)) = (e1))\/(((op (e2) (e2)) = (e1))\/((op (e3) (e2)) = (e1))))) -> (~((op (e2) (op (e1) (e2))) = (op (e1) (e2)))) -> (~((op (e0) (e2)) = (op (e0) (e3)))) -> (((op (e0) (e1)) = (e1))\/(((op (e1) (e1)) = (e1))\/(((op (e2) (e1)) = (e1))\/((op (e3) (e1)) = (e1))))) -> (((op (e0) (e0)) = (e1))\/(((op (e1) (e0)) = (e1))\/(((op (e2) (e0)) = (e1))\/((op (e3) (e0)) = (e1))))) -> (((op (e2) (e0)) = (e1))\/(((op (e2) (e1)) = (e1))\/(((op (e2) (e2)) = (e1))\/((op (e2) (e3)) = (e1))))) -> (~((op (e1) (e3)) = (op (e2) (e3)))) -> (~((op (e0) (e1)) = (op (e2) (e1)))) -> (~((op (e3) (e0)) = (op (e3) (e2)))) -> (((op (e0) (e0)) = (e3))\/(((op (e1) (e0)) = (e3))\/(((op (e2) (e0)) = (e3))\/((op (e3) (e0)) = (e3))))) -> ((~((op (e2) (e2)) = (e1)))\/((op (e2) (e1)) = (e2))) -> (~((op (e0) (e3)) = (op (e1) (e3)))) -> (~((e1) = (e2))) -> (~((op (e1) (e2)) = (op (e2) (e2)))) -> ((op (e2) (e2)) = (e2)) -> (((op (e1) (e0)) = (e3))\/(((op (e1) (e1)) = (e3))\/(((op (e1) (e2)) = (e3))\/((op (e1) (e3)) = (e3))))) -> (~((e2) = (e3))) -> (((op (e1) (e1)) = (e0))\/(((op (e1) (e1)) = (e1))\/(((op (e1) (e1)) = (e2))\/((op (e1) (e1)) = (e3))))) -> (((op (e1) (e0)) = (e2))\/(((op (e1) (e1)) = (e2))\/(((op (e1) (e2)) = (e2))\/((op (e1) (e3)) = (e2))))) -> (~((op (e0) (e0)) = (e0))) -> (((op (e0) (e2)) = (e3))\/(((op (e1) (e2)) = (e3))\/(((op (e2) (e2)) = (e3))\/((op (e3) (e2)) = (e3))))) -> ((~((op (e0) (e0)) = (e3)))\/((op (e0) (e3)) = (e0))) -> (~((op (e3) (e3)) = (e3))) -> ((op (e1) (e1)) = (e3)) -> (~((op (e3) (e3)) = (e1))) -> (~((op (e3) (e3)) = (e0))) -> (((op (e3) (e3)) = (e0))\/(((op (e3) (e3)) = (e1))\/(((op (e3) (e3)) = (e2))\/((op (e3) (e3)) = (e3))))) -> (~((op (e2) (e2)) = (e0))) -> (~((e0) = (e3))) -> ((op (e3) (e2)) = (e3)) -> False). % 15.36/15.52 do 0 intro. intros zenon_H1e4 zenon_H1d5 zenon_H140 zenon_H1d8 zenon_Hd7 zenon_Hce zenon_H1d0 zenon_H27b zenon_He6 zenon_He3 zenon_H16f zenon_Hf0 zenon_H22e zenon_H26e zenon_H163 zenon_H261 zenon_H1d2 zenon_H17d zenon_Heb zenon_H17a zenon_H1d4 zenon_H1c3 zenon_H12d zenon_H121 zenon_H87 zenon_H8b zenon_H2d zenon_Haa zenon_H166 zenon_H1d3 zenon_H45 zenon_H8e zenon_H28 zenon_H23 zenon_Ha3 zenon_H1c5 zenon_H144 zenon_H15f zenon_H1cd zenon_H157 zenon_H1a2 zenon_H135 zenon_H10d zenon_H10e zenon_H173 zenon_H58 zenon_H36 zenon_H9e zenon_Hd3 zenon_H5e zenon_H160 zenon_H44 zenon_Hbb zenon_H10f zenon_H1cf zenon_H109 zenon_H10c zenon_H11b zenon_H277 zenon_Hc9 zenon_H228 zenon_Hf1 zenon_Hb7 zenon_H244 zenon_Hde zenon_H105 zenon_Hbe zenon_H1e3 zenon_H80 zenon_Ha7 zenon_H7d zenon_H35 zenon_H90 zenon_H6a zenon_H1b3 zenon_H84 zenon_H20 zenon_H175 zenon_H236 zenon_H3e zenon_H96 zenon_H104 zenon_H3c zenon_H3b zenon_H2e zenon_H4b zenon_H106. % 15.36/15.52 apply (zenon_or_s _ _ zenon_H16f); [ zenon_intro zenon_Hab | zenon_intro zenon_H170 ]. % 15.36/15.52 apply (zenon_L770_); trivial. % 15.36/15.52 apply (zenon_or_s _ _ zenon_H170); [ zenon_intro zenon_H15d | zenon_intro zenon_H171 ]. % 15.36/15.52 apply (zenon_L489_); trivial. % 15.36/15.52 apply (zenon_or_s _ _ zenon_H171); [ zenon_intro zenon_H32 | zenon_intro zenon_H167 ]. % 15.36/15.52 exact (zenon_H2e zenon_H32). % 15.36/15.52 apply (zenon_L589_); trivial. % 15.36/15.52 (* end of lemma zenon_L771_ *) % 15.36/15.52 assert (zenon_L772_ : ((op (e1) (e3)) = (e1)) -> ((op (e1) (e3)) = (e3)) -> (~((e1) = (e3))) -> False). % 15.36/15.52 do 0 intro. intros zenon_H11f zenon_H8a zenon_Ha3. % 15.36/15.52 elim (classic ((e3) = (e3))); [ zenon_intro zenon_H4c | zenon_intro zenon_H4d ]. % 15.36/15.52 cut (((e3) = (e3)) = ((e1) = (e3))). % 15.36/15.52 intro zenon_D_pnotp. % 15.36/15.52 apply zenon_Ha3. % 15.36/15.52 rewrite <- zenon_D_pnotp. % 15.36/15.52 exact zenon_H4c. % 15.36/15.52 cut (((e3) = (e3))); [idtac | apply NNPP; zenon_intro zenon_H4d]. % 15.36/15.52 cut (((e3) = (e1))); [idtac | apply NNPP; zenon_intro zenon_Ha4]. % 15.36/15.52 congruence. % 15.36/15.52 cut (((op (e1) (e3)) = (e1)) = ((e3) = (e1))). % 15.36/15.52 intro zenon_D_pnotp. % 15.36/15.52 apply zenon_Ha4. % 15.36/15.52 rewrite <- zenon_D_pnotp. % 15.36/15.52 exact zenon_H11f. % 15.36/15.52 cut (((e1) = (e1))); [idtac | apply NNPP; zenon_intro zenon_Ha0]. % 15.36/15.52 cut (((op (e1) (e3)) = (e3))); [idtac | apply NNPP; zenon_intro zenon_H181]. % 15.36/15.52 congruence. % 15.36/15.52 exact (zenon_H181 zenon_H8a). % 15.36/15.52 apply zenon_Ha0. apply refl_equal. % 15.36/15.52 apply zenon_H4d. apply refl_equal. % 15.36/15.52 apply zenon_H4d. apply refl_equal. % 15.36/15.52 (* end of lemma zenon_L772_ *) % 15.36/15.52 assert (zenon_L773_ : (((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) (e3)) = (e3))) -> (~((op (e3) (e3)) = (e1))) -> (~((op (e3) (e3)) = (e0))) -> (((op (e3) (e3)) = (e0))\/(((op (e3) (e3)) = (e1))\/(((op (e3) (e3)) = (e2))\/((op (e3) (e3)) = (e3))))) -> (~((op (e1) (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) (e3)) = (op (e1) (e3)))) -> ((op (e0) (e3)) = (e0)) -> False). % 15.36/15.52 do 0 intro. intros zenon_H163 zenon_H22e zenon_Hdb zenon_H3e zenon_H104 zenon_H3c zenon_H3b zenon_Hd6 zenon_H1b4 zenon_H145 zenon_H1b3 zenon_H80 zenon_Hca. % 15.36/15.52 apply (zenon_or_s _ _ zenon_H163); [ zenon_intro zenon_Had | zenon_intro zenon_H164 ]. % 15.36/15.52 apply (zenon_L756_); trivial. % 15.36/15.52 apply (zenon_or_s _ _ zenon_H164); [ zenon_intro zenon_H149 | zenon_intro zenon_H165 ]. % 15.36/15.52 exact (zenon_H145 zenon_H149). % 15.36/15.52 apply (zenon_or_s _ _ zenon_H165); [ zenon_intro zenon_H15d | zenon_intro zenon_Hcc ]. % 15.36/15.52 apply (zenon_L490_); trivial. % 15.36/15.52 apply (zenon_L155_); trivial. % 15.36/15.52 (* end of lemma zenon_L773_ *) % 15.36/15.52 assert (zenon_L774_ : (~((op (e0) (e0)) = (e0))) -> ((op (e1) (e3)) = (e1)) -> ((~((op (e0) (e0)) = (e3)))\/((op (e0) (e3)) = (e0))) -> (((op (e0) (e2)) = (e3))\/(((op (e1) (e2)) = (e3))\/(((op (e2) (e2)) = (e3))\/((op (e3) (e2)) = (e3))))) -> (((op (e1) (e0)) = (e2))\/(((op (e1) (e1)) = (e2))\/(((op (e1) (e2)) = (e2))\/((op (e1) (e3)) = (e2))))) -> (((op (e1) (e1)) = (e0))\/(((op (e1) (e1)) = (e1))\/(((op (e1) (e1)) = (e2))\/((op (e1) (e1)) = (e3))))) -> (~((e2) = (e3))) -> (((op (e1) (e0)) = (e3))\/(((op (e1) (e1)) = (e3))\/(((op (e1) (e2)) = (e3))\/((op (e1) (e3)) = (e3))))) -> ((op (e2) (e2)) = (e2)) -> (~((op (e1) (e2)) = (op (e2) (e2)))) -> (~((e1) = (e2))) -> (~((op (e0) (e3)) = (op (e1) (e3)))) -> ((~((op (e2) (e2)) = (e1)))\/((op (e2) (e1)) = (e2))) -> (((op (e0) (e0)) = (e3))\/(((op (e1) (e0)) = (e3))\/(((op (e2) (e0)) = (e3))\/((op (e3) (e0)) = (e3))))) -> (~((op (e3) (e0)) = (op (e3) (e2)))) -> (~((op (e0) (e1)) = (op (e2) (e1)))) -> (~((op (e1) (e3)) = (op (e2) (e3)))) -> (((op (e2) (e0)) = (e1))\/(((op (e2) (e1)) = (e1))\/(((op (e2) (e2)) = (e1))\/((op (e2) (e3)) = (e1))))) -> (((op (e0) (e0)) = (e1))\/(((op (e1) (e0)) = (e1))\/(((op (e2) (e0)) = (e1))\/((op (e3) (e0)) = (e1))))) -> (((op (e0) (e1)) = (e1))\/(((op (e1) (e1)) = (e1))\/(((op (e2) (e1)) = (e1))\/((op (e3) (e1)) = (e1))))) -> (~((op (e0) (e2)) = (op (e0) (e3)))) -> (~((op (e2) (op (e1) (e2))) = (op (e1) (e2)))) -> (((op (e0) (e2)) = (e1))\/(((op (e1) (e2)) = (e1))\/(((op (e2) (e2)) = (e1))\/((op (e3) (e2)) = (e1))))) -> ((~((op (e3) (e3)) = (e1)))\/((op (e3) (e1)) = (e3))) -> (~((op (e3) (e0)) = (op (e3) (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) (e3)) = (e0)))\/((op (e3) (e0)) = (e3))) -> (~((op (e3) (e0)) = (op (e3) (e3)))) -> (((op (e0) (e0)) = (e1))\/(((op (e0) (e1)) = (e1))\/(((op (e0) (e2)) = (e1))\/((op (e0) (e3)) = (e1))))) -> (((op (e0) (e3)) = (e2))\/(((op (e1) (e3)) = (e2))\/(((op (e2) (e3)) = (e2))\/((op (e3) (e3)) = (e2))))) -> (~((e0) = (e2))) -> (((op (e0) (e3)) = (e0))\/(((op (e1) (e3)) = (e0))\/(((op (e2) (e3)) = (e0))\/((op (e3) (e3)) = (e0))))) -> (~((e0) = (e1))) -> (~((op (e0) (e3)) = (op (e3) (e3)))) -> (((op (e0) (e0)) = (e3))\/(((op (e0) (e1)) = (e3))\/(((op (e0) (e2)) = (e3))\/((op (e0) (e3)) = (e3))))) -> (~((op (e3) (e2)) = (op (e3) (e3)))) -> ((~((op (e3) (e3)) = (e2)))\/((op (e3) (e2)) = (e3))) -> ((~((op (e3) (e3)) = (e3)))\/((op (e3) (e3)) = (e3))) -> (~((op (e3) (e1)) = (op (e3) (e2)))) -> (((op (e0) (e1)) = (e2))\/(((op (e1) (e1)) = (e2))\/(((op (e2) (e1)) = (e2))\/((op (e3) (e1)) = (e2))))) -> (~((op (e2) (e1)) = (op (e2) (e2)))) -> (~((op (e0) (e1)) = (op (e0) (e3)))) -> (~((op (e2) (e2)) = (op (e2) (e3)))) -> (((op (e0) (e1)) = (e0))\/(((op (e1) (e1)) = (e0))\/(((op (e2) (e1)) = (e0))\/((op (e3) (e1)) = (e0))))) -> (((op (e1) (e0)) = (e1))\/(((op (e1) (e1)) = (e1))\/(((op (e1) (e2)) = (e1))\/((op (e1) (e3)) = (e1))))) -> (~((e1) = (e3))) -> (~((op (e0) (e1)) = (op (e1) (e1)))) -> (~((op (e0) (e2)) = (op (e2) (e2)))) -> (((op (e0) (e0)) = (e2))\/(((op (e0) (e1)) = (e2))\/(((op (e0) (e2)) = (e2))\/((op (e0) (e3)) = (e2))))) -> (~((op (e0) (e0)) = (e1))) -> ((~((op (e1) (e1)) = (e2)))\/((op (e1) (e2)) = (e1))) -> (~((op (e1) (e0)) = (op (e1) (e2)))) -> ((~((op (e2) (e2)) = (e2)))\/((op (e2) (e2)) = (e2))) -> (((op (e2) (e2)) = (e0))\/(((op (e2) (e2)) = (e1))\/(((op (e2) (e2)) = (e2))\/((op (e2) (e2)) = (e3))))) -> (~((op (e1) (e3)) = (op (e3) (e3)))) -> (~((op (e0) (e2)) = (op (e1) (e2)))) -> (((op (e0) (e3)) = (e1))\/(((op (e1) (e3)) = (e1))\/(((op (e2) (e3)) = (e1))\/((op (e3) (e3)) = (e1))))) -> (~((op (e3) (e1)) = (op (e3) (e3)))) -> ((~((op (e2) (e2)) = (e3)))\/((op (e2) (e3)) = (e2))) -> ((~((op (e2) (e2)) = (e0)))\/((op (e2) (e0)) = (e2))) -> (~((op (e2) (e0)) = (op (e2) (e2)))) -> (((op (e0) (e0)) = (e2))\/(((op (e1) (e0)) = (e2))\/(((op (e2) (e0)) = (e2))\/((op (e3) (e0)) = (e2))))) -> (~((op (e1) (e2)) = (op (e3) (e2)))) -> ((~((op (e1) (e1)) = (e3)))\/((op (e1) (e3)) = (e1))) -> (~((op (e0) (op (e1) (e0))) = (op (e1) (e0)))) -> (((op (e1) (e0)) = (e0))\/(((op (e1) (e1)) = (e0))\/(((op (e1) (e2)) = (e0))\/((op (e1) (e3)) = (e0))))) -> (~((op (e3) (op (e1) (e3))) = (op (e1) (e3)))) -> (~((op (e1) (e0)) = (op (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))))) -> (~((op (e2) (e3)) = (op (e3) (e3)))) -> (((op (e2) (e0)) = (e3))\/(((op (e2) (e1)) = (e3))\/(((op (e2) (e2)) = (e3))\/((op (e2) (e3)) = (e3))))) -> (~((op (e1) (op (e1) (e1))) = (op (e1) (e1)))) -> (~((op (e1) (e2)) = (op (e1) (e3)))) -> (~((op (e2) (e0)) = (op (e2) (e3)))) -> (~((op (e1) (e0)) = (op (e1) (e1)))) -> ((~((op (e1) (e1)) = (e1)))\/((op (e1) (e1)) = (e1))) -> (~((op (e0) (e2)) = (op (e3) (e2)))) -> (((op (e1) (e2)) = (e0))\/(((op (e1) (e2)) = (e1))\/(((op (e1) (e2)) = (e2))\/((op (e1) (e2)) = (e3))))) -> ((~((op (e1) (e1)) = (e0)))\/((op (e1) (e0)) = (e1))) -> (~((op (e3) (e3)) = (e1))) -> (~((op (e3) (e3)) = (e0))) -> (~((op (e2) (e2)) = (e0))) -> ((op (e3) (e2)) = (e3)) -> (~((e0) = (e3))) -> ((op (e0) (e3)) = (e0)) -> (~((op (e2) (e0)) = (op (e2) (e1)))) -> (~((op (e1) (e1)) = (e0))) -> (~((op (e0) (e0)) = (e2))) -> (~((op (e1) (e1)) = (e1))) -> (~((op (e1) (e1)) = (e2))) -> False). % 15.36/15.52 do 0 intro. intros zenon_H20 zenon_H11f zenon_H236 zenon_H175 zenon_H84 zenon_H1b3 zenon_H6a zenon_H90 zenon_H35 zenon_H7d zenon_Ha7 zenon_H80 zenon_H1e3 zenon_Hbe zenon_H105 zenon_Hde zenon_H244 zenon_Hb7 zenon_Hf1 zenon_H228 zenon_Hc9 zenon_H277 zenon_H11b zenon_H10c zenon_H109 zenon_H1cf zenon_H3b zenon_H10f zenon_Hbb zenon_H44 zenon_H160 zenon_H5e zenon_Hd3 zenon_H9e zenon_H36 zenon_H58 zenon_H173 zenon_H10e zenon_H10d zenon_H135 zenon_H1a2 zenon_H157 zenon_H1cd zenon_H15f zenon_H144 zenon_H1c5 zenon_Ha3 zenon_H23 zenon_H28 zenon_H8e zenon_H45 zenon_H1d3 zenon_H166 zenon_Haa zenon_H2d zenon_H8b zenon_H87 zenon_H121 zenon_H12d zenon_H1c3 zenon_H1d4 zenon_H17a zenon_Heb zenon_H17d zenon_H1d2 zenon_H261 zenon_H163 zenon_H26e zenon_H22e zenon_Hf0 zenon_H16f zenon_He3 zenon_He6 zenon_H27b zenon_H1d0 zenon_Hce zenon_Hd7 zenon_H1d8 zenon_H140 zenon_H1d5 zenon_H1e4 zenon_H104 zenon_H3c zenon_H2e zenon_H106 zenon_H4b zenon_Hca zenon_H154 zenon_H145 zenon_H8f zenon_H1b4 zenon_Hd6. % 15.36/15.52 apply (zenon_or_s _ _ zenon_H10d); [ zenon_intro zenon_H3e | zenon_intro zenon_H42 ]. % 15.36/15.52 apply (zenon_or_s _ _ zenon_Hf0); [ zenon_intro zenon_H1f | zenon_intro zenon_Hf2 ]. % 15.36/15.52 exact (zenon_H20 zenon_H1f). % 15.36/15.52 apply (zenon_or_s _ _ zenon_Hf2); [ zenon_intro zenon_Had | zenon_intro zenon_Hf3 ]. % 15.36/15.52 apply (zenon_or_s _ _ zenon_H90); [ zenon_intro zenon_H69 | zenon_intro zenon_H94 ]. % 15.36/15.52 apply (zenon_L38_); trivial. % 15.36/15.52 apply (zenon_or_s _ _ zenon_H94); [ zenon_intro zenon_H96 | zenon_intro zenon_H95 ]. % 15.36/15.52 apply (zenon_L771_); trivial. % 15.36/15.52 apply (zenon_or_s _ _ zenon_H95); [ zenon_intro zenon_H88 | zenon_intro zenon_H8a ]. % 15.36/15.52 apply (zenon_L164_); trivial. % 15.36/15.52 apply (zenon_L772_); trivial. % 15.36/15.52 apply (zenon_or_s _ _ zenon_Hf3); [ zenon_intro zenon_Hcf | zenon_intro zenon_Hdb ]. % 15.36/15.52 apply (zenon_or_s _ _ zenon_H8e); [ zenon_intro zenon_H92 | zenon_intro zenon_H91 ]. % 15.36/15.52 exact (zenon_H8f zenon_H92). % 15.36/15.52 apply (zenon_or_s _ _ zenon_H91); [ zenon_intro zenon_H5d | zenon_intro zenon_H93 ]. % 15.36/15.52 apply (zenon_or_s _ _ zenon_H163); [ zenon_intro zenon_Had | zenon_intro zenon_H164 ]. % 15.36/15.52 apply (zenon_L151_); trivial. % 15.36/15.52 apply (zenon_or_s _ _ zenon_H164); [ zenon_intro zenon_H149 | zenon_intro zenon_H165 ]. % 15.36/15.52 exact (zenon_H145 zenon_H149). % 15.36/15.52 apply (zenon_or_s _ _ zenon_H165); [ zenon_intro zenon_H15d | zenon_intro zenon_Hcc ]. % 15.36/15.52 apply (zenon_L720_); trivial. % 15.36/15.52 apply (zenon_L208_); trivial. % 15.36/15.52 apply (zenon_or_s _ _ zenon_H93); [ zenon_intro zenon_H63 | zenon_intro zenon_H81 ]. % 15.36/15.52 apply (zenon_L15_); trivial. % 15.36/15.52 apply (zenon_L373_); trivial. % 15.36/15.52 apply (zenon_L773_); trivial. % 15.36/15.52 apply (zenon_L153_); trivial. % 15.36/15.52 (* end of lemma zenon_L774_ *) % 15.36/15.52 assert (zenon_L775_ : (((op (e0) (e0)) = (e2))\/(((op (e1) (e0)) = (e2))\/(((op (e2) (e0)) = (e2))\/((op (e3) (e0)) = (e2))))) -> (((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 (e2) (e2)) = (e2)) -> (~((op (e2) (e0)) = (op (e2) (e2)))) -> ((op (e1) (e0)) = (e1)) -> (~((e1) = (e2))) -> (~((op (e0) (e0)) = (e2))) -> ((~((op (e0) (e0)) = (e0)))\/((op (e0) (e0)) = (e0))) -> (~((op (e0) (e0)) = (op (e0) (e1)))) -> (((op (e1) (e3)) = (e0))\/(((op (e1) (e3)) = (e1))\/(((op (e1) (e3)) = (e2))\/((op (e1) (e3)) = (e3))))) -> (~((op (e0) (e0)) = (op (e1) (e0)))) -> (~((op (e0) (e0)) = (op (e2) (e0)))) -> (~((op (e1) (e3)) = (op (e2) (e3)))) -> (~((op (e0) (e0)) = (op (e0) (e3)))) -> (~((op (e0) (e3)) = (op (e2) (e3)))) -> (((op (e0) (e3)) = (e0))\/(((op (e0) (e3)) = (e1))\/(((op (e0) (e3)) = (e2))\/((op (e0) (e3)) = (e3))))) -> (~((op (e0) (e0)) = (op (e0) (e2)))) -> (((op (e3) (e2)) = (e0))\/(((op (e3) (e2)) = (e1))\/(((op (e3) (e2)) = (e2))\/((op (e3) (e2)) = (e3))))) -> ((~((op (e0) (e0)) = (e2)))\/((op (e0) (e2)) = (e0))) -> ((~((op (e1) (e1)) = (e3)))\/((op (e1) (e3)) = (e1))) -> ((~((op (e2) (e2)) = (e1)))\/((op (e2) (e1)) = (e2))) -> ((~((op (e2) (e2)) = (e3)))\/((op (e2) (e3)) = (e2))) -> (~((op (e2) (e1)) = (op (e2) (e3)))) -> (((op (e0) (e1)) = (e3))\/(((op (e1) (e1)) = (e3))\/(((op (e2) (e1)) = (e3))\/((op (e3) (e1)) = (e3))))) -> (~((op (e2) (e0)) = (op (e2) (e3)))) -> (((op (e2) (e0)) = (e0))\/(((op (e2) (e1)) = (e0))\/(((op (e2) (e2)) = (e0))\/((op (e2) (e3)) = (e0))))) -> (((op (e0) (e1)) = (e1))\/(((op (e1) (e1)) = (e1))\/(((op (e2) (e1)) = (e1))\/((op (e3) (e1)) = (e1))))) -> (~((op (e0) (e1)) = (op (e2) (e1)))) -> (~((op (e2) (e1)) = (op (e2) (e2)))) -> (((op (e0) (e0)) = (e3))\/(((op (e0) (e1)) = (e3))\/(((op (e0) (e2)) = (e3))\/((op (e0) (e3)) = (e3))))) -> (~((op (e0) (e3)) = (op (e3) (e3)))) -> (~((op (e0) (e2)) = (op (e2) (e2)))) -> (((op (e2) (e2)) = (e0))\/(((op (e2) (e2)) = (e1))\/(((op (e2) (e2)) = (e2))\/((op (e2) (e2)) = (e3))))) -> (~((e0) = (e3))) -> ((~((op (e3) (e3)) = (e0)))\/((op (e3) (e0)) = (e3))) -> (~((op (e3) (e0)) = (op (e3) (e3)))) -> (((op (e0) (e0)) = (e1))\/(((op (e0) (e1)) = (e1))\/(((op (e0) (e2)) = (e1))\/((op (e0) (e3)) = (e1))))) -> (((op (e0) (e3)) = (e0))\/(((op (e1) (e3)) = (e0))\/(((op (e2) (e3)) = (e0))\/((op (e3) (e3)) = (e0))))) -> (~((op (e0) (e1)) = (op (e0) (e3)))) -> (((op (e0) (e3)) = (e2))\/(((op (e1) (e3)) = (e2))\/(((op (e2) (e3)) = (e2))\/((op (e3) (e3)) = (e2))))) -> (~((e1) = (e3))) -> (~((e0) = (e1))) -> (~((e0) = (e2))) -> (((op (e1) (e0)) = (e2))\/(((op (e1) (e1)) = (e2))\/(((op (e1) (e2)) = (e2))\/((op (e1) (e3)) = (e2))))) -> (~((op (e0) (e3)) = (op (e1) (e3)))) -> (~((op (e1) (e2)) = (op (e2) (e2)))) -> (~((e2) = (e3))) -> (~((op (e0) (e2)) = (op (e1) (e2)))) -> (~((op (e1) (e3)) = (op (e3) (e3)))) -> (((op (e1) (e0)) = (e3))\/(((op (e1) (e1)) = (e3))\/(((op (e1) (e2)) = (e3))\/((op (e1) (e3)) = (e3))))) -> (((op (e0) (e0)) = (e2))\/(((op (e0) (e1)) = (e2))\/(((op (e0) (e2)) = (e2))\/((op (e0) (e3)) = (e2))))) -> (~((op (e3) (e2)) = (op (e3) (e3)))) -> ((~((op (e3) (e3)) = (e2)))\/((op (e3) (e2)) = (e3))) -> ((~((op (e2) (e2)) = (e2)))\/((op (e2) (e2)) = (e2))) -> (~((op (e2) (e0)) = (op (e2) (e1)))) -> (((op (e2) (e0)) = (e3))\/(((op (e2) (e1)) = (e3))\/(((op (e2) (e2)) = (e3))\/((op (e2) (e3)) = (e3))))) -> (~((op (e2) (e3)) = (op (e3) (e3)))) -> ((~((op (e2) (e2)) = (e0)))\/((op (e2) (e0)) = (e2))) -> (~((op (e0) (e1)) = (op (e1) (e1)))) -> (((op (e0) (e0)) = (e3))\/(((op (e1) (e0)) = (e3))\/(((op (e2) (e0)) = (e3))\/((op (e3) (e0)) = (e3))))) -> (~((op (e0) (e2)) = (op (e0) (e3)))) -> (((op (e0) (e2)) = (e3))\/(((op (e1) (e2)) = (e3))\/(((op (e2) (e2)) = (e3))\/((op (e3) (e2)) = (e3))))) -> (((op (e1) (e0)) = (e1))\/(((op (e1) (e1)) = (e1))\/(((op (e1) (e2)) = (e1))\/((op (e1) (e3)) = (e1))))) -> (((op (e0) (e1)) = (e0))\/(((op (e1) (e1)) = (e0))\/(((op (e2) (e1)) = (e0))\/((op (e3) (e1)) = (e0))))) -> (((op (e0) (e0)) = (e0))\/(((op (e1) (e0)) = (e0))\/(((op (e2) (e0)) = (e0))\/((op (e3) (e0)) = (e0))))) -> (((op (e0) (e2)) = (e0))\/(((op (e1) (e2)) = (e0))\/(((op (e2) (e2)) = (e0))\/((op (e3) (e2)) = (e0))))) -> (~((op (e3) (e1)) = (op (e3) (e2)))) -> (~((op (e3) (e0)) = (op (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 (e1) (e1)) = (e0)))\/((op (e1) (e0)) = (e1))) -> (~((op (e1) (e0)) = (op (e1) (e2)))) -> (~((op (e1) (e0)) = (op (e1) (e1)))) -> ((~((op (e1) (e1)) = (e2)))\/((op (e1) (e2)) = (e1))) -> (~((op (e1) (e2)) = (op (e1) (e3)))) -> (~((op (e1) (op (e1) (e1))) = (op (e1) (e1)))) -> ((~((op (e1) (e1)) = (e1)))\/((op (e1) (e1)) = (e1))) -> ((~((op (e0) (e0)) = (e3)))\/((op (e0) (e3)) = (e0))) -> (~((op (e1) (e0)) = (op (e1) (e3)))) -> (((op (e0) (e3)) = (e1))\/(((op (e1) (e3)) = (e1))\/(((op (e2) (e3)) = (e1))\/((op (e3) (e3)) = (e1))))) -> (~((op (e0) (op (e1) (e0))) = (op (e1) (e0)))) -> (((op (e2) (e0)) = (e1))\/(((op (e2) (e1)) = (e1))\/(((op (e2) (e2)) = (e1))\/((op (e2) (e3)) = (e1))))) -> (((op (e0) (e0)) = (e1))\/(((op (e1) (e0)) = (e1))\/(((op (e2) (e0)) = (e1))\/((op (e3) (e0)) = (e1))))) -> (~((op (e3) (e1)) = (op (e3) (e3)))) -> ((~((op (e3) (e3)) = (e1)))\/((op (e3) (e1)) = (e3))) -> (((op (e0) (e0)) = (e0))\/(((op (e0) (e1)) = (e0))\/(((op (e0) (e2)) = (e0))\/((op (e0) (e3)) = (e0))))) -> ((~((op (e3) (e3)) = (e3)))\/((op (e3) (e3)) = (e3))) -> (((op (e0) (e0)) = (e0))\/(((op (e0) (e0)) = (e1))\/(((op (e0) (e0)) = (e2))\/((op (e0) (e0)) = (e3))))) -> (((op (e0) (e1)) = (e2))\/(((op (e1) (e1)) = (e2))\/(((op (e2) (e1)) = (e2))\/((op (e3) (e1)) = (e2))))) -> (~((op (e2) (e2)) = (op (e2) (e3)))) -> (((op (e3) (e0)) = (e1))\/(((op (e3) (e1)) = (e1))\/(((op (e3) (e2)) = (e1))\/((op (e3) (e3)) = (e1))))) -> (~((op (e0) (e2)) = (op (e3) (e2)))) -> (~((op (e3) (op (e1) (e3))) = (op (e1) (e3)))) -> (((op (e2) (e0)) = (e2))\/(((op (e2) (e1)) = (e2))\/(((op (e2) (e2)) = (e2))\/((op (e2) (e3)) = (e2))))) -> (((op (e0) (e2)) = (e0))\/(((op (e0) (e2)) = (e1))\/(((op (e0) (e2)) = (e2))\/((op (e0) (e2)) = (e3))))) -> (((op (e3) (e0)) = (e2))\/(((op (e3) (e1)) = (e2))\/(((op (e3) (e2)) = (e2))\/((op (e3) (e3)) = (e2))))) -> (((op (e0) (e2)) = (e2))\/(((op (e1) (e2)) = (e2))\/(((op (e2) (e2)) = (e2))\/((op (e3) (e2)) = (e2))))) -> (~((op (e2) (e1)) = (op (e3) (e1)))) -> (((op (e0) (e2)) = (e1))\/(((op (e1) (e2)) = (e1))\/(((op (e2) (e2)) = (e1))\/((op (e3) (e2)) = (e1))))) -> (~((op (e2) (op (e1) (e2))) = (op (e1) (e2)))) -> (((op (e1) (e0)) = (e0))\/(((op (e1) (e1)) = (e0))\/(((op (e1) (e2)) = (e0))\/((op (e1) (e3)) = (e0))))) -> (~((op (e3) (e0)) = (op (e3) (e2)))) -> (~((op (e1) (e2)) = (op (e3) (e2)))) -> (~((op (e1) (e0)) = (op (e3) (e0)))) -> (~((op (e0) (e1)) = (op (e0) (e2)))) -> ((~((op (e0) (e0)) = (e1)))\/((op (e0) (e1)) = (e0))) -> False). % 15.36/15.53 do 0 intro. intros zenon_Heb zenon_H3b zenon_H1b3 zenon_H35 zenon_H17a zenon_Hd8 zenon_Ha7 zenon_H8f zenon_H249 zenon_H25a zenon_H25b zenon_H24c zenon_H258 zenon_H244 zenon_H24f zenon_Hb4 zenon_H254 zenon_H250 zenon_H25e zenon_H24a zenon_H1d2 zenon_H1e3 zenon_H1c3 zenon_H1e2 zenon_H199 zenon_Hce zenon_H1f5 zenon_H228 zenon_Hde zenon_H157 zenon_H58 zenon_H36 zenon_H28 zenon_H2d zenon_H4b zenon_H10f zenon_Hbb zenon_H44 zenon_Hd3 zenon_H1cd zenon_H160 zenon_Ha3 zenon_H9e zenon_H5e zenon_H84 zenon_H80 zenon_H7d zenon_H6a zenon_H87 zenon_H8b zenon_H90 zenon_H8e zenon_H173 zenon_H10e zenon_Haa zenon_H154 zenon_He6 zenon_He3 zenon_H1d4 zenon_H23 zenon_Hbe zenon_Hc9 zenon_H175 zenon_H1c5 zenon_H144 zenon_Hf0 zenon_H16f zenon_H135 zenon_H109 zenon_H138 zenon_H16c zenon_H1e4 zenon_H166 zenon_Hd7 zenon_H1d3 zenon_H1d0 zenon_H27b zenon_H1d8 zenon_H236 zenon_H1cf zenon_H121 zenon_H261 zenon_Hb7 zenon_Hf1 zenon_H12d zenon_H10c zenon_H110 zenon_H10d zenon_H12a zenon_H1a2 zenon_H15f zenon_H146 zenon_H140 zenon_H26e zenon_H237 zenon_H251 zenon_H1df zenon_H27c zenon_H13c zenon_H11b zenon_H277 zenon_H163 zenon_H105 zenon_H17d zenon_H22e zenon_H23e zenon_H24b. % 15.36/15.53 apply (zenon_or_s _ _ zenon_H1d8); [ zenon_intro zenon_H1b4 | zenon_intro zenon_H21 ]. % 15.36/15.53 apply (zenon_or_s _ _ zenon_H1d3); [ zenon_intro zenon_Hd6 | zenon_intro zenon_H117 ]. % 15.36/15.53 apply (zenon_L751_); trivial. % 15.36/15.53 apply (zenon_L248_); trivial. % 15.36/15.53 apply (zenon_L61_); trivial. % 15.36/15.53 (* end of lemma zenon_L775_ *) % 15.36/15.53 assert (zenon_L776_ : (~((op (e3) (op (e2) (e3))) = (op (e2) (e3)))) -> ((op (e3) (e3)) = (e3)) -> ((op (e2) (e3)) = (e3)) -> False). % 15.36/15.53 do 0 intro. intros zenon_H28a zenon_H42 zenon_He2. % 15.36/15.53 cut (((op (e3) (e3)) = (e3)) = ((op (e3) (op (e2) (e3))) = (op (e2) (e3)))). % 15.36/15.53 intro zenon_D_pnotp. % 15.36/15.53 apply zenon_H28a. % 15.36/15.53 rewrite <- zenon_D_pnotp. % 15.36/15.53 exact zenon_H42. % 15.36/15.53 cut (((e3) = (op (e2) (e3)))); [idtac | apply NNPP; zenon_intro zenon_He5]. % 15.36/15.53 cut (((op (e3) (e3)) = (op (e3) (op (e2) (e3))))); [idtac | apply NNPP; zenon_intro zenon_H28b]. % 15.36/15.53 congruence. % 15.36/15.53 elim (classic ((op (e3) (op (e2) (e3))) = (op (e3) (op (e2) (e3))))); [ zenon_intro zenon_H28c | zenon_intro zenon_H28d ]. % 15.36/15.53 cut (((op (e3) (op (e2) (e3))) = (op (e3) (op (e2) (e3)))) = ((op (e3) (e3)) = (op (e3) (op (e2) (e3))))). % 15.36/15.53 intro zenon_D_pnotp. % 15.36/15.53 apply zenon_H28b. % 15.36/15.53 rewrite <- zenon_D_pnotp. % 15.36/15.53 exact zenon_H28c. % 15.36/15.53 cut (((op (e3) (op (e2) (e3))) = (op (e3) (op (e2) (e3))))); [idtac | apply NNPP; zenon_intro zenon_H28d]. % 15.36/15.53 cut (((op (e3) (op (e2) (e3))) = (op (e3) (e3)))); [idtac | apply NNPP; zenon_intro zenon_H28e]. % 15.36/15.53 congruence. % 15.36/15.53 cut (((op (e2) (e3)) = (e3))); [idtac | apply NNPP; zenon_intro zenon_H129]. % 15.36/15.53 cut (((e3) = (e3))); [idtac | apply NNPP; zenon_intro zenon_H4d]. % 15.36/15.53 congruence. % 15.36/15.53 apply zenon_H4d. apply refl_equal. % 15.36/15.53 exact (zenon_H129 zenon_He2). % 15.36/15.53 apply zenon_H28d. apply refl_equal. % 15.36/15.53 apply zenon_H28d. apply refl_equal. % 15.36/15.53 apply zenon_He5. apply sym_equal. exact zenon_He2. % 15.36/15.53 (* end of lemma zenon_L776_ *) % 15.36/15.53 assert (zenon_L777_ : (((op (e2) (e0)) = (e3))\/(((op (e2) (e1)) = (e3))\/(((op (e2) (e2)) = (e3))\/((op (e2) (e3)) = (e3))))) -> (~((e2) = (e3))) -> ((op (e2) (e0)) = (e2)) -> ((op (e0) (e1)) = (e3)) -> (~((op (e0) (e1)) = (op (e2) (e1)))) -> (~((op (e2) (e2)) = (e3))) -> (~((op (e3) (op (e2) (e3))) = (op (e2) (e3)))) -> ((op (e3) (e3)) = (e3)) -> False). % 15.36/15.53 do 0 intro. intros zenon_He6 zenon_H6a zenon_Hdd zenon_H4a zenon_Hde zenon_H30 zenon_H28a zenon_H42. % 15.36/15.53 apply (zenon_or_s _ _ zenon_He6); [ zenon_intro zenon_Haf | zenon_intro zenon_He7 ]. % 15.36/15.53 apply (zenon_L64_); trivial. % 15.36/15.53 apply (zenon_or_s _ _ zenon_He7); [ zenon_intro zenon_Hdf | zenon_intro zenon_He8 ]. % 15.36/15.53 apply (zenon_L65_); trivial. % 15.36/15.53 apply (zenon_or_s _ _ zenon_He8); [ zenon_intro zenon_H34 | zenon_intro zenon_He2 ]. % 15.36/15.53 exact (zenon_H30 zenon_H34). % 15.36/15.53 apply (zenon_L776_); trivial. % 15.36/15.53 (* end of lemma zenon_L777_ *) % 15.36/15.53 assert (zenon_L778_ : (((op (e0) (e0)) = (e3))\/(((op (e0) (e1)) = (e3))\/(((op (e0) (e2)) = (e3))\/((op (e0) (e3)) = (e3))))) -> (~((op (e0) (e0)) = (e3))) -> (~((op (e3) (op (e2) (e3))) = (op (e2) (e3)))) -> (~((op (e2) (e2)) = (e3))) -> (~((op (e0) (e1)) = (op (e2) (e1)))) -> ((op (e2) (e0)) = (e2)) -> (~((e2) = (e3))) -> (((op (e2) (e0)) = (e3))\/(((op (e2) (e1)) = (e3))\/(((op (e2) (e2)) = (e3))\/((op (e2) (e3)) = (e3))))) -> (~((op (e1) (e3)) = (op (e3) (e3)))) -> (~((op (e0) (e2)) = (op (e1) (e2)))) -> (~((op (e1) (e1)) = (e3))) -> ((op (e1) (e0)) = (e1)) -> (~((e1) = (e3))) -> (((op (e1) (e0)) = (e3))\/(((op (e1) (e1)) = (e3))\/(((op (e1) (e2)) = (e3))\/((op (e1) (e3)) = (e3))))) -> ((op (e3) (e3)) = (e3)) -> (~((op (e0) (e3)) = (op (e3) (e3)))) -> False). % 15.36/15.53 do 0 intro. intros zenon_H58 zenon_H59 zenon_H28a zenon_H30 zenon_Hde zenon_Hdd zenon_H6a zenon_He6 zenon_H8b zenon_H87 zenon_H182 zenon_Hd8 zenon_Ha3 zenon_H90 zenon_H42 zenon_H36. % 15.36/15.53 apply (zenon_or_s _ _ zenon_H58); [ zenon_intro zenon_H5b | zenon_intro zenon_H5a ]. % 15.36/15.53 exact (zenon_H59 zenon_H5b). % 15.36/15.53 apply (zenon_or_s _ _ zenon_H5a); [ zenon_intro zenon_H4a | zenon_intro zenon_H5c ]. % 15.36/15.53 apply (zenon_L777_); trivial. % 15.36/15.53 apply (zenon_or_s _ _ zenon_H5c); [ zenon_intro zenon_H50 | zenon_intro zenon_H53 ]. % 15.36/15.53 apply (zenon_L226_); trivial. % 15.36/15.53 apply (zenon_L12_); trivial. % 15.36/15.53 (* end of lemma zenon_L778_ *) % 15.36/15.53 assert (zenon_L779_ : ((~((op (e2) (e2)) = (e3)))\/((op (e2) (e3)) = (e2))) -> (~((op (e2) (e0)) = (op (e2) (e3)))) -> (~((op (e0) (e0)) = (e3))) -> (((op (e2) (e0)) = (e3))\/(((op (e2) (e1)) = (e3))\/(((op (e2) (e2)) = (e3))\/((op (e2) (e3)) = (e3))))) -> ((op (e3) (e3)) = (e3)) -> (~((op (e3) (op (e2) (e3))) = (op (e2) (e3)))) -> (~((op (e0) (e1)) = (op (e2) (e1)))) -> ((op (e2) (e0)) = (e2)) -> (~((e2) = (e3))) -> (((op (e1) (e0)) = (e3))\/(((op (e1) (e1)) = (e3))\/(((op (e1) (e2)) = (e3))\/((op (e1) (e3)) = (e3))))) -> (~((op (e1) (e3)) = (op (e3) (e3)))) -> (~((op (e0) (e2)) = (op (e1) (e2)))) -> (~((op (e1) (e1)) = (e3))) -> ((op (e1) (e0)) = (e1)) -> (~((e1) = (e3))) -> (~((op (e0) (e3)) = (op (e3) (e3)))) -> (((op (e0) (e0)) = (e3))\/(((op (e0) (e1)) = (e3))\/(((op (e0) (e2)) = (e3))\/((op (e0) (e3)) = (e3))))) -> False). % 15.36/15.53 do 0 intro. intros zenon_H1c3 zenon_Hce zenon_H59 zenon_He6 zenon_H42 zenon_H28a zenon_Hde zenon_Hdd zenon_H6a zenon_H90 zenon_H8b zenon_H87 zenon_H182 zenon_Hd8 zenon_Ha3 zenon_H36 zenon_H58. % 15.36/15.53 apply (zenon_or_s _ _ zenon_H1c3); [ zenon_intro zenon_H30 | zenon_intro zenon_H124 ]. % 15.36/15.53 apply (zenon_L778_); trivial. % 15.36/15.53 apply (zenon_L119_); trivial. % 15.36/15.53 (* end of lemma zenon_L779_ *) % 15.36/15.53 assert (zenon_L780_ : (((op (e0) (e0)) = (e2))\/(((op (e1) (e0)) = (e2))\/(((op (e2) (e0)) = (e2))\/((op (e3) (e0)) = (e2))))) -> (~((op (e0) (e0)) = (e2))) -> (~((e1) = (e2))) -> (((op (e0) (e0)) = (e3))\/(((op (e0) (e1)) = (e3))\/(((op (e0) (e2)) = (e3))\/((op (e0) (e3)) = (e3))))) -> (~((op (e0) (e3)) = (op (e3) (e3)))) -> (~((e1) = (e3))) -> ((op (e1) (e0)) = (e1)) -> (~((op (e1) (e1)) = (e3))) -> (~((op (e0) (e2)) = (op (e1) (e2)))) -> (~((op (e1) (e3)) = (op (e3) (e3)))) -> (((op (e1) (e0)) = (e3))\/(((op (e1) (e1)) = (e3))\/(((op (e1) (e2)) = (e3))\/((op (e1) (e3)) = (e3))))) -> (~((op (e0) (e1)) = (op (e2) (e1)))) -> (~((op (e3) (op (e2) (e3))) = (op (e2) (e3)))) -> ((op (e3) (e3)) = (e3)) -> (((op (e2) (e0)) = (e3))\/(((op (e2) (e1)) = (e3))\/(((op (e2) (e2)) = (e3))\/((op (e2) (e3)) = (e3))))) -> (~((op (e0) (e0)) = (e3))) -> (~((op (e2) (e0)) = (op (e2) (e3)))) -> ((~((op (e2) (e2)) = (e3)))\/((op (e2) (e3)) = (e2))) -> (~((e2) = (e3))) -> ((op (e3) (e0)) = (e3)) -> False). % 15.36/15.53 do 0 intro. intros zenon_Heb zenon_H8f zenon_Ha7 zenon_H58 zenon_H36 zenon_Ha3 zenon_Hd8 zenon_H182 zenon_H87 zenon_H8b zenon_H90 zenon_Hde zenon_H28a zenon_H42 zenon_He6 zenon_H59 zenon_Hce zenon_H1c3 zenon_H6a zenon_Hba. % 15.36/15.53 apply (zenon_or_s _ _ zenon_Heb); [ zenon_intro zenon_H92 | zenon_intro zenon_Hec ]. % 15.36/15.53 exact (zenon_H8f zenon_H92). % 15.36/15.53 apply (zenon_or_s _ _ zenon_Hec); [ zenon_intro zenon_H68 | zenon_intro zenon_Hed ]. % 15.36/15.53 apply (zenon_L162_); trivial. % 15.36/15.53 apply (zenon_or_s _ _ zenon_Hed); [ zenon_intro zenon_Hdd | zenon_intro zenon_He9 ]. % 15.36/15.53 apply (zenon_L779_); trivial. % 15.36/15.53 apply (zenon_L220_); trivial. % 15.36/15.53 (* end of lemma zenon_L780_ *) % 15.36/15.53 assert (zenon_L781_ : (((op (e0) (e0)) = (e3))\/(((op (e1) (e0)) = (e3))\/(((op (e2) (e0)) = (e3))\/((op (e3) (e0)) = (e3))))) -> (~((op (e1) (e1)) = (e2))) -> (~((op (e1) (e1)) = (e1))) -> (((op (e2) (e2)) = (e0))\/(((op (e2) (e2)) = (e1))\/(((op (e2) (e2)) = (e2))\/((op (e2) (e2)) = (e3))))) -> (~((op (e2) (e2)) = (e0))) -> (~((op (e2) (e2)) = (e2))) -> (~((op (e2) (e2)) = (e3))) -> (((op (e1) (e1)) = (e0))\/(((op (e1) (e1)) = (e1))\/(((op (e1) (e1)) = (e2))\/((op (e1) (e1)) = (e3))))) -> (((op (e0) (e0)) = (e2))\/(((op (e1) (e0)) = (e2))\/(((op (e2) (e0)) = (e2))\/((op (e3) (e0)) = (e2))))) -> (~((op (e0) (e0)) = (e2))) -> (~((e1) = (e2))) -> (((op (e0) (e0)) = (e3))\/(((op (e0) (e1)) = (e3))\/(((op (e0) (e2)) = (e3))\/((op (e0) (e3)) = (e3))))) -> (~((op (e0) (e3)) = (op (e3) (e3)))) -> (~((e1) = (e3))) -> ((op (e1) (e0)) = (e1)) -> (~((op (e1) (e1)) = (e3))) -> (~((op (e0) (e2)) = (op (e1) (e2)))) -> (~((op (e1) (e3)) = (op (e3) (e3)))) -> (((op (e1) (e0)) = (e3))\/(((op (e1) (e1)) = (e3))\/(((op (e1) (e2)) = (e3))\/((op (e1) (e3)) = (e3))))) -> (~((op (e0) (e1)) = (op (e2) (e1)))) -> (~((op (e3) (op (e2) (e3))) = (op (e2) (e3)))) -> ((op (e3) (e3)) = (e3)) -> (((op (e2) (e0)) = (e3))\/(((op (e2) (e1)) = (e3))\/(((op (e2) (e2)) = (e3))\/((op (e2) (e3)) = (e3))))) -> (~((op (e0) (e0)) = (e3))) -> (~((op (e2) (e0)) = (op (e2) (e3)))) -> ((~((op (e2) (e2)) = (e3)))\/((op (e2) (e3)) = (e2))) -> (~((e2) = (e3))) -> False). % 15.36/15.53 do 0 intro. intros zenon_Hbe zenon_Hd6 zenon_H1b4 zenon_H2d zenon_H2e zenon_H2f zenon_H30 zenon_H1b3 zenon_Heb zenon_H8f zenon_Ha7 zenon_H58 zenon_H36 zenon_Ha3 zenon_Hd8 zenon_H182 zenon_H87 zenon_H8b zenon_H90 zenon_Hde zenon_H28a zenon_H42 zenon_He6 zenon_H59 zenon_Hce zenon_H1c3 zenon_H6a. % 15.36/15.53 apply (zenon_or_s _ _ zenon_Hbe); [ zenon_intro zenon_H5b | zenon_intro zenon_Hbf ]. % 15.36/15.53 exact (zenon_H59 zenon_H5b). % 15.36/15.53 apply (zenon_or_s _ _ zenon_Hbf); [ zenon_intro zenon_H69 | zenon_intro zenon_Hc0 ]. % 15.36/15.53 apply (zenon_L163_); trivial. % 15.36/15.53 apply (zenon_or_s _ _ zenon_Hc0); [ zenon_intro zenon_Haf | zenon_intro zenon_Hba ]. % 15.36/15.53 apply (zenon_L219_); trivial. % 15.36/15.53 apply (zenon_L780_); trivial. % 15.36/15.53 (* end of lemma zenon_L781_ *) % 15.36/15.53 assert (zenon_L782_ : (~((op (e1) (op (e2) (e1))) = (op (e1) (e0)))) -> ((op (e2) (e1)) = (e0)) -> False). % 15.36/15.53 do 0 intro. intros zenon_H28f zenon_H14a. % 15.36/15.53 cut (((op (e2) (e1)) = (e0))); [idtac | apply NNPP; zenon_intro zenon_H21b]. % 15.36/15.53 cut (((e1) = (e1))); [idtac | apply NNPP; zenon_intro zenon_Ha0]. % 15.36/15.53 congruence. % 15.36/15.53 apply zenon_Ha0. apply refl_equal. % 15.36/15.53 exact (zenon_H21b zenon_H14a). % 15.36/15.53 (* end of lemma zenon_L782_ *) % 15.36/15.53 assert (zenon_L783_ : (~((op (e1) (op (e2) (e1))) = (op (e2) (e1)))) -> ((op (e1) (e0)) = (e1)) -> ((op (e2) (e1)) = (e0)) -> ((op (e2) (e1)) = (e1)) -> False). % 15.36/15.53 do 0 intro. intros zenon_H290 zenon_Hd8 zenon_H14a zenon_Hb2. % 15.36/15.53 cut (((op (e1) (e0)) = (e1)) = ((op (e1) (op (e2) (e1))) = (op (e2) (e1)))). % 15.36/15.53 intro zenon_D_pnotp. % 15.36/15.53 apply zenon_H290. % 15.36/15.53 rewrite <- zenon_D_pnotp. % 15.36/15.53 exact zenon_Hd8. % 15.36/15.53 cut (((e1) = (op (e2) (e1)))); [idtac | apply NNPP; zenon_intro zenon_Hb3]. % 15.36/15.53 cut (((op (e1) (e0)) = (op (e1) (op (e2) (e1))))); [idtac | apply NNPP; zenon_intro zenon_H291]. % 15.36/15.53 congruence. % 15.36/15.53 elim (classic ((op (e1) (op (e2) (e1))) = (op (e1) (op (e2) (e1))))); [ zenon_intro zenon_H292 | zenon_intro zenon_H293 ]. % 15.36/15.53 cut (((op (e1) (op (e2) (e1))) = (op (e1) (op (e2) (e1)))) = ((op (e1) (e0)) = (op (e1) (op (e2) (e1))))). % 15.36/15.53 intro zenon_D_pnotp. % 15.36/15.53 apply zenon_H291. % 15.36/15.53 rewrite <- zenon_D_pnotp. % 15.36/15.53 exact zenon_H292. % 15.36/15.53 cut (((op (e1) (op (e2) (e1))) = (op (e1) (op (e2) (e1))))); [idtac | apply NNPP; zenon_intro zenon_H293]. % 15.36/15.53 cut (((op (e1) (op (e2) (e1))) = (op (e1) (e0)))); [idtac | apply NNPP; zenon_intro zenon_H28f]. % 15.36/15.53 congruence. % 15.36/15.53 apply (zenon_L782_); trivial. % 15.36/15.53 apply zenon_H293. apply refl_equal. % 15.36/15.53 apply zenon_H293. apply refl_equal. % 15.36/15.53 apply zenon_Hb3. apply sym_equal. exact zenon_Hb2. % 15.36/15.53 (* end of lemma zenon_L783_ *) % 15.36/15.53 assert (zenon_L784_ : (((op (e2) (e0)) = (e1))\/(((op (e2) (e1)) = (e1))\/(((op (e2) (e2)) = (e1))\/((op (e2) (e3)) = (e1))))) -> (~((e1) = (e3))) -> ((op (e2) (e0)) = (e3)) -> ((op (e2) (e1)) = (e0)) -> ((op (e1) (e0)) = (e1)) -> (~((op (e1) (op (e2) (e1))) = (op (e2) (e1)))) -> (~((op (e2) (e2)) = (e1))) -> (~((e1) = (e2))) -> ((op (e2) (e3)) = (e2)) -> False). % 15.36/15.53 do 0 intro. intros zenon_Hb7 zenon_Ha3 zenon_Haf zenon_H14a zenon_Hd8 zenon_H290 zenon_H52 zenon_Ha7 zenon_H124. % 15.36/15.53 apply (zenon_or_s _ _ zenon_Hb7); [ zenon_intro zenon_Hae | zenon_intro zenon_Hb8 ]. % 15.36/15.53 apply (zenon_L39_); trivial. % 15.36/15.53 apply (zenon_or_s _ _ zenon_Hb8); [ zenon_intro zenon_Hb2 | zenon_intro zenon_Hb9 ]. % 15.36/15.53 apply (zenon_L783_); trivial. % 15.36/15.53 apply (zenon_or_s _ _ zenon_Hb9); [ zenon_intro zenon_H2a | zenon_intro zenon_Hb5 ]. % 15.36/15.53 exact (zenon_H52 zenon_H2a). % 15.36/15.53 apply (zenon_L93_); trivial. % 15.36/15.53 (* end of lemma zenon_L784_ *) % 15.36/15.53 assert (zenon_L785_ : (((op (e0) (e0)) = (e3))\/(((op (e1) (e0)) = (e3))\/(((op (e2) (e0)) = (e3))\/((op (e3) (e0)) = (e3))))) -> ((op (e2) (e3)) = (e2)) -> (~((e0) = (e2))) -> (~((op (e2) (e2)) = (e0))) -> (((op (e2) (e0)) = (e1))\/(((op (e2) (e1)) = (e1))\/(((op (e2) (e2)) = (e1))\/((op (e2) (e3)) = (e1))))) -> (~((op (e1) (op (e2) (e1))) = (op (e2) (e1)))) -> (~((op (e2) (e2)) = (e1))) -> (~((op (e0) (e0)) = (op (e2) (e0)))) -> ((op (e0) (e0)) = (e0)) -> (((op (e2) (e0)) = (e0))\/(((op (e2) (e1)) = (e0))\/(((op (e2) (e2)) = (e0))\/((op (e2) (e3)) = (e0))))) -> (((op (e0) (e0)) = (e2))\/(((op (e1) (e0)) = (e2))\/(((op (e2) (e0)) = (e2))\/((op (e3) (e0)) = (e2))))) -> (~((op (e0) (e0)) = (e2))) -> (~((e1) = (e2))) -> (((op (e0) (e0)) = (e3))\/(((op (e0) (e1)) = (e3))\/(((op (e0) (e2)) = (e3))\/((op (e0) (e3)) = (e3))))) -> (~((op (e0) (e3)) = (op (e3) (e3)))) -> (~((e1) = (e3))) -> ((op (e1) (e0)) = (e1)) -> (~((op (e1) (e1)) = (e3))) -> (~((op (e0) (e2)) = (op (e1) (e2)))) -> (~((op (e1) (e3)) = (op (e3) (e3)))) -> (((op (e1) (e0)) = (e3))\/(((op (e1) (e1)) = (e3))\/(((op (e1) (e2)) = (e3))\/((op (e1) (e3)) = (e3))))) -> (~((op (e0) (e1)) = (op (e2) (e1)))) -> (~((op (e3) (op (e2) (e3))) = (op (e2) (e3)))) -> ((op (e3) (e3)) = (e3)) -> (((op (e2) (e0)) = (e3))\/(((op (e2) (e1)) = (e3))\/(((op (e2) (e2)) = (e3))\/((op (e2) (e3)) = (e3))))) -> (~((op (e0) (e0)) = (e3))) -> (~((op (e2) (e0)) = (op (e2) (e3)))) -> ((~((op (e2) (e2)) = (e3)))\/((op (e2) (e3)) = (e2))) -> (~((e2) = (e3))) -> False). % 15.36/15.53 do 0 intro. intros zenon_Hbe zenon_H124 zenon_H5e zenon_H2e zenon_Hb7 zenon_H290 zenon_H52 zenon_H258 zenon_H1f zenon_H1f5 zenon_Heb zenon_H8f zenon_Ha7 zenon_H58 zenon_H36 zenon_Ha3 zenon_Hd8 zenon_H182 zenon_H87 zenon_H8b zenon_H90 zenon_Hde zenon_H28a zenon_H42 zenon_He6 zenon_H59 zenon_Hce zenon_H1c3 zenon_H6a. % 15.36/15.53 apply (zenon_or_s _ _ zenon_Hbe); [ zenon_intro zenon_H5b | zenon_intro zenon_Hbf ]. % 15.36/15.53 exact (zenon_H59 zenon_H5b). % 15.36/15.53 apply (zenon_or_s _ _ zenon_Hbf); [ zenon_intro zenon_H69 | zenon_intro zenon_Hc0 ]. % 15.36/15.53 apply (zenon_L163_); trivial. % 15.36/15.53 apply (zenon_or_s _ _ zenon_Hc0); [ zenon_intro zenon_Haf | zenon_intro zenon_Hba ]. % 15.36/15.53 apply (zenon_or_s _ _ zenon_H1f5); [ zenon_intro zenon_Hcf | zenon_intro zenon_H1f9 ]. % 15.36/15.53 apply (zenon_L598_); trivial. % 15.36/15.53 apply (zenon_or_s _ _ zenon_H1f9); [ zenon_intro zenon_H14a | zenon_intro zenon_H1fa ]. % 15.36/15.53 apply (zenon_L784_); trivial. % 15.36/15.53 apply (zenon_or_s _ _ zenon_H1fa); [ zenon_intro zenon_H32 | zenon_intro zenon_Hd0 ]. % 15.36/15.53 exact (zenon_H2e zenon_H32). % 15.36/15.53 apply (zenon_L201_); trivial. % 15.36/15.53 apply (zenon_L780_); trivial. % 15.36/15.53 (* end of lemma zenon_L785_ *) % 15.36/15.53 assert (zenon_L786_ : (((op (e2) (e0)) = (e0))\/(((op (e2) (e1)) = (e0))\/(((op (e2) (e2)) = (e0))\/((op (e2) (e3)) = (e0))))) -> (~((e0) = (e2))) -> (~((op (e1) (op (e2) (e1))) = (op (e2) (e1)))) -> (~((op (e2) (e2)) = (e1))) -> (((op (e2) (e0)) = (e1))\/(((op (e2) (e1)) = (e1))\/(((op (e2) (e2)) = (e1))\/((op (e2) (e3)) = (e1))))) -> ((op (e0) (e0)) = (e0)) -> (~((op (e0) (e0)) = (op (e2) (e0)))) -> (~((op (e0) (e0)) = (e3))) -> (~((e1) = (e3))) -> ((op (e1) (e0)) = (e1)) -> (((op (e1) (e1)) = (e0))\/(((op (e1) (e1)) = (e1))\/(((op (e1) (e1)) = (e2))\/((op (e1) (e1)) = (e3))))) -> (~((op (e1) (e1)) = (e3))) -> (~((op (e1) (e1)) = (e2))) -> (~((op (e1) (e1)) = (e1))) -> (~((op (e2) (e2)) = (e0))) -> (~((op (e2) (e2)) = (e2))) -> (((op (e2) (e2)) = (e0))\/(((op (e2) (e2)) = (e1))\/(((op (e2) (e2)) = (e2))\/((op (e2) (e2)) = (e3))))) -> (((op (e0) (e0)) = (e2))\/(((op (e1) (e0)) = (e2))\/(((op (e2) (e0)) = (e2))\/((op (e3) (e0)) = (e2))))) -> (((op (e0) (e0)) = (e3))\/(((op (e0) (e1)) = (e3))\/(((op (e0) (e2)) = (e3))\/((op (e0) (e3)) = (e3))))) -> (~((op (e0) (e3)) = (op (e3) (e3)))) -> (~((op (e0) (e2)) = (op (e1) (e2)))) -> (~((op (e1) (e3)) = (op (e3) (e3)))) -> (((op (e1) (e0)) = (e3))\/(((op (e1) (e1)) = (e3))\/(((op (e1) (e2)) = (e3))\/((op (e1) (e3)) = (e3))))) -> (~((e2) = (e3))) -> (~((op (e0) (e1)) = (op (e2) (e1)))) -> (~((op (e3) (op (e2) (e3))) = (op (e2) (e3)))) -> ((op (e3) (e3)) = (e3)) -> (((op (e2) (e0)) = (e3))\/(((op (e2) (e1)) = (e3))\/(((op (e2) (e2)) = (e3))\/((op (e2) (e3)) = (e3))))) -> (~((op (e2) (e0)) = (op (e2) (e3)))) -> ((~((op (e2) (e2)) = (e3)))\/((op (e2) (e3)) = (e2))) -> (~((e1) = (e2))) -> (~((op (e0) (e0)) = (e2))) -> (((op (e0) (e0)) = (e3))\/(((op (e1) (e0)) = (e3))\/(((op (e2) (e0)) = (e3))\/((op (e3) (e0)) = (e3))))) -> False). % 15.36/15.53 do 0 intro. intros zenon_H1f5 zenon_H5e zenon_H290 zenon_H52 zenon_Hb7 zenon_H1f zenon_H258 zenon_H59 zenon_Ha3 zenon_Hd8 zenon_H1b3 zenon_H182 zenon_Hd6 zenon_H1b4 zenon_H2e zenon_H2f zenon_H2d zenon_Heb zenon_H58 zenon_H36 zenon_H87 zenon_H8b zenon_H90 zenon_H6a zenon_Hde zenon_H28a zenon_H42 zenon_He6 zenon_Hce zenon_H1c3 zenon_Ha7 zenon_H8f zenon_Hbe. % 15.36/15.53 apply (zenon_or_s _ _ zenon_H1c3); [ zenon_intro zenon_H30 | zenon_intro zenon_H124 ]. % 15.36/15.53 apply (zenon_L781_); trivial. % 15.36/15.53 apply (zenon_L785_); trivial. % 15.36/15.53 (* end of lemma zenon_L786_ *) % 15.36/15.53 assert (zenon_L787_ : (((op (e2) (e0)) = (e3))\/(((op (e2) (e1)) = (e3))\/(((op (e2) (e2)) = (e3))\/((op (e2) (e3)) = (e3))))) -> (~((e1) = (e3))) -> ((op (e2) (e0)) = (e1)) -> ((op (e0) (e1)) = (e3)) -> (~((op (e0) (e1)) = (op (e2) (e1)))) -> (~((op (e2) (e2)) = (e3))) -> (~((op (e3) (op (e2) (e3))) = (op (e2) (e3)))) -> ((op (e3) (e3)) = (e3)) -> False). % 15.36/15.53 do 0 intro. intros zenon_He6 zenon_Ha3 zenon_Hae zenon_H4a zenon_Hde zenon_H30 zenon_H28a zenon_H42. % 15.36/15.53 apply (zenon_or_s _ _ zenon_He6); [ zenon_intro zenon_Haf | zenon_intro zenon_He7 ]. % 15.36/15.53 apply (zenon_L39_); trivial. % 15.36/15.53 apply (zenon_or_s _ _ zenon_He7); [ zenon_intro zenon_Hdf | zenon_intro zenon_He8 ]. % 15.36/15.53 apply (zenon_L65_); trivial. % 15.36/15.53 apply (zenon_or_s _ _ zenon_He8); [ zenon_intro zenon_H34 | zenon_intro zenon_He2 ]. % 15.36/15.53 exact (zenon_H30 zenon_H34). % 15.36/15.53 apply (zenon_L776_); trivial. % 15.36/15.53 (* end of lemma zenon_L787_ *) % 15.36/15.53 assert (zenon_L788_ : (((op (e0) (e0)) = (e3))\/(((op (e0) (e1)) = (e3))\/(((op (e0) (e2)) = (e3))\/((op (e0) (e3)) = (e3))))) -> (~((op (e0) (e0)) = (e3))) -> (~((op (e3) (op (e2) (e3))) = (op (e2) (e3)))) -> (~((op (e2) (e2)) = (e3))) -> (~((op (e0) (e1)) = (op (e2) (e1)))) -> ((op (e2) (e0)) = (e1)) -> (~((e1) = (e3))) -> (((op (e2) (e0)) = (e3))\/(((op (e2) (e1)) = (e3))\/(((op (e2) (e2)) = (e3))\/((op (e2) (e3)) = (e3))))) -> (~((op (e0) (e2)) = (op (e2) (e2)))) -> (~((op (e2) (e2)) = (e2))) -> (~((op (e2) (e2)) = (e1))) -> (~((op (e2) (e2)) = (e0))) -> (((op (e2) (e2)) = (e0))\/(((op (e2) (e2)) = (e1))\/(((op (e2) (e2)) = (e2))\/((op (e2) (e2)) = (e3))))) -> ((op (e3) (e3)) = (e3)) -> (~((op (e0) (e3)) = (op (e3) (e3)))) -> False). % 15.36/15.53 do 0 intro. intros zenon_H58 zenon_H59 zenon_H28a zenon_H30 zenon_Hde zenon_Hae zenon_Ha3 zenon_He6 zenon_H28 zenon_H2f zenon_H52 zenon_H2e zenon_H2d zenon_H42 zenon_H36. % 15.36/15.53 apply (zenon_or_s _ _ zenon_H58); [ zenon_intro zenon_H5b | zenon_intro zenon_H5a ]. % 15.36/15.53 exact (zenon_H59 zenon_H5b). % 15.36/15.53 apply (zenon_or_s _ _ zenon_H5a); [ zenon_intro zenon_H4a | zenon_intro zenon_H5c ]. % 15.36/15.53 apply (zenon_L787_); trivial. % 15.36/15.53 apply (zenon_or_s _ _ zenon_H5c); [ zenon_intro zenon_H50 | zenon_intro zenon_H53 ]. % 15.36/15.53 apply (zenon_L11_); trivial. % 15.36/15.53 apply (zenon_L12_); trivial. % 15.36/15.53 (* end of lemma zenon_L788_ *) % 15.36/15.53 assert (zenon_L789_ : (((op (e0) (e0)) = (e3))\/(((op (e0) (e1)) = (e3))\/(((op (e0) (e2)) = (e3))\/((op (e0) (e3)) = (e3))))) -> (~((op (e0) (e0)) = (e3))) -> (~((op (e3) (op (e2) (e3))) = (op (e2) (e3)))) -> (~((op (e2) (e2)) = (e3))) -> (~((op (e0) (e1)) = (op (e2) (e1)))) -> ((op (e2) (e0)) = (e2)) -> (((op (e2) (e0)) = (e3))\/(((op (e2) (e1)) = (e3))\/(((op (e2) (e2)) = (e3))\/((op (e2) (e3)) = (e3))))) -> (~((e2) = (e3))) -> ((op (e0) (e2)) = (e2)) -> ((op (e3) (e3)) = (e3)) -> (~((op (e0) (e3)) = (op (e3) (e3)))) -> False). % 15.36/15.53 do 0 intro. intros zenon_H58 zenon_H59 zenon_H28a zenon_H30 zenon_Hde zenon_Hdd zenon_He6 zenon_H6a zenon_H63 zenon_H42 zenon_H36. % 15.36/15.53 apply (zenon_or_s _ _ zenon_H58); [ zenon_intro zenon_H5b | zenon_intro zenon_H5a ]. % 15.36/15.53 exact (zenon_H59 zenon_H5b). % 15.36/15.53 apply (zenon_or_s _ _ zenon_H5a); [ zenon_intro zenon_H4a | zenon_intro zenon_H5c ]. % 15.36/15.53 apply (zenon_L777_); trivial. % 15.36/15.53 apply (zenon_or_s _ _ zenon_H5c); [ zenon_intro zenon_H50 | zenon_intro zenon_H53 ]. % 15.36/15.53 apply (zenon_L31_); trivial. % 15.36/15.53 apply (zenon_L12_); trivial. % 15.36/15.53 (* end of lemma zenon_L789_ *) % 15.36/15.53 assert (zenon_L790_ : (((op (e0) (e0)) = (e2))\/(((op (e1) (e0)) = (e2))\/(((op (e2) (e0)) = (e2))\/((op (e3) (e0)) = (e2))))) -> (~((op (e0) (e0)) = (e2))) -> (~((op (e1) (e3)) = (op (e3) (e3)))) -> ((op (e1) (e2)) = (e1)) -> (~((e1) = (e3))) -> (~((op (e1) (e1)) = (e3))) -> (((op (e1) (e0)) = (e3))\/(((op (e1) (e1)) = (e3))\/(((op (e1) (e2)) = (e3))\/((op (e1) (e3)) = (e3))))) -> (~((op (e0) (e3)) = (op (e3) (e3)))) -> ((op (e3) (e3)) = (e3)) -> ((op (e0) (e2)) = (e2)) -> (~((e2) = (e3))) -> (((op (e2) (e0)) = (e3))\/(((op (e2) (e1)) = (e3))\/(((op (e2) (e2)) = (e3))\/((op (e2) (e3)) = (e3))))) -> (~((op (e0) (e1)) = (op (e2) (e1)))) -> (~((op (e2) (e2)) = (e3))) -> (~((op (e3) (op (e2) (e3))) = (op (e2) (e3)))) -> (~((op (e0) (e0)) = (e3))) -> (((op (e0) (e0)) = (e3))\/(((op (e0) (e1)) = (e3))\/(((op (e0) (e2)) = (e3))\/((op (e0) (e3)) = (e3))))) -> ((op (e3) (e0)) = (e1)) -> (~((e1) = (e2))) -> False). % 15.36/15.53 do 0 intro. intros zenon_Heb zenon_H8f zenon_H8b zenon_H117 zenon_Ha3 zenon_H182 zenon_H90 zenon_H36 zenon_H42 zenon_H63 zenon_H6a zenon_He6 zenon_Hde zenon_H30 zenon_H28a zenon_H59 zenon_H58 zenon_Hee zenon_Ha7. % 15.36/15.53 apply (zenon_or_s _ _ zenon_Heb); [ zenon_intro zenon_H92 | zenon_intro zenon_Hec ]. % 15.36/15.53 exact (zenon_H8f zenon_H92). % 15.36/15.53 apply (zenon_or_s _ _ zenon_Hec); [ zenon_intro zenon_H68 | zenon_intro zenon_Hed ]. % 15.36/15.53 apply (zenon_L198_); trivial. % 15.36/15.53 apply (zenon_or_s _ _ zenon_Hed); [ zenon_intro zenon_Hdd | zenon_intro zenon_He9 ]. % 15.36/15.53 apply (zenon_L789_); trivial. % 15.36/15.53 apply (zenon_L122_); trivial. % 15.36/15.53 (* end of lemma zenon_L790_ *) % 15.36/15.53 assert (zenon_L791_ : (((op (e0) (e0)) = (e1))\/(((op (e1) (e0)) = (e1))\/(((op (e2) (e0)) = (e1))\/((op (e3) (e0)) = (e1))))) -> (~((op (e0) (e0)) = (e1))) -> (~((op (e1) (e0)) = (op (e1) (e2)))) -> (~((op (e2) (e2)) = (e0))) -> (~((op (e0) (e2)) = (op (e2) (e2)))) -> (((op (e0) (e0)) = (e2))\/(((op (e0) (e1)) = (e2))\/(((op (e0) (e2)) = (e2))\/((op (e0) (e3)) = (e2))))) -> (~((op (e0) (e1)) = (op (e1) (e1)))) -> (~((op (e1) (e1)) = (e1))) -> (~((op (e1) (e1)) = (e0))) -> (((op (e1) (e1)) = (e0))\/(((op (e1) (e1)) = (e1))\/(((op (e1) (e1)) = (e2))\/((op (e1) (e1)) = (e3))))) -> (((op (e0) (e0)) = (e3))\/(((op (e0) (e1)) = (e3))\/(((op (e0) (e2)) = (e3))\/((op (e0) (e3)) = (e3))))) -> (~((op (e3) (op (e2) (e3))) = (op (e2) (e3)))) -> (~((op (e0) (e1)) = (op (e2) (e1)))) -> (((op (e2) (e0)) = (e3))\/(((op (e2) (e1)) = (e3))\/(((op (e2) (e2)) = (e3))\/((op (e2) (e3)) = (e3))))) -> (~((op (e0) (e3)) = (op (e3) (e3)))) -> (((op (e0) (e0)) = (e2))\/(((op (e1) (e0)) = (e2))\/(((op (e2) (e0)) = (e2))\/((op (e3) (e0)) = (e2))))) -> (~((op (e0) (e0)) = (e2))) -> (~((op (e1) (e3)) = (op (e3) (e3)))) -> ((op (e3) (e3)) = (e3)) -> (~((op (e1) (e1)) = (e3))) -> (((op (e1) (e0)) = (e3))\/(((op (e1) (e1)) = (e3))\/(((op (e1) (e2)) = (e3))\/((op (e1) (e3)) = (e3))))) -> (~((e1) = (e3))) -> (~((e2) = (e3))) -> (((op (e1) (e0)) = (e2))\/(((op (e1) (e1)) = (e2))\/(((op (e1) (e2)) = (e2))\/((op (e1) (e3)) = (e2))))) -> (~((op (e2) (e2)) = (e3))) -> (~((op (e2) (e2)) = (e2))) -> (~((op (e2) (e2)) = (e1))) -> (((op (e2) (e2)) = (e0))\/(((op (e2) (e2)) = (e1))\/(((op (e2) (e2)) = (e2))\/((op (e2) (e2)) = (e3))))) -> ((op (e1) (e2)) = (e1)) -> (~((op (e0) (e3)) = (op (e1) (e3)))) -> (~((op (e0) (e0)) = (e3))) -> (((op (e0) (e0)) = (e3))\/(((op (e1) (e0)) = (e3))\/(((op (e2) (e0)) = (e3))\/((op (e3) (e0)) = (e3))))) -> (~((e1) = (e2))) -> False). % 15.36/15.53 do 0 intro. intros zenon_Hf1 zenon_H45 zenon_H166 zenon_H2e zenon_H28 zenon_H8e zenon_H23 zenon_H1b4 zenon_H145 zenon_H1b3 zenon_H58 zenon_H28a zenon_Hde zenon_He6 zenon_H36 zenon_Heb zenon_H8f zenon_H8b zenon_H42 zenon_H182 zenon_H90 zenon_Ha3 zenon_H6a zenon_H84 zenon_H30 zenon_H2f zenon_H52 zenon_H2d zenon_H117 zenon_H80 zenon_H59 zenon_Hbe zenon_Ha7. % 15.36/15.53 apply (zenon_or_s _ _ zenon_Hf1); [ zenon_intro zenon_H47 | zenon_intro zenon_Hf4 ]. % 15.36/15.53 exact (zenon_H45 zenon_H47). % 15.36/15.53 apply (zenon_or_s _ _ zenon_Hf4); [ zenon_intro zenon_Hd8 | zenon_intro zenon_Hf5 ]. % 15.36/15.53 apply (zenon_L248_); trivial. % 15.36/15.53 apply (zenon_or_s _ _ zenon_Hf5); [ zenon_intro zenon_Hae | zenon_intro zenon_Hee ]. % 15.36/15.53 apply (zenon_L788_); trivial. % 15.36/15.53 apply (zenon_or_s _ _ zenon_H8e); [ zenon_intro zenon_H92 | zenon_intro zenon_H91 ]. % 15.36/15.53 exact (zenon_H8f zenon_H92). % 15.36/15.53 apply (zenon_or_s _ _ zenon_H91); [ zenon_intro zenon_H5d | zenon_intro zenon_H93 ]. % 15.36/15.53 apply (zenon_L214_); trivial. % 15.36/15.53 apply (zenon_or_s _ _ zenon_H93); [ zenon_intro zenon_H63 | zenon_intro zenon_H81 ]. % 15.36/15.53 apply (zenon_L790_); trivial. % 15.36/15.53 apply (zenon_L581_); trivial. % 15.36/15.53 (* end of lemma zenon_L791_ *) % 15.36/15.53 assert (zenon_L792_ : (((op (e1) (e0)) = (e2))\/(((op (e1) (e1)) = (e2))\/(((op (e1) (e2)) = (e2))\/((op (e1) (e3)) = (e2))))) -> (~((e2) = (e3))) -> ((op (e1) (e0)) = (e3)) -> ((op (e3) (e3)) = (e3)) -> (~((op (e3) (op (e2) (e3))) = (op (e2) (e3)))) -> (~((op (e0) (e1)) = (op (e2) (e1)))) -> ((op (e0) (e1)) = (e3)) -> ((op (e2) (e0)) = (e1)) -> (~((e1) = (e3))) -> (((op (e2) (e0)) = (e3))\/(((op (e2) (e1)) = (e3))\/(((op (e2) (e2)) = (e3))\/((op (e2) (e3)) = (e3))))) -> (~((e1) = (e2))) -> ((op (e1) (e2)) = (e1)) -> ((op (e1) (e3)) = (e0)) -> (~((e0) = (e2))) -> False). % 15.36/15.53 do 0 intro. intros zenon_H84 zenon_H6a zenon_H69 zenon_H42 zenon_H28a zenon_Hde zenon_H4a zenon_Hae zenon_Ha3 zenon_He6 zenon_Ha7 zenon_H117 zenon_Hcc zenon_H5e. % 15.36/15.53 apply (zenon_or_s _ _ zenon_H84); [ zenon_intro zenon_H68 | zenon_intro zenon_H85 ]. % 15.36/15.53 apply (zenon_L17_); trivial. % 15.36/15.53 apply (zenon_or_s _ _ zenon_H85); [ zenon_intro zenon_H6e | zenon_intro zenon_H86 ]. % 15.36/15.53 apply (zenon_or_s _ _ zenon_He6); [ zenon_intro zenon_Haf | zenon_intro zenon_He7 ]. % 15.36/15.53 apply (zenon_L39_); trivial. % 15.36/15.53 apply (zenon_or_s _ _ zenon_He7); [ zenon_intro zenon_Hdf | zenon_intro zenon_He8 ]. % 15.36/15.53 apply (zenon_L65_); trivial. % 15.36/15.53 apply (zenon_or_s _ _ zenon_He8); [ zenon_intro zenon_H34 | zenon_intro zenon_He2 ]. % 15.36/15.53 apply (zenon_L200_); trivial. % 15.36/15.53 apply (zenon_L776_); trivial. % 15.36/15.53 apply (zenon_or_s _ _ zenon_H86); [ zenon_intro zenon_H7c | zenon_intro zenon_H82 ]. % 15.36/15.53 apply (zenon_L204_); trivial. % 15.36/15.53 apply (zenon_L54_); trivial. % 15.36/15.53 (* end of lemma zenon_L792_ *) % 15.36/15.53 assert (zenon_L793_ : (((op (e0) (e0)) = (e1))\/(((op (e1) (e0)) = (e1))\/(((op (e2) (e0)) = (e1))\/((op (e3) (e0)) = (e1))))) -> (~((op (e0) (e0)) = (e1))) -> ((~((op (e2) (e2)) = (e3)))\/((op (e2) (e3)) = (e2))) -> (~((op (e0) (e2)) = (op (e1) (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) (e0)) = (op (e2) (e0)))) -> (~((op (e1) (op (e2) (e1))) = (op (e2) (e1)))) -> (((op (e2) (e0)) = (e1))\/(((op (e2) (e1)) = (e1))\/(((op (e2) (e2)) = (e1))\/((op (e2) (e3)) = (e1))))) -> (~((op (e3) (e3)) = (e1))) -> (~((op (e1) (e2)) = (op (e1) (e3)))) -> (((op (e0) (e3)) = (e1))\/(((op (e1) (e3)) = (e1))\/(((op (e2) (e3)) = (e1))\/((op (e3) (e3)) = (e1))))) -> (((op (e2) (e2)) = (e0))\/(((op (e2) (e2)) = (e1))\/(((op (e2) (e2)) = (e2))\/((op (e2) (e2)) = (e3))))) -> (~((op (e2) (e2)) = (e0))) -> (~((op (e2) (e2)) = (e1))) -> (~((op (e2) (e2)) = (e2))) -> (~((op (e0) (e2)) = (op (e2) (e2)))) -> (((op (e0) (e0)) = (e3))\/(((op (e1) (e0)) = (e3))\/(((op (e2) (e0)) = (e3))\/((op (e3) (e0)) = (e3))))) -> (~((op (e0) (e0)) = (e3))) -> (~((e0) = (e2))) -> (((op (e2) (e0)) = (e3))\/(((op (e2) (e1)) = (e3))\/(((op (e2) (e2)) = (e3))\/((op (e2) (e3)) = (e3))))) -> (~((op (e0) (e1)) = (op (e2) (e1)))) -> (~((op (e3) (op (e2) (e3))) = (op (e2) (e3)))) -> (((op (e1) (e0)) = (e2))\/(((op (e1) (e1)) = (e2))\/(((op (e1) (e2)) = (e2))\/((op (e1) (e3)) = (e2))))) -> (~((e0) = (e1))) -> (~((op (e1) (e1)) = (e0))) -> (~((op (e0) (e0)) = (op (e1) (e0)))) -> ((op (e0) (e0)) = (e0)) -> (((op (e1) (e0)) = (e0))\/(((op (e1) (e1)) = (e0))\/(((op (e1) (e2)) = (e0))\/((op (e1) (e3)) = (e0))))) -> (((op (e0) (e0)) = (e3))\/(((op (e0) (e1)) = (e3))\/(((op (e0) (e2)) = (e3))\/((op (e0) (e3)) = (e3))))) -> (((op (e0) (e0)) = (e2))\/(((op (e1) (e0)) = (e2))\/(((op (e2) (e0)) = (e2))\/((op (e3) (e0)) = (e2))))) -> (~((op (e0) (e0)) = (e2))) -> (~((op (e1) (e3)) = (op (e3) (e3)))) -> ((op (e3) (e3)) = (e3)) -> ((op (e1) (e2)) = (e1)) -> (~((e1) = (e3))) -> (~((op (e1) (e1)) = (e3))) -> (~((e2) = (e3))) -> (((op (e1) (e0)) = (e3))\/(((op (e1) (e1)) = (e3))\/(((op (e1) (e2)) = (e3))\/((op (e1) (e3)) = (e3))))) -> ((op (e2) (e3)) = (e2)) -> (~((op (e2) (e0)) = (op (e2) (e3)))) -> (~((e1) = (e2))) -> False). % 15.36/15.53 do 0 intro. intros zenon_Hf1 zenon_H45 zenon_H1c3 zenon_H87 zenon_H36 zenon_H1f5 zenon_H258 zenon_H290 zenon_Hb7 zenon_H104 zenon_H1d0 zenon_H121 zenon_H2d zenon_H2e zenon_H52 zenon_H2f zenon_H28 zenon_Hbe zenon_H59 zenon_H5e zenon_He6 zenon_Hde zenon_H28a zenon_H84 zenon_H9e zenon_H145 zenon_H24c zenon_H1f zenon_H163 zenon_H58 zenon_Heb zenon_H8f zenon_H8b zenon_H42 zenon_H117 zenon_Ha3 zenon_H182 zenon_H6a zenon_H90 zenon_H124 zenon_Hce zenon_Ha7. % 15.36/15.53 apply (zenon_or_s _ _ zenon_Hf1); [ zenon_intro zenon_H47 | zenon_intro zenon_Hf4 ]. % 15.36/15.53 exact (zenon_H45 zenon_H47). % 15.36/15.53 apply (zenon_or_s _ _ zenon_Hf4); [ zenon_intro zenon_Hd8 | zenon_intro zenon_Hf5 ]. % 15.36/15.53 apply (zenon_L785_); trivial. % 15.36/15.53 apply (zenon_or_s _ _ zenon_Hf5); [ zenon_intro zenon_Hae | zenon_intro zenon_Hee ]. % 15.36/15.53 apply (zenon_or_s _ _ zenon_Heb); [ zenon_intro zenon_H92 | zenon_intro zenon_Hec ]. % 15.36/15.53 exact (zenon_H8f zenon_H92). % 15.36/15.53 apply (zenon_or_s _ _ zenon_Hec); [ zenon_intro zenon_H68 | zenon_intro zenon_Hed ]. % 15.36/15.53 apply (zenon_L198_); trivial. % 15.36/15.53 apply (zenon_or_s _ _ zenon_Hed); [ zenon_intro zenon_Hdd | zenon_intro zenon_He9 ]. % 15.36/15.53 apply (zenon_L304_); trivial. % 15.36/15.53 apply (zenon_or_s _ _ zenon_H58); [ zenon_intro zenon_H5b | zenon_intro zenon_H5a ]. % 15.36/15.53 exact (zenon_H59 zenon_H5b). % 15.36/15.53 apply (zenon_or_s _ _ zenon_H5a); [ zenon_intro zenon_H4a | zenon_intro zenon_H5c ]. % 15.36/15.53 apply (zenon_or_s _ _ zenon_Hbe); [ zenon_intro zenon_H5b | zenon_intro zenon_Hbf ]. % 15.36/15.53 exact (zenon_H59 zenon_H5b). % 15.36/15.53 apply (zenon_or_s _ _ zenon_Hbf); [ zenon_intro zenon_H69 | zenon_intro zenon_Hc0 ]. % 15.36/15.53 apply (zenon_or_s _ _ zenon_H163); [ zenon_intro zenon_Had | zenon_intro zenon_H164 ]. % 15.36/15.53 apply (zenon_L559_); trivial. % 15.36/15.53 apply (zenon_or_s _ _ zenon_H164); [ zenon_intro zenon_H149 | zenon_intro zenon_H165 ]. % 15.36/15.53 exact (zenon_H145 zenon_H149). % 15.36/15.53 apply (zenon_or_s _ _ zenon_H165); [ zenon_intro zenon_H15d | zenon_intro zenon_Hcc ]. % 15.36/15.53 apply (zenon_L496_); trivial. % 15.36/15.53 apply (zenon_L792_); trivial. % 15.36/15.53 apply (zenon_or_s _ _ zenon_Hc0); [ zenon_intro zenon_Haf | zenon_intro zenon_Hba ]. % 15.36/15.53 apply (zenon_L39_); trivial. % 15.36/15.53 apply (zenon_L220_); trivial. % 15.36/15.53 apply (zenon_or_s _ _ zenon_H5c); [ zenon_intro zenon_H50 | zenon_intro zenon_H53 ]. % 15.36/15.53 apply (zenon_L11_); trivial. % 15.36/15.53 apply (zenon_L549_); trivial. % 15.36/15.53 apply (zenon_L591_); trivial. % 15.36/15.53 (* end of lemma zenon_L793_ *) % 15.36/15.53 assert (zenon_L794_ : (~((op (e2) (op (e2) (e2))) = (op (e2) (e2)))) -> ((op (e2) (e2)) = (e2)) -> False). % 15.36/15.53 do 0 intro. intros zenon_H294 zenon_H35. % 15.36/15.53 cut (((op (e2) (e2)) = (e2))); [idtac | apply NNPP; zenon_intro zenon_H2f]. % 15.36/15.53 cut (((e2) = (e2))); [idtac | apply NNPP; zenon_intro zenon_H60]. % 15.36/15.53 congruence. % 15.36/15.53 apply zenon_H60. apply refl_equal. % 15.36/15.53 exact (zenon_H2f zenon_H35). % 15.36/15.53 (* end of lemma zenon_L794_ *) % 15.36/15.53 assert (zenon_L795_ : ((~((op (e2) (e2)) = (e2)))\/((op (e2) (e2)) = (e2))) -> (~((op (e2) (op (e2) (e2))) = (op (e2) (e2)))) -> (((op (e0) (e0)) = (e1))\/(((op (e1) (e0)) = (e1))\/(((op (e2) (e0)) = (e1))\/((op (e3) (e0)) = (e1))))) -> (~((op (e0) (e0)) = (e2))) -> (((op (e1) (e1)) = (e0))\/(((op (e1) (e1)) = (e1))\/(((op (e1) (e1)) = (e2))\/((op (e1) (e1)) = (e3))))) -> (~((op (e1) (e1)) = (e3))) -> (~((op (e0) (e1)) = (op (e1) (e1)))) -> (~((op (e1) (e1)) = (e1))) -> (~((op (e1) (e1)) = (e0))) -> (((op (e0) (e0)) = (e2))\/(((op (e1) (e0)) = (e2))\/(((op (e2) (e0)) = (e2))\/((op (e3) (e0)) = (e2))))) -> (~((e1) = (e2))) -> (~((e2) = (e3))) -> (~((op (e1) (e3)) = (op (e3) (e3)))) -> (((op (e1) (e0)) = (e3))\/(((op (e1) (e1)) = (e3))\/(((op (e1) (e2)) = (e3))\/((op (e1) (e3)) = (e3))))) -> (((op (e1) (e0)) = (e2))\/(((op (e1) (e1)) = (e2))\/(((op (e1) (e2)) = (e2))\/((op (e1) (e3)) = (e2))))) -> (~((op (e0) (e3)) = (op (e1) (e3)))) -> (((op (e0) (e0)) = (e3))\/(((op (e1) (e0)) = (e3))\/(((op (e2) (e0)) = (e3))\/((op (e3) (e0)) = (e3))))) -> (((op (e0) (e0)) = (e2))\/(((op (e0) (e1)) = (e2))\/(((op (e0) (e2)) = (e2))\/((op (e0) (e3)) = (e2))))) -> (~((op (e0) (e0)) = (e3))) -> (((op (e2) (e0)) = (e3))\/(((op (e2) (e1)) = (e3))\/(((op (e2) (e2)) = (e3))\/((op (e2) (e3)) = (e3))))) -> ((op (e3) (e3)) = (e3)) -> (~((op (e3) (op (e2) (e3))) = (op (e2) (e3)))) -> (~((op (e0) (e1)) = (op (e2) (e1)))) -> (~((e1) = (e3))) -> (((op (e2) (e2)) = (e0))\/(((op (e2) (e2)) = (e1))\/(((op (e2) (e2)) = (e2))\/((op (e2) (e2)) = (e3))))) -> (~((op (e0) (e2)) = (op (e2) (e2)))) -> (~((op (e2) (e2)) = (e1))) -> (~((op (e2) (e2)) = (e0))) -> (~((op (e0) (e3)) = (op (e3) (e3)))) -> (((op (e0) (e0)) = (e3))\/(((op (e0) (e1)) = (e3))\/(((op (e0) (e2)) = (e3))\/((op (e0) (e3)) = (e3))))) -> ((op (e1) (e2)) = (e1)) -> (~((op (e1) (e0)) = (op (e1) (e2)))) -> (~((op (e0) (e0)) = (e1))) -> ((~((op (e3) (e3)) = (e1)))\/((op (e3) (e1)) = (e3))) -> (~((op (e3) (e1)) = (op (e3) (e3)))) -> ((~((op (e2) (e2)) = (e3)))\/((op (e2) (e3)) = (e2))) -> (~((op (e2) (e0)) = (op (e2) (e3)))) -> (~((op (e0) (e2)) = (op (e1) (e2)))) -> (~((op (e0) (e0)) = (op (e2) (e0)))) -> ((op (e0) (e0)) = (e0)) -> (((op (e2) (e0)) = (e1))\/(((op (e2) (e1)) = (e1))\/(((op (e2) (e2)) = (e1))\/((op (e2) (e3)) = (e1))))) -> (~((op (e1) (op (e2) (e1))) = (op (e2) (e1)))) -> (~((e0) = (e2))) -> (((op (e2) (e0)) = (e0))\/(((op (e2) (e1)) = (e0))\/(((op (e2) (e2)) = (e0))\/((op (e2) (e3)) = (e0))))) -> (~((op (e0) (e0)) = (op (e1) (e0)))) -> (~((e0) = (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) (e2)) = (op (e1) (e3)))) -> False). % 15.36/15.53 do 0 intro. intros zenon_Haa zenon_H294 zenon_Hf1 zenon_H8f zenon_H1b3 zenon_H182 zenon_H23 zenon_H1b4 zenon_H145 zenon_Heb zenon_Ha7 zenon_H6a zenon_H8b zenon_H90 zenon_H84 zenon_H80 zenon_Hbe zenon_H8e zenon_H59 zenon_He6 zenon_H42 zenon_H28a zenon_Hde zenon_Ha3 zenon_H2d zenon_H28 zenon_H52 zenon_H2e zenon_H36 zenon_H58 zenon_H117 zenon_H166 zenon_H45 zenon_H10c zenon_H12d zenon_H1c3 zenon_Hce zenon_H87 zenon_H258 zenon_H1f zenon_Hb7 zenon_H290 zenon_H5e zenon_H1f5 zenon_H24c zenon_H9e zenon_H163 zenon_H121 zenon_H1d0. % 15.36/15.53 apply (zenon_or_s _ _ zenon_Haa); [ zenon_intro zenon_H2f | zenon_intro zenon_H35 ]. % 15.36/15.53 apply (zenon_or_s _ _ zenon_H1c3); [ zenon_intro zenon_H30 | zenon_intro zenon_H124 ]. % 15.36/15.53 apply (zenon_L791_); trivial. % 15.36/15.53 apply (zenon_or_s _ _ zenon_H10c); [ zenon_intro zenon_H104 | zenon_intro zenon_H10a ]. % 15.36/15.53 apply (zenon_L793_); trivial. % 15.36/15.53 apply (zenon_L102_); trivial. % 15.36/15.53 apply (zenon_L794_); trivial. % 15.36/15.53 (* end of lemma zenon_L795_ *) % 15.36/15.53 assert (zenon_L796_ : (((op (e2) (e0)) = (e3))\/(((op (e2) (e1)) = (e3))\/(((op (e2) (e2)) = (e3))\/((op (e2) (e3)) = (e3))))) -> (~((e1) = (e3))) -> ((op (e2) (e0)) = (e1)) -> (~((e2) = (e3))) -> ((op (e2) (e1)) = (e2)) -> (~((op (e2) (e2)) = (e3))) -> (~((op (e3) (op (e2) (e3))) = (op (e2) (e3)))) -> ((op (e3) (e3)) = (e3)) -> False). % 15.36/15.53 do 0 intro. intros zenon_He6 zenon_Ha3 zenon_Hae zenon_H6a zenon_H156 zenon_H30 zenon_H28a zenon_H42. % 15.36/15.53 apply (zenon_or_s _ _ zenon_He6); [ zenon_intro zenon_Haf | zenon_intro zenon_He7 ]. % 15.36/15.53 apply (zenon_L39_); trivial. % 15.36/15.53 apply (zenon_or_s _ _ zenon_He7); [ zenon_intro zenon_Hdf | zenon_intro zenon_He8 ]. % 15.36/15.53 apply (zenon_L183_); trivial. % 15.36/15.53 apply (zenon_or_s _ _ zenon_He8); [ zenon_intro zenon_H34 | zenon_intro zenon_He2 ]. % 15.36/15.53 exact (zenon_H30 zenon_H34). % 15.36/15.53 apply (zenon_L776_); trivial. % 15.36/15.53 (* end of lemma zenon_L796_ *) % 15.36/15.53 assert (zenon_L797_ : (((op (e0) (e0)) = (e1))\/(((op (e1) (e0)) = (e1))\/(((op (e2) (e0)) = (e1))\/((op (e3) (e0)) = (e1))))) -> (~((op (e0) (e0)) = (e1))) -> (~((op (e1) (e0)) = (op (e1) (e3)))) -> (~((op (e3) (op (e2) (e3))) = (op (e2) (e3)))) -> (~((op (e2) (e2)) = (e3))) -> (((op (e2) (e0)) = (e3))\/(((op (e2) (e1)) = (e3))\/(((op (e2) (e2)) = (e3))\/((op (e2) (e3)) = (e3))))) -> (((op (e0) (e0)) = (e2))\/(((op (e1) (e0)) = (e2))\/(((op (e2) (e0)) = (e2))\/((op (e3) (e0)) = (e2))))) -> (~((op (e0) (e0)) = (e2))) -> (~((e1) = (e3))) -> (((op (e1) (e0)) = (e0))\/(((op (e1) (e1)) = (e0))\/(((op (e1) (e2)) = (e0))\/((op (e1) (e3)) = (e0))))) -> (~((op (e0) (e0)) = (op (e1) (e0)))) -> (~((op (e1) (e1)) = (e0))) -> (~((op (e1) (e3)) = (op (e3) (e3)))) -> ((op (e3) (e3)) = (e3)) -> (((op (e2) (e0)) = (e0))\/(((op (e2) (e1)) = (e0))\/(((op (e2) (e2)) = (e0))\/((op (e2) (e3)) = (e0))))) -> (~((op (e0) (e0)) = (op (e2) (e0)))) -> (~((e0) = (e2))) -> (~((op (e2) (e2)) = (e0))) -> (((op (e2) (e0)) = (e1))\/(((op (e2) (e1)) = (e1))\/(((op (e2) (e2)) = (e1))\/((op (e2) (e3)) = (e1))))) -> (~((op (e3) (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 (e3) (e2)))) -> (~((op (e0) (e2)) = (op (e1) (e2)))) -> (~((op (e2) (e1)) = (op (e3) (e1)))) -> (((op (e3) (e0)) = (e2))\/(((op (e3) (e1)) = (e2))\/(((op (e3) (e2)) = (e2))\/((op (e3) (e3)) = (e2))))) -> (((op (e1) (e3)) = (e0))\/(((op (e1) (e3)) = (e1))\/(((op (e1) (e3)) = (e2))\/((op (e1) (e3)) = (e3))))) -> (~((op (e1) (e3)) = (op (e2) (e3)))) -> (~((op (e0) (e3)) = (op (e3) (e3)))) -> (~((op (e0) (e3)) = (op (e1) (e3)))) -> (~((op (e0) (e3)) = (op (e2) (e3)))) -> (~((op (e0) (e0)) = (op (e0) (e3)))) -> ((op (e0) (e0)) = (e0)) -> (((op (e0) (e3)) = (e0))\/(((op (e0) (e3)) = (e1))\/(((op (e0) (e3)) = (e2))\/((op (e0) (e3)) = (e3))))) -> (~((e2) = (e3))) -> (((op (e1) (e0)) = (e3))\/(((op (e1) (e1)) = (e3))\/(((op (e1) (e2)) = (e3))\/((op (e1) (e3)) = (e3))))) -> (~((e0) = (e1))) -> ((op (e1) (e3)) = (e1)) -> (~((op (e0) (e0)) = (e3))) -> (((op (e0) (e0)) = (e3))\/(((op (e1) (e0)) = (e3))\/(((op (e2) (e0)) = (e3))\/((op (e3) (e0)) = (e3))))) -> ((op (e2) (e1)) = (e2)) -> (~((op (e2) (e0)) = (op (e2) (e1)))) -> (~((e1) = (e2))) -> False). % 15.36/15.53 do 0 intro. intros zenon_Hf1 zenon_H45 zenon_H1cf zenon_H28a zenon_H30 zenon_He6 zenon_Heb zenon_H8f zenon_Ha3 zenon_H163 zenon_H24c zenon_H145 zenon_H8b zenon_H42 zenon_H1f5 zenon_H258 zenon_H5e zenon_H2e zenon_Hb7 zenon_H3d zenon_H251 zenon_H28 zenon_H140 zenon_H87 zenon_H13c zenon_H1df zenon_H25b zenon_H244 zenon_H36 zenon_H80 zenon_Hb4 zenon_H24f zenon_H1f zenon_H254 zenon_H6a zenon_H90 zenon_H9e zenon_H11f zenon_H59 zenon_Hbe zenon_H156 zenon_H154 zenon_Ha7. % 15.36/15.53 apply (zenon_or_s _ _ zenon_Hf1); [ zenon_intro zenon_H47 | zenon_intro zenon_Hf4 ]. % 15.36/15.53 exact (zenon_H45 zenon_H47). % 15.36/15.53 apply (zenon_or_s _ _ zenon_Hf4); [ zenon_intro zenon_Hd8 | zenon_intro zenon_Hf5 ]. % 15.36/15.53 apply (zenon_L224_); trivial. % 15.36/15.53 apply (zenon_or_s _ _ zenon_Hf5); [ zenon_intro zenon_Hae | zenon_intro zenon_Hee ]. % 15.36/15.53 apply (zenon_L796_); trivial. % 15.36/15.53 apply (zenon_L617_); trivial. % 15.36/15.53 (* end of lemma zenon_L797_ *) % 15.36/15.53 assert (zenon_L798_ : ((~((op (e2) (e2)) = (e1)))\/((op (e2) (e1)) = (e2))) -> ((~((op (e3) (e3)) = (e2)))\/((op (e3) (e2)) = (e3))) -> (~((op (e3) (e2)) = (op (e3) (e3)))) -> (~((op (e0) (e0)) = (e1))) -> (~((op (e1) (e0)) = (op (e1) (e3)))) -> (((op (e2) (e0)) = (e3))\/(((op (e2) (e1)) = (e3))\/(((op (e2) (e2)) = (e3))\/((op (e2) (e3)) = (e3))))) -> (~((op (e3) (op (e2) (e3))) = (op (e2) (e3)))) -> (~((e2) = (e3))) -> (~((e1) = (e3))) -> (((op (e0) (e0)) = (e2))\/(((op (e1) (e0)) = (e2))\/(((op (e2) (e0)) = (e2))\/((op (e3) (e0)) = (e2))))) -> (~((op (e2) (e0)) = (op (e2) (e1)))) -> (~((op (e0) (e0)) = (e3))) -> (((op (e2) (e0)) = (e0))\/(((op (e2) (e1)) = (e0))\/(((op (e2) (e2)) = (e0))\/((op (e2) (e3)) = (e0))))) -> (~((e1) = (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) (e2)) = (e0))) -> (~((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 (e1) (e2)))) -> (~((op (e0) (e2)) = (op (e2) (e2)))) -> (~((op (e0) (e2)) = (op (e3) (e2)))) -> (((op (e0) (e2)) = (e0))\/(((op (e0) (e2)) = (e1))\/(((op (e0) (e2)) = (e2))\/((op (e0) (e2)) = (e3))))) -> (~((op (e2) (e1)) = (op (e3) (e1)))) -> (((op (e1) (e3)) = (e0))\/(((op (e1) (e3)) = (e1))\/(((op (e1) (e3)) = (e2))\/((op (e1) (e3)) = (e3))))) -> (~((op (e1) (e3)) = (op (e3) (e3)))) -> (~((op (e0) (e3)) = (op (e2) (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 (e1) (e0)) = (e3))\/(((op (e1) (e1)) = (e3))\/(((op (e1) (e2)) = (e3))\/((op (e1) (e3)) = (e3))))) -> (((op (e0) (e0)) = (e3))\/(((op (e1) (e0)) = (e3))\/(((op (e2) (e0)) = (e3))\/((op (e3) (e0)) = (e3))))) -> (~((op (e0) (e0)) = (e2))) -> (((op (e0) (e0)) = (e1))\/(((op (e1) (e0)) = (e1))\/(((op (e2) (e0)) = (e1))\/((op (e3) (e0)) = (e1))))) -> (~((op (e2) (e1)) = (op (e2) (e3)))) -> ((~((op (e2) (e2)) = (e3)))\/((op (e2) (e3)) = (e2))) -> (((op (e0) (e3)) = (e0))\/(((op (e1) (e3)) = (e0))\/(((op (e2) (e3)) = (e0))\/((op (e3) (e3)) = (e0))))) -> (~((e0) = (e2))) -> (~((op (e0) (e0)) = (op (e0) (e3)))) -> (~((op (e3) (e0)) = (op (e3) (e3)))) -> ((op (e3) (e3)) = (e3)) -> ((~((op (e3) (e3)) = (e0)))\/((op (e3) (e0)) = (e3))) -> (~((op (e0) (e0)) = (op (e1) (e0)))) -> ((op (e0) (e0)) = (e0)) -> (~((op (e1) (e1)) = (e0))) -> (((op (e2) (e2)) = (e0))\/(((op (e2) (e2)) = (e1))\/(((op (e2) (e2)) = (e2))\/((op (e2) (e2)) = (e3))))) -> (~((op (e1) (e2)) = (op (e2) (e2)))) -> (~((e0) = (e1))) -> ((op (e1) (e3)) = (e1)) -> (((op (e1) (e0)) = (e0))\/(((op (e1) (e1)) = (e0))\/(((op (e1) (e2)) = (e0))\/((op (e1) (e3)) = (e0))))) -> (~((op (e2) (op (e2) (e2))) = (op (e2) (e2)))) -> ((~((op (e2) (e2)) = (e2)))\/((op (e2) (e2)) = (e2))) -> False). % 15.36/15.53 do 0 intro. intros zenon_H1e3 zenon_H10e zenon_H173 zenon_H45 zenon_H1cf zenon_He6 zenon_H28a zenon_H6a zenon_Ha3 zenon_Heb zenon_H154 zenon_H59 zenon_H1f5 zenon_Ha7 zenon_H244 zenon_Hb7 zenon_H2e zenon_H258 zenon_H1df zenon_H87 zenon_H28 zenon_H140 zenon_H251 zenon_H13c zenon_H25b zenon_H8b zenon_Hb4 zenon_H80 zenon_H36 zenon_H254 zenon_H90 zenon_Hbe zenon_H8f zenon_Hf1 zenon_H1e2 zenon_H1c3 zenon_Hd3 zenon_H5e zenon_H24f zenon_Hbb zenon_H42 zenon_H10f zenon_H24c zenon_H1f zenon_H145 zenon_H2d zenon_H7d zenon_H9e zenon_H11f zenon_H163 zenon_H294 zenon_Haa. % 15.36/15.53 apply (zenon_or_s _ _ zenon_H1e3); [ zenon_intro zenon_H52 | zenon_intro zenon_H156 ]. % 15.36/15.53 apply (zenon_or_s _ _ zenon_Haa); [ zenon_intro zenon_H2f | zenon_intro zenon_H35 ]. % 15.36/15.53 apply (zenon_L605_); trivial. % 15.36/15.53 apply (zenon_L794_); trivial. % 15.36/15.53 apply (zenon_or_s _ _ zenon_H1c3); [ zenon_intro zenon_H30 | zenon_intro zenon_H124 ]. % 15.36/15.53 apply (zenon_or_s _ _ zenon_H10e); [ zenon_intro zenon_H3d | zenon_intro zenon_H106 ]. % 15.36/15.53 apply (zenon_L797_); trivial. % 15.36/15.53 apply (zenon_L153_); trivial. % 15.36/15.53 apply (zenon_L256_); trivial. % 15.36/15.53 (* end of lemma zenon_L798_ *) % 15.36/15.53 assert (zenon_L799_ : (((op (e2) (e0)) = (e0))\/(((op (e2) (e1)) = (e0))\/(((op (e2) (e2)) = (e0))\/((op (e2) (e3)) = (e0))))) -> (~((e0) = (e2))) -> (~((op (e1) (op (e2) (e1))) = (op (e2) (e1)))) -> (~((op (e2) (e2)) = (e1))) -> (((op (e2) (e0)) = (e1))\/(((op (e2) (e1)) = (e1))\/(((op (e2) (e2)) = (e1))\/((op (e2) (e3)) = (e1))))) -> ((op (e0) (e0)) = (e0)) -> (~((op (e0) (e0)) = (op (e2) (e0)))) -> (~((op (e0) (e0)) = (e3))) -> (~((e1) = (e3))) -> (((op (e1) (e1)) = (e0))\/(((op (e1) (e1)) = (e1))\/(((op (e1) (e1)) = (e2))\/((op (e1) (e1)) = (e3))))) -> (~((op (e1) (e1)) = (e3))) -> (~((op (e1) (e1)) = (e2))) -> (~((op (e1) (e1)) = (e1))) -> (~((op (e2) (e2)) = (e0))) -> (((op (e2) (e2)) = (e0))\/(((op (e2) (e2)) = (e1))\/(((op (e2) (e2)) = (e2))\/((op (e2) (e2)) = (e3))))) -> (((op (e0) (e0)) = (e2))\/(((op (e1) (e0)) = (e2))\/(((op (e2) (e0)) = (e2))\/((op (e3) (e0)) = (e2))))) -> (((op (e0) (e0)) = (e3))\/(((op (e0) (e1)) = (e3))\/(((op (e0) (e2)) = (e3))\/((op (e0) (e3)) = (e3))))) -> (~((op (e0) (e3)) = (op (e3) (e3)))) -> (~((op (e0) (e2)) = (op (e1) (e2)))) -> (~((op (e1) (e3)) = (op (e3) (e3)))) -> (((op (e1) (e0)) = (e3))\/(((op (e1) (e1)) = (e3))\/(((op (e1) (e2)) = (e3))\/((op (e1) (e3)) = (e3))))) -> (~((e2) = (e3))) -> (~((op (e0) (e1)) = (op (e2) (e1)))) -> (~((op (e3) (op (e2) (e3))) = (op (e2) (e3)))) -> ((op (e3) (e3)) = (e3)) -> (((op (e2) (e0)) = (e3))\/(((op (e2) (e1)) = (e3))\/(((op (e2) (e2)) = (e3))\/((op (e2) (e3)) = (e3))))) -> (~((op (e2) (e0)) = (op (e2) (e3)))) -> ((~((op (e2) (e2)) = (e3)))\/((op (e2) (e3)) = (e2))) -> (~((e1) = (e2))) -> (~((op (e0) (e0)) = (e2))) -> (((op (e0) (e0)) = (e3))\/(((op (e1) (e0)) = (e3))\/(((op (e2) (e0)) = (e3))\/((op (e3) (e0)) = (e3))))) -> ((~((op (e2) (e2)) = (e2)))\/((op (e2) (e2)) = (e2))) -> (~((op (e2) (op (e2) (e2))) = (op (e2) (e2)))) -> (((op (e0) (e0)) = (e1))\/(((op (e1) (e0)) = (e1))\/(((op (e2) (e0)) = (e1))\/((op (e3) (e0)) = (e1))))) -> (~((op (e0) (e1)) = (op (e1) (e1)))) -> (~((op (e1) (e1)) = (e0))) -> (((op (e1) (e0)) = (e2))\/(((op (e1) (e1)) = (e2))\/(((op (e1) (e2)) = (e2))\/((op (e1) (e3)) = (e2))))) -> (~((op (e0) (e3)) = (op (e1) (e3)))) -> (((op (e0) (e0)) = (e2))\/(((op (e0) (e1)) = (e2))\/(((op (e0) (e2)) = (e2))\/((op (e0) (e3)) = (e2))))) -> (~((op (e0) (e2)) = (op (e2) (e2)))) -> (~((op (e1) (e0)) = (op (e1) (e2)))) -> (~((op (e0) (e0)) = (e1))) -> ((~((op (e3) (e3)) = (e1)))\/((op (e3) (e1)) = (e3))) -> (~((op (e3) (e1)) = (op (e3) (e3)))) -> (~((op (e0) (e0)) = (op (e1) (e0)))) -> (~((e0) = (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) (e2)) = (op (e1) (e3)))) -> ((~((op (e2) (e2)) = (e1)))\/((op (e2) (e1)) = (e2))) -> ((~((op (e3) (e3)) = (e2)))\/((op (e3) (e2)) = (e3))) -> (~((op (e3) (e2)) = (op (e3) (e3)))) -> (~((op (e1) (e0)) = (op (e1) (e3)))) -> (~((op (e2) (e0)) = (op (e2) (e1)))) -> (~((op (e1) (e3)) = (op (e2) (e3)))) -> (((op (e3) (e0)) = (e2))\/(((op (e3) (e1)) = (e2))\/(((op (e3) (e2)) = (e2))\/((op (e3) (e3)) = (e2))))) -> (~((op (e0) (e2)) = (op (e3) (e2)))) -> (((op (e0) (e2)) = (e0))\/(((op (e0) (e2)) = (e1))\/(((op (e0) (e2)) = (e2))\/((op (e0) (e2)) = (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) (e3)) = (e0))\/(((op (e0) (e3)) = (e1))\/(((op (e0) (e3)) = (e2))\/((op (e0) (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 (e0) (e0)) = (op (e0) (e3)))) -> (~((op (e3) (e0)) = (op (e3) (e3)))) -> ((~((op (e3) (e3)) = (e0)))\/((op (e3) (e0)) = (e3))) -> (~((op (e1) (e2)) = (op (e2) (e2)))) -> (((op (e1) (e0)) = (e1))\/(((op (e1) (e1)) = (e1))\/(((op (e1) (e2)) = (e1))\/((op (e1) (e3)) = (e1))))) -> False). % 15.36/15.53 do 0 intro. intros zenon_H1f5 zenon_H5e zenon_H290 zenon_H52 zenon_Hb7 zenon_H1f zenon_H258 zenon_H59 zenon_Ha3 zenon_H1b3 zenon_H182 zenon_Hd6 zenon_H1b4 zenon_H2e zenon_H2d zenon_Heb zenon_H58 zenon_H36 zenon_H87 zenon_H8b zenon_H90 zenon_H6a zenon_Hde zenon_H28a zenon_H42 zenon_He6 zenon_Hce zenon_H1c3 zenon_Ha7 zenon_H8f zenon_Hbe zenon_Haa zenon_H294 zenon_Hf1 zenon_H23 zenon_H145 zenon_H84 zenon_H80 zenon_H8e zenon_H28 zenon_H166 zenon_H45 zenon_H10c zenon_H12d zenon_H24c zenon_H9e zenon_H163 zenon_H121 zenon_H1d0 zenon_H1e3 zenon_H10e zenon_H173 zenon_H1cf zenon_H154 zenon_H244 zenon_H1df zenon_H140 zenon_H251 zenon_H13c zenon_H25b zenon_Hb4 zenon_H254 zenon_H1e2 zenon_Hd3 zenon_H24f zenon_Hbb zenon_H10f zenon_H7d zenon_H1c5. % 15.36/15.53 apply (zenon_or_s _ _ zenon_Haa); [ zenon_intro zenon_H2f | zenon_intro zenon_H35 ]. % 15.36/15.53 apply (zenon_or_s _ _ zenon_H1c5); [ zenon_intro zenon_Hd8 | zenon_intro zenon_H1c6 ]. % 15.36/15.53 apply (zenon_L786_); trivial. % 15.36/15.53 apply (zenon_or_s _ _ zenon_H1c6); [ zenon_intro zenon_H21 | zenon_intro zenon_H1c7 ]. % 15.36/15.53 exact (zenon_H1b4 zenon_H21). % 15.36/15.53 apply (zenon_or_s _ _ zenon_H1c7); [ zenon_intro zenon_H117 | zenon_intro zenon_H11f ]. % 15.36/15.53 apply (zenon_L795_); trivial. % 15.36/15.53 apply (zenon_L798_); trivial. % 15.36/15.53 apply (zenon_L794_); trivial. % 15.36/15.53 (* end of lemma zenon_L799_ *) % 15.36/15.53 assert (zenon_L800_ : (((op (e0) (e0)) = (e1))\/(((op (e1) (e0)) = (e1))\/(((op (e2) (e0)) = (e1))\/((op (e3) (e0)) = (e1))))) -> (~((op (e0) (e0)) = (e1))) -> ((~((op (e2) (e2)) = (e3)))\/((op (e2) (e3)) = (e2))) -> (~((op (e2) (e0)) = (op (e2) (e3)))) -> (~((op (e0) (e1)) = (op (e2) (e1)))) -> (((op (e1) (e0)) = (e3))\/(((op (e1) (e1)) = (e3))\/(((op (e1) (e2)) = (e3))\/((op (e1) (e3)) = (e3))))) -> (~((op (e1) (e3)) = (op (e3) (e3)))) -> (~((op (e0) (e2)) = (op (e1) (e2)))) -> (~((op (e0) (e3)) = (op (e3) (e3)))) -> (((op (e0) (e0)) = (e3))\/(((op (e0) (e1)) = (e3))\/(((op (e0) (e2)) = (e3))\/((op (e0) (e3)) = (e3))))) -> ((op (e3) (e3)) = (e3)) -> (~((op (e3) (op (e2) (e3))) = (op (e2) (e3)))) -> (((op (e2) (e0)) = (e3))\/(((op (e2) (e1)) = (e3))\/(((op (e2) (e2)) = (e3))\/((op (e2) (e3)) = (e3))))) -> (((op (e0) (e0)) = (e2))\/(((op (e1) (e0)) = (e2))\/(((op (e2) (e0)) = (e2))\/((op (e3) (e0)) = (e2))))) -> (~((op (e0) (e0)) = (e2))) -> (~((e1) = (e3))) -> (((op (e1) (e1)) = (e0))\/(((op (e1) (e1)) = (e1))\/(((op (e1) (e1)) = (e2))\/((op (e1) (e1)) = (e3))))) -> (~((op (e2) (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) (e1)) = (e1))) -> (~((op (e1) (e1)) = (e2))) -> (~((op (e1) (e1)) = (e3))) -> (~((e2) = (e3))) -> (~((op (e0) (e0)) = (e3))) -> (((op (e0) (e0)) = (e3))\/(((op (e1) (e0)) = (e3))\/(((op (e2) (e0)) = (e3))\/((op (e3) (e0)) = (e3))))) -> ((op (e2) (e1)) = (e2)) -> (~((op (e2) (e0)) = (op (e2) (e1)))) -> (~((e1) = (e2))) -> False). % 15.36/15.53 do 0 intro. intros zenon_Hf1 zenon_H45 zenon_H1c3 zenon_Hce zenon_Hde zenon_H90 zenon_H8b zenon_H87 zenon_H36 zenon_H58 zenon_H42 zenon_H28a zenon_He6 zenon_Heb zenon_H8f zenon_Ha3 zenon_H1b3 zenon_H30 zenon_H2f zenon_H2e zenon_H2d zenon_H1b4 zenon_Hd6 zenon_H182 zenon_H6a zenon_H59 zenon_Hbe zenon_H156 zenon_H154 zenon_Ha7. % 15.36/15.53 apply (zenon_or_s _ _ zenon_Hf1); [ zenon_intro zenon_H47 | zenon_intro zenon_Hf4 ]. % 15.36/15.53 exact (zenon_H45 zenon_H47). % 15.36/15.53 apply (zenon_or_s _ _ zenon_Hf4); [ zenon_intro zenon_Hd8 | zenon_intro zenon_Hf5 ]. % 15.36/15.53 apply (zenon_L781_); trivial. % 15.36/15.53 apply (zenon_or_s _ _ zenon_Hf5); [ zenon_intro zenon_Hae | zenon_intro zenon_Hee ]. % 15.36/15.53 apply (zenon_L796_); trivial. % 15.36/15.53 apply (zenon_L624_); trivial. % 15.36/15.53 (* end of lemma zenon_L800_ *) % 15.36/15.53 assert (zenon_L801_ : ((~((op (e2) (e2)) = (e2)))\/((op (e2) (e2)) = (e2))) -> (~((op (e2) (e1)) = (op (e2) (e2)))) -> (((op (e0) (e0)) = (e1))\/(((op (e1) (e0)) = (e1))\/(((op (e2) (e0)) = (e1))\/((op (e3) (e0)) = (e1))))) -> (~((op (e2) (e0)) = (op (e2) (e1)))) -> ((op (e2) (e1)) = (e2)) -> (~((op (e0) (e0)) = (e3))) -> (~((e1) = (e3))) -> (((op (e1) (e1)) = (e0))\/(((op (e1) (e1)) = (e1))\/(((op (e1) (e1)) = (e2))\/((op (e1) (e1)) = (e3))))) -> (~((op (e1) (e1)) = (e3))) -> (~((op (e1) (e1)) = (e2))) -> (~((op (e1) (e1)) = (e1))) -> (~((op (e2) (e2)) = (e0))) -> (((op (e2) (e2)) = (e0))\/(((op (e2) (e2)) = (e1))\/(((op (e2) (e2)) = (e2))\/((op (e2) (e2)) = (e3))))) -> (((op (e0) (e0)) = (e2))\/(((op (e1) (e0)) = (e2))\/(((op (e2) (e0)) = (e2))\/((op (e3) (e0)) = (e2))))) -> (((op (e0) (e0)) = (e3))\/(((op (e0) (e1)) = (e3))\/(((op (e0) (e2)) = (e3))\/((op (e0) (e3)) = (e3))))) -> (~((op (e0) (e3)) = (op (e3) (e3)))) -> (~((op (e0) (e2)) = (op (e1) (e2)))) -> (~((op (e1) (e3)) = (op (e3) (e3)))) -> (((op (e1) (e0)) = (e3))\/(((op (e1) (e1)) = (e3))\/(((op (e1) (e2)) = (e3))\/((op (e1) (e3)) = (e3))))) -> (~((e2) = (e3))) -> (~((op (e0) (e1)) = (op (e2) (e1)))) -> (~((op (e3) (op (e2) (e3))) = (op (e2) (e3)))) -> ((op (e3) (e3)) = (e3)) -> (((op (e2) (e0)) = (e3))\/(((op (e2) (e1)) = (e3))\/(((op (e2) (e2)) = (e3))\/((op (e2) (e3)) = (e3))))) -> (~((op (e2) (e0)) = (op (e2) (e3)))) -> ((~((op (e2) (e2)) = (e3)))\/((op (e2) (e3)) = (e2))) -> (~((e1) = (e2))) -> (~((op (e0) (e0)) = (e2))) -> (((op (e0) (e0)) = (e3))\/(((op (e1) (e0)) = (e3))\/(((op (e2) (e0)) = (e3))\/((op (e3) (e0)) = (e3))))) -> (~((op (e0) (e0)) = (e1))) -> (~((op (e2) (e1)) = (op (e2) (e3)))) -> False). % 15.36/15.53 do 0 intro. intros zenon_Haa zenon_H157 zenon_Hf1 zenon_H154 zenon_H156 zenon_H59 zenon_Ha3 zenon_H1b3 zenon_H182 zenon_Hd6 zenon_H1b4 zenon_H2e zenon_H2d zenon_Heb zenon_H58 zenon_H36 zenon_H87 zenon_H8b zenon_H90 zenon_H6a zenon_Hde zenon_H28a zenon_H42 zenon_He6 zenon_Hce zenon_H1c3 zenon_Ha7 zenon_H8f zenon_Hbe zenon_H45 zenon_H1e2. % 15.36/15.53 apply (zenon_or_s _ _ zenon_Haa); [ zenon_intro zenon_H2f | zenon_intro zenon_H35 ]. % 15.36/15.53 apply (zenon_or_s _ _ zenon_H1c3); [ zenon_intro zenon_H30 | zenon_intro zenon_H124 ]. % 15.36/15.53 apply (zenon_L800_); trivial. % 15.36/15.53 apply (zenon_L256_); trivial. % 15.36/15.53 apply (zenon_L134_); trivial. % 15.36/15.53 (* end of lemma zenon_L801_ *) % 15.36/15.53 assert (zenon_L802_ : (~((op (e2) (e1)) = (op (e2) (e2)))) -> (((op (e1) (e0)) = (e1))\/(((op (e1) (e1)) = (e1))\/(((op (e1) (e2)) = (e1))\/((op (e1) (e3)) = (e1))))) -> (~((op (e1) (e2)) = (op (e2) (e2)))) -> ((~((op (e3) (e3)) = (e0)))\/((op (e3) (e0)) = (e3))) -> (~((op (e3) (e0)) = (op (e3) (e3)))) -> (~((op (e0) (e0)) = (op (e0) (e3)))) -> (((op (e0) (e3)) = (e0))\/(((op (e1) (e3)) = (e0))\/(((op (e2) (e3)) = (e0))\/((op (e3) (e3)) = (e0))))) -> (~((op (e2) (e1)) = (op (e2) (e3)))) -> (((op (e0) (e3)) = (e0))\/(((op (e0) (e3)) = (e1))\/(((op (e0) (e3)) = (e2))\/((op (e0) (e3)) = (e3))))) -> (~((op (e0) (e3)) = (op (e2) (e3)))) -> (((op (e1) (e3)) = (e0))\/(((op (e1) (e3)) = (e1))\/(((op (e1) (e3)) = (e2))\/((op (e1) (e3)) = (e3))))) -> (~((op (e2) (e1)) = (op (e3) (e1)))) -> (((op (e0) (e2)) = (e0))\/(((op (e0) (e2)) = (e1))\/(((op (e0) (e2)) = (e2))\/((op (e0) (e2)) = (e3))))) -> (~((op (e0) (e2)) = (op (e3) (e2)))) -> (((op (e3) (e0)) = (e2))\/(((op (e3) (e1)) = (e2))\/(((op (e3) (e2)) = (e2))\/((op (e3) (e3)) = (e2))))) -> (~((op (e1) (e3)) = (op (e2) (e3)))) -> (~((op (e2) (e0)) = (op (e2) (e1)))) -> (~((op (e1) (e0)) = (op (e1) (e3)))) -> (~((op (e3) (e2)) = (op (e3) (e3)))) -> ((~((op (e3) (e3)) = (e2)))\/((op (e3) (e2)) = (e3))) -> ((~((op (e2) (e2)) = (e1)))\/((op (e2) (e1)) = (e2))) -> (~((op (e1) (e2)) = (op (e1) (e3)))) -> (((op (e0) (e3)) = (e1))\/(((op (e1) (e3)) = (e1))\/(((op (e2) (e3)) = (e1))\/((op (e3) (e3)) = (e1))))) -> (((op (e1) (e0)) = (e0))\/(((op (e1) (e1)) = (e0))\/(((op (e1) (e2)) = (e0))\/((op (e1) (e3)) = (e0))))) -> (~((e0) = (e1))) -> (~((op (e0) (e0)) = (op (e1) (e0)))) -> (~((op (e3) (e1)) = (op (e3) (e3)))) -> ((~((op (e3) (e3)) = (e1)))\/((op (e3) (e1)) = (e3))) -> (~((op (e0) (e0)) = (e1))) -> (~((op (e1) (e0)) = (op (e1) (e2)))) -> (~((op (e0) (e2)) = (op (e2) (e2)))) -> (((op (e0) (e0)) = (e2))\/(((op (e0) (e1)) = (e2))\/(((op (e0) (e2)) = (e2))\/((op (e0) (e3)) = (e2))))) -> (~((op (e0) (e3)) = (op (e1) (e3)))) -> (((op (e1) (e0)) = (e2))\/(((op (e1) (e1)) = (e2))\/(((op (e1) (e2)) = (e2))\/((op (e1) (e3)) = (e2))))) -> (~((op (e1) (e1)) = (e0))) -> (~((op (e0) (e1)) = (op (e1) (e1)))) -> (((op (e0) (e0)) = (e1))\/(((op (e1) (e0)) = (e1))\/(((op (e2) (e0)) = (e1))\/((op (e3) (e0)) = (e1))))) -> (~((op (e2) (op (e2) (e2))) = (op (e2) (e2)))) -> ((~((op (e2) (e2)) = (e2)))\/((op (e2) (e2)) = (e2))) -> (((op (e0) (e0)) = (e3))\/(((op (e1) (e0)) = (e3))\/(((op (e2) (e0)) = (e3))\/((op (e3) (e0)) = (e3))))) -> (~((op (e0) (e0)) = (e2))) -> (~((e1) = (e2))) -> ((~((op (e2) (e2)) = (e3)))\/((op (e2) (e3)) = (e2))) -> (~((op (e2) (e0)) = (op (e2) (e3)))) -> (((op (e2) (e0)) = (e3))\/(((op (e2) (e1)) = (e3))\/(((op (e2) (e2)) = (e3))\/((op (e2) (e3)) = (e3))))) -> ((op (e3) (e3)) = (e3)) -> (~((op (e3) (op (e2) (e3))) = (op (e2) (e3)))) -> (~((op (e0) (e1)) = (op (e2) (e1)))) -> (~((e2) = (e3))) -> (((op (e1) (e0)) = (e3))\/(((op (e1) (e1)) = (e3))\/(((op (e1) (e2)) = (e3))\/((op (e1) (e3)) = (e3))))) -> (~((op (e1) (e3)) = (op (e3) (e3)))) -> (~((op (e0) (e2)) = (op (e1) (e2)))) -> (~((op (e0) (e3)) = (op (e3) (e3)))) -> (((op (e0) (e0)) = (e3))\/(((op (e0) (e1)) = (e3))\/(((op (e0) (e2)) = (e3))\/((op (e0) (e3)) = (e3))))) -> (((op (e0) (e0)) = (e2))\/(((op (e1) (e0)) = (e2))\/(((op (e2) (e0)) = (e2))\/((op (e3) (e0)) = (e2))))) -> (((op (e2) (e2)) = (e0))\/(((op (e2) (e2)) = (e1))\/(((op (e2) (e2)) = (e2))\/((op (e2) (e2)) = (e3))))) -> (~((op (e2) (e2)) = (e0))) -> (~((op (e1) (e1)) = (e1))) -> (~((op (e1) (e1)) = (e2))) -> (~((op (e1) (e1)) = (e3))) -> (((op (e1) (e1)) = (e0))\/(((op (e1) (e1)) = (e1))\/(((op (e1) (e1)) = (e2))\/((op (e1) (e1)) = (e3))))) -> (~((e1) = (e3))) -> (~((op (e0) (e0)) = (e3))) -> (~((op (e0) (e0)) = (op (e2) (e0)))) -> ((op (e0) (e0)) = (e0)) -> (((op (e2) (e0)) = (e1))\/(((op (e2) (e1)) = (e1))\/(((op (e2) (e2)) = (e1))\/((op (e2) (e3)) = (e1))))) -> (~((op (e1) (op (e2) (e1))) = (op (e2) (e1)))) -> (~((e0) = (e2))) -> (((op (e2) (e0)) = (e0))\/(((op (e2) (e1)) = (e0))\/(((op (e2) (e2)) = (e0))\/((op (e2) (e3)) = (e0))))) -> False). % 15.36/15.53 do 0 intro. intros zenon_H157 zenon_H1c5 zenon_H7d zenon_H10f zenon_Hbb zenon_H24f zenon_Hd3 zenon_H1e2 zenon_H254 zenon_Hb4 zenon_H25b zenon_H13c zenon_H251 zenon_H140 zenon_H1df zenon_H244 zenon_H154 zenon_H1cf zenon_H173 zenon_H10e zenon_H1e3 zenon_H1d0 zenon_H121 zenon_H163 zenon_H9e zenon_H24c zenon_H12d zenon_H10c zenon_H45 zenon_H166 zenon_H28 zenon_H8e zenon_H80 zenon_H84 zenon_H145 zenon_H23 zenon_Hf1 zenon_H294 zenon_Haa zenon_Hbe zenon_H8f zenon_Ha7 zenon_H1c3 zenon_Hce zenon_He6 zenon_H42 zenon_H28a zenon_Hde zenon_H6a zenon_H90 zenon_H8b zenon_H87 zenon_H36 zenon_H58 zenon_Heb zenon_H2d zenon_H2e zenon_H1b4 zenon_Hd6 zenon_H182 zenon_H1b3 zenon_Ha3 zenon_H59 zenon_H258 zenon_H1f zenon_Hb7 zenon_H290 zenon_H5e zenon_H1f5. % 15.36/15.53 apply (zenon_or_s _ _ zenon_H1e3); [ zenon_intro zenon_H52 | zenon_intro zenon_H156 ]. % 15.36/15.53 apply (zenon_L799_); trivial. % 15.36/15.53 apply (zenon_L801_); trivial. % 15.36/15.53 (* end of lemma zenon_L802_ *) % 15.36/15.53 assert (zenon_L803_ : (~((op (e0) (op (e2) (e0))) = (op (e2) (e0)))) -> ((op (e0) (e3)) = (e3)) -> ((op (e2) (e0)) = (e3)) -> False). % 15.36/15.53 do 0 intro. intros zenon_H295 zenon_H53 zenon_Haf. % 15.36/15.53 cut (((op (e0) (e3)) = (e3)) = ((op (e0) (op (e2) (e0))) = (op (e2) (e0)))). % 15.36/15.53 intro zenon_D_pnotp. % 15.36/15.53 apply zenon_H295. % 15.36/15.53 rewrite <- zenon_D_pnotp. % 15.36/15.53 exact zenon_H53. % 15.36/15.53 cut (((e3) = (op (e2) (e0)))); [idtac | apply NNPP; zenon_intro zenon_H1e8]. % 15.36/15.53 cut (((op (e0) (e3)) = (op (e0) (op (e2) (e0))))); [idtac | apply NNPP; zenon_intro zenon_H296]. % 15.36/15.53 congruence. % 15.36/15.53 elim (classic ((op (e0) (op (e2) (e0))) = (op (e0) (op (e2) (e0))))); [ zenon_intro zenon_H297 | zenon_intro zenon_H298 ]. % 15.36/15.53 cut (((op (e0) (op (e2) (e0))) = (op (e0) (op (e2) (e0)))) = ((op (e0) (e3)) = (op (e0) (op (e2) (e0))))). % 15.36/15.53 intro zenon_D_pnotp. % 15.36/15.53 apply zenon_H296. % 15.36/15.53 rewrite <- zenon_D_pnotp. % 15.36/15.53 exact zenon_H297. % 15.36/15.53 cut (((op (e0) (op (e2) (e0))) = (op (e0) (op (e2) (e0))))); [idtac | apply NNPP; zenon_intro zenon_H298]. % 15.36/15.53 cut (((op (e0) (op (e2) (e0))) = (op (e0) (e3)))); [idtac | apply NNPP; zenon_intro zenon_H299]. % 15.36/15.53 congruence. % 15.36/15.53 cut (((op (e2) (e0)) = (e3))); [idtac | apply NNPP; zenon_intro zenon_Hb0]. % 15.36/15.53 cut (((e0) = (e0))); [idtac | apply NNPP; zenon_intro zenon_H1d]. % 15.36/15.53 congruence. % 15.36/15.53 apply zenon_H1d. apply refl_equal. % 15.36/15.53 exact (zenon_Hb0 zenon_Haf). % 15.36/15.53 apply zenon_H298. apply refl_equal. % 15.36/15.53 apply zenon_H298. apply refl_equal. % 15.36/15.53 apply zenon_H1e8. apply sym_equal. exact zenon_Haf. % 15.36/15.53 (* end of lemma zenon_L803_ *) % 15.36/15.53 assert (zenon_L804_ : (~((op (e3) (op (e2) (e3))) = (op (e3) (e1)))) -> ((op (e2) (e3)) = (e1)) -> False). % 15.36/15.53 do 0 intro. intros zenon_H29a zenon_Hb5. % 15.36/15.53 cut (((op (e2) (e3)) = (e1))); [idtac | apply NNPP; zenon_intro zenon_H125]. % 15.36/15.53 cut (((e3) = (e3))); [idtac | apply NNPP; zenon_intro zenon_H4d]. % 15.36/15.53 congruence. % 15.36/15.53 apply zenon_H4d. apply refl_equal. % 15.36/15.53 exact (zenon_H125 zenon_Hb5). % 15.36/15.53 (* end of lemma zenon_L804_ *) % 15.36/15.53 assert (zenon_L805_ : (~((op (e3) (op (e2) (e3))) = (op (e2) (e3)))) -> ((op (e3) (e1)) = (e1)) -> ((op (e2) (e3)) = (e1)) -> False). % 15.36/15.53 do 0 intro. intros zenon_H28a zenon_H13e zenon_Hb5. % 15.36/15.53 cut (((op (e3) (e1)) = (e1)) = ((op (e3) (op (e2) (e3))) = (op (e2) (e3)))). % 15.36/15.53 intro zenon_D_pnotp. % 15.36/15.53 apply zenon_H28a. % 15.36/15.53 rewrite <- zenon_D_pnotp. % 15.36/15.53 exact zenon_H13e. % 15.36/15.53 cut (((e1) = (op (e2) (e3)))); [idtac | apply NNPP; zenon_intro zenon_Hb6]. % 15.36/15.53 cut (((op (e3) (e1)) = (op (e3) (op (e2) (e3))))); [idtac | apply NNPP; zenon_intro zenon_H29b]. % 15.36/15.53 congruence. % 15.36/15.53 elim (classic ((op (e3) (op (e2) (e3))) = (op (e3) (op (e2) (e3))))); [ zenon_intro zenon_H28c | zenon_intro zenon_H28d ]. % 15.36/15.53 cut (((op (e3) (op (e2) (e3))) = (op (e3) (op (e2) (e3)))) = ((op (e3) (e1)) = (op (e3) (op (e2) (e3))))). % 15.36/15.53 intro zenon_D_pnotp. % 15.36/15.53 apply zenon_H29b. % 15.36/15.53 rewrite <- zenon_D_pnotp. % 15.36/15.53 exact zenon_H28c. % 15.36/15.53 cut (((op (e3) (op (e2) (e3))) = (op (e3) (op (e2) (e3))))); [idtac | apply NNPP; zenon_intro zenon_H28d]. % 15.36/15.53 cut (((op (e3) (op (e2) (e3))) = (op (e3) (e1)))); [idtac | apply NNPP; zenon_intro zenon_H29a]. % 15.36/15.53 congruence. % 15.36/15.53 apply (zenon_L804_); trivial. % 15.36/15.53 apply zenon_H28d. apply refl_equal. % 15.36/15.53 apply zenon_H28d. apply refl_equal. % 15.36/15.53 apply zenon_Hb6. apply sym_equal. exact zenon_Hb5. % 15.36/15.53 (* end of lemma zenon_L805_ *) % 15.36/15.53 assert (zenon_L806_ : (((op (e0) (e3)) = (e1))\/(((op (e1) (e3)) = (e1))\/(((op (e2) (e3)) = (e1))\/((op (e3) (e3)) = (e1))))) -> (~((op (e3) (e1)) = (op (e3) (e2)))) -> (~((op (e2) (e2)) = (e1))) -> ((op (e1) (e2)) = (e3)) -> (~((e1) = (e3))) -> (~((op (e0) (e2)) = (op (e0) (e3)))) -> (((op (e0) (e2)) = (e1))\/(((op (e1) (e2)) = (e1))\/(((op (e2) (e2)) = (e1))\/((op (e3) (e2)) = (e1))))) -> ((op (e1) (e0)) = (e1)) -> (~((op (e1) (e0)) = (op (e1) (e3)))) -> ((op (e3) (e1)) = (e1)) -> (~((op (e3) (op (e2) (e3))) = (op (e2) (e3)))) -> (~((op (e3) (e3)) = (e1))) -> False). % 15.36/15.53 do 0 intro. intros zenon_H121 zenon_H135 zenon_H52 zenon_H88 zenon_Ha3 zenon_Hc9 zenon_H11b zenon_Hd8 zenon_H1cf zenon_H13e zenon_H28a zenon_H104. % 15.36/15.53 apply (zenon_or_s _ _ zenon_H121); [ zenon_intro zenon_H37 | zenon_intro zenon_H122 ]. % 15.36/15.53 apply (zenon_L395_); trivial. % 15.36/15.53 apply (zenon_or_s _ _ zenon_H122); [ zenon_intro zenon_H11f | zenon_intro zenon_H123 ]. % 15.36/15.53 apply (zenon_L224_); trivial. % 15.36/15.53 apply (zenon_or_s _ _ zenon_H123); [ zenon_intro zenon_Hb5 | zenon_intro zenon_H38 ]. % 15.36/15.53 apply (zenon_L805_); trivial. % 15.36/15.53 exact (zenon_H104 zenon_H38). % 15.36/15.53 (* end of lemma zenon_L806_ *) % 15.36/15.53 assert (zenon_L807_ : (((op (e1) (e0)) = (e3))\/(((op (e1) (e1)) = (e3))\/(((op (e1) (e2)) = (e3))\/((op (e1) (e3)) = (e3))))) -> (~((op (e1) (e1)) = (e3))) -> (~((op (e3) (e3)) = (e1))) -> (~((op (e3) (op (e2) (e3))) = (op (e2) (e3)))) -> ((op (e3) (e1)) = (e1)) -> (~((op (e1) (e0)) = (op (e1) (e3)))) -> ((op (e1) (e0)) = (e1)) -> (((op (e0) (e2)) = (e1))\/(((op (e1) (e2)) = (e1))\/(((op (e2) (e2)) = (e1))\/((op (e3) (e2)) = (e1))))) -> (~((op (e0) (e2)) = (op (e0) (e3)))) -> (~((e1) = (e3))) -> (~((op (e2) (e2)) = (e1))) -> (~((op (e3) (e1)) = (op (e3) (e2)))) -> (((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) (e1)) = (op (e0) (e3)))) -> ((op (e0) (e1)) = (e2)) -> (~((e2) = (e3))) -> ((op (e2) (e0)) = (e2)) -> (~((op (e2) (e0)) = (op (e2) (e3)))) -> (~((op (e3) (e3)) = (e2))) -> False). % 15.36/15.53 do 0 intro. intros zenon_H90 zenon_H182 zenon_H104 zenon_H28a zenon_H13e zenon_H1cf zenon_Hd8 zenon_H11b zenon_Hc9 zenon_Ha3 zenon_H52 zenon_H135 zenon_H121 zenon_H160 zenon_H1cd zenon_H5d zenon_H6a zenon_Hdd zenon_Hce zenon_H3d. % 15.36/15.53 apply (zenon_or_s _ _ zenon_H90); [ zenon_intro zenon_H69 | zenon_intro zenon_H94 ]. % 15.36/15.53 apply (zenon_L163_); trivial. % 15.36/15.53 apply (zenon_or_s _ _ zenon_H94); [ zenon_intro zenon_H96 | zenon_intro zenon_H95 ]. % 15.36/15.53 exact (zenon_H182 zenon_H96). % 15.36/15.53 apply (zenon_or_s _ _ zenon_H95); [ zenon_intro zenon_H88 | zenon_intro zenon_H8a ]. % 15.36/15.53 apply (zenon_L806_); trivial. % 15.36/15.53 apply (zenon_L410_); trivial. % 15.36/15.53 (* end of lemma zenon_L807_ *) % 15.36/15.53 assert (zenon_L808_ : (((op (e3) (e0)) = (e1))\/(((op (e3) (e1)) = (e1))\/(((op (e3) (e2)) = (e1))\/((op (e3) (e3)) = (e1))))) -> (~((op (e1) (e0)) = (op (e3) (e0)))) -> (~((op (e3) (e3)) = (e2))) -> (~((op (e2) (e0)) = (op (e2) (e3)))) -> ((op (e2) (e0)) = (e2)) -> (~((e2) = (e3))) -> ((op (e0) (e1)) = (e2)) -> (~((op (e0) (e1)) = (op (e0) (e3)))) -> (((op (e0) (e3)) = (e2))\/(((op (e1) (e3)) = (e2))\/(((op (e2) (e3)) = (e2))\/((op (e3) (e3)) = (e2))))) -> (((op (e0) (e3)) = (e1))\/(((op (e1) (e3)) = (e1))\/(((op (e2) (e3)) = (e1))\/((op (e3) (e3)) = (e1))))) -> (~((op (e3) (e1)) = (op (e3) (e2)))) -> (~((op (e2) (e2)) = (e1))) -> (~((e1) = (e3))) -> (~((op (e0) (e2)) = (op (e0) (e3)))) -> (((op (e0) (e2)) = (e1))\/(((op (e1) (e2)) = (e1))\/(((op (e2) (e2)) = (e1))\/((op (e3) (e2)) = (e1))))) -> ((op (e1) (e0)) = (e1)) -> (~((op (e1) (e0)) = (op (e1) (e3)))) -> (~((op (e3) (op (e2) (e3))) = (op (e2) (e3)))) -> (~((op (e1) (e1)) = (e3))) -> (((op (e1) (e0)) = (e3))\/(((op (e1) (e1)) = (e3))\/(((op (e1) (e2)) = (e3))\/((op (e1) (e3)) = (e3))))) -> ((op (e0) (e2)) = (e1)) -> (~((op (e0) (e2)) = (op (e3) (e2)))) -> (~((op (e3) (e3)) = (e1))) -> False). % 15.41/15.54 do 0 intro. intros zenon_H146 zenon_H22e zenon_H3d zenon_Hce zenon_Hdd zenon_H6a zenon_H5d zenon_H1cd zenon_H160 zenon_H121 zenon_H135 zenon_H52 zenon_Ha3 zenon_Hc9 zenon_H11b zenon_Hd8 zenon_H1cf zenon_H28a zenon_H182 zenon_H90 zenon_H29 zenon_H140 zenon_H104. % 15.41/15.54 apply (zenon_or_s _ _ zenon_H146); [ zenon_intro zenon_Hee | zenon_intro zenon_H14b ]. % 15.41/15.54 apply (zenon_L393_); trivial. % 15.41/15.54 apply (zenon_or_s _ _ zenon_H14b); [ zenon_intro zenon_H13e | zenon_intro zenon_H14c ]. % 15.41/15.54 apply (zenon_L807_); trivial. % 15.41/15.54 apply (zenon_or_s _ _ zenon_H14c); [ zenon_intro zenon_H119 | zenon_intro zenon_H38 ]. % 15.41/15.54 apply (zenon_L124_); trivial. % 15.41/15.54 exact (zenon_H104 zenon_H38). % 15.41/15.54 (* end of lemma zenon_L808_ *) % 15.41/15.54 assert (zenon_L809_ : (((op (e0) (e0)) = (e2))\/(((op (e0) (e1)) = (e2))\/(((op (e0) (e2)) = (e2))\/((op (e0) (e3)) = (e2))))) -> (~((op (e0) (e0)) = (e2))) -> (((op (e1) (e0)) = (e3))\/(((op (e1) (e1)) = (e3))\/(((op (e1) (e2)) = (e3))\/((op (e1) (e3)) = (e3))))) -> (~((op (e1) (e1)) = (e3))) -> (~((op (e3) (op (e2) (e3))) = (op (e2) (e3)))) -> (~((op (e1) (e0)) = (op (e1) (e3)))) -> (((op (e0) (e2)) = (e1))\/(((op (e1) (e2)) = (e1))\/(((op (e2) (e2)) = (e1))\/((op (e3) (e2)) = (e1))))) -> (~((op (e0) (e2)) = (op (e0) (e3)))) -> (~((e1) = (e3))) -> (~((op (e2) (e2)) = (e1))) -> (~((op (e3) (e1)) = (op (e3) (e2)))) -> (((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))))) -> (~((e2) = (e3))) -> (~((op (e2) (e0)) = (op (e2) (e3)))) -> (~((op (e3) (e3)) = (e2))) -> (((op (e3) (e0)) = (e1))\/(((op (e3) (e1)) = (e1))\/(((op (e3) (e2)) = (e1))\/((op (e3) (e3)) = (e1))))) -> ((op (e1) (e0)) = (e1)) -> (~((op (e1) (e0)) = (op (e3) (e0)))) -> (~((e1) = (e2))) -> (~((op (e2) (e0)) = (op (e2) (e1)))) -> ((op (e2) (e0)) = (e2)) -> (~((op (e1) (e1)) = (e2))) -> (~((op (e0) (e1)) = (op (e0) (e3)))) -> (((op (e0) (e1)) = (e2))\/(((op (e1) (e1)) = (e2))\/(((op (e2) (e1)) = (e2))\/((op (e3) (e1)) = (e2))))) -> ((op (e0) (e2)) = (e1)) -> (~((op (e0) (e2)) = (op (e3) (e2)))) -> (~((op (e3) (e3)) = (e1))) -> False). % 15.41/15.54 do 0 intro. intros zenon_H8e zenon_H8f zenon_H90 zenon_H182 zenon_H28a zenon_H1cf zenon_H11b zenon_Hc9 zenon_Ha3 zenon_H52 zenon_H135 zenon_H121 zenon_H160 zenon_H6a zenon_Hce zenon_H3d zenon_H146 zenon_Hd8 zenon_H22e zenon_Ha7 zenon_H154 zenon_Hdd zenon_Hd6 zenon_H1cd zenon_H1a2 zenon_H29 zenon_H140 zenon_H104. % 15.41/15.54 apply (zenon_or_s _ _ zenon_H8e); [ zenon_intro zenon_H92 | zenon_intro zenon_H91 ]. % 15.41/15.54 exact (zenon_H8f zenon_H92). % 15.41/15.54 apply (zenon_or_s _ _ zenon_H91); [ zenon_intro zenon_H5d | zenon_intro zenon_H93 ]. % 15.41/15.54 apply (zenon_L808_); trivial. % 15.41/15.54 apply (zenon_or_s _ _ zenon_H93); [ zenon_intro zenon_H63 | zenon_intro zenon_H81 ]. % 15.41/15.54 apply (zenon_L104_); trivial. % 15.41/15.54 apply (zenon_L416_); trivial. % 15.41/15.54 (* end of lemma zenon_L809_ *) % 15.41/15.54 assert (zenon_L810_ : (((op (e0) (e2)) = (e0))\/(((op (e0) (e2)) = (e1))\/(((op (e0) (e2)) = (e2))\/((op (e0) (e2)) = (e3))))) -> ((op (e0) (e0)) = (e0)) -> (~((op (e0) (e0)) = (op (e0) (e2)))) -> (~((op (e3) (e3)) = (e1))) -> (((op (e0) (e1)) = (e2))\/(((op (e1) (e1)) = (e2))\/(((op (e2) (e1)) = (e2))\/((op (e3) (e1)) = (e2))))) -> (~((op (e1) (e1)) = (e2))) -> (~((op (e2) (e0)) = (op (e2) (e1)))) -> (~((e1) = (e2))) -> (~((op (e1) (e0)) = (op (e3) (e0)))) -> (((op (e3) (e0)) = (e1))\/(((op (e3) (e1)) = (e1))\/(((op (e3) (e2)) = (e1))\/((op (e3) (e3)) = (e1))))) -> (((op (e0) (e3)) = (e1))\/(((op (e1) (e3)) = (e1))\/(((op (e2) (e3)) = (e1))\/((op (e3) (e3)) = (e1))))) -> (~((op (e3) (e1)) = (op (e3) (e2)))) -> (~((op (e2) (e2)) = (e1))) -> (~((op (e0) (e2)) = (op (e0) (e3)))) -> (((op (e0) (e2)) = (e1))\/(((op (e1) (e2)) = (e1))\/(((op (e2) (e2)) = (e1))\/((op (e3) (e2)) = (e1))))) -> (~((op (e1) (e0)) = (op (e1) (e3)))) -> (~((op (e3) (op (e2) (e3))) = (op (e2) (e3)))) -> (~((op (e0) (e0)) = (e2))) -> (((op (e0) (e0)) = (e2))\/(((op (e0) (e1)) = (e2))\/(((op (e0) (e2)) = (e2))\/((op (e0) (e3)) = (e2))))) -> ((op (e3) (e2)) = (e2)) -> (~((op (e0) (e2)) = (op (e3) (e2)))) -> (((op (e1) (e0)) = (e3))\/(((op (e1) (e1)) = (e3))\/(((op (e1) (e2)) = (e3))\/((op (e1) (e3)) = (e3))))) -> (~((e1) = (e3))) -> ((op (e1) (e0)) = (e1)) -> (~((op (e1) (e1)) = (e3))) -> (~((op (e0) (e2)) = (op (e1) (e2)))) -> (((op (e0) (e3)) = (e2))\/(((op (e1) (e3)) = (e2))\/(((op (e2) (e3)) = (e2))\/((op (e3) (e3)) = (e2))))) -> (~((op (e0) (e1)) = (op (e0) (e3)))) -> ((op (e0) (e1)) = (e2)) -> (~((e2) = (e3))) -> ((op (e2) (e0)) = (e2)) -> (~((op (e2) (e0)) = (op (e2) (e3)))) -> (~((op (e3) (e3)) = (e2))) -> False). % 15.41/15.54 do 0 intro. intros zenon_H251 zenon_H1f zenon_H250 zenon_H104 zenon_H1a2 zenon_Hd6 zenon_H154 zenon_Ha7 zenon_H22e zenon_H146 zenon_H121 zenon_H135 zenon_H52 zenon_Hc9 zenon_H11b zenon_H1cf zenon_H28a zenon_H8f zenon_H8e zenon_H1dd zenon_H140 zenon_H90 zenon_Ha3 zenon_Hd8 zenon_H182 zenon_H87 zenon_H160 zenon_H1cd zenon_H5d zenon_H6a zenon_Hdd zenon_Hce zenon_H3d. % 15.41/15.54 apply (zenon_or_s _ _ zenon_H251); [ zenon_intro zenon_Hab | zenon_intro zenon_H252 ]. % 15.41/15.54 apply (zenon_L567_); trivial. % 15.41/15.54 apply (zenon_or_s _ _ zenon_H252); [ zenon_intro zenon_H29 | zenon_intro zenon_H253 ]. % 15.41/15.54 apply (zenon_L809_); trivial. % 15.41/15.54 apply (zenon_or_s _ _ zenon_H253); [ zenon_intro zenon_H63 | zenon_intro zenon_H50 ]. % 15.41/15.54 apply (zenon_L253_); trivial. % 15.41/15.54 apply (zenon_L411_); trivial. % 15.41/15.54 (* end of lemma zenon_L810_ *) % 15.41/15.54 assert (zenon_L811_ : (((op (e3) (e0)) = (e2))\/(((op (e3) (e1)) = (e2))\/(((op (e3) (e2)) = (e2))\/((op (e3) (e3)) = (e2))))) -> ((op (e3) (e0)) = (e3)) -> (~((op (e0) (e1)) = (op (e3) (e1)))) -> (~((op (e2) (e0)) = (op (e2) (e3)))) -> ((op (e2) (e0)) = (e2)) -> (~((e2) = (e3))) -> ((op (e0) (e1)) = (e2)) -> (~((op (e0) (e1)) = (op (e0) (e3)))) -> (((op (e0) (e3)) = (e2))\/(((op (e1) (e3)) = (e2))\/(((op (e2) (e3)) = (e2))\/((op (e3) (e3)) = (e2))))) -> (~((op (e0) (e2)) = (op (e1) (e2)))) -> (~((op (e1) (e1)) = (e3))) -> ((op (e1) (e0)) = (e1)) -> (~((e1) = (e3))) -> (((op (e1) (e0)) = (e3))\/(((op (e1) (e1)) = (e3))\/(((op (e1) (e2)) = (e3))\/((op (e1) (e3)) = (e3))))) -> (~((op (e0) (e2)) = (op (e3) (e2)))) -> (((op (e0) (e0)) = (e2))\/(((op (e0) (e1)) = (e2))\/(((op (e0) (e2)) = (e2))\/((op (e0) (e3)) = (e2))))) -> (~((op (e0) (e0)) = (e2))) -> (~((op (e3) (op (e2) (e3))) = (op (e2) (e3)))) -> (~((op (e1) (e0)) = (op (e1) (e3)))) -> (((op (e0) (e2)) = (e1))\/(((op (e1) (e2)) = (e1))\/(((op (e2) (e2)) = (e1))\/((op (e3) (e2)) = (e1))))) -> (~((op (e0) (e2)) = (op (e0) (e3)))) -> (~((op (e2) (e2)) = (e1))) -> (~((op (e3) (e1)) = (op (e3) (e2)))) -> (((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 (e1) (e0)) = (op (e3) (e0)))) -> (~((e1) = (e2))) -> (~((op (e2) (e0)) = (op (e2) (e1)))) -> (~((op (e1) (e1)) = (e2))) -> (((op (e0) (e1)) = (e2))\/(((op (e1) (e1)) = (e2))\/(((op (e2) (e1)) = (e2))\/((op (e3) (e1)) = (e2))))) -> (~((op (e3) (e3)) = (e1))) -> (~((op (e0) (e0)) = (op (e0) (e2)))) -> ((op (e0) (e0)) = (e0)) -> (((op (e0) (e2)) = (e0))\/(((op (e0) (e2)) = (e1))\/(((op (e0) (e2)) = (e2))\/((op (e0) (e2)) = (e3))))) -> (~((op (e3) (e3)) = (e2))) -> False). % 15.41/15.54 do 0 intro. intros zenon_H1df zenon_Hba zenon_H138 zenon_Hce zenon_Hdd zenon_H6a zenon_H5d zenon_H1cd zenon_H160 zenon_H87 zenon_H182 zenon_Hd8 zenon_Ha3 zenon_H90 zenon_H140 zenon_H8e zenon_H8f zenon_H28a zenon_H1cf zenon_H11b zenon_Hc9 zenon_H52 zenon_H135 zenon_H121 zenon_H146 zenon_H22e zenon_Ha7 zenon_H154 zenon_Hd6 zenon_H1a2 zenon_H104 zenon_H250 zenon_H1f zenon_H251 zenon_H3d. % 15.41/15.54 apply (zenon_or_s _ _ zenon_H1df); [ zenon_intro zenon_He9 | zenon_intro zenon_H1e0 ]. % 15.41/15.54 apply (zenon_L220_); trivial. % 15.41/15.54 apply (zenon_or_s _ _ zenon_H1e0); [ zenon_intro zenon_H16a | zenon_intro zenon_H1e1 ]. % 15.41/15.54 apply (zenon_L146_); trivial. % 15.41/15.54 apply (zenon_or_s _ _ zenon_H1e1); [ zenon_intro zenon_H1dd | zenon_intro zenon_H43 ]. % 15.41/15.54 apply (zenon_L810_); trivial. % 15.41/15.54 exact (zenon_H3d zenon_H43). % 15.41/15.54 (* end of lemma zenon_L811_ *) % 15.41/15.54 assert (zenon_L812_ : (~((op (e0) (op (e2) (e0))) = (op (e2) (e0)))) -> ((op (e0) (e2)) = (e2)) -> ((op (e2) (e0)) = (e2)) -> False). % 15.41/15.54 do 0 intro. intros zenon_H295 zenon_H63 zenon_Hdd. % 15.41/15.54 cut (((op (e0) (e2)) = (e2)) = ((op (e0) (op (e2) (e0))) = (op (e2) (e0)))). % 15.41/15.54 intro zenon_D_pnotp. % 15.41/15.54 apply zenon_H295. % 15.41/15.54 rewrite <- zenon_D_pnotp. % 15.41/15.54 exact zenon_H63. % 15.41/15.54 cut (((e2) = (op (e2) (e0)))); [idtac | apply NNPP; zenon_intro zenon_H17c]. % 15.41/15.54 cut (((op (e0) (e2)) = (op (e0) (op (e2) (e0))))); [idtac | apply NNPP; zenon_intro zenon_H29c]. % 15.41/15.54 congruence. % 15.41/15.54 elim (classic ((op (e0) (op (e2) (e0))) = (op (e0) (op (e2) (e0))))); [ zenon_intro zenon_H297 | zenon_intro zenon_H298 ]. % 15.41/15.54 cut (((op (e0) (op (e2) (e0))) = (op (e0) (op (e2) (e0)))) = ((op (e0) (e2)) = (op (e0) (op (e2) (e0))))). % 15.41/15.54 intro zenon_D_pnotp. % 15.41/15.54 apply zenon_H29c. % 15.41/15.54 rewrite <- zenon_D_pnotp. % 15.41/15.54 exact zenon_H297. % 15.41/15.54 cut (((op (e0) (op (e2) (e0))) = (op (e0) (op (e2) (e0))))); [idtac | apply NNPP; zenon_intro zenon_H298]. % 15.41/15.54 cut (((op (e0) (op (e2) (e0))) = (op (e0) (e2)))); [idtac | apply NNPP; zenon_intro zenon_H29d]. % 15.41/15.54 congruence. % 15.41/15.54 cut (((op (e2) (e0)) = (e2))); [idtac | apply NNPP; zenon_intro zenon_H29e]. % 15.41/15.54 cut (((e0) = (e0))); [idtac | apply NNPP; zenon_intro zenon_H1d]. % 15.41/15.54 congruence. % 15.41/15.54 apply zenon_H1d. apply refl_equal. % 15.41/15.54 exact (zenon_H29e zenon_Hdd). % 15.41/15.54 apply zenon_H298. apply refl_equal. % 15.41/15.54 apply zenon_H298. apply refl_equal. % 15.41/15.54 apply zenon_H17c. apply sym_equal. exact zenon_Hdd. % 15.41/15.54 (* end of lemma zenon_L812_ *) % 15.41/15.54 assert (zenon_L813_ : (~((op (e3) (e3)) = (e2))) -> (((op (e0) (e2)) = (e0))\/(((op (e0) (e2)) = (e1))\/(((op (e0) (e2)) = (e2))\/((op (e0) (e2)) = (e3))))) -> ((op (e0) (e0)) = (e0)) -> (~((op (e0) (e0)) = (op (e0) (e2)))) -> (((op (e0) (e1)) = (e2))\/(((op (e1) (e1)) = (e2))\/(((op (e2) (e1)) = (e2))\/((op (e3) (e1)) = (e2))))) -> (~((op (e1) (e1)) = (e2))) -> (~((op (e2) (e0)) = (op (e2) (e1)))) -> (~((e1) = (e2))) -> (~((op (e1) (e0)) = (op (e3) (e0)))) -> (((op (e3) (e0)) = (e1))\/(((op (e3) (e1)) = (e1))\/(((op (e3) (e2)) = (e1))\/((op (e3) (e3)) = (e1))))) -> (((op (e0) (e3)) = (e1))\/(((op (e1) (e3)) = (e1))\/(((op (e2) (e3)) = (e1))\/((op (e3) (e3)) = (e1))))) -> (~((op (e3) (e1)) = (op (e3) (e2)))) -> (~((op (e2) (e2)) = (e1))) -> (~((op (e0) (e2)) = (op (e0) (e3)))) -> (((op (e0) (e2)) = (e1))\/(((op (e1) (e2)) = (e1))\/(((op (e2) (e2)) = (e1))\/((op (e3) (e2)) = (e1))))) -> (~((op (e1) (e0)) = (op (e1) (e3)))) -> (~((op (e3) (op (e2) (e3))) = (op (e2) (e3)))) -> (~((op (e0) (e0)) = (e2))) -> (((op (e0) (e0)) = (e2))\/(((op (e0) (e1)) = (e2))\/(((op (e0) (e2)) = (e2))\/((op (e0) (e3)) = (e2))))) -> (~((op (e0) (e2)) = (op (e3) (e2)))) -> (((op (e1) (e0)) = (e3))\/(((op (e1) (e1)) = (e3))\/(((op (e1) (e2)) = (e3))\/((op (e1) (e3)) = (e3))))) -> (~((e1) = (e3))) -> ((op (e1) (e0)) = (e1)) -> (~((op (e1) (e1)) = (e3))) -> (~((op (e0) (e2)) = (op (e1) (e2)))) -> (((op (e0) (e3)) = (e2))\/(((op (e1) (e3)) = (e2))\/(((op (e2) (e3)) = (e2))\/((op (e3) (e3)) = (e2))))) -> (~((op (e0) (e1)) = (op (e0) (e3)))) -> (~((e2) = (e3))) -> (~((op (e2) (e0)) = (op (e2) (e3)))) -> (~((op (e0) (e1)) = (op (e3) (e1)))) -> (((op (e3) (e0)) = (e2))\/(((op (e3) (e1)) = (e2))\/(((op (e3) (e2)) = (e2))\/((op (e3) (e3)) = (e2))))) -> (~((op (e0) (e0)) = (e3))) -> (((op (e0) (e0)) = (e3))\/(((op (e1) (e0)) = (e3))\/(((op (e2) (e0)) = (e3))\/((op (e3) (e0)) = (e3))))) -> (((op (e0) (e0)) = (e3))\/(((op (e0) (e1)) = (e3))\/(((op (e0) (e2)) = (e3))\/((op (e0) (e3)) = (e3))))) -> ((op (e2) (e0)) = (e2)) -> (~((op (e0) (op (e2) (e0))) = (op (e2) (e0)))) -> (((op (e3) (e3)) = (e0))\/(((op (e3) (e3)) = (e1))\/(((op (e3) (e3)) = (e2))\/((op (e3) (e3)) = (e3))))) -> (~((op (e3) (e3)) = (e0))) -> (~((op (e3) (e3)) = (e1))) -> (~((op (e0) (e3)) = (op (e3) (e3)))) -> (~((op (e3) (e3)) = (e3))) -> False). % 15.41/15.54 do 0 intro. intros zenon_H3d zenon_H251 zenon_H1f zenon_H250 zenon_H1a2 zenon_Hd6 zenon_H154 zenon_Ha7 zenon_H22e zenon_H146 zenon_H121 zenon_H135 zenon_H52 zenon_Hc9 zenon_H11b zenon_H1cf zenon_H28a zenon_H8f zenon_H8e zenon_H140 zenon_H90 zenon_Ha3 zenon_Hd8 zenon_H182 zenon_H87 zenon_H160 zenon_H1cd zenon_H6a zenon_Hce zenon_H138 zenon_H1df zenon_H59 zenon_Hbe zenon_H58 zenon_Hdd zenon_H295 zenon_H3b zenon_H3c zenon_H104 zenon_H36 zenon_H3e. % 15.41/15.54 apply (zenon_or_s _ _ zenon_H8e); [ zenon_intro zenon_H92 | zenon_intro zenon_H91 ]. % 15.41/15.54 exact (zenon_H8f zenon_H92). % 15.41/15.54 apply (zenon_or_s _ _ zenon_H91); [ zenon_intro zenon_H5d | zenon_intro zenon_H93 ]. % 15.41/15.54 apply (zenon_or_s _ _ zenon_H58); [ zenon_intro zenon_H5b | zenon_intro zenon_H5a ]. % 15.41/15.54 exact (zenon_H59 zenon_H5b). % 15.41/15.54 apply (zenon_or_s _ _ zenon_H5a); [ zenon_intro zenon_H4a | zenon_intro zenon_H5c ]. % 15.41/15.54 apply (zenon_L50_); trivial. % 15.41/15.54 apply (zenon_or_s _ _ zenon_H5c); [ zenon_intro zenon_H50 | zenon_intro zenon_H53 ]. % 15.41/15.54 apply (zenon_L411_); trivial. % 15.41/15.54 apply (zenon_or_s _ _ zenon_Hbe); [ zenon_intro zenon_H5b | zenon_intro zenon_Hbf ]. % 15.41/15.54 exact (zenon_H59 zenon_H5b). % 15.41/15.54 apply (zenon_or_s _ _ zenon_Hbf); [ zenon_intro zenon_H69 | zenon_intro zenon_Hc0 ]. % 15.41/15.54 apply (zenon_L163_); trivial. % 15.41/15.54 apply (zenon_or_s _ _ zenon_Hc0); [ zenon_intro zenon_Haf | zenon_intro zenon_Hba ]. % 15.41/15.54 apply (zenon_L803_); trivial. % 15.41/15.54 apply (zenon_L811_); trivial. % 15.41/15.54 apply (zenon_or_s _ _ zenon_H93); [ zenon_intro zenon_H63 | zenon_intro zenon_H81 ]. % 15.41/15.54 apply (zenon_L812_); trivial. % 15.41/15.54 apply (zenon_L107_); trivial. % 15.41/15.54 (* end of lemma zenon_L813_ *) % 15.41/15.54 assert (zenon_L814_ : ((~((op (e2) (e2)) = (e1)))\/((op (e2) (e1)) = (e2))) -> (~((op (e2) (e1)) = (op (e2) (e3)))) -> (~((op (e2) (e1)) = (op (e2) (e2)))) -> (((op (e2) (e0)) = (e0))\/(((op (e2) (e1)) = (e0))\/(((op (e2) (e2)) = (e0))\/((op (e2) (e3)) = (e0))))) -> (~((e0) = (e2))) -> (~((op (e1) (op (e2) (e1))) = (op (e2) (e1)))) -> (((op (e2) (e0)) = (e1))\/(((op (e2) (e1)) = (e1))\/(((op (e2) (e2)) = (e1))\/((op (e2) (e3)) = (e1))))) -> ((op (e0) (e0)) = (e0)) -> (~((op (e0) (e0)) = (op (e2) (e0)))) -> (~((op (e0) (e0)) = (e3))) -> (~((e1) = (e3))) -> ((op (e1) (e0)) = (e1)) -> (((op (e1) (e1)) = (e0))\/(((op (e1) (e1)) = (e1))\/(((op (e1) (e1)) = (e2))\/((op (e1) (e1)) = (e3))))) -> (~((op (e1) (e1)) = (e3))) -> (~((op (e1) (e1)) = (e2))) -> (~((op (e1) (e1)) = (e1))) -> (~((op (e2) (e2)) = (e0))) -> (((op (e2) (e2)) = (e0))\/(((op (e2) (e2)) = (e1))\/(((op (e2) (e2)) = (e2))\/((op (e2) (e2)) = (e3))))) -> (((op (e0) (e0)) = (e2))\/(((op (e1) (e0)) = (e2))\/(((op (e2) (e0)) = (e2))\/((op (e3) (e0)) = (e2))))) -> (((op (e0) (e0)) = (e3))\/(((op (e0) (e1)) = (e3))\/(((op (e0) (e2)) = (e3))\/((op (e0) (e3)) = (e3))))) -> (~((op (e0) (e3)) = (op (e3) (e3)))) -> (~((op (e0) (e2)) = (op (e1) (e2)))) -> (~((op (e1) (e3)) = (op (e3) (e3)))) -> (((op (e1) (e0)) = (e3))\/(((op (e1) (e1)) = (e3))\/(((op (e1) (e2)) = (e3))\/((op (e1) (e3)) = (e3))))) -> (~((e2) = (e3))) -> (~((op (e0) (e1)) = (op (e2) (e1)))) -> (~((op (e3) (op (e2) (e3))) = (op (e2) (e3)))) -> ((op (e3) (e3)) = (e3)) -> (((op (e2) (e0)) = (e3))\/(((op (e2) (e1)) = (e3))\/(((op (e2) (e2)) = (e3))\/((op (e2) (e3)) = (e3))))) -> (~((op (e2) (e0)) = (op (e2) (e3)))) -> ((~((op (e2) (e2)) = (e3)))\/((op (e2) (e3)) = (e2))) -> (~((e1) = (e2))) -> (~((op (e0) (e0)) = (e2))) -> (((op (e0) (e0)) = (e3))\/(((op (e1) (e0)) = (e3))\/(((op (e2) (e0)) = (e3))\/((op (e3) (e0)) = (e3))))) -> ((~((op (e3) (e3)) = (e1)))\/((op (e3) (e1)) = (e3))) -> (~((op (e0) (e1)) = (op (e3) (e1)))) -> (~((op (e1) (e2)) = (op (e2) (e2)))) -> (((op (e0) (e3)) = (e1))\/(((op (e1) (e3)) = (e1))\/(((op (e2) (e3)) = (e1))\/((op (e3) (e3)) = (e1))))) -> (~((op (e0) (e0)) = (op (e0) (e3)))) -> (~((op (e0) (e3)) = (op (e2) (e3)))) -> (~((op (e0) (e3)) = (op (e1) (e3)))) -> (((op (e0) (e3)) = (e0))\/(((op (e0) (e3)) = (e1))\/(((op (e0) (e3)) = (e2))\/((op (e0) (e3)) = (e3))))) -> (~((op (e1) (e0)) = (op (e1) (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) (e2)) = (op (e3) (e2)))) -> (~((op (e0) (e2)) = (op (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 (e1) (e0)) = (e2))\/(((op (e1) (e1)) = (e2))\/(((op (e1) (e2)) = (e2))\/((op (e1) (e3)) = (e2))))) -> ((~((op (e2) (e2)) = (e2)))\/((op (e2) (e2)) = (e2))) -> False). % 15.41/15.54 do 0 intro. intros zenon_H1e3 zenon_H1e2 zenon_H157 zenon_H1f5 zenon_H5e zenon_H290 zenon_Hb7 zenon_H1f zenon_H258 zenon_H59 zenon_Ha3 zenon_Hd8 zenon_H1b3 zenon_H182 zenon_Hd6 zenon_H1b4 zenon_H2e zenon_H2d zenon_Heb zenon_H58 zenon_H36 zenon_H87 zenon_H8b zenon_H90 zenon_H6a zenon_Hde zenon_H28a zenon_H42 zenon_He6 zenon_Hce zenon_H1c3 zenon_Ha7 zenon_H8f zenon_Hbe zenon_H10c zenon_H138 zenon_H7d zenon_H121 zenon_H24f zenon_Hb4 zenon_H80 zenon_H254 zenon_H1cf zenon_H11b zenon_H250 zenon_H140 zenon_H28 zenon_H251 zenon_Hc9 zenon_H84 zenon_Haa. % 15.41/15.54 apply (zenon_or_s _ _ zenon_H1e3); [ zenon_intro zenon_H52 | zenon_intro zenon_H156 ]. % 15.41/15.54 apply (zenon_or_s _ _ zenon_Haa); [ zenon_intro zenon_H2f | zenon_intro zenon_H35 ]. % 15.41/15.54 apply (zenon_L786_); trivial. % 15.41/15.54 apply (zenon_L573_); trivial. % 15.41/15.54 apply (zenon_or_s _ _ zenon_Haa); [ zenon_intro zenon_H2f | zenon_intro zenon_H35 ]. % 15.41/15.54 apply (zenon_or_s _ _ zenon_H1c3); [ zenon_intro zenon_H30 | zenon_intro zenon_H124 ]. % 15.41/15.54 apply (zenon_L781_); trivial. % 15.41/15.54 apply (zenon_L256_); trivial. % 15.41/15.54 apply (zenon_L134_); trivial. % 15.41/15.54 (* end of lemma zenon_L814_ *) % 15.41/15.54 assert (zenon_L815_ : ((~((op (e3) (e3)) = (e2)))\/((op (e3) (e2)) = (e3))) -> (~((op (e0) (e0)) = (e1))) -> (~((op (e3) (e0)) = (op (e3) (e2)))) -> (~((op (e2) (e2)) = (e3))) -> (~((op (e2) (e2)) = (e2))) -> (((op (e0) (e0)) = (e1))\/(((op (e1) (e0)) = (e1))\/(((op (e2) (e0)) = (e1))\/((op (e3) (e0)) = (e1))))) -> (~((op (e1) (e2)) = (op (e3) (e2)))) -> (((op (e0) (e0)) = (e2))\/(((op (e1) (e0)) = (e2))\/(((op (e2) (e0)) = (e2))\/((op (e3) (e0)) = (e2))))) -> (~((op (e1) (e1)) = (e1))) -> (((op (e1) (e1)) = (e0))\/(((op (e1) (e1)) = (e1))\/(((op (e1) (e1)) = (e2))\/((op (e1) (e1)) = (e3))))) -> (((op (e0) (e0)) = (e3))\/(((op (e0) (e1)) = (e3))\/(((op (e0) (e2)) = (e3))\/((op (e0) (e3)) = (e3))))) -> (~((op (e0) (op (e2) (e0))) = (op (e2) (e0)))) -> (((op (e3) (e0)) = (e2))\/(((op (e3) (e1)) = (e2))\/(((op (e3) (e2)) = (e2))\/((op (e3) (e3)) = (e2))))) -> (~((op (e0) (e0)) = (op (e0) (e2)))) -> ((op (e0) (e0)) = (e0)) -> (((op (e0) (e0)) = (e2))\/(((op (e0) (e1)) = (e2))\/(((op (e0) (e2)) = (e2))\/((op (e0) (e3)) = (e2))))) -> (((op (e0) (e1)) = (e2))\/(((op (e1) (e1)) = (e2))\/(((op (e2) (e1)) = (e2))\/((op (e3) (e1)) = (e2))))) -> (~((op (e2) (e0)) = (op (e2) (e1)))) -> (~((op (e1) (e1)) = (e2))) -> (~((op (e1) (e0)) = (op (e3) (e0)))) -> (((op (e0) (e2)) = (e1))\/(((op (e1) (e2)) = (e1))\/(((op (e2) (e2)) = (e1))\/((op (e3) (e2)) = (e1))))) -> (~((op (e3) (e1)) = (op (e3) (e2)))) -> (~((op (e2) (e2)) = (e1))) -> (~((op (e0) (e2)) = (op (e0) (e3)))) -> (~((op (e1) (e0)) = (op (e1) (e3)))) -> (~((op (e3) (op (e2) (e3))) = (op (e2) (e3)))) -> (~((op (e3) (e3)) = (e1))) -> (((op (e0) (e3)) = (e1))\/(((op (e1) (e3)) = (e1))\/(((op (e2) (e3)) = (e1))\/((op (e3) (e3)) = (e1))))) -> (~((op (e0) (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)) = (e1))\/(((op (e0) (e2)) = (e2))\/((op (e0) (e2)) = (e3))))) -> (~((op (e0) (e1)) = (op (e3) (e1)))) -> (((op (e0) (e0)) = (e3))\/(((op (e1) (e0)) = (e3))\/(((op (e2) (e0)) = (e3))\/((op (e3) (e0)) = (e3))))) -> (~((e1) = (e3))) -> (~((op (e1) (e1)) = (e3))) -> (~((op (e0) (e2)) = (op (e1) (e2)))) -> (((op (e0) (e3)) = (e2))\/(((op (e1) (e3)) = (e2))\/(((op (e2) (e3)) = (e2))\/((op (e3) (e3)) = (e2))))) -> (~((op (e2) (e0)) = (op (e2) (e3)))) -> (~((op (e0) (e1)) = (op (e0) (e3)))) -> (((op (e1) (e0)) = (e3))\/(((op (e1) (e1)) = (e3))\/(((op (e1) (e2)) = (e3))\/((op (e1) (e3)) = (e3))))) -> (~((e2) = (e3))) -> (~((op (e0) (e0)) = (e3))) -> (((op (e3) (e3)) = (e0))\/(((op (e3) (e3)) = (e1))\/(((op (e3) (e3)) = (e2))\/((op (e3) (e3)) = (e3))))) -> (~((op (e0) (e3)) = (op (e3) (e3)))) -> (~((op (e3) (e3)) = (e0))) -> ((op (e1) (e0)) = (e1)) -> (~((e1) = (e2))) -> (~((op (e0) (e0)) = (e2))) -> ((~((op (e2) (e2)) = (e1)))\/((op (e2) (e1)) = (e2))) -> (~((op (e2) (e1)) = (op (e2) (e3)))) -> (~((op (e2) (e1)) = (op (e2) (e2)))) -> (((op (e2) (e0)) = (e0))\/(((op (e2) (e1)) = (e0))\/(((op (e2) (e2)) = (e0))\/((op (e2) (e3)) = (e0))))) -> (~((e0) = (e2))) -> (~((op (e1) (op (e2) (e1))) = (op (e2) (e1)))) -> (((op (e2) (e0)) = (e1))\/(((op (e2) (e1)) = (e1))\/(((op (e2) (e2)) = (e1))\/((op (e2) (e3)) = (e1))))) -> (~((op (e0) (e0)) = (op (e2) (e0)))) -> (~((op (e2) (e2)) = (e0))) -> (((op (e2) (e2)) = (e0))\/(((op (e2) (e2)) = (e1))\/(((op (e2) (e2)) = (e2))\/((op (e2) (e2)) = (e3))))) -> (~((op (e1) (e3)) = (op (e3) (e3)))) -> (~((op (e0) (e1)) = (op (e2) (e1)))) -> (((op (e2) (e0)) = (e3))\/(((op (e2) (e1)) = (e3))\/(((op (e2) (e2)) = (e3))\/((op (e2) (e3)) = (e3))))) -> ((~((op (e2) (e2)) = (e3)))\/((op (e2) (e3)) = (e2))) -> ((~((op (e3) (e3)) = (e1)))\/((op (e3) (e1)) = (e3))) -> (~((op (e1) (e2)) = (op (e2) (e2)))) -> (~((op (e0) (e0)) = (op (e0) (e3)))) -> (~((op (e0) (e3)) = (op (e2) (e3)))) -> (~((op (e0) (e3)) = (op (e1) (e3)))) -> (((op (e0) (e3)) = (e0))\/(((op (e0) (e3)) = (e1))\/(((op (e0) (e3)) = (e2))\/((op (e0) (e3)) = (e3))))) -> (~((op (e0) (e2)) = (op (e2) (e2)))) -> (((op (e1) (e0)) = (e2))\/(((op (e1) (e1)) = (e2))\/(((op (e1) (e2)) = (e2))\/((op (e1) (e3)) = (e2))))) -> ((~((op (e2) (e2)) = (e2)))\/((op (e2) (e2)) = (e2))) -> ((~((op (e3) (e3)) = (e3)))\/((op (e3) (e3)) = (e3))) -> False). % 15.41/15.54 do 0 intro. intros zenon_H10e zenon_H45 zenon_H105 zenon_H30 zenon_H2f zenon_Hf1 zenon_H17d zenon_Heb zenon_H1b4 zenon_H1b3 zenon_H58 zenon_H295 zenon_H1df zenon_H250 zenon_H1f zenon_H8e zenon_H1a2 zenon_H154 zenon_Hd6 zenon_H22e zenon_H11b zenon_H135 zenon_H52 zenon_Hc9 zenon_H1cf zenon_H28a zenon_H104 zenon_H121 zenon_H140 zenon_H146 zenon_H251 zenon_H138 zenon_Hbe zenon_Ha3 zenon_H182 zenon_H87 zenon_H160 zenon_Hce zenon_H1cd zenon_H90 zenon_H6a zenon_H59 zenon_H3b zenon_H36 zenon_H3c zenon_Hd8 zenon_Ha7 zenon_H8f zenon_H1e3 zenon_H1e2 zenon_H157 zenon_H1f5 zenon_H5e zenon_H290 zenon_Hb7 zenon_H258 zenon_H2e zenon_H2d zenon_H8b zenon_Hde zenon_He6 zenon_H1c3 zenon_H10c zenon_H7d zenon_H24f zenon_Hb4 zenon_H80 zenon_H254 zenon_H28 zenon_H84 zenon_Haa zenon_H10d. % 15.41/15.54 apply (zenon_or_s _ _ zenon_H10e); [ zenon_intro zenon_H3d | zenon_intro zenon_H106 ]. % 15.41/15.54 apply (zenon_or_s _ _ zenon_H10d); [ zenon_intro zenon_H3e | zenon_intro zenon_H42 ]. % 15.41/15.54 apply (zenon_or_s _ _ zenon_Heb); [ zenon_intro zenon_H92 | zenon_intro zenon_Hec ]. % 15.41/15.54 exact (zenon_H8f zenon_H92). % 15.41/15.54 apply (zenon_or_s _ _ zenon_Hec); [ zenon_intro zenon_H68 | zenon_intro zenon_Hed ]. % 15.41/15.54 apply (zenon_L162_); trivial. % 15.41/15.54 apply (zenon_or_s _ _ zenon_Hed); [ zenon_intro zenon_Hdd | zenon_intro zenon_He9 ]. % 15.41/15.54 apply (zenon_L813_); trivial. % 15.41/15.54 apply (zenon_L406_); trivial. % 15.41/15.54 apply (zenon_L814_); trivial. % 15.41/15.54 apply (zenon_L748_); trivial. % 15.41/15.54 (* end of lemma zenon_L815_ *) % 15.41/15.54 assert (zenon_L816_ : (~((op (e0) (op (e2) (e0))) = (op (e2) (e0)))) -> ((op (e0) (e1)) = (e1)) -> ((op (e2) (e0)) = (e1)) -> False). % 15.41/15.54 do 0 intro. intros zenon_H295 zenon_H22 zenon_Hae. % 15.41/15.54 cut (((op (e0) (e1)) = (e1)) = ((op (e0) (op (e2) (e0))) = (op (e2) (e0)))). % 15.41/15.54 intro zenon_D_pnotp. % 15.41/15.54 apply zenon_H295. % 15.41/15.54 rewrite <- zenon_D_pnotp. % 15.41/15.54 exact zenon_H22. % 15.41/15.54 cut (((e1) = (op (e2) (e0)))); [idtac | apply NNPP; zenon_intro zenon_H248]. % 15.41/15.54 cut (((op (e0) (e1)) = (op (e0) (op (e2) (e0))))); [idtac | apply NNPP; zenon_intro zenon_H29f]. % 15.41/15.54 congruence. % 15.41/15.54 elim (classic ((op (e0) (op (e2) (e0))) = (op (e0) (op (e2) (e0))))); [ zenon_intro zenon_H297 | zenon_intro zenon_H298 ]. % 15.41/15.54 cut (((op (e0) (op (e2) (e0))) = (op (e0) (op (e2) (e0)))) = ((op (e0) (e1)) = (op (e0) (op (e2) (e0))))). % 15.41/15.54 intro zenon_D_pnotp. % 15.41/15.54 apply zenon_H29f. % 15.41/15.54 rewrite <- zenon_D_pnotp. % 15.41/15.54 exact zenon_H297. % 15.41/15.54 cut (((op (e0) (op (e2) (e0))) = (op (e0) (op (e2) (e0))))); [idtac | apply NNPP; zenon_intro zenon_H298]. % 15.41/15.54 cut (((op (e0) (op (e2) (e0))) = (op (e0) (e1)))); [idtac | apply NNPP; zenon_intro zenon_H2a0]. % 15.41/15.54 congruence. % 15.41/15.54 cut (((op (e2) (e0)) = (e1))); [idtac | apply NNPP; zenon_intro zenon_H1f4]. % 15.41/15.54 cut (((e0) = (e0))); [idtac | apply NNPP; zenon_intro zenon_H1d]. % 15.41/15.54 congruence. % 15.41/15.54 apply zenon_H1d. apply refl_equal. % 15.41/15.54 exact (zenon_H1f4 zenon_Hae). % 15.41/15.54 apply zenon_H298. apply refl_equal. % 15.41/15.54 apply zenon_H298. apply refl_equal. % 15.41/15.54 apply zenon_H248. apply sym_equal. exact zenon_Hae. % 15.41/15.54 (* end of lemma zenon_L816_ *) % 15.41/15.54 assert (zenon_L817_ : (((op (e0) (e0)) = (e3))\/(((op (e0) (e1)) = (e3))\/(((op (e0) (e2)) = (e3))\/((op (e0) (e3)) = (e3))))) -> (~((op (e0) (e0)) = (e3))) -> (~((op (e3) (op (e2) (e3))) = (op (e2) (e3)))) -> (~((op (e2) (e2)) = (e3))) -> (~((op (e0) (e1)) = (op (e2) (e1)))) -> ((op (e2) (e0)) = (e1)) -> (~((e1) = (e3))) -> (((op (e2) (e0)) = (e3))\/(((op (e2) (e1)) = (e3))\/(((op (e2) (e2)) = (e3))\/((op (e2) (e3)) = (e3))))) -> (~((op (e0) (e2)) = (op (e3) (e2)))) -> ((op (e3) (e2)) = (e3)) -> ((op (e3) (e3)) = (e3)) -> (~((op (e0) (e3)) = (op (e3) (e3)))) -> False). % 15.41/15.54 do 0 intro. intros zenon_H58 zenon_H59 zenon_H28a zenon_H30 zenon_Hde zenon_Hae zenon_Ha3 zenon_He6 zenon_H140 zenon_H106 zenon_H42 zenon_H36. % 15.41/15.54 apply (zenon_or_s _ _ zenon_H58); [ zenon_intro zenon_H5b | zenon_intro zenon_H5a ]. % 15.41/15.54 exact (zenon_H59 zenon_H5b). % 15.41/15.54 apply (zenon_or_s _ _ zenon_H5a); [ zenon_intro zenon_H4a | zenon_intro zenon_H5c ]. % 15.41/15.54 apply (zenon_L787_); trivial. % 15.41/15.54 apply (zenon_or_s _ _ zenon_H5c); [ zenon_intro zenon_H50 | zenon_intro zenon_H53 ]. % 15.41/15.54 apply (zenon_L533_); trivial. % 15.41/15.54 apply (zenon_L12_); trivial. % 15.41/15.54 (* end of lemma zenon_L817_ *) % 15.41/15.54 assert (zenon_L818_ : (((op (e1) (e0)) = (e3))\/(((op (e1) (e1)) = (e3))\/(((op (e1) (e2)) = (e3))\/((op (e1) (e3)) = (e3))))) -> (~((e2) = (e3))) -> ((op (e1) (e0)) = (e2)) -> (~((op (e1) (e1)) = (e3))) -> (~((op (e1) (e2)) = (op (e3) (e2)))) -> ((op (e3) (e2)) = (e3)) -> ((op (e3) (e3)) = (e3)) -> (~((op (e1) (e3)) = (op (e3) (e3)))) -> False). % 15.41/15.54 do 0 intro. intros zenon_H90 zenon_H6a zenon_H68 zenon_H182 zenon_H17d zenon_H106 zenon_H42 zenon_H8b. % 15.41/15.54 apply (zenon_or_s _ _ zenon_H90); [ zenon_intro zenon_H69 | zenon_intro zenon_H94 ]. % 15.41/15.54 apply (zenon_L17_); trivial. % 15.41/15.54 apply (zenon_or_s _ _ zenon_H94); [ zenon_intro zenon_H96 | zenon_intro zenon_H95 ]. % 15.41/15.54 exact (zenon_H182 zenon_H96). % 15.41/15.54 apply (zenon_or_s _ _ zenon_H95); [ zenon_intro zenon_H88 | zenon_intro zenon_H8a ]. % 15.41/15.54 apply (zenon_L164_); trivial. % 15.41/15.54 apply (zenon_L25_); trivial. % 15.41/15.54 (* end of lemma zenon_L818_ *) % 15.41/15.54 assert (zenon_L819_ : (((op (e0) (e0)) = (e3))\/(((op (e0) (e1)) = (e3))\/(((op (e0) (e2)) = (e3))\/((op (e0) (e3)) = (e3))))) -> (~((op (e0) (e0)) = (e3))) -> (~((op (e3) (op (e2) (e3))) = (op (e2) (e3)))) -> (~((op (e2) (e2)) = (e3))) -> (~((op (e0) (e1)) = (op (e2) (e1)))) -> ((op (e2) (e0)) = (e2)) -> (~((e2) = (e3))) -> (((op (e2) (e0)) = (e3))\/(((op (e2) (e1)) = (e3))\/(((op (e2) (e2)) = (e3))\/((op (e2) (e3)) = (e3))))) -> (~((op (e0) (e2)) = (op (e3) (e2)))) -> ((op (e3) (e2)) = (e3)) -> ((op (e3) (e3)) = (e3)) -> (~((op (e0) (e3)) = (op (e3) (e3)))) -> False). % 15.41/15.54 do 0 intro. intros zenon_H58 zenon_H59 zenon_H28a zenon_H30 zenon_Hde zenon_Hdd zenon_H6a zenon_He6 zenon_H140 zenon_H106 zenon_H42 zenon_H36. % 15.41/15.54 apply (zenon_or_s _ _ zenon_H58); [ zenon_intro zenon_H5b | zenon_intro zenon_H5a ]. % 15.41/15.54 exact (zenon_H59 zenon_H5b). % 15.41/15.54 apply (zenon_or_s _ _ zenon_H5a); [ zenon_intro zenon_H4a | zenon_intro zenon_H5c ]. % 15.41/15.54 apply (zenon_L777_); trivial. % 15.41/15.54 apply (zenon_or_s _ _ zenon_H5c); [ zenon_intro zenon_H50 | zenon_intro zenon_H53 ]. % 15.41/15.54 apply (zenon_L533_); trivial. % 15.41/15.54 apply (zenon_L12_); trivial. % 15.41/15.54 (* end of lemma zenon_L819_ *) % 15.41/15.54 assert (zenon_L820_ : (((op (e0) (e0)) = (e1))\/(((op (e1) (e0)) = (e1))\/(((op (e2) (e0)) = (e1))\/((op (e3) (e0)) = (e1))))) -> (~((op (e0) (e0)) = (e1))) -> (~((e1) = (e3))) -> (((op (e0) (e0)) = (e2))\/(((op (e1) (e0)) = (e2))\/(((op (e2) (e0)) = (e2))\/((op (e3) (e0)) = (e2))))) -> (~((op (e0) (e0)) = (e2))) -> (~((op (e1) (e3)) = (op (e3) (e3)))) -> (~((op (e1) (e2)) = (op (e3) (e2)))) -> (~((op (e1) (e1)) = (e3))) -> (((op (e1) (e0)) = (e3))\/(((op (e1) (e1)) = (e3))\/(((op (e1) (e2)) = (e3))\/((op (e1) (e3)) = (e3))))) -> (~((op (e0) (e3)) = (op (e3) (e3)))) -> ((op (e3) (e3)) = (e3)) -> ((op (e3) (e2)) = (e3)) -> (~((op (e0) (e2)) = (op (e3) (e2)))) -> (((op (e2) (e0)) = (e3))\/(((op (e2) (e1)) = (e3))\/(((op (e2) (e2)) = (e3))\/((op (e2) (e3)) = (e3))))) -> (~((e2) = (e3))) -> (~((op (e0) (e1)) = (op (e2) (e1)))) -> (~((op (e2) (e2)) = (e3))) -> (~((op (e3) (op (e2) (e3))) = (op (e2) (e3)))) -> (~((op (e0) (e0)) = (e3))) -> (((op (e0) (e0)) = (e3))\/(((op (e0) (e1)) = (e3))\/(((op (e0) (e2)) = (e3))\/((op (e0) (e3)) = (e3))))) -> (~((e1) = (e2))) -> False). % 15.41/15.54 do 0 intro. intros zenon_Hf1 zenon_H45 zenon_Ha3 zenon_Heb zenon_H8f zenon_H8b zenon_H17d zenon_H182 zenon_H90 zenon_H36 zenon_H42 zenon_H106 zenon_H140 zenon_He6 zenon_H6a zenon_Hde zenon_H30 zenon_H28a zenon_H59 zenon_H58 zenon_Ha7. % 15.41/15.54 apply (zenon_or_s _ _ zenon_Hf1); [ zenon_intro zenon_H47 | zenon_intro zenon_Hf4 ]. % 15.41/15.54 exact (zenon_H45 zenon_H47). % 15.41/15.54 apply (zenon_or_s _ _ zenon_Hf4); [ zenon_intro zenon_Hd8 | zenon_intro zenon_Hf5 ]. % 15.41/15.54 apply (zenon_L417_); trivial. % 15.41/15.54 apply (zenon_or_s _ _ zenon_Hf5); [ zenon_intro zenon_Hae | zenon_intro zenon_Hee ]. % 15.41/15.54 apply (zenon_L817_); trivial. % 15.41/15.54 apply (zenon_or_s _ _ zenon_Heb); [ zenon_intro zenon_H92 | zenon_intro zenon_Hec ]. % 15.41/15.54 exact (zenon_H8f zenon_H92). % 15.41/15.54 apply (zenon_or_s _ _ zenon_Hec); [ zenon_intro zenon_H68 | zenon_intro zenon_Hed ]. % 15.41/15.54 apply (zenon_L818_); trivial. % 15.41/15.54 apply (zenon_or_s _ _ zenon_Hed); [ zenon_intro zenon_Hdd | zenon_intro zenon_He9 ]. % 15.41/15.54 apply (zenon_L819_); trivial. % 15.41/15.54 apply (zenon_L122_); trivial. % 15.41/15.54 (* end of lemma zenon_L820_ *) % 15.41/15.54 assert (zenon_L821_ : ((~((op (e3) (e3)) = (e3)))\/((op (e3) (e3)) = (e3))) -> (((op (e1) (e0)) = (e3))\/(((op (e1) (e1)) = (e3))\/(((op (e1) (e2)) = (e3))\/((op (e1) (e3)) = (e3))))) -> (~((op (e1) (e3)) = (op (e3) (e3)))) -> (~((op (e1) (e2)) = (op (e3) (e2)))) -> (~((op (e1) (e1)) = (e3))) -> (((op (e0) (e0)) = (e3))\/(((op (e0) (e1)) = (e3))\/(((op (e0) (e2)) = (e3))\/((op (e0) (e3)) = (e3))))) -> (~((op (e0) (e3)) = (op (e3) (e3)))) -> (~((op (e0) (e2)) = (op (e3) (e2)))) -> (~((op (e0) (e1)) = (op (e2) (e1)))) -> (~((op (e3) (op (e2) (e3))) = (op (e2) (e3)))) -> (((op (e2) (e0)) = (e3))\/(((op (e2) (e1)) = (e3))\/(((op (e2) (e2)) = (e3))\/((op (e2) (e3)) = (e3))))) -> (((op (e0) (e0)) = (e2))\/(((op (e1) (e0)) = (e2))\/(((op (e2) (e0)) = (e2))\/((op (e3) (e0)) = (e2))))) -> (~((op (e0) (e0)) = (e2))) -> (~((op (e0) (e0)) = (e1))) -> (((op (e0) (e0)) = (e3))\/(((op (e1) (e0)) = (e3))\/(((op (e2) (e0)) = (e3))\/((op (e3) (e0)) = (e3))))) -> ((op (e3) (e2)) = (e3)) -> (~((op (e3) (e0)) = (op (e3) (e2)))) -> ((op (e2) (e0)) = (e2)) -> (~((e2) = (e3))) -> (~((e1) = (e3))) -> (~((op (e0) (e0)) = (e3))) -> (~((e1) = (e2))) -> (((op (e2) (e2)) = (e0))\/(((op (e2) (e2)) = (e1))\/(((op (e2) (e2)) = (e2))\/((op (e2) (e2)) = (e3))))) -> (~((op (e2) (e2)) = (e3))) -> (~((op (e2) (e2)) = (e2))) -> (~((op (e2) (e2)) = (e1))) -> (~((op (e3) (e3)) = (e0))) -> (~((op (e3) (e3)) = (e1))) -> (((op (e3) (e3)) = (e0))\/(((op (e3) (e3)) = (e1))\/(((op (e3) (e3)) = (e2))\/((op (e3) (e3)) = (e3))))) -> (((op (e0) (e0)) = (e1))\/(((op (e1) (e0)) = (e1))\/(((op (e2) (e0)) = (e1))\/((op (e3) (e0)) = (e1))))) -> False). % 15.41/15.54 do 0 intro. intros zenon_H10d zenon_H90 zenon_H8b zenon_H17d zenon_H182 zenon_H58 zenon_H36 zenon_H140 zenon_Hde zenon_H28a zenon_He6 zenon_Heb zenon_H8f zenon_H45 zenon_Hbe zenon_H106 zenon_H105 zenon_Hdd zenon_H6a zenon_Ha3 zenon_H59 zenon_Ha7 zenon_H2d zenon_H30 zenon_H2f zenon_H52 zenon_H3c zenon_H104 zenon_H3b zenon_Hf1. % 15.41/15.54 apply (zenon_or_s _ _ zenon_H10d); [ zenon_intro zenon_H3e | zenon_intro zenon_H42 ]. % 15.41/15.54 apply (zenon_L457_); trivial. % 15.41/15.54 apply (zenon_L820_); trivial. % 15.41/15.54 (* end of lemma zenon_L821_ *) % 15.41/15.54 assert (zenon_L822_ : (((op (e0) (e0)) = (e3))\/(((op (e1) (e0)) = (e3))\/(((op (e2) (e0)) = (e3))\/((op (e3) (e0)) = (e3))))) -> (~((op (e0) (e0)) = (e3))) -> (~((e1) = (e3))) -> ((op (e1) (e0)) = (e1)) -> ((op (e0) (e3)) = (e3)) -> (~((op (e0) (op (e2) (e0))) = (op (e2) (e0)))) -> (~((op (e3) (e0)) = (op (e3) (e1)))) -> ((op (e3) (e1)) = (e3)) -> False). % 15.41/15.54 do 0 intro. intros zenon_Hbe zenon_H59 zenon_Ha3 zenon_Hd8 zenon_H53 zenon_H295 zenon_H109 zenon_H10a. % 15.41/15.54 apply (zenon_or_s _ _ zenon_Hbe); [ zenon_intro zenon_H5b | zenon_intro zenon_Hbf ]. % 15.41/15.54 exact (zenon_H59 zenon_H5b). % 15.41/15.54 apply (zenon_or_s _ _ zenon_Hbf); [ zenon_intro zenon_H69 | zenon_intro zenon_Hc0 ]. % 15.41/15.54 apply (zenon_L163_); trivial. % 15.41/15.54 apply (zenon_or_s _ _ zenon_Hc0); [ zenon_intro zenon_Haf | zenon_intro zenon_Hba ]. % 15.41/15.54 apply (zenon_L803_); trivial. % 15.41/15.54 apply (zenon_L82_); trivial. % 15.41/15.54 (* end of lemma zenon_L822_ *) % 15.41/15.54 assert (zenon_L823_ : (~((op (e1) (op (e2) (e1))) = (op (e1) (e2)))) -> ((op (e2) (e1)) = (e2)) -> False). % 15.41/15.54 do 0 intro. intros zenon_H2a1 zenon_H156. % 15.41/15.54 cut (((op (e2) (e1)) = (e2))); [idtac | apply NNPP; zenon_intro zenon_H2a2]. % 15.41/15.54 cut (((e1) = (e1))); [idtac | apply NNPP; zenon_intro zenon_Ha0]. % 15.41/15.54 congruence. % 15.41/15.54 apply zenon_Ha0. apply refl_equal. % 15.41/15.54 exact (zenon_H2a2 zenon_H156). % 15.41/15.54 (* end of lemma zenon_L823_ *) % 15.41/15.54 assert (zenon_L824_ : (~((op (e1) (op (e2) (e1))) = (op (e2) (e1)))) -> ((op (e1) (e2)) = (e2)) -> ((op (e2) (e1)) = (e2)) -> False). % 15.41/15.54 do 0 intro. intros zenon_H290 zenon_H7c zenon_H156. % 15.41/15.54 cut (((op (e1) (e2)) = (e2)) = ((op (e1) (op (e2) (e1))) = (op (e2) (e1)))). % 15.41/15.54 intro zenon_D_pnotp. % 15.41/15.54 apply zenon_H290. % 15.41/15.54 rewrite <- zenon_D_pnotp. % 15.41/15.54 exact zenon_H7c. % 15.41/15.54 cut (((e2) = (op (e2) (e1)))); [idtac | apply NNPP; zenon_intro zenon_H159]. % 15.41/15.54 cut (((op (e1) (e2)) = (op (e1) (op (e2) (e1))))); [idtac | apply NNPP; zenon_intro zenon_H2a3]. % 15.41/15.54 congruence. % 15.41/15.54 elim (classic ((op (e1) (op (e2) (e1))) = (op (e1) (op (e2) (e1))))); [ zenon_intro zenon_H292 | zenon_intro zenon_H293 ]. % 15.41/15.54 cut (((op (e1) (op (e2) (e1))) = (op (e1) (op (e2) (e1)))) = ((op (e1) (e2)) = (op (e1) (op (e2) (e1))))). % 15.41/15.54 intro zenon_D_pnotp. % 15.41/15.54 apply zenon_H2a3. % 15.41/15.54 rewrite <- zenon_D_pnotp. % 15.41/15.54 exact zenon_H292. % 15.41/15.54 cut (((op (e1) (op (e2) (e1))) = (op (e1) (op (e2) (e1))))); [idtac | apply NNPP; zenon_intro zenon_H293]. % 15.41/15.54 cut (((op (e1) (op (e2) (e1))) = (op (e1) (e2)))); [idtac | apply NNPP; zenon_intro zenon_H2a1]. % 15.41/15.54 congruence. % 15.41/15.54 apply (zenon_L823_); trivial. % 15.41/15.54 apply zenon_H293. apply refl_equal. % 15.41/15.54 apply zenon_H293. apply refl_equal. % 15.41/15.54 apply zenon_H159. apply sym_equal. exact zenon_H156. % 15.41/15.54 (* end of lemma zenon_L824_ *) % 15.41/15.54 assert (zenon_L825_ : (~((op (e1) (op (e2) (e1))) = (op (e1) (e3)))) -> ((op (e2) (e1)) = (e3)) -> False). % 15.41/15.54 do 0 intro. intros zenon_H2a4 zenon_Hdf. % 15.41/15.54 cut (((op (e2) (e1)) = (e3))); [idtac | apply NNPP; zenon_intro zenon_H198]. % 15.41/15.54 cut (((e1) = (e1))); [idtac | apply NNPP; zenon_intro zenon_Ha0]. % 15.41/15.54 congruence. % 15.41/15.54 apply zenon_Ha0. apply refl_equal. % 15.41/15.54 exact (zenon_H198 zenon_Hdf). % 15.41/15.54 (* end of lemma zenon_L825_ *) % 15.41/15.54 assert (zenon_L826_ : (~((op (e1) (op (e2) (e1))) = (op (e2) (e1)))) -> ((op (e1) (e3)) = (e3)) -> ((op (e2) (e1)) = (e3)) -> False). % 15.41/15.54 do 0 intro. intros zenon_H290 zenon_H8a zenon_Hdf. % 15.41/15.54 cut (((op (e1) (e3)) = (e3)) = ((op (e1) (op (e2) (e1))) = (op (e2) (e1)))). % 15.41/15.54 intro zenon_D_pnotp. % 15.41/15.54 apply zenon_H290. % 15.41/15.54 rewrite <- zenon_D_pnotp. % 15.41/15.54 exact zenon_H8a. % 15.41/15.54 cut (((e3) = (op (e2) (e1)))); [idtac | apply NNPP; zenon_intro zenon_He0]. % 15.41/15.54 cut (((op (e1) (e3)) = (op (e1) (op (e2) (e1))))); [idtac | apply NNPP; zenon_intro zenon_H2a5]. % 15.41/15.54 congruence. % 15.41/15.54 elim (classic ((op (e1) (op (e2) (e1))) = (op (e1) (op (e2) (e1))))); [ zenon_intro zenon_H292 | zenon_intro zenon_H293 ]. % 15.41/15.54 cut (((op (e1) (op (e2) (e1))) = (op (e1) (op (e2) (e1)))) = ((op (e1) (e3)) = (op (e1) (op (e2) (e1))))). % 15.41/15.54 intro zenon_D_pnotp. % 15.41/15.54 apply zenon_H2a5. % 15.41/15.54 rewrite <- zenon_D_pnotp. % 15.41/15.54 exact zenon_H292. % 15.41/15.54 cut (((op (e1) (op (e2) (e1))) = (op (e1) (op (e2) (e1))))); [idtac | apply NNPP; zenon_intro zenon_H293]. % 15.41/15.54 cut (((op (e1) (op (e2) (e1))) = (op (e1) (e3)))); [idtac | apply NNPP; zenon_intro zenon_H2a4]. % 15.41/15.54 congruence. % 15.41/15.54 apply (zenon_L825_); trivial. % 15.41/15.54 apply zenon_H293. apply refl_equal. % 15.41/15.54 apply zenon_H293. apply refl_equal. % 15.41/15.54 apply zenon_He0. apply sym_equal. exact zenon_Hdf. % 15.41/15.54 (* end of lemma zenon_L826_ *) % 15.41/15.54 assert (zenon_L827_ : (((op (e0) (e0)) = (e3))\/(((op (e0) (e1)) = (e3))\/(((op (e0) (e2)) = (e3))\/((op (e0) (e3)) = (e3))))) -> (~((op (e0) (e0)) = (e3))) -> (~((op (e0) (e3)) = (op (e1) (e3)))) -> (((op (e0) (e1)) = (e2))\/(((op (e1) (e1)) = (e2))\/(((op (e2) (e1)) = (e2))\/((op (e3) (e1)) = (e2))))) -> (~((op (e0) (e1)) = (op (e0) (e3)))) -> (~((op (e1) (e1)) = (e2))) -> (((op (e1) (e0)) = (e3))\/(((op (e1) (e1)) = (e3))\/(((op (e1) (e2)) = (e3))\/((op (e1) (e3)) = (e3))))) -> ((op (e1) (e0)) = (e1)) -> (~((op (e0) (e2)) = (op (e1) (e2)))) -> (((op (e0) (e1)) = (e3))\/(((op (e1) (e1)) = (e3))\/(((op (e2) (e1)) = (e3))\/((op (e3) (e1)) = (e3))))) -> (~((e1) = (e3))) -> ((op (e0) (e1)) = (e1)) -> (~((op (e1) (e1)) = (e3))) -> (~((op (e1) (op (e2) (e1))) = (op (e2) (e1)))) -> (~((e1) = (e2))) -> (((op (e1) (e0)) = (e2))\/(((op (e1) (e1)) = (e2))\/(((op (e1) (e2)) = (e2))\/((op (e1) (e3)) = (e2))))) -> ((op (e0) (e3)) = (e2)) -> (~((e2) = (e3))) -> False). % 15.41/15.54 do 0 intro. intros zenon_H58 zenon_H59 zenon_H80 zenon_H1a2 zenon_H1cd zenon_Hd6 zenon_H90 zenon_Hd8 zenon_H87 zenon_H199 zenon_Ha3 zenon_H22 zenon_H182 zenon_H290 zenon_Ha7 zenon_H84 zenon_H81 zenon_H6a. % 15.41/15.54 apply (zenon_or_s _ _ zenon_H58); [ zenon_intro zenon_H5b | zenon_intro zenon_H5a ]. % 15.41/15.54 exact (zenon_H59 zenon_H5b). % 15.41/15.54 apply (zenon_or_s _ _ zenon_H5a); [ zenon_intro zenon_H4a | zenon_intro zenon_H5c ]. % 15.41/15.54 apply (zenon_L59_); trivial. % 15.41/15.54 apply (zenon_or_s _ _ zenon_H5c); [ zenon_intro zenon_H50 | zenon_intro zenon_H53 ]. % 15.41/15.54 apply (zenon_or_s _ _ zenon_H84); [ zenon_intro zenon_H68 | zenon_intro zenon_H85 ]. % 15.41/15.54 apply (zenon_L162_); trivial. % 15.41/15.54 apply (zenon_or_s _ _ zenon_H85); [ zenon_intro zenon_H6e | zenon_intro zenon_H86 ]. % 15.41/15.54 exact (zenon_Hd6 zenon_H6e). % 15.41/15.54 apply (zenon_or_s _ _ zenon_H86); [ zenon_intro zenon_H7c | zenon_intro zenon_H82 ]. % 15.41/15.54 apply (zenon_or_s _ _ zenon_H1a2); [ zenon_intro zenon_H5d | zenon_intro zenon_H1a3 ]. % 15.41/15.54 apply (zenon_L350_); trivial. % 15.41/15.54 apply (zenon_or_s _ _ zenon_H1a3); [ zenon_intro zenon_H6e | zenon_intro zenon_H1a4 ]. % 15.41/15.54 exact (zenon_Hd6 zenon_H6e). % 15.41/15.54 apply (zenon_or_s _ _ zenon_H1a4); [ zenon_intro zenon_H156 | zenon_intro zenon_H16a ]. % 15.41/15.54 apply (zenon_L824_); trivial. % 15.41/15.54 apply (zenon_or_s _ _ zenon_H90); [ zenon_intro zenon_H69 | zenon_intro zenon_H94 ]. % 15.41/15.54 apply (zenon_L163_); trivial. % 15.41/15.54 apply (zenon_or_s _ _ zenon_H94); [ zenon_intro zenon_H96 | zenon_intro zenon_H95 ]. % 15.41/15.54 exact (zenon_H182 zenon_H96). % 15.41/15.54 apply (zenon_or_s _ _ zenon_H95); [ zenon_intro zenon_H88 | zenon_intro zenon_H8a ]. % 15.41/15.54 apply (zenon_L24_); trivial. % 15.41/15.54 apply (zenon_or_s _ _ zenon_H199); [ zenon_intro zenon_H4a | zenon_intro zenon_H19a ]. % 15.41/15.54 apply (zenon_L59_); trivial. % 15.41/15.54 apply (zenon_or_s _ _ zenon_H19a); [ zenon_intro zenon_H96 | zenon_intro zenon_H19b ]. % 15.41/15.54 exact (zenon_H182 zenon_H96). % 15.41/15.54 apply (zenon_or_s _ _ zenon_H19b); [ zenon_intro zenon_Hdf | zenon_intro zenon_H10a ]. % 15.41/15.54 apply (zenon_L826_); trivial. % 15.41/15.54 apply (zenon_L297_); trivial. % 15.41/15.54 apply (zenon_L22_); trivial. % 15.41/15.54 apply (zenon_L128_); trivial. % 15.41/15.54 (* end of lemma zenon_L827_ *) % 15.41/15.54 assert (zenon_L828_ : (((op (e0) (e0)) = (e2))\/(((op (e0) (e1)) = (e2))\/(((op (e0) (e2)) = (e2))\/((op (e0) (e3)) = (e2))))) -> (~((op (e0) (e0)) = (e2))) -> ((op (e3) (e1)) = (e3)) -> (~((op (e3) (e0)) = (op (e3) (e1)))) -> (((op (e0) (e0)) = (e3))\/(((op (e1) (e0)) = (e3))\/(((op (e2) (e0)) = (e3))\/((op (e3) (e0)) = (e3))))) -> (((op (e0) (e3)) = (e2))\/(((op (e1) (e3)) = (e2))\/(((op (e2) (e3)) = (e2))\/((op (e3) (e3)) = (e2))))) -> (~((op (e2) (e0)) = (op (e2) (e3)))) -> (~((op (e3) (e3)) = (e2))) -> ((op (e2) (e0)) = (e2)) -> (~((op (e0) (op (e2) (e0))) = (op (e2) (e0)))) -> (((op (e0) (e0)) = (e3))\/(((op (e0) (e1)) = (e3))\/(((op (e0) (e2)) = (e3))\/((op (e0) (e3)) = (e3))))) -> (~((op (e0) (e0)) = (e3))) -> (~((op (e0) (e3)) = (op (e1) (e3)))) -> (((op (e0) (e1)) = (e2))\/(((op (e1) (e1)) = (e2))\/(((op (e2) (e1)) = (e2))\/((op (e3) (e1)) = (e2))))) -> (~((op (e0) (e1)) = (op (e0) (e3)))) -> (~((op (e1) (e1)) = (e2))) -> (((op (e1) (e0)) = (e3))\/(((op (e1) (e1)) = (e3))\/(((op (e1) (e2)) = (e3))\/((op (e1) (e3)) = (e3))))) -> ((op (e1) (e0)) = (e1)) -> (~((op (e0) (e2)) = (op (e1) (e2)))) -> (((op (e0) (e1)) = (e3))\/(((op (e1) (e1)) = (e3))\/(((op (e2) (e1)) = (e3))\/((op (e3) (e1)) = (e3))))) -> (~((e1) = (e3))) -> ((op (e0) (e1)) = (e1)) -> (~((op (e1) (e1)) = (e3))) -> (~((op (e1) (op (e2) (e1))) = (op (e2) (e1)))) -> (~((e1) = (e2))) -> (((op (e1) (e0)) = (e2))\/(((op (e1) (e1)) = (e2))\/(((op (e1) (e2)) = (e2))\/((op (e1) (e3)) = (e2))))) -> (~((e2) = (e3))) -> False). % 15.41/15.54 do 0 intro. intros zenon_H8e zenon_H8f zenon_H10a zenon_H109 zenon_Hbe zenon_H160 zenon_Hce zenon_H3d zenon_Hdd zenon_H295 zenon_H58 zenon_H59 zenon_H80 zenon_H1a2 zenon_H1cd zenon_Hd6 zenon_H90 zenon_Hd8 zenon_H87 zenon_H199 zenon_Ha3 zenon_H22 zenon_H182 zenon_H290 zenon_Ha7 zenon_H84 zenon_H6a. % 15.41/15.54 apply (zenon_or_s _ _ zenon_H8e); [ zenon_intro zenon_H92 | zenon_intro zenon_H91 ]. % 15.41/15.54 exact (zenon_H8f zenon_H92). % 15.41/15.54 apply (zenon_or_s _ _ zenon_H91); [ zenon_intro zenon_H5d | zenon_intro zenon_H93 ]. % 15.41/15.54 apply (zenon_or_s _ _ zenon_H58); [ zenon_intro zenon_H5b | zenon_intro zenon_H5a ]. % 15.41/15.54 exact (zenon_H59 zenon_H5b). % 15.41/15.54 apply (zenon_or_s _ _ zenon_H5a); [ zenon_intro zenon_H4a | zenon_intro zenon_H5c ]. % 15.41/15.54 apply (zenon_L50_); trivial. % 15.41/15.54 apply (zenon_or_s _ _ zenon_H5c); [ zenon_intro zenon_H50 | zenon_intro zenon_H53 ]. % 15.41/15.54 apply (zenon_L411_); trivial. % 15.41/15.54 apply (zenon_L822_); trivial. % 15.41/15.54 apply (zenon_or_s _ _ zenon_H93); [ zenon_intro zenon_H63 | zenon_intro zenon_H81 ]. % 15.41/15.54 apply (zenon_L812_); trivial. % 15.41/15.54 apply (zenon_L827_); trivial. % 15.41/15.54 (* end of lemma zenon_L828_ *) % 15.41/15.54 assert (zenon_L829_ : (((op (e0) (e0)) = (e3))\/(((op (e0) (e1)) = (e3))\/(((op (e0) (e2)) = (e3))\/((op (e0) (e3)) = (e3))))) -> (~((op (e0) (e1)) = (op (e3) (e1)))) -> ((op (e0) (e2)) = (e1)) -> (((op (e0) (e0)) = (e3))\/(((op (e1) (e0)) = (e3))\/(((op (e2) (e0)) = (e3))\/((op (e3) (e0)) = (e3))))) -> (~((op (e0) (e0)) = (e3))) -> (~((e1) = (e3))) -> ((op (e1) (e0)) = (e1)) -> (~((op (e0) (op (e2) (e0))) = (op (e2) (e0)))) -> (~((op (e3) (e0)) = (op (e3) (e1)))) -> ((op (e3) (e1)) = (e3)) -> False). % 15.41/15.54 do 0 intro. intros zenon_H58 zenon_H138 zenon_H29 zenon_Hbe zenon_H59 zenon_Ha3 zenon_Hd8 zenon_H295 zenon_H109 zenon_H10a. % 15.41/15.54 apply (zenon_or_s _ _ zenon_H58); [ zenon_intro zenon_H5b | zenon_intro zenon_H5a ]. % 15.41/15.54 exact (zenon_H59 zenon_H5b). % 15.41/15.54 apply (zenon_or_s _ _ zenon_H5a); [ zenon_intro zenon_H4a | zenon_intro zenon_H5c ]. % 15.41/15.54 apply (zenon_L120_); trivial. % 15.41/15.54 apply (zenon_or_s _ _ zenon_H5c); [ zenon_intro zenon_H50 | zenon_intro zenon_H53 ]. % 15.41/15.54 apply (zenon_L29_); trivial. % 15.41/15.54 apply (zenon_L822_); trivial. % 15.41/15.54 (* end of lemma zenon_L829_ *) % 15.41/15.54 assert (zenon_L830_ : ((~((op (e3) (e3)) = (e3)))\/((op (e3) (e3)) = (e3))) -> (~((op (e1) (e3)) = (op (e3) (e3)))) -> (~((op (e0) (e0)) = (e1))) -> (((op (e0) (e0)) = (e2))\/(((op (e0) (e1)) = (e2))\/(((op (e0) (e2)) = (e2))\/((op (e0) (e3)) = (e2))))) -> (((op (e1) (e0)) = (e2))\/(((op (e1) (e1)) = (e2))\/(((op (e1) (e2)) = (e2))\/((op (e1) (e3)) = (e2))))) -> (~((op (e0) (e3)) = (op (e1) (e3)))) -> (~((op (e1) (op (e2) (e1))) = (op (e2) (e1)))) -> (((op (e0) (e1)) = (e3))\/(((op (e1) (e1)) = (e3))\/(((op (e2) (e1)) = (e3))\/((op (e3) (e1)) = (e3))))) -> (((op (e0) (e1)) = (e2))\/(((op (e1) (e1)) = (e2))\/(((op (e2) (e1)) = (e2))\/((op (e3) (e1)) = (e2))))) -> (~((op (e1) (e1)) = (e2))) -> (~((e1) = (e2))) -> (~((op (e0) (e0)) = (e3))) -> (~((e2) = (e3))) -> (((op (e1) (e0)) = (e3))\/(((op (e1) (e1)) = (e3))\/(((op (e1) (e2)) = (e3))\/((op (e1) (e3)) = (e3))))) -> (~((op (e0) (e1)) = (op (e0) (e3)))) -> (~((op (e2) (e0)) = (op (e2) (e3)))) -> ((op (e2) (e0)) = (e2)) -> (~((op (e3) (e3)) = (e2))) -> (((op (e0) (e3)) = (e2))\/(((op (e1) (e3)) = (e2))\/(((op (e2) (e3)) = (e2))\/((op (e3) (e3)) = (e2))))) -> (~((op (e0) (e2)) = (op (e1) (e2)))) -> (~((op (e1) (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 (e3) (e1)) = (e3)) -> (~((op (e3) (e0)) = (op (e3) (e1)))) -> (~((op (e0) (op (e2) (e0))) = (op (e2) (e0)))) -> (((op (e0) (e0)) = (e3))\/(((op (e0) (e1)) = (e3))\/(((op (e0) (e2)) = (e3))\/((op (e0) (e3)) = (e3))))) -> (~((op (e0) (e0)) = (e2))) -> (~((op (e0) (e1)) = (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 (e3) (e3)) = (e0))) -> (((op (e0) (e0)) = (e1))\/(((op (e0) (e1)) = (e1))\/(((op (e0) (e2)) = (e1))\/((op (e0) (e3)) = (e1))))) -> False). % 15.41/15.54 do 0 intro. intros zenon_H10d zenon_H8b zenon_H45 zenon_H8e zenon_H84 zenon_H80 zenon_H290 zenon_H199 zenon_H1a2 zenon_Hd6 zenon_Ha7 zenon_H59 zenon_H6a zenon_H90 zenon_H1cd zenon_Hce zenon_Hdd zenon_H3d zenon_H160 zenon_H87 zenon_H182 zenon_Hd8 zenon_Ha3 zenon_Hbe zenon_H10a zenon_H109 zenon_H295 zenon_H58 zenon_H8f zenon_H138 zenon_H3b zenon_H36 zenon_H3c zenon_H44. % 15.41/15.54 apply (zenon_or_s _ _ zenon_H10d); [ zenon_intro zenon_H3e | zenon_intro zenon_H42 ]. % 15.41/15.54 apply (zenon_or_s _ _ zenon_H44); [ zenon_intro zenon_H47 | zenon_intro zenon_H46 ]. % 15.41/15.54 exact (zenon_H45 zenon_H47). % 15.41/15.54 apply (zenon_or_s _ _ zenon_H46); [ zenon_intro zenon_H22 | zenon_intro zenon_H48 ]. % 15.41/15.54 apply (zenon_L828_); trivial. % 15.41/15.54 apply (zenon_or_s _ _ zenon_H48); [ zenon_intro zenon_H29 | zenon_intro zenon_H37 ]. % 15.41/15.54 apply (zenon_L829_); trivial. % 15.41/15.54 apply (zenon_L7_); trivial. % 15.41/15.54 apply (zenon_L572_); trivial. % 15.41/15.54 (* end of lemma zenon_L830_ *) % 15.41/15.54 assert (zenon_L831_ : (((op (e0) (e0)) = (e2))\/(((op (e1) (e0)) = (e2))\/(((op (e2) (e0)) = (e2))\/((op (e3) (e0)) = (e2))))) -> (~((op (e3) (e3)) = (e2))) -> (((op (e0) (e2)) = (e0))\/(((op (e0) (e2)) = (e1))\/(((op (e0) (e2)) = (e2))\/((op (e0) (e2)) = (e3))))) -> ((op (e0) (e0)) = (e0)) -> (~((op (e0) (e0)) = (op (e0) (e2)))) -> (~((op (e3) (e3)) = (e1))) -> (((op (e0) (e1)) = (e2))\/(((op (e1) (e1)) = (e2))\/(((op (e2) (e1)) = (e2))\/((op (e3) (e1)) = (e2))))) -> (~((op (e1) (e1)) = (e2))) -> (~((op (e2) (e0)) = (op (e2) (e1)))) -> (~((e1) = (e2))) -> (~((op (e1) (e0)) = (op (e3) (e0)))) -> (((op (e3) (e0)) = (e1))\/(((op (e3) (e1)) = (e1))\/(((op (e3) (e2)) = (e1))\/((op (e3) (e3)) = (e1))))) -> (((op (e0) (e3)) = (e1))\/(((op (e1) (e3)) = (e1))\/(((op (e2) (e3)) = (e1))\/((op (e3) (e3)) = (e1))))) -> (~((op (e3) (e1)) = (op (e3) (e2)))) -> (~((op (e2) (e2)) = (e1))) -> (~((op (e0) (e2)) = (op (e0) (e3)))) -> (((op (e0) (e2)) = (e1))\/(((op (e1) (e2)) = (e1))\/(((op (e2) (e2)) = (e1))\/((op (e3) (e2)) = (e1))))) -> (~((op (e1) (e0)) = (op (e1) (e3)))) -> (~((op (e3) (op (e2) (e3))) = (op (e2) (e3)))) -> (~((op (e0) (e0)) = (e2))) -> (((op (e0) (e0)) = (e2))\/(((op (e0) (e1)) = (e2))\/(((op (e0) (e2)) = (e2))\/((op (e0) (e3)) = (e2))))) -> (~((op (e0) (e2)) = (op (e3) (e2)))) -> (((op (e1) (e0)) = (e3))\/(((op (e1) (e1)) = (e3))\/(((op (e1) (e2)) = (e3))\/((op (e1) (e3)) = (e3))))) -> (~((e1) = (e3))) -> ((op (e1) (e0)) = (e1)) -> (~((op (e1) (e1)) = (e3))) -> (~((op (e0) (e2)) = (op (e1) (e2)))) -> (((op (e0) (e3)) = (e2))\/(((op (e1) (e3)) = (e2))\/(((op (e2) (e3)) = (e2))\/((op (e3) (e3)) = (e2))))) -> (~((op (e0) (e1)) = (op (e0) (e3)))) -> ((op (e0) (e1)) = (e2)) -> (~((op (e2) (e0)) = (op (e2) (e3)))) -> (~((op (e0) (e1)) = (op (e3) (e1)))) -> (((op (e3) (e0)) = (e2))\/(((op (e3) (e1)) = (e2))\/(((op (e3) (e2)) = (e2))\/((op (e3) (e3)) = (e2))))) -> (~((e2) = (e3))) -> ((op (e3) (e0)) = (e3)) -> False). % 15.41/15.54 do 0 intro. intros zenon_Heb zenon_H3d zenon_H251 zenon_H1f zenon_H250 zenon_H104 zenon_H1a2 zenon_Hd6 zenon_H154 zenon_Ha7 zenon_H22e zenon_H146 zenon_H121 zenon_H135 zenon_H52 zenon_Hc9 zenon_H11b zenon_H1cf zenon_H28a zenon_H8f zenon_H8e zenon_H140 zenon_H90 zenon_Ha3 zenon_Hd8 zenon_H182 zenon_H87 zenon_H160 zenon_H1cd zenon_H5d zenon_Hce zenon_H138 zenon_H1df zenon_H6a zenon_Hba. % 15.41/15.54 apply (zenon_or_s _ _ zenon_Heb); [ zenon_intro zenon_H92 | zenon_intro zenon_Hec ]. % 15.41/15.54 exact (zenon_H8f zenon_H92). % 15.41/15.54 apply (zenon_or_s _ _ zenon_Hec); [ zenon_intro zenon_H68 | zenon_intro zenon_Hed ]. % 15.41/15.54 apply (zenon_L162_); trivial. % 15.41/15.54 apply (zenon_or_s _ _ zenon_Hed); [ zenon_intro zenon_Hdd | zenon_intro zenon_He9 ]. % 15.41/15.54 apply (zenon_L811_); trivial. % 15.41/15.54 apply (zenon_L220_); trivial. % 15.41/15.54 (* end of lemma zenon_L831_ *) % 15.41/15.54 assert (zenon_L832_ : (((op (e0) (e0)) = (e2))\/(((op (e1) (e0)) = (e2))\/(((op (e2) (e0)) = (e2))\/((op (e3) (e0)) = (e2))))) -> (~((op (e0) (e0)) = (e2))) -> (~((e1) = (e2))) -> ((op (e0) (e2)) = (e2)) -> (~((op (e0) (op (e2) (e0))) = (op (e2) (e0)))) -> (((op (e0) (e0)) = (e3))\/(((op (e1) (e0)) = (e3))\/(((op (e2) (e0)) = (e3))\/((op (e3) (e0)) = (e3))))) -> (~((op (e0) (e0)) = (e3))) -> (~((e1) = (e3))) -> ((op (e1) (e0)) = (e1)) -> (~((op (e1) (e1)) = (e3))) -> (~((op (e1) (e1)) = (e2))) -> (~((op (e1) (e1)) = (e1))) -> (((op (e2) (e2)) = (e0))\/(((op (e2) (e2)) = (e1))\/(((op (e2) (e2)) = (e2))\/((op (e2) (e2)) = (e3))))) -> (~((op (e2) (e2)) = (e0))) -> (~((op (e2) (e2)) = (e2))) -> (~((op (e2) (e2)) = (e3))) -> (((op (e1) (e1)) = (e0))\/(((op (e1) (e1)) = (e1))\/(((op (e1) (e1)) = (e2))\/((op (e1) (e1)) = (e3))))) -> (~((e2) = (e3))) -> False). % 15.41/15.54 do 0 intro. intros zenon_Heb zenon_H8f zenon_Ha7 zenon_H63 zenon_H295 zenon_Hbe zenon_H59 zenon_Ha3 zenon_Hd8 zenon_H182 zenon_Hd6 zenon_H1b4 zenon_H2d zenon_H2e zenon_H2f zenon_H30 zenon_H1b3 zenon_H6a. % 15.41/15.54 apply (zenon_or_s _ _ zenon_Heb); [ zenon_intro zenon_H92 | zenon_intro zenon_Hec ]. % 15.41/15.54 exact (zenon_H8f zenon_H92). % 15.41/15.54 apply (zenon_or_s _ _ zenon_Hec); [ zenon_intro zenon_H68 | zenon_intro zenon_Hed ]. % 15.41/15.54 apply (zenon_L162_); trivial. % 15.41/15.54 apply (zenon_or_s _ _ zenon_Hed); [ zenon_intro zenon_Hdd | zenon_intro zenon_He9 ]. % 15.41/15.54 apply (zenon_L812_); trivial. % 15.41/15.54 apply (zenon_L746_); trivial. % 15.41/15.54 (* end of lemma zenon_L832_ *) % 15.41/15.54 assert (zenon_L833_ : ((~((op (e3) (e3)) = (e1)))\/((op (e3) (e1)) = (e3))) -> (~((op (e3) (e0)) = (op (e3) (e1)))) -> (((op (e0) (e0)) = (e1))\/(((op (e0) (e1)) = (e1))\/(((op (e0) (e2)) = (e1))\/((op (e0) (e3)) = (e1))))) -> (~((op (e0) (e2)) = (op (e2) (e2)))) -> (~((op (e0) (e0)) = (e2))) -> (((op (e0) (e0)) = (e2))\/(((op (e1) (e0)) = (e2))\/(((op (e2) (e0)) = (e2))\/((op (e3) (e0)) = (e2))))) -> (~((e2) = (e3))) -> ((op (e3) (e0)) = (e3)) -> (~((op (e0) (e1)) = (op (e3) (e1)))) -> (((op (e0) (e2)) = (e0))\/(((op (e0) (e2)) = (e1))\/(((op (e0) (e2)) = (e2))\/((op (e0) (e2)) = (e3))))) -> (~((op (e0) (e2)) = (op (e1) (e2)))) -> (((op (e3) (e0)) = (e1))\/(((op (e3) (e1)) = (e1))\/(((op (e3) (e2)) = (e1))\/((op (e3) (e3)) = (e1))))) -> (~((op (e0) (e2)) = (op (e3) (e2)))) -> (~((e1) = (e3))) -> (~((op (e1) (e1)) = (e3))) -> (((op (e0) (e3)) = (e1))\/(((op (e1) (e3)) = (e1))\/(((op (e2) (e3)) = (e1))\/((op (e3) (e3)) = (e1))))) -> (~((op (e3) (op (e2) (e3))) = (op (e2) (e3)))) -> (~((op (e1) (e0)) = (op (e1) (e3)))) -> (~((op (e0) (e2)) = (op (e0) (e3)))) -> (~((op (e2) (e2)) = (e1))) -> (~((op (e3) (e1)) = (op (e3) (e2)))) -> (((op (e0) (e2)) = (e1))\/(((op (e1) (e2)) = (e1))\/(((op (e2) (e2)) = (e1))\/((op (e3) (e2)) = (e1))))) -> (((op (e0) (e3)) = (e2))\/(((op (e1) (e3)) = (e2))\/(((op (e2) (e3)) = (e2))\/((op (e3) (e3)) = (e2))))) -> (~((op (e2) (e0)) = (op (e2) (e3)))) -> (~((op (e0) (e1)) = (op (e0) (e3)))) -> (((op (e1) (e0)) = (e3))\/(((op (e1) (e1)) = (e3))\/(((op (e1) (e2)) = (e3))\/((op (e1) (e3)) = (e3))))) -> (~((op (e1) (e0)) = (op (e3) (e0)))) -> (~((op (e1) (e1)) = (e2))) -> (~((op (e2) (e0)) = (op (e2) (e1)))) -> (((op (e0) (e1)) = (e2))\/(((op (e1) (e1)) = (e2))\/(((op (e2) (e1)) = (e2))\/((op (e3) (e1)) = (e2))))) -> (((op (e0) (e0)) = (e2))\/(((op (e0) (e1)) = (e2))\/(((op (e0) (e2)) = (e2))\/((op (e0) (e3)) = (e2))))) -> ((op (e0) (e0)) = (e0)) -> (~((op (e0) (e0)) = (op (e0) (e2)))) -> (((op (e3) (e0)) = (e2))\/(((op (e3) (e1)) = (e2))\/(((op (e3) (e2)) = (e2))\/((op (e3) (e3)) = (e2))))) -> ((op (e1) (e0)) = (e1)) -> (~((e1) = (e2))) -> (~((op (e0) (e0)) = (e3))) -> (((op (e1) (e1)) = (e0))\/(((op (e1) (e1)) = (e1))\/(((op (e1) (e1)) = (e2))\/((op (e1) (e1)) = (e3))))) -> (~((op (e1) (e1)) = (e1))) -> (~((op (e2) (e2)) = (e0))) -> (~((op (e2) (e2)) = (e2))) -> (~((op (e2) (e2)) = (e3))) -> (((op (e2) (e2)) = (e0))\/(((op (e2) (e2)) = (e1))\/(((op (e2) (e2)) = (e2))\/((op (e2) (e2)) = (e3))))) -> (((op (e0) (e0)) = (e3))\/(((op (e1) (e0)) = (e3))\/(((op (e2) (e0)) = (e3))\/((op (e3) (e0)) = (e3))))) -> (~((op (e0) (op (e2) (e0))) = (op (e2) (e0)))) -> (((op (e0) (e0)) = (e3))\/(((op (e0) (e1)) = (e3))\/(((op (e0) (e2)) = (e3))\/((op (e0) (e3)) = (e3))))) -> (((op (e0) (e1)) = (e3))\/(((op (e1) (e1)) = (e3))\/(((op (e2) (e1)) = (e3))\/((op (e3) (e1)) = (e3))))) -> (~((op (e1) (op (e2) (e1))) = (op (e2) (e1)))) -> (~((op (e0) (e3)) = (op (e1) (e3)))) -> (((op (e1) (e0)) = (e2))\/(((op (e1) (e1)) = (e2))\/(((op (e1) (e2)) = (e2))\/((op (e1) (e3)) = (e2))))) -> (~((op (e0) (e0)) = (e1))) -> (~((op (e3) (e0)) = (op (e3) (e2)))) -> ((~((op (e3) (e3)) = (e2)))\/((op (e3) (e2)) = (e3))) -> False). % 15.41/15.54 do 0 intro. intros zenon_H10c zenon_H109 zenon_H44 zenon_H28 zenon_H8f zenon_Heb zenon_H6a zenon_Hba zenon_H138 zenon_H251 zenon_H87 zenon_H146 zenon_H140 zenon_Ha3 zenon_H182 zenon_H121 zenon_H28a zenon_H1cf zenon_Hc9 zenon_H52 zenon_H135 zenon_H11b zenon_H160 zenon_Hce zenon_H1cd zenon_H90 zenon_H22e zenon_Hd6 zenon_H154 zenon_H1a2 zenon_H8e zenon_H1f zenon_H250 zenon_H1df zenon_Hd8 zenon_Ha7 zenon_H59 zenon_H1b3 zenon_H1b4 zenon_H2e zenon_H2f zenon_H30 zenon_H2d zenon_Hbe zenon_H295 zenon_H58 zenon_H199 zenon_H290 zenon_H80 zenon_H84 zenon_H45 zenon_H105 zenon_H10e. % 15.41/15.54 apply (zenon_or_s _ _ zenon_H10c); [ zenon_intro zenon_H104 | zenon_intro zenon_H10a ]. % 15.41/15.54 apply (zenon_or_s _ _ zenon_H10e); [ zenon_intro zenon_H3d | zenon_intro zenon_H106 ]. % 15.41/15.54 apply (zenon_or_s _ _ zenon_H44); [ zenon_intro zenon_H47 | zenon_intro zenon_H46 ]. % 15.41/15.54 exact (zenon_H45 zenon_H47). % 15.41/15.54 apply (zenon_or_s _ _ zenon_H46); [ zenon_intro zenon_H22 | zenon_intro zenon_H48 ]. % 15.41/15.54 apply (zenon_or_s _ _ zenon_H8e); [ zenon_intro zenon_H92 | zenon_intro zenon_H91 ]. % 15.41/15.54 exact (zenon_H8f zenon_H92). % 15.41/15.54 apply (zenon_or_s _ _ zenon_H91); [ zenon_intro zenon_H5d | zenon_intro zenon_H93 ]. % 15.41/15.54 apply (zenon_L831_); trivial. % 15.41/15.54 apply (zenon_or_s _ _ zenon_H93); [ zenon_intro zenon_H63 | zenon_intro zenon_H81 ]. % 15.41/15.54 apply (zenon_L832_); trivial. % 15.41/15.54 apply (zenon_L827_); trivial. % 15.41/15.54 apply (zenon_or_s _ _ zenon_H48); [ zenon_intro zenon_H29 | zenon_intro zenon_H37 ]. % 15.41/15.54 apply (zenon_L5_); trivial. % 15.41/15.54 apply (zenon_or_s _ _ zenon_H8e); [ zenon_intro zenon_H92 | zenon_intro zenon_H91 ]. % 15.41/15.54 exact (zenon_H8f zenon_H92). % 15.41/15.54 apply (zenon_or_s _ _ zenon_H91); [ zenon_intro zenon_H5d | zenon_intro zenon_H93 ]. % 15.41/15.54 apply (zenon_L831_); trivial. % 15.41/15.54 apply (zenon_or_s _ _ zenon_H93); [ zenon_intro zenon_H63 | zenon_intro zenon_H81 ]. % 15.41/15.54 apply (zenon_L832_); trivial. % 15.41/15.54 apply (zenon_L33_); trivial. % 15.41/15.54 apply (zenon_L81_); trivial. % 15.41/15.54 apply (zenon_L82_); trivial. % 15.41/15.54 (* end of lemma zenon_L833_ *) % 15.41/15.54 assert (zenon_L834_ : (((op (e0) (e0)) = (e2))\/(((op (e1) (e0)) = (e2))\/(((op (e2) (e0)) = (e2))\/((op (e3) (e0)) = (e2))))) -> (~((op (e3) (e3)) = (e1))) -> (~((op (e0) (e2)) = (op (e3) (e2)))) -> ((op (e0) (e2)) = (e1)) -> (((op (e0) (e1)) = (e2))\/(((op (e1) (e1)) = (e2))\/(((op (e2) (e1)) = (e2))\/((op (e3) (e1)) = (e2))))) -> (~((op (e0) (e1)) = (op (e0) (e3)))) -> (~((op (e2) (e0)) = (op (e2) (e1)))) -> (~((e1) = (e2))) -> (~((op (e1) (e0)) = (op (e3) (e0)))) -> ((op (e1) (e0)) = (e1)) -> (((op (e3) (e0)) = (e1))\/(((op (e3) (e1)) = (e1))\/(((op (e3) (e2)) = (e1))\/((op (e3) (e3)) = (e1))))) -> (~((op (e2) (e0)) = (op (e2) (e3)))) -> (~((e2) = (e3))) -> (((op (e0) (e3)) = (e2))\/(((op (e1) (e3)) = (e2))\/(((op (e2) (e3)) = (e2))\/((op (e3) (e3)) = (e2))))) -> (((op (e0) (e3)) = (e1))\/(((op (e1) (e3)) = (e1))\/(((op (e2) (e3)) = (e1))\/((op (e3) (e3)) = (e1))))) -> (~((op (e3) (e1)) = (op (e3) (e2)))) -> (~((op (e2) (e2)) = (e1))) -> (~((e1) = (e3))) -> (~((op (e0) (e2)) = (op (e0) (e3)))) -> (((op (e0) (e2)) = (e1))\/(((op (e1) (e2)) = (e1))\/(((op (e2) (e2)) = (e1))\/((op (e3) (e2)) = (e1))))) -> (~((op (e1) (e0)) = (op (e1) (e3)))) -> (~((op (e3) (op (e2) (e3))) = (op (e2) (e3)))) -> (((op (e1) (e0)) = (e3))\/(((op (e1) (e1)) = (e3))\/(((op (e1) (e2)) = (e3))\/((op (e1) (e3)) = (e3))))) -> (~((op (e0) (e0)) = (e2))) -> (((op (e0) (e0)) = (e2))\/(((op (e0) (e1)) = (e2))\/(((op (e0) (e2)) = (e2))\/((op (e0) (e3)) = (e2))))) -> (((op (e1) (e1)) = (e0))\/(((op (e1) (e1)) = (e1))\/(((op (e1) (e1)) = (e2))\/((op (e1) (e1)) = (e3))))) -> (~((op (e3) (e3)) = (e3))) -> (~((op (e3) (e3)) = (e2))) -> (~((op (e3) (e3)) = (e0))) -> (((op (e3) (e3)) = (e0))\/(((op (e3) (e3)) = (e1))\/(((op (e3) (e3)) = (e2))\/((op (e3) (e3)) = (e3))))) -> (~((op (e1) (e1)) = (e1))) -> (~((op (e1) (e1)) = (e2))) -> (~((op (e1) (e1)) = (e3))) -> False). % 15.41/15.54 do 0 intro. intros zenon_Heb zenon_H104 zenon_H140 zenon_H29 zenon_H1a2 zenon_H1cd zenon_H154 zenon_Ha7 zenon_H22e zenon_Hd8 zenon_H146 zenon_Hce zenon_H6a zenon_H160 zenon_H121 zenon_H135 zenon_H52 zenon_Ha3 zenon_Hc9 zenon_H11b zenon_H1cf zenon_H28a zenon_H90 zenon_H8f zenon_H8e zenon_H1b3 zenon_H3e zenon_H3d zenon_H3c zenon_H3b zenon_H1b4 zenon_Hd6 zenon_H182. % 15.41/15.54 apply (zenon_or_s _ _ zenon_Heb); [ zenon_intro zenon_H92 | zenon_intro zenon_Hec ]. % 15.41/15.54 exact (zenon_H8f zenon_H92). % 15.41/15.54 apply (zenon_or_s _ _ zenon_Hec); [ zenon_intro zenon_H68 | zenon_intro zenon_Hed ]. % 15.41/15.54 apply (zenon_L162_); trivial. % 15.41/15.54 apply (zenon_or_s _ _ zenon_Hed); [ zenon_intro zenon_Hdd | zenon_intro zenon_He9 ]. % 15.41/15.54 apply (zenon_L809_); trivial. % 15.41/15.54 apply (zenon_L406_); trivial. % 15.41/15.54 (* end of lemma zenon_L834_ *) % 15.41/15.54 assert (zenon_L835_ : (((op (e2) (e0)) = (e0))\/(((op (e2) (e1)) = (e0))\/(((op (e2) (e2)) = (e0))\/((op (e2) (e3)) = (e0))))) -> (~((e0) = (e3))) -> (~((e1) = (e2))) -> (~((op (e2) (e2)) = (e1))) -> (~((op (e1) (op (e2) (e1))) = (op (e2) (e1)))) -> ((op (e1) (e0)) = (e1)) -> ((op (e2) (e0)) = (e3)) -> (~((e1) = (e3))) -> (((op (e2) (e0)) = (e1))\/(((op (e2) (e1)) = (e1))\/(((op (e2) (e2)) = (e1))\/((op (e2) (e3)) = (e1))))) -> (~((op (e2) (e2)) = (e0))) -> (~((e0) = (e2))) -> ((op (e2) (e3)) = (e2)) -> False). % 15.41/15.54 do 0 intro. intros zenon_H1f5 zenon_H4b zenon_Ha7 zenon_H52 zenon_H290 zenon_Hd8 zenon_Haf zenon_Ha3 zenon_Hb7 zenon_H2e zenon_H5e zenon_H124. % 15.41/15.54 apply (zenon_or_s _ _ zenon_H1f5); [ zenon_intro zenon_Hcf | zenon_intro zenon_H1f9 ]. % 15.41/15.54 apply (zenon_L57_); trivial. % 15.41/15.54 apply (zenon_or_s _ _ zenon_H1f9); [ zenon_intro zenon_H14a | zenon_intro zenon_H1fa ]. % 15.41/15.54 apply (zenon_L784_); trivial. % 15.41/15.54 apply (zenon_or_s _ _ zenon_H1fa); [ zenon_intro zenon_H32 | zenon_intro zenon_Hd0 ]. % 15.41/15.54 exact (zenon_H2e zenon_H32). % 15.41/15.54 apply (zenon_L201_); trivial. % 15.41/15.54 (* end of lemma zenon_L835_ *) % 15.41/15.54 assert (zenon_L836_ : (((op (e0) (e0)) = (e3))\/(((op (e1) (e0)) = (e3))\/(((op (e2) (e0)) = (e3))\/((op (e3) (e0)) = (e3))))) -> (~((op (e0) (e0)) = (e3))) -> ((op (e2) (e3)) = (e2)) -> (~((e0) = (e2))) -> (~((op (e2) (e2)) = (e0))) -> (((op (e2) (e0)) = (e1))\/(((op (e2) (e1)) = (e1))\/(((op (e2) (e2)) = (e1))\/((op (e2) (e3)) = (e1))))) -> (~((e1) = (e3))) -> ((op (e1) (e0)) = (e1)) -> (~((op (e1) (op (e2) (e1))) = (op (e2) (e1)))) -> (~((op (e2) (e2)) = (e1))) -> (~((e1) = (e2))) -> (~((e0) = (e3))) -> (((op (e2) (e0)) = (e0))\/(((op (e2) (e1)) = (e0))\/(((op (e2) (e2)) = (e0))\/((op (e2) (e3)) = (e0))))) -> (~((e2) = (e3))) -> ((op (e3) (e0)) = (e2)) -> False). % 15.41/15.54 do 0 intro. intros zenon_Hbe zenon_H59 zenon_H124 zenon_H5e zenon_H2e zenon_Hb7 zenon_Ha3 zenon_Hd8 zenon_H290 zenon_H52 zenon_Ha7 zenon_H4b zenon_H1f5 zenon_H6a zenon_He9. % 15.41/15.54 apply (zenon_or_s _ _ zenon_Hbe); [ zenon_intro zenon_H5b | zenon_intro zenon_Hbf ]. % 15.41/15.54 exact (zenon_H59 zenon_H5b). % 15.41/15.54 apply (zenon_or_s _ _ zenon_Hbf); [ zenon_intro zenon_H69 | zenon_intro zenon_Hc0 ]. % 15.41/15.54 apply (zenon_L163_); trivial. % 15.41/15.54 apply (zenon_or_s _ _ zenon_Hc0); [ zenon_intro zenon_Haf | zenon_intro zenon_Hba ]. % 15.41/15.54 apply (zenon_L835_); trivial. % 15.41/15.54 apply (zenon_L220_); trivial. % 15.41/15.54 (* end of lemma zenon_L836_ *) % 15.41/15.54 assert (zenon_L837_ : (((op (e0) (e0)) = (e2))\/(((op (e1) (e0)) = (e2))\/(((op (e2) (e0)) = (e2))\/((op (e3) (e0)) = (e2))))) -> (~((op (e0) (e0)) = (e2))) -> ((op (e3) (e2)) = (e3)) -> (~((op (e3) (e0)) = (op (e3) (e2)))) -> (((op (e0) (e0)) = (e3))\/(((op (e1) (e0)) = (e3))\/(((op (e2) (e0)) = (e3))\/((op (e3) (e0)) = (e3))))) -> (~((op (e0) (e0)) = (e3))) -> ((op (e2) (e3)) = (e2)) -> (~((e0) = (e2))) -> (~((op (e2) (e2)) = (e0))) -> (((op (e2) (e0)) = (e1))\/(((op (e2) (e1)) = (e1))\/(((op (e2) (e2)) = (e1))\/((op (e2) (e3)) = (e1))))) -> (~((e1) = (e3))) -> ((op (e1) (e0)) = (e1)) -> (~((op (e1) (op (e2) (e1))) = (op (e2) (e1)))) -> (~((op (e2) (e2)) = (e1))) -> (~((e1) = (e2))) -> (~((e0) = (e3))) -> (((op (e2) (e0)) = (e0))\/(((op (e2) (e1)) = (e0))\/(((op (e2) (e2)) = (e0))\/((op (e2) (e3)) = (e0))))) -> (~((e2) = (e3))) -> False). % 15.41/15.54 do 0 intro. intros zenon_Heb zenon_H8f zenon_H106 zenon_H105 zenon_Hbe zenon_H59 zenon_H124 zenon_H5e zenon_H2e zenon_Hb7 zenon_Ha3 zenon_Hd8 zenon_H290 zenon_H52 zenon_Ha7 zenon_H4b zenon_H1f5 zenon_H6a. % 15.41/15.54 apply (zenon_or_s _ _ zenon_Heb); [ zenon_intro zenon_H92 | zenon_intro zenon_Hec ]. % 15.41/15.54 exact (zenon_H8f zenon_H92). % 15.41/15.54 apply (zenon_or_s _ _ zenon_Hec); [ zenon_intro zenon_H68 | zenon_intro zenon_Hed ]. % 15.41/15.54 apply (zenon_L162_); trivial. % 15.41/15.54 apply (zenon_or_s _ _ zenon_Hed); [ zenon_intro zenon_Hdd | zenon_intro zenon_He9 ]. % 15.41/15.54 apply (zenon_L456_); trivial. % 15.41/15.54 apply (zenon_L836_); trivial. % 15.41/15.54 (* end of lemma zenon_L837_ *) % 15.41/15.54 assert (zenon_L838_ : (((op (e0) (e0)) = (e2))\/(((op (e1) (e0)) = (e2))\/(((op (e2) (e0)) = (e2))\/((op (e3) (e0)) = (e2))))) -> (~((op (e0) (e0)) = (e2))) -> (~((op (e3) (e3)) = (e1))) -> (~((op (e0) (e2)) = (op (e3) (e2)))) -> ((op (e0) (e2)) = (e1)) -> (((op (e0) (e1)) = (e2))\/(((op (e1) (e1)) = (e2))\/(((op (e2) (e1)) = (e2))\/((op (e3) (e1)) = (e2))))) -> (~((op (e0) (e1)) = (op (e0) (e3)))) -> ((op (e0) (e3)) = (e2)) -> (~((op (e1) (e1)) = (e2))) -> (~((op (e2) (e0)) = (op (e2) (e1)))) -> (~((op (e1) (e0)) = (op (e3) (e0)))) -> (((op (e3) (e0)) = (e1))\/(((op (e3) (e1)) = (e1))\/(((op (e3) (e2)) = (e1))\/((op (e3) (e3)) = (e1))))) -> (((op (e0) (e0)) = (e3))\/(((op (e1) (e0)) = (e3))\/(((op (e2) (e0)) = (e3))\/((op (e3) (e0)) = (e3))))) -> (~((op (e0) (e0)) = (e3))) -> ((op (e2) (e3)) = (e2)) -> (~((e0) = (e2))) -> (~((op (e2) (e2)) = (e0))) -> (((op (e2) (e0)) = (e1))\/(((op (e2) (e1)) = (e1))\/(((op (e2) (e2)) = (e1))\/((op (e2) (e3)) = (e1))))) -> (~((e1) = (e3))) -> ((op (e1) (e0)) = (e1)) -> (~((op (e1) (op (e2) (e1))) = (op (e2) (e1)))) -> (~((op (e2) (e2)) = (e1))) -> (~((e1) = (e2))) -> (~((e0) = (e3))) -> (((op (e2) (e0)) = (e0))\/(((op (e2) (e1)) = (e0))\/(((op (e2) (e2)) = (e0))\/((op (e2) (e3)) = (e0))))) -> (~((e2) = (e3))) -> False). % 15.41/15.54 do 0 intro. intros zenon_Heb zenon_H8f zenon_H104 zenon_H140 zenon_H29 zenon_H1a2 zenon_H1cd zenon_H81 zenon_Hd6 zenon_H154 zenon_H22e zenon_H146 zenon_Hbe zenon_H59 zenon_H124 zenon_H5e zenon_H2e zenon_Hb7 zenon_Ha3 zenon_Hd8 zenon_H290 zenon_H52 zenon_Ha7 zenon_H4b zenon_H1f5 zenon_H6a. % 15.41/15.54 apply (zenon_or_s _ _ zenon_Heb); [ zenon_intro zenon_H92 | zenon_intro zenon_Hec ]. % 15.41/15.54 exact (zenon_H8f zenon_H92). % 15.41/15.54 apply (zenon_or_s _ _ zenon_Hec); [ zenon_intro zenon_H68 | zenon_intro zenon_Hed ]. % 15.41/15.54 apply (zenon_L162_); trivial. % 15.41/15.54 apply (zenon_or_s _ _ zenon_Hed); [ zenon_intro zenon_Hdd | zenon_intro zenon_He9 ]. % 15.41/15.54 apply (zenon_L416_); trivial. % 15.41/15.54 apply (zenon_L836_); trivial. % 15.41/15.54 (* end of lemma zenon_L838_ *) % 15.41/15.54 assert (zenon_L839_ : (((op (e0) (e2)) = (e1))\/(((op (e1) (e2)) = (e1))\/(((op (e2) (e2)) = (e1))\/((op (e3) (e2)) = (e1))))) -> (~((e1) = (e2))) -> ((op (e0) (e2)) = (e2)) -> ((op (e1) (e0)) = (e1)) -> (~((op (e1) (e0)) = (op (e1) (e2)))) -> (~((op (e2) (e2)) = (e1))) -> (~((op (e3) (e1)) = (op (e3) (e2)))) -> ((op (e3) (e1)) = (e1)) -> False). % 15.41/15.54 do 0 intro. intros zenon_H11b zenon_Ha7 zenon_H63 zenon_Hd8 zenon_H166 zenon_H52 zenon_H135 zenon_H13e. % 15.41/15.54 apply (zenon_or_s _ _ zenon_H11b); [ zenon_intro zenon_H29 | zenon_intro zenon_H11c ]. % 15.41/15.54 apply (zenon_L104_); trivial. % 15.41/15.54 apply (zenon_or_s _ _ zenon_H11c); [ zenon_intro zenon_H117 | zenon_intro zenon_H11d ]. % 15.41/15.54 apply (zenon_L248_); trivial. % 15.41/15.54 apply (zenon_or_s _ _ zenon_H11d); [ zenon_intro zenon_H2a | zenon_intro zenon_H119 ]. % 15.41/15.54 exact (zenon_H52 zenon_H2a). % 15.41/15.54 apply (zenon_L394_); trivial. % 15.41/15.54 (* end of lemma zenon_L839_ *) % 15.41/15.54 assert (zenon_L840_ : (((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 (e2) (e3)) = (e2)) -> (~((e0) = (e2))) -> (~((op (e2) (e2)) = (e0))) -> (~((op (e1) (op (e2) (e1))) = (op (e2) (e1)))) -> (~((op (e0) (e0)) = (op (e2) (e0)))) -> ((op (e0) (e0)) = (e0)) -> (((op (e2) (e0)) = (e0))\/(((op (e2) (e1)) = (e0))\/(((op (e2) (e2)) = (e0))\/((op (e2) (e3)) = (e0))))) -> (((op (e0) (e2)) = (e1))\/(((op (e1) (e2)) = (e1))\/(((op (e2) (e2)) = (e1))\/((op (e3) (e2)) = (e1))))) -> (~((e1) = (e2))) -> ((op (e0) (e2)) = (e2)) -> ((op (e1) (e0)) = (e1)) -> (~((op (e1) (e0)) = (op (e1) (e2)))) -> (~((op (e2) (e2)) = (e1))) -> (~((op (e3) (e1)) = (op (e3) (e2)))) -> False). % 15.41/15.55 do 0 intro. intros zenon_H228 zenon_H1cd zenon_H37 zenon_H1b4 zenon_H124 zenon_H5e zenon_H2e zenon_H290 zenon_H258 zenon_H1f zenon_H1f5 zenon_H11b zenon_Ha7 zenon_H63 zenon_Hd8 zenon_H166 zenon_H52 zenon_H135. % 15.41/15.55 apply (zenon_or_s _ _ zenon_H228); [ zenon_intro zenon_H22 | zenon_intro zenon_H229 ]. % 15.41/15.55 apply (zenon_L223_); trivial. % 15.41/15.55 apply (zenon_or_s _ _ zenon_H229); [ zenon_intro zenon_H21 | zenon_intro zenon_H22a ]. % 15.41/15.55 exact (zenon_H1b4 zenon_H21). % 15.41/15.55 apply (zenon_or_s _ _ zenon_H22a); [ zenon_intro zenon_Hb2 | zenon_intro zenon_H13e ]. % 15.41/15.55 apply (zenon_or_s _ _ zenon_H1f5); [ zenon_intro zenon_Hcf | zenon_intro zenon_H1f9 ]. % 15.41/15.55 apply (zenon_L598_); trivial. % 15.41/15.55 apply (zenon_or_s _ _ zenon_H1f9); [ zenon_intro zenon_H14a | zenon_intro zenon_H1fa ]. % 15.41/15.55 apply (zenon_L783_); trivial. % 15.41/15.55 apply (zenon_or_s _ _ zenon_H1fa); [ zenon_intro zenon_H32 | zenon_intro zenon_Hd0 ]. % 15.41/15.55 exact (zenon_H2e zenon_H32). % 15.41/15.55 apply (zenon_L201_); trivial. % 15.41/15.55 apply (zenon_L839_); trivial. % 15.41/15.55 (* end of lemma zenon_L840_ *) % 15.41/15.55 assert (zenon_L841_ : (((op (e0) (e0)) = (e2))\/(((op (e0) (e1)) = (e2))\/(((op (e0) (e2)) = (e2))\/((op (e0) (e3)) = (e2))))) -> (~((op (e0) (e1)) = (op (e2) (e1)))) -> ((op (e2) (e1)) = (e2)) -> (((op (e1) (e1)) = (e0))\/(((op (e1) (e1)) = (e1))\/(((op (e1) (e1)) = (e2))\/((op (e1) (e1)) = (e3))))) -> (~((op (e2) (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) (e1)) = (e1))) -> (((op (e0) (e0)) = (e3))\/(((op (e1) (e0)) = (e3))\/(((op (e2) (e0)) = (e3))\/((op (e3) (e0)) = (e3))))) -> (~((op (e0) (op (e2) (e0))) = (op (e2) (e0)))) -> (~((op (e0) (e0)) = (e2))) -> (((op (e0) (e0)) = (e2))\/(((op (e1) (e0)) = (e2))\/(((op (e2) (e0)) = (e2))\/((op (e3) (e0)) = (e2))))) -> (((op (e0) (e0)) = (e3))\/(((op (e0) (e1)) = (e3))\/(((op (e0) (e2)) = (e3))\/((op (e0) (e3)) = (e3))))) -> (~((op (e0) (e0)) = (e3))) -> (~((op (e0) (e3)) = (op (e1) (e3)))) -> (((op (e0) (e1)) = (e2))\/(((op (e1) (e1)) = (e2))\/(((op (e2) (e1)) = (e2))\/((op (e3) (e1)) = (e2))))) -> (~((op (e0) (e1)) = (op (e0) (e3)))) -> (~((op (e1) (e1)) = (e2))) -> (((op (e1) (e0)) = (e3))\/(((op (e1) (e1)) = (e3))\/(((op (e1) (e2)) = (e3))\/((op (e1) (e3)) = (e3))))) -> ((op (e1) (e0)) = (e1)) -> (~((op (e0) (e2)) = (op (e1) (e2)))) -> (((op (e0) (e1)) = (e3))\/(((op (e1) (e1)) = (e3))\/(((op (e2) (e1)) = (e3))\/((op (e3) (e1)) = (e3))))) -> (~((e1) = (e3))) -> ((op (e0) (e1)) = (e1)) -> (~((op (e1) (e1)) = (e3))) -> (~((op (e1) (op (e2) (e1))) = (op (e2) (e1)))) -> (~((e1) = (e2))) -> (((op (e1) (e0)) = (e2))\/(((op (e1) (e1)) = (e2))\/(((op (e1) (e2)) = (e2))\/((op (e1) (e3)) = (e2))))) -> (~((e2) = (e3))) -> False). % 15.41/15.55 do 0 intro. intros zenon_H8e zenon_Hde zenon_H156 zenon_H1b3 zenon_H30 zenon_H2f zenon_H2e zenon_H2d zenon_H1b4 zenon_Hbe zenon_H295 zenon_H8f zenon_Heb zenon_H58 zenon_H59 zenon_H80 zenon_H1a2 zenon_H1cd zenon_Hd6 zenon_H90 zenon_Hd8 zenon_H87 zenon_H199 zenon_Ha3 zenon_H22 zenon_H182 zenon_H290 zenon_Ha7 zenon_H84 zenon_H6a. % 15.41/15.55 apply (zenon_or_s _ _ zenon_H8e); [ zenon_intro zenon_H92 | zenon_intro zenon_H91 ]. % 15.41/15.55 exact (zenon_H8f zenon_H92). % 15.41/15.55 apply (zenon_or_s _ _ zenon_H91); [ zenon_intro zenon_H5d | zenon_intro zenon_H93 ]. % 15.41/15.55 apply (zenon_L251_); trivial. % 15.41/15.55 apply (zenon_or_s _ _ zenon_H93); [ zenon_intro zenon_H63 | zenon_intro zenon_H81 ]. % 15.41/15.55 apply (zenon_L832_); trivial. % 15.41/15.55 apply (zenon_L827_); trivial. % 15.41/15.55 (* end of lemma zenon_L841_ *) % 15.41/15.55 assert (zenon_L842_ : (~((op (e3) (e1)) = (op (e3) (e3)))) -> (~((e0) = (e3))) -> (((op (e0) (e1)) = (e1))\/(((op (e1) (e1)) = (e1))\/(((op (e2) (e1)) = (e1))\/((op (e3) (e1)) = (e1))))) -> (~((op (e1) (e0)) = (op (e1) (e2)))) -> (((op (e0) (e1)) = (e3))\/(((op (e1) (e1)) = (e3))\/(((op (e2) (e1)) = (e3))\/((op (e3) (e1)) = (e3))))) -> (~((op (e3) (e0)) = (op (e3) (e1)))) -> (((op (e0) (e0)) = (e1))\/(((op (e0) (e1)) = (e1))\/(((op (e0) (e2)) = (e1))\/((op (e0) (e3)) = (e1))))) -> ((~((op (e3) (e3)) = (e3)))\/((op (e3) (e3)) = (e3))) -> ((~((op (e2) (e2)) = (e2)))\/((op (e2) (e2)) = (e2))) -> (((op (e1) (e0)) = (e2))\/(((op (e1) (e1)) = (e2))\/(((op (e1) (e2)) = (e2))\/((op (e1) (e3)) = (e2))))) -> (~((op (e0) (e2)) = (op (e2) (e2)))) -> (((op (e0) (e3)) = (e0))\/(((op (e0) (e3)) = (e1))\/(((op (e0) (e3)) = (e2))\/((op (e0) (e3)) = (e3))))) -> (~((op (e0) (e3)) = (op (e1) (e3)))) -> (~((op (e0) (e3)) = (op (e2) (e3)))) -> (~((op (e0) (e0)) = (op (e0) (e3)))) -> (~((op (e1) (e2)) = (op (e2) (e2)))) -> ((~((op (e3) (e3)) = (e1)))\/((op (e3) (e1)) = (e3))) -> ((~((op (e2) (e2)) = (e3)))\/((op (e2) (e3)) = (e2))) -> (((op (e2) (e0)) = (e3))\/(((op (e2) (e1)) = (e3))\/(((op (e2) (e2)) = (e3))\/((op (e2) (e3)) = (e3))))) -> (~((op (e0) (e1)) = (op (e2) (e1)))) -> (~((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)) = (e0))) -> (~((op (e0) (e0)) = (op (e2) (e0)))) -> (((op (e2) (e0)) = (e1))\/(((op (e2) (e1)) = (e1))\/(((op (e2) (e2)) = (e1))\/((op (e2) (e3)) = (e1))))) -> (~((op (e1) (op (e2) (e1))) = (op (e2) (e1)))) -> (~((e0) = (e2))) -> (((op (e2) (e0)) = (e0))\/(((op (e2) (e1)) = (e0))\/(((op (e2) (e2)) = (e0))\/((op (e2) (e3)) = (e0))))) -> (~((op (e2) (e1)) = (op (e2) (e2)))) -> (~((op (e2) (e1)) = (op (e2) (e3)))) -> ((~((op (e2) (e2)) = (e1)))\/((op (e2) (e1)) = (e2))) -> (~((op (e0) (e0)) = (e2))) -> (~((e1) = (e2))) -> ((op (e1) (e0)) = (e1)) -> (~((op (e0) (e3)) = (op (e3) (e3)))) -> (((op (e3) (e3)) = (e0))\/(((op (e3) (e3)) = (e1))\/(((op (e3) (e3)) = (e2))\/((op (e3) (e3)) = (e3))))) -> (~((op (e0) (e0)) = (e3))) -> (~((e2) = (e3))) -> (((op (e1) (e0)) = (e3))\/(((op (e1) (e1)) = (e3))\/(((op (e1) (e2)) = (e3))\/((op (e1) (e3)) = (e3))))) -> (~((op (e0) (e1)) = (op (e0) (e3)))) -> (~((op (e2) (e0)) = (op (e2) (e3)))) -> (((op (e0) (e3)) = (e2))\/(((op (e1) (e3)) = (e2))\/(((op (e2) (e3)) = (e2))\/((op (e3) (e3)) = (e2))))) -> (~((op (e0) (e2)) = (op (e1) (e2)))) -> (~((op (e1) (e1)) = (e3))) -> (~((e1) = (e3))) -> (((op (e0) (e0)) = (e3))\/(((op (e1) (e0)) = (e3))\/(((op (e2) (e0)) = (e3))\/((op (e3) (e0)) = (e3))))) -> (~((op (e0) (e1)) = (op (e3) (e1)))) -> (((op (e0) (e2)) = (e0))\/(((op (e0) (e2)) = (e1))\/(((op (e0) (e2)) = (e2))\/((op (e0) (e2)) = (e3))))) -> (((op (e3) (e0)) = (e1))\/(((op (e3) (e1)) = (e1))\/(((op (e3) (e2)) = (e1))\/((op (e3) (e3)) = (e1))))) -> (~((op (e0) (e2)) = (op (e3) (e2)))) -> (((op (e0) (e3)) = (e1))\/(((op (e1) (e3)) = (e1))\/(((op (e2) (e3)) = (e1))\/((op (e3) (e3)) = (e1))))) -> (~((op (e3) (op (e2) (e3))) = (op (e2) (e3)))) -> (~((op (e1) (e0)) = (op (e1) (e3)))) -> (~((op (e0) (e2)) = (op (e0) (e3)))) -> (~((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 (e3) (e0)))) -> (~((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 (e0) (e0)) = (e2))\/(((op (e0) (e1)) = (e2))\/(((op (e0) (e2)) = (e2))\/((op (e0) (e3)) = (e2))))) -> ((op (e0) (e0)) = (e0)) -> (~((op (e0) (e0)) = (op (e0) (e2)))) -> (((op (e3) (e0)) = (e2))\/(((op (e3) (e1)) = (e2))\/(((op (e3) (e2)) = (e2))\/((op (e3) (e3)) = (e2))))) -> (~((op (e0) (op (e2) (e0))) = (op (e2) (e0)))) -> (((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 (e0) (e0)) = (e2))\/(((op (e1) (e0)) = (e2))\/(((op (e2) (e0)) = (e2))\/((op (e3) (e0)) = (e2))))) -> (~((op (e1) (e2)) = (op (e3) (e2)))) -> (((op (e0) (e0)) = (e1))\/(((op (e1) (e0)) = (e1))\/(((op (e2) (e0)) = (e1))\/((op (e3) (e0)) = (e1))))) -> (~((op (e3) (e0)) = (op (e3) (e2)))) -> (~((op (e0) (e0)) = (e1))) -> ((~((op (e3) (e3)) = (e2)))\/((op (e3) (e2)) = (e3))) -> ((~((op (e3) (e3)) = (e0)))\/((op (e3) (e0)) = (e3))) -> (~((op (e2) (op (e2) (e2))) = (op (e2) (e2)))) -> False). % 15.41/15.55 do 0 intro. intros zenon_H12d zenon_H4b zenon_H228 zenon_H166 zenon_H199 zenon_H109 zenon_H44 zenon_H10d zenon_Haa zenon_H84 zenon_H28 zenon_H254 zenon_H80 zenon_Hb4 zenon_H24f zenon_H7d zenon_H10c zenon_H1c3 zenon_He6 zenon_Hde zenon_H8b zenon_H2d zenon_H2e zenon_H258 zenon_Hb7 zenon_H290 zenon_H5e zenon_H1f5 zenon_H157 zenon_H1e2 zenon_H1e3 zenon_H8f zenon_Ha7 zenon_Hd8 zenon_H36 zenon_H3b zenon_H59 zenon_H6a zenon_H90 zenon_H1cd zenon_Hce zenon_H160 zenon_H87 zenon_H182 zenon_Ha3 zenon_Hbe zenon_H138 zenon_H251 zenon_H146 zenon_H140 zenon_H121 zenon_H28a zenon_H1cf zenon_Hc9 zenon_H135 zenon_H11b zenon_H22e zenon_Hd6 zenon_H154 zenon_H1a2 zenon_H8e zenon_H1f zenon_H250 zenon_H1df zenon_H295 zenon_H58 zenon_H1b3 zenon_H1b4 zenon_Heb zenon_H17d zenon_Hf1 zenon_H105 zenon_H45 zenon_H10e zenon_H10f zenon_H294. % 15.41/15.55 apply (zenon_or_s _ _ zenon_H1e3); [ zenon_intro zenon_H52 | zenon_intro zenon_H156 ]. % 15.41/15.55 apply (zenon_or_s _ _ zenon_Haa); [ zenon_intro zenon_H2f | zenon_intro zenon_H35 ]. % 15.41/15.55 apply (zenon_or_s _ _ zenon_H1c3); [ zenon_intro zenon_H30 | zenon_intro zenon_H124 ]. % 15.41/15.55 apply (zenon_or_s _ _ zenon_H10f); [ zenon_intro zenon_H3c | zenon_intro zenon_Hba ]. % 15.41/15.55 apply (zenon_or_s _ _ zenon_H10c); [ zenon_intro zenon_H104 | zenon_intro zenon_H10a ]. % 15.41/15.55 apply (zenon_L815_); trivial. % 15.41/15.55 apply (zenon_or_s _ _ zenon_H10e); [ zenon_intro zenon_H3d | zenon_intro zenon_H106 ]. % 15.41/15.55 apply (zenon_or_s _ _ zenon_H10d); [ zenon_intro zenon_H3e | zenon_intro zenon_H42 ]. % 15.41/15.55 apply (zenon_or_s _ _ zenon_Heb); [ zenon_intro zenon_H92 | zenon_intro zenon_Hec ]. % 15.41/15.55 exact (zenon_H8f zenon_H92). % 15.41/15.55 apply (zenon_or_s _ _ zenon_Hec); [ zenon_intro zenon_H68 | zenon_intro zenon_Hed ]. % 15.41/15.55 apply (zenon_L162_); trivial. % 15.41/15.55 apply (zenon_or_s _ _ zenon_Hed); [ zenon_intro zenon_Hdd | zenon_intro zenon_He9 ]. % 15.41/15.55 apply (zenon_L830_); trivial. % 15.41/15.55 apply (zenon_L406_); trivial. % 15.41/15.55 apply (zenon_L572_); trivial. % 15.41/15.55 apply (zenon_L115_); trivial. % 15.41/15.55 apply (zenon_L833_); trivial. % 15.41/15.55 apply (zenon_or_s _ _ zenon_H10f); [ zenon_intro zenon_H3c | zenon_intro zenon_Hba ]. % 15.41/15.55 apply (zenon_or_s _ _ zenon_H10c); [ zenon_intro zenon_H104 | zenon_intro zenon_H10a ]. % 15.41/15.55 apply (zenon_or_s _ _ zenon_H10e); [ zenon_intro zenon_H3d | zenon_intro zenon_H106 ]. % 15.41/15.55 apply (zenon_or_s _ _ zenon_H10d); [ zenon_intro zenon_H3e | zenon_intro zenon_H42 ]. % 15.41/15.55 apply (zenon_or_s _ _ zenon_H44); [ zenon_intro zenon_H47 | zenon_intro zenon_H46 ]. % 15.41/15.55 exact (zenon_H45 zenon_H47). % 15.41/15.55 apply (zenon_or_s _ _ zenon_H46); [ zenon_intro zenon_H22 | zenon_intro zenon_H48 ]. % 15.41/15.55 apply (zenon_L225_); trivial. % 15.41/15.55 apply (zenon_or_s _ _ zenon_H48); [ zenon_intro zenon_H29 | zenon_intro zenon_H37 ]. % 15.41/15.55 apply (zenon_L834_); trivial. % 15.41/15.55 apply (zenon_L7_); trivial. % 15.41/15.55 apply (zenon_L814_); trivial. % 15.41/15.55 apply (zenon_L837_); trivial. % 15.41/15.55 apply (zenon_or_s _ _ zenon_H10e); [ zenon_intro zenon_H3d | zenon_intro zenon_H106 ]. % 15.41/15.55 apply (zenon_or_s _ _ zenon_H10d); [ zenon_intro zenon_H3e | zenon_intro zenon_H42 ]. % 15.41/15.55 apply (zenon_or_s _ _ zenon_H44); [ zenon_intro zenon_H47 | zenon_intro zenon_H46 ]. % 15.41/15.55 exact (zenon_H45 zenon_H47). % 15.41/15.55 apply (zenon_or_s _ _ zenon_H46); [ zenon_intro zenon_H22 | zenon_intro zenon_H48 ]. % 15.41/15.55 apply (zenon_or_s _ _ zenon_Heb); [ zenon_intro zenon_H92 | zenon_intro zenon_Hec ]. % 15.41/15.55 exact (zenon_H8f zenon_H92). % 15.41/15.55 apply (zenon_or_s _ _ zenon_Hec); [ zenon_intro zenon_H68 | zenon_intro zenon_Hed ]. % 15.41/15.55 apply (zenon_L162_); trivial. % 15.41/15.55 apply (zenon_or_s _ _ zenon_Hed); [ zenon_intro zenon_Hdd | zenon_intro zenon_He9 ]. % 15.41/15.55 apply (zenon_L828_); trivial. % 15.41/15.55 apply (zenon_L836_); trivial. % 15.41/15.55 apply (zenon_or_s _ _ zenon_H48); [ zenon_intro zenon_H29 | zenon_intro zenon_H37 ]. % 15.41/15.55 apply (zenon_L829_); trivial. % 15.41/15.55 apply (zenon_L7_); trivial. % 15.41/15.55 apply (zenon_L102_); trivial. % 15.41/15.55 apply (zenon_L115_); trivial. % 15.41/15.55 apply (zenon_or_s _ _ zenon_H10c); [ zenon_intro zenon_H104 | zenon_intro zenon_H10a ]. % 15.41/15.55 apply (zenon_or_s _ _ zenon_H10e); [ zenon_intro zenon_H3d | zenon_intro zenon_H106 ]. % 15.41/15.55 apply (zenon_or_s _ _ zenon_H44); [ zenon_intro zenon_H47 | zenon_intro zenon_H46 ]. % 15.41/15.55 exact (zenon_H45 zenon_H47). % 15.41/15.55 apply (zenon_or_s _ _ zenon_H46); [ zenon_intro zenon_H22 | zenon_intro zenon_H48 ]. % 15.41/15.55 apply (zenon_L225_); trivial. % 15.41/15.55 apply (zenon_or_s _ _ zenon_H48); [ zenon_intro zenon_H29 | zenon_intro zenon_H37 ]. % 15.41/15.55 apply (zenon_or_s _ _ zenon_H8e); [ zenon_intro zenon_H92 | zenon_intro zenon_H91 ]. % 15.41/15.55 exact (zenon_H8f zenon_H92). % 15.41/15.55 apply (zenon_or_s _ _ zenon_H91); [ zenon_intro zenon_H5d | zenon_intro zenon_H93 ]. % 15.41/15.55 apply (zenon_L831_); trivial. % 15.41/15.55 apply (zenon_or_s _ _ zenon_H93); [ zenon_intro zenon_H63 | zenon_intro zenon_H81 ]. % 15.41/15.55 apply (zenon_L104_); trivial. % 15.41/15.55 apply (zenon_L838_); trivial. % 15.41/15.55 apply (zenon_or_s _ _ zenon_H8e); [ zenon_intro zenon_H92 | zenon_intro zenon_H91 ]. % 15.41/15.55 exact (zenon_H8f zenon_H92). % 15.41/15.55 apply (zenon_or_s _ _ zenon_H91); [ zenon_intro zenon_H5d | zenon_intro zenon_H93 ]. % 15.41/15.55 apply (zenon_L831_); trivial. % 15.41/15.55 apply (zenon_or_s _ _ zenon_H93); [ zenon_intro zenon_H63 | zenon_intro zenon_H81 ]. % 15.41/15.55 apply (zenon_L840_); trivial. % 15.41/15.55 apply (zenon_L33_); trivial. % 15.41/15.55 apply (zenon_L81_); trivial. % 15.41/15.55 apply (zenon_L82_); trivial. % 15.41/15.55 apply (zenon_L794_); trivial. % 15.41/15.55 apply (zenon_or_s _ _ zenon_Haa); [ zenon_intro zenon_H2f | zenon_intro zenon_H35 ]. % 15.41/15.55 apply (zenon_or_s _ _ zenon_H1c3); [ zenon_intro zenon_H30 | zenon_intro zenon_H124 ]. % 15.41/15.55 apply (zenon_or_s _ _ zenon_H44); [ zenon_intro zenon_H47 | zenon_intro zenon_H46 ]. % 15.41/15.55 exact (zenon_H45 zenon_H47). % 15.41/15.55 apply (zenon_or_s _ _ zenon_H46); [ zenon_intro zenon_H22 | zenon_intro zenon_H48 ]. % 15.41/15.55 apply (zenon_L841_); trivial. % 15.41/15.55 apply (zenon_or_s _ _ zenon_H48); [ zenon_intro zenon_H29 | zenon_intro zenon_H37 ]. % 15.41/15.55 apply (zenon_L5_); trivial. % 15.41/15.55 apply (zenon_or_s _ _ zenon_H8e); [ zenon_intro zenon_H92 | zenon_intro zenon_H91 ]. % 15.41/15.55 exact (zenon_H8f zenon_H92). % 15.41/15.55 apply (zenon_or_s _ _ zenon_H91); [ zenon_intro zenon_H5d | zenon_intro zenon_H93 ]. % 15.41/15.55 apply (zenon_L251_); trivial. % 15.41/15.55 apply (zenon_or_s _ _ zenon_H93); [ zenon_intro zenon_H63 | zenon_intro zenon_H81 ]. % 15.41/15.55 apply (zenon_L832_); trivial. % 15.41/15.55 apply (zenon_L33_); trivial. % 15.41/15.55 apply (zenon_L256_); trivial. % 15.41/15.55 apply (zenon_L134_); trivial. % 15.41/15.55 (* end of lemma zenon_L842_ *) % 15.41/15.55 assert (zenon_L843_ : (((op (e0) (e0)) = (e2))\/(((op (e0) (e1)) = (e2))\/(((op (e0) (e2)) = (e2))\/((op (e0) (e3)) = (e2))))) -> (~((op (e0) (e0)) = (e2))) -> (~((e1) = (e3))) -> (((op (e1) (e0)) = (e3))\/(((op (e1) (e1)) = (e3))\/(((op (e1) (e2)) = (e3))\/((op (e1) (e3)) = (e3))))) -> ((op (e1) (e0)) = (e1)) -> (~((op (e1) (e1)) = (e3))) -> (~((op (e0) (e2)) = (op (e1) (e2)))) -> (((op (e0) (e3)) = (e2))\/(((op (e1) (e3)) = (e2))\/(((op (e2) (e3)) = (e2))\/((op (e3) (e3)) = (e2))))) -> (~((op (e0) (e1)) = (op (e0) (e3)))) -> (~((e2) = (e3))) -> (~((op (e2) (e0)) = (op (e2) (e3)))) -> (~((op (e3) (e3)) = (e2))) -> (~((op (e0) (e0)) = (e3))) -> (((op (e0) (e0)) = (e3))\/(((op (e0) (e1)) = (e3))\/(((op (e0) (e2)) = (e3))\/((op (e0) (e3)) = (e3))))) -> ((op (e2) (e0)) = (e2)) -> (~((op (e0) (op (e2) (e0))) = (op (e2) (e0)))) -> ((op (e0) (e3)) = (e1)) -> (~((e1) = (e2))) -> False). % 15.41/15.55 do 0 intro. intros zenon_H8e zenon_H8f zenon_Ha3 zenon_H90 zenon_Hd8 zenon_H182 zenon_H87 zenon_H160 zenon_H1cd zenon_H6a zenon_Hce zenon_H3d zenon_H59 zenon_H58 zenon_Hdd zenon_H295 zenon_H37 zenon_Ha7. % 15.41/15.55 apply (zenon_or_s _ _ zenon_H8e); [ zenon_intro zenon_H92 | zenon_intro zenon_H91 ]. % 15.41/15.55 exact (zenon_H8f zenon_H92). % 15.41/15.55 apply (zenon_or_s _ _ zenon_H91); [ zenon_intro zenon_H5d | zenon_intro zenon_H93 ]. % 15.41/15.55 apply (zenon_L656_); trivial. % 15.41/15.55 apply (zenon_or_s _ _ zenon_H93); [ zenon_intro zenon_H63 | zenon_intro zenon_H81 ]. % 15.41/15.55 apply (zenon_L812_); trivial. % 15.41/15.55 apply (zenon_L33_); trivial. % 15.41/15.55 (* end of lemma zenon_L843_ *) % 15.41/15.55 assert (zenon_L844_ : ((~((op (e1) (e1)) = (e3)))\/((op (e1) (e3)) = (e1))) -> (~((op (e3) (e1)) = (op (e3) (e3)))) -> (~((e0) = (e3))) -> (((op (e0) (e1)) = (e1))\/(((op (e1) (e1)) = (e1))\/(((op (e2) (e1)) = (e1))\/((op (e3) (e1)) = (e1))))) -> (~((op (e1) (e0)) = (op (e1) (e2)))) -> (((op (e0) (e1)) = (e3))\/(((op (e1) (e1)) = (e3))\/(((op (e2) (e1)) = (e3))\/((op (e3) (e1)) = (e3))))) -> (~((op (e3) (e0)) = (op (e3) (e1)))) -> (((op (e0) (e0)) = (e1))\/(((op (e0) (e1)) = (e1))\/(((op (e0) (e2)) = (e1))\/((op (e0) (e3)) = (e1))))) -> ((~((op (e3) (e3)) = (e3)))\/((op (e3) (e3)) = (e3))) -> ((~((op (e2) (e2)) = (e2)))\/((op (e2) (e2)) = (e2))) -> (((op (e1) (e0)) = (e2))\/(((op (e1) (e1)) = (e2))\/(((op (e1) (e2)) = (e2))\/((op (e1) (e3)) = (e2))))) -> (~((op (e0) (e2)) = (op (e2) (e2)))) -> (((op (e0) (e3)) = (e0))\/(((op (e0) (e3)) = (e1))\/(((op (e0) (e3)) = (e2))\/((op (e0) (e3)) = (e3))))) -> (~((op (e0) (e3)) = (op (e1) (e3)))) -> (~((op (e0) (e3)) = (op (e2) (e3)))) -> (~((op (e0) (e0)) = (op (e0) (e3)))) -> (~((op (e1) (e2)) = (op (e2) (e2)))) -> ((~((op (e3) (e3)) = (e1)))\/((op (e3) (e1)) = (e3))) -> ((~((op (e2) (e2)) = (e3)))\/((op (e2) (e3)) = (e2))) -> (((op (e2) (e0)) = (e3))\/(((op (e2) (e1)) = (e3))\/(((op (e2) (e2)) = (e3))\/((op (e2) (e3)) = (e3))))) -> (~((op (e0) (e1)) = (op (e2) (e1)))) -> (~((op (e1) (e3)) = (op (e3) (e3)))) -> (((op (e2) (e2)) = (e0))\/(((op (e2) (e2)) = (e1))\/(((op (e2) (e2)) = (e2))\/((op (e2) (e2)) = (e3))))) -> (~((op (e0) (e0)) = (op (e2) (e0)))) -> (((op (e2) (e0)) = (e1))\/(((op (e2) (e1)) = (e1))\/(((op (e2) (e2)) = (e1))\/((op (e2) (e3)) = (e1))))) -> (~((op (e1) (op (e2) (e1))) = (op (e2) (e1)))) -> (~((e0) = (e2))) -> (((op (e2) (e0)) = (e0))\/(((op (e2) (e1)) = (e0))\/(((op (e2) (e2)) = (e0))\/((op (e2) (e3)) = (e0))))) -> (~((op (e2) (e1)) = (op (e2) (e2)))) -> (~((op (e2) (e1)) = (op (e2) (e3)))) -> ((~((op (e2) (e2)) = (e1)))\/((op (e2) (e1)) = (e2))) -> (~((op (e0) (e0)) = (e2))) -> (~((e1) = (e2))) -> ((op (e1) (e0)) = (e1)) -> (~((op (e0) (e3)) = (op (e3) (e3)))) -> (((op (e3) (e3)) = (e0))\/(((op (e3) (e3)) = (e1))\/(((op (e3) (e3)) = (e2))\/((op (e3) (e3)) = (e3))))) -> (~((op (e0) (e0)) = (e3))) -> (~((e2) = (e3))) -> (((op (e1) (e0)) = (e3))\/(((op (e1) (e1)) = (e3))\/(((op (e1) (e2)) = (e3))\/((op (e1) (e3)) = (e3))))) -> (~((op (e0) (e1)) = (op (e0) (e3)))) -> (~((op (e2) (e0)) = (op (e2) (e3)))) -> (((op (e0) (e3)) = (e2))\/(((op (e1) (e3)) = (e2))\/(((op (e2) (e3)) = (e2))\/((op (e3) (e3)) = (e2))))) -> (~((op (e0) (e2)) = (op (e1) (e2)))) -> (~((e1) = (e3))) -> (((op (e0) (e0)) = (e3))\/(((op (e1) (e0)) = (e3))\/(((op (e2) (e0)) = (e3))\/((op (e3) (e0)) = (e3))))) -> (~((op (e0) (e1)) = (op (e3) (e1)))) -> (((op (e0) (e2)) = (e0))\/(((op (e0) (e2)) = (e1))\/(((op (e0) (e2)) = (e2))\/((op (e0) (e2)) = (e3))))) -> (((op (e3) (e0)) = (e1))\/(((op (e3) (e1)) = (e1))\/(((op (e3) (e2)) = (e1))\/((op (e3) (e3)) = (e1))))) -> (~((op (e0) (e2)) = (op (e3) (e2)))) -> (((op (e0) (e3)) = (e1))\/(((op (e1) (e3)) = (e1))\/(((op (e2) (e3)) = (e1))\/((op (e3) (e3)) = (e1))))) -> (~((op (e3) (op (e2) (e3))) = (op (e2) (e3)))) -> (~((op (e1) (e0)) = (op (e1) (e3)))) -> (~((op (e0) (e2)) = (op (e0) (e3)))) -> (~((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 (e3) (e0)))) -> (~((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 (e0) (e0)) = (e2))\/(((op (e0) (e1)) = (e2))\/(((op (e0) (e2)) = (e2))\/((op (e0) (e3)) = (e2))))) -> ((op (e0) (e0)) = (e0)) -> (~((op (e0) (e0)) = (op (e0) (e2)))) -> (((op (e3) (e0)) = (e2))\/(((op (e3) (e1)) = (e2))\/(((op (e3) (e2)) = (e2))\/((op (e3) (e3)) = (e2))))) -> (~((op (e0) (op (e2) (e0))) = (op (e2) (e0)))) -> (((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 (e0) (e0)) = (e2))\/(((op (e1) (e0)) = (e2))\/(((op (e2) (e0)) = (e2))\/((op (e3) (e0)) = (e2))))) -> (~((op (e1) (e2)) = (op (e3) (e2)))) -> (((op (e0) (e0)) = (e1))\/(((op (e1) (e0)) = (e1))\/(((op (e2) (e0)) = (e1))\/((op (e3) (e0)) = (e1))))) -> (~((op (e3) (e0)) = (op (e3) (e2)))) -> (~((op (e0) (e0)) = (e1))) -> ((~((op (e3) (e3)) = (e2)))\/((op (e3) (e2)) = (e3))) -> ((~((op (e3) (e3)) = (e0)))\/((op (e3) (e0)) = (e3))) -> (~((op (e2) (op (e2) (e2))) = (op (e2) (e2)))) -> (~((op (e2) (e0)) = (op (e2) (e2)))) -> ((~((op (e2) (e2)) = (e0)))\/((op (e2) (e0)) = (e2))) -> False). % 15.41/15.55 do 0 intro. intros zenon_H1d2 zenon_H12d zenon_H4b zenon_H228 zenon_H166 zenon_H199 zenon_H109 zenon_H44 zenon_H10d zenon_Haa zenon_H84 zenon_H28 zenon_H254 zenon_H80 zenon_Hb4 zenon_H24f zenon_H7d zenon_H10c zenon_H1c3 zenon_He6 zenon_Hde zenon_H8b zenon_H2d zenon_H258 zenon_Hb7 zenon_H290 zenon_H5e zenon_H1f5 zenon_H157 zenon_H1e2 zenon_H1e3 zenon_H8f zenon_Ha7 zenon_Hd8 zenon_H36 zenon_H3b zenon_H59 zenon_H6a zenon_H90 zenon_H1cd zenon_Hce zenon_H160 zenon_H87 zenon_Ha3 zenon_Hbe zenon_H138 zenon_H251 zenon_H146 zenon_H140 zenon_H121 zenon_H28a zenon_H1cf zenon_Hc9 zenon_H135 zenon_H11b zenon_H22e zenon_Hd6 zenon_H154 zenon_H1a2 zenon_H8e zenon_H1f zenon_H250 zenon_H1df zenon_H295 zenon_H58 zenon_H1b3 zenon_H1b4 zenon_Heb zenon_H17d zenon_Hf1 zenon_H105 zenon_H45 zenon_H10e zenon_H10f zenon_H294 zenon_H17a zenon_H1d4. % 15.41/15.55 apply (zenon_or_s _ _ zenon_H1d2); [ zenon_intro zenon_H182 | zenon_intro zenon_H11f ]. % 15.41/15.55 apply (zenon_or_s _ _ zenon_H1d4); [ zenon_intro zenon_H2e | zenon_intro zenon_Hdd ]. % 15.41/15.55 apply (zenon_L842_); trivial. % 15.41/15.55 apply (zenon_or_s _ _ zenon_H1e3); [ zenon_intro zenon_H52 | zenon_intro zenon_H156 ]. % 15.41/15.55 apply (zenon_or_s _ _ zenon_Haa); [ zenon_intro zenon_H2f | zenon_intro zenon_H35 ]. % 15.41/15.55 apply (zenon_or_s _ _ zenon_H1c3); [ zenon_intro zenon_H30 | zenon_intro zenon_H124 ]. % 15.41/15.55 apply (zenon_or_s _ _ zenon_H10f); [ zenon_intro zenon_H3c | zenon_intro zenon_Hba ]. % 15.41/15.55 apply (zenon_or_s _ _ zenon_H10c); [ zenon_intro zenon_H104 | zenon_intro zenon_H10a ]. % 15.41/15.55 apply (zenon_or_s _ _ zenon_H10e); [ zenon_intro zenon_H3d | zenon_intro zenon_H106 ]. % 15.41/15.55 apply (zenon_or_s _ _ zenon_H10d); [ zenon_intro zenon_H3e | zenon_intro zenon_H42 ]. % 15.41/15.55 apply (zenon_L813_); trivial. % 15.41/15.55 apply (zenon_L778_); trivial. % 15.41/15.55 apply (zenon_L821_); trivial. % 15.41/15.55 apply (zenon_or_s _ _ zenon_H10e); [ zenon_intro zenon_H3d | zenon_intro zenon_H106 ]. % 15.41/15.55 apply (zenon_L830_); trivial. % 15.41/15.55 apply (zenon_L115_); trivial. % 15.41/15.55 apply (zenon_or_s _ _ zenon_H10c); [ zenon_intro zenon_H104 | zenon_intro zenon_H10a ]. % 15.41/15.55 apply (zenon_or_s _ _ zenon_H10e); [ zenon_intro zenon_H3d | zenon_intro zenon_H106 ]. % 15.41/15.55 apply (zenon_or_s _ _ zenon_H44); [ zenon_intro zenon_H47 | zenon_intro zenon_H46 ]. % 15.41/15.55 exact (zenon_H45 zenon_H47). % 15.41/15.55 apply (zenon_or_s _ _ zenon_H46); [ zenon_intro zenon_H22 | zenon_intro zenon_H48 ]. % 15.41/15.55 apply (zenon_or_s _ _ zenon_H8e); [ zenon_intro zenon_H92 | zenon_intro zenon_H91 ]. % 15.41/15.55 exact (zenon_H8f zenon_H92). % 15.41/15.55 apply (zenon_or_s _ _ zenon_H91); [ zenon_intro zenon_H5d | zenon_intro zenon_H93 ]. % 15.41/15.55 apply (zenon_L811_); trivial. % 15.41/15.55 apply (zenon_or_s _ _ zenon_H93); [ zenon_intro zenon_H63 | zenon_intro zenon_H81 ]. % 15.41/15.55 apply (zenon_L812_); trivial. % 15.41/15.55 apply (zenon_L827_); trivial. % 15.41/15.55 apply (zenon_or_s _ _ zenon_H48); [ zenon_intro zenon_H29 | zenon_intro zenon_H37 ]. % 15.41/15.55 apply (zenon_L809_); trivial. % 15.41/15.55 apply (zenon_L843_); trivial. % 15.41/15.55 apply (zenon_L81_); trivial. % 15.41/15.55 apply (zenon_L82_); trivial. % 15.41/15.55 apply (zenon_L119_); trivial. % 15.41/15.55 apply (zenon_L161_); trivial. % 15.41/15.55 apply (zenon_L284_); trivial. % 15.41/15.55 apply (zenon_L224_); trivial. % 15.41/15.55 (* end of lemma zenon_L844_ *) % 15.41/15.55 assert (zenon_L845_ : ((~((op (e1) (e1)) = (e1)))\/((op (e1) (e1)) = (e1))) -> (~((op (e1) (e0)) = (op (e1) (e1)))) -> ((~((op (e1) (e1)) = (e3)))\/((op (e1) (e3)) = (e1))) -> (~((op (e3) (e1)) = (op (e3) (e3)))) -> (~((e0) = (e3))) -> (((op (e0) (e1)) = (e1))\/(((op (e1) (e1)) = (e1))\/(((op (e2) (e1)) = (e1))\/((op (e3) (e1)) = (e1))))) -> (~((op (e1) (e0)) = (op (e1) (e2)))) -> (((op (e0) (e1)) = (e3))\/(((op (e1) (e1)) = (e3))\/(((op (e2) (e1)) = (e3))\/((op (e3) (e1)) = (e3))))) -> (~((op (e3) (e0)) = (op (e3) (e1)))) -> (((op (e0) (e0)) = (e1))\/(((op (e0) (e1)) = (e1))\/(((op (e0) (e2)) = (e1))\/((op (e0) (e3)) = (e1))))) -> ((~((op (e3) (e3)) = (e3)))\/((op (e3) (e3)) = (e3))) -> ((~((op (e2) (e2)) = (e2)))\/((op (e2) (e2)) = (e2))) -> (((op (e1) (e0)) = (e2))\/(((op (e1) (e1)) = (e2))\/(((op (e1) (e2)) = (e2))\/((op (e1) (e3)) = (e2))))) -> (~((op (e0) (e2)) = (op (e2) (e2)))) -> (((op (e0) (e3)) = (e0))\/(((op (e0) (e3)) = (e1))\/(((op (e0) (e3)) = (e2))\/((op (e0) (e3)) = (e3))))) -> (~((op (e0) (e3)) = (op (e1) (e3)))) -> (~((op (e0) (e3)) = (op (e2) (e3)))) -> (~((op (e0) (e0)) = (op (e0) (e3)))) -> (~((op (e1) (e2)) = (op (e2) (e2)))) -> ((~((op (e3) (e3)) = (e1)))\/((op (e3) (e1)) = (e3))) -> ((~((op (e2) (e2)) = (e3)))\/((op (e2) (e3)) = (e2))) -> (((op (e2) (e0)) = (e3))\/(((op (e2) (e1)) = (e3))\/(((op (e2) (e2)) = (e3))\/((op (e2) (e3)) = (e3))))) -> (~((op (e0) (e1)) = (op (e2) (e1)))) -> (~((op (e1) (e3)) = (op (e3) (e3)))) -> (((op (e2) (e2)) = (e0))\/(((op (e2) (e2)) = (e1))\/(((op (e2) (e2)) = (e2))\/((op (e2) (e2)) = (e3))))) -> (~((op (e0) (e0)) = (op (e2) (e0)))) -> (((op (e2) (e0)) = (e1))\/(((op (e2) (e1)) = (e1))\/(((op (e2) (e2)) = (e1))\/((op (e2) (e3)) = (e1))))) -> (~((op (e1) (op (e2) (e1))) = (op (e2) (e1)))) -> (~((e0) = (e2))) -> (((op (e2) (e0)) = (e0))\/(((op (e2) (e1)) = (e0))\/(((op (e2) (e2)) = (e0))\/((op (e2) (e3)) = (e0))))) -> (~((op (e2) (e1)) = (op (e2) (e2)))) -> (~((op (e2) (e1)) = (op (e2) (e3)))) -> ((~((op (e2) (e2)) = (e1)))\/((op (e2) (e1)) = (e2))) -> (~((op (e0) (e0)) = (e2))) -> (~((e1) = (e2))) -> ((op (e1) (e0)) = (e1)) -> (~((op (e0) (e3)) = (op (e3) (e3)))) -> (((op (e3) (e3)) = (e0))\/(((op (e3) (e3)) = (e1))\/(((op (e3) (e3)) = (e2))\/((op (e3) (e3)) = (e3))))) -> (~((op (e0) (e0)) = (e3))) -> (~((e2) = (e3))) -> (((op (e1) (e0)) = (e3))\/(((op (e1) (e1)) = (e3))\/(((op (e1) (e2)) = (e3))\/((op (e1) (e3)) = (e3))))) -> (~((op (e0) (e1)) = (op (e0) (e3)))) -> (~((op (e2) (e0)) = (op (e2) (e3)))) -> (((op (e0) (e3)) = (e2))\/(((op (e1) (e3)) = (e2))\/(((op (e2) (e3)) = (e2))\/((op (e3) (e3)) = (e2))))) -> (~((op (e0) (e2)) = (op (e1) (e2)))) -> (~((e1) = (e3))) -> (((op (e0) (e0)) = (e3))\/(((op (e1) (e0)) = (e3))\/(((op (e2) (e0)) = (e3))\/((op (e3) (e0)) = (e3))))) -> (~((op (e0) (e1)) = (op (e3) (e1)))) -> (((op (e0) (e2)) = (e0))\/(((op (e0) (e2)) = (e1))\/(((op (e0) (e2)) = (e2))\/((op (e0) (e2)) = (e3))))) -> (((op (e3) (e0)) = (e1))\/(((op (e3) (e1)) = (e1))\/(((op (e3) (e2)) = (e1))\/((op (e3) (e3)) = (e1))))) -> (~((op (e0) (e2)) = (op (e3) (e2)))) -> (((op (e0) (e3)) = (e1))\/(((op (e1) (e3)) = (e1))\/(((op (e2) (e3)) = (e1))\/((op (e3) (e3)) = (e1))))) -> (~((op (e3) (op (e2) (e3))) = (op (e2) (e3)))) -> (~((op (e1) (e0)) = (op (e1) (e3)))) -> (~((op (e0) (e2)) = (op (e0) (e3)))) -> (~((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 (e3) (e0)))) -> (~((op (e2) (e0)) = (op (e2) (e1)))) -> (((op (e0) (e1)) = (e2))\/(((op (e1) (e1)) = (e2))\/(((op (e2) (e1)) = (e2))\/((op (e3) (e1)) = (e2))))) -> (((op (e0) (e0)) = (e2))\/(((op (e0) (e1)) = (e2))\/(((op (e0) (e2)) = (e2))\/((op (e0) (e3)) = (e2))))) -> ((op (e0) (e0)) = (e0)) -> (~((op (e0) (e0)) = (op (e0) (e2)))) -> (((op (e3) (e0)) = (e2))\/(((op (e3) (e1)) = (e2))\/(((op (e3) (e2)) = (e2))\/((op (e3) (e3)) = (e2))))) -> (~((op (e0) (op (e2) (e0))) = (op (e2) (e0)))) -> (((op (e0) (e0)) = (e3))\/(((op (e0) (e1)) = (e3))\/(((op (e0) (e2)) = (e3))\/((op (e0) (e3)) = (e3))))) -> (((op (e1) (e1)) = (e0))\/(((op (e1) (e1)) = (e1))\/(((op (e1) (e1)) = (e2))\/((op (e1) (e1)) = (e3))))) -> (((op (e0) (e0)) = (e2))\/(((op (e1) (e0)) = (e2))\/(((op (e2) (e0)) = (e2))\/((op (e3) (e0)) = (e2))))) -> (~((op (e1) (e2)) = (op (e3) (e2)))) -> (((op (e0) (e0)) = (e1))\/(((op (e1) (e0)) = (e1))\/(((op (e2) (e0)) = (e1))\/((op (e3) (e0)) = (e1))))) -> (~((op (e3) (e0)) = (op (e3) (e2)))) -> (~((op (e0) (e0)) = (e1))) -> ((~((op (e3) (e3)) = (e2)))\/((op (e3) (e2)) = (e3))) -> ((~((op (e3) (e3)) = (e0)))\/((op (e3) (e0)) = (e3))) -> (~((op (e2) (op (e2) (e2))) = (op (e2) (e2)))) -> (~((op (e2) (e0)) = (op (e2) (e2)))) -> ((~((op (e2) (e2)) = (e0)))\/((op (e2) (e0)) = (e2))) -> ((~((op (e1) (e1)) = (e2)))\/((op (e1) (e2)) = (e1))) -> False). % 15.41/15.55 do 0 intro. intros zenon_H1d8 zenon_Hd7 zenon_H1d2 zenon_H12d zenon_H4b zenon_H228 zenon_H166 zenon_H199 zenon_H109 zenon_H44 zenon_H10d zenon_Haa zenon_H84 zenon_H28 zenon_H254 zenon_H80 zenon_Hb4 zenon_H24f zenon_H7d zenon_H10c zenon_H1c3 zenon_He6 zenon_Hde zenon_H8b zenon_H2d zenon_H258 zenon_Hb7 zenon_H290 zenon_H5e zenon_H1f5 zenon_H157 zenon_H1e2 zenon_H1e3 zenon_H8f zenon_Ha7 zenon_Hd8 zenon_H36 zenon_H3b zenon_H59 zenon_H6a zenon_H90 zenon_H1cd zenon_Hce zenon_H160 zenon_H87 zenon_Ha3 zenon_Hbe zenon_H138 zenon_H251 zenon_H146 zenon_H140 zenon_H121 zenon_H28a zenon_H1cf zenon_Hc9 zenon_H135 zenon_H11b zenon_H22e zenon_H154 zenon_H1a2 zenon_H8e zenon_H1f zenon_H250 zenon_H1df zenon_H295 zenon_H58 zenon_H1b3 zenon_Heb zenon_H17d zenon_Hf1 zenon_H105 zenon_H45 zenon_H10e zenon_H10f zenon_H294 zenon_H17a zenon_H1d4 zenon_H1d3. % 15.41/15.55 apply (zenon_or_s _ _ zenon_H1d8); [ zenon_intro zenon_H1b4 | zenon_intro zenon_H21 ]. % 15.41/15.55 apply (zenon_or_s _ _ zenon_H1d3); [ zenon_intro zenon_Hd6 | zenon_intro zenon_H117 ]. % 15.41/15.55 apply (zenon_L844_); trivial. % 15.41/15.55 apply (zenon_L248_); trivial. % 15.41/15.55 apply (zenon_L61_); trivial. % 15.41/15.55 (* end of lemma zenon_L845_ *) % 15.41/15.55 assert (zenon_L846_ : ((~((op (e1) (e1)) = (e2)))\/((op (e1) (e2)) = (e1))) -> ((~((op (e2) (e2)) = (e0)))\/((op (e2) (e0)) = (e2))) -> (~((op (e2) (e0)) = (op (e2) (e2)))) -> (~((op (e2) (op (e2) (e2))) = (op (e2) (e2)))) -> ((~((op (e3) (e3)) = (e0)))\/((op (e3) (e0)) = (e3))) -> ((~((op (e3) (e3)) = (e2)))\/((op (e3) (e2)) = (e3))) -> (~((op (e0) (e0)) = (e1))) -> (~((op (e3) (e0)) = (op (e3) (e2)))) -> (((op (e0) (e0)) = (e1))\/(((op (e1) (e0)) = (e1))\/(((op (e2) (e0)) = (e1))\/((op (e3) (e0)) = (e1))))) -> (~((op (e1) (e2)) = (op (e3) (e2)))) -> (((op (e0) (e0)) = (e2))\/(((op (e1) (e0)) = (e2))\/(((op (e2) (e0)) = (e2))\/((op (e3) (e0)) = (e2))))) -> (((op (e1) (e1)) = (e0))\/(((op (e1) (e1)) = (e1))\/(((op (e1) (e1)) = (e2))\/((op (e1) (e1)) = (e3))))) -> (((op (e0) (e0)) = (e3))\/(((op (e0) (e1)) = (e3))\/(((op (e0) (e2)) = (e3))\/((op (e0) (e3)) = (e3))))) -> (((op (e3) (e0)) = (e2))\/(((op (e3) (e1)) = (e2))\/(((op (e3) (e2)) = (e2))\/((op (e3) (e3)) = (e2))))) -> (~((op (e0) (e0)) = (op (e0) (e2)))) -> ((op (e0) (e0)) = (e0)) -> (((op (e0) (e0)) = (e2))\/(((op (e0) (e1)) = (e2))\/(((op (e0) (e2)) = (e2))\/((op (e0) (e3)) = (e2))))) -> (((op (e0) (e1)) = (e2))\/(((op (e1) (e1)) = (e2))\/(((op (e2) (e1)) = (e2))\/((op (e3) (e1)) = (e2))))) -> (~((op (e2) (e0)) = (op (e2) (e1)))) -> (~((op (e1) (e0)) = (op (e3) (e0)))) -> (((op (e0) (e2)) = (e1))\/(((op (e1) (e2)) = (e1))\/(((op (e2) (e2)) = (e1))\/((op (e3) (e2)) = (e1))))) -> (~((op (e3) (e1)) = (op (e3) (e2)))) -> (~((op (e0) (e2)) = (op (e0) (e3)))) -> (~((op (e1) (e0)) = (op (e1) (e3)))) -> (~((op (e3) (op (e2) (e3))) = (op (e2) (e3)))) -> (((op (e0) (e3)) = (e1))\/(((op (e1) (e3)) = (e1))\/(((op (e2) (e3)) = (e1))\/((op (e3) (e3)) = (e1))))) -> (~((op (e0) (e2)) = (op (e3) (e2)))) -> (((op (e3) (e0)) = (e1))\/(((op (e3) (e1)) = (e1))\/(((op (e3) (e2)) = (e1))\/((op (e3) (e3)) = (e1))))) -> (((op (e0) (e2)) = (e0))\/(((op (e0) (e2)) = (e1))\/(((op (e0) (e2)) = (e2))\/((op (e0) (e2)) = (e3))))) -> (~((op (e0) (e1)) = (op (e3) (e1)))) -> (((op (e0) (e0)) = (e3))\/(((op (e1) (e0)) = (e3))\/(((op (e2) (e0)) = (e3))\/((op (e3) (e0)) = (e3))))) -> (~((op (e0) (e2)) = (op (e1) (e2)))) -> (((op (e0) (e3)) = (e2))\/(((op (e1) (e3)) = (e2))\/(((op (e2) (e3)) = (e2))\/((op (e3) (e3)) = (e2))))) -> (~((op (e2) (e0)) = (op (e2) (e3)))) -> (~((op (e0) (e1)) = (op (e0) (e3)))) -> (((op (e1) (e0)) = (e3))\/(((op (e1) (e1)) = (e3))\/(((op (e1) (e2)) = (e3))\/((op (e1) (e3)) = (e3))))) -> (~((e2) = (e3))) -> (~((op (e0) (e0)) = (e3))) -> (((op (e3) (e3)) = (e0))\/(((op (e3) (e3)) = (e1))\/(((op (e3) (e3)) = (e2))\/((op (e3) (e3)) = (e3))))) -> (~((op (e0) (e3)) = (op (e3) (e3)))) -> (~((e1) = (e2))) -> (~((op (e0) (e0)) = (e2))) -> ((~((op (e2) (e2)) = (e1)))\/((op (e2) (e1)) = (e2))) -> (~((op (e2) (e1)) = (op (e2) (e3)))) -> (~((op (e2) (e1)) = (op (e2) (e2)))) -> (((op (e2) (e0)) = (e0))\/(((op (e2) (e1)) = (e0))\/(((op (e2) (e2)) = (e0))\/((op (e2) (e3)) = (e0))))) -> (~((e0) = (e2))) -> (~((op (e1) (op (e2) (e1))) = (op (e2) (e1)))) -> (((op (e2) (e0)) = (e1))\/(((op (e2) (e1)) = (e1))\/(((op (e2) (e2)) = (e1))\/((op (e2) (e3)) = (e1))))) -> (~((op (e0) (e0)) = (op (e2) (e0)))) -> (((op (e2) (e2)) = (e0))\/(((op (e2) (e2)) = (e1))\/(((op (e2) (e2)) = (e2))\/((op (e2) (e2)) = (e3))))) -> (~((op (e1) (e3)) = (op (e3) (e3)))) -> (~((op (e0) (e1)) = (op (e2) (e1)))) -> (((op (e2) (e0)) = (e3))\/(((op (e2) (e1)) = (e3))\/(((op (e2) (e2)) = (e3))\/((op (e2) (e3)) = (e3))))) -> ((~((op (e2) (e2)) = (e3)))\/((op (e2) (e3)) = (e2))) -> ((~((op (e3) (e3)) = (e1)))\/((op (e3) (e1)) = (e3))) -> (~((op (e1) (e2)) = (op (e2) (e2)))) -> (~((op (e0) (e0)) = (op (e0) (e3)))) -> (~((op (e0) (e3)) = (op (e2) (e3)))) -> (~((op (e0) (e3)) = (op (e1) (e3)))) -> (((op (e0) (e3)) = (e0))\/(((op (e0) (e3)) = (e1))\/(((op (e0) (e3)) = (e2))\/((op (e0) (e3)) = (e3))))) -> (~((op (e0) (e2)) = (op (e2) (e2)))) -> (((op (e1) (e0)) = (e2))\/(((op (e1) (e1)) = (e2))\/(((op (e1) (e2)) = (e2))\/((op (e1) (e3)) = (e2))))) -> ((~((op (e2) (e2)) = (e2)))\/((op (e2) (e2)) = (e2))) -> ((~((op (e3) (e3)) = (e3)))\/((op (e3) (e3)) = (e3))) -> (((op (e0) (e0)) = (e1))\/(((op (e0) (e1)) = (e1))\/(((op (e0) (e2)) = (e1))\/((op (e0) (e3)) = (e1))))) -> (~((op (e3) (e0)) = (op (e3) (e1)))) -> (((op (e0) (e1)) = (e3))\/(((op (e1) (e1)) = (e3))\/(((op (e2) (e1)) = (e3))\/((op (e3) (e1)) = (e3))))) -> (~((op (e1) (e0)) = (op (e1) (e2)))) -> (((op (e0) (e1)) = (e1))\/(((op (e1) (e1)) = (e1))\/(((op (e2) (e1)) = (e1))\/((op (e3) (e1)) = (e1))))) -> (~((e0) = (e3))) -> (~((op (e3) (e1)) = (op (e3) (e3)))) -> ((~((op (e1) (e1)) = (e3)))\/((op (e1) (e3)) = (e1))) -> (~((op (e1) (e0)) = (op (e1) (e1)))) -> ((~((op (e1) (e1)) = (e1)))\/((op (e1) (e1)) = (e1))) -> ((op (e0) (e1)) = (e1)) -> (~((op (e0) (op (e2) (e0))) = (op (e2) (e0)))) -> (~((e1) = (e3))) -> ((op (e3) (e0)) = (e3)) -> False). % 15.41/15.55 do 0 intro. intros zenon_H1d3 zenon_H1d4 zenon_H17a zenon_H294 zenon_H10f zenon_H10e zenon_H45 zenon_H105 zenon_Hf1 zenon_H17d zenon_Heb zenon_H1b3 zenon_H58 zenon_H1df zenon_H250 zenon_H1f zenon_H8e zenon_H1a2 zenon_H154 zenon_H22e zenon_H11b zenon_H135 zenon_Hc9 zenon_H1cf zenon_H28a zenon_H121 zenon_H140 zenon_H146 zenon_H251 zenon_H138 zenon_Hbe zenon_H87 zenon_H160 zenon_Hce zenon_H1cd zenon_H90 zenon_H6a zenon_H59 zenon_H3b zenon_H36 zenon_Ha7 zenon_H8f zenon_H1e3 zenon_H1e2 zenon_H157 zenon_H1f5 zenon_H5e zenon_H290 zenon_Hb7 zenon_H258 zenon_H2d zenon_H8b zenon_Hde zenon_He6 zenon_H1c3 zenon_H10c zenon_H7d zenon_H24f zenon_Hb4 zenon_H80 zenon_H254 zenon_H28 zenon_H84 zenon_Haa zenon_H10d zenon_H44 zenon_H109 zenon_H199 zenon_H166 zenon_H228 zenon_H4b zenon_H12d zenon_H1d2 zenon_Hd7 zenon_H1d8 zenon_H22 zenon_H295 zenon_Ha3 zenon_Hba. % 15.41/15.55 apply (zenon_or_s _ _ zenon_Hf1); [ zenon_intro zenon_H47 | zenon_intro zenon_Hf4 ]. % 15.41/15.55 exact (zenon_H45 zenon_H47). % 15.41/15.55 apply (zenon_or_s _ _ zenon_Hf4); [ zenon_intro zenon_Hd8 | zenon_intro zenon_Hf5 ]. % 15.41/15.55 apply (zenon_L845_); trivial. % 15.41/15.55 apply (zenon_or_s _ _ zenon_Hf5); [ zenon_intro zenon_Hae | zenon_intro zenon_Hee ]. % 15.41/15.55 apply (zenon_L816_); trivial. % 15.41/15.55 apply (zenon_L79_); trivial. % 15.41/15.55 (* end of lemma zenon_L846_ *) % 15.41/15.55 assert (zenon_L847_ : ((op (e1) (e0)) = (e2)) -> ((op (e0) (e3)) = (e3)) -> ((~((op (e1) (e1)) = (e2)))\/((op (e1) (e2)) = (e1))) -> ((~((op (e2) (e2)) = (e0)))\/((op (e2) (e0)) = (e2))) -> (~((op (e2) (e0)) = (op (e2) (e2)))) -> (~((op (e2) (op (e2) (e2))) = (op (e2) (e2)))) -> ((~((op (e3) (e3)) = (e0)))\/((op (e3) (e0)) = (e3))) -> ((~((op (e3) (e3)) = (e2)))\/((op (e3) (e2)) = (e3))) -> (~((op (e0) (e0)) = (e1))) -> (~((op (e3) (e0)) = (op (e3) (e2)))) -> (((op (e0) (e0)) = (e1))\/(((op (e1) (e0)) = (e1))\/(((op (e2) (e0)) = (e1))\/((op (e3) (e0)) = (e1))))) -> (~((op (e1) (e2)) = (op (e3) (e2)))) -> (((op (e0) (e0)) = (e2))\/(((op (e1) (e0)) = (e2))\/(((op (e2) (e0)) = (e2))\/((op (e3) (e0)) = (e2))))) -> (((op (e1) (e1)) = (e0))\/(((op (e1) (e1)) = (e1))\/(((op (e1) (e1)) = (e2))\/((op (e1) (e1)) = (e3))))) -> (((op (e0) (e0)) = (e3))\/(((op (e0) (e1)) = (e3))\/(((op (e0) (e2)) = (e3))\/((op (e0) (e3)) = (e3))))) -> (((op (e3) (e0)) = (e2))\/(((op (e3) (e1)) = (e2))\/(((op (e3) (e2)) = (e2))\/((op (e3) (e3)) = (e2))))) -> (~((op (e0) (e0)) = (op (e0) (e2)))) -> ((op (e0) (e0)) = (e0)) -> (((op (e0) (e0)) = (e2))\/(((op (e0) (e1)) = (e2))\/(((op (e0) (e2)) = (e2))\/((op (e0) (e3)) = (e2))))) -> (((op (e0) (e1)) = (e2))\/(((op (e1) (e1)) = (e2))\/(((op (e2) (e1)) = (e2))\/((op (e3) (e1)) = (e2))))) -> (~((op (e2) (e0)) = (op (e2) (e1)))) -> (~((op (e1) (e0)) = (op (e3) (e0)))) -> (((op (e0) (e2)) = (e1))\/(((op (e1) (e2)) = (e1))\/(((op (e2) (e2)) = (e1))\/((op (e3) (e2)) = (e1))))) -> (~((op (e3) (e1)) = (op (e3) (e2)))) -> (~((op (e0) (e2)) = (op (e0) (e3)))) -> (~((op (e1) (e0)) = (op (e1) (e3)))) -> (~((op (e3) (op (e2) (e3))) = (op (e2) (e3)))) -> (((op (e0) (e3)) = (e1))\/(((op (e1) (e3)) = (e1))\/(((op (e2) (e3)) = (e1))\/((op (e3) (e3)) = (e1))))) -> (~((op (e0) (e2)) = (op (e3) (e2)))) -> (((op (e3) (e0)) = (e1))\/(((op (e3) (e1)) = (e1))\/(((op (e3) (e2)) = (e1))\/((op (e3) (e3)) = (e1))))) -> (((op (e0) (e2)) = (e0))\/(((op (e0) (e2)) = (e1))\/(((op (e0) (e2)) = (e2))\/((op (e0) (e2)) = (e3))))) -> (~((op (e0) (e1)) = (op (e3) (e1)))) -> (((op (e0) (e0)) = (e3))\/(((op (e1) (e0)) = (e3))\/(((op (e2) (e0)) = (e3))\/((op (e3) (e0)) = (e3))))) -> (~((op (e0) (e2)) = (op (e1) (e2)))) -> (((op (e0) (e3)) = (e2))\/(((op (e1) (e3)) = (e2))\/(((op (e2) (e3)) = (e2))\/((op (e3) (e3)) = (e2))))) -> (~((op (e2) (e0)) = (op (e2) (e3)))) -> (~((op (e0) (e1)) = (op (e0) (e3)))) -> (((op (e1) (e0)) = (e3))\/(((op (e1) (e1)) = (e3))\/(((op (e1) (e2)) = (e3))\/((op (e1) (e3)) = (e3))))) -> (~((e2) = (e3))) -> (~((op (e0) (e0)) = (e3))) -> (((op (e3) (e3)) = (e0))\/(((op (e3) (e3)) = (e1))\/(((op (e3) (e3)) = (e2))\/((op (e3) (e3)) = (e3))))) -> (~((op (e0) (e3)) = (op (e3) (e3)))) -> (~((e1) = (e2))) -> (~((op (e0) (e0)) = (e2))) -> ((~((op (e2) (e2)) = (e1)))\/((op (e2) (e1)) = (e2))) -> (~((op (e2) (e1)) = (op (e2) (e3)))) -> (~((op (e2) (e1)) = (op (e2) (e2)))) -> (((op (e2) (e0)) = (e0))\/(((op (e2) (e1)) = (e0))\/(((op (e2) (e2)) = (e0))\/((op (e2) (e3)) = (e0))))) -> (~((e0) = (e2))) -> (~((op (e1) (op (e2) (e1))) = (op (e2) (e1)))) -> (((op (e2) (e0)) = (e1))\/(((op (e2) (e1)) = (e1))\/(((op (e2) (e2)) = (e1))\/((op (e2) (e3)) = (e1))))) -> (~((op (e0) (e0)) = (op (e2) (e0)))) -> (((op (e2) (e2)) = (e0))\/(((op (e2) (e2)) = (e1))\/(((op (e2) (e2)) = (e2))\/((op (e2) (e2)) = (e3))))) -> (~((op (e1) (e3)) = (op (e3) (e3)))) -> (~((op (e0) (e1)) = (op (e2) (e1)))) -> (((op (e2) (e0)) = (e3))\/(((op (e2) (e1)) = (e3))\/(((op (e2) (e2)) = (e3))\/((op (e2) (e3)) = (e3))))) -> ((~((op (e2) (e2)) = (e3)))\/((op (e2) (e3)) = (e2))) -> ((~((op (e3) (e3)) = (e1)))\/((op (e3) (e1)) = (e3))) -> (~((op (e1) (e2)) = (op (e2) (e2)))) -> (~((op (e0) (e0)) = (op (e0) (e3)))) -> (~((op (e0) (e3)) = (op (e2) (e3)))) -> (~((op (e0) (e3)) = (op (e1) (e3)))) -> (((op (e0) (e3)) = (e0))\/(((op (e0) (e3)) = (e1))\/(((op (e0) (e3)) = (e2))\/((op (e0) (e3)) = (e3))))) -> (~((op (e0) (e2)) = (op (e2) (e2)))) -> (((op (e1) (e0)) = (e2))\/(((op (e1) (e1)) = (e2))\/(((op (e1) (e2)) = (e2))\/((op (e1) (e3)) = (e2))))) -> ((~((op (e2) (e2)) = (e2)))\/((op (e2) (e2)) = (e2))) -> ((~((op (e3) (e3)) = (e3)))\/((op (e3) (e3)) = (e3))) -> (((op (e0) (e0)) = (e1))\/(((op (e0) (e1)) = (e1))\/(((op (e0) (e2)) = (e1))\/((op (e0) (e3)) = (e1))))) -> (~((op (e3) (e0)) = (op (e3) (e1)))) -> (((op (e0) (e1)) = (e3))\/(((op (e1) (e1)) = (e3))\/(((op (e2) (e1)) = (e3))\/((op (e3) (e1)) = (e3))))) -> (~((op (e1) (e0)) = (op (e1) (e2)))) -> (((op (e0) (e1)) = (e1))\/(((op (e1) (e1)) = (e1))\/(((op (e2) (e1)) = (e1))\/((op (e3) (e1)) = (e1))))) -> (~((e0) = (e3))) -> (~((op (e3) (e1)) = (op (e3) (e3)))) -> ((~((op (e1) (e1)) = (e3)))\/((op (e1) (e3)) = (e1))) -> (~((op (e1) (e0)) = (op (e1) (e1)))) -> ((~((op (e1) (e1)) = (e1)))\/((op (e1) (e1)) = (e1))) -> ((op (e0) (e1)) = (e1)) -> (~((op (e0) (op (e2) (e0))) = (op (e2) (e0)))) -> (~((e1) = (e3))) -> False). % 15.41/15.55 do 0 intro. intros zenon_H68 zenon_H53 zenon_H1d3 zenon_H1d4 zenon_H17a zenon_H294 zenon_H10f zenon_H10e zenon_H45 zenon_H105 zenon_Hf1 zenon_H17d zenon_Heb zenon_H1b3 zenon_H58 zenon_H1df zenon_H250 zenon_H1f zenon_H8e zenon_H1a2 zenon_H154 zenon_H22e zenon_H11b zenon_H135 zenon_Hc9 zenon_H1cf zenon_H28a zenon_H121 zenon_H140 zenon_H146 zenon_H251 zenon_H138 zenon_Hbe zenon_H87 zenon_H160 zenon_Hce zenon_H1cd zenon_H90 zenon_H6a zenon_H59 zenon_H3b zenon_H36 zenon_Ha7 zenon_H8f zenon_H1e3 zenon_H1e2 zenon_H157 zenon_H1f5 zenon_H5e zenon_H290 zenon_Hb7 zenon_H258 zenon_H2d zenon_H8b zenon_Hde zenon_He6 zenon_H1c3 zenon_H10c zenon_H7d zenon_H24f zenon_Hb4 zenon_H80 zenon_H254 zenon_H28 zenon_H84 zenon_Haa zenon_H10d zenon_H44 zenon_H109 zenon_H199 zenon_H166 zenon_H228 zenon_H4b zenon_H12d zenon_H1d2 zenon_Hd7 zenon_H1d8 zenon_H22 zenon_H295 zenon_Ha3. % 15.41/15.55 apply (zenon_or_s _ _ zenon_Hbe); [ zenon_intro zenon_H5b | zenon_intro zenon_Hbf ]. % 15.41/15.55 exact (zenon_H59 zenon_H5b). % 15.41/15.55 apply (zenon_or_s _ _ zenon_Hbf); [ zenon_intro zenon_H69 | zenon_intro zenon_Hc0 ]. % 15.41/15.55 apply (zenon_L17_); trivial. % 15.41/15.55 apply (zenon_or_s _ _ zenon_Hc0); [ zenon_intro zenon_Haf | zenon_intro zenon_Hba ]. % 15.41/15.55 apply (zenon_L803_); trivial. % 15.41/15.55 apply (zenon_L846_); trivial. % 15.41/15.55 (* end of lemma zenon_L847_ *) % 15.41/15.55 assert (zenon_L848_ : (~((e1) = (e3))) -> ((op (e0) (e1)) = (e1)) -> ((~((op (e1) (e1)) = (e1)))\/((op (e1) (e1)) = (e1))) -> (~((op (e1) (e0)) = (op (e1) (e1)))) -> ((~((op (e1) (e1)) = (e3)))\/((op (e1) (e3)) = (e1))) -> (~((op (e3) (e1)) = (op (e3) (e3)))) -> (~((e0) = (e3))) -> (((op (e0) (e1)) = (e1))\/(((op (e1) (e1)) = (e1))\/(((op (e2) (e1)) = (e1))\/((op (e3) (e1)) = (e1))))) -> (~((op (e1) (e0)) = (op (e1) (e2)))) -> (((op (e0) (e1)) = (e3))\/(((op (e1) (e1)) = (e3))\/(((op (e2) (e1)) = (e3))\/((op (e3) (e1)) = (e3))))) -> (~((op (e3) (e0)) = (op (e3) (e1)))) -> (((op (e0) (e0)) = (e1))\/(((op (e0) (e1)) = (e1))\/(((op (e0) (e2)) = (e1))\/((op (e0) (e3)) = (e1))))) -> ((~((op (e3) (e3)) = (e3)))\/((op (e3) (e3)) = (e3))) -> ((~((op (e2) (e2)) = (e2)))\/((op (e2) (e2)) = (e2))) -> (((op (e1) (e0)) = (e2))\/(((op (e1) (e1)) = (e2))\/(((op (e1) (e2)) = (e2))\/((op (e1) (e3)) = (e2))))) -> (~((op (e0) (e2)) = (op (e2) (e2)))) -> (((op (e0) (e3)) = (e0))\/(((op (e0) (e3)) = (e1))\/(((op (e0) (e3)) = (e2))\/((op (e0) (e3)) = (e3))))) -> (~((op (e0) (e3)) = (op (e1) (e3)))) -> (~((op (e0) (e3)) = (op (e2) (e3)))) -> (~((op (e0) (e0)) = (op (e0) (e3)))) -> (~((op (e1) (e2)) = (op (e2) (e2)))) -> ((~((op (e3) (e3)) = (e1)))\/((op (e3) (e1)) = (e3))) -> ((~((op (e2) (e2)) = (e3)))\/((op (e2) (e3)) = (e2))) -> (((op (e2) (e0)) = (e3))\/(((op (e2) (e1)) = (e3))\/(((op (e2) (e2)) = (e3))\/((op (e2) (e3)) = (e3))))) -> (~((op (e0) (e1)) = (op (e2) (e1)))) -> (~((op (e1) (e3)) = (op (e3) (e3)))) -> (((op (e2) (e2)) = (e0))\/(((op (e2) (e2)) = (e1))\/(((op (e2) (e2)) = (e2))\/((op (e2) (e2)) = (e3))))) -> (~((op (e0) (e0)) = (op (e2) (e0)))) -> (((op (e2) (e0)) = (e1))\/(((op (e2) (e1)) = (e1))\/(((op (e2) (e2)) = (e1))\/((op (e2) (e3)) = (e1))))) -> (~((op (e1) (op (e2) (e1))) = (op (e2) (e1)))) -> (~((e0) = (e2))) -> (((op (e2) (e0)) = (e0))\/(((op (e2) (e1)) = (e0))\/(((op (e2) (e2)) = (e0))\/((op (e2) (e3)) = (e0))))) -> (~((op (e2) (e1)) = (op (e2) (e2)))) -> (~((op (e2) (e1)) = (op (e2) (e3)))) -> ((~((op (e2) (e2)) = (e1)))\/((op (e2) (e1)) = (e2))) -> (~((op (e0) (e0)) = (e2))) -> (~((op (e0) (e3)) = (op (e3) (e3)))) -> (((op (e3) (e3)) = (e0))\/(((op (e3) (e3)) = (e1))\/(((op (e3) (e3)) = (e2))\/((op (e3) (e3)) = (e3))))) -> (~((op (e0) (e0)) = (e3))) -> (~((e2) = (e3))) -> (((op (e1) (e0)) = (e3))\/(((op (e1) (e1)) = (e3))\/(((op (e1) (e2)) = (e3))\/((op (e1) (e3)) = (e3))))) -> (~((op (e0) (e1)) = (op (e0) (e3)))) -> (~((op (e2) (e0)) = (op (e2) (e3)))) -> (((op (e0) (e3)) = (e2))\/(((op (e1) (e3)) = (e2))\/(((op (e2) (e3)) = (e2))\/((op (e3) (e3)) = (e2))))) -> (~((op (e0) (e2)) = (op (e1) (e2)))) -> (((op (e0) (e0)) = (e3))\/(((op (e1) (e0)) = (e3))\/(((op (e2) (e0)) = (e3))\/((op (e3) (e0)) = (e3))))) -> (~((op (e0) (e1)) = (op (e3) (e1)))) -> (((op (e0) (e2)) = (e0))\/(((op (e0) (e2)) = (e1))\/(((op (e0) (e2)) = (e2))\/((op (e0) (e2)) = (e3))))) -> (((op (e3) (e0)) = (e1))\/(((op (e3) (e1)) = (e1))\/(((op (e3) (e2)) = (e1))\/((op (e3) (e3)) = (e1))))) -> (~((op (e0) (e2)) = (op (e3) (e2)))) -> (((op (e0) (e3)) = (e1))\/(((op (e1) (e3)) = (e1))\/(((op (e2) (e3)) = (e1))\/((op (e3) (e3)) = (e1))))) -> (~((op (e3) (op (e2) (e3))) = (op (e2) (e3)))) -> (~((op (e1) (e0)) = (op (e1) (e3)))) -> (~((op (e0) (e2)) = (op (e0) (e3)))) -> (~((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 (e3) (e0)))) -> (~((op (e2) (e0)) = (op (e2) (e1)))) -> (((op (e0) (e1)) = (e2))\/(((op (e1) (e1)) = (e2))\/(((op (e2) (e1)) = (e2))\/((op (e3) (e1)) = (e2))))) -> (((op (e0) (e0)) = (e2))\/(((op (e0) (e1)) = (e2))\/(((op (e0) (e2)) = (e2))\/((op (e0) (e3)) = (e2))))) -> ((op (e0) (e0)) = (e0)) -> (~((op (e0) (e0)) = (op (e0) (e2)))) -> (((op (e3) (e0)) = (e2))\/(((op (e3) (e1)) = (e2))\/(((op (e3) (e2)) = (e2))\/((op (e3) (e3)) = (e2))))) -> (((op (e0) (e0)) = (e3))\/(((op (e0) (e1)) = (e3))\/(((op (e0) (e2)) = (e3))\/((op (e0) (e3)) = (e3))))) -> (((op (e1) (e1)) = (e0))\/(((op (e1) (e1)) = (e1))\/(((op (e1) (e1)) = (e2))\/((op (e1) (e1)) = (e3))))) -> (((op (e0) (e0)) = (e2))\/(((op (e1) (e0)) = (e2))\/(((op (e2) (e0)) = (e2))\/((op (e3) (e0)) = (e2))))) -> (~((op (e1) (e2)) = (op (e3) (e2)))) -> (((op (e0) (e0)) = (e1))\/(((op (e1) (e0)) = (e1))\/(((op (e2) (e0)) = (e1))\/((op (e3) (e0)) = (e1))))) -> (~((op (e3) (e0)) = (op (e3) (e2)))) -> (~((op (e0) (e0)) = (e1))) -> ((~((op (e3) (e3)) = (e2)))\/((op (e3) (e2)) = (e3))) -> ((~((op (e3) (e3)) = (e0)))\/((op (e3) (e0)) = (e3))) -> (~((op (e2) (op (e2) (e2))) = (op (e2) (e2)))) -> (~((op (e2) (e0)) = (op (e2) (e2)))) -> ((~((op (e2) (e2)) = (e0)))\/((op (e2) (e0)) = (e2))) -> ((~((op (e1) (e1)) = (e2)))\/((op (e1) (e2)) = (e1))) -> (~((op (e2) (e2)) = (e0))) -> (~((op (e2) (e2)) = (e1))) -> (~((op (e2) (e2)) = (e2))) -> ((op (e3) (e1)) = (e3)) -> ((op (e0) (e2)) = (e2)) -> (~((op (e0) (op (e2) (e0))) = (op (e2) (e0)))) -> ((op (e3) (e0)) = (e1)) -> (~((e1) = (e2))) -> False). % 15.41/15.55 do 0 intro. intros zenon_Ha3 zenon_H22 zenon_H1d8 zenon_Hd7 zenon_H1d2 zenon_H12d zenon_H4b zenon_H228 zenon_H166 zenon_H199 zenon_H109 zenon_H44 zenon_H10d zenon_Haa zenon_H84 zenon_H28 zenon_H254 zenon_H80 zenon_Hb4 zenon_H24f zenon_H7d zenon_H10c zenon_H1c3 zenon_He6 zenon_Hde zenon_H8b zenon_H2d zenon_H258 zenon_Hb7 zenon_H290 zenon_H5e zenon_H1f5 zenon_H157 zenon_H1e2 zenon_H1e3 zenon_H8f zenon_H36 zenon_H3b zenon_H59 zenon_H6a zenon_H90 zenon_H1cd zenon_Hce zenon_H160 zenon_H87 zenon_Hbe zenon_H138 zenon_H251 zenon_H146 zenon_H140 zenon_H121 zenon_H28a zenon_H1cf zenon_Hc9 zenon_H135 zenon_H11b zenon_H22e zenon_H154 zenon_H1a2 zenon_H8e zenon_H1f zenon_H250 zenon_H1df zenon_H58 zenon_H1b3 zenon_Heb zenon_H17d zenon_Hf1 zenon_H105 zenon_H45 zenon_H10e zenon_H10f zenon_H294 zenon_H17a zenon_H1d4 zenon_H1d3 zenon_H2e zenon_H52 zenon_H2f zenon_H10a zenon_H63 zenon_H295 zenon_Hee zenon_Ha7. % 15.41/15.55 apply (zenon_or_s _ _ zenon_Heb); [ zenon_intro zenon_H92 | zenon_intro zenon_Hec ]. % 15.41/15.55 exact (zenon_H8f zenon_H92). % 15.41/15.55 apply (zenon_or_s _ _ zenon_Hec); [ zenon_intro zenon_H68 | zenon_intro zenon_Hed ]. % 15.41/15.55 apply (zenon_or_s _ _ zenon_H58); [ zenon_intro zenon_H5b | zenon_intro zenon_H5a ]. % 15.41/15.55 exact (zenon_H59 zenon_H5b). % 15.41/15.55 apply (zenon_or_s _ _ zenon_H5a); [ zenon_intro zenon_H4a | zenon_intro zenon_H5c ]. % 15.41/15.55 apply (zenon_L120_); trivial. % 15.41/15.55 apply (zenon_or_s _ _ zenon_H5c); [ zenon_intro zenon_H50 | zenon_intro zenon_H53 ]. % 15.41/15.55 apply (zenon_L11_); trivial. % 15.41/15.55 apply (zenon_L847_); trivial. % 15.41/15.55 apply (zenon_or_s _ _ zenon_Hed); [ zenon_intro zenon_Hdd | zenon_intro zenon_He9 ]. % 15.41/15.55 apply (zenon_L812_); trivial. % 15.41/15.55 apply (zenon_L122_); trivial. % 15.41/15.55 (* end of lemma zenon_L848_ *) % 15.41/15.55 assert (zenon_L849_ : (~((op (e3) (e3)) = (e0))) -> ((~((op (e1) (e1)) = (e1)))\/((op (e1) (e1)) = (e1))) -> (~((op (e1) (e0)) = (op (e1) (e1)))) -> ((~((op (e1) (e1)) = (e3)))\/((op (e1) (e3)) = (e1))) -> (~((op (e3) (e1)) = (op (e3) (e3)))) -> (~((e0) = (e3))) -> (((op (e0) (e1)) = (e1))\/(((op (e1) (e1)) = (e1))\/(((op (e2) (e1)) = (e1))\/((op (e3) (e1)) = (e1))))) -> (~((op (e1) (e0)) = (op (e1) (e2)))) -> (((op (e0) (e1)) = (e3))\/(((op (e1) (e1)) = (e3))\/(((op (e2) (e1)) = (e3))\/((op (e3) (e1)) = (e3))))) -> (~((op (e3) (e0)) = (op (e3) (e1)))) -> (((op (e0) (e0)) = (e1))\/(((op (e0) (e1)) = (e1))\/(((op (e0) (e2)) = (e1))\/((op (e0) (e3)) = (e1))))) -> ((~((op (e3) (e3)) = (e3)))\/((op (e3) (e3)) = (e3))) -> ((~((op (e2) (e2)) = (e2)))\/((op (e2) (e2)) = (e2))) -> (((op (e1) (e0)) = (e2))\/(((op (e1) (e1)) = (e2))\/(((op (e1) (e2)) = (e2))\/((op (e1) (e3)) = (e2))))) -> (~((op (e0) (e2)) = (op (e2) (e2)))) -> (((op (e0) (e3)) = (e0))\/(((op (e0) (e3)) = (e1))\/(((op (e0) (e3)) = (e2))\/((op (e0) (e3)) = (e3))))) -> (~((op (e0) (e3)) = (op (e1) (e3)))) -> (~((op (e0) (e3)) = (op (e2) (e3)))) -> (~((op (e0) (e0)) = (op (e0) (e3)))) -> (~((op (e1) (e2)) = (op (e2) (e2)))) -> ((~((op (e3) (e3)) = (e1)))\/((op (e3) (e1)) = (e3))) -> ((~((op (e2) (e2)) = (e3)))\/((op (e2) (e3)) = (e2))) -> (((op (e2) (e0)) = (e3))\/(((op (e2) (e1)) = (e3))\/(((op (e2) (e2)) = (e3))\/((op (e2) (e3)) = (e3))))) -> (~((op (e0) (e1)) = (op (e2) (e1)))) -> (~((op (e1) (e3)) = (op (e3) (e3)))) -> (((op (e2) (e2)) = (e0))\/(((op (e2) (e2)) = (e1))\/(((op (e2) (e2)) = (e2))\/((op (e2) (e2)) = (e3))))) -> (~((op (e0) (e0)) = (op (e2) (e0)))) -> (((op (e2) (e0)) = (e1))\/(((op (e2) (e1)) = (e1))\/(((op (e2) (e2)) = (e1))\/((op (e2) (e3)) = (e1))))) -> (~((op (e1) (op (e2) (e1))) = (op (e2) (e1)))) -> (~((e0) = (e2))) -> (((op (e2) (e0)) = (e0))\/(((op (e2) (e1)) = (e0))\/(((op (e2) (e2)) = (e0))\/((op (e2) (e3)) = (e0))))) -> (~((op (e2) (e1)) = (op (e2) (e2)))) -> (~((op (e2) (e1)) = (op (e2) (e3)))) -> ((~((op (e2) (e2)) = (e1)))\/((op (e2) (e1)) = (e2))) -> (~((op (e0) (e0)) = (e2))) -> (~((e1) = (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) (e0)) = (e3))) -> (~((e2) = (e3))) -> (((op (e1) (e0)) = (e3))\/(((op (e1) (e1)) = (e3))\/(((op (e1) (e2)) = (e3))\/((op (e1) (e3)) = (e3))))) -> (~((op (e0) (e1)) = (op (e0) (e3)))) -> (~((op (e2) (e0)) = (op (e2) (e3)))) -> (((op (e0) (e3)) = (e2))\/(((op (e1) (e3)) = (e2))\/(((op (e2) (e3)) = (e2))\/((op (e3) (e3)) = (e2))))) -> (~((op (e0) (e2)) = (op (e1) (e2)))) -> (~((e1) = (e3))) -> (((op (e0) (e0)) = (e3))\/(((op (e1) (e0)) = (e3))\/(((op (e2) (e0)) = (e3))\/((op (e3) (e0)) = (e3))))) -> (~((op (e0) (e1)) = (op (e3) (e1)))) -> (((op (e0) (e2)) = (e0))\/(((op (e0) (e2)) = (e1))\/(((op (e0) (e2)) = (e2))\/((op (e0) (e2)) = (e3))))) -> (((op (e3) (e0)) = (e1))\/(((op (e3) (e1)) = (e1))\/(((op (e3) (e2)) = (e1))\/((op (e3) (e3)) = (e1))))) -> (~((op (e0) (e2)) = (op (e3) (e2)))) -> (((op (e0) (e3)) = (e1))\/(((op (e1) (e3)) = (e1))\/(((op (e2) (e3)) = (e1))\/((op (e3) (e3)) = (e1))))) -> (~((op (e3) (op (e2) (e3))) = (op (e2) (e3)))) -> (~((op (e1) (e0)) = (op (e1) (e3)))) -> (~((op (e0) (e2)) = (op (e0) (e3)))) -> (~((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 (e3) (e0)))) -> (~((op (e2) (e0)) = (op (e2) (e1)))) -> (((op (e0) (e1)) = (e2))\/(((op (e1) (e1)) = (e2))\/(((op (e2) (e1)) = (e2))\/((op (e3) (e1)) = (e2))))) -> (((op (e0) (e0)) = (e2))\/(((op (e0) (e1)) = (e2))\/(((op (e0) (e2)) = (e2))\/((op (e0) (e3)) = (e2))))) -> ((op (e0) (e0)) = (e0)) -> (~((op (e0) (e0)) = (op (e0) (e2)))) -> (((op (e3) (e0)) = (e2))\/(((op (e3) (e1)) = (e2))\/(((op (e3) (e2)) = (e2))\/((op (e3) (e3)) = (e2))))) -> (~((op (e0) (op (e2) (e0))) = (op (e2) (e0)))) -> (((op (e0) (e0)) = (e3))\/(((op (e0) (e1)) = (e3))\/(((op (e0) (e2)) = (e3))\/((op (e0) (e3)) = (e3))))) -> (((op (e1) (e1)) = (e0))\/(((op (e1) (e1)) = (e1))\/(((op (e1) (e1)) = (e2))\/((op (e1) (e1)) = (e3))))) -> (((op (e0) (e0)) = (e2))\/(((op (e1) (e0)) = (e2))\/(((op (e2) (e0)) = (e2))\/((op (e3) (e0)) = (e2))))) -> (~((op (e1) (e2)) = (op (e3) (e2)))) -> (((op (e0) (e0)) = (e1))\/(((op (e1) (e0)) = (e1))\/(((op (e2) (e0)) = (e1))\/((op (e3) (e0)) = (e1))))) -> (~((op (e3) (e0)) = (op (e3) (e2)))) -> ((~((op (e3) (e3)) = (e2)))\/((op (e3) (e2)) = (e3))) -> ((~((op (e3) (e3)) = (e0)))\/((op (e3) (e0)) = (e3))) -> (~((op (e2) (op (e2) (e2))) = (op (e2) (e2)))) -> (~((op (e2) (e0)) = (op (e2) (e2)))) -> ((~((op (e2) (e2)) = (e0)))\/((op (e2) (e0)) = (e2))) -> ((~((op (e1) (e1)) = (e2)))\/((op (e1) (e2)) = (e1))) -> (~((op (e2) (e2)) = (e0))) -> (~((op (e2) (e2)) = (e1))) -> (~((op (e2) (e2)) = (e2))) -> ((op (e3) (e1)) = (e3)) -> (~((op (e1) (e1)) = (e0))) -> (~((op (e1) (e1)) = (e1))) -> (~((op (e0) (e1)) = (op (e1) (e1)))) -> (~((op (e1) (e1)) = (e3))) -> (~((op (e0) (e0)) = (e1))) -> False). % 15.41/15.55 do 0 intro. intros zenon_H3c zenon_H1d8 zenon_Hd7 zenon_H1d2 zenon_H12d zenon_H4b zenon_H228 zenon_H166 zenon_H199 zenon_H109 zenon_H44 zenon_H10d zenon_Haa zenon_H84 zenon_H28 zenon_H254 zenon_H80 zenon_Hb4 zenon_H24f zenon_H7d zenon_H10c zenon_H1c3 zenon_He6 zenon_Hde zenon_H8b zenon_H2d zenon_H258 zenon_Hb7 zenon_H290 zenon_H5e zenon_H1f5 zenon_H157 zenon_H1e2 zenon_H1e3 zenon_H8f zenon_Ha7 zenon_H36 zenon_H3b zenon_H59 zenon_H6a zenon_H90 zenon_H1cd zenon_Hce zenon_H160 zenon_H87 zenon_Ha3 zenon_Hbe zenon_H138 zenon_H251 zenon_H146 zenon_H140 zenon_H121 zenon_H28a zenon_H1cf zenon_Hc9 zenon_H135 zenon_H11b zenon_H22e zenon_H154 zenon_H1a2 zenon_H8e zenon_H1f zenon_H250 zenon_H1df zenon_H295 zenon_H58 zenon_H1b3 zenon_Heb zenon_H17d zenon_Hf1 zenon_H105 zenon_H10e zenon_H10f zenon_H294 zenon_H17a zenon_H1d4 zenon_H1d3 zenon_H2e zenon_H52 zenon_H2f zenon_H10a zenon_H145 zenon_H1b4 zenon_H23 zenon_H182 zenon_H45. % 15.41/15.55 apply (zenon_or_s _ _ zenon_H10e); [ zenon_intro zenon_H3d | zenon_intro zenon_H106 ]. % 15.41/15.55 apply (zenon_or_s _ _ zenon_H10d); [ zenon_intro zenon_H3e | zenon_intro zenon_H42 ]. % 15.41/15.55 apply (zenon_or_s _ _ zenon_H44); [ zenon_intro zenon_H47 | zenon_intro zenon_H46 ]. % 15.41/15.55 exact (zenon_H45 zenon_H47). % 15.41/15.55 apply (zenon_or_s _ _ zenon_H46); [ zenon_intro zenon_H22 | zenon_intro zenon_H48 ]. % 15.41/15.55 apply (zenon_or_s _ _ zenon_Hf1); [ zenon_intro zenon_H47 | zenon_intro zenon_Hf4 ]. % 15.41/15.55 exact (zenon_H45 zenon_H47). % 15.41/15.55 apply (zenon_or_s _ _ zenon_Hf4); [ zenon_intro zenon_Hd8 | zenon_intro zenon_Hf5 ]. % 15.41/15.55 apply (zenon_L845_); trivial. % 15.41/15.55 apply (zenon_or_s _ _ zenon_Hf5); [ zenon_intro zenon_Hae | zenon_intro zenon_Hee ]. % 15.41/15.55 apply (zenon_L816_); trivial. % 15.41/15.55 apply (zenon_or_s _ _ zenon_H8e); [ zenon_intro zenon_H92 | zenon_intro zenon_H91 ]. % 15.41/15.55 exact (zenon_H8f zenon_H92). % 15.41/15.55 apply (zenon_or_s _ _ zenon_H91); [ zenon_intro zenon_H5d | zenon_intro zenon_H93 ]. % 15.41/15.55 apply (zenon_L214_); trivial. % 15.41/15.55 apply (zenon_or_s _ _ zenon_H93); [ zenon_intro zenon_H63 | zenon_intro zenon_H81 ]. % 15.41/15.55 apply (zenon_L848_); trivial. % 15.41/15.55 apply (zenon_L663_); trivial. % 15.41/15.55 apply (zenon_or_s _ _ zenon_H48); [ zenon_intro zenon_H29 | zenon_intro zenon_H37 ]. % 15.41/15.55 apply (zenon_L666_); trivial. % 15.41/15.55 apply (zenon_L7_); trivial. % 15.41/15.55 apply (zenon_L102_); trivial. % 15.41/15.55 apply (zenon_L115_); trivial. % 15.41/15.55 (* end of lemma zenon_L849_ *) % 15.41/15.55 assert (zenon_L850_ : (~((op (e3) (op (e2) (e3))) = (op (e3) (e2)))) -> ((op (e2) (e3)) = (e2)) -> False). % 15.41/15.55 do 0 intro. intros zenon_H2a6 zenon_H124. % 15.41/15.55 cut (((op (e2) (e3)) = (e2))); [idtac | apply NNPP; zenon_intro zenon_H2a7]. % 15.41/15.55 cut (((e3) = (e3))); [idtac | apply NNPP; zenon_intro zenon_H4d]. % 15.41/15.55 congruence. % 15.41/15.55 apply zenon_H4d. apply refl_equal. % 15.41/15.55 exact (zenon_H2a7 zenon_H124). % 15.41/15.55 (* end of lemma zenon_L850_ *) % 15.41/15.55 assert (zenon_L851_ : (~((op (e3) (op (e2) (e3))) = (op (e2) (e3)))) -> ((op (e3) (e2)) = (e2)) -> ((op (e2) (e3)) = (e2)) -> False). % 15.41/15.55 do 0 intro. intros zenon_H28a zenon_H1dd zenon_H124. % 15.41/15.55 cut (((op (e3) (e2)) = (e2)) = ((op (e3) (op (e2) (e3))) = (op (e2) (e3)))). % 15.41/15.55 intro zenon_D_pnotp. % 15.41/15.55 apply zenon_H28a. % 15.41/15.55 rewrite <- zenon_D_pnotp. % 15.41/15.55 exact zenon_H1dd. % 15.41/15.55 cut (((e2) = (op (e2) (e3)))); [idtac | apply NNPP; zenon_intro zenon_H137]. % 15.41/15.55 cut (((op (e3) (e2)) = (op (e3) (op (e2) (e3))))); [idtac | apply NNPP; zenon_intro zenon_H2a8]. % 15.41/15.55 congruence. % 15.41/15.55 elim (classic ((op (e3) (op (e2) (e3))) = (op (e3) (op (e2) (e3))))); [ zenon_intro zenon_H28c | zenon_intro zenon_H28d ]. % 15.41/15.55 cut (((op (e3) (op (e2) (e3))) = (op (e3) (op (e2) (e3)))) = ((op (e3) (e2)) = (op (e3) (op (e2) (e3))))). % 15.41/15.55 intro zenon_D_pnotp. % 15.41/15.55 apply zenon_H2a8. % 15.41/15.55 rewrite <- zenon_D_pnotp. % 15.41/15.55 exact zenon_H28c. % 15.41/15.55 cut (((op (e3) (op (e2) (e3))) = (op (e3) (op (e2) (e3))))); [idtac | apply NNPP; zenon_intro zenon_H28d]. % 15.41/15.55 cut (((op (e3) (op (e2) (e3))) = (op (e3) (e2)))); [idtac | apply NNPP; zenon_intro zenon_H2a6]. % 15.41/15.55 congruence. % 15.41/15.55 apply (zenon_L850_); trivial. % 15.41/15.55 apply zenon_H28d. apply refl_equal. % 15.41/15.55 apply zenon_H28d. apply refl_equal. % 15.41/15.55 apply zenon_H137. apply sym_equal. exact zenon_H124. % 15.41/15.55 (* end of lemma zenon_L851_ *) % 15.41/15.55 assert (zenon_L852_ : (((op (e3) (e0)) = (e2))\/(((op (e3) (e1)) = (e2))\/(((op (e3) (e2)) = (e2))\/((op (e3) (e3)) = (e2))))) -> (~((e1) = (e2))) -> ((op (e3) (e0)) = (e1)) -> ((op (e0) (e1)) = (e2)) -> (~((op (e0) (e1)) = (op (e3) (e1)))) -> ((op (e2) (e3)) = (e2)) -> (~((op (e3) (op (e2) (e3))) = (op (e2) (e3)))) -> (~((op (e3) (e3)) = (e2))) -> False). % 15.41/15.55 do 0 intro. intros zenon_H1df zenon_Ha7 zenon_Hee zenon_H5d zenon_H138 zenon_H124 zenon_H28a zenon_H3d. % 15.41/15.55 apply (zenon_or_s _ _ zenon_H1df); [ zenon_intro zenon_He9 | zenon_intro zenon_H1e0 ]. % 15.41/15.55 apply (zenon_L122_); trivial. % 15.41/15.55 apply (zenon_or_s _ _ zenon_H1e0); [ zenon_intro zenon_H16a | zenon_intro zenon_H1e1 ]. % 15.41/15.55 apply (zenon_L146_); trivial. % 15.41/15.55 apply (zenon_or_s _ _ zenon_H1e1); [ zenon_intro zenon_H1dd | zenon_intro zenon_H43 ]. % 15.41/15.55 apply (zenon_L851_); trivial. % 15.41/15.55 exact (zenon_H3d zenon_H43). % 15.41/15.55 (* end of lemma zenon_L852_ *) % 15.41/15.55 assert (zenon_L853_ : ((op (e0) (e2)) = (e2)) -> ((op (e1) (e0)) = (e2)) -> ((~((op (e1) (e1)) = (e2)))\/((op (e1) (e2)) = (e1))) -> ((~((op (e2) (e2)) = (e0)))\/((op (e2) (e0)) = (e2))) -> (~((op (e2) (e0)) = (op (e2) (e2)))) -> (~((op (e2) (op (e2) (e2))) = (op (e2) (e2)))) -> ((~((op (e3) (e3)) = (e0)))\/((op (e3) (e0)) = (e3))) -> ((~((op (e3) (e3)) = (e2)))\/((op (e3) (e2)) = (e3))) -> (~((op (e0) (e0)) = (e1))) -> (~((op (e3) (e0)) = (op (e3) (e2)))) -> (((op (e0) (e0)) = (e1))\/(((op (e1) (e0)) = (e1))\/(((op (e2) (e0)) = (e1))\/((op (e3) (e0)) = (e1))))) -> (~((op (e1) (e2)) = (op (e3) (e2)))) -> (((op (e0) (e0)) = (e2))\/(((op (e1) (e0)) = (e2))\/(((op (e2) (e0)) = (e2))\/((op (e3) (e0)) = (e2))))) -> (((op (e1) (e1)) = (e0))\/(((op (e1) (e1)) = (e1))\/(((op (e1) (e1)) = (e2))\/((op (e1) (e1)) = (e3))))) -> (((op (e0) (e0)) = (e3))\/(((op (e0) (e1)) = (e3))\/(((op (e0) (e2)) = (e3))\/((op (e0) (e3)) = (e3))))) -> (((op (e3) (e0)) = (e2))\/(((op (e3) (e1)) = (e2))\/(((op (e3) (e2)) = (e2))\/((op (e3) (e3)) = (e2))))) -> (~((op (e0) (e0)) = (op (e0) (e2)))) -> ((op (e0) (e0)) = (e0)) -> (((op (e0) (e0)) = (e2))\/(((op (e0) (e1)) = (e2))\/(((op (e0) (e2)) = (e2))\/((op (e0) (e3)) = (e2))))) -> (((op (e0) (e1)) = (e2))\/(((op (e1) (e1)) = (e2))\/(((op (e2) (e1)) = (e2))\/((op (e3) (e1)) = (e2))))) -> (~((op (e2) (e0)) = (op (e2) (e1)))) -> (~((op (e1) (e0)) = (op (e3) (e0)))) -> (((op (e0) (e2)) = (e1))\/(((op (e1) (e2)) = (e1))\/(((op (e2) (e2)) = (e1))\/((op (e3) (e2)) = (e1))))) -> (~((op (e3) (e1)) = (op (e3) (e2)))) -> (~((op (e0) (e2)) = (op (e0) (e3)))) -> (~((op (e1) (e0)) = (op (e1) (e3)))) -> (~((op (e3) (op (e2) (e3))) = (op (e2) (e3)))) -> (((op (e0) (e3)) = (e1))\/(((op (e1) (e3)) = (e1))\/(((op (e2) (e3)) = (e1))\/((op (e3) (e3)) = (e1))))) -> (~((op (e0) (e2)) = (op (e3) (e2)))) -> (((op (e3) (e0)) = (e1))\/(((op (e3) (e1)) = (e1))\/(((op (e3) (e2)) = (e1))\/((op (e3) (e3)) = (e1))))) -> (((op (e0) (e2)) = (e0))\/(((op (e0) (e2)) = (e1))\/(((op (e0) (e2)) = (e2))\/((op (e0) (e2)) = (e3))))) -> (~((op (e0) (e1)) = (op (e3) (e1)))) -> (((op (e0) (e0)) = (e3))\/(((op (e1) (e0)) = (e3))\/(((op (e2) (e0)) = (e3))\/((op (e3) (e0)) = (e3))))) -> (~((op (e0) (e2)) = (op (e1) (e2)))) -> (((op (e0) (e3)) = (e2))\/(((op (e1) (e3)) = (e2))\/(((op (e2) (e3)) = (e2))\/((op (e3) (e3)) = (e2))))) -> (~((op (e2) (e0)) = (op (e2) (e3)))) -> (~((op (e0) (e1)) = (op (e0) (e3)))) -> (((op (e1) (e0)) = (e3))\/(((op (e1) (e1)) = (e3))\/(((op (e1) (e2)) = (e3))\/((op (e1) (e3)) = (e3))))) -> (~((e2) = (e3))) -> (~((op (e0) (e0)) = (e3))) -> (((op (e3) (e3)) = (e0))\/(((op (e3) (e3)) = (e1))\/(((op (e3) (e3)) = (e2))\/((op (e3) (e3)) = (e3))))) -> (~((op (e0) (e3)) = (op (e3) (e3)))) -> (~((e1) = (e2))) -> (~((op (e0) (e0)) = (e2))) -> ((~((op (e2) (e2)) = (e1)))\/((op (e2) (e1)) = (e2))) -> (~((op (e2) (e1)) = (op (e2) (e3)))) -> (~((op (e2) (e1)) = (op (e2) (e2)))) -> (((op (e2) (e0)) = (e0))\/(((op (e2) (e1)) = (e0))\/(((op (e2) (e2)) = (e0))\/((op (e2) (e3)) = (e0))))) -> (~((e0) = (e2))) -> (~((op (e1) (op (e2) (e1))) = (op (e2) (e1)))) -> (((op (e2) (e0)) = (e1))\/(((op (e2) (e1)) = (e1))\/(((op (e2) (e2)) = (e1))\/((op (e2) (e3)) = (e1))))) -> (~((op (e0) (e0)) = (op (e2) (e0)))) -> (((op (e2) (e2)) = (e0))\/(((op (e2) (e2)) = (e1))\/(((op (e2) (e2)) = (e2))\/((op (e2) (e2)) = (e3))))) -> (~((op (e1) (e3)) = (op (e3) (e3)))) -> (~((op (e0) (e1)) = (op (e2) (e1)))) -> (((op (e2) (e0)) = (e3))\/(((op (e2) (e1)) = (e3))\/(((op (e2) (e2)) = (e3))\/((op (e2) (e3)) = (e3))))) -> ((~((op (e2) (e2)) = (e3)))\/((op (e2) (e3)) = (e2))) -> ((~((op (e3) (e3)) = (e1)))\/((op (e3) (e1)) = (e3))) -> (~((op (e1) (e2)) = (op (e2) (e2)))) -> (~((op (e0) (e0)) = (op (e0) (e3)))) -> (~((op (e0) (e3)) = (op (e2) (e3)))) -> (~((op (e0) (e3)) = (op (e1) (e3)))) -> (((op (e0) (e3)) = (e0))\/(((op (e0) (e3)) = (e1))\/(((op (e0) (e3)) = (e2))\/((op (e0) (e3)) = (e3))))) -> (~((op (e0) (e2)) = (op (e2) (e2)))) -> (((op (e1) (e0)) = (e2))\/(((op (e1) (e1)) = (e2))\/(((op (e1) (e2)) = (e2))\/((op (e1) (e3)) = (e2))))) -> ((~((op (e2) (e2)) = (e2)))\/((op (e2) (e2)) = (e2))) -> ((~((op (e3) (e3)) = (e3)))\/((op (e3) (e3)) = (e3))) -> (((op (e0) (e0)) = (e1))\/(((op (e0) (e1)) = (e1))\/(((op (e0) (e2)) = (e1))\/((op (e0) (e3)) = (e1))))) -> (~((op (e3) (e0)) = (op (e3) (e1)))) -> (((op (e0) (e1)) = (e3))\/(((op (e1) (e1)) = (e3))\/(((op (e2) (e1)) = (e3))\/((op (e3) (e1)) = (e3))))) -> (~((op (e1) (e0)) = (op (e1) (e2)))) -> (((op (e0) (e1)) = (e1))\/(((op (e1) (e1)) = (e1))\/(((op (e2) (e1)) = (e1))\/((op (e3) (e1)) = (e1))))) -> (~((e0) = (e3))) -> (~((op (e3) (e1)) = (op (e3) (e3)))) -> ((~((op (e1) (e1)) = (e3)))\/((op (e1) (e3)) = (e1))) -> (~((op (e1) (e0)) = (op (e1) (e1)))) -> ((~((op (e1) (e1)) = (e1)))\/((op (e1) (e1)) = (e1))) -> ((op (e0) (e1)) = (e1)) -> (~((op (e0) (op (e2) (e0))) = (op (e2) (e0)))) -> (~((e1) = (e3))) -> False). % 15.41/15.55 do 0 intro. intros zenon_H63 zenon_H68 zenon_H1d3 zenon_H1d4 zenon_H17a zenon_H294 zenon_H10f zenon_H10e zenon_H45 zenon_H105 zenon_Hf1 zenon_H17d zenon_Heb zenon_H1b3 zenon_H58 zenon_H1df zenon_H250 zenon_H1f zenon_H8e zenon_H1a2 zenon_H154 zenon_H22e zenon_H11b zenon_H135 zenon_Hc9 zenon_H1cf zenon_H28a zenon_H121 zenon_H140 zenon_H146 zenon_H251 zenon_H138 zenon_Hbe zenon_H87 zenon_H160 zenon_Hce zenon_H1cd zenon_H90 zenon_H6a zenon_H59 zenon_H3b zenon_H36 zenon_Ha7 zenon_H8f zenon_H1e3 zenon_H1e2 zenon_H157 zenon_H1f5 zenon_H5e zenon_H290 zenon_Hb7 zenon_H258 zenon_H2d zenon_H8b zenon_Hde zenon_He6 zenon_H1c3 zenon_H10c zenon_H7d zenon_H24f zenon_Hb4 zenon_H80 zenon_H254 zenon_H28 zenon_H84 zenon_Haa zenon_H10d zenon_H44 zenon_H109 zenon_H199 zenon_H166 zenon_H228 zenon_H4b zenon_H12d zenon_H1d2 zenon_Hd7 zenon_H1d8 zenon_H22 zenon_H295 zenon_Ha3. % 15.41/15.55 apply (zenon_or_s _ _ zenon_H58); [ zenon_intro zenon_H5b | zenon_intro zenon_H5a ]. % 15.41/15.55 exact (zenon_H59 zenon_H5b). % 15.41/15.55 apply (zenon_or_s _ _ zenon_H5a); [ zenon_intro zenon_H4a | zenon_intro zenon_H5c ]. % 15.41/15.55 apply (zenon_L59_); trivial. % 15.41/15.55 apply (zenon_or_s _ _ zenon_H5c); [ zenon_intro zenon_H50 | zenon_intro zenon_H53 ]. % 15.41/15.55 apply (zenon_L31_); trivial. % 15.41/15.55 apply (zenon_L847_); trivial. % 15.41/15.55 (* end of lemma zenon_L853_ *) % 15.41/15.55 assert (zenon_L854_ : (~((e1) = (e3))) -> (~((op (e0) (op (e2) (e0))) = (op (e2) (e0)))) -> ((~((op (e1) (e1)) = (e1)))\/((op (e1) (e1)) = (e1))) -> (~((op (e1) (e0)) = (op (e1) (e1)))) -> ((~((op (e1) (e1)) = (e3)))\/((op (e1) (e3)) = (e1))) -> (~((op (e3) (e1)) = (op (e3) (e3)))) -> (~((e0) = (e3))) -> (((op (e0) (e1)) = (e1))\/(((op (e1) (e1)) = (e1))\/(((op (e2) (e1)) = (e1))\/((op (e3) (e1)) = (e1))))) -> (~((op (e1) (e0)) = (op (e1) (e2)))) -> (((op (e0) (e1)) = (e3))\/(((op (e1) (e1)) = (e3))\/(((op (e2) (e1)) = (e3))\/((op (e3) (e1)) = (e3))))) -> (~((op (e3) (e0)) = (op (e3) (e1)))) -> (((op (e0) (e0)) = (e1))\/(((op (e0) (e1)) = (e1))\/(((op (e0) (e2)) = (e1))\/((op (e0) (e3)) = (e1))))) -> ((~((op (e3) (e3)) = (e3)))\/((op (e3) (e3)) = (e3))) -> ((~((op (e2) (e2)) = (e2)))\/((op (e2) (e2)) = (e2))) -> (((op (e1) (e0)) = (e2))\/(((op (e1) (e1)) = (e2))\/(((op (e1) (e2)) = (e2))\/((op (e1) (e3)) = (e2))))) -> (~((op (e0) (e2)) = (op (e2) (e2)))) -> (((op (e0) (e3)) = (e0))\/(((op (e0) (e3)) = (e1))\/(((op (e0) (e3)) = (e2))\/((op (e0) (e3)) = (e3))))) -> (~((op (e0) (e3)) = (op (e1) (e3)))) -> (~((op (e0) (e3)) = (op (e2) (e3)))) -> (~((op (e0) (e0)) = (op (e0) (e3)))) -> (~((op (e1) (e2)) = (op (e2) (e2)))) -> ((~((op (e3) (e3)) = (e1)))\/((op (e3) (e1)) = (e3))) -> ((~((op (e2) (e2)) = (e3)))\/((op (e2) (e3)) = (e2))) -> (((op (e2) (e0)) = (e3))\/(((op (e2) (e1)) = (e3))\/(((op (e2) (e2)) = (e3))\/((op (e2) (e3)) = (e3))))) -> (~((op (e0) (e1)) = (op (e2) (e1)))) -> (~((op (e1) (e3)) = (op (e3) (e3)))) -> (((op (e2) (e2)) = (e0))\/(((op (e2) (e2)) = (e1))\/(((op (e2) (e2)) = (e2))\/((op (e2) (e2)) = (e3))))) -> (~((op (e0) (e0)) = (op (e2) (e0)))) -> (((op (e2) (e0)) = (e1))\/(((op (e2) (e1)) = (e1))\/(((op (e2) (e2)) = (e1))\/((op (e2) (e3)) = (e1))))) -> (~((op (e1) (op (e2) (e1))) = (op (e2) (e1)))) -> (~((e0) = (e2))) -> (((op (e2) (e0)) = (e0))\/(((op (e2) (e1)) = (e0))\/(((op (e2) (e2)) = (e0))\/((op (e2) (e3)) = (e0))))) -> (~((op (e2) (e1)) = (op (e2) (e2)))) -> (~((op (e2) (e1)) = (op (e2) (e3)))) -> ((~((op (e2) (e2)) = (e1)))\/((op (e2) (e1)) = (e2))) -> (~((op (e0) (e0)) = (e3))) -> (~((e2) = (e3))) -> (((op (e1) (e0)) = (e3))\/(((op (e1) (e1)) = (e3))\/(((op (e1) (e2)) = (e3))\/((op (e1) (e3)) = (e3))))) -> (~((op (e0) (e1)) = (op (e0) (e3)))) -> (((op (e0) (e3)) = (e2))\/(((op (e1) (e3)) = (e2))\/(((op (e2) (e3)) = (e2))\/((op (e3) (e3)) = (e2))))) -> (~((op (e0) (e2)) = (op (e1) (e2)))) -> (((op (e0) (e0)) = (e3))\/(((op (e1) (e0)) = (e3))\/(((op (e2) (e0)) = (e3))\/((op (e3) (e0)) = (e3))))) -> (~((op (e0) (e1)) = (op (e3) (e1)))) -> (((op (e0) (e2)) = (e0))\/(((op (e0) (e2)) = (e1))\/(((op (e0) (e2)) = (e2))\/((op (e0) (e2)) = (e3))))) -> (((op (e3) (e0)) = (e1))\/(((op (e3) (e1)) = (e1))\/(((op (e3) (e2)) = (e1))\/((op (e3) (e3)) = (e1))))) -> (~((op (e0) (e2)) = (op (e3) (e2)))) -> (((op (e0) (e3)) = (e1))\/(((op (e1) (e3)) = (e1))\/(((op (e2) (e3)) = (e1))\/((op (e3) (e3)) = (e1))))) -> (~((op (e3) (op (e2) (e3))) = (op (e2) (e3)))) -> (~((op (e1) (e0)) = (op (e1) (e3)))) -> (~((op (e0) (e2)) = (op (e0) (e3)))) -> (~((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 (e3) (e0)))) -> (~((op (e2) (e0)) = (op (e2) (e1)))) -> (((op (e0) (e1)) = (e2))\/(((op (e1) (e1)) = (e2))\/(((op (e2) (e1)) = (e2))\/((op (e3) (e1)) = (e2))))) -> ((op (e0) (e0)) = (e0)) -> (~((op (e0) (e0)) = (op (e0) (e2)))) -> (((op (e3) (e0)) = (e2))\/(((op (e3) (e1)) = (e2))\/(((op (e3) (e2)) = (e2))\/((op (e3) (e3)) = (e2))))) -> (((op (e0) (e0)) = (e3))\/(((op (e0) (e1)) = (e3))\/(((op (e0) (e2)) = (e3))\/((op (e0) (e3)) = (e3))))) -> (((op (e0) (e0)) = (e2))\/(((op (e1) (e0)) = (e2))\/(((op (e2) (e0)) = (e2))\/((op (e3) (e0)) = (e2))))) -> (~((op (e1) (e2)) = (op (e3) (e2)))) -> (((op (e0) (e0)) = (e1))\/(((op (e1) (e0)) = (e1))\/(((op (e2) (e0)) = (e1))\/((op (e3) (e0)) = (e1))))) -> (~((op (e3) (e0)) = (op (e3) (e2)))) -> (~((op (e0) (e0)) = (e1))) -> ((~((op (e3) (e3)) = (e2)))\/((op (e3) (e2)) = (e3))) -> ((~((op (e3) (e3)) = (e0)))\/((op (e3) (e0)) = (e3))) -> (~((op (e2) (op (e2) (e2))) = (op (e2) (e2)))) -> (~((op (e2) (e0)) = (op (e2) (e2)))) -> ((~((op (e2) (e2)) = (e0)))\/((op (e2) (e0)) = (e2))) -> ((~((op (e1) (e1)) = (e2)))\/((op (e1) (e2)) = (e1))) -> ((op (e2) (e3)) = (e2)) -> (~((op (e2) (e0)) = (op (e2) (e3)))) -> (~((op (e3) (e3)) = (e1))) -> (~((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 (e0) (e1)) = (op (e1) (e1)))) -> (~((op (e1) (e1)) = (e3))) -> (~((op (e0) (e0)) = (e2))) -> (((op (e0) (e0)) = (e2))\/(((op (e0) (e1)) = (e2))\/(((op (e0) (e2)) = (e2))\/((op (e0) (e3)) = (e2))))) -> (((op (e3) (e3)) = (e0))\/(((op (e3) (e3)) = (e1))\/(((op (e3) (e3)) = (e2))\/((op (e3) (e3)) = (e3))))) -> (~((op (e3) (e3)) = (e0))) -> (~((op (e0) (e3)) = (op (e3) (e3)))) -> (~((op (e3) (e3)) = (e2))) -> (~((op (e3) (e3)) = (e3))) -> False). % 15.41/15.56 do 0 intro. intros zenon_Ha3 zenon_H295 zenon_H1d8 zenon_Hd7 zenon_H1d2 zenon_H12d zenon_H4b zenon_H228 zenon_H166 zenon_H199 zenon_H109 zenon_H44 zenon_H10d zenon_Haa zenon_H84 zenon_H28 zenon_H254 zenon_H80 zenon_Hb4 zenon_H24f zenon_H7d zenon_H10c zenon_H1c3 zenon_He6 zenon_Hde zenon_H8b zenon_H2d zenon_H258 zenon_Hb7 zenon_H290 zenon_H5e zenon_H1f5 zenon_H157 zenon_H1e2 zenon_H1e3 zenon_H59 zenon_H6a zenon_H90 zenon_H1cd zenon_H160 zenon_H87 zenon_Hbe zenon_H138 zenon_H251 zenon_H146 zenon_H140 zenon_H121 zenon_H28a zenon_H1cf zenon_Hc9 zenon_H135 zenon_H11b zenon_H22e zenon_H154 zenon_H1a2 zenon_H1f zenon_H250 zenon_H1df zenon_H58 zenon_Heb zenon_H17d zenon_Hf1 zenon_H105 zenon_H45 zenon_H10e zenon_H10f zenon_H294 zenon_H17a zenon_H1d4 zenon_H1d3 zenon_H124 zenon_Hce zenon_H104 zenon_Ha7 zenon_H1b3 zenon_H145 zenon_H1b4 zenon_H23 zenon_H182 zenon_H8f zenon_H8e zenon_H3b zenon_H3c zenon_H36 zenon_H3d zenon_H3e. % 15.41/15.56 apply (zenon_or_s _ _ zenon_H44); [ zenon_intro zenon_H47 | zenon_intro zenon_H46 ]. % 15.41/15.56 exact (zenon_H45 zenon_H47). % 15.41/15.56 apply (zenon_or_s _ _ zenon_H46); [ zenon_intro zenon_H22 | zenon_intro zenon_H48 ]. % 15.41/15.56 apply (zenon_or_s _ _ zenon_Hf1); [ zenon_intro zenon_H47 | zenon_intro zenon_Hf4 ]. % 15.41/15.56 exact (zenon_H45 zenon_H47). % 15.41/15.56 apply (zenon_or_s _ _ zenon_Hf4); [ zenon_intro zenon_Hd8 | zenon_intro zenon_Hf5 ]. % 15.41/15.56 apply (zenon_L845_); trivial. % 15.41/15.56 apply (zenon_or_s _ _ zenon_Hf5); [ zenon_intro zenon_Hae | zenon_intro zenon_Hee ]. % 15.41/15.56 apply (zenon_L816_); trivial. % 15.41/15.56 apply (zenon_or_s _ _ zenon_H8e); [ zenon_intro zenon_H92 | zenon_intro zenon_H91 ]. % 15.41/15.56 exact (zenon_H8f zenon_H92). % 15.41/15.56 apply (zenon_or_s _ _ zenon_H91); [ zenon_intro zenon_H5d | zenon_intro zenon_H93 ]. % 15.41/15.56 apply (zenon_L852_); trivial. % 15.41/15.56 apply (zenon_or_s _ _ zenon_H93); [ zenon_intro zenon_H63 | zenon_intro zenon_H81 ]. % 15.41/15.56 apply (zenon_or_s _ _ zenon_Heb); [ zenon_intro zenon_H92 | zenon_intro zenon_Hec ]. % 15.41/15.56 exact (zenon_H8f zenon_H92). % 15.41/15.56 apply (zenon_or_s _ _ zenon_Hec); [ zenon_intro zenon_H68 | zenon_intro zenon_Hed ]. % 15.41/15.56 apply (zenon_L853_); trivial. % 15.41/15.56 apply (zenon_or_s _ _ zenon_Hed); [ zenon_intro zenon_Hdd | zenon_intro zenon_He9 ]. % 15.41/15.56 apply (zenon_L119_); trivial. % 15.41/15.56 apply (zenon_L122_); trivial. % 15.41/15.56 apply (zenon_L107_); trivial. % 15.41/15.56 apply (zenon_or_s _ _ zenon_H48); [ zenon_intro zenon_H29 | zenon_intro zenon_H37 ]. % 15.41/15.56 apply (zenon_L665_); trivial. % 15.41/15.56 apply (zenon_L7_); trivial. % 15.41/15.56 (* end of lemma zenon_L854_ *) % 15.41/15.56 assert (zenon_L855_ : (((op (e0) (e2)) = (e0))\/(((op (e1) (e2)) = (e0))\/(((op (e2) (e2)) = (e0))\/((op (e3) (e2)) = (e0))))) -> (~((op (e1) (e1)) = (e3))) -> (~((op (e0) (e1)) = (op (e1) (e1)))) -> (~((op (e1) (e1)) = (e1))) -> (~((op (e1) (e1)) = (e0))) -> ((~((op (e1) (e1)) = (e1)))\/((op (e1) (e1)) = (e1))) -> (~((op (e1) (e0)) = (op (e1) (e1)))) -> ((~((op (e1) (e1)) = (e3)))\/((op (e1) (e3)) = (e1))) -> (~((op (e3) (e1)) = (op (e3) (e3)))) -> (~((e0) = (e3))) -> (((op (e0) (e1)) = (e1))\/(((op (e1) (e1)) = (e1))\/(((op (e2) (e1)) = (e1))\/((op (e3) (e1)) = (e1))))) -> (~((op (e1) (e0)) = (op (e1) (e2)))) -> (((op (e0) (e1)) = (e3))\/(((op (e1) (e1)) = (e3))\/(((op (e2) (e1)) = (e3))\/((op (e3) (e1)) = (e3))))) -> (~((op (e3) (e0)) = (op (e3) (e1)))) -> (((op (e0) (e0)) = (e1))\/(((op (e0) (e1)) = (e1))\/(((op (e0) (e2)) = (e1))\/((op (e0) (e3)) = (e1))))) -> ((~((op (e3) (e3)) = (e3)))\/((op (e3) (e3)) = (e3))) -> ((~((op (e2) (e2)) = (e2)))\/((op (e2) (e2)) = (e2))) -> (((op (e1) (e0)) = (e2))\/(((op (e1) (e1)) = (e2))\/(((op (e1) (e2)) = (e2))\/((op (e1) (e3)) = (e2))))) -> (~((op (e0) (e2)) = (op (e2) (e2)))) -> (((op (e0) (e3)) = (e0))\/(((op (e0) (e3)) = (e1))\/(((op (e0) (e3)) = (e2))\/((op (e0) (e3)) = (e3))))) -> (~((op (e0) (e3)) = (op (e1) (e3)))) -> (~((op (e0) (e3)) = (op (e2) (e3)))) -> (~((op (e0) (e0)) = (op (e0) (e3)))) -> (~((op (e1) (e2)) = (op (e2) (e2)))) -> ((~((op (e3) (e3)) = (e1)))\/((op (e3) (e1)) = (e3))) -> ((~((op (e2) (e2)) = (e3)))\/((op (e2) (e3)) = (e2))) -> (((op (e2) (e0)) = (e3))\/(((op (e2) (e1)) = (e3))\/(((op (e2) (e2)) = (e3))\/((op (e2) (e3)) = (e3))))) -> (~((op (e0) (e1)) = (op (e2) (e1)))) -> (~((op (e1) (e3)) = (op (e3) (e3)))) -> (((op (e2) (e2)) = (e0))\/(((op (e2) (e2)) = (e1))\/(((op (e2) (e2)) = (e2))\/((op (e2) (e2)) = (e3))))) -> (~((op (e0) (e0)) = (op (e2) (e0)))) -> (((op (e2) (e0)) = (e1))\/(((op (e2) (e1)) = (e1))\/(((op (e2) (e2)) = (e1))\/((op (e2) (e3)) = (e1))))) -> (~((op (e1) (op (e2) (e1))) = (op (e2) (e1)))) -> (~((e0) = (e2))) -> (((op (e2) (e0)) = (e0))\/(((op (e2) (e1)) = (e0))\/(((op (e2) (e2)) = (e0))\/((op (e2) (e3)) = (e0))))) -> (~((op (e2) (e1)) = (op (e2) (e2)))) -> (~((op (e2) (e1)) = (op (e2) (e3)))) -> ((~((op (e2) (e2)) = (e1)))\/((op (e2) (e1)) = (e2))) -> (~((op (e0) (e0)) = (e2))) -> (~((e1) = (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) (e0)) = (e3))) -> (~((e2) = (e3))) -> (((op (e1) (e0)) = (e3))\/(((op (e1) (e1)) = (e3))\/(((op (e1) (e2)) = (e3))\/((op (e1) (e3)) = (e3))))) -> (~((op (e0) (e1)) = (op (e0) (e3)))) -> (~((op (e2) (e0)) = (op (e2) (e3)))) -> (((op (e0) (e3)) = (e2))\/(((op (e1) (e3)) = (e2))\/(((op (e2) (e3)) = (e2))\/((op (e3) (e3)) = (e2))))) -> (~((op (e0) (e2)) = (op (e1) (e2)))) -> (~((e1) = (e3))) -> (((op (e0) (e0)) = (e3))\/(((op (e1) (e0)) = (e3))\/(((op (e2) (e0)) = (e3))\/((op (e3) (e0)) = (e3))))) -> (~((op (e0) (e1)) = (op (e3) (e1)))) -> (((op (e0) (e2)) = (e0))\/(((op (e0) (e2)) = (e1))\/(((op (e0) (e2)) = (e2))\/((op (e0) (e2)) = (e3))))) -> (((op (e3) (e0)) = (e1))\/(((op (e3) (e1)) = (e1))\/(((op (e3) (e2)) = (e1))\/((op (e3) (e3)) = (e1))))) -> (~((op (e0) (e2)) = (op (e3) (e2)))) -> (((op (e0) (e3)) = (e1))\/(((op (e1) (e3)) = (e1))\/(((op (e2) (e3)) = (e1))\/((op (e3) (e3)) = (e1))))) -> (~((op (e3) (op (e2) (e3))) = (op (e2) (e3)))) -> (~((op (e1) (e0)) = (op (e1) (e3)))) -> (~((op (e0) (e2)) = (op (e0) (e3)))) -> (~((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 (e3) (e0)))) -> (~((op (e2) (e0)) = (op (e2) (e1)))) -> (((op (e0) (e1)) = (e2))\/(((op (e1) (e1)) = (e2))\/(((op (e2) (e1)) = (e2))\/((op (e3) (e1)) = (e2))))) -> (((op (e0) (e0)) = (e2))\/(((op (e0) (e1)) = (e2))\/(((op (e0) (e2)) = (e2))\/((op (e0) (e3)) = (e2))))) -> ((op (e0) (e0)) = (e0)) -> (~((op (e0) (e0)) = (op (e0) (e2)))) -> (((op (e3) (e0)) = (e2))\/(((op (e3) (e1)) = (e2))\/(((op (e3) (e2)) = (e2))\/((op (e3) (e3)) = (e2))))) -> (~((op (e0) (op (e2) (e0))) = (op (e2) (e0)))) -> (((op (e0) (e0)) = (e3))\/(((op (e0) (e1)) = (e3))\/(((op (e0) (e2)) = (e3))\/((op (e0) (e3)) = (e3))))) -> (((op (e1) (e1)) = (e0))\/(((op (e1) (e1)) = (e1))\/(((op (e1) (e1)) = (e2))\/((op (e1) (e1)) = (e3))))) -> (((op (e0) (e0)) = (e2))\/(((op (e1) (e0)) = (e2))\/(((op (e2) (e0)) = (e2))\/((op (e3) (e0)) = (e2))))) -> (~((op (e1) (e2)) = (op (e3) (e2)))) -> (((op (e0) (e0)) = (e1))\/(((op (e1) (e0)) = (e1))\/(((op (e2) (e0)) = (e1))\/((op (e3) (e0)) = (e1))))) -> (~((op (e3) (e0)) = (op (e3) (e2)))) -> ((~((op (e3) (e3)) = (e2)))\/((op (e3) (e2)) = (e3))) -> ((~((op (e3) (e3)) = (e0)))\/((op (e3) (e0)) = (e3))) -> (~((op (e2) (op (e2) (e2))) = (op (e2) (e2)))) -> (~((op (e2) (e0)) = (op (e2) (e2)))) -> ((~((op (e2) (e2)) = (e0)))\/((op (e2) (e0)) = (e2))) -> ((~((op (e1) (e1)) = (e2)))\/((op (e1) (e2)) = (e1))) -> (~((op (e3) (e3)) = (e0))) -> (~((op (e3) (e3)) = (e1))) -> ((op (e2) (e3)) = (e2)) -> (~((op (e0) (e0)) = (e1))) -> ((op (e1) (e2)) = (e1)) -> (~((op (e1) (e2)) = (op (e1) (e3)))) -> (~((op (e2) (e2)) = (e2))) -> (((op (e1) (e0)) = (e0))\/(((op (e1) (e1)) = (e0))\/(((op (e1) (e2)) = (e0))\/((op (e1) (e3)) = (e0))))) -> (~((e0) = (e1))) -> (~((op (e0) (e0)) = (op (e1) (e0)))) -> (~((op (e2) (e2)) = (e0))) -> (~((op (e2) (e2)) = (e1))) -> False). % 15.41/15.56 do 0 intro. intros zenon_H16f zenon_H182 zenon_H23 zenon_H1b4 zenon_H145 zenon_H1d8 zenon_Hd7 zenon_H1d2 zenon_H12d zenon_H4b zenon_H228 zenon_H166 zenon_H199 zenon_H109 zenon_H44 zenon_H10d zenon_Haa zenon_H84 zenon_H28 zenon_H254 zenon_H80 zenon_Hb4 zenon_H24f zenon_H7d zenon_H10c zenon_H1c3 zenon_He6 zenon_Hde zenon_H8b zenon_H2d zenon_H258 zenon_Hb7 zenon_H290 zenon_H5e zenon_H1f5 zenon_H157 zenon_H1e2 zenon_H1e3 zenon_H8f zenon_Ha7 zenon_H36 zenon_H3b zenon_H59 zenon_H6a zenon_H90 zenon_H1cd zenon_Hce zenon_H160 zenon_H87 zenon_Ha3 zenon_Hbe zenon_H138 zenon_H251 zenon_H146 zenon_H140 zenon_H121 zenon_H28a zenon_H1cf zenon_Hc9 zenon_H135 zenon_H11b zenon_H22e zenon_H154 zenon_H1a2 zenon_H8e zenon_H1f zenon_H250 zenon_H1df zenon_H295 zenon_H58 zenon_H1b3 zenon_Heb zenon_H17d zenon_Hf1 zenon_H105 zenon_H10e zenon_H10f zenon_H294 zenon_H17a zenon_H1d4 zenon_H1d3 zenon_H3c zenon_H104 zenon_H124 zenon_H45 zenon_H117 zenon_H1d0 zenon_H2f zenon_H163 zenon_H9e zenon_H24c zenon_H2e zenon_H52. % 15.41/15.56 apply (zenon_or_s _ _ zenon_H10e); [ zenon_intro zenon_H3d | zenon_intro zenon_H106 ]. % 15.41/15.56 apply (zenon_or_s _ _ zenon_H10d); [ zenon_intro zenon_H3e | zenon_intro zenon_H42 ]. % 15.41/15.56 apply (zenon_L854_); trivial. % 15.41/15.56 apply (zenon_L793_); trivial. % 15.41/15.56 apply (zenon_L590_); trivial. % 15.41/15.56 (* end of lemma zenon_L855_ *) % 15.41/15.56 assert (zenon_L856_ : (((op (e2) (e0)) = (e0))\/(((op (e2) (e1)) = (e0))\/(((op (e2) (e2)) = (e0))\/((op (e2) (e3)) = (e0))))) -> ((op (e0) (e0)) = (e0)) -> (~((op (e0) (e0)) = (op (e2) (e0)))) -> ((op (e2) (e1)) = (e1)) -> ((op (e1) (e0)) = (e1)) -> (~((op (e1) (op (e2) (e1))) = (op (e2) (e1)))) -> (~((op (e2) (e2)) = (e0))) -> (~((op (e1) (e3)) = (op (e2) (e3)))) -> ((op (e1) (e3)) = (e0)) -> False). % 15.41/15.56 do 0 intro. intros zenon_H1f5 zenon_H1f zenon_H258 zenon_Hb2 zenon_Hd8 zenon_H290 zenon_H2e zenon_H244 zenon_Hcc. % 15.41/15.56 apply (zenon_or_s _ _ zenon_H1f5); [ zenon_intro zenon_Hcf | zenon_intro zenon_H1f9 ]. % 15.41/15.56 apply (zenon_L598_); trivial. % 15.41/15.56 apply (zenon_or_s _ _ zenon_H1f9); [ zenon_intro zenon_H14a | zenon_intro zenon_H1fa ]. % 15.41/15.56 apply (zenon_L783_); trivial. % 15.41/15.56 apply (zenon_or_s _ _ zenon_H1fa); [ zenon_intro zenon_H32 | zenon_intro zenon_Hd0 ]. % 15.41/15.56 exact (zenon_H2e zenon_H32). % 15.41/15.56 apply (zenon_L599_); trivial. % 15.41/15.56 (* end of lemma zenon_L856_ *) % 15.41/15.56 assert (zenon_L857_ : (((op (e2) (e0)) = (e1))\/(((op (e2) (e1)) = (e1))\/(((op (e2) (e2)) = (e1))\/((op (e2) (e3)) = (e1))))) -> (~((e1) = (e3))) -> ((op (e2) (e0)) = (e3)) -> ((op (e1) (e3)) = (e0)) -> (~((op (e1) (e3)) = (op (e2) (e3)))) -> (~((op (e2) (e2)) = (e0))) -> (~((op (e1) (op (e2) (e1))) = (op (e2) (e1)))) -> ((op (e1) (e0)) = (e1)) -> (~((op (e0) (e0)) = (op (e2) (e0)))) -> ((op (e0) (e0)) = (e0)) -> (((op (e2) (e0)) = (e0))\/(((op (e2) (e1)) = (e0))\/(((op (e2) (e2)) = (e0))\/((op (e2) (e3)) = (e0))))) -> (~((op (e2) (e2)) = (e1))) -> (~((e1) = (e2))) -> ((op (e2) (e3)) = (e2)) -> False). % 15.41/15.56 do 0 intro. intros zenon_Hb7 zenon_Ha3 zenon_Haf zenon_Hcc zenon_H244 zenon_H2e zenon_H290 zenon_Hd8 zenon_H258 zenon_H1f zenon_H1f5 zenon_H52 zenon_Ha7 zenon_H124. % 15.41/15.56 apply (zenon_or_s _ _ zenon_Hb7); [ zenon_intro zenon_Hae | zenon_intro zenon_Hb8 ]. % 15.41/15.56 apply (zenon_L39_); trivial. % 15.41/15.56 apply (zenon_or_s _ _ zenon_Hb8); [ zenon_intro zenon_Hb2 | zenon_intro zenon_Hb9 ]. % 15.41/15.56 apply (zenon_L856_); trivial. % 15.41/15.56 apply (zenon_or_s _ _ zenon_Hb9); [ zenon_intro zenon_H2a | zenon_intro zenon_Hb5 ]. % 15.41/15.56 exact (zenon_H52 zenon_H2a). % 15.41/15.56 apply (zenon_L93_); trivial. % 15.41/15.56 (* end of lemma zenon_L857_ *) % 15.41/15.56 assert (zenon_L858_ : (((op (e1) (e0)) = (e1))\/(((op (e1) (e1)) = (e1))\/(((op (e1) (e2)) = (e1))\/((op (e1) (e3)) = (e1))))) -> ((op (e2) (e3)) = (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 (e1) (op (e2) (e1))) = (op (e2) (e1)))) -> (~((op (e1) (e3)) = (op (e2) (e3)))) -> ((op (e2) (e0)) = (e3)) -> (~((e1) = (e3))) -> (((op (e2) (e0)) = (e1))\/(((op (e2) (e1)) = (e1))\/(((op (e2) (e2)) = (e1))\/((op (e2) (e3)) = (e1))))) -> (~((op (e1) (e1)) = (e1))) -> ((op (e3) (e1)) = (e0)) -> (~((op (e3) (e1)) = (op (e3) (e2)))) -> (~((op (e2) (e2)) = (e0))) -> (~((op (e0) (e0)) = (op (e0) (e2)))) -> ((op (e0) (e0)) = (e0)) -> (((op (e0) (e2)) = (e0))\/(((op (e1) (e2)) = (e0))\/(((op (e2) (e2)) = (e0))\/((op (e3) (e2)) = (e0))))) -> (~((e0) = (e1))) -> ((op (e1) (e3)) = (e0)) -> False). % 15.41/15.56 do 0 intro. intros zenon_H1c5 zenon_H124 zenon_Ha7 zenon_H52 zenon_H1f5 zenon_H258 zenon_H290 zenon_H244 zenon_Haf zenon_Ha3 zenon_Hb7 zenon_H1b4 zenon_H142 zenon_H135 zenon_H2e zenon_H250 zenon_H1f zenon_H16f zenon_H9e zenon_Hcc. % 15.41/15.56 apply (zenon_or_s _ _ zenon_H1c5); [ zenon_intro zenon_Hd8 | zenon_intro zenon_H1c6 ]. % 15.41/15.56 apply (zenon_L857_); trivial. % 15.41/15.56 apply (zenon_or_s _ _ zenon_H1c6); [ zenon_intro zenon_H21 | zenon_intro zenon_H1c7 ]. % 15.41/15.56 exact (zenon_H1b4 zenon_H21). % 15.41/15.56 apply (zenon_or_s _ _ zenon_H1c7); [ zenon_intro zenon_H117 | zenon_intro zenon_H11f ]. % 15.41/15.56 apply (zenon_L622_); trivial. % 15.41/15.56 apply (zenon_L208_); trivial. % 15.41/15.56 (* end of lemma zenon_L858_ *) % 15.41/15.56 assert (zenon_L859_ : (~((op (e3) (e3)) = (e3))) -> (~((op (e1) (e1)) = (e2))) -> (((op (e0) (e1)) = (e0))\/(((op (e1) (e1)) = (e0))\/(((op (e2) (e1)) = (e0))\/((op (e3) (e1)) = (e0))))) -> ((op (e0) (e1)) = (e3)) -> (~((op (e1) (e1)) = (e3))) -> (~((op (e0) (e1)) = (op (e1) (e1)))) -> (~((op (e1) (e1)) = (e0))) -> ((~((op (e1) (e1)) = (e1)))\/((op (e1) (e1)) = (e1))) -> (~((op (e1) (e0)) = (op (e1) (e1)))) -> ((~((op (e1) (e1)) = (e3)))\/((op (e1) (e3)) = (e1))) -> (~((op (e3) (e1)) = (op (e3) (e3)))) -> (~((e0) = (e3))) -> (((op (e0) (e1)) = (e1))\/(((op (e1) (e1)) = (e1))\/(((op (e2) (e1)) = (e1))\/((op (e3) (e1)) = (e1))))) -> (~((op (e1) (e0)) = (op (e1) (e2)))) -> (((op (e0) (e1)) = (e3))\/(((op (e1) (e1)) = (e3))\/(((op (e2) (e1)) = (e3))\/((op (e3) (e1)) = (e3))))) -> (~((op (e3) (e0)) = (op (e3) (e1)))) -> (((op (e0) (e0)) = (e1))\/(((op (e0) (e1)) = (e1))\/(((op (e0) (e2)) = (e1))\/((op (e0) (e3)) = (e1))))) -> ((~((op (e3) (e3)) = (e3)))\/((op (e3) (e3)) = (e3))) -> ((~((op (e2) (e2)) = (e2)))\/((op (e2) (e2)) = (e2))) -> (((op (e1) (e0)) = (e2))\/(((op (e1) (e1)) = (e2))\/(((op (e1) (e2)) = (e2))\/((op (e1) (e3)) = (e2))))) -> (~((op (e0) (e2)) = (op (e2) (e2)))) -> (((op (e0) (e3)) = (e0))\/(((op (e0) (e3)) = (e1))\/(((op (e0) (e3)) = (e2))\/((op (e0) (e3)) = (e3))))) -> (~((op (e0) (e3)) = (op (e1) (e3)))) -> (~((op (e0) (e3)) = (op (e2) (e3)))) -> (~((op (e0) (e0)) = (op (e0) (e3)))) -> (~((op (e1) (e2)) = (op (e2) (e2)))) -> ((~((op (e3) (e3)) = (e1)))\/((op (e3) (e1)) = (e3))) -> ((~((op (e2) (e2)) = (e3)))\/((op (e2) (e3)) = (e2))) -> (((op (e2) (e0)) = (e3))\/(((op (e2) (e1)) = (e3))\/(((op (e2) (e2)) = (e3))\/((op (e2) (e3)) = (e3))))) -> (~((op (e0) (e1)) = (op (e2) (e1)))) -> (~((op (e1) (e3)) = (op (e3) (e3)))) -> (((op (e2) (e2)) = (e0))\/(((op (e2) (e2)) = (e1))\/(((op (e2) (e2)) = (e2))\/((op (e2) (e2)) = (e3))))) -> (~((e0) = (e2))) -> (~((op (e2) (e1)) = (op (e2) (e2)))) -> (~((op (e2) (e1)) = (op (e2) (e3)))) -> ((~((op (e2) (e2)) = (e1)))\/((op (e2) (e1)) = (e2))) -> (~((op (e0) (e0)) = (e2))) -> (~((op (e0) (e3)) = (op (e3) (e3)))) -> (((op (e3) (e3)) = (e0))\/(((op (e3) (e3)) = (e1))\/(((op (e3) (e3)) = (e2))\/((op (e3) (e3)) = (e3))))) -> (~((op (e0) (e0)) = (e3))) -> (~((e2) = (e3))) -> (((op (e1) (e0)) = (e3))\/(((op (e1) (e1)) = (e3))\/(((op (e1) (e2)) = (e3))\/((op (e1) (e3)) = (e3))))) -> (~((op (e0) (e1)) = (op (e0) (e3)))) -> (~((op (e2) (e0)) = (op (e2) (e3)))) -> (((op (e0) (e3)) = (e2))\/(((op (e1) (e3)) = (e2))\/(((op (e2) (e3)) = (e2))\/((op (e3) (e3)) = (e2))))) -> (~((op (e0) (e2)) = (op (e1) (e2)))) -> (((op (e0) (e0)) = (e3))\/(((op (e1) (e0)) = (e3))\/(((op (e2) (e0)) = (e3))\/((op (e3) (e0)) = (e3))))) -> (~((op (e0) (e1)) = (op (e3) (e1)))) -> (((op (e0) (e2)) = (e0))\/(((op (e0) (e2)) = (e1))\/(((op (e0) (e2)) = (e2))\/((op (e0) (e2)) = (e3))))) -> (((op (e3) (e0)) = (e1))\/(((op (e3) (e1)) = (e1))\/(((op (e3) (e2)) = (e1))\/((op (e3) (e3)) = (e1))))) -> (~((op (e0) (e2)) = (op (e3) (e2)))) -> (((op (e0) (e3)) = (e1))\/(((op (e1) (e3)) = (e1))\/(((op (e2) (e3)) = (e1))\/((op (e3) (e3)) = (e1))))) -> (~((op (e3) (op (e2) (e3))) = (op (e2) (e3)))) -> (~((op (e1) (e0)) = (op (e1) (e3)))) -> (~((op (e0) (e2)) = (op (e0) (e3)))) -> (((op (e0) (e2)) = (e1))\/(((op (e1) (e2)) = (e1))\/(((op (e2) (e2)) = (e1))\/((op (e3) (e2)) = (e1))))) -> (~((op (e1) (e0)) = (op (e3) (e0)))) -> (~((op (e2) (e0)) = (op (e2) (e1)))) -> (((op (e0) (e1)) = (e2))\/(((op (e1) (e1)) = (e2))\/(((op (e2) (e1)) = (e2))\/((op (e3) (e1)) = (e2))))) -> (((op (e0) (e0)) = (e2))\/(((op (e0) (e1)) = (e2))\/(((op (e0) (e2)) = (e2))\/((op (e0) (e3)) = (e2))))) -> (((op (e3) (e0)) = (e2))\/(((op (e3) (e1)) = (e2))\/(((op (e3) (e2)) = (e2))\/((op (e3) (e3)) = (e2))))) -> (~((op (e0) (op (e2) (e0))) = (op (e2) (e0)))) -> (((op (e0) (e0)) = (e3))\/(((op (e0) (e1)) = (e3))\/(((op (e0) (e2)) = (e3))\/((op (e0) (e3)) = (e3))))) -> (((op (e1) (e1)) = (e0))\/(((op (e1) (e1)) = (e1))\/(((op (e1) (e1)) = (e2))\/((op (e1) (e1)) = (e3))))) -> (((op (e0) (e0)) = (e2))\/(((op (e1) (e0)) = (e2))\/(((op (e2) (e0)) = (e2))\/((op (e3) (e0)) = (e2))))) -> (~((op (e1) (e2)) = (op (e3) (e2)))) -> (((op (e0) (e0)) = (e1))\/(((op (e1) (e0)) = (e1))\/(((op (e2) (e0)) = (e1))\/((op (e3) (e0)) = (e1))))) -> (~((op (e3) (e0)) = (op (e3) (e2)))) -> ((~((op (e3) (e3)) = (e2)))\/((op (e3) (e2)) = (e3))) -> ((~((op (e3) (e3)) = (e0)))\/((op (e3) (e0)) = (e3))) -> (~((op (e2) (op (e2) (e2))) = (op (e2) (e2)))) -> (~((op (e2) (e0)) = (op (e2) (e2)))) -> ((~((op (e2) (e2)) = (e0)))\/((op (e2) (e0)) = (e2))) -> ((~((op (e1) (e1)) = (e2)))\/((op (e1) (e2)) = (e1))) -> (~((op (e3) (e3)) = (e0))) -> (~((op (e3) (e3)) = (e1))) -> (~((op (e0) (e0)) = (e1))) -> (~((op (e1) (e2)) = (op (e1) (e3)))) -> (~((op (e2) (e2)) = (e2))) -> (((op (e1) (e0)) = (e0))\/(((op (e1) (e1)) = (e0))\/(((op (e1) (e2)) = (e0))\/((op (e1) (e3)) = (e0))))) -> (~((op (e0) (e0)) = (op (e1) (e0)))) -> (((op (e1) (e0)) = (e1))\/(((op (e1) (e1)) = (e1))\/(((op (e1) (e2)) = (e1))\/((op (e1) (e3)) = (e1))))) -> ((op (e2) (e3)) = (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 (e1) (op (e2) (e1))) = (op (e2) (e1)))) -> (~((op (e1) (e3)) = (op (e2) (e3)))) -> ((op (e2) (e0)) = (e3)) -> (~((e1) = (e3))) -> (((op (e2) (e0)) = (e1))\/(((op (e2) (e1)) = (e1))\/(((op (e2) (e2)) = (e1))\/((op (e2) (e3)) = (e1))))) -> (~((op (e1) (e1)) = (e1))) -> (~((op (e3) (e1)) = (op (e3) (e2)))) -> (~((op (e2) (e2)) = (e0))) -> (~((op (e0) (e0)) = (op (e0) (e2)))) -> ((op (e0) (e0)) = (e0)) -> (((op (e0) (e2)) = (e0))\/(((op (e1) (e2)) = (e0))\/(((op (e2) (e2)) = (e0))\/((op (e3) (e2)) = (e0))))) -> (~((e0) = (e1))) -> False). % 15.41/15.56 do 0 intro. intros zenon_H3e zenon_Hd6 zenon_H144 zenon_H4a zenon_H182 zenon_H23 zenon_H145 zenon_H1d8 zenon_Hd7 zenon_H1d2 zenon_H12d zenon_H4b zenon_H228 zenon_H166 zenon_H199 zenon_H109 zenon_H44 zenon_H10d zenon_Haa zenon_H84 zenon_H28 zenon_H254 zenon_H80 zenon_Hb4 zenon_H24f zenon_H7d zenon_H10c zenon_H1c3 zenon_He6 zenon_Hde zenon_H8b zenon_H2d zenon_H5e zenon_H157 zenon_H1e2 zenon_H1e3 zenon_H8f zenon_H36 zenon_H3b zenon_H59 zenon_H6a zenon_H90 zenon_H1cd zenon_Hce zenon_H160 zenon_H87 zenon_Hbe zenon_H138 zenon_H251 zenon_H146 zenon_H140 zenon_H121 zenon_H28a zenon_H1cf zenon_Hc9 zenon_H11b zenon_H22e zenon_H154 zenon_H1a2 zenon_H8e zenon_H1df zenon_H295 zenon_H58 zenon_H1b3 zenon_Heb zenon_H17d zenon_Hf1 zenon_H105 zenon_H10e zenon_H10f zenon_H294 zenon_H17a zenon_H1d4 zenon_H1d3 zenon_H3c zenon_H104 zenon_H45 zenon_H1d0 zenon_H2f zenon_H163 zenon_H24c zenon_H1c5 zenon_H124 zenon_Ha7 zenon_H52 zenon_H1f5 zenon_H258 zenon_H290 zenon_H244 zenon_Haf zenon_Ha3 zenon_Hb7 zenon_H1b4 zenon_H135 zenon_H2e zenon_H250 zenon_H1f zenon_H16f zenon_H9e. % 15.41/15.56 apply (zenon_or_s _ _ zenon_H163); [ zenon_intro zenon_Had | zenon_intro zenon_H164 ]. % 15.41/15.56 apply (zenon_L559_); trivial. % 15.41/15.56 apply (zenon_or_s _ _ zenon_H164); [ zenon_intro zenon_H149 | zenon_intro zenon_H165 ]. % 15.41/15.56 exact (zenon_H145 zenon_H149). % 15.41/15.56 apply (zenon_or_s _ _ zenon_H165); [ zenon_intro zenon_H15d | zenon_intro zenon_Hcc ]. % 15.41/15.56 apply (zenon_L490_); trivial. % 15.41/15.56 apply (zenon_or_s _ _ zenon_H144); [ zenon_intro zenon_H49 | zenon_intro zenon_H147 ]. % 15.41/15.56 apply (zenon_L9_); trivial. % 15.41/15.56 apply (zenon_or_s _ _ zenon_H147); [ zenon_intro zenon_H149 | zenon_intro zenon_H148 ]. % 15.41/15.56 exact (zenon_H145 zenon_H149). % 15.41/15.56 apply (zenon_or_s _ _ zenon_H148); [ zenon_intro zenon_H14a | zenon_intro zenon_H142 ]. % 15.41/15.56 apply (zenon_or_s _ _ zenon_H1c5); [ zenon_intro zenon_Hd8 | zenon_intro zenon_H1c6 ]. % 15.41/15.56 apply (zenon_L784_); trivial. % 15.41/15.56 apply (zenon_or_s _ _ zenon_H1c6); [ zenon_intro zenon_H21 | zenon_intro zenon_H1c7 ]. % 15.41/15.56 exact (zenon_H1b4 zenon_H21). % 15.41/15.56 apply (zenon_or_s _ _ zenon_H1c7); [ zenon_intro zenon_H117 | zenon_intro zenon_H11f ]. % 15.41/15.56 apply (zenon_L855_); trivial. % 15.41/15.56 apply (zenon_L208_); trivial. % 15.41/15.56 apply (zenon_L858_); trivial. % 15.41/15.56 (* end of lemma zenon_L859_ *) % 15.41/15.56 assert (zenon_L860_ : (~((op (e0) (e3)) = (op (e1) (e3)))) -> ((op (e3) (e2)) = (e3)) -> (~((op (e1) (e2)) = (op (e3) (e2)))) -> (~((op (e1) (e1)) = (e3))) -> (~((e2) = (e3))) -> (((op (e1) (e0)) = (e3))\/(((op (e1) (e1)) = (e3))\/(((op (e1) (e2)) = (e3))\/((op (e1) (e3)) = (e3))))) -> (~((e0) = (e1))) -> (((op (e0) (e2)) = (e0))\/(((op (e1) (e2)) = (e0))\/(((op (e2) (e2)) = (e0))\/((op (e3) (e2)) = (e0))))) -> ((op (e0) (e0)) = (e0)) -> (~((op (e0) (e0)) = (op (e0) (e2)))) -> (~((op (e2) (e2)) = (e0))) -> (~((op (e3) (e1)) = (op (e3) (e2)))) -> (~((op (e1) (e1)) = (e1))) -> (((op (e2) (e0)) = (e1))\/(((op (e2) (e1)) = (e1))\/(((op (e2) (e2)) = (e1))\/((op (e2) (e3)) = (e1))))) -> (~((op (e1) (e3)) = (op (e2) (e3)))) -> (~((op (e1) (op (e2) (e1))) = (op (e2) (e1)))) -> (~((op (e0) (e0)) = (op (e2) (e0)))) -> (((op (e2) (e0)) = (e0))\/(((op (e2) (e1)) = (e0))\/(((op (e2) (e2)) = (e0))\/((op (e2) (e3)) = (e0))))) -> (~((op (e2) (e2)) = (e1))) -> ((op (e2) (e3)) = (e2)) -> (((op (e1) (e0)) = (e1))\/(((op (e1) (e1)) = (e1))\/(((op (e1) (e2)) = (e1))\/((op (e1) (e3)) = (e1))))) -> (~((op (e0) (e0)) = (op (e1) (e0)))) -> (((op (e1) (e0)) = (e0))\/(((op (e1) (e1)) = (e0))\/(((op (e1) (e2)) = (e0))\/((op (e1) (e3)) = (e0))))) -> (~((op (e2) (e2)) = (e2))) -> (~((op (e1) (e2)) = (op (e1) (e3)))) -> (~((op (e0) (e0)) = (e1))) -> (~((op (e3) (e3)) = (e1))) -> (~((op (e3) (e3)) = (e0))) -> ((~((op (e1) (e1)) = (e2)))\/((op (e1) (e2)) = (e1))) -> ((~((op (e2) (e2)) = (e0)))\/((op (e2) (e0)) = (e2))) -> (~((op (e2) (e0)) = (op (e2) (e2)))) -> (~((op (e2) (op (e2) (e2))) = (op (e2) (e2)))) -> ((~((op (e3) (e3)) = (e0)))\/((op (e3) (e0)) = (e3))) -> ((~((op (e3) (e3)) = (e2)))\/((op (e3) (e2)) = (e3))) -> (~((op (e3) (e0)) = (op (e3) (e2)))) -> (((op (e0) (e0)) = (e1))\/(((op (e1) (e0)) = (e1))\/(((op (e2) (e0)) = (e1))\/((op (e3) (e0)) = (e1))))) -> (((op (e0) (e0)) = (e2))\/(((op (e1) (e0)) = (e2))\/(((op (e2) (e0)) = (e2))\/((op (e3) (e0)) = (e2))))) -> (((op (e1) (e1)) = (e0))\/(((op (e1) (e1)) = (e1))\/(((op (e1) (e1)) = (e2))\/((op (e1) (e1)) = (e3))))) -> (((op (e0) (e0)) = (e3))\/(((op (e0) (e1)) = (e3))\/(((op (e0) (e2)) = (e3))\/((op (e0) (e3)) = (e3))))) -> (((op (e3) (e0)) = (e2))\/(((op (e3) (e1)) = (e2))\/(((op (e3) (e2)) = (e2))\/((op (e3) (e3)) = (e2))))) -> (((op (e0) (e0)) = (e2))\/(((op (e0) (e1)) = (e2))\/(((op (e0) (e2)) = (e2))\/((op (e0) (e3)) = (e2))))) -> (((op (e0) (e1)) = (e2))\/(((op (e1) (e1)) = (e2))\/(((op (e2) (e1)) = (e2))\/((op (e3) (e1)) = (e2))))) -> (~((op (e2) (e0)) = (op (e2) (e1)))) -> (~((op (e1) (e0)) = (op (e3) (e0)))) -> (((op (e0) (e2)) = (e1))\/(((op (e1) (e2)) = (e1))\/(((op (e2) (e2)) = (e1))\/((op (e3) (e2)) = (e1))))) -> (~((op (e0) (e2)) = (op (e0) (e3)))) -> (~((op (e1) (e0)) = (op (e1) (e3)))) -> (~((op (e3) (op (e2) (e3))) = (op (e2) (e3)))) -> (((op (e0) (e3)) = (e1))\/(((op (e1) (e3)) = (e1))\/(((op (e2) (e3)) = (e1))\/((op (e3) (e3)) = (e1))))) -> (~((op (e0) (e2)) = (op (e3) (e2)))) -> (((op (e3) (e0)) = (e1))\/(((op (e3) (e1)) = (e1))\/(((op (e3) (e2)) = (e1))\/((op (e3) (e3)) = (e1))))) -> (((op (e0) (e2)) = (e0))\/(((op (e0) (e2)) = (e1))\/(((op (e0) (e2)) = (e2))\/((op (e0) (e2)) = (e3))))) -> (~((op (e0) (e1)) = (op (e3) (e1)))) -> (((op (e0) (e0)) = (e3))\/(((op (e1) (e0)) = (e3))\/(((op (e2) (e0)) = (e3))\/((op (e3) (e0)) = (e3))))) -> (~((op (e0) (e2)) = (op (e1) (e2)))) -> (((op (e0) (e3)) = (e2))\/(((op (e1) (e3)) = (e2))\/(((op (e2) (e3)) = (e2))\/((op (e3) (e3)) = (e2))))) -> (~((op (e2) (e0)) = (op (e2) (e3)))) -> (~((op (e0) (e1)) = (op (e0) (e3)))) -> (~((op (e0) (e0)) = (e3))) -> (((op (e3) (e3)) = (e0))\/(((op (e3) (e3)) = (e1))\/(((op (e3) (e3)) = (e2))\/((op (e3) (e3)) = (e3))))) -> (~((op (e0) (e3)) = (op (e3) (e3)))) -> (~((op (e0) (e0)) = (e2))) -> ((~((op (e2) (e2)) = (e1)))\/((op (e2) (e1)) = (e2))) -> (~((op (e2) (e1)) = (op (e2) (e3)))) -> (~((op (e2) (e1)) = (op (e2) (e2)))) -> (~((e0) = (e2))) -> (((op (e2) (e2)) = (e0))\/(((op (e2) (e2)) = (e1))\/(((op (e2) (e2)) = (e2))\/((op (e2) (e2)) = (e3))))) -> (~((op (e1) (e3)) = (op (e3) (e3)))) -> (~((op (e0) (e1)) = (op (e2) (e1)))) -> (((op (e2) (e0)) = (e3))\/(((op (e2) (e1)) = (e3))\/(((op (e2) (e2)) = (e3))\/((op (e2) (e3)) = (e3))))) -> ((~((op (e2) (e2)) = (e3)))\/((op (e2) (e3)) = (e2))) -> ((~((op (e3) (e3)) = (e1)))\/((op (e3) (e1)) = (e3))) -> (~((op (e1) (e2)) = (op (e2) (e2)))) -> (~((op (e0) (e0)) = (op (e0) (e3)))) -> (~((op (e0) (e3)) = (op (e2) (e3)))) -> (((op (e0) (e3)) = (e0))\/(((op (e0) (e3)) = (e1))\/(((op (e0) (e3)) = (e2))\/((op (e0) (e3)) = (e3))))) -> (~((op (e0) (e2)) = (op (e2) (e2)))) -> (((op (e1) (e0)) = (e2))\/(((op (e1) (e1)) = (e2))\/(((op (e1) (e2)) = (e2))\/((op (e1) (e3)) = (e2))))) -> ((~((op (e2) (e2)) = (e2)))\/((op (e2) (e2)) = (e2))) -> ((~((op (e3) (e3)) = (e3)))\/((op (e3) (e3)) = (e3))) -> (((op (e0) (e0)) = (e1))\/(((op (e0) (e1)) = (e1))\/(((op (e0) (e2)) = (e1))\/((op (e0) (e3)) = (e1))))) -> (~((op (e3) (e0)) = (op (e3) (e1)))) -> (((op (e0) (e1)) = (e3))\/(((op (e1) (e1)) = (e3))\/(((op (e2) (e1)) = (e3))\/((op (e3) (e1)) = (e3))))) -> (~((op (e1) (e0)) = (op (e1) (e2)))) -> (((op (e0) (e1)) = (e1))\/(((op (e1) (e1)) = (e1))\/(((op (e2) (e1)) = (e1))\/((op (e3) (e1)) = (e1))))) -> (~((e0) = (e3))) -> (~((op (e3) (e1)) = (op (e3) (e3)))) -> ((~((op (e1) (e1)) = (e3)))\/((op (e1) (e3)) = (e1))) -> (~((op (e1) (e0)) = (op (e1) (e1)))) -> ((~((op (e1) (e1)) = (e1)))\/((op (e1) (e1)) = (e1))) -> (~((op (e1) (e1)) = (e0))) -> (~((op (e0) (e1)) = (op (e1) (e1)))) -> (((op (e0) (e1)) = (e0))\/(((op (e1) (e1)) = (e0))\/(((op (e2) (e1)) = (e0))\/((op (e3) (e1)) = (e0))))) -> (~((op (e1) (e1)) = (e2))) -> (~((op (e3) (e3)) = (e3))) -> (~((e1) = (e3))) -> ((op (e0) (e2)) = (e2)) -> (~((op (e0) (op (e2) (e0))) = (op (e2) (e0)))) -> ((op (e3) (e0)) = (e1)) -> (~((e1) = (e2))) -> False). % 15.41/15.56 do 0 intro. intros zenon_H80 zenon_H106 zenon_H17d zenon_H182 zenon_H6a zenon_H90 zenon_H9e zenon_H16f zenon_H1f zenon_H250 zenon_H2e zenon_H135 zenon_H1b4 zenon_Hb7 zenon_H244 zenon_H290 zenon_H258 zenon_H1f5 zenon_H52 zenon_H124 zenon_H1c5 zenon_H24c zenon_H163 zenon_H2f zenon_H1d0 zenon_H45 zenon_H104 zenon_H3c zenon_H1d3 zenon_H1d4 zenon_H17a zenon_H294 zenon_H10f zenon_H10e zenon_H105 zenon_Hf1 zenon_Heb zenon_H1b3 zenon_H58 zenon_H1df zenon_H8e zenon_H1a2 zenon_H154 zenon_H22e zenon_H11b zenon_Hc9 zenon_H1cf zenon_H28a zenon_H121 zenon_H140 zenon_H146 zenon_H251 zenon_H138 zenon_Hbe zenon_H87 zenon_H160 zenon_Hce zenon_H1cd zenon_H59 zenon_H3b zenon_H36 zenon_H8f zenon_H1e3 zenon_H1e2 zenon_H157 zenon_H5e zenon_H2d zenon_H8b zenon_Hde zenon_He6 zenon_H1c3 zenon_H10c zenon_H7d zenon_H24f zenon_Hb4 zenon_H254 zenon_H28 zenon_H84 zenon_Haa zenon_H10d zenon_H44 zenon_H109 zenon_H199 zenon_H166 zenon_H228 zenon_H4b zenon_H12d zenon_H1d2 zenon_Hd7 zenon_H1d8 zenon_H145 zenon_H23 zenon_H144 zenon_Hd6 zenon_H3e zenon_Ha3 zenon_H63 zenon_H295 zenon_Hee zenon_Ha7. % 15.41/15.56 apply (zenon_or_s _ _ zenon_Heb); [ zenon_intro zenon_H92 | zenon_intro zenon_Hec ]. % 15.41/15.56 exact (zenon_H8f zenon_H92). % 15.41/15.56 apply (zenon_or_s _ _ zenon_Hec); [ zenon_intro zenon_H68 | zenon_intro zenon_Hed ]. % 15.41/15.56 apply (zenon_or_s _ _ zenon_H58); [ zenon_intro zenon_H5b | zenon_intro zenon_H5a ]. % 15.41/15.56 exact (zenon_H59 zenon_H5b). % 15.41/15.56 apply (zenon_or_s _ _ zenon_H5a); [ zenon_intro zenon_H4a | zenon_intro zenon_H5c ]. % 15.41/15.56 apply (zenon_or_s _ _ zenon_Hbe); [ zenon_intro zenon_H5b | zenon_intro zenon_Hbf ]. % 15.41/15.56 exact (zenon_H59 zenon_H5b). % 15.41/15.56 apply (zenon_or_s _ _ zenon_Hbf); [ zenon_intro zenon_H69 | zenon_intro zenon_Hc0 ]. % 15.41/15.56 apply (zenon_L17_); trivial. % 15.41/15.56 apply (zenon_or_s _ _ zenon_Hc0); [ zenon_intro zenon_Haf | zenon_intro zenon_Hba ]. % 15.41/15.56 apply (zenon_L859_); trivial. % 15.41/15.56 apply (zenon_L79_); trivial. % 15.41/15.56 apply (zenon_or_s _ _ zenon_H5c); [ zenon_intro zenon_H50 | zenon_intro zenon_H53 ]. % 15.41/15.56 apply (zenon_L31_); trivial. % 15.41/15.56 apply (zenon_L294_); trivial. % 15.41/15.56 apply (zenon_or_s _ _ zenon_Hed); [ zenon_intro zenon_Hdd | zenon_intro zenon_He9 ]. % 15.41/15.56 apply (zenon_L812_); trivial. % 15.41/15.56 apply (zenon_L122_); trivial. % 15.41/15.56 (* end of lemma zenon_L860_ *) % 15.41/15.56 assert (zenon_L861_ : (~((op (e3) (e0)) = (op (e3) (e3)))) -> (~((op (e0) (e0)) = (e1))) -> ((~((op (e1) (e1)) = (e1)))\/((op (e1) (e1)) = (e1))) -> (~((op (e1) (e0)) = (op (e1) (e1)))) -> ((~((op (e1) (e1)) = (e3)))\/((op (e1) (e3)) = (e1))) -> (~((op (e3) (e1)) = (op (e3) (e3)))) -> (~((e0) = (e3))) -> (((op (e0) (e1)) = (e1))\/(((op (e1) (e1)) = (e1))\/(((op (e2) (e1)) = (e1))\/((op (e3) (e1)) = (e1))))) -> (~((op (e1) (e0)) = (op (e1) (e2)))) -> (((op (e0) (e1)) = (e3))\/(((op (e1) (e1)) = (e3))\/(((op (e2) (e1)) = (e3))\/((op (e3) (e1)) = (e3))))) -> (~((op (e3) (e0)) = (op (e3) (e1)))) -> (((op (e0) (e0)) = (e1))\/(((op (e0) (e1)) = (e1))\/(((op (e0) (e2)) = (e1))\/((op (e0) (e3)) = (e1))))) -> ((~((op (e3) (e3)) = (e3)))\/((op (e3) (e3)) = (e3))) -> ((~((op (e2) (e2)) = (e2)))\/((op (e2) (e2)) = (e2))) -> (((op (e1) (e0)) = (e2))\/(((op (e1) (e1)) = (e2))\/(((op (e1) (e2)) = (e2))\/((op (e1) (e3)) = (e2))))) -> (~((op (e0) (e2)) = (op (e2) (e2)))) -> (((op (e0) (e3)) = (e0))\/(((op (e0) (e3)) = (e1))\/(((op (e0) (e3)) = (e2))\/((op (e0) (e3)) = (e3))))) -> (~((op (e0) (e3)) = (op (e1) (e3)))) -> (~((op (e0) (e3)) = (op (e2) (e3)))) -> (~((op (e0) (e0)) = (op (e0) (e3)))) -> (~((op (e1) (e2)) = (op (e2) (e2)))) -> ((~((op (e3) (e3)) = (e1)))\/((op (e3) (e1)) = (e3))) -> ((~((op (e2) (e2)) = (e3)))\/((op (e2) (e3)) = (e2))) -> (((op (e2) (e0)) = (e3))\/(((op (e2) (e1)) = (e3))\/(((op (e2) (e2)) = (e3))\/((op (e2) (e3)) = (e3))))) -> (~((op (e0) (e1)) = (op (e2) (e1)))) -> (~((op (e1) (e3)) = (op (e3) (e3)))) -> (((op (e2) (e2)) = (e0))\/(((op (e2) (e2)) = (e1))\/(((op (e2) (e2)) = (e2))\/((op (e2) (e2)) = (e3))))) -> (~((op (e0) (e0)) = (op (e2) (e0)))) -> (((op (e2) (e0)) = (e1))\/(((op (e2) (e1)) = (e1))\/(((op (e2) (e2)) = (e1))\/((op (e2) (e3)) = (e1))))) -> (~((op (e1) (op (e2) (e1))) = (op (e2) (e1)))) -> (~((e0) = (e2))) -> (((op (e2) (e0)) = (e0))\/(((op (e2) (e1)) = (e0))\/(((op (e2) (e2)) = (e0))\/((op (e2) (e3)) = (e0))))) -> (~((op (e2) (e1)) = (op (e2) (e2)))) -> (~((op (e2) (e1)) = (op (e2) (e3)))) -> ((~((op (e2) (e2)) = (e1)))\/((op (e2) (e1)) = (e2))) -> (~((op (e0) (e0)) = (e2))) -> (~((e1) = (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) (e0)) = (e3))) -> (~((e2) = (e3))) -> (((op (e1) (e0)) = (e3))\/(((op (e1) (e1)) = (e3))\/(((op (e1) (e2)) = (e3))\/((op (e1) (e3)) = (e3))))) -> (~((op (e0) (e1)) = (op (e0) (e3)))) -> (~((op (e2) (e0)) = (op (e2) (e3)))) -> (((op (e0) (e3)) = (e2))\/(((op (e1) (e3)) = (e2))\/(((op (e2) (e3)) = (e2))\/((op (e3) (e3)) = (e2))))) -> (~((op (e0) (e2)) = (op (e1) (e2)))) -> (~((e1) = (e3))) -> (((op (e0) (e0)) = (e3))\/(((op (e1) (e0)) = (e3))\/(((op (e2) (e0)) = (e3))\/((op (e3) (e0)) = (e3))))) -> (~((op (e0) (e1)) = (op (e3) (e1)))) -> (((op (e0) (e2)) = (e0))\/(((op (e0) (e2)) = (e1))\/(((op (e0) (e2)) = (e2))\/((op (e0) (e2)) = (e3))))) -> (((op (e3) (e0)) = (e1))\/(((op (e3) (e1)) = (e1))\/(((op (e3) (e2)) = (e1))\/((op (e3) (e3)) = (e1))))) -> (~((op (e0) (e2)) = (op (e3) (e2)))) -> (((op (e0) (e3)) = (e1))\/(((op (e1) (e3)) = (e1))\/(((op (e2) (e3)) = (e1))\/((op (e3) (e3)) = (e1))))) -> (~((op (e3) (op (e2) (e3))) = (op (e2) (e3)))) -> (~((op (e1) (e0)) = (op (e1) (e3)))) -> (~((op (e0) (e2)) = (op (e0) (e3)))) -> (~((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 (e3) (e0)))) -> (~((op (e2) (e0)) = (op (e2) (e1)))) -> (((op (e0) (e1)) = (e2))\/(((op (e1) (e1)) = (e2))\/(((op (e2) (e1)) = (e2))\/((op (e3) (e1)) = (e2))))) -> (((op (e0) (e0)) = (e2))\/(((op (e0) (e1)) = (e2))\/(((op (e0) (e2)) = (e2))\/((op (e0) (e3)) = (e2))))) -> ((op (e0) (e0)) = (e0)) -> (~((op (e0) (e0)) = (op (e0) (e2)))) -> (((op (e3) (e0)) = (e2))\/(((op (e3) (e1)) = (e2))\/(((op (e3) (e2)) = (e2))\/((op (e3) (e3)) = (e2))))) -> (~((op (e0) (op (e2) (e0))) = (op (e2) (e0)))) -> (((op (e0) (e0)) = (e3))\/(((op (e0) (e1)) = (e3))\/(((op (e0) (e2)) = (e3))\/((op (e0) (e3)) = (e3))))) -> (((op (e1) (e1)) = (e0))\/(((op (e1) (e1)) = (e1))\/(((op (e1) (e1)) = (e2))\/((op (e1) (e1)) = (e3))))) -> (((op (e0) (e0)) = (e2))\/(((op (e1) (e0)) = (e2))\/(((op (e2) (e0)) = (e2))\/((op (e3) (e0)) = (e2))))) -> (~((op (e1) (e2)) = (op (e3) (e2)))) -> (((op (e0) (e0)) = (e1))\/(((op (e1) (e0)) = (e1))\/(((op (e2) (e0)) = (e1))\/((op (e3) (e0)) = (e1))))) -> (~((op (e3) (e0)) = (op (e3) (e2)))) -> ((~((op (e3) (e3)) = (e2)))\/((op (e3) (e2)) = (e3))) -> ((~((op (e3) (e3)) = (e0)))\/((op (e3) (e0)) = (e3))) -> (~((op (e2) (op (e2) (e2))) = (op (e2) (e2)))) -> (~((op (e2) (e0)) = (op (e2) (e2)))) -> ((~((op (e2) (e2)) = (e0)))\/((op (e2) (e0)) = (e2))) -> ((~((op (e1) (e1)) = (e2)))\/((op (e1) (e2)) = (e1))) -> (((op (e0) (e3)) = (e0))\/(((op (e1) (e3)) = (e0))\/(((op (e2) (e3)) = (e0))\/((op (e3) (e3)) = (e0))))) -> (~((op (e2) (e2)) = (e0))) -> (~((op (e2) (e2)) = (e1))) -> (~((op (e2) (e2)) = (e2))) -> ((op (e2) (e3)) = (e2)) -> ((op (e3) (e0)) = (e3)) -> False). % 15.41/15.56 do 0 intro. intros zenon_Hbb zenon_H45 zenon_H1d8 zenon_Hd7 zenon_H1d2 zenon_H12d zenon_H4b zenon_H228 zenon_H166 zenon_H199 zenon_H109 zenon_H44 zenon_H10d zenon_Haa zenon_H84 zenon_H28 zenon_H254 zenon_H80 zenon_Hb4 zenon_H24f zenon_H7d zenon_H10c zenon_H1c3 zenon_He6 zenon_Hde zenon_H8b zenon_H2d zenon_H258 zenon_Hb7 zenon_H290 zenon_H5e zenon_H1f5 zenon_H157 zenon_H1e2 zenon_H1e3 zenon_H8f zenon_Ha7 zenon_H36 zenon_H3b zenon_H59 zenon_H6a zenon_H90 zenon_H1cd zenon_Hce zenon_H160 zenon_H87 zenon_Ha3 zenon_Hbe zenon_H138 zenon_H251 zenon_H146 zenon_H140 zenon_H121 zenon_H28a zenon_H1cf zenon_Hc9 zenon_H135 zenon_H11b zenon_H22e zenon_H154 zenon_H1a2 zenon_H8e zenon_H1f zenon_H250 zenon_H1df zenon_H295 zenon_H58 zenon_H1b3 zenon_Heb zenon_H17d zenon_Hf1 zenon_H105 zenon_H10e zenon_H10f zenon_H294 zenon_H17a zenon_H1d4 zenon_H1d3 zenon_Hd3 zenon_H2e zenon_H52 zenon_H2f zenon_H124 zenon_Hba. % 15.41/15.56 apply (zenon_or_s _ _ zenon_H10c); [ zenon_intro zenon_H104 | zenon_intro zenon_H10a ]. % 15.41/15.56 apply (zenon_or_s _ _ zenon_H10e); [ zenon_intro zenon_H3d | zenon_intro zenon_H106 ]. % 15.41/15.56 apply (zenon_or_s _ _ zenon_H10d); [ zenon_intro zenon_H3e | zenon_intro zenon_H42 ]. % 15.41/15.56 apply (zenon_or_s _ _ zenon_Hf1); [ zenon_intro zenon_H47 | zenon_intro zenon_Hf4 ]. % 15.41/15.56 exact (zenon_H45 zenon_H47). % 15.41/15.56 apply (zenon_or_s _ _ zenon_Hf4); [ zenon_intro zenon_Hd8 | zenon_intro zenon_Hf5 ]. % 15.41/15.56 apply (zenon_L845_); trivial. % 15.41/15.56 apply (zenon_or_s _ _ zenon_Hf5); [ zenon_intro zenon_Hae | zenon_intro zenon_Hee ]. % 15.41/15.56 apply (zenon_L684_); trivial. % 15.41/15.56 apply (zenon_L79_); trivial. % 15.41/15.56 apply (zenon_L43_); trivial. % 15.41/15.56 apply (zenon_L81_); trivial. % 15.41/15.56 apply (zenon_L82_); trivial. % 15.41/15.56 (* end of lemma zenon_L861_ *) % 15.41/15.56 assert (zenon_L862_ : (((op (e0) (e0)) = (e1))\/(((op (e1) (e0)) = (e1))\/(((op (e2) (e0)) = (e1))\/((op (e3) (e0)) = (e1))))) -> (~((op (e0) (e0)) = (e1))) -> (((op (e1) (e0)) = (e2))\/(((op (e1) (e1)) = (e2))\/(((op (e1) (e2)) = (e2))\/((op (e1) (e3)) = (e2))))) -> (~((op (e1) (op (e2) (e1))) = (op (e2) (e1)))) -> (((op (e0) (e1)) = (e3))\/(((op (e1) (e1)) = (e3))\/(((op (e2) (e1)) = (e3))\/((op (e3) (e1)) = (e3))))) -> (~((op (e0) (e2)) = (op (e1) (e2)))) -> (((op (e1) (e0)) = (e3))\/(((op (e1) (e1)) = (e3))\/(((op (e1) (e2)) = (e3))\/((op (e1) (e3)) = (e3))))) -> (~((op (e0) (e1)) = (op (e0) (e3)))) -> (((op (e0) (e1)) = (e2))\/(((op (e1) (e1)) = (e2))\/(((op (e2) (e1)) = (e2))\/((op (e3) (e1)) = (e2))))) -> (~((op (e0) (e3)) = (op (e1) (e3)))) -> (((op (e0) (e0)) = (e3))\/(((op (e0) (e1)) = (e3))\/(((op (e0) (e2)) = (e3))\/((op (e0) (e3)) = (e3))))) -> (~((op (e0) (e1)) = (op (e2) (e1)))) -> (((op (e0) (e0)) = (e2))\/(((op (e0) (e1)) = (e2))\/(((op (e0) (e2)) = (e2))\/((op (e0) (e3)) = (e2))))) -> ((op (e0) (e1)) = (e1)) -> (~((op (e0) (op (e2) (e0))) = (op (e2) (e0)))) -> (((op (e0) (e0)) = (e2))\/(((op (e1) (e0)) = (e2))\/(((op (e2) (e0)) = (e2))\/((op (e3) (e0)) = (e2))))) -> (~((op (e0) (e0)) = (e2))) -> (~((e1) = (e3))) -> (((op (e1) (e1)) = (e0))\/(((op (e1) (e1)) = (e1))\/(((op (e1) (e1)) = (e2))\/((op (e1) (e1)) = (e3))))) -> (~((op (e2) (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) (e1)) = (e1))) -> (~((op (e1) (e1)) = (e2))) -> (~((op (e1) (e1)) = (e3))) -> (~((e2) = (e3))) -> (~((op (e0) (e0)) = (e3))) -> (((op (e0) (e0)) = (e3))\/(((op (e1) (e0)) = (e3))\/(((op (e2) (e0)) = (e3))\/((op (e3) (e0)) = (e3))))) -> ((op (e2) (e1)) = (e2)) -> (~((op (e2) (e0)) = (op (e2) (e1)))) -> (~((e1) = (e2))) -> False). % 15.41/15.56 do 0 intro. intros zenon_Hf1 zenon_H45 zenon_H84 zenon_H290 zenon_H199 zenon_H87 zenon_H90 zenon_H1cd zenon_H1a2 zenon_H80 zenon_H58 zenon_Hde zenon_H8e zenon_H22 zenon_H295 zenon_Heb zenon_H8f zenon_Ha3 zenon_H1b3 zenon_H30 zenon_H2f zenon_H2e zenon_H2d zenon_H1b4 zenon_Hd6 zenon_H182 zenon_H6a zenon_H59 zenon_Hbe zenon_H156 zenon_H154 zenon_Ha7. % 15.41/15.56 apply (zenon_or_s _ _ zenon_Hf1); [ zenon_intro zenon_H47 | zenon_intro zenon_Hf4 ]. % 15.41/15.56 exact (zenon_H45 zenon_H47). % 15.41/15.56 apply (zenon_or_s _ _ zenon_Hf4); [ zenon_intro zenon_Hd8 | zenon_intro zenon_Hf5 ]. % 15.41/15.56 apply (zenon_L841_); trivial. % 15.41/15.56 apply (zenon_or_s _ _ zenon_Hf5); [ zenon_intro zenon_Hae | zenon_intro zenon_Hee ]. % 15.41/15.56 apply (zenon_L816_); trivial. % 15.41/15.56 apply (zenon_L624_); trivial. % 15.41/15.56 (* end of lemma zenon_L862_ *) % 15.41/15.56 assert (zenon_L863_ : (((op (e1) (e0)) = (e2))\/(((op (e1) (e1)) = (e2))\/(((op (e1) (e2)) = (e2))\/((op (e1) (e3)) = (e2))))) -> (~((e2) = (e3))) -> ((op (e1) (e0)) = (e3)) -> (~((op (e1) (e1)) = (e2))) -> ((op (e2) (e1)) = (e2)) -> (~((op (e1) (op (e2) (e1))) = (op (e2) (e1)))) -> ((op (e1) (e3)) = (e0)) -> (~((e0) = (e2))) -> False). % 15.41/15.56 do 0 intro. intros zenon_H84 zenon_H6a zenon_H69 zenon_Hd6 zenon_H156 zenon_H290 zenon_Hcc zenon_H5e. % 15.41/15.56 apply (zenon_or_s _ _ zenon_H84); [ zenon_intro zenon_H68 | zenon_intro zenon_H85 ]. % 15.41/15.56 apply (zenon_L17_); trivial. % 15.41/15.56 apply (zenon_or_s _ _ zenon_H85); [ zenon_intro zenon_H6e | zenon_intro zenon_H86 ]. % 15.41/15.56 exact (zenon_Hd6 zenon_H6e). % 15.41/15.56 apply (zenon_or_s _ _ zenon_H86); [ zenon_intro zenon_H7c | zenon_intro zenon_H82 ]. % 15.41/15.56 apply (zenon_L824_); trivial. % 15.41/15.56 apply (zenon_L54_); trivial. % 15.41/15.56 (* end of lemma zenon_L863_ *) % 15.41/15.56 assert (zenon_L864_ : ((~((op (e2) (e2)) = (e0)))\/((op (e2) (e0)) = (e2))) -> (~((op (e2) (e0)) = (op (e2) (e2)))) -> (~((op (e2) (op (e2) (e2))) = (op (e2) (e2)))) -> ((~((op (e3) (e3)) = (e0)))\/((op (e3) (e0)) = (e3))) -> ((~((op (e3) (e3)) = (e2)))\/((op (e3) (e2)) = (e3))) -> (~((op (e0) (e0)) = (e1))) -> (((op (e0) (e0)) = (e1))\/(((op (e1) (e0)) = (e1))\/(((op (e2) (e0)) = (e1))\/((op (e3) (e0)) = (e1))))) -> (~((op (e1) (e2)) = (op (e3) (e2)))) -> (((op (e0) (e0)) = (e3))\/(((op (e0) (e1)) = (e3))\/(((op (e0) (e2)) = (e3))\/((op (e0) (e3)) = (e3))))) -> (((op (e3) (e0)) = (e2))\/(((op (e3) (e1)) = (e2))\/(((op (e3) (e2)) = (e2))\/((op (e3) (e3)) = (e2))))) -> (~((op (e0) (e0)) = (op (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) (e0)) = (op (e3) (e0)))) -> (((op (e0) (e2)) = (e1))\/(((op (e1) (e2)) = (e1))\/(((op (e2) (e2)) = (e1))\/((op (e3) (e2)) = (e1))))) -> (~((op (e3) (e1)) = (op (e3) (e2)))) -> (~((op (e0) (e2)) = (op (e0) (e3)))) -> (~((op (e1) (e0)) = (op (e1) (e3)))) -> (~((op (e3) (op (e2) (e3))) = (op (e2) (e3)))) -> (((op (e0) (e3)) = (e1))\/(((op (e1) (e3)) = (e1))\/(((op (e2) (e3)) = (e1))\/((op (e3) (e3)) = (e1))))) -> (~((op (e0) (e2)) = (op (e3) (e2)))) -> (((op (e3) (e0)) = (e1))\/(((op (e3) (e1)) = (e1))\/(((op (e3) (e2)) = (e1))\/((op (e3) (e3)) = (e1))))) -> (((op (e0) (e2)) = (e0))\/(((op (e0) (e2)) = (e1))\/(((op (e0) (e2)) = (e2))\/((op (e0) (e2)) = (e3))))) -> (~((op (e0) (e1)) = (op (e3) (e1)))) -> (~((op (e0) (e2)) = (op (e1) (e2)))) -> (((op (e0) (e3)) = (e2))\/(((op (e1) (e3)) = (e2))\/(((op (e2) (e3)) = (e2))\/((op (e3) (e3)) = (e2))))) -> (~((op (e2) (e0)) = (op (e2) (e3)))) -> (((op (e1) (e0)) = (e3))\/(((op (e1) (e1)) = (e3))\/(((op (e1) (e2)) = (e3))\/((op (e1) (e3)) = (e3))))) -> (~((op (e0) (e3)) = (op (e3) (e3)))) -> ((~((op (e2) (e2)) = (e1)))\/((op (e2) (e1)) = (e2))) -> (~((op (e2) (e1)) = (op (e2) (e3)))) -> (~((op (e2) (e1)) = (op (e2) (e2)))) -> (((op (e2) (e0)) = (e0))\/(((op (e2) (e1)) = (e0))\/(((op (e2) (e2)) = (e0))\/((op (e2) (e3)) = (e0))))) -> (((op (e2) (e0)) = (e1))\/(((op (e2) (e1)) = (e1))\/(((op (e2) (e2)) = (e1))\/((op (e2) (e3)) = (e1))))) -> (~((op (e0) (e0)) = (op (e2) (e0)))) -> (((op (e2) (e2)) = (e0))\/(((op (e2) (e2)) = (e1))\/(((op (e2) (e2)) = (e2))\/((op (e2) (e2)) = (e3))))) -> (~((op (e1) (e3)) = (op (e3) (e3)))) -> (((op (e2) (e0)) = (e3))\/(((op (e2) (e1)) = (e3))\/(((op (e2) (e2)) = (e3))\/((op (e2) (e3)) = (e3))))) -> ((~((op (e2) (e2)) = (e3)))\/((op (e2) (e3)) = (e2))) -> ((~((op (e3) (e3)) = (e1)))\/((op (e3) (e1)) = (e3))) -> (~((op (e1) (e2)) = (op (e2) (e2)))) -> (~((op (e0) (e0)) = (op (e0) (e3)))) -> (~((op (e0) (e3)) = (op (e2) (e3)))) -> (~((op (e0) (e3)) = (op (e1) (e3)))) -> (((op (e0) (e3)) = (e0))\/(((op (e0) (e3)) = (e1))\/(((op (e0) (e3)) = (e2))\/((op (e0) (e3)) = (e3))))) -> (~((op (e0) (e2)) = (op (e2) (e2)))) -> ((~((op (e2) (e2)) = (e2)))\/((op (e2) (e2)) = (e2))) -> ((~((op (e3) (e3)) = (e3)))\/((op (e3) (e3)) = (e3))) -> (((op (e0) (e0)) = (e1))\/(((op (e0) (e1)) = (e1))\/(((op (e0) (e2)) = (e1))\/((op (e0) (e3)) = (e1))))) -> (((op (e0) (e1)) = (e3))\/(((op (e1) (e1)) = (e3))\/(((op (e2) (e1)) = (e3))\/((op (e3) (e1)) = (e3))))) -> (~((op (e1) (e0)) = (op (e1) (e2)))) -> (~((e0) = (e3))) -> (~((op (e3) (e1)) = (op (e3) (e3)))) -> ((~((op (e1) (e1)) = (e3)))\/((op (e1) (e3)) = (e1))) -> (((op (e0) (e0)) = (e2))\/(((op (e1) (e0)) = (e2))\/(((op (e2) (e0)) = (e2))\/((op (e3) (e0)) = (e2))))) -> (~((op (e0) (e0)) = (e2))) -> ((op (e3) (e2)) = (e3)) -> (~((op (e3) (e0)) = (op (e3) (e2)))) -> (~((op (e0) (op (e2) (e0))) = (op (e2) (e0)))) -> (((op (e0) (e0)) = (e3))\/(((op (e1) (e0)) = (e3))\/(((op (e2) (e0)) = (e3))\/((op (e3) (e0)) = (e3))))) -> (~((op (e0) (e0)) = (e3))) -> (~((e0) = (e2))) -> (~((op (e1) (op (e2) (e1))) = (op (e2) (e1)))) -> (~((op (e1) (e1)) = (e2))) -> (((op (e1) (e0)) = (e2))\/(((op (e1) (e1)) = (e2))\/(((op (e1) (e2)) = (e2))\/((op (e1) (e3)) = (e2))))) -> (((op (e1) (e1)) = (e0))\/(((op (e1) (e1)) = (e1))\/(((op (e1) (e1)) = (e2))\/((op (e1) (e1)) = (e3))))) -> (~((op (e1) (e1)) = (e0))) -> (((op (e3) (e3)) = (e0))\/(((op (e3) (e3)) = (e1))\/(((op (e3) (e3)) = (e2))\/((op (e3) (e3)) = (e3))))) -> (~((op (e3) (e3)) = (e0))) -> (~((op (e3) (e3)) = (e1))) -> (~((op (e3) (e3)) = (e3))) -> (~((op (e0) (e0)) = (op (e1) (e0)))) -> ((op (e0) (e0)) = (e0)) -> (((op (e1) (e0)) = (e0))\/(((op (e1) (e1)) = (e0))\/(((op (e1) (e2)) = (e0))\/((op (e1) (e3)) = (e0))))) -> (~((e1) = (e3))) -> (~((e2) = (e3))) -> (~((op (e0) (e1)) = (op (e2) (e1)))) -> (((op (e0) (e0)) = (e2))\/(((op (e0) (e1)) = (e2))\/(((op (e0) (e2)) = (e2))\/((op (e0) (e3)) = (e2))))) -> (((op (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 (e2) (e1)) = (e2)) -> (~((e1) = (e2))) -> (~((op (e3) (e0)) = (op (e3) (e1)))) -> False). % 15.41/15.56 do 0 intro. intros zenon_H1d4 zenon_H17a zenon_H294 zenon_H10f zenon_H10e zenon_H45 zenon_Hf1 zenon_H17d zenon_H58 zenon_H1df zenon_H250 zenon_H1a2 zenon_H154 zenon_H22e zenon_H11b zenon_H135 zenon_Hc9 zenon_H1cf zenon_H28a zenon_H121 zenon_H140 zenon_H146 zenon_H251 zenon_H138 zenon_H87 zenon_H160 zenon_Hce zenon_H90 zenon_H36 zenon_H1e3 zenon_H1e2 zenon_H157 zenon_H1f5 zenon_Hb7 zenon_H258 zenon_H2d zenon_H8b zenon_He6 zenon_H1c3 zenon_H10c zenon_H7d zenon_H24f zenon_Hb4 zenon_H80 zenon_H254 zenon_H28 zenon_Haa zenon_H10d zenon_H44 zenon_H199 zenon_H166 zenon_H4b zenon_H12d zenon_H1d2 zenon_Heb zenon_H8f zenon_H106 zenon_H105 zenon_H295 zenon_Hbe zenon_H59 zenon_H5e zenon_H290 zenon_Hd6 zenon_H84 zenon_H1b3 zenon_H145 zenon_H3b zenon_H3c zenon_H104 zenon_H3e zenon_H24c zenon_H1f zenon_H163 zenon_Ha3 zenon_H6a zenon_Hde zenon_H8e zenon_H228 zenon_H1cd zenon_H37 zenon_H1b4 zenon_H156 zenon_Ha7 zenon_H109. % 15.41/15.56 apply (zenon_or_s _ _ zenon_Hf1); [ zenon_intro zenon_H47 | zenon_intro zenon_Hf4 ]. % 15.41/15.56 exact (zenon_H45 zenon_H47). % 15.41/15.56 apply (zenon_or_s _ _ zenon_Hf4); [ zenon_intro zenon_Hd8 | zenon_intro zenon_Hf5 ]. % 15.41/15.56 apply (zenon_L844_); trivial. % 15.41/15.56 apply (zenon_or_s _ _ zenon_Hf5); [ zenon_intro zenon_Hae | zenon_intro zenon_Hee ]. % 15.41/15.56 apply (zenon_or_s _ _ zenon_H8e); [ zenon_intro zenon_H92 | zenon_intro zenon_H91 ]. % 15.41/15.56 exact (zenon_H8f zenon_H92). % 15.41/15.56 apply (zenon_or_s _ _ zenon_H91); [ zenon_intro zenon_H5d | zenon_intro zenon_H93 ]. % 15.41/15.56 apply (zenon_L251_); trivial. % 15.41/15.56 apply (zenon_or_s _ _ zenon_H93); [ zenon_intro zenon_H63 | zenon_intro zenon_H81 ]. % 15.41/15.56 apply (zenon_or_s _ _ zenon_Heb); [ zenon_intro zenon_H92 | zenon_intro zenon_Hec ]. % 15.41/15.56 exact (zenon_H8f zenon_H92). % 15.41/15.56 apply (zenon_or_s _ _ zenon_Hec); [ zenon_intro zenon_H68 | zenon_intro zenon_Hed ]. % 15.41/15.56 apply (zenon_L528_); trivial. % 15.41/15.56 apply (zenon_or_s _ _ zenon_Hed); [ zenon_intro zenon_Hdd | zenon_intro zenon_He9 ]. % 15.41/15.56 apply (zenon_L812_); trivial. % 15.41/15.56 apply (zenon_or_s _ _ zenon_Hbe); [ zenon_intro zenon_H5b | zenon_intro zenon_Hbf ]. % 15.41/15.56 exact (zenon_H59 zenon_H5b). % 15.41/15.56 apply (zenon_or_s _ _ zenon_Hbf); [ zenon_intro zenon_H69 | zenon_intro zenon_Hc0 ]. % 15.41/15.56 apply (zenon_or_s _ _ zenon_H163); [ zenon_intro zenon_Had | zenon_intro zenon_H164 ]. % 15.41/15.56 apply (zenon_L559_); trivial. % 15.41/15.56 apply (zenon_or_s _ _ zenon_H164); [ zenon_intro zenon_H149 | zenon_intro zenon_H165 ]. % 15.41/15.56 exact (zenon_H145 zenon_H149). % 15.41/15.56 apply (zenon_or_s _ _ zenon_H165); [ zenon_intro zenon_H15d | zenon_intro zenon_Hcc ]. % 15.41/15.56 apply (zenon_L490_); trivial. % 15.41/15.56 apply (zenon_L863_); trivial. % 15.41/15.56 apply (zenon_or_s _ _ zenon_Hc0); [ zenon_intro zenon_Haf | zenon_intro zenon_Hba ]. % 15.41/15.56 apply (zenon_L39_); trivial. % 15.41/15.56 apply (zenon_L220_); trivial. % 15.41/15.56 apply (zenon_L33_); trivial. % 15.41/15.56 apply (zenon_L618_); trivial. % 15.41/15.56 (* end of lemma zenon_L864_ *) % 15.41/15.56 assert (zenon_L865_ : (~((op (e0) (e0)) = (e1))) -> ((op (e3) (e0)) = (e3)) -> ((~((op (e1) (e1)) = (e2)))\/((op (e1) (e2)) = (e1))) -> ((~((op (e2) (e2)) = (e0)))\/((op (e2) (e0)) = (e2))) -> (~((op (e2) (e0)) = (op (e2) (e2)))) -> (~((op (e2) (op (e2) (e2))) = (op (e2) (e2)))) -> ((~((op (e3) (e3)) = (e0)))\/((op (e3) (e0)) = (e3))) -> ((~((op (e3) (e3)) = (e2)))\/((op (e3) (e2)) = (e3))) -> (~((op (e3) (e0)) = (op (e3) (e2)))) -> (((op (e0) (e0)) = (e1))\/(((op (e1) (e0)) = (e1))\/(((op (e2) (e0)) = (e1))\/((op (e3) (e0)) = (e1))))) -> (~((op (e1) (e2)) = (op (e3) (e2)))) -> (((op (e0) (e0)) = (e2))\/(((op (e1) (e0)) = (e2))\/(((op (e2) (e0)) = (e2))\/((op (e3) (e0)) = (e2))))) -> (((op (e1) (e1)) = (e0))\/(((op (e1) (e1)) = (e1))\/(((op (e1) (e1)) = (e2))\/((op (e1) (e1)) = (e3))))) -> (((op (e0) (e0)) = (e3))\/(((op (e0) (e1)) = (e3))\/(((op (e0) (e2)) = (e3))\/((op (e0) (e3)) = (e3))))) -> (~((op (e0) (op (e2) (e0))) = (op (e2) (e0)))) -> (((op (e3) (e0)) = (e2))\/(((op (e3) (e1)) = (e2))\/(((op (e3) (e2)) = (e2))\/((op (e3) (e3)) = (e2))))) -> (~((op (e0) (e0)) = (op (e0) (e2)))) -> ((op (e0) (e0)) = (e0)) -> (((op (e0) (e0)) = (e2))\/(((op (e0) (e1)) = (e2))\/(((op (e0) (e2)) = (e2))\/((op (e0) (e3)) = (e2))))) -> (((op (e0) (e1)) = (e2))\/(((op (e1) (e1)) = (e2))\/(((op (e2) (e1)) = (e2))\/((op (e3) (e1)) = (e2))))) -> (~((op (e2) (e0)) = (op (e2) (e1)))) -> (~((op (e1) (e0)) = (op (e3) (e0)))) -> (((op (e0) (e2)) = (e1))\/(((op (e1) (e2)) = (e1))\/(((op (e2) (e2)) = (e1))\/((op (e3) (e2)) = (e1))))) -> (~((op (e3) (e1)) = (op (e3) (e2)))) -> (~((op (e0) (e2)) = (op (e0) (e3)))) -> (~((op (e1) (e0)) = (op (e1) (e3)))) -> (~((op (e3) (op (e2) (e3))) = (op (e2) (e3)))) -> (((op (e0) (e3)) = (e1))\/(((op (e1) (e3)) = (e1))\/(((op (e2) (e3)) = (e1))\/((op (e3) (e3)) = (e1))))) -> (~((op (e0) (e2)) = (op (e3) (e2)))) -> (((op (e3) (e0)) = (e1))\/(((op (e3) (e1)) = (e1))\/(((op (e3) (e2)) = (e1))\/((op (e3) (e3)) = (e1))))) -> (((op (e0) (e2)) = (e0))\/(((op (e0) (e2)) = (e1))\/(((op (e0) (e2)) = (e2))\/((op (e0) (e2)) = (e3))))) -> (~((op (e0) (e1)) = (op (e3) (e1)))) -> (((op (e0) (e0)) = (e3))\/(((op (e1) (e0)) = (e3))\/(((op (e2) (e0)) = (e3))\/((op (e3) (e0)) = (e3))))) -> (~((e1) = (e3))) -> (~((op (e0) (e2)) = (op (e1) (e2)))) -> (((op (e0) (e3)) = (e2))\/(((op (e1) (e3)) = (e2))\/(((op (e2) (e3)) = (e2))\/((op (e3) (e3)) = (e2))))) -> (~((op (e2) (e0)) = (op (e2) (e3)))) -> (~((op (e0) (e1)) = (op (e0) (e3)))) -> (((op (e1) (e0)) = (e3))\/(((op (e1) (e1)) = (e3))\/(((op (e1) (e2)) = (e3))\/((op (e1) (e3)) = (e3))))) -> (~((e2) = (e3))) -> (~((op (e0) (e0)) = (e3))) -> (((op (e3) (e3)) = (e0))\/(((op (e3) (e3)) = (e1))\/(((op (e3) (e3)) = (e2))\/((op (e3) (e3)) = (e3))))) -> (~((op (e0) (e3)) = (op (e3) (e3)))) -> (~((e1) = (e2))) -> (~((op (e0) (e0)) = (e2))) -> ((~((op (e2) (e2)) = (e1)))\/((op (e2) (e1)) = (e2))) -> (~((op (e2) (e1)) = (op (e2) (e3)))) -> (~((op (e2) (e1)) = (op (e2) (e2)))) -> (((op (e2) (e0)) = (e0))\/(((op (e2) (e1)) = (e0))\/(((op (e2) (e2)) = (e0))\/((op (e2) (e3)) = (e0))))) -> (~((e0) = (e2))) -> (~((op (e1) (op (e2) (e1))) = (op (e2) (e1)))) -> (((op (e2) (e0)) = (e1))\/(((op (e2) (e1)) = (e1))\/(((op (e2) (e2)) = (e1))\/((op (e2) (e3)) = (e1))))) -> (~((op (e0) (e0)) = (op (e2) (e0)))) -> (((op (e2) (e2)) = (e0))\/(((op (e2) (e2)) = (e1))\/(((op (e2) (e2)) = (e2))\/((op (e2) (e2)) = (e3))))) -> (~((op (e1) (e3)) = (op (e3) (e3)))) -> (~((op (e0) (e1)) = (op (e2) (e1)))) -> (((op (e2) (e0)) = (e3))\/(((op (e2) (e1)) = (e3))\/(((op (e2) (e2)) = (e3))\/((op (e2) (e3)) = (e3))))) -> ((~((op (e2) (e2)) = (e3)))\/((op (e2) (e3)) = (e2))) -> ((~((op (e3) (e3)) = (e1)))\/((op (e3) (e1)) = (e3))) -> (~((op (e1) (e2)) = (op (e2) (e2)))) -> (~((op (e0) (e0)) = (op (e0) (e3)))) -> (~((op (e0) (e3)) = (op (e2) (e3)))) -> (~((op (e0) (e3)) = (op (e1) (e3)))) -> (((op (e0) (e3)) = (e0))\/(((op (e0) (e3)) = (e1))\/(((op (e0) (e3)) = (e2))\/((op (e0) (e3)) = (e3))))) -> (~((op (e0) (e2)) = (op (e2) (e2)))) -> (((op (e1) (e0)) = (e2))\/(((op (e1) (e1)) = (e2))\/(((op (e1) (e2)) = (e2))\/((op (e1) (e3)) = (e2))))) -> ((~((op (e2) (e2)) = (e2)))\/((op (e2) (e2)) = (e2))) -> ((~((op (e3) (e3)) = (e3)))\/((op (e3) (e3)) = (e3))) -> (((op (e0) (e0)) = (e1))\/(((op (e0) (e1)) = (e1))\/(((op (e0) (e2)) = (e1))\/((op (e0) (e3)) = (e1))))) -> (~((op (e3) (e0)) = (op (e3) (e1)))) -> (((op (e0) (e1)) = (e3))\/(((op (e1) (e1)) = (e3))\/(((op (e2) (e1)) = (e3))\/((op (e3) (e1)) = (e3))))) -> (~((op (e1) (e0)) = (op (e1) (e2)))) -> (((op (e0) (e1)) = (e1))\/(((op (e1) (e1)) = (e1))\/(((op (e2) (e1)) = (e1))\/((op (e3) (e1)) = (e1))))) -> (~((e0) = (e3))) -> (~((op (e3) (e1)) = (op (e3) (e3)))) -> ((~((op (e1) (e1)) = (e3)))\/((op (e1) (e3)) = (e1))) -> (~((op (e1) (e0)) = (op (e1) (e1)))) -> ((~((op (e1) (e1)) = (e1)))\/((op (e1) (e1)) = (e1))) -> (~((op (e2) (e2)) = (e3))) -> (~((op (e2) (e2)) = (e2))) -> (~((op (e2) (e2)) = (e0))) -> (~((op (e2) (e1)) = (op (e3) (e1)))) -> ((op (e2) (e1)) = (e2)) -> False). % 15.41/15.56 do 0 intro. intros zenon_H45 zenon_Hba zenon_H1d3 zenon_H1d4 zenon_H17a zenon_H294 zenon_H10f zenon_H10e zenon_H105 zenon_Hf1 zenon_H17d zenon_Heb zenon_H1b3 zenon_H58 zenon_H295 zenon_H1df zenon_H250 zenon_H1f zenon_H8e zenon_H1a2 zenon_H154 zenon_H22e zenon_H11b zenon_H135 zenon_Hc9 zenon_H1cf zenon_H28a zenon_H121 zenon_H140 zenon_H146 zenon_H251 zenon_H138 zenon_Hbe zenon_Ha3 zenon_H87 zenon_H160 zenon_Hce zenon_H1cd zenon_H90 zenon_H6a zenon_H59 zenon_H3b zenon_H36 zenon_Ha7 zenon_H8f zenon_H1e3 zenon_H1e2 zenon_H157 zenon_H1f5 zenon_H5e zenon_H290 zenon_Hb7 zenon_H258 zenon_H2d zenon_H8b zenon_Hde zenon_He6 zenon_H1c3 zenon_H10c zenon_H7d zenon_H24f zenon_Hb4 zenon_H80 zenon_H254 zenon_H28 zenon_H84 zenon_Haa zenon_H10d zenon_H44 zenon_H109 zenon_H199 zenon_H166 zenon_H228 zenon_H4b zenon_H12d zenon_H1d2 zenon_Hd7 zenon_H1d8 zenon_H30 zenon_H2f zenon_H2e zenon_H13c zenon_H156. % 15.41/15.56 apply (zenon_or_s _ _ zenon_H10e); [ zenon_intro zenon_H3d | zenon_intro zenon_H106 ]. % 15.41/15.56 apply (zenon_or_s _ _ zenon_H44); [ zenon_intro zenon_H47 | zenon_intro zenon_H46 ]. % 15.41/15.56 exact (zenon_H45 zenon_H47). % 15.41/15.56 apply (zenon_or_s _ _ zenon_H46); [ zenon_intro zenon_H22 | zenon_intro zenon_H48 ]. % 15.41/15.56 apply (zenon_L846_); trivial. % 15.41/15.56 apply (zenon_or_s _ _ zenon_H48); [ zenon_intro zenon_H29 | zenon_intro zenon_H37 ]. % 15.41/15.56 apply (zenon_L5_); trivial. % 15.41/15.56 apply (zenon_L688_); trivial. % 15.41/15.56 apply (zenon_L81_); trivial. % 15.41/15.56 (* end of lemma zenon_L865_ *) % 15.41/15.56 assert (zenon_L866_ : (((op (e0) (e0)) = (e2))\/(((op (e0) (e1)) = (e2))\/(((op (e0) (e2)) = (e2))\/((op (e0) (e3)) = (e2))))) -> (~((op (e0) (e0)) = (e2))) -> (~((op (e1) (e1)) = (e3))) -> (~((op (e0) (e1)) = (op (e1) (e1)))) -> (~((op (e1) (e1)) = (e1))) -> (~((op (e1) (e1)) = (e0))) -> (((op (e1) (e1)) = (e0))\/(((op (e1) (e1)) = (e1))\/(((op (e1) (e1)) = (e2))\/((op (e1) (e1)) = (e3))))) -> (~((op (e0) (e3)) = (op (e3) (e3)))) -> ((op (e3) (e3)) = (e3)) -> (((op (e2) (e0)) = (e3))\/(((op (e2) (e1)) = (e3))\/(((op (e2) (e2)) = (e3))\/((op (e2) (e3)) = (e3))))) -> (~((op (e0) (e1)) = (op (e2) (e1)))) -> (~((op (e3) (op (e2) (e3))) = (op (e2) (e3)))) -> (((op (e0) (e0)) = (e3))\/(((op (e0) (e1)) = (e3))\/(((op (e0) (e2)) = (e3))\/((op (e0) (e3)) = (e3))))) -> (((op (e0) (e0)) = (e3))\/(((op (e1) (e0)) = (e3))\/(((op (e2) (e0)) = (e3))\/((op (e3) (e0)) = (e3))))) -> (~((op (e0) (e0)) = (e3))) -> (~((op (e0) (e3)) = (op (e1) (e3)))) -> ((op (e1) (e2)) = (e1)) -> (~((e1) = (e2))) -> (((op (e2) (e2)) = (e0))\/(((op (e2) (e2)) = (e1))\/(((op (e2) (e2)) = (e2))\/((op (e2) (e2)) = (e3))))) -> (~((op (e2) (e2)) = (e1))) -> (~((op (e2) (e2)) = (e2))) -> (~((op (e2) (e2)) = (e3))) -> (((op (e1) (e0)) = (e2))\/(((op (e1) (e1)) = (e2))\/(((op (e1) (e2)) = (e2))\/((op (e1) (e3)) = (e2))))) -> (~((e2) = (e3))) -> ((op (e2) (e0)) = (e2)) -> (~((e1) = (e3))) -> ((op (e3) (e0)) = (e1)) -> False). % 15.41/15.56 do 0 intro. intros zenon_H8e zenon_H8f zenon_H182 zenon_H23 zenon_H1b4 zenon_H145 zenon_H1b3 zenon_H36 zenon_H42 zenon_He6 zenon_Hde zenon_H28a zenon_H58 zenon_Hbe zenon_H59 zenon_H80 zenon_H117 zenon_Ha7 zenon_H2d zenon_H52 zenon_H2f zenon_H30 zenon_H84 zenon_H6a zenon_Hdd zenon_Ha3 zenon_Hee. % 15.41/15.56 apply (zenon_or_s _ _ zenon_H8e); [ zenon_intro zenon_H92 | zenon_intro zenon_H91 ]. % 15.41/15.56 exact (zenon_H8f zenon_H92). % 15.41/15.56 apply (zenon_or_s _ _ zenon_H91); [ zenon_intro zenon_H5d | zenon_intro zenon_H93 ]. % 15.41/15.56 apply (zenon_L214_); trivial. % 15.41/15.56 apply (zenon_or_s _ _ zenon_H93); [ zenon_intro zenon_H63 | zenon_intro zenon_H81 ]. % 15.41/15.56 apply (zenon_L789_); trivial. % 15.41/15.56 apply (zenon_L580_); trivial. % 15.41/15.56 (* end of lemma zenon_L866_ *) % 15.41/15.56 assert (zenon_L867_ : (((op (e0) (e0)) = (e1))\/(((op (e1) (e0)) = (e1))\/(((op (e2) (e0)) = (e1))\/((op (e3) (e0)) = (e1))))) -> (~((op (e0) (e0)) = (e1))) -> (((op (e1) (e0)) = (e3))\/(((op (e1) (e1)) = (e3))\/(((op (e1) (e2)) = (e3))\/((op (e1) (e3)) = (e3))))) -> (~((op (e0) (e2)) = (op (e1) (e2)))) -> (~((op (e1) (e3)) = (op (e3) (e3)))) -> (((op (e0) (e0)) = (e2))\/(((op (e0) (e1)) = (e2))\/(((op (e0) (e2)) = (e2))\/((op (e0) (e3)) = (e2))))) -> (~((op (e0) (e0)) = (e2))) -> (~((op (e1) (e1)) = (e3))) -> (~((op (e0) (e1)) = (op (e1) (e1)))) -> (~((op (e1) (e1)) = (e1))) -> (~((op (e1) (e1)) = (e0))) -> (((op (e1) (e1)) = (e0))\/(((op (e1) (e1)) = (e1))\/(((op (e1) (e1)) = (e2))\/((op (e1) (e1)) = (e3))))) -> (~((op (e0) (e3)) = (op (e3) (e3)))) -> ((op (e3) (e3)) = (e3)) -> (((op (e2) (e0)) = (e3))\/(((op (e2) (e1)) = (e3))\/(((op (e2) (e2)) = (e3))\/((op (e2) (e3)) = (e3))))) -> (~((op (e0) (e1)) = (op (e2) (e1)))) -> (~((op (e3) (op (e2) (e3))) = (op (e2) (e3)))) -> (((op (e0) (e0)) = (e3))\/(((op (e0) (e1)) = (e3))\/(((op (e0) (e2)) = (e3))\/((op (e0) (e3)) = (e3))))) -> (((op (e0) (e0)) = (e3))\/(((op (e1) (e0)) = (e3))\/(((op (e2) (e0)) = (e3))\/((op (e3) (e0)) = (e3))))) -> (~((op (e0) (e0)) = (e3))) -> (~((op (e0) (e3)) = (op (e1) (e3)))) -> ((op (e1) (e2)) = (e1)) -> (~((e1) = (e2))) -> (((op (e2) (e2)) = (e0))\/(((op (e2) (e2)) = (e1))\/(((op (e2) (e2)) = (e2))\/((op (e2) (e2)) = (e3))))) -> (~((op (e2) (e2)) = (e1))) -> (~((op (e2) (e2)) = (e2))) -> (~((op (e2) (e2)) = (e3))) -> (((op (e1) (e0)) = (e2))\/(((op (e1) (e1)) = (e2))\/(((op (e1) (e2)) = (e2))\/((op (e1) (e3)) = (e2))))) -> (~((e2) = (e3))) -> ((op (e2) (e0)) = (e2)) -> (~((e1) = (e3))) -> False). % 15.41/15.56 do 0 intro. intros zenon_Hf1 zenon_H45 zenon_H90 zenon_H87 zenon_H8b zenon_H8e zenon_H8f zenon_H182 zenon_H23 zenon_H1b4 zenon_H145 zenon_H1b3 zenon_H36 zenon_H42 zenon_He6 zenon_Hde zenon_H28a zenon_H58 zenon_Hbe zenon_H59 zenon_H80 zenon_H117 zenon_Ha7 zenon_H2d zenon_H52 zenon_H2f zenon_H30 zenon_H84 zenon_H6a zenon_Hdd zenon_Ha3. % 15.41/15.56 apply (zenon_or_s _ _ zenon_Hf1); [ zenon_intro zenon_H47 | zenon_intro zenon_Hf4 ]. % 15.41/15.56 exact (zenon_H45 zenon_H47). % 15.41/15.56 apply (zenon_or_s _ _ zenon_Hf4); [ zenon_intro zenon_Hd8 | zenon_intro zenon_Hf5 ]. % 15.41/15.56 apply (zenon_L778_); trivial. % 15.41/15.56 apply (zenon_or_s _ _ zenon_Hf5); [ zenon_intro zenon_Hae | zenon_intro zenon_Hee ]. % 15.41/15.56 apply (zenon_L304_); trivial. % 15.41/15.56 apply (zenon_L866_); trivial. % 15.41/15.56 (* end of lemma zenon_L867_ *) % 15.41/15.56 assert (zenon_L868_ : (((op (e1) (e0)) = (e0))\/(((op (e1) (e1)) = (e0))\/(((op (e1) (e2)) = (e0))\/((op (e1) (e3)) = (e0))))) -> (~((e0) = (e1))) -> (~((op (e1) (e2)) = (op (e2) (e2)))) -> (~((op (e2) (e2)) = (e1))) -> (~((op (e2) (e2)) = (e2))) -> (((op (e2) (e2)) = (e0))\/(((op (e2) (e2)) = (e1))\/(((op (e2) (e2)) = (e2))\/((op (e2) (e2)) = (e3))))) -> (~((op (e1) (e1)) = (e0))) -> ((op (e0) (e0)) = (e0)) -> (~((op (e0) (e0)) = (op (e1) (e0)))) -> ((~((op (e3) (e3)) = (e0)))\/((op (e3) (e0)) = (e3))) -> ((op (e3) (e3)) = (e3)) -> (~((op (e3) (e0)) = (op (e3) (e3)))) -> (~((op (e0) (e0)) = (op (e0) (e3)))) -> (~((e0) = (e2))) -> (((op (e0) (e3)) = (e0))\/(((op (e1) (e3)) = (e0))\/(((op (e2) (e3)) = (e0))\/((op (e3) (e3)) = (e0))))) -> ((~((op (e2) (e2)) = (e3)))\/((op (e2) (e3)) = (e2))) -> (((op (e0) (e0)) = (e1))\/(((op (e1) (e0)) = (e1))\/(((op (e2) (e0)) = (e1))\/((op (e3) (e0)) = (e1))))) -> (~((op (e0) (e0)) = (e1))) -> (((op (e1) (e0)) = (e3))\/(((op (e1) (e1)) = (e3))\/(((op (e1) (e2)) = (e3))\/((op (e1) (e3)) = (e3))))) -> (~((op (e0) (e2)) = (op (e1) (e2)))) -> (~((op (e1) (e3)) = (op (e3) (e3)))) -> (((op (e0) (e0)) = (e2))\/(((op (e0) (e1)) = (e2))\/(((op (e0) (e2)) = (e2))\/((op (e0) (e3)) = (e2))))) -> (~((op (e0) (e0)) = (e2))) -> (~((op (e1) (e1)) = (e3))) -> (~((op (e0) (e1)) = (op (e1) (e1)))) -> (~((op (e1) (e1)) = (e1))) -> (((op (e1) (e1)) = (e0))\/(((op (e1) (e1)) = (e1))\/(((op (e1) (e1)) = (e2))\/((op (e1) (e1)) = (e3))))) -> (~((op (e0) (e3)) = (op (e3) (e3)))) -> (((op (e2) (e0)) = (e3))\/(((op (e2) (e1)) = (e3))\/(((op (e2) (e2)) = (e3))\/((op (e2) (e3)) = (e3))))) -> (~((op (e0) (e1)) = (op (e2) (e1)))) -> (~((op (e3) (op (e2) (e3))) = (op (e2) (e3)))) -> (((op (e0) (e0)) = (e3))\/(((op (e0) (e1)) = (e3))\/(((op (e0) (e2)) = (e3))\/((op (e0) (e3)) = (e3))))) -> (((op (e0) (e0)) = (e3))\/(((op (e1) (e0)) = (e3))\/(((op (e2) (e0)) = (e3))\/((op (e3) (e0)) = (e3))))) -> (~((op (e0) (e0)) = (e3))) -> (~((op (e0) (e3)) = (op (e1) (e3)))) -> (~((e1) = (e2))) -> (~((op (e2) (e2)) = (e3))) -> (((op (e1) (e0)) = (e2))\/(((op (e1) (e1)) = (e2))\/(((op (e1) (e2)) = (e2))\/((op (e1) (e3)) = (e2))))) -> (((op (e1) (e0)) = (e1))\/(((op (e1) (e1)) = (e1))\/(((op (e1) (e2)) = (e1))\/((op (e1) (e3)) = (e1))))) -> (~((e2) = (e3))) -> ((op (e2) (e0)) = (e2)) -> (~((e1) = (e3))) -> False). % 15.41/15.56 do 0 intro. intros zenon_H163 zenon_H9e zenon_H7d zenon_H52 zenon_H2f zenon_H2d zenon_H145 zenon_H1f zenon_H24c zenon_H10f zenon_H42 zenon_Hbb zenon_H24f zenon_H5e zenon_Hd3 zenon_H1c3 zenon_Hf1 zenon_H45 zenon_H90 zenon_H87 zenon_H8b zenon_H8e zenon_H8f zenon_H182 zenon_H23 zenon_H1b4 zenon_H1b3 zenon_H36 zenon_He6 zenon_Hde zenon_H28a zenon_H58 zenon_Hbe zenon_H59 zenon_H80 zenon_Ha7 zenon_H30 zenon_H84 zenon_H1c5 zenon_H6a zenon_Hdd zenon_Ha3. % 15.41/15.56 apply (zenon_or_s _ _ zenon_Hf1); [ zenon_intro zenon_H47 | zenon_intro zenon_Hf4 ]. % 15.41/15.56 exact (zenon_H45 zenon_H47). % 15.41/15.56 apply (zenon_or_s _ _ zenon_Hf4); [ zenon_intro zenon_Hd8 | zenon_intro zenon_Hf5 ]. % 15.41/15.56 apply (zenon_L778_); trivial. % 15.41/15.56 apply (zenon_or_s _ _ zenon_Hf5); [ zenon_intro zenon_Hae | zenon_intro zenon_Hee ]. % 15.41/15.56 apply (zenon_L304_); trivial. % 15.41/15.56 apply (zenon_or_s _ _ zenon_Hbe); [ zenon_intro zenon_H5b | zenon_intro zenon_Hbf ]. % 15.41/15.56 exact (zenon_H59 zenon_H5b). % 15.41/15.56 apply (zenon_or_s _ _ zenon_Hbf); [ zenon_intro zenon_H69 | zenon_intro zenon_Hc0 ]. % 15.41/15.56 apply (zenon_or_s _ _ zenon_H1c5); [ zenon_intro zenon_Hd8 | zenon_intro zenon_H1c6 ]. % 15.41/15.56 apply (zenon_L163_); trivial. % 15.41/15.56 apply (zenon_or_s _ _ zenon_H1c6); [ zenon_intro zenon_H21 | zenon_intro zenon_H1c7 ]. % 15.41/15.56 exact (zenon_H1b4 zenon_H21). % 15.41/15.56 apply (zenon_or_s _ _ zenon_H1c7); [ zenon_intro zenon_H117 | zenon_intro zenon_H11f ]. % 15.41/15.57 apply (zenon_L867_); trivial. % 15.41/15.57 apply (zenon_L605_); trivial. % 15.41/15.57 apply (zenon_or_s _ _ zenon_Hc0); [ zenon_intro zenon_Haf | zenon_intro zenon_Hba ]. % 15.41/15.57 apply (zenon_L64_); trivial. % 15.41/15.57 apply (zenon_L79_); trivial. % 15.41/15.57 (* end of lemma zenon_L868_ *) % 15.41/15.57 assert (zenon_L869_ : (((op (e0) (e0)) = (e1))\/(((op (e1) (e0)) = (e1))\/(((op (e2) (e0)) = (e1))\/((op (e3) (e0)) = (e1))))) -> (~((op (e0) (e0)) = (e1))) -> (~((op (e1) (e0)) = (op (e1) (e2)))) -> ((op (e0) (e1)) = (e1)) -> (((op (e0) (e0)) = (e2))\/(((op (e0) (e1)) = (e2))\/(((op (e0) (e2)) = (e2))\/((op (e0) (e3)) = (e2))))) -> (~((op (e0) (e0)) = (e2))) -> (~((op (e1) (e1)) = (e3))) -> (~((op (e0) (e1)) = (op (e1) (e1)))) -> (~((op (e1) (e1)) = (e1))) -> (~((op (e1) (e1)) = (e0))) -> (((op (e1) (e1)) = (e0))\/(((op (e1) (e1)) = (e1))\/(((op (e1) (e1)) = (e2))\/((op (e1) (e1)) = (e3))))) -> (~((op (e0) (op (e2) (e0))) = (op (e2) (e0)))) -> (((op (e0) (e0)) = (e3))\/(((op (e1) (e0)) = (e3))\/(((op (e2) (e0)) = (e3))\/((op (e3) (e0)) = (e3))))) -> (~((op (e0) (e0)) = (e3))) -> (~((op (e0) (e3)) = (op (e1) (e3)))) -> ((op (e1) (e2)) = (e1)) -> (~((e1) = (e2))) -> (((op (e2) (e2)) = (e0))\/(((op (e2) (e2)) = (e1))\/(((op (e2) (e2)) = (e2))\/((op (e2) (e2)) = (e3))))) -> (~((op (e2) (e2)) = (e1))) -> (~((op (e2) (e2)) = (e2))) -> (~((op (e2) (e2)) = (e3))) -> (((op (e1) (e0)) = (e2))\/(((op (e1) (e1)) = (e2))\/(((op (e1) (e2)) = (e2))\/((op (e1) (e3)) = (e2))))) -> (~((e2) = (e3))) -> ((op (e2) (e0)) = (e2)) -> (~((e1) = (e3))) -> False). % 15.41/15.57 do 0 intro. intros zenon_Hf1 zenon_H45 zenon_H166 zenon_H22 zenon_H8e zenon_H8f zenon_H182 zenon_H23 zenon_H1b4 zenon_H145 zenon_H1b3 zenon_H295 zenon_Hbe zenon_H59 zenon_H80 zenon_H117 zenon_Ha7 zenon_H2d zenon_H52 zenon_H2f zenon_H30 zenon_H84 zenon_H6a zenon_Hdd zenon_Ha3. % 15.41/15.57 apply (zenon_or_s _ _ zenon_Hf1); [ zenon_intro zenon_H47 | zenon_intro zenon_Hf4 ]. % 15.41/15.57 exact (zenon_H45 zenon_H47). % 15.41/15.57 apply (zenon_or_s _ _ zenon_Hf4); [ zenon_intro zenon_Hd8 | zenon_intro zenon_Hf5 ]. % 15.41/15.57 apply (zenon_L248_); trivial. % 15.41/15.57 apply (zenon_or_s _ _ zenon_Hf5); [ zenon_intro zenon_Hae | zenon_intro zenon_Hee ]. % 15.41/15.57 apply (zenon_L816_); trivial. % 15.41/15.57 apply (zenon_or_s _ _ zenon_H8e); [ zenon_intro zenon_H92 | zenon_intro zenon_H91 ]. % 15.41/15.57 exact (zenon_H8f zenon_H92). % 15.41/15.57 apply (zenon_or_s _ _ zenon_H91); [ zenon_intro zenon_H5d | zenon_intro zenon_H93 ]. % 15.41/15.57 apply (zenon_L214_); trivial. % 15.41/15.57 apply (zenon_or_s _ _ zenon_H93); [ zenon_intro zenon_H63 | zenon_intro zenon_H81 ]. % 15.41/15.57 apply (zenon_L812_); trivial. % 15.41/15.57 apply (zenon_L580_); trivial. % 15.41/15.57 (* end of lemma zenon_L869_ *) % 15.41/15.57 assert (zenon_L870_ : (((op (e0) (e0)) = (e1))\/(((op (e0) (e1)) = (e1))\/(((op (e0) (e2)) = (e1))\/((op (e0) (e3)) = (e1))))) -> (((op (e1) (e0)) = (e2))\/(((op (e1) (e1)) = (e2))\/(((op (e1) (e2)) = (e2))\/((op (e1) (e3)) = (e2))))) -> ((op (e1) (e2)) = (e1)) -> (~((op (e0) (e3)) = (op (e1) (e3)))) -> (((op (e0) (e0)) = (e3))\/(((op (e1) (e0)) = (e3))\/(((op (e2) (e0)) = (e3))\/((op (e3) (e0)) = (e3))))) -> (~((op (e0) (op (e2) (e0))) = (op (e2) (e0)))) -> (((op (e1) (e1)) = (e0))\/(((op (e1) (e1)) = (e1))\/(((op (e1) (e1)) = (e2))\/((op (e1) (e1)) = (e3))))) -> (~((op (e1) (e1)) = (e1))) -> (~((op (e0) (e1)) = (op (e1) (e1)))) -> (~((op (e1) (e1)) = (e3))) -> (~((op (e1) (e0)) = (op (e1) (e2)))) -> (~((op (e0) (e0)) = (e1))) -> (((op (e0) (e0)) = (e1))\/(((op (e1) (e0)) = (e1))\/(((op (e2) (e0)) = (e1))\/((op (e3) (e0)) = (e1))))) -> (~((e2) = (e3))) -> (~((e1) = (e3))) -> ((op (e3) (e1)) = (e3)) -> (~((op (e0) (e1)) = (op (e3) (e1)))) -> (~((op (e0) (e0)) = (e3))) -> (((op (e0) (e0)) = (e3))\/(((op (e0) (e1)) = (e3))\/(((op (e0) (e2)) = (e3))\/((op (e0) (e3)) = (e3))))) -> (~((e1) = (e2))) -> (((op (e1) (e0)) = (e0))\/(((op (e1) (e1)) = (e0))\/(((op (e1) (e2)) = (e0))\/((op (e1) (e3)) = (e0))))) -> ((op (e0) (e0)) = (e0)) -> (~((op (e0) (e0)) = (op (e1) (e0)))) -> (~((op (e1) (e1)) = (e0))) -> (~((op (e2) (e2)) = (e3))) -> (~((op (e2) (e2)) = (e2))) -> (~((op (e2) (e2)) = (e1))) -> (~((op (e1) (e2)) = (op (e2) (e2)))) -> (((op (e2) (e2)) = (e0))\/(((op (e2) (e2)) = (e1))\/(((op (e2) (e2)) = (e2))\/((op (e2) (e2)) = (e3))))) -> (((op (e0) (e3)) = (e2))\/(((op (e1) (e3)) = (e2))\/(((op (e2) (e3)) = (e2))\/((op (e3) (e3)) = (e2))))) -> (~((e0) = (e2))) -> ((op (e2) (e0)) = (e2)) -> (~((op (e2) (e0)) = (op (e2) (e3)))) -> (~((op (e0) (e0)) = (e2))) -> (((op (e0) (e0)) = (e2))\/(((op (e0) (e1)) = (e2))\/(((op (e0) (e2)) = (e2))\/((op (e0) (e3)) = (e2))))) -> (((op (e3) (e3)) = (e0))\/(((op (e3) (e3)) = (e1))\/(((op (e3) (e3)) = (e2))\/((op (e3) (e3)) = (e3))))) -> (~((op (e3) (e3)) = (e0))) -> (~((op (e0) (e3)) = (op (e3) (e3)))) -> (~((op (e3) (e3)) = (e2))) -> (~((op (e3) (e3)) = (e3))) -> False). % 15.41/15.57 do 0 intro. intros zenon_H44 zenon_H84 zenon_H117 zenon_H80 zenon_Hbe zenon_H295 zenon_H1b3 zenon_H1b4 zenon_H23 zenon_H182 zenon_H166 zenon_H45 zenon_Hf1 zenon_H6a zenon_Ha3 zenon_H10a zenon_H138 zenon_H59 zenon_H58 zenon_Ha7 zenon_H163 zenon_H1f zenon_H24c zenon_H145 zenon_H30 zenon_H2f zenon_H52 zenon_H7d zenon_H2d zenon_H160 zenon_H5e zenon_Hdd zenon_Hce zenon_H8f zenon_H8e zenon_H3b zenon_H3c zenon_H36 zenon_H3d zenon_H3e. % 15.41/15.57 apply (zenon_or_s _ _ zenon_H44); [ zenon_intro zenon_H47 | zenon_intro zenon_H46 ]. % 15.41/15.57 exact (zenon_H45 zenon_H47). % 15.41/15.57 apply (zenon_or_s _ _ zenon_H46); [ zenon_intro zenon_H22 | zenon_intro zenon_H48 ]. % 15.41/15.57 apply (zenon_L869_); trivial. % 15.41/15.57 apply (zenon_or_s _ _ zenon_H48); [ zenon_intro zenon_H29 | zenon_intro zenon_H37 ]. % 15.41/15.57 apply (zenon_L646_); trivial. % 15.41/15.57 apply (zenon_L7_); trivial. % 15.41/15.57 (* end of lemma zenon_L870_ *) % 15.41/15.57 assert (zenon_L871_ : (((op (e0) (e0)) = (e1))\/(((op (e1) (e0)) = (e1))\/(((op (e2) (e0)) = (e1))\/((op (e3) (e0)) = (e1))))) -> (~((op (e0) (e0)) = (e1))) -> ((op (e0) (e3)) = (e1)) -> (~((op (e0) (op (e2) (e0))) = (op (e2) (e0)))) -> (((op (e0) (e0)) = (e3))\/(((op (e0) (e1)) = (e3))\/(((op (e0) (e2)) = (e3))\/((op (e0) (e3)) = (e3))))) -> (~((op (e0) (e0)) = (e3))) -> (~((op (e3) (e3)) = (e2))) -> (~((op (e2) (e0)) = (op (e2) (e3)))) -> (~((e2) = (e3))) -> (~((op (e0) (e1)) = (op (e0) (e3)))) -> (((op (e0) (e3)) = (e2))\/(((op (e1) (e3)) = (e2))\/(((op (e2) (e3)) = (e2))\/((op (e3) (e3)) = (e2))))) -> (~((op (e0) (e2)) = (op (e1) (e2)))) -> (~((op (e1) (e1)) = (e3))) -> (((op (e1) (e0)) = (e3))\/(((op (e1) (e1)) = (e3))\/(((op (e1) (e2)) = (e3))\/((op (e1) (e3)) = (e3))))) -> (~((op (e0) (e0)) = (e2))) -> (((op (e0) (e0)) = (e2))\/(((op (e0) (e1)) = (e2))\/(((op (e0) (e2)) = (e2))\/((op (e0) (e3)) = (e2))))) -> ((op (e2) (e0)) = (e2)) -> (~((e1) = (e2))) -> (~((e1) = (e3))) -> ((op (e3) (e0)) = (e3)) -> False). % 15.41/15.57 do 0 intro. intros zenon_Hf1 zenon_H45 zenon_H37 zenon_H295 zenon_H58 zenon_H59 zenon_H3d zenon_Hce zenon_H6a zenon_H1cd zenon_H160 zenon_H87 zenon_H182 zenon_H90 zenon_H8f zenon_H8e zenon_Hdd zenon_Ha7 zenon_Ha3 zenon_Hba. % 15.41/15.57 apply (zenon_or_s _ _ zenon_Hf1); [ zenon_intro zenon_H47 | zenon_intro zenon_Hf4 ]. % 15.41/15.57 exact (zenon_H45 zenon_H47). % 15.41/15.57 apply (zenon_or_s _ _ zenon_Hf4); [ zenon_intro zenon_Hd8 | zenon_intro zenon_Hf5 ]. % 15.41/15.57 apply (zenon_L843_); trivial. % 15.41/15.57 apply (zenon_or_s _ _ zenon_Hf5); [ zenon_intro zenon_Hae | zenon_intro zenon_Hee ]. % 15.41/15.57 apply (zenon_L304_); trivial. % 15.41/15.57 apply (zenon_L79_); trivial. % 15.41/15.57 (* end of lemma zenon_L871_ *) % 15.41/15.57 assert (zenon_L872_ : (((op (e1) (e0)) = (e2))\/(((op (e1) (e1)) = (e2))\/(((op (e1) (e2)) = (e2))\/((op (e1) (e3)) = (e2))))) -> (~((e2) = (e3))) -> ((op (e1) (e0)) = (e3)) -> (~((op (e1) (e1)) = (e2))) -> ((op (e2) (e1)) = (e2)) -> (~((op (e1) (op (e2) (e1))) = (op (e2) (e1)))) -> (~((op (e0) (e3)) = (op (e1) (e3)))) -> ((op (e0) (e3)) = (e2)) -> False). % 15.41/15.57 do 0 intro. intros zenon_H84 zenon_H6a zenon_H69 zenon_Hd6 zenon_H156 zenon_H290 zenon_H80 zenon_H81. % 15.41/15.57 apply (zenon_or_s _ _ zenon_H84); [ zenon_intro zenon_H68 | zenon_intro zenon_H85 ]. % 15.41/15.57 apply (zenon_L17_); trivial. % 15.41/15.57 apply (zenon_or_s _ _ zenon_H85); [ zenon_intro zenon_H6e | zenon_intro zenon_H86 ]. % 15.41/15.57 exact (zenon_Hd6 zenon_H6e). % 15.41/15.57 apply (zenon_or_s _ _ zenon_H86); [ zenon_intro zenon_H7c | zenon_intro zenon_H82 ]. % 15.41/15.57 apply (zenon_L824_); trivial. % 15.41/15.57 apply (zenon_L22_); trivial. % 15.41/15.57 (* end of lemma zenon_L872_ *) % 15.41/15.57 assert (zenon_L873_ : (((op (e1) (e0)) = (e3))\/(((op (e1) (e1)) = (e3))\/(((op (e1) (e2)) = (e3))\/((op (e1) (e3)) = (e3))))) -> (~((e2) = (e3))) -> ((op (e1) (e0)) = (e2)) -> (~((op (e1) (e3)) = (op (e2) (e3)))) -> (~((e1) = (e2))) -> ((op (e2) (e1)) = (e2)) -> ((op (e2) (e0)) = (e3)) -> (((op (e2) (e0)) = (e1))\/(((op (e2) (e1)) = (e1))\/(((op (e2) (e2)) = (e1))\/((op (e2) (e3)) = (e1))))) -> (~((op (e2) (e2)) = (e0))) -> (~((e0) = (e2))) -> (~((op (e0) (e0)) = (op (e2) (e0)))) -> ((op (e0) (e0)) = (e0)) -> (((op (e2) (e0)) = (e0))\/(((op (e2) (e1)) = (e0))\/(((op (e2) (e2)) = (e0))\/((op (e2) (e3)) = (e0))))) -> ((op (e0) (e2)) = (e3)) -> (~((op (e0) (e2)) = (op (e1) (e2)))) -> ((op (e1) (e3)) = (e1)) -> (~((e1) = (e3))) -> False). % 15.41/15.57 do 0 intro. intros zenon_H90 zenon_H6a zenon_H68 zenon_H244 zenon_Ha7 zenon_H156 zenon_Haf zenon_Hb7 zenon_H2e zenon_H5e zenon_H258 zenon_H1f zenon_H1f5 zenon_H50 zenon_H87 zenon_H11f zenon_Ha3. % 15.41/15.57 apply (zenon_or_s _ _ zenon_H90); [ zenon_intro zenon_H69 | zenon_intro zenon_H94 ]. % 15.41/15.57 apply (zenon_L17_); trivial. % 15.41/15.57 apply (zenon_or_s _ _ zenon_H94); [ zenon_intro zenon_H96 | zenon_intro zenon_H95 ]. % 15.41/15.57 apply (zenon_L614_); trivial. % 15.41/15.57 apply (zenon_or_s _ _ zenon_H95); [ zenon_intro zenon_H88 | zenon_intro zenon_H8a ]. % 15.41/15.57 apply (zenon_L24_); trivial. % 15.41/15.57 apply (zenon_L772_); trivial. % 15.41/15.57 (* end of lemma zenon_L873_ *) % 15.41/15.57 assert (zenon_L874_ : (~((e1) = (e3))) -> (~((op (e0) (op (e2) (e0))) = (op (e2) (e0)))) -> ((op (e0) (e1)) = (e1)) -> ((~((op (e1) (e1)) = (e1)))\/((op (e1) (e1)) = (e1))) -> (~((op (e1) (e0)) = (op (e1) (e1)))) -> ((~((op (e1) (e1)) = (e3)))\/((op (e1) (e3)) = (e1))) -> (~((op (e3) (e1)) = (op (e3) (e3)))) -> (~((e0) = (e3))) -> (((op (e0) (e1)) = (e1))\/(((op (e1) (e1)) = (e1))\/(((op (e2) (e1)) = (e1))\/((op (e3) (e1)) = (e1))))) -> (~((op (e1) (e0)) = (op (e1) (e2)))) -> (((op (e0) (e1)) = (e3))\/(((op (e1) (e1)) = (e3))\/(((op (e2) (e1)) = (e3))\/((op (e3) (e1)) = (e3))))) -> (~((op (e3) (e0)) = (op (e3) (e1)))) -> (((op (e0) (e0)) = (e1))\/(((op (e0) (e1)) = (e1))\/(((op (e0) (e2)) = (e1))\/((op (e0) (e3)) = (e1))))) -> ((~((op (e3) (e3)) = (e3)))\/((op (e3) (e3)) = (e3))) -> ((~((op (e2) (e2)) = (e2)))\/((op (e2) (e2)) = (e2))) -> (((op (e1) (e0)) = (e2))\/(((op (e1) (e1)) = (e2))\/(((op (e1) (e2)) = (e2))\/((op (e1) (e3)) = (e2))))) -> (~((op (e0) (e2)) = (op (e2) (e2)))) -> (((op (e0) (e3)) = (e0))\/(((op (e0) (e3)) = (e1))\/(((op (e0) (e3)) = (e2))\/((op (e0) (e3)) = (e3))))) -> (~((op (e0) (e3)) = (op (e1) (e3)))) -> (~((op (e0) (e3)) = (op (e2) (e3)))) -> (~((op (e0) (e0)) = (op (e0) (e3)))) -> (~((op (e1) (e2)) = (op (e2) (e2)))) -> ((~((op (e3) (e3)) = (e1)))\/((op (e3) (e1)) = (e3))) -> ((~((op (e2) (e2)) = (e3)))\/((op (e2) (e3)) = (e2))) -> (((op (e2) (e0)) = (e3))\/(((op (e2) (e1)) = (e3))\/(((op (e2) (e2)) = (e3))\/((op (e2) (e3)) = (e3))))) -> (~((op (e0) (e1)) = (op (e2) (e1)))) -> (~((op (e1) (e3)) = (op (e3) (e3)))) -> (((op (e2) (e2)) = (e0))\/(((op (e2) (e2)) = (e1))\/(((op (e2) (e2)) = (e2))\/((op (e2) (e2)) = (e3))))) -> (~((op (e0) (e0)) = (op (e2) (e0)))) -> (((op (e2) (e0)) = (e1))\/(((op (e2) (e1)) = (e1))\/(((op (e2) (e2)) = (e1))\/((op (e2) (e3)) = (e1))))) -> (~((op (e1) (op (e2) (e1))) = (op (e2) (e1)))) -> (~((e0) = (e2))) -> (((op (e2) (e0)) = (e0))\/(((op (e2) (e1)) = (e0))\/(((op (e2) (e2)) = (e0))\/((op (e2) (e3)) = (e0))))) -> (~((op (e2) (e1)) = (op (e2) (e2)))) -> (~((op (e2) (e1)) = (op (e2) (e3)))) -> ((~((op (e2) (e2)) = (e1)))\/((op (e2) (e1)) = (e2))) -> (~((op (e0) (e0)) = (e2))) -> (~((op (e0) (e3)) = (op (e3) (e3)))) -> (((op (e3) (e3)) = (e0))\/(((op (e3) (e3)) = (e1))\/(((op (e3) (e3)) = (e2))\/((op (e3) (e3)) = (e3))))) -> (~((op (e0) (e0)) = (e3))) -> (~((e2) = (e3))) -> (((op (e1) (e0)) = (e3))\/(((op (e1) (e1)) = (e3))\/(((op (e1) (e2)) = (e3))\/((op (e1) (e3)) = (e3))))) -> (~((op (e0) (e1)) = (op (e0) (e3)))) -> (~((op (e2) (e0)) = (op (e2) (e3)))) -> (((op (e0) (e3)) = (e2))\/(((op (e1) (e3)) = (e2))\/(((op (e2) (e3)) = (e2))\/((op (e3) (e3)) = (e2))))) -> (~((op (e0) (e2)) = (op (e1) (e2)))) -> (((op (e0) (e0)) = (e3))\/(((op (e1) (e0)) = (e3))\/(((op (e2) (e0)) = (e3))\/((op (e3) (e0)) = (e3))))) -> (~((op (e0) (e1)) = (op (e3) (e1)))) -> (((op (e0) (e2)) = (e0))\/(((op (e0) (e2)) = (e1))\/(((op (e0) (e2)) = (e2))\/((op (e0) (e2)) = (e3))))) -> (((op (e3) (e0)) = (e1))\/(((op (e3) (e1)) = (e1))\/(((op (e3) (e2)) = (e1))\/((op (e3) (e3)) = (e1))))) -> (~((op (e0) (e2)) = (op (e3) (e2)))) -> (((op (e0) (e3)) = (e1))\/(((op (e1) (e3)) = (e1))\/(((op (e2) (e3)) = (e1))\/((op (e3) (e3)) = (e1))))) -> (~((op (e3) (op (e2) (e3))) = (op (e2) (e3)))) -> (~((op (e1) (e0)) = (op (e1) (e3)))) -> (~((op (e0) (e2)) = (op (e0) (e3)))) -> (~((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 (e3) (e0)))) -> (((op (e0) (e1)) = (e2))\/(((op (e1) (e1)) = (e2))\/(((op (e2) (e1)) = (e2))\/((op (e3) (e1)) = (e2))))) -> (((op (e0) (e0)) = (e2))\/(((op (e0) (e1)) = (e2))\/(((op (e0) (e2)) = (e2))\/((op (e0) (e3)) = (e2))))) -> ((op (e0) (e0)) = (e0)) -> (~((op (e0) (e0)) = (op (e0) (e2)))) -> (((op (e3) (e0)) = (e2))\/(((op (e3) (e1)) = (e2))\/(((op (e3) (e2)) = (e2))\/((op (e3) (e3)) = (e2))))) -> (((op (e0) (e0)) = (e3))\/(((op (e0) (e1)) = (e3))\/(((op (e0) (e2)) = (e3))\/((op (e0) (e3)) = (e3))))) -> (((op (e1) (e1)) = (e0))\/(((op (e1) (e1)) = (e1))\/(((op (e1) (e1)) = (e2))\/((op (e1) (e1)) = (e3))))) -> (((op (e0) (e0)) = (e2))\/(((op (e1) (e0)) = (e2))\/(((op (e2) (e0)) = (e2))\/((op (e3) (e0)) = (e2))))) -> (~((op (e1) (e2)) = (op (e3) (e2)))) -> (((op (e0) (e0)) = (e1))\/(((op (e1) (e0)) = (e1))\/(((op (e2) (e0)) = (e1))\/((op (e3) (e0)) = (e1))))) -> (~((op (e3) (e0)) = (op (e3) (e2)))) -> (~((op (e0) (e0)) = (e1))) -> ((~((op (e3) (e3)) = (e2)))\/((op (e3) (e2)) = (e3))) -> ((~((op (e3) (e3)) = (e0)))\/((op (e3) (e0)) = (e3))) -> (~((op (e2) (op (e2) (e2))) = (op (e2) (e2)))) -> (~((op (e2) (e0)) = (op (e2) (e2)))) -> ((~((op (e2) (e2)) = (e0)))\/((op (e2) (e0)) = (e2))) -> ((~((op (e1) (e1)) = (e2)))\/((op (e1) (e2)) = (e1))) -> ((op (e0) (e3)) = (e2)) -> (~((op (e1) (e1)) = (e2))) -> ((op (e1) (e3)) = (e1)) -> (~((op (e2) (e2)) = (e0))) -> (~((op (e1) (e3)) = (op (e2) (e3)))) -> ((op (e2) (e1)) = (e2)) -> (~((op (e2) (e0)) = (op (e2) (e1)))) -> ((op (e3) (e0)) = (e1)) -> (~((e1) = (e2))) -> False). % 15.41/15.57 do 0 intro. intros zenon_Ha3 zenon_H295 zenon_H22 zenon_H1d8 zenon_Hd7 zenon_H1d2 zenon_H12d zenon_H4b zenon_H228 zenon_H166 zenon_H199 zenon_H109 zenon_H44 zenon_H10d zenon_Haa zenon_H84 zenon_H28 zenon_H254 zenon_H80 zenon_Hb4 zenon_H24f zenon_H7d zenon_H10c zenon_H1c3 zenon_He6 zenon_Hde zenon_H8b zenon_H2d zenon_H258 zenon_Hb7 zenon_H290 zenon_H5e zenon_H1f5 zenon_H157 zenon_H1e2 zenon_H1e3 zenon_H8f zenon_H36 zenon_H3b zenon_H59 zenon_H6a zenon_H90 zenon_H1cd zenon_Hce zenon_H160 zenon_H87 zenon_Hbe zenon_H138 zenon_H251 zenon_H146 zenon_H140 zenon_H121 zenon_H28a zenon_H1cf zenon_Hc9 zenon_H135 zenon_H11b zenon_H22e zenon_H1a2 zenon_H8e zenon_H1f zenon_H250 zenon_H1df zenon_H58 zenon_H1b3 zenon_Heb zenon_H17d zenon_Hf1 zenon_H105 zenon_H45 zenon_H10e zenon_H10f zenon_H294 zenon_H17a zenon_H1d4 zenon_H1d3 zenon_H81 zenon_Hd6 zenon_H11f zenon_H2e zenon_H244 zenon_H156 zenon_H154 zenon_Hee zenon_Ha7. % 15.41/15.57 apply (zenon_or_s _ _ zenon_Heb); [ zenon_intro zenon_H92 | zenon_intro zenon_Hec ]. % 15.41/15.57 exact (zenon_H8f zenon_H92). % 15.41/15.57 apply (zenon_or_s _ _ zenon_Hec); [ zenon_intro zenon_H68 | zenon_intro zenon_Hed ]. % 15.41/15.57 apply (zenon_or_s _ _ zenon_H58); [ zenon_intro zenon_H5b | zenon_intro zenon_H5a ]. % 15.41/15.57 exact (zenon_H59 zenon_H5b). % 15.41/15.57 apply (zenon_or_s _ _ zenon_H5a); [ zenon_intro zenon_H4a | zenon_intro zenon_H5c ]. % 15.41/15.57 apply (zenon_L59_); trivial. % 15.41/15.57 apply (zenon_or_s _ _ zenon_H5c); [ zenon_intro zenon_H50 | zenon_intro zenon_H53 ]. % 15.41/15.57 apply (zenon_or_s _ _ zenon_Hbe); [ zenon_intro zenon_H5b | zenon_intro zenon_Hbf ]. % 15.41/15.57 exact (zenon_H59 zenon_H5b). % 15.41/15.57 apply (zenon_or_s _ _ zenon_Hbf); [ zenon_intro zenon_H69 | zenon_intro zenon_Hc0 ]. % 15.41/15.57 apply (zenon_L872_); trivial. % 15.41/15.57 apply (zenon_or_s _ _ zenon_Hc0); [ zenon_intro zenon_Haf | zenon_intro zenon_Hba ]. % 15.41/15.57 apply (zenon_L873_); trivial. % 15.41/15.57 apply (zenon_L79_); trivial. % 15.41/15.57 apply (zenon_L847_); trivial. % 15.41/15.57 apply (zenon_or_s _ _ zenon_Hed); [ zenon_intro zenon_Hdd | zenon_intro zenon_He9 ]. % 15.41/15.57 apply (zenon_L284_); trivial. % 15.41/15.57 apply (zenon_L122_); trivial. % 15.41/15.57 (* end of lemma zenon_L874_ *) % 15.41/15.57 assert (zenon_L875_ : (~((op (e2) (e0)) = (op (e2) (e3)))) -> (~((op (e0) (e0)) = (e1))) -> (((op (e0) (e0)) = (e3))\/(((op (e0) (e1)) = (e3))\/(((op (e0) (e2)) = (e3))\/((op (e0) (e3)) = (e3))))) -> (~((op (e0) (e3)) = (op (e3) (e3)))) -> (~((e1) = (e3))) -> (~((op (e1) (e1)) = (e3))) -> (~((op (e0) (e2)) = (op (e1) (e2)))) -> (~((op (e1) (e3)) = (op (e3) (e3)))) -> (((op (e1) (e0)) = (e3))\/(((op (e1) (e1)) = (e3))\/(((op (e1) (e2)) = (e3))\/((op (e1) (e3)) = (e3))))) -> (~((e2) = (e3))) -> ((op (e2) (e0)) = (e2)) -> (~((op (e0) (e1)) = (op (e2) (e1)))) -> (~((op (e3) (op (e2) (e3))) = (op (e2) (e3)))) -> ((op (e3) (e3)) = (e3)) -> (((op (e2) (e0)) = (e3))\/(((op (e2) (e1)) = (e3))\/(((op (e2) (e2)) = (e3))\/((op (e2) (e3)) = (e3))))) -> (~((op (e0) (e0)) = (e3))) -> (~((e1) = (e2))) -> (~((op (e1) (e1)) = (e1))) -> (((op (e0) (e0)) = (e1))\/(((op (e1) (e0)) = (e1))\/(((op (e2) (e0)) = (e1))\/((op (e3) (e0)) = (e1))))) -> (~((op (e0) (e0)) = (e2))) -> (((op (e1) (e1)) = (e0))\/(((op (e1) (e1)) = (e1))\/(((op (e1) (e1)) = (e2))\/((op (e1) (e1)) = (e3))))) -> (~((op (e0) (e1)) = (op (e1) (e1)))) -> (~((op (e1) (e1)) = (e0))) -> (((op (e0) (e0)) = (e3))\/(((op (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) (e2)) = (e2))) -> (~((op (e2) (e2)) = (e1))) -> (~((op (e0) (e3)) = (op (e1) (e3)))) -> (((op (e1) (e0)) = (e2))\/(((op (e1) (e1)) = (e2))\/(((op (e1) (e2)) = (e2))\/((op (e1) (e3)) = (e2))))) -> (((op (e0) (e0)) = (e2))\/(((op (e0) (e1)) = (e2))\/(((op (e0) (e2)) = (e2))\/((op (e0) (e3)) = (e2))))) -> ((~((op (e2) (e2)) = (e3)))\/((op (e2) (e3)) = (e2))) -> (((op (e0) (e3)) = (e0))\/(((op (e1) (e3)) = (e0))\/(((op (e2) (e3)) = (e0))\/((op (e3) (e3)) = (e0))))) -> (~((e0) = (e2))) -> (~((op (e0) (e0)) = (op (e0) (e3)))) -> (~((op (e3) (e0)) = (op (e3) (e3)))) -> ((~((op (e3) (e3)) = (e0)))\/((op (e3) (e0)) = (e3))) -> (~((op (e0) (e0)) = (op (e1) (e0)))) -> ((op (e0) (e0)) = (e0)) -> (~((op (e1) (e2)) = (op (e2) (e2)))) -> (~((e0) = (e1))) -> (((op (e1) (e0)) = (e0))\/(((op (e1) (e1)) = (e0))\/(((op (e1) (e2)) = (e0))\/((op (e1) (e3)) = (e0))))) -> (((op (e1) (e0)) = (e1))\/(((op (e1) (e1)) = (e1))\/(((op (e1) (e2)) = (e1))\/((op (e1) (e3)) = (e1))))) -> False). % 15.41/15.57 do 0 intro. intros zenon_Hce zenon_H45 zenon_H58 zenon_H36 zenon_Ha3 zenon_H182 zenon_H87 zenon_H8b zenon_H90 zenon_H6a zenon_Hdd zenon_Hde zenon_H28a zenon_H42 zenon_He6 zenon_H59 zenon_Ha7 zenon_H1b4 zenon_Hf1 zenon_H8f zenon_H1b3 zenon_H23 zenon_H145 zenon_Hbe zenon_H2d zenon_H2f zenon_H52 zenon_H80 zenon_H84 zenon_H8e zenon_H1c3 zenon_Hd3 zenon_H5e zenon_H24f zenon_Hbb zenon_H10f zenon_H24c zenon_H1f zenon_H7d zenon_H9e zenon_H163 zenon_H1c5. % 15.41/15.57 apply (zenon_or_s _ _ zenon_H1c3); [ zenon_intro zenon_H30 | zenon_intro zenon_H124 ]. % 15.41/15.57 apply (zenon_L868_); trivial. % 15.41/15.57 apply (zenon_L119_); trivial. % 15.41/15.57 (* end of lemma zenon_L875_ *) % 15.41/15.57 assert (zenon_L876_ : (((op (e0) (e0)) = (e1))\/(((op (e1) (e0)) = (e1))\/(((op (e2) (e0)) = (e1))\/((op (e3) (e0)) = (e1))))) -> (~((op (e0) (e0)) = (e1))) -> (~((op (e1) (e0)) = (op (e1) (e2)))) -> (~((op (e3) (e3)) = (e1))) -> (~((op (e2) (e0)) = (op (e2) (e3)))) -> (~((op (e1) (e2)) = (op (e1) (e3)))) -> ((op (e1) (e2)) = (e1)) -> ((op (e0) (e2)) = (e1)) -> (~((op (e0) (e2)) = (op (e0) (e3)))) -> (((op (e0) (e3)) = (e1))\/(((op (e1) (e3)) = (e1))\/(((op (e2) (e3)) = (e1))\/((op (e3) (e3)) = (e1))))) -> (~((e1) = (e3))) -> ((op (e3) (e0)) = (e3)) -> False). % 15.41/15.57 do 0 intro. intros zenon_Hf1 zenon_H45 zenon_H166 zenon_H104 zenon_Hce zenon_H1d0 zenon_H117 zenon_H29 zenon_Hc9 zenon_H121 zenon_Ha3 zenon_Hba. % 15.41/15.57 apply (zenon_or_s _ _ zenon_Hf1); [ zenon_intro zenon_H47 | zenon_intro zenon_Hf4 ]. % 15.41/15.57 exact (zenon_H45 zenon_H47). % 15.41/15.57 apply (zenon_or_s _ _ zenon_Hf4); [ zenon_intro zenon_Hd8 | zenon_intro zenon_Hf5 ]. % 15.41/15.57 apply (zenon_L248_); trivial. % 15.41/15.57 apply (zenon_or_s _ _ zenon_Hf5); [ zenon_intro zenon_Hae | zenon_intro zenon_Hee ]. % 15.41/15.57 apply (zenon_L551_); trivial. % 15.41/15.57 apply (zenon_L79_); trivial. % 15.41/15.57 (* end of lemma zenon_L876_ *) % 15.41/15.57 assert (zenon_L877_ : ((~((op (e1) (e1)) = (e3)))\/((op (e1) (e3)) = (e1))) -> ((~((op (e2) (e2)) = (e1)))\/((op (e2) (e1)) = (e2))) -> (~((op (e2) (e1)) = (op (e2) (e3)))) -> (~((op (e2) (e1)) = (op (e2) (e2)))) -> (((op (e2) (e0)) = (e0))\/(((op (e2) (e1)) = (e0))\/(((op (e2) (e2)) = (e0))\/((op (e2) (e3)) = (e0))))) -> (~((e0) = (e2))) -> (~((op (e1) (op (e2) (e1))) = (op (e2) (e1)))) -> (((op (e2) (e0)) = (e1))\/(((op (e2) (e1)) = (e1))\/(((op (e2) (e2)) = (e1))\/((op (e2) (e3)) = (e1))))) -> ((op (e0) (e0)) = (e0)) -> (~((op (e0) (e0)) = (op (e2) (e0)))) -> (~((op (e0) (e0)) = (e3))) -> (~((e1) = (e3))) -> ((op (e1) (e0)) = (e1)) -> (((op (e1) (e1)) = (e0))\/(((op (e1) (e1)) = (e1))\/(((op (e1) (e1)) = (e2))\/((op (e1) (e1)) = (e3))))) -> (~((op (e1) (e1)) = (e2))) -> (~((op (e1) (e1)) = (e1))) -> (((op (e2) (e2)) = (e0))\/(((op (e2) (e2)) = (e1))\/(((op (e2) (e2)) = (e2))\/((op (e2) (e2)) = (e3))))) -> (((op (e0) (e0)) = (e2))\/(((op (e1) (e0)) = (e2))\/(((op (e2) (e0)) = (e2))\/((op (e3) (e0)) = (e2))))) -> (((op (e0) (e0)) = (e3))\/(((op (e0) (e1)) = (e3))\/(((op (e0) (e2)) = (e3))\/((op (e0) (e3)) = (e3))))) -> (~((op (e0) (e3)) = (op (e3) (e3)))) -> (~((op (e0) (e2)) = (op (e1) (e2)))) -> (~((op (e1) (e3)) = (op (e3) (e3)))) -> (((op (e1) (e0)) = (e3))\/(((op (e1) (e1)) = (e3))\/(((op (e1) (e2)) = (e3))\/((op (e1) (e3)) = (e3))))) -> (~((e2) = (e3))) -> (~((op (e0) (e1)) = (op (e2) (e1)))) -> (~((op (e3) (op (e2) (e3))) = (op (e2) (e3)))) -> ((op (e3) (e3)) = (e3)) -> (((op (e2) (e0)) = (e3))\/(((op (e2) (e1)) = (e3))\/(((op (e2) (e2)) = (e3))\/((op (e2) (e3)) = (e3))))) -> (~((op (e2) (e0)) = (op (e2) (e3)))) -> ((~((op (e2) (e2)) = (e3)))\/((op (e2) (e3)) = (e2))) -> (~((e1) = (e2))) -> (~((op (e0) (e0)) = (e2))) -> (((op (e0) (e0)) = (e3))\/(((op (e1) (e0)) = (e3))\/(((op (e2) (e0)) = (e3))\/((op (e3) (e0)) = (e3))))) -> ((~((op (e3) (e3)) = (e1)))\/((op (e3) (e1)) = (e3))) -> (~((op (e0) (e1)) = (op (e3) (e1)))) -> (~((op (e1) (e2)) = (op (e2) (e2)))) -> (((op (e0) (e3)) = (e1))\/(((op (e1) (e3)) = (e1))\/(((op (e2) (e3)) = (e1))\/((op (e3) (e3)) = (e1))))) -> (~((op (e0) (e0)) = (op (e0) (e3)))) -> (~((op (e0) (e3)) = (op (e2) (e3)))) -> (~((op (e0) (e3)) = (op (e1) (e3)))) -> (((op (e0) (e3)) = (e0))\/(((op (e0) (e3)) = (e1))\/(((op (e0) (e3)) = (e2))\/((op (e0) (e3)) = (e3))))) -> (~((op (e1) (e0)) = (op (e1) (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) (e2)) = (op (e3) (e2)))) -> (~((op (e0) (e2)) = (op (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 (e1) (e0)) = (e2))\/(((op (e1) (e1)) = (e2))\/(((op (e1) (e2)) = (e2))\/((op (e1) (e3)) = (e2))))) -> ((~((op (e2) (e2)) = (e2)))\/((op (e2) (e2)) = (e2))) -> ((~((op (e2) (e2)) = (e0)))\/((op (e2) (e0)) = (e2))) -> False). % 15.41/15.57 do 0 intro. intros zenon_H1d2 zenon_H1e3 zenon_H1e2 zenon_H157 zenon_H1f5 zenon_H5e zenon_H290 zenon_Hb7 zenon_H1f zenon_H258 zenon_H59 zenon_Ha3 zenon_Hd8 zenon_H1b3 zenon_Hd6 zenon_H1b4 zenon_H2d zenon_Heb zenon_H58 zenon_H36 zenon_H87 zenon_H8b zenon_H90 zenon_H6a zenon_Hde zenon_H28a zenon_H42 zenon_He6 zenon_Hce zenon_H1c3 zenon_Ha7 zenon_H8f zenon_Hbe zenon_H10c zenon_H138 zenon_H7d zenon_H121 zenon_H24f zenon_Hb4 zenon_H80 zenon_H254 zenon_H1cf zenon_H11b zenon_H250 zenon_H140 zenon_H28 zenon_H251 zenon_Hc9 zenon_H84 zenon_Haa zenon_H1d4. % 15.41/15.57 apply (zenon_or_s _ _ zenon_H1d2); [ zenon_intro zenon_H182 | zenon_intro zenon_H11f ]. % 15.41/15.57 apply (zenon_or_s _ _ zenon_H1d4); [ zenon_intro zenon_H2e | zenon_intro zenon_Hdd ]. % 15.41/15.57 apply (zenon_L814_); trivial. % 15.41/15.57 apply (zenon_L779_); trivial. % 15.41/15.57 apply (zenon_L224_); trivial. % 15.41/15.57 (* end of lemma zenon_L877_ *) % 15.41/15.57 assert (zenon_L878_ : ((~((op (e1) (e1)) = (e2)))\/((op (e1) (e2)) = (e1))) -> (~((op (e1) (e0)) = (op (e1) (e2)))) -> ((~((op (e2) (e2)) = (e0)))\/((op (e2) (e0)) = (e2))) -> ((~((op (e2) (e2)) = (e2)))\/((op (e2) (e2)) = (e2))) -> (((op (e1) (e0)) = (e2))\/(((op (e1) (e1)) = (e2))\/(((op (e1) (e2)) = (e2))\/((op (e1) (e3)) = (e2))))) -> (~((op (e0) (e2)) = (op (e0) (e3)))) -> (((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 (e3) (e2)))) -> (~((op (e0) (e0)) = (op (e0) (e2)))) -> (((op (e0) (e2)) = (e1))\/(((op (e1) (e2)) = (e1))\/(((op (e2) (e2)) = (e1))\/((op (e3) (e2)) = (e1))))) -> (~((op (e1) (e0)) = (op (e1) (e3)))) -> (((op (e0) (e3)) = (e0))\/(((op (e0) (e3)) = (e1))\/(((op (e0) (e3)) = (e2))\/((op (e0) (e3)) = (e3))))) -> (~((op (e0) (e3)) = (op (e1) (e3)))) -> (~((op (e0) (e3)) = (op (e2) (e3)))) -> (~((op (e0) (e0)) = (op (e0) (e3)))) -> (((op (e0) (e3)) = (e1))\/(((op (e1) (e3)) = (e1))\/(((op (e2) (e3)) = (e1))\/((op (e3) (e3)) = (e1))))) -> (~((op (e1) (e2)) = (op (e2) (e2)))) -> (~((op (e0) (e1)) = (op (e3) (e1)))) -> ((~((op (e3) (e3)) = (e1)))\/((op (e3) (e1)) = (e3))) -> (((op (e0) (e0)) = (e3))\/(((op (e1) (e0)) = (e3))\/(((op (e2) (e0)) = (e3))\/((op (e3) (e0)) = (e3))))) -> (~((op (e0) (e0)) = (e2))) -> (~((e1) = (e2))) -> ((~((op (e2) (e2)) = (e3)))\/((op (e2) (e3)) = (e2))) -> (~((op (e2) (e0)) = (op (e2) (e3)))) -> (((op (e2) (e0)) = (e3))\/(((op (e2) (e1)) = (e3))\/(((op (e2) (e2)) = (e3))\/((op (e2) (e3)) = (e3))))) -> ((op (e3) (e3)) = (e3)) -> (~((op (e3) (op (e2) (e3))) = (op (e2) (e3)))) -> (~((op (e0) (e1)) = (op (e2) (e1)))) -> (~((e2) = (e3))) -> (((op (e1) (e0)) = (e3))\/(((op (e1) (e1)) = (e3))\/(((op (e1) (e2)) = (e3))\/((op (e1) (e3)) = (e3))))) -> (~((op (e1) (e3)) = (op (e3) (e3)))) -> (~((op (e0) (e2)) = (op (e1) (e2)))) -> (~((op (e0) (e3)) = (op (e3) (e3)))) -> (((op (e0) (e0)) = (e3))\/(((op (e0) (e1)) = (e3))\/(((op (e0) (e2)) = (e3))\/((op (e0) (e3)) = (e3))))) -> (((op (e0) (e0)) = (e2))\/(((op (e1) (e0)) = (e2))\/(((op (e2) (e0)) = (e2))\/((op (e3) (e0)) = (e2))))) -> (((op (e2) (e2)) = (e0))\/(((op (e2) (e2)) = (e1))\/(((op (e2) (e2)) = (e2))\/((op (e2) (e2)) = (e3))))) -> (~((op (e1) (e1)) = (e1))) -> (((op (e1) (e1)) = (e0))\/(((op (e1) (e1)) = (e1))\/(((op (e1) (e1)) = (e2))\/((op (e1) (e1)) = (e3))))) -> ((op (e1) (e0)) = (e1)) -> (~((e1) = (e3))) -> (~((op (e0) (e0)) = (e3))) -> (~((op (e0) (e0)) = (op (e2) (e0)))) -> ((op (e0) (e0)) = (e0)) -> (((op (e2) (e0)) = (e1))\/(((op (e2) (e1)) = (e1))\/(((op (e2) (e2)) = (e1))\/((op (e2) (e3)) = (e1))))) -> (~((op (e1) (op (e2) (e1))) = (op (e2) (e1)))) -> (~((e0) = (e2))) -> (((op (e2) (e0)) = (e0))\/(((op (e2) (e1)) = (e0))\/(((op (e2) (e2)) = (e0))\/((op (e2) (e3)) = (e0))))) -> (~((op (e2) (e1)) = (op (e2) (e2)))) -> (~((op (e2) (e1)) = (op (e2) (e3)))) -> ((~((op (e2) (e2)) = (e1)))\/((op (e2) (e1)) = (e2))) -> ((~((op (e1) (e1)) = (e3)))\/((op (e1) (e3)) = (e1))) -> False). % 15.41/15.57 do 0 intro. intros zenon_H1d3 zenon_H166 zenon_H1d4 zenon_Haa zenon_H84 zenon_Hc9 zenon_H251 zenon_H28 zenon_H140 zenon_H250 zenon_H11b zenon_H1cf zenon_H254 zenon_H80 zenon_Hb4 zenon_H24f zenon_H121 zenon_H7d zenon_H138 zenon_H10c zenon_Hbe zenon_H8f zenon_Ha7 zenon_H1c3 zenon_Hce zenon_He6 zenon_H42 zenon_H28a zenon_Hde zenon_H6a zenon_H90 zenon_H8b zenon_H87 zenon_H36 zenon_H58 zenon_Heb zenon_H2d zenon_H1b4 zenon_H1b3 zenon_Hd8 zenon_Ha3 zenon_H59 zenon_H258 zenon_H1f zenon_Hb7 zenon_H290 zenon_H5e zenon_H1f5 zenon_H157 zenon_H1e2 zenon_H1e3 zenon_H1d2. % 15.41/15.57 apply (zenon_or_s _ _ zenon_H1d3); [ zenon_intro zenon_Hd6 | zenon_intro zenon_H117 ]. % 15.41/15.57 apply (zenon_L877_); trivial. % 15.41/15.57 apply (zenon_L248_); trivial. % 15.41/15.57 (* end of lemma zenon_L878_ *) % 15.41/15.57 assert (zenon_L879_ : ((~((op (e1) (e1)) = (e1)))\/((op (e1) (e1)) = (e1))) -> (~((op (e1) (e0)) = (op (e1) (e1)))) -> ((~((op (e1) (e1)) = (e3)))\/((op (e1) (e3)) = (e1))) -> ((~((op (e2) (e2)) = (e1)))\/((op (e2) (e1)) = (e2))) -> (~((op (e2) (e1)) = (op (e2) (e3)))) -> (~((op (e2) (e1)) = (op (e2) (e2)))) -> (((op (e2) (e0)) = (e0))\/(((op (e2) (e1)) = (e0))\/(((op (e2) (e2)) = (e0))\/((op (e2) (e3)) = (e0))))) -> (~((e0) = (e2))) -> (~((op (e1) (op (e2) (e1))) = (op (e2) (e1)))) -> (((op (e2) (e0)) = (e1))\/(((op (e2) (e1)) = (e1))\/(((op (e2) (e2)) = (e1))\/((op (e2) (e3)) = (e1))))) -> ((op (e0) (e0)) = (e0)) -> (~((op (e0) (e0)) = (op (e2) (e0)))) -> (~((op (e0) (e0)) = (e3))) -> (~((e1) = (e3))) -> ((op (e1) (e0)) = (e1)) -> (((op (e1) (e1)) = (e0))\/(((op (e1) (e1)) = (e1))\/(((op (e1) (e1)) = (e2))\/((op (e1) (e1)) = (e3))))) -> (((op (e2) (e2)) = (e0))\/(((op (e2) (e2)) = (e1))\/(((op (e2) (e2)) = (e2))\/((op (e2) (e2)) = (e3))))) -> (((op (e0) (e0)) = (e2))\/(((op (e1) (e0)) = (e2))\/(((op (e2) (e0)) = (e2))\/((op (e3) (e0)) = (e2))))) -> (((op (e0) (e0)) = (e3))\/(((op (e0) (e1)) = (e3))\/(((op (e0) (e2)) = (e3))\/((op (e0) (e3)) = (e3))))) -> (~((op (e0) (e3)) = (op (e3) (e3)))) -> (~((op (e0) (e2)) = (op (e1) (e2)))) -> (~((op (e1) (e3)) = (op (e3) (e3)))) -> (((op (e1) (e0)) = (e3))\/(((op (e1) (e1)) = (e3))\/(((op (e1) (e2)) = (e3))\/((op (e1) (e3)) = (e3))))) -> (~((e2) = (e3))) -> (~((op (e0) (e1)) = (op (e2) (e1)))) -> (~((op (e3) (op (e2) (e3))) = (op (e2) (e3)))) -> ((op (e3) (e3)) = (e3)) -> (((op (e2) (e0)) = (e3))\/(((op (e2) (e1)) = (e3))\/(((op (e2) (e2)) = (e3))\/((op (e2) (e3)) = (e3))))) -> (~((op (e2) (e0)) = (op (e2) (e3)))) -> ((~((op (e2) (e2)) = (e3)))\/((op (e2) (e3)) = (e2))) -> (~((e1) = (e2))) -> (~((op (e0) (e0)) = (e2))) -> (((op (e0) (e0)) = (e3))\/(((op (e1) (e0)) = (e3))\/(((op (e2) (e0)) = (e3))\/((op (e3) (e0)) = (e3))))) -> ((~((op (e3) (e3)) = (e1)))\/((op (e3) (e1)) = (e3))) -> (~((op (e0) (e1)) = (op (e3) (e1)))) -> (~((op (e1) (e2)) = (op (e2) (e2)))) -> (((op (e0) (e3)) = (e1))\/(((op (e1) (e3)) = (e1))\/(((op (e2) (e3)) = (e1))\/((op (e3) (e3)) = (e1))))) -> (~((op (e0) (e0)) = (op (e0) (e3)))) -> (~((op (e0) (e3)) = (op (e2) (e3)))) -> (~((op (e0) (e3)) = (op (e1) (e3)))) -> (((op (e0) (e3)) = (e0))\/(((op (e0) (e3)) = (e1))\/(((op (e0) (e3)) = (e2))\/((op (e0) (e3)) = (e3))))) -> (~((op (e1) (e0)) = (op (e1) (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) (e2)) = (op (e3) (e2)))) -> (~((op (e0) (e2)) = (op (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 (e1) (e0)) = (e2))\/(((op (e1) (e1)) = (e2))\/(((op (e1) (e2)) = (e2))\/((op (e1) (e3)) = (e2))))) -> ((~((op (e2) (e2)) = (e2)))\/((op (e2) (e2)) = (e2))) -> ((~((op (e2) (e2)) = (e0)))\/((op (e2) (e0)) = (e2))) -> (~((op (e1) (e0)) = (op (e1) (e2)))) -> ((~((op (e1) (e1)) = (e2)))\/((op (e1) (e2)) = (e1))) -> False). % 15.41/15.57 do 0 intro. intros zenon_H1d8 zenon_Hd7 zenon_H1d2 zenon_H1e3 zenon_H1e2 zenon_H157 zenon_H1f5 zenon_H5e zenon_H290 zenon_Hb7 zenon_H1f zenon_H258 zenon_H59 zenon_Ha3 zenon_Hd8 zenon_H1b3 zenon_H2d zenon_Heb zenon_H58 zenon_H36 zenon_H87 zenon_H8b zenon_H90 zenon_H6a zenon_Hde zenon_H28a zenon_H42 zenon_He6 zenon_Hce zenon_H1c3 zenon_Ha7 zenon_H8f zenon_Hbe zenon_H10c zenon_H138 zenon_H7d zenon_H121 zenon_H24f zenon_Hb4 zenon_H80 zenon_H254 zenon_H1cf zenon_H11b zenon_H250 zenon_H140 zenon_H28 zenon_H251 zenon_Hc9 zenon_H84 zenon_Haa zenon_H1d4 zenon_H166 zenon_H1d3. % 15.41/15.57 apply (zenon_or_s _ _ zenon_H1d8); [ zenon_intro zenon_H1b4 | zenon_intro zenon_H21 ]. % 15.41/15.57 apply (zenon_L878_); trivial. % 15.41/15.57 apply (zenon_L61_); trivial. % 15.41/15.57 (* end of lemma zenon_L879_ *) % 15.41/15.57 assert (zenon_L880_ : (((op (e0) (e0)) = (e3))\/(((op (e0) (e1)) = (e3))\/(((op (e0) (e2)) = (e3))\/((op (e0) (e3)) = (e3))))) -> (~((op (e0) (e0)) = (e3))) -> (~((op (e3) (op (e2) (e3))) = (op (e2) (e3)))) -> (~((op (e2) (e2)) = (e3))) -> (~((op (e0) (e1)) = (op (e2) (e1)))) -> ((op (e2) (e0)) = (e2)) -> (~((e2) = (e3))) -> (((op (e2) (e0)) = (e3))\/(((op (e2) (e1)) = (e3))\/(((op (e2) (e2)) = (e3))\/((op (e2) (e3)) = (e3))))) -> (~((e1) = (e3))) -> ((op (e0) (e2)) = (e1)) -> ((op (e3) (e3)) = (e3)) -> (~((op (e0) (e3)) = (op (e3) (e3)))) -> False). % 15.41/15.57 do 0 intro. intros zenon_H58 zenon_H59 zenon_H28a zenon_H30 zenon_Hde zenon_Hdd zenon_H6a zenon_He6 zenon_Ha3 zenon_H29 zenon_H42 zenon_H36. % 15.41/15.57 apply (zenon_or_s _ _ zenon_H58); [ zenon_intro zenon_H5b | zenon_intro zenon_H5a ]. % 15.41/15.57 exact (zenon_H59 zenon_H5b). % 15.41/15.57 apply (zenon_or_s _ _ zenon_H5a); [ zenon_intro zenon_H4a | zenon_intro zenon_H5c ]. % 15.41/15.57 apply (zenon_L777_); trivial. % 15.41/15.57 apply (zenon_or_s _ _ zenon_H5c); [ zenon_intro zenon_H50 | zenon_intro zenon_H53 ]. % 15.41/15.57 apply (zenon_L29_); trivial. % 15.41/15.57 apply (zenon_L12_); trivial. % 15.41/15.57 (* end of lemma zenon_L880_ *) % 15.41/15.57 assert (zenon_L881_ : (((op (e0) (e0)) = (e2))\/(((op (e1) (e0)) = (e2))\/(((op (e2) (e0)) = (e2))\/((op (e3) (e0)) = (e2))))) -> (~((op (e0) (e0)) = (e2))) -> (~((op (e1) (e3)) = (op (e2) (e3)))) -> (~((op (e2) (e2)) = (e0))) -> (~((e0) = (e2))) -> ((op (e2) (e1)) = (e2)) -> (~((op (e0) (e0)) = (op (e2) (e0)))) -> ((op (e0) (e0)) = (e0)) -> (((op (e2) (e0)) = (e0))\/(((op (e2) (e1)) = (e0))\/(((op (e2) (e2)) = (e0))\/((op (e2) (e3)) = (e0))))) -> (((op (e1) (e0)) = (e3))\/(((op (e1) (e1)) = (e3))\/(((op (e1) (e2)) = (e3))\/((op (e1) (e3)) = (e3))))) -> (~((op (e1) (e1)) = (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 (e1) (e3)))) -> (~((op (e0) (e3)) = (op (e2) (e3)))) -> (~((op (e0) (e0)) = (op (e0) (e3)))) -> (((op (e0) (e3)) = (e0))\/(((op (e0) (e3)) = (e1))\/(((op (e0) (e3)) = (e2))\/((op (e0) (e3)) = (e3))))) -> (~((op (e1) (e1)) = (op (e1) (e3)))) -> ((op (e1) (e1)) = (e1)) -> (((op (e3) (e0)) = (e2))\/(((op (e3) (e1)) = (e2))\/(((op (e3) (e2)) = (e2))\/((op (e3) (e3)) = (e2))))) -> (~((op (e2) (e1)) = (op (e3) (e1)))) -> (~((op (e0) (e2)) = (op (e1) (e2)))) -> (~((op (e0) (e2)) = (op (e3) (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) (e3)) = (e2))) -> (((op (e0) (e3)) = (e1))\/(((op (e1) (e3)) = (e1))\/(((op (e2) (e3)) = (e1))\/((op (e3) (e3)) = (e1))))) -> (~((op (e1) (e3)) = (op (e3) (e3)))) -> (~((op (e1) (e1)) = (e0))) -> (~((op (e0) (e0)) = (op (e1) (e0)))) -> (((op (e1) (e0)) = (e0))\/(((op (e1) (e1)) = (e0))\/(((op (e1) (e2)) = (e0))\/((op (e1) (e3)) = (e0))))) -> (~((op (e0) (e3)) = (op (e3) (e3)))) -> ((op (e3) (e3)) = (e3)) -> ((op (e0) (e2)) = (e1)) -> (~((e1) = (e3))) -> (((op (e2) (e0)) = (e3))\/(((op (e2) (e1)) = (e3))\/(((op (e2) (e2)) = (e3))\/((op (e2) (e3)) = (e3))))) -> (~((e2) = (e3))) -> (~((op (e0) (e1)) = (op (e2) (e1)))) -> (~((op (e2) (e2)) = (e3))) -> (~((op (e3) (op (e2) (e3))) = (op (e2) (e3)))) -> (~((op (e0) (e0)) = (e3))) -> (((op (e0) (e0)) = (e3))\/(((op (e0) (e1)) = (e3))\/(((op (e0) (e2)) = (e3))\/((op (e0) (e3)) = (e3))))) -> ((op (e3) (e0)) = (e1)) -> (~((e1) = (e2))) -> False). % 15.41/15.57 do 0 intro. intros zenon_Heb zenon_H8f zenon_H244 zenon_H2e zenon_H5e zenon_H156 zenon_H258 zenon_H1f zenon_H1f5 zenon_H90 zenon_H182 zenon_H104 zenon_H25b zenon_H80 zenon_Hb4 zenon_H24f zenon_H254 zenon_H11e zenon_H21 zenon_H1df zenon_H13c zenon_H87 zenon_H140 zenon_Hc9 zenon_H251 zenon_H3d zenon_H121 zenon_H8b zenon_H145 zenon_H24c zenon_H163 zenon_H36 zenon_H42 zenon_H29 zenon_Ha3 zenon_He6 zenon_H6a zenon_Hde zenon_H30 zenon_H28a zenon_H59 zenon_H58 zenon_Hee zenon_Ha7. % 15.41/15.57 apply (zenon_or_s _ _ zenon_Heb); [ zenon_intro zenon_H92 | zenon_intro zenon_Hec ]. % 15.41/15.57 exact (zenon_H8f zenon_H92). % 15.41/15.57 apply (zenon_or_s _ _ zenon_Hec); [ zenon_intro zenon_H68 | zenon_intro zenon_Hed ]. % 15.41/15.57 apply (zenon_or_s _ _ zenon_H163); [ zenon_intro zenon_Had | zenon_intro zenon_H164 ]. % 15.41/15.57 apply (zenon_L559_); trivial. % 15.41/15.57 apply (zenon_or_s _ _ zenon_H164); [ zenon_intro zenon_H149 | zenon_intro zenon_H165 ]. % 15.41/15.57 exact (zenon_H145 zenon_H149). % 15.41/15.57 apply (zenon_or_s _ _ zenon_H165); [ zenon_intro zenon_H15d | zenon_intro zenon_Hcc ]. % 15.41/15.57 apply (zenon_or_s _ _ zenon_H90); [ zenon_intro zenon_H69 | zenon_intro zenon_H94 ]. % 15.41/15.57 apply (zenon_L17_); trivial. % 15.41/15.57 apply (zenon_or_s _ _ zenon_H94); [ zenon_intro zenon_H96 | zenon_intro zenon_H95 ]. % 15.41/15.57 exact (zenon_H182 zenon_H96). % 15.41/15.57 apply (zenon_or_s _ _ zenon_H95); [ zenon_intro zenon_H88 | zenon_intro zenon_H8a ]. % 15.41/15.57 apply (zenon_or_s _ _ zenon_H1f5); [ zenon_intro zenon_Hcf | zenon_intro zenon_H1f9 ]. % 15.41/15.57 apply (zenon_L598_); trivial. % 15.41/15.57 apply (zenon_or_s _ _ zenon_H1f9); [ zenon_intro zenon_H14a | zenon_intro zenon_H1fa ]. % 15.41/15.57 apply (zenon_L351_); trivial. % 15.41/15.57 apply (zenon_or_s _ _ zenon_H1fa); [ zenon_intro zenon_H32 | zenon_intro zenon_Hd0 ]. % 15.41/15.57 exact (zenon_H2e zenon_H32). % 15.41/15.57 apply (zenon_or_s _ _ zenon_H121); [ zenon_intro zenon_H37 | zenon_intro zenon_H122 ]. % 15.41/15.57 apply (zenon_L632_); trivial. % 15.41/15.57 apply (zenon_or_s _ _ zenon_H122); [ zenon_intro zenon_H11f | zenon_intro zenon_H123 ]. % 15.41/15.57 apply (zenon_L90_); trivial. % 15.41/15.57 apply (zenon_or_s _ _ zenon_H123); [ zenon_intro zenon_Hb5 | zenon_intro zenon_H38 ]. % 15.41/15.57 apply (zenon_L616_); trivial. % 15.41/15.57 exact (zenon_H104 zenon_H38). % 15.41/15.57 apply (zenon_L25_); trivial. % 15.41/15.57 apply (zenon_L600_); trivial. % 15.41/15.57 apply (zenon_or_s _ _ zenon_Hed); [ zenon_intro zenon_Hdd | zenon_intro zenon_He9 ]. % 15.41/15.57 apply (zenon_L880_); trivial. % 15.41/15.57 apply (zenon_L122_); trivial. % 15.41/15.57 (* end of lemma zenon_L881_ *) % 15.41/15.57 assert (zenon_L882_ : (((op (e0) (e0)) = (e3))\/(((op (e1) (e0)) = (e3))\/(((op (e2) (e0)) = (e3))\/((op (e3) (e0)) = (e3))))) -> ((op (e1) (e0)) = (e2)) -> (~((e1) = (e2))) -> (~((op (e2) (e2)) = (e1))) -> (~((op (e1) (e1)) = (op (e2) (e1)))) -> ((op (e1) (e1)) = (e1)) -> (((op (e2) (e0)) = (e1))\/(((op (e2) (e1)) = (e1))\/(((op (e2) (e2)) = (e1))\/((op (e2) (e3)) = (e1))))) -> (~((op (e2) (e2)) = (e2))) -> (((op (e0) (e0)) = (e2))\/(((op (e1) (e0)) = (e2))\/(((op (e2) (e0)) = (e2))\/((op (e3) (e0)) = (e2))))) -> (~((op (e0) (e0)) = (e2))) -> (~((op (e1) (e3)) = (op (e2) (e3)))) -> (~((op (e2) (e2)) = (e0))) -> (~((e0) = (e2))) -> (~((op (e0) (e0)) = (op (e2) (e0)))) -> ((op (e0) (e0)) = (e0)) -> (((op (e2) (e0)) = (e0))\/(((op (e2) (e1)) = (e0))\/(((op (e2) (e2)) = (e0))\/((op (e2) (e3)) = (e0))))) -> (((op (e1) (e0)) = (e3))\/(((op (e1) (e1)) = (e3))\/(((op (e1) (e2)) = (e3))\/((op (e1) (e3)) = (e3))))) -> (~((op (e1) (e1)) = (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 (e1) (e3)))) -> (~((op (e0) (e3)) = (op (e2) (e3)))) -> (~((op (e0) (e0)) = (op (e0) (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) (e0)) = (e2))\/(((op (e3) (e1)) = (e2))\/(((op (e3) (e2)) = (e2))\/((op (e3) (e3)) = (e2))))) -> (~((op (e2) (e1)) = (op (e3) (e1)))) -> (~((op (e0) (e2)) = (op (e1) (e2)))) -> (~((op (e0) (e2)) = (op (e3) (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) (e3)) = (e2))) -> (((op (e0) (e3)) = (e1))\/(((op (e1) (e3)) = (e1))\/(((op (e2) (e3)) = (e1))\/((op (e3) (e3)) = (e1))))) -> (~((op (e1) (e3)) = (op (e3) (e3)))) -> (~((op (e1) (e1)) = (e0))) -> (~((op (e0) (e0)) = (op (e1) (e0)))) -> (((op (e1) (e0)) = (e0))\/(((op (e1) (e1)) = (e0))\/(((op (e1) (e2)) = (e0))\/((op (e1) (e3)) = (e0))))) -> (~((op (e0) (e3)) = (op (e3) (e3)))) -> ((op (e3) (e3)) = (e3)) -> ((op (e0) (e2)) = (e1)) -> (((op (e2) (e0)) = (e3))\/(((op (e2) (e1)) = (e3))\/(((op (e2) (e2)) = (e3))\/((op (e2) (e3)) = (e3))))) -> (~((e2) = (e3))) -> (~((op (e0) (e1)) = (op (e2) (e1)))) -> (~((op (e2) (e2)) = (e3))) -> (~((op (e3) (op (e2) (e3))) = (op (e2) (e3)))) -> (~((op (e0) (e0)) = (e3))) -> (((op (e0) (e0)) = (e3))\/(((op (e0) (e1)) = (e3))\/(((op (e0) (e2)) = (e3))\/((op (e0) (e3)) = (e3))))) -> (((op (e2) (e0)) = (e2))\/(((op (e2) (e1)) = (e2))\/(((op (e2) (e2)) = (e2))\/((op (e2) (e3)) = (e2))))) -> (~((e1) = (e3))) -> ((op (e3) (e0)) = (e1)) -> False). % 15.41/15.57 do 0 intro. intros zenon_Hbe zenon_H68 zenon_Ha7 zenon_H52 zenon_Hb1 zenon_H21 zenon_Hb7 zenon_H2f zenon_Heb zenon_H8f zenon_H244 zenon_H2e zenon_H5e zenon_H258 zenon_H1f zenon_H1f5 zenon_H90 zenon_H182 zenon_H104 zenon_H25b zenon_H80 zenon_Hb4 zenon_H24f zenon_H254 zenon_H11e zenon_H1df zenon_H13c zenon_H87 zenon_H140 zenon_Hc9 zenon_H251 zenon_H3d zenon_H121 zenon_H8b zenon_H145 zenon_H24c zenon_H163 zenon_H36 zenon_H42 zenon_H29 zenon_He6 zenon_H6a zenon_Hde zenon_H30 zenon_H28a zenon_H59 zenon_H58 zenon_H237 zenon_Ha3 zenon_Hee. % 15.41/15.57 apply (zenon_or_s _ _ zenon_Hbe); [ zenon_intro zenon_H5b | zenon_intro zenon_Hbf ]. % 15.41/15.57 exact (zenon_H59 zenon_H5b). % 15.41/15.57 apply (zenon_or_s _ _ zenon_Hbf); [ zenon_intro zenon_H69 | zenon_intro zenon_Hc0 ]. % 15.41/15.57 apply (zenon_L17_); trivial. % 15.41/15.57 apply (zenon_or_s _ _ zenon_Hc0); [ zenon_intro zenon_Haf | zenon_intro zenon_Hba ]. % 15.41/15.57 apply (zenon_or_s _ _ zenon_H237); [ zenon_intro zenon_Hdd | zenon_intro zenon_H238 ]. % 15.41/15.57 apply (zenon_L64_); trivial. % 15.41/15.57 apply (zenon_or_s _ _ zenon_H238); [ zenon_intro zenon_H156 | zenon_intro zenon_H239 ]. % 15.41/15.57 apply (zenon_L881_); trivial. % 15.41/15.57 apply (zenon_or_s _ _ zenon_H239); [ zenon_intro zenon_H35 | zenon_intro zenon_H124 ]. % 15.41/15.57 exact (zenon_H2f zenon_H35). % 15.41/15.57 apply (zenon_L96_); trivial. % 15.41/15.57 apply (zenon_L79_); trivial. % 15.41/15.57 (* end of lemma zenon_L882_ *) % 15.41/15.57 assert (zenon_L883_ : (((op (e0) (e0)) = (e3))\/(((op (e0) (e1)) = (e3))\/(((op (e0) (e2)) = (e3))\/((op (e0) (e3)) = (e3))))) -> (~((op (e0) (e0)) = (e3))) -> ((op (e3) (e3)) = (e3)) -> (~((op (e3) (op (e2) (e3))) = (op (e2) (e3)))) -> (~((op (e2) (e2)) = (e3))) -> (~((op (e0) (e1)) = (op (e2) (e1)))) -> ((op (e2) (e0)) = (e1)) -> (((op (e2) (e0)) = (e3))\/(((op (e2) (e1)) = (e3))\/(((op (e2) (e2)) = (e3))\/((op (e2) (e3)) = (e3))))) -> (~((op (e0) (e2)) = (op (e2) (e2)))) -> (~((op (e2) (e2)) = (e2))) -> (~((op (e2) (e2)) = (e1))) -> (~((op (e2) (e2)) = (e0))) -> (((op (e2) (e2)) = (e0))\/(((op (e2) (e2)) = (e1))\/(((op (e2) (e2)) = (e2))\/((op (e2) (e2)) = (e3))))) -> ((op (e0) (e3)) = (e1)) -> (~((e1) = (e3))) -> False). % 15.41/15.57 do 0 intro. intros zenon_H58 zenon_H59 zenon_H42 zenon_H28a zenon_H30 zenon_Hde zenon_Hae zenon_He6 zenon_H28 zenon_H2f zenon_H52 zenon_H2e zenon_H2d zenon_H37 zenon_Ha3. % 15.41/15.57 apply (zenon_or_s _ _ zenon_H58); [ zenon_intro zenon_H5b | zenon_intro zenon_H5a ]. % 15.41/15.57 exact (zenon_H59 zenon_H5b). % 15.41/15.57 apply (zenon_or_s _ _ zenon_H5a); [ zenon_intro zenon_H4a | zenon_intro zenon_H5c ]. % 15.41/15.57 apply (zenon_L787_); trivial. % 15.41/15.57 apply (zenon_or_s _ _ zenon_H5c); [ zenon_intro zenon_H50 | zenon_intro zenon_H53 ]. % 15.41/15.57 apply (zenon_L11_); trivial. % 15.41/15.57 apply (zenon_L32_); trivial. % 15.41/15.57 (* end of lemma zenon_L883_ *) % 15.41/15.57 assert (zenon_L884_ : (((op (e0) (e0)) = (e3))\/(((op (e1) (e0)) = (e3))\/(((op (e2) (e0)) = (e3))\/((op (e3) (e0)) = (e3))))) -> (~((op (e0) (e0)) = (e3))) -> (~((e2) = (e3))) -> ((op (e1) (e0)) = (e2)) -> ((op (e0) (e3)) = (e1)) -> (~((op (e0) (e3)) = (op (e2) (e3)))) -> (~((op (e2) (e2)) = (e1))) -> (~((op (e1) (e1)) = (op (e2) (e1)))) -> ((op (e1) (e1)) = (e1)) -> (((op (e2) (e0)) = (e1))\/(((op (e2) (e1)) = (e1))\/(((op (e2) (e2)) = (e1))\/((op (e2) (e3)) = (e1))))) -> (~((e1) = (e3))) -> ((op (e3) (e0)) = (e1)) -> False). % 15.41/15.57 do 0 intro. intros zenon_Hbe zenon_H59 zenon_H6a zenon_H68 zenon_H37 zenon_Hb4 zenon_H52 zenon_Hb1 zenon_H21 zenon_Hb7 zenon_Ha3 zenon_Hee. % 15.41/15.57 apply (zenon_or_s _ _ zenon_Hbe); [ zenon_intro zenon_H5b | zenon_intro zenon_Hbf ]. % 15.41/15.57 exact (zenon_H59 zenon_H5b). % 15.41/15.57 apply (zenon_or_s _ _ zenon_Hbf); [ zenon_intro zenon_H69 | zenon_intro zenon_Hc0 ]. % 15.41/15.57 apply (zenon_L17_); trivial. % 15.41/15.57 apply (zenon_or_s _ _ zenon_Hc0); [ zenon_intro zenon_Haf | zenon_intro zenon_Hba ]. % 15.41/15.57 apply (zenon_L42_); trivial. % 15.41/15.57 apply (zenon_L79_); trivial. % 15.41/15.57 (* end of lemma zenon_L884_ *) % 15.41/15.57 assert (zenon_L885_ : (((op (e0) (e0)) = (e2))\/(((op (e1) (e0)) = (e2))\/(((op (e2) (e0)) = (e2))\/((op (e3) (e0)) = (e2))))) -> (~((op (e0) (e0)) = (e2))) -> (~((e1) = (e3))) -> (~((e2) = (e3))) -> (~((op (e0) (e0)) = (e3))) -> (((op (e0) (e0)) = (e3))\/(((op (e1) (e0)) = (e3))\/(((op (e2) (e0)) = (e3))\/((op (e3) (e0)) = (e3))))) -> ((op (e0) (e3)) = (e1)) -> (~((op (e0) (e3)) = (op (e2) (e3)))) -> (~((op (e2) (e2)) = (e1))) -> (~((op (e1) (e1)) = (op (e2) (e1)))) -> ((op (e1) (e1)) = (e1)) -> (((op (e2) (e0)) = (e1))\/(((op (e2) (e1)) = (e1))\/(((op (e2) (e2)) = (e1))\/((op (e2) (e3)) = (e1))))) -> ((op (e3) (e0)) = (e1)) -> (~((e1) = (e2))) -> False). % 15.41/15.57 do 0 intro. intros zenon_Heb zenon_H8f zenon_Ha3 zenon_H6a zenon_H59 zenon_Hbe zenon_H37 zenon_Hb4 zenon_H52 zenon_Hb1 zenon_H21 zenon_Hb7 zenon_Hee zenon_Ha7. % 15.41/15.57 apply (zenon_or_s _ _ zenon_Heb); [ zenon_intro zenon_H92 | zenon_intro zenon_Hec ]. % 15.41/15.57 exact (zenon_H8f zenon_H92). % 15.41/15.57 apply (zenon_or_s _ _ zenon_Hec); [ zenon_intro zenon_H68 | zenon_intro zenon_Hed ]. % 15.41/15.57 apply (zenon_L884_); trivial. % 15.41/15.57 apply (zenon_or_s _ _ zenon_Hed); [ zenon_intro zenon_Hdd | zenon_intro zenon_He9 ]. % 15.41/15.57 apply (zenon_L322_); trivial. % 15.41/15.57 apply (zenon_L122_); trivial. % 15.41/15.57 (* end of lemma zenon_L885_ *) % 15.41/15.57 assert (zenon_L886_ : (((op (e0) (e0)) = (e1))\/(((op (e0) (e1)) = (e1))\/(((op (e0) (e2)) = (e1))\/((op (e0) (e3)) = (e1))))) -> (~((op (e0) (e1)) = (op (e1) (e1)))) -> (~((op (e0) (e3)) = (op (e3) (e3)))) -> (~((op (e1) (e3)) = (op (e2) (e3)))) -> (~((e0) = (e2))) -> (~((op (e0) (e0)) = (op (e2) (e0)))) -> ((op (e0) (e0)) = (e0)) -> (((op (e2) (e0)) = (e0))\/(((op (e2) (e1)) = (e0))\/(((op (e2) (e2)) = (e0))\/((op (e2) (e3)) = (e0))))) -> (((op (e1) (e0)) = (e3))\/(((op (e1) (e1)) = (e3))\/(((op (e1) (e2)) = (e3))\/((op (e1) (e3)) = (e3))))) -> (~((op (e1) (e1)) = (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 (e1) (e3)))) -> (~((op (e0) (e0)) = (op (e0) (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) (e0)) = (e2))\/(((op (e3) (e1)) = (e2))\/(((op (e3) (e2)) = (e2))\/((op (e3) (e3)) = (e2))))) -> (~((op (e2) (e1)) = (op (e3) (e1)))) -> (~((op (e0) (e2)) = (op (e1) (e2)))) -> (~((op (e0) (e2)) = (op (e3) (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) (e3)) = (e2))) -> (((op (e0) (e3)) = (e1))\/(((op (e1) (e3)) = (e1))\/(((op (e2) (e3)) = (e1))\/((op (e3) (e3)) = (e1))))) -> (~((op (e1) (e3)) = (op (e3) (e3)))) -> (~((op (e1) (e1)) = (e0))) -> (~((op (e0) (e0)) = (op (e1) (e0)))) -> (((op (e1) (e0)) = (e0))\/(((op (e1) (e1)) = (e0))\/(((op (e1) (e2)) = (e0))\/((op (e1) (e3)) = (e0))))) -> (((op (e2) (e0)) = (e2))\/(((op (e2) (e1)) = (e2))\/(((op (e2) (e2)) = (e2))\/((op (e2) (e3)) = (e2))))) -> ((~((op (e1) (e1)) = (e1)))\/((op (e1) (e1)) = (e1))) -> ((~((op (e1) (e1)) = (e3)))\/((op (e1) (e3)) = (e1))) -> ((~((op (e2) (e2)) = (e1)))\/((op (e2) (e1)) = (e2))) -> (~((op (e2) (e1)) = (op (e2) (e3)))) -> (~((op (e2) (e1)) = (op (e2) (e2)))) -> (~((op (e1) (op (e2) (e1))) = (op (e2) (e1)))) -> (((op (e1) (e1)) = (e0))\/(((op (e1) (e1)) = (e1))\/(((op (e1) (e1)) = (e2))\/((op (e1) (e1)) = (e3))))) -> (~((op (e2) (e0)) = (op (e2) (e3)))) -> ((~((op (e2) (e2)) = (e3)))\/((op (e2) (e3)) = (e2))) -> ((~((op (e3) (e3)) = (e1)))\/((op (e3) (e1)) = (e3))) -> (~((op (e0) (e1)) = (op (e3) (e1)))) -> (~((op (e1) (e2)) = (op (e2) (e2)))) -> (~((op (e1) (e0)) = (op (e1) (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) (e0)) = (e2))\/(((op (e1) (e1)) = (e2))\/(((op (e1) (e2)) = (e2))\/((op (e1) (e3)) = (e2))))) -> ((~((op (e2) (e2)) = (e2)))\/((op (e2) (e2)) = (e2))) -> ((~((op (e2) (e2)) = (e0)))\/((op (e2) (e0)) = (e2))) -> (~((op (e1) (e0)) = (op (e1) (e2)))) -> ((~((op (e1) (e1)) = (e2)))\/((op (e1) (e2)) = (e1))) -> (((op (e0) (e0)) = (e1))\/(((op (e1) (e0)) = (e1))\/(((op (e2) (e0)) = (e1))\/((op (e3) (e0)) = (e1))))) -> (~((op (e0) (e0)) = (e1))) -> (~((op (e1) (e0)) = (op (e1) (e1)))) -> (((op (e2) (e2)) = (e0))\/(((op (e2) (e2)) = (e1))\/(((op (e2) (e2)) = (e2))\/((op (e2) (e2)) = (e3))))) -> (~((op (e2) (e2)) = (e0))) -> (~((op (e2) (e2)) = (e2))) -> (~((op (e0) (e2)) = (op (e2) (e2)))) -> (((op (e2) (e0)) = (e3))\/(((op (e2) (e1)) = (e3))\/(((op (e2) (e2)) = (e3))\/((op (e2) (e3)) = (e3))))) -> (~((op (e0) (e1)) = (op (e2) (e1)))) -> (~((op (e2) (e2)) = (e3))) -> (~((op (e3) (op (e2) (e3))) = (op (e2) (e3)))) -> ((op (e3) (e3)) = (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 (e0) (e0)) = (e2))) -> (~((e1) = (e3))) -> (~((e2) = (e3))) -> (~((op (e0) (e0)) = (e3))) -> (((op (e0) (e0)) = (e3))\/(((op (e1) (e0)) = (e3))\/(((op (e2) (e0)) = (e3))\/((op (e3) (e0)) = (e3))))) -> (~((op (e0) (e3)) = (op (e2) (e3)))) -> (~((op (e2) (e2)) = (e1))) -> (~((op (e1) (e1)) = (op (e2) (e1)))) -> ((op (e1) (e1)) = (e1)) -> (((op (e2) (e0)) = (e1))\/(((op (e2) (e1)) = (e1))\/(((op (e2) (e2)) = (e1))\/((op (e2) (e3)) = (e1))))) -> (~((e1) = (e2))) -> False). % 15.41/15.57 do 0 intro. intros zenon_H44 zenon_H23 zenon_H36 zenon_H244 zenon_H5e zenon_H258 zenon_H1f zenon_H1f5 zenon_H90 zenon_H182 zenon_H104 zenon_H25b zenon_H80 zenon_H24f zenon_H254 zenon_H11e zenon_H1df zenon_H13c zenon_H87 zenon_H140 zenon_Hc9 zenon_H251 zenon_H3d zenon_H121 zenon_H8b zenon_H145 zenon_H24c zenon_H163 zenon_H237 zenon_H1d8 zenon_H1d2 zenon_H1e3 zenon_H1e2 zenon_H157 zenon_H290 zenon_H1b3 zenon_Hce zenon_H1c3 zenon_H10c zenon_H138 zenon_H7d zenon_H1cf zenon_H11b zenon_H250 zenon_H84 zenon_Haa zenon_H1d4 zenon_H166 zenon_H1d3 zenon_Hf1 zenon_H45 zenon_Hd7 zenon_H2d zenon_H2e zenon_H2f zenon_H28 zenon_He6 zenon_Hde zenon_H30 zenon_H28a zenon_H42 zenon_H58 zenon_Heb zenon_H8f zenon_Ha3 zenon_H6a zenon_H59 zenon_Hbe zenon_Hb4 zenon_H52 zenon_Hb1 zenon_H21 zenon_Hb7 zenon_Ha7. % 15.41/15.57 apply (zenon_or_s _ _ zenon_H44); [ zenon_intro zenon_H47 | zenon_intro zenon_H46 ]. % 15.41/15.57 exact (zenon_H45 zenon_H47). % 15.41/15.57 apply (zenon_or_s _ _ zenon_H46); [ zenon_intro zenon_H22 | zenon_intro zenon_H48 ]. % 15.41/15.57 apply (zenon_L3_); trivial. % 15.41/15.57 apply (zenon_or_s _ _ zenon_H48); [ zenon_intro zenon_H29 | zenon_intro zenon_H37 ]. % 15.41/15.57 apply (zenon_or_s _ _ zenon_Hf1); [ zenon_intro zenon_H47 | zenon_intro zenon_Hf4 ]. % 15.41/15.57 exact (zenon_H45 zenon_H47). % 15.41/15.57 apply (zenon_or_s _ _ zenon_Hf4); [ zenon_intro zenon_Hd8 | zenon_intro zenon_Hf5 ]. % 15.41/15.57 apply (zenon_L879_); trivial. % 15.41/15.57 apply (zenon_or_s _ _ zenon_Hf5); [ zenon_intro zenon_Hae | zenon_intro zenon_Hee ]. % 15.41/15.57 apply (zenon_L788_); trivial. % 15.41/15.57 apply (zenon_or_s _ _ zenon_Heb); [ zenon_intro zenon_H92 | zenon_intro zenon_Hec ]. % 15.41/15.57 exact (zenon_H8f zenon_H92). % 15.41/15.57 apply (zenon_or_s _ _ zenon_Hec); [ zenon_intro zenon_H68 | zenon_intro zenon_Hed ]. % 15.41/15.57 apply (zenon_L882_); trivial. % 15.41/15.57 apply (zenon_or_s _ _ zenon_Hed); [ zenon_intro zenon_Hdd | zenon_intro zenon_He9 ]. % 15.41/15.57 apply (zenon_L880_); trivial. % 15.41/15.57 apply (zenon_L122_); trivial. % 15.41/15.57 apply (zenon_or_s _ _ zenon_Hf1); [ zenon_intro zenon_H47 | zenon_intro zenon_Hf4 ]. % 15.41/15.57 exact (zenon_H45 zenon_H47). % 15.41/15.57 apply (zenon_or_s _ _ zenon_Hf4); [ zenon_intro zenon_Hd8 | zenon_intro zenon_Hf5 ]. % 15.41/15.57 apply (zenon_L61_); trivial. % 15.41/15.57 apply (zenon_or_s _ _ zenon_Hf5); [ zenon_intro zenon_Hae | zenon_intro zenon_Hee ]. % 15.41/15.57 apply (zenon_L883_); trivial. % 15.41/15.57 apply (zenon_L885_); trivial. % 15.41/15.57 (* end of lemma zenon_L886_ *) % 15.41/15.57 assert (zenon_L887_ : (((op (e0) (e0)) = (e3))\/(((op (e1) (e0)) = (e3))\/(((op (e2) (e0)) = (e3))\/((op (e3) (e0)) = (e3))))) -> (~((op (e0) (e0)) = (e3))) -> (~((op (e3) (e3)) = (e0))) -> (~((e0) = (e2))) -> ((op (e2) (e3)) = (e2)) -> (~((op (e0) (e0)) = (op (e0) (e3)))) -> ((op (e0) (e0)) = (e0)) -> (((op (e0) (e3)) = (e0))\/(((op (e1) (e3)) = (e0))\/(((op (e2) (e3)) = (e0))\/((op (e3) (e3)) = (e0))))) -> (~((op (e0) (e2)) = (op (e1) (e2)))) -> ((op (e0) (e2)) = (e2)) -> (~((op (e1) (e1)) = (e2))) -> (~((e2) = (e3))) -> (((op (e1) (e0)) = (e2))\/(((op (e1) (e1)) = (e2))\/(((op (e1) (e2)) = (e2))\/((op (e1) (e3)) = (e2))))) -> ((op (e0) (e3)) = (e1)) -> (~((op (e0) (e3)) = (op (e2) (e3)))) -> (~((op (e2) (e2)) = (e1))) -> (~((op (e1) (e1)) = (op (e2) (e1)))) -> ((op (e1) (e1)) = (e1)) -> (~((e1) = (e3))) -> (((op (e2) (e0)) = (e1))\/(((op (e2) (e1)) = (e1))\/(((op (e2) (e2)) = (e1))\/((op (e2) (e3)) = (e1))))) -> ((op (e3) (e3)) = (e3)) -> (~((op (e3) (e0)) = (op (e3) (e3)))) -> False). % 15.41/15.57 do 0 intro. intros zenon_Hbe zenon_H59 zenon_H3c zenon_H5e zenon_H124 zenon_H24f zenon_H1f zenon_Hd3 zenon_H87 zenon_H63 zenon_Hd6 zenon_H6a zenon_H84 zenon_H37 zenon_Hb4 zenon_H52 zenon_Hb1 zenon_H21 zenon_Ha3 zenon_Hb7 zenon_H42 zenon_Hbb. % 15.41/15.57 apply (zenon_or_s _ _ zenon_Hbe); [ zenon_intro zenon_H5b | zenon_intro zenon_Hbf ]. % 15.41/15.57 exact (zenon_H59 zenon_H5b). % 15.41/15.57 apply (zenon_or_s _ _ zenon_Hbf); [ zenon_intro zenon_H69 | zenon_intro zenon_Hc0 ]. % 15.41/15.57 apply (zenon_L679_); trivial. % 15.41/15.57 apply (zenon_or_s _ _ zenon_Hc0); [ zenon_intro zenon_Haf | zenon_intro zenon_Hba ]. % 15.41/15.57 apply (zenon_L42_); trivial. % 15.41/15.57 apply (zenon_L43_); trivial. % 15.41/15.57 (* end of lemma zenon_L887_ *) % 15.41/15.57 assert (zenon_L888_ : (((op (e0) (e2)) = (e0))\/(((op (e0) (e2)) = (e1))\/(((op (e0) (e2)) = (e2))\/((op (e0) (e2)) = (e3))))) -> ((op (e1) (e2)) = (e0)) -> ((op (e3) (e2)) = (e1)) -> (~((op (e0) (e2)) = (op (e3) (e2)))) -> (~((op (e3) (e0)) = (op (e3) (e3)))) -> ((op (e3) (e3)) = (e3)) -> (((op (e2) (e0)) = (e1))\/(((op (e2) (e1)) = (e1))\/(((op (e2) (e2)) = (e1))\/((op (e2) (e3)) = (e1))))) -> (~((e1) = (e3))) -> ((op (e1) (e1)) = (e1)) -> (~((op (e1) (e1)) = (op (e2) (e1)))) -> (~((op (e2) (e2)) = (e1))) -> (~((op (e0) (e3)) = (op (e2) (e3)))) -> ((op (e0) (e3)) = (e1)) -> (((op (e1) (e0)) = (e2))\/(((op (e1) (e1)) = (e2))\/(((op (e1) (e2)) = (e2))\/((op (e1) (e3)) = (e2))))) -> (~((e2) = (e3))) -> (~((op (e1) (e1)) = (e2))) -> (~((op (e0) (e2)) = (op (e1) (e2)))) -> (((op (e0) (e3)) = (e0))\/(((op (e1) (e3)) = (e0))\/(((op (e2) (e3)) = (e0))\/((op (e3) (e3)) = (e0))))) -> ((op (e0) (e0)) = (e0)) -> (~((op (e0) (e0)) = (op (e0) (e3)))) -> ((op (e2) (e3)) = (e2)) -> (~((e0) = (e2))) -> (~((op (e3) (e3)) = (e0))) -> (~((op (e0) (e0)) = (e3))) -> (((op (e0) (e0)) = (e3))\/(((op (e1) (e0)) = (e3))\/(((op (e2) (e0)) = (e3))\/((op (e3) (e0)) = (e3))))) -> (~((op (e0) (e2)) = (op (e2) (e2)))) -> ((op (e2) (e2)) = (e3)) -> False). % 15.41/15.57 do 0 intro. intros zenon_H251 zenon_H15d zenon_H119 zenon_H140 zenon_Hbb zenon_H42 zenon_Hb7 zenon_Ha3 zenon_H21 zenon_Hb1 zenon_H52 zenon_Hb4 zenon_H37 zenon_H84 zenon_H6a zenon_Hd6 zenon_H87 zenon_Hd3 zenon_H1f zenon_H24f zenon_H124 zenon_H5e zenon_H3c zenon_H59 zenon_Hbe zenon_H28 zenon_H34. % 15.41/15.57 apply (zenon_or_s _ _ zenon_H251); [ zenon_intro zenon_Hab | zenon_intro zenon_H252 ]. % 15.41/15.57 apply (zenon_L136_); trivial. % 15.41/15.57 apply (zenon_or_s _ _ zenon_H252); [ zenon_intro zenon_H29 | zenon_intro zenon_H253 ]. % 15.41/15.57 apply (zenon_L124_); trivial. % 15.41/15.57 apply (zenon_or_s _ _ zenon_H253); [ zenon_intro zenon_H63 | zenon_intro zenon_H50 ]. % 15.41/15.57 apply (zenon_L887_); trivial. % 15.41/15.57 apply (zenon_L10_); trivial. % 15.41/15.57 (* end of lemma zenon_L888_ *) % 15.41/15.57 assert (zenon_L889_ : (((op (e0) (e2)) = (e0))\/(((op (e0) (e2)) = (e1))\/(((op (e0) (e2)) = (e2))\/((op (e0) (e2)) = (e3))))) -> ((op (e3) (e2)) = (e0)) -> ((op (e3) (e2)) = (e1)) -> (~((op (e0) (e2)) = (op (e3) (e2)))) -> (~((e0) = (e2))) -> ((op (e1) (e3)) = (e0)) -> (~((op (e0) (e2)) = (op (e1) (e2)))) -> (~((op (e1) (e1)) = (e2))) -> ((op (e1) (e0)) = (e3)) -> (~((e2) = (e3))) -> (((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). % 15.41/15.57 do 0 intro. intros zenon_H251 zenon_H167 zenon_H119 zenon_H140 zenon_H5e zenon_Hcc zenon_H87 zenon_Hd6 zenon_H69 zenon_H6a zenon_H84 zenon_H28 zenon_H34. % 15.41/15.57 apply (zenon_or_s _ _ zenon_H251); [ zenon_intro zenon_Hab | zenon_intro zenon_H252 ]. % 15.41/15.57 apply (zenon_L267_); trivial. % 15.41/15.57 apply (zenon_or_s _ _ zenon_H252); [ zenon_intro zenon_H29 | zenon_intro zenon_H253 ]. % 15.41/15.57 apply (zenon_L124_); trivial. % 15.41/15.57 apply (zenon_or_s _ _ zenon_H253); [ zenon_intro zenon_H63 | zenon_intro zenon_H50 ]. % 15.41/15.57 apply (zenon_L630_); trivial. % 15.41/15.57 apply (zenon_L10_); trivial. % 15.41/15.57 (* end of lemma zenon_L889_ *) % 15.41/15.57 assert (zenon_L890_ : (((op (e0) (e2)) = (e1))\/(((op (e1) (e2)) = (e1))\/(((op (e2) (e2)) = (e1))\/((op (e3) (e2)) = (e1))))) -> (~((op (e0) (e2)) = (op (e0) (e3)))) -> ((op (e0) (e3)) = (e1)) -> (~((op (e1) (e1)) = (op (e1) (e2)))) -> (((op (e2) (e0)) = (e3))\/(((op (e2) (e1)) = (e3))\/(((op (e2) (e2)) = (e3))\/((op (e2) (e3)) = (e3))))) -> ((op (e2) (e3)) = (e2)) -> (~((e1) = (e2))) -> (~((op (e2) (e2)) = (e1))) -> (~((op (e1) (e1)) = (op (e2) (e1)))) -> ((op (e1) (e1)) = (e1)) -> (~((e1) = (e3))) -> (((op (e2) (e0)) = (e1))\/(((op (e2) (e1)) = (e1))\/(((op (e2) (e2)) = (e1))\/((op (e2) (e3)) = (e1))))) -> ((op (e0) (e1)) = (e3)) -> (~((op (e0) (e1)) = (op (e2) (e1)))) -> (~((op (e0) (e2)) = (op (e2) (e2)))) -> (((op (e1) (e0)) = (e2))\/(((op (e1) (e1)) = (e2))\/(((op (e1) (e2)) = (e2))\/((op (e1) (e3)) = (e2))))) -> (~((e2) = (e3))) -> ((op (e1) (e0)) = (e3)) -> (~((op (e1) (e1)) = (e2))) -> (~((op (e0) (e2)) = (op (e1) (e2)))) -> ((op (e1) (e3)) = (e0)) -> (~((e0) = (e2))) -> (~((op (e0) (e2)) = (op (e3) (e2)))) -> ((op (e3) (e2)) = (e0)) -> (((op (e0) (e2)) = (e0))\/(((op (e0) (e2)) = (e1))\/(((op (e0) (e2)) = (e2))\/((op (e0) (e2)) = (e3))))) -> (~((op (e3) (op (e2) (e3))) = (op (e2) (e3)))) -> ((op (e3) (e3)) = (e3)) -> False). % 15.41/15.57 do 0 intro. intros zenon_H11b zenon_Hc9 zenon_H37 zenon_H116 zenon_He6 zenon_H124 zenon_Ha7 zenon_H52 zenon_Hb1 zenon_H21 zenon_Ha3 zenon_Hb7 zenon_H4a zenon_Hde zenon_H28 zenon_H84 zenon_H6a zenon_H69 zenon_Hd6 zenon_H87 zenon_Hcc zenon_H5e zenon_H140 zenon_H167 zenon_H251 zenon_H28a zenon_H42. % 15.41/15.57 apply (zenon_or_s _ _ zenon_H11b); [ zenon_intro zenon_H29 | zenon_intro zenon_H11c ]. % 15.41/15.57 apply (zenon_L85_); trivial. % 15.41/15.57 apply (zenon_or_s _ _ zenon_H11c); [ zenon_intro zenon_H117 | zenon_intro zenon_H11d ]. % 15.41/15.57 apply (zenon_L86_); trivial. % 15.41/15.57 apply (zenon_or_s _ _ zenon_H11d); [ zenon_intro zenon_H2a | zenon_intro zenon_H119 ]. % 15.41/15.57 exact (zenon_H52 zenon_H2a). % 15.41/15.57 apply (zenon_or_s _ _ zenon_He6); [ zenon_intro zenon_Haf | zenon_intro zenon_He7 ]. % 15.41/15.57 apply (zenon_L96_); trivial. % 15.41/15.57 apply (zenon_or_s _ _ zenon_He7); [ zenon_intro zenon_Hdf | zenon_intro zenon_He8 ]. % 15.41/15.57 apply (zenon_L65_); trivial. % 15.41/15.57 apply (zenon_or_s _ _ zenon_He8); [ zenon_intro zenon_H34 | zenon_intro zenon_He2 ]. % 15.41/15.57 apply (zenon_L889_); trivial. % 15.41/15.57 apply (zenon_L776_); trivial. % 15.41/15.57 (* end of lemma zenon_L890_ *) % 15.41/15.57 assert (zenon_L891_ : (((op (e0) (e0)) = (e3))\/(((op (e0) (e1)) = (e3))\/(((op (e0) (e2)) = (e3))\/((op (e0) (e3)) = (e3))))) -> (~((op (e3) (e0)) = (op (e3) (e3)))) -> (((op (e2) (e0)) = (e1))\/(((op (e2) (e1)) = (e1))\/(((op (e2) (e2)) = (e1))\/((op (e2) (e3)) = (e1))))) -> (~((e1) = (e3))) -> ((op (e1) (e1)) = (e1)) -> (~((op (e1) (e1)) = (op (e2) (e1)))) -> (~((op (e0) (e3)) = (op (e2) (e3)))) -> ((op (e0) (e3)) = (e1)) -> (((op (e1) (e0)) = (e0))\/(((op (e1) (e1)) = (e0))\/(((op (e1) (e2)) = (e0))\/((op (e1) (e3)) = (e0))))) -> (~((op (e0) (e0)) = (op (e1) (e0)))) -> (~((op (e1) (e1)) = (e0))) -> (((op (e0) (e2)) = (e0))\/(((op (e1) (e2)) = (e0))\/(((op (e2) (e2)) = (e0))\/((op (e3) (e2)) = (e0))))) -> (~((op (e0) (e0)) = (op (e0) (e2)))) -> (~((op (e3) (e3)) = (e2))) -> (((op (e0) (e3)) = (e2))\/(((op (e1) (e3)) = (e2))\/(((op (e2) (e3)) = (e2))\/((op (e3) (e3)) = (e2))))) -> (((op (e0) (e3)) = (e0))\/(((op (e1) (e3)) = (e0))\/(((op (e2) (e3)) = (e0))\/((op (e3) (e3)) = (e0))))) -> ((op (e0) (e0)) = (e0)) -> (~((op (e0) (e0)) = (op (e0) (e3)))) -> (~((op (e3) (e3)) = (e0))) -> (~((op (e0) (e0)) = (e3))) -> (((op (e0) (e0)) = (e3))\/(((op (e1) (e0)) = (e3))\/(((op (e2) (e0)) = (e3))\/((op (e3) (e0)) = (e3))))) -> (~((e0) = (e1))) -> (((op (e0) (e2)) = (e1))\/(((op (e1) (e2)) = (e1))\/(((op (e2) (e2)) = (e1))\/((op (e3) (e2)) = (e1))))) -> (~((op (e0) (e2)) = (op (e0) (e3)))) -> (~((op (e1) (e1)) = (op (e1) (e2)))) -> (((op (e2) (e0)) = (e3))\/(((op (e2) (e1)) = (e3))\/(((op (e2) (e2)) = (e3))\/((op (e2) (e3)) = (e3))))) -> ((op (e2) (e3)) = (e2)) -> (~((e1) = (e2))) -> (~((op (e0) (e1)) = (op (e2) (e1)))) -> (((op (e1) (e0)) = (e2))\/(((op (e1) (e1)) = (e2))\/(((op (e1) (e2)) = (e2))\/((op (e1) (e3)) = (e2))))) -> (~((e2) = (e3))) -> (~((op (e1) (e1)) = (e2))) -> (~((op (e0) (e2)) = (op (e1) (e2)))) -> (~((e0) = (e2))) -> (~((op (e0) (e2)) = (op (e3) (e2)))) -> (((op (e0) (e2)) = (e0))\/(((op (e0) (e2)) = (e1))\/(((op (e0) (e2)) = (e2))\/((op (e0) (e2)) = (e3))))) -> (~((op (e3) (op (e2) (e3))) = (op (e2) (e3)))) -> (~((op (e0) (e2)) = (op (e2) (e2)))) -> (~((op (e2) (e2)) = (e2))) -> (~((op (e2) (e2)) = (e1))) -> (~((op (e2) (e2)) = (e0))) -> (((op (e2) (e2)) = (e0))\/(((op (e2) (e2)) = (e1))\/(((op (e2) (e2)) = (e2))\/((op (e2) (e2)) = (e3))))) -> ((op (e3) (e3)) = (e3)) -> (~((op (e0) (e3)) = (op (e3) (e3)))) -> False). % 15.41/15.57 do 0 intro. intros zenon_H58 zenon_Hbb zenon_Hb7 zenon_Ha3 zenon_H21 zenon_Hb1 zenon_Hb4 zenon_H37 zenon_H163 zenon_H24c zenon_H145 zenon_H16f zenon_H250 zenon_H3d zenon_H160 zenon_Hd3 zenon_H1f zenon_H24f zenon_H3c zenon_H59 zenon_Hbe zenon_H9e zenon_H11b zenon_Hc9 zenon_H116 zenon_He6 zenon_H124 zenon_Ha7 zenon_Hde zenon_H84 zenon_H6a zenon_Hd6 zenon_H87 zenon_H5e zenon_H140 zenon_H251 zenon_H28a zenon_H28 zenon_H2f zenon_H52 zenon_H2e zenon_H2d zenon_H42 zenon_H36. % 15.41/15.57 apply (zenon_or_s _ _ zenon_H58); [ zenon_intro zenon_H5b | zenon_intro zenon_H5a ]. % 15.41/15.57 exact (zenon_H59 zenon_H5b). % 15.41/15.57 apply (zenon_or_s _ _ zenon_H5a); [ zenon_intro zenon_H4a | zenon_intro zenon_H5c ]. % 15.41/15.57 apply (zenon_or_s _ _ zenon_Hbe); [ zenon_intro zenon_H5b | zenon_intro zenon_Hbf ]. % 15.41/15.57 exact (zenon_H59 zenon_H5b). % 15.41/15.57 apply (zenon_or_s _ _ zenon_Hbf); [ zenon_intro zenon_H69 | zenon_intro zenon_Hc0 ]. % 15.41/15.57 apply (zenon_or_s _ _ zenon_H163); [ zenon_intro zenon_Had | zenon_intro zenon_H164 ]. % 15.41/15.57 apply (zenon_L559_); trivial. % 15.41/15.57 apply (zenon_or_s _ _ zenon_H164); [ zenon_intro zenon_H149 | zenon_intro zenon_H165 ]. % 15.41/15.57 exact (zenon_H145 zenon_H149). % 15.41/15.57 apply (zenon_or_s _ _ zenon_H165); [ zenon_intro zenon_H15d | zenon_intro zenon_Hcc ]. % 15.41/15.57 apply (zenon_or_s _ _ zenon_H11b); [ zenon_intro zenon_H29 | zenon_intro zenon_H11c ]. % 15.41/15.57 apply (zenon_L85_); trivial. % 15.41/15.57 apply (zenon_or_s _ _ zenon_H11c); [ zenon_intro zenon_H117 | zenon_intro zenon_H11d ]. % 15.41/15.57 apply (zenon_L86_); trivial. % 15.41/15.57 apply (zenon_or_s _ _ zenon_H11d); [ zenon_intro zenon_H2a | zenon_intro zenon_H119 ]. % 15.41/15.57 exact (zenon_H52 zenon_H2a). % 15.41/15.57 apply (zenon_or_s _ _ zenon_He6); [ zenon_intro zenon_Haf | zenon_intro zenon_He7 ]. % 15.41/15.57 apply (zenon_L96_); trivial. % 15.41/15.57 apply (zenon_or_s _ _ zenon_He7); [ zenon_intro zenon_Hdf | zenon_intro zenon_He8 ]. % 15.41/15.57 apply (zenon_L65_); trivial. % 15.41/15.57 apply (zenon_or_s _ _ zenon_He8); [ zenon_intro zenon_H34 | zenon_intro zenon_He2 ]. % 15.41/15.57 apply (zenon_L888_); trivial. % 15.41/15.57 apply (zenon_L776_); trivial. % 15.41/15.57 apply (zenon_or_s _ _ zenon_H16f); [ zenon_intro zenon_Hab | zenon_intro zenon_H170 ]. % 15.41/15.57 apply (zenon_L567_); trivial. % 15.41/15.57 apply (zenon_or_s _ _ zenon_H170); [ zenon_intro zenon_H15d | zenon_intro zenon_H171 ]. % 15.41/15.57 apply (zenon_or_s _ _ zenon_H11b); [ zenon_intro zenon_H29 | zenon_intro zenon_H11c ]. % 15.41/15.57 apply (zenon_L85_); trivial. % 15.41/15.57 apply (zenon_or_s _ _ zenon_H11c); [ zenon_intro zenon_H117 | zenon_intro zenon_H11d ]. % 15.41/15.57 apply (zenon_L496_); trivial. % 15.41/15.57 apply (zenon_or_s _ _ zenon_H11d); [ zenon_intro zenon_H2a | zenon_intro zenon_H119 ]. % 15.41/15.57 exact (zenon_H52 zenon_H2a). % 15.41/15.57 apply (zenon_or_s _ _ zenon_He6); [ zenon_intro zenon_Haf | zenon_intro zenon_He7 ]. % 15.41/15.57 apply (zenon_L42_); trivial. % 15.41/15.57 apply (zenon_or_s _ _ zenon_He7); [ zenon_intro zenon_Hdf | zenon_intro zenon_He8 ]. % 15.41/15.57 apply (zenon_L65_); trivial. % 15.41/15.57 apply (zenon_or_s _ _ zenon_He8); [ zenon_intro zenon_H34 | zenon_intro zenon_He2 ]. % 15.41/15.57 apply (zenon_L888_); trivial. % 15.41/15.57 apply (zenon_L263_); trivial. % 15.41/15.57 apply (zenon_or_s _ _ zenon_H171); [ zenon_intro zenon_H32 | zenon_intro zenon_H167 ]. % 15.41/15.57 exact (zenon_H2e zenon_H32). % 15.41/15.57 apply (zenon_L890_); trivial. % 15.41/15.57 apply (zenon_or_s _ _ zenon_Hc0); [ zenon_intro zenon_Haf | zenon_intro zenon_Hba ]. % 15.41/15.57 apply (zenon_L42_); trivial. % 15.41/15.57 apply (zenon_L43_); trivial. % 15.41/15.57 apply (zenon_or_s _ _ zenon_H5c); [ zenon_intro zenon_H50 | zenon_intro zenon_H53 ]. % 15.41/15.57 apply (zenon_L11_); trivial. % 15.41/15.57 apply (zenon_L12_); trivial. % 15.41/15.57 (* end of lemma zenon_L891_ *) % 15.41/15.57 assert (zenon_L892_ : (((op (e0) (e3)) = (e1))\/(((op (e1) (e3)) = (e1))\/(((op (e2) (e3)) = (e1))\/((op (e3) (e3)) = (e1))))) -> ((op (e3) (e2)) = (e3)) -> (~((e1) = (e3))) -> (~((op (e2) (e2)) = (e1))) -> (~((op (e1) (e1)) = (op (e1) (e2)))) -> ((op (e1) (e1)) = (e1)) -> (~((op (e0) (e2)) = (op (e0) (e3)))) -> (((op (e0) (e2)) = (e1))\/(((op (e1) (e2)) = (e1))\/(((op (e2) (e2)) = (e1))\/((op (e3) (e2)) = (e1))))) -> ((op (e1) (e3)) = (e0)) -> (~((e0) = (e1))) -> ((op (e2) (e3)) = (e2)) -> (~((e1) = (e2))) -> (~((op (e3) (e3)) = (e1))) -> False). % 15.41/15.57 do 0 intro. intros zenon_H121 zenon_H106 zenon_Ha3 zenon_H52 zenon_H116 zenon_H21 zenon_Hc9 zenon_H11b zenon_Hcc zenon_H9e zenon_H124 zenon_Ha7 zenon_H104. % 15.41/15.57 apply (zenon_or_s _ _ zenon_H121); [ zenon_intro zenon_H37 | zenon_intro zenon_H122 ]. % 15.41/15.57 apply (zenon_L88_); trivial. % 15.41/15.57 apply (zenon_or_s _ _ zenon_H122); [ zenon_intro zenon_H11f | zenon_intro zenon_H123 ]. % 15.41/15.57 apply (zenon_L208_); trivial. % 15.41/15.57 apply (zenon_or_s _ _ zenon_H123); [ zenon_intro zenon_Hb5 | zenon_intro zenon_H38 ]. % 15.41/15.57 apply (zenon_L93_); trivial. % 15.41/15.57 exact (zenon_H104 zenon_H38). % 15.41/15.57 (* end of lemma zenon_L892_ *) % 15.41/15.57 assert (zenon_L893_ : (((op (e0) (e3)) = (e0))\/(((op (e1) (e3)) = (e0))\/(((op (e2) (e3)) = (e0))\/((op (e3) (e3)) = (e0))))) -> ((op (e0) (e0)) = (e0)) -> (~((op (e0) (e0)) = (op (e0) (e3)))) -> (~((op (e3) (e3)) = (e1))) -> (~((e1) = (e2))) -> (~((e0) = (e1))) -> (((op (e0) (e2)) = (e1))\/(((op (e1) (e2)) = (e1))\/(((op (e2) (e2)) = (e1))\/((op (e3) (e2)) = (e1))))) -> (~((op (e0) (e2)) = (op (e0) (e3)))) -> ((op (e1) (e1)) = (e1)) -> (~((op (e1) (e1)) = (op (e1) (e2)))) -> (~((op (e2) (e2)) = (e1))) -> (~((e1) = (e3))) -> ((op (e3) (e2)) = (e3)) -> (((op (e0) (e3)) = (e1))\/(((op (e1) (e3)) = (e1))\/(((op (e2) (e3)) = (e1))\/((op (e3) (e3)) = (e1))))) -> ((op (e2) (e3)) = (e2)) -> (~((e0) = (e2))) -> (~((op (e3) (e3)) = (e0))) -> False). % 15.41/15.57 do 0 intro. intros zenon_Hd3 zenon_H1f zenon_H24f zenon_H104 zenon_Ha7 zenon_H9e zenon_H11b zenon_Hc9 zenon_H21 zenon_H116 zenon_H52 zenon_Ha3 zenon_H106 zenon_H121 zenon_H124 zenon_H5e zenon_H3c. % 15.41/15.57 apply (zenon_or_s _ _ zenon_Hd3); [ zenon_intro zenon_Hca | zenon_intro zenon_Hd4 ]. % 15.41/15.57 apply (zenon_L562_); trivial. % 15.41/15.57 apply (zenon_or_s _ _ zenon_Hd4); [ zenon_intro zenon_Hcc | zenon_intro zenon_Hd5 ]. % 15.41/15.57 apply (zenon_L892_); trivial. % 15.41/15.57 apply (zenon_or_s _ _ zenon_Hd5); [ zenon_intro zenon_Hd0 | zenon_intro zenon_H40 ]. % 15.41/15.57 apply (zenon_L201_); trivial. % 15.41/15.57 exact (zenon_H3c zenon_H40). % 15.41/15.57 (* end of lemma zenon_L893_ *) % 15.41/15.57 assert (zenon_L894_ : ((~((op (e3) (e3)) = (e2)))\/((op (e3) (e2)) = (e3))) -> (((op (e0) (e0)) = (e3))\/(((op (e0) (e1)) = (e3))\/(((op (e0) (e2)) = (e3))\/((op (e0) (e3)) = (e3))))) -> (~((op (e0) (e3)) = (op (e3) (e3)))) -> (~((op (e2) (e2)) = (e2))) -> (((op (e2) (e2)) = (e0))\/(((op (e2) (e2)) = (e1))\/(((op (e2) (e2)) = (e2))\/((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) (e2)))) -> (((op (e0) (e3)) = (e2))\/(((op (e1) (e3)) = (e2))\/(((op (e2) (e3)) = (e2))\/((op (e3) (e3)) = (e2))))) -> (~((e0) = (e1))) -> (~((op (e2) (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) (e1)) = (op (e1) (e2)))) -> ((op (e1) (e1)) = (e1)) -> (~((op (e2) (e2)) = (e1))) -> (((op (e2) (e0)) = (e3))\/(((op (e2) (e1)) = (e3))\/(((op (e2) (e2)) = (e3))\/((op (e2) (e3)) = (e3))))) -> (~((op (e3) (op (e2) (e3))) = (op (e2) (e3)))) -> (~((op (e0) (e2)) = (op (e1) (e2)))) -> (~((op (e0) (e2)) = (op (e3) (e2)))) -> (((op (e0) (e0)) = (e3))\/(((op (e1) (e0)) = (e3))\/(((op (e2) (e0)) = (e3))\/((op (e3) (e0)) = (e3))))) -> ((op (e3) (e3)) = (e3)) -> (~((op (e3) (e0)) = (op (e3) (e3)))) -> (~((op (e0) (e3)) = (op (e2) (e3)))) -> (~((e2) = (e3))) -> (~((op (e1) (e1)) = (e2))) -> (((op (e0) (e3)) = (e0))\/(((op (e1) (e3)) = (e0))\/(((op (e2) (e3)) = (e0))\/((op (e3) (e3)) = (e0))))) -> (~((op (e3) (e3)) = (e0))) -> (~((e0) = (e2))) -> (~((op (e0) (e0)) = (op (e0) (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) (e2)) = (e0))\/(((op (e0) (e2)) = (e1))\/(((op (e0) (e2)) = (e2))\/((op (e0) (e2)) = (e3))))) -> (~((op (e0) (e1)) = (op (e2) (e1)))) -> (~((e1) = (e3))) -> (~((op (e1) (e1)) = (op (e2) (e1)))) -> (~((e1) = (e2))) -> ((op (e2) (e3)) = (e2)) -> (((op (e2) (e0)) = (e1))\/(((op (e2) (e1)) = (e1))\/(((op (e2) (e2)) = (e1))\/((op (e2) (e3)) = (e1))))) -> (((op (e0) (e2)) = (e1))\/(((op (e1) (e2)) = (e1))\/(((op (e2) (e2)) = (e1))\/((op (e3) (e2)) = (e1))))) -> (~((op (e1) (e1)) = (e0))) -> ((op (e0) (e0)) = (e0)) -> (~((op (e0) (e0)) = (op (e1) (e0)))) -> (~((op (e0) (e0)) = (e3))) -> (~((op (e1) (e1)) = (op (e1) (e3)))) -> (~((op (e3) (e3)) = (e1))) -> (((op (e0) (e3)) = (e1))\/(((op (e1) (e3)) = (e1))\/(((op (e2) (e3)) = (e1))\/((op (e3) (e3)) = (e1))))) -> False). % 15.41/15.58 do 0 intro. intros zenon_H10e zenon_H58 zenon_H36 zenon_H2f zenon_H2d zenon_H163 zenon_H250 zenon_H160 zenon_H9e zenon_H2e zenon_H16f zenon_Hc9 zenon_H116 zenon_H21 zenon_H52 zenon_He6 zenon_H28a zenon_H87 zenon_H140 zenon_Hbe zenon_H42 zenon_Hbb zenon_Hb4 zenon_H6a zenon_Hd6 zenon_Hd3 zenon_H3c zenon_H5e zenon_H24f zenon_H84 zenon_H28 zenon_H251 zenon_Hde zenon_Ha3 zenon_Hb1 zenon_Ha7 zenon_H124 zenon_Hb7 zenon_H11b zenon_H145 zenon_H1f zenon_H24c zenon_H59 zenon_H11e zenon_H104 zenon_H121. % 15.41/15.58 apply (zenon_or_s _ _ zenon_H10e); [ zenon_intro zenon_H3d | zenon_intro zenon_H106 ]. % 15.41/15.58 apply (zenon_or_s _ _ zenon_H121); [ zenon_intro zenon_H37 | zenon_intro zenon_H122 ]. % 15.41/15.58 apply (zenon_L891_); trivial. % 15.41/15.58 apply (zenon_or_s _ _ zenon_H122); [ zenon_intro zenon_H11f | zenon_intro zenon_H123 ]. % 15.41/15.58 apply (zenon_L90_); trivial. % 15.41/15.58 apply (zenon_or_s _ _ zenon_H123); [ zenon_intro zenon_Hb5 | zenon_intro zenon_H38 ]. % 15.41/15.58 apply (zenon_L93_); trivial. % 15.41/15.58 exact (zenon_H104 zenon_H38). % 15.41/15.58 apply (zenon_L893_); trivial. % 15.41/15.58 (* end of lemma zenon_L894_ *) % 15.41/15.58 assert (zenon_L895_ : (((op (e0) (e0)) = (e1))\/(((op (e1) (e0)) = (e1))\/(((op (e2) (e0)) = (e1))\/((op (e3) (e0)) = (e1))))) -> (~((op (e0) (e0)) = (e1))) -> ((op (e1) (e1)) = (e1)) -> (~((op (e1) (e0)) = (op (e1) (e1)))) -> (~((op (e2) (e2)) = (e2))) -> (~((op (e2) (e2)) = (e1))) -> (~((op (e2) (e2)) = (e0))) -> (((op (e2) (e2)) = (e0))\/(((op (e2) (e2)) = (e1))\/(((op (e2) (e2)) = (e2))\/((op (e2) (e2)) = (e3))))) -> (~((e0) = (e2))) -> ((op (e2) (e3)) = (e2)) -> (((op (e3) (e3)) = (e0))\/(((op (e3) (e3)) = (e1))\/(((op (e3) (e3)) = (e2))\/((op (e3) (e3)) = (e3))))) -> (~((op (e1) (e3)) = (op (e3) (e3)))) -> (~((op (e3) (e3)) = (e1))) -> (~((op (e3) (e3)) = (e2))) -> (~((op (e3) (e3)) = (e3))) -> (~((op (e0) (e0)) = (op (e0) (e3)))) -> ((op (e0) (e0)) = (e0)) -> (((op (e0) (e3)) = (e0))\/(((op (e1) (e3)) = (e0))\/(((op (e2) (e3)) = (e0))\/((op (e3) (e3)) = (e0))))) -> (~((e1) = (e3))) -> ((op (e3) (e0)) = (e3)) -> False). % 15.41/15.58 do 0 intro. intros zenon_Hf1 zenon_H45 zenon_H21 zenon_Hd7 zenon_H2f zenon_H52 zenon_H2e zenon_H2d zenon_H5e zenon_H124 zenon_H3b zenon_H8b zenon_H104 zenon_H3d zenon_H3e zenon_H24f zenon_H1f zenon_Hd3 zenon_Ha3 zenon_Hba. % 15.41/15.58 apply (zenon_or_s _ _ zenon_Hf1); [ zenon_intro zenon_H47 | zenon_intro zenon_Hf4 ]. % 15.41/15.58 exact (zenon_H45 zenon_H47). % 15.41/15.58 apply (zenon_or_s _ _ zenon_Hf4); [ zenon_intro zenon_Hd8 | zenon_intro zenon_Hf5 ]. % 15.41/15.58 apply (zenon_L61_); trivial. % 15.41/15.58 apply (zenon_or_s _ _ zenon_Hf5); [ zenon_intro zenon_Hae | zenon_intro zenon_Hee ]. % 15.41/15.58 apply (zenon_L684_); trivial. % 15.41/15.58 apply (zenon_L79_); trivial. % 15.41/15.58 (* end of lemma zenon_L895_ *) % 15.41/15.58 assert (zenon_L896_ : (((op (e0) (e0)) = (e3))\/(((op (e0) (e1)) = (e3))\/(((op (e0) (e2)) = (e3))\/((op (e0) (e3)) = (e3))))) -> (~((op (e0) (e0)) = (e3))) -> (~((op (e0) (e1)) = (op (e3) (e1)))) -> ((op (e3) (e1)) = (e3)) -> (~((e1) = (e3))) -> ((op (e0) (e2)) = (e1)) -> ((op (e3) (e3)) = (e3)) -> (~((op (e0) (e3)) = (op (e3) (e3)))) -> False). % 15.41/15.58 do 0 intro. intros zenon_H58 zenon_H59 zenon_H138 zenon_H10a zenon_Ha3 zenon_H29 zenon_H42 zenon_H36. % 15.41/15.58 apply (zenon_or_s _ _ zenon_H58); [ zenon_intro zenon_H5b | zenon_intro zenon_H5a ]. % 15.41/15.58 exact (zenon_H59 zenon_H5b). % 15.41/15.58 apply (zenon_or_s _ _ zenon_H5a); [ zenon_intro zenon_H4a | zenon_intro zenon_H5c ]. % 15.41/15.58 apply (zenon_L120_); trivial. % 15.41/15.58 apply (zenon_or_s _ _ zenon_H5c); [ zenon_intro zenon_H50 | zenon_intro zenon_H53 ]. % 15.41/15.58 apply (zenon_L29_); trivial. % 15.41/15.58 apply (zenon_L12_); trivial. % 15.41/15.58 (* end of lemma zenon_L896_ *) % 15.41/15.58 assert (zenon_L897_ : (((op (e2) (e0)) = (e3))\/(((op (e2) (e1)) = (e3))\/(((op (e2) (e2)) = (e3))\/((op (e2) (e3)) = (e3))))) -> (~((e1) = (e3))) -> ((op (e2) (e0)) = (e1)) -> (~((op (e2) (e1)) = (op (e3) (e1)))) -> ((op (e3) (e1)) = (e3)) -> (~((op (e2) (e2)) = (e3))) -> (~((op (e3) (op (e2) (e3))) = (op (e2) (e3)))) -> ((op (e3) (e3)) = (e3)) -> False). % 15.41/15.58 do 0 intro. intros zenon_He6 zenon_Ha3 zenon_Hae zenon_H13c zenon_H10a zenon_H30 zenon_H28a zenon_H42. % 15.41/15.58 apply (zenon_or_s _ _ zenon_He6); [ zenon_intro zenon_Haf | zenon_intro zenon_He7 ]. % 15.41/15.58 apply (zenon_L39_); trivial. % 15.41/15.58 apply (zenon_or_s _ _ zenon_He7); [ zenon_intro zenon_Hdf | zenon_intro zenon_He8 ]. % 15.41/15.58 apply (zenon_L121_); trivial. % 15.41/15.58 apply (zenon_or_s _ _ zenon_He8); [ zenon_intro zenon_H34 | zenon_intro zenon_He2 ]. % 15.41/15.58 exact (zenon_H30 zenon_H34). % 15.41/15.58 apply (zenon_L776_); trivial. % 15.41/15.58 (* end of lemma zenon_L897_ *) % 15.41/15.58 assert (zenon_L898_ : (((op (e0) (e0)) = (e3))\/(((op (e0) (e1)) = (e3))\/(((op (e0) (e2)) = (e3))\/((op (e0) (e3)) = (e3))))) -> (~((op (e0) (e0)) = (e3))) -> (~((op (e0) (e1)) = (op (e3) (e1)))) -> ((op (e3) (e1)) = (e3)) -> (~((op (e1) (e3)) = (op (e3) (e3)))) -> ((op (e3) (e3)) = (e3)) -> (~((op (e0) (e2)) = (op (e1) (e2)))) -> (~((op (e1) (e1)) = (e3))) -> ((op (e1) (e0)) = (e2)) -> (~((e2) = (e3))) -> (((op (e1) (e0)) = (e3))\/(((op (e1) (e1)) = (e3))\/(((op (e1) (e2)) = (e3))\/((op (e1) (e3)) = (e3))))) -> ((op (e0) (e3)) = (e1)) -> (~((e1) = (e3))) -> False). % 15.41/15.58 do 0 intro. intros zenon_H58 zenon_H59 zenon_H138 zenon_H10a zenon_H8b zenon_H42 zenon_H87 zenon_H182 zenon_H68 zenon_H6a zenon_H90 zenon_H37 zenon_Ha3. % 15.41/15.58 apply (zenon_or_s _ _ zenon_H58); [ zenon_intro zenon_H5b | zenon_intro zenon_H5a ]. % 15.41/15.58 exact (zenon_H59 zenon_H5b). % 15.41/15.58 apply (zenon_or_s _ _ zenon_H5a); [ zenon_intro zenon_H4a | zenon_intro zenon_H5c ]. % 15.41/15.58 apply (zenon_L120_); trivial. % 15.41/15.58 apply (zenon_or_s _ _ zenon_H5c); [ zenon_intro zenon_H50 | zenon_intro zenon_H53 ]. % 15.41/15.58 apply (zenon_L379_); trivial. % 15.41/15.58 apply (zenon_L32_); trivial. % 15.41/15.58 (* end of lemma zenon_L898_ *) % 15.41/15.58 assert (zenon_L899_ : (((op (e0) (e0)) = (e1))\/(((op (e0) (e1)) = (e1))\/(((op (e0) (e2)) = (e1))\/((op (e0) (e3)) = (e1))))) -> (~((op (e0) (e1)) = (op (e1) (e1)))) -> ((op (e1) (e1)) = (e1)) -> (((op (e0) (e0)) = (e1))\/(((op (e1) (e0)) = (e1))\/(((op (e2) (e0)) = (e1))\/((op (e3) (e0)) = (e1))))) -> (~((op (e0) (e0)) = (e1))) -> (~((op (e0) (e3)) = (op (e3) (e3)))) -> (~((op (e3) (op (e2) (e3))) = (op (e2) (e3)))) -> (~((op (e2) (e2)) = (e3))) -> (~((op (e2) (e1)) = (op (e3) (e1)))) -> (((op (e2) (e0)) = (e3))\/(((op (e2) (e1)) = (e3))\/(((op (e2) (e2)) = (e3))\/((op (e2) (e3)) = (e3))))) -> (((op (e0) (e0)) = (e2))\/(((op (e1) (e0)) = (e2))\/(((op (e2) (e0)) = (e2))\/((op (e3) (e0)) = (e2))))) -> (~((op (e0) (e0)) = (e2))) -> (~((e1) = (e3))) -> (((op (e1) (e0)) = (e3))\/(((op (e1) (e1)) = (e3))\/(((op (e1) (e2)) = (e3))\/((op (e1) (e3)) = (e3))))) -> (~((e2) = (e3))) -> (~((op (e1) (e1)) = (e3))) -> (~((op (e0) (e2)) = (op (e1) (e2)))) -> ((op (e3) (e3)) = (e3)) -> (~((op (e1) (e3)) = (op (e3) (e3)))) -> ((op (e3) (e1)) = (e3)) -> (~((op (e0) (e1)) = (op (e3) (e1)))) -> (~((op (e0) (e0)) = (e3))) -> (((op (e0) (e0)) = (e3))\/(((op (e0) (e1)) = (e3))\/(((op (e0) (e2)) = (e3))\/((op (e0) (e3)) = (e3))))) -> ((op (e2) (e1)) = (e2)) -> (~((op (e2) (e0)) = (op (e2) (e1)))) -> (~((e1) = (e2))) -> False). % 15.41/15.58 do 0 intro. intros zenon_H44 zenon_H23 zenon_H21 zenon_Hf1 zenon_H45 zenon_H36 zenon_H28a zenon_H30 zenon_H13c zenon_He6 zenon_Heb zenon_H8f zenon_Ha3 zenon_H90 zenon_H6a zenon_H182 zenon_H87 zenon_H42 zenon_H8b zenon_H10a zenon_H138 zenon_H59 zenon_H58 zenon_H156 zenon_H154 zenon_Ha7. % 15.41/15.58 apply (zenon_or_s _ _ zenon_H44); [ zenon_intro zenon_H47 | zenon_intro zenon_H46 ]. % 15.41/15.58 exact (zenon_H45 zenon_H47). % 15.41/15.58 apply (zenon_or_s _ _ zenon_H46); [ zenon_intro zenon_H22 | zenon_intro zenon_H48 ]. % 15.41/15.58 apply (zenon_L3_); trivial. % 15.41/15.58 apply (zenon_or_s _ _ zenon_H48); [ zenon_intro zenon_H29 | zenon_intro zenon_H37 ]. % 15.41/15.58 apply (zenon_L896_); trivial. % 15.41/15.58 apply (zenon_or_s _ _ zenon_Hf1); [ zenon_intro zenon_H47 | zenon_intro zenon_Hf4 ]. % 15.41/15.58 exact (zenon_H45 zenon_H47). % 15.41/15.58 apply (zenon_or_s _ _ zenon_Hf4); [ zenon_intro zenon_Hd8 | zenon_intro zenon_Hf5 ]. % 15.41/15.58 apply (zenon_L572_); trivial. % 15.41/15.58 apply (zenon_or_s _ _ zenon_Hf5); [ zenon_intro zenon_Hae | zenon_intro zenon_Hee ]. % 15.41/15.58 apply (zenon_L897_); trivial. % 15.41/15.58 apply (zenon_or_s _ _ zenon_Heb); [ zenon_intro zenon_H92 | zenon_intro zenon_Hec ]. % 15.41/15.58 exact (zenon_H8f zenon_H92). % 15.41/15.58 apply (zenon_or_s _ _ zenon_Hec); [ zenon_intro zenon_H68 | zenon_intro zenon_Hed ]. % 15.41/15.58 apply (zenon_L898_); trivial. % 15.41/15.58 apply (zenon_or_s _ _ zenon_Hed); [ zenon_intro zenon_Hdd | zenon_intro zenon_He9 ]. % 15.41/15.58 apply (zenon_L284_); trivial. % 15.41/15.58 apply (zenon_L122_); trivial. % 15.41/15.58 (* end of lemma zenon_L899_ *) % 15.41/15.58 assert (zenon_L900_ : (((op (e0) (e1)) = (e3))\/(((op (e1) (e1)) = (e3))\/(((op (e2) (e1)) = (e3))\/((op (e3) (e1)) = (e3))))) -> (~((op (e0) (e1)) = (op (e2) (e1)))) -> ((op (e2) (e0)) = (e1)) -> (((op (e0) (e0)) = (e1))\/(((op (e0) (e1)) = (e1))\/(((op (e0) (e2)) = (e1))\/((op (e0) (e3)) = (e1))))) -> (~((op (e0) (e1)) = (op (e1) (e1)))) -> ((op (e1) (e1)) = (e1)) -> (((op (e0) (e0)) = (e1))\/(((op (e1) (e0)) = (e1))\/(((op (e2) (e0)) = (e1))\/((op (e3) (e0)) = (e1))))) -> (~((op (e0) (e0)) = (e1))) -> (~((op (e0) (e3)) = (op (e3) (e3)))) -> (~((op (e3) (op (e2) (e3))) = (op (e2) (e3)))) -> (~((op (e2) (e2)) = (e3))) -> (~((op (e2) (e1)) = (op (e3) (e1)))) -> (((op (e2) (e0)) = (e3))\/(((op (e2) (e1)) = (e3))\/(((op (e2) (e2)) = (e3))\/((op (e2) (e3)) = (e3))))) -> (((op (e0) (e0)) = (e2))\/(((op (e1) (e0)) = (e2))\/(((op (e2) (e0)) = (e2))\/((op (e3) (e0)) = (e2))))) -> (~((op (e0) (e0)) = (e2))) -> (~((e1) = (e3))) -> (((op (e1) (e0)) = (e3))\/(((op (e1) (e1)) = (e3))\/(((op (e1) (e2)) = (e3))\/((op (e1) (e3)) = (e3))))) -> (~((e2) = (e3))) -> (~((op (e1) (e1)) = (e3))) -> (~((op (e0) (e2)) = (op (e1) (e2)))) -> ((op (e3) (e3)) = (e3)) -> (~((op (e1) (e3)) = (op (e3) (e3)))) -> (~((op (e0) (e1)) = (op (e3) (e1)))) -> (~((op (e0) (e0)) = (e3))) -> (((op (e0) (e0)) = (e3))\/(((op (e0) (e1)) = (e3))\/(((op (e0) (e2)) = (e3))\/((op (e0) (e3)) = (e3))))) -> ((op (e2) (e1)) = (e2)) -> (~((op (e2) (e0)) = (op (e2) (e1)))) -> (~((e1) = (e2))) -> False). % 15.41/15.58 do 0 intro. intros zenon_H199 zenon_Hde zenon_Hae zenon_H44 zenon_H23 zenon_H21 zenon_Hf1 zenon_H45 zenon_H36 zenon_H28a zenon_H30 zenon_H13c zenon_He6 zenon_Heb zenon_H8f zenon_Ha3 zenon_H90 zenon_H6a zenon_H182 zenon_H87 zenon_H42 zenon_H8b zenon_H138 zenon_H59 zenon_H58 zenon_H156 zenon_H154 zenon_Ha7. % 15.41/15.58 apply (zenon_or_s _ _ zenon_H199); [ zenon_intro zenon_H4a | zenon_intro zenon_H19a ]. % 15.41/15.58 apply (zenon_L787_); trivial. % 15.41/15.58 apply (zenon_or_s _ _ zenon_H19a); [ zenon_intro zenon_H96 | zenon_intro zenon_H19b ]. % 15.41/15.58 exact (zenon_H182 zenon_H96). % 15.41/15.58 apply (zenon_or_s _ _ zenon_H19b); [ zenon_intro zenon_Hdf | zenon_intro zenon_H10a ]. % 15.41/15.58 apply (zenon_L183_); trivial. % 15.41/15.58 apply (zenon_L899_); trivial. % 15.41/15.58 (* end of lemma zenon_L900_ *) % 15.41/15.58 assert (zenon_L901_ : (~((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)) = (e1))) -> (~((op (e2) (e2)) = (e0))) -> (~((op (e1) (e3)) = (op (e2) (e3)))) -> ((~((op (e1) (e1)) = (e2)))\/((op (e1) (e2)) = (e1))) -> (~((op (e1) (e0)) = (op (e1) (e2)))) -> ((~((op (e2) (e2)) = (e0)))\/((op (e2) (e0)) = (e2))) -> ((~((op (e2) (e2)) = (e2)))\/((op (e2) (e2)) = (e2))) -> (((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)) = (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) (e3)) = (e0))\/(((op (e0) (e3)) = (e1))\/(((op (e0) (e3)) = (e2))\/((op (e0) (e3)) = (e3))))) -> (~((op (e0) (e3)) = (op (e1) (e3)))) -> (~((op (e0) (e3)) = (op (e2) (e3)))) -> (~((op (e0) (e0)) = (op (e0) (e3)))) -> (((op (e0) (e3)) = (e1))\/(((op (e1) (e3)) = (e1))\/(((op (e2) (e3)) = (e1))\/((op (e3) (e3)) = (e1))))) -> (~((op (e1) (e2)) = (op (e2) (e2)))) -> ((~((op (e3) (e3)) = (e1)))\/((op (e3) (e1)) = (e3))) -> (((op (e0) (e0)) = (e3))\/(((op (e1) (e0)) = (e3))\/(((op (e2) (e0)) = (e3))\/((op (e3) (e0)) = (e3))))) -> ((~((op (e2) (e2)) = (e3)))\/((op (e2) (e3)) = (e2))) -> (~((op (e2) (e0)) = (op (e2) (e3)))) -> (((op (e2) (e2)) = (e0))\/(((op (e2) (e2)) = (e1))\/(((op (e2) (e2)) = (e2))\/((op (e2) (e2)) = (e3))))) -> (((op (e1) (e1)) = (e0))\/(((op (e1) (e1)) = (e1))\/(((op (e1) (e1)) = (e2))\/((op (e1) (e1)) = (e3))))) -> (~((op (e0) (e0)) = (op (e2) (e0)))) -> (((op (e2) (e0)) = (e1))\/(((op (e2) (e1)) = (e1))\/(((op (e2) (e2)) = (e1))\/((op (e2) (e3)) = (e1))))) -> (~((op (e1) (op (e2) (e1))) = (op (e2) (e1)))) -> (((op (e2) (e0)) = (e0))\/(((op (e2) (e1)) = (e0))\/(((op (e2) (e2)) = (e0))\/((op (e2) (e3)) = (e0))))) -> (~((op (e2) (e1)) = (op (e2) (e2)))) -> ((~((op (e2) (e2)) = (e1)))\/((op (e2) (e1)) = (e2))) -> ((~((op (e1) (e1)) = (e3)))\/((op (e1) (e3)) = (e1))) -> (~((op (e1) (e0)) = (op (e1) (e1)))) -> ((~((op (e1) (e1)) = (e1)))\/((op (e1) (e1)) = (e1))) -> (((op (e0) (e0)) = (e3))\/(((op (e0) (e1)) = (e3))\/(((op (e0) (e2)) = (e3))\/((op (e0) (e3)) = (e3))))) -> (~((op (e0) (e0)) = (e3))) -> (~((op (e0) (e1)) = (op (e3) (e1)))) -> (~((e1) = (e3))) -> (((op (e2) (e0)) = (e3))\/(((op (e2) (e1)) = (e3))\/(((op (e2) (e2)) = (e3))\/((op (e2) (e3)) = (e3))))) -> (~((op (e2) (e2)) = (e3))) -> (~((op (e3) (op (e2) (e3))) = (op (e2) (e3)))) -> (~((op (e0) (e3)) = (op (e3) (e3)))) -> (~((op (e0) (e0)) = (e1))) -> (((op (e0) (e0)) = (e1))\/(((op (e1) (e0)) = (e1))\/(((op (e2) (e0)) = (e1))\/((op (e3) (e0)) = (e1))))) -> ((op (e1) (e1)) = (e1)) -> (~((op (e0) (e1)) = (op (e1) (e1)))) -> (((op (e0) (e0)) = (e1))\/(((op (e0) (e1)) = (e1))\/(((op (e0) (e2)) = (e1))\/((op (e0) (e3)) = (e1))))) -> (~((op (e0) (e1)) = (op (e2) (e1)))) -> (((op (e0) (e1)) = (e3))\/(((op (e1) (e1)) = (e3))\/(((op (e2) (e1)) = (e3))\/((op (e3) (e1)) = (e3))))) -> (((op (e0) (e0)) = (e2))\/(((op (e1) (e0)) = (e2))\/(((op (e2) (e0)) = (e2))\/((op (e3) (e0)) = (e2))))) -> (~((op (e0) (e0)) = (e2))) -> (~((op (e3) (e3)) = (e2))) -> (~((op (e2) (e1)) = (op (e2) (e3)))) -> (~((e0) = (e2))) -> (((op (e0) (e3)) = (e2))\/(((op (e1) (e3)) = (e2))\/(((op (e2) (e3)) = (e2))\/((op (e3) (e3)) = (e2))))) -> (((op (e1) (e0)) = (e3))\/(((op (e1) (e1)) = (e3))\/(((op (e1) (e2)) = (e3))\/((op (e1) (e3)) = (e3))))) -> (~((e2) = (e3))) -> (~((op (e1) (e1)) = (e3))) -> (((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)) = (op (e1) (e2)))) -> (~((op (e2) (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 (e1) (e3)) = (op (e3) (e3)))) -> (~((op (e1) (e1)) = (e0))) -> (~((op (e0) (e0)) = (op (e1) (e0)))) -> ((op (e0) (e0)) = (e0)) -> (((op (e1) (e0)) = (e0))\/(((op (e1) (e1)) = (e0))\/(((op (e1) (e2)) = (e0))\/((op (e1) (e3)) = (e0))))) -> ((op (e2) (e1)) = (e2)) -> (~((op (e2) (e0)) = (op (e2) (e1)))) -> (~((e1) = (e2))) -> False). % 15.41/15.58 do 0 intro. intros zenon_H11e zenon_H25b zenon_H104 zenon_H2e zenon_H244 zenon_H1d3 zenon_H166 zenon_H1d4 zenon_Haa zenon_H84 zenon_H28 zenon_H250 zenon_H11b zenon_H1cf zenon_H254 zenon_H80 zenon_Hb4 zenon_H24f zenon_H121 zenon_H7d zenon_H10c zenon_Hbe zenon_H1c3 zenon_Hce zenon_H2d zenon_H1b3 zenon_H258 zenon_Hb7 zenon_H290 zenon_H1f5 zenon_H157 zenon_H1e3 zenon_H1d2 zenon_Hd7 zenon_H1d8 zenon_H58 zenon_H59 zenon_H138 zenon_Ha3 zenon_He6 zenon_H30 zenon_H28a zenon_H36 zenon_H45 zenon_Hf1 zenon_H21 zenon_H23 zenon_H44 zenon_Hde zenon_H199 zenon_Heb zenon_H8f zenon_H3d zenon_H1e2 zenon_H5e zenon_H160 zenon_H90 zenon_H6a zenon_H182 zenon_H251 zenon_Hc9 zenon_H140 zenon_H87 zenon_H13c zenon_H1df zenon_H42 zenon_H8b zenon_H145 zenon_H24c zenon_H1f zenon_H163 zenon_H156 zenon_H154 zenon_Ha7. % 15.41/15.58 apply (zenon_or_s _ _ zenon_H44); [ zenon_intro zenon_H47 | zenon_intro zenon_H46 ]. % 15.41/15.58 exact (zenon_H45 zenon_H47). % 15.41/15.58 apply (zenon_or_s _ _ zenon_H46); [ zenon_intro zenon_H22 | zenon_intro zenon_H48 ]. % 15.41/15.58 apply (zenon_L3_); trivial. % 15.41/15.58 apply (zenon_or_s _ _ zenon_H48); [ zenon_intro zenon_H29 | zenon_intro zenon_H37 ]. % 15.41/15.58 apply (zenon_or_s _ _ zenon_Hf1); [ zenon_intro zenon_H47 | zenon_intro zenon_Hf4 ]. % 15.41/15.58 exact (zenon_H45 zenon_H47). % 15.41/15.58 apply (zenon_or_s _ _ zenon_Hf4); [ zenon_intro zenon_Hd8 | zenon_intro zenon_Hf5 ]. % 15.41/15.58 apply (zenon_L61_); trivial. % 15.41/15.58 apply (zenon_or_s _ _ zenon_Hf5); [ zenon_intro zenon_Hae | zenon_intro zenon_Hee ]. % 15.41/15.58 apply (zenon_L900_); trivial. % 15.41/15.58 apply (zenon_L881_); trivial. % 15.41/15.58 apply (zenon_or_s _ _ zenon_Hf1); [ zenon_intro zenon_H47 | zenon_intro zenon_Hf4 ]. % 15.41/15.58 exact (zenon_H45 zenon_H47). % 15.41/15.58 apply (zenon_or_s _ _ zenon_Hf4); [ zenon_intro zenon_Hd8 | zenon_intro zenon_Hf5 ]. % 15.41/15.58 apply (zenon_L879_); trivial. % 15.41/15.58 apply (zenon_or_s _ _ zenon_Hf5); [ zenon_intro zenon_Hae | zenon_intro zenon_Hee ]. % 15.41/15.58 apply (zenon_L900_); trivial. % 15.41/15.58 apply (zenon_L634_); trivial. % 15.41/15.58 (* end of lemma zenon_L901_ *) % 15.41/15.58 assert (zenon_L902_ : (((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 (e3) (e3)) = (e1))) -> (~((op (e3) (e3)) = (e0))) -> (((op (e3) (e3)) = (e0))\/(((op (e3) (e3)) = (e1))\/(((op (e3) (e3)) = (e2))\/((op (e3) (e3)) = (e3))))) -> (~((e2) = (e3))) -> ((op (e1) (e3)) = (e3)) -> ((op (e2) (e1)) = (e2)) -> (~((op (e2) (e1)) = (op (e2) (e3)))) -> ((op (e3) (e1)) = (e0)) -> ((op (e2) (e2)) = (e1)) -> False). % 15.41/15.58 do 0 intro. intros zenon_H160 zenon_H3e zenon_H36 zenon_H104 zenon_H3c zenon_H3b zenon_H6a zenon_H8a zenon_H156 zenon_H1e2 zenon_H142 zenon_H2a. % 15.41/15.58 apply (zenon_or_s _ _ zenon_H160); [ zenon_intro zenon_H81 | zenon_intro zenon_H161 ]. % 15.41/15.58 apply (zenon_L107_); trivial. % 15.41/15.58 apply (zenon_or_s _ _ zenon_H161); [ zenon_intro zenon_H82 | zenon_intro zenon_H162 ]. % 15.41/15.58 apply (zenon_L165_); trivial. % 15.41/15.58 apply (zenon_or_s _ _ zenon_H162); [ zenon_intro zenon_H124 | zenon_intro zenon_H43 ]. % 15.41/15.58 apply (zenon_L256_); trivial. % 15.41/15.58 apply (zenon_L171_); trivial. % 15.41/15.58 (* end of lemma zenon_L902_ *) % 15.41/15.58 assert (zenon_L903_ : (((op (e0) (e3)) = (e0))\/(((op (e0) (e3)) = (e1))\/(((op (e0) (e3)) = (e2))\/((op (e0) (e3)) = (e3))))) -> ((op (e0) (e0)) = (e0)) -> (~((op (e0) (e0)) = (op (e0) (e3)))) -> ((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). % 15.41/15.58 do 0 intro. intros zenon_H254 zenon_H1f zenon_H24f zenon_Hb5 zenon_Hb4 zenon_H43 zenon_H36 zenon_H80 zenon_H8a. % 15.41/15.58 apply (zenon_or_s _ _ zenon_H254); [ zenon_intro zenon_Hca | zenon_intro zenon_H255 ]. % 15.41/15.58 apply (zenon_L562_); trivial. % 15.41/15.58 apply (zenon_or_s _ _ zenon_H255); [ zenon_intro zenon_H37 | zenon_intro zenon_H256 ]. % 15.41/15.58 apply (zenon_L41_); trivial. % 15.41/15.58 apply (zenon_or_s _ _ zenon_H256); [ zenon_intro zenon_H81 | zenon_intro zenon_H53 ]. % 15.41/15.58 apply (zenon_L106_); trivial. % 15.41/15.58 apply (zenon_L293_); trivial. % 15.41/15.58 (* end of lemma zenon_L903_ *) % 15.41/15.58 assert (zenon_L904_ : (((op (e0) (e3)) = (e2))\/(((op (e1) (e3)) = (e2))\/(((op (e2) (e3)) = (e2))\/((op (e3) (e3)) = (e2))))) -> (~((op (e3) (e3)) = (e3))) -> (~((op (e3) (e3)) = (e1))) -> (~((op (e3) (e3)) = (e0))) -> (((op (e3) (e3)) = (e0))\/(((op (e3) (e3)) = (e1))\/(((op (e3) (e3)) = (e2))\/((op (e3) (e3)) = (e3))))) -> (~((e2) = (e3))) -> ((op (e2) (e1)) = (e2)) -> (~((op (e2) (e1)) = (op (e2) (e3)))) -> (((op (e0) (e3)) = (e0))\/(((op (e0) (e3)) = (e1))\/(((op (e0) (e3)) = (e2))\/((op (e0) (e3)) = (e3))))) -> ((op (e0) (e0)) = (e0)) -> (~((op (e0) (e0)) = (op (e0) (e3)))) -> ((op (e2) (e3)) = (e1)) -> (~((op (e0) (e3)) = (op (e2) (e3)))) -> (~((op (e0) (e3)) = (op (e3) (e3)))) -> (~((op (e0) (e3)) = (op (e1) (e3)))) -> ((op (e1) (e3)) = (e3)) -> False). % 15.41/15.58 do 0 intro. intros zenon_H160 zenon_H3e zenon_H104 zenon_H3c zenon_H3b zenon_H6a zenon_H156 zenon_H1e2 zenon_H254 zenon_H1f zenon_H24f zenon_Hb5 zenon_Hb4 zenon_H36 zenon_H80 zenon_H8a. % 15.41/15.58 apply (zenon_or_s _ _ zenon_H160); [ zenon_intro zenon_H81 | zenon_intro zenon_H161 ]. % 15.41/15.58 apply (zenon_L107_); trivial. % 15.41/15.58 apply (zenon_or_s _ _ zenon_H161); [ zenon_intro zenon_H82 | zenon_intro zenon_H162 ]. % 15.41/15.58 apply (zenon_L165_); trivial. % 15.41/15.58 apply (zenon_or_s _ _ zenon_H162); [ zenon_intro zenon_H124 | zenon_intro zenon_H43 ]. % 15.41/15.58 apply (zenon_L256_); trivial. % 15.41/15.58 apply (zenon_L903_); trivial. % 15.41/15.58 (* end of lemma zenon_L904_ *) % 15.41/15.58 assert (zenon_L905_ : (((op (e2) (e0)) = (e1))\/(((op (e2) (e1)) = (e1))\/(((op (e2) (e2)) = (e1))\/((op (e2) (e3)) = (e1))))) -> (~((e1) = (e3))) -> ((op (e2) (e0)) = (e3)) -> ((op (e1) (e1)) = (e1)) -> (~((op (e1) (e1)) = (op (e2) (e1)))) -> ((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 (e3) (e3)) = (e1))) -> (~((op (e3) (e3)) = (e0))) -> (((op (e3) (e3)) = (e0))\/(((op (e3) (e3)) = (e1))\/(((op (e3) (e3)) = (e2))\/((op (e3) (e3)) = (e3))))) -> (~((e2) = (e3))) -> ((op (e2) (e1)) = (e2)) -> (~((op (e2) (e1)) = (op (e2) (e3)))) -> (((op (e0) (e3)) = (e0))\/(((op (e0) (e3)) = (e1))\/(((op (e0) (e3)) = (e2))\/((op (e0) (e3)) = (e3))))) -> ((op (e0) (e0)) = (e0)) -> (~((op (e0) (e0)) = (op (e0) (e3)))) -> (~((op (e0) (e3)) = (op (e2) (e3)))) -> (~((op (e0) (e3)) = (op (e3) (e3)))) -> (~((op (e0) (e3)) = (op (e1) (e3)))) -> ((op (e1) (e3)) = (e3)) -> False). % 15.41/15.58 do 0 intro. intros zenon_Hb7 zenon_Ha3 zenon_Haf zenon_H21 zenon_Hb1 zenon_H142 zenon_H160 zenon_H3e zenon_H104 zenon_H3c zenon_H3b zenon_H6a zenon_H156 zenon_H1e2 zenon_H254 zenon_H1f zenon_H24f zenon_Hb4 zenon_H36 zenon_H80 zenon_H8a. % 15.41/15.58 apply (zenon_or_s _ _ zenon_Hb7); [ zenon_intro zenon_Hae | zenon_intro zenon_Hb8 ]. % 15.41/15.58 apply (zenon_L39_); trivial. % 15.41/15.58 apply (zenon_or_s _ _ zenon_Hb8); [ zenon_intro zenon_Hb2 | zenon_intro zenon_Hb9 ]. % 15.41/15.58 apply (zenon_L40_); trivial. % 15.41/15.58 apply (zenon_or_s _ _ zenon_Hb9); [ zenon_intro zenon_H2a | zenon_intro zenon_Hb5 ]. % 15.41/15.58 apply (zenon_L902_); trivial. % 15.41/15.58 apply (zenon_L904_); trivial. % 15.41/15.58 (* end of lemma zenon_L905_ *) % 15.41/15.58 assert (zenon_L906_ : (((op (e0) (e0)) = (e1))\/(((op (e0) (e1)) = (e1))\/(((op (e0) (e2)) = (e1))\/((op (e0) (e3)) = (e1))))) -> (~((op (e0) (e0)) = (e1))) -> (~((op (e0) (e1)) = (op (e1) (e1)))) -> (~((op (e0) (e3)) = (op (e3) (e3)))) -> ((op (e3) (e3)) = (e3)) -> (~((e1) = (e3))) -> (((op (e2) (e0)) = (e3))\/(((op (e2) (e1)) = (e3))\/(((op (e2) (e2)) = (e3))\/((op (e2) (e3)) = (e3))))) -> (~((e2) = (e3))) -> (~((op (e0) (e1)) = (op (e2) (e1)))) -> (~((op (e2) (e2)) = (e3))) -> (~((op (e3) (op (e2) (e3))) = (op (e2) (e3)))) -> (~((op (e0) (e0)) = (e3))) -> (((op (e0) (e0)) = (e3))\/(((op (e0) (e1)) = (e3))\/(((op (e0) (e2)) = (e3))\/((op (e0) (e3)) = (e3))))) -> (((op (e2) (e0)) = (e1))\/(((op (e2) (e1)) = (e1))\/(((op (e2) (e2)) = (e1))\/((op (e2) (e3)) = (e1))))) -> ((op (e2) (e0)) = (e2)) -> (~((e1) = (e2))) -> ((op (e1) (e1)) = (e1)) -> (~((op (e1) (e1)) = (op (e2) (e1)))) -> (~((op (e2) (e2)) = (e1))) -> (~((op (e0) (e3)) = (op (e2) (e3)))) -> False). % 15.41/15.58 do 0 intro. intros zenon_H44 zenon_H45 zenon_H23 zenon_H36 zenon_H42 zenon_Ha3 zenon_He6 zenon_H6a zenon_Hde zenon_H30 zenon_H28a zenon_H59 zenon_H58 zenon_Hb7 zenon_Hdd zenon_Ha7 zenon_H21 zenon_Hb1 zenon_H52 zenon_Hb4. % 15.41/15.58 apply (zenon_or_s _ _ zenon_H44); [ zenon_intro zenon_H47 | zenon_intro zenon_H46 ]. % 15.41/15.58 exact (zenon_H45 zenon_H47). % 15.41/15.58 apply (zenon_or_s _ _ zenon_H46); [ zenon_intro zenon_H22 | zenon_intro zenon_H48 ]. % 15.41/15.58 apply (zenon_L3_); trivial. % 15.41/15.58 apply (zenon_or_s _ _ zenon_H48); [ zenon_intro zenon_H29 | zenon_intro zenon_H37 ]. % 15.41/15.58 apply (zenon_L880_); trivial. % 15.41/15.58 apply (zenon_L322_); trivial. % 15.41/15.58 (* end of lemma zenon_L906_ *) % 15.41/15.58 assert (zenon_L907_ : ((~((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 (e0) (e3)) = (op (e3) (e3)))) -> (~((e1) = (e3))) -> (~((e2) = (e3))) -> (~((op (e0) (e1)) = (op (e2) (e1)))) -> (~((op (e3) (op (e2) (e3))) = (op (e2) (e3)))) -> (((op (e2) (e0)) = (e3))\/(((op (e2) (e1)) = (e3))\/(((op (e2) (e2)) = (e3))\/((op (e2) (e3)) = (e3))))) -> (~((op (e0) (e0)) = (e3))) -> (((op (e2) (e0)) = (e1))\/(((op (e2) (e1)) = (e1))\/(((op (e2) (e2)) = (e1))\/((op (e2) (e3)) = (e1))))) -> (~((op (e0) (e3)) = (op (e2) (e3)))) -> (~((op (e1) (e1)) = (op (e2) (e1)))) -> (((op (e0) (e0)) = (e1))\/(((op (e0) (e1)) = (e1))\/(((op (e0) (e2)) = (e1))\/((op (e0) (e3)) = (e1))))) -> (~((op (e0) (e0)) = (e1))) -> (~((op (e1) (e0)) = (op (e1) (e1)))) -> ((op (e1) (e1)) = (e1)) -> (~((e1) = (e2))) -> ((op (e2) (e0)) = (e2)) -> (((op (e2) (e2)) = (e0))\/(((op (e2) (e2)) = (e1))\/(((op (e2) (e2)) = (e2))\/((op (e2) (e2)) = (e3))))) -> (~((op (e2) (e2)) = (e3))) -> (~((op (e2) (e2)) = (e2))) -> (~((op (e2) (e2)) = (e1))) -> (~((op (e3) (e3)) = (e0))) -> (~((op (e3) (e3)) = (e1))) -> (((op (e3) (e3)) = (e0))\/(((op (e3) (e3)) = (e1))\/(((op (e3) (e3)) = (e2))\/((op (e3) (e3)) = (e3))))) -> (((op (e0) (e0)) = (e1))\/(((op (e1) (e0)) = (e1))\/(((op (e2) (e0)) = (e1))\/((op (e3) (e0)) = (e1))))) -> False). % 15.41/15.58 do 0 intro. intros zenon_H10d zenon_H23 zenon_H58 zenon_H36 zenon_Ha3 zenon_H6a zenon_Hde zenon_H28a zenon_He6 zenon_H59 zenon_Hb7 zenon_Hb4 zenon_Hb1 zenon_H44 zenon_H45 zenon_Hd7 zenon_H21 zenon_Ha7 zenon_Hdd zenon_H2d zenon_H30 zenon_H2f zenon_H52 zenon_H3c zenon_H104 zenon_H3b zenon_Hf1. % 15.41/15.58 apply (zenon_or_s _ _ zenon_H10d); [ zenon_intro zenon_H3e | zenon_intro zenon_H42 ]. % 15.41/15.58 apply (zenon_L307_); trivial. % 15.41/15.58 apply (zenon_L906_); trivial. % 15.41/15.58 (* end of lemma zenon_L907_ *) % 15.41/15.58 assert (zenon_L908_ : ((~((op (e3) (e3)) = (e2)))\/((op (e3) (e2)) = (e3))) -> (~((op (e3) (e1)) = (op (e3) (e2)))) -> (((op (e0) (e0)) = (e1))\/(((op (e0) (e1)) = (e1))\/(((op (e0) (e2)) = (e1))\/((op (e0) (e3)) = (e1))))) -> (~((op (e3) (e3)) = (e0))) -> (~((op (e0) (e3)) = (op (e3) (e3)))) -> (((op (e3) (e3)) = (e0))\/(((op (e3) (e3)) = (e1))\/(((op (e3) (e3)) = (e2))\/((op (e3) (e3)) = (e3))))) -> (~((op (e0) (e0)) = (e2))) -> (((op (e0) (e0)) = (e3))\/(((op (e0) (e1)) = (e3))\/(((op (e0) (e2)) = (e3))\/((op (e0) (e3)) = (e3))))) -> (~((op (e0) (e0)) = (op (e1) (e0)))) -> ((op (e0) (e0)) = (e0)) -> (~((op (e1) (e1)) = (e0))) -> (((op (e2) (e2)) = (e0))\/(((op (e2) (e2)) = (e1))\/(((op (e2) (e2)) = (e2))\/((op (e2) (e2)) = (e3))))) -> (~((op (e2) (e2)) = (e3))) -> (~((op (e2) (e2)) = (e2))) -> (~((op (e2) (e2)) = (e1))) -> (~((op (e1) (e2)) = (op (e2) (e2)))) -> (((op (e0) (e3)) = (e2))\/(((op (e1) (e3)) = (e2))\/(((op (e2) (e3)) = (e2))\/((op (e3) (e3)) = (e2))))) -> ((op (e2) (e0)) = (e2)) -> (~((op (e2) (e0)) = (op (e2) (e3)))) -> (~((e0) = (e2))) -> (((op (e1) (e0)) = (e0))\/(((op (e1) (e1)) = (e0))\/(((op (e1) (e2)) = (e0))\/((op (e1) (e3)) = (e0))))) -> (~((e1) = (e3))) -> (~((e2) = (e3))) -> (~((op (e0) (e0)) = (e3))) -> (~((e1) = (e2))) -> ((op (e3) (e1)) = (e3)) -> (~((op (e0) (e1)) = (op (e3) (e1)))) -> (((op (e0) (e0)) = (e2))\/(((op (e0) (e1)) = (e2))\/(((op (e0) (e2)) = (e2))\/((op (e0) (e3)) = (e2))))) -> ((op (e1) (e1)) = (e1)) -> (~((op (e0) (e1)) = (op (e1) (e1)))) -> (~((op (e0) (e0)) = (e1))) -> (~((op (e3) (e1)) = (op (e3) (e3)))) -> ((~((op (e3) (e3)) = (e3)))\/((op (e3) (e3)) = (e3))) -> False). % 15.41/15.58 do 0 intro. intros zenon_H10e zenon_H135 zenon_H44 zenon_H3c zenon_H36 zenon_H3b zenon_H8f zenon_H58 zenon_H24c zenon_H1f zenon_H145 zenon_H2d zenon_H30 zenon_H2f zenon_H52 zenon_H7d zenon_H160 zenon_Hdd zenon_Hce zenon_H5e zenon_H163 zenon_Ha3 zenon_H6a zenon_H59 zenon_Ha7 zenon_H10a zenon_H138 zenon_H8e zenon_H21 zenon_H23 zenon_H45 zenon_H12d zenon_H10d. % 15.41/15.58 apply (zenon_or_s _ _ zenon_H10e); [ zenon_intro zenon_H3d | zenon_intro zenon_H106 ]. % 15.41/15.58 apply (zenon_or_s _ _ zenon_H10d); [ zenon_intro zenon_H3e | zenon_intro zenon_H42 ]. % 15.41/15.58 apply (zenon_or_s _ _ zenon_H44); [ zenon_intro zenon_H47 | zenon_intro zenon_H46 ]. % 15.41/15.58 exact (zenon_H45 zenon_H47). % 15.41/15.58 apply (zenon_or_s _ _ zenon_H46); [ zenon_intro zenon_H22 | zenon_intro zenon_H48 ]. % 15.41/15.58 apply (zenon_L3_); trivial. % 15.41/15.58 apply (zenon_or_s _ _ zenon_H48); [ zenon_intro zenon_H29 | zenon_intro zenon_H37 ]. % 15.41/15.58 apply (zenon_L646_); trivial. % 15.41/15.58 apply (zenon_L7_); trivial. % 15.41/15.58 apply (zenon_L102_); trivial. % 15.41/15.58 apply (zenon_L115_); trivial. % 15.41/15.58 (* end of lemma zenon_L908_ *) % 15.41/15.58 assert (zenon_L909_ : ((~((op (e2) (e2)) = (e1)))\/((op (e2) (e1)) = (e2))) -> (~((op (e2) (e0)) = (op (e2) (e1)))) -> ((~((op (e2) (e2)) = (e3)))\/((op (e2) (e3)) = (e2))) -> ((~((op (e3) (e3)) = (e1)))\/((op (e3) (e1)) = (e3))) -> (~((op (e3) (e1)) = (op (e3) (e3)))) -> (((op (e0) (e0)) = (e2))\/(((op (e0) (e1)) = (e2))\/(((op (e0) (e2)) = (e2))\/((op (e0) (e3)) = (e2))))) -> (~((op (e0) (e1)) = (op (e3) (e1)))) -> (((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 (e0) (e3)) = (e2))\/(((op (e1) (e3)) = (e2))\/(((op (e2) (e3)) = (e2))\/((op (e3) (e3)) = (e2))))) -> (~((op (e1) (e2)) = (op (e2) (e2)))) -> (~((op (e1) (e1)) = (e0))) -> ((op (e0) (e0)) = (e0)) -> (~((op (e0) (e0)) = (op (e1) (e0)))) -> (~((op (e0) (e0)) = (e2))) -> (~((op (e3) (e1)) = (op (e3) (e2)))) -> ((~((op (e3) (e3)) = (e2)))\/((op (e3) (e2)) = (e3))) -> (((op (e0) (e0)) = (e1))\/(((op (e1) (e0)) = (e1))\/(((op (e2) (e0)) = (e1))\/((op (e3) (e0)) = (e1))))) -> (((op (e3) (e3)) = (e0))\/(((op (e3) (e3)) = (e1))\/(((op (e3) (e3)) = (e2))\/((op (e3) (e3)) = (e3))))) -> (((op (e2) (e2)) = (e0))\/(((op (e2) (e2)) = (e1))\/(((op (e2) (e2)) = (e2))\/((op (e2) (e2)) = (e3))))) -> ((op (e2) (e0)) = (e2)) -> (~((e1) = (e2))) -> ((op (e1) (e1)) = (e1)) -> (~((op (e1) (e0)) = (op (e1) (e1)))) -> (~((op (e0) (e0)) = (e1))) -> (((op (e0) (e0)) = (e1))\/(((op (e0) (e1)) = (e1))\/(((op (e0) (e2)) = (e1))\/((op (e0) (e3)) = (e1))))) -> (~((op (e1) (e1)) = (op (e2) (e1)))) -> (~((op (e0) (e3)) = (op (e2) (e3)))) -> (((op (e2) (e0)) = (e1))\/(((op (e2) (e1)) = (e1))\/(((op (e2) (e2)) = (e1))\/((op (e2) (e3)) = (e1))))) -> (~((op (e0) (e0)) = (e3))) -> (((op (e2) (e0)) = (e3))\/(((op (e2) (e1)) = (e3))\/(((op (e2) (e2)) = (e3))\/((op (e2) (e3)) = (e3))))) -> (~((op (e3) (op (e2) (e3))) = (op (e2) (e3)))) -> (~((op (e0) (e1)) = (op (e2) (e1)))) -> (~((e2) = (e3))) -> (~((e1) = (e3))) -> (~((op (e0) (e3)) = (op (e3) (e3)))) -> (((op (e0) (e0)) = (e3))\/(((op (e0) (e1)) = (e3))\/(((op (e0) (e2)) = (e3))\/((op (e0) (e3)) = (e3))))) -> (~((op (e0) (e1)) = (op (e1) (e1)))) -> ((~((op (e3) (e3)) = (e3)))\/((op (e3) (e3)) = (e3))) -> ((~((op (e3) (e3)) = (e0)))\/((op (e3) (e0)) = (e3))) -> (~((op (e2) (e0)) = (op (e2) (e2)))) -> ((~((op (e2) (e2)) = (e2)))\/((op (e2) (e2)) = (e2))) -> False). % 15.41/15.58 do 0 intro. intros zenon_H1e3 zenon_H154 zenon_H1c3 zenon_H10c zenon_H12d zenon_H8e zenon_H138 zenon_H163 zenon_H5e zenon_Hce zenon_H160 zenon_H7d zenon_H145 zenon_H1f zenon_H24c zenon_H8f zenon_H135 zenon_H10e zenon_Hf1 zenon_H3b zenon_H2d zenon_Hdd zenon_Ha7 zenon_H21 zenon_Hd7 zenon_H45 zenon_H44 zenon_Hb1 zenon_Hb4 zenon_Hb7 zenon_H59 zenon_He6 zenon_H28a zenon_Hde zenon_H6a zenon_Ha3 zenon_H36 zenon_H58 zenon_H23 zenon_H10d zenon_H10f zenon_H17a zenon_Haa. % 15.41/15.58 apply (zenon_or_s _ _ zenon_H1e3); [ zenon_intro zenon_H52 | zenon_intro zenon_H156 ]. % 15.41/15.58 apply (zenon_or_s _ _ zenon_Haa); [ zenon_intro zenon_H2f | zenon_intro zenon_H35 ]. % 15.41/15.58 apply (zenon_or_s _ _ zenon_H1c3); [ zenon_intro zenon_H30 | zenon_intro zenon_H124 ]. % 15.41/15.58 apply (zenon_or_s _ _ zenon_H10f); [ zenon_intro zenon_H3c | zenon_intro zenon_Hba ]. % 15.41/15.58 apply (zenon_or_s _ _ zenon_H10c); [ zenon_intro zenon_H104 | zenon_intro zenon_H10a ]. % 15.41/15.58 apply (zenon_L907_); trivial. % 15.41/15.58 apply (zenon_L908_); trivial. % 15.41/15.58 apply (zenon_L310_); trivial. % 15.41/15.58 apply (zenon_L119_); trivial. % 15.41/15.58 apply (zenon_L161_); trivial. % 15.41/15.58 apply (zenon_L284_); trivial. % 15.41/15.58 (* end of lemma zenon_L909_ *) % 15.41/15.58 assert (zenon_L910_ : (((op (e0) (e1)) = (e0))\/(((op (e0) (e1)) = (e1))\/(((op (e0) (e1)) = (e2))\/((op (e0) (e1)) = (e3))))) -> ((op (e0) (e0)) = (e0)) -> (~((op (e0) (e0)) = (op (e0) (e1)))) -> (~((op (e0) (e1)) = (op (e1) (e1)))) -> ((op (e1) (e1)) = (e1)) -> ((op (e3) (e1)) = (e2)) -> (~((op (e0) (e1)) = (op (e3) (e1)))) -> (~((op (e0) (e1)) = (op (e2) (e1)))) -> ((op (e2) (e1)) = (e3)) -> False). % 15.41/15.58 do 0 intro. intros zenon_H1e9 zenon_H1f zenon_H25a zenon_H23 zenon_H21 zenon_H16a zenon_H138 zenon_Hde zenon_Hdf. % 15.41/15.58 apply (zenon_or_s _ _ zenon_H1e9); [ zenon_intro zenon_H49 | zenon_intro zenon_H1ea ]. % 15.41/15.58 apply (zenon_L610_); trivial. % 15.41/15.58 apply (zenon_or_s _ _ zenon_H1ea); [ zenon_intro zenon_H22 | zenon_intro zenon_H1eb ]. % 15.41/15.58 apply (zenon_L3_); trivial. % 15.41/15.58 apply (zenon_or_s _ _ zenon_H1eb); [ zenon_intro zenon_H5d | zenon_intro zenon_H4a ]. % 15.41/15.58 apply (zenon_L146_); trivial. % 15.41/15.58 apply (zenon_L65_); trivial. % 15.41/15.58 (* end of lemma zenon_L910_ *) % 15.41/15.58 assert (zenon_L911_ : (((op (e3) (e0)) = (e2))\/(((op (e3) (e1)) = (e2))\/(((op (e3) (e2)) = (e2))\/((op (e3) (e3)) = (e2))))) -> ((op (e3) (e0)) = (e3)) -> (~((e2) = (e3))) -> ((op (e2) (e1)) = (e3)) -> (~((op (e0) (e1)) = (op (e2) (e1)))) -> (~((op (e0) (e1)) = (op (e3) (e1)))) -> ((op (e1) (e1)) = (e1)) -> (~((op (e0) (e1)) = (op (e1) (e1)))) -> (~((op (e0) (e0)) = (op (e0) (e1)))) -> ((op (e0) (e0)) = (e0)) -> (((op (e0) (e1)) = (e0))\/(((op (e0) (e1)) = (e1))\/(((op (e0) (e1)) = (e2))\/((op (e0) (e1)) = (e3))))) -> ((op (e0) (e2)) = (e2)) -> (~((op (e0) (e2)) = (op (e3) (e2)))) -> (~((op (e3) (e3)) = (e2))) -> False). % 15.41/15.58 do 0 intro. intros zenon_H1df zenon_Hba zenon_H6a zenon_Hdf zenon_Hde zenon_H138 zenon_H21 zenon_H23 zenon_H25a zenon_H1f zenon_H1e9 zenon_H63 zenon_H140 zenon_H3d. % 15.41/15.58 apply (zenon_or_s _ _ zenon_H1df); [ zenon_intro zenon_He9 | zenon_intro zenon_H1e0 ]. % 15.41/15.58 apply (zenon_L220_); trivial. % 15.41/15.58 apply (zenon_or_s _ _ zenon_H1e0); [ zenon_intro zenon_H16a | zenon_intro zenon_H1e1 ]. % 15.41/15.58 apply (zenon_L910_); trivial. % 15.41/15.58 apply (zenon_or_s _ _ zenon_H1e1); [ zenon_intro zenon_H1dd | zenon_intro zenon_H43 ]. % 15.41/15.58 apply (zenon_L253_); trivial. % 15.41/15.58 exact (zenon_H3d zenon_H43). % 15.41/15.58 (* end of lemma zenon_L911_ *) % 15.41/15.58 assert (zenon_L912_ : (((op (e0) (e3)) = (e2))\/(((op (e1) (e3)) = (e2))\/(((op (e2) (e3)) = (e2))\/((op (e3) (e3)) = (e2))))) -> (~((e1) = (e2))) -> ((op (e0) (e3)) = (e1)) -> ((op (e1) (e3)) = (e3)) -> (~((e2) = (e3))) -> ((op (e2) (e3)) = (e3)) -> (~((op (e3) (e3)) = (e2))) -> False). % 15.41/15.58 do 0 intro. intros zenon_H160 zenon_Ha7 zenon_H37 zenon_H8a zenon_H6a zenon_He2 zenon_H3d. % 15.41/15.58 apply (zenon_or_s _ _ zenon_H160); [ zenon_intro zenon_H81 | zenon_intro zenon_H161 ]. % 15.41/15.58 apply (zenon_L33_); trivial. % 15.41/15.58 apply (zenon_or_s _ _ zenon_H161); [ zenon_intro zenon_H82 | zenon_intro zenon_H162 ]. % 15.41/15.58 apply (zenon_L165_); trivial. % 15.41/15.58 apply (zenon_or_s _ _ zenon_H162); [ zenon_intro zenon_H124 | zenon_intro zenon_H43 ]. % 15.41/15.58 apply (zenon_L98_); trivial. % 15.41/15.58 exact (zenon_H3d zenon_H43). % 15.41/15.58 (* end of lemma zenon_L912_ *) % 15.41/15.58 assert (zenon_L913_ : (~((op (e2) (op (e2) (e2))) = (op (e2) (e2)))) -> ((~((op (e3) (e3)) = (e0)))\/((op (e3) (e0)) = (e3))) -> (~((op (e3) (e0)) = (op (e3) (e2)))) -> (~((op (e3) (e0)) = (op (e3) (e1)))) -> ((~((op (e3) (e3)) = (e2)))\/((op (e3) (e2)) = (e3))) -> (~((op (e1) (e1)) = (op (e1) (e2)))) -> (((op (e0) (e0)) = (e1))\/(((op (e0) (e1)) = (e1))\/(((op (e0) (e2)) = (e1))\/((op (e0) (e3)) = (e1))))) -> (~((op (e0) (e3)) = (op (e3) (e3)))) -> (((op (e3) (e3)) = (e0))\/(((op (e3) (e3)) = (e1))\/(((op (e3) (e3)) = (e2))\/((op (e3) (e3)) = (e3))))) -> (~((op (e0) (e2)) = (op (e2) (e2)))) -> (((op (e2) (e2)) = (e0))\/(((op (e2) (e2)) = (e1))\/(((op (e2) (e2)) = (e2))\/((op (e2) (e2)) = (e3))))) -> ((op (e1) (e1)) = (e1)) -> (~((op (e0) (e1)) = (op (e1) (e1)))) -> (~((op (e0) (e0)) = (e1))) -> ((~((op (e1) (e1)) = (e1)))\/((op (e1) (e1)) = (e1))) -> (~((op (e1) (e0)) = (op (e1) (e1)))) -> ((~((op (e1) (e1)) = (e3)))\/((op (e1) (e3)) = (e1))) -> ((~((op (e2) (e2)) = (e1)))\/((op (e2) (e1)) = (e2))) -> (~((op (e2) (e1)) = (op (e2) (e3)))) -> (~((op (e2) (e1)) = (op (e2) (e2)))) -> (((op (e2) (e0)) = (e0))\/(((op (e2) (e1)) = (e0))\/(((op (e2) (e2)) = (e0))\/((op (e2) (e3)) = (e0))))) -> (~((e0) = (e2))) -> (~((op (e1) (op (e2) (e1))) = (op (e2) (e1)))) -> (((op (e2) (e0)) = (e1))\/(((op (e2) (e1)) = (e1))\/(((op (e2) (e2)) = (e1))\/((op (e2) (e3)) = (e1))))) -> ((op (e0) (e0)) = (e0)) -> (~((op (e0) (e0)) = (op (e2) (e0)))) -> (~((op (e0) (e0)) = (e3))) -> (~((e1) = (e3))) -> (((op (e1) (e1)) = (e0))\/(((op (e1) (e1)) = (e1))\/(((op (e1) (e1)) = (e2))\/((op (e1) (e1)) = (e3))))) -> (((op (e0) (e0)) = (e2))\/(((op (e1) (e0)) = (e2))\/(((op (e2) (e0)) = (e2))\/((op (e3) (e0)) = (e2))))) -> (((op (e0) (e0)) = (e3))\/(((op (e0) (e1)) = (e3))\/(((op (e0) (e2)) = (e3))\/((op (e0) (e3)) = (e3))))) -> (~((op (e0) (e2)) = (op (e1) (e2)))) -> (~((op (e1) (e3)) = (op (e3) (e3)))) -> (((op (e1) (e0)) = (e3))\/(((op (e1) (e1)) = (e3))\/(((op (e1) (e2)) = (e3))\/((op (e1) (e3)) = (e3))))) -> (~((e2) = (e3))) -> (~((op (e0) (e1)) = (op (e2) (e1)))) -> (~((op (e3) (op (e2) (e3))) = (op (e2) (e3)))) -> (((op (e2) (e0)) = (e3))\/(((op (e2) (e1)) = (e3))\/(((op (e2) (e2)) = (e3))\/((op (e2) (e3)) = (e3))))) -> (~((op (e2) (e0)) = (op (e2) (e3)))) -> ((~((op (e2) (e2)) = (e3)))\/((op (e2) (e3)) = (e2))) -> (~((e1) = (e2))) -> (~((op (e0) (e0)) = (e2))) -> (((op (e0) (e0)) = (e3))\/(((op (e1) (e0)) = (e3))\/(((op (e2) (e0)) = (e3))\/((op (e3) (e0)) = (e3))))) -> ((~((op (e3) (e3)) = (e1)))\/((op (e3) (e1)) = (e3))) -> (~((op (e0) (e1)) = (op (e3) (e1)))) -> (~((op (e1) (e2)) = (op (e2) (e2)))) -> (((op (e0) (e3)) = (e1))\/(((op (e1) (e3)) = (e1))\/(((op (e2) (e3)) = (e1))\/((op (e3) (e3)) = (e1))))) -> (~((op (e0) (e0)) = (op (e0) (e3)))) -> (~((op (e0) (e3)) = (op (e2) (e3)))) -> (~((op (e0) (e3)) = (op (e1) (e3)))) -> (((op (e0) (e3)) = (e0))\/(((op (e0) (e3)) = (e1))\/(((op (e0) (e3)) = (e2))\/((op (e0) (e3)) = (e3))))) -> (~((op (e1) (e0)) = (op (e1) (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) (e2)) = (op (e3) (e2)))) -> (((op (e0) (e2)) = (e0))\/(((op (e0) (e2)) = (e1))\/(((op (e0) (e2)) = (e2))\/((op (e0) (e2)) = (e3))))) -> (~((op (e0) (e2)) = (op (e0) (e3)))) -> (((op (e1) (e0)) = (e2))\/(((op (e1) (e1)) = (e2))\/(((op (e1) (e2)) = (e2))\/((op (e1) (e3)) = (e2))))) -> ((~((op (e2) (e2)) = (e2)))\/((op (e2) (e2)) = (e2))) -> ((~((op (e2) (e2)) = (e0)))\/((op (e2) (e0)) = (e2))) -> (~((op (e1) (e0)) = (op (e1) (e2)))) -> ((~((op (e1) (e1)) = (e2)))\/((op (e1) (e2)) = (e1))) -> (((op (e2) (e0)) = (e2))\/(((op (e2) (e1)) = (e2))\/(((op (e2) (e2)) = (e2))\/((op (e2) (e3)) = (e2))))) -> (~((op (e1) (e1)) = (op (e2) (e1)))) -> (((op (e1) (e0)) = (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 (e2) (e1)) = (op (e3) (e1)))) -> (~((op (e1) (e1)) = (op (e1) (e3)))) -> (((op (e1) (e3)) = (e0))\/(((op (e1) (e3)) = (e1))\/(((op (e1) (e3)) = (e2))\/((op (e1) (e3)) = (e3))))) -> (~((op (e1) (e3)) = (op (e2) (e3)))) -> (~((op (e1) (e1)) = (e0))) -> (~((op (e0) (e0)) = (op (e1) (e0)))) -> (((op (e0) (e0)) = (e1))\/(((op (e1) (e0)) = (e1))\/(((op (e2) (e0)) = (e1))\/((op (e3) (e0)) = (e1))))) -> ((~((op (e3) (e3)) = (e3)))\/((op (e3) (e3)) = (e3))) -> (~((op (e3) (e1)) = (op (e3) (e2)))) -> (~((op (e3) (e1)) = (op (e3) (e3)))) -> (((op (e0) (e3)) = (e2))\/(((op (e1) (e3)) = (e2))\/(((op (e2) (e3)) = (e2))\/((op (e3) (e3)) = (e2))))) -> (~((e0) = (e1))) -> (((op (e0) (e2)) = (e0))\/(((op (e1) (e2)) = (e0))\/(((op (e2) (e2)) = (e0))\/((op (e3) (e2)) = (e0))))) -> (~((op (e3) (e0)) = (op (e3) (e3)))) -> (((op (e0) (e3)) = (e0))\/(((op (e1) (e3)) = (e0))\/(((op (e2) (e3)) = (e0))\/((op (e3) (e3)) = (e0))))) -> (((op (e0) (e1)) = (e0))\/(((op (e1) (e1)) = (e0))\/(((op (e2) (e1)) = (e0))\/((op (e3) (e1)) = (e0))))) -> (~((e0) = (e3))) -> (((op (e3) (e0)) = (e1))\/(((op (e3) (e1)) = (e1))\/(((op (e3) (e2)) = (e1))\/((op (e3) (e3)) = (e1))))) -> (((op (e0) (e0)) = (e2))\/(((op (e0) (e1)) = (e2))\/(((op (e0) (e2)) = (e2))\/((op (e0) (e3)) = (e2))))) -> (((op (e0) (e1)) = (e0))\/(((op (e0) (e1)) = (e1))\/(((op (e0) (e1)) = (e2))\/((op (e0) (e1)) = (e3))))) -> (~((op (e0) (op (e2) (e0))) = (op (e2) (e0)))) -> (~((op (e1) (e2)) = (op (e3) (e2)))) -> (~((op (e2) (e0)) = (op (e2) (e2)))) -> (~((op (e0) (e0)) = (op (e0) (e1)))) -> (((op (e0) (e1)) = (e3))\/(((op (e1) (e1)) = (e3))\/(((op (e2) (e1)) = (e3))\/((op (e3) (e1)) = (e3))))) -> (~((op (e2) (e0)) = (op (e2) (e1)))) -> False). % 15.41/15.58 do 0 intro. intros zenon_H294 zenon_H10f zenon_H105 zenon_H109 zenon_H10e zenon_H116 zenon_H44 zenon_H36 zenon_H3b zenon_H28 zenon_H2d zenon_H21 zenon_H23 zenon_H45 zenon_H1d8 zenon_Hd7 zenon_H1d2 zenon_H1e3 zenon_H1e2 zenon_H157 zenon_H1f5 zenon_H5e zenon_H290 zenon_Hb7 zenon_H1f zenon_H258 zenon_H59 zenon_Ha3 zenon_H1b3 zenon_Heb zenon_H58 zenon_H87 zenon_H8b zenon_H90 zenon_H6a zenon_Hde zenon_H28a zenon_He6 zenon_Hce zenon_H1c3 zenon_Ha7 zenon_H8f zenon_Hbe zenon_H10c zenon_H138 zenon_H7d zenon_H121 zenon_H24f zenon_Hb4 zenon_H80 zenon_H254 zenon_H1cf zenon_H11b zenon_H250 zenon_H140 zenon_H251 zenon_Hc9 zenon_H84 zenon_Haa zenon_H1d4 zenon_H166 zenon_H1d3 zenon_H237 zenon_Hb1 zenon_H163 zenon_H1df zenon_H13c zenon_H11e zenon_H25b zenon_H244 zenon_H145 zenon_H24c zenon_Hf1 zenon_H10d zenon_H135 zenon_H12d zenon_H160 zenon_H9e zenon_H16f zenon_Hbb zenon_Hd3 zenon_H144 zenon_H4b zenon_H146 zenon_H8e zenon_H1e9 zenon_H295 zenon_H17d zenon_H17a zenon_H25a zenon_H199 zenon_H154. % 15.41/15.58 apply (zenon_or_s _ _ zenon_H1d3); [ zenon_intro zenon_Hd6 | zenon_intro zenon_H117 ]. % 15.41/15.58 apply (zenon_or_s _ _ zenon_H1d2); [ zenon_intro zenon_H182 | zenon_intro zenon_H11f ]. % 15.41/15.58 apply (zenon_or_s _ _ zenon_H1d4); [ zenon_intro zenon_H2e | zenon_intro zenon_Hdd ]. % 15.41/15.58 apply (zenon_or_s _ _ zenon_H1e3); [ zenon_intro zenon_H52 | zenon_intro zenon_H156 ]. % 15.41/15.58 apply (zenon_or_s _ _ zenon_Haa); [ zenon_intro zenon_H2f | zenon_intro zenon_H35 ]. % 15.41/15.58 apply (zenon_or_s _ _ zenon_H1c3); [ zenon_intro zenon_H30 | zenon_intro zenon_H124 ]. % 15.41/15.58 apply (zenon_or_s _ _ zenon_H10f); [ zenon_intro zenon_H3c | zenon_intro zenon_Hba ]. % 15.41/15.58 apply (zenon_or_s _ _ zenon_H10c); [ zenon_intro zenon_H104 | zenon_intro zenon_H10a ]. % 15.41/15.58 apply (zenon_or_s _ _ zenon_H10e); [ zenon_intro zenon_H3d | zenon_intro zenon_H106 ]. % 15.41/15.58 apply (zenon_or_s _ _ zenon_H10d); [ zenon_intro zenon_H3e | zenon_intro zenon_H42 ]. % 15.41/15.58 apply (zenon_L8_); trivial. % 15.41/15.58 apply (zenon_L886_); trivial. % 15.41/15.58 apply (zenon_L89_); trivial. % 15.41/15.58 apply (zenon_L325_); trivial. % 15.41/15.58 apply (zenon_or_s _ _ zenon_H10c); [ zenon_intro zenon_H104 | zenon_intro zenon_H10a ]. % 15.41/15.58 apply (zenon_or_s _ _ zenon_H10e); [ zenon_intro zenon_H3d | zenon_intro zenon_H106 ]. % 15.41/15.58 apply (zenon_or_s _ _ zenon_H10d); [ zenon_intro zenon_H3e | zenon_intro zenon_H42 ]. % 15.41/15.58 apply (zenon_L80_); trivial. % 15.41/15.58 apply (zenon_L886_); trivial. % 15.41/15.58 apply (zenon_L81_); trivial. % 15.41/15.58 apply (zenon_L82_); trivial. % 15.41/15.58 apply (zenon_or_s _ _ zenon_H10f); [ zenon_intro zenon_H3c | zenon_intro zenon_Hba ]. % 15.41/15.58 apply (zenon_or_s _ _ zenon_H10c); [ zenon_intro zenon_H104 | zenon_intro zenon_H10a ]. % 15.41/15.58 apply (zenon_or_s _ _ zenon_H10e); [ zenon_intro zenon_H3d | zenon_intro zenon_H106 ]. % 15.41/15.58 apply (zenon_or_s _ _ zenon_H10d); [ zenon_intro zenon_H3e | zenon_intro zenon_H42 ]. % 15.41/15.58 apply (zenon_L95_); trivial. % 15.41/15.58 apply (zenon_L894_); trivial. % 15.41/15.58 apply (zenon_L893_); trivial. % 15.41/15.58 apply (zenon_L130_); trivial. % 15.41/15.58 apply (zenon_or_s _ _ zenon_H10c); [ zenon_intro zenon_H104 | zenon_intro zenon_H10a ]. % 15.41/15.58 apply (zenon_or_s _ _ zenon_H10e); [ zenon_intro zenon_H3d | zenon_intro zenon_H106 ]. % 15.41/15.58 apply (zenon_or_s _ _ zenon_H10d); [ zenon_intro zenon_H3e | zenon_intro zenon_H42 ]. % 15.41/15.58 apply (zenon_L895_); trivial. % 15.41/15.58 apply (zenon_L43_); trivial. % 15.41/15.58 apply (zenon_L81_); trivial. % 15.41/15.58 apply (zenon_L82_); trivial. % 15.41/15.58 apply (zenon_L794_); trivial. % 15.41/15.58 apply (zenon_or_s _ _ zenon_Haa); [ zenon_intro zenon_H2f | zenon_intro zenon_H35 ]. % 15.41/15.58 apply (zenon_or_s _ _ zenon_H1c3); [ zenon_intro zenon_H30 | zenon_intro zenon_H124 ]. % 15.41/15.58 apply (zenon_or_s _ _ zenon_H10f); [ zenon_intro zenon_H3c | zenon_intro zenon_Hba ]. % 15.41/15.58 apply (zenon_or_s _ _ zenon_H10c); [ zenon_intro zenon_H104 | zenon_intro zenon_H10a ]. % 15.41/15.58 apply (zenon_or_s _ _ zenon_H10e); [ zenon_intro zenon_H3d | zenon_intro zenon_H106 ]. % 15.41/15.58 apply (zenon_or_s _ _ zenon_H10d); [ zenon_intro zenon_H3e | zenon_intro zenon_H42 ]. % 15.41/15.58 apply (zenon_L8_); trivial. % 15.41/15.58 apply (zenon_L901_); trivial. % 15.41/15.58 apply (zenon_or_s _ _ zenon_H10d); [ zenon_intro zenon_H3e | zenon_intro zenon_H42 ]. % 15.41/15.58 apply (zenon_or_s _ _ zenon_Hf1); [ zenon_intro zenon_H47 | zenon_intro zenon_Hf4 ]. % 15.41/15.58 exact (zenon_H45 zenon_H47). % 15.41/15.58 apply (zenon_or_s _ _ zenon_Hf4); [ zenon_intro zenon_Hd8 | zenon_intro zenon_Hf5 ]. % 15.41/15.58 apply (zenon_L61_); trivial. % 15.41/15.58 apply (zenon_or_s _ _ zenon_Hf5); [ zenon_intro zenon_Hae | zenon_intro zenon_Hee ]. % 15.41/15.58 apply (zenon_or_s _ _ zenon_H144); [ zenon_intro zenon_H49 | zenon_intro zenon_H147 ]. % 15.41/15.58 apply (zenon_L610_); trivial. % 15.41/15.58 apply (zenon_or_s _ _ zenon_H147); [ zenon_intro zenon_H149 | zenon_intro zenon_H148 ]. % 15.41/15.58 exact (zenon_H145 zenon_H149). % 15.41/15.58 apply (zenon_or_s _ _ zenon_H148); [ zenon_intro zenon_H14a | zenon_intro zenon_H142 ]. % 15.41/15.58 apply (zenon_L351_); trivial. % 15.41/15.58 apply (zenon_or_s _ _ zenon_H11b); [ zenon_intro zenon_H29 | zenon_intro zenon_H11c ]. % 15.41/15.58 apply (zenon_L92_); trivial. % 15.41/15.58 apply (zenon_or_s _ _ zenon_H11c); [ zenon_intro zenon_H117 | zenon_intro zenon_H11d ]. % 15.41/15.58 apply (zenon_L622_); trivial. % 15.41/15.58 apply (zenon_or_s _ _ zenon_H11d); [ zenon_intro zenon_H2a | zenon_intro zenon_H119 ]. % 15.41/15.58 apply (zenon_L172_); trivial. % 15.41/15.58 apply (zenon_L87_); trivial. % 15.41/15.58 apply (zenon_or_s _ _ zenon_Heb); [ zenon_intro zenon_H92 | zenon_intro zenon_Hec ]. % 15.41/15.58 exact (zenon_H8f zenon_H92). % 15.41/15.58 apply (zenon_or_s _ _ zenon_Hec); [ zenon_intro zenon_H68 | zenon_intro zenon_Hed ]. % 15.41/15.58 apply (zenon_or_s _ _ zenon_H58); [ zenon_intro zenon_H5b | zenon_intro zenon_H5a ]. % 15.41/15.58 exact (zenon_H59 zenon_H5b). % 15.41/15.58 apply (zenon_or_s _ _ zenon_H5a); [ zenon_intro zenon_H4a | zenon_intro zenon_H5c ]. % 15.41/15.58 apply (zenon_or_s _ _ zenon_Hbe); [ zenon_intro zenon_H5b | zenon_intro zenon_Hbf ]. % 15.41/15.58 exact (zenon_H59 zenon_H5b). % 15.41/15.58 apply (zenon_or_s _ _ zenon_Hbf); [ zenon_intro zenon_H69 | zenon_intro zenon_Hc0 ]. % 15.41/15.58 apply (zenon_L17_); trivial. % 15.41/15.58 apply (zenon_or_s _ _ zenon_Hc0); [ zenon_intro zenon_Haf | zenon_intro zenon_Hba ]. % 15.41/15.58 apply (zenon_or_s _ _ zenon_H163); [ zenon_intro zenon_Had | zenon_intro zenon_H164 ]. % 15.41/15.58 apply (zenon_L559_); trivial. % 15.41/15.58 apply (zenon_or_s _ _ zenon_H164); [ zenon_intro zenon_H149 | zenon_intro zenon_H165 ]. % 15.41/15.58 exact (zenon_H145 zenon_H149). % 15.41/15.58 apply (zenon_or_s _ _ zenon_H165); [ zenon_intro zenon_H15d | zenon_intro zenon_Hcc ]. % 15.41/15.58 apply (zenon_or_s _ _ zenon_H144); [ zenon_intro zenon_H49 | zenon_intro zenon_H147 ]. % 15.41/15.58 apply (zenon_L9_); trivial. % 15.41/15.58 apply (zenon_or_s _ _ zenon_H147); [ zenon_intro zenon_H149 | zenon_intro zenon_H148 ]. % 15.41/15.58 exact (zenon_H145 zenon_H149). % 15.41/15.58 apply (zenon_or_s _ _ zenon_H148); [ zenon_intro zenon_H14a | zenon_intro zenon_H142 ]. % 15.41/15.58 apply (zenon_L351_); trivial. % 15.41/15.58 apply (zenon_or_s _ _ zenon_H90); [ zenon_intro zenon_H69 | zenon_intro zenon_H94 ]. % 15.41/15.58 apply (zenon_L17_); trivial. % 15.41/15.58 apply (zenon_or_s _ _ zenon_H94); [ zenon_intro zenon_H96 | zenon_intro zenon_H95 ]. % 15.41/15.58 exact (zenon_H182 zenon_H96). % 15.41/15.58 apply (zenon_or_s _ _ zenon_H95); [ zenon_intro zenon_H88 | zenon_intro zenon_H8a ]. % 15.41/15.58 apply (zenon_L152_); trivial. % 15.41/15.58 apply (zenon_L905_); trivial. % 15.41/15.58 apply (zenon_L600_); trivial. % 15.41/15.58 apply (zenon_L79_); trivial. % 15.41/15.58 apply (zenon_or_s _ _ zenon_H5c); [ zenon_intro zenon_H50 | zenon_intro zenon_H53 ]. % 15.41/15.58 apply (zenon_L533_); trivial. % 15.41/15.58 apply (zenon_L294_); trivial. % 15.41/15.58 apply (zenon_or_s _ _ zenon_Hed); [ zenon_intro zenon_Hdd | zenon_intro zenon_He9 ]. % 15.41/15.58 apply (zenon_L909_); trivial. % 15.41/15.58 apply (zenon_L122_); trivial. % 15.41/15.58 apply (zenon_L820_); trivial. % 15.41/15.58 apply (zenon_L325_); trivial. % 15.41/15.58 apply (zenon_or_s _ _ zenon_H10e); [ zenon_intro zenon_H3d | zenon_intro zenon_H106 ]. % 15.41/15.58 apply (zenon_or_s _ _ zenon_H44); [ zenon_intro zenon_H47 | zenon_intro zenon_H46 ]. % 15.41/15.58 exact (zenon_H45 zenon_H47). % 15.41/15.58 apply (zenon_or_s _ _ zenon_H46); [ zenon_intro zenon_H22 | zenon_intro zenon_H48 ]. % 15.41/15.58 apply (zenon_L3_); trivial. % 15.41/15.58 apply (zenon_or_s _ _ zenon_H48); [ zenon_intro zenon_H29 | zenon_intro zenon_H37 ]. % 15.41/15.58 apply (zenon_L5_); trivial. % 15.41/15.58 apply (zenon_or_s _ _ zenon_Hf1); [ zenon_intro zenon_H47 | zenon_intro zenon_Hf4 ]. % 15.41/15.58 exact (zenon_H45 zenon_H47). % 15.41/15.58 apply (zenon_or_s _ _ zenon_Hf4); [ zenon_intro zenon_Hd8 | zenon_intro zenon_Hf5 ]. % 15.41/15.58 apply (zenon_L61_); trivial. % 15.41/15.58 apply (zenon_or_s _ _ zenon_Hf5); [ zenon_intro zenon_Hae | zenon_intro zenon_Hee ]. % 15.41/15.58 apply (zenon_or_s _ _ zenon_H8e); [ zenon_intro zenon_H92 | zenon_intro zenon_H91 ]. % 15.41/15.58 exact (zenon_H8f zenon_H92). % 15.41/15.58 apply (zenon_or_s _ _ zenon_H91); [ zenon_intro zenon_H5d | zenon_intro zenon_H93 ]. % 15.41/15.58 apply (zenon_L251_); trivial. % 15.41/15.58 apply (zenon_or_s _ _ zenon_H93); [ zenon_intro zenon_H63 | zenon_intro zenon_H81 ]. % 15.41/15.58 apply (zenon_or_s _ _ zenon_Heb); [ zenon_intro zenon_H92 | zenon_intro zenon_Hec ]. % 15.41/15.58 exact (zenon_H8f zenon_H92). % 15.41/15.58 apply (zenon_or_s _ _ zenon_Hec); [ zenon_intro zenon_H68 | zenon_intro zenon_Hed ]. % 15.41/15.58 apply (zenon_or_s _ _ zenon_H163); [ zenon_intro zenon_Had | zenon_intro zenon_H164 ]. % 15.41/15.58 apply (zenon_L559_); trivial. % 15.41/15.58 apply (zenon_or_s _ _ zenon_H164); [ zenon_intro zenon_H149 | zenon_intro zenon_H165 ]. % 15.41/15.58 exact (zenon_H145 zenon_H149). % 15.41/15.58 apply (zenon_or_s _ _ zenon_H165); [ zenon_intro zenon_H15d | zenon_intro zenon_Hcc ]. % 15.41/15.58 apply (zenon_or_s _ _ zenon_H90); [ zenon_intro zenon_H69 | zenon_intro zenon_H94 ]. % 15.41/15.58 apply (zenon_L17_); trivial. % 15.41/15.58 apply (zenon_or_s _ _ zenon_H94); [ zenon_intro zenon_H96 | zenon_intro zenon_H95 ]. % 15.41/15.58 exact (zenon_H182 zenon_H96). % 15.41/15.58 apply (zenon_or_s _ _ zenon_H95); [ zenon_intro zenon_H88 | zenon_intro zenon_H8a ]. % 15.41/15.58 apply (zenon_L152_); trivial. % 15.41/15.58 apply (zenon_or_s _ _ zenon_He6); [ zenon_intro zenon_Haf | zenon_intro zenon_He7 ]. % 15.41/15.58 apply (zenon_L39_); trivial. % 15.41/15.58 apply (zenon_or_s _ _ zenon_He7); [ zenon_intro zenon_Hdf | zenon_intro zenon_He8 ]. % 15.41/15.58 apply (zenon_L911_); trivial. % 15.41/15.58 apply (zenon_or_s _ _ zenon_He8); [ zenon_intro zenon_H34 | zenon_intro zenon_He2 ]. % 15.41/15.58 exact (zenon_H30 zenon_H34). % 15.41/15.58 apply (zenon_L912_); trivial. % 15.41/15.58 apply (zenon_L625_); trivial. % 15.41/15.58 apply (zenon_or_s _ _ zenon_Hed); [ zenon_intro zenon_Hdd | zenon_intro zenon_He9 ]. % 15.41/15.58 apply (zenon_L812_); trivial. % 15.41/15.58 apply (zenon_L220_); trivial. % 15.41/15.58 apply (zenon_L33_); trivial. % 15.41/15.58 apply (zenon_L79_); trivial. % 15.41/15.58 apply (zenon_L81_); trivial. % 15.41/15.58 apply (zenon_L256_); trivial. % 15.41/15.58 apply (zenon_L134_); trivial. % 15.41/15.58 apply (zenon_L909_); trivial. % 15.41/15.58 apply (zenon_L90_); trivial. % 15.41/15.58 apply (zenon_L86_); trivial. % 15.41/15.58 (* end of lemma zenon_L913_ *) % 15.41/15.58 assert (zenon_L914_ : ((~((op (e2) (e2)) = (e2)))\/((op (e2) (e2)) = (e2))) -> (~((op (e2) (op (e2) (e2))) = (op (e2) (e2)))) -> (~((op (e0) (e0)) = (e3))) -> (~((e0) = (e3))) -> ((op (e0) (e1)) = (e0)) -> (((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)) = (e1))) -> (~((op (e2) (e2)) = (e0))) -> (~((op (e0) (e3)) = (op (e3) (e3)))) -> ((op (e3) (e3)) = (e3)) -> (((op (e0) (e0)) = (e3))\/(((op (e0) (e1)) = (e3))\/(((op (e0) (e2)) = (e3))\/((op (e0) (e3)) = (e3))))) -> False). % 15.41/15.58 do 0 intro. intros zenon_Haa zenon_H294 zenon_H59 zenon_H4b zenon_H49 zenon_H2d zenon_H28 zenon_H52 zenon_H2e zenon_H36 zenon_H42 zenon_H58. % 15.41/15.58 apply (zenon_or_s _ _ zenon_Haa); [ zenon_intro zenon_H2f | zenon_intro zenon_H35 ]. % 15.41/15.58 apply (zenon_L13_); trivial. % 15.41/15.58 apply (zenon_L794_); trivial. % 15.41/15.58 (* end of lemma zenon_L914_ *) % 15.41/15.58 assert (zenon_L915_ : ((~((op (e2) (e2)) = (e1)))\/((op (e2) (e1)) = (e2))) -> (~((op (e1) (e1)) = (e3))) -> (~((e2) = (e3))) -> (~((op (e3) (e1)) = (op (e3) (e3)))) -> (((op (e0) (e1)) = (e3))\/(((op (e1) (e1)) = (e3))\/(((op (e2) (e1)) = (e3))\/((op (e3) (e1)) = (e3))))) -> (((op (e0) (e0)) = (e3))\/(((op (e0) (e1)) = (e3))\/(((op (e0) (e2)) = (e3))\/((op (e0) (e3)) = (e3))))) -> ((op (e3) (e3)) = (e3)) -> (~((op (e0) (e3)) = (op (e3) (e3)))) -> (~((op (e2) (e2)) = (e0))) -> (~((op (e0) (e2)) = (op (e2) (e2)))) -> (((op (e2) (e2)) = (e0))\/(((op (e2) (e2)) = (e1))\/(((op (e2) (e2)) = (e2))\/((op (e2) (e2)) = (e3))))) -> ((op (e0) (e1)) = (e0)) -> (~((e0) = (e3))) -> (~((op (e0) (e0)) = (e3))) -> (~((op (e2) (op (e2) (e2))) = (op (e2) (e2)))) -> ((~((op (e2) (e2)) = (e2)))\/((op (e2) (e2)) = (e2))) -> False). % 15.41/15.58 do 0 intro. intros zenon_H1e3 zenon_H182 zenon_H6a zenon_H12d zenon_H199 zenon_H58 zenon_H42 zenon_H36 zenon_H2e zenon_H28 zenon_H2d zenon_H49 zenon_H4b zenon_H59 zenon_H294 zenon_Haa. % 15.41/15.58 apply (zenon_or_s _ _ zenon_H1e3); [ zenon_intro zenon_H52 | zenon_intro zenon_H156 ]. % 15.41/15.58 apply (zenon_L914_); trivial. % 15.41/15.58 apply (zenon_L278_); trivial. % 15.41/15.58 (* end of lemma zenon_L915_ *) % 15.41/15.58 assert (zenon_L916_ : (((op (e0) (e0)) = (e1))\/(((op (e0) (e1)) = (e1))\/(((op (e0) (e2)) = (e1))\/((op (e0) (e3)) = (e1))))) -> (~((op (e0) (e0)) = (e1))) -> (~((op (e0) (e1)) = (op (e1) (e1)))) -> (~((op (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 (e0) (e0)) = (e3))\/(((op (e0) (e1)) = (e3))\/(((op (e0) (e2)) = (e3))\/((op (e0) (e3)) = (e3))))) -> (~((op (e0) (e0)) = (e3))) -> (~((op (e0) (e3)) = (op (e2) (e3)))) -> (~((op (e2) (e2)) = (e1))) -> (~((op (e1) (e1)) = (op (e2) (e1)))) -> ((op (e1) (e1)) = (e1)) -> (((op (e2) (e0)) = (e3))\/(((op (e2) (e1)) = (e3))\/(((op (e2) (e2)) = (e3))\/((op (e2) (e3)) = (e3))))) -> (~((e1) = (e3))) -> (~((op (e0) (e1)) = (op (e2) (e1)))) -> (~((op (e2) (e2)) = (e3))) -> (~((op (e3) (op (e2) (e3))) = (op (e2) (e3)))) -> (((op (e2) (e0)) = (e1))\/(((op (e2) (e1)) = (e1))\/(((op (e2) (e2)) = (e1))\/((op (e2) (e3)) = (e1))))) -> (~((e0) = (e3))) -> ((op (e0) (e2)) = (e0)) -> ((op (e3) (e3)) = (e3)) -> (~((op (e0) (e3)) = (op (e3) (e3)))) -> False). % 15.41/15.58 do 0 intro. intros zenon_H44 zenon_H45 zenon_H23 zenon_H2f zenon_H28 zenon_H2e zenon_H2d zenon_H58 zenon_H59 zenon_Hb4 zenon_H52 zenon_Hb1 zenon_H21 zenon_He6 zenon_Ha3 zenon_Hde zenon_H30 zenon_H28a zenon_Hb7 zenon_H4b zenon_Hab zenon_H42 zenon_H36. % 15.41/15.58 apply (zenon_or_s _ _ zenon_H44); [ zenon_intro zenon_H47 | zenon_intro zenon_H46 ]. % 15.41/15.58 exact (zenon_H45 zenon_H47). % 15.41/15.58 apply (zenon_or_s _ _ zenon_H46); [ zenon_intro zenon_H22 | zenon_intro zenon_H48 ]. % 15.41/15.58 apply (zenon_L3_); trivial. % 15.41/15.58 apply (zenon_or_s _ _ zenon_H48); [ zenon_intro zenon_H29 | zenon_intro zenon_H37 ]. % 15.41/15.58 apply (zenon_L5_); trivial. % 15.41/15.58 apply (zenon_or_s _ _ zenon_H58); [ zenon_intro zenon_H5b | zenon_intro zenon_H5a ]. % 15.41/15.58 exact (zenon_H59 zenon_H5b). % 15.41/15.58 apply (zenon_or_s _ _ zenon_H5a); [ zenon_intro zenon_H4a | zenon_intro zenon_H5c ]. % 15.41/15.58 apply (zenon_or_s _ _ zenon_Hb7); [ zenon_intro zenon_Hae | zenon_intro zenon_Hb8 ]. % 15.41/15.58 apply (zenon_L787_); trivial. % 15.41/15.58 apply (zenon_or_s _ _ zenon_Hb8); [ zenon_intro zenon_Hb2 | zenon_intro zenon_Hb9 ]. % 15.41/15.58 apply (zenon_L40_); trivial. % 15.41/15.58 apply (zenon_or_s _ _ zenon_Hb9); [ zenon_intro zenon_H2a | zenon_intro zenon_Hb5 ]. % 15.41/15.58 exact (zenon_H52 zenon_H2a). % 15.41/15.58 apply (zenon_L41_); trivial. % 15.41/15.58 apply (zenon_or_s _ _ zenon_H5c); [ zenon_intro zenon_H50 | zenon_intro zenon_H53 ]. % 15.41/15.58 apply (zenon_L48_); trivial. % 15.41/15.58 apply (zenon_L12_); trivial. % 15.41/15.58 (* end of lemma zenon_L916_ *) % 15.41/15.58 assert (zenon_L917_ : ((~((op (e2) (e2)) = (e2)))\/((op (e2) (e2)) = (e2))) -> (~((op (e2) (op (e2) (e2))) = (op (e2) (e2)))) -> (((op (e0) (e0)) = (e1))\/(((op (e0) (e1)) = (e1))\/(((op (e0) (e2)) = (e1))\/((op (e0) (e3)) = (e1))))) -> ((op (e0) (e3)) = (e0)) -> (~((e0) = (e1))) -> (~((op (e2) (e2)) = (e0))) -> (~((op (e0) (e2)) = (op (e2) (e2)))) -> (((op (e2) (e2)) = (e0))\/(((op (e2) (e2)) = (e1))\/(((op (e2) (e2)) = (e2))\/((op (e2) (e2)) = (e3))))) -> ((op (e1) (e1)) = (e1)) -> (~((op (e0) (e1)) = (op (e1) (e1)))) -> (~((op (e0) (e0)) = (e1))) -> ((~((op (e3) (e3)) = (e1)))\/((op (e3) (e1)) = (e3))) -> ((op (e3) (e3)) = (e3)) -> (~((op (e3) (e1)) = (op (e3) (e3)))) -> (((op (e2) (e0)) = (e1))\/(((op (e2) (e1)) = (e1))\/(((op (e2) (e2)) = (e1))\/((op (e2) (e3)) = (e1))))) -> (~((e1) = (e2))) -> (~((op (e2) (e2)) = (e1))) -> (~((op (e1) (e1)) = (op (e2) (e1)))) -> (~((op (e0) (e2)) = (op (e0) (e3)))) -> (~((op (e1) (e1)) = (op (e1) (e3)))) -> (~((op (e2) (e0)) = (op (e2) (e3)))) -> (((op (e0) (e3)) = (e1))\/(((op (e1) (e3)) = (e1))\/(((op (e2) (e3)) = (e1))\/((op (e3) (e3)) = (e1))))) -> ((~((op (e2) (e2)) = (e3)))\/((op (e2) (e3)) = (e2))) -> False). % 15.41/15.58 do 0 intro. intros zenon_Haa zenon_H294 zenon_H44 zenon_Hca zenon_H9e zenon_H2e zenon_H28 zenon_H2d zenon_H21 zenon_H23 zenon_H45 zenon_H10c zenon_H42 zenon_H12d zenon_Hb7 zenon_Ha7 zenon_H52 zenon_Hb1 zenon_Hc9 zenon_H11e zenon_Hce zenon_H121 zenon_H1c3. % 15.41/15.58 apply (zenon_or_s _ _ zenon_Haa); [ zenon_intro zenon_H2f | zenon_intro zenon_H35 ]. % 15.41/15.58 apply (zenon_or_s _ _ zenon_H1c3); [ zenon_intro zenon_H30 | zenon_intro zenon_H124 ]. % 15.41/15.58 apply (zenon_L74_); trivial. % 15.41/15.58 apply (zenon_or_s _ _ zenon_H10c); [ zenon_intro zenon_H104 | zenon_intro zenon_H10a ]. % 15.41/15.58 apply (zenon_L100_); trivial. % 15.41/15.58 apply (zenon_L102_); trivial. % 15.41/15.58 apply (zenon_L794_); trivial. % 15.41/15.58 (* end of lemma zenon_L917_ *) % 15.41/15.58 assert (zenon_L918_ : (((op (e0) (e0)) = (e0))\/(((op (e0) (e1)) = (e0))\/(((op (e0) (e2)) = (e0))\/((op (e0) (e3)) = (e0))))) -> (~((op (e0) (e0)) = (e0))) -> (((op (e0) (e1)) = (e3))\/(((op (e1) (e1)) = (e3))\/(((op (e2) (e1)) = (e3))\/((op (e3) (e1)) = (e3))))) -> (~((e2) = (e3))) -> (~((op (e1) (e1)) = (e3))) -> ((~((op (e2) (e2)) = (e1)))\/((op (e2) (e1)) = (e2))) -> (~((op (e0) (e3)) = (op (e3) (e3)))) -> (~((e0) = (e3))) -> (~((op (e3) (op (e2) (e3))) = (op (e2) (e3)))) -> (~((op (e2) (e2)) = (e3))) -> (~((op (e0) (e1)) = (op (e2) (e1)))) -> (~((e1) = (e3))) -> (((op (e2) (e0)) = (e3))\/(((op (e2) (e1)) = (e3))\/(((op (e2) (e2)) = (e3))\/((op (e2) (e3)) = (e3))))) -> (~((op (e0) (e3)) = (op (e2) (e3)))) -> (~((op (e0) (e0)) = (e3))) -> (((op (e0) (e0)) = (e3))\/(((op (e0) (e1)) = (e3))\/(((op (e0) (e2)) = (e3))\/((op (e0) (e3)) = (e3))))) -> (~((op (e2) (e2)) = (e2))) -> ((~((op (e2) (e2)) = (e2)))\/((op (e2) (e2)) = (e2))) -> (~((op (e2) (op (e2) (e2))) = (op (e2) (e2)))) -> (((op (e0) (e0)) = (e1))\/(((op (e0) (e1)) = (e1))\/(((op (e0) (e2)) = (e1))\/((op (e0) (e3)) = (e1))))) -> (~((e0) = (e1))) -> (~((op (e2) (e2)) = (e0))) -> (~((op (e0) (e2)) = (op (e2) (e2)))) -> (((op (e2) (e2)) = (e0))\/(((op (e2) (e2)) = (e1))\/(((op (e2) (e2)) = (e2))\/((op (e2) (e2)) = (e3))))) -> ((op (e1) (e1)) = (e1)) -> (~((op (e0) (e1)) = (op (e1) (e1)))) -> (~((op (e0) (e0)) = (e1))) -> ((~((op (e3) (e3)) = (e1)))\/((op (e3) (e1)) = (e3))) -> ((op (e3) (e3)) = (e3)) -> (~((op (e3) (e1)) = (op (e3) (e3)))) -> (((op (e2) (e0)) = (e1))\/(((op (e2) (e1)) = (e1))\/(((op (e2) (e2)) = (e1))\/((op (e2) (e3)) = (e1))))) -> (~((e1) = (e2))) -> (~((op (e2) (e2)) = (e1))) -> (~((op (e1) (e1)) = (op (e2) (e1)))) -> (~((op (e0) (e2)) = (op (e0) (e3)))) -> (~((op (e1) (e1)) = (op (e1) (e3)))) -> (~((op (e2) (e0)) = (op (e2) (e3)))) -> (((op (e0) (e3)) = (e1))\/(((op (e1) (e3)) = (e1))\/(((op (e2) (e3)) = (e1))\/((op (e3) (e3)) = (e1))))) -> ((~((op (e2) (e2)) = (e3)))\/((op (e2) (e3)) = (e2))) -> False). % 15.41/15.58 do 0 intro. intros zenon_H110 zenon_H20 zenon_H199 zenon_H6a zenon_H182 zenon_H1e3 zenon_H36 zenon_H4b zenon_H28a zenon_H30 zenon_Hde zenon_Ha3 zenon_He6 zenon_Hb4 zenon_H59 zenon_H58 zenon_H2f zenon_Haa zenon_H294 zenon_H44 zenon_H9e zenon_H2e zenon_H28 zenon_H2d zenon_H21 zenon_H23 zenon_H45 zenon_H10c zenon_H42 zenon_H12d zenon_Hb7 zenon_Ha7 zenon_H52 zenon_Hb1 zenon_Hc9 zenon_H11e zenon_Hce zenon_H121 zenon_H1c3. % 15.41/15.58 apply (zenon_or_s _ _ zenon_H110); [ zenon_intro zenon_H1f | zenon_intro zenon_H111 ]. % 15.41/15.58 exact (zenon_H20 zenon_H1f). % 15.41/15.58 apply (zenon_or_s _ _ zenon_H111); [ zenon_intro zenon_H49 | zenon_intro zenon_H112 ]. % 15.41/15.58 apply (zenon_L915_); trivial. % 15.41/15.58 apply (zenon_or_s _ _ zenon_H112); [ zenon_intro zenon_Hab | zenon_intro zenon_Hca ]. % 15.41/15.58 apply (zenon_L916_); trivial. % 15.41/15.58 apply (zenon_L917_); trivial. % 15.41/15.58 (* end of lemma zenon_L918_ *) % 15.41/15.58 assert (zenon_L919_ : ((~((op (e3) (e3)) = (e3)))\/((op (e3) (e3)) = (e3))) -> (~((op (e0) (e0)) = (e0))) -> ((~((op (e2) (e2)) = (e1)))\/((op (e2) (e1)) = (e2))) -> (~((op (e1) (e1)) = (e3))) -> (~((e2) = (e3))) -> (~((op (e3) (e1)) = (op (e3) (e3)))) -> (((op (e0) (e1)) = (e3))\/(((op (e1) (e1)) = (e3))\/(((op (e2) (e1)) = (e3))\/((op (e3) (e1)) = (e3))))) -> (((op (e0) (e0)) = (e3))\/(((op (e0) (e1)) = (e3))\/(((op (e0) (e2)) = (e3))\/((op (e0) (e3)) = (e3))))) -> (~((e0) = (e3))) -> (~((op (e0) (e0)) = (e3))) -> (~((op (e2) (op (e2) (e2))) = (op (e2) (e2)))) -> ((~((op (e2) (e2)) = (e2)))\/((op (e2) (e2)) = (e2))) -> (((op (e2) (e0)) = (e1))\/(((op (e2) (e1)) = (e1))\/(((op (e2) (e2)) = (e1))\/((op (e2) (e3)) = (e1))))) -> (~((op (e0) (e3)) = (op (e2) (e3)))) -> (~((op (e2) (e2)) = (e1))) -> (~((op (e1) (e1)) = (op (e2) (e1)))) -> (~((e1) = (e3))) -> (~((op (e0) (e1)) = (op (e2) (e1)))) -> (~((op (e3) (op (e2) (e3))) = (op (e2) (e3)))) -> (((op (e2) (e0)) = (e3))\/(((op (e2) (e1)) = (e3))\/(((op (e2) (e2)) = (e3))\/((op (e2) (e3)) = (e3))))) -> (~((e0) = (e1))) -> ((~((op (e3) (e3)) = (e1)))\/((op (e3) (e1)) = (e3))) -> (~((e1) = (e2))) -> (~((op (e0) (e2)) = (op (e0) (e3)))) -> (~((op (e1) (e1)) = (op (e1) (e3)))) -> (~((op (e2) (e0)) = (op (e2) (e3)))) -> (((op (e0) (e3)) = (e1))\/(((op (e1) (e3)) = (e1))\/(((op (e2) (e3)) = (e1))\/((op (e3) (e3)) = (e1))))) -> ((~((op (e2) (e2)) = (e3)))\/((op (e2) (e3)) = (e2))) -> (((op (e0) (e0)) = (e0))\/(((op (e0) (e1)) = (e0))\/(((op (e0) (e2)) = (e0))\/((op (e0) (e3)) = (e0))))) -> (~((op (e0) (e0)) = (e1))) -> (~((op (e0) (e1)) = (op (e1) (e1)))) -> ((op (e1) (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 (e0) (e2)) = (op (e2) (e2)))) -> (~((op (e2) (e2)) = (e0))) -> (((op (e3) (e3)) = (e0))\/(((op (e3) (e3)) = (e1))\/(((op (e3) (e3)) = (e2))\/((op (e3) (e3)) = (e3))))) -> (~((op (e3) (e3)) = (e2))) -> (~((op (e0) (e3)) = (op (e3) (e3)))) -> (~((op (e3) (e3)) = (e0))) -> (((op (e0) (e0)) = (e1))\/(((op (e0) (e1)) = (e1))\/(((op (e0) (e2)) = (e1))\/((op (e0) (e3)) = (e1))))) -> False). % 15.41/15.58 do 0 intro. intros zenon_H10d zenon_H20 zenon_H1e3 zenon_H182 zenon_H6a zenon_H12d zenon_H199 zenon_H58 zenon_H4b zenon_H59 zenon_H294 zenon_Haa zenon_Hb7 zenon_Hb4 zenon_H52 zenon_Hb1 zenon_Ha3 zenon_Hde zenon_H28a zenon_He6 zenon_H9e zenon_H10c zenon_Ha7 zenon_Hc9 zenon_H11e zenon_Hce zenon_H121 zenon_H1c3 zenon_H110 zenon_H45 zenon_H23 zenon_H21 zenon_H2d zenon_H30 zenon_H2f zenon_H28 zenon_H2e zenon_H3b zenon_H3d zenon_H36 zenon_H3c zenon_H44. % 15.41/15.58 apply (zenon_or_s _ _ zenon_H10d); [ zenon_intro zenon_H3e | zenon_intro zenon_H42 ]. % 15.41/15.58 apply (zenon_L8_); trivial. % 15.41/15.58 apply (zenon_L918_); trivial. % 15.41/15.58 (* end of lemma zenon_L919_ *) % 15.41/15.58 assert (zenon_L920_ : (((op (e0) (e0)) = (e3))\/(((op (e0) (e1)) = (e3))\/(((op (e0) (e2)) = (e3))\/((op (e0) (e3)) = (e3))))) -> (~((op (e0) (e0)) = (e3))) -> (~((op (e3) (op (e2) (e3))) = (op (e2) (e3)))) -> (~((op (e2) (e2)) = (e3))) -> (~((op (e0) (e1)) = (op (e2) (e1)))) -> ((op (e2) (e0)) = (e2)) -> (~((e2) = (e3))) -> (((op (e2) (e0)) = (e3))\/(((op (e2) (e1)) = (e3))\/(((op (e2) (e2)) = (e3))\/((op (e2) (e3)) = (e3))))) -> (~((e0) = (e3))) -> ((op (e0) (e2)) = (e0)) -> ((op (e3) (e3)) = (e3)) -> (~((op (e0) (e3)) = (op (e3) (e3)))) -> False). % 15.41/15.58 do 0 intro. intros zenon_H58 zenon_H59 zenon_H28a zenon_H30 zenon_Hde zenon_Hdd zenon_H6a zenon_He6 zenon_H4b zenon_Hab zenon_H42 zenon_H36. % 15.41/15.58 apply (zenon_or_s _ _ zenon_H58); [ zenon_intro zenon_H5b | zenon_intro zenon_H5a ]. % 15.41/15.58 exact (zenon_H59 zenon_H5b). % 15.41/15.58 apply (zenon_or_s _ _ zenon_H5a); [ zenon_intro zenon_H4a | zenon_intro zenon_H5c ]. % 15.41/15.58 apply (zenon_L777_); trivial. % 15.41/15.58 apply (zenon_or_s _ _ zenon_H5c); [ zenon_intro zenon_H50 | zenon_intro zenon_H53 ]. % 15.41/15.58 apply (zenon_L48_); trivial. % 15.41/15.58 apply (zenon_L12_); trivial. % 15.41/15.58 (* end of lemma zenon_L920_ *) % 15.41/15.58 assert (zenon_L921_ : (((op (e2) (e0)) = (e2))\/(((op (e2) (e1)) = (e2))\/(((op (e2) (e2)) = (e2))\/((op (e2) (e3)) = (e2))))) -> (~((op (e0) (e3)) = (op (e3) (e3)))) -> ((op (e3) (e3)) = (e3)) -> (~((e0) = (e3))) -> (((op (e2) (e0)) = (e3))\/(((op (e2) (e1)) = (e3))\/(((op (e2) (e2)) = (e3))\/((op (e2) (e3)) = (e3))))) -> (~((e2) = (e3))) -> (~((op (e2) (e2)) = (e3))) -> (~((op (e3) (op (e2) (e3))) = (op (e2) (e3)))) -> (~((op (e0) (e0)) = (e3))) -> (((op (e0) (e0)) = (e3))\/(((op (e0) (e1)) = (e3))\/(((op (e0) (e2)) = (e3))\/((op (e0) (e3)) = (e3))))) -> (~((op (e0) (e1)) = (op (e2) (e1)))) -> ((op (e0) (e1)) = (e2)) -> (~((op (e2) (e2)) = (e2))) -> (((op (e0) (e3)) = (e0))\/(((op (e1) (e3)) = (e0))\/(((op (e2) (e3)) = (e0))\/((op (e3) (e3)) = (e0))))) -> ((op (e0) (e2)) = (e0)) -> (~((op (e0) (e2)) = (op (e0) (e3)))) -> ((op (e1) (e3)) = (e1)) -> (~((e0) = (e1))) -> (~((e0) = (e2))) -> (~((op (e3) (e3)) = (e0))) -> False). % 15.41/15.58 do 0 intro. intros zenon_H237 zenon_H36 zenon_H42 zenon_H4b zenon_He6 zenon_H6a zenon_H30 zenon_H28a zenon_H59 zenon_H58 zenon_Hde zenon_H5d zenon_H2f zenon_Hd3 zenon_Hab zenon_Hc9 zenon_H11f zenon_H9e zenon_H5e zenon_H3c. % 15.41/15.58 apply (zenon_or_s _ _ zenon_H237); [ zenon_intro zenon_Hdd | zenon_intro zenon_H238 ]. % 15.41/15.58 apply (zenon_L920_); trivial. % 15.41/15.58 apply (zenon_or_s _ _ zenon_H238); [ zenon_intro zenon_H156 | zenon_intro zenon_H239 ]. % 15.41/15.58 apply (zenon_L251_); trivial. % 15.41/15.58 apply (zenon_or_s _ _ zenon_H239); [ zenon_intro zenon_H35 | zenon_intro zenon_H124 ]. % 15.41/15.58 exact (zenon_H2f zenon_H35). % 15.41/15.58 apply (zenon_L711_); trivial. % 15.41/15.58 (* end of lemma zenon_L921_ *) % 15.41/15.58 assert (zenon_L922_ : (((op (e2) (e0)) = (e1))\/(((op (e2) (e1)) = (e1))\/(((op (e2) (e2)) = (e1))\/((op (e2) (e3)) = (e1))))) -> ((op (e3) (e3)) = (e3)) -> (~((op (e3) (op (e2) (e3))) = (op (e2) (e3)))) -> (~((op (e2) (e2)) = (e3))) -> (~((op (e0) (e1)) = (op (e2) (e1)))) -> (~((e1) = (e3))) -> (((op (e2) (e0)) = (e3))\/(((op (e2) (e1)) = (e3))\/(((op (e2) (e2)) = (e3))\/((op (e2) (e3)) = (e3))))) -> ((op (e2) (e1)) = (e2)) -> (~((e1) = (e2))) -> ((op (e0) (e0)) = (e2)) -> ((op (e0) (e1)) = (e3)) -> (~((op (e1) (e3)) = (op (e2) (e3)))) -> ((op (e1) (e3)) = (e1)) -> False). % 15.41/15.58 do 0 intro. intros zenon_Hb7 zenon_H42 zenon_H28a zenon_H30 zenon_Hde zenon_Ha3 zenon_He6 zenon_H156 zenon_Ha7 zenon_H92 zenon_H4a zenon_H244 zenon_H11f. % 15.41/15.58 apply (zenon_or_s _ _ zenon_Hb7); [ zenon_intro zenon_Hae | zenon_intro zenon_Hb8 ]. % 15.41/15.58 apply (zenon_L787_); trivial. % 15.41/15.58 apply (zenon_or_s _ _ zenon_Hb8); [ zenon_intro zenon_Hb2 | zenon_intro zenon_Hb9 ]. % 15.41/15.58 apply (zenon_L372_); trivial. % 15.41/15.59 apply (zenon_or_s _ _ zenon_Hb9); [ zenon_intro zenon_H2a | zenon_intro zenon_Hb5 ]. % 15.41/15.59 apply (zenon_L46_); trivial. % 15.41/15.59 apply (zenon_L529_); trivial. % 15.41/15.59 (* end of lemma zenon_L922_ *) % 15.41/15.59 assert (zenon_L923_ : (((op (e0) (e0)) = (e3))\/(((op (e0) (e1)) = (e3))\/(((op (e0) (e2)) = (e3))\/((op (e0) (e3)) = (e3))))) -> (~((op (e0) (e0)) = (e3))) -> ((op (e1) (e3)) = (e1)) -> (~((op (e1) (e3)) = (op (e2) (e3)))) -> ((op (e0) (e0)) = (e2)) -> (~((e1) = (e2))) -> ((op (e2) (e1)) = (e2)) -> (((op (e2) (e0)) = (e3))\/(((op (e2) (e1)) = (e3))\/(((op (e2) (e2)) = (e3))\/((op (e2) (e3)) = (e3))))) -> (~((e1) = (e3))) -> (~((op (e0) (e1)) = (op (e2) (e1)))) -> (~((op (e2) (e2)) = (e3))) -> (~((op (e3) (op (e2) (e3))) = (op (e2) (e3)))) -> (((op (e2) (e0)) = (e1))\/(((op (e2) (e1)) = (e1))\/(((op (e2) (e2)) = (e1))\/((op (e2) (e3)) = (e1))))) -> (~((e0) = (e3))) -> ((op (e0) (e2)) = (e0)) -> ((op (e3) (e3)) = (e3)) -> (~((op (e0) (e3)) = (op (e3) (e3)))) -> False). % 15.41/15.59 do 0 intro. intros zenon_H58 zenon_H59 zenon_H11f zenon_H244 zenon_H92 zenon_Ha7 zenon_H156 zenon_He6 zenon_Ha3 zenon_Hde zenon_H30 zenon_H28a zenon_Hb7 zenon_H4b zenon_Hab zenon_H42 zenon_H36. % 15.41/15.59 apply (zenon_or_s _ _ zenon_H58); [ zenon_intro zenon_H5b | zenon_intro zenon_H5a ]. % 15.41/15.59 exact (zenon_H59 zenon_H5b). % 15.41/15.59 apply (zenon_or_s _ _ zenon_H5a); [ zenon_intro zenon_H4a | zenon_intro zenon_H5c ]. % 15.41/15.59 apply (zenon_L922_); trivial. % 15.41/15.59 apply (zenon_or_s _ _ zenon_H5c); [ zenon_intro zenon_H50 | zenon_intro zenon_H53 ]. % 15.41/15.59 apply (zenon_L48_); trivial. % 15.41/15.59 apply (zenon_L12_); trivial. % 15.41/15.59 (* end of lemma zenon_L923_ *) % 15.41/15.59 assert (zenon_L924_ : (((op (e2) (e0)) = (e3))\/(((op (e2) (e1)) = (e3))\/(((op (e2) (e2)) = (e3))\/((op (e2) (e3)) = (e3))))) -> (~((e0) = (e3))) -> ((op (e2) (e0)) = (e0)) -> (~((e2) = (e3))) -> ((op (e2) (e1)) = (e2)) -> (~((op (e2) (e2)) = (e3))) -> (~((op (e3) (op (e2) (e3))) = (op (e2) (e3)))) -> ((op (e3) (e3)) = (e3)) -> False). % 15.41/15.59 do 0 intro. intros zenon_He6 zenon_H4b zenon_Hcf zenon_H6a zenon_H156 zenon_H30 zenon_H28a zenon_H42. % 15.41/15.59 apply (zenon_or_s _ _ zenon_He6); [ zenon_intro zenon_Haf | zenon_intro zenon_He7 ]. % 15.41/15.59 apply (zenon_L57_); trivial. % 15.41/15.59 apply (zenon_or_s _ _ zenon_He7); [ zenon_intro zenon_Hdf | zenon_intro zenon_He8 ]. % 15.41/15.59 apply (zenon_L183_); trivial. % 15.41/15.59 apply (zenon_or_s _ _ zenon_He8); [ zenon_intro zenon_H34 | zenon_intro zenon_He2 ]. % 15.41/15.59 exact (zenon_H30 zenon_H34). % 15.41/15.59 apply (zenon_L776_); trivial. % 15.41/15.59 (* end of lemma zenon_L924_ *) % 15.41/15.59 assert (zenon_L925_ : (((op (e2) (e0)) = (e2))\/(((op (e2) (e1)) = (e2))\/(((op (e2) (e2)) = (e2))\/((op (e2) (e3)) = (e2))))) -> (~((op (e0) (e1)) = (op (e2) (e1)))) -> ((op (e0) (e1)) = (e3)) -> ((op (e3) (e3)) = (e3)) -> (~((op (e3) (op (e2) (e3))) = (op (e2) (e3)))) -> (~((op (e2) (e2)) = (e3))) -> (~((e2) = (e3))) -> ((op (e2) (e0)) = (e0)) -> (~((e0) = (e3))) -> (((op (e2) (e0)) = (e3))\/(((op (e2) (e1)) = (e3))\/(((op (e2) (e2)) = (e3))\/((op (e2) (e3)) = (e3))))) -> (~((op (e2) (e2)) = (e2))) -> (((op (e0) (e3)) = (e0))\/(((op (e1) (e3)) = (e0))\/(((op (e2) (e3)) = (e0))\/((op (e3) (e3)) = (e0))))) -> ((op (e0) (e2)) = (e0)) -> (~((op (e0) (e2)) = (op (e0) (e3)))) -> ((op (e1) (e3)) = (e1)) -> (~((e0) = (e1))) -> (~((e0) = (e2))) -> (~((op (e3) (e3)) = (e0))) -> False). % 15.41/15.59 do 0 intro. intros zenon_H237 zenon_Hde zenon_H4a zenon_H42 zenon_H28a zenon_H30 zenon_H6a zenon_Hcf zenon_H4b zenon_He6 zenon_H2f zenon_Hd3 zenon_Hab zenon_Hc9 zenon_H11f zenon_H9e zenon_H5e zenon_H3c. % 15.41/15.59 apply (zenon_or_s _ _ zenon_H237); [ zenon_intro zenon_Hdd | zenon_intro zenon_H238 ]. % 15.41/15.59 apply (zenon_L777_); trivial. % 15.41/15.59 apply (zenon_or_s _ _ zenon_H238); [ zenon_intro zenon_H156 | zenon_intro zenon_H239 ]. % 15.41/15.59 apply (zenon_L924_); trivial. % 15.41/15.59 apply (zenon_or_s _ _ zenon_H239); [ zenon_intro zenon_H35 | zenon_intro zenon_H124 ]. % 15.41/15.59 exact (zenon_H2f zenon_H35). % 15.41/15.59 apply (zenon_L711_); trivial. % 15.41/15.59 (* end of lemma zenon_L925_ *) % 15.41/15.59 assert (zenon_L926_ : (((op (e0) (e0)) = (e3))\/(((op (e0) (e1)) = (e3))\/(((op (e0) (e2)) = (e3))\/((op (e0) (e3)) = (e3))))) -> (~((op (e0) (e0)) = (e3))) -> (~((op (e3) (e3)) = (e0))) -> (~((e0) = (e2))) -> (~((e0) = (e1))) -> ((op (e1) (e3)) = (e1)) -> (~((op (e0) (e2)) = (op (e0) (e3)))) -> ((op (e0) (e2)) = (e0)) -> (((op (e0) (e3)) = (e0))\/(((op (e1) (e3)) = (e0))\/(((op (e2) (e3)) = (e0))\/((op (e3) (e3)) = (e0))))) -> (((op (e2) (e0)) = (e3))\/(((op (e2) (e1)) = (e3))\/(((op (e2) (e2)) = (e3))\/((op (e2) (e3)) = (e3))))) -> (~((e0) = (e3))) -> ((op (e2) (e0)) = (e0)) -> (~((e2) = (e3))) -> (~((op (e2) (e2)) = (e3))) -> (~((op (e3) (op (e2) (e3))) = (op (e2) (e3)))) -> (~((op (e0) (e1)) = (op (e2) (e1)))) -> (((op (e2) (e0)) = (e2))\/(((op (e2) (e1)) = (e2))\/(((op (e2) (e2)) = (e2))\/((op (e2) (e3)) = (e2))))) -> (~((op (e0) (e2)) = (op (e2) (e2)))) -> (~((op (e2) (e2)) = (e2))) -> (~((op (e2) (e2)) = (e1))) -> (~((op (e2) (e2)) = (e0))) -> (((op (e2) (e2)) = (e0))\/(((op (e2) (e2)) = (e1))\/(((op (e2) (e2)) = (e2))\/((op (e2) (e2)) = (e3))))) -> ((op (e3) (e3)) = (e3)) -> (~((op (e0) (e3)) = (op (e3) (e3)))) -> False). % 15.41/15.59 do 0 intro. intros zenon_H58 zenon_H59 zenon_H3c zenon_H5e zenon_H9e zenon_H11f zenon_Hc9 zenon_Hab zenon_Hd3 zenon_He6 zenon_H4b zenon_Hcf zenon_H6a zenon_H30 zenon_H28a zenon_Hde zenon_H237 zenon_H28 zenon_H2f zenon_H52 zenon_H2e zenon_H2d zenon_H42 zenon_H36. % 15.41/15.59 apply (zenon_or_s _ _ zenon_H58); [ zenon_intro zenon_H5b | zenon_intro zenon_H5a ]. % 15.41/15.59 exact (zenon_H59 zenon_H5b). % 15.41/15.59 apply (zenon_or_s _ _ zenon_H5a); [ zenon_intro zenon_H4a | zenon_intro zenon_H5c ]. % 15.41/15.59 apply (zenon_L925_); trivial. % 15.41/15.59 apply (zenon_or_s _ _ zenon_H5c); [ zenon_intro zenon_H50 | zenon_intro zenon_H53 ]. % 15.41/15.59 apply (zenon_L11_); trivial. % 15.41/15.59 apply (zenon_L12_); trivial. % 15.41/15.59 (* end of lemma zenon_L926_ *) % 15.41/15.59 assert (zenon_L927_ : (((op (e2) (e0)) = (e2))\/(((op (e2) (e1)) = (e2))\/(((op (e2) (e2)) = (e2))\/((op (e2) (e3)) = (e2))))) -> (~((op (e0) (e3)) = (op (e3) (e3)))) -> ((op (e3) (e3)) = (e3)) -> (~((e0) = (e3))) -> (((op (e2) (e0)) = (e3))\/(((op (e2) (e1)) = (e3))\/(((op (e2) (e2)) = (e3))\/((op (e2) (e3)) = (e3))))) -> (~((e2) = (e3))) -> (~((op (e0) (e1)) = (op (e2) (e1)))) -> (~((op (e2) (e2)) = (e3))) -> (~((op (e3) (op (e2) (e3))) = (op (e2) (e3)))) -> (~((op (e0) (e0)) = (e3))) -> (((op (e0) (e0)) = (e3))\/(((op (e0) (e1)) = (e3))\/(((op (e0) (e2)) = (e3))\/((op (e0) (e3)) = (e3))))) -> ((op (e2) (e1)) = (e0)) -> (~((op (e2) (e2)) = (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 (e0) (e3)))) -> ((op (e1) (e3)) = (e1)) -> (~((e0) = (e1))) -> (~((e0) = (e2))) -> (~((op (e3) (e3)) = (e0))) -> False). % 15.41/15.59 do 0 intro. intros zenon_H237 zenon_H36 zenon_H42 zenon_H4b zenon_He6 zenon_H6a zenon_Hde zenon_H30 zenon_H28a zenon_H59 zenon_H58 zenon_H14a zenon_H2f zenon_Hd3 zenon_Hab zenon_Hc9 zenon_H11f zenon_H9e zenon_H5e zenon_H3c. % 15.41/15.59 apply (zenon_or_s _ _ zenon_H237); [ zenon_intro zenon_Hdd | zenon_intro zenon_H238 ]. % 15.41/15.59 apply (zenon_L920_); trivial. % 15.41/15.59 apply (zenon_or_s _ _ zenon_H238); [ zenon_intro zenon_H156 | zenon_intro zenon_H239 ]. % 15.41/15.59 apply (zenon_L351_); trivial. % 15.41/15.59 apply (zenon_or_s _ _ zenon_H239); [ zenon_intro zenon_H35 | zenon_intro zenon_H124 ]. % 15.41/15.59 exact (zenon_H2f zenon_H35). % 15.41/15.59 apply (zenon_L711_); trivial. % 15.41/15.59 (* end of lemma zenon_L927_ *) % 15.41/15.59 assert (zenon_L928_ : (((op (e2) (e0)) = (e2))\/(((op (e2) (e1)) = (e2))\/(((op (e2) (e2)) = (e2))\/((op (e2) (e3)) = (e2))))) -> ((op (e3) (e3)) = (e3)) -> (~((op (e3) (op (e2) (e3))) = (op (e2) (e3)))) -> (~((op (e2) (e2)) = (e3))) -> (~((op (e0) (e1)) = (op (e2) (e1)))) -> ((op (e0) (e1)) = (e3)) -> (~((e2) = (e3))) -> (((op (e2) (e0)) = (e3))\/(((op (e2) (e1)) = (e3))\/(((op (e2) (e2)) = (e3))\/((op (e2) (e3)) = (e3))))) -> ((op (e3) (e1)) = (e2)) -> (~((op (e2) (e1)) = (op (e3) (e1)))) -> (~((op (e2) (e2)) = (e2))) -> (~((e0) = (e2))) -> ((op (e2) (e3)) = (e0)) -> False). % 15.41/15.59 do 0 intro. intros zenon_H237 zenon_H42 zenon_H28a zenon_H30 zenon_Hde zenon_H4a zenon_H6a zenon_He6 zenon_H16a zenon_H13c zenon_H2f zenon_H5e zenon_Hd0. % 15.41/15.59 apply (zenon_or_s _ _ zenon_H237); [ zenon_intro zenon_Hdd | zenon_intro zenon_H238 ]. % 15.41/15.59 apply (zenon_L777_); trivial. % 15.41/15.59 apply (zenon_or_s _ _ zenon_H238); [ zenon_intro zenon_H156 | zenon_intro zenon_H239 ]. % 15.41/15.59 apply (zenon_L252_); trivial. % 15.41/15.59 apply (zenon_or_s _ _ zenon_H239); [ zenon_intro zenon_H35 | zenon_intro zenon_H124 ]. % 15.41/15.59 exact (zenon_H2f zenon_H35). % 15.41/15.59 apply (zenon_L201_); trivial. % 15.41/15.59 (* end of lemma zenon_L928_ *) % 15.41/15.59 assert (zenon_L929_ : (((op (e2) (e0)) = (e0))\/(((op (e2) (e1)) = (e0))\/(((op (e2) (e2)) = (e0))\/((op (e2) (e3)) = (e0))))) -> (((op (e2) (e2)) = (e0))\/(((op (e2) (e2)) = (e1))\/(((op (e2) (e2)) = (e2))\/((op (e2) (e2)) = (e3))))) -> (~((op (e2) (e2)) = (e1))) -> (~((op (e0) (e2)) = (op (e2) (e2)))) -> (~((op (e3) (e3)) = (e0))) -> (~((e0) = (e1))) -> ((op (e1) (e3)) = (e1)) -> (~((op (e0) (e2)) = (op (e0) (e3)))) -> ((op (e0) (e2)) = (e0)) -> (((op (e0) (e3)) = (e0))\/(((op (e1) (e3)) = (e0))\/(((op (e2) (e3)) = (e0))\/((op (e3) (e3)) = (e0))))) -> (((op (e0) (e0)) = (e3))\/(((op (e0) (e1)) = (e3))\/(((op (e0) (e2)) = (e3))\/((op (e0) (e3)) = (e3))))) -> (~((op (e0) (e0)) = (e3))) -> (~((e0) = (e3))) -> (~((op (e0) (e3)) = (op (e3) (e3)))) -> (~((op (e2) (e2)) = (e0))) -> (((op (e2) (e0)) = (e2))\/(((op (e2) (e1)) = (e2))\/(((op (e2) (e2)) = (e2))\/((op (e2) (e3)) = (e2))))) -> ((op (e3) (e3)) = (e3)) -> (~((op (e3) (op (e2) (e3))) = (op (e2) (e3)))) -> (~((op (e2) (e2)) = (e3))) -> (~((op (e0) (e1)) = (op (e2) (e1)))) -> ((op (e0) (e1)) = (e3)) -> (~((e2) = (e3))) -> (((op (e2) (e0)) = (e3))\/(((op (e2) (e1)) = (e3))\/(((op (e2) (e2)) = (e3))\/((op (e2) (e3)) = (e3))))) -> ((op (e3) (e1)) = (e2)) -> (~((op (e2) (e1)) = (op (e3) (e1)))) -> (~((op (e2) (e2)) = (e2))) -> (~((e0) = (e2))) -> False). % 15.41/15.59 do 0 intro. intros zenon_H1f5 zenon_H2d zenon_H52 zenon_H28 zenon_H3c zenon_H9e zenon_H11f zenon_Hc9 zenon_Hab zenon_Hd3 zenon_H58 zenon_H59 zenon_H4b zenon_H36 zenon_H2e zenon_H237 zenon_H42 zenon_H28a zenon_H30 zenon_Hde zenon_H4a zenon_H6a zenon_He6 zenon_H16a zenon_H13c zenon_H2f zenon_H5e. % 15.41/15.59 apply (zenon_or_s _ _ zenon_H1f5); [ zenon_intro zenon_Hcf | zenon_intro zenon_H1f9 ]. % 15.41/15.59 apply (zenon_L926_); trivial. % 15.41/15.59 apply (zenon_or_s _ _ zenon_H1f9); [ zenon_intro zenon_H14a | zenon_intro zenon_H1fa ]. % 15.41/15.59 apply (zenon_L927_); trivial. % 15.41/15.59 apply (zenon_or_s _ _ zenon_H1fa); [ zenon_intro zenon_H32 | zenon_intro zenon_Hd0 ]. % 15.41/15.59 exact (zenon_H2e zenon_H32). % 15.41/15.59 apply (zenon_L928_); trivial. % 15.41/15.59 (* end of lemma zenon_L929_ *) % 15.41/15.59 assert (zenon_L930_ : (((op (e0) (e1)) = (e2))\/(((op (e1) (e1)) = (e2))\/(((op (e2) (e1)) = (e2))\/((op (e3) (e1)) = (e2))))) -> (~((op (e1) (e1)) = (e2))) -> (((op (e2) (e0)) = (e1))\/(((op (e2) (e1)) = (e1))\/(((op (e2) (e2)) = (e1))\/((op (e2) (e3)) = (e1))))) -> (~((e1) = (e3))) -> (~((e1) = (e2))) -> ((op (e0) (e0)) = (e2)) -> (~((op (e1) (e3)) = (op (e2) (e3)))) -> (((op (e2) (e0)) = (e0))\/(((op (e2) (e1)) = (e0))\/(((op (e2) (e2)) = (e0))\/((op (e2) (e3)) = (e0))))) -> (((op (e2) (e2)) = (e0))\/(((op (e2) (e2)) = (e1))\/(((op (e2) (e2)) = (e2))\/((op (e2) (e2)) = (e3))))) -> (~((op (e2) (e2)) = (e1))) -> (~((op (e0) (e2)) = (op (e2) (e2)))) -> (~((op (e3) (e3)) = (e0))) -> (~((e0) = (e1))) -> ((op (e1) (e3)) = (e1)) -> (~((op (e0) (e2)) = (op (e0) (e3)))) -> ((op (e0) (e2)) = (e0)) -> (((op (e0) (e3)) = (e0))\/(((op (e1) (e3)) = (e0))\/(((op (e2) (e3)) = (e0))\/((op (e3) (e3)) = (e0))))) -> (((op (e0) (e0)) = (e3))\/(((op (e0) (e1)) = (e3))\/(((op (e0) (e2)) = (e3))\/((op (e0) (e3)) = (e3))))) -> (~((op (e0) (e0)) = (e3))) -> (~((e0) = (e3))) -> (~((op (e0) (e3)) = (op (e3) (e3)))) -> (~((op (e2) (e2)) = (e0))) -> (((op (e2) (e0)) = (e2))\/(((op (e2) (e1)) = (e2))\/(((op (e2) (e2)) = (e2))\/((op (e2) (e3)) = (e2))))) -> ((op (e3) (e3)) = (e3)) -> (~((op (e3) (op (e2) (e3))) = (op (e2) (e3)))) -> (~((op (e2) (e2)) = (e3))) -> (~((op (e0) (e1)) = (op (e2) (e1)))) -> ((op (e0) (e1)) = (e3)) -> (~((e2) = (e3))) -> (((op (e2) (e0)) = (e3))\/(((op (e2) (e1)) = (e3))\/(((op (e2) (e2)) = (e3))\/((op (e2) (e3)) = (e3))))) -> (~((op (e2) (e1)) = (op (e3) (e1)))) -> (~((op (e2) (e2)) = (e2))) -> (~((e0) = (e2))) -> False). % 15.41/15.59 do 0 intro. intros zenon_H1a2 zenon_Hd6 zenon_Hb7 zenon_Ha3 zenon_Ha7 zenon_H92 zenon_H244 zenon_H1f5 zenon_H2d zenon_H52 zenon_H28 zenon_H3c zenon_H9e zenon_H11f zenon_Hc9 zenon_Hab zenon_Hd3 zenon_H58 zenon_H59 zenon_H4b zenon_H36 zenon_H2e zenon_H237 zenon_H42 zenon_H28a zenon_H30 zenon_Hde zenon_H4a zenon_H6a zenon_He6 zenon_H13c zenon_H2f zenon_H5e. % 15.41/15.59 apply (zenon_or_s _ _ zenon_H1a2); [ zenon_intro zenon_H5d | zenon_intro zenon_H1a3 ]. % 15.41/15.59 apply (zenon_L921_); trivial. % 15.41/15.59 apply (zenon_or_s _ _ zenon_H1a3); [ zenon_intro zenon_H6e | zenon_intro zenon_H1a4 ]. % 15.41/15.59 exact (zenon_Hd6 zenon_H6e). % 15.41/15.59 apply (zenon_or_s _ _ zenon_H1a4); [ zenon_intro zenon_H156 | zenon_intro zenon_H16a ]. % 15.41/15.59 apply (zenon_L923_); trivial. % 15.41/15.59 apply (zenon_L929_); trivial. % 15.41/15.59 (* end of lemma zenon_L930_ *) % 15.41/15.59 assert (zenon_L931_ : (((op (e0) (e0)) = (e3))\/(((op (e1) (e0)) = (e3))\/(((op (e2) (e0)) = (e3))\/((op (e3) (e0)) = (e3))))) -> (~((e0) = (e2))) -> (~((op (e2) (e1)) = (op (e3) (e1)))) -> (((op (e2) (e0)) = (e3))\/(((op (e2) (e1)) = (e3))\/(((op (e2) (e2)) = (e3))\/((op (e2) (e3)) = (e3))))) -> (~((e2) = (e3))) -> ((op (e0) (e1)) = (e3)) -> (~((op (e0) (e1)) = (op (e2) (e1)))) -> (~((op (e3) (op (e2) (e3))) = (op (e2) (e3)))) -> (((op (e2) (e0)) = (e2))\/(((op (e2) (e1)) = (e2))\/(((op (e2) (e2)) = (e2))\/((op (e2) (e3)) = (e2))))) -> (~((op (e0) (e3)) = (op (e3) (e3)))) -> (~((e0) = (e3))) -> (~((op (e0) (e0)) = (e3))) -> (((op (e0) (e0)) = (e3))\/(((op (e0) (e1)) = (e3))\/(((op (e0) (e2)) = (e3))\/((op (e0) (e3)) = (e3))))) -> (((op (e0) (e3)) = (e0))\/(((op (e1) (e3)) = (e0))\/(((op (e2) (e3)) = (e0))\/((op (e3) (e3)) = (e0))))) -> ((op (e0) (e2)) = (e0)) -> (~((op (e0) (e2)) = (op (e0) (e3)))) -> (~((e0) = (e1))) -> (~((op (e3) (e3)) = (e0))) -> (~((op (e0) (e2)) = (op (e2) (e2)))) -> (~((op (e2) (e2)) = (e1))) -> (((op (e2) (e0)) = (e0))\/(((op (e2) (e1)) = (e0))\/(((op (e2) (e2)) = (e0))\/((op (e2) (e3)) = (e0))))) -> (~((op (e1) (e3)) = (op (e2) (e3)))) -> ((op (e0) (e0)) = (e2)) -> (~((e1) = (e2))) -> (~((e1) = (e3))) -> (((op (e2) (e0)) = (e1))\/(((op (e2) (e1)) = (e1))\/(((op (e2) (e2)) = (e1))\/((op (e2) (e3)) = (e1))))) -> (((op (e0) (e1)) = (e2))\/(((op (e1) (e1)) = (e2))\/(((op (e2) (e1)) = (e2))\/((op (e3) (e1)) = (e2))))) -> (((op (e0) (e2)) = (e3))\/(((op (e1) (e2)) = (e3))\/(((op (e2) (e2)) = (e3))\/((op (e3) (e2)) = (e3))))) -> (~((op (e3) (e2)) = (op (e3) (e3)))) -> (((op (e1) (e0)) = (e1))\/(((op (e1) (e1)) = (e1))\/(((op (e1) (e2)) = (e1))\/((op (e1) (e3)) = (e1))))) -> (~((op (e1) (e1)) = (e3))) -> (~((op (e1) (e1)) = (e2))) -> (~((op (e1) (e1)) = (e1))) -> (((op (e2) (e2)) = (e0))\/(((op (e2) (e2)) = (e1))\/(((op (e2) (e2)) = (e2))\/((op (e2) (e2)) = (e3))))) -> (~((op (e2) (e2)) = (e0))) -> (~((op (e2) (e2)) = (e2))) -> (~((op (e2) (e2)) = (e3))) -> (((op (e1) (e1)) = (e0))\/(((op (e1) (e1)) = (e1))\/(((op (e1) (e1)) = (e2))\/((op (e1) (e1)) = (e3))))) -> ((op (e3) (e3)) = (e3)) -> (~((op (e3) (e0)) = (op (e3) (e3)))) -> False). % 15.41/15.59 do 0 intro. intros zenon_Hbe zenon_H5e zenon_H13c zenon_He6 zenon_H6a zenon_H4a zenon_Hde zenon_H28a zenon_H237 zenon_H36 zenon_H4b zenon_H59 zenon_H58 zenon_Hd3 zenon_Hab zenon_Hc9 zenon_H9e zenon_H3c zenon_H28 zenon_H52 zenon_H1f5 zenon_H244 zenon_H92 zenon_Ha7 zenon_Ha3 zenon_Hb7 zenon_H1a2 zenon_H175 zenon_H173 zenon_H1c5 zenon_H182 zenon_Hd6 zenon_H1b4 zenon_H2d zenon_H2e zenon_H2f zenon_H30 zenon_H1b3 zenon_H42 zenon_Hbb. % 15.41/15.59 apply (zenon_or_s _ _ zenon_Hbe); [ zenon_intro zenon_H5b | zenon_intro zenon_Hbf ]. % 15.41/15.59 exact (zenon_H59 zenon_H5b). % 15.41/15.59 apply (zenon_or_s _ _ zenon_Hbf); [ zenon_intro zenon_H69 | zenon_intro zenon_Hc0 ]. % 15.41/15.59 apply (zenon_or_s _ _ zenon_H1c5); [ zenon_intro zenon_Hd8 | zenon_intro zenon_H1c6 ]. % 15.41/15.59 apply (zenon_L163_); trivial. % 15.41/15.59 apply (zenon_or_s _ _ zenon_H1c6); [ zenon_intro zenon_H21 | zenon_intro zenon_H1c7 ]. % 15.41/15.59 exact (zenon_H1b4 zenon_H21). % 15.41/15.59 apply (zenon_or_s _ _ zenon_H1c7); [ zenon_intro zenon_H117 | zenon_intro zenon_H11f ]. % 15.41/15.59 apply (zenon_L197_); trivial. % 15.41/15.59 apply (zenon_L930_); trivial. % 15.41/15.59 apply (zenon_or_s _ _ zenon_Hc0); [ zenon_intro zenon_Haf | zenon_intro zenon_Hba ]. % 15.41/15.59 apply (zenon_L219_); trivial. % 15.41/15.59 apply (zenon_L43_); trivial. % 15.41/15.59 (* end of lemma zenon_L931_ *) % 15.41/15.59 assert (zenon_L932_ : (((op (e0) (e0)) = (e1))\/(((op (e1) (e0)) = (e1))\/(((op (e2) (e0)) = (e1))\/((op (e3) (e0)) = (e1))))) -> (~((op (e0) (e0)) = (e1))) -> (((op (e0) (e0)) = (e2))\/(((op (e0) (e1)) = (e2))\/(((op (e0) (e2)) = (e2))\/((op (e0) (e3)) = (e2))))) -> (~((op (e0) (e1)) = (op (e1) (e1)))) -> (~((op (e1) (e1)) = (e0))) -> (~((op (e3) (e0)) = (op (e3) (e3)))) -> (~((op (e3) (e2)) = (op (e3) (e3)))) -> (((op (e0) (e2)) = (e3))\/(((op (e1) (e2)) = (e3))\/(((op (e2) (e2)) = (e3))\/((op (e3) (e2)) = (e3))))) -> (((op (e0) (e0)) = (e2))\/(((op (e1) (e0)) = (e2))\/(((op (e2) (e0)) = (e2))\/((op (e3) (e0)) = (e2))))) -> (~((e0) = (e2))) -> (~((op (e2) (e1)) = (op (e3) (e1)))) -> (((op (e2) (e0)) = (e2))\/(((op (e2) (e1)) = (e2))\/(((op (e2) (e2)) = (e2))\/((op (e2) (e3)) = (e2))))) -> (((op (e0) (e3)) = (e0))\/(((op (e1) (e3)) = (e0))\/(((op (e2) (e3)) = (e0))\/((op (e3) (e3)) = (e0))))) -> (~((op (e0) (e2)) = (op (e0) (e3)))) -> (~((e0) = (e1))) -> (~((op (e3) (e3)) = (e0))) -> (~((op (e0) (e2)) = (op (e2) (e2)))) -> (~((op (e2) (e2)) = (e1))) -> (((op (e2) (e0)) = (e0))\/(((op (e2) (e1)) = (e0))\/(((op (e2) (e2)) = (e0))\/((op (e2) (e3)) = (e0))))) -> (~((op (e1) (e3)) = (op (e2) (e3)))) -> (((op (e2) (e0)) = (e1))\/(((op (e2) (e1)) = (e1))\/(((op (e2) (e2)) = (e1))\/((op (e2) (e3)) = (e1))))) -> (((op (e0) (e1)) = (e2))\/(((op (e1) (e1)) = (e2))\/(((op (e2) (e1)) = (e2))\/((op (e3) (e1)) = (e2))))) -> (((op (e1) (e0)) = (e2))\/(((op (e1) (e1)) = (e2))\/(((op (e1) (e2)) = (e2))\/((op (e1) (e3)) = (e2))))) -> (~((op (e0) (e3)) = (op (e1) (e3)))) -> (((op (e1) (e0)) = (e1))\/(((op (e1) (e1)) = (e1))\/(((op (e1) (e2)) = (e1))\/((op (e1) (e3)) = (e1))))) -> (~((e1) = (e3))) -> (((op (e1) (e1)) = (e0))\/(((op (e1) (e1)) = (e1))\/(((op (e1) (e1)) = (e2))\/((op (e1) (e1)) = (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) (e1)) = (e1))) -> (~((op (e1) (e1)) = (e2))) -> (~((op (e1) (e1)) = (e3))) -> (((op (e0) (e0)) = (e3))\/(((op (e1) (e0)) = (e3))\/(((op (e2) (e0)) = (e3))\/((op (e3) (e0)) = (e3))))) -> (~((op (e0) (e3)) = (op (e3) (e3)))) -> ((op (e3) (e3)) = (e3)) -> ((op (e0) (e2)) = (e0)) -> (~((e0) = (e3))) -> (((op (e2) (e0)) = (e3))\/(((op (e2) (e1)) = (e3))\/(((op (e2) (e2)) = (e3))\/((op (e2) (e3)) = (e3))))) -> (~((e2) = (e3))) -> (~((op (e0) (e1)) = (op (e2) (e1)))) -> (~((op (e2) (e2)) = (e3))) -> (~((op (e3) (op (e2) (e3))) = (op (e2) (e3)))) -> (~((op (e0) (e0)) = (e3))) -> (((op (e0) (e0)) = (e3))\/(((op (e0) (e1)) = (e3))\/(((op (e0) (e2)) = (e3))\/((op (e0) (e3)) = (e3))))) -> (~((e1) = (e2))) -> False). % 15.41/15.59 do 0 intro. intros zenon_Hf1 zenon_H45 zenon_H8e zenon_H23 zenon_H145 zenon_Hbb zenon_H173 zenon_H175 zenon_Heb zenon_H5e zenon_H13c zenon_H237 zenon_Hd3 zenon_Hc9 zenon_H9e zenon_H3c zenon_H28 zenon_H52 zenon_H1f5 zenon_H244 zenon_Hb7 zenon_H1a2 zenon_H84 zenon_H80 zenon_H1c5 zenon_Ha3 zenon_H1b3 zenon_H2f zenon_H2e zenon_H2d zenon_H1b4 zenon_Hd6 zenon_H182 zenon_Hbe zenon_H36 zenon_H42 zenon_Hab zenon_H4b zenon_He6 zenon_H6a zenon_Hde zenon_H30 zenon_H28a zenon_H59 zenon_H58 zenon_Ha7. % 15.41/15.59 apply (zenon_or_s _ _ zenon_Hf1); [ zenon_intro zenon_H47 | zenon_intro zenon_Hf4 ]. % 15.41/15.59 exact (zenon_H45 zenon_H47). % 15.41/15.59 apply (zenon_or_s _ _ zenon_Hf4); [ zenon_intro zenon_Hd8 | zenon_intro zenon_Hf5 ]. % 15.41/15.59 apply (zenon_L241_); trivial. % 15.41/15.59 apply (zenon_or_s _ _ zenon_Hf5); [ zenon_intro zenon_Hae | zenon_intro zenon_Hee ]. % 15.41/15.59 apply (zenon_L788_); trivial. % 15.41/15.59 apply (zenon_or_s _ _ zenon_H8e); [ zenon_intro zenon_H92 | zenon_intro zenon_H91 ]. % 15.41/15.59 apply (zenon_or_s _ _ zenon_H58); [ zenon_intro zenon_H5b | zenon_intro zenon_H5a ]. % 15.41/15.59 exact (zenon_H59 zenon_H5b). % 15.41/15.59 apply (zenon_or_s _ _ zenon_H5a); [ zenon_intro zenon_H4a | zenon_intro zenon_H5c ]. % 15.41/15.59 apply (zenon_L931_); trivial. % 15.41/15.59 apply (zenon_or_s _ _ zenon_H5c); [ zenon_intro zenon_H50 | zenon_intro zenon_H53 ]. % 15.41/15.59 apply (zenon_L48_); trivial. % 15.41/15.59 apply (zenon_L12_); trivial. % 15.41/15.59 apply (zenon_or_s _ _ zenon_H91); [ zenon_intro zenon_H5d | zenon_intro zenon_H93 ]. % 15.41/15.59 apply (zenon_L214_); trivial. % 15.41/15.59 apply (zenon_or_s _ _ zenon_H93); [ zenon_intro zenon_H63 | zenon_intro zenon_H81 ]. % 15.41/15.59 apply (zenon_or_s _ _ zenon_Heb); [ zenon_intro zenon_H92 | zenon_intro zenon_Hec ]. % 15.41/15.59 apply (zenon_or_s _ _ zenon_H58); [ zenon_intro zenon_H5b | zenon_intro zenon_H5a ]. % 15.41/15.59 exact (zenon_H59 zenon_H5b). % 15.41/15.59 apply (zenon_or_s _ _ zenon_H5a); [ zenon_intro zenon_H4a | zenon_intro zenon_H5c ]. % 15.41/15.59 apply (zenon_L931_); trivial. % 15.41/15.59 apply (zenon_or_s _ _ zenon_H5c); [ zenon_intro zenon_H50 | zenon_intro zenon_H53 ]. % 15.41/15.59 apply (zenon_L31_); trivial. % 15.41/15.59 apply (zenon_L12_); trivial. % 15.41/15.59 apply (zenon_or_s _ _ zenon_Hec); [ zenon_intro zenon_H68 | zenon_intro zenon_Hed ]. % 15.41/15.59 apply (zenon_L623_); trivial. % 15.41/15.59 apply (zenon_or_s _ _ zenon_Hed); [ zenon_intro zenon_Hdd | zenon_intro zenon_He9 ]. % 15.41/15.59 apply (zenon_L789_); trivial. % 15.41/15.59 apply (zenon_L122_); trivial. % 15.41/15.59 apply (zenon_or_s _ _ zenon_Heb); [ zenon_intro zenon_H92 | zenon_intro zenon_Hec ]. % 15.41/15.59 apply (zenon_or_s _ _ zenon_H58); [ zenon_intro zenon_H5b | zenon_intro zenon_H5a ]. % 15.41/15.59 exact (zenon_H59 zenon_H5b). % 15.41/15.59 apply (zenon_or_s _ _ zenon_H5a); [ zenon_intro zenon_H4a | zenon_intro zenon_H5c ]. % 15.41/15.59 apply (zenon_or_s _ _ zenon_Hbe); [ zenon_intro zenon_H5b | zenon_intro zenon_Hbf ]. % 15.41/15.59 exact (zenon_H59 zenon_H5b). % 15.41/15.59 apply (zenon_or_s _ _ zenon_Hbf); [ zenon_intro zenon_H69 | zenon_intro zenon_Hc0 ]. % 15.41/15.59 apply (zenon_or_s _ _ zenon_H1c5); [ zenon_intro zenon_Hd8 | zenon_intro zenon_H1c6 ]. % 15.41/15.59 apply (zenon_L163_); trivial. % 15.41/15.59 apply (zenon_or_s _ _ zenon_H1c6); [ zenon_intro zenon_H21 | zenon_intro zenon_H1c7 ]. % 15.41/15.59 exact (zenon_H1b4 zenon_H21). % 15.41/15.59 apply (zenon_or_s _ _ zenon_H1c7); [ zenon_intro zenon_H117 | zenon_intro zenon_H11f ]. % 15.41/15.59 apply (zenon_L385_); trivial. % 15.41/15.59 apply (zenon_L930_); trivial. % 15.41/15.59 apply (zenon_or_s _ _ zenon_Hc0); [ zenon_intro zenon_Haf | zenon_intro zenon_Hba ]. % 15.41/15.59 apply (zenon_L219_); trivial. % 15.41/15.59 apply (zenon_L79_); trivial. % 15.41/15.59 apply (zenon_or_s _ _ zenon_H5c); [ zenon_intro zenon_H50 | zenon_intro zenon_H53 ]. % 15.41/15.59 apply (zenon_L48_); trivial. % 15.41/15.59 apply (zenon_L128_); trivial. % 15.41/15.59 apply (zenon_or_s _ _ zenon_Hec); [ zenon_intro zenon_H68 | zenon_intro zenon_Hed ]. % 15.41/15.59 apply (zenon_L623_); trivial. % 15.41/15.59 apply (zenon_or_s _ _ zenon_Hed); [ zenon_intro zenon_Hdd | zenon_intro zenon_He9 ]. % 15.41/15.59 apply (zenon_L920_); trivial. % 15.41/15.59 apply (zenon_L122_); trivial. % 15.41/15.59 (* end of lemma zenon_L932_ *) % 15.41/15.59 assert (zenon_L933_ : (((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 (e0) (e3)) = (e2)) -> (~((op (e0) (e3)) = (op (e1) (e3)))) -> ((op (e3) (e3)) = (e3)) -> (~((op (e1) (e3)) = (op (e3) (e3)))) -> False). % 15.41/15.59 do 0 intro. intros zenon_H25b zenon_Hd0 zenon_Hb5 zenon_H244 zenon_H81 zenon_H80 zenon_H42 zenon_H8b. % 15.41/15.59 apply (zenon_or_s _ _ zenon_H25b); [ zenon_intro zenon_Hcc | zenon_intro zenon_H25c ]. % 15.41/15.59 apply (zenon_L599_); trivial. % 15.41/15.59 apply (zenon_or_s _ _ zenon_H25c); [ zenon_intro zenon_H11f | zenon_intro zenon_H25d ]. % 15.41/15.59 apply (zenon_L529_); trivial. % 15.41/15.59 apply (zenon_or_s _ _ zenon_H25d); [ zenon_intro zenon_H82 | zenon_intro zenon_H8a ]. % 15.41/15.59 apply (zenon_L22_); trivial. % 15.41/15.59 apply (zenon_L25_); trivial. % 15.41/15.59 (* end of lemma zenon_L933_ *) % 15.41/15.59 assert (zenon_L934_ : (((op (e0) (e0)) = (e2))\/(((op (e0) (e1)) = (e2))\/(((op (e0) (e2)) = (e2))\/((op (e0) (e3)) = (e2))))) -> (~((op (e0) (e0)) = (e2))) -> (~((op (e0) (e3)) = (op (e3) (e3)))) -> (~((op (e0) (e0)) = (e3))) -> (((op (e0) (e0)) = (e3))\/(((op (e0) (e1)) = (e3))\/(((op (e0) (e2)) = (e3))\/((op (e0) (e3)) = (e3))))) -> (((op (e0) (e1)) = (e3))\/(((op (e1) (e1)) = (e3))\/(((op (e2) (e1)) = (e3))\/((op (e3) (e1)) = (e3))))) -> (~((e0) = (e3))) -> (~((op (e1) (e3)) = (op (e3) (e3)))) -> (~((op (e0) (e3)) = (op (e1) (e3)))) -> (~((op (e1) (e3)) = (op (e2) (e3)))) -> (((op (e1) (e3)) = (e0))\/(((op (e1) (e3)) = (e1))\/(((op (e1) (e3)) = (e2))\/((op (e1) (e3)) = (e3))))) -> (~((e1) = (e2))) -> (((op (e2) (e0)) = (e3))\/(((op (e2) (e1)) = (e3))\/(((op (e2) (e2)) = (e3))\/((op (e2) (e3)) = (e3))))) -> (~((e1) = (e3))) -> (~((op (e2) (e2)) = (e3))) -> (~((op (e3) (op (e2) (e3))) = (op (e2) (e3)))) -> (((op (e2) (e0)) = (e1))\/(((op (e2) (e1)) = (e1))\/(((op (e2) (e2)) = (e1))\/((op (e2) (e3)) = (e1))))) -> (~((op (e2) (e2)) = (e0))) -> (~((op (e0) (e1)) = (op (e2) (e1)))) -> ((op (e0) (e1)) = (e0)) -> (((op (e0) (e3)) = (e0))\/(((op (e1) (e3)) = (e0))\/(((op (e2) (e3)) = (e0))\/((op (e3) (e3)) = (e0))))) -> (~((e0) = (e2))) -> ((op (e1) (e3)) = (e1)) -> (~((e0) = (e1))) -> (~((op (e2) (e0)) = (op (e2) (e3)))) -> (~((op (e3) (e3)) = (e0))) -> (((op (e2) (e0)) = (e0))\/(((op (e2) (e1)) = (e0))\/(((op (e2) (e2)) = (e0))\/((op (e2) (e3)) = (e0))))) -> (~((e2) = (e3))) -> ((op (e2) (e1)) = (e2)) -> ((op (e3) (e3)) = (e3)) -> (~((op (e3) (e1)) = (op (e3) (e3)))) -> False). % 15.41/15.59 do 0 intro. intros zenon_H8e zenon_H8f zenon_H36 zenon_H59 zenon_H58 zenon_H199 zenon_H4b zenon_H8b zenon_H80 zenon_H244 zenon_H25b zenon_Ha7 zenon_He6 zenon_Ha3 zenon_H30 zenon_H28a zenon_Hb7 zenon_H2e zenon_Hde zenon_H49 zenon_Hd3 zenon_H5e zenon_H11f zenon_H9e zenon_Hce zenon_H3c zenon_H1f5 zenon_H6a zenon_H156 zenon_H42 zenon_H12d. % 15.41/15.59 apply (zenon_or_s _ _ zenon_H8e); [ zenon_intro zenon_H92 | zenon_intro zenon_H91 ]. % 15.41/15.59 exact (zenon_H8f zenon_H92). % 15.41/15.59 apply (zenon_or_s _ _ zenon_H91); [ zenon_intro zenon_H5d | zenon_intro zenon_H93 ]. % 15.41/15.59 apply (zenon_L14_); trivial. % 15.41/15.59 apply (zenon_or_s _ _ zenon_H93); [ zenon_intro zenon_H63 | zenon_intro zenon_H81 ]. % 15.41/15.59 apply (zenon_L371_); trivial. % 15.41/15.59 apply (zenon_or_s _ _ zenon_H199); [ zenon_intro zenon_H4a | zenon_intro zenon_H19a ]. % 15.41/15.59 apply (zenon_L9_); trivial. % 15.41/15.59 apply (zenon_or_s _ _ zenon_H19a); [ zenon_intro zenon_H96 | zenon_intro zenon_H19b ]. % 15.41/15.59 apply (zenon_or_s _ _ zenon_H1f5); [ zenon_intro zenon_Hcf | zenon_intro zenon_H1f9 ]. % 15.41/15.59 apply (zenon_L373_); trivial. % 15.41/15.59 apply (zenon_or_s _ _ zenon_H1f9); [ zenon_intro zenon_H14a | zenon_intro zenon_H1fa ]. % 15.41/15.59 apply (zenon_L180_); trivial. % 15.41/15.59 apply (zenon_or_s _ _ zenon_H1fa); [ zenon_intro zenon_H32 | zenon_intro zenon_Hd0 ]. % 15.41/15.59 exact (zenon_H2e zenon_H32). % 15.41/15.59 apply (zenon_or_s _ _ zenon_Hb7); [ zenon_intro zenon_Hae | zenon_intro zenon_Hb8 ]. % 15.41/15.59 apply (zenon_L796_); trivial. % 15.41/15.59 apply (zenon_or_s _ _ zenon_Hb8); [ zenon_intro zenon_Hb2 | zenon_intro zenon_Hb9 ]. % 15.41/15.59 apply (zenon_L372_); trivial. % 15.41/15.59 apply (zenon_or_s _ _ zenon_Hb9); [ zenon_intro zenon_H2a | zenon_intro zenon_Hb5 ]. % 15.41/15.59 apply (zenon_L374_); trivial. % 15.41/15.59 apply (zenon_L933_); trivial. % 15.41/15.59 apply (zenon_or_s _ _ zenon_H19b); [ zenon_intro zenon_Hdf | zenon_intro zenon_H10a ]. % 15.41/15.59 apply (zenon_L183_); trivial. % 15.41/15.59 apply (zenon_L102_); trivial. % 15.41/15.59 (* end of lemma zenon_L934_ *) % 15.41/15.59 assert (zenon_L935_ : (((op (e0) (e0)) = (e0))\/(((op (e0) (e0)) = (e1))\/(((op (e0) (e0)) = (e2))\/((op (e0) (e0)) = (e3))))) -> (~((op (e0) (e0)) = (e0))) -> (~((op (e2) (e2)) = (e3))) -> (~((op (e2) (e2)) = (e2))) -> (~((op (e2) (e2)) = (e1))) -> ((op (e2) (e1)) = (e3)) -> (((op (e2) (e2)) = (e0))\/(((op (e2) (e2)) = (e1))\/(((op (e2) (e2)) = (e2))\/((op (e2) (e2)) = (e3))))) -> (~((op (e0) (e0)) = (e2))) -> (~((op (e0) (e0)) = (e3))) -> False). % 15.41/15.59 do 0 intro. intros zenon_H12a zenon_H20 zenon_H30 zenon_H2f zenon_H52 zenon_Hdf zenon_H2d zenon_H8f zenon_H59. % 15.41/15.59 apply (zenon_or_s _ _ zenon_H12a); [ zenon_intro zenon_H1f | zenon_intro zenon_H12b ]. % 15.41/15.59 exact (zenon_H20 zenon_H1f). % 15.41/15.59 apply (zenon_or_s _ _ zenon_H12b); [ zenon_intro zenon_H47 | zenon_intro zenon_H12c ]. % 15.41/15.59 apply (zenon_L282_); trivial. % 15.41/15.59 apply (zenon_or_s _ _ zenon_H12c); [ zenon_intro zenon_H92 | zenon_intro zenon_H5b ]. % 15.41/15.59 exact (zenon_H8f zenon_H92). % 15.41/15.59 exact (zenon_H59 zenon_H5b). % 15.41/15.59 (* end of lemma zenon_L935_ *) % 15.41/15.59 assert (zenon_L936_ : (((op (e2) (e0)) = (e3))\/(((op (e2) (e1)) = (e3))\/(((op (e2) (e2)) = (e3))\/((op (e2) (e3)) = (e3))))) -> (~((e2) = (e3))) -> ((op (e2) (e0)) = (e2)) -> (~((op (e0) (e0)) = (e3))) -> (~((op (e0) (e0)) = (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 (e0) (e0)) = (e0))) -> (((op (e0) (e0)) = (e0))\/(((op (e0) (e0)) = (e1))\/(((op (e0) (e0)) = (e2))\/((op (e0) (e0)) = (e3))))) -> (~((op (e2) (e2)) = (e3))) -> (~((op (e3) (op (e2) (e3))) = (op (e2) (e3)))) -> ((op (e3) (e3)) = (e3)) -> False). % 15.41/15.59 do 0 intro. intros zenon_He6 zenon_H6a zenon_Hdd zenon_H59 zenon_H8f zenon_H2d zenon_H52 zenon_H2f zenon_H20 zenon_H12a zenon_H30 zenon_H28a zenon_H42. % 15.41/15.59 apply (zenon_or_s _ _ zenon_He6); [ zenon_intro zenon_Haf | zenon_intro zenon_He7 ]. % 15.41/15.59 apply (zenon_L64_); trivial. % 15.41/15.59 apply (zenon_or_s _ _ zenon_He7); [ zenon_intro zenon_Hdf | zenon_intro zenon_He8 ]. % 15.41/15.59 apply (zenon_L935_); trivial. % 15.41/15.59 apply (zenon_or_s _ _ zenon_He8); [ zenon_intro zenon_H34 | zenon_intro zenon_He2 ]. % 15.41/15.59 exact (zenon_H30 zenon_H34). % 15.41/15.59 apply (zenon_L776_); trivial. % 15.41/15.59 (* end of lemma zenon_L936_ *) % 15.41/15.59 assert (zenon_L937_ : ((~((op (e2) (e2)) = (e1)))\/((op (e2) (e1)) = (e2))) -> (~((op (e2) (e0)) = (op (e2) (e1)))) -> ((~((op (e2) (e2)) = (e3)))\/((op (e2) (e3)) = (e2))) -> (~((op (e2) (e0)) = (op (e2) (e3)))) -> (~((e2) = (e3))) -> ((op (e2) (e0)) = (e2)) -> (((op (e0) (e0)) = (e0))\/(((op (e0) (e0)) = (e1))\/(((op (e0) (e0)) = (e2))\/((op (e0) (e0)) = (e3))))) -> (~((op (e0) (e0)) = (e3))) -> (~((op (e0) (e0)) = (e2))) -> (((op (e2) (e2)) = (e0))\/(((op (e2) (e2)) = (e1))\/(((op (e2) (e2)) = (e2))\/((op (e2) (e2)) = (e3))))) -> (~((op (e0) (e0)) = (e0))) -> (~((op (e3) (op (e2) (e3))) = (op (e2) (e3)))) -> ((op (e3) (e3)) = (e3)) -> (((op (e2) (e0)) = (e3))\/(((op (e2) (e1)) = (e3))\/(((op (e2) (e2)) = (e3))\/((op (e2) (e3)) = (e3))))) -> (~((op (e2) (op (e2) (e2))) = (op (e2) (e2)))) -> ((~((op (e2) (e2)) = (e2)))\/((op (e2) (e2)) = (e2))) -> False). % 15.41/15.59 do 0 intro. intros zenon_H1e3 zenon_H154 zenon_H1c3 zenon_Hce zenon_H6a zenon_Hdd zenon_H12a zenon_H59 zenon_H8f zenon_H2d zenon_H20 zenon_H28a zenon_H42 zenon_He6 zenon_H294 zenon_Haa. % 15.41/15.59 apply (zenon_or_s _ _ zenon_H1e3); [ zenon_intro zenon_H52 | zenon_intro zenon_H156 ]. % 15.41/15.59 apply (zenon_or_s _ _ zenon_Haa); [ zenon_intro zenon_H2f | zenon_intro zenon_H35 ]. % 15.41/15.59 apply (zenon_or_s _ _ zenon_H1c3); [ zenon_intro zenon_H30 | zenon_intro zenon_H124 ]. % 15.41/15.59 apply (zenon_L936_); trivial. % 15.41/15.59 apply (zenon_L119_); trivial. % 15.41/15.59 apply (zenon_L794_); trivial. % 15.41/15.59 apply (zenon_L284_); trivial. % 15.41/15.59 (* end of lemma zenon_L937_ *) % 15.41/15.59 assert (zenon_L938_ : ((~((op (e2) (e2)) = (e1)))\/((op (e2) (e1)) = (e2))) -> ((~((op (e2) (e2)) = (e3)))\/((op (e2) (e3)) = (e2))) -> (~((op (e2) (e0)) = (op (e2) (e3)))) -> (((op (e0) (e0)) = (e2))\/(((op (e0) (e1)) = (e2))\/(((op (e0) (e2)) = (e2))\/((op (e0) (e3)) = (e2))))) -> (~((op (e0) (e1)) = (op (e0) (e3)))) -> (~((op (e1) (e1)) = (e2))) -> (~((op (e2) (e0)) = (op (e2) (e1)))) -> (((op (e0) (e1)) = (e3))\/(((op (e1) (e1)) = (e3))\/(((op (e2) (e1)) = (e3))\/((op (e3) (e1)) = (e3))))) -> (((op (e2) (e2)) = (e0))\/(((op (e2) (e2)) = (e1))\/(((op (e2) (e2)) = (e2))\/((op (e2) (e2)) = (e3))))) -> (~((op (e1) (e1)) = (e3))) -> (((op (e0) (e1)) = (e2))\/(((op (e1) (e1)) = (e2))\/(((op (e2) (e1)) = (e2))\/((op (e3) (e1)) = (e2))))) -> (~((op (e0) (e0)) = (e3))) -> (((op (e2) (e0)) = (e3))\/(((op (e2) (e1)) = (e3))\/(((op (e2) (e2)) = (e3))\/((op (e2) (e3)) = (e3))))) -> ((op (e3) (e3)) = (e3)) -> (~((op (e3) (op (e2) (e3))) = (op (e2) (e3)))) -> (~((op (e0) (e1)) = (op (e2) (e1)))) -> ((op (e2) (e0)) = (e2)) -> (~((e2) = (e3))) -> (~((op (e0) (e3)) = (op (e3) (e3)))) -> (((op (e0) (e0)) = (e3))\/(((op (e0) (e1)) = (e3))\/(((op (e0) (e2)) = (e3))\/((op (e0) (e3)) = (e3))))) -> ((op (e0) (e1)) = (e0)) -> (~((e0) = (e2))) -> (~((op (e0) (e0)) = (e2))) -> (~((op (e0) (e1)) = (op (e1) (e1)))) -> ((op (e1) (e1)) = (e1)) -> (~((e1) = (e3))) -> (((op (e2) (e0)) = (e1))\/(((op (e2) (e1)) = (e1))\/(((op (e2) (e2)) = (e1))\/((op (e2) (e3)) = (e1))))) -> (~((op (e0) (e3)) = (op (e2) (e3)))) -> (~((op (e1) (e1)) = (op (e2) (e1)))) -> (~((e1) = (e2))) -> (((op (e0) (e0)) = (e1))\/(((op (e0) (e1)) = (e1))\/(((op (e0) (e2)) = (e1))\/((op (e0) (e3)) = (e1))))) -> (~((op (e2) (e0)) = (op (e2) (e2)))) -> ((~((op (e2) (e2)) = (e2)))\/((op (e2) (e2)) = (e2))) -> False). % 15.41/15.59 do 0 intro. intros zenon_H1e3 zenon_H1c3 zenon_Hce zenon_H8e zenon_H1cd zenon_Hd6 zenon_H154 zenon_H199 zenon_H2d zenon_H182 zenon_H1a2 zenon_H59 zenon_He6 zenon_H42 zenon_H28a zenon_Hde zenon_Hdd zenon_H6a zenon_H36 zenon_H58 zenon_H49 zenon_H5e zenon_H8f zenon_H23 zenon_H21 zenon_Ha3 zenon_Hb7 zenon_Hb4 zenon_Hb1 zenon_Ha7 zenon_H44 zenon_H17a zenon_Haa. % 15.41/15.59 apply (zenon_or_s _ _ zenon_H1e3); [ zenon_intro zenon_H52 | zenon_intro zenon_H156 ]. % 15.41/15.59 apply (zenon_or_s _ _ zenon_Haa); [ zenon_intro zenon_H2f | zenon_intro zenon_H35 ]. % 15.41/15.59 apply (zenon_or_s _ _ zenon_H1c3); [ zenon_intro zenon_H30 | zenon_intro zenon_H124 ]. % 15.41/15.59 apply (zenon_or_s _ _ zenon_H44); [ zenon_intro zenon_H47 | zenon_intro zenon_H46 ]. % 15.41/15.59 apply (zenon_or_s _ _ zenon_H8e); [ zenon_intro zenon_H92 | zenon_intro zenon_H91 ]. % 15.41/15.59 exact (zenon_H8f zenon_H92). % 15.41/15.59 apply (zenon_or_s _ _ zenon_H91); [ zenon_intro zenon_H5d | zenon_intro zenon_H93 ]. % 15.41/15.59 apply (zenon_L14_); trivial. % 15.41/15.59 apply (zenon_or_s _ _ zenon_H93); [ zenon_intro zenon_H63 | zenon_intro zenon_H81 ]. % 15.41/15.59 apply (zenon_L789_); trivial. % 15.41/15.59 apply (zenon_or_s _ _ zenon_H1a2); [ zenon_intro zenon_H5d | zenon_intro zenon_H1a3 ]. % 15.41/15.59 apply (zenon_L350_); trivial. % 15.41/15.59 apply (zenon_or_s _ _ zenon_H1a3); [ zenon_intro zenon_H6e | zenon_intro zenon_H1a4 ]. % 15.41/15.59 exact (zenon_Hd6 zenon_H6e). % 15.41/15.59 apply (zenon_or_s _ _ zenon_H1a4); [ zenon_intro zenon_H156 | zenon_intro zenon_H16a ]. % 15.41/15.59 apply (zenon_L284_); trivial. % 15.41/15.59 apply (zenon_or_s _ _ zenon_H199); [ zenon_intro zenon_H4a | zenon_intro zenon_H19a ]. % 15.41/15.59 apply (zenon_L777_); trivial. % 15.41/15.59 apply (zenon_or_s _ _ zenon_H19a); [ zenon_intro zenon_H96 | zenon_intro zenon_H19b ]. % 15.41/15.59 exact (zenon_H182 zenon_H96). % 15.41/15.59 apply (zenon_or_s _ _ zenon_H19b); [ zenon_intro zenon_Hdf | zenon_intro zenon_H10a ]. % 15.41/15.59 apply (zenon_L282_); trivial. % 15.41/15.59 apply (zenon_L297_); trivial. % 15.41/15.59 apply (zenon_or_s _ _ zenon_H46); [ zenon_intro zenon_H22 | zenon_intro zenon_H48 ]. % 15.41/15.59 apply (zenon_L3_); trivial. % 15.41/15.59 apply (zenon_or_s _ _ zenon_H48); [ zenon_intro zenon_H29 | zenon_intro zenon_H37 ]. % 15.41/15.59 apply (zenon_L880_); trivial. % 15.41/15.59 apply (zenon_L322_); trivial. % 15.41/15.59 apply (zenon_L119_); trivial. % 15.41/15.59 apply (zenon_L161_); trivial. % 15.41/15.59 apply (zenon_L284_); trivial. % 15.41/15.59 (* end of lemma zenon_L938_ *) % 15.41/15.59 assert (zenon_L939_ : ((~((op (e0) (e0)) = (e3)))\/((op (e0) (e3)) = (e0))) -> ((~((op (e1) (e1)) = (e2)))\/((op (e1) (e2)) = (e1))) -> (~((op (e2) (e0)) = (op (e2) (e2)))) -> (((op (e1) (e0)) = (e2))\/(((op (e1) (e1)) = (e2))\/(((op (e1) (e2)) = (e2))\/((op (e1) (e3)) = (e2))))) -> (((op (e0) (e0)) = (e3))\/(((op (e1) (e0)) = (e3))\/(((op (e2) (e0)) = (e3))\/((op (e3) (e0)) = (e3))))) -> (~((op (e1) (e2)) = (op (e1) (e3)))) -> (((op (e1) (e1)) = (e0))\/(((op (e1) (e1)) = (e1))\/(((op (e1) (e1)) = (e2))\/((op (e1) (e1)) = (e3))))) -> ((op (e0) (e1)) = (e0)) -> (~((op (e0) (e1)) = (op (e1) (e1)))) -> ((~((op (e2) (e2)) = (e0)))\/((op (e2) (e0)) = (e2))) -> (~((op (e0) (e0)) = (e0))) -> (((op (e0) (e0)) = (e0))\/(((op (e0) (e0)) = (e1))\/(((op (e0) (e0)) = (e2))\/((op (e0) (e0)) = (e3))))) -> (~((op (e2) (e0)) = (op (e2) (e1)))) -> ((~((op (e2) (e2)) = (e2)))\/((op (e2) (e2)) = (e2))) -> (~((op (e2) (op (e2) (e2))) = (op (e2) (e2)))) -> (~((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 (e0) (e3)) = (op (e3) (e3)))) -> ((op (e3) (e3)) = (e3)) -> (((op (e0) (e0)) = (e3))\/(((op (e0) (e1)) = (e3))\/(((op (e0) (e2)) = (e3))\/((op (e0) (e3)) = (e3))))) -> ((~((op (e2) (e2)) = (e3)))\/((op (e2) (e3)) = (e2))) -> (~((op (e2) (e1)) = (op (e2) (e3)))) -> (((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) (e0)) = (e3))\/(((op (e2) (e1)) = (e3))\/(((op (e2) (e2)) = (e3))\/((op (e2) (e3)) = (e3))))) -> (~((op (e3) (op (e2) (e3))) = (op (e2) (e3)))) -> (~((e1) = (e3))) -> (~((e1) = (e2))) -> (((op (e1) (e3)) = (e0))\/(((op (e1) (e3)) = (e1))\/(((op (e1) (e3)) = (e2))\/((op (e1) (e3)) = (e3))))) -> (~((op (e1) (e3)) = (op (e3) (e3)))) -> (~((op (e0) (e3)) = (op (e1) (e3)))) -> (~((op (e1) (e3)) = (op (e2) (e3)))) -> (((op (e2) (e0)) = (e1))\/(((op (e2) (e1)) = (e1))\/(((op (e2) (e2)) = (e1))\/((op (e2) (e3)) = (e1))))) -> (~((op (e0) (e1)) = (op (e2) (e1)))) -> (~((e0) = (e1))) -> (~((op (e2) (e0)) = (op (e2) (e3)))) -> (((op (e0) (e3)) = (e0))\/(((op (e1) (e3)) = (e0))\/(((op (e2) (e3)) = (e0))\/((op (e3) (e3)) = (e0))))) -> (~((op (e3) (e1)) = (op (e3) (e3)))) -> (((op (e0) (e1)) = (e3))\/(((op (e1) (e1)) = (e3))\/(((op (e2) (e1)) = (e3))\/((op (e3) (e1)) = (e3))))) -> (~((e2) = (e3))) -> (~((e0) = (e2))) -> (~((op (e0) (e0)) = (e2))) -> (~((op (e3) (e0)) = (op (e3) (e3)))) -> ((~((op (e3) (e3)) = (e0)))\/((op (e3) (e0)) = (e3))) -> ((~((op (e2) (e2)) = (e1)))\/((op (e2) (e1)) = (e2))) -> ((~((op (e1) (e1)) = (e3)))\/((op (e1) (e3)) = (e1))) -> (~((op (e1) (e1)) = (op (e1) (e2)))) -> (((op (e0) (e0)) = (e1))\/(((op (e0) (e1)) = (e1))\/(((op (e0) (e2)) = (e1))\/((op (e0) (e3)) = (e1))))) -> (~((op (e1) (e1)) = (op (e2) (e1)))) -> (~((op (e0) (e3)) = (op (e2) (e3)))) -> (((op (e0) (e1)) = (e2))\/(((op (e1) (e1)) = (e2))\/(((op (e2) (e1)) = (e2))\/((op (e3) (e1)) = (e2))))) -> (~((op (e0) (e1)) = (op (e0) (e3)))) -> (~((op (e1) (e1)) = (op (e1) (e3)))) -> ((~((op (e1) (e1)) = (e1)))\/((op (e1) (e1)) = (e1))) -> False). % 15.41/15.59 do 0 intro. intros zenon_H236 zenon_H1d3 zenon_H17a zenon_H84 zenon_Hbe zenon_H1d0 zenon_H1b3 zenon_H49 zenon_H23 zenon_H1d4 zenon_H20 zenon_H12a zenon_H154 zenon_Haa zenon_H294 zenon_H4b zenon_H2d zenon_H28 zenon_H36 zenon_H42 zenon_H58 zenon_H1c3 zenon_H1e2 zenon_H8e zenon_H1f5 zenon_He6 zenon_H28a zenon_Ha3 zenon_Ha7 zenon_H25b zenon_H8b zenon_H80 zenon_H244 zenon_Hb7 zenon_Hde zenon_H9e zenon_Hce zenon_Hd3 zenon_H12d zenon_H199 zenon_H6a zenon_H5e zenon_H8f zenon_Hbb zenon_H10f zenon_H1e3 zenon_H1d2 zenon_H116 zenon_H44 zenon_Hb1 zenon_Hb4 zenon_H1a2 zenon_H1cd zenon_H11e zenon_H1d8. % 15.41/15.59 apply (zenon_or_s _ _ zenon_H236); [ zenon_intro zenon_H59 | zenon_intro zenon_Hca ]. % 15.41/15.59 apply (zenon_or_s _ _ zenon_H1d8); [ zenon_intro zenon_H1b4 | zenon_intro zenon_H21 ]. % 15.41/15.59 apply (zenon_or_s _ _ zenon_H1d3); [ zenon_intro zenon_Hd6 | zenon_intro zenon_H117 ]. % 15.41/15.59 apply (zenon_or_s _ _ zenon_H1d2); [ zenon_intro zenon_H182 | zenon_intro zenon_H11f ]. % 15.41/15.59 apply (zenon_L347_); trivial. % 15.41/15.59 apply (zenon_or_s _ _ zenon_H1d4); [ zenon_intro zenon_H2e | zenon_intro zenon_Hdd ]. % 15.41/15.59 apply (zenon_or_s _ _ zenon_H1e3); [ zenon_intro zenon_H52 | zenon_intro zenon_H156 ]. % 15.41/15.59 apply (zenon_L914_); trivial. % 15.41/15.59 apply (zenon_or_s _ _ zenon_H1c3); [ zenon_intro zenon_H30 | zenon_intro zenon_H124 ]. % 15.41/15.59 apply (zenon_or_s _ _ zenon_H10f); [ zenon_intro zenon_H3c | zenon_intro zenon_Hba ]. % 15.41/15.59 apply (zenon_L934_); trivial. % 15.41/15.59 apply (zenon_L43_); trivial. % 15.41/15.59 apply (zenon_L256_); trivial. % 15.41/15.59 apply (zenon_L937_); trivial. % 15.41/15.59 apply (zenon_or_s _ _ zenon_H1d2); [ zenon_intro zenon_H182 | zenon_intro zenon_H11f ]. % 15.41/15.59 apply (zenon_or_s _ _ zenon_H1d4); [ zenon_intro zenon_H2e | zenon_intro zenon_Hdd ]. % 15.41/15.59 apply (zenon_L915_); trivial. % 15.41/15.59 apply (zenon_or_s _ _ zenon_H1e3); [ zenon_intro zenon_H52 | zenon_intro zenon_H156 ]. % 15.41/15.59 apply (zenon_or_s _ _ zenon_Haa); [ zenon_intro zenon_H2f | zenon_intro zenon_H35 ]. % 15.41/15.59 apply (zenon_or_s _ _ zenon_H1c3); [ zenon_intro zenon_H30 | zenon_intro zenon_H124 ]. % 15.41/15.59 apply (zenon_or_s _ _ zenon_H8e); [ zenon_intro zenon_H92 | zenon_intro zenon_H91 ]. % 15.41/15.59 exact (zenon_H8f zenon_H92). % 15.41/15.59 apply (zenon_or_s _ _ zenon_H91); [ zenon_intro zenon_H5d | zenon_intro zenon_H93 ]. % 15.41/15.59 apply (zenon_L14_); trivial. % 15.41/15.59 apply (zenon_or_s _ _ zenon_H93); [ zenon_intro zenon_H63 | zenon_intro zenon_H81 ]. % 15.41/15.59 apply (zenon_L789_); trivial. % 15.41/15.59 apply (zenon_L386_); trivial. % 15.41/15.59 apply (zenon_L119_); trivial. % 15.41/15.59 apply (zenon_L161_); trivial. % 15.41/15.59 apply (zenon_L284_); trivial. % 15.41/15.59 apply (zenon_L237_); trivial. % 15.41/15.59 apply (zenon_or_s _ _ zenon_H1d3); [ zenon_intro zenon_Hd6 | zenon_intro zenon_H117 ]. % 15.41/15.59 apply (zenon_or_s _ _ zenon_H1d2); [ zenon_intro zenon_H182 | zenon_intro zenon_H11f ]. % 15.41/15.59 apply (zenon_or_s _ _ zenon_H1d4); [ zenon_intro zenon_H2e | zenon_intro zenon_Hdd ]. % 15.41/15.59 apply (zenon_L915_); trivial. % 15.41/15.59 apply (zenon_L938_); trivial. % 15.41/15.59 apply (zenon_L90_); trivial. % 15.41/15.59 apply (zenon_L86_); trivial. % 15.41/15.59 apply (zenon_L463_); trivial. % 15.41/15.59 (* end of lemma zenon_L939_ *) % 15.41/15.59 assert (zenon_L940_ : (~((op (e1) (op (e2) (e1))) = (op (e2) (e1)))) -> ((op (e1) (e0)) = (e0)) -> ((op (e2) (e1)) = (e0)) -> False). % 15.41/15.59 do 0 intro. intros zenon_H290 zenon_Had zenon_H14a. % 15.41/15.59 cut (((op (e1) (e0)) = (e0)) = ((op (e1) (op (e2) (e1))) = (op (e2) (e1)))). % 15.41/15.59 intro zenon_D_pnotp. % 15.41/15.59 apply zenon_H290. % 15.41/15.59 rewrite <- zenon_D_pnotp. % 15.41/15.59 exact zenon_Had. % 15.41/15.59 cut (((e0) = (op (e2) (e1)))); [idtac | apply NNPP; zenon_intro zenon_H155]. % 15.41/15.59 cut (((op (e1) (e0)) = (op (e1) (op (e2) (e1))))); [idtac | apply NNPP; zenon_intro zenon_H291]. % 15.41/15.59 congruence. % 15.41/15.59 elim (classic ((op (e1) (op (e2) (e1))) = (op (e1) (op (e2) (e1))))); [ zenon_intro zenon_H292 | zenon_intro zenon_H293 ]. % 15.41/15.59 cut (((op (e1) (op (e2) (e1))) = (op (e1) (op (e2) (e1)))) = ((op (e1) (e0)) = (op (e1) (op (e2) (e1))))). % 15.41/15.59 intro zenon_D_pnotp. % 15.41/15.59 apply zenon_H291. % 15.41/15.59 rewrite <- zenon_D_pnotp. % 15.41/15.59 exact zenon_H292. % 15.41/15.59 cut (((op (e1) (op (e2) (e1))) = (op (e1) (op (e2) (e1))))); [idtac | apply NNPP; zenon_intro zenon_H293]. % 15.41/15.59 cut (((op (e1) (op (e2) (e1))) = (op (e1) (e0)))); [idtac | apply NNPP; zenon_intro zenon_H28f]. % 15.41/15.59 congruence. % 15.41/15.59 apply (zenon_L782_); trivial. % 15.41/15.59 apply zenon_H293. apply refl_equal. % 15.41/15.59 apply zenon_H293. apply refl_equal. % 15.41/15.59 apply zenon_H155. apply sym_equal. exact zenon_H14a. % 15.41/15.59 (* end of lemma zenon_L940_ *) % 15.41/15.59 assert (zenon_L941_ : (((op (e0) (e0)) = (e3))\/(((op (e1) (e0)) = (e3))\/(((op (e2) (e0)) = (e3))\/((op (e3) (e0)) = (e3))))) -> (~((op (e0) (e0)) = (e3))) -> ((op (e2) (e3)) = (e2)) -> (~((e0) = (e2))) -> (~((op (e2) (e2)) = (e0))) -> (((op (e2) (e0)) = (e1))\/(((op (e2) (e1)) = (e1))\/(((op (e2) (e2)) = (e1))\/((op (e2) (e3)) = (e1))))) -> (~((e1) = (e3))) -> ((op (e1) (e0)) = (e1)) -> (~((op (e1) (op (e2) (e1))) = (op (e2) (e1)))) -> (~((op (e2) (e2)) = (e1))) -> (~((e1) = (e2))) -> (~((e0) = (e3))) -> (((op (e2) (e0)) = (e0))\/(((op (e2) (e1)) = (e0))\/(((op (e2) (e2)) = (e0))\/((op (e2) (e3)) = (e0))))) -> ((op (e3) (e3)) = (e3)) -> (~((op (e3) (e0)) = (op (e3) (e3)))) -> False). % 15.41/15.59 do 0 intro. intros zenon_Hbe zenon_H59 zenon_H124 zenon_H5e zenon_H2e zenon_Hb7 zenon_Ha3 zenon_Hd8 zenon_H290 zenon_H52 zenon_Ha7 zenon_H4b zenon_H1f5 zenon_H42 zenon_Hbb. % 15.41/15.59 apply (zenon_or_s _ _ zenon_Hbe); [ zenon_intro zenon_H5b | zenon_intro zenon_Hbf ]. % 15.41/15.59 exact (zenon_H59 zenon_H5b). % 15.41/15.59 apply (zenon_or_s _ _ zenon_Hbf); [ zenon_intro zenon_H69 | zenon_intro zenon_Hc0 ]. % 15.41/15.59 apply (zenon_L163_); trivial. % 15.41/15.59 apply (zenon_or_s _ _ zenon_Hc0); [ zenon_intro zenon_Haf | zenon_intro zenon_Hba ]. % 15.41/15.59 apply (zenon_L835_); trivial. % 15.41/15.59 apply (zenon_L43_); trivial. % 15.41/15.59 (* end of lemma zenon_L941_ *) % 15.41/15.59 assert (zenon_L942_ : (~((e0) = (e2))) -> (~((op (e2) (e2)) = (e2))) -> (~((op (e2) (e1)) = (op (e3) (e1)))) -> (((op (e2) (e0)) = (e3))\/(((op (e2) (e1)) = (e3))\/(((op (e2) (e2)) = (e3))\/((op (e2) (e3)) = (e3))))) -> (~((e2) = (e3))) -> (~((op (e0) (e1)) = (op (e2) (e1)))) -> (~((op (e2) (e2)) = (e3))) -> (~((op (e3) (op (e2) (e3))) = (op (e2) (e3)))) -> (((op (e2) (e0)) = (e2))\/(((op (e2) (e1)) = (e2))\/(((op (e2) (e2)) = (e2))\/((op (e2) (e3)) = (e2))))) -> (~((op (e2) (e2)) = (e0))) -> (~((op (e0) (e0)) = (e3))) -> (((op (e0) (e0)) = (e3))\/(((op (e0) (e1)) = (e3))\/(((op (e0) (e2)) = (e3))\/((op (e0) (e3)) = (e3))))) -> (((op (e0) (e3)) = (e0))\/(((op (e1) (e3)) = (e0))\/(((op (e2) (e3)) = (e0))\/((op (e3) (e3)) = (e0))))) -> (~((op (e0) (e2)) = (op (e0) (e3)))) -> ((op (e1) (e3)) = (e1)) -> (~((e0) = (e1))) -> (~((op (e3) (e3)) = (e0))) -> (~((op (e0) (e2)) = (op (e2) (e2)))) -> (~((op (e2) (e2)) = (e1))) -> (((op (e2) (e2)) = (e0))\/(((op (e2) (e2)) = (e1))\/(((op (e2) (e2)) = (e2))\/((op (e2) (e2)) = (e3))))) -> (((op (e2) (e0)) = (e0))\/(((op (e2) (e1)) = (e0))\/(((op (e2) (e2)) = (e0))\/((op (e2) (e3)) = (e0))))) -> (~((op (e1) (e3)) = (op (e2) (e3)))) -> ((op (e0) (e0)) = (e2)) -> (~((e1) = (e2))) -> (~((e1) = (e3))) -> (((op (e2) (e0)) = (e1))\/(((op (e2) (e1)) = (e1))\/(((op (e2) (e2)) = (e1))\/((op (e2) (e3)) = (e1))))) -> (~((op (e1) (e1)) = (e2))) -> (((op (e0) (e1)) = (e2))\/(((op (e1) (e1)) = (e2))\/(((op (e2) (e1)) = (e2))\/((op (e3) (e1)) = (e2))))) -> (~((e0) = (e3))) -> ((op (e0) (e2)) = (e0)) -> ((op (e3) (e3)) = (e3)) -> (~((op (e0) (e3)) = (op (e3) (e3)))) -> False). % 15.41/15.59 do 0 intro. intros zenon_H5e zenon_H2f zenon_H13c zenon_He6 zenon_H6a zenon_Hde zenon_H30 zenon_H28a zenon_H237 zenon_H2e zenon_H59 zenon_H58 zenon_Hd3 zenon_Hc9 zenon_H11f zenon_H9e zenon_H3c zenon_H28 zenon_H52 zenon_H2d zenon_H1f5 zenon_H244 zenon_H92 zenon_Ha7 zenon_Ha3 zenon_Hb7 zenon_Hd6 zenon_H1a2 zenon_H4b zenon_Hab zenon_H42 zenon_H36. % 15.41/15.59 apply (zenon_or_s _ _ zenon_H58); [ zenon_intro zenon_H5b | zenon_intro zenon_H5a ]. % 15.41/15.59 exact (zenon_H59 zenon_H5b). % 15.41/15.59 apply (zenon_or_s _ _ zenon_H5a); [ zenon_intro zenon_H4a | zenon_intro zenon_H5c ]. % 15.41/15.59 apply (zenon_L930_); trivial. % 15.41/15.59 apply (zenon_or_s _ _ zenon_H5c); [ zenon_intro zenon_H50 | zenon_intro zenon_H53 ]. % 15.41/15.59 apply (zenon_L48_); trivial. % 15.41/15.59 apply (zenon_L12_); trivial. % 15.41/15.59 (* end of lemma zenon_L942_ *) % 15.41/15.59 assert (zenon_L943_ : ((~((op (e1) (e1)) = (e1)))\/((op (e1) (e1)) = (e1))) -> (~((op (e1) (e0)) = (op (e1) (e1)))) -> ((~((op (e1) (e1)) = (e3)))\/((op (e1) (e3)) = (e1))) -> (~((op (e1) (e0)) = (op (e1) (e3)))) -> ((~((op (e2) (e2)) = (e1)))\/((op (e2) (e1)) = (e2))) -> (~((op (e2) (e1)) = (op (e2) (e3)))) -> ((~((op (e2) (e2)) = (e3)))\/((op (e2) (e3)) = (e2))) -> (((op (e2) (e0)) = (e0))\/(((op (e2) (e1)) = (e0))\/(((op (e2) (e2)) = (e0))\/((op (e2) (e3)) = (e0))))) -> (~((e0) = (e2))) -> (~((op (e1) (op (e2) (e1))) = (op (e2) (e1)))) -> (~((e1) = (e2))) -> (((op (e2) (e0)) = (e1))\/(((op (e2) (e1)) = (e1))\/(((op (e2) (e2)) = (e1))\/((op (e2) (e3)) = (e1))))) -> (~((e0) = (e3))) -> (~((op (e0) (e0)) = (e3))) -> (~((e1) = (e3))) -> ((op (e1) (e0)) = (e1)) -> (((op (e1) (e1)) = (e0))\/(((op (e1) (e1)) = (e1))\/(((op (e1) (e1)) = (e2))\/((op (e1) (e1)) = (e3))))) -> (((op (e2) (e2)) = (e0))\/(((op (e2) (e2)) = (e1))\/(((op (e2) (e2)) = (e2))\/((op (e2) (e2)) = (e3))))) -> (~((op (e3) (e0)) = (op (e3) (e3)))) -> ((op (e3) (e3)) = (e3)) -> (((op (e0) (e0)) = (e3))\/(((op (e1) (e0)) = (e3))\/(((op (e2) (e0)) = (e3))\/((op (e3) (e0)) = (e3))))) -> (~((op (e2) (op (e2) (e2))) = (op (e2) (e2)))) -> ((~((op (e2) (e2)) = (e2)))\/((op (e2) (e2)) = (e2))) -> (~((op (e2) (e0)) = (op (e2) (e3)))) -> (((op (e2) (e0)) = (e3))\/(((op (e2) (e1)) = (e3))\/(((op (e2) (e2)) = (e3))\/((op (e2) (e3)) = (e3))))) -> (~((op (e3) (op (e2) (e3))) = (op (e2) (e3)))) -> (~((op (e0) (e1)) = (op (e2) (e1)))) -> (~((e2) = (e3))) -> (((op (e1) (e0)) = (e3))\/(((op (e1) (e1)) = (e3))\/(((op (e1) (e2)) = (e3))\/((op (e1) (e3)) = (e3))))) -> (~((op (e1) (e3)) = (op (e3) (e3)))) -> (~((op (e0) (e2)) = (op (e1) (e2)))) -> (~((op (e0) (e3)) = (op (e3) (e3)))) -> (((op (e0) (e0)) = (e3))\/(((op (e0) (e1)) = (e3))\/(((op (e0) (e2)) = (e3))\/((op (e0) (e3)) = (e3))))) -> ((~((op (e2) (e2)) = (e0)))\/((op (e2) (e0)) = (e2))) -> (~((op (e1) (e0)) = (op (e1) (e2)))) -> ((~((op (e1) (e1)) = (e2)))\/((op (e1) (e2)) = (e1))) -> False). % 15.41/15.59 do 0 intro. intros zenon_H1d8 zenon_Hd7 zenon_H1d2 zenon_H1cf zenon_H1e3 zenon_H1e2 zenon_H1c3 zenon_H1f5 zenon_H5e zenon_H290 zenon_Ha7 zenon_Hb7 zenon_H4b zenon_H59 zenon_Ha3 zenon_Hd8 zenon_H1b3 zenon_H2d zenon_Hbb zenon_H42 zenon_Hbe zenon_H294 zenon_Haa zenon_Hce zenon_He6 zenon_H28a zenon_Hde zenon_H6a zenon_H90 zenon_H8b zenon_H87 zenon_H36 zenon_H58 zenon_H1d4 zenon_H166 zenon_H1d3. % 15.41/15.59 apply (zenon_or_s _ _ zenon_H1d8); [ zenon_intro zenon_H1b4 | zenon_intro zenon_H21 ]. % 15.41/15.59 apply (zenon_or_s _ _ zenon_H1d3); [ zenon_intro zenon_Hd6 | zenon_intro zenon_H117 ]. % 15.41/15.59 apply (zenon_or_s _ _ zenon_H1d2); [ zenon_intro zenon_H182 | zenon_intro zenon_H11f ]. % 15.41/15.59 apply (zenon_or_s _ _ zenon_H1d4); [ zenon_intro zenon_H2e | zenon_intro zenon_Hdd ]. % 15.41/15.59 apply (zenon_or_s _ _ zenon_H1e3); [ zenon_intro zenon_H52 | zenon_intro zenon_H156 ]. % 15.41/15.59 apply (zenon_or_s _ _ zenon_Haa); [ zenon_intro zenon_H2f | zenon_intro zenon_H35 ]. % 15.41/15.59 apply (zenon_or_s _ _ zenon_H1c3); [ zenon_intro zenon_H30 | zenon_intro zenon_H124 ]. % 15.41/15.59 apply (zenon_L241_); trivial. % 15.41/15.59 apply (zenon_L941_); trivial. % 15.41/15.59 apply (zenon_L794_); trivial. % 15.41/15.59 apply (zenon_or_s _ _ zenon_Haa); [ zenon_intro zenon_H2f | zenon_intro zenon_H35 ]. % 15.41/15.59 apply (zenon_L446_); trivial. % 15.41/15.59 apply (zenon_L794_); trivial. % 15.41/15.59 apply (zenon_L779_); trivial. % 15.41/15.59 apply (zenon_L224_); trivial. % 15.41/15.59 apply (zenon_L248_); trivial. % 15.41/15.59 apply (zenon_L61_); trivial. % 15.41/15.59 (* end of lemma zenon_L943_ *) % 15.41/15.59 assert (zenon_L944_ : (((op (e2) (e0)) = (e1))\/(((op (e2) (e1)) = (e1))\/(((op (e2) (e2)) = (e1))\/((op (e2) (e3)) = (e1))))) -> (~((e1) = (e3))) -> ((op (e2) (e0)) = (e3)) -> ((op (e2) (e1)) = (e2)) -> (~((e1) = (e2))) -> (~((op (e0) (e0)) = (e3))) -> ((op (e0) (e1)) = (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)) = (op (e2) (e3)))) -> ((op (e1) (e3)) = (e1)) -> False). % 15.41/15.59 do 0 intro. intros zenon_Hb7 zenon_Ha3 zenon_Haf zenon_H156 zenon_Ha7 zenon_H59 zenon_H4a zenon_H45 zenon_H20 zenon_H12a zenon_H244 zenon_H11f. % 15.41/15.59 apply (zenon_or_s _ _ zenon_Hb7); [ zenon_intro zenon_Hae | zenon_intro zenon_Hb8 ]. % 15.41/15.59 apply (zenon_L39_); trivial. % 15.41/15.59 apply (zenon_or_s _ _ zenon_Hb8); [ zenon_intro zenon_Hb2 | zenon_intro zenon_Hb9 ]. % 15.41/15.59 apply (zenon_L372_); trivial. % 15.41/15.59 apply (zenon_or_s _ _ zenon_Hb9); [ zenon_intro zenon_H2a | zenon_intro zenon_Hb5 ]. % 15.41/15.59 apply (zenon_or_s _ _ zenon_H12a); [ zenon_intro zenon_H1f | zenon_intro zenon_H12b ]. % 15.41/15.59 exact (zenon_H20 zenon_H1f). % 15.41/15.59 apply (zenon_or_s _ _ zenon_H12b); [ zenon_intro zenon_H47 | zenon_intro zenon_H12c ]. % 15.41/15.59 exact (zenon_H45 zenon_H47). % 15.41/15.59 apply (zenon_or_s _ _ zenon_H12c); [ zenon_intro zenon_H92 | zenon_intro zenon_H5b ]. % 15.41/15.59 apply (zenon_L46_); trivial. % 15.41/15.59 exact (zenon_H59 zenon_H5b). % 15.41/15.59 apply (zenon_L529_); trivial. % 15.41/15.59 (* end of lemma zenon_L944_ *) % 15.41/15.59 assert (zenon_L945_ : (((op (e2) (e0)) = (e0))\/(((op (e2) (e1)) = (e0))\/(((op (e2) (e2)) = (e0))\/((op (e2) (e3)) = (e0))))) -> (~((op (e3) (e3)) = (e0))) -> (~((op (e2) (e0)) = (op (e2) (e3)))) -> (~((e0) = (e1))) -> ((op (e0) (e3)) = (e2)) -> (((op (e0) (e3)) = (e0))\/(((op (e1) (e3)) = (e0))\/(((op (e2) (e3)) = (e0))\/((op (e3) (e3)) = (e0))))) -> (~((e0) = (e2))) -> (~((op (e2) (e2)) = (e0))) -> (((op (e2) (e0)) = (e1))\/(((op (e2) (e1)) = (e1))\/(((op (e2) (e2)) = (e1))\/((op (e2) (e3)) = (e1))))) -> (~((e1) = (e3))) -> ((op (e2) (e0)) = (e3)) -> ((op (e2) (e1)) = (e2)) -> (~((e1) = (e2))) -> ((op (e1) (e1)) = (e3)) -> (~((op (e1) (e3)) = (op (e2) (e3)))) -> ((op (e1) (e3)) = (e1)) -> False). % 15.41/15.59 do 0 intro. intros zenon_H1f5 zenon_H3c zenon_Hce zenon_H9e zenon_H81 zenon_Hd3 zenon_H5e zenon_H2e zenon_Hb7 zenon_Ha3 zenon_Haf zenon_H156 zenon_Ha7 zenon_H96 zenon_H244 zenon_H11f. % 15.41/15.59 apply (zenon_or_s _ _ zenon_H1f5); [ zenon_intro zenon_Hcf | zenon_intro zenon_H1f9 ]. % 15.41/15.59 apply (zenon_L373_); trivial. % 15.41/15.59 apply (zenon_or_s _ _ zenon_H1f9); [ zenon_intro zenon_H14a | zenon_intro zenon_H1fa ]. % 15.41/15.59 apply (zenon_L351_); trivial. % 15.41/15.59 apply (zenon_or_s _ _ zenon_H1fa); [ zenon_intro zenon_H32 | zenon_intro zenon_Hd0 ]. % 15.41/15.59 exact (zenon_H2e zenon_H32). % 15.41/15.59 apply (zenon_L613_); trivial. % 15.41/15.59 (* end of lemma zenon_L945_ *) % 15.41/15.59 assert (zenon_L946_ : (((op (e0) (e0)) = (e3))\/(((op (e1) (e0)) = (e3))\/(((op (e2) (e0)) = (e3))\/((op (e3) (e0)) = (e3))))) -> (~((op (e0) (e0)) = (e3))) -> (~((op (e1) (e3)) = (op (e3) (e3)))) -> ((op (e3) (e3)) = (e3)) -> (~((op (e0) (e2)) = (op (e1) (e2)))) -> ((op (e0) (e2)) = (e3)) -> (((op (e2) (e0)) = (e0))\/(((op (e2) (e1)) = (e0))\/(((op (e2) (e2)) = (e0))\/((op (e2) (e3)) = (e0))))) -> (~((op (e3) (e3)) = (e0))) -> (~((op (e2) (e0)) = (op (e2) (e3)))) -> (~((e0) = (e1))) -> ((op (e0) (e3)) = (e2)) -> (((op (e0) (e3)) = (e0))\/(((op (e1) (e3)) = (e0))\/(((op (e2) (e3)) = (e0))\/((op (e3) (e3)) = (e0))))) -> (~((e0) = (e2))) -> (~((op (e2) (e2)) = (e0))) -> (((op (e2) (e0)) = (e1))\/(((op (e2) (e1)) = (e1))\/(((op (e2) (e2)) = (e1))\/((op (e2) (e3)) = (e1))))) -> ((op (e2) (e1)) = (e2)) -> (~((e1) = (e2))) -> (~((op (e1) (e3)) = (op (e2) (e3)))) -> ((op (e1) (e3)) = (e1)) -> ((op (e1) (e0)) = (e2)) -> (~((e2) = (e3))) -> (((op (e1) (e0)) = (e3))\/(((op (e1) (e1)) = (e3))\/(((op (e1) (e2)) = (e3))\/((op (e1) (e3)) = (e3))))) -> (~((e1) = (e3))) -> ((op (e3) (e0)) = (e1)) -> False). % 15.41/15.59 do 0 intro. intros zenon_Hbe zenon_H59 zenon_H8b zenon_H42 zenon_H87 zenon_H50 zenon_H1f5 zenon_H3c zenon_Hce zenon_H9e zenon_H81 zenon_Hd3 zenon_H5e zenon_H2e zenon_Hb7 zenon_H156 zenon_Ha7 zenon_H244 zenon_H11f zenon_H68 zenon_H6a zenon_H90 zenon_Ha3 zenon_Hee. % 15.41/15.59 apply (zenon_or_s _ _ zenon_Hbe); [ zenon_intro zenon_H5b | zenon_intro zenon_Hbf ]. % 15.41/15.59 exact (zenon_H59 zenon_H5b). % 15.41/15.59 apply (zenon_or_s _ _ zenon_Hbf); [ zenon_intro zenon_H69 | zenon_intro zenon_Hc0 ]. % 15.41/15.59 apply (zenon_L17_); trivial. % 15.41/15.59 apply (zenon_or_s _ _ zenon_Hc0); [ zenon_intro zenon_Haf | zenon_intro zenon_Hba ]. % 15.41/15.59 apply (zenon_or_s _ _ zenon_H90); [ zenon_intro zenon_H69 | zenon_intro zenon_H94 ]. % 15.41/15.59 apply (zenon_L17_); trivial. % 15.41/15.59 apply (zenon_or_s _ _ zenon_H94); [ zenon_intro zenon_H96 | zenon_intro zenon_H95 ]. % 15.41/15.59 apply (zenon_L945_); trivial. % 15.41/15.59 apply (zenon_or_s _ _ zenon_H95); [ zenon_intro zenon_H88 | zenon_intro zenon_H8a ]. % 15.41/15.59 apply (zenon_L24_); trivial. % 15.41/15.59 apply (zenon_L25_); trivial. % 15.41/15.59 apply (zenon_L79_); trivial. % 15.41/15.59 (* end of lemma zenon_L946_ *) % 15.41/15.59 assert (zenon_L947_ : (((op (e0) (e0)) = (e1))\/(((op (e1) (e0)) = (e1))\/(((op (e2) (e0)) = (e1))\/((op (e3) (e0)) = (e1))))) -> ((~((op (e1) (e1)) = (e2)))\/((op (e1) (e2)) = (e1))) -> (~((op (e1) (e0)) = (op (e1) (e2)))) -> ((~((op (e2) (e2)) = (e0)))\/((op (e2) (e0)) = (e2))) -> ((~((op (e2) (e2)) = (e2)))\/((op (e2) (e2)) = (e2))) -> (~((op (e2) (op (e2) (e2))) = (op (e2) (e2)))) -> (~((op (e3) (e0)) = (op (e3) (e3)))) -> (((op (e2) (e2)) = (e0))\/(((op (e2) (e2)) = (e1))\/(((op (e2) (e2)) = (e2))\/((op (e2) (e2)) = (e3))))) -> (((op (e1) (e1)) = (e0))\/(((op (e1) (e1)) = (e1))\/(((op (e1) (e1)) = (e2))\/((op (e1) (e1)) = (e3))))) -> (~((op (e1) (op (e2) (e1))) = (op (e2) (e1)))) -> ((~((op (e2) (e2)) = (e3)))\/((op (e2) (e3)) = (e2))) -> (~((op (e2) (e1)) = (op (e2) (e3)))) -> ((~((op (e2) (e2)) = (e1)))\/((op (e2) (e1)) = (e2))) -> (~((op (e1) (e0)) = (op (e1) (e3)))) -> ((~((op (e1) (e1)) = (e3)))\/((op (e1) (e3)) = (e1))) -> (~((op (e1) (e0)) = (op (e1) (e1)))) -> ((~((op (e1) (e1)) = (e1)))\/((op (e1) (e1)) = (e1))) -> (((op (e0) (e0)) = (e2))\/(((op (e0) (e1)) = (e2))\/(((op (e0) (e2)) = (e2))\/((op (e0) (e3)) = (e2))))) -> (~((op (e3) (e3)) = (e2))) -> (~((op (e0) (e2)) = (op (e3) (e2)))) -> (~((op (e2) (e1)) = (op (e3) (e1)))) -> (((op (e3) (e0)) = (e2))\/(((op (e3) (e1)) = (e2))\/(((op (e3) (e2)) = (e2))\/((op (e3) (e3)) = (e2))))) -> (((op (e0) (e0)) = (e2))\/(((op (e1) (e0)) = (e2))\/(((op (e2) (e0)) = (e2))\/((op (e3) (e0)) = (e2))))) -> (((op (e1) (e3)) = (e0))\/(((op (e1) (e3)) = (e1))\/(((op (e1) (e3)) = (e2))\/((op (e1) (e3)) = (e3))))) -> (~((op (e0) (e3)) = (op (e1) (e3)))) -> (((op (e0) (e0)) = (e3))\/(((op (e1) (e0)) = (e3))\/(((op (e2) (e0)) = (e3))\/((op (e3) (e0)) = (e3))))) -> (~((op (e1) (e3)) = (op (e3) (e3)))) -> (~((op (e0) (e2)) = (op (e1) (e2)))) -> (((op (e2) (e0)) = (e0))\/(((op (e2) (e1)) = (e0))\/(((op (e2) (e2)) = (e0))\/((op (e2) (e3)) = (e0))))) -> (~((op (e3) (e3)) = (e0))) -> (~((op (e2) (e0)) = (op (e2) (e3)))) -> (~((e0) = (e1))) -> (((op (e0) (e3)) = (e0))\/(((op (e1) (e3)) = (e0))\/(((op (e2) (e3)) = (e0))\/((op (e3) (e3)) = (e0))))) -> (~((e0) = (e2))) -> (~((op (e2) (e2)) = (e0))) -> (((op (e2) (e0)) = (e1))\/(((op (e2) (e1)) = (e1))\/(((op (e2) (e2)) = (e1))\/((op (e2) (e3)) = (e1))))) -> ((op (e2) (e1)) = (e2)) -> (~((op (e1) (e3)) = (op (e2) (e3)))) -> ((op (e1) (e3)) = (e1)) -> (((op (e1) (e0)) = (e3))\/(((op (e1) (e1)) = (e3))\/(((op (e1) (e2)) = (e3))\/((op (e1) (e3)) = (e3))))) -> (~((e1) = (e3))) -> (((op (e0) (e0)) = (e0))\/(((op (e0) (e0)) = (e1))\/(((op (e0) (e0)) = (e2))\/((op (e0) (e0)) = (e3))))) -> (~((op (e0) (e0)) = (e0))) -> (~((op (e0) (e0)) = (e1))) -> (~((op (e0) (e3)) = (op (e3) (e3)))) -> ((op (e3) (e3)) = (e3)) -> ((op (e0) (e2)) = (e0)) -> (~((e0) = (e3))) -> (((op (e2) (e0)) = (e3))\/(((op (e2) (e1)) = (e3))\/(((op (e2) (e2)) = (e3))\/((op (e2) (e3)) = (e3))))) -> (~((e2) = (e3))) -> (~((op (e0) (e1)) = (op (e2) (e1)))) -> (~((op (e2) (e2)) = (e3))) -> (~((op (e3) (op (e2) (e3))) = (op (e2) (e3)))) -> (~((op (e0) (e0)) = (e3))) -> (((op (e0) (e0)) = (e3))\/(((op (e0) (e1)) = (e3))\/(((op (e0) (e2)) = (e3))\/((op (e0) (e3)) = (e3))))) -> (~((e1) = (e2))) -> False). % 15.41/15.59 do 0 intro. intros zenon_Hf1 zenon_H1d3 zenon_H166 zenon_H1d4 zenon_Haa zenon_H294 zenon_Hbb zenon_H2d zenon_H1b3 zenon_H290 zenon_H1c3 zenon_H1e2 zenon_H1e3 zenon_H1cf zenon_H1d2 zenon_Hd7 zenon_H1d8 zenon_H8e zenon_H3d zenon_H140 zenon_H13c zenon_H1df zenon_Heb zenon_H25b zenon_H80 zenon_Hbe zenon_H8b zenon_H87 zenon_H1f5 zenon_H3c zenon_Hce zenon_H9e zenon_Hd3 zenon_H5e zenon_H2e zenon_Hb7 zenon_H156 zenon_H244 zenon_H11f zenon_H90 zenon_Ha3 zenon_H12a zenon_H20 zenon_H45 zenon_H36 zenon_H42 zenon_Hab zenon_H4b zenon_He6 zenon_H6a zenon_Hde zenon_H30 zenon_H28a zenon_H59 zenon_H58 zenon_Ha7. % 15.41/15.59 apply (zenon_or_s _ _ zenon_Hf1); [ zenon_intro zenon_H47 | zenon_intro zenon_Hf4 ]. % 15.41/15.59 exact (zenon_H45 zenon_H47). % 15.41/15.59 apply (zenon_or_s _ _ zenon_Hf4); [ zenon_intro zenon_Hd8 | zenon_intro zenon_Hf5 ]. % 15.41/15.59 apply (zenon_L943_); trivial. % 15.41/15.59 apply (zenon_or_s _ _ zenon_Hf5); [ zenon_intro zenon_Hae | zenon_intro zenon_Hee ]. % 15.41/15.59 apply (zenon_L796_); trivial. % 15.41/15.59 apply (zenon_or_s _ _ zenon_H8e); [ zenon_intro zenon_H92 | zenon_intro zenon_H91 ]. % 15.41/15.59 apply (zenon_L923_); trivial. % 15.41/15.59 apply (zenon_or_s _ _ zenon_H91); [ zenon_intro zenon_H5d | zenon_intro zenon_H93 ]. % 15.41/15.59 apply (zenon_L251_); trivial. % 15.41/15.59 apply (zenon_or_s _ _ zenon_H93); [ zenon_intro zenon_H63 | zenon_intro zenon_H81 ]. % 15.41/15.59 apply (zenon_L254_); trivial. % 15.41/15.59 apply (zenon_or_s _ _ zenon_Heb); [ zenon_intro zenon_H92 | zenon_intro zenon_Hec ]. % 15.41/15.59 apply (zenon_or_s _ _ zenon_H58); [ zenon_intro zenon_H5b | zenon_intro zenon_H5a ]. % 15.41/15.59 exact (zenon_H59 zenon_H5b). % 15.41/15.59 apply (zenon_or_s _ _ zenon_H5a); [ zenon_intro zenon_H4a | zenon_intro zenon_H5c ]. % 15.41/15.59 apply (zenon_or_s _ _ zenon_H1f5); [ zenon_intro zenon_Hcf | zenon_intro zenon_H1f9 ]. % 15.41/15.59 apply (zenon_L373_); trivial. % 15.41/15.59 apply (zenon_or_s _ _ zenon_H1f9); [ zenon_intro zenon_H14a | zenon_intro zenon_H1fa ]. % 15.41/15.59 apply (zenon_L351_); trivial. % 15.41/15.59 apply (zenon_or_s _ _ zenon_H1fa); [ zenon_intro zenon_H32 | zenon_intro zenon_Hd0 ]. % 15.41/15.59 exact (zenon_H2e zenon_H32). % 15.41/15.59 apply (zenon_or_s _ _ zenon_Hb7); [ zenon_intro zenon_Hae | zenon_intro zenon_Hb8 ]. % 15.41/15.59 apply (zenon_L787_); trivial. % 15.41/15.59 apply (zenon_or_s _ _ zenon_Hb8); [ zenon_intro zenon_Hb2 | zenon_intro zenon_Hb9 ]. % 15.41/15.59 apply (zenon_L372_); trivial. % 15.41/15.59 apply (zenon_or_s _ _ zenon_Hb9); [ zenon_intro zenon_H2a | zenon_intro zenon_Hb5 ]. % 15.41/15.59 apply (zenon_L46_); trivial. % 15.41/15.59 apply (zenon_L933_); trivial. % 15.41/15.59 apply (zenon_or_s _ _ zenon_H5c); [ zenon_intro zenon_H50 | zenon_intro zenon_H53 ]. % 15.41/15.59 apply (zenon_L48_); trivial. % 15.41/15.59 apply (zenon_L12_); trivial. % 15.41/15.59 apply (zenon_or_s _ _ zenon_Hec); [ zenon_intro zenon_H68 | zenon_intro zenon_Hed ]. % 15.41/15.59 apply (zenon_or_s _ _ zenon_H58); [ zenon_intro zenon_H5b | zenon_intro zenon_H5a ]. % 15.41/15.59 exact (zenon_H59 zenon_H5b). % 15.41/15.59 apply (zenon_or_s _ _ zenon_H5a); [ zenon_intro zenon_H4a | zenon_intro zenon_H5c ]. % 15.41/15.59 apply (zenon_or_s _ _ zenon_Hbe); [ zenon_intro zenon_H5b | zenon_intro zenon_Hbf ]. % 15.41/15.59 exact (zenon_H59 zenon_H5b). % 15.41/15.59 apply (zenon_or_s _ _ zenon_Hbf); [ zenon_intro zenon_H69 | zenon_intro zenon_Hc0 ]. % 15.41/15.59 apply (zenon_L17_); trivial. % 15.41/15.59 apply (zenon_or_s _ _ zenon_Hc0); [ zenon_intro zenon_Haf | zenon_intro zenon_Hba ]. % 15.41/15.59 apply (zenon_L944_); trivial. % 15.41/15.59 apply (zenon_L79_); trivial. % 15.41/15.59 apply (zenon_or_s _ _ zenon_H5c); [ zenon_intro zenon_H50 | zenon_intro zenon_H53 ]. % 15.41/15.59 apply (zenon_L946_); trivial. % 15.41/15.59 apply (zenon_L128_); trivial. % 15.41/15.59 apply (zenon_or_s _ _ zenon_Hed); [ zenon_intro zenon_Hdd | zenon_intro zenon_He9 ]. % 15.41/15.59 apply (zenon_L920_); trivial. % 15.41/15.59 apply (zenon_L122_); trivial. % 15.41/15.59 (* end of lemma zenon_L947_ *) % 15.41/15.59 assert (zenon_L948_ : ((~((op (e3) (e3)) = (e2)))\/((op (e3) (e2)) = (e3))) -> (~((op (e3) (e2)) = (op (e3) (e3)))) -> (~((op (e0) (e0)) = (e1))) -> ((~((op (e1) (e1)) = (e1)))\/((op (e1) (e1)) = (e1))) -> (~((op (e1) (e0)) = (op (e1) (e1)))) -> ((~((op (e1) (e1)) = (e3)))\/((op (e1) (e3)) = (e1))) -> (~((op (e1) (e0)) = (op (e1) (e3)))) -> ((~((op (e2) (e2)) = (e1)))\/((op (e2) (e1)) = (e2))) -> (~((op (e2) (e1)) = (op (e2) (e3)))) -> ((~((op (e2) (e2)) = (e3)))\/((op (e2) (e3)) = (e2))) -> (((op (e2) (e0)) = (e0))\/(((op (e2) (e1)) = (e0))\/(((op (e2) (e2)) = (e0))\/((op (e2) (e3)) = (e0))))) -> (~((e0) = (e2))) -> (~((op (e1) (op (e2) (e1))) = (op (e2) (e1)))) -> (~((e1) = (e2))) -> (((op (e2) (e0)) = (e1))\/(((op (e2) (e1)) = (e1))\/(((op (e2) (e2)) = (e1))\/((op (e2) (e3)) = (e1))))) -> (~((e0) = (e3))) -> (~((op (e0) (e0)) = (e3))) -> (~((e1) = (e3))) -> (((op (e1) (e1)) = (e0))\/(((op (e1) (e1)) = (e1))\/(((op (e1) (e1)) = (e2))\/((op (e1) (e1)) = (e3))))) -> (((op (e2) (e2)) = (e0))\/(((op (e2) (e2)) = (e1))\/(((op (e2) (e2)) = (e2))\/((op (e2) (e2)) = (e3))))) -> (~((op (e3) (e0)) = (op (e3) (e3)))) -> ((op (e3) (e3)) = (e3)) -> (((op (e0) (e0)) = (e3))\/(((op (e1) (e0)) = (e3))\/(((op (e2) (e0)) = (e3))\/((op (e3) (e0)) = (e3))))) -> (~((op (e2) (op (e2) (e2))) = (op (e2) (e2)))) -> ((~((op (e2) (e2)) = (e2)))\/((op (e2) (e2)) = (e2))) -> (~((op (e2) (e0)) = (op (e2) (e3)))) -> (((op (e2) (e0)) = (e3))\/(((op (e2) (e1)) = (e3))\/(((op (e2) (e2)) = (e3))\/((op (e2) (e3)) = (e3))))) -> (~((op (e3) (op (e2) (e3))) = (op (e2) (e3)))) -> (~((op (e0) (e1)) = (op (e2) (e1)))) -> (~((e2) = (e3))) -> (((op (e1) (e0)) = (e3))\/(((op (e1) (e1)) = (e3))\/(((op (e1) (e2)) = (e3))\/((op (e1) (e3)) = (e3))))) -> (~((op (e1) (e3)) = (op (e3) (e3)))) -> (~((op (e0) (e2)) = (op (e1) (e2)))) -> (~((op (e0) (e3)) = (op (e3) (e3)))) -> (((op (e0) (e0)) = (e3))\/(((op (e0) (e1)) = (e3))\/(((op (e0) (e2)) = (e3))\/((op (e0) (e3)) = (e3))))) -> ((~((op (e2) (e2)) = (e0)))\/((op (e2) (e0)) = (e2))) -> (~((op (e1) (e0)) = (op (e1) (e2)))) -> ((~((op (e1) (e1)) = (e2)))\/((op (e1) (e2)) = (e1))) -> (~((op (e2) (e2)) = (e3))) -> ((op (e2) (e1)) = (e2)) -> (((op (e0) (e0)) = (e2))\/(((op (e0) (e1)) = (e2))\/(((op (e0) (e2)) = (e2))\/((op (e0) (e3)) = (e2))))) -> (((op (e0) (e3)) = (e0))\/(((op (e1) (e3)) = (e0))\/(((op (e2) (e3)) = (e0))\/((op (e3) (e3)) = (e0))))) -> (~((op (e3) (e3)) = (e0))) -> (~((e0) = (e1))) -> (~((op (e2) (e2)) = (e0))) -> (~((op (e0) (e3)) = (op (e1) (e3)))) -> (((op (e1) (e3)) = (e0))\/(((op (e1) (e3)) = (e1))\/(((op (e1) (e3)) = (e2))\/((op (e1) (e3)) = (e3))))) -> (~((op (e0) (e0)) = (e0))) -> (((op (e0) (e0)) = (e0))\/(((op (e0) (e0)) = (e1))\/(((op (e0) (e0)) = (e2))\/((op (e0) (e0)) = (e3))))) -> (((op (e0) (e0)) = (e2))\/(((op (e1) (e0)) = (e2))\/(((op (e2) (e0)) = (e2))\/((op (e3) (e0)) = (e2))))) -> (~((op (e2) (e1)) = (op (e3) (e1)))) -> (~((op (e0) (e2)) = (op (e3) (e2)))) -> (((op (e3) (e0)) = (e2))\/(((op (e3) (e1)) = (e2))\/(((op (e3) (e2)) = (e2))\/((op (e3) (e3)) = (e2))))) -> ((op (e1) (e3)) = (e1)) -> (~((op (e1) (e3)) = (op (e2) (e3)))) -> ((op (e0) (e2)) = (e0)) -> (((op (e0) (e0)) = (e1))\/(((op (e1) (e0)) = (e1))\/(((op (e2) (e0)) = (e1))\/((op (e3) (e0)) = (e1))))) -> False). % 15.41/15.59 do 0 intro. intros zenon_H10e zenon_H173 zenon_H45 zenon_H1d8 zenon_Hd7 zenon_H1d2 zenon_H1cf zenon_H1e3 zenon_H1e2 zenon_H1c3 zenon_H1f5 zenon_H5e zenon_H290 zenon_Ha7 zenon_Hb7 zenon_H4b zenon_H59 zenon_Ha3 zenon_H1b3 zenon_H2d zenon_Hbb zenon_H42 zenon_Hbe zenon_H294 zenon_Haa zenon_Hce zenon_He6 zenon_H28a zenon_Hde zenon_H6a zenon_H90 zenon_H8b zenon_H87 zenon_H36 zenon_H58 zenon_H1d4 zenon_H166 zenon_H1d3 zenon_H30 zenon_H156 zenon_H8e zenon_Hd3 zenon_H3c zenon_H9e zenon_H2e zenon_H80 zenon_H25b zenon_H20 zenon_H12a zenon_Heb zenon_H13c zenon_H140 zenon_H1df zenon_H11f zenon_H244 zenon_Hab zenon_Hf1. % 15.41/15.59 apply (zenon_or_s _ _ zenon_H10e); [ zenon_intro zenon_H3d | zenon_intro zenon_H106 ]. % 15.41/15.59 apply (zenon_L947_); trivial. % 15.41/15.59 apply (zenon_L153_); trivial. % 15.41/15.59 (* end of lemma zenon_L948_ *) % 15.41/15.59 assert (zenon_L949_ : (((op (e2) (e0)) = (e2))\/(((op (e2) (e1)) = (e2))\/(((op (e2) (e2)) = (e2))\/((op (e2) (e3)) = (e2))))) -> ((op (e0) (e2)) = (e2)) -> (((op (e0) (e0)) = (e1))\/(((op (e1) (e0)) = (e1))\/(((op (e2) (e0)) = (e1))\/((op (e3) (e0)) = (e1))))) -> (~((op (e1) (e3)) = (op (e2) (e3)))) -> (((op (e3) (e0)) = (e2))\/(((op (e3) (e1)) = (e2))\/(((op (e3) (e2)) = (e2))\/((op (e3) (e3)) = (e2))))) -> (~((op (e0) (e2)) = (op (e3) (e2)))) -> (~((op (e2) (e1)) = (op (e3) (e1)))) -> (((op (e0) (e0)) = (e2))\/(((op (e1) (e0)) = (e2))\/(((op (e2) (e0)) = (e2))\/((op (e3) (e0)) = (e2))))) -> (((op (e0) (e0)) = (e0))\/(((op (e0) (e0)) = (e1))\/(((op (e0) (e0)) = (e2))\/((op (e0) (e0)) = (e3))))) -> (~((op (e0) (e0)) = (e0))) -> (((op (e1) (e3)) = (e0))\/(((op (e1) (e3)) = (e1))\/(((op (e1) (e3)) = (e2))\/((op (e1) (e3)) = (e3))))) -> (~((op (e0) (e3)) = (op (e1) (e3)))) -> (~((op (e2) (e2)) = (e0))) -> (((op (e0) (e0)) = (e2))\/(((op (e0) (e1)) = (e2))\/(((op (e0) (e2)) = (e2))\/((op (e0) (e3)) = (e2))))) -> (~((op (e2) (e2)) = (e3))) -> ((~((op (e1) (e1)) = (e2)))\/((op (e1) (e2)) = (e1))) -> (~((op (e1) (e0)) = (op (e1) (e2)))) -> ((~((op (e2) (e2)) = (e0)))\/((op (e2) (e0)) = (e2))) -> (((op (e0) (e0)) = (e3))\/(((op (e0) (e1)) = (e3))\/(((op (e0) (e2)) = (e3))\/((op (e0) (e3)) = (e3))))) -> (~((op (e0) (e3)) = (op (e3) (e3)))) -> (~((op (e0) (e2)) = (op (e1) (e2)))) -> (~((op (e1) (e3)) = (op (e3) (e3)))) -> (((op (e1) (e0)) = (e3))\/(((op (e1) (e1)) = (e3))\/(((op (e1) (e2)) = (e3))\/((op (e1) (e3)) = (e3))))) -> (~((e2) = (e3))) -> (~((op (e0) (e1)) = (op (e2) (e1)))) -> (~((op (e3) (op (e2) (e3))) = (op (e2) (e3)))) -> (((op (e2) (e0)) = (e3))\/(((op (e2) (e1)) = (e3))\/(((op (e2) (e2)) = (e3))\/((op (e2) (e3)) = (e3))))) -> (~((op (e2) (e0)) = (op (e2) (e3)))) -> ((~((op (e2) (e2)) = (e2)))\/((op (e2) (e2)) = (e2))) -> (~((op (e2) (op (e2) (e2))) = (op (e2) (e2)))) -> (((op (e0) (e0)) = (e3))\/(((op (e1) (e0)) = (e3))\/(((op (e2) (e0)) = (e3))\/((op (e3) (e0)) = (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 (e1) (e1)) = (e0))\/(((op (e1) (e1)) = (e1))\/(((op (e1) (e1)) = (e2))\/((op (e1) (e1)) = (e3))))) -> (~((e1) = (e3))) -> (~((op (e0) (e0)) = (e3))) -> (~((e0) = (e3))) -> (((op (e2) (e0)) = (e1))\/(((op (e2) (e1)) = (e1))\/(((op (e2) (e2)) = (e1))\/((op (e2) (e3)) = (e1))))) -> (~((e1) = (e2))) -> (~((op (e1) (op (e2) (e1))) = (op (e2) (e1)))) -> (((op (e2) (e0)) = (e0))\/(((op (e2) (e1)) = (e0))\/(((op (e2) (e2)) = (e0))\/((op (e2) (e3)) = (e0))))) -> ((~((op (e2) (e2)) = (e3)))\/((op (e2) (e3)) = (e2))) -> (~((op (e2) (e1)) = (op (e2) (e3)))) -> ((~((op (e2) (e2)) = (e1)))\/((op (e2) (e1)) = (e2))) -> (~((op (e1) (e0)) = (op (e1) (e3)))) -> ((~((op (e1) (e1)) = (e3)))\/((op (e1) (e3)) = (e1))) -> (~((op (e1) (e0)) = (op (e1) (e1)))) -> ((~((op (e1) (e1)) = (e1)))\/((op (e1) (e1)) = (e1))) -> (~((op (e0) (e0)) = (e1))) -> (~((op (e3) (e2)) = (op (e3) (e3)))) -> ((~((op (e3) (e3)) = (e2)))\/((op (e3) (e2)) = (e3))) -> (~((op (e2) (e2)) = (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 (e0) (e3)))) -> ((op (e1) (e3)) = (e1)) -> (~((e0) = (e1))) -> (~((e0) = (e2))) -> (~((op (e3) (e3)) = (e0))) -> False). % 15.41/15.59 do 0 intro. intros zenon_H237 zenon_H63 zenon_Hf1 zenon_H244 zenon_H1df zenon_H140 zenon_H13c zenon_Heb zenon_H12a zenon_H20 zenon_H25b zenon_H80 zenon_H2e zenon_H8e zenon_H30 zenon_H1d3 zenon_H166 zenon_H1d4 zenon_H58 zenon_H36 zenon_H87 zenon_H8b zenon_H90 zenon_H6a zenon_Hde zenon_H28a zenon_He6 zenon_Hce zenon_Haa zenon_H294 zenon_Hbe zenon_H42 zenon_Hbb zenon_H2d zenon_H1b3 zenon_Ha3 zenon_H59 zenon_H4b zenon_Hb7 zenon_Ha7 zenon_H290 zenon_H1f5 zenon_H1c3 zenon_H1e2 zenon_H1e3 zenon_H1cf zenon_H1d2 zenon_Hd7 zenon_H1d8 zenon_H45 zenon_H173 zenon_H10e zenon_H2f zenon_Hd3 zenon_Hab zenon_Hc9 zenon_H11f zenon_H9e zenon_H5e zenon_H3c. % 15.41/15.59 apply (zenon_or_s _ _ zenon_H237); [ zenon_intro zenon_Hdd | zenon_intro zenon_H238 ]. % 15.41/15.59 apply (zenon_L789_); trivial. % 15.41/15.59 apply (zenon_or_s _ _ zenon_H238); [ zenon_intro zenon_H156 | zenon_intro zenon_H239 ]. % 15.41/15.59 apply (zenon_L948_); trivial. % 15.41/15.59 apply (zenon_or_s _ _ zenon_H239); [ zenon_intro zenon_H35 | zenon_intro zenon_H124 ]. % 15.41/15.59 exact (zenon_H2f zenon_H35). % 15.41/15.59 apply (zenon_L711_); trivial. % 15.41/15.59 (* end of lemma zenon_L949_ *) % 15.41/15.59 assert (zenon_L950_ : (((op (e2) (e0)) = (e2))\/(((op (e2) (e1)) = (e2))\/(((op (e2) (e2)) = (e2))\/((op (e2) (e3)) = (e2))))) -> (~((op (e0) (e2)) = (op (e0) (e3)))) -> (~((e0) = (e1))) -> (~((e0) = (e2))) -> (((op (e0) (e3)) = (e0))\/(((op (e1) (e3)) = (e0))\/(((op (e2) (e3)) = (e0))\/((op (e3) (e3)) = (e0))))) -> (~((e2) = (e3))) -> (~((e0) = (e3))) -> ((op (e0) (e2)) = (e0)) -> (~((op (e1) (e1)) = (e2))) -> (~((e1) = (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)) = (e0))\/(((op (e2) (e1)) = (e0))\/(((op (e2) (e2)) = (e0))\/((op (e2) (e3)) = (e0))))) -> (~((op (e2) (e1)) = (op (e3) (e1)))) -> (((op (e0) (e1)) = (e2))\/(((op (e1) (e1)) = (e2))\/(((op (e2) (e1)) = (e2))\/((op (e3) (e1)) = (e2))))) -> (((op (e0) (e0)) = (e1))\/(((op (e1) (e0)) = (e1))\/(((op (e2) (e0)) = (e1))\/((op (e3) (e0)) = (e1))))) -> (((op (e3) (e0)) = (e2))\/(((op (e3) (e1)) = (e2))\/(((op (e3) (e2)) = (e2))\/((op (e3) (e3)) = (e2))))) -> (~((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)) = (e0))\/(((op (e0) (e0)) = (e1))\/(((op (e0) (e0)) = (e2))\/((op (e0) (e0)) = (e3))))) -> (~((op (e0) (e0)) = (e0))) -> (((op (e1) (e3)) = (e0))\/(((op (e1) (e3)) = (e1))\/(((op (e1) (e3)) = (e2))\/((op (e1) (e3)) = (e3))))) -> (~((op (e0) (e3)) = (op (e1) (e3)))) -> (((op (e0) (e0)) = (e2))\/(((op (e0) (e1)) = (e2))\/(((op (e0) (e2)) = (e2))\/((op (e0) (e3)) = (e2))))) -> ((~((op (e1) (e1)) = (e2)))\/((op (e1) (e2)) = (e1))) -> (~((op (e1) (e0)) = (op (e1) (e2)))) -> ((~((op (e2) (e2)) = (e0)))\/((op (e2) (e0)) = (e2))) -> (~((op (e0) (e2)) = (op (e1) (e2)))) -> (~((op (e1) (e3)) = (op (e3) (e3)))) -> (((op (e1) (e0)) = (e3))\/(((op (e1) (e1)) = (e3))\/(((op (e1) (e2)) = (e3))\/((op (e1) (e3)) = (e3))))) -> (~((op (e2) (e0)) = (op (e2) (e3)))) -> ((~((op (e2) (e2)) = (e2)))\/((op (e2) (e2)) = (e2))) -> (~((op (e2) (op (e2) (e2))) = (op (e2) (e2)))) -> (((op (e0) (e0)) = (e3))\/(((op (e1) (e0)) = (e3))\/(((op (e2) (e0)) = (e3))\/((op (e3) (e0)) = (e3))))) -> (~((op (e3) (e0)) = (op (e3) (e3)))) -> (((op (e1) (e1)) = (e0))\/(((op (e1) (e1)) = (e1))\/(((op (e1) (e1)) = (e2))\/((op (e1) (e1)) = (e3))))) -> (~((op (e1) (op (e2) (e1))) = (op (e2) (e1)))) -> ((~((op (e2) (e2)) = (e3)))\/((op (e2) (e3)) = (e2))) -> (~((op (e2) (e1)) = (op (e2) (e3)))) -> ((~((op (e2) (e2)) = (e1)))\/((op (e2) (e1)) = (e2))) -> ((~((op (e1) (e1)) = (e3)))\/((op (e1) (e3)) = (e1))) -> (~((op (e1) (e0)) = (op (e1) (e1)))) -> ((~((op (e1) (e1)) = (e1)))\/((op (e1) (e1)) = (e1))) -> (~((op (e3) (e2)) = (op (e3) (e3)))) -> ((~((op (e3) (e3)) = (e2)))\/((op (e3) (e2)) = (e3))) -> (~((op (e0) (e1)) = (op (e0) (e3)))) -> (~((op (e0) (e0)) = (e3))) -> (((op (e2) (e0)) = (e3))\/(((op (e2) (e1)) = (e3))\/(((op (e2) (e2)) = (e3))\/((op (e2) (e3)) = (e3))))) -> ((op (e3) (e3)) = (e3)) -> (~((op (e3) (op (e2) (e3))) = (op (e2) (e3)))) -> (~((op (e0) (e1)) = (op (e2) (e1)))) -> (~((e1) = (e3))) -> (((op (e2) (e2)) = (e0))\/(((op (e2) (e2)) = (e1))\/(((op (e2) (e2)) = (e2))\/((op (e2) (e2)) = (e3))))) -> (~((op (e0) (e2)) = (op (e2) (e2)))) -> (~((op (e2) (e2)) = (e2))) -> (~((op (e2) (e2)) = (e1))) -> (~((op (e2) (e2)) = (e0))) -> (~((op (e0) (e3)) = (op (e3) (e3)))) -> (((op (e0) (e0)) = (e3))\/(((op (e0) (e1)) = (e3))\/(((op (e0) (e2)) = (e3))\/((op (e0) (e3)) = (e3))))) -> ((op (e1) (e3)) = (e1)) -> (~((op (e1) (e0)) = (op (e1) (e3)))) -> (~((op (e0) (e0)) = (e1))) -> ((~((op (e3) (e3)) = (e0)))\/((op (e3) (e0)) = (e3))) -> False). % 15.41/15.59 do 0 intro. intros zenon_H237 zenon_Hc9 zenon_H9e zenon_H5e zenon_Hd3 zenon_H6a zenon_H4b zenon_Hab zenon_Hd6 zenon_Ha7 zenon_H244 zenon_Hb7 zenon_H1f5 zenon_H13c zenon_H1a2 zenon_Hf1 zenon_H1df zenon_H140 zenon_Heb zenon_H12a zenon_H20 zenon_H25b zenon_H80 zenon_H8e zenon_H1d3 zenon_H166 zenon_H1d4 zenon_H87 zenon_H8b zenon_H90 zenon_Hce zenon_Haa zenon_H294 zenon_Hbe zenon_Hbb zenon_H1b3 zenon_H290 zenon_H1c3 zenon_H1e2 zenon_H1e3 zenon_H1d2 zenon_Hd7 zenon_H1d8 zenon_H173 zenon_H10e zenon_H1cd zenon_H59 zenon_He6 zenon_H42 zenon_H28a zenon_Hde zenon_Ha3 zenon_H2d zenon_H28 zenon_H2f zenon_H52 zenon_H2e zenon_H36 zenon_H58 zenon_H11f zenon_H1cf zenon_H45 zenon_H10f. % 15.41/15.59 apply (zenon_or_s _ _ zenon_H1c3); [ zenon_intro zenon_H30 | zenon_intro zenon_H124 ]. % 15.41/15.59 apply (zenon_or_s _ _ zenon_H10f); [ zenon_intro zenon_H3c | zenon_intro zenon_Hba ]. % 15.41/15.59 apply (zenon_or_s _ _ zenon_Hf1); [ zenon_intro zenon_H47 | zenon_intro zenon_Hf4 ]. % 15.41/15.59 exact (zenon_H45 zenon_H47). % 15.41/15.59 apply (zenon_or_s _ _ zenon_Hf4); [ zenon_intro zenon_Hd8 | zenon_intro zenon_Hf5 ]. % 15.41/15.59 apply (zenon_L224_); trivial. % 15.41/15.59 apply (zenon_or_s _ _ zenon_Hf5); [ zenon_intro zenon_Hae | zenon_intro zenon_Hee ]. % 15.41/15.59 apply (zenon_L788_); trivial. % 15.41/15.59 apply (zenon_or_s _ _ zenon_H8e); [ zenon_intro zenon_H92 | zenon_intro zenon_H91 ]. % 15.41/15.59 apply (zenon_L942_); trivial. % 15.41/15.59 apply (zenon_or_s _ _ zenon_H91); [ zenon_intro zenon_H5d | zenon_intro zenon_H93 ]. % 15.41/15.59 apply (zenon_L921_); trivial. % 15.41/15.59 apply (zenon_or_s _ _ zenon_H93); [ zenon_intro zenon_H63 | zenon_intro zenon_H81 ]. % 15.41/15.59 apply (zenon_L949_); trivial. % 15.41/15.59 apply (zenon_or_s _ _ zenon_Heb); [ zenon_intro zenon_H92 | zenon_intro zenon_Hec ]. % 15.41/15.59 apply (zenon_L942_); trivial. % 15.41/15.59 apply (zenon_or_s _ _ zenon_Hec); [ zenon_intro zenon_H68 | zenon_intro zenon_Hed ]. % 15.41/15.59 apply (zenon_or_s _ _ zenon_H58); [ zenon_intro zenon_H5b | zenon_intro zenon_H5a ]. % 15.41/15.59 exact (zenon_H59 zenon_H5b). % 15.41/15.59 apply (zenon_or_s _ _ zenon_H5a); [ zenon_intro zenon_H4a | zenon_intro zenon_H5c ]. % 15.41/15.59 apply (zenon_or_s _ _ zenon_Hbe); [ zenon_intro zenon_H5b | zenon_intro zenon_Hbf ]. % 15.41/15.59 exact (zenon_H59 zenon_H5b). % 15.41/15.59 apply (zenon_or_s _ _ zenon_Hbf); [ zenon_intro zenon_H69 | zenon_intro zenon_Hc0 ]. % 15.41/15.59 apply (zenon_L17_); trivial. % 15.41/15.59 apply (zenon_or_s _ _ zenon_Hc0); [ zenon_intro zenon_Haf | zenon_intro zenon_Hba ]. % 15.41/15.59 apply (zenon_or_s _ _ zenon_H1a2); [ zenon_intro zenon_H5d | zenon_intro zenon_H1a3 ]. % 15.41/15.59 apply (zenon_L350_); trivial. % 15.41/15.59 apply (zenon_or_s _ _ zenon_H1a3); [ zenon_intro zenon_H6e | zenon_intro zenon_H1a4 ]. % 15.41/15.59 exact (zenon_Hd6 zenon_H6e). % 15.41/15.59 apply (zenon_or_s _ _ zenon_H1a4); [ zenon_intro zenon_H156 | zenon_intro zenon_H16a ]. % 15.41/15.59 apply (zenon_L944_); trivial. % 15.41/15.59 apply (zenon_L929_); trivial. % 15.41/15.59 apply (zenon_L79_); trivial. % 15.41/15.59 apply (zenon_or_s _ _ zenon_H5c); [ zenon_intro zenon_H50 | zenon_intro zenon_H53 ]. % 15.41/15.59 apply (zenon_L11_); trivial. % 15.41/15.59 apply (zenon_L128_); trivial. % 15.41/15.59 apply (zenon_or_s _ _ zenon_Hed); [ zenon_intro zenon_Hdd | zenon_intro zenon_He9 ]. % 15.41/15.59 apply (zenon_L920_); trivial. % 15.41/15.59 apply (zenon_L122_); trivial. % 15.41/15.59 apply (zenon_L43_); trivial. % 15.41/15.59 apply (zenon_L712_); trivial. % 15.41/15.59 (* end of lemma zenon_L950_ *) % 15.41/15.59 assert (zenon_L951_ : (((op (e1) (e0)) = (e1))\/(((op (e1) (e1)) = (e1))\/(((op (e1) (e2)) = (e1))\/((op (e1) (e3)) = (e1))))) -> ((op (e2) (e3)) = (e2)) -> (~((op (e1) (e1)) = (e1))) -> (((op (e0) (e2)) = (e3))\/(((op (e1) (e2)) = (e3))\/(((op (e2) (e2)) = (e3))\/((op (e3) (e2)) = (e3))))) -> (~((op (e1) (e1)) = (e3))) -> (((op (e1) (e0)) = (e2))\/(((op (e1) (e1)) = (e2))\/(((op (e1) (e2)) = (e2))\/((op (e1) (e3)) = (e2))))) -> (((op (e2) (e0)) = (e2))\/(((op (e2) (e1)) = (e2))\/(((op (e2) (e2)) = (e2))\/((op (e2) (e3)) = (e2))))) -> (~((op (e0) (e2)) = (op (e0) (e3)))) -> (~((e0) = (e1))) -> (~((e0) = (e2))) -> (((op (e0) (e3)) = (e0))\/(((op (e1) (e3)) = (e0))\/(((op (e2) (e3)) = (e0))\/((op (e3) (e3)) = (e0))))) -> (~((e2) = (e3))) -> (~((e0) = (e3))) -> ((op (e0) (e2)) = (e0)) -> (~((op (e1) (e1)) = (e2))) -> (~((e1) = (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)) = (e0))\/(((op (e2) (e1)) = (e0))\/(((op (e2) (e2)) = (e0))\/((op (e2) (e3)) = (e0))))) -> (~((op (e2) (e1)) = (op (e3) (e1)))) -> (((op (e0) (e1)) = (e2))\/(((op (e1) (e1)) = (e2))\/(((op (e2) (e1)) = (e2))\/((op (e3) (e1)) = (e2))))) -> (((op (e0) (e0)) = (e1))\/(((op (e1) (e0)) = (e1))\/(((op (e2) (e0)) = (e1))\/((op (e3) (e0)) = (e1))))) -> (((op (e3) (e0)) = (e2))\/(((op (e3) (e1)) = (e2))\/(((op (e3) (e2)) = (e2))\/((op (e3) (e3)) = (e2))))) -> (~((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)) = (e0))\/(((op (e0) (e0)) = (e1))\/(((op (e0) (e0)) = (e2))\/((op (e0) (e0)) = (e3))))) -> (~((op (e0) (e0)) = (e0))) -> (((op (e1) (e3)) = (e0))\/(((op (e1) (e3)) = (e1))\/(((op (e1) (e3)) = (e2))\/((op (e1) (e3)) = (e3))))) -> (~((op (e0) (e3)) = (op (e1) (e3)))) -> (((op (e0) (e0)) = (e2))\/(((op (e0) (e1)) = (e2))\/(((op (e0) (e2)) = (e2))\/((op (e0) (e3)) = (e2))))) -> ((~((op (e1) (e1)) = (e2)))\/((op (e1) (e2)) = (e1))) -> (~((op (e1) (e0)) = (op (e1) (e2)))) -> ((~((op (e2) (e2)) = (e0)))\/((op (e2) (e0)) = (e2))) -> (~((op (e0) (e2)) = (op (e1) (e2)))) -> (~((op (e1) (e3)) = (op (e3) (e3)))) -> (((op (e1) (e0)) = (e3))\/(((op (e1) (e1)) = (e3))\/(((op (e1) (e2)) = (e3))\/((op (e1) (e3)) = (e3))))) -> (~((op (e2) (e0)) = (op (e2) (e3)))) -> ((~((op (e2) (e2)) = (e2)))\/((op (e2) (e2)) = (e2))) -> (~((op (e2) (op (e2) (e2))) = (op (e2) (e2)))) -> (((op (e0) (e0)) = (e3))\/(((op (e1) (e0)) = (e3))\/(((op (e2) (e0)) = (e3))\/((op (e3) (e0)) = (e3))))) -> (~((op (e3) (e0)) = (op (e3) (e3)))) -> (((op (e1) (e1)) = (e0))\/(((op (e1) (e1)) = (e1))\/(((op (e1) (e1)) = (e2))\/((op (e1) (e1)) = (e3))))) -> (~((op (e1) (op (e2) (e1))) = (op (e2) (e1)))) -> ((~((op (e2) (e2)) = (e3)))\/((op (e2) (e3)) = (e2))) -> (~((op (e2) (e1)) = (op (e2) (e3)))) -> ((~((op (e2) (e2)) = (e1)))\/((op (e2) (e1)) = (e2))) -> ((~((op (e1) (e1)) = (e3)))\/((op (e1) (e3)) = (e1))) -> (~((op (e1) (e0)) = (op (e1) (e1)))) -> ((~((op (e1) (e1)) = (e1)))\/((op (e1) (e1)) = (e1))) -> (~((op (e3) (e2)) = (op (e3) (e3)))) -> ((~((op (e3) (e3)) = (e2)))\/((op (e3) (e2)) = (e3))) -> (~((op (e0) (e1)) = (op (e0) (e3)))) -> (~((op (e0) (e0)) = (e3))) -> (((op (e2) (e0)) = (e3))\/(((op (e2) (e1)) = (e3))\/(((op (e2) (e2)) = (e3))\/((op (e2) (e3)) = (e3))))) -> ((op (e3) (e3)) = (e3)) -> (~((op (e3) (op (e2) (e3))) = (op (e2) (e3)))) -> (~((op (e0) (e1)) = (op (e2) (e1)))) -> (~((e1) = (e3))) -> (((op (e2) (e2)) = (e0))\/(((op (e2) (e2)) = (e1))\/(((op (e2) (e2)) = (e2))\/((op (e2) (e2)) = (e3))))) -> (~((op (e0) (e2)) = (op (e2) (e2)))) -> (~((op (e2) (e2)) = (e2))) -> (~((op (e2) (e2)) = (e1))) -> (~((op (e2) (e2)) = (e0))) -> (~((op (e0) (e3)) = (op (e3) (e3)))) -> (((op (e0) (e0)) = (e3))\/(((op (e0) (e1)) = (e3))\/(((op (e0) (e2)) = (e3))\/((op (e0) (e3)) = (e3))))) -> (~((op (e1) (e0)) = (op (e1) (e3)))) -> (~((op (e0) (e0)) = (e1))) -> ((~((op (e3) (e3)) = (e0)))\/((op (e3) (e0)) = (e3))) -> False). % 15.41/15.59 do 0 intro. intros zenon_H1c5 zenon_H124 zenon_H1b4 zenon_H175 zenon_H182 zenon_H84 zenon_H237 zenon_Hc9 zenon_H9e zenon_H5e zenon_Hd3 zenon_H6a zenon_H4b zenon_Hab zenon_Hd6 zenon_Ha7 zenon_H244 zenon_Hb7 zenon_H1f5 zenon_H13c zenon_H1a2 zenon_Hf1 zenon_H1df zenon_H140 zenon_Heb zenon_H12a zenon_H20 zenon_H25b zenon_H80 zenon_H8e zenon_H1d3 zenon_H166 zenon_H1d4 zenon_H87 zenon_H8b zenon_H90 zenon_Hce zenon_Haa zenon_H294 zenon_Hbe zenon_Hbb zenon_H1b3 zenon_H290 zenon_H1c3 zenon_H1e2 zenon_H1e3 zenon_H1d2 zenon_Hd7 zenon_H1d8 zenon_H173 zenon_H10e zenon_H1cd zenon_H59 zenon_He6 zenon_H42 zenon_H28a zenon_Hde zenon_Ha3 zenon_H2d zenon_H28 zenon_H2f zenon_H52 zenon_H2e zenon_H36 zenon_H58 zenon_H1cf zenon_H45 zenon_H10f. % 15.41/15.59 apply (zenon_or_s _ _ zenon_H1c5); [ zenon_intro zenon_Hd8 | zenon_intro zenon_H1c6 ]. % 15.41/15.59 apply (zenon_L941_); trivial. % 15.41/15.59 apply (zenon_or_s _ _ zenon_H1c6); [ zenon_intro zenon_H21 | zenon_intro zenon_H1c7 ]. % 15.41/15.59 exact (zenon_H1b4 zenon_H21). % 15.41/15.59 apply (zenon_or_s _ _ zenon_H1c7); [ zenon_intro zenon_H117 | zenon_intro zenon_H11f ]. % 15.41/15.59 apply (zenon_L207_); trivial. % 15.41/15.59 apply (zenon_L950_); trivial. % 15.41/15.59 (* end of lemma zenon_L951_ *) % 15.41/15.59 assert (zenon_L952_ : (((op (e0) (e1)) = (e3))\/(((op (e1) (e1)) = (e3))\/(((op (e2) (e1)) = (e3))\/((op (e3) (e1)) = (e3))))) -> ((op (e3) (e3)) = (e3)) -> (~((op (e3) (op (e2) (e3))) = (op (e2) (e3)))) -> (~((op (e2) (e2)) = (e3))) -> (~((op (e0) (e1)) = (op (e2) (e1)))) -> ((op (e2) (e0)) = (e1)) -> (~((e1) = (e3))) -> (((op (e2) (e0)) = (e3))\/(((op (e2) (e1)) = (e3))\/(((op (e2) (e2)) = (e3))\/((op (e2) (e3)) = (e3))))) -> (~((op (e1) (e1)) = (e3))) -> (~((e2) = (e3))) -> ((op (e2) (e1)) = (e2)) -> (~((e0) = (e3))) -> ((op (e3) (e1)) = (e0)) -> False). % 15.41/15.59 do 0 intro. intros zenon_H199 zenon_H42 zenon_H28a zenon_H30 zenon_Hde zenon_Hae zenon_Ha3 zenon_He6 zenon_H182 zenon_H6a zenon_H156 zenon_H4b zenon_H142. % 15.41/15.59 apply (zenon_or_s _ _ zenon_H199); [ zenon_intro zenon_H4a | zenon_intro zenon_H19a ]. % 15.41/15.59 apply (zenon_L787_); trivial. % 15.41/15.59 apply (zenon_or_s _ _ zenon_H19a); [ zenon_intro zenon_H96 | zenon_intro zenon_H19b ]. % 15.41/15.59 exact (zenon_H182 zenon_H96). % 15.41/15.59 apply (zenon_or_s _ _ zenon_H19b); [ zenon_intro zenon_Hdf | zenon_intro zenon_H10a ]. % 15.41/15.59 apply (zenon_L183_); trivial. % 15.41/15.59 apply (zenon_L126_); trivial. % 15.41/15.59 (* end of lemma zenon_L952_ *) % 15.41/15.59 assert (zenon_L953_ : (((op (e2) (e0)) = (e1))\/(((op (e2) (e1)) = (e1))\/(((op (e2) (e2)) = (e1))\/((op (e2) (e3)) = (e1))))) -> ((op (e3) (e1)) = (e0)) -> (~((e0) = (e3))) -> (~((e2) = (e3))) -> (~((op (e1) (e1)) = (e3))) -> (((op (e2) (e0)) = (e3))\/(((op (e2) (e1)) = (e3))\/(((op (e2) (e2)) = (e3))\/((op (e2) (e3)) = (e3))))) -> (~((e1) = (e3))) -> (~((op (e0) (e1)) = (op (e2) (e1)))) -> (~((op (e2) (e2)) = (e3))) -> (~((op (e3) (op (e2) (e3))) = (op (e2) (e3)))) -> (((op (e0) (e1)) = (e3))\/(((op (e1) (e1)) = (e3))\/(((op (e2) (e1)) = (e3))\/((op (e3) (e1)) = (e3))))) -> ((op (e2) (e1)) = (e2)) -> (~((e1) = (e2))) -> ((op (e0) (e0)) = (e2)) -> ((op (e0) (e1)) = (e3)) -> (((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 (e0) (e3)) = (e2)) -> (~((op (e0) (e3)) = (op (e1) (e3)))) -> ((op (e3) (e3)) = (e3)) -> (~((op (e1) (e3)) = (op (e3) (e3)))) -> False). % 15.41/15.60 do 0 intro. intros zenon_Hb7 zenon_H142 zenon_H4b zenon_H6a zenon_H182 zenon_He6 zenon_Ha3 zenon_Hde zenon_H30 zenon_H28a zenon_H199 zenon_H156 zenon_Ha7 zenon_H92 zenon_H4a zenon_H25b zenon_Hd0 zenon_H244 zenon_H81 zenon_H80 zenon_H42 zenon_H8b. % 15.41/15.60 apply (zenon_or_s _ _ zenon_Hb7); [ zenon_intro zenon_Hae | zenon_intro zenon_Hb8 ]. % 15.41/15.60 apply (zenon_L952_); trivial. % 15.41/15.60 apply (zenon_or_s _ _ zenon_Hb8); [ zenon_intro zenon_Hb2 | zenon_intro zenon_Hb9 ]. % 15.41/15.60 apply (zenon_L372_); trivial. % 15.41/15.60 apply (zenon_or_s _ _ zenon_Hb9); [ zenon_intro zenon_H2a | zenon_intro zenon_Hb5 ]. % 15.41/15.60 apply (zenon_L46_); trivial. % 15.41/15.60 apply (zenon_L933_); trivial. % 15.41/15.60 (* end of lemma zenon_L953_ *) % 15.41/15.60 assert (zenon_L954_ : (~((op (e1) (e3)) = (op (e3) (e3)))) -> ((op (e3) (e3)) = (e3)) -> (~((op (e0) (e3)) = (op (e1) (e3)))) -> (~((op (e1) (e3)) = (op (e2) (e3)))) -> (((op (e1) (e3)) = (e0))\/(((op (e1) (e3)) = (e1))\/(((op (e1) (e3)) = (e2))\/((op (e1) (e3)) = (e3))))) -> ((op (e0) (e0)) = (e2)) -> (~((e1) = (e2))) -> ((op (e2) (e1)) = (e2)) -> (((op (e0) (e1)) = (e3))\/(((op (e1) (e1)) = (e3))\/(((op (e2) (e1)) = (e3))\/((op (e3) (e1)) = (e3))))) -> (~((op (e3) (op (e2) (e3))) = (op (e2) (e3)))) -> (~((op (e2) (e2)) = (e3))) -> (~((op (e0) (e1)) = (op (e2) (e1)))) -> (~((e1) = (e3))) -> (((op (e2) (e0)) = (e3))\/(((op (e2) (e1)) = (e3))\/(((op (e2) (e2)) = (e3))\/((op (e2) (e3)) = (e3))))) -> (~((op (e1) (e1)) = (e3))) -> (((op (e2) (e0)) = (e1))\/(((op (e2) (e1)) = (e1))\/(((op (e2) (e2)) = (e1))\/((op (e2) (e3)) = (e1))))) -> (~((op (e2) (e2)) = (e0))) -> (~((e0) = (e2))) -> (((op (e2) (e0)) = (e0))\/(((op (e2) (e1)) = (e0))\/(((op (e2) (e2)) = (e0))\/((op (e2) (e3)) = (e0))))) -> (~((op (e1) (e1)) = (e0))) -> ((~((op (e2) (e2)) = (e1)))\/((op (e2) (e1)) = (e2))) -> (~((op (e3) (e1)) = (op (e3) (e3)))) -> (((op (e0) (e0)) = (e3))\/(((op (e0) (e1)) = (e3))\/(((op (e0) (e2)) = (e3))\/((op (e0) (e3)) = (e3))))) -> (~((op (e0) (e3)) = (op (e3) (e3)))) -> (~((op (e0) (e2)) = (op (e2) (e2)))) -> (((op (e2) (e2)) = (e0))\/(((op (e2) (e2)) = (e1))\/(((op (e2) (e2)) = (e2))\/((op (e2) (e2)) = (e3))))) -> (~((op (e0) (e0)) = (e3))) -> (~((op (e2) (op (e2) (e2))) = (op (e2) (e2)))) -> ((~((op (e2) (e2)) = (e2)))\/((op (e2) (e2)) = (e2))) -> (((op (e0) (e1)) = (e0))\/(((op (e1) (e1)) = (e0))\/(((op (e2) (e1)) = (e0))\/((op (e3) (e1)) = (e0))))) -> (~((e0) = (e3))) -> ((op (e0) (e2)) = (e0)) -> ((op (e0) (e3)) = (e2)) -> (~((e2) = (e3))) -> False). % 15.41/15.60 do 0 intro. intros zenon_H8b zenon_H42 zenon_H80 zenon_H244 zenon_H25b zenon_H92 zenon_Ha7 zenon_H156 zenon_H199 zenon_H28a zenon_H30 zenon_Hde zenon_Ha3 zenon_He6 zenon_H182 zenon_Hb7 zenon_H2e zenon_H5e zenon_H1f5 zenon_H145 zenon_H1e3 zenon_H12d zenon_H58 zenon_H36 zenon_H28 zenon_H2d zenon_H59 zenon_H294 zenon_Haa zenon_H144 zenon_H4b zenon_Hab zenon_H81 zenon_H6a. % 15.41/15.60 apply (zenon_or_s _ _ zenon_H58); [ zenon_intro zenon_H5b | zenon_intro zenon_H5a ]. % 15.41/15.60 exact (zenon_H59 zenon_H5b). % 15.41/15.60 apply (zenon_or_s _ _ zenon_H5a); [ zenon_intro zenon_H4a | zenon_intro zenon_H5c ]. % 15.41/15.60 apply (zenon_or_s _ _ zenon_H144); [ zenon_intro zenon_H49 | zenon_intro zenon_H147 ]. % 15.41/15.60 apply (zenon_L915_); trivial. % 15.41/15.60 apply (zenon_or_s _ _ zenon_H147); [ zenon_intro zenon_H149 | zenon_intro zenon_H148 ]. % 15.41/15.60 exact (zenon_H145 zenon_H149). % 15.41/15.60 apply (zenon_or_s _ _ zenon_H148); [ zenon_intro zenon_H14a | zenon_intro zenon_H142 ]. % 15.41/15.60 apply (zenon_L351_); trivial. % 15.41/15.60 apply (zenon_or_s _ _ zenon_H1f5); [ zenon_intro zenon_Hcf | zenon_intro zenon_H1f9 ]. % 15.41/15.60 apply (zenon_L924_); trivial. % 15.41/15.60 apply (zenon_or_s _ _ zenon_H1f9); [ zenon_intro zenon_H14a | zenon_intro zenon_H1fa ]. % 15.41/15.60 apply (zenon_L351_); trivial. % 15.41/15.60 apply (zenon_or_s _ _ zenon_H1fa); [ zenon_intro zenon_H32 | zenon_intro zenon_Hd0 ]. % 15.41/15.60 exact (zenon_H2e zenon_H32). % 15.41/15.60 apply (zenon_L953_); trivial. % 15.41/15.60 apply (zenon_or_s _ _ zenon_H5c); [ zenon_intro zenon_H50 | zenon_intro zenon_H53 ]. % 15.41/15.60 apply (zenon_L48_); trivial. % 15.41/15.60 apply (zenon_L128_); trivial. % 15.41/15.60 (* end of lemma zenon_L954_ *) % 15.41/15.60 assert (zenon_L955_ : ((~((op (e2) (e2)) = (e3)))\/((op (e2) (e3)) = (e2))) -> (~((op (e2) (e0)) = (op (e2) (e3)))) -> (~((op (e0) (e0)) = (e3))) -> (((op (e2) (e0)) = (e3))\/(((op (e2) (e1)) = (e3))\/(((op (e2) (e2)) = (e3))\/((op (e2) (e3)) = (e3))))) -> ((op (e3) (e3)) = (e3)) -> (~((op (e3) (op (e2) (e3))) = (op (e2) (e3)))) -> (~((op (e0) (e1)) = (op (e2) (e1)))) -> ((op (e2) (e0)) = (e2)) -> (~((e2) = (e3))) -> (~((e0) = (e3))) -> ((op (e0) (e2)) = (e0)) -> (~((op (e0) (e3)) = (op (e3) (e3)))) -> (((op (e0) (e0)) = (e3))\/(((op (e0) (e1)) = (e3))\/(((op (e0) (e2)) = (e3))\/((op (e0) (e3)) = (e3))))) -> False). % 15.41/15.60 do 0 intro. intros zenon_H1c3 zenon_Hce zenon_H59 zenon_He6 zenon_H42 zenon_H28a zenon_Hde zenon_Hdd zenon_H6a zenon_H4b zenon_Hab zenon_H36 zenon_H58. % 15.41/15.60 apply (zenon_or_s _ _ zenon_H1c3); [ zenon_intro zenon_H30 | zenon_intro zenon_H124 ]. % 15.41/15.60 apply (zenon_L920_); trivial. % 15.41/15.60 apply (zenon_L119_); trivial. % 15.41/15.60 (* end of lemma zenon_L955_ *) % 15.41/15.60 assert (zenon_L956_ : (((op (e0) (e0)) = (e1))\/(((op (e1) (e0)) = (e1))\/(((op (e2) (e0)) = (e1))\/((op (e3) (e0)) = (e1))))) -> (~((op (e0) (e0)) = (e1))) -> ((~((op (e1) (e1)) = (e2)))\/((op (e1) (e2)) = (e1))) -> (~((op (e1) (e0)) = (op (e1) (e2)))) -> ((~((op (e2) (e2)) = (e0)))\/((op (e2) (e0)) = (e2))) -> (~((op (e0) (e2)) = (op (e1) (e2)))) -> (~((op (e1) (e3)) = (op (e3) (e3)))) -> (((op (e1) (e0)) = (e3))\/(((op (e1) (e1)) = (e3))\/(((op (e1) (e2)) = (e3))\/((op (e1) (e3)) = (e3))))) -> (~((op (e2) (e0)) = (op (e2) (e3)))) -> ((~((op (e2) (e2)) = (e2)))\/((op (e2) (e2)) = (e2))) -> (~((op (e2) (op (e2) (e2))) = (op (e2) (e2)))) -> (((op (e0) (e0)) = (e3))\/(((op (e1) (e0)) = (e3))\/(((op (e2) (e0)) = (e3))\/((op (e3) (e0)) = (e3))))) -> (~((op (e3) (e0)) = (op (e3) (e3)))) -> (((op (e2) (e2)) = (e0))\/(((op (e2) (e2)) = (e1))\/(((op (e2) (e2)) = (e2))\/((op (e2) (e2)) = (e3))))) -> (((op (e1) (e1)) = (e0))\/(((op (e1) (e1)) = (e1))\/(((op (e1) (e1)) = (e2))\/((op (e1) (e1)) = (e3))))) -> (~((op (e1) (op (e2) (e1))) = (op (e2) (e1)))) -> (((op (e2) (e0)) = (e0))\/(((op (e2) (e1)) = (e0))\/(((op (e2) (e2)) = (e0))\/((op (e2) (e3)) = (e0))))) -> ((~((op (e2) (e2)) = (e3)))\/((op (e2) (e3)) = (e2))) -> (~((op (e2) (e1)) = (op (e2) (e3)))) -> ((~((op (e2) (e2)) = (e1)))\/((op (e2) (e1)) = (e2))) -> (~((op (e1) (e0)) = (op (e1) (e3)))) -> ((~((op (e1) (e1)) = (e3)))\/((op (e1) (e3)) = (e1))) -> (~((op (e1) (e0)) = (op (e1) (e1)))) -> ((~((op (e1) (e1)) = (e1)))\/((op (e1) (e1)) = (e1))) -> (((op (e0) (e0)) = (e2))\/(((op (e0) (e1)) = (e2))\/(((op (e0) (e2)) = (e2))\/((op (e0) (e3)) = (e2))))) -> (~((op (e0) (e3)) = (op (e3) (e3)))) -> ((op (e3) (e3)) = (e3)) -> ((op (e0) (e2)) = (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)) = (e0))) -> (~((e0) = (e2))) -> (((op (e2) (e0)) = (e1))\/(((op (e2) (e1)) = (e1))\/(((op (e2) (e2)) = (e1))\/((op (e2) (e3)) = (e1))))) -> (~((e2) = (e3))) -> (~((op (e1) (e1)) = (e3))) -> (((op (e2) (e0)) = (e3))\/(((op (e2) (e1)) = (e3))\/(((op (e2) (e2)) = (e3))\/((op (e2) (e3)) = (e3))))) -> (~((e1) = (e3))) -> (~((op (e2) (e2)) = (e3))) -> (~((op (e3) (op (e2) (e3))) = (op (e2) (e3)))) -> (((op (e0) (e1)) = (e3))\/(((op (e1) (e1)) = (e3))\/(((op (e2) (e1)) = (e3))\/((op (e3) (e1)) = (e3))))) -> (~((op (e0) (e3)) = (op (e2) (e3)))) -> (~((op (e0) (e0)) = (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) (e3)) = (e2))) -> (~((op (e0) (e2)) = (op (e3) (e2)))) -> (~((op (e2) (e1)) = (op (e3) (e1)))) -> ((op (e2) (e1)) = (e2)) -> (((op (e3) (e0)) = (e2))\/(((op (e3) (e1)) = (e2))\/(((op (e3) (e2)) = (e2))\/((op (e3) (e3)) = (e2))))) -> ((op (e0) (e3)) = (e1)) -> (~((e1) = (e2))) -> False). % 15.41/15.60 do 0 intro. intros zenon_Hf1 zenon_H45 zenon_H1d3 zenon_H166 zenon_H1d4 zenon_H87 zenon_H8b zenon_H90 zenon_Hce zenon_Haa zenon_H294 zenon_Hbe zenon_Hbb zenon_H2d zenon_H1b3 zenon_H290 zenon_H1f5 zenon_H1c3 zenon_H1e2 zenon_H1e3 zenon_H1cf zenon_H1d2 zenon_Hd7 zenon_H1d8 zenon_H8e zenon_H36 zenon_H42 zenon_Hab zenon_H4b zenon_H144 zenon_H12d zenon_H145 zenon_H5e zenon_Hb7 zenon_H6a zenon_H182 zenon_He6 zenon_Ha3 zenon_H30 zenon_H28a zenon_H199 zenon_Hb4 zenon_H59 zenon_H58 zenon_Hde zenon_H3d zenon_H140 zenon_H13c zenon_H156 zenon_H1df zenon_H37 zenon_Ha7. % 15.41/15.60 apply (zenon_or_s _ _ zenon_Hf1); [ zenon_intro zenon_H47 | zenon_intro zenon_Hf4 ]. % 15.41/15.60 exact (zenon_H45 zenon_H47). % 15.41/15.60 apply (zenon_or_s _ _ zenon_Hf4); [ zenon_intro zenon_Hd8 | zenon_intro zenon_Hf5 ]. % 15.41/15.60 apply (zenon_L943_); trivial. % 15.41/15.60 apply (zenon_or_s _ _ zenon_Hf5); [ zenon_intro zenon_Hae | zenon_intro zenon_Hee ]. % 15.41/15.60 apply (zenon_L796_); trivial. % 15.41/15.60 apply (zenon_or_s _ _ zenon_H8e); [ zenon_intro zenon_H92 | zenon_intro zenon_H91 ]. % 15.41/15.60 apply (zenon_or_s _ _ zenon_H58); [ zenon_intro zenon_H5b | zenon_intro zenon_H5a ]. % 15.41/15.60 exact (zenon_H59 zenon_H5b). % 15.41/15.60 apply (zenon_or_s _ _ zenon_H5a); [ zenon_intro zenon_H4a | zenon_intro zenon_H5c ]. % 15.41/15.60 apply (zenon_or_s _ _ zenon_H144); [ zenon_intro zenon_H49 | zenon_intro zenon_H147 ]. % 15.41/15.60 apply (zenon_L278_); trivial. % 15.41/15.60 apply (zenon_or_s _ _ zenon_H147); [ zenon_intro zenon_H149 | zenon_intro zenon_H148 ]. % 15.41/15.60 exact (zenon_H145 zenon_H149). % 15.41/15.60 apply (zenon_or_s _ _ zenon_H148); [ zenon_intro zenon_H14a | zenon_intro zenon_H142 ]. % 15.41/15.60 apply (zenon_L351_); trivial. % 15.41/15.60 apply (zenon_or_s _ _ zenon_Hb7); [ zenon_intro zenon_Hae | zenon_intro zenon_Hb8 ]. % 15.41/15.60 apply (zenon_L952_); trivial. % 15.41/15.60 apply (zenon_or_s _ _ zenon_Hb8); [ zenon_intro zenon_Hb2 | zenon_intro zenon_Hb9 ]. % 15.41/15.60 apply (zenon_L372_); trivial. % 15.41/15.60 apply (zenon_or_s _ _ zenon_Hb9); [ zenon_intro zenon_H2a | zenon_intro zenon_Hb5 ]. % 15.41/15.60 apply (zenon_L46_); trivial. % 15.41/15.60 apply (zenon_L41_); trivial. % 15.41/15.60 apply (zenon_or_s _ _ zenon_H5c); [ zenon_intro zenon_H50 | zenon_intro zenon_H53 ]. % 15.41/15.60 apply (zenon_L48_); trivial. % 15.41/15.60 apply (zenon_L12_); trivial. % 15.41/15.60 apply (zenon_or_s _ _ zenon_H91); [ zenon_intro zenon_H5d | zenon_intro zenon_H93 ]. % 15.41/15.60 apply (zenon_L251_); trivial. % 15.41/15.60 apply (zenon_or_s _ _ zenon_H93); [ zenon_intro zenon_H63 | zenon_intro zenon_H81 ]. % 15.41/15.60 apply (zenon_L254_); trivial. % 15.41/15.60 apply (zenon_L33_); trivial. % 15.41/15.60 (* end of lemma zenon_L956_ *) % 15.41/15.60 assert (zenon_L957_ : (((op (e0) (e0)) = (e1))\/(((op (e0) (e1)) = (e1))\/(((op (e0) (e2)) = (e1))\/((op (e0) (e3)) = (e1))))) -> (~((op (e0) (e1)) = (op (e1) (e1)))) -> ((op (e1) (e1)) = (e1)) -> (~((op (e2) (e2)) = (e2))) -> (~((op (e0) (e2)) = (op (e2) (e2)))) -> (~((op (e2) (e2)) = (e0))) -> (((op (e0) (e0)) = (e1))\/(((op (e1) (e0)) = (e1))\/(((op (e2) (e0)) = (e1))\/((op (e3) (e0)) = (e1))))) -> (~((op (e0) (e0)) = (e1))) -> ((~((op (e1) (e1)) = (e2)))\/((op (e1) (e2)) = (e1))) -> (~((op (e1) (e0)) = (op (e1) (e2)))) -> ((~((op (e2) (e2)) = (e0)))\/((op (e2) (e0)) = (e2))) -> (~((op (e0) (e2)) = (op (e1) (e2)))) -> (~((op (e1) (e3)) = (op (e3) (e3)))) -> (((op (e1) (e0)) = (e3))\/(((op (e1) (e1)) = (e3))\/(((op (e1) (e2)) = (e3))\/((op (e1) (e3)) = (e3))))) -> (~((op (e2) (e0)) = (op (e2) (e3)))) -> ((~((op (e2) (e2)) = (e2)))\/((op (e2) (e2)) = (e2))) -> (~((op (e2) (op (e2) (e2))) = (op (e2) (e2)))) -> (((op (e0) (e0)) = (e3))\/(((op (e1) (e0)) = (e3))\/(((op (e2) (e0)) = (e3))\/((op (e3) (e0)) = (e3))))) -> (~((op (e3) (e0)) = (op (e3) (e3)))) -> (((op (e2) (e2)) = (e0))\/(((op (e2) (e2)) = (e1))\/(((op (e2) (e2)) = (e2))\/((op (e2) (e2)) = (e3))))) -> (((op (e1) (e1)) = (e0))\/(((op (e1) (e1)) = (e1))\/(((op (e1) (e1)) = (e2))\/((op (e1) (e1)) = (e3))))) -> (~((op (e1) (op (e2) (e1))) = (op (e2) (e1)))) -> (((op (e2) (e0)) = (e0))\/(((op (e2) (e1)) = (e0))\/(((op (e2) (e2)) = (e0))\/((op (e2) (e3)) = (e0))))) -> ((~((op (e2) (e2)) = (e3)))\/((op (e2) (e3)) = (e2))) -> (~((op (e2) (e1)) = (op (e2) (e3)))) -> ((~((op (e2) (e2)) = (e1)))\/((op (e2) (e1)) = (e2))) -> (~((op (e1) (e0)) = (op (e1) (e3)))) -> ((~((op (e1) (e1)) = (e3)))\/((op (e1) (e3)) = (e1))) -> (~((op (e1) (e0)) = (op (e1) (e1)))) -> ((~((op (e1) (e1)) = (e1)))\/((op (e1) (e1)) = (e1))) -> (((op (e0) (e0)) = (e2))\/(((op (e0) (e1)) = (e2))\/(((op (e0) (e2)) = (e2))\/((op (e0) (e3)) = (e2))))) -> (~((op (e0) (e3)) = (op (e3) (e3)))) -> ((op (e3) (e3)) = (e3)) -> ((op (e0) (e2)) = (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)) = (e0))) -> (~((e0) = (e2))) -> (((op (e2) (e0)) = (e1))\/(((op (e2) (e1)) = (e1))\/(((op (e2) (e2)) = (e1))\/((op (e2) (e3)) = (e1))))) -> (~((e2) = (e3))) -> (~((op (e1) (e1)) = (e3))) -> (((op (e2) (e0)) = (e3))\/(((op (e2) (e1)) = (e3))\/(((op (e2) (e2)) = (e3))\/((op (e2) (e3)) = (e3))))) -> (~((e1) = (e3))) -> (~((op (e2) (e2)) = (e3))) -> (~((op (e3) (op (e2) (e3))) = (op (e2) (e3)))) -> (((op (e0) (e1)) = (e3))\/(((op (e1) (e1)) = (e3))\/(((op (e2) (e1)) = (e3))\/((op (e3) (e1)) = (e3))))) -> (~((op (e0) (e3)) = (op (e2) (e3)))) -> (~((op (e0) (e0)) = (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) (e3)) = (e2))) -> (~((op (e0) (e2)) = (op (e3) (e2)))) -> (~((op (e2) (e1)) = (op (e3) (e1)))) -> ((op (e2) (e1)) = (e2)) -> (((op (e3) (e0)) = (e2))\/(((op (e3) (e1)) = (e2))\/(((op (e3) (e2)) = (e2))\/((op (e3) (e3)) = (e2))))) -> (~((e1) = (e2))) -> False). % 15.41/15.60 do 0 intro. intros zenon_H44 zenon_H23 zenon_H21 zenon_H2f zenon_H28 zenon_H2e zenon_Hf1 zenon_H45 zenon_H1d3 zenon_H166 zenon_H1d4 zenon_H87 zenon_H8b zenon_H90 zenon_Hce zenon_Haa zenon_H294 zenon_Hbe zenon_Hbb zenon_H2d zenon_H1b3 zenon_H290 zenon_H1f5 zenon_H1c3 zenon_H1e2 zenon_H1e3 zenon_H1cf zenon_H1d2 zenon_Hd7 zenon_H1d8 zenon_H8e zenon_H36 zenon_H42 zenon_Hab zenon_H4b zenon_H144 zenon_H12d zenon_H145 zenon_H5e zenon_Hb7 zenon_H6a zenon_H182 zenon_He6 zenon_Ha3 zenon_H30 zenon_H28a zenon_H199 zenon_Hb4 zenon_H59 zenon_H58 zenon_Hde zenon_H3d zenon_H140 zenon_H13c zenon_H156 zenon_H1df zenon_Ha7. % 15.41/15.60 apply (zenon_or_s _ _ zenon_H44); [ zenon_intro zenon_H47 | zenon_intro zenon_H46 ]. % 15.41/15.60 exact (zenon_H45 zenon_H47). % 15.41/15.60 apply (zenon_or_s _ _ zenon_H46); [ zenon_intro zenon_H22 | zenon_intro zenon_H48 ]. % 15.41/15.60 apply (zenon_L3_); trivial. % 15.41/15.60 apply (zenon_or_s _ _ zenon_H48); [ zenon_intro zenon_H29 | zenon_intro zenon_H37 ]. % 15.41/15.60 apply (zenon_L5_); trivial. % 15.41/15.60 apply (zenon_L956_); trivial. % 15.41/15.60 (* end of lemma zenon_L957_ *) % 15.41/15.60 assert (zenon_L958_ : ((~((op (e2) (e2)) = (e3)))\/((op (e2) (e3)) = (e2))) -> (~((op (e2) (e0)) = (op (e2) (e3)))) -> (~((op (e0) (e0)) = (e1))) -> (~((op (e0) (e1)) = (op (e1) (e1)))) -> ((op (e1) (e1)) = (e1)) -> (((op (e0) (e0)) = (e3))\/(((op (e0) (e1)) = (e3))\/(((op (e0) (e2)) = (e3))\/((op (e0) (e3)) = (e3))))) -> (~((op (e0) (e3)) = (op (e3) (e3)))) -> (~((e1) = (e3))) -> (~((e2) = (e3))) -> ((op (e2) (e0)) = (e2)) -> (~((op (e0) (e1)) = (op (e2) (e1)))) -> (~((op (e3) (op (e2) (e3))) = (op (e2) (e3)))) -> ((op (e3) (e3)) = (e3)) -> (((op (e2) (e0)) = (e3))\/(((op (e2) (e1)) = (e3))\/(((op (e2) (e2)) = (e3))\/((op (e2) (e3)) = (e3))))) -> (~((op (e0) (e0)) = (e3))) -> (((op (e2) (e0)) = (e1))\/(((op (e2) (e1)) = (e1))\/(((op (e2) (e2)) = (e1))\/((op (e2) (e3)) = (e1))))) -> (~((op (e0) (e3)) = (op (e2) (e3)))) -> (~((op (e2) (e2)) = (e1))) -> (~((op (e1) (e1)) = (op (e2) (e1)))) -> (~((e1) = (e2))) -> (((op (e0) (e0)) = (e1))\/(((op (e0) (e1)) = (e1))\/(((op (e0) (e2)) = (e1))\/((op (e0) (e3)) = (e1))))) -> False). % 15.41/15.60 do 0 intro. intros zenon_H1c3 zenon_Hce zenon_H45 zenon_H23 zenon_H21 zenon_H58 zenon_H36 zenon_Ha3 zenon_H6a zenon_Hdd zenon_Hde zenon_H28a zenon_H42 zenon_He6 zenon_H59 zenon_Hb7 zenon_Hb4 zenon_H52 zenon_Hb1 zenon_Ha7 zenon_H44. % 15.41/15.60 apply (zenon_or_s _ _ zenon_H1c3); [ zenon_intro zenon_H30 | zenon_intro zenon_H124 ]. % 15.41/15.60 apply (zenon_L906_); trivial. % 15.41/15.60 apply (zenon_L119_); trivial. % 15.41/15.60 (* end of lemma zenon_L958_ *) % 15.41/15.60 assert (zenon_L959_ : ((~((op (e2) (e2)) = (e1)))\/((op (e2) (e1)) = (e2))) -> (~((op (e2) (e0)) = (op (e2) (e1)))) -> (((op (e0) (e0)) = (e1))\/(((op (e0) (e1)) = (e1))\/(((op (e0) (e2)) = (e1))\/((op (e0) (e3)) = (e1))))) -> (~((e1) = (e2))) -> (~((op (e1) (e1)) = (op (e2) (e1)))) -> (~((op (e0) (e3)) = (op (e2) (e3)))) -> (((op (e2) (e0)) = (e1))\/(((op (e2) (e1)) = (e1))\/(((op (e2) (e2)) = (e1))\/((op (e2) (e3)) = (e1))))) -> (~((op (e0) (e0)) = (e3))) -> (((op (e2) (e0)) = (e3))\/(((op (e2) (e1)) = (e3))\/(((op (e2) (e2)) = (e3))\/((op (e2) (e3)) = (e3))))) -> ((op (e3) (e3)) = (e3)) -> (~((op (e3) (op (e2) (e3))) = (op (e2) (e3)))) -> (~((op (e0) (e1)) = (op (e2) (e1)))) -> ((op (e2) (e0)) = (e2)) -> (~((e2) = (e3))) -> (~((e1) = (e3))) -> (~((op (e0) (e3)) = (op (e3) (e3)))) -> (((op (e0) (e0)) = (e3))\/(((op (e0) (e1)) = (e3))\/(((op (e0) (e2)) = (e3))\/((op (e0) (e3)) = (e3))))) -> ((op (e1) (e1)) = (e1)) -> (~((op (e0) (e1)) = (op (e1) (e1)))) -> (~((op (e0) (e0)) = (e1))) -> (~((op (e2) (e0)) = (op (e2) (e3)))) -> ((~((op (e2) (e2)) = (e3)))\/((op (e2) (e3)) = (e2))) -> False). % 15.41/15.60 do 0 intro. intros zenon_H1e3 zenon_H154 zenon_H44 zenon_Ha7 zenon_Hb1 zenon_Hb4 zenon_Hb7 zenon_H59 zenon_He6 zenon_H42 zenon_H28a zenon_Hde zenon_Hdd zenon_H6a zenon_Ha3 zenon_H36 zenon_H58 zenon_H21 zenon_H23 zenon_H45 zenon_Hce zenon_H1c3. % 15.41/15.60 apply (zenon_or_s _ _ zenon_H1e3); [ zenon_intro zenon_H52 | zenon_intro zenon_H156 ]. % 15.41/15.60 apply (zenon_L958_); trivial. % 15.41/15.60 apply (zenon_L284_); trivial. % 15.41/15.60 (* end of lemma zenon_L959_ *) % 15.41/15.60 assert (zenon_L960_ : ((~((op (e0) (e0)) = (e3)))\/((op (e0) (e3)) = (e0))) -> (~((op (e2) (e0)) = (op (e2) (e1)))) -> (((op (e0) (e0)) = (e1))\/(((op (e0) (e1)) = (e1))\/(((op (e0) (e2)) = (e1))\/((op (e0) (e3)) = (e1))))) -> (~((op (e0) (e3)) = (op (e2) (e3)))) -> (~((op (e1) (e1)) = (op (e2) (e1)))) -> (~((op (e1) (e1)) = (op (e1) (e3)))) -> (((op (e0) (e1)) = (e0))\/(((op (e1) (e1)) = (e0))\/(((op (e2) (e1)) = (e0))\/((op (e3) (e1)) = (e0))))) -> (((op (e0) (e1)) = (e3))\/(((op (e1) (e1)) = (e3))\/(((op (e2) (e1)) = (e3))\/((op (e3) (e1)) = (e3))))) -> (~((op (e3) (e1)) = (op (e3) (e3)))) -> (~((op (e2) (e1)) = (op (e2) (e2)))) -> (~((op (e1) (op (e2) (e1))) = (op (e2) (e1)))) -> ((~((op (e2) (e2)) = (e3)))\/((op (e2) (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 (e3) (e0)) = (e2))\/(((op (e3) (e1)) = (e2))\/(((op (e3) (e2)) = (e2))\/((op (e3) (e3)) = (e2))))) -> (~((op (e0) (e2)) = (op (e3) (e2)))) -> (((op (e0) (e0)) = (e0))\/(((op (e0) (e0)) = (e1))\/(((op (e0) (e0)) = (e2))\/((op (e0) (e0)) = (e3))))) -> (~((op (e0) (e0)) = (e0))) -> (((op (e1) (e3)) = (e0))\/(((op (e1) (e3)) = (e1))\/(((op (e1) (e3)) = (e2))\/((op (e1) (e3)) = (e3))))) -> ((~((op (e1) (e1)) = (e2)))\/((op (e1) (e2)) = (e1))) -> (~((op (e1) (e0)) = (op (e1) (e2)))) -> ((~((op (e2) (e2)) = (e0)))\/((op (e2) (e0)) = (e2))) -> (~((op (e0) (e2)) = (op (e1) (e2)))) -> (~((op (e2) (e0)) = (op (e2) (e3)))) -> ((~((op (e2) (e2)) = (e2)))\/((op (e2) (e2)) = (e2))) -> (~((op (e2) (op (e2) (e2))) = (op (e2) (e2)))) -> (~((op (e2) (e1)) = (op (e2) (e3)))) -> ((~((op (e2) (e2)) = (e1)))\/((op (e2) (e1)) = (e2))) -> ((~((op (e1) (e1)) = (e3)))\/((op (e1) (e3)) = (e1))) -> (~((op (e1) (e0)) = (op (e1) (e1)))) -> ((~((op (e1) (e1)) = (e1)))\/((op (e1) (e1)) = (e1))) -> ((~((op (e3) (e3)) = (e2)))\/((op (e3) (e2)) = (e3))) -> (~((op (e0) (e1)) = (op (e0) (e3)))) -> (~((op (e1) (e0)) = (op (e1) (e3)))) -> (((op (e0) (e0)) = (e1))\/(((op (e1) (e0)) = (e1))\/(((op (e2) (e0)) = (e1))\/((op (e3) (e0)) = (e1))))) -> (((op (e1) (e0)) = (e1))\/(((op (e1) (e1)) = (e1))\/(((op (e1) (e2)) = (e1))\/((op (e1) (e3)) = (e1))))) -> (((op (e2) (e0)) = (e2))\/(((op (e2) (e1)) = (e2))\/(((op (e2) (e2)) = (e2))\/((op (e2) (e3)) = (e2))))) -> (~((op (e0) (e2)) = (op (e0) (e3)))) -> (~((e0) = (e1))) -> (~((e0) = (e2))) -> (((op (e0) (e3)) = (e0))\/(((op (e1) (e3)) = (e0))\/(((op (e2) (e3)) = (e0))\/((op (e3) (e3)) = (e0))))) -> (~((e2) = (e3))) -> (~((e1) = (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)) = (e0))\/(((op (e2) (e1)) = (e0))\/(((op (e2) (e2)) = (e0))\/((op (e2) (e3)) = (e0))))) -> (~((op (e2) (e1)) = (op (e3) (e1)))) -> (((op (e0) (e1)) = (e2))\/(((op (e1) (e1)) = (e2))\/(((op (e2) (e1)) = (e2))\/((op (e3) (e1)) = (e2))))) -> (~((e0) = (e3))) -> ((op (e0) (e2)) = (e0)) -> (~((op (e3) (e2)) = (op (e3) (e3)))) -> (((op (e0) (e2)) = (e3))\/(((op (e1) (e2)) = (e3))\/(((op (e2) (e2)) = (e3))\/((op (e3) (e2)) = (e3))))) -> (~((op (e0) (e1)) = (op (e1) (e1)))) -> (((op (e0) (e0)) = (e2))\/(((op (e1) (e0)) = (e2))\/(((op (e2) (e0)) = (e2))\/((op (e3) (e0)) = (e2))))) -> (((op (e1) (e0)) = (e2))\/(((op (e1) (e1)) = (e2))\/(((op (e1) (e2)) = (e2))\/((op (e1) (e3)) = (e2))))) -> (~((op (e0) (e3)) = (op (e1) (e3)))) -> (((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 (e3) (op (e2) (e3))) = (op (e2) (e3)))) -> (~((op (e0) (e1)) = (op (e2) (e1)))) -> (~((op (e0) (e2)) = (op (e2) (e2)))) -> (~((op (e0) (e3)) = (op (e3) (e3)))) -> (((op (e0) (e0)) = (e3))\/(((op (e0) (e1)) = (e3))\/(((op (e0) (e2)) = (e3))\/((op (e0) (e3)) = (e3))))) -> (~((e1) = (e3))) -> (((op (e1) (e1)) = (e0))\/(((op (e1) (e1)) = (e1))\/(((op (e1) (e1)) = (e2))\/((op (e1) (e1)) = (e3))))) -> (((op (e2) (e2)) = (e0))\/(((op (e2) (e2)) = (e1))\/(((op (e2) (e2)) = (e2))\/((op (e2) (e2)) = (e3))))) -> (~((op (e3) (e0)) = (op (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)) = (e1))) -> ((~((op (e3) (e3)) = (e0)))\/((op (e3) (e0)) = (e3))) -> (~((op (e1) (e2)) = (op (e1) (e3)))) -> ((~((op (e1) (e1)) = (e0)))\/((op (e1) (e0)) = (e1))) -> False). % 15.41/15.60 do 0 intro. intros zenon_H236 zenon_H154 zenon_H44 zenon_Hb4 zenon_Hb1 zenon_H11e zenon_H144 zenon_H199 zenon_H12d zenon_H157 zenon_H290 zenon_H1c3 zenon_H8b zenon_H90 zenon_H1df zenon_H140 zenon_H12a zenon_H20 zenon_H25b zenon_H1d3 zenon_H166 zenon_H1d4 zenon_H87 zenon_Hce zenon_Haa zenon_H294 zenon_H1e2 zenon_H1e3 zenon_H1d2 zenon_Hd7 zenon_H1d8 zenon_H10e zenon_H1cd zenon_H1cf zenon_Hf1 zenon_H1c5 zenon_H237 zenon_Hc9 zenon_H9e zenon_H5e zenon_Hd3 zenon_H6a zenon_Ha7 zenon_H244 zenon_Hb7 zenon_H1f5 zenon_H13c zenon_H1a2 zenon_H4b zenon_Hab zenon_H173 zenon_H175 zenon_H23 zenon_Heb zenon_H84 zenon_H80 zenon_H8e zenon_He6 zenon_H28a zenon_Hde zenon_H28 zenon_H36 zenon_H58 zenon_Ha3 zenon_H1b3 zenon_H2d zenon_Hbb zenon_H42 zenon_Hbe zenon_H45 zenon_H10f zenon_H1d0 zenon_H1e4. % 15.41/15.60 apply (zenon_or_s _ _ zenon_H236); [ zenon_intro zenon_H59 | zenon_intro zenon_Hca ]. % 15.41/15.60 apply (zenon_or_s _ _ zenon_H1e4); [ zenon_intro zenon_H145 | zenon_intro zenon_Hd8 ]. % 15.41/15.60 apply (zenon_or_s _ _ zenon_H1d8); [ zenon_intro zenon_H1b4 | zenon_intro zenon_H21 ]. % 15.41/15.60 apply (zenon_or_s _ _ zenon_H1d3); [ zenon_intro zenon_Hd6 | zenon_intro zenon_H117 ]. % 15.41/15.60 apply (zenon_or_s _ _ zenon_H1d2); [ zenon_intro zenon_H182 | zenon_intro zenon_H11f ]. % 15.41/15.60 apply (zenon_or_s _ _ zenon_H1d4); [ zenon_intro zenon_H2e | zenon_intro zenon_Hdd ]. % 15.41/15.60 apply (zenon_or_s _ _ zenon_H1e3); [ zenon_intro zenon_H52 | zenon_intro zenon_H156 ]. % 15.41/15.60 apply (zenon_or_s _ _ zenon_Haa); [ zenon_intro zenon_H2f | zenon_intro zenon_H35 ]. % 15.41/15.60 apply (zenon_or_s _ _ zenon_H1c3); [ zenon_intro zenon_H30 | zenon_intro zenon_H124 ]. % 15.41/15.60 apply (zenon_or_s _ _ zenon_H10f); [ zenon_intro zenon_H3c | zenon_intro zenon_Hba ]. % 15.41/15.60 apply (zenon_L932_); trivial. % 15.41/15.60 apply (zenon_L43_); trivial. % 15.41/15.60 apply (zenon_L951_); trivial. % 15.41/15.60 apply (zenon_L794_); trivial. % 15.41/15.60 apply (zenon_or_s _ _ zenon_Haa); [ zenon_intro zenon_H2f | zenon_intro zenon_H35 ]. % 15.41/15.60 apply (zenon_or_s _ _ zenon_H1c3); [ zenon_intro zenon_H30 | zenon_intro zenon_H124 ]. % 15.41/15.60 apply (zenon_or_s _ _ zenon_H10e); [ zenon_intro zenon_H3d | zenon_intro zenon_H106 ]. % 15.41/15.60 apply (zenon_or_s _ _ zenon_Hf1); [ zenon_intro zenon_H47 | zenon_intro zenon_Hf4 ]. % 15.41/15.60 exact (zenon_H45 zenon_H47). % 15.41/15.60 apply (zenon_or_s _ _ zenon_Hf4); [ zenon_intro zenon_Hd8 | zenon_intro zenon_Hf5 ]. % 15.41/15.60 apply (zenon_L446_); trivial. % 15.41/15.60 apply (zenon_or_s _ _ zenon_Hf5); [ zenon_intro zenon_Hae | zenon_intro zenon_Hee ]. % 15.41/15.60 apply (zenon_L796_); trivial. % 15.41/15.60 apply (zenon_or_s _ _ zenon_H8e); [ zenon_intro zenon_H92 | zenon_intro zenon_H91 ]. % 15.41/15.60 apply (zenon_or_s _ _ zenon_H58); [ zenon_intro zenon_H5b | zenon_intro zenon_H5a ]. % 15.41/15.60 exact (zenon_H59 zenon_H5b). % 15.41/15.60 apply (zenon_or_s _ _ zenon_H5a); [ zenon_intro zenon_H4a | zenon_intro zenon_H5c ]. % 15.41/15.60 apply (zenon_or_s _ _ zenon_Hbe); [ zenon_intro zenon_H5b | zenon_intro zenon_Hbf ]. % 15.41/15.60 exact (zenon_H59 zenon_H5b). % 15.41/15.60 apply (zenon_or_s _ _ zenon_Hbf); [ zenon_intro zenon_H69 | zenon_intro zenon_Hc0 ]. % 15.41/15.60 apply (zenon_or_s _ _ zenon_H1c5); [ zenon_intro zenon_Hd8 | zenon_intro zenon_H1c6 ]. % 15.41/15.60 apply (zenon_L163_); trivial. % 15.41/15.60 apply (zenon_or_s _ _ zenon_H1c6); [ zenon_intro zenon_H21 | zenon_intro zenon_H1c7 ]. % 15.41/15.60 exact (zenon_H1b4 zenon_H21). % 15.41/15.60 apply (zenon_or_s _ _ zenon_H1c7); [ zenon_intro zenon_H117 | zenon_intro zenon_H11f ]. % 15.41/15.60 apply (zenon_L207_); trivial. % 15.41/15.60 apply (zenon_L922_); trivial. % 15.41/15.60 apply (zenon_or_s _ _ zenon_Hc0); [ zenon_intro zenon_Haf | zenon_intro zenon_Hba ]. % 15.41/15.60 apply (zenon_L219_); trivial. % 15.41/15.60 apply (zenon_L79_); trivial. % 15.41/15.60 apply (zenon_or_s _ _ zenon_H5c); [ zenon_intro zenon_H50 | zenon_intro zenon_H53 ]. % 15.41/15.60 apply (zenon_L48_); trivial. % 15.41/15.60 apply (zenon_L12_); trivial. % 15.41/15.60 apply (zenon_or_s _ _ zenon_H91); [ zenon_intro zenon_H5d | zenon_intro zenon_H93 ]. % 15.41/15.60 apply (zenon_L251_); trivial. % 15.41/15.60 apply (zenon_or_s _ _ zenon_H93); [ zenon_intro zenon_H63 | zenon_intro zenon_H81 ]. % 15.41/15.60 apply (zenon_L254_); trivial. % 15.41/15.60 apply (zenon_or_s _ _ zenon_Heb); [ zenon_intro zenon_H92 | zenon_intro zenon_Hec ]. % 15.41/15.60 apply (zenon_L954_); trivial. % 15.41/15.60 apply (zenon_or_s _ _ zenon_Hec); [ zenon_intro zenon_H68 | zenon_intro zenon_Hed ]. % 15.41/15.60 apply (zenon_L623_); trivial. % 15.41/15.60 apply (zenon_or_s _ _ zenon_Hed); [ zenon_intro zenon_Hdd | zenon_intro zenon_He9 ]. % 15.41/15.60 apply (zenon_L920_); trivial. % 15.41/15.60 apply (zenon_L122_); trivial. % 15.41/15.60 apply (zenon_L153_); trivial. % 15.41/15.60 apply (zenon_L256_); trivial. % 15.41/15.60 apply (zenon_L134_); trivial. % 15.41/15.60 apply (zenon_L955_); trivial. % 15.41/15.60 apply (zenon_or_s _ _ zenon_H1d4); [ zenon_intro zenon_H2e | zenon_intro zenon_Hdd ]. % 15.41/15.60 apply (zenon_or_s _ _ zenon_H1e3); [ zenon_intro zenon_H52 | zenon_intro zenon_H156 ]. % 15.41/15.60 apply (zenon_or_s _ _ zenon_Haa); [ zenon_intro zenon_H2f | zenon_intro zenon_H35 ]. % 15.41/15.60 apply (zenon_L950_); trivial. % 15.41/15.60 apply (zenon_L794_); trivial. % 15.41/15.60 apply (zenon_or_s _ _ zenon_H1c3); [ zenon_intro zenon_H30 | zenon_intro zenon_H124 ]. % 15.41/15.60 apply (zenon_or_s _ _ zenon_H10f); [ zenon_intro zenon_H3c | zenon_intro zenon_Hba ]. % 15.41/15.60 apply (zenon_L948_); trivial. % 15.41/15.60 apply (zenon_L43_); trivial. % 15.41/15.60 apply (zenon_L256_); trivial. % 15.41/15.60 apply (zenon_L955_); trivial. % 15.41/15.60 apply (zenon_L238_); trivial. % 15.41/15.60 apply (zenon_or_s _ _ zenon_H1d2); [ zenon_intro zenon_H182 | zenon_intro zenon_H11f ]. % 15.41/15.60 apply (zenon_or_s _ _ zenon_H1d4); [ zenon_intro zenon_H2e | zenon_intro zenon_Hdd ]. % 15.41/15.60 apply (zenon_or_s _ _ zenon_H1e3); [ zenon_intro zenon_H52 | zenon_intro zenon_H156 ]. % 15.41/15.60 apply (zenon_or_s _ _ zenon_Haa); [ zenon_intro zenon_H2f | zenon_intro zenon_H35 ]. % 15.41/15.60 apply (zenon_or_s _ _ zenon_H1c3); [ zenon_intro zenon_H30 | zenon_intro zenon_H124 ]. % 15.41/15.60 apply (zenon_L916_); trivial. % 15.41/15.60 apply (zenon_L99_); trivial. % 15.41/15.60 apply (zenon_L794_); trivial. % 15.41/15.60 apply (zenon_or_s _ _ zenon_Haa); [ zenon_intro zenon_H2f | zenon_intro zenon_H35 ]. % 15.41/15.60 apply (zenon_or_s _ _ zenon_H1c3); [ zenon_intro zenon_H30 | zenon_intro zenon_H124 ]. % 15.41/15.60 apply (zenon_or_s _ _ zenon_H10e); [ zenon_intro zenon_H3d | zenon_intro zenon_H106 ]. % 15.41/15.60 apply (zenon_L957_); trivial. % 15.41/15.60 apply (zenon_L153_); trivial. % 15.41/15.60 apply (zenon_L256_); trivial. % 15.41/15.60 apply (zenon_L134_); trivial. % 15.41/15.60 apply (zenon_L959_); trivial. % 15.41/15.60 apply (zenon_L90_); trivial. % 15.41/15.60 apply (zenon_L943_); trivial. % 15.41/15.60 apply (zenon_L53_); trivial. % 15.41/15.60 (* end of lemma zenon_L960_ *) % 15.41/15.60 assert (zenon_L961_ : (((op (e0) (e2)) = (e0))\/(((op (e1) (e2)) = (e0))\/(((op (e2) (e2)) = (e0))\/((op (e3) (e2)) = (e0))))) -> ((~((op (e1) (e1)) = (e0)))\/((op (e1) (e0)) = (e1))) -> (~((op (e1) (e2)) = (op (e1) (e3)))) -> ((~((op (e3) (e3)) = (e0)))\/((op (e3) (e0)) = (e3))) -> (~((op (e0) (e0)) = (e1))) -> (((op (e0) (e0)) = (e3))\/(((op (e1) (e0)) = (e3))\/(((op (e2) (e0)) = (e3))\/((op (e3) (e0)) = (e3))))) -> ((op (e3) (e3)) = (e3)) -> (~((op (e3) (e0)) = (op (e3) (e3)))) -> (((op (e1) (e1)) = (e0))\/(((op (e1) (e1)) = (e1))\/(((op (e1) (e1)) = (e2))\/((op (e1) (e1)) = (e3))))) -> (~((e1) = (e3))) -> (((op (e0) (e0)) = (e3))\/(((op (e0) (e1)) = (e3))\/(((op (e0) (e2)) = (e3))\/((op (e0) (e3)) = (e3))))) -> (~((op (e0) (e3)) = (op (e3) (e3)))) -> (~((op (e0) (e2)) = (op (e2) (e2)))) -> (~((op (e0) (e1)) = (op (e2) (e1)))) -> (~((op (e3) (op (e2) (e3))) = (op (e2) (e3)))) -> (((op (e2) (e0)) = (e3))\/(((op (e2) (e1)) = (e3))\/(((op (e2) (e2)) = (e3))\/((op (e2) (e3)) = (e3))))) -> (((op (e0) (e0)) = (e2))\/(((op (e0) (e1)) = (e2))\/(((op (e0) (e2)) = (e2))\/((op (e0) (e3)) = (e2))))) -> (~((op (e0) (e3)) = (op (e1) (e3)))) -> (((op (e1) (e0)) = (e2))\/(((op (e1) (e1)) = (e2))\/(((op (e1) (e2)) = (e2))\/((op (e1) (e3)) = (e2))))) -> (((op (e0) (e0)) = (e2))\/(((op (e1) (e0)) = (e2))\/(((op (e2) (e0)) = (e2))\/((op (e3) (e0)) = (e2))))) -> (~((op (e0) (e1)) = (op (e1) (e1)))) -> (((op (e0) (e2)) = (e3))\/(((op (e1) (e2)) = (e3))\/(((op (e2) (e2)) = (e3))\/((op (e3) (e2)) = (e3))))) -> (~((op (e3) (e2)) = (op (e3) (e3)))) -> (~((e0) = (e3))) -> (((op (e0) (e1)) = (e2))\/(((op (e1) (e1)) = (e2))\/(((op (e2) (e1)) = (e2))\/((op (e3) (e1)) = (e2))))) -> (~((op (e2) (e1)) = (op (e3) (e1)))) -> (((op (e2) (e0)) = (e0))\/(((op (e2) (e1)) = (e0))\/(((op (e2) (e2)) = (e0))\/((op (e2) (e3)) = (e0))))) -> (((op (e2) (e0)) = (e1))\/(((op (e2) (e1)) = (e1))\/(((op (e2) (e2)) = (e1))\/((op (e2) (e3)) = (e1))))) -> (~((op (e1) (e3)) = (op (e2) (e3)))) -> (~((e1) = (e2))) -> (~((e2) = (e3))) -> (((op (e0) (e3)) = (e0))\/(((op (e1) (e3)) = (e0))\/(((op (e2) (e3)) = (e0))\/((op (e3) (e3)) = (e0))))) -> (~((e0) = (e2))) -> (~((e0) = (e1))) -> (~((op (e0) (e2)) = (op (e0) (e3)))) -> (((op (e2) (e0)) = (e2))\/(((op (e2) (e1)) = (e2))\/(((op (e2) (e2)) = (e2))\/((op (e2) (e3)) = (e2))))) -> (((op (e1) (e0)) = (e1))\/(((op (e1) (e1)) = (e1))\/(((op (e1) (e2)) = (e1))\/((op (e1) (e3)) = (e1))))) -> (((op (e0) (e0)) = (e1))\/(((op (e1) (e0)) = (e1))\/(((op (e2) (e0)) = (e1))\/((op (e3) (e0)) = (e1))))) -> (~((op (e1) (e0)) = (op (e1) (e3)))) -> (~((op (e0) (e1)) = (op (e0) (e3)))) -> ((~((op (e3) (e3)) = (e2)))\/((op (e3) (e2)) = (e3))) -> ((~((op (e1) (e1)) = (e1)))\/((op (e1) (e1)) = (e1))) -> (~((op (e1) (e0)) = (op (e1) (e1)))) -> ((~((op (e1) (e1)) = (e3)))\/((op (e1) (e3)) = (e1))) -> ((~((op (e2) (e2)) = (e1)))\/((op (e2) (e1)) = (e2))) -> (~((op (e2) (e1)) = (op (e2) (e3)))) -> (~((op (e2) (op (e2) (e2))) = (op (e2) (e2)))) -> ((~((op (e2) (e2)) = (e2)))\/((op (e2) (e2)) = (e2))) -> (~((op (e2) (e0)) = (op (e2) (e3)))) -> (~((op (e0) (e2)) = (op (e1) (e2)))) -> ((~((op (e2) (e2)) = (e0)))\/((op (e2) (e0)) = (e2))) -> (~((op (e1) (e0)) = (op (e1) (e2)))) -> ((~((op (e1) (e1)) = (e2)))\/((op (e1) (e2)) = (e1))) -> (((op (e1) (e3)) = (e0))\/(((op (e1) (e3)) = (e1))\/(((op (e1) (e3)) = (e2))\/((op (e1) (e3)) = (e3))))) -> (~((op (e0) (e0)) = (e0))) -> (((op (e0) (e0)) = (e0))\/(((op (e0) (e0)) = (e1))\/(((op (e0) (e0)) = (e2))\/((op (e0) (e0)) = (e3))))) -> (~((op (e0) (e2)) = (op (e3) (e2)))) -> (((op (e3) (e0)) = (e2))\/(((op (e3) (e1)) = (e2))\/(((op (e3) (e2)) = (e2))\/((op (e3) (e3)) = (e2))))) -> (((op (e1) (e0)) = (e3))\/(((op (e1) (e1)) = (e3))\/(((op (e1) (e2)) = (e3))\/((op (e1) (e3)) = (e3))))) -> (~((op (e1) (e3)) = (op (e3) (e3)))) -> ((~((op (e2) (e2)) = (e3)))\/((op (e2) (e3)) = (e2))) -> (~((op (e1) (op (e2) (e1))) = (op (e2) (e1)))) -> (~((op (e2) (e1)) = (op (e2) (e2)))) -> (~((op (e3) (e1)) = (op (e3) (e3)))) -> (((op (e0) (e1)) = (e3))\/(((op (e1) (e1)) = (e3))\/(((op (e2) (e1)) = (e3))\/((op (e3) (e1)) = (e3))))) -> (((op (e0) (e1)) = (e0))\/(((op (e1) (e1)) = (e0))\/(((op (e2) (e1)) = (e0))\/((op (e3) (e1)) = (e0))))) -> (~((op (e1) (e1)) = (op (e1) (e3)))) -> (~((op (e1) (e1)) = (op (e2) (e1)))) -> (~((op (e0) (e3)) = (op (e2) (e3)))) -> (((op (e0) (e0)) = (e1))\/(((op (e0) (e1)) = (e1))\/(((op (e0) (e2)) = (e1))\/((op (e0) (e3)) = (e1))))) -> (~((op (e2) (e0)) = (op (e2) (e1)))) -> ((~((op (e0) (e0)) = (e3)))\/((op (e0) (e3)) = (e0))) -> (~((op (e2) (e2)) = (e3))) -> (~((op (e2) (e2)) = (e2))) -> (~((op (e2) (e2)) = (e1))) -> (~((op (e1) (e2)) = (op (e2) (e2)))) -> (((op (e2) (e2)) = (e0))\/(((op (e2) (e2)) = (e1))\/(((op (e2) (e2)) = (e2))\/((op (e2) (e2)) = (e3))))) -> (~((op (e2) (e2)) = (e0))) -> (~((op (e3) (e1)) = (op (e3) (e2)))) -> ((op (e3) (e1)) = (e0)) -> False). % 15.41/15.60 do 0 intro. intros zenon_H16f zenon_H1e4 zenon_H1d0 zenon_H10f zenon_H45 zenon_Hbe zenon_H42 zenon_Hbb zenon_H1b3 zenon_Ha3 zenon_H58 zenon_H36 zenon_H28 zenon_Hde zenon_H28a zenon_He6 zenon_H8e zenon_H80 zenon_H84 zenon_Heb zenon_H23 zenon_H175 zenon_H173 zenon_H4b zenon_H1a2 zenon_H13c zenon_H1f5 zenon_Hb7 zenon_H244 zenon_Ha7 zenon_H6a zenon_Hd3 zenon_H5e zenon_H9e zenon_Hc9 zenon_H237 zenon_H1c5 zenon_Hf1 zenon_H1cf zenon_H1cd zenon_H10e zenon_H1d8 zenon_Hd7 zenon_H1d2 zenon_H1e3 zenon_H1e2 zenon_H294 zenon_Haa zenon_Hce zenon_H87 zenon_H1d4 zenon_H166 zenon_H1d3 zenon_H25b zenon_H20 zenon_H12a zenon_H140 zenon_H1df zenon_H90 zenon_H8b zenon_H1c3 zenon_H290 zenon_H157 zenon_H12d zenon_H199 zenon_H144 zenon_H11e zenon_Hb1 zenon_Hb4 zenon_H44 zenon_H154 zenon_H236 zenon_H30 zenon_H2f zenon_H52 zenon_H7d zenon_H2d zenon_H2e zenon_H135 zenon_H142. % 15.41/15.60 apply (zenon_or_s _ _ zenon_H16f); [ zenon_intro zenon_Hab | zenon_intro zenon_H170 ]. % 15.41/15.60 apply (zenon_L960_); trivial. % 15.41/15.60 apply (zenon_or_s _ _ zenon_H170); [ zenon_intro zenon_H15d | zenon_intro zenon_H171 ]. % 15.41/15.60 apply (zenon_L335_); trivial. % 15.41/15.60 apply (zenon_or_s _ _ zenon_H171); [ zenon_intro zenon_H32 | zenon_intro zenon_H167 ]. % 15.41/15.60 exact (zenon_H2e zenon_H32). % 15.41/15.60 apply (zenon_L144_); trivial. % 15.41/15.60 (* end of lemma zenon_L961_ *) % 15.41/15.60 assert (zenon_L962_ : (~((op (e1) (e1)) = (op (e1) (e2)))) -> (~((op (e0) (e0)) = (e2))) -> (~((op (e2) (e0)) = (op (e2) (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 (e1) (e1)) = (e0)))\/((op (e1) (e0)) = (e1))) -> (~((op (e1) (e2)) = (op (e1) (e3)))) -> ((~((op (e3) (e3)) = (e0)))\/((op (e3) (e0)) = (e3))) -> (~((op (e0) (e0)) = (e1))) -> (((op (e0) (e0)) = (e3))\/(((op (e1) (e0)) = (e3))\/(((op (e2) (e0)) = (e3))\/((op (e3) (e0)) = (e3))))) -> ((op (e3) (e3)) = (e3)) -> (~((op (e3) (e0)) = (op (e3) (e3)))) -> (((op (e1) (e1)) = (e0))\/(((op (e1) (e1)) = (e1))\/(((op (e1) (e1)) = (e2))\/((op (e1) (e1)) = (e3))))) -> (~((e1) = (e3))) -> (((op (e0) (e0)) = (e3))\/(((op (e0) (e1)) = (e3))\/(((op (e0) (e2)) = (e3))\/((op (e0) (e3)) = (e3))))) -> (~((op (e0) (e3)) = (op (e3) (e3)))) -> (~((op (e0) (e2)) = (op (e2) (e2)))) -> (~((op (e0) (e1)) = (op (e2) (e1)))) -> (~((op (e3) (op (e2) (e3))) = (op (e2) (e3)))) -> (((op (e2) (e0)) = (e3))\/(((op (e2) (e1)) = (e3))\/(((op (e2) (e2)) = (e3))\/((op (e2) (e3)) = (e3))))) -> (((op (e0) (e0)) = (e2))\/(((op (e0) (e1)) = (e2))\/(((op (e0) (e2)) = (e2))\/((op (e0) (e3)) = (e2))))) -> (~((op (e0) (e3)) = (op (e1) (e3)))) -> (((op (e1) (e0)) = (e2))\/(((op (e1) (e1)) = (e2))\/(((op (e1) (e2)) = (e2))\/((op (e1) (e3)) = (e2))))) -> (((op (e0) (e0)) = (e2))\/(((op (e1) (e0)) = (e2))\/(((op (e2) (e0)) = (e2))\/((op (e3) (e0)) = (e2))))) -> (~((op (e0) (e1)) = (op (e1) (e1)))) -> (((op (e0) (e2)) = (e3))\/(((op (e1) (e2)) = (e3))\/(((op (e2) (e2)) = (e3))\/((op (e3) (e2)) = (e3))))) -> (~((op (e3) (e2)) = (op (e3) (e3)))) -> (~((e0) = (e3))) -> (((op (e0) (e1)) = (e2))\/(((op (e1) (e1)) = (e2))\/(((op (e2) (e1)) = (e2))\/((op (e3) (e1)) = (e2))))) -> (~((op (e2) (e1)) = (op (e3) (e1)))) -> (((op (e2) (e0)) = (e0))\/(((op (e2) (e1)) = (e0))\/(((op (e2) (e2)) = (e0))\/((op (e2) (e3)) = (e0))))) -> (((op (e2) (e0)) = (e1))\/(((op (e2) (e1)) = (e1))\/(((op (e2) (e2)) = (e1))\/((op (e2) (e3)) = (e1))))) -> (~((op (e1) (e3)) = (op (e2) (e3)))) -> (~((e1) = (e2))) -> (~((e2) = (e3))) -> (((op (e0) (e3)) = (e0))\/(((op (e1) (e3)) = (e0))\/(((op (e2) (e3)) = (e0))\/((op (e3) (e3)) = (e0))))) -> (~((e0) = (e2))) -> (~((e0) = (e1))) -> (~((op (e0) (e2)) = (op (e0) (e3)))) -> (((op (e2) (e0)) = (e2))\/(((op (e2) (e1)) = (e2))\/(((op (e2) (e2)) = (e2))\/((op (e2) (e3)) = (e2))))) -> (((op (e1) (e0)) = (e1))\/(((op (e1) (e1)) = (e1))\/(((op (e1) (e2)) = (e1))\/((op (e1) (e3)) = (e1))))) -> (((op (e0) (e0)) = (e1))\/(((op (e1) (e0)) = (e1))\/(((op (e2) (e0)) = (e1))\/((op (e3) (e0)) = (e1))))) -> (~((op (e1) (e0)) = (op (e1) (e3)))) -> (~((op (e0) (e1)) = (op (e0) (e3)))) -> ((~((op (e3) (e3)) = (e2)))\/((op (e3) (e2)) = (e3))) -> ((~((op (e1) (e1)) = (e1)))\/((op (e1) (e1)) = (e1))) -> (~((op (e1) (e0)) = (op (e1) (e1)))) -> ((~((op (e1) (e1)) = (e3)))\/((op (e1) (e3)) = (e1))) -> ((~((op (e2) (e2)) = (e1)))\/((op (e2) (e1)) = (e2))) -> (~((op (e2) (e1)) = (op (e2) (e3)))) -> (~((op (e2) (op (e2) (e2))) = (op (e2) (e2)))) -> ((~((op (e2) (e2)) = (e2)))\/((op (e2) (e2)) = (e2))) -> (~((op (e2) (e0)) = (op (e2) (e3)))) -> (~((op (e0) (e2)) = (op (e1) (e2)))) -> ((~((op (e2) (e2)) = (e0)))\/((op (e2) (e0)) = (e2))) -> (~((op (e1) (e0)) = (op (e1) (e2)))) -> ((~((op (e1) (e1)) = (e2)))\/((op (e1) (e2)) = (e1))) -> (((op (e1) (e3)) = (e0))\/(((op (e1) (e3)) = (e1))\/(((op (e1) (e3)) = (e2))\/((op (e1) (e3)) = (e3))))) -> (~((op (e0) (e0)) = (e0))) -> (((op (e0) (e0)) = (e0))\/(((op (e0) (e0)) = (e1))\/(((op (e0) (e0)) = (e2))\/((op (e0) (e0)) = (e3))))) -> (~((op (e0) (e2)) = (op (e3) (e2)))) -> (((op (e3) (e0)) = (e2))\/(((op (e3) (e1)) = (e2))\/(((op (e3) (e2)) = (e2))\/((op (e3) (e3)) = (e2))))) -> (((op (e1) (e0)) = (e3))\/(((op (e1) (e1)) = (e3))\/(((op (e1) (e2)) = (e3))\/((op (e1) (e3)) = (e3))))) -> (~((op (e1) (e3)) = (op (e3) (e3)))) -> ((~((op (e2) (e2)) = (e3)))\/((op (e2) (e3)) = (e2))) -> (~((op (e1) (op (e2) (e1))) = (op (e2) (e1)))) -> (~((op (e2) (e1)) = (op (e2) (e2)))) -> (~((op (e3) (e1)) = (op (e3) (e3)))) -> (((op (e0) (e1)) = (e3))\/(((op (e1) (e1)) = (e3))\/(((op (e2) (e1)) = (e3))\/((op (e3) (e1)) = (e3))))) -> (((op (e0) (e1)) = (e0))\/(((op (e1) (e1)) = (e0))\/(((op (e2) (e1)) = (e0))\/((op (e3) (e1)) = (e0))))) -> (~((op (e1) (e1)) = (op (e1) (e3)))) -> (~((op (e1) (e1)) = (op (e2) (e1)))) -> (~((op (e0) (e3)) = (op (e2) (e3)))) -> (((op (e0) (e0)) = (e1))\/(((op (e0) (e1)) = (e1))\/(((op (e0) (e2)) = (e1))\/((op (e0) (e3)) = (e1))))) -> (~((op (e2) (e0)) = (op (e2) (e1)))) -> ((~((op (e0) (e0)) = (e3)))\/((op (e0) (e3)) = (e0))) -> (~((op (e2) (e2)) = (e3))) -> (~((op (e2) (e2)) = (e2))) -> (~((op (e2) (e2)) = (e1))) -> (~((op (e1) (e2)) = (op (e2) (e2)))) -> (((op (e2) (e2)) = (e0))\/(((op (e2) (e2)) = (e1))\/(((op (e2) (e2)) = (e2))\/((op (e2) (e2)) = (e3))))) -> (~((op (e2) (e2)) = (e0))) -> (~((op (e3) (e1)) = (op (e3) (e2)))) -> False). % 15.41/15.60 do 0 intro. intros zenon_H116 zenon_H8f zenon_H17a zenon_H145 zenon_Had zenon_H16f zenon_H1e4 zenon_H1d0 zenon_H10f zenon_H45 zenon_Hbe zenon_H42 zenon_Hbb zenon_H1b3 zenon_Ha3 zenon_H58 zenon_H36 zenon_H28 zenon_Hde zenon_H28a zenon_He6 zenon_H8e zenon_H80 zenon_H84 zenon_Heb zenon_H23 zenon_H175 zenon_H173 zenon_H4b zenon_H1a2 zenon_H13c zenon_H1f5 zenon_Hb7 zenon_H244 zenon_Ha7 zenon_H6a zenon_Hd3 zenon_H5e zenon_H9e zenon_Hc9 zenon_H237 zenon_H1c5 zenon_Hf1 zenon_H1cf zenon_H1cd zenon_H10e zenon_H1d8 zenon_Hd7 zenon_H1d2 zenon_H1e3 zenon_H1e2 zenon_H294 zenon_Haa zenon_Hce zenon_H87 zenon_H1d4 zenon_H166 zenon_H1d3 zenon_H25b zenon_H20 zenon_H12a zenon_H140 zenon_H1df zenon_H90 zenon_H8b zenon_H1c3 zenon_H290 zenon_H157 zenon_H12d zenon_H199 zenon_H144 zenon_H11e zenon_Hb1 zenon_Hb4 zenon_H44 zenon_H154 zenon_H236 zenon_H30 zenon_H2f zenon_H52 zenon_H7d zenon_H2d zenon_H2e zenon_H135. % 15.41/15.60 apply (zenon_or_s _ _ zenon_H144); [ zenon_intro zenon_H49 | zenon_intro zenon_H147 ]. % 15.41/15.60 apply (zenon_L939_); trivial. % 15.41/15.60 apply (zenon_or_s _ _ zenon_H147); [ zenon_intro zenon_H149 | zenon_intro zenon_H148 ]. % 15.41/15.60 exact (zenon_H145 zenon_H149). % 15.41/15.60 apply (zenon_or_s _ _ zenon_H148); [ zenon_intro zenon_H14a | zenon_intro zenon_H142 ]. % 15.41/15.60 apply (zenon_L940_); trivial. % 15.41/15.60 apply (zenon_L961_); trivial. % 15.41/15.60 (* end of lemma zenon_L962_ *) % 15.41/15.60 assert (zenon_L963_ : (~((op (e0) (e3)) = (op (e2) (e3)))) -> ((op (e0) (e3)) = (e0)) -> ((op (e2) (e3)) = (e0)) -> False). % 15.41/15.60 do 0 intro. intros zenon_Hb4 zenon_Hca zenon_Hd0. % 15.41/15.60 cut (((op (e0) (e3)) = (e0)) = ((op (e0) (e3)) = (op (e2) (e3)))). % 15.41/15.60 intro zenon_D_pnotp. % 15.41/15.60 apply zenon_Hb4. % 15.41/15.60 rewrite <- zenon_D_pnotp. % 15.41/15.60 exact zenon_Hca. % 15.41/15.60 cut (((e0) = (op (e2) (e3)))); [idtac | apply NNPP; zenon_intro zenon_Hd1]. % 15.41/15.60 cut (((op (e0) (e3)) = (op (e0) (e3)))); [idtac | apply NNPP; zenon_intro zenon_H3a]. % 15.41/15.60 congruence. % 15.41/15.60 apply zenon_H3a. apply refl_equal. % 15.41/15.60 apply zenon_Hd1. apply sym_equal. exact zenon_Hd0. % 15.41/15.60 (* end of lemma zenon_L963_ *) % 15.41/15.60 assert (zenon_L964_ : (((op (e2) (e0)) = (e0))\/(((op (e2) (e1)) = (e0))\/(((op (e2) (e2)) = (e0))\/((op (e2) (e3)) = (e0))))) -> ((op (e2) (e3)) = (e2)) -> (~((e1) = (e2))) -> (~((op (e2) (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) (e0)) = (e0)) -> (~((op (e1) (op (e2) (e1))) = (op (e2) (e1)))) -> (~((op (e2) (e2)) = (e0))) -> (~((op (e0) (e3)) = (op (e2) (e3)))) -> ((op (e0) (e3)) = (e0)) -> False). % 15.41/15.60 do 0 intro. intros zenon_H1f5 zenon_H124 zenon_Ha7 zenon_H52 zenon_Hde zenon_H22 zenon_H9e zenon_Hb7 zenon_Had zenon_H290 zenon_H2e zenon_Hb4 zenon_Hca. % 15.41/15.60 apply (zenon_or_s _ _ zenon_H1f5); [ zenon_intro zenon_Hcf | zenon_intro zenon_H1f9 ]. % 15.41/15.60 apply (zenon_L340_); trivial. % 15.41/15.60 apply (zenon_or_s _ _ zenon_H1f9); [ zenon_intro zenon_H14a | zenon_intro zenon_H1fa ]. % 15.41/15.60 apply (zenon_L940_); trivial. % 15.41/15.60 apply (zenon_or_s _ _ zenon_H1fa); [ zenon_intro zenon_H32 | zenon_intro zenon_Hd0 ]. % 15.41/15.60 exact (zenon_H2e zenon_H32). % 15.41/15.60 apply (zenon_L963_); trivial. % 15.41/15.60 (* end of lemma zenon_L964_ *) % 15.41/15.60 assert (zenon_L965_ : (((op (e3) (e0)) = (e2))\/(((op (e3) (e1)) = (e2))\/(((op (e3) (e2)) = (e2))\/((op (e3) (e3)) = (e2))))) -> (~((e0) = (e2))) -> ((op (e3) (e0)) = (e0)) -> (~((e1) = (e2))) -> ((op (e3) (e1)) = (e1)) -> ((op (e2) (e3)) = (e2)) -> (~((op (e3) (op (e2) (e3))) = (op (e2) (e3)))) -> (~((op (e3) (e3)) = (e2))) -> False). % 15.41/15.60 do 0 intro. intros zenon_H1df zenon_H5e zenon_Hdb zenon_Ha7 zenon_H13e zenon_H124 zenon_H28a zenon_H3d. % 15.41/15.60 apply (zenon_or_s _ _ zenon_H1df); [ zenon_intro zenon_He9 | zenon_intro zenon_H1e0 ]. % 15.41/15.60 apply (zenon_L69_); trivial. % 15.41/15.60 apply (zenon_or_s _ _ zenon_H1e0); [ zenon_intro zenon_H16a | zenon_intro zenon_H1e1 ]. % 15.41/15.60 apply (zenon_L414_); trivial. % 15.41/15.60 apply (zenon_or_s _ _ zenon_H1e1); [ zenon_intro zenon_H1dd | zenon_intro zenon_H43 ]. % 15.41/15.60 apply (zenon_L851_); trivial. % 15.41/15.60 exact (zenon_H3d zenon_H43). % 15.41/15.60 (* end of lemma zenon_L965_ *) % 15.41/15.60 assert (zenon_L966_ : (((op (e0) (e0)) = (e1))\/(((op (e0) (e1)) = (e1))\/(((op (e0) (e2)) = (e1))\/((op (e0) (e3)) = (e1))))) -> (~((op (e0) (op (e2) (e0))) = (op (e2) (e0)))) -> (((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 (e0) (e0)) = (e1))) -> (((op (e0) (e0)) = (e1))\/(((op (e1) (e0)) = (e1))\/(((op (e2) (e0)) = (e1))\/((op (e3) (e0)) = (e1))))) -> (~((op (e3) (e3)) = (e1))) -> (~((op (e0) (e2)) = (op (e3) (e2)))) -> (((op (e3) (e0)) = (e2))\/(((op (e3) (e1)) = (e2))\/(((op (e3) (e2)) = (e2))\/((op (e3) (e3)) = (e2))))) -> (~((e0) = (e2))) -> ((op (e3) (e0)) = (e0)) -> (~((e1) = (e2))) -> ((op (e2) (e3)) = (e2)) -> (~((op (e3) (op (e2) (e3))) = (op (e2) (e3)))) -> (~((op (e3) (e3)) = (e2))) -> (((op (e3) (e0)) = (e1))\/(((op (e3) (e1)) = (e1))\/(((op (e3) (e2)) = (e1))\/((op (e3) (e3)) = (e1))))) -> ((op (e0) (e3)) = (e0)) -> (~((e0) = (e1))) -> False). % 15.41/15.60 do 0 intro. intros zenon_H44 zenon_H295 zenon_H121 zenon_H1cd zenon_H1cf zenon_H45 zenon_Hf1 zenon_H104 zenon_H140 zenon_H1df zenon_H5e zenon_Hdb zenon_Ha7 zenon_H124 zenon_H28a zenon_H3d zenon_H146 zenon_Hca zenon_H9e. % 15.41/15.60 apply (zenon_or_s _ _ zenon_H44); [ zenon_intro zenon_H47 | zenon_intro zenon_H46 ]. % 15.41/15.60 exact (zenon_H45 zenon_H47). % 15.41/15.60 apply (zenon_or_s _ _ zenon_H46); [ zenon_intro zenon_H22 | zenon_intro zenon_H48 ]. % 15.41/15.60 apply (zenon_or_s _ _ zenon_Hf1); [ zenon_intro zenon_H47 | zenon_intro zenon_Hf4 ]. % 15.41/15.60 exact (zenon_H45 zenon_H47). % 15.41/15.60 apply (zenon_or_s _ _ zenon_Hf4); [ zenon_intro zenon_Hd8 | zenon_intro zenon_Hf5 ]. % 15.41/15.60 apply (zenon_L225_); trivial. % 15.41/15.60 apply (zenon_or_s _ _ zenon_Hf5); [ zenon_intro zenon_Hae | zenon_intro zenon_Hee ]. % 15.41/15.60 apply (zenon_L816_); trivial. % 15.41/15.60 apply (zenon_L71_); trivial. % 15.41/15.60 apply (zenon_or_s _ _ zenon_H48); [ zenon_intro zenon_H29 | zenon_intro zenon_H37 ]. % 15.41/15.60 apply (zenon_or_s _ _ zenon_H146); [ zenon_intro zenon_Hee | zenon_intro zenon_H14b ]. % 15.41/15.60 apply (zenon_L71_); trivial. % 15.41/15.60 apply (zenon_or_s _ _ zenon_H14b); [ zenon_intro zenon_H13e | zenon_intro zenon_H14c ]. % 15.41/15.60 apply (zenon_L965_); trivial. % 15.41/15.60 apply (zenon_or_s _ _ zenon_H14c); [ zenon_intro zenon_H119 | zenon_intro zenon_H38 ]. % 15.41/15.60 apply (zenon_L124_); trivial. % 15.41/15.60 exact (zenon_H104 zenon_H38). % 15.41/15.60 apply (zenon_L73_); trivial. % 15.41/15.60 (* end of lemma zenon_L966_ *) % 15.41/15.60 assert (zenon_L967_ : (((op (e0) (e0)) = (e0))\/(((op (e1) (e0)) = (e0))\/(((op (e2) (e0)) = (e0))\/((op (e3) (e0)) = (e0))))) -> (~((op (e0) (e0)) = (e0))) -> (((op (e2) (e0)) = (e0))\/(((op (e2) (e1)) = (e0))\/(((op (e2) (e2)) = (e0))\/((op (e2) (e3)) = (e0))))) -> (~((op (e1) (op (e2) (e1))) = (op (e2) (e1)))) -> (~((op (e2) (e2)) = (e0))) -> (~((op (e0) (e3)) = (op (e2) (e3)))) -> (((op (e0) (e0)) = (e2))\/(((op (e0) (e1)) = (e2))\/(((op (e0) (e2)) = (e2))\/((op (e0) (e3)) = (e2))))) -> (~((op (e0) (e0)) = (e2))) -> (~((op (e1) (e1)) = (e3))) -> (~((op (e0) (e1)) = (op (e1) (e1)))) -> (~((op (e1) (e1)) = (e1))) -> (~((op (e1) (e1)) = (e0))) -> (((op (e1) (e1)) = (e0))\/(((op (e1) (e1)) = (e1))\/(((op (e1) (e1)) = (e2))\/((op (e1) (e1)) = (e3))))) -> (((op (e2) (e0)) = (e1))\/(((op (e2) (e1)) = (e1))\/(((op (e2) (e2)) = (e1))\/((op (e2) (e3)) = (e1))))) -> (~((op (e0) (e1)) = (op (e2) (e1)))) -> (~((op (e2) (e2)) = (e1))) -> (((op (e0) (e0)) = (e1))\/(((op (e0) (e1)) = (e1))\/(((op (e0) (e2)) = (e1))\/((op (e0) (e3)) = (e1))))) -> (~((op (e0) (op (e2) (e0))) = (op (e2) (e0)))) -> (((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 (e0) (e0)) = (e1))) -> (((op (e0) (e0)) = (e1))\/(((op (e1) (e0)) = (e1))\/(((op (e2) (e0)) = (e1))\/((op (e3) (e0)) = (e1))))) -> (~((op (e3) (e3)) = (e1))) -> (~((op (e0) (e2)) = (op (e3) (e2)))) -> (((op (e3) (e0)) = (e2))\/(((op (e3) (e1)) = (e2))\/(((op (e3) (e2)) = (e2))\/((op (e3) (e3)) = (e2))))) -> (~((e0) = (e2))) -> (~((e1) = (e2))) -> ((op (e2) (e3)) = (e2)) -> (~((op (e3) (op (e2) (e3))) = (op (e2) (e3)))) -> (~((op (e3) (e3)) = (e2))) -> (((op (e3) (e0)) = (e1))\/(((op (e3) (e1)) = (e1))\/(((op (e3) (e2)) = (e1))\/((op (e3) (e3)) = (e1))))) -> ((op (e0) (e3)) = (e0)) -> (~((e0) = (e1))) -> False). % 15.41/15.60 do 0 intro. intros zenon_Hf0 zenon_H20 zenon_H1f5 zenon_H290 zenon_H2e zenon_Hb4 zenon_H8e zenon_H8f zenon_H182 zenon_H23 zenon_H1b4 zenon_H145 zenon_H1b3 zenon_Hb7 zenon_Hde zenon_H52 zenon_H44 zenon_H295 zenon_H121 zenon_H1cd zenon_H1cf zenon_H45 zenon_Hf1 zenon_H104 zenon_H140 zenon_H1df zenon_H5e zenon_Ha7 zenon_H124 zenon_H28a zenon_H3d zenon_H146 zenon_Hca zenon_H9e. % 15.41/15.60 apply (zenon_or_s _ _ zenon_Hf0); [ zenon_intro zenon_H1f | zenon_intro zenon_Hf2 ]. % 15.41/15.60 exact (zenon_H20 zenon_H1f). % 15.41/15.60 apply (zenon_or_s _ _ zenon_Hf2); [ zenon_intro zenon_Had | zenon_intro zenon_Hf3 ]. % 15.41/15.60 apply (zenon_or_s _ _ zenon_H44); [ zenon_intro zenon_H47 | zenon_intro zenon_H46 ]. % 15.41/15.60 exact (zenon_H45 zenon_H47). % 15.41/15.60 apply (zenon_or_s _ _ zenon_H46); [ zenon_intro zenon_H22 | zenon_intro zenon_H48 ]. % 15.41/15.60 apply (zenon_L964_); trivial. % 15.41/15.60 apply (zenon_or_s _ _ zenon_H48); [ zenon_intro zenon_H29 | zenon_intro zenon_H37 ]. % 15.41/15.60 apply (zenon_L339_); trivial. % 15.41/15.60 apply (zenon_L73_); trivial. % 15.41/15.60 apply (zenon_or_s _ _ zenon_Hf3); [ zenon_intro zenon_Hcf | zenon_intro zenon_Hdb ]. % 15.41/15.60 apply (zenon_L341_); trivial. % 15.48/15.60 apply (zenon_L966_); trivial. % 15.48/15.60 (* end of lemma zenon_L967_ *) % 15.48/15.60 assert (zenon_L968_ : (((op (e1) (e0)) = (e0))\/(((op (e1) (e1)) = (e0))\/(((op (e1) (e2)) = (e0))\/((op (e1) (e3)) = (e0))))) -> ((op (e0) (e3)) = (e0)) -> ((~((op (e0) (e0)) = (e3)))\/((op (e0) (e3)) = (e0))) -> ((~((op (e1) (e1)) = (e2)))\/((op (e1) (e2)) = (e1))) -> (~((op (e2) (e0)) = (op (e2) (e2)))) -> (((op (e1) (e0)) = (e2))\/(((op (e1) (e1)) = (e2))\/(((op (e1) (e2)) = (e2))\/((op (e1) (e3)) = (e2))))) -> (((op (e0) (e0)) = (e3))\/(((op (e1) (e0)) = (e3))\/(((op (e2) (e0)) = (e3))\/((op (e3) (e0)) = (e3))))) -> (~((op (e1) (e2)) = (op (e1) (e3)))) -> (((op (e1) (e1)) = (e0))\/(((op (e1) (e1)) = (e1))\/(((op (e1) (e1)) = (e2))\/((op (e1) (e1)) = (e3))))) -> (~((op (e0) (e1)) = (op (e1) (e1)))) -> ((~((op (e2) (e2)) = (e0)))\/((op (e2) (e0)) = (e2))) -> (~((op (e0) (e0)) = (e0))) -> (((op (e0) (e0)) = (e0))\/(((op (e0) (e0)) = (e1))\/(((op (e0) (e0)) = (e2))\/((op (e0) (e0)) = (e3))))) -> (~((op (e2) (e0)) = (op (e2) (e1)))) -> ((~((op (e2) (e2)) = (e2)))\/((op (e2) (e2)) = (e2))) -> (~((op (e2) (op (e2) (e2))) = (op (e2) (e2)))) -> (~((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 (e0) (e3)) = (op (e3) (e3)))) -> ((op (e3) (e3)) = (e3)) -> (((op (e0) (e0)) = (e3))\/(((op (e0) (e1)) = (e3))\/(((op (e0) (e2)) = (e3))\/((op (e0) (e3)) = (e3))))) -> ((~((op (e2) (e2)) = (e3)))\/((op (e2) (e3)) = (e2))) -> (~((op (e2) (e1)) = (op (e2) (e3)))) -> (((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) (e0)) = (e3))\/(((op (e2) (e1)) = (e3))\/(((op (e2) (e2)) = (e3))\/((op (e2) (e3)) = (e3))))) -> (~((op (e3) (op (e2) (e3))) = (op (e2) (e3)))) -> (~((e1) = (e3))) -> (~((e1) = (e2))) -> (((op (e1) (e3)) = (e0))\/(((op (e1) (e3)) = (e1))\/(((op (e1) (e3)) = (e2))\/((op (e1) (e3)) = (e3))))) -> (~((op (e1) (e3)) = (op (e3) (e3)))) -> (~((op (e0) (e3)) = (op (e1) (e3)))) -> (~((op (e1) (e3)) = (op (e2) (e3)))) -> (((op (e2) (e0)) = (e1))\/(((op (e2) (e1)) = (e1))\/(((op (e2) (e2)) = (e1))\/((op (e2) (e3)) = (e1))))) -> (~((op (e0) (e1)) = (op (e2) (e1)))) -> (~((e0) = (e1))) -> (~((op (e2) (e0)) = (op (e2) (e3)))) -> (((op (e0) (e3)) = (e0))\/(((op (e1) (e3)) = (e0))\/(((op (e2) (e3)) = (e0))\/((op (e3) (e3)) = (e0))))) -> (~((op (e3) (e1)) = (op (e3) (e3)))) -> (((op (e0) (e1)) = (e3))\/(((op (e1) (e1)) = (e3))\/(((op (e2) (e1)) = (e3))\/((op (e3) (e1)) = (e3))))) -> (~((e2) = (e3))) -> (~((e0) = (e2))) -> (~((op (e0) (e0)) = (e2))) -> (~((op (e3) (e0)) = (op (e3) (e3)))) -> ((~((op (e3) (e3)) = (e0)))\/((op (e3) (e0)) = (e3))) -> ((~((op (e2) (e2)) = (e1)))\/((op (e2) (e1)) = (e2))) -> ((~((op (e1) (e1)) = (e3)))\/((op (e1) (e3)) = (e1))) -> (~((op (e1) (e1)) = (op (e1) (e2)))) -> (((op (e0) (e0)) = (e1))\/(((op (e0) (e1)) = (e1))\/(((op (e0) (e2)) = (e1))\/((op (e0) (e3)) = (e1))))) -> (~((op (e1) (e1)) = (op (e2) (e1)))) -> (~((op (e0) (e3)) = (op (e2) (e3)))) -> (((op (e0) (e1)) = (e2))\/(((op (e1) (e1)) = (e2))\/(((op (e2) (e1)) = (e2))\/((op (e3) (e1)) = (e2))))) -> (~((op (e0) (e1)) = (op (e0) (e3)))) -> (~((op (e1) (e1)) = (op (e1) (e3)))) -> ((~((op (e1) (e1)) = (e1)))\/((op (e1) (e1)) = (e1))) -> (~((op (e1) (e1)) = (e0))) -> (~((op (e1) (op (e2) (e1))) = (op (e2) (e1)))) -> (((op (e0) (e2)) = (e0))\/(((op (e1) (e2)) = (e0))\/(((op (e2) (e2)) = (e0))\/((op (e3) (e2)) = (e0))))) -> (~((op (e3) (e1)) = (op (e3) (e2)))) -> (~((op (e2) (e2)) = (e0))) -> (~((op (e1) (e2)) = (op (e2) (e2)))) -> (~((op (e2) (e2)) = (e1))) -> ((~((op (e1) (e1)) = (e0)))\/((op (e1) (e0)) = (e1))) -> (~((op (e0) (e0)) = (e1))) -> (((op (e0) (e0)) = (e2))\/(((op (e1) (e0)) = (e2))\/(((op (e2) (e0)) = (e2))\/((op (e3) (e0)) = (e2))))) -> (((op (e0) (e2)) = (e3))\/(((op (e1) (e2)) = (e3))\/(((op (e2) (e2)) = (e3))\/((op (e3) (e2)) = (e3))))) -> (~((op (e3) (e2)) = (op (e3) (e3)))) -> (~((op (e2) (e1)) = (op (e3) (e1)))) -> (~((op (e0) (e2)) = (op (e0) (e3)))) -> (((op (e2) (e0)) = (e2))\/(((op (e2) (e1)) = (e2))\/(((op (e2) (e2)) = (e2))\/((op (e2) (e3)) = (e2))))) -> (((op (e1) (e0)) = (e1))\/(((op (e1) (e1)) = (e1))\/(((op (e1) (e2)) = (e1))\/((op (e1) (e3)) = (e1))))) -> (((op (e0) (e0)) = (e1))\/(((op (e1) (e0)) = (e1))\/(((op (e2) (e0)) = (e1))\/((op (e3) (e0)) = (e1))))) -> (~((op (e1) (e0)) = (op (e1) (e3)))) -> ((~((op (e3) (e3)) = (e2)))\/((op (e3) (e2)) = (e3))) -> (~((op (e1) (e0)) = (op (e1) (e1)))) -> (~((op (e0) (e2)) = (op (e1) (e2)))) -> (~((op (e1) (e0)) = (op (e1) (e2)))) -> (~((op (e0) (e2)) = (op (e3) (e2)))) -> (((op (e3) (e0)) = (e2))\/(((op (e3) (e1)) = (e2))\/(((op (e3) (e2)) = (e2))\/((op (e3) (e3)) = (e2))))) -> (((op (e1) (e0)) = (e3))\/(((op (e1) (e1)) = (e3))\/(((op (e1) (e2)) = (e3))\/((op (e1) (e3)) = (e3))))) -> (~((op (e2) (e1)) = (op (e2) (e2)))) -> (((op (e0) (e1)) = (e0))\/(((op (e1) (e1)) = (e0))\/(((op (e2) (e1)) = (e0))\/((op (e3) (e1)) = (e0))))) -> ((~((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 (e0) (op (e2) (e0))) = (op (e2) (e0)))) -> (((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 (e1) (e1)) = (e1))) -> (~((op (e1) (e1)) = (e3))) -> False). % 15.48/15.60 do 0 intro. intros zenon_H163 zenon_Hca zenon_H236 zenon_H1d3 zenon_H17a zenon_H84 zenon_Hbe zenon_H1d0 zenon_H1b3 zenon_H23 zenon_H1d4 zenon_H20 zenon_H12a zenon_H154 zenon_Haa zenon_H294 zenon_H4b zenon_H2d zenon_H28 zenon_H36 zenon_H42 zenon_H58 zenon_H1c3 zenon_H1e2 zenon_H8e zenon_H1f5 zenon_He6 zenon_H28a zenon_Ha3 zenon_Ha7 zenon_H25b zenon_H8b zenon_H80 zenon_H244 zenon_Hb7 zenon_Hde zenon_H9e zenon_Hce zenon_Hd3 zenon_H12d zenon_H199 zenon_H6a zenon_H5e zenon_H8f zenon_Hbb zenon_H10f zenon_H1e3 zenon_H1d2 zenon_H116 zenon_H44 zenon_Hb1 zenon_Hb4 zenon_H1a2 zenon_H1cd zenon_H11e zenon_H1d8 zenon_H145 zenon_H290 zenon_H16f zenon_H135 zenon_H2e zenon_H7d zenon_H52 zenon_H1e4 zenon_H45 zenon_Heb zenon_H175 zenon_H173 zenon_H13c zenon_Hc9 zenon_H237 zenon_H1c5 zenon_Hf1 zenon_H1cf zenon_H10e zenon_Hd7 zenon_H87 zenon_H166 zenon_H140 zenon_H1df zenon_H90 zenon_H157 zenon_H144 zenon_H10c zenon_Hf0 zenon_H295 zenon_H121 zenon_H146 zenon_H1b4 zenon_H182. % 15.48/15.60 apply (zenon_or_s _ _ zenon_Haa); [ zenon_intro zenon_H2f | zenon_intro zenon_H35 ]. % 15.48/15.60 apply (zenon_or_s _ _ zenon_H1c3); [ zenon_intro zenon_H30 | zenon_intro zenon_H124 ]. % 15.48/15.60 apply (zenon_or_s _ _ zenon_H163); [ zenon_intro zenon_Had | zenon_intro zenon_H164 ]. % 15.48/15.60 apply (zenon_L962_); trivial. % 15.48/15.60 apply (zenon_or_s _ _ zenon_H164); [ zenon_intro zenon_H149 | zenon_intro zenon_H165 ]. % 15.48/15.60 exact (zenon_H145 zenon_H149). % 15.48/15.60 apply (zenon_or_s _ _ zenon_H165); [ zenon_intro zenon_H15d | zenon_intro zenon_Hcc ]. % 15.48/15.60 apply (zenon_L335_); trivial. % 15.48/15.60 apply (zenon_L155_); trivial. % 15.48/15.60 apply (zenon_or_s _ _ zenon_H10c); [ zenon_intro zenon_H104 | zenon_intro zenon_H10a ]. % 15.48/15.60 apply (zenon_or_s _ _ zenon_H10e); [ zenon_intro zenon_H3d | zenon_intro zenon_H106 ]. % 15.48/15.60 apply (zenon_L967_); trivial. % 15.48/15.60 apply (zenon_L153_); trivial. % 15.48/15.60 apply (zenon_L102_); trivial. % 15.48/15.60 apply (zenon_L343_); trivial. % 15.48/15.60 (* end of lemma zenon_L968_ *) % 15.48/15.60 assert (zenon_L969_ : (((op (e1) (e0)) = (e0))\/(((op (e1) (e1)) = (e0))\/(((op (e1) (e2)) = (e0))\/((op (e1) (e3)) = (e0))))) -> (~((op (e3) (e1)) = (op (e3) (e2)))) -> (~((op (e2) (e2)) = (e0))) -> ((~((op (e0) (e0)) = (e3)))\/((op (e0) (e3)) = (e0))) -> (~((op (e2) (e0)) = (op (e2) (e1)))) -> (((op (e0) (e0)) = (e1))\/(((op (e0) (e1)) = (e1))\/(((op (e0) (e2)) = (e1))\/((op (e0) (e3)) = (e1))))) -> (~((op (e0) (e3)) = (op (e2) (e3)))) -> (~((op (e1) (e1)) = (op (e2) (e1)))) -> (~((op (e1) (e1)) = (op (e1) (e3)))) -> (((op (e0) (e1)) = (e0))\/(((op (e1) (e1)) = (e0))\/(((op (e2) (e1)) = (e0))\/((op (e3) (e1)) = (e0))))) -> (((op (e0) (e1)) = (e3))\/(((op (e1) (e1)) = (e3))\/(((op (e2) (e1)) = (e3))\/((op (e3) (e1)) = (e3))))) -> (~((op (e3) (e1)) = (op (e3) (e3)))) -> (~((op (e2) (e1)) = (op (e2) (e2)))) -> (~((op (e1) (op (e2) (e1))) = (op (e2) (e1)))) -> ((~((op (e2) (e2)) = (e3)))\/((op (e2) (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 (e3) (e0)) = (e2))\/(((op (e3) (e1)) = (e2))\/(((op (e3) (e2)) = (e2))\/((op (e3) (e3)) = (e2))))) -> (~((op (e0) (e2)) = (op (e3) (e2)))) -> (((op (e0) (e0)) = (e0))\/(((op (e0) (e0)) = (e1))\/(((op (e0) (e0)) = (e2))\/((op (e0) (e0)) = (e3))))) -> (~((op (e0) (e0)) = (e0))) -> (((op (e1) (e3)) = (e0))\/(((op (e1) (e3)) = (e1))\/(((op (e1) (e3)) = (e2))\/((op (e1) (e3)) = (e3))))) -> ((~((op (e1) (e1)) = (e2)))\/((op (e1) (e2)) = (e1))) -> (~((op (e1) (e0)) = (op (e1) (e2)))) -> ((~((op (e2) (e2)) = (e0)))\/((op (e2) (e0)) = (e2))) -> (~((op (e0) (e2)) = (op (e1) (e2)))) -> (~((op (e2) (e0)) = (op (e2) (e3)))) -> ((~((op (e2) (e2)) = (e2)))\/((op (e2) (e2)) = (e2))) -> (~((op (e2) (op (e2) (e2))) = (op (e2) (e2)))) -> (~((op (e2) (e1)) = (op (e2) (e3)))) -> ((~((op (e2) (e2)) = (e1)))\/((op (e2) (e1)) = (e2))) -> ((~((op (e1) (e1)) = (e3)))\/((op (e1) (e3)) = (e1))) -> (~((op (e1) (e0)) = (op (e1) (e1)))) -> ((~((op (e1) (e1)) = (e1)))\/((op (e1) (e1)) = (e1))) -> ((~((op (e3) (e3)) = (e2)))\/((op (e3) (e2)) = (e3))) -> (~((op (e0) (e1)) = (op (e0) (e3)))) -> (~((op (e1) (e0)) = (op (e1) (e3)))) -> (((op (e0) (e0)) = (e1))\/(((op (e1) (e0)) = (e1))\/(((op (e2) (e0)) = (e1))\/((op (e3) (e0)) = (e1))))) -> (((op (e1) (e0)) = (e1))\/(((op (e1) (e1)) = (e1))\/(((op (e1) (e2)) = (e1))\/((op (e1) (e3)) = (e1))))) -> (((op (e2) (e0)) = (e2))\/(((op (e2) (e1)) = (e2))\/(((op (e2) (e2)) = (e2))\/((op (e2) (e3)) = (e2))))) -> (~((op (e0) (e2)) = (op (e0) (e3)))) -> (~((e0) = (e2))) -> (((op (e0) (e3)) = (e0))\/(((op (e1) (e3)) = (e0))\/(((op (e2) (e3)) = (e0))\/((op (e3) (e3)) = (e0))))) -> (~((e2) = (e3))) -> (~((e1) = (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)) = (e0))\/(((op (e2) (e1)) = (e0))\/(((op (e2) (e2)) = (e0))\/((op (e2) (e3)) = (e0))))) -> (~((op (e2) (e1)) = (op (e3) (e1)))) -> (((op (e0) (e1)) = (e2))\/(((op (e1) (e1)) = (e2))\/(((op (e2) (e1)) = (e2))\/((op (e3) (e1)) = (e2))))) -> (~((e0) = (e3))) -> (~((op (e3) (e2)) = (op (e3) (e3)))) -> (((op (e0) (e2)) = (e3))\/(((op (e1) (e2)) = (e3))\/(((op (e2) (e2)) = (e3))\/((op (e3) (e2)) = (e3))))) -> (~((op (e0) (e1)) = (op (e1) (e1)))) -> (((op (e0) (e0)) = (e2))\/(((op (e1) (e0)) = (e2))\/(((op (e2) (e0)) = (e2))\/((op (e3) (e0)) = (e2))))) -> (((op (e1) (e0)) = (e2))\/(((op (e1) (e1)) = (e2))\/(((op (e1) (e2)) = (e2))\/((op (e1) (e3)) = (e2))))) -> (~((op (e0) (e3)) = (op (e1) (e3)))) -> (((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 (e3) (op (e2) (e3))) = (op (e2) (e3)))) -> (~((op (e0) (e1)) = (op (e2) (e1)))) -> (~((op (e0) (e2)) = (op (e2) (e2)))) -> (~((op (e0) (e3)) = (op (e3) (e3)))) -> (((op (e0) (e0)) = (e3))\/(((op (e0) (e1)) = (e3))\/(((op (e0) (e2)) = (e3))\/((op (e0) (e3)) = (e3))))) -> (~((e1) = (e3))) -> (((op (e1) (e1)) = (e0))\/(((op (e1) (e1)) = (e1))\/(((op (e1) (e1)) = (e2))\/((op (e1) (e1)) = (e3))))) -> (~((op (e3) (e0)) = (op (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)) = (e1))) -> ((~((op (e3) (e3)) = (e0)))\/((op (e3) (e0)) = (e3))) -> (~((op (e1) (e2)) = (op (e1) (e3)))) -> ((~((op (e1) (e1)) = (e0)))\/((op (e1) (e0)) = (e1))) -> (((op (e0) (e2)) = (e0))\/(((op (e1) (e2)) = (e0))\/(((op (e2) (e2)) = (e0))\/((op (e3) (e2)) = (e0))))) -> (~((op (e2) (e0)) = (op (e2) (e2)))) -> (~((op (e0) (e0)) = (e2))) -> (~((op (e1) (e1)) = (op (e1) (e2)))) -> (~((op (e1) (e1)) = (e0))) -> (~((op (e2) (e2)) = (e3))) -> (~((op (e2) (e2)) = (e2))) -> (~((op (e2) (e2)) = (e1))) -> (~((op (e1) (e2)) = (op (e2) (e2)))) -> (((op (e2) (e2)) = (e0))\/(((op (e2) (e2)) = (e1))\/(((op (e2) (e2)) = (e2))\/((op (e2) (e2)) = (e3))))) -> (~((e0) = (e1))) -> ((op (e1) (e3)) = (e1)) -> False). % 15.48/15.60 do 0 intro. intros zenon_H163 zenon_H135 zenon_H2e zenon_H236 zenon_H154 zenon_H44 zenon_Hb4 zenon_Hb1 zenon_H11e zenon_H144 zenon_H199 zenon_H12d zenon_H157 zenon_H290 zenon_H1c3 zenon_H8b zenon_H90 zenon_H1df zenon_H140 zenon_H12a zenon_H20 zenon_H25b zenon_H1d3 zenon_H166 zenon_H1d4 zenon_H87 zenon_Hce zenon_Haa zenon_H294 zenon_H1e2 zenon_H1e3 zenon_H1d2 zenon_Hd7 zenon_H1d8 zenon_H10e zenon_H1cd zenon_H1cf zenon_Hf1 zenon_H1c5 zenon_H237 zenon_Hc9 zenon_H5e zenon_Hd3 zenon_H6a zenon_Ha7 zenon_H244 zenon_Hb7 zenon_H1f5 zenon_H13c zenon_H1a2 zenon_H4b zenon_H173 zenon_H175 zenon_H23 zenon_Heb zenon_H84 zenon_H80 zenon_H8e zenon_He6 zenon_H28a zenon_Hde zenon_H28 zenon_H36 zenon_H58 zenon_Ha3 zenon_H1b3 zenon_Hbb zenon_H42 zenon_Hbe zenon_H45 zenon_H10f zenon_H1d0 zenon_H1e4 zenon_H16f zenon_H17a zenon_H8f zenon_H116 zenon_H145 zenon_H30 zenon_H2f zenon_H52 zenon_H7d zenon_H2d zenon_H9e zenon_H11f. % 15.48/15.60 apply (zenon_or_s _ _ zenon_H163); [ zenon_intro zenon_Had | zenon_intro zenon_H164 ]. % 15.48/15.60 apply (zenon_L962_); trivial. % 15.48/15.60 apply (zenon_or_s _ _ zenon_H164); [ zenon_intro zenon_H149 | zenon_intro zenon_H165 ]. % 15.48/15.60 exact (zenon_H145 zenon_H149). % 15.48/15.60 apply (zenon_or_s _ _ zenon_H165); [ zenon_intro zenon_H15d | zenon_intro zenon_Hcc ]. % 15.48/15.60 apply (zenon_L335_); trivial. % 15.48/15.60 apply (zenon_L208_); trivial. % 15.48/15.60 (* end of lemma zenon_L969_ *) % 15.48/15.60 assert (zenon_L970_ : (((op (e0) (e0)) = (e1))\/(((op (e1) (e0)) = (e1))\/(((op (e2) (e0)) = (e1))\/((op (e3) (e0)) = (e1))))) -> (~((op (e0) (e0)) = (e1))) -> (~((op (e1) (e0)) = (op (e1) (e3)))) -> (((op (e0) (e0)) = (e2))\/(((op (e0) (e1)) = (e2))\/(((op (e0) (e2)) = (e2))\/((op (e0) (e3)) = (e2))))) -> (~((op (e0) (e0)) = (e2))) -> (~((op (e3) (e3)) = (e2))) -> (~((op (e3) (op (e2) (e3))) = (op (e2) (e3)))) -> ((op (e2) (e3)) = (e2)) -> (~((op (e0) (e1)) = (op (e3) (e1)))) -> (((op (e3) (e0)) = (e2))\/(((op (e3) (e1)) = (e2))\/(((op (e3) (e2)) = (e2))\/((op (e3) (e3)) = (e2))))) -> (~((e1) = (e2))) -> ((op (e0) (e2)) = (e1)) -> (((op (e0) (e3)) = (e0))\/(((op (e1) (e3)) = (e0))\/(((op (e2) (e3)) = (e0))\/((op (e3) (e3)) = (e0))))) -> (~((e0) = (e2))) -> ((op (e1) (e3)) = (e1)) -> (~((e0) = (e1))) -> ((op (e2) (e0)) = (e0)) -> (~((op (e2) (e0)) = (op (e2) (e3)))) -> (~((op (e3) (e3)) = (e0))) -> False). % 15.48/15.60 do 0 intro. intros zenon_Hf1 zenon_H45 zenon_H1cf zenon_H8e zenon_H8f zenon_H3d zenon_H28a zenon_H124 zenon_H138 zenon_H1df zenon_Ha7 zenon_H29 zenon_Hd3 zenon_H5e zenon_H11f zenon_H9e zenon_Hcf zenon_Hce zenon_H3c. % 15.48/15.60 apply (zenon_or_s _ _ zenon_Hf1); [ zenon_intro zenon_H47 | zenon_intro zenon_Hf4 ]. % 15.48/15.60 exact (zenon_H45 zenon_H47). % 15.48/15.60 apply (zenon_or_s _ _ zenon_Hf4); [ zenon_intro zenon_Hd8 | zenon_intro zenon_Hf5 ]. % 15.48/15.60 apply (zenon_L224_); trivial. % 15.48/15.60 apply (zenon_or_s _ _ zenon_Hf5); [ zenon_intro zenon_Hae | zenon_intro zenon_Hee ]. % 15.48/15.60 apply (zenon_L269_); trivial. % 15.48/15.60 apply (zenon_or_s _ _ zenon_H8e); [ zenon_intro zenon_H92 | zenon_intro zenon_H91 ]. % 15.48/15.60 exact (zenon_H8f zenon_H92). % 15.48/15.60 apply (zenon_or_s _ _ zenon_H91); [ zenon_intro zenon_H5d | zenon_intro zenon_H93 ]. % 15.48/15.60 apply (zenon_L852_); trivial. % 15.48/15.60 apply (zenon_or_s _ _ zenon_H93); [ zenon_intro zenon_H63 | zenon_intro zenon_H81 ]. % 15.48/15.60 apply (zenon_L104_); trivial. % 15.48/15.60 apply (zenon_L373_); trivial. % 15.48/15.60 (* end of lemma zenon_L970_ *) % 15.48/15.60 assert (zenon_L971_ : (((op (e0) (e0)) = (e0))\/(((op (e1) (e0)) = (e0))\/(((op (e2) (e0)) = (e0))\/((op (e3) (e0)) = (e0))))) -> (~((op (e0) (e0)) = (e0))) -> (((op (e2) (e0)) = (e0))\/(((op (e2) (e1)) = (e0))\/(((op (e2) (e2)) = (e0))\/((op (e2) (e3)) = (e0))))) -> (~((op (e1) (op (e2) (e1))) = (op (e2) (e1)))) -> (~((op (e2) (e2)) = (e0))) -> (~((op (e0) (e3)) = (op (e2) (e3)))) -> (((op (e0) (e0)) = (e2))\/(((op (e0) (e1)) = (e2))\/(((op (e0) (e2)) = (e2))\/((op (e0) (e3)) = (e2))))) -> (~((op (e0) (e0)) = (e2))) -> (~((op (e0) (e1)) = (op (e3) (e1)))) -> (((op (e0) (e3)) = (e0))\/(((op (e1) (e3)) = (e0))\/(((op (e2) (e3)) = (e0))\/((op (e3) (e3)) = (e0))))) -> ((op (e1) (e3)) = (e1)) -> (~((op (e2) (e0)) = (op (e2) (e3)))) -> (~((op (e3) (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 (e2) (e2)) = (e1))) -> (((op (e0) (e0)) = (e1))\/(((op (e0) (e1)) = (e1))\/(((op (e0) (e2)) = (e1))\/((op (e0) (e3)) = (e1))))) -> (~((op (e0) (op (e2) (e0))) = (op (e2) (e0)))) -> (((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 (e0) (e0)) = (e1))) -> (((op (e0) (e0)) = (e1))\/(((op (e1) (e0)) = (e1))\/(((op (e2) (e0)) = (e1))\/((op (e3) (e0)) = (e1))))) -> (~((op (e3) (e3)) = (e1))) -> (~((op (e0) (e2)) = (op (e3) (e2)))) -> (((op (e3) (e0)) = (e2))\/(((op (e3) (e1)) = (e2))\/(((op (e3) (e2)) = (e2))\/((op (e3) (e3)) = (e2))))) -> (~((e0) = (e2))) -> (~((e1) = (e2))) -> ((op (e2) (e3)) = (e2)) -> (~((op (e3) (op (e2) (e3))) = (op (e2) (e3)))) -> (~((op (e3) (e3)) = (e2))) -> (((op (e3) (e0)) = (e1))\/(((op (e3) (e1)) = (e1))\/(((op (e3) (e2)) = (e1))\/((op (e3) (e3)) = (e1))))) -> ((op (e0) (e3)) = (e0)) -> (~((e0) = (e1))) -> False). % 15.48/15.60 do 0 intro. intros zenon_Hf0 zenon_H20 zenon_H1f5 zenon_H290 zenon_H2e zenon_Hb4 zenon_H8e zenon_H8f zenon_H138 zenon_Hd3 zenon_H11f zenon_Hce zenon_H3c zenon_Hb7 zenon_Hde zenon_H52 zenon_H44 zenon_H295 zenon_H121 zenon_H1cd zenon_H1cf zenon_H45 zenon_Hf1 zenon_H104 zenon_H140 zenon_H1df zenon_H5e zenon_Ha7 zenon_H124 zenon_H28a zenon_H3d zenon_H146 zenon_Hca zenon_H9e. % 15.48/15.60 apply (zenon_or_s _ _ zenon_Hf0); [ zenon_intro zenon_H1f | zenon_intro zenon_Hf2 ]. % 15.48/15.60 exact (zenon_H20 zenon_H1f). % 15.48/15.60 apply (zenon_or_s _ _ zenon_Hf2); [ zenon_intro zenon_Had | zenon_intro zenon_Hf3 ]. % 15.48/15.60 apply (zenon_or_s _ _ zenon_H44); [ zenon_intro zenon_H47 | zenon_intro zenon_H46 ]. % 15.48/15.60 exact (zenon_H45 zenon_H47). % 15.48/15.60 apply (zenon_or_s _ _ zenon_H46); [ zenon_intro zenon_H22 | zenon_intro zenon_H48 ]. % 15.48/15.60 apply (zenon_L964_); trivial. % 15.48/15.60 apply (zenon_or_s _ _ zenon_H48); [ zenon_intro zenon_H29 | zenon_intro zenon_H37 ]. % 15.48/15.60 apply (zenon_or_s _ _ zenon_H1f5); [ zenon_intro zenon_Hcf | zenon_intro zenon_H1f9 ]. % 15.48/15.60 apply (zenon_L970_); trivial. % 15.48/15.60 apply (zenon_or_s _ _ zenon_H1f9); [ zenon_intro zenon_H14a | zenon_intro zenon_H1fa ]. % 15.48/15.60 apply (zenon_L940_); trivial. % 15.48/15.60 apply (zenon_or_s _ _ zenon_H1fa); [ zenon_intro zenon_H32 | zenon_intro zenon_Hd0 ]. % 15.48/15.60 exact (zenon_H2e zenon_H32). % 15.48/15.60 apply (zenon_L963_); trivial. % 15.48/15.60 apply (zenon_L73_); trivial. % 15.48/15.60 apply (zenon_or_s _ _ zenon_Hf3); [ zenon_intro zenon_Hcf | zenon_intro zenon_Hdb ]. % 15.48/15.60 apply (zenon_or_s _ _ zenon_H44); [ zenon_intro zenon_H47 | zenon_intro zenon_H46 ]. % 15.48/15.60 exact (zenon_H45 zenon_H47). % 15.48/15.60 apply (zenon_or_s _ _ zenon_H46); [ zenon_intro zenon_H22 | zenon_intro zenon_H48 ]. % 15.48/15.60 apply (zenon_L340_); trivial. % 15.48/15.60 apply (zenon_or_s _ _ zenon_H48); [ zenon_intro zenon_H29 | zenon_intro zenon_H37 ]. % 15.48/15.60 apply (zenon_L970_); trivial. % 15.48/15.60 apply (zenon_L73_); trivial. % 15.48/15.60 apply (zenon_L966_); trivial. % 15.48/15.60 (* end of lemma zenon_L971_ *) % 15.48/15.60 assert (zenon_L972_ : (((op (e2) (e0)) = (e0))\/(((op (e2) (e1)) = (e0))\/(((op (e2) (e2)) = (e0))\/((op (e2) (e3)) = (e0))))) -> ((op (e3) (e3)) = (e3)) -> (~((op (e3) (op (e2) (e3))) = (op (e2) (e3)))) -> (~((op (e2) (e2)) = (e3))) -> (~((e2) = (e3))) -> (~((e0) = (e3))) -> (((op (e2) (e0)) = (e3))\/(((op (e2) (e1)) = (e3))\/(((op (e2) (e2)) = (e3))\/((op (e2) (e3)) = (e3))))) -> ((op (e2) (e1)) = (e2)) -> (~((e0) = (e2))) -> (~((op (e2) (e2)) = (e0))) -> (~((op (e0) (e3)) = (op (e2) (e3)))) -> ((op (e0) (e3)) = (e0)) -> False). % 15.48/15.60 do 0 intro. intros zenon_H1f5 zenon_H42 zenon_H28a zenon_H30 zenon_H6a zenon_H4b zenon_He6 zenon_H156 zenon_H5e zenon_H2e zenon_Hb4 zenon_Hca. % 15.48/15.60 apply (zenon_or_s _ _ zenon_H1f5); [ zenon_intro zenon_Hcf | zenon_intro zenon_H1f9 ]. % 15.48/15.60 apply (zenon_L924_); trivial. % 15.48/15.60 apply (zenon_or_s _ _ zenon_H1f9); [ zenon_intro zenon_H14a | zenon_intro zenon_H1fa ]. % 15.48/15.60 apply (zenon_L351_); trivial. % 15.48/15.60 apply (zenon_or_s _ _ zenon_H1fa); [ zenon_intro zenon_H32 | zenon_intro zenon_Hd0 ]. % 15.48/15.60 exact (zenon_H2e zenon_H32). % 15.48/15.60 apply (zenon_L963_); trivial. % 15.48/15.60 (* end of lemma zenon_L972_ *) % 15.48/15.60 assert (zenon_L973_ : ((~((op (e2) (e2)) = (e3)))\/((op (e2) (e3)) = (e2))) -> ((op (e2) (e1)) = (e2)) -> (~((op (e2) (e1)) = (op (e2) (e3)))) -> (~((e0) = (e3))) -> ((op (e0) (e2)) = (e0)) -> (~((e1) = (e3))) -> ((op (e1) (e2)) = (e1)) -> (~((op (e3) (e2)) = (op (e3) (e3)))) -> ((op (e3) (e3)) = (e3)) -> (((op (e0) (e2)) = (e3))\/(((op (e1) (e2)) = (e3))\/(((op (e2) (e2)) = (e3))\/((op (e3) (e2)) = (e3))))) -> False). % 15.48/15.60 do 0 intro. intros zenon_H1c3 zenon_H156 zenon_H1e2 zenon_H4b zenon_Hab zenon_Ha3 zenon_H117 zenon_H173 zenon_H42 zenon_H175. % 15.48/15.60 apply (zenon_or_s _ _ zenon_H1c3); [ zenon_intro zenon_H30 | zenon_intro zenon_H124 ]. % 15.48/15.60 apply (zenon_L197_); trivial. % 15.48/15.60 apply (zenon_L256_); trivial. % 15.48/15.60 (* end of lemma zenon_L973_ *) % 15.48/15.60 assert (zenon_L974_ : ((~((op (e2) (e2)) = (e1)))\/((op (e2) (e1)) = (e2))) -> (~((op (e2) (e0)) = (op (e2) (e1)))) -> ((~((op (e2) (e2)) = (e3)))\/((op (e2) (e3)) = (e2))) -> (~((op (e2) (e0)) = (op (e2) (e3)))) -> (~((op (e0) (e0)) = (e1))) -> (((op (e0) (e0)) = (e3))\/(((op (e0) (e1)) = (e3))\/(((op (e0) (e2)) = (e3))\/((op (e0) (e3)) = (e3))))) -> (~((op (e0) (e3)) = (op (e3) (e3)))) -> (~((e1) = (e3))) -> (~((op (e1) (e1)) = (e3))) -> (~((op (e0) (e2)) = (op (e1) (e2)))) -> (~((op (e1) (e3)) = (op (e3) (e3)))) -> (((op (e1) (e0)) = (e3))\/(((op (e1) (e1)) = (e3))\/(((op (e1) (e2)) = (e3))\/((op (e1) (e3)) = (e3))))) -> (~((e2) = (e3))) -> ((op (e2) (e0)) = (e2)) -> (~((op (e0) (e1)) = (op (e2) (e1)))) -> (~((op (e3) (op (e2) (e3))) = (op (e2) (e3)))) -> ((op (e3) (e3)) = (e3)) -> (((op (e2) (e0)) = (e3))\/(((op (e2) (e1)) = (e3))\/(((op (e2) (e2)) = (e3))\/((op (e2) (e3)) = (e3))))) -> (~((op (e0) (e0)) = (e3))) -> (~((e1) = (e2))) -> (((op (e0) (e0)) = (e2))\/(((op (e0) (e1)) = (e2))\/(((op (e0) (e2)) = (e2))\/((op (e0) (e3)) = (e2))))) -> (((op (e1) (e0)) = (e2))\/(((op (e1) (e1)) = (e2))\/(((op (e1) (e2)) = (e2))\/((op (e1) (e3)) = (e2))))) -> (~((op (e0) (e3)) = (op (e1) (e3)))) -> ((op (e1) (e2)) = (e1)) -> (((op (e2) (e2)) = (e0))\/(((op (e2) (e2)) = (e1))\/(((op (e2) (e2)) = (e2))\/((op (e2) (e2)) = (e3))))) -> (((op (e0) (e0)) = (e3))\/(((op (e1) (e0)) = (e3))\/(((op (e2) (e0)) = (e3))\/((op (e3) (e0)) = (e3))))) -> (~((op (e1) (e1)) = (e0))) -> (~((op (e1) (e1)) = (e1))) -> (~((op (e0) (e1)) = (op (e1) (e1)))) -> (((op (e1) (e1)) = (e0))\/(((op (e1) (e1)) = (e1))\/(((op (e1) (e1)) = (e2))\/((op (e1) (e1)) = (e3))))) -> (~((op (e0) (e0)) = (e2))) -> (((op (e0) (e0)) = (e1))\/(((op (e1) (e0)) = (e1))\/(((op (e2) (e0)) = (e1))\/((op (e3) (e0)) = (e1))))) -> (~((op (e2) (e0)) = (op (e2) (e2)))) -> ((~((op (e2) (e2)) = (e2)))\/((op (e2) (e2)) = (e2))) -> False). % 15.48/15.60 do 0 intro. intros zenon_H1e3 zenon_H154 zenon_H1c3 zenon_Hce zenon_H45 zenon_H58 zenon_H36 zenon_Ha3 zenon_H182 zenon_H87 zenon_H8b zenon_H90 zenon_H6a zenon_Hdd zenon_Hde zenon_H28a zenon_H42 zenon_He6 zenon_H59 zenon_Ha7 zenon_H8e zenon_H84 zenon_H80 zenon_H117 zenon_H2d zenon_Hbe zenon_H145 zenon_H1b4 zenon_H23 zenon_H1b3 zenon_H8f zenon_Hf1 zenon_H17a zenon_Haa. % 15.48/15.60 apply (zenon_or_s _ _ zenon_H1e3); [ zenon_intro zenon_H52 | zenon_intro zenon_H156 ]. % 15.48/15.60 apply (zenon_or_s _ _ zenon_Haa); [ zenon_intro zenon_H2f | zenon_intro zenon_H35 ]. % 15.48/15.60 apply (zenon_or_s _ _ zenon_H1c3); [ zenon_intro zenon_H30 | zenon_intro zenon_H124 ]. % 15.48/15.60 apply (zenon_L867_); trivial. % 15.48/15.60 apply (zenon_L119_); trivial. % 15.48/15.60 apply (zenon_L161_); trivial. % 15.48/15.60 apply (zenon_L284_); trivial. % 15.48/15.60 (* end of lemma zenon_L974_ *) % 15.48/15.60 assert (zenon_L975_ : (((op (e0) (e0)) = (e0))\/(((op (e0) (e1)) = (e0))\/(((op (e0) (e2)) = (e0))\/((op (e0) (e3)) = (e0))))) -> (~((op (e0) (e0)) = (e0))) -> (~((e1) = (e2))) -> (((op (e3) (e0)) = (e2))\/(((op (e3) (e1)) = (e2))\/(((op (e3) (e2)) = (e2))\/((op (e3) (e3)) = (e2))))) -> (~((op (e2) (e1)) = (op (e3) (e1)))) -> (~((op (e0) (e2)) = (op (e3) (e2)))) -> (~((op (e3) (e3)) = (e2))) -> (~((op (e0) (e1)) = (op (e2) (e1)))) -> (((op (e0) (e0)) = (e3))\/(((op (e0) (e1)) = (e3))\/(((op (e0) (e2)) = (e3))\/((op (e0) (e3)) = (e3))))) -> (~((op (e0) (e0)) = (e3))) -> (((op (e0) (e1)) = (e3))\/(((op (e1) (e1)) = (e3))\/(((op (e2) (e1)) = (e3))\/((op (e3) (e1)) = (e3))))) -> (~((e1) = (e3))) -> (~((op (e1) (e1)) = (e3))) -> (((op (e2) (e0)) = (e1))\/(((op (e2) (e1)) = (e1))\/(((op (e2) (e2)) = (e1))\/((op (e2) (e3)) = (e1))))) -> (~((op (e1) (e1)) = (e0))) -> (~((op (e3) (e1)) = (op (e3) (e3)))) -> (((op (e0) (e1)) = (e0))\/(((op (e1) (e1)) = (e0))\/(((op (e2) (e1)) = (e0))\/((op (e3) (e1)) = (e0))))) -> (~((op (e0) (e3)) = (op (e3) (e3)))) -> (((op (e0) (e0)) = (e2))\/(((op (e0) (e1)) = (e2))\/(((op (e0) (e2)) = (e2))\/((op (e0) (e3)) = (e2))))) -> ((~((op (e1) (e1)) = (e1)))\/((op (e1) (e1)) = (e1))) -> (~((op (e1) (e0)) = (op (e1) (e1)))) -> ((~((op (e1) (e1)) = (e3)))\/((op (e1) (e3)) = (e1))) -> (~((op (e1) (e0)) = (op (e1) (e3)))) -> ((~((op (e2) (e2)) = (e1)))\/((op (e2) (e1)) = (e2))) -> (~((op (e2) (e1)) = (op (e2) (e3)))) -> ((~((op (e2) (e2)) = (e3)))\/((op (e2) (e3)) = (e2))) -> (~((op (e1) (op (e2) (e1))) = (op (e2) (e1)))) -> (((op (e1) (e1)) = (e0))\/(((op (e1) (e1)) = (e1))\/(((op (e1) (e1)) = (e2))\/((op (e1) (e1)) = (e3))))) -> (((op (e2) (e2)) = (e0))\/(((op (e2) (e2)) = (e1))\/(((op (e2) (e2)) = (e2))\/((op (e2) (e2)) = (e3))))) -> (~((op (e3) (e0)) = (op (e3) (e3)))) -> (((op (e0) (e0)) = (e3))\/(((op (e1) (e0)) = (e3))\/(((op (e2) (e0)) = (e3))\/((op (e3) (e0)) = (e3))))) -> (~((op (e2) (op (e2) (e2))) = (op (e2) (e2)))) -> ((~((op (e2) (e2)) = (e2)))\/((op (e2) (e2)) = (e2))) -> (~((op (e2) (e0)) = (op (e2) (e3)))) -> (((op (e1) (e0)) = (e3))\/(((op (e1) (e1)) = (e3))\/(((op (e1) (e2)) = (e3))\/((op (e1) (e3)) = (e3))))) -> (~((op (e1) (e3)) = (op (e3) (e3)))) -> (~((op (e0) (e2)) = (op (e1) (e2)))) -> ((~((op (e2) (e2)) = (e0)))\/((op (e2) (e0)) = (e2))) -> (~((op (e1) (e0)) = (op (e1) (e2)))) -> ((~((op (e1) (e1)) = (e2)))\/((op (e1) (e2)) = (e1))) -> (~((op (e0) (e0)) = (e1))) -> (((op (e0) (e0)) = (e1))\/(((op (e1) (e0)) = (e1))\/(((op (e2) (e0)) = (e1))\/((op (e3) (e0)) = (e1))))) -> (~((op (e0) (e2)) = (op (e2) (e2)))) -> (~((op (e2) (e2)) = (e2))) -> ((op (e1) (e1)) = (e1)) -> (~((op (e0) (e1)) = (op (e1) (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) (e3)) = (e0))))) -> ((op (e3) (e3)) = (e3)) -> (~((op (e3) (op (e2) (e3))) = (op (e2) (e3)))) -> (~((op (e2) (e2)) = (e3))) -> (~((e2) = (e3))) -> (~((e0) = (e3))) -> (((op (e2) (e0)) = (e3))\/(((op (e2) (e1)) = (e3))\/(((op (e2) (e2)) = (e3))\/((op (e2) (e3)) = (e3))))) -> ((op (e2) (e1)) = (e2)) -> (~((e0) = (e2))) -> (~((op (e2) (e2)) = (e0))) -> (~((op (e0) (e3)) = (op (e2) (e3)))) -> False). % 15.48/15.60 do 0 intro. intros zenon_H110 zenon_H20 zenon_Ha7 zenon_H1df zenon_H13c zenon_H140 zenon_H3d zenon_Hde zenon_H58 zenon_H59 zenon_H199 zenon_Ha3 zenon_H182 zenon_Hb7 zenon_H145 zenon_H12d zenon_H144 zenon_H36 zenon_H8e zenon_H1d8 zenon_Hd7 zenon_H1d2 zenon_H1cf zenon_H1e3 zenon_H1e2 zenon_H1c3 zenon_H290 zenon_H1b3 zenon_H2d zenon_Hbb zenon_Hbe zenon_H294 zenon_Haa zenon_Hce zenon_H90 zenon_H8b zenon_H87 zenon_H1d4 zenon_H166 zenon_H1d3 zenon_H45 zenon_Hf1 zenon_H28 zenon_H2f zenon_H21 zenon_H23 zenon_H44 zenon_H1f5 zenon_H42 zenon_H28a zenon_H30 zenon_H6a zenon_H4b zenon_He6 zenon_H156 zenon_H5e zenon_H2e zenon_Hb4. % 15.48/15.60 apply (zenon_or_s _ _ zenon_H110); [ zenon_intro zenon_H1f | zenon_intro zenon_H111 ]. % 15.48/15.60 exact (zenon_H20 zenon_H1f). % 15.48/15.60 apply (zenon_or_s _ _ zenon_H111); [ zenon_intro zenon_H49 | zenon_intro zenon_H112 ]. % 15.48/15.60 apply (zenon_L915_); trivial. % 15.48/15.60 apply (zenon_or_s _ _ zenon_H112); [ zenon_intro zenon_Hab | zenon_intro zenon_Hca ]. % 15.48/15.60 apply (zenon_L957_); trivial. % 15.48/15.60 apply (zenon_L972_); trivial. % 15.48/15.60 (* end of lemma zenon_L975_ *) % 15.48/15.60 assert (zenon_L976_ : (~((op (e1) (e2)) = (op (e3) (e2)))) -> (~((op (e0) (e1)) = (op (e3) (e1)))) -> (((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) (e3)) = (e1))\/(((op (e1) (e3)) = (e1))\/(((op (e2) (e3)) = (e1))\/((op (e3) (e3)) = (e1))))) -> (~((op (e0) (op (e2) (e0))) = (op (e2) (e0)))) -> (((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 (e0) (e1)) = (e0))\/(((op (e1) (e1)) = (e0))\/(((op (e2) (e1)) = (e0))\/((op (e3) (e1)) = (e0))))) -> (~((op (e2) (e1)) = (op (e2) (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 (e0) (e2)) = (op (e3) (e2)))) -> (~((op (e1) (e0)) = (op (e1) (e2)))) -> (~((op (e0) (e2)) = (op (e1) (e2)))) -> (~((op (e1) (e0)) = (op (e1) (e1)))) -> ((~((op (e3) (e3)) = (e2)))\/((op (e3) (e2)) = (e3))) -> (~((op (e1) (e0)) = (op (e1) (e3)))) -> ((~((op (e1) (e1)) = (e0)))\/((op (e1) (e0)) = (e1))) -> (~((op (e1) (e2)) = (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) (op (e2) (e1))) = (op (e2) (e1)))) -> ((~((op (e1) (e1)) = (e1)))\/((op (e1) (e1)) = (e1))) -> (~((op (e1) (e1)) = (op (e1) (e3)))) -> (~((op (e0) (e1)) = (op (e0) (e3)))) -> (~((op (e0) (e3)) = (op (e2) (e3)))) -> (~((op (e1) (e1)) = (op (e2) (e1)))) -> (((op (e0) (e0)) = (e1))\/(((op (e0) (e1)) = (e1))\/(((op (e0) (e2)) = (e1))\/((op (e0) (e3)) = (e1))))) -> (~((op (e1) (e1)) = (op (e1) (e2)))) -> ((~((op (e1) (e1)) = (e3)))\/((op (e1) (e3)) = (e1))) -> ((~((op (e2) (e2)) = (e1)))\/((op (e2) (e1)) = (e2))) -> ((~((op (e3) (e3)) = (e0)))\/((op (e3) (e0)) = (e3))) -> (~((op (e0) (e0)) = (e2))) -> (((op (e0) (e1)) = (e3))\/(((op (e1) (e1)) = (e3))\/(((op (e2) (e1)) = (e3))\/((op (e3) (e1)) = (e3))))) -> (~((op (e3) (e1)) = (op (e3) (e3)))) -> (~((op (e2) (e0)) = (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) (e1)) = (op (e2) (e3)))) -> ((~((op (e2) (e2)) = (e3)))\/((op (e2) (e3)) = (e2))) -> (~((op (e2) (op (e2) (e2))) = (op (e2) (e2)))) -> ((~((op (e2) (e2)) = (e2)))\/((op (e2) (e2)) = (e2))) -> (~((op (e2) (e0)) = (op (e2) (e1)))) -> (((op (e0) (e0)) = (e0))\/(((op (e0) (e0)) = (e1))\/(((op (e0) (e0)) = (e2))\/((op (e0) (e0)) = (e3))))) -> ((~((op (e2) (e2)) = (e0)))\/((op (e2) (e0)) = (e2))) -> (~((op (e1) (e2)) = (op (e1) (e3)))) -> (~((op (e2) (e0)) = (op (e2) (e2)))) -> ((~((op (e1) (e1)) = (e2)))\/((op (e1) (e2)) = (e1))) -> ((~((op (e0) (e0)) = (e3)))\/((op (e0) (e3)) = (e0))) -> (((op (e1) (e0)) = (e0))\/(((op (e1) (e1)) = (e0))\/(((op (e1) (e2)) = (e0))\/((op (e1) (e3)) = (e0))))) -> (~((op (e0) (e0)) = (e1))) -> (((op (e0) (e0)) = (e3))\/(((op (e1) (e0)) = (e3))\/(((op (e2) (e0)) = (e3))\/((op (e3) (e0)) = (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))))) -> (~((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 (e0) (e2)) = (op (e2) (e2)))) -> (~((op (e0) (e1)) = (op (e2) (e1)))) -> (~((op (e3) (op (e2) (e3))) = (op (e2) (e3)))) -> (((op (e2) (e0)) = (e3))\/(((op (e2) (e1)) = (e3))\/(((op (e2) (e2)) = (e3))\/((op (e2) (e3)) = (e3))))) -> (((op (e0) (e0)) = (e2))\/(((op (e0) (e1)) = (e2))\/(((op (e0) (e2)) = (e2))\/((op (e0) (e3)) = (e2))))) -> (~((op (e0) (e3)) = (op (e1) (e3)))) -> (((op (e1) (e0)) = (e2))\/(((op (e1) (e1)) = (e2))\/(((op (e1) (e2)) = (e2))\/((op (e1) (e3)) = (e2))))) -> (((op (e0) (e0)) = (e2))\/(((op (e1) (e0)) = (e2))\/(((op (e2) (e0)) = (e2))\/((op (e3) (e0)) = (e2))))) -> (~((op (e1) (e1)) = (e0))) -> (((op (e0) (e2)) = (e3))\/(((op (e1) (e2)) = (e3))\/(((op (e2) (e2)) = (e3))\/((op (e3) (e2)) = (e3))))) -> (~((op (e3) (e2)) = (op (e3) (e3)))) -> (~((e0) = (e3))) -> (((op (e0) (e1)) = (e2))\/(((op (e1) (e1)) = (e2))\/(((op (e2) (e1)) = (e2))\/((op (e3) (e1)) = (e2))))) -> (~((op (e2) (e1)) = (op (e3) (e1)))) -> (((op (e2) (e0)) = (e0))\/(((op (e2) (e1)) = (e0))\/(((op (e2) (e2)) = (e0))\/((op (e2) (e3)) = (e0))))) -> (((op (e2) (e0)) = (e1))\/(((op (e2) (e1)) = (e1))\/(((op (e2) (e2)) = (e1))\/((op (e2) (e3)) = (e1))))) -> (~((op (e1) (e3)) = (op (e2) (e3)))) -> (~((e1) = (e2))) -> (~((e2) = (e3))) -> (((op (e0) (e3)) = (e0))\/(((op (e1) (e3)) = (e0))\/(((op (e2) (e3)) = (e0))\/((op (e3) (e3)) = (e0))))) -> (~((e0) = (e2))) -> (~((e0) = (e1))) -> (~((op (e0) (e2)) = (op (e0) (e3)))) -> (((op (e2) (e0)) = (e2))\/(((op (e2) (e1)) = (e2))\/(((op (e2) (e2)) = (e2))\/((op (e2) (e3)) = (e2))))) -> (((op (e1) (e0)) = (e1))\/(((op (e1) (e1)) = (e1))\/(((op (e1) (e2)) = (e1))\/((op (e1) (e3)) = (e1))))) -> (((op (e0) (e0)) = (e1))\/(((op (e1) (e0)) = (e1))\/(((op (e2) (e0)) = (e1))\/((op (e3) (e0)) = (e1))))) -> (~((op (e0) (e1)) = (op (e1) (e1)))) -> (((op (e1) (e1)) = (e0))\/(((op (e1) (e1)) = (e1))\/(((op (e1) (e1)) = (e2))\/((op (e1) (e1)) = (e3))))) -> (~((op (e0) (e0)) = (e0))) -> False). % 15.48/15.60 do 0 intro. intros zenon_H17d zenon_H138 zenon_H110 zenon_H146 zenon_H121 zenon_H295 zenon_Hf0 zenon_H10c zenon_H144 zenon_H157 zenon_H90 zenon_H1df zenon_H140 zenon_H166 zenon_H87 zenon_Hd7 zenon_H10e zenon_H1cf zenon_H1e4 zenon_H7d zenon_H135 zenon_H16f zenon_H290 zenon_H1d8 zenon_H11e zenon_H1cd zenon_Hb4 zenon_Hb1 zenon_H44 zenon_H116 zenon_H1d2 zenon_H1e3 zenon_H10f zenon_H8f zenon_H199 zenon_H12d zenon_Hce zenon_H8b zenon_H25b zenon_H1e2 zenon_H1c3 zenon_H294 zenon_Haa zenon_H154 zenon_H12a zenon_H1d4 zenon_H1d0 zenon_H17a zenon_H1d3 zenon_H236 zenon_H163 zenon_H45 zenon_Hbe zenon_H42 zenon_Hbb zenon_H2d zenon_Ha3 zenon_H59 zenon_H58 zenon_H36 zenon_H28 zenon_Hde zenon_H28a zenon_He6 zenon_H8e zenon_H80 zenon_H84 zenon_Heb zenon_H145 zenon_H175 zenon_H173 zenon_H4b zenon_H1a2 zenon_H13c zenon_H1f5 zenon_Hb7 zenon_H244 zenon_Ha7 zenon_H6a zenon_Hd3 zenon_H5e zenon_H9e zenon_Hc9 zenon_H237 zenon_H1c5 zenon_Hf1 zenon_H23 zenon_H1b3 zenon_H20. % 15.48/15.60 apply (zenon_or_s _ _ zenon_H1d8); [ zenon_intro zenon_H1b4 | zenon_intro zenon_H21 ]. % 15.48/15.60 apply (zenon_or_s _ _ zenon_H1d3); [ zenon_intro zenon_Hd6 | zenon_intro zenon_H117 ]. % 15.48/15.60 apply (zenon_or_s _ _ zenon_H1d2); [ zenon_intro zenon_H182 | zenon_intro zenon_H11f ]. % 15.48/15.60 apply (zenon_or_s _ _ zenon_H1d4); [ zenon_intro zenon_H2e | zenon_intro zenon_Hdd ]. % 15.48/15.60 apply (zenon_or_s _ _ zenon_H1e3); [ zenon_intro zenon_H52 | zenon_intro zenon_H156 ]. % 15.48/15.60 apply (zenon_or_s _ _ zenon_Haa); [ zenon_intro zenon_H2f | zenon_intro zenon_H35 ]. % 15.48/15.60 apply (zenon_or_s _ _ zenon_H1c3); [ zenon_intro zenon_H30 | zenon_intro zenon_H124 ]. % 15.48/15.60 apply (zenon_or_s _ _ zenon_H10f); [ zenon_intro zenon_H3c | zenon_intro zenon_Hba ]. % 15.48/15.60 apply (zenon_or_s _ _ zenon_H110); [ zenon_intro zenon_H1f | zenon_intro zenon_H111 ]. % 15.48/15.60 exact (zenon_H20 zenon_H1f). % 15.48/15.60 apply (zenon_or_s _ _ zenon_H111); [ zenon_intro zenon_H49 | zenon_intro zenon_H112 ]. % 15.48/15.60 apply (zenon_L347_); trivial. % 15.48/15.60 apply (zenon_or_s _ _ zenon_H112); [ zenon_intro zenon_Hab | zenon_intro zenon_Hca ]. % 15.48/15.60 apply (zenon_L932_); trivial. % 15.48/15.60 apply (zenon_L968_); trivial. % 15.48/15.60 apply (zenon_L43_); trivial. % 15.48/15.60 apply (zenon_or_s _ _ zenon_H10c); [ zenon_intro zenon_H104 | zenon_intro zenon_H10a ]. % 15.48/15.60 apply (zenon_or_s _ _ zenon_H10e); [ zenon_intro zenon_H3d | zenon_intro zenon_H106 ]. % 15.48/15.60 apply (zenon_or_s _ _ zenon_H110); [ zenon_intro zenon_H1f | zenon_intro zenon_H111 ]. % 15.48/15.60 exact (zenon_H20 zenon_H1f). % 15.48/15.60 apply (zenon_or_s _ _ zenon_H111); [ zenon_intro zenon_H49 | zenon_intro zenon_H112 ]. % 15.48/15.60 apply (zenon_L13_); trivial. % 15.48/15.60 apply (zenon_or_s _ _ zenon_H112); [ zenon_intro zenon_Hab | zenon_intro zenon_Hca ]. % 15.48/15.60 apply (zenon_L951_); trivial. % 15.48/15.60 apply (zenon_L967_); trivial. % 15.48/15.60 apply (zenon_L153_); trivial. % 15.48/15.60 apply (zenon_L102_); trivial. % 15.48/15.60 apply (zenon_L794_); trivial. % 15.48/15.60 apply (zenon_L801_); trivial. % 15.48/15.60 apply (zenon_L937_); trivial. % 15.48/15.60 apply (zenon_or_s _ _ zenon_H1d4); [ zenon_intro zenon_H2e | zenon_intro zenon_Hdd ]. % 15.48/15.60 apply (zenon_or_s _ _ zenon_H1e3); [ zenon_intro zenon_H52 | zenon_intro zenon_H156 ]. % 15.48/15.60 apply (zenon_or_s _ _ zenon_Haa); [ zenon_intro zenon_H2f | zenon_intro zenon_H35 ]. % 15.48/15.60 apply (zenon_or_s _ _ zenon_H1c3); [ zenon_intro zenon_H30 | zenon_intro zenon_H124 ]. % 15.48/15.60 apply (zenon_L969_); trivial. % 15.48/15.60 apply (zenon_or_s _ _ zenon_H10f); [ zenon_intro zenon_H3c | zenon_intro zenon_Hba ]. % 15.48/15.60 apply (zenon_or_s _ _ zenon_H10c); [ zenon_intro zenon_H104 | zenon_intro zenon_H10a ]. % 15.48/15.60 apply (zenon_or_s _ _ zenon_H10e); [ zenon_intro zenon_H3d | zenon_intro zenon_H106 ]. % 15.48/15.60 apply (zenon_or_s _ _ zenon_H110); [ zenon_intro zenon_H1f | zenon_intro zenon_H111 ]. % 15.48/15.60 exact (zenon_H20 zenon_H1f). % 15.48/15.60 apply (zenon_or_s _ _ zenon_H111); [ zenon_intro zenon_H49 | zenon_intro zenon_H112 ]. % 15.48/15.60 apply (zenon_L13_); trivial. % 15.48/15.60 apply (zenon_or_s _ _ zenon_H112); [ zenon_intro zenon_Hab | zenon_intro zenon_Hca ]. % 15.48/15.60 apply (zenon_L711_); trivial. % 15.48/15.60 apply (zenon_L971_); trivial. % 15.48/15.60 apply (zenon_L153_); trivial. % 15.48/15.60 apply (zenon_L102_); trivial. % 15.48/15.60 apply (zenon_L43_); trivial. % 15.48/15.60 apply (zenon_L794_); trivial. % 15.48/15.60 apply (zenon_or_s _ _ zenon_H1c3); [ zenon_intro zenon_H30 | zenon_intro zenon_H124 ]. % 15.48/15.60 apply (zenon_or_s _ _ zenon_H10f); [ zenon_intro zenon_H3c | zenon_intro zenon_Hba ]. % 15.48/15.60 apply (zenon_or_s _ _ zenon_H10e); [ zenon_intro zenon_H3d | zenon_intro zenon_H106 ]. % 15.48/15.60 apply (zenon_or_s _ _ zenon_H110); [ zenon_intro zenon_H1f | zenon_intro zenon_H111 ]. % 15.48/15.60 exact (zenon_H20 zenon_H1f). % 15.48/15.60 apply (zenon_or_s _ _ zenon_H111); [ zenon_intro zenon_H49 | zenon_intro zenon_H112 ]. % 15.48/15.60 apply (zenon_L934_); trivial. % 15.48/15.60 apply (zenon_or_s _ _ zenon_H112); [ zenon_intro zenon_Hab | zenon_intro zenon_Hca ]. % 15.48/15.60 apply (zenon_L947_); trivial. % 15.48/15.60 apply (zenon_L972_); trivial. % 15.48/15.60 apply (zenon_L153_); trivial. % 15.48/15.60 apply (zenon_L43_); trivial. % 15.48/15.60 apply (zenon_L256_); trivial. % 15.48/15.60 apply (zenon_L937_); trivial. % 15.48/15.60 apply (zenon_or_s _ _ zenon_H1d2); [ zenon_intro zenon_H182 | zenon_intro zenon_H11f ]. % 15.48/15.60 apply (zenon_or_s _ _ zenon_H1d4); [ zenon_intro zenon_H2e | zenon_intro zenon_Hdd ]. % 15.48/15.60 apply (zenon_or_s _ _ zenon_H1e3); [ zenon_intro zenon_H52 | zenon_intro zenon_H156 ]. % 15.48/15.60 apply (zenon_or_s _ _ zenon_Haa); [ zenon_intro zenon_H2f | zenon_intro zenon_H35 ]. % 15.48/15.60 apply (zenon_or_s _ _ zenon_H1c3); [ zenon_intro zenon_H30 | zenon_intro zenon_H124 ]. % 15.48/15.60 apply (zenon_L791_); trivial. % 15.48/15.60 apply (zenon_or_s _ _ zenon_H10f); [ zenon_intro zenon_H3c | zenon_intro zenon_Hba ]. % 15.48/15.60 apply (zenon_or_s _ _ zenon_H10c); [ zenon_intro zenon_H104 | zenon_intro zenon_H10a ]. % 15.48/15.60 apply (zenon_or_s _ _ zenon_H10e); [ zenon_intro zenon_H3d | zenon_intro zenon_H106 ]. % 15.48/15.60 apply (zenon_or_s _ _ zenon_H110); [ zenon_intro zenon_H1f | zenon_intro zenon_H111 ]. % 15.48/15.60 exact (zenon_H20 zenon_H1f). % 15.48/15.60 apply (zenon_or_s _ _ zenon_H111); [ zenon_intro zenon_H49 | zenon_intro zenon_H112 ]. % 15.48/15.60 apply (zenon_L13_); trivial. % 15.48/15.60 apply (zenon_or_s _ _ zenon_H112); [ zenon_intro zenon_Hab | zenon_intro zenon_Hca ]. % 15.48/15.60 apply (zenon_L206_); trivial. % 15.48/15.60 apply (zenon_L967_); trivial. % 15.48/15.60 apply (zenon_L153_); trivial. % 15.48/15.60 apply (zenon_L102_); trivial. % 15.48/15.60 apply (zenon_L43_); trivial. % 15.48/15.60 apply (zenon_L794_); trivial. % 15.48/15.60 apply (zenon_or_s _ _ zenon_H1c3); [ zenon_intro zenon_H30 | zenon_intro zenon_H124 ]. % 15.48/15.60 apply (zenon_or_s _ _ zenon_H110); [ zenon_intro zenon_H1f | zenon_intro zenon_H111 ]. % 15.48/15.60 exact (zenon_H20 zenon_H1f). % 15.48/15.60 apply (zenon_or_s _ _ zenon_H111); [ zenon_intro zenon_H49 | zenon_intro zenon_H112 ]. % 15.48/15.60 apply (zenon_L278_); trivial. % 15.48/15.60 apply (zenon_or_s _ _ zenon_H112); [ zenon_intro zenon_Hab | zenon_intro zenon_Hca ]. % 15.48/15.60 apply (zenon_L973_); trivial. % 15.48/15.60 apply (zenon_L972_); trivial. % 15.48/15.60 apply (zenon_L256_); trivial. % 15.48/15.60 apply (zenon_L974_); trivial. % 15.48/15.60 apply (zenon_L237_); trivial. % 15.48/15.60 apply (zenon_or_s _ _ zenon_H1d2); [ zenon_intro zenon_H182 | zenon_intro zenon_H11f ]. % 15.48/15.60 apply (zenon_or_s _ _ zenon_H1d4); [ zenon_intro zenon_H2e | zenon_intro zenon_Hdd ]. % 15.48/15.60 apply (zenon_or_s _ _ zenon_H1e3); [ zenon_intro zenon_H52 | zenon_intro zenon_H156 ]. % 15.48/15.60 apply (zenon_or_s _ _ zenon_Haa); [ zenon_intro zenon_H2f | zenon_intro zenon_H35 ]. % 15.48/15.60 apply (zenon_or_s _ _ zenon_H1c3); [ zenon_intro zenon_H30 | zenon_intro zenon_H124 ]. % 15.48/15.60 apply (zenon_L918_); trivial. % 15.48/15.60 apply (zenon_L103_); trivial. % 15.48/15.60 apply (zenon_L794_); trivial. % 15.48/15.60 apply (zenon_or_s _ _ zenon_Haa); [ zenon_intro zenon_H2f | zenon_intro zenon_H35 ]. % 15.48/15.60 apply (zenon_or_s _ _ zenon_H1c3); [ zenon_intro zenon_H30 | zenon_intro zenon_H124 ]. % 15.48/15.60 apply (zenon_or_s _ _ zenon_H10e); [ zenon_intro zenon_H3d | zenon_intro zenon_H106 ]. % 15.48/15.60 apply (zenon_L975_); trivial. % 15.48/15.60 apply (zenon_L820_); trivial. % 15.48/15.60 apply (zenon_L256_); trivial. % 15.48/15.60 apply (zenon_L134_); trivial. % 15.48/15.60 apply (zenon_L959_); trivial. % 15.48/15.60 apply (zenon_L90_); trivial. % 15.48/15.60 (* end of lemma zenon_L976_ *) % 15.48/15.60 assert (zenon_L977_ : ((~((op (e3) (e3)) = (e3)))\/((op (e3) (e3)) = (e3))) -> (~((op (e0) (e0)) = (e0))) -> ((~((op (e2) (e2)) = (e1)))\/((op (e2) (e1)) = (e2))) -> (~((op (e1) (e1)) = (e3))) -> (~((e2) = (e3))) -> (~((op (e3) (e1)) = (op (e3) (e3)))) -> (((op (e0) (e1)) = (e3))\/(((op (e1) (e1)) = (e3))\/(((op (e2) (e1)) = (e3))\/((op (e3) (e1)) = (e3))))) -> (((op (e0) (e0)) = (e3))\/(((op (e0) (e1)) = (e3))\/(((op (e0) (e2)) = (e3))\/((op (e0) (e3)) = (e3))))) -> (~((e0) = (e3))) -> (~((op (e0) (e0)) = (e3))) -> (~((op (e2) (op (e2) (e2))) = (op (e2) (e2)))) -> ((~((op (e2) (e2)) = (e2)))\/((op (e2) (e2)) = (e2))) -> ((~((op (e1) (e1)) = (e1)))\/((op (e1) (e1)) = (e1))) -> (~((op (e1) (e0)) = (op (e1) (e1)))) -> ((~((op (e1) (e1)) = (e3)))\/((op (e1) (e3)) = (e1))) -> (~((op (e1) (e0)) = (op (e1) (e3)))) -> (~((op (e2) (e1)) = (op (e2) (e3)))) -> ((~((op (e2) (e2)) = (e3)))\/((op (e2) (e3)) = (e2))) -> (((op (e2) (e0)) = (e0))\/(((op (e2) (e1)) = (e0))\/(((op (e2) (e2)) = (e0))\/((op (e2) (e3)) = (e0))))) -> (~((e0) = (e2))) -> (~((op (e1) (op (e2) (e1))) = (op (e2) (e1)))) -> (~((e1) = (e2))) -> (((op (e2) (e0)) = (e1))\/(((op (e2) (e1)) = (e1))\/(((op (e2) (e2)) = (e1))\/((op (e2) (e3)) = (e1))))) -> (~((e1) = (e3))) -> (((op (e1) (e1)) = (e0))\/(((op (e1) (e1)) = (e1))\/(((op (e1) (e1)) = (e2))\/((op (e1) (e1)) = (e3))))) -> (~((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)) = (op (e2) (e3)))) -> (((op (e2) (e0)) = (e3))\/(((op (e2) (e1)) = (e3))\/(((op (e2) (e2)) = (e3))\/((op (e2) (e3)) = (e3))))) -> (~((op (e3) (op (e2) (e3))) = (op (e2) (e3)))) -> (~((op (e0) (e1)) = (op (e2) (e1)))) -> (((op (e1) (e0)) = (e3))\/(((op (e1) (e1)) = (e3))\/(((op (e1) (e2)) = (e3))\/((op (e1) (e3)) = (e3))))) -> (~((op (e1) (e3)) = (op (e3) (e3)))) -> (~((op (e0) (e2)) = (op (e1) (e2)))) -> ((~((op (e2) (e2)) = (e0)))\/((op (e2) (e0)) = (e2))) -> (~((op (e1) (e0)) = (op (e1) (e2)))) -> ((~((op (e1) (e1)) = (e2)))\/((op (e1) (e2)) = (e1))) -> ((op (e2) (e1)) = (e2)) -> (((op (e0) (e0)) = (e2))\/(((op (e0) (e1)) = (e2))\/(((op (e0) (e2)) = (e2))\/((op (e0) (e3)) = (e2))))) -> (~((op (e2) (e1)) = (op (e3) (e1)))) -> (~((op (e0) (e2)) = (op (e3) (e2)))) -> (((op (e3) (e0)) = (e2))\/(((op (e3) (e1)) = (e2))\/(((op (e3) (e2)) = (e2))\/((op (e3) (e3)) = (e2))))) -> (((op (e0) (e1)) = (e0))\/(((op (e1) (e1)) = (e0))\/(((op (e2) (e1)) = (e0))\/((op (e3) (e1)) = (e0))))) -> (~((op (e0) (e3)) = (op (e2) (e3)))) -> (~((op (e1) (e1)) = (e0))) -> (((op (e0) (e0)) = (e1))\/(((op (e1) (e0)) = (e1))\/(((op (e2) (e0)) = (e1))\/((op (e3) (e0)) = (e1))))) -> (((op (e0) (e0)) = (e0))\/(((op (e0) (e1)) = (e0))\/(((op (e0) (e2)) = (e0))\/((op (e0) (e3)) = (e0))))) -> (~((op (e0) (e0)) = (e1))) -> (~((op (e0) (e1)) = (op (e1) (e1)))) -> ((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 (e0) (e2)) = (op (e2) (e2)))) -> (~((op (e2) (e2)) = (e0))) -> (((op (e3) (e3)) = (e0))\/(((op (e3) (e3)) = (e1))\/(((op (e3) (e3)) = (e2))\/((op (e3) (e3)) = (e3))))) -> (~((op (e3) (e3)) = (e2))) -> (~((op (e0) (e3)) = (op (e3) (e3)))) -> (~((op (e3) (e3)) = (e0))) -> (((op (e0) (e0)) = (e1))\/(((op (e0) (e1)) = (e1))\/(((op (e0) (e2)) = (e1))\/((op (e0) (e3)) = (e1))))) -> False). % 15.48/15.61 do 0 intro. intros zenon_H10d zenon_H20 zenon_H1e3 zenon_H182 zenon_H6a zenon_H12d zenon_H199 zenon_H58 zenon_H4b zenon_H59 zenon_H294 zenon_Haa zenon_H1d8 zenon_Hd7 zenon_H1d2 zenon_H1cf zenon_H1e2 zenon_H1c3 zenon_H1f5 zenon_H5e zenon_H290 zenon_Ha7 zenon_Hb7 zenon_Ha3 zenon_H1b3 zenon_Hbb zenon_Hbe zenon_Hce zenon_He6 zenon_H28a zenon_Hde zenon_H90 zenon_H8b zenon_H87 zenon_H1d4 zenon_H166 zenon_H1d3 zenon_H156 zenon_H8e zenon_H13c zenon_H140 zenon_H1df zenon_H144 zenon_Hb4 zenon_H145 zenon_Hf1 zenon_H110 zenon_H45 zenon_H23 zenon_H21 zenon_H2d zenon_H30 zenon_H2f zenon_H28 zenon_H2e zenon_H3b zenon_H3d zenon_H36 zenon_H3c zenon_H44. % 15.48/15.61 apply (zenon_or_s _ _ zenon_H10d); [ zenon_intro zenon_H3e | zenon_intro zenon_H42 ]. % 15.48/15.61 apply (zenon_L8_); trivial. % 15.48/15.61 apply (zenon_L975_); trivial. % 15.48/15.61 (* end of lemma zenon_L977_ *) % 15.48/15.61 assert (zenon_L978_ : (((op (e2) (e0)) = (e3))\/(((op (e2) (e1)) = (e3))\/(((op (e2) (e2)) = (e3))\/((op (e2) (e3)) = (e3))))) -> (~((op (e0) (op (e2) (e0))) = (op (e2) (e0)))) -> (~((e2) = (e3))) -> ((op (e2) (e1)) = (e2)) -> (~((op (e2) (e2)) = (e3))) -> (~((op (e0) (e3)) = (op (e2) (e3)))) -> ((op (e0) (e3)) = (e3)) -> False). % 15.48/15.61 do 0 intro. intros zenon_He6 zenon_H295 zenon_H6a zenon_H156 zenon_H30 zenon_Hb4 zenon_H53. % 15.48/15.61 apply (zenon_or_s _ _ zenon_He6); [ zenon_intro zenon_Haf | zenon_intro zenon_He7 ]. % 15.48/15.61 apply (zenon_L803_); trivial. % 15.48/15.61 apply (zenon_or_s _ _ zenon_He7); [ zenon_intro zenon_Hdf | zenon_intro zenon_He8 ]. % 15.48/15.61 apply (zenon_L183_); trivial. % 15.48/15.61 apply (zenon_or_s _ _ zenon_He8); [ zenon_intro zenon_H34 | zenon_intro zenon_He2 ]. % 15.48/15.61 exact (zenon_H30 zenon_H34). % 15.48/15.61 apply (zenon_L125_); trivial. % 15.48/15.61 (* end of lemma zenon_L978_ *) % 15.48/15.61 assert (zenon_L979_ : (((op (e0) (e0)) = (e2))\/(((op (e0) (e1)) = (e2))\/(((op (e0) (e2)) = (e2))\/((op (e0) (e3)) = (e2))))) -> (~((op (e0) (e0)) = (e2))) -> (~((op (e0) (e1)) = (op (e2) (e1)))) -> (~((op (e0) (e3)) = (op (e2) (e3)))) -> (~((op (e2) (e2)) = (e3))) -> ((op (e2) (e1)) = (e2)) -> (~((e2) = (e3))) -> (~((op (e0) (op (e2) (e0))) = (op (e2) (e0)))) -> (((op (e2) (e0)) = (e3))\/(((op (e2) (e1)) = (e3))\/(((op (e2) (e2)) = (e3))\/((op (e2) (e3)) = (e3))))) -> ((op (e0) (e1)) = (e0)) -> (~((e0) = (e3))) -> (~((op (e0) (e0)) = (e3))) -> (((op (e0) (e0)) = (e3))\/(((op (e0) (e1)) = (e3))\/(((op (e0) (e2)) = (e3))\/((op (e0) (e3)) = (e3))))) -> (((op (e3) (e3)) = (e0))\/(((op (e3) (e3)) = (e1))\/(((op (e3) (e3)) = (e2))\/((op (e3) (e3)) = (e3))))) -> (~((op (e3) (e3)) = (e0))) -> (~((op (e3) (e3)) = (e1))) -> (~((op (e0) (e3)) = (op (e3) (e3)))) -> (~((op (e3) (e3)) = (e3))) -> False). % 15.48/15.61 do 0 intro. intros zenon_H8e zenon_H8f zenon_Hde zenon_Hb4 zenon_H30 zenon_H156 zenon_H6a zenon_H295 zenon_He6 zenon_H49 zenon_H4b zenon_H59 zenon_H58 zenon_H3b zenon_H3c zenon_H104 zenon_H36 zenon_H3e. % 15.48/15.61 apply (zenon_or_s _ _ zenon_H8e); [ zenon_intro zenon_H92 | zenon_intro zenon_H91 ]. % 15.48/15.61 exact (zenon_H8f zenon_H92). % 15.48/15.61 apply (zenon_or_s _ _ zenon_H91); [ zenon_intro zenon_H5d | zenon_intro zenon_H93 ]. % 15.48/15.61 apply (zenon_L251_); trivial. % 15.48/15.61 apply (zenon_or_s _ _ zenon_H93); [ zenon_intro zenon_H63 | zenon_intro zenon_H81 ]. % 15.48/15.61 apply (zenon_or_s _ _ zenon_H58); [ zenon_intro zenon_H5b | zenon_intro zenon_H5a ]. % 15.48/15.61 exact (zenon_H59 zenon_H5b). % 15.48/15.61 apply (zenon_or_s _ _ zenon_H5a); [ zenon_intro zenon_H4a | zenon_intro zenon_H5c ]. % 15.48/15.61 apply (zenon_L9_); trivial. % 15.48/15.61 apply (zenon_or_s _ _ zenon_H5c); [ zenon_intro zenon_H50 | zenon_intro zenon_H53 ]. % 15.48/15.61 apply (zenon_L31_); trivial. % 15.48/15.61 apply (zenon_L978_); trivial. % 15.48/15.61 apply (zenon_L107_); trivial. % 15.48/15.61 (* end of lemma zenon_L979_ *) % 15.48/15.61 assert (zenon_L980_ : ((op (e3) (e0)) = (e0)) -> ((op (e2) (e0)) = (e0)) -> (~((op (e2) (e0)) = (op (e3) (e0)))) -> False). % 15.48/15.61 do 0 intro. intros zenon_Hdb zenon_Hcf zenon_H1e5. % 15.48/15.61 elim (classic ((op (e3) (e0)) = (op (e3) (e0)))); [ zenon_intro zenon_H1e6 | zenon_intro zenon_H108 ]. % 15.48/15.61 cut (((op (e3) (e0)) = (op (e3) (e0))) = ((op (e2) (e0)) = (op (e3) (e0)))). % 15.48/15.61 intro zenon_D_pnotp. % 15.48/15.61 apply zenon_H1e5. % 15.48/15.61 rewrite <- zenon_D_pnotp. % 15.48/15.61 exact zenon_H1e6. % 15.48/15.61 cut (((op (e3) (e0)) = (op (e3) (e0)))); [idtac | apply NNPP; zenon_intro zenon_H108]. % 15.48/15.61 cut (((op (e3) (e0)) = (op (e2) (e0)))); [idtac | apply NNPP; zenon_intro zenon_H1e7]. % 15.48/15.61 congruence. % 15.48/15.61 cut (((op (e3) (e0)) = (e0)) = ((op (e3) (e0)) = (op (e2) (e0)))). % 15.48/15.61 intro zenon_D_pnotp. % 15.48/15.61 apply zenon_H1e7. % 15.48/15.61 rewrite <- zenon_D_pnotp. % 15.48/15.61 exact zenon_Hdb. % 15.48/15.61 cut (((e0) = (op (e2) (e0)))); [idtac | apply NNPP; zenon_intro zenon_H259]. % 15.48/15.61 cut (((op (e3) (e0)) = (op (e3) (e0)))); [idtac | apply NNPP; zenon_intro zenon_H108]. % 15.48/15.61 congruence. % 15.48/15.61 apply zenon_H108. apply refl_equal. % 15.48/15.61 apply zenon_H259. apply sym_equal. exact zenon_Hcf. % 15.48/15.61 apply zenon_H108. apply refl_equal. % 15.48/15.61 apply zenon_H108. apply refl_equal. % 15.48/15.61 (* end of lemma zenon_L980_ *) % 15.48/15.61 assert (zenon_L981_ : (~((op (e3) (op (e2) (e3))) = (op (e3) (e0)))) -> ((op (e2) (e3)) = (e0)) -> False). % 15.48/15.61 do 0 intro. intros zenon_H2a9 zenon_Hd0. % 15.48/15.61 cut (((op (e2) (e3)) = (e0))); [idtac | apply NNPP; zenon_intro zenon_H1c1]. % 15.48/15.61 cut (((e3) = (e3))); [idtac | apply NNPP; zenon_intro zenon_H4d]. % 15.48/15.61 congruence. % 15.48/15.61 apply zenon_H4d. apply refl_equal. % 15.48/15.61 exact (zenon_H1c1 zenon_Hd0). % 15.48/15.61 (* end of lemma zenon_L981_ *) % 15.48/15.61 assert (zenon_L982_ : (~((op (e3) (op (e2) (e3))) = (op (e2) (e3)))) -> ((op (e3) (e0)) = (e0)) -> ((op (e2) (e3)) = (e0)) -> False). % 15.48/15.61 do 0 intro. intros zenon_H28a zenon_Hdb zenon_Hd0. % 15.48/15.61 cut (((op (e3) (e0)) = (e0)) = ((op (e3) (op (e2) (e3))) = (op (e2) (e3)))). % 15.48/15.61 intro zenon_D_pnotp. % 15.48/15.61 apply zenon_H28a. % 15.48/15.61 rewrite <- zenon_D_pnotp. % 15.48/15.61 exact zenon_Hdb. % 15.48/15.61 cut (((e0) = (op (e2) (e3)))); [idtac | apply NNPP; zenon_intro zenon_Hd1]. % 15.48/15.61 cut (((op (e3) (e0)) = (op (e3) (op (e2) (e3))))); [idtac | apply NNPP; zenon_intro zenon_H2aa]. % 15.48/15.61 congruence. % 15.48/15.61 elim (classic ((op (e3) (op (e2) (e3))) = (op (e3) (op (e2) (e3))))); [ zenon_intro zenon_H28c | zenon_intro zenon_H28d ]. % 15.48/15.61 cut (((op (e3) (op (e2) (e3))) = (op (e3) (op (e2) (e3)))) = ((op (e3) (e0)) = (op (e3) (op (e2) (e3))))). % 15.48/15.61 intro zenon_D_pnotp. % 15.48/15.61 apply zenon_H2aa. % 15.48/15.61 rewrite <- zenon_D_pnotp. % 15.48/15.61 exact zenon_H28c. % 15.48/15.61 cut (((op (e3) (op (e2) (e3))) = (op (e3) (op (e2) (e3))))); [idtac | apply NNPP; zenon_intro zenon_H28d]. % 15.48/15.61 cut (((op (e3) (op (e2) (e3))) = (op (e3) (e0)))); [idtac | apply NNPP; zenon_intro zenon_H2a9]. % 15.48/15.61 congruence. % 15.48/15.61 apply (zenon_L981_); trivial. % 15.48/15.61 apply zenon_H28d. apply refl_equal. % 15.48/15.61 apply zenon_H28d. apply refl_equal. % 15.48/15.61 apply zenon_Hd1. apply sym_equal. exact zenon_Hd0. % 15.48/15.61 (* end of lemma zenon_L982_ *) % 15.48/15.61 assert (zenon_L983_ : (((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)) = (e2)) -> (~((e0) = (e2))) -> (~((op (e2) (e2)) = (e0))) -> (~((op (e3) (op (e2) (e3))) = (op (e2) (e3)))) -> ((op (e3) (e0)) = (e0)) -> False). % 15.48/15.61 do 0 intro. intros zenon_H1f5 zenon_H1e5 zenon_H156 zenon_H5e zenon_H2e zenon_H28a zenon_Hdb. % 15.48/15.61 apply (zenon_or_s _ _ zenon_H1f5); [ zenon_intro zenon_Hcf | zenon_intro zenon_H1f9 ]. % 15.48/15.61 apply (zenon_L980_); trivial. % 15.48/15.61 apply (zenon_or_s _ _ zenon_H1f9); [ zenon_intro zenon_H14a | zenon_intro zenon_H1fa ]. % 15.48/15.61 apply (zenon_L351_); trivial. % 15.48/15.61 apply (zenon_or_s _ _ zenon_H1fa); [ zenon_intro zenon_H32 | zenon_intro zenon_Hd0 ]. % 15.48/15.61 exact (zenon_H2e zenon_H32). % 15.48/15.61 apply (zenon_L982_); trivial. % 15.48/15.61 (* end of lemma zenon_L983_ *) % 15.48/15.61 assert (zenon_L984_ : (((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 (e1) (e1)) = (e1)) -> (~((op (e1) (e1)) = (op (e1) (e2)))) -> ((op (e2) (e1)) = (e2)) -> (~((op (e1) (op (e2) (e1))) = (op (e2) (e1)))) -> (~((op (e0) (e2)) = (op (e1) (e2)))) -> ((op (e0) (e2)) = (e3)) -> False). % 15.48/15.61 do 0 intro. intros zenon_H1d5 zenon_H167 zenon_H17d zenon_H21 zenon_H116 zenon_H156 zenon_H290 zenon_H87 zenon_H50. % 15.48/15.61 apply (zenon_or_s _ _ zenon_H1d5); [ zenon_intro zenon_H15d | zenon_intro zenon_H1d6 ]. % 15.48/15.61 apply (zenon_L626_); trivial. % 15.48/15.61 apply (zenon_or_s _ _ zenon_H1d6); [ zenon_intro zenon_H117 | zenon_intro zenon_H1d7 ]. % 15.48/15.61 apply (zenon_L86_); trivial. % 15.48/15.61 apply (zenon_or_s _ _ zenon_H1d7); [ zenon_intro zenon_H7c | zenon_intro zenon_H88 ]. % 15.48/15.61 apply (zenon_L824_); trivial. % 15.48/15.61 apply (zenon_L24_); trivial. % 15.48/15.61 (* end of lemma zenon_L984_ *) % 15.48/15.61 assert (zenon_L985_ : (((op (e3) (e0)) = (e0))\/(((op (e3) (e1)) = (e0))\/(((op (e3) (e2)) = (e0))\/((op (e3) (e3)) = (e0))))) -> (~((op (e3) (op (e2) (e3))) = (op (e2) (e3)))) -> (~((op (e2) (e2)) = (e0))) -> (~((e0) = (e2))) -> (~((op (e2) (e0)) = (op (e3) (e0)))) -> (((op (e2) (e0)) = (e0))\/(((op (e2) (e1)) = (e0))\/(((op (e2) (e2)) = (e0))\/((op (e2) (e3)) = (e0))))) -> ((op (e3) (e1)) = (e3)) -> (~((e0) = (e3))) -> ((op (e0) (e2)) = (e3)) -> (~((op (e0) (e2)) = (op (e1) (e2)))) -> (~((op (e1) (op (e2) (e1))) = (op (e2) (e1)))) -> ((op (e2) (e1)) = (e2)) -> (~((op (e1) (e1)) = (op (e1) (e2)))) -> ((op (e1) (e1)) = (e1)) -> (~((op (e1) (e2)) = (op (e3) (e2)))) -> (((op (e1) (e2)) = (e0))\/(((op (e1) (e2)) = (e1))\/(((op (e1) (e2)) = (e2))\/((op (e1) (e2)) = (e3))))) -> (~((op (e3) (e3)) = (e0))) -> False). % 15.48/15.61 do 0 intro. intros zenon_H1f6 zenon_H28a zenon_H2e zenon_H5e zenon_H1e5 zenon_H1f5 zenon_H10a zenon_H4b zenon_H50 zenon_H87 zenon_H290 zenon_H156 zenon_H116 zenon_H21 zenon_H17d zenon_H1d5 zenon_H3c. % 15.48/15.61 apply (zenon_or_s _ _ zenon_H1f6); [ zenon_intro zenon_Hdb | zenon_intro zenon_H1f7 ]. % 15.48/15.61 apply (zenon_L983_); trivial. % 15.48/15.61 apply (zenon_or_s _ _ zenon_H1f7); [ zenon_intro zenon_H142 | zenon_intro zenon_H1f8 ]. % 15.48/15.61 apply (zenon_L126_); trivial. % 15.48/15.61 apply (zenon_or_s _ _ zenon_H1f8); [ zenon_intro zenon_H167 | zenon_intro zenon_H40 ]. % 15.48/15.61 apply (zenon_L984_); trivial. % 15.48/15.61 exact (zenon_H3c zenon_H40). % 15.48/15.61 (* end of lemma zenon_L985_ *) % 15.48/15.61 assert (zenon_L986_ : (((op (e0) (e0)) = (e3))\/(((op (e0) (e1)) = (e3))\/(((op (e0) (e2)) = (e3))\/((op (e0) (e3)) = (e3))))) -> (~((op (e0) (e0)) = (e3))) -> (~((op (e0) (e1)) = (op (e3) (e1)))) -> (~((op (e3) (e3)) = (e0))) -> (((op (e1) (e2)) = (e0))\/(((op (e1) (e2)) = (e1))\/(((op (e1) (e2)) = (e2))\/((op (e1) (e2)) = (e3))))) -> (~((op (e1) (e2)) = (op (e3) (e2)))) -> ((op (e1) (e1)) = (e1)) -> (~((op (e1) (e1)) = (op (e1) (e2)))) -> (~((op (e1) (op (e2) (e1))) = (op (e2) (e1)))) -> (~((op (e0) (e2)) = (op (e1) (e2)))) -> (~((e0) = (e3))) -> ((op (e3) (e1)) = (e3)) -> (((op (e2) (e0)) = (e0))\/(((op (e2) (e1)) = (e0))\/(((op (e2) (e2)) = (e0))\/((op (e2) (e3)) = (e0))))) -> (~((op (e2) (e0)) = (op (e3) (e0)))) -> (~((e0) = (e2))) -> (~((op (e2) (e2)) = (e0))) -> (~((op (e3) (op (e2) (e3))) = (op (e2) (e3)))) -> (((op (e3) (e0)) = (e0))\/(((op (e3) (e1)) = (e0))\/(((op (e3) (e2)) = (e0))\/((op (e3) (e3)) = (e0))))) -> (((op (e2) (e0)) = (e3))\/(((op (e2) (e1)) = (e3))\/(((op (e2) (e2)) = (e3))\/((op (e2) (e3)) = (e3))))) -> (~((op (e0) (op (e2) (e0))) = (op (e2) (e0)))) -> (~((e2) = (e3))) -> ((op (e2) (e1)) = (e2)) -> (~((op (e2) (e2)) = (e3))) -> (~((op (e0) (e3)) = (op (e2) (e3)))) -> False). % 15.48/15.61 do 0 intro. intros zenon_H58 zenon_H59 zenon_H138 zenon_H3c zenon_H1d5 zenon_H17d zenon_H21 zenon_H116 zenon_H290 zenon_H87 zenon_H4b zenon_H10a zenon_H1f5 zenon_H1e5 zenon_H5e zenon_H2e zenon_H28a zenon_H1f6 zenon_He6 zenon_H295 zenon_H6a zenon_H156 zenon_H30 zenon_Hb4. % 15.48/15.61 apply (zenon_or_s _ _ zenon_H58); [ zenon_intro zenon_H5b | zenon_intro zenon_H5a ]. % 15.48/15.61 exact (zenon_H59 zenon_H5b). % 15.48/15.61 apply (zenon_or_s _ _ zenon_H5a); [ zenon_intro zenon_H4a | zenon_intro zenon_H5c ]. % 15.48/15.61 apply (zenon_L120_); trivial. % 15.48/15.61 apply (zenon_or_s _ _ zenon_H5c); [ zenon_intro zenon_H50 | zenon_intro zenon_H53 ]. % 15.48/15.61 apply (zenon_L985_); trivial. % 15.48/15.61 apply (zenon_L978_); trivial. % 15.48/15.61 (* end of lemma zenon_L986_ *) % 15.48/15.61 assert (zenon_L987_ : ((~((op (e2) (e2)) = (e3)))\/((op (e2) (e3)) = (e2))) -> (~((op (e2) (e1)) = (op (e2) (e3)))) -> ((~((op (e3) (e3)) = (e1)))\/((op (e3) (e1)) = (e3))) -> (~((op (e0) (e1)) = (op (e3) (e1)))) -> (((op (e3) (e0)) = (e0))\/(((op (e3) (e1)) = (e0))\/(((op (e3) (e2)) = (e0))\/((op (e3) (e3)) = (e0))))) -> (~((op (e1) (e2)) = (op (e3) (e2)))) -> (~((op (e1) (e1)) = (op (e1) (e2)))) -> ((op (e1) (e1)) = (e1)) -> (~((op (e1) (op (e2) (e1))) = (op (e2) (e1)))) -> (~((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)) = (op (e3) (e0)))) -> (~((e0) = (e2))) -> (~((op (e3) (op (e2) (e3))) = (op (e2) (e3)))) -> (((op (e2) (e0)) = (e0))\/(((op (e2) (e1)) = (e0))\/(((op (e2) (e2)) = (e0))\/((op (e2) (e3)) = (e0))))) -> (((op (e0) (e0)) = (e2))\/(((op (e0) (e1)) = (e2))\/(((op (e0) (e2)) = (e2))\/((op (e0) (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) (e0)) = (e3))) -> (~((e0) = (e3))) -> ((op (e0) (e1)) = (e0)) -> (~((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) (op (e2) (e0))) = (op (e2) (e0)))) -> (((op (e0) (e0)) = (e3))\/(((op (e0) (e1)) = (e3))\/(((op (e0) (e2)) = (e3))\/((op (e0) (e3)) = (e3))))) -> ((op (e2) (e1)) = (e2)) -> (~((op (e0) (e1)) = (op (e2) (e1)))) -> (~((op (e0) (e0)) = (e2))) -> ((~((op (e2) (e2)) = (e1)))\/((op (e2) (e1)) = (e2))) -> (~((op (e1) (e1)) = (e3))) -> (~((op (e3) (e1)) = (op (e3) (e3)))) -> (((op (e0) (e1)) = (e3))\/(((op (e1) (e1)) = (e3))\/(((op (e2) (e1)) = (e3))\/((op (e3) (e1)) = (e3))))) -> (~((op (e2) (e2)) = (e0))) -> (~((op (e0) (e2)) = (op (e2) (e2)))) -> (((op (e2) (e2)) = (e0))\/(((op (e2) (e2)) = (e1))\/(((op (e2) (e2)) = (e2))\/((op (e2) (e2)) = (e3))))) -> (~((op (e2) (op (e2) (e2))) = (op (e2) (e2)))) -> ((~((op (e2) (e2)) = (e2)))\/((op (e2) (e2)) = (e2))) -> ((~((op (e3) (e3)) = (e3)))\/((op (e3) (e3)) = (e3))) -> (~((op (e3) (e0)) = (op (e3) (e1)))) -> ((~((op (e3) (e3)) = (e0)))\/((op (e3) (e0)) = (e3))) -> False). % 15.48/15.61 do 0 intro. intros zenon_H1c3 zenon_H1e2 zenon_H10c zenon_H138 zenon_H1f6 zenon_H17d zenon_H116 zenon_H21 zenon_H290 zenon_H87 zenon_H1d5 zenon_H1e5 zenon_H5e zenon_H28a zenon_H1f5 zenon_H8e zenon_H36 zenon_H3b zenon_H59 zenon_H4b zenon_H49 zenon_H6a zenon_He6 zenon_Hb4 zenon_H295 zenon_H58 zenon_H156 zenon_Hde zenon_H8f zenon_H1e3 zenon_H182 zenon_H12d zenon_H199 zenon_H2e zenon_H28 zenon_H2d zenon_H294 zenon_Haa zenon_H10d zenon_H109 zenon_H10f. % 15.48/15.61 apply (zenon_or_s _ _ zenon_H1c3); [ zenon_intro zenon_H30 | zenon_intro zenon_H124 ]. % 15.48/15.61 apply (zenon_or_s _ _ zenon_H10f); [ zenon_intro zenon_H3c | zenon_intro zenon_Hba ]. % 15.48/15.61 apply (zenon_or_s _ _ zenon_H10c); [ zenon_intro zenon_H104 | zenon_intro zenon_H10a ]. % 15.48/15.61 apply (zenon_or_s _ _ zenon_H10d); [ zenon_intro zenon_H3e | zenon_intro zenon_H42 ]. % 15.48/15.61 apply (zenon_L979_); trivial. % 15.48/15.61 apply (zenon_L915_); trivial. % 15.48/15.61 apply (zenon_L986_); trivial. % 15.48/15.61 apply (zenon_L184_); trivial. % 15.48/15.61 apply (zenon_L256_); trivial. % 15.48/15.61 (* end of lemma zenon_L987_ *) % 15.48/15.61 assert (zenon_L988_ : (((op (e0) (e1)) = (e2))\/(((op (e1) (e1)) = (e2))\/(((op (e2) (e1)) = (e2))\/((op (e3) (e1)) = (e2))))) -> (~((op (e1) (e1)) = (e2))) -> ((~((op (e3) (e3)) = (e0)))\/((op (e3) (e0)) = (e3))) -> (~((op (e3) (e0)) = (op (e3) (e1)))) -> ((~((op (e3) (e3)) = (e3)))\/((op (e3) (e3)) = (e3))) -> ((~((op (e2) (e2)) = (e2)))\/((op (e2) (e2)) = (e2))) -> (~((op (e2) (op (e2) (e2))) = (op (e2) (e2)))) -> (((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)) = (e0))) -> (((op (e0) (e1)) = (e3))\/(((op (e1) (e1)) = (e3))\/(((op (e2) (e1)) = (e3))\/((op (e3) (e1)) = (e3))))) -> (~((op (e3) (e1)) = (op (e3) (e3)))) -> (~((op (e1) (e1)) = (e3))) -> ((~((op (e2) (e2)) = (e1)))\/((op (e2) (e1)) = (e2))) -> (~((op (e0) (e0)) = (e2))) -> (~((op (e0) (e1)) = (op (e2) (e1)))) -> (((op (e0) (e0)) = (e3))\/(((op (e0) (e1)) = (e3))\/(((op (e0) (e2)) = (e3))\/((op (e0) (e3)) = (e3))))) -> (~((op (e0) (op (e2) (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 (e0) (e1)) = (e0)) -> (~((e0) = (e3))) -> (~((op (e0) (e0)) = (e3))) -> (((op (e3) (e3)) = (e0))\/(((op (e3) (e3)) = (e1))\/(((op (e3) (e3)) = (e2))\/((op (e3) (e3)) = (e3))))) -> (~((op (e0) (e3)) = (op (e3) (e3)))) -> (((op (e0) (e0)) = (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 (e3) (op (e2) (e3))) = (op (e2) (e3)))) -> (~((e0) = (e2))) -> (~((op (e2) (e0)) = (op (e3) (e0)))) -> (((op (e1) (e2)) = (e0))\/(((op (e1) (e2)) = (e1))\/(((op (e1) (e2)) = (e2))\/((op (e1) (e2)) = (e3))))) -> (~((op (e0) (e2)) = (op (e1) (e2)))) -> (~((op (e1) (op (e2) (e1))) = (op (e2) (e1)))) -> ((op (e1) (e1)) = (e1)) -> (~((op (e1) (e1)) = (op (e1) (e2)))) -> (~((op (e1) (e2)) = (op (e3) (e2)))) -> (((op (e3) (e0)) = (e0))\/(((op (e3) (e1)) = (e0))\/(((op (e3) (e2)) = (e0))\/((op (e3) (e3)) = (e0))))) -> (~((op (e0) (e1)) = (op (e3) (e1)))) -> ((~((op (e3) (e3)) = (e1)))\/((op (e3) (e1)) = (e3))) -> (~((op (e2) (e1)) = (op (e2) (e3)))) -> ((~((op (e2) (e2)) = (e3)))\/((op (e2) (e3)) = (e2))) -> (~((e2) = (e3))) -> ((op (e3) (e1)) = (e3)) -> False). % 15.48/15.61 do 0 intro. intros zenon_H1a2 zenon_Hd6 zenon_H10f zenon_H109 zenon_H10d zenon_Haa zenon_H294 zenon_H2d zenon_H28 zenon_H2e zenon_H199 zenon_H12d zenon_H182 zenon_H1e3 zenon_H8f zenon_Hde zenon_H58 zenon_H295 zenon_Hb4 zenon_He6 zenon_H49 zenon_H4b zenon_H59 zenon_H3b zenon_H36 zenon_H8e zenon_H1f5 zenon_H28a zenon_H5e zenon_H1e5 zenon_H1d5 zenon_H87 zenon_H290 zenon_H21 zenon_H116 zenon_H17d zenon_H1f6 zenon_H138 zenon_H10c zenon_H1e2 zenon_H1c3 zenon_H6a zenon_H10a. % 15.48/15.61 apply (zenon_or_s _ _ zenon_H1a2); [ zenon_intro zenon_H5d | zenon_intro zenon_H1a3 ]. % 15.48/15.61 apply (zenon_L14_); trivial. % 15.48/15.61 apply (zenon_or_s _ _ zenon_H1a3); [ zenon_intro zenon_H6e | zenon_intro zenon_H1a4 ]. % 15.48/15.61 exact (zenon_Hd6 zenon_H6e). % 15.48/15.61 apply (zenon_or_s _ _ zenon_H1a4); [ zenon_intro zenon_H156 | zenon_intro zenon_H16a ]. % 15.48/15.61 apply (zenon_L987_); trivial. % 15.48/15.61 apply (zenon_L297_); trivial. % 15.48/15.61 (* end of lemma zenon_L988_ *) % 15.48/15.61 assert (zenon_L989_ : ((~((op (e3) (e3)) = (e2)))\/((op (e3) (e2)) = (e3))) -> (((op (e0) (e0)) = (e2))\/(((op (e0) (e1)) = (e2))\/(((op (e0) (e2)) = (e2))\/((op (e0) (e3)) = (e2))))) -> (~((op (e3) (e3)) = (e0))) -> (~((op (e0) (e3)) = (op (e3) (e3)))) -> (~((e1) = (e2))) -> (~((op (e1) (e1)) = (op (e1) (e2)))) -> ((op (e1) (e1)) = (e1)) -> (~((e1) = (e3))) -> (((op (e0) (e2)) = (e1))\/(((op (e1) (e2)) = (e1))\/(((op (e2) (e2)) = (e1))\/((op (e3) (e2)) = (e1))))) -> (~((op (e3) (e2)) = (op (e3) (e3)))) -> (((op (e0) (e1)) = (e2))\/(((op (e1) (e1)) = (e2))\/(((op (e2) (e1)) = (e2))\/((op (e3) (e1)) = (e2))))) -> (((op (e0) (e0)) = (e0))\/(((op (e0) (e0)) = (e1))\/(((op (e0) (e0)) = (e2))\/((op (e0) (e0)) = (e3))))) -> (~((op (e0) (e0)) = (e3))) -> (~((op (e0) (e0)) = (e2))) -> (~((op (e0) (e0)) = (e0))) -> (~((op (e3) (e3)) = (e1))) -> (((op (e3) (e3)) = (e0))\/(((op (e3) (e3)) = (e1))\/(((op (e3) (e3)) = (e2))\/((op (e3) (e3)) = (e3))))) -> ((op (e2) (e0)) = (e2)) -> (~((op (e2) (e0)) = (op (e2) (e1)))) -> (~((op (e1) (e1)) = (e2))) -> ((op (e0) (e1)) = (e0)) -> (~((e0) = (e2))) -> (((op (e2) (e0)) = (e3))\/(((op (e2) (e1)) = (e3))\/(((op (e2) (e2)) = (e3))\/((op (e2) (e3)) = (e3))))) -> (~((op (e3) (op (e2) (e3))) = (op (e2) (e3)))) -> (((op (e2) (e2)) = (e0))\/(((op (e2) (e2)) = (e1))\/(((op (e2) (e2)) = (e2))\/((op (e2) (e2)) = (e3))))) -> (~((op (e2) (e2)) = (e3))) -> (~((op (e2) (e2)) = (e2))) -> (~((op (e2) (e2)) = (e1))) -> (~((e2) = (e3))) -> ((~((op (e3) (e3)) = (e3)))\/((op (e3) (e3)) = (e3))) -> False). % 15.48/15.61 do 0 intro. intros zenon_H10e zenon_H8e zenon_H3c zenon_H36 zenon_Ha7 zenon_H116 zenon_H21 zenon_Ha3 zenon_H11b zenon_H173 zenon_H1a2 zenon_H12a zenon_H59 zenon_H8f zenon_H20 zenon_H104 zenon_H3b zenon_Hdd zenon_H154 zenon_Hd6 zenon_H49 zenon_H5e zenon_He6 zenon_H28a zenon_H2d zenon_H30 zenon_H2f zenon_H52 zenon_H6a zenon_H10d. % 15.48/15.61 apply (zenon_or_s _ _ zenon_H10e); [ zenon_intro zenon_H3d | zenon_intro zenon_H106 ]. % 15.48/15.61 apply (zenon_or_s _ _ zenon_H10d); [ zenon_intro zenon_H3e | zenon_intro zenon_H42 ]. % 15.48/15.61 apply (zenon_L295_); trivial. % 15.48/15.61 apply (zenon_L936_); trivial. % 15.48/15.61 apply (zenon_L296_); trivial. % 15.48/15.61 (* end of lemma zenon_L989_ *) % 15.48/15.61 assert (zenon_L990_ : ((~((op (e3) (e3)) = (e1)))\/((op (e3) (e1)) = (e3))) -> ((~((op (e3) (e3)) = (e3)))\/((op (e3) (e3)) = (e3))) -> (~((e2) = (e3))) -> (~((op (e2) (e2)) = (e1))) -> (~((op (e2) (e2)) = (e2))) -> (~((op (e2) (e2)) = (e3))) -> (((op (e2) (e2)) = (e0))\/(((op (e2) (e2)) = (e1))\/(((op (e2) (e2)) = (e2))\/((op (e2) (e2)) = (e3))))) -> (~((op (e3) (op (e2) (e3))) = (op (e2) (e3)))) -> (((op (e2) (e0)) = (e3))\/(((op (e2) (e1)) = (e3))\/(((op (e2) (e2)) = (e3))\/((op (e2) (e3)) = (e3))))) -> (~((e0) = (e2))) -> ((op (e0) (e1)) = (e0)) -> (~((op (e1) (e1)) = (e2))) -> (~((op (e2) (e0)) = (op (e2) (e1)))) -> ((op (e2) (e0)) = (e2)) -> (((op (e3) (e3)) = (e0))\/(((op (e3) (e3)) = (e1))\/(((op (e3) (e3)) = (e2))\/((op (e3) (e3)) = (e3))))) -> (~((op (e0) (e0)) = (e0))) -> (~((op (e0) (e0)) = (e2))) -> (~((op (e0) (e0)) = (e3))) -> (((op (e0) (e0)) = (e0))\/(((op (e0) (e0)) = (e1))\/(((op (e0) (e0)) = (e2))\/((op (e0) (e0)) = (e3))))) -> (((op (e0) (e1)) = (e2))\/(((op (e1) (e1)) = (e2))\/(((op (e2) (e1)) = (e2))\/((op (e3) (e1)) = (e2))))) -> (~((op (e3) (e2)) = (op (e3) (e3)))) -> (((op (e0) (e2)) = (e1))\/(((op (e1) (e2)) = (e1))\/(((op (e2) (e2)) = (e1))\/((op (e3) (e2)) = (e1))))) -> (~((e1) = (e3))) -> ((op (e1) (e1)) = (e1)) -> (~((op (e1) (e1)) = (op (e1) (e2)))) -> (~((e1) = (e2))) -> (~((op (e0) (e3)) = (op (e3) (e3)))) -> (~((op (e3) (e3)) = (e0))) -> (((op (e0) (e0)) = (e2))\/(((op (e0) (e1)) = (e2))\/(((op (e0) (e2)) = (e2))\/((op (e0) (e3)) = (e2))))) -> ((~((op (e3) (e3)) = (e2)))\/((op (e3) (e2)) = (e3))) -> False). % 15.48/15.61 do 0 intro. intros zenon_H10c zenon_H10d zenon_H6a zenon_H52 zenon_H2f zenon_H30 zenon_H2d zenon_H28a zenon_He6 zenon_H5e zenon_H49 zenon_Hd6 zenon_H154 zenon_Hdd zenon_H3b zenon_H20 zenon_H8f zenon_H59 zenon_H12a zenon_H1a2 zenon_H173 zenon_H11b zenon_Ha3 zenon_H21 zenon_H116 zenon_Ha7 zenon_H36 zenon_H3c zenon_H8e zenon_H10e. % 15.48/15.61 apply (zenon_or_s _ _ zenon_H10c); [ zenon_intro zenon_H104 | zenon_intro zenon_H10a ]. % 15.48/15.61 apply (zenon_L989_); trivial. % 15.48/15.61 apply (zenon_L298_); trivial. % 15.48/15.61 (* end of lemma zenon_L990_ *) % 15.48/15.61 assert (zenon_L991_ : ((~((op (e0) (e0)) = (e2)))\/((op (e0) (e2)) = (e0))) -> (~((op (e0) (e1)) = (op (e0) (e2)))) -> ((~((op (e1) (e1)) = (e2)))\/((op (e1) (e2)) = (e1))) -> ((~((op (e2) (e2)) = (e0)))\/((op (e2) (e0)) = (e2))) -> (~((op (e2) (e0)) = (op (e2) (e2)))) -> (~((op (e2) (e0)) = (op (e2) (e1)))) -> (~((op (e2) (e0)) = (op (e2) (e3)))) -> (~((op (e3) (e0)) = (op (e3) (e2)))) -> (~((op (e3) (e0)) = (op (e3) (e3)))) -> ((~((op (e3) (e3)) = (e2)))\/((op (e3) (e2)) = (e3))) -> (~((e1) = (e2))) -> (~((op (e1) (e1)) = (op (e1) (e2)))) -> ((op (e1) (e1)) = (e1)) -> (~((e1) = (e3))) -> (((op (e0) (e2)) = (e1))\/(((op (e1) (e2)) = (e1))\/(((op (e2) (e2)) = (e1))\/((op (e3) (e2)) = (e1))))) -> (~((op (e3) (e2)) = (op (e3) (e3)))) -> (((op (e0) (e0)) = (e2))\/(((op (e0) (e1)) = (e2))\/(((op (e0) (e2)) = (e2))\/((op (e0) (e3)) = (e2))))) -> (~((op (e0) (e3)) = (op (e3) (e3)))) -> (~((e0) = (e3))) -> (~((e2) = (e3))) -> (((op (e0) (e1)) = (e2))\/(((op (e1) (e1)) = (e2))\/(((op (e2) (e1)) = (e2))\/((op (e3) (e1)) = (e2))))) -> (((op (e0) (e0)) = (e0))\/(((op (e0) (e0)) = (e1))\/(((op (e0) (e0)) = (e2))\/((op (e0) (e0)) = (e3))))) -> (~((op (e0) (e0)) = (e0))) -> (((op (e3) (e3)) = (e0))\/(((op (e3) (e3)) = (e1))\/(((op (e3) (e3)) = (e2))\/((op (e3) (e3)) = (e3))))) -> (~((op (e0) (op (e2) (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 (e0) (e0)) = (e3))\/(((op (e0) (e1)) = (e3))\/(((op (e0) (e2)) = (e3))\/((op (e0) (e3)) = (e3))))) -> ((op (e0) (e1)) = (e0)) -> (~((e0) = (e2))) -> ((~((op (e2) (e2)) = (e2)))\/((op (e2) (e2)) = (e2))) -> (~((op (e2) (op (e2) (e2))) = (op (e2) (e2)))) -> (((op (e2) (e2)) = (e0))\/(((op (e2) (e2)) = (e1))\/(((op (e2) (e2)) = (e2))\/((op (e2) (e2)) = (e3))))) -> (~((op (e0) (e2)) = (op (e2) (e2)))) -> ((~((op (e3) (e3)) = (e3)))\/((op (e3) (e3)) = (e3))) -> ((~((op (e3) (e3)) = (e0)))\/((op (e3) (e0)) = (e3))) -> (~((op (e3) (e0)) = (op (e3) (e1)))) -> (((op (e0) (e1)) = (e3))\/(((op (e1) (e1)) = (e3))\/(((op (e2) (e1)) = (e3))\/((op (e3) (e1)) = (e3))))) -> (~((op (e3) (e1)) = (op (e3) (e3)))) -> ((~((op (e2) (e2)) = (e1)))\/((op (e2) (e1)) = (e2))) -> (~((op (e0) (e1)) = (op (e2) (e1)))) -> (((op (e2) (e0)) = (e0))\/(((op (e2) (e1)) = (e0))\/(((op (e2) (e2)) = (e0))\/((op (e2) (e3)) = (e0))))) -> (~((op (e3) (op (e2) (e3))) = (op (e2) (e3)))) -> (~((op (e2) (e0)) = (op (e3) (e0)))) -> (((op (e1) (e2)) = (e0))\/(((op (e1) (e2)) = (e1))\/(((op (e1) (e2)) = (e2))\/((op (e1) (e2)) = (e3))))) -> (~((op (e0) (e2)) = (op (e1) (e2)))) -> (~((op (e1) (op (e2) (e1))) = (op (e2) (e1)))) -> (~((op (e1) (e2)) = (op (e3) (e2)))) -> (((op (e3) (e0)) = (e0))\/(((op (e3) (e1)) = (e0))\/(((op (e3) (e2)) = (e0))\/((op (e3) (e3)) = (e0))))) -> (~((op (e0) (e1)) = (op (e3) (e1)))) -> ((~((op (e3) (e3)) = (e1)))\/((op (e3) (e1)) = (e3))) -> (~((op (e2) (e1)) = (op (e2) (e3)))) -> ((~((op (e2) (e2)) = (e3)))\/((op (e2) (e3)) = (e2))) -> (~((op (e1) (e1)) = (op (e1) (e3)))) -> ((~((op (e1) (e1)) = (e3)))\/((op (e1) (e3)) = (e1))) -> (~((op (e0) (e1)) = (op (e0) (e3)))) -> ((~((op (e0) (e0)) = (e3)))\/((op (e0) (e3)) = (e0))) -> False). % 15.48/15.61 do 0 intro. intros zenon_H24a zenon_H23e zenon_H1d3 zenon_H1d4 zenon_H17a zenon_H154 zenon_Hce zenon_H105 zenon_Hbb zenon_H10e zenon_Ha7 zenon_H116 zenon_H21 zenon_Ha3 zenon_H11b zenon_H173 zenon_H8e zenon_H36 zenon_H4b zenon_H6a zenon_H1a2 zenon_H12a zenon_H20 zenon_H3b zenon_H295 zenon_Hb4 zenon_He6 zenon_H58 zenon_H49 zenon_H5e zenon_Haa zenon_H294 zenon_H2d zenon_H28 zenon_H10d zenon_H10f zenon_H109 zenon_H199 zenon_H12d zenon_H1e3 zenon_Hde zenon_H1f5 zenon_H28a zenon_H1e5 zenon_H1d5 zenon_H87 zenon_H290 zenon_H17d zenon_H1f6 zenon_H138 zenon_H10c zenon_H1e2 zenon_H1c3 zenon_H11e zenon_H1d2 zenon_H1cd zenon_H236. % 15.48/15.61 apply (zenon_or_s _ _ zenon_H24a); [ zenon_intro zenon_H8f | zenon_intro zenon_Hab ]. % 15.48/15.61 apply (zenon_or_s _ _ zenon_H236); [ zenon_intro zenon_H59 | zenon_intro zenon_Hca ]. % 15.48/15.61 apply (zenon_or_s _ _ zenon_H1d3); [ zenon_intro zenon_Hd6 | zenon_intro zenon_H117 ]. % 15.48/15.61 apply (zenon_or_s _ _ zenon_H1d2); [ zenon_intro zenon_H182 | zenon_intro zenon_H11f ]. % 15.48/15.61 apply (zenon_or_s _ _ zenon_H1d4); [ zenon_intro zenon_H2e | zenon_intro zenon_Hdd ]. % 15.48/15.61 apply (zenon_or_s _ _ zenon_H1e3); [ zenon_intro zenon_H52 | zenon_intro zenon_H156 ]. % 15.48/15.61 apply (zenon_or_s _ _ zenon_Haa); [ zenon_intro zenon_H2f | zenon_intro zenon_H35 ]. % 15.48/15.61 apply (zenon_or_s _ _ zenon_H1c3); [ zenon_intro zenon_H30 | zenon_intro zenon_H124 ]. % 15.48/15.61 apply (zenon_or_s _ _ zenon_H10f); [ zenon_intro zenon_H3c | zenon_intro zenon_Hba ]. % 15.48/15.61 apply (zenon_or_s _ _ zenon_H10c); [ zenon_intro zenon_H104 | zenon_intro zenon_H10a ]. % 15.48/15.61 apply (zenon_or_s _ _ zenon_H10e); [ zenon_intro zenon_H3d | zenon_intro zenon_H106 ]. % 15.48/15.61 apply (zenon_or_s _ _ zenon_H10d); [ zenon_intro zenon_H3e | zenon_intro zenon_H42 ]. % 15.48/15.61 apply (zenon_or_s _ _ zenon_H8e); [ zenon_intro zenon_H92 | zenon_intro zenon_H91 ]. % 15.48/15.61 exact (zenon_H8f zenon_H92). % 15.48/15.61 apply (zenon_or_s _ _ zenon_H91); [ zenon_intro zenon_H5d | zenon_intro zenon_H93 ]. % 15.48/15.61 apply (zenon_L14_); trivial. % 15.48/15.61 apply (zenon_or_s _ _ zenon_H93); [ zenon_intro zenon_H63 | zenon_intro zenon_H81 ]. % 15.48/15.61 apply (zenon_or_s _ _ zenon_H58); [ zenon_intro zenon_H5b | zenon_intro zenon_H5a ]. % 15.48/15.61 exact (zenon_H59 zenon_H5b). % 15.48/15.61 apply (zenon_or_s _ _ zenon_H5a); [ zenon_intro zenon_H4a | zenon_intro zenon_H5c ]. % 15.48/15.61 apply (zenon_L9_); trivial. % 15.48/15.61 apply (zenon_or_s _ _ zenon_H5c); [ zenon_intro zenon_H50 | zenon_intro zenon_H53 ]. % 15.48/15.61 apply (zenon_L31_); trivial. % 15.48/15.61 apply (zenon_or_s _ _ zenon_H1a2); [ zenon_intro zenon_H5d | zenon_intro zenon_H1a3 ]. % 15.48/15.61 apply (zenon_L14_); trivial. % 15.48/15.61 apply (zenon_or_s _ _ zenon_H1a3); [ zenon_intro zenon_H6e | zenon_intro zenon_H1a4 ]. % 15.48/15.61 exact (zenon_Hd6 zenon_H6e). % 15.48/15.61 apply (zenon_or_s _ _ zenon_H1a4); [ zenon_intro zenon_H156 | zenon_intro zenon_H16a ]. % 15.48/15.61 apply (zenon_L978_); trivial. % 15.48/15.61 apply (zenon_L188_); trivial. % 15.48/15.61 apply (zenon_L107_); trivial. % 15.48/15.61 apply (zenon_L914_); trivial. % 15.48/15.61 apply (zenon_L296_); trivial. % 15.48/15.61 apply (zenon_L988_); trivial. % 15.48/15.61 apply (zenon_L475_); trivial. % 15.48/15.61 apply (zenon_or_s _ _ zenon_H10f); [ zenon_intro zenon_H3c | zenon_intro zenon_Hba ]. % 15.48/15.61 apply (zenon_or_s _ _ zenon_H10c); [ zenon_intro zenon_H104 | zenon_intro zenon_H10a ]. % 15.48/15.61 apply (zenon_L476_); trivial. % 15.48/15.61 apply (zenon_L988_); trivial. % 15.48/15.61 apply (zenon_L475_); trivial. % 15.48/15.61 apply (zenon_L794_); trivial. % 15.48/15.61 apply (zenon_L987_); trivial. % 15.48/15.61 apply (zenon_or_s _ _ zenon_H1e3); [ zenon_intro zenon_H52 | zenon_intro zenon_H156 ]. % 15.48/15.61 apply (zenon_or_s _ _ zenon_Haa); [ zenon_intro zenon_H2f | zenon_intro zenon_H35 ]. % 15.48/15.61 apply (zenon_or_s _ _ zenon_H1c3); [ zenon_intro zenon_H30 | zenon_intro zenon_H124 ]. % 15.48/15.61 apply (zenon_or_s _ _ zenon_H10f); [ zenon_intro zenon_H3c | zenon_intro zenon_Hba ]. % 15.48/15.61 apply (zenon_L990_); trivial. % 15.48/15.61 apply (zenon_L301_); trivial. % 15.48/15.61 apply (zenon_L119_); trivial. % 15.48/15.61 apply (zenon_L161_); trivial. % 15.48/15.61 apply (zenon_L284_); trivial. % 15.48/15.61 apply (zenon_L90_); trivial. % 15.48/15.61 apply (zenon_L86_); trivial. % 15.48/15.61 apply (zenon_L463_); trivial. % 15.48/15.61 apply (zenon_L485_); trivial. % 15.48/15.61 (* end of lemma zenon_L991_ *) % 15.48/15.61 assert (zenon_L992_ : (((op (e0) (e0)) = (e3))\/(((op (e0) (e1)) = (e3))\/(((op (e0) (e2)) = (e3))\/((op (e0) (e3)) = (e3))))) -> (~((op (e0) (e0)) = (e3))) -> (~((op (e2) (e2)) = (e2))) -> ((op (e0) (e0)) = (e2)) -> (~((op (e2) (e2)) = (e0))) -> (((op (e2) (e2)) = (e0))\/(((op (e2) (e2)) = (e1))\/(((op (e2) (e2)) = (e2))\/((op (e2) (e2)) = (e3))))) -> (~((e0) = (e3))) -> ((op (e0) (e2)) = (e0)) -> (((op (e2) (e0)) = (e3))\/(((op (e2) (e1)) = (e3))\/(((op (e2) (e2)) = (e3))\/((op (e2) (e3)) = (e3))))) -> (~((op (e0) (op (e2) (e0))) = (op (e2) (e0)))) -> (~((e2) = (e3))) -> ((op (e2) (e1)) = (e2)) -> (~((op (e2) (e2)) = (e3))) -> (~((op (e0) (e3)) = (op (e2) (e3)))) -> False). % 15.48/15.61 do 0 intro. intros zenon_H58 zenon_H59 zenon_H2f zenon_H92 zenon_H2e zenon_H2d zenon_H4b zenon_Hab zenon_He6 zenon_H295 zenon_H6a zenon_H156 zenon_H30 zenon_Hb4. % 15.48/15.61 apply (zenon_or_s _ _ zenon_H58); [ zenon_intro zenon_H5b | zenon_intro zenon_H5a ]. % 15.48/15.61 exact (zenon_H59 zenon_H5b). % 15.48/15.61 apply (zenon_or_s _ _ zenon_H5a); [ zenon_intro zenon_H4a | zenon_intro zenon_H5c ]. % 15.48/15.61 apply (zenon_L47_); trivial. % 15.48/15.61 apply (zenon_or_s _ _ zenon_H5c); [ zenon_intro zenon_H50 | zenon_intro zenon_H53 ]. % 15.48/15.61 apply (zenon_L48_); trivial. % 15.48/15.61 apply (zenon_L978_); trivial. % 15.48/15.61 (* end of lemma zenon_L992_ *) % 15.48/15.61 assert (zenon_L993_ : (((op (e0) (e0)) = (e3))\/(((op (e1) (e0)) = (e3))\/(((op (e2) (e0)) = (e3))\/((op (e3) (e0)) = (e3))))) -> (~((op (e0) (e0)) = (e3))) -> (~((e2) = (e3))) -> ((op (e1) (e0)) = (e2)) -> (~((e0) = (e3))) -> ((op (e2) (e0)) = (e0)) -> (~((e1) = (e3))) -> ((op (e3) (e0)) = (e1)) -> False). % 15.48/15.61 do 0 intro. intros zenon_Hbe zenon_H59 zenon_H6a zenon_H68 zenon_H4b zenon_Hcf zenon_Ha3 zenon_Hee. % 15.48/15.61 apply (zenon_or_s _ _ zenon_Hbe); [ zenon_intro zenon_H5b | zenon_intro zenon_Hbf ]. % 15.48/15.61 exact (zenon_H59 zenon_H5b). % 15.48/15.61 apply (zenon_or_s _ _ zenon_Hbf); [ zenon_intro zenon_H69 | zenon_intro zenon_Hc0 ]. % 15.48/15.61 apply (zenon_L17_); trivial. % 15.48/15.61 apply (zenon_or_s _ _ zenon_Hc0); [ zenon_intro zenon_Haf | zenon_intro zenon_Hba ]. % 15.48/15.61 apply (zenon_L57_); trivial. % 15.48/15.61 apply (zenon_L79_); trivial. % 15.48/15.61 (* end of lemma zenon_L993_ *) % 15.48/15.61 assert (zenon_L994_ : (((op (e0) (e0)) = (e0))\/(((op (e1) (e0)) = (e0))\/(((op (e2) (e0)) = (e0))\/((op (e3) (e0)) = (e0))))) -> (~((op (e0) (e3)) = (op (e1) (e3)))) -> ((op (e3) (e2)) = (e3)) -> (~((op (e1) (e2)) = (op (e3) (e2)))) -> (~((op (e1) (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) (e3)) = (e3))) -> (~((op (e0) (e3)) = (op (e3) (e3)))) -> (~((op (e3) (e3)) = (e1))) -> (~((op (e3) (e3)) = (e0))) -> (((op (e3) (e3)) = (e0))\/(((op (e3) (e3)) = (e1))\/(((op (e3) (e3)) = (e2))\/((op (e3) (e3)) = (e3))))) -> (~((op (e2) (e1)) = (op (e2) (e3)))) -> (~((op (e1) (e1)) = (op (e2) (e1)))) -> (((op (e2) (e0)) = (e1))\/(((op (e2) (e1)) = (e1))\/(((op (e2) (e2)) = (e1))\/((op (e2) (e3)) = (e1))))) -> (~((op (e1) (op (e2) (e1))) = (op (e2) (e1)))) -> (~((op (e1) (e1)) = (e0))) -> (((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) (e1)) = (e2))\/(((op (e0) (e2)) = (e2))\/((op (e0) (e3)) = (e2))))) -> ((~((op (e0) (e0)) = (e3)))\/((op (e0) (e3)) = (e0))) -> (~((op (e0) (e1)) = (op (e0) (e3)))) -> ((~((op (e1) (e1)) = (e3)))\/((op (e1) (e3)) = (e1))) -> ((~((op (e2) (e2)) = (e3)))\/((op (e2) (e3)) = (e2))) -> ((~((op (e3) (e3)) = (e1)))\/((op (e3) (e1)) = (e3))) -> (~((op (e0) (e1)) = (op (e3) (e1)))) -> (((op (e3) (e0)) = (e0))\/(((op (e3) (e1)) = (e0))\/(((op (e3) (e2)) = (e0))\/((op (e3) (e3)) = (e0))))) -> (~((op (e0) (e2)) = (op (e1) (e2)))) -> (((op (e1) (e2)) = (e0))\/(((op (e1) (e2)) = (e1))\/(((op (e1) (e2)) = (e2))\/((op (e1) (e2)) = (e3))))) -> ((~((op (e2) (e2)) = (e1)))\/((op (e2) (e1)) = (e2))) -> (~((op (e3) (e1)) = (op (e3) (e3)))) -> (((op (e0) (e1)) = (e3))\/(((op (e1) (e1)) = (e3))\/(((op (e2) (e1)) = (e3))\/((op (e3) (e1)) = (e3))))) -> (~((op (e3) (e0)) = (op (e3) (e1)))) -> ((~((op (e3) (e3)) = (e0)))\/((op (e3) (e0)) = (e3))) -> ((~((op (e3) (e3)) = (e3)))\/((op (e3) (e3)) = (e3))) -> (~((op (e0) (e2)) = (op (e2) (e2)))) -> (~((op (e2) (op (e2) (e2))) = (op (e2) (e2)))) -> ((~((op (e2) (e2)) = (e2)))\/((op (e2) (e2)) = (e2))) -> (~((op (e0) (e0)) = (e0))) -> (((op (e0) (e0)) = (e0))\/(((op (e0) (e0)) = (e1))\/(((op (e0) (e0)) = (e2))\/((op (e0) (e0)) = (e3))))) -> (((op (e0) (e1)) = (e2))\/(((op (e1) (e1)) = (e2))\/(((op (e2) (e1)) = (e2))\/((op (e3) (e1)) = (e2))))) -> (~((op (e3) (e2)) = (op (e3) (e3)))) -> ((~((op (e3) (e3)) = (e2)))\/((op (e3) (e2)) = (e3))) -> (~((op (e3) (e0)) = (op (e3) (e3)))) -> (~((op (e3) (e0)) = (op (e3) (e2)))) -> (~((op (e2) (e0)) = (op (e2) (e1)))) -> (~((op (e2) (e0)) = (op (e2) (e2)))) -> ((~((op (e2) (e2)) = (e0)))\/((op (e2) (e0)) = (e2))) -> ((~((op (e1) (e1)) = (e2)))\/((op (e1) (e2)) = (e1))) -> (~((op (e0) (e1)) = (op (e0) (e2)))) -> ((~((op (e0) (e0)) = (e2)))\/((op (e0) (e2)) = (e0))) -> (((op (e0) (e2)) = (e1))\/(((op (e1) (e2)) = (e1))\/(((op (e2) (e2)) = (e1))\/((op (e3) (e2)) = (e1))))) -> (~((op (e2) (e0)) = (op (e2) (e3)))) -> (~((op (e1) (e1)) = (op (e1) (e3)))) -> (~((op (e0) (e2)) = (op (e0) (e3)))) -> (((op (e0) (e3)) = (e1))\/(((op (e1) (e3)) = (e1))\/(((op (e2) (e3)) = (e1))\/((op (e3) (e3)) = (e1))))) -> (~((op (e1) (e1)) = (op (e1) (e2)))) -> (~((op (e0) (e1)) = (op (e1) (e1)))) -> (((op (e0) (e0)) = (e1))\/(((op (e0) (e1)) = (e1))\/(((op (e0) (e2)) = (e1))\/((op (e0) (e3)) = (e1))))) -> (~((e1) = (e2))) -> (((op (e0) (e0)) = (e3))\/(((op (e1) (e0)) = (e3))\/(((op (e2) (e0)) = (e3))\/((op (e3) (e0)) = (e3))))) -> (~((op (e0) (e0)) = (e3))) -> (~((e2) = (e3))) -> (~((e0) = (e3))) -> (~((e1) = (e3))) -> (((op (e0) (e0)) = (e3))\/(((op (e0) (e1)) = (e3))\/(((op (e0) (e2)) = (e3))\/((op (e0) (e3)) = (e3))))) -> (~((op (e2) (e2)) = (e2))) -> (((op (e2) (e2)) = (e0))\/(((op (e2) (e2)) = (e1))\/(((op (e2) (e2)) = (e2))\/((op (e2) (e2)) = (e3))))) -> ((op (e0) (e2)) = (e0)) -> (((op (e2) (e0)) = (e3))\/(((op (e2) (e1)) = (e3))\/(((op (e2) (e2)) = (e3))\/((op (e2) (e3)) = (e3))))) -> (~((op (e0) (op (e2) (e0))) = (op (e2) (e0)))) -> (~((op (e2) (e2)) = (e3))) -> (~((op (e0) (e3)) = (op (e2) (e3)))) -> (((op (e0) (e0)) = (e2))\/(((op (e1) (e0)) = (e2))\/(((op (e2) (e0)) = (e2))\/((op (e3) (e0)) = (e2))))) -> (~((e0) = (e1))) -> (~((op (e1) (e0)) = (op (e1) (e1)))) -> ((op (e1) (e1)) = (e1)) -> (~((op (e0) (e0)) = (e1))) -> (((op (e0) (e0)) = (e1))\/(((op (e1) (e0)) = (e1))\/(((op (e2) (e0)) = (e1))\/((op (e3) (e0)) = (e1))))) -> (((op (e2) (e0)) = (e0))\/(((op (e2) (e1)) = (e0))\/(((op (e2) (e2)) = (e0))\/((op (e2) (e3)) = (e0))))) -> (~((op (e2) (e0)) = (op (e3) (e0)))) -> ((op (e2) (e1)) = (e2)) -> (~((e0) = (e2))) -> (~((op (e2) (e2)) = (e0))) -> (~((op (e3) (op (e2) (e3))) = (op (e2) (e3)))) -> False). % 15.48/15.61 do 0 intro. intros zenon_Hf0 zenon_H80 zenon_H106 zenon_H17d zenon_H182 zenon_H90 zenon_H160 zenon_H3e zenon_H36 zenon_H104 zenon_H3c zenon_H3b zenon_H1e2 zenon_Hb1 zenon_Hb7 zenon_H290 zenon_H145 zenon_H144 zenon_Hde zenon_H8e zenon_H236 zenon_H1cd zenon_H1d2 zenon_H1c3 zenon_H10c zenon_H138 zenon_H1f6 zenon_H87 zenon_H1d5 zenon_H1e3 zenon_H12d zenon_H199 zenon_H109 zenon_H10f zenon_H10d zenon_H28 zenon_H294 zenon_Haa zenon_H20 zenon_H12a zenon_H1a2 zenon_H173 zenon_H10e zenon_Hbb zenon_H105 zenon_H154 zenon_H17a zenon_H1d4 zenon_H1d3 zenon_H23e zenon_H24a zenon_H11b zenon_Hce zenon_H11e zenon_Hc9 zenon_H121 zenon_H116 zenon_H23 zenon_H44 zenon_Ha7 zenon_Hbe zenon_H59 zenon_H6a zenon_H4b zenon_Ha3 zenon_H58 zenon_H2f zenon_H2d zenon_Hab zenon_He6 zenon_H295 zenon_H30 zenon_Hb4 zenon_Heb zenon_H9e zenon_Hd7 zenon_H21 zenon_H45 zenon_Hf1 zenon_H1f5 zenon_H1e5 zenon_H156 zenon_H5e zenon_H2e zenon_H28a. % 15.48/15.61 apply (zenon_or_s _ _ zenon_Hf0); [ zenon_intro zenon_H1f | zenon_intro zenon_Hf2 ]. % 15.48/15.61 exact (zenon_H20 zenon_H1f). % 15.48/15.61 apply (zenon_or_s _ _ zenon_Hf2); [ zenon_intro zenon_Had | zenon_intro zenon_Hf3 ]. % 15.48/15.61 apply (zenon_or_s _ _ zenon_H44); [ zenon_intro zenon_H47 | zenon_intro zenon_H46 ]. % 15.48/15.61 exact (zenon_H45 zenon_H47). % 15.48/15.61 apply (zenon_or_s _ _ zenon_H46); [ zenon_intro zenon_H22 | zenon_intro zenon_H48 ]. % 15.48/15.61 apply (zenon_L3_); trivial. % 15.48/15.61 apply (zenon_or_s _ _ zenon_H48); [ zenon_intro zenon_H29 | zenon_intro zenon_H37 ]. % 15.48/15.61 apply (zenon_L5_); trivial. % 15.48/15.61 apply (zenon_or_s _ _ zenon_Hf1); [ zenon_intro zenon_H47 | zenon_intro zenon_Hf4 ]. % 15.48/15.61 exact (zenon_H45 zenon_H47). % 15.48/15.61 apply (zenon_or_s _ _ zenon_Hf4); [ zenon_intro zenon_Hd8 | zenon_intro zenon_Hf5 ]. % 15.48/15.61 apply (zenon_L61_); trivial. % 15.48/15.61 apply (zenon_or_s _ _ zenon_Hf5); [ zenon_intro zenon_Hae | zenon_intro zenon_Hee ]. % 15.48/15.61 apply (zenon_or_s _ _ zenon_H144); [ zenon_intro zenon_H49 | zenon_intro zenon_H147 ]. % 15.48/15.61 apply (zenon_L991_); trivial. % 15.48/15.61 apply (zenon_or_s _ _ zenon_H147); [ zenon_intro zenon_H149 | zenon_intro zenon_H148 ]. % 15.48/15.61 exact (zenon_H145 zenon_H149). % 15.48/15.61 apply (zenon_or_s _ _ zenon_H148); [ zenon_intro zenon_H14a | zenon_intro zenon_H142 ]. % 15.48/15.61 apply (zenon_L351_); trivial. % 15.48/15.61 apply (zenon_L173_); trivial. % 15.48/15.61 apply (zenon_or_s _ _ zenon_H8e); [ zenon_intro zenon_H92 | zenon_intro zenon_H91 ]. % 15.48/15.61 apply (zenon_L992_); trivial. % 15.48/15.61 apply (zenon_or_s _ _ zenon_H91); [ zenon_intro zenon_H5d | zenon_intro zenon_H93 ]. % 15.48/15.61 apply (zenon_L251_); trivial. % 15.48/15.61 apply (zenon_or_s _ _ zenon_H93); [ zenon_intro zenon_H63 | zenon_intro zenon_H81 ]. % 15.48/15.61 apply (zenon_or_s _ _ zenon_Heb); [ zenon_intro zenon_H92 | zenon_intro zenon_Hec ]. % 15.48/15.61 apply (zenon_L992_); trivial. % 15.48/15.61 apply (zenon_or_s _ _ zenon_Hec); [ zenon_intro zenon_H68 | zenon_intro zenon_Hed ]. % 15.48/15.61 apply (zenon_or_s _ _ zenon_H58); [ zenon_intro zenon_H5b | zenon_intro zenon_H5a ]. % 15.48/15.61 exact (zenon_H59 zenon_H5b). % 15.48/15.61 apply (zenon_or_s _ _ zenon_H5a); [ zenon_intro zenon_H4a | zenon_intro zenon_H5c ]. % 15.48/15.61 apply (zenon_or_s _ _ zenon_Hbe); [ zenon_intro zenon_H5b | zenon_intro zenon_Hbf ]. % 15.48/15.61 exact (zenon_H59 zenon_H5b). % 15.48/15.61 apply (zenon_or_s _ _ zenon_Hbf); [ zenon_intro zenon_H69 | zenon_intro zenon_Hc0 ]. % 15.48/15.61 apply (zenon_L17_); trivial. % 15.48/15.61 apply (zenon_or_s _ _ zenon_Hc0); [ zenon_intro zenon_Haf | zenon_intro zenon_Hba ]. % 15.48/15.61 apply (zenon_or_s _ _ zenon_H144); [ zenon_intro zenon_H49 | zenon_intro zenon_H147 ]. % 15.48/15.61 apply (zenon_L9_); trivial. % 15.48/15.61 apply (zenon_or_s _ _ zenon_H147); [ zenon_intro zenon_H149 | zenon_intro zenon_H148 ]. % 15.48/15.61 exact (zenon_H145 zenon_H149). % 15.48/15.61 apply (zenon_or_s _ _ zenon_H148); [ zenon_intro zenon_H14a | zenon_intro zenon_H142 ]. % 15.48/15.61 apply (zenon_L940_); trivial. % 15.48/15.61 apply (zenon_or_s _ _ zenon_H90); [ zenon_intro zenon_H69 | zenon_intro zenon_H94 ]. % 15.48/15.61 apply (zenon_L17_); trivial. % 15.48/15.61 apply (zenon_or_s _ _ zenon_H94); [ zenon_intro zenon_H96 | zenon_intro zenon_H95 ]. % 15.48/15.61 exact (zenon_H182 zenon_H96). % 15.48/15.61 apply (zenon_or_s _ _ zenon_H95); [ zenon_intro zenon_H88 | zenon_intro zenon_H8a ]. % 15.48/15.61 apply (zenon_L164_); trivial. % 15.48/15.61 apply (zenon_or_s _ _ zenon_Hb7); [ zenon_intro zenon_Hae | zenon_intro zenon_Hb8 ]. % 15.48/15.61 apply (zenon_L39_); trivial. % 15.48/15.61 apply (zenon_or_s _ _ zenon_Hb8); [ zenon_intro zenon_Hb2 | zenon_intro zenon_Hb9 ]. % 15.48/15.61 apply (zenon_L40_); trivial. % 15.48/15.61 apply (zenon_or_s _ _ zenon_Hb9); [ zenon_intro zenon_H2a | zenon_intro zenon_Hb5 ]. % 15.48/15.61 apply (zenon_L902_); trivial. % 15.48/15.61 apply (zenon_L41_); trivial. % 15.48/15.61 apply (zenon_L79_); trivial. % 15.48/15.61 apply (zenon_or_s _ _ zenon_H5c); [ zenon_intro zenon_H50 | zenon_intro zenon_H53 ]. % 15.48/15.61 apply (zenon_L31_); trivial. % 15.48/15.61 apply (zenon_L294_); trivial. % 15.48/15.61 apply (zenon_or_s _ _ zenon_Hed); [ zenon_intro zenon_Hdd | zenon_intro zenon_He9 ]. % 15.48/15.61 apply (zenon_L812_); trivial. % 15.48/15.61 apply (zenon_L122_); trivial. % 15.48/15.61 apply (zenon_L33_); trivial. % 15.48/15.61 apply (zenon_or_s _ _ zenon_Hf3); [ zenon_intro zenon_Hcf | zenon_intro zenon_Hdb ]. % 15.48/15.61 apply (zenon_or_s _ _ zenon_Hf1); [ zenon_intro zenon_H47 | zenon_intro zenon_Hf4 ]. % 15.48/15.61 exact (zenon_H45 zenon_H47). % 15.48/15.61 apply (zenon_or_s _ _ zenon_Hf4); [ zenon_intro zenon_Hd8 | zenon_intro zenon_Hf5 ]. % 15.48/15.61 apply (zenon_L61_); trivial. % 15.48/15.61 apply (zenon_or_s _ _ zenon_Hf5); [ zenon_intro zenon_Hae | zenon_intro zenon_Hee ]. % 15.48/15.61 apply (zenon_L269_); trivial. % 15.48/15.61 apply (zenon_or_s _ _ zenon_Heb); [ zenon_intro zenon_H92 | zenon_intro zenon_Hec ]. % 15.48/15.61 apply (zenon_L992_); trivial. % 15.48/15.61 apply (zenon_or_s _ _ zenon_Hec); [ zenon_intro zenon_H68 | zenon_intro zenon_Hed ]. % 15.48/15.61 apply (zenon_L993_); trivial. % 15.48/15.61 apply (zenon_or_s _ _ zenon_Hed); [ zenon_intro zenon_Hdd | zenon_intro zenon_He9 ]. % 15.48/15.61 apply (zenon_L177_); trivial. % 15.48/15.61 apply (zenon_L122_); trivial. % 15.48/15.61 apply (zenon_L983_); trivial. % 15.48/15.61 (* end of lemma zenon_L994_ *) % 15.48/15.61 assert (zenon_L995_ : (((op (e0) (e0)) = (e1))\/(((op (e0) (e1)) = (e1))\/(((op (e0) (e2)) = (e1))\/((op (e0) (e3)) = (e1))))) -> (~((op (e0) (e0)) = (e1))) -> (~((op (e0) (e1)) = (op (e1) (e1)))) -> ((op (e1) (e1)) = (e1)) -> (~((e0) = (e1))) -> (((op (e0) (e0)) = (e2))\/(((op (e0) (e1)) = (e2))\/(((op (e0) (e2)) = (e2))\/((op (e0) (e3)) = (e2))))) -> (~((op (e0) (e3)) = (op (e2) (e3)))) -> (~((op (e2) (e2)) = (e3))) -> (~((op (e0) (op (e2) (e0))) = (op (e2) (e0)))) -> (((op (e2) (e0)) = (e3))\/(((op (e2) (e1)) = (e3))\/(((op (e2) (e2)) = (e3))\/((op (e2) (e3)) = (e3))))) -> ((op (e0) (e2)) = (e0)) -> (~((e0) = (e3))) -> (((op (e2) (e2)) = (e0))\/(((op (e2) (e2)) = (e1))\/(((op (e2) (e2)) = (e2))\/((op (e2) (e2)) = (e3))))) -> (~((op (e2) (e2)) = (e0))) -> (~((op (e2) (e2)) = (e2))) -> (~((op (e0) (e0)) = (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) (e3)) = (e2))) -> (~((op (e0) (e2)) = (op (e3) (e2)))) -> (~((op (e2) (e1)) = (op (e3) (e1)))) -> ((op (e2) (e1)) = (e2)) -> (~((e2) = (e3))) -> ((op (e3) (e0)) = (e3)) -> (((op (e3) (e0)) = (e2))\/(((op (e3) (e1)) = (e2))\/(((op (e3) (e2)) = (e2))\/((op (e3) (e3)) = (e2))))) -> (~((e1) = (e2))) -> False). % 15.48/15.61 do 0 intro. intros zenon_H44 zenon_H45 zenon_H23 zenon_H21 zenon_H9e zenon_H8e zenon_Hb4 zenon_H30 zenon_H295 zenon_He6 zenon_Hab zenon_H4b zenon_H2d zenon_H2e zenon_H2f zenon_H59 zenon_H58 zenon_Hde zenon_H3d zenon_H140 zenon_H13c zenon_H156 zenon_H6a zenon_Hba zenon_H1df zenon_Ha7. % 15.48/15.61 apply (zenon_or_s _ _ zenon_H44); [ zenon_intro zenon_H47 | zenon_intro zenon_H46 ]. % 15.48/15.61 exact (zenon_H45 zenon_H47). % 15.48/15.61 apply (zenon_or_s _ _ zenon_H46); [ zenon_intro zenon_H22 | zenon_intro zenon_H48 ]. % 15.48/15.61 apply (zenon_L3_); trivial. % 15.48/15.61 apply (zenon_or_s _ _ zenon_H48); [ zenon_intro zenon_H29 | zenon_intro zenon_H37 ]. % 15.48/15.61 apply (zenon_L37_); trivial. % 15.48/15.61 apply (zenon_or_s _ _ zenon_H8e); [ zenon_intro zenon_H92 | zenon_intro zenon_H91 ]. % 15.48/15.61 apply (zenon_L992_); trivial. % 15.48/15.61 apply (zenon_or_s _ _ zenon_H91); [ zenon_intro zenon_H5d | zenon_intro zenon_H93 ]. % 15.48/15.61 apply (zenon_L251_); trivial. % 15.48/15.61 apply (zenon_or_s _ _ zenon_H93); [ zenon_intro zenon_H63 | zenon_intro zenon_H81 ]. % 15.48/15.61 apply (zenon_L326_); trivial. % 15.48/15.61 apply (zenon_L33_); trivial. % 15.48/15.61 (* end of lemma zenon_L995_ *) % 15.48/15.61 assert (zenon_L996_ : (((op (e0) (e0)) = (e2))\/(((op (e1) (e0)) = (e2))\/(((op (e2) (e0)) = (e2))\/((op (e3) (e0)) = (e2))))) -> (~((op (e0) (e0)) = (e2))) -> (((op (e1) (e0)) = (e3))\/(((op (e1) (e1)) = (e3))\/(((op (e1) (e2)) = (e3))\/((op (e1) (e3)) = (e3))))) -> (~((op (e1) (e1)) = (e3))) -> (~((op (e0) (e2)) = (op (e1) (e2)))) -> (~((op (e1) (e3)) = (op (e3) (e3)))) -> ((op (e2) (e0)) = (e1)) -> (~((op (e2) (e2)) = (e3))) -> ((~((op (e2) (e2)) = (e3)))\/((op (e2) (e3)) = (e2))) -> (~((op (e2) (e0)) = (op (e2) (e3)))) -> (~((op (e0) (e0)) = (e1))) -> (~((op (e0) (e1)) = (op (e1) (e1)))) -> ((op (e1) (e1)) = (e1)) -> (((op (e0) (e0)) = (e3))\/(((op (e0) (e1)) = (e3))\/(((op (e0) (e2)) = (e3))\/((op (e0) (e3)) = (e3))))) -> (~((op (e0) (e3)) = (op (e3) (e3)))) -> (~((e1) = (e3))) -> (~((op (e0) (e1)) = (op (e2) (e1)))) -> (~((op (e3) (op (e2) (e3))) = (op (e2) (e3)))) -> ((op (e3) (e3)) = (e3)) -> (((op (e2) (e0)) = (e3))\/(((op (e2) (e1)) = (e3))\/(((op (e2) (e2)) = (e3))\/((op (e2) (e3)) = (e3))))) -> (~((op (e0) (e0)) = (e3))) -> (((op (e2) (e0)) = (e1))\/(((op (e2) (e1)) = (e1))\/(((op (e2) (e2)) = (e1))\/((op (e2) (e3)) = (e1))))) -> (~((op (e0) (e3)) = (op (e2) (e3)))) -> (~((op (e1) (e1)) = (op (e2) (e1)))) -> (~((e1) = (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) (e2)) = (e1)))\/((op (e2) (e1)) = (e2))) -> (~((e2) = (e3))) -> ((op (e3) (e0)) = (e3)) -> False). % 15.48/15.61 do 0 intro. intros zenon_Heb zenon_H8f zenon_H90 zenon_H182 zenon_H87 zenon_H8b zenon_Hae zenon_H30 zenon_H1c3 zenon_Hce zenon_H45 zenon_H23 zenon_H21 zenon_H58 zenon_H36 zenon_Ha3 zenon_Hde zenon_H28a zenon_H42 zenon_He6 zenon_H59 zenon_Hb7 zenon_Hb4 zenon_Hb1 zenon_Ha7 zenon_H44 zenon_H154 zenon_H1e3 zenon_H6a zenon_Hba. % 15.48/15.61 apply (zenon_or_s _ _ zenon_Heb); [ zenon_intro zenon_H92 | zenon_intro zenon_Hec ]. % 15.48/15.61 exact (zenon_H8f zenon_H92). % 15.48/15.61 apply (zenon_or_s _ _ zenon_Hec); [ zenon_intro zenon_H68 | zenon_intro zenon_Hed ]. % 15.48/15.61 apply (zenon_or_s _ _ zenon_H58); [ zenon_intro zenon_H5b | zenon_intro zenon_H5a ]. % 15.48/15.61 exact (zenon_H59 zenon_H5b). % 15.48/15.61 apply (zenon_or_s _ _ zenon_H5a); [ zenon_intro zenon_H4a | zenon_intro zenon_H5c ]. % 15.48/15.61 apply (zenon_L787_); trivial. % 15.48/15.61 apply (zenon_or_s _ _ zenon_H5c); [ zenon_intro zenon_H50 | zenon_intro zenon_H53 ]. % 15.48/15.61 apply (zenon_L379_); trivial. % 15.48/15.61 apply (zenon_L12_); trivial. % 15.48/15.61 apply (zenon_or_s _ _ zenon_Hed); [ zenon_intro zenon_Hdd | zenon_intro zenon_He9 ]. % 15.48/15.61 apply (zenon_L959_); trivial. % 15.48/15.61 apply (zenon_L220_); trivial. % 15.48/15.61 (* end of lemma zenon_L996_ *) % 15.48/15.61 assert (zenon_L997_ : (((op (e0) (e0)) = (e1))\/(((op (e1) (e0)) = (e1))\/(((op (e2) (e0)) = (e1))\/((op (e3) (e0)) = (e1))))) -> (~((e2) = (e3))) -> ((~((op (e2) (e2)) = (e1)))\/((op (e2) (e1)) = (e2))) -> (~((op (e2) (e0)) = (op (e2) (e1)))) -> (((op (e0) (e0)) = (e1))\/(((op (e0) (e1)) = (e1))\/(((op (e0) (e2)) = (e1))\/((op (e0) (e3)) = (e1))))) -> (~((e1) = (e2))) -> (~((op (e1) (e1)) = (op (e2) (e1)))) -> (~((op (e0) (e3)) = (op (e2) (e3)))) -> (((op (e2) (e0)) = (e1))\/(((op (e2) (e1)) = (e1))\/(((op (e2) (e2)) = (e1))\/((op (e2) (e3)) = (e1))))) -> (~((op (e0) (e0)) = (e3))) -> (((op (e2) (e0)) = (e3))\/(((op (e2) (e1)) = (e3))\/(((op (e2) (e2)) = (e3))\/((op (e2) (e3)) = (e3))))) -> ((op (e3) (e3)) = (e3)) -> (~((op (e3) (op (e2) (e3))) = (op (e2) (e3)))) -> (~((op (e0) (e1)) = (op (e2) (e1)))) -> (~((op (e0) (e3)) = (op (e3) (e3)))) -> (((op (e0) (e0)) = (e3))\/(((op (e0) (e1)) = (e3))\/(((op (e0) (e2)) = (e3))\/((op (e0) (e3)) = (e3))))) -> ((op (e1) (e1)) = (e1)) -> (~((op (e0) (e1)) = (op (e1) (e1)))) -> (~((op (e0) (e0)) = (e1))) -> (~((op (e2) (e0)) = (op (e2) (e3)))) -> ((~((op (e2) (e2)) = (e3)))\/((op (e2) (e3)) = (e2))) -> (~((op (e2) (e2)) = (e3))) -> (~((op (e1) (e3)) = (op (e3) (e3)))) -> (~((op (e0) (e2)) = (op (e1) (e2)))) -> (~((op (e1) (e1)) = (e3))) -> (((op (e1) (e0)) = (e3))\/(((op (e1) (e1)) = (e3))\/(((op (e1) (e2)) = (e3))\/((op (e1) (e3)) = (e3))))) -> (~((op (e0) (e0)) = (e2))) -> (((op (e0) (e0)) = (e2))\/(((op (e1) (e0)) = (e2))\/(((op (e2) (e0)) = (e2))\/((op (e3) (e0)) = (e2))))) -> (~((e1) = (e3))) -> ((op (e3) (e0)) = (e3)) -> False). % 15.48/15.61 do 0 intro. intros zenon_Hf1 zenon_H6a zenon_H1e3 zenon_H154 zenon_H44 zenon_Ha7 zenon_Hb1 zenon_Hb4 zenon_Hb7 zenon_H59 zenon_He6 zenon_H42 zenon_H28a zenon_Hde zenon_H36 zenon_H58 zenon_H21 zenon_H23 zenon_H45 zenon_Hce zenon_H1c3 zenon_H30 zenon_H8b zenon_H87 zenon_H182 zenon_H90 zenon_H8f zenon_Heb zenon_Ha3 zenon_Hba. % 15.48/15.61 apply (zenon_or_s _ _ zenon_Hf1); [ zenon_intro zenon_H47 | zenon_intro zenon_Hf4 ]. % 15.48/15.61 exact (zenon_H45 zenon_H47). % 15.48/15.61 apply (zenon_or_s _ _ zenon_Hf4); [ zenon_intro zenon_Hd8 | zenon_intro zenon_Hf5 ]. % 15.48/15.61 apply (zenon_L780_); trivial. % 15.48/15.61 apply (zenon_or_s _ _ zenon_Hf5); [ zenon_intro zenon_Hae | zenon_intro zenon_Hee ]. % 15.48/15.61 apply (zenon_L996_); trivial. % 15.48/15.61 apply (zenon_L79_); trivial. % 15.48/15.61 (* end of lemma zenon_L997_ *) % 15.48/15.61 assert (zenon_L998_ : ((~((op (e1) (e1)) = (e0)))\/((op (e1) (e0)) = (e1))) -> ((~((op (e3) (e3)) = (e0)))\/((op (e3) (e0)) = (e3))) -> (~((op (e3) (e0)) = (op (e3) (e2)))) -> (((op (e0) (e0)) = (e1))\/(((op (e1) (e0)) = (e1))\/(((op (e2) (e0)) = (e1))\/((op (e3) (e0)) = (e1))))) -> (~((op (e1) (e0)) = (op (e1) (e1)))) -> (~((op (e3) (e0)) = (op (e3) (e3)))) -> (~((op (e3) (e0)) = (op (e3) (e1)))) -> ((~((op (e3) (e3)) = (e3)))\/((op (e3) (e3)) = (e3))) -> (~((op (e0) (e0)) = (e0))) -> ((~((op (e2) (e2)) = (e1)))\/((op (e2) (e1)) = (e2))) -> (~((e2) = (e3))) -> (~((op (e3) (e1)) = (op (e3) (e3)))) -> (((op (e0) (e1)) = (e3))\/(((op (e1) (e1)) = (e3))\/(((op (e2) (e1)) = (e3))\/((op (e3) (e1)) = (e3))))) -> (((op (e0) (e0)) = (e3))\/(((op (e0) (e1)) = (e3))\/(((op (e0) (e2)) = (e3))\/((op (e0) (e3)) = (e3))))) -> (~((e0) = (e3))) -> (~((op (e0) (e0)) = (e3))) -> (~((op (e2) (op (e2) (e2))) = (op (e2) (e2)))) -> ((~((op (e2) (e2)) = (e2)))\/((op (e2) (e2)) = (e2))) -> (((op (e2) (e0)) = (e1))\/(((op (e2) (e1)) = (e1))\/(((op (e2) (e2)) = (e1))\/((op (e2) (e3)) = (e1))))) -> (~((op (e0) (e3)) = (op (e2) (e3)))) -> (~((op (e1) (e1)) = (op (e2) (e1)))) -> (~((e1) = (e3))) -> (~((op (e0) (e1)) = (op (e2) (e1)))) -> (~((op (e3) (op (e2) (e3))) = (op (e2) (e3)))) -> (((op (e2) (e0)) = (e3))\/(((op (e2) (e1)) = (e3))\/(((op (e2) (e2)) = (e3))\/((op (e2) (e3)) = (e3))))) -> (~((e0) = (e1))) -> ((~((op (e3) (e3)) = (e1)))\/((op (e3) (e1)) = (e3))) -> (~((e1) = (e2))) -> (~((op (e0) (e2)) = (op (e0) (e3)))) -> (~((op (e1) (e1)) = (op (e1) (e3)))) -> (~((op (e2) (e0)) = (op (e2) (e3)))) -> (((op (e0) (e3)) = (e1))\/(((op (e1) (e3)) = (e1))\/(((op (e2) (e3)) = (e1))\/((op (e3) (e3)) = (e1))))) -> ((~((op (e2) (e2)) = (e3)))\/((op (e2) (e3)) = (e2))) -> (((op (e0) (e0)) = (e0))\/(((op (e0) (e1)) = (e0))\/(((op (e0) (e2)) = (e0))\/((op (e0) (e3)) = (e0))))) -> (~((op (e0) (e0)) = (e1))) -> (~((op (e0) (e1)) = (op (e1) (e1)))) -> ((op (e1) (e1)) = (e1)) -> (((op (e2) (e2)) = (e0))\/(((op (e2) (e2)) = (e1))\/(((op (e2) (e2)) = (e2))\/((op (e2) (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 (e0) (e3)) = (op (e3) (e3)))) -> (((op (e0) (e0)) = (e1))\/(((op (e0) (e1)) = (e1))\/(((op (e0) (e2)) = (e1))\/((op (e0) (e3)) = (e1))))) -> (~((op (e1) (e1)) = (op (e1) (e2)))) -> (((op (e0) (e2)) = (e1))\/(((op (e1) (e2)) = (e1))\/(((op (e2) (e2)) = (e1))\/((op (e3) (e2)) = (e1))))) -> ((op (e0) (e2)) = (e0)) -> ((~((op (e3) (e3)) = (e2)))\/((op (e3) (e2)) = (e3))) -> (((op (e0) (e0)) = (e0))\/(((op (e0) (e0)) = (e1))\/(((op (e0) (e0)) = (e2))\/((op (e0) (e0)) = (e3))))) -> (~((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)) = (e2))\/(((op (e1) (e0)) = (e2))\/(((op (e2) (e0)) = (e2))\/((op (e3) (e0)) = (e2))))) -> (((op (e0) (e3)) = (e2))\/(((op (e1) (e3)) = (e2))\/(((op (e2) (e3)) = (e2))\/((op (e3) (e3)) = (e2))))) -> (~((op (e0) (e3)) = (op (e1) (e3)))) -> ((~((op (e0) (e0)) = (e2)))\/((op (e0) (e2)) = (e0))) -> (~((op (e0) (e1)) = (op (e0) (e2)))) -> (~((op (e2) (e0)) = (op (e2) (e2)))) -> (~((op (e2) (e0)) = (op (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) (op (e2) (e0))) = (op (e2) (e0)))) -> (~((op (e2) (e0)) = (op (e3) (e0)))) -> (((op (e1) (e2)) = (e0))\/(((op (e1) (e2)) = (e1))\/(((op (e1) (e2)) = (e2))\/((op (e1) (e2)) = (e3))))) -> (~((op (e1) (e2)) = (op (e3) (e2)))) -> (((op (e3) (e0)) = (e0))\/(((op (e3) (e1)) = (e0))\/(((op (e3) (e2)) = (e0))\/((op (e3) (e3)) = (e0))))) -> (~((op (e0) (e1)) = (op (e3) (e1)))) -> (~((op (e0) (e1)) = (op (e0) (e3)))) -> ((~((op (e0) (e0)) = (e3)))\/((op (e0) (e3)) = (e0))) -> (((op (e0) (e1)) = (e0))\/(((op (e1) (e1)) = (e0))\/(((op (e2) (e1)) = (e0))\/((op (e3) (e1)) = (e0))))) -> (((op (e3) (e0)) = (e2))\/(((op (e3) (e1)) = (e2))\/(((op (e3) (e2)) = (e2))\/((op (e3) (e3)) = (e2))))) -> (~((op (e0) (e2)) = (op (e3) (e2)))) -> (~((op (e2) (e1)) = (op (e3) (e1)))) -> (((op (e0) (e0)) = (e2))\/(((op (e0) (e1)) = (e2))\/(((op (e0) (e2)) = (e2))\/((op (e0) (e3)) = (e2))))) -> ((~((op (e1) (e1)) = (e2)))\/((op (e1) (e2)) = (e1))) -> (~((op (e1) (e0)) = (op (e1) (e2)))) -> ((~((op (e2) (e2)) = (e0)))\/((op (e2) (e0)) = (e2))) -> (~((op (e0) (e2)) = (op (e1) (e2)))) -> (~((op (e1) (e3)) = (op (e3) (e3)))) -> (((op (e1) (e0)) = (e3))\/(((op (e1) (e1)) = (e3))\/(((op (e1) (e2)) = (e3))\/((op (e1) (e3)) = (e3))))) -> (((op (e0) (e0)) = (e3))\/(((op (e1) (e0)) = (e3))\/(((op (e2) (e0)) = (e3))\/((op (e3) (e0)) = (e3))))) -> (((op (e1) (e1)) = (e0))\/(((op (e1) (e1)) = (e1))\/(((op (e1) (e1)) = (e2))\/((op (e1) (e1)) = (e3))))) -> (~((op (e1) (op (e2) (e1))) = (op (e2) (e1)))) -> (~((e0) = (e2))) -> (((op (e2) (e0)) = (e0))\/(((op (e2) (e1)) = (e0))\/(((op (e2) (e2)) = (e0))\/((op (e2) (e3)) = (e0))))) -> (~((op (e2) (e1)) = (op (e2) (e3)))) -> (~((op (e1) (e0)) = (op (e1) (e3)))) -> ((~((op (e1) (e1)) = (e3)))\/((op (e1) (e3)) = (e1))) -> ((~((op (e1) (e1)) = (e1)))\/((op (e1) (e1)) = (e1))) -> (~((op (e3) (e1)) = (op (e3) (e2)))) -> False). % 15.48/15.61 do 0 intro. intros zenon_H1e4 zenon_H10f zenon_H105 zenon_Hf1 zenon_Hd7 zenon_Hbb zenon_H109 zenon_H10d zenon_H20 zenon_H1e3 zenon_H6a zenon_H12d zenon_H199 zenon_H58 zenon_H4b zenon_H59 zenon_H294 zenon_Haa zenon_Hb7 zenon_Hb4 zenon_Hb1 zenon_Ha3 zenon_Hde zenon_H28a zenon_He6 zenon_H9e zenon_H10c zenon_Ha7 zenon_Hc9 zenon_H11e zenon_Hce zenon_H121 zenon_H1c3 zenon_H110 zenon_H45 zenon_H23 zenon_H21 zenon_H2d zenon_H28 zenon_H3b zenon_H36 zenon_H44 zenon_H116 zenon_H11b zenon_Hab zenon_H10e zenon_H12a zenon_H157 zenon_Hf0 zenon_Heb zenon_H160 zenon_H80 zenon_H24a zenon_H23e zenon_H17a zenon_H154 zenon_H173 zenon_H1a2 zenon_H295 zenon_H1e5 zenon_H1d5 zenon_H17d zenon_H1f6 zenon_H138 zenon_H1cd zenon_H236 zenon_H144 zenon_H1df zenon_H140 zenon_H13c zenon_H8e zenon_H1d3 zenon_H166 zenon_H1d4 zenon_H87 zenon_H8b zenon_H90 zenon_Hbe zenon_H1b3 zenon_H290 zenon_H5e zenon_H1f5 zenon_H1e2 zenon_H1cf zenon_H1d2 zenon_H1d8 zenon_H135. % 15.48/15.61 apply (zenon_or_s _ _ zenon_H1e4); [ zenon_intro zenon_H145 | zenon_intro zenon_Hd8 ]. % 15.48/15.61 apply (zenon_or_s _ _ zenon_H1d2); [ zenon_intro zenon_H182 | zenon_intro zenon_H11f ]. % 15.48/15.61 apply (zenon_or_s _ _ zenon_H1d4); [ zenon_intro zenon_H2e | zenon_intro zenon_Hdd ]. % 15.48/15.61 apply (zenon_or_s _ _ zenon_H1e3); [ zenon_intro zenon_H52 | zenon_intro zenon_H156 ]. % 15.48/15.61 apply (zenon_or_s _ _ zenon_Haa); [ zenon_intro zenon_H2f | zenon_intro zenon_H35 ]. % 15.48/15.61 apply (zenon_or_s _ _ zenon_H1c3); [ zenon_intro zenon_H30 | zenon_intro zenon_H124 ]. % 15.48/15.61 apply (zenon_or_s _ _ zenon_H10f); [ zenon_intro zenon_H3c | zenon_intro zenon_Hba ]. % 15.48/15.61 apply (zenon_or_s _ _ zenon_H10e); [ zenon_intro zenon_H3d | zenon_intro zenon_H106 ]. % 15.48/15.61 apply (zenon_L919_); trivial. % 15.48/15.61 apply (zenon_L109_); trivial. % 15.48/15.61 apply (zenon_L83_); trivial. % 15.48/15.61 apply (zenon_L99_); trivial. % 15.48/15.61 apply (zenon_L794_); trivial. % 15.48/15.61 apply (zenon_or_s _ _ zenon_Haa); [ zenon_intro zenon_H2f | zenon_intro zenon_H35 ]. % 15.48/15.61 apply (zenon_or_s _ _ zenon_H1c3); [ zenon_intro zenon_H30 | zenon_intro zenon_H124 ]. % 15.48/15.61 apply (zenon_or_s _ _ zenon_H10f); [ zenon_intro zenon_H3c | zenon_intro zenon_Hba ]. % 15.48/15.61 apply (zenon_or_s _ _ zenon_H10c); [ zenon_intro zenon_H104 | zenon_intro zenon_H10a ]. % 15.48/15.61 apply (zenon_or_s _ _ zenon_H10e); [ zenon_intro zenon_H3d | zenon_intro zenon_H106 ]. % 15.48/15.61 apply (zenon_L977_); trivial. % 15.48/15.61 apply (zenon_or_s _ _ zenon_H10d); [ zenon_intro zenon_H3e | zenon_intro zenon_H42 ]. % 15.48/15.61 apply (zenon_L994_); trivial. % 15.48/15.61 apply (zenon_L153_); trivial. % 15.48/15.61 apply (zenon_L309_); trivial. % 15.48/15.61 apply (zenon_or_s _ _ zenon_H10e); [ zenon_intro zenon_H3d | zenon_intro zenon_H106 ]. % 15.48/15.61 apply (zenon_L995_); trivial. % 15.48/15.61 apply (zenon_L81_); trivial. % 15.48/15.61 apply (zenon_L256_); trivial. % 15.48/15.61 apply (zenon_L134_); trivial. % 15.48/15.61 apply (zenon_or_s _ _ zenon_H1e3); [ zenon_intro zenon_H52 | zenon_intro zenon_H156 ]. % 15.48/15.61 apply (zenon_or_s _ _ zenon_Haa); [ zenon_intro zenon_H2f | zenon_intro zenon_H35 ]. % 15.48/15.61 apply (zenon_or_s _ _ zenon_H1c3); [ zenon_intro zenon_H30 | zenon_intro zenon_H124 ]. % 15.48/15.61 apply (zenon_or_s _ _ zenon_H10f); [ zenon_intro zenon_H3c | zenon_intro zenon_Hba ]. % 15.48/15.61 apply (zenon_or_s _ _ zenon_H10c); [ zenon_intro zenon_H104 | zenon_intro zenon_H10a ]. % 15.48/15.61 apply (zenon_L907_); trivial. % 15.48/15.61 apply (zenon_L309_); trivial. % 15.48/15.61 apply (zenon_L310_); trivial. % 15.48/15.61 apply (zenon_L119_); trivial. % 15.48/15.61 apply (zenon_L161_); trivial. % 15.48/15.61 apply (zenon_L284_); trivial. % 15.48/15.61 apply (zenon_L90_); trivial. % 15.48/15.61 apply (zenon_L61_); trivial. % 15.48/15.61 (* end of lemma zenon_L998_ *) % 15.48/15.61 assert (zenon_L999_ : (((op (e0) (e0)) = (e1))\/(((op (e0) (e1)) = (e1))\/(((op (e0) (e2)) = (e1))\/((op (e0) (e3)) = (e1))))) -> (~((op (e0) (e0)) = (e1))) -> (~((op (e0) (e1)) = (op (e1) (e1)))) -> (~((op (e0) (e3)) = (op (e3) (e3)))) -> ((op (e3) (e3)) = (e3)) -> (~((e1) = (e3))) -> ((op (e3) (e1)) = (e3)) -> (~((op (e0) (e1)) = (op (e3) (e1)))) -> (~((op (e0) (e0)) = (e3))) -> (((op (e0) (e0)) = (e3))\/(((op (e0) (e1)) = (e3))\/(((op (e0) (e2)) = (e3))\/((op (e0) (e3)) = (e3))))) -> (((op (e2) (e0)) = (e1))\/(((op (e2) (e1)) = (e1))\/(((op (e2) (e2)) = (e1))\/((op (e2) (e3)) = (e1))))) -> ((op (e2) (e0)) = (e2)) -> (~((e1) = (e2))) -> ((op (e1) (e1)) = (e1)) -> (~((op (e1) (e1)) = (op (e2) (e1)))) -> (~((op (e2) (e2)) = (e1))) -> (~((op (e0) (e3)) = (op (e2) (e3)))) -> False). % 15.48/15.61 do 0 intro. intros zenon_H44 zenon_H45 zenon_H23 zenon_H36 zenon_H42 zenon_Ha3 zenon_H10a zenon_H138 zenon_H59 zenon_H58 zenon_Hb7 zenon_Hdd zenon_Ha7 zenon_H21 zenon_Hb1 zenon_H52 zenon_Hb4. % 15.48/15.61 apply (zenon_or_s _ _ zenon_H44); [ zenon_intro zenon_H47 | zenon_intro zenon_H46 ]. % 15.48/15.61 exact (zenon_H45 zenon_H47). % 15.48/15.61 apply (zenon_or_s _ _ zenon_H46); [ zenon_intro zenon_H22 | zenon_intro zenon_H48 ]. % 15.48/15.61 apply (zenon_L3_); trivial. % 15.48/15.61 apply (zenon_or_s _ _ zenon_H48); [ zenon_intro zenon_H29 | zenon_intro zenon_H37 ]. % 15.48/15.61 apply (zenon_L896_); trivial. % 15.48/15.61 apply (zenon_L322_); trivial. % 15.48/15.61 (* end of lemma zenon_L999_ *) % 15.48/15.61 assert (zenon_L1000_ : (((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) (e2)) = (e0)) -> ((op (e0) (e0)) = (e3)) -> ((op (e2) (e0)) = (e2)) -> (~((op (e2) (e0)) = (op (e2) (e3)))) -> (~((op (e3) (op (e2) (e3))) = (op (e2) (e3)))) -> ((op (e3) (e3)) = (e3)) -> False). % 15.48/15.61 do 0 intro. intros zenon_H2ab zenon_Hca zenon_Hb4 zenon_H32 zenon_H5b zenon_Hdd zenon_Hce zenon_H28a zenon_H42. % 15.48/15.61 apply (zenon_or_s _ _ zenon_H2ab); [ zenon_intro zenon_Hd0 | zenon_intro zenon_H2ac ]. % 15.48/15.61 apply (zenon_L963_); trivial. % 15.48/15.61 apply (zenon_or_s _ _ zenon_H2ac); [ zenon_intro zenon_Hb5 | zenon_intro zenon_H2ad ]. % 15.48/15.61 apply (zenon_L319_); trivial. % 15.48/15.61 apply (zenon_or_s _ _ zenon_H2ad); [ zenon_intro zenon_H124 | zenon_intro zenon_He2 ]. % 15.48/15.61 apply (zenon_L119_); trivial. % 15.48/15.61 apply (zenon_L776_); trivial. % 15.48/15.61 (* end of lemma zenon_L1000_ *) % 15.48/15.61 assert (zenon_L1001_ : (((op (e2) (e2)) = (e0))\/(((op (e2) (e2)) = (e1))\/(((op (e2) (e2)) = (e2))\/((op (e2) (e2)) = (e3))))) -> ((op (e3) (e3)) = (e3)) -> (~((op (e3) (op (e2) (e3))) = (op (e2) (e3)))) -> (~((op (e2) (e0)) = (op (e2) (e3)))) -> ((op (e2) (e0)) = (e2)) -> ((op (e0) (e0)) = (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) (e2)) = (e1))) -> (~((op (e2) (e2)) = (e2))) -> (~((op (e2) (e2)) = (e3))) -> False). % 15.48/15.61 do 0 intro. intros zenon_H2d zenon_H42 zenon_H28a zenon_Hce zenon_Hdd zenon_H5b zenon_Hb4 zenon_Hca zenon_H2ab zenon_H52 zenon_H2f zenon_H30. % 15.48/15.61 apply (zenon_or_s _ _ zenon_H2d); [ zenon_intro zenon_H32 | zenon_intro zenon_H31 ]. % 15.48/15.61 apply (zenon_L1000_); trivial. % 15.48/15.61 apply (zenon_or_s _ _ zenon_H31); [ zenon_intro zenon_H2a | zenon_intro zenon_H33 ]. % 15.48/15.61 exact (zenon_H52 zenon_H2a). % 15.48/15.61 apply (zenon_or_s _ _ zenon_H33); [ zenon_intro zenon_H35 | zenon_intro zenon_H34 ]. % 15.48/15.61 exact (zenon_H2f zenon_H35). % 15.48/15.61 exact (zenon_H30 zenon_H34). % 15.48/15.61 (* end of lemma zenon_L1001_ *) % 15.48/15.61 assert (zenon_L1002_ : (((op (e0) (e0)) = (e0))\/(((op (e0) (e0)) = (e1))\/(((op (e0) (e0)) = (e2))\/((op (e0) (e0)) = (e3))))) -> (~((op (e0) (e0)) = (e0))) -> (~((op (e0) (e0)) = (e1))) -> (~((op (e0) (e0)) = (e2))) -> (((op (e2) (e2)) = (e0))\/(((op (e2) (e2)) = (e1))\/(((op (e2) (e2)) = (e2))\/((op (e2) (e2)) = (e3))))) -> ((op (e3) (e3)) = (e3)) -> (~((op (e3) (op (e2) (e3))) = (op (e2) (e3)))) -> (~((op (e2) (e0)) = (op (e2) (e3)))) -> ((op (e2) (e0)) = (e2)) -> (~((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) (e2)) = (e1))) -> (~((op (e2) (e2)) = (e2))) -> (~((op (e2) (e2)) = (e3))) -> False). % 15.48/15.61 do 0 intro. intros zenon_H12a zenon_H20 zenon_H45 zenon_H8f zenon_H2d zenon_H42 zenon_H28a zenon_Hce zenon_Hdd zenon_Hb4 zenon_Hca zenon_H2ab zenon_H52 zenon_H2f zenon_H30. % 15.48/15.61 apply (zenon_or_s _ _ zenon_H12a); [ zenon_intro zenon_H1f | zenon_intro zenon_H12b ]. % 15.48/15.61 exact (zenon_H20 zenon_H1f). % 15.48/15.61 apply (zenon_or_s _ _ zenon_H12b); [ zenon_intro zenon_H47 | zenon_intro zenon_H12c ]. % 15.48/15.61 exact (zenon_H45 zenon_H47). % 15.48/15.61 apply (zenon_or_s _ _ zenon_H12c); [ zenon_intro zenon_H92 | zenon_intro zenon_H5b ]. % 15.48/15.61 exact (zenon_H8f zenon_H92). % 15.48/15.61 apply (zenon_L1001_); trivial. % 15.48/15.61 (* end of lemma zenon_L1002_ *) % 15.48/15.61 assert (zenon_L1003_ : ((~((op (e2) (e2)) = (e3)))\/((op (e2) (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 (e3) (e3)) = (e3)) -> (~((op (e3) (op (e2) (e3))) = (op (e2) (e3)))) -> ((op (e2) (e1)) = (e2)) -> (~((e2) = (e3))) -> (~((e0) = (e3))) -> (~((e0) = (e2))) -> (~((op (e2) (e2)) = (e0))) -> (~((op (e0) (e3)) = (op (e2) (e3)))) -> ((op (e0) (e3)) = (e0)) -> (((op (e2) (e0)) = (e0))\/(((op (e2) (e1)) = (e0))\/(((op (e2) (e2)) = (e0))\/((op (e2) (e3)) = (e0))))) -> False). % 15.48/15.61 do 0 intro. intros zenon_H1c3 zenon_H1e2 zenon_He6 zenon_H42 zenon_H28a zenon_H156 zenon_H6a zenon_H4b zenon_H5e zenon_H2e zenon_Hb4 zenon_Hca zenon_H1f5. % 15.48/15.61 apply (zenon_or_s _ _ zenon_H1c3); [ zenon_intro zenon_H30 | zenon_intro zenon_H124 ]. % 15.48/15.61 apply (zenon_L972_); trivial. % 15.48/15.61 apply (zenon_L256_); trivial. % 15.48/15.61 (* end of lemma zenon_L1003_ *) % 15.48/15.61 assert (zenon_L1004_ : (((op (e0) (e0)) = (e2))\/(((op (e0) (e1)) = (e2))\/(((op (e0) (e2)) = (e2))\/((op (e0) (e3)) = (e2))))) -> (~((op (e0) (e0)) = (e2))) -> (~((op (e1) (e1)) = (e3))) -> (~((op (e0) (e1)) = (op (e1) (e1)))) -> (~((op (e1) (e1)) = (e1))) -> (~((op (e1) (e1)) = (e0))) -> (((op (e1) (e1)) = (e0))\/(((op (e1) (e1)) = (e1))\/(((op (e1) (e1)) = (e2))\/((op (e1) (e1)) = (e3))))) -> ((op (e2) (e0)) = (e2)) -> (~((op (e0) (op (e2) (e0))) = (op (e2) (e0)))) -> ((op (e0) (e3)) = (e0)) -> (~((e0) = (e2))) -> False). % 15.48/15.61 do 0 intro. intros zenon_H8e zenon_H8f zenon_H182 zenon_H23 zenon_H1b4 zenon_H145 zenon_H1b3 zenon_Hdd zenon_H295 zenon_Hca zenon_H5e. % 15.48/15.61 apply (zenon_or_s _ _ zenon_H8e); [ zenon_intro zenon_H92 | zenon_intro zenon_H91 ]. % 15.48/15.61 exact (zenon_H8f zenon_H92). % 15.48/15.61 apply (zenon_or_s _ _ zenon_H91); [ zenon_intro zenon_H5d | zenon_intro zenon_H93 ]. % 15.48/15.61 apply (zenon_L214_); trivial. % 15.48/15.61 apply (zenon_or_s _ _ zenon_H93); [ zenon_intro zenon_H63 | zenon_intro zenon_H81 ]. % 15.48/15.61 apply (zenon_L812_); trivial. % 15.48/15.61 apply (zenon_L113_); trivial. % 15.48/15.61 (* end of lemma zenon_L1004_ *) % 15.48/15.61 assert (zenon_L1005_ : ((~((op (e2) (e2)) = (e1)))\/((op (e2) (e1)) = (e2))) -> (~((op (e2) (e0)) = (op (e2) (e1)))) -> ((~((op (e2) (e2)) = (e3)))\/((op (e2) (e3)) = (e2))) -> (~((op (e2) (e0)) = (op (e2) (e3)))) -> (~((op (e0) (e0)) = (e1))) -> (~((op (e0) (e1)) = (op (e1) (e1)))) -> ((op (e1) (e1)) = (e1)) -> (((op (e0) (e0)) = (e3))\/(((op (e0) (e1)) = (e3))\/(((op (e0) (e2)) = (e3))\/((op (e0) (e3)) = (e3))))) -> (~((op (e0) (e3)) = (op (e3) (e3)))) -> (~((e1) = (e3))) -> (~((e2) = (e3))) -> (~((op (e0) (e1)) = (op (e2) (e1)))) -> (~((op (e3) (op (e2) (e3))) = (op (e2) (e3)))) -> ((op (e3) (e3)) = (e3)) -> (((op (e2) (e0)) = (e3))\/(((op (e2) (e1)) = (e3))\/(((op (e2) (e2)) = (e3))\/((op (e2) (e3)) = (e3))))) -> (~((e1) = (e2))) -> ((op (e2) (e0)) = (e2)) -> (~((op (e1) (e1)) = (op (e2) (e1)))) -> (((op (e2) (e2)) = (e0))\/(((op (e2) (e2)) = (e1))\/(((op (e2) (e2)) = (e2))\/((op (e2) (e2)) = (e3))))) -> (((op (e2) (e0)) = (e1))\/(((op (e2) (e1)) = (e1))\/(((op (e2) (e2)) = (e1))\/((op (e2) (e3)) = (e1))))) -> (~((e0) = (e1))) -> ((op (e0) (e3)) = (e0)) -> (((op (e0) (e0)) = (e1))\/(((op (e0) (e1)) = (e1))\/(((op (e0) (e2)) = (e1))\/((op (e0) (e3)) = (e1))))) -> (~((op (e2) (e0)) = (op (e2) (e2)))) -> ((~((op (e2) (e2)) = (e2)))\/((op (e2) (e2)) = (e2))) -> False). % 15.48/15.61 do 0 intro. intros zenon_H1e3 zenon_H154 zenon_H1c3 zenon_Hce zenon_H45 zenon_H23 zenon_H21 zenon_H58 zenon_H36 zenon_Ha3 zenon_H6a zenon_Hde zenon_H28a zenon_H42 zenon_He6 zenon_Ha7 zenon_Hdd zenon_Hb1 zenon_H2d zenon_Hb7 zenon_H9e zenon_Hca zenon_H44 zenon_H17a zenon_Haa. % 15.48/15.61 apply (zenon_or_s _ _ zenon_H1e3); [ zenon_intro zenon_H52 | zenon_intro zenon_H156 ]. % 15.48/15.61 apply (zenon_or_s _ _ zenon_Haa); [ zenon_intro zenon_H2f | zenon_intro zenon_H35 ]. % 15.48/15.61 apply (zenon_or_s _ _ zenon_H1c3); [ zenon_intro zenon_H30 | zenon_intro zenon_H124 ]. % 15.48/15.61 apply (zenon_or_s _ _ zenon_H44); [ zenon_intro zenon_H47 | zenon_intro zenon_H46 ]. % 15.48/15.61 exact (zenon_H45 zenon_H47). % 15.48/15.61 apply (zenon_or_s _ _ zenon_H46); [ zenon_intro zenon_H22 | zenon_intro zenon_H48 ]. % 15.48/15.61 apply (zenon_L3_); trivial. % 15.48/15.61 apply (zenon_or_s _ _ zenon_H48); [ zenon_intro zenon_H29 | zenon_intro zenon_H37 ]. % 15.48/15.61 apply (zenon_or_s _ _ zenon_H58); [ zenon_intro zenon_H5b | zenon_intro zenon_H5a ]. % 15.48/15.61 apply (zenon_L321_); trivial. % 15.48/15.61 apply (zenon_or_s _ _ zenon_H5a); [ zenon_intro zenon_H4a | zenon_intro zenon_H5c ]. % 15.48/15.61 apply (zenon_L777_); trivial. % 15.48/15.61 apply (zenon_or_s _ _ zenon_H5c); [ zenon_intro zenon_H50 | zenon_intro zenon_H53 ]. % 15.48/15.61 apply (zenon_L29_); trivial. % 15.48/15.61 apply (zenon_L12_); trivial. % 15.48/15.61 apply (zenon_L73_); trivial. % 15.48/15.61 apply (zenon_L119_); trivial. % 15.48/15.61 apply (zenon_L161_); trivial. % 15.48/15.61 apply (zenon_L284_); trivial. % 15.48/15.61 (* end of lemma zenon_L1005_ *) % 15.48/15.61 assert (zenon_L1006_ : (((op (e3) (e0)) = (e1))\/(((op (e3) (e1)) = (e1))\/(((op (e3) (e2)) = (e1))\/((op (e3) (e3)) = (e1))))) -> (~((op (e1) (e0)) = (op (e3) (e0)))) -> (~((op (e3) (op (e2) (e3))) = (op (e2) (e3)))) -> (~((op (e1) (e0)) = (op (e1) (e3)))) -> ((op (e1) (e0)) = (e1)) -> (((op (e0) (e2)) = (e1))\/(((op (e1) (e2)) = (e1))\/(((op (e2) (e2)) = (e1))\/((op (e3) (e2)) = (e1))))) -> (~((op (e0) (e2)) = (op (e0) (e3)))) -> (~((e1) = (e3))) -> ((op (e1) (e2)) = (e3)) -> (~((op (e2) (e2)) = (e1))) -> (~((op (e3) (e1)) = (op (e3) (e2)))) -> (((op (e0) (e3)) = (e1))\/(((op (e1) (e3)) = (e1))\/(((op (e2) (e3)) = (e1))\/((op (e3) (e3)) = (e1))))) -> ((op (e0) (e2)) = (e1)) -> (~((op (e0) (e2)) = (op (e3) (e2)))) -> (~((op (e3) (e3)) = (e1))) -> False). % 15.48/15.61 do 0 intro. intros zenon_H146 zenon_H22e zenon_H28a zenon_H1cf zenon_Hd8 zenon_H11b zenon_Hc9 zenon_Ha3 zenon_H88 zenon_H52 zenon_H135 zenon_H121 zenon_H29 zenon_H140 zenon_H104. % 15.48/15.61 apply (zenon_or_s _ _ zenon_H146); [ zenon_intro zenon_Hee | zenon_intro zenon_H14b ]. % 15.48/15.61 apply (zenon_L393_); trivial. % 15.48/15.61 apply (zenon_or_s _ _ zenon_H14b); [ zenon_intro zenon_H13e | zenon_intro zenon_H14c ]. % 15.48/15.61 apply (zenon_L806_); trivial. % 15.48/15.61 apply (zenon_or_s _ _ zenon_H14c); [ zenon_intro zenon_H119 | zenon_intro zenon_H38 ]. % 15.48/15.61 apply (zenon_L124_); trivial. % 15.48/15.61 exact (zenon_H104 zenon_H38). % 15.48/15.61 (* end of lemma zenon_L1006_ *) % 15.48/15.61 assert (zenon_L1007_ : (((op (e0) (e2)) = (e0))\/(((op (e0) (e2)) = (e1))\/(((op (e0) (e2)) = (e2))\/((op (e0) (e2)) = (e3))))) -> ((~((op (e1) (e1)) = (e0)))\/((op (e1) (e0)) = (e1))) -> (~((op (e1) (e2)) = (op (e1) (e3)))) -> ((~((op (e3) (e3)) = (e0)))\/((op (e3) (e0)) = (e3))) -> (~((op (e0) (e0)) = (e1))) -> (((op (e0) (e0)) = (e3))\/(((op (e1) (e0)) = (e3))\/(((op (e2) (e0)) = (e3))\/((op (e3) (e0)) = (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 (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)) = (op (e3) (e3)))) -> (~((op (e0) (e2)) = (op (e2) (e2)))) -> (~((op (e0) (e1)) = (op (e2) (e1)))) -> (~((op (e3) (op (e2) (e3))) = (op (e2) (e3)))) -> (((op (e2) (e0)) = (e3))\/(((op (e2) (e1)) = (e3))\/(((op (e2) (e2)) = (e3))\/((op (e2) (e3)) = (e3))))) -> (((op (e0) (e0)) = (e2))\/(((op (e0) (e1)) = (e2))\/(((op (e0) (e2)) = (e2))\/((op (e0) (e3)) = (e2))))) -> (~((op (e0) (e3)) = (op (e1) (e3)))) -> (((op (e1) (e0)) = (e2))\/(((op (e1) (e1)) = (e2))\/(((op (e1) (e2)) = (e2))\/((op (e1) (e3)) = (e2))))) -> (((op (e0) (e0)) = (e2))\/(((op (e1) (e0)) = (e2))\/(((op (e2) (e0)) = (e2))\/((op (e3) (e0)) = (e2))))) -> (~((op (e0) (e1)) = (op (e1) (e1)))) -> (((op (e0) (e2)) = (e3))\/(((op (e1) (e2)) = (e3))\/(((op (e2) (e2)) = (e3))\/((op (e3) (e2)) = (e3))))) -> (~((op (e3) (e2)) = (op (e3) (e3)))) -> (~((e0) = (e3))) -> (((op (e0) (e1)) = (e2))\/(((op (e1) (e1)) = (e2))\/(((op (e2) (e1)) = (e2))\/((op (e3) (e1)) = (e2))))) -> (~((op (e2) (e1)) = (op (e3) (e1)))) -> (((op (e2) (e0)) = (e0))\/(((op (e2) (e1)) = (e0))\/(((op (e2) (e2)) = (e0))\/((op (e2) (e3)) = (e0))))) -> (((op (e2) (e0)) = (e1))\/(((op (e2) (e1)) = (e1))\/(((op (e2) (e2)) = (e1))\/((op (e2) (e3)) = (e1))))) -> (~((op (e1) (e3)) = (op (e2) (e3)))) -> (~((e1) = (e2))) -> (((op (e0) (e3)) = (e0))\/(((op (e1) (e3)) = (e0))\/(((op (e2) (e3)) = (e0))\/((op (e3) (e3)) = (e0))))) -> (~((e0) = (e2))) -> (~((e0) = (e1))) -> (~((op (e0) (e2)) = (op (e0) (e3)))) -> (((op (e2) (e0)) = (e2))\/(((op (e2) (e1)) = (e2))\/(((op (e2) (e2)) = (e2))\/((op (e2) (e3)) = (e2))))) -> (((op (e1) (e0)) = (e1))\/(((op (e1) (e1)) = (e1))\/(((op (e1) (e2)) = (e1))\/((op (e1) (e3)) = (e1))))) -> (((op (e0) (e0)) = (e1))\/(((op (e1) (e0)) = (e1))\/(((op (e2) (e0)) = (e1))\/((op (e3) (e0)) = (e1))))) -> (~((op (e1) (e0)) = (op (e1) (e3)))) -> ((~((op (e3) (e3)) = (e2)))\/((op (e3) (e2)) = (e3))) -> ((~((op (e1) (e1)) = (e1)))\/((op (e1) (e1)) = (e1))) -> (~((op (e1) (e0)) = (op (e1) (e1)))) -> ((~((op (e1) (e1)) = (e3)))\/((op (e1) (e3)) = (e1))) -> ((~((op (e2) (e2)) = (e1)))\/((op (e2) (e1)) = (e2))) -> (~((op (e2) (e1)) = (op (e2) (e3)))) -> (~((op (e2) (op (e2) (e2))) = (op (e2) (e2)))) -> ((~((op (e2) (e2)) = (e2)))\/((op (e2) (e2)) = (e2))) -> ((~((op (e2) (e2)) = (e0)))\/((op (e2) (e0)) = (e2))) -> (~((op (e1) (e0)) = (op (e1) (e2)))) -> ((~((op (e1) (e1)) = (e2)))\/((op (e1) (e2)) = (e1))) -> (((op (e1) (e3)) = (e0))\/(((op (e1) (e3)) = (e1))\/(((op (e1) (e3)) = (e2))\/((op (e1) (e3)) = (e3))))) -> (~((op (e0) (e0)) = (e0))) -> (((op (e0) (e0)) = (e0))\/(((op (e0) (e0)) = (e1))\/(((op (e0) (e0)) = (e2))\/((op (e0) (e0)) = (e3))))) -> (((op (e3) (e0)) = (e2))\/(((op (e3) (e1)) = (e2))\/(((op (e3) (e2)) = (e2))\/((op (e3) (e3)) = (e2))))) -> (~((op (e1) (e3)) = (op (e3) (e3)))) -> ((~((op (e2) (e2)) = (e3)))\/((op (e2) (e3)) = (e2))) -> (~((op (e1) (op (e2) (e1))) = (op (e2) (e1)))) -> (~((op (e2) (e1)) = (op (e2) (e2)))) -> (~((op (e3) (e1)) = (op (e3) (e3)))) -> (((op (e0) (e1)) = (e3))\/(((op (e1) (e1)) = (e3))\/(((op (e2) (e1)) = (e3))\/((op (e3) (e1)) = (e3))))) -> (((op (e0) (e1)) = (e0))\/(((op (e1) (e1)) = (e0))\/(((op (e2) (e1)) = (e0))\/((op (e3) (e1)) = (e0))))) -> (~((op (e1) (e1)) = (op (e1) (e3)))) -> (~((op (e1) (e1)) = (op (e2) (e1)))) -> (~((op (e0) (e3)) = (op (e2) (e3)))) -> (((op (e0) (e0)) = (e1))\/(((op (e0) (e1)) = (e1))\/(((op (e0) (e2)) = (e1))\/((op (e0) (e3)) = (e1))))) -> (~((op (e2) (e0)) = (op (e2) (e1)))) -> ((~((op (e0) (e0)) = (e3)))\/((op (e0) (e3)) = (e0))) -> ((op (e3) (e2)) = (e1)) -> ((op (e3) (e2)) = (e2)) -> (~((op (e0) (e2)) = (op (e3) (e2)))) -> (((op (e1) (e0)) = (e3))\/(((op (e1) (e1)) = (e3))\/(((op (e1) (e2)) = (e3))\/((op (e1) (e3)) = (e3))))) -> (~((e1) = (e3))) -> ((op (e1) (e0)) = (e1)) -> (~((op (e1) (e1)) = (e3))) -> (~((op (e0) (e2)) = (op (e1) (e2)))) -> (((op (e0) (e3)) = (e2))\/(((op (e1) (e3)) = (e2))\/(((op (e2) (e3)) = (e2))\/((op (e3) (e3)) = (e2))))) -> (~((op (e0) (e1)) = (op (e0) (e3)))) -> ((op (e0) (e1)) = (e2)) -> (~((e2) = (e3))) -> ((op (e2) (e0)) = (e2)) -> (~((op (e2) (e0)) = (op (e2) (e3)))) -> (~((op (e3) (e3)) = (e2))) -> False). % 15.48/15.61 do 0 intro. intros zenon_H251 zenon_H1e4 zenon_H1d0 zenon_H10f zenon_H45 zenon_Hbe zenon_H42 zenon_Hbb zenon_H2d zenon_H1b3 zenon_H58 zenon_H36 zenon_H28 zenon_Hde zenon_H28a zenon_He6 zenon_H8e zenon_H80 zenon_H84 zenon_Heb zenon_H23 zenon_H175 zenon_H173 zenon_H4b zenon_H1a2 zenon_H13c zenon_H1f5 zenon_Hb7 zenon_H244 zenon_Ha7 zenon_Hd3 zenon_H5e zenon_H9e zenon_Hc9 zenon_H237 zenon_H1c5 zenon_Hf1 zenon_H1cf zenon_H10e zenon_H1d8 zenon_Hd7 zenon_H1d2 zenon_H1e3 zenon_H1e2 zenon_H294 zenon_Haa zenon_H1d4 zenon_H166 zenon_H1d3 zenon_H25b zenon_H20 zenon_H12a zenon_H1df zenon_H8b zenon_H1c3 zenon_H290 zenon_H157 zenon_H12d zenon_H199 zenon_H144 zenon_H11e zenon_Hb1 zenon_Hb4 zenon_H44 zenon_H154 zenon_H236 zenon_H119 zenon_H1dd zenon_H140 zenon_H90 zenon_Ha3 zenon_Hd8 zenon_H182 zenon_H87 zenon_H160 zenon_H1cd zenon_H5d zenon_H6a zenon_Hdd zenon_Hce zenon_H3d. % 15.48/15.61 apply (zenon_or_s _ _ zenon_H251); [ zenon_intro zenon_Hab | zenon_intro zenon_H252 ]. % 15.48/15.61 apply (zenon_L960_); trivial. % 15.48/15.61 apply (zenon_or_s _ _ zenon_H252); [ zenon_intro zenon_H29 | zenon_intro zenon_H253 ]. % 15.48/15.61 apply (zenon_L124_); trivial. % 15.48/15.61 apply (zenon_or_s _ _ zenon_H253); [ zenon_intro zenon_H63 | zenon_intro zenon_H50 ]. % 15.48/15.61 apply (zenon_L253_); trivial. % 15.48/15.61 apply (zenon_L411_); trivial. % 15.48/15.61 (* end of lemma zenon_L1007_ *) % 15.48/15.61 assert (zenon_L1008_ : (((op (e0) (e2)) = (e2))\/(((op (e1) (e2)) = (e2))\/(((op (e2) (e2)) = (e2))\/((op (e3) (e2)) = (e2))))) -> (~((op (e0) (op (e2) (e0))) = (op (e2) (e0)))) -> ((op (e1) (e2)) = (e3)) -> (~((op (e2) (e2)) = (e2))) -> (((op (e0) (e2)) = (e0))\/(((op (e0) (e2)) = (e1))\/(((op (e0) (e2)) = (e2))\/((op (e0) (e2)) = (e3))))) -> ((~((op (e1) (e1)) = (e0)))\/((op (e1) (e0)) = (e1))) -> (~((op (e1) (e2)) = (op (e1) (e3)))) -> ((~((op (e3) (e3)) = (e0)))\/((op (e3) (e0)) = (e3))) -> (~((op (e0) (e0)) = (e1))) -> (((op (e0) (e0)) = (e3))\/(((op (e1) (e0)) = (e3))\/(((op (e2) (e0)) = (e3))\/((op (e3) (e0)) = (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 (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)) = (op (e3) (e3)))) -> (~((op (e0) (e2)) = (op (e2) (e2)))) -> (~((op (e0) (e1)) = (op (e2) (e1)))) -> (~((op (e3) (op (e2) (e3))) = (op (e2) (e3)))) -> (((op (e2) (e0)) = (e3))\/(((op (e2) (e1)) = (e3))\/(((op (e2) (e2)) = (e3))\/((op (e2) (e3)) = (e3))))) -> (((op (e0) (e0)) = (e2))\/(((op (e0) (e1)) = (e2))\/(((op (e0) (e2)) = (e2))\/((op (e0) (e3)) = (e2))))) -> (~((op (e0) (e3)) = (op (e1) (e3)))) -> (((op (e1) (e0)) = (e2))\/(((op (e1) (e1)) = (e2))\/(((op (e1) (e2)) = (e2))\/((op (e1) (e3)) = (e2))))) -> (((op (e0) (e0)) = (e2))\/(((op (e1) (e0)) = (e2))\/(((op (e2) (e0)) = (e2))\/((op (e3) (e0)) = (e2))))) -> (~((op (e0) (e1)) = (op (e1) (e1)))) -> (((op (e0) (e2)) = (e3))\/(((op (e1) (e2)) = (e3))\/(((op (e2) (e2)) = (e3))\/((op (e3) (e2)) = (e3))))) -> (~((op (e3) (e2)) = (op (e3) (e3)))) -> (~((e0) = (e3))) -> (((op (e0) (e1)) = (e2))\/(((op (e1) (e1)) = (e2))\/(((op (e2) (e1)) = (e2))\/((op (e3) (e1)) = (e2))))) -> (~((op (e2) (e1)) = (op (e3) (e1)))) -> (((op (e2) (e0)) = (e0))\/(((op (e2) (e1)) = (e0))\/(((op (e2) (e2)) = (e0))\/((op (e2) (e3)) = (e0))))) -> (((op (e2) (e0)) = (e1))\/(((op (e2) (e1)) = (e1))\/(((op (e2) (e2)) = (e1))\/((op (e2) (e3)) = (e1))))) -> (~((op (e1) (e3)) = (op (e2) (e3)))) -> (~((e1) = (e2))) -> (((op (e0) (e3)) = (e0))\/(((op (e1) (e3)) = (e0))\/(((op (e2) (e3)) = (e0))\/((op (e3) (e3)) = (e0))))) -> (~((e0) = (e2))) -> (~((e0) = (e1))) -> (~((op (e0) (e2)) = (op (e0) (e3)))) -> (((op (e2) (e0)) = (e2))\/(((op (e2) (e1)) = (e2))\/(((op (e2) (e2)) = (e2))\/((op (e2) (e3)) = (e2))))) -> (((op (e1) (e0)) = (e1))\/(((op (e1) (e1)) = (e1))\/(((op (e1) (e2)) = (e1))\/((op (e1) (e3)) = (e1))))) -> (((op (e0) (e0)) = (e1))\/(((op (e1) (e0)) = (e1))\/(((op (e2) (e0)) = (e1))\/((op (e3) (e0)) = (e1))))) -> (~((op (e1) (e0)) = (op (e1) (e3)))) -> ((~((op (e3) (e3)) = (e2)))\/((op (e3) (e2)) = (e3))) -> ((~((op (e1) (e1)) = (e1)))\/((op (e1) (e1)) = (e1))) -> (~((op (e1) (e0)) = (op (e1) (e1)))) -> ((~((op (e1) (e1)) = (e3)))\/((op (e1) (e3)) = (e1))) -> ((~((op (e2) (e2)) = (e1)))\/((op (e2) (e1)) = (e2))) -> (~((op (e2) (e1)) = (op (e2) (e3)))) -> (~((op (e2) (op (e2) (e2))) = (op (e2) (e2)))) -> ((~((op (e2) (e2)) = (e2)))\/((op (e2) (e2)) = (e2))) -> ((~((op (e2) (e2)) = (e0)))\/((op (e2) (e0)) = (e2))) -> (~((op (e1) (e0)) = (op (e1) (e2)))) -> ((~((op (e1) (e1)) = (e2)))\/((op (e1) (e2)) = (e1))) -> (((op (e1) (e3)) = (e0))\/(((op (e1) (e3)) = (e1))\/(((op (e1) (e3)) = (e2))\/((op (e1) (e3)) = (e3))))) -> (~((op (e0) (e0)) = (e0))) -> (((op (e0) (e0)) = (e0))\/(((op (e0) (e0)) = (e1))\/(((op (e0) (e0)) = (e2))\/((op (e0) (e0)) = (e3))))) -> (((op (e3) (e0)) = (e2))\/(((op (e3) (e1)) = (e2))\/(((op (e3) (e2)) = (e2))\/((op (e3) (e3)) = (e2))))) -> (~((op (e1) (e3)) = (op (e3) (e3)))) -> ((~((op (e2) (e2)) = (e3)))\/((op (e2) (e3)) = (e2))) -> (~((op (e1) (op (e2) (e1))) = (op (e2) (e1)))) -> (~((op (e2) (e1)) = (op (e2) (e2)))) -> (~((op (e3) (e1)) = (op (e3) (e3)))) -> (((op (e0) (e1)) = (e3))\/(((op (e1) (e1)) = (e3))\/(((op (e2) (e1)) = (e3))\/((op (e3) (e1)) = (e3))))) -> (((op (e0) (e1)) = (e0))\/(((op (e1) (e1)) = (e0))\/(((op (e2) (e1)) = (e0))\/((op (e3) (e1)) = (e0))))) -> (~((op (e1) (e1)) = (op (e1) (e3)))) -> (~((op (e1) (e1)) = (op (e2) (e1)))) -> (~((op (e0) (e3)) = (op (e2) (e3)))) -> (((op (e0) (e0)) = (e1))\/(((op (e0) (e1)) = (e1))\/(((op (e0) (e2)) = (e1))\/((op (e0) (e3)) = (e1))))) -> (~((op (e2) (e0)) = (op (e2) (e1)))) -> ((~((op (e0) (e0)) = (e3)))\/((op (e0) (e3)) = (e0))) -> ((op (e3) (e2)) = (e1)) -> (~((op (e0) (e2)) = (op (e3) (e2)))) -> (((op (e1) (e0)) = (e3))\/(((op (e1) (e1)) = (e3))\/(((op (e1) (e2)) = (e3))\/((op (e1) (e3)) = (e3))))) -> (~((e1) = (e3))) -> ((op (e1) (e0)) = (e1)) -> (~((op (e1) (e1)) = (e3))) -> (~((op (e0) (e2)) = (op (e1) (e2)))) -> (((op (e0) (e3)) = (e2))\/(((op (e1) (e3)) = (e2))\/(((op (e2) (e3)) = (e2))\/((op (e3) (e3)) = (e2))))) -> (~((op (e0) (e1)) = (op (e0) (e3)))) -> ((op (e0) (e1)) = (e2)) -> (~((e2) = (e3))) -> ((op (e2) (e0)) = (e2)) -> (~((op (e2) (e0)) = (op (e2) (e3)))) -> (~((op (e3) (e3)) = (e2))) -> False). % 15.48/15.61 do 0 intro. intros zenon_H27c zenon_H295 zenon_H88 zenon_H2f zenon_H251 zenon_H1e4 zenon_H1d0 zenon_H10f zenon_H45 zenon_Hbe zenon_H42 zenon_Hbb zenon_H2d zenon_H1b3 zenon_H58 zenon_H36 zenon_H28 zenon_Hde zenon_H28a zenon_He6 zenon_H8e zenon_H80 zenon_H84 zenon_Heb zenon_H23 zenon_H175 zenon_H173 zenon_H4b zenon_H1a2 zenon_H13c zenon_H1f5 zenon_Hb7 zenon_H244 zenon_Ha7 zenon_Hd3 zenon_H5e zenon_H9e zenon_Hc9 zenon_H237 zenon_H1c5 zenon_Hf1 zenon_H1cf zenon_H10e zenon_H1d8 zenon_Hd7 zenon_H1d2 zenon_H1e3 zenon_H1e2 zenon_H294 zenon_Haa zenon_H1d4 zenon_H166 zenon_H1d3 zenon_H25b zenon_H20 zenon_H12a zenon_H1df zenon_H8b zenon_H1c3 zenon_H290 zenon_H157 zenon_H12d zenon_H199 zenon_H144 zenon_H11e zenon_Hb1 zenon_Hb4 zenon_H44 zenon_H154 zenon_H236 zenon_H119 zenon_H140 zenon_H90 zenon_Ha3 zenon_Hd8 zenon_H182 zenon_H87 zenon_H160 zenon_H1cd zenon_H5d zenon_H6a zenon_Hdd zenon_Hce zenon_H3d. % 15.48/15.61 apply (zenon_or_s _ _ zenon_H27c); [ zenon_intro zenon_H63 | zenon_intro zenon_H27d ]. % 15.48/15.61 apply (zenon_L812_); trivial. % 15.48/15.61 apply (zenon_or_s _ _ zenon_H27d); [ zenon_intro zenon_H7c | zenon_intro zenon_H27e ]. % 15.48/15.61 apply (zenon_or_s _ _ zenon_H251); [ zenon_intro zenon_Hab | zenon_intro zenon_H252 ]. % 15.48/15.61 apply (zenon_L960_); trivial. % 15.48/15.61 apply (zenon_or_s _ _ zenon_H252); [ zenon_intro zenon_H29 | zenon_intro zenon_H253 ]. % 15.48/15.61 apply (zenon_L124_); trivial. % 15.48/15.61 apply (zenon_or_s _ _ zenon_H253); [ zenon_intro zenon_H63 | zenon_intro zenon_H50 ]. % 15.48/15.61 apply (zenon_L52_); trivial. % 15.48/15.61 apply (zenon_L24_); trivial. % 15.48/15.61 apply (zenon_or_s _ _ zenon_H27e); [ zenon_intro zenon_H35 | zenon_intro zenon_H1dd ]. % 15.48/15.61 exact (zenon_H2f zenon_H35). % 15.48/15.61 apply (zenon_L1007_); trivial. % 15.48/15.61 (* end of lemma zenon_L1008_ *) % 15.48/15.61 assert (zenon_L1009_ : (((op (e1) (e0)) = (e3))\/(((op (e1) (e1)) = (e3))\/(((op (e1) (e2)) = (e3))\/((op (e1) (e3)) = (e3))))) -> (~((op (e1) (e1)) = (e3))) -> (~((op (e3) (e3)) = (e1))) -> (~((op (e0) (e2)) = (op (e3) (e2)))) -> ((op (e0) (e2)) = (e1)) -> (((op (e0) (e3)) = (e1))\/(((op (e1) (e3)) = (e1))\/(((op (e2) (e3)) = (e1))\/((op (e3) (e3)) = (e1))))) -> (~((op (e3) (e1)) = (op (e3) (e2)))) -> (~((op (e2) (e2)) = (e1))) -> (~((e1) = (e3))) -> (~((op (e0) (e2)) = (op (e0) (e3)))) -> (((op (e0) (e2)) = (e1))\/(((op (e1) (e2)) = (e1))\/(((op (e2) (e2)) = (e1))\/((op (e3) (e2)) = (e1))))) -> ((op (e1) (e0)) = (e1)) -> (~((op (e1) (e0)) = (op (e1) (e3)))) -> (~((op (e3) (op (e2) (e3))) = (op (e2) (e3)))) -> (~((op (e1) (e0)) = (op (e3) (e0)))) -> (((op (e3) (e0)) = (e1))\/(((op (e3) (e1)) = (e1))\/(((op (e3) (e2)) = (e1))\/((op (e3) (e3)) = (e1))))) -> ((op (e3) (e3)) = (e3)) -> (~((op (e1) (e3)) = (op (e3) (e3)))) -> False). % 15.48/15.62 do 0 intro. intros zenon_H90 zenon_H182 zenon_H104 zenon_H140 zenon_H29 zenon_H121 zenon_H135 zenon_H52 zenon_Ha3 zenon_Hc9 zenon_H11b zenon_Hd8 zenon_H1cf zenon_H28a zenon_H22e zenon_H146 zenon_H42 zenon_H8b. % 15.48/15.62 apply (zenon_or_s _ _ zenon_H90); [ zenon_intro zenon_H69 | zenon_intro zenon_H94 ]. % 15.48/15.62 apply (zenon_L163_); trivial. % 15.48/15.62 apply (zenon_or_s _ _ zenon_H94); [ zenon_intro zenon_H96 | zenon_intro zenon_H95 ]. % 15.48/15.62 exact (zenon_H182 zenon_H96). % 15.48/15.62 apply (zenon_or_s _ _ zenon_H95); [ zenon_intro zenon_H88 | zenon_intro zenon_H8a ]. % 15.48/15.62 apply (zenon_L1006_); trivial. % 15.48/15.62 apply (zenon_L25_); trivial. % 15.48/15.62 (* end of lemma zenon_L1009_ *) % 15.48/15.62 assert (zenon_L1010_ : ((~((op (e3) (e3)) = (e1)))\/((op (e3) (e1)) = (e3))) -> (~((op (e3) (e1)) = (op (e3) (e3)))) -> (~((op (e0) (e0)) = (e1))) -> (((op (e0) (e3)) = (e1))\/(((op (e1) (e3)) = (e1))\/(((op (e2) (e3)) = (e1))\/((op (e3) (e3)) = (e1))))) -> ((op (e2) (e3)) = (e2)) -> (~((e1) = (e2))) -> ((op (e1) (e0)) = (e1)) -> (~((op (e1) (e0)) = (op (e1) (e3)))) -> (~((op (e0) (e1)) = (op (e0) (e3)))) -> (((op (e1) (e0)) = (e3))\/(((op (e1) (e1)) = (e3))\/(((op (e1) (e2)) = (e3))\/((op (e1) (e3)) = (e3))))) -> ((op (e3) (e3)) = (e3)) -> (~((op (e1) (e3)) = (op (e3) (e3)))) -> (~((op (e1) (e0)) = (op (e3) (e0)))) -> (~((op (e3) (op (e2) (e3))) = (op (e2) (e3)))) -> (~((op (e0) (e2)) = (op (e0) (e3)))) -> (~((op (e2) (e2)) = (e1))) -> (~((op (e3) (e1)) = (op (e3) (e2)))) -> (((op (e0) (e2)) = (e1))\/(((op (e1) (e2)) = (e1))\/(((op (e2) (e2)) = (e1))\/((op (e3) (e2)) = (e1))))) -> (~((op (e0) (e2)) = (op (e3) (e2)))) -> (((op (e3) (e0)) = (e1))\/(((op (e3) (e1)) = (e1))\/(((op (e3) (e2)) = (e1))\/((op (e3) (e3)) = (e1))))) -> (~((op (e1) (e1)) = (e3))) -> (~((e1) = (e3))) -> (~((e0) = (e1))) -> ((op (e0) (e3)) = (e0)) -> (((op (e0) (e0)) = (e1))\/(((op (e0) (e1)) = (e1))\/(((op (e0) (e2)) = (e1))\/((op (e0) (e3)) = (e1))))) -> False). % 15.48/15.62 do 0 intro. intros zenon_H10c zenon_H12d zenon_H45 zenon_H121 zenon_H124 zenon_Ha7 zenon_Hd8 zenon_H1cf zenon_H1cd zenon_H90 zenon_H42 zenon_H8b zenon_H22e zenon_H28a zenon_Hc9 zenon_H52 zenon_H135 zenon_H11b zenon_H140 zenon_H146 zenon_H182 zenon_Ha3 zenon_H9e zenon_Hca zenon_H44. % 15.48/15.62 apply (zenon_or_s _ _ zenon_H10c); [ zenon_intro zenon_H104 | zenon_intro zenon_H10a ]. % 15.48/15.62 apply (zenon_or_s _ _ zenon_H44); [ zenon_intro zenon_H47 | zenon_intro zenon_H46 ]. % 15.48/15.62 exact (zenon_H45 zenon_H47). % 15.48/15.62 apply (zenon_or_s _ _ zenon_H46); [ zenon_intro zenon_H22 | zenon_intro zenon_H48 ]. % 15.48/15.62 apply (zenon_L225_); trivial. % 15.48/15.62 apply (zenon_or_s _ _ zenon_H48); [ zenon_intro zenon_H29 | zenon_intro zenon_H37 ]. % 15.48/15.62 apply (zenon_L1009_); trivial. % 15.48/15.62 apply (zenon_L73_); trivial. % 15.48/15.62 apply (zenon_L102_); trivial. % 15.48/15.62 (* end of lemma zenon_L1010_ *) % 15.48/15.62 assert (zenon_L1011_ : (~((op (e3) (e3)) = (e1))) -> (~((op (e3) (e3)) = (e2))) -> (~((op (e2) (e0)) = (op (e2) (e3)))) -> (~((e2) = (e3))) -> ((op (e0) (e1)) = (e2)) -> (((op (e0) (e3)) = (e2))\/(((op (e1) (e3)) = (e2))\/(((op (e2) (e3)) = (e2))\/((op (e3) (e3)) = (e2))))) -> (~((op (e0) (e2)) = (op (e1) (e2)))) -> ((~((op (e0) (e0)) = (e3)))\/((op (e0) (e3)) = (e0))) -> (~((op (e2) (e0)) = (op (e2) (e1)))) -> (~((op (e0) (e3)) = (op (e2) (e3)))) -> (~((op (e1) (e1)) = (op (e2) (e1)))) -> (~((op (e1) (e1)) = (op (e1) (e3)))) -> (((op (e0) (e1)) = (e0))\/(((op (e1) (e1)) = (e0))\/(((op (e2) (e1)) = (e0))\/((op (e3) (e1)) = (e0))))) -> (((op (e0) (e1)) = (e3))\/(((op (e1) (e1)) = (e3))\/(((op (e2) (e1)) = (e3))\/((op (e3) (e1)) = (e3))))) -> (~((op (e2) (e1)) = (op (e2) (e2)))) -> (~((op (e1) (op (e2) (e1))) = (op (e2) (e1)))) -> ((~((op (e2) (e2)) = (e3)))\/((op (e2) (e3)) = (e2))) -> (((op (e3) (e0)) = (e2))\/(((op (e3) (e1)) = (e2))\/(((op (e3) (e2)) = (e2))\/((op (e3) (e3)) = (e2))))) -> (((op (e0) (e0)) = (e0))\/(((op (e0) (e0)) = (e1))\/(((op (e0) (e0)) = (e2))\/((op (e0) (e0)) = (e3))))) -> (~((op (e0) (e0)) = (e0))) -> (((op (e1) (e3)) = (e0))\/(((op (e1) (e3)) = (e1))\/(((op (e1) (e3)) = (e2))\/((op (e1) (e3)) = (e3))))) -> ((~((op (e1) (e1)) = (e2)))\/((op (e1) (e2)) = (e1))) -> (~((op (e1) (e0)) = (op (e1) (e2)))) -> ((~((op (e2) (e2)) = (e0)))\/((op (e2) (e0)) = (e2))) -> ((~((op (e2) (e2)) = (e2)))\/((op (e2) (e2)) = (e2))) -> (~((op (e2) (op (e2) (e2))) = (op (e2) (e2)))) -> (~((op (e2) (e1)) = (op (e2) (e3)))) -> ((~((op (e2) (e2)) = (e1)))\/((op (e2) (e1)) = (e2))) -> ((~((op (e1) (e1)) = (e3)))\/((op (e1) (e3)) = (e1))) -> (~((op (e1) (e0)) = (op (e1) (e1)))) -> ((~((op (e1) (e1)) = (e1)))\/((op (e1) (e1)) = (e1))) -> ((~((op (e3) (e3)) = (e2)))\/((op (e3) (e2)) = (e3))) -> (((op (e0) (e0)) = (e1))\/(((op (e1) (e0)) = (e1))\/(((op (e2) (e0)) = (e1))\/((op (e3) (e0)) = (e1))))) -> (((op (e1) (e0)) = (e1))\/(((op (e1) (e1)) = (e1))\/(((op (e1) (e2)) = (e1))\/((op (e1) (e3)) = (e1))))) -> (((op (e2) (e0)) = (e2))\/(((op (e2) (e1)) = (e2))\/(((op (e2) (e2)) = (e2))\/((op (e2) (e3)) = (e2))))) -> (~((e0) = (e2))) -> (((op (e0) (e3)) = (e0))\/(((op (e1) (e3)) = (e0))\/(((op (e2) (e3)) = (e0))\/((op (e3) (e3)) = (e0))))) -> (~((op (e1) (e3)) = (op (e2) (e3)))) -> (((op (e2) (e0)) = (e1))\/(((op (e2) (e1)) = (e1))\/(((op (e2) (e2)) = (e1))\/((op (e2) (e3)) = (e1))))) -> (((op (e2) (e0)) = (e0))\/(((op (e2) (e1)) = (e0))\/(((op (e2) (e2)) = (e0))\/((op (e2) (e3)) = (e0))))) -> (((op (e0) (e1)) = (e2))\/(((op (e1) (e1)) = (e2))\/(((op (e2) (e1)) = (e2))\/((op (e3) (e1)) = (e2))))) -> (~((e0) = (e3))) -> (~((op (e3) (e2)) = (op (e3) (e3)))) -> (((op (e0) (e2)) = (e3))\/(((op (e1) (e2)) = (e3))\/(((op (e2) (e2)) = (e3))\/((op (e3) (e2)) = (e3))))) -> (~((op (e0) (e1)) = (op (e1) (e1)))) -> (((op (e0) (e0)) = (e2))\/(((op (e1) (e0)) = (e2))\/(((op (e2) (e0)) = (e2))\/((op (e3) (e0)) = (e2))))) -> (((op (e1) (e0)) = (e2))\/(((op (e1) (e1)) = (e2))\/(((op (e1) (e2)) = (e2))\/((op (e1) (e3)) = (e2))))) -> (~((op (e0) (e3)) = (op (e1) (e3)))) -> (((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 (e0) (e1)) = (op (e2) (e1)))) -> (~((op (e0) (e2)) = (op (e2) (e2)))) -> (~((op (e0) (e3)) = (op (e3) (e3)))) -> (((op (e0) (e0)) = (e3))\/(((op (e0) (e1)) = (e3))\/(((op (e0) (e2)) = (e3))\/((op (e0) (e3)) = (e3))))) -> (((op (e1) (e1)) = (e0))\/(((op (e1) (e1)) = (e1))\/(((op (e1) (e1)) = (e2))\/((op (e1) (e1)) = (e3))))) -> (((op (e2) (e2)) = (e0))\/(((op (e2) (e2)) = (e1))\/(((op (e2) (e2)) = (e2))\/((op (e2) (e2)) = (e3))))) -> (~((op (e3) (e0)) = (op (e3) (e3)))) -> (((op (e0) (e0)) = (e3))\/(((op (e1) (e0)) = (e3))\/(((op (e2) (e0)) = (e3))\/((op (e3) (e0)) = (e3))))) -> ((~((op (e3) (e3)) = (e0)))\/((op (e3) (e0)) = (e3))) -> (~((op (e1) (e2)) = (op (e1) (e3)))) -> ((~((op (e1) (e1)) = (e0)))\/((op (e1) (e0)) = (e1))) -> (((op (e0) (e2)) = (e0))\/(((op (e0) (e2)) = (e1))\/(((op (e0) (e2)) = (e2))\/((op (e0) (e2)) = (e3))))) -> ((op (e1) (e2)) = (e3)) -> (~((op (e0) (op (e2) (e0))) = (op (e2) (e0)))) -> (((op (e0) (e2)) = (e2))\/(((op (e1) (e2)) = (e2))\/(((op (e2) (e2)) = (e2))\/((op (e3) (e2)) = (e2))))) -> (~((op (e2) (e1)) = (op (e3) (e1)))) -> ((op (e3) (e2)) = (e0)) -> (((op (e3) (e1)) = (e0))\/(((op (e3) (e1)) = (e1))\/(((op (e3) (e1)) = (e2))\/((op (e3) (e1)) = (e3))))) -> (~((op (e2) (e2)) = (e2))) -> ((~((op (e3) (e3)) = (e1)))\/((op (e3) (e1)) = (e3))) -> (~((op (e3) (e1)) = (op (e3) (e3)))) -> (~((op (e0) (e0)) = (e1))) -> (((op (e0) (e3)) = (e1))\/(((op (e1) (e3)) = (e1))\/(((op (e2) (e3)) = (e1))\/((op (e3) (e3)) = (e1))))) -> (~((e1) = (e2))) -> ((op (e1) (e0)) = (e1)) -> (~((op (e1) (e0)) = (op (e1) (e3)))) -> (~((op (e0) (e1)) = (op (e0) (e3)))) -> (((op (e1) (e0)) = (e3))\/(((op (e1) (e1)) = (e3))\/(((op (e1) (e2)) = (e3))\/((op (e1) (e3)) = (e3))))) -> ((op (e3) (e3)) = (e3)) -> (~((op (e1) (e3)) = (op (e3) (e3)))) -> (~((op (e1) (e0)) = (op (e3) (e0)))) -> (~((op (e3) (op (e2) (e3))) = (op (e2) (e3)))) -> (~((op (e0) (e2)) = (op (e0) (e3)))) -> (~((op (e2) (e2)) = (e1))) -> (~((op (e3) (e1)) = (op (e3) (e2)))) -> (((op (e0) (e2)) = (e1))\/(((op (e1) (e2)) = (e1))\/(((op (e2) (e2)) = (e1))\/((op (e3) (e2)) = (e1))))) -> (~((op (e0) (e2)) = (op (e3) (e2)))) -> (((op (e3) (e0)) = (e1))\/(((op (e3) (e1)) = (e1))\/(((op (e3) (e2)) = (e1))\/((op (e3) (e3)) = (e1))))) -> (~((op (e1) (e1)) = (e3))) -> (~((e1) = (e3))) -> (~((e0) = (e1))) -> ((op (e0) (e3)) = (e0)) -> (((op (e0) (e0)) = (e1))\/(((op (e0) (e1)) = (e1))\/(((op (e0) (e2)) = (e1))\/((op (e0) (e3)) = (e1))))) -> False). % 15.48/15.62 do 0 intro. intros zenon_H104 zenon_H3d zenon_Hce zenon_H6a zenon_H5d zenon_H160 zenon_H87 zenon_H236 zenon_H154 zenon_Hb4 zenon_Hb1 zenon_H11e zenon_H144 zenon_H199 zenon_H157 zenon_H290 zenon_H1c3 zenon_H1df zenon_H12a zenon_H20 zenon_H25b zenon_H1d3 zenon_H166 zenon_H1d4 zenon_Haa zenon_H294 zenon_H1e2 zenon_H1e3 zenon_H1d2 zenon_Hd7 zenon_H1d8 zenon_H10e zenon_Hf1 zenon_H1c5 zenon_H237 zenon_H5e zenon_Hd3 zenon_H244 zenon_Hb7 zenon_H1f5 zenon_H1a2 zenon_H4b zenon_H173 zenon_H175 zenon_H23 zenon_Heb zenon_H84 zenon_H80 zenon_H8e zenon_He6 zenon_Hde zenon_H28 zenon_H36 zenon_H58 zenon_H1b3 zenon_H2d zenon_Hbb zenon_Hbe zenon_H10f zenon_H1d0 zenon_H1e4 zenon_H251 zenon_H88 zenon_H295 zenon_H27c zenon_H13c zenon_H167 zenon_H16c zenon_H2f zenon_H10c zenon_H12d zenon_H45 zenon_H121 zenon_Ha7 zenon_Hd8 zenon_H1cf zenon_H1cd zenon_H90 zenon_H42 zenon_H8b zenon_H22e zenon_H28a zenon_Hc9 zenon_H52 zenon_H135 zenon_H11b zenon_H140 zenon_H146 zenon_H182 zenon_Ha3 zenon_H9e zenon_Hca zenon_H44. % 15.48/15.62 apply (zenon_or_s _ _ zenon_H11b); [ zenon_intro zenon_H29 | zenon_intro zenon_H11c ]. % 15.48/15.62 apply (zenon_L1006_); trivial. % 15.48/15.62 apply (zenon_or_s _ _ zenon_H11c); [ zenon_intro zenon_H117 | zenon_intro zenon_H11d ]. % 15.48/15.62 apply (zenon_L196_); trivial. % 15.48/15.62 apply (zenon_or_s _ _ zenon_H11d); [ zenon_intro zenon_H2a | zenon_intro zenon_H119 ]. % 15.48/15.62 exact (zenon_H52 zenon_H2a). % 15.48/15.62 apply (zenon_or_s _ _ zenon_H237); [ zenon_intro zenon_Hdd | zenon_intro zenon_H238 ]. % 15.48/15.62 apply (zenon_L1008_); trivial. % 15.48/15.62 apply (zenon_or_s _ _ zenon_H238); [ zenon_intro zenon_H156 | zenon_intro zenon_H239 ]. % 15.48/15.62 apply (zenon_L707_); trivial. % 15.48/15.62 apply (zenon_or_s _ _ zenon_H239); [ zenon_intro zenon_H35 | zenon_intro zenon_H124 ]. % 15.48/15.62 exact (zenon_H2f zenon_H35). % 15.48/15.62 apply (zenon_L1010_); trivial. % 15.48/15.62 (* end of lemma zenon_L1011_ *) % 15.48/15.62 assert (zenon_L1012_ : (((op (e0) (e0)) = (e1))\/(((op (e0) (e1)) = (e1))\/(((op (e0) (e2)) = (e1))\/((op (e0) (e3)) = (e1))))) -> ((op (e0) (e3)) = (e0)) -> (~((e0) = (e1))) -> (~((e1) = (e3))) -> (~((op (e1) (e1)) = (e3))) -> (((op (e3) (e0)) = (e1))\/(((op (e3) (e1)) = (e1))\/(((op (e3) (e2)) = (e1))\/((op (e3) (e3)) = (e1))))) -> (~((op (e0) (e2)) = (op (e3) (e2)))) -> (((op (e0) (e2)) = (e1))\/(((op (e1) (e2)) = (e1))\/(((op (e2) (e2)) = (e1))\/((op (e3) (e2)) = (e1))))) -> (~((op (e3) (e1)) = (op (e3) (e2)))) -> (~((op (e2) (e2)) = (e1))) -> (~((op (e0) (e2)) = (op (e0) (e3)))) -> (~((op (e3) (op (e2) (e3))) = (op (e2) (e3)))) -> (~((op (e1) (e0)) = (op (e3) (e0)))) -> (((op (e1) (e0)) = (e3))\/(((op (e1) (e1)) = (e3))\/(((op (e1) (e2)) = (e3))\/((op (e1) (e3)) = (e3))))) -> (~((op (e0) (e1)) = (op (e0) (e3)))) -> (~((op (e1) (e0)) = (op (e1) (e3)))) -> ((op (e1) (e0)) = (e1)) -> (~((e1) = (e2))) -> (((op (e0) (e3)) = (e1))\/(((op (e1) (e3)) = (e1))\/(((op (e2) (e3)) = (e1))\/((op (e3) (e3)) = (e1))))) -> (~((op (e0) (e0)) = (e1))) -> (~((op (e3) (e1)) = (op (e3) (e3)))) -> ((~((op (e3) (e3)) = (e1)))\/((op (e3) (e1)) = (e3))) -> (~((op (e2) (e2)) = (e2))) -> (((op (e3) (e1)) = (e0))\/(((op (e3) (e1)) = (e1))\/(((op (e3) (e1)) = (e2))\/((op (e3) (e1)) = (e3))))) -> (~((op (e2) (e1)) = (op (e3) (e1)))) -> (((op (e0) (e2)) = (e2))\/(((op (e1) (e2)) = (e2))\/(((op (e2) (e2)) = (e2))\/((op (e3) (e2)) = (e2))))) -> (~((op (e0) (op (e2) (e0))) = (op (e2) (e0)))) -> (((op (e0) (e2)) = (e0))\/(((op (e0) (e2)) = (e1))\/(((op (e0) (e2)) = (e2))\/((op (e0) (e2)) = (e3))))) -> ((~((op (e1) (e1)) = (e0)))\/((op (e1) (e0)) = (e1))) -> (~((op (e1) (e2)) = (op (e1) (e3)))) -> ((~((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) (e0)) = (op (e3) (e3)))) -> (((op (e2) (e2)) = (e0))\/(((op (e2) (e2)) = (e1))\/(((op (e2) (e2)) = (e2))\/((op (e2) (e2)) = (e3))))) -> (((op (e1) (e1)) = (e0))\/(((op (e1) (e1)) = (e1))\/(((op (e1) (e1)) = (e2))\/((op (e1) (e1)) = (e3))))) -> (((op (e0) (e0)) = (e3))\/(((op (e0) (e1)) = (e3))\/(((op (e0) (e2)) = (e3))\/((op (e0) (e3)) = (e3))))) -> (~((op (e0) (e3)) = (op (e3) (e3)))) -> (~((op (e0) (e2)) = (op (e2) (e2)))) -> (~((op (e0) (e1)) = (op (e2) (e1)))) -> (((op (e2) (e0)) = (e3))\/(((op (e2) (e1)) = (e3))\/(((op (e2) (e2)) = (e3))\/((op (e2) (e3)) = (e3))))) -> (((op (e0) (e0)) = (e2))\/(((op (e0) (e1)) = (e2))\/(((op (e0) (e2)) = (e2))\/((op (e0) (e3)) = (e2))))) -> (~((op (e0) (e3)) = (op (e1) (e3)))) -> (((op (e1) (e0)) = (e2))\/(((op (e1) (e1)) = (e2))\/(((op (e1) (e2)) = (e2))\/((op (e1) (e3)) = (e2))))) -> (((op (e0) (e0)) = (e2))\/(((op (e1) (e0)) = (e2))\/(((op (e2) (e0)) = (e2))\/((op (e3) (e0)) = (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) (e2)) = (op (e3) (e3)))) -> (~((e0) = (e3))) -> (((op (e0) (e1)) = (e2))\/(((op (e1) (e1)) = (e2))\/(((op (e2) (e1)) = (e2))\/((op (e3) (e1)) = (e2))))) -> (((op (e2) (e0)) = (e0))\/(((op (e2) (e1)) = (e0))\/(((op (e2) (e2)) = (e0))\/((op (e2) (e3)) = (e0))))) -> (((op (e2) (e0)) = (e1))\/(((op (e2) (e1)) = (e1))\/(((op (e2) (e2)) = (e1))\/((op (e2) (e3)) = (e1))))) -> (~((op (e1) (e3)) = (op (e2) (e3)))) -> (((op (e0) (e3)) = (e0))\/(((op (e1) (e3)) = (e0))\/(((op (e2) (e3)) = (e0))\/((op (e3) (e3)) = (e0))))) -> (~((e0) = (e2))) -> (((op (e2) (e0)) = (e2))\/(((op (e2) (e1)) = (e2))\/(((op (e2) (e2)) = (e2))\/((op (e2) (e3)) = (e2))))) -> (((op (e1) (e0)) = (e1))\/(((op (e1) (e1)) = (e1))\/(((op (e1) (e2)) = (e1))\/((op (e1) (e3)) = (e1))))) -> (((op (e0) (e0)) = (e1))\/(((op (e1) (e0)) = (e1))\/(((op (e2) (e0)) = (e1))\/((op (e3) (e0)) = (e1))))) -> ((~((op (e3) (e3)) = (e2)))\/((op (e3) (e2)) = (e3))) -> ((~((op (e1) (e1)) = (e1)))\/((op (e1) (e1)) = (e1))) -> (~((op (e1) (e0)) = (op (e1) (e1)))) -> ((~((op (e1) (e1)) = (e3)))\/((op (e1) (e3)) = (e1))) -> ((~((op (e2) (e2)) = (e1)))\/((op (e2) (e1)) = (e2))) -> (~((op (e2) (e1)) = (op (e2) (e3)))) -> (~((op (e2) (op (e2) (e2))) = (op (e2) (e2)))) -> ((~((op (e2) (e2)) = (e2)))\/((op (e2) (e2)) = (e2))) -> ((~((op (e2) (e2)) = (e0)))\/((op (e2) (e0)) = (e2))) -> (~((op (e1) (e0)) = (op (e1) (e2)))) -> ((~((op (e1) (e1)) = (e2)))\/((op (e1) (e2)) = (e1))) -> (((op (e1) (e3)) = (e0))\/(((op (e1) (e3)) = (e1))\/(((op (e1) (e3)) = (e2))\/((op (e1) (e3)) = (e3))))) -> (~((op (e0) (e0)) = (e0))) -> (((op (e0) (e0)) = (e0))\/(((op (e0) (e0)) = (e1))\/(((op (e0) (e0)) = (e2))\/((op (e0) (e0)) = (e3))))) -> (((op (e3) (e0)) = (e2))\/(((op (e3) (e1)) = (e2))\/(((op (e3) (e2)) = (e2))\/((op (e3) (e3)) = (e2))))) -> ((~((op (e2) (e2)) = (e3)))\/((op (e2) (e3)) = (e2))) -> (~((op (e1) (op (e2) (e1))) = (op (e2) (e1)))) -> (~((op (e2) (e1)) = (op (e2) (e2)))) -> (((op (e0) (e1)) = (e3))\/(((op (e1) (e1)) = (e3))\/(((op (e2) (e1)) = (e3))\/((op (e3) (e1)) = (e3))))) -> (((op (e0) (e1)) = (e0))\/(((op (e1) (e1)) = (e0))\/(((op (e2) (e1)) = (e0))\/((op (e3) (e1)) = (e0))))) -> (~((op (e1) (e1)) = (op (e1) (e3)))) -> (~((op (e1) (e1)) = (op (e2) (e1)))) -> (~((op (e0) (e3)) = (op (e2) (e3)))) -> (~((op (e2) (e0)) = (op (e2) (e1)))) -> ((~((op (e0) (e0)) = (e3)))\/((op (e0) (e3)) = (e0))) -> (~((op (e0) (e2)) = (op (e1) (e2)))) -> (((op (e0) (e3)) = (e2))\/(((op (e1) (e3)) = (e2))\/(((op (e2) (e3)) = (e2))\/((op (e3) (e3)) = (e2))))) -> ((op (e0) (e1)) = (e2)) -> (~((e2) = (e3))) -> (~((op (e2) (e0)) = (op (e2) (e3)))) -> (~((op (e3) (e3)) = (e2))) -> (~((op (e3) (e3)) = (e1))) -> (~((op (e2) (e2)) = (e0))) -> (~((op (e1) (e2)) = (op (e2) (e2)))) -> (~((op (e2) (e2)) = (e3))) -> (((op (e0) (e2)) = (e0))\/(((op (e1) (e2)) = (e0))\/(((op (e2) (e2)) = (e0))\/((op (e3) (e2)) = (e0))))) -> ((op (e3) (e3)) = (e3)) -> (~((op (e1) (e3)) = (op (e3) (e3)))) -> False). % 15.48/15.62 do 0 intro. intros zenon_H44 zenon_Hca zenon_H9e zenon_Ha3 zenon_H182 zenon_H146 zenon_H140 zenon_H11b zenon_H135 zenon_H52 zenon_Hc9 zenon_H28a zenon_H22e zenon_H90 zenon_H1cd zenon_H1cf zenon_Hd8 zenon_Ha7 zenon_H121 zenon_H45 zenon_H12d zenon_H10c zenon_H2f zenon_H16c zenon_H13c zenon_H27c zenon_H295 zenon_H251 zenon_H1e4 zenon_H1d0 zenon_H10f zenon_Hbe zenon_Hbb zenon_H2d zenon_H1b3 zenon_H58 zenon_H36 zenon_H28 zenon_Hde zenon_He6 zenon_H8e zenon_H80 zenon_H84 zenon_Heb zenon_H23 zenon_H175 zenon_H173 zenon_H4b zenon_H1a2 zenon_H1f5 zenon_Hb7 zenon_H244 zenon_Hd3 zenon_H5e zenon_H237 zenon_H1c5 zenon_Hf1 zenon_H10e zenon_H1d8 zenon_Hd7 zenon_H1d2 zenon_H1e3 zenon_H1e2 zenon_H294 zenon_Haa zenon_H1d4 zenon_H166 zenon_H1d3 zenon_H25b zenon_H20 zenon_H12a zenon_H1df zenon_H1c3 zenon_H290 zenon_H157 zenon_H199 zenon_H144 zenon_H11e zenon_Hb1 zenon_Hb4 zenon_H154 zenon_H236 zenon_H87 zenon_H160 zenon_H5d zenon_H6a zenon_Hce zenon_H3d zenon_H104 zenon_H2e zenon_H7d zenon_H30 zenon_H16f zenon_H42 zenon_H8b. % 15.48/15.62 apply (zenon_or_s _ _ zenon_H90); [ zenon_intro zenon_H69 | zenon_intro zenon_H94 ]. % 15.48/15.62 apply (zenon_L163_); trivial. % 15.48/15.62 apply (zenon_or_s _ _ zenon_H94); [ zenon_intro zenon_H96 | zenon_intro zenon_H95 ]. % 15.48/15.62 exact (zenon_H182 zenon_H96). % 15.48/15.62 apply (zenon_or_s _ _ zenon_H95); [ zenon_intro zenon_H88 | zenon_intro zenon_H8a ]. % 15.48/15.62 apply (zenon_or_s _ _ zenon_H16f); [ zenon_intro zenon_Hab | zenon_intro zenon_H170 ]. % 15.48/15.62 apply (zenon_L53_); trivial. % 15.48/15.62 apply (zenon_or_s _ _ zenon_H170); [ zenon_intro zenon_H15d | zenon_intro zenon_H171 ]. % 15.48/15.62 apply (zenon_L335_); trivial. % 15.48/15.62 apply (zenon_or_s _ _ zenon_H171); [ zenon_intro zenon_H32 | zenon_intro zenon_H167 ]. % 15.48/15.62 exact (zenon_H2e zenon_H32). % 15.48/15.62 apply (zenon_L1011_); trivial. % 15.48/15.62 apply (zenon_L25_); trivial. % 15.48/15.62 (* end of lemma zenon_L1012_ *) % 15.48/15.62 assert (zenon_L1013_ : (((op (e0) (e2)) = (e1))\/(((op (e1) (e2)) = (e1))\/(((op (e2) (e2)) = (e1))\/((op (e3) (e2)) = (e1))))) -> (~((op (e1) (e0)) = (op (e1) (e2)))) -> (~((op (e2) (e2)) = (e1))) -> (((op (e2) (e0)) = (e2))\/(((op (e2) (e1)) = (e2))\/(((op (e2) (e2)) = (e2))\/((op (e2) (e3)) = (e2))))) -> ((op (e0) (e2)) = (e2)) -> (~((op (e0) (op (e2) (e0))) = (op (e2) (e0)))) -> (~((op (e3) (e1)) = (op (e3) (e3)))) -> ((op (e3) (e3)) = (e3)) -> (~((op (e2) (e1)) = (op (e3) (e1)))) -> (~((op (e3) (e1)) = (op (e3) (e2)))) -> ((op (e3) (e2)) = (e0)) -> (((op (e3) (e1)) = (e0))\/(((op (e3) (e1)) = (e1))\/(((op (e3) (e1)) = (e2))\/((op (e3) (e1)) = (e3))))) -> (~((op (e2) (e2)) = (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)) = (e1)) -> (~((op (e1) (e0)) = (op (e1) (e3)))) -> (~((e1) = (e2))) -> (~((op (e3) (e3)) = (e1))) -> False). % 15.48/15.62 do 0 intro. intros zenon_H11b zenon_H166 zenon_H52 zenon_H237 zenon_H63 zenon_H295 zenon_H12d zenon_H42 zenon_H13c zenon_H135 zenon_H167 zenon_H16c zenon_H2f zenon_H121 zenon_H1cd zenon_H22 zenon_Hd8 zenon_H1cf zenon_Ha7 zenon_H104. % 15.48/15.62 apply (zenon_or_s _ _ zenon_H11b); [ zenon_intro zenon_H29 | zenon_intro zenon_H11c ]. % 15.48/15.62 apply (zenon_L104_); trivial. % 15.48/15.62 apply (zenon_or_s _ _ zenon_H11c); [ zenon_intro zenon_H117 | zenon_intro zenon_H11d ]. % 15.48/15.62 apply (zenon_L248_); trivial. % 15.48/15.62 apply (zenon_or_s _ _ zenon_H11d); [ zenon_intro zenon_H2a | zenon_intro zenon_H119 ]. % 15.48/15.62 exact (zenon_H52 zenon_H2a). % 15.48/15.62 apply (zenon_or_s _ _ zenon_H237); [ zenon_intro zenon_Hdd | zenon_intro zenon_H238 ]. % 15.48/15.62 apply (zenon_L812_); trivial. % 15.48/15.62 apply (zenon_or_s _ _ zenon_H238); [ zenon_intro zenon_H156 | zenon_intro zenon_H239 ]. % 15.48/15.62 apply (zenon_L707_); trivial. % 15.48/15.62 apply (zenon_or_s _ _ zenon_H239); [ zenon_intro zenon_H35 | zenon_intro zenon_H124 ]. % 15.48/15.62 exact (zenon_H2f zenon_H35). % 15.48/15.62 apply (zenon_L225_); trivial. % 15.48/15.62 (* end of lemma zenon_L1013_ *) % 15.48/15.62 assert (zenon_L1014_ : (~((op (e0) (e0)) = (e2))) -> (~((op (e1) (e3)) = (op (e3) (e3)))) -> (~((op (e3) (e3)) = (e2))) -> (~((op (e2) (e0)) = (op (e2) (e3)))) -> (~((e2) = (e3))) -> (((op (e0) (e3)) = (e2))\/(((op (e1) (e3)) = (e2))\/(((op (e2) (e3)) = (e2))\/((op (e3) (e3)) = (e2))))) -> (~((op (e0) (e2)) = (op (e1) (e2)))) -> ((~((op (e0) (e0)) = (e3)))\/((op (e0) (e3)) = (e0))) -> (~((op (e2) (e0)) = (op (e2) (e1)))) -> (~((op (e0) (e3)) = (op (e2) (e3)))) -> (~((op (e1) (e1)) = (op (e2) (e1)))) -> (~((op (e1) (e1)) = (op (e1) (e3)))) -> (((op (e0) (e1)) = (e0))\/(((op (e1) (e1)) = (e0))\/(((op (e2) (e1)) = (e0))\/((op (e3) (e1)) = (e0))))) -> (((op (e0) (e1)) = (e3))\/(((op (e1) (e1)) = (e3))\/(((op (e2) (e1)) = (e3))\/((op (e3) (e1)) = (e3))))) -> (~((op (e2) (e1)) = (op (e2) (e2)))) -> (~((op (e1) (op (e2) (e1))) = (op (e2) (e1)))) -> ((~((op (e2) (e2)) = (e3)))\/((op (e2) (e3)) = (e2))) -> (((op (e3) (e0)) = (e2))\/(((op (e3) (e1)) = (e2))\/(((op (e3) (e2)) = (e2))\/((op (e3) (e3)) = (e2))))) -> (((op (e0) (e0)) = (e0))\/(((op (e0) (e0)) = (e1))\/(((op (e0) (e0)) = (e2))\/((op (e0) (e0)) = (e3))))) -> (~((op (e0) (e0)) = (e0))) -> (((op (e1) (e3)) = (e0))\/(((op (e1) (e3)) = (e1))\/(((op (e1) (e3)) = (e2))\/((op (e1) (e3)) = (e3))))) -> ((~((op (e1) (e1)) = (e2)))\/((op (e1) (e2)) = (e1))) -> ((~((op (e2) (e2)) = (e0)))\/((op (e2) (e0)) = (e2))) -> ((~((op (e2) (e2)) = (e2)))\/((op (e2) (e2)) = (e2))) -> (~((op (e2) (op (e2) (e2))) = (op (e2) (e2)))) -> (~((op (e2) (e1)) = (op (e2) (e3)))) -> ((~((op (e2) (e2)) = (e1)))\/((op (e2) (e1)) = (e2))) -> ((~((op (e1) (e1)) = (e3)))\/((op (e1) (e3)) = (e1))) -> (~((op (e1) (e0)) = (op (e1) (e1)))) -> ((~((op (e1) (e1)) = (e1)))\/((op (e1) (e1)) = (e1))) -> ((~((op (e3) (e3)) = (e2)))\/((op (e3) (e2)) = (e3))) -> (((op (e0) (e0)) = (e1))\/(((op (e1) (e0)) = (e1))\/(((op (e2) (e0)) = (e1))\/((op (e3) (e0)) = (e1))))) -> (((op (e1) (e0)) = (e1))\/(((op (e1) (e1)) = (e1))\/(((op (e1) (e2)) = (e1))\/((op (e1) (e3)) = (e1))))) -> (((op (e0) (e3)) = (e0))\/(((op (e1) (e3)) = (e0))\/(((op (e2) (e3)) = (e0))\/((op (e3) (e3)) = (e0))))) -> (~((op (e1) (e3)) = (op (e2) (e3)))) -> (((op (e2) (e0)) = (e1))\/(((op (e2) (e1)) = (e1))\/(((op (e2) (e2)) = (e1))\/((op (e2) (e3)) = (e1))))) -> (((op (e2) (e0)) = (e0))\/(((op (e2) (e1)) = (e0))\/(((op (e2) (e2)) = (e0))\/((op (e2) (e3)) = (e0))))) -> (((op (e0) (e1)) = (e2))\/(((op (e1) (e1)) = (e2))\/(((op (e2) (e1)) = (e2))\/((op (e3) (e1)) = (e2))))) -> (~((e0) = (e3))) -> (~((op (e3) (e2)) = (op (e3) (e3)))) -> (((op (e0) (e2)) = (e3))\/(((op (e1) (e2)) = (e3))\/(((op (e2) (e2)) = (e3))\/((op (e3) (e2)) = (e3))))) -> (~((op (e0) (e1)) = (op (e1) (e1)))) -> (((op (e0) (e0)) = (e2))\/(((op (e1) (e0)) = (e2))\/(((op (e2) (e0)) = (e2))\/((op (e3) (e0)) = (e2))))) -> (((op (e1) (e0)) = (e2))\/(((op (e1) (e1)) = (e2))\/(((op (e1) (e2)) = (e2))\/((op (e1) (e3)) = (e2))))) -> (~((op (e0) (e3)) = (op (e1) (e3)))) -> (((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 (e0) (e1)) = (op (e2) (e1)))) -> (~((op (e0) (e2)) = (op (e2) (e2)))) -> (~((op (e0) (e3)) = (op (e3) (e3)))) -> (((op (e0) (e0)) = (e3))\/(((op (e0) (e1)) = (e3))\/(((op (e0) (e2)) = (e3))\/((op (e0) (e3)) = (e3))))) -> (((op (e1) (e1)) = (e0))\/(((op (e1) (e1)) = (e1))\/(((op (e1) (e1)) = (e2))\/((op (e1) (e1)) = (e3))))) -> (~((op (e3) (e0)) = (op (e3) (e3)))) -> (((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 (e1) (e2)) = (op (e1) (e3)))) -> ((~((op (e1) (e1)) = (e0)))\/((op (e1) (e0)) = (e1))) -> (((op (e0) (e2)) = (e0))\/(((op (e0) (e2)) = (e1))\/(((op (e0) (e2)) = (e2))\/((op (e0) (e2)) = (e3))))) -> (((op (e0) (e2)) = (e2))\/(((op (e1) (e2)) = (e2))\/(((op (e2) (e2)) = (e2))\/((op (e3) (e2)) = (e2))))) -> ((~((op (e3) (e3)) = (e1)))\/((op (e3) (e1)) = (e3))) -> (~((op (e0) (e0)) = (e1))) -> (((op (e1) (e0)) = (e3))\/(((op (e1) (e1)) = (e3))\/(((op (e1) (e2)) = (e3))\/((op (e1) (e3)) = (e3))))) -> (~((op (e1) (e0)) = (op (e3) (e0)))) -> (~((op (e3) (op (e2) (e3))) = (op (e2) (e3)))) -> (~((op (e0) (e2)) = (op (e3) (e2)))) -> (((op (e3) (e0)) = (e1))\/(((op (e3) (e1)) = (e1))\/(((op (e3) (e2)) = (e1))\/((op (e3) (e3)) = (e1))))) -> (~((op (e1) (e1)) = (e3))) -> (~((e1) = (e3))) -> (~((e0) = (e1))) -> (((op (e0) (e0)) = (e1))\/(((op (e0) (e1)) = (e1))\/(((op (e0) (e2)) = (e1))\/((op (e0) (e3)) = (e1))))) -> (~((op (e3) (e3)) = (e1))) -> (~((e1) = (e2))) -> (~((op (e1) (e0)) = (op (e1) (e3)))) -> ((op (e1) (e0)) = (e1)) -> ((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)) = (e2))) -> (((op (e3) (e1)) = (e0))\/(((op (e3) (e1)) = (e1))\/(((op (e3) (e1)) = (e2))\/((op (e3) (e1)) = (e3))))) -> (~((op (e3) (e1)) = (op (e3) (e2)))) -> (~((op (e2) (e1)) = (op (e3) (e1)))) -> ((op (e3) (e3)) = (e3)) -> (~((op (e3) (e1)) = (op (e3) (e3)))) -> (~((op (e0) (op (e2) (e0))) = (op (e2) (e0)))) -> (((op (e2) (e0)) = (e2))\/(((op (e2) (e1)) = (e2))\/(((op (e2) (e2)) = (e2))\/((op (e2) (e3)) = (e2))))) -> (~((op (e2) (e2)) = (e1))) -> (~((op (e1) (e0)) = (op (e1) (e2)))) -> (((op (e0) (e2)) = (e1))\/(((op (e1) (e2)) = (e1))\/(((op (e2) (e2)) = (e1))\/((op (e3) (e2)) = (e1))))) -> (~((op (e2) (e2)) = (e0))) -> (((op (e2) (e2)) = (e0))\/(((op (e2) (e2)) = (e1))\/(((op (e2) (e2)) = (e2))\/((op (e2) (e2)) = (e3))))) -> (~((op (e1) (e2)) = (op (e2) (e2)))) -> (~((op (e2) (e2)) = (e3))) -> (~((op (e0) (e2)) = (op (e0) (e3)))) -> (((op (e0) (e2)) = (e0))\/(((op (e1) (e2)) = (e0))\/(((op (e2) (e2)) = (e0))\/((op (e3) (e2)) = (e0))))) -> ((op (e0) (e3)) = (e0)) -> (~((e0) = (e2))) -> False). % 15.48/15.62 do 0 intro. intros zenon_H8f zenon_H8b zenon_H3d zenon_Hce zenon_H6a zenon_H160 zenon_H87 zenon_H236 zenon_H154 zenon_Hb4 zenon_Hb1 zenon_H11e zenon_H144 zenon_H199 zenon_H157 zenon_H290 zenon_H1c3 zenon_H1df zenon_H12a zenon_H20 zenon_H25b zenon_H1d3 zenon_H1d4 zenon_Haa zenon_H294 zenon_H1e2 zenon_H1e3 zenon_H1d2 zenon_Hd7 zenon_H1d8 zenon_H10e zenon_Hf1 zenon_H1c5 zenon_Hd3 zenon_H244 zenon_Hb7 zenon_H1f5 zenon_H1a2 zenon_H4b zenon_H173 zenon_H175 zenon_H23 zenon_Heb zenon_H84 zenon_H80 zenon_H8e zenon_He6 zenon_Hde zenon_H28 zenon_H36 zenon_H58 zenon_H1b3 zenon_Hbb zenon_Hbe zenon_H10f zenon_H1d0 zenon_H1e4 zenon_H251 zenon_H27c zenon_H10c zenon_H45 zenon_H90 zenon_H22e zenon_H28a zenon_H140 zenon_H146 zenon_H182 zenon_Ha3 zenon_H9e zenon_H44 zenon_H104 zenon_Ha7 zenon_H1cf zenon_Hd8 zenon_H22 zenon_H1cd zenon_H121 zenon_H2f zenon_H16c zenon_H135 zenon_H13c zenon_H42 zenon_H12d zenon_H295 zenon_H237 zenon_H52 zenon_H166 zenon_H11b zenon_H2e zenon_H2d zenon_H7d zenon_H30 zenon_Hc9 zenon_H16f zenon_Hca zenon_H5e. % 15.48/15.62 apply (zenon_or_s _ _ zenon_H8e); [ zenon_intro zenon_H92 | zenon_intro zenon_H91 ]. % 15.48/15.62 exact (zenon_H8f zenon_H92). % 15.48/15.62 apply (zenon_or_s _ _ zenon_H91); [ zenon_intro zenon_H5d | zenon_intro zenon_H93 ]. % 15.48/15.62 apply (zenon_L1012_); trivial. % 15.48/15.62 apply (zenon_or_s _ _ zenon_H93); [ zenon_intro zenon_H63 | zenon_intro zenon_H81 ]. % 15.48/15.62 apply (zenon_or_s _ _ zenon_H16f); [ zenon_intro zenon_Hab | zenon_intro zenon_H170 ]. % 15.48/15.62 apply (zenon_L53_); trivial. % 15.48/15.62 apply (zenon_or_s _ _ zenon_H170); [ zenon_intro zenon_H15d | zenon_intro zenon_H171 ]. % 15.48/15.62 apply (zenon_L335_); trivial. % 15.48/15.62 apply (zenon_or_s _ _ zenon_H171); [ zenon_intro zenon_H32 | zenon_intro zenon_H167 ]. % 15.48/15.62 exact (zenon_H2e zenon_H32). % 15.48/15.62 apply (zenon_L1013_); trivial. % 15.48/15.62 apply (zenon_L113_); trivial. % 15.48/15.62 (* end of lemma zenon_L1014_ *) % 15.48/15.62 assert (zenon_L1015_ : (~((op (e0) (e0)) = (e2))) -> (~((op (e0) (e2)) = (op (e0) (e3)))) -> ((op (e0) (e3)) = (e0)) -> (((op (e2) (e2)) = (e0))\/(((op (e2) (e2)) = (e1))\/(((op (e2) (e2)) = (e2))\/((op (e2) (e2)) = (e3))))) -> (~((op (e2) (e2)) = (e1))) -> (~((op (e1) (e2)) = (op (e2) (e2)))) -> (~((op (e2) (e2)) = (e0))) -> (((op (e0) (e2)) = (e2))\/(((op (e1) (e2)) = (e2))\/(((op (e2) (e2)) = (e2))\/((op (e3) (e2)) = (e2))))) -> (((op (e0) (e3)) = (e2))\/(((op (e1) (e3)) = (e2))\/(((op (e2) (e3)) = (e2))\/((op (e3) (e3)) = (e2))))) -> ((~((op (e0) (e0)) = (e3)))\/((op (e0) (e3)) = (e0))) -> (~((op (e2) (e0)) = (op (e2) (e1)))) -> (((op (e0) (e0)) = (e1))\/(((op (e0) (e1)) = (e1))\/(((op (e0) (e2)) = (e1))\/((op (e0) (e3)) = (e1))))) -> (~((op (e0) (e3)) = (op (e2) (e3)))) -> (~((op (e1) (e1)) = (op (e2) (e1)))) -> (~((op (e1) (e1)) = (op (e1) (e3)))) -> (((op (e0) (e1)) = (e0))\/(((op (e1) (e1)) = (e0))\/(((op (e2) (e1)) = (e0))\/((op (e3) (e1)) = (e0))))) -> (((op (e0) (e1)) = (e3))\/(((op (e1) (e1)) = (e3))\/(((op (e2) (e1)) = (e3))\/((op (e3) (e1)) = (e3))))) -> (~((op (e3) (e1)) = (op (e3) (e3)))) -> (~((op (e2) (e1)) = (op (e2) (e2)))) -> (~((op (e1) (op (e2) (e1))) = (op (e2) (e1)))) -> ((~((op (e2) (e2)) = (e3)))\/((op (e2) (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 (e3) (e0)) = (e2))\/(((op (e3) (e1)) = (e2))\/(((op (e3) (e2)) = (e2))\/((op (e3) (e3)) = (e2))))) -> (((op (e0) (e0)) = (e0))\/(((op (e0) (e0)) = (e1))\/(((op (e0) (e0)) = (e2))\/((op (e0) (e0)) = (e3))))) -> (~((op (e0) (e0)) = (e0))) -> (((op (e1) (e3)) = (e0))\/(((op (e1) (e3)) = (e1))\/(((op (e1) (e3)) = (e2))\/((op (e1) (e3)) = (e3))))) -> ((~((op (e1) (e1)) = (e2)))\/((op (e1) (e2)) = (e1))) -> (~((op (e1) (e0)) = (op (e1) (e2)))) -> ((~((op (e2) (e2)) = (e0)))\/((op (e2) (e0)) = (e2))) -> (~((op (e0) (e2)) = (op (e1) (e2)))) -> (~((op (e2) (e0)) = (op (e2) (e3)))) -> ((~((op (e2) (e2)) = (e2)))\/((op (e2) (e2)) = (e2))) -> (~((op (e2) (op (e2) (e2))) = (op (e2) (e2)))) -> (~((op (e2) (e1)) = (op (e2) (e3)))) -> ((~((op (e2) (e2)) = (e1)))\/((op (e2) (e1)) = (e2))) -> ((~((op (e1) (e1)) = (e3)))\/((op (e1) (e3)) = (e1))) -> (~((op (e1) (e0)) = (op (e1) (e1)))) -> ((~((op (e1) (e1)) = (e1)))\/((op (e1) (e1)) = (e1))) -> ((~((op (e3) (e3)) = (e2)))\/((op (e3) (e2)) = (e3))) -> (~((op (e0) (e1)) = (op (e0) (e3)))) -> (((op (e0) (e0)) = (e1))\/(((op (e1) (e0)) = (e1))\/(((op (e2) (e0)) = (e1))\/((op (e3) (e0)) = (e1))))) -> (((op (e1) (e0)) = (e1))\/(((op (e1) (e1)) = (e1))\/(((op (e1) (e2)) = (e1))\/((op (e1) (e3)) = (e1))))) -> (((op (e2) (e0)) = (e2))\/(((op (e2) (e1)) = (e2))\/(((op (e2) (e2)) = (e2))\/((op (e2) (e3)) = (e2))))) -> (~((e0) = (e1))) -> (~((e0) = (e2))) -> (((op (e0) (e3)) = (e0))\/(((op (e1) (e3)) = (e0))\/(((op (e2) (e3)) = (e0))\/((op (e3) (e3)) = (e0))))) -> (~((e2) = (e3))) -> (~((e1) = (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)) = (e0))\/(((op (e2) (e1)) = (e0))\/(((op (e2) (e2)) = (e0))\/((op (e2) (e3)) = (e0))))) -> (~((op (e2) (e1)) = (op (e3) (e1)))) -> (((op (e0) (e1)) = (e2))\/(((op (e1) (e1)) = (e2))\/(((op (e2) (e1)) = (e2))\/((op (e3) (e1)) = (e2))))) -> (~((e0) = (e3))) -> (~((op (e3) (e2)) = (op (e3) (e3)))) -> (((op (e0) (e2)) = (e3))\/(((op (e1) (e2)) = (e3))\/(((op (e2) (e2)) = (e3))\/((op (e3) (e2)) = (e3))))) -> (~((op (e0) (e1)) = (op (e1) (e1)))) -> (((op (e0) (e0)) = (e2))\/(((op (e1) (e0)) = (e2))\/(((op (e2) (e0)) = (e2))\/((op (e3) (e0)) = (e2))))) -> (((op (e1) (e0)) = (e2))\/(((op (e1) (e1)) = (e2))\/(((op (e1) (e2)) = (e2))\/((op (e1) (e3)) = (e2))))) -> (~((op (e0) (e3)) = (op (e1) (e3)))) -> (((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 (e0) (e1)) = (op (e2) (e1)))) -> (~((op (e0) (e2)) = (op (e2) (e2)))) -> (~((op (e0) (e3)) = (op (e3) (e3)))) -> (((op (e0) (e0)) = (e3))\/(((op (e0) (e1)) = (e3))\/(((op (e0) (e2)) = (e3))\/((op (e0) (e3)) = (e3))))) -> (((op (e1) (e1)) = (e0))\/(((op (e1) (e1)) = (e1))\/(((op (e1) (e1)) = (e2))\/((op (e1) (e1)) = (e3))))) -> (~((op (e3) (e0)) = (op (e3) (e3)))) -> ((op (e3) (e3)) = (e3)) -> (((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 (e1) (e2)) = (op (e1) (e3)))) -> ((~((op (e1) (e1)) = (e0)))\/((op (e1) (e0)) = (e1))) -> (((op (e0) (e2)) = (e0))\/(((op (e0) (e2)) = (e1))\/(((op (e0) (e2)) = (e2))\/((op (e0) (e2)) = (e3))))) -> (~((op (e0) (op (e2) (e0))) = (op (e2) (e0)))) -> (((op (e3) (e1)) = (e0))\/(((op (e3) (e1)) = (e1))\/(((op (e3) (e1)) = (e2))\/((op (e3) (e1)) = (e3))))) -> ((~((op (e3) (e3)) = (e1)))\/((op (e3) (e1)) = (e3))) -> (~((op (e1) (e0)) = (op (e3) (e0)))) -> (((op (e0) (e3)) = (e1))\/(((op (e1) (e3)) = (e1))\/(((op (e2) (e3)) = (e1))\/((op (e3) (e3)) = (e1))))) -> (~((op (e3) (op (e2) (e3))) = (op (e2) (e3)))) -> (~((op (e1) (e0)) = (op (e1) (e3)))) -> (~((op (e3) (e1)) = (op (e3) (e2)))) -> (((op (e0) (e2)) = (e1))\/(((op (e1) (e2)) = (e1))\/(((op (e2) (e2)) = (e1))\/((op (e3) (e2)) = (e1))))) -> (~((op (e0) (e2)) = (op (e3) (e2)))) -> (((op (e3) (e0)) = (e1))\/(((op (e3) (e1)) = (e1))\/(((op (e3) (e2)) = (e1))\/((op (e3) (e3)) = (e1))))) -> (((op (e0) (e2)) = (e0))\/(((op (e1) (e2)) = (e0))\/(((op (e2) (e2)) = (e0))\/((op (e3) (e2)) = (e0))))) -> (~((op (e1) (e1)) = (e3))) -> ((op (e1) (e0)) = (e1)) -> (~((e1) = (e3))) -> (~((op (e0) (e0)) = (e1))) -> False). % 15.48/15.62 do 0 intro. intros zenon_H8f zenon_Hc9 zenon_Hca zenon_H2d zenon_H52 zenon_H7d zenon_H2e zenon_H27c zenon_H160 zenon_H236 zenon_H154 zenon_H44 zenon_Hb4 zenon_Hb1 zenon_H11e zenon_H144 zenon_H199 zenon_H12d zenon_H157 zenon_H290 zenon_H1c3 zenon_H8b zenon_H90 zenon_H1df zenon_H12a zenon_H20 zenon_H25b zenon_H1d3 zenon_H166 zenon_H1d4 zenon_H87 zenon_Hce zenon_Haa zenon_H294 zenon_H1e2 zenon_H1e3 zenon_H1d2 zenon_Hd7 zenon_H1d8 zenon_H10e zenon_H1cd zenon_Hf1 zenon_H1c5 zenon_H237 zenon_H9e zenon_H5e zenon_Hd3 zenon_H6a zenon_Ha7 zenon_H244 zenon_Hb7 zenon_H1f5 zenon_H13c zenon_H1a2 zenon_H4b zenon_H173 zenon_H175 zenon_H23 zenon_Heb zenon_H84 zenon_H80 zenon_H8e zenon_He6 zenon_Hde zenon_H28 zenon_H36 zenon_H58 zenon_H1b3 zenon_Hbb zenon_H42 zenon_Hbe zenon_H10f zenon_H1d0 zenon_H1e4 zenon_H251 zenon_H295 zenon_H16c zenon_H10c zenon_H22e zenon_H121 zenon_H28a zenon_H1cf zenon_H135 zenon_H11b zenon_H140 zenon_H146 zenon_H16f zenon_H182 zenon_Hd8 zenon_Ha3 zenon_H45. % 15.48/15.62 apply (zenon_or_s _ _ zenon_Haa); [ zenon_intro zenon_H2f | zenon_intro zenon_H35 ]. % 15.48/15.62 apply (zenon_or_s _ _ zenon_H1c3); [ zenon_intro zenon_H30 | zenon_intro zenon_H124 ]. % 15.48/15.62 apply (zenon_or_s _ _ zenon_H10c); [ zenon_intro zenon_H104 | zenon_intro zenon_H10a ]. % 15.48/15.62 apply (zenon_or_s _ _ zenon_H10e); [ zenon_intro zenon_H3d | zenon_intro zenon_H106 ]. % 15.48/15.62 apply (zenon_or_s _ _ zenon_H44); [ zenon_intro zenon_H47 | zenon_intro zenon_H46 ]. % 15.48/15.62 exact (zenon_H45 zenon_H47). % 15.48/15.62 apply (zenon_or_s _ _ zenon_H46); [ zenon_intro zenon_H22 | zenon_intro zenon_H48 ]. % 15.48/15.62 apply (zenon_L1014_); trivial. % 15.48/15.62 apply (zenon_or_s _ _ zenon_H48); [ zenon_intro zenon_H29 | zenon_intro zenon_H37 ]. % 15.48/15.62 apply (zenon_L1009_); trivial. % 15.48/15.62 apply (zenon_L73_); trivial. % 15.48/15.62 apply (zenon_L153_); trivial. % 15.48/15.62 apply (zenon_L102_); trivial. % 15.48/15.62 apply (zenon_L1010_); trivial. % 15.48/15.62 apply (zenon_L794_); trivial. % 15.48/15.62 (* end of lemma zenon_L1015_ *) % 15.48/15.62 assert (zenon_L1016_ : (~((op (e3) (e3)) = (e1))) -> (~((op (e1) (e1)) = (e2))) -> (~((op (e1) (e0)) = (op (e3) (e0)))) -> (((op (e3) (e0)) = (e1))\/(((op (e3) (e1)) = (e1))\/(((op (e3) (e2)) = (e1))\/((op (e3) (e3)) = (e1))))) -> (((op (e0) (e3)) = (e1))\/(((op (e1) (e3)) = (e1))\/(((op (e2) (e3)) = (e1))\/((op (e3) (e3)) = (e1))))) -> (~((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)) = (e2))) -> (~((op (e2) (e2)) = (e1))) -> (((op (e0) (e2)) = (e2))\/(((op (e1) (e2)) = (e2))\/(((op (e2) (e2)) = (e2))\/((op (e3) (e2)) = (e2))))) -> (~((op (e0) (op (e2) (e0))) = (op (e2) (e0)))) -> ((op (e1) (e2)) = (e3)) -> (~((op (e2) (e2)) = (e2))) -> (((op (e0) (e2)) = (e0))\/(((op (e0) (e2)) = (e1))\/(((op (e0) (e2)) = (e2))\/((op (e0) (e2)) = (e3))))) -> ((~((op (e1) (e1)) = (e0)))\/((op (e1) (e0)) = (e1))) -> (~((op (e1) (e2)) = (op (e1) (e3)))) -> ((~((op (e3) (e3)) = (e0)))\/((op (e3) (e0)) = (e3))) -> (~((op (e0) (e0)) = (e1))) -> (((op (e0) (e0)) = (e3))\/(((op (e1) (e0)) = (e3))\/(((op (e2) (e0)) = (e3))\/((op (e3) (e0)) = (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 (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)) = (op (e3) (e3)))) -> (~((op (e0) (e2)) = (op (e2) (e2)))) -> (~((op (e0) (e1)) = (op (e2) (e1)))) -> (~((op (e3) (op (e2) (e3))) = (op (e2) (e3)))) -> (((op (e2) (e0)) = (e3))\/(((op (e2) (e1)) = (e3))\/(((op (e2) (e2)) = (e3))\/((op (e2) (e3)) = (e3))))) -> (((op (e0) (e0)) = (e2))\/(((op (e0) (e1)) = (e2))\/(((op (e0) (e2)) = (e2))\/((op (e0) (e3)) = (e2))))) -> (~((op (e0) (e3)) = (op (e1) (e3)))) -> (((op (e1) (e0)) = (e2))\/(((op (e1) (e1)) = (e2))\/(((op (e1) (e2)) = (e2))\/((op (e1) (e3)) = (e2))))) -> (((op (e0) (e0)) = (e2))\/(((op (e1) (e0)) = (e2))\/(((op (e2) (e0)) = (e2))\/((op (e3) (e0)) = (e2))))) -> (~((op (e0) (e1)) = (op (e1) (e1)))) -> (((op (e0) (e2)) = (e3))\/(((op (e1) (e2)) = (e3))\/(((op (e2) (e2)) = (e3))\/((op (e3) (e2)) = (e3))))) -> (~((op (e3) (e2)) = (op (e3) (e3)))) -> (~((e0) = (e3))) -> (((op (e0) (e1)) = (e2))\/(((op (e1) (e1)) = (e2))\/(((op (e2) (e1)) = (e2))\/((op (e3) (e1)) = (e2))))) -> (~((op (e2) (e1)) = (op (e3) (e1)))) -> (((op (e2) (e0)) = (e0))\/(((op (e2) (e1)) = (e0))\/(((op (e2) (e2)) = (e0))\/((op (e2) (e3)) = (e0))))) -> (((op (e2) (e0)) = (e1))\/(((op (e2) (e1)) = (e1))\/(((op (e2) (e2)) = (e1))\/((op (e2) (e3)) = (e1))))) -> (~((op (e1) (e3)) = (op (e2) (e3)))) -> (~((e1) = (e2))) -> (((op (e0) (e3)) = (e0))\/(((op (e1) (e3)) = (e0))\/(((op (e2) (e3)) = (e0))\/((op (e3) (e3)) = (e0))))) -> (~((e0) = (e2))) -> (~((e0) = (e1))) -> (~((op (e0) (e2)) = (op (e0) (e3)))) -> (((op (e2) (e0)) = (e2))\/(((op (e2) (e1)) = (e2))\/(((op (e2) (e2)) = (e2))\/((op (e2) (e3)) = (e2))))) -> (((op (e1) (e0)) = (e1))\/(((op (e1) (e1)) = (e1))\/(((op (e1) (e2)) = (e1))\/((op (e1) (e3)) = (e1))))) -> (((op (e0) (e0)) = (e1))\/(((op (e1) (e0)) = (e1))\/(((op (e2) (e0)) = (e1))\/((op (e3) (e0)) = (e1))))) -> (~((op (e1) (e0)) = (op (e1) (e3)))) -> ((~((op (e3) (e3)) = (e2)))\/((op (e3) (e2)) = (e3))) -> ((~((op (e1) (e1)) = (e1)))\/((op (e1) (e1)) = (e1))) -> (~((op (e1) (e0)) = (op (e1) (e1)))) -> ((~((op (e1) (e1)) = (e3)))\/((op (e1) (e3)) = (e1))) -> ((~((op (e2) (e2)) = (e1)))\/((op (e2) (e1)) = (e2))) -> (~((op (e2) (e1)) = (op (e2) (e3)))) -> (~((op (e2) (op (e2) (e2))) = (op (e2) (e2)))) -> ((~((op (e2) (e2)) = (e2)))\/((op (e2) (e2)) = (e2))) -> ((~((op (e2) (e2)) = (e0)))\/((op (e2) (e0)) = (e2))) -> (~((op (e1) (e0)) = (op (e1) (e2)))) -> ((~((op (e1) (e1)) = (e2)))\/((op (e1) (e2)) = (e1))) -> (((op (e1) (e3)) = (e0))\/(((op (e1) (e3)) = (e1))\/(((op (e1) (e3)) = (e2))\/((op (e1) (e3)) = (e3))))) -> (~((op (e0) (e0)) = (e0))) -> (((op (e0) (e0)) = (e0))\/(((op (e0) (e0)) = (e1))\/(((op (e0) (e0)) = (e2))\/((op (e0) (e0)) = (e3))))) -> (((op (e3) (e0)) = (e2))\/(((op (e3) (e1)) = (e2))\/(((op (e3) (e2)) = (e2))\/((op (e3) (e3)) = (e2))))) -> (~((op (e1) (e3)) = (op (e3) (e3)))) -> ((~((op (e2) (e2)) = (e3)))\/((op (e2) (e3)) = (e2))) -> (~((op (e1) (op (e2) (e1))) = (op (e2) (e1)))) -> (~((op (e2) (e1)) = (op (e2) (e2)))) -> (~((op (e3) (e1)) = (op (e3) (e3)))) -> (((op (e0) (e1)) = (e3))\/(((op (e1) (e1)) = (e3))\/(((op (e2) (e1)) = (e3))\/((op (e3) (e1)) = (e3))))) -> (((op (e0) (e1)) = (e0))\/(((op (e1) (e1)) = (e0))\/(((op (e2) (e1)) = (e0))\/((op (e3) (e1)) = (e0))))) -> (~((op (e1) (e1)) = (op (e1) (e3)))) -> (~((op (e1) (e1)) = (op (e2) (e1)))) -> (~((op (e0) (e3)) = (op (e2) (e3)))) -> (((op (e0) (e0)) = (e1))\/(((op (e0) (e1)) = (e1))\/(((op (e0) (e2)) = (e1))\/((op (e0) (e3)) = (e1))))) -> (~((op (e2) (e0)) = (op (e2) (e1)))) -> ((~((op (e0) (e0)) = (e3)))\/((op (e0) (e3)) = (e0))) -> (~((op (e0) (e2)) = (op (e3) (e2)))) -> (((op (e1) (e0)) = (e3))\/(((op (e1) (e1)) = (e3))\/(((op (e1) (e2)) = (e3))\/((op (e1) (e3)) = (e3))))) -> (~((e1) = (e3))) -> ((op (e1) (e0)) = (e1)) -> (~((op (e1) (e1)) = (e3))) -> (~((op (e0) (e2)) = (op (e1) (e2)))) -> (((op (e0) (e3)) = (e2))\/(((op (e1) (e3)) = (e2))\/(((op (e2) (e3)) = (e2))\/((op (e3) (e3)) = (e2))))) -> (~((op (e0) (e1)) = (op (e0) (e3)))) -> ((op (e0) (e1)) = (e2)) -> (~((e2) = (e3))) -> ((op (e2) (e0)) = (e2)) -> (~((op (e2) (e0)) = (op (e2) (e3)))) -> (~((op (e3) (e3)) = (e2))) -> False). % 15.48/15.62 do 0 intro. intros zenon_H104 zenon_Hd6 zenon_H22e zenon_H146 zenon_H121 zenon_H135 zenon_H11b zenon_H8f zenon_H52 zenon_H27c zenon_H295 zenon_H88 zenon_H2f zenon_H251 zenon_H1e4 zenon_H1d0 zenon_H10f zenon_H45 zenon_Hbe zenon_H42 zenon_Hbb zenon_H2d zenon_H1b3 zenon_H58 zenon_H36 zenon_H28 zenon_Hde zenon_H28a zenon_He6 zenon_H8e zenon_H80 zenon_H84 zenon_Heb zenon_H23 zenon_H175 zenon_H173 zenon_H4b zenon_H1a2 zenon_H13c zenon_H1f5 zenon_Hb7 zenon_H244 zenon_Ha7 zenon_Hd3 zenon_H5e zenon_H9e zenon_Hc9 zenon_H237 zenon_H1c5 zenon_Hf1 zenon_H1cf zenon_H10e zenon_H1d8 zenon_Hd7 zenon_H1d2 zenon_H1e3 zenon_H1e2 zenon_H294 zenon_Haa zenon_H1d4 zenon_H166 zenon_H1d3 zenon_H25b zenon_H20 zenon_H12a zenon_H1df zenon_H8b zenon_H1c3 zenon_H290 zenon_H157 zenon_H12d zenon_H199 zenon_H144 zenon_H11e zenon_Hb1 zenon_Hb4 zenon_H44 zenon_H154 zenon_H236 zenon_H140 zenon_H90 zenon_Ha3 zenon_Hd8 zenon_H182 zenon_H87 zenon_H160 zenon_H1cd zenon_H5d zenon_H6a zenon_Hdd zenon_Hce zenon_H3d. % 15.48/15.62 apply (zenon_or_s _ _ zenon_H11b); [ zenon_intro zenon_H29 | zenon_intro zenon_H11c ]. % 15.48/15.62 apply (zenon_L809_); trivial. % 15.48/15.62 apply (zenon_or_s _ _ zenon_H11c); [ zenon_intro zenon_H117 | zenon_intro zenon_H11d ]. % 15.48/15.62 apply (zenon_L196_); trivial. % 15.48/15.62 apply (zenon_or_s _ _ zenon_H11d); [ zenon_intro zenon_H2a | zenon_intro zenon_H119 ]. % 15.48/15.62 exact (zenon_H52 zenon_H2a). % 15.48/15.62 apply (zenon_L1008_); trivial. % 15.48/15.62 (* end of lemma zenon_L1016_ *) % 15.48/15.62 assert (zenon_L1017_ : (~((op (e0) (e2)) = (op (e1) (e2)))) -> (~((op (e1) (e1)) = (e3))) -> ((op (e1) (e0)) = (e1)) -> (~((e1) = (e3))) -> (((op (e1) (e0)) = (e3))\/(((op (e1) (e1)) = (e3))\/(((op (e1) (e2)) = (e3))\/((op (e1) (e3)) = (e3))))) -> (~((op (e0) (e2)) = (op (e3) (e2)))) -> ((~((op (e0) (e0)) = (e3)))\/((op (e0) (e3)) = (e0))) -> (~((op (e2) (e0)) = (op (e2) (e1)))) -> (((op (e0) (e0)) = (e1))\/(((op (e0) (e1)) = (e1))\/(((op (e0) (e2)) = (e1))\/((op (e0) (e3)) = (e1))))) -> (~((op (e0) (e3)) = (op (e2) (e3)))) -> (~((op (e1) (e1)) = (op (e2) (e1)))) -> (~((op (e1) (e1)) = (op (e1) (e3)))) -> (((op (e0) (e1)) = (e0))\/(((op (e1) (e1)) = (e0))\/(((op (e2) (e1)) = (e0))\/((op (e3) (e1)) = (e0))))) -> (((op (e0) (e1)) = (e3))\/(((op (e1) (e1)) = (e3))\/(((op (e2) (e1)) = (e3))\/((op (e3) (e1)) = (e3))))) -> (~((op (e3) (e1)) = (op (e3) (e3)))) -> (~((op (e2) (e1)) = (op (e2) (e2)))) -> (~((op (e1) (op (e2) (e1))) = (op (e2) (e1)))) -> ((~((op (e2) (e2)) = (e3)))\/((op (e2) (e3)) = (e2))) -> (~((op (e1) (e3)) = (op (e3) (e3)))) -> (((op (e3) (e0)) = (e2))\/(((op (e3) (e1)) = (e2))\/(((op (e3) (e2)) = (e2))\/((op (e3) (e3)) = (e2))))) -> (((op (e0) (e0)) = (e0))\/(((op (e0) (e0)) = (e1))\/(((op (e0) (e0)) = (e2))\/((op (e0) (e0)) = (e3))))) -> (~((op (e0) (e0)) = (e0))) -> (((op (e1) (e3)) = (e0))\/(((op (e1) (e3)) = (e1))\/(((op (e1) (e3)) = (e2))\/((op (e1) (e3)) = (e3))))) -> ((~((op (e1) (e1)) = (e2)))\/((op (e1) (e2)) = (e1))) -> (~((op (e1) (e0)) = (op (e1) (e2)))) -> ((~((op (e2) (e2)) = (e0)))\/((op (e2) (e0)) = (e2))) -> ((~((op (e2) (e2)) = (e2)))\/((op (e2) (e2)) = (e2))) -> (~((op (e2) (op (e2) (e2))) = (op (e2) (e2)))) -> (~((op (e2) (e1)) = (op (e2) (e3)))) -> ((~((op (e2) (e2)) = (e1)))\/((op (e2) (e1)) = (e2))) -> ((~((op (e1) (e1)) = (e3)))\/((op (e1) (e3)) = (e1))) -> (~((op (e1) (e0)) = (op (e1) (e1)))) -> ((~((op (e1) (e1)) = (e1)))\/((op (e1) (e1)) = (e1))) -> ((~((op (e3) (e3)) = (e2)))\/((op (e3) (e2)) = (e3))) -> (~((op (e1) (e0)) = (op (e1) (e3)))) -> (((op (e0) (e0)) = (e1))\/(((op (e1) (e0)) = (e1))\/(((op (e2) (e0)) = (e1))\/((op (e3) (e0)) = (e1))))) -> (((op (e1) (e0)) = (e1))\/(((op (e1) (e1)) = (e1))\/(((op (e1) (e2)) = (e1))\/((op (e1) (e3)) = (e1))))) -> (((op (e2) (e0)) = (e2))\/(((op (e2) (e1)) = (e2))\/(((op (e2) (e2)) = (e2))\/((op (e2) (e3)) = (e2))))) -> (~((op (e0) (e2)) = (op (e0) (e3)))) -> (~((e0) = (e1))) -> (~((e0) = (e2))) -> (((op (e0) (e3)) = (e0))\/(((op (e1) (e3)) = (e0))\/(((op (e2) (e3)) = (e0))\/((op (e3) (e3)) = (e0))))) -> (~((e1) = (e2))) -> (~((op (e1) (e3)) = (op (e2) (e3)))) -> (((op (e2) (e0)) = (e1))\/(((op (e2) (e1)) = (e1))\/(((op (e2) (e2)) = (e1))\/((op (e2) (e3)) = (e1))))) -> (((op (e2) (e0)) = (e0))\/(((op (e2) (e1)) = (e0))\/(((op (e2) (e2)) = (e0))\/((op (e2) (e3)) = (e0))))) -> (~((op (e2) (e1)) = (op (e3) (e1)))) -> (((op (e0) (e1)) = (e2))\/(((op (e1) (e1)) = (e2))\/(((op (e2) (e1)) = (e2))\/((op (e3) (e1)) = (e2))))) -> (~((e0) = (e3))) -> (~((op (e3) (e2)) = (op (e3) (e3)))) -> (((op (e0) (e2)) = (e3))\/(((op (e1) (e2)) = (e3))\/(((op (e2) (e2)) = (e3))\/((op (e3) (e2)) = (e3))))) -> (~((op (e0) (e1)) = (op (e1) (e1)))) -> (((op (e0) (e0)) = (e2))\/(((op (e1) (e0)) = (e2))\/(((op (e2) (e0)) = (e2))\/((op (e3) (e0)) = (e2))))) -> (((op (e1) (e0)) = (e2))\/(((op (e1) (e1)) = (e2))\/(((op (e1) (e2)) = (e2))\/((op (e1) (e3)) = (e2))))) -> (~((op (e0) (e3)) = (op (e1) (e3)))) -> (((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 (e3) (op (e2) (e3))) = (op (e2) (e3)))) -> (~((op (e0) (e1)) = (op (e2) (e1)))) -> (~((op (e0) (e2)) = (op (e2) (e2)))) -> (~((op (e0) (e3)) = (op (e3) (e3)))) -> (((op (e0) (e0)) = (e3))\/(((op (e0) (e1)) = (e3))\/(((op (e0) (e2)) = (e3))\/((op (e0) (e3)) = (e3))))) -> (((op (e1) (e1)) = (e0))\/(((op (e1) (e1)) = (e1))\/(((op (e1) (e1)) = (e2))\/((op (e1) (e1)) = (e3))))) -> (((op (e2) (e2)) = (e0))\/(((op (e2) (e2)) = (e1))\/(((op (e2) (e2)) = (e2))\/((op (e2) (e2)) = (e3))))) -> (~((op (e3) (e0)) = (op (e3) (e3)))) -> ((op (e3) (e3)) = (e3)) -> (((op (e0) (e0)) = (e3))\/(((op (e1) (e0)) = (e3))\/(((op (e2) (e0)) = (e3))\/((op (e3) (e0)) = (e3))))) -> (~((op (e0) (e0)) = (e1))) -> ((~((op (e3) (e3)) = (e0)))\/((op (e3) (e0)) = (e3))) -> (~((op (e1) (e2)) = (op (e1) (e3)))) -> ((~((op (e1) (e1)) = (e0)))\/((op (e1) (e0)) = (e1))) -> (((op (e0) (e2)) = (e0))\/(((op (e0) (e2)) = (e1))\/(((op (e0) (e2)) = (e2))\/((op (e0) (e2)) = (e3))))) -> (~((op (e2) (e2)) = (e2))) -> (~((op (e0) (op (e2) (e0))) = (op (e2) (e0)))) -> (((op (e0) (e2)) = (e2))\/(((op (e1) (e2)) = (e2))\/(((op (e2) (e2)) = (e2))\/((op (e3) (e2)) = (e2))))) -> (~((op (e2) (e2)) = (e1))) -> (~((op (e0) (e0)) = (e2))) -> (((op (e0) (e2)) = (e1))\/(((op (e1) (e2)) = (e1))\/(((op (e2) (e2)) = (e1))\/((op (e3) (e2)) = (e1))))) -> (~((op (e3) (e1)) = (op (e3) (e2)))) -> (((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 (e1) (e0)) = (op (e3) (e0)))) -> (~((op (e1) (e1)) = (e2))) -> (~((op (e3) (e3)) = (e1))) -> (((op (e0) (e3)) = (e2))\/(((op (e1) (e3)) = (e2))\/(((op (e2) (e3)) = (e2))\/((op (e3) (e3)) = (e2))))) -> (~((op (e0) (e1)) = (op (e0) (e3)))) -> ((op (e0) (e1)) = (e2)) -> (~((e2) = (e3))) -> ((op (e2) (e0)) = (e2)) -> (~((op (e2) (e0)) = (op (e2) (e3)))) -> (~((op (e3) (e3)) = (e2))) -> False). % 15.48/15.62 do 0 intro. intros zenon_H87 zenon_H182 zenon_Hd8 zenon_Ha3 zenon_H90 zenon_H140 zenon_H236 zenon_H154 zenon_H44 zenon_Hb4 zenon_Hb1 zenon_H11e zenon_H144 zenon_H199 zenon_H12d zenon_H157 zenon_H290 zenon_H1c3 zenon_H8b zenon_H1df zenon_H12a zenon_H20 zenon_H25b zenon_H1d3 zenon_H166 zenon_H1d4 zenon_Haa zenon_H294 zenon_H1e2 zenon_H1e3 zenon_H1d2 zenon_Hd7 zenon_H1d8 zenon_H10e zenon_H1cf zenon_Hf1 zenon_H1c5 zenon_H237 zenon_Hc9 zenon_H9e zenon_H5e zenon_Hd3 zenon_Ha7 zenon_H244 zenon_Hb7 zenon_H1f5 zenon_H13c zenon_H1a2 zenon_H4b zenon_H173 zenon_H175 zenon_H23 zenon_Heb zenon_H84 zenon_H80 zenon_H8e zenon_He6 zenon_H28a zenon_Hde zenon_H28 zenon_H36 zenon_H58 zenon_H1b3 zenon_H2d zenon_Hbb zenon_H42 zenon_Hbe zenon_H45 zenon_H10f zenon_H1d0 zenon_H1e4 zenon_H251 zenon_H2f zenon_H295 zenon_H27c zenon_H52 zenon_H8f zenon_H11b zenon_H135 zenon_H121 zenon_H146 zenon_H22e zenon_Hd6 zenon_H104 zenon_H160 zenon_H1cd zenon_H5d zenon_H6a zenon_Hdd zenon_Hce zenon_H3d. % 15.48/15.62 apply (zenon_or_s _ _ zenon_H90); [ zenon_intro zenon_H69 | zenon_intro zenon_H94 ]. % 15.48/15.62 apply (zenon_L163_); trivial. % 15.48/15.62 apply (zenon_or_s _ _ zenon_H94); [ zenon_intro zenon_H96 | zenon_intro zenon_H95 ]. % 15.48/15.62 exact (zenon_H182 zenon_H96). % 15.48/15.62 apply (zenon_or_s _ _ zenon_H95); [ zenon_intro zenon_H88 | zenon_intro zenon_H8a ]. % 15.48/15.62 apply (zenon_L1016_); trivial. % 15.48/15.62 apply (zenon_L410_); trivial. % 15.48/15.62 (* end of lemma zenon_L1017_ *) % 15.48/15.62 assert (zenon_L1018_ : (~((op (e2) (e0)) = (op (e2) (e2)))) -> (~((op (e1) (e2)) = (op (e3) (e2)))) -> (~((op (e0) (e0)) = (e2))) -> (~((op (e0) (e2)) = (op (e0) (e3)))) -> ((op (e0) (e3)) = (e0)) -> (((op (e2) (e2)) = (e0))\/(((op (e2) (e2)) = (e1))\/(((op (e2) (e2)) = (e2))\/((op (e2) (e2)) = (e3))))) -> (~((op (e1) (e2)) = (op (e2) (e2)))) -> (((op (e0) (e2)) = (e2))\/(((op (e1) (e2)) = (e2))\/(((op (e2) (e2)) = (e2))\/((op (e3) (e2)) = (e2))))) -> (((op (e0) (e3)) = (e2))\/(((op (e1) (e3)) = (e2))\/(((op (e2) (e3)) = (e2))\/((op (e3) (e3)) = (e2))))) -> ((~((op (e0) (e0)) = (e3)))\/((op (e0) (e3)) = (e0))) -> (~((op (e2) (e0)) = (op (e2) (e1)))) -> (((op (e0) (e0)) = (e1))\/(((op (e0) (e1)) = (e1))\/(((op (e0) (e2)) = (e1))\/((op (e0) (e3)) = (e1))))) -> (~((op (e0) (e3)) = (op (e2) (e3)))) -> (~((op (e1) (e1)) = (op (e2) (e1)))) -> (~((op (e1) (e1)) = (op (e1) (e3)))) -> (((op (e0) (e1)) = (e0))\/(((op (e1) (e1)) = (e0))\/(((op (e2) (e1)) = (e0))\/((op (e3) (e1)) = (e0))))) -> (((op (e0) (e1)) = (e3))\/(((op (e1) (e1)) = (e3))\/(((op (e2) (e1)) = (e3))\/((op (e3) (e1)) = (e3))))) -> (~((op (e3) (e1)) = (op (e3) (e3)))) -> (~((op (e2) (e1)) = (op (e2) (e2)))) -> (~((op (e1) (op (e2) (e1))) = (op (e2) (e1)))) -> ((~((op (e2) (e2)) = (e3)))\/((op (e2) (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 (e3) (e0)) = (e2))\/(((op (e3) (e1)) = (e2))\/(((op (e3) (e2)) = (e2))\/((op (e3) (e3)) = (e2))))) -> (((op (e0) (e0)) = (e0))\/(((op (e0) (e0)) = (e1))\/(((op (e0) (e0)) = (e2))\/((op (e0) (e0)) = (e3))))) -> (~((op (e0) (e0)) = (e0))) -> (((op (e1) (e3)) = (e0))\/(((op (e1) (e3)) = (e1))\/(((op (e1) (e3)) = (e2))\/((op (e1) (e3)) = (e3))))) -> ((~((op (e1) (e1)) = (e2)))\/((op (e1) (e2)) = (e1))) -> (~((op (e1) (e0)) = (op (e1) (e2)))) -> ((~((op (e2) (e2)) = (e0)))\/((op (e2) (e0)) = (e2))) -> (~((op (e0) (e2)) = (op (e1) (e2)))) -> (~((op (e2) (e0)) = (op (e2) (e3)))) -> ((~((op (e2) (e2)) = (e2)))\/((op (e2) (e2)) = (e2))) -> (~((op (e2) (op (e2) (e2))) = (op (e2) (e2)))) -> (~((op (e2) (e1)) = (op (e2) (e3)))) -> ((~((op (e2) (e2)) = (e1)))\/((op (e2) (e1)) = (e2))) -> ((~((op (e1) (e1)) = (e3)))\/((op (e1) (e3)) = (e1))) -> (~((op (e1) (e0)) = (op (e1) (e1)))) -> ((~((op (e1) (e1)) = (e1)))\/((op (e1) (e1)) = (e1))) -> ((~((op (e3) (e3)) = (e2)))\/((op (e3) (e2)) = (e3))) -> (~((op (e0) (e1)) = (op (e0) (e3)))) -> (((op (e0) (e0)) = (e1))\/(((op (e1) (e0)) = (e1))\/(((op (e2) (e0)) = (e1))\/((op (e3) (e0)) = (e1))))) -> (((op (e1) (e0)) = (e1))\/(((op (e1) (e1)) = (e1))\/(((op (e1) (e2)) = (e1))\/((op (e1) (e3)) = (e1))))) -> (((op (e2) (e0)) = (e2))\/(((op (e2) (e1)) = (e2))\/(((op (e2) (e2)) = (e2))\/((op (e2) (e3)) = (e2))))) -> (~((e0) = (e1))) -> (~((e0) = (e2))) -> (((op (e0) (e3)) = (e0))\/(((op (e1) (e3)) = (e0))\/(((op (e2) (e3)) = (e0))\/((op (e3) (e3)) = (e0))))) -> (~((e2) = (e3))) -> (~((e1) = (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)) = (e0))\/(((op (e2) (e1)) = (e0))\/(((op (e2) (e2)) = (e0))\/((op (e2) (e3)) = (e0))))) -> (~((op (e2) (e1)) = (op (e3) (e1)))) -> (((op (e0) (e1)) = (e2))\/(((op (e1) (e1)) = (e2))\/(((op (e2) (e1)) = (e2))\/((op (e3) (e1)) = (e2))))) -> (~((e0) = (e3))) -> (~((op (e3) (e2)) = (op (e3) (e3)))) -> (((op (e0) (e2)) = (e3))\/(((op (e1) (e2)) = (e3))\/(((op (e2) (e2)) = (e3))\/((op (e3) (e2)) = (e3))))) -> (~((op (e0) (e1)) = (op (e1) (e1)))) -> (((op (e0) (e0)) = (e2))\/(((op (e1) (e0)) = (e2))\/(((op (e2) (e0)) = (e2))\/((op (e3) (e0)) = (e2))))) -> (((op (e1) (e0)) = (e2))\/(((op (e1) (e1)) = (e2))\/(((op (e1) (e2)) = (e2))\/((op (e1) (e3)) = (e2))))) -> (~((op (e0) (e3)) = (op (e1) (e3)))) -> (((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 (e0) (e1)) = (op (e2) (e1)))) -> (~((op (e0) (e2)) = (op (e2) (e2)))) -> (~((op (e0) (e3)) = (op (e3) (e3)))) -> (((op (e0) (e0)) = (e3))\/(((op (e0) (e1)) = (e3))\/(((op (e0) (e2)) = (e3))\/((op (e0) (e3)) = (e3))))) -> (((op (e1) (e1)) = (e0))\/(((op (e1) (e1)) = (e1))\/(((op (e1) (e1)) = (e2))\/((op (e1) (e1)) = (e3))))) -> (~((op (e3) (e0)) = (op (e3) (e3)))) -> ((op (e3) (e3)) = (e3)) -> (((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 (e1) (e2)) = (op (e1) (e3)))) -> ((~((op (e1) (e1)) = (e0)))\/((op (e1) (e0)) = (e1))) -> (((op (e0) (e2)) = (e0))\/(((op (e0) (e2)) = (e1))\/(((op (e0) (e2)) = (e2))\/((op (e0) (e2)) = (e3))))) -> (~((op (e0) (op (e2) (e0))) = (op (e2) (e0)))) -> (((op (e3) (e1)) = (e0))\/(((op (e3) (e1)) = (e1))\/(((op (e3) (e1)) = (e2))\/((op (e3) (e1)) = (e3))))) -> ((~((op (e3) (e3)) = (e1)))\/((op (e3) (e1)) = (e3))) -> (~((op (e1) (e0)) = (op (e3) (e0)))) -> (((op (e0) (e3)) = (e1))\/(((op (e1) (e3)) = (e1))\/(((op (e2) (e3)) = (e1))\/((op (e3) (e3)) = (e1))))) -> (~((op (e3) (op (e2) (e3))) = (op (e2) (e3)))) -> (~((op (e1) (e0)) = (op (e1) (e3)))) -> (~((op (e3) (e1)) = (op (e3) (e2)))) -> (((op (e0) (e2)) = (e1))\/(((op (e1) (e2)) = (e1))\/(((op (e2) (e2)) = (e1))\/((op (e3) (e2)) = (e1))))) -> (~((op (e0) (e2)) = (op (e3) (e2)))) -> (((op (e3) (e0)) = (e1))\/(((op (e3) (e1)) = (e1))\/(((op (e3) (e2)) = (e1))\/((op (e3) (e3)) = (e1))))) -> (((op (e0) (e2)) = (e0))\/(((op (e1) (e2)) = (e0))\/(((op (e2) (e2)) = (e0))\/((op (e3) (e2)) = (e0))))) -> ((op (e1) (e0)) = (e1)) -> (~((e1) = (e3))) -> (~((op (e0) (e0)) = (e1))) -> False). % 15.48/15.62 do 0 intro. intros zenon_H17a zenon_H17d zenon_H8f zenon_Hc9 zenon_Hca zenon_H2d zenon_H7d zenon_H27c zenon_H160 zenon_H236 zenon_H154 zenon_H44 zenon_Hb4 zenon_Hb1 zenon_H11e zenon_H144 zenon_H199 zenon_H12d zenon_H157 zenon_H290 zenon_H1c3 zenon_H8b zenon_H90 zenon_H1df zenon_H12a zenon_H20 zenon_H25b zenon_H1d3 zenon_H166 zenon_H1d4 zenon_H87 zenon_Hce zenon_Haa zenon_H294 zenon_H1e2 zenon_H1e3 zenon_H1d2 zenon_Hd7 zenon_H1d8 zenon_H10e zenon_H1cd zenon_Hf1 zenon_H1c5 zenon_H237 zenon_H9e zenon_H5e zenon_Hd3 zenon_H6a zenon_Ha7 zenon_H244 zenon_Hb7 zenon_H1f5 zenon_H13c zenon_H1a2 zenon_H4b zenon_H173 zenon_H175 zenon_H23 zenon_Heb zenon_H84 zenon_H80 zenon_H8e zenon_He6 zenon_Hde zenon_H28 zenon_H36 zenon_H58 zenon_H1b3 zenon_Hbb zenon_H42 zenon_Hbe zenon_H10f zenon_H1d0 zenon_H1e4 zenon_H251 zenon_H295 zenon_H16c zenon_H10c zenon_H22e zenon_H121 zenon_H28a zenon_H1cf zenon_H135 zenon_H11b zenon_H140 zenon_H146 zenon_H16f zenon_Hd8 zenon_Ha3 zenon_H45. % 15.48/15.62 apply (zenon_or_s _ _ zenon_H1d3); [ zenon_intro zenon_Hd6 | zenon_intro zenon_H117 ]. % 15.48/15.62 apply (zenon_or_s _ _ zenon_H1d2); [ zenon_intro zenon_H182 | zenon_intro zenon_H11f ]. % 15.48/15.62 apply (zenon_or_s _ _ zenon_H1d4); [ zenon_intro zenon_H2e | zenon_intro zenon_Hdd ]. % 15.48/15.62 apply (zenon_or_s _ _ zenon_H1e3); [ zenon_intro zenon_H52 | zenon_intro zenon_H156 ]. % 15.48/15.62 apply (zenon_L1015_); trivial. % 15.48/15.62 apply (zenon_L1003_); trivial. % 15.48/15.62 apply (zenon_or_s _ _ zenon_H1e3); [ zenon_intro zenon_H52 | zenon_intro zenon_H156 ]. % 15.48/15.62 apply (zenon_or_s _ _ zenon_Haa); [ zenon_intro zenon_H2f | zenon_intro zenon_H35 ]. % 15.48/15.62 apply (zenon_or_s _ _ zenon_H10c); [ zenon_intro zenon_H104 | zenon_intro zenon_H10a ]. % 15.48/15.62 apply (zenon_or_s _ _ zenon_H10e); [ zenon_intro zenon_H3d | zenon_intro zenon_H106 ]. % 15.48/15.62 apply (zenon_or_s _ _ zenon_H8e); [ zenon_intro zenon_H92 | zenon_intro zenon_H91 ]. % 15.48/15.62 exact (zenon_H8f zenon_H92). % 15.48/15.62 apply (zenon_or_s _ _ zenon_H91); [ zenon_intro zenon_H5d | zenon_intro zenon_H93 ]. % 15.48/15.62 apply (zenon_L1017_); trivial. % 15.48/15.62 apply (zenon_or_s _ _ zenon_H93); [ zenon_intro zenon_H63 | zenon_intro zenon_H81 ]. % 15.48/15.62 apply (zenon_L812_); trivial. % 15.48/15.62 apply (zenon_L113_); trivial. % 15.48/15.62 apply (zenon_L417_); trivial. % 15.48/15.62 apply (zenon_L102_); trivial. % 15.48/15.62 apply (zenon_L161_); trivial. % 15.48/15.62 apply (zenon_L284_); trivial. % 15.48/15.62 apply (zenon_L224_); trivial. % 15.48/15.62 apply (zenon_L248_); trivial. % 15.48/15.62 (* end of lemma zenon_L1018_ *) % 15.48/15.62 assert (zenon_L1019_ : ((~((op (e0) (e0)) = (e2)))\/((op (e0) (e2)) = (e0))) -> (~((op (e0) (e1)) = (op (e0) (e2)))) -> ((~((op (e1) (e1)) = (e1)))\/((op (e1) (e1)) = (e1))) -> (~((op (e1) (e1)) = (op (e1) (e3)))) -> (~((op (e0) (e1)) = (op (e0) (e3)))) -> (((op (e0) (e1)) = (e2))\/(((op (e1) (e1)) = (e2))\/(((op (e2) (e1)) = (e2))\/((op (e3) (e1)) = (e2))))) -> (~((op (e0) (e3)) = (op (e2) (e3)))) -> (~((op (e1) (e1)) = (op (e2) (e1)))) -> (((op (e0) (e0)) = (e1))\/(((op (e0) (e1)) = (e1))\/(((op (e0) (e2)) = (e1))\/((op (e0) (e3)) = (e1))))) -> (~((op (e1) (e1)) = (op (e1) (e2)))) -> ((~((op (e1) (e1)) = (e3)))\/((op (e1) (e3)) = (e1))) -> ((~((op (e2) (e2)) = (e1)))\/((op (e2) (e1)) = (e2))) -> ((~((op (e3) (e3)) = (e0)))\/((op (e3) (e0)) = (e3))) -> (~((op (e3) (e0)) = (op (e3) (e3)))) -> (~((e0) = (e2))) -> (~((e2) = (e3))) -> (((op (e0) (e1)) = (e3))\/(((op (e1) (e1)) = (e3))\/(((op (e2) (e1)) = (e3))\/((op (e3) (e1)) = (e3))))) -> (~((op (e3) (e1)) = (op (e3) (e3)))) -> (((op (e0) (e3)) = (e0))\/(((op (e1) (e3)) = (e0))\/(((op (e2) (e3)) = (e0))\/((op (e3) (e3)) = (e0))))) -> (~((op (e2) (e0)) = (op (e2) (e3)))) -> (~((e0) = (e1))) -> (~((op (e0) (e1)) = (op (e2) (e1)))) -> (((op (e2) (e0)) = (e1))\/(((op (e2) (e1)) = (e1))\/(((op (e2) (e2)) = (e1))\/((op (e2) (e3)) = (e1))))) -> (~((op (e1) (e3)) = (op (e2) (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))))) -> (~((e1) = (e2))) -> (~((e1) = (e3))) -> (~((op (e3) (op (e2) (e3))) = (op (e2) (e3)))) -> (((op (e2) (e0)) = (e3))\/(((op (e2) (e1)) = (e3))\/(((op (e2) (e2)) = (e3))\/((op (e2) (e3)) = (e3))))) -> (((op (e2) (e0)) = (e0))\/(((op (e2) (e1)) = (e0))\/(((op (e2) (e2)) = (e0))\/((op (e2) (e3)) = (e0))))) -> (((op (e0) (e0)) = (e2))\/(((op (e0) (e1)) = (e2))\/(((op (e0) (e2)) = (e2))\/((op (e0) (e3)) = (e2))))) -> (~((op (e2) (e1)) = (op (e2) (e3)))) -> ((~((op (e2) (e2)) = (e3)))\/((op (e2) (e3)) = (e2))) -> (((op (e0) (e0)) = (e3))\/(((op (e0) (e1)) = (e3))\/(((op (e0) (e2)) = (e3))\/((op (e0) (e3)) = (e3))))) -> ((op (e3) (e3)) = (e3)) -> (~((op (e0) (e3)) = (op (e3) (e3)))) -> (~((op (e0) (e2)) = (op (e2) (e2)))) -> (((op (e2) (e2)) = (e0))\/(((op (e2) (e2)) = (e1))\/(((op (e2) (e2)) = (e2))\/((op (e2) (e2)) = (e3))))) -> (~((e0) = (e3))) -> (~((op (e2) (op (e2) (e2))) = (op (e2) (e2)))) -> ((~((op (e2) (e2)) = (e2)))\/((op (e2) (e2)) = (e2))) -> (~((op (e2) (e0)) = (op (e2) (e1)))) -> (((op (e0) (e0)) = (e0))\/(((op (e0) (e0)) = (e1))\/(((op (e0) (e0)) = (e2))\/((op (e0) (e0)) = (e3))))) -> (~((op (e0) (e0)) = (e0))) -> ((~((op (e2) (e2)) = (e0)))\/((op (e2) (e0)) = (e2))) -> (~((op (e0) (e1)) = (op (e1) (e1)))) -> ((op (e0) (e1)) = (e0)) -> (((op (e1) (e1)) = (e0))\/(((op (e1) (e1)) = (e1))\/(((op (e1) (e1)) = (e2))\/((op (e1) (e1)) = (e3))))) -> (~((op (e1) (e2)) = (op (e1) (e3)))) -> (((op (e0) (e0)) = (e3))\/(((op (e1) (e0)) = (e3))\/(((op (e2) (e0)) = (e3))\/((op (e3) (e0)) = (e3))))) -> (((op (e1) (e0)) = (e2))\/(((op (e1) (e1)) = (e2))\/(((op (e1) (e2)) = (e2))\/((op (e1) (e3)) = (e2))))) -> (~((op (e2) (e0)) = (op (e2) (e2)))) -> ((~((op (e1) (e1)) = (e2)))\/((op (e1) (e2)) = (e1))) -> ((~((op (e0) (e0)) = (e3)))\/((op (e0) (e3)) = (e0))) -> False). % 15.48/15.62 do 0 intro. intros zenon_H24a zenon_H23e zenon_H1d8 zenon_H11e zenon_H1cd zenon_H1a2 zenon_Hb4 zenon_Hb1 zenon_H44 zenon_H116 zenon_H1d2 zenon_H1e3 zenon_H10f zenon_Hbb zenon_H5e zenon_H6a zenon_H199 zenon_H12d zenon_Hd3 zenon_Hce zenon_H9e zenon_Hde zenon_Hb7 zenon_H244 zenon_H80 zenon_H8b zenon_H25b zenon_Ha7 zenon_Ha3 zenon_H28a zenon_He6 zenon_H1f5 zenon_H8e zenon_H1e2 zenon_H1c3 zenon_H58 zenon_H42 zenon_H36 zenon_H28 zenon_H2d zenon_H4b zenon_H294 zenon_Haa zenon_H154 zenon_H12a zenon_H20 zenon_H1d4 zenon_H23 zenon_H49 zenon_H1b3 zenon_H1d0 zenon_Hbe zenon_H84 zenon_H17a zenon_H1d3 zenon_H236. % 15.48/15.62 apply (zenon_or_s _ _ zenon_H24a); [ zenon_intro zenon_H8f | zenon_intro zenon_Hab ]. % 15.48/15.62 apply (zenon_L939_); trivial. % 15.48/15.62 apply (zenon_L485_); trivial. % 15.48/15.62 (* end of lemma zenon_L1019_ *) % 15.48/15.62 assert (zenon_L1020_ : (((op (e0) (e0)) = (e2))\/(((op (e1) (e0)) = (e2))\/(((op (e2) (e0)) = (e2))\/((op (e3) (e0)) = (e2))))) -> (~((op (e0) (e0)) = (e2))) -> ((op (e0) (e3)) = (e1)) -> (((op (e1) (e0)) = (e3))\/(((op (e1) (e1)) = (e3))\/(((op (e1) (e2)) = (e3))\/((op (e1) (e3)) = (e3))))) -> (~((e2) = (e3))) -> (~((op (e1) (e1)) = (e3))) -> (~((op (e0) (e2)) = (op (e1) (e2)))) -> (~((op (e1) (e3)) = (op (e3) (e3)))) -> (~((op (e0) (e3)) = (op (e2) (e3)))) -> (~((op (e2) (e2)) = (e1))) -> (~((op (e1) (e1)) = (op (e2) (e1)))) -> ((op (e1) (e1)) = (e1)) -> (((op (e2) (e0)) = (e1))\/(((op (e2) (e1)) = (e1))\/(((op (e2) (e2)) = (e1))\/((op (e2) (e3)) = (e1))))) -> (((op (e0) (e0)) = (e3))\/(((op (e0) (e1)) = (e3))\/(((op (e0) (e2)) = (e3))\/((op (e0) (e3)) = (e3))))) -> (~((op (e0) (e0)) = (e3))) -> (~((op (e0) (e1)) = (op (e3) (e1)))) -> ((op (e3) (e1)) = (e3)) -> (~((e1) = (e3))) -> ((op (e3) (e3)) = (e3)) -> (~((op (e0) (e3)) = (op (e3) (e3)))) -> (~((op (e0) (e1)) = (op (e1) (e1)))) -> (~((op (e0) (e0)) = (e1))) -> (((op (e0) (e0)) = (e1))\/(((op (e0) (e1)) = (e1))\/(((op (e0) (e2)) = (e1))\/((op (e0) (e3)) = (e1))))) -> ((op (e3) (e0)) = (e1)) -> (~((e1) = (e2))) -> False). % 15.48/15.62 do 0 intro. intros zenon_Heb zenon_H8f zenon_H37 zenon_H90 zenon_H6a zenon_H182 zenon_H87 zenon_H8b zenon_Hb4 zenon_H52 zenon_Hb1 zenon_H21 zenon_Hb7 zenon_H58 zenon_H59 zenon_H138 zenon_H10a zenon_Ha3 zenon_H42 zenon_H36 zenon_H23 zenon_H45 zenon_H44 zenon_Hee zenon_Ha7. % 15.48/15.62 apply (zenon_or_s _ _ zenon_Heb); [ zenon_intro zenon_H92 | zenon_intro zenon_Hec ]. % 15.48/15.62 exact (zenon_H8f zenon_H92). % 15.48/15.62 apply (zenon_or_s _ _ zenon_Hec); [ zenon_intro zenon_H68 | zenon_intro zenon_Hed ]. % 15.48/15.62 apply (zenon_L898_); trivial. % 15.48/15.62 apply (zenon_or_s _ _ zenon_Hed); [ zenon_intro zenon_Hdd | zenon_intro zenon_He9 ]. % 15.48/15.62 apply (zenon_L999_); trivial. % 15.48/15.62 apply (zenon_L122_); trivial. % 15.48/15.62 (* end of lemma zenon_L1020_ *) % 15.48/15.62 assert (zenon_L1021_ : (((op (e0) (e0)) = (e1))\/(((op (e1) (e0)) = (e1))\/(((op (e2) (e0)) = (e1))\/((op (e3) (e0)) = (e1))))) -> (~((op (e3) (op (e2) (e3))) = (op (e2) (e3)))) -> (~((op (e2) (e2)) = (e3))) -> (~((op (e2) (e1)) = (op (e3) (e1)))) -> (((op (e2) (e0)) = (e3))\/(((op (e2) (e1)) = (e3))\/(((op (e2) (e2)) = (e3))\/((op (e2) (e3)) = (e3))))) -> (((op (e0) (e0)) = (e2))\/(((op (e1) (e0)) = (e2))\/(((op (e2) (e0)) = (e2))\/((op (e3) (e0)) = (e2))))) -> (~((op (e0) (e0)) = (e2))) -> (((op (e1) (e0)) = (e3))\/(((op (e1) (e1)) = (e3))\/(((op (e1) (e2)) = (e3))\/((op (e1) (e3)) = (e3))))) -> (~((e2) = (e3))) -> (~((op (e1) (e1)) = (e3))) -> (~((op (e0) (e2)) = (op (e1) (e2)))) -> (~((op (e1) (e3)) = (op (e3) (e3)))) -> (~((op (e0) (e3)) = (op (e2) (e3)))) -> (~((op (e2) (e2)) = (e1))) -> (~((op (e1) (e1)) = (op (e2) (e1)))) -> ((op (e1) (e1)) = (e1)) -> (((op (e2) (e0)) = (e1))\/(((op (e2) (e1)) = (e1))\/(((op (e2) (e2)) = (e1))\/((op (e2) (e3)) = (e1))))) -> (((op (e0) (e0)) = (e3))\/(((op (e0) (e1)) = (e3))\/(((op (e0) (e2)) = (e3))\/((op (e0) (e3)) = (e3))))) -> (~((op (e0) (e0)) = (e3))) -> (~((op (e0) (e1)) = (op (e3) (e1)))) -> ((op (e3) (e1)) = (e3)) -> (~((e1) = (e3))) -> ((op (e3) (e3)) = (e3)) -> (~((op (e0) (e3)) = (op (e3) (e3)))) -> (~((op (e0) (e1)) = (op (e1) (e1)))) -> (~((op (e0) (e0)) = (e1))) -> (((op (e0) (e0)) = (e1))\/(((op (e0) (e1)) = (e1))\/(((op (e0) (e2)) = (e1))\/((op (e0) (e3)) = (e1))))) -> (~((e1) = (e2))) -> False). % 15.48/15.62 do 0 intro. intros zenon_Hf1 zenon_H28a zenon_H30 zenon_H13c zenon_He6 zenon_Heb zenon_H8f zenon_H90 zenon_H6a zenon_H182 zenon_H87 zenon_H8b zenon_Hb4 zenon_H52 zenon_Hb1 zenon_H21 zenon_Hb7 zenon_H58 zenon_H59 zenon_H138 zenon_H10a zenon_Ha3 zenon_H42 zenon_H36 zenon_H23 zenon_H45 zenon_H44 zenon_Ha7. % 15.48/15.62 apply (zenon_or_s _ _ zenon_H44); [ zenon_intro zenon_H47 | zenon_intro zenon_H46 ]. % 15.48/15.63 exact (zenon_H45 zenon_H47). % 15.48/15.63 apply (zenon_or_s _ _ zenon_H46); [ zenon_intro zenon_H22 | zenon_intro zenon_H48 ]. % 15.48/15.63 apply (zenon_L3_); trivial. % 15.48/15.63 apply (zenon_or_s _ _ zenon_H48); [ zenon_intro zenon_H29 | zenon_intro zenon_H37 ]. % 15.48/15.63 apply (zenon_L896_); trivial. % 15.48/15.63 apply (zenon_or_s _ _ zenon_Hf1); [ zenon_intro zenon_H47 | zenon_intro zenon_Hf4 ]. % 15.48/15.63 exact (zenon_H45 zenon_H47). % 15.48/15.63 apply (zenon_or_s _ _ zenon_Hf4); [ zenon_intro zenon_Hd8 | zenon_intro zenon_Hf5 ]. % 15.48/15.63 apply (zenon_L572_); trivial. % 15.48/15.63 apply (zenon_or_s _ _ zenon_Hf5); [ zenon_intro zenon_Hae | zenon_intro zenon_Hee ]. % 15.48/15.63 apply (zenon_L897_); trivial. % 15.48/15.63 apply (zenon_L1020_); trivial. % 15.48/15.63 (* end of lemma zenon_L1021_ *) % 15.48/15.63 assert (zenon_L1022_ : ((~((op (e3) (e3)) = (e2)))\/((op (e3) (e2)) = (e3))) -> (~((op (e1) (e2)) = (op (e3) (e2)))) -> (~((op (e0) (e0)) = (e1))) -> (~((op (e0) (e1)) = (op (e1) (e1)))) -> ((op (e1) (e1)) = (e1)) -> (((op (e1) (e0)) = (e0))\/(((op (e1) (e1)) = (e0))\/(((op (e1) (e2)) = (e0))\/((op (e1) (e3)) = (e0))))) -> (((op (e2) (e0)) = (e0))\/(((op (e2) (e1)) = (e0))\/(((op (e2) (e2)) = (e0))\/((op (e2) (e3)) = (e0))))) -> (((op (e3) (e0)) = (e2))\/(((op (e3) (e1)) = (e2))\/(((op (e3) (e2)) = (e2))\/((op (e3) (e3)) = (e2))))) -> (~((op (e0) (e2)) = (op (e0) (e3)))) -> (~((op (e0) (e2)) = (op (e3) (e2)))) -> (((op (e0) (e2)) = (e0))\/(((op (e0) (e2)) = (e1))\/(((op (e0) (e2)) = (e2))\/((op (e0) (e2)) = (e3))))) -> (~((op (e1) (e1)) = (op (e1) (e3)))) -> (((op (e1) (e3)) = (e0))\/(((op (e1) (e3)) = (e1))\/(((op (e1) (e3)) = (e2))\/((op (e1) (e3)) = (e3))))) -> (~((op (e0) (e0)) = (op (e0) (e3)))) -> (~((op (e0) (e3)) = (op (e2) (e3)))) -> (~((op (e0) (e3)) = (op (e1) (e3)))) -> (((op (e0) (e3)) = (e0))\/(((op (e0) (e3)) = (e1))\/(((op (e0) (e3)) = (e2))\/((op (e0) (e3)) = (e3))))) -> (~((op (e1) (e3)) = (op (e2) (e3)))) -> (((op (e0) (e3)) = (e1))\/(((op (e1) (e3)) = (e1))\/(((op (e2) (e3)) = (e1))\/((op (e3) (e3)) = (e1))))) -> (~((op (e2) (e2)) = (e0))) -> (~((e0) = (e2))) -> (~((op (e0) (e0)) = (op (e2) (e0)))) -> (~((op (e1) (e1)) = (e0))) -> ((op (e0) (e0)) = (e0)) -> (~((op (e0) (e0)) = (op (e1) (e0)))) -> (((op (e2) (e0)) = (e3))\/(((op (e2) (e1)) = (e3))\/(((op (e2) (e2)) = (e3))\/((op (e2) (e3)) = (e3))))) -> ((op (e3) (e3)) = (e3)) -> (~((op (e3) (op (e2) (e3))) = (op (e2) (e3)))) -> (~((op (e0) (e1)) = (op (e2) (e1)))) -> (~((e1) = (e3))) -> (~((op (e1) (e1)) = (e3))) -> (~((e2) = (e3))) -> ((op (e2) (e1)) = (e2)) -> (((op (e0) (e0)) = (e1))\/(((op (e0) (e1)) = (e1))\/(((op (e0) (e2)) = (e1))\/((op (e0) (e3)) = (e1))))) -> (~((op (e0) (e2)) = (op (e1) (e2)))) -> (~((op (e1) (e3)) = (op (e3) (e3)))) -> (((op (e1) (e0)) = (e3))\/(((op (e1) (e1)) = (e3))\/(((op (e1) (e2)) = (e3))\/((op (e1) (e3)) = (e3))))) -> (~((op (e2) (e1)) = (op (e3) (e1)))) -> (((op (e0) (e0)) = (e2))\/(((op (e1) (e0)) = (e2))\/(((op (e2) (e0)) = (e2))\/((op (e3) (e0)) = (e2))))) -> (~((e1) = (e2))) -> (~((op (e2) (e0)) = (op (e2) (e1)))) -> (~((op (e0) (e0)) = (e2))) -> (((op (e0) (e0)) = (e1))\/(((op (e1) (e0)) = (e1))\/(((op (e2) (e0)) = (e1))\/((op (e3) (e0)) = (e1))))) -> (~((op (e0) (e0)) = (e3))) -> (~((op (e0) (e1)) = (op (e3) (e1)))) -> (~((op (e0) (e3)) = (op (e3) (e3)))) -> (((op (e0) (e0)) = (e3))\/(((op (e0) (e1)) = (e3))\/(((op (e0) (e2)) = (e3))\/((op (e0) (e3)) = (e3))))) -> (((op (e0) (e1)) = (e3))\/(((op (e1) (e1)) = (e3))\/(((op (e2) (e1)) = (e3))\/((op (e3) (e1)) = (e3))))) -> (~((op (e1) (e0)) = (op (e1) (e1)))) -> (((op (e0) (e3)) = (e2))\/(((op (e1) (e3)) = (e2))\/(((op (e2) (e3)) = (e2))\/((op (e3) (e3)) = (e2))))) -> ((~((op (e1) (e1)) = (e2)))\/((op (e1) (e2)) = (e1))) -> (~((op (e1) (e0)) = (op (e1) (e2)))) -> ((~((op (e2) (e2)) = (e0)))\/((op (e2) (e0)) = (e2))) -> ((~((op (e2) (e2)) = (e2)))\/((op (e2) (e2)) = (e2))) -> (((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)) = (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 (e1) (e2)) = (op (e2) (e2)))) -> ((~((op (e3) (e3)) = (e1)))\/((op (e3) (e1)) = (e3))) -> (((op (e0) (e0)) = (e3))\/(((op (e1) (e0)) = (e3))\/(((op (e2) (e0)) = (e3))\/((op (e3) (e0)) = (e3))))) -> ((~((op (e2) (e2)) = (e3)))\/((op (e2) (e3)) = (e2))) -> (~((op (e2) (e0)) = (op (e2) (e3)))) -> (((op (e2) (e2)) = (e0))\/(((op (e2) (e2)) = (e1))\/(((op (e2) (e2)) = (e2))\/((op (e2) (e2)) = (e3))))) -> (((op (e1) (e1)) = (e0))\/(((op (e1) (e1)) = (e1))\/(((op (e1) (e1)) = (e2))\/((op (e1) (e1)) = (e3))))) -> (((op (e2) (e0)) = (e1))\/(((op (e2) (e1)) = (e1))\/(((op (e2) (e2)) = (e1))\/((op (e2) (e3)) = (e1))))) -> (~((op (e1) (op (e2) (e1))) = (op (e2) (e1)))) -> (~((op (e2) (e1)) = (op (e2) (e2)))) -> (~((op (e2) (e1)) = (op (e2) (e3)))) -> ((~((op (e2) (e2)) = (e1)))\/((op (e2) (e1)) = (e2))) -> ((~((op (e1) (e1)) = (e3)))\/((op (e1) (e3)) = (e1))) -> ((~((op (e1) (e1)) = (e1)))\/((op (e1) (e1)) = (e1))) -> False). % 15.48/15.63 do 0 intro. intros zenon_H10e zenon_H17d zenon_H45 zenon_H23 zenon_H21 zenon_H163 zenon_H1f5 zenon_H1df zenon_Hc9 zenon_H140 zenon_H251 zenon_H11e zenon_H25b zenon_H24f zenon_Hb4 zenon_H80 zenon_H254 zenon_H244 zenon_H121 zenon_H2e zenon_H5e zenon_H258 zenon_H145 zenon_H1f zenon_H24c zenon_He6 zenon_H42 zenon_H28a zenon_Hde zenon_Ha3 zenon_H182 zenon_H6a zenon_H156 zenon_H44 zenon_H87 zenon_H8b zenon_H90 zenon_H13c zenon_Heb zenon_Ha7 zenon_H154 zenon_H8f zenon_Hf1 zenon_H59 zenon_H138 zenon_H36 zenon_H58 zenon_H199 zenon_Hd7 zenon_H160 zenon_H1d3 zenon_H166 zenon_H1d4 zenon_Haa zenon_H84 zenon_H28 zenon_H250 zenon_H11b zenon_H1cf zenon_H7d zenon_H10c zenon_Hbe zenon_H1c3 zenon_Hce zenon_H2d zenon_H1b3 zenon_Hb7 zenon_H290 zenon_H157 zenon_H1e2 zenon_H1e3 zenon_H1d2 zenon_H1d8. % 15.48/15.63 apply (zenon_or_s _ _ zenon_H1c3); [ zenon_intro zenon_H30 | zenon_intro zenon_H124 ]. % 15.48/15.63 apply (zenon_or_s _ _ zenon_H10c); [ zenon_intro zenon_H104 | zenon_intro zenon_H10a ]. % 15.48/15.63 apply (zenon_or_s _ _ zenon_H10e); [ zenon_intro zenon_H3d | zenon_intro zenon_H106 ]. % 15.48/15.63 apply (zenon_L901_); trivial. % 15.48/15.63 apply (zenon_L820_); trivial. % 15.48/15.63 apply (zenon_L899_); trivial. % 15.48/15.63 apply (zenon_L256_); trivial. % 15.48/15.63 (* end of lemma zenon_L1022_ *) % 15.48/15.63 assert (zenon_L1023_ : (~((op (e2) (op (e3) (e2))) = (op (e2) (e1)))) -> ((op (e3) (e2)) = (e1)) -> False). % 15.48/15.63 do 0 intro. intros zenon_H2ae zenon_H119. % 15.48/15.63 cut (((op (e3) (e2)) = (e1))); [idtac | apply NNPP; zenon_intro zenon_H11a]. % 15.48/15.63 cut (((e2) = (e2))); [idtac | apply NNPP; zenon_intro zenon_H60]. % 15.48/15.63 congruence. % 15.48/15.63 apply zenon_H60. apply refl_equal. % 15.48/15.63 exact (zenon_H11a zenon_H119). % 15.48/15.63 (* end of lemma zenon_L1023_ *) % 15.48/15.63 assert (zenon_L1024_ : (~((op (e2) (op (e3) (e2))) = (op (e3) (e2)))) -> ((op (e2) (e1)) = (e1)) -> ((op (e3) (e2)) = (e1)) -> False). % 15.48/15.63 do 0 intro. intros zenon_H2af zenon_Hb2 zenon_H119. % 15.48/15.63 cut (((op (e2) (e1)) = (e1)) = ((op (e2) (op (e3) (e2))) = (op (e3) (e2)))). % 15.48/15.63 intro zenon_D_pnotp. % 15.48/15.63 apply zenon_H2af. % 15.48/15.63 rewrite <- zenon_D_pnotp. % 15.48/15.63 exact zenon_Hb2. % 15.48/15.63 cut (((e1) = (op (e3) (e2)))); [idtac | apply NNPP; zenon_intro zenon_H141]. % 15.48/15.63 cut (((op (e2) (e1)) = (op (e2) (op (e3) (e2))))); [idtac | apply NNPP; zenon_intro zenon_H2b0]. % 15.48/15.63 congruence. % 15.48/15.63 elim (classic ((op (e2) (op (e3) (e2))) = (op (e2) (op (e3) (e2))))); [ zenon_intro zenon_H2b1 | zenon_intro zenon_H2b2 ]. % 15.48/15.63 cut (((op (e2) (op (e3) (e2))) = (op (e2) (op (e3) (e2)))) = ((op (e2) (e1)) = (op (e2) (op (e3) (e2))))). % 15.48/15.63 intro zenon_D_pnotp. % 15.48/15.63 apply zenon_H2b0. % 15.48/15.63 rewrite <- zenon_D_pnotp. % 15.48/15.63 exact zenon_H2b1. % 15.48/15.63 cut (((op (e2) (op (e3) (e2))) = (op (e2) (op (e3) (e2))))); [idtac | apply NNPP; zenon_intro zenon_H2b2]. % 15.48/15.63 cut (((op (e2) (op (e3) (e2))) = (op (e2) (e1)))); [idtac | apply NNPP; zenon_intro zenon_H2ae]. % 15.48/15.63 congruence. % 15.48/15.63 apply (zenon_L1023_); trivial. % 15.48/15.63 apply zenon_H2b2. apply refl_equal. % 15.48/15.63 apply zenon_H2b2. apply refl_equal. % 15.48/15.63 apply zenon_H141. apply sym_equal. exact zenon_H119. % 15.48/15.63 (* end of lemma zenon_L1024_ *) % 15.48/15.63 assert (zenon_L1025_ : (((op (e0) (e2)) = (e1))\/(((op (e1) (e2)) = (e1))\/(((op (e2) (e2)) = (e1))\/((op (e3) (e2)) = (e1))))) -> (~((op (e0) (e2)) = (op (e0) (e3)))) -> ((op (e0) (e3)) = (e1)) -> ((op (e1) (e0)) = (e1)) -> (~((op (e1) (e0)) = (op (e1) (e2)))) -> (~((op (e2) (e2)) = (e1))) -> (~((op (e2) (op (e3) (e2))) = (op (e3) (e2)))) -> ((op (e2) (e1)) = (e1)) -> False). % 15.48/15.63 do 0 intro. intros zenon_H11b zenon_Hc9 zenon_H37 zenon_Hd8 zenon_H166 zenon_H52 zenon_H2af zenon_Hb2. % 15.48/15.63 apply (zenon_or_s _ _ zenon_H11b); [ zenon_intro zenon_H29 | zenon_intro zenon_H11c ]. % 15.48/15.63 apply (zenon_L85_); trivial. % 15.48/15.63 apply (zenon_or_s _ _ zenon_H11c); [ zenon_intro zenon_H117 | zenon_intro zenon_H11d ]. % 15.48/15.63 apply (zenon_L248_); trivial. % 15.48/15.63 apply (zenon_or_s _ _ zenon_H11d); [ zenon_intro zenon_H2a | zenon_intro zenon_H119 ]. % 15.48/15.63 exact (zenon_H52 zenon_H2a). % 15.48/15.63 apply (zenon_L1024_); trivial. % 15.48/15.63 (* end of lemma zenon_L1025_ *) % 15.48/15.63 assert (zenon_L1026_ : (((op (e0) (e3)) = (e0))\/(((op (e0) (e3)) = (e1))\/(((op (e0) (e3)) = (e2))\/((op (e0) (e3)) = (e3))))) -> ((op (e0) (e0)) = (e0)) -> (~((op (e0) (e0)) = (op (e0) (e3)))) -> ((op (e2) (e3)) = (e1)) -> ((op (e1) (e3)) = (e2)) -> (~((op (e0) (e3)) = (op (e1) (e3)))) -> (~((op (e0) (e3)) = (op (e2) (e3)))) -> ((op (e2) (e3)) = (e3)) -> False). % 15.48/15.63 do 0 intro. intros zenon_H254 zenon_H1f zenon_H24f zenon_Hb5 zenon_H82 zenon_H80 zenon_Hb4 zenon_He2. % 15.48/15.63 apply (zenon_or_s _ _ zenon_H254); [ zenon_intro zenon_Hca | zenon_intro zenon_H255 ]. % 15.48/15.63 apply (zenon_L562_); trivial. % 15.48/15.63 apply (zenon_or_s _ _ zenon_H255); [ zenon_intro zenon_H37 | zenon_intro zenon_H256 ]. % 15.48/15.63 apply (zenon_L41_); trivial. % 15.48/15.63 apply (zenon_or_s _ _ zenon_H256); [ zenon_intro zenon_H81 | zenon_intro zenon_H53 ]. % 15.48/15.63 apply (zenon_L22_); trivial. % 15.48/15.63 apply (zenon_L125_); trivial. % 15.48/15.63 (* end of lemma zenon_L1026_ *) % 15.48/15.63 assert (zenon_L1027_ : (((op (e0) (e3)) = (e2))\/(((op (e1) (e3)) = (e2))\/(((op (e2) (e3)) = (e2))\/((op (e3) (e3)) = (e2))))) -> (~((op (e0) (e1)) = (op (e0) (e3)))) -> ((op (e0) (e1)) = (e2)) -> (~((op (e0) (e3)) = (op (e2) (e3)))) -> (~((op (e0) (e3)) = (op (e1) (e3)))) -> ((op (e2) (e3)) = (e1)) -> (~((op (e0) (e0)) = (op (e0) (e3)))) -> ((op (e0) (e0)) = (e0)) -> (((op (e0) (e3)) = (e0))\/(((op (e0) (e3)) = (e1))\/(((op (e0) (e3)) = (e2))\/((op (e0) (e3)) = (e3))))) -> (~((e2) = (e3))) -> ((op (e2) (e3)) = (e3)) -> (~((op (e3) (e3)) = (e2))) -> False). % 15.48/15.63 do 0 intro. intros zenon_H160 zenon_H1cd zenon_H5d zenon_Hb4 zenon_H80 zenon_Hb5 zenon_H24f zenon_H1f zenon_H254 zenon_H6a zenon_He2 zenon_H3d. % 15.48/15.63 apply (zenon_or_s _ _ zenon_H160); [ zenon_intro zenon_H81 | zenon_intro zenon_H161 ]. % 15.48/15.63 apply (zenon_L350_); trivial. % 15.48/15.63 apply (zenon_or_s _ _ zenon_H161); [ zenon_intro zenon_H82 | zenon_intro zenon_H162 ]. % 15.48/15.63 apply (zenon_L1026_); trivial. % 15.48/15.63 apply (zenon_or_s _ _ zenon_H162); [ zenon_intro zenon_H124 | zenon_intro zenon_H43 ]. % 15.48/15.63 apply (zenon_L98_); trivial. % 15.48/15.63 exact (zenon_H3d zenon_H43). % 15.48/15.63 (* end of lemma zenon_L1027_ *) % 15.48/15.63 assert (zenon_L1028_ : (((op (e2) (e0)) = (e3))\/(((op (e2) (e1)) = (e3))\/(((op (e2) (e2)) = (e3))\/((op (e2) (e3)) = (e3))))) -> ((op (e2) (e0)) = (e2)) -> ((op (e0) (e1)) = (e3)) -> (~((op (e0) (e1)) = (op (e2) (e1)))) -> (~((op (e2) (e2)) = (e3))) -> (((op (e0) (e3)) = (e2))\/(((op (e1) (e3)) = (e2))\/(((op (e2) (e3)) = (e2))\/((op (e3) (e3)) = (e2))))) -> (~((op (e0) (e1)) = (op (e0) (e3)))) -> ((op (e0) (e1)) = (e2)) -> (~((op (e0) (e3)) = (op (e2) (e3)))) -> (~((op (e0) (e3)) = (op (e1) (e3)))) -> ((op (e2) (e3)) = (e1)) -> (~((op (e0) (e0)) = (op (e0) (e3)))) -> ((op (e0) (e0)) = (e0)) -> (((op (e0) (e3)) = (e0))\/(((op (e0) (e3)) = (e1))\/(((op (e0) (e3)) = (e2))\/((op (e0) (e3)) = (e3))))) -> (~((e2) = (e3))) -> (~((op (e3) (e3)) = (e2))) -> False). % 15.48/15.63 do 0 intro. intros zenon_He6 zenon_Hdd zenon_H4a zenon_Hde zenon_H30 zenon_H160 zenon_H1cd zenon_H5d zenon_Hb4 zenon_H80 zenon_Hb5 zenon_H24f zenon_H1f zenon_H254 zenon_H6a zenon_H3d. % 15.48/15.63 apply (zenon_or_s _ _ zenon_He6); [ zenon_intro zenon_Haf | zenon_intro zenon_He7 ]. % 15.48/15.63 apply (zenon_L64_); trivial. % 15.48/15.63 apply (zenon_or_s _ _ zenon_He7); [ zenon_intro zenon_Hdf | zenon_intro zenon_He8 ]. % 15.48/15.63 apply (zenon_L65_); trivial. % 15.48/15.63 apply (zenon_or_s _ _ zenon_He8); [ zenon_intro zenon_H34 | zenon_intro zenon_He2 ]. % 15.48/15.63 exact (zenon_H30 zenon_H34). % 15.48/15.63 apply (zenon_L1027_); trivial. % 15.48/15.63 (* end of lemma zenon_L1028_ *) % 15.48/15.63 assert (zenon_L1029_ : (((op (e2) (e0)) = (e1))\/(((op (e2) (e1)) = (e1))\/(((op (e2) (e2)) = (e1))\/((op (e2) (e3)) = (e1))))) -> (~((e1) = (e2))) -> (~((op (e3) (e3)) = (e1))) -> (~((op (e1) (e0)) = (op (e1) (e3)))) -> ((op (e1) (e0)) = (e1)) -> (((op (e0) (e2)) = (e1))\/(((op (e1) (e2)) = (e1))\/(((op (e2) (e2)) = (e1))\/((op (e3) (e2)) = (e1))))) -> (~((op (e0) (e2)) = (op (e0) (e3)))) -> (~((op (e1) (e0)) = (op (e1) (e2)))) -> (~((op (e2) (op (e3) (e2))) = (op (e3) (e2)))) -> (((op (e0) (e3)) = (e1))\/(((op (e1) (e3)) = (e1))\/(((op (e2) (e3)) = (e1))\/((op (e3) (e3)) = (e1))))) -> (~((op (e2) (e2)) = (e1))) -> (((op (e2) (e0)) = (e3))\/(((op (e2) (e1)) = (e3))\/(((op (e2) (e2)) = (e3))\/((op (e2) (e3)) = (e3))))) -> ((op (e2) (e0)) = (e2)) -> ((op (e0) (e1)) = (e3)) -> (~((op (e0) (e1)) = (op (e2) (e1)))) -> (~((op (e2) (e2)) = (e3))) -> (((op (e0) (e3)) = (e2))\/(((op (e1) (e3)) = (e2))\/(((op (e2) (e3)) = (e2))\/((op (e3) (e3)) = (e2))))) -> (~((op (e0) (e1)) = (op (e0) (e3)))) -> ((op (e0) (e1)) = (e2)) -> (~((op (e0) (e3)) = (op (e2) (e3)))) -> (~((op (e0) (e3)) = (op (e1) (e3)))) -> (~((op (e0) (e0)) = (op (e0) (e3)))) -> ((op (e0) (e0)) = (e0)) -> (((op (e0) (e3)) = (e0))\/(((op (e0) (e3)) = (e1))\/(((op (e0) (e3)) = (e2))\/((op (e0) (e3)) = (e3))))) -> (~((e2) = (e3))) -> (~((op (e3) (e3)) = (e2))) -> False). % 15.48/15.63 do 0 intro. intros zenon_Hb7 zenon_Ha7 zenon_H104 zenon_H1cf zenon_Hd8 zenon_H11b zenon_Hc9 zenon_H166 zenon_H2af zenon_H121 zenon_H52 zenon_He6 zenon_Hdd zenon_H4a zenon_Hde zenon_H30 zenon_H160 zenon_H1cd zenon_H5d zenon_Hb4 zenon_H80 zenon_H24f zenon_H1f zenon_H254 zenon_H6a zenon_H3d. % 15.48/15.63 apply (zenon_or_s _ _ zenon_Hb7); [ zenon_intro zenon_Hae | zenon_intro zenon_Hb8 ]. % 15.48/15.63 apply (zenon_L304_); trivial. % 15.48/15.63 apply (zenon_or_s _ _ zenon_Hb8); [ zenon_intro zenon_Hb2 | zenon_intro zenon_Hb9 ]. % 15.48/15.63 apply (zenon_or_s _ _ zenon_He6); [ zenon_intro zenon_Haf | zenon_intro zenon_He7 ]. % 15.48/15.63 apply (zenon_L64_); trivial. % 15.48/15.63 apply (zenon_or_s _ _ zenon_He7); [ zenon_intro zenon_Hdf | zenon_intro zenon_He8 ]. % 15.48/15.63 apply (zenon_L65_); trivial. % 15.48/15.63 apply (zenon_or_s _ _ zenon_He8); [ zenon_intro zenon_H34 | zenon_intro zenon_He2 ]. % 15.48/15.63 exact (zenon_H30 zenon_H34). % 15.48/15.63 apply (zenon_or_s _ _ zenon_H121); [ zenon_intro zenon_H37 | zenon_intro zenon_H122 ]. % 15.48/15.63 apply (zenon_L1025_); trivial. % 15.48/15.63 apply (zenon_or_s _ _ zenon_H122); [ zenon_intro zenon_H11f | zenon_intro zenon_H123 ]. % 15.48/15.63 apply (zenon_L224_); trivial. % 15.48/15.63 apply (zenon_or_s _ _ zenon_H123); [ zenon_intro zenon_Hb5 | zenon_intro zenon_H38 ]. % 15.48/15.63 apply (zenon_L1027_); trivial. % 15.48/15.63 exact (zenon_H104 zenon_H38). % 15.48/15.63 apply (zenon_or_s _ _ zenon_Hb9); [ zenon_intro zenon_H2a | zenon_intro zenon_Hb5 ]. % 15.48/15.63 exact (zenon_H52 zenon_H2a). % 15.48/15.63 apply (zenon_L1028_); trivial. % 15.48/15.63 (* end of lemma zenon_L1029_ *) % 15.48/15.63 assert (zenon_L1030_ : (~((op (e1) (op (e3) (e1))) = (op (e1) (e2)))) -> ((op (e3) (e1)) = (e2)) -> False). % 15.48/15.63 do 0 intro. intros zenon_H2b3 zenon_H16a. % 15.48/15.63 cut (((op (e3) (e1)) = (e2))); [idtac | apply NNPP; zenon_intro zenon_H206]. % 15.48/15.63 cut (((e1) = (e1))); [idtac | apply NNPP; zenon_intro zenon_Ha0]. % 15.48/15.63 congruence. % 15.48/15.63 apply zenon_Ha0. apply refl_equal. % 15.48/15.63 exact (zenon_H206 zenon_H16a). % 15.48/15.63 (* end of lemma zenon_L1030_ *) % 15.48/15.63 assert (zenon_L1031_ : (~((op (e1) (op (e3) (e1))) = (op (e3) (e1)))) -> ((op (e1) (e2)) = (e2)) -> ((op (e3) (e1)) = (e2)) -> False). % 15.48/15.63 do 0 intro. intros zenon_H2b4 zenon_H7c zenon_H16a. % 15.48/15.63 cut (((op (e1) (e2)) = (e2)) = ((op (e1) (op (e3) (e1))) = (op (e3) (e1)))). % 15.48/15.63 intro zenon_D_pnotp. % 15.48/15.63 apply zenon_H2b4. % 15.48/15.63 rewrite <- zenon_D_pnotp. % 15.48/15.63 exact zenon_H7c. % 15.48/15.63 cut (((e2) = (op (e3) (e1)))); [idtac | apply NNPP; zenon_intro zenon_H16b]. % 15.48/15.63 cut (((op (e1) (e2)) = (op (e1) (op (e3) (e1))))); [idtac | apply NNPP; zenon_intro zenon_H2b5]. % 15.48/15.63 congruence. % 15.48/15.63 elim (classic ((op (e1) (op (e3) (e1))) = (op (e1) (op (e3) (e1))))); [ zenon_intro zenon_H2b6 | zenon_intro zenon_H2b7 ]. % 15.48/15.63 cut (((op (e1) (op (e3) (e1))) = (op (e1) (op (e3) (e1)))) = ((op (e1) (e2)) = (op (e1) (op (e3) (e1))))). % 15.48/15.63 intro zenon_D_pnotp. % 15.48/15.63 apply zenon_H2b5. % 15.48/15.63 rewrite <- zenon_D_pnotp. % 15.48/15.63 exact zenon_H2b6. % 15.48/15.63 cut (((op (e1) (op (e3) (e1))) = (op (e1) (op (e3) (e1))))); [idtac | apply NNPP; zenon_intro zenon_H2b7]. % 15.48/15.63 cut (((op (e1) (op (e3) (e1))) = (op (e1) (e2)))); [idtac | apply NNPP; zenon_intro zenon_H2b3]. % 15.48/15.63 congruence. % 15.48/15.63 apply (zenon_L1030_); trivial. % 15.48/15.63 apply zenon_H2b7. apply refl_equal. % 15.48/15.63 apply zenon_H2b7. apply refl_equal. % 15.48/15.63 apply zenon_H16b. apply sym_equal. exact zenon_H16a. % 15.48/15.63 (* end of lemma zenon_L1031_ *) % 15.48/15.63 assert (zenon_L1032_ : (((op (e0) (e1)) = (e2))\/(((op (e1) (e1)) = (e2))\/(((op (e2) (e1)) = (e2))\/((op (e3) (e1)) = (e2))))) -> (~((op (e0) (e1)) = (op (e0) (e3)))) -> ((op (e0) (e3)) = (e2)) -> (~((op (e1) (e1)) = (e2))) -> ((op (e2) (e0)) = (e2)) -> (~((op (e2) (e0)) = (op (e2) (e1)))) -> (~((op (e1) (op (e3) (e1))) = (op (e3) (e1)))) -> ((op (e1) (e2)) = (e2)) -> False). % 15.48/15.63 do 0 intro. intros zenon_H1a2 zenon_H1cd zenon_H81 zenon_Hd6 zenon_Hdd zenon_H154 zenon_H2b4 zenon_H7c. % 15.48/15.63 apply (zenon_or_s _ _ zenon_H1a2); [ zenon_intro zenon_H5d | zenon_intro zenon_H1a3 ]. % 15.48/15.63 apply (zenon_L350_); trivial. % 15.48/15.63 apply (zenon_or_s _ _ zenon_H1a3); [ zenon_intro zenon_H6e | zenon_intro zenon_H1a4 ]. % 15.48/15.63 exact (zenon_Hd6 zenon_H6e). % 15.48/15.63 apply (zenon_or_s _ _ zenon_H1a4); [ zenon_intro zenon_H156 | zenon_intro zenon_H16a ]. % 15.48/15.63 apply (zenon_L284_); trivial. % 15.48/15.63 apply (zenon_L1031_); trivial. % 15.48/15.63 (* end of lemma zenon_L1032_ *) % 15.48/15.63 assert (zenon_L1033_ : (((op (e1) (e0)) = (e3))\/(((op (e1) (e1)) = (e3))\/(((op (e1) (e2)) = (e3))\/((op (e1) (e3)) = (e3))))) -> (~((e1) = (e3))) -> ((op (e1) (e0)) = (e1)) -> (~((op (e1) (e1)) = (e3))) -> ((op (e0) (e2)) = (e3)) -> (~((op (e0) (e2)) = (op (e1) (e2)))) -> ((op (e1) (e3)) = (e2)) -> (~((e2) = (e3))) -> False). % 15.48/15.63 do 0 intro. intros zenon_H90 zenon_Ha3 zenon_Hd8 zenon_H182 zenon_H50 zenon_H87 zenon_H82 zenon_H6a. % 15.48/15.63 apply (zenon_or_s _ _ zenon_H90); [ zenon_intro zenon_H69 | zenon_intro zenon_H94 ]. % 15.48/15.63 apply (zenon_L163_); trivial. % 15.48/15.63 apply (zenon_or_s _ _ zenon_H94); [ zenon_intro zenon_H96 | zenon_intro zenon_H95 ]. % 15.48/15.63 exact (zenon_H182 zenon_H96). % 15.48/15.63 apply (zenon_or_s _ _ zenon_H95); [ zenon_intro zenon_H88 | zenon_intro zenon_H8a ]. % 15.48/15.63 apply (zenon_L24_); trivial. % 15.48/15.63 apply (zenon_L165_); trivial. % 15.48/15.63 (* end of lemma zenon_L1033_ *) % 15.48/15.63 assert (zenon_L1034_ : (((op (e1) (e0)) = (e2))\/(((op (e1) (e1)) = (e2))\/(((op (e1) (e2)) = (e2))\/((op (e1) (e3)) = (e2))))) -> (~((op (e3) (e3)) = (e2))) -> (~((e1) = (e2))) -> (((op (e0) (e1)) = (e2))\/(((op (e1) (e1)) = (e2))\/(((op (e2) (e1)) = (e2))\/((op (e3) (e1)) = (e2))))) -> (~((op (e0) (e1)) = (op (e0) (e3)))) -> (~((op (e1) (e1)) = (e2))) -> ((op (e2) (e0)) = (e2)) -> (~((op (e2) (e0)) = (op (e2) (e1)))) -> (~((op (e1) (op (e3) (e1))) = (op (e3) (e1)))) -> (((op (e0) (e3)) = (e2))\/(((op (e1) (e3)) = (e2))\/(((op (e2) (e3)) = (e2))\/((op (e3) (e3)) = (e2))))) -> (~((op (e2) (e2)) = (e1))) -> (((op (e0) (e2)) = (e1))\/(((op (e1) (e2)) = (e1))\/(((op (e2) (e2)) = (e1))\/((op (e3) (e2)) = (e1))))) -> (~((op (e1) (e0)) = (op (e1) (e2)))) -> (~((op (e2) (op (e3) (e2))) = (op (e3) (e2)))) -> (~((op (e1) (e0)) = (op (e2) (e0)))) -> (((op (e2) (e0)) = (e1))\/(((op (e2) (e1)) = (e1))\/(((op (e2) (e2)) = (e1))\/((op (e2) (e3)) = (e1))))) -> (((op (e1) (e0)) = (e3))\/(((op (e1) (e1)) = (e3))\/(((op (e1) (e2)) = (e3))\/((op (e1) (e3)) = (e3))))) -> (~((e1) = (e3))) -> ((op (e1) (e0)) = (e1)) -> (~((op (e1) (e1)) = (e3))) -> ((op (e0) (e2)) = (e3)) -> (~((op (e0) (e2)) = (op (e1) (e2)))) -> (~((e2) = (e3))) -> False). % 15.48/15.63 do 0 intro. intros zenon_H84 zenon_H3d zenon_Ha7 zenon_H1a2 zenon_H1cd zenon_Hd6 zenon_Hdd zenon_H154 zenon_H2b4 zenon_H160 zenon_H52 zenon_H11b zenon_H166 zenon_H2af zenon_H247 zenon_Hb7 zenon_H90 zenon_Ha3 zenon_Hd8 zenon_H182 zenon_H50 zenon_H87 zenon_H6a. % 15.48/15.63 apply (zenon_or_s _ _ zenon_H84); [ zenon_intro zenon_H68 | zenon_intro zenon_H85 ]. % 15.48/15.63 apply (zenon_L162_); trivial. % 15.48/15.63 apply (zenon_or_s _ _ zenon_H85); [ zenon_intro zenon_H6e | zenon_intro zenon_H86 ]. % 15.48/15.63 exact (zenon_Hd6 zenon_H6e). % 15.48/15.63 apply (zenon_or_s _ _ zenon_H86); [ zenon_intro zenon_H7c | zenon_intro zenon_H82 ]. % 15.48/15.63 apply (zenon_or_s _ _ zenon_H90); [ zenon_intro zenon_H69 | zenon_intro zenon_H94 ]. % 15.48/15.63 apply (zenon_L163_); trivial. % 15.48/15.63 apply (zenon_or_s _ _ zenon_H94); [ zenon_intro zenon_H96 | zenon_intro zenon_H95 ]. % 15.48/15.63 exact (zenon_H182 zenon_H96). % 15.48/15.63 apply (zenon_or_s _ _ zenon_H95); [ zenon_intro zenon_H88 | zenon_intro zenon_H8a ]. % 15.48/15.63 apply (zenon_L24_); trivial. % 15.48/15.63 apply (zenon_or_s _ _ zenon_Hb7); [ zenon_intro zenon_Hae | zenon_intro zenon_Hb8 ]. % 15.48/15.63 apply (zenon_L540_); trivial. % 15.48/15.63 apply (zenon_or_s _ _ zenon_Hb8); [ zenon_intro zenon_Hb2 | zenon_intro zenon_Hb9 ]. % 15.48/15.63 apply (zenon_or_s _ _ zenon_H11b); [ zenon_intro zenon_H29 | zenon_intro zenon_H11c ]. % 15.48/15.63 apply (zenon_L29_); trivial. % 15.48/15.63 apply (zenon_or_s _ _ zenon_H11c); [ zenon_intro zenon_H117 | zenon_intro zenon_H11d ]. % 15.48/15.63 apply (zenon_L248_); trivial. % 15.48/15.63 apply (zenon_or_s _ _ zenon_H11d); [ zenon_intro zenon_H2a | zenon_intro zenon_H119 ]. % 15.48/15.63 exact (zenon_H52 zenon_H2a). % 15.48/15.63 apply (zenon_L1024_); trivial. % 15.48/15.63 apply (zenon_or_s _ _ zenon_Hb9); [ zenon_intro zenon_H2a | zenon_intro zenon_Hb5 ]. % 15.48/15.63 exact (zenon_H52 zenon_H2a). % 15.48/15.63 apply (zenon_or_s _ _ zenon_H160); [ zenon_intro zenon_H81 | zenon_intro zenon_H161 ]. % 15.48/15.63 apply (zenon_L1032_); trivial. % 15.48/15.63 apply (zenon_or_s _ _ zenon_H161); [ zenon_intro zenon_H82 | zenon_intro zenon_H162 ]. % 15.48/15.63 apply (zenon_L165_); trivial. % 15.48/15.63 apply (zenon_or_s _ _ zenon_H162); [ zenon_intro zenon_H124 | zenon_intro zenon_H43 ]. % 15.48/15.63 apply (zenon_L93_); trivial. % 15.48/15.63 exact (zenon_H3d zenon_H43). % 15.48/15.63 apply (zenon_L1033_); trivial. % 15.48/15.63 (* end of lemma zenon_L1034_ *) % 15.48/15.63 assert (zenon_L1035_ : (~((op (e0) (op (e3) (e0))) = (op (e3) (e0)))) -> ((op (e0) (e3)) = (e3)) -> ((op (e3) (e0)) = (e3)) -> False). % 15.48/15.63 do 0 intro. intros zenon_H2b8 zenon_H53 zenon_Hba. % 15.48/15.63 cut (((op (e0) (e3)) = (e3)) = ((op (e0) (op (e3) (e0))) = (op (e3) (e0)))). % 15.48/15.63 intro zenon_D_pnotp. % 15.48/15.63 apply zenon_H2b8. % 15.48/15.63 rewrite <- zenon_D_pnotp. % 15.48/15.63 exact zenon_H53. % 15.48/15.63 cut (((e3) = (op (e3) (e0)))); [idtac | apply NNPP; zenon_intro zenon_Hbd]. % 15.48/15.63 cut (((op (e0) (e3)) = (op (e0) (op (e3) (e0))))); [idtac | apply NNPP; zenon_intro zenon_H2b9]. % 15.48/15.63 congruence. % 15.48/15.63 elim (classic ((op (e0) (op (e3) (e0))) = (op (e0) (op (e3) (e0))))); [ zenon_intro zenon_H2ba | zenon_intro zenon_H2bb ]. % 15.48/15.63 cut (((op (e0) (op (e3) (e0))) = (op (e0) (op (e3) (e0)))) = ((op (e0) (e3)) = (op (e0) (op (e3) (e0))))). % 15.48/15.63 intro zenon_D_pnotp. % 15.48/15.63 apply zenon_H2b9. % 15.48/15.63 rewrite <- zenon_D_pnotp. % 15.48/15.63 exact zenon_H2ba. % 15.48/15.63 cut (((op (e0) (op (e3) (e0))) = (op (e0) (op (e3) (e0))))); [idtac | apply NNPP; zenon_intro zenon_H2bb]. % 15.48/15.63 cut (((op (e0) (op (e3) (e0))) = (op (e0) (e3)))); [idtac | apply NNPP; zenon_intro zenon_H2bc]. % 15.48/15.63 congruence. % 15.48/15.63 cut (((op (e3) (e0)) = (e3))); [idtac | apply NNPP; zenon_intro zenon_H2bd]. % 15.48/15.63 cut (((e0) = (e0))); [idtac | apply NNPP; zenon_intro zenon_H1d]. % 15.48/15.63 congruence. % 15.48/15.63 apply zenon_H1d. apply refl_equal. % 15.48/15.63 exact (zenon_H2bd zenon_Hba). % 15.48/15.63 apply zenon_H2bb. apply refl_equal. % 15.48/15.63 apply zenon_H2bb. apply refl_equal. % 15.48/15.63 apply zenon_Hbd. apply sym_equal. exact zenon_Hba. % 15.48/15.63 (* end of lemma zenon_L1035_ *) % 15.48/15.63 assert (zenon_L1036_ : (((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)) -> (~((e2) = (e3))) -> ((op (e2) (e0)) = (e2)) -> (~((op (e0) (op (e3) (e0))) = (op (e3) (e0)))) -> ((op (e0) (e3)) = (e3)) -> False). % 15.48/15.63 do 0 intro. intros zenon_Hbe zenon_H59 zenon_Ha3 zenon_Hd8 zenon_H6a zenon_Hdd zenon_H2b8 zenon_H53. % 15.48/15.63 apply (zenon_or_s _ _ zenon_Hbe); [ zenon_intro zenon_H5b | zenon_intro zenon_Hbf ]. % 15.48/15.63 exact (zenon_H59 zenon_H5b). % 15.48/15.63 apply (zenon_or_s _ _ zenon_Hbf); [ zenon_intro zenon_H69 | zenon_intro zenon_Hc0 ]. % 15.48/15.63 apply (zenon_L163_); trivial. % 15.48/15.63 apply (zenon_or_s _ _ zenon_Hc0); [ zenon_intro zenon_Haf | zenon_intro zenon_Hba ]. % 15.48/15.63 apply (zenon_L64_); trivial. % 15.48/15.63 apply (zenon_L1035_); trivial. % 15.48/15.63 (* end of lemma zenon_L1036_ *) % 15.48/15.63 assert (zenon_L1037_ : (((op (e0) (e0)) = (e3))\/(((op (e0) (e1)) = (e3))\/(((op (e0) (e2)) = (e3))\/((op (e0) (e3)) = (e3))))) -> (((op (e0) (e3)) = (e0))\/(((op (e0) (e3)) = (e1))\/(((op (e0) (e3)) = (e2))\/((op (e0) (e3)) = (e3))))) -> ((op (e0) (e0)) = (e0)) -> (~((op (e0) (e0)) = (op (e0) (e3)))) -> (~((op (e0) (e3)) = (op (e1) (e3)))) -> (~((op (e0) (e3)) = (op (e2) (e3)))) -> ((op (e0) (e1)) = (e2)) -> (~((op (e2) (e2)) = (e3))) -> (~((op (e0) (e1)) = (op (e2) (e1)))) -> (((op (e2) (e0)) = (e3))\/(((op (e2) (e1)) = (e3))\/(((op (e2) (e2)) = (e3))\/((op (e2) (e3)) = (e3))))) -> (((op (e0) (e3)) = (e1))\/(((op (e1) (e3)) = (e1))\/(((op (e2) (e3)) = (e1))\/((op (e3) (e3)) = (e1))))) -> (~((op (e0) (e2)) = (op (e0) (e3)))) -> (~((op (e1) (e0)) = (op (e1) (e3)))) -> (~((op (e3) (e3)) = (e1))) -> (~((op (e0) (e2)) = (op (e1) (e2)))) -> (~((op (e1) (e1)) = (e3))) -> (((op (e1) (e0)) = (e3))\/(((op (e1) (e1)) = (e3))\/(((op (e1) (e2)) = (e3))\/((op (e1) (e3)) = (e3))))) -> (((op (e2) (e0)) = (e1))\/(((op (e2) (e1)) = (e1))\/(((op (e2) (e2)) = (e1))\/((op (e2) (e3)) = (e1))))) -> (~((op (e1) (e0)) = (op (e2) (e0)))) -> (~((op (e2) (op (e3) (e2))) = (op (e3) (e2)))) -> (~((op (e1) (e0)) = (op (e1) (e2)))) -> (((op (e0) (e2)) = (e1))\/(((op (e1) (e2)) = (e1))\/(((op (e2) (e2)) = (e1))\/((op (e3) (e2)) = (e1))))) -> (~((op (e2) (e2)) = (e1))) -> (((op (e0) (e3)) = (e2))\/(((op (e1) (e3)) = (e2))\/(((op (e2) (e3)) = (e2))\/((op (e3) (e3)) = (e2))))) -> (~((op (e1) (op (e3) (e1))) = (op (e3) (e1)))) -> (~((op (e2) (e0)) = (op (e2) (e1)))) -> (~((op (e1) (e1)) = (e2))) -> (~((op (e0) (e1)) = (op (e0) (e3)))) -> (((op (e0) (e1)) = (e2))\/(((op (e1) (e1)) = (e2))\/(((op (e2) (e1)) = (e2))\/((op (e3) (e1)) = (e2))))) -> (~((e1) = (e2))) -> (~((op (e3) (e3)) = (e2))) -> (((op (e1) (e0)) = (e2))\/(((op (e1) (e1)) = (e2))\/(((op (e1) (e2)) = (e2))\/((op (e1) (e3)) = (e2))))) -> (((op (e0) (e0)) = (e3))\/(((op (e1) (e0)) = (e3))\/(((op (e2) (e0)) = (e3))\/((op (e3) (e0)) = (e3))))) -> (~((op (e0) (e0)) = (e3))) -> (~((e1) = (e3))) -> ((op (e1) (e0)) = (e1)) -> (~((e2) = (e3))) -> ((op (e2) (e0)) = (e2)) -> (~((op (e0) (op (e3) (e0))) = (op (e3) (e0)))) -> False). % 15.48/15.63 do 0 intro. intros zenon_H58 zenon_H254 zenon_H1f zenon_H24f zenon_H80 zenon_Hb4 zenon_H5d zenon_H30 zenon_Hde zenon_He6 zenon_H121 zenon_Hc9 zenon_H1cf zenon_H104 zenon_H87 zenon_H182 zenon_H90 zenon_Hb7 zenon_H247 zenon_H2af zenon_H166 zenon_H11b zenon_H52 zenon_H160 zenon_H2b4 zenon_H154 zenon_Hd6 zenon_H1cd zenon_H1a2 zenon_Ha7 zenon_H3d zenon_H84 zenon_Hbe zenon_H59 zenon_Ha3 zenon_Hd8 zenon_H6a zenon_Hdd zenon_H2b8. % 15.48/15.63 apply (zenon_or_s _ _ zenon_H58); [ zenon_intro zenon_H5b | zenon_intro zenon_H5a ]. % 15.48/15.63 exact (zenon_H59 zenon_H5b). % 15.48/15.63 apply (zenon_or_s _ _ zenon_H5a); [ zenon_intro zenon_H4a | zenon_intro zenon_H5c ]. % 15.48/15.63 apply (zenon_L1029_); trivial. % 15.48/15.63 apply (zenon_or_s _ _ zenon_H5c); [ zenon_intro zenon_H50 | zenon_intro zenon_H53 ]. % 15.48/15.63 apply (zenon_L1034_); trivial. % 15.48/15.63 apply (zenon_L1036_); trivial. % 15.48/15.63 (* end of lemma zenon_L1037_ *) % 15.48/15.63 assert (zenon_L1038_ : (((op (e2) (e0)) = (e3))\/(((op (e2) (e1)) = (e3))\/(((op (e2) (e2)) = (e3))\/((op (e2) (e3)) = (e3))))) -> (~((op (e2) (e0)) = (op (e3) (e0)))) -> ((op (e3) (e0)) = (e3)) -> ((op (e0) (e1)) = (e3)) -> (~((op (e0) (e1)) = (op (e2) (e1)))) -> (~((op (e2) (e2)) = (e3))) -> (((op (e0) (e3)) = (e1))\/(((op (e1) (e3)) = (e1))\/(((op (e2) (e3)) = (e1))\/((op (e3) (e3)) = (e1))))) -> (~((op (e0) (e2)) = (op (e0) (e3)))) -> ((op (e0) (e2)) = (e1)) -> ((op (e1) (e0)) = (e1)) -> (~((op (e1) (e0)) = (op (e1) (e3)))) -> (~((op (e0) (e3)) = (op (e2) (e3)))) -> (~((op (e0) (e3)) = (op (e1) (e3)))) -> ((op (e1) (e3)) = (e2)) -> (~((op (e0) (e0)) = (op (e0) (e3)))) -> ((op (e0) (e0)) = (e0)) -> (((op (e0) (e3)) = (e0))\/(((op (e0) (e3)) = (e1))\/(((op (e0) (e3)) = (e2))\/((op (e0) (e3)) = (e3))))) -> (~((op (e3) (e3)) = (e1))) -> False). % 15.48/15.63 do 0 intro. intros zenon_He6 zenon_H1e5 zenon_Hba zenon_H4a zenon_Hde zenon_H30 zenon_H121 zenon_Hc9 zenon_H29 zenon_Hd8 zenon_H1cf zenon_Hb4 zenon_H80 zenon_H82 zenon_H24f zenon_H1f zenon_H254 zenon_H104. % 15.48/15.63 apply (zenon_or_s _ _ zenon_He6); [ zenon_intro zenon_Haf | zenon_intro zenon_He7 ]. % 15.48/15.63 apply (zenon_L261_); trivial. % 15.48/15.63 apply (zenon_or_s _ _ zenon_He7); [ zenon_intro zenon_Hdf | zenon_intro zenon_He8 ]. % 15.48/15.63 apply (zenon_L65_); trivial. % 15.48/15.63 apply (zenon_or_s _ _ zenon_He8); [ zenon_intro zenon_H34 | zenon_intro zenon_He2 ]. % 15.48/15.63 exact (zenon_H30 zenon_H34). % 15.48/15.63 apply (zenon_or_s _ _ zenon_H121); [ zenon_intro zenon_H37 | zenon_intro zenon_H122 ]. % 15.48/15.63 apply (zenon_L85_); trivial. % 15.48/15.63 apply (zenon_or_s _ _ zenon_H122); [ zenon_intro zenon_H11f | zenon_intro zenon_H123 ]. % 15.48/15.63 apply (zenon_L224_); trivial. % 15.48/15.63 apply (zenon_or_s _ _ zenon_H123); [ zenon_intro zenon_Hb5 | zenon_intro zenon_H38 ]. % 15.48/15.63 apply (zenon_L1026_); trivial. % 15.48/15.63 exact (zenon_H104 zenon_H38). % 15.48/15.63 (* end of lemma zenon_L1038_ *) % 15.48/15.63 assert (zenon_L1039_ : (((op (e2) (e0)) = (e3))\/(((op (e2) (e1)) = (e3))\/(((op (e2) (e2)) = (e3))\/((op (e2) (e3)) = (e3))))) -> (~((e2) = (e3))) -> ((op (e2) (e0)) = (e2)) -> ((op (e0) (e1)) = (e3)) -> (~((op (e0) (e1)) = (op (e2) (e1)))) -> (~((op (e2) (e2)) = (e3))) -> (((op (e0) (e3)) = (e0))\/(((op (e0) (e3)) = (e1))\/(((op (e0) (e3)) = (e2))\/((op (e0) (e3)) = (e3))))) -> ((op (e0) (e0)) = (e0)) -> (~((op (e0) (e0)) = (op (e0) (e3)))) -> ((op (e2) (e3)) = (e1)) -> ((op (e1) (e3)) = (e2)) -> (~((op (e0) (e3)) = (op (e1) (e3)))) -> (~((op (e0) (e3)) = (op (e2) (e3)))) -> False). % 15.48/15.63 do 0 intro. intros zenon_He6 zenon_H6a zenon_Hdd zenon_H4a zenon_Hde zenon_H30 zenon_H254 zenon_H1f zenon_H24f zenon_Hb5 zenon_H82 zenon_H80 zenon_Hb4. % 15.48/15.63 apply (zenon_or_s _ _ zenon_He6); [ zenon_intro zenon_Haf | zenon_intro zenon_He7 ]. % 15.48/15.63 apply (zenon_L64_); trivial. % 15.48/15.63 apply (zenon_or_s _ _ zenon_He7); [ zenon_intro zenon_Hdf | zenon_intro zenon_He8 ]. % 15.48/15.63 apply (zenon_L65_); trivial. % 15.48/15.63 apply (zenon_or_s _ _ zenon_He8); [ zenon_intro zenon_H34 | zenon_intro zenon_He2 ]. % 15.48/15.63 exact (zenon_H30 zenon_H34). % 15.48/15.63 apply (zenon_L1026_); trivial. % 15.48/15.63 (* end of lemma zenon_L1039_ *) % 15.48/15.63 assert (zenon_L1040_ : (((op (e0) (e0)) = (e3))\/(((op (e0) (e1)) = (e3))\/(((op (e0) (e2)) = (e3))\/((op (e0) (e3)) = (e3))))) -> (~((op (e0) (e0)) = (e3))) -> (((op (e2) (e0)) = (e1))\/(((op (e2) (e1)) = (e1))\/(((op (e2) (e2)) = (e1))\/((op (e2) (e3)) = (e1))))) -> (~((e1) = (e2))) -> (~((op (e2) (op (e3) (e2))) = (op (e3) (e2)))) -> (~((e1) = (e3))) -> (~((op (e2) (e0)) = (op (e3) (e0)))) -> (((op (e0) (e3)) = (e1))\/(((op (e1) (e3)) = (e1))\/(((op (e2) (e3)) = (e1))\/((op (e3) (e3)) = (e1))))) -> (~((op (e0) (e2)) = (op (e0) (e3)))) -> ((op (e1) (e0)) = (e1)) -> (~((op (e1) (e0)) = (op (e1) (e3)))) -> (~((op (e3) (e3)) = (e1))) -> (((op (e0) (e2)) = (e1))\/(((op (e1) (e2)) = (e1))\/(((op (e2) (e2)) = (e1))\/((op (e3) (e2)) = (e1))))) -> (~((op (e2) (e2)) = (e1))) -> (((op (e2) (e0)) = (e3))\/(((op (e2) (e1)) = (e3))\/(((op (e2) (e2)) = (e3))\/((op (e2) (e3)) = (e3))))) -> ((op (e2) (e0)) = (e2)) -> (~((op (e0) (e1)) = (op (e2) (e1)))) -> (~((op (e2) (e2)) = (e3))) -> (((op (e0) (e3)) = (e0))\/(((op (e0) (e3)) = (e1))\/(((op (e0) (e3)) = (e2))\/((op (e0) (e3)) = (e3))))) -> ((op (e0) (e0)) = (e0)) -> (~((op (e0) (e0)) = (op (e0) (e3)))) -> (~((op (e0) (e3)) = (op (e1) (e3)))) -> (~((op (e0) (e3)) = (op (e2) (e3)))) -> (~((op (e1) (e1)) = (e3))) -> (((op (e1) (e0)) = (e3))\/(((op (e1) (e1)) = (e3))\/(((op (e1) (e2)) = (e3))\/((op (e1) (e3)) = (e3))))) -> (((op (e0) (e1)) = (e2))\/(((op (e1) (e1)) = (e2))\/(((op (e2) (e1)) = (e2))\/((op (e3) (e1)) = (e2))))) -> (~((op (e3) (e3)) = (e2))) -> (~((op (e0) (e1)) = (op (e0) (e3)))) -> (((op (e0) (e3)) = (e2))\/(((op (e1) (e3)) = (e2))\/(((op (e2) (e3)) = (e2))\/((op (e3) (e3)) = (e2))))) -> (~((op (e1) (e0)) = (op (e1) (e2)))) -> (~((op (e1) (e1)) = (e2))) -> (~((op (e2) (e0)) = (op (e2) (e1)))) -> (~((op (e1) (op (e3) (e1))) = (op (e3) (e1)))) -> (((op (e1) (e0)) = (e2))\/(((op (e1) (e1)) = (e2))\/(((op (e1) (e2)) = (e2))\/((op (e1) (e3)) = (e2))))) -> (~((e2) = (e3))) -> ((op (e0) (e2)) = (e2)) -> (~((op (e0) (op (e3) (e0))) = (op (e3) (e0)))) -> ((op (e3) (e0)) = (e3)) -> False). % 15.48/15.63 do 0 intro. intros zenon_H58 zenon_H59 zenon_Hb7 zenon_Ha7 zenon_H2af zenon_Ha3 zenon_H1e5 zenon_H121 zenon_Hc9 zenon_Hd8 zenon_H1cf zenon_H104 zenon_H11b zenon_H52 zenon_He6 zenon_Hdd zenon_Hde zenon_H30 zenon_H254 zenon_H1f zenon_H24f zenon_H80 zenon_Hb4 zenon_H182 zenon_H90 zenon_H1a2 zenon_H3d zenon_H1cd zenon_H160 zenon_H166 zenon_Hd6 zenon_H154 zenon_H2b4 zenon_H84 zenon_H6a zenon_H63 zenon_H2b8 zenon_Hba. % 15.48/15.63 apply (zenon_or_s _ _ zenon_H58); [ zenon_intro zenon_H5b | zenon_intro zenon_H5a ]. % 15.48/15.63 exact (zenon_H59 zenon_H5b). % 15.48/15.63 apply (zenon_or_s _ _ zenon_H5a); [ zenon_intro zenon_H4a | zenon_intro zenon_H5c ]. % 15.48/15.63 apply (zenon_or_s _ _ zenon_H84); [ zenon_intro zenon_H68 | zenon_intro zenon_H85 ]. % 15.48/15.63 apply (zenon_L162_); trivial. % 15.48/15.63 apply (zenon_or_s _ _ zenon_H85); [ zenon_intro zenon_H6e | zenon_intro zenon_H86 ]. % 15.48/15.63 exact (zenon_Hd6 zenon_H6e). % 15.48/15.63 apply (zenon_or_s _ _ zenon_H86); [ zenon_intro zenon_H7c | zenon_intro zenon_H82 ]. % 15.48/15.63 apply (zenon_or_s _ _ zenon_H1a2); [ zenon_intro zenon_H5d | zenon_intro zenon_H1a3 ]. % 15.48/15.63 apply (zenon_L1029_); trivial. % 15.48/15.63 apply (zenon_or_s _ _ zenon_H1a3); [ zenon_intro zenon_H6e | zenon_intro zenon_H1a4 ]. % 15.48/15.63 exact (zenon_Hd6 zenon_H6e). % 15.48/15.63 apply (zenon_or_s _ _ zenon_H1a4); [ zenon_intro zenon_H156 | zenon_intro zenon_H16a ]. % 15.48/15.63 apply (zenon_L284_); trivial. % 15.48/15.63 apply (zenon_L1031_); trivial. % 15.48/15.63 apply (zenon_or_s _ _ zenon_H90); [ zenon_intro zenon_H69 | zenon_intro zenon_H94 ]. % 15.48/15.63 apply (zenon_L163_); trivial. % 15.48/15.63 apply (zenon_or_s _ _ zenon_H94); [ zenon_intro zenon_H96 | zenon_intro zenon_H95 ]. % 15.48/15.63 exact (zenon_H182 zenon_H96). % 15.48/15.63 apply (zenon_or_s _ _ zenon_H95); [ zenon_intro zenon_H88 | zenon_intro zenon_H8a ]. % 15.48/15.63 apply (zenon_or_s _ _ zenon_Hb7); [ zenon_intro zenon_Hae | zenon_intro zenon_Hb8 ]. % 15.48/15.63 apply (zenon_L304_); trivial. % 15.48/15.63 apply (zenon_or_s _ _ zenon_Hb8); [ zenon_intro zenon_Hb2 | zenon_intro zenon_Hb9 ]. % 15.48/15.63 apply (zenon_or_s _ _ zenon_H11b); [ zenon_intro zenon_H29 | zenon_intro zenon_H11c ]. % 15.48/15.63 apply (zenon_L1038_); trivial. % 15.48/15.63 apply (zenon_or_s _ _ zenon_H11c); [ zenon_intro zenon_H117 | zenon_intro zenon_H11d ]. % 15.48/15.63 apply (zenon_L196_); trivial. % 15.48/15.63 apply (zenon_or_s _ _ zenon_H11d); [ zenon_intro zenon_H2a | zenon_intro zenon_H119 ]. % 15.48/15.63 exact (zenon_H52 zenon_H2a). % 15.48/15.63 apply (zenon_L1024_); trivial. % 15.48/15.63 apply (zenon_or_s _ _ zenon_Hb9); [ zenon_intro zenon_H2a | zenon_intro zenon_Hb5 ]. % 15.48/15.63 exact (zenon_H52 zenon_H2a). % 15.48/15.63 apply (zenon_L1039_); trivial. % 15.48/15.63 apply (zenon_L165_); trivial. % 15.48/15.63 apply (zenon_or_s _ _ zenon_H5c); [ zenon_intro zenon_H50 | zenon_intro zenon_H53 ]. % 15.48/15.63 apply (zenon_L31_); trivial. % 15.48/15.63 apply (zenon_L1035_); trivial. % 15.48/15.63 (* end of lemma zenon_L1040_ *) % 15.48/15.63 assert (zenon_L1041_ : (~((op (e3) (op (e3) (e3))) = (op (e3) (e3)))) -> ((op (e3) (e3)) = (e3)) -> False). % 15.48/15.63 do 0 intro. intros zenon_H2be zenon_H42. % 15.48/15.63 cut (((op (e3) (e3)) = (e3))); [idtac | apply NNPP; zenon_intro zenon_H3e]. % 15.48/15.63 cut (((e3) = (e3))); [idtac | apply NNPP; zenon_intro zenon_H4d]. % 15.48/15.63 congruence. % 15.48/15.63 apply zenon_H4d. apply refl_equal. % 15.48/15.63 exact (zenon_H3e zenon_H42). % 15.48/15.63 (* end of lemma zenon_L1041_ *) % 15.48/15.63 assert (zenon_L1042_ : (((op (e0) (e0)) = (e3))\/(((op (e0) (e1)) = (e3))\/(((op (e0) (e2)) = (e3))\/((op (e0) (e3)) = (e3))))) -> (~((op (e0) (e1)) = (op (e3) (e1)))) -> ((op (e3) (e1)) = (e3)) -> (~((op (e0) (e2)) = (op (e1) (e2)))) -> (~((op (e1) (e1)) = (e3))) -> (((op (e1) (e0)) = (e3))\/(((op (e1) (e1)) = (e3))\/(((op (e1) (e2)) = (e3))\/((op (e1) (e3)) = (e3))))) -> (((op (e2) (e0)) = (e1))\/(((op (e2) (e1)) = (e1))\/(((op (e2) (e2)) = (e1))\/((op (e2) (e3)) = (e1))))) -> (~((op (e1) (e0)) = (op (e2) (e0)))) -> (~((op (e2) (op (e3) (e2))) = (op (e3) (e2)))) -> (~((op (e1) (e0)) = (op (e1) (e2)))) -> (((op (e0) (e2)) = (e1))\/(((op (e1) (e2)) = (e1))\/(((op (e2) (e2)) = (e1))\/((op (e3) (e2)) = (e1))))) -> (~((op (e2) (e2)) = (e1))) -> (((op (e0) (e3)) = (e2))\/(((op (e1) (e3)) = (e2))\/(((op (e2) (e3)) = (e2))\/((op (e3) (e3)) = (e2))))) -> (~((op (e1) (op (e3) (e1))) = (op (e3) (e1)))) -> (~((op (e2) (e0)) = (op (e2) (e1)))) -> (~((op (e1) (e1)) = (e2))) -> (~((op (e0) (e1)) = (op (e0) (e3)))) -> (((op (e0) (e1)) = (e2))\/(((op (e1) (e1)) = (e2))\/(((op (e2) (e1)) = (e2))\/((op (e3) (e1)) = (e2))))) -> (~((e1) = (e2))) -> (~((op (e3) (e3)) = (e2))) -> (((op (e1) (e0)) = (e2))\/(((op (e1) (e1)) = (e2))\/(((op (e1) (e2)) = (e2))\/((op (e1) (e3)) = (e2))))) -> (((op (e0) (e0)) = (e3))\/(((op (e1) (e0)) = (e3))\/(((op (e2) (e0)) = (e3))\/((op (e3) (e0)) = (e3))))) -> (~((op (e0) (e0)) = (e3))) -> (~((e1) = (e3))) -> ((op (e1) (e0)) = (e1)) -> (~((e2) = (e3))) -> ((op (e2) (e0)) = (e2)) -> (~((op (e0) (op (e3) (e0))) = (op (e3) (e0)))) -> False). % 15.48/15.63 do 0 intro. intros zenon_H58 zenon_H138 zenon_H10a zenon_H87 zenon_H182 zenon_H90 zenon_Hb7 zenon_H247 zenon_H2af zenon_H166 zenon_H11b zenon_H52 zenon_H160 zenon_H2b4 zenon_H154 zenon_Hd6 zenon_H1cd zenon_H1a2 zenon_Ha7 zenon_H3d zenon_H84 zenon_Hbe zenon_H59 zenon_Ha3 zenon_Hd8 zenon_H6a zenon_Hdd zenon_H2b8. % 15.48/15.63 apply (zenon_or_s _ _ zenon_H58); [ zenon_intro zenon_H5b | zenon_intro zenon_H5a ]. % 15.48/15.63 exact (zenon_H59 zenon_H5b). % 15.48/15.63 apply (zenon_or_s _ _ zenon_H5a); [ zenon_intro zenon_H4a | zenon_intro zenon_H5c ]. % 15.48/15.63 apply (zenon_L120_); trivial. % 15.48/15.63 apply (zenon_or_s _ _ zenon_H5c); [ zenon_intro zenon_H50 | zenon_intro zenon_H53 ]. % 15.48/15.63 apply (zenon_L1034_); trivial. % 15.48/15.63 apply (zenon_L1036_); trivial. % 15.48/15.63 (* end of lemma zenon_L1042_ *) % 15.48/15.63 assert (zenon_L1043_ : (((op (e1) (e0)) = (e2))\/(((op (e1) (e1)) = (e2))\/(((op (e1) (e2)) = (e2))\/((op (e1) (e3)) = (e2))))) -> (~((e1) = (e2))) -> ((op (e1) (e0)) = (e1)) -> (~((op (e1) (op (e3) (e1))) = (op (e3) (e1)))) -> (~((op (e2) (e0)) = (op (e2) (e1)))) -> ((op (e2) (e0)) = (e2)) -> (~((op (e1) (e1)) = (e2))) -> (~((op (e0) (e1)) = (op (e0) (e3)))) -> (((op (e0) (e1)) = (e2))\/(((op (e1) (e1)) = (e2))\/(((op (e2) (e1)) = (e2))\/((op (e3) (e1)) = (e2))))) -> (~((op (e0) (e3)) = (op (e1) (e3)))) -> ((op (e0) (e3)) = (e2)) -> False). % 15.48/15.63 do 0 intro. intros zenon_H84 zenon_Ha7 zenon_Hd8 zenon_H2b4 zenon_H154 zenon_Hdd zenon_Hd6 zenon_H1cd zenon_H1a2 zenon_H80 zenon_H81. % 15.48/15.63 apply (zenon_or_s _ _ zenon_H84); [ zenon_intro zenon_H68 | zenon_intro zenon_H85 ]. % 15.48/15.63 apply (zenon_L162_); trivial. % 15.48/15.63 apply (zenon_or_s _ _ zenon_H85); [ zenon_intro zenon_H6e | zenon_intro zenon_H86 ]. % 15.48/15.63 exact (zenon_Hd6 zenon_H6e). % 15.48/15.63 apply (zenon_or_s _ _ zenon_H86); [ zenon_intro zenon_H7c | zenon_intro zenon_H82 ]. % 15.48/15.63 apply (zenon_L1032_); trivial. % 15.48/15.63 apply (zenon_L22_); trivial. % 15.48/15.63 (* end of lemma zenon_L1043_ *) % 15.48/15.63 assert (zenon_L1044_ : ((~((op (e2) (e2)) = (e1)))\/((op (e2) (e1)) = (e2))) -> ((~((op (e3) (e3)) = (e0)))\/((op (e3) (e0)) = (e3))) -> (~((op (e3) (e0)) = (op (e3) (e1)))) -> ((~((op (e3) (e3)) = (e2)))\/((op (e3) (e2)) = (e3))) -> (~((op (e3) (e0)) = (op (e3) (e2)))) -> (((op (e0) (e0)) = (e2))\/(((op (e0) (e1)) = (e2))\/(((op (e0) (e2)) = (e2))\/((op (e0) (e3)) = (e2))))) -> (~((op (e0) (e3)) = (op (e3) (e3)))) -> (((op (e3) (e3)) = (e0))\/(((op (e3) (e3)) = (e1))\/(((op (e3) (e3)) = (e2))\/((op (e3) (e3)) = (e3))))) -> (~((op (e2) (e0)) = (op (e3) (e0)))) -> (~((op (e0) (e0)) = (e3))) -> (((op (e2) (e0)) = (e1))\/(((op (e2) (e1)) = (e1))\/(((op (e2) (e2)) = (e1))\/((op (e2) (e3)) = (e1))))) -> (~((e2) = (e3))) -> (~((op (e0) (e1)) = (op (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) (e3)) = (e0))\/(((op (e0) (e3)) = (e1))\/(((op (e0) (e3)) = (e2))\/((op (e0) (e3)) = (e3))))) -> (~((op (e0) (e3)) = (op (e1) (e3)))) -> (~((op (e0) (e3)) = (op (e2) (e3)))) -> ((op (e0) (e0)) = (e0)) -> (~((op (e0) (e0)) = (op (e0) (e3)))) -> (((op (e0) (e3)) = (e2))\/(((op (e1) (e3)) = (e2))\/(((op (e2) (e3)) = (e2))\/((op (e3) (e3)) = (e2))))) -> (~((op (e1) (e0)) = (op (e1) (e3)))) -> (~((op (e0) (e2)) = (op (e0) (e3)))) -> (~((op (e1) (e0)) = (op (e1) (e2)))) -> ((op (e1) (e0)) = (e1)) -> (~((op (e2) (op (e3) (e2))) = (op (e3) (e2)))) -> (((op (e0) (e2)) = (e1))\/(((op (e1) (e2)) = (e1))\/(((op (e2) (e2)) = (e1))\/((op (e3) (e2)) = (e1))))) -> (((op (e2) (e0)) = (e3))\/(((op (e2) (e1)) = (e3))\/(((op (e2) (e2)) = (e3))\/((op (e2) (e3)) = (e3))))) -> ((op (e2) (e0)) = (e2)) -> (~((e1) = (e2))) -> (((op (e1) (e0)) = (e2))\/(((op (e1) (e1)) = (e2))\/(((op (e1) (e2)) = (e2))\/((op (e1) (e3)) = (e2))))) -> (~((e1) = (e3))) -> (~((op (e1) (e1)) = (e3))) -> (~((op (e0) (e2)) = (op (e1) (e2)))) -> (((op (e0) (e1)) = (e2))\/(((op (e1) (e1)) = (e2))\/(((op (e2) (e1)) = (e2))\/((op (e3) (e1)) = (e2))))) -> (~((op (e1) (op (e3) (e1))) = (op (e3) (e1)))) -> (~((op (e2) (e0)) = (op (e2) (e1)))) -> (~((op (e1) (e0)) = (op (e2) (e0)))) -> (((op (e1) (e0)) = (e3))\/(((op (e1) (e1)) = (e3))\/(((op (e1) (e2)) = (e3))\/((op (e1) (e3)) = (e3))))) -> (~((op (e1) (e1)) = (e2))) -> (((op (e0) (e0)) = (e3))\/(((op (e1) (e0)) = (e3))\/(((op (e2) (e0)) = (e3))\/((op (e3) (e0)) = (e3))))) -> (~((op (e0) (op (e3) (e0))) = (op (e3) (e0)))) -> (((op (e0) (e0)) = (e3))\/(((op (e0) (e1)) = (e3))\/(((op (e0) (e2)) = (e3))\/((op (e0) (e3)) = (e3))))) -> (~((op (e0) (e0)) = (e2))) -> (~((op (e3) (op (e3) (e3))) = (op (e3) (e3)))) -> ((~((op (e3) (e3)) = (e3)))\/((op (e3) (e3)) = (e3))) -> (~((op (e3) (e1)) = (op (e3) (e2)))) -> (~((op (e0) (e1)) = (op (e3) (e1)))) -> ((~((op (e3) (e3)) = (e1)))\/((op (e3) (e1)) = (e3))) -> (~((op (e2) (e0)) = (op (e2) (e3)))) -> ((~((op (e2) (e2)) = (e3)))\/((op (e2) (e3)) = (e2))) -> False). % 15.48/15.63 do 0 intro. intros zenon_H1e3 zenon_H10f zenon_H109 zenon_H10e zenon_H105 zenon_H8e zenon_H36 zenon_H3b zenon_H1e5 zenon_H59 zenon_Hb7 zenon_H6a zenon_Hde zenon_H121 zenon_H1cd zenon_H254 zenon_H80 zenon_Hb4 zenon_H1f zenon_H24f zenon_H160 zenon_H1cf zenon_Hc9 zenon_H166 zenon_Hd8 zenon_H2af zenon_H11b zenon_He6 zenon_Hdd zenon_Ha7 zenon_H84 zenon_Ha3 zenon_H182 zenon_H87 zenon_H1a2 zenon_H2b4 zenon_H154 zenon_H247 zenon_H90 zenon_Hd6 zenon_Hbe zenon_H2b8 zenon_H58 zenon_H8f zenon_H2be zenon_H10d zenon_H135 zenon_H138 zenon_H10c zenon_Hce zenon_H1c3. % 15.48/15.63 apply (zenon_or_s _ _ zenon_H1e3); [ zenon_intro zenon_H52 | zenon_intro zenon_H156 ]. % 15.48/15.63 apply (zenon_or_s _ _ zenon_H1c3); [ zenon_intro zenon_H30 | zenon_intro zenon_H124 ]. % 15.48/15.63 apply (zenon_or_s _ _ zenon_H10f); [ zenon_intro zenon_H3c | zenon_intro zenon_Hba ]. % 15.48/15.63 apply (zenon_or_s _ _ zenon_H10c); [ zenon_intro zenon_H104 | zenon_intro zenon_H10a ]. % 15.48/15.63 apply (zenon_or_s _ _ zenon_H10e); [ zenon_intro zenon_H3d | zenon_intro zenon_H106 ]. % 15.48/15.63 apply (zenon_or_s _ _ zenon_H10d); [ zenon_intro zenon_H3e | zenon_intro zenon_H42 ]. % 15.48/15.63 apply (zenon_or_s _ _ zenon_H8e); [ zenon_intro zenon_H92 | zenon_intro zenon_H91 ]. % 15.48/15.63 exact (zenon_H8f zenon_H92). % 15.48/15.63 apply (zenon_or_s _ _ zenon_H91); [ zenon_intro zenon_H5d | zenon_intro zenon_H93 ]. % 15.48/15.63 apply (zenon_L1037_); trivial. % 15.48/15.63 apply (zenon_or_s _ _ zenon_H93); [ zenon_intro zenon_H63 | zenon_intro zenon_H81 ]. % 15.48/15.63 apply (zenon_or_s _ _ zenon_Hbe); [ zenon_intro zenon_H5b | zenon_intro zenon_Hbf ]. % 15.48/15.63 exact (zenon_H59 zenon_H5b). % 15.48/15.63 apply (zenon_or_s _ _ zenon_Hbf); [ zenon_intro zenon_H69 | zenon_intro zenon_Hc0 ]. % 15.48/15.63 apply (zenon_L163_); trivial. % 15.48/15.63 apply (zenon_or_s _ _ zenon_Hc0); [ zenon_intro zenon_Haf | zenon_intro zenon_Hba ]. % 15.48/15.63 apply (zenon_L64_); trivial. % 15.48/15.63 apply (zenon_L1040_); trivial. % 15.48/15.63 apply (zenon_L107_); trivial. % 15.48/15.63 apply (zenon_L1041_); trivial. % 15.48/15.63 apply (zenon_L456_); trivial. % 15.48/15.63 apply (zenon_or_s _ _ zenon_H10e); [ zenon_intro zenon_H3d | zenon_intro zenon_H106 ]. % 15.48/15.63 apply (zenon_L1042_); trivial. % 15.48/15.63 apply (zenon_L115_); trivial. % 15.48/15.63 apply (zenon_or_s _ _ zenon_H10c); [ zenon_intro zenon_H104 | zenon_intro zenon_H10a ]. % 15.48/15.63 apply (zenon_or_s _ _ zenon_H10e); [ zenon_intro zenon_H3d | zenon_intro zenon_H106 ]. % 15.48/15.63 apply (zenon_or_s _ _ zenon_H8e); [ zenon_intro zenon_H92 | zenon_intro zenon_H91 ]. % 15.48/15.63 exact (zenon_H8f zenon_H92). % 15.48/15.63 apply (zenon_or_s _ _ zenon_H91); [ zenon_intro zenon_H5d | zenon_intro zenon_H93 ]. % 15.48/15.63 apply (zenon_or_s _ _ zenon_H58); [ zenon_intro zenon_H5b | zenon_intro zenon_H5a ]. % 15.48/15.63 exact (zenon_H59 zenon_H5b). % 15.48/15.63 apply (zenon_or_s _ _ zenon_H5a); [ zenon_intro zenon_H4a | zenon_intro zenon_H5c ]. % 15.48/15.63 apply (zenon_L1029_); trivial. % 15.48/15.63 apply (zenon_or_s _ _ zenon_H5c); [ zenon_intro zenon_H50 | zenon_intro zenon_H53 ]. % 15.48/15.63 apply (zenon_L1034_); trivial. % 15.48/15.63 apply (zenon_L1035_); trivial. % 15.48/15.63 apply (zenon_or_s _ _ zenon_H93); [ zenon_intro zenon_H63 | zenon_intro zenon_H81 ]. % 15.48/15.63 apply (zenon_L1040_); trivial. % 15.48/15.63 apply (zenon_L1043_); trivial. % 15.48/15.63 apply (zenon_L81_); trivial. % 15.48/15.63 apply (zenon_L82_); trivial. % 15.48/15.63 apply (zenon_L119_); trivial. % 15.48/15.63 apply (zenon_L284_); trivial. % 15.48/15.63 (* end of lemma zenon_L1044_ *) % 15.48/15.63 assert (zenon_L1045_ : (~((op (e0) (op (e3) (e0))) = (op (e3) (e0)))) -> ((op (e0) (e0)) = (e0)) -> ((op (e3) (e0)) = (e0)) -> False). % 15.48/15.63 do 0 intro. intros zenon_H2b8 zenon_H1f zenon_Hdb. % 15.48/15.63 cut (((op (e0) (e0)) = (e0)) = ((op (e0) (op (e3) (e0))) = (op (e3) (e0)))). % 15.48/15.63 intro zenon_D_pnotp. % 15.48/15.63 apply zenon_H2b8. % 15.48/15.63 rewrite <- zenon_D_pnotp. % 15.48/15.63 exact zenon_H1f. % 15.48/15.63 cut (((e0) = (op (e3) (e0)))); [idtac | apply NNPP; zenon_intro zenon_H2bf]. % 15.48/15.63 cut (((op (e0) (e0)) = (op (e0) (op (e3) (e0))))); [idtac | apply NNPP; zenon_intro zenon_H2c0]. % 15.48/15.63 congruence. % 15.48/15.63 elim (classic ((op (e0) (op (e3) (e0))) = (op (e0) (op (e3) (e0))))); [ zenon_intro zenon_H2ba | zenon_intro zenon_H2bb ]. % 15.48/15.63 cut (((op (e0) (op (e3) (e0))) = (op (e0) (op (e3) (e0)))) = ((op (e0) (e0)) = (op (e0) (op (e3) (e0))))). % 15.48/15.63 intro zenon_D_pnotp. % 15.48/15.63 apply zenon_H2c0. % 15.48/15.63 rewrite <- zenon_D_pnotp. % 15.48/15.63 exact zenon_H2ba. % 15.48/15.63 cut (((op (e0) (op (e3) (e0))) = (op (e0) (op (e3) (e0))))); [idtac | apply NNPP; zenon_intro zenon_H2bb]. % 15.48/15.63 cut (((op (e0) (op (e3) (e0))) = (op (e0) (e0)))); [idtac | apply NNPP; zenon_intro zenon_H2c1]. % 15.48/15.63 congruence. % 15.48/15.63 cut (((op (e3) (e0)) = (e0))); [idtac | apply NNPP; zenon_intro zenon_Hdc]. % 15.48/15.63 cut (((e0) = (e0))); [idtac | apply NNPP; zenon_intro zenon_H1d]. % 15.48/15.63 congruence. % 15.48/15.63 apply zenon_H1d. apply refl_equal. % 15.48/15.63 exact (zenon_Hdc zenon_Hdb). % 15.48/15.63 apply zenon_H2bb. apply refl_equal. % 15.48/15.63 apply zenon_H2bb. apply refl_equal. % 15.48/15.63 apply zenon_H2bf. apply sym_equal. exact zenon_Hdb. % 15.48/15.63 (* end of lemma zenon_L1045_ *) % 15.48/15.63 assert (zenon_L1046_ : (~((op (e1) (op (e3) (e1))) = (op (e1) (e0)))) -> ((op (e3) (e1)) = (e0)) -> False). % 15.48/15.63 do 0 intro. intros zenon_H2c2 zenon_H142. % 15.48/15.63 cut (((op (e3) (e1)) = (e0))); [idtac | apply NNPP; zenon_intro zenon_H143]. % 15.48/15.63 cut (((e1) = (e1))); [idtac | apply NNPP; zenon_intro zenon_Ha0]. % 15.48/15.63 congruence. % 15.48/15.63 apply zenon_Ha0. apply refl_equal. % 15.48/15.63 exact (zenon_H143 zenon_H142). % 15.48/15.63 (* end of lemma zenon_L1046_ *) % 15.48/15.63 assert (zenon_L1047_ : (~((op (e1) (op (e3) (e1))) = (op (e3) (e1)))) -> ((op (e1) (e0)) = (e1)) -> ((op (e3) (e1)) = (e0)) -> ((op (e3) (e1)) = (e1)) -> False). % 15.48/15.63 do 0 intro. intros zenon_H2b4 zenon_Hd8 zenon_H142 zenon_H13e. % 15.48/15.63 cut (((op (e1) (e0)) = (e1)) = ((op (e1) (op (e3) (e1))) = (op (e3) (e1)))). % 15.48/15.63 intro zenon_D_pnotp. % 15.48/15.63 apply zenon_H2b4. % 15.48/15.63 rewrite <- zenon_D_pnotp. % 15.48/15.63 exact zenon_Hd8. % 15.48/15.63 cut (((e1) = (op (e3) (e1)))); [idtac | apply NNPP; zenon_intro zenon_H169]. % 15.48/15.63 cut (((op (e1) (e0)) = (op (e1) (op (e3) (e1))))); [idtac | apply NNPP; zenon_intro zenon_H2c3]. % 15.48/15.63 congruence. % 15.48/15.63 elim (classic ((op (e1) (op (e3) (e1))) = (op (e1) (op (e3) (e1))))); [ zenon_intro zenon_H2b6 | zenon_intro zenon_H2b7 ]. % 15.48/15.63 cut (((op (e1) (op (e3) (e1))) = (op (e1) (op (e3) (e1)))) = ((op (e1) (e0)) = (op (e1) (op (e3) (e1))))). % 15.48/15.63 intro zenon_D_pnotp. % 15.48/15.63 apply zenon_H2c3. % 15.48/15.63 rewrite <- zenon_D_pnotp. % 15.48/15.63 exact zenon_H2b6. % 15.48/15.63 cut (((op (e1) (op (e3) (e1))) = (op (e1) (op (e3) (e1))))); [idtac | apply NNPP; zenon_intro zenon_H2b7]. % 15.48/15.63 cut (((op (e1) (op (e3) (e1))) = (op (e1) (e0)))); [idtac | apply NNPP; zenon_intro zenon_H2c2]. % 15.48/15.63 congruence. % 15.48/15.63 apply (zenon_L1046_); trivial. % 15.48/15.63 apply zenon_H2b7. apply refl_equal. % 15.48/15.63 apply zenon_H2b7. apply refl_equal. % 15.48/15.63 apply zenon_H169. apply sym_equal. exact zenon_H13e. % 15.48/15.63 (* end of lemma zenon_L1047_ *) % 15.48/15.63 assert (zenon_L1048_ : (((op (e3) (e0)) = (e1))\/(((op (e3) (e1)) = (e1))\/(((op (e3) (e2)) = (e1))\/((op (e3) (e3)) = (e1))))) -> (~((op (e1) (e0)) = (op (e3) (e0)))) -> ((op (e3) (e1)) = (e0)) -> ((op (e1) (e0)) = (e1)) -> (~((op (e1) (op (e3) (e1))) = (op (e3) (e1)))) -> ((op (e3) (e2)) = (e3)) -> (~((e1) = (e3))) -> (~((op (e3) (e3)) = (e1))) -> False). % 15.48/15.63 do 0 intro. intros zenon_H146 zenon_H22e zenon_H142 zenon_Hd8 zenon_H2b4 zenon_H106 zenon_Ha3 zenon_H104. % 15.48/15.63 apply (zenon_or_s _ _ zenon_H146); [ zenon_intro zenon_Hee | zenon_intro zenon_H14b ]. % 15.48/15.63 apply (zenon_L393_); trivial. % 15.48/15.63 apply (zenon_or_s _ _ zenon_H14b); [ zenon_intro zenon_H13e | zenon_intro zenon_H14c ]. % 15.48/15.63 apply (zenon_L1047_); trivial. % 15.48/15.63 apply (zenon_or_s _ _ zenon_H14c); [ zenon_intro zenon_H119 | zenon_intro zenon_H38 ]. % 15.48/15.63 apply (zenon_L87_); trivial. % 15.48/15.63 exact (zenon_H104 zenon_H38). % 15.48/15.63 (* end of lemma zenon_L1048_ *) % 15.48/15.63 assert (zenon_L1049_ : (((op (e3) (e0)) = (e0))\/(((op (e3) (e1)) = (e0))\/(((op (e3) (e2)) = (e0))\/((op (e3) (e3)) = (e0))))) -> ((op (e0) (e0)) = (e0)) -> (~((op (e0) (op (e3) (e0))) = (op (e3) (e0)))) -> (~((op (e3) (e3)) = (e1))) -> (~((e1) = (e3))) -> ((op (e3) (e2)) = (e3)) -> (~((op (e1) (op (e3) (e1))) = (op (e3) (e1)))) -> ((op (e1) (e0)) = (e1)) -> (~((op (e1) (e0)) = (op (e3) (e0)))) -> (((op (e3) (e0)) = (e1))\/(((op (e3) (e1)) = (e1))\/(((op (e3) (e2)) = (e1))\/((op (e3) (e3)) = (e1))))) -> ((op (e1) (e2)) = (e0)) -> (~((op (e1) (e2)) = (op (e3) (e2)))) -> (~((op (e3) (e3)) = (e0))) -> False). % 15.48/15.63 do 0 intro. intros zenon_H1f6 zenon_H1f zenon_H2b8 zenon_H104 zenon_Ha3 zenon_H106 zenon_H2b4 zenon_Hd8 zenon_H22e zenon_H146 zenon_H15d zenon_H17d zenon_H3c. % 15.48/15.63 apply (zenon_or_s _ _ zenon_H1f6); [ zenon_intro zenon_Hdb | zenon_intro zenon_H1f7 ]. % 15.48/15.63 apply (zenon_L1045_); trivial. % 15.48/15.63 apply (zenon_or_s _ _ zenon_H1f7); [ zenon_intro zenon_H142 | zenon_intro zenon_H1f8 ]. % 15.48/15.63 apply (zenon_L1048_); trivial. % 15.48/15.63 apply (zenon_or_s _ _ zenon_H1f8); [ zenon_intro zenon_H167 | zenon_intro zenon_H40 ]. % 15.48/15.63 apply (zenon_L626_); trivial. % 15.48/15.63 exact (zenon_H3c zenon_H40). % 15.48/15.63 (* end of lemma zenon_L1049_ *) % 15.48/15.63 assert (zenon_L1050_ : (((op (e0) (e2)) = (e0))\/(((op (e1) (e2)) = (e0))\/(((op (e2) (e2)) = (e0))\/((op (e3) (e2)) = (e0))))) -> (~((op (e0) (e0)) = (op (e0) (e2)))) -> (~((op (e3) (e3)) = (e0))) -> (~((op (e1) (e2)) = (op (e3) (e2)))) -> (((op (e3) (e0)) = (e1))\/(((op (e3) (e1)) = (e1))\/(((op (e3) (e2)) = (e1))\/((op (e3) (e3)) = (e1))))) -> (~((op (e1) (e0)) = (op (e3) (e0)))) -> ((op (e1) (e0)) = (e1)) -> (~((op (e1) (op (e3) (e1))) = (op (e3) (e1)))) -> (~((e1) = (e3))) -> (~((op (e3) (e3)) = (e1))) -> (~((op (e0) (op (e3) (e0))) = (op (e3) (e0)))) -> ((op (e0) (e0)) = (e0)) -> (((op (e3) (e0)) = (e0))\/(((op (e3) (e1)) = (e0))\/(((op (e3) (e2)) = (e0))\/((op (e3) (e3)) = (e0))))) -> (~((op (e2) (e2)) = (e0))) -> (~((e0) = (e3))) -> ((op (e3) (e2)) = (e3)) -> False). % 15.48/15.63 do 0 intro. intros zenon_H16f zenon_H250 zenon_H3c zenon_H17d zenon_H146 zenon_H22e zenon_Hd8 zenon_H2b4 zenon_Ha3 zenon_H104 zenon_H2b8 zenon_H1f zenon_H1f6 zenon_H2e zenon_H4b zenon_H106. % 15.48/15.63 apply (zenon_or_s _ _ zenon_H16f); [ zenon_intro zenon_Hab | zenon_intro zenon_H170 ]. % 15.48/15.63 apply (zenon_L567_); trivial. % 15.48/15.63 apply (zenon_or_s _ _ zenon_H170); [ zenon_intro zenon_H15d | zenon_intro zenon_H171 ]. % 15.48/15.63 apply (zenon_L1049_); trivial. % 15.48/15.63 apply (zenon_or_s _ _ zenon_H171); [ zenon_intro zenon_H32 | zenon_intro zenon_H167 ]. % 15.48/15.63 exact (zenon_H2e zenon_H32). % 15.48/15.63 apply (zenon_L589_); trivial. % 15.48/15.63 (* end of lemma zenon_L1050_ *) % 15.48/15.63 assert (zenon_L1051_ : (~((op (e0) (e0)) = (op (e0) (e2)))) -> (((op (e3) (e0)) = (e0))\/(((op (e3) (e1)) = (e0))\/(((op (e3) (e2)) = (e0))\/((op (e3) (e3)) = (e0))))) -> (~((op (e1) (e2)) = (op (e3) (e2)))) -> (~((op (e1) (e0)) = (op (e3) (e0)))) -> (~((op (e3) (e3)) = (e1))) -> (((op (e3) (e0)) = (e1))\/(((op (e3) (e1)) = (e1))\/(((op (e3) (e2)) = (e1))\/((op (e3) (e3)) = (e1))))) -> (~((op (e2) (e2)) = (e0))) -> (~((e0) = (e3))) -> (((op (e0) (e2)) = (e0))\/(((op (e1) (e2)) = (e0))\/(((op (e2) (e2)) = (e0))\/((op (e3) (e2)) = (e0))))) -> (((op (e0) (e0)) = (e2))\/(((op (e1) (e0)) = (e2))\/(((op (e2) (e0)) = (e2))\/((op (e3) (e0)) = (e2))))) -> (~((op (e3) (e3)) = (e0))) -> (~((op (e1) (e1)) = (e1))) -> (((op (e1) (e1)) = (e0))\/(((op (e1) (e1)) = (e1))\/(((op (e1) (e1)) = (e2))\/((op (e1) (e1)) = (e3))))) -> ((~((op (e2) (e2)) = (e3)))\/((op (e2) (e3)) = (e2))) -> (~((op (e2) (e0)) = (op (e2) (e3)))) -> ((~((op (e3) (e3)) = (e1)))\/((op (e3) (e1)) = (e3))) -> (~((op (e0) (e1)) = (op (e3) (e1)))) -> (~((op (e3) (e1)) = (op (e3) (e2)))) -> ((~((op (e3) (e3)) = (e3)))\/((op (e3) (e3)) = (e3))) -> (~((op (e3) (op (e3) (e3))) = (op (e3) (e3)))) -> (((op (e0) (e0)) = (e3))\/(((op (e0) (e1)) = (e3))\/(((op (e0) (e2)) = (e3))\/((op (e0) (e3)) = (e3))))) -> (~((op (e0) (op (e3) (e0))) = (op (e3) (e0)))) -> (((op (e0) (e0)) = (e3))\/(((op (e1) (e0)) = (e3))\/(((op (e2) (e0)) = (e3))\/((op (e3) (e0)) = (e3))))) -> (~((op (e1) (e1)) = (e2))) -> (((op (e1) (e0)) = (e3))\/(((op (e1) (e1)) = (e3))\/(((op (e1) (e2)) = (e3))\/((op (e1) (e3)) = (e3))))) -> (~((op (e1) (e0)) = (op (e2) (e0)))) -> (~((op (e2) (e0)) = (op (e2) (e1)))) -> (~((op (e1) (op (e3) (e1))) = (op (e3) (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) (e1)) = (e3))) -> (~((e1) = (e3))) -> (((op (e1) (e0)) = (e2))\/(((op (e1) (e1)) = (e2))\/(((op (e1) (e2)) = (e2))\/((op (e1) (e3)) = (e2))))) -> (((op (e2) (e0)) = (e3))\/(((op (e2) (e1)) = (e3))\/(((op (e2) (e2)) = (e3))\/((op (e2) (e3)) = (e3))))) -> (((op (e0) (e2)) = (e1))\/(((op (e1) (e2)) = (e1))\/(((op (e2) (e2)) = (e1))\/((op (e3) (e2)) = (e1))))) -> (~((op (e2) (op (e3) (e2))) = (op (e3) (e2)))) -> (~((op (e1) (e0)) = (op (e1) (e2)))) -> (~((op (e0) (e2)) = (op (e0) (e3)))) -> (~((op (e1) (e0)) = (op (e1) (e3)))) -> (((op (e0) (e3)) = (e2))\/(((op (e1) (e3)) = (e2))\/(((op (e2) (e3)) = (e2))\/((op (e3) (e3)) = (e2))))) -> (~((op (e0) (e0)) = (op (e0) (e3)))) -> ((op (e0) (e0)) = (e0)) -> (~((op (e0) (e3)) = (op (e2) (e3)))) -> (~((op (e0) (e3)) = (op (e1) (e3)))) -> (((op (e0) (e3)) = (e0))\/(((op (e0) (e3)) = (e1))\/(((op (e0) (e3)) = (e2))\/((op (e0) (e3)) = (e3))))) -> (~((op (e0) (e1)) = (op (e0) (e3)))) -> (((op (e0) (e3)) = (e1))\/(((op (e1) (e3)) = (e1))\/(((op (e2) (e3)) = (e1))\/((op (e3) (e3)) = (e1))))) -> (~((op (e0) (e1)) = (op (e2) (e1)))) -> (~((e2) = (e3))) -> (((op (e2) (e0)) = (e1))\/(((op (e2) (e1)) = (e1))\/(((op (e2) (e2)) = (e1))\/((op (e2) (e3)) = (e1))))) -> (~((op (e0) (e0)) = (e3))) -> (~((op (e2) (e0)) = (op (e3) (e0)))) -> (((op (e3) (e3)) = (e0))\/(((op (e3) (e3)) = (e1))\/(((op (e3) (e3)) = (e2))\/((op (e3) (e3)) = (e3))))) -> (~((op (e0) (e3)) = (op (e3) (e3)))) -> (((op (e0) (e0)) = (e2))\/(((op (e0) (e1)) = (e2))\/(((op (e0) (e2)) = (e2))\/((op (e0) (e3)) = (e2))))) -> (~((op (e3) (e0)) = (op (e3) (e2)))) -> ((~((op (e3) (e3)) = (e2)))\/((op (e3) (e2)) = (e3))) -> (~((op (e3) (e0)) = (op (e3) (e1)))) -> ((~((op (e3) (e3)) = (e0)))\/((op (e3) (e0)) = (e3))) -> ((~((op (e2) (e2)) = (e1)))\/((op (e2) (e1)) = (e2))) -> ((op (e1) (e0)) = (e1)) -> (~((e1) = (e2))) -> (~((op (e0) (e0)) = (e2))) -> False). % 15.48/15.63 do 0 intro. intros zenon_H250 zenon_H1f6 zenon_H17d zenon_H22e zenon_H104 zenon_H146 zenon_H2e zenon_H4b zenon_H16f zenon_Heb zenon_H3c zenon_H1b4 zenon_H1b3 zenon_H1c3 zenon_Hce zenon_H10c zenon_H138 zenon_H135 zenon_H10d zenon_H2be zenon_H58 zenon_H2b8 zenon_Hbe zenon_Hd6 zenon_H90 zenon_H247 zenon_H154 zenon_H2b4 zenon_H1a2 zenon_H87 zenon_H182 zenon_Ha3 zenon_H84 zenon_He6 zenon_H11b zenon_H2af zenon_H166 zenon_Hc9 zenon_H1cf zenon_H160 zenon_H24f zenon_H1f zenon_Hb4 zenon_H80 zenon_H254 zenon_H1cd zenon_H121 zenon_Hde zenon_H6a zenon_Hb7 zenon_H59 zenon_H1e5 zenon_H3b zenon_H36 zenon_H8e zenon_H105 zenon_H10e zenon_H109 zenon_H10f zenon_H1e3 zenon_Hd8 zenon_Ha7 zenon_H8f. % 15.48/15.63 apply (zenon_or_s _ _ zenon_H10e); [ zenon_intro zenon_H3d | zenon_intro zenon_H106 ]. % 15.48/15.63 apply (zenon_or_s _ _ zenon_H10d); [ zenon_intro zenon_H3e | zenon_intro zenon_H42 ]. % 15.48/15.63 apply (zenon_or_s _ _ zenon_Heb); [ zenon_intro zenon_H92 | zenon_intro zenon_Hec ]. % 15.48/15.63 exact (zenon_H8f zenon_H92). % 15.48/15.63 apply (zenon_or_s _ _ zenon_Hec); [ zenon_intro zenon_H68 | zenon_intro zenon_Hed ]. % 15.48/15.63 apply (zenon_L162_); trivial. % 15.48/15.63 apply (zenon_or_s _ _ zenon_Hed); [ zenon_intro zenon_Hdd | zenon_intro zenon_He9 ]. % 15.48/15.63 apply (zenon_L1044_); trivial. % 15.48/15.63 apply (zenon_L406_); trivial. % 15.48/15.63 apply (zenon_L1041_); trivial. % 15.48/15.63 apply (zenon_L1050_); trivial. % 15.48/15.63 (* end of lemma zenon_L1051_ *) % 15.48/15.63 assert (zenon_L1052_ : (((op (e0) (e0)) = (e2))\/(((op (e1) (e0)) = (e2))\/(((op (e2) (e0)) = (e2))\/((op (e3) (e0)) = (e2))))) -> (~((op (e0) (e0)) = (e2))) -> (~((op (e0) (op (e3) (e0))) = (op (e3) (e0)))) -> (~((e2) = (e3))) -> ((op (e1) (e0)) = (e1)) -> (~((e1) = (e3))) -> (~((op (e0) (e0)) = (e3))) -> (((op (e0) (e0)) = (e3))\/(((op (e1) (e0)) = (e3))\/(((op (e2) (e0)) = (e3))\/((op (e3) (e0)) = (e3))))) -> (((op (e1) (e0)) = (e2))\/(((op (e1) (e1)) = (e2))\/(((op (e1) (e2)) = (e2))\/((op (e1) (e3)) = (e2))))) -> (~((e1) = (e2))) -> (((op (e0) (e1)) = (e2))\/(((op (e1) (e1)) = (e2))\/(((op (e2) (e1)) = (e2))\/((op (e3) (e1)) = (e2))))) -> (~((op (e0) (e1)) = (op (e0) (e3)))) -> (~((op (e2) (e0)) = (op (e2) (e1)))) -> (~((op (e1) (op (e3) (e1))) = (op (e3) (e1)))) -> (((op (e0) (e3)) = (e2))\/(((op (e1) (e3)) = (e2))\/(((op (e2) (e3)) = (e2))\/((op (e3) (e3)) = (e2))))) -> (~((op (e2) (e2)) = (e1))) -> (((op (e0) (e2)) = (e1))\/(((op (e1) (e2)) = (e1))\/(((op (e2) (e2)) = (e1))\/((op (e3) (e2)) = (e1))))) -> (~((op (e1) (e0)) = (op (e1) (e2)))) -> (~((op (e2) (op (e3) (e2))) = (op (e3) (e2)))) -> (~((op (e1) (e0)) = (op (e2) (e0)))) -> (((op (e2) (e0)) = (e1))\/(((op (e2) (e1)) = (e1))\/(((op (e2) (e2)) = (e1))\/((op (e2) (e3)) = (e1))))) -> (((op (e1) (e0)) = (e3))\/(((op (e1) (e1)) = (e3))\/(((op (e1) (e2)) = (e3))\/((op (e1) (e3)) = (e3))))) -> (~((op (e0) (e2)) = (op (e1) (e2)))) -> ((op (e3) (e1)) = (e3)) -> (~((op (e0) (e1)) = (op (e3) (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 (e3) (e3)) = (e3))) -> (~((op (e3) (e3)) = (e2))) -> (~((op (e3) (e3)) = (e0))) -> (((op (e3) (e3)) = (e0))\/(((op (e3) (e3)) = (e1))\/(((op (e3) (e3)) = (e2))\/((op (e3) (e3)) = (e3))))) -> (~((op (e1) (e1)) = (e1))) -> (~((op (e1) (e1)) = (e2))) -> (~((op (e1) (e1)) = (e3))) -> False). % 15.48/15.63 do 0 intro. intros zenon_Heb zenon_H8f zenon_H2b8 zenon_H6a zenon_Hd8 zenon_Ha3 zenon_H59 zenon_Hbe zenon_H84 zenon_Ha7 zenon_H1a2 zenon_H1cd zenon_H154 zenon_H2b4 zenon_H160 zenon_H52 zenon_H11b zenon_H166 zenon_H2af zenon_H247 zenon_Hb7 zenon_H90 zenon_H87 zenon_H10a zenon_H138 zenon_H58 zenon_H1b3 zenon_H3e zenon_H3d zenon_H3c zenon_H3b zenon_H1b4 zenon_Hd6 zenon_H182. % 15.48/15.63 apply (zenon_or_s _ _ zenon_Heb); [ zenon_intro zenon_H92 | zenon_intro zenon_Hec ]. % 15.48/15.63 exact (zenon_H8f zenon_H92). % 15.48/15.63 apply (zenon_or_s _ _ zenon_Hec); [ zenon_intro zenon_H68 | zenon_intro zenon_Hed ]. % 15.48/15.63 apply (zenon_L162_); trivial. % 15.48/15.63 apply (zenon_or_s _ _ zenon_Hed); [ zenon_intro zenon_Hdd | zenon_intro zenon_He9 ]. % 15.48/15.63 apply (zenon_L1042_); trivial. % 15.48/15.63 apply (zenon_L406_); trivial. % 15.48/15.63 (* end of lemma zenon_L1052_ *) % 15.48/15.63 assert (zenon_L1053_ : (~((op (e2) (e2)) = (e1))) -> (~((op (e0) (e0)) = (e2))) -> (~((e1) = (e2))) -> ((op (e1) (e0)) = (e1)) -> ((~((op (e2) (e2)) = (e1)))\/((op (e2) (e1)) = (e2))) -> ((~((op (e3) (e3)) = (e0)))\/((op (e3) (e0)) = (e3))) -> (~((op (e3) (e0)) = (op (e3) (e1)))) -> ((~((op (e3) (e3)) = (e2)))\/((op (e3) (e2)) = (e3))) -> (~((op (e3) (e0)) = (op (e3) (e2)))) -> (((op (e0) (e0)) = (e2))\/(((op (e0) (e1)) = (e2))\/(((op (e0) (e2)) = (e2))\/((op (e0) (e3)) = (e2))))) -> (~((op (e0) (e3)) = (op (e3) (e3)))) -> (((op (e3) (e3)) = (e0))\/(((op (e3) (e3)) = (e1))\/(((op (e3) (e3)) = (e2))\/((op (e3) (e3)) = (e3))))) -> (~((op (e2) (e0)) = (op (e3) (e0)))) -> (~((op (e0) (e0)) = (e3))) -> (((op (e2) (e0)) = (e1))\/(((op (e2) (e1)) = (e1))\/(((op (e2) (e2)) = (e1))\/((op (e2) (e3)) = (e1))))) -> (~((e2) = (e3))) -> (~((op (e0) (e1)) = (op (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) (e3)) = (e0))\/(((op (e0) (e3)) = (e1))\/(((op (e0) (e3)) = (e2))\/((op (e0) (e3)) = (e3))))) -> (~((op (e0) (e3)) = (op (e1) (e3)))) -> (~((op (e0) (e3)) = (op (e2) (e3)))) -> ((op (e0) (e0)) = (e0)) -> (~((op (e0) (e0)) = (op (e0) (e3)))) -> (((op (e0) (e3)) = (e2))\/(((op (e1) (e3)) = (e2))\/(((op (e2) (e3)) = (e2))\/((op (e3) (e3)) = (e2))))) -> (~((op (e1) (e0)) = (op (e1) (e3)))) -> (~((op (e0) (e2)) = (op (e0) (e3)))) -> (~((op (e1) (e0)) = (op (e1) (e2)))) -> (~((op (e2) (op (e3) (e2))) = (op (e3) (e2)))) -> (((op (e0) (e2)) = (e1))\/(((op (e1) (e2)) = (e1))\/(((op (e2) (e2)) = (e1))\/((op (e3) (e2)) = (e1))))) -> (((op (e2) (e0)) = (e3))\/(((op (e2) (e1)) = (e3))\/(((op (e2) (e2)) = (e3))\/((op (e2) (e3)) = (e3))))) -> (((op (e1) (e0)) = (e2))\/(((op (e1) (e1)) = (e2))\/(((op (e1) (e2)) = (e2))\/((op (e1) (e3)) = (e2))))) -> (~((e1) = (e3))) -> (~((op (e1) (e1)) = (e3))) -> (~((op (e0) (e2)) = (op (e1) (e2)))) -> (((op (e0) (e1)) = (e2))\/(((op (e1) (e1)) = (e2))\/(((op (e2) (e1)) = (e2))\/((op (e3) (e1)) = (e2))))) -> (~((op (e1) (op (e3) (e1))) = (op (e3) (e1)))) -> (~((op (e2) (e0)) = (op (e2) (e1)))) -> (~((op (e1) (e0)) = (op (e2) (e0)))) -> (((op (e1) (e0)) = (e3))\/(((op (e1) (e1)) = (e3))\/(((op (e1) (e2)) = (e3))\/((op (e1) (e3)) = (e3))))) -> (~((op (e1) (e1)) = (e2))) -> (((op (e0) (e0)) = (e3))\/(((op (e1) (e0)) = (e3))\/(((op (e2) (e0)) = (e3))\/((op (e3) (e0)) = (e3))))) -> (~((op (e0) (op (e3) (e0))) = (op (e3) (e0)))) -> (((op (e0) (e0)) = (e3))\/(((op (e0) (e1)) = (e3))\/(((op (e0) (e2)) = (e3))\/((op (e0) (e3)) = (e3))))) -> (~((op (e3) (op (e3) (e3))) = (op (e3) (e3)))) -> ((~((op (e3) (e3)) = (e3)))\/((op (e3) (e3)) = (e3))) -> (~((op (e3) (e1)) = (op (e3) (e2)))) -> (~((op (e0) (e1)) = (op (e3) (e1)))) -> ((~((op (e3) (e3)) = (e1)))\/((op (e3) (e1)) = (e3))) -> (~((op (e2) (e0)) = (op (e2) (e3)))) -> ((~((op (e2) (e2)) = (e3)))\/((op (e2) (e3)) = (e2))) -> (((op (e1) (e1)) = (e0))\/(((op (e1) (e1)) = (e1))\/(((op (e1) (e1)) = (e2))\/((op (e1) (e1)) = (e3))))) -> (~((op (e1) (e1)) = (e1))) -> (~((op (e3) (e3)) = (e0))) -> (((op (e0) (e0)) = (e2))\/(((op (e1) (e0)) = (e2))\/(((op (e2) (e0)) = (e2))\/((op (e3) (e0)) = (e2))))) -> (((op (e0) (e2)) = (e0))\/(((op (e1) (e2)) = (e0))\/(((op (e2) (e2)) = (e0))\/((op (e3) (e2)) = (e0))))) -> (~((e0) = (e3))) -> (~((op (e2) (e2)) = (e0))) -> (((op (e3) (e0)) = (e1))\/(((op (e3) (e1)) = (e1))\/(((op (e3) (e2)) = (e1))\/((op (e3) (e3)) = (e1))))) -> (~((op (e1) (e0)) = (op (e3) (e0)))) -> (~((op (e1) (e2)) = (op (e3) (e2)))) -> (((op (e3) (e0)) = (e0))\/(((op (e3) (e1)) = (e0))\/(((op (e3) (e2)) = (e0))\/((op (e3) (e3)) = (e0))))) -> (~((op (e0) (e0)) = (op (e0) (e2)))) -> False). % 15.48/15.63 do 0 intro. intros zenon_H52 zenon_H8f zenon_Ha7 zenon_Hd8 zenon_H1e3 zenon_H10f zenon_H109 zenon_H10e zenon_H105 zenon_H8e zenon_H36 zenon_H3b zenon_H1e5 zenon_H59 zenon_Hb7 zenon_H6a zenon_Hde zenon_H121 zenon_H1cd zenon_H254 zenon_H80 zenon_Hb4 zenon_H1f zenon_H24f zenon_H160 zenon_H1cf zenon_Hc9 zenon_H166 zenon_H2af zenon_H11b zenon_He6 zenon_H84 zenon_Ha3 zenon_H182 zenon_H87 zenon_H1a2 zenon_H2b4 zenon_H154 zenon_H247 zenon_H90 zenon_Hd6 zenon_Hbe zenon_H2b8 zenon_H58 zenon_H2be zenon_H10d zenon_H135 zenon_H138 zenon_H10c zenon_Hce zenon_H1c3 zenon_H1b3 zenon_H1b4 zenon_H3c zenon_Heb zenon_H16f zenon_H4b zenon_H2e zenon_H146 zenon_H22e zenon_H17d zenon_H1f6 zenon_H250. % 15.48/15.63 apply (zenon_or_s _ _ zenon_H10c); [ zenon_intro zenon_H104 | zenon_intro zenon_H10a ]. % 15.48/15.63 apply (zenon_L1051_); trivial. % 15.48/15.63 apply (zenon_or_s _ _ zenon_H10e); [ zenon_intro zenon_H3d | zenon_intro zenon_H106 ]. % 15.48/15.63 apply (zenon_or_s _ _ zenon_H10d); [ zenon_intro zenon_H3e | zenon_intro zenon_H42 ]. % 15.48/15.63 apply (zenon_L1052_); trivial. % 15.48/15.63 apply (zenon_L1041_); trivial. % 15.48/15.63 apply (zenon_L115_); trivial. % 15.48/15.63 (* end of lemma zenon_L1053_ *) % 15.48/15.63 assert (zenon_L1054_ : (~((op (e0) (op (e3) (e0))) = (op (e3) (e0)))) -> ((op (e0) (e1)) = (e1)) -> ((op (e3) (e0)) = (e1)) -> False). % 15.48/15.63 do 0 intro. intros zenon_H2b8 zenon_H22 zenon_Hee. % 15.48/15.63 cut (((op (e0) (e1)) = (e1)) = ((op (e0) (op (e3) (e0))) = (op (e3) (e0)))). % 15.48/15.63 intro zenon_D_pnotp. % 15.48/15.63 apply zenon_H2b8. % 15.48/15.63 rewrite <- zenon_D_pnotp. % 15.48/15.63 exact zenon_H22. % 15.48/15.63 cut (((e1) = (op (e3) (e0)))); [idtac | apply NNPP; zenon_intro zenon_H22f]. % 15.48/15.63 cut (((op (e0) (e1)) = (op (e0) (op (e3) (e0))))); [idtac | apply NNPP; zenon_intro zenon_H2c4]. % 15.48/15.63 congruence. % 15.48/15.63 elim (classic ((op (e0) (op (e3) (e0))) = (op (e0) (op (e3) (e0))))); [ zenon_intro zenon_H2ba | zenon_intro zenon_H2bb ]. % 15.48/15.63 cut (((op (e0) (op (e3) (e0))) = (op (e0) (op (e3) (e0)))) = ((op (e0) (e1)) = (op (e0) (op (e3) (e0))))). % 15.48/15.63 intro zenon_D_pnotp. % 15.48/15.63 apply zenon_H2c4. % 15.48/15.63 rewrite <- zenon_D_pnotp. % 15.48/15.63 exact zenon_H2ba. % 15.48/15.63 cut (((op (e0) (op (e3) (e0))) = (op (e0) (op (e3) (e0))))); [idtac | apply NNPP; zenon_intro zenon_H2bb]. % 15.48/15.63 cut (((op (e0) (op (e3) (e0))) = (op (e0) (e1)))); [idtac | apply NNPP; zenon_intro zenon_H2c5]. % 15.48/15.63 congruence. % 15.48/15.63 cut (((op (e3) (e0)) = (e1))); [idtac | apply NNPP; zenon_intro zenon_Hef]. % 15.48/15.63 cut (((e0) = (e0))); [idtac | apply NNPP; zenon_intro zenon_H1d]. % 15.48/15.63 congruence. % 15.48/15.63 apply zenon_H1d. apply refl_equal. % 15.48/15.63 exact (zenon_Hef zenon_Hee). % 15.48/15.63 apply zenon_H2bb. apply refl_equal. % 15.48/15.63 apply zenon_H2bb. apply refl_equal. % 15.48/15.63 apply zenon_H22f. apply sym_equal. exact zenon_Hee. % 15.48/15.63 (* end of lemma zenon_L1054_ *) % 15.48/15.63 assert (zenon_L1055_ : (((op (e0) (e0)) = (e1))\/(((op (e1) (e0)) = (e1))\/(((op (e2) (e0)) = (e1))\/((op (e3) (e0)) = (e1))))) -> (~((op (e0) (e0)) = (e1))) -> (~((op (e1) (e0)) = (op (e1) (e2)))) -> (~((op (e3) (e3)) = (e1))) -> (~((op (e2) (e0)) = (op (e2) (e3)))) -> (~((op (e1) (e2)) = (op (e1) (e3)))) -> ((op (e1) (e2)) = (e1)) -> (((op (e3) (e3)) = (e0))\/(((op (e3) (e3)) = (e1))\/(((op (e3) (e3)) = (e2))\/((op (e3) (e3)) = (e3))))) -> (~((op (e3) (e3)) = (e0))) -> (~((op (e0) (e3)) = (op (e3) (e3)))) -> (~((op (e3) (e3)) = (e2))) -> (~((op (e3) (e3)) = (e3))) -> (((op (e0) (e3)) = (e1))\/(((op (e1) (e3)) = (e1))\/(((op (e2) (e3)) = (e1))\/((op (e3) (e3)) = (e1))))) -> (~((op (e0) (op (e3) (e0))) = (op (e3) (e0)))) -> ((op (e0) (e1)) = (e1)) -> False). % 15.48/15.64 do 0 intro. intros zenon_Hf1 zenon_H45 zenon_H166 zenon_H104 zenon_Hce zenon_H1d0 zenon_H117 zenon_H3b zenon_H3c zenon_H36 zenon_H3d zenon_H3e zenon_H121 zenon_H2b8 zenon_H22. % 15.48/15.64 apply (zenon_or_s _ _ zenon_Hf1); [ zenon_intro zenon_H47 | zenon_intro zenon_Hf4 ]. % 15.48/15.64 exact (zenon_H45 zenon_H47). % 15.48/15.64 apply (zenon_or_s _ _ zenon_Hf4); [ zenon_intro zenon_Hd8 | zenon_intro zenon_Hf5 ]. % 15.48/15.64 apply (zenon_L248_); trivial. % 15.48/15.64 apply (zenon_or_s _ _ zenon_Hf5); [ zenon_intro zenon_Hae | zenon_intro zenon_Hee ]. % 15.48/15.64 apply (zenon_L763_); trivial. % 15.48/15.64 apply (zenon_L1054_); trivial. % 15.48/15.64 (* end of lemma zenon_L1055_ *) % 15.48/15.64 assert (zenon_L1056_ : ((~((op (e3) (e3)) = (e3)))\/((op (e3) (e3)) = (e3))) -> (~((op (e3) (op (e3) (e3))) = (op (e3) (e3)))) -> (~((op (e0) (e0)) = (e1))) -> (((op (e0) (e0)) = (e1))\/(((op (e1) (e0)) = (e1))\/(((op (e2) (e0)) = (e1))\/((op (e3) (e0)) = (e1))))) -> (~((op (e0) (op (e3) (e0))) = (op (e3) (e0)))) -> (((op (e3) (e3)) = (e0))\/(((op (e3) (e3)) = (e1))\/(((op (e3) (e3)) = (e2))\/((op (e3) (e3)) = (e3))))) -> (~((op (e3) (e3)) = (e2))) -> (~((op (e0) (e3)) = (op (e3) (e3)))) -> (~((op (e3) (e3)) = (e0))) -> (~((op (e1) (e2)) = (op (e1) (e3)))) -> (~((op (e2) (e0)) = (op (e2) (e3)))) -> (~((op (e3) (e3)) = (e1))) -> (((op (e0) (e3)) = (e1))\/(((op (e1) (e3)) = (e1))\/(((op (e2) (e3)) = (e1))\/((op (e3) (e3)) = (e1))))) -> ((op (e1) (e2)) = (e1)) -> (~((op (e1) (e0)) = (op (e1) (e2)))) -> (((op (e0) (e0)) = (e2))\/(((op (e0) (e1)) = (e2))\/(((op (e0) (e2)) = (e2))\/((op (e0) (e3)) = (e2))))) -> (~((e1) = (e2))) -> (~((op (e1) (e1)) = (e0))) -> (~((op (e1) (e1)) = (e1))) -> (~((op (e0) (e1)) = (op (e1) (e1)))) -> (~((op (e1) (e1)) = (e3))) -> (((op (e1) (e1)) = (e0))\/(((op (e1) (e1)) = (e1))\/(((op (e1) (e1)) = (e2))\/((op (e1) (e1)) = (e3))))) -> (~((op (e0) (e0)) = (e2))) -> (((op (e0) (e0)) = (e1))\/(((op (e0) (e1)) = (e1))\/(((op (e0) (e2)) = (e1))\/((op (e0) (e3)) = (e1))))) -> False). % 15.48/15.64 do 0 intro. intros zenon_H10d zenon_H2be zenon_H45 zenon_Hf1 zenon_H2b8 zenon_H3b zenon_H3d zenon_H36 zenon_H3c zenon_H1d0 zenon_Hce zenon_H104 zenon_H121 zenon_H117 zenon_H166 zenon_H8e zenon_Ha7 zenon_H145 zenon_H1b4 zenon_H23 zenon_H182 zenon_H1b3 zenon_H8f zenon_H44. % 15.48/15.64 apply (zenon_or_s _ _ zenon_H10d); [ zenon_intro zenon_H3e | zenon_intro zenon_H42 ]. % 15.48/15.64 apply (zenon_or_s _ _ zenon_H44); [ zenon_intro zenon_H47 | zenon_intro zenon_H46 ]. % 15.48/15.64 exact (zenon_H45 zenon_H47). % 15.48/15.64 apply (zenon_or_s _ _ zenon_H46); [ zenon_intro zenon_H22 | zenon_intro zenon_H48 ]. % 15.48/15.64 apply (zenon_L1055_); trivial. % 15.48/15.64 apply (zenon_or_s _ _ zenon_H48); [ zenon_intro zenon_H29 | zenon_intro zenon_H37 ]. % 15.48/15.64 apply (zenon_L665_); trivial. % 15.48/15.64 apply (zenon_L7_); trivial. % 15.48/15.64 apply (zenon_L1041_); trivial. % 15.48/15.64 (* end of lemma zenon_L1056_ *) % 15.48/15.64 assert (zenon_L1057_ : (((op (e3) (e0)) = (e0))\/(((op (e3) (e1)) = (e0))\/(((op (e3) (e2)) = (e0))\/((op (e3) (e3)) = (e0))))) -> ((op (e0) (e0)) = (e0)) -> (~((op (e0) (op (e3) (e0))) = (op (e3) (e0)))) -> ((op (e3) (e1)) = (e3)) -> (~((e0) = (e3))) -> ((op (e1) (e2)) = (e0)) -> (~((op (e1) (e2)) = (op (e3) (e2)))) -> (~((op (e3) (e3)) = (e0))) -> False). % 15.48/15.64 do 0 intro. intros zenon_H1f6 zenon_H1f zenon_H2b8 zenon_H10a zenon_H4b zenon_H15d zenon_H17d zenon_H3c. % 15.48/15.64 apply (zenon_or_s _ _ zenon_H1f6); [ zenon_intro zenon_Hdb | zenon_intro zenon_H1f7 ]. % 15.48/15.64 apply (zenon_L1045_); trivial. % 15.48/15.64 apply (zenon_or_s _ _ zenon_H1f7); [ zenon_intro zenon_H142 | zenon_intro zenon_H1f8 ]. % 15.48/15.64 apply (zenon_L126_); trivial. % 15.48/15.64 apply (zenon_or_s _ _ zenon_H1f8); [ zenon_intro zenon_H167 | zenon_intro zenon_H40 ]. % 15.48/15.64 apply (zenon_L626_); trivial. % 15.48/15.64 exact (zenon_H3c zenon_H40). % 15.48/15.64 (* end of lemma zenon_L1057_ *) % 15.48/15.64 assert (zenon_L1058_ : (((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) (e3)) = (e3))) -> (~((op (e3) (e3)) = (e2))) -> ((op (e3) (e2)) = (e0)) -> (~((op (e3) (e3)) = (e0))) -> (((op (e3) (e3)) = (e0))\/(((op (e3) (e3)) = (e1))\/(((op (e3) (e3)) = (e2))\/((op (e3) (e3)) = (e3))))) -> (~((op (e1) (e1)) = (e3))) -> False). % 15.48/15.64 do 0 intro. intros zenon_H1b3 zenon_H145 zenon_H1b4 zenon_H3e zenon_H3d zenon_H167 zenon_H3c zenon_H3b zenon_H182. % 15.48/15.64 apply (zenon_or_s _ _ zenon_H1b3); [ zenon_intro zenon_H149 | zenon_intro zenon_H1b5 ]. % 15.48/15.64 exact (zenon_H145 zenon_H149). % 15.48/15.64 apply (zenon_or_s _ _ zenon_H1b5); [ zenon_intro zenon_H21 | zenon_intro zenon_H1b6 ]. % 15.48/15.64 exact (zenon_H1b4 zenon_H21). % 15.48/15.64 apply (zenon_or_s _ _ zenon_H1b6); [ zenon_intro zenon_H6e | zenon_intro zenon_H96 ]. % 15.48/15.64 apply (zenon_L498_); trivial. % 15.48/15.64 exact (zenon_H182 zenon_H96). % 15.48/15.64 (* end of lemma zenon_L1058_ *) % 15.48/15.64 assert (zenon_L1059_ : ((~((op (e3) (e3)) = (e2)))\/((op (e3) (e2)) = (e3))) -> (~((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)) = (e0))) -> (~((op (e1) (e1)) = (e1))) -> (((op (e3) (e3)) = (e0))\/(((op (e3) (e3)) = (e1))\/(((op (e3) (e3)) = (e2))\/((op (e3) (e3)) = (e3))))) -> (~((op (e1) (e1)) = (e3))) -> (((op (e1) (e1)) = (e0))\/(((op (e1) (e1)) = (e1))\/(((op (e1) (e1)) = (e2))\/((op (e1) (e1)) = (e3))))) -> (~((op (e2) (e2)) = (e0))) -> (~((op (e0) (op (e3) (e0))) = (op (e3) (e0)))) -> (~((e0) = (e3))) -> ((op (e3) (e1)) = (e3)) -> (~((op (e1) (e2)) = (op (e3) (e2)))) -> (~((op (e3) (e3)) = (e0))) -> (((op (e3) (e0)) = (e0))\/(((op (e3) (e1)) = (e0))\/(((op (e3) (e2)) = (e0))\/((op (e3) (e3)) = (e0))))) -> ((op (e0) (e0)) = (e0)) -> (~((op (e0) (e0)) = (op (e0) (e2)))) -> (~((op (e3) (op (e3) (e3))) = (op (e3) (e3)))) -> ((~((op (e3) (e3)) = (e3)))\/((op (e3) (e3)) = (e3))) -> False). % 15.48/15.64 do 0 intro. intros zenon_H10e zenon_H135 zenon_H16f zenon_H145 zenon_H1b4 zenon_H3b zenon_H182 zenon_H1b3 zenon_H2e zenon_H2b8 zenon_H4b zenon_H10a zenon_H17d zenon_H3c zenon_H1f6 zenon_H1f zenon_H250 zenon_H2be zenon_H10d. % 15.48/15.64 apply (zenon_or_s _ _ zenon_H10e); [ zenon_intro zenon_H3d | zenon_intro zenon_H106 ]. % 15.48/15.64 apply (zenon_or_s _ _ zenon_H10d); [ zenon_intro zenon_H3e | zenon_intro zenon_H42 ]. % 15.48/15.64 apply (zenon_or_s _ _ zenon_H16f); [ zenon_intro zenon_Hab | zenon_intro zenon_H170 ]. % 15.48/15.64 apply (zenon_L567_); trivial. % 15.48/15.64 apply (zenon_or_s _ _ zenon_H170); [ zenon_intro zenon_H15d | zenon_intro zenon_H171 ]. % 15.48/15.64 apply (zenon_L1057_); trivial. % 15.48/15.64 apply (zenon_or_s _ _ zenon_H171); [ zenon_intro zenon_H32 | zenon_intro zenon_H167 ]. % 15.48/15.64 exact (zenon_H2e zenon_H32). % 15.48/15.64 apply (zenon_L1058_); trivial. % 15.48/15.64 apply (zenon_L1041_); trivial. % 15.48/15.64 apply (zenon_L115_); trivial. % 15.48/15.64 (* end of lemma zenon_L1059_ *) % 15.48/15.64 assert (zenon_L1060_ : ((~((op (e3) (e3)) = (e1)))\/((op (e3) (e1)) = (e3))) -> (((op (e3) (e0)) = (e0))\/(((op (e3) (e1)) = (e0))\/(((op (e3) (e2)) = (e0))\/((op (e3) (e3)) = (e0))))) -> (~((op (e1) (e2)) = (op (e3) (e2)))) -> (~((op (e3) (e1)) = (op (e3) (e2)))) -> ((~((op (e3) (e3)) = (e3)))\/((op (e3) (e3)) = (e3))) -> (~((op (e3) (op (e3) (e3))) = (op (e3) (e3)))) -> (~((op (e0) (e0)) = (e1))) -> (((op (e0) (e0)) = (e1))\/(((op (e1) (e0)) = (e1))\/(((op (e2) (e0)) = (e1))\/((op (e3) (e0)) = (e1))))) -> (~((op (e0) (op (e3) (e0))) = (op (e3) (e0)))) -> (((op (e3) (e3)) = (e0))\/(((op (e3) (e3)) = (e1))\/(((op (e3) (e3)) = (e2))\/((op (e3) (e3)) = (e3))))) -> (~((op (e0) (e3)) = (op (e3) (e3)))) -> (~((op (e3) (e3)) = (e0))) -> (~((op (e1) (e2)) = (op (e1) (e3)))) -> (~((op (e2) (e0)) = (op (e2) (e3)))) -> (((op (e0) (e3)) = (e1))\/(((op (e1) (e3)) = (e1))\/(((op (e2) (e3)) = (e1))\/((op (e3) (e3)) = (e1))))) -> ((op (e1) (e2)) = (e1)) -> (~((op (e1) (e0)) = (op (e1) (e2)))) -> (((op (e0) (e0)) = (e2))\/(((op (e0) (e1)) = (e2))\/(((op (e0) (e2)) = (e2))\/((op (e0) (e3)) = (e2))))) -> (~((e1) = (e2))) -> (~((op (e1) (e1)) = (e0))) -> (~((op (e1) (e1)) = (e1))) -> (~((op (e0) (e1)) = (op (e1) (e1)))) -> (~((op (e1) (e1)) = (e3))) -> (((op (e1) (e1)) = (e0))\/(((op (e1) (e1)) = (e1))\/(((op (e1) (e1)) = (e2))\/((op (e1) (e1)) = (e3))))) -> (~((op (e0) (e0)) = (e2))) -> (((op (e0) (e0)) = (e1))\/(((op (e0) (e1)) = (e1))\/(((op (e0) (e2)) = (e1))\/((op (e0) (e3)) = (e1))))) -> (((op (e0) (e2)) = (e0))\/(((op (e1) (e2)) = (e0))\/(((op (e2) (e2)) = (e0))\/((op (e3) (e2)) = (e0))))) -> (~((e0) = (e3))) -> (~((op (e2) (e2)) = (e0))) -> (~((e0) = (e1))) -> ((op (e0) (e0)) = (e0)) -> (~((op (e0) (e0)) = (op (e0) (e2)))) -> ((~((op (e3) (e3)) = (e2)))\/((op (e3) (e2)) = (e3))) -> False). % 15.48/15.64 do 0 intro. intros zenon_H10c zenon_H1f6 zenon_H17d zenon_H135 zenon_H10d zenon_H2be zenon_H45 zenon_Hf1 zenon_H2b8 zenon_H3b zenon_H36 zenon_H3c zenon_H1d0 zenon_Hce zenon_H121 zenon_H117 zenon_H166 zenon_H8e zenon_Ha7 zenon_H145 zenon_H1b4 zenon_H23 zenon_H182 zenon_H1b3 zenon_H8f zenon_H44 zenon_H16f zenon_H4b zenon_H2e zenon_H9e zenon_H1f zenon_H250 zenon_H10e. % 15.48/15.64 apply (zenon_or_s _ _ zenon_H10c); [ zenon_intro zenon_H104 | zenon_intro zenon_H10a ]. % 15.48/15.64 apply (zenon_or_s _ _ zenon_H10e); [ zenon_intro zenon_H3d | zenon_intro zenon_H106 ]. % 15.48/15.64 apply (zenon_L1056_); trivial. % 15.48/15.64 apply (zenon_L590_); trivial. % 15.48/15.64 apply (zenon_L1059_); trivial. % 15.48/15.64 (* end of lemma zenon_L1060_ *) % 15.48/15.64 assert (zenon_L1061_ : (((op (e0) (e0)) = (e2))\/(((op (e1) (e0)) = (e2))\/(((op (e2) (e0)) = (e2))\/((op (e3) (e0)) = (e2))))) -> ((~((op (e2) (e2)) = (e3)))\/((op (e2) (e3)) = (e2))) -> (~((op (e2) (e0)) = (op (e2) (e3)))) -> ((~((op (e3) (e3)) = (e1)))\/((op (e3) (e1)) = (e3))) -> (~((op (e0) (e1)) = (op (e3) (e1)))) -> (~((op (e3) (e1)) = (op (e3) (e2)))) -> ((~((op (e3) (e3)) = (e3)))\/((op (e3) (e3)) = (e3))) -> (~((op (e3) (op (e3) (e3))) = (op (e3) (e3)))) -> (~((op (e0) (e0)) = (e2))) -> (((op (e0) (e0)) = (e3))\/(((op (e0) (e1)) = (e3))\/(((op (e0) (e2)) = (e3))\/((op (e0) (e3)) = (e3))))) -> (~((op (e0) (op (e3) (e0))) = (op (e3) (e0)))) -> (((op (e0) (e0)) = (e3))\/(((op (e1) (e0)) = (e3))\/(((op (e2) (e0)) = (e3))\/((op (e3) (e0)) = (e3))))) -> (~((op (e1) (e1)) = (e2))) -> (((op (e1) (e0)) = (e3))\/(((op (e1) (e1)) = (e3))\/(((op (e1) (e2)) = (e3))\/((op (e1) (e3)) = (e3))))) -> (~((op (e1) (e0)) = (op (e2) (e0)))) -> (~((op (e2) (e0)) = (op (e2) (e1)))) -> (~((op (e1) (op (e3) (e1))) = (op (e3) (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) (e1)) = (e3))) -> (~((e1) = (e3))) -> (((op (e1) (e0)) = (e2))\/(((op (e1) (e1)) = (e2))\/(((op (e1) (e2)) = (e2))\/((op (e1) (e3)) = (e2))))) -> (~((e1) = (e2))) -> (((op (e2) (e0)) = (e3))\/(((op (e2) (e1)) = (e3))\/(((op (e2) (e2)) = (e3))\/((op (e2) (e3)) = (e3))))) -> (((op (e0) (e2)) = (e1))\/(((op (e1) (e2)) = (e1))\/(((op (e2) (e2)) = (e1))\/((op (e3) (e2)) = (e1))))) -> (~((op (e2) (op (e3) (e2))) = (op (e3) (e2)))) -> ((op (e1) (e0)) = (e1)) -> (~((op (e1) (e0)) = (op (e1) (e2)))) -> (~((op (e0) (e2)) = (op (e0) (e3)))) -> (~((op (e1) (e0)) = (op (e1) (e3)))) -> (((op (e0) (e3)) = (e2))\/(((op (e1) (e3)) = (e2))\/(((op (e2) (e3)) = (e2))\/((op (e3) (e3)) = (e2))))) -> (~((op (e0) (e0)) = (op (e0) (e3)))) -> ((op (e0) (e0)) = (e0)) -> (~((op (e0) (e3)) = (op (e2) (e3)))) -> (~((op (e0) (e3)) = (op (e1) (e3)))) -> (((op (e0) (e3)) = (e0))\/(((op (e0) (e3)) = (e1))\/(((op (e0) (e3)) = (e2))\/((op (e0) (e3)) = (e3))))) -> (~((op (e0) (e1)) = (op (e0) (e3)))) -> (((op (e0) (e3)) = (e1))\/(((op (e1) (e3)) = (e1))\/(((op (e2) (e3)) = (e1))\/((op (e3) (e3)) = (e1))))) -> (~((op (e0) (e1)) = (op (e2) (e1)))) -> (((op (e2) (e0)) = (e1))\/(((op (e2) (e1)) = (e1))\/(((op (e2) (e2)) = (e1))\/((op (e2) (e3)) = (e1))))) -> (~((op (e0) (e0)) = (e3))) -> (~((op (e2) (e0)) = (op (e3) (e0)))) -> (((op (e3) (e3)) = (e0))\/(((op (e3) (e3)) = (e1))\/(((op (e3) (e3)) = (e2))\/((op (e3) (e3)) = (e3))))) -> (~((op (e0) (e3)) = (op (e3) (e3)))) -> (((op (e0) (e0)) = (e2))\/(((op (e0) (e1)) = (e2))\/(((op (e0) (e2)) = (e2))\/((op (e0) (e3)) = (e2))))) -> (~((op (e3) (e0)) = (op (e3) (e2)))) -> ((~((op (e3) (e3)) = (e2)))\/((op (e3) (e2)) = (e3))) -> (~((op (e3) (e0)) = (op (e3) (e1)))) -> ((~((op (e3) (e3)) = (e0)))\/((op (e3) (e0)) = (e3))) -> ((~((op (e2) (e2)) = (e1)))\/((op (e2) (e1)) = (e2))) -> (~((e2) = (e3))) -> ((op (e3) (e0)) = (e3)) -> False). % 15.48/15.64 do 0 intro. intros zenon_Heb zenon_H1c3 zenon_Hce zenon_H10c zenon_H138 zenon_H135 zenon_H10d zenon_H2be zenon_H8f zenon_H58 zenon_H2b8 zenon_Hbe zenon_Hd6 zenon_H90 zenon_H247 zenon_H154 zenon_H2b4 zenon_H1a2 zenon_H87 zenon_H182 zenon_Ha3 zenon_H84 zenon_Ha7 zenon_He6 zenon_H11b zenon_H2af zenon_Hd8 zenon_H166 zenon_Hc9 zenon_H1cf zenon_H160 zenon_H24f zenon_H1f zenon_Hb4 zenon_H80 zenon_H254 zenon_H1cd zenon_H121 zenon_Hde zenon_Hb7 zenon_H59 zenon_H1e5 zenon_H3b zenon_H36 zenon_H8e zenon_H105 zenon_H10e zenon_H109 zenon_H10f zenon_H1e3 zenon_H6a zenon_Hba. % 15.48/15.64 apply (zenon_or_s _ _ zenon_Heb); [ zenon_intro zenon_H92 | zenon_intro zenon_Hec ]. % 15.48/15.64 exact (zenon_H8f zenon_H92). % 15.48/15.64 apply (zenon_or_s _ _ zenon_Hec); [ zenon_intro zenon_H68 | zenon_intro zenon_Hed ]. % 15.48/15.64 apply (zenon_L162_); trivial. % 15.48/15.64 apply (zenon_or_s _ _ zenon_Hed); [ zenon_intro zenon_Hdd | zenon_intro zenon_He9 ]. % 15.48/15.64 apply (zenon_L1044_); trivial. % 15.48/15.64 apply (zenon_L220_); trivial. % 15.48/15.64 (* end of lemma zenon_L1061_ *) % 15.48/15.64 assert (zenon_L1062_ : ((~((op (e3) (e3)) = (e3)))\/((op (e3) (e3)) = (e3))) -> (~((op (e3) (op (e3) (e3))) = (op (e3) (e3)))) -> (~((op (e0) (e0)) = (e2))) -> (~((e1) = (e2))) -> ((op (e1) (e0)) = (e1)) -> (~((op (e2) (e0)) = (op (e2) (e1)))) -> ((op (e2) (e1)) = (e2)) -> (((op (e1) (e1)) = (e0))\/(((op (e1) (e1)) = (e1))\/(((op (e1) (e1)) = (e2))\/((op (e1) (e1)) = (e3))))) -> (~((op (e1) (e1)) = (e3))) -> (~((op (e1) (e1)) = (e2))) -> (~((op (e1) (e1)) = (e1))) -> (~((op (e3) (e3)) = (e0))) -> (~((op (e3) (e3)) = (e2))) -> (((op (e3) (e3)) = (e0))\/(((op (e3) (e3)) = (e1))\/(((op (e3) (e3)) = (e2))\/((op (e3) (e3)) = (e3))))) -> (((op (e0) (e0)) = (e2))\/(((op (e1) (e0)) = (e2))\/(((op (e2) (e0)) = (e2))\/((op (e3) (e0)) = (e2))))) -> False). % 15.48/15.64 do 0 intro. intros zenon_H10d zenon_H2be zenon_H8f zenon_Ha7 zenon_Hd8 zenon_H154 zenon_H156 zenon_H1b3 zenon_H182 zenon_Hd6 zenon_H1b4 zenon_H3c zenon_H3d zenon_H3b zenon_Heb. % 15.48/15.64 apply (zenon_or_s _ _ zenon_H10d); [ zenon_intro zenon_H3e | zenon_intro zenon_H42 ]. % 15.48/15.64 apply (zenon_L407_); trivial. % 15.48/15.64 apply (zenon_L1041_); trivial. % 15.48/15.64 (* end of lemma zenon_L1062_ *) % 15.48/15.64 assert (zenon_L1063_ : ((~((op (e1) (e1)) = (e1)))\/((op (e1) (e1)) = (e1))) -> (~((op (e1) (e0)) = (op (e1) (e1)))) -> ((~((op (e1) (e1)) = (e3)))\/((op (e1) (e3)) = (e1))) -> (~((op (e0) (e0)) = (e2))) -> (~((e1) = (e2))) -> ((op (e1) (e0)) = (e1)) -> ((~((op (e2) (e2)) = (e1)))\/((op (e2) (e1)) = (e2))) -> ((~((op (e3) (e3)) = (e0)))\/((op (e3) (e0)) = (e3))) -> (~((op (e3) (e0)) = (op (e3) (e1)))) -> ((~((op (e3) (e3)) = (e2)))\/((op (e3) (e2)) = (e3))) -> (~((op (e3) (e0)) = (op (e3) (e2)))) -> (((op (e0) (e0)) = (e2))\/(((op (e0) (e1)) = (e2))\/(((op (e0) (e2)) = (e2))\/((op (e0) (e3)) = (e2))))) -> (~((op (e0) (e3)) = (op (e3) (e3)))) -> (((op (e3) (e3)) = (e0))\/(((op (e3) (e3)) = (e1))\/(((op (e3) (e3)) = (e2))\/((op (e3) (e3)) = (e3))))) -> (~((op (e2) (e0)) = (op (e3) (e0)))) -> (~((op (e0) (e0)) = (e3))) -> (((op (e2) (e0)) = (e1))\/(((op (e2) (e1)) = (e1))\/(((op (e2) (e2)) = (e1))\/((op (e2) (e3)) = (e1))))) -> (~((e2) = (e3))) -> (~((op (e0) (e1)) = (op (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) (e3)) = (e0))\/(((op (e0) (e3)) = (e1))\/(((op (e0) (e3)) = (e2))\/((op (e0) (e3)) = (e3))))) -> (~((op (e0) (e3)) = (op (e1) (e3)))) -> (~((op (e0) (e3)) = (op (e2) (e3)))) -> ((op (e0) (e0)) = (e0)) -> (~((op (e0) (e0)) = (op (e0) (e3)))) -> (((op (e0) (e3)) = (e2))\/(((op (e1) (e3)) = (e2))\/(((op (e2) (e3)) = (e2))\/((op (e3) (e3)) = (e2))))) -> (~((op (e1) (e0)) = (op (e1) (e3)))) -> (~((op (e0) (e2)) = (op (e0) (e3)))) -> (~((op (e1) (e0)) = (op (e1) (e2)))) -> (~((op (e2) (op (e3) (e2))) = (op (e3) (e2)))) -> (((op (e0) (e2)) = (e1))\/(((op (e1) (e2)) = (e1))\/(((op (e2) (e2)) = (e1))\/((op (e3) (e2)) = (e1))))) -> (((op (e2) (e0)) = (e3))\/(((op (e2) (e1)) = (e3))\/(((op (e2) (e2)) = (e3))\/((op (e2) (e3)) = (e3))))) -> (((op (e1) (e0)) = (e2))\/(((op (e1) (e1)) = (e2))\/(((op (e1) (e2)) = (e2))\/((op (e1) (e3)) = (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))))) -> (~((op (e1) (op (e3) (e1))) = (op (e3) (e1)))) -> (~((op (e2) (e0)) = (op (e2) (e1)))) -> (~((op (e1) (e0)) = (op (e2) (e0)))) -> (((op (e1) (e0)) = (e3))\/(((op (e1) (e1)) = (e3))\/(((op (e1) (e2)) = (e3))\/((op (e1) (e3)) = (e3))))) -> (((op (e0) (e0)) = (e3))\/(((op (e1) (e0)) = (e3))\/(((op (e2) (e0)) = (e3))\/((op (e3) (e0)) = (e3))))) -> (~((op (e0) (op (e3) (e0))) = (op (e3) (e0)))) -> (((op (e0) (e0)) = (e3))\/(((op (e0) (e1)) = (e3))\/(((op (e0) (e2)) = (e3))\/((op (e0) (e3)) = (e3))))) -> (~((op (e3) (op (e3) (e3))) = (op (e3) (e3)))) -> ((~((op (e3) (e3)) = (e3)))\/((op (e3) (e3)) = (e3))) -> (~((op (e3) (e1)) = (op (e3) (e2)))) -> (~((op (e0) (e1)) = (op (e3) (e1)))) -> ((~((op (e3) (e3)) = (e1)))\/((op (e3) (e1)) = (e3))) -> (~((op (e2) (e0)) = (op (e2) (e3)))) -> ((~((op (e2) (e2)) = (e3)))\/((op (e2) (e3)) = (e2))) -> (((op (e1) (e1)) = (e0))\/(((op (e1) (e1)) = (e1))\/(((op (e1) (e1)) = (e2))\/((op (e1) (e1)) = (e3))))) -> (((op (e0) (e0)) = (e2))\/(((op (e1) (e0)) = (e2))\/(((op (e2) (e0)) = (e2))\/((op (e3) (e0)) = (e2))))) -> (((op (e0) (e2)) = (e0))\/(((op (e1) (e2)) = (e0))\/(((op (e2) (e2)) = (e0))\/((op (e3) (e2)) = (e0))))) -> (~((e0) = (e3))) -> (((op (e3) (e0)) = (e1))\/(((op (e3) (e1)) = (e1))\/(((op (e3) (e2)) = (e1))\/((op (e3) (e3)) = (e1))))) -> (~((op (e1) (e0)) = (op (e3) (e0)))) -> (~((op (e1) (e2)) = (op (e3) (e2)))) -> (((op (e3) (e0)) = (e0))\/(((op (e3) (e1)) = (e0))\/(((op (e3) (e2)) = (e0))\/((op (e3) (e3)) = (e0))))) -> (~((op (e0) (e0)) = (op (e0) (e2)))) -> ((~((op (e2) (e2)) = (e0)))\/((op (e2) (e0)) = (e2))) -> ((~((op (e1) (e1)) = (e2)))\/((op (e1) (e2)) = (e1))) -> False). % 15.48/15.64 do 0 intro. intros zenon_H1d8 zenon_Hd7 zenon_H1d2 zenon_H8f zenon_Ha7 zenon_Hd8 zenon_H1e3 zenon_H10f zenon_H109 zenon_H10e zenon_H105 zenon_H8e zenon_H36 zenon_H3b zenon_H1e5 zenon_H59 zenon_Hb7 zenon_H6a zenon_Hde zenon_H121 zenon_H1cd zenon_H254 zenon_H80 zenon_Hb4 zenon_H1f zenon_H24f zenon_H160 zenon_H1cf zenon_Hc9 zenon_H166 zenon_H2af zenon_H11b zenon_He6 zenon_H84 zenon_Ha3 zenon_H87 zenon_H1a2 zenon_H2b4 zenon_H154 zenon_H247 zenon_H90 zenon_Hbe zenon_H2b8 zenon_H58 zenon_H2be zenon_H10d zenon_H135 zenon_H138 zenon_H10c zenon_Hce zenon_H1c3 zenon_H1b3 zenon_Heb zenon_H16f zenon_H4b zenon_H146 zenon_H22e zenon_H17d zenon_H1f6 zenon_H250 zenon_H1d4 zenon_H1d3. % 15.48/15.64 apply (zenon_or_s _ _ zenon_H1d8); [ zenon_intro zenon_H1b4 | zenon_intro zenon_H21 ]. % 15.48/15.64 apply (zenon_or_s _ _ zenon_H1d3); [ zenon_intro zenon_Hd6 | zenon_intro zenon_H117 ]. % 15.48/15.64 apply (zenon_or_s _ _ zenon_H1d2); [ zenon_intro zenon_H182 | zenon_intro zenon_H11f ]. % 15.48/15.64 apply (zenon_or_s _ _ zenon_H1d4); [ zenon_intro zenon_H2e | zenon_intro zenon_Hdd ]. % 15.48/15.64 apply (zenon_or_s _ _ zenon_H1e3); [ zenon_intro zenon_H52 | zenon_intro zenon_H156 ]. % 15.48/15.64 apply (zenon_or_s _ _ zenon_H10f); [ zenon_intro zenon_H3c | zenon_intro zenon_Hba ]. % 15.48/15.64 apply (zenon_L1053_); trivial. % 15.48/15.64 apply (zenon_L1061_); trivial. % 15.48/15.64 apply (zenon_or_s _ _ zenon_H10f); [ zenon_intro zenon_H3c | zenon_intro zenon_Hba ]. % 15.48/15.64 apply (zenon_or_s _ _ zenon_H10c); [ zenon_intro zenon_H104 | zenon_intro zenon_H10a ]. % 15.48/15.64 apply (zenon_or_s _ _ zenon_H10e); [ zenon_intro zenon_H3d | zenon_intro zenon_H106 ]. % 15.48/15.64 apply (zenon_L1062_); trivial. % 15.48/15.64 apply (zenon_L1050_); trivial. % 15.48/15.64 apply (zenon_or_s _ _ zenon_H10e); [ zenon_intro zenon_H3d | zenon_intro zenon_H106 ]. % 15.48/15.64 apply (zenon_L1062_); trivial. % 15.48/15.64 apply (zenon_L115_); trivial. % 15.48/15.64 apply (zenon_L1061_); trivial. % 15.48/15.64 apply (zenon_L1044_); trivial. % 15.48/15.64 apply (zenon_L224_); trivial. % 15.48/15.64 apply (zenon_L248_); trivial. % 15.48/15.64 apply (zenon_L61_); trivial. % 15.48/15.64 (* end of lemma zenon_L1063_ *) % 15.48/15.64 assert (zenon_L1064_ : (~((op (e2) (op (e3) (e2))) = (op (e2) (e3)))) -> ((op (e3) (e2)) = (e3)) -> False). % 15.48/15.64 do 0 intro. intros zenon_H2c6 zenon_H106. % 15.48/15.64 cut (((op (e3) (e2)) = (e3))); [idtac | apply NNPP; zenon_intro zenon_H2c7]. % 15.48/15.64 cut (((e2) = (e2))); [idtac | apply NNPP; zenon_intro zenon_H60]. % 15.48/15.64 congruence. % 15.48/15.64 apply zenon_H60. apply refl_equal. % 15.48/15.64 exact (zenon_H2c7 zenon_H106). % 15.48/15.64 (* end of lemma zenon_L1064_ *) % 15.48/15.64 assert (zenon_L1065_ : (~((op (e2) (op (e3) (e2))) = (op (e3) (e2)))) -> ((op (e2) (e3)) = (e3)) -> ((op (e3) (e2)) = (e3)) -> False). % 15.48/15.64 do 0 intro. intros zenon_H2af zenon_He2 zenon_H106. % 15.48/15.64 cut (((op (e2) (e3)) = (e3)) = ((op (e2) (op (e3) (e2))) = (op (e3) (e2)))). % 15.48/15.64 intro zenon_D_pnotp. % 15.48/15.64 apply zenon_H2af. % 15.48/15.64 rewrite <- zenon_D_pnotp. % 15.48/15.64 exact zenon_He2. % 15.48/15.64 cut (((e3) = (op (e3) (e2)))); [idtac | apply NNPP; zenon_intro zenon_H107]. % 15.48/15.64 cut (((op (e2) (e3)) = (op (e2) (op (e3) (e2))))); [idtac | apply NNPP; zenon_intro zenon_H2c8]. % 15.48/15.64 congruence. % 15.48/15.64 elim (classic ((op (e2) (op (e3) (e2))) = (op (e2) (op (e3) (e2))))); [ zenon_intro zenon_H2b1 | zenon_intro zenon_H2b2 ]. % 15.48/15.64 cut (((op (e2) (op (e3) (e2))) = (op (e2) (op (e3) (e2)))) = ((op (e2) (e3)) = (op (e2) (op (e3) (e2))))). % 15.48/15.64 intro zenon_D_pnotp. % 15.48/15.64 apply zenon_H2c8. % 15.48/15.64 rewrite <- zenon_D_pnotp. % 15.48/15.64 exact zenon_H2b1. % 15.48/15.64 cut (((op (e2) (op (e3) (e2))) = (op (e2) (op (e3) (e2))))); [idtac | apply NNPP; zenon_intro zenon_H2b2]. % 15.48/15.64 cut (((op (e2) (op (e3) (e2))) = (op (e2) (e3)))); [idtac | apply NNPP; zenon_intro zenon_H2c6]. % 15.48/15.64 congruence. % 15.48/15.64 apply (zenon_L1064_); trivial. % 15.48/15.64 apply zenon_H2b2. apply refl_equal. % 15.48/15.64 apply zenon_H2b2. apply refl_equal. % 15.48/15.64 apply zenon_H107. apply sym_equal. exact zenon_H106. % 15.48/15.64 (* end of lemma zenon_L1065_ *) % 15.48/15.64 assert (zenon_L1066_ : (((op (e0) (e0)) = (e3))\/(((op (e0) (e1)) = (e3))\/(((op (e0) (e2)) = (e3))\/((op (e0) (e3)) = (e3))))) -> (~((op (e0) (e0)) = (e3))) -> (~((op (e2) (op (e3) (e2))) = (op (e3) (e2)))) -> (~((op (e2) (e2)) = (e3))) -> (((op (e0) (e2)) = (e3))\/(((op (e1) (e2)) = (e3))\/(((op (e2) (e2)) = (e3))\/((op (e3) (e2)) = (e3))))) -> (~((op (e0) (e1)) = (op (e2) (e1)))) -> (((op (e2) (e0)) = (e3))\/(((op (e2) (e1)) = (e3))\/(((op (e2) (e2)) = (e3))\/((op (e2) (e3)) = (e3))))) -> (~((e2) = (e3))) -> ((op (e0) (e2)) = (e2)) -> (((op (e0) (e3)) = (e1))\/(((op (e1) (e3)) = (e1))\/(((op (e2) (e3)) = (e1))\/((op (e3) (e3)) = (e1))))) -> (~((e1) = (e3))) -> ((op (e1) (e2)) = (e1)) -> (~((op (e1) (e2)) = (op (e1) (e3)))) -> ((op (e2) (e0)) = (e1)) -> (~((op (e2) (e0)) = (op (e2) (e3)))) -> (~((op (e3) (e3)) = (e1))) -> False). % 15.48/15.64 do 0 intro. intros zenon_H58 zenon_H59 zenon_H2af zenon_H30 zenon_H175 zenon_Hde zenon_He6 zenon_H6a zenon_H63 zenon_H121 zenon_Ha3 zenon_H117 zenon_H1d0 zenon_Hae zenon_Hce zenon_H104. % 15.48/15.64 apply (zenon_or_s _ _ zenon_H58); [ zenon_intro zenon_H5b | zenon_intro zenon_H5a ]. % 15.48/15.64 exact (zenon_H59 zenon_H5b). % 15.48/15.64 apply (zenon_or_s _ _ zenon_H5a); [ zenon_intro zenon_H4a | zenon_intro zenon_H5c ]. % 15.48/15.64 apply (zenon_or_s _ _ zenon_He6); [ zenon_intro zenon_Haf | zenon_intro zenon_He7 ]. % 15.48/15.64 apply (zenon_L39_); trivial. % 15.48/15.64 apply (zenon_or_s _ _ zenon_He7); [ zenon_intro zenon_Hdf | zenon_intro zenon_He8 ]. % 15.48/15.64 apply (zenon_L65_); trivial. % 15.48/15.64 apply (zenon_or_s _ _ zenon_He8); [ zenon_intro zenon_H34 | zenon_intro zenon_He2 ]. % 15.48/15.64 exact (zenon_H30 zenon_H34). % 15.48/15.64 apply (zenon_or_s _ _ zenon_H175); [ zenon_intro zenon_H50 | zenon_intro zenon_H176 ]. % 15.48/15.64 apply (zenon_L31_); trivial. % 15.48/15.64 apply (zenon_or_s _ _ zenon_H176); [ zenon_intro zenon_H88 | zenon_intro zenon_H177 ]. % 15.48/15.64 apply (zenon_L196_); trivial. % 15.48/15.64 apply (zenon_or_s _ _ zenon_H177); [ zenon_intro zenon_H34 | zenon_intro zenon_H106 ]. % 15.48/15.64 exact (zenon_H30 zenon_H34). % 15.48/15.64 apply (zenon_L1065_); trivial. % 15.48/15.64 apply (zenon_or_s _ _ zenon_H5c); [ zenon_intro zenon_H50 | zenon_intro zenon_H53 ]. % 15.48/15.64 apply (zenon_L31_); trivial. % 15.48/15.64 apply (zenon_L549_); trivial. % 15.48/15.64 (* end of lemma zenon_L1066_ *) % 15.48/15.64 assert (zenon_L1067_ : (((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) (e0)) = (e1)) -> (~((op (e2) (e0)) = (op (e2) (e3)))) -> (~((op (e3) (e3)) = (e1))) -> False). % 15.48/15.64 do 0 intro. intros zenon_H121 zenon_Ha7 zenon_H81 zenon_Ha3 zenon_H8a zenon_Hae zenon_Hce zenon_H104. % 15.48/15.64 apply (zenon_or_s _ _ zenon_H121); [ zenon_intro zenon_H37 | zenon_intro zenon_H122 ]. % 15.48/15.64 apply (zenon_L33_); trivial. % 15.48/15.64 apply (zenon_or_s _ _ zenon_H122); [ zenon_intro zenon_H11f | zenon_intro zenon_H123 ]. % 15.48/15.64 apply (zenon_L772_); trivial. % 15.48/15.64 apply (zenon_or_s _ _ zenon_H123); [ zenon_intro zenon_Hb5 | zenon_intro zenon_H38 ]. % 15.48/15.64 apply (zenon_L91_); trivial. % 15.48/15.64 exact (zenon_H104 zenon_H38). % 15.48/15.64 (* end of lemma zenon_L1067_ *) % 15.48/15.64 assert (zenon_L1068_ : (((op (e1) (e0)) = (e3))\/(((op (e1) (e1)) = (e3))\/(((op (e1) (e2)) = (e3))\/((op (e1) (e3)) = (e3))))) -> (~((e2) = (e3))) -> ((op (e1) (e0)) = (e2)) -> (~((op (e1) (e1)) = (e3))) -> ((op (e1) (e2)) = (e1)) -> (((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 (e2) (e0)) = (e1)) -> (~((op (e2) (e0)) = (op (e2) (e3)))) -> (~((op (e3) (e3)) = (e1))) -> False). % 15.48/15.64 do 0 intro. intros zenon_H90 zenon_H6a zenon_H68 zenon_H182 zenon_H117 zenon_H121 zenon_Ha7 zenon_H81 zenon_Ha3 zenon_Hae zenon_Hce zenon_H104. % 15.48/15.64 apply (zenon_or_s _ _ zenon_H90); [ zenon_intro zenon_H69 | zenon_intro zenon_H94 ]. % 15.48/15.64 apply (zenon_L17_); trivial. % 15.48/15.64 apply (zenon_or_s _ _ zenon_H94); [ zenon_intro zenon_H96 | zenon_intro zenon_H95 ]. % 15.48/15.64 exact (zenon_H182 zenon_H96). % 15.48/15.64 apply (zenon_or_s _ _ zenon_H95); [ zenon_intro zenon_H88 | zenon_intro zenon_H8a ]. % 15.48/15.64 apply (zenon_L196_); trivial. % 15.48/15.64 apply (zenon_L1067_); trivial. % 15.48/15.64 (* end of lemma zenon_L1068_ *) % 15.48/15.64 assert (zenon_L1069_ : (((op (e0) (e0)) = (e1))\/(((op (e1) (e0)) = (e1))\/(((op (e2) (e0)) = (e1))\/((op (e3) (e0)) = (e1))))) -> (~((op (e0) (e0)) = (e1))) -> ((op (e1) (e2)) = (e1)) -> (~((op (e1) (e0)) = (op (e1) (e2)))) -> ((op (e2) (e0)) = (e2)) -> (~((e1) = (e2))) -> (~((op (e0) (op (e3) (e0))) = (op (e3) (e0)))) -> ((op (e0) (e1)) = (e1)) -> False). % 15.48/15.64 do 0 intro. intros zenon_Hf1 zenon_H45 zenon_H117 zenon_H166 zenon_Hdd zenon_Ha7 zenon_H2b8 zenon_H22. % 15.48/15.64 apply (zenon_or_s _ _ zenon_Hf1); [ zenon_intro zenon_H47 | zenon_intro zenon_Hf4 ]. % 15.48/15.64 exact (zenon_H45 zenon_H47). % 15.48/15.64 apply (zenon_or_s _ _ zenon_Hf4); [ zenon_intro zenon_Hd8 | zenon_intro zenon_Hf5 ]. % 15.48/15.64 apply (zenon_L248_); trivial. % 15.48/15.64 apply (zenon_or_s _ _ zenon_Hf5); [ zenon_intro zenon_Hae | zenon_intro zenon_Hee ]. % 15.48/15.64 apply (zenon_L304_); trivial. % 15.48/15.64 apply (zenon_L1054_); trivial. % 15.48/15.64 (* end of lemma zenon_L1069_ *) % 15.48/15.64 assert (zenon_L1070_ : (((op (e0) (e0)) = (e2))\/(((op (e0) (e1)) = (e2))\/(((op (e0) (e2)) = (e2))\/((op (e0) (e3)) = (e2))))) -> (~((op (e0) (e0)) = (e2))) -> (~((op (e1) (e1)) = (e3))) -> (~((op (e0) (e1)) = (op (e1) (e1)))) -> (~((op (e1) (e1)) = (e1))) -> (~((op (e1) (e1)) = (e0))) -> (((op (e1) (e1)) = (e0))\/(((op (e1) (e1)) = (e1))\/(((op (e1) (e1)) = (e2))\/((op (e1) (e1)) = (e3))))) -> (~((op (e3) (e3)) = (e1))) -> (~((op (e2) (e0)) = (op (e2) (e3)))) -> ((op (e2) (e0)) = (e1)) -> (~((op (e1) (e2)) = (op (e1) (e3)))) -> ((op (e1) (e2)) = (e1)) -> (~((e1) = (e3))) -> (((op (e0) (e3)) = (e1))\/(((op (e1) (e3)) = (e1))\/(((op (e2) (e3)) = (e1))\/((op (e3) (e3)) = (e1))))) -> (~((e2) = (e3))) -> (((op (e2) (e0)) = (e3))\/(((op (e2) (e1)) = (e3))\/(((op (e2) (e2)) = (e3))\/((op (e2) (e3)) = (e3))))) -> (~((op (e0) (e1)) = (op (e2) (e1)))) -> (((op (e0) (e2)) = (e3))\/(((op (e1) (e2)) = (e3))\/(((op (e2) (e2)) = (e3))\/((op (e3) (e2)) = (e3))))) -> (~((op (e2) (e2)) = (e3))) -> (~((op (e2) (op (e3) (e2))) = (op (e3) (e2)))) -> (~((op (e0) (e0)) = (e3))) -> (((op (e0) (e0)) = (e3))\/(((op (e0) (e1)) = (e3))\/(((op (e0) (e2)) = (e3))\/((op (e0) (e3)) = (e3))))) -> ((op (e0) (e3)) = (e1)) -> (~((e1) = (e2))) -> False). % 15.48/15.64 do 0 intro. intros zenon_H8e zenon_H8f zenon_H182 zenon_H23 zenon_H1b4 zenon_H145 zenon_H1b3 zenon_H104 zenon_Hce zenon_Hae zenon_H1d0 zenon_H117 zenon_Ha3 zenon_H121 zenon_H6a zenon_He6 zenon_Hde zenon_H175 zenon_H30 zenon_H2af zenon_H59 zenon_H58 zenon_H37 zenon_Ha7. % 15.48/15.64 apply (zenon_or_s _ _ zenon_H8e); [ zenon_intro zenon_H92 | zenon_intro zenon_H91 ]. % 15.48/15.64 exact (zenon_H8f zenon_H92). % 15.48/15.64 apply (zenon_or_s _ _ zenon_H91); [ zenon_intro zenon_H5d | zenon_intro zenon_H93 ]. % 15.48/15.64 apply (zenon_L214_); trivial. % 15.48/15.64 apply (zenon_or_s _ _ zenon_H93); [ zenon_intro zenon_H63 | zenon_intro zenon_H81 ]. % 15.48/15.64 apply (zenon_L1066_); trivial. % 15.48/15.64 apply (zenon_L33_); trivial. % 15.48/15.64 (* end of lemma zenon_L1070_ *) % 15.48/15.64 assert (zenon_L1071_ : (~((op (e0) (e0)) = (e1))) -> (~((op (e1) (e1)) = (e3))) -> (~((op (e0) (e1)) = (op (e1) (e1)))) -> (~((op (e1) (e1)) = (e1))) -> (~((op (e1) (e1)) = (e0))) -> (~((op (e1) (e2)) = (op (e1) (e3)))) -> (~((op (e2) (e2)) = (e3))) -> (((op (e0) (e2)) = (e3))\/(((op (e1) (e2)) = (e3))\/(((op (e2) (e2)) = (e3))\/((op (e3) (e2)) = (e3))))) -> ((op (e1) (e2)) = (e1)) -> ((op (e3) (e0)) = (e3)) -> (((op (e0) (e0)) = (e1))\/(((op (e1) (e0)) = (e1))\/(((op (e2) (e0)) = (e1))\/((op (e3) (e0)) = (e1))))) -> ((~((op (e1) (e1)) = (e2)))\/((op (e1) (e2)) = (e1))) -> ((~((op (e2) (e2)) = (e0)))\/((op (e2) (e0)) = (e2))) -> (~((op (e0) (e0)) = (op (e0) (e2)))) -> (((op (e3) (e0)) = (e0))\/(((op (e3) (e1)) = (e0))\/(((op (e3) (e2)) = (e0))\/((op (e3) (e3)) = (e0))))) -> (~((op (e1) (e2)) = (op (e3) (e2)))) -> (~((op (e1) (e0)) = (op (e3) (e0)))) -> (((op (e3) (e0)) = (e1))\/(((op (e3) (e1)) = (e1))\/(((op (e3) (e2)) = (e1))\/((op (e3) (e3)) = (e1))))) -> (~((e0) = (e3))) -> (((op (e0) (e2)) = (e0))\/(((op (e1) (e2)) = (e0))\/(((op (e2) (e2)) = (e0))\/((op (e3) (e2)) = (e0))))) -> (((op (e0) (e0)) = (e2))\/(((op (e1) (e0)) = (e2))\/(((op (e2) (e0)) = (e2))\/((op (e3) (e0)) = (e2))))) -> (((op (e1) (e1)) = (e0))\/(((op (e1) (e1)) = (e1))\/(((op (e1) (e1)) = (e2))\/((op (e1) (e1)) = (e3))))) -> ((~((op (e2) (e2)) = (e3)))\/((op (e2) (e3)) = (e2))) -> (~((op (e2) (e0)) = (op (e2) (e3)))) -> ((~((op (e3) (e3)) = (e1)))\/((op (e3) (e1)) = (e3))) -> (~((op (e0) (e1)) = (op (e3) (e1)))) -> (~((op (e3) (e1)) = (op (e3) (e2)))) -> ((~((op (e3) (e3)) = (e3)))\/((op (e3) (e3)) = (e3))) -> (~((op (e3) (op (e3) (e3))) = (op (e3) (e3)))) -> (((op (e0) (e0)) = (e3))\/(((op (e0) (e1)) = (e3))\/(((op (e0) (e2)) = (e3))\/((op (e0) (e3)) = (e3))))) -> (~((op (e0) (op (e3) (e0))) = (op (e3) (e0)))) -> (((op (e0) (e0)) = (e3))\/(((op (e1) (e0)) = (e3))\/(((op (e2) (e0)) = (e3))\/((op (e3) (e0)) = (e3))))) -> (((op (e1) (e0)) = (e3))\/(((op (e1) (e1)) = (e3))\/(((op (e1) (e2)) = (e3))\/((op (e1) (e3)) = (e3))))) -> (~((op (e1) (e0)) = (op (e2) (e0)))) -> (~((op (e2) (e0)) = (op (e2) (e1)))) -> (~((op (e1) (op (e3) (e1))) = (op (e3) (e1)))) -> (((op (e0) (e1)) = (e2))\/(((op (e1) (e1)) = (e2))\/(((op (e2) (e1)) = (e2))\/((op (e3) (e1)) = (e2))))) -> (~((op (e0) (e2)) = (op (e1) (e2)))) -> (~((e1) = (e3))) -> (((op (e1) (e0)) = (e2))\/(((op (e1) (e1)) = (e2))\/(((op (e1) (e2)) = (e2))\/((op (e1) (e3)) = (e2))))) -> (((op (e2) (e0)) = (e3))\/(((op (e2) (e1)) = (e3))\/(((op (e2) (e2)) = (e3))\/((op (e2) (e3)) = (e3))))) -> (((op (e0) (e2)) = (e1))\/(((op (e1) (e2)) = (e1))\/(((op (e2) (e2)) = (e1))\/((op (e3) (e2)) = (e1))))) -> (~((op (e2) (op (e3) (e2))) = (op (e3) (e2)))) -> (~((op (e1) (e0)) = (op (e1) (e2)))) -> (~((op (e0) (e2)) = (op (e0) (e3)))) -> (~((op (e1) (e0)) = (op (e1) (e3)))) -> (((op (e0) (e3)) = (e2))\/(((op (e1) (e3)) = (e2))\/(((op (e2) (e3)) = (e2))\/((op (e3) (e3)) = (e2))))) -> (~((op (e0) (e0)) = (op (e0) (e3)))) -> ((op (e0) (e0)) = (e0)) -> (~((op (e0) (e3)) = (op (e2) (e3)))) -> (~((op (e0) (e3)) = (op (e1) (e3)))) -> (((op (e0) (e3)) = (e0))\/(((op (e0) (e3)) = (e1))\/(((op (e0) (e3)) = (e2))\/((op (e0) (e3)) = (e3))))) -> (~((op (e0) (e1)) = (op (e0) (e3)))) -> (((op (e0) (e3)) = (e1))\/(((op (e1) (e3)) = (e1))\/(((op (e2) (e3)) = (e1))\/((op (e3) (e3)) = (e1))))) -> (~((op (e0) (e1)) = (op (e2) (e1)))) -> (~((e2) = (e3))) -> (((op (e2) (e0)) = (e1))\/(((op (e2) (e1)) = (e1))\/(((op (e2) (e2)) = (e1))\/((op (e2) (e3)) = (e1))))) -> (~((op (e0) (e0)) = (e3))) -> (~((op (e2) (e0)) = (op (e3) (e0)))) -> (((op (e3) (e3)) = (e0))\/(((op (e3) (e3)) = (e1))\/(((op (e3) (e3)) = (e2))\/((op (e3) (e3)) = (e3))))) -> (~((op (e0) (e3)) = (op (e3) (e3)))) -> (((op (e0) (e0)) = (e2))\/(((op (e0) (e1)) = (e2))\/(((op (e0) (e2)) = (e2))\/((op (e0) (e3)) = (e2))))) -> (~((op (e3) (e0)) = (op (e3) (e2)))) -> ((~((op (e3) (e3)) = (e2)))\/((op (e3) (e2)) = (e3))) -> (~((op (e3) (e0)) = (op (e3) (e1)))) -> ((~((op (e3) (e3)) = (e0)))\/((op (e3) (e0)) = (e3))) -> ((~((op (e2) (e2)) = (e1)))\/((op (e2) (e1)) = (e2))) -> (~((e1) = (e2))) -> (~((op (e0) (e0)) = (e2))) -> ((~((op (e1) (e1)) = (e3)))\/((op (e1) (e3)) = (e1))) -> (~((op (e1) (e0)) = (op (e1) (e1)))) -> ((~((op (e1) (e1)) = (e1)))\/((op (e1) (e1)) = (e1))) -> (((op (e0) (e0)) = (e1))\/(((op (e0) (e1)) = (e1))\/(((op (e0) (e2)) = (e1))\/((op (e0) (e3)) = (e1))))) -> False). % 15.48/15.64 do 0 intro. intros zenon_H45 zenon_H182 zenon_H23 zenon_H1b4 zenon_H145 zenon_H1d0 zenon_H30 zenon_H175 zenon_H117 zenon_Hba zenon_Hf1 zenon_H1d3 zenon_H1d4 zenon_H250 zenon_H1f6 zenon_H17d zenon_H22e zenon_H146 zenon_H4b zenon_H16f zenon_Heb zenon_H1b3 zenon_H1c3 zenon_Hce zenon_H10c zenon_H138 zenon_H135 zenon_H10d zenon_H2be zenon_H58 zenon_H2b8 zenon_Hbe zenon_H90 zenon_H247 zenon_H154 zenon_H2b4 zenon_H1a2 zenon_H87 zenon_Ha3 zenon_H84 zenon_He6 zenon_H11b zenon_H2af zenon_H166 zenon_Hc9 zenon_H1cf zenon_H160 zenon_H24f zenon_H1f zenon_Hb4 zenon_H80 zenon_H254 zenon_H1cd zenon_H121 zenon_Hde zenon_H6a zenon_Hb7 zenon_H59 zenon_H1e5 zenon_H3b zenon_H36 zenon_H8e zenon_H105 zenon_H10e zenon_H109 zenon_H10f zenon_H1e3 zenon_Ha7 zenon_H8f zenon_H1d2 zenon_Hd7 zenon_H1d8 zenon_H44. % 15.48/15.64 apply (zenon_or_s _ _ zenon_H10c); [ zenon_intro zenon_H104 | zenon_intro zenon_H10a ]. % 15.48/15.64 apply (zenon_or_s _ _ zenon_H44); [ zenon_intro zenon_H47 | zenon_intro zenon_H46 ]. % 15.48/15.64 exact (zenon_H45 zenon_H47). % 15.48/15.64 apply (zenon_or_s _ _ zenon_H46); [ zenon_intro zenon_H22 | zenon_intro zenon_H48 ]. % 15.48/15.64 apply (zenon_or_s _ _ zenon_Hf1); [ zenon_intro zenon_H47 | zenon_intro zenon_Hf4 ]. % 15.48/15.64 exact (zenon_H45 zenon_H47). % 15.48/15.64 apply (zenon_or_s _ _ zenon_Hf4); [ zenon_intro zenon_Hd8 | zenon_intro zenon_Hf5 ]. % 15.48/15.64 apply (zenon_L1063_); trivial. % 15.48/15.64 apply (zenon_or_s _ _ zenon_Hf5); [ zenon_intro zenon_Hae | zenon_intro zenon_Hee ]. % 15.48/15.64 apply (zenon_or_s _ _ zenon_H8e); [ zenon_intro zenon_H92 | zenon_intro zenon_H91 ]. % 15.48/15.64 exact (zenon_H8f zenon_H92). % 15.48/15.64 apply (zenon_or_s _ _ zenon_H91); [ zenon_intro zenon_H5d | zenon_intro zenon_H93 ]. % 15.48/15.64 apply (zenon_L214_); trivial. % 15.48/15.64 apply (zenon_or_s _ _ zenon_H93); [ zenon_intro zenon_H63 | zenon_intro zenon_H81 ]. % 15.48/15.64 apply (zenon_L1066_); trivial. % 15.48/15.64 apply (zenon_or_s _ _ zenon_Heb); [ zenon_intro zenon_H92 | zenon_intro zenon_Hec ]. % 15.48/15.64 exact (zenon_H8f zenon_H92). % 15.48/15.64 apply (zenon_or_s _ _ zenon_Hec); [ zenon_intro zenon_H68 | zenon_intro zenon_Hed ]. % 15.48/15.64 apply (zenon_L1068_); trivial. % 15.48/15.64 apply (zenon_or_s _ _ zenon_Hed); [ zenon_intro zenon_Hdd | zenon_intro zenon_He9 ]. % 15.48/15.64 apply (zenon_L1069_); trivial. % 15.48/15.64 apply (zenon_L220_); trivial. % 15.48/15.64 apply (zenon_L79_); trivial. % 15.48/15.64 apply (zenon_or_s _ _ zenon_H48); [ zenon_intro zenon_H29 | zenon_intro zenon_H37 ]. % 15.48/15.64 apply (zenon_L876_); trivial. % 15.48/15.64 apply (zenon_or_s _ _ zenon_Hf1); [ zenon_intro zenon_H47 | zenon_intro zenon_Hf4 ]. % 15.48/15.64 exact (zenon_H45 zenon_H47). % 15.48/15.64 apply (zenon_or_s _ _ zenon_Hf4); [ zenon_intro zenon_Hd8 | zenon_intro zenon_Hf5 ]. % 15.48/15.64 apply (zenon_L1063_); trivial. % 15.48/15.64 apply (zenon_or_s _ _ zenon_Hf5); [ zenon_intro zenon_Hae | zenon_intro zenon_Hee ]. % 15.48/15.64 apply (zenon_L1070_); trivial. % 15.48/15.64 apply (zenon_L79_); trivial. % 15.48/15.64 apply (zenon_L82_); trivial. % 15.48/15.64 (* end of lemma zenon_L1071_ *) % 15.48/15.64 assert (zenon_L1072_ : (~((op (e0) (e0)) = (e1))) -> ((~((op (e1) (e1)) = (e1)))\/((op (e1) (e1)) = (e1))) -> (~((op (e1) (e0)) = (op (e1) (e1)))) -> ((~((op (e1) (e1)) = (e3)))\/((op (e1) (e3)) = (e1))) -> (~((op (e0) (e0)) = (e2))) -> (~((e1) = (e2))) -> ((~((op (e2) (e2)) = (e1)))\/((op (e2) (e1)) = (e2))) -> ((~((op (e3) (e3)) = (e0)))\/((op (e3) (e0)) = (e3))) -> (~((op (e3) (e0)) = (op (e3) (e1)))) -> ((~((op (e3) (e3)) = (e2)))\/((op (e3) (e2)) = (e3))) -> (~((op (e3) (e0)) = (op (e3) (e2)))) -> (((op (e0) (e0)) = (e2))\/(((op (e0) (e1)) = (e2))\/(((op (e0) (e2)) = (e2))\/((op (e0) (e3)) = (e2))))) -> (~((op (e0) (e3)) = (op (e3) (e3)))) -> (((op (e3) (e3)) = (e0))\/(((op (e3) (e3)) = (e1))\/(((op (e3) (e3)) = (e2))\/((op (e3) (e3)) = (e3))))) -> (~((op (e2) (e0)) = (op (e3) (e0)))) -> (~((op (e0) (e0)) = (e3))) -> (((op (e2) (e0)) = (e1))\/(((op (e2) (e1)) = (e1))\/(((op (e2) (e2)) = (e1))\/((op (e2) (e3)) = (e1))))) -> (~((e2) = (e3))) -> (~((op (e0) (e1)) = (op (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) (e3)) = (e0))\/(((op (e0) (e3)) = (e1))\/(((op (e0) (e3)) = (e2))\/((op (e0) (e3)) = (e3))))) -> (~((op (e0) (e3)) = (op (e1) (e3)))) -> (~((op (e0) (e3)) = (op (e2) (e3)))) -> ((op (e0) (e0)) = (e0)) -> (~((op (e0) (e0)) = (op (e0) (e3)))) -> (((op (e0) (e3)) = (e2))\/(((op (e1) (e3)) = (e2))\/(((op (e2) (e3)) = (e2))\/((op (e3) (e3)) = (e2))))) -> (~((op (e1) (e0)) = (op (e1) (e3)))) -> (~((op (e0) (e2)) = (op (e0) (e3)))) -> (~((op (e1) (e0)) = (op (e1) (e2)))) -> (~((op (e2) (op (e3) (e2))) = (op (e3) (e2)))) -> (((op (e0) (e2)) = (e1))\/(((op (e1) (e2)) = (e1))\/(((op (e2) (e2)) = (e1))\/((op (e3) (e2)) = (e1))))) -> (((op (e2) (e0)) = (e3))\/(((op (e2) (e1)) = (e3))\/(((op (e2) (e2)) = (e3))\/((op (e2) (e3)) = (e3))))) -> (((op (e1) (e0)) = (e2))\/(((op (e1) (e1)) = (e2))\/(((op (e1) (e2)) = (e2))\/((op (e1) (e3)) = (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))))) -> (~((op (e1) (op (e3) (e1))) = (op (e3) (e1)))) -> (~((op (e2) (e0)) = (op (e2) (e1)))) -> (~((op (e1) (e0)) = (op (e2) (e0)))) -> (((op (e1) (e0)) = (e3))\/(((op (e1) (e1)) = (e3))\/(((op (e1) (e2)) = (e3))\/((op (e1) (e3)) = (e3))))) -> (((op (e0) (e0)) = (e3))\/(((op (e1) (e0)) = (e3))\/(((op (e2) (e0)) = (e3))\/((op (e3) (e0)) = (e3))))) -> (~((op (e0) (op (e3) (e0))) = (op (e3) (e0)))) -> (((op (e0) (e0)) = (e3))\/(((op (e0) (e1)) = (e3))\/(((op (e0) (e2)) = (e3))\/((op (e0) (e3)) = (e3))))) -> (~((op (e3) (op (e3) (e3))) = (op (e3) (e3)))) -> ((~((op (e3) (e3)) = (e3)))\/((op (e3) (e3)) = (e3))) -> (~((op (e3) (e1)) = (op (e3) (e2)))) -> (~((op (e0) (e1)) = (op (e3) (e1)))) -> ((~((op (e3) (e3)) = (e1)))\/((op (e3) (e1)) = (e3))) -> (~((op (e2) (e0)) = (op (e2) (e3)))) -> ((~((op (e2) (e2)) = (e3)))\/((op (e2) (e3)) = (e2))) -> (((op (e1) (e1)) = (e0))\/(((op (e1) (e1)) = (e1))\/(((op (e1) (e1)) = (e2))\/((op (e1) (e1)) = (e3))))) -> (((op (e0) (e0)) = (e2))\/(((op (e1) (e0)) = (e2))\/(((op (e2) (e0)) = (e2))\/((op (e3) (e0)) = (e2))))) -> (((op (e0) (e2)) = (e0))\/(((op (e1) (e2)) = (e0))\/(((op (e2) (e2)) = (e0))\/((op (e3) (e2)) = (e0))))) -> (~((e0) = (e3))) -> (((op (e3) (e0)) = (e1))\/(((op (e3) (e1)) = (e1))\/(((op (e3) (e2)) = (e1))\/((op (e3) (e3)) = (e1))))) -> (~((op (e1) (e0)) = (op (e3) (e0)))) -> (~((op (e1) (e2)) = (op (e3) (e2)))) -> (((op (e3) (e0)) = (e0))\/(((op (e3) (e1)) = (e0))\/(((op (e3) (e2)) = (e0))\/((op (e3) (e3)) = (e0))))) -> (~((op (e0) (e0)) = (op (e0) (e2)))) -> ((~((op (e2) (e2)) = (e0)))\/((op (e2) (e0)) = (e2))) -> ((~((op (e1) (e1)) = (e2)))\/((op (e1) (e2)) = (e1))) -> (((op (e0) (e3)) = (e0))\/(((op (e1) (e3)) = (e0))\/(((op (e2) (e3)) = (e0))\/((op (e3) (e3)) = (e0))))) -> (~((op (e2) (e2)) = (e0))) -> (~((op (e2) (e2)) = (e1))) -> (~((op (e2) (e2)) = (e2))) -> (((op (e2) (e2)) = (e0))\/(((op (e2) (e2)) = (e1))\/(((op (e2) (e2)) = (e2))\/((op (e2) (e2)) = (e3))))) -> ((op (e2) (e3)) = (e2)) -> (~((e0) = (e2))) -> (~((op (e1) (e3)) = (op (e3) (e3)))) -> ((op (e3) (e0)) = (e3)) -> (((op (e0) (e0)) = (e1))\/(((op (e1) (e0)) = (e1))\/(((op (e2) (e0)) = (e1))\/((op (e3) (e0)) = (e1))))) -> False). % 15.48/15.64 do 0 intro. intros zenon_H45 zenon_H1d8 zenon_Hd7 zenon_H1d2 zenon_H8f zenon_Ha7 zenon_H1e3 zenon_H10f zenon_H109 zenon_H10e zenon_H105 zenon_H8e zenon_H36 zenon_H3b zenon_H1e5 zenon_H59 zenon_Hb7 zenon_H6a zenon_Hde zenon_H121 zenon_H1cd zenon_H254 zenon_H80 zenon_Hb4 zenon_H1f zenon_H24f zenon_H160 zenon_H1cf zenon_Hc9 zenon_H166 zenon_H2af zenon_H11b zenon_He6 zenon_H84 zenon_Ha3 zenon_H87 zenon_H1a2 zenon_H2b4 zenon_H154 zenon_H247 zenon_H90 zenon_Hbe zenon_H2b8 zenon_H58 zenon_H2be zenon_H10d zenon_H135 zenon_H138 zenon_H10c zenon_Hce zenon_H1c3 zenon_H1b3 zenon_Heb zenon_H16f zenon_H4b zenon_H146 zenon_H22e zenon_H17d zenon_H1f6 zenon_H250 zenon_H1d4 zenon_H1d3 zenon_Hd3 zenon_H2e zenon_H52 zenon_H2f zenon_H2d zenon_H124 zenon_H5e zenon_H8b zenon_Hba zenon_Hf1. % 15.48/15.64 apply (zenon_or_s _ _ zenon_H10c); [ zenon_intro zenon_H104 | zenon_intro zenon_H10a ]. % 15.48/15.64 apply (zenon_or_s _ _ zenon_H10e); [ zenon_intro zenon_H3d | zenon_intro zenon_H106 ]. % 15.48/15.64 apply (zenon_or_s _ _ zenon_H10d); [ zenon_intro zenon_H3e | zenon_intro zenon_H42 ]. % 15.48/15.64 apply (zenon_or_s _ _ zenon_Hf1); [ zenon_intro zenon_H47 | zenon_intro zenon_Hf4 ]. % 15.48/15.64 exact (zenon_H45 zenon_H47). % 15.48/15.64 apply (zenon_or_s _ _ zenon_Hf4); [ zenon_intro zenon_Hd8 | zenon_intro zenon_Hf5 ]. % 15.48/15.64 apply (zenon_L1063_); trivial. % 15.48/15.64 apply (zenon_or_s _ _ zenon_Hf5); [ zenon_intro zenon_Hae | zenon_intro zenon_Hee ]. % 15.48/15.64 apply (zenon_L684_); trivial. % 15.48/15.64 apply (zenon_L79_); trivial. % 15.48/15.64 apply (zenon_L1041_); trivial. % 15.48/15.64 apply (zenon_L81_); trivial. % 15.48/15.64 apply (zenon_L82_); trivial. % 15.48/15.64 (* end of lemma zenon_L1072_ *) % 15.48/15.64 assert (zenon_L1073_ : ((~((op (e3) (e3)) = (e3)))\/((op (e3) (e3)) = (e3))) -> (~((op (e3) (op (e3) (e3))) = (op (e3) (e3)))) -> (~((op (e0) (e0)) = (e2))) -> (~((e1) = (e2))) -> ((op (e1) (e0)) = (e1)) -> (~((op (e2) (e0)) = (op (e2) (e2)))) -> ((op (e2) (e2)) = (e2)) -> (((op (e1) (e1)) = (e0))\/(((op (e1) (e1)) = (e1))\/(((op (e1) (e1)) = (e2))\/((op (e1) (e1)) = (e3))))) -> (~((op (e1) (e1)) = (e3))) -> (~((op (e1) (e1)) = (e2))) -> (~((op (e1) (e1)) = (e1))) -> (~((op (e3) (e3)) = (e0))) -> (~((op (e3) (e3)) = (e2))) -> (((op (e3) (e3)) = (e0))\/(((op (e3) (e3)) = (e1))\/(((op (e3) (e3)) = (e2))\/((op (e3) (e3)) = (e3))))) -> (((op (e0) (e0)) = (e2))\/(((op (e1) (e0)) = (e2))\/(((op (e2) (e0)) = (e2))\/((op (e3) (e0)) = (e2))))) -> False). % 15.48/15.64 do 0 intro. intros zenon_H10d zenon_H2be zenon_H8f zenon_Ha7 zenon_Hd8 zenon_H17a zenon_H35 zenon_H1b3 zenon_H182 zenon_Hd6 zenon_H1b4 zenon_H3c zenon_H3d zenon_H3b zenon_Heb. % 15.48/15.64 apply (zenon_or_s _ _ zenon_H10d); [ zenon_intro zenon_H3e | zenon_intro zenon_H42 ]. % 15.48/15.64 apply (zenon_L508_); trivial. % 15.48/15.64 apply (zenon_L1041_); trivial. % 15.48/15.64 (* end of lemma zenon_L1073_ *) % 15.48/15.64 assert (zenon_L1074_ : (((op (e3) (e0)) = (e0))\/(((op (e3) (e1)) = (e0))\/(((op (e3) (e2)) = (e0))\/((op (e3) (e3)) = (e0))))) -> ((op (e0) (e0)) = (e0)) -> (~((op (e0) (op (e3) (e0))) = (op (e3) (e0)))) -> ((op (e3) (e1)) = (e1)) -> ((op (e1) (e0)) = (e1)) -> (~((op (e1) (op (e3) (e1))) = (op (e3) (e1)))) -> ((op (e1) (e2)) = (e0)) -> (~((op (e1) (e2)) = (op (e3) (e2)))) -> (~((op (e3) (e3)) = (e0))) -> False). % 15.48/15.64 do 0 intro. intros zenon_H1f6 zenon_H1f zenon_H2b8 zenon_H13e zenon_Hd8 zenon_H2b4 zenon_H15d zenon_H17d zenon_H3c. % 15.48/15.64 apply (zenon_or_s _ _ zenon_H1f6); [ zenon_intro zenon_Hdb | zenon_intro zenon_H1f7 ]. % 15.48/15.64 apply (zenon_L1045_); trivial. % 15.48/15.64 apply (zenon_or_s _ _ zenon_H1f7); [ zenon_intro zenon_H142 | zenon_intro zenon_H1f8 ]. % 15.48/15.64 apply (zenon_L1047_); trivial. % 15.48/15.64 apply (zenon_or_s _ _ zenon_H1f8); [ zenon_intro zenon_H167 | zenon_intro zenon_H40 ]. % 15.48/15.64 apply (zenon_L626_); trivial. % 15.48/15.64 exact (zenon_H3c zenon_H40). % 15.48/15.64 (* end of lemma zenon_L1074_ *) % 15.48/15.64 assert (zenon_L1075_ : (((op (e1) (e2)) = (e0))\/(((op (e1) (e2)) = (e1))\/(((op (e1) (e2)) = (e2))\/((op (e1) (e2)) = (e3))))) -> (~((op (e3) (e3)) = (e0))) -> (~((op (e1) (op (e3) (e1))) = (op (e3) (e1)))) -> ((op (e3) (e1)) = (e1)) -> (~((op (e0) (op (e3) (e0))) = (op (e3) (e0)))) -> ((op (e0) (e0)) = (e0)) -> (((op (e3) (e0)) = (e0))\/(((op (e3) (e1)) = (e0))\/(((op (e3) (e2)) = (e0))\/((op (e3) (e3)) = (e0))))) -> ((op (e1) (e0)) = (e1)) -> (~((op (e1) (e0)) = (op (e1) (e2)))) -> (~((op (e1) (e2)) = (op (e2) (e2)))) -> ((op (e2) (e2)) = (e2)) -> ((op (e3) (e2)) = (e3)) -> (~((op (e1) (e2)) = (op (e3) (e2)))) -> False). % 15.48/15.64 do 0 intro. intros zenon_H1d5 zenon_H3c zenon_H2b4 zenon_H13e zenon_H2b8 zenon_H1f zenon_H1f6 zenon_Hd8 zenon_H166 zenon_H7d zenon_H35 zenon_H106 zenon_H17d. % 15.48/15.64 apply (zenon_or_s _ _ zenon_H1d5); [ zenon_intro zenon_H15d | zenon_intro zenon_H1d6 ]. % 15.48/15.64 apply (zenon_L1074_); trivial. % 15.48/15.64 apply (zenon_or_s _ _ zenon_H1d6); [ zenon_intro zenon_H117 | zenon_intro zenon_H1d7 ]. % 15.48/15.64 apply (zenon_L248_); trivial. % 15.48/15.64 apply (zenon_or_s _ _ zenon_H1d7); [ zenon_intro zenon_H7c | zenon_intro zenon_H88 ]. % 15.48/15.64 apply (zenon_L21_); trivial. % 15.48/15.64 apply (zenon_L164_); trivial. % 15.48/15.64 (* end of lemma zenon_L1075_ *) % 15.48/15.64 assert (zenon_L1076_ : (((op (e3) (e0)) = (e1))\/(((op (e3) (e1)) = (e1))\/(((op (e3) (e2)) = (e1))\/((op (e3) (e3)) = (e1))))) -> (~((op (e1) (e0)) = (op (e3) (e0)))) -> (~((op (e1) (e2)) = (op (e3) (e2)))) -> ((op (e2) (e2)) = (e2)) -> (~((op (e1) (e2)) = (op (e2) (e2)))) -> (~((op (e1) (e0)) = (op (e1) (e2)))) -> ((op (e1) (e0)) = (e1)) -> (((op (e3) (e0)) = (e0))\/(((op (e3) (e1)) = (e0))\/(((op (e3) (e2)) = (e0))\/((op (e3) (e3)) = (e0))))) -> ((op (e0) (e0)) = (e0)) -> (~((op (e0) (op (e3) (e0))) = (op (e3) (e0)))) -> (~((op (e1) (op (e3) (e1))) = (op (e3) (e1)))) -> (~((op (e3) (e3)) = (e0))) -> (((op (e1) (e2)) = (e0))\/(((op (e1) (e2)) = (e1))\/(((op (e1) (e2)) = (e2))\/((op (e1) (e2)) = (e3))))) -> ((op (e3) (e2)) = (e3)) -> (~((e1) = (e3))) -> (~((op (e3) (e3)) = (e1))) -> False). % 15.48/15.64 do 0 intro. intros zenon_H146 zenon_H22e zenon_H17d zenon_H35 zenon_H7d zenon_H166 zenon_Hd8 zenon_H1f6 zenon_H1f zenon_H2b8 zenon_H2b4 zenon_H3c zenon_H1d5 zenon_H106 zenon_Ha3 zenon_H104. % 15.48/15.64 apply (zenon_or_s _ _ zenon_H146); [ zenon_intro zenon_Hee | zenon_intro zenon_H14b ]. % 15.48/15.64 apply (zenon_L393_); trivial. % 15.48/15.64 apply (zenon_or_s _ _ zenon_H14b); [ zenon_intro zenon_H13e | zenon_intro zenon_H14c ]. % 15.48/15.64 apply (zenon_L1075_); trivial. % 15.48/15.64 apply (zenon_or_s _ _ zenon_H14c); [ zenon_intro zenon_H119 | zenon_intro zenon_H38 ]. % 15.48/15.64 apply (zenon_L87_); trivial. % 15.48/15.64 exact (zenon_H104 zenon_H38). % 15.48/15.64 (* end of lemma zenon_L1076_ *) % 15.48/15.64 assert (zenon_L1077_ : ((~((op (e3) (e3)) = (e2)))\/((op (e3) (e2)) = (e3))) -> ((op (e3) (e1)) = (e3)) -> (~((op (e3) (e1)) = (op (e3) (e2)))) -> (((op (e0) (e0)) = (e2))\/(((op (e1) (e0)) = (e2))\/(((op (e2) (e0)) = (e2))\/((op (e3) (e0)) = (e2))))) -> (((op (e3) (e3)) = (e0))\/(((op (e3) (e3)) = (e1))\/(((op (e3) (e3)) = (e2))\/((op (e3) (e3)) = (e3))))) -> (~((op (e3) (e3)) = (e0))) -> (~((op (e1) (e1)) = (e1))) -> (~((op (e1) (e1)) = (e2))) -> (~((op (e1) (e1)) = (e3))) -> (((op (e1) (e1)) = (e0))\/(((op (e1) (e1)) = (e1))\/(((op (e1) (e1)) = (e2))\/((op (e1) (e1)) = (e3))))) -> ((op (e2) (e2)) = (e2)) -> (~((op (e2) (e0)) = (op (e2) (e2)))) -> ((op (e1) (e0)) = (e1)) -> (~((e1) = (e2))) -> (~((op (e0) (e0)) = (e2))) -> (~((op (e3) (op (e3) (e3))) = (op (e3) (e3)))) -> ((~((op (e3) (e3)) = (e3)))\/((op (e3) (e3)) = (e3))) -> False). % 15.48/15.64 do 0 intro. intros zenon_H10e zenon_H10a zenon_H135 zenon_Heb zenon_H3b zenon_H3c zenon_H1b4 zenon_Hd6 zenon_H182 zenon_H1b3 zenon_H35 zenon_H17a zenon_Hd8 zenon_Ha7 zenon_H8f zenon_H2be zenon_H10d. % 15.48/15.64 apply (zenon_or_s _ _ zenon_H10e); [ zenon_intro zenon_H3d | zenon_intro zenon_H106 ]. % 15.48/15.64 apply (zenon_L1073_); trivial. % 15.48/15.64 apply (zenon_L115_); trivial. % 15.48/15.64 (* end of lemma zenon_L1077_ *) % 15.48/15.64 assert (zenon_L1078_ : ((~((op (e3) (e3)) = (e0)))\/((op (e3) (e0)) = (e3))) -> (~((op (e0) (e0)) = (op (e2) (e0)))) -> (~((op (e1) (e0)) = (op (e2) (e0)))) -> (~((op (e2) (e0)) = (op (e3) (e0)))) -> (((op (e2) (e0)) = (e0))\/(((op (e2) (e0)) = (e1))\/(((op (e2) (e0)) = (e2))\/((op (e2) (e0)) = (e3))))) -> ((~((op (e3) (e3)) = (e2)))\/((op (e3) (e2)) = (e3))) -> (~((op (e1) (e0)) = (op (e3) (e0)))) -> (((op (e1) (e2)) = (e0))\/(((op (e1) (e2)) = (e1))\/(((op (e1) (e2)) = (e2))\/((op (e1) (e2)) = (e3))))) -> (~((op (e1) (e2)) = (op (e2) (e2)))) -> (~((op (e1) (e0)) = (op (e1) (e2)))) -> (~((op (e0) (op (e3) (e0))) = (op (e3) (e0)))) -> ((op (e0) (e0)) = (e0)) -> (~((op (e1) (op (e3) (e1))) = (op (e3) (e1)))) -> (~((op (e1) (e2)) = (op (e3) (e2)))) -> (((op (e3) (e0)) = (e0))\/(((op (e3) (e1)) = (e0))\/(((op (e3) (e2)) = (e0))\/((op (e3) (e3)) = (e0))))) -> (~((e1) = (e3))) -> (((op (e3) (e0)) = (e1))\/(((op (e3) (e1)) = (e1))\/(((op (e3) (e2)) = (e1))\/((op (e3) (e3)) = (e1))))) -> (((op (e0) (e0)) = (e2))\/(((op (e1) (e0)) = (e2))\/(((op (e2) (e0)) = (e2))\/((op (e3) (e0)) = (e2))))) -> (((op (e3) (e3)) = (e0))\/(((op (e3) (e3)) = (e1))\/(((op (e3) (e3)) = (e2))\/((op (e3) (e3)) = (e3))))) -> (~((op (e1) (e1)) = (e1))) -> (~((op (e1) (e1)) = (e2))) -> (~((op (e1) (e1)) = (e3))) -> (((op (e1) (e1)) = (e0))\/(((op (e1) (e1)) = (e1))\/(((op (e1) (e1)) = (e2))\/((op (e1) (e1)) = (e3))))) -> ((op (e2) (e2)) = (e2)) -> (~((op (e2) (e0)) = (op (e2) (e2)))) -> ((op (e1) (e0)) = (e1)) -> (~((e1) = (e2))) -> (~((op (e0) (e0)) = (e2))) -> (~((op (e3) (op (e3) (e3))) = (op (e3) (e3)))) -> ((~((op (e3) (e3)) = (e3)))\/((op (e3) (e3)) = (e3))) -> (~((op (e3) (e1)) = (op (e3) (e2)))) -> ((~((op (e3) (e3)) = (e1)))\/((op (e3) (e1)) = (e3))) -> False). % 15.48/15.64 do 0 intro. intros zenon_H10f zenon_H258 zenon_H247 zenon_H1e5 zenon_H281 zenon_H10e zenon_H22e zenon_H1d5 zenon_H7d zenon_H166 zenon_H2b8 zenon_H1f zenon_H2b4 zenon_H17d zenon_H1f6 zenon_Ha3 zenon_H146 zenon_Heb zenon_H3b zenon_H1b4 zenon_Hd6 zenon_H182 zenon_H1b3 zenon_H35 zenon_H17a zenon_Hd8 zenon_Ha7 zenon_H8f zenon_H2be zenon_H10d zenon_H135 zenon_H10c. % 15.48/15.64 apply (zenon_or_s _ _ zenon_H10f); [ zenon_intro zenon_H3c | zenon_intro zenon_Hba ]. % 15.48/15.64 apply (zenon_or_s _ _ zenon_H10c); [ zenon_intro zenon_H104 | zenon_intro zenon_H10a ]. % 15.48/15.64 apply (zenon_or_s _ _ zenon_H10e); [ zenon_intro zenon_H3d | zenon_intro zenon_H106 ]. % 15.48/15.64 apply (zenon_L1073_); trivial. % 15.48/15.64 apply (zenon_L1076_); trivial. % 15.48/15.64 apply (zenon_L1077_); trivial. % 15.48/15.64 apply (zenon_L735_); trivial. % 15.48/15.64 (* end of lemma zenon_L1078_ *) % 15.48/15.64 assert (zenon_L1079_ : ((~((op (e1) (e1)) = (e3)))\/((op (e1) (e3)) = (e1))) -> (~((op (e1) (e0)) = (op (e1) (e3)))) -> ((~((op (e3) (e3)) = (e1)))\/((op (e3) (e1)) = (e3))) -> (~((op (e3) (e1)) = (op (e3) (e2)))) -> ((~((op (e3) (e3)) = (e3)))\/((op (e3) (e3)) = (e3))) -> (~((op (e3) (op (e3) (e3))) = (op (e3) (e3)))) -> (~((op (e0) (e0)) = (e2))) -> (~((e1) = (e2))) -> ((op (e1) (e0)) = (e1)) -> (~((op (e2) (e0)) = (op (e2) (e2)))) -> ((op (e2) (e2)) = (e2)) -> (((op (e1) (e1)) = (e0))\/(((op (e1) (e1)) = (e1))\/(((op (e1) (e1)) = (e2))\/((op (e1) (e1)) = (e3))))) -> (~((op (e1) (e1)) = (e2))) -> (~((op (e1) (e1)) = (e1))) -> (((op (e3) (e3)) = (e0))\/(((op (e3) (e3)) = (e1))\/(((op (e3) (e3)) = (e2))\/((op (e3) (e3)) = (e3))))) -> (((op (e0) (e0)) = (e2))\/(((op (e1) (e0)) = (e2))\/(((op (e2) (e0)) = (e2))\/((op (e3) (e0)) = (e2))))) -> (((op (e3) (e0)) = (e1))\/(((op (e3) (e1)) = (e1))\/(((op (e3) (e2)) = (e1))\/((op (e3) (e3)) = (e1))))) -> (~((e1) = (e3))) -> (((op (e3) (e0)) = (e0))\/(((op (e3) (e1)) = (e0))\/(((op (e3) (e2)) = (e0))\/((op (e3) (e3)) = (e0))))) -> (~((op (e1) (e2)) = (op (e3) (e2)))) -> (~((op (e1) (op (e3) (e1))) = (op (e3) (e1)))) -> ((op (e0) (e0)) = (e0)) -> (~((op (e0) (op (e3) (e0))) = (op (e3) (e0)))) -> (~((op (e1) (e0)) = (op (e1) (e2)))) -> (~((op (e1) (e2)) = (op (e2) (e2)))) -> (((op (e1) (e2)) = (e0))\/(((op (e1) (e2)) = (e1))\/(((op (e1) (e2)) = (e2))\/((op (e1) (e2)) = (e3))))) -> (~((op (e1) (e0)) = (op (e3) (e0)))) -> ((~((op (e3) (e3)) = (e2)))\/((op (e3) (e2)) = (e3))) -> (((op (e2) (e0)) = (e0))\/(((op (e2) (e0)) = (e1))\/(((op (e2) (e0)) = (e2))\/((op (e2) (e0)) = (e3))))) -> (~((op (e2) (e0)) = (op (e3) (e0)))) -> (~((op (e1) (e0)) = (op (e2) (e0)))) -> (~((op (e0) (e0)) = (op (e2) (e0)))) -> ((~((op (e3) (e3)) = (e0)))\/((op (e3) (e0)) = (e3))) -> False). % 15.48/15.64 do 0 intro. intros zenon_H1d2 zenon_H1cf zenon_H10c zenon_H135 zenon_H10d zenon_H2be zenon_H8f zenon_Ha7 zenon_Hd8 zenon_H17a zenon_H35 zenon_H1b3 zenon_Hd6 zenon_H1b4 zenon_H3b zenon_Heb zenon_H146 zenon_Ha3 zenon_H1f6 zenon_H17d zenon_H2b4 zenon_H1f zenon_H2b8 zenon_H166 zenon_H7d zenon_H1d5 zenon_H22e zenon_H10e zenon_H281 zenon_H1e5 zenon_H247 zenon_H258 zenon_H10f. % 15.48/15.64 apply (zenon_or_s _ _ zenon_H1d2); [ zenon_intro zenon_H182 | zenon_intro zenon_H11f ]. % 15.48/15.64 apply (zenon_L1078_); trivial. % 15.48/15.64 apply (zenon_L224_); trivial. % 15.48/15.64 (* end of lemma zenon_L1079_ *) % 15.48/15.64 assert (zenon_L1080_ : ((~((op (e1) (e1)) = (e2)))\/((op (e1) (e2)) = (e1))) -> ((~((op (e3) (e3)) = (e0)))\/((op (e3) (e0)) = (e3))) -> (~((op (e0) (e0)) = (op (e2) (e0)))) -> (~((op (e1) (e0)) = (op (e2) (e0)))) -> (~((op (e2) (e0)) = (op (e3) (e0)))) -> (((op (e2) (e0)) = (e0))\/(((op (e2) (e0)) = (e1))\/(((op (e2) (e0)) = (e2))\/((op (e2) (e0)) = (e3))))) -> ((~((op (e3) (e3)) = (e2)))\/((op (e3) (e2)) = (e3))) -> (~((op (e1) (e0)) = (op (e3) (e0)))) -> (((op (e1) (e2)) = (e0))\/(((op (e1) (e2)) = (e1))\/(((op (e1) (e2)) = (e2))\/((op (e1) (e2)) = (e3))))) -> (~((op (e1) (e2)) = (op (e2) (e2)))) -> (~((op (e1) (e0)) = (op (e1) (e2)))) -> (~((op (e0) (op (e3) (e0))) = (op (e3) (e0)))) -> ((op (e0) (e0)) = (e0)) -> (~((op (e1) (op (e3) (e1))) = (op (e3) (e1)))) -> (~((op (e1) (e2)) = (op (e3) (e2)))) -> (((op (e3) (e0)) = (e0))\/(((op (e3) (e1)) = (e0))\/(((op (e3) (e2)) = (e0))\/((op (e3) (e3)) = (e0))))) -> (~((e1) = (e3))) -> (((op (e3) (e0)) = (e1))\/(((op (e3) (e1)) = (e1))\/(((op (e3) (e2)) = (e1))\/((op (e3) (e3)) = (e1))))) -> (((op (e0) (e0)) = (e2))\/(((op (e1) (e0)) = (e2))\/(((op (e2) (e0)) = (e2))\/((op (e3) (e0)) = (e2))))) -> (((op (e3) (e3)) = (e0))\/(((op (e3) (e3)) = (e1))\/(((op (e3) (e3)) = (e2))\/((op (e3) (e3)) = (e3))))) -> (~((op (e1) (e1)) = (e1))) -> (((op (e1) (e1)) = (e0))\/(((op (e1) (e1)) = (e1))\/(((op (e1) (e1)) = (e2))\/((op (e1) (e1)) = (e3))))) -> ((op (e2) (e2)) = (e2)) -> (~((op (e2) (e0)) = (op (e2) (e2)))) -> ((op (e1) (e0)) = (e1)) -> (~((e1) = (e2))) -> (~((op (e0) (e0)) = (e2))) -> (~((op (e3) (op (e3) (e3))) = (op (e3) (e3)))) -> ((~((op (e3) (e3)) = (e3)))\/((op (e3) (e3)) = (e3))) -> (~((op (e3) (e1)) = (op (e3) (e2)))) -> ((~((op (e3) (e3)) = (e1)))\/((op (e3) (e1)) = (e3))) -> (~((op (e1) (e0)) = (op (e1) (e3)))) -> ((~((op (e1) (e1)) = (e3)))\/((op (e1) (e3)) = (e1))) -> False). % 15.48/15.64 do 0 intro. intros zenon_H1d3 zenon_H10f zenon_H258 zenon_H247 zenon_H1e5 zenon_H281 zenon_H10e zenon_H22e zenon_H1d5 zenon_H7d zenon_H166 zenon_H2b8 zenon_H1f zenon_H2b4 zenon_H17d zenon_H1f6 zenon_Ha3 zenon_H146 zenon_Heb zenon_H3b zenon_H1b4 zenon_H1b3 zenon_H35 zenon_H17a zenon_Hd8 zenon_Ha7 zenon_H8f zenon_H2be zenon_H10d zenon_H135 zenon_H10c zenon_H1cf zenon_H1d2. % 15.48/15.64 apply (zenon_or_s _ _ zenon_H1d3); [ zenon_intro zenon_Hd6 | zenon_intro zenon_H117 ]. % 15.48/15.64 apply (zenon_L1079_); trivial. % 15.48/15.64 apply (zenon_L248_); trivial. % 15.48/15.64 (* end of lemma zenon_L1080_ *) % 15.48/15.64 assert (zenon_L1081_ : (~((op (e0) (op (e3) (e0))) = (op (e0) (e2)))) -> ((op (e3) (e0)) = (e2)) -> False). % 15.48/15.64 do 0 intro. intros zenon_H2c9 zenon_He9. % 15.48/15.64 cut (((op (e3) (e0)) = (e2))); [idtac | apply NNPP; zenon_intro zenon_Hea]. % 15.48/15.64 cut (((e0) = (e0))); [idtac | apply NNPP; zenon_intro zenon_H1d]. % 15.48/15.64 congruence. % 15.48/15.64 apply zenon_H1d. apply refl_equal. % 15.48/15.64 exact (zenon_Hea zenon_He9). % 15.48/15.64 (* end of lemma zenon_L1081_ *) % 15.48/15.64 assert (zenon_L1082_ : (~((op (e0) (op (e3) (e0))) = (op (e3) (e0)))) -> ((op (e0) (e2)) = (e1)) -> ((op (e3) (e0)) = (e2)) -> ((op (e3) (e0)) = (e1)) -> False). % 15.48/15.64 do 0 intro. intros zenon_H2b8 zenon_H29 zenon_He9 zenon_Hee. % 15.48/15.64 cut (((op (e0) (e2)) = (e1)) = ((op (e0) (op (e3) (e0))) = (op (e3) (e0)))). % 15.48/15.64 intro zenon_D_pnotp. % 15.48/15.64 apply zenon_H2b8. % 15.48/15.64 rewrite <- zenon_D_pnotp. % 15.48/15.64 exact zenon_H29. % 15.48/15.64 cut (((e1) = (op (e3) (e0)))); [idtac | apply NNPP; zenon_intro zenon_H22f]. % 15.48/15.64 cut (((op (e0) (e2)) = (op (e0) (op (e3) (e0))))); [idtac | apply NNPP; zenon_intro zenon_H2ca]. % 15.48/15.64 congruence. % 15.48/15.64 elim (classic ((op (e0) (op (e3) (e0))) = (op (e0) (op (e3) (e0))))); [ zenon_intro zenon_H2ba | zenon_intro zenon_H2bb ]. % 15.48/15.64 cut (((op (e0) (op (e3) (e0))) = (op (e0) (op (e3) (e0)))) = ((op (e0) (e2)) = (op (e0) (op (e3) (e0))))). % 15.48/15.64 intro zenon_D_pnotp. % 15.48/15.64 apply zenon_H2ca. % 15.48/15.64 rewrite <- zenon_D_pnotp. % 15.48/15.64 exact zenon_H2ba. % 15.48/15.64 cut (((op (e0) (op (e3) (e0))) = (op (e0) (op (e3) (e0))))); [idtac | apply NNPP; zenon_intro zenon_H2bb]. % 15.48/15.64 cut (((op (e0) (op (e3) (e0))) = (op (e0) (e2)))); [idtac | apply NNPP; zenon_intro zenon_H2c9]. % 15.48/15.64 congruence. % 15.48/15.64 apply (zenon_L1081_); trivial. % 15.48/15.64 apply zenon_H2bb. apply refl_equal. % 15.48/15.64 apply zenon_H2bb. apply refl_equal. % 15.48/15.64 apply zenon_H22f. apply sym_equal. exact zenon_Hee. % 15.48/15.64 (* end of lemma zenon_L1082_ *) % 15.48/15.64 assert (zenon_L1083_ : (~((op (e2) (op (e3) (e2))) = (op (e3) (e2)))) -> ((op (e2) (e2)) = (e2)) -> ((op (e3) (e2)) = (e2)) -> False). % 15.48/15.64 do 0 intro. intros zenon_H2af zenon_H35 zenon_H1dd. % 15.48/15.64 cut (((op (e2) (e2)) = (e2)) = ((op (e2) (op (e3) (e2))) = (op (e3) (e2)))). % 15.48/15.64 intro zenon_D_pnotp. % 15.48/15.64 apply zenon_H2af. % 15.48/15.64 rewrite <- zenon_D_pnotp. % 15.48/15.64 exact zenon_H35. % 15.48/15.64 cut (((e2) = (op (e3) (e2)))); [idtac | apply NNPP; zenon_intro zenon_H1de]. % 15.48/15.64 cut (((op (e2) (e2)) = (op (e2) (op (e3) (e2))))); [idtac | apply NNPP; zenon_intro zenon_H2cb]. % 15.48/15.64 congruence. % 15.48/15.64 elim (classic ((op (e2) (op (e3) (e2))) = (op (e2) (op (e3) (e2))))); [ zenon_intro zenon_H2b1 | zenon_intro zenon_H2b2 ]. % 15.48/15.64 cut (((op (e2) (op (e3) (e2))) = (op (e2) (op (e3) (e2)))) = ((op (e2) (e2)) = (op (e2) (op (e3) (e2))))). % 15.48/15.64 intro zenon_D_pnotp. % 15.48/15.64 apply zenon_H2cb. % 15.48/15.64 rewrite <- zenon_D_pnotp. % 15.48/15.64 exact zenon_H2b1. % 15.48/15.64 cut (((op (e2) (op (e3) (e2))) = (op (e2) (op (e3) (e2))))); [idtac | apply NNPP; zenon_intro zenon_H2b2]. % 15.48/15.64 cut (((op (e2) (op (e3) (e2))) = (op (e2) (e2)))); [idtac | apply NNPP; zenon_intro zenon_H2cc]. % 15.48/15.64 congruence. % 15.48/15.64 cut (((op (e3) (e2)) = (e2))); [idtac | apply NNPP; zenon_intro zenon_H2cd]. % 15.48/15.64 cut (((e2) = (e2))); [idtac | apply NNPP; zenon_intro zenon_H60]. % 15.48/15.64 congruence. % 15.48/15.64 apply zenon_H60. apply refl_equal. % 15.48/15.64 exact (zenon_H2cd zenon_H1dd). % 15.48/15.64 apply zenon_H2b2. apply refl_equal. % 15.48/15.64 apply zenon_H2b2. apply refl_equal. % 15.48/15.64 apply zenon_H1de. apply sym_equal. exact zenon_H1dd. % 15.48/15.64 (* end of lemma zenon_L1083_ *) % 15.48/15.64 assert (zenon_L1084_ : (((op (e3) (e0)) = (e2))\/(((op (e3) (e1)) = (e2))\/(((op (e3) (e2)) = (e2))\/((op (e3) (e3)) = (e2))))) -> ((op (e3) (e0)) = (e1)) -> ((op (e0) (e2)) = (e1)) -> (~((op (e0) (op (e3) (e0))) = (op (e3) (e0)))) -> ((op (e0) (e1)) = (e2)) -> (~((op (e0) (e1)) = (op (e3) (e1)))) -> ((op (e2) (e2)) = (e2)) -> (~((op (e2) (op (e3) (e2))) = (op (e3) (e2)))) -> (~((op (e3) (e3)) = (e2))) -> False). % 15.48/15.64 do 0 intro. intros zenon_H1df zenon_Hee zenon_H29 zenon_H2b8 zenon_H5d zenon_H138 zenon_H35 zenon_H2af zenon_H3d. % 15.48/15.64 apply (zenon_or_s _ _ zenon_H1df); [ zenon_intro zenon_He9 | zenon_intro zenon_H1e0 ]. % 15.48/15.64 apply (zenon_L1082_); trivial. % 15.48/15.64 apply (zenon_or_s _ _ zenon_H1e0); [ zenon_intro zenon_H16a | zenon_intro zenon_H1e1 ]. % 15.48/15.64 apply (zenon_L146_); trivial. % 15.48/15.64 apply (zenon_or_s _ _ zenon_H1e1); [ zenon_intro zenon_H1dd | zenon_intro zenon_H43 ]. % 15.48/15.64 apply (zenon_L1083_); trivial. % 15.48/15.64 exact (zenon_H3d zenon_H43). % 15.48/15.64 (* end of lemma zenon_L1084_ *) % 15.48/15.64 assert (zenon_L1085_ : (((op (e0) (e0)) = (e2))\/(((op (e0) (e1)) = (e2))\/(((op (e0) (e2)) = (e2))\/((op (e0) (e3)) = (e2))))) -> (~((op (e0) (e0)) = (e2))) -> (~((op (e3) (e3)) = (e2))) -> (~((op (e2) (op (e3) (e2))) = (op (e3) (e2)))) -> (~((op (e0) (e1)) = (op (e3) (e1)))) -> (~((op (e0) (op (e3) (e0))) = (op (e3) (e0)))) -> ((op (e0) (e2)) = (e1)) -> ((op (e3) (e0)) = (e1)) -> (((op (e3) (e0)) = (e2))\/(((op (e3) (e1)) = (e2))\/(((op (e3) (e2)) = (e2))\/((op (e3) (e3)) = (e2))))) -> (~((op (e0) (e2)) = (op (e2) (e2)))) -> ((op (e2) (e2)) = (e2)) -> (((op (e3) (e3)) = (e0))\/(((op (e3) (e3)) = (e1))\/(((op (e3) (e3)) = (e2))\/((op (e3) (e3)) = (e3))))) -> (~((op (e3) (e3)) = (e0))) -> (~((op (e3) (e3)) = (e1))) -> (~((op (e0) (e3)) = (op (e3) (e3)))) -> (~((op (e3) (e3)) = (e3))) -> False). % 15.48/15.64 do 0 intro. intros zenon_H8e zenon_H8f zenon_H3d zenon_H2af zenon_H138 zenon_H2b8 zenon_H29 zenon_Hee zenon_H1df zenon_H28 zenon_H35 zenon_H3b zenon_H3c zenon_H104 zenon_H36 zenon_H3e. % 15.48/15.64 apply (zenon_or_s _ _ zenon_H8e); [ zenon_intro zenon_H92 | zenon_intro zenon_H91 ]. % 15.48/15.64 exact (zenon_H8f zenon_H92). % 15.48/15.64 apply (zenon_or_s _ _ zenon_H91); [ zenon_intro zenon_H5d | zenon_intro zenon_H93 ]. % 15.48/15.64 apply (zenon_L1084_); trivial. % 15.48/15.64 apply (zenon_or_s _ _ zenon_H93); [ zenon_intro zenon_H63 | zenon_intro zenon_H81 ]. % 15.48/15.64 apply (zenon_L15_); trivial. % 15.48/15.64 apply (zenon_L107_); trivial. % 15.48/15.64 (* end of lemma zenon_L1085_ *) % 15.48/15.64 assert (zenon_L1086_ : (((op (e0) (e2)) = (e0))\/(((op (e0) (e2)) = (e1))\/(((op (e0) (e2)) = (e2))\/((op (e0) (e2)) = (e3))))) -> ((op (e0) (e0)) = (e0)) -> (~((op (e0) (e0)) = (op (e0) (e2)))) -> (~((op (e0) (e2)) = (op (e0) (e3)))) -> ((op (e0) (e3)) = (e1)) -> (~((op (e0) (e2)) = (op (e2) (e2)))) -> ((op (e2) (e2)) = (e2)) -> ((op (e3) (e2)) = (e3)) -> (~((op (e0) (e2)) = (op (e3) (e2)))) -> False). % 15.48/15.64 do 0 intro. intros zenon_H251 zenon_H1f zenon_H250 zenon_Hc9 zenon_H37 zenon_H28 zenon_H35 zenon_H106 zenon_H140. % 15.48/15.64 apply (zenon_or_s _ _ zenon_H251); [ zenon_intro zenon_Hab | zenon_intro zenon_H252 ]. % 15.48/15.64 apply (zenon_L567_); trivial. % 15.48/15.64 apply (zenon_or_s _ _ zenon_H252); [ zenon_intro zenon_H29 | zenon_intro zenon_H253 ]. % 15.48/15.64 apply (zenon_L85_); trivial. % 15.48/15.64 apply (zenon_or_s _ _ zenon_H253); [ zenon_intro zenon_H63 | zenon_intro zenon_H50 ]. % 15.48/15.64 apply (zenon_L15_); trivial. % 15.48/15.64 apply (zenon_L533_); trivial. % 15.48/15.64 (* end of lemma zenon_L1086_ *) % 15.48/15.64 assert (zenon_L1087_ : (((op (e3) (e0)) = (e2))\/(((op (e3) (e1)) = (e2))\/(((op (e3) (e2)) = (e2))\/((op (e3) (e3)) = (e2))))) -> ((op (e3) (e0)) = (e1)) -> ((op (e0) (e2)) = (e1)) -> (~((op (e0) (op (e3) (e0))) = (op (e3) (e0)))) -> ((op (e0) (e1)) = (e2)) -> (~((op (e0) (e1)) = (op (e3) (e1)))) -> ((op (e2) (e2)) = (e2)) -> (~((op (e2) (op (e3) (e2))) = (op (e3) (e2)))) -> (((op (e0) (e3)) = (e0))\/(((op (e0) (e3)) = (e1))\/(((op (e0) (e3)) = (e2))\/((op (e0) (e3)) = (e3))))) -> ((op (e0) (e0)) = (e0)) -> (~((op (e0) (e0)) = (op (e0) (e3)))) -> ((op (e2) (e3)) = (e1)) -> (~((op (e0) (e3)) = (op (e2) (e3)))) -> (~((op (e0) (e3)) = (op (e3) (e3)))) -> (~((op (e0) (e3)) = (op (e1) (e3)))) -> ((op (e1) (e3)) = (e3)) -> False). % 15.48/15.64 do 0 intro. intros zenon_H1df zenon_Hee zenon_H29 zenon_H2b8 zenon_H5d zenon_H138 zenon_H35 zenon_H2af zenon_H254 zenon_H1f zenon_H24f zenon_Hb5 zenon_Hb4 zenon_H36 zenon_H80 zenon_H8a. % 15.48/15.64 apply (zenon_or_s _ _ zenon_H1df); [ zenon_intro zenon_He9 | zenon_intro zenon_H1e0 ]. % 15.48/15.64 apply (zenon_L1082_); trivial. % 15.48/15.64 apply (zenon_or_s _ _ zenon_H1e0); [ zenon_intro zenon_H16a | zenon_intro zenon_H1e1 ]. % 15.48/15.64 apply (zenon_L146_); trivial. % 15.48/15.64 apply (zenon_or_s _ _ zenon_H1e1); [ zenon_intro zenon_H1dd | zenon_intro zenon_H43 ]. % 15.48/15.64 apply (zenon_L1083_); trivial. % 15.48/15.64 apply (zenon_L903_); trivial. % 15.48/15.64 (* end of lemma zenon_L1087_ *) % 15.48/15.64 assert (zenon_L1088_ : (((op (e3) (e0)) = (e1))\/(((op (e3) (e1)) = (e1))\/(((op (e3) (e2)) = (e1))\/((op (e3) (e3)) = (e1))))) -> ((op (e0) (e1)) = (e1)) -> (~((op (e0) (op (e3) (e0))) = (op (e3) (e0)))) -> ((op (e3) (e1)) = (e3)) -> (~((e1) = (e3))) -> ((op (e1) (e2)) = (e1)) -> (~((op (e1) (e2)) = (op (e3) (e2)))) -> ((op (e3) (e2)) = (e0)) -> ((op (e1) (e1)) = (e2)) -> False). % 15.48/15.64 do 0 intro. intros zenon_H146 zenon_H22 zenon_H2b8 zenon_H10a zenon_Ha3 zenon_H117 zenon_H17d zenon_H167 zenon_H6e. % 15.48/15.64 apply (zenon_or_s _ _ zenon_H146); [ zenon_intro zenon_Hee | zenon_intro zenon_H14b ]. % 15.48/15.64 apply (zenon_L1054_); trivial. % 15.48/15.64 apply (zenon_or_s _ _ zenon_H14b); [ zenon_intro zenon_H13e | zenon_intro zenon_H14c ]. % 15.48/15.64 apply (zenon_L123_); trivial. % 15.48/15.64 apply (zenon_or_s _ _ zenon_H14c); [ zenon_intro zenon_H119 | zenon_intro zenon_H38 ]. % 15.48/15.64 apply (zenon_L759_); trivial. % 15.48/15.64 apply (zenon_L497_); trivial. % 15.48/15.64 (* end of lemma zenon_L1088_ *) % 15.48/15.64 assert (zenon_L1089_ : (((op (e0) (e2)) = (e0))\/(((op (e1) (e2)) = (e0))\/(((op (e2) (e2)) = (e0))\/((op (e3) (e2)) = (e0))))) -> (~((op (e0) (e0)) = (op (e0) (e2)))) -> (~((op (e3) (e3)) = (e0))) -> (~((e0) = (e3))) -> ((op (e0) (e0)) = (e0)) -> (((op (e3) (e0)) = (e0))\/(((op (e3) (e1)) = (e0))\/(((op (e3) (e2)) = (e0))\/((op (e3) (e3)) = (e0))))) -> (~((op (e2) (e2)) = (e0))) -> (((op (e3) (e0)) = (e1))\/(((op (e3) (e1)) = (e1))\/(((op (e3) (e2)) = (e1))\/((op (e3) (e3)) = (e1))))) -> ((op (e0) (e1)) = (e1)) -> (~((op (e0) (op (e3) (e0))) = (op (e3) (e0)))) -> ((op (e3) (e1)) = (e3)) -> (~((e1) = (e3))) -> ((op (e1) (e2)) = (e1)) -> (~((op (e1) (e2)) = (op (e3) (e2)))) -> ((op (e1) (e1)) = (e2)) -> False). % 15.48/15.64 do 0 intro. intros zenon_H16f zenon_H250 zenon_H3c zenon_H4b zenon_H1f zenon_H1f6 zenon_H2e zenon_H146 zenon_H22 zenon_H2b8 zenon_H10a zenon_Ha3 zenon_H117 zenon_H17d zenon_H6e. % 15.48/15.64 apply (zenon_or_s _ _ zenon_H16f); [ zenon_intro zenon_Hab | zenon_intro zenon_H170 ]. % 15.48/15.64 apply (zenon_L567_); trivial. % 15.48/15.64 apply (zenon_or_s _ _ zenon_H170); [ zenon_intro zenon_H15d | zenon_intro zenon_H171 ]. % 15.48/15.64 apply (zenon_L1057_); trivial. % 15.48/15.64 apply (zenon_or_s _ _ zenon_H171); [ zenon_intro zenon_H32 | zenon_intro zenon_H167 ]. % 15.48/15.64 exact (zenon_H2e zenon_H32). % 15.48/15.64 apply (zenon_L1088_); trivial. % 15.48/15.64 (* end of lemma zenon_L1089_ *) % 15.48/15.64 assert (zenon_L1090_ : (((op (e2) (e0)) = (e3))\/(((op (e2) (e1)) = (e3))\/(((op (e2) (e2)) = (e3))\/((op (e2) (e3)) = (e3))))) -> ((op (e2) (e0)) = (e1)) -> (~((op (e2) (e1)) = (op (e3) (e1)))) -> (~((op (e2) (e2)) = (e3))) -> (((op (e3) (e0)) = (e1))\/(((op (e3) (e1)) = (e1))\/(((op (e3) (e2)) = (e1))\/((op (e3) (e3)) = (e1))))) -> ((op (e0) (e1)) = (e1)) -> (~((op (e0) (op (e3) (e0))) = (op (e3) (e0)))) -> ((op (e3) (e1)) = (e3)) -> (~((e1) = (e3))) -> ((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) (e0)) = (e0)) -> (~((op (e0) (e0)) = (op (e0) (e3)))) -> (~((op (e0) (e3)) = (op (e3) (e3)))) -> ((op (e1) (e3)) = (e2)) -> (~((op (e0) (e3)) = (op (e1) (e3)))) -> (~((op (e0) (e3)) = (op (e2) (e3)))) -> False). % 15.48/15.64 do 0 intro. intros zenon_He6 zenon_Hae zenon_H13c zenon_H30 zenon_H146 zenon_H22 zenon_H2b8 zenon_H10a zenon_Ha3 zenon_H117 zenon_H17d zenon_H254 zenon_H1f zenon_H24f zenon_H36 zenon_H82 zenon_H80 zenon_Hb4. % 15.48/15.65 apply (zenon_or_s _ _ zenon_He6); [ zenon_intro zenon_Haf | zenon_intro zenon_He7 ]. % 15.48/15.65 apply (zenon_L39_); trivial. % 15.48/15.65 apply (zenon_or_s _ _ zenon_He7); [ zenon_intro zenon_Hdf | zenon_intro zenon_He8 ]. % 15.48/15.65 apply (zenon_L121_); trivial. % 15.48/15.65 apply (zenon_or_s _ _ zenon_He8); [ zenon_intro zenon_H34 | zenon_intro zenon_He2 ]. % 15.48/15.65 exact (zenon_H30 zenon_H34). % 15.48/15.65 apply (zenon_or_s _ _ zenon_H146); [ zenon_intro zenon_Hee | zenon_intro zenon_H14b ]. % 15.48/15.65 apply (zenon_L1054_); trivial. % 15.48/15.65 apply (zenon_or_s _ _ zenon_H14b); [ zenon_intro zenon_H13e | zenon_intro zenon_H14c ]. % 15.48/15.65 apply (zenon_L123_); trivial. % 15.48/15.65 apply (zenon_or_s _ _ zenon_H14c); [ zenon_intro zenon_H119 | zenon_intro zenon_H38 ]. % 15.48/15.65 apply (zenon_L759_); trivial. % 15.48/15.65 apply (zenon_or_s _ _ zenon_H254); [ zenon_intro zenon_Hca | zenon_intro zenon_H255 ]. % 15.48/15.65 apply (zenon_L562_); trivial. % 15.48/15.65 apply (zenon_or_s _ _ zenon_H255); [ zenon_intro zenon_H37 | zenon_intro zenon_H256 ]. % 15.48/15.65 apply (zenon_L6_); trivial. % 15.48/15.65 apply (zenon_or_s _ _ zenon_H256); [ zenon_intro zenon_H81 | zenon_intro zenon_H53 ]. % 15.48/15.65 apply (zenon_L22_); trivial. % 15.48/15.65 apply (zenon_L125_); trivial. % 15.48/15.65 (* end of lemma zenon_L1090_ *) % 15.48/15.65 assert (zenon_L1091_ : (((op (e3) (e0)) = (e2))\/(((op (e3) (e1)) = (e2))\/(((op (e3) (e2)) = (e2))\/((op (e3) (e3)) = (e2))))) -> ((op (e3) (e0)) = (e3)) -> (~((e2) = (e3))) -> ((op (e0) (e1)) = (e2)) -> (~((op (e0) (e1)) = (op (e3) (e1)))) -> ((op (e2) (e2)) = (e2)) -> (~((op (e2) (op (e3) (e2))) = (op (e3) (e2)))) -> (~((op (e3) (e3)) = (e2))) -> False). % 15.48/15.65 do 0 intro. intros zenon_H1df zenon_Hba zenon_H6a zenon_H5d zenon_H138 zenon_H35 zenon_H2af zenon_H3d. % 15.48/15.65 apply (zenon_or_s _ _ zenon_H1df); [ zenon_intro zenon_He9 | zenon_intro zenon_H1e0 ]. % 15.48/15.65 apply (zenon_L220_); trivial. % 15.48/15.65 apply (zenon_or_s _ _ zenon_H1e0); [ zenon_intro zenon_H16a | zenon_intro zenon_H1e1 ]. % 15.48/15.65 apply (zenon_L146_); trivial. % 15.48/15.65 apply (zenon_or_s _ _ zenon_H1e1); [ zenon_intro zenon_H1dd | zenon_intro zenon_H43 ]. % 15.48/15.65 apply (zenon_L1083_); trivial. % 15.48/15.65 exact (zenon_H3d zenon_H43). % 15.48/15.65 (* end of lemma zenon_L1091_ *) % 15.48/15.65 assert (zenon_L1092_ : (~((op (e1) (op (e3) (e1))) = (op (e3) (e1)))) -> ((op (e1) (e2)) = (e1)) -> ((op (e3) (e1)) = (e2)) -> ((op (e3) (e1)) = (e1)) -> False). % 15.48/15.65 do 0 intro. intros zenon_H2b4 zenon_H117 zenon_H16a zenon_H13e. % 15.48/15.65 cut (((op (e1) (e2)) = (e1)) = ((op (e1) (op (e3) (e1))) = (op (e3) (e1)))). % 15.48/15.65 intro zenon_D_pnotp. % 15.48/15.65 apply zenon_H2b4. % 15.48/15.65 rewrite <- zenon_D_pnotp. % 15.48/15.65 exact zenon_H117. % 15.48/15.65 cut (((e1) = (op (e3) (e1)))); [idtac | apply NNPP; zenon_intro zenon_H169]. % 15.48/15.65 cut (((op (e1) (e2)) = (op (e1) (op (e3) (e1))))); [idtac | apply NNPP; zenon_intro zenon_H2b5]. % 15.48/15.65 congruence. % 15.48/15.65 elim (classic ((op (e1) (op (e3) (e1))) = (op (e1) (op (e3) (e1))))); [ zenon_intro zenon_H2b6 | zenon_intro zenon_H2b7 ]. % 15.48/15.65 cut (((op (e1) (op (e3) (e1))) = (op (e1) (op (e3) (e1)))) = ((op (e1) (e2)) = (op (e1) (op (e3) (e1))))). % 15.48/15.65 intro zenon_D_pnotp. % 15.48/15.65 apply zenon_H2b5. % 15.48/15.65 rewrite <- zenon_D_pnotp. % 15.48/15.65 exact zenon_H2b6. % 15.48/15.65 cut (((op (e1) (op (e3) (e1))) = (op (e1) (op (e3) (e1))))); [idtac | apply NNPP; zenon_intro zenon_H2b7]. % 15.48/15.65 cut (((op (e1) (op (e3) (e1))) = (op (e1) (e2)))); [idtac | apply NNPP; zenon_intro zenon_H2b3]. % 15.48/15.65 congruence. % 15.48/15.65 apply (zenon_L1030_); trivial. % 15.48/15.65 apply zenon_H2b7. apply refl_equal. % 15.48/15.65 apply zenon_H2b7. apply refl_equal. % 15.48/15.65 apply zenon_H169. apply sym_equal. exact zenon_H13e. % 15.48/15.65 (* end of lemma zenon_L1092_ *) % 15.48/15.65 assert (zenon_L1093_ : (((op (e3) (e0)) = (e2))\/(((op (e3) (e1)) = (e2))\/(((op (e3) (e2)) = (e2))\/((op (e3) (e3)) = (e2))))) -> ((op (e3) (e0)) = (e3)) -> (~((e2) = (e3))) -> ((op (e3) (e1)) = (e1)) -> ((op (e1) (e2)) = (e1)) -> (~((op (e1) (op (e3) (e1))) = (op (e3) (e1)))) -> ((op (e2) (e2)) = (e2)) -> (~((op (e2) (op (e3) (e2))) = (op (e3) (e2)))) -> (~((op (e3) (e3)) = (e2))) -> False). % 15.48/15.65 do 0 intro. intros zenon_H1df zenon_Hba zenon_H6a zenon_H13e zenon_H117 zenon_H2b4 zenon_H35 zenon_H2af zenon_H3d. % 15.48/15.65 apply (zenon_or_s _ _ zenon_H1df); [ zenon_intro zenon_He9 | zenon_intro zenon_H1e0 ]. % 15.48/15.65 apply (zenon_L220_); trivial. % 15.48/15.65 apply (zenon_or_s _ _ zenon_H1e0); [ zenon_intro zenon_H16a | zenon_intro zenon_H1e1 ]. % 15.48/15.65 apply (zenon_L1092_); trivial. % 15.48/15.65 apply (zenon_or_s _ _ zenon_H1e1); [ zenon_intro zenon_H1dd | zenon_intro zenon_H43 ]. % 15.48/15.65 apply (zenon_L1083_); trivial. % 15.48/15.65 exact (zenon_H3d zenon_H43). % 15.48/15.65 (* end of lemma zenon_L1093_ *) % 15.48/15.65 assert (zenon_L1094_ : (((op (e3) (e0)) = (e1))\/(((op (e3) (e1)) = (e1))\/(((op (e3) (e2)) = (e1))\/((op (e3) (e3)) = (e1))))) -> (~((e1) = (e3))) -> (~((op (e3) (e3)) = (e2))) -> (~((op (e2) (op (e3) (e2))) = (op (e3) (e2)))) -> ((op (e2) (e2)) = (e2)) -> (~((op (e1) (op (e3) (e1))) = (op (e3) (e1)))) -> (~((e2) = (e3))) -> ((op (e3) (e0)) = (e3)) -> (((op (e3) (e0)) = (e2))\/(((op (e3) (e1)) = (e2))\/(((op (e3) (e2)) = (e2))\/((op (e3) (e3)) = (e2))))) -> ((op (e1) (e2)) = (e1)) -> (~((op (e1) (e2)) = (op (e3) (e2)))) -> (~((op (e3) (e3)) = (e1))) -> False). % 15.48/15.65 do 0 intro. intros zenon_H146 zenon_Ha3 zenon_H3d zenon_H2af zenon_H35 zenon_H2b4 zenon_H6a zenon_Hba zenon_H1df zenon_H117 zenon_H17d zenon_H104. % 15.48/15.65 apply (zenon_or_s _ _ zenon_H146); [ zenon_intro zenon_Hee | zenon_intro zenon_H14b ]. % 15.48/15.65 apply (zenon_L79_); trivial. % 15.48/15.65 apply (zenon_or_s _ _ zenon_H14b); [ zenon_intro zenon_H13e | zenon_intro zenon_H14c ]. % 15.48/15.65 apply (zenon_L1093_); trivial. % 15.48/15.65 apply (zenon_or_s _ _ zenon_H14c); [ zenon_intro zenon_H119 | zenon_intro zenon_H38 ]. % 15.48/15.65 apply (zenon_L759_); trivial. % 15.48/15.65 exact (zenon_H104 zenon_H38). % 15.48/15.65 (* end of lemma zenon_L1094_ *) % 15.48/15.65 assert (zenon_L1095_ : ((~((op (e3) (e3)) = (e1)))\/((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 (e1) (e2)) = (op (e3) (e2)))) -> (~((e2) = (e3))) -> (~((op (e1) (op (e3) (e1))) = (op (e3) (e1)))) -> ((op (e1) (e2)) = (e1)) -> (~((op (e2) (op (e3) (e2))) = (op (e3) (e2)))) -> ((op (e2) (e2)) = (e2)) -> (((op (e3) (e0)) = (e2))\/(((op (e3) (e1)) = (e2))\/(((op (e3) (e2)) = (e2))\/((op (e3) (e3)) = (e2))))) -> ((op (e3) (e0)) = (e3)) -> (~((e1) = (e3))) -> (~((op (e3) (e0)) = (op (e3) (e2)))) -> ((~((op (e3) (e3)) = (e2)))\/((op (e3) (e2)) = (e3))) -> False). % 15.48/15.65 do 0 intro. intros zenon_H10c zenon_H109 zenon_H146 zenon_H17d zenon_H6a zenon_H2b4 zenon_H117 zenon_H2af zenon_H35 zenon_H1df zenon_Hba zenon_Ha3 zenon_H105 zenon_H10e. % 15.48/15.65 apply (zenon_or_s _ _ zenon_H10c); [ zenon_intro zenon_H104 | zenon_intro zenon_H10a ]. % 15.48/15.65 apply (zenon_or_s _ _ zenon_H10e); [ zenon_intro zenon_H3d | zenon_intro zenon_H106 ]. % 15.48/15.65 apply (zenon_L1094_); trivial. % 15.48/15.65 apply (zenon_L81_); trivial. % 15.48/15.65 apply (zenon_L82_); trivial. % 15.48/15.65 (* end of lemma zenon_L1095_ *) % 15.48/15.65 assert (zenon_L1096_ : (((op (e0) (e0)) = (e2))\/(((op (e0) (e1)) = (e2))\/(((op (e0) (e2)) = (e2))\/((op (e0) (e3)) = (e2))))) -> (~((op (e0) (e0)) = (e2))) -> (~((op (e3) (e3)) = (e2))) -> (~((op (e0) (e1)) = (op (e3) (e1)))) -> (((op (e2) (e0)) = (e3))\/(((op (e2) (e1)) = (e3))\/(((op (e2) (e2)) = (e3))\/((op (e2) (e3)) = (e3))))) -> (~((op (e2) (e1)) = (op (e3) (e1)))) -> (~((op (e2) (e2)) = (e3))) -> (((op (e0) (e3)) = (e0))\/(((op (e0) (e3)) = (e1))\/(((op (e0) (e3)) = (e2))\/((op (e0) (e3)) = (e3))))) -> (~((op (e0) (e0)) = (op (e0) (e3)))) -> (~((op (e0) (e3)) = (op (e3) (e3)))) -> (~((op (e0) (e3)) = (op (e2) (e3)))) -> (~((op (e0) (e2)) = (op (e2) (e2)))) -> (((op (e0) (e0)) = (e3))\/(((op (e1) (e0)) = (e3))\/(((op (e2) (e0)) = (e3))\/((op (e3) (e0)) = (e3))))) -> (~((op (e0) (e0)) = (e3))) -> (~((op (e0) (e3)) = (op (e1) (e3)))) -> (~((op (e1) (e2)) = (op (e2) (e2)))) -> (((op (e0) (e2)) = (e0))\/(((op (e1) (e2)) = (e0))\/(((op (e2) (e2)) = (e0))\/((op (e3) (e2)) = (e0))))) -> (~((op (e0) (e0)) = (op (e0) (e2)))) -> (~((op (e3) (e3)) = (e0))) -> (~((e0) = (e3))) -> ((op (e0) (e0)) = (e0)) -> (((op (e3) (e0)) = (e0))\/(((op (e3) (e1)) = (e0))\/(((op (e3) (e2)) = (e0))\/((op (e3) (e3)) = (e0))))) -> (~((op (e2) (e2)) = (e0))) -> ((op (e0) (e1)) = (e1)) -> (~((op (e0) (op (e3) (e0))) = (op (e3) (e0)))) -> ((op (e3) (e1)) = (e3)) -> (((op (e1) (e0)) = (e2))\/(((op (e1) (e1)) = (e2))\/(((op (e1) (e2)) = (e2))\/((op (e1) (e3)) = (e2))))) -> ((op (e2) (e0)) = (e1)) -> ((~((op (e3) (e3)) = (e1)))\/((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 (e1) (e2)) = (op (e3) (e2)))) -> (~((e2) = (e3))) -> (~((op (e1) (op (e3) (e1))) = (op (e3) (e1)))) -> ((op (e1) (e2)) = (e1)) -> (~((op (e2) (op (e3) (e2))) = (op (e3) (e2)))) -> ((op (e2) (e2)) = (e2)) -> (((op (e3) (e0)) = (e2))\/(((op (e3) (e1)) = (e2))\/(((op (e3) (e2)) = (e2))\/((op (e3) (e3)) = (e2))))) -> (~((e1) = (e3))) -> (~((op (e3) (e0)) = (op (e3) (e2)))) -> ((~((op (e3) (e3)) = (e2)))\/((op (e3) (e2)) = (e3))) -> False). % 15.48/15.65 do 0 intro. intros zenon_H8e zenon_H8f zenon_H3d zenon_H138 zenon_He6 zenon_H13c zenon_H30 zenon_H254 zenon_H24f zenon_H36 zenon_Hb4 zenon_H28 zenon_Hbe zenon_H59 zenon_H80 zenon_H7d zenon_H16f zenon_H250 zenon_H3c zenon_H4b zenon_H1f zenon_H1f6 zenon_H2e zenon_H22 zenon_H2b8 zenon_H10a zenon_H84 zenon_Hae zenon_H10c zenon_H109 zenon_H146 zenon_H17d zenon_H6a zenon_H2b4 zenon_H117 zenon_H2af zenon_H35 zenon_H1df zenon_Ha3 zenon_H105 zenon_H10e. % 15.48/15.65 apply (zenon_or_s _ _ zenon_H8e); [ zenon_intro zenon_H92 | zenon_intro zenon_H91 ]. % 15.48/15.65 exact (zenon_H8f zenon_H92). % 15.48/15.65 apply (zenon_or_s _ _ zenon_H91); [ zenon_intro zenon_H5d | zenon_intro zenon_H93 ]. % 15.48/15.65 apply (zenon_or_s _ _ zenon_Hbe); [ zenon_intro zenon_H5b | zenon_intro zenon_Hbf ]. % 15.48/15.65 exact (zenon_H59 zenon_H5b). % 15.48/15.65 apply (zenon_or_s _ _ zenon_Hbf); [ zenon_intro zenon_H69 | zenon_intro zenon_Hc0 ]. % 15.48/15.65 apply (zenon_or_s _ _ zenon_H84); [ zenon_intro zenon_H68 | zenon_intro zenon_H85 ]. % 15.48/15.65 apply (zenon_L17_); trivial. % 15.48/15.65 apply (zenon_or_s _ _ zenon_H85); [ zenon_intro zenon_H6e | zenon_intro zenon_H86 ]. % 15.48/15.65 apply (zenon_L1089_); trivial. % 15.48/15.65 apply (zenon_or_s _ _ zenon_H86); [ zenon_intro zenon_H7c | zenon_intro zenon_H82 ]. % 15.48/15.65 apply (zenon_L21_); trivial. % 15.48/15.65 apply (zenon_L1090_); trivial. % 15.48/15.65 apply (zenon_or_s _ _ zenon_Hc0); [ zenon_intro zenon_Haf | zenon_intro zenon_Hba ]. % 15.48/15.65 apply (zenon_L39_); trivial. % 15.48/15.65 apply (zenon_L1091_); trivial. % 15.48/15.65 apply (zenon_or_s _ _ zenon_H93); [ zenon_intro zenon_H63 | zenon_intro zenon_H81 ]. % 15.48/15.65 apply (zenon_L15_); trivial. % 15.48/15.65 apply (zenon_or_s _ _ zenon_Hbe); [ zenon_intro zenon_H5b | zenon_intro zenon_Hbf ]. % 15.48/15.65 exact (zenon_H59 zenon_H5b). % 15.48/15.65 apply (zenon_or_s _ _ zenon_Hbf); [ zenon_intro zenon_H69 | zenon_intro zenon_Hc0 ]. % 15.48/15.65 apply (zenon_or_s _ _ zenon_H84); [ zenon_intro zenon_H68 | zenon_intro zenon_H85 ]. % 15.48/15.65 apply (zenon_L17_); trivial. % 15.48/15.65 apply (zenon_or_s _ _ zenon_H85); [ zenon_intro zenon_H6e | zenon_intro zenon_H86 ]. % 15.48/15.65 apply (zenon_L1089_); trivial. % 15.48/15.65 apply (zenon_or_s _ _ zenon_H86); [ zenon_intro zenon_H7c | zenon_intro zenon_H82 ]. % 15.48/15.65 apply (zenon_L21_); trivial. % 15.48/15.65 apply (zenon_L22_); trivial. % 15.48/15.65 apply (zenon_or_s _ _ zenon_Hc0); [ zenon_intro zenon_Haf | zenon_intro zenon_Hba ]. % 15.48/15.65 apply (zenon_L39_); trivial. % 15.48/15.65 apply (zenon_L1095_); trivial. % 15.48/15.65 (* end of lemma zenon_L1096_ *) % 15.48/15.65 assert (zenon_L1097_ : (((op (e0) (e0)) = (e3))\/(((op (e0) (e1)) = (e3))\/(((op (e0) (e2)) = (e3))\/((op (e0) (e3)) = (e3))))) -> (~((op (e0) (e0)) = (e3))) -> (~((op (e0) (e1)) = (op (e3) (e1)))) -> ((op (e0) (e2)) = (e1)) -> (((op (e2) (e0)) = (e3))\/(((op (e2) (e1)) = (e3))\/(((op (e2) (e2)) = (e3))\/((op (e2) (e3)) = (e3))))) -> (~((e1) = (e3))) -> ((op (e2) (e0)) = (e1)) -> (~((op (e2) (e1)) = (op (e3) (e1)))) -> ((op (e3) (e1)) = (e3)) -> (~((op (e2) (e2)) = (e3))) -> (~((op (e0) (e3)) = (op (e2) (e3)))) -> False). % 15.48/15.65 do 0 intro. intros zenon_H58 zenon_H59 zenon_H138 zenon_H29 zenon_He6 zenon_Ha3 zenon_Hae zenon_H13c zenon_H10a zenon_H30 zenon_Hb4. % 15.48/15.65 apply (zenon_or_s _ _ zenon_H58); [ zenon_intro zenon_H5b | zenon_intro zenon_H5a ]. % 15.48/15.65 exact (zenon_H59 zenon_H5b). % 15.48/15.65 apply (zenon_or_s _ _ zenon_H5a); [ zenon_intro zenon_H4a | zenon_intro zenon_H5c ]. % 15.48/15.65 apply (zenon_L120_); trivial. % 15.48/15.65 apply (zenon_or_s _ _ zenon_H5c); [ zenon_intro zenon_H50 | zenon_intro zenon_H53 ]. % 15.48/15.65 apply (zenon_L29_); trivial. % 15.48/15.65 apply (zenon_L536_); trivial. % 15.48/15.65 (* end of lemma zenon_L1097_ *) % 15.48/15.65 assert (zenon_L1098_ : (((op (e3) (e0)) = (e2))\/(((op (e3) (e1)) = (e2))\/(((op (e3) (e2)) = (e2))\/((op (e3) (e3)) = (e2))))) -> ((op (e3) (e0)) = (e1)) -> ((op (e0) (e2)) = (e1)) -> (~((op (e0) (op (e3) (e0))) = (op (e3) (e0)))) -> ((op (e3) (e1)) = (e3)) -> (~((e2) = (e3))) -> ((op (e2) (e2)) = (e2)) -> (~((op (e2) (op (e3) (e2))) = (op (e3) (e2)))) -> (~((op (e3) (e3)) = (e2))) -> False). % 15.48/15.65 do 0 intro. intros zenon_H1df zenon_Hee zenon_H29 zenon_H2b8 zenon_H10a zenon_H6a zenon_H35 zenon_H2af zenon_H3d. % 15.48/15.65 apply (zenon_or_s _ _ zenon_H1df); [ zenon_intro zenon_He9 | zenon_intro zenon_H1e0 ]. % 15.48/15.65 apply (zenon_L1082_); trivial. % 15.48/15.65 apply (zenon_or_s _ _ zenon_H1e0); [ zenon_intro zenon_H16a | zenon_intro zenon_H1e1 ]. % 15.48/15.65 apply (zenon_L297_); trivial. % 15.48/15.65 apply (zenon_or_s _ _ zenon_H1e1); [ zenon_intro zenon_H1dd | zenon_intro zenon_H43 ]. % 15.48/15.65 apply (zenon_L1083_); trivial. % 15.48/15.65 exact (zenon_H3d zenon_H43). % 15.48/15.65 (* end of lemma zenon_L1098_ *) % 15.48/15.65 assert (zenon_L1099_ : (((op (e0) (e0)) = (e1))\/(((op (e1) (e0)) = (e1))\/(((op (e2) (e0)) = (e1))\/((op (e3) (e0)) = (e1))))) -> (~((op (e0) (e0)) = (e1))) -> ((~((op (e1) (e1)) = (e3)))\/((op (e1) (e3)) = (e1))) -> (~((op (e1) (e0)) = (op (e1) (e3)))) -> ((~((op (e3) (e3)) = (e1)))\/((op (e3) (e1)) = (e3))) -> (~((op (e3) (e1)) = (op (e3) (e2)))) -> ((~((op (e3) (e3)) = (e3)))\/((op (e3) (e3)) = (e3))) -> (~((op (e3) (op (e3) (e3))) = (op (e3) (e3)))) -> (~((op (e0) (e0)) = (e2))) -> (~((e1) = (e2))) -> (~((op (e2) (e0)) = (op (e2) (e2)))) -> (((op (e1) (e1)) = (e0))\/(((op (e1) (e1)) = (e1))\/(((op (e1) (e1)) = (e2))\/((op (e1) (e1)) = (e3))))) -> (~((op (e1) (e1)) = (e1))) -> (((op (e3) (e3)) = (e0))\/(((op (e3) (e3)) = (e1))\/(((op (e3) (e3)) = (e2))\/((op (e3) (e3)) = (e3))))) -> (((op (e0) (e0)) = (e2))\/(((op (e1) (e0)) = (e2))\/(((op (e2) (e0)) = (e2))\/((op (e3) (e0)) = (e2))))) -> (((op (e3) (e0)) = (e1))\/(((op (e3) (e1)) = (e1))\/(((op (e3) (e2)) = (e1))\/((op (e3) (e3)) = (e1))))) -> (((op (e3) (e0)) = (e0))\/(((op (e3) (e1)) = (e0))\/(((op (e3) (e2)) = (e0))\/((op (e3) (e3)) = (e0))))) -> (~((op (e1) (e2)) = (op (e3) (e2)))) -> (~((op (e1) (op (e3) (e1))) = (op (e3) (e1)))) -> ((op (e0) (e0)) = (e0)) -> (~((op (e1) (e0)) = (op (e1) (e2)))) -> (~((op (e1) (e2)) = (op (e2) (e2)))) -> (((op (e1) (e2)) = (e0))\/(((op (e1) (e2)) = (e1))\/(((op (e1) (e2)) = (e2))\/((op (e1) (e2)) = (e3))))) -> (~((op (e1) (e0)) = (op (e3) (e0)))) -> ((~((op (e3) (e3)) = (e2)))\/((op (e3) (e2)) = (e3))) -> (((op (e2) (e0)) = (e0))\/(((op (e2) (e0)) = (e1))\/(((op (e2) (e0)) = (e2))\/((op (e2) (e0)) = (e3))))) -> (~((op (e2) (e0)) = (op (e3) (e0)))) -> (~((op (e1) (e0)) = (op (e2) (e0)))) -> (~((op (e0) (e0)) = (op (e2) (e0)))) -> ((~((op (e3) (e3)) = (e0)))\/((op (e3) (e0)) = (e3))) -> ((~((op (e1) (e1)) = (e2)))\/((op (e1) (e2)) = (e1))) -> (~((op (e0) (e3)) = (op (e2) (e3)))) -> (~((op (e2) (e2)) = (e3))) -> (~((op (e2) (e1)) = (op (e3) (e1)))) -> (~((e1) = (e3))) -> (((op (e2) (e0)) = (e3))\/(((op (e2) (e1)) = (e3))\/(((op (e2) (e2)) = (e3))\/((op (e2) (e3)) = (e3))))) -> (~((op (e0) (e1)) = (op (e3) (e1)))) -> (~((op (e0) (e0)) = (e3))) -> (((op (e0) (e0)) = (e3))\/(((op (e0) (e1)) = (e3))\/(((op (e0) (e2)) = (e3))\/((op (e0) (e3)) = (e3))))) -> (((op (e3) (e0)) = (e2))\/(((op (e3) (e1)) = (e2))\/(((op (e3) (e2)) = (e2))\/((op (e3) (e3)) = (e2))))) -> ((op (e0) (e2)) = (e1)) -> (~((op (e0) (op (e3) (e0))) = (op (e3) (e0)))) -> ((op (e3) (e1)) = (e3)) -> (~((e2) = (e3))) -> ((op (e2) (e2)) = (e2)) -> (~((op (e2) (op (e3) (e2))) = (op (e3) (e2)))) -> (~((op (e3) (e3)) = (e2))) -> False). % 15.48/15.65 do 0 intro. intros zenon_Hf1 zenon_H45 zenon_H1d2 zenon_H1cf zenon_H10c zenon_H135 zenon_H10d zenon_H2be zenon_H8f zenon_Ha7 zenon_H17a zenon_H1b3 zenon_H1b4 zenon_H3b zenon_Heb zenon_H146 zenon_H1f6 zenon_H17d zenon_H2b4 zenon_H1f zenon_H166 zenon_H7d zenon_H1d5 zenon_H22e zenon_H10e zenon_H281 zenon_H1e5 zenon_H247 zenon_H258 zenon_H10f zenon_H1d3 zenon_Hb4 zenon_H30 zenon_H13c zenon_Ha3 zenon_He6 zenon_H138 zenon_H59 zenon_H58 zenon_H1df zenon_H29 zenon_H2b8 zenon_H10a zenon_H6a zenon_H35 zenon_H2af zenon_H3d. % 15.48/15.65 apply (zenon_or_s _ _ zenon_Hf1); [ zenon_intro zenon_H47 | zenon_intro zenon_Hf4 ]. % 15.48/15.65 exact (zenon_H45 zenon_H47). % 15.48/15.65 apply (zenon_or_s _ _ zenon_Hf4); [ zenon_intro zenon_Hd8 | zenon_intro zenon_Hf5 ]. % 15.48/15.65 apply (zenon_L1080_); trivial. % 15.48/15.65 apply (zenon_or_s _ _ zenon_Hf5); [ zenon_intro zenon_Hae | zenon_intro zenon_Hee ]. % 15.48/15.65 apply (zenon_L1097_); trivial. % 15.48/15.65 apply (zenon_L1098_); trivial. % 15.48/15.65 (* end of lemma zenon_L1099_ *) % 15.48/15.65 assert (zenon_L1100_ : ((~((op (e2) (e2)) = (e3)))\/((op (e2) (e3)) = (e2))) -> (~((op (e2) (e2)) = (op (e2) (e3)))) -> (((op (e0) (e0)) = (e3))\/(((op (e1) (e0)) = (e3))\/(((op (e2) (e0)) = (e3))\/((op (e3) (e0)) = (e3))))) -> (((op (e0) (e2)) = (e0))\/(((op (e1) (e2)) = (e0))\/(((op (e2) (e2)) = (e0))\/((op (e3) (e2)) = (e0))))) -> (~((op (e2) (e2)) = (e0))) -> (~((e0) = (e3))) -> (((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)) = (e2))\/(((op (e1) (e1)) = (e2))\/(((op (e1) (e2)) = (e2))\/((op (e1) (e3)) = (e2))))) -> (~((op (e0) (e0)) = (e3))) -> (~((op (e3) (e0)) = (op (e3) (e2)))) -> (~((op (e3) (e0)) = (op (e3) (e1)))) -> (((op (e0) (e0)) = (e3))\/(((op (e0) (e1)) = (e3))\/(((op (e0) (e2)) = (e3))\/((op (e0) (e3)) = (e3))))) -> (~((op (e0) (e0)) = (e1))) -> (((op (e0) (e0)) = (e1))\/(((op (e1) (e0)) = (e1))\/(((op (e2) (e0)) = (e1))\/((op (e3) (e0)) = (e1))))) -> (~((op (e0) (op (e3) (e0))) = (op (e3) (e0)))) -> (((op (e3) (e3)) = (e0))\/(((op (e3) (e3)) = (e1))\/(((op (e3) (e3)) = (e2))\/((op (e3) (e3)) = (e3))))) -> (~((op (e0) (e3)) = (op (e3) (e3)))) -> (~((op (e1) (e2)) = (op (e1) (e3)))) -> (~((op (e2) (e0)) = (op (e2) (e3)))) -> (((op (e0) (e3)) = (e1))\/(((op (e1) (e3)) = (e1))\/(((op (e2) (e3)) = (e1))\/((op (e3) (e3)) = (e1))))) -> ((op (e1) (e2)) = (e1)) -> (~((op (e1) (e0)) = (op (e1) (e2)))) -> (((op (e3) (e0)) = (e2))\/(((op (e3) (e1)) = (e2))\/(((op (e3) (e2)) = (e2))\/((op (e3) (e3)) = (e2))))) -> (~((op (e2) (op (e3) (e2))) = (op (e3) (e2)))) -> (~((op (e0) (e1)) = (op (e3) (e1)))) -> (~((op (e0) (e2)) = (op (e2) (e2)))) -> (((op (e0) (e0)) = (e2))\/(((op (e0) (e1)) = (e2))\/(((op (e0) (e2)) = (e2))\/((op (e0) (e3)) = (e2))))) -> (~((op (e0) (e2)) = (op (e0) (e3)))) -> ((~((op (e1) (e1)) = (e3)))\/((op (e1) (e3)) = (e1))) -> (~((op (e1) (e0)) = (op (e1) (e3)))) -> ((~((op (e3) (e3)) = (e1)))\/((op (e3) (e1)) = (e3))) -> (~((op (e3) (e1)) = (op (e3) (e2)))) -> ((~((op (e3) (e3)) = (e3)))\/((op (e3) (e3)) = (e3))) -> (~((op (e3) (op (e3) (e3))) = (op (e3) (e3)))) -> (~((op (e0) (e0)) = (e2))) -> (~((e1) = (e2))) -> (~((op (e2) (e0)) = (op (e2) (e2)))) -> ((op (e2) (e2)) = (e2)) -> (((op (e1) (e1)) = (e0))\/(((op (e1) (e1)) = (e1))\/(((op (e1) (e1)) = (e2))\/((op (e1) (e1)) = (e3))))) -> (~((op (e1) (e1)) = (e1))) -> (((op (e0) (e0)) = (e2))\/(((op (e1) (e0)) = (e2))\/(((op (e2) (e0)) = (e2))\/((op (e3) (e0)) = (e2))))) -> (((op (e3) (e0)) = (e1))\/(((op (e3) (e1)) = (e1))\/(((op (e3) (e2)) = (e1))\/((op (e3) (e3)) = (e1))))) -> (~((e1) = (e3))) -> (((op (e3) (e0)) = (e0))\/(((op (e3) (e1)) = (e0))\/(((op (e3) (e2)) = (e0))\/((op (e3) (e3)) = (e0))))) -> (~((op (e1) (e2)) = (op (e3) (e2)))) -> (~((op (e1) (op (e3) (e1))) = (op (e3) (e1)))) -> ((op (e0) (e0)) = (e0)) -> (~((op (e1) (e2)) = (op (e2) (e2)))) -> (((op (e1) (e2)) = (e0))\/(((op (e1) (e2)) = (e1))\/(((op (e1) (e2)) = (e2))\/((op (e1) (e2)) = (e3))))) -> (~((op (e1) (e0)) = (op (e3) (e0)))) -> ((~((op (e3) (e3)) = (e2)))\/((op (e3) (e2)) = (e3))) -> (((op (e2) (e0)) = (e0))\/(((op (e2) (e0)) = (e1))\/(((op (e2) (e0)) = (e2))\/((op (e2) (e0)) = (e3))))) -> (~((op (e2) (e0)) = (op (e3) (e0)))) -> (~((op (e1) (e0)) = (op (e2) (e0)))) -> (~((op (e0) (e0)) = (op (e2) (e0)))) -> ((~((op (e3) (e3)) = (e0)))\/((op (e3) (e0)) = (e3))) -> ((~((op (e1) (e1)) = (e2)))\/((op (e1) (e2)) = (e1))) -> (((op (e0) (e0)) = (e1))\/(((op (e0) (e1)) = (e1))\/(((op (e0) (e2)) = (e1))\/((op (e0) (e3)) = (e1))))) -> (((op (e0) (e2)) = (e0))\/(((op (e0) (e2)) = (e1))\/(((op (e0) (e2)) = (e2))\/((op (e0) (e2)) = (e3))))) -> (~((op (e0) (e2)) = (op (e3) (e2)))) -> (~((op (e0) (e0)) = (op (e0) (e2)))) -> (~((e2) = (e3))) -> (~((op (e1) (e1)) = (e3))) -> (((op (e0) (e3)) = (e0))\/(((op (e0) (e3)) = (e1))\/(((op (e0) (e3)) = (e2))\/((op (e0) (e3)) = (e3))))) -> (~((op (e0) (e3)) = (op (e1) (e3)))) -> (~((op (e0) (e3)) = (op (e2) (e3)))) -> (~((op (e0) (e0)) = (op (e0) (e3)))) -> (((op (e1) (e0)) = (e3))\/(((op (e1) (e1)) = (e3))\/(((op (e1) (e2)) = (e3))\/((op (e1) (e3)) = (e3))))) -> False). % 15.48/15.65 do 0 intro. intros zenon_H1c3 zenon_H15f zenon_Hbe zenon_H16f zenon_H2e zenon_H4b zenon_He6 zenon_H13c zenon_H84 zenon_H59 zenon_H105 zenon_H109 zenon_H58 zenon_H45 zenon_Hf1 zenon_H2b8 zenon_H3b zenon_H36 zenon_H1d0 zenon_Hce zenon_H121 zenon_H117 zenon_H166 zenon_H1df zenon_H2af zenon_H138 zenon_H28 zenon_H8e zenon_Hc9 zenon_H1d2 zenon_H1cf zenon_H10c zenon_H135 zenon_H10d zenon_H2be zenon_H8f zenon_Ha7 zenon_H17a zenon_H35 zenon_H1b3 zenon_H1b4 zenon_Heb zenon_H146 zenon_Ha3 zenon_H1f6 zenon_H17d zenon_H2b4 zenon_H1f zenon_H7d zenon_H1d5 zenon_H22e zenon_H10e zenon_H281 zenon_H1e5 zenon_H247 zenon_H258 zenon_H10f zenon_H1d3 zenon_H44 zenon_H251 zenon_H140 zenon_H250 zenon_H6a zenon_H182 zenon_H254 zenon_H80 zenon_Hb4 zenon_H24f zenon_H90. % 15.48/15.65 apply (zenon_or_s _ _ zenon_H1c3); [ zenon_intro zenon_H30 | zenon_intro zenon_H124 ]. % 15.48/15.65 apply (zenon_or_s _ _ zenon_H10f); [ zenon_intro zenon_H3c | zenon_intro zenon_Hba ]. % 15.48/15.65 apply (zenon_or_s _ _ zenon_H10c); [ zenon_intro zenon_H104 | zenon_intro zenon_H10a ]. % 15.48/15.65 apply (zenon_or_s _ _ zenon_H10e); [ zenon_intro zenon_H3d | zenon_intro zenon_H106 ]. % 15.48/15.65 apply (zenon_or_s _ _ zenon_H10d); [ zenon_intro zenon_H3e | zenon_intro zenon_H42 ]. % 15.48/15.65 apply (zenon_or_s _ _ zenon_H44); [ zenon_intro zenon_H47 | zenon_intro zenon_H46 ]. % 15.48/15.65 exact (zenon_H45 zenon_H47). % 15.48/15.65 apply (zenon_or_s _ _ zenon_H46); [ zenon_intro zenon_H22 | zenon_intro zenon_H48 ]. % 15.48/15.65 apply (zenon_L1055_); trivial. % 15.48/15.65 apply (zenon_or_s _ _ zenon_H48); [ zenon_intro zenon_H29 | zenon_intro zenon_H37 ]. % 15.48/15.65 apply (zenon_or_s _ _ zenon_Hf1); [ zenon_intro zenon_H47 | zenon_intro zenon_Hf4 ]. % 15.48/15.65 exact (zenon_H45 zenon_H47). % 15.48/15.65 apply (zenon_or_s _ _ zenon_Hf4); [ zenon_intro zenon_Hd8 | zenon_intro zenon_Hf5 ]. % 15.48/15.65 apply (zenon_L1080_); trivial. % 15.48/15.65 apply (zenon_or_s _ _ zenon_Hf5); [ zenon_intro zenon_Hae | zenon_intro zenon_Hee ]. % 15.48/15.65 apply (zenon_L551_); trivial. % 15.48/15.65 apply (zenon_L1085_); trivial. % 15.48/15.65 apply (zenon_L7_); trivial. % 15.48/15.65 apply (zenon_L1041_); trivial. % 15.48/15.65 apply (zenon_or_s _ _ zenon_H10d); [ zenon_intro zenon_H3e | zenon_intro zenon_H42 ]. % 15.48/15.65 apply (zenon_or_s _ _ zenon_H44); [ zenon_intro zenon_H47 | zenon_intro zenon_H46 ]. % 15.48/15.65 exact (zenon_H45 zenon_H47). % 15.48/15.65 apply (zenon_or_s _ _ zenon_H46); [ zenon_intro zenon_H22 | zenon_intro zenon_H48 ]. % 15.48/15.65 apply (zenon_or_s _ _ zenon_Hf1); [ zenon_intro zenon_H47 | zenon_intro zenon_Hf4 ]. % 15.48/15.65 exact (zenon_H45 zenon_H47). % 15.48/15.65 apply (zenon_or_s _ _ zenon_Hf4); [ zenon_intro zenon_Hd8 | zenon_intro zenon_Hf5 ]. % 15.48/15.65 apply (zenon_L248_); trivial. % 15.48/15.65 apply (zenon_or_s _ _ zenon_Hf5); [ zenon_intro zenon_Hae | zenon_intro zenon_Hee ]. % 15.48/15.65 apply (zenon_or_s _ _ zenon_H121); [ zenon_intro zenon_H37 | zenon_intro zenon_H122 ]. % 15.48/15.65 apply (zenon_L1086_); trivial. % 15.48/15.65 apply (zenon_or_s _ _ zenon_H122); [ zenon_intro zenon_H11f | zenon_intro zenon_H123 ]. % 15.48/15.65 apply (zenon_L237_); trivial. % 15.48/15.65 apply (zenon_or_s _ _ zenon_H123); [ zenon_intro zenon_Hb5 | zenon_intro zenon_H38 ]. % 15.48/15.65 apply (zenon_L91_); trivial. % 15.48/15.65 exact (zenon_H104 zenon_H38). % 15.48/15.65 apply (zenon_L1054_); trivial. % 15.48/15.65 apply (zenon_or_s _ _ zenon_H48); [ zenon_intro zenon_H29 | zenon_intro zenon_H37 ]. % 15.48/15.65 apply (zenon_or_s _ _ zenon_Hf1); [ zenon_intro zenon_H47 | zenon_intro zenon_Hf4 ]. % 15.48/15.65 exact (zenon_H45 zenon_H47). % 15.48/15.65 apply (zenon_or_s _ _ zenon_Hf4); [ zenon_intro zenon_Hd8 | zenon_intro zenon_Hf5 ]. % 15.48/15.65 apply (zenon_L1076_); trivial. % 15.48/15.65 apply (zenon_or_s _ _ zenon_Hf5); [ zenon_intro zenon_Hae | zenon_intro zenon_Hee ]. % 15.48/15.65 apply (zenon_L551_); trivial. % 15.48/15.65 apply (zenon_or_s _ _ zenon_H8e); [ zenon_intro zenon_H92 | zenon_intro zenon_H91 ]. % 15.48/15.65 exact (zenon_H8f zenon_H92). % 15.48/15.65 apply (zenon_or_s _ _ zenon_H91); [ zenon_intro zenon_H5d | zenon_intro zenon_H93 ]. % 15.48/15.65 apply (zenon_or_s _ _ zenon_Heb); [ zenon_intro zenon_H92 | zenon_intro zenon_Hec ]. % 15.48/15.65 exact (zenon_H8f zenon_H92). % 15.48/15.65 apply (zenon_or_s _ _ zenon_Hec); [ zenon_intro zenon_H68 | zenon_intro zenon_Hed ]. % 15.48/15.65 apply (zenon_or_s _ _ zenon_H90); [ zenon_intro zenon_H69 | zenon_intro zenon_H94 ]. % 15.48/15.65 apply (zenon_L17_); trivial. % 15.48/15.65 apply (zenon_or_s _ _ zenon_H94); [ zenon_intro zenon_H96 | zenon_intro zenon_H95 ]. % 15.48/15.65 exact (zenon_H182 zenon_H96). % 15.48/15.65 apply (zenon_or_s _ _ zenon_H95); [ zenon_intro zenon_H88 | zenon_intro zenon_H8a ]. % 15.48/15.65 apply (zenon_L164_); trivial. % 15.48/15.65 apply (zenon_or_s _ _ zenon_H121); [ zenon_intro zenon_H37 | zenon_intro zenon_H122 ]. % 15.48/15.65 apply (zenon_L85_); trivial. % 15.48/15.65 apply (zenon_or_s _ _ zenon_H122); [ zenon_intro zenon_H11f | zenon_intro zenon_H123 ]. % 15.48/15.65 apply (zenon_L237_); trivial. % 15.48/15.65 apply (zenon_or_s _ _ zenon_H123); [ zenon_intro zenon_Hb5 | zenon_intro zenon_H38 ]. % 15.48/15.65 apply (zenon_L1087_); trivial. % 15.48/15.65 exact (zenon_H104 zenon_H38). % 15.48/15.65 apply (zenon_or_s _ _ zenon_Hed); [ zenon_intro zenon_Hdd | zenon_intro zenon_He9 ]. % 15.48/15.65 apply (zenon_L161_); trivial. % 15.48/15.65 apply (zenon_L1082_); trivial. % 15.48/15.65 apply (zenon_or_s _ _ zenon_H93); [ zenon_intro zenon_H63 | zenon_intro zenon_H81 ]. % 15.48/15.65 apply (zenon_L15_); trivial. % 15.48/15.65 apply (zenon_L107_); trivial. % 15.48/15.65 apply (zenon_L1086_); trivial. % 15.48/15.65 apply (zenon_L1041_); trivial. % 15.48/15.65 apply (zenon_or_s _ _ zenon_H10e); [ zenon_intro zenon_H3d | zenon_intro zenon_H106 ]. % 15.48/15.65 apply (zenon_or_s _ _ zenon_H10d); [ zenon_intro zenon_H3e | zenon_intro zenon_H42 ]. % 15.48/15.65 apply (zenon_or_s _ _ zenon_H44); [ zenon_intro zenon_H47 | zenon_intro zenon_H46 ]. % 15.48/15.65 exact (zenon_H45 zenon_H47). % 15.48/15.65 apply (zenon_or_s _ _ zenon_H46); [ zenon_intro zenon_H22 | zenon_intro zenon_H48 ]. % 15.48/15.65 apply (zenon_or_s _ _ zenon_Hf1); [ zenon_intro zenon_H47 | zenon_intro zenon_Hf4 ]. % 15.48/15.65 exact (zenon_H45 zenon_H47). % 15.48/15.65 apply (zenon_or_s _ _ zenon_Hf4); [ zenon_intro zenon_Hd8 | zenon_intro zenon_Hf5 ]. % 15.48/15.65 apply (zenon_L248_); trivial. % 15.48/15.65 apply (zenon_or_s _ _ zenon_Hf5); [ zenon_intro zenon_Hae | zenon_intro zenon_Hee ]. % 15.48/15.65 apply (zenon_L1096_); trivial. % 15.48/15.65 apply (zenon_L1054_); trivial. % 15.48/15.65 apply (zenon_or_s _ _ zenon_H48); [ zenon_intro zenon_H29 | zenon_intro zenon_H37 ]. % 15.48/15.65 apply (zenon_L1099_); trivial. % 15.48/15.65 apply (zenon_L7_); trivial. % 15.48/15.65 apply (zenon_L1041_); trivial. % 15.48/15.65 apply (zenon_L115_); trivial. % 15.48/15.65 apply (zenon_L1095_); trivial. % 15.48/15.65 apply (zenon_L137_); trivial. % 15.48/15.65 (* end of lemma zenon_L1100_ *) % 15.48/15.65 assert (zenon_L1101_ : ((~((op (e2) (e2)) = (e0)))\/((op (e2) (e0)) = (e2))) -> (((op (e1) (e0)) = (e3))\/(((op (e1) (e1)) = (e3))\/(((op (e1) (e2)) = (e3))\/((op (e1) (e3)) = (e3))))) -> (~((op (e0) (e0)) = (op (e0) (e3)))) -> (~((op (e0) (e3)) = (op (e2) (e3)))) -> (~((op (e0) (e3)) = (op (e1) (e3)))) -> (((op (e0) (e3)) = (e0))\/(((op (e0) (e3)) = (e1))\/(((op (e0) (e3)) = (e2))\/((op (e0) (e3)) = (e3))))) -> (~((op (e1) (e1)) = (e3))) -> (~((e2) = (e3))) -> (~((op (e0) (e0)) = (op (e0) (e2)))) -> (~((op (e0) (e2)) = (op (e3) (e2)))) -> (((op (e0) (e2)) = (e0))\/(((op (e0) (e2)) = (e1))\/(((op (e0) (e2)) = (e2))\/((op (e0) (e2)) = (e3))))) -> (((op (e0) (e0)) = (e1))\/(((op (e0) (e1)) = (e1))\/(((op (e0) (e2)) = (e1))\/((op (e0) (e3)) = (e1))))) -> ((~((op (e1) (e1)) = (e2)))\/((op (e1) (e2)) = (e1))) -> ((~((op (e3) (e3)) = (e0)))\/((op (e3) (e0)) = (e3))) -> (~((op (e0) (e0)) = (op (e2) (e0)))) -> (~((op (e1) (e0)) = (op (e2) (e0)))) -> (~((op (e2) (e0)) = (op (e3) (e0)))) -> (((op (e2) (e0)) = (e0))\/(((op (e2) (e0)) = (e1))\/(((op (e2) (e0)) = (e2))\/((op (e2) (e0)) = (e3))))) -> ((~((op (e3) (e3)) = (e2)))\/((op (e3) (e2)) = (e3))) -> (~((op (e1) (e0)) = (op (e3) (e0)))) -> (((op (e1) (e2)) = (e0))\/(((op (e1) (e2)) = (e1))\/(((op (e1) (e2)) = (e2))\/((op (e1) (e2)) = (e3))))) -> (~((op (e1) (e2)) = (op (e2) (e2)))) -> ((op (e0) (e0)) = (e0)) -> (~((op (e1) (op (e3) (e1))) = (op (e3) (e1)))) -> (~((op (e1) (e2)) = (op (e3) (e2)))) -> (((op (e3) (e0)) = (e0))\/(((op (e3) (e1)) = (e0))\/(((op (e3) (e2)) = (e0))\/((op (e3) (e3)) = (e0))))) -> (~((e1) = (e3))) -> (((op (e3) (e0)) = (e1))\/(((op (e3) (e1)) = (e1))\/(((op (e3) (e2)) = (e1))\/((op (e3) (e3)) = (e1))))) -> (((op (e0) (e0)) = (e2))\/(((op (e1) (e0)) = (e2))\/(((op (e2) (e0)) = (e2))\/((op (e3) (e0)) = (e2))))) -> (~((op (e1) (e1)) = (e1))) -> (((op (e1) (e1)) = (e0))\/(((op (e1) (e1)) = (e1))\/(((op (e1) (e1)) = (e2))\/((op (e1) (e1)) = (e3))))) -> ((op (e2) (e2)) = (e2)) -> (~((op (e2) (e0)) = (op (e2) (e2)))) -> (~((e1) = (e2))) -> (~((op (e0) (e0)) = (e2))) -> (~((op (e3) (op (e3) (e3))) = (op (e3) (e3)))) -> ((~((op (e3) (e3)) = (e3)))\/((op (e3) (e3)) = (e3))) -> (~((op (e3) (e1)) = (op (e3) (e2)))) -> ((~((op (e3) (e3)) = (e1)))\/((op (e3) (e1)) = (e3))) -> (~((op (e1) (e0)) = (op (e1) (e3)))) -> ((~((op (e1) (e1)) = (e3)))\/((op (e1) (e3)) = (e1))) -> (~((op (e0) (e2)) = (op (e0) (e3)))) -> (((op (e0) (e0)) = (e2))\/(((op (e0) (e1)) = (e2))\/(((op (e0) (e2)) = (e2))\/((op (e0) (e3)) = (e2))))) -> (~((op (e0) (e2)) = (op (e2) (e2)))) -> (~((op (e0) (e1)) = (op (e3) (e1)))) -> (~((op (e2) (op (e3) (e2))) = (op (e3) (e2)))) -> (((op (e3) (e0)) = (e2))\/(((op (e3) (e1)) = (e2))\/(((op (e3) (e2)) = (e2))\/((op (e3) (e3)) = (e2))))) -> (~((op (e1) (e0)) = (op (e1) (e2)))) -> ((op (e1) (e2)) = (e1)) -> (((op (e0) (e3)) = (e1))\/(((op (e1) (e3)) = (e1))\/(((op (e2) (e3)) = (e1))\/((op (e3) (e3)) = (e1))))) -> (~((op (e2) (e0)) = (op (e2) (e3)))) -> (~((op (e1) (e2)) = (op (e1) (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) (op (e3) (e0))) = (op (e3) (e0)))) -> (((op (e0) (e0)) = (e1))\/(((op (e1) (e0)) = (e1))\/(((op (e2) (e0)) = (e1))\/((op (e3) (e0)) = (e1))))) -> (~((op (e0) (e0)) = (e1))) -> (((op (e0) (e0)) = (e3))\/(((op (e0) (e1)) = (e3))\/(((op (e0) (e2)) = (e3))\/((op (e0) (e3)) = (e3))))) -> (~((op (e3) (e0)) = (op (e3) (e1)))) -> (~((op (e3) (e0)) = (op (e3) (e2)))) -> (~((op (e0) (e0)) = (e3))) -> (((op (e1) (e0)) = (e2))\/(((op (e1) (e1)) = (e2))\/(((op (e1) (e2)) = (e2))\/((op (e1) (e3)) = (e2))))) -> (~((op (e2) (e1)) = (op (e3) (e1)))) -> (((op (e2) (e0)) = (e3))\/(((op (e2) (e1)) = (e3))\/(((op (e2) (e2)) = (e3))\/((op (e2) (e3)) = (e3))))) -> (~((e0) = (e3))) -> (((op (e0) (e2)) = (e0))\/(((op (e1) (e2)) = (e0))\/(((op (e2) (e2)) = (e0))\/((op (e3) (e2)) = (e0))))) -> (((op (e0) (e0)) = (e3))\/(((op (e1) (e0)) = (e3))\/(((op (e2) (e0)) = (e3))\/((op (e3) (e0)) = (e3))))) -> (~((op (e2) (e2)) = (op (e2) (e3)))) -> ((~((op (e2) (e2)) = (e3)))\/((op (e2) (e3)) = (e2))) -> False). % 15.48/15.65 do 0 intro. intros zenon_H1d4 zenon_H90 zenon_H24f zenon_Hb4 zenon_H80 zenon_H254 zenon_H182 zenon_H6a zenon_H250 zenon_H140 zenon_H251 zenon_H44 zenon_H1d3 zenon_H10f zenon_H258 zenon_H247 zenon_H1e5 zenon_H281 zenon_H10e zenon_H22e zenon_H1d5 zenon_H7d zenon_H1f zenon_H2b4 zenon_H17d zenon_H1f6 zenon_Ha3 zenon_H146 zenon_Heb zenon_H1b4 zenon_H1b3 zenon_H35 zenon_H17a zenon_Ha7 zenon_H8f zenon_H2be zenon_H10d zenon_H135 zenon_H10c zenon_H1cf zenon_H1d2 zenon_Hc9 zenon_H8e zenon_H28 zenon_H138 zenon_H2af zenon_H1df zenon_H166 zenon_H117 zenon_H121 zenon_Hce zenon_H1d0 zenon_H36 zenon_H3b zenon_H2b8 zenon_Hf1 zenon_H45 zenon_H58 zenon_H109 zenon_H105 zenon_H59 zenon_H84 zenon_H13c zenon_He6 zenon_H4b zenon_H16f zenon_Hbe zenon_H15f zenon_H1c3. % 15.48/15.65 apply (zenon_or_s _ _ zenon_H1d4); [ zenon_intro zenon_H2e | zenon_intro zenon_Hdd ]. % 15.48/15.65 apply (zenon_L1100_); trivial. % 15.48/15.65 apply (zenon_L161_); trivial. % 15.48/15.65 (* end of lemma zenon_L1101_ *) % 15.48/15.65 assert (zenon_L1102_ : (((op (e2) (e0)) = (e3))\/(((op (e2) (e1)) = (e3))\/(((op (e2) (e2)) = (e3))\/((op (e2) (e3)) = (e3))))) -> (~((e1) = (e3))) -> ((op (e2) (e0)) = (e1)) -> ((op (e0) (e1)) = (e3)) -> (~((op (e0) (e1)) = (op (e2) (e1)))) -> (~((op (e2) (e2)) = (e3))) -> (~((op (e2) (op (e3) (e2))) = (op (e3) (e2)))) -> ((op (e3) (e2)) = (e3)) -> False). % 15.48/15.65 do 0 intro. intros zenon_He6 zenon_Ha3 zenon_Hae zenon_H4a zenon_Hde zenon_H30 zenon_H2af zenon_H106. % 15.48/15.65 apply (zenon_or_s _ _ zenon_He6); [ zenon_intro zenon_Haf | zenon_intro zenon_He7 ]. % 15.48/15.65 apply (zenon_L39_); trivial. % 15.48/15.65 apply (zenon_or_s _ _ zenon_He7); [ zenon_intro zenon_Hdf | zenon_intro zenon_He8 ]. % 15.48/15.65 apply (zenon_L65_); trivial. % 15.48/15.65 apply (zenon_or_s _ _ zenon_He8); [ zenon_intro zenon_H34 | zenon_intro zenon_He2 ]. % 15.48/15.65 exact (zenon_H30 zenon_H34). % 15.48/15.65 apply (zenon_L1065_); trivial. % 15.48/15.65 (* end of lemma zenon_L1102_ *) % 15.48/15.65 assert (zenon_L1103_ : (((op (e0) (e0)) = (e3))\/(((op (e0) (e1)) = (e3))\/(((op (e0) (e2)) = (e3))\/((op (e0) (e3)) = (e3))))) -> (~((op (e0) (e0)) = (e3))) -> (~((op (e2) (op (e3) (e2))) = (op (e3) (e2)))) -> (~((op (e2) (e2)) = (e3))) -> (~((op (e0) (e1)) = (op (e2) (e1)))) -> (((op (e2) (e0)) = (e3))\/(((op (e2) (e1)) = (e3))\/(((op (e2) (e2)) = (e3))\/((op (e2) (e3)) = (e3))))) -> (~((op (e0) (e2)) = (op (e3) (e2)))) -> ((op (e3) (e2)) = (e3)) -> (((op (e0) (e3)) = (e1))\/(((op (e1) (e3)) = (e1))\/(((op (e2) (e3)) = (e1))\/((op (e3) (e3)) = (e1))))) -> (~((e1) = (e3))) -> ((op (e1) (e2)) = (e1)) -> (~((op (e1) (e2)) = (op (e1) (e3)))) -> ((op (e2) (e0)) = (e1)) -> (~((op (e2) (e0)) = (op (e2) (e3)))) -> (~((op (e3) (e3)) = (e1))) -> False). % 15.48/15.65 do 0 intro. intros zenon_H58 zenon_H59 zenon_H2af zenon_H30 zenon_Hde zenon_He6 zenon_H140 zenon_H106 zenon_H121 zenon_Ha3 zenon_H117 zenon_H1d0 zenon_Hae zenon_Hce zenon_H104. % 15.48/15.65 apply (zenon_or_s _ _ zenon_H58); [ zenon_intro zenon_H5b | zenon_intro zenon_H5a ]. % 15.48/15.65 exact (zenon_H59 zenon_H5b). % 15.48/15.65 apply (zenon_or_s _ _ zenon_H5a); [ zenon_intro zenon_H4a | zenon_intro zenon_H5c ]. % 15.48/15.65 apply (zenon_L1102_); trivial. % 15.48/15.65 apply (zenon_or_s _ _ zenon_H5c); [ zenon_intro zenon_H50 | zenon_intro zenon_H53 ]. % 15.48/15.65 apply (zenon_L533_); trivial. % 15.48/15.65 apply (zenon_L549_); trivial. % 15.48/15.65 (* end of lemma zenon_L1103_ *) % 15.48/15.65 assert (zenon_L1104_ : (~((op (e1) (op (e3) (e1))) = (op (e3) (e1)))) -> ((op (e1) (e0)) = (e2)) -> ((op (e3) (e1)) = (e0)) -> ((op (e3) (e1)) = (e2)) -> False). % 15.48/15.65 do 0 intro. intros zenon_H2b4 zenon_H68 zenon_H142 zenon_H16a. % 15.48/15.65 cut (((op (e1) (e0)) = (e2)) = ((op (e1) (op (e3) (e1))) = (op (e3) (e1)))). % 15.48/15.65 intro zenon_D_pnotp. % 15.48/15.65 apply zenon_H2b4. % 15.48/15.65 rewrite <- zenon_D_pnotp. % 15.48/15.65 exact zenon_H68. % 15.48/15.65 cut (((e2) = (op (e3) (e1)))); [idtac | apply NNPP; zenon_intro zenon_H16b]. % 15.48/15.65 cut (((op (e1) (e0)) = (op (e1) (op (e3) (e1))))); [idtac | apply NNPP; zenon_intro zenon_H2c3]. % 15.48/15.65 congruence. % 15.48/15.65 elim (classic ((op (e1) (op (e3) (e1))) = (op (e1) (op (e3) (e1))))); [ zenon_intro zenon_H2b6 | zenon_intro zenon_H2b7 ]. % 15.48/15.65 cut (((op (e1) (op (e3) (e1))) = (op (e1) (op (e3) (e1)))) = ((op (e1) (e0)) = (op (e1) (op (e3) (e1))))). % 15.48/15.65 intro zenon_D_pnotp. % 15.48/15.65 apply zenon_H2c3. % 15.48/15.65 rewrite <- zenon_D_pnotp. % 15.48/15.65 exact zenon_H2b6. % 15.48/15.65 cut (((op (e1) (op (e3) (e1))) = (op (e1) (op (e3) (e1))))); [idtac | apply NNPP; zenon_intro zenon_H2b7]. % 15.48/15.65 cut (((op (e1) (op (e3) (e1))) = (op (e1) (e0)))); [idtac | apply NNPP; zenon_intro zenon_H2c2]. % 15.48/15.65 congruence. % 15.48/15.65 apply (zenon_L1046_); trivial. % 15.48/15.65 apply zenon_H2b7. apply refl_equal. % 15.48/15.65 apply zenon_H2b7. apply refl_equal. % 15.48/15.65 apply zenon_H16b. apply sym_equal. exact zenon_H16a. % 15.48/15.65 (* end of lemma zenon_L1104_ *) % 15.48/15.65 assert (zenon_L1105_ : (((op (e3) (e0)) = (e2))\/(((op (e3) (e1)) = (e2))\/(((op (e3) (e2)) = (e2))\/((op (e3) (e3)) = (e2))))) -> (~((e1) = (e2))) -> ((op (e3) (e0)) = (e1)) -> ((op (e1) (e0)) = (e2)) -> (~((op (e1) (op (e3) (e1))) = (op (e3) (e1)))) -> ((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 (e2) (e2)) = (e0))) -> ((op (e3) (e1)) = (e0)) -> (~((op (e2) (e2)) = (e2))) -> (~((op (e2) (e2)) = (e3))) -> False). % 15.48/15.65 do 0 intro. intros zenon_H1df zenon_Ha7 zenon_Hee zenon_H68 zenon_H2b4 zenon_H63 zenon_H140 zenon_H2d zenon_H2e zenon_H142 zenon_H2f zenon_H30. % 15.48/15.65 apply (zenon_or_s _ _ zenon_H1df); [ zenon_intro zenon_He9 | zenon_intro zenon_H1e0 ]. % 15.48/15.65 apply (zenon_L122_); trivial. % 15.48/15.65 apply (zenon_or_s _ _ zenon_H1e0); [ zenon_intro zenon_H16a | zenon_intro zenon_H1e1 ]. % 15.48/15.65 apply (zenon_L1104_); trivial. % 15.48/15.65 apply (zenon_or_s _ _ zenon_H1e1); [ zenon_intro zenon_H1dd | zenon_intro zenon_H43 ]. % 15.48/15.65 apply (zenon_L253_); trivial. % 15.48/15.65 apply (zenon_or_s _ _ zenon_H2d); [ zenon_intro zenon_H32 | zenon_intro zenon_H31 ]. % 15.48/15.65 exact (zenon_H2e zenon_H32). % 15.48/15.65 apply (zenon_or_s _ _ zenon_H31); [ zenon_intro zenon_H2a | zenon_intro zenon_H33 ]. % 15.48/15.65 apply (zenon_L171_); trivial. % 15.48/15.65 apply (zenon_or_s _ _ zenon_H33); [ zenon_intro zenon_H35 | zenon_intro zenon_H34 ]. % 15.48/15.65 exact (zenon_H2f zenon_H35). % 15.48/15.65 exact (zenon_H30 zenon_H34). % 15.48/15.65 (* end of lemma zenon_L1105_ *) % 15.48/15.65 assert (zenon_L1106_ : (~((op (e0) (op (e3) (e0))) = (op (e3) (e0)))) -> ((op (e0) (e2)) = (e2)) -> ((op (e3) (e0)) = (e2)) -> False). % 15.48/15.65 do 0 intro. intros zenon_H2b8 zenon_H63 zenon_He9. % 15.48/15.65 cut (((op (e0) (e2)) = (e2)) = ((op (e0) (op (e3) (e0))) = (op (e3) (e0)))). % 15.48/15.65 intro zenon_D_pnotp. % 15.48/15.65 apply zenon_H2b8. % 15.48/15.65 rewrite <- zenon_D_pnotp. % 15.48/15.65 exact zenon_H63. % 15.48/15.65 cut (((e2) = (op (e3) (e0)))); [idtac | apply NNPP; zenon_intro zenon_H2ce]. % 15.48/15.65 cut (((op (e0) (e2)) = (op (e0) (op (e3) (e0))))); [idtac | apply NNPP; zenon_intro zenon_H2ca]. % 15.48/15.65 congruence. % 15.48/15.65 elim (classic ((op (e0) (op (e3) (e0))) = (op (e0) (op (e3) (e0))))); [ zenon_intro zenon_H2ba | zenon_intro zenon_H2bb ]. % 15.48/15.65 cut (((op (e0) (op (e3) (e0))) = (op (e0) (op (e3) (e0)))) = ((op (e0) (e2)) = (op (e0) (op (e3) (e0))))). % 15.48/15.65 intro zenon_D_pnotp. % 15.48/15.65 apply zenon_H2ca. % 15.48/15.65 rewrite <- zenon_D_pnotp. % 15.48/15.65 exact zenon_H2ba. % 15.48/15.65 cut (((op (e0) (op (e3) (e0))) = (op (e0) (op (e3) (e0))))); [idtac | apply NNPP; zenon_intro zenon_H2bb]. % 15.48/15.65 cut (((op (e0) (op (e3) (e0))) = (op (e0) (e2)))); [idtac | apply NNPP; zenon_intro zenon_H2c9]. % 15.48/15.65 congruence. % 15.48/15.65 apply (zenon_L1081_); trivial. % 15.48/15.65 apply zenon_H2bb. apply refl_equal. % 15.48/15.65 apply zenon_H2bb. apply refl_equal. % 15.48/15.65 apply zenon_H2ce. apply sym_equal. exact zenon_He9. % 15.48/15.65 (* end of lemma zenon_L1106_ *) % 15.48/15.65 assert (zenon_L1107_ : (((op (e0) (e0)) = (e2))\/(((op (e1) (e0)) = (e2))\/(((op (e2) (e0)) = (e2))\/((op (e3) (e0)) = (e2))))) -> (~((op (e0) (e0)) = (e2))) -> (~((op (e3) (e3)) = (e0))) -> (~((e0) = (e3))) -> ((op (e3) (e2)) = (e3)) -> (((op (e3) (e0)) = (e2))\/(((op (e3) (e1)) = (e2))\/(((op (e3) (e2)) = (e2))\/((op (e3) (e3)) = (e2))))) -> (~((e1) = (e2))) -> ((op (e3) (e0)) = (e1)) -> (~((op (e1) (op (e3) (e1))) = (op (e3) (e1)))) -> (~((op (e0) (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 (e2) (e2)) = (e3))) -> ((op (e0) (e0)) = (e0)) -> (((op (e3) (e0)) = (e0))\/(((op (e3) (e1)) = (e0))\/(((op (e3) (e2)) = (e0))\/((op (e3) (e3)) = (e0))))) -> ((op (e2) (e1)) = (e2)) -> (~((op (e2) (e0)) = (op (e2) (e1)))) -> (~((op (e0) (op (e3) (e0))) = (op (e3) (e0)))) -> ((op (e0) (e2)) = (e2)) -> False). % 15.48/15.65 do 0 intro. intros zenon_Heb zenon_H8f zenon_H3c zenon_H4b zenon_H106 zenon_H1df zenon_Ha7 zenon_Hee zenon_H2b4 zenon_H140 zenon_H2d zenon_H2e zenon_H2f zenon_H30 zenon_H1f zenon_H1f6 zenon_H156 zenon_H154 zenon_H2b8 zenon_H63. % 15.48/15.65 apply (zenon_or_s _ _ zenon_Heb); [ zenon_intro zenon_H92 | zenon_intro zenon_Hec ]. % 15.48/15.65 exact (zenon_H8f zenon_H92). % 15.48/15.65 apply (zenon_or_s _ _ zenon_Hec); [ zenon_intro zenon_H68 | zenon_intro zenon_Hed ]. % 15.48/15.65 apply (zenon_or_s _ _ zenon_H1f6); [ zenon_intro zenon_Hdb | zenon_intro zenon_H1f7 ]. % 15.48/15.65 apply (zenon_L1045_); trivial. % 15.48/15.65 apply (zenon_or_s _ _ zenon_H1f7); [ zenon_intro zenon_H142 | zenon_intro zenon_H1f8 ]. % 15.48/15.65 apply (zenon_L1105_); trivial. % 15.48/15.65 apply (zenon_or_s _ _ zenon_H1f8); [ zenon_intro zenon_H167 | zenon_intro zenon_H40 ]. % 15.48/15.65 apply (zenon_L589_); trivial. % 15.48/15.65 exact (zenon_H3c zenon_H40). % 15.48/15.65 apply (zenon_or_s _ _ zenon_Hed); [ zenon_intro zenon_Hdd | zenon_intro zenon_He9 ]. % 15.48/15.65 apply (zenon_L284_); trivial. % 15.48/15.65 apply (zenon_L1106_); trivial. % 15.48/15.65 (* end of lemma zenon_L1107_ *) % 15.48/15.65 assert (zenon_L1108_ : (((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)) = (e0))) -> (((op (e1) (e1)) = (e0))\/(((op (e1) (e1)) = (e1))\/(((op (e1) (e1)) = (e2))\/((op (e1) (e1)) = (e3))))) -> (~((op (e0) (op (e3) (e0))) = (op (e3) (e0)))) -> (~((op (e2) (e0)) = (op (e2) (e1)))) -> ((op (e2) (e1)) = (e2)) -> (((op (e3) (e0)) = (e0))\/(((op (e3) (e1)) = (e0))\/(((op (e3) (e2)) = (e0))\/((op (e3) (e3)) = (e0))))) -> ((op (e0) (e0)) = (e0)) -> (~((op (e2) (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 (e0) (e2)) = (op (e3) (e2)))) -> (~((op (e1) (op (e3) (e1))) = (op (e3) (e1)))) -> ((op (e3) (e0)) = (e1)) -> (~((e1) = (e2))) -> (((op (e3) (e0)) = (e2))\/(((op (e3) (e1)) = (e2))\/(((op (e3) (e2)) = (e2))\/((op (e3) (e3)) = (e2))))) -> ((op (e3) (e2)) = (e3)) -> (~((e0) = (e3))) -> (~((op (e0) (e0)) = (e2))) -> (((op (e0) (e0)) = (e2))\/(((op (e1) (e0)) = (e2))\/(((op (e2) (e0)) = (e2))\/((op (e3) (e0)) = (e2))))) -> (((op (e3) (e3)) = (e0))\/(((op (e3) (e3)) = (e1))\/(((op (e3) (e3)) = (e2))\/((op (e3) (e3)) = (e3))))) -> (~((op (e3) (e3)) = (e0))) -> (~((op (e3) (e3)) = (e1))) -> (~((op (e0) (e3)) = (op (e3) (e3)))) -> (~((op (e3) (e3)) = (e3))) -> False). % 15.48/15.65 do 0 intro. intros zenon_H8e zenon_H182 zenon_H23 zenon_H1b4 zenon_H145 zenon_H1b3 zenon_H2b8 zenon_H154 zenon_H156 zenon_H1f6 zenon_H1f zenon_H30 zenon_H2f zenon_H2e zenon_H2d zenon_H140 zenon_H2b4 zenon_Hee zenon_Ha7 zenon_H1df zenon_H106 zenon_H4b zenon_H8f zenon_Heb zenon_H3b zenon_H3c zenon_H104 zenon_H36 zenon_H3e. % 15.48/15.65 apply (zenon_or_s _ _ zenon_H8e); [ zenon_intro zenon_H92 | zenon_intro zenon_H91 ]. % 15.48/15.65 exact (zenon_H8f zenon_H92). % 15.48/15.65 apply (zenon_or_s _ _ zenon_H91); [ zenon_intro zenon_H5d | zenon_intro zenon_H93 ]. % 15.48/15.65 apply (zenon_L214_); trivial. % 15.48/15.65 apply (zenon_or_s _ _ zenon_H93); [ zenon_intro zenon_H63 | zenon_intro zenon_H81 ]. % 15.48/15.65 apply (zenon_L1107_); trivial. % 15.48/15.65 apply (zenon_L107_); trivial. % 15.48/15.65 (* end of lemma zenon_L1108_ *) % 15.48/15.65 assert (zenon_L1109_ : (((op (e2) (e0)) = (e1))\/(((op (e2) (e1)) = (e1))\/(((op (e2) (e2)) = (e1))\/((op (e2) (e3)) = (e1))))) -> ((op (e2) (e0)) = (e2)) -> (~((e1) = (e2))) -> (~((op (e2) (op (e3) (e2))) = (op (e3) (e2)))) -> (~((op (e1) (e0)) = (op (e1) (e2)))) -> ((op (e1) (e0)) = (e1)) -> (~((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)) = (e1))) -> (~((op (e0) (e3)) = (op (e2) (e3)))) -> ((op (e0) (e3)) = (e1)) -> False). % 15.48/15.65 do 0 intro. intros zenon_Hb7 zenon_Hdd zenon_Ha7 zenon_H2af zenon_H166 zenon_Hd8 zenon_Hc9 zenon_H11b zenon_H52 zenon_Hb4 zenon_H37. % 15.48/15.65 apply (zenon_or_s _ _ zenon_Hb7); [ zenon_intro zenon_Hae | zenon_intro zenon_Hb8 ]. % 15.48/15.65 apply (zenon_L304_); trivial. % 15.48/15.65 apply (zenon_or_s _ _ zenon_Hb8); [ zenon_intro zenon_Hb2 | zenon_intro zenon_Hb9 ]. % 15.48/15.65 apply (zenon_L1025_); trivial. % 15.48/15.65 apply (zenon_or_s _ _ zenon_Hb9); [ zenon_intro zenon_H2a | zenon_intro zenon_Hb5 ]. % 15.48/15.65 exact (zenon_H52 zenon_H2a). % 15.48/15.65 apply (zenon_L41_); trivial. % 15.48/15.65 (* end of lemma zenon_L1109_ *) % 15.48/15.65 assert (zenon_L1110_ : (((op (e0) (e0)) = (e3))\/(((op (e0) (e1)) = (e3))\/(((op (e0) (e2)) = (e3))\/((op (e0) (e3)) = (e3))))) -> (~((op (e0) (e0)) = (e3))) -> (~((op (e2) (op (e3) (e2))) = (op (e3) (e2)))) -> (~((op (e2) (e2)) = (e3))) -> (~((op (e0) (e1)) = (op (e2) (e1)))) -> ((op (e2) (e0)) = (e1)) -> (((op (e2) (e0)) = (e3))\/(((op (e2) (e1)) = (e3))\/(((op (e2) (e2)) = (e3))\/((op (e2) (e3)) = (e3))))) -> (~((op (e0) (e2)) = (op (e3) (e2)))) -> ((op (e3) (e2)) = (e3)) -> ((op (e0) (e3)) = (e1)) -> (~((e1) = (e3))) -> False). % 15.48/15.65 do 0 intro. intros zenon_H58 zenon_H59 zenon_H2af zenon_H30 zenon_Hde zenon_Hae zenon_He6 zenon_H140 zenon_H106 zenon_H37 zenon_Ha3. % 15.48/15.65 apply (zenon_or_s _ _ zenon_H58); [ zenon_intro zenon_H5b | zenon_intro zenon_H5a ]. % 15.48/15.65 exact (zenon_H59 zenon_H5b). % 15.48/15.65 apply (zenon_or_s _ _ zenon_H5a); [ zenon_intro zenon_H4a | zenon_intro zenon_H5c ]. % 15.48/15.65 apply (zenon_L1102_); trivial. % 15.48/15.65 apply (zenon_or_s _ _ zenon_H5c); [ zenon_intro zenon_H50 | zenon_intro zenon_H53 ]. % 15.48/15.65 apply (zenon_L533_); trivial. % 15.48/15.65 apply (zenon_L32_); trivial. % 15.48/15.65 (* end of lemma zenon_L1110_ *) % 15.48/15.65 assert (zenon_L1111_ : (((op (e0) (e0)) = (e1))\/(((op (e1) (e0)) = (e1))\/(((op (e2) (e0)) = (e1))\/((op (e3) (e0)) = (e1))))) -> (~((op (e0) (e0)) = (e1))) -> (~((op (e0) (e3)) = (op (e2) (e3)))) -> (((op (e0) (e2)) = (e1))\/(((op (e1) (e2)) = (e1))\/(((op (e2) (e2)) = (e1))\/((op (e3) (e2)) = (e1))))) -> (~((op (e0) (e2)) = (op (e0) (e3)))) -> (~((op (e1) (e0)) = (op (e1) (e2)))) -> (~((e1) = (e2))) -> ((op (e2) (e0)) = (e2)) -> (((op (e2) (e0)) = (e1))\/(((op (e2) (e1)) = (e1))\/(((op (e2) (e2)) = (e1))\/((op (e2) (e3)) = (e1))))) -> (~((e1) = (e3))) -> ((op (e0) (e3)) = (e1)) -> ((op (e3) (e2)) = (e3)) -> (~((op (e0) (e2)) = (op (e3) (e2)))) -> (((op (e2) (e0)) = (e3))\/(((op (e2) (e1)) = (e3))\/(((op (e2) (e2)) = (e3))\/((op (e2) (e3)) = (e3))))) -> (~((op (e0) (e1)) = (op (e2) (e1)))) -> (~((op (e2) (op (e3) (e2))) = (op (e3) (e2)))) -> (~((op (e0) (e0)) = (e3))) -> (((op (e0) (e0)) = (e3))\/(((op (e0) (e1)) = (e3))\/(((op (e0) (e2)) = (e3))\/((op (e0) (e3)) = (e3))))) -> (((op (e2) (e2)) = (e0))\/(((op (e2) (e2)) = (e1))\/(((op (e2) (e2)) = (e2))\/((op (e2) (e2)) = (e3))))) -> (~((op (e3) (e3)) = (e3))) -> (~((op (e3) (e3)) = (e1))) -> (~((op (e3) (e3)) = (e0))) -> (((op (e3) (e3)) = (e0))\/(((op (e3) (e3)) = (e1))\/(((op (e3) (e3)) = (e2))\/((op (e3) (e3)) = (e3))))) -> (~((op (e2) (e2)) = (e1))) -> (~((op (e2) (e2)) = (e2))) -> (~((op (e2) (e2)) = (e3))) -> False). % 15.48/15.65 do 0 intro. intros zenon_Hf1 zenon_H45 zenon_Hb4 zenon_H11b zenon_Hc9 zenon_H166 zenon_Ha7 zenon_Hdd zenon_Hb7 zenon_Ha3 zenon_H37 zenon_H106 zenon_H140 zenon_He6 zenon_Hde zenon_H2af zenon_H59 zenon_H58 zenon_H2d zenon_H3e zenon_H104 zenon_H3c zenon_H3b zenon_H52 zenon_H2f zenon_H30. % 15.48/15.65 apply (zenon_or_s _ _ zenon_Hf1); [ zenon_intro zenon_H47 | zenon_intro zenon_Hf4 ]. % 15.48/15.65 exact (zenon_H45 zenon_H47). % 15.48/15.65 apply (zenon_or_s _ _ zenon_Hf4); [ zenon_intro zenon_Hd8 | zenon_intro zenon_Hf5 ]. % 15.48/15.65 apply (zenon_L1109_); trivial. % 15.48/15.65 apply (zenon_or_s _ _ zenon_Hf5); [ zenon_intro zenon_Hae | zenon_intro zenon_Hee ]. % 15.48/15.65 apply (zenon_L1110_); trivial. % 15.48/15.65 apply (zenon_L306_); trivial. % 15.48/15.65 (* end of lemma zenon_L1111_ *) % 15.48/15.65 assert (zenon_L1112_ : (((op (e0) (e0)) = (e3))\/(((op (e0) (e1)) = (e3))\/(((op (e0) (e2)) = (e3))\/((op (e0) (e3)) = (e3))))) -> (~((op (e0) (e0)) = (e3))) -> (~((op (e0) (e1)) = (op (e3) (e1)))) -> (~((e1) = (e3))) -> ((op (e0) (e2)) = (e1)) -> (((op (e1) (e0)) = (e0))\/(((op (e1) (e1)) = (e0))\/(((op (e1) (e2)) = (e0))\/((op (e1) (e3)) = (e0))))) -> (~((op (e0) (e0)) = (op (e1) (e0)))) -> (~((op (e1) (e1)) = (e0))) -> (~((op (e3) (e3)) = (e0))) -> (~((op (e1) (e2)) = (op (e3) (e2)))) -> (~((e0) = (e3))) -> ((op (e3) (e1)) = (e3)) -> (~((op (e0) (op (e3) (e0))) = (op (e3) (e0)))) -> ((op (e0) (e0)) = (e0)) -> (((op (e3) (e0)) = (e0))\/(((op (e3) (e1)) = (e0))\/(((op (e3) (e2)) = (e0))\/((op (e3) (e3)) = (e0))))) -> (((op (e0) (e3)) = (e2))\/(((op (e1) (e3)) = (e2))\/(((op (e2) (e3)) = (e2))\/((op (e3) (e3)) = (e2))))) -> (~((e2) = (e3))) -> (~((e0) = (e2))) -> ((op (e2) (e0)) = (e2)) -> (~((op (e2) (e0)) = (op (e2) (e3)))) -> (~((op (e3) (e3)) = (e2))) -> False). % 15.48/15.65 do 0 intro. intros zenon_H58 zenon_H59 zenon_H138 zenon_Ha3 zenon_H29 zenon_H163 zenon_H24c zenon_H145 zenon_H3c zenon_H17d zenon_H4b zenon_H10a zenon_H2b8 zenon_H1f zenon_H1f6 zenon_H160 zenon_H6a zenon_H5e zenon_Hdd zenon_Hce zenon_H3d. % 15.48/15.65 apply (zenon_or_s _ _ zenon_H58); [ zenon_intro zenon_H5b | zenon_intro zenon_H5a ]. % 15.48/15.65 exact (zenon_H59 zenon_H5b). % 15.48/15.65 apply (zenon_or_s _ _ zenon_H5a); [ zenon_intro zenon_H4a | zenon_intro zenon_H5c ]. % 15.48/15.65 apply (zenon_L120_); trivial. % 15.48/15.65 apply (zenon_or_s _ _ zenon_H5c); [ zenon_intro zenon_H50 | zenon_intro zenon_H53 ]. % 15.48/15.65 apply (zenon_L29_); trivial. % 15.48/15.65 apply (zenon_or_s _ _ zenon_H163); [ zenon_intro zenon_Had | zenon_intro zenon_H164 ]. % 15.48/15.65 apply (zenon_L559_); trivial. % 15.48/15.65 apply (zenon_or_s _ _ zenon_H164); [ zenon_intro zenon_H149 | zenon_intro zenon_H165 ]. % 15.48/15.65 exact (zenon_H145 zenon_H149). % 15.48/15.65 apply (zenon_or_s _ _ zenon_H165); [ zenon_intro zenon_H15d | zenon_intro zenon_Hcc ]. % 15.48/15.65 apply (zenon_L1057_); trivial. % 15.48/15.65 apply (zenon_L459_); trivial. % 15.48/15.65 (* end of lemma zenon_L1112_ *) % 15.48/15.65 assert (zenon_L1113_ : (((op (e0) (e0)) = (e1))\/(((op (e1) (e0)) = (e1))\/(((op (e2) (e0)) = (e1))\/((op (e3) (e0)) = (e1))))) -> (~((op (e0) (e0)) = (e1))) -> ((~((op (e1) (e1)) = (e2)))\/((op (e1) (e2)) = (e1))) -> ((~((op (e2) (e2)) = (e0)))\/((op (e2) (e0)) = (e2))) -> (~((op (e0) (e0)) = (op (e0) (e2)))) -> (((op (e3) (e0)) = (e0))\/(((op (e3) (e1)) = (e0))\/(((op (e3) (e2)) = (e0))\/((op (e3) (e3)) = (e0))))) -> (~((op (e1) (e2)) = (op (e3) (e2)))) -> (~((op (e1) (e0)) = (op (e3) (e0)))) -> (((op (e3) (e0)) = (e1))\/(((op (e3) (e1)) = (e1))\/(((op (e3) (e2)) = (e1))\/((op (e3) (e3)) = (e1))))) -> (~((e0) = (e3))) -> (((op (e0) (e2)) = (e0))\/(((op (e1) (e2)) = (e0))\/(((op (e2) (e2)) = (e0))\/((op (e3) (e2)) = (e0))))) -> (((op (e0) (e0)) = (e2))\/(((op (e1) (e0)) = (e2))\/(((op (e2) (e0)) = (e2))\/((op (e3) (e0)) = (e2))))) -> (((op (e1) (e1)) = (e0))\/(((op (e1) (e1)) = (e1))\/(((op (e1) (e1)) = (e2))\/((op (e1) (e1)) = (e3))))) -> ((~((op (e2) (e2)) = (e3)))\/((op (e2) (e3)) = (e2))) -> (~((op (e2) (e0)) = (op (e2) (e3)))) -> ((~((op (e3) (e3)) = (e1)))\/((op (e3) (e1)) = (e3))) -> (~((op (e0) (e1)) = (op (e3) (e1)))) -> (~((op (e3) (e1)) = (op (e3) (e2)))) -> ((~((op (e3) (e3)) = (e3)))\/((op (e3) (e3)) = (e3))) -> (~((op (e3) (op (e3) (e3))) = (op (e3) (e3)))) -> (((op (e0) (e0)) = (e3))\/(((op (e0) (e1)) = (e3))\/(((op (e0) (e2)) = (e3))\/((op (e0) (e3)) = (e3))))) -> (~((op (e0) (op (e3) (e0))) = (op (e3) (e0)))) -> (((op (e0) (e0)) = (e3))\/(((op (e1) (e0)) = (e3))\/(((op (e2) (e0)) = (e3))\/((op (e3) (e0)) = (e3))))) -> (((op (e1) (e0)) = (e3))\/(((op (e1) (e1)) = (e3))\/(((op (e1) (e2)) = (e3))\/((op (e1) (e3)) = (e3))))) -> (~((op (e1) (e0)) = (op (e2) (e0)))) -> (~((op (e2) (e0)) = (op (e2) (e1)))) -> (~((op (e1) (op (e3) (e1))) = (op (e3) (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)) = (e2))\/(((op (e1) (e1)) = (e2))\/(((op (e1) (e2)) = (e2))\/((op (e1) (e3)) = (e2))))) -> (((op (e2) (e0)) = (e3))\/(((op (e2) (e1)) = (e3))\/(((op (e2) (e2)) = (e3))\/((op (e2) (e3)) = (e3))))) -> (((op (e0) (e2)) = (e1))\/(((op (e1) (e2)) = (e1))\/(((op (e2) (e2)) = (e1))\/((op (e3) (e2)) = (e1))))) -> (~((op (e2) (op (e3) (e2))) = (op (e3) (e2)))) -> (~((op (e1) (e0)) = (op (e1) (e2)))) -> (~((op (e0) (e2)) = (op (e0) (e3)))) -> (~((op (e1) (e0)) = (op (e1) (e3)))) -> (((op (e0) (e3)) = (e2))\/(((op (e1) (e3)) = (e2))\/(((op (e2) (e3)) = (e2))\/((op (e3) (e3)) = (e2))))) -> (~((op (e0) (e0)) = (op (e0) (e3)))) -> ((op (e0) (e0)) = (e0)) -> (~((op (e0) (e3)) = (op (e2) (e3)))) -> (~((op (e0) (e3)) = (op (e1) (e3)))) -> (((op (e0) (e3)) = (e0))\/(((op (e0) (e3)) = (e1))\/(((op (e0) (e3)) = (e2))\/((op (e0) (e3)) = (e3))))) -> (~((op (e0) (e1)) = (op (e0) (e3)))) -> (((op (e0) (e3)) = (e1))\/(((op (e1) (e3)) = (e1))\/(((op (e2) (e3)) = (e1))\/((op (e3) (e3)) = (e1))))) -> (~((op (e0) (e1)) = (op (e2) (e1)))) -> (~((e2) = (e3))) -> (((op (e2) (e0)) = (e1))\/(((op (e2) (e1)) = (e1))\/(((op (e2) (e2)) = (e1))\/((op (e2) (e3)) = (e1))))) -> (~((op (e0) (e0)) = (e3))) -> (~((op (e2) (e0)) = (op (e3) (e0)))) -> (((op (e3) (e3)) = (e0))\/(((op (e3) (e3)) = (e1))\/(((op (e3) (e3)) = (e2))\/((op (e3) (e3)) = (e3))))) -> (~((op (e0) (e3)) = (op (e3) (e3)))) -> (((op (e0) (e0)) = (e2))\/(((op (e0) (e1)) = (e2))\/(((op (e0) (e2)) = (e2))\/((op (e0) (e3)) = (e2))))) -> (~((op (e3) (e0)) = (op (e3) (e2)))) -> ((~((op (e3) (e3)) = (e2)))\/((op (e3) (e2)) = (e3))) -> (~((op (e3) (e0)) = (op (e3) (e1)))) -> ((~((op (e3) (e3)) = (e0)))\/((op (e3) (e0)) = (e3))) -> ((~((op (e2) (e2)) = (e1)))\/((op (e2) (e1)) = (e2))) -> (~((op (e0) (e0)) = (e2))) -> ((~((op (e1) (e1)) = (e3)))\/((op (e1) (e3)) = (e1))) -> (~((op (e1) (e0)) = (op (e1) (e1)))) -> ((~((op (e1) (e1)) = (e1)))\/((op (e1) (e1)) = (e1))) -> ((op (e2) (e0)) = (e2)) -> (~((e1) = (e2))) -> (~((e1) = (e3))) -> ((op (e3) (e0)) = (e3)) -> False). % 15.48/15.65 do 0 intro. intros zenon_Hf1 zenon_H45 zenon_H1d3 zenon_H1d4 zenon_H250 zenon_H1f6 zenon_H17d zenon_H22e zenon_H146 zenon_H4b zenon_H16f zenon_Heb zenon_H1b3 zenon_H1c3 zenon_Hce zenon_H10c zenon_H138 zenon_H135 zenon_H10d zenon_H2be zenon_H58 zenon_H2b8 zenon_Hbe zenon_H90 zenon_H247 zenon_H154 zenon_H2b4 zenon_H1a2 zenon_H87 zenon_H84 zenon_He6 zenon_H11b zenon_H2af zenon_H166 zenon_Hc9 zenon_H1cf zenon_H160 zenon_H24f zenon_H1f zenon_Hb4 zenon_H80 zenon_H254 zenon_H1cd zenon_H121 zenon_Hde zenon_H6a zenon_Hb7 zenon_H59 zenon_H1e5 zenon_H3b zenon_H36 zenon_H8e zenon_H105 zenon_H10e zenon_H109 zenon_H10f zenon_H1e3 zenon_H8f zenon_H1d2 zenon_Hd7 zenon_H1d8 zenon_Hdd zenon_Ha7 zenon_Ha3 zenon_Hba. % 15.48/15.65 apply (zenon_or_s _ _ zenon_Hf1); [ zenon_intro zenon_H47 | zenon_intro zenon_Hf4 ]. % 15.48/15.65 exact (zenon_H45 zenon_H47). % 15.48/15.65 apply (zenon_or_s _ _ zenon_Hf4); [ zenon_intro zenon_Hd8 | zenon_intro zenon_Hf5 ]. % 15.48/15.65 apply (zenon_L1063_); trivial. % 15.48/15.65 apply (zenon_or_s _ _ zenon_Hf5); [ zenon_intro zenon_Hae | zenon_intro zenon_Hee ]. % 15.48/15.65 apply (zenon_L304_); trivial. % 15.48/15.65 apply (zenon_L79_); trivial. % 15.48/15.65 (* end of lemma zenon_L1113_ *) % 15.48/15.65 assert (zenon_L1114_ : (((op (e1) (e0)) = (e0))\/(((op (e1) (e1)) = (e0))\/(((op (e1) (e2)) = (e0))\/((op (e1) (e3)) = (e0))))) -> (~((op (e0) (e0)) = (op (e1) (e0)))) -> ((~((op (e2) (e2)) = (e2)))\/((op (e2) (e2)) = (e2))) -> (~((op (e2) (e2)) = (op (e2) (e3)))) -> (~((op (e2) (e1)) = (op (e3) (e1)))) -> (((op (e3) (e0)) = (e2))\/(((op (e3) (e1)) = (e2))\/(((op (e3) (e2)) = (e2))\/((op (e3) (e3)) = (e2))))) -> (~((op (e0) (e2)) = (op (e2) (e2)))) -> (~((op (e2) (e0)) = (op (e2) (e2)))) -> (~((op (e1) (e2)) = (op (e2) (e2)))) -> (((op (e1) (e2)) = (e0))\/(((op (e1) (e2)) = (e1))\/(((op (e1) (e2)) = (e2))\/((op (e1) (e2)) = (e3))))) -> (((op (e2) (e0)) = (e0))\/(((op (e2) (e0)) = (e1))\/(((op (e2) (e0)) = (e2))\/((op (e2) (e0)) = (e3))))) -> (~((op (e0) (e0)) = (op (e2) (e0)))) -> (((op (e0) (e2)) = (e0))\/(((op (e0) (e2)) = (e1))\/(((op (e0) (e2)) = (e2))\/((op (e0) (e2)) = (e3))))) -> (~((op (e0) (e2)) = (op (e3) (e2)))) -> ((~((op (e1) (e1)) = (e1)))\/((op (e1) (e1)) = (e1))) -> (~((op (e1) (e0)) = (op (e1) (e1)))) -> ((~((op (e1) (e1)) = (e3)))\/((op (e1) (e3)) = (e1))) -> ((~((op (e2) (e2)) = (e1)))\/((op (e2) (e1)) = (e2))) -> ((~((op (e3) (e3)) = (e0)))\/((op (e3) (e0)) = (e3))) -> (~((op (e3) (e0)) = (op (e3) (e1)))) -> (~((op (e3) (e0)) = (op (e3) (e2)))) -> (~((op (e2) (e0)) = (op (e3) (e0)))) -> (~((op (e0) (e0)) = (e3))) -> (((op (e2) (e0)) = (e1))\/(((op (e2) (e1)) = (e1))\/(((op (e2) (e2)) = (e1))\/((op (e2) (e3)) = (e1))))) -> (~((e2) = (e3))) -> (~((op (e0) (e1)) = (op (e2) (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) (e3)) = (op (e1) (e3)))) -> (~((op (e0) (e3)) = (op (e2) (e3)))) -> (~((op (e0) (e0)) = (op (e0) (e3)))) -> (((op (e0) (e3)) = (e2))\/(((op (e1) (e3)) = (e2))\/(((op (e2) (e3)) = (e2))\/((op (e3) (e3)) = (e2))))) -> (~((op (e1) (e0)) = (op (e1) (e3)))) -> (~((op (e0) (e2)) = (op (e0) (e3)))) -> (~((op (e2) (op (e3) (e2))) = (op (e3) (e2)))) -> (((op (e0) (e2)) = (e1))\/(((op (e1) (e2)) = (e1))\/(((op (e2) (e2)) = (e1))\/((op (e3) (e2)) = (e1))))) -> (((op (e2) (e0)) = (e3))\/(((op (e2) (e1)) = (e3))\/(((op (e2) (e2)) = (e3))\/((op (e2) (e3)) = (e3))))) -> (((op (e1) (e0)) = (e2))\/(((op (e1) (e1)) = (e2))\/(((op (e1) (e2)) = (e2))\/((op (e1) (e3)) = (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))))) -> (~((op (e1) (op (e3) (e1))) = (op (e3) (e1)))) -> (~((op (e2) (e0)) = (op (e2) (e1)))) -> (~((op (e1) (e0)) = (op (e2) (e0)))) -> (((op (e1) (e0)) = (e3))\/(((op (e1) (e1)) = (e3))\/(((op (e1) (e2)) = (e3))\/((op (e1) (e3)) = (e3))))) -> (((op (e0) (e0)) = (e3))\/(((op (e1) (e0)) = (e3))\/(((op (e2) (e0)) = (e3))\/((op (e3) (e0)) = (e3))))) -> (((op (e0) (e0)) = (e3))\/(((op (e0) (e1)) = (e3))\/(((op (e0) (e2)) = (e3))\/((op (e0) (e3)) = (e3))))) -> (~((op (e0) (e1)) = (op (e3) (e1)))) -> ((~((op (e2) (e2)) = (e3)))\/((op (e2) (e3)) = (e2))) -> (((op (e0) (e0)) = (e2))\/(((op (e1) (e0)) = (e2))\/(((op (e2) (e0)) = (e2))\/((op (e3) (e0)) = (e2))))) -> (((op (e3) (e0)) = (e1))\/(((op (e3) (e1)) = (e1))\/(((op (e3) (e2)) = (e1))\/((op (e3) (e3)) = (e1))))) -> (~((op (e1) (e0)) = (op (e3) (e0)))) -> ((~((op (e2) (e2)) = (e0)))\/((op (e2) (e0)) = (e2))) -> ((~((op (e1) (e1)) = (e2)))\/((op (e1) (e2)) = (e1))) -> (((op (e0) (e2)) = (e3))\/(((op (e1) (e2)) = (e3))\/(((op (e2) (e2)) = (e3))\/((op (e3) (e2)) = (e3))))) -> ((~((op (e3) (e3)) = (e2)))\/((op (e3) (e2)) = (e3))) -> (~((op (e0) (e0)) = (op (e0) (e2)))) -> ((op (e0) (e0)) = (e0)) -> (~((e0) = (e1))) -> (~((e0) = (e3))) -> (((op (e0) (e2)) = (e0))\/(((op (e1) (e2)) = (e0))\/(((op (e2) (e2)) = (e0))\/((op (e3) (e2)) = (e0))))) -> (((op (e0) (e0)) = (e1))\/(((op (e0) (e1)) = (e1))\/(((op (e0) (e2)) = (e1))\/((op (e0) (e3)) = (e1))))) -> (~((op (e0) (e0)) = (e2))) -> (((op (e1) (e1)) = (e0))\/(((op (e1) (e1)) = (e1))\/(((op (e1) (e1)) = (e2))\/((op (e1) (e1)) = (e3))))) -> (~((op (e1) (e1)) = (e3))) -> (~((op (e0) (e1)) = (op (e1) (e1)))) -> (~((op (e1) (e1)) = (e1))) -> (~((op (e1) (e1)) = (e0))) -> (~((e1) = (e2))) -> (((op (e0) (e0)) = (e2))\/(((op (e0) (e1)) = (e2))\/(((op (e0) (e2)) = (e2))\/((op (e0) (e3)) = (e2))))) -> (~((op (e1) (e0)) = (op (e1) (e2)))) -> ((op (e1) (e2)) = (e1)) -> (((op (e0) (e3)) = (e1))\/(((op (e1) (e3)) = (e1))\/(((op (e2) (e3)) = (e1))\/((op (e3) (e3)) = (e1))))) -> (~((op (e2) (e0)) = (op (e2) (e3)))) -> (~((op (e1) (e2)) = (op (e1) (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) (op (e3) (e0))) = (op (e3) (e0)))) -> (((op (e0) (e0)) = (e1))\/(((op (e1) (e0)) = (e1))\/(((op (e2) (e0)) = (e1))\/((op (e3) (e0)) = (e1))))) -> (~((op (e0) (e0)) = (e1))) -> (~((op (e3) (op (e3) (e3))) = (op (e3) (e3)))) -> ((~((op (e3) (e3)) = (e3)))\/((op (e3) (e3)) = (e3))) -> (~((op (e3) (e1)) = (op (e3) (e2)))) -> (~((op (e1) (e2)) = (op (e3) (e2)))) -> (((op (e3) (e0)) = (e0))\/(((op (e3) (e1)) = (e0))\/(((op (e3) (e2)) = (e0))\/((op (e3) (e3)) = (e0))))) -> ((~((op (e3) (e3)) = (e1)))\/((op (e3) (e1)) = (e3))) -> (~((op (e1) (e3)) = (op (e3) (e3)))) -> (~((e0) = (e2))) -> (((op (e2) (e2)) = (e0))\/(((op (e2) (e2)) = (e1))\/(((op (e2) (e2)) = (e2))\/((op (e2) (e2)) = (e3))))) -> (((op (e0) (e3)) = (e0))\/(((op (e1) (e3)) = (e0))\/(((op (e2) (e3)) = (e0))\/((op (e3) (e3)) = (e0))))) -> (~((op (e2) (e1)) = (op (e2) (e2)))) -> (~((op (e2) (e1)) = (op (e2) (e3)))) -> False). % 15.48/15.65 do 0 intro. intros zenon_H163 zenon_H24c zenon_Haa zenon_H15f zenon_H13c zenon_H1df zenon_H28 zenon_H17a zenon_H7d zenon_H1d5 zenon_H281 zenon_H258 zenon_H251 zenon_H140 zenon_H1d8 zenon_Hd7 zenon_H1d2 zenon_H1e3 zenon_H10f zenon_H109 zenon_H105 zenon_H1e5 zenon_H59 zenon_Hb7 zenon_H6a zenon_Hde zenon_H1cd zenon_H254 zenon_H80 zenon_Hb4 zenon_H24f zenon_H160 zenon_H1cf zenon_Hc9 zenon_H2af zenon_H11b zenon_He6 zenon_H84 zenon_Ha3 zenon_H87 zenon_H1a2 zenon_H2b4 zenon_H154 zenon_H247 zenon_H90 zenon_Hbe zenon_H58 zenon_H138 zenon_H1c3 zenon_Heb zenon_H146 zenon_H22e zenon_H1d4 zenon_H1d3 zenon_H175 zenon_H10e zenon_H250 zenon_H1f zenon_H9e zenon_H4b zenon_H16f zenon_H44 zenon_H8f zenon_H1b3 zenon_H182 zenon_H23 zenon_H1b4 zenon_H145 zenon_Ha7 zenon_H8e zenon_H166 zenon_H117 zenon_H121 zenon_Hce zenon_H1d0 zenon_H36 zenon_H3b zenon_H2b8 zenon_Hf1 zenon_H45 zenon_H2be zenon_H10d zenon_H135 zenon_H17d zenon_H1f6 zenon_H10c zenon_H8b zenon_H5e zenon_H2d zenon_Hd3 zenon_H157 zenon_H1e2. % 15.48/15.65 apply (zenon_or_s _ _ zenon_H1d4); [ zenon_intro zenon_H2e | zenon_intro zenon_Hdd ]. % 15.48/15.65 apply (zenon_or_s _ _ zenon_H1e3); [ zenon_intro zenon_H52 | zenon_intro zenon_H156 ]. % 15.48/15.65 apply (zenon_or_s _ _ zenon_Haa); [ zenon_intro zenon_H2f | zenon_intro zenon_H35 ]. % 15.48/15.65 apply (zenon_or_s _ _ zenon_H1c3); [ zenon_intro zenon_H30 | zenon_intro zenon_H124 ]. % 15.48/15.65 apply (zenon_or_s _ _ zenon_H10f); [ zenon_intro zenon_H3c | zenon_intro zenon_Hba ]. % 15.48/15.65 apply (zenon_L1060_); trivial. % 15.48/15.65 apply (zenon_L1071_); trivial. % 15.48/15.65 apply (zenon_or_s _ _ zenon_H10f); [ zenon_intro zenon_H3c | zenon_intro zenon_Hba ]. % 15.48/15.65 apply (zenon_L1060_); trivial. % 15.48/15.65 apply (zenon_L1072_); trivial. % 15.48/15.65 apply (zenon_L1101_); trivial. % 15.48/15.65 apply (zenon_or_s _ _ zenon_Haa); [ zenon_intro zenon_H2f | zenon_intro zenon_H35 ]. % 15.48/15.65 apply (zenon_or_s _ _ zenon_H1c3); [ zenon_intro zenon_H30 | zenon_intro zenon_H124 ]. % 15.48/15.65 apply (zenon_or_s _ _ zenon_H10f); [ zenon_intro zenon_H3c | zenon_intro zenon_Hba ]. % 15.48/15.65 apply (zenon_or_s _ _ zenon_H10c); [ zenon_intro zenon_H104 | zenon_intro zenon_H10a ]. % 15.48/15.65 apply (zenon_or_s _ _ zenon_H10e); [ zenon_intro zenon_H3d | zenon_intro zenon_H106 ]. % 15.48/15.65 apply (zenon_L1056_); trivial. % 15.48/15.65 apply (zenon_or_s _ _ zenon_H10d); [ zenon_intro zenon_H3e | zenon_intro zenon_H42 ]. % 15.48/15.65 apply (zenon_or_s _ _ zenon_Hf1); [ zenon_intro zenon_H47 | zenon_intro zenon_Hf4 ]. % 15.48/15.65 exact (zenon_H45 zenon_H47). % 15.48/15.65 apply (zenon_or_s _ _ zenon_Hf4); [ zenon_intro zenon_Hd8 | zenon_intro zenon_Hf5 ]. % 15.48/15.65 apply (zenon_L1050_); trivial. % 15.48/15.65 apply (zenon_or_s _ _ zenon_Hf5); [ zenon_intro zenon_Hae | zenon_intro zenon_Hee ]. % 15.48/15.65 apply (zenon_L1103_); trivial. % 15.48/15.65 apply (zenon_L1108_); trivial. % 15.48/15.65 apply (zenon_L1041_); trivial. % 15.48/15.65 apply (zenon_L1059_); trivial. % 15.48/15.65 apply (zenon_L1071_); trivial. % 15.48/15.65 apply (zenon_L256_); trivial. % 15.48/15.65 apply (zenon_L134_); trivial. % 15.48/15.65 apply (zenon_or_s _ _ zenon_H1e3); [ zenon_intro zenon_H52 | zenon_intro zenon_H156 ]. % 15.48/15.65 apply (zenon_or_s _ _ zenon_Haa); [ zenon_intro zenon_H2f | zenon_intro zenon_H35 ]. % 15.48/15.65 apply (zenon_or_s _ _ zenon_H1c3); [ zenon_intro zenon_H30 | zenon_intro zenon_H124 ]. % 15.48/15.65 apply (zenon_or_s _ _ zenon_H10f); [ zenon_intro zenon_H3c | zenon_intro zenon_Hba ]. % 15.48/15.65 apply (zenon_or_s _ _ zenon_H10c); [ zenon_intro zenon_H104 | zenon_intro zenon_H10a ]. % 15.48/15.65 apply (zenon_or_s _ _ zenon_H10e); [ zenon_intro zenon_H3d | zenon_intro zenon_H106 ]. % 15.48/15.65 apply (zenon_or_s _ _ zenon_H10d); [ zenon_intro zenon_H3e | zenon_intro zenon_H42 ]. % 15.48/15.65 apply (zenon_or_s _ _ zenon_H44); [ zenon_intro zenon_H47 | zenon_intro zenon_H46 ]. % 15.48/15.65 exact (zenon_H45 zenon_H47). % 15.48/15.65 apply (zenon_or_s _ _ zenon_H46); [ zenon_intro zenon_H22 | zenon_intro zenon_H48 ]. % 15.48/15.65 apply (zenon_L1055_); trivial. % 15.48/15.65 apply (zenon_or_s _ _ zenon_H48); [ zenon_intro zenon_H29 | zenon_intro zenon_H37 ]. % 15.48/15.65 apply (zenon_L740_); trivial. % 15.48/15.65 apply (zenon_L7_); trivial. % 15.48/15.65 apply (zenon_L1041_); trivial. % 15.48/15.65 apply (zenon_or_s _ _ zenon_H10d); [ zenon_intro zenon_H3e | zenon_intro zenon_H42 ]. % 15.48/15.65 apply (zenon_or_s _ _ zenon_H44); [ zenon_intro zenon_H47 | zenon_intro zenon_H46 ]. % 15.48/15.65 exact (zenon_H45 zenon_H47). % 15.48/15.65 apply (zenon_or_s _ _ zenon_H46); [ zenon_intro zenon_H22 | zenon_intro zenon_H48 ]. % 15.48/15.65 apply (zenon_L1069_); trivial. % 15.48/15.65 apply (zenon_or_s _ _ zenon_H48); [ zenon_intro zenon_H29 | zenon_intro zenon_H37 ]. % 15.48/15.65 apply (zenon_L740_); trivial. % 15.48/15.65 apply (zenon_L1111_); trivial. % 15.48/15.65 apply (zenon_L1041_); trivial. % 15.48/15.65 apply (zenon_or_s _ _ zenon_H10e); [ zenon_intro zenon_H3d | zenon_intro zenon_H106 ]. % 15.48/15.65 apply (zenon_or_s _ _ zenon_H10d); [ zenon_intro zenon_H3e | zenon_intro zenon_H42 ]. % 15.48/15.65 apply (zenon_or_s _ _ zenon_H44); [ zenon_intro zenon_H47 | zenon_intro zenon_H46 ]. % 15.48/15.65 exact (zenon_H45 zenon_H47). % 15.48/15.65 apply (zenon_or_s _ _ zenon_H46); [ zenon_intro zenon_H22 | zenon_intro zenon_H48 ]. % 15.48/15.65 apply (zenon_L1069_); trivial. % 15.48/15.65 apply (zenon_or_s _ _ zenon_H48); [ zenon_intro zenon_H29 | zenon_intro zenon_H37 ]. % 15.48/15.65 apply (zenon_L1112_); trivial. % 15.48/15.65 apply (zenon_L7_); trivial. % 15.48/15.65 apply (zenon_L1041_); trivial. % 15.48/15.65 apply (zenon_L115_); trivial. % 15.48/15.65 apply (zenon_L1113_); trivial. % 15.48/15.65 apply (zenon_L119_); trivial. % 15.48/15.65 apply (zenon_L1101_); trivial. % 15.48/15.65 apply (zenon_L284_); trivial. % 15.48/15.65 (* end of lemma zenon_L1114_ *) % 15.48/15.65 assert (zenon_L1115_ : (~((op (e2) (e1)) = (op (e2) (e3)))) -> (~((op (e2) (e1)) = (op (e2) (e2)))) -> (((op (e0) (e3)) = (e0))\/(((op (e1) (e3)) = (e0))\/(((op (e2) (e3)) = (e0))\/((op (e3) (e3)) = (e0))))) -> (((op (e2) (e2)) = (e0))\/(((op (e2) (e2)) = (e1))\/(((op (e2) (e2)) = (e2))\/((op (e2) (e2)) = (e3))))) -> (~((e0) = (e2))) -> (~((op (e1) (e3)) = (op (e3) (e3)))) -> ((~((op (e3) (e3)) = (e1)))\/((op (e3) (e1)) = (e3))) -> (((op (e3) (e0)) = (e0))\/(((op (e3) (e1)) = (e0))\/(((op (e3) (e2)) = (e0))\/((op (e3) (e3)) = (e0))))) -> (~((op (e1) (e2)) = (op (e3) (e2)))) -> (~((op (e3) (e1)) = (op (e3) (e2)))) -> ((~((op (e3) (e3)) = (e3)))\/((op (e3) (e3)) = (e3))) -> (~((op (e3) (op (e3) (e3))) = (op (e3) (e3)))) -> (~((op (e0) (e0)) = (e1))) -> (((op (e0) (e0)) = (e1))\/(((op (e1) (e0)) = (e1))\/(((op (e2) (e0)) = (e1))\/((op (e3) (e0)) = (e1))))) -> (~((op (e0) (op (e3) (e0))) = (op (e3) (e0)))) -> (((op (e3) (e3)) = (e0))\/(((op (e3) (e3)) = (e1))\/(((op (e3) (e3)) = (e2))\/((op (e3) (e3)) = (e3))))) -> (~((op (e0) (e3)) = (op (e3) (e3)))) -> (~((op (e1) (e2)) = (op (e1) (e3)))) -> (~((op (e2) (e0)) = (op (e2) (e3)))) -> (((op (e0) (e3)) = (e1))\/(((op (e1) (e3)) = (e1))\/(((op (e2) (e3)) = (e1))\/((op (e3) (e3)) = (e1))))) -> ((op (e1) (e2)) = (e1)) -> (~((op (e1) (e0)) = (op (e1) (e2)))) -> (((op (e0) (e0)) = (e2))\/(((op (e0) (e1)) = (e2))\/(((op (e0) (e2)) = (e2))\/((op (e0) (e3)) = (e2))))) -> (~((e1) = (e2))) -> (~((op (e1) (e1)) = (e0))) -> (~((op (e1) (e1)) = (e1))) -> (~((op (e0) (e1)) = (op (e1) (e1)))) -> (((op (e1) (e1)) = (e0))\/(((op (e1) (e1)) = (e1))\/(((op (e1) (e1)) = (e2))\/((op (e1) (e1)) = (e3))))) -> (~((op (e0) (e0)) = (e2))) -> (((op (e0) (e0)) = (e1))\/(((op (e0) (e1)) = (e1))\/(((op (e0) (e2)) = (e1))\/((op (e0) (e3)) = (e1))))) -> (((op (e0) (e2)) = (e0))\/(((op (e1) (e2)) = (e0))\/(((op (e2) (e2)) = (e0))\/((op (e3) (e2)) = (e0))))) -> (~((e0) = (e3))) -> (~((e0) = (e1))) -> ((op (e0) (e0)) = (e0)) -> (~((op (e0) (e0)) = (op (e0) (e2)))) -> ((~((op (e3) (e3)) = (e2)))\/((op (e3) (e2)) = (e3))) -> (((op (e0) (e2)) = (e3))\/(((op (e1) (e2)) = (e3))\/(((op (e2) (e2)) = (e3))\/((op (e3) (e2)) = (e3))))) -> ((~((op (e1) (e1)) = (e2)))\/((op (e1) (e2)) = (e1))) -> ((~((op (e2) (e2)) = (e0)))\/((op (e2) (e0)) = (e2))) -> (~((op (e1) (e0)) = (op (e3) (e0)))) -> (((op (e3) (e0)) = (e1))\/(((op (e3) (e1)) = (e1))\/(((op (e3) (e2)) = (e1))\/((op (e3) (e3)) = (e1))))) -> (((op (e0) (e0)) = (e2))\/(((op (e1) (e0)) = (e2))\/(((op (e2) (e0)) = (e2))\/((op (e3) (e0)) = (e2))))) -> ((~((op (e2) (e2)) = (e3)))\/((op (e2) (e3)) = (e2))) -> (~((op (e0) (e1)) = (op (e3) (e1)))) -> (((op (e0) (e0)) = (e3))\/(((op (e0) (e1)) = (e3))\/(((op (e0) (e2)) = (e3))\/((op (e0) (e3)) = (e3))))) -> (((op (e0) (e0)) = (e3))\/(((op (e1) (e0)) = (e3))\/(((op (e2) (e0)) = (e3))\/((op (e3) (e0)) = (e3))))) -> (((op (e1) (e0)) = (e3))\/(((op (e1) (e1)) = (e3))\/(((op (e1) (e2)) = (e3))\/((op (e1) (e3)) = (e3))))) -> (~((op (e1) (e0)) = (op (e2) (e0)))) -> (~((op (e2) (e0)) = (op (e2) (e1)))) -> (~((op (e1) (op (e3) (e1))) = (op (e3) (e1)))) -> (((op (e0) (e1)) = (e2))\/(((op (e1) (e1)) = (e2))\/(((op (e2) (e1)) = (e2))\/((op (e3) (e1)) = (e2))))) -> (~((op (e0) (e2)) = (op (e1) (e2)))) -> (~((e1) = (e3))) -> (((op (e1) (e0)) = (e2))\/(((op (e1) (e1)) = (e2))\/(((op (e1) (e2)) = (e2))\/((op (e1) (e3)) = (e2))))) -> (((op (e2) (e0)) = (e3))\/(((op (e2) (e1)) = (e3))\/(((op (e2) (e2)) = (e3))\/((op (e2) (e3)) = (e3))))) -> (((op (e0) (e2)) = (e1))\/(((op (e1) (e2)) = (e1))\/(((op (e2) (e2)) = (e1))\/((op (e3) (e2)) = (e1))))) -> (~((op (e2) (op (e3) (e2))) = (op (e3) (e2)))) -> (~((op (e0) (e2)) = (op (e0) (e3)))) -> (~((op (e1) (e0)) = (op (e1) (e3)))) -> (((op (e0) (e3)) = (e2))\/(((op (e1) (e3)) = (e2))\/(((op (e2) (e3)) = (e2))\/((op (e3) (e3)) = (e2))))) -> (~((op (e0) (e0)) = (op (e0) (e3)))) -> (~((op (e0) (e3)) = (op (e2) (e3)))) -> (~((op (e0) (e3)) = (op (e1) (e3)))) -> (((op (e0) (e3)) = (e0))\/(((op (e0) (e3)) = (e1))\/(((op (e0) (e3)) = (e2))\/((op (e0) (e3)) = (e3))))) -> (~((op (e0) (e1)) = (op (e0) (e3)))) -> (~((op (e0) (e1)) = (op (e2) (e1)))) -> (~((e2) = (e3))) -> (((op (e2) (e0)) = (e1))\/(((op (e2) (e1)) = (e1))\/(((op (e2) (e2)) = (e1))\/((op (e2) (e3)) = (e1))))) -> (~((op (e0) (e0)) = (e3))) -> (~((op (e2) (e0)) = (op (e3) (e0)))) -> (~((op (e3) (e0)) = (op (e3) (e2)))) -> (~((op (e3) (e0)) = (op (e3) (e1)))) -> ((~((op (e3) (e3)) = (e0)))\/((op (e3) (e0)) = (e3))) -> ((~((op (e2) (e2)) = (e1)))\/((op (e2) (e1)) = (e2))) -> ((~((op (e1) (e1)) = (e3)))\/((op (e1) (e3)) = (e1))) -> (~((op (e1) (e0)) = (op (e1) (e1)))) -> ((~((op (e1) (e1)) = (e1)))\/((op (e1) (e1)) = (e1))) -> (~((op (e0) (e2)) = (op (e3) (e2)))) -> (((op (e0) (e2)) = (e0))\/(((op (e0) (e2)) = (e1))\/(((op (e0) (e2)) = (e2))\/((op (e0) (e2)) = (e3))))) -> (~((op (e0) (e0)) = (op (e2) (e0)))) -> (((op (e2) (e0)) = (e0))\/(((op (e2) (e0)) = (e1))\/(((op (e2) (e0)) = (e2))\/((op (e2) (e0)) = (e3))))) -> (((op (e1) (e2)) = (e0))\/(((op (e1) (e2)) = (e1))\/(((op (e1) (e2)) = (e2))\/((op (e1) (e2)) = (e3))))) -> (~((op (e1) (e2)) = (op (e2) (e2)))) -> (~((op (e2) (e0)) = (op (e2) (e2)))) -> (~((op (e0) (e2)) = (op (e2) (e2)))) -> (((op (e3) (e0)) = (e2))\/(((op (e3) (e1)) = (e2))\/(((op (e3) (e2)) = (e2))\/((op (e3) (e3)) = (e2))))) -> (~((op (e2) (e1)) = (op (e3) (e1)))) -> (~((op (e2) (e2)) = (op (e2) (e3)))) -> ((~((op (e2) (e2)) = (e2)))\/((op (e2) (e2)) = (e2))) -> (~((op (e0) (e0)) = (op (e1) (e0)))) -> (((op (e1) (e0)) = (e0))\/(((op (e1) (e1)) = (e0))\/(((op (e1) (e2)) = (e0))\/((op (e1) (e3)) = (e0))))) -> False). % 15.48/15.66 do 0 intro. intros zenon_H1e2 zenon_H157 zenon_Hd3 zenon_H2d zenon_H5e zenon_H8b zenon_H10c zenon_H1f6 zenon_H17d zenon_H135 zenon_H10d zenon_H2be zenon_H45 zenon_Hf1 zenon_H2b8 zenon_H3b zenon_H36 zenon_H1d0 zenon_Hce zenon_H121 zenon_H117 zenon_H166 zenon_H8e zenon_Ha7 zenon_H145 zenon_H1b4 zenon_H23 zenon_H1b3 zenon_H8f zenon_H44 zenon_H16f zenon_H4b zenon_H9e zenon_H1f zenon_H250 zenon_H10e zenon_H175 zenon_H1d3 zenon_H1d4 zenon_H22e zenon_H146 zenon_Heb zenon_H1c3 zenon_H138 zenon_H58 zenon_Hbe zenon_H90 zenon_H247 zenon_H154 zenon_H2b4 zenon_H1a2 zenon_H87 zenon_Ha3 zenon_H84 zenon_He6 zenon_H11b zenon_H2af zenon_Hc9 zenon_H1cf zenon_H160 zenon_H24f zenon_Hb4 zenon_H80 zenon_H254 zenon_H1cd zenon_Hde zenon_H6a zenon_Hb7 zenon_H59 zenon_H1e5 zenon_H105 zenon_H109 zenon_H10f zenon_H1e3 zenon_H1d2 zenon_Hd7 zenon_H1d8 zenon_H140 zenon_H251 zenon_H258 zenon_H281 zenon_H1d5 zenon_H7d zenon_H17a zenon_H28 zenon_H1df zenon_H13c zenon_H15f zenon_Haa zenon_H24c zenon_H163. % 15.48/15.66 apply (zenon_or_s _ _ zenon_H1d2); [ zenon_intro zenon_H182 | zenon_intro zenon_H11f ]. % 15.48/15.66 apply (zenon_L1114_); trivial. % 15.48/15.66 apply (zenon_L237_); trivial. % 15.48/15.66 (* end of lemma zenon_L1115_ *) % 15.48/15.66 assert (zenon_L1116_ : ((~((op (e3) (e3)) = (e3)))\/((op (e3) (e3)) = (e3))) -> (~((op (e3) (op (e3) (e3))) = (op (e3) (e3)))) -> (~((op (e0) (e0)) = (op (e1) (e0)))) -> ((op (e0) (e0)) = (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)) = (e0))\/(((op (e3) (e3)) = (e1))\/(((op (e3) (e3)) = (e2))\/((op (e3) (e3)) = (e3))))) -> (~((op (e1) (e1)) = (e2))) -> (~((op (e1) (e1)) = (e1))) -> (~((op (e3) (e3)) = (e2))) -> (~((op (e1) (e3)) = (op (e3) (e3)))) -> (((op (e1) (e0)) = (e0))\/(((op (e1) (e1)) = (e0))\/(((op (e1) (e2)) = (e0))\/((op (e1) (e3)) = (e0))))) -> False). % 15.48/15.66 do 0 intro. intros zenon_H10d zenon_H2be zenon_H24c zenon_H1f zenon_H145 zenon_H1b3 zenon_H3c zenon_H104 zenon_H3b zenon_Hd6 zenon_H1b4 zenon_H3d zenon_H8b zenon_H163. % 15.48/15.66 apply (zenon_or_s _ _ zenon_H10d); [ zenon_intro zenon_H3e | zenon_intro zenon_H42 ]. % 15.48/15.66 apply (zenon_L560_); trivial. % 15.48/15.66 apply (zenon_L1041_); trivial. % 15.48/15.66 (* end of lemma zenon_L1116_ *) % 15.48/15.66 assert (zenon_L1117_ : (((op (e0) (e0)) = (e1))\/(((op (e1) (e0)) = (e1))\/(((op (e2) (e0)) = (e1))\/((op (e3) (e0)) = (e1))))) -> (~((op (e0) (e0)) = (e1))) -> ((op (e1) (e3)) = (e1)) -> (~((op (e1) (e0)) = (op (e1) (e3)))) -> ((op (e2) (e0)) = (e2)) -> (~((e1) = (e2))) -> (~((op (e0) (op (e3) (e0))) = (op (e3) (e0)))) -> ((op (e0) (e1)) = (e1)) -> False). % 15.48/15.66 do 0 intro. intros zenon_Hf1 zenon_H45 zenon_H11f zenon_H1cf zenon_Hdd zenon_Ha7 zenon_H2b8 zenon_H22. % 15.48/15.66 apply (zenon_or_s _ _ zenon_Hf1); [ zenon_intro zenon_H47 | zenon_intro zenon_Hf4 ]. % 15.48/15.66 exact (zenon_H45 zenon_H47). % 15.48/15.66 apply (zenon_or_s _ _ zenon_Hf4); [ zenon_intro zenon_Hd8 | zenon_intro zenon_Hf5 ]. % 15.48/15.66 apply (zenon_L224_); trivial. % 15.48/15.66 apply (zenon_or_s _ _ zenon_Hf5); [ zenon_intro zenon_Hae | zenon_intro zenon_Hee ]. % 15.48/15.66 apply (zenon_L304_); trivial. % 15.48/15.66 apply (zenon_L1054_); trivial. % 15.48/15.66 (* end of lemma zenon_L1117_ *) % 15.48/15.66 assert (zenon_L1118_ : (((op (e1) (e0)) = (e0))\/(((op (e1) (e1)) = (e0))\/(((op (e1) (e2)) = (e0))\/((op (e1) (e3)) = (e0))))) -> ((op (e0) (e0)) = (e0)) -> (~((op (e0) (e0)) = (op (e1) (e0)))) -> (~((op (e3) (e3)) = (e3))) -> (~((op (e3) (e3)) = (e1))) -> (~((op (e3) (e3)) = (e0))) -> (((op (e3) (e3)) = (e0))\/(((op (e3) (e3)) = (e1))\/(((op (e3) (e3)) = (e2))\/((op (e3) (e3)) = (e3))))) -> (~((op (e1) (e1)) = (e1))) -> (~((op (e1) (e1)) = (e0))) -> (((op (e1) (e1)) = (e0))\/(((op (e1) (e1)) = (e1))\/(((op (e1) (e1)) = (e2))\/((op (e1) (e1)) = (e3))))) -> (((op (e1) (e0)) = (e2))\/(((op (e1) (e1)) = (e2))\/(((op (e1) (e2)) = (e2))\/((op (e1) (e3)) = (e2))))) -> (~((e2) = (e3))) -> ((op (e1) (e0)) = (e3)) -> (~((op (e1) (e1)) = (e2))) -> (~((op (e1) (e2)) = (op (e2) (e2)))) -> ((op (e2) (e2)) = (e2)) -> (~((e0) = (e2))) -> False). % 15.48/15.66 do 0 intro. intros zenon_H163 zenon_H1f zenon_H24c zenon_H3e zenon_H104 zenon_H3c zenon_H3b zenon_H1b4 zenon_H145 zenon_H1b3 zenon_H84 zenon_H6a zenon_H69 zenon_Hd6 zenon_H7d zenon_H35 zenon_H5e. % 15.48/15.66 apply (zenon_or_s _ _ zenon_H163); [ zenon_intro zenon_Had | zenon_intro zenon_H164 ]. % 15.48/15.66 apply (zenon_L559_); trivial. % 15.48/15.66 apply (zenon_or_s _ _ zenon_H164); [ zenon_intro zenon_H149 | zenon_intro zenon_H165 ]. % 15.48/15.66 exact (zenon_H145 zenon_H149). % 15.48/15.66 apply (zenon_or_s _ _ zenon_H165); [ zenon_intro zenon_H15d | zenon_intro zenon_Hcc ]. % 15.48/15.66 apply (zenon_L490_); trivial. % 15.48/15.66 apply (zenon_L524_); trivial. % 15.48/15.66 (* end of lemma zenon_L1118_ *) % 15.48/15.66 assert (zenon_L1119_ : (((op (e3) (e0)) = (e0))\/(((op (e3) (e1)) = (e0))\/(((op (e3) (e2)) = (e0))\/((op (e3) (e3)) = (e0))))) -> ((op (e0) (e0)) = (e0)) -> (~((op (e0) (op (e3) (e0))) = (op (e3) (e0)))) -> ((op (e3) (e1)) = (e2)) -> (~((op (e1) (op (e3) (e1))) = (op (e3) (e1)))) -> ((op (e1) (e2)) = (e0)) -> (~((op (e1) (e2)) = (op (e3) (e2)))) -> ((op (e1) (e0)) = (e2)) -> ((op (e1) (e1)) = (e3)) -> False). % 15.48/15.66 do 0 intro. intros zenon_H1f6 zenon_H1f zenon_H2b8 zenon_H16a zenon_H2b4 zenon_H15d zenon_H17d zenon_H68 zenon_H96. % 15.48/15.66 apply (zenon_or_s _ _ zenon_H1f6); [ zenon_intro zenon_Hdb | zenon_intro zenon_H1f7 ]. % 15.48/15.66 apply (zenon_L1045_); trivial. % 15.48/15.66 apply (zenon_or_s _ _ zenon_H1f7); [ zenon_intro zenon_H142 | zenon_intro zenon_H1f8 ]. % 15.48/15.66 apply (zenon_L1104_); trivial. % 15.48/15.66 apply (zenon_or_s _ _ zenon_H1f8); [ zenon_intro zenon_H167 | zenon_intro zenon_H40 ]. % 15.48/15.66 apply (zenon_L626_); trivial. % 15.48/15.66 apply (zenon_L356_); trivial. % 15.48/15.66 (* end of lemma zenon_L1119_ *) % 15.48/15.66 assert (zenon_L1120_ : (((op (e3) (e2)) = (e0))\/(((op (e3) (e2)) = (e1))\/(((op (e3) (e2)) = (e2))\/((op (e3) (e2)) = (e3))))) -> ((op (e1) (e2)) = (e0)) -> ((op (e0) (e2)) = (e1)) -> (~((op (e0) (e2)) = (op (e3) (e2)))) -> ((op (e2) (e2)) = (e2)) -> (~((op (e2) (op (e3) (e2))) = (op (e3) (e2)))) -> ((op (e1) (e2)) = (e3)) -> (~((op (e1) (e2)) = (op (e3) (e2)))) -> False). % 15.48/15.66 do 0 intro. intros zenon_H25e zenon_H15d zenon_H29 zenon_H140 zenon_H35 zenon_H2af zenon_H88 zenon_H17d. % 15.48/15.66 apply (zenon_or_s _ _ zenon_H25e); [ zenon_intro zenon_H167 | zenon_intro zenon_H25f ]. % 15.48/15.66 apply (zenon_L626_); trivial. % 15.48/15.66 apply (zenon_or_s _ _ zenon_H25f); [ zenon_intro zenon_H119 | zenon_intro zenon_H260 ]. % 15.48/15.66 apply (zenon_L124_); trivial. % 15.48/15.66 apply (zenon_or_s _ _ zenon_H260); [ zenon_intro zenon_H1dd | zenon_intro zenon_H106 ]. % 15.48/15.66 apply (zenon_L1083_); trivial. % 15.48/15.66 apply (zenon_L164_); trivial. % 15.48/15.66 (* end of lemma zenon_L1120_ *) % 15.48/15.66 assert (zenon_L1121_ : (((op (e0) (e2)) = (e1))\/(((op (e1) (e2)) = (e1))\/(((op (e2) (e2)) = (e1))\/((op (e3) (e2)) = (e1))))) -> (~((op (e1) (e2)) = (op (e3) (e2)))) -> (~((op (e2) (op (e3) (e2))) = (op (e3) (e2)))) -> ((op (e1) (e2)) = (e0)) -> (((op (e3) (e2)) = (e0))\/(((op (e3) (e2)) = (e1))\/(((op (e3) (e2)) = (e2))\/((op (e3) (e2)) = (e3))))) -> (~((e1) = (e3))) -> (~((op (e2) (e2)) = (e1))) -> (((op (e0) (e2)) = (e0))\/(((op (e0) (e2)) = (e1))\/(((op (e0) (e2)) = (e2))\/((op (e0) (e2)) = (e3))))) -> ((op (e0) (e0)) = (e0)) -> (~((op (e0) (e0)) = (op (e0) (e2)))) -> (~((op (e0) (e2)) = (op (e3) (e2)))) -> (~((op (e0) (e2)) = (op (e2) (e2)))) -> ((op (e2) (e2)) = (e2)) -> (~((op (e0) (e2)) = (op (e1) (e2)))) -> ((op (e1) (e2)) = (e3)) -> False). % 15.48/15.66 do 0 intro. intros zenon_H11b zenon_H17d zenon_H2af zenon_H15d zenon_H25e zenon_Ha3 zenon_H52 zenon_H251 zenon_H1f zenon_H250 zenon_H140 zenon_H28 zenon_H35 zenon_H87 zenon_H88. % 15.48/15.66 apply (zenon_or_s _ _ zenon_H11b); [ zenon_intro zenon_H29 | zenon_intro zenon_H11c ]. % 15.48/15.66 apply (zenon_L1120_); trivial. % 15.48/15.66 apply (zenon_or_s _ _ zenon_H11c); [ zenon_intro zenon_H117 | zenon_intro zenon_H11d ]. % 15.48/15.66 apply (zenon_L196_); trivial. % 15.48/15.66 apply (zenon_or_s _ _ zenon_H11d); [ zenon_intro zenon_H2a | zenon_intro zenon_H119 ]. % 15.48/15.66 exact (zenon_H52 zenon_H2a). % 15.48/15.66 apply (zenon_L568_); trivial. % 15.48/15.66 (* end of lemma zenon_L1121_ *) % 15.48/15.66 assert (zenon_L1122_ : (((op (e0) (e1)) = (e2))\/(((op (e1) (e1)) = (e2))\/(((op (e2) (e1)) = (e2))\/((op (e3) (e1)) = (e2))))) -> (~((op (e3) (e3)) = (e2))) -> (~((op (e0) (e1)) = (op (e3) (e1)))) -> ((op (e3) (e0)) = (e3)) -> (((op (e3) (e0)) = (e2))\/(((op (e3) (e1)) = (e2))\/(((op (e3) (e2)) = (e2))\/((op (e3) (e3)) = (e2))))) -> (~((op (e1) (e1)) = (e2))) -> (~((op (e2) (e1)) = (op (e2) (e2)))) -> (((op (e1) (e0)) = (e3))\/(((op (e1) (e1)) = (e3))\/(((op (e1) (e2)) = (e3))\/((op (e1) (e3)) = (e3))))) -> (~((e2) = (e3))) -> ((op (e1) (e0)) = (e2)) -> (~((op (e1) (op (e3) (e1))) = (op (e3) (e1)))) -> (~((op (e0) (op (e3) (e0))) = (op (e3) (e0)))) -> (((op (e3) (e0)) = (e0))\/(((op (e3) (e1)) = (e0))\/(((op (e3) (e2)) = (e0))\/((op (e3) (e3)) = (e0))))) -> (~((op (e0) (e2)) = (op (e1) (e2)))) -> ((op (e2) (e2)) = (e2)) -> (~((op (e0) (e2)) = (op (e2) (e2)))) -> (~((op (e0) (e2)) = (op (e3) (e2)))) -> (~((op (e0) (e0)) = (op (e0) (e2)))) -> ((op (e0) (e0)) = (e0)) -> (((op (e0) (e2)) = (e0))\/(((op (e0) (e2)) = (e1))\/(((op (e0) (e2)) = (e2))\/((op (e0) (e2)) = (e3))))) -> (~((op (e2) (e2)) = (e1))) -> (((op (e3) (e2)) = (e0))\/(((op (e3) (e2)) = (e1))\/(((op (e3) (e2)) = (e2))\/((op (e3) (e2)) = (e3))))) -> ((op (e1) (e2)) = (e0)) -> (~((op (e2) (op (e3) (e2))) = (op (e3) (e2)))) -> (~((op (e1) (e2)) = (op (e3) (e2)))) -> (((op (e0) (e2)) = (e1))\/(((op (e1) (e2)) = (e1))\/(((op (e2) (e2)) = (e1))\/((op (e3) (e2)) = (e1))))) -> ((op (e1) (e3)) = (e1)) -> (~((e1) = (e3))) -> False). % 15.48/15.66 do 0 intro. intros zenon_H1a2 zenon_H3d zenon_H138 zenon_Hba zenon_H1df zenon_Hd6 zenon_H157 zenon_H90 zenon_H6a zenon_H68 zenon_H2b4 zenon_H2b8 zenon_H1f6 zenon_H87 zenon_H35 zenon_H28 zenon_H140 zenon_H250 zenon_H1f zenon_H251 zenon_H52 zenon_H25e zenon_H15d zenon_H2af zenon_H17d zenon_H11b zenon_H11f zenon_Ha3. % 15.48/15.66 apply (zenon_or_s _ _ zenon_H1a2); [ zenon_intro zenon_H5d | zenon_intro zenon_H1a3 ]. % 15.48/15.66 apply (zenon_L1091_); trivial. % 15.48/15.66 apply (zenon_or_s _ _ zenon_H1a3); [ zenon_intro zenon_H6e | zenon_intro zenon_H1a4 ]. % 15.48/15.66 exact (zenon_Hd6 zenon_H6e). % 15.48/15.66 apply (zenon_or_s _ _ zenon_H1a4); [ zenon_intro zenon_H156 | zenon_intro zenon_H16a ]. % 15.48/15.66 apply (zenon_L134_); trivial. % 15.48/15.66 apply (zenon_or_s _ _ zenon_H90); [ zenon_intro zenon_H69 | zenon_intro zenon_H94 ]. % 15.48/15.66 apply (zenon_L17_); trivial. % 15.48/15.66 apply (zenon_or_s _ _ zenon_H94); [ zenon_intro zenon_H96 | zenon_intro zenon_H95 ]. % 15.48/15.66 apply (zenon_L1119_); trivial. % 15.48/15.66 apply (zenon_or_s _ _ zenon_H95); [ zenon_intro zenon_H88 | zenon_intro zenon_H8a ]. % 15.48/15.66 apply (zenon_L1121_); trivial. % 15.48/15.66 apply (zenon_L772_); trivial. % 15.48/15.66 (* end of lemma zenon_L1122_ *) % 15.48/15.66 assert (zenon_L1123_ : ((~((op (e3) (e3)) = (e2)))\/((op (e3) (e2)) = (e3))) -> (~((op (e3) (e0)) = (op (e3) (e2)))) -> (~((op (e0) (e0)) = (e2))) -> (((op (e1) (e0)) = (e0))\/(((op (e1) (e1)) = (e0))\/(((op (e1) (e2)) = (e0))\/((op (e1) (e3)) = (e0))))) -> (~((e0) = (e1))) -> (((op (e3) (e0)) = (e2))\/(((op (e3) (e1)) = (e2))\/(((op (e3) (e2)) = (e2))\/((op (e3) (e3)) = (e2))))) -> ((op (e2) (e2)) = (e2)) -> (~((op (e2) (op (e3) (e2))) = (op (e3) (e2)))) -> (~((op (e0) (e1)) = (op (e3) (e1)))) -> ((op (e3) (e0)) = (e3)) -> (~((e2) = (e3))) -> (~((op (e1) (e1)) = (e2))) -> (~((op (e2) (e1)) = (op (e2) (e2)))) -> (((op (e1) (e0)) = (e3))\/(((op (e1) (e1)) = (e3))\/(((op (e1) (e2)) = (e3))\/((op (e1) (e3)) = (e3))))) -> ((op (e1) (e3)) = (e1)) -> (((op (e3) (e2)) = (e0))\/(((op (e3) (e2)) = (e1))\/(((op (e3) (e2)) = (e2))\/((op (e3) (e2)) = (e3))))) -> (~((op (e0) (e2)) = (op (e3) (e2)))) -> (~((e1) = (e3))) -> (~((op (e2) (e2)) = (e1))) -> (((op (e0) (e2)) = (e0))\/(((op (e0) (e2)) = (e1))\/(((op (e0) (e2)) = (e2))\/((op (e0) (e2)) = (e3))))) -> (~((op (e0) (e2)) = (op (e1) (e2)))) -> (~((op (e0) (e2)) = (op (e2) (e2)))) -> (~((op (e0) (e0)) = (op (e0) (e2)))) -> (((op (e0) (e2)) = (e1))\/(((op (e1) (e2)) = (e1))\/(((op (e2) (e2)) = (e1))\/((op (e3) (e2)) = (e1))))) -> (~((op (e0) (op (e3) (e0))) = (op (e3) (e0)))) -> (~((op (e1) (op (e3) (e1))) = (op (e3) (e1)))) -> (~((op (e1) (e2)) = (op (e3) (e2)))) -> (((op (e3) (e0)) = (e0))\/(((op (e3) (e1)) = (e0))\/(((op (e3) (e2)) = (e0))\/((op (e3) (e3)) = (e0))))) -> (((op (e0) (e1)) = (e2))\/(((op (e1) (e1)) = (e2))\/(((op (e2) (e1)) = (e2))\/((op (e3) (e1)) = (e2))))) -> (~((op (e1) (e1)) = (e0))) -> ((op (e0) (e0)) = (e0)) -> (~((op (e0) (e0)) = (op (e1) (e0)))) -> (~((op (e2) (e0)) = (op (e2) (e2)))) -> (((op (e0) (e0)) = (e2))\/(((op (e1) (e0)) = (e2))\/(((op (e2) (e0)) = (e2))\/((op (e3) (e0)) = (e2))))) -> False). % 15.48/15.66 do 0 intro. intros zenon_H10e zenon_H105 zenon_H8f zenon_H163 zenon_H9e zenon_H1df zenon_H35 zenon_H2af zenon_H138 zenon_Hba zenon_H6a zenon_Hd6 zenon_H157 zenon_H90 zenon_H11f zenon_H25e zenon_H140 zenon_Ha3 zenon_H52 zenon_H251 zenon_H87 zenon_H28 zenon_H250 zenon_H11b zenon_H2b8 zenon_H2b4 zenon_H17d zenon_H1f6 zenon_H1a2 zenon_H145 zenon_H1f zenon_H24c zenon_H17a zenon_Heb. % 15.48/15.66 apply (zenon_or_s _ _ zenon_H10e); [ zenon_intro zenon_H3d | zenon_intro zenon_H106 ]. % 15.48/15.66 apply (zenon_or_s _ _ zenon_Heb); [ zenon_intro zenon_H92 | zenon_intro zenon_Hec ]. % 15.48/15.66 exact (zenon_H8f zenon_H92). % 15.48/15.66 apply (zenon_or_s _ _ zenon_Hec); [ zenon_intro zenon_H68 | zenon_intro zenon_Hed ]. % 15.48/15.66 apply (zenon_or_s _ _ zenon_H163); [ zenon_intro zenon_Had | zenon_intro zenon_H164 ]. % 15.48/15.66 apply (zenon_L559_); trivial. % 15.48/15.66 apply (zenon_or_s _ _ zenon_H164); [ zenon_intro zenon_H149 | zenon_intro zenon_H165 ]. % 15.48/15.66 exact (zenon_H145 zenon_H149). % 15.48/15.66 apply (zenon_or_s _ _ zenon_H165); [ zenon_intro zenon_H15d | zenon_intro zenon_Hcc ]. % 15.48/15.66 apply (zenon_L1122_); trivial. % 15.48/15.66 apply (zenon_L208_); trivial. % 15.48/15.66 apply (zenon_or_s _ _ zenon_Hed); [ zenon_intro zenon_Hdd | zenon_intro zenon_He9 ]. % 15.48/15.66 apply (zenon_L161_); trivial. % 15.48/15.66 apply (zenon_L220_); trivial. % 15.48/15.66 apply (zenon_L81_); trivial. % 15.48/15.66 (* end of lemma zenon_L1123_ *) % 15.48/15.66 assert (zenon_L1124_ : (((op (e0) (e0)) = (e3))\/(((op (e1) (e0)) = (e3))\/(((op (e2) (e0)) = (e3))\/((op (e3) (e0)) = (e3))))) -> (~((op (e0) (e0)) = (e3))) -> (~((e0) = (e2))) -> (~((op (e1) (e2)) = (op (e2) (e2)))) -> (((op (e1) (e0)) = (e2))\/(((op (e1) (e1)) = (e2))\/(((op (e1) (e2)) = (e2))\/((op (e1) (e3)) = (e2))))) -> (((op (e1) (e1)) = (e0))\/(((op (e1) (e1)) = (e1))\/(((op (e1) (e1)) = (e2))\/((op (e1) (e1)) = (e3))))) -> (~((op (e1) (e1)) = (e1))) -> (((op (e3) (e3)) = (e0))\/(((op (e3) (e3)) = (e1))\/(((op (e3) (e3)) = (e2))\/((op (e3) (e3)) = (e3))))) -> (~((op (e3) (e3)) = (e0))) -> (~((op (e3) (e3)) = (e1))) -> (~((op (e3) (e3)) = (e3))) -> ((op (e2) (e0)) = (e1)) -> ((~((op (e3) (e3)) = (e2)))\/((op (e3) (e2)) = (e3))) -> (~((op (e3) (e0)) = (op (e3) (e2)))) -> (~((op (e0) (e0)) = (e2))) -> (((op (e1) (e0)) = (e0))\/(((op (e1) (e1)) = (e0))\/(((op (e1) (e2)) = (e0))\/((op (e1) (e3)) = (e0))))) -> (~((e0) = (e1))) -> (((op (e3) (e0)) = (e2))\/(((op (e3) (e1)) = (e2))\/(((op (e3) (e2)) = (e2))\/((op (e3) (e3)) = (e2))))) -> ((op (e2) (e2)) = (e2)) -> (~((op (e2) (op (e3) (e2))) = (op (e3) (e2)))) -> (~((op (e0) (e1)) = (op (e3) (e1)))) -> (~((e2) = (e3))) -> (~((op (e1) (e1)) = (e2))) -> (~((op (e2) (e1)) = (op (e2) (e2)))) -> (((op (e1) (e0)) = (e3))\/(((op (e1) (e1)) = (e3))\/(((op (e1) (e2)) = (e3))\/((op (e1) (e3)) = (e3))))) -> ((op (e1) (e3)) = (e1)) -> (((op (e3) (e2)) = (e0))\/(((op (e3) (e2)) = (e1))\/(((op (e3) (e2)) = (e2))\/((op (e3) (e2)) = (e3))))) -> (~((op (e0) (e2)) = (op (e3) (e2)))) -> (~((e1) = (e3))) -> (~((op (e2) (e2)) = (e1))) -> (((op (e0) (e2)) = (e0))\/(((op (e0) (e2)) = (e1))\/(((op (e0) (e2)) = (e2))\/((op (e0) (e2)) = (e3))))) -> (~((op (e0) (e2)) = (op (e1) (e2)))) -> (~((op (e0) (e2)) = (op (e2) (e2)))) -> (~((op (e0) (e0)) = (op (e0) (e2)))) -> (((op (e0) (e2)) = (e1))\/(((op (e1) (e2)) = (e1))\/(((op (e2) (e2)) = (e1))\/((op (e3) (e2)) = (e1))))) -> (~((op (e0) (op (e3) (e0))) = (op (e3) (e0)))) -> (~((op (e1) (op (e3) (e1))) = (op (e3) (e1)))) -> (~((op (e1) (e2)) = (op (e3) (e2)))) -> (((op (e3) (e0)) = (e0))\/(((op (e3) (e1)) = (e0))\/(((op (e3) (e2)) = (e0))\/((op (e3) (e3)) = (e0))))) -> (((op (e0) (e1)) = (e2))\/(((op (e1) (e1)) = (e2))\/(((op (e2) (e1)) = (e2))\/((op (e3) (e1)) = (e2))))) -> (~((op (e1) (e1)) = (e0))) -> ((op (e0) (e0)) = (e0)) -> (~((op (e0) (e0)) = (op (e1) (e0)))) -> (~((op (e2) (e0)) = (op (e2) (e2)))) -> (((op (e0) (e0)) = (e2))\/(((op (e1) (e0)) = (e2))\/(((op (e2) (e0)) = (e2))\/((op (e3) (e0)) = (e2))))) -> False). % 15.48/15.66 do 0 intro. intros zenon_Hbe zenon_H59 zenon_H5e zenon_H7d zenon_H84 zenon_H1b3 zenon_H1b4 zenon_H3b zenon_H3c zenon_H104 zenon_H3e zenon_Hae zenon_H10e zenon_H105 zenon_H8f zenon_H163 zenon_H9e zenon_H1df zenon_H35 zenon_H2af zenon_H138 zenon_H6a zenon_Hd6 zenon_H157 zenon_H90 zenon_H11f zenon_H25e zenon_H140 zenon_Ha3 zenon_H52 zenon_H251 zenon_H87 zenon_H28 zenon_H250 zenon_H11b zenon_H2b8 zenon_H2b4 zenon_H17d zenon_H1f6 zenon_H1a2 zenon_H145 zenon_H1f zenon_H24c zenon_H17a zenon_Heb. % 15.48/15.66 apply (zenon_or_s _ _ zenon_Hbe); [ zenon_intro zenon_H5b | zenon_intro zenon_Hbf ]. % 15.48/15.66 exact (zenon_H59 zenon_H5b). % 15.48/15.66 apply (zenon_or_s _ _ zenon_Hbf); [ zenon_intro zenon_H69 | zenon_intro zenon_Hc0 ]. % 15.48/15.66 apply (zenon_L1118_); trivial. % 15.48/15.66 apply (zenon_or_s _ _ zenon_Hc0); [ zenon_intro zenon_Haf | zenon_intro zenon_Hba ]. % 15.48/15.66 apply (zenon_L39_); trivial. % 15.48/15.66 apply (zenon_L1123_); trivial. % 15.48/15.66 (* end of lemma zenon_L1124_ *) % 15.48/15.66 assert (zenon_L1125_ : (((op (e0) (e0)) = (e1))\/(((op (e1) (e0)) = (e1))\/(((op (e2) (e0)) = (e1))\/((op (e3) (e0)) = (e1))))) -> (~((op (e0) (e0)) = (e1))) -> (~((op (e1) (e0)) = (op (e1) (e3)))) -> (((op (e0) (e0)) = (e2))\/(((op (e1) (e0)) = (e2))\/(((op (e2) (e0)) = (e2))\/((op (e3) (e0)) = (e2))))) -> (~((op (e2) (e0)) = (op (e2) (e2)))) -> (~((op (e0) (e0)) = (op (e1) (e0)))) -> ((op (e0) (e0)) = (e0)) -> (~((op (e1) (e1)) = (e0))) -> (((op (e0) (e1)) = (e2))\/(((op (e1) (e1)) = (e2))\/(((op (e2) (e1)) = (e2))\/((op (e3) (e1)) = (e2))))) -> (((op (e3) (e0)) = (e0))\/(((op (e3) (e1)) = (e0))\/(((op (e3) (e2)) = (e0))\/((op (e3) (e3)) = (e0))))) -> (~((op (e1) (e2)) = (op (e3) (e2)))) -> (~((op (e1) (op (e3) (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) (e2)) = (op (e2) (e2)))) -> (~((op (e0) (e2)) = (op (e1) (e2)))) -> (((op (e0) (e2)) = (e0))\/(((op (e0) (e2)) = (e1))\/(((op (e0) (e2)) = (e2))\/((op (e0) (e2)) = (e3))))) -> (~((op (e2) (e2)) = (e1))) -> (~((e1) = (e3))) -> (~((op (e0) (e2)) = (op (e3) (e2)))) -> (((op (e3) (e2)) = (e0))\/(((op (e3) (e2)) = (e1))\/(((op (e3) (e2)) = (e2))\/((op (e3) (e2)) = (e3))))) -> ((op (e1) (e3)) = (e1)) -> (((op (e1) (e0)) = (e3))\/(((op (e1) (e1)) = (e3))\/(((op (e1) (e2)) = (e3))\/((op (e1) (e3)) = (e3))))) -> (~((op (e2) (e1)) = (op (e2) (e2)))) -> (~((op (e1) (e1)) = (e2))) -> (~((e2) = (e3))) -> (~((op (e0) (e1)) = (op (e3) (e1)))) -> (~((op (e2) (op (e3) (e2))) = (op (e3) (e2)))) -> ((op (e2) (e2)) = (e2)) -> (((op (e3) (e0)) = (e2))\/(((op (e3) (e1)) = (e2))\/(((op (e3) (e2)) = (e2))\/((op (e3) (e3)) = (e2))))) -> (~((e0) = (e1))) -> (((op (e1) (e0)) = (e0))\/(((op (e1) (e1)) = (e0))\/(((op (e1) (e2)) = (e0))\/((op (e1) (e3)) = (e0))))) -> (~((op (e0) (e0)) = (e2))) -> (~((op (e3) (e0)) = (op (e3) (e2)))) -> ((~((op (e3) (e3)) = (e2)))\/((op (e3) (e2)) = (e3))) -> (~((op (e3) (e3)) = (e3))) -> (~((op (e3) (e3)) = (e1))) -> (~((op (e3) (e3)) = (e0))) -> (((op (e3) (e3)) = (e0))\/(((op (e3) (e3)) = (e1))\/(((op (e3) (e3)) = (e2))\/((op (e3) (e3)) = (e3))))) -> (~((op (e1) (e1)) = (e1))) -> (((op (e1) (e1)) = (e0))\/(((op (e1) (e1)) = (e1))\/(((op (e1) (e1)) = (e2))\/((op (e1) (e1)) = (e3))))) -> (((op (e1) (e0)) = (e2))\/(((op (e1) (e1)) = (e2))\/(((op (e1) (e2)) = (e2))\/((op (e1) (e3)) = (e2))))) -> (~((op (e1) (e2)) = (op (e2) (e2)))) -> (~((e0) = (e2))) -> (~((op (e0) (e0)) = (e3))) -> (((op (e0) (e0)) = (e3))\/(((op (e1) (e0)) = (e3))\/(((op (e2) (e0)) = (e3))\/((op (e3) (e0)) = (e3))))) -> (~((op (e0) (op (e3) (e0))) = (op (e3) (e0)))) -> ((op (e0) (e1)) = (e1)) -> False). % 15.48/15.66 do 0 intro. intros zenon_Hf1 zenon_H45 zenon_H1cf zenon_Heb zenon_H17a zenon_H24c zenon_H1f zenon_H145 zenon_H1a2 zenon_H1f6 zenon_H17d zenon_H2b4 zenon_H11b zenon_H250 zenon_H28 zenon_H87 zenon_H251 zenon_H52 zenon_Ha3 zenon_H140 zenon_H25e zenon_H11f zenon_H90 zenon_H157 zenon_Hd6 zenon_H6a zenon_H138 zenon_H2af zenon_H35 zenon_H1df zenon_H9e zenon_H163 zenon_H8f zenon_H105 zenon_H10e zenon_H3e zenon_H104 zenon_H3c zenon_H3b zenon_H1b4 zenon_H1b3 zenon_H84 zenon_H7d zenon_H5e zenon_H59 zenon_Hbe zenon_H2b8 zenon_H22. % 15.48/15.66 apply (zenon_or_s _ _ zenon_Hf1); [ zenon_intro zenon_H47 | zenon_intro zenon_Hf4 ]. % 15.48/15.66 exact (zenon_H45 zenon_H47). % 15.48/15.66 apply (zenon_or_s _ _ zenon_Hf4); [ zenon_intro zenon_Hd8 | zenon_intro zenon_Hf5 ]. % 15.48/15.66 apply (zenon_L224_); trivial. % 15.48/15.66 apply (zenon_or_s _ _ zenon_Hf5); [ zenon_intro zenon_Hae | zenon_intro zenon_Hee ]. % 15.48/15.66 apply (zenon_L1124_); trivial. % 15.48/15.66 apply (zenon_L1054_); trivial. % 15.48/15.66 (* end of lemma zenon_L1125_ *) % 15.48/15.66 assert (zenon_L1126_ : (((op (e3) (e0)) = (e2))\/(((op (e3) (e1)) = (e2))\/(((op (e3) (e2)) = (e2))\/((op (e3) (e3)) = (e2))))) -> ((op (e3) (e0)) = (e1)) -> ((op (e0) (e2)) = (e1)) -> (~((op (e0) (op (e3) (e0))) = (op (e3) (e0)))) -> ((op (e3) (e1)) = (e0)) -> ((op (e1) (e0)) = (e2)) -> (~((op (e1) (op (e3) (e1))) = (op (e3) (e1)))) -> ((op (e2) (e2)) = (e2)) -> (~((op (e2) (op (e3) (e2))) = (op (e3) (e2)))) -> ((op (e1) (e2)) = (e0)) -> ((op (e1) (e1)) = (e3)) -> False). % 15.48/15.66 do 0 intro. intros zenon_H1df zenon_Hee zenon_H29 zenon_H2b8 zenon_H142 zenon_H68 zenon_H2b4 zenon_H35 zenon_H2af zenon_H15d zenon_H96. % 15.48/15.66 apply (zenon_or_s _ _ zenon_H1df); [ zenon_intro zenon_He9 | zenon_intro zenon_H1e0 ]. % 15.48/15.66 apply (zenon_L1082_); trivial. % 15.48/15.66 apply (zenon_or_s _ _ zenon_H1e0); [ zenon_intro zenon_H16a | zenon_intro zenon_H1e1 ]. % 15.48/15.66 apply (zenon_L1104_); trivial. % 15.48/15.66 apply (zenon_or_s _ _ zenon_H1e1); [ zenon_intro zenon_H1dd | zenon_intro zenon_H43 ]. % 15.48/15.66 apply (zenon_L1083_); trivial. % 15.48/15.66 apply (zenon_L488_); trivial. % 15.48/15.66 (* end of lemma zenon_L1126_ *) % 15.48/15.66 assert (zenon_L1127_ : (((op (e3) (e0)) = (e0))\/(((op (e3) (e1)) = (e0))\/(((op (e3) (e2)) = (e0))\/((op (e3) (e3)) = (e0))))) -> ((op (e0) (e0)) = (e0)) -> ((op (e1) (e1)) = (e3)) -> (~((op (e2) (op (e3) (e2))) = (op (e3) (e2)))) -> ((op (e2) (e2)) = (e2)) -> (~((op (e1) (op (e3) (e1))) = (op (e3) (e1)))) -> ((op (e1) (e0)) = (e2)) -> (~((op (e0) (op (e3) (e0))) = (op (e3) (e0)))) -> ((op (e0) (e2)) = (e1)) -> ((op (e3) (e0)) = (e1)) -> (((op (e3) (e0)) = (e2))\/(((op (e3) (e1)) = (e2))\/(((op (e3) (e2)) = (e2))\/((op (e3) (e3)) = (e2))))) -> ((op (e1) (e2)) = (e0)) -> (~((op (e1) (e2)) = (op (e3) (e2)))) -> (~((op (e3) (e3)) = (e0))) -> False). % 15.48/15.66 do 0 intro. intros zenon_H1f6 zenon_H1f zenon_H96 zenon_H2af zenon_H35 zenon_H2b4 zenon_H68 zenon_H2b8 zenon_H29 zenon_Hee zenon_H1df zenon_H15d zenon_H17d zenon_H3c. % 15.48/15.66 apply (zenon_or_s _ _ zenon_H1f6); [ zenon_intro zenon_Hdb | zenon_intro zenon_H1f7 ]. % 15.48/15.66 apply (zenon_L1045_); trivial. % 15.48/15.66 apply (zenon_or_s _ _ zenon_H1f7); [ zenon_intro zenon_H142 | zenon_intro zenon_H1f8 ]. % 15.48/15.66 apply (zenon_L1126_); trivial. % 15.48/15.66 apply (zenon_or_s _ _ zenon_H1f8); [ zenon_intro zenon_H167 | zenon_intro zenon_H40 ]. % 15.48/15.66 apply (zenon_L626_); trivial. % 15.48/15.66 exact (zenon_H3c zenon_H40). % 15.48/15.66 (* end of lemma zenon_L1127_ *) % 15.48/15.66 assert (zenon_L1128_ : (((op (e1) (e0)) = (e0))\/(((op (e1) (e1)) = (e0))\/(((op (e1) (e2)) = (e0))\/((op (e1) (e3)) = (e0))))) -> (~((op (e0) (e0)) = (op (e1) (e0)))) -> (~((op (e1) (e1)) = (e0))) -> (~((op (e3) (e3)) = (e0))) -> (~((op (e1) (e2)) = (op (e3) (e2)))) -> (~((e0) = (e3))) -> ((op (e3) (e1)) = (e3)) -> (~((op (e0) (op (e3) (e0))) = (op (e3) (e0)))) -> ((op (e0) (e0)) = (e0)) -> (((op (e3) (e0)) = (e0))\/(((op (e3) (e1)) = (e0))\/(((op (e3) (e2)) = (e0))\/((op (e3) (e3)) = (e0))))) -> (((op (e1) (e0)) = (e2))\/(((op (e1) (e1)) = (e2))\/(((op (e1) (e2)) = (e2))\/((op (e1) (e3)) = (e2))))) -> (~((e2) = (e3))) -> ((op (e1) (e0)) = (e3)) -> (~((op (e1) (e1)) = (e2))) -> (~((op (e1) (e2)) = (op (e2) (e2)))) -> ((op (e2) (e2)) = (e2)) -> (~((e0) = (e2))) -> False). % 15.48/15.66 do 0 intro. intros zenon_H163 zenon_H24c zenon_H145 zenon_H3c zenon_H17d zenon_H4b zenon_H10a zenon_H2b8 zenon_H1f zenon_H1f6 zenon_H84 zenon_H6a zenon_H69 zenon_Hd6 zenon_H7d zenon_H35 zenon_H5e. % 15.48/15.66 apply (zenon_or_s _ _ zenon_H163); [ zenon_intro zenon_Had | zenon_intro zenon_H164 ]. % 15.48/15.66 apply (zenon_L559_); trivial. % 15.48/15.66 apply (zenon_or_s _ _ zenon_H164); [ zenon_intro zenon_H149 | zenon_intro zenon_H165 ]. % 15.48/15.66 exact (zenon_H145 zenon_H149). % 15.48/15.66 apply (zenon_or_s _ _ zenon_H165); [ zenon_intro zenon_H15d | zenon_intro zenon_Hcc ]. % 15.48/15.66 apply (zenon_L1057_); trivial. % 15.48/15.66 apply (zenon_L524_); trivial. % 15.48/15.66 (* end of lemma zenon_L1128_ *) % 15.48/15.66 assert (zenon_L1129_ : (((op (e0) (e1)) = (e2))\/(((op (e1) (e1)) = (e2))\/(((op (e2) (e1)) = (e2))\/((op (e3) (e1)) = (e2))))) -> (~((op (e3) (e3)) = (e2))) -> (~((op (e2) (op (e3) (e2))) = (op (e3) (e2)))) -> (~((op (e0) (e1)) = (op (e3) (e1)))) -> ((op (e3) (e0)) = (e3)) -> (((op (e3) (e0)) = (e2))\/(((op (e3) (e1)) = (e2))\/(((op (e3) (e2)) = (e2))\/((op (e3) (e3)) = (e2))))) -> (~((op (e1) (e1)) = (e2))) -> (~((op (e2) (e1)) = (op (e2) (e2)))) -> ((op (e2) (e2)) = (e2)) -> (((op (e1) (e0)) = (e3))\/(((op (e1) (e1)) = (e3))\/(((op (e1) (e2)) = (e3))\/((op (e1) (e3)) = (e3))))) -> (~((e2) = (e3))) -> ((op (e1) (e0)) = (e2)) -> (~((op (e1) (e2)) = (op (e3) (e2)))) -> ((op (e1) (e2)) = (e0)) -> (~((op (e1) (op (e3) (e1))) = (op (e3) (e1)))) -> (~((op (e0) (op (e3) (e0))) = (op (e3) (e0)))) -> ((op (e0) (e0)) = (e0)) -> (((op (e3) (e0)) = (e0))\/(((op (e3) (e1)) = (e0))\/(((op (e3) (e2)) = (e0))\/((op (e3) (e3)) = (e0))))) -> ((op (e0) (e2)) = (e3)) -> (~((op (e0) (e2)) = (op (e1) (e2)))) -> ((op (e1) (e3)) = (e1)) -> (~((e1) = (e3))) -> False). % 15.48/15.66 do 0 intro. intros zenon_H1a2 zenon_H3d zenon_H2af zenon_H138 zenon_Hba zenon_H1df zenon_Hd6 zenon_H157 zenon_H35 zenon_H90 zenon_H6a zenon_H68 zenon_H17d zenon_H15d zenon_H2b4 zenon_H2b8 zenon_H1f zenon_H1f6 zenon_H50 zenon_H87 zenon_H11f zenon_Ha3. % 15.48/15.66 apply (zenon_or_s _ _ zenon_H1a2); [ zenon_intro zenon_H5d | zenon_intro zenon_H1a3 ]. % 15.48/15.66 apply (zenon_L1091_); trivial. % 15.48/15.66 apply (zenon_or_s _ _ zenon_H1a3); [ zenon_intro zenon_H6e | zenon_intro zenon_H1a4 ]. % 15.48/15.66 exact (zenon_Hd6 zenon_H6e). % 15.48/15.66 apply (zenon_or_s _ _ zenon_H1a4); [ zenon_intro zenon_H156 | zenon_intro zenon_H16a ]. % 15.48/15.66 apply (zenon_L134_); trivial. % 15.48/15.66 apply (zenon_or_s _ _ zenon_H90); [ zenon_intro zenon_H69 | zenon_intro zenon_H94 ]. % 15.48/15.66 apply (zenon_L17_); trivial. % 15.48/15.66 apply (zenon_or_s _ _ zenon_H94); [ zenon_intro zenon_H96 | zenon_intro zenon_H95 ]. % 15.48/15.66 apply (zenon_L1119_); trivial. % 15.48/15.66 apply (zenon_or_s _ _ zenon_H95); [ zenon_intro zenon_H88 | zenon_intro zenon_H8a ]. % 15.48/15.66 apply (zenon_L24_); trivial. % 15.48/15.66 apply (zenon_L772_); trivial. % 15.48/15.66 (* end of lemma zenon_L1129_ *) % 15.48/15.66 assert (zenon_L1130_ : (((op (e1) (e0)) = (e0))\/(((op (e1) (e1)) = (e0))\/(((op (e1) (e2)) = (e0))\/((op (e1) (e3)) = (e0))))) -> (~((op (e0) (e0)) = (op (e1) (e0)))) -> (~((op (e1) (e1)) = (e0))) -> (~((e1) = (e3))) -> (~((op (e0) (e2)) = (op (e1) (e2)))) -> ((op (e0) (e2)) = (e3)) -> (((op (e3) (e0)) = (e0))\/(((op (e3) (e1)) = (e0))\/(((op (e3) (e2)) = (e0))\/((op (e3) (e3)) = (e0))))) -> ((op (e0) (e0)) = (e0)) -> (~((op (e0) (op (e3) (e0))) = (op (e3) (e0)))) -> (~((op (e1) (op (e3) (e1))) = (op (e3) (e1)))) -> (~((op (e1) (e2)) = (op (e3) (e2)))) -> ((op (e1) (e0)) = (e2)) -> (~((e2) = (e3))) -> (((op (e1) (e0)) = (e3))\/(((op (e1) (e1)) = (e3))\/(((op (e1) (e2)) = (e3))\/((op (e1) (e3)) = (e3))))) -> ((op (e2) (e2)) = (e2)) -> (~((op (e2) (e1)) = (op (e2) (e2)))) -> (~((op (e1) (e1)) = (e2))) -> (((op (e3) (e0)) = (e2))\/(((op (e3) (e1)) = (e2))\/(((op (e3) (e2)) = (e2))\/((op (e3) (e3)) = (e2))))) -> ((op (e3) (e0)) = (e3)) -> (~((op (e0) (e1)) = (op (e3) (e1)))) -> (~((op (e2) (op (e3) (e2))) = (op (e3) (e2)))) -> (~((op (e3) (e3)) = (e2))) -> (((op (e0) (e1)) = (e2))\/(((op (e1) (e1)) = (e2))\/(((op (e2) (e1)) = (e2))\/((op (e3) (e1)) = (e2))))) -> (~((e0) = (e1))) -> ((op (e1) (e3)) = (e1)) -> False). % 15.48/15.66 do 0 intro. intros zenon_H163 zenon_H24c zenon_H145 zenon_Ha3 zenon_H87 zenon_H50 zenon_H1f6 zenon_H1f zenon_H2b8 zenon_H2b4 zenon_H17d zenon_H68 zenon_H6a zenon_H90 zenon_H35 zenon_H157 zenon_Hd6 zenon_H1df zenon_Hba zenon_H138 zenon_H2af zenon_H3d zenon_H1a2 zenon_H9e zenon_H11f. % 15.48/15.66 apply (zenon_or_s _ _ zenon_H163); [ zenon_intro zenon_Had | zenon_intro zenon_H164 ]. % 15.48/15.66 apply (zenon_L559_); trivial. % 15.48/15.66 apply (zenon_or_s _ _ zenon_H164); [ zenon_intro zenon_H149 | zenon_intro zenon_H165 ]. % 15.48/15.66 exact (zenon_H145 zenon_H149). % 15.48/15.66 apply (zenon_or_s _ _ zenon_H165); [ zenon_intro zenon_H15d | zenon_intro zenon_Hcc ]. % 15.48/15.66 apply (zenon_L1129_); trivial. % 15.48/15.66 apply (zenon_L208_); trivial. % 15.48/15.66 (* end of lemma zenon_L1130_ *) % 15.48/15.66 assert (zenon_L1131_ : (((op (e0) (e0)) = (e3))\/(((op (e1) (e0)) = (e3))\/(((op (e2) (e0)) = (e3))\/((op (e3) (e0)) = (e3))))) -> (~((op (e0) (e0)) = (e3))) -> (~((e0) = (e2))) -> (~((op (e1) (e2)) = (op (e2) (e2)))) -> (((op (e1) (e0)) = (e2))\/(((op (e1) (e1)) = (e2))\/(((op (e1) (e2)) = (e2))\/((op (e1) (e3)) = (e2))))) -> ((op (e3) (e1)) = (e3)) -> (~((e0) = (e3))) -> (~((op (e3) (e3)) = (e0))) -> ((op (e2) (e0)) = (e1)) -> (((op (e1) (e0)) = (e0))\/(((op (e1) (e1)) = (e0))\/(((op (e1) (e2)) = (e0))\/((op (e1) (e3)) = (e0))))) -> (~((op (e0) (e0)) = (op (e1) (e0)))) -> (~((op (e1) (e1)) = (e0))) -> (~((e1) = (e3))) -> (~((op (e0) (e2)) = (op (e1) (e2)))) -> ((op (e0) (e2)) = (e3)) -> (((op (e3) (e0)) = (e0))\/(((op (e3) (e1)) = (e0))\/(((op (e3) (e2)) = (e0))\/((op (e3) (e3)) = (e0))))) -> ((op (e0) (e0)) = (e0)) -> (~((op (e0) (op (e3) (e0))) = (op (e3) (e0)))) -> (~((op (e1) (op (e3) (e1))) = (op (e3) (e1)))) -> (~((op (e1) (e2)) = (op (e3) (e2)))) -> ((op (e1) (e0)) = (e2)) -> (~((e2) = (e3))) -> (((op (e1) (e0)) = (e3))\/(((op (e1) (e1)) = (e3))\/(((op (e1) (e2)) = (e3))\/((op (e1) (e3)) = (e3))))) -> ((op (e2) (e2)) = (e2)) -> (~((op (e2) (e1)) = (op (e2) (e2)))) -> (~((op (e1) (e1)) = (e2))) -> (((op (e3) (e0)) = (e2))\/(((op (e3) (e1)) = (e2))\/(((op (e3) (e2)) = (e2))\/((op (e3) (e3)) = (e2))))) -> (~((op (e0) (e1)) = (op (e3) (e1)))) -> (~((op (e2) (op (e3) (e2))) = (op (e3) (e2)))) -> (~((op (e3) (e3)) = (e2))) -> (((op (e0) (e1)) = (e2))\/(((op (e1) (e1)) = (e2))\/(((op (e2) (e1)) = (e2))\/((op (e3) (e1)) = (e2))))) -> (~((e0) = (e1))) -> ((op (e1) (e3)) = (e1)) -> False). % 15.48/15.66 do 0 intro. intros zenon_Hbe zenon_H59 zenon_H5e zenon_H7d zenon_H84 zenon_H10a zenon_H4b zenon_H3c zenon_Hae zenon_H163 zenon_H24c zenon_H145 zenon_Ha3 zenon_H87 zenon_H50 zenon_H1f6 zenon_H1f zenon_H2b8 zenon_H2b4 zenon_H17d zenon_H68 zenon_H6a zenon_H90 zenon_H35 zenon_H157 zenon_Hd6 zenon_H1df zenon_H138 zenon_H2af zenon_H3d zenon_H1a2 zenon_H9e zenon_H11f. % 15.48/15.66 apply (zenon_or_s _ _ zenon_Hbe); [ zenon_intro zenon_H5b | zenon_intro zenon_Hbf ]. % 15.48/15.66 exact (zenon_H59 zenon_H5b). % 15.48/15.66 apply (zenon_or_s _ _ zenon_Hbf); [ zenon_intro zenon_H69 | zenon_intro zenon_Hc0 ]. % 15.48/15.66 apply (zenon_L1128_); trivial. % 15.48/15.66 apply (zenon_or_s _ _ zenon_Hc0); [ zenon_intro zenon_Haf | zenon_intro zenon_Hba ]. % 15.48/15.66 apply (zenon_L39_); trivial. % 15.48/15.66 apply (zenon_L1130_); trivial. % 15.48/15.66 (* end of lemma zenon_L1131_ *) % 15.48/15.66 assert (zenon_L1132_ : (((op (e0) (e0)) = (e3))\/(((op (e1) (e0)) = (e3))\/(((op (e2) (e0)) = (e3))\/((op (e3) (e0)) = (e3))))) -> (~((op (e0) (e0)) = (e3))) -> (~((e0) = (e2))) -> ((op (e2) (e2)) = (e2)) -> (~((op (e1) (e2)) = (op (e2) (e2)))) -> (~((op (e1) (e1)) = (e2))) -> (((op (e1) (e0)) = (e2))\/(((op (e1) (e1)) = (e2))\/(((op (e1) (e2)) = (e2))\/((op (e1) (e3)) = (e2))))) -> (((op (e3) (e0)) = (e0))\/(((op (e3) (e1)) = (e0))\/(((op (e3) (e2)) = (e0))\/((op (e3) (e3)) = (e0))))) -> ((op (e0) (e0)) = (e0)) -> (~((op (e0) (op (e3) (e0))) = (op (e3) (e0)))) -> ((op (e3) (e1)) = (e3)) -> (~((e0) = (e3))) -> (~((op (e1) (e2)) = (op (e3) (e2)))) -> (~((op (e3) (e3)) = (e0))) -> (~((op (e1) (e1)) = (e0))) -> (~((op (e0) (e0)) = (op (e1) (e0)))) -> (((op (e1) (e0)) = (e0))\/(((op (e1) (e1)) = (e0))\/(((op (e1) (e2)) = (e0))\/((op (e1) (e3)) = (e0))))) -> (~((e1) = (e3))) -> ((op (e2) (e0)) = (e1)) -> (~((e2) = (e3))) -> ((op (e3) (e0)) = (e2)) -> False). % 15.48/15.66 do 0 intro. intros zenon_Hbe zenon_H59 zenon_H5e zenon_H35 zenon_H7d zenon_Hd6 zenon_H84 zenon_H1f6 zenon_H1f zenon_H2b8 zenon_H10a zenon_H4b zenon_H17d zenon_H3c zenon_H145 zenon_H24c zenon_H163 zenon_Ha3 zenon_Hae zenon_H6a zenon_He9. % 15.48/15.66 apply (zenon_or_s _ _ zenon_Hbe); [ zenon_intro zenon_H5b | zenon_intro zenon_Hbf ]. % 15.48/15.66 exact (zenon_H59 zenon_H5b). % 15.48/15.66 apply (zenon_or_s _ _ zenon_Hbf); [ zenon_intro zenon_H69 | zenon_intro zenon_Hc0 ]. % 15.48/15.66 apply (zenon_L1128_); trivial. % 15.48/15.66 apply (zenon_or_s _ _ zenon_Hc0); [ zenon_intro zenon_Haf | zenon_intro zenon_Hba ]. % 15.48/15.66 apply (zenon_L39_); trivial. % 15.48/15.66 apply (zenon_L220_); trivial. % 15.48/15.66 (* end of lemma zenon_L1132_ *) % 15.48/15.66 assert (zenon_L1133_ : ((~((op (e2) (e2)) = (e3)))\/((op (e2) (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 (e2) (e1)) = (op (e3) (e1)))) -> (~((op (e0) (e3)) = (op (e2) (e3)))) -> (((op (e2) (e0)) = (e3))\/(((op (e2) (e1)) = (e3))\/(((op (e2) (e2)) = (e3))\/((op (e2) (e3)) = (e3))))) -> (~((e0) = (e3))) -> ((~((op (e1) (e1)) = (e2)))\/((op (e1) (e2)) = (e1))) -> (~((op (e0) (e0)) = (e1))) -> (((op (e0) (e0)) = (e1))\/(((op (e1) (e0)) = (e1))\/(((op (e2) (e0)) = (e1))\/((op (e3) (e0)) = (e1))))) -> (~((op (e0) (e0)) = (e3))) -> (((op (e1) (e0)) = (e0))\/(((op (e1) (e1)) = (e0))\/(((op (e1) (e2)) = (e0))\/((op (e1) (e3)) = (e0))))) -> (~((e2) = (e3))) -> (~((op (e1) (e2)) = (op (e2) (e2)))) -> ((op (e2) (e2)) = (e2)) -> (~((e0) = (e2))) -> (((op (e1) (e0)) = (e2))\/(((op (e1) (e1)) = (e2))\/(((op (e1) (e2)) = (e2))\/((op (e1) (e3)) = (e2))))) -> (~((op (e1) (e1)) = (e1))) -> (~((op (e1) (e1)) = (e2))) -> (((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)) = (e0))) -> ((op (e0) (e0)) = (e0)) -> (~((op (e0) (e0)) = (op (e1) (e0)))) -> (~((e1) = (e3))) -> ((~((op (e3) (e3)) = (e2)))\/((op (e3) (e2)) = (e3))) -> (~((op (e3) (e0)) = (op (e3) (e2)))) -> (~((op (e0) (e0)) = (e2))) -> (~((e0) = (e1))) -> (((op (e3) (e0)) = (e2))\/(((op (e3) (e1)) = (e2))\/(((op (e3) (e2)) = (e2))\/((op (e3) (e3)) = (e2))))) -> (~((op (e2) (op (e3) (e2))) = (op (e3) (e2)))) -> (~((op (e0) (e1)) = (op (e3) (e1)))) -> (~((op (e2) (e1)) = (op (e2) (e2)))) -> (((op (e1) (e0)) = (e3))\/(((op (e1) (e1)) = (e3))\/(((op (e1) (e2)) = (e3))\/((op (e1) (e3)) = (e3))))) -> (((op (e3) (e2)) = (e0))\/(((op (e3) (e2)) = (e1))\/(((op (e3) (e2)) = (e2))\/((op (e3) (e2)) = (e3))))) -> (~((op (e0) (e2)) = (op (e3) (e2)))) -> (~((op (e2) (e2)) = (e1))) -> (((op (e0) (e2)) = (e0))\/(((op (e0) (e2)) = (e1))\/(((op (e0) (e2)) = (e2))\/((op (e0) (e2)) = (e3))))) -> (~((op (e0) (e2)) = (op (e1) (e2)))) -> (~((op (e0) (e2)) = (op (e2) (e2)))) -> (~((op (e0) (e0)) = (op (e0) (e2)))) -> (((op (e0) (e2)) = (e1))\/(((op (e1) (e2)) = (e1))\/(((op (e2) (e2)) = (e1))\/((op (e3) (e2)) = (e1))))) -> (~((op (e0) (op (e3) (e0))) = (op (e3) (e0)))) -> (~((op (e1) (op (e3) (e1))) = (op (e3) (e1)))) -> (~((op (e1) (e2)) = (op (e3) (e2)))) -> (((op (e3) (e0)) = (e0))\/(((op (e3) (e1)) = (e0))\/(((op (e3) (e2)) = (e0))\/((op (e3) (e3)) = (e0))))) -> (((op (e0) (e1)) = (e2))\/(((op (e1) (e1)) = (e2))\/(((op (e2) (e1)) = (e2))\/((op (e3) (e1)) = (e2))))) -> (~((op (e2) (e0)) = (op (e2) (e2)))) -> (((op (e0) (e0)) = (e2))\/(((op (e1) (e0)) = (e2))\/(((op (e2) (e0)) = (e2))\/((op (e3) (e0)) = (e2))))) -> (((op (e0) (e0)) = (e3))\/(((op (e1) (e0)) = (e3))\/(((op (e2) (e0)) = (e3))\/((op (e3) (e0)) = (e3))))) -> ((op (e1) (e3)) = (e1)) -> (~((op (e1) (e0)) = (op (e1) (e3)))) -> (~((op (e0) (e3)) = (op (e3) (e3)))) -> (((op (e0) (e0)) = (e2))\/(((op (e0) (e1)) = (e2))\/(((op (e0) (e2)) = (e2))\/((op (e0) (e3)) = (e2))))) -> ((~((op (e3) (e3)) = (e0)))\/((op (e3) (e0)) = (e3))) -> (~((op (e0) (e0)) = (op (e2) (e0)))) -> (~((op (e1) (e0)) = (op (e2) (e0)))) -> (~((op (e2) (e0)) = (op (e3) (e0)))) -> (((op (e2) (e0)) = (e0))\/(((op (e2) (e0)) = (e1))\/(((op (e2) (e0)) = (e2))\/((op (e2) (e0)) = (e3))))) -> (~((op (e1) (e0)) = (op (e3) (e0)))) -> (((op (e1) (e2)) = (e0))\/(((op (e1) (e2)) = (e1))\/(((op (e1) (e2)) = (e2))\/((op (e1) (e2)) = (e3))))) -> (~((op (e1) (e0)) = (op (e1) (e2)))) -> (((op (e3) (e0)) = (e1))\/(((op (e3) (e1)) = (e1))\/(((op (e3) (e2)) = (e1))\/((op (e3) (e3)) = (e1))))) -> (~((e1) = (e2))) -> (~((op (e3) (op (e3) (e3))) = (op (e3) (e3)))) -> ((~((op (e3) (e3)) = (e3)))\/((op (e3) (e3)) = (e3))) -> (~((op (e3) (e1)) = (op (e3) (e2)))) -> ((~((op (e3) (e3)) = (e1)))\/((op (e3) (e1)) = (e3))) -> ((~((op (e1) (e1)) = (e3)))\/((op (e1) (e3)) = (e1))) -> (((op (e0) (e0)) = (e1))\/(((op (e0) (e1)) = (e1))\/(((op (e0) (e2)) = (e1))\/((op (e0) (e3)) = (e1))))) -> (~((op (e0) (e2)) = (op (e0) (e3)))) -> False). % 15.48/15.66 do 0 intro. intros zenon_H1c3 zenon_H15f zenon_H58 zenon_H13c zenon_Hb4 zenon_He6 zenon_H4b zenon_H1d3 zenon_H45 zenon_Hf1 zenon_H59 zenon_H163 zenon_H6a zenon_H7d zenon_H35 zenon_H5e zenon_H84 zenon_H1b4 zenon_Hd6 zenon_H3b zenon_H1b3 zenon_H145 zenon_H1f zenon_H24c zenon_Ha3 zenon_H10e zenon_H105 zenon_H8f zenon_H9e zenon_H1df zenon_H2af zenon_H138 zenon_H157 zenon_H90 zenon_H25e zenon_H140 zenon_H52 zenon_H251 zenon_H87 zenon_H28 zenon_H250 zenon_H11b zenon_H2b8 zenon_H2b4 zenon_H17d zenon_H1f6 zenon_H1a2 zenon_H17a zenon_Heb zenon_Hbe zenon_H11f zenon_H1cf zenon_H36 zenon_H8e zenon_H10f zenon_H258 zenon_H247 zenon_H1e5 zenon_H281 zenon_H22e zenon_H1d5 zenon_H166 zenon_H146 zenon_Ha7 zenon_H2be zenon_H10d zenon_H135 zenon_H10c zenon_H1d2 zenon_H44 zenon_Hc9. % 15.48/15.66 apply (zenon_or_s _ _ zenon_H1c3); [ zenon_intro zenon_H30 | zenon_intro zenon_H124 ]. % 15.48/15.66 apply (zenon_or_s _ _ zenon_H10f); [ zenon_intro zenon_H3c | zenon_intro zenon_Hba ]. % 15.48/15.66 apply (zenon_or_s _ _ zenon_H10c); [ zenon_intro zenon_H104 | zenon_intro zenon_H10a ]. % 15.48/15.66 apply (zenon_or_s _ _ zenon_H10e); [ zenon_intro zenon_H3d | zenon_intro zenon_H106 ]. % 15.48/15.66 apply (zenon_or_s _ _ zenon_H10d); [ zenon_intro zenon_H3e | zenon_intro zenon_H42 ]. % 15.48/15.66 apply (zenon_or_s _ _ zenon_H44); [ zenon_intro zenon_H47 | zenon_intro zenon_H46 ]. % 15.48/15.66 exact (zenon_H45 zenon_H47). % 15.48/15.66 apply (zenon_or_s _ _ zenon_H46); [ zenon_intro zenon_H22 | zenon_intro zenon_H48 ]. % 15.48/15.66 apply (zenon_L1125_); trivial. % 15.48/15.66 apply (zenon_or_s _ _ zenon_H48); [ zenon_intro zenon_H29 | zenon_intro zenon_H37 ]. % 15.48/15.66 apply (zenon_or_s _ _ zenon_Hf1); [ zenon_intro zenon_H47 | zenon_intro zenon_Hf4 ]. % 15.48/15.66 exact (zenon_H45 zenon_H47). % 15.48/15.66 apply (zenon_or_s _ _ zenon_Hf4); [ zenon_intro zenon_Hd8 | zenon_intro zenon_Hf5 ]. % 15.48/15.66 apply (zenon_L1079_); trivial. % 15.48/15.66 apply (zenon_or_s _ _ zenon_Hf5); [ zenon_intro zenon_Hae | zenon_intro zenon_Hee ]. % 15.48/15.66 apply (zenon_L1124_); trivial. % 15.48/15.66 apply (zenon_L1085_); trivial. % 15.48/15.66 apply (zenon_L7_); trivial. % 15.48/15.66 apply (zenon_L1041_); trivial. % 15.48/15.66 apply (zenon_or_s _ _ zenon_H10d); [ zenon_intro zenon_H3e | zenon_intro zenon_H42 ]. % 15.48/15.66 apply (zenon_or_s _ _ zenon_H44); [ zenon_intro zenon_H47 | zenon_intro zenon_H46 ]. % 15.48/15.66 exact (zenon_H45 zenon_H47). % 15.48/15.66 apply (zenon_or_s _ _ zenon_H46); [ zenon_intro zenon_H22 | zenon_intro zenon_H48 ]. % 15.48/15.66 apply (zenon_L1125_); trivial. % 15.48/15.66 apply (zenon_or_s _ _ zenon_H48); [ zenon_intro zenon_H29 | zenon_intro zenon_H37 ]. % 15.48/15.66 apply (zenon_or_s _ _ zenon_Hf1); [ zenon_intro zenon_H47 | zenon_intro zenon_Hf4 ]. % 15.48/15.66 exact (zenon_H45 zenon_H47). % 15.48/15.66 apply (zenon_or_s _ _ zenon_Hf4); [ zenon_intro zenon_Hd8 | zenon_intro zenon_Hf5 ]. % 15.48/15.66 apply (zenon_L1076_); trivial. % 15.48/15.66 apply (zenon_or_s _ _ zenon_Hf5); [ zenon_intro zenon_Hae | zenon_intro zenon_Hee ]. % 15.48/15.66 apply (zenon_L1124_); trivial. % 15.48/15.66 apply (zenon_or_s _ _ zenon_Heb); [ zenon_intro zenon_H92 | zenon_intro zenon_Hec ]. % 15.48/15.66 exact (zenon_H8f zenon_H92). % 15.48/15.66 apply (zenon_or_s _ _ zenon_Hec); [ zenon_intro zenon_H68 | zenon_intro zenon_Hed ]. % 15.48/15.66 apply (zenon_or_s _ _ zenon_H163); [ zenon_intro zenon_Had | zenon_intro zenon_H164 ]. % 15.48/15.66 apply (zenon_L559_); trivial. % 15.48/15.66 apply (zenon_or_s _ _ zenon_H164); [ zenon_intro zenon_H149 | zenon_intro zenon_H165 ]. % 15.48/15.66 exact (zenon_H145 zenon_H149). % 15.48/15.66 apply (zenon_or_s _ _ zenon_H165); [ zenon_intro zenon_H15d | zenon_intro zenon_Hcc ]. % 15.48/15.66 apply (zenon_or_s _ _ zenon_H90); [ zenon_intro zenon_H69 | zenon_intro zenon_H94 ]. % 15.48/15.66 apply (zenon_L17_); trivial. % 15.48/15.66 apply (zenon_or_s _ _ zenon_H94); [ zenon_intro zenon_H96 | zenon_intro zenon_H95 ]. % 15.48/15.66 apply (zenon_L1127_); trivial. % 15.48/15.66 apply (zenon_or_s _ _ zenon_H95); [ zenon_intro zenon_H88 | zenon_intro zenon_H8a ]. % 15.48/15.66 apply (zenon_L164_); trivial. % 15.48/15.66 apply (zenon_L772_); trivial. % 15.48/15.66 apply (zenon_L208_); trivial. % 15.48/15.66 apply (zenon_or_s _ _ zenon_Hed); [ zenon_intro zenon_Hdd | zenon_intro zenon_He9 ]. % 15.48/15.66 apply (zenon_L161_); trivial. % 15.48/15.66 apply (zenon_L1082_); trivial. % 15.48/15.66 apply (zenon_L1086_); trivial. % 15.48/15.66 apply (zenon_L1041_); trivial. % 15.48/15.66 apply (zenon_or_s _ _ zenon_H10e); [ zenon_intro zenon_H3d | zenon_intro zenon_H106 ]. % 15.48/15.66 apply (zenon_or_s _ _ zenon_H10d); [ zenon_intro zenon_H3e | zenon_intro zenon_H42 ]. % 15.48/15.66 apply (zenon_or_s _ _ zenon_H44); [ zenon_intro zenon_H47 | zenon_intro zenon_H46 ]. % 15.48/15.66 exact (zenon_H45 zenon_H47). % 15.48/15.66 apply (zenon_or_s _ _ zenon_H46); [ zenon_intro zenon_H22 | zenon_intro zenon_H48 ]. % 15.48/15.66 apply (zenon_or_s _ _ zenon_Hf1); [ zenon_intro zenon_H47 | zenon_intro zenon_Hf4 ]. % 15.48/15.66 exact (zenon_H45 zenon_H47). % 15.48/15.66 apply (zenon_or_s _ _ zenon_Hf4); [ zenon_intro zenon_Hd8 | zenon_intro zenon_Hf5 ]. % 15.48/15.66 apply (zenon_L224_); trivial. % 15.48/15.66 apply (zenon_or_s _ _ zenon_Hf5); [ zenon_intro zenon_Hae | zenon_intro zenon_Hee ]. % 15.48/15.66 apply (zenon_or_s _ _ zenon_Heb); [ zenon_intro zenon_H92 | zenon_intro zenon_Hec ]. % 15.48/15.66 exact (zenon_H8f zenon_H92). % 15.48/15.66 apply (zenon_or_s _ _ zenon_Hec); [ zenon_intro zenon_H68 | zenon_intro zenon_Hed ]. % 15.48/15.66 apply (zenon_or_s _ _ zenon_H58); [ zenon_intro zenon_H5b | zenon_intro zenon_H5a ]. % 15.48/15.66 exact (zenon_H59 zenon_H5b). % 15.48/15.66 apply (zenon_or_s _ _ zenon_H5a); [ zenon_intro zenon_H4a | zenon_intro zenon_H5c ]. % 15.48/15.66 apply (zenon_L120_); trivial. % 15.48/15.66 apply (zenon_or_s _ _ zenon_H5c); [ zenon_intro zenon_H50 | zenon_intro zenon_H53 ]. % 15.48/15.66 apply (zenon_L1131_); trivial. % 15.48/15.66 apply (zenon_L536_); trivial. % 15.48/15.66 apply (zenon_or_s _ _ zenon_Hed); [ zenon_intro zenon_Hdd | zenon_intro zenon_He9 ]. % 15.48/15.66 apply (zenon_L161_); trivial. % 15.48/15.66 apply (zenon_L1132_); trivial. % 15.48/15.66 apply (zenon_L1054_); trivial. % 15.48/15.66 apply (zenon_or_s _ _ zenon_H48); [ zenon_intro zenon_H29 | zenon_intro zenon_H37 ]. % 15.48/15.66 apply (zenon_L1099_); trivial. % 15.48/15.66 apply (zenon_L7_); trivial. % 15.48/15.66 apply (zenon_L1041_); trivial. % 15.48/15.66 apply (zenon_L115_); trivial. % 15.48/15.66 apply (zenon_L1123_); trivial. % 15.48/15.66 apply (zenon_L137_); trivial. % 15.48/15.66 (* end of lemma zenon_L1133_ *) % 15.48/15.66 assert (zenon_L1134_ : ((~((op (e3) (e3)) = (e1)))\/((op (e3) (e1)) = (e3))) -> (~((op (e0) (op (e3) (e0))) = (op (e3) (e0)))) -> (((op (e0) (e0)) = (e3))\/(((op (e0) (e1)) = (e3))\/(((op (e0) (e2)) = (e3))\/((op (e0) (e3)) = (e3))))) -> (~((op (e0) (e0)) = (op (e1) (e0)))) -> ((op (e0) (e0)) = (e0)) -> (~((op (e1) (e1)) = (e0))) -> (((op (e3) (e0)) = (e0))\/(((op (e3) (e1)) = (e0))\/(((op (e3) (e2)) = (e0))\/((op (e3) (e3)) = (e0))))) -> (~((op (e1) (e2)) = (op (e3) (e2)))) -> (~((e0) = (e3))) -> (((op (e0) (e3)) = (e2))\/(((op (e1) (e3)) = (e2))\/(((op (e2) (e3)) = (e2))\/((op (e3) (e3)) = (e2))))) -> (~((op (e2) (e0)) = (op (e2) (e3)))) -> (~((e0) = (e2))) -> (~((e2) = (e3))) -> (((op (e1) (e0)) = (e0))\/(((op (e1) (e1)) = (e0))\/(((op (e1) (e2)) = (e0))\/((op (e1) (e3)) = (e0))))) -> (~((e1) = (e3))) -> (~((op (e0) (e1)) = (op (e3) (e1)))) -> (~((op (e0) (e0)) = (e3))) -> (~((op (e0) (e3)) = (op (e3) (e3)))) -> (((op (e0) (e0)) = (e1))\/(((op (e0) (e1)) = (e1))\/(((op (e0) (e2)) = (e1))\/((op (e0) (e3)) = (e1))))) -> (~((op (e3) (e1)) = (op (e3) (e2)))) -> ((~((op (e3) (e3)) = (e2)))\/((op (e3) (e2)) = (e3))) -> (((op (e0) (e0)) = (e1))\/(((op (e1) (e0)) = (e1))\/(((op (e2) (e0)) = (e1))\/((op (e3) (e0)) = (e1))))) -> (((op (e3) (e3)) = (e0))\/(((op (e3) (e3)) = (e1))\/(((op (e3) (e3)) = (e2))\/((op (e3) (e3)) = (e3))))) -> (((op (e2) (e2)) = (e0))\/(((op (e2) (e2)) = (e1))\/(((op (e2) (e2)) = (e2))\/((op (e2) (e2)) = (e3))))) -> ((op (e2) (e0)) = (e2)) -> (~((e1) = (e2))) -> ((op (e1) (e3)) = (e1)) -> (~((op (e1) (e0)) = (op (e1) (e3)))) -> (~((op (e0) (e0)) = (e1))) -> (~((op (e3) (op (e3) (e3))) = (op (e3) (e3)))) -> ((~((op (e3) (e3)) = (e3)))\/((op (e3) (e3)) = (e3))) -> ((~((op (e1) (e1)) = (e2)))\/((op (e1) (e2)) = (e1))) -> ((~((op (e2) (e2)) = (e0)))\/((op (e2) (e0)) = (e2))) -> (~((op (e0) (e0)) = (op (e0) (e2)))) -> (~((op (e1) (e0)) = (op (e3) (e0)))) -> (((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) (e0)) = (e2))\/(((op (e1) (e0)) = (e2))\/(((op (e2) (e0)) = (e2))\/((op (e3) (e0)) = (e2))))) -> (((op (e1) (e1)) = (e0))\/(((op (e1) (e1)) = (e1))\/(((op (e1) (e1)) = (e2))\/((op (e1) (e1)) = (e3))))) -> ((~((op (e2) (e2)) = (e3)))\/((op (e2) (e3)) = (e2))) -> (((op (e0) (e0)) = (e3))\/(((op (e1) (e0)) = (e3))\/(((op (e2) (e0)) = (e3))\/((op (e3) (e0)) = (e3))))) -> (((op (e1) (e0)) = (e3))\/(((op (e1) (e1)) = (e3))\/(((op (e1) (e2)) = (e3))\/((op (e1) (e3)) = (e3))))) -> (~((op (e1) (e0)) = (op (e2) (e0)))) -> (~((op (e2) (e0)) = (op (e2) (e1)))) -> (~((op (e1) (op (e3) (e1))) = (op (e3) (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)) = (e2))\/(((op (e1) (e1)) = (e2))\/(((op (e1) (e2)) = (e2))\/((op (e1) (e3)) = (e2))))) -> (((op (e2) (e0)) = (e3))\/(((op (e2) (e1)) = (e3))\/(((op (e2) (e2)) = (e3))\/((op (e2) (e3)) = (e3))))) -> (((op (e0) (e2)) = (e1))\/(((op (e1) (e2)) = (e1))\/(((op (e2) (e2)) = (e1))\/((op (e3) (e2)) = (e1))))) -> (~((op (e2) (op (e3) (e2))) = (op (e3) (e2)))) -> (~((op (e1) (e0)) = (op (e1) (e2)))) -> (~((op (e0) (e2)) = (op (e0) (e3)))) -> (~((op (e0) (e0)) = (op (e0) (e3)))) -> (~((op (e0) (e3)) = (op (e2) (e3)))) -> (~((op (e0) (e3)) = (op (e1) (e3)))) -> (((op (e0) (e3)) = (e0))\/(((op (e0) (e3)) = (e1))\/(((op (e0) (e3)) = (e2))\/((op (e0) (e3)) = (e3))))) -> (~((op (e0) (e1)) = (op (e0) (e3)))) -> (((op (e0) (e3)) = (e1))\/(((op (e1) (e3)) = (e1))\/(((op (e2) (e3)) = (e1))\/((op (e3) (e3)) = (e1))))) -> (~((op (e0) (e1)) = (op (e2) (e1)))) -> (((op (e2) (e0)) = (e1))\/(((op (e2) (e1)) = (e1))\/(((op (e2) (e2)) = (e1))\/((op (e2) (e3)) = (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)) = (op (e3) (e2)))) -> (~((op (e3) (e0)) = (op (e3) (e1)))) -> ((~((op (e3) (e3)) = (e0)))\/((op (e3) (e0)) = (e3))) -> ((~((op (e2) (e2)) = (e1)))\/((op (e2) (e1)) = (e2))) -> (~((op (e0) (e0)) = (e2))) -> ((~((op (e1) (e1)) = (e3)))\/((op (e1) (e3)) = (e1))) -> (~((op (e1) (e0)) = (op (e1) (e1)))) -> ((~((op (e1) (e1)) = (e1)))\/((op (e1) (e1)) = (e1))) -> (~((op (e2) (e2)) = (op (e2) (e3)))) -> (~((op (e2) (e1)) = (op (e3) (e1)))) -> (~((op (e1) (e2)) = (op (e2) (e2)))) -> (~((op (e1) (e1)) = (e1))) -> (~((op (e1) (e1)) = (e2))) -> (~((e0) = (e1))) -> (((op (e3) (e0)) = (e2))\/(((op (e3) (e1)) = (e2))\/(((op (e3) (e2)) = (e2))\/((op (e3) (e3)) = (e2))))) -> (~((op (e2) (e1)) = (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 (e0) (e2)) = (e0))\/(((op (e0) (e2)) = (e1))\/(((op (e0) (e2)) = (e2))\/((op (e0) (e2)) = (e3))))) -> (~((op (e0) (e2)) = (op (e2) (e2)))) -> (~((op (e2) (e0)) = (op (e2) (e2)))) -> (~((op (e0) (e0)) = (op (e2) (e0)))) -> (((op (e2) (e0)) = (e0))\/(((op (e2) (e0)) = (e1))\/(((op (e2) (e0)) = (e2))\/((op (e2) (e0)) = (e3))))) -> (((op (e1) (e2)) = (e0))\/(((op (e1) (e2)) = (e1))\/(((op (e1) (e2)) = (e2))\/((op (e1) (e2)) = (e3))))) -> ((~((op (e2) (e2)) = (e2)))\/((op (e2) (e2)) = (e2))) -> False). % 15.48/15.66 do 0 intro. intros zenon_H10c zenon_H2b8 zenon_H58 zenon_H24c zenon_H1f zenon_H145 zenon_H1f6 zenon_H17d zenon_H4b zenon_H160 zenon_Hce zenon_H5e zenon_H6a zenon_H163 zenon_Ha3 zenon_H138 zenon_H59 zenon_H36 zenon_H44 zenon_H135 zenon_H10e zenon_Hf1 zenon_H3b zenon_H2d zenon_Hdd zenon_Ha7 zenon_H11f zenon_H1cf zenon_H45 zenon_H2be zenon_H10d zenon_H1d3 zenon_H1d4 zenon_H250 zenon_H22e zenon_H146 zenon_H16f zenon_Heb zenon_H1b3 zenon_H1c3 zenon_Hbe zenon_H90 zenon_H247 zenon_H154 zenon_H2b4 zenon_H1a2 zenon_H87 zenon_H84 zenon_He6 zenon_H11b zenon_H2af zenon_H166 zenon_Hc9 zenon_H24f zenon_Hb4 zenon_H80 zenon_H254 zenon_H1cd zenon_H121 zenon_Hde zenon_Hb7 zenon_H1e5 zenon_H8e zenon_H105 zenon_H109 zenon_H10f zenon_H1e3 zenon_H8f zenon_H1d2 zenon_Hd7 zenon_H1d8 zenon_H15f zenon_H13c zenon_H7d zenon_H1b4 zenon_Hd6 zenon_H9e zenon_H1df zenon_H157 zenon_H25e zenon_H140 zenon_H251 zenon_H28 zenon_H17a zenon_H258 zenon_H281 zenon_H1d5 zenon_Haa. % 15.48/15.66 apply (zenon_or_s _ _ zenon_H1e3); [ zenon_intro zenon_H52 | zenon_intro zenon_H156 ]. % 15.48/15.66 apply (zenon_or_s _ _ zenon_Haa); [ zenon_intro zenon_H2f | zenon_intro zenon_H35 ]. % 15.48/15.66 apply (zenon_or_s _ _ zenon_H1c3); [ zenon_intro zenon_H30 | zenon_intro zenon_H124 ]. % 15.48/15.66 apply (zenon_or_s _ _ zenon_H10f); [ zenon_intro zenon_H3c | zenon_intro zenon_Hba ]. % 15.48/15.66 apply (zenon_or_s _ _ zenon_H10c); [ zenon_intro zenon_H104 | zenon_intro zenon_H10a ]. % 15.48/15.66 apply (zenon_or_s _ _ zenon_H10d); [ zenon_intro zenon_H3e | zenon_intro zenon_H42 ]. % 15.48/15.66 apply (zenon_or_s _ _ zenon_Hf1); [ zenon_intro zenon_H47 | zenon_intro zenon_Hf4 ]. % 15.48/15.66 exact (zenon_H45 zenon_H47). % 15.48/15.66 apply (zenon_or_s _ _ zenon_Hf4); [ zenon_intro zenon_Hd8 | zenon_intro zenon_Hf5 ]. % 15.48/15.66 apply (zenon_L224_); trivial. % 15.48/15.66 apply (zenon_or_s _ _ zenon_Hf5); [ zenon_intro zenon_Hae | zenon_intro zenon_Hee ]. % 15.48/15.66 apply (zenon_L304_); trivial. % 15.48/15.66 apply (zenon_L306_); trivial. % 15.48/15.66 apply (zenon_L1041_); trivial. % 15.48/15.66 apply (zenon_or_s _ _ zenon_H10e); [ zenon_intro zenon_H3d | zenon_intro zenon_H106 ]. % 15.48/15.66 apply (zenon_or_s _ _ zenon_H10d); [ zenon_intro zenon_H3e | zenon_intro zenon_H42 ]. % 15.48/15.66 apply (zenon_or_s _ _ zenon_H44); [ zenon_intro zenon_H47 | zenon_intro zenon_H46 ]. % 15.48/15.66 exact (zenon_H45 zenon_H47). % 15.48/15.66 apply (zenon_or_s _ _ zenon_H46); [ zenon_intro zenon_H22 | zenon_intro zenon_H48 ]. % 15.48/15.66 apply (zenon_L1117_); trivial. % 15.48/15.66 apply (zenon_or_s _ _ zenon_H48); [ zenon_intro zenon_H29 | zenon_intro zenon_H37 ]. % 15.48/15.66 apply (zenon_L1112_); trivial. % 15.48/15.66 apply (zenon_L7_); trivial. % 15.48/15.66 apply (zenon_L1041_); trivial. % 15.48/15.66 apply (zenon_L115_); trivial. % 15.48/15.66 apply (zenon_L1113_); trivial. % 15.48/15.66 apply (zenon_L119_); trivial. % 15.48/15.66 apply (zenon_L1133_); trivial. % 15.48/15.66 apply (zenon_L284_); trivial. % 15.48/15.66 (* end of lemma zenon_L1134_ *) % 15.48/15.66 assert (zenon_L1135_ : (~((op (e0) (op (e3) (e0))) = (op (e3) (e0)))) -> ((op (e0) (e2)) = (e0)) -> ((op (e3) (e0)) = (e2)) -> ((op (e3) (e0)) = (e0)) -> False). % 15.48/15.66 do 0 intro. intros zenon_H2b8 zenon_Hab zenon_He9 zenon_Hdb. % 15.48/15.66 cut (((op (e0) (e2)) = (e0)) = ((op (e0) (op (e3) (e0))) = (op (e3) (e0)))). % 15.48/15.66 intro zenon_D_pnotp. % 15.48/15.66 apply zenon_H2b8. % 15.48/15.66 rewrite <- zenon_D_pnotp. % 15.48/15.66 exact zenon_Hab. % 15.48/15.66 cut (((e0) = (op (e3) (e0)))); [idtac | apply NNPP; zenon_intro zenon_H2bf]. % 15.48/15.66 cut (((op (e0) (e2)) = (op (e0) (op (e3) (e0))))); [idtac | apply NNPP; zenon_intro zenon_H2ca]. % 15.48/15.66 congruence. % 15.48/15.66 elim (classic ((op (e0) (op (e3) (e0))) = (op (e0) (op (e3) (e0))))); [ zenon_intro zenon_H2ba | zenon_intro zenon_H2bb ]. % 15.48/15.66 cut (((op (e0) (op (e3) (e0))) = (op (e0) (op (e3) (e0)))) = ((op (e0) (e2)) = (op (e0) (op (e3) (e0))))). % 15.48/15.66 intro zenon_D_pnotp. % 15.48/15.66 apply zenon_H2ca. % 15.48/15.66 rewrite <- zenon_D_pnotp. % 15.48/15.66 exact zenon_H2ba. % 15.48/15.66 cut (((op (e0) (op (e3) (e0))) = (op (e0) (op (e3) (e0))))); [idtac | apply NNPP; zenon_intro zenon_H2bb]. % 15.48/15.66 cut (((op (e0) (op (e3) (e0))) = (op (e0) (e2)))); [idtac | apply NNPP; zenon_intro zenon_H2c9]. % 15.48/15.66 congruence. % 15.48/15.66 apply (zenon_L1081_); trivial. % 15.48/15.66 apply zenon_H2bb. apply refl_equal. % 15.48/15.66 apply zenon_H2bb. apply refl_equal. % 15.48/15.66 apply zenon_H2bf. apply sym_equal. exact zenon_Hdb. % 15.48/15.66 (* end of lemma zenon_L1135_ *) % 15.48/15.66 assert (zenon_L1136_ : (~((op (e1) (op (e3) (e1))) = (op (e3) (e1)))) -> ((op (e1) (e0)) = (e0)) -> ((op (e3) (e1)) = (e0)) -> False). % 15.48/15.66 do 0 intro. intros zenon_H2b4 zenon_Had zenon_H142. % 15.48/15.66 cut (((op (e1) (e0)) = (e0)) = ((op (e1) (op (e3) (e1))) = (op (e3) (e1)))). % 15.48/15.66 intro zenon_D_pnotp. % 15.48/15.66 apply zenon_H2b4. % 15.48/15.66 rewrite <- zenon_D_pnotp. % 15.48/15.66 exact zenon_Had. % 15.48/15.66 cut (((e0) = (op (e3) (e1)))); [idtac | apply NNPP; zenon_intro zenon_H2cf]. % 15.48/15.66 cut (((op (e1) (e0)) = (op (e1) (op (e3) (e1))))); [idtac | apply NNPP; zenon_intro zenon_H2c3]. % 15.48/15.66 congruence. % 15.48/15.66 elim (classic ((op (e1) (op (e3) (e1))) = (op (e1) (op (e3) (e1))))); [ zenon_intro zenon_H2b6 | zenon_intro zenon_H2b7 ]. % 15.48/15.66 cut (((op (e1) (op (e3) (e1))) = (op (e1) (op (e3) (e1)))) = ((op (e1) (e0)) = (op (e1) (op (e3) (e1))))). % 15.55/15.66 intro zenon_D_pnotp. % 15.55/15.66 apply zenon_H2c3. % 15.55/15.66 rewrite <- zenon_D_pnotp. % 15.55/15.66 exact zenon_H2b6. % 15.55/15.66 cut (((op (e1) (op (e3) (e1))) = (op (e1) (op (e3) (e1))))); [idtac | apply NNPP; zenon_intro zenon_H2b7]. % 15.55/15.66 cut (((op (e1) (op (e3) (e1))) = (op (e1) (e0)))); [idtac | apply NNPP; zenon_intro zenon_H2c2]. % 15.55/15.66 congruence. % 15.55/15.66 apply (zenon_L1046_); trivial. % 15.55/15.66 apply zenon_H2b7. apply refl_equal. % 15.55/15.66 apply zenon_H2b7. apply refl_equal. % 15.55/15.66 apply zenon_H2cf. apply sym_equal. exact zenon_H142. % 15.55/15.66 (* end of lemma zenon_L1136_ *) % 15.55/15.66 assert (zenon_L1137_ : (((op (e3) (e0)) = (e0))\/(((op (e3) (e1)) = (e0))\/(((op (e3) (e2)) = (e0))\/((op (e3) (e3)) = (e0))))) -> ((op (e3) (e0)) = (e2)) -> (~((op (e0) (op (e3) (e0))) = (op (e3) (e0)))) -> ((op (e1) (e0)) = (e0)) -> (~((op (e1) (op (e3) (e1))) = (op (e3) (e1)))) -> ((op (e0) (e2)) = (e0)) -> (~((op (e0) (e2)) = (op (e3) (e2)))) -> (~((op (e3) (e3)) = (e0))) -> False). % 15.55/15.66 do 0 intro. intros zenon_H1f6 zenon_He9 zenon_H2b8 zenon_Had zenon_H2b4 zenon_Hab zenon_H140 zenon_H3c. % 15.55/15.66 apply (zenon_or_s _ _ zenon_H1f6); [ zenon_intro zenon_Hdb | zenon_intro zenon_H1f7 ]. % 15.55/15.66 apply (zenon_L1135_); trivial. % 15.55/15.66 apply (zenon_or_s _ _ zenon_H1f7); [ zenon_intro zenon_H142 | zenon_intro zenon_H1f8 ]. % 15.55/15.66 apply (zenon_L1136_); trivial. % 15.55/15.66 apply (zenon_or_s _ _ zenon_H1f8); [ zenon_intro zenon_H167 | zenon_intro zenon_H40 ]. % 15.55/15.66 apply (zenon_L267_); trivial. % 15.55/15.66 exact (zenon_H3c zenon_H40). % 15.55/15.66 (* end of lemma zenon_L1137_ *) % 15.55/15.66 assert (zenon_L1138_ : (((op (e0) (e2)) = (e0))\/(((op (e1) (e2)) = (e0))\/(((op (e2) (e2)) = (e0))\/((op (e3) (e2)) = (e0))))) -> (~((op (e0) (e2)) = (op (e3) (e2)))) -> (~((op (e0) (op (e3) (e0))) = (op (e3) (e0)))) -> (~((op (e3) (e3)) = (e0))) -> (~((op (e1) (e2)) = (op (e3) (e2)))) -> (~((op (e1) (op (e3) (e1))) = (op (e3) (e1)))) -> ((op (e1) (e0)) = (e0)) -> ((op (e3) (e0)) = (e2)) -> (~((e0) = (e2))) -> (((op (e3) (e0)) = (e0))\/(((op (e3) (e1)) = (e0))\/(((op (e3) (e2)) = (e0))\/((op (e3) (e3)) = (e0))))) -> (~((op (e2) (e2)) = (e0))) -> (~((e0) = (e3))) -> ((op (e3) (e2)) = (e3)) -> False). % 15.55/15.66 do 0 intro. intros zenon_H16f zenon_H140 zenon_H2b8 zenon_H3c zenon_H17d zenon_H2b4 zenon_Had zenon_He9 zenon_H5e zenon_H1f6 zenon_H2e zenon_H4b zenon_H106. % 15.55/15.66 apply (zenon_or_s _ _ zenon_H16f); [ zenon_intro zenon_Hab | zenon_intro zenon_H170 ]. % 15.55/15.66 apply (zenon_L1137_); trivial. % 15.55/15.66 apply (zenon_or_s _ _ zenon_H170); [ zenon_intro zenon_H15d | zenon_intro zenon_H171 ]. % 15.55/15.66 apply (zenon_or_s _ _ zenon_H1f6); [ zenon_intro zenon_Hdb | zenon_intro zenon_H1f7 ]. % 15.55/15.66 apply (zenon_L69_); trivial. % 15.55/15.66 apply (zenon_or_s _ _ zenon_H1f7); [ zenon_intro zenon_H142 | zenon_intro zenon_H1f8 ]. % 15.55/15.66 apply (zenon_L1136_); trivial. % 15.55/15.66 apply (zenon_or_s _ _ zenon_H1f8); [ zenon_intro zenon_H167 | zenon_intro zenon_H40 ]. % 15.55/15.66 apply (zenon_L626_); trivial. % 15.55/15.66 exact (zenon_H3c zenon_H40). % 15.55/15.66 apply (zenon_or_s _ _ zenon_H171); [ zenon_intro zenon_H32 | zenon_intro zenon_H167 ]. % 15.55/15.66 exact (zenon_H2e zenon_H32). % 15.55/15.66 apply (zenon_L589_); trivial. % 15.55/15.66 (* end of lemma zenon_L1138_ *) % 15.55/15.66 assert (zenon_L1139_ : (((op (e1) (e0)) = (e0))\/(((op (e1) (e1)) = (e0))\/(((op (e1) (e2)) = (e0))\/((op (e1) (e3)) = (e0))))) -> ((op (e3) (e2)) = (e3)) -> (~((e0) = (e3))) -> (~((op (e2) (e2)) = (e0))) -> (((op (e3) (e0)) = (e0))\/(((op (e3) (e1)) = (e0))\/(((op (e3) (e2)) = (e0))\/((op (e3) (e3)) = (e0))))) -> (~((e0) = (e2))) -> ((op (e3) (e0)) = (e2)) -> (~((op (e1) (op (e3) (e1))) = (op (e3) (e1)))) -> (~((op (e1) (e2)) = (op (e3) (e2)))) -> (~((op (e0) (op (e3) (e0))) = (op (e3) (e0)))) -> (~((op (e0) (e2)) = (op (e3) (e2)))) -> (((op (e0) (e2)) = (e0))\/(((op (e1) (e2)) = (e0))\/(((op (e2) (e2)) = (e0))\/((op (e3) (e2)) = (e0))))) -> (~((op (e3) (e3)) = (e3))) -> (~((op (e3) (e3)) = (e1))) -> (~((op (e3) (e3)) = (e0))) -> (((op (e3) (e3)) = (e0))\/(((op (e3) (e3)) = (e1))\/(((op (e3) (e3)) = (e2))\/((op (e3) (e3)) = (e3))))) -> (~((op (e1) (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))))) -> (~((e0) = (e1))) -> ((op (e1) (e3)) = (e1)) -> False). % 15.55/15.66 do 0 intro. intros zenon_H163 zenon_H106 zenon_H4b zenon_H2e zenon_H1f6 zenon_H5e zenon_He9 zenon_H2b4 zenon_H17d zenon_H2b8 zenon_H140 zenon_H16f zenon_H3e zenon_H104 zenon_H3c zenon_H3b zenon_Hd6 zenon_H1b4 zenon_H145 zenon_H1b3 zenon_H9e zenon_H11f. % 15.55/15.66 apply (zenon_or_s _ _ zenon_H163); [ zenon_intro zenon_Had | zenon_intro zenon_H164 ]. % 15.55/15.66 apply (zenon_L1138_); trivial. % 15.55/15.66 apply (zenon_or_s _ _ zenon_H164); [ zenon_intro zenon_H149 | zenon_intro zenon_H165 ]. % 15.55/15.66 exact (zenon_H145 zenon_H149). % 15.55/15.66 apply (zenon_or_s _ _ zenon_H165); [ zenon_intro zenon_H15d | zenon_intro zenon_Hcc ]. % 15.55/15.66 apply (zenon_L490_); trivial. % 15.55/15.66 apply (zenon_L208_); trivial. % 15.55/15.66 (* end of lemma zenon_L1139_ *) % 15.55/15.66 assert (zenon_L1140_ : (((op (e3) (e0)) = (e0))\/(((op (e3) (e1)) = (e0))\/(((op (e3) (e2)) = (e0))\/((op (e3) (e3)) = (e0))))) -> (~((e0) = (e1))) -> ((op (e3) (e0)) = (e1)) -> ((op (e1) (e0)) = (e0)) -> (~((op (e1) (op (e3) (e1))) = (op (e3) (e1)))) -> ((op (e3) (e2)) = (e3)) -> (~((e0) = (e3))) -> (~((op (e3) (e3)) = (e0))) -> False). % 15.55/15.66 do 0 intro. intros zenon_H1f6 zenon_H9e zenon_Hee zenon_Had zenon_H2b4 zenon_H106 zenon_H4b zenon_H3c. % 15.55/15.67 apply (zenon_or_s _ _ zenon_H1f6); [ zenon_intro zenon_Hdb | zenon_intro zenon_H1f7 ]. % 15.55/15.67 apply (zenon_L71_); trivial. % 15.55/15.67 apply (zenon_or_s _ _ zenon_H1f7); [ zenon_intro zenon_H142 | zenon_intro zenon_H1f8 ]. % 15.55/15.67 apply (zenon_L1136_); trivial. % 15.55/15.67 apply (zenon_or_s _ _ zenon_H1f8); [ zenon_intro zenon_H167 | zenon_intro zenon_H40 ]. % 15.55/15.67 apply (zenon_L589_); trivial. % 15.55/15.67 exact (zenon_H3c zenon_H40). % 15.55/15.67 (* end of lemma zenon_L1140_ *) % 15.55/15.67 assert (zenon_L1141_ : (((op (e1) (e0)) = (e0))\/(((op (e1) (e1)) = (e0))\/(((op (e1) (e2)) = (e0))\/((op (e1) (e3)) = (e0))))) -> (~((e0) = (e3))) -> ((op (e3) (e2)) = (e3)) -> (~((op (e1) (op (e3) (e1))) = (op (e3) (e1)))) -> ((op (e3) (e0)) = (e1)) -> (((op (e3) (e0)) = (e0))\/(((op (e3) (e1)) = (e0))\/(((op (e3) (e2)) = (e0))\/((op (e3) (e3)) = (e0))))) -> (~((op (e3) (e3)) = (e3))) -> (~((op (e3) (e3)) = (e1))) -> (~((op (e3) (e3)) = (e0))) -> (((op (e3) (e3)) = (e0))\/(((op (e3) (e3)) = (e1))\/(((op (e3) (e3)) = (e2))\/((op (e3) (e3)) = (e3))))) -> (~((op (e1) (e1)) = (e2))) -> (~((op (e1) (e1)) = (e1))) -> (~((op (e1) (e1)) = (e0))) -> (((op (e1) (e1)) = (e0))\/(((op (e1) (e1)) = (e1))\/(((op (e1) (e1)) = (e2))\/((op (e1) (e1)) = (e3))))) -> (~((e0) = (e1))) -> ((op (e1) (e3)) = (e1)) -> False). % 15.55/15.67 do 0 intro. intros zenon_H163 zenon_H4b zenon_H106 zenon_H2b4 zenon_Hee zenon_H1f6 zenon_H3e zenon_H104 zenon_H3c zenon_H3b zenon_Hd6 zenon_H1b4 zenon_H145 zenon_H1b3 zenon_H9e zenon_H11f. % 15.55/15.67 apply (zenon_or_s _ _ zenon_H163); [ zenon_intro zenon_Had | zenon_intro zenon_H164 ]. % 15.55/15.67 apply (zenon_L1140_); trivial. % 15.55/15.67 apply (zenon_or_s _ _ zenon_H164); [ zenon_intro zenon_H149 | zenon_intro zenon_H165 ]. % 15.55/15.67 exact (zenon_H145 zenon_H149). % 15.55/15.67 apply (zenon_or_s _ _ zenon_H165); [ zenon_intro zenon_H15d | zenon_intro zenon_Hcc ]. % 15.55/15.67 apply (zenon_L490_); trivial. % 15.55/15.67 apply (zenon_L208_); trivial. % 15.55/15.67 (* end of lemma zenon_L1141_ *) % 15.55/15.67 assert (zenon_L1142_ : (((op (e1) (e0)) = (e0))\/(((op (e1) (e1)) = (e0))\/(((op (e1) (e2)) = (e0))\/((op (e1) (e3)) = (e0))))) -> (~((op (e0) (e0)) = (op (e1) (e0)))) -> (~((op (e1) (e1)) = (e0))) -> (~((op (e3) (e3)) = (e0))) -> (~((op (e1) (e2)) = (op (e3) (e2)))) -> (~((e0) = (e3))) -> ((op (e3) (e1)) = (e3)) -> (~((op (e0) (op (e3) (e0))) = (op (e3) (e0)))) -> ((op (e0) (e0)) = (e0)) -> (((op (e3) (e0)) = (e0))\/(((op (e3) (e1)) = (e0))\/(((op (e3) (e2)) = (e0))\/((op (e3) (e3)) = (e0))))) -> (~((e0) = (e1))) -> ((op (e1) (e3)) = (e1)) -> False). % 15.55/15.67 do 0 intro. intros zenon_H163 zenon_H24c zenon_H145 zenon_H3c zenon_H17d zenon_H4b zenon_H10a zenon_H2b8 zenon_H1f zenon_H1f6 zenon_H9e zenon_H11f. % 15.55/15.67 apply (zenon_or_s _ _ zenon_H163); [ zenon_intro zenon_Had | zenon_intro zenon_H164 ]. % 15.55/15.67 apply (zenon_L559_); trivial. % 15.55/15.67 apply (zenon_or_s _ _ zenon_H164); [ zenon_intro zenon_H149 | zenon_intro zenon_H165 ]. % 15.55/15.67 exact (zenon_H145 zenon_H149). % 15.55/15.67 apply (zenon_or_s _ _ zenon_H165); [ zenon_intro zenon_H15d | zenon_intro zenon_Hcc ]. % 15.55/15.67 apply (zenon_L1057_); trivial. % 15.55/15.67 apply (zenon_L208_); trivial. % 15.55/15.67 (* end of lemma zenon_L1142_ *) % 15.55/15.67 assert (zenon_L1143_ : ((~((op (e3) (e3)) = (e3)))\/((op (e3) (e3)) = (e3))) -> (~((op (e3) (op (e3) (e3))) = (op (e3) (e3)))) -> (~((op (e0) (e0)) = (op (e1) (e0)))) -> ((op (e0) (e0)) = (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)) = (e0))\/(((op (e3) (e3)) = (e1))\/(((op (e3) (e3)) = (e2))\/((op (e3) (e3)) = (e3))))) -> (~((op (e1) (e1)) = (e2))) -> (~((op (e1) (e1)) = (e1))) -> (~((op (e1) (e3)) = (op (e3) (e3)))) -> (((op (e1) (e0)) = (e0))\/(((op (e1) (e1)) = (e0))\/(((op (e1) (e2)) = (e0))\/((op (e1) (e3)) = (e0))))) -> (~((op (e0) (e0)) = (e1))) -> (((op (e0) (e2)) = (e0))\/(((op (e1) (e2)) = (e0))\/(((op (e2) (e2)) = (e0))\/((op (e3) (e2)) = (e0))))) -> (~((e0) = (e3))) -> (~((op (e2) (e2)) = (e0))) -> (~((op (e0) (op (e3) (e0))) = (op (e3) (e0)))) -> (((op (e3) (e0)) = (e1))\/(((op (e3) (e1)) = (e1))\/(((op (e3) (e2)) = (e1))\/((op (e3) (e3)) = (e1))))) -> (~((e1) = (e3))) -> (~((op (e1) (op (e3) (e1))) = (op (e3) (e1)))) -> (~((op (e1) (e0)) = (op (e3) (e0)))) -> (~((op (e1) (e2)) = (op (e3) (e2)))) -> (((op (e3) (e0)) = (e0))\/(((op (e3) (e1)) = (e0))\/(((op (e3) (e2)) = (e0))\/((op (e3) (e3)) = (e0))))) -> (~((op (e0) (e0)) = (op (e0) (e2)))) -> ((~((op (e2) (e2)) = (e2)))\/((op (e2) (e2)) = (e2))) -> (((op (e1) (e2)) = (e0))\/(((op (e1) (e2)) = (e1))\/(((op (e1) (e2)) = (e2))\/((op (e1) (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)) = (op (e2) (e2)))) -> (~((op (e0) (e2)) = (op (e2) (e2)))) -> (((op (e0) (e2)) = (e0))\/(((op (e0) (e2)) = (e1))\/(((op (e0) (e2)) = (e2))\/((op (e0) (e2)) = (e3))))) -> (~((op (e0) (e2)) = (op (e3) (e2)))) -> (((op (e3) (e2)) = (e0))\/(((op (e3) (e2)) = (e1))\/(((op (e3) (e2)) = (e2))\/((op (e3) (e2)) = (e3))))) -> (~((op (e2) (e1)) = (op (e2) (e2)))) -> (((op (e3) (e0)) = (e2))\/(((op (e3) (e1)) = (e2))\/(((op (e3) (e2)) = (e2))\/((op (e3) (e3)) = (e2))))) -> (~((e0) = (e1))) -> (~((op (e1) (e2)) = (op (e2) (e2)))) -> (~((op (e2) (e1)) = (op (e3) (e1)))) -> (~((op (e2) (e2)) = (op (e2) (e3)))) -> ((~((op (e1) (e1)) = (e1)))\/((op (e1) (e1)) = (e1))) -> (~((op (e1) (e0)) = (op (e1) (e1)))) -> ((~((op (e1) (e1)) = (e3)))\/((op (e1) (e3)) = (e1))) -> ((~((op (e2) (e2)) = (e1)))\/((op (e2) (e1)) = (e2))) -> ((~((op (e3) (e3)) = (e0)))\/((op (e3) (e0)) = (e3))) -> (~((op (e3) (e0)) = (op (e3) (e1)))) -> (((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)) = (e1))\/(((op (e2) (e1)) = (e1))\/(((op (e2) (e2)) = (e1))\/((op (e2) (e3)) = (e1))))) -> (~((op (e0) (e1)) = (op (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) (e3)) = (e0))\/(((op (e0) (e3)) = (e1))\/(((op (e0) (e3)) = (e2))\/((op (e0) (e3)) = (e3))))) -> (~((op (e0) (e3)) = (op (e1) (e3)))) -> (~((op (e0) (e3)) = (op (e2) (e3)))) -> (~((op (e0) (e0)) = (op (e0) (e3)))) -> (~((op (e0) (e2)) = (op (e0) (e3)))) -> (~((op (e1) (e0)) = (op (e1) (e2)))) -> (~((op (e2) (op (e3) (e2))) = (op (e3) (e2)))) -> (((op (e0) (e2)) = (e1))\/(((op (e1) (e2)) = (e1))\/(((op (e2) (e2)) = (e1))\/((op (e3) (e2)) = (e1))))) -> (((op (e2) (e0)) = (e3))\/(((op (e2) (e1)) = (e3))\/(((op (e2) (e2)) = (e3))\/((op (e2) (e3)) = (e3))))) -> (((op (e1) (e0)) = (e2))\/(((op (e1) (e1)) = (e2))\/(((op (e1) (e2)) = (e2))\/((op (e1) (e3)) = (e2))))) -> (~((op (e0) (e2)) = (op (e1) (e2)))) -> (((op (e0) (e1)) = (e2))\/(((op (e1) (e1)) = (e2))\/(((op (e2) (e1)) = (e2))\/((op (e3) (e1)) = (e2))))) -> (~((op (e2) (e0)) = (op (e2) (e1)))) -> (~((op (e1) (e0)) = (op (e2) (e0)))) -> (((op (e1) (e0)) = (e3))\/(((op (e1) (e1)) = (e3))\/(((op (e1) (e2)) = (e3))\/((op (e1) (e3)) = (e3))))) -> ((~((op (e2) (e2)) = (e3)))\/((op (e2) (e3)) = (e2))) -> (((op (e0) (e0)) = (e2))\/(((op (e1) (e0)) = (e2))\/(((op (e2) (e0)) = (e2))\/((op (e3) (e0)) = (e2))))) -> ((~((op (e2) (e2)) = (e0)))\/((op (e2) (e0)) = (e2))) -> ((~((op (e1) (e1)) = (e2)))\/((op (e1) (e2)) = (e1))) -> (~((op (e1) (e0)) = (op (e1) (e3)))) -> ((op (e1) (e3)) = (e1)) -> (~((e1) = (e2))) -> (((op (e2) (e2)) = (e0))\/(((op (e2) (e2)) = (e1))\/(((op (e2) (e2)) = (e2))\/((op (e2) (e2)) = (e3))))) -> (((op (e0) (e0)) = (e1))\/(((op (e1) (e0)) = (e1))\/(((op (e2) (e0)) = (e1))\/((op (e3) (e0)) = (e1))))) -> ((~((op (e3) (e3)) = (e2)))\/((op (e3) (e2)) = (e3))) -> (~((op (e3) (e1)) = (op (e3) (e2)))) -> (((op (e0) (e0)) = (e1))\/(((op (e0) (e1)) = (e1))\/(((op (e0) (e2)) = (e1))\/((op (e0) (e3)) = (e1))))) -> (~((op (e0) (e3)) = (op (e3) (e3)))) -> (~((op (e0) (e1)) = (op (e3) (e1)))) -> (~((e0) = (e2))) -> (~((op (e2) (e0)) = (op (e2) (e3)))) -> (((op (e0) (e3)) = (e2))\/(((op (e1) (e3)) = (e2))\/(((op (e2) (e3)) = (e2))\/((op (e3) (e3)) = (e2))))) -> (((op (e0) (e0)) = (e3))\/(((op (e0) (e1)) = (e3))\/(((op (e0) (e2)) = (e3))\/((op (e0) (e3)) = (e3))))) -> ((~((op (e3) (e3)) = (e1)))\/((op (e3) (e1)) = (e3))) -> (~((op (e0) (e0)) = (e3))) -> (~((e2) = (e3))) -> (~((op (e3) (e0)) = (op (e3) (e2)))) -> (((op (e0) (e0)) = (e3))\/(((op (e1) (e0)) = (e3))\/(((op (e2) (e0)) = (e3))\/((op (e3) (e0)) = (e3))))) -> (~((op (e0) (e0)) = (e2))) -> False). % 15.55/15.67 do 0 intro. intros zenon_H10d zenon_H2be zenon_H24c zenon_H1f zenon_H145 zenon_H1b3 zenon_H3c zenon_H3b zenon_Hd6 zenon_H1b4 zenon_H8b zenon_H163 zenon_H45 zenon_H16f zenon_H4b zenon_H2e zenon_H2b8 zenon_H146 zenon_Ha3 zenon_H2b4 zenon_H22e zenon_H17d zenon_H1f6 zenon_H250 zenon_Haa zenon_H1d5 zenon_H281 zenon_H258 zenon_H17a zenon_H28 zenon_H251 zenon_H140 zenon_H25e zenon_H157 zenon_H1df zenon_H9e zenon_H7d zenon_H13c zenon_H15f zenon_H1d8 zenon_Hd7 zenon_H1d2 zenon_H1e3 zenon_H10f zenon_H109 zenon_H8e zenon_H1e5 zenon_Hb7 zenon_Hde zenon_H121 zenon_H1cd zenon_H254 zenon_H80 zenon_Hb4 zenon_H24f zenon_Hc9 zenon_H166 zenon_H2af zenon_H11b zenon_He6 zenon_H84 zenon_H87 zenon_H1a2 zenon_H154 zenon_H247 zenon_H90 zenon_H1c3 zenon_Heb zenon_H1d4 zenon_H1d3 zenon_H1cf zenon_H11f zenon_Ha7 zenon_H2d zenon_Hf1 zenon_H10e zenon_H135 zenon_H44 zenon_H36 zenon_H138 zenon_H5e zenon_Hce zenon_H160 zenon_H58 zenon_H10c zenon_H59 zenon_H6a zenon_H105 zenon_Hbe zenon_H8f. % 15.55/15.67 apply (zenon_or_s _ _ zenon_H10c); [ zenon_intro zenon_H104 | zenon_intro zenon_H10a ]. % 15.55/15.67 apply (zenon_or_s _ _ zenon_H10e); [ zenon_intro zenon_H3d | zenon_intro zenon_H106 ]. % 15.55/15.67 apply (zenon_L1116_); trivial. % 15.55/15.67 apply (zenon_or_s _ _ zenon_H10d); [ zenon_intro zenon_H3e | zenon_intro zenon_H42 ]. % 15.55/15.67 apply (zenon_or_s _ _ zenon_Hf1); [ zenon_intro zenon_H47 | zenon_intro zenon_Hf4 ]. % 15.55/15.67 exact (zenon_H45 zenon_H47). % 15.55/15.67 apply (zenon_or_s _ _ zenon_Hf4); [ zenon_intro zenon_Hd8 | zenon_intro zenon_Hf5 ]. % 15.55/15.67 apply (zenon_L1050_); trivial. % 15.55/15.67 apply (zenon_or_s _ _ zenon_Hf5); [ zenon_intro zenon_Hae | zenon_intro zenon_Hee ]. % 15.55/15.67 apply (zenon_or_s _ _ zenon_Heb); [ zenon_intro zenon_H92 | zenon_intro zenon_Hec ]. % 15.55/15.67 exact (zenon_H8f zenon_H92). % 15.55/15.67 apply (zenon_or_s _ _ zenon_Hec); [ zenon_intro zenon_H68 | zenon_intro zenon_Hed ]. % 15.55/15.67 apply (zenon_L528_); trivial. % 15.55/15.67 apply (zenon_or_s _ _ zenon_Hed); [ zenon_intro zenon_Hdd | zenon_intro zenon_He9 ]. % 15.55/15.67 apply (zenon_L1134_); trivial. % 15.55/15.67 apply (zenon_L1139_); trivial. % 15.55/15.67 apply (zenon_L1141_); trivial. % 15.55/15.67 apply (zenon_L1041_); trivial. % 15.55/15.67 apply (zenon_L1142_); trivial. % 15.55/15.67 (* end of lemma zenon_L1143_ *) % 15.55/15.67 assert (zenon_L1144_ : (~((op (e0) (e0)) = (e2))) -> (((op (e1) (e1)) = (e0))\/(((op (e1) (e1)) = (e1))\/(((op (e1) (e1)) = (e2))\/((op (e1) (e1)) = (e3))))) -> (~((op (e3) (e3)) = (e1))) -> (~((op (e3) (e3)) = (e2))) -> (((op (e3) (e3)) = (e0))\/(((op (e3) (e3)) = (e1))\/(((op (e3) (e3)) = (e2))\/((op (e3) (e3)) = (e3))))) -> (~((op (e1) (e1)) = (e2))) -> (~((op (e1) (e1)) = (e1))) -> (~((op (e1) (e1)) = (e0))) -> (((op (e0) (e0)) = (e1))\/(((op (e1) (e0)) = (e1))\/(((op (e2) (e0)) = (e1))\/((op (e3) (e0)) = (e1))))) -> ((op (e3) (e0)) = (e3)) -> ((~((op (e1) (e1)) = (e2)))\/((op (e1) (e2)) = (e1))) -> ((~((op (e2) (e2)) = (e0)))\/((op (e2) (e0)) = (e2))) -> (~((op (e0) (e0)) = (op (e0) (e2)))) -> (((op (e3) (e0)) = (e0))\/(((op (e3) (e1)) = (e0))\/(((op (e3) (e2)) = (e0))\/((op (e3) (e3)) = (e0))))) -> (~((op (e1) (e2)) = (op (e3) (e2)))) -> (~((op (e1) (e0)) = (op (e3) (e0)))) -> (((op (e3) (e0)) = (e1))\/(((op (e3) (e1)) = (e1))\/(((op (e3) (e2)) = (e1))\/((op (e3) (e3)) = (e1))))) -> (~((e0) = (e3))) -> (((op (e0) (e2)) = (e0))\/(((op (e1) (e2)) = (e0))\/(((op (e2) (e2)) = (e0))\/((op (e3) (e2)) = (e0))))) -> (((op (e0) (e0)) = (e2))\/(((op (e1) (e0)) = (e2))\/(((op (e2) (e0)) = (e2))\/((op (e3) (e0)) = (e2))))) -> ((~((op (e2) (e2)) = (e3)))\/((op (e2) (e3)) = (e2))) -> (~((op (e2) (e0)) = (op (e2) (e3)))) -> ((~((op (e3) (e3)) = (e1)))\/((op (e3) (e1)) = (e3))) -> (~((op (e0) (e1)) = (op (e3) (e1)))) -> (~((op (e3) (e1)) = (op (e3) (e2)))) -> ((~((op (e3) (e3)) = (e3)))\/((op (e3) (e3)) = (e3))) -> (~((op (e3) (op (e3) (e3))) = (op (e3) (e3)))) -> (((op (e0) (e0)) = (e3))\/(((op (e0) (e1)) = (e3))\/(((op (e0) (e2)) = (e3))\/((op (e0) (e3)) = (e3))))) -> (~((op (e0) (op (e3) (e0))) = (op (e3) (e0)))) -> (((op (e0) (e0)) = (e3))\/(((op (e1) (e0)) = (e3))\/(((op (e2) (e0)) = (e3))\/((op (e3) (e0)) = (e3))))) -> (((op (e1) (e0)) = (e3))\/(((op (e1) (e1)) = (e3))\/(((op (e1) (e2)) = (e3))\/((op (e1) (e3)) = (e3))))) -> (~((op (e1) (e0)) = (op (e2) (e0)))) -> (~((op (e2) (e0)) = (op (e2) (e1)))) -> (~((op (e1) (op (e3) (e1))) = (op (e3) (e1)))) -> (((op (e0) (e1)) = (e2))\/(((op (e1) (e1)) = (e2))\/(((op (e2) (e1)) = (e2))\/((op (e3) (e1)) = (e2))))) -> (~((op (e0) (e2)) = (op (e1) (e2)))) -> (~((e1) = (e3))) -> (((op (e1) (e0)) = (e2))\/(((op (e1) (e1)) = (e2))\/(((op (e1) (e2)) = (e2))\/((op (e1) (e3)) = (e2))))) -> (((op (e2) (e0)) = (e3))\/(((op (e2) (e1)) = (e3))\/(((op (e2) (e2)) = (e3))\/((op (e2) (e3)) = (e3))))) -> (((op (e0) (e2)) = (e1))\/(((op (e1) (e2)) = (e1))\/(((op (e2) (e2)) = (e1))\/((op (e3) (e2)) = (e1))))) -> (~((op (e2) (op (e3) (e2))) = (op (e3) (e2)))) -> (~((op (e1) (e0)) = (op (e1) (e2)))) -> (~((op (e0) (e2)) = (op (e0) (e3)))) -> (~((op (e1) (e0)) = (op (e1) (e3)))) -> (((op (e0) (e3)) = (e2))\/(((op (e1) (e3)) = (e2))\/(((op (e2) (e3)) = (e2))\/((op (e3) (e3)) = (e2))))) -> (~((op (e0) (e0)) = (op (e0) (e3)))) -> ((op (e0) (e0)) = (e0)) -> (~((op (e0) (e3)) = (op (e2) (e3)))) -> (~((op (e0) (e3)) = (op (e1) (e3)))) -> (((op (e0) (e3)) = (e0))\/(((op (e0) (e3)) = (e1))\/(((op (e0) (e3)) = (e2))\/((op (e0) (e3)) = (e3))))) -> (~((op (e0) (e1)) = (op (e0) (e3)))) -> (((op (e0) (e3)) = (e1))\/(((op (e1) (e3)) = (e1))\/(((op (e2) (e3)) = (e1))\/((op (e3) (e3)) = (e1))))) -> (~((op (e0) (e1)) = (op (e2) (e1)))) -> (~((e2) = (e3))) -> (((op (e2) (e0)) = (e1))\/(((op (e2) (e1)) = (e1))\/(((op (e2) (e2)) = (e1))\/((op (e2) (e3)) = (e1))))) -> (~((op (e0) (e0)) = (e3))) -> (~((op (e2) (e0)) = (op (e3) (e0)))) -> (~((op (e0) (e3)) = (op (e3) (e3)))) -> (((op (e0) (e0)) = (e2))\/(((op (e0) (e1)) = (e2))\/(((op (e0) (e2)) = (e2))\/((op (e0) (e3)) = (e2))))) -> (~((op (e3) (e0)) = (op (e3) (e2)))) -> ((~((op (e3) (e3)) = (e2)))\/((op (e3) (e2)) = (e3))) -> (~((op (e3) (e0)) = (op (e3) (e1)))) -> ((~((op (e3) (e3)) = (e0)))\/((op (e3) (e0)) = (e3))) -> ((~((op (e2) (e2)) = (e1)))\/((op (e2) (e1)) = (e2))) -> (~((e1) = (e2))) -> ((~((op (e1) (e1)) = (e3)))\/((op (e1) (e3)) = (e1))) -> (~((op (e1) (e0)) = (op (e1) (e1)))) -> ((~((op (e1) (e1)) = (e1)))\/((op (e1) (e1)) = (e1))) -> (~((op (e0) (e0)) = (e1))) -> False). % 15.55/15.67 do 0 intro. intros zenon_H8f zenon_H1b3 zenon_H104 zenon_H3d zenon_H3b zenon_Hd6 zenon_H1b4 zenon_H145 zenon_Hf1 zenon_Hba zenon_H1d3 zenon_H1d4 zenon_H250 zenon_H1f6 zenon_H17d zenon_H22e zenon_H146 zenon_H4b zenon_H16f zenon_Heb zenon_H1c3 zenon_Hce zenon_H10c zenon_H138 zenon_H135 zenon_H10d zenon_H2be zenon_H58 zenon_H2b8 zenon_Hbe zenon_H90 zenon_H247 zenon_H154 zenon_H2b4 zenon_H1a2 zenon_H87 zenon_Ha3 zenon_H84 zenon_He6 zenon_H11b zenon_H2af zenon_H166 zenon_Hc9 zenon_H1cf zenon_H160 zenon_H24f zenon_H1f zenon_Hb4 zenon_H80 zenon_H254 zenon_H1cd zenon_H121 zenon_Hde zenon_H6a zenon_Hb7 zenon_H59 zenon_H1e5 zenon_H36 zenon_H8e zenon_H105 zenon_H10e zenon_H109 zenon_H10f zenon_H1e3 zenon_Ha7 zenon_H1d2 zenon_Hd7 zenon_H1d8 zenon_H45. % 15.55/15.67 apply (zenon_or_s _ _ zenon_H10d); [ zenon_intro zenon_H3e | zenon_intro zenon_H42 ]. % 15.55/15.67 apply (zenon_or_s _ _ zenon_Heb); [ zenon_intro zenon_H92 | zenon_intro zenon_Hec ]. % 15.55/15.67 exact (zenon_H8f zenon_H92). % 15.55/15.67 apply (zenon_or_s _ _ zenon_Hec); [ zenon_intro zenon_H68 | zenon_intro zenon_Hed ]. % 15.55/15.67 apply (zenon_L357_); trivial. % 15.55/15.67 apply (zenon_or_s _ _ zenon_Hed); [ zenon_intro zenon_Hdd | zenon_intro zenon_He9 ]. % 15.55/15.67 apply (zenon_L1113_); trivial. % 15.55/15.67 apply (zenon_L220_); trivial. % 15.55/15.67 apply (zenon_L1041_); trivial. % 15.55/15.67 (* end of lemma zenon_L1144_ *) % 15.55/15.67 assert (zenon_L1145_ : (~((op (e0) (e0)) = (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 (e1) (e1)) = (e2))) -> (~((op (e1) (e1)) = (e1))) -> (~((op (e1) (e1)) = (e0))) -> (((op (e0) (e0)) = (e1))\/(((op (e1) (e0)) = (e1))\/(((op (e2) (e0)) = (e1))\/((op (e3) (e0)) = (e1))))) -> ((op (e3) (e0)) = (e3)) -> ((~((op (e1) (e1)) = (e2)))\/((op (e1) (e2)) = (e1))) -> ((~((op (e2) (e2)) = (e0)))\/((op (e2) (e0)) = (e2))) -> (~((op (e0) (e0)) = (op (e0) (e2)))) -> (((op (e3) (e0)) = (e0))\/(((op (e3) (e1)) = (e0))\/(((op (e3) (e2)) = (e0))\/((op (e3) (e3)) = (e0))))) -> (~((op (e1) (e2)) = (op (e3) (e2)))) -> (~((op (e1) (e0)) = (op (e3) (e0)))) -> (((op (e3) (e0)) = (e1))\/(((op (e3) (e1)) = (e1))\/(((op (e3) (e2)) = (e1))\/((op (e3) (e3)) = (e1))))) -> (~((e0) = (e3))) -> (((op (e0) (e2)) = (e0))\/(((op (e1) (e2)) = (e0))\/(((op (e2) (e2)) = (e0))\/((op (e3) (e2)) = (e0))))) -> (((op (e0) (e0)) = (e2))\/(((op (e1) (e0)) = (e2))\/(((op (e2) (e0)) = (e2))\/((op (e3) (e0)) = (e2))))) -> ((~((op (e2) (e2)) = (e3)))\/((op (e2) (e3)) = (e2))) -> (~((op (e2) (e0)) = (op (e2) (e3)))) -> ((~((op (e3) (e3)) = (e1)))\/((op (e3) (e1)) = (e3))) -> (~((op (e0) (e1)) = (op (e3) (e1)))) -> (~((op (e3) (e1)) = (op (e3) (e2)))) -> ((~((op (e3) (e3)) = (e3)))\/((op (e3) (e3)) = (e3))) -> (~((op (e3) (op (e3) (e3))) = (op (e3) (e3)))) -> (((op (e0) (e0)) = (e3))\/(((op (e0) (e1)) = (e3))\/(((op (e0) (e2)) = (e3))\/((op (e0) (e3)) = (e3))))) -> (~((op (e0) (op (e3) (e0))) = (op (e3) (e0)))) -> (((op (e0) (e0)) = (e3))\/(((op (e1) (e0)) = (e3))\/(((op (e2) (e0)) = (e3))\/((op (e3) (e0)) = (e3))))) -> (((op (e1) (e0)) = (e3))\/(((op (e1) (e1)) = (e3))\/(((op (e1) (e2)) = (e3))\/((op (e1) (e3)) = (e3))))) -> (~((op (e1) (e0)) = (op (e2) (e0)))) -> (~((op (e2) (e0)) = (op (e2) (e1)))) -> (~((op (e1) (op (e3) (e1))) = (op (e3) (e1)))) -> (((op (e0) (e1)) = (e2))\/(((op (e1) (e1)) = (e2))\/(((op (e2) (e1)) = (e2))\/((op (e3) (e1)) = (e2))))) -> (~((op (e0) (e2)) = (op (e1) (e2)))) -> (~((e1) = (e3))) -> (((op (e1) (e0)) = (e2))\/(((op (e1) (e1)) = (e2))\/(((op (e1) (e2)) = (e2))\/((op (e1) (e3)) = (e2))))) -> (((op (e2) (e0)) = (e3))\/(((op (e2) (e1)) = (e3))\/(((op (e2) (e2)) = (e3))\/((op (e2) (e3)) = (e3))))) -> (((op (e0) (e2)) = (e1))\/(((op (e1) (e2)) = (e1))\/(((op (e2) (e2)) = (e1))\/((op (e3) (e2)) = (e1))))) -> (~((op (e2) (op (e3) (e2))) = (op (e3) (e2)))) -> (~((op (e1) (e0)) = (op (e1) (e2)))) -> (~((op (e0) (e2)) = (op (e0) (e3)))) -> (~((op (e1) (e0)) = (op (e1) (e3)))) -> (((op (e0) (e3)) = (e2))\/(((op (e1) (e3)) = (e2))\/(((op (e2) (e3)) = (e2))\/((op (e3) (e3)) = (e2))))) -> (~((op (e0) (e0)) = (op (e0) (e3)))) -> ((op (e0) (e0)) = (e0)) -> (~((op (e0) (e3)) = (op (e2) (e3)))) -> (~((op (e0) (e3)) = (op (e1) (e3)))) -> (((op (e0) (e3)) = (e0))\/(((op (e0) (e3)) = (e1))\/(((op (e0) (e3)) = (e2))\/((op (e0) (e3)) = (e3))))) -> (~((op (e0) (e1)) = (op (e0) (e3)))) -> (((op (e0) (e3)) = (e1))\/(((op (e1) (e3)) = (e1))\/(((op (e2) (e3)) = (e1))\/((op (e3) (e3)) = (e1))))) -> (~((op (e0) (e1)) = (op (e2) (e1)))) -> (~((e2) = (e3))) -> (((op (e2) (e0)) = (e1))\/(((op (e2) (e1)) = (e1))\/(((op (e2) (e2)) = (e1))\/((op (e2) (e3)) = (e1))))) -> (~((op (e0) (e0)) = (e3))) -> (~((op (e2) (e0)) = (op (e3) (e0)))) -> (~((op (e0) (e3)) = (op (e3) (e3)))) -> (((op (e0) (e0)) = (e2))\/(((op (e0) (e1)) = (e2))\/(((op (e0) (e2)) = (e2))\/((op (e0) (e3)) = (e2))))) -> (~((op (e3) (e0)) = (op (e3) (e2)))) -> ((~((op (e3) (e3)) = (e2)))\/((op (e3) (e2)) = (e3))) -> (~((op (e3) (e0)) = (op (e3) (e1)))) -> ((~((op (e3) (e3)) = (e0)))\/((op (e3) (e0)) = (e3))) -> ((~((op (e2) (e2)) = (e1)))\/((op (e2) (e1)) = (e2))) -> (~((e1) = (e2))) -> ((~((op (e1) (e1)) = (e3)))\/((op (e1) (e3)) = (e1))) -> (~((op (e1) (e0)) = (op (e1) (e1)))) -> ((~((op (e1) (e1)) = (e1)))\/((op (e1) (e1)) = (e1))) -> (~((op (e0) (e0)) = (e1))) -> False). % 15.55/15.67 do 0 intro. intros zenon_H8f zenon_H1b3 zenon_H3b zenon_Hd6 zenon_H1b4 zenon_H145 zenon_Hf1 zenon_Hba zenon_H1d3 zenon_H1d4 zenon_H250 zenon_H1f6 zenon_H17d zenon_H22e zenon_H146 zenon_H4b zenon_H16f zenon_Heb zenon_H1c3 zenon_Hce zenon_H10c zenon_H138 zenon_H135 zenon_H10d zenon_H2be zenon_H58 zenon_H2b8 zenon_Hbe zenon_H90 zenon_H247 zenon_H154 zenon_H2b4 zenon_H1a2 zenon_H87 zenon_Ha3 zenon_H84 zenon_He6 zenon_H11b zenon_H2af zenon_H166 zenon_Hc9 zenon_H1cf zenon_H160 zenon_H24f zenon_H1f zenon_Hb4 zenon_H80 zenon_H254 zenon_H1cd zenon_H121 zenon_Hde zenon_H6a zenon_Hb7 zenon_H59 zenon_H1e5 zenon_H36 zenon_H8e zenon_H105 zenon_H10e zenon_H109 zenon_H10f zenon_H1e3 zenon_Ha7 zenon_H1d2 zenon_Hd7 zenon_H1d8 zenon_H45. % 15.55/15.67 apply (zenon_or_s _ _ zenon_H10c); [ zenon_intro zenon_H104 | zenon_intro zenon_H10a ]. % 15.55/15.67 apply (zenon_or_s _ _ zenon_H10e); [ zenon_intro zenon_H3d | zenon_intro zenon_H106 ]. % 15.55/15.67 apply (zenon_L1144_); trivial. % 15.55/15.67 apply (zenon_L81_); trivial. % 15.55/15.67 apply (zenon_L82_); trivial. % 15.55/15.67 (* end of lemma zenon_L1145_ *) % 15.55/15.67 assert (zenon_L1146_ : ((~((op (e3) (e3)) = (e3)))\/((op (e3) (e3)) = (e3))) -> (~((op (e3) (op (e3) (e3))) = (op (e3) (e3)))) -> (~((op (e0) (e0)) = (op (e1) (e0)))) -> ((op (e0) (e0)) = (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 (e1) (e1)) = (e2))) -> (~((op (e1) (e1)) = (e1))) -> (~((op (e1) (e3)) = (op (e3) (e3)))) -> (((op (e1) (e0)) = (e0))\/(((op (e1) (e1)) = (e0))\/(((op (e1) (e2)) = (e0))\/((op (e1) (e3)) = (e0))))) -> (~((op (e0) (e0)) = (e1))) -> (((op (e0) (e2)) = (e0))\/(((op (e1) (e2)) = (e0))\/(((op (e2) (e2)) = (e0))\/((op (e3) (e2)) = (e0))))) -> (~((e0) = (e3))) -> (~((op (e0) (op (e3) (e0))) = (op (e3) (e0)))) -> (((op (e3) (e0)) = (e1))\/(((op (e3) (e1)) = (e1))\/(((op (e3) (e2)) = (e1))\/((op (e3) (e3)) = (e1))))) -> (~((e1) = (e3))) -> (~((op (e1) (op (e3) (e1))) = (op (e3) (e1)))) -> (~((op (e1) (e0)) = (op (e3) (e0)))) -> (~((op (e1) (e2)) = (op (e3) (e2)))) -> (((op (e3) (e0)) = (e0))\/(((op (e3) (e1)) = (e0))\/(((op (e3) (e2)) = (e0))\/((op (e3) (e3)) = (e0))))) -> (~((op (e0) (e0)) = (op (e0) (e2)))) -> ((~((op (e2) (e2)) = (e2)))\/((op (e2) (e2)) = (e2))) -> (((op (e1) (e2)) = (e0))\/(((op (e1) (e2)) = (e1))\/(((op (e1) (e2)) = (e2))\/((op (e1) (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)) = (op (e2) (e2)))) -> (~((op (e0) (e2)) = (op (e2) (e2)))) -> (((op (e0) (e2)) = (e0))\/(((op (e0) (e2)) = (e1))\/(((op (e0) (e2)) = (e2))\/((op (e0) (e2)) = (e3))))) -> (~((op (e0) (e2)) = (op (e3) (e2)))) -> (((op (e3) (e2)) = (e0))\/(((op (e3) (e2)) = (e1))\/(((op (e3) (e2)) = (e2))\/((op (e3) (e2)) = (e3))))) -> (~((op (e2) (e1)) = (op (e2) (e2)))) -> (((op (e3) (e0)) = (e2))\/(((op (e3) (e1)) = (e2))\/(((op (e3) (e2)) = (e2))\/((op (e3) (e3)) = (e2))))) -> (~((e0) = (e1))) -> (~((op (e1) (e2)) = (op (e2) (e2)))) -> (~((op (e2) (e1)) = (op (e3) (e1)))) -> (~((op (e2) (e2)) = (op (e2) (e3)))) -> ((~((op (e1) (e1)) = (e1)))\/((op (e1) (e1)) = (e1))) -> (~((op (e1) (e0)) = (op (e1) (e1)))) -> ((~((op (e1) (e1)) = (e3)))\/((op (e1) (e3)) = (e1))) -> ((~((op (e2) (e2)) = (e1)))\/((op (e2) (e1)) = (e2))) -> ((~((op (e3) (e3)) = (e0)))\/((op (e3) (e0)) = (e3))) -> (~((op (e3) (e0)) = (op (e3) (e1)))) -> (((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)) = (e1))\/(((op (e2) (e1)) = (e1))\/(((op (e2) (e2)) = (e1))\/((op (e2) (e3)) = (e1))))) -> (~((op (e0) (e1)) = (op (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) (e3)) = (e0))\/(((op (e0) (e3)) = (e1))\/(((op (e0) (e3)) = (e2))\/((op (e0) (e3)) = (e3))))) -> (~((op (e0) (e3)) = (op (e1) (e3)))) -> (~((op (e0) (e3)) = (op (e2) (e3)))) -> (~((op (e0) (e0)) = (op (e0) (e3)))) -> (~((op (e0) (e2)) = (op (e0) (e3)))) -> (~((op (e1) (e0)) = (op (e1) (e2)))) -> (~((op (e2) (op (e3) (e2))) = (op (e3) (e2)))) -> (((op (e0) (e2)) = (e1))\/(((op (e1) (e2)) = (e1))\/(((op (e2) (e2)) = (e1))\/((op (e3) (e2)) = (e1))))) -> (((op (e2) (e0)) = (e3))\/(((op (e2) (e1)) = (e3))\/(((op (e2) (e2)) = (e3))\/((op (e2) (e3)) = (e3))))) -> (((op (e1) (e0)) = (e2))\/(((op (e1) (e1)) = (e2))\/(((op (e1) (e2)) = (e2))\/((op (e1) (e3)) = (e2))))) -> (~((op (e0) (e2)) = (op (e1) (e2)))) -> (((op (e0) (e1)) = (e2))\/(((op (e1) (e1)) = (e2))\/(((op (e2) (e1)) = (e2))\/((op (e3) (e1)) = (e2))))) -> (~((op (e2) (e0)) = (op (e2) (e1)))) -> (~((op (e1) (e0)) = (op (e2) (e0)))) -> (((op (e1) (e0)) = (e3))\/(((op (e1) (e1)) = (e3))\/(((op (e1) (e2)) = (e3))\/((op (e1) (e3)) = (e3))))) -> ((~((op (e2) (e2)) = (e3)))\/((op (e2) (e3)) = (e2))) -> (((op (e0) (e0)) = (e2))\/(((op (e1) (e0)) = (e2))\/(((op (e2) (e0)) = (e2))\/((op (e3) (e0)) = (e2))))) -> ((~((op (e2) (e2)) = (e0)))\/((op (e2) (e0)) = (e2))) -> ((~((op (e1) (e1)) = (e2)))\/((op (e1) (e2)) = (e1))) -> (~((op (e1) (e0)) = (op (e1) (e3)))) -> ((op (e1) (e3)) = (e1)) -> (~((e1) = (e2))) -> (((op (e2) (e2)) = (e0))\/(((op (e2) (e2)) = (e1))\/(((op (e2) (e2)) = (e2))\/((op (e2) (e2)) = (e3))))) -> (((op (e0) (e0)) = (e1))\/(((op (e1) (e0)) = (e1))\/(((op (e2) (e0)) = (e1))\/((op (e3) (e0)) = (e1))))) -> ((~((op (e3) (e3)) = (e2)))\/((op (e3) (e2)) = (e3))) -> (~((op (e3) (e1)) = (op (e3) (e2)))) -> (((op (e0) (e0)) = (e1))\/(((op (e0) (e1)) = (e1))\/(((op (e0) (e2)) = (e1))\/((op (e0) (e3)) = (e1))))) -> (~((op (e0) (e3)) = (op (e3) (e3)))) -> (~((op (e0) (e1)) = (op (e3) (e1)))) -> (~((e0) = (e2))) -> (~((op (e2) (e0)) = (op (e2) (e3)))) -> (((op (e0) (e3)) = (e2))\/(((op (e1) (e3)) = (e2))\/(((op (e2) (e3)) = (e2))\/((op (e3) (e3)) = (e2))))) -> (((op (e0) (e0)) = (e3))\/(((op (e0) (e1)) = (e3))\/(((op (e0) (e2)) = (e3))\/((op (e0) (e3)) = (e3))))) -> ((~((op (e3) (e3)) = (e1)))\/((op (e3) (e1)) = (e3))) -> (~((op (e0) (e0)) = (e3))) -> (~((e2) = (e3))) -> (~((op (e3) (e0)) = (op (e3) (e2)))) -> (((op (e0) (e0)) = (e3))\/(((op (e1) (e0)) = (e3))\/(((op (e2) (e0)) = (e3))\/((op (e3) (e0)) = (e3))))) -> (~((op (e0) (e0)) = (e2))) -> False). % 15.55/15.67 do 0 intro. intros zenon_H10d zenon_H2be zenon_H24c zenon_H1f zenon_H145 zenon_H1b3 zenon_H3b zenon_Hd6 zenon_H1b4 zenon_H8b zenon_H163 zenon_H45 zenon_H16f zenon_H4b zenon_H2b8 zenon_H146 zenon_Ha3 zenon_H2b4 zenon_H22e zenon_H17d zenon_H1f6 zenon_H250 zenon_Haa zenon_H1d5 zenon_H281 zenon_H258 zenon_H17a zenon_H28 zenon_H251 zenon_H140 zenon_H25e zenon_H157 zenon_H1df zenon_H9e zenon_H7d zenon_H13c zenon_H15f zenon_H1d8 zenon_Hd7 zenon_H1d2 zenon_H1e3 zenon_H10f zenon_H109 zenon_H8e zenon_H1e5 zenon_Hb7 zenon_Hde zenon_H121 zenon_H1cd zenon_H254 zenon_H80 zenon_Hb4 zenon_H24f zenon_Hc9 zenon_H166 zenon_H2af zenon_H11b zenon_He6 zenon_H84 zenon_H87 zenon_H1a2 zenon_H154 zenon_H247 zenon_H90 zenon_H1c3 zenon_Heb zenon_H1d4 zenon_H1d3 zenon_H1cf zenon_H11f zenon_Ha7 zenon_H2d zenon_Hf1 zenon_H10e zenon_H135 zenon_H44 zenon_H36 zenon_H138 zenon_H5e zenon_Hce zenon_H160 zenon_H58 zenon_H10c zenon_H59 zenon_H6a zenon_H105 zenon_Hbe zenon_H8f. % 15.55/15.67 apply (zenon_or_s _ _ zenon_H1d4); [ zenon_intro zenon_H2e | zenon_intro zenon_Hdd ]. % 15.55/15.67 apply (zenon_or_s _ _ zenon_H10f); [ zenon_intro zenon_H3c | zenon_intro zenon_Hba ]. % 15.55/15.67 apply (zenon_L1143_); trivial. % 15.55/15.67 apply (zenon_L1145_); trivial. % 15.55/15.67 apply (zenon_L1134_); trivial. % 15.55/15.67 (* end of lemma zenon_L1146_ *) % 15.55/15.67 assert (zenon_L1147_ : (((op (e1) (e0)) = (e1))\/(((op (e1) (e1)) = (e1))\/(((op (e1) (e2)) = (e1))\/((op (e1) (e3)) = (e1))))) -> (~((op (e2) (e2)) = (e0))) -> (~((op (e3) (e3)) = (e0))) -> (~((op (e1) (e1)) = (e3))) -> (~((op (e2) (e2)) = (e1))) -> (((op (e0) (e2)) = (e3))\/(((op (e1) (e2)) = (e3))\/(((op (e2) (e2)) = (e3))\/((op (e3) (e2)) = (e3))))) -> (~((op (e0) (e1)) = (op (e1) (e1)))) -> (~((op (e1) (e2)) = (op (e1) (e3)))) -> (((op (e0) (e3)) = (e0))\/(((op (e1) (e3)) = (e0))\/(((op (e2) (e3)) = (e0))\/((op (e3) (e3)) = (e0))))) -> (~((op (e2) (e1)) = (op (e2) (e3)))) -> ((~((op (e3) (e3)) = (e3)))\/((op (e3) (e3)) = (e3))) -> (~((op (e3) (op (e3) (e3))) = (op (e3) (e3)))) -> (~((op (e0) (e0)) = (op (e1) (e0)))) -> ((op (e0) (e0)) = (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 (e1) (e1)) = (e2))) -> (~((op (e1) (e1)) = (e1))) -> (~((op (e1) (e3)) = (op (e3) (e3)))) -> (((op (e1) (e0)) = (e0))\/(((op (e1) (e1)) = (e0))\/(((op (e1) (e2)) = (e0))\/((op (e1) (e3)) = (e0))))) -> (~((op (e0) (e0)) = (e1))) -> (((op (e0) (e2)) = (e0))\/(((op (e1) (e2)) = (e0))\/(((op (e2) (e2)) = (e0))\/((op (e3) (e2)) = (e0))))) -> (~((e0) = (e3))) -> (~((op (e0) (op (e3) (e0))) = (op (e3) (e0)))) -> (((op (e3) (e0)) = (e1))\/(((op (e3) (e1)) = (e1))\/(((op (e3) (e2)) = (e1))\/((op (e3) (e3)) = (e1))))) -> (~((e1) = (e3))) -> (~((op (e1) (op (e3) (e1))) = (op (e3) (e1)))) -> (~((op (e1) (e0)) = (op (e3) (e0)))) -> (~((op (e1) (e2)) = (op (e3) (e2)))) -> (((op (e3) (e0)) = (e0))\/(((op (e3) (e1)) = (e0))\/(((op (e3) (e2)) = (e0))\/((op (e3) (e3)) = (e0))))) -> (~((op (e0) (e0)) = (op (e0) (e2)))) -> ((~((op (e2) (e2)) = (e2)))\/((op (e2) (e2)) = (e2))) -> (((op (e1) (e2)) = (e0))\/(((op (e1) (e2)) = (e1))\/(((op (e1) (e2)) = (e2))\/((op (e1) (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)) = (op (e2) (e2)))) -> (~((op (e0) (e2)) = (op (e2) (e2)))) -> (((op (e0) (e2)) = (e0))\/(((op (e0) (e2)) = (e1))\/(((op (e0) (e2)) = (e2))\/((op (e0) (e2)) = (e3))))) -> (~((op (e0) (e2)) = (op (e3) (e2)))) -> (((op (e3) (e2)) = (e0))\/(((op (e3) (e2)) = (e1))\/(((op (e3) (e2)) = (e2))\/((op (e3) (e2)) = (e3))))) -> (~((op (e2) (e1)) = (op (e2) (e2)))) -> (((op (e3) (e0)) = (e2))\/(((op (e3) (e1)) = (e2))\/(((op (e3) (e2)) = (e2))\/((op (e3) (e3)) = (e2))))) -> (~((e0) = (e1))) -> (~((op (e1) (e2)) = (op (e2) (e2)))) -> (~((op (e2) (e1)) = (op (e3) (e1)))) -> (~((op (e2) (e2)) = (op (e2) (e3)))) -> ((~((op (e1) (e1)) = (e1)))\/((op (e1) (e1)) = (e1))) -> (~((op (e1) (e0)) = (op (e1) (e1)))) -> ((~((op (e1) (e1)) = (e3)))\/((op (e1) (e3)) = (e1))) -> ((~((op (e2) (e2)) = (e1)))\/((op (e2) (e1)) = (e2))) -> ((~((op (e3) (e3)) = (e0)))\/((op (e3) (e0)) = (e3))) -> (~((op (e3) (e0)) = (op (e3) (e1)))) -> (((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)) = (e1))\/(((op (e2) (e1)) = (e1))\/(((op (e2) (e2)) = (e1))\/((op (e2) (e3)) = (e1))))) -> (~((op (e0) (e1)) = (op (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) (e3)) = (e0))\/(((op (e0) (e3)) = (e1))\/(((op (e0) (e3)) = (e2))\/((op (e0) (e3)) = (e3))))) -> (~((op (e0) (e3)) = (op (e1) (e3)))) -> (~((op (e0) (e3)) = (op (e2) (e3)))) -> (~((op (e0) (e0)) = (op (e0) (e3)))) -> (~((op (e0) (e2)) = (op (e0) (e3)))) -> (~((op (e1) (e0)) = (op (e1) (e2)))) -> (~((op (e2) (op (e3) (e2))) = (op (e3) (e2)))) -> (((op (e0) (e2)) = (e1))\/(((op (e1) (e2)) = (e1))\/(((op (e2) (e2)) = (e1))\/((op (e3) (e2)) = (e1))))) -> (((op (e2) (e0)) = (e3))\/(((op (e2) (e1)) = (e3))\/(((op (e2) (e2)) = (e3))\/((op (e2) (e3)) = (e3))))) -> (((op (e1) (e0)) = (e2))\/(((op (e1) (e1)) = (e2))\/(((op (e1) (e2)) = (e2))\/((op (e1) (e3)) = (e2))))) -> (~((op (e0) (e2)) = (op (e1) (e2)))) -> (((op (e0) (e1)) = (e2))\/(((op (e1) (e1)) = (e2))\/(((op (e2) (e1)) = (e2))\/((op (e3) (e1)) = (e2))))) -> (~((op (e2) (e0)) = (op (e2) (e1)))) -> (~((op (e1) (e0)) = (op (e2) (e0)))) -> (((op (e1) (e0)) = (e3))\/(((op (e1) (e1)) = (e3))\/(((op (e1) (e2)) = (e3))\/((op (e1) (e3)) = (e3))))) -> ((~((op (e2) (e2)) = (e3)))\/((op (e2) (e3)) = (e2))) -> (((op (e0) (e0)) = (e2))\/(((op (e1) (e0)) = (e2))\/(((op (e2) (e0)) = (e2))\/((op (e3) (e0)) = (e2))))) -> ((~((op (e2) (e2)) = (e0)))\/((op (e2) (e0)) = (e2))) -> ((~((op (e1) (e1)) = (e2)))\/((op (e1) (e2)) = (e1))) -> (~((op (e1) (e0)) = (op (e1) (e3)))) -> (~((e1) = (e2))) -> (((op (e2) (e2)) = (e0))\/(((op (e2) (e2)) = (e1))\/(((op (e2) (e2)) = (e2))\/((op (e2) (e2)) = (e3))))) -> (((op (e0) (e0)) = (e1))\/(((op (e1) (e0)) = (e1))\/(((op (e2) (e0)) = (e1))\/((op (e3) (e0)) = (e1))))) -> ((~((op (e3) (e3)) = (e2)))\/((op (e3) (e2)) = (e3))) -> (~((op (e3) (e1)) = (op (e3) (e2)))) -> (((op (e0) (e0)) = (e1))\/(((op (e0) (e1)) = (e1))\/(((op (e0) (e2)) = (e1))\/((op (e0) (e3)) = (e1))))) -> (~((op (e0) (e3)) = (op (e3) (e3)))) -> (~((op (e0) (e1)) = (op (e3) (e1)))) -> (~((e0) = (e2))) -> (~((op (e2) (e0)) = (op (e2) (e3)))) -> (((op (e0) (e3)) = (e2))\/(((op (e1) (e3)) = (e2))\/(((op (e2) (e3)) = (e2))\/((op (e3) (e3)) = (e2))))) -> (((op (e0) (e0)) = (e3))\/(((op (e0) (e1)) = (e3))\/(((op (e0) (e2)) = (e3))\/((op (e0) (e3)) = (e3))))) -> ((~((op (e3) (e3)) = (e1)))\/((op (e3) (e1)) = (e3))) -> (~((op (e0) (e0)) = (e3))) -> (~((e2) = (e3))) -> (~((op (e3) (e0)) = (op (e3) (e2)))) -> (((op (e0) (e0)) = (e3))\/(((op (e1) (e0)) = (e3))\/(((op (e2) (e0)) = (e3))\/((op (e3) (e0)) = (e3))))) -> (~((op (e0) (e0)) = (e2))) -> False). % 15.55/15.67 do 0 intro. intros zenon_H1c5 zenon_H2e zenon_H3c zenon_H182 zenon_H52 zenon_H175 zenon_H23 zenon_H1d0 zenon_Hd3 zenon_H1e2 zenon_H10d zenon_H2be zenon_H24c zenon_H1f zenon_H145 zenon_H1b3 zenon_H3b zenon_Hd6 zenon_H1b4 zenon_H8b zenon_H163 zenon_H45 zenon_H16f zenon_H4b zenon_H2b8 zenon_H146 zenon_Ha3 zenon_H2b4 zenon_H22e zenon_H17d zenon_H1f6 zenon_H250 zenon_Haa zenon_H1d5 zenon_H281 zenon_H258 zenon_H17a zenon_H28 zenon_H251 zenon_H140 zenon_H25e zenon_H157 zenon_H1df zenon_H9e zenon_H7d zenon_H13c zenon_H15f zenon_H1d8 zenon_Hd7 zenon_H1d2 zenon_H1e3 zenon_H10f zenon_H109 zenon_H8e zenon_H1e5 zenon_Hb7 zenon_Hde zenon_H121 zenon_H1cd zenon_H254 zenon_H80 zenon_Hb4 zenon_H24f zenon_Hc9 zenon_H166 zenon_H2af zenon_H11b zenon_He6 zenon_H84 zenon_H87 zenon_H1a2 zenon_H154 zenon_H247 zenon_H90 zenon_H1c3 zenon_Heb zenon_H1d4 zenon_H1d3 zenon_H1cf zenon_Ha7 zenon_H2d zenon_Hf1 zenon_H10e zenon_H135 zenon_H44 zenon_H36 zenon_H138 zenon_H5e zenon_Hce zenon_H160 zenon_H58 zenon_H10c zenon_H59 zenon_H6a zenon_H105 zenon_Hbe zenon_H8f. % 15.55/15.67 apply (zenon_or_s _ _ zenon_H1c5); [ zenon_intro zenon_Hd8 | zenon_intro zenon_H1c6 ]. % 15.55/15.67 apply (zenon_L1053_); trivial. % 15.55/15.67 apply (zenon_or_s _ _ zenon_H1c6); [ zenon_intro zenon_H21 | zenon_intro zenon_H1c7 ]. % 15.55/15.67 exact (zenon_H1b4 zenon_H21). % 15.55/15.67 apply (zenon_or_s _ _ zenon_H1c7); [ zenon_intro zenon_H117 | zenon_intro zenon_H11f ]. % 15.55/15.67 apply (zenon_L1115_); trivial. % 15.55/15.67 apply (zenon_L1146_); trivial. % 15.55/15.67 (* end of lemma zenon_L1147_ *) % 15.55/15.67 assert (zenon_L1148_ : (((op (e0) (e0)) = (e3))\/(((op (e0) (e1)) = (e3))\/(((op (e0) (e2)) = (e3))\/((op (e0) (e3)) = (e3))))) -> (~((op (e0) (e0)) = (e3))) -> (~((op (e2) (op (e3) (e2))) = (op (e3) (e2)))) -> (~((op (e2) (e2)) = (e3))) -> (~((op (e0) (e1)) = (op (e2) (e1)))) -> ((op (e2) (e0)) = (e1)) -> (~((e1) = (e3))) -> (((op (e2) (e0)) = (e3))\/(((op (e2) (e1)) = (e3))\/(((op (e2) (e2)) = (e3))\/((op (e2) (e3)) = (e3))))) -> (~((op (e0) (e2)) = (op (e3) (e2)))) -> (((op (e1) (e0)) = (e3))\/(((op (e1) (e1)) = (e3))\/(((op (e1) (e2)) = (e3))\/((op (e1) (e3)) = (e3))))) -> (~((e2) = (e3))) -> ((op (e1) (e0)) = (e2)) -> (~((op (e1) (e1)) = (e3))) -> (~((op (e1) (e2)) = (op (e3) (e2)))) -> ((op (e3) (e2)) = (e3)) -> (~((op (e0) (e3)) = (op (e1) (e3)))) -> False). % 15.55/15.67 do 0 intro. intros zenon_H58 zenon_H59 zenon_H2af zenon_H30 zenon_Hde zenon_Hae zenon_Ha3 zenon_He6 zenon_H140 zenon_H90 zenon_H6a zenon_H68 zenon_H182 zenon_H17d zenon_H106 zenon_H80. % 15.55/15.67 apply (zenon_or_s _ _ zenon_H58); [ zenon_intro zenon_H5b | zenon_intro zenon_H5a ]. % 15.55/15.67 exact (zenon_H59 zenon_H5b). % 15.55/15.67 apply (zenon_or_s _ _ zenon_H5a); [ zenon_intro zenon_H4a | zenon_intro zenon_H5c ]. % 15.55/15.67 apply (zenon_L1102_); trivial. % 15.55/15.67 apply (zenon_or_s _ _ zenon_H5c); [ zenon_intro zenon_H50 | zenon_intro zenon_H53 ]. % 15.55/15.67 apply (zenon_L533_); trivial. % 15.55/15.67 apply (zenon_L294_); trivial. % 15.55/15.67 (* end of lemma zenon_L1148_ *) % 15.55/15.67 assert (zenon_L1149_ : (((op (e2) (e3)) = (e0))\/(((op (e2) (e3)) = (e1))\/(((op (e2) (e3)) = (e2))\/((op (e2) (e3)) = (e3))))) -> ((op (e1) (e3)) = (e0)) -> (~((op (e1) (e3)) = (op (e2) (e3)))) -> ((op (e1) (e3)) = (e3)) -> (~((op (e0) (e3)) = (op (e1) (e3)))) -> (~((op (e0) (e3)) = (op (e3) (e3)))) -> ((op (e3) (e3)) = (e2)) -> (~((op (e0) (e3)) = (op (e2) (e3)))) -> (~((op (e0) (e0)) = (op (e0) (e3)))) -> ((op (e0) (e0)) = (e0)) -> (((op (e0) (e3)) = (e0))\/(((op (e0) (e3)) = (e1))\/(((op (e0) (e3)) = (e2))\/((op (e0) (e3)) = (e3))))) -> ((op (e2) (e1)) = (e2)) -> (~((op (e2) (e1)) = (op (e2) (e3)))) -> (~((op (e2) (op (e3) (e2))) = (op (e3) (e2)))) -> ((op (e3) (e2)) = (e3)) -> False). % 15.55/15.67 do 0 intro. intros zenon_H2ab zenon_Hcc zenon_H244 zenon_H8a zenon_H80 zenon_H36 zenon_H43 zenon_Hb4 zenon_H24f zenon_H1f zenon_H254 zenon_H156 zenon_H1e2 zenon_H2af zenon_H106. % 15.55/15.67 apply (zenon_or_s _ _ zenon_H2ab); [ zenon_intro zenon_Hd0 | zenon_intro zenon_H2ac ]. % 15.55/15.67 apply (zenon_L599_); trivial. % 15.55/15.67 apply (zenon_or_s _ _ zenon_H2ac); [ zenon_intro zenon_Hb5 | zenon_intro zenon_H2ad ]. % 15.55/15.67 apply (zenon_L903_); trivial. % 15.55/15.67 apply (zenon_or_s _ _ zenon_H2ad); [ zenon_intro zenon_H124 | zenon_intro zenon_He2 ]. % 15.55/15.67 apply (zenon_L256_); trivial. % 15.55/15.67 apply (zenon_L1065_); trivial. % 15.55/15.67 (* end of lemma zenon_L1149_ *) % 15.55/15.67 assert (zenon_L1150_ : (((op (e0) (e3)) = (e2))\/(((op (e1) (e3)) = (e2))\/(((op (e2) (e3)) = (e2))\/((op (e3) (e3)) = (e2))))) -> (~((e1) = (e2))) -> (~((e0) = (e2))) -> (((op (e0) (e3)) = (e3))\/(((op (e1) (e3)) = (e3))\/(((op (e2) (e3)) = (e3))\/((op (e3) (e3)) = (e3))))) -> (~((e1) = (e3))) -> ((op (e0) (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 (e0) (e0)) = (e0)) -> (~((op (e0) (e0)) = (op (e0) (e3)))) -> (~((op (e0) (e3)) = (op (e2) (e3)))) -> (~((op (e0) (e3)) = (op (e3) (e3)))) -> (~((op (e0) (e3)) = (op (e1) (e3)))) -> (~((op (e1) (e3)) = (op (e2) (e3)))) -> ((op (e1) (e3)) = (e0)) -> (((op (e2) (e3)) = (e0))\/(((op (e2) (e3)) = (e1))\/(((op (e2) (e3)) = (e2))\/((op (e2) (e3)) = (e3))))) -> ((op (e3) (e2)) = (e3)) -> (~((op (e2) (op (e3) (e2))) = (op (e3) (e2)))) -> (~((op (e3) (e3)) = (e3))) -> False). % 15.55/15.67 do 0 intro. intros zenon_H160 zenon_Ha7 zenon_H5e zenon_H2d0 zenon_Ha3 zenon_H37 zenon_H1e2 zenon_H156 zenon_H254 zenon_H1f zenon_H24f zenon_Hb4 zenon_H36 zenon_H80 zenon_H244 zenon_Hcc zenon_H2ab zenon_H106 zenon_H2af zenon_H3e. % 15.55/15.67 apply (zenon_or_s _ _ zenon_H160); [ zenon_intro zenon_H81 | zenon_intro zenon_H161 ]. % 15.55/15.67 apply (zenon_L33_); trivial. % 15.55/15.67 apply (zenon_or_s _ _ zenon_H161); [ zenon_intro zenon_H82 | zenon_intro zenon_H162 ]. % 15.55/15.67 apply (zenon_L54_); trivial. % 15.55/15.67 apply (zenon_or_s _ _ zenon_H162); [ zenon_intro zenon_H124 | zenon_intro zenon_H43 ]. % 15.55/15.67 apply (zenon_L256_); trivial. % 15.55/15.67 apply (zenon_or_s _ _ zenon_H2d0); [ zenon_intro zenon_H53 | zenon_intro zenon_H2d1 ]. % 15.55/15.67 apply (zenon_L32_); trivial. % 15.55/15.67 apply (zenon_or_s _ _ zenon_H2d1); [ zenon_intro zenon_H8a | zenon_intro zenon_H2d2 ]. % 15.55/15.67 apply (zenon_L1149_); trivial. % 15.55/15.67 apply (zenon_or_s _ _ zenon_H2d2); [ zenon_intro zenon_He2 | zenon_intro zenon_H42 ]. % 15.55/15.67 apply (zenon_L1065_); trivial. % 15.55/15.67 exact (zenon_H3e zenon_H42). % 15.55/15.67 (* end of lemma zenon_L1150_ *) % 15.55/15.67 assert (zenon_L1151_ : (((op (e0) (e0)) = (e1))\/(((op (e1) (e0)) = (e1))\/(((op (e2) (e0)) = (e1))\/((op (e3) (e0)) = (e1))))) -> (~((op (e0) (e0)) = (e1))) -> (~((op (e2) (e2)) = (e0))) -> (~((op (e0) (op (e3) (e0))) = (op (e3) (e0)))) -> (~((op (e1) (e0)) = (op (e3) (e0)))) -> (((op (e3) (e0)) = (e1))\/(((op (e3) (e1)) = (e1))\/(((op (e3) (e2)) = (e1))\/((op (e3) (e3)) = (e1))))) -> (~((op (e1) (e2)) = (op (e3) (e2)))) -> (~((op (e0) (e0)) = (op (e0) (e2)))) -> (((op (e0) (e2)) = (e0))\/(((op (e1) (e2)) = (e0))\/(((op (e2) (e2)) = (e0))\/((op (e3) (e2)) = (e0))))) -> (~((op (e0) (e2)) = (op (e3) (e2)))) -> (((op (e2) (e0)) = (e3))\/(((op (e2) (e1)) = (e3))\/(((op (e2) (e2)) = (e3))\/((op (e2) (e3)) = (e3))))) -> (~((op (e0) (e1)) = (op (e2) (e1)))) -> (~((op (e2) (e2)) = (e3))) -> (~((op (e0) (e0)) = (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))))) -> (~((e0) = (e3))) -> (~((op (e1) (op (e3) (e1))) = (op (e3) (e1)))) -> (~((e0) = (e1))) -> (((op (e3) (e0)) = (e0))\/(((op (e3) (e1)) = (e0))\/(((op (e3) (e2)) = (e0))\/((op (e3) (e3)) = (e0))))) -> (~((op (e3) (e3)) = (e1))) -> (~((op (e3) (e3)) = (e0))) -> (((op (e3) (e3)) = (e0))\/(((op (e3) (e3)) = (e1))\/(((op (e3) (e3)) = (e2))\/((op (e3) (e3)) = (e3))))) -> (~((op (e1) (e1)) = (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) (e3)) = (e2))\/(((op (e1) (e3)) = (e2))\/(((op (e2) (e3)) = (e2))\/((op (e3) (e3)) = (e2))))) -> (~((e1) = (e2))) -> (~((e0) = (e2))) -> (((op (e0) (e3)) = (e3))\/(((op (e1) (e3)) = (e3))\/(((op (e2) (e3)) = (e3))\/((op (e3) (e3)) = (e3))))) -> (~((e1) = (e3))) -> ((op (e0) (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 (e0) (e0)) = (e0)) -> (~((op (e0) (e0)) = (op (e0) (e3)))) -> (~((op (e0) (e3)) = (op (e2) (e3)))) -> (~((op (e0) (e3)) = (op (e3) (e3)))) -> (~((op (e0) (e3)) = (op (e1) (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) (e2)) = (e3)) -> (~((op (e2) (op (e3) (e2))) = (op (e3) (e2)))) -> (~((op (e3) (e3)) = (e3))) -> False). % 15.55/15.67 do 0 intro. intros zenon_Hf1 zenon_H45 zenon_H2e zenon_H2b8 zenon_H22e zenon_H146 zenon_H17d zenon_H250 zenon_H16f zenon_H140 zenon_He6 zenon_Hde zenon_H30 zenon_H59 zenon_H58 zenon_H163 zenon_H4b zenon_H2b4 zenon_H9e zenon_H1f6 zenon_H104 zenon_H3c zenon_H3b zenon_Hd6 zenon_H1b4 zenon_H145 zenon_H1b3 zenon_H160 zenon_Ha7 zenon_H5e zenon_H2d0 zenon_Ha3 zenon_H37 zenon_H1e2 zenon_H156 zenon_H254 zenon_H1f zenon_H24f zenon_Hb4 zenon_H36 zenon_H80 zenon_H244 zenon_H2ab zenon_H106 zenon_H2af zenon_H3e. % 15.55/15.67 apply (zenon_or_s _ _ zenon_Hf1); [ zenon_intro zenon_H47 | zenon_intro zenon_Hf4 ]. % 15.55/15.67 exact (zenon_H45 zenon_H47). % 15.55/15.67 apply (zenon_or_s _ _ zenon_Hf4); [ zenon_intro zenon_Hd8 | zenon_intro zenon_Hf5 ]. % 15.55/15.67 apply (zenon_L1050_); trivial. % 15.55/15.67 apply (zenon_or_s _ _ zenon_Hf5); [ zenon_intro zenon_Hae | zenon_intro zenon_Hee ]. % 15.55/15.67 apply (zenon_L1110_); trivial. % 15.55/15.67 apply (zenon_or_s _ _ zenon_H163); [ zenon_intro zenon_Had | zenon_intro zenon_H164 ]. % 15.55/15.67 apply (zenon_L1140_); trivial. % 15.55/15.67 apply (zenon_or_s _ _ zenon_H164); [ zenon_intro zenon_H149 | zenon_intro zenon_H165 ]. % 15.55/15.67 exact (zenon_H145 zenon_H149). % 15.55/15.67 apply (zenon_or_s _ _ zenon_H165); [ zenon_intro zenon_H15d | zenon_intro zenon_Hcc ]. % 15.55/15.67 apply (zenon_L490_); trivial. % 15.55/15.67 apply (zenon_L1150_); trivial. % 15.55/15.67 (* end of lemma zenon_L1151_ *) % 15.55/15.67 assert (zenon_L1152_ : ((~((op (e3) (e3)) = (e3)))\/((op (e3) (e3)) = (e3))) -> (~((op (e3) (op (e3) (e3))) = (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) (e2)) = (e3)) -> (~((op (e3) (e0)) = (op (e3) (e2)))) -> ((op (e2) (e0)) = (e2)) -> (~((e2) = (e3))) -> (~((e1) = (e3))) -> (~((op (e0) (e0)) = (e3))) -> (~((e1) = (e2))) -> (((op (e2) (e2)) = (e0))\/(((op (e2) (e2)) = (e1))\/(((op (e2) (e2)) = (e2))\/((op (e2) (e2)) = (e3))))) -> (~((op (e2) (e2)) = (e3))) -> (~((op (e2) (e2)) = (e2))) -> (~((op (e2) (e2)) = (e1))) -> (~((op (e3) (e3)) = (e0))) -> (~((op (e3) (e3)) = (e1))) -> (((op (e3) (e3)) = (e0))\/(((op (e3) (e3)) = (e1))\/(((op (e3) (e3)) = (e2))\/((op (e3) (e3)) = (e3))))) -> (((op (e0) (e0)) = (e1))\/(((op (e1) (e0)) = (e1))\/(((op (e2) (e0)) = (e1))\/((op (e3) (e0)) = (e1))))) -> False). % 15.55/15.67 do 0 intro. intros zenon_H10d zenon_H2be zenon_H45 zenon_Hbe zenon_H106 zenon_H105 zenon_Hdd zenon_H6a zenon_Ha3 zenon_H59 zenon_Ha7 zenon_H2d zenon_H30 zenon_H2f zenon_H52 zenon_H3c zenon_H104 zenon_H3b zenon_Hf1. % 15.55/15.67 apply (zenon_or_s _ _ zenon_H10d); [ zenon_intro zenon_H3e | zenon_intro zenon_H42 ]. % 15.55/15.67 apply (zenon_L457_); trivial. % 15.55/15.67 apply (zenon_L1041_); trivial. % 15.55/15.67 (* end of lemma zenon_L1152_ *) % 15.55/15.67 assert (zenon_L1153_ : (((op (e1) (e0)) = (e2))\/(((op (e1) (e1)) = (e2))\/(((op (e1) (e2)) = (e2))\/((op (e1) (e3)) = (e2))))) -> (~((e1) = (e2))) -> ((op (e1) (e0)) = (e1)) -> (~((op (e1) (e1)) = (e2))) -> (~((op (e1) (e2)) = (op (e2) (e2)))) -> ((op (e2) (e2)) = (e2)) -> ((op (e1) (e3)) = (e0)) -> (~((e0) = (e2))) -> False). % 15.55/15.67 do 0 intro. intros zenon_H84 zenon_Ha7 zenon_Hd8 zenon_Hd6 zenon_H7d zenon_H35 zenon_Hcc zenon_H5e. % 15.55/15.67 apply (zenon_or_s _ _ zenon_H84); [ zenon_intro zenon_H68 | zenon_intro zenon_H85 ]. % 15.55/15.67 apply (zenon_L162_); trivial. % 15.55/15.67 apply (zenon_or_s _ _ zenon_H85); [ zenon_intro zenon_H6e | zenon_intro zenon_H86 ]. % 15.55/15.67 exact (zenon_Hd6 zenon_H6e). % 15.55/15.67 apply (zenon_or_s _ _ zenon_H86); [ zenon_intro zenon_H7c | zenon_intro zenon_H82 ]. % 15.55/15.67 apply (zenon_L21_); trivial. % 15.55/15.67 apply (zenon_L54_); trivial. % 15.55/15.67 (* end of lemma zenon_L1153_ *) % 15.55/15.67 assert (zenon_L1154_ : (((op (e1) (e0)) = (e1))\/(((op (e1) (e1)) = (e1))\/(((op (e1) (e2)) = (e1))\/((op (e1) (e3)) = (e1))))) -> (~((e0) = (e2))) -> (~((op (e1) (e1)) = (e2))) -> (((op (e1) (e0)) = (e3))\/(((op (e1) (e1)) = (e3))\/(((op (e1) (e2)) = (e3))\/((op (e1) (e3)) = (e3))))) -> (~((op (e0) (e0)) = (op (e0) (e3)))) -> (~((op (e0) (e3)) = (op (e2) (e3)))) -> (~((op (e0) (e3)) = (op (e1) (e3)))) -> (((op (e0) (e3)) = (e0))\/(((op (e0) (e3)) = (e1))\/(((op (e0) (e3)) = (e2))\/((op (e0) (e3)) = (e3))))) -> (~((op (e1) (e1)) = (e3))) -> (~((e2) = (e3))) -> (~((op (e0) (e0)) = (op (e0) (e2)))) -> (~((op (e0) (e2)) = (op (e3) (e2)))) -> (((op (e0) (e2)) = (e0))\/(((op (e0) (e2)) = (e1))\/(((op (e0) (e2)) = (e2))\/((op (e0) (e2)) = (e3))))) -> (((op (e0) (e0)) = (e1))\/(((op (e0) (e1)) = (e1))\/(((op (e0) (e2)) = (e1))\/((op (e0) (e3)) = (e1))))) -> ((~((op (e1) (e1)) = (e2)))\/((op (e1) (e2)) = (e1))) -> ((~((op (e3) (e3)) = (e0)))\/((op (e3) (e0)) = (e3))) -> (~((op (e0) (e0)) = (op (e2) (e0)))) -> (~((op (e1) (e0)) = (op (e2) (e0)))) -> (~((op (e2) (e0)) = (op (e3) (e0)))) -> (((op (e2) (e0)) = (e0))\/(((op (e2) (e0)) = (e1))\/(((op (e2) (e0)) = (e2))\/((op (e2) (e0)) = (e3))))) -> ((~((op (e3) (e3)) = (e2)))\/((op (e3) (e2)) = (e3))) -> (~((op (e1) (e0)) = (op (e3) (e0)))) -> (((op (e1) (e2)) = (e0))\/(((op (e1) (e2)) = (e1))\/(((op (e1) (e2)) = (e2))\/((op (e1) (e2)) = (e3))))) -> (~((op (e1) (e2)) = (op (e2) (e2)))) -> ((op (e0) (e0)) = (e0)) -> (~((op (e1) (op (e3) (e1))) = (op (e3) (e1)))) -> (~((op (e1) (e2)) = (op (e3) (e2)))) -> (((op (e3) (e0)) = (e0))\/(((op (e3) (e1)) = (e0))\/(((op (e3) (e2)) = (e0))\/((op (e3) (e3)) = (e0))))) -> (~((e1) = (e3))) -> (((op (e3) (e0)) = (e1))\/(((op (e3) (e1)) = (e1))\/(((op (e3) (e2)) = (e1))\/((op (e3) (e3)) = (e1))))) -> (((op (e0) (e0)) = (e2))\/(((op (e1) (e0)) = (e2))\/(((op (e2) (e0)) = (e2))\/((op (e3) (e0)) = (e2))))) -> (~((op (e1) (e1)) = (e1))) -> (((op (e1) (e1)) = (e0))\/(((op (e1) (e1)) = (e1))\/(((op (e1) (e1)) = (e2))\/((op (e1) (e1)) = (e3))))) -> ((op (e2) (e2)) = (e2)) -> (~((op (e2) (e0)) = (op (e2) (e2)))) -> (~((e1) = (e2))) -> (~((op (e0) (e0)) = (e2))) -> (~((op (e3) (op (e3) (e3))) = (op (e3) (e3)))) -> ((~((op (e3) (e3)) = (e3)))\/((op (e3) (e3)) = (e3))) -> (~((op (e3) (e1)) = (op (e3) (e2)))) -> ((~((op (e3) (e3)) = (e1)))\/((op (e3) (e1)) = (e3))) -> (~((op (e1) (e0)) = (op (e1) (e3)))) -> ((~((op (e1) (e1)) = (e3)))\/((op (e1) (e3)) = (e1))) -> (~((op (e0) (e2)) = (op (e0) (e3)))) -> (((op (e0) (e0)) = (e2))\/(((op (e0) (e1)) = (e2))\/(((op (e0) (e2)) = (e2))\/((op (e0) (e3)) = (e2))))) -> (~((op (e0) (e2)) = (op (e2) (e2)))) -> (~((op (e0) (e1)) = (op (e3) (e1)))) -> (~((op (e2) (op (e3) (e2))) = (op (e3) (e2)))) -> (((op (e3) (e0)) = (e2))\/(((op (e3) (e1)) = (e2))\/(((op (e3) (e2)) = (e2))\/((op (e3) (e3)) = (e2))))) -> (~((op (e1) (e0)) = (op (e1) (e2)))) -> (((op (e0) (e3)) = (e1))\/(((op (e1) (e3)) = (e1))\/(((op (e2) (e3)) = (e1))\/((op (e3) (e3)) = (e1))))) -> (~((op (e2) (e0)) = (op (e2) (e3)))) -> (~((op (e1) (e2)) = (op (e1) (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) (op (e3) (e0))) = (op (e3) (e0)))) -> (((op (e0) (e0)) = (e1))\/(((op (e1) (e0)) = (e1))\/(((op (e2) (e0)) = (e1))\/((op (e3) (e0)) = (e1))))) -> (~((op (e0) (e0)) = (e1))) -> (((op (e0) (e0)) = (e3))\/(((op (e0) (e1)) = (e3))\/(((op (e0) (e2)) = (e3))\/((op (e0) (e3)) = (e3))))) -> (~((op (e3) (e0)) = (op (e3) (e1)))) -> (~((op (e3) (e0)) = (op (e3) (e2)))) -> (~((op (e0) (e0)) = (e3))) -> (((op (e1) (e0)) = (e2))\/(((op (e1) (e1)) = (e2))\/(((op (e1) (e2)) = (e2))\/((op (e1) (e3)) = (e2))))) -> (~((op (e2) (e1)) = (op (e3) (e1)))) -> (((op (e2) (e0)) = (e3))\/(((op (e2) (e1)) = (e3))\/(((op (e2) (e2)) = (e3))\/((op (e2) (e3)) = (e3))))) -> (~((e0) = (e3))) -> (~((op (e2) (e2)) = (e0))) -> (((op (e0) (e2)) = (e0))\/(((op (e1) (e2)) = (e0))\/(((op (e2) (e2)) = (e0))\/((op (e3) (e2)) = (e0))))) -> (((op (e0) (e0)) = (e3))\/(((op (e1) (e0)) = (e3))\/(((op (e2) (e0)) = (e3))\/((op (e3) (e0)) = (e3))))) -> (~((op (e2) (e2)) = (op (e2) (e3)))) -> ((~((op (e2) (e2)) = (e3)))\/((op (e2) (e3)) = (e2))) -> (~((e0) = (e1))) -> ((op (e1) (e3)) = (e0)) -> False). % 15.55/15.67 do 0 intro. intros zenon_H1c5 zenon_H5e zenon_Hd6 zenon_H90 zenon_H24f zenon_Hb4 zenon_H80 zenon_H254 zenon_H182 zenon_H6a zenon_H250 zenon_H140 zenon_H251 zenon_H44 zenon_H1d3 zenon_H10f zenon_H258 zenon_H247 zenon_H1e5 zenon_H281 zenon_H10e zenon_H22e zenon_H1d5 zenon_H7d zenon_H1f zenon_H2b4 zenon_H17d zenon_H1f6 zenon_Ha3 zenon_H146 zenon_Heb zenon_H1b4 zenon_H1b3 zenon_H35 zenon_H17a zenon_Ha7 zenon_H8f zenon_H2be zenon_H10d zenon_H135 zenon_H10c zenon_H1cf zenon_H1d2 zenon_Hc9 zenon_H8e zenon_H28 zenon_H138 zenon_H2af zenon_H1df zenon_H166 zenon_H121 zenon_Hce zenon_H1d0 zenon_H36 zenon_H3b zenon_H2b8 zenon_Hf1 zenon_H45 zenon_H58 zenon_H109 zenon_H105 zenon_H59 zenon_H84 zenon_H13c zenon_He6 zenon_H4b zenon_H2e zenon_H16f zenon_Hbe zenon_H15f zenon_H1c3 zenon_H9e zenon_Hcc. % 15.55/15.67 apply (zenon_or_s _ _ zenon_H1c5); [ zenon_intro zenon_Hd8 | zenon_intro zenon_H1c6 ]. % 15.55/15.67 apply (zenon_L1153_); trivial. % 15.55/15.67 apply (zenon_or_s _ _ zenon_H1c6); [ zenon_intro zenon_H21 | zenon_intro zenon_H1c7 ]. % 15.55/15.67 exact (zenon_H1b4 zenon_H21). % 15.55/15.67 apply (zenon_or_s _ _ zenon_H1c7); [ zenon_intro zenon_H117 | zenon_intro zenon_H11f ]. % 15.55/15.67 apply (zenon_L1100_); trivial. % 15.55/15.67 apply (zenon_L208_); trivial. % 15.55/15.67 (* end of lemma zenon_L1154_ *) % 15.55/15.67 assert (zenon_L1155_ : (~((e0) = (e1))) -> ((~((op (e2) (e2)) = (e3)))\/((op (e2) (e3)) = (e2))) -> (~((op (e2) (e2)) = (op (e2) (e3)))) -> (((op (e0) (e0)) = (e3))\/(((op (e1) (e0)) = (e3))\/(((op (e2) (e0)) = (e3))\/((op (e3) (e0)) = (e3))))) -> (((op (e0) (e2)) = (e0))\/(((op (e1) (e2)) = (e0))\/(((op (e2) (e2)) = (e0))\/((op (e3) (e2)) = (e0))))) -> (~((op (e2) (e2)) = (e0))) -> (~((e0) = (e3))) -> (((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)) = (e2))\/(((op (e1) (e1)) = (e2))\/(((op (e1) (e2)) = (e2))\/((op (e1) (e3)) = (e2))))) -> (~((op (e0) (e0)) = (e3))) -> (~((op (e3) (e0)) = (op (e3) (e2)))) -> (~((op (e3) (e0)) = (op (e3) (e1)))) -> (((op (e0) (e0)) = (e3))\/(((op (e0) (e1)) = (e3))\/(((op (e0) (e2)) = (e3))\/((op (e0) (e3)) = (e3))))) -> (~((op (e0) (e0)) = (e1))) -> (((op (e0) (e0)) = (e1))\/(((op (e1) (e0)) = (e1))\/(((op (e2) (e0)) = (e1))\/((op (e3) (e0)) = (e1))))) -> (~((op (e0) (op (e3) (e0))) = (op (e3) (e0)))) -> (((op (e3) (e3)) = (e0))\/(((op (e3) (e3)) = (e1))\/(((op (e3) (e3)) = (e2))\/((op (e3) (e3)) = (e3))))) -> (~((op (e0) (e3)) = (op (e3) (e3)))) -> (~((op (e1) (e2)) = (op (e1) (e3)))) -> (~((op (e2) (e0)) = (op (e2) (e3)))) -> (((op (e0) (e3)) = (e1))\/(((op (e1) (e3)) = (e1))\/(((op (e2) (e3)) = (e1))\/((op (e3) (e3)) = (e1))))) -> (~((op (e1) (e0)) = (op (e1) (e2)))) -> (((op (e3) (e0)) = (e2))\/(((op (e3) (e1)) = (e2))\/(((op (e3) (e2)) = (e2))\/((op (e3) (e3)) = (e2))))) -> (~((op (e2) (op (e3) (e2))) = (op (e3) (e2)))) -> (~((op (e0) (e1)) = (op (e3) (e1)))) -> (~((op (e0) (e2)) = (op (e2) (e2)))) -> (((op (e0) (e0)) = (e2))\/(((op (e0) (e1)) = (e2))\/(((op (e0) (e2)) = (e2))\/((op (e0) (e3)) = (e2))))) -> (~((op (e0) (e2)) = (op (e0) (e3)))) -> ((~((op (e1) (e1)) = (e3)))\/((op (e1) (e3)) = (e1))) -> (~((op (e1) (e0)) = (op (e1) (e3)))) -> ((~((op (e3) (e3)) = (e1)))\/((op (e3) (e1)) = (e3))) -> (~((op (e3) (e1)) = (op (e3) (e2)))) -> ((~((op (e3) (e3)) = (e3)))\/((op (e3) (e3)) = (e3))) -> (~((op (e3) (op (e3) (e3))) = (op (e3) (e3)))) -> (~((op (e0) (e0)) = (e2))) -> (~((e1) = (e2))) -> (((op (e1) (e1)) = (e0))\/(((op (e1) (e1)) = (e1))\/(((op (e1) (e1)) = (e2))\/((op (e1) (e1)) = (e3))))) -> (~((op (e1) (e1)) = (e1))) -> (((op (e0) (e0)) = (e2))\/(((op (e1) (e0)) = (e2))\/(((op (e2) (e0)) = (e2))\/((op (e3) (e0)) = (e2))))) -> (((op (e3) (e0)) = (e1))\/(((op (e3) (e1)) = (e1))\/(((op (e3) (e2)) = (e1))\/((op (e3) (e3)) = (e1))))) -> (~((e1) = (e3))) -> (((op (e3) (e0)) = (e0))\/(((op (e3) (e1)) = (e0))\/(((op (e3) (e2)) = (e0))\/((op (e3) (e3)) = (e0))))) -> (~((op (e1) (e2)) = (op (e3) (e2)))) -> (~((op (e1) (op (e3) (e1))) = (op (e3) (e1)))) -> ((op (e0) (e0)) = (e0)) -> (~((op (e1) (e2)) = (op (e2) (e2)))) -> (((op (e1) (e2)) = (e0))\/(((op (e1) (e2)) = (e1))\/(((op (e1) (e2)) = (e2))\/((op (e1) (e2)) = (e3))))) -> (~((op (e1) (e0)) = (op (e3) (e0)))) -> ((~((op (e3) (e3)) = (e2)))\/((op (e3) (e2)) = (e3))) -> (((op (e2) (e0)) = (e0))\/(((op (e2) (e0)) = (e1))\/(((op (e2) (e0)) = (e2))\/((op (e2) (e0)) = (e3))))) -> (~((op (e2) (e0)) = (op (e3) (e0)))) -> (~((op (e1) (e0)) = (op (e2) (e0)))) -> (~((op (e0) (e0)) = (op (e2) (e0)))) -> ((~((op (e3) (e3)) = (e0)))\/((op (e3) (e0)) = (e3))) -> ((~((op (e1) (e1)) = (e2)))\/((op (e1) (e2)) = (e1))) -> (((op (e0) (e0)) = (e1))\/(((op (e0) (e1)) = (e1))\/(((op (e0) (e2)) = (e1))\/((op (e0) (e3)) = (e1))))) -> (((op (e0) (e2)) = (e0))\/(((op (e0) (e2)) = (e1))\/(((op (e0) (e2)) = (e2))\/((op (e0) (e2)) = (e3))))) -> (~((op (e0) (e2)) = (op (e3) (e2)))) -> (~((op (e0) (e0)) = (op (e0) (e2)))) -> (~((op (e1) (e1)) = (e3))) -> (((op (e0) (e3)) = (e0))\/(((op (e0) (e3)) = (e1))\/(((op (e0) (e3)) = (e2))\/((op (e0) (e3)) = (e3))))) -> (~((op (e0) (e3)) = (op (e1) (e3)))) -> (~((op (e0) (e3)) = (op (e2) (e3)))) -> (~((op (e0) (e0)) = (op (e0) (e3)))) -> (((op (e1) (e0)) = (e3))\/(((op (e1) (e1)) = (e3))\/(((op (e1) (e2)) = (e3))\/((op (e1) (e3)) = (e3))))) -> (~((op (e1) (e1)) = (e2))) -> (~((e0) = (e2))) -> (((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 (e2) (e1)) = (e2))\/((op (e3) (e1)) = (e2))))) -> (~((op (e3) (e3)) = (e2))) -> (~((op (e2) (e1)) = (op (e2) (e2)))) -> (~((op (e0) (e2)) = (op (e1) (e2)))) -> (~((op (e2) (e2)) = (e1))) -> (((op (e3) (e2)) = (e0))\/(((op (e3) (e2)) = (e1))\/(((op (e3) (e2)) = (e2))\/((op (e3) (e2)) = (e3))))) -> (((op (e0) (e2)) = (e1))\/(((op (e1) (e2)) = (e1))\/(((op (e2) (e2)) = (e1))\/((op (e3) (e2)) = (e1))))) -> (~((op (e1) (e1)) = (e0))) -> (~((op (e0) (e0)) = (op (e1) (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) (e2)) = (e2)) -> (~((e2) = (e3))) -> ((op (e3) (e0)) = (e3)) -> False). % 15.55/15.67 do 0 intro. intros zenon_H9e zenon_H1c3 zenon_H15f zenon_Hbe zenon_H16f zenon_H2e zenon_H4b zenon_He6 zenon_H13c zenon_H84 zenon_H59 zenon_H105 zenon_H109 zenon_H58 zenon_H45 zenon_Hf1 zenon_H2b8 zenon_H3b zenon_H36 zenon_H1d0 zenon_Hce zenon_H121 zenon_H166 zenon_H1df zenon_H2af zenon_H138 zenon_H28 zenon_H8e zenon_Hc9 zenon_H1d2 zenon_H1cf zenon_H10c zenon_H135 zenon_H10d zenon_H2be zenon_H8f zenon_Ha7 zenon_H1b3 zenon_H1b4 zenon_Heb zenon_H146 zenon_Ha3 zenon_H1f6 zenon_H17d zenon_H2b4 zenon_H1f zenon_H7d zenon_H1d5 zenon_H22e zenon_H10e zenon_H281 zenon_H1e5 zenon_H247 zenon_H258 zenon_H10f zenon_H1d3 zenon_H44 zenon_H251 zenon_H140 zenon_H250 zenon_H182 zenon_H254 zenon_H80 zenon_Hb4 zenon_H24f zenon_H90 zenon_Hd6 zenon_H5e zenon_H1c5 zenon_H1a2 zenon_H3d zenon_H157 zenon_H87 zenon_H52 zenon_H25e zenon_H11b zenon_H145 zenon_H24c zenon_H163 zenon_H17a zenon_H35 zenon_H6a zenon_Hba. % 15.55/15.67 apply (zenon_or_s _ _ zenon_Heb); [ zenon_intro zenon_H92 | zenon_intro zenon_Hec ]. % 15.55/15.67 exact (zenon_H8f zenon_H92). % 15.55/15.67 apply (zenon_or_s _ _ zenon_Hec); [ zenon_intro zenon_H68 | zenon_intro zenon_Hed ]. % 15.55/15.67 apply (zenon_or_s _ _ zenon_H163); [ zenon_intro zenon_Had | zenon_intro zenon_H164 ]. % 15.55/15.67 apply (zenon_L559_); trivial. % 15.55/15.67 apply (zenon_or_s _ _ zenon_H164); [ zenon_intro zenon_H149 | zenon_intro zenon_H165 ]. % 15.55/15.67 exact (zenon_H145 zenon_H149). % 15.55/15.67 apply (zenon_or_s _ _ zenon_H165); [ zenon_intro zenon_H15d | zenon_intro zenon_Hcc ]. % 15.55/15.67 apply (zenon_or_s _ _ zenon_H1c5); [ zenon_intro zenon_Hd8 | zenon_intro zenon_H1c6 ]. % 15.55/15.67 apply (zenon_L735_); trivial. % 15.55/15.67 apply (zenon_or_s _ _ zenon_H1c6); [ zenon_intro zenon_H21 | zenon_intro zenon_H1c7 ]. % 15.55/15.67 exact (zenon_H1b4 zenon_H21). % 15.55/15.67 apply (zenon_or_s _ _ zenon_H1c7); [ zenon_intro zenon_H117 | zenon_intro zenon_H11f ]. % 15.55/15.67 apply (zenon_L1100_); trivial. % 15.55/15.67 apply (zenon_L1122_); trivial. % 15.55/15.67 apply (zenon_L1154_); trivial. % 15.55/15.67 apply (zenon_or_s _ _ zenon_Hed); [ zenon_intro zenon_Hdd | zenon_intro zenon_He9 ]. % 15.55/15.67 apply (zenon_L161_); trivial. % 15.55/15.67 apply (zenon_L220_); trivial. % 15.55/15.67 (* end of lemma zenon_L1155_ *) % 15.55/15.67 assert (zenon_L1156_ : (~((op (e2) (e1)) = (op (e2) (e2)))) -> (((op (e3) (e2)) = (e0))\/(((op (e3) (e2)) = (e1))\/(((op (e3) (e2)) = (e2))\/((op (e3) (e2)) = (e3))))) -> (~((op (e2) (e2)) = (e1))) -> (~((op (e0) (e2)) = (op (e1) (e2)))) -> (((op (e0) (e2)) = (e1))\/(((op (e1) (e2)) = (e1))\/(((op (e2) (e2)) = (e1))\/((op (e3) (e2)) = (e1))))) -> (((op (e0) (e1)) = (e2))\/(((op (e1) (e1)) = (e2))\/(((op (e2) (e1)) = (e2))\/((op (e3) (e1)) = (e2))))) -> (((op (e1) (e0)) = (e0))\/(((op (e1) (e1)) = (e0))\/(((op (e1) (e2)) = (e0))\/((op (e1) (e3)) = (e0))))) -> (((op (e1) (e0)) = (e2))\/(((op (e1) (e1)) = (e2))\/(((op (e1) (e2)) = (e2))\/((op (e1) (e3)) = (e2))))) -> (~((e0) = (e2))) -> ((op (e2) (e2)) = (e2)) -> (~((op (e1) (e2)) = (op (e2) (e2)))) -> (~((e1) = (e2))) -> ((~((op (e2) (e2)) = (e3)))\/((op (e2) (e3)) = (e2))) -> (~((op (e2) (e2)) = (op (e2) (e3)))) -> (((op (e0) (e0)) = (e3))\/(((op (e1) (e0)) = (e3))\/(((op (e2) (e0)) = (e3))\/((op (e3) (e0)) = (e3))))) -> (((op (e0) (e2)) = (e0))\/(((op (e1) (e2)) = (e0))\/(((op (e2) (e2)) = (e0))\/((op (e3) (e2)) = (e0))))) -> (~((op (e2) (e2)) = (e0))) -> (~((e0) = (e3))) -> (((op (e2) (e0)) = (e3))\/(((op (e2) (e1)) = (e3))\/(((op (e2) (e2)) = (e3))\/((op (e2) (e3)) = (e3))))) -> (~((op (e2) (e1)) = (op (e3) (e1)))) -> (~((op (e0) (e0)) = (e3))) -> (~((op (e3) (e0)) = (op (e3) (e2)))) -> (~((op (e3) (e0)) = (op (e3) (e1)))) -> (((op (e0) (e0)) = (e3))\/(((op (e0) (e1)) = (e3))\/(((op (e0) (e2)) = (e3))\/((op (e0) (e3)) = (e3))))) -> (~((op (e0) (e0)) = (e1))) -> (((op (e0) (e0)) = (e1))\/(((op (e1) (e0)) = (e1))\/(((op (e2) (e0)) = (e1))\/((op (e3) (e0)) = (e1))))) -> (~((op (e0) (op (e3) (e0))) = (op (e3) (e0)))) -> (~((op (e0) (e3)) = (op (e3) (e3)))) -> (~((op (e1) (e2)) = (op (e1) (e3)))) -> (~((op (e2) (e0)) = (op (e2) (e3)))) -> (((op (e0) (e3)) = (e1))\/(((op (e1) (e3)) = (e1))\/(((op (e2) (e3)) = (e1))\/((op (e3) (e3)) = (e1))))) -> (~((op (e1) (e0)) = (op (e1) (e2)))) -> (((op (e3) (e0)) = (e2))\/(((op (e3) (e1)) = (e2))\/(((op (e3) (e2)) = (e2))\/((op (e3) (e3)) = (e2))))) -> (~((op (e2) (op (e3) (e2))) = (op (e3) (e2)))) -> (~((op (e0) (e1)) = (op (e3) (e1)))) -> (~((op (e0) (e2)) = (op (e2) (e2)))) -> (((op (e0) (e0)) = (e2))\/(((op (e0) (e1)) = (e2))\/(((op (e0) (e2)) = (e2))\/((op (e0) (e3)) = (e2))))) -> (~((op (e0) (e2)) = (op (e0) (e3)))) -> ((~((op (e1) (e1)) = (e3)))\/((op (e1) (e3)) = (e1))) -> (~((op (e1) (e0)) = (op (e1) (e3)))) -> ((~((op (e3) (e3)) = (e1)))\/((op (e3) (e1)) = (e3))) -> (~((op (e3) (e1)) = (op (e3) (e2)))) -> ((~((op (e3) (e3)) = (e3)))\/((op (e3) (e3)) = (e3))) -> (~((op (e3) (op (e3) (e3))) = (op (e3) (e3)))) -> (~((op (e0) (e0)) = (e2))) -> (~((op (e2) (e0)) = (op (e2) (e2)))) -> (((op (e0) (e0)) = (e2))\/(((op (e1) (e0)) = (e2))\/(((op (e2) (e0)) = (e2))\/((op (e3) (e0)) = (e2))))) -> (((op (e3) (e0)) = (e1))\/(((op (e3) (e1)) = (e1))\/(((op (e3) (e2)) = (e1))\/((op (e3) (e3)) = (e1))))) -> (~((e1) = (e3))) -> (((op (e3) (e0)) = (e0))\/(((op (e3) (e1)) = (e0))\/(((op (e3) (e2)) = (e0))\/((op (e3) (e3)) = (e0))))) -> (~((op (e1) (e2)) = (op (e3) (e2)))) -> (~((op (e1) (op (e3) (e1))) = (op (e3) (e1)))) -> (((op (e1) (e2)) = (e0))\/(((op (e1) (e2)) = (e1))\/(((op (e1) (e2)) = (e2))\/((op (e1) (e2)) = (e3))))) -> (~((op (e1) (e0)) = (op (e3) (e0)))) -> ((~((op (e3) (e3)) = (e2)))\/((op (e3) (e2)) = (e3))) -> (((op (e2) (e0)) = (e0))\/(((op (e2) (e0)) = (e1))\/(((op (e2) (e0)) = (e2))\/((op (e2) (e0)) = (e3))))) -> (~((op (e2) (e0)) = (op (e3) (e0)))) -> (~((op (e1) (e0)) = (op (e2) (e0)))) -> (~((op (e0) (e0)) = (op (e2) (e0)))) -> ((~((op (e3) (e3)) = (e0)))\/((op (e3) (e0)) = (e3))) -> ((~((op (e1) (e1)) = (e2)))\/((op (e1) (e2)) = (e1))) -> (((op (e0) (e0)) = (e1))\/(((op (e0) (e1)) = (e1))\/(((op (e0) (e2)) = (e1))\/((op (e0) (e3)) = (e1))))) -> (((op (e0) (e2)) = (e0))\/(((op (e0) (e2)) = (e1))\/(((op (e0) (e2)) = (e2))\/((op (e0) (e2)) = (e3))))) -> (~((op (e0) (e2)) = (op (e3) (e2)))) -> (~((op (e0) (e0)) = (op (e0) (e2)))) -> (~((e2) = (e3))) -> (~((op (e1) (e1)) = (e3))) -> (((op (e0) (e3)) = (e0))\/(((op (e0) (e3)) = (e1))\/(((op (e0) (e3)) = (e2))\/((op (e0) (e3)) = (e3))))) -> (~((op (e0) (e3)) = (op (e1) (e3)))) -> (~((op (e0) (e3)) = (op (e2) (e3)))) -> (~((op (e0) (e0)) = (op (e0) (e3)))) -> (((op (e1) (e0)) = (e3))\/(((op (e1) (e1)) = (e3))\/(((op (e1) (e2)) = (e3))\/((op (e1) (e3)) = (e3))))) -> (~((e0) = (e1))) -> (((op (e1) (e0)) = (e1))\/(((op (e1) (e1)) = (e1))\/(((op (e1) (e2)) = (e1))\/((op (e1) (e3)) = (e1))))) -> (~((op (e1) (e1)) = (e1))) -> (~((op (e1) (e1)) = (e2))) -> (((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)) = (e0))) -> ((op (e0) (e0)) = (e0)) -> (~((op (e0) (e0)) = (op (e1) (e0)))) -> False). % 15.55/15.67 do 0 intro. intros zenon_H157 zenon_H25e zenon_H52 zenon_H87 zenon_H11b zenon_H1a2 zenon_H163 zenon_H84 zenon_H5e zenon_H35 zenon_H7d zenon_Ha7 zenon_H1c3 zenon_H15f zenon_Hbe zenon_H16f zenon_H2e zenon_H4b zenon_He6 zenon_H13c zenon_H59 zenon_H105 zenon_H109 zenon_H58 zenon_H45 zenon_Hf1 zenon_H2b8 zenon_H36 zenon_H1d0 zenon_Hce zenon_H121 zenon_H166 zenon_H1df zenon_H2af zenon_H138 zenon_H28 zenon_H8e zenon_Hc9 zenon_H1d2 zenon_H1cf zenon_H10c zenon_H135 zenon_H10d zenon_H2be zenon_H8f zenon_H17a zenon_Heb zenon_H146 zenon_Ha3 zenon_H1f6 zenon_H17d zenon_H2b4 zenon_H1d5 zenon_H22e zenon_H10e zenon_H281 zenon_H1e5 zenon_H247 zenon_H258 zenon_H10f zenon_H1d3 zenon_H44 zenon_H251 zenon_H140 zenon_H250 zenon_H6a zenon_H182 zenon_H254 zenon_H80 zenon_Hb4 zenon_H24f zenon_H90 zenon_H9e zenon_H1c5 zenon_H1b4 zenon_Hd6 zenon_H3b zenon_H1b3 zenon_H145 zenon_H1f zenon_H24c. % 15.55/15.67 apply (zenon_or_s _ _ zenon_H1c3); [ zenon_intro zenon_H30 | zenon_intro zenon_H124 ]. % 15.55/15.67 apply (zenon_or_s _ _ zenon_H10f); [ zenon_intro zenon_H3c | zenon_intro zenon_Hba ]. % 15.55/15.67 apply (zenon_or_s _ _ zenon_H10c); [ zenon_intro zenon_H104 | zenon_intro zenon_H10a ]. % 15.55/15.67 apply (zenon_or_s _ _ zenon_H10d); [ zenon_intro zenon_H3e | zenon_intro zenon_H42 ]. % 15.55/15.67 apply (zenon_or_s _ _ zenon_H163); [ zenon_intro zenon_Had | zenon_intro zenon_H164 ]. % 15.55/15.67 apply (zenon_L559_); trivial. % 15.55/15.67 apply (zenon_or_s _ _ zenon_H164); [ zenon_intro zenon_H149 | zenon_intro zenon_H165 ]. % 15.55/15.67 exact (zenon_H145 zenon_H149). % 15.55/15.67 apply (zenon_or_s _ _ zenon_H165); [ zenon_intro zenon_H15d | zenon_intro zenon_Hcc ]. % 15.55/15.67 apply (zenon_L490_); trivial. % 15.55/15.67 apply (zenon_L1154_); trivial. % 15.55/15.67 apply (zenon_L1041_); trivial. % 15.55/15.67 apply (zenon_or_s _ _ zenon_H10e); [ zenon_intro zenon_H3d | zenon_intro zenon_H106 ]. % 15.55/15.67 apply (zenon_or_s _ _ zenon_H10d); [ zenon_intro zenon_H3e | zenon_intro zenon_H42 ]. % 15.55/15.67 apply (zenon_or_s _ _ zenon_H44); [ zenon_intro zenon_H47 | zenon_intro zenon_H46 ]. % 15.55/15.67 exact (zenon_H45 zenon_H47). % 15.55/15.67 apply (zenon_or_s _ _ zenon_H46); [ zenon_intro zenon_H22 | zenon_intro zenon_H48 ]. % 15.55/15.67 apply (zenon_or_s _ _ zenon_Hf1); [ zenon_intro zenon_H47 | zenon_intro zenon_Hf4 ]. % 15.55/15.67 exact (zenon_H45 zenon_H47). % 15.55/15.67 apply (zenon_or_s _ _ zenon_Hf4); [ zenon_intro zenon_Hd8 | zenon_intro zenon_Hf5 ]. % 15.55/15.67 apply (zenon_L1073_); trivial. % 15.55/15.67 apply (zenon_or_s _ _ zenon_Hf5); [ zenon_intro zenon_Hae | zenon_intro zenon_Hee ]. % 15.55/15.67 apply (zenon_or_s _ _ zenon_Hbe); [ zenon_intro zenon_H5b | zenon_intro zenon_Hbf ]. % 15.55/15.67 exact (zenon_H59 zenon_H5b). % 15.55/15.67 apply (zenon_or_s _ _ zenon_Hbf); [ zenon_intro zenon_H69 | zenon_intro zenon_Hc0 ]. % 15.55/15.67 apply (zenon_L1128_); trivial. % 15.55/15.67 apply (zenon_or_s _ _ zenon_Hc0); [ zenon_intro zenon_Haf | zenon_intro zenon_Hba ]. % 15.55/15.67 apply (zenon_L39_); trivial. % 15.55/15.67 apply (zenon_L1155_); trivial. % 15.55/15.67 apply (zenon_L1054_); trivial. % 15.55/15.67 apply (zenon_or_s _ _ zenon_H48); [ zenon_intro zenon_H29 | zenon_intro zenon_H37 ]. % 15.55/15.67 apply (zenon_L1099_); trivial. % 15.55/15.67 apply (zenon_L7_); trivial. % 15.55/15.67 apply (zenon_L1041_); trivial. % 15.55/15.67 apply (zenon_L115_); trivial. % 15.55/15.67 apply (zenon_or_s _ _ zenon_H10e); [ zenon_intro zenon_H3d | zenon_intro zenon_H106 ]. % 15.55/15.67 apply (zenon_L1155_); trivial. % 15.55/15.67 apply (zenon_L81_); trivial. % 15.55/15.67 apply (zenon_L137_); trivial. % 15.55/15.67 (* end of lemma zenon_L1156_ *) % 15.55/15.67 assert (zenon_L1157_ : ((~((op (e2) (e2)) = (e0)))\/((op (e2) (e0)) = (e2))) -> (~((op (e2) (e1)) = (op (e2) (e2)))) -> (((op (e3) (e2)) = (e0))\/(((op (e3) (e2)) = (e1))\/(((op (e3) (e2)) = (e2))\/((op (e3) (e2)) = (e3))))) -> (~((op (e0) (e2)) = (op (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 (e1) (e0)) = (e0))\/(((op (e1) (e1)) = (e0))\/(((op (e1) (e2)) = (e0))\/((op (e1) (e3)) = (e0))))) -> (((op (e1) (e0)) = (e2))\/(((op (e1) (e1)) = (e2))\/(((op (e1) (e2)) = (e2))\/((op (e1) (e3)) = (e2))))) -> (~((e0) = (e2))) -> ((op (e2) (e2)) = (e2)) -> (~((op (e1) (e2)) = (op (e2) (e2)))) -> (~((e1) = (e2))) -> ((~((op (e2) (e2)) = (e3)))\/((op (e2) (e3)) = (e2))) -> (~((op (e2) (e2)) = (op (e2) (e3)))) -> (((op (e0) (e0)) = (e3))\/(((op (e1) (e0)) = (e3))\/(((op (e2) (e0)) = (e3))\/((op (e3) (e0)) = (e3))))) -> (((op (e0) (e2)) = (e0))\/(((op (e1) (e2)) = (e0))\/(((op (e2) (e2)) = (e0))\/((op (e3) (e2)) = (e0))))) -> (~((e0) = (e3))) -> (((op (e2) (e0)) = (e3))\/(((op (e2) (e1)) = (e3))\/(((op (e2) (e2)) = (e3))\/((op (e2) (e3)) = (e3))))) -> (~((op (e2) (e1)) = (op (e3) (e1)))) -> (~((op (e0) (e0)) = (e3))) -> (~((op (e3) (e0)) = (op (e3) (e2)))) -> (~((op (e3) (e0)) = (op (e3) (e1)))) -> (((op (e0) (e0)) = (e3))\/(((op (e0) (e1)) = (e3))\/(((op (e0) (e2)) = (e3))\/((op (e0) (e3)) = (e3))))) -> (~((op (e0) (e0)) = (e1))) -> (((op (e0) (e0)) = (e1))\/(((op (e1) (e0)) = (e1))\/(((op (e2) (e0)) = (e1))\/((op (e3) (e0)) = (e1))))) -> (~((op (e0) (op (e3) (e0))) = (op (e3) (e0)))) -> (~((op (e0) (e3)) = (op (e3) (e3)))) -> (~((op (e1) (e2)) = (op (e1) (e3)))) -> (~((op (e2) (e0)) = (op (e2) (e3)))) -> (((op (e0) (e3)) = (e1))\/(((op (e1) (e3)) = (e1))\/(((op (e2) (e3)) = (e1))\/((op (e3) (e3)) = (e1))))) -> (~((op (e1) (e0)) = (op (e1) (e2)))) -> (((op (e3) (e0)) = (e2))\/(((op (e3) (e1)) = (e2))\/(((op (e3) (e2)) = (e2))\/((op (e3) (e3)) = (e2))))) -> (~((op (e2) (op (e3) (e2))) = (op (e3) (e2)))) -> (~((op (e0) (e1)) = (op (e3) (e1)))) -> (~((op (e0) (e2)) = (op (e2) (e2)))) -> (((op (e0) (e0)) = (e2))\/(((op (e0) (e1)) = (e2))\/(((op (e0) (e2)) = (e2))\/((op (e0) (e3)) = (e2))))) -> (~((op (e0) (e2)) = (op (e0) (e3)))) -> ((~((op (e1) (e1)) = (e3)))\/((op (e1) (e3)) = (e1))) -> (~((op (e1) (e0)) = (op (e1) (e3)))) -> ((~((op (e3) (e3)) = (e1)))\/((op (e3) (e1)) = (e3))) -> (~((op (e3) (e1)) = (op (e3) (e2)))) -> ((~((op (e3) (e3)) = (e3)))\/((op (e3) (e3)) = (e3))) -> (~((op (e3) (op (e3) (e3))) = (op (e3) (e3)))) -> (~((op (e0) (e0)) = (e2))) -> (~((op (e2) (e0)) = (op (e2) (e2)))) -> (((op (e0) (e0)) = (e2))\/(((op (e1) (e0)) = (e2))\/(((op (e2) (e0)) = (e2))\/((op (e3) (e0)) = (e2))))) -> (((op (e3) (e0)) = (e1))\/(((op (e3) (e1)) = (e1))\/(((op (e3) (e2)) = (e1))\/((op (e3) (e3)) = (e1))))) -> (~((e1) = (e3))) -> (((op (e3) (e0)) = (e0))\/(((op (e3) (e1)) = (e0))\/(((op (e3) (e2)) = (e0))\/((op (e3) (e3)) = (e0))))) -> (~((op (e1) (e2)) = (op (e3) (e2)))) -> (~((op (e1) (op (e3) (e1))) = (op (e3) (e1)))) -> (((op (e1) (e2)) = (e0))\/(((op (e1) (e2)) = (e1))\/(((op (e1) (e2)) = (e2))\/((op (e1) (e2)) = (e3))))) -> (~((op (e1) (e0)) = (op (e3) (e0)))) -> ((~((op (e3) (e3)) = (e2)))\/((op (e3) (e2)) = (e3))) -> (((op (e2) (e0)) = (e0))\/(((op (e2) (e0)) = (e1))\/(((op (e2) (e0)) = (e2))\/((op (e2) (e0)) = (e3))))) -> (~((op (e2) (e0)) = (op (e3) (e0)))) -> (~((op (e1) (e0)) = (op (e2) (e0)))) -> (~((op (e0) (e0)) = (op (e2) (e0)))) -> ((~((op (e3) (e3)) = (e0)))\/((op (e3) (e0)) = (e3))) -> ((~((op (e1) (e1)) = (e2)))\/((op (e1) (e2)) = (e1))) -> (((op (e0) (e0)) = (e1))\/(((op (e0) (e1)) = (e1))\/(((op (e0) (e2)) = (e1))\/((op (e0) (e3)) = (e1))))) -> (((op (e0) (e2)) = (e0))\/(((op (e0) (e2)) = (e1))\/(((op (e0) (e2)) = (e2))\/((op (e0) (e2)) = (e3))))) -> (~((op (e0) (e2)) = (op (e3) (e2)))) -> (~((op (e0) (e0)) = (op (e0) (e2)))) -> (~((e2) = (e3))) -> (~((op (e1) (e1)) = (e3))) -> (((op (e0) (e3)) = (e0))\/(((op (e0) (e3)) = (e1))\/(((op (e0) (e3)) = (e2))\/((op (e0) (e3)) = (e3))))) -> (~((op (e0) (e3)) = (op (e1) (e3)))) -> (~((op (e0) (e3)) = (op (e2) (e3)))) -> (~((op (e0) (e0)) = (op (e0) (e3)))) -> (((op (e1) (e0)) = (e3))\/(((op (e1) (e1)) = (e3))\/(((op (e1) (e2)) = (e3))\/((op (e1) (e3)) = (e3))))) -> (~((e0) = (e1))) -> (((op (e1) (e0)) = (e1))\/(((op (e1) (e1)) = (e1))\/(((op (e1) (e2)) = (e1))\/((op (e1) (e3)) = (e1))))) -> (~((op (e1) (e1)) = (e1))) -> (~((op (e1) (e1)) = (e2))) -> (((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)) = (e0))) -> ((op (e0) (e0)) = (e0)) -> (~((op (e0) (e0)) = (op (e1) (e0)))) -> ((~((op (e2) (e2)) = (e1)))\/((op (e2) (e1)) = (e2))) -> False). % 15.55/15.68 do 0 intro. intros zenon_H1d4 zenon_H157 zenon_H25e zenon_H87 zenon_H11b zenon_H1a2 zenon_H163 zenon_H84 zenon_H5e zenon_H35 zenon_H7d zenon_Ha7 zenon_H1c3 zenon_H15f zenon_Hbe zenon_H16f zenon_H4b zenon_He6 zenon_H13c zenon_H59 zenon_H105 zenon_H109 zenon_H58 zenon_H45 zenon_Hf1 zenon_H2b8 zenon_H36 zenon_H1d0 zenon_Hce zenon_H121 zenon_H166 zenon_H1df zenon_H2af zenon_H138 zenon_H28 zenon_H8e zenon_Hc9 zenon_H1d2 zenon_H1cf zenon_H10c zenon_H135 zenon_H10d zenon_H2be zenon_H8f zenon_H17a zenon_Heb zenon_H146 zenon_Ha3 zenon_H1f6 zenon_H17d zenon_H2b4 zenon_H1d5 zenon_H22e zenon_H10e zenon_H281 zenon_H1e5 zenon_H247 zenon_H258 zenon_H10f zenon_H1d3 zenon_H44 zenon_H251 zenon_H140 zenon_H250 zenon_H6a zenon_H182 zenon_H254 zenon_H80 zenon_Hb4 zenon_H24f zenon_H90 zenon_H9e zenon_H1c5 zenon_H1b4 zenon_Hd6 zenon_H3b zenon_H1b3 zenon_H145 zenon_H1f zenon_H24c zenon_H1e3. % 15.55/15.68 apply (zenon_or_s _ _ zenon_H1d4); [ zenon_intro zenon_H2e | zenon_intro zenon_Hdd ]. % 15.55/15.68 apply (zenon_or_s _ _ zenon_H1e3); [ zenon_intro zenon_H52 | zenon_intro zenon_H156 ]. % 15.55/15.68 apply (zenon_L1156_); trivial. % 15.55/15.68 apply (zenon_L134_); trivial. % 15.55/15.68 apply (zenon_L161_); trivial. % 15.55/15.68 (* end of lemma zenon_L1157_ *) % 15.55/15.68 assert (zenon_L1158_ : (~((op (e1) (op (e3) (e1))) = (op (e3) (e1)))) -> ((op (e1) (e1)) = (e1)) -> ((op (e3) (e1)) = (e1)) -> False). % 15.55/15.68 do 0 intro. intros zenon_H2b4 zenon_H21 zenon_H13e. % 15.55/15.68 cut (((op (e1) (e1)) = (e1)) = ((op (e1) (op (e3) (e1))) = (op (e3) (e1)))). % 15.55/15.68 intro zenon_D_pnotp. % 15.55/15.68 apply zenon_H2b4. % 15.55/15.68 rewrite <- zenon_D_pnotp. % 15.55/15.68 exact zenon_H21. % 15.55/15.68 cut (((e1) = (op (e3) (e1)))); [idtac | apply NNPP; zenon_intro zenon_H169]. % 15.55/15.68 cut (((op (e1) (e1)) = (op (e1) (op (e3) (e1))))); [idtac | apply NNPP; zenon_intro zenon_H2d3]. % 15.55/15.68 congruence. % 15.55/15.68 elim (classic ((op (e1) (op (e3) (e1))) = (op (e1) (op (e3) (e1))))); [ zenon_intro zenon_H2b6 | zenon_intro zenon_H2b7 ]. % 15.55/15.68 cut (((op (e1) (op (e3) (e1))) = (op (e1) (op (e3) (e1)))) = ((op (e1) (e1)) = (op (e1) (op (e3) (e1))))). % 15.55/15.68 intro zenon_D_pnotp. % 15.55/15.68 apply zenon_H2d3. % 15.55/15.68 rewrite <- zenon_D_pnotp. % 15.55/15.68 exact zenon_H2b6. % 15.55/15.68 cut (((op (e1) (op (e3) (e1))) = (op (e1) (op (e3) (e1))))); [idtac | apply NNPP; zenon_intro zenon_H2b7]. % 15.55/15.68 cut (((op (e1) (op (e3) (e1))) = (op (e1) (e1)))); [idtac | apply NNPP; zenon_intro zenon_H2d4]. % 15.55/15.68 congruence. % 15.55/15.68 cut (((op (e3) (e1)) = (e1))); [idtac | apply NNPP; zenon_intro zenon_H13f]. % 15.55/15.68 cut (((e1) = (e1))); [idtac | apply NNPP; zenon_intro zenon_Ha0]. % 15.55/15.68 congruence. % 15.55/15.68 apply zenon_Ha0. apply refl_equal. % 15.55/15.68 exact (zenon_H13f zenon_H13e). % 15.55/15.68 apply zenon_H2b7. apply refl_equal. % 15.55/15.68 apply zenon_H2b7. apply refl_equal. % 15.55/15.68 apply zenon_H169. apply sym_equal. exact zenon_H13e. % 15.55/15.68 (* end of lemma zenon_L1158_ *) % 15.55/15.68 assert (zenon_L1159_ : (((op (e3) (e0)) = (e1))\/(((op (e3) (e1)) = (e1))\/(((op (e3) (e2)) = (e1))\/((op (e3) (e3)) = (e1))))) -> ((op (e3) (e0)) = (e3)) -> (~((e1) = (e3))) -> ((op (e1) (e1)) = (e1)) -> (~((op (e1) (op (e3) (e1))) = (op (e3) (e1)))) -> ((op (e0) (e2)) = (e1)) -> (~((op (e0) (e2)) = (op (e3) (e2)))) -> (~((op (e3) (e3)) = (e1))) -> False). % 15.55/15.68 do 0 intro. intros zenon_H146 zenon_Hba zenon_Ha3 zenon_H21 zenon_H2b4 zenon_H29 zenon_H140 zenon_H104. % 15.55/15.68 apply (zenon_or_s _ _ zenon_H146); [ zenon_intro zenon_Hee | zenon_intro zenon_H14b ]. % 15.55/15.68 apply (zenon_L79_); trivial. % 15.55/15.68 apply (zenon_or_s _ _ zenon_H14b); [ zenon_intro zenon_H13e | zenon_intro zenon_H14c ]. % 15.55/15.68 apply (zenon_L1158_); trivial. % 15.55/15.68 apply (zenon_or_s _ _ zenon_H14c); [ zenon_intro zenon_H119 | zenon_intro zenon_H38 ]. % 15.55/15.68 apply (zenon_L124_); trivial. % 15.55/15.68 exact (zenon_H104 zenon_H38). % 15.55/15.68 (* end of lemma zenon_L1159_ *) % 15.55/15.68 assert (zenon_L1160_ : (~((op (e2) (op (e3) (e2))) = (op (e3) (e2)))) -> ((op (e2) (e1)) = (e2)) -> ((op (e3) (e2)) = (e1)) -> ((op (e3) (e2)) = (e2)) -> False). % 15.55/15.68 do 0 intro. intros zenon_H2af zenon_H156 zenon_H119 zenon_H1dd. % 15.55/15.68 cut (((op (e2) (e1)) = (e2)) = ((op (e2) (op (e3) (e2))) = (op (e3) (e2)))). % 15.55/15.68 intro zenon_D_pnotp. % 15.55/15.68 apply zenon_H2af. % 15.55/15.68 rewrite <- zenon_D_pnotp. % 15.55/15.68 exact zenon_H156. % 15.55/15.68 cut (((e2) = (op (e3) (e2)))); [idtac | apply NNPP; zenon_intro zenon_H1de]. % 15.55/15.68 cut (((op (e2) (e1)) = (op (e2) (op (e3) (e2))))); [idtac | apply NNPP; zenon_intro zenon_H2b0]. % 15.55/15.68 congruence. % 15.55/15.68 elim (classic ((op (e2) (op (e3) (e2))) = (op (e2) (op (e3) (e2))))); [ zenon_intro zenon_H2b1 | zenon_intro zenon_H2b2 ]. % 15.55/15.68 cut (((op (e2) (op (e3) (e2))) = (op (e2) (op (e3) (e2)))) = ((op (e2) (e1)) = (op (e2) (op (e3) (e2))))). % 15.55/15.68 intro zenon_D_pnotp. % 15.55/15.68 apply zenon_H2b0. % 15.55/15.68 rewrite <- zenon_D_pnotp. % 15.55/15.68 exact zenon_H2b1. % 15.55/15.68 cut (((op (e2) (op (e3) (e2))) = (op (e2) (op (e3) (e2))))); [idtac | apply NNPP; zenon_intro zenon_H2b2]. % 15.55/15.68 cut (((op (e2) (op (e3) (e2))) = (op (e2) (e1)))); [idtac | apply NNPP; zenon_intro zenon_H2ae]. % 15.55/15.68 congruence. % 15.55/15.68 apply (zenon_L1023_); trivial. % 15.55/15.68 apply zenon_H2b2. apply refl_equal. % 15.55/15.68 apply zenon_H2b2. apply refl_equal. % 15.55/15.68 apply zenon_H1de. apply sym_equal. exact zenon_H1dd. % 15.55/15.68 (* end of lemma zenon_L1160_ *) % 15.55/15.68 assert (zenon_L1161_ : (((op (e3) (e0)) = (e2))\/(((op (e3) (e1)) = (e2))\/(((op (e3) (e2)) = (e2))\/((op (e3) (e3)) = (e2))))) -> ((op (e3) (e0)) = (e3)) -> (~((e2) = (e3))) -> (~((op (e2) (e1)) = (op (e3) (e1)))) -> ((op (e3) (e2)) = (e1)) -> ((op (e2) (e1)) = (e2)) -> (~((op (e2) (op (e3) (e2))) = (op (e3) (e2)))) -> (~((op (e3) (e3)) = (e2))) -> False). % 15.55/15.68 do 0 intro. intros zenon_H1df zenon_Hba zenon_H6a zenon_H13c zenon_H119 zenon_H156 zenon_H2af zenon_H3d. % 15.55/15.68 apply (zenon_or_s _ _ zenon_H1df); [ zenon_intro zenon_He9 | zenon_intro zenon_H1e0 ]. % 15.55/15.68 apply (zenon_L220_); trivial. % 15.55/15.68 apply (zenon_or_s _ _ zenon_H1e0); [ zenon_intro zenon_H16a | zenon_intro zenon_H1e1 ]. % 15.55/15.68 apply (zenon_L252_); trivial. % 15.55/15.68 apply (zenon_or_s _ _ zenon_H1e1); [ zenon_intro zenon_H1dd | zenon_intro zenon_H43 ]. % 15.55/15.68 apply (zenon_L1160_); trivial. % 15.55/15.68 exact (zenon_H3d zenon_H43). % 15.55/15.68 (* end of lemma zenon_L1161_ *) % 15.55/15.68 assert (zenon_L1162_ : (((op (e0) (e0)) = (e3))\/(((op (e1) (e0)) = (e3))\/(((op (e2) (e0)) = (e3))\/((op (e3) (e0)) = (e3))))) -> (~((op (e0) (e0)) = (e3))) -> (~((e2) = (e3))) -> ((op (e1) (e0)) = (e2)) -> ((op (e2) (e3)) = (e2)) -> (~((e1) = (e2))) -> (~((op (e2) (e2)) = (e1))) -> (~((op (e1) (e1)) = (op (e2) (e1)))) -> (((op (e2) (e0)) = (e1))\/(((op (e2) (e1)) = (e1))\/(((op (e2) (e2)) = (e1))\/((op (e2) (e3)) = (e1))))) -> (((op (e3) (e0)) = (e1))\/(((op (e3) (e1)) = (e1))\/(((op (e3) (e2)) = (e1))\/((op (e3) (e3)) = (e1))))) -> (~((e1) = (e3))) -> ((op (e1) (e1)) = (e1)) -> (~((op (e1) (op (e3) (e1))) = (op (e3) (e1)))) -> ((op (e0) (e2)) = (e1)) -> (~((op (e0) (e2)) = (op (e3) (e2)))) -> (~((op (e3) (e3)) = (e1))) -> False). % 15.55/15.68 do 0 intro. intros zenon_Hbe zenon_H59 zenon_H6a zenon_H68 zenon_H124 zenon_Ha7 zenon_H52 zenon_Hb1 zenon_Hb7 zenon_H146 zenon_Ha3 zenon_H21 zenon_H2b4 zenon_H29 zenon_H140 zenon_H104. % 15.55/15.68 apply (zenon_or_s _ _ zenon_Hbe); [ zenon_intro zenon_H5b | zenon_intro zenon_Hbf ]. % 15.55/15.68 exact (zenon_H59 zenon_H5b). % 15.55/15.68 apply (zenon_or_s _ _ zenon_Hbf); [ zenon_intro zenon_H69 | zenon_intro zenon_Hc0 ]. % 15.55/15.68 apply (zenon_L17_); trivial. % 15.55/15.68 apply (zenon_or_s _ _ zenon_Hc0); [ zenon_intro zenon_Haf | zenon_intro zenon_Hba ]. % 15.55/15.68 apply (zenon_L96_); trivial. % 15.55/15.68 apply (zenon_L1159_); trivial. % 15.55/15.68 (* end of lemma zenon_L1162_ *) % 15.55/15.68 assert (zenon_L1163_ : (((op (e3) (e0)) = (e1))\/(((op (e3) (e1)) = (e1))\/(((op (e3) (e2)) = (e1))\/((op (e3) (e3)) = (e1))))) -> ((op (e3) (e0)) = (e2)) -> (~((op (e0) (op (e3) (e0))) = (op (e3) (e0)))) -> ((op (e1) (e1)) = (e1)) -> (~((op (e1) (op (e3) (e1))) = (op (e3) (e1)))) -> ((op (e0) (e2)) = (e1)) -> (~((op (e0) (e2)) = (op (e3) (e2)))) -> (~((op (e3) (e3)) = (e1))) -> False). % 15.55/15.68 do 0 intro. intros zenon_H146 zenon_He9 zenon_H2b8 zenon_H21 zenon_H2b4 zenon_H29 zenon_H140 zenon_H104. % 15.55/15.68 apply (zenon_or_s _ _ zenon_H146); [ zenon_intro zenon_Hee | zenon_intro zenon_H14b ]. % 15.55/15.68 apply (zenon_L1082_); trivial. % 15.55/15.68 apply (zenon_or_s _ _ zenon_H14b); [ zenon_intro zenon_H13e | zenon_intro zenon_H14c ]. % 15.55/15.68 apply (zenon_L1158_); trivial. % 15.55/15.68 apply (zenon_or_s _ _ zenon_H14c); [ zenon_intro zenon_H119 | zenon_intro zenon_H38 ]. % 15.55/15.68 apply (zenon_L124_); trivial. % 15.55/15.68 exact (zenon_H104 zenon_H38). % 15.55/15.68 (* end of lemma zenon_L1163_ *) % 15.55/15.68 assert (zenon_L1164_ : (((op (e0) (e2)) = (e1))\/(((op (e1) (e2)) = (e1))\/(((op (e2) (e2)) = (e1))\/((op (e3) (e2)) = (e1))))) -> ((op (e3) (e0)) = (e1)) -> ((op (e3) (e0)) = (e2)) -> (~((op (e0) (op (e3) (e0))) = (op (e3) (e0)))) -> ((op (e1) (e1)) = (e1)) -> (~((op (e1) (e1)) = (op (e1) (e2)))) -> (~((op (e2) (e2)) = (e1))) -> (~((e1) = (e3))) -> ((op (e3) (e2)) = (e3)) -> False). % 15.55/15.68 do 0 intro. intros zenon_H11b zenon_Hee zenon_He9 zenon_H2b8 zenon_H21 zenon_H116 zenon_H52 zenon_Ha3 zenon_H106. % 15.55/15.68 apply (zenon_or_s _ _ zenon_H11b); [ zenon_intro zenon_H29 | zenon_intro zenon_H11c ]. % 15.55/15.68 apply (zenon_L1082_); trivial. % 15.55/15.68 apply (zenon_or_s _ _ zenon_H11c); [ zenon_intro zenon_H117 | zenon_intro zenon_H11d ]. % 15.55/15.68 apply (zenon_L86_); trivial. % 15.55/15.68 apply (zenon_or_s _ _ zenon_H11d); [ zenon_intro zenon_H2a | zenon_intro zenon_H119 ]. % 15.55/15.68 exact (zenon_H52 zenon_H2a). % 15.55/15.68 apply (zenon_L87_); trivial. % 15.55/15.68 (* end of lemma zenon_L1164_ *) % 15.55/15.68 assert (zenon_L1165_ : (((op (e0) (e0)) = (e1))\/(((op (e0) (e1)) = (e1))\/(((op (e0) (e2)) = (e1))\/((op (e0) (e3)) = (e1))))) -> (~((op (e0) (e1)) = (op (e1) (e1)))) -> (~((op (e0) (op (e3) (e0))) = (op (e3) (e0)))) -> (~((op (e2) (e0)) = (op (e2) (e3)))) -> ((op (e2) (e3)) = (e2)) -> (((op (e0) (e0)) = (e3))\/(((op (e1) (e0)) = (e3))\/(((op (e2) (e0)) = (e3))\/((op (e3) (e0)) = (e3))))) -> (~((op (e0) (e0)) = (e3))) -> (~((e2) = (e3))) -> (~((e1) = (e2))) -> (~((op (e1) (e1)) = (op (e2) (e1)))) -> (((op (e2) (e0)) = (e1))\/(((op (e2) (e1)) = (e1))\/(((op (e2) (e2)) = (e1))\/((op (e2) (e3)) = (e1))))) -> (((op (e3) (e0)) = (e1))\/(((op (e3) (e1)) = (e1))\/(((op (e3) (e2)) = (e1))\/((op (e3) (e3)) = (e1))))) -> (~((op (e1) (op (e3) (e1))) = (op (e3) (e1)))) -> (~((op (e0) (e2)) = (op (e3) (e2)))) -> (~((op (e3) (e3)) = (e1))) -> (~((op (e0) (e0)) = (e2))) -> (((op (e0) (e0)) = (e2))\/(((op (e1) (e0)) = (e2))\/(((op (e2) (e0)) = (e2))\/((op (e3) (e0)) = (e2))))) -> (~((op (e1) (e0)) = (op (e1) (e1)))) -> (~((op (e0) (e0)) = (e1))) -> (((op (e0) (e0)) = (e1))\/(((op (e1) (e0)) = (e1))\/(((op (e2) (e0)) = (e1))\/((op (e3) (e0)) = (e1))))) -> (((op (e0) (e2)) = (e1))\/(((op (e1) (e2)) = (e1))\/(((op (e2) (e2)) = (e1))\/((op (e3) (e2)) = (e1))))) -> (~((op (e0) (e2)) = (op (e0) (e3)))) -> ((op (e1) (e1)) = (e1)) -> (~((op (e1) (e1)) = (op (e1) (e2)))) -> (~((op (e2) (e2)) = (e1))) -> (~((e1) = (e3))) -> ((op (e3) (e2)) = (e3)) -> False). % 15.55/15.68 do 0 intro. intros zenon_H44 zenon_H23 zenon_H2b8 zenon_Hce zenon_H124 zenon_Hbe zenon_H59 zenon_H6a zenon_Ha7 zenon_Hb1 zenon_Hb7 zenon_H146 zenon_H2b4 zenon_H140 zenon_H104 zenon_H8f zenon_Heb zenon_Hd7 zenon_H45 zenon_Hf1 zenon_H11b zenon_Hc9 zenon_H21 zenon_H116 zenon_H52 zenon_Ha3 zenon_H106. % 15.55/15.68 apply (zenon_or_s _ _ zenon_H44); [ zenon_intro zenon_H47 | zenon_intro zenon_H46 ]. % 15.55/15.68 exact (zenon_H45 zenon_H47). % 15.55/15.68 apply (zenon_or_s _ _ zenon_H46); [ zenon_intro zenon_H22 | zenon_intro zenon_H48 ]. % 15.55/15.68 apply (zenon_L3_); trivial. % 15.55/15.68 apply (zenon_or_s _ _ zenon_H48); [ zenon_intro zenon_H29 | zenon_intro zenon_H37 ]. % 15.55/15.68 apply (zenon_or_s _ _ zenon_Hf1); [ zenon_intro zenon_H47 | zenon_intro zenon_Hf4 ]. % 15.55/15.68 exact (zenon_H45 zenon_H47). % 15.55/15.68 apply (zenon_or_s _ _ zenon_Hf4); [ zenon_intro zenon_Hd8 | zenon_intro zenon_Hf5 ]. % 15.55/15.68 apply (zenon_L61_); trivial. % 15.55/15.68 apply (zenon_or_s _ _ zenon_Hf5); [ zenon_intro zenon_Hae | zenon_intro zenon_Hee ]. % 15.55/15.68 apply (zenon_or_s _ _ zenon_Heb); [ zenon_intro zenon_H92 | zenon_intro zenon_Hec ]. % 15.55/15.68 exact (zenon_H8f zenon_H92). % 15.55/15.68 apply (zenon_or_s _ _ zenon_Hec); [ zenon_intro zenon_H68 | zenon_intro zenon_Hed ]. % 15.55/15.68 apply (zenon_L1162_); trivial. % 15.55/15.68 apply (zenon_or_s _ _ zenon_Hed); [ zenon_intro zenon_Hdd | zenon_intro zenon_He9 ]. % 15.55/15.68 apply (zenon_L304_); trivial. % 15.55/15.68 apply (zenon_L1163_); trivial. % 15.55/15.68 apply (zenon_or_s _ _ zenon_Heb); [ zenon_intro zenon_H92 | zenon_intro zenon_Hec ]. % 15.55/15.68 exact (zenon_H8f zenon_H92). % 15.55/15.68 apply (zenon_or_s _ _ zenon_Hec); [ zenon_intro zenon_H68 | zenon_intro zenon_Hed ]. % 15.55/15.68 apply (zenon_L1162_); trivial. % 15.55/15.68 apply (zenon_or_s _ _ zenon_Hed); [ zenon_intro zenon_Hdd | zenon_intro zenon_He9 ]. % 15.55/15.68 apply (zenon_L119_); trivial. % 15.55/15.68 apply (zenon_L1164_); trivial. % 15.55/15.68 apply (zenon_L88_); trivial. % 15.55/15.68 (* end of lemma zenon_L1165_ *) % 15.55/15.68 assert (zenon_L1166_ : (((op (e0) (e0)) = (e3))\/(((op (e1) (e0)) = (e3))\/(((op (e2) (e0)) = (e3))\/((op (e3) (e0)) = (e3))))) -> (~((op (e0) (e0)) = (e3))) -> (~((e2) = (e3))) -> ((op (e1) (e0)) = (e2)) -> ((op (e2) (e3)) = (e2)) -> (~((e1) = (e2))) -> (~((op (e2) (e2)) = (e1))) -> (~((op (e1) (e1)) = (op (e2) (e1)))) -> ((op (e1) (e1)) = (e1)) -> (~((e1) = (e3))) -> (((op (e2) (e0)) = (e1))\/(((op (e2) (e1)) = (e1))\/(((op (e2) (e2)) = (e1))\/((op (e2) (e3)) = (e1))))) -> (~((op (e0) (op (e3) (e0))) = (op (e3) (e0)))) -> ((op (e0) (e3)) = (e3)) -> False). % 15.55/15.68 do 0 intro. intros zenon_Hbe zenon_H59 zenon_H6a zenon_H68 zenon_H124 zenon_Ha7 zenon_H52 zenon_Hb1 zenon_H21 zenon_Ha3 zenon_Hb7 zenon_H2b8 zenon_H53. % 15.55/15.68 apply (zenon_or_s _ _ zenon_Hbe); [ zenon_intro zenon_H5b | zenon_intro zenon_Hbf ]. % 15.55/15.68 exact (zenon_H59 zenon_H5b). % 15.55/15.68 apply (zenon_or_s _ _ zenon_Hbf); [ zenon_intro zenon_H69 | zenon_intro zenon_Hc0 ]. % 15.55/15.68 apply (zenon_L17_); trivial. % 15.55/15.68 apply (zenon_or_s _ _ zenon_Hc0); [ zenon_intro zenon_Haf | zenon_intro zenon_Hba ]. % 15.55/15.68 apply (zenon_L96_); trivial. % 15.55/15.68 apply (zenon_L1035_); trivial. % 15.55/15.68 (* end of lemma zenon_L1166_ *) % 15.55/15.68 assert (zenon_L1167_ : (((op (e0) (e0)) = (e3))\/(((op (e0) (e1)) = (e3))\/(((op (e0) (e2)) = (e3))\/((op (e0) (e3)) = (e3))))) -> (~((op (e0) (e1)) = (op (e3) (e1)))) -> ((op (e3) (e1)) = (e3)) -> ((op (e0) (e2)) = (e1)) -> (((op (e0) (e0)) = (e3))\/(((op (e1) (e0)) = (e3))\/(((op (e2) (e0)) = (e3))\/((op (e3) (e0)) = (e3))))) -> (~((op (e0) (e0)) = (e3))) -> (~((e2) = (e3))) -> ((op (e1) (e0)) = (e2)) -> ((op (e2) (e3)) = (e2)) -> (~((e1) = (e2))) -> (~((op (e2) (e2)) = (e1))) -> (~((op (e1) (e1)) = (op (e2) (e1)))) -> ((op (e1) (e1)) = (e1)) -> (~((e1) = (e3))) -> (((op (e2) (e0)) = (e1))\/(((op (e2) (e1)) = (e1))\/(((op (e2) (e2)) = (e1))\/((op (e2) (e3)) = (e1))))) -> (~((op (e0) (op (e3) (e0))) = (op (e3) (e0)))) -> False). % 15.55/15.68 do 0 intro. intros zenon_H58 zenon_H138 zenon_H10a zenon_H29 zenon_Hbe zenon_H59 zenon_H6a zenon_H68 zenon_H124 zenon_Ha7 zenon_H52 zenon_Hb1 zenon_H21 zenon_Ha3 zenon_Hb7 zenon_H2b8. % 15.55/15.68 apply (zenon_or_s _ _ zenon_H58); [ zenon_intro zenon_H5b | zenon_intro zenon_H5a ]. % 15.55/15.68 exact (zenon_H59 zenon_H5b). % 15.55/15.68 apply (zenon_or_s _ _ zenon_H5a); [ zenon_intro zenon_H4a | zenon_intro zenon_H5c ]. % 15.55/15.68 apply (zenon_L120_); trivial. % 15.55/15.68 apply (zenon_or_s _ _ zenon_H5c); [ zenon_intro zenon_H50 | zenon_intro zenon_H53 ]. % 15.55/15.68 apply (zenon_L29_); trivial. % 15.55/15.68 apply (zenon_L1166_); trivial. % 15.55/15.68 (* end of lemma zenon_L1167_ *) % 15.55/15.68 assert (zenon_L1168_ : ((~((op (e3) (e3)) = (e0)))\/((op (e3) (e0)) = (e3))) -> (~((op (e3) (e0)) = (op (e3) (e2)))) -> (~((op (e3) (e0)) = (op (e3) (e1)))) -> ((~((op (e3) (e3)) = (e2)))\/((op (e3) (e2)) = (e3))) -> (((op (e0) (e2)) = (e1))\/(((op (e1) (e2)) = (e1))\/(((op (e2) (e2)) = (e1))\/((op (e3) (e2)) = (e1))))) -> (~((op (e1) (e1)) = (op (e1) (e2)))) -> (~((op (e0) (op (e3) (e0))) = (op (e3) (e0)))) -> (~((op (e0) (e2)) = (op (e0) (e3)))) -> (((op (e0) (e0)) = (e1))\/(((op (e0) (e1)) = (e1))\/(((op (e0) (e2)) = (e1))\/((op (e0) (e3)) = (e1))))) -> (~((op (e0) (e3)) = (op (e3) (e3)))) -> (~((op (e1) (e0)) = (op (e1) (e1)))) -> (((op (e0) (e3)) = (e0))\/(((op (e1) (e3)) = (e0))\/(((op (e2) (e3)) = (e0))\/((op (e3) (e3)) = (e0))))) -> (~((op (e2) (e2)) = (e0))) -> (~((op (e2) (e2)) = (e1))) -> (~((op (e2) (e2)) = (e2))) -> (((op (e2) (e2)) = (e0))\/(((op (e2) (e2)) = (e1))\/(((op (e2) (e2)) = (e2))\/((op (e2) (e2)) = (e3))))) -> ((op (e2) (e3)) = (e2)) -> (~((e0) = (e2))) -> (~((op (e1) (e3)) = (op (e3) (e3)))) -> (((op (e3) (e3)) = (e0))\/(((op (e3) (e3)) = (e1))\/(((op (e3) (e3)) = (e2))\/((op (e3) (e3)) = (e3))))) -> ((op (e0) (e0)) = (e0)) -> (~((op (e0) (e0)) = (op (e0) (e3)))) -> (((op (e0) (e0)) = (e2))\/(((op (e1) (e0)) = (e2))\/(((op (e2) (e0)) = (e2))\/((op (e3) (e0)) = (e2))))) -> (~((op (e2) (e0)) = (op (e2) (e3)))) -> (~((op (e0) (e0)) = (e3))) -> (~((e2) = (e3))) -> (((op (e2) (e0)) = (e1))\/(((op (e2) (e1)) = (e1))\/(((op (e2) (e2)) = (e1))\/((op (e2) (e3)) = (e1))))) -> (~((e1) = (e2))) -> (~((op (e1) (e1)) = (op (e2) (e1)))) -> (~((e1) = (e3))) -> (((op (e3) (e0)) = (e1))\/(((op (e3) (e1)) = (e1))\/(((op (e3) (e2)) = (e1))\/((op (e3) (e3)) = (e1))))) -> (~((op (e0) (e2)) = (op (e3) (e2)))) -> (~((op (e1) (op (e3) (e1))) = (op (e3) (e1)))) -> (((op (e0) (e0)) = (e3))\/(((op (e1) (e0)) = (e3))\/(((op (e2) (e0)) = (e3))\/((op (e3) (e0)) = (e3))))) -> (~((op (e0) (e0)) = (e2))) -> (((op (e0) (e0)) = (e1))\/(((op (e1) (e0)) = (e1))\/(((op (e2) (e0)) = (e1))\/((op (e3) (e0)) = (e1))))) -> ((op (e1) (e1)) = (e1)) -> (~((op (e0) (e1)) = (op (e1) (e1)))) -> (~((op (e0) (e0)) = (e1))) -> (~((op (e3) (op (e3) (e3))) = (op (e3) (e3)))) -> ((~((op (e3) (e3)) = (e3)))\/((op (e3) (e3)) = (e3))) -> (~((op (e3) (e1)) = (op (e3) (e2)))) -> (((op (e0) (e0)) = (e2))\/(((op (e0) (e1)) = (e2))\/(((op (e0) (e2)) = (e2))\/((op (e0) (e3)) = (e2))))) -> (((op (e0) (e0)) = (e3))\/(((op (e0) (e1)) = (e3))\/(((op (e0) (e2)) = (e3))\/((op (e0) (e3)) = (e3))))) -> (~((op (e0) (e1)) = (op (e3) (e1)))) -> (~((op (e1) (e1)) = (e0))) -> (((op (e2) (e0)) = (e3))\/(((op (e2) (e1)) = (e3))\/(((op (e2) (e2)) = (e3))\/((op (e2) (e3)) = (e3))))) -> (~((op (e0) (e3)) = (op (e2) (e3)))) -> (~((op (e2) (e1)) = (op (e3) (e1)))) -> (~((e0) = (e3))) -> (((op (e0) (e1)) = (e0))\/(((op (e1) (e1)) = (e0))\/(((op (e2) (e1)) = (e0))\/((op (e3) (e1)) = (e0))))) -> (((op (e1) (e0)) = (e0))\/(((op (e1) (e1)) = (e0))\/(((op (e1) (e2)) = (e0))\/((op (e1) (e3)) = (e0))))) -> (((op (e0) (e3)) = (e2))\/(((op (e1) (e3)) = (e2))\/(((op (e2) (e3)) = (e2))\/((op (e3) (e3)) = (e2))))) -> (~((op (e1) (e2)) = (op (e3) (e2)))) -> (((op (e3) (e0)) = (e0))\/(((op (e3) (e1)) = (e0))\/(((op (e3) (e2)) = (e0))\/((op (e3) (e3)) = (e0))))) -> (~((op (e0) (e0)) = (op (e1) (e0)))) -> ((~((op (e3) (e3)) = (e1)))\/((op (e3) (e1)) = (e3))) -> False). % 15.55/15.68 do 0 intro. intros zenon_H10f zenon_H105 zenon_H109 zenon_H10e zenon_H11b zenon_H116 zenon_H2b8 zenon_Hc9 zenon_H44 zenon_H36 zenon_Hd7 zenon_Hd3 zenon_H2e zenon_H52 zenon_H2f zenon_H2d zenon_H124 zenon_H5e zenon_H8b zenon_H3b zenon_H1f zenon_H24f zenon_Heb zenon_Hce zenon_H59 zenon_H6a zenon_Hb7 zenon_Ha7 zenon_Hb1 zenon_Ha3 zenon_H146 zenon_H140 zenon_H2b4 zenon_Hbe zenon_H8f zenon_Hf1 zenon_H21 zenon_H23 zenon_H45 zenon_H2be zenon_H10d zenon_H135 zenon_H8e zenon_H58 zenon_H138 zenon_H145 zenon_He6 zenon_Hb4 zenon_H13c zenon_H4b zenon_H144 zenon_H163 zenon_H160 zenon_H17d zenon_H1f6 zenon_H24c zenon_H10c. % 15.55/15.68 apply (zenon_or_s _ _ zenon_H10f); [ zenon_intro zenon_H3c | zenon_intro zenon_Hba ]. % 15.55/15.68 apply (zenon_or_s _ _ zenon_H10c); [ zenon_intro zenon_H104 | zenon_intro zenon_H10a ]. % 15.55/15.68 apply (zenon_or_s _ _ zenon_H10e); [ zenon_intro zenon_H3d | zenon_intro zenon_H106 ]. % 15.55/15.68 apply (zenon_or_s _ _ zenon_H10d); [ zenon_intro zenon_H3e | zenon_intro zenon_H42 ]. % 15.55/15.68 apply (zenon_or_s _ _ zenon_H44); [ zenon_intro zenon_H47 | zenon_intro zenon_H46 ]. % 15.55/15.68 exact (zenon_H45 zenon_H47). % 15.55/15.68 apply (zenon_or_s _ _ zenon_H46); [ zenon_intro zenon_H22 | zenon_intro zenon_H48 ]. % 15.55/15.68 apply (zenon_L3_); trivial. % 15.55/15.68 apply (zenon_or_s _ _ zenon_H48); [ zenon_intro zenon_H29 | zenon_intro zenon_H37 ]. % 15.55/15.68 apply (zenon_or_s _ _ zenon_Hf1); [ zenon_intro zenon_H47 | zenon_intro zenon_Hf4 ]. % 15.55/15.68 exact (zenon_H45 zenon_H47). % 15.55/15.68 apply (zenon_or_s _ _ zenon_Hf4); [ zenon_intro zenon_Hd8 | zenon_intro zenon_Hf5 ]. % 15.55/15.68 apply (zenon_L61_); trivial. % 15.55/15.68 apply (zenon_or_s _ _ zenon_Hf5); [ zenon_intro zenon_Hae | zenon_intro zenon_Hee ]. % 15.55/15.68 apply (zenon_L684_); trivial. % 15.55/15.68 apply (zenon_or_s _ _ zenon_Heb); [ zenon_intro zenon_H92 | zenon_intro zenon_Hec ]. % 15.55/15.68 exact (zenon_H8f zenon_H92). % 15.55/15.68 apply (zenon_or_s _ _ zenon_Hec); [ zenon_intro zenon_H68 | zenon_intro zenon_Hed ]. % 15.55/15.68 apply (zenon_L1162_); trivial. % 15.55/15.68 apply (zenon_or_s _ _ zenon_Hed); [ zenon_intro zenon_Hdd | zenon_intro zenon_He9 ]. % 15.55/15.68 apply (zenon_L119_); trivial. % 15.55/15.68 apply (zenon_L122_); trivial. % 15.55/15.68 apply (zenon_L7_); trivial. % 15.55/15.68 apply (zenon_L1041_); trivial. % 15.55/15.68 apply (zenon_L1165_); trivial. % 15.55/15.68 apply (zenon_or_s _ _ zenon_H10e); [ zenon_intro zenon_H3d | zenon_intro zenon_H106 ]. % 15.55/15.68 apply (zenon_or_s _ _ zenon_H10d); [ zenon_intro zenon_H3e | zenon_intro zenon_H42 ]. % 15.55/15.68 apply (zenon_or_s _ _ zenon_H44); [ zenon_intro zenon_H47 | zenon_intro zenon_H46 ]. % 15.55/15.68 exact (zenon_H45 zenon_H47). % 15.55/15.68 apply (zenon_or_s _ _ zenon_H46); [ zenon_intro zenon_H22 | zenon_intro zenon_H48 ]. % 15.55/15.68 apply (zenon_L3_); trivial. % 15.55/15.68 apply (zenon_or_s _ _ zenon_H48); [ zenon_intro zenon_H29 | zenon_intro zenon_H37 ]. % 15.55/15.68 apply (zenon_or_s _ _ zenon_Hf1); [ zenon_intro zenon_H47 | zenon_intro zenon_Hf4 ]. % 15.55/15.68 exact (zenon_H45 zenon_H47). % 15.55/15.68 apply (zenon_or_s _ _ zenon_Hf4); [ zenon_intro zenon_Hd8 | zenon_intro zenon_Hf5 ]. % 15.55/15.68 apply (zenon_L61_); trivial. % 15.55/15.68 apply (zenon_or_s _ _ zenon_Hf5); [ zenon_intro zenon_Hae | zenon_intro zenon_Hee ]. % 15.55/15.68 apply (zenon_or_s _ _ zenon_H8e); [ zenon_intro zenon_H92 | zenon_intro zenon_H91 ]. % 15.55/15.68 exact (zenon_H8f zenon_H92). % 15.55/15.68 apply (zenon_or_s _ _ zenon_H91); [ zenon_intro zenon_H5d | zenon_intro zenon_H93 ]. % 15.55/15.68 apply (zenon_or_s _ _ zenon_Heb); [ zenon_intro zenon_H92 | zenon_intro zenon_Hec ]. % 15.55/15.68 exact (zenon_H8f zenon_H92). % 15.55/15.68 apply (zenon_or_s _ _ zenon_Hec); [ zenon_intro zenon_H68 | zenon_intro zenon_Hed ]. % 15.55/15.68 apply (zenon_L1167_); trivial. % 15.55/15.68 apply (zenon_or_s _ _ zenon_Hed); [ zenon_intro zenon_Hdd | zenon_intro zenon_He9 ]. % 15.55/15.68 apply (zenon_L304_); trivial. % 15.55/15.68 apply (zenon_L127_); trivial. % 15.55/15.68 apply (zenon_or_s _ _ zenon_H93); [ zenon_intro zenon_H63 | zenon_intro zenon_H81 ]. % 15.55/15.68 apply (zenon_L104_); trivial. % 15.55/15.68 apply (zenon_L129_); trivial. % 15.55/15.68 apply (zenon_or_s _ _ zenon_Heb); [ zenon_intro zenon_H92 | zenon_intro zenon_Hec ]. % 15.55/15.68 exact (zenon_H8f zenon_H92). % 15.55/15.68 apply (zenon_or_s _ _ zenon_Hec); [ zenon_intro zenon_H68 | zenon_intro zenon_Hed ]. % 15.55/15.68 apply (zenon_L1167_); trivial. % 15.55/15.68 apply (zenon_or_s _ _ zenon_Hed); [ zenon_intro zenon_Hdd | zenon_intro zenon_He9 ]. % 15.55/15.68 apply (zenon_L1112_); trivial. % 15.55/15.68 apply (zenon_L122_); trivial. % 15.55/15.68 apply (zenon_L7_); trivial. % 15.55/15.68 apply (zenon_L1041_); trivial. % 15.55/15.68 apply (zenon_L115_); trivial. % 15.55/15.68 apply (zenon_or_s _ _ zenon_H10c); [ zenon_intro zenon_H104 | zenon_intro zenon_H10a ]. % 15.55/15.68 apply (zenon_or_s _ _ zenon_H10e); [ zenon_intro zenon_H3d | zenon_intro zenon_H106 ]. % 15.55/15.68 apply (zenon_or_s _ _ zenon_H10d); [ zenon_intro zenon_H3e | zenon_intro zenon_H42 ]. % 15.55/15.68 apply (zenon_L895_); trivial. % 15.55/15.68 apply (zenon_L1041_); trivial. % 15.55/15.68 apply (zenon_L81_); trivial. % 15.55/15.68 apply (zenon_L82_); trivial. % 15.55/15.68 (* end of lemma zenon_L1168_ *) % 15.55/15.68 assert (zenon_L1169_ : (((op (e2) (e0)) = (e2))\/(((op (e2) (e1)) = (e2))\/(((op (e2) (e2)) = (e2))\/((op (e2) (e3)) = (e2))))) -> (~((op (e3) (e3)) = (e2))) -> (~((op (e2) (op (e3) (e2))) = (op (e3) (e2)))) -> ((op (e3) (e2)) = (e1)) -> ((op (e3) (e0)) = (e3)) -> (((op (e3) (e0)) = (e2))\/(((op (e3) (e1)) = (e2))\/(((op (e3) (e2)) = (e2))\/((op (e3) (e3)) = (e2))))) -> ((~((op (e3) (e3)) = (e0)))\/((op (e3) (e0)) = (e3))) -> (~((op (e3) (e0)) = (op (e3) (e2)))) -> (~((op (e3) (e0)) = (op (e3) (e1)))) -> ((~((op (e3) (e3)) = (e2)))\/((op (e3) (e2)) = (e3))) -> (((op (e0) (e2)) = (e1))\/(((op (e1) (e2)) = (e1))\/(((op (e2) (e2)) = (e1))\/((op (e3) (e2)) = (e1))))) -> (~((op (e1) (e1)) = (op (e1) (e2)))) -> (~((op (e0) (op (e3) (e0))) = (op (e3) (e0)))) -> (~((op (e0) (e2)) = (op (e0) (e3)))) -> (((op (e0) (e0)) = (e1))\/(((op (e0) (e1)) = (e1))\/(((op (e0) (e2)) = (e1))\/((op (e0) (e3)) = (e1))))) -> (~((op (e0) (e3)) = (op (e3) (e3)))) -> (~((op (e1) (e0)) = (op (e1) (e1)))) -> (((op (e0) (e3)) = (e0))\/(((op (e1) (e3)) = (e0))\/(((op (e2) (e3)) = (e0))\/((op (e3) (e3)) = (e0))))) -> (~((op (e2) (e2)) = (e0))) -> (~((op (e2) (e2)) = (e1))) -> (~((op (e2) (e2)) = (e2))) -> (((op (e2) (e2)) = (e0))\/(((op (e2) (e2)) = (e1))\/(((op (e2) (e2)) = (e2))\/((op (e2) (e2)) = (e3))))) -> (~((e0) = (e2))) -> (~((op (e1) (e3)) = (op (e3) (e3)))) -> (((op (e3) (e3)) = (e0))\/(((op (e3) (e3)) = (e1))\/(((op (e3) (e3)) = (e2))\/((op (e3) (e3)) = (e3))))) -> ((op (e0) (e0)) = (e0)) -> (~((op (e0) (e0)) = (op (e0) (e3)))) -> (((op (e0) (e0)) = (e2))\/(((op (e1) (e0)) = (e2))\/(((op (e2) (e0)) = (e2))\/((op (e3) (e0)) = (e2))))) -> (~((op (e2) (e0)) = (op (e2) (e3)))) -> (~((op (e0) (e0)) = (e3))) -> (~((e2) = (e3))) -> (((op (e2) (e0)) = (e1))\/(((op (e2) (e1)) = (e1))\/(((op (e2) (e2)) = (e1))\/((op (e2) (e3)) = (e1))))) -> (~((e1) = (e2))) -> (~((op (e1) (e1)) = (op (e2) (e1)))) -> (~((e1) = (e3))) -> (((op (e3) (e0)) = (e1))\/(((op (e3) (e1)) = (e1))\/(((op (e3) (e2)) = (e1))\/((op (e3) (e3)) = (e1))))) -> (~((op (e0) (e2)) = (op (e3) (e2)))) -> (~((op (e1) (op (e3) (e1))) = (op (e3) (e1)))) -> (((op (e0) (e0)) = (e3))\/(((op (e1) (e0)) = (e3))\/(((op (e2) (e0)) = (e3))\/((op (e3) (e0)) = (e3))))) -> (~((op (e0) (e0)) = (e2))) -> (((op (e0) (e0)) = (e1))\/(((op (e1) (e0)) = (e1))\/(((op (e2) (e0)) = (e1))\/((op (e3) (e0)) = (e1))))) -> ((op (e1) (e1)) = (e1)) -> (~((op (e0) (e1)) = (op (e1) (e1)))) -> (~((op (e0) (e0)) = (e1))) -> (~((op (e3) (op (e3) (e3))) = (op (e3) (e3)))) -> ((~((op (e3) (e3)) = (e3)))\/((op (e3) (e3)) = (e3))) -> (~((op (e3) (e1)) = (op (e3) (e2)))) -> (((op (e0) (e0)) = (e2))\/(((op (e0) (e1)) = (e2))\/(((op (e0) (e2)) = (e2))\/((op (e0) (e3)) = (e2))))) -> (((op (e0) (e0)) = (e3))\/(((op (e0) (e1)) = (e3))\/(((op (e0) (e2)) = (e3))\/((op (e0) (e3)) = (e3))))) -> (~((op (e0) (e1)) = (op (e3) (e1)))) -> (~((op (e1) (e1)) = (e0))) -> (((op (e2) (e0)) = (e3))\/(((op (e2) (e1)) = (e3))\/(((op (e2) (e2)) = (e3))\/((op (e2) (e3)) = (e3))))) -> (~((op (e0) (e3)) = (op (e2) (e3)))) -> (~((op (e2) (e1)) = (op (e3) (e1)))) -> (~((e0) = (e3))) -> (((op (e0) (e1)) = (e0))\/(((op (e1) (e1)) = (e0))\/(((op (e2) (e1)) = (e0))\/((op (e3) (e1)) = (e0))))) -> (((op (e1) (e0)) = (e0))\/(((op (e1) (e1)) = (e0))\/(((op (e1) (e2)) = (e0))\/((op (e1) (e3)) = (e0))))) -> (((op (e0) (e3)) = (e2))\/(((op (e1) (e3)) = (e2))\/(((op (e2) (e3)) = (e2))\/((op (e3) (e3)) = (e2))))) -> (~((op (e1) (e2)) = (op (e3) (e2)))) -> (((op (e3) (e0)) = (e0))\/(((op (e3) (e1)) = (e0))\/(((op (e3) (e2)) = (e0))\/((op (e3) (e3)) = (e0))))) -> (~((op (e0) (e0)) = (op (e1) (e0)))) -> ((~((op (e3) (e3)) = (e1)))\/((op (e3) (e1)) = (e3))) -> False). % 15.55/15.68 do 0 intro. intros zenon_H237 zenon_H3d zenon_H2af zenon_H119 zenon_Hba zenon_H1df zenon_H10f zenon_H105 zenon_H109 zenon_H10e zenon_H11b zenon_H116 zenon_H2b8 zenon_Hc9 zenon_H44 zenon_H36 zenon_Hd7 zenon_Hd3 zenon_H2e zenon_H52 zenon_H2f zenon_H2d zenon_H5e zenon_H8b zenon_H3b zenon_H1f zenon_H24f zenon_Heb zenon_Hce zenon_H59 zenon_H6a zenon_Hb7 zenon_Ha7 zenon_Hb1 zenon_Ha3 zenon_H146 zenon_H140 zenon_H2b4 zenon_Hbe zenon_H8f zenon_Hf1 zenon_H21 zenon_H23 zenon_H45 zenon_H2be zenon_H10d zenon_H135 zenon_H8e zenon_H58 zenon_H138 zenon_H145 zenon_He6 zenon_Hb4 zenon_H13c zenon_H4b zenon_H144 zenon_H163 zenon_H160 zenon_H17d zenon_H1f6 zenon_H24c zenon_H10c. % 15.55/15.68 apply (zenon_or_s _ _ zenon_H237); [ zenon_intro zenon_Hdd | zenon_intro zenon_H238 ]. % 15.55/15.68 apply (zenon_L310_); trivial. % 15.55/15.68 apply (zenon_or_s _ _ zenon_H238); [ zenon_intro zenon_H156 | zenon_intro zenon_H239 ]. % 15.55/15.68 apply (zenon_L1161_); trivial. % 15.55/15.68 apply (zenon_or_s _ _ zenon_H239); [ zenon_intro zenon_H35 | zenon_intro zenon_H124 ]. % 15.55/15.68 exact (zenon_H2f zenon_H35). % 15.55/15.68 apply (zenon_L1168_); trivial. % 15.55/15.68 (* end of lemma zenon_L1169_ *) % 15.55/15.68 assert (zenon_L1170_ : (~((op (e3) (e3)) = (e1))) -> (((op (e2) (e0)) = (e2))\/(((op (e2) (e1)) = (e2))\/(((op (e2) (e2)) = (e2))\/((op (e2) (e3)) = (e2))))) -> (~((op (e3) (e3)) = (e2))) -> (~((op (e2) (op (e3) (e2))) = (op (e3) (e2)))) -> ((op (e3) (e0)) = (e3)) -> (((op (e3) (e0)) = (e2))\/(((op (e3) (e1)) = (e2))\/(((op (e3) (e2)) = (e2))\/((op (e3) (e3)) = (e2))))) -> ((~((op (e3) (e3)) = (e0)))\/((op (e3) (e0)) = (e3))) -> (~((op (e3) (e0)) = (op (e3) (e2)))) -> (~((op (e3) (e0)) = (op (e3) (e1)))) -> ((~((op (e3) (e3)) = (e2)))\/((op (e3) (e2)) = (e3))) -> (((op (e0) (e2)) = (e1))\/(((op (e1) (e2)) = (e1))\/(((op (e2) (e2)) = (e1))\/((op (e3) (e2)) = (e1))))) -> (~((op (e1) (e1)) = (op (e1) (e2)))) -> (~((op (e0) (op (e3) (e0))) = (op (e3) (e0)))) -> (~((op (e0) (e2)) = (op (e0) (e3)))) -> (((op (e0) (e0)) = (e1))\/(((op (e0) (e1)) = (e1))\/(((op (e0) (e2)) = (e1))\/((op (e0) (e3)) = (e1))))) -> (~((op (e0) (e3)) = (op (e3) (e3)))) -> (~((op (e1) (e0)) = (op (e1) (e1)))) -> (((op (e0) (e3)) = (e0))\/(((op (e1) (e3)) = (e0))\/(((op (e2) (e3)) = (e0))\/((op (e3) (e3)) = (e0))))) -> (~((op (e2) (e2)) = (e0))) -> (~((op (e2) (e2)) = (e1))) -> (~((op (e2) (e2)) = (e2))) -> (((op (e2) (e2)) = (e0))\/(((op (e2) (e2)) = (e1))\/(((op (e2) (e2)) = (e2))\/((op (e2) (e2)) = (e3))))) -> (~((e0) = (e2))) -> (~((op (e1) (e3)) = (op (e3) (e3)))) -> (((op (e3) (e3)) = (e0))\/(((op (e3) (e3)) = (e1))\/(((op (e3) (e3)) = (e2))\/((op (e3) (e3)) = (e3))))) -> ((op (e0) (e0)) = (e0)) -> (~((op (e0) (e0)) = (op (e0) (e3)))) -> (((op (e0) (e0)) = (e2))\/(((op (e1) (e0)) = (e2))\/(((op (e2) (e0)) = (e2))\/((op (e3) (e0)) = (e2))))) -> (~((op (e2) (e0)) = (op (e2) (e3)))) -> (~((op (e0) (e0)) = (e3))) -> (~((e2) = (e3))) -> (((op (e2) (e0)) = (e1))\/(((op (e2) (e1)) = (e1))\/(((op (e2) (e2)) = (e1))\/((op (e2) (e3)) = (e1))))) -> (~((e1) = (e2))) -> (~((op (e1) (e1)) = (op (e2) (e1)))) -> (~((e1) = (e3))) -> (((op (e3) (e0)) = (e1))\/(((op (e3) (e1)) = (e1))\/(((op (e3) (e2)) = (e1))\/((op (e3) (e3)) = (e1))))) -> (~((op (e0) (e2)) = (op (e3) (e2)))) -> (~((op (e1) (op (e3) (e1))) = (op (e3) (e1)))) -> (((op (e0) (e0)) = (e3))\/(((op (e1) (e0)) = (e3))\/(((op (e2) (e0)) = (e3))\/((op (e3) (e0)) = (e3))))) -> (~((op (e0) (e0)) = (e2))) -> (((op (e0) (e0)) = (e1))\/(((op (e1) (e0)) = (e1))\/(((op (e2) (e0)) = (e1))\/((op (e3) (e0)) = (e1))))) -> ((op (e1) (e1)) = (e1)) -> (~((op (e0) (e1)) = (op (e1) (e1)))) -> (~((op (e0) (e0)) = (e1))) -> (~((op (e3) (op (e3) (e3))) = (op (e3) (e3)))) -> ((~((op (e3) (e3)) = (e3)))\/((op (e3) (e3)) = (e3))) -> (~((op (e3) (e1)) = (op (e3) (e2)))) -> (((op (e0) (e0)) = (e2))\/(((op (e0) (e1)) = (e2))\/(((op (e0) (e2)) = (e2))\/((op (e0) (e3)) = (e2))))) -> (((op (e0) (e0)) = (e3))\/(((op (e0) (e1)) = (e3))\/(((op (e0) (e2)) = (e3))\/((op (e0) (e3)) = (e3))))) -> (~((op (e0) (e1)) = (op (e3) (e1)))) -> (~((op (e1) (e1)) = (e0))) -> (((op (e2) (e0)) = (e3))\/(((op (e2) (e1)) = (e3))\/(((op (e2) (e2)) = (e3))\/((op (e2) (e3)) = (e3))))) -> (~((op (e0) (e3)) = (op (e2) (e3)))) -> (~((op (e2) (e1)) = (op (e3) (e1)))) -> (~((e0) = (e3))) -> (((op (e0) (e1)) = (e0))\/(((op (e1) (e1)) = (e0))\/(((op (e2) (e1)) = (e0))\/((op (e3) (e1)) = (e0))))) -> (((op (e1) (e0)) = (e0))\/(((op (e1) (e1)) = (e0))\/(((op (e1) (e2)) = (e0))\/((op (e1) (e3)) = (e0))))) -> (((op (e0) (e3)) = (e2))\/(((op (e1) (e3)) = (e2))\/(((op (e2) (e3)) = (e2))\/((op (e3) (e3)) = (e2))))) -> (~((op (e1) (e2)) = (op (e3) (e2)))) -> (((op (e3) (e0)) = (e0))\/(((op (e3) (e1)) = (e0))\/(((op (e3) (e2)) = (e0))\/((op (e3) (e3)) = (e0))))) -> (~((op (e0) (e0)) = (op (e1) (e0)))) -> ((~((op (e3) (e3)) = (e1)))\/((op (e3) (e1)) = (e3))) -> False). % 15.55/15.68 do 0 intro. intros zenon_H104 zenon_H237 zenon_H3d zenon_H2af zenon_Hba zenon_H1df zenon_H10f zenon_H105 zenon_H109 zenon_H10e zenon_H11b zenon_H116 zenon_H2b8 zenon_Hc9 zenon_H44 zenon_H36 zenon_Hd7 zenon_Hd3 zenon_H2e zenon_H52 zenon_H2f zenon_H2d zenon_H5e zenon_H8b zenon_H3b zenon_H1f zenon_H24f zenon_Heb zenon_Hce zenon_H59 zenon_H6a zenon_Hb7 zenon_Ha7 zenon_Hb1 zenon_Ha3 zenon_H146 zenon_H140 zenon_H2b4 zenon_Hbe zenon_H8f zenon_Hf1 zenon_H21 zenon_H23 zenon_H45 zenon_H2be zenon_H10d zenon_H135 zenon_H8e zenon_H58 zenon_H138 zenon_H145 zenon_He6 zenon_Hb4 zenon_H13c zenon_H4b zenon_H144 zenon_H163 zenon_H160 zenon_H17d zenon_H1f6 zenon_H24c zenon_H10c. % 15.55/15.68 apply (zenon_or_s _ _ zenon_H44); [ zenon_intro zenon_H47 | zenon_intro zenon_H46 ]. % 15.55/15.68 exact (zenon_H45 zenon_H47). % 15.55/15.68 apply (zenon_or_s _ _ zenon_H46); [ zenon_intro zenon_H22 | zenon_intro zenon_H48 ]. % 15.55/15.68 apply (zenon_L3_); trivial. % 15.55/15.68 apply (zenon_or_s _ _ zenon_H48); [ zenon_intro zenon_H29 | zenon_intro zenon_H37 ]. % 15.55/15.68 apply (zenon_L1159_); trivial. % 15.55/15.68 apply (zenon_or_s _ _ zenon_H11b); [ zenon_intro zenon_H29 | zenon_intro zenon_H11c ]. % 15.55/15.68 apply (zenon_L85_); trivial. % 15.55/15.68 apply (zenon_or_s _ _ zenon_H11c); [ zenon_intro zenon_H117 | zenon_intro zenon_H11d ]. % 15.55/15.68 apply (zenon_L86_); trivial. % 15.55/15.68 apply (zenon_or_s _ _ zenon_H11d); [ zenon_intro zenon_H2a | zenon_intro zenon_H119 ]. % 15.55/15.68 exact (zenon_H52 zenon_H2a). % 15.55/15.68 apply (zenon_L1169_); trivial. % 15.55/15.68 (* end of lemma zenon_L1170_ *) % 15.55/15.68 assert (zenon_L1171_ : ((~((op (e3) (e3)) = (e3)))\/((op (e3) (e3)) = (e3))) -> (~((op (e3) (op (e3) (e3))) = (op (e3) (e3)))) -> (~((op (e0) (e0)) = (e1))) -> (~((op (e1) (e0)) = (op (e1) (e1)))) -> ((op (e1) (e1)) = (e1)) -> (~((e1) = (e2))) -> ((op (e2) (e0)) = (e2)) -> (((op (e2) (e2)) = (e0))\/(((op (e2) (e2)) = (e1))\/(((op (e2) (e2)) = (e2))\/((op (e2) (e2)) = (e3))))) -> (~((op (e2) (e2)) = (e3))) -> (~((op (e2) (e2)) = (e2))) -> (~((op (e2) (e2)) = (e1))) -> (~((op (e3) (e3)) = (e0))) -> (~((op (e3) (e3)) = (e1))) -> (((op (e3) (e3)) = (e0))\/(((op (e3) (e3)) = (e1))\/(((op (e3) (e3)) = (e2))\/((op (e3) (e3)) = (e3))))) -> (((op (e0) (e0)) = (e1))\/(((op (e1) (e0)) = (e1))\/(((op (e2) (e0)) = (e1))\/((op (e3) (e0)) = (e1))))) -> False). % 15.55/15.68 do 0 intro. intros zenon_H10d zenon_H2be zenon_H45 zenon_Hd7 zenon_H21 zenon_Ha7 zenon_Hdd zenon_H2d zenon_H30 zenon_H2f zenon_H52 zenon_H3c zenon_H104 zenon_H3b zenon_Hf1. % 15.55/15.68 apply (zenon_or_s _ _ zenon_H10d); [ zenon_intro zenon_H3e | zenon_intro zenon_H42 ]. % 15.55/15.68 apply (zenon_L307_); trivial. % 15.55/15.68 apply (zenon_L1041_); trivial. % 15.55/15.68 (* end of lemma zenon_L1171_ *) % 15.55/15.68 assert (zenon_L1172_ : (((op (e0) (e0)) = (e1))\/(((op (e0) (e1)) = (e1))\/(((op (e0) (e2)) = (e1))\/((op (e0) (e3)) = (e1))))) -> (~((op (e0) (e0)) = (e1))) -> (~((op (e0) (e1)) = (op (e1) (e1)))) -> ((op (e1) (e1)) = (e1)) -> (~((op (e2) (e0)) = (op (e2) (e3)))) -> ((op (e2) (e0)) = (e2)) -> (~((e0) = (e2))) -> (~((e2) = (e3))) -> (((op (e0) (e3)) = (e2))\/(((op (e1) (e3)) = (e2))\/(((op (e2) (e3)) = (e2))\/((op (e3) (e3)) = (e2))))) -> (((op (e3) (e0)) = (e0))\/(((op (e3) (e1)) = (e0))\/(((op (e3) (e2)) = (e0))\/((op (e3) (e3)) = (e0))))) -> ((op (e0) (e0)) = (e0)) -> (~((op (e0) (op (e3) (e0))) = (op (e3) (e0)))) -> ((op (e3) (e1)) = (e3)) -> (~((e0) = (e3))) -> (~((op (e1) (e2)) = (op (e3) (e2)))) -> (~((op (e1) (e1)) = (e0))) -> (~((op (e0) (e0)) = (op (e1) (e0)))) -> (((op (e1) (e0)) = (e0))\/(((op (e1) (e1)) = (e0))\/(((op (e1) (e2)) = (e0))\/((op (e1) (e3)) = (e0))))) -> (~((e1) = (e3))) -> (~((op (e0) (e1)) = (op (e3) (e1)))) -> (~((op (e0) (e0)) = (e3))) -> (((op (e0) (e0)) = (e3))\/(((op (e0) (e1)) = (e3))\/(((op (e0) (e2)) = (e3))\/((op (e0) (e3)) = (e3))))) -> (((op (e3) (e3)) = (e0))\/(((op (e3) (e3)) = (e1))\/(((op (e3) (e3)) = (e2))\/((op (e3) (e3)) = (e3))))) -> (~((op (e3) (e3)) = (e0))) -> (~((op (e0) (e3)) = (op (e3) (e3)))) -> (~((op (e3) (e3)) = (e2))) -> (~((op (e3) (e3)) = (e3))) -> False). % 15.55/15.68 do 0 intro. intros zenon_H44 zenon_H45 zenon_H23 zenon_H21 zenon_Hce zenon_Hdd zenon_H5e zenon_H6a zenon_H160 zenon_H1f6 zenon_H1f zenon_H2b8 zenon_H10a zenon_H4b zenon_H17d zenon_H145 zenon_H24c zenon_H163 zenon_Ha3 zenon_H138 zenon_H59 zenon_H58 zenon_H3b zenon_H3c zenon_H36 zenon_H3d zenon_H3e. % 15.55/15.68 apply (zenon_or_s _ _ zenon_H44); [ zenon_intro zenon_H47 | zenon_intro zenon_H46 ]. % 15.55/15.68 exact (zenon_H45 zenon_H47). % 15.55/15.68 apply (zenon_or_s _ _ zenon_H46); [ zenon_intro zenon_H22 | zenon_intro zenon_H48 ]. % 15.55/15.68 apply (zenon_L3_); trivial. % 15.55/15.68 apply (zenon_or_s _ _ zenon_H48); [ zenon_intro zenon_H29 | zenon_intro zenon_H37 ]. % 15.55/15.68 apply (zenon_L1112_); trivial. % 15.55/15.68 apply (zenon_L7_); trivial. % 15.55/15.68 (* end of lemma zenon_L1172_ *) % 15.55/15.68 assert (zenon_L1173_ : ((~((op (e3) (e3)) = (e2)))\/((op (e3) (e2)) = (e3))) -> (~((op (e3) (e1)) = (op (e3) (e2)))) -> (((op (e0) (e0)) = (e1))\/(((op (e0) (e1)) = (e1))\/(((op (e0) (e2)) = (e1))\/((op (e0) (e3)) = (e1))))) -> (~((op (e0) (e3)) = (op (e3) (e3)))) -> (((op (e3) (e3)) = (e0))\/(((op (e3) (e3)) = (e1))\/(((op (e3) (e3)) = (e2))\/((op (e3) (e3)) = (e3))))) -> (~((op (e0) (e0)) = (e3))) -> (~((op (e0) (e1)) = (op (e3) (e1)))) -> ((op (e3) (e1)) = (e3)) -> (~((e1) = (e3))) -> (((op (e1) (e0)) = (e0))\/(((op (e1) (e1)) = (e0))\/(((op (e1) (e2)) = (e0))\/((op (e1) (e3)) = (e0))))) -> (~((e2) = (e3))) -> (~((e0) = (e2))) -> (~((op (e2) (e0)) = (op (e2) (e3)))) -> ((op (e2) (e0)) = (e2)) -> (((op (e0) (e3)) = (e2))\/(((op (e1) (e3)) = (e2))\/(((op (e2) (e3)) = (e2))\/((op (e3) (e3)) = (e2))))) -> (~((op (e0) (op (e3) (e0))) = (op (e3) (e0)))) -> (~((e0) = (e3))) -> (~((op (e1) (e2)) = (op (e3) (e2)))) -> (~((op (e3) (e3)) = (e0))) -> (((op (e3) (e0)) = (e0))\/(((op (e3) (e1)) = (e0))\/(((op (e3) (e2)) = (e0))\/((op (e3) (e3)) = (e0))))) -> (~((op (e1) (e1)) = (e0))) -> ((op (e0) (e0)) = (e0)) -> (~((op (e0) (e0)) = (op (e1) (e0)))) -> (((op (e0) (e0)) = (e3))\/(((op (e0) (e1)) = (e3))\/(((op (e0) (e2)) = (e3))\/((op (e0) (e3)) = (e3))))) -> ((op (e1) (e1)) = (e1)) -> (~((op (e0) (e1)) = (op (e1) (e1)))) -> (~((op (e0) (e0)) = (e1))) -> (~((op (e3) (op (e3) (e3))) = (op (e3) (e3)))) -> ((~((op (e3) (e3)) = (e3)))\/((op (e3) (e3)) = (e3))) -> False). % 15.55/15.68 do 0 intro. intros zenon_H10e zenon_H135 zenon_H44 zenon_H36 zenon_H3b zenon_H59 zenon_H138 zenon_H10a zenon_Ha3 zenon_H163 zenon_H6a zenon_H5e zenon_Hce zenon_Hdd zenon_H160 zenon_H2b8 zenon_H4b zenon_H17d zenon_H3c zenon_H1f6 zenon_H145 zenon_H1f zenon_H24c zenon_H58 zenon_H21 zenon_H23 zenon_H45 zenon_H2be zenon_H10d. % 15.55/15.68 apply (zenon_or_s _ _ zenon_H10e); [ zenon_intro zenon_H3d | zenon_intro zenon_H106 ]. % 15.55/15.68 apply (zenon_or_s _ _ zenon_H10d); [ zenon_intro zenon_H3e | zenon_intro zenon_H42 ]. % 15.55/15.68 apply (zenon_L1172_); trivial. % 15.55/15.68 apply (zenon_L1041_); trivial. % 15.55/15.68 apply (zenon_L115_); trivial. % 15.55/15.68 (* end of lemma zenon_L1173_ *) % 15.55/15.68 assert (zenon_L1174_ : ((~((op (e3) (e3)) = (e1)))\/((op (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 (e0) (e0)) = (op (e1) (e0)))) -> ((op (e0) (e0)) = (e0)) -> (~((op (e1) (e1)) = (e0))) -> (((op (e3) (e0)) = (e0))\/(((op (e3) (e1)) = (e0))\/(((op (e3) (e2)) = (e0))\/((op (e3) (e3)) = (e0))))) -> (~((op (e1) (e2)) = (op (e3) (e2)))) -> (~((e0) = (e3))) -> (~((op (e0) (op (e3) (e0))) = (op (e3) (e0)))) -> (((op (e0) (e3)) = (e2))\/(((op (e1) (e3)) = (e2))\/(((op (e2) (e3)) = (e2))\/((op (e3) (e3)) = (e2))))) -> (~((op (e2) (e0)) = (op (e2) (e3)))) -> (~((e0) = (e2))) -> (~((e2) = (e3))) -> (((op (e1) (e0)) = (e0))\/(((op (e1) (e1)) = (e0))\/(((op (e1) (e2)) = (e0))\/((op (e1) (e3)) = (e0))))) -> (~((e1) = (e3))) -> (~((op (e0) (e1)) = (op (e3) (e1)))) -> (~((op (e0) (e0)) = (e3))) -> (~((op (e0) (e3)) = (op (e3) (e3)))) -> (((op (e0) (e0)) = (e1))\/(((op (e0) (e1)) = (e1))\/(((op (e0) (e2)) = (e1))\/((op (e0) (e3)) = (e1))))) -> (~((op (e3) (e1)) = (op (e3) (e2)))) -> ((~((op (e3) (e3)) = (e2)))\/((op (e3) (e2)) = (e3))) -> (((op (e0) (e0)) = (e1))\/(((op (e1) (e0)) = (e1))\/(((op (e2) (e0)) = (e1))\/((op (e3) (e0)) = (e1))))) -> (((op (e3) (e3)) = (e0))\/(((op (e3) (e3)) = (e1))\/(((op (e3) (e3)) = (e2))\/((op (e3) (e3)) = (e3))))) -> (~((op (e3) (e3)) = (e0))) -> (~((op (e2) (e2)) = (e1))) -> (~((op (e2) (e2)) = (e2))) -> (~((op (e2) (e2)) = (e3))) -> (((op (e2) (e2)) = (e0))\/(((op (e2) (e2)) = (e1))\/(((op (e2) (e2)) = (e2))\/((op (e2) (e2)) = (e3))))) -> ((op (e2) (e0)) = (e2)) -> (~((e1) = (e2))) -> ((op (e1) (e1)) = (e1)) -> (~((op (e1) (e0)) = (op (e1) (e1)))) -> (~((op (e0) (e0)) = (e1))) -> (~((op (e3) (op (e3) (e3))) = (op (e3) (e3)))) -> ((~((op (e3) (e3)) = (e3)))\/((op (e3) (e3)) = (e3))) -> False). % 15.55/15.68 do 0 intro. intros zenon_H10c zenon_H23 zenon_H58 zenon_H24c zenon_H1f zenon_H145 zenon_H1f6 zenon_H17d zenon_H4b zenon_H2b8 zenon_H160 zenon_Hce zenon_H5e zenon_H6a zenon_H163 zenon_Ha3 zenon_H138 zenon_H59 zenon_H36 zenon_H44 zenon_H135 zenon_H10e zenon_Hf1 zenon_H3b zenon_H3c zenon_H52 zenon_H2f zenon_H30 zenon_H2d zenon_Hdd zenon_Ha7 zenon_H21 zenon_Hd7 zenon_H45 zenon_H2be zenon_H10d. % 15.55/15.68 apply (zenon_or_s _ _ zenon_H10c); [ zenon_intro zenon_H104 | zenon_intro zenon_H10a ]. % 15.55/15.68 apply (zenon_L1171_); trivial. % 15.55/15.68 apply (zenon_L1173_); trivial. % 15.55/15.68 (* end of lemma zenon_L1174_ *) % 15.55/15.68 assert (zenon_L1175_ : (((op (e0) (e2)) = (e1))\/(((op (e1) (e2)) = (e1))\/(((op (e2) (e2)) = (e1))\/((op (e3) (e2)) = (e1))))) -> (~((op (e3) (e3)) = (e1))) -> (~((op (e0) (e2)) = (op (e3) (e2)))) -> (~((op (e1) (op (e3) (e1))) = (op (e3) (e1)))) -> (~((op (e0) (op (e3) (e0))) = (op (e3) (e0)))) -> ((op (e3) (e0)) = (e2)) -> (((op (e3) (e0)) = (e1))\/(((op (e3) (e1)) = (e1))\/(((op (e3) (e2)) = (e1))\/((op (e3) (e3)) = (e1))))) -> ((op (e1) (e1)) = (e1)) -> (~((op (e1) (e1)) = (op (e1) (e2)))) -> (~((op (e2) (e2)) = (e1))) -> (~((e1) = (e3))) -> ((op (e3) (e2)) = (e3)) -> False). % 15.55/15.68 do 0 intro. intros zenon_H11b zenon_H104 zenon_H140 zenon_H2b4 zenon_H2b8 zenon_He9 zenon_H146 zenon_H21 zenon_H116 zenon_H52 zenon_Ha3 zenon_H106. % 15.55/15.68 apply (zenon_or_s _ _ zenon_H11b); [ zenon_intro zenon_H29 | zenon_intro zenon_H11c ]. % 15.55/15.68 apply (zenon_L1163_); trivial. % 15.55/15.68 apply (zenon_or_s _ _ zenon_H11c); [ zenon_intro zenon_H117 | zenon_intro zenon_H11d ]. % 15.55/15.68 apply (zenon_L86_); trivial. % 15.55/15.68 apply (zenon_or_s _ _ zenon_H11d); [ zenon_intro zenon_H2a | zenon_intro zenon_H119 ]. % 15.55/15.68 exact (zenon_H52 zenon_H2a). % 15.55/15.68 apply (zenon_L87_); trivial. % 15.55/15.68 (* end of lemma zenon_L1175_ *) % 15.55/15.68 assert (zenon_L1176_ : ((~((op (e1) (e1)) = (e1)))\/((op (e1) (e1)) = (e1))) -> (~((op (e1) (e0)) = (op (e1) (e1)))) -> ((~((op (e1) (e1)) = (e3)))\/((op (e1) (e3)) = (e1))) -> (~((op (e1) (e0)) = (op (e1) (e3)))) -> ((~((op (e3) (e3)) = (e1)))\/((op (e3) (e1)) = (e3))) -> (~((op (e3) (e1)) = (op (e3) (e2)))) -> ((~((op (e3) (e3)) = (e3)))\/((op (e3) (e3)) = (e3))) -> (~((op (e3) (op (e3) (e3))) = (op (e3) (e3)))) -> (~((op (e0) (e0)) = (e2))) -> (~((e1) = (e2))) -> ((op (e1) (e0)) = (e1)) -> (~((op (e2) (e0)) = (op (e2) (e2)))) -> ((op (e2) (e2)) = (e2)) -> (((op (e1) (e1)) = (e0))\/(((op (e1) (e1)) = (e1))\/(((op (e1) (e1)) = (e2))\/((op (e1) (e1)) = (e3))))) -> (((op (e3) (e3)) = (e0))\/(((op (e3) (e3)) = (e1))\/(((op (e3) (e3)) = (e2))\/((op (e3) (e3)) = (e3))))) -> (((op (e0) (e0)) = (e2))\/(((op (e1) (e0)) = (e2))\/(((op (e2) (e0)) = (e2))\/((op (e3) (e0)) = (e2))))) -> (((op (e3) (e0)) = (e1))\/(((op (e3) (e1)) = (e1))\/(((op (e3) (e2)) = (e1))\/((op (e3) (e3)) = (e1))))) -> (~((e1) = (e3))) -> (((op (e3) (e0)) = (e0))\/(((op (e3) (e1)) = (e0))\/(((op (e3) (e2)) = (e0))\/((op (e3) (e3)) = (e0))))) -> (~((op (e1) (e2)) = (op (e3) (e2)))) -> (~((op (e1) (op (e3) (e1))) = (op (e3) (e1)))) -> ((op (e0) (e0)) = (e0)) -> (~((op (e0) (op (e3) (e0))) = (op (e3) (e0)))) -> (~((op (e1) (e0)) = (op (e1) (e2)))) -> (~((op (e1) (e2)) = (op (e2) (e2)))) -> (((op (e1) (e2)) = (e0))\/(((op (e1) (e2)) = (e1))\/(((op (e1) (e2)) = (e2))\/((op (e1) (e2)) = (e3))))) -> (~((op (e1) (e0)) = (op (e3) (e0)))) -> ((~((op (e3) (e3)) = (e2)))\/((op (e3) (e2)) = (e3))) -> (((op (e2) (e0)) = (e0))\/(((op (e2) (e0)) = (e1))\/(((op (e2) (e0)) = (e2))\/((op (e2) (e0)) = (e3))))) -> (~((op (e2) (e0)) = (op (e3) (e0)))) -> (~((op (e1) (e0)) = (op (e2) (e0)))) -> (~((op (e0) (e0)) = (op (e2) (e0)))) -> ((~((op (e3) (e3)) = (e0)))\/((op (e3) (e0)) = (e3))) -> ((~((op (e1) (e1)) = (e2)))\/((op (e1) (e2)) = (e1))) -> False). % 15.55/15.68 do 0 intro. intros zenon_H1d8 zenon_Hd7 zenon_H1d2 zenon_H1cf zenon_H10c zenon_H135 zenon_H10d zenon_H2be zenon_H8f zenon_Ha7 zenon_Hd8 zenon_H17a zenon_H35 zenon_H1b3 zenon_H3b zenon_Heb zenon_H146 zenon_Ha3 zenon_H1f6 zenon_H17d zenon_H2b4 zenon_H1f zenon_H2b8 zenon_H166 zenon_H7d zenon_H1d5 zenon_H22e zenon_H10e zenon_H281 zenon_H1e5 zenon_H247 zenon_H258 zenon_H10f zenon_H1d3. % 15.55/15.68 apply (zenon_or_s _ _ zenon_H1d8); [ zenon_intro zenon_H1b4 | zenon_intro zenon_H21 ]. % 15.55/15.68 apply (zenon_L1080_); trivial. % 15.55/15.68 apply (zenon_L61_); trivial. % 15.55/15.68 (* end of lemma zenon_L1176_ *) % 15.55/15.68 assert (zenon_L1177_ : (((op (e0) (e0)) = (e2))\/(((op (e0) (e1)) = (e2))\/(((op (e0) (e2)) = (e2))\/((op (e0) (e3)) = (e2))))) -> (~((op (e0) (e0)) = (e2))) -> (~((op (e3) (e3)) = (e2))) -> (~((op (e2) (op (e3) (e2))) = (op (e3) (e2)))) -> (~((op (e0) (e1)) = (op (e3) (e1)))) -> (~((e2) = (e3))) -> ((op (e3) (e0)) = (e3)) -> (((op (e3) (e0)) = (e2))\/(((op (e3) (e1)) = (e2))\/(((op (e3) (e2)) = (e2))\/((op (e3) (e3)) = (e2))))) -> (~((op (e0) (e2)) = (op (e2) (e2)))) -> ((op (e2) (e2)) = (e2)) -> ((op (e0) (e3)) = (e1)) -> (~((e1) = (e2))) -> False). % 15.55/15.68 do 0 intro. intros zenon_H8e zenon_H8f zenon_H3d zenon_H2af zenon_H138 zenon_H6a zenon_Hba zenon_H1df zenon_H28 zenon_H35 zenon_H37 zenon_Ha7. % 15.55/15.68 apply (zenon_or_s _ _ zenon_H8e); [ zenon_intro zenon_H92 | zenon_intro zenon_H91 ]. % 15.55/15.68 exact (zenon_H8f zenon_H92). % 15.55/15.68 apply (zenon_or_s _ _ zenon_H91); [ zenon_intro zenon_H5d | zenon_intro zenon_H93 ]. % 15.55/15.68 apply (zenon_L1091_); trivial. % 15.55/15.68 apply (zenon_or_s _ _ zenon_H93); [ zenon_intro zenon_H63 | zenon_intro zenon_H81 ]. % 15.55/15.68 apply (zenon_L15_); trivial. % 15.55/15.68 apply (zenon_L33_); trivial. % 15.55/15.68 (* end of lemma zenon_L1177_ *) % 15.55/15.68 assert (zenon_L1178_ : ((~((op (e3) (e3)) = (e1)))\/((op (e3) (e1)) = (e3))) -> (~((op (e3) (e0)) = (op (e3) (e1)))) -> (((op (e0) (e0)) = (e1))\/(((op (e0) (e1)) = (e1))\/(((op (e0) (e2)) = (e1))\/((op (e0) (e3)) = (e1))))) -> (~((op (e0) (e0)) = (e2))) -> (((op (e3) (e0)) = (e2))\/(((op (e3) (e1)) = (e2))\/(((op (e3) (e2)) = (e2))\/((op (e3) (e3)) = (e2))))) -> ((op (e2) (e2)) = (e2)) -> (~((op (e2) (op (e3) (e2))) = (op (e3) (e2)))) -> (~((op (e0) (e1)) = (op (e3) (e1)))) -> (~((e2) = (e3))) -> (~((op (e0) (e2)) = (op (e2) (e2)))) -> (~((e1) = (e2))) -> (((op (e0) (e0)) = (e2))\/(((op (e0) (e1)) = (e2))\/(((op (e0) (e2)) = (e2))\/((op (e0) (e3)) = (e2))))) -> (~((e1) = (e3))) -> ((op (e3) (e0)) = (e3)) -> (~((op (e1) (op (e3) (e1))) = (op (e3) (e1)))) -> (~((op (e0) (e2)) = (op (e3) (e2)))) -> (((op (e3) (e0)) = (e1))\/(((op (e3) (e1)) = (e1))\/(((op (e3) (e2)) = (e1))\/((op (e3) (e3)) = (e1))))) -> ((op (e1) (e1)) = (e1)) -> (~((op (e0) (e1)) = (op (e1) (e1)))) -> (~((op (e0) (e0)) = (e1))) -> (~((op (e3) (e0)) = (op (e3) (e2)))) -> ((~((op (e3) (e3)) = (e2)))\/((op (e3) (e2)) = (e3))) -> False). % 15.55/15.68 do 0 intro. intros zenon_H10c zenon_H109 zenon_H44 zenon_H8f zenon_H1df zenon_H35 zenon_H2af zenon_H138 zenon_H6a zenon_H28 zenon_Ha7 zenon_H8e zenon_Ha3 zenon_Hba zenon_H2b4 zenon_H140 zenon_H146 zenon_H21 zenon_H23 zenon_H45 zenon_H105 zenon_H10e. % 15.55/15.68 apply (zenon_or_s _ _ zenon_H10c); [ zenon_intro zenon_H104 | zenon_intro zenon_H10a ]. % 15.55/15.68 apply (zenon_or_s _ _ zenon_H10e); [ zenon_intro zenon_H3d | zenon_intro zenon_H106 ]. % 15.55/15.68 apply (zenon_or_s _ _ zenon_H44); [ zenon_intro zenon_H47 | zenon_intro zenon_H46 ]. % 15.55/15.68 exact (zenon_H45 zenon_H47). % 15.55/15.68 apply (zenon_or_s _ _ zenon_H46); [ zenon_intro zenon_H22 | zenon_intro zenon_H48 ]. % 15.55/15.68 apply (zenon_L3_); trivial. % 15.55/15.68 apply (zenon_or_s _ _ zenon_H48); [ zenon_intro zenon_H29 | zenon_intro zenon_H37 ]. % 15.55/15.68 apply (zenon_L1159_); trivial. % 15.55/15.68 apply (zenon_L1177_); trivial. % 15.55/15.68 apply (zenon_L81_); trivial. % 15.55/15.68 apply (zenon_L82_); trivial. % 15.55/15.68 (* end of lemma zenon_L1178_ *) % 15.55/15.68 assert (zenon_L1179_ : (((op (e0) (e0)) = (e2))\/(((op (e1) (e0)) = (e2))\/(((op (e2) (e0)) = (e2))\/((op (e3) (e0)) = (e2))))) -> (~((op (e0) (e0)) = (e2))) -> (~((op (e3) (e3)) = (e1))) -> (~((op (e0) (e2)) = (op (e3) (e2)))) -> ((op (e0) (e2)) = (e1)) -> (~((op (e1) (op (e3) (e1))) = (op (e3) (e1)))) -> (((op (e3) (e0)) = (e1))\/(((op (e3) (e1)) = (e1))\/(((op (e3) (e2)) = (e1))\/((op (e3) (e3)) = (e1))))) -> (((op (e1) (e0)) = (e3))\/(((op (e1) (e1)) = (e3))\/(((op (e1) (e2)) = (e3))\/((op (e1) (e3)) = (e3))))) -> (~((e2) = (e3))) -> (~((op (e1) (e1)) = (e3))) -> (~((op (e1) (e2)) = (op (e3) (e2)))) -> (((op (e2) (e0)) = (e1))\/(((op (e2) (e1)) = (e1))\/(((op (e2) (e2)) = (e1))\/((op (e2) (e3)) = (e1))))) -> (~((op (e1) (e1)) = (op (e2) (e1)))) -> (((op (e3) (e0)) = (e2))\/(((op (e3) (e1)) = (e2))\/(((op (e3) (e2)) = (e2))\/((op (e3) (e3)) = (e2))))) -> ((op (e0) (e1)) = (e2)) -> (~((op (e0) (e1)) = (op (e3) (e1)))) -> (~((op (e2) (op (e3) (e2))) = (op (e3) (e2)))) -> (((op (e0) (e3)) = (e0))\/(((op (e0) (e3)) = (e1))\/(((op (e0) (e3)) = (e2))\/((op (e0) (e3)) = (e3))))) -> ((op (e0) (e0)) = (e0)) -> (~((op (e0) (e0)) = (op (e0) (e3)))) -> (~((op (e0) (e3)) = (op (e2) (e3)))) -> (~((op (e0) (e3)) = (op (e3) (e3)))) -> (~((op (e0) (e3)) = (op (e1) (e3)))) -> (~((op (e0) (e0)) = (e3))) -> (((op (e0) (e0)) = (e3))\/(((op (e1) (e0)) = (e3))\/(((op (e2) (e0)) = (e3))\/((op (e3) (e0)) = (e3))))) -> (~((op (e2) (e0)) = (op (e2) (e2)))) -> ((op (e2) (e2)) = (e2)) -> (((op (e0) (e2)) = (e1))\/(((op (e1) (e2)) = (e1))\/(((op (e2) (e2)) = (e1))\/((op (e3) (e2)) = (e1))))) -> ((op (e3) (e0)) = (e1)) -> (~((op (e0) (op (e3) (e0))) = (op (e3) (e0)))) -> ((op (e1) (e1)) = (e1)) -> (~((op (e1) (e1)) = (op (e1) (e2)))) -> (~((op (e2) (e2)) = (e1))) -> (~((e1) = (e3))) -> ((op (e3) (e2)) = (e3)) -> False). % 15.55/15.68 do 0 intro. intros zenon_Heb zenon_H8f zenon_H104 zenon_H140 zenon_H29 zenon_H2b4 zenon_H146 zenon_H90 zenon_H6a zenon_H182 zenon_H17d zenon_Hb7 zenon_Hb1 zenon_H1df zenon_H5d zenon_H138 zenon_H2af zenon_H254 zenon_H1f zenon_H24f zenon_Hb4 zenon_H36 zenon_H80 zenon_H59 zenon_Hbe zenon_H17a zenon_H35 zenon_H11b zenon_Hee zenon_H2b8 zenon_H21 zenon_H116 zenon_H52 zenon_Ha3 zenon_H106. % 15.55/15.68 apply (zenon_or_s _ _ zenon_Heb); [ zenon_intro zenon_H92 | zenon_intro zenon_Hec ]. % 15.55/15.68 exact (zenon_H8f zenon_H92). % 15.55/15.68 apply (zenon_or_s _ _ zenon_Hec); [ zenon_intro zenon_H68 | zenon_intro zenon_Hed ]. % 15.55/15.68 apply (zenon_or_s _ _ zenon_Hbe); [ zenon_intro zenon_H5b | zenon_intro zenon_Hbf ]. % 15.55/15.68 exact (zenon_H59 zenon_H5b). % 15.55/15.68 apply (zenon_or_s _ _ zenon_Hbf); [ zenon_intro zenon_H69 | zenon_intro zenon_Hc0 ]. % 15.55/15.68 apply (zenon_L17_); trivial. % 15.55/15.68 apply (zenon_or_s _ _ zenon_Hc0); [ zenon_intro zenon_Haf | zenon_intro zenon_Hba ]. % 15.55/15.68 apply (zenon_or_s _ _ zenon_H90); [ zenon_intro zenon_H69 | zenon_intro zenon_H94 ]. % 15.55/15.68 apply (zenon_L17_); trivial. % 15.55/15.68 apply (zenon_or_s _ _ zenon_H94); [ zenon_intro zenon_H96 | zenon_intro zenon_H95 ]. % 15.55/15.68 exact (zenon_H182 zenon_H96). % 15.55/15.68 apply (zenon_or_s _ _ zenon_H95); [ zenon_intro zenon_H88 | zenon_intro zenon_H8a ]. % 15.55/15.68 apply (zenon_L164_); trivial. % 15.55/15.68 apply (zenon_or_s _ _ zenon_Hb7); [ zenon_intro zenon_Hae | zenon_intro zenon_Hb8 ]. % 15.55/15.68 apply (zenon_L39_); trivial. % 15.55/15.68 apply (zenon_or_s _ _ zenon_Hb8); [ zenon_intro zenon_Hb2 | zenon_intro zenon_Hb9 ]. % 15.55/15.68 apply (zenon_L40_); trivial. % 15.55/15.68 apply (zenon_or_s _ _ zenon_Hb9); [ zenon_intro zenon_H2a | zenon_intro zenon_Hb5 ]. % 15.55/15.68 exact (zenon_H52 zenon_H2a). % 15.55/15.68 apply (zenon_L1087_); trivial. % 15.55/15.68 apply (zenon_L1159_); trivial. % 15.55/15.68 apply (zenon_or_s _ _ zenon_Hed); [ zenon_intro zenon_Hdd | zenon_intro zenon_He9 ]. % 15.55/15.68 apply (zenon_L161_); trivial. % 15.55/15.68 apply (zenon_L1164_); trivial. % 15.55/15.68 (* end of lemma zenon_L1179_ *) % 15.55/15.68 assert (zenon_L1180_ : (((op (e0) (e0)) = (e2))\/(((op (e0) (e1)) = (e2))\/(((op (e0) (e2)) = (e2))\/((op (e0) (e3)) = (e2))))) -> (~((e1) = (e3))) -> ((op (e3) (e2)) = (e3)) -> (~((op (e1) (op (e3) (e1))) = (op (e3) (e1)))) -> ((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) (e2)) = (op (e3) (e2)))) -> ((op (e0) (e2)) = (e1)) -> (((op (e3) (e0)) = (e1))\/(((op (e3) (e1)) = (e1))\/(((op (e3) (e2)) = (e1))\/((op (e3) (e3)) = (e1))))) -> (((op (e1) (e0)) = (e3))\/(((op (e1) (e1)) = (e3))\/(((op (e1) (e2)) = (e3))\/((op (e1) (e3)) = (e3))))) -> (~((e2) = (e3))) -> (~((op (e1) (e1)) = (e3))) -> (~((op (e1) (e2)) = (op (e3) (e2)))) -> (((op (e2) (e0)) = (e1))\/(((op (e2) (e1)) = (e1))\/(((op (e2) (e2)) = (e1))\/((op (e2) (e3)) = (e1))))) -> (~((op (e1) (e1)) = (op (e2) (e1)))) -> (((op (e3) (e0)) = (e2))\/(((op (e3) (e1)) = (e2))\/(((op (e3) (e2)) = (e2))\/((op (e3) (e3)) = (e2))))) -> (~((op (e0) (e1)) = (op (e3) (e1)))) -> (~((op (e2) (op (e3) (e2))) = (op (e3) (e2)))) -> (((op (e0) (e3)) = (e0))\/(((op (e0) (e3)) = (e1))\/(((op (e0) (e3)) = (e2))\/((op (e0) (e3)) = (e3))))) -> ((op (e0) (e0)) = (e0)) -> (~((op (e0) (e0)) = (op (e0) (e3)))) -> (~((op (e0) (e3)) = (op (e2) (e3)))) -> (~((op (e0) (e3)) = (op (e1) (e3)))) -> (~((op (e0) (e0)) = (e3))) -> (((op (e0) (e0)) = (e3))\/(((op (e1) (e0)) = (e3))\/(((op (e2) (e0)) = (e3))\/((op (e3) (e0)) = (e3))))) -> (~((op (e2) (e0)) = (op (e2) (e2)))) -> (((op (e0) (e2)) = (e1))\/(((op (e1) (e2)) = (e1))\/(((op (e2) (e2)) = (e1))\/((op (e3) (e2)) = (e1))))) -> (~((op (e0) (op (e3) (e0))) = (op (e3) (e0)))) -> (~((op (e1) (e1)) = (op (e1) (e2)))) -> (~((op (e2) (e2)) = (e1))) -> (~((op (e0) (e2)) = (op (e2) (e2)))) -> ((op (e2) (e2)) = (e2)) -> (((op (e3) (e3)) = (e0))\/(((op (e3) (e3)) = (e1))\/(((op (e3) (e3)) = (e2))\/((op (e3) (e3)) = (e3))))) -> (~((op (e3) (e3)) = (e0))) -> (~((op (e3) (e3)) = (e1))) -> (~((op (e0) (e3)) = (op (e3) (e3)))) -> (~((op (e3) (e3)) = (e3))) -> False). % 15.55/15.68 do 0 intro. intros zenon_H8e zenon_Ha3 zenon_H106 zenon_H2b4 zenon_H21 zenon_Heb zenon_H8f zenon_H140 zenon_H29 zenon_H146 zenon_H90 zenon_H6a zenon_H182 zenon_H17d zenon_Hb7 zenon_Hb1 zenon_H1df zenon_H138 zenon_H2af zenon_H254 zenon_H1f zenon_H24f zenon_Hb4 zenon_H80 zenon_H59 zenon_Hbe zenon_H17a zenon_H11b zenon_H2b8 zenon_H116 zenon_H52 zenon_H28 zenon_H35 zenon_H3b zenon_H3c zenon_H104 zenon_H36 zenon_H3e. % 15.55/15.68 apply (zenon_or_s _ _ zenon_H8e); [ zenon_intro zenon_H92 | zenon_intro zenon_H91 ]. % 15.55/15.68 exact (zenon_H8f zenon_H92). % 15.55/15.68 apply (zenon_or_s _ _ zenon_H91); [ zenon_intro zenon_H5d | zenon_intro zenon_H93 ]. % 15.55/15.68 apply (zenon_or_s _ _ zenon_H146); [ zenon_intro zenon_Hee | zenon_intro zenon_H14b ]. % 15.55/15.68 apply (zenon_L1179_); trivial. % 15.55/15.68 apply (zenon_or_s _ _ zenon_H14b); [ zenon_intro zenon_H13e | zenon_intro zenon_H14c ]. % 15.55/15.68 apply (zenon_L1158_); trivial. % 15.55/15.68 apply (zenon_or_s _ _ zenon_H14c); [ zenon_intro zenon_H119 | zenon_intro zenon_H38 ]. % 15.55/15.68 apply (zenon_L87_); trivial. % 15.55/15.68 exact (zenon_H104 zenon_H38). % 15.55/15.68 apply (zenon_or_s _ _ zenon_H93); [ zenon_intro zenon_H63 | zenon_intro zenon_H81 ]. % 15.55/15.68 apply (zenon_L15_); trivial. % 15.55/15.68 apply (zenon_L107_); trivial. % 15.55/15.68 (* end of lemma zenon_L1180_ *) % 15.55/15.68 assert (zenon_L1181_ : (((op (e0) (e1)) = (e2))\/(((op (e1) (e1)) = (e2))\/(((op (e2) (e1)) = (e2))\/((op (e3) (e1)) = (e2))))) -> (~((op (e3) (e3)) = (e2))) -> (~((op (e2) (op (e3) (e2))) = (op (e3) (e2)))) -> (~((op (e0) (e1)) = (op (e3) (e1)))) -> (~((op (e0) (op (e3) (e0))) = (op (e3) (e0)))) -> ((op (e0) (e2)) = (e1)) -> ((op (e3) (e0)) = (e1)) -> (((op (e3) (e0)) = (e2))\/(((op (e3) (e1)) = (e2))\/(((op (e3) (e2)) = (e2))\/((op (e3) (e3)) = (e2))))) -> (~((op (e1) (e1)) = (e2))) -> (~((op (e2) (e1)) = (op (e2) (e2)))) -> ((op (e2) (e2)) = (e2)) -> (~((e2) = (e3))) -> ((op (e3) (e1)) = (e3)) -> False). % 15.55/15.68 do 0 intro. intros zenon_H1a2 zenon_H3d zenon_H2af zenon_H138 zenon_H2b8 zenon_H29 zenon_Hee zenon_H1df zenon_Hd6 zenon_H157 zenon_H35 zenon_H6a zenon_H10a. % 15.55/15.68 apply (zenon_or_s _ _ zenon_H1a2); [ zenon_intro zenon_H5d | zenon_intro zenon_H1a3 ]. % 15.55/15.68 apply (zenon_L1084_); trivial. % 15.55/15.68 apply (zenon_or_s _ _ zenon_H1a3); [ zenon_intro zenon_H6e | zenon_intro zenon_H1a4 ]. % 15.55/15.68 exact (zenon_Hd6 zenon_H6e). % 15.55/15.68 apply (zenon_or_s _ _ zenon_H1a4); [ zenon_intro zenon_H156 | zenon_intro zenon_H16a ]. % 15.55/15.68 apply (zenon_L134_); trivial. % 15.55/15.68 apply (zenon_L297_); trivial. % 15.55/15.68 (* end of lemma zenon_L1181_ *) % 15.55/15.68 assert (zenon_L1182_ : (((op (e0) (e0)) = (e1))\/(((op (e0) (e1)) = (e1))\/(((op (e0) (e2)) = (e1))\/((op (e0) (e3)) = (e1))))) -> (~((op (e0) (e1)) = (op (e1) (e1)))) -> ((op (e3) (e1)) = (e3)) -> (~((e2) = (e3))) -> ((op (e2) (e2)) = (e2)) -> (~((op (e2) (e1)) = (op (e2) (e2)))) -> (~((op (e1) (e1)) = (e2))) -> (((op (e3) (e0)) = (e2))\/(((op (e3) (e1)) = (e2))\/(((op (e3) (e2)) = (e2))\/((op (e3) (e3)) = (e2))))) -> (~((op (e0) (op (e3) (e0))) = (op (e3) (e0)))) -> (~((op (e0) (e1)) = (op (e3) (e1)))) -> (~((op (e2) (op (e3) (e2))) = (op (e3) (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) (e0)) = (e3))) -> (((op (e2) (e0)) = (e3))\/(((op (e2) (e1)) = (e3))\/(((op (e2) (e2)) = (e3))\/((op (e2) (e3)) = (e3))))) -> (~((e1) = (e3))) -> (~((op (e2) (e1)) = (op (e3) (e1)))) -> (~((op (e2) (e2)) = (e3))) -> (~((op (e0) (e3)) = (op (e2) (e3)))) -> (~((op (e1) (e0)) = (op (e1) (e1)))) -> ((op (e1) (e1)) = (e1)) -> (~((op (e0) (e0)) = (e1))) -> (((op (e0) (e0)) = (e1))\/(((op (e1) (e0)) = (e1))\/(((op (e2) (e0)) = (e1))\/((op (e3) (e0)) = (e1))))) -> (((op (e3) (e3)) = (e0))\/(((op (e3) (e3)) = (e1))\/(((op (e3) (e3)) = (e2))\/((op (e3) (e3)) = (e3))))) -> (~((op (e3) (e3)) = (e0))) -> (~((op (e0) (e3)) = (op (e3) (e3)))) -> (~((op (e3) (e3)) = (e2))) -> (~((op (e3) (e3)) = (e3))) -> False). % 15.55/15.68 do 0 intro. intros zenon_H44 zenon_H23 zenon_H10a zenon_H6a zenon_H35 zenon_H157 zenon_Hd6 zenon_H1df zenon_H2b8 zenon_H138 zenon_H2af zenon_H1a2 zenon_H58 zenon_H59 zenon_He6 zenon_Ha3 zenon_H13c zenon_H30 zenon_Hb4 zenon_Hd7 zenon_H21 zenon_H45 zenon_Hf1 zenon_H3b zenon_H3c zenon_H36 zenon_H3d zenon_H3e. % 15.55/15.68 apply (zenon_or_s _ _ zenon_H44); [ zenon_intro zenon_H47 | zenon_intro zenon_H46 ]. % 15.55/15.68 exact (zenon_H45 zenon_H47). % 15.55/15.68 apply (zenon_or_s _ _ zenon_H46); [ zenon_intro zenon_H22 | zenon_intro zenon_H48 ]. % 15.55/15.68 apply (zenon_L3_); trivial. % 15.55/15.68 apply (zenon_or_s _ _ zenon_H48); [ zenon_intro zenon_H29 | zenon_intro zenon_H37 ]. % 15.55/15.68 apply (zenon_or_s _ _ zenon_Hf1); [ zenon_intro zenon_H47 | zenon_intro zenon_Hf4 ]. % 15.55/15.68 exact (zenon_H45 zenon_H47). % 15.55/15.68 apply (zenon_or_s _ _ zenon_Hf4); [ zenon_intro zenon_Hd8 | zenon_intro zenon_Hf5 ]. % 15.55/15.68 apply (zenon_L61_); trivial. % 15.55/15.68 apply (zenon_or_s _ _ zenon_Hf5); [ zenon_intro zenon_Hae | zenon_intro zenon_Hee ]. % 15.55/15.68 apply (zenon_L1097_); trivial. % 15.55/15.68 apply (zenon_L1181_); trivial. % 15.55/15.68 apply (zenon_L7_); trivial. % 15.55/15.68 (* end of lemma zenon_L1182_ *) % 15.55/15.68 assert (zenon_L1183_ : ((~((op (e3) (e3)) = (e2)))\/((op (e3) (e2)) = (e3))) -> (~((op (e3) (e1)) = (op (e3) (e2)))) -> (((op (e0) (e0)) = (e1))\/(((op (e0) (e1)) = (e1))\/(((op (e0) (e2)) = (e1))\/((op (e0) (e3)) = (e1))))) -> (~((op (e3) (e3)) = (e0))) -> (~((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) (e1)))) -> (((op (e0) (e0)) = (e3))\/(((op (e0) (e1)) = (e3))\/(((op (e0) (e2)) = (e3))\/((op (e0) (e3)) = (e3))))) -> (~((op (e2) (e1)) = (op (e3) (e1)))) -> (~((op (e2) (e2)) = (e3))) -> (~((op (e0) (e3)) = (op (e2) (e3)))) -> (((op (e2) (e0)) = (e3))\/(((op (e2) (e1)) = (e3))\/(((op (e2) (e2)) = (e3))\/((op (e2) (e3)) = (e3))))) -> (~((e1) = (e3))) -> ((op (e3) (e1)) = (e3)) -> (~((op (e0) (e1)) = (op (e3) (e1)))) -> (~((op (e0) (e0)) = (e3))) -> (((op (e0) (e1)) = (e2))\/(((op (e1) (e1)) = (e2))\/(((op (e2) (e1)) = (e2))\/((op (e3) (e1)) = (e2))))) -> (~((e2) = (e3))) -> (~((op (e2) (e1)) = (op (e2) (e2)))) -> (~((op (e1) (e1)) = (e2))) -> (~((op (e0) (op (e3) (e0))) = (op (e3) (e0)))) -> (~((op (e2) (op (e3) (e2))) = (op (e3) (e2)))) -> ((op (e2) (e2)) = (e2)) -> (((op (e3) (e0)) = (e2))\/(((op (e3) (e1)) = (e2))\/(((op (e3) (e2)) = (e2))\/((op (e3) (e3)) = (e2))))) -> (((op (e0) (e0)) = (e1))\/(((op (e1) (e0)) = (e1))\/(((op (e2) (e0)) = (e1))\/((op (e3) (e0)) = (e1))))) -> ((op (e1) (e1)) = (e1)) -> (~((op (e0) (e1)) = (op (e1) (e1)))) -> (~((op (e0) (e0)) = (e1))) -> (~((op (e3) (op (e3) (e3))) = (op (e3) (e3)))) -> ((~((op (e3) (e3)) = (e3)))\/((op (e3) (e3)) = (e3))) -> False). % 15.55/15.68 do 0 intro. intros zenon_H10e zenon_H135 zenon_H44 zenon_H3c zenon_H36 zenon_H3b zenon_Hd7 zenon_H58 zenon_H13c zenon_H30 zenon_Hb4 zenon_He6 zenon_Ha3 zenon_H10a zenon_H138 zenon_H59 zenon_H1a2 zenon_H6a zenon_H157 zenon_Hd6 zenon_H2b8 zenon_H2af zenon_H35 zenon_H1df zenon_Hf1 zenon_H21 zenon_H23 zenon_H45 zenon_H2be zenon_H10d. % 15.55/15.68 apply (zenon_or_s _ _ zenon_H10e); [ zenon_intro zenon_H3d | zenon_intro zenon_H106 ]. % 15.55/15.68 apply (zenon_or_s _ _ zenon_H10d); [ zenon_intro zenon_H3e | zenon_intro zenon_H42 ]. % 15.55/15.68 apply (zenon_L1182_); trivial. % 15.55/15.68 apply (zenon_L1041_); trivial. % 15.55/15.68 apply (zenon_L115_); trivial. % 15.55/15.68 (* end of lemma zenon_L1183_ *) % 15.55/15.68 assert (zenon_L1184_ : ((~((op (e2) (e2)) = (e3)))\/((op (e2) (e3)) = (e2))) -> (~((op (e2) (e2)) = (op (e2) (e3)))) -> (~((op (e1) (e1)) = (e2))) -> (~((op (e2) (e1)) = (op (e2) (e2)))) -> (((op (e0) (e1)) = (e2))\/(((op (e1) (e1)) = (e2))\/(((op (e2) (e1)) = (e2))\/((op (e3) (e1)) = (e2))))) -> (((op (e2) (e0)) = (e3))\/(((op (e2) (e1)) = (e3))\/(((op (e2) (e2)) = (e3))\/((op (e2) (e3)) = (e3))))) -> (~((op (e2) (e1)) = (op (e3) (e1)))) -> (((op (e0) (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)) = (e1)) -> (((op (e0) (e0)) = (e1))\/(((op (e1) (e0)) = (e1))\/(((op (e2) (e0)) = (e1))\/((op (e3) (e0)) = (e1))))) -> (~((op (e0) (e3)) = (op (e3) (e3)))) -> (((op (e0) (e0)) = (e3))\/(((op (e1) (e0)) = (e3))\/(((op (e2) (e0)) = (e3))\/((op (e3) (e0)) = (e3))))) -> (~((op (e3) (e0)) = (op (e3) (e2)))) -> (~((op (e0) (e2)) = (op (e3) (e2)))) -> (((op (e0) (e0)) = (e2))\/(((op (e0) (e1)) = (e2))\/(((op (e0) (e2)) = (e2))\/((op (e0) (e3)) = (e2))))) -> (~((op (e0) (e2)) = (op (e2) (e2)))) -> (~((op (e0) (e1)) = (op (e3) (e1)))) -> (~((op (e2) (op (e3) (e2))) = (op (e3) (e2)))) -> (((op (e3) (e0)) = (e2))\/(((op (e3) (e1)) = (e2))\/(((op (e3) (e2)) = (e2))\/((op (e3) (e3)) = (e2))))) -> (((op (e0) (e0)) = (e1))\/(((op (e0) (e1)) = (e1))\/(((op (e0) (e2)) = (e1))\/((op (e0) (e3)) = (e1))))) -> (~((op (e3) (e0)) = (op (e3) (e1)))) -> (~((e2) = (e3))) -> (~((op (e0) (e0)) = (e3))) -> ((~((op (e1) (e1)) = (e2)))\/((op (e1) (e2)) = (e1))) -> ((~((op (e3) (e3)) = (e0)))\/((op (e3) (e0)) = (e3))) -> (~((op (e0) (e0)) = (op (e2) (e0)))) -> (~((op (e1) (e0)) = (op (e2) (e0)))) -> (~((op (e2) (e0)) = (op (e3) (e0)))) -> (((op (e2) (e0)) = (e0))\/(((op (e2) (e0)) = (e1))\/(((op (e2) (e0)) = (e2))\/((op (e2) (e0)) = (e3))))) -> ((~((op (e3) (e3)) = (e2)))\/((op (e3) (e2)) = (e3))) -> (~((op (e1) (e0)) = (op (e3) (e0)))) -> (((op (e1) (e2)) = (e0))\/(((op (e1) (e2)) = (e1))\/(((op (e1) (e2)) = (e2))\/((op (e1) (e2)) = (e3))))) -> (~((op (e1) (e2)) = (op (e2) (e2)))) -> (~((op (e1) (e0)) = (op (e1) (e2)))) -> (~((op (e0) (op (e3) (e0))) = (op (e3) (e0)))) -> ((op (e0) (e0)) = (e0)) -> (~((op (e1) (op (e3) (e1))) = (op (e3) (e1)))) -> (~((op (e1) (e2)) = (op (e3) (e2)))) -> (((op (e3) (e0)) = (e0))\/(((op (e3) (e1)) = (e0))\/(((op (e3) (e2)) = (e0))\/((op (e3) (e3)) = (e0))))) -> (~((e1) = (e3))) -> (((op (e3) (e0)) = (e1))\/(((op (e3) (e1)) = (e1))\/(((op (e3) (e2)) = (e1))\/((op (e3) (e3)) = (e1))))) -> (((op (e0) (e0)) = (e2))\/(((op (e1) (e0)) = (e2))\/(((op (e2) (e0)) = (e2))\/((op (e3) (e0)) = (e2))))) -> (((op (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 (e2) (e2)) = (e2)) -> (~((op (e2) (e0)) = (op (e2) (e2)))) -> (~((e1) = (e2))) -> (~((op (e0) (e0)) = (e2))) -> (~((op (e3) (op (e3) (e3))) = (op (e3) (e3)))) -> ((~((op (e3) (e3)) = (e3)))\/((op (e3) (e3)) = (e3))) -> (~((op (e3) (e1)) = (op (e3) (e2)))) -> ((~((op (e3) (e3)) = (e1)))\/((op (e3) (e1)) = (e3))) -> (~((op (e1) (e0)) = (op (e1) (e3)))) -> ((~((op (e1) (e1)) = (e3)))\/((op (e1) (e3)) = (e1))) -> (~((op (e1) (e0)) = (op (e1) (e1)))) -> ((~((op (e1) (e1)) = (e1)))\/((op (e1) (e1)) = (e1))) -> (~((op (e1) (e1)) = (op (e1) (e2)))) -> (((op (e0) (e2)) = (e1))\/(((op (e1) (e2)) = (e1))\/(((op (e2) (e2)) = (e1))\/((op (e3) (e2)) = (e1))))) -> (((op (e1) (e0)) = (e3))\/(((op (e1) (e1)) = (e3))\/(((op (e1) (e2)) = (e3))\/((op (e1) (e3)) = (e3))))) -> (~((op (e1) (e1)) = (op (e2) (e1)))) -> (~((op (e2) (e2)) = (e1))) -> (~((op (e0) (e0)) = (op (e0) (e3)))) -> (~((op (e0) (e3)) = (op (e2) (e3)))) -> (~((op (e0) (e3)) = (op (e1) (e3)))) -> (((op (e0) (e3)) = (e0))\/(((op (e0) (e3)) = (e1))\/(((op (e0) (e3)) = (e2))\/((op (e0) (e3)) = (e3))))) -> (((op (e2) (e0)) = (e1))\/(((op (e2) (e1)) = (e1))\/(((op (e2) (e2)) = (e1))\/((op (e2) (e3)) = (e1))))) -> (~((op (e1) (e1)) = (e3))) -> (~((op (e0) (e2)) = (op (e0) (e3)))) -> False). % 15.55/15.68 do 0 intro. intros zenon_H1c3 zenon_H15f zenon_Hd6 zenon_H157 zenon_H1a2 zenon_He6 zenon_H13c zenon_H58 zenon_H45 zenon_H23 zenon_H21 zenon_Hf1 zenon_H36 zenon_Hbe zenon_H105 zenon_H140 zenon_H8e zenon_H28 zenon_H138 zenon_H2af zenon_H1df zenon_H44 zenon_H109 zenon_H6a zenon_H59 zenon_H1d3 zenon_H10f zenon_H258 zenon_H247 zenon_H1e5 zenon_H281 zenon_H10e zenon_H22e zenon_H1d5 zenon_H7d zenon_H166 zenon_H2b8 zenon_H1f zenon_H2b4 zenon_H17d zenon_H1f6 zenon_Ha3 zenon_H146 zenon_Heb zenon_H3b zenon_H1b3 zenon_H35 zenon_H17a zenon_Ha7 zenon_H8f zenon_H2be zenon_H10d zenon_H135 zenon_H10c zenon_H1cf zenon_H1d2 zenon_Hd7 zenon_H1d8 zenon_H116 zenon_H11b zenon_H90 zenon_Hb1 zenon_H52 zenon_H24f zenon_Hb4 zenon_H80 zenon_H254 zenon_Hb7 zenon_H182 zenon_Hc9. % 15.55/15.69 apply (zenon_or_s _ _ zenon_H1c3); [ zenon_intro zenon_H30 | zenon_intro zenon_H124 ]. % 15.55/15.69 apply (zenon_or_s _ _ zenon_H10f); [ zenon_intro zenon_H3c | zenon_intro zenon_Hba ]. % 15.55/15.69 apply (zenon_or_s _ _ zenon_H10c); [ zenon_intro zenon_H104 | zenon_intro zenon_H10a ]. % 15.55/15.69 apply (zenon_or_s _ _ zenon_H10e); [ zenon_intro zenon_H3d | zenon_intro zenon_H106 ]. % 15.55/15.69 apply (zenon_or_s _ _ zenon_H10d); [ zenon_intro zenon_H3e | zenon_intro zenon_H42 ]. % 15.55/15.69 apply (zenon_or_s _ _ zenon_H44); [ zenon_intro zenon_H47 | zenon_intro zenon_H46 ]. % 15.55/15.69 exact (zenon_H45 zenon_H47). % 15.55/15.69 apply (zenon_or_s _ _ zenon_H46); [ zenon_intro zenon_H22 | zenon_intro zenon_H48 ]. % 15.55/15.69 apply (zenon_L3_); trivial. % 15.55/15.69 apply (zenon_or_s _ _ zenon_H48); [ zenon_intro zenon_H29 | zenon_intro zenon_H37 ]. % 15.55/15.69 apply (zenon_or_s _ _ zenon_Hf1); [ zenon_intro zenon_H47 | zenon_intro zenon_Hf4 ]. % 15.55/15.69 exact (zenon_H45 zenon_H47). % 15.55/15.69 apply (zenon_or_s _ _ zenon_Hf4); [ zenon_intro zenon_Hd8 | zenon_intro zenon_Hf5 ]. % 15.55/15.69 apply (zenon_L1176_); trivial. % 15.55/15.69 apply (zenon_or_s _ _ zenon_Hf5); [ zenon_intro zenon_Hae | zenon_intro zenon_Hee ]. % 15.55/15.69 apply (zenon_or_s _ _ zenon_Heb); [ zenon_intro zenon_H92 | zenon_intro zenon_Hec ]. % 15.55/15.69 exact (zenon_H8f zenon_H92). % 15.55/15.69 apply (zenon_or_s _ _ zenon_Hec); [ zenon_intro zenon_H68 | zenon_intro zenon_Hed ]. % 15.55/15.69 apply (zenon_or_s _ _ zenon_Hbe); [ zenon_intro zenon_H5b | zenon_intro zenon_Hbf ]. % 15.55/15.69 exact (zenon_H59 zenon_H5b). % 15.55/15.69 apply (zenon_or_s _ _ zenon_Hbf); [ zenon_intro zenon_H69 | zenon_intro zenon_Hc0 ]. % 15.55/15.69 apply (zenon_L17_); trivial. % 15.55/15.69 apply (zenon_or_s _ _ zenon_Hc0); [ zenon_intro zenon_Haf | zenon_intro zenon_Hba ]. % 15.55/15.69 apply (zenon_L39_); trivial. % 15.55/15.69 apply (zenon_L1178_); trivial. % 15.55/15.69 apply (zenon_or_s _ _ zenon_Hed); [ zenon_intro zenon_Hdd | zenon_intro zenon_He9 ]. % 15.55/15.69 apply (zenon_L161_); trivial. % 15.55/15.69 apply (zenon_L1163_); trivial. % 15.55/15.69 apply (zenon_L1085_); trivial. % 15.55/15.69 apply (zenon_L7_); trivial. % 15.55/15.69 apply (zenon_L1041_); trivial. % 15.55/15.69 apply (zenon_or_s _ _ zenon_H10d); [ zenon_intro zenon_H3e | zenon_intro zenon_H42 ]. % 15.55/15.69 apply (zenon_or_s _ _ zenon_H44); [ zenon_intro zenon_H47 | zenon_intro zenon_H46 ]. % 15.55/15.69 exact (zenon_H45 zenon_H47). % 15.55/15.69 apply (zenon_or_s _ _ zenon_H46); [ zenon_intro zenon_H22 | zenon_intro zenon_H48 ]. % 15.55/15.69 apply (zenon_L3_); trivial. % 15.55/15.69 apply (zenon_or_s _ _ zenon_H48); [ zenon_intro zenon_H29 | zenon_intro zenon_H37 ]. % 15.55/15.69 apply (zenon_L1180_); trivial. % 15.55/15.69 apply (zenon_L88_); trivial. % 15.55/15.69 apply (zenon_L1041_); trivial. % 15.55/15.69 apply (zenon_L1183_); trivial. % 15.55/15.69 apply (zenon_L1178_); trivial. % 15.55/15.69 apply (zenon_L137_); trivial. % 15.55/15.69 (* end of lemma zenon_L1184_ *) % 15.55/15.69 assert (zenon_L1185_ : (((op (e3) (e0)) = (e1))\/(((op (e3) (e1)) = (e1))\/(((op (e3) (e2)) = (e1))\/((op (e3) (e3)) = (e1))))) -> (~((e0) = (e1))) -> ((op (e3) (e0)) = (e0)) -> ((op (e1) (e1)) = (e1)) -> (~((op (e1) (op (e3) (e1))) = (op (e3) (e1)))) -> ((op (e0) (e2)) = (e1)) -> (~((op (e0) (e2)) = (op (e3) (e2)))) -> (~((op (e3) (e3)) = (e1))) -> False). % 15.55/15.69 do 0 intro. intros zenon_H146 zenon_H9e zenon_Hdb zenon_H21 zenon_H2b4 zenon_H29 zenon_H140 zenon_H104. % 15.55/15.69 apply (zenon_or_s _ _ zenon_H146); [ zenon_intro zenon_Hee | zenon_intro zenon_H14b ]. % 15.55/15.69 apply (zenon_L71_); trivial. % 15.55/15.69 apply (zenon_or_s _ _ zenon_H14b); [ zenon_intro zenon_H13e | zenon_intro zenon_H14c ]. % 15.55/15.69 apply (zenon_L1158_); trivial. % 15.55/15.69 apply (zenon_or_s _ _ zenon_H14c); [ zenon_intro zenon_H119 | zenon_intro zenon_H38 ]. % 15.55/15.69 apply (zenon_L124_); trivial. % 15.55/15.69 exact (zenon_H104 zenon_H38). % 15.55/15.69 (* end of lemma zenon_L1185_ *) % 15.55/15.69 assert (zenon_L1186_ : (((op (e0) (e0)) = (e1))\/(((op (e0) (e1)) = (e1))\/(((op (e0) (e2)) = (e1))\/((op (e0) (e3)) = (e1))))) -> (~((op (e0) (e0)) = (e1))) -> (~((op (e0) (e1)) = (op (e1) (e1)))) -> (~((op (e3) (e3)) = (e1))) -> (~((op (e0) (e2)) = (op (e3) (e2)))) -> (~((op (e1) (op (e3) (e1))) = (op (e3) (e1)))) -> ((op (e1) (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 (e3) (e3)) = (e0))\/(((op (e3) (e3)) = (e1))\/(((op (e3) (e3)) = (e2))\/((op (e3) (e3)) = (e3))))) -> (~((op (e3) (e3)) = (e0))) -> (~((op (e0) (e3)) = (op (e3) (e3)))) -> (~((op (e3) (e3)) = (e2))) -> (~((op (e3) (e3)) = (e3))) -> False). % 15.55/15.69 do 0 intro. intros zenon_H44 zenon_H45 zenon_H23 zenon_H104 zenon_H140 zenon_H2b4 zenon_H21 zenon_Hdb zenon_H9e zenon_H146 zenon_H3b zenon_H3c zenon_H36 zenon_H3d zenon_H3e. % 15.55/15.69 apply (zenon_or_s _ _ zenon_H44); [ zenon_intro zenon_H47 | zenon_intro zenon_H46 ]. % 15.55/15.69 exact (zenon_H45 zenon_H47). % 15.55/15.69 apply (zenon_or_s _ _ zenon_H46); [ zenon_intro zenon_H22 | zenon_intro zenon_H48 ]. % 15.55/15.69 apply (zenon_L3_); trivial. % 15.55/15.69 apply (zenon_or_s _ _ zenon_H48); [ zenon_intro zenon_H29 | zenon_intro zenon_H37 ]. % 15.55/15.69 apply (zenon_L1185_); trivial. % 15.55/15.69 apply (zenon_L7_); trivial. % 15.55/15.69 (* end of lemma zenon_L1186_ *) % 15.55/15.69 assert (zenon_L1187_ : (((op (e3) (e0)) = (e2))\/(((op (e3) (e1)) = (e2))\/(((op (e3) (e2)) = (e2))\/((op (e3) (e3)) = (e2))))) -> ((op (e3) (e0)) = (e3)) -> (~((e2) = (e3))) -> ((op (e3) (e1)) = (e0)) -> ((op (e1) (e0)) = (e2)) -> (~((op (e1) (op (e3) (e1))) = (op (e3) (e1)))) -> ((op (e3) (e2)) = (e1)) -> ((op (e2) (e1)) = (e2)) -> (~((op (e2) (op (e3) (e2))) = (op (e3) (e2)))) -> (~((op (e3) (e3)) = (e2))) -> False). % 15.55/15.69 do 0 intro. intros zenon_H1df zenon_Hba zenon_H6a zenon_H142 zenon_H68 zenon_H2b4 zenon_H119 zenon_H156 zenon_H2af zenon_H3d. % 15.55/15.69 apply (zenon_or_s _ _ zenon_H1df); [ zenon_intro zenon_He9 | zenon_intro zenon_H1e0 ]. % 15.55/15.69 apply (zenon_L220_); trivial. % 15.55/15.69 apply (zenon_or_s _ _ zenon_H1e0); [ zenon_intro zenon_H16a | zenon_intro zenon_H1e1 ]. % 15.55/15.69 apply (zenon_L1104_); trivial. % 15.55/15.69 apply (zenon_or_s _ _ zenon_H1e1); [ zenon_intro zenon_H1dd | zenon_intro zenon_H43 ]. % 15.55/15.69 apply (zenon_L1160_); trivial. % 15.55/15.69 exact (zenon_H3d zenon_H43). % 15.55/15.69 (* end of lemma zenon_L1187_ *) % 15.55/15.69 assert (zenon_L1188_ : (((op (e3) (e0)) = (e1))\/(((op (e3) (e1)) = (e1))\/(((op (e3) (e2)) = (e1))\/((op (e3) (e3)) = (e1))))) -> (~((e1) = (e3))) -> ((op (e1) (e1)) = (e1)) -> (~((op (e3) (e3)) = (e2))) -> (~((op (e2) (op (e3) (e2))) = (op (e3) (e2)))) -> ((op (e2) (e1)) = (e2)) -> (~((op (e1) (op (e3) (e1))) = (op (e3) (e1)))) -> ((op (e1) (e0)) = (e2)) -> ((op (e3) (e1)) = (e0)) -> (~((e2) = (e3))) -> ((op (e3) (e0)) = (e3)) -> (((op (e3) (e0)) = (e2))\/(((op (e3) (e1)) = (e2))\/(((op (e3) (e2)) = (e2))\/((op (e3) (e3)) = (e2))))) -> (~((op (e3) (e3)) = (e1))) -> False). % 15.55/15.69 do 0 intro. intros zenon_H146 zenon_Ha3 zenon_H21 zenon_H3d zenon_H2af zenon_H156 zenon_H2b4 zenon_H68 zenon_H142 zenon_H6a zenon_Hba zenon_H1df zenon_H104. % 15.55/15.69 apply (zenon_or_s _ _ zenon_H146); [ zenon_intro zenon_Hee | zenon_intro zenon_H14b ]. % 15.55/15.69 apply (zenon_L79_); trivial. % 15.55/15.69 apply (zenon_or_s _ _ zenon_H14b); [ zenon_intro zenon_H13e | zenon_intro zenon_H14c ]. % 15.55/15.69 apply (zenon_L1158_); trivial. % 15.55/15.69 apply (zenon_or_s _ _ zenon_H14c); [ zenon_intro zenon_H119 | zenon_intro zenon_H38 ]. % 15.55/15.69 apply (zenon_L1187_); trivial. % 15.55/15.69 exact (zenon_H104 zenon_H38). % 15.55/15.69 (* end of lemma zenon_L1188_ *) % 15.55/15.69 assert (zenon_L1189_ : (((op (e3) (e0)) = (e3))\/(((op (e3) (e1)) = (e3))\/(((op (e3) (e2)) = (e3))\/((op (e3) (e3)) = (e3))))) -> (~((op (e3) (e3)) = (e1))) -> (((op (e3) (e0)) = (e2))\/(((op (e3) (e1)) = (e2))\/(((op (e3) (e2)) = (e2))\/((op (e3) (e3)) = (e2))))) -> (~((e2) = (e3))) -> ((op (e1) (e0)) = (e2)) -> (~((op (e1) (op (e3) (e1))) = (op (e3) (e1)))) -> ((op (e2) (e1)) = (e2)) -> (~((op (e2) (op (e3) (e2))) = (op (e3) (e2)))) -> (~((op (e3) (e3)) = (e2))) -> ((op (e1) (e1)) = (e1)) -> (~((e1) = (e3))) -> (((op (e3) (e0)) = (e1))\/(((op (e3) (e1)) = (e1))\/(((op (e3) (e2)) = (e1))\/((op (e3) (e3)) = (e1))))) -> ((op (e3) (e1)) = (e0)) -> (~((e0) = (e3))) -> (~((op (e1) (e2)) = (op (e3) (e2)))) -> ((op (e1) (e2)) = (e3)) -> (~((op (e3) (e3)) = (e3))) -> False). % 15.55/15.69 do 0 intro. intros zenon_H2d5 zenon_H104 zenon_H1df zenon_H6a zenon_H68 zenon_H2b4 zenon_H156 zenon_H2af zenon_H3d zenon_H21 zenon_Ha3 zenon_H146 zenon_H142 zenon_H4b zenon_H17d zenon_H88 zenon_H3e. % 15.55/15.69 apply (zenon_or_s _ _ zenon_H2d5); [ zenon_intro zenon_Hba | zenon_intro zenon_H2d6 ]. % 15.55/15.69 apply (zenon_L1188_); trivial. % 15.55/15.69 apply (zenon_or_s _ _ zenon_H2d6); [ zenon_intro zenon_H10a | zenon_intro zenon_H2d7 ]. % 15.55/15.69 apply (zenon_L126_); trivial. % 15.55/15.69 apply (zenon_or_s _ _ zenon_H2d7); [ zenon_intro zenon_H106 | zenon_intro zenon_H42 ]. % 15.55/15.69 apply (zenon_L164_); trivial. % 15.55/15.69 exact (zenon_H3e zenon_H42). % 15.55/15.69 (* end of lemma zenon_L1189_ *) % 15.55/15.69 assert (zenon_L1190_ : (((op (e3) (e0)) = (e0))\/(((op (e3) (e1)) = (e0))\/(((op (e3) (e2)) = (e0))\/((op (e3) (e3)) = (e0))))) -> (~((op (e0) (e3)) = (op (e3) (e3)))) -> (((op (e3) (e3)) = (e0))\/(((op (e3) (e3)) = (e1))\/(((op (e3) (e3)) = (e2))\/((op (e3) (e3)) = (e3))))) -> (~((e0) = (e1))) -> (~((op (e0) (e2)) = (op (e3) (e2)))) -> (~((op (e0) (e1)) = (op (e1) (e1)))) -> (~((op (e0) (e0)) = (e1))) -> (((op (e0) (e0)) = (e1))\/(((op (e0) (e1)) = (e1))\/(((op (e0) (e2)) = (e1))\/((op (e0) (e3)) = (e1))))) -> (~((op (e3) (e3)) = (e3))) -> ((op (e1) (e2)) = (e3)) -> (~((e0) = (e3))) -> (((op (e3) (e0)) = (e1))\/(((op (e3) (e1)) = (e1))\/(((op (e3) (e2)) = (e1))\/((op (e3) (e3)) = (e1))))) -> (~((e1) = (e3))) -> ((op (e1) (e1)) = (e1)) -> (~((op (e3) (e3)) = (e2))) -> (~((op (e2) (op (e3) (e2))) = (op (e3) (e2)))) -> ((op (e2) (e1)) = (e2)) -> (~((op (e1) (op (e3) (e1))) = (op (e3) (e1)))) -> ((op (e1) (e0)) = (e2)) -> (~((e2) = (e3))) -> (((op (e3) (e0)) = (e2))\/(((op (e3) (e1)) = (e2))\/(((op (e3) (e2)) = (e2))\/((op (e3) (e3)) = (e2))))) -> (~((op (e3) (e3)) = (e1))) -> (((op (e3) (e0)) = (e3))\/(((op (e3) (e1)) = (e3))\/(((op (e3) (e2)) = (e3))\/((op (e3) (e3)) = (e3))))) -> ((op (e1) (e2)) = (e0)) -> (~((op (e1) (e2)) = (op (e3) (e2)))) -> (~((op (e3) (e3)) = (e0))) -> False). % 15.55/15.69 do 0 intro. intros zenon_H1f6 zenon_H36 zenon_H3b zenon_H9e zenon_H140 zenon_H23 zenon_H45 zenon_H44 zenon_H3e zenon_H88 zenon_H4b zenon_H146 zenon_Ha3 zenon_H21 zenon_H3d zenon_H2af zenon_H156 zenon_H2b4 zenon_H68 zenon_H6a zenon_H1df zenon_H104 zenon_H2d5 zenon_H15d zenon_H17d zenon_H3c. % 15.55/15.69 apply (zenon_or_s _ _ zenon_H1f6); [ zenon_intro zenon_Hdb | zenon_intro zenon_H1f7 ]. % 15.55/15.69 apply (zenon_L1186_); trivial. % 15.55/15.69 apply (zenon_or_s _ _ zenon_H1f7); [ zenon_intro zenon_H142 | zenon_intro zenon_H1f8 ]. % 15.55/15.69 apply (zenon_L1189_); trivial. % 15.55/15.69 apply (zenon_or_s _ _ zenon_H1f8); [ zenon_intro zenon_H167 | zenon_intro zenon_H40 ]. % 15.55/15.69 apply (zenon_L626_); trivial. % 15.55/15.69 exact (zenon_H3c zenon_H40). % 15.55/15.69 (* end of lemma zenon_L1190_ *) % 15.55/15.69 assert (zenon_L1191_ : (((op (e3) (e0)) = (e0))\/(((op (e3) (e1)) = (e0))\/(((op (e3) (e2)) = (e0))\/((op (e3) (e3)) = (e0))))) -> ((op (e0) (e0)) = (e0)) -> (~((op (e0) (op (e3) (e0))) = (op (e3) (e0)))) -> ((op (e2) (e2)) = (e1)) -> (~((op (e2) (e1)) = (op (e2) (e3)))) -> ((op (e2) (e1)) = (e2)) -> ((op (e1) (e3)) = (e3)) -> (~((e2) = (e3))) -> (((op (e3) (e3)) = (e0))\/(((op (e3) (e3)) = (e1))\/(((op (e3) (e3)) = (e2))\/((op (e3) (e3)) = (e3))))) -> (~((op (e3) (e3)) = (e1))) -> (~((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) (e2)) = (e3)) -> (~((e0) = (e3))) -> (~((op (e3) (e3)) = (e0))) -> False). % 15.55/15.69 do 0 intro. intros zenon_H1f6 zenon_H1f zenon_H2b8 zenon_H2a zenon_H1e2 zenon_H156 zenon_H8a zenon_H6a zenon_H3b zenon_H104 zenon_H36 zenon_H3e zenon_H160 zenon_H106 zenon_H4b zenon_H3c. % 15.55/15.69 apply (zenon_or_s _ _ zenon_H1f6); [ zenon_intro zenon_Hdb | zenon_intro zenon_H1f7 ]. % 15.55/15.69 apply (zenon_L1045_); trivial. % 15.55/15.69 apply (zenon_or_s _ _ zenon_H1f7); [ zenon_intro zenon_H142 | zenon_intro zenon_H1f8 ]. % 15.55/15.69 apply (zenon_L902_); trivial. % 15.55/15.69 apply (zenon_or_s _ _ zenon_H1f8); [ zenon_intro zenon_H167 | zenon_intro zenon_H40 ]. % 15.55/15.69 apply (zenon_L589_); trivial. % 15.55/15.69 exact (zenon_H3c zenon_H40). % 15.55/15.69 (* end of lemma zenon_L1191_ *) % 15.55/15.69 assert (zenon_L1192_ : (((op (e0) (e0)) = (e3))\/(((op (e1) (e0)) = (e3))\/(((op (e2) (e0)) = (e3))\/((op (e3) (e0)) = (e3))))) -> (~((op (e0) (e0)) = (e3))) -> (~((op (e3) (e3)) = (e3))) -> (~((op (e3) (e3)) = (e2))) -> (~((op (e1) (e3)) = (op (e3) (e3)))) -> (((op (e3) (e3)) = (e0))\/(((op (e3) (e3)) = (e1))\/(((op (e3) (e3)) = (e2))\/((op (e3) (e3)) = (e3))))) -> (((op (e1) (e0)) = (e3))\/(((op (e1) (e1)) = (e3))\/(((op (e1) (e2)) = (e3))\/((op (e1) (e3)) = (e3))))) -> (~((op (e1) (e1)) = (e3))) -> (((op (e2) (e0)) = (e1))\/(((op (e2) (e1)) = (e1))\/(((op (e2) (e2)) = (e1))\/((op (e2) (e3)) = (e1))))) -> (~((op (e1) (e1)) = (op (e2) (e1)))) -> (~((e0) = (e3))) -> (~((op (e0) (op (e3) (e0))) = (op (e3) (e0)))) -> (((op (e3) (e0)) = (e0))\/(((op (e3) (e1)) = (e0))\/(((op (e3) (e2)) = (e0))\/((op (e3) (e3)) = (e0))))) -> (~((op (e2) (e2)) = (e3))) -> (~((e0) = (e1))) -> (~((op (e0) (e1)) = (op (e1) (e1)))) -> (~((op (e0) (e0)) = (e1))) -> (((op (e0) (e0)) = (e1))\/(((op (e0) (e1)) = (e1))\/(((op (e0) (e2)) = (e1))\/((op (e0) (e3)) = (e1))))) -> (~((op (e2) (op (e3) (e2))) = (op (e3) (e2)))) -> ((op (e1) (e0)) = (e2)) -> (((op (e3) (e0)) = (e2))\/(((op (e3) (e1)) = (e2))\/(((op (e3) (e2)) = (e2))\/((op (e3) (e3)) = (e2))))) -> (((op (e3) (e0)) = (e3))\/(((op (e3) (e1)) = (e3))\/(((op (e3) (e2)) = (e3))\/((op (e3) (e3)) = (e3))))) -> (~((op (e1) (e2)) = (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) (e3)) = (e0))) -> (~((e2) = (e3))) -> ((op (e2) (e1)) = (e2)) -> (~((op (e2) (e1)) = (op (e2) (e3)))) -> (((op (e0) (e3)) = (e0))\/(((op (e0) (e3)) = (e1))\/(((op (e0) (e3)) = (e2))\/((op (e0) (e3)) = (e3))))) -> ((op (e0) (e0)) = (e0)) -> (~((op (e0) (e0)) = (op (e0) (e3)))) -> (~((op (e0) (e3)) = (op (e2) (e3)))) -> (~((op (e0) (e3)) = (op (e3) (e3)))) -> (~((op (e0) (e3)) = (op (e1) (e3)))) -> (~((op (e1) (e1)) = (e0))) -> (~((op (e0) (e0)) = (op (e1) (e0)))) -> (((op (e1) (e0)) = (e0))\/(((op (e1) (e1)) = (e0))\/(((op (e1) (e2)) = (e0))\/((op (e1) (e3)) = (e0))))) -> (((op (e3) (e0)) = (e1))\/(((op (e3) (e1)) = (e1))\/(((op (e3) (e2)) = (e1))\/((op (e3) (e3)) = (e1))))) -> (~((e1) = (e3))) -> ((op (e1) (e1)) = (e1)) -> (~((op (e1) (op (e3) (e1))) = (op (e3) (e1)))) -> ((op (e0) (e2)) = (e1)) -> (~((op (e0) (e2)) = (op (e3) (e2)))) -> (~((op (e3) (e3)) = (e1))) -> False). % 15.55/15.69 do 0 intro. intros zenon_Hbe zenon_H59 zenon_H3e zenon_H3d zenon_H8b zenon_H3b zenon_H90 zenon_H182 zenon_Hb7 zenon_Hb1 zenon_H4b zenon_H2b8 zenon_H1f6 zenon_H30 zenon_H9e zenon_H23 zenon_H45 zenon_H44 zenon_H2af zenon_H68 zenon_H1df zenon_H2d5 zenon_H17d zenon_H175 zenon_H160 zenon_H3c zenon_H6a zenon_H156 zenon_H1e2 zenon_H254 zenon_H1f zenon_H24f zenon_Hb4 zenon_H36 zenon_H80 zenon_H145 zenon_H24c zenon_H163 zenon_H146 zenon_Ha3 zenon_H21 zenon_H2b4 zenon_H29 zenon_H140 zenon_H104. % 15.55/15.69 apply (zenon_or_s _ _ zenon_Hbe); [ zenon_intro zenon_H5b | zenon_intro zenon_Hbf ]. % 15.55/15.69 exact (zenon_H59 zenon_H5b). % 15.55/15.69 apply (zenon_or_s _ _ zenon_Hbf); [ zenon_intro zenon_H69 | zenon_intro zenon_Hc0 ]. % 15.55/15.69 apply (zenon_L17_); trivial. % 15.55/15.69 apply (zenon_or_s _ _ zenon_Hc0); [ zenon_intro zenon_Haf | zenon_intro zenon_Hba ]. % 15.55/15.69 apply (zenon_or_s _ _ zenon_H163); [ zenon_intro zenon_Had | zenon_intro zenon_H164 ]. % 15.55/15.69 apply (zenon_L559_); trivial. % 15.55/15.69 apply (zenon_or_s _ _ zenon_H164); [ zenon_intro zenon_H149 | zenon_intro zenon_H165 ]. % 15.55/15.69 exact (zenon_H145 zenon_H149). % 15.55/15.69 apply (zenon_or_s _ _ zenon_H165); [ zenon_intro zenon_H15d | zenon_intro zenon_Hcc ]. % 15.55/15.69 apply (zenon_or_s _ _ zenon_H90); [ zenon_intro zenon_H69 | zenon_intro zenon_H94 ]. % 15.55/15.69 apply (zenon_L17_); trivial. % 15.55/15.69 apply (zenon_or_s _ _ zenon_H94); [ zenon_intro zenon_H96 | zenon_intro zenon_H95 ]. % 15.55/15.69 exact (zenon_H182 zenon_H96). % 15.55/15.69 apply (zenon_or_s _ _ zenon_H95); [ zenon_intro zenon_H88 | zenon_intro zenon_H8a ]. % 15.55/15.69 apply (zenon_L1190_); trivial. % 15.55/15.69 apply (zenon_or_s _ _ zenon_Hb7); [ zenon_intro zenon_Hae | zenon_intro zenon_Hb8 ]. % 15.55/15.69 apply (zenon_L39_); trivial. % 15.55/15.69 apply (zenon_or_s _ _ zenon_Hb8); [ zenon_intro zenon_Hb2 | zenon_intro zenon_Hb9 ]. % 15.55/15.69 apply (zenon_L40_); trivial. % 15.55/15.69 apply (zenon_or_s _ _ zenon_Hb9); [ zenon_intro zenon_H2a | zenon_intro zenon_Hb5 ]. % 15.55/15.69 apply (zenon_or_s _ _ zenon_H175); [ zenon_intro zenon_H50 | zenon_intro zenon_H176 ]. % 15.55/15.69 apply (zenon_L29_); trivial. % 15.55/15.69 apply (zenon_or_s _ _ zenon_H176); [ zenon_intro zenon_H88 | zenon_intro zenon_H177 ]. % 15.55/15.69 apply (zenon_L1190_); trivial. % 15.55/15.69 apply (zenon_or_s _ _ zenon_H177); [ zenon_intro zenon_H34 | zenon_intro zenon_H106 ]. % 15.55/15.69 exact (zenon_H30 zenon_H34). % 15.55/15.69 apply (zenon_L1191_); trivial. % 15.55/15.69 apply (zenon_L904_); trivial. % 15.55/15.69 apply (zenon_L465_); trivial. % 15.55/15.69 apply (zenon_L1159_); trivial. % 15.55/15.69 (* end of lemma zenon_L1192_ *) % 15.55/15.69 assert (zenon_L1193_ : (((op (e0) (e0)) = (e3))\/(((op (e1) (e0)) = (e3))\/(((op (e2) (e0)) = (e3))\/((op (e3) (e0)) = (e3))))) -> (~((op (e0) (e0)) = (e3))) -> (~((op (e0) (e3)) = (op (e1) (e3)))) -> (~((op (e0) (e3)) = (op (e3) (e3)))) -> (~((op (e0) (e3)) = (op (e2) (e3)))) -> (~((op (e0) (e0)) = (op (e0) (e3)))) -> ((op (e0) (e0)) = (e0)) -> (((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)) -> (~((e2) = (e3))) -> (((op (e3) (e3)) = (e0))\/(((op (e3) (e3)) = (e1))\/(((op (e3) (e3)) = (e2))\/((op (e3) (e3)) = (e3))))) -> (~((op (e3) (e3)) = (e0))) -> (~((op (e3) (e3)) = (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 (e0) (op (e3) (e0))) = (op (e3) (e0)))) -> ((op (e3) (e2)) = (e3)) -> (~((e0) = (e3))) -> (~((op (e1) (e1)) = (op (e2) (e1)))) -> (((op (e2) (e0)) = (e1))\/(((op (e2) (e1)) = (e1))\/(((op (e2) (e2)) = (e1))\/((op (e2) (e3)) = (e1))))) -> (~((op (e1) (e2)) = (op (e3) (e2)))) -> (~((op (e1) (e1)) = (e3))) -> ((op (e1) (e0)) = (e2)) -> (((op (e1) (e0)) = (e3))\/(((op (e1) (e1)) = (e3))\/(((op (e1) (e2)) = (e3))\/((op (e1) (e3)) = (e3))))) -> (((op (e3) (e0)) = (e1))\/(((op (e3) (e1)) = (e1))\/(((op (e3) (e2)) = (e1))\/((op (e3) (e3)) = (e1))))) -> (~((e1) = (e3))) -> ((op (e1) (e1)) = (e1)) -> (~((op (e1) (op (e3) (e1))) = (op (e3) (e1)))) -> ((op (e0) (e2)) = (e1)) -> (~((op (e0) (e2)) = (op (e3) (e2)))) -> (~((op (e3) (e3)) = (e1))) -> False). % 15.55/15.69 do 0 intro. intros zenon_Hbe zenon_H59 zenon_H80 zenon_H36 zenon_Hb4 zenon_H24f zenon_H1f zenon_H254 zenon_H1e2 zenon_H156 zenon_H6a zenon_H3b zenon_H3c zenon_H3e zenon_H160 zenon_H1f6 zenon_H2b8 zenon_H106 zenon_H4b zenon_Hb1 zenon_Hb7 zenon_H17d zenon_H182 zenon_H68 zenon_H90 zenon_H146 zenon_Ha3 zenon_H21 zenon_H2b4 zenon_H29 zenon_H140 zenon_H104. % 15.55/15.69 apply (zenon_or_s _ _ zenon_Hbe); [ zenon_intro zenon_H5b | zenon_intro zenon_Hbf ]. % 15.55/15.69 exact (zenon_H59 zenon_H5b). % 15.55/15.69 apply (zenon_or_s _ _ zenon_Hbf); [ zenon_intro zenon_H69 | zenon_intro zenon_Hc0 ]. % 15.55/15.69 apply (zenon_L17_); trivial. % 15.55/15.69 apply (zenon_or_s _ _ zenon_Hc0); [ zenon_intro zenon_Haf | zenon_intro zenon_Hba ]. % 15.55/15.69 apply (zenon_or_s _ _ zenon_H90); [ zenon_intro zenon_H69 | zenon_intro zenon_H94 ]. % 15.55/15.69 apply (zenon_L17_); trivial. % 15.55/15.69 apply (zenon_or_s _ _ zenon_H94); [ zenon_intro zenon_H96 | zenon_intro zenon_H95 ]. % 15.55/15.69 exact (zenon_H182 zenon_H96). % 15.55/15.69 apply (zenon_or_s _ _ zenon_H95); [ zenon_intro zenon_H88 | zenon_intro zenon_H8a ]. % 15.55/15.69 apply (zenon_L164_); trivial. % 15.55/15.69 apply (zenon_or_s _ _ zenon_Hb7); [ zenon_intro zenon_Hae | zenon_intro zenon_Hb8 ]. % 15.55/15.69 apply (zenon_L39_); trivial. % 15.55/15.69 apply (zenon_or_s _ _ zenon_Hb8); [ zenon_intro zenon_Hb2 | zenon_intro zenon_Hb9 ]. % 15.55/15.69 apply (zenon_L40_); trivial. % 15.55/15.69 apply (zenon_or_s _ _ zenon_Hb9); [ zenon_intro zenon_H2a | zenon_intro zenon_Hb5 ]. % 15.55/15.69 apply (zenon_L1191_); trivial. % 15.55/15.69 apply (zenon_L904_); trivial. % 15.55/15.69 apply (zenon_L1159_); trivial. % 15.55/15.69 (* end of lemma zenon_L1193_ *) % 15.55/15.69 assert (zenon_L1194_ : ((~((op (e3) (e3)) = (e0)))\/((op (e3) (e0)) = (e3))) -> ((~((op (e3) (e3)) = (e3)))\/((op (e3) (e3)) = (e3))) -> (~((op (e3) (op (e3) (e3))) = (op (e3) (e3)))) -> (~((op (e0) (e0)) = (e1))) -> (~((op (e1) (e0)) = (op (e1) (e1)))) -> ((op (e1) (e1)) = (e1)) -> (~((e1) = (e2))) -> ((op (e2) (e0)) = (e2)) -> (((op (e2) (e2)) = (e0))\/(((op (e2) (e2)) = (e1))\/(((op (e2) (e2)) = (e2))\/((op (e2) (e2)) = (e3))))) -> (~((op (e2) (e2)) = (e3))) -> (~((op (e2) (e2)) = (e2))) -> (~((op (e2) (e2)) = (e1))) -> (((op (e3) (e3)) = (e0))\/(((op (e3) (e3)) = (e1))\/(((op (e3) (e3)) = (e2))\/((op (e3) (e3)) = (e3))))) -> (((op (e0) (e0)) = (e1))\/(((op (e1) (e0)) = (e1))\/(((op (e2) (e0)) = (e1))\/((op (e3) (e0)) = (e1))))) -> ((~((op (e3) (e3)) = (e2)))\/((op (e3) (e2)) = (e3))) -> (~((op (e3) (e1)) = (op (e3) (e2)))) -> (((op (e0) (e0)) = (e1))\/(((op (e0) (e1)) = (e1))\/(((op (e0) (e2)) = (e1))\/((op (e0) (e3)) = (e1))))) -> (~((op (e0) (e3)) = (op (e3) (e3)))) -> (~((op (e0) (e0)) = (e3))) -> (~((op (e0) (e1)) = (op (e3) (e1)))) -> (~((e1) = (e3))) -> (((op (e1) (e0)) = (e0))\/(((op (e1) (e1)) = (e0))\/(((op (e1) (e2)) = (e0))\/((op (e1) (e3)) = (e0))))) -> (~((e2) = (e3))) -> (~((e0) = (e2))) -> (~((op (e2) (e0)) = (op (e2) (e3)))) -> (((op (e0) (e3)) = (e2))\/(((op (e1) (e3)) = (e2))\/(((op (e2) (e3)) = (e2))\/((op (e3) (e3)) = (e2))))) -> (~((op (e0) (op (e3) (e0))) = (op (e3) (e0)))) -> (~((e0) = (e3))) -> (~((op (e1) (e2)) = (op (e3) (e2)))) -> (((op (e3) (e0)) = (e0))\/(((op (e3) (e1)) = (e0))\/(((op (e3) (e2)) = (e0))\/((op (e3) (e3)) = (e0))))) -> (~((op (e1) (e1)) = (e0))) -> ((op (e0) (e0)) = (e0)) -> (~((op (e0) (e0)) = (op (e1) (e0)))) -> (((op (e0) (e0)) = (e3))\/(((op (e0) (e1)) = (e3))\/(((op (e0) (e2)) = (e3))\/((op (e0) (e3)) = (e3))))) -> (~((op (e0) (e1)) = (op (e1) (e1)))) -> ((~((op (e3) (e3)) = (e1)))\/((op (e3) (e1)) = (e3))) -> False). % 15.55/15.69 do 0 intro. intros zenon_H10f zenon_H10d zenon_H2be zenon_H45 zenon_Hd7 zenon_H21 zenon_Ha7 zenon_Hdd zenon_H2d zenon_H30 zenon_H2f zenon_H52 zenon_H3b zenon_Hf1 zenon_H10e zenon_H135 zenon_H44 zenon_H36 zenon_H59 zenon_H138 zenon_Ha3 zenon_H163 zenon_H6a zenon_H5e zenon_Hce zenon_H160 zenon_H2b8 zenon_H4b zenon_H17d zenon_H1f6 zenon_H145 zenon_H1f zenon_H24c zenon_H58 zenon_H23 zenon_H10c. % 15.55/15.69 apply (zenon_or_s _ _ zenon_H10f); [ zenon_intro zenon_H3c | zenon_intro zenon_Hba ]. % 15.55/15.69 apply (zenon_L1174_); trivial. % 15.55/15.69 apply (zenon_L310_); trivial. % 15.55/15.69 (* end of lemma zenon_L1194_ *) % 15.55/15.69 assert (zenon_L1195_ : ((~((op (e2) (e2)) = (e2)))\/((op (e2) (e2)) = (e2))) -> (~((op (e0) (e2)) = (op (e0) (e3)))) -> (~((op (e1) (e1)) = (e3))) -> (((op (e2) (e0)) = (e1))\/(((op (e2) (e1)) = (e1))\/(((op (e2) (e2)) = (e1))\/((op (e2) (e3)) = (e1))))) -> (((op (e0) (e3)) = (e0))\/(((op (e0) (e3)) = (e1))\/(((op (e0) (e3)) = (e2))\/((op (e0) (e3)) = (e3))))) -> (~((op (e0) (e3)) = (op (e1) (e3)))) -> (~((op (e0) (e3)) = (op (e2) (e3)))) -> (~((op (e0) (e0)) = (op (e0) (e3)))) -> (~((op (e1) (e1)) = (op (e2) (e1)))) -> (((op (e1) (e0)) = (e3))\/(((op (e1) (e1)) = (e3))\/(((op (e1) (e2)) = (e3))\/((op (e1) (e3)) = (e3))))) -> (((op (e0) (e2)) = (e1))\/(((op (e1) (e2)) = (e1))\/(((op (e2) (e2)) = (e1))\/((op (e3) (e2)) = (e1))))) -> (~((op (e1) (e1)) = (op (e1) (e2)))) -> ((~((op (e1) (e1)) = (e1)))\/((op (e1) (e1)) = (e1))) -> ((~((op (e1) (e1)) = (e3)))\/((op (e1) (e3)) = (e1))) -> (~((op (e1) (e0)) = (op (e1) (e3)))) -> (~((op (e0) (e0)) = (e2))) -> (~((op (e2) (e0)) = (op (e2) (e2)))) -> (((op (e1) (e1)) = (e0))\/(((op (e1) (e1)) = (e1))\/(((op (e1) (e1)) = (e2))\/((op (e1) (e1)) = (e3))))) -> (((op (e0) (e0)) = (e2))\/(((op (e1) (e0)) = (e2))\/(((op (e2) (e0)) = (e2))\/((op (e3) (e0)) = (e2))))) -> (((op (e3) (e0)) = (e1))\/(((op (e3) (e1)) = (e1))\/(((op (e3) (e2)) = (e1))\/((op (e3) (e3)) = (e1))))) -> (~((op (e1) (op (e3) (e1))) = (op (e3) (e1)))) -> (~((op (e1) (e0)) = (op (e1) (e2)))) -> (~((op (e1) (e2)) = (op (e2) (e2)))) -> (((op (e1) (e2)) = (e0))\/(((op (e1) (e2)) = (e1))\/(((op (e1) (e2)) = (e2))\/((op (e1) (e2)) = (e3))))) -> (~((op (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 (e1) (e0)) = (op (e2) (e0)))) -> (~((op (e0) (e0)) = (op (e2) (e0)))) -> ((~((op (e1) (e1)) = (e2)))\/((op (e1) (e2)) = (e1))) -> (~((op (e3) (e0)) = (op (e3) (e1)))) -> (((op (e3) (e0)) = (e2))\/(((op (e3) (e1)) = (e2))\/(((op (e3) (e2)) = (e2))\/((op (e3) (e3)) = (e2))))) -> (~((op (e2) (op (e3) (e2))) = (op (e3) (e2)))) -> (~((op (e0) (e2)) = (op (e2) (e2)))) -> (((op (e0) (e0)) = (e2))\/(((op (e0) (e1)) = (e2))\/(((op (e0) (e2)) = (e2))\/((op (e0) (e3)) = (e2))))) -> (~((op (e0) (e2)) = (op (e3) (e2)))) -> (~((op (e3) (e0)) = (op (e3) (e2)))) -> (((op (e0) (e0)) = (e3))\/(((op (e1) (e0)) = (e3))\/(((op (e2) (e0)) = (e3))\/((op (e3) (e0)) = (e3))))) -> (~((op (e2) (e1)) = (op (e3) (e1)))) -> (((op (e2) (e0)) = (e3))\/(((op (e2) (e1)) = (e3))\/(((op (e2) (e2)) = (e3))\/((op (e2) (e3)) = (e3))))) -> (((op (e0) (e1)) = (e2))\/(((op (e1) (e1)) = (e2))\/(((op (e2) (e1)) = (e2))\/((op (e3) (e1)) = (e2))))) -> (~((op (e2) (e1)) = (op (e2) (e2)))) -> (~((op (e1) (e1)) = (e2))) -> (~((op (e2) (e2)) = (op (e2) (e3)))) -> ((~((op (e3) (e3)) = (e0)))\/((op (e3) (e0)) = (e3))) -> ((~((op (e3) (e3)) = (e3)))\/((op (e3) (e3)) = (e3))) -> (~((op (e3) (op (e3) (e3))) = (op (e3) (e3)))) -> (~((op (e0) (e0)) = (e1))) -> (~((op (e1) (e0)) = (op (e1) (e1)))) -> ((op (e1) (e1)) = (e1)) -> (~((e1) = (e2))) -> ((op (e2) (e0)) = (e2)) -> (((op (e2) (e2)) = (e0))\/(((op (e2) (e2)) = (e1))\/(((op (e2) (e2)) = (e2))\/((op (e2) (e2)) = (e3))))) -> (~((op (e2) (e2)) = (e1))) -> (((op (e3) (e3)) = (e0))\/(((op (e3) (e3)) = (e1))\/(((op (e3) (e3)) = (e2))\/((op (e3) (e3)) = (e3))))) -> (((op (e0) (e0)) = (e1))\/(((op (e1) (e0)) = (e1))\/(((op (e2) (e0)) = (e1))\/((op (e3) (e0)) = (e1))))) -> ((~((op (e3) (e3)) = (e2)))\/((op (e3) (e2)) = (e3))) -> (~((op (e3) (e1)) = (op (e3) (e2)))) -> (((op (e0) (e0)) = (e1))\/(((op (e0) (e1)) = (e1))\/(((op (e0) (e2)) = (e1))\/((op (e0) (e3)) = (e1))))) -> (~((op (e0) (e3)) = (op (e3) (e3)))) -> (~((op (e0) (e0)) = (e3))) -> (~((op (e0) (e1)) = (op (e3) (e1)))) -> (~((e1) = (e3))) -> (((op (e1) (e0)) = (e0))\/(((op (e1) (e1)) = (e0))\/(((op (e1) (e2)) = (e0))\/((op (e1) (e3)) = (e0))))) -> (~((e2) = (e3))) -> (~((e0) = (e2))) -> (~((op (e2) (e0)) = (op (e2) (e3)))) -> (((op (e0) (e3)) = (e2))\/(((op (e1) (e3)) = (e2))\/(((op (e2) (e3)) = (e2))\/((op (e3) (e3)) = (e2))))) -> (~((op (e0) (op (e3) (e0))) = (op (e3) (e0)))) -> (~((e0) = (e3))) -> (~((op (e1) (e2)) = (op (e3) (e2)))) -> (((op (e3) (e0)) = (e0))\/(((op (e3) (e1)) = (e0))\/(((op (e3) (e2)) = (e0))\/((op (e3) (e3)) = (e0))))) -> (~((op (e1) (e1)) = (e0))) -> ((op (e0) (e0)) = (e0)) -> (~((op (e0) (e0)) = (op (e1) (e0)))) -> (((op (e0) (e0)) = (e3))\/(((op (e0) (e1)) = (e3))\/(((op (e0) (e2)) = (e3))\/((op (e0) (e3)) = (e3))))) -> (~((op (e0) (e1)) = (op (e1) (e1)))) -> ((~((op (e3) (e3)) = (e1)))\/((op (e3) (e1)) = (e3))) -> ((~((op (e2) (e2)) = (e3)))\/((op (e2) (e3)) = (e2))) -> False). % 15.55/15.69 do 0 intro. intros zenon_Haa zenon_Hc9 zenon_H182 zenon_Hb7 zenon_H254 zenon_H80 zenon_Hb4 zenon_H24f zenon_Hb1 zenon_H90 zenon_H11b zenon_H116 zenon_H1d8 zenon_H1d2 zenon_H1cf zenon_H8f zenon_H17a zenon_H1b3 zenon_Heb zenon_H146 zenon_H2b4 zenon_H166 zenon_H7d zenon_H1d5 zenon_H22e zenon_H281 zenon_H1e5 zenon_H247 zenon_H258 zenon_H1d3 zenon_H109 zenon_H1df zenon_H2af zenon_H28 zenon_H8e zenon_H140 zenon_H105 zenon_Hbe zenon_H13c zenon_He6 zenon_H1a2 zenon_H157 zenon_Hd6 zenon_H15f zenon_H10f zenon_H10d zenon_H2be zenon_H45 zenon_Hd7 zenon_H21 zenon_Ha7 zenon_Hdd zenon_H2d zenon_H52 zenon_H3b zenon_Hf1 zenon_H10e zenon_H135 zenon_H44 zenon_H36 zenon_H59 zenon_H138 zenon_Ha3 zenon_H163 zenon_H6a zenon_H5e zenon_Hce zenon_H160 zenon_H2b8 zenon_H4b zenon_H17d zenon_H1f6 zenon_H145 zenon_H1f zenon_H24c zenon_H58 zenon_H23 zenon_H10c zenon_H1c3. % 15.55/15.69 apply (zenon_or_s _ _ zenon_Haa); [ zenon_intro zenon_H2f | zenon_intro zenon_H35 ]. % 15.55/15.69 apply (zenon_or_s _ _ zenon_H1c3); [ zenon_intro zenon_H30 | zenon_intro zenon_H124 ]. % 15.55/15.69 apply (zenon_L1194_); trivial. % 15.55/15.69 apply (zenon_L119_); trivial. % 15.55/15.69 apply (zenon_L1184_); trivial. % 15.55/15.69 (* end of lemma zenon_L1195_ *) % 15.55/15.69 assert (zenon_L1196_ : ((~((op (e2) (e2)) = (e1)))\/((op (e2) (e1)) = (e2))) -> (~((op (e2) (e0)) = (op (e2) (e1)))) -> ((~((op (e2) (e2)) = (e3)))\/((op (e2) (e3)) = (e2))) -> ((~((op (e3) (e3)) = (e1)))\/((op (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 (e0) (e0)) = (op (e1) (e0)))) -> ((op (e0) (e0)) = (e0)) -> (~((op (e1) (e1)) = (e0))) -> (((op (e3) (e0)) = (e0))\/(((op (e3) (e1)) = (e0))\/(((op (e3) (e2)) = (e0))\/((op (e3) (e3)) = (e0))))) -> (~((op (e1) (e2)) = (op (e3) (e2)))) -> (~((e0) = (e3))) -> (~((op (e0) (op (e3) (e0))) = (op (e3) (e0)))) -> (((op (e0) (e3)) = (e2))\/(((op (e1) (e3)) = (e2))\/(((op (e2) (e3)) = (e2))\/((op (e3) (e3)) = (e2))))) -> (~((op (e2) (e0)) = (op (e2) (e3)))) -> (~((e0) = (e2))) -> (~((e2) = (e3))) -> (((op (e1) (e0)) = (e0))\/(((op (e1) (e1)) = (e0))\/(((op (e1) (e2)) = (e0))\/((op (e1) (e3)) = (e0))))) -> (~((e1) = (e3))) -> (~((op (e0) (e1)) = (op (e3) (e1)))) -> (~((op (e0) (e0)) = (e3))) -> (~((op (e0) (e3)) = (op (e3) (e3)))) -> (((op (e0) (e0)) = (e1))\/(((op (e0) (e1)) = (e1))\/(((op (e0) (e2)) = (e1))\/((op (e0) (e3)) = (e1))))) -> (~((op (e3) (e1)) = (op (e3) (e2)))) -> ((~((op (e3) (e3)) = (e2)))\/((op (e3) (e2)) = (e3))) -> (((op (e0) (e0)) = (e1))\/(((op (e1) (e0)) = (e1))\/(((op (e2) (e0)) = (e1))\/((op (e3) (e0)) = (e1))))) -> (((op (e3) (e3)) = (e0))\/(((op (e3) (e3)) = (e1))\/(((op (e3) (e3)) = (e2))\/((op (e3) (e3)) = (e3))))) -> (((op (e2) (e2)) = (e0))\/(((op (e2) (e2)) = (e1))\/(((op (e2) (e2)) = (e2))\/((op (e2) (e2)) = (e3))))) -> ((op (e2) (e0)) = (e2)) -> (~((e1) = (e2))) -> ((op (e1) (e1)) = (e1)) -> (~((op (e1) (e0)) = (op (e1) (e1)))) -> (~((op (e0) (e0)) = (e1))) -> (~((op (e3) (op (e3) (e3))) = (op (e3) (e3)))) -> ((~((op (e3) (e3)) = (e3)))\/((op (e3) (e3)) = (e3))) -> ((~((op (e3) (e3)) = (e0)))\/((op (e3) (e0)) = (e3))) -> (~((op (e2) (e2)) = (op (e2) (e3)))) -> (~((op (e1) (e1)) = (e2))) -> (~((op (e2) (e1)) = (op (e2) (e2)))) -> (((op (e0) (e1)) = (e2))\/(((op (e1) (e1)) = (e2))\/(((op (e2) (e1)) = (e2))\/((op (e3) (e1)) = (e2))))) -> (((op (e2) (e0)) = (e3))\/(((op (e2) (e1)) = (e3))\/(((op (e2) (e2)) = (e3))\/((op (e2) (e3)) = (e3))))) -> (~((op (e2) (e1)) = (op (e3) (e1)))) -> (((op (e0) (e0)) = (e3))\/(((op (e1) (e0)) = (e3))\/(((op (e2) (e0)) = (e3))\/((op (e3) (e0)) = (e3))))) -> (~((op (e3) (e0)) = (op (e3) (e2)))) -> (~((op (e0) (e2)) = (op (e3) (e2)))) -> (((op (e0) (e0)) = (e2))\/(((op (e0) (e1)) = (e2))\/(((op (e0) (e2)) = (e2))\/((op (e0) (e3)) = (e2))))) -> (~((op (e0) (e2)) = (op (e2) (e2)))) -> (~((op (e2) (op (e3) (e2))) = (op (e3) (e2)))) -> (((op (e3) (e0)) = (e2))\/(((op (e3) (e1)) = (e2))\/(((op (e3) (e2)) = (e2))\/((op (e3) (e3)) = (e2))))) -> (~((op (e3) (e0)) = (op (e3) (e1)))) -> ((~((op (e1) (e1)) = (e2)))\/((op (e1) (e2)) = (e1))) -> (~((op (e0) (e0)) = (op (e2) (e0)))) -> (~((op (e1) (e0)) = (op (e2) (e0)))) -> (~((op (e2) (e0)) = (op (e3) (e0)))) -> (((op (e2) (e0)) = (e0))\/(((op (e2) (e0)) = (e1))\/(((op (e2) (e0)) = (e2))\/((op (e2) (e0)) = (e3))))) -> (~((op (e1) (e0)) = (op (e3) (e0)))) -> (((op (e1) (e2)) = (e0))\/(((op (e1) (e2)) = (e1))\/(((op (e1) (e2)) = (e2))\/((op (e1) (e2)) = (e3))))) -> (~((op (e1) (e2)) = (op (e2) (e2)))) -> (~((op (e1) (e0)) = (op (e1) (e2)))) -> (~((op (e1) (op (e3) (e1))) = (op (e3) (e1)))) -> (((op (e3) (e0)) = (e1))\/(((op (e3) (e1)) = (e1))\/(((op (e3) (e2)) = (e1))\/((op (e3) (e3)) = (e1))))) -> (((op (e0) (e0)) = (e2))\/(((op (e1) (e0)) = (e2))\/(((op (e2) (e0)) = (e2))\/((op (e3) (e0)) = (e2))))) -> (((op (e1) (e1)) = (e0))\/(((op (e1) (e1)) = (e1))\/(((op (e1) (e1)) = (e2))\/((op (e1) (e1)) = (e3))))) -> (~((op (e2) (e0)) = (op (e2) (e2)))) -> (~((op (e0) (e0)) = (e2))) -> (~((op (e1) (e0)) = (op (e1) (e3)))) -> ((~((op (e1) (e1)) = (e3)))\/((op (e1) (e3)) = (e1))) -> ((~((op (e1) (e1)) = (e1)))\/((op (e1) (e1)) = (e1))) -> (~((op (e1) (e1)) = (op (e1) (e2)))) -> (((op (e0) (e2)) = (e1))\/(((op (e1) (e2)) = (e1))\/(((op (e2) (e2)) = (e1))\/((op (e3) (e2)) = (e1))))) -> (((op (e1) (e0)) = (e3))\/(((op (e1) (e1)) = (e3))\/(((op (e1) (e2)) = (e3))\/((op (e1) (e3)) = (e3))))) -> (~((op (e1) (e1)) = (op (e2) (e1)))) -> (~((op (e0) (e0)) = (op (e0) (e3)))) -> (~((op (e0) (e3)) = (op (e2) (e3)))) -> (~((op (e0) (e3)) = (op (e1) (e3)))) -> (((op (e0) (e3)) = (e0))\/(((op (e0) (e3)) = (e1))\/(((op (e0) (e3)) = (e2))\/((op (e0) (e3)) = (e3))))) -> (((op (e2) (e0)) = (e1))\/(((op (e2) (e1)) = (e1))\/(((op (e2) (e2)) = (e1))\/((op (e2) (e3)) = (e1))))) -> (~((op (e1) (e1)) = (e3))) -> (~((op (e0) (e2)) = (op (e0) (e3)))) -> ((~((op (e2) (e2)) = (e2)))\/((op (e2) (e2)) = (e2))) -> False). % 15.55/15.69 do 0 intro. intros zenon_H1e3 zenon_H154 zenon_H1c3 zenon_H10c zenon_H23 zenon_H58 zenon_H24c zenon_H1f zenon_H145 zenon_H1f6 zenon_H17d zenon_H4b zenon_H2b8 zenon_H160 zenon_Hce zenon_H5e zenon_H6a zenon_H163 zenon_Ha3 zenon_H138 zenon_H59 zenon_H36 zenon_H44 zenon_H135 zenon_H10e zenon_Hf1 zenon_H3b zenon_H2d zenon_Hdd zenon_Ha7 zenon_H21 zenon_Hd7 zenon_H45 zenon_H2be zenon_H10d zenon_H10f zenon_H15f zenon_Hd6 zenon_H157 zenon_H1a2 zenon_He6 zenon_H13c zenon_Hbe zenon_H105 zenon_H140 zenon_H8e zenon_H28 zenon_H2af zenon_H1df zenon_H109 zenon_H1d3 zenon_H258 zenon_H247 zenon_H1e5 zenon_H281 zenon_H22e zenon_H1d5 zenon_H7d zenon_H166 zenon_H2b4 zenon_H146 zenon_Heb zenon_H1b3 zenon_H17a zenon_H8f zenon_H1cf zenon_H1d2 zenon_H1d8 zenon_H116 zenon_H11b zenon_H90 zenon_Hb1 zenon_H24f zenon_Hb4 zenon_H80 zenon_H254 zenon_Hb7 zenon_H182 zenon_Hc9 zenon_Haa. % 15.55/15.69 apply (zenon_or_s _ _ zenon_H1e3); [ zenon_intro zenon_H52 | zenon_intro zenon_H156 ]. % 15.55/15.69 apply (zenon_L1195_); trivial. % 15.55/15.69 apply (zenon_L284_); trivial. % 15.55/15.69 (* end of lemma zenon_L1196_ *) % 15.55/15.69 assert (zenon_L1197_ : (~((op (e0) (e0)) = (e1))) -> (~((op (e0) (e1)) = (op (e1) (e1)))) -> ((op (e1) (e1)) = (e1)) -> (((op (e0) (e0)) = (e1))\/(((op (e1) (e0)) = (e1))\/(((op (e2) (e0)) = (e1))\/((op (e3) (e0)) = (e1))))) -> (~((op (e2) (e0)) = (op (e2) (e1)))) -> (~((op (e0) (e0)) = (e2))) -> (((op (e0) (e0)) = (e3))\/(((op (e1) (e0)) = (e3))\/(((op (e2) (e0)) = (e3))\/((op (e3) (e0)) = (e3))))) -> (~((op (e1) (op (e3) (e1))) = (op (e3) (e1)))) -> (~((op (e0) (e2)) = (op (e3) (e2)))) -> (((op (e3) (e0)) = (e1))\/(((op (e3) (e1)) = (e1))\/(((op (e3) (e2)) = (e1))\/((op (e3) (e3)) = (e1))))) -> (~((op (e1) (e1)) = (e3))) -> (~((op (e1) (e2)) = (op (e3) (e2)))) -> ((op (e3) (e2)) = (e3)) -> (((op (e2) (e0)) = (e1))\/(((op (e2) (e1)) = (e1))\/(((op (e2) (e2)) = (e1))\/((op (e2) (e3)) = (e1))))) -> (((op (e0) (e3)) = (e0))\/(((op (e0) (e3)) = (e1))\/(((op (e0) (e3)) = (e2))\/((op (e0) (e3)) = (e3))))) -> (~((op (e0) (e3)) = (op (e1) (e3)))) -> (~((op (e0) (e3)) = (op (e2) (e3)))) -> (~((op (e0) (e0)) = (op (e0) (e3)))) -> (~((op (e0) (op (e3) (e0))) = (op (e3) (e0)))) -> ((op (e0) (e0)) = (e0)) -> (((op (e0) (e3)) = (e2))\/(((op (e1) (e3)) = (e2))\/(((op (e2) (e3)) = (e2))\/((op (e3) (e3)) = (e2))))) -> ((op (e2) (e1)) = (e2)) -> (~((op (e2) (e1)) = (op (e2) (e3)))) -> (~((op (e3) (e3)) = (e0))) -> (~((op (e3) (e3)) = (e1))) -> (~((op (e0) (e3)) = (op (e3) (e3)))) -> (((op (e3) (e3)) = (e0))\/(((op (e3) (e3)) = (e1))\/(((op (e3) (e3)) = (e2))\/((op (e3) (e3)) = (e3))))) -> (~((e0) = (e3))) -> (((op (e3) (e0)) = (e0))\/(((op (e3) (e1)) = (e0))\/(((op (e3) (e2)) = (e0))\/((op (e3) (e3)) = (e0))))) -> (~((op (e1) (e1)) = (op (e2) (e1)))) -> (~((e1) = (e3))) -> (((op (e1) (e0)) = (e3))\/(((op (e1) (e1)) = (e3))\/(((op (e1) (e2)) = (e3))\/((op (e1) (e3)) = (e3))))) -> (~((e2) = (e3))) -> (~((op (e0) (e0)) = (e3))) -> (~((e1) = (e2))) -> (((op (e0) (e0)) = (e2))\/(((op (e1) (e0)) = (e2))\/(((op (e2) (e0)) = (e2))\/((op (e3) (e0)) = (e2))))) -> (~((op (e1) (e0)) = (op (e1) (e1)))) -> ((~((op (e2) (e2)) = (e1)))\/((op (e2) (e1)) = (e2))) -> ((~((op (e2) (e2)) = (e3)))\/((op (e2) (e3)) = (e2))) -> ((~((op (e3) (e3)) = (e1)))\/((op (e3) (e1)) = (e3))) -> (~((op (e0) (e0)) = (op (e1) (e0)))) -> (~((op (e1) (e1)) = (e0))) -> (~((op (e2) (e0)) = (op (e2) (e3)))) -> (~((e0) = (e2))) -> (((op (e1) (e0)) = (e0))\/(((op (e1) (e1)) = (e0))\/(((op (e1) (e2)) = (e0))\/((op (e1) (e3)) = (e0))))) -> (~((op (e0) (e1)) = (op (e3) (e1)))) -> (((op (e0) (e0)) = (e1))\/(((op (e0) (e1)) = (e1))\/(((op (e0) (e2)) = (e1))\/((op (e0) (e3)) = (e1))))) -> (~((op (e3) (e1)) = (op (e3) (e2)))) -> ((~((op (e3) (e3)) = (e2)))\/((op (e3) (e2)) = (e3))) -> (((op (e2) (e2)) = (e0))\/(((op (e2) (e2)) = (e1))\/(((op (e2) (e2)) = (e2))\/((op (e2) (e2)) = (e3))))) -> (~((op (e3) (op (e3) (e3))) = (op (e3) (e3)))) -> ((~((op (e3) (e3)) = (e3)))\/((op (e3) (e3)) = (e3))) -> ((~((op (e3) (e3)) = (e0)))\/((op (e3) (e0)) = (e3))) -> (~((op (e2) (e2)) = (op (e2) (e3)))) -> (~((op (e1) (e1)) = (e2))) -> (~((op (e2) (e1)) = (op (e2) (e2)))) -> (((op (e0) (e1)) = (e2))\/(((op (e1) (e1)) = (e2))\/(((op (e2) (e1)) = (e2))\/((op (e3) (e1)) = (e2))))) -> (~((op (e2) (e1)) = (op (e3) (e1)))) -> (~((op (e3) (e0)) = (op (e3) (e2)))) -> (((op (e0) (e0)) = (e2))\/(((op (e0) (e1)) = (e2))\/(((op (e0) (e2)) = (e2))\/((op (e0) (e3)) = (e2))))) -> (~((op (e0) (e2)) = (op (e2) (e2)))) -> (((op (e3) (e0)) = (e2))\/(((op (e3) (e1)) = (e2))\/(((op (e3) (e2)) = (e2))\/((op (e3) (e3)) = (e2))))) -> (~((op (e3) (e0)) = (op (e3) (e1)))) -> ((~((op (e1) (e1)) = (e2)))\/((op (e1) (e2)) = (e1))) -> (~((op (e0) (e0)) = (op (e2) (e0)))) -> (~((op (e1) (e0)) = (op (e2) (e0)))) -> (~((op (e2) (e0)) = (op (e3) (e0)))) -> (((op (e2) (e0)) = (e0))\/(((op (e2) (e0)) = (e1))\/(((op (e2) (e0)) = (e2))\/((op (e2) (e0)) = (e3))))) -> (~((op (e1) (e0)) = (op (e3) (e0)))) -> (((op (e1) (e2)) = (e0))\/(((op (e1) (e2)) = (e1))\/(((op (e1) (e2)) = (e2))\/((op (e1) (e2)) = (e3))))) -> (~((op (e1) (e2)) = (op (e2) (e2)))) -> (~((op (e1) (e0)) = (op (e1) (e2)))) -> (((op (e1) (e1)) = (e0))\/(((op (e1) (e1)) = (e1))\/(((op (e1) (e1)) = (e2))\/((op (e1) (e1)) = (e3))))) -> (~((op (e2) (e0)) = (op (e2) (e2)))) -> (~((op (e1) (e0)) = (op (e1) (e3)))) -> ((~((op (e1) (e1)) = (e3)))\/((op (e1) (e3)) = (e1))) -> ((~((op (e1) (e1)) = (e1)))\/((op (e1) (e1)) = (e1))) -> (~((op (e1) (e1)) = (op (e1) (e2)))) -> (((op (e0) (e2)) = (e1))\/(((op (e1) (e2)) = (e1))\/(((op (e2) (e2)) = (e1))\/((op (e3) (e2)) = (e1))))) -> (~((op (e0) (e2)) = (op (e0) (e3)))) -> ((~((op (e2) (e2)) = (e2)))\/((op (e2) (e2)) = (e2))) -> (((op (e2) (e0)) = (e3))\/(((op (e2) (e1)) = (e3))\/(((op (e2) (e2)) = (e3))\/((op (e2) (e3)) = (e3))))) -> (~((op (e2) (op (e3) (e2))) = (op (e3) (e2)))) -> (~((op (e2) (e2)) = (e3))) -> (~((op (e0) (e1)) = (op (e2) (e1)))) -> (((op (e0) (e0)) = (e3))\/(((op (e0) (e1)) = (e3))\/(((op (e0) (e2)) = (e3))\/((op (e0) (e3)) = (e3))))) -> False). % 15.55/15.69 do 0 intro. intros zenon_H45 zenon_H23 zenon_H21 zenon_Hf1 zenon_H154 zenon_H8f zenon_Hbe zenon_H2b4 zenon_H140 zenon_H146 zenon_H182 zenon_H17d zenon_H106 zenon_Hb7 zenon_H254 zenon_H80 zenon_Hb4 zenon_H24f zenon_H2b8 zenon_H1f zenon_H160 zenon_H156 zenon_H1e2 zenon_H3c zenon_H104 zenon_H36 zenon_H3b zenon_H4b zenon_H1f6 zenon_Hb1 zenon_Ha3 zenon_H90 zenon_H6a zenon_H59 zenon_Ha7 zenon_Heb zenon_Hd7 zenon_H1e3 zenon_H1c3 zenon_H10c zenon_H24c zenon_H145 zenon_Hce zenon_H5e zenon_H163 zenon_H138 zenon_H44 zenon_H135 zenon_H10e zenon_H2d zenon_H2be zenon_H10d zenon_H10f zenon_H15f zenon_Hd6 zenon_H157 zenon_H1a2 zenon_H13c zenon_H105 zenon_H8e zenon_H28 zenon_H1df zenon_H109 zenon_H1d3 zenon_H258 zenon_H247 zenon_H1e5 zenon_H281 zenon_H22e zenon_H1d5 zenon_H7d zenon_H166 zenon_H1b3 zenon_H17a zenon_H1cf zenon_H1d2 zenon_H1d8 zenon_H116 zenon_H11b zenon_Hc9 zenon_Haa zenon_He6 zenon_H2af zenon_H30 zenon_Hde zenon_H58. % 15.55/15.69 apply (zenon_or_s _ _ zenon_H10d); [ zenon_intro zenon_H3e | zenon_intro zenon_H42 ]. % 15.55/15.69 apply (zenon_or_s _ _ zenon_H44); [ zenon_intro zenon_H47 | zenon_intro zenon_H46 ]. % 15.55/15.69 exact (zenon_H45 zenon_H47). % 15.55/15.69 apply (zenon_or_s _ _ zenon_H46); [ zenon_intro zenon_H22 | zenon_intro zenon_H48 ]. % 15.55/15.69 apply (zenon_L3_); trivial. % 15.55/15.69 apply (zenon_or_s _ _ zenon_H48); [ zenon_intro zenon_H29 | zenon_intro zenon_H37 ]. % 15.55/15.69 apply (zenon_or_s _ _ zenon_Hf1); [ zenon_intro zenon_H47 | zenon_intro zenon_Hf4 ]. % 15.55/15.69 exact (zenon_H45 zenon_H47). % 15.55/15.69 apply (zenon_or_s _ _ zenon_Hf4); [ zenon_intro zenon_Hd8 | zenon_intro zenon_Hf5 ]. % 15.55/15.69 apply (zenon_L61_); trivial. % 15.55/15.69 apply (zenon_or_s _ _ zenon_Hf5); [ zenon_intro zenon_Hae | zenon_intro zenon_Hee ]. % 15.55/15.69 apply (zenon_or_s _ _ zenon_Heb); [ zenon_intro zenon_H92 | zenon_intro zenon_Hec ]. % 15.55/15.69 exact (zenon_H8f zenon_H92). % 15.55/15.69 apply (zenon_or_s _ _ zenon_Hec); [ zenon_intro zenon_H68 | zenon_intro zenon_Hed ]. % 15.55/15.69 apply (zenon_L1193_); trivial. % 15.55/15.69 apply (zenon_or_s _ _ zenon_Hed); [ zenon_intro zenon_Hdd | zenon_intro zenon_He9 ]. % 15.55/15.69 apply (zenon_L304_); trivial. % 15.55/15.69 apply (zenon_L1163_); trivial. % 15.55/15.69 apply (zenon_or_s _ _ zenon_Heb); [ zenon_intro zenon_H92 | zenon_intro zenon_Hec ]. % 15.55/15.69 exact (zenon_H8f zenon_H92). % 15.55/15.69 apply (zenon_or_s _ _ zenon_Hec); [ zenon_intro zenon_H68 | zenon_intro zenon_Hed ]. % 15.55/15.69 apply (zenon_L1193_); trivial. % 15.55/15.69 apply (zenon_or_s _ _ zenon_Hed); [ zenon_intro zenon_Hdd | zenon_intro zenon_He9 ]. % 15.55/15.69 apply (zenon_L284_); trivial. % 15.55/15.69 apply (zenon_L1082_); trivial. % 15.55/15.69 apply (zenon_or_s _ _ zenon_Hf1); [ zenon_intro zenon_H47 | zenon_intro zenon_Hf4 ]. % 15.55/15.69 exact (zenon_H45 zenon_H47). % 15.55/15.69 apply (zenon_or_s _ _ zenon_Hf4); [ zenon_intro zenon_Hd8 | zenon_intro zenon_Hf5 ]. % 15.55/15.69 apply (zenon_L61_); trivial. % 15.55/15.69 apply (zenon_or_s _ _ zenon_Hf5); [ zenon_intro zenon_Hae | zenon_intro zenon_Hee ]. % 15.55/15.69 apply (zenon_L1110_); trivial. % 15.55/15.69 apply (zenon_or_s _ _ zenon_Heb); [ zenon_intro zenon_H92 | zenon_intro zenon_Hec ]. % 15.55/15.69 exact (zenon_H8f zenon_H92). % 15.55/15.69 apply (zenon_or_s _ _ zenon_Hec); [ zenon_intro zenon_H68 | zenon_intro zenon_Hed ]. % 15.55/15.69 apply (zenon_or_s _ _ zenon_Hbe); [ zenon_intro zenon_H5b | zenon_intro zenon_Hbf ]. % 15.55/15.69 exact (zenon_H59 zenon_H5b). % 15.55/15.69 apply (zenon_or_s _ _ zenon_Hbf); [ zenon_intro zenon_H69 | zenon_intro zenon_Hc0 ]. % 15.55/15.69 apply (zenon_L17_); trivial. % 15.55/15.69 apply (zenon_or_s _ _ zenon_Hc0); [ zenon_intro zenon_Haf | zenon_intro zenon_Hba ]. % 15.55/15.69 apply (zenon_or_s _ _ zenon_H90); [ zenon_intro zenon_H69 | zenon_intro zenon_H94 ]. % 15.55/15.69 apply (zenon_L17_); trivial. % 15.55/15.69 apply (zenon_or_s _ _ zenon_H94); [ zenon_intro zenon_H96 | zenon_intro zenon_H95 ]. % 15.55/15.69 exact (zenon_H182 zenon_H96). % 15.55/15.69 apply (zenon_or_s _ _ zenon_H95); [ zenon_intro zenon_H88 | zenon_intro zenon_H8a ]. % 15.55/15.69 apply (zenon_L164_); trivial. % 15.55/15.69 apply (zenon_or_s _ _ zenon_Hb7); [ zenon_intro zenon_Hae | zenon_intro zenon_Hb8 ]. % 15.55/15.69 apply (zenon_L39_); trivial. % 15.55/15.69 apply (zenon_or_s _ _ zenon_Hb8); [ zenon_intro zenon_Hb2 | zenon_intro zenon_Hb9 ]. % 15.55/15.69 apply (zenon_L40_); trivial. % 15.55/15.69 apply (zenon_or_s _ _ zenon_Hb9); [ zenon_intro zenon_H2a | zenon_intro zenon_Hb5 ]. % 15.55/15.69 apply (zenon_L1191_); trivial. % 15.55/15.69 apply (zenon_L41_); trivial. % 15.55/15.69 apply (zenon_L79_); trivial. % 15.55/15.69 apply (zenon_or_s _ _ zenon_Hed); [ zenon_intro zenon_Hdd | zenon_intro zenon_He9 ]. % 15.55/15.69 apply (zenon_L1196_); trivial. % 15.55/15.69 apply (zenon_L122_); trivial. % 15.55/15.69 apply (zenon_L1041_); trivial. % 15.55/15.69 (* end of lemma zenon_L1197_ *) % 15.55/15.69 assert (zenon_L1198_ : (((op (e1) (e0)) = (e0))\/(((op (e1) (e1)) = (e0))\/(((op (e1) (e2)) = (e0))\/((op (e1) (e3)) = (e0))))) -> (~((op (e0) (e0)) = (op (e1) (e0)))) -> (~((op (e1) (e1)) = (e0))) -> (~((op (e3) (e3)) = (e0))) -> (~((op (e1) (e2)) = (op (e3) (e2)))) -> (~((e0) = (e3))) -> ((op (e3) (e1)) = (e3)) -> (~((op (e0) (op (e3) (e0))) = (op (e3) (e0)))) -> ((op (e0) (e0)) = (e0)) -> (((op (e3) (e0)) = (e0))\/(((op (e3) (e1)) = (e0))\/(((op (e3) (e2)) = (e0))\/((op (e3) (e3)) = (e0))))) -> (((op (e0) (e3)) = (e2))\/(((op (e1) (e3)) = (e2))\/(((op (e2) (e3)) = (e2))\/((op (e3) (e3)) = (e2))))) -> (~((e2) = (e3))) -> ((op (e0) (e3)) = (e3)) -> (~((e0) = (e2))) -> ((op (e2) (e1)) = (e2)) -> (~((op (e2) (e1)) = (op (e2) (e3)))) -> (~((op (e3) (e3)) = (e2))) -> False). % 15.55/15.69 do 0 intro. intros zenon_H163 zenon_H24c zenon_H145 zenon_H3c zenon_H17d zenon_H4b zenon_H10a zenon_H2b8 zenon_H1f zenon_H1f6 zenon_H160 zenon_H6a zenon_H53 zenon_H5e zenon_H156 zenon_H1e2 zenon_H3d. % 15.55/15.69 apply (zenon_or_s _ _ zenon_H163); [ zenon_intro zenon_Had | zenon_intro zenon_H164 ]. % 15.55/15.69 apply (zenon_L559_); trivial. % 15.55/15.69 apply (zenon_or_s _ _ zenon_H164); [ zenon_intro zenon_H149 | zenon_intro zenon_H165 ]. % 15.55/15.69 exact (zenon_H145 zenon_H149). % 15.55/15.69 apply (zenon_or_s _ _ zenon_H165); [ zenon_intro zenon_H15d | zenon_intro zenon_Hcc ]. % 15.55/15.69 apply (zenon_L1057_); trivial. % 15.55/15.69 apply (zenon_L460_); trivial. % 15.55/15.69 (* end of lemma zenon_L1198_ *) % 15.55/15.69 assert (zenon_L1199_ : (((op (e0) (e0)) = (e3))\/(((op (e0) (e1)) = (e3))\/(((op (e0) (e2)) = (e3))\/((op (e0) (e3)) = (e3))))) -> (~((op (e0) (e0)) = (e3))) -> (~((op (e0) (e1)) = (op (e3) (e1)))) -> (~((e1) = (e3))) -> ((op (e0) (e2)) = (e1)) -> (((op (e1) (e0)) = (e0))\/(((op (e1) (e1)) = (e0))\/(((op (e1) (e2)) = (e0))\/((op (e1) (e3)) = (e0))))) -> (~((op (e0) (e0)) = (op (e1) (e0)))) -> (~((op (e1) (e1)) = (e0))) -> (~((op (e3) (e3)) = (e0))) -> (~((op (e1) (e2)) = (op (e3) (e2)))) -> (~((e0) = (e3))) -> ((op (e3) (e1)) = (e3)) -> (~((op (e0) (op (e3) (e0))) = (op (e3) (e0)))) -> ((op (e0) (e0)) = (e0)) -> (((op (e3) (e0)) = (e0))\/(((op (e3) (e1)) = (e0))\/(((op (e3) (e2)) = (e0))\/((op (e3) (e3)) = (e0))))) -> (((op (e0) (e3)) = (e2))\/(((op (e1) (e3)) = (e2))\/(((op (e2) (e3)) = (e2))\/((op (e3) (e3)) = (e2))))) -> (~((e2) = (e3))) -> (~((e0) = (e2))) -> ((op (e2) (e1)) = (e2)) -> (~((op (e2) (e1)) = (op (e2) (e3)))) -> (~((op (e3) (e3)) = (e2))) -> False). % 15.55/15.69 do 0 intro. intros zenon_H58 zenon_H59 zenon_H138 zenon_Ha3 zenon_H29 zenon_H163 zenon_H24c zenon_H145 zenon_H3c zenon_H17d zenon_H4b zenon_H10a zenon_H2b8 zenon_H1f zenon_H1f6 zenon_H160 zenon_H6a zenon_H5e zenon_H156 zenon_H1e2 zenon_H3d. % 15.55/15.69 apply (zenon_or_s _ _ zenon_H58); [ zenon_intro zenon_H5b | zenon_intro zenon_H5a ]. % 15.55/15.69 exact (zenon_H59 zenon_H5b). % 15.55/15.69 apply (zenon_or_s _ _ zenon_H5a); [ zenon_intro zenon_H4a | zenon_intro zenon_H5c ]. % 15.55/15.69 apply (zenon_L120_); trivial. % 15.55/15.69 apply (zenon_or_s _ _ zenon_H5c); [ zenon_intro zenon_H50 | zenon_intro zenon_H53 ]. % 15.55/15.69 apply (zenon_L29_); trivial. % 15.55/15.69 apply (zenon_L1198_); trivial. % 15.55/15.69 (* end of lemma zenon_L1199_ *) % 15.55/15.69 assert (zenon_L1200_ : ((~((op (e3) (e3)) = (e2)))\/((op (e3) (e2)) = (e3))) -> (~((op (e3) (e1)) = (op (e3) (e2)))) -> (((op (e0) (e0)) = (e1))\/(((op (e0) (e1)) = (e1))\/(((op (e0) (e2)) = (e1))\/((op (e0) (e3)) = (e1))))) -> (~((op (e0) (e3)) = (op (e3) (e3)))) -> (((op (e3) (e3)) = (e0))\/(((op (e3) (e3)) = (e1))\/(((op (e3) (e3)) = (e2))\/((op (e3) (e3)) = (e3))))) -> (~((op (e0) (e0)) = (e3))) -> (~((op (e0) (e1)) = (op (e3) (e1)))) -> ((op (e3) (e1)) = (e3)) -> (~((e1) = (e3))) -> (((op (e1) (e0)) = (e0))\/(((op (e1) (e1)) = (e0))\/(((op (e1) (e2)) = (e0))\/((op (e1) (e3)) = (e0))))) -> (~((e2) = (e3))) -> (~((e0) = (e2))) -> (~((op (e2) (e1)) = (op (e2) (e3)))) -> ((op (e2) (e1)) = (e2)) -> (((op (e0) (e3)) = (e2))\/(((op (e1) (e3)) = (e2))\/(((op (e2) (e3)) = (e2))\/((op (e3) (e3)) = (e2))))) -> (~((op (e0) (op (e3) (e0))) = (op (e3) (e0)))) -> (~((e0) = (e3))) -> (~((op (e1) (e2)) = (op (e3) (e2)))) -> (~((op (e3) (e3)) = (e0))) -> (((op (e3) (e0)) = (e0))\/(((op (e3) (e1)) = (e0))\/(((op (e3) (e2)) = (e0))\/((op (e3) (e3)) = (e0))))) -> (~((op (e1) (e1)) = (e0))) -> ((op (e0) (e0)) = (e0)) -> (~((op (e0) (e0)) = (op (e1) (e0)))) -> (((op (e0) (e0)) = (e3))\/(((op (e0) (e1)) = (e3))\/(((op (e0) (e2)) = (e3))\/((op (e0) (e3)) = (e3))))) -> ((op (e1) (e1)) = (e1)) -> (~((op (e0) (e1)) = (op (e1) (e1)))) -> (~((op (e0) (e0)) = (e1))) -> (~((op (e3) (op (e3) (e3))) = (op (e3) (e3)))) -> ((~((op (e3) (e3)) = (e3)))\/((op (e3) (e3)) = (e3))) -> False). % 15.55/15.69 do 0 intro. intros zenon_H10e zenon_H135 zenon_H44 zenon_H36 zenon_H3b zenon_H59 zenon_H138 zenon_H10a zenon_Ha3 zenon_H163 zenon_H6a zenon_H5e zenon_H1e2 zenon_H156 zenon_H160 zenon_H2b8 zenon_H4b zenon_H17d zenon_H3c zenon_H1f6 zenon_H145 zenon_H1f zenon_H24c zenon_H58 zenon_H21 zenon_H23 zenon_H45 zenon_H2be zenon_H10d. % 15.55/15.69 apply (zenon_or_s _ _ zenon_H10e); [ zenon_intro zenon_H3d | zenon_intro zenon_H106 ]. % 15.55/15.69 apply (zenon_or_s _ _ zenon_H10d); [ zenon_intro zenon_H3e | zenon_intro zenon_H42 ]. % 15.55/15.69 apply (zenon_or_s _ _ zenon_H44); [ zenon_intro zenon_H47 | zenon_intro zenon_H46 ]. % 15.55/15.69 exact (zenon_H45 zenon_H47). % 15.55/15.69 apply (zenon_or_s _ _ zenon_H46); [ zenon_intro zenon_H22 | zenon_intro zenon_H48 ]. % 15.55/15.69 apply (zenon_L3_); trivial. % 15.55/15.69 apply (zenon_or_s _ _ zenon_H48); [ zenon_intro zenon_H29 | zenon_intro zenon_H37 ]. % 15.55/15.69 apply (zenon_L1199_); trivial. % 15.55/15.69 apply (zenon_L7_); trivial. % 15.55/15.69 apply (zenon_L1041_); trivial. % 15.55/15.69 apply (zenon_L115_); trivial. % 15.55/15.69 (* end of lemma zenon_L1200_ *) % 15.55/15.69 assert (zenon_L1201_ : (((op (e3) (e0)) = (e1))\/(((op (e3) (e1)) = (e1))\/(((op (e3) (e2)) = (e1))\/((op (e3) (e3)) = (e1))))) -> (~((e1) = (e3))) -> ((op (e1) (e1)) = (e1)) -> (~((op (e1) (op (e3) (e1))) = (op (e3) (e1)))) -> (~((op (e3) (e3)) = (e2))) -> (~((op (e2) (op (e3) (e2))) = (op (e3) (e2)))) -> ((op (e2) (e1)) = (e2)) -> (~((op (e2) (e1)) = (op (e3) (e1)))) -> (~((e2) = (e3))) -> ((op (e3) (e0)) = (e3)) -> (((op (e3) (e0)) = (e2))\/(((op (e3) (e1)) = (e2))\/(((op (e3) (e2)) = (e2))\/((op (e3) (e3)) = (e2))))) -> (~((op (e3) (e3)) = (e1))) -> False). % 15.55/15.69 do 0 intro. intros zenon_H146 zenon_Ha3 zenon_H21 zenon_H2b4 zenon_H3d zenon_H2af zenon_H156 zenon_H13c zenon_H6a zenon_Hba zenon_H1df zenon_H104. % 15.55/15.69 apply (zenon_or_s _ _ zenon_H146); [ zenon_intro zenon_Hee | zenon_intro zenon_H14b ]. % 15.55/15.69 apply (zenon_L79_); trivial. % 15.55/15.69 apply (zenon_or_s _ _ zenon_H14b); [ zenon_intro zenon_H13e | zenon_intro zenon_H14c ]. % 15.55/15.69 apply (zenon_L1158_); trivial. % 15.55/15.69 apply (zenon_or_s _ _ zenon_H14c); [ zenon_intro zenon_H119 | zenon_intro zenon_H38 ]. % 15.55/15.69 apply (zenon_L1161_); trivial. % 15.55/15.69 exact (zenon_H104 zenon_H38). % 15.55/15.69 (* end of lemma zenon_L1201_ *) % 15.55/15.69 assert (zenon_L1202_ : ((~((op (e3) (e3)) = (e1)))\/((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))))) -> (~((e2) = (e3))) -> (~((op (e2) (e1)) = (op (e3) (e1)))) -> ((op (e2) (e1)) = (e2)) -> (~((op (e2) (op (e3) (e2))) = (op (e3) (e2)))) -> (((op (e3) (e0)) = (e2))\/(((op (e3) (e1)) = (e2))\/(((op (e3) (e2)) = (e2))\/((op (e3) (e3)) = (e2))))) -> ((op (e1) (e1)) = (e1)) -> (~((op (e1) (op (e3) (e1))) = (op (e3) (e1)))) -> ((op (e3) (e0)) = (e3)) -> (~((e1) = (e3))) -> (~((op (e3) (e0)) = (op (e3) (e2)))) -> ((~((op (e3) (e3)) = (e2)))\/((op (e3) (e2)) = (e3))) -> False). % 15.55/15.69 do 0 intro. intros zenon_H10c zenon_H109 zenon_H146 zenon_H6a zenon_H13c zenon_H156 zenon_H2af zenon_H1df zenon_H21 zenon_H2b4 zenon_Hba zenon_Ha3 zenon_H105 zenon_H10e. % 15.55/15.69 apply (zenon_or_s _ _ zenon_H10c); [ zenon_intro zenon_H104 | zenon_intro zenon_H10a ]. % 15.55/15.69 apply (zenon_or_s _ _ zenon_H10e); [ zenon_intro zenon_H3d | zenon_intro zenon_H106 ]. % 15.55/15.69 apply (zenon_L1201_); trivial. % 15.55/15.69 apply (zenon_L81_); trivial. % 15.55/15.69 apply (zenon_L82_); trivial. % 15.55/15.69 (* end of lemma zenon_L1202_ *) % 15.55/15.69 assert (zenon_L1203_ : (((op (e0) (e0)) = (e3))\/(((op (e0) (e1)) = (e3))\/(((op (e0) (e2)) = (e3))\/((op (e0) (e3)) = (e3))))) -> (~((op (e0) (e1)) = (op (e2) (e1)))) -> (((op (e2) (e0)) = (e3))\/(((op (e2) (e1)) = (e3))\/(((op (e2) (e2)) = (e3))\/((op (e2) (e3)) = (e3))))) -> ((~((op (e2) (e2)) = (e2)))\/((op (e2) (e2)) = (e2))) -> (~((op (e0) (e2)) = (op (e0) (e3)))) -> (((op (e0) (e2)) = (e1))\/(((op (e1) (e2)) = (e1))\/(((op (e2) (e2)) = (e1))\/((op (e3) (e2)) = (e1))))) -> (~((op (e1) (e1)) = (op (e1) (e2)))) -> ((~((op (e1) (e1)) = (e1)))\/((op (e1) (e1)) = (e1))) -> ((~((op (e1) (e1)) = (e3)))\/((op (e1) (e3)) = (e1))) -> (~((op (e1) (e0)) = (op (e1) (e3)))) -> (~((op (e2) (e0)) = (op (e2) (e2)))) -> (((op (e1) (e1)) = (e0))\/(((op (e1) (e1)) = (e1))\/(((op (e1) (e1)) = (e2))\/((op (e1) (e1)) = (e3))))) -> (~((op (e1) (e0)) = (op (e1) (e2)))) -> (~((op (e1) (e2)) = (op (e2) (e2)))) -> (((op (e1) (e2)) = (e0))\/(((op (e1) (e2)) = (e1))\/(((op (e1) (e2)) = (e2))\/((op (e1) (e2)) = (e3))))) -> (~((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 (e1) (e0)) = (op (e2) (e0)))) -> (~((op (e0) (e0)) = (op (e2) (e0)))) -> ((~((op (e1) (e1)) = (e2)))\/((op (e1) (e2)) = (e1))) -> (~((op (e3) (e0)) = (op (e3) (e1)))) -> (~((op (e0) (e2)) = (op (e2) (e2)))) -> (((op (e0) (e0)) = (e2))\/(((op (e0) (e1)) = (e2))\/(((op (e0) (e2)) = (e2))\/((op (e0) (e3)) = (e2))))) -> (~((op (e3) (e0)) = (op (e3) (e2)))) -> (~((op (e2) (e1)) = (op (e3) (e1)))) -> (((op (e0) (e1)) = (e2))\/(((op (e1) (e1)) = (e2))\/(((op (e2) (e1)) = (e2))\/((op (e3) (e1)) = (e2))))) -> (~((op (e2) (e1)) = (op (e2) (e2)))) -> (~((op (e1) (e1)) = (e2))) -> (~((op (e2) (e2)) = (op (e2) (e3)))) -> ((~((op (e3) (e3)) = (e0)))\/((op (e3) (e0)) = (e3))) -> (((op (e2) (e2)) = (e0))\/(((op (e2) (e2)) = (e1))\/(((op (e2) (e2)) = (e2))\/((op (e2) (e2)) = (e3))))) -> ((~((op (e3) (e3)) = (e2)))\/((op (e3) (e2)) = (e3))) -> (~((op (e3) (e1)) = (op (e3) (e2)))) -> (~((op (e0) (e1)) = (op (e3) (e1)))) -> (~((e0) = (e2))) -> (~((op (e2) (e0)) = (op (e2) (e3)))) -> ((~((op (e3) (e3)) = (e1)))\/((op (e3) (e1)) = (e3))) -> ((~((op (e2) (e2)) = (e3)))\/((op (e2) (e3)) = (e2))) -> ((~((op (e2) (e2)) = (e1)))\/((op (e2) (e1)) = (e2))) -> (~((op (e1) (e0)) = (op (e1) (e1)))) -> (((op (e0) (e0)) = (e2))\/(((op (e1) (e0)) = (e2))\/(((op (e2) (e0)) = (e2))\/((op (e3) (e0)) = (e2))))) -> (~((e1) = (e2))) -> (~((op (e0) (e0)) = (e3))) -> (~((e2) = (e3))) -> (((op (e1) (e0)) = (e0))\/(((op (e1) (e1)) = (e0))\/(((op (e1) (e2)) = (e0))\/((op (e1) (e3)) = (e0))))) -> (~((op (e1) (e3)) = (op (e3) (e3)))) -> (~((op (e1) (e1)) = (e3))) -> (((op (e3) (e0)) = (e0))\/(((op (e3) (e1)) = (e0))\/(((op (e3) (e2)) = (e0))\/((op (e3) (e3)) = (e0))))) -> (~((op (e2) (op (e3) (e2))) = (op (e3) (e2)))) -> ((op (e2) (e1)) = (e2)) -> (((op (e3) (e0)) = (e2))\/(((op (e3) (e1)) = (e2))\/(((op (e3) (e2)) = (e2))\/((op (e3) (e3)) = (e2))))) -> (~((e1) = (e3))) -> (~((e0) = (e3))) -> (~((op (e1) (e2)) = (op (e3) (e2)))) -> (((op (e3) (e0)) = (e3))\/(((op (e3) (e1)) = (e3))\/(((op (e3) (e2)) = (e3))\/((op (e3) (e3)) = (e3))))) -> (((op (e3) (e0)) = (e1))\/(((op (e3) (e1)) = (e1))\/(((op (e3) (e2)) = (e1))\/((op (e3) (e3)) = (e1))))) -> (~((op (e0) (e2)) = (op (e3) (e2)))) -> (~((op (e1) (op (e3) (e1))) = (op (e3) (e1)))) -> (~((e0) = (e1))) -> (((op (e3) (e3)) = (e0))\/(((op (e3) (e3)) = (e1))\/(((op (e3) (e3)) = (e2))\/((op (e3) (e3)) = (e3))))) -> (~((op (e0) (e3)) = (op (e3) (e3)))) -> (((op (e0) (e0)) = (e1))\/(((op (e0) (e1)) = (e1))\/(((op (e0) (e2)) = (e1))\/((op (e0) (e3)) = (e1))))) -> (((op (e2) (e0)) = (e1))\/(((op (e2) (e1)) = (e1))\/(((op (e2) (e2)) = (e1))\/((op (e2) (e3)) = (e1))))) -> (((op (e0) (e3)) = (e0))\/(((op (e0) (e3)) = (e1))\/(((op (e0) (e3)) = (e2))\/((op (e0) (e3)) = (e3))))) -> (~((op (e0) (e3)) = (op (e1) (e3)))) -> (~((op (e0) (e3)) = (op (e2) (e3)))) -> (~((op (e0) (e0)) = (op (e0) (e3)))) -> (~((op (e2) (e2)) = (e3))) -> (~((op (e2) (e1)) = (op (e2) (e3)))) -> (((op (e0) (e3)) = (e2))\/(((op (e1) (e3)) = (e2))\/(((op (e2) (e3)) = (e2))\/((op (e3) (e3)) = (e2))))) -> (~((op (e0) (op (e3) (e0))) = (op (e3) (e0)))) -> (((op (e0) (e2)) = (e3))\/(((op (e1) (e2)) = (e3))\/(((op (e2) (e2)) = (e3))\/((op (e3) (e2)) = (e3))))) -> (~((op (e1) (e1)) = (op (e2) (e1)))) -> (((op (e1) (e0)) = (e3))\/(((op (e1) (e1)) = (e3))\/(((op (e1) (e2)) = (e3))\/((op (e1) (e3)) = (e3))))) -> (~((op (e1) (e1)) = (e0))) -> ((op (e0) (e0)) = (e0)) -> (~((op (e0) (e0)) = (op (e1) (e0)))) -> (((op (e0) (e0)) = (e3))\/(((op (e1) (e0)) = (e3))\/(((op (e2) (e0)) = (e3))\/((op (e3) (e0)) = (e3))))) -> (~((op (e0) (e0)) = (e2))) -> (~((op (e2) (e0)) = (op (e2) (e1)))) -> (((op (e0) (e0)) = (e1))\/(((op (e1) (e0)) = (e1))\/(((op (e2) (e0)) = (e1))\/((op (e3) (e0)) = (e1))))) -> ((op (e1) (e1)) = (e1)) -> (~((op (e0) (e1)) = (op (e1) (e1)))) -> (~((op (e0) (e0)) = (e1))) -> (~((op (e3) (op (e3) (e3))) = (op (e3) (e3)))) -> ((~((op (e3) (e3)) = (e3)))\/((op (e3) (e3)) = (e3))) -> False). % 15.55/15.69 do 0 intro. intros zenon_H58 zenon_Hde zenon_He6 zenon_Haa zenon_Hc9 zenon_H11b zenon_H116 zenon_H1d8 zenon_H1d2 zenon_H1cf zenon_H17a zenon_H1b3 zenon_H166 zenon_H7d zenon_H1d5 zenon_H22e zenon_H281 zenon_H1e5 zenon_H247 zenon_H258 zenon_H1d3 zenon_H109 zenon_H28 zenon_H8e zenon_H105 zenon_H13c zenon_H1a2 zenon_H157 zenon_Hd6 zenon_H15f zenon_H10f zenon_H2d zenon_H10e zenon_H135 zenon_H138 zenon_H5e zenon_Hce zenon_H10c zenon_H1c3 zenon_H1e3 zenon_Hd7 zenon_Heb zenon_Ha7 zenon_H59 zenon_H6a zenon_H163 zenon_H8b zenon_H182 zenon_H1f6 zenon_H2af zenon_H156 zenon_H1df zenon_Ha3 zenon_H4b zenon_H17d zenon_H2d5 zenon_H146 zenon_H140 zenon_H2b4 zenon_H9e zenon_H3b zenon_H36 zenon_H44 zenon_Hb7 zenon_H254 zenon_H80 zenon_Hb4 zenon_H24f zenon_H30 zenon_H1e2 zenon_H160 zenon_H2b8 zenon_H175 zenon_Hb1 zenon_H90 zenon_H145 zenon_H1f zenon_H24c zenon_Hbe zenon_H8f zenon_H154 zenon_Hf1 zenon_H21 zenon_H23 zenon_H45 zenon_H2be zenon_H10d. % 15.55/15.69 apply (zenon_or_s _ _ zenon_H10f); [ zenon_intro zenon_H3c | zenon_intro zenon_Hba ]. % 15.55/15.69 apply (zenon_or_s _ _ zenon_H10c); [ zenon_intro zenon_H104 | zenon_intro zenon_H10a ]. % 15.55/15.69 apply (zenon_or_s _ _ zenon_H10e); [ zenon_intro zenon_H3d | zenon_intro zenon_H106 ]. % 15.55/15.69 apply (zenon_or_s _ _ zenon_H10d); [ zenon_intro zenon_H3e | zenon_intro zenon_H42 ]. % 15.55/15.69 apply (zenon_or_s _ _ zenon_H44); [ zenon_intro zenon_H47 | zenon_intro zenon_H46 ]. % 15.55/15.69 exact (zenon_H45 zenon_H47). % 15.55/15.69 apply (zenon_or_s _ _ zenon_H46); [ zenon_intro zenon_H22 | zenon_intro zenon_H48 ]. % 15.55/15.69 apply (zenon_L3_); trivial. % 15.55/15.69 apply (zenon_or_s _ _ zenon_H48); [ zenon_intro zenon_H29 | zenon_intro zenon_H37 ]. % 15.55/15.69 apply (zenon_or_s _ _ zenon_Hf1); [ zenon_intro zenon_H47 | zenon_intro zenon_Hf4 ]. % 15.55/15.69 exact (zenon_H45 zenon_H47). % 15.55/15.69 apply (zenon_or_s _ _ zenon_Hf4); [ zenon_intro zenon_Hd8 | zenon_intro zenon_Hf5 ]. % 15.55/15.69 apply (zenon_L61_); trivial. % 15.55/15.69 apply (zenon_or_s _ _ zenon_Hf5); [ zenon_intro zenon_Hae | zenon_intro zenon_Hee ]. % 15.55/15.69 apply (zenon_or_s _ _ zenon_Heb); [ zenon_intro zenon_H92 | zenon_intro zenon_Hec ]. % 15.55/15.69 exact (zenon_H8f zenon_H92). % 15.55/15.69 apply (zenon_or_s _ _ zenon_Hec); [ zenon_intro zenon_H68 | zenon_intro zenon_Hed ]. % 15.55/15.69 apply (zenon_L1192_); trivial. % 15.55/15.69 apply (zenon_or_s _ _ zenon_Hed); [ zenon_intro zenon_Hdd | zenon_intro zenon_He9 ]. % 15.55/15.69 apply (zenon_L304_); trivial. % 15.55/15.69 apply (zenon_L1163_); trivial. % 15.55/15.69 apply (zenon_or_s _ _ zenon_Heb); [ zenon_intro zenon_H92 | zenon_intro zenon_Hec ]. % 15.55/15.69 exact (zenon_H8f zenon_H92). % 15.55/15.69 apply (zenon_or_s _ _ zenon_Hec); [ zenon_intro zenon_H68 | zenon_intro zenon_Hed ]. % 15.55/15.69 apply (zenon_L1192_); trivial. % 15.55/15.69 apply (zenon_or_s _ _ zenon_Hed); [ zenon_intro zenon_Hdd | zenon_intro zenon_He9 ]. % 15.55/15.69 apply (zenon_L284_); trivial. % 15.55/15.69 apply (zenon_L122_); trivial. % 15.55/15.69 apply (zenon_L7_); trivial. % 15.55/15.69 apply (zenon_L1041_); trivial. % 15.55/15.69 apply (zenon_L1197_); trivial. % 15.55/15.69 apply (zenon_L1200_); trivial. % 15.55/15.69 apply (zenon_L1202_); trivial. % 15.55/15.69 (* end of lemma zenon_L1203_ *) % 15.55/15.69 assert (zenon_L1204_ : ((~((op (e3) (e3)) = (e3)))\/((op (e3) (e3)) = (e3))) -> (~((op (e3) (op (e3) (e3))) = (op (e3) (e3)))) -> (~((op (e0) (e0)) = (e1))) -> (~((op (e0) (e1)) = (op (e1) (e1)))) -> ((op (e1) (e1)) = (e1)) -> (((op (e0) (e0)) = (e1))\/(((op (e1) (e0)) = (e1))\/(((op (e2) (e0)) = (e1))\/((op (e3) (e0)) = (e1))))) -> (~((op (e2) (e0)) = (op (e2) (e1)))) -> (~((op (e0) (e0)) = (e2))) -> (((op (e0) (e0)) = (e3))\/(((op (e1) (e0)) = (e3))\/(((op (e2) (e0)) = (e3))\/((op (e3) (e0)) = (e3))))) -> (~((op (e0) (e0)) = (op (e1) (e0)))) -> ((op (e0) (e0)) = (e0)) -> (~((op (e1) (e1)) = (e0))) -> (((op (e1) (e0)) = (e3))\/(((op (e1) (e1)) = (e3))\/(((op (e1) (e2)) = (e3))\/((op (e1) (e3)) = (e3))))) -> (~((op (e1) (e1)) = (op (e2) (e1)))) -> (((op (e0) (e2)) = (e3))\/(((op (e1) (e2)) = (e3))\/(((op (e2) (e2)) = (e3))\/((op (e3) (e2)) = (e3))))) -> (~((op (e0) (op (e3) (e0))) = (op (e3) (e0)))) -> (((op (e0) (e3)) = (e2))\/(((op (e1) (e3)) = (e2))\/(((op (e2) (e3)) = (e2))\/((op (e3) (e3)) = (e2))))) -> (~((op (e2) (e1)) = (op (e2) (e3)))) -> (~((op (e0) (e0)) = (op (e0) (e3)))) -> (~((op (e0) (e3)) = (op (e2) (e3)))) -> (~((op (e0) (e3)) = (op (e1) (e3)))) -> (((op (e0) (e3)) = (e0))\/(((op (e0) (e3)) = (e1))\/(((op (e0) (e3)) = (e2))\/((op (e0) (e3)) = (e3))))) -> (((op (e2) (e0)) = (e1))\/(((op (e2) (e1)) = (e1))\/(((op (e2) (e2)) = (e1))\/((op (e2) (e3)) = (e1))))) -> (((op (e0) (e0)) = (e1))\/(((op (e0) (e1)) = (e1))\/(((op (e0) (e2)) = (e1))\/((op (e0) (e3)) = (e1))))) -> (~((op (e0) (e3)) = (op (e3) (e3)))) -> (((op (e3) (e3)) = (e0))\/(((op (e3) (e3)) = (e1))\/(((op (e3) (e3)) = (e2))\/((op (e3) (e3)) = (e3))))) -> (~((e0) = (e1))) -> (~((op (e1) (op (e3) (e1))) = (op (e3) (e1)))) -> (~((op (e0) (e2)) = (op (e3) (e2)))) -> (((op (e3) (e0)) = (e1))\/(((op (e3) (e1)) = (e1))\/(((op (e3) (e2)) = (e1))\/((op (e3) (e3)) = (e1))))) -> (((op (e3) (e0)) = (e3))\/(((op (e3) (e1)) = (e3))\/(((op (e3) (e2)) = (e3))\/((op (e3) (e3)) = (e3))))) -> (~((op (e1) (e2)) = (op (e3) (e2)))) -> (~((e0) = (e3))) -> (~((e1) = (e3))) -> (((op (e3) (e0)) = (e2))\/(((op (e3) (e1)) = (e2))\/(((op (e3) (e2)) = (e2))\/((op (e3) (e3)) = (e2))))) -> ((op (e2) (e1)) = (e2)) -> (~((op (e2) (op (e3) (e2))) = (op (e3) (e2)))) -> (((op (e3) (e0)) = (e0))\/(((op (e3) (e1)) = (e0))\/(((op (e3) (e2)) = (e0))\/((op (e3) (e3)) = (e0))))) -> (~((op (e1) (e1)) = (e3))) -> (~((op (e1) (e3)) = (op (e3) (e3)))) -> (((op (e1) (e0)) = (e0))\/(((op (e1) (e1)) = (e0))\/(((op (e1) (e2)) = (e0))\/((op (e1) (e3)) = (e0))))) -> (~((e2) = (e3))) -> (~((op (e0) (e0)) = (e3))) -> (~((e1) = (e2))) -> (((op (e0) (e0)) = (e2))\/(((op (e1) (e0)) = (e2))\/(((op (e2) (e0)) = (e2))\/((op (e3) (e0)) = (e2))))) -> (~((op (e1) (e0)) = (op (e1) (e1)))) -> ((~((op (e2) (e2)) = (e1)))\/((op (e2) (e1)) = (e2))) -> ((~((op (e2) (e2)) = (e3)))\/((op (e2) (e3)) = (e2))) -> ((~((op (e3) (e3)) = (e1)))\/((op (e3) (e1)) = (e3))) -> (~((op (e2) (e0)) = (op (e2) (e3)))) -> (~((e0) = (e2))) -> (~((op (e0) (e1)) = (op (e3) (e1)))) -> (~((op (e3) (e1)) = (op (e3) (e2)))) -> ((~((op (e3) (e3)) = (e2)))\/((op (e3) (e2)) = (e3))) -> (((op (e2) (e2)) = (e0))\/(((op (e2) (e2)) = (e1))\/(((op (e2) (e2)) = (e2))\/((op (e2) (e2)) = (e3))))) -> ((~((op (e3) (e3)) = (e0)))\/((op (e3) (e0)) = (e3))) -> (~((op (e2) (e2)) = (op (e2) (e3)))) -> (~((op (e1) (e1)) = (e2))) -> (~((op (e2) (e1)) = (op (e2) (e2)))) -> (((op (e0) (e1)) = (e2))\/(((op (e1) (e1)) = (e2))\/(((op (e2) (e1)) = (e2))\/((op (e3) (e1)) = (e2))))) -> (~((op (e2) (e1)) = (op (e3) (e1)))) -> (~((op (e3) (e0)) = (op (e3) (e2)))) -> (((op (e0) (e0)) = (e2))\/(((op (e0) (e1)) = (e2))\/(((op (e0) (e2)) = (e2))\/((op (e0) (e3)) = (e2))))) -> (~((op (e0) (e2)) = (op (e2) (e2)))) -> (~((op (e3) (e0)) = (op (e3) (e1)))) -> ((~((op (e1) (e1)) = (e2)))\/((op (e1) (e2)) = (e1))) -> (~((op (e0) (e0)) = (op (e2) (e0)))) -> (~((op (e1) (e0)) = (op (e2) (e0)))) -> (~((op (e2) (e0)) = (op (e3) (e0)))) -> (((op (e2) (e0)) = (e0))\/(((op (e2) (e0)) = (e1))\/(((op (e2) (e0)) = (e2))\/((op (e2) (e0)) = (e3))))) -> (~((op (e1) (e0)) = (op (e3) (e0)))) -> (((op (e1) (e2)) = (e0))\/(((op (e1) (e2)) = (e1))\/(((op (e1) (e2)) = (e2))\/((op (e1) (e2)) = (e3))))) -> (~((op (e1) (e2)) = (op (e2) (e2)))) -> (~((op (e1) (e0)) = (op (e1) (e2)))) -> (((op (e1) (e1)) = (e0))\/(((op (e1) (e1)) = (e1))\/(((op (e1) (e1)) = (e2))\/((op (e1) (e1)) = (e3))))) -> (~((op (e2) (e0)) = (op (e2) (e2)))) -> (~((op (e1) (e0)) = (op (e1) (e3)))) -> ((~((op (e1) (e1)) = (e3)))\/((op (e1) (e3)) = (e1))) -> ((~((op (e1) (e1)) = (e1)))\/((op (e1) (e1)) = (e1))) -> (~((op (e1) (e1)) = (op (e1) (e2)))) -> (((op (e0) (e2)) = (e1))\/(((op (e1) (e2)) = (e1))\/(((op (e2) (e2)) = (e1))\/((op (e3) (e2)) = (e1))))) -> (~((op (e0) (e2)) = (op (e0) (e3)))) -> ((~((op (e2) (e2)) = (e2)))\/((op (e2) (e2)) = (e2))) -> (((op (e2) (e0)) = (e3))\/(((op (e2) (e1)) = (e3))\/(((op (e2) (e2)) = (e3))\/((op (e2) (e3)) = (e3))))) -> (~((op (e0) (e1)) = (op (e2) (e1)))) -> (((op (e0) (e0)) = (e3))\/(((op (e0) (e1)) = (e3))\/(((op (e0) (e2)) = (e3))\/((op (e0) (e3)) = (e3))))) -> False). % 15.55/15.69 do 0 intro. intros zenon_H10d zenon_H2be zenon_H45 zenon_H23 zenon_H21 zenon_Hf1 zenon_H154 zenon_H8f zenon_Hbe zenon_H24c zenon_H1f zenon_H145 zenon_H90 zenon_Hb1 zenon_H175 zenon_H2b8 zenon_H160 zenon_H1e2 zenon_H24f zenon_Hb4 zenon_H80 zenon_H254 zenon_Hb7 zenon_H44 zenon_H36 zenon_H3b zenon_H9e zenon_H2b4 zenon_H140 zenon_H146 zenon_H2d5 zenon_H17d zenon_H4b zenon_Ha3 zenon_H1df zenon_H156 zenon_H2af zenon_H1f6 zenon_H182 zenon_H8b zenon_H163 zenon_H6a zenon_H59 zenon_Ha7 zenon_Heb zenon_Hd7 zenon_H1e3 zenon_H1c3 zenon_H10c zenon_Hce zenon_H5e zenon_H138 zenon_H135 zenon_H10e zenon_H2d zenon_H10f zenon_H15f zenon_Hd6 zenon_H157 zenon_H1a2 zenon_H13c zenon_H105 zenon_H8e zenon_H28 zenon_H109 zenon_H1d3 zenon_H258 zenon_H247 zenon_H1e5 zenon_H281 zenon_H22e zenon_H1d5 zenon_H7d zenon_H166 zenon_H1b3 zenon_H17a zenon_H1cf zenon_H1d2 zenon_H1d8 zenon_H116 zenon_H11b zenon_Hc9 zenon_Haa zenon_He6 zenon_Hde zenon_H58. % 15.55/15.69 apply (zenon_or_s _ _ zenon_H1c3); [ zenon_intro zenon_H30 | zenon_intro zenon_H124 ]. % 15.55/15.69 apply (zenon_L1203_); trivial. % 15.55/15.69 apply (zenon_L256_); trivial. % 15.55/15.69 (* end of lemma zenon_L1204_ *) % 15.55/15.69 assert (zenon_L1205_ : ((~((op (e2) (e2)) = (e0)))\/((op (e2) (e0)) = (e2))) -> ((~((op (e2) (e2)) = (e2)))\/((op (e2) (e2)) = (e2))) -> (((op (e0) (e3)) = (e0))\/(((op (e0) (e3)) = (e1))\/(((op (e0) (e3)) = (e2))\/((op (e0) (e3)) = (e3))))) -> ((~((op (e1) (e1)) = (e1)))\/((op (e1) (e1)) = (e1))) -> ((~((op (e1) (e1)) = (e3)))\/((op (e1) (e3)) = (e1))) -> (~((op (e1) (e0)) = (op (e1) (e3)))) -> (~((op (e2) (e0)) = (op (e2) (e2)))) -> (((op (e1) (e1)) = (e0))\/(((op (e1) (e1)) = (e1))\/(((op (e1) (e1)) = (e2))\/((op (e1) (e1)) = (e3))))) -> (~((op (e1) (e0)) = (op (e1) (e2)))) -> (~((op (e1) (e2)) = (op (e2) (e2)))) -> (((op (e1) (e2)) = (e0))\/(((op (e1) (e2)) = (e1))\/(((op (e1) (e2)) = (e2))\/((op (e1) (e2)) = (e3))))) -> (~((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 (e1) (e0)) = (op (e2) (e0)))) -> (~((op (e0) (e0)) = (op (e2) (e0)))) -> ((~((op (e1) (e1)) = (e2)))\/((op (e1) (e2)) = (e1))) -> (~((op (e0) (e2)) = (op (e2) (e2)))) -> (((op (e0) (e1)) = (e2))\/(((op (e1) (e1)) = (e2))\/(((op (e2) (e1)) = (e2))\/((op (e3) (e1)) = (e2))))) -> (~((op (e2) (e1)) = (op (e2) (e2)))) -> (~((op (e2) (e2)) = (op (e2) (e3)))) -> (~((op (e0) (e3)) = (op (e1) (e3)))) -> (((op (e1) (e0)) = (e3))\/(((op (e1) (e1)) = (e3))\/(((op (e1) (e2)) = (e3))\/((op (e1) (e3)) = (e3))))) -> (~((op (e0) (e1)) = (op (e2) (e1)))) -> (~((op (e1) (e0)) = (op (e1) (e1)))) -> (~((op (e0) (e0)) = (e3))) -> (~((e2) = (e3))) -> (~((e1) = (e3))) -> (~((op (e0) (e2)) = (op (e0) (e3)))) -> (~((op (e1) (e1)) = (op (e1) (e2)))) -> (((op (e2) (e0)) = (e2))\/(((op (e2) (e1)) = (e2))\/(((op (e2) (e2)) = (e2))\/((op (e2) (e3)) = (e2))))) -> ((~((op (e3) (e3)) = (e1)))\/((op (e3) (e1)) = (e3))) -> (~((op (e0) (e0)) = (op (e1) (e0)))) -> (((op (e3) (e0)) = (e0))\/(((op (e3) (e1)) = (e0))\/(((op (e3) (e2)) = (e0))\/((op (e3) (e3)) = (e0))))) -> (~((op (e1) (e2)) = (op (e3) (e2)))) -> (((op (e0) (e3)) = (e2))\/(((op (e1) (e3)) = (e2))\/(((op (e2) (e3)) = (e2))\/((op (e3) (e3)) = (e2))))) -> (((op (e1) (e0)) = (e0))\/(((op (e1) (e1)) = (e0))\/(((op (e1) (e2)) = (e0))\/((op (e1) (e3)) = (e0))))) -> (((op (e0) (e1)) = (e0))\/(((op (e1) (e1)) = (e0))\/(((op (e2) (e1)) = (e0))\/((op (e3) (e1)) = (e0))))) -> (~((e0) = (e3))) -> (~((op (e0) (e3)) = (op (e2) (e3)))) -> (((op (e2) (e0)) = (e3))\/(((op (e2) (e1)) = (e3))\/(((op (e2) (e2)) = (e3))\/((op (e2) (e3)) = (e3))))) -> (~((op (e1) (e1)) = (e0))) -> (~((op (e0) (e1)) = (op (e3) (e1)))) -> (((op (e0) (e0)) = (e3))\/(((op (e0) (e1)) = (e3))\/(((op (e0) (e2)) = (e3))\/((op (e0) (e3)) = (e3))))) -> (((op (e0) (e0)) = (e2))\/(((op (e0) (e1)) = (e2))\/(((op (e0) (e2)) = (e2))\/((op (e0) (e3)) = (e2))))) -> (~((op (e3) (e1)) = (op (e3) (e2)))) -> ((~((op (e3) (e3)) = (e3)))\/((op (e3) (e3)) = (e3))) -> (~((op (e3) (op (e3) (e3))) = (op (e3) (e3)))) -> (((op (e0) (e0)) = (e3))\/(((op (e1) (e0)) = (e3))\/(((op (e2) (e0)) = (e3))\/((op (e3) (e0)) = (e3))))) -> (~((op (e1) (e1)) = (op (e2) (e1)))) -> (((op (e2) (e0)) = (e1))\/(((op (e2) (e1)) = (e1))\/(((op (e2) (e2)) = (e1))\/((op (e2) (e3)) = (e1))))) -> (~((op (e2) (e0)) = (op (e2) (e3)))) -> (((op (e0) (e0)) = (e2))\/(((op (e1) (e0)) = (e2))\/(((op (e2) (e0)) = (e2))\/((op (e3) (e0)) = (e2))))) -> (~((op (e0) (e0)) = (op (e0) (e3)))) -> ((op (e0) (e0)) = (e0)) -> (((op (e3) (e3)) = (e0))\/(((op (e3) (e3)) = (e1))\/(((op (e3) (e3)) = (e2))\/((op (e3) (e3)) = (e3))))) -> (~((op (e1) (e3)) = (op (e3) (e3)))) -> (~((e0) = (e2))) -> (((op (e2) (e2)) = (e0))\/(((op (e2) (e2)) = (e1))\/(((op (e2) (e2)) = (e2))\/((op (e2) (e2)) = (e3))))) -> (((op (e0) (e3)) = (e0))\/(((op (e1) (e3)) = (e0))\/(((op (e2) (e3)) = (e0))\/((op (e3) (e3)) = (e0))))) -> (~((op (e0) (e3)) = (op (e3) (e3)))) -> (((op (e0) (e0)) = (e1))\/(((op (e0) (e1)) = (e1))\/(((op (e0) (e2)) = (e1))\/((op (e0) (e3)) = (e1))))) -> (~((op (e0) (op (e3) (e0))) = (op (e3) (e0)))) -> (((op (e0) (e2)) = (e1))\/(((op (e1) (e2)) = (e1))\/(((op (e2) (e2)) = (e1))\/((op (e3) (e2)) = (e1))))) -> ((~((op (e3) (e3)) = (e2)))\/((op (e3) (e2)) = (e3))) -> (~((op (e3) (e0)) = (op (e3) (e1)))) -> (~((op (e3) (e0)) = (op (e3) (e2)))) -> ((~((op (e3) (e3)) = (e0)))\/((op (e3) (e0)) = (e3))) -> (~((op (e2) (e1)) = (op (e3) (e1)))) -> (~((op (e2) (op (e3) (e2))) = (op (e3) (e2)))) -> (((op (e3) (e0)) = (e2))\/(((op (e3) (e1)) = (e2))\/(((op (e3) (e2)) = (e2))\/((op (e3) (e3)) = (e2))))) -> (~((e1) = (e2))) -> (((op (e0) (e0)) = (e1))\/(((op (e1) (e0)) = (e1))\/(((op (e2) (e0)) = (e1))\/((op (e3) (e0)) = (e1))))) -> (~((op (e1) (op (e3) (e1))) = (op (e3) (e1)))) -> (~((op (e0) (e2)) = (op (e3) (e2)))) -> (((op (e3) (e0)) = (e1))\/(((op (e3) (e1)) = (e1))\/(((op (e3) (e2)) = (e1))\/((op (e3) (e3)) = (e1))))) -> (~((op (e0) (e0)) = (e2))) -> ((op (e1) (e1)) = (e1)) -> (~((op (e0) (e1)) = (op (e1) (e1)))) -> (~((op (e0) (e0)) = (e1))) -> (~((op (e2) (e1)) = (op (e2) (e3)))) -> ((~((op (e2) (e2)) = (e3)))\/((op (e2) (e3)) = (e2))) -> (~((op (e2) (e0)) = (op (e2) (e1)))) -> (((op (e0) (e2)) = (e3))\/(((op (e1) (e2)) = (e3))\/(((op (e2) (e2)) = (e3))\/((op (e3) (e2)) = (e3))))) -> (~((e0) = (e1))) -> (((op (e3) (e0)) = (e3))\/(((op (e3) (e1)) = (e3))\/(((op (e3) (e2)) = (e3))\/((op (e3) (e3)) = (e3))))) -> ((~((op (e2) (e2)) = (e1)))\/((op (e2) (e1)) = (e2))) -> (~((op (e1) (e1)) = (op (e1) (e3)))) -> False). % 15.55/15.69 do 0 intro. intros zenon_H1d4 zenon_Haa zenon_H254 zenon_H1d8 zenon_H1d2 zenon_H1cf zenon_H17a zenon_H1b3 zenon_H166 zenon_H7d zenon_H1d5 zenon_H22e zenon_H281 zenon_H1e5 zenon_H247 zenon_H258 zenon_H1d3 zenon_H28 zenon_H1a2 zenon_H157 zenon_H15f zenon_H80 zenon_H90 zenon_Hde zenon_Hd7 zenon_H59 zenon_H6a zenon_Ha3 zenon_Hc9 zenon_H116 zenon_H237 zenon_H10c zenon_H24c zenon_H1f6 zenon_H17d zenon_H160 zenon_H163 zenon_H144 zenon_H4b zenon_Hb4 zenon_He6 zenon_H145 zenon_H138 zenon_H58 zenon_H8e zenon_H135 zenon_H10d zenon_H2be zenon_Hbe zenon_Hb1 zenon_Hb7 zenon_Hce zenon_Heb zenon_H24f zenon_H1f zenon_H3b zenon_H8b zenon_H5e zenon_H2d zenon_Hd3 zenon_H36 zenon_H44 zenon_H2b8 zenon_H11b zenon_H10e zenon_H109 zenon_H105 zenon_H10f zenon_H13c zenon_H2af zenon_H1df zenon_Ha7 zenon_Hf1 zenon_H2b4 zenon_H140 zenon_H146 zenon_H8f zenon_H21 zenon_H23 zenon_H45 zenon_H1e2 zenon_H1c3 zenon_H154 zenon_H175 zenon_H9e zenon_H2d5 zenon_H1e3 zenon_H11e. % 15.55/15.69 apply (zenon_or_s _ _ zenon_H1d3); [ zenon_intro zenon_Hd6 | zenon_intro zenon_H117 ]. % 15.55/15.69 apply (zenon_or_s _ _ zenon_H1d2); [ zenon_intro zenon_H182 | zenon_intro zenon_H11f ]. % 15.55/15.69 apply (zenon_or_s _ _ zenon_H1d4); [ zenon_intro zenon_H2e | zenon_intro zenon_Hdd ]. % 15.55/15.69 apply (zenon_or_s _ _ zenon_H1e3); [ zenon_intro zenon_H52 | zenon_intro zenon_H156 ]. % 15.55/15.69 apply (zenon_or_s _ _ zenon_Haa); [ zenon_intro zenon_H2f | zenon_intro zenon_H35 ]. % 15.55/15.69 apply (zenon_or_s _ _ zenon_H1c3); [ zenon_intro zenon_H30 | zenon_intro zenon_H124 ]. % 15.55/15.69 apply (zenon_or_s _ _ zenon_H10f); [ zenon_intro zenon_H3c | zenon_intro zenon_Hba ]. % 15.55/15.69 apply (zenon_or_s _ _ zenon_H10c); [ zenon_intro zenon_H104 | zenon_intro zenon_H10a ]. % 15.55/15.69 apply (zenon_or_s _ _ zenon_H10e); [ zenon_intro zenon_H3d | zenon_intro zenon_H106 ]. % 15.55/15.69 apply (zenon_or_s _ _ zenon_H10d); [ zenon_intro zenon_H3e | zenon_intro zenon_H42 ]. % 15.55/15.69 apply (zenon_or_s _ _ zenon_H44); [ zenon_intro zenon_H47 | zenon_intro zenon_H46 ]. % 15.55/15.69 exact (zenon_H45 zenon_H47). % 15.55/15.69 apply (zenon_or_s _ _ zenon_H46); [ zenon_intro zenon_H22 | zenon_intro zenon_H48 ]. % 15.55/15.69 apply (zenon_L3_); trivial. % 15.55/15.69 apply (zenon_or_s _ _ zenon_H48); [ zenon_intro zenon_H29 | zenon_intro zenon_H37 ]. % 15.55/15.69 apply (zenon_or_s _ _ zenon_Hf1); [ zenon_intro zenon_H47 | zenon_intro zenon_Hf4 ]. % 15.55/15.69 exact (zenon_H45 zenon_H47). % 15.55/15.69 apply (zenon_or_s _ _ zenon_Hf4); [ zenon_intro zenon_Hd8 | zenon_intro zenon_Hf5 ]. % 15.55/15.69 apply (zenon_L61_); trivial. % 15.55/15.69 apply (zenon_or_s _ _ zenon_Hf5); [ zenon_intro zenon_Hae | zenon_intro zenon_Hee ]. % 15.55/15.69 apply (zenon_or_s _ _ zenon_Heb); [ zenon_intro zenon_H92 | zenon_intro zenon_Hec ]. % 15.55/15.69 exact (zenon_H8f zenon_H92). % 15.55/15.69 apply (zenon_or_s _ _ zenon_Hec); [ zenon_intro zenon_H68 | zenon_intro zenon_Hed ]. % 15.55/15.69 apply (zenon_or_s _ _ zenon_Hbe); [ zenon_intro zenon_H5b | zenon_intro zenon_Hbf ]. % 15.55/15.69 exact (zenon_H59 zenon_H5b). % 15.55/15.69 apply (zenon_or_s _ _ zenon_Hbf); [ zenon_intro zenon_H69 | zenon_intro zenon_Hc0 ]. % 15.55/15.69 apply (zenon_L17_); trivial. % 15.55/15.69 apply (zenon_or_s _ _ zenon_Hc0); [ zenon_intro zenon_Haf | zenon_intro zenon_Hba ]. % 15.55/15.69 apply (zenon_L39_); trivial. % 15.55/15.69 apply (zenon_L1170_); trivial. % 15.55/15.69 apply (zenon_or_s _ _ zenon_Hed); [ zenon_intro zenon_Hdd | zenon_intro zenon_He9 ]. % 15.55/15.69 apply (zenon_L304_); trivial. % 15.55/15.69 apply (zenon_L1163_); trivial. % 15.55/15.69 apply (zenon_L306_); trivial. % 15.55/15.69 apply (zenon_L7_); trivial. % 15.55/15.69 apply (zenon_L1041_); trivial. % 15.55/15.69 apply (zenon_or_s _ _ zenon_H10d); [ zenon_intro zenon_H3e | zenon_intro zenon_H42 ]. % 15.55/15.69 apply (zenon_or_s _ _ zenon_Hf1); [ zenon_intro zenon_H47 | zenon_intro zenon_Hf4 ]. % 15.55/15.69 exact (zenon_H45 zenon_H47). % 15.55/15.69 apply (zenon_or_s _ _ zenon_Hf4); [ zenon_intro zenon_Hd8 | zenon_intro zenon_Hf5 ]. % 15.55/15.69 apply (zenon_L61_); trivial. % 15.55/15.69 apply (zenon_or_s _ _ zenon_Hf5); [ zenon_intro zenon_Hae | zenon_intro zenon_Hee ]. % 15.55/15.69 apply (zenon_or_s _ _ zenon_Heb); [ zenon_intro zenon_H92 | zenon_intro zenon_Hec ]. % 15.55/15.69 exact (zenon_H8f zenon_H92). % 15.55/15.69 apply (zenon_or_s _ _ zenon_Hec); [ zenon_intro zenon_H68 | zenon_intro zenon_Hed ]. % 15.55/15.69 apply (zenon_L1148_); trivial. % 15.55/15.69 apply (zenon_or_s _ _ zenon_Hed); [ zenon_intro zenon_Hdd | zenon_intro zenon_He9 ]. % 15.55/15.69 apply (zenon_L1174_); trivial. % 15.55/15.69 apply (zenon_L1175_); trivial. % 15.55/15.69 apply (zenon_L306_); trivial. % 15.55/15.69 apply (zenon_L1041_); trivial. % 15.55/15.69 apply (zenon_or_s _ _ zenon_H10e); [ zenon_intro zenon_H3d | zenon_intro zenon_H106 ]. % 15.55/15.69 apply (zenon_or_s _ _ zenon_H10d); [ zenon_intro zenon_H3e | zenon_intro zenon_H42 ]. % 15.55/15.69 apply (zenon_or_s _ _ zenon_H44); [ zenon_intro zenon_H47 | zenon_intro zenon_H46 ]. % 15.55/15.69 exact (zenon_H45 zenon_H47). % 15.55/15.69 apply (zenon_or_s _ _ zenon_H46); [ zenon_intro zenon_H22 | zenon_intro zenon_H48 ]. % 15.55/15.69 apply (zenon_L3_); trivial. % 15.55/15.69 apply (zenon_or_s _ _ zenon_H48); [ zenon_intro zenon_H29 | zenon_intro zenon_H37 ]. % 15.55/15.69 apply (zenon_or_s _ _ zenon_Hf1); [ zenon_intro zenon_H47 | zenon_intro zenon_Hf4 ]. % 15.55/15.69 exact (zenon_H45 zenon_H47). % 15.55/15.69 apply (zenon_or_s _ _ zenon_Hf4); [ zenon_intro zenon_Hd8 | zenon_intro zenon_Hf5 ]. % 15.55/15.69 apply (zenon_L61_); trivial. % 15.55/15.69 apply (zenon_or_s _ _ zenon_Hf5); [ zenon_intro zenon_Hae | zenon_intro zenon_Hee ]. % 15.55/15.69 apply (zenon_L1097_); trivial. % 15.55/15.69 apply (zenon_or_s _ _ zenon_Heb); [ zenon_intro zenon_H92 | zenon_intro zenon_Hec ]. % 15.55/15.69 exact (zenon_H8f zenon_H92). % 15.55/15.69 apply (zenon_or_s _ _ zenon_Hec); [ zenon_intro zenon_H68 | zenon_intro zenon_Hed ]. % 15.55/15.69 apply (zenon_or_s _ _ zenon_H58); [ zenon_intro zenon_H5b | zenon_intro zenon_H5a ]. % 15.55/15.69 exact (zenon_H59 zenon_H5b). % 15.55/15.69 apply (zenon_or_s _ _ zenon_H5a); [ zenon_intro zenon_H4a | zenon_intro zenon_H5c ]. % 15.55/15.69 apply (zenon_L120_); trivial. % 15.55/15.69 apply (zenon_or_s _ _ zenon_H5c); [ zenon_intro zenon_H50 | zenon_intro zenon_H53 ]. % 15.55/15.69 apply (zenon_L29_); trivial. % 15.55/15.69 apply (zenon_or_s _ _ zenon_Hbe); [ zenon_intro zenon_H5b | zenon_intro zenon_Hbf ]. % 15.55/15.69 exact (zenon_H59 zenon_H5b). % 15.55/15.69 apply (zenon_or_s _ _ zenon_Hbf); [ zenon_intro zenon_H69 | zenon_intro zenon_Hc0 ]. % 15.55/15.69 apply (zenon_L17_); trivial. % 15.55/15.69 apply (zenon_or_s _ _ zenon_Hc0); [ zenon_intro zenon_Haf | zenon_intro zenon_Hba ]. % 15.55/15.69 apply (zenon_or_s _ _ zenon_H163); [ zenon_intro zenon_Had | zenon_intro zenon_H164 ]. % 15.55/15.69 apply (zenon_L559_); trivial. % 15.55/15.69 apply (zenon_or_s _ _ zenon_H164); [ zenon_intro zenon_H149 | zenon_intro zenon_H165 ]. % 15.55/15.69 exact (zenon_H145 zenon_H149). % 15.55/15.69 apply (zenon_or_s _ _ zenon_H165); [ zenon_intro zenon_H15d | zenon_intro zenon_Hcc ]. % 15.55/15.69 apply (zenon_L1057_); trivial. % 15.55/15.69 apply (zenon_L461_); trivial. % 15.55/15.69 apply (zenon_L1035_); trivial. % 15.55/15.69 apply (zenon_or_s _ _ zenon_Hed); [ zenon_intro zenon_Hdd | zenon_intro zenon_He9 ]. % 15.55/15.69 apply (zenon_L1172_); trivial. % 15.55/15.69 apply (zenon_L122_); trivial. % 15.55/15.69 apply (zenon_L7_); trivial. % 15.55/15.69 apply (zenon_L1041_); trivial. % 15.55/15.69 apply (zenon_L115_); trivial. % 15.55/15.69 apply (zenon_or_s _ _ zenon_H10c); [ zenon_intro zenon_H104 | zenon_intro zenon_H10a ]. % 15.55/15.69 apply (zenon_or_s _ _ zenon_H10e); [ zenon_intro zenon_H3d | zenon_intro zenon_H106 ]. % 15.55/15.69 apply (zenon_L1170_); trivial. % 15.55/15.69 apply (zenon_L81_); trivial. % 15.55/15.69 apply (zenon_L82_); trivial. % 15.55/15.69 apply (zenon_L1168_); trivial. % 15.55/15.69 apply (zenon_L1184_); trivial. % 15.55/15.69 apply (zenon_L1204_); trivial. % 15.55/15.69 apply (zenon_L1196_); trivial. % 15.55/15.69 apply (zenon_L90_); trivial. % 15.55/15.69 apply (zenon_L86_); trivial. % 15.55/15.69 (* end of lemma zenon_L1205_ *) % 15.55/15.69 assert (zenon_L1206_ : (((op (e3) (e0)) = (e2))\/(((op (e3) (e1)) = (e2))\/(((op (e3) (e2)) = (e2))\/((op (e3) (e3)) = (e2))))) -> ((op (e0) (e2)) = (e2)) -> (~((op (e0) (op (e3) (e0))) = (op (e3) (e0)))) -> (~((op (e2) (e1)) = (op (e3) (e1)))) -> ((op (e3) (e2)) = (e1)) -> ((op (e2) (e1)) = (e2)) -> (~((op (e2) (op (e3) (e2))) = (op (e3) (e2)))) -> (~((op (e3) (e3)) = (e2))) -> False). % 15.55/15.69 do 0 intro. intros zenon_H1df zenon_H63 zenon_H2b8 zenon_H13c zenon_H119 zenon_H156 zenon_H2af zenon_H3d. % 15.55/15.69 apply (zenon_or_s _ _ zenon_H1df); [ zenon_intro zenon_He9 | zenon_intro zenon_H1e0 ]. % 15.55/15.69 apply (zenon_L1106_); trivial. % 15.55/15.69 apply (zenon_or_s _ _ zenon_H1e0); [ zenon_intro zenon_H16a | zenon_intro zenon_H1e1 ]. % 15.55/15.69 apply (zenon_L252_); trivial. % 15.55/15.69 apply (zenon_or_s _ _ zenon_H1e1); [ zenon_intro zenon_H1dd | zenon_intro zenon_H43 ]. % 15.55/15.69 apply (zenon_L1160_); trivial. % 15.55/15.69 exact (zenon_H3d zenon_H43). % 15.55/15.69 (* end of lemma zenon_L1206_ *) % 15.55/15.69 assert (zenon_L1207_ : (((op (e3) (e0)) = (e1))\/(((op (e3) (e1)) = (e1))\/(((op (e3) (e2)) = (e1))\/((op (e3) (e3)) = (e1))))) -> (~((op (e0) (e2)) = (op (e3) (e2)))) -> (((op (e3) (e3)) = (e0))\/(((op (e3) (e3)) = (e1))\/(((op (e3) (e3)) = (e2))\/((op (e3) (e3)) = (e3))))) -> (~((op (e0) (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 (e3) (e3)) = (e3))) -> (~((e1) = (e2))) -> ((op (e1) (e1)) = (e1)) -> (~((op (e1) (op (e3) (e1))) = (op (e3) (e1)))) -> (~((op (e3) (e3)) = (e2))) -> (~((op (e2) (op (e3) (e2))) = (op (e3) (e2)))) -> ((op (e2) (e1)) = (e2)) -> (~((op (e2) (e1)) = (op (e3) (e1)))) -> (~((op (e0) (op (e3) (e0))) = (op (e3) (e0)))) -> ((op (e0) (e2)) = (e2)) -> (((op (e3) (e0)) = (e2))\/(((op (e3) (e1)) = (e2))\/(((op (e3) (e2)) = (e2))\/((op (e3) (e3)) = (e2))))) -> (~((op (e3) (e3)) = (e1))) -> False). % 15.55/15.69 do 0 intro. intros zenon_H146 zenon_H140 zenon_H3b zenon_H59 zenon_H8f zenon_H20 zenon_H12a zenon_H3e zenon_Ha7 zenon_H21 zenon_H2b4 zenon_H3d zenon_H2af zenon_H156 zenon_H13c zenon_H2b8 zenon_H63 zenon_H1df zenon_H104. % 15.55/15.69 apply (zenon_or_s _ _ zenon_H146); [ zenon_intro zenon_Hee | zenon_intro zenon_H14b ]. % 15.55/15.69 apply (zenon_or_s _ _ zenon_H1df); [ zenon_intro zenon_He9 | zenon_intro zenon_H1e0 ]. % 15.55/15.69 apply (zenon_L122_); trivial. % 15.55/15.69 apply (zenon_or_s _ _ zenon_H1e0); [ zenon_intro zenon_H16a | zenon_intro zenon_H1e1 ]. % 15.55/15.69 apply (zenon_L188_); trivial. % 15.55/15.69 apply (zenon_or_s _ _ zenon_H1e1); [ zenon_intro zenon_H1dd | zenon_intro zenon_H43 ]. % 15.55/15.69 apply (zenon_L253_); trivial. % 15.55/15.69 exact (zenon_H3d zenon_H43). % 15.55/15.69 apply (zenon_or_s _ _ zenon_H14b); [ zenon_intro zenon_H13e | zenon_intro zenon_H14c ]. % 15.55/15.69 apply (zenon_L1158_); trivial. % 15.55/15.69 apply (zenon_or_s _ _ zenon_H14c); [ zenon_intro zenon_H119 | zenon_intro zenon_H38 ]. % 15.55/15.69 apply (zenon_L1206_); trivial. % 15.55/15.69 exact (zenon_H104 zenon_H38). % 15.55/15.69 (* end of lemma zenon_L1207_ *) % 15.55/15.69 assert (zenon_L1208_ : (((op (e0) (e0)) = (e2))\/(((op (e0) (e1)) = (e2))\/(((op (e0) (e2)) = (e2))\/((op (e0) (e3)) = (e2))))) -> (~((op (e3) (e3)) = (e2))) -> (((op (e0) (e0)) = (e0))\/(((op (e0) (e0)) = (e1))\/(((op (e0) (e0)) = (e2))\/((op (e0) (e0)) = (e3))))) -> (~((op (e0) (e0)) = (e0))) -> (~((op (e0) (e0)) = (e2))) -> (~((op (e0) (e0)) = (e3))) -> (((op (e3) (e0)) = (e1))\/(((op (e3) (e1)) = (e1))\/(((op (e3) (e2)) = (e1))\/((op (e3) (e3)) = (e1))))) -> (~((op (e0) (e2)) = (op (e3) (e2)))) -> (~((e1) = (e2))) -> ((op (e1) (e1)) = (e1)) -> (~((op (e1) (op (e3) (e1))) = (op (e3) (e1)))) -> (~((op (e2) (op (e3) (e2))) = (op (e3) (e2)))) -> (~((op (e2) (e1)) = (op (e3) (e1)))) -> (~((op (e0) (op (e3) (e0))) = (op (e3) (e0)))) -> (((op (e3) (e0)) = (e2))\/(((op (e3) (e1)) = (e2))\/(((op (e3) (e2)) = (e2))\/((op (e3) (e3)) = (e2))))) -> (~((op (e1) (e1)) = (e2))) -> ((op (e0) (e1)) = (e0)) -> (~((e0) = (e2))) -> (((op (e0) (e1)) = (e2))\/(((op (e1) (e1)) = (e2))\/(((op (e2) (e1)) = (e2))\/((op (e3) (e1)) = (e2))))) -> (((op (e3) (e3)) = (e0))\/(((op (e3) (e3)) = (e1))\/(((op (e3) (e3)) = (e2))\/((op (e3) (e3)) = (e3))))) -> (~((op (e3) (e3)) = (e0))) -> (~((op (e3) (e3)) = (e1))) -> (~((op (e0) (e3)) = (op (e3) (e3)))) -> (~((op (e3) (e3)) = (e3))) -> False). % 15.55/15.69 do 0 intro. intros zenon_H8e zenon_H3d zenon_H12a zenon_H20 zenon_H8f zenon_H59 zenon_H146 zenon_H140 zenon_Ha7 zenon_H21 zenon_H2b4 zenon_H2af zenon_H13c zenon_H2b8 zenon_H1df zenon_Hd6 zenon_H49 zenon_H5e zenon_H1a2 zenon_H3b zenon_H3c zenon_H104 zenon_H36 zenon_H3e. % 15.55/15.69 apply (zenon_or_s _ _ zenon_H8e); [ zenon_intro zenon_H92 | zenon_intro zenon_H91 ]. % 15.55/15.69 exact (zenon_H8f zenon_H92). % 15.55/15.69 apply (zenon_or_s _ _ zenon_H91); [ zenon_intro zenon_H5d | zenon_intro zenon_H93 ]. % 15.55/15.69 apply (zenon_L14_); trivial. % 15.55/15.69 apply (zenon_or_s _ _ zenon_H93); [ zenon_intro zenon_H63 | zenon_intro zenon_H81 ]. % 15.55/15.69 apply (zenon_or_s _ _ zenon_H1a2); [ zenon_intro zenon_H5d | zenon_intro zenon_H1a3 ]. % 15.55/15.69 apply (zenon_L14_); trivial. % 15.55/15.69 apply (zenon_or_s _ _ zenon_H1a3); [ zenon_intro zenon_H6e | zenon_intro zenon_H1a4 ]. % 15.55/15.69 exact (zenon_Hd6 zenon_H6e). % 15.55/15.69 apply (zenon_or_s _ _ zenon_H1a4); [ zenon_intro zenon_H156 | zenon_intro zenon_H16a ]. % 15.55/15.69 apply (zenon_L1207_); trivial. % 15.55/15.69 apply (zenon_L188_); trivial. % 15.55/15.69 apply (zenon_L107_); trivial. % 15.55/15.69 (* end of lemma zenon_L1208_ *) % 15.55/15.69 assert (zenon_L1209_ : ((~((op (e3) (e3)) = (e3)))\/((op (e3) (e3)) = (e3))) -> (~((op (e3) (op (e3) (e3))) = (op (e3) (e3)))) -> (~((op (e0) (e0)) = (e0))) -> (((op (e0) (e0)) = (e2))\/(((op (e0) (e1)) = (e2))\/(((op (e0) (e2)) = (e2))\/((op (e0) (e3)) = (e2))))) -> (~((op (e3) (e3)) = (e0))) -> (~((op (e0) (e3)) = (op (e3) (e3)))) -> (~((op (e1) (e1)) = (e2))) -> (((op (e3) (e0)) = (e1))\/(((op (e3) (e1)) = (e1))\/(((op (e3) (e2)) = (e1))\/((op (e3) (e3)) = (e1))))) -> (~((op (e0) (op (e3) (e0))) = (op (e3) (e0)))) -> (~((op (e2) (e1)) = (op (e3) (e1)))) -> (~((op (e2) (op (e3) (e2))) = (op (e3) (e2)))) -> ((op (e1) (e1)) = (e1)) -> (~((op (e1) (op (e3) (e1))) = (op (e3) (e1)))) -> (~((e1) = (e2))) -> (((op (e3) (e3)) = (e0))\/(((op (e3) (e3)) = (e1))\/(((op (e3) (e3)) = (e2))\/((op (e3) (e3)) = (e3))))) -> (~((op (e3) (e3)) = (e2))) -> (~((op (e3) (e3)) = (e1))) -> (~((op (e0) (e0)) = (e3))) -> (((op (e0) (e0)) = (e0))\/(((op (e0) (e0)) = (e1))\/(((op (e0) (e0)) = (e2))\/((op (e0) (e0)) = (e3))))) -> (~((op (e0) (e2)) = (op (e3) (e2)))) -> (((op (e3) (e0)) = (e2))\/(((op (e3) (e1)) = (e2))\/(((op (e3) (e2)) = (e2))\/((op (e3) (e3)) = (e2))))) -> (((op (e0) (e1)) = (e2))\/(((op (e1) (e1)) = (e2))\/(((op (e2) (e1)) = (e2))\/((op (e3) (e1)) = (e2))))) -> (~((e0) = (e2))) -> (~((op (e0) (e0)) = (e2))) -> (((op (e0) (e0)) = (e1))\/(((op (e0) (e1)) = (e1))\/(((op (e0) (e2)) = (e1))\/((op (e0) (e3)) = (e1))))) -> (~((e0) = (e1))) -> (~((op (e0) (e1)) = (op (e1) (e1)))) -> (~((op (e0) (e0)) = (e1))) -> (((op (e0) (e0)) = (e0))\/(((op (e0) (e1)) = (e0))\/(((op (e0) (e2)) = (e0))\/((op (e0) (e3)) = (e0))))) -> False). % 15.55/15.69 do 0 intro. intros zenon_H10d zenon_H2be zenon_H20 zenon_H8e zenon_H3c zenon_H36 zenon_Hd6 zenon_H146 zenon_H2b8 zenon_H13c zenon_H2af zenon_H21 zenon_H2b4 zenon_Ha7 zenon_H3b zenon_H3d zenon_H104 zenon_H59 zenon_H12a zenon_H140 zenon_H1df zenon_H1a2 zenon_H5e zenon_H8f zenon_H44 zenon_H9e zenon_H23 zenon_H45 zenon_H110. % 15.55/15.69 apply (zenon_or_s _ _ zenon_H10d); [ zenon_intro zenon_H3e | zenon_intro zenon_H42 ]. % 15.55/15.69 apply (zenon_or_s _ _ zenon_H110); [ zenon_intro zenon_H1f | zenon_intro zenon_H111 ]. % 15.55/15.69 exact (zenon_H20 zenon_H1f). % 15.55/15.69 apply (zenon_or_s _ _ zenon_H111); [ zenon_intro zenon_H49 | zenon_intro zenon_H112 ]. % 15.55/15.69 apply (zenon_L1208_); trivial. % 15.55/15.69 apply (zenon_or_s _ _ zenon_H112); [ zenon_intro zenon_Hab | zenon_intro zenon_Hca ]. % 15.55/15.69 apply (zenon_L132_); trivial. % 15.55/15.69 apply (zenon_L114_); trivial. % 15.55/15.69 apply (zenon_L1041_); trivial. % 15.55/15.69 (* end of lemma zenon_L1209_ *) % 15.55/15.69 assert (zenon_L1210_ : (((op (e3) (e0)) = (e0))\/(((op (e3) (e1)) = (e0))\/(((op (e3) (e2)) = (e0))\/((op (e3) (e3)) = (e0))))) -> (~((op (e3) (e3)) = (e1))) -> (~((op (e0) (e2)) = (op (e3) (e2)))) -> ((op (e0) (e2)) = (e1)) -> ((op (e1) (e1)) = (e1)) -> (~((e0) = (e1))) -> (((op (e3) (e0)) = (e1))\/(((op (e3) (e1)) = (e1))\/(((op (e3) (e2)) = (e1))\/((op (e3) (e3)) = (e1))))) -> ((op (e1) (e0)) = (e0)) -> (~((op (e1) (op (e3) (e1))) = (op (e3) (e1)))) -> ((op (e3) (e2)) = (e3)) -> (~((e0) = (e3))) -> (~((op (e3) (e3)) = (e0))) -> False). % 15.55/15.69 do 0 intro. intros zenon_H1f6 zenon_H104 zenon_H140 zenon_H29 zenon_H21 zenon_H9e zenon_H146 zenon_Had zenon_H2b4 zenon_H106 zenon_H4b zenon_H3c. % 15.55/15.69 apply (zenon_or_s _ _ zenon_H1f6); [ zenon_intro zenon_Hdb | zenon_intro zenon_H1f7 ]. % 15.55/15.69 apply (zenon_L1185_); trivial. % 15.55/15.69 apply (zenon_or_s _ _ zenon_H1f7); [ zenon_intro zenon_H142 | zenon_intro zenon_H1f8 ]. % 15.55/15.69 apply (zenon_L1136_); trivial. % 15.55/15.69 apply (zenon_or_s _ _ zenon_H1f8); [ zenon_intro zenon_H167 | zenon_intro zenon_H40 ]. % 15.55/15.69 apply (zenon_L589_); trivial. % 15.55/15.69 exact (zenon_H3c zenon_H40). % 15.55/15.69 (* end of lemma zenon_L1210_ *) % 15.55/15.69 assert (zenon_L1211_ : (((op (e0) (e0)) = (e1))\/(((op (e0) (e1)) = (e1))\/(((op (e0) (e2)) = (e1))\/((op (e0) (e3)) = (e1))))) -> (~((op (e0) (e0)) = (e1))) -> (~((op (e0) (e1)) = (op (e1) (e1)))) -> (~((op (e3) (e3)) = (e0))) -> (~((e0) = (e3))) -> (~((op (e1) (op (e3) (e1))) = (op (e3) (e1)))) -> ((op (e1) (e0)) = (e0)) -> (((op (e3) (e0)) = (e1))\/(((op (e3) (e1)) = (e1))\/(((op (e3) (e2)) = (e1))\/((op (e3) (e3)) = (e1))))) -> (~((e0) = (e1))) -> (~((op (e0) (e2)) = (op (e3) (e2)))) -> (~((op (e3) (e3)) = (e1))) -> (((op (e3) (e0)) = (e0))\/(((op (e3) (e1)) = (e0))\/(((op (e3) (e2)) = (e0))\/((op (e3) (e3)) = (e0))))) -> (((op (e0) (e2)) = (e1))\/(((op (e1) (e2)) = (e1))\/(((op (e2) (e2)) = (e1))\/((op (e3) (e2)) = (e1))))) -> (~((op (e0) (e2)) = (op (e0) (e3)))) -> ((op (e1) (e1)) = (e1)) -> (~((op (e1) (e1)) = (op (e1) (e2)))) -> (~((op (e2) (e2)) = (e1))) -> (~((e1) = (e3))) -> ((op (e3) (e2)) = (e3)) -> False). % 15.55/15.69 do 0 intro. intros zenon_H44 zenon_H45 zenon_H23 zenon_H3c zenon_H4b zenon_H2b4 zenon_Had zenon_H146 zenon_H9e zenon_H140 zenon_H104 zenon_H1f6 zenon_H11b zenon_Hc9 zenon_H21 zenon_H116 zenon_H52 zenon_Ha3 zenon_H106. % 15.55/15.69 apply (zenon_or_s _ _ zenon_H44); [ zenon_intro zenon_H47 | zenon_intro zenon_H46 ]. % 15.55/15.69 exact (zenon_H45 zenon_H47). % 15.55/15.69 apply (zenon_or_s _ _ zenon_H46); [ zenon_intro zenon_H22 | zenon_intro zenon_H48 ]. % 15.55/15.69 apply (zenon_L3_); trivial. % 15.55/15.69 apply (zenon_or_s _ _ zenon_H48); [ zenon_intro zenon_H29 | zenon_intro zenon_H37 ]. % 15.55/15.69 apply (zenon_L1210_); trivial. % 15.55/15.69 apply (zenon_L88_); trivial. % 15.55/15.69 (* end of lemma zenon_L1211_ *) % 15.55/15.69 assert (zenon_L1212_ : (((op (e3) (e0)) = (e1))\/(((op (e3) (e1)) = (e1))\/(((op (e3) (e2)) = (e1))\/((op (e3) (e3)) = (e1))))) -> (~((e0) = (e1))) -> ((op (e3) (e0)) = (e0)) -> ((op (e1) (e1)) = (e1)) -> (~((op (e1) (op (e3) (e1))) = (op (e3) (e1)))) -> ((op (e3) (e2)) = (e3)) -> (~((e1) = (e3))) -> (~((op (e3) (e3)) = (e1))) -> False). % 15.55/15.69 do 0 intro. intros zenon_H146 zenon_H9e zenon_Hdb zenon_H21 zenon_H2b4 zenon_H106 zenon_Ha3 zenon_H104. % 15.55/15.69 apply (zenon_or_s _ _ zenon_H146); [ zenon_intro zenon_Hee | zenon_intro zenon_H14b ]. % 15.55/15.69 apply (zenon_L71_); trivial. % 15.55/15.69 apply (zenon_or_s _ _ zenon_H14b); [ zenon_intro zenon_H13e | zenon_intro zenon_H14c ]. % 15.55/15.69 apply (zenon_L1158_); trivial. % 15.55/15.69 apply (zenon_or_s _ _ zenon_H14c); [ zenon_intro zenon_H119 | zenon_intro zenon_H38 ]. % 15.55/15.69 apply (zenon_L87_); trivial. % 15.55/15.69 exact (zenon_H104 zenon_H38). % 15.55/15.69 (* end of lemma zenon_L1212_ *) % 15.55/15.69 assert (zenon_L1213_ : ((~((op (e3) (e3)) = (e3)))\/((op (e3) (e3)) = (e3))) -> (~((op (e3) (op (e3) (e3))) = (op (e3) (e3)))) -> (~((op (e0) (e0)) = (e0))) -> (((op (e0) (e0)) = (e1))\/(((op (e0) (e1)) = (e1))\/(((op (e0) (e2)) = (e1))\/((op (e0) (e3)) = (e1))))) -> (~((op (e0) (e2)) = (op (e0) (e3)))) -> (~((op (e1) (e1)) = (op (e1) (e2)))) -> (~((op (e2) (e2)) = (e1))) -> (~((e1) = (e3))) -> (((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) (e3)) = (e1))) -> (~((op (e0) (e2)) = (op (e3) (e2)))) -> (~((op (e1) (op (e3) (e1))) = (op (e3) (e1)))) -> (~((e0) = (e1))) -> (~((e0) = (e3))) -> ((op (e3) (e2)) = (e3)) -> (~((op (e3) (e3)) = (e0))) -> (((op (e3) (e0)) = (e0))\/(((op (e3) (e1)) = (e0))\/(((op (e3) (e2)) = (e0))\/((op (e3) (e3)) = (e0))))) -> ((op (e1) (e1)) = (e1)) -> (~((op (e0) (e1)) = (op (e1) (e1)))) -> (~((op (e0) (e0)) = (e1))) -> (((op (e0) (e0)) = (e1))\/(((op (e1) (e0)) = (e1))\/(((op (e2) (e0)) = (e1))\/((op (e3) (e0)) = (e1))))) -> (((op (e3) (e3)) = (e0))\/(((op (e3) (e3)) = (e1))\/(((op (e3) (e3)) = (e2))\/((op (e3) (e3)) = (e3))))) -> (~((op (e2) (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)) = (op (e1) (e1)))) -> (((op (e0) (e0)) = (e0))\/(((op (e1) (e0)) = (e0))\/(((op (e2) (e0)) = (e0))\/((op (e3) (e0)) = (e0))))) -> False). % 15.55/15.69 do 0 intro. intros zenon_H10d zenon_H2be zenon_H20 zenon_H44 zenon_Hc9 zenon_H116 zenon_H52 zenon_Ha3 zenon_H11b zenon_H146 zenon_H104 zenon_H140 zenon_H2b4 zenon_H9e zenon_H4b zenon_H106 zenon_H3c zenon_H1f6 zenon_H21 zenon_H23 zenon_H45 zenon_Hf1 zenon_H3b zenon_H2f zenon_H30 zenon_H2d zenon_Hd7 zenon_Hf0. % 15.55/15.69 apply (zenon_or_s _ _ zenon_H10d); [ zenon_intro zenon_H3e | zenon_intro zenon_H42 ]. % 15.55/15.69 apply (zenon_or_s _ _ zenon_Hf0); [ zenon_intro zenon_H1f | zenon_intro zenon_Hf2 ]. % 15.55/15.69 exact (zenon_H20 zenon_H1f). % 15.55/15.69 apply (zenon_or_s _ _ zenon_Hf2); [ zenon_intro zenon_Had | zenon_intro zenon_Hf3 ]. % 15.55/15.69 apply (zenon_L1211_); trivial. % 15.55/15.69 apply (zenon_or_s _ _ zenon_Hf3); [ zenon_intro zenon_Hcf | zenon_intro zenon_Hdb ]. % 15.55/15.69 apply (zenon_or_s _ _ zenon_Hf1); [ zenon_intro zenon_H47 | zenon_intro zenon_Hf4 ]. % 15.55/15.69 exact (zenon_H45 zenon_H47). % 15.55/15.69 apply (zenon_or_s _ _ zenon_Hf4); [ zenon_intro zenon_Hd8 | zenon_intro zenon_Hf5 ]. % 15.55/15.69 apply (zenon_L61_); trivial. % 15.55/15.69 apply (zenon_or_s _ _ zenon_Hf5); [ zenon_intro zenon_Hae | zenon_intro zenon_Hee ]. % 15.55/15.69 apply (zenon_L269_); trivial. % 15.55/15.69 apply (zenon_L306_); trivial. % 15.55/15.69 apply (zenon_L1212_); trivial. % 15.55/15.69 apply (zenon_L1041_); trivial. % 15.55/15.69 (* end of lemma zenon_L1213_ *) % 15.55/15.69 assert (zenon_L1214_ : (((op (e3) (e0)) = (e2))\/(((op (e3) (e1)) = (e2))\/(((op (e3) (e2)) = (e2))\/((op (e3) (e3)) = (e2))))) -> (~((op (e0) (op (e3) (e0))) = (op (e3) (e0)))) -> ((op (e3) (e1)) = (e3)) -> (~((e2) = (e3))) -> ((op (e0) (e2)) = (e2)) -> (~((op (e0) (e2)) = (op (e3) (e2)))) -> (~((op (e3) (e3)) = (e2))) -> False). % 15.55/15.69 do 0 intro. intros zenon_H1df zenon_H2b8 zenon_H10a zenon_H6a zenon_H63 zenon_H140 zenon_H3d. % 15.55/15.69 apply (zenon_or_s _ _ zenon_H1df); [ zenon_intro zenon_He9 | zenon_intro zenon_H1e0 ]. % 15.55/15.69 apply (zenon_L1106_); trivial. % 15.55/15.69 apply (zenon_or_s _ _ zenon_H1e0); [ zenon_intro zenon_H16a | zenon_intro zenon_H1e1 ]. % 15.55/15.69 apply (zenon_L297_); trivial. % 15.55/15.69 apply (zenon_or_s _ _ zenon_H1e1); [ zenon_intro zenon_H1dd | zenon_intro zenon_H43 ]. % 15.55/15.69 apply (zenon_L253_); trivial. % 15.55/15.69 exact (zenon_H3d zenon_H43). % 15.55/15.69 (* end of lemma zenon_L1214_ *) % 15.55/15.69 assert (zenon_L1215_ : (((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 (e3) (e1)) = (e3)) -> (~((e0) = (e3))) -> ((op (e1) (e2)) = (e0)) -> (~((op (e1) (e2)) = (op (e3) (e2)))) -> (~((op (e3) (e3)) = (e0))) -> False). % 15.55/15.69 do 0 intro. intros zenon_H1f6 zenon_H1e5 zenon_Hcf zenon_H10a zenon_H4b zenon_H15d zenon_H17d zenon_H3c. % 15.55/15.69 apply (zenon_or_s _ _ zenon_H1f6); [ zenon_intro zenon_Hdb | zenon_intro zenon_H1f7 ]. % 15.55/15.69 apply (zenon_L980_); trivial. % 15.55/15.69 apply (zenon_or_s _ _ zenon_H1f7); [ zenon_intro zenon_H142 | zenon_intro zenon_H1f8 ]. % 15.55/15.69 apply (zenon_L126_); trivial. % 15.55/15.69 apply (zenon_or_s _ _ zenon_H1f8); [ zenon_intro zenon_H167 | zenon_intro zenon_H40 ]. % 15.55/15.69 apply (zenon_L626_); trivial. % 15.55/15.69 exact (zenon_H3c zenon_H40). % 15.55/15.69 (* end of lemma zenon_L1215_ *) % 15.55/15.69 assert (zenon_L1216_ : (~((op (e2) (op (e3) (e2))) = (op (e2) (e0)))) -> ((op (e3) (e2)) = (e0)) -> False). % 15.55/15.69 do 0 intro. intros zenon_H2d8 zenon_H167. % 15.55/15.69 cut (((op (e3) (e2)) = (e0))); [idtac | apply NNPP; zenon_intro zenon_H257]. % 15.55/15.69 cut (((e2) = (e2))); [idtac | apply NNPP; zenon_intro zenon_H60]. % 15.55/15.69 congruence. % 15.55/15.69 apply zenon_H60. apply refl_equal. % 15.55/15.69 exact (zenon_H257 zenon_H167). % 15.55/15.69 (* end of lemma zenon_L1216_ *) % 15.55/15.69 assert (zenon_L1217_ : (~((op (e2) (op (e3) (e2))) = (op (e3) (e2)))) -> ((op (e2) (e0)) = (e0)) -> ((op (e3) (e2)) = (e0)) -> False). % 15.55/15.69 do 0 intro. intros zenon_H2af zenon_Hcf zenon_H167. % 15.55/15.69 cut (((op (e2) (e0)) = (e0)) = ((op (e2) (op (e3) (e2))) = (op (e3) (e2)))). % 15.55/15.69 intro zenon_D_pnotp. % 15.55/15.69 apply zenon_H2af. % 15.55/15.69 rewrite <- zenon_D_pnotp. % 15.55/15.69 exact zenon_Hcf. % 15.55/15.69 cut (((e0) = (op (e3) (e2)))); [idtac | apply NNPP; zenon_intro zenon_H168]. % 15.55/15.69 cut (((op (e2) (e0)) = (op (e2) (op (e3) (e2))))); [idtac | apply NNPP; zenon_intro zenon_H2d9]. % 15.55/15.69 congruence. % 15.55/15.69 elim (classic ((op (e2) (op (e3) (e2))) = (op (e2) (op (e3) (e2))))); [ zenon_intro zenon_H2b1 | zenon_intro zenon_H2b2 ]. % 15.55/15.69 cut (((op (e2) (op (e3) (e2))) = (op (e2) (op (e3) (e2)))) = ((op (e2) (e0)) = (op (e2) (op (e3) (e2))))). % 15.55/15.69 intro zenon_D_pnotp. % 15.55/15.69 apply zenon_H2d9. % 15.55/15.69 rewrite <- zenon_D_pnotp. % 15.55/15.69 exact zenon_H2b1. % 15.55/15.69 cut (((op (e2) (op (e3) (e2))) = (op (e2) (op (e3) (e2))))); [idtac | apply NNPP; zenon_intro zenon_H2b2]. % 15.55/15.69 cut (((op (e2) (op (e3) (e2))) = (op (e2) (e0)))); [idtac | apply NNPP; zenon_intro zenon_H2d8]. % 15.55/15.69 congruence. % 15.55/15.69 apply (zenon_L1216_); trivial. % 15.55/15.69 apply zenon_H2b2. apply refl_equal. % 15.55/15.69 apply zenon_H2b2. apply refl_equal. % 15.55/15.69 apply zenon_H168. apply sym_equal. exact zenon_H167. % 15.55/15.69 (* end of lemma zenon_L1217_ *) % 15.55/15.69 assert (zenon_L1218_ : (((op (e0) (e2)) = (e0))\/(((op (e1) (e2)) = (e0))\/(((op (e2) (e2)) = (e0))\/((op (e3) (e2)) = (e0))))) -> ((op (e0) (e1)) = (e0)) -> (~((op (e0) (e1)) = (op (e0) (e2)))) -> (~((op (e3) (e3)) = (e0))) -> (~((op (e1) (e2)) = (op (e3) (e2)))) -> (~((e0) = (e3))) -> ((op (e3) (e1)) = (e3)) -> (~((op (e2) (e0)) = (op (e3) (e0)))) -> (((op (e3) (e0)) = (e0))\/(((op (e3) (e1)) = (e0))\/(((op (e3) (e2)) = (e0))\/((op (e3) (e3)) = (e0))))) -> (~((op (e2) (e2)) = (e0))) -> (~((op (e2) (op (e3) (e2))) = (op (e3) (e2)))) -> ((op (e2) (e0)) = (e0)) -> False). % 15.55/15.69 do 0 intro. intros zenon_H16f zenon_H49 zenon_H23e zenon_H3c zenon_H17d zenon_H4b zenon_H10a zenon_H1e5 zenon_H1f6 zenon_H2e zenon_H2af zenon_Hcf. % 15.55/15.69 apply (zenon_or_s _ _ zenon_H16f); [ zenon_intro zenon_Hab | zenon_intro zenon_H170 ]. % 15.55/15.69 apply (zenon_L485_); trivial. % 15.55/15.69 apply (zenon_or_s _ _ zenon_H170); [ zenon_intro zenon_H15d | zenon_intro zenon_H171 ]. % 15.55/15.69 apply (zenon_L1215_); trivial. % 15.55/15.69 apply (zenon_or_s _ _ zenon_H171); [ zenon_intro zenon_H32 | zenon_intro zenon_H167 ]. % 15.55/15.69 exact (zenon_H2e zenon_H32). % 15.55/15.69 apply (zenon_L1217_); trivial. % 15.55/15.69 (* end of lemma zenon_L1218_ *) % 15.55/15.69 assert (zenon_L1219_ : (~((op (e1) (op (e3) (e1))) = (op (e1) (e3)))) -> ((op (e3) (e1)) = (e3)) -> False). % 15.55/15.69 do 0 intro. intros zenon_H2da zenon_H10a. % 15.55/15.69 cut (((op (e3) (e1)) = (e3))); [idtac | apply NNPP; zenon_intro zenon_H2db]. % 15.55/15.69 cut (((e1) = (e1))); [idtac | apply NNPP; zenon_intro zenon_Ha0]. % 15.55/15.69 congruence. % 15.55/15.69 apply zenon_Ha0. apply refl_equal. % 15.55/15.69 exact (zenon_H2db zenon_H10a). % 15.55/15.69 (* end of lemma zenon_L1219_ *) % 15.55/15.69 assert (zenon_L1220_ : (~((op (e1) (op (e3) (e1))) = (op (e3) (e1)))) -> ((op (e1) (e3)) = (e3)) -> ((op (e3) (e1)) = (e3)) -> False). % 15.55/15.69 do 0 intro. intros zenon_H2b4 zenon_H8a zenon_H10a. % 15.55/15.69 cut (((op (e1) (e3)) = (e3)) = ((op (e1) (op (e3) (e1))) = (op (e3) (e1)))). % 15.55/15.69 intro zenon_D_pnotp. % 15.55/15.69 apply zenon_H2b4. % 15.55/15.69 rewrite <- zenon_D_pnotp. % 15.55/15.69 exact zenon_H8a. % 15.55/15.69 cut (((e3) = (op (e3) (e1)))); [idtac | apply NNPP; zenon_intro zenon_H10b]. % 15.55/15.69 cut (((op (e1) (e3)) = (op (e1) (op (e3) (e1))))); [idtac | apply NNPP; zenon_intro zenon_H2dc]. % 15.55/15.69 congruence. % 15.55/15.69 elim (classic ((op (e1) (op (e3) (e1))) = (op (e1) (op (e3) (e1))))); [ zenon_intro zenon_H2b6 | zenon_intro zenon_H2b7 ]. % 15.55/15.69 cut (((op (e1) (op (e3) (e1))) = (op (e1) (op (e3) (e1)))) = ((op (e1) (e3)) = (op (e1) (op (e3) (e1))))). % 15.55/15.69 intro zenon_D_pnotp. % 15.55/15.69 apply zenon_H2dc. % 15.55/15.69 rewrite <- zenon_D_pnotp. % 15.55/15.69 exact zenon_H2b6. % 15.55/15.69 cut (((op (e1) (op (e3) (e1))) = (op (e1) (op (e3) (e1))))); [idtac | apply NNPP; zenon_intro zenon_H2b7]. % 15.55/15.69 cut (((op (e1) (op (e3) (e1))) = (op (e1) (e3)))); [idtac | apply NNPP; zenon_intro zenon_H2da]. % 15.55/15.69 congruence. % 15.55/15.69 apply (zenon_L1219_); trivial. % 15.55/15.69 apply zenon_H2b7. apply refl_equal. % 15.55/15.69 apply zenon_H2b7. apply refl_equal. % 15.55/15.69 apply zenon_H10b. apply sym_equal. exact zenon_H10a. % 15.55/15.69 (* end of lemma zenon_L1220_ *) % 15.55/15.69 assert (zenon_L1221_ : (((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 (e0) (e3)) = (e2)) -> (~((op (e0) (e3)) = (op (e1) (e3)))) -> (~((op (e1) (op (e3) (e1))) = (op (e3) (e1)))) -> ((op (e3) (e1)) = (e3)) -> False). % 15.55/15.69 do 0 intro. intros zenon_H25b zenon_Hd0 zenon_Hb5 zenon_H244 zenon_H81 zenon_H80 zenon_H2b4 zenon_H10a. % 15.55/15.69 apply (zenon_or_s _ _ zenon_H25b); [ zenon_intro zenon_Hcc | zenon_intro zenon_H25c ]. % 15.55/15.69 apply (zenon_L599_); trivial. % 15.55/15.69 apply (zenon_or_s _ _ zenon_H25c); [ zenon_intro zenon_H11f | zenon_intro zenon_H25d ]. % 15.55/15.69 apply (zenon_L529_); trivial. % 15.55/15.69 apply (zenon_or_s _ _ zenon_H25d); [ zenon_intro zenon_H82 | zenon_intro zenon_H8a ]. % 15.55/15.69 apply (zenon_L22_); trivial. % 15.55/15.69 apply (zenon_L1220_); trivial. % 15.55/15.69 (* end of lemma zenon_L1221_ *) % 15.55/15.69 assert (zenon_L1222_ : (((op (e0) (e3)) = (e0))\/(((op (e0) (e3)) = (e1))\/(((op (e0) (e3)) = (e2))\/((op (e0) (e3)) = (e3))))) -> ((op (e0) (e1)) = (e0)) -> (~((op (e0) (e1)) = (op (e0) (e3)))) -> ((op (e3) (e3)) = (e1)) -> (~((op (e0) (e3)) = (op (e3) (e3)))) -> ((op (e1) (e3)) = (e2)) -> (~((op (e0) (e3)) = (op (e1) (e3)))) -> (~((op (e0) (e3)) = (op (e2) (e3)))) -> ((op (e2) (e3)) = (e3)) -> False). % 15.55/15.69 do 0 intro. intros zenon_H254 zenon_H49 zenon_H1cd zenon_H38 zenon_H36 zenon_H82 zenon_H80 zenon_Hb4 zenon_He2. % 15.55/15.69 apply (zenon_or_s _ _ zenon_H254); [ zenon_intro zenon_Hca | zenon_intro zenon_H255 ]. % 15.55/15.69 apply (zenon_L463_); trivial. % 15.55/15.69 apply (zenon_or_s _ _ zenon_H255); [ zenon_intro zenon_H37 | zenon_intro zenon_H256 ]. % 15.55/15.69 apply (zenon_L6_); trivial. % 15.55/15.69 apply (zenon_or_s _ _ zenon_H256); [ zenon_intro zenon_H81 | zenon_intro zenon_H53 ]. % 15.55/15.69 apply (zenon_L22_); trivial. % 15.55/15.69 apply (zenon_L125_); trivial. % 15.55/15.69 (* end of lemma zenon_L1222_ *) % 15.55/15.69 assert (zenon_L1223_ : (((op (e0) (e3)) = (e3))\/(((op (e1) (e3)) = (e3))\/(((op (e2) (e3)) = (e3))\/((op (e3) (e3)) = (e3))))) -> (~((e2) = (e3))) -> ((op (e0) (e3)) = (e2)) -> ((op (e3) (e1)) = (e3)) -> (~((op (e1) (op (e3) (e1))) = (op (e3) (e1)))) -> (((op (e0) (e3)) = (e0))\/(((op (e0) (e3)) = (e1))\/(((op (e0) (e3)) = (e2))\/((op (e0) (e3)) = (e3))))) -> ((op (e0) (e1)) = (e0)) -> (~((op (e0) (e1)) = (op (e0) (e3)))) -> ((op (e3) (e3)) = (e1)) -> (~((op (e0) (e3)) = (op (e3) (e3)))) -> (~((op (e0) (e3)) = (op (e1) (e3)))) -> (~((op (e0) (e3)) = (op (e2) (e3)))) -> (~((op (e1) (e1)) = (op (e1) (e3)))) -> ((op (e1) (e1)) = (e1)) -> (~((op (e1) (e3)) = (op (e2) (e3)))) -> ((op (e2) (e3)) = (e0)) -> (((op (e1) (e3)) = (e0))\/(((op (e1) (e3)) = (e1))\/(((op (e1) (e3)) = (e2))\/((op (e1) (e3)) = (e3))))) -> (~((op (e3) (e3)) = (e3))) -> False). % 15.55/15.70 do 0 intro. intros zenon_H2d0 zenon_H6a zenon_H81 zenon_H10a zenon_H2b4 zenon_H254 zenon_H49 zenon_H1cd zenon_H38 zenon_H36 zenon_H80 zenon_Hb4 zenon_H11e zenon_H21 zenon_H244 zenon_Hd0 zenon_H25b zenon_H3e. % 15.55/15.70 apply (zenon_or_s _ _ zenon_H2d0); [ zenon_intro zenon_H53 | zenon_intro zenon_H2d1 ]. % 15.55/15.70 apply (zenon_L128_); trivial. % 15.55/15.70 apply (zenon_or_s _ _ zenon_H2d1); [ zenon_intro zenon_H8a | zenon_intro zenon_H2d2 ]. % 15.55/15.70 apply (zenon_L1220_); trivial. % 15.55/15.70 apply (zenon_or_s _ _ zenon_H2d2); [ zenon_intro zenon_He2 | zenon_intro zenon_H42 ]. % 15.55/15.70 apply (zenon_or_s _ _ zenon_H25b); [ zenon_intro zenon_Hcc | zenon_intro zenon_H25c ]. % 15.55/15.70 apply (zenon_L599_); trivial. % 15.55/15.70 apply (zenon_or_s _ _ zenon_H25c); [ zenon_intro zenon_H11f | zenon_intro zenon_H25d ]. % 15.55/15.70 apply (zenon_L90_); trivial. % 15.55/15.70 apply (zenon_or_s _ _ zenon_H25d); [ zenon_intro zenon_H82 | zenon_intro zenon_H8a ]. % 15.55/15.70 apply (zenon_L1222_); trivial. % 15.55/15.70 apply (zenon_L1220_); trivial. % 15.55/15.70 exact (zenon_H3e zenon_H42). % 15.55/15.70 (* end of lemma zenon_L1223_ *) % 15.55/15.70 assert (zenon_L1224_ : (((op (e0) (e0)) = (e2))\/(((op (e0) (e1)) = (e2))\/(((op (e0) (e2)) = (e2))\/((op (e0) (e3)) = (e2))))) -> (~((op (e0) (e0)) = (e2))) -> (~((e0) = (e2))) -> (~((op (e3) (e3)) = (e2))) -> (~((op (e0) (e2)) = (op (e3) (e2)))) -> (~((op (e0) (op (e3) (e0))) = (op (e3) (e0)))) -> (((op (e3) (e0)) = (e2))\/(((op (e3) (e1)) = (e2))\/(((op (e3) (e2)) = (e2))\/((op (e3) (e3)) = (e2))))) -> (((op (e2) (e0)) = (e0))\/(((op (e2) (e1)) = (e0))\/(((op (e2) (e2)) = (e0))\/((op (e2) (e3)) = (e0))))) -> (~((op (e2) (op (e3) (e2))) = (op (e3) (e2)))) -> (((op (e3) (e0)) = (e0))\/(((op (e3) (e1)) = (e0))\/(((op (e3) (e2)) = (e0))\/((op (e3) (e3)) = (e0))))) -> (~((op (e2) (e0)) = (op (e3) (e0)))) -> (~((e0) = (e3))) -> (~((op (e1) (e2)) = (op (e3) (e2)))) -> (~((op (e3) (e3)) = (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) (e1)) = (op (e2) (e1)))) -> (~((op (e2) (e2)) = (e0))) -> (((op (e0) (e3)) = (e1))\/(((op (e1) (e3)) = (e1))\/(((op (e2) (e3)) = (e1))\/((op (e3) (e3)) = (e1))))) -> (~((e1) = (e2))) -> (((op (e0) (e3)) = (e3))\/(((op (e1) (e3)) = (e3))\/(((op (e2) (e3)) = (e3))\/((op (e3) (e3)) = (e3))))) -> (~((e2) = (e3))) -> ((op (e3) (e1)) = (e3)) -> (~((op (e1) (op (e3) (e1))) = (op (e3) (e1)))) -> (((op (e0) (e3)) = (e0))\/(((op (e0) (e3)) = (e1))\/(((op (e0) (e3)) = (e2))\/((op (e0) (e3)) = (e3))))) -> ((op (e0) (e1)) = (e0)) -> (~((op (e0) (e1)) = (op (e0) (e3)))) -> (~((op (e0) (e3)) = (op (e3) (e3)))) -> (~((op (e0) (e3)) = (op (e1) (e3)))) -> (~((op (e0) (e3)) = (op (e2) (e3)))) -> (~((op (e1) (e1)) = (op (e1) (e3)))) -> ((op (e1) (e1)) = (e1)) -> (~((op (e1) (e3)) = (op (e2) (e3)))) -> (((op (e1) (e3)) = (e0))\/(((op (e1) (e3)) = (e1))\/(((op (e1) (e3)) = (e2))\/((op (e1) (e3)) = (e3))))) -> (~((op (e3) (e3)) = (e3))) -> False). % 15.55/15.70 do 0 intro. intros zenon_H8e zenon_H8f zenon_H5e zenon_H3d zenon_H140 zenon_H2b8 zenon_H1df zenon_H1f5 zenon_H2af zenon_H1f6 zenon_H1e5 zenon_H4b zenon_H17d zenon_H3c zenon_H23e zenon_H16f zenon_Hde zenon_H2e zenon_H121 zenon_Ha7 zenon_H2d0 zenon_H6a zenon_H10a zenon_H2b4 zenon_H254 zenon_H49 zenon_H1cd zenon_H36 zenon_H80 zenon_Hb4 zenon_H11e zenon_H21 zenon_H244 zenon_H25b zenon_H3e. % 15.55/15.70 apply (zenon_or_s _ _ zenon_H8e); [ zenon_intro zenon_H92 | zenon_intro zenon_H91 ]. % 15.55/15.70 exact (zenon_H8f zenon_H92). % 15.55/15.70 apply (zenon_or_s _ _ zenon_H91); [ zenon_intro zenon_H5d | zenon_intro zenon_H93 ]. % 15.55/15.70 apply (zenon_L14_); trivial. % 15.55/15.70 apply (zenon_or_s _ _ zenon_H93); [ zenon_intro zenon_H63 | zenon_intro zenon_H81 ]. % 15.55/15.70 apply (zenon_L1214_); trivial. % 15.55/15.70 apply (zenon_or_s _ _ zenon_H1f5); [ zenon_intro zenon_Hcf | zenon_intro zenon_H1f9 ]. % 15.55/15.70 apply (zenon_L1218_); trivial. % 15.55/15.70 apply (zenon_or_s _ _ zenon_H1f9); [ zenon_intro zenon_H14a | zenon_intro zenon_H1fa ]. % 15.55/15.70 apply (zenon_L180_); trivial. % 15.55/15.70 apply (zenon_or_s _ _ zenon_H1fa); [ zenon_intro zenon_H32 | zenon_intro zenon_Hd0 ]. % 15.55/15.70 exact (zenon_H2e zenon_H32). % 15.55/15.70 apply (zenon_or_s _ _ zenon_H121); [ zenon_intro zenon_H37 | zenon_intro zenon_H122 ]. % 15.55/15.70 apply (zenon_L33_); trivial. % 15.55/15.70 apply (zenon_or_s _ _ zenon_H122); [ zenon_intro zenon_H11f | zenon_intro zenon_H123 ]. % 15.55/15.70 apply (zenon_L90_); trivial. % 15.55/15.70 apply (zenon_or_s _ _ zenon_H123); [ zenon_intro zenon_Hb5 | zenon_intro zenon_H38 ]. % 15.55/15.70 apply (zenon_L1221_); trivial. % 15.55/15.70 apply (zenon_L1223_); trivial. % 15.55/15.70 (* end of lemma zenon_L1224_ *) % 15.55/15.70 assert (zenon_L1225_ : ((~((op (e3) (e3)) = (e2)))\/((op (e3) (e2)) = (e3))) -> (~((op (e3) (e1)) = (op (e3) (e2)))) -> (((op (e0) (e0)) = (e0))\/(((op (e0) (e1)) = (e0))\/(((op (e0) (e2)) = (e0))\/((op (e0) (e3)) = (e0))))) -> (((op (e0) (e0)) = (e0))\/(((op (e0) (e0)) = (e1))\/(((op (e0) (e0)) = (e2))\/((op (e0) (e0)) = (e3))))) -> (~((op (e0) (e0)) = (e1))) -> (~((op (e0) (e1)) = (op (e1) (e1)))) -> (~((e0) = (e1))) -> (((op (e3) (e3)) = (e0))\/(((op (e3) (e3)) = (e1))\/(((op (e3) (e3)) = (e2))\/((op (e3) (e3)) = (e3))))) -> (((op (e0) (e0)) = (e1))\/(((op (e0) (e1)) = (e1))\/(((op (e0) (e2)) = (e1))\/((op (e0) (e3)) = (e1))))) -> (~((op (e0) (e0)) = (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) (e1)) = (e3)) -> (~((e2) = (e3))) -> (~((op (e0) (op (e3) (e0))) = (op (e3) (e0)))) -> (((op (e2) (e0)) = (e0))\/(((op (e2) (e1)) = (e0))\/(((op (e2) (e2)) = (e0))\/((op (e2) (e3)) = (e0))))) -> (~((e1) = (e2))) -> (~((op (e1) (e1)) = (op (e1) (e3)))) -> ((op (e1) (e1)) = (e1)) -> (((op (e1) (e3)) = (e0))\/(((op (e1) (e3)) = (e1))\/(((op (e1) (e3)) = (e2))\/((op (e1) (e3)) = (e3))))) -> (~((op (e1) (op (e3) (e1))) = (op (e3) (e1)))) -> (~((op (e0) (e3)) = (op (e1) (e3)))) -> (~((op (e1) (e3)) = (op (e2) (e3)))) -> (((op (e0) (e3)) = (e3))\/(((op (e1) (e3)) = (e3))\/(((op (e2) (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 (e2) (e3)))) -> (~((op (e0) (e3)) = (op (e3) (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) (e1)) = (op (e2) (e1)))) -> (~((op (e0) (e1)) = (op (e0) (e2)))) -> (((op (e3) (e0)) = (e0))\/(((op (e3) (e1)) = (e0))\/(((op (e3) (e2)) = (e0))\/((op (e3) (e3)) = (e0))))) -> (~((op (e3) (e3)) = (e0))) -> (~((op (e1) (e2)) = (op (e3) (e2)))) -> (~((e0) = (e3))) -> (~((op (e2) (e0)) = (op (e3) (e0)))) -> (~((op (e2) (e2)) = (e0))) -> (~((op (e2) (op (e3) (e2))) = (op (e3) (e2)))) -> (((op (e0) (e2)) = (e0))\/(((op (e1) (e2)) = (e0))\/(((op (e2) (e2)) = (e0))\/((op (e3) (e2)) = (e0))))) -> (((op (e0) (e0)) = (e2))\/(((op (e0) (e1)) = (e2))\/(((op (e0) (e2)) = (e2))\/((op (e0) (e3)) = (e2))))) -> (~((op (e0) (e0)) = (e0))) -> (~((op (e3) (op (e3) (e3))) = (op (e3) (e3)))) -> ((~((op (e3) (e3)) = (e3)))\/((op (e3) (e3)) = (e3))) -> False). % 15.55/15.70 do 0 intro. intros zenon_H10e zenon_H135 zenon_H110 zenon_H12a zenon_H45 zenon_H23 zenon_H9e zenon_H3b zenon_H44 zenon_H8f zenon_H5e zenon_H1df zenon_H140 zenon_H10a zenon_H6a zenon_H2b8 zenon_H1f5 zenon_Ha7 zenon_H11e zenon_H21 zenon_H25b zenon_H2b4 zenon_H80 zenon_H244 zenon_H2d0 zenon_H254 zenon_Hb4 zenon_H36 zenon_H1cd zenon_H121 zenon_Hde zenon_H23e zenon_H1f6 zenon_H3c zenon_H17d zenon_H4b zenon_H1e5 zenon_H2e zenon_H2af zenon_H16f zenon_H8e zenon_H20 zenon_H2be zenon_H10d. % 15.55/15.70 apply (zenon_or_s _ _ zenon_H10e); [ zenon_intro zenon_H3d | zenon_intro zenon_H106 ]. % 15.55/15.70 apply (zenon_or_s _ _ zenon_H10d); [ zenon_intro zenon_H3e | zenon_intro zenon_H42 ]. % 15.55/15.70 apply (zenon_or_s _ _ zenon_H110); [ zenon_intro zenon_H1f | zenon_intro zenon_H111 ]. % 15.55/15.70 exact (zenon_H20 zenon_H1f). % 15.55/15.70 apply (zenon_or_s _ _ zenon_H111); [ zenon_intro zenon_H49 | zenon_intro zenon_H112 ]. % 15.55/15.70 apply (zenon_L1224_); trivial. % 15.55/15.70 apply (zenon_or_s _ _ zenon_H112); [ zenon_intro zenon_Hab | zenon_intro zenon_Hca ]. % 15.55/15.70 apply (zenon_L132_); trivial. % 15.55/15.70 apply (zenon_L114_); trivial. % 15.55/15.70 apply (zenon_L1041_); trivial. % 15.55/15.70 apply (zenon_L115_); trivial. % 15.55/15.70 (* end of lemma zenon_L1225_ *) % 15.55/15.70 assert (zenon_L1226_ : ((~((op (e3) (e3)) = (e1)))\/((op (e3) (e1)) = (e3))) -> (~((op (e3) (e0)) = (op (e3) (e1)))) -> ((~((op (e3) (e3)) = (e3)))\/((op (e3) (e3)) = (e3))) -> (~((op (e3) (op (e3) (e3))) = (op (e3) (e3)))) -> (~((op (e0) (e0)) = (e1))) -> (~((op (e1) (e0)) = (op (e1) (e1)))) -> ((op (e1) (e1)) = (e1)) -> (((op (e2) (e2)) = (e0))\/(((op (e2) (e2)) = (e1))\/(((op (e2) (e2)) = (e2))\/((op (e2) (e2)) = (e3))))) -> (((op (e3) (e3)) = (e0))\/(((op (e3) (e3)) = (e1))\/(((op (e3) (e3)) = (e2))\/((op (e3) (e3)) = (e3))))) -> (~((op (e2) (e2)) = (e2))) -> (~((op (e2) (e2)) = (e1))) -> (~((op (e2) (e2)) = (e0))) -> (~((e1) = (e3))) -> ((op (e3) (e0)) = (e3)) -> (((op (e0) (e0)) = (e1))\/(((op (e1) (e0)) = (e1))\/(((op (e2) (e0)) = (e1))\/((op (e3) (e0)) = (e1))))) -> (~((op (e3) (e0)) = (op (e3) (e2)))) -> ((~((op (e3) (e3)) = (e2)))\/((op (e3) (e2)) = (e3))) -> False). % 15.55/15.70 do 0 intro. intros zenon_H10c zenon_H109 zenon_H10d zenon_H2be zenon_H45 zenon_Hd7 zenon_H21 zenon_H2d zenon_H3b zenon_H2f zenon_H52 zenon_H2e zenon_Ha3 zenon_Hba zenon_Hf1 zenon_H105 zenon_H10e. % 15.55/15.70 apply (zenon_or_s _ _ zenon_H10c); [ zenon_intro zenon_H104 | zenon_intro zenon_H10a ]. % 15.55/15.70 apply (zenon_or_s _ _ zenon_H10e); [ zenon_intro zenon_H3d | zenon_intro zenon_H106 ]. % 15.55/15.70 apply (zenon_or_s _ _ zenon_H10d); [ zenon_intro zenon_H3e | zenon_intro zenon_H42 ]. % 15.55/15.70 apply (zenon_L80_); trivial. % 15.55/15.70 apply (zenon_L1041_); trivial. % 15.55/15.70 apply (zenon_L81_); trivial. % 15.55/15.70 apply (zenon_L82_); trivial. % 15.55/15.70 (* end of lemma zenon_L1226_ *) % 15.55/15.70 assert (zenon_L1227_ : (((op (e3) (e0)) = (e1))\/(((op (e3) (e1)) = (e1))\/(((op (e3) (e2)) = (e1))\/((op (e3) (e3)) = (e1))))) -> (~((op (e3) (e3)) = (e2))) -> (~((op (e2) (op (e3) (e2))) = (op (e3) (e2)))) -> ((op (e2) (e2)) = (e2)) -> (~((op (e0) (e1)) = (op (e3) (e1)))) -> ((op (e0) (e1)) = (e2)) -> (~((op (e0) (op (e3) (e0))) = (op (e3) (e0)))) -> (((op (e3) (e0)) = (e2))\/(((op (e3) (e1)) = (e2))\/(((op (e3) (e2)) = (e2))\/((op (e3) (e3)) = (e2))))) -> ((op (e1) (e1)) = (e1)) -> (~((op (e1) (op (e3) (e1))) = (op (e3) (e1)))) -> ((op (e0) (e2)) = (e1)) -> (~((op (e0) (e2)) = (op (e3) (e2)))) -> (~((op (e3) (e3)) = (e1))) -> False). % 15.55/15.70 do 0 intro. intros zenon_H146 zenon_H3d zenon_H2af zenon_H35 zenon_H138 zenon_H5d zenon_H2b8 zenon_H1df zenon_H21 zenon_H2b4 zenon_H29 zenon_H140 zenon_H104. % 15.55/15.70 apply (zenon_or_s _ _ zenon_H146); [ zenon_intro zenon_Hee | zenon_intro zenon_H14b ]. % 15.55/15.70 apply (zenon_L1084_); trivial. % 15.55/15.70 apply (zenon_or_s _ _ zenon_H14b); [ zenon_intro zenon_H13e | zenon_intro zenon_H14c ]. % 15.55/15.70 apply (zenon_L1158_); trivial. % 15.55/15.70 apply (zenon_or_s _ _ zenon_H14c); [ zenon_intro zenon_H119 | zenon_intro zenon_H38 ]. % 15.55/15.70 apply (zenon_L124_); trivial. % 15.55/15.70 exact (zenon_H104 zenon_H38). % 15.55/15.70 (* end of lemma zenon_L1227_ *) % 15.55/15.70 assert (zenon_L1228_ : (((op (e0) (e0)) = (e2))\/(((op (e0) (e1)) = (e2))\/(((op (e0) (e2)) = (e2))\/((op (e0) (e3)) = (e2))))) -> (~((op (e0) (e0)) = (e2))) -> (~((op (e0) (e2)) = (op (e3) (e2)))) -> ((op (e0) (e2)) = (e1)) -> (~((op (e1) (op (e3) (e1))) = (op (e3) (e1)))) -> ((op (e1) (e1)) = (e1)) -> (((op (e3) (e0)) = (e2))\/(((op (e3) (e1)) = (e2))\/(((op (e3) (e2)) = (e2))\/((op (e3) (e3)) = (e2))))) -> (~((op (e0) (op (e3) (e0))) = (op (e3) (e0)))) -> (~((op (e0) (e1)) = (op (e3) (e1)))) -> (~((op (e2) (op (e3) (e2))) = (op (e3) (e2)))) -> (~((op (e3) (e3)) = (e2))) -> (((op (e3) (e0)) = (e1))\/(((op (e3) (e1)) = (e1))\/(((op (e3) (e2)) = (e1))\/((op (e3) (e3)) = (e1))))) -> (~((op (e0) (e2)) = (op (e2) (e2)))) -> ((op (e2) (e2)) = (e2)) -> (((op (e3) (e3)) = (e0))\/(((op (e3) (e3)) = (e1))\/(((op (e3) (e3)) = (e2))\/((op (e3) (e3)) = (e3))))) -> (~((op (e3) (e3)) = (e0))) -> (~((op (e3) (e3)) = (e1))) -> (~((op (e0) (e3)) = (op (e3) (e3)))) -> (~((op (e3) (e3)) = (e3))) -> False). % 15.55/15.70 do 0 intro. intros zenon_H8e zenon_H8f zenon_H140 zenon_H29 zenon_H2b4 zenon_H21 zenon_H1df zenon_H2b8 zenon_H138 zenon_H2af zenon_H3d zenon_H146 zenon_H28 zenon_H35 zenon_H3b zenon_H3c zenon_H104 zenon_H36 zenon_H3e. % 15.55/15.70 apply (zenon_or_s _ _ zenon_H8e); [ zenon_intro zenon_H92 | zenon_intro zenon_H91 ]. % 15.55/15.70 exact (zenon_H8f zenon_H92). % 15.55/15.70 apply (zenon_or_s _ _ zenon_H91); [ zenon_intro zenon_H5d | zenon_intro zenon_H93 ]. % 15.55/15.70 apply (zenon_L1227_); trivial. % 15.55/15.70 apply (zenon_or_s _ _ zenon_H93); [ zenon_intro zenon_H63 | zenon_intro zenon_H81 ]. % 15.55/15.70 apply (zenon_L15_); trivial. % 15.55/15.70 apply (zenon_L107_); trivial. % 15.55/15.70 (* end of lemma zenon_L1228_ *) % 15.55/15.70 assert (zenon_L1229_ : ((~((op (e3) (e3)) = (e3)))\/((op (e3) (e3)) = (e3))) -> (~((op (e3) (op (e3) (e3))) = (op (e3) (e3)))) -> (~((op (e0) (e0)) = (e1))) -> (~((op (e0) (e1)) = (op (e1) (e1)))) -> ((op (e1) (e1)) = (e1)) -> (((op (e0) (e0)) = (e2))\/(((op (e0) (e1)) = (e2))\/(((op (e0) (e2)) = (e2))\/((op (e0) (e3)) = (e2))))) -> (~((op (e3) (e3)) = (e0))) -> (~((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 (e2) (e2)))) -> (((op (e3) (e0)) = (e2))\/(((op (e3) (e1)) = (e2))\/(((op (e3) (e2)) = (e2))\/((op (e3) (e3)) = (e2))))) -> (~((op (e3) (e3)) = (e2))) -> ((op (e2) (e2)) = (e2)) -> (~((op (e2) (op (e3) (e2))) = (op (e3) (e2)))) -> (~((op (e0) (e1)) = (op (e3) (e1)))) -> (~((op (e0) (op (e3) (e0))) = (op (e3) (e0)))) -> (~((op (e1) (op (e3) (e1))) = (op (e3) (e1)))) -> (~((op (e0) (e2)) = (op (e3) (e2)))) -> (~((op (e3) (e3)) = (e1))) -> (((op (e3) (e0)) = (e1))\/(((op (e3) (e1)) = (e1))\/(((op (e3) (e2)) = (e1))\/((op (e3) (e3)) = (e1))))) -> (~((op (e0) (e0)) = (e2))) -> (((op (e0) (e0)) = (e1))\/(((op (e0) (e1)) = (e1))\/(((op (e0) (e2)) = (e1))\/((op (e0) (e3)) = (e1))))) -> False). % 15.55/15.70 do 0 intro. intros zenon_H10d zenon_H2be zenon_H45 zenon_H23 zenon_H21 zenon_H8e zenon_H3c zenon_H36 zenon_H3b zenon_H28 zenon_H1df zenon_H3d zenon_H35 zenon_H2af zenon_H138 zenon_H2b8 zenon_H2b4 zenon_H140 zenon_H104 zenon_H146 zenon_H8f zenon_H44. % 15.55/15.70 apply (zenon_or_s _ _ zenon_H10d); [ zenon_intro zenon_H3e | zenon_intro zenon_H42 ]. % 15.55/15.70 apply (zenon_or_s _ _ zenon_H44); [ zenon_intro zenon_H47 | zenon_intro zenon_H46 ]. % 15.55/15.70 exact (zenon_H45 zenon_H47). % 15.55/15.70 apply (zenon_or_s _ _ zenon_H46); [ zenon_intro zenon_H22 | zenon_intro zenon_H48 ]. % 15.55/15.70 apply (zenon_L3_); trivial. % 15.55/15.70 apply (zenon_or_s _ _ zenon_H48); [ zenon_intro zenon_H29 | zenon_intro zenon_H37 ]. % 15.55/15.70 apply (zenon_L1228_); trivial. % 15.55/15.70 apply (zenon_L7_); trivial. % 15.55/15.70 apply (zenon_L1041_); trivial. % 15.55/15.70 (* end of lemma zenon_L1229_ *) % 15.55/15.70 assert (zenon_L1230_ : (((op (e0) (e3)) = (e0))\/(((op (e0) (e3)) = (e1))\/(((op (e0) (e3)) = (e2))\/((op (e0) (e3)) = (e3))))) -> ((op (e0) (e1)) = (e0)) -> (~((op (e0) (e1)) = (op (e0) (e3)))) -> ((op (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). % 15.55/15.70 do 0 intro. intros zenon_H254 zenon_H49 zenon_H1cd zenon_Hb5 zenon_Hb4 zenon_H43 zenon_H36 zenon_H80 zenon_H8a. % 15.55/15.70 apply (zenon_or_s _ _ zenon_H254); [ zenon_intro zenon_Hca | zenon_intro zenon_H255 ]. % 15.55/15.70 apply (zenon_L463_); trivial. % 15.55/15.70 apply (zenon_or_s _ _ zenon_H255); [ zenon_intro zenon_H37 | zenon_intro zenon_H256 ]. % 15.55/15.70 apply (zenon_L41_); trivial. % 15.55/15.70 apply (zenon_or_s _ _ zenon_H256); [ zenon_intro zenon_H81 | zenon_intro zenon_H53 ]. % 15.55/15.70 apply (zenon_L106_); trivial. % 15.55/15.70 apply (zenon_L293_); trivial. % 15.55/15.70 (* end of lemma zenon_L1230_ *) % 15.55/15.70 assert (zenon_L1231_ : (((op (e3) (e0)) = (e2))\/(((op (e3) (e1)) = (e2))\/(((op (e3) (e2)) = (e2))\/((op (e3) (e3)) = (e2))))) -> (~((op (e3) (e3)) = (e1))) -> (~((op (e0) (e2)) = (op (e3) (e2)))) -> ((op (e0) (e2)) = (e1)) -> (~((op (e1) (op (e3) (e1))) = (op (e3) (e1)))) -> ((op (e1) (e1)) = (e1)) -> (~((op (e0) (op (e3) (e0))) = (op (e3) (e0)))) -> (((op (e3) (e0)) = (e1))\/(((op (e3) (e1)) = (e1))\/(((op (e3) (e2)) = (e1))\/((op (e3) (e3)) = (e1))))) -> ((op (e0) (e1)) = (e2)) -> (~((op (e0) (e1)) = (op (e3) (e1)))) -> ((op (e2) (e2)) = (e2)) -> (~((op (e2) (op (e3) (e2))) = (op (e3) (e2)))) -> (((op (e0) (e3)) = (e0))\/(((op (e0) (e3)) = (e1))\/(((op (e0) (e3)) = (e2))\/((op (e0) (e3)) = (e3))))) -> ((op (e0) (e1)) = (e0)) -> (~((op (e0) (e1)) = (op (e0) (e3)))) -> ((op (e2) (e3)) = (e1)) -> (~((op (e0) (e3)) = (op (e2) (e3)))) -> (~((op (e0) (e3)) = (op (e3) (e3)))) -> (~((op (e0) (e3)) = (op (e1) (e3)))) -> ((op (e1) (e3)) = (e3)) -> False). % 15.55/15.70 do 0 intro. intros zenon_H1df zenon_H104 zenon_H140 zenon_H29 zenon_H2b4 zenon_H21 zenon_H2b8 zenon_H146 zenon_H5d zenon_H138 zenon_H35 zenon_H2af zenon_H254 zenon_H49 zenon_H1cd zenon_Hb5 zenon_Hb4 zenon_H36 zenon_H80 zenon_H8a. % 15.55/15.70 apply (zenon_or_s _ _ zenon_H1df); [ zenon_intro zenon_He9 | zenon_intro zenon_H1e0 ]. % 15.55/15.70 apply (zenon_L1163_); trivial. % 15.55/15.70 apply (zenon_or_s _ _ zenon_H1e0); [ zenon_intro zenon_H16a | zenon_intro zenon_H1e1 ]. % 15.55/15.70 apply (zenon_L146_); trivial. % 15.55/15.70 apply (zenon_or_s _ _ zenon_H1e1); [ zenon_intro zenon_H1dd | zenon_intro zenon_H43 ]. % 15.55/15.70 apply (zenon_L1083_); trivial. % 15.55/15.70 apply (zenon_L1230_); trivial. % 15.55/15.70 (* end of lemma zenon_L1231_ *) % 15.55/15.70 assert (zenon_L1232_ : (((op (e2) (e0)) = (e1))\/(((op (e2) (e1)) = (e1))\/(((op (e2) (e2)) = (e1))\/((op (e2) (e3)) = (e1))))) -> ((op (e2) (e0)) = (e3)) -> (~((op (e1) (e1)) = (op (e2) (e1)))) -> (((op (e0) (e2)) = (e1))\/(((op (e1) (e2)) = (e1))\/(((op (e2) (e2)) = (e1))\/((op (e3) (e2)) = (e1))))) -> ((op (e1) (e3)) = (e3)) -> (~((op (e0) (e3)) = (op (e1) (e3)))) -> (~((op (e0) (e3)) = (op (e3) (e3)))) -> (~((op (e0) (e3)) = (op (e2) (e3)))) -> (~((op (e0) (e1)) = (op (e0) (e3)))) -> ((op (e0) (e1)) = (e0)) -> (((op (e0) (e3)) = (e0))\/(((op (e0) (e3)) = (e1))\/(((op (e0) (e3)) = (e2))\/((op (e0) (e3)) = (e3))))) -> (~((op (e2) (op (e3) (e2))) = (op (e3) (e2)))) -> ((op (e2) (e2)) = (e2)) -> (~((op (e0) (e1)) = (op (e3) (e1)))) -> ((op (e0) (e1)) = (e2)) -> (((op (e3) (e0)) = (e1))\/(((op (e3) (e1)) = (e1))\/(((op (e3) (e2)) = (e1))\/((op (e3) (e3)) = (e1))))) -> (~((op (e0) (op (e3) (e0))) = (op (e3) (e0)))) -> (~((op (e1) (op (e3) (e1))) = (op (e3) (e1)))) -> (~((op (e0) (e2)) = (op (e3) (e2)))) -> (~((op (e3) (e3)) = (e1))) -> (((op (e3) (e0)) = (e2))\/(((op (e3) (e1)) = (e2))\/(((op (e3) (e2)) = (e2))\/((op (e3) (e3)) = (e2))))) -> ((op (e1) (e1)) = (e1)) -> (~((op (e1) (e1)) = (op (e1) (e2)))) -> (~((op (e2) (e2)) = (e1))) -> (~((e1) = (e3))) -> ((op (e3) (e2)) = (e3)) -> False). % 15.55/15.70 do 0 intro. intros zenon_Hb7 zenon_Haf zenon_Hb1 zenon_H11b zenon_H8a zenon_H80 zenon_H36 zenon_Hb4 zenon_H1cd zenon_H49 zenon_H254 zenon_H2af zenon_H35 zenon_H138 zenon_H5d zenon_H146 zenon_H2b8 zenon_H2b4 zenon_H140 zenon_H104 zenon_H1df zenon_H21 zenon_H116 zenon_H52 zenon_Ha3 zenon_H106. % 15.55/15.70 apply (zenon_or_s _ _ zenon_Hb7); [ zenon_intro zenon_Hae | zenon_intro zenon_Hb8 ]. % 15.55/15.70 apply (zenon_L39_); trivial. % 15.55/15.70 apply (zenon_or_s _ _ zenon_Hb8); [ zenon_intro zenon_Hb2 | zenon_intro zenon_Hb9 ]. % 15.55/15.70 apply (zenon_L40_); trivial. % 15.55/15.70 apply (zenon_or_s _ _ zenon_Hb9); [ zenon_intro zenon_H2a | zenon_intro zenon_Hb5 ]. % 15.55/15.70 exact (zenon_H52 zenon_H2a). % 15.55/15.70 apply (zenon_or_s _ _ zenon_H11b); [ zenon_intro zenon_H29 | zenon_intro zenon_H11c ]. % 15.55/15.70 apply (zenon_L1231_); trivial. % 15.55/15.70 apply (zenon_or_s _ _ zenon_H11c); [ zenon_intro zenon_H117 | zenon_intro zenon_H11d ]. % 15.55/15.70 apply (zenon_L86_); trivial. % 15.55/15.70 apply (zenon_or_s _ _ zenon_H11d); [ zenon_intro zenon_H2a | zenon_intro zenon_H119 ]. % 15.55/15.70 exact (zenon_H52 zenon_H2a). % 15.55/15.70 apply (zenon_L87_); trivial. % 15.55/15.70 (* end of lemma zenon_L1232_ *) % 15.55/15.70 assert (zenon_L1233_ : (((op (e3) (e0)) = (e1))\/(((op (e3) (e1)) = (e1))\/(((op (e3) (e2)) = (e1))\/((op (e3) (e3)) = (e1))))) -> ((op (e3) (e0)) = (e3)) -> (~((e1) = (e3))) -> ((op (e3) (e1)) = (e2)) -> (~((op (e1) (op (e3) (e1))) = (op (e3) (e1)))) -> ((op (e1) (e2)) = (e1)) -> (~((op (e1) (e2)) = (op (e3) (e2)))) -> (~((op (e3) (e3)) = (e1))) -> False). % 15.55/15.70 do 0 intro. intros zenon_H146 zenon_Hba zenon_Ha3 zenon_H16a zenon_H2b4 zenon_H117 zenon_H17d zenon_H104. % 15.55/15.70 apply (zenon_or_s _ _ zenon_H146); [ zenon_intro zenon_Hee | zenon_intro zenon_H14b ]. % 15.55/15.70 apply (zenon_L79_); trivial. % 15.55/15.70 apply (zenon_or_s _ _ zenon_H14b); [ zenon_intro zenon_H13e | zenon_intro zenon_H14c ]. % 15.55/15.70 apply (zenon_L1092_); trivial. % 15.55/15.70 apply (zenon_or_s _ _ zenon_H14c); [ zenon_intro zenon_H119 | zenon_intro zenon_H38 ]. % 15.55/15.70 apply (zenon_L759_); trivial. % 15.55/15.70 exact (zenon_H104 zenon_H38). % 15.55/15.70 (* end of lemma zenon_L1233_ *) % 15.55/15.70 assert (zenon_L1234_ : (((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 (e1) (e2)) = (op (e3) (e2)))) -> (~((op (e1) (e2)) = (op (e2) (e2)))) -> ((op (e2) (e2)) = (e2)) -> (~((op (e0) (e2)) = (op (e1) (e2)))) -> ((op (e0) (e2)) = (e3)) -> False). % 15.55/15.70 do 0 intro. intros zenon_H1d5 zenon_H167 zenon_H119 zenon_H17d zenon_H7d zenon_H35 zenon_H87 zenon_H50. % 15.55/15.70 apply (zenon_or_s _ _ zenon_H1d5); [ zenon_intro zenon_H15d | zenon_intro zenon_H1d6 ]. % 15.55/15.70 apply (zenon_L626_); trivial. % 15.55/15.70 apply (zenon_or_s _ _ zenon_H1d6); [ zenon_intro zenon_H117 | zenon_intro zenon_H1d7 ]. % 15.55/15.70 apply (zenon_L759_); trivial. % 15.55/15.70 apply (zenon_or_s _ _ zenon_H1d7); [ zenon_intro zenon_H7c | zenon_intro zenon_H88 ]. % 15.55/15.70 apply (zenon_L21_); trivial. % 15.55/15.70 apply (zenon_L24_); trivial. % 15.55/15.70 (* end of lemma zenon_L1234_ *) % 15.55/15.70 assert (zenon_L1235_ : (((op (e3) (e0)) = (e0))\/(((op (e3) (e1)) = (e0))\/(((op (e3) (e2)) = (e0))\/((op (e3) (e3)) = (e0))))) -> ((op (e3) (e0)) = (e3)) -> (~((e0) = (e3))) -> ((op (e1) (e0)) = (e2)) -> (~((op (e1) (op (e3) (e1))) = (op (e3) (e1)))) -> ((op (e0) (e2)) = (e3)) -> (~((op (e0) (e2)) = (op (e1) (e2)))) -> ((op (e2) (e2)) = (e2)) -> (~((op (e1) (e2)) = (op (e2) (e2)))) -> (~((op (e1) (e2)) = (op (e3) (e2)))) -> ((op (e3) (e2)) = (e1)) -> (((op (e1) (e2)) = (e0))\/(((op (e1) (e2)) = (e1))\/(((op (e1) (e2)) = (e2))\/((op (e1) (e2)) = (e3))))) -> ((op (e3) (e1)) = (e2)) -> ((op (e0) (e0)) = (e1)) -> False). % 15.55/15.70 do 0 intro. intros zenon_H1f6 zenon_Hba zenon_H4b zenon_H68 zenon_H2b4 zenon_H50 zenon_H87 zenon_H35 zenon_H7d zenon_H17d zenon_H119 zenon_H1d5 zenon_H16a zenon_H47. % 15.55/15.70 apply (zenon_or_s _ _ zenon_H1f6); [ zenon_intro zenon_Hdb | zenon_intro zenon_H1f7 ]. % 15.55/15.70 apply (zenon_L62_); trivial. % 15.55/15.70 apply (zenon_or_s _ _ zenon_H1f7); [ zenon_intro zenon_H142 | zenon_intro zenon_H1f8 ]. % 15.55/15.70 apply (zenon_L1104_); trivial. % 15.55/15.70 apply (zenon_or_s _ _ zenon_H1f8); [ zenon_intro zenon_H167 | zenon_intro zenon_H40 ]. % 15.55/15.70 apply (zenon_L1234_); trivial. % 15.55/15.70 apply (zenon_L186_); trivial. % 15.55/15.70 (* end of lemma zenon_L1235_ *) % 15.55/15.70 assert (zenon_L1236_ : (((op (e0) (e2)) = (e0))\/(((op (e0) (e2)) = (e1))\/(((op (e0) (e2)) = (e2))\/((op (e0) (e2)) = (e3))))) -> ((op (e0) (e1)) = (e0)) -> (~((op (e0) (e1)) = (op (e0) (e2)))) -> ((op (e3) (e2)) = (e1)) -> (~((op (e0) (e2)) = (op (e3) (e2)))) -> (~((op (e0) (e2)) = (op (e2) (e2)))) -> ((op (e2) (e2)) = (e2)) -> (~((op (e0) (e2)) = (op (e1) (e2)))) -> ((op (e1) (e2)) = (e3)) -> False). % 15.55/15.70 do 0 intro. intros zenon_H251 zenon_H49 zenon_H23e zenon_H119 zenon_H140 zenon_H28 zenon_H35 zenon_H87 zenon_H88. % 15.55/15.70 apply (zenon_or_s _ _ zenon_H251); [ zenon_intro zenon_Hab | zenon_intro zenon_H252 ]. % 15.55/15.70 apply (zenon_L485_); trivial. % 15.55/15.70 apply (zenon_or_s _ _ zenon_H252); [ zenon_intro zenon_H29 | zenon_intro zenon_H253 ]. % 15.55/15.70 apply (zenon_L124_); trivial. % 15.55/15.70 apply (zenon_or_s _ _ zenon_H253); [ zenon_intro zenon_H63 | zenon_intro zenon_H50 ]. % 15.55/15.70 apply (zenon_L15_); trivial. % 15.55/15.70 apply (zenon_L24_); trivial. % 15.55/15.70 (* end of lemma zenon_L1236_ *) % 15.55/15.70 assert (zenon_L1237_ : (((op (e0) (e1)) = (e2))\/(((op (e1) (e1)) = (e2))\/(((op (e2) (e1)) = (e2))\/((op (e3) (e1)) = (e2))))) -> (~((op (e3) (e3)) = (e2))) -> (~((op (e2) (op (e3) (e2))) = (op (e3) (e2)))) -> (~((op (e0) (e1)) = (op (e3) (e1)))) -> (~((e2) = (e3))) -> (((op (e3) (e0)) = (e2))\/(((op (e3) (e1)) = (e2))\/(((op (e3) (e2)) = (e2))\/((op (e3) (e3)) = (e2))))) -> (~((op (e1) (e1)) = (e2))) -> (~((op (e2) (e1)) = (op (e2) (e2)))) -> (((op (e0) (e2)) = (e1))\/(((op (e1) (e2)) = (e1))\/(((op (e2) (e2)) = (e1))\/((op (e3) (e2)) = (e1))))) -> ((op (e1) (e1)) = (e1)) -> (~((op (e3) (e3)) = (e1))) -> (((op (e3) (e0)) = (e1))\/(((op (e3) (e1)) = (e1))\/(((op (e3) (e2)) = (e1))\/((op (e3) (e3)) = (e1))))) -> (~((op (e2) (e2)) = (e1))) -> (((op (e0) (e2)) = (e3))\/(((op (e1) (e2)) = (e3))\/(((op (e2) (e2)) = (e3))\/((op (e3) (e2)) = (e3))))) -> ((op (e0) (e0)) = (e1)) -> (((op (e1) (e2)) = (e0))\/(((op (e1) (e2)) = (e1))\/(((op (e1) (e2)) = (e2))\/((op (e1) (e2)) = (e3))))) -> (~((op (e1) (e2)) = (op (e3) (e2)))) -> (~((op (e1) (e2)) = (op (e2) (e2)))) -> (~((op (e1) (op (e3) (e1))) = (op (e3) (e1)))) -> ((op (e1) (e0)) = (e2)) -> (~((e0) = (e3))) -> ((op (e3) (e0)) = (e3)) -> (((op (e3) (e0)) = (e0))\/(((op (e3) (e1)) = (e0))\/(((op (e3) (e2)) = (e0))\/((op (e3) (e3)) = (e0))))) -> (~((op (e0) (e2)) = (op (e1) (e2)))) -> ((op (e2) (e2)) = (e2)) -> (~((op (e0) (e2)) = (op (e2) (e2)))) -> (~((op (e0) (e2)) = (op (e3) (e2)))) -> (~((op (e0) (e1)) = (op (e0) (e2)))) -> ((op (e0) (e1)) = (e0)) -> (((op (e0) (e2)) = (e0))\/(((op (e0) (e2)) = (e1))\/(((op (e0) (e2)) = (e2))\/((op (e0) (e2)) = (e3))))) -> (~((op (e2) (e2)) = (e3))) -> (~((e1) = (e3))) -> False). % 15.55/15.70 do 0 intro. intros zenon_H1a2 zenon_H3d zenon_H2af zenon_H138 zenon_H6a zenon_H1df zenon_Hd6 zenon_H157 zenon_H11b zenon_H21 zenon_H104 zenon_H146 zenon_H52 zenon_H175 zenon_H47 zenon_H1d5 zenon_H17d zenon_H7d zenon_H2b4 zenon_H68 zenon_H4b zenon_Hba zenon_H1f6 zenon_H87 zenon_H35 zenon_H28 zenon_H140 zenon_H23e zenon_H49 zenon_H251 zenon_H30 zenon_Ha3. % 15.55/15.70 apply (zenon_or_s _ _ zenon_H1a2); [ zenon_intro zenon_H5d | zenon_intro zenon_H1a3 ]. % 15.55/15.70 apply (zenon_L1091_); trivial. % 15.55/15.70 apply (zenon_or_s _ _ zenon_H1a3); [ zenon_intro zenon_H6e | zenon_intro zenon_H1a4 ]. % 15.55/15.70 exact (zenon_Hd6 zenon_H6e). % 15.55/15.70 apply (zenon_or_s _ _ zenon_H1a4); [ zenon_intro zenon_H156 | zenon_intro zenon_H16a ]. % 15.55/15.70 apply (zenon_L134_); trivial. % 15.55/15.70 apply (zenon_or_s _ _ zenon_H11b); [ zenon_intro zenon_H29 | zenon_intro zenon_H11c ]. % 15.55/15.70 apply (zenon_L1159_); trivial. % 15.55/15.70 apply (zenon_or_s _ _ zenon_H11c); [ zenon_intro zenon_H117 | zenon_intro zenon_H11d ]. % 15.55/15.70 apply (zenon_L1233_); trivial. % 15.55/15.70 apply (zenon_or_s _ _ zenon_H11d); [ zenon_intro zenon_H2a | zenon_intro zenon_H119 ]. % 15.55/15.70 exact (zenon_H52 zenon_H2a). % 15.55/15.70 apply (zenon_or_s _ _ zenon_H175); [ zenon_intro zenon_H50 | zenon_intro zenon_H176 ]. % 15.55/15.70 apply (zenon_L1235_); trivial. % 15.55/15.70 apply (zenon_or_s _ _ zenon_H176); [ zenon_intro zenon_H88 | zenon_intro zenon_H177 ]. % 15.55/15.70 apply (zenon_L1236_); trivial. % 15.55/15.70 apply (zenon_or_s _ _ zenon_H177); [ zenon_intro zenon_H34 | zenon_intro zenon_H106 ]. % 15.55/15.70 exact (zenon_H30 zenon_H34). % 15.55/15.70 apply (zenon_L87_); trivial. % 15.55/15.70 (* end of lemma zenon_L1237_ *) % 15.55/15.70 assert (zenon_L1238_ : ((~((op (e3) (e3)) = (e2)))\/((op (e3) (e2)) = (e3))) -> (~((op (e3) (e0)) = (op (e3) (e2)))) -> (((op (e0) (e0)) = (e2))\/(((op (e1) (e0)) = (e2))\/(((op (e2) (e0)) = (e2))\/((op (e3) (e0)) = (e2))))) -> (~((op (e2) (e0)) = (op (e2) (e2)))) -> (((op (e3) (e0)) = (e2))\/(((op (e3) (e1)) = (e2))\/(((op (e3) (e2)) = (e2))\/((op (e3) (e3)) = (e2))))) -> ((op (e2) (e2)) = (e2)) -> (~((op (e2) (op (e3) (e2))) = (op (e3) (e2)))) -> (~((op (e0) (e1)) = (op (e3) (e1)))) -> ((op (e3) (e0)) = (e3)) -> (~((e2) = (e3))) -> (~((op (e1) (e1)) = (e2))) -> (~((op (e2) (e1)) = (op (e2) (e2)))) -> (((op (e0) (e2)) = (e1))\/(((op (e1) (e2)) = (e1))\/(((op (e2) (e2)) = (e1))\/((op (e3) (e2)) = (e1))))) -> (((op (e3) (e0)) = (e0))\/(((op (e3) (e1)) = (e0))\/(((op (e3) (e2)) = (e0))\/((op (e3) (e3)) = (e0))))) -> (~((op (e1) (e2)) = (op (e2) (e2)))) -> (~((op (e0) (e2)) = (op (e1) (e2)))) -> (((op (e1) (e2)) = (e0))\/(((op (e1) (e2)) = (e1))\/(((op (e1) (e2)) = (e2))\/((op (e1) (e2)) = (e3))))) -> (~((e0) = (e3))) -> (((op (e0) (e2)) = (e0))\/(((op (e0) (e2)) = (e1))\/(((op (e0) (e2)) = (e2))\/((op (e0) (e2)) = (e3))))) -> (~((op (e0) (e2)) = (op (e2) (e2)))) -> ((op (e0) (e1)) = (e0)) -> (~((op (e0) (e1)) = (op (e0) (e2)))) -> (~((op (e2) (e2)) = (e3))) -> (((op (e0) (e2)) = (e3))\/(((op (e1) (e2)) = (e3))\/(((op (e2) (e2)) = (e3))\/((op (e3) (e2)) = (e3))))) -> (~((op (e2) (e2)) = (e1))) -> (~((op (e1) (e2)) = (op (e3) (e2)))) -> (~((e1) = (e3))) -> (~((op (e1) (op (e3) (e1))) = (op (e3) (e1)))) -> ((op (e1) (e1)) = (e1)) -> (~((op (e0) (e2)) = (op (e3) (e2)))) -> (~((op (e3) (e3)) = (e1))) -> (((op (e3) (e0)) = (e1))\/(((op (e3) (e1)) = (e1))\/(((op (e3) (e2)) = (e1))\/((op (e3) (e3)) = (e1))))) -> (((op (e0) (e1)) = (e2))\/(((op (e1) (e1)) = (e2))\/(((op (e2) (e1)) = (e2))\/((op (e3) (e1)) = (e2))))) -> (~((op (e0) (e0)) = (e2))) -> (~((op (e0) (e1)) = (op (e1) (e1)))) -> (((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)) = (e1))\/(((op (e0) (e2)) = (e1))\/((op (e0) (e3)) = (e1))))) -> False). % 15.55/15.70 do 0 intro. intros zenon_H10e zenon_H105 zenon_Heb zenon_H17a zenon_H1df zenon_H35 zenon_H2af zenon_H138 zenon_Hba zenon_H6a zenon_Hd6 zenon_H157 zenon_H11b zenon_H1f6 zenon_H7d zenon_H87 zenon_H1d5 zenon_H4b zenon_H251 zenon_H28 zenon_H49 zenon_H23e zenon_H30 zenon_H175 zenon_H52 zenon_H17d zenon_Ha3 zenon_H2b4 zenon_H21 zenon_H140 zenon_H104 zenon_H146 zenon_H1a2 zenon_H8f zenon_H23 zenon_H8e zenon_Ha7 zenon_H44. % 15.55/15.70 apply (zenon_or_s _ _ zenon_H10e); [ zenon_intro zenon_H3d | zenon_intro zenon_H106 ]. % 15.55/15.70 apply (zenon_or_s _ _ zenon_H44); [ zenon_intro zenon_H47 | zenon_intro zenon_H46 ]. % 15.55/15.70 apply (zenon_or_s _ _ zenon_Heb); [ zenon_intro zenon_H92 | zenon_intro zenon_Hec ]. % 15.55/15.70 exact (zenon_H8f zenon_H92). % 15.55/15.70 apply (zenon_or_s _ _ zenon_Hec); [ zenon_intro zenon_H68 | zenon_intro zenon_Hed ]. % 15.55/15.70 apply (zenon_L1237_); trivial. % 15.55/15.70 apply (zenon_or_s _ _ zenon_Hed); [ zenon_intro zenon_Hdd | zenon_intro zenon_He9 ]. % 15.55/15.70 apply (zenon_L161_); trivial. % 15.55/15.70 apply (zenon_L220_); trivial. % 15.55/15.70 apply (zenon_or_s _ _ zenon_H46); [ zenon_intro zenon_H22 | zenon_intro zenon_H48 ]. % 15.55/15.70 apply (zenon_L3_); trivial. % 15.55/15.70 apply (zenon_or_s _ _ zenon_H48); [ zenon_intro zenon_H29 | zenon_intro zenon_H37 ]. % 15.55/15.70 apply (zenon_L1159_); trivial. % 15.55/15.70 apply (zenon_L1177_); trivial. % 15.55/15.70 apply (zenon_L81_); trivial. % 15.55/15.70 (* end of lemma zenon_L1238_ *) % 15.55/15.70 assert (zenon_L1239_ : ((op (e3) (e2)) = (e3)) -> (~((e1) = (e3))) -> (~((op (e2) (e2)) = (e1))) -> (~((op (e1) (e1)) = (op (e1) (e2)))) -> ((op (e1) (e1)) = (e1)) -> (((op (e3) (e0)) = (e1))\/(((op (e3) (e1)) = (e1))\/(((op (e3) (e2)) = (e1))\/((op (e3) (e3)) = (e1))))) -> (~((op (e0) (op (e3) (e0))) = (op (e3) (e0)))) -> (~((op (e1) (op (e3) (e1))) = (op (e3) (e1)))) -> (~((op (e0) (e2)) = (op (e3) (e2)))) -> (((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)) = (e3))\/(((op (e1) (e0)) = (e3))\/(((op (e2) (e0)) = (e3))\/((op (e3) (e0)) = (e3))))) -> (~((op (e0) (e0)) = (e3))) -> (((op (e0) (e3)) = (e0))\/(((op (e0) (e3)) = (e1))\/(((op (e0) (e3)) = (e2))\/((op (e0) (e3)) = (e3))))) -> (~((op (e0) (e1)) = (op (e0) (e3)))) -> (~((op (e0) (e3)) = (op (e2) (e3)))) -> (~((op (e0) (e3)) = (op (e1) (e3)))) -> (~((op (e1) (e1)) = (op (e2) (e1)))) -> (((op (e2) (e0)) = (e1))\/(((op (e2) (e1)) = (e1))\/(((op (e2) (e2)) = (e1))\/((op (e2) (e3)) = (e1))))) -> (~((op (e1) (e1)) = (e3))) -> (((op (e1) (e0)) = (e3))\/(((op (e1) (e1)) = (e3))\/(((op (e1) (e2)) = (e3))\/((op (e1) (e3)) = (e3))))) -> ((~((op (e3) (e3)) = (e2)))\/((op (e3) (e2)) = (e3))) -> (~((op (e3) (e0)) = (op (e3) (e2)))) -> (((op (e0) (e0)) = (e2))\/(((op (e1) (e0)) = (e2))\/(((op (e2) (e0)) = (e2))\/((op (e3) (e0)) = (e2))))) -> (((op (e3) (e0)) = (e2))\/(((op (e3) (e1)) = (e2))\/(((op (e3) (e2)) = (e2))\/((op (e3) (e3)) = (e2))))) -> (~((op (e2) (op (e3) (e2))) = (op (e3) (e2)))) -> (~((op (e0) (e1)) = (op (e3) (e1)))) -> (~((e2) = (e3))) -> (~((op (e1) (e1)) = (e2))) -> (~((op (e2) (e1)) = (op (e2) (e2)))) -> (((op (e3) (e0)) = (e0))\/(((op (e3) (e1)) = (e0))\/(((op (e3) (e2)) = (e0))\/((op (e3) (e3)) = (e0))))) -> (~((op (e1) (e2)) = (op (e2) (e2)))) -> (~((op (e0) (e2)) = (op (e1) (e2)))) -> (((op (e1) (e2)) = (e0))\/(((op (e1) (e2)) = (e1))\/(((op (e1) (e2)) = (e2))\/((op (e1) (e2)) = (e3))))) -> (~((e0) = (e3))) -> (((op (e0) (e2)) = (e0))\/(((op (e0) (e2)) = (e1))\/(((op (e0) (e2)) = (e2))\/((op (e0) (e2)) = (e3))))) -> ((op (e0) (e1)) = (e0)) -> (~((op (e0) (e1)) = (op (e0) (e2)))) -> (~((op (e2) (e2)) = (e3))) -> (((op (e0) (e2)) = (e3))\/(((op (e1) (e2)) = (e3))\/(((op (e2) (e2)) = (e3))\/((op (e3) (e2)) = (e3))))) -> (~((op (e1) (e2)) = (op (e3) (e2)))) -> (((op (e0) (e1)) = (e2))\/(((op (e1) (e1)) = (e2))\/(((op (e2) (e1)) = (e2))\/((op (e3) (e1)) = (e2))))) -> (~((op (e0) (e0)) = (e2))) -> (~((op (e0) (e1)) = (op (e1) (e1)))) -> (((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)) = (e1))\/(((op (e0) (e2)) = (e1))\/((op (e0) (e3)) = (e1))))) -> (~((op (e0) (e2)) = (op (e2) (e2)))) -> ((op (e2) (e2)) = (e2)) -> (((op (e3) (e3)) = (e0))\/(((op (e3) (e3)) = (e1))\/(((op (e3) (e3)) = (e2))\/((op (e3) (e3)) = (e3))))) -> (~((op (e3) (e3)) = (e0))) -> (~((op (e3) (e3)) = (e1))) -> (~((op (e0) (e3)) = (op (e3) (e3)))) -> (~((op (e3) (e3)) = (e3))) -> False). % 15.55/15.70 do 0 intro. intros zenon_H106 zenon_Ha3 zenon_H52 zenon_H116 zenon_H21 zenon_H146 zenon_H2b8 zenon_H2b4 zenon_H140 zenon_H11b zenon_H17a zenon_Hbe zenon_H59 zenon_H254 zenon_H1cd zenon_Hb4 zenon_H80 zenon_Hb1 zenon_Hb7 zenon_H182 zenon_H90 zenon_H10e zenon_H105 zenon_Heb zenon_H1df zenon_H2af zenon_H138 zenon_H6a zenon_Hd6 zenon_H157 zenon_H1f6 zenon_H7d zenon_H87 zenon_H1d5 zenon_H4b zenon_H251 zenon_H49 zenon_H23e zenon_H30 zenon_H175 zenon_H17d zenon_H1a2 zenon_H8f zenon_H23 zenon_H8e zenon_Ha7 zenon_H44 zenon_H28 zenon_H35 zenon_H3b zenon_H3c zenon_H104 zenon_H36 zenon_H3e. % 15.55/15.70 apply (zenon_or_s _ _ zenon_H8e); [ zenon_intro zenon_H92 | zenon_intro zenon_H91 ]. % 15.55/15.70 exact (zenon_H8f zenon_H92). % 15.55/15.70 apply (zenon_or_s _ _ zenon_H91); [ zenon_intro zenon_H5d | zenon_intro zenon_H93 ]. % 15.55/15.70 apply (zenon_or_s _ _ zenon_Heb); [ zenon_intro zenon_H92 | zenon_intro zenon_Hec ]. % 15.55/15.70 exact (zenon_H8f zenon_H92). % 15.55/15.70 apply (zenon_or_s _ _ zenon_Hec); [ zenon_intro zenon_H68 | zenon_intro zenon_Hed ]. % 15.55/15.70 apply (zenon_or_s _ _ zenon_Hbe); [ zenon_intro zenon_H5b | zenon_intro zenon_Hbf ]. % 15.55/15.70 exact (zenon_H59 zenon_H5b). % 15.55/15.70 apply (zenon_or_s _ _ zenon_Hbf); [ zenon_intro zenon_H69 | zenon_intro zenon_Hc0 ]. % 15.55/15.70 apply (zenon_L17_); trivial. % 15.55/15.70 apply (zenon_or_s _ _ zenon_Hc0); [ zenon_intro zenon_Haf | zenon_intro zenon_Hba ]. % 15.55/15.70 apply (zenon_or_s _ _ zenon_H90); [ zenon_intro zenon_H69 | zenon_intro zenon_H94 ]. % 15.55/15.70 apply (zenon_L17_); trivial. % 15.55/15.70 apply (zenon_or_s _ _ zenon_H94); [ zenon_intro zenon_H96 | zenon_intro zenon_H95 ]. % 15.55/15.70 exact (zenon_H182 zenon_H96). % 15.55/15.70 apply (zenon_or_s _ _ zenon_H95); [ zenon_intro zenon_H88 | zenon_intro zenon_H8a ]. % 15.55/15.70 apply (zenon_L164_); trivial. % 15.55/15.70 apply (zenon_L1232_); trivial. % 15.55/15.70 apply (zenon_L1238_); trivial. % 15.55/15.70 apply (zenon_or_s _ _ zenon_Hed); [ zenon_intro zenon_Hdd | zenon_intro zenon_He9 ]. % 15.55/15.70 apply (zenon_L161_); trivial. % 15.55/15.70 apply (zenon_L1175_); trivial. % 15.55/15.70 apply (zenon_or_s _ _ zenon_H93); [ zenon_intro zenon_H63 | zenon_intro zenon_H81 ]. % 15.55/15.70 apply (zenon_L15_); trivial. % 15.55/15.70 apply (zenon_L107_); trivial. % 15.55/15.70 (* end of lemma zenon_L1239_ *) % 15.55/15.70 assert (zenon_L1240_ : (((op (e3) (e0)) = (e0))\/(((op (e3) (e1)) = (e0))\/(((op (e3) (e2)) = (e0))\/((op (e3) (e3)) = (e0))))) -> ((op (e3) (e0)) = (e3)) -> (~((e0) = (e3))) -> ((op (e1) (e0)) = (e0)) -> (~((op (e1) (op (e3) (e1))) = (op (e3) (e1)))) -> ((op (e0) (e2)) = (e0)) -> (~((op (e0) (e2)) = (op (e3) (e2)))) -> ((op (e3) (e2)) = (e1)) -> ((op (e0) (e0)) = (e2)) -> False). % 15.55/15.70 do 0 intro. intros zenon_H1f6 zenon_Hba zenon_H4b zenon_Had zenon_H2b4 zenon_Hab zenon_H140 zenon_H119 zenon_H92. % 15.55/15.70 apply (zenon_or_s _ _ zenon_H1f6); [ zenon_intro zenon_Hdb | zenon_intro zenon_H1f7 ]. % 15.55/15.70 apply (zenon_L62_); trivial. % 15.55/15.70 apply (zenon_or_s _ _ zenon_H1f7); [ zenon_intro zenon_H142 | zenon_intro zenon_H1f8 ]. % 15.55/15.70 apply (zenon_L1136_); trivial. % 15.55/15.70 apply (zenon_or_s _ _ zenon_H1f8); [ zenon_intro zenon_H167 | zenon_intro zenon_H40 ]. % 15.55/15.70 apply (zenon_L267_); trivial. % 15.55/15.70 apply (zenon_L265_); trivial. % 15.55/15.70 (* end of lemma zenon_L1240_ *) % 15.55/15.70 assert (zenon_L1241_ : (((op (e0) (e2)) = (e1))\/(((op (e1) (e2)) = (e1))\/(((op (e2) (e2)) = (e1))\/((op (e3) (e2)) = (e1))))) -> (~((op (e3) (e3)) = (e1))) -> (~((e1) = (e3))) -> (((op (e3) (e0)) = (e1))\/(((op (e3) (e1)) = (e1))\/(((op (e3) (e2)) = (e1))\/((op (e3) (e3)) = (e1))))) -> ((op (e1) (e1)) = (e1)) -> (~((op (e1) (e1)) = (op (e1) (e2)))) -> (~((op (e2) (e2)) = (e1))) -> (((op (e3) (e0)) = (e0))\/(((op (e3) (e1)) = (e0))\/(((op (e3) (e2)) = (e0))\/((op (e3) (e3)) = (e0))))) -> ((op (e3) (e0)) = (e3)) -> (~((e0) = (e3))) -> ((op (e1) (e0)) = (e0)) -> (~((op (e1) (op (e3) (e1))) = (op (e3) (e1)))) -> ((op (e0) (e2)) = (e0)) -> (~((op (e0) (e2)) = (op (e3) (e2)))) -> ((op (e0) (e0)) = (e2)) -> False). % 15.55/15.70 do 0 intro. intros zenon_H11b zenon_H104 zenon_Ha3 zenon_H146 zenon_H21 zenon_H116 zenon_H52 zenon_H1f6 zenon_Hba zenon_H4b zenon_Had zenon_H2b4 zenon_Hab zenon_H140 zenon_H92. % 15.55/15.70 apply (zenon_or_s _ _ zenon_H11b); [ zenon_intro zenon_H29 | zenon_intro zenon_H11c ]. % 15.55/15.70 apply (zenon_L1159_); trivial. % 15.55/15.70 apply (zenon_or_s _ _ zenon_H11c); [ zenon_intro zenon_H117 | zenon_intro zenon_H11d ]. % 15.55/15.70 apply (zenon_L86_); trivial. % 15.55/15.70 apply (zenon_or_s _ _ zenon_H11d); [ zenon_intro zenon_H2a | zenon_intro zenon_H119 ]. % 15.55/15.70 exact (zenon_H52 zenon_H2a). % 15.55/15.70 apply (zenon_L1240_); trivial. % 15.55/15.70 (* end of lemma zenon_L1241_ *) % 15.55/15.70 assert (zenon_L1242_ : (((op (e0) (e0)) = (e1))\/(((op (e0) (e1)) = (e1))\/(((op (e0) (e2)) = (e1))\/((op (e0) (e3)) = (e1))))) -> (~((op (e0) (e0)) = (e1))) -> (~((op (e0) (e1)) = (op (e1) (e1)))) -> (((op (e0) (e0)) = (e2))\/(((op (e0) (e1)) = (e2))\/(((op (e0) (e2)) = (e2))\/((op (e0) (e3)) = (e2))))) -> (~((op (e0) (e2)) = (op (e3) (e2)))) -> ((op (e0) (e2)) = (e0)) -> (~((op (e1) (op (e3) (e1))) = (op (e3) (e1)))) -> ((op (e1) (e0)) = (e0)) -> (~((e0) = (e3))) -> (((op (e3) (e0)) = (e0))\/(((op (e3) (e1)) = (e0))\/(((op (e3) (e2)) = (e0))\/((op (e3) (e3)) = (e0))))) -> (~((op (e2) (e2)) = (e1))) -> (~((op (e1) (e1)) = (op (e1) (e2)))) -> ((op (e1) (e1)) = (e1)) -> (((op (e3) (e0)) = (e1))\/(((op (e3) (e1)) = (e1))\/(((op (e3) (e2)) = (e1))\/((op (e3) (e3)) = (e1))))) -> (~((e1) = (e3))) -> (~((op (e3) (e3)) = (e1))) -> (((op (e0) (e2)) = (e1))\/(((op (e1) (e2)) = (e1))\/(((op (e2) (e2)) = (e1))\/((op (e3) (e2)) = (e1))))) -> (~((op (e3) (e3)) = (e2))) -> (~((op (e2) (op (e3) (e2))) = (op (e3) (e2)))) -> (~((op (e0) (e1)) = (op (e3) (e1)))) -> (~((e2) = (e3))) -> ((op (e3) (e0)) = (e3)) -> (((op (e3) (e0)) = (e2))\/(((op (e3) (e1)) = (e2))\/(((op (e3) (e2)) = (e2))\/((op (e3) (e3)) = (e2))))) -> (~((op (e0) (e2)) = (op (e2) (e2)))) -> ((op (e2) (e2)) = (e2)) -> (~((e1) = (e2))) -> False). % 15.55/15.70 do 0 intro. intros zenon_H44 zenon_H45 zenon_H23 zenon_H8e zenon_H140 zenon_Hab zenon_H2b4 zenon_Had zenon_H4b zenon_H1f6 zenon_H52 zenon_H116 zenon_H21 zenon_H146 zenon_Ha3 zenon_H104 zenon_H11b zenon_H3d zenon_H2af zenon_H138 zenon_H6a zenon_Hba zenon_H1df zenon_H28 zenon_H35 zenon_Ha7. % 15.55/15.70 apply (zenon_or_s _ _ zenon_H44); [ zenon_intro zenon_H47 | zenon_intro zenon_H46 ]. % 15.55/15.70 exact (zenon_H45 zenon_H47). % 15.55/15.70 apply (zenon_or_s _ _ zenon_H46); [ zenon_intro zenon_H22 | zenon_intro zenon_H48 ]. % 15.55/15.70 apply (zenon_L3_); trivial. % 15.55/15.70 apply (zenon_or_s _ _ zenon_H48); [ zenon_intro zenon_H29 | zenon_intro zenon_H37 ]. % 15.55/15.70 apply (zenon_L1159_); trivial. % 15.55/15.70 apply (zenon_or_s _ _ zenon_H8e); [ zenon_intro zenon_H92 | zenon_intro zenon_H91 ]. % 15.55/15.70 apply (zenon_L1241_); trivial. % 15.55/15.70 apply (zenon_or_s _ _ zenon_H91); [ zenon_intro zenon_H5d | zenon_intro zenon_H93 ]. % 15.55/15.70 apply (zenon_L1091_); trivial. % 15.55/15.70 apply (zenon_or_s _ _ zenon_H93); [ zenon_intro zenon_H63 | zenon_intro zenon_H81 ]. % 15.55/15.70 apply (zenon_L15_); trivial. % 15.55/15.70 apply (zenon_L33_); trivial. % 15.55/15.70 (* end of lemma zenon_L1242_ *) % 15.55/15.70 assert (zenon_L1243_ : (((op (e2) (e0)) = (e1))\/(((op (e2) (e1)) = (e1))\/(((op (e2) (e2)) = (e1))\/((op (e2) (e3)) = (e1))))) -> (~((e1) = (e3))) -> ((op (e2) (e0)) = (e3)) -> (~((op (e2) (op (e3) (e2))) = (op (e3) (e2)))) -> (~((op (e1) (e0)) = (op (e1) (e2)))) -> ((op (e1) (e0)) = (e1)) -> (~((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)) = (e1))) -> (~((op (e0) (e3)) = (op (e2) (e3)))) -> ((op (e0) (e3)) = (e1)) -> False). % 15.55/15.70 do 0 intro. intros zenon_Hb7 zenon_Ha3 zenon_Haf zenon_H2af zenon_H166 zenon_Hd8 zenon_Hc9 zenon_H11b zenon_H52 zenon_Hb4 zenon_H37. % 15.55/15.70 apply (zenon_or_s _ _ zenon_Hb7); [ zenon_intro zenon_Hae | zenon_intro zenon_Hb8 ]. % 15.55/15.70 apply (zenon_L39_); trivial. % 15.55/15.70 apply (zenon_or_s _ _ zenon_Hb8); [ zenon_intro zenon_Hb2 | zenon_intro zenon_Hb9 ]. % 15.55/15.70 apply (zenon_L1025_); trivial. % 15.55/15.70 apply (zenon_or_s _ _ zenon_Hb9); [ zenon_intro zenon_H2a | zenon_intro zenon_Hb5 ]. % 15.55/15.70 exact (zenon_H52 zenon_H2a). % 15.55/15.70 apply (zenon_L41_); trivial. % 15.55/15.70 (* end of lemma zenon_L1243_ *) % 15.55/15.70 assert (zenon_L1244_ : (((op (e0) (e2)) = (e1))\/(((op (e1) (e2)) = (e1))\/(((op (e2) (e2)) = (e1))\/((op (e3) (e2)) = (e1))))) -> (~((op (e0) (e2)) = (op (e0) (e3)))) -> ((op (e0) (e3)) = (e1)) -> (~((op (e3) (e3)) = (e1))) -> (~((op (e1) (e2)) = (op (e3) (e2)))) -> (~((op (e1) (op (e3) (e1))) = (op (e3) (e1)))) -> ((op (e3) (e1)) = (e2)) -> (~((e1) = (e3))) -> ((op (e3) (e0)) = (e3)) -> (((op (e3) (e0)) = (e1))\/(((op (e3) (e1)) = (e1))\/(((op (e3) (e2)) = (e1))\/((op (e3) (e3)) = (e1))))) -> (~((op (e2) (e2)) = (e1))) -> (~((op (e2) (op (e3) (e2))) = (op (e3) (e2)))) -> ((op (e2) (e1)) = (e1)) -> False). % 15.55/15.70 do 0 intro. intros zenon_H11b zenon_Hc9 zenon_H37 zenon_H104 zenon_H17d zenon_H2b4 zenon_H16a zenon_Ha3 zenon_Hba zenon_H146 zenon_H52 zenon_H2af zenon_Hb2. % 15.55/15.70 apply (zenon_or_s _ _ zenon_H11b); [ zenon_intro zenon_H29 | zenon_intro zenon_H11c ]. % 15.55/15.70 apply (zenon_L85_); trivial. % 15.55/15.70 apply (zenon_or_s _ _ zenon_H11c); [ zenon_intro zenon_H117 | zenon_intro zenon_H11d ]. % 15.55/15.70 apply (zenon_L1233_); trivial. % 15.55/15.70 apply (zenon_or_s _ _ zenon_H11d); [ zenon_intro zenon_H2a | zenon_intro zenon_H119 ]. % 15.55/15.70 exact (zenon_H52 zenon_H2a). % 15.55/15.70 apply (zenon_L1024_); trivial. % 15.55/15.70 (* end of lemma zenon_L1244_ *) % 15.55/15.70 assert (zenon_L1245_ : (((op (e2) (e0)) = (e1))\/(((op (e2) (e1)) = (e1))\/(((op (e2) (e2)) = (e1))\/((op (e2) (e3)) = (e1))))) -> ((op (e1) (e0)) = (e1)) -> (~((op (e1) (e0)) = (op (e2) (e0)))) -> (~((op (e2) (op (e3) (e2))) = (op (e3) (e2)))) -> (((op (e3) (e0)) = (e1))\/(((op (e3) (e1)) = (e1))\/(((op (e3) (e2)) = (e1))\/((op (e3) (e3)) = (e1))))) -> ((op (e3) (e0)) = (e3)) -> (~((e1) = (e3))) -> ((op (e3) (e1)) = (e2)) -> (~((op (e1) (op (e3) (e1))) = (op (e3) (e1)))) -> (~((op (e1) (e2)) = (op (e3) (e2)))) -> (~((op (e3) (e3)) = (e1))) -> (~((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)) = (e1))) -> (~((op (e0) (e3)) = (op (e2) (e3)))) -> ((op (e0) (e3)) = (e1)) -> False). % 15.55/15.70 do 0 intro. intros zenon_Hb7 zenon_Hd8 zenon_H247 zenon_H2af zenon_H146 zenon_Hba zenon_Ha3 zenon_H16a zenon_H2b4 zenon_H17d zenon_H104 zenon_Hc9 zenon_H11b zenon_H52 zenon_Hb4 zenon_H37. % 15.55/15.70 apply (zenon_or_s _ _ zenon_Hb7); [ zenon_intro zenon_Hae | zenon_intro zenon_Hb8 ]. % 15.55/15.70 apply (zenon_L540_); trivial. % 15.55/15.70 apply (zenon_or_s _ _ zenon_Hb8); [ zenon_intro zenon_Hb2 | zenon_intro zenon_Hb9 ]. % 15.55/15.70 apply (zenon_L1244_); trivial. % 15.55/15.70 apply (zenon_or_s _ _ zenon_Hb9); [ zenon_intro zenon_H2a | zenon_intro zenon_Hb5 ]. % 15.55/15.70 exact (zenon_H52 zenon_H2a). % 15.55/15.70 apply (zenon_L41_); trivial. % 15.55/15.70 (* end of lemma zenon_L1245_ *) % 15.55/15.70 assert (zenon_L1246_ : (((op (e0) (e1)) = (e2))\/(((op (e1) (e1)) = (e2))\/(((op (e2) (e1)) = (e2))\/((op (e3) (e1)) = (e2))))) -> (~((op (e3) (e3)) = (e2))) -> (~((op (e0) (e1)) = (op (e3) (e1)))) -> (~((e2) = (e3))) -> (((op (e3) (e0)) = (e2))\/(((op (e3) (e1)) = (e2))\/(((op (e3) (e2)) = (e2))\/((op (e3) (e3)) = (e2))))) -> (~((op (e1) (e1)) = (e2))) -> (~((op (e2) (e1)) = (op (e2) (e2)))) -> ((op (e2) (e2)) = (e2)) -> (((op (e2) (e0)) = (e1))\/(((op (e2) (e1)) = (e1))\/(((op (e2) (e2)) = (e1))\/((op (e2) (e3)) = (e1))))) -> ((op (e1) (e0)) = (e1)) -> (~((op (e1) (e0)) = (op (e2) (e0)))) -> (~((op (e2) (op (e3) (e2))) = (op (e3) (e2)))) -> (((op (e3) (e0)) = (e1))\/(((op (e3) (e1)) = (e1))\/(((op (e3) (e2)) = (e1))\/((op (e3) (e3)) = (e1))))) -> ((op (e3) (e0)) = (e3)) -> (~((e1) = (e3))) -> (~((op (e1) (op (e3) (e1))) = (op (e3) (e1)))) -> (~((op (e1) (e2)) = (op (e3) (e2)))) -> (~((op (e3) (e3)) = (e1))) -> (~((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)) = (e1))) -> (~((op (e0) (e3)) = (op (e2) (e3)))) -> ((op (e0) (e3)) = (e1)) -> False). % 15.55/15.70 do 0 intro. intros zenon_H1a2 zenon_H3d zenon_H138 zenon_H6a zenon_H1df zenon_Hd6 zenon_H157 zenon_H35 zenon_Hb7 zenon_Hd8 zenon_H247 zenon_H2af zenon_H146 zenon_Hba zenon_Ha3 zenon_H2b4 zenon_H17d zenon_H104 zenon_Hc9 zenon_H11b zenon_H52 zenon_Hb4 zenon_H37. % 15.55/15.70 apply (zenon_or_s _ _ zenon_H1a2); [ zenon_intro zenon_H5d | zenon_intro zenon_H1a3 ]. % 15.55/15.70 apply (zenon_L1091_); trivial. % 15.55/15.70 apply (zenon_or_s _ _ zenon_H1a3); [ zenon_intro zenon_H6e | zenon_intro zenon_H1a4 ]. % 15.55/15.70 exact (zenon_Hd6 zenon_H6e). % 15.55/15.70 apply (zenon_or_s _ _ zenon_H1a4); [ zenon_intro zenon_H156 | zenon_intro zenon_H16a ]. % 15.55/15.70 apply (zenon_L134_); trivial. % 15.55/15.70 apply (zenon_L1245_); trivial. % 15.55/15.70 (* end of lemma zenon_L1246_ *) % 15.55/15.70 assert (zenon_L1247_ : (((op (e0) (e3)) = (e0))\/(((op (e0) (e3)) = (e1))\/(((op (e0) (e3)) = (e2))\/((op (e0) (e3)) = (e3))))) -> ((op (e0) (e2)) = (e0)) -> (~((op (e0) (e3)) = (op (e2) (e3)))) -> (~((op (e2) (e2)) = (e1))) -> (((op (e0) (e2)) = (e1))\/(((op (e1) (e2)) = (e1))\/(((op (e2) (e2)) = (e1))\/((op (e3) (e2)) = (e1))))) -> (~((op (e0) (e2)) = (op (e0) (e3)))) -> (~((op (e3) (e3)) = (e1))) -> (~((op (e1) (e2)) = (op (e3) (e2)))) -> (~((op (e1) (op (e3) (e1))) = (op (e3) (e1)))) -> (~((e1) = (e3))) -> (((op (e3) (e0)) = (e1))\/(((op (e3) (e1)) = (e1))\/(((op (e3) (e2)) = (e1))\/((op (e3) (e3)) = (e1))))) -> (~((op (e2) (op (e3) (e2))) = (op (e3) (e2)))) -> (~((op (e1) (e0)) = (op (e2) (e0)))) -> (((op (e2) (e0)) = (e1))\/(((op (e2) (e1)) = (e1))\/(((op (e2) (e2)) = (e1))\/((op (e2) (e3)) = (e1))))) -> (~((op (e2) (e1)) = (op (e2) (e2)))) -> (((op (e3) (e0)) = (e2))\/(((op (e3) (e1)) = (e2))\/(((op (e3) (e2)) = (e2))\/((op (e3) (e3)) = (e2))))) -> (~((e2) = (e3))) -> (~((op (e0) (e1)) = (op (e3) (e1)))) -> (~((op (e3) (e3)) = (e2))) -> (((op (e0) (e1)) = (e2))\/(((op (e1) (e1)) = (e2))\/(((op (e2) (e1)) = (e2))\/((op (e3) (e1)) = (e2))))) -> (~((op (e0) (e3)) = (op (e1) (e3)))) -> ((op (e2) (e2)) = (e2)) -> (~((op (e1) (e2)) = (op (e2) (e2)))) -> (~((op (e1) (e1)) = (e2))) -> ((op (e1) (e0)) = (e1)) -> (~((e1) = (e2))) -> (((op (e1) (e0)) = (e2))\/(((op (e1) (e1)) = (e2))\/(((op (e1) (e2)) = (e2))\/((op (e1) (e3)) = (e2))))) -> (~((op (e0) (op (e3) (e0))) = (op (e3) (e0)))) -> ((op (e3) (e0)) = (e3)) -> False). % 15.55/15.70 do 0 intro. intros zenon_H254 zenon_Hab zenon_Hb4 zenon_H52 zenon_H11b zenon_Hc9 zenon_H104 zenon_H17d zenon_H2b4 zenon_Ha3 zenon_H146 zenon_H2af zenon_H247 zenon_Hb7 zenon_H157 zenon_H1df zenon_H6a zenon_H138 zenon_H3d zenon_H1a2 zenon_H80 zenon_H35 zenon_H7d zenon_Hd6 zenon_Hd8 zenon_Ha7 zenon_H84 zenon_H2b8 zenon_Hba. % 15.55/15.70 apply (zenon_or_s _ _ zenon_H254); [ zenon_intro zenon_Hca | zenon_intro zenon_H255 ]. % 15.55/15.70 apply (zenon_L53_); trivial. % 15.55/15.70 apply (zenon_or_s _ _ zenon_H255); [ zenon_intro zenon_H37 | zenon_intro zenon_H256 ]. % 15.55/15.70 apply (zenon_L1246_); trivial. % 15.55/15.70 apply (zenon_or_s _ _ zenon_H256); [ zenon_intro zenon_H81 | zenon_intro zenon_H53 ]. % 15.55/15.70 apply (zenon_L243_); trivial. % 15.55/15.70 apply (zenon_L1035_); trivial. % 15.55/15.70 (* end of lemma zenon_L1247_ *) % 15.55/15.70 assert (zenon_L1248_ : ((~((op (e3) (e3)) = (e2)))\/((op (e3) (e2)) = (e3))) -> (~((op (e3) (e0)) = (op (e3) (e2)))) -> (~((op (e0) (e2)) = (op (e0) (e3)))) -> ((op (e0) (e2)) = (e0)) -> (((op (e0) (e1)) = (e2))\/(((op (e1) (e1)) = (e2))\/(((op (e2) (e1)) = (e2))\/((op (e3) (e1)) = (e2))))) -> (~((op (e1) (e0)) = (op (e2) (e0)))) -> ((op (e1) (e0)) = (e1)) -> (((op (e0) (e2)) = (e1))\/(((op (e1) (e2)) = (e1))\/(((op (e2) (e2)) = (e1))\/((op (e3) (e2)) = (e1))))) -> (~((op (e2) (e2)) = (e1))) -> (~((e1) = (e3))) -> (~((op (e1) (op (e3) (e1))) = (op (e3) (e1)))) -> (~((op (e1) (e2)) = (op (e3) (e2)))) -> (~((op (e3) (e3)) = (e1))) -> (((op (e3) (e0)) = (e1))\/(((op (e3) (e1)) = (e1))\/(((op (e3) (e2)) = (e1))\/((op (e3) (e3)) = (e1))))) -> (~((op (e0) (e3)) = (op (e2) (e3)))) -> (((op (e2) (e0)) = (e1))\/(((op (e2) (e1)) = (e1))\/(((op (e2) (e2)) = (e1))\/((op (e2) (e3)) = (e1))))) -> (~((op (e2) (e1)) = (op (e2) (e2)))) -> (~((op (e1) (e1)) = (e2))) -> (~((e2) = (e3))) -> ((op (e3) (e0)) = (e3)) -> (~((op (e0) (e1)) = (op (e3) (e1)))) -> (~((op (e2) (op (e3) (e2))) = (op (e3) (e2)))) -> ((op (e2) (e2)) = (e2)) -> (((op (e3) (e0)) = (e2))\/(((op (e3) (e1)) = (e2))\/(((op (e3) (e2)) = (e2))\/((op (e3) (e3)) = (e2))))) -> (((op (e1) (e0)) = (e2))\/(((op (e1) (e1)) = (e2))\/(((op (e1) (e2)) = (e2))\/((op (e1) (e3)) = (e2))))) -> (~((op (e0) (e3)) = (op (e1) (e3)))) -> (~((op (e1) (e2)) = (op (e2) (e2)))) -> (~((e1) = (e2))) -> (~((op (e0) (op (e3) (e0))) = (op (e3) (e0)))) -> (((op (e0) (e3)) = (e0))\/(((op (e0) (e3)) = (e1))\/(((op (e0) (e3)) = (e2))\/((op (e0) (e3)) = (e3))))) -> False). % 15.55/15.70 do 0 intro. intros zenon_H10e zenon_H105 zenon_Hc9 zenon_Hab zenon_H1a2 zenon_H247 zenon_Hd8 zenon_H11b zenon_H52 zenon_Ha3 zenon_H2b4 zenon_H17d zenon_H104 zenon_H146 zenon_Hb4 zenon_Hb7 zenon_H157 zenon_Hd6 zenon_H6a zenon_Hba zenon_H138 zenon_H2af zenon_H35 zenon_H1df zenon_H84 zenon_H80 zenon_H7d zenon_Ha7 zenon_H2b8 zenon_H254. % 15.55/15.70 apply (zenon_or_s _ _ zenon_H10e); [ zenon_intro zenon_H3d | zenon_intro zenon_H106 ]. % 15.55/15.70 apply (zenon_L1247_); trivial. % 15.55/15.70 apply (zenon_L81_); trivial. % 15.55/15.70 (* end of lemma zenon_L1248_ *) % 15.55/15.70 assert (zenon_L1249_ : ((~((op (e3) (e3)) = (e1)))\/((op (e3) (e1)) = (e3))) -> (~((op (e3) (e0)) = (op (e3) (e1)))) -> (((op (e0) (e3)) = (e0))\/(((op (e0) (e3)) = (e1))\/(((op (e0) (e3)) = (e2))\/((op (e0) (e3)) = (e3))))) -> (~((op (e0) (op (e3) (e0))) = (op (e3) (e0)))) -> (~((e1) = (e2))) -> (~((op (e1) (e2)) = (op (e2) (e2)))) -> (~((op (e0) (e3)) = (op (e1) (e3)))) -> (((op (e1) (e0)) = (e2))\/(((op (e1) (e1)) = (e2))\/(((op (e1) (e2)) = (e2))\/((op (e1) (e3)) = (e2))))) -> (((op (e3) (e0)) = (e2))\/(((op (e3) (e1)) = (e2))\/(((op (e3) (e2)) = (e2))\/((op (e3) (e3)) = (e2))))) -> ((op (e2) (e2)) = (e2)) -> (~((op (e2) (op (e3) (e2))) = (op (e3) (e2)))) -> (~((op (e0) (e1)) = (op (e3) (e1)))) -> ((op (e3) (e0)) = (e3)) -> (~((e2) = (e3))) -> (~((op (e1) (e1)) = (e2))) -> (~((op (e2) (e1)) = (op (e2) (e2)))) -> (((op (e2) (e0)) = (e1))\/(((op (e2) (e1)) = (e1))\/(((op (e2) (e2)) = (e1))\/((op (e2) (e3)) = (e1))))) -> (~((op (e0) (e3)) = (op (e2) (e3)))) -> (((op (e3) (e0)) = (e1))\/(((op (e3) (e1)) = (e1))\/(((op (e3) (e2)) = (e1))\/((op (e3) (e3)) = (e1))))) -> (~((op (e1) (e2)) = (op (e3) (e2)))) -> (~((op (e1) (op (e3) (e1))) = (op (e3) (e1)))) -> (~((e1) = (e3))) -> (~((op (e2) (e2)) = (e1))) -> (((op (e0) (e2)) = (e1))\/(((op (e1) (e2)) = (e1))\/(((op (e2) (e2)) = (e1))\/((op (e3) (e2)) = (e1))))) -> ((op (e1) (e0)) = (e1)) -> (~((op (e1) (e0)) = (op (e2) (e0)))) -> (((op (e0) (e1)) = (e2))\/(((op (e1) (e1)) = (e2))\/(((op (e2) (e1)) = (e2))\/((op (e3) (e1)) = (e2))))) -> ((op (e0) (e2)) = (e0)) -> (~((op (e0) (e2)) = (op (e0) (e3)))) -> (~((op (e3) (e0)) = (op (e3) (e2)))) -> ((~((op (e3) (e3)) = (e2)))\/((op (e3) (e2)) = (e3))) -> False). % 15.55/15.70 do 0 intro. intros zenon_H10c zenon_H109 zenon_H254 zenon_H2b8 zenon_Ha7 zenon_H7d zenon_H80 zenon_H84 zenon_H1df zenon_H35 zenon_H2af zenon_H138 zenon_Hba zenon_H6a zenon_Hd6 zenon_H157 zenon_Hb7 zenon_Hb4 zenon_H146 zenon_H17d zenon_H2b4 zenon_Ha3 zenon_H52 zenon_H11b zenon_Hd8 zenon_H247 zenon_H1a2 zenon_Hab zenon_Hc9 zenon_H105 zenon_H10e. % 15.55/15.70 apply (zenon_or_s _ _ zenon_H10c); [ zenon_intro zenon_H104 | zenon_intro zenon_H10a ]. % 15.55/15.70 apply (zenon_L1248_); trivial. % 15.55/15.70 apply (zenon_L82_); trivial. % 15.55/15.70 (* end of lemma zenon_L1249_ *) % 15.55/15.70 assert (zenon_L1250_ : (((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 (e1) (e0)) = (op (e1) (e2)))) -> ((~((op (e3) (e3)) = (e1)))\/((op (e3) (e1)) = (e3))) -> (~((op (e3) (e0)) = (op (e3) (e1)))) -> (((op (e0) (e3)) = (e0))\/(((op (e0) (e3)) = (e1))\/(((op (e0) (e3)) = (e2))\/((op (e0) (e3)) = (e3))))) -> (~((op (e0) (op (e3) (e0))) = (op (e3) (e0)))) -> (~((e1) = (e2))) -> (~((op (e1) (e2)) = (op (e2) (e2)))) -> (~((op (e0) (e3)) = (op (e1) (e3)))) -> (((op (e1) (e0)) = (e2))\/(((op (e1) (e1)) = (e2))\/(((op (e1) (e2)) = (e2))\/((op (e1) (e3)) = (e2))))) -> (((op (e3) (e0)) = (e2))\/(((op (e3) (e1)) = (e2))\/(((op (e3) (e2)) = (e2))\/((op (e3) (e3)) = (e2))))) -> ((op (e2) (e2)) = (e2)) -> (~((op (e2) (op (e3) (e2))) = (op (e3) (e2)))) -> (~((op (e0) (e1)) = (op (e3) (e1)))) -> (~((e2) = (e3))) -> (~((op (e1) (e1)) = (e2))) -> (~((op (e2) (e1)) = (op (e2) (e2)))) -> (((op (e2) (e0)) = (e1))\/(((op (e2) (e1)) = (e1))\/(((op (e2) (e2)) = (e1))\/((op (e2) (e3)) = (e1))))) -> (~((op (e0) (e3)) = (op (e2) (e3)))) -> (((op (e3) (e0)) = (e1))\/(((op (e3) (e1)) = (e1))\/(((op (e3) (e2)) = (e1))\/((op (e3) (e3)) = (e1))))) -> (~((op (e1) (e2)) = (op (e3) (e2)))) -> (~((op (e1) (op (e3) (e1))) = (op (e3) (e1)))) -> (~((e1) = (e3))) -> (~((op (e2) (e2)) = (e1))) -> (((op (e0) (e2)) = (e1))\/(((op (e1) (e2)) = (e1))\/(((op (e2) (e2)) = (e1))\/((op (e3) (e2)) = (e1))))) -> ((op (e1) (e0)) = (e1)) -> (~((op (e1) (e0)) = (op (e2) (e0)))) -> (((op (e0) (e1)) = (e2))\/(((op (e1) (e1)) = (e2))\/(((op (e2) (e1)) = (e2))\/((op (e3) (e1)) = (e2))))) -> ((op (e0) (e2)) = (e0)) -> (~((op (e0) (e2)) = (op (e0) (e3)))) -> (~((op (e3) (e0)) = (op (e3) (e2)))) -> ((~((op (e3) (e3)) = (e2)))\/((op (e3) (e2)) = (e3))) -> False). % 15.55/15.70 do 0 intro. intros zenon_Hbe zenon_H59 zenon_H37 zenon_H166 zenon_H10c zenon_H109 zenon_H254 zenon_H2b8 zenon_Ha7 zenon_H7d zenon_H80 zenon_H84 zenon_H1df zenon_H35 zenon_H2af zenon_H138 zenon_H6a zenon_Hd6 zenon_H157 zenon_Hb7 zenon_Hb4 zenon_H146 zenon_H17d zenon_H2b4 zenon_Ha3 zenon_H52 zenon_H11b zenon_Hd8 zenon_H247 zenon_H1a2 zenon_Hab zenon_Hc9 zenon_H105 zenon_H10e. % 15.55/15.70 apply (zenon_or_s _ _ zenon_Hbe); [ zenon_intro zenon_H5b | zenon_intro zenon_Hbf ]. % 15.55/15.70 exact (zenon_H59 zenon_H5b). % 15.55/15.70 apply (zenon_or_s _ _ zenon_Hbf); [ zenon_intro zenon_H69 | zenon_intro zenon_Hc0 ]. % 15.55/15.70 apply (zenon_L163_); trivial. % 15.55/15.70 apply (zenon_or_s _ _ zenon_Hc0); [ zenon_intro zenon_Haf | zenon_intro zenon_Hba ]. % 15.55/15.70 apply (zenon_L1243_); trivial. % 15.55/15.70 apply (zenon_L1249_); trivial. % 15.55/15.70 (* end of lemma zenon_L1250_ *) % 15.55/15.70 assert (zenon_L1251_ : (((op (e0) (e0)) = (e1))\/(((op (e1) (e0)) = (e1))\/(((op (e2) (e0)) = (e1))\/((op (e3) (e0)) = (e1))))) -> (~((op (e0) (e0)) = (e1))) -> ((~((op (e3) (e3)) = (e2)))\/((op (e3) (e2)) = (e3))) -> (~((op (e3) (e0)) = (op (e3) (e2)))) -> (~((op (e0) (e2)) = (op (e0) (e3)))) -> ((op (e0) (e2)) = (e0)) -> (((op (e0) (e1)) = (e2))\/(((op (e1) (e1)) = (e2))\/(((op (e2) (e1)) = (e2))\/((op (e3) (e1)) = (e2))))) -> (~((op (e1) (e0)) = (op (e2) (e0)))) -> (((op (e0) (e2)) = (e1))\/(((op (e1) (e2)) = (e1))\/(((op (e2) (e2)) = (e1))\/((op (e3) (e2)) = (e1))))) -> (~((op (e2) (e2)) = (e1))) -> (~((op (e1) (op (e3) (e1))) = (op (e3) (e1)))) -> (~((op (e1) (e2)) = (op (e3) (e2)))) -> (((op (e3) (e0)) = (e1))\/(((op (e3) (e1)) = (e1))\/(((op (e3) (e2)) = (e1))\/((op (e3) (e3)) = (e1))))) -> (~((op (e0) (e3)) = (op (e2) (e3)))) -> (((op (e2) (e0)) = (e1))\/(((op (e2) (e1)) = (e1))\/(((op (e2) (e2)) = (e1))\/((op (e2) (e3)) = (e1))))) -> (~((op (e2) (e1)) = (op (e2) (e2)))) -> (~((op (e1) (e1)) = (e2))) -> (~((e2) = (e3))) -> (~((op (e0) (e1)) = (op (e3) (e1)))) -> (~((op (e2) (op (e3) (e2))) = (op (e3) (e2)))) -> ((op (e2) (e2)) = (e2)) -> (((op (e3) (e0)) = (e2))\/(((op (e3) (e1)) = (e2))\/(((op (e3) (e2)) = (e2))\/((op (e3) (e3)) = (e2))))) -> (((op (e1) (e0)) = (e2))\/(((op (e1) (e1)) = (e2))\/(((op (e1) (e2)) = (e2))\/((op (e1) (e3)) = (e2))))) -> (~((op (e0) (e3)) = (op (e1) (e3)))) -> (~((op (e1) (e2)) = (op (e2) (e2)))) -> (~((e1) = (e2))) -> (~((op (e0) (op (e3) (e0))) = (op (e3) (e0)))) -> (((op (e0) (e3)) = (e0))\/(((op (e0) (e3)) = (e1))\/(((op (e0) (e3)) = (e2))\/((op (e0) (e3)) = (e3))))) -> (~((op (e3) (e0)) = (op (e3) (e1)))) -> ((~((op (e3) (e3)) = (e1)))\/((op (e3) (e1)) = (e3))) -> (~((op (e1) (e0)) = (op (e1) (e2)))) -> ((op (e0) (e3)) = (e1)) -> (~((op (e0) (e0)) = (e3))) -> (((op (e0) (e0)) = (e3))\/(((op (e1) (e0)) = (e3))\/(((op (e2) (e0)) = (e3))\/((op (e3) (e0)) = (e3))))) -> (~((e0) = (e1))) -> ((op (e2) (e0)) = (e0)) -> (~((e1) = (e3))) -> ((op (e3) (e0)) = (e3)) -> False). % 15.55/15.70 do 0 intro. intros zenon_Hf1 zenon_H45 zenon_H10e zenon_H105 zenon_Hc9 zenon_Hab zenon_H1a2 zenon_H247 zenon_H11b zenon_H52 zenon_H2b4 zenon_H17d zenon_H146 zenon_Hb4 zenon_Hb7 zenon_H157 zenon_Hd6 zenon_H6a zenon_H138 zenon_H2af zenon_H35 zenon_H1df zenon_H84 zenon_H80 zenon_H7d zenon_Ha7 zenon_H2b8 zenon_H254 zenon_H109 zenon_H10c zenon_H166 zenon_H37 zenon_H59 zenon_Hbe zenon_H9e zenon_Hcf zenon_Ha3 zenon_Hba. % 15.55/15.70 apply (zenon_or_s _ _ zenon_Hf1); [ zenon_intro zenon_H47 | zenon_intro zenon_Hf4 ]. % 15.55/15.70 exact (zenon_H45 zenon_H47). % 15.55/15.70 apply (zenon_or_s _ _ zenon_Hf4); [ zenon_intro zenon_Hd8 | zenon_intro zenon_Hf5 ]. % 15.55/15.70 apply (zenon_L1250_); trivial. % 15.55/15.70 apply (zenon_or_s _ _ zenon_Hf5); [ zenon_intro zenon_Hae | zenon_intro zenon_Hee ]. % 15.55/15.70 apply (zenon_L269_); trivial. % 15.55/15.70 apply (zenon_L79_); trivial. % 15.55/15.70 (* end of lemma zenon_L1251_ *) % 15.55/15.70 assert (zenon_L1252_ : (((op (e0) (e0)) = (e0))\/(((op (e1) (e0)) = (e0))\/(((op (e2) (e0)) = (e0))\/((op (e3) (e0)) = (e0))))) -> (~((op (e0) (e0)) = (e0))) -> (~((op (e0) (e2)) = (op (e2) (e2)))) -> (~((op (e3) (e3)) = (e2))) -> (~((op (e1) (e1)) = (op (e1) (e2)))) -> (((op (e3) (e0)) = (e0))\/(((op (e3) (e1)) = (e0))\/(((op (e3) (e2)) = (e0))\/((op (e3) (e3)) = (e0))))) -> (((op (e0) (e0)) = (e2))\/(((op (e0) (e1)) = (e2))\/(((op (e0) (e2)) = (e2))\/((op (e0) (e3)) = (e2))))) -> (~((e1) = (e3))) -> (~((e0) = (e1))) -> (((op (e0) (e0)) = (e3))\/(((op (e1) (e0)) = (e3))\/(((op (e2) (e0)) = (e3))\/((op (e3) (e0)) = (e3))))) -> (~((op (e0) (e0)) = (e3))) -> (~((op (e1) (e0)) = (op (e1) (e2)))) -> ((~((op (e3) (e3)) = (e1)))\/((op (e3) (e1)) = (e3))) -> (~((op (e3) (e0)) = (op (e3) (e1)))) -> (((op (e0) (e3)) = (e0))\/(((op (e0) (e3)) = (e1))\/(((op (e0) (e3)) = (e2))\/((op (e0) (e3)) = (e3))))) -> (~((op (e0) (op (e3) (e0))) = (op (e3) (e0)))) -> (~((e1) = (e2))) -> (~((op (e1) (e2)) = (op (e2) (e2)))) -> (~((op (e0) (e3)) = (op (e1) (e3)))) -> (((op (e1) (e0)) = (e2))\/(((op (e1) (e1)) = (e2))\/(((op (e1) (e2)) = (e2))\/((op (e1) (e3)) = (e2))))) -> (((op (e3) (e0)) = (e2))\/(((op (e3) (e1)) = (e2))\/(((op (e3) (e2)) = (e2))\/((op (e3) (e3)) = (e2))))) -> ((op (e2) (e2)) = (e2)) -> (~((op (e2) (op (e3) (e2))) = (op (e3) (e2)))) -> (~((op (e0) (e1)) = (op (e3) (e1)))) -> (~((e2) = (e3))) -> (~((op (e1) (e1)) = (e2))) -> (~((op (e2) (e1)) = (op (e2) (e2)))) -> (((op (e2) (e0)) = (e1))\/(((op (e2) (e1)) = (e1))\/(((op (e2) (e2)) = (e1))\/((op (e2) (e3)) = (e1))))) -> (~((op (e0) (e3)) = (op (e2) (e3)))) -> (((op (e3) (e0)) = (e1))\/(((op (e3) (e1)) = (e1))\/(((op (e3) (e2)) = (e1))\/((op (e3) (e3)) = (e1))))) -> (~((op (e1) (e2)) = (op (e3) (e2)))) -> (~((op (e1) (op (e3) (e1))) = (op (e3) (e1)))) -> (~((op (e2) (e2)) = (e1))) -> (((op (e0) (e2)) = (e1))\/(((op (e1) (e2)) = (e1))\/(((op (e2) (e2)) = (e1))\/((op (e3) (e2)) = (e1))))) -> (~((op (e1) (e0)) = (op (e2) (e0)))) -> (((op (e0) (e1)) = (e2))\/(((op (e1) (e1)) = (e2))\/(((op (e2) (e1)) = (e2))\/((op (e3) (e1)) = (e2))))) -> ((op (e0) (e2)) = (e0)) -> (~((op (e0) (e2)) = (op (e0) (e3)))) -> (~((op (e3) (e0)) = (op (e3) (e2)))) -> ((~((op (e3) (e3)) = (e2)))\/((op (e3) (e2)) = (e3))) -> (~((op (e0) (e0)) = (e1))) -> (((op (e0) (e0)) = (e1))\/(((op (e1) (e0)) = (e1))\/(((op (e2) (e0)) = (e1))\/((op (e3) (e0)) = (e1))))) -> ((op (e1) (e1)) = (e1)) -> (~((op (e0) (e2)) = (op (e3) (e2)))) -> (~((op (e3) (e3)) = (e1))) -> (~((op (e0) (e1)) = (op (e1) (e1)))) -> (((op (e0) (e0)) = (e1))\/(((op (e0) (e1)) = (e1))\/(((op (e0) (e2)) = (e1))\/((op (e0) (e3)) = (e1))))) -> (~((e0) = (e3))) -> ((op (e3) (e0)) = (e3)) -> False). % 15.55/15.70 do 0 intro. intros zenon_Hf0 zenon_H20 zenon_H28 zenon_H3d zenon_H116 zenon_H1f6 zenon_H8e zenon_Ha3 zenon_H9e zenon_Hbe zenon_H59 zenon_H166 zenon_H10c zenon_H109 zenon_H254 zenon_H2b8 zenon_Ha7 zenon_H7d zenon_H80 zenon_H84 zenon_H1df zenon_H35 zenon_H2af zenon_H138 zenon_H6a zenon_Hd6 zenon_H157 zenon_Hb7 zenon_Hb4 zenon_H146 zenon_H17d zenon_H2b4 zenon_H52 zenon_H11b zenon_H247 zenon_H1a2 zenon_Hab zenon_Hc9 zenon_H105 zenon_H10e zenon_H45 zenon_Hf1 zenon_H21 zenon_H140 zenon_H104 zenon_H23 zenon_H44 zenon_H4b zenon_Hba. % 15.55/15.70 apply (zenon_or_s _ _ zenon_Hf0); [ zenon_intro zenon_H1f | zenon_intro zenon_Hf2 ]. % 15.55/15.70 exact (zenon_H20 zenon_H1f). % 15.55/15.70 apply (zenon_or_s _ _ zenon_Hf2); [ zenon_intro zenon_Had | zenon_intro zenon_Hf3 ]. % 15.55/15.70 apply (zenon_L1242_); trivial. % 15.55/15.70 apply (zenon_or_s _ _ zenon_Hf3); [ zenon_intro zenon_Hcf | zenon_intro zenon_Hdb ]. % 15.55/15.70 apply (zenon_or_s _ _ zenon_H44); [ zenon_intro zenon_H47 | zenon_intro zenon_H46 ]. % 15.55/15.70 exact (zenon_H45 zenon_H47). % 15.55/15.70 apply (zenon_or_s _ _ zenon_H46); [ zenon_intro zenon_H22 | zenon_intro zenon_H48 ]. % 15.55/15.70 apply (zenon_L3_); trivial. % 15.55/15.70 apply (zenon_or_s _ _ zenon_H48); [ zenon_intro zenon_H29 | zenon_intro zenon_H37 ]. % 15.55/15.70 apply (zenon_L1159_); trivial. % 15.55/15.70 apply (zenon_L1251_); trivial. % 15.55/15.70 apply (zenon_L62_); trivial. % 15.55/15.70 (* end of lemma zenon_L1252_ *) % 15.55/15.70 assert (zenon_L1253_ : (((op (e3) (e0)) = (e3))\/(((op (e3) (e1)) = (e3))\/(((op (e3) (e2)) = (e3))\/((op (e3) (e3)) = (e3))))) -> (~((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) (e3)) = (e1))) -> (~((op (e0) (e2)) = (op (e3) (e2)))) -> (((op (e0) (e0)) = (e1))\/(((op (e1) (e0)) = (e1))\/(((op (e2) (e0)) = (e1))\/((op (e3) (e0)) = (e1))))) -> (~((op (e0) (e0)) = (e1))) -> ((~((op (e3) (e3)) = (e2)))\/((op (e3) (e2)) = (e3))) -> (~((op (e3) (e0)) = (op (e3) (e2)))) -> (~((op (e0) (e2)) = (op (e0) (e3)))) -> (((op (e0) (e1)) = (e2))\/(((op (e1) (e1)) = (e2))\/(((op (e2) (e1)) = (e2))\/((op (e3) (e1)) = (e2))))) -> (~((op (e1) (e0)) = (op (e2) (e0)))) -> (((op (e0) (e2)) = (e1))\/(((op (e1) (e2)) = (e1))\/(((op (e2) (e2)) = (e1))\/((op (e3) (e2)) = (e1))))) -> (~((op (e2) (e2)) = (e1))) -> (~((op (e1) (op (e3) (e1))) = (op (e3) (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) (e0)) = (e1))\/(((op (e2) (e1)) = (e1))\/(((op (e2) (e2)) = (e1))\/((op (e2) (e3)) = (e1))))) -> (~((op (e2) (e1)) = (op (e2) (e2)))) -> (~((op (e1) (e1)) = (e2))) -> (~((op (e0) (e1)) = (op (e3) (e1)))) -> (~((op (e2) (op (e3) (e2))) = (op (e3) (e2)))) -> (((op (e3) (e0)) = (e2))\/(((op (e3) (e1)) = (e2))\/(((op (e3) (e2)) = (e2))\/((op (e3) (e3)) = (e2))))) -> (((op (e1) (e0)) = (e2))\/(((op (e1) (e1)) = (e2))\/(((op (e1) (e2)) = (e2))\/((op (e1) (e3)) = (e2))))) -> (~((op (e0) (e3)) = (op (e1) (e3)))) -> (~((e1) = (e2))) -> (~((op (e0) (op (e3) (e0))) = (op (e3) (e0)))) -> (((op (e0) (e3)) = (e0))\/(((op (e0) (e3)) = (e1))\/(((op (e0) (e3)) = (e2))\/((op (e0) (e3)) = (e3))))) -> (~((op (e3) (e0)) = (op (e3) (e1)))) -> ((~((op (e3) (e3)) = (e1)))\/((op (e3) (e1)) = (e3))) -> (~((op (e1) (e0)) = (op (e1) (e2)))) -> (~((op (e0) (e0)) = (e3))) -> (((op (e0) (e0)) = (e3))\/(((op (e1) (e0)) = (e3))\/(((op (e2) (e0)) = (e3))\/((op (e3) (e0)) = (e3))))) -> (~((e0) = (e1))) -> (~((e1) = (e3))) -> (((op (e0) (e0)) = (e2))\/(((op (e0) (e1)) = (e2))\/(((op (e0) (e2)) = (e2))\/((op (e0) (e3)) = (e2))))) -> (((op (e3) (e0)) = (e0))\/(((op (e3) (e1)) = (e0))\/(((op (e3) (e2)) = (e0))\/((op (e3) (e3)) = (e0))))) -> (~((op (e3) (e3)) = (e2))) -> (~((op (e0) (e2)) = (op (e2) (e2)))) -> (~((op (e0) (e0)) = (e0))) -> (((op (e0) (e0)) = (e0))\/(((op (e1) (e0)) = (e0))\/(((op (e2) (e0)) = (e0))\/((op (e3) (e0)) = (e0))))) -> ((op (e3) (e1)) = (e2)) -> (~((e2) = (e3))) -> (~((op (e1) (e2)) = (op (e3) (e2)))) -> ((op (e2) (e2)) = (e2)) -> (~((op (e1) (e2)) = (op (e2) (e2)))) -> (~((op (e1) (e1)) = (op (e1) (e2)))) -> ((op (e1) (e1)) = (e1)) -> (~((op (e0) (e2)) = (op (e1) (e2)))) -> ((op (e0) (e2)) = (e0)) -> (((op (e1) (e2)) = (e0))\/(((op (e1) (e2)) = (e1))\/(((op (e1) (e2)) = (e2))\/((op (e1) (e2)) = (e3))))) -> (~((op (e3) (e3)) = (e3))) -> False). % 15.55/15.70 do 0 intro. intros zenon_H2d5 zenon_H4b zenon_H44 zenon_H23 zenon_H104 zenon_H140 zenon_Hf1 zenon_H45 zenon_H10e zenon_H105 zenon_Hc9 zenon_H1a2 zenon_H247 zenon_H11b zenon_H52 zenon_H2b4 zenon_H146 zenon_Hb4 zenon_Hb7 zenon_H157 zenon_Hd6 zenon_H138 zenon_H2af zenon_H1df zenon_H84 zenon_H80 zenon_Ha7 zenon_H2b8 zenon_H254 zenon_H109 zenon_H10c zenon_H166 zenon_H59 zenon_Hbe zenon_H9e zenon_Ha3 zenon_H8e zenon_H1f6 zenon_H3d zenon_H28 zenon_H20 zenon_Hf0 zenon_H16a zenon_H6a zenon_H17d zenon_H35 zenon_H7d zenon_H116 zenon_H21 zenon_H87 zenon_Hab zenon_H1d5 zenon_H3e. % 15.55/15.70 apply (zenon_or_s _ _ zenon_H2d5); [ zenon_intro zenon_Hba | zenon_intro zenon_H2d6 ]. % 15.55/15.70 apply (zenon_L1252_); trivial. % 15.55/15.70 apply (zenon_or_s _ _ zenon_H2d6); [ zenon_intro zenon_H10a | zenon_intro zenon_H2d7 ]. % 15.55/15.70 apply (zenon_L297_); trivial. % 15.55/15.70 apply (zenon_or_s _ _ zenon_H2d7); [ zenon_intro zenon_H106 | zenon_intro zenon_H42 ]. % 15.55/15.70 apply (zenon_L240_); trivial. % 15.55/15.70 exact (zenon_H3e zenon_H42). % 15.55/15.70 (* end of lemma zenon_L1253_ *) % 15.55/15.70 assert (zenon_L1254_ : (~((op (e3) (e3)) = (e0))) -> (~((op (e0) (e3)) = (op (e3) (e3)))) -> (((op (e3) (e3)) = (e0))\/(((op (e3) (e3)) = (e1))\/(((op (e3) (e3)) = (e2))\/((op (e3) (e3)) = (e3))))) -> (((op (e3) (e0)) = (e1))\/(((op (e3) (e1)) = (e1))\/(((op (e3) (e2)) = (e1))\/((op (e3) (e3)) = (e1))))) -> (~((op (e3) (e3)) = (e1))) -> (~((op (e0) (e2)) = (op (e3) (e2)))) -> (~((op (e1) (op (e3) (e1))) = (op (e3) (e1)))) -> (~((op (e0) (op (e3) (e0))) = (op (e3) (e0)))) -> (~((op (e0) (e1)) = (op (e3) (e1)))) -> (~((op (e2) (op (e3) (e2))) = (op (e3) (e2)))) -> ((op (e2) (e2)) = (e2)) -> (((op (e3) (e0)) = (e2))\/(((op (e3) (e1)) = (e2))\/(((op (e3) (e2)) = (e2))\/((op (e3) (e3)) = (e2))))) -> (~((op (e1) (e1)) = (e2))) -> (~((op (e2) (e1)) = (op (e2) (e2)))) -> (((op (e3) (e0)) = (e3))\/(((op (e3) (e1)) = (e3))\/(((op (e3) (e2)) = (e3))\/((op (e3) (e3)) = (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)) = (e0))) -> (((op (e0) (e0)) = (e1))\/(((op (e0) (e1)) = (e1))\/(((op (e0) (e2)) = (e1))\/((op (e0) (e3)) = (e1))))) -> (((op (e0) (e2)) = (e1))\/(((op (e1) (e2)) = (e1))\/(((op (e2) (e2)) = (e1))\/((op (e3) (e2)) = (e1))))) -> (~((e0) = (e3))) -> ((op (e0) (e2)) = (e0)) -> (((op (e3) (e0)) = (e0))\/(((op (e3) (e1)) = (e0))\/(((op (e3) (e2)) = (e0))\/((op (e3) (e3)) = (e0))))) -> (~((op (e2) (e2)) = (e1))) -> (~((op (e1) (e1)) = (op (e1) (e2)))) -> (~((e2) = (e3))) -> (~((op (e0) (e2)) = (op (e2) (e2)))) -> (~((e1) = (e2))) -> (((op (e0) (e0)) = (e2))\/(((op (e0) (e1)) = (e2))\/(((op (e0) (e2)) = (e2))\/((op (e0) (e3)) = (e2))))) -> (~((e1) = (e3))) -> (((op (e0) (e0)) = (e3))\/(((op (e1) (e0)) = (e3))\/(((op (e2) (e0)) = (e3))\/((op (e3) (e0)) = (e3))))) -> ((~((op (e3) (e3)) = (e2)))\/((op (e3) (e2)) = (e3))) -> (~((op (e3) (e0)) = (op (e3) (e2)))) -> (((op (e0) (e1)) = (e2))\/(((op (e1) (e1)) = (e2))\/(((op (e2) (e1)) = (e2))\/((op (e3) (e1)) = (e2))))) -> (~((op (e1) (e0)) = (op (e2) (e0)))) -> (~((op (e1) (e2)) = (op (e3) (e2)))) -> (((op (e1) (e0)) = (e2))\/(((op (e1) (e1)) = (e2))\/(((op (e1) (e2)) = (e2))\/((op (e1) (e3)) = (e2))))) -> (~((op (e0) (e3)) = (op (e1) (e3)))) -> (~((op (e1) (e2)) = (op (e2) (e2)))) -> (((op (e0) (e3)) = (e0))\/(((op (e0) (e3)) = (e1))\/(((op (e0) (e3)) = (e2))\/((op (e0) (e3)) = (e3))))) -> (~((op (e3) (e0)) = (op (e3) (e1)))) -> ((~((op (e3) (e3)) = (e1)))\/((op (e3) (e1)) = (e3))) -> (~((op (e1) (e0)) = (op (e1) (e2)))) -> (~((op (e0) (e2)) = (op (e0) (e3)))) -> (~((op (e0) (e3)) = (op (e2) (e3)))) -> (((op (e2) (e0)) = (e1))\/(((op (e2) (e1)) = (e1))\/(((op (e2) (e2)) = (e1))\/((op (e2) (e3)) = (e1))))) -> (~((op (e0) (e0)) = (e3))) -> (~((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 (e2) (e0)) = (e0))\/((op (e3) (e0)) = (e0))))) -> ((op (e1) (e1)) = (e1)) -> (~((op (e0) (e1)) = (op (e1) (e1)))) -> (~((op (e0) (e0)) = (e1))) -> (~((op (e3) (op (e3) (e3))) = (op (e3) (e3)))) -> ((~((op (e3) (e3)) = (e3)))\/((op (e3) (e3)) = (e3))) -> False). % 15.55/15.70 do 0 intro. intros zenon_H3c zenon_H36 zenon_H3b zenon_H146 zenon_H104 zenon_H140 zenon_H2b4 zenon_H2b8 zenon_H138 zenon_H2af zenon_H35 zenon_H1df zenon_Hd6 zenon_H157 zenon_H2d5 zenon_H87 zenon_H1d5 zenon_H20 zenon_H44 zenon_H11b zenon_H4b zenon_Hab zenon_H1f6 zenon_H52 zenon_H116 zenon_H6a zenon_H28 zenon_Ha7 zenon_H8e zenon_Ha3 zenon_Hbe zenon_H10e zenon_H105 zenon_H1a2 zenon_H247 zenon_H17d zenon_H84 zenon_H80 zenon_H7d zenon_H254 zenon_H109 zenon_H10c zenon_H166 zenon_Hc9 zenon_Hb4 zenon_Hb7 zenon_H59 zenon_H9e zenon_Hf1 zenon_Hf0 zenon_H21 zenon_H23 zenon_H45 zenon_H2be zenon_H10d. % 15.55/15.70 apply (zenon_or_s _ _ zenon_H10e); [ zenon_intro zenon_H3d | zenon_intro zenon_H106 ]. % 15.55/15.70 apply (zenon_or_s _ _ zenon_H10d); [ zenon_intro zenon_H3e | zenon_intro zenon_H42 ]. % 15.55/15.70 apply (zenon_or_s _ _ zenon_H44); [ zenon_intro zenon_H47 | zenon_intro zenon_H46 ]. % 15.55/15.70 exact (zenon_H45 zenon_H47). % 15.55/15.70 apply (zenon_or_s _ _ zenon_H46); [ zenon_intro zenon_H22 | zenon_intro zenon_H48 ]. % 15.55/15.70 apply (zenon_L3_); trivial. % 15.55/15.70 apply (zenon_or_s _ _ zenon_H48); [ zenon_intro zenon_H29 | zenon_intro zenon_H37 ]. % 15.55/15.70 apply (zenon_or_s _ _ zenon_H1a2); [ zenon_intro zenon_H5d | zenon_intro zenon_H1a3 ]. % 15.55/15.70 apply (zenon_L1227_); trivial. % 15.55/15.70 apply (zenon_or_s _ _ zenon_H1a3); [ zenon_intro zenon_H6e | zenon_intro zenon_H1a4 ]. % 15.55/15.70 exact (zenon_Hd6 zenon_H6e). % 15.55/15.70 apply (zenon_or_s _ _ zenon_H1a4); [ zenon_intro zenon_H156 | zenon_intro zenon_H16a ]. % 15.55/15.70 apply (zenon_L134_); trivial. % 15.55/15.70 apply (zenon_L1253_); trivial. % 15.55/15.70 apply (zenon_L7_); trivial. % 15.55/15.70 apply (zenon_L1041_); trivial. % 15.55/15.70 apply (zenon_L240_); trivial. % 15.55/15.70 (* end of lemma zenon_L1254_ *) % 15.55/15.70 assert (zenon_L1255_ : ((~((op (e1) (e1)) = (e2)))\/((op (e1) (e2)) = (e1))) -> (~((op (e1) (e0)) = (op (e1) (e2)))) -> ((~((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 (e0) (e3)) = (op (e1) (e3)))) -> (~((op (e0) (e2)) = (op (e2) (e2)))) -> (~((op (e0) (e1)) = (op (e3) (e1)))) -> (~((op (e2) (op (e3) (e2))) = (op (e3) (e2)))) -> (((op (e3) (e0)) = (e2))\/(((op (e3) (e1)) = (e2))\/(((op (e3) (e2)) = (e2))\/((op (e3) (e3)) = (e2))))) -> (~((op (e3) (e0)) = (op (e3) (e2)))) -> ((~((op (e3) (e3)) = (e3)))\/((op (e3) (e3)) = (e3))) -> (~((op (e3) (op (e3) (e3))) = (op (e3) (e3)))) -> (~((op (e0) (e0)) = (e2))) -> (~((e1) = (e2))) -> ((op (e1) (e0)) = (e1)) -> (~((op (e2) (e0)) = (op (e2) (e2)))) -> ((op (e2) (e2)) = (e2)) -> (((op (e1) (e1)) = (e0))\/(((op (e1) (e1)) = (e1))\/(((op (e1) (e1)) = (e2))\/((op (e1) (e1)) = (e3))))) -> (~((op (e1) (e1)) = (e1))) -> (((op (e3) (e3)) = (e0))\/(((op (e3) (e3)) = (e1))\/(((op (e3) (e3)) = (e2))\/((op (e3) (e3)) = (e3))))) -> (((op (e0) (e0)) = (e2))\/(((op (e1) (e0)) = (e2))\/(((op (e2) (e0)) = (e2))\/((op (e3) (e0)) = (e2))))) -> (((op (e1) (e0)) = (e2))\/(((op (e1) (e1)) = (e2))\/(((op (e1) (e2)) = (e2))\/((op (e1) (e3)) = (e2))))) -> (~((e1) = (e3))) -> (~((op (e1) (e2)) = (op (e3) (e2)))) -> (~((e2) = (e3))) -> (((op (e1) (e0)) = (e3))\/(((op (e1) (e1)) = (e3))\/(((op (e1) (e2)) = (e3))\/((op (e1) (e3)) = (e3))))) -> (~((op (e1) (e2)) = (op (e2) (e2)))) -> ((~((op (e3) (e3)) = (e2)))\/((op (e3) (e2)) = (e3))) -> (~((op (e1) (e0)) = (op (e1) (e3)))) -> ((~((op (e1) (e1)) = (e3)))\/((op (e1) (e3)) = (e1))) -> False). % 15.55/15.70 do 0 intro. intros zenon_H1d3 zenon_H166 zenon_H10f zenon_H8e zenon_H80 zenon_H28 zenon_H138 zenon_H2af zenon_H1df zenon_H105 zenon_H10d zenon_H2be zenon_H8f zenon_Ha7 zenon_Hd8 zenon_H17a zenon_H35 zenon_H1b3 zenon_H1b4 zenon_H3b zenon_Heb zenon_H84 zenon_Ha3 zenon_H17d zenon_H6a zenon_H90 zenon_H7d zenon_H10e zenon_H1cf zenon_H1d2. % 15.55/15.70 apply (zenon_or_s _ _ zenon_H1d3); [ zenon_intro zenon_Hd6 | zenon_intro zenon_H117 ]. % 15.55/15.70 apply (zenon_or_s _ _ zenon_H1d2); [ zenon_intro zenon_H182 | zenon_intro zenon_H11f ]. % 15.55/15.70 apply (zenon_or_s _ _ zenon_H10f); [ zenon_intro zenon_H3c | zenon_intro zenon_Hba ]. % 15.55/15.70 apply (zenon_or_s _ _ zenon_H10e); [ zenon_intro zenon_H3d | zenon_intro zenon_H106 ]. % 15.55/15.70 apply (zenon_L1073_); trivial. % 15.55/15.70 apply (zenon_L167_); trivial. % 15.55/15.70 apply (zenon_or_s _ _ zenon_H10e); [ zenon_intro zenon_H3d | zenon_intro zenon_H106 ]. % 15.55/15.70 apply (zenon_or_s _ _ zenon_H8e); [ zenon_intro zenon_H92 | zenon_intro zenon_H91 ]. % 15.55/15.70 exact (zenon_H8f zenon_H92). % 15.55/15.70 apply (zenon_or_s _ _ zenon_H91); [ zenon_intro zenon_H5d | zenon_intro zenon_H93 ]. % 15.55/15.70 apply (zenon_L1091_); trivial. % 15.55/15.70 apply (zenon_or_s _ _ zenon_H93); [ zenon_intro zenon_H63 | zenon_intro zenon_H81 ]. % 15.55/15.70 apply (zenon_L15_); trivial. % 15.55/15.70 apply (zenon_L243_); trivial. % 15.55/15.70 apply (zenon_L81_); trivial. % 15.55/15.70 apply (zenon_L224_); trivial. % 15.55/15.70 apply (zenon_L248_); trivial. % 15.55/15.70 (* end of lemma zenon_L1255_ *) % 15.55/15.70 assert (zenon_L1256_ : ((~((op (e1) (e1)) = (e1)))\/((op (e1) (e1)) = (e1))) -> (~((op (e1) (e0)) = (op (e1) (e1)))) -> ((~((op (e1) (e1)) = (e3)))\/((op (e1) (e3)) = (e1))) -> (~((op (e1) (e0)) = (op (e1) (e3)))) -> ((~((op (e3) (e3)) = (e2)))\/((op (e3) (e2)) = (e3))) -> (~((op (e1) (e2)) = (op (e2) (e2)))) -> (((op (e1) (e0)) = (e3))\/(((op (e1) (e1)) = (e3))\/(((op (e1) (e2)) = (e3))\/((op (e1) (e3)) = (e3))))) -> (~((e2) = (e3))) -> (~((op (e1) (e2)) = (op (e3) (e2)))) -> (~((e1) = (e3))) -> (((op (e1) (e0)) = (e2))\/(((op (e1) (e1)) = (e2))\/(((op (e1) (e2)) = (e2))\/((op (e1) (e3)) = (e2))))) -> (((op (e0) (e0)) = (e2))\/(((op (e1) (e0)) = (e2))\/(((op (e2) (e0)) = (e2))\/((op (e3) (e0)) = (e2))))) -> (((op (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 (e2) (e2)) = (e2)) -> (~((op (e2) (e0)) = (op (e2) (e2)))) -> ((op (e1) (e0)) = (e1)) -> (~((e1) = (e2))) -> (~((op (e0) (e0)) = (e2))) -> (~((op (e3) (op (e3) (e3))) = (op (e3) (e3)))) -> ((~((op (e3) (e3)) = (e3)))\/((op (e3) (e3)) = (e3))) -> (~((op (e3) (e0)) = (op (e3) (e2)))) -> (((op (e3) (e0)) = (e2))\/(((op (e3) (e1)) = (e2))\/(((op (e3) (e2)) = (e2))\/((op (e3) (e3)) = (e2))))) -> (~((op (e2) (op (e3) (e2))) = (op (e3) (e2)))) -> (~((op (e0) (e1)) = (op (e3) (e1)))) -> (~((op (e0) (e2)) = (op (e2) (e2)))) -> (~((op (e0) (e3)) = (op (e1) (e3)))) -> (((op (e0) (e0)) = (e2))\/(((op (e0) (e1)) = (e2))\/(((op (e0) (e2)) = (e2))\/((op (e0) (e3)) = (e2))))) -> ((~((op (e3) (e3)) = (e0)))\/((op (e3) (e0)) = (e3))) -> (~((op (e1) (e0)) = (op (e1) (e2)))) -> ((~((op (e1) (e1)) = (e2)))\/((op (e1) (e2)) = (e1))) -> False). % 15.55/15.70 do 0 intro. intros zenon_H1d8 zenon_Hd7 zenon_H1d2 zenon_H1cf zenon_H10e zenon_H7d zenon_H90 zenon_H6a zenon_H17d zenon_Ha3 zenon_H84 zenon_Heb zenon_H3b zenon_H1b3 zenon_H35 zenon_H17a zenon_Hd8 zenon_Ha7 zenon_H8f zenon_H2be zenon_H10d zenon_H105 zenon_H1df zenon_H2af zenon_H138 zenon_H28 zenon_H80 zenon_H8e zenon_H10f zenon_H166 zenon_H1d3. % 15.55/15.70 apply (zenon_or_s _ _ zenon_H1d8); [ zenon_intro zenon_H1b4 | zenon_intro zenon_H21 ]. % 15.55/15.70 apply (zenon_L1255_); trivial. % 15.55/15.70 apply (zenon_L61_); trivial. % 15.55/15.70 (* end of lemma zenon_L1256_ *) % 15.55/15.70 assert (zenon_L1257_ : (((op (e0) (e0)) = (e1))\/(((op (e0) (e1)) = (e1))\/(((op (e0) (e2)) = (e1))\/((op (e0) (e3)) = (e1))))) -> (~((op (e0) (e0)) = (e1))) -> (~((op (e0) (e1)) = (op (e1) (e1)))) -> (~((op (e3) (e3)) = (e1))) -> (~((op (e0) (e2)) = (op (e3) (e2)))) -> (~((op (e1) (op (e3) (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)) = (e1))\/(((op (e1) (e2)) = (e1))\/(((op (e2) (e2)) = (e1))\/((op (e3) (e2)) = (e1))))) -> (~((op (e0) (e2)) = (op (e0) (e3)))) -> ((op (e1) (e1)) = (e1)) -> (~((op (e1) (e1)) = (op (e1) (e2)))) -> (~((op (e2) (e2)) = (e1))) -> (~((e1) = (e3))) -> ((op (e3) (e2)) = (e3)) -> False). % 15.55/15.70 do 0 intro. intros zenon_H44 zenon_H45 zenon_H23 zenon_H104 zenon_H140 zenon_H2b4 zenon_Hdb zenon_H9e zenon_H146 zenon_H11b zenon_Hc9 zenon_H21 zenon_H116 zenon_H52 zenon_Ha3 zenon_H106. % 15.55/15.70 apply (zenon_or_s _ _ zenon_H44); [ zenon_intro zenon_H47 | zenon_intro zenon_H46 ]. % 15.55/15.70 exact (zenon_H45 zenon_H47). % 15.55/15.70 apply (zenon_or_s _ _ zenon_H46); [ zenon_intro zenon_H22 | zenon_intro zenon_H48 ]. % 15.55/15.70 apply (zenon_L3_); trivial. % 15.55/15.70 apply (zenon_or_s _ _ zenon_H48); [ zenon_intro zenon_H29 | zenon_intro zenon_H37 ]. % 15.55/15.70 apply (zenon_L1185_); trivial. % 15.55/15.70 apply (zenon_L88_); trivial. % 15.55/15.70 (* end of lemma zenon_L1257_ *) % 15.55/15.70 assert (zenon_L1258_ : (((op (e3) (e0)) = (e2))\/(((op (e3) (e1)) = (e2))\/(((op (e3) (e2)) = (e2))\/((op (e3) (e3)) = (e2))))) -> ((op (e3) (e2)) = (e3)) -> (~((e1) = (e3))) -> (~((op (e2) (e2)) = (e1))) -> (~((op (e1) (e1)) = (op (e1) (e2)))) -> ((op (e1) (e1)) = (e1)) -> (((op (e3) (e0)) = (e1))\/(((op (e3) (e1)) = (e1))\/(((op (e3) (e2)) = (e1))\/((op (e3) (e3)) = (e1))))) -> (~((op (e0) (op (e3) (e0))) = (op (e3) (e0)))) -> (~((op (e0) (e2)) = (op (e3) (e2)))) -> (~((op (e3) (e3)) = (e1))) -> (((op (e0) (e2)) = (e1))\/(((op (e1) (e2)) = (e1))\/(((op (e2) (e2)) = (e1))\/((op (e3) (e2)) = (e1))))) -> ((op (e3) (e1)) = (e0)) -> ((op (e1) (e0)) = (e2)) -> (~((op (e1) (op (e3) (e1))) = (op (e3) (e1)))) -> ((op (e2) (e2)) = (e2)) -> (~((op (e2) (op (e3) (e2))) = (op (e3) (e2)))) -> ((op (e0) (e2)) = (e1)) -> ((op (e0) (e0)) = (e3)) -> False). % 15.55/15.70 do 0 intro. intros zenon_H1df zenon_H106 zenon_Ha3 zenon_H52 zenon_H116 zenon_H21 zenon_H146 zenon_H2b8 zenon_H140 zenon_H104 zenon_H11b zenon_H142 zenon_H68 zenon_H2b4 zenon_H35 zenon_H2af zenon_H29 zenon_H5b. % 15.55/15.70 apply (zenon_or_s _ _ zenon_H1df); [ zenon_intro zenon_He9 | zenon_intro zenon_H1e0 ]. % 15.55/15.70 apply (zenon_L1175_); trivial. % 15.55/15.70 apply (zenon_or_s _ _ zenon_H1e0); [ zenon_intro zenon_H16a | zenon_intro zenon_H1e1 ]. % 15.55/15.70 apply (zenon_L1104_); trivial. % 15.55/15.70 apply (zenon_or_s _ _ zenon_H1e1); [ zenon_intro zenon_H1dd | zenon_intro zenon_H43 ]. % 15.55/15.70 apply (zenon_L1083_); trivial. % 15.55/15.70 apply (zenon_L174_); trivial. % 15.55/15.70 (* end of lemma zenon_L1258_ *) % 15.55/15.70 assert (zenon_L1259_ : (((op (e1) (e2)) = (e0))\/(((op (e1) (e2)) = (e1))\/(((op (e1) (e2)) = (e2))\/((op (e1) (e2)) = (e3))))) -> ((op (e3) (e2)) = (e0)) -> ((op (e1) (e1)) = (e1)) -> (~((op (e1) (e1)) = (op (e1) (e2)))) -> (~((op (e1) (e2)) = (op (e2) (e2)))) -> ((op (e2) (e2)) = (e2)) -> ((op (e3) (e2)) = (e3)) -> (~((op (e1) (e2)) = (op (e3) (e2)))) -> False). % 15.55/15.70 do 0 intro. intros zenon_H1d5 zenon_H167 zenon_H21 zenon_H116 zenon_H7d zenon_H35 zenon_H106 zenon_H17d. % 15.55/15.70 apply (zenon_or_s _ _ zenon_H1d5); [ zenon_intro zenon_H15d | zenon_intro zenon_H1d6 ]. % 15.55/15.70 apply (zenon_L626_); trivial. % 15.55/15.70 apply (zenon_or_s _ _ zenon_H1d6); [ zenon_intro zenon_H117 | zenon_intro zenon_H1d7 ]. % 15.55/15.70 apply (zenon_L86_); trivial. % 15.55/15.70 apply (zenon_or_s _ _ zenon_H1d7); [ zenon_intro zenon_H7c | zenon_intro zenon_H88 ]. % 15.55/15.70 apply (zenon_L21_); trivial. % 15.55/15.70 apply (zenon_L164_); trivial. % 15.55/15.70 (* end of lemma zenon_L1259_ *) % 15.55/15.70 assert (zenon_L1260_ : (((op (e3) (e0)) = (e0))\/(((op (e3) (e1)) = (e0))\/(((op (e3) (e2)) = (e0))\/((op (e3) (e3)) = (e0))))) -> (~((op (e0) (e2)) = (op (e0) (e3)))) -> (~((e0) = (e1))) -> (~((op (e0) (e1)) = (op (e1) (e1)))) -> (~((op (e0) (e0)) = (e1))) -> (((op (e0) (e0)) = (e1))\/(((op (e0) (e1)) = (e1))\/(((op (e0) (e2)) = (e1))\/((op (e0) (e3)) = (e1))))) -> ((op (e0) (e0)) = (e3)) -> ((op (e0) (e2)) = (e1)) -> (~((op (e2) (op (e3) (e2))) = (op (e3) (e2)))) -> (~((op (e1) (op (e3) (e1))) = (op (e3) (e1)))) -> ((op (e1) (e0)) = (e2)) -> (((op (e0) (e2)) = (e1))\/(((op (e1) (e2)) = (e1))\/(((op (e2) (e2)) = (e1))\/((op (e3) (e2)) = (e1))))) -> (~((op (e3) (e3)) = (e1))) -> (~((op (e0) (e2)) = (op (e3) (e2)))) -> (~((op (e0) (op (e3) (e0))) = (op (e3) (e0)))) -> (((op (e3) (e0)) = (e1))\/(((op (e3) (e1)) = (e1))\/(((op (e3) (e2)) = (e1))\/((op (e3) (e3)) = (e1))))) -> (~((op (e2) (e2)) = (e1))) -> (~((e1) = (e3))) -> (((op (e3) (e0)) = (e2))\/(((op (e3) (e1)) = (e2))\/(((op (e3) (e2)) = (e2))\/((op (e3) (e3)) = (e2))))) -> (~((op (e1) (e2)) = (op (e3) (e2)))) -> ((op (e3) (e2)) = (e3)) -> ((op (e2) (e2)) = (e2)) -> (~((op (e1) (e2)) = (op (e2) (e2)))) -> (~((op (e1) (e1)) = (op (e1) (e2)))) -> ((op (e1) (e1)) = (e1)) -> (((op (e1) (e2)) = (e0))\/(((op (e1) (e2)) = (e1))\/(((op (e1) (e2)) = (e2))\/((op (e1) (e2)) = (e3))))) -> (~((op (e3) (e3)) = (e0))) -> False). % 15.55/15.70 do 0 intro. intros zenon_H1f6 zenon_Hc9 zenon_H9e zenon_H23 zenon_H45 zenon_H44 zenon_H5b zenon_H29 zenon_H2af zenon_H2b4 zenon_H68 zenon_H11b zenon_H104 zenon_H140 zenon_H2b8 zenon_H146 zenon_H52 zenon_Ha3 zenon_H1df zenon_H17d zenon_H106 zenon_H35 zenon_H7d zenon_H116 zenon_H21 zenon_H1d5 zenon_H3c. % 15.55/15.70 apply (zenon_or_s _ _ zenon_H1f6); [ zenon_intro zenon_Hdb | zenon_intro zenon_H1f7 ]. % 15.55/15.70 apply (zenon_L1257_); trivial. % 15.55/15.70 apply (zenon_or_s _ _ zenon_H1f7); [ zenon_intro zenon_H142 | zenon_intro zenon_H1f8 ]. % 15.55/15.70 apply (zenon_L1258_); trivial. % 15.55/15.70 apply (zenon_or_s _ _ zenon_H1f8); [ zenon_intro zenon_H167 | zenon_intro zenon_H40 ]. % 15.55/15.70 apply (zenon_L1259_); trivial. % 15.55/15.70 exact (zenon_H3c zenon_H40). % 15.55/15.70 (* end of lemma zenon_L1260_ *) % 15.55/15.70 assert (zenon_L1261_ : (~((op (e3) (e0)) = (op (e3) (e1)))) -> ((op (e3) (e0)) = (e0)) -> ((op (e3) (e1)) = (e0)) -> False). % 15.55/15.70 do 0 intro. intros zenon_H109 zenon_Hdb zenon_H142. % 15.55/15.70 cut (((op (e3) (e0)) = (e0)) = ((op (e3) (e0)) = (op (e3) (e1)))). % 15.55/15.70 intro zenon_D_pnotp. % 15.55/15.70 apply zenon_H109. % 15.55/15.70 rewrite <- zenon_D_pnotp. % 15.55/15.70 exact zenon_Hdb. % 15.55/15.70 cut (((e0) = (op (e3) (e1)))); [idtac | apply NNPP; zenon_intro zenon_H2cf]. % 15.55/15.70 cut (((op (e3) (e0)) = (op (e3) (e0)))); [idtac | apply NNPP; zenon_intro zenon_H108]. % 15.55/15.70 congruence. % 15.55/15.70 apply zenon_H108. apply refl_equal. % 15.55/15.70 apply zenon_H2cf. apply sym_equal. exact zenon_H142. % 15.55/15.70 (* end of lemma zenon_L1261_ *) % 15.55/15.70 assert (zenon_L1262_ : (((op (e3) (e1)) = (e0))\/(((op (e3) (e1)) = (e1))\/(((op (e3) (e1)) = (e2))\/((op (e3) (e1)) = (e3))))) -> ((op (e3) (e0)) = (e0)) -> ((op (e3) (e0)) = (e1)) -> (~((op (e3) (e0)) = (op (e3) (e1)))) -> ((op (e0) (e1)) = (e2)) -> ((op (e0) (e1)) = (e3)) -> (~((op (e0) (e1)) = (op (e3) (e1)))) -> False). % 15.55/15.70 do 0 intro. intros zenon_H16c zenon_Hdb zenon_Hee zenon_H109 zenon_H5d zenon_H4a zenon_H138. % 15.55/15.70 apply (zenon_or_s _ _ zenon_H16c); [ zenon_intro zenon_H142 | zenon_intro zenon_H16d ]. % 15.55/15.70 apply (zenon_L1261_); trivial. % 15.55/15.70 apply (zenon_or_s _ _ zenon_H16d); [ zenon_intro zenon_H13e | zenon_intro zenon_H16e ]. % 15.55/15.70 apply (zenon_L145_); trivial. % 15.55/15.70 apply (zenon_or_s _ _ zenon_H16e); [ zenon_intro zenon_H16a | zenon_intro zenon_H10a ]. % 15.55/15.70 apply (zenon_L146_); trivial. % 15.55/15.70 apply (zenon_L120_); trivial. % 15.55/15.70 (* end of lemma zenon_L1262_ *) % 15.55/15.70 assert (zenon_L1263_ : (((op (e0) (e0)) = (e2))\/(((op (e1) (e0)) = (e2))\/(((op (e2) (e0)) = (e2))\/((op (e3) (e0)) = (e2))))) -> (~((op (e0) (e0)) = (e2))) -> (~((op (e3) (e3)) = (e1))) -> (((op (e3) (e0)) = (e2))\/(((op (e3) (e1)) = (e2))\/(((op (e3) (e2)) = (e2))\/((op (e3) (e3)) = (e2))))) -> ((op (e0) (e1)) = (e2)) -> (~((op (e0) (e1)) = (op (e3) (e1)))) -> (~((op (e2) (op (e3) (e2))) = (op (e3) (e2)))) -> (((op (e0) (e3)) = (e0))\/(((op (e0) (e3)) = (e1))\/(((op (e0) (e3)) = (e2))\/((op (e0) (e3)) = (e3))))) -> ((op (e0) (e1)) = (e0)) -> (~((op (e0) (e1)) = (op (e0) (e3)))) -> (~((op (e0) (e3)) = (op (e2) (e3)))) -> (~((op (e0) (e3)) = (op (e3) (e3)))) -> (~((op (e0) (e3)) = (op (e1) (e3)))) -> (~((e1) = (e3))) -> (~((op (e0) (e2)) = (op (e0) (e3)))) -> (((op (e0) (e3)) = (e1))\/(((op (e1) (e3)) = (e1))\/(((op (e2) (e3)) = (e1))\/((op (e3) (e3)) = (e1))))) -> ((op (e3) (e2)) = (e3)) -> (~((op (e1) (e2)) = (op (e3) (e2)))) -> (~((op (e1) (e1)) = (e3))) -> (~((e2) = (e3))) -> (((op (e1) (e0)) = (e3))\/(((op (e1) (e1)) = (e3))\/(((op (e1) (e2)) = (e3))\/((op (e1) (e3)) = (e3))))) -> (~((op (e2) (e0)) = (op (e2) (e2)))) -> ((op (e2) (e2)) = (e2)) -> (~((op (e0) (op (e3) (e0))) = (op (e3) (e0)))) -> ((op (e0) (e2)) = (e1)) -> ((op (e3) (e0)) = (e1)) -> False). % 15.55/15.70 do 0 intro. intros zenon_Heb zenon_H8f zenon_H104 zenon_H1df zenon_H5d zenon_H138 zenon_H2af zenon_H254 zenon_H49 zenon_H1cd zenon_Hb4 zenon_H36 zenon_H80 zenon_Ha3 zenon_Hc9 zenon_H121 zenon_H106 zenon_H17d zenon_H182 zenon_H6a zenon_H90 zenon_H17a zenon_H35 zenon_H2b8 zenon_H29 zenon_Hee. % 15.55/15.70 apply (zenon_or_s _ _ zenon_Heb); [ zenon_intro zenon_H92 | zenon_intro zenon_Hec ]. % 15.55/15.70 exact (zenon_H8f zenon_H92). % 15.55/15.70 apply (zenon_or_s _ _ zenon_Hec); [ zenon_intro zenon_H68 | zenon_intro zenon_Hed ]. % 15.55/15.70 apply (zenon_or_s _ _ zenon_H90); [ zenon_intro zenon_H69 | zenon_intro zenon_H94 ]. % 15.55/15.70 apply (zenon_L17_); trivial. % 15.55/15.70 apply (zenon_or_s _ _ zenon_H94); [ zenon_intro zenon_H96 | zenon_intro zenon_H95 ]. % 15.55/15.70 exact (zenon_H182 zenon_H96). % 15.55/15.70 apply (zenon_or_s _ _ zenon_H95); [ zenon_intro zenon_H88 | zenon_intro zenon_H8a ]. % 15.55/15.70 apply (zenon_L164_); trivial. % 15.55/15.70 apply (zenon_or_s _ _ zenon_H121); [ zenon_intro zenon_H37 | zenon_intro zenon_H122 ]. % 15.55/15.70 apply (zenon_L85_); trivial. % 15.55/15.70 apply (zenon_or_s _ _ zenon_H122); [ zenon_intro zenon_H11f | zenon_intro zenon_H123 ]. % 15.55/15.70 apply (zenon_L772_); trivial. % 15.55/15.70 apply (zenon_or_s _ _ zenon_H123); [ zenon_intro zenon_Hb5 | zenon_intro zenon_H38 ]. % 15.55/15.70 apply (zenon_or_s _ _ zenon_H1df); [ zenon_intro zenon_He9 | zenon_intro zenon_H1e0 ]. % 15.55/15.70 apply (zenon_L1082_); trivial. % 15.55/15.70 apply (zenon_or_s _ _ zenon_H1e0); [ zenon_intro zenon_H16a | zenon_intro zenon_H1e1 ]. % 15.55/15.70 apply (zenon_L146_); trivial. % 15.55/15.70 apply (zenon_or_s _ _ zenon_H1e1); [ zenon_intro zenon_H1dd | zenon_intro zenon_H43 ]. % 15.55/15.70 apply (zenon_L1083_); trivial. % 15.55/15.70 apply (zenon_L1230_); trivial. % 15.55/15.70 exact (zenon_H104 zenon_H38). % 15.55/15.70 apply (zenon_or_s _ _ zenon_Hed); [ zenon_intro zenon_Hdd | zenon_intro zenon_He9 ]. % 15.55/15.70 apply (zenon_L161_); trivial. % 15.55/15.70 apply (zenon_L1082_); trivial. % 15.55/15.70 (* end of lemma zenon_L1263_ *) % 15.55/15.70 assert (zenon_L1264_ : (((op (e2) (e3)) = (e0))\/(((op (e2) (e3)) = (e1))\/(((op (e2) (e3)) = (e2))\/((op (e2) (e3)) = (e3))))) -> ((op (e2) (e0)) = (e0)) -> (~((op (e2) (e0)) = (op (e2) (e3)))) -> ((op (e0) (e3)) = (e1)) -> (~((op (e0) (e3)) = (op (e2) (e3)))) -> ((op (e2) (e2)) = (e2)) -> (~((op (e2) (e2)) = (op (e2) (e3)))) -> (~((op (e2) (op (e3) (e2))) = (op (e3) (e2)))) -> ((op (e3) (e2)) = (e3)) -> False). % 15.55/15.70 do 0 intro. intros zenon_H2ab zenon_Hcf zenon_Hce zenon_H37 zenon_Hb4 zenon_H35 zenon_H15f zenon_H2af zenon_H106. % 15.55/15.70 apply (zenon_or_s _ _ zenon_H2ab); [ zenon_intro zenon_Hd0 | zenon_intro zenon_H2ac ]. % 15.55/15.70 apply (zenon_L55_); trivial. % 15.55/15.70 apply (zenon_or_s _ _ zenon_H2ac); [ zenon_intro zenon_Hb5 | zenon_intro zenon_H2ad ]. % 15.55/15.70 apply (zenon_L41_); trivial. % 15.55/15.70 apply (zenon_or_s _ _ zenon_H2ad); [ zenon_intro zenon_H124 | zenon_intro zenon_He2 ]. % 15.55/15.70 apply (zenon_L137_); trivial. % 15.55/15.70 apply (zenon_L1065_); trivial. % 15.55/15.70 (* end of lemma zenon_L1264_ *) % 15.55/15.70 assert (zenon_L1265_ : (((op (e0) (e0)) = (e0))\/(((op (e1) (e0)) = (e0))\/(((op (e2) (e0)) = (e0))\/((op (e3) (e0)) = (e0))))) -> (~((op (e0) (e0)) = (e0))) -> ((~((op (e1) (e1)) = (e2)))\/((op (e1) (e2)) = (e1))) -> (~((op (e1) (e0)) = (op (e1) (e2)))) -> ((~((op (e3) (e3)) = (e0)))\/((op (e3) (e0)) = (e3))) -> (~((op (e3) (e0)) = (op (e3) (e2)))) -> ((~((op (e3) (e3)) = (e3)))\/((op (e3) (e3)) = (e3))) -> (~((op (e3) (op (e3) (e3))) = (op (e3) (e3)))) -> (((op (e1) (e1)) = (e0))\/(((op (e1) (e1)) = (e1))\/(((op (e1) (e1)) = (e2))\/((op (e1) (e1)) = (e3))))) -> ((~((op (e3) (e3)) = (e2)))\/((op (e3) (e2)) = (e3))) -> (~((op (e1) (e0)) = (op (e1) (e3)))) -> ((~((op (e1) (e1)) = (e3)))\/((op (e1) (e3)) = (e1))) -> (~((op (e1) (e0)) = (op (e1) (e1)))) -> ((~((op (e1) (e1)) = (e1)))\/((op (e1) (e1)) = (e1))) -> (~((op (e2) (e2)) = (e3))) -> (((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) (e1)) = (e0))\/(((op (e3) (e1)) = (e1))\/(((op (e3) (e1)) = (e2))\/((op (e3) (e1)) = (e3))))) -> (~((op (e3) (e0)) = (op (e3) (e1)))) -> (((op (e3) (e0)) = (e0))\/(((op (e3) (e1)) = (e0))\/(((op (e3) (e2)) = (e0))\/((op (e3) (e3)) = (e0))))) -> (((op (e3) (e3)) = (e0))\/(((op (e3) (e3)) = (e1))\/(((op (e3) (e3)) = (e2))\/((op (e3) (e3)) = (e3))))) -> (~((op (e3) (e3)) = (e0))) -> (~((op (e3) (e3)) = (e3))) -> (~((op (e2) (op (e3) (e2))) = (op (e3) (e2)))) -> (~((op (e2) (e2)) = (op (e2) (e3)))) -> ((op (e2) (e2)) = (e2)) -> (~((op (e0) (e3)) = (op (e2) (e3)))) -> (~((op (e2) (e0)) = (op (e2) (e3)))) -> (((op (e2) (e3)) = (e0))\/(((op (e2) (e3)) = (e1))\/(((op (e2) (e3)) = (e2))\/((op (e2) (e3)) = (e3))))) -> (((op (e0) (e0)) = (e1))\/(((op (e1) (e0)) = (e1))\/(((op (e2) (e0)) = (e1))\/((op (e3) (e0)) = (e1))))) -> (~((op (e1) (e2)) = (op (e2) (e2)))) -> (~((op (e1) (e1)) = (e2))) -> (~((e1) = (e2))) -> (((op (e1) (e0)) = (e2))\/(((op (e1) (e1)) = (e2))\/(((op (e1) (e2)) = (e2))\/((op (e1) (e3)) = (e2))))) -> (((op (e0) (e0)) = (e2))\/(((op (e0) (e1)) = (e2))\/(((op (e0) (e2)) = (e2))\/((op (e0) (e3)) = (e2))))) -> (~((op (e0) (op (e3) (e0))) = (op (e3) (e0)))) -> (~((op (e2) (e0)) = (op (e2) (e2)))) -> (((op (e0) (e0)) = (e3))\/(((op (e0) (e1)) = (e3))\/(((op (e0) (e2)) = (e3))\/((op (e0) (e3)) = (e3))))) -> (((op (e3) (e0)) = (e2))\/(((op (e3) (e1)) = (e2))\/(((op (e3) (e2)) = (e2))\/((op (e3) (e3)) = (e2))))) -> (~((op (e1) (e1)) = (e0))) -> (((op (e0) (e0)) = (e2))\/(((op (e1) (e0)) = (e2))\/(((op (e2) (e0)) = (e2))\/((op (e3) (e0)) = (e2))))) -> (~((op (e0) (e0)) = (e2))) -> (~((op (e0) (e1)) = (op (e3) (e1)))) -> (((op (e0) (e3)) = (e0))\/(((op (e0) (e3)) = (e1))\/(((op (e0) (e3)) = (e2))\/((op (e0) (e3)) = (e3))))) -> (~((op (e0) (e1)) = (op (e0) (e3)))) -> (~((op (e0) (e3)) = (op (e3) (e3)))) -> (((op (e0) (e3)) = (e1))\/(((op (e1) (e3)) = (e1))\/(((op (e2) (e3)) = (e1))\/((op (e3) (e3)) = (e1))))) -> (((op (e0) (e1)) = (e0))\/(((op (e1) (e1)) = (e0))\/(((op (e2) (e1)) = (e0))\/((op (e3) (e1)) = (e0))))) -> (~((op (e0) (e1)) = (op (e2) (e1)))) -> (~((op (e2) (e1)) = (op (e2) (e2)))) -> (~((op (e1) (e1)) = (op (e2) (e1)))) -> (~((op (e2) (e0)) = (op (e2) (e1)))) -> (((op (e2) (e1)) = (e0))\/(((op (e2) (e1)) = (e1))\/(((op (e2) (e1)) = (e2))\/((op (e2) (e1)) = (e3))))) -> (((op (e1) (e0)) = (e3))\/(((op (e1) (e1)) = (e3))\/(((op (e1) (e2)) = (e3))\/((op (e1) (e3)) = (e3))))) -> (~((e2) = (e3))) -> (~((op (e1) (e1)) = (e3))) -> (~((op (e1) (e2)) = (op (e3) (e2)))) -> (~((op (e0) (e3)) = (op (e1) (e3)))) -> (~((op (e0) (e2)) = (op (e2) (e2)))) -> ((op (e0) (e3)) = (e0)) -> (~((e0) = (e2))) -> (((op (e0) (e0)) = (e1))\/(((op (e0) (e1)) = (e1))\/(((op (e0) (e2)) = (e1))\/((op (e0) (e3)) = (e1))))) -> (~((op (e0) (e0)) = (e1))) -> (~((op (e0) (e1)) = (op (e1) (e1)))) -> (~((op (e3) (e3)) = (e1))) -> (~((op (e0) (e2)) = (op (e3) (e2)))) -> (~((op (e1) (op (e3) (e1))) = (op (e3) (e1)))) -> (~((e0) = (e1))) -> (((op (e3) (e0)) = (e1))\/(((op (e3) (e1)) = (e1))\/(((op (e3) (e2)) = (e1))\/((op (e3) (e3)) = (e1))))) -> (((op (e0) (e2)) = (e1))\/(((op (e1) (e2)) = (e1))\/(((op (e2) (e2)) = (e1))\/((op (e3) (e2)) = (e1))))) -> (~((op (e0) (e2)) = (op (e0) (e3)))) -> ((op (e1) (e1)) = (e1)) -> (~((op (e1) (e1)) = (op (e1) (e2)))) -> (~((op (e2) (e2)) = (e1))) -> (~((e1) = (e3))) -> ((op (e3) (e2)) = (e3)) -> False). % 15.55/15.70 do 0 intro. intros zenon_Hf0 zenon_H20 zenon_H1d3 zenon_H166 zenon_H10f zenon_H105 zenon_H10d zenon_H2be zenon_H1b3 zenon_H10e zenon_H1cf zenon_H1d2 zenon_Hd7 zenon_H1d8 zenon_H30 zenon_He6 zenon_H1d5 zenon_H16c zenon_H109 zenon_H1f6 zenon_H3b zenon_H3c zenon_H3e zenon_H2af zenon_H15f zenon_H35 zenon_Hb4 zenon_Hce zenon_H2ab zenon_Hf1 zenon_H7d zenon_Hd6 zenon_Ha7 zenon_H84 zenon_H8e zenon_H2b8 zenon_H17a zenon_H58 zenon_H1df zenon_H145 zenon_Heb zenon_H8f zenon_H138 zenon_H254 zenon_H1cd zenon_H36 zenon_H121 zenon_H144 zenon_Hde zenon_H157 zenon_Hb1 zenon_H154 zenon_H15a zenon_H90 zenon_H6a zenon_H182 zenon_H17d zenon_H80 zenon_H28 zenon_Hca zenon_H5e zenon_H44 zenon_H45 zenon_H23 zenon_H104 zenon_H140 zenon_H2b4 zenon_H9e zenon_H146 zenon_H11b zenon_Hc9 zenon_H21 zenon_H116 zenon_H52 zenon_Ha3 zenon_H106. % 15.55/15.70 apply (zenon_or_s _ _ zenon_Hf0); [ zenon_intro zenon_H1f | zenon_intro zenon_Hf2 ]. % 15.55/15.70 exact (zenon_H20 zenon_H1f). % 15.55/15.70 apply (zenon_or_s _ _ zenon_Hf2); [ zenon_intro zenon_Had | zenon_intro zenon_Hf3 ]. % 15.55/15.70 apply (zenon_or_s _ _ zenon_H44); [ zenon_intro zenon_H47 | zenon_intro zenon_H46 ]. % 15.55/15.70 exact (zenon_H45 zenon_H47). % 15.55/15.70 apply (zenon_or_s _ _ zenon_H46); [ zenon_intro zenon_H22 | zenon_intro zenon_H48 ]. % 15.55/15.70 apply (zenon_L3_); trivial. % 15.55/15.70 apply (zenon_or_s _ _ zenon_H48); [ zenon_intro zenon_H29 | zenon_intro zenon_H37 ]. % 15.55/15.70 apply (zenon_or_s _ _ zenon_Hf1); [ zenon_intro zenon_H47 | zenon_intro zenon_Hf4 ]. % 15.55/15.70 exact (zenon_H45 zenon_H47). % 15.55/15.70 apply (zenon_or_s _ _ zenon_Hf4); [ zenon_intro zenon_Hd8 | zenon_intro zenon_Hf5 ]. % 15.55/15.70 apply (zenon_L1256_); trivial. % 15.55/15.70 apply (zenon_or_s _ _ zenon_Hf5); [ zenon_intro zenon_Hae | zenon_intro zenon_Hee ]. % 15.55/15.70 apply (zenon_or_s _ _ zenon_Heb); [ zenon_intro zenon_H92 | zenon_intro zenon_Hec ]. % 15.55/15.70 exact (zenon_H8f zenon_H92). % 15.55/15.70 apply (zenon_or_s _ _ zenon_Hec); [ zenon_intro zenon_H68 | zenon_intro zenon_Hed ]. % 15.55/15.70 apply (zenon_or_s _ _ zenon_H58); [ zenon_intro zenon_H5b | zenon_intro zenon_H5a ]. % 15.55/15.70 apply (zenon_L1260_); trivial. % 15.55/15.70 apply (zenon_or_s _ _ zenon_H5a); [ zenon_intro zenon_H4a | zenon_intro zenon_H5c ]. % 15.55/15.70 apply (zenon_L1102_); trivial. % 15.55/15.70 apply (zenon_or_s _ _ zenon_H5c); [ zenon_intro zenon_H50 | zenon_intro zenon_H53 ]. % 15.55/15.70 apply (zenon_L29_); trivial. % 15.55/15.70 apply (zenon_L294_); trivial. % 15.55/15.70 apply (zenon_or_s _ _ zenon_Hed); [ zenon_intro zenon_Hdd | zenon_intro zenon_He9 ]. % 15.55/15.70 apply (zenon_L161_); trivial. % 15.55/15.70 apply (zenon_L1175_); trivial. % 15.55/15.70 apply (zenon_or_s _ _ zenon_H8e); [ zenon_intro zenon_H92 | zenon_intro zenon_H91 ]. % 15.55/15.70 exact (zenon_H8f zenon_H92). % 15.55/15.70 apply (zenon_or_s _ _ zenon_H91); [ zenon_intro zenon_H5d | zenon_intro zenon_H93 ]. % 15.55/15.70 apply (zenon_or_s _ _ zenon_Heb); [ zenon_intro zenon_H92 | zenon_intro zenon_Hec ]. % 15.55/15.70 exact (zenon_H8f zenon_H92). % 15.55/15.70 apply (zenon_or_s _ _ zenon_Hec); [ zenon_intro zenon_H68 | zenon_intro zenon_Hed ]. % 15.55/15.70 apply (zenon_or_s _ _ zenon_H58); [ zenon_intro zenon_H5b | zenon_intro zenon_H5a ]. % 15.55/15.70 apply (zenon_L1260_); trivial. % 15.55/15.70 apply (zenon_or_s _ _ zenon_H5a); [ zenon_intro zenon_H4a | zenon_intro zenon_H5c ]. % 15.55/15.70 apply (zenon_or_s _ _ zenon_H1f6); [ zenon_intro zenon_Hdb | zenon_intro zenon_H1f7 ]. % 15.55/15.70 apply (zenon_L1262_); trivial. % 15.55/15.70 apply (zenon_or_s _ _ zenon_H1f7); [ zenon_intro zenon_H142 | zenon_intro zenon_H1f8 ]. % 15.55/15.70 apply (zenon_L1136_); trivial. % 15.55/15.70 apply (zenon_or_s _ _ zenon_H1f8); [ zenon_intro zenon_H167 | zenon_intro zenon_H40 ]. % 15.55/15.70 apply (zenon_L1259_); trivial. % 15.55/15.70 exact (zenon_H3c zenon_H40). % 15.55/15.70 apply (zenon_or_s _ _ zenon_H5c); [ zenon_intro zenon_H50 | zenon_intro zenon_H53 ]. % 15.55/15.70 apply (zenon_L533_); trivial. % 15.55/15.70 apply (zenon_L294_); trivial. % 15.55/15.70 apply (zenon_or_s _ _ zenon_Hed); [ zenon_intro zenon_Hdd | zenon_intro zenon_He9 ]. % 15.55/15.70 apply (zenon_L161_); trivial. % 15.55/15.70 apply (zenon_L1164_); trivial. % 15.55/15.70 apply (zenon_or_s _ _ zenon_H93); [ zenon_intro zenon_H63 | zenon_intro zenon_H81 ]. % 15.55/15.70 apply (zenon_L15_); trivial. % 15.55/15.70 apply (zenon_L107_); trivial. % 15.55/15.70 apply (zenon_L88_); trivial. % 15.55/15.70 apply (zenon_or_s _ _ zenon_Hf3); [ zenon_intro zenon_Hcf | zenon_intro zenon_Hdb ]. % 15.55/15.70 apply (zenon_or_s _ _ zenon_H44); [ zenon_intro zenon_H47 | zenon_intro zenon_H46 ]. % 15.55/15.70 exact (zenon_H45 zenon_H47). % 15.55/15.70 apply (zenon_or_s _ _ zenon_H46); [ zenon_intro zenon_H22 | zenon_intro zenon_H48 ]. % 15.55/15.70 apply (zenon_L3_); trivial. % 15.55/15.70 apply (zenon_or_s _ _ zenon_H48); [ zenon_intro zenon_H29 | zenon_intro zenon_H37 ]. % 15.55/15.70 apply (zenon_or_s _ _ zenon_Hf1); [ zenon_intro zenon_H47 | zenon_intro zenon_Hf4 ]. % 15.55/15.70 exact (zenon_H45 zenon_H47). % 15.55/15.70 apply (zenon_or_s _ _ zenon_Hf4); [ zenon_intro zenon_Hd8 | zenon_intro zenon_Hf5 ]. % 15.55/15.70 apply (zenon_L167_); trivial. % 15.55/15.70 apply (zenon_or_s _ _ zenon_Hf5); [ zenon_intro zenon_Hae | zenon_intro zenon_Hee ]. % 15.55/15.70 apply (zenon_L269_); trivial. % 15.55/15.70 apply (zenon_or_s _ _ zenon_H8e); [ zenon_intro zenon_H92 | zenon_intro zenon_H91 ]. % 15.55/15.70 exact (zenon_H8f zenon_H92). % 15.55/15.70 apply (zenon_or_s _ _ zenon_H91); [ zenon_intro zenon_H5d | zenon_intro zenon_H93 ]. % 15.55/15.70 apply (zenon_or_s _ _ zenon_Heb); [ zenon_intro zenon_H92 | zenon_intro zenon_Hec ]. % 15.55/15.70 exact (zenon_H8f zenon_H92). % 15.55/15.70 apply (zenon_or_s _ _ zenon_Hec); [ zenon_intro zenon_H68 | zenon_intro zenon_Hed ]. % 15.55/15.70 apply (zenon_or_s _ _ zenon_H58); [ zenon_intro zenon_H5b | zenon_intro zenon_H5a ]. % 15.55/15.70 apply (zenon_or_s _ _ zenon_H144); [ zenon_intro zenon_H49 | zenon_intro zenon_H147 ]. % 15.55/15.70 apply (zenon_L1263_); trivial. % 15.55/15.70 apply (zenon_or_s _ _ zenon_H147); [ zenon_intro zenon_H149 | zenon_intro zenon_H148 ]. % 15.55/15.70 exact (zenon_H145 zenon_H149). % 15.55/15.70 apply (zenon_or_s _ _ zenon_H148); [ zenon_intro zenon_H14a | zenon_intro zenon_H142 ]. % 15.55/15.70 apply (zenon_L133_); trivial. % 15.55/15.70 apply (zenon_L1258_); trivial. % 15.55/15.70 apply (zenon_or_s _ _ zenon_H5a); [ zenon_intro zenon_H4a | zenon_intro zenon_H5c ]. % 15.55/15.71 apply (zenon_L135_); trivial. % 15.55/15.71 apply (zenon_or_s _ _ zenon_H5c); [ zenon_intro zenon_H50 | zenon_intro zenon_H53 ]. % 15.55/15.71 apply (zenon_L29_); trivial. % 15.55/15.71 apply (zenon_L294_); trivial. % 15.55/15.71 apply (zenon_or_s _ _ zenon_Hed); [ zenon_intro zenon_Hdd | zenon_intro zenon_He9 ]. % 15.55/15.71 apply (zenon_L161_); trivial. % 15.55/15.71 apply (zenon_L1164_); trivial. % 15.55/15.71 apply (zenon_or_s _ _ zenon_H93); [ zenon_intro zenon_H63 | zenon_intro zenon_H81 ]. % 15.55/15.71 apply (zenon_L15_); trivial. % 15.55/15.71 apply (zenon_L113_); trivial. % 15.55/15.71 apply (zenon_L1264_); trivial. % 15.55/15.71 apply (zenon_L1257_); trivial. % 15.55/15.71 (* end of lemma zenon_L1265_ *) % 15.55/15.71 assert (zenon_L1266_ : ((~((op (e2) (e2)) = (e3)))\/((op (e2) (e3)) = (e2))) -> (~((op (e2) (e1)) = (op (e3) (e1)))) -> (~((op (e3) (e1)) = (op (e3) (e2)))) -> ((~((op (e3) (e3)) = (e3)))\/((op (e3) (e3)) = (e3))) -> (~((op (e3) (op (e3) (e3))) = (op (e3) (e3)))) -> (~((op (e0) (e0)) = (e1))) -> (~((op (e0) (e1)) = (op (e1) (e1)))) -> ((op (e1) (e1)) = (e1)) -> (((op (e0) (e0)) = (e2))\/(((op (e0) (e1)) = (e2))\/(((op (e0) (e2)) = (e2))\/((op (e0) (e3)) = (e2))))) -> (~((op (e0) (e3)) = (op (e3) (e3)))) -> (((op (e3) (e3)) = (e0))\/(((op (e3) (e3)) = (e1))\/(((op (e3) (e3)) = (e2))\/((op (e3) (e3)) = (e3))))) -> (~((op (e0) (e2)) = (op (e2) (e2)))) -> (((op (e3) (e0)) = (e2))\/(((op (e3) (e1)) = (e2))\/(((op (e3) (e2)) = (e2))\/((op (e3) (e3)) = (e2))))) -> ((op (e2) (e2)) = (e2)) -> (~((op (e2) (op (e3) (e2))) = (op (e3) (e2)))) -> (~((op (e0) (e1)) = (op (e3) (e1)))) -> (~((op (e0) (op (e3) (e0))) = (op (e3) (e0)))) -> (~((op (e1) (op (e3) (e1))) = (op (e3) (e1)))) -> (~((op (e0) (e2)) = (op (e3) (e2)))) -> (((op (e3) (e0)) = (e1))\/(((op (e3) (e1)) = (e1))\/(((op (e3) (e2)) = (e1))\/((op (e3) (e3)) = (e1))))) -> (~((op (e0) (e0)) = (e2))) -> (((op (e0) (e0)) = (e1))\/(((op (e0) (e1)) = (e1))\/(((op (e0) (e2)) = (e1))\/((op (e0) (e3)) = (e1))))) -> (~((op (e0) (e0)) = (e0))) -> (((op (e0) (e0)) = (e3))\/(((op (e1) (e0)) = (e3))\/(((op (e2) (e0)) = (e3))\/((op (e3) (e0)) = (e3))))) -> (~((e1) = (e2))) -> (((op (e0) (e1)) = (e2))\/(((op (e1) (e1)) = (e2))\/(((op (e2) (e1)) = (e2))\/((op (e3) (e1)) = (e2))))) -> (((op (e0) (e2)) = (e3))\/(((op (e1) (e2)) = (e3))\/(((op (e2) (e2)) = (e3))\/((op (e3) (e2)) = (e3))))) -> (~((op (e0) (e1)) = (op (e0) (e2)))) -> (((op (e0) (e2)) = (e0))\/(((op (e0) (e2)) = (e1))\/(((op (e0) (e2)) = (e2))\/((op (e0) (e2)) = (e3))))) -> (~((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 (e1) (e2)) = (op (e2) (e2)))) -> (((op (e3) (e0)) = (e0))\/(((op (e3) (e1)) = (e0))\/(((op (e3) (e2)) = (e0))\/((op (e3) (e3)) = (e0))))) -> (~((op (e2) (e1)) = (op (e2) (e2)))) -> (~((op (e1) (e1)) = (e2))) -> (~((op (e2) (e0)) = (op (e2) (e2)))) -> (((op (e0) (e0)) = (e2))\/(((op (e1) (e0)) = (e2))\/(((op (e2) (e0)) = (e2))\/((op (e3) (e0)) = (e2))))) -> (~((op (e3) (e0)) = (op (e3) (e2)))) -> ((~((op (e3) (e3)) = (e2)))\/((op (e3) (e2)) = (e3))) -> (~((op (e1) (e1)) = (e3))) -> (~((op (e1) (e2)) = (op (e3) (e2)))) -> (((op (e2) (e0)) = (e1))\/(((op (e2) (e1)) = (e1))\/(((op (e2) (e2)) = (e1))\/((op (e2) (e3)) = (e1))))) -> (~((op (e0) (e1)) = (op (e0) (e3)))) -> (~((op (e0) (e3)) = (op (e2) (e3)))) -> (~((op (e0) (e3)) = (op (e1) (e3)))) -> (((op (e0) (e3)) = (e0))\/(((op (e0) (e3)) = (e1))\/(((op (e0) (e3)) = (e2))\/((op (e0) (e3)) = (e3))))) -> (~((op (e1) (e1)) = (op (e1) (e2)))) -> (((op (e0) (e2)) = (e1))\/(((op (e1) (e2)) = (e1))\/(((op (e2) (e2)) = (e1))\/((op (e3) (e2)) = (e1))))) -> (~((op (e2) (e2)) = (e1))) -> (~((op (e1) (e1)) = (op (e2) (e1)))) -> (~((e1) = (e3))) -> (((op (e1) (e0)) = (e3))\/(((op (e1) (e1)) = (e3))\/(((op (e1) (e2)) = (e3))\/((op (e1) (e3)) = (e3))))) -> (~((e2) = (e3))) -> (~((op (e0) (e0)) = (e3))) -> (((op (e3) (e0)) = (e3))\/(((op (e3) (e1)) = (e3))\/(((op (e3) (e2)) = (e3))\/((op (e3) (e3)) = (e3))))) -> (~((op (e1) (e0)) = (op (e2) (e0)))) -> (((op (e1) (e0)) = (e2))\/(((op (e1) (e1)) = (e2))\/(((op (e1) (e2)) = (e2))\/((op (e1) (e3)) = (e2))))) -> (~((op (e3) (e0)) = (op (e3) (e1)))) -> ((~((op (e3) (e3)) = (e1)))\/((op (e3) (e1)) = (e3))) -> (~((op (e1) (e0)) = (op (e1) (e2)))) -> (~((op (e0) (e2)) = (op (e0) (e3)))) -> (~((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 (e2) (e0)) = (e0))\/((op (e3) (e0)) = (e0))))) -> (((op (e0) (e1)) = (e0))\/(((op (e1) (e1)) = (e0))\/(((op (e2) (e1)) = (e0))\/((op (e3) (e1)) = (e0))))) -> (~((op (e2) (e0)) = (op (e2) (e1)))) -> (~((op (e1) (e1)) = (e0))) -> (((op (e0) (e3)) = (e1))\/(((op (e1) (e3)) = (e1))\/(((op (e2) (e3)) = (e1))\/((op (e3) (e3)) = (e1))))) -> (((op (e2) (e1)) = (e0))\/(((op (e2) (e1)) = (e1))\/(((op (e2) (e1)) = (e2))\/((op (e2) (e1)) = (e3))))) -> (~((e0) = (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) (e0)) = (op (e2) (e3)))) -> (((op (e3) (e1)) = (e0))\/(((op (e3) (e1)) = (e1))\/(((op (e3) (e1)) = (e2))\/((op (e3) (e1)) = (e3))))) -> (((op (e0) (e0)) = (e3))\/(((op (e0) (e1)) = (e3))\/(((op (e0) (e2)) = (e3))\/((op (e0) (e3)) = (e3))))) -> (~((op (e0) (e1)) = (op (e2) (e1)))) -> (((op (e2) (e0)) = (e3))\/(((op (e2) (e1)) = (e3))\/(((op (e2) (e2)) = (e3))\/((op (e2) (e3)) = (e3))))) -> ((~((op (e1) (e1)) = (e2)))\/((op (e1) (e2)) = (e1))) -> ((~((op (e3) (e3)) = (e0)))\/((op (e3) (e0)) = (e3))) -> (((op (e1) (e1)) = (e0))\/(((op (e1) (e1)) = (e1))\/(((op (e1) (e1)) = (e2))\/((op (e1) (e1)) = (e3))))) -> (~((op (e1) (e0)) = (op (e1) (e3)))) -> ((~((op (e1) (e1)) = (e3)))\/((op (e1) (e3)) = (e1))) -> (~((op (e1) (e0)) = (op (e1) (e1)))) -> ((~((op (e1) (e1)) = (e1)))\/((op (e1) (e1)) = (e1))) -> (((op (e0) (e0)) = (e0))\/(((op (e0) (e1)) = (e0))\/(((op (e0) (e2)) = (e0))\/((op (e0) (e3)) = (e0))))) -> False). % 15.55/15.71 do 0 intro. intros zenon_H1c3 zenon_H13c zenon_H135 zenon_H10d zenon_H2be zenon_H45 zenon_H23 zenon_H21 zenon_H8e zenon_H36 zenon_H3b zenon_H28 zenon_H1df zenon_H35 zenon_H2af zenon_H138 zenon_H2b8 zenon_H2b4 zenon_H140 zenon_H146 zenon_H8f zenon_H44 zenon_H20 zenon_Hbe zenon_Ha7 zenon_H1a2 zenon_H175 zenon_H23e zenon_H251 zenon_H4b zenon_H1d5 zenon_H87 zenon_H7d zenon_H1f6 zenon_H157 zenon_Hd6 zenon_H17a zenon_Heb zenon_H105 zenon_H10e zenon_H182 zenon_H17d zenon_Hb7 zenon_H1cd zenon_Hb4 zenon_H80 zenon_H254 zenon_H116 zenon_H11b zenon_H52 zenon_Hb1 zenon_Ha3 zenon_H90 zenon_H6a zenon_H59 zenon_H2d5 zenon_H247 zenon_H84 zenon_H109 zenon_H10c zenon_H166 zenon_Hc9 zenon_H9e zenon_Hf1 zenon_Hf0 zenon_H144 zenon_H154 zenon_H145 zenon_H121 zenon_H15a zenon_H5e zenon_H2ab zenon_H15f zenon_Hce zenon_H16c zenon_H58 zenon_Hde zenon_He6 zenon_H1d3 zenon_H10f zenon_H1b3 zenon_H1cf zenon_H1d2 zenon_Hd7 zenon_H1d8 zenon_H110. % 15.55/15.71 apply (zenon_or_s _ _ zenon_H1c3); [ zenon_intro zenon_H30 | zenon_intro zenon_H124 ]. % 15.55/15.71 apply (zenon_or_s _ _ zenon_H10f); [ zenon_intro zenon_H3c | zenon_intro zenon_Hba ]. % 15.55/15.71 apply (zenon_or_s _ _ zenon_H10c); [ zenon_intro zenon_H104 | zenon_intro zenon_H10a ]. % 15.55/15.71 apply (zenon_or_s _ _ zenon_H10e); [ zenon_intro zenon_H3d | zenon_intro zenon_H106 ]. % 15.55/15.71 apply (zenon_L1229_); trivial. % 15.55/15.71 apply (zenon_or_s _ _ zenon_H10d); [ zenon_intro zenon_H3e | zenon_intro zenon_H42 ]. % 15.55/15.71 apply (zenon_or_s _ _ zenon_H110); [ zenon_intro zenon_H1f | zenon_intro zenon_H111 ]. % 15.55/15.71 exact (zenon_H20 zenon_H1f). % 15.55/15.71 apply (zenon_or_s _ _ zenon_H111); [ zenon_intro zenon_H49 | zenon_intro zenon_H112 ]. % 15.55/15.71 apply (zenon_L1239_); trivial. % 15.55/15.71 apply (zenon_or_s _ _ zenon_H112); [ zenon_intro zenon_Hab | zenon_intro zenon_Hca ]. % 15.55/15.71 apply (zenon_L1254_); trivial. % 15.55/15.71 apply (zenon_L1265_); trivial. % 15.55/15.71 apply (zenon_L1041_); trivial. % 15.55/15.71 apply (zenon_L1183_); trivial. % 15.55/15.71 apply (zenon_L1178_); trivial. % 15.55/15.71 apply (zenon_L137_); trivial. % 15.55/15.71 (* end of lemma zenon_L1266_ *) % 15.55/15.71 assert (zenon_L1267_ : (((op (e0) (e0)) = (e2))\/(((op (e0) (e1)) = (e2))\/(((op (e0) (e2)) = (e2))\/((op (e0) (e3)) = (e2))))) -> (~((e0) = (e2))) -> ((op (e0) (e1)) = (e0)) -> (((op (e3) (e0)) = (e2))\/(((op (e3) (e1)) = (e2))\/(((op (e3) (e2)) = (e2))\/((op (e3) (e3)) = (e2))))) -> (~((op (e0) (op (e3) (e0))) = (op (e3) (e0)))) -> (~((op (e2) (e1)) = (op (e3) (e1)))) -> ((op (e2) (e1)) = (e2)) -> (~((op (e2) (op (e3) (e2))) = (op (e3) (e2)))) -> (~((op (e3) (e3)) = (e2))) -> (~((op (e1) (op (e3) (e1))) = (op (e3) (e1)))) -> ((op (e1) (e1)) = (e1)) -> (~((e1) = (e2))) -> (((op (e0) (e0)) = (e0))\/(((op (e0) (e0)) = (e1))\/(((op (e0) (e0)) = (e2))\/((op (e0) (e0)) = (e3))))) -> (~((op (e0) (e0)) = (e0))) -> (~((op (e0) (e0)) = (e2))) -> (~((op (e0) (e0)) = (e3))) -> (~((op (e0) (e2)) = (op (e3) (e2)))) -> (((op (e3) (e0)) = (e1))\/(((op (e3) (e1)) = (e1))\/(((op (e3) (e2)) = (e1))\/((op (e3) (e3)) = (e1))))) -> (((op (e3) (e3)) = (e0))\/(((op (e3) (e3)) = (e1))\/(((op (e3) (e3)) = (e2))\/((op (e3) (e3)) = (e3))))) -> (~((op (e3) (e3)) = (e0))) -> (~((op (e3) (e3)) = (e1))) -> (~((op (e0) (e3)) = (op (e3) (e3)))) -> (~((op (e3) (e3)) = (e3))) -> False). % 15.55/15.71 do 0 intro. intros zenon_H8e zenon_H5e zenon_H49 zenon_H1df zenon_H2b8 zenon_H13c zenon_H156 zenon_H2af zenon_H3d zenon_H2b4 zenon_H21 zenon_Ha7 zenon_H12a zenon_H20 zenon_H8f zenon_H59 zenon_H140 zenon_H146 zenon_H3b zenon_H3c zenon_H104 zenon_H36 zenon_H3e. % 15.55/15.71 apply (zenon_or_s _ _ zenon_H8e); [ zenon_intro zenon_H92 | zenon_intro zenon_H91 ]. % 15.55/15.71 exact (zenon_H8f zenon_H92). % 15.55/15.71 apply (zenon_or_s _ _ zenon_H91); [ zenon_intro zenon_H5d | zenon_intro zenon_H93 ]. % 15.55/15.71 apply (zenon_L14_); trivial. % 15.55/15.71 apply (zenon_or_s _ _ zenon_H93); [ zenon_intro zenon_H63 | zenon_intro zenon_H81 ]. % 15.55/15.71 apply (zenon_L1207_); trivial. % 15.55/15.71 apply (zenon_L107_); trivial. % 15.55/15.71 (* end of lemma zenon_L1267_ *) % 15.55/15.71 assert (zenon_L1268_ : (((op (e3) (e0)) = (e0))\/(((op (e3) (e1)) = (e0))\/(((op (e3) (e2)) = (e0))\/((op (e3) (e3)) = (e0))))) -> (~((e1) = (e3))) -> (~((op (e1) (op (e3) (e1))) = (op (e3) (e1)))) -> ((op (e1) (e1)) = (e1)) -> (~((e0) = (e1))) -> (((op (e3) (e0)) = (e1))\/(((op (e3) (e1)) = (e1))\/(((op (e3) (e2)) = (e1))\/((op (e3) (e3)) = (e1))))) -> ((op (e2) (e2)) = (e1)) -> (~((op (e2) (e1)) = (op (e2) (e3)))) -> ((op (e2) (e1)) = (e2)) -> ((op (e1) (e3)) = (e3)) -> (~((e2) = (e3))) -> (((op (e3) (e3)) = (e0))\/(((op (e3) (e3)) = (e1))\/(((op (e3) (e3)) = (e2))\/((op (e3) (e3)) = (e3))))) -> (~((op (e3) (e3)) = (e1))) -> (~((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) (e2)) = (e3)) -> (~((e0) = (e3))) -> (~((op (e3) (e3)) = (e0))) -> False). % 15.55/15.71 do 0 intro. intros zenon_H1f6 zenon_Ha3 zenon_H2b4 zenon_H21 zenon_H9e zenon_H146 zenon_H2a zenon_H1e2 zenon_H156 zenon_H8a zenon_H6a zenon_H3b zenon_H104 zenon_H36 zenon_H3e zenon_H160 zenon_H106 zenon_H4b zenon_H3c. % 15.55/15.71 apply (zenon_or_s _ _ zenon_H1f6); [ zenon_intro zenon_Hdb | zenon_intro zenon_H1f7 ]. % 15.55/15.71 apply (zenon_L1212_); trivial. % 15.55/15.71 apply (zenon_or_s _ _ zenon_H1f7); [ zenon_intro zenon_H142 | zenon_intro zenon_H1f8 ]. % 15.55/15.71 apply (zenon_L902_); trivial. % 15.55/15.71 apply (zenon_or_s _ _ zenon_H1f8); [ zenon_intro zenon_H167 | zenon_intro zenon_H40 ]. % 15.55/15.71 apply (zenon_L589_); trivial. % 15.55/15.71 exact (zenon_H3c zenon_H40). % 15.55/15.71 (* end of lemma zenon_L1268_ *) % 15.55/15.71 assert (zenon_L1269_ : (((op (e1) (e0)) = (e3))\/(((op (e1) (e1)) = (e3))\/(((op (e1) (e2)) = (e3))\/((op (e1) (e3)) = (e3))))) -> ((op (e1) (e0)) = (e2)) -> (~((op (e1) (e1)) = (e3))) -> (~((op (e1) (e2)) = (op (e3) (e2)))) -> (((op (e0) (e2)) = (e1))\/(((op (e1) (e2)) = (e1))\/(((op (e2) (e2)) = (e1))\/((op (e3) (e2)) = (e1))))) -> (~((e1) = (e2))) -> ((op (e0) (e2)) = (e2)) -> (~((op (e1) (e1)) = (op (e1) (e2)))) -> (~((op (e3) (e3)) = (e0))) -> (~((e0) = (e3))) -> (((op (e0) (e3)) = (e2))\/(((op (e1) (e3)) = (e2))\/(((op (e2) (e3)) = (e2))\/((op (e3) (e3)) = (e2))))) -> (~((op (e3) (e3)) = (e3))) -> (~((op (e0) (e3)) = (op (e3) (e3)))) -> (~((op (e3) (e3)) = (e1))) -> (((op (e3) (e3)) = (e0))\/(((op (e3) (e3)) = (e1))\/(((op (e3) (e3)) = (e2))\/((op (e3) (e3)) = (e3))))) -> (~((e2) = (e3))) -> ((op (e2) (e1)) = (e2)) -> (~((op (e2) (e1)) = (op (e2) (e3)))) -> (((op (e3) (e0)) = (e1))\/(((op (e3) (e1)) = (e1))\/(((op (e3) (e2)) = (e1))\/((op (e3) (e3)) = (e1))))) -> (~((e0) = (e1))) -> ((op (e1) (e1)) = (e1)) -> (~((op (e1) (op (e3) (e1))) = (op (e3) (e1)))) -> (((op (e3) (e0)) = (e0))\/(((op (e3) (e1)) = (e0))\/(((op (e3) (e2)) = (e0))\/((op (e3) (e3)) = (e0))))) -> (~((e1) = (e3))) -> ((op (e3) (e2)) = (e3)) -> False). % 15.55/15.71 do 0 intro. intros zenon_H90 zenon_H68 zenon_H182 zenon_H17d zenon_H11b zenon_Ha7 zenon_H63 zenon_H116 zenon_H3c zenon_H4b zenon_H160 zenon_H3e zenon_H36 zenon_H104 zenon_H3b zenon_H6a zenon_H156 zenon_H1e2 zenon_H146 zenon_H9e zenon_H21 zenon_H2b4 zenon_H1f6 zenon_Ha3 zenon_H106. % 15.55/15.71 apply (zenon_or_s _ _ zenon_H90); [ zenon_intro zenon_H69 | zenon_intro zenon_H94 ]. % 15.55/15.71 apply (zenon_L17_); trivial. % 15.55/15.71 apply (zenon_or_s _ _ zenon_H94); [ zenon_intro zenon_H96 | zenon_intro zenon_H95 ]. % 15.55/15.71 exact (zenon_H182 zenon_H96). % 15.55/15.71 apply (zenon_or_s _ _ zenon_H95); [ zenon_intro zenon_H88 | zenon_intro zenon_H8a ]. % 15.55/15.71 apply (zenon_L164_); trivial. % 15.55/15.71 apply (zenon_or_s _ _ zenon_H11b); [ zenon_intro zenon_H29 | zenon_intro zenon_H11c ]. % 15.55/15.71 apply (zenon_L104_); trivial. % 15.55/15.71 apply (zenon_or_s _ _ zenon_H11c); [ zenon_intro zenon_H117 | zenon_intro zenon_H11d ]. % 15.55/15.71 apply (zenon_L86_); trivial. % 15.55/15.71 apply (zenon_or_s _ _ zenon_H11d); [ zenon_intro zenon_H2a | zenon_intro zenon_H119 ]. % 15.55/15.71 apply (zenon_L1268_); trivial. % 15.55/15.71 apply (zenon_L87_); trivial. % 15.55/15.71 (* end of lemma zenon_L1269_ *) % 15.55/15.71 assert (zenon_L1270_ : ((~((op (e3) (e3)) = (e3)))\/((op (e3) (e3)) = (e3))) -> (~((op (e3) (op (e3) (e3))) = (op (e3) (e3)))) -> (~((op (e0) (e0)) = (e2))) -> (~((e0) = (e2))) -> ((op (e0) (e1)) = (e0)) -> (((op (e0) (e2)) = (e1))\/(((op (e1) (e2)) = (e1))\/(((op (e2) (e2)) = (e1))\/((op (e3) (e2)) = (e1))))) -> ((op (e3) (e2)) = (e3)) -> (~((e1) = (e3))) -> (~((op (e2) (e2)) = (e1))) -> ((op (e1) (e1)) = (e1)) -> (~((op (e1) (e1)) = (op (e1) (e2)))) -> (~((e1) = (e2))) -> (((op (e3) (e3)) = (e0))\/(((op (e3) (e3)) = (e1))\/(((op (e3) (e3)) = (e2))\/((op (e3) (e3)) = (e3))))) -> (~((op (e0) (e3)) = (op (e3) (e3)))) -> (~((op (e3) (e3)) = (e1))) -> (~((op (e3) (e3)) = (e0))) -> (((op (e0) (e0)) = (e2))\/(((op (e0) (e1)) = (e2))\/(((op (e0) (e2)) = (e2))\/((op (e0) (e3)) = (e2))))) -> False). % 15.55/15.71 do 0 intro. intros zenon_H10d zenon_H2be zenon_H8f zenon_H5e zenon_H49 zenon_H11b zenon_H106 zenon_Ha3 zenon_H52 zenon_H21 zenon_H116 zenon_Ha7 zenon_H3b zenon_H36 zenon_H104 zenon_H3c zenon_H8e. % 15.55/15.71 apply (zenon_or_s _ _ zenon_H10d); [ zenon_intro zenon_H3e | zenon_intro zenon_H42 ]. % 15.55/15.71 apply (zenon_L108_); trivial. % 15.55/15.71 apply (zenon_L1041_); trivial. % 15.55/15.71 (* end of lemma zenon_L1270_ *) % 15.55/15.71 assert (zenon_L1271_ : ((~((op (e3) (e3)) = (e2)))\/((op (e3) (e2)) = (e3))) -> (((op (e0) (e0)) = (e2))\/(((op (e0) (e1)) = (e2))\/(((op (e0) (e2)) = (e2))\/((op (e0) (e3)) = (e2))))) -> (~((op (e3) (e3)) = (e0))) -> (~((op (e0) (e3)) = (op (e3) (e3)))) -> (~((e1) = (e2))) -> (~((op (e1) (e1)) = (op (e1) (e2)))) -> ((op (e1) (e1)) = (e1)) -> (~((op (e2) (e2)) = (e1))) -> (~((e1) = (e3))) -> (((op (e0) (e2)) = (e1))\/(((op (e1) (e2)) = (e1))\/(((op (e2) (e2)) = (e1))\/((op (e3) (e2)) = (e1))))) -> (((op (e0) (e1)) = (e2))\/(((op (e1) (e1)) = (e2))\/(((op (e2) (e1)) = (e2))\/((op (e3) (e1)) = (e2))))) -> (((op (e0) (e0)) = (e0))\/(((op (e0) (e0)) = (e1))\/(((op (e0) (e0)) = (e2))\/((op (e0) (e0)) = (e3))))) -> (~((op (e0) (e0)) = (e3))) -> (~((op (e0) (e0)) = (e2))) -> (~((op (e0) (e0)) = (e0))) -> (~((op (e3) (e3)) = (e1))) -> (((op (e3) (e3)) = (e0))\/(((op (e3) (e3)) = (e1))\/(((op (e3) (e3)) = (e2))\/((op (e3) (e3)) = (e3))))) -> ((op (e2) (e0)) = (e2)) -> (~((op (e2) (e0)) = (op (e2) (e1)))) -> (~((op (e1) (e1)) = (e2))) -> ((op (e0) (e1)) = (e0)) -> (~((e0) = (e2))) -> (~((op (e3) (op (e3) (e3))) = (op (e3) (e3)))) -> ((~((op (e3) (e3)) = (e3)))\/((op (e3) (e3)) = (e3))) -> False). % 15.55/15.71 do 0 intro. intros zenon_H10e zenon_H8e zenon_H3c zenon_H36 zenon_Ha7 zenon_H116 zenon_H21 zenon_H52 zenon_Ha3 zenon_H11b zenon_H1a2 zenon_H12a zenon_H59 zenon_H8f zenon_H20 zenon_H104 zenon_H3b zenon_Hdd zenon_H154 zenon_Hd6 zenon_H49 zenon_H5e zenon_H2be zenon_H10d. % 15.55/15.71 apply (zenon_or_s _ _ zenon_H10e); [ zenon_intro zenon_H3d | zenon_intro zenon_H106 ]. % 15.55/15.71 apply (zenon_or_s _ _ zenon_H10d); [ zenon_intro zenon_H3e | zenon_intro zenon_H42 ]. % 15.55/15.71 apply (zenon_L295_); trivial. % 15.55/15.71 apply (zenon_L1041_); trivial. % 15.55/15.71 apply (zenon_L1270_); trivial. % 15.55/15.71 (* end of lemma zenon_L1271_ *) % 15.55/15.71 assert (zenon_L1272_ : ((~((op (e3) (e3)) = (e1)))\/((op (e3) (e1)) = (e3))) -> (~((e2) = (e3))) -> ((~((op (e3) (e3)) = (e3)))\/((op (e3) (e3)) = (e3))) -> (~((op (e3) (op (e3) (e3))) = (op (e3) (e3)))) -> (~((e0) = (e2))) -> ((op (e0) (e1)) = (e0)) -> (~((op (e1) (e1)) = (e2))) -> (~((op (e2) (e0)) = (op (e2) (e1)))) -> ((op (e2) (e0)) = (e2)) -> (((op (e3) (e3)) = (e0))\/(((op (e3) (e3)) = (e1))\/(((op (e3) (e3)) = (e2))\/((op (e3) (e3)) = (e3))))) -> (~((op (e0) (e0)) = (e0))) -> (~((op (e0) (e0)) = (e2))) -> (~((op (e0) (e0)) = (e3))) -> (((op (e0) (e0)) = (e0))\/(((op (e0) (e0)) = (e1))\/(((op (e0) (e0)) = (e2))\/((op (e0) (e0)) = (e3))))) -> (((op (e0) (e1)) = (e2))\/(((op (e1) (e1)) = (e2))\/(((op (e2) (e1)) = (e2))\/((op (e3) (e1)) = (e2))))) -> (((op (e0) (e2)) = (e1))\/(((op (e1) (e2)) = (e1))\/(((op (e2) (e2)) = (e1))\/((op (e3) (e2)) = (e1))))) -> (~((e1) = (e3))) -> (~((op (e2) (e2)) = (e1))) -> ((op (e1) (e1)) = (e1)) -> (~((op (e1) (e1)) = (op (e1) (e2)))) -> (~((e1) = (e2))) -> (~((op (e0) (e3)) = (op (e3) (e3)))) -> (~((op (e3) (e3)) = (e0))) -> (((op (e0) (e0)) = (e2))\/(((op (e0) (e1)) = (e2))\/(((op (e0) (e2)) = (e2))\/((op (e0) (e3)) = (e2))))) -> ((~((op (e3) (e3)) = (e2)))\/((op (e3) (e2)) = (e3))) -> False). % 15.55/15.71 do 0 intro. intros zenon_H10c zenon_H6a zenon_H10d zenon_H2be zenon_H5e zenon_H49 zenon_Hd6 zenon_H154 zenon_Hdd zenon_H3b zenon_H20 zenon_H8f zenon_H59 zenon_H12a zenon_H1a2 zenon_H11b zenon_Ha3 zenon_H52 zenon_H21 zenon_H116 zenon_Ha7 zenon_H36 zenon_H3c zenon_H8e zenon_H10e. % 15.55/15.71 apply (zenon_or_s _ _ zenon_H10c); [ zenon_intro zenon_H104 | zenon_intro zenon_H10a ]. % 15.55/15.71 apply (zenon_L1271_); trivial. % 15.55/15.71 apply (zenon_L298_); trivial. % 15.55/15.71 (* end of lemma zenon_L1272_ *) % 15.55/15.71 assert (zenon_L1273_ : (((op (e0) (e1)) = (e2))\/(((op (e1) (e1)) = (e2))\/(((op (e2) (e1)) = (e2))\/((op (e3) (e1)) = (e2))))) -> (~((e0) = (e2))) -> ((op (e0) (e1)) = (e0)) -> (~((op (e1) (e1)) = (e2))) -> (((op (e3) (e0)) = (e2))\/(((op (e3) (e1)) = (e2))\/(((op (e3) (e2)) = (e2))\/((op (e3) (e3)) = (e2))))) -> ((op (e3) (e0)) = (e3)) -> (~((e2) = (e3))) -> (~((op (e2) (e1)) = (op (e3) (e1)))) -> (~((op (e2) (op (e3) (e2))) = (op (e3) (e2)))) -> (~((op (e1) (op (e3) (e1))) = (op (e3) (e1)))) -> ((op (e1) (e1)) = (e1)) -> (~((e1) = (e3))) -> (((op (e3) (e0)) = (e1))\/(((op (e3) (e1)) = (e1))\/(((op (e3) (e2)) = (e1))\/((op (e3) (e3)) = (e1))))) -> (((op (e3) (e3)) = (e0))\/(((op (e3) (e3)) = (e1))\/(((op (e3) (e3)) = (e2))\/((op (e3) (e3)) = (e3))))) -> (~((op (e0) (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 (e3) (e3)) = (e1))) -> (~((op (e3) (e3)) = (e2))) -> (~((op (e3) (e3)) = (e3))) -> False). % 15.55/15.71 do 0 intro. intros zenon_H1a2 zenon_H5e zenon_H49 zenon_Hd6 zenon_H1df zenon_Hba zenon_H6a zenon_H13c zenon_H2af zenon_H2b4 zenon_H21 zenon_Ha3 zenon_H146 zenon_H3b zenon_H59 zenon_H8f zenon_H20 zenon_H12a zenon_H104 zenon_H3d zenon_H3e. % 15.55/15.71 apply (zenon_or_s _ _ zenon_H1a2); [ zenon_intro zenon_H5d | zenon_intro zenon_H1a3 ]. % 15.55/15.71 apply (zenon_L14_); trivial. % 15.55/15.71 apply (zenon_or_s _ _ zenon_H1a3); [ zenon_intro zenon_H6e | zenon_intro zenon_H1a4 ]. % 15.55/15.71 exact (zenon_Hd6 zenon_H6e). % 15.55/15.71 apply (zenon_or_s _ _ zenon_H1a4); [ zenon_intro zenon_H156 | zenon_intro zenon_H16a ]. % 15.55/15.71 apply (zenon_L1201_); trivial. % 15.55/15.71 apply (zenon_L188_); trivial. % 15.55/15.71 (* end of lemma zenon_L1273_ *) % 15.55/15.71 assert (zenon_L1274_ : ((~((op (e3) (e3)) = (e1)))\/((op (e3) (e1)) = (e3))) -> (~((op (e3) (e0)) = (op (e3) (e1)))) -> ((~((op (e3) (e3)) = (e3)))\/((op (e3) (e3)) = (e3))) -> (~((op (e3) (op (e3) (e3))) = (op (e3) (e3)))) -> (~((e0) = (e2))) -> ((op (e0) (e1)) = (e0)) -> (~((op (e1) (e1)) = (e2))) -> (((op (e3) (e0)) = (e1))\/(((op (e3) (e1)) = (e1))\/(((op (e3) (e2)) = (e1))\/((op (e3) (e3)) = (e1))))) -> (~((e2) = (e3))) -> (~((op (e2) (e1)) = (op (e3) (e1)))) -> (~((op (e2) (op (e3) (e2))) = (op (e3) (e2)))) -> (((op (e3) (e0)) = (e2))\/(((op (e3) (e1)) = (e2))\/(((op (e3) (e2)) = (e2))\/((op (e3) (e3)) = (e2))))) -> ((op (e1) (e1)) = (e1)) -> (~((op (e1) (op (e3) (e1))) = (op (e3) (e1)))) -> ((op (e3) (e0)) = (e3)) -> (~((e1) = (e3))) -> (((op (e3) (e3)) = (e0))\/(((op (e3) (e3)) = (e1))\/(((op (e3) (e3)) = (e2))\/((op (e3) (e3)) = (e3))))) -> (~((op (e0) (e0)) = (e0))) -> (~((op (e0) (e0)) = (e2))) -> (~((op (e0) (e0)) = (e3))) -> (((op (e0) (e0)) = (e0))\/(((op (e0) (e0)) = (e1))\/(((op (e0) (e0)) = (e2))\/((op (e0) (e0)) = (e3))))) -> (((op (e0) (e1)) = (e2))\/(((op (e1) (e1)) = (e2))\/(((op (e2) (e1)) = (e2))\/((op (e3) (e1)) = (e2))))) -> (~((op (e3) (e0)) = (op (e3) (e2)))) -> ((~((op (e3) (e3)) = (e2)))\/((op (e3) (e2)) = (e3))) -> False). % 15.55/15.71 do 0 intro. intros zenon_H10c zenon_H109 zenon_H10d zenon_H2be zenon_H5e zenon_H49 zenon_Hd6 zenon_H146 zenon_H6a zenon_H13c zenon_H2af zenon_H1df zenon_H21 zenon_H2b4 zenon_Hba zenon_Ha3 zenon_H3b zenon_H20 zenon_H8f zenon_H59 zenon_H12a zenon_H1a2 zenon_H105 zenon_H10e. % 15.55/15.71 apply (zenon_or_s _ _ zenon_H10c); [ zenon_intro zenon_H104 | zenon_intro zenon_H10a ]. % 15.55/15.71 apply (zenon_or_s _ _ zenon_H10e); [ zenon_intro zenon_H3d | zenon_intro zenon_H106 ]. % 15.55/15.71 apply (zenon_or_s _ _ zenon_H10d); [ zenon_intro zenon_H3e | zenon_intro zenon_H42 ]. % 15.55/15.71 apply (zenon_L1273_); trivial. % 15.55/15.71 apply (zenon_L1041_); trivial. % 15.55/15.71 apply (zenon_L81_); trivial. % 15.55/15.71 apply (zenon_L82_); trivial. % 15.55/15.71 (* end of lemma zenon_L1274_ *) % 15.55/15.71 assert (zenon_L1275_ : ((~((op (e2) (e2)) = (e1)))\/((op (e2) (e1)) = (e2))) -> ((~((op (e3) (e3)) = (e1)))\/((op (e3) (e1)) = (e3))) -> (~((e2) = (e3))) -> ((~((op (e3) (e3)) = (e3)))\/((op (e3) (e3)) = (e3))) -> (~((op (e3) (op (e3) (e3))) = (op (e3) (e3)))) -> (~((e0) = (e2))) -> ((op (e0) (e1)) = (e0)) -> (~((op (e1) (e1)) = (e2))) -> (~((op (e2) (e0)) = (op (e2) (e1)))) -> ((op (e2) (e0)) = (e2)) -> (((op (e3) (e3)) = (e0))\/(((op (e3) (e3)) = (e1))\/(((op (e3) (e3)) = (e2))\/((op (e3) (e3)) = (e3))))) -> (~((op (e0) (e0)) = (e0))) -> (~((op (e0) (e0)) = (e2))) -> (~((op (e0) (e0)) = (e3))) -> (((op (e0) (e0)) = (e0))\/(((op (e0) (e0)) = (e1))\/(((op (e0) (e0)) = (e2))\/((op (e0) (e0)) = (e3))))) -> (((op (e0) (e1)) = (e2))\/(((op (e1) (e1)) = (e2))\/(((op (e2) (e1)) = (e2))\/((op (e3) (e1)) = (e2))))) -> (((op (e0) (e2)) = (e1))\/(((op (e1) (e2)) = (e1))\/(((op (e2) (e2)) = (e1))\/((op (e3) (e2)) = (e1))))) -> (~((e1) = (e3))) -> ((op (e1) (e1)) = (e1)) -> (~((op (e1) (e1)) = (op (e1) (e2)))) -> (~((e1) = (e2))) -> (~((op (e0) (e3)) = (op (e3) (e3)))) -> (((op (e0) (e0)) = (e2))\/(((op (e0) (e1)) = (e2))\/(((op (e0) (e2)) = (e2))\/((op (e0) (e3)) = (e2))))) -> ((~((op (e3) (e3)) = (e2)))\/((op (e3) (e2)) = (e3))) -> (~((op (e3) (e0)) = (op (e3) (e1)))) -> (((op (e3) (e0)) = (e1))\/(((op (e3) (e1)) = (e1))\/(((op (e3) (e2)) = (e1))\/((op (e3) (e3)) = (e1))))) -> (~((op (e2) (e1)) = (op (e3) (e1)))) -> (~((op (e2) (op (e3) (e2))) = (op (e3) (e2)))) -> (((op (e3) (e0)) = (e2))\/(((op (e3) (e1)) = (e2))\/(((op (e3) (e2)) = (e2))\/((op (e3) (e3)) = (e2))))) -> (~((op (e1) (op (e3) (e1))) = (op (e3) (e1)))) -> (~((op (e3) (e0)) = (op (e3) (e2)))) -> ((~((op (e3) (e3)) = (e0)))\/((op (e3) (e0)) = (e3))) -> False). % 15.55/15.71 do 0 intro. intros zenon_H1e3 zenon_H10c zenon_H6a zenon_H10d zenon_H2be zenon_H5e zenon_H49 zenon_Hd6 zenon_H154 zenon_Hdd zenon_H3b zenon_H20 zenon_H8f zenon_H59 zenon_H12a zenon_H1a2 zenon_H11b zenon_Ha3 zenon_H21 zenon_H116 zenon_Ha7 zenon_H36 zenon_H8e zenon_H10e zenon_H109 zenon_H146 zenon_H13c zenon_H2af zenon_H1df zenon_H2b4 zenon_H105 zenon_H10f. % 15.55/15.71 apply (zenon_or_s _ _ zenon_H1e3); [ zenon_intro zenon_H52 | zenon_intro zenon_H156 ]. % 15.55/15.71 apply (zenon_or_s _ _ zenon_H10f); [ zenon_intro zenon_H3c | zenon_intro zenon_Hba ]. % 15.55/15.71 apply (zenon_L1272_); trivial. % 15.55/15.71 apply (zenon_L1274_); trivial. % 15.55/15.71 apply (zenon_L284_); trivial. % 15.55/15.71 (* end of lemma zenon_L1275_ *) % 15.55/15.71 assert (zenon_L1276_ : (~((op (e0) (op (e3) (e0))) = (op (e3) (e0)))) -> ((~((op (e2) (e2)) = (e1)))\/((op (e2) (e1)) = (e2))) -> ((~((op (e3) (e3)) = (e1)))\/((op (e3) (e1)) = (e3))) -> (~((e2) = (e3))) -> ((~((op (e3) (e3)) = (e3)))\/((op (e3) (e3)) = (e3))) -> (~((op (e3) (op (e3) (e3))) = (op (e3) (e3)))) -> (~((e0) = (e2))) -> ((op (e0) (e1)) = (e0)) -> (~((op (e1) (e1)) = (e2))) -> (~((op (e2) (e0)) = (op (e2) (e1)))) -> (~((op (e0) (e0)) = (e0))) -> (~((op (e0) (e0)) = (e2))) -> (~((op (e0) (e0)) = (e3))) -> (((op (e0) (e0)) = (e0))\/(((op (e0) (e0)) = (e1))\/(((op (e0) (e0)) = (e2))\/((op (e0) (e0)) = (e3))))) -> (((op (e0) (e1)) = (e2))\/(((op (e1) (e1)) = (e2))\/(((op (e2) (e1)) = (e2))\/((op (e3) (e1)) = (e2))))) -> (((op (e0) (e2)) = (e1))\/(((op (e1) (e2)) = (e1))\/(((op (e2) (e2)) = (e1))\/((op (e3) (e2)) = (e1))))) -> (~((e1) = (e3))) -> ((op (e1) (e1)) = (e1)) -> (~((op (e1) (e1)) = (op (e1) (e2)))) -> (~((e1) = (e2))) -> (((op (e0) (e0)) = (e2))\/(((op (e0) (e1)) = (e2))\/(((op (e0) (e2)) = (e2))\/((op (e0) (e3)) = (e2))))) -> ((~((op (e3) (e3)) = (e2)))\/((op (e3) (e2)) = (e3))) -> (~((op (e3) (e0)) = (op (e3) (e1)))) -> (((op (e3) (e0)) = (e1))\/(((op (e3) (e1)) = (e1))\/(((op (e3) (e2)) = (e1))\/((op (e3) (e3)) = (e1))))) -> (~((op (e2) (e1)) = (op (e3) (e1)))) -> (~((op (e2) (op (e3) (e2))) = (op (e3) (e2)))) -> (((op (e3) (e0)) = (e2))\/(((op (e3) (e1)) = (e2))\/(((op (e3) (e2)) = (e2))\/((op (e3) (e3)) = (e2))))) -> (~((op (e1) (op (e3) (e1))) = (op (e3) (e1)))) -> (~((op (e3) (e0)) = (op (e3) (e2)))) -> ((~((op (e3) (e3)) = (e0)))\/((op (e3) (e0)) = (e3))) -> (((op (e1) (e0)) = (e3))\/(((op (e1) (e1)) = (e3))\/(((op (e1) (e2)) = (e3))\/((op (e1) (e3)) = (e3))))) -> (~((op (e1) (e1)) = (e3))) -> (~((op (e1) (e2)) = (op (e3) (e2)))) -> (~((e0) = (e3))) -> (((op (e0) (e3)) = (e2))\/(((op (e1) (e3)) = (e2))\/(((op (e2) (e3)) = (e2))\/((op (e3) (e3)) = (e2))))) -> ((op (e2) (e1)) = (e2)) -> (~((op (e2) (e1)) = (op (e2) (e3)))) -> (~((e0) = (e1))) -> (((op (e3) (e0)) = (e0))\/(((op (e3) (e1)) = (e0))\/(((op (e3) (e2)) = (e0))\/((op (e3) (e3)) = (e0))))) -> ((op (e3) (e2)) = (e3)) -> (((op (e0) (e0)) = (e2))\/(((op (e1) (e0)) = (e2))\/(((op (e2) (e0)) = (e2))\/((op (e3) (e0)) = (e2))))) -> (((op (e3) (e3)) = (e0))\/(((op (e3) (e3)) = (e1))\/(((op (e3) (e3)) = (e2))\/((op (e3) (e3)) = (e3))))) -> (~((op (e3) (e3)) = (e0))) -> (~((op (e3) (e3)) = (e1))) -> (~((op (e0) (e3)) = (op (e3) (e3)))) -> (~((op (e3) (e3)) = (e3))) -> False). % 15.55/15.71 do 0 intro. intros zenon_H2b8 zenon_H1e3 zenon_H10c zenon_H6a zenon_H10d zenon_H2be zenon_H5e zenon_H49 zenon_Hd6 zenon_H154 zenon_H20 zenon_H8f zenon_H59 zenon_H12a zenon_H1a2 zenon_H11b zenon_Ha3 zenon_H21 zenon_H116 zenon_Ha7 zenon_H8e zenon_H10e zenon_H109 zenon_H146 zenon_H13c zenon_H2af zenon_H1df zenon_H2b4 zenon_H105 zenon_H10f zenon_H90 zenon_H182 zenon_H17d zenon_H4b zenon_H160 zenon_H156 zenon_H1e2 zenon_H9e zenon_H1f6 zenon_H106 zenon_Heb zenon_H3b zenon_H3c zenon_H104 zenon_H36 zenon_H3e. % 15.55/15.71 apply (zenon_or_s _ _ zenon_H8e); [ zenon_intro zenon_H92 | zenon_intro zenon_H91 ]. % 15.55/15.71 exact (zenon_H8f zenon_H92). % 15.55/15.71 apply (zenon_or_s _ _ zenon_H91); [ zenon_intro zenon_H5d | zenon_intro zenon_H93 ]. % 15.55/15.71 apply (zenon_L14_); trivial. % 15.55/15.71 apply (zenon_or_s _ _ zenon_H93); [ zenon_intro zenon_H63 | zenon_intro zenon_H81 ]. % 15.55/15.71 apply (zenon_or_s _ _ zenon_Heb); [ zenon_intro zenon_H92 | zenon_intro zenon_Hec ]. % 15.55/15.71 exact (zenon_H8f zenon_H92). % 15.55/15.71 apply (zenon_or_s _ _ zenon_Hec); [ zenon_intro zenon_H68 | zenon_intro zenon_Hed ]. % 15.55/15.71 apply (zenon_L1269_); trivial. % 15.55/15.71 apply (zenon_or_s _ _ zenon_Hed); [ zenon_intro zenon_Hdd | zenon_intro zenon_He9 ]. % 15.55/15.71 apply (zenon_L1275_); trivial. % 15.55/15.71 apply (zenon_L1106_); trivial. % 15.55/15.71 apply (zenon_L107_); trivial. % 15.55/15.71 (* end of lemma zenon_L1276_ *) % 15.55/15.71 assert (zenon_L1277_ : (((op (e3) (e0)) = (e0))\/(((op (e3) (e1)) = (e0))\/(((op (e3) (e2)) = (e0))\/((op (e3) (e3)) = (e0))))) -> (~((e0) = (e1))) -> ((op (e3) (e0)) = (e1)) -> ((op (e1) (e0)) = (e0)) -> (~((op (e1) (op (e3) (e1))) = (op (e3) (e1)))) -> ((op (e0) (e2)) = (e0)) -> (~((op (e0) (e2)) = (op (e3) (e2)))) -> (~((op (e3) (e3)) = (e0))) -> False). % 15.55/15.71 do 0 intro. intros zenon_H1f6 zenon_H9e zenon_Hee zenon_Had zenon_H2b4 zenon_Hab zenon_H140 zenon_H3c. % 15.55/15.71 apply (zenon_or_s _ _ zenon_H1f6); [ zenon_intro zenon_Hdb | zenon_intro zenon_H1f7 ]. % 15.55/15.71 apply (zenon_L71_); trivial. % 15.55/15.71 apply (zenon_or_s _ _ zenon_H1f7); [ zenon_intro zenon_H142 | zenon_intro zenon_H1f8 ]. % 15.55/15.71 apply (zenon_L1136_); trivial. % 15.55/15.71 apply (zenon_or_s _ _ zenon_H1f8); [ zenon_intro zenon_H167 | zenon_intro zenon_H40 ]. % 15.55/15.71 apply (zenon_L267_); trivial. % 15.55/15.71 exact (zenon_H3c zenon_H40). % 15.55/15.71 (* end of lemma zenon_L1277_ *) % 15.55/15.71 assert (zenon_L1278_ : (((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 (e3) (e3)) = (e1))) -> (~((op (e3) (e3)) = (e0))) -> (((op (e3) (e3)) = (e0))\/(((op (e3) (e3)) = (e1))\/(((op (e3) (e3)) = (e2))\/((op (e3) (e3)) = (e3))))) -> (~((e0) = (e2))) -> ((op (e1) (e3)) = (e0)) -> ((op (e2) (e1)) = (e2)) -> (~((op (e2) (e1)) = (op (e2) (e3)))) -> ((op (e3) (e1)) = (e0)) -> ((op (e2) (e2)) = (e1)) -> False). % 15.55/15.71 do 0 intro. intros zenon_H160 zenon_H3e zenon_H36 zenon_H104 zenon_H3c zenon_H3b zenon_H5e zenon_Hcc zenon_H156 zenon_H1e2 zenon_H142 zenon_H2a. % 15.55/15.71 apply (zenon_or_s _ _ zenon_H160); [ zenon_intro zenon_H81 | zenon_intro zenon_H161 ]. % 15.55/15.71 apply (zenon_L107_); trivial. % 15.55/15.71 apply (zenon_or_s _ _ zenon_H161); [ zenon_intro zenon_H82 | zenon_intro zenon_H162 ]. % 15.55/15.71 apply (zenon_L54_); trivial. % 15.55/15.71 apply (zenon_or_s _ _ zenon_H162); [ zenon_intro zenon_H124 | zenon_intro zenon_H43 ]. % 15.55/15.71 apply (zenon_L256_); trivial. % 15.55/15.71 apply (zenon_L171_); trivial. % 15.55/15.71 (* end of lemma zenon_L1278_ *) % 15.55/15.71 assert (zenon_L1279_ : (((op (e0) (e0)) = (e0))\/(((op (e1) (e0)) = (e0))\/(((op (e2) (e0)) = (e0))\/((op (e3) (e0)) = (e0))))) -> (~((op (e0) (e0)) = (e0))) -> (((op (e0) (e0)) = (e3))\/(((op (e0) (e1)) = (e3))\/(((op (e0) (e2)) = (e3))\/((op (e0) (e3)) = (e3))))) -> (~((op (e0) (e0)) = (e3))) -> (~((op (e2) (op (e3) (e2))) = (op (e3) (e2)))) -> (~((op (e2) (e2)) = (e3))) -> (~((op (e0) (e1)) = (op (e2) (e1)))) -> (((op (e2) (e0)) = (e3))\/(((op (e2) (e1)) = (e3))\/(((op (e2) (e2)) = (e3))\/((op (e2) (e3)) = (e3))))) -> (~((op (e0) (e3)) = (op (e2) (e3)))) -> (((op (e0) (e3)) = (e2))\/(((op (e1) (e3)) = (e2))\/(((op (e2) (e3)) = (e2))\/((op (e3) (e3)) = (e2))))) -> (~((op (e3) (e3)) = (e3))) -> (~((op (e0) (e3)) = (op (e3) (e3)))) -> (~((op (e3) (e3)) = (e0))) -> (((op (e3) (e3)) = (e0))\/(((op (e3) (e3)) = (e1))\/(((op (e3) (e3)) = (e2))\/((op (e3) (e3)) = (e3))))) -> (~((e0) = (e2))) -> ((op (e2) (e1)) = (e2)) -> (~((op (e2) (e1)) = (op (e2) (e3)))) -> (~((op (e1) (e1)) = (op (e2) (e1)))) -> (((op (e2) (e0)) = (e1))\/(((op (e2) (e1)) = (e1))\/(((op (e2) (e2)) = (e1))\/((op (e2) (e3)) = (e1))))) -> (~((op (e2) (e0)) = (op (e2) (e1)))) -> (~((op (e1) (e1)) = (e0))) -> (~((op (e0) (e1)) = (op (e0) (e2)))) -> ((op (e0) (e2)) = (e0)) -> (((op (e0) (e1)) = (e0))\/(((op (e1) (e1)) = (e0))\/(((op (e2) (e1)) = (e0))\/((op (e3) (e1)) = (e0))))) -> (~((op (e0) (e2)) = (op (e1) (e2)))) -> (((op (e3) (e0)) = (e0))\/(((op (e3) (e1)) = (e0))\/(((op (e3) (e2)) = (e0))\/((op (e3) (e3)) = (e0))))) -> (~((op (e0) (e2)) = (op (e3) (e2)))) -> (((op (e1) (e0)) = (e0))\/(((op (e1) (e1)) = (e0))\/(((op (e1) (e2)) = (e0))\/((op (e1) (e3)) = (e0))))) -> (~((op (e1) (e0)) = (op (e1) (e1)))) -> (~((op (e0) (e0)) = (e1))) -> (((op (e0) (e0)) = (e1))\/(((op (e1) (e0)) = (e1))\/(((op (e2) (e0)) = (e1))\/((op (e3) (e0)) = (e1))))) -> (~((op (e0) (e1)) = (op (e1) (e1)))) -> (((op (e0) (e0)) = (e1))\/(((op (e0) (e1)) = (e1))\/(((op (e0) (e2)) = (e1))\/((op (e0) (e3)) = (e1))))) -> (((op (e3) (e0)) = (e1))\/(((op (e3) (e1)) = (e1))\/(((op (e3) (e2)) = (e1))\/((op (e3) (e3)) = (e1))))) -> (~((e0) = (e1))) -> ((op (e1) (e1)) = (e1)) -> (~((op (e1) (op (e3) (e1))) = (op (e3) (e1)))) -> ((op (e3) (e2)) = (e3)) -> (~((e1) = (e3))) -> (~((op (e3) (e3)) = (e1))) -> False). % 15.55/15.71 do 0 intro. intros zenon_Hf0 zenon_H20 zenon_H58 zenon_H59 zenon_H2af zenon_H30 zenon_Hde zenon_He6 zenon_Hb4 zenon_H160 zenon_H3e zenon_H36 zenon_H3c zenon_H3b zenon_H5e zenon_H156 zenon_H1e2 zenon_Hb1 zenon_Hb7 zenon_H154 zenon_H145 zenon_H23e zenon_Hab zenon_H144 zenon_H87 zenon_H1f6 zenon_H140 zenon_H163 zenon_Hd7 zenon_H45 zenon_Hf1 zenon_H23 zenon_H44 zenon_H146 zenon_H9e zenon_H21 zenon_H2b4 zenon_H106 zenon_Ha3 zenon_H104. % 15.55/15.71 apply (zenon_or_s _ _ zenon_Hf0); [ zenon_intro zenon_H1f | zenon_intro zenon_Hf2 ]. % 15.55/15.71 exact (zenon_H20 zenon_H1f). % 15.55/15.71 apply (zenon_or_s _ _ zenon_Hf2); [ zenon_intro zenon_Had | zenon_intro zenon_Hf3 ]. % 15.55/15.71 apply (zenon_or_s _ _ zenon_H44); [ zenon_intro zenon_H47 | zenon_intro zenon_H46 ]. % 15.55/15.71 exact (zenon_H45 zenon_H47). % 15.55/15.71 apply (zenon_or_s _ _ zenon_H46); [ zenon_intro zenon_H22 | zenon_intro zenon_H48 ]. % 15.55/15.71 apply (zenon_L3_); trivial. % 15.55/15.71 apply (zenon_or_s _ _ zenon_H48); [ zenon_intro zenon_H29 | zenon_intro zenon_H37 ]. % 15.55/15.71 apply (zenon_L37_); trivial. % 15.55/15.71 apply (zenon_or_s _ _ zenon_Hf1); [ zenon_intro zenon_H47 | zenon_intro zenon_Hf4 ]. % 15.55/15.71 exact (zenon_H45 zenon_H47). % 15.55/15.71 apply (zenon_or_s _ _ zenon_Hf4); [ zenon_intro zenon_Hd8 | zenon_intro zenon_Hf5 ]. % 15.55/15.71 apply (zenon_L61_); trivial. % 15.55/15.71 apply (zenon_or_s _ _ zenon_Hf5); [ zenon_intro zenon_Hae | zenon_intro zenon_Hee ]. % 15.55/15.71 apply (zenon_L1110_); trivial. % 15.55/15.71 apply (zenon_L1277_); trivial. % 15.55/15.71 apply (zenon_or_s _ _ zenon_Hf3); [ zenon_intro zenon_Hcf | zenon_intro zenon_Hdb ]. % 15.55/15.71 apply (zenon_or_s _ _ zenon_H44); [ zenon_intro zenon_H47 | zenon_intro zenon_H46 ]. % 15.55/15.71 exact (zenon_H45 zenon_H47). % 15.55/15.71 apply (zenon_or_s _ _ zenon_H46); [ zenon_intro zenon_H22 | zenon_intro zenon_H48 ]. % 15.55/15.71 apply (zenon_L3_); trivial. % 15.55/15.71 apply (zenon_or_s _ _ zenon_H48); [ zenon_intro zenon_H29 | zenon_intro zenon_H37 ]. % 15.55/15.71 apply (zenon_L37_); trivial. % 15.55/15.71 apply (zenon_or_s _ _ zenon_Hf1); [ zenon_intro zenon_H47 | zenon_intro zenon_Hf4 ]. % 15.55/15.71 exact (zenon_H45 zenon_H47). % 15.55/15.71 apply (zenon_or_s _ _ zenon_Hf4); [ zenon_intro zenon_Hd8 | zenon_intro zenon_Hf5 ]. % 15.55/15.71 apply (zenon_L61_); trivial. % 15.55/15.71 apply (zenon_or_s _ _ zenon_Hf5); [ zenon_intro zenon_Hae | zenon_intro zenon_Hee ]. % 15.55/15.71 apply (zenon_L269_); trivial. % 15.55/15.71 apply (zenon_or_s _ _ zenon_H163); [ zenon_intro zenon_Had | zenon_intro zenon_H164 ]. % 15.55/15.71 apply (zenon_L1277_); trivial. % 15.55/15.71 apply (zenon_or_s _ _ zenon_H164); [ zenon_intro zenon_H149 | zenon_intro zenon_H165 ]. % 15.55/15.71 exact (zenon_H145 zenon_H149). % 15.55/15.71 apply (zenon_or_s _ _ zenon_H165); [ zenon_intro zenon_H15d | zenon_intro zenon_Hcc ]. % 15.55/15.71 apply (zenon_L136_); trivial. % 15.55/15.71 apply (zenon_or_s _ _ zenon_H144); [ zenon_intro zenon_H49 | zenon_intro zenon_H147 ]. % 15.55/15.71 apply (zenon_L485_); trivial. % 15.55/15.71 apply (zenon_or_s _ _ zenon_H147); [ zenon_intro zenon_H149 | zenon_intro zenon_H148 ]. % 15.55/15.71 exact (zenon_H145 zenon_H149). % 15.55/15.71 apply (zenon_or_s _ _ zenon_H148); [ zenon_intro zenon_H14a | zenon_intro zenon_H142 ]. % 15.55/15.71 apply (zenon_L133_); trivial. % 15.55/15.71 apply (zenon_or_s _ _ zenon_Hb7); [ zenon_intro zenon_Hae | zenon_intro zenon_Hb8 ]. % 15.55/15.71 apply (zenon_L269_); trivial. % 15.55/15.71 apply (zenon_or_s _ _ zenon_Hb8); [ zenon_intro zenon_Hb2 | zenon_intro zenon_Hb9 ]. % 15.55/15.71 apply (zenon_L40_); trivial. % 15.55/15.71 apply (zenon_or_s _ _ zenon_Hb9); [ zenon_intro zenon_H2a | zenon_intro zenon_Hb5 ]. % 15.55/15.71 apply (zenon_L1278_); trivial. % 15.55/15.71 apply (zenon_L41_); trivial. % 15.55/15.71 apply (zenon_L1212_); trivial. % 15.55/15.71 (* end of lemma zenon_L1279_ *) % 15.55/15.71 assert (zenon_L1280_ : (((op (e0) (e2)) = (e1))\/(((op (e1) (e2)) = (e1))\/(((op (e2) (e2)) = (e1))\/((op (e3) (e2)) = (e1))))) -> (~((op (e0) (e2)) = (op (e0) (e3)))) -> ((op (e0) (e3)) = (e1)) -> (~((op (e1) (e1)) = (op (e1) (e2)))) -> (~((op (e3) (e3)) = (e0))) -> (~((e0) = (e3))) -> (((op (e0) (e3)) = (e2))\/(((op (e1) (e3)) = (e2))\/(((op (e2) (e3)) = (e2))\/((op (e3) (e3)) = (e2))))) -> (~((op (e3) (e3)) = (e3))) -> (~((op (e0) (e3)) = (op (e3) (e3)))) -> (~((op (e3) (e3)) = (e1))) -> (((op (e3) (e3)) = (e0))\/(((op (e3) (e3)) = (e1))\/(((op (e3) (e3)) = (e2))\/((op (e3) (e3)) = (e3))))) -> (~((e2) = (e3))) -> ((op (e1) (e3)) = (e3)) -> ((op (e2) (e1)) = (e2)) -> (~((op (e2) (e1)) = (op (e2) (e3)))) -> (((op (e3) (e0)) = (e1))\/(((op (e3) (e1)) = (e1))\/(((op (e3) (e2)) = (e1))\/((op (e3) (e3)) = (e1))))) -> (~((e0) = (e1))) -> ((op (e1) (e1)) = (e1)) -> (~((op (e1) (op (e3) (e1))) = (op (e3) (e1)))) -> (((op (e3) (e0)) = (e0))\/(((op (e3) (e1)) = (e0))\/(((op (e3) (e2)) = (e0))\/((op (e3) (e3)) = (e0))))) -> (~((e1) = (e3))) -> ((op (e3) (e2)) = (e3)) -> False). % 15.55/15.71 do 0 intro. intros zenon_H11b zenon_Hc9 zenon_H37 zenon_H116 zenon_H3c zenon_H4b zenon_H160 zenon_H3e zenon_H36 zenon_H104 zenon_H3b zenon_H6a zenon_H8a zenon_H156 zenon_H1e2 zenon_H146 zenon_H9e zenon_H21 zenon_H2b4 zenon_H1f6 zenon_Ha3 zenon_H106. % 15.55/15.71 apply (zenon_or_s _ _ zenon_H11b); [ zenon_intro zenon_H29 | zenon_intro zenon_H11c ]. % 15.55/15.71 apply (zenon_L85_); trivial. % 15.55/15.71 apply (zenon_or_s _ _ zenon_H11c); [ zenon_intro zenon_H117 | zenon_intro zenon_H11d ]. % 15.55/15.71 apply (zenon_L86_); trivial. % 15.55/15.71 apply (zenon_or_s _ _ zenon_H11d); [ zenon_intro zenon_H2a | zenon_intro zenon_H119 ]. % 15.55/15.71 apply (zenon_L1268_); trivial. % 15.55/15.71 apply (zenon_L87_); trivial. % 15.55/15.71 (* end of lemma zenon_L1280_ *) % 15.55/15.71 assert (zenon_L1281_ : (((op (e1) (e0)) = (e3))\/(((op (e1) (e1)) = (e3))\/(((op (e1) (e2)) = (e3))\/((op (e1) (e3)) = (e3))))) -> ((op (e1) (e0)) = (e2)) -> (~((op (e1) (e1)) = (e3))) -> (~((op (e1) (e2)) = (op (e3) (e2)))) -> (((op (e0) (e2)) = (e1))\/(((op (e1) (e2)) = (e1))\/(((op (e2) (e2)) = (e1))\/((op (e3) (e2)) = (e1))))) -> (~((op (e0) (e2)) = (op (e0) (e3)))) -> ((op (e0) (e3)) = (e1)) -> (~((op (e1) (e1)) = (op (e1) (e2)))) -> (~((op (e3) (e3)) = (e0))) -> (~((e0) = (e3))) -> (((op (e0) (e3)) = (e2))\/(((op (e1) (e3)) = (e2))\/(((op (e2) (e3)) = (e2))\/((op (e3) (e3)) = (e2))))) -> (~((op (e3) (e3)) = (e3))) -> (~((op (e0) (e3)) = (op (e3) (e3)))) -> (~((op (e3) (e3)) = (e1))) -> (((op (e3) (e3)) = (e0))\/(((op (e3) (e3)) = (e1))\/(((op (e3) (e3)) = (e2))\/((op (e3) (e3)) = (e3))))) -> (~((e2) = (e3))) -> ((op (e2) (e1)) = (e2)) -> (~((op (e2) (e1)) = (op (e2) (e3)))) -> (((op (e3) (e0)) = (e1))\/(((op (e3) (e1)) = (e1))\/(((op (e3) (e2)) = (e1))\/((op (e3) (e3)) = (e1))))) -> (~((e0) = (e1))) -> ((op (e1) (e1)) = (e1)) -> (~((op (e1) (op (e3) (e1))) = (op (e3) (e1)))) -> (((op (e3) (e0)) = (e0))\/(((op (e3) (e1)) = (e0))\/(((op (e3) (e2)) = (e0))\/((op (e3) (e3)) = (e0))))) -> (~((e1) = (e3))) -> ((op (e3) (e2)) = (e3)) -> False). % 15.55/15.71 do 0 intro. intros zenon_H90 zenon_H68 zenon_H182 zenon_H17d zenon_H11b zenon_Hc9 zenon_H37 zenon_H116 zenon_H3c zenon_H4b zenon_H160 zenon_H3e zenon_H36 zenon_H104 zenon_H3b zenon_H6a zenon_H156 zenon_H1e2 zenon_H146 zenon_H9e zenon_H21 zenon_H2b4 zenon_H1f6 zenon_Ha3 zenon_H106. % 15.55/15.71 apply (zenon_or_s _ _ zenon_H90); [ zenon_intro zenon_H69 | zenon_intro zenon_H94 ]. % 15.55/15.71 apply (zenon_L17_); trivial. % 15.55/15.71 apply (zenon_or_s _ _ zenon_H94); [ zenon_intro zenon_H96 | zenon_intro zenon_H95 ]. % 15.55/15.71 exact (zenon_H182 zenon_H96). % 15.55/15.71 apply (zenon_or_s _ _ zenon_H95); [ zenon_intro zenon_H88 | zenon_intro zenon_H8a ]. % 15.55/15.71 apply (zenon_L164_); trivial. % 15.55/15.71 apply (zenon_L1280_); trivial. % 15.55/15.71 (* end of lemma zenon_L1281_ *) % 15.55/15.71 assert (zenon_L1282_ : ((~((op (e3) (e3)) = (e3)))\/((op (e3) (e3)) = (e3))) -> (~((op (e3) (op (e3) (e3))) = (op (e3) (e3)))) -> (~((op (e0) (e0)) = (e1))) -> (~((op (e0) (e1)) = (op (e1) (e1)))) -> ((op (e1) (e1)) = (e1)) -> (((op (e0) (e0)) = (e2))\/(((op (e0) (e1)) = (e2))\/(((op (e0) (e2)) = (e2))\/((op (e0) (e3)) = (e2))))) -> ((op (e0) (e3)) = (e0)) -> (~((e0) = (e2))) -> (~((e1) = (e2))) -> (~((op (e0) (e0)) = (e0))) -> (((op (e3) (e3)) = (e0))\/(((op (e3) (e3)) = (e1))\/(((op (e3) (e3)) = (e2))\/((op (e3) (e3)) = (e3))))) -> (~((op (e3) (e3)) = (e2))) -> (~((op (e3) (e3)) = (e0))) -> (((op (e0) (e0)) = (e0))\/(((op (e0) (e0)) = (e1))\/(((op (e0) (e0)) = (e2))\/((op (e0) (e0)) = (e3))))) -> (~((op (e0) (e0)) = (e2))) -> (~((op (e0) (e3)) = (op (e3) (e3)))) -> (((op (e0) (e0)) = (e1))\/(((op (e0) (e1)) = (e1))\/(((op (e0) (e2)) = (e1))\/((op (e0) (e3)) = (e1))))) -> False). % 15.55/15.71 do 0 intro. intros zenon_H10d zenon_H2be zenon_H45 zenon_H23 zenon_H21 zenon_H8e zenon_Hca zenon_H5e zenon_Ha7 zenon_H20 zenon_H3b zenon_H3d zenon_H3c zenon_H12a zenon_H8f zenon_H36 zenon_H44. % 15.55/15.71 apply (zenon_or_s _ _ zenon_H10d); [ zenon_intro zenon_H3e | zenon_intro zenon_H42 ]. % 15.55/15.71 apply (zenon_L114_); trivial. % 15.55/15.71 apply (zenon_L1041_); trivial. % 15.55/15.71 (* end of lemma zenon_L1282_ *) % 15.55/15.71 assert (zenon_L1283_ : ((~((op (e3) (e3)) = (e2)))\/((op (e3) (e2)) = (e3))) -> ((op (e3) (e1)) = (e3)) -> (~((op (e3) (e1)) = (op (e3) (e2)))) -> (((op (e0) (e0)) = (e1))\/(((op (e0) (e1)) = (e1))\/(((op (e0) (e2)) = (e1))\/((op (e0) (e3)) = (e1))))) -> (~((op (e0) (e3)) = (op (e3) (e3)))) -> (~((op (e0) (e0)) = (e2))) -> (((op (e0) (e0)) = (e0))\/(((op (e0) (e0)) = (e1))\/(((op (e0) (e0)) = (e2))\/((op (e0) (e0)) = (e3))))) -> (~((op (e3) (e3)) = (e0))) -> (((op (e3) (e3)) = (e0))\/(((op (e3) (e3)) = (e1))\/(((op (e3) (e3)) = (e2))\/((op (e3) (e3)) = (e3))))) -> (~((op (e0) (e0)) = (e0))) -> (~((e1) = (e2))) -> (~((e0) = (e2))) -> ((op (e0) (e3)) = (e0)) -> (((op (e0) (e0)) = (e2))\/(((op (e0) (e1)) = (e2))\/(((op (e0) (e2)) = (e2))\/((op (e0) (e3)) = (e2))))) -> ((op (e1) (e1)) = (e1)) -> (~((op (e0) (e1)) = (op (e1) (e1)))) -> (~((op (e0) (e0)) = (e1))) -> (~((op (e3) (op (e3) (e3))) = (op (e3) (e3)))) -> ((~((op (e3) (e3)) = (e3)))\/((op (e3) (e3)) = (e3))) -> False). % 15.55/15.71 do 0 intro. intros zenon_H10e zenon_H10a zenon_H135 zenon_H44 zenon_H36 zenon_H8f zenon_H12a zenon_H3c zenon_H3b zenon_H20 zenon_Ha7 zenon_H5e zenon_Hca zenon_H8e zenon_H21 zenon_H23 zenon_H45 zenon_H2be zenon_H10d. % 15.55/15.71 apply (zenon_or_s _ _ zenon_H10e); [ zenon_intro zenon_H3d | zenon_intro zenon_H106 ]. % 15.55/15.71 apply (zenon_L1282_); trivial. % 15.55/15.71 apply (zenon_L115_); trivial. % 15.55/15.71 (* end of lemma zenon_L1283_ *) % 15.55/15.71 assert (zenon_L1284_ : ((~((op (e2) (e2)) = (e3)))\/((op (e2) (e3)) = (e2))) -> ((~((op (e3) (e3)) = (e1)))\/((op (e3) (e1)) = (e3))) -> (~((op (e2) (e1)) = (op (e3) (e1)))) -> (~((op (e3) (e1)) = (op (e3) (e2)))) -> ((~((op (e3) (e3)) = (e3)))\/((op (e3) (e3)) = (e3))) -> (~((op (e3) (op (e3) (e3))) = (op (e3) (e3)))) -> (~((op (e0) (e0)) = (e1))) -> (~((op (e0) (e1)) = (op (e1) (e1)))) -> ((op (e1) (e1)) = (e1)) -> (((op (e0) (e0)) = (e2))\/(((op (e0) (e1)) = (e2))\/(((op (e0) (e2)) = (e2))\/((op (e0) (e3)) = (e2))))) -> (~((op (e0) (e3)) = (op (e3) (e3)))) -> (((op (e3) (e3)) = (e0))\/(((op (e3) (e3)) = (e1))\/(((op (e3) (e3)) = (e2))\/((op (e3) (e3)) = (e3))))) -> (~((op (e0) (e2)) = (op (e2) (e2)))) -> (((op (e3) (e0)) = (e2))\/(((op (e3) (e1)) = (e2))\/(((op (e3) (e2)) = (e2))\/((op (e3) (e3)) = (e2))))) -> ((op (e2) (e2)) = (e2)) -> (~((op (e2) (op (e3) (e2))) = (op (e3) (e2)))) -> (~((op (e0) (e1)) = (op (e3) (e1)))) -> (~((op (e0) (op (e3) (e0))) = (op (e3) (e0)))) -> (~((op (e1) (op (e3) (e1))) = (op (e3) (e1)))) -> (~((op (e0) (e2)) = (op (e3) (e2)))) -> (((op (e3) (e0)) = (e1))\/(((op (e3) (e1)) = (e1))\/(((op (e3) (e2)) = (e1))\/((op (e3) (e3)) = (e1))))) -> (~((op (e0) (e0)) = (e2))) -> (((op (e0) (e0)) = (e1))\/(((op (e0) (e1)) = (e1))\/(((op (e0) (e2)) = (e1))\/((op (e0) (e3)) = (e1))))) -> (~((op (e0) (e0)) = (e0))) -> ((~((op (e1) (e1)) = (e1)))\/((op (e1) (e1)) = (e1))) -> (~((op (e1) (e0)) = (op (e1) (e1)))) -> ((~((op (e1) (e1)) = (e3)))\/((op (e1) (e3)) = (e1))) -> (~((op (e1) (e0)) = (op (e1) (e3)))) -> ((~((op (e3) (e3)) = (e2)))\/((op (e3) (e2)) = (e3))) -> (~((op (e1) (e2)) = (op (e2) (e2)))) -> (((op (e1) (e0)) = (e3))\/(((op (e1) (e1)) = (e3))\/(((op (e1) (e2)) = (e3))\/((op (e1) (e3)) = (e3))))) -> (~((e2) = (e3))) -> (~((op (e1) (e2)) = (op (e3) (e2)))) -> (~((e1) = (e3))) -> (((op (e1) (e0)) = (e2))\/(((op (e1) (e1)) = (e2))\/(((op (e1) (e2)) = (e2))\/((op (e1) (e3)) = (e2))))) -> (((op (e0) (e0)) = (e2))\/(((op (e1) (e0)) = (e2))\/(((op (e2) (e0)) = (e2))\/((op (e3) (e0)) = (e2))))) -> (((op (e1) (e1)) = (e0))\/(((op (e1) (e1)) = (e1))\/(((op (e1) (e1)) = (e2))\/((op (e1) (e1)) = (e3))))) -> (~((op (e2) (e0)) = (op (e2) (e2)))) -> (~((e1) = (e2))) -> (~((op (e3) (e0)) = (op (e3) (e2)))) -> (~((op (e0) (e3)) = (op (e1) (e3)))) -> ((~((op (e3) (e3)) = (e0)))\/((op (e3) (e0)) = (e3))) -> (~((op (e1) (e0)) = (op (e1) (e2)))) -> ((~((op (e1) (e1)) = (e2)))\/((op (e1) (e2)) = (e1))) -> (((op (e3) (e0)) = (e0))\/(((op (e3) (e1)) = (e0))\/(((op (e3) (e2)) = (e0))\/((op (e3) (e3)) = (e0))))) -> (((op (e1) (e2)) = (e0))\/(((op (e1) (e2)) = (e1))\/(((op (e1) (e2)) = (e2))\/((op (e1) (e2)) = (e3))))) -> (~((e0) = (e1))) -> (((op (e0) (e2)) = (e1))\/(((op (e1) (e2)) = (e1))\/(((op (e2) (e2)) = (e1))\/((op (e3) (e2)) = (e1))))) -> (~((op (e2) (e2)) = (e1))) -> (~((op (e1) (e1)) = (op (e1) (e2)))) -> (~((op (e0) (e2)) = (op (e0) (e3)))) -> (((op (e2) (e0)) = (e3))\/(((op (e2) (e1)) = (e3))\/(((op (e2) (e2)) = (e3))\/((op (e2) (e3)) = (e3))))) -> (~((op (e0) (e1)) = (op (e2) (e1)))) -> (~((op (e1) (e1)) = (e3))) -> (((op (e0) (e0)) = (e3))\/(((op (e0) (e1)) = (e3))\/(((op (e0) (e2)) = (e3))\/((op (e0) (e3)) = (e3))))) -> (((op (e3) (e1)) = (e0))\/(((op (e3) (e1)) = (e1))\/(((op (e3) (e1)) = (e2))\/((op (e3) (e1)) = (e3))))) -> (~((op (e3) (e0)) = (op (e3) (e1)))) -> (((op (e0) (e0)) = (e1))\/(((op (e1) (e0)) = (e1))\/(((op (e2) (e0)) = (e1))\/((op (e3) (e0)) = (e1))))) -> (~((op (e2) (e0)) = (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 (e1) (e1)) = (e2))) -> ((op (e0) (e3)) = (e0)) -> (~((e0) = (e2))) -> (~((op (e1) (e1)) = (op (e2) (e1)))) -> (~((op (e2) (e1)) = (op (e2) (e2)))) -> (((op (e2) (e1)) = (e0))\/(((op (e2) (e1)) = (e1))\/(((op (e2) (e1)) = (e2))\/((op (e2) (e1)) = (e3))))) -> (((op (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 (e2) (e3)))) -> (~((op (e0) (e1)) = (op (e0) (e3)))) -> (~((op (e1) (e1)) = (e0))) -> (~((op (e2) (e0)) = (op (e2) (e1)))) -> (((op (e0) (e1)) = (e0))\/(((op (e1) (e1)) = (e0))\/(((op (e2) (e1)) = (e0))\/((op (e3) (e1)) = (e0))))) -> (((op (e0) (e0)) = (e0))\/(((op (e1) (e0)) = (e0))\/(((op (e2) (e0)) = (e0))\/((op (e3) (e0)) = (e0))))) -> False). % 15.55/15.71 do 0 intro. intros zenon_H1c3 zenon_H10c zenon_H13c zenon_H135 zenon_H10d zenon_H2be zenon_H45 zenon_H23 zenon_H21 zenon_H8e zenon_H36 zenon_H3b zenon_H28 zenon_H1df zenon_H35 zenon_H2af zenon_H138 zenon_H2b8 zenon_H2b4 zenon_H140 zenon_H146 zenon_H8f zenon_H44 zenon_H20 zenon_H1d8 zenon_Hd7 zenon_H1d2 zenon_H1cf zenon_H10e zenon_H7d zenon_H90 zenon_H6a zenon_H17d zenon_Ha3 zenon_H84 zenon_Heb zenon_H1b3 zenon_H17a zenon_Ha7 zenon_H105 zenon_H80 zenon_H10f zenon_H166 zenon_H1d3 zenon_H1f6 zenon_H1d5 zenon_H9e zenon_H11b zenon_H52 zenon_H116 zenon_Hc9 zenon_He6 zenon_Hde zenon_H182 zenon_H58 zenon_H16c zenon_H109 zenon_Hf1 zenon_Hce zenon_H15f zenon_H2ab zenon_Hd6 zenon_Hca zenon_H5e zenon_Hb1 zenon_H157 zenon_H15a zenon_H121 zenon_H254 zenon_Hb4 zenon_H1cd zenon_H145 zenon_H154 zenon_H144 zenon_Hf0. % 15.55/15.71 apply (zenon_or_s _ _ zenon_H1c3); [ zenon_intro zenon_H30 | zenon_intro zenon_H124 ]. % 15.55/15.71 apply (zenon_or_s _ _ zenon_H10f); [ zenon_intro zenon_H3c | zenon_intro zenon_Hba ]. % 15.55/15.71 apply (zenon_or_s _ _ zenon_H10c); [ zenon_intro zenon_H104 | zenon_intro zenon_H10a ]. % 15.55/15.71 apply (zenon_or_s _ _ zenon_H10e); [ zenon_intro zenon_H3d | zenon_intro zenon_H106 ]. % 15.55/15.71 apply (zenon_L1229_); trivial. % 15.55/15.71 apply (zenon_or_s _ _ zenon_H10d); [ zenon_intro zenon_H3e | zenon_intro zenon_H42 ]. % 15.55/15.71 apply (zenon_L1265_); trivial. % 15.55/15.71 apply (zenon_L1041_); trivial. % 15.55/15.71 apply (zenon_or_s _ _ zenon_H10e); [ zenon_intro zenon_H3d | zenon_intro zenon_H106 ]. % 15.55/15.71 apply (zenon_or_s _ _ zenon_H10d); [ zenon_intro zenon_H3e | zenon_intro zenon_H42 ]. % 15.55/15.71 apply (zenon_or_s _ _ zenon_H44); [ zenon_intro zenon_H47 | zenon_intro zenon_H46 ]. % 15.55/15.71 exact (zenon_H45 zenon_H47). % 15.55/15.71 apply (zenon_or_s _ _ zenon_H46); [ zenon_intro zenon_H22 | zenon_intro zenon_H48 ]. % 15.55/15.71 apply (zenon_L3_); trivial. % 15.55/15.71 apply (zenon_or_s _ _ zenon_H48); [ zenon_intro zenon_H29 | zenon_intro zenon_H37 ]. % 15.55/15.71 apply (zenon_or_s _ _ zenon_Hf1); [ zenon_intro zenon_H47 | zenon_intro zenon_Hf4 ]. % 15.55/15.71 exact (zenon_H45 zenon_H47). % 15.55/15.71 apply (zenon_or_s _ _ zenon_Hf4); [ zenon_intro zenon_Hd8 | zenon_intro zenon_Hf5 ]. % 15.55/15.71 apply (zenon_L1256_); trivial. % 15.55/15.71 apply (zenon_or_s _ _ zenon_Hf5); [ zenon_intro zenon_Hae | zenon_intro zenon_Hee ]. % 15.55/15.71 apply (zenon_or_s _ _ zenon_H8e); [ zenon_intro zenon_H92 | zenon_intro zenon_H91 ]. % 15.55/15.71 exact (zenon_H8f zenon_H92). % 15.55/15.71 apply (zenon_or_s _ _ zenon_H91); [ zenon_intro zenon_H5d | zenon_intro zenon_H93 ]. % 15.55/15.71 apply (zenon_or_s _ _ zenon_H58); [ zenon_intro zenon_H5b | zenon_intro zenon_H5a ]. % 15.55/15.71 apply (zenon_or_s _ _ zenon_H146); [ zenon_intro zenon_Hee | zenon_intro zenon_H14b ]. % 15.55/15.71 apply (zenon_L1098_); trivial. % 15.55/15.71 apply (zenon_or_s _ _ zenon_H14b); [ zenon_intro zenon_H13e | zenon_intro zenon_H14c ]. % 15.55/15.71 apply (zenon_L1158_); trivial. % 15.55/15.71 apply (zenon_or_s _ _ zenon_H14c); [ zenon_intro zenon_H119 | zenon_intro zenon_H38 ]. % 15.55/15.71 apply (zenon_L124_); trivial. % 15.55/15.71 apply (zenon_L111_); trivial. % 15.55/15.71 apply (zenon_or_s _ _ zenon_H5a); [ zenon_intro zenon_H4a | zenon_intro zenon_H5c ]. % 15.55/15.71 apply (zenon_L120_); trivial. % 15.55/15.71 apply (zenon_or_s _ _ zenon_H5c); [ zenon_intro zenon_H50 | zenon_intro zenon_H53 ]. % 15.55/15.71 apply (zenon_L29_); trivial. % 15.55/15.71 apply (zenon_L536_); trivial. % 15.55/15.71 apply (zenon_or_s _ _ zenon_H93); [ zenon_intro zenon_H63 | zenon_intro zenon_H81 ]. % 15.55/15.71 apply (zenon_L15_); trivial. % 15.55/15.71 apply (zenon_L113_); trivial. % 15.55/15.71 apply (zenon_L1098_); trivial. % 15.55/15.71 apply (zenon_L7_); trivial. % 15.55/15.71 apply (zenon_L1041_); trivial. % 15.55/15.71 apply (zenon_L115_); trivial. % 15.55/15.71 apply (zenon_L1178_); trivial. % 15.55/15.71 apply (zenon_L137_); trivial. % 15.55/15.71 (* end of lemma zenon_L1284_ *) % 15.55/15.71 assert (zenon_L1285_ : ((~((op (e2) (e2)) = (e1)))\/((op (e2) (e1)) = (e2))) -> ((~((op (e2) (e2)) = (e3)))\/((op (e2) (e3)) = (e2))) -> (~((op (e2) (e0)) = (op (e2) (e3)))) -> ((~((op (e3) (e3)) = (e1)))\/((op (e3) (e1)) = (e3))) -> (~((op (e0) (e1)) = (op (e1) (e1)))) -> (((op (e0) (e0)) = (e2))\/(((op (e0) (e1)) = (e2))\/(((op (e0) (e2)) = (e2))\/((op (e0) (e3)) = (e2))))) -> ((op (e0) (e3)) = (e0)) -> (~((e0) = (e2))) -> (~((op (e0) (e0)) = (e0))) -> (((op (e0) (e0)) = (e0))\/(((op (e0) (e0)) = (e1))\/(((op (e0) (e0)) = (e2))\/((op (e0) (e0)) = (e3))))) -> (~((op (e0) (e0)) = (e2))) -> (~((op (e0) (e3)) = (op (e3) (e3)))) -> (((op (e0) (e0)) = (e1))\/(((op (e0) (e1)) = (e1))\/(((op (e0) (e2)) = (e1))\/((op (e0) (e3)) = (e1))))) -> (~((op (e3) (e1)) = (op (e3) (e2)))) -> ((~((op (e3) (e3)) = (e2)))\/((op (e3) (e2)) = (e3))) -> (((op (e0) (e0)) = (e1))\/(((op (e1) (e0)) = (e1))\/(((op (e2) (e0)) = (e1))\/((op (e3) (e0)) = (e1))))) -> (((op (e3) (e3)) = (e0))\/(((op (e3) (e3)) = (e1))\/(((op (e3) (e3)) = (e2))\/((op (e3) (e3)) = (e3))))) -> (((op (e2) (e2)) = (e0))\/(((op (e2) (e2)) = (e1))\/(((op (e2) (e2)) = (e2))\/((op (e2) (e2)) = (e3))))) -> ((op (e2) (e0)) = (e2)) -> (~((e1) = (e2))) -> ((op (e1) (e1)) = (e1)) -> (~((op (e1) (e0)) = (op (e1) (e1)))) -> (~((op (e0) (e0)) = (e1))) -> (~((op (e3) (op (e3) (e3))) = (op (e3) (e3)))) -> ((~((op (e3) (e3)) = (e3)))\/((op (e3) (e3)) = (e3))) -> (~((e1) = (e3))) -> ((~((op (e3) (e3)) = (e0)))\/((op (e3) (e0)) = (e3))) -> (~((op (e2) (e1)) = (op (e3) (e1)))) -> (~((op (e0) (e2)) = (op (e2) (e2)))) -> (((op (e3) (e0)) = (e2))\/(((op (e3) (e1)) = (e2))\/(((op (e3) (e2)) = (e2))\/((op (e3) (e3)) = (e2))))) -> (~((op (e2) (op (e3) (e2))) = (op (e3) (e2)))) -> (~((op (e0) (e1)) = (op (e3) (e1)))) -> (~((op (e0) (op (e3) (e0))) = (op (e3) (e0)))) -> (~((op (e1) (op (e3) (e1))) = (op (e3) (e1)))) -> (~((op (e0) (e2)) = (op (e3) (e2)))) -> (((op (e3) (e0)) = (e1))\/(((op (e3) (e1)) = (e1))\/(((op (e3) (e2)) = (e1))\/((op (e3) (e3)) = (e1))))) -> ((~((op (e1) (e1)) = (e1)))\/((op (e1) (e1)) = (e1))) -> ((~((op (e1) (e1)) = (e3)))\/((op (e1) (e3)) = (e1))) -> (~((op (e1) (e0)) = (op (e1) (e3)))) -> (~((op (e1) (e2)) = (op (e2) (e2)))) -> (((op (e1) (e0)) = (e3))\/(((op (e1) (e1)) = (e3))\/(((op (e1) (e2)) = (e3))\/((op (e1) (e3)) = (e3))))) -> (~((e2) = (e3))) -> (~((op (e1) (e2)) = (op (e3) (e2)))) -> (((op (e1) (e0)) = (e2))\/(((op (e1) (e1)) = (e2))\/(((op (e1) (e2)) = (e2))\/((op (e1) (e3)) = (e2))))) -> (((op (e0) (e0)) = (e2))\/(((op (e1) (e0)) = (e2))\/(((op (e2) (e0)) = (e2))\/((op (e3) (e0)) = (e2))))) -> (((op (e1) (e1)) = (e0))\/(((op (e1) (e1)) = (e1))\/(((op (e1) (e1)) = (e2))\/((op (e1) (e1)) = (e3))))) -> (~((op (e2) (e0)) = (op (e2) (e2)))) -> (~((op (e3) (e0)) = (op (e3) (e2)))) -> (~((op (e0) (e3)) = (op (e1) (e3)))) -> (~((op (e1) (e0)) = (op (e1) (e2)))) -> ((~((op (e1) (e1)) = (e2)))\/((op (e1) (e2)) = (e1))) -> (((op (e3) (e0)) = (e0))\/(((op (e3) (e1)) = (e0))\/(((op (e3) (e2)) = (e0))\/((op (e3) (e3)) = (e0))))) -> (((op (e1) (e2)) = (e0))\/(((op (e1) (e2)) = (e1))\/(((op (e1) (e2)) = (e2))\/((op (e1) (e2)) = (e3))))) -> (~((e0) = (e1))) -> (((op (e0) (e2)) = (e1))\/(((op (e1) (e2)) = (e1))\/(((op (e2) (e2)) = (e1))\/((op (e3) (e2)) = (e1))))) -> (~((op (e1) (e1)) = (op (e1) (e2)))) -> (~((op (e0) (e2)) = (op (e0) (e3)))) -> (((op (e2) (e0)) = (e3))\/(((op (e2) (e1)) = (e3))\/(((op (e2) (e2)) = (e3))\/((op (e2) (e3)) = (e3))))) -> (~((op (e0) (e1)) = (op (e2) (e1)))) -> (~((op (e1) (e1)) = (e3))) -> (((op (e0) (e0)) = (e3))\/(((op (e0) (e1)) = (e3))\/(((op (e0) (e2)) = (e3))\/((op (e0) (e3)) = (e3))))) -> (((op (e3) (e1)) = (e0))\/(((op (e3) (e1)) = (e1))\/(((op (e3) (e1)) = (e2))\/((op (e3) (e1)) = (e3))))) -> (~((op (e3) (e0)) = (op (e3) (e1)))) -> (~((op (e2) (e2)) = (op (e2) (e3)))) -> (((op (e2) (e3)) = (e0))\/(((op (e2) (e3)) = (e1))\/(((op (e2) (e3)) = (e2))\/((op (e2) (e3)) = (e3))))) -> (~((op (e1) (e1)) = (e2))) -> (~((op (e1) (e1)) = (op (e2) (e1)))) -> (~((op (e2) (e1)) = (op (e2) (e2)))) -> (((op (e2) (e1)) = (e0))\/(((op (e2) (e1)) = (e1))\/(((op (e2) (e1)) = (e2))\/((op (e2) (e1)) = (e3))))) -> (((op (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 (e2) (e3)))) -> (~((op (e0) (e1)) = (op (e0) (e3)))) -> (~((op (e1) (e1)) = (e0))) -> (~((op (e2) (e0)) = (op (e2) (e1)))) -> (((op (e0) (e1)) = (e0))\/(((op (e1) (e1)) = (e0))\/(((op (e2) (e1)) = (e0))\/((op (e3) (e1)) = (e0))))) -> (((op (e0) (e0)) = (e0))\/(((op (e1) (e0)) = (e0))\/(((op (e2) (e0)) = (e0))\/((op (e3) (e0)) = (e0))))) -> ((~((op (e2) (e2)) = (e2)))\/((op (e2) (e2)) = (e2))) -> False). % 15.55/15.71 do 0 intro. intros zenon_H1e3 zenon_H1c3 zenon_Hce zenon_H10c zenon_H23 zenon_H8e zenon_Hca zenon_H5e zenon_H20 zenon_H12a zenon_H8f zenon_H36 zenon_H44 zenon_H135 zenon_H10e zenon_Hf1 zenon_H3b zenon_H2d zenon_Hdd zenon_Ha7 zenon_H21 zenon_Hd7 zenon_H45 zenon_H2be zenon_H10d zenon_Ha3 zenon_H10f zenon_H13c zenon_H28 zenon_H1df zenon_H2af zenon_H138 zenon_H2b8 zenon_H2b4 zenon_H140 zenon_H146 zenon_H1d8 zenon_H1d2 zenon_H1cf zenon_H7d zenon_H90 zenon_H6a zenon_H17d zenon_H84 zenon_Heb zenon_H1b3 zenon_H17a zenon_H105 zenon_H80 zenon_H166 zenon_H1d3 zenon_H1f6 zenon_H1d5 zenon_H9e zenon_H11b zenon_H116 zenon_Hc9 zenon_He6 zenon_Hde zenon_H182 zenon_H58 zenon_H16c zenon_H109 zenon_H15f zenon_H2ab zenon_Hd6 zenon_Hb1 zenon_H157 zenon_H15a zenon_H121 zenon_H254 zenon_Hb4 zenon_H1cd zenon_H145 zenon_H154 zenon_H144 zenon_Hf0 zenon_Haa. % 15.55/15.71 apply (zenon_or_s _ _ zenon_H1e3); [ zenon_intro zenon_H52 | zenon_intro zenon_H156 ]. % 15.55/15.71 apply (zenon_or_s _ _ zenon_Haa); [ zenon_intro zenon_H2f | zenon_intro zenon_H35 ]. % 15.55/15.71 apply (zenon_or_s _ _ zenon_H1c3); [ zenon_intro zenon_H30 | zenon_intro zenon_H124 ]. % 15.55/15.71 apply (zenon_or_s _ _ zenon_H10f); [ zenon_intro zenon_H3c | zenon_intro zenon_Hba ]. % 15.55/15.71 apply (zenon_or_s _ _ zenon_H10c); [ zenon_intro zenon_H104 | zenon_intro zenon_H10a ]. % 15.55/15.71 apply (zenon_L1171_); trivial. % 15.55/15.71 apply (zenon_L1283_); trivial. % 15.55/15.71 apply (zenon_L310_); trivial. % 15.55/15.71 apply (zenon_L119_); trivial. % 15.55/15.71 apply (zenon_L1284_); trivial. % 15.55/15.71 apply (zenon_L284_); trivial. % 15.55/15.71 (* end of lemma zenon_L1285_ *) % 15.55/15.71 assert (zenon_L1286_ : (((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)) = (e1)) -> (~((op (e2) (e1)) = (op (e2) (e3)))) -> ((op (e2) (e1)) = (e2)) -> ((op (e1) (e3)) = (e3)) -> (~((e2) = (e3))) -> (((op (e3) (e3)) = (e0))\/(((op (e3) (e3)) = (e1))\/(((op (e3) (e3)) = (e2))\/((op (e3) (e3)) = (e3))))) -> (~((op (e3) (e3)) = (e1))) -> (~((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 (e2) (e0)) = (e0)) -> (~((op (e2) (op (e3) (e2))) = (op (e3) (e2)))) -> (~((op (e3) (e3)) = (e0))) -> False). % 15.55/15.71 do 0 intro. intros zenon_H1f6 zenon_H1e5 zenon_H2a zenon_H1e2 zenon_H156 zenon_H8a zenon_H6a zenon_H3b zenon_H104 zenon_H36 zenon_H3e zenon_H160 zenon_Hcf zenon_H2af zenon_H3c. % 15.55/15.71 apply (zenon_or_s _ _ zenon_H1f6); [ zenon_intro zenon_Hdb | zenon_intro zenon_H1f7 ]. % 15.55/15.71 apply (zenon_L980_); trivial. % 15.55/15.71 apply (zenon_or_s _ _ zenon_H1f7); [ zenon_intro zenon_H142 | zenon_intro zenon_H1f8 ]. % 15.55/15.71 apply (zenon_L902_); trivial. % 15.55/15.71 apply (zenon_or_s _ _ zenon_H1f8); [ zenon_intro zenon_H167 | zenon_intro zenon_H40 ]. % 15.55/15.71 apply (zenon_L1217_); trivial. % 15.55/15.71 exact (zenon_H3c zenon_H40). % 15.55/15.71 (* end of lemma zenon_L1286_ *) % 15.55/15.71 assert (zenon_L1287_ : ((~((op (e3) (e3)) = (e3)))\/((op (e3) (e3)) = (e3))) -> (~((op (e3) (op (e3) (e3))) = (op (e3) (e3)))) -> (~((op (e0) (e0)) = (e2))) -> (~((e0) = (e2))) -> ((op (e0) (e1)) = (e0)) -> (((op (e3) (e0)) = (e2))\/(((op (e3) (e1)) = (e2))\/(((op (e3) (e2)) = (e2))\/((op (e3) (e3)) = (e2))))) -> (~((op (e3) (e3)) = (e2))) -> (~((op (e0) (e2)) = (op (e3) (e2)))) -> ((op (e3) (e1)) = (e3)) -> (~((e2) = (e3))) -> (~((op (e0) (op (e3) (e0))) = (op (e3) (e0)))) -> (((op (e2) (e0)) = (e0))\/(((op (e2) (e1)) = (e0))\/(((op (e2) (e2)) = (e0))\/((op (e2) (e3)) = (e0))))) -> (~((e1) = (e2))) -> (~((op (e1) (e1)) = (op (e1) (e3)))) -> ((op (e1) (e1)) = (e1)) -> (((op (e1) (e3)) = (e0))\/(((op (e1) (e3)) = (e1))\/(((op (e1) (e3)) = (e2))\/((op (e1) (e3)) = (e3))))) -> (~((op (e1) (op (e3) (e1))) = (op (e3) (e1)))) -> (~((op (e0) (e3)) = (op (e1) (e3)))) -> (~((op (e1) (e3)) = (op (e2) (e3)))) -> (((op (e0) (e3)) = (e3))\/(((op (e1) (e3)) = (e3))\/(((op (e2) (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 (e2) (e3)))) -> (~((op (e0) (e3)) = (op (e3) (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) (e1)) = (op (e2) (e1)))) -> (~((op (e0) (e1)) = (op (e0) (e2)))) -> (((op (e3) (e0)) = (e0))\/(((op (e3) (e1)) = (e0))\/(((op (e3) (e2)) = (e0))\/((op (e3) (e3)) = (e0))))) -> (~((op (e3) (e3)) = (e0))) -> (~((op (e1) (e2)) = (op (e3) (e2)))) -> (~((e0) = (e3))) -> (~((op (e2) (e0)) = (op (e3) (e0)))) -> (~((op (e2) (e2)) = (e0))) -> (~((op (e2) (op (e3) (e2))) = (op (e3) (e2)))) -> (((op (e0) (e2)) = (e0))\/(((op (e1) (e2)) = (e0))\/(((op (e2) (e2)) = (e0))\/((op (e3) (e2)) = (e0))))) -> (((op (e0) (e0)) = (e2))\/(((op (e0) (e1)) = (e2))\/(((op (e0) (e2)) = (e2))\/((op (e0) (e3)) = (e2))))) -> False). % 15.55/15.71 do 0 intro. intros zenon_H10d zenon_H2be zenon_H8f zenon_H5e zenon_H49 zenon_H1df zenon_H3d zenon_H140 zenon_H10a zenon_H6a zenon_H2b8 zenon_H1f5 zenon_Ha7 zenon_H11e zenon_H21 zenon_H25b zenon_H2b4 zenon_H80 zenon_H244 zenon_H2d0 zenon_H254 zenon_Hb4 zenon_H36 zenon_H1cd zenon_H121 zenon_Hde zenon_H23e zenon_H1f6 zenon_H3c zenon_H17d zenon_H4b zenon_H1e5 zenon_H2e zenon_H2af zenon_H16f zenon_H8e. % 15.55/15.71 apply (zenon_or_s _ _ zenon_H10d); [ zenon_intro zenon_H3e | zenon_intro zenon_H42 ]. % 15.55/15.71 apply (zenon_L1224_); trivial. % 15.55/15.71 apply (zenon_L1041_); trivial. % 15.55/15.71 (* end of lemma zenon_L1287_ *) % 15.55/15.71 assert (zenon_L1288_ : ((~((op (e3) (e3)) = (e2)))\/((op (e3) (e2)) = (e3))) -> (~((op (e3) (e1)) = (op (e3) (e2)))) -> (((op (e0) (e0)) = (e2))\/(((op (e0) (e1)) = (e2))\/(((op (e0) (e2)) = (e2))\/((op (e0) (e3)) = (e2))))) -> (((op (e0) (e2)) = (e0))\/(((op (e1) (e2)) = (e0))\/(((op (e2) (e2)) = (e0))\/((op (e3) (e2)) = (e0))))) -> (~((op (e2) (op (e3) (e2))) = (op (e3) (e2)))) -> (~((op (e2) (e2)) = (e0))) -> (~((op (e2) (e0)) = (op (e3) (e0)))) -> (~((e0) = (e3))) -> (~((op (e1) (e2)) = (op (e3) (e2)))) -> (~((op (e3) (e3)) = (e0))) -> (((op (e3) (e0)) = (e0))\/(((op (e3) (e1)) = (e0))\/(((op (e3) (e2)) = (e0))\/((op (e3) (e3)) = (e0))))) -> (~((op (e0) (e1)) = (op (e0) (e2)))) -> (~((op (e0) (e1)) = (op (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) (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) (e3)) = (e3))\/(((op (e1) (e3)) = (e3))\/(((op (e2) (e3)) = (e3))\/((op (e3) (e3)) = (e3))))) -> (~((op (e1) (e3)) = (op (e2) (e3)))) -> (~((op (e0) (e3)) = (op (e1) (e3)))) -> (~((op (e1) (op (e3) (e1))) = (op (e3) (e1)))) -> (((op (e1) (e3)) = (e0))\/(((op (e1) (e3)) = (e1))\/(((op (e1) (e3)) = (e2))\/((op (e1) (e3)) = (e3))))) -> ((op (e1) (e1)) = (e1)) -> (~((op (e1) (e1)) = (op (e1) (e3)))) -> (~((e1) = (e2))) -> (((op (e2) (e0)) = (e0))\/(((op (e2) (e1)) = (e0))\/(((op (e2) (e2)) = (e0))\/((op (e2) (e3)) = (e0))))) -> (~((op (e0) (op (e3) (e0))) = (op (e3) (e0)))) -> (~((e2) = (e3))) -> ((op (e3) (e1)) = (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) (e1)) = (e0)) -> (~((e0) = (e2))) -> (~((op (e0) (e0)) = (e2))) -> (~((op (e3) (op (e3) (e3))) = (op (e3) (e3)))) -> ((~((op (e3) (e3)) = (e3)))\/((op (e3) (e3)) = (e3))) -> False). % 15.55/15.71 do 0 intro. intros zenon_H10e zenon_H135 zenon_H8e zenon_H16f zenon_H2af zenon_H2e zenon_H1e5 zenon_H4b zenon_H17d zenon_H3c zenon_H1f6 zenon_H23e zenon_Hde zenon_H121 zenon_H1cd zenon_H36 zenon_Hb4 zenon_H254 zenon_H2d0 zenon_H244 zenon_H80 zenon_H2b4 zenon_H25b zenon_H21 zenon_H11e zenon_Ha7 zenon_H1f5 zenon_H2b8 zenon_H6a zenon_H10a zenon_H140 zenon_H1df zenon_H49 zenon_H5e zenon_H8f zenon_H2be zenon_H10d. % 15.55/15.71 apply (zenon_or_s _ _ zenon_H10e); [ zenon_intro zenon_H3d | zenon_intro zenon_H106 ]. % 15.55/15.71 apply (zenon_L1287_); trivial. % 15.55/15.71 apply (zenon_L115_); trivial. % 15.55/15.71 (* end of lemma zenon_L1288_ *) % 15.55/15.71 assert (zenon_L1289_ : ((~((op (e0) (e0)) = (e2)))\/((op (e0) (e2)) = (e0))) -> ((~((op (e1) (e1)) = (e2)))\/((op (e1) (e2)) = (e1))) -> ((~((op (e2) (e2)) = (e0)))\/((op (e2) (e0)) = (e2))) -> ((~((op (e3) (e3)) = (e0)))\/((op (e3) (e0)) = (e3))) -> (~((op (e3) (e0)) = (op (e3) (e2)))) -> (~((op (e3) (e0)) = (op (e3) (e1)))) -> ((~((op (e3) (e3)) = (e2)))\/((op (e3) (e2)) = (e3))) -> (~((op (e1) (e1)) = (op (e1) (e2)))) -> (~((e1) = (e3))) -> (((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 (e0) (e3)) = (op (e3) (e3)))) -> (((op (e3) (e0)) = (e1))\/(((op (e3) (e1)) = (e1))\/(((op (e3) (e2)) = (e1))\/((op (e3) (e3)) = (e1))))) -> (~((op (e0) (op (e3) (e0))) = (op (e3) (e0)))) -> (~((op (e2) (e1)) = (op (e3) (e1)))) -> (~((op (e2) (op (e3) (e2))) = (op (e3) (e2)))) -> ((op (e1) (e1)) = (e1)) -> (~((op (e1) (op (e3) (e1))) = (op (e3) (e1)))) -> (~((e1) = (e2))) -> (((op (e3) (e3)) = (e0))\/(((op (e3) (e3)) = (e1))\/(((op (e3) (e3)) = (e2))\/((op (e3) (e3)) = (e3))))) -> (~((op (e0) (e0)) = (e0))) -> (((op (e0) (e0)) = (e0))\/(((op (e0) (e0)) = (e1))\/(((op (e0) (e0)) = (e2))\/((op (e0) (e0)) = (e3))))) -> (~((op (e0) (e2)) = (op (e3) (e2)))) -> (((op (e3) (e0)) = (e2))\/(((op (e3) (e1)) = (e2))\/(((op (e3) (e2)) = (e2))\/((op (e3) (e3)) = (e2))))) -> (((op (e0) (e1)) = (e2))\/(((op (e1) (e1)) = (e2))\/(((op (e2) (e1)) = (e2))\/((op (e3) (e1)) = (e2))))) -> ((op (e0) (e1)) = (e0)) -> (~((e0) = (e2))) -> (~((op (e3) (op (e3) (e3))) = (op (e3) (e3)))) -> ((~((op (e3) (e3)) = (e3)))\/((op (e3) (e3)) = (e3))) -> (~((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)) = (op (e3) (e0)))) -> (~((e0) = (e3))) -> (~((op (e1) (e2)) = (op (e3) (e2)))) -> (((op (e3) (e0)) = (e0))\/(((op (e3) (e1)) = (e0))\/(((op (e3) (e2)) = (e0))\/((op (e3) (e3)) = (e0))))) -> (~((op (e0) (e1)) = (op (e0) (e2)))) -> (~((op (e0) (e1)) = (op (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) (e3)) = (op (e2) (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 (e1) (e3)) = (op (e2) (e3)))) -> (~((op (e0) (e3)) = (op (e1) (e3)))) -> (((op (e1) (e3)) = (e0))\/(((op (e1) (e3)) = (e1))\/(((op (e1) (e3)) = (e2))\/((op (e1) (e3)) = (e3))))) -> (~((op (e1) (e1)) = (op (e1) (e3)))) -> (((op (e2) (e0)) = (e0))\/(((op (e2) (e1)) = (e0))\/(((op (e2) (e2)) = (e0))\/((op (e2) (e3)) = (e0))))) -> (~((e2) = (e3))) -> ((~((op (e3) (e3)) = (e1)))\/((op (e3) (e1)) = (e3))) -> (((op (e1) (e0)) = (e3))\/(((op (e1) (e1)) = (e3))\/(((op (e1) (e2)) = (e3))\/((op (e1) (e3)) = (e3))))) -> (~((op (e2) (e1)) = (op (e2) (e3)))) -> (((op (e0) (e3)) = (e2))\/(((op (e1) (e3)) = (e2))\/(((op (e2) (e3)) = (e2))\/((op (e3) (e3)) = (e2))))) -> (~((e0) = (e1))) -> ((~((op (e2) (e2)) = (e1)))\/((op (e2) (e1)) = (e2))) -> (~((op (e2) (e0)) = (op (e2) (e1)))) -> (((op (e0) (e0)) = (e2))\/(((op (e1) (e0)) = (e2))\/(((op (e2) (e0)) = (e2))\/((op (e3) (e0)) = (e2))))) -> ((~((op (e1) (e1)) = (e3)))\/((op (e1) (e3)) = (e1))) -> ((~((op (e0) (e0)) = (e3)))\/((op (e0) (e3)) = (e0))) -> False). % 15.55/15.72 do 0 intro. intros zenon_H24a zenon_H1d3 zenon_H1d4 zenon_H10f zenon_H105 zenon_H109 zenon_H10e zenon_H116 zenon_Ha3 zenon_H11b zenon_H8e zenon_H36 zenon_H146 zenon_H2b8 zenon_H13c zenon_H2af zenon_H21 zenon_H2b4 zenon_Ha7 zenon_H3b zenon_H20 zenon_H12a zenon_H140 zenon_H1df zenon_H1a2 zenon_H49 zenon_H5e zenon_H2be zenon_H10d zenon_H135 zenon_H16f zenon_H1e5 zenon_H4b zenon_H17d zenon_H1f6 zenon_H23e zenon_Hde zenon_H121 zenon_H1cd zenon_Hb4 zenon_H254 zenon_H2d0 zenon_H244 zenon_H80 zenon_H25b zenon_H11e zenon_H1f5 zenon_H6a zenon_H10c zenon_H90 zenon_H1e2 zenon_H160 zenon_H9e zenon_H1e3 zenon_H154 zenon_Heb zenon_H1d2 zenon_H236. % 15.55/15.72 apply (zenon_or_s _ _ zenon_H24a); [ zenon_intro zenon_H8f | zenon_intro zenon_Hab ]. % 15.55/15.72 apply (zenon_or_s _ _ zenon_H236); [ zenon_intro zenon_H59 | zenon_intro zenon_Hca ]. % 15.55/15.72 apply (zenon_or_s _ _ zenon_H1d3); [ zenon_intro zenon_Hd6 | zenon_intro zenon_H117 ]. % 15.55/15.72 apply (zenon_or_s _ _ zenon_H1d2); [ zenon_intro zenon_H182 | zenon_intro zenon_H11f ]. % 15.55/15.72 apply (zenon_or_s _ _ zenon_H1d4); [ zenon_intro zenon_H2e | zenon_intro zenon_Hdd ]. % 15.55/15.72 apply (zenon_or_s _ _ zenon_H1e3); [ zenon_intro zenon_H52 | zenon_intro zenon_H156 ]. % 15.55/15.72 apply (zenon_or_s _ _ zenon_H10f); [ zenon_intro zenon_H3c | zenon_intro zenon_Hba ]. % 15.55/15.72 apply (zenon_or_s _ _ zenon_H10c); [ zenon_intro zenon_H104 | zenon_intro zenon_H10a ]. % 15.55/15.72 apply (zenon_or_s _ _ zenon_H10e); [ zenon_intro zenon_H3d | zenon_intro zenon_H106 ]. % 15.55/15.72 apply (zenon_or_s _ _ zenon_H10d); [ zenon_intro zenon_H3e | zenon_intro zenon_H42 ]. % 15.55/15.72 apply (zenon_L1208_); trivial. % 15.55/15.72 apply (zenon_L1041_); trivial. % 15.55/15.72 apply (zenon_L1270_); trivial. % 15.55/15.72 apply (zenon_L1288_); trivial. % 15.55/15.72 apply (zenon_L1274_); trivial. % 15.55/15.72 apply (zenon_or_s _ _ zenon_H10f); [ zenon_intro zenon_H3c | zenon_intro zenon_Hba ]. % 15.55/15.72 apply (zenon_or_s _ _ zenon_H10c); [ zenon_intro zenon_H104 | zenon_intro zenon_H10a ]. % 15.55/15.72 apply (zenon_or_s _ _ zenon_H10e); [ zenon_intro zenon_H3d | zenon_intro zenon_H106 ]. % 15.55/15.72 apply (zenon_or_s _ _ zenon_H10d); [ zenon_intro zenon_H3e | zenon_intro zenon_H42 ]. % 15.55/15.72 apply (zenon_L1267_); trivial. % 15.55/15.72 apply (zenon_L1041_); trivial. % 15.55/15.72 apply (zenon_or_s _ _ zenon_H10d); [ zenon_intro zenon_H3e | zenon_intro zenon_H42 ]. % 15.55/15.72 apply (zenon_L1276_); trivial. % 15.55/15.72 apply (zenon_L1041_); trivial. % 15.55/15.72 apply (zenon_L1288_); trivial. % 15.55/15.72 apply (zenon_L1202_); trivial. % 15.55/15.72 apply (zenon_L1275_); trivial. % 15.55/15.72 apply (zenon_L90_); trivial. % 15.55/15.72 apply (zenon_L86_); trivial. % 15.55/15.72 apply (zenon_L463_); trivial. % 15.55/15.72 apply (zenon_L485_); trivial. % 15.55/15.72 (* end of lemma zenon_L1289_ *) % 15.55/15.72 assert (zenon_L1290_ : (~((op (e0) (e0)) = (e0))) -> (~((op (e1) (e0)) = (op (e1) (e1)))) -> (((op (e0) (e0)) = (e2))\/(((op (e1) (e0)) = (e2))\/(((op (e2) (e0)) = (e2))\/((op (e3) (e0)) = (e2))))) -> (~((op (e0) (op (e3) (e0))) = (op (e3) (e0)))) -> (~((e0) = (e2))) -> (~((op (e2) (e2)) = (e0))) -> (((op (e0) (e2)) = (e0))\/(((op (e1) (e2)) = (e0))\/(((op (e2) (e2)) = (e0))\/((op (e3) (e2)) = (e0))))) -> (~((e1) = (e2))) -> (~((e2) = (e3))) -> (~((op (e1) (e1)) = (e3))) -> (~((op (e1) (e2)) = (op (e3) (e2)))) -> (((op (e0) (e2)) = (e1))\/(((op (e1) (e2)) = (e1))\/(((op (e2) (e2)) = (e1))\/((op (e3) (e2)) = (e1))))) -> (~((e1) = (e3))) -> (((op (e0) (e3)) = (e2))\/(((op (e1) (e3)) = (e2))\/(((op (e2) (e3)) = (e2))\/((op (e3) (e3)) = (e2))))) -> ((op (e2) (e1)) = (e2)) -> (~((op (e2) (e1)) = (op (e2) (e3)))) -> (~((op (e0) (e3)) = (op (e3) (e3)))) -> (((op (e3) (e3)) = (e0))\/(((op (e3) (e3)) = (e1))\/(((op (e3) (e3)) = (e2))\/((op (e3) (e3)) = (e3))))) -> (~((op (e1) (e1)) = (op (e1) (e2)))) -> (~((op (e0) (e2)) = (op (e0) (e3)))) -> (((op (e1) (e0)) = (e3))\/(((op (e1) (e1)) = (e3))\/(((op (e1) (e2)) = (e3))\/((op (e1) (e3)) = (e3))))) -> (~((op (e0) (e0)) = (e2))) -> ((~((op (e2) (e2)) = (e2)))\/((op (e2) (e2)) = (e2))) -> (((op (e0) (e0)) = (e0))\/(((op (e1) (e0)) = (e0))\/(((op (e2) (e0)) = (e0))\/((op (e3) (e0)) = (e0))))) -> (((op (e0) (e1)) = (e0))\/(((op (e1) (e1)) = (e0))\/(((op (e2) (e1)) = (e0))\/((op (e3) (e1)) = (e0))))) -> (~((op (e2) (e0)) = (op (e2) (e1)))) -> (~((op (e1) (e1)) = (e0))) -> (~((op (e0) (e1)) = (op (e0) (e3)))) -> (~((op (e0) (e3)) = (op (e2) (e3)))) -> (((op (e0) (e3)) = (e0))\/(((op (e0) (e3)) = (e1))\/(((op (e0) (e3)) = (e2))\/((op (e0) (e3)) = (e3))))) -> (((op (e0) (e3)) = (e1))\/(((op (e1) (e3)) = (e1))\/(((op (e2) (e3)) = (e1))\/((op (e3) (e3)) = (e1))))) -> (((op (e2) (e1)) = (e0))\/(((op (e2) (e1)) = (e1))\/(((op (e2) (e1)) = (e2))\/((op (e2) (e1)) = (e3))))) -> (~((op (e2) (e1)) = (op (e2) (e2)))) -> (~((op (e1) (e1)) = (op (e2) (e1)))) -> (~((op (e1) (e1)) = (e2))) -> (((op (e2) (e3)) = (e0))\/(((op (e2) (e3)) = (e1))\/(((op (e2) (e3)) = (e2))\/((op (e2) (e3)) = (e3))))) -> (~((op (e2) (e2)) = (op (e2) (e3)))) -> (~((op (e3) (e0)) = (op (e3) (e1)))) -> (((op (e3) (e1)) = (e0))\/(((op (e3) (e1)) = (e1))\/(((op (e3) (e1)) = (e2))\/((op (e3) (e1)) = (e3))))) -> (((op (e0) (e0)) = (e3))\/(((op (e0) (e1)) = (e3))\/(((op (e0) (e2)) = (e3))\/((op (e0) (e3)) = (e3))))) -> (~((op (e0) (e1)) = (op (e2) (e1)))) -> (((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 (e1) (e1)) = (e2)))\/((op (e1) (e2)) = (e1))) -> (~((op (e1) (e0)) = (op (e1) (e2)))) -> (~((op (e0) (e3)) = (op (e1) (e3)))) -> (~((op (e3) (e0)) = (op (e3) (e2)))) -> (~((op (e2) (e0)) = (op (e2) (e2)))) -> (((op (e1) (e1)) = (e0))\/(((op (e1) (e1)) = (e1))\/(((op (e1) (e1)) = (e2))\/((op (e1) (e1)) = (e3))))) -> (((op (e1) (e0)) = (e2))\/(((op (e1) (e1)) = (e2))\/(((op (e1) (e2)) = (e2))\/((op (e1) (e3)) = (e2))))) -> (~((op (e1) (e2)) = (op (e2) (e2)))) -> (~((op (e1) (e0)) = (op (e1) (e3)))) -> ((~((op (e1) (e1)) = (e3)))\/((op (e1) (e3)) = (e1))) -> ((~((op (e1) (e1)) = (e1)))\/((op (e1) (e1)) = (e1))) -> (~((op (e0) (e1)) = (op (e3) (e1)))) -> (~((op (e2) (op (e3) (e2))) = (op (e3) (e2)))) -> (((op (e3) (e0)) = (e2))\/(((op (e3) (e1)) = (e2))\/(((op (e3) (e2)) = (e2))\/((op (e3) (e3)) = (e2))))) -> (~((op (e0) (e2)) = (op (e2) (e2)))) -> (~((op (e2) (e1)) = (op (e3) (e1)))) -> ((~((op (e3) (e3)) = (e0)))\/((op (e3) (e0)) = (e3))) -> ((~((op (e3) (e3)) = (e3)))\/((op (e3) (e3)) = (e3))) -> (~((op (e3) (op (e3) (e3))) = (op (e3) (e3)))) -> (((op (e2) (e2)) = (e0))\/(((op (e2) (e2)) = (e1))\/(((op (e2) (e2)) = (e2))\/((op (e2) (e2)) = (e3))))) -> (((op (e0) (e0)) = (e1))\/(((op (e1) (e0)) = (e1))\/(((op (e2) (e0)) = (e1))\/((op (e3) (e0)) = (e1))))) -> ((~((op (e3) (e3)) = (e2)))\/((op (e3) (e2)) = (e3))) -> (~((op (e3) (e1)) = (op (e3) (e2)))) -> (((op (e0) (e0)) = (e1))\/(((op (e0) (e1)) = (e1))\/(((op (e0) (e2)) = (e1))\/((op (e0) (e3)) = (e1))))) -> (((op (e0) (e0)) = (e0))\/(((op (e0) (e0)) = (e1))\/(((op (e0) (e0)) = (e2))\/((op (e0) (e0)) = (e3))))) -> ((op (e0) (e3)) = (e0)) -> (((op (e0) (e0)) = (e2))\/(((op (e0) (e1)) = (e2))\/(((op (e0) (e2)) = (e2))\/((op (e0) (e3)) = (e2))))) -> ((~((op (e3) (e3)) = (e1)))\/((op (e3) (e1)) = (e3))) -> (~((op (e2) (e0)) = (op (e2) (e3)))) -> ((~((op (e2) (e2)) = (e3)))\/((op (e2) (e3)) = (e2))) -> ((~((op (e2) (e2)) = (e1)))\/((op (e2) (e1)) = (e2))) -> (((op (e3) (e0)) = (e1))\/(((op (e3) (e1)) = (e1))\/(((op (e3) (e2)) = (e1))\/((op (e3) (e3)) = (e1))))) -> (~((op (e3) (e3)) = (e1))) -> (~((op (e0) (e2)) = (op (e3) (e2)))) -> (~((op (e1) (op (e3) (e1))) = (op (e3) (e1)))) -> (~((e0) = (e1))) -> (~((e0) = (e3))) -> ((op (e3) (e2)) = (e3)) -> (~((op (e3) (e3)) = (e0))) -> (((op (e3) (e0)) = (e0))\/(((op (e3) (e1)) = (e0))\/(((op (e3) (e2)) = (e0))\/((op (e3) (e3)) = (e0))))) -> ((op (e1) (e1)) = (e1)) -> (~((op (e0) (e1)) = (op (e1) (e1)))) -> (~((op (e0) (e0)) = (e1))) -> ((~((op (e0) (e0)) = (e2)))\/((op (e0) (e2)) = (e0))) -> ((~((op (e2) (e2)) = (e0)))\/((op (e2) (e0)) = (e2))) -> (((op (e0) (e1)) = (e2))\/(((op (e1) (e1)) = (e2))\/(((op (e2) (e1)) = (e2))\/((op (e3) (e1)) = (e2))))) -> (~((op (e0) (e1)) = (op (e0) (e2)))) -> (((op (e0) (e3)) = (e3))\/(((op (e1) (e3)) = (e3))\/(((op (e2) (e3)) = (e3))\/((op (e3) (e3)) = (e3))))) -> (~((op (e1) (e3)) = (op (e2) (e3)))) -> (((op (e1) (e3)) = (e0))\/(((op (e1) (e3)) = (e1))\/(((op (e1) (e3)) = (e2))\/((op (e1) (e3)) = (e3))))) -> (~((op (e1) (e1)) = (op (e1) (e3)))) -> (((op (e2) (e0)) = (e0))\/(((op (e2) (e1)) = (e0))\/(((op (e2) (e2)) = (e0))\/((op (e2) (e3)) = (e0))))) -> ((~((op (e0) (e0)) = (e3)))\/((op (e0) (e3)) = (e0))) -> (((op (e2) (e0)) = (e1))\/(((op (e2) (e1)) = (e1))\/(((op (e2) (e2)) = (e1))\/((op (e2) (e3)) = (e1))))) -> (~((op (e2) (e0)) = (op (e3) (e0)))) -> False). % 15.55/15.72 do 0 intro. intros zenon_H20 zenon_Hd7 zenon_Heb zenon_H2b8 zenon_H5e zenon_H2e zenon_H16f zenon_Ha7 zenon_H6a zenon_H182 zenon_H17d zenon_H11b zenon_Ha3 zenon_H160 zenon_H156 zenon_H1e2 zenon_H36 zenon_H3b zenon_H116 zenon_Hc9 zenon_H90 zenon_H8f zenon_Haa zenon_Hf0 zenon_H144 zenon_H154 zenon_H145 zenon_H1cd zenon_Hb4 zenon_H254 zenon_H121 zenon_H15a zenon_H157 zenon_Hb1 zenon_Hd6 zenon_H2ab zenon_H15f zenon_H109 zenon_H16c zenon_H58 zenon_Hde zenon_He6 zenon_H1d5 zenon_H1d3 zenon_H166 zenon_H80 zenon_H105 zenon_H17a zenon_H1b3 zenon_H84 zenon_H7d zenon_H1cf zenon_H1d2 zenon_H1d8 zenon_H138 zenon_H2af zenon_H1df zenon_H28 zenon_H13c zenon_H10f zenon_H10d zenon_H2be zenon_H2d zenon_Hf1 zenon_H10e zenon_H135 zenon_H44 zenon_H12a zenon_Hca zenon_H8e zenon_H10c zenon_Hce zenon_H1c3 zenon_H1e3 zenon_H146 zenon_H104 zenon_H140 zenon_H2b4 zenon_H9e zenon_H4b zenon_H106 zenon_H3c zenon_H1f6 zenon_H21 zenon_H23 zenon_H45 zenon_H24a zenon_H1d4 zenon_H1a2 zenon_H23e zenon_H2d0 zenon_H244 zenon_H25b zenon_H11e zenon_H1f5 zenon_H236 zenon_Hb7 zenon_H1e5. % 15.55/15.72 apply (zenon_or_s _ _ zenon_H10d); [ zenon_intro zenon_H3e | zenon_intro zenon_H42 ]. % 15.55/15.72 apply (zenon_or_s _ _ zenon_Hf0); [ zenon_intro zenon_H1f | zenon_intro zenon_Hf2 ]. % 15.55/15.72 exact (zenon_H20 zenon_H1f). % 15.55/15.72 apply (zenon_or_s _ _ zenon_Hf2); [ zenon_intro zenon_Had | zenon_intro zenon_Hf3 ]. % 15.55/15.72 apply (zenon_or_s _ _ zenon_H44); [ zenon_intro zenon_H47 | zenon_intro zenon_H46 ]. % 15.55/15.72 exact (zenon_H45 zenon_H47). % 15.55/15.72 apply (zenon_or_s _ _ zenon_H46); [ zenon_intro zenon_H22 | zenon_intro zenon_H48 ]. % 15.55/15.72 apply (zenon_L3_); trivial. % 15.55/15.72 apply (zenon_or_s _ _ zenon_H48); [ zenon_intro zenon_H29 | zenon_intro zenon_H37 ]. % 15.55/15.72 apply (zenon_L1210_); trivial. % 15.55/15.72 apply (zenon_or_s _ _ zenon_Hf1); [ zenon_intro zenon_H47 | zenon_intro zenon_Hf4 ]. % 15.55/15.72 exact (zenon_H45 zenon_H47). % 15.55/15.72 apply (zenon_or_s _ _ zenon_Hf4); [ zenon_intro zenon_Hd8 | zenon_intro zenon_Hf5 ]. % 15.55/15.72 apply (zenon_L61_); trivial. % 15.55/15.72 apply (zenon_or_s _ _ zenon_Hf5); [ zenon_intro zenon_Hae | zenon_intro zenon_Hee ]. % 15.55/15.72 apply (zenon_or_s _ _ zenon_Heb); [ zenon_intro zenon_H92 | zenon_intro zenon_Hec ]. % 15.55/15.72 exact (zenon_H8f zenon_H92). % 15.55/15.72 apply (zenon_or_s _ _ zenon_Hec); [ zenon_intro zenon_H68 | zenon_intro zenon_Hed ]. % 15.55/15.72 apply (zenon_L1281_); trivial. % 15.55/15.72 apply (zenon_or_s _ _ zenon_Hed); [ zenon_intro zenon_Hdd | zenon_intro zenon_He9 ]. % 15.55/15.72 apply (zenon_L304_); trivial. % 15.55/15.72 apply (zenon_L1138_); trivial. % 15.55/15.72 apply (zenon_or_s _ _ zenon_Heb); [ zenon_intro zenon_H92 | zenon_intro zenon_Hec ]. % 15.55/15.72 exact (zenon_H8f zenon_H92). % 15.55/15.72 apply (zenon_or_s _ _ zenon_Hec); [ zenon_intro zenon_H68 | zenon_intro zenon_Hed ]. % 15.55/15.72 apply (zenon_L1281_); trivial. % 15.55/15.72 apply (zenon_or_s _ _ zenon_Hed); [ zenon_intro zenon_Hdd | zenon_intro zenon_He9 ]. % 15.55/15.72 apply (zenon_L1285_); trivial. % 15.55/15.72 apply (zenon_L122_); trivial. % 15.55/15.72 apply (zenon_or_s _ _ zenon_Hf3); [ zenon_intro zenon_Hcf | zenon_intro zenon_Hdb ]. % 15.55/15.72 apply (zenon_or_s _ _ zenon_H44); [ zenon_intro zenon_H47 | zenon_intro zenon_H46 ]. % 15.55/15.72 exact (zenon_H45 zenon_H47). % 15.55/15.72 apply (zenon_or_s _ _ zenon_H46); [ zenon_intro zenon_H22 | zenon_intro zenon_H48 ]. % 15.55/15.72 apply (zenon_L3_); trivial. % 15.55/15.72 apply (zenon_or_s _ _ zenon_H48); [ zenon_intro zenon_H29 | zenon_intro zenon_H37 ]. % 15.55/15.72 apply (zenon_or_s _ _ zenon_Hf1); [ zenon_intro zenon_H47 | zenon_intro zenon_Hf4 ]. % 15.55/15.72 exact (zenon_H45 zenon_H47). % 15.55/15.72 apply (zenon_or_s _ _ zenon_Hf4); [ zenon_intro zenon_Hd8 | zenon_intro zenon_Hf5 ]. % 15.55/15.72 apply (zenon_L61_); trivial. % 15.55/15.72 apply (zenon_or_s _ _ zenon_Hf5); [ zenon_intro zenon_Hae | zenon_intro zenon_Hee ]. % 15.55/15.72 apply (zenon_L269_); trivial. % 15.55/15.72 apply (zenon_or_s _ _ zenon_Heb); [ zenon_intro zenon_H92 | zenon_intro zenon_Hec ]. % 15.55/15.72 exact (zenon_H8f zenon_H92). % 15.55/15.72 apply (zenon_or_s _ _ zenon_Hec); [ zenon_intro zenon_H68 | zenon_intro zenon_Hed ]. % 15.55/15.72 apply (zenon_or_s _ _ zenon_H90); [ zenon_intro zenon_H69 | zenon_intro zenon_H94 ]. % 15.55/15.72 apply (zenon_L17_); trivial. % 15.55/15.72 apply (zenon_or_s _ _ zenon_H94); [ zenon_intro zenon_H96 | zenon_intro zenon_H95 ]. % 15.55/15.72 exact (zenon_H182 zenon_H96). % 15.55/15.72 apply (zenon_or_s _ _ zenon_H95); [ zenon_intro zenon_H88 | zenon_intro zenon_H8a ]. % 15.55/15.72 apply (zenon_L164_); trivial. % 15.55/15.72 apply (zenon_or_s _ _ zenon_Hb7); [ zenon_intro zenon_Hae | zenon_intro zenon_Hb8 ]. % 15.55/15.72 apply (zenon_L269_); trivial. % 15.55/15.72 apply (zenon_or_s _ _ zenon_Hb8); [ zenon_intro zenon_Hb2 | zenon_intro zenon_Hb9 ]. % 15.55/15.72 apply (zenon_L40_); trivial. % 15.55/15.72 apply (zenon_or_s _ _ zenon_Hb9); [ zenon_intro zenon_H2a | zenon_intro zenon_Hb5 ]. % 15.55/15.72 apply (zenon_L1286_); trivial. % 15.55/15.72 apply (zenon_L176_); trivial. % 15.55/15.72 apply (zenon_or_s _ _ zenon_Hed); [ zenon_intro zenon_Hdd | zenon_intro zenon_He9 ]. % 15.55/15.72 apply (zenon_L1285_); trivial. % 15.55/15.72 apply (zenon_L1082_); trivial. % 15.55/15.72 apply (zenon_or_s _ _ zenon_Hf1); [ zenon_intro zenon_H47 | zenon_intro zenon_Hf4 ]. % 15.55/15.72 exact (zenon_H45 zenon_H47). % 15.55/15.72 apply (zenon_or_s _ _ zenon_Hf4); [ zenon_intro zenon_Hd8 | zenon_intro zenon_Hf5 ]. % 15.55/15.72 apply (zenon_L61_); trivial. % 15.55/15.72 apply (zenon_or_s _ _ zenon_Hf5); [ zenon_intro zenon_Hae | zenon_intro zenon_Hee ]. % 15.55/15.72 apply (zenon_L269_); trivial. % 15.55/15.72 apply (zenon_or_s _ _ zenon_Heb); [ zenon_intro zenon_H92 | zenon_intro zenon_Hec ]. % 15.55/15.72 exact (zenon_H8f zenon_H92). % 15.55/15.72 apply (zenon_or_s _ _ zenon_Hec); [ zenon_intro zenon_H68 | zenon_intro zenon_Hed ]. % 15.55/15.72 apply (zenon_or_s _ _ zenon_H144); [ zenon_intro zenon_H49 | zenon_intro zenon_H147 ]. % 15.55/15.72 apply (zenon_L1289_); trivial. % 15.55/15.72 apply (zenon_or_s _ _ zenon_H147); [ zenon_intro zenon_H149 | zenon_intro zenon_H148 ]. % 15.55/15.72 exact (zenon_H145 zenon_H149). % 15.55/15.72 apply (zenon_or_s _ _ zenon_H148); [ zenon_intro zenon_H14a | zenon_intro zenon_H142 ]. % 15.55/15.72 apply (zenon_L133_); trivial. % 15.55/15.72 apply (zenon_or_s _ _ zenon_H90); [ zenon_intro zenon_H69 | zenon_intro zenon_H94 ]. % 15.55/15.72 apply (zenon_L17_); trivial. % 15.55/15.72 apply (zenon_or_s _ _ zenon_H94); [ zenon_intro zenon_H96 | zenon_intro zenon_H95 ]. % 15.55/15.72 exact (zenon_H182 zenon_H96). % 15.55/15.72 apply (zenon_or_s _ _ zenon_H95); [ zenon_intro zenon_H88 | zenon_intro zenon_H8a ]. % 15.55/15.72 apply (zenon_L164_); trivial. % 15.55/15.72 apply (zenon_or_s _ _ zenon_Hb7); [ zenon_intro zenon_Hae | zenon_intro zenon_Hb8 ]. % 15.55/15.72 apply (zenon_L269_); trivial. % 15.55/15.72 apply (zenon_or_s _ _ zenon_Hb8); [ zenon_intro zenon_Hb2 | zenon_intro zenon_Hb9 ]. % 15.55/15.72 apply (zenon_L40_); trivial. % 15.55/15.72 apply (zenon_or_s _ _ zenon_Hb9); [ zenon_intro zenon_H2a | zenon_intro zenon_Hb5 ]. % 15.55/15.72 apply (zenon_L902_); trivial. % 15.55/15.72 apply (zenon_L41_); trivial. % 15.55/15.72 apply (zenon_or_s _ _ zenon_Hed); [ zenon_intro zenon_Hdd | zenon_intro zenon_He9 ]. % 15.55/15.72 apply (zenon_L284_); trivial. % 15.55/15.72 apply (zenon_L122_); trivial. % 15.55/15.72 apply (zenon_L1212_); trivial. % 15.55/15.72 apply (zenon_L1041_); trivial. % 15.55/15.72 (* end of lemma zenon_L1290_ *) % 15.55/15.72 assert (zenon_L1291_ : ((~((op (e3) (e3)) = (e3)))\/((op (e3) (e3)) = (e3))) -> (~((op (e3) (op (e3) (e3))) = (op (e3) (e3)))) -> (~((op (e0) (e0)) = (e1))) -> (~((op (e0) (e1)) = (op (e1) (e1)))) -> ((op (e1) (e1)) = (e1)) -> (~((e0) = (e1))) -> ((op (e0) (e2)) = (e0)) -> (((op (e3) (e3)) = (e0))\/(((op (e3) (e3)) = (e1))\/(((op (e3) (e3)) = (e2))\/((op (e3) (e3)) = (e3))))) -> (~((op (e3) (e3)) = (e2))) -> (~((op (e0) (e3)) = (op (e3) (e3)))) -> (~((op (e3) (e3)) = (e0))) -> (((op (e0) (e0)) = (e1))\/(((op (e0) (e1)) = (e1))\/(((op (e0) (e2)) = (e1))\/((op (e0) (e3)) = (e1))))) -> False). % 15.55/15.72 do 0 intro. intros zenon_H10d zenon_H2be zenon_H45 zenon_H23 zenon_H21 zenon_H9e zenon_Hab zenon_H3b zenon_H3d zenon_H36 zenon_H3c zenon_H44. % 15.55/15.72 apply (zenon_or_s _ _ zenon_H10d); [ zenon_intro zenon_H3e | zenon_intro zenon_H42 ]. % 15.55/15.72 apply (zenon_L132_); trivial. % 15.55/15.72 apply (zenon_L1041_); trivial. % 15.55/15.72 (* end of lemma zenon_L1291_ *) % 15.55/15.72 assert (zenon_L1292_ : ((~((op (e3) (e3)) = (e2)))\/((op (e3) (e2)) = (e3))) -> ((op (e3) (e1)) = (e3)) -> (~((op (e3) (e1)) = (op (e3) (e2)))) -> (((op (e0) (e0)) = (e1))\/(((op (e0) (e1)) = (e1))\/(((op (e0) (e2)) = (e1))\/((op (e0) (e3)) = (e1))))) -> (~((op (e3) (e3)) = (e0))) -> (~((op (e0) (e3)) = (op (e3) (e3)))) -> (((op (e3) (e3)) = (e0))\/(((op (e3) (e3)) = (e1))\/(((op (e3) (e3)) = (e2))\/((op (e3) (e3)) = (e3))))) -> ((op (e0) (e2)) = (e0)) -> (~((e0) = (e1))) -> ((op (e1) (e1)) = (e1)) -> (~((op (e0) (e1)) = (op (e1) (e1)))) -> (~((op (e0) (e0)) = (e1))) -> (~((op (e3) (op (e3) (e3))) = (op (e3) (e3)))) -> ((~((op (e3) (e3)) = (e3)))\/((op (e3) (e3)) = (e3))) -> False). % 15.55/15.72 do 0 intro. intros zenon_H10e zenon_H10a zenon_H135 zenon_H44 zenon_H3c zenon_H36 zenon_H3b zenon_Hab zenon_H9e zenon_H21 zenon_H23 zenon_H45 zenon_H2be zenon_H10d. % 15.55/15.72 apply (zenon_or_s _ _ zenon_H10e); [ zenon_intro zenon_H3d | zenon_intro zenon_H106 ]. % 15.55/15.72 apply (zenon_L1291_); trivial. % 15.55/15.72 apply (zenon_L115_); trivial. % 15.55/15.72 (* end of lemma zenon_L1292_ *) % 15.55/15.72 assert (zenon_L1293_ : ((~((op (e2) (e2)) = (e3)))\/((op (e2) (e3)) = (e2))) -> (~((op (e2) (e0)) = (op (e2) (e3)))) -> ((~((op (e3) (e3)) = (e1)))\/((op (e3) (e1)) = (e3))) -> (~((op (e0) (e1)) = (op (e1) (e1)))) -> (~((e0) = (e1))) -> ((op (e0) (e2)) = (e0)) -> (~((op (e0) (e3)) = (op (e3) (e3)))) -> (((op (e0) (e0)) = (e1))\/(((op (e0) (e1)) = (e1))\/(((op (e0) (e2)) = (e1))\/((op (e0) (e3)) = (e1))))) -> (~((op (e3) (e1)) = (op (e3) (e2)))) -> ((~((op (e3) (e3)) = (e2)))\/((op (e3) (e2)) = (e3))) -> (((op (e0) (e0)) = (e1))\/(((op (e1) (e0)) = (e1))\/(((op (e2) (e0)) = (e1))\/((op (e3) (e0)) = (e1))))) -> (((op (e3) (e3)) = (e0))\/(((op (e3) (e3)) = (e1))\/(((op (e3) (e3)) = (e2))\/((op (e3) (e3)) = (e3))))) -> (~((op (e2) (e2)) = (e1))) -> (~((op (e2) (e2)) = (e2))) -> (((op (e2) (e2)) = (e0))\/(((op (e2) (e2)) = (e1))\/(((op (e2) (e2)) = (e2))\/((op (e2) (e2)) = (e3))))) -> ((op (e2) (e0)) = (e2)) -> (~((e1) = (e2))) -> ((op (e1) (e1)) = (e1)) -> (~((op (e1) (e0)) = (op (e1) (e1)))) -> (~((op (e0) (e0)) = (e1))) -> (~((op (e3) (op (e3) (e3))) = (op (e3) (e3)))) -> ((~((op (e3) (e3)) = (e3)))\/((op (e3) (e3)) = (e3))) -> (~((e1) = (e3))) -> ((~((op (e3) (e3)) = (e0)))\/((op (e3) (e0)) = (e3))) -> False). % 15.55/15.72 do 0 intro. intros zenon_H1c3 zenon_Hce zenon_H10c zenon_H23 zenon_H9e zenon_Hab zenon_H36 zenon_H44 zenon_H135 zenon_H10e zenon_Hf1 zenon_H3b zenon_H52 zenon_H2f zenon_H2d zenon_Hdd zenon_Ha7 zenon_H21 zenon_Hd7 zenon_H45 zenon_H2be zenon_H10d zenon_Ha3 zenon_H10f. % 15.55/15.72 apply (zenon_or_s _ _ zenon_H1c3); [ zenon_intro zenon_H30 | zenon_intro zenon_H124 ]. % 15.55/15.72 apply (zenon_or_s _ _ zenon_H10f); [ zenon_intro zenon_H3c | zenon_intro zenon_Hba ]. % 15.55/15.72 apply (zenon_or_s _ _ zenon_H10c); [ zenon_intro zenon_H104 | zenon_intro zenon_H10a ]. % 15.55/15.72 apply (zenon_L1171_); trivial. % 15.55/15.72 apply (zenon_L1292_); trivial. % 15.55/15.72 apply (zenon_L310_); trivial. % 15.55/15.72 apply (zenon_L119_); trivial. % 15.55/15.72 (* end of lemma zenon_L1293_ *) % 15.55/15.72 assert (zenon_L1294_ : ((~((op (e2) (e2)) = (e3)))\/((op (e2) (e3)) = (e2))) -> (~((op (e2) (e2)) = (op (e2) (e3)))) -> (((op (e2) (e0)) = (e3))\/(((op (e2) (e1)) = (e3))\/(((op (e2) (e2)) = (e3))\/((op (e2) (e3)) = (e3))))) -> (~((op (e2) (e1)) = (op (e3) (e1)))) -> (((op (e0) (e0)) = (e3))\/(((op (e0) (e1)) = (e3))\/(((op (e0) (e2)) = (e3))\/((op (e0) (e3)) = (e3))))) -> (~((op (e1) (e0)) = (op (e1) (e1)))) -> (~((op (e3) (e1)) = (op (e3) (e2)))) -> ((~((op (e3) (e3)) = (e3)))\/((op (e3) (e3)) = (e3))) -> (~((op (e3) (op (e3) (e3))) = (op (e3) (e3)))) -> (~((op (e0) (e0)) = (e1))) -> (~((op (e0) (e1)) = (op (e1) (e1)))) -> ((op (e1) (e1)) = (e1)) -> (((op (e0) (e0)) = (e0))\/(((op (e1) (e0)) = (e0))\/(((op (e2) (e0)) = (e0))\/((op (e3) (e0)) = (e0))))) -> (((op (e0) (e0)) = (e1))\/(((op (e1) (e0)) = (e1))\/(((op (e2) (e0)) = (e1))\/((op (e3) (e0)) = (e1))))) -> (~((e0) = (e1))) -> (~((op (e0) (e0)) = (e3))) -> (((op (e2) (e0)) = (e1))\/(((op (e2) (e1)) = (e1))\/(((op (e2) (e2)) = (e1))\/((op (e2) (e3)) = (e1))))) -> (~((op (e0) (e3)) = (op (e2) (e3)))) -> (~((op (e0) (e2)) = (op (e0) (e3)))) -> (~((op (e1) (e0)) = (op (e1) (e2)))) -> ((~((op (e3) (e3)) = (e1)))\/((op (e3) (e1)) = (e3))) -> (~((op (e3) (e0)) = (op (e3) (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) (e3)) = (op (e1) (e3)))) -> (((op (e1) (e0)) = (e2))\/(((op (e1) (e1)) = (e2))\/(((op (e1) (e2)) = (e2))\/((op (e1) (e3)) = (e2))))) -> (~((op (e1) (e2)) = (op (e3) (e2)))) -> (~((op (e1) (e0)) = (op (e2) (e0)))) -> (((op (e0) (e1)) = (e2))\/(((op (e1) (e1)) = (e2))\/(((op (e2) (e1)) = (e2))\/((op (e3) (e1)) = (e2))))) -> (~((op (e3) (e0)) = (op (e3) (e2)))) -> ((~((op (e3) (e3)) = (e2)))\/((op (e3) (e2)) = (e3))) -> (((op (e0) (e0)) = (e3))\/(((op (e1) (e0)) = (e3))\/(((op (e2) (e0)) = (e3))\/((op (e3) (e0)) = (e3))))) -> (~((e1) = (e3))) -> (((op (e0) (e0)) = (e2))\/(((op (e0) (e1)) = (e2))\/(((op (e0) (e2)) = (e2))\/((op (e0) (e3)) = (e2))))) -> (~((e1) = (e2))) -> (~((op (e0) (e2)) = (op (e2) (e2)))) -> (~((e2) = (e3))) -> (~((op (e1) (e1)) = (op (e1) (e2)))) -> (~((op (e2) (e2)) = (e1))) -> (((op (e3) (e0)) = (e0))\/(((op (e3) (e1)) = (e0))\/(((op (e3) (e2)) = (e0))\/((op (e3) (e3)) = (e0))))) -> ((op (e0) (e2)) = (e0)) -> (~((e0) = (e3))) -> (((op (e0) (e2)) = (e1))\/(((op (e1) (e2)) = (e1))\/(((op (e2) (e2)) = (e1))\/((op (e3) (e2)) = (e1))))) -> (((op (e0) (e0)) = (e1))\/(((op (e0) (e1)) = (e1))\/(((op (e0) (e2)) = (e1))\/((op (e0) (e3)) = (e1))))) -> (~((op (e0) (e0)) = (e0))) -> (((op (e1) (e2)) = (e0))\/(((op (e1) (e2)) = (e1))\/(((op (e1) (e2)) = (e2))\/((op (e1) (e2)) = (e3))))) -> (~((op (e0) (e2)) = (op (e1) (e2)))) -> (((op (e3) (e0)) = (e3))\/(((op (e3) (e1)) = (e3))\/(((op (e3) (e2)) = (e3))\/((op (e3) (e3)) = (e3))))) -> (~((op (e2) (e1)) = (op (e2) (e2)))) -> (~((op (e1) (e1)) = (e2))) -> (((op (e3) (e0)) = (e2))\/(((op (e3) (e1)) = (e2))\/(((op (e3) (e2)) = (e2))\/((op (e3) (e3)) = (e2))))) -> ((op (e2) (e2)) = (e2)) -> (~((op (e2) (op (e3) (e2))) = (op (e3) (e2)))) -> (~((op (e0) (e1)) = (op (e3) (e1)))) -> (~((op (e0) (op (e3) (e0))) = (op (e3) (e0)))) -> (~((op (e1) (op (e3) (e1))) = (op (e3) (e1)))) -> (~((op (e0) (e2)) = (op (e3) (e2)))) -> (((op (e3) (e0)) = (e1))\/(((op (e3) (e1)) = (e1))\/(((op (e3) (e2)) = (e1))\/((op (e3) (e3)) = (e1))))) -> (((op (e3) (e3)) = (e0))\/(((op (e3) (e3)) = (e1))\/(((op (e3) (e3)) = (e2))\/((op (e3) (e3)) = (e3))))) -> (~((op (e0) (e3)) = (op (e3) (e3)))) -> ((~((op (e3) (e3)) = (e0)))\/((op (e3) (e0)) = (e3))) -> False). % 15.55/15.72 do 0 intro. intros zenon_H1c3 zenon_H15f zenon_He6 zenon_H13c zenon_H58 zenon_Hd7 zenon_H135 zenon_H10d zenon_H2be zenon_H45 zenon_H23 zenon_H21 zenon_Hf0 zenon_Hf1 zenon_H9e zenon_H59 zenon_Hb7 zenon_Hb4 zenon_Hc9 zenon_H166 zenon_H10c zenon_H109 zenon_H254 zenon_H7d zenon_H80 zenon_H84 zenon_H17d zenon_H247 zenon_H1a2 zenon_H105 zenon_H10e zenon_Hbe zenon_Ha3 zenon_H8e zenon_Ha7 zenon_H28 zenon_H6a zenon_H116 zenon_H52 zenon_H1f6 zenon_Hab zenon_H4b zenon_H11b zenon_H44 zenon_H20 zenon_H1d5 zenon_H87 zenon_H2d5 zenon_H157 zenon_Hd6 zenon_H1df zenon_H35 zenon_H2af zenon_H138 zenon_H2b8 zenon_H2b4 zenon_H140 zenon_H146 zenon_H3b zenon_H36 zenon_H10f. % 15.55/15.72 apply (zenon_or_s _ _ zenon_H1c3); [ zenon_intro zenon_H30 | zenon_intro zenon_H124 ]. % 15.55/15.72 apply (zenon_or_s _ _ zenon_H10f); [ zenon_intro zenon_H3c | zenon_intro zenon_Hba ]. % 15.55/15.72 apply (zenon_or_s _ _ zenon_H10c); [ zenon_intro zenon_H104 | zenon_intro zenon_H10a ]. % 15.55/15.72 apply (zenon_L1254_); trivial. % 15.55/15.72 apply (zenon_L1183_); trivial. % 15.55/15.72 apply (zenon_or_s _ _ zenon_H10c); [ zenon_intro zenon_H104 | zenon_intro zenon_H10a ]. % 15.55/15.72 apply (zenon_or_s _ _ zenon_H10e); [ zenon_intro zenon_H3d | zenon_intro zenon_H106 ]. % 15.55/15.72 apply (zenon_L1252_); trivial. % 15.55/15.72 apply (zenon_L81_); trivial. % 15.55/15.72 apply (zenon_L82_); trivial. % 15.55/15.72 apply (zenon_L137_); trivial. % 15.55/15.72 (* end of lemma zenon_L1294_ *) % 15.55/15.72 assert (zenon_L1295_ : ((~((op (e2) (e2)) = (e2)))\/((op (e2) (e2)) = (e2))) -> (((op (e3) (e0)) = (e1))\/(((op (e3) (e1)) = (e1))\/(((op (e3) (e2)) = (e1))\/((op (e3) (e3)) = (e1))))) -> (~((op (e0) (e2)) = (op (e3) (e2)))) -> (~((op (e1) (op (e3) (e1))) = (op (e3) (e1)))) -> (~((op (e0) (op (e3) (e0))) = (op (e3) (e0)))) -> (~((op (e0) (e1)) = (op (e3) (e1)))) -> (~((op (e2) (op (e3) (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 (e2) (e1)) = (op (e2) (e2)))) -> (((op (e3) (e0)) = (e3))\/(((op (e3) (e1)) = (e3))\/(((op (e3) (e2)) = (e3))\/((op (e3) (e3)) = (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)) = (e0))) -> (((op (e0) (e2)) = (e1))\/(((op (e1) (e2)) = (e1))\/(((op (e2) (e2)) = (e1))\/((op (e3) (e2)) = (e1))))) -> (~((e0) = (e3))) -> (((op (e3) (e0)) = (e0))\/(((op (e3) (e1)) = (e0))\/(((op (e3) (e2)) = (e0))\/((op (e3) (e3)) = (e0))))) -> (~((op (e1) (e1)) = (op (e1) (e2)))) -> (~((e2) = (e3))) -> (~((op (e0) (e2)) = (op (e2) (e2)))) -> (((op (e0) (e0)) = (e2))\/(((op (e0) (e1)) = (e2))\/(((op (e0) (e2)) = (e2))\/((op (e0) (e3)) = (e2))))) -> (((op (e0) (e0)) = (e3))\/(((op (e1) (e0)) = (e3))\/(((op (e2) (e0)) = (e3))\/((op (e3) (e0)) = (e3))))) -> (~((op (e3) (e0)) = (op (e3) (e2)))) -> (((op (e0) (e1)) = (e2))\/(((op (e1) (e1)) = (e2))\/(((op (e2) (e1)) = (e2))\/((op (e3) (e1)) = (e2))))) -> (~((op (e1) (e0)) = (op (e2) (e0)))) -> (~((op (e1) (e2)) = (op (e3) (e2)))) -> (((op (e1) (e0)) = (e2))\/(((op (e1) (e1)) = (e2))\/(((op (e1) (e2)) = (e2))\/((op (e1) (e3)) = (e2))))) -> (~((op (e0) (e3)) = (op (e1) (e3)))) -> (~((op (e1) (e2)) = (op (e2) (e2)))) -> (((op (e0) (e3)) = (e0))\/(((op (e0) (e3)) = (e1))\/(((op (e0) (e3)) = (e2))\/((op (e0) (e3)) = (e3))))) -> (~((op (e3) (e0)) = (op (e3) (e1)))) -> (~((op (e1) (e0)) = (op (e1) (e2)))) -> (~((op (e0) (e2)) = (op (e0) (e3)))) -> (~((op (e0) (e3)) = (op (e2) (e3)))) -> (((op (e2) (e0)) = (e1))\/(((op (e2) (e1)) = (e1))\/(((op (e2) (e2)) = (e1))\/((op (e2) (e3)) = (e1))))) -> (~((op (e0) (e0)) = (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) (e1)) = (op (e3) (e1)))) -> (((op (e2) (e0)) = (e3))\/(((op (e2) (e1)) = (e3))\/(((op (e2) (e2)) = (e3))\/((op (e2) (e3)) = (e3))))) -> (~((op (e2) (e2)) = (op (e2) (e3)))) -> ((~((op (e3) (e3)) = (e0)))\/((op (e3) (e0)) = (e3))) -> (~((e1) = (e3))) -> ((~((op (e3) (e3)) = (e3)))\/((op (e3) (e3)) = (e3))) -> (~((op (e3) (op (e3) (e3))) = (op (e3) (e3)))) -> (~((op (e0) (e0)) = (e1))) -> (~((op (e1) (e0)) = (op (e1) (e1)))) -> ((op (e1) (e1)) = (e1)) -> (~((e1) = (e2))) -> ((op (e2) (e0)) = (e2)) -> (((op (e2) (e2)) = (e0))\/(((op (e2) (e2)) = (e1))\/(((op (e2) (e2)) = (e2))\/((op (e2) (e2)) = (e3))))) -> (~((op (e2) (e2)) = (e1))) -> (((op (e3) (e3)) = (e0))\/(((op (e3) (e3)) = (e1))\/(((op (e3) (e3)) = (e2))\/((op (e3) (e3)) = (e3))))) -> (((op (e0) (e0)) = (e1))\/(((op (e1) (e0)) = (e1))\/(((op (e2) (e0)) = (e1))\/((op (e3) (e0)) = (e1))))) -> ((~((op (e3) (e3)) = (e2)))\/((op (e3) (e2)) = (e3))) -> (~((op (e3) (e1)) = (op (e3) (e2)))) -> (((op (e0) (e0)) = (e1))\/(((op (e0) (e1)) = (e1))\/(((op (e0) (e2)) = (e1))\/((op (e0) (e3)) = (e1))))) -> (~((op (e0) (e3)) = (op (e3) (e3)))) -> ((op (e0) (e2)) = (e0)) -> (~((e0) = (e1))) -> (~((op (e0) (e1)) = (op (e1) (e1)))) -> ((~((op (e3) (e3)) = (e1)))\/((op (e3) (e1)) = (e3))) -> (~((op (e2) (e0)) = (op (e2) (e3)))) -> ((~((op (e2) (e2)) = (e3)))\/((op (e2) (e3)) = (e2))) -> False). % 15.55/15.72 do 0 intro. intros zenon_Haa zenon_H146 zenon_H140 zenon_H2b4 zenon_H2b8 zenon_H138 zenon_H2af zenon_H1df zenon_Hd6 zenon_H157 zenon_H2d5 zenon_H87 zenon_H1d5 zenon_H20 zenon_H11b zenon_H4b zenon_H1f6 zenon_H116 zenon_H6a zenon_H28 zenon_H8e zenon_Hbe zenon_H105 zenon_H1a2 zenon_H247 zenon_H17d zenon_H84 zenon_H80 zenon_H7d zenon_H254 zenon_H109 zenon_H166 zenon_Hc9 zenon_Hb4 zenon_Hb7 zenon_H59 zenon_Hf0 zenon_H58 zenon_H13c zenon_He6 zenon_H15f zenon_H10f zenon_Ha3 zenon_H10d zenon_H2be zenon_H45 zenon_Hd7 zenon_H21 zenon_Ha7 zenon_Hdd zenon_H2d zenon_H52 zenon_H3b zenon_Hf1 zenon_H10e zenon_H135 zenon_H44 zenon_H36 zenon_Hab zenon_H9e zenon_H23 zenon_H10c zenon_Hce zenon_H1c3. % 15.55/15.72 apply (zenon_or_s _ _ zenon_Haa); [ zenon_intro zenon_H2f | zenon_intro zenon_H35 ]. % 15.55/15.72 apply (zenon_L1293_); trivial. % 15.55/15.72 apply (zenon_L1294_); trivial. % 15.55/15.72 (* end of lemma zenon_L1295_ *) % 15.55/15.72 assert (zenon_L1296_ : ((~((op (e2) (e2)) = (e1)))\/((op (e2) (e1)) = (e2))) -> (((op (e0) (e0)) = (e0))\/(((op (e0) (e1)) = (e0))\/(((op (e0) (e2)) = (e0))\/((op (e0) (e3)) = (e0))))) -> ((~((op (e1) (e1)) = (e1)))\/((op (e1) (e1)) = (e1))) -> (~((op (e1) (e0)) = (op (e1) (e1)))) -> ((~((op (e1) (e1)) = (e3)))\/((op (e1) (e3)) = (e1))) -> (~((op (e1) (e0)) = (op (e1) (e3)))) -> (((op (e1) (e1)) = (e0))\/(((op (e1) (e1)) = (e1))\/(((op (e1) (e1)) = (e2))\/((op (e1) (e1)) = (e3))))) -> ((~((op (e3) (e3)) = (e0)))\/((op (e3) (e0)) = (e3))) -> ((~((op (e1) (e1)) = (e2)))\/((op (e1) (e2)) = (e1))) -> (((op (e2) (e0)) = (e3))\/(((op (e2) (e1)) = (e3))\/(((op (e2) (e2)) = (e3))\/((op (e2) (e3)) = (e3))))) -> (~((op (e0) (e1)) = (op (e2) (e1)))) -> (((op (e0) (e0)) = (e3))\/(((op (e0) (e1)) = (e3))\/(((op (e0) (e2)) = (e3))\/((op (e0) (e3)) = (e3))))) -> (((op (e3) (e1)) = (e0))\/(((op (e3) (e1)) = (e1))\/(((op (e3) (e1)) = (e2))\/((op (e3) (e1)) = (e3))))) -> (~((op (e2) (e0)) = (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))))) -> (~((e0) = (e2))) -> (((op (e2) (e1)) = (e0))\/(((op (e2) (e1)) = (e1))\/(((op (e2) (e1)) = (e2))\/((op (e2) (e1)) = (e3))))) -> (((op (e0) (e3)) = (e1))\/(((op (e1) (e3)) = (e1))\/(((op (e2) (e3)) = (e1))\/((op (e3) (e3)) = (e1))))) -> (~((op (e1) (e1)) = (e0))) -> (~((op (e2) (e0)) = (op (e2) (e1)))) -> (((op (e0) (e1)) = (e0))\/(((op (e1) (e1)) = (e0))\/(((op (e2) (e1)) = (e0))\/((op (e3) (e1)) = (e0))))) -> (((op (e0) (e0)) = (e0))\/(((op (e1) (e0)) = (e0))\/(((op (e2) (e0)) = (e0))\/((op (e3) (e0)) = (e0))))) -> (((op (e0) (e0)) = (e1))\/(((op (e1) (e0)) = (e1))\/(((op (e2) (e0)) = (e1))\/((op (e3) (e0)) = (e1))))) -> (~((e0) = (e1))) -> (~((op (e0) (e2)) = (op (e0) (e3)))) -> (~((op (e1) (e0)) = (op (e1) (e2)))) -> ((~((op (e3) (e3)) = (e1)))\/((op (e3) (e1)) = (e3))) -> (~((op (e3) (e0)) = (op (e3) (e1)))) -> (((op (e1) (e0)) = (e2))\/(((op (e1) (e1)) = (e2))\/(((op (e1) (e2)) = (e2))\/((op (e1) (e3)) = (e2))))) -> (~((op (e1) (e0)) = (op (e2) (e0)))) -> (((op (e3) (e0)) = (e3))\/(((op (e3) (e1)) = (e3))\/(((op (e3) (e2)) = (e3))\/((op (e3) (e3)) = (e3))))) -> (~((op (e0) (e0)) = (e3))) -> (~((e2) = (e3))) -> (((op (e1) (e0)) = (e3))\/(((op (e1) (e1)) = (e3))\/(((op (e1) (e2)) = (e3))\/((op (e1) (e3)) = (e3))))) -> (~((e1) = (e3))) -> (~((op (e1) (e1)) = (op (e2) (e1)))) -> (((op (e0) (e2)) = (e1))\/(((op (e1) (e2)) = (e1))\/(((op (e2) (e2)) = (e1))\/((op (e3) (e2)) = (e1))))) -> (~((op (e1) (e1)) = (op (e1) (e2)))) -> (((op (e0) (e3)) = (e0))\/(((op (e0) (e3)) = (e1))\/(((op (e0) (e3)) = (e2))\/((op (e0) (e3)) = (e3))))) -> (~((op (e0) (e3)) = (op (e1) (e3)))) -> (~((op (e0) (e3)) = (op (e2) (e3)))) -> (~((op (e0) (e1)) = (op (e0) (e3)))) -> (((op (e2) (e0)) = (e1))\/(((op (e2) (e1)) = (e1))\/(((op (e2) (e2)) = (e1))\/((op (e2) (e3)) = (e1))))) -> (~((op (e1) (e2)) = (op (e3) (e2)))) -> (~((op (e1) (e1)) = (e3))) -> ((~((op (e3) (e3)) = (e2)))\/((op (e3) (e2)) = (e3))) -> (~((op (e3) (e0)) = (op (e3) (e2)))) -> (((op (e0) (e0)) = (e2))\/(((op (e1) (e0)) = (e2))\/(((op (e2) (e0)) = (e2))\/((op (e3) (e0)) = (e2))))) -> (~((op (e2) (e0)) = (op (e2) (e2)))) -> (~((op (e1) (e1)) = (e2))) -> (~((op (e2) (e1)) = (op (e2) (e2)))) -> (((op (e3) (e0)) = (e0))\/(((op (e3) (e1)) = (e0))\/(((op (e3) (e2)) = (e0))\/((op (e3) (e3)) = (e0))))) -> (~((op (e1) (e2)) = (op (e2) (e2)))) -> (~((op (e0) (e2)) = (op (e1) (e2)))) -> (((op (e1) (e2)) = (e0))\/(((op (e1) (e2)) = (e1))\/(((op (e1) (e2)) = (e2))\/((op (e1) (e2)) = (e3))))) -> (~((e0) = (e3))) -> (((op (e0) (e2)) = (e0))\/(((op (e0) (e2)) = (e1))\/(((op (e0) (e2)) = (e2))\/((op (e0) (e2)) = (e3))))) -> (~((op (e0) (e1)) = (op (e0) (e2)))) -> (((op (e0) (e2)) = (e3))\/(((op (e1) (e2)) = (e3))\/(((op (e2) (e2)) = (e3))\/((op (e3) (e2)) = (e3))))) -> (((op (e0) (e1)) = (e2))\/(((op (e1) (e1)) = (e2))\/(((op (e2) (e1)) = (e2))\/((op (e3) (e1)) = (e2))))) -> (~((e1) = (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) (e1)) = (e1))\/(((op (e0) (e2)) = (e1))\/((op (e0) (e3)) = (e1))))) -> (~((op (e0) (e0)) = (e2))) -> (((op (e3) (e0)) = (e1))\/(((op (e3) (e1)) = (e1))\/(((op (e3) (e2)) = (e1))\/((op (e3) (e3)) = (e1))))) -> (~((op (e0) (e2)) = (op (e3) (e2)))) -> (~((op (e1) (op (e3) (e1))) = (op (e3) (e1)))) -> (~((op (e0) (op (e3) (e0))) = (op (e3) (e0)))) -> (~((op (e0) (e1)) = (op (e3) (e1)))) -> (~((op (e2) (op (e3) (e2))) = (op (e3) (e2)))) -> ((op (e2) (e2)) = (e2)) -> (((op (e3) (e0)) = (e2))\/(((op (e3) (e1)) = (e2))\/(((op (e3) (e2)) = (e2))\/((op (e3) (e3)) = (e2))))) -> (~((op (e0) (e2)) = (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 (e0) (e0)) = (e2))\/(((op (e0) (e1)) = (e2))\/(((op (e0) (e2)) = (e2))\/((op (e0) (e3)) = (e2))))) -> ((op (e1) (e1)) = (e1)) -> (~((op (e0) (e1)) = (op (e1) (e1)))) -> (~((op (e0) (e0)) = (e1))) -> (~((op (e3) (op (e3) (e3))) = (op (e3) (e3)))) -> ((~((op (e3) (e3)) = (e3)))\/((op (e3) (e3)) = (e3))) -> (~((op (e3) (e1)) = (op (e3) (e2)))) -> (~((op (e2) (e1)) = (op (e3) (e1)))) -> ((~((op (e2) (e2)) = (e3)))\/((op (e2) (e3)) = (e2))) -> False). % 15.55/15.72 do 0 intro. intros zenon_H1e3 zenon_H110 zenon_H1d8 zenon_Hd7 zenon_H1d2 zenon_H1cf zenon_H1b3 zenon_H10f zenon_H1d3 zenon_He6 zenon_Hde zenon_H58 zenon_H16c zenon_Hce zenon_H15f zenon_H2ab zenon_H5e zenon_H15a zenon_H121 zenon_H145 zenon_H154 zenon_H144 zenon_Hf0 zenon_Hf1 zenon_H9e zenon_Hc9 zenon_H166 zenon_H10c zenon_H109 zenon_H84 zenon_H247 zenon_H2d5 zenon_H59 zenon_H6a zenon_H90 zenon_Ha3 zenon_Hb1 zenon_H11b zenon_H116 zenon_H254 zenon_H80 zenon_Hb4 zenon_H1cd zenon_Hb7 zenon_H17d zenon_H182 zenon_H10e zenon_H105 zenon_Heb zenon_H17a zenon_Hd6 zenon_H157 zenon_H1f6 zenon_H7d zenon_H87 zenon_H1d5 zenon_H4b zenon_H251 zenon_H23e zenon_H175 zenon_H1a2 zenon_Ha7 zenon_Hbe zenon_H20 zenon_H44 zenon_H8f zenon_H146 zenon_H140 zenon_H2b4 zenon_H2b8 zenon_H138 zenon_H2af zenon_H35 zenon_H1df zenon_H28 zenon_H3b zenon_H36 zenon_H8e zenon_H21 zenon_H23 zenon_H45 zenon_H2be zenon_H10d zenon_H135 zenon_H13c zenon_H1c3. % 15.55/15.72 apply (zenon_or_s _ _ zenon_H1e3); [ zenon_intro zenon_H52 | zenon_intro zenon_H156 ]. % 15.55/15.72 apply (zenon_L1266_); trivial. % 15.55/15.72 apply (zenon_L134_); trivial. % 15.55/15.72 (* end of lemma zenon_L1296_ *) % 15.55/15.72 assert (zenon_L1297_ : ((~((op (e2) (e2)) = (e1)))\/((op (e2) (e1)) = (e2))) -> (~((op (e2) (e0)) = (op (e2) (e1)))) -> ((~((op (e2) (e2)) = (e3)))\/((op (e2) (e3)) = (e2))) -> (~((op (e2) (e0)) = (op (e2) (e3)))) -> ((~((op (e3) (e3)) = (e1)))\/((op (e3) (e1)) = (e3))) -> (~((op (e0) (e1)) = (op (e1) (e1)))) -> (~((e0) = (e1))) -> ((op (e0) (e2)) = (e0)) -> (~((op (e0) (e3)) = (op (e3) (e3)))) -> (((op (e0) (e0)) = (e1))\/(((op (e0) (e1)) = (e1))\/(((op (e0) (e2)) = (e1))\/((op (e0) (e3)) = (e1))))) -> (~((op (e3) (e1)) = (op (e3) (e2)))) -> ((~((op (e3) (e3)) = (e2)))\/((op (e3) (e2)) = (e3))) -> (((op (e0) (e0)) = (e1))\/(((op (e1) (e0)) = (e1))\/(((op (e2) (e0)) = (e1))\/((op (e3) (e0)) = (e1))))) -> (((op (e3) (e3)) = (e0))\/(((op (e3) (e3)) = (e1))\/(((op (e3) (e3)) = (e2))\/((op (e3) (e3)) = (e3))))) -> (((op (e2) (e2)) = (e0))\/(((op (e2) (e2)) = (e1))\/(((op (e2) (e2)) = (e2))\/((op (e2) (e2)) = (e3))))) -> ((op (e2) (e0)) = (e2)) -> (~((e1) = (e2))) -> ((op (e1) (e1)) = (e1)) -> (~((op (e1) (e0)) = (op (e1) (e1)))) -> (~((op (e0) (e0)) = (e1))) -> (~((op (e3) (op (e3) (e3))) = (op (e3) (e3)))) -> ((~((op (e3) (e3)) = (e3)))\/((op (e3) (e3)) = (e3))) -> (~((e1) = (e3))) -> ((~((op (e3) (e3)) = (e0)))\/((op (e3) (e0)) = (e3))) -> (~((op (e2) (e2)) = (op (e2) (e3)))) -> (((op (e2) (e0)) = (e3))\/(((op (e2) (e1)) = (e3))\/(((op (e2) (e2)) = (e3))\/((op (e2) (e3)) = (e3))))) -> (~((op (e2) (e1)) = (op (e3) (e1)))) -> (((op (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)) = (e3))) -> (((op (e2) (e0)) = (e1))\/(((op (e2) (e1)) = (e1))\/(((op (e2) (e2)) = (e1))\/((op (e2) (e3)) = (e1))))) -> (~((op (e0) (e3)) = (op (e2) (e3)))) -> (~((op (e0) (e2)) = (op (e0) (e3)))) -> (~((op (e1) (e0)) = (op (e1) (e2)))) -> (~((op (e3) (e0)) = (op (e3) (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) (e3)) = (op (e1) (e3)))) -> (((op (e1) (e0)) = (e2))\/(((op (e1) (e1)) = (e2))\/(((op (e1) (e2)) = (e2))\/((op (e1) (e3)) = (e2))))) -> (~((op (e1) (e2)) = (op (e3) (e2)))) -> (~((op (e1) (e0)) = (op (e2) (e0)))) -> (((op (e0) (e1)) = (e2))\/(((op (e1) (e1)) = (e2))\/(((op (e2) (e1)) = (e2))\/((op (e3) (e1)) = (e2))))) -> (~((op (e3) (e0)) = (op (e3) (e2)))) -> (((op (e0) (e0)) = (e3))\/(((op (e1) (e0)) = (e3))\/(((op (e2) (e0)) = (e3))\/((op (e3) (e0)) = (e3))))) -> (((op (e0) (e0)) = (e2))\/(((op (e0) (e1)) = (e2))\/(((op (e0) (e2)) = (e2))\/((op (e0) (e3)) = (e2))))) -> (~((op (e0) (e2)) = (op (e2) (e2)))) -> (~((e2) = (e3))) -> (~((op (e1) (e1)) = (op (e1) (e2)))) -> (((op (e3) (e0)) = (e0))\/(((op (e3) (e1)) = (e0))\/(((op (e3) (e2)) = (e0))\/((op (e3) (e3)) = (e0))))) -> (~((e0) = (e3))) -> (((op (e0) (e2)) = (e1))\/(((op (e1) (e2)) = (e1))\/(((op (e2) (e2)) = (e1))\/((op (e3) (e2)) = (e1))))) -> (~((op (e0) (e0)) = (e0))) -> (((op (e1) (e2)) = (e0))\/(((op (e1) (e2)) = (e1))\/(((op (e1) (e2)) = (e2))\/((op (e1) (e2)) = (e3))))) -> (~((op (e0) (e2)) = (op (e1) (e2)))) -> (((op (e3) (e0)) = (e3))\/(((op (e3) (e1)) = (e3))\/(((op (e3) (e2)) = (e3))\/((op (e3) (e3)) = (e3))))) -> (~((op (e2) (e1)) = (op (e2) (e2)))) -> (~((op (e1) (e1)) = (e2))) -> (((op (e3) (e0)) = (e2))\/(((op (e3) (e1)) = (e2))\/(((op (e3) (e2)) = (e2))\/((op (e3) (e3)) = (e2))))) -> (~((op (e2) (op (e3) (e2))) = (op (e3) (e2)))) -> (~((op (e0) (e1)) = (op (e3) (e1)))) -> (~((op (e0) (op (e3) (e0))) = (op (e3) (e0)))) -> (~((op (e1) (op (e3) (e1))) = (op (e3) (e1)))) -> (~((op (e0) (e2)) = (op (e3) (e2)))) -> (((op (e3) (e0)) = (e1))\/(((op (e3) (e1)) = (e1))\/(((op (e3) (e2)) = (e1))\/((op (e3) (e3)) = (e1))))) -> ((~((op (e2) (e2)) = (e2)))\/((op (e2) (e2)) = (e2))) -> False). % 15.55/15.72 do 0 intro. intros zenon_H1e3 zenon_H154 zenon_H1c3 zenon_Hce zenon_H10c zenon_H23 zenon_H9e zenon_Hab zenon_H36 zenon_H44 zenon_H135 zenon_H10e zenon_Hf1 zenon_H3b zenon_H2d zenon_Hdd zenon_Ha7 zenon_H21 zenon_Hd7 zenon_H45 zenon_H2be zenon_H10d zenon_Ha3 zenon_H10f zenon_H15f zenon_He6 zenon_H13c zenon_H58 zenon_Hf0 zenon_H59 zenon_Hb7 zenon_Hb4 zenon_Hc9 zenon_H166 zenon_H109 zenon_H254 zenon_H7d zenon_H80 zenon_H84 zenon_H17d zenon_H247 zenon_H1a2 zenon_H105 zenon_Hbe zenon_H8e zenon_H28 zenon_H6a zenon_H116 zenon_H1f6 zenon_H4b zenon_H11b zenon_H20 zenon_H1d5 zenon_H87 zenon_H2d5 zenon_H157 zenon_Hd6 zenon_H1df zenon_H2af zenon_H138 zenon_H2b8 zenon_H2b4 zenon_H140 zenon_H146 zenon_Haa. % 15.55/15.72 apply (zenon_or_s _ _ zenon_H1e3); [ zenon_intro zenon_H52 | zenon_intro zenon_H156 ]. % 15.55/15.72 apply (zenon_L1295_); trivial. % 15.55/15.72 apply (zenon_L284_); trivial. % 15.55/15.72 (* end of lemma zenon_L1297_ *) % 15.55/15.72 assert (zenon_L1298_ : (((op (e3) (e2)) = (e0))\/(((op (e3) (e2)) = (e1))\/(((op (e3) (e2)) = (e2))\/((op (e3) (e2)) = (e3))))) -> ((op (e0) (e2)) = (e0)) -> (~((op (e0) (e2)) = (op (e3) (e2)))) -> ((op (e3) (e1)) = (e1)) -> (~((op (e3) (e1)) = (op (e3) (e2)))) -> ((op (e2) (e2)) = (e2)) -> (~((op (e2) (op (e3) (e2))) = (op (e3) (e2)))) -> (((op (e1) (e0)) = (e3))\/(((op (e1) (e1)) = (e3))\/(((op (e1) (e2)) = (e3))\/((op (e1) (e3)) = (e3))))) -> (~((e1) = (e3))) -> ((op (e1) (e0)) = (e1)) -> (~((op (e1) (e1)) = (e3))) -> (~((op (e1) (e2)) = (op (e3) (e2)))) -> (~((op (e0) (e3)) = (op (e1) (e3)))) -> ((op (e0) (e3)) = (e3)) -> False). % 15.55/15.72 do 0 intro. intros zenon_H25e zenon_Hab zenon_H140 zenon_H13e zenon_H135 zenon_H35 zenon_H2af zenon_H90 zenon_Ha3 zenon_Hd8 zenon_H182 zenon_H17d zenon_H80 zenon_H53. % 15.55/15.72 apply (zenon_or_s _ _ zenon_H25e); [ zenon_intro zenon_H167 | zenon_intro zenon_H25f ]. % 15.55/15.72 apply (zenon_L267_); trivial. % 15.55/15.72 apply (zenon_or_s _ _ zenon_H25f); [ zenon_intro zenon_H119 | zenon_intro zenon_H260 ]. % 15.55/15.72 apply (zenon_L394_); trivial. % 15.55/15.72 apply (zenon_or_s _ _ zenon_H260); [ zenon_intro zenon_H1dd | zenon_intro zenon_H106 ]. % 15.55/15.72 apply (zenon_L1083_); trivial. % 15.55/15.72 apply (zenon_L527_); trivial. % 15.55/15.72 (* end of lemma zenon_L1298_ *) % 15.55/15.72 assert (zenon_L1299_ : (((op (e0) (e1)) = (e1))\/(((op (e1) (e1)) = (e1))\/(((op (e2) (e1)) = (e1))\/((op (e3) (e1)) = (e1))))) -> ((op (e0) (e2)) = (e1)) -> (~((op (e0) (op (e3) (e0))) = (op (e3) (e0)))) -> (~((op (e1) (e1)) = (e1))) -> (~((op (e3) (e3)) = (e1))) -> (~((op (e1) (e0)) = (op (e3) (e0)))) -> (((op (e3) (e0)) = (e1))\/(((op (e3) (e1)) = (e1))\/(((op (e3) (e2)) = (e1))\/((op (e3) (e3)) = (e1))))) -> (((op (e3) (e2)) = (e0))\/(((op (e3) (e2)) = (e1))\/(((op (e3) (e2)) = (e2))\/((op (e3) (e2)) = (e3))))) -> ((op (e0) (e2)) = (e0)) -> (~((op (e0) (e2)) = (op (e3) (e2)))) -> (~((op (e3) (e1)) = (op (e3) (e2)))) -> ((op (e2) (e2)) = (e2)) -> (~((op (e2) (op (e3) (e2))) = (op (e3) (e2)))) -> (((op (e1) (e0)) = (e3))\/(((op (e1) (e1)) = (e3))\/(((op (e1) (e2)) = (e3))\/((op (e1) (e3)) = (e3))))) -> (~((e1) = (e3))) -> ((op (e1) (e0)) = (e1)) -> (~((op (e1) (e1)) = (e3))) -> (~((op (e1) (e2)) = (op (e3) (e2)))) -> (~((op (e0) (e3)) = (op (e1) (e3)))) -> ((op (e0) (e3)) = (e3)) -> False). % 15.55/15.72 do 0 intro. intros zenon_H228 zenon_H29 zenon_H2b8 zenon_H1b4 zenon_H104 zenon_H22e zenon_H146 zenon_H25e zenon_Hab zenon_H140 zenon_H135 zenon_H35 zenon_H2af zenon_H90 zenon_Ha3 zenon_Hd8 zenon_H182 zenon_H17d zenon_H80 zenon_H53. % 15.55/15.72 apply (zenon_or_s _ _ zenon_H228); [ zenon_intro zenon_H22 | zenon_intro zenon_H229 ]. % 15.55/15.72 apply (zenon_or_s _ _ zenon_H146); [ zenon_intro zenon_Hee | zenon_intro zenon_H14b ]. % 15.55/15.72 apply (zenon_L1054_); trivial. % 15.55/15.72 apply (zenon_or_s _ _ zenon_H14b); [ zenon_intro zenon_H13e | zenon_intro zenon_H14c ]. % 15.55/15.72 apply (zenon_L1298_); trivial. % 15.55/15.72 apply (zenon_or_s _ _ zenon_H14c); [ zenon_intro zenon_H119 | zenon_intro zenon_H38 ]. % 15.55/15.72 apply (zenon_L124_); trivial. % 15.55/15.72 exact (zenon_H104 zenon_H38). % 15.55/15.72 apply (zenon_or_s _ _ zenon_H229); [ zenon_intro zenon_H21 | zenon_intro zenon_H22a ]. % 15.55/15.72 exact (zenon_H1b4 zenon_H21). % 15.55/15.72 apply (zenon_or_s _ _ zenon_H22a); [ zenon_intro zenon_Hb2 | zenon_intro zenon_H13e ]. % 15.55/15.72 apply (zenon_or_s _ _ zenon_H146); [ zenon_intro zenon_Hee | zenon_intro zenon_H14b ]. % 15.55/15.72 apply (zenon_L393_); trivial. % 15.55/15.72 apply (zenon_or_s _ _ zenon_H14b); [ zenon_intro zenon_H13e | zenon_intro zenon_H14c ]. % 15.55/15.72 apply (zenon_L1298_); trivial. % 15.55/15.72 apply (zenon_or_s _ _ zenon_H14c); [ zenon_intro zenon_H119 | zenon_intro zenon_H38 ]. % 15.55/15.72 apply (zenon_L1024_); trivial. % 15.55/15.72 exact (zenon_H104 zenon_H38). % 15.55/15.72 apply (zenon_L1298_); trivial. % 15.55/15.72 (* end of lemma zenon_L1299_ *) % 15.55/15.72 assert (zenon_L1300_ : (((op (e0) (e3)) = (e0))\/(((op (e0) (e3)) = (e1))\/(((op (e0) (e3)) = (e2))\/((op (e0) (e3)) = (e3))))) -> (~((op (e0) (e2)) = (op (e0) (e3)))) -> (~((op (e1) (e2)) = (op (e2) (e2)))) -> (~((op (e1) (e1)) = (e2))) -> (~((e1) = (e2))) -> (((op (e1) (e0)) = (e2))\/(((op (e1) (e1)) = (e2))\/(((op (e1) (e2)) = (e2))\/((op (e1) (e3)) = (e2))))) -> (((op (e0) (e1)) = (e1))\/(((op (e1) (e1)) = (e1))\/(((op (e2) (e1)) = (e1))\/((op (e3) (e1)) = (e1))))) -> ((op (e0) (e2)) = (e1)) -> (~((op (e0) (op (e3) (e0))) = (op (e3) (e0)))) -> (~((op (e1) (e1)) = (e1))) -> (~((op (e3) (e3)) = (e1))) -> (~((op (e1) (e0)) = (op (e3) (e0)))) -> (((op (e3) (e0)) = (e1))\/(((op (e3) (e1)) = (e1))\/(((op (e3) (e2)) = (e1))\/((op (e3) (e3)) = (e1))))) -> (((op (e3) (e2)) = (e0))\/(((op (e3) (e2)) = (e1))\/(((op (e3) (e2)) = (e2))\/((op (e3) (e2)) = (e3))))) -> ((op (e0) (e2)) = (e0)) -> (~((op (e0) (e2)) = (op (e3) (e2)))) -> (~((op (e3) (e1)) = (op (e3) (e2)))) -> ((op (e2) (e2)) = (e2)) -> (~((op (e2) (op (e3) (e2))) = (op (e3) (e2)))) -> (((op (e1) (e0)) = (e3))\/(((op (e1) (e1)) = (e3))\/(((op (e1) (e2)) = (e3))\/((op (e1) (e3)) = (e3))))) -> (~((e1) = (e3))) -> ((op (e1) (e0)) = (e1)) -> (~((op (e1) (e1)) = (e3))) -> (~((op (e1) (e2)) = (op (e3) (e2)))) -> (~((op (e0) (e3)) = (op (e1) (e3)))) -> False). % 15.55/15.72 do 0 intro. intros zenon_H254 zenon_Hc9 zenon_H7d zenon_Hd6 zenon_Ha7 zenon_H84 zenon_H228 zenon_H29 zenon_H2b8 zenon_H1b4 zenon_H104 zenon_H22e zenon_H146 zenon_H25e zenon_Hab zenon_H140 zenon_H135 zenon_H35 zenon_H2af zenon_H90 zenon_Ha3 zenon_Hd8 zenon_H182 zenon_H17d zenon_H80. % 15.55/15.72 apply (zenon_or_s _ _ zenon_H254); [ zenon_intro zenon_Hca | zenon_intro zenon_H255 ]. % 15.55/15.72 apply (zenon_L53_); trivial. % 15.55/15.72 apply (zenon_or_s _ _ zenon_H255); [ zenon_intro zenon_H37 | zenon_intro zenon_H256 ]. % 15.55/15.72 apply (zenon_L85_); trivial. % 15.55/15.72 apply (zenon_or_s _ _ zenon_H256); [ zenon_intro zenon_H81 | zenon_intro zenon_H53 ]. % 15.55/15.72 apply (zenon_L243_); trivial. % 15.55/15.72 apply (zenon_L1299_); trivial. % 15.55/15.72 (* end of lemma zenon_L1300_ *) % 15.55/15.72 assert (zenon_L1301_ : (((op (e3) (e0)) = (e2))\/(((op (e3) (e1)) = (e2))\/(((op (e3) (e2)) = (e2))\/((op (e3) (e3)) = (e2))))) -> (~((op (e1) (e1)) = (e3))) -> (~((op (e1) (e1)) = (e2))) -> (~((op (e1) (e1)) = (e1))) -> (((op (e3) (e3)) = (e0))\/(((op (e3) (e3)) = (e1))\/(((op (e3) (e3)) = (e2))\/((op (e3) (e3)) = (e3))))) -> (~((op (e3) (e3)) = (e0))) -> (~((op (e3) (e3)) = (e3))) -> (((op (e1) (e1)) = (e0))\/(((op (e1) (e1)) = (e1))\/(((op (e1) (e1)) = (e2))\/((op (e1) (e1)) = (e3))))) -> ((op (e0) (e1)) = (e2)) -> (~((op (e0) (e1)) = (op (e3) (e1)))) -> ((op (e2) (e2)) = (e2)) -> (~((op (e2) (op (e3) (e2))) = (op (e3) (e2)))) -> (~((op (e3) (e3)) = (e2))) -> False). % 15.55/15.72 do 0 intro. intros zenon_H1df zenon_H182 zenon_Hd6 zenon_H1b4 zenon_H3b zenon_H3c zenon_H3e zenon_H1b3 zenon_H5d zenon_H138 zenon_H35 zenon_H2af zenon_H3d. % 15.55/15.72 apply (zenon_or_s _ _ zenon_H1df); [ zenon_intro zenon_He9 | zenon_intro zenon_H1e0 ]. % 15.55/15.72 apply (zenon_L406_); trivial. % 15.55/15.72 apply (zenon_or_s _ _ zenon_H1e0); [ zenon_intro zenon_H16a | zenon_intro zenon_H1e1 ]. % 15.55/15.72 apply (zenon_L146_); trivial. % 15.55/15.72 apply (zenon_or_s _ _ zenon_H1e1); [ zenon_intro zenon_H1dd | zenon_intro zenon_H43 ]. % 15.55/15.72 apply (zenon_L1083_); trivial. % 15.55/15.72 exact (zenon_H3d zenon_H43). % 15.55/15.72 (* end of lemma zenon_L1301_ *) % 15.55/15.72 assert (zenon_L1302_ : ((~((op (e3) (e3)) = (e2)))\/((op (e3) (e2)) = (e3))) -> (~((op (e3) (e1)) = (op (e3) (e2)))) -> (((op (e0) (e1)) = (e2))\/(((op (e1) (e1)) = (e2))\/(((op (e2) (e1)) = (e2))\/((op (e3) (e1)) = (e2))))) -> ((op (e3) (e1)) = (e3)) -> (~((e2) = (e3))) -> (~((op (e2) (e1)) = (op (e2) (e2)))) -> (((op (e1) (e1)) = (e0))\/(((op (e1) (e1)) = (e1))\/(((op (e1) (e1)) = (e2))\/((op (e1) (e1)) = (e3))))) -> (~((op (e1) (e1)) = (e3))) -> (~((op (e1) (e1)) = (e2))) -> (~((op (e1) (e1)) = (e1))) -> (~((op (e3) (e3)) = (e0))) -> (((op (e3) (e3)) = (e0))\/(((op (e3) (e3)) = (e1))\/(((op (e3) (e3)) = (e2))\/((op (e3) (e3)) = (e3))))) -> (~((op (e0) (e1)) = (op (e3) (e1)))) -> (~((op (e2) (op (e3) (e2))) = (op (e3) (e2)))) -> ((op (e2) (e2)) = (e2)) -> (((op (e3) (e0)) = (e2))\/(((op (e3) (e1)) = (e2))\/(((op (e3) (e2)) = (e2))\/((op (e3) (e3)) = (e2))))) -> (~((op (e3) (op (e3) (e3))) = (op (e3) (e3)))) -> ((~((op (e3) (e3)) = (e3)))\/((op (e3) (e3)) = (e3))) -> False). % 15.55/15.72 do 0 intro. intros zenon_H10e zenon_H135 zenon_H1a2 zenon_H10a zenon_H6a zenon_H157 zenon_H1b3 zenon_H182 zenon_Hd6 zenon_H1b4 zenon_H3c zenon_H3b zenon_H138 zenon_H2af zenon_H35 zenon_H1df zenon_H2be zenon_H10d. % 15.55/15.72 apply (zenon_or_s _ _ zenon_H10e); [ zenon_intro zenon_H3d | zenon_intro zenon_H106 ]. % 15.55/15.72 apply (zenon_or_s _ _ zenon_H10d); [ zenon_intro zenon_H3e | zenon_intro zenon_H42 ]. % 15.55/15.72 apply (zenon_or_s _ _ zenon_H1a2); [ zenon_intro zenon_H5d | zenon_intro zenon_H1a3 ]. % 15.55/15.72 apply (zenon_L1301_); trivial. % 15.55/15.72 apply (zenon_or_s _ _ zenon_H1a3); [ zenon_intro zenon_H6e | zenon_intro zenon_H1a4 ]. % 15.55/15.72 exact (zenon_Hd6 zenon_H6e). % 15.55/15.72 apply (zenon_or_s _ _ zenon_H1a4); [ zenon_intro zenon_H156 | zenon_intro zenon_H16a ]. % 15.55/15.72 apply (zenon_L134_); trivial. % 15.55/15.72 apply (zenon_L297_); trivial. % 15.55/15.72 apply (zenon_L1041_); trivial. % 15.55/15.72 apply (zenon_L115_); trivial. % 15.55/15.72 (* end of lemma zenon_L1302_ *) % 15.55/15.72 assert (zenon_L1303_ : (((op (e3) (e0)) = (e3))\/(((op (e3) (e1)) = (e3))\/(((op (e3) (e2)) = (e3))\/((op (e3) (e3)) = (e3))))) -> (~((op (e2) (e0)) = (op (e3) (e0)))) -> ((op (e2) (e0)) = (e3)) -> ((~((op (e3) (e3)) = (e3)))\/((op (e3) (e3)) = (e3))) -> (~((op (e3) (op (e3) (e3))) = (op (e3) (e3)))) -> (((op (e3) (e0)) = (e2))\/(((op (e3) (e1)) = (e2))\/(((op (e3) (e2)) = (e2))\/((op (e3) (e3)) = (e2))))) -> ((op (e2) (e2)) = (e2)) -> (~((op (e2) (op (e3) (e2))) = (op (e3) (e2)))) -> (~((op (e0) (e1)) = (op (e3) (e1)))) -> (((op (e3) (e3)) = (e0))\/(((op (e3) (e3)) = (e1))\/(((op (e3) (e3)) = (e2))\/((op (e3) (e3)) = (e3))))) -> (~((op (e3) (e3)) = (e0))) -> (~((op (e1) (e1)) = (e1))) -> (~((op (e1) (e1)) = (e2))) -> (~((op (e1) (e1)) = (e3))) -> (((op (e1) (e1)) = (e0))\/(((op (e1) (e1)) = (e1))\/(((op (e1) (e1)) = (e2))\/((op (e1) (e1)) = (e3))))) -> (~((op (e2) (e1)) = (op (e2) (e2)))) -> (~((e2) = (e3))) -> (((op (e0) (e1)) = (e2))\/(((op (e1) (e1)) = (e2))\/(((op (e2) (e1)) = (e2))\/((op (e3) (e1)) = (e2))))) -> (~((op (e3) (e1)) = (op (e3) (e2)))) -> ((~((op (e3) (e3)) = (e2)))\/((op (e3) (e2)) = (e3))) -> (~((op (e1) (e2)) = (op (e3) (e2)))) -> ((op (e1) (e2)) = (e3)) -> (~((op (e3) (e3)) = (e3))) -> False). % 15.55/15.72 do 0 intro. intros zenon_H2d5 zenon_H1e5 zenon_Haf zenon_H10d zenon_H2be zenon_H1df zenon_H35 zenon_H2af zenon_H138 zenon_H3b zenon_H3c zenon_H1b4 zenon_Hd6 zenon_H182 zenon_H1b3 zenon_H157 zenon_H6a zenon_H1a2 zenon_H135 zenon_H10e zenon_H17d zenon_H88 zenon_H3e. % 15.55/15.72 apply (zenon_or_s _ _ zenon_H2d5); [ zenon_intro zenon_Hba | zenon_intro zenon_H2d6 ]. % 15.55/15.72 apply (zenon_L261_); trivial. % 15.55/15.72 apply (zenon_or_s _ _ zenon_H2d6); [ zenon_intro zenon_H10a | zenon_intro zenon_H2d7 ]. % 15.55/15.72 apply (zenon_L1302_); trivial. % 15.55/15.72 apply (zenon_or_s _ _ zenon_H2d7); [ zenon_intro zenon_H106 | zenon_intro zenon_H42 ]. % 15.55/15.72 apply (zenon_L164_); trivial. % 15.55/15.72 exact (zenon_H3e zenon_H42). % 15.55/15.72 (* end of lemma zenon_L1303_ *) % 15.55/15.72 assert (zenon_L1304_ : (((op (e0) (e0)) = (e3))\/(((op (e1) (e0)) = (e3))\/(((op (e2) (e0)) = (e3))\/((op (e3) (e0)) = (e3))))) -> (~((op (e0) (e0)) = (e3))) -> (~((op (e2) (e2)) = (e3))) -> (((op (e3) (e0)) = (e3))\/(((op (e3) (e1)) = (e3))\/(((op (e3) (e2)) = (e3))\/((op (e3) (e3)) = (e3))))) -> (~((op (e2) (e0)) = (op (e3) (e0)))) -> ((~((op (e3) (e3)) = (e3)))\/((op (e3) (e3)) = (e3))) -> (~((op (e3) (op (e3) (e3))) = (op (e3) (e3)))) -> (((op (e3) (e3)) = (e0))\/(((op (e3) (e3)) = (e1))\/(((op (e3) (e3)) = (e2))\/((op (e3) (e3)) = (e3))))) -> (~((op (e3) (e3)) = (e0))) -> (~((op (e1) (e1)) = (e1))) -> (~((op (e1) (e1)) = (e3))) -> (((op (e1) (e1)) = (e0))\/(((op (e1) (e1)) = (e1))\/(((op (e1) (e1)) = (e2))\/((op (e1) (e1)) = (e3))))) -> (~((op (e3) (e1)) = (op (e3) (e2)))) -> (~((op (e3) (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 (e0) (e2)) = (e3))\/(((op (e1) (e2)) = (e3))\/(((op (e2) (e2)) = (e3))\/((op (e3) (e2)) = (e3))))) -> (((op (e0) (e0)) = (e1))\/(((op (e1) (e0)) = (e1))\/(((op (e2) (e0)) = (e1))\/((op (e3) (e0)) = (e1))))) -> (~((op (e0) (e0)) = (e1))) -> (~((op (e1) (e0)) = (op (e1) (e2)))) -> (~((op (e2) (e0)) = (op (e2) (e3)))) -> (~((op (e1) (e2)) = (op (e1) (e3)))) -> (~((op (e0) (e3)) = (op (e3) (e3)))) -> (~((op (e3) (e3)) = (e2))) -> (((op (e0) (e3)) = (e1))\/(((op (e1) (e3)) = (e1))\/(((op (e2) (e3)) = (e1))\/((op (e3) (e3)) = (e1))))) -> ((op (e0) (e1)) = (e1)) -> (((op (e0) (e1)) = (e1))\/(((op (e1) (e1)) = (e1))\/(((op (e2) (e1)) = (e1))\/((op (e3) (e1)) = (e1))))) -> (~((op (e1) (e0)) = (op (e3) (e0)))) -> (((op (e3) (e2)) = (e0))\/(((op (e3) (e2)) = (e1))\/(((op (e3) (e2)) = (e2))\/((op (e3) (e2)) = (e3))))) -> (~((op (e0) (e2)) = (op (e3) (e2)))) -> (((op (e1) (e0)) = (e3))\/(((op (e1) (e1)) = (e3))\/(((op (e1) (e2)) = (e3))\/((op (e1) (e3)) = (e3))))) -> ((~((op (e3) (e3)) = (e2)))\/((op (e3) (e2)) = (e3))) -> (~((op (e3) (e0)) = (op (e3) (e2)))) -> (~((op (e0) (e2)) = (op (e0) (e3)))) -> ((op (e0) (e2)) = (e0)) -> (((op (e0) (e1)) = (e2))\/(((op (e1) (e1)) = (e2))\/(((op (e2) (e1)) = (e2))\/((op (e3) (e1)) = (e2))))) -> (~((op (e1) (e0)) = (op (e2) (e0)))) -> ((op (e1) (e0)) = (e1)) -> (((op (e0) (e2)) = (e1))\/(((op (e1) (e2)) = (e1))\/(((op (e2) (e2)) = (e1))\/((op (e3) (e2)) = (e1))))) -> (~((op (e2) (e2)) = (e1))) -> (~((e1) = (e3))) -> (~((op (e1) (op (e3) (e1))) = (op (e3) (e1)))) -> (~((op (e1) (e2)) = (op (e3) (e2)))) -> (~((op (e3) (e3)) = (e1))) -> (((op (e3) (e0)) = (e1))\/(((op (e3) (e1)) = (e1))\/(((op (e3) (e2)) = (e1))\/((op (e3) (e3)) = (e1))))) -> (~((op (e0) (e3)) = (op (e2) (e3)))) -> (((op (e2) (e0)) = (e1))\/(((op (e2) (e1)) = (e1))\/(((op (e2) (e2)) = (e1))\/((op (e2) (e3)) = (e1))))) -> (~((op (e2) (e1)) = (op (e2) (e2)))) -> (~((op (e1) (e1)) = (e2))) -> (~((e2) = (e3))) -> (~((op (e0) (e1)) = (op (e3) (e1)))) -> (~((op (e2) (op (e3) (e2))) = (op (e3) (e2)))) -> ((op (e2) (e2)) = (e2)) -> (((op (e3) (e0)) = (e2))\/(((op (e3) (e1)) = (e2))\/(((op (e3) (e2)) = (e2))\/((op (e3) (e3)) = (e2))))) -> (((op (e1) (e0)) = (e2))\/(((op (e1) (e1)) = (e2))\/(((op (e1) (e2)) = (e2))\/((op (e1) (e3)) = (e2))))) -> (~((op (e0) (e3)) = (op (e1) (e3)))) -> (~((op (e1) (e2)) = (op (e2) (e2)))) -> (~((e1) = (e2))) -> (~((op (e0) (op (e3) (e0))) = (op (e3) (e0)))) -> (((op (e0) (e3)) = (e0))\/(((op (e0) (e3)) = (e1))\/(((op (e0) (e3)) = (e2))\/((op (e0) (e3)) = (e3))))) -> False). % 15.55/15.72 do 0 intro. intros zenon_Hbe zenon_H59 zenon_H30 zenon_H2d5 zenon_H1e5 zenon_H10d zenon_H2be zenon_H3b zenon_H3c zenon_H1b4 zenon_H182 zenon_H1b3 zenon_H135 zenon_H3e zenon_H1d5 zenon_H87 zenon_H175 zenon_Hf1 zenon_H45 zenon_H166 zenon_Hce zenon_H1d0 zenon_H36 zenon_H3d zenon_H121 zenon_H22 zenon_H228 zenon_H22e zenon_H25e zenon_H140 zenon_H90 zenon_H10e zenon_H105 zenon_Hc9 zenon_Hab zenon_H1a2 zenon_H247 zenon_Hd8 zenon_H11b zenon_H52 zenon_Ha3 zenon_H2b4 zenon_H17d zenon_H104 zenon_H146 zenon_Hb4 zenon_Hb7 zenon_H157 zenon_Hd6 zenon_H6a zenon_H138 zenon_H2af zenon_H35 zenon_H1df zenon_H84 zenon_H80 zenon_H7d zenon_Ha7 zenon_H2b8 zenon_H254. % 15.55/15.72 apply (zenon_or_s _ _ zenon_Hbe); [ zenon_intro zenon_H5b | zenon_intro zenon_Hbf ]. % 15.55/15.72 exact (zenon_H59 zenon_H5b). % 15.55/15.72 apply (zenon_or_s _ _ zenon_Hbf); [ zenon_intro zenon_H69 | zenon_intro zenon_Hc0 ]. % 15.55/15.72 apply (zenon_L163_); trivial. % 15.55/15.72 apply (zenon_or_s _ _ zenon_Hc0); [ zenon_intro zenon_Haf | zenon_intro zenon_Hba ]. % 15.55/15.72 apply (zenon_or_s _ _ zenon_H11b); [ zenon_intro zenon_H29 | zenon_intro zenon_H11c ]. % 15.55/15.72 apply (zenon_L1300_); trivial. % 15.55/15.72 apply (zenon_or_s _ _ zenon_H11c); [ zenon_intro zenon_H117 | zenon_intro zenon_H11d ]. % 15.55/15.72 apply (zenon_L1055_); trivial. % 15.55/15.72 apply (zenon_or_s _ _ zenon_H11d); [ zenon_intro zenon_H2a | zenon_intro zenon_H119 ]. % 15.55/15.72 exact (zenon_H52 zenon_H2a). % 15.55/15.72 apply (zenon_or_s _ _ zenon_H175); [ zenon_intro zenon_H50 | zenon_intro zenon_H176 ]. % 15.55/15.72 apply (zenon_L760_); trivial. % 15.55/15.72 apply (zenon_or_s _ _ zenon_H176); [ zenon_intro zenon_H88 | zenon_intro zenon_H177 ]. % 15.55/15.72 apply (zenon_L1303_); trivial. % 15.55/15.72 apply (zenon_or_s _ _ zenon_H177); [ zenon_intro zenon_H34 | zenon_intro zenon_H106 ]. % 15.55/15.72 exact (zenon_H30 zenon_H34). % 15.55/15.72 apply (zenon_L87_); trivial. % 15.55/15.72 apply (zenon_L1248_); trivial. % 15.55/15.72 (* end of lemma zenon_L1304_ *) % 15.55/15.72 assert (zenon_L1305_ : (((op (e0) (e0)) = (e1))\/(((op (e0) (e1)) = (e1))\/(((op (e0) (e2)) = (e1))\/((op (e0) (e3)) = (e1))))) -> (~((op (e0) (op (e3) (e0))) = (op (e3) (e0)))) -> (((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 (e2) (e0)) = (op (e2) (e3)))) -> (~((op (e3) (e3)) = (e1))) -> (~((op (e1) (e0)) = (op (e1) (e2)))) -> (~((op (e0) (e0)) = (e1))) -> (((op (e0) (e0)) = (e1))\/(((op (e1) (e0)) = (e1))\/(((op (e2) (e0)) = (e1))\/((op (e3) (e0)) = (e1))))) -> (~((e0) = (e1))) -> ((op (e0) (e2)) = (e0)) -> (((op (e3) (e3)) = (e0))\/(((op (e3) (e3)) = (e1))\/(((op (e3) (e3)) = (e2))\/((op (e3) (e3)) = (e3))))) -> (~((op (e3) (e3)) = (e0))) -> (~((op (e0) (e3)) = (op (e3) (e3)))) -> (~((op (e3) (e3)) = (e2))) -> (~((op (e3) (e3)) = (e3))) -> False). % 15.55/15.72 do 0 intro. intros zenon_H44 zenon_H2b8 zenon_H121 zenon_H117 zenon_H1d0 zenon_Hce zenon_H104 zenon_H166 zenon_H45 zenon_Hf1 zenon_H9e zenon_Hab zenon_H3b zenon_H3c zenon_H36 zenon_H3d zenon_H3e. % 15.55/15.72 apply (zenon_or_s _ _ zenon_H44); [ zenon_intro zenon_H47 | zenon_intro zenon_H46 ]. % 15.55/15.72 exact (zenon_H45 zenon_H47). % 15.55/15.72 apply (zenon_or_s _ _ zenon_H46); [ zenon_intro zenon_H22 | zenon_intro zenon_H48 ]. % 15.55/15.72 apply (zenon_L1055_); trivial. % 15.55/15.72 apply (zenon_or_s _ _ zenon_H48); [ zenon_intro zenon_H29 | zenon_intro zenon_H37 ]. % 15.55/15.72 apply (zenon_L37_); trivial. % 15.55/15.72 apply (zenon_L7_); trivial. % 15.55/15.72 (* end of lemma zenon_L1305_ *) % 15.55/15.72 assert (zenon_L1306_ : ((~((op (e2) (e2)) = (e1)))\/((op (e2) (e1)) = (e2))) -> ((~((op (e3) (e3)) = (e0)))\/((op (e3) (e0)) = (e3))) -> (~((op (e3) (e0)) = (op (e3) (e1)))) -> (((op (e0) (e0)) = (e1))\/(((op (e0) (e1)) = (e1))\/(((op (e0) (e2)) = (e1))\/((op (e0) (e3)) = (e1))))) -> (~((op (e0) (e0)) = (e3))) -> (~((e1) = (e3))) -> ((op (e1) (e0)) = (e1)) -> (((op (e0) (e2)) = (e1))\/(((op (e1) (e2)) = (e1))\/(((op (e2) (e2)) = (e1))\/((op (e3) (e2)) = (e1))))) -> (((op (e1) (e2)) = (e0))\/(((op (e1) (e2)) = (e1))\/(((op (e1) (e2)) = (e2))\/((op (e1) (e2)) = (e3))))) -> (~((op (e0) (e2)) = (op (e1) (e2)))) -> (((op (e3) (e0)) = (e3))\/(((op (e3) (e1)) = (e3))\/(((op (e3) (e2)) = (e3))\/((op (e3) (e3)) = (e3))))) -> ((~((op (e3) (e3)) = (e3)))\/((op (e3) (e3)) = (e3))) -> (~((op (e3) (op (e3) (e3))) = (op (e3) (e3)))) -> (((op (e3) (e0)) = (e2))\/(((op (e3) (e1)) = (e2))\/(((op (e3) (e2)) = (e2))\/((op (e3) (e3)) = (e2))))) -> (~((op (e0) (e1)) = (op (e3) (e1)))) -> (((op (e1) (e1)) = (e0))\/(((op (e1) (e1)) = (e1))\/(((op (e1) (e1)) = (e2))\/((op (e1) (e1)) = (e3))))) -> (~((op (e2) (e1)) = (op (e2) (e2)))) -> (~((e2) = (e3))) -> (((op (e0) (e1)) = (e2))\/(((op (e1) (e1)) = (e2))\/(((op (e2) (e1)) = (e2))\/((op (e3) (e1)) = (e2))))) -> ((~((op (e3) (e3)) = (e2)))\/((op (e3) (e2)) = (e3))) -> (~((op (e2) (e0)) = (op (e3) (e0)))) -> (((op (e0) (e2)) = (e3))\/(((op (e1) (e2)) = (e3))\/(((op (e2) (e2)) = (e3))\/((op (e3) (e2)) = (e3))))) -> (~((op (e1) (e0)) = (op (e1) (e2)))) -> (((op (e0) (e3)) = (e1))\/(((op (e1) (e3)) = (e1))\/(((op (e2) (e3)) = (e1))\/((op (e3) (e3)) = (e1))))) -> (~((op (e2) (e0)) = (op (e2) (e3)))) -> (~((op (e1) (e2)) = (op (e1) (e3)))) -> (~((op (e0) (e3)) = (op (e3) (e3)))) -> (((op (e3) (e3)) = (e0))\/(((op (e3) (e3)) = (e1))\/(((op (e3) (e3)) = (e2))\/((op (e3) (e3)) = (e3))))) -> (((op (e0) (e0)) = (e1))\/(((op (e1) (e0)) = (e1))\/(((op (e2) (e0)) = (e1))\/((op (e3) (e0)) = (e1))))) -> (~((op (e0) (e2)) = (op (e0) (e3)))) -> ((op (e0) (e2)) = (e0)) -> (((op (e1) (e0)) = (e2))\/(((op (e1) (e1)) = (e2))\/(((op (e1) (e2)) = (e2))\/((op (e1) (e3)) = (e2))))) -> (~((op (e0) (e3)) = (op (e1) (e3)))) -> ((op (e2) (e2)) = (e2)) -> (~((op (e1) (e2)) = (op (e2) (e2)))) -> (~((op (e1) (e1)) = (e2))) -> (~((e1) = (e2))) -> (((op (e0) (e1)) = (e1))\/(((op (e1) (e1)) = (e1))\/(((op (e2) (e1)) = (e1))\/((op (e3) (e1)) = (e1))))) -> (~((op (e1) (e0)) = (op (e3) (e0)))) -> (~((op (e1) (e1)) = (e1))) -> (~((op (e0) (op (e3) (e0))) = (op (e3) (e0)))) -> (((op (e3) (e2)) = (e0))\/(((op (e3) (e2)) = (e1))\/(((op (e3) (e2)) = (e2))\/((op (e3) (e2)) = (e3))))) -> (~((op (e1) (e1)) = (e3))) -> (~((op (e1) (e2)) = (op (e3) (e2)))) -> (((op (e1) (e0)) = (e3))\/(((op (e1) (e1)) = (e3))\/(((op (e1) (e2)) = (e3))\/((op (e1) (e3)) = (e3))))) -> (~((op (e2) (op (e3) (e2))) = (op (e3) (e2)))) -> (~((op (e3) (e1)) = (op (e3) (e2)))) -> (~((op (e0) (e2)) = (op (e3) (e2)))) -> (((op (e3) (e0)) = (e1))\/(((op (e3) (e1)) = (e1))\/(((op (e3) (e2)) = (e1))\/((op (e3) (e3)) = (e1))))) -> (((op (e0) (e3)) = (e0))\/(((op (e0) (e3)) = (e1))\/(((op (e0) (e3)) = (e2))\/((op (e0) (e3)) = (e3))))) -> (~((op (e3) (e0)) = (op (e3) (e2)))) -> (~((op (e1) (e0)) = (op (e2) (e0)))) -> (~((op (e1) (op (e3) (e1))) = (op (e3) (e1)))) -> (~((op (e0) (e3)) = (op (e2) (e3)))) -> (((op (e2) (e0)) = (e1))\/(((op (e2) (e1)) = (e1))\/(((op (e2) (e2)) = (e1))\/((op (e2) (e3)) = (e1))))) -> (((op (e0) (e0)) = (e3))\/(((op (e1) (e0)) = (e3))\/(((op (e2) (e0)) = (e3))\/((op (e3) (e0)) = (e3))))) -> (~((op (e0) (e0)) = (e1))) -> ((~((op (e3) (e3)) = (e1)))\/((op (e3) (e1)) = (e3))) -> (~((op (e2) (e2)) = (op (e2) (e3)))) -> ((~((op (e2) (e2)) = (e3)))\/((op (e2) (e3)) = (e2))) -> False). % 15.55/15.72 do 0 intro. intros zenon_H1e3 zenon_H10f zenon_H109 zenon_H44 zenon_H59 zenon_Ha3 zenon_Hd8 zenon_H11b zenon_H1d5 zenon_H87 zenon_H2d5 zenon_H10d zenon_H2be zenon_H1df zenon_H138 zenon_H1b3 zenon_H157 zenon_H6a zenon_H1a2 zenon_H10e zenon_H1e5 zenon_H175 zenon_H166 zenon_H121 zenon_Hce zenon_H1d0 zenon_H36 zenon_H3b zenon_Hf1 zenon_Hc9 zenon_Hab zenon_H84 zenon_H80 zenon_H35 zenon_H7d zenon_Hd6 zenon_Ha7 zenon_H228 zenon_H22e zenon_H1b4 zenon_H2b8 zenon_H25e zenon_H182 zenon_H17d zenon_H90 zenon_H2af zenon_H135 zenon_H140 zenon_H146 zenon_H254 zenon_H105 zenon_H247 zenon_H2b4 zenon_Hb4 zenon_Hb7 zenon_Hbe zenon_H45 zenon_H10c zenon_H15f zenon_H1c3. % 15.55/15.72 apply (zenon_or_s _ _ zenon_H1e3); [ zenon_intro zenon_H52 | zenon_intro zenon_H156 ]. % 15.55/15.72 apply (zenon_or_s _ _ zenon_H1c3); [ zenon_intro zenon_H30 | zenon_intro zenon_H124 ]. % 15.55/15.72 apply (zenon_or_s _ _ zenon_H10f); [ zenon_intro zenon_H3c | zenon_intro zenon_Hba ]. % 15.55/15.72 apply (zenon_or_s _ _ zenon_H10c); [ zenon_intro zenon_H104 | zenon_intro zenon_H10a ]. % 15.55/15.72 apply (zenon_or_s _ _ zenon_H10e); [ zenon_intro zenon_H3d | zenon_intro zenon_H106 ]. % 15.55/15.72 apply (zenon_or_s _ _ zenon_H10d); [ zenon_intro zenon_H3e | zenon_intro zenon_H42 ]. % 15.55/15.72 apply (zenon_or_s _ _ zenon_H44); [ zenon_intro zenon_H47 | zenon_intro zenon_H46 ]. % 15.55/15.72 exact (zenon_H45 zenon_H47). % 15.55/15.72 apply (zenon_or_s _ _ zenon_H46); [ zenon_intro zenon_H22 | zenon_intro zenon_H48 ]. % 15.55/15.72 apply (zenon_L1304_); trivial. % 15.55/15.72 apply (zenon_or_s _ _ zenon_H48); [ zenon_intro zenon_H29 | zenon_intro zenon_H37 ]. % 15.55/15.72 apply (zenon_L1300_); trivial. % 15.55/15.72 apply (zenon_L7_); trivial. % 15.55/15.72 apply (zenon_L1041_); trivial. % 15.55/15.72 apply (zenon_or_s _ _ zenon_H11b); [ zenon_intro zenon_H29 | zenon_intro zenon_H11c ]. % 15.55/15.72 apply (zenon_L1300_); trivial. % 15.55/15.72 apply (zenon_or_s _ _ zenon_H11c); [ zenon_intro zenon_H117 | zenon_intro zenon_H11d ]. % 15.55/15.72 apply (zenon_L248_); trivial. % 15.55/15.72 apply (zenon_or_s _ _ zenon_H11d); [ zenon_intro zenon_H2a | zenon_intro zenon_H119 ]. % 15.55/15.72 exact (zenon_H52 zenon_H2a). % 15.55/15.72 apply (zenon_L87_); trivial. % 15.55/15.72 apply (zenon_L1302_); trivial. % 15.55/15.72 apply (zenon_L1249_); trivial. % 15.55/15.72 apply (zenon_L137_); trivial. % 15.55/15.72 apply (zenon_L134_); trivial. % 15.55/15.72 (* end of lemma zenon_L1306_ *) % 15.55/15.72 assert (zenon_L1307_ : ((~((op (e1) (e1)) = (e2)))\/((op (e1) (e2)) = (e1))) -> ((~((op (e2) (e2)) = (e1)))\/((op (e2) (e1)) = (e2))) -> ((~((op (e3) (e3)) = (e0)))\/((op (e3) (e0)) = (e3))) -> (~((op (e3) (e0)) = (op (e3) (e1)))) -> (((op (e0) (e0)) = (e1))\/(((op (e0) (e1)) = (e1))\/(((op (e0) (e2)) = (e1))\/((op (e0) (e3)) = (e1))))) -> (~((op (e0) (e0)) = (e3))) -> (~((e1) = (e3))) -> ((op (e1) (e0)) = (e1)) -> (((op (e0) (e2)) = (e1))\/(((op (e1) (e2)) = (e1))\/(((op (e2) (e2)) = (e1))\/((op (e3) (e2)) = (e1))))) -> (((op (e1) (e2)) = (e0))\/(((op (e1) (e2)) = (e1))\/(((op (e1) (e2)) = (e2))\/((op (e1) (e2)) = (e3))))) -> (~((op (e0) (e2)) = (op (e1) (e2)))) -> (((op (e3) (e0)) = (e3))\/(((op (e3) (e1)) = (e3))\/(((op (e3) (e2)) = (e3))\/((op (e3) (e3)) = (e3))))) -> ((~((op (e3) (e3)) = (e3)))\/((op (e3) (e3)) = (e3))) -> (~((op (e3) (op (e3) (e3))) = (op (e3) (e3)))) -> (((op (e3) (e0)) = (e2))\/(((op (e3) (e1)) = (e2))\/(((op (e3) (e2)) = (e2))\/((op (e3) (e3)) = (e2))))) -> (~((op (e0) (e1)) = (op (e3) (e1)))) -> (((op (e1) (e1)) = (e0))\/(((op (e1) (e1)) = (e1))\/(((op (e1) (e1)) = (e2))\/((op (e1) (e1)) = (e3))))) -> (~((op (e2) (e1)) = (op (e2) (e2)))) -> (~((e2) = (e3))) -> (((op (e0) (e1)) = (e2))\/(((op (e1) (e1)) = (e2))\/(((op (e2) (e1)) = (e2))\/((op (e3) (e1)) = (e2))))) -> ((~((op (e3) (e3)) = (e2)))\/((op (e3) (e2)) = (e3))) -> (~((op (e2) (e0)) = (op (e3) (e0)))) -> (((op (e0) (e2)) = (e3))\/(((op (e1) (e2)) = (e3))\/(((op (e2) (e2)) = (e3))\/((op (e3) (e2)) = (e3))))) -> (~((op (e1) (e0)) = (op (e1) (e2)))) -> (((op (e0) (e3)) = (e1))\/(((op (e1) (e3)) = (e1))\/(((op (e2) (e3)) = (e1))\/((op (e3) (e3)) = (e1))))) -> (~((op (e2) (e0)) = (op (e2) (e3)))) -> (~((op (e1) (e2)) = (op (e1) (e3)))) -> (~((op (e0) (e3)) = (op (e3) (e3)))) -> (((op (e3) (e3)) = (e0))\/(((op (e3) (e3)) = (e1))\/(((op (e3) (e3)) = (e2))\/((op (e3) (e3)) = (e3))))) -> (((op (e0) (e0)) = (e1))\/(((op (e1) (e0)) = (e1))\/(((op (e2) (e0)) = (e1))\/((op (e3) (e0)) = (e1))))) -> (~((op (e0) (e2)) = (op (e0) (e3)))) -> ((op (e0) (e2)) = (e0)) -> (((op (e1) (e0)) = (e2))\/(((op (e1) (e1)) = (e2))\/(((op (e1) (e2)) = (e2))\/((op (e1) (e3)) = (e2))))) -> (~((op (e0) (e3)) = (op (e1) (e3)))) -> ((op (e2) (e2)) = (e2)) -> (~((op (e1) (e2)) = (op (e2) (e2)))) -> (~((e1) = (e2))) -> (((op (e0) (e1)) = (e1))\/(((op (e1) (e1)) = (e1))\/(((op (e2) (e1)) = (e1))\/((op (e3) (e1)) = (e1))))) -> (~((op (e1) (e0)) = (op (e3) (e0)))) -> (~((op (e1) (e1)) = (e1))) -> (~((op (e0) (op (e3) (e0))) = (op (e3) (e0)))) -> (((op (e3) (e2)) = (e0))\/(((op (e3) (e2)) = (e1))\/(((op (e3) (e2)) = (e2))\/((op (e3) (e2)) = (e3))))) -> (~((op (e1) (e2)) = (op (e3) (e2)))) -> (((op (e1) (e0)) = (e3))\/(((op (e1) (e1)) = (e3))\/(((op (e1) (e2)) = (e3))\/((op (e1) (e3)) = (e3))))) -> (~((op (e2) (op (e3) (e2))) = (op (e3) (e2)))) -> (~((op (e3) (e1)) = (op (e3) (e2)))) -> (~((op (e0) (e2)) = (op (e3) (e2)))) -> (((op (e3) (e0)) = (e1))\/(((op (e3) (e1)) = (e1))\/(((op (e3) (e2)) = (e1))\/((op (e3) (e3)) = (e1))))) -> (((op (e0) (e3)) = (e0))\/(((op (e0) (e3)) = (e1))\/(((op (e0) (e3)) = (e2))\/((op (e0) (e3)) = (e3))))) -> (~((op (e3) (e0)) = (op (e3) (e2)))) -> (~((op (e1) (e0)) = (op (e2) (e0)))) -> (~((op (e1) (op (e3) (e1))) = (op (e3) (e1)))) -> (~((op (e0) (e3)) = (op (e2) (e3)))) -> (((op (e2) (e0)) = (e1))\/(((op (e2) (e1)) = (e1))\/(((op (e2) (e2)) = (e1))\/((op (e2) (e3)) = (e1))))) -> (((op (e0) (e0)) = (e3))\/(((op (e1) (e0)) = (e3))\/(((op (e2) (e0)) = (e3))\/((op (e3) (e0)) = (e3))))) -> (~((op (e0) (e0)) = (e1))) -> ((~((op (e3) (e3)) = (e1)))\/((op (e3) (e1)) = (e3))) -> (~((op (e2) (e2)) = (op (e2) (e3)))) -> ((~((op (e2) (e2)) = (e3)))\/((op (e2) (e3)) = (e2))) -> (~((op (e1) (e0)) = (op (e1) (e3)))) -> ((~((op (e1) (e1)) = (e3)))\/((op (e1) (e3)) = (e1))) -> False). % 15.55/15.73 do 0 intro. intros zenon_H1d3 zenon_H1e3 zenon_H10f zenon_H109 zenon_H44 zenon_H59 zenon_Ha3 zenon_Hd8 zenon_H11b zenon_H1d5 zenon_H87 zenon_H2d5 zenon_H10d zenon_H2be zenon_H1df zenon_H138 zenon_H1b3 zenon_H157 zenon_H6a zenon_H1a2 zenon_H10e zenon_H1e5 zenon_H175 zenon_H166 zenon_H121 zenon_Hce zenon_H1d0 zenon_H36 zenon_H3b zenon_Hf1 zenon_Hc9 zenon_Hab zenon_H84 zenon_H80 zenon_H35 zenon_H7d zenon_Ha7 zenon_H228 zenon_H22e zenon_H1b4 zenon_H2b8 zenon_H25e zenon_H17d zenon_H90 zenon_H2af zenon_H135 zenon_H140 zenon_H146 zenon_H254 zenon_H105 zenon_H247 zenon_H2b4 zenon_Hb4 zenon_Hb7 zenon_Hbe zenon_H45 zenon_H10c zenon_H15f zenon_H1c3 zenon_H1cf zenon_H1d2. % 15.55/15.73 apply (zenon_or_s _ _ zenon_H1d3); [ zenon_intro zenon_Hd6 | zenon_intro zenon_H117 ]. % 15.55/15.73 apply (zenon_or_s _ _ zenon_H1d2); [ zenon_intro zenon_H182 | zenon_intro zenon_H11f ]. % 15.55/15.73 apply (zenon_L1306_); trivial. % 15.55/15.73 apply (zenon_L224_); trivial. % 15.55/15.73 apply (zenon_L248_); trivial. % 15.55/15.73 (* end of lemma zenon_L1307_ *) % 15.55/15.73 assert (zenon_L1308_ : ((~((op (e1) (e1)) = (e1)))\/((op (e1) (e1)) = (e1))) -> (~((op (e1) (e0)) = (op (e1) (e1)))) -> ((~((op (e1) (e1)) = (e3)))\/((op (e1) (e3)) = (e1))) -> (~((op (e1) (e0)) = (op (e1) (e3)))) -> ((~((op (e2) (e2)) = (e3)))\/((op (e2) (e3)) = (e2))) -> (~((op (e2) (e2)) = (op (e2) (e3)))) -> ((~((op (e3) (e3)) = (e1)))\/((op (e3) (e1)) = (e3))) -> (~((op (e0) (e0)) = (e1))) -> (((op (e0) (e0)) = (e3))\/(((op (e1) (e0)) = (e3))\/(((op (e2) (e0)) = (e3))\/((op (e3) (e0)) = (e3))))) -> (((op (e2) (e0)) = (e1))\/(((op (e2) (e1)) = (e1))\/(((op (e2) (e2)) = (e1))\/((op (e2) (e3)) = (e1))))) -> (~((op (e0) (e3)) = (op (e2) (e3)))) -> (~((op (e1) (op (e3) (e1))) = (op (e3) (e1)))) -> (~((op (e1) (e0)) = (op (e2) (e0)))) -> (~((op (e3) (e0)) = (op (e3) (e2)))) -> (((op (e0) (e3)) = (e0))\/(((op (e0) (e3)) = (e1))\/(((op (e0) (e3)) = (e2))\/((op (e0) (e3)) = (e3))))) -> (((op (e3) (e0)) = (e1))\/(((op (e3) (e1)) = (e1))\/(((op (e3) (e2)) = (e1))\/((op (e3) (e3)) = (e1))))) -> (~((op (e0) (e2)) = (op (e3) (e2)))) -> (~((op (e3) (e1)) = (op (e3) (e2)))) -> (~((op (e2) (op (e3) (e2))) = (op (e3) (e2)))) -> (((op (e1) (e0)) = (e3))\/(((op (e1) (e1)) = (e3))\/(((op (e1) (e2)) = (e3))\/((op (e1) (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 (e0) (op (e3) (e0))) = (op (e3) (e0)))) -> (~((op (e1) (e0)) = (op (e3) (e0)))) -> (((op (e0) (e1)) = (e1))\/(((op (e1) (e1)) = (e1))\/(((op (e2) (e1)) = (e1))\/((op (e3) (e1)) = (e1))))) -> (~((e1) = (e2))) -> (~((op (e1) (e2)) = (op (e2) (e2)))) -> ((op (e2) (e2)) = (e2)) -> (~((op (e0) (e3)) = (op (e1) (e3)))) -> (((op (e1) (e0)) = (e2))\/(((op (e1) (e1)) = (e2))\/(((op (e1) (e2)) = (e2))\/((op (e1) (e3)) = (e2))))) -> ((op (e0) (e2)) = (e0)) -> (~((op (e0) (e2)) = (op (e0) (e3)))) -> (((op (e0) (e0)) = (e1))\/(((op (e1) (e0)) = (e1))\/(((op (e2) (e0)) = (e1))\/((op (e3) (e0)) = (e1))))) -> (((op (e3) (e3)) = (e0))\/(((op (e3) (e3)) = (e1))\/(((op (e3) (e3)) = (e2))\/((op (e3) (e3)) = (e3))))) -> (~((op (e0) (e3)) = (op (e3) (e3)))) -> (~((op (e1) (e2)) = (op (e1) (e3)))) -> (~((op (e2) (e0)) = (op (e2) (e3)))) -> (((op (e0) (e3)) = (e1))\/(((op (e1) (e3)) = (e1))\/(((op (e2) (e3)) = (e1))\/((op (e3) (e3)) = (e1))))) -> (~((op (e1) (e0)) = (op (e1) (e2)))) -> (((op (e0) (e2)) = (e3))\/(((op (e1) (e2)) = (e3))\/(((op (e2) (e2)) = (e3))\/((op (e3) (e2)) = (e3))))) -> (~((op (e2) (e0)) = (op (e3) (e0)))) -> ((~((op (e3) (e3)) = (e2)))\/((op (e3) (e2)) = (e3))) -> (((op (e0) (e1)) = (e2))\/(((op (e1) (e1)) = (e2))\/(((op (e2) (e1)) = (e2))\/((op (e3) (e1)) = (e2))))) -> (~((e2) = (e3))) -> (~((op (e2) (e1)) = (op (e2) (e2)))) -> (((op (e1) (e1)) = (e0))\/(((op (e1) (e1)) = (e1))\/(((op (e1) (e1)) = (e2))\/((op (e1) (e1)) = (e3))))) -> (~((op (e0) (e1)) = (op (e3) (e1)))) -> (((op (e3) (e0)) = (e2))\/(((op (e3) (e1)) = (e2))\/(((op (e3) (e2)) = (e2))\/((op (e3) (e3)) = (e2))))) -> (~((op (e3) (op (e3) (e3))) = (op (e3) (e3)))) -> ((~((op (e3) (e3)) = (e3)))\/((op (e3) (e3)) = (e3))) -> (((op (e3) (e0)) = (e3))\/(((op (e3) (e1)) = (e3))\/(((op (e3) (e2)) = (e3))\/((op (e3) (e3)) = (e3))))) -> (~((op (e0) (e2)) = (op (e1) (e2)))) -> (((op (e1) (e2)) = (e0))\/(((op (e1) (e2)) = (e1))\/(((op (e1) (e2)) = (e2))\/((op (e1) (e2)) = (e3))))) -> (((op (e0) (e2)) = (e1))\/(((op (e1) (e2)) = (e1))\/(((op (e2) (e2)) = (e1))\/((op (e3) (e2)) = (e1))))) -> ((op (e1) (e0)) = (e1)) -> (~((e1) = (e3))) -> (~((op (e0) (e0)) = (e3))) -> (((op (e0) (e0)) = (e1))\/(((op (e0) (e1)) = (e1))\/(((op (e0) (e2)) = (e1))\/((op (e0) (e3)) = (e1))))) -> (~((op (e3) (e0)) = (op (e3) (e1)))) -> ((~((op (e3) (e3)) = (e0)))\/((op (e3) (e0)) = (e3))) -> ((~((op (e2) (e2)) = (e1)))\/((op (e2) (e1)) = (e2))) -> ((~((op (e1) (e1)) = (e2)))\/((op (e1) (e2)) = (e1))) -> False). % 15.55/15.73 do 0 intro. intros zenon_H1d8 zenon_Hd7 zenon_H1d2 zenon_H1cf zenon_H1c3 zenon_H15f zenon_H10c zenon_H45 zenon_Hbe zenon_Hb7 zenon_Hb4 zenon_H2b4 zenon_H247 zenon_H105 zenon_H254 zenon_H146 zenon_H140 zenon_H135 zenon_H2af zenon_H90 zenon_H17d zenon_H25e zenon_H2b8 zenon_H22e zenon_H228 zenon_Ha7 zenon_H7d zenon_H35 zenon_H80 zenon_H84 zenon_Hab zenon_Hc9 zenon_Hf1 zenon_H3b zenon_H36 zenon_H1d0 zenon_Hce zenon_H121 zenon_H166 zenon_H175 zenon_H1e5 zenon_H10e zenon_H1a2 zenon_H6a zenon_H157 zenon_H1b3 zenon_H138 zenon_H1df zenon_H2be zenon_H10d zenon_H2d5 zenon_H87 zenon_H1d5 zenon_H11b zenon_Hd8 zenon_Ha3 zenon_H59 zenon_H44 zenon_H109 zenon_H10f zenon_H1e3 zenon_H1d3. % 15.55/15.73 apply (zenon_or_s _ _ zenon_H1d8); [ zenon_intro zenon_H1b4 | zenon_intro zenon_H21 ]. % 15.55/15.73 apply (zenon_L1307_); trivial. % 15.55/15.73 apply (zenon_L61_); trivial. % 15.55/15.73 (* end of lemma zenon_L1308_ *) % 15.55/15.73 assert (zenon_L1309_ : ((~((op (e1) (e1)) = (e2)))\/((op (e1) (e2)) = (e1))) -> ((~((op (e2) (e2)) = (e1)))\/((op (e2) (e1)) = (e2))) -> ((~((op (e3) (e3)) = (e0)))\/((op (e3) (e0)) = (e3))) -> (~((op (e3) (e0)) = (op (e3) (e1)))) -> (((op (e0) (e0)) = (e1))\/(((op (e0) (e1)) = (e1))\/(((op (e0) (e2)) = (e1))\/((op (e0) (e3)) = (e1))))) -> (((op (e0) (e2)) = (e1))\/(((op (e1) (e2)) = (e1))\/(((op (e2) (e2)) = (e1))\/((op (e3) (e2)) = (e1))))) -> (((op (e1) (e2)) = (e0))\/(((op (e1) (e2)) = (e1))\/(((op (e1) (e2)) = (e2))\/((op (e1) (e2)) = (e3))))) -> (~((op (e0) (e2)) = (op (e1) (e2)))) -> (((op (e3) (e0)) = (e3))\/(((op (e3) (e1)) = (e3))\/(((op (e3) (e2)) = (e3))\/((op (e3) (e3)) = (e3))))) -> ((~((op (e3) (e3)) = (e3)))\/((op (e3) (e3)) = (e3))) -> (~((op (e3) (op (e3) (e3))) = (op (e3) (e3)))) -> (((op (e3) (e0)) = (e2))\/(((op (e3) (e1)) = (e2))\/(((op (e3) (e2)) = (e2))\/((op (e3) (e3)) = (e2))))) -> (~((op (e0) (e1)) = (op (e3) (e1)))) -> (((op (e1) (e1)) = (e0))\/(((op (e1) (e1)) = (e1))\/(((op (e1) (e1)) = (e2))\/((op (e1) (e1)) = (e3))))) -> (~((op (e2) (e1)) = (op (e2) (e2)))) -> (~((e2) = (e3))) -> (((op (e0) (e1)) = (e2))\/(((op (e1) (e1)) = (e2))\/(((op (e2) (e1)) = (e2))\/((op (e3) (e1)) = (e2))))) -> ((~((op (e3) (e3)) = (e2)))\/((op (e3) (e2)) = (e3))) -> (~((op (e2) (e0)) = (op (e3) (e0)))) -> (((op (e0) (e2)) = (e3))\/(((op (e1) (e2)) = (e3))\/(((op (e2) (e2)) = (e3))\/((op (e3) (e2)) = (e3))))) -> (~((op (e1) (e0)) = (op (e1) (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) (e0)) = (e1))\/(((op (e1) (e0)) = (e1))\/(((op (e2) (e0)) = (e1))\/((op (e3) (e0)) = (e1))))) -> (~((op (e0) (e2)) = (op (e0) (e3)))) -> ((op (e0) (e2)) = (e0)) -> (((op (e1) (e0)) = (e2))\/(((op (e1) (e1)) = (e2))\/(((op (e1) (e2)) = (e2))\/((op (e1) (e3)) = (e2))))) -> (~((op (e0) (e3)) = (op (e1) (e3)))) -> ((op (e2) (e2)) = (e2)) -> (~((op (e1) (e2)) = (op (e2) (e2)))) -> (~((e1) = (e2))) -> (((op (e0) (e1)) = (e1))\/(((op (e1) (e1)) = (e1))\/(((op (e2) (e1)) = (e1))\/((op (e3) (e1)) = (e1))))) -> (~((op (e1) (e0)) = (op (e3) (e0)))) -> (((op (e3) (e2)) = (e0))\/(((op (e3) (e2)) = (e1))\/(((op (e3) (e2)) = (e2))\/((op (e3) (e2)) = (e3))))) -> (~((op (e1) (e2)) = (op (e3) (e2)))) -> (((op (e1) (e0)) = (e3))\/(((op (e1) (e1)) = (e3))\/(((op (e1) (e2)) = (e3))\/((op (e1) (e3)) = (e3))))) -> (~((op (e3) (e1)) = (op (e3) (e2)))) -> (((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 (e3) (e0)) = (op (e3) (e2)))) -> (~((op (e1) (e0)) = (op (e2) (e0)))) -> (~((op (e1) (op (e3) (e1))) = (op (e3) (e1)))) -> (~((op (e0) (e3)) = (op (e2) (e3)))) -> (((op (e2) (e0)) = (e1))\/(((op (e2) (e1)) = (e1))\/(((op (e2) (e2)) = (e1))\/((op (e2) (e3)) = (e1))))) -> (((op (e0) (e0)) = (e3))\/(((op (e1) (e0)) = (e3))\/(((op (e2) (e0)) = (e3))\/((op (e3) (e0)) = (e3))))) -> (~((op (e0) (e0)) = (e1))) -> ((~((op (e3) (e3)) = (e1)))\/((op (e3) (e1)) = (e3))) -> (~((op (e2) (e2)) = (op (e2) (e3)))) -> ((~((op (e2) (e2)) = (e3)))\/((op (e2) (e3)) = (e2))) -> (~((op (e1) (e0)) = (op (e1) (e3)))) -> ((~((op (e1) (e1)) = (e3)))\/((op (e1) (e3)) = (e1))) -> (~((op (e1) (e0)) = (op (e1) (e1)))) -> ((~((op (e1) (e1)) = (e1)))\/((op (e1) (e1)) = (e1))) -> (~((op (e3) (e3)) = (e1))) -> (~((op (e2) (e0)) = (op (e2) (e3)))) -> (~((op (e1) (e2)) = (op (e1) (e3)))) -> ((op (e1) (e2)) = (e1)) -> (~((e1) = (e3))) -> (((op (e0) (e3)) = (e1))\/(((op (e1) (e3)) = (e1))\/(((op (e2) (e3)) = (e1))\/((op (e3) (e3)) = (e1))))) -> ((op (e3) (e2)) = (e3)) -> (~((op (e0) (e2)) = (op (e3) (e2)))) -> (((op (e2) (e0)) = (e3))\/(((op (e2) (e1)) = (e3))\/(((op (e2) (e2)) = (e3))\/((op (e2) (e3)) = (e3))))) -> (~((op (e0) (e1)) = (op (e2) (e1)))) -> (~((op (e2) (e2)) = (e3))) -> (~((op (e2) (op (e3) (e2))) = (op (e3) (e2)))) -> (~((op (e0) (e0)) = (e3))) -> (((op (e0) (e0)) = (e3))\/(((op (e0) (e1)) = (e3))\/(((op (e0) (e2)) = (e3))\/((op (e0) (e3)) = (e3))))) -> (~((op (e0) (op (e3) (e0))) = (op (e3) (e0)))) -> ((op (e0) (e1)) = (e1)) -> False). % 15.55/15.73 do 0 intro. intros zenon_H1d3 zenon_H1e3 zenon_H10f zenon_H109 zenon_H44 zenon_H11b zenon_H1d5 zenon_H87 zenon_H2d5 zenon_H10d zenon_H2be zenon_H1df zenon_H138 zenon_H1b3 zenon_H157 zenon_H6a zenon_H1a2 zenon_H10e zenon_H1e5 zenon_H175 zenon_H166 zenon_H36 zenon_H3b zenon_Hf1 zenon_Hc9 zenon_Hab zenon_H84 zenon_H80 zenon_H35 zenon_H7d zenon_Ha7 zenon_H228 zenon_H22e zenon_H25e zenon_H17d zenon_H90 zenon_H135 zenon_H146 zenon_H254 zenon_H105 zenon_H247 zenon_H2b4 zenon_Hb4 zenon_Hb7 zenon_Hbe zenon_H45 zenon_H10c zenon_H15f zenon_H1c3 zenon_H1cf zenon_H1d2 zenon_Hd7 zenon_H1d8 zenon_H104 zenon_Hce zenon_H1d0 zenon_H117 zenon_Ha3 zenon_H121 zenon_H106 zenon_H140 zenon_He6 zenon_Hde zenon_H30 zenon_H2af zenon_H59 zenon_H58 zenon_H2b8 zenon_H22. % 15.55/15.73 apply (zenon_or_s _ _ zenon_Hf1); [ zenon_intro zenon_H47 | zenon_intro zenon_Hf4 ]. % 15.55/15.73 exact (zenon_H45 zenon_H47). % 15.55/15.73 apply (zenon_or_s _ _ zenon_Hf4); [ zenon_intro zenon_Hd8 | zenon_intro zenon_Hf5 ]. % 15.55/15.73 apply (zenon_L1308_); trivial. % 15.55/15.73 apply (zenon_or_s _ _ zenon_Hf5); [ zenon_intro zenon_Hae | zenon_intro zenon_Hee ]. % 15.55/15.73 apply (zenon_L1103_); trivial. % 15.55/15.73 apply (zenon_L1054_); trivial. % 15.55/15.73 (* end of lemma zenon_L1309_ *) % 15.55/15.73 assert (zenon_L1310_ : ((op (e1) (e2)) = (e1)) -> (~((op (e3) (e3)) = (e1))) -> ((~((op (e1) (e1)) = (e1)))\/((op (e1) (e1)) = (e1))) -> (~((op (e1) (e0)) = (op (e1) (e1)))) -> ((~((op (e1) (e1)) = (e3)))\/((op (e1) (e3)) = (e1))) -> (~((op (e1) (e0)) = (op (e1) (e3)))) -> ((~((op (e2) (e2)) = (e3)))\/((op (e2) (e3)) = (e2))) -> (~((op (e2) (e2)) = (op (e2) (e3)))) -> ((~((op (e3) (e3)) = (e1)))\/((op (e3) (e1)) = (e3))) -> (~((op (e0) (e0)) = (e1))) -> (((op (e0) (e0)) = (e3))\/(((op (e1) (e0)) = (e3))\/(((op (e2) (e0)) = (e3))\/((op (e3) (e0)) = (e3))))) -> (((op (e2) (e0)) = (e1))\/(((op (e2) (e1)) = (e1))\/(((op (e2) (e2)) = (e1))\/((op (e2) (e3)) = (e1))))) -> (~((op (e0) (e3)) = (op (e2) (e3)))) -> (~((op (e1) (e0)) = (op (e2) (e0)))) -> (~((op (e3) (e0)) = (op (e3) (e2)))) -> (((op (e0) (e3)) = (e0))\/(((op (e0) (e3)) = (e1))\/(((op (e0) (e3)) = (e2))\/((op (e0) (e3)) = (e3))))) -> (((op (e3) (e0)) = (e1))\/(((op (e3) (e1)) = (e1))\/(((op (e3) (e2)) = (e1))\/((op (e3) (e3)) = (e1))))) -> (~((op (e3) (e1)) = (op (e3) (e2)))) -> (((op (e1) (e0)) = (e3))\/(((op (e1) (e1)) = (e3))\/(((op (e1) (e2)) = (e3))\/((op (e1) (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 (e0) (op (e3) (e0))) = (op (e3) (e0)))) -> (~((op (e1) (e1)) = (e1))) -> (~((op (e1) (e0)) = (op (e3) (e0)))) -> (((op (e0) (e1)) = (e1))\/(((op (e1) (e1)) = (e1))\/(((op (e2) (e1)) = (e1))\/((op (e3) (e1)) = (e1))))) -> (~((e1) = (e2))) -> (~((op (e1) (e2)) = (op (e2) (e2)))) -> ((op (e2) (e2)) = (e2)) -> (~((op (e0) (e3)) = (op (e1) (e3)))) -> (((op (e1) (e0)) = (e2))\/(((op (e1) (e1)) = (e2))\/(((op (e1) (e2)) = (e2))\/((op (e1) (e3)) = (e2))))) -> (~((op (e0) (e2)) = (op (e0) (e3)))) -> (((op (e0) (e0)) = (e1))\/(((op (e1) (e0)) = (e1))\/(((op (e2) (e0)) = (e1))\/((op (e3) (e0)) = (e1))))) -> (((op (e3) (e3)) = (e0))\/(((op (e3) (e3)) = (e1))\/(((op (e3) (e3)) = (e2))\/((op (e3) (e3)) = (e3))))) -> (~((op (e0) (e3)) = (op (e3) (e3)))) -> (~((op (e1) (e2)) = (op (e1) (e3)))) -> (~((op (e2) (e0)) = (op (e2) (e3)))) -> (((op (e0) (e3)) = (e1))\/(((op (e1) (e3)) = (e1))\/(((op (e2) (e3)) = (e1))\/((op (e3) (e3)) = (e1))))) -> (~((op (e1) (e0)) = (op (e1) (e2)))) -> (((op (e0) (e2)) = (e3))\/(((op (e1) (e2)) = (e3))\/(((op (e2) (e2)) = (e3))\/((op (e3) (e2)) = (e3))))) -> (~((op (e2) (e0)) = (op (e3) (e0)))) -> ((~((op (e3) (e3)) = (e2)))\/((op (e3) (e2)) = (e3))) -> (((op (e0) (e1)) = (e2))\/(((op (e1) (e1)) = (e2))\/(((op (e2) (e1)) = (e2))\/((op (e3) (e1)) = (e2))))) -> (~((e2) = (e3))) -> (~((op (e2) (e1)) = (op (e2) (e2)))) -> (((op (e1) (e1)) = (e0))\/(((op (e1) (e1)) = (e1))\/(((op (e1) (e1)) = (e2))\/((op (e1) (e1)) = (e3))))) -> (~((op (e0) (e1)) = (op (e3) (e1)))) -> (((op (e3) (e0)) = (e2))\/(((op (e3) (e1)) = (e2))\/(((op (e3) (e2)) = (e2))\/((op (e3) (e3)) = (e2))))) -> (~((op (e3) (op (e3) (e3))) = (op (e3) (e3)))) -> ((~((op (e3) (e3)) = (e3)))\/((op (e3) (e3)) = (e3))) -> (((op (e3) (e0)) = (e3))\/(((op (e3) (e1)) = (e3))\/(((op (e3) (e2)) = (e3))\/((op (e3) (e3)) = (e3))))) -> (~((op (e0) (e2)) = (op (e1) (e2)))) -> (((op (e1) (e2)) = (e0))\/(((op (e1) (e2)) = (e1))\/(((op (e1) (e2)) = (e2))\/((op (e1) (e2)) = (e3))))) -> (((op (e0) (e2)) = (e1))\/(((op (e1) (e2)) = (e1))\/(((op (e2) (e2)) = (e1))\/((op (e3) (e2)) = (e1))))) -> (((op (e0) (e0)) = (e1))\/(((op (e0) (e1)) = (e1))\/(((op (e0) (e2)) = (e1))\/((op (e0) (e3)) = (e1))))) -> (~((op (e3) (e0)) = (op (e3) (e1)))) -> ((~((op (e3) (e3)) = (e0)))\/((op (e3) (e0)) = (e3))) -> ((~((op (e2) (e2)) = (e1)))\/((op (e2) (e1)) = (e2))) -> ((~((op (e1) (e1)) = (e2)))\/((op (e1) (e2)) = (e1))) -> (~((e1) = (e3))) -> ((op (e3) (e2)) = (e3)) -> (((op (e2) (e0)) = (e3))\/(((op (e2) (e1)) = (e3))\/(((op (e2) (e2)) = (e3))\/((op (e2) (e3)) = (e3))))) -> (~((op (e0) (e1)) = (op (e2) (e1)))) -> (~((op (e2) (e2)) = (e3))) -> (~((op (e2) (op (e3) (e2))) = (op (e3) (e2)))) -> (~((op (e0) (e0)) = (e3))) -> (((op (e0) (e0)) = (e3))\/(((op (e0) (e1)) = (e3))\/(((op (e0) (e2)) = (e3))\/((op (e0) (e3)) = (e3))))) -> (((op (e3) (e0)) = (e0))\/(((op (e3) (e1)) = (e0))\/(((op (e3) (e2)) = (e0))\/((op (e3) (e3)) = (e0))))) -> (~((e0) = (e1))) -> ((op (e1) (e0)) = (e0)) -> (~((op (e1) (op (e3) (e1))) = (op (e3) (e1)))) -> ((op (e0) (e2)) = (e0)) -> (~((op (e0) (e2)) = (op (e3) (e2)))) -> (~((op (e3) (e3)) = (e0))) -> False). % 15.55/15.73 do 0 intro. intros zenon_H117 zenon_H104 zenon_H1d8 zenon_Hd7 zenon_H1d2 zenon_H1cf zenon_H1c3 zenon_H15f zenon_H10c zenon_H45 zenon_Hbe zenon_Hb7 zenon_Hb4 zenon_H247 zenon_H105 zenon_H254 zenon_H146 zenon_H135 zenon_H90 zenon_H17d zenon_H25e zenon_H2b8 zenon_H1b4 zenon_H22e zenon_H228 zenon_Ha7 zenon_H7d zenon_H35 zenon_H80 zenon_H84 zenon_Hc9 zenon_Hf1 zenon_H3b zenon_H36 zenon_H1d0 zenon_Hce zenon_H121 zenon_H166 zenon_H175 zenon_H1e5 zenon_H10e zenon_H1a2 zenon_H6a zenon_H157 zenon_H1b3 zenon_H138 zenon_H1df zenon_H2be zenon_H10d zenon_H2d5 zenon_H87 zenon_H1d5 zenon_H11b zenon_H44 zenon_H109 zenon_H10f zenon_H1e3 zenon_H1d3 zenon_Ha3 zenon_H106 zenon_He6 zenon_Hde zenon_H30 zenon_H2af zenon_H59 zenon_H58 zenon_H1f6 zenon_H9e zenon_Had zenon_H2b4 zenon_Hab zenon_H140 zenon_H3c. % 15.55/15.73 apply (zenon_or_s _ _ zenon_H44); [ zenon_intro zenon_H47 | zenon_intro zenon_H46 ]. % 15.55/15.73 exact (zenon_H45 zenon_H47). % 15.55/15.73 apply (zenon_or_s _ _ zenon_H46); [ zenon_intro zenon_H22 | zenon_intro zenon_H48 ]. % 15.55/15.73 apply (zenon_L1309_); trivial. % 15.55/15.73 apply (zenon_or_s _ _ zenon_H48); [ zenon_intro zenon_H29 | zenon_intro zenon_H37 ]. % 15.55/15.73 apply (zenon_L37_); trivial. % 15.55/15.73 apply (zenon_or_s _ _ zenon_Hf1); [ zenon_intro zenon_H47 | zenon_intro zenon_Hf4 ]. % 15.55/15.73 exact (zenon_H45 zenon_H47). % 15.55/15.73 apply (zenon_or_s _ _ zenon_Hf4); [ zenon_intro zenon_Hd8 | zenon_intro zenon_Hf5 ]. % 15.55/15.73 apply (zenon_L1307_); trivial. % 15.55/15.73 apply (zenon_or_s _ _ zenon_Hf5); [ zenon_intro zenon_Hae | zenon_intro zenon_Hee ]. % 15.55/15.73 apply (zenon_L1110_); trivial. % 15.55/15.73 apply (zenon_L1277_); trivial. % 15.55/15.73 (* end of lemma zenon_L1310_ *) % 15.55/15.73 assert (zenon_L1311_ : (((op (e0) (e0)) = (e0))\/(((op (e1) (e0)) = (e0))\/(((op (e2) (e0)) = (e0))\/((op (e3) (e0)) = (e0))))) -> (~((op (e0) (e0)) = (e0))) -> (~((op (e3) (e3)) = (e0))) -> (((op (e3) (e0)) = (e0))\/(((op (e3) (e1)) = (e0))\/(((op (e3) (e2)) = (e0))\/((op (e3) (e3)) = (e0))))) -> (((op (e2) (e3)) = (e0))\/(((op (e2) (e3)) = (e1))\/(((op (e2) (e3)) = (e2))\/((op (e2) (e3)) = (e3))))) -> (~((op (e1) (e0)) = (op (e1) (e1)))) -> ((~((op (e1) (e1)) = (e1)))\/((op (e1) (e1)) = (e1))) -> ((~((op (e1) (e1)) = (e3)))\/((op (e1) (e3)) = (e1))) -> (~((op (e1) (e0)) = (op (e1) (e3)))) -> ((~((op (e2) (e2)) = (e3)))\/((op (e2) (e3)) = (e2))) -> (~((op (e2) (e2)) = (op (e2) (e3)))) -> ((~((op (e3) (e3)) = (e1)))\/((op (e3) (e1)) = (e3))) -> (~((op (e0) (e0)) = (e1))) -> (((op (e0) (e0)) = (e3))\/(((op (e1) (e0)) = (e3))\/(((op (e2) (e0)) = (e3))\/((op (e3) (e0)) = (e3))))) -> (((op (e2) (e0)) = (e1))\/(((op (e2) (e1)) = (e1))\/(((op (e2) (e2)) = (e1))\/((op (e2) (e3)) = (e1))))) -> (~((op (e0) (e3)) = (op (e2) (e3)))) -> (~((op (e1) (op (e3) (e1))) = (op (e3) (e1)))) -> (~((op (e1) (e0)) = (op (e2) (e0)))) -> (~((op (e3) (e0)) = (op (e3) (e2)))) -> (((op (e0) (e3)) = (e0))\/(((op (e0) (e3)) = (e1))\/(((op (e0) (e3)) = (e2))\/((op (e0) (e3)) = (e3))))) -> (((op (e3) (e0)) = (e1))\/(((op (e3) (e1)) = (e1))\/(((op (e3) (e2)) = (e1))\/((op (e3) (e3)) = (e1))))) -> (~((op (e3) (e1)) = (op (e3) (e2)))) -> (((op (e1) (e0)) = (e3))\/(((op (e1) (e1)) = (e3))\/(((op (e1) (e2)) = (e3))\/((op (e1) (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 (e0) (op (e3) (e0))) = (op (e3) (e0)))) -> (~((op (e1) (e1)) = (e1))) -> (~((op (e1) (e0)) = (op (e3) (e0)))) -> (((op (e0) (e1)) = (e1))\/(((op (e1) (e1)) = (e1))\/(((op (e2) (e1)) = (e1))\/((op (e3) (e1)) = (e1))))) -> (~((e1) = (e2))) -> (~((op (e1) (e2)) = (op (e2) (e2)))) -> ((op (e2) (e2)) = (e2)) -> (~((op (e0) (e3)) = (op (e1) (e3)))) -> (((op (e1) (e0)) = (e2))\/(((op (e1) (e1)) = (e2))\/(((op (e1) (e2)) = (e2))\/((op (e1) (e3)) = (e2))))) -> ((op (e0) (e2)) = (e0)) -> (~((op (e0) (e2)) = (op (e0) (e3)))) -> (((op (e0) (e0)) = (e1))\/(((op (e1) (e0)) = (e1))\/(((op (e2) (e0)) = (e1))\/((op (e3) (e0)) = (e1))))) -> (((op (e3) (e3)) = (e0))\/(((op (e3) (e3)) = (e1))\/(((op (e3) (e3)) = (e2))\/((op (e3) (e3)) = (e3))))) -> (~((op (e0) (e3)) = (op (e3) (e3)))) -> (~((op (e1) (e0)) = (op (e1) (e2)))) -> (((op (e0) (e2)) = (e3))\/(((op (e1) (e2)) = (e3))\/(((op (e2) (e2)) = (e3))\/((op (e3) (e2)) = (e3))))) -> (~((op (e2) (e0)) = (op (e3) (e0)))) -> ((~((op (e3) (e3)) = (e2)))\/((op (e3) (e2)) = (e3))) -> (((op (e0) (e1)) = (e2))\/(((op (e1) (e1)) = (e2))\/(((op (e2) (e1)) = (e2))\/((op (e3) (e1)) = (e2))))) -> (~((e2) = (e3))) -> (~((op (e2) (e1)) = (op (e2) (e2)))) -> (((op (e1) (e1)) = (e0))\/(((op (e1) (e1)) = (e1))\/(((op (e1) (e1)) = (e2))\/((op (e1) (e1)) = (e3))))) -> (~((op (e0) (e1)) = (op (e3) (e1)))) -> (((op (e3) (e0)) = (e2))\/(((op (e3) (e1)) = (e2))\/(((op (e3) (e2)) = (e2))\/((op (e3) (e3)) = (e2))))) -> (~((op (e3) (op (e3) (e3))) = (op (e3) (e3)))) -> ((~((op (e3) (e3)) = (e3)))\/((op (e3) (e3)) = (e3))) -> (((op (e3) (e0)) = (e3))\/(((op (e3) (e1)) = (e3))\/(((op (e3) (e2)) = (e3))\/((op (e3) (e3)) = (e3))))) -> (~((op (e0) (e2)) = (op (e1) (e2)))) -> (((op (e1) (e2)) = (e0))\/(((op (e1) (e2)) = (e1))\/(((op (e1) (e2)) = (e2))\/((op (e1) (e2)) = (e3))))) -> (((op (e0) (e2)) = (e1))\/(((op (e1) (e2)) = (e1))\/(((op (e2) (e2)) = (e1))\/((op (e3) (e2)) = (e1))))) -> (((op (e0) (e0)) = (e1))\/(((op (e0) (e1)) = (e1))\/(((op (e0) (e2)) = (e1))\/((op (e0) (e3)) = (e1))))) -> (~((op (e3) (e0)) = (op (e3) (e1)))) -> ((~((op (e3) (e3)) = (e0)))\/((op (e3) (e0)) = (e3))) -> ((~((op (e2) (e2)) = (e1)))\/((op (e2) (e1)) = (e2))) -> ((~((op (e1) (e1)) = (e2)))\/((op (e1) (e2)) = (e1))) -> (~((op (e3) (e3)) = (e1))) -> (~((op (e2) (e0)) = (op (e2) (e3)))) -> (~((op (e1) (e2)) = (op (e1) (e3)))) -> ((op (e1) (e2)) = (e1)) -> (~((e1) = (e3))) -> (((op (e0) (e3)) = (e1))\/(((op (e1) (e3)) = (e1))\/(((op (e2) (e3)) = (e1))\/((op (e3) (e3)) = (e1))))) -> ((op (e3) (e2)) = (e3)) -> (~((op (e0) (e2)) = (op (e3) (e2)))) -> (((op (e2) (e0)) = (e3))\/(((op (e2) (e1)) = (e3))\/(((op (e2) (e2)) = (e3))\/((op (e2) (e3)) = (e3))))) -> (~((op (e0) (e1)) = (op (e2) (e1)))) -> (~((op (e2) (e2)) = (e3))) -> (~((op (e2) (op (e3) (e2))) = (op (e3) (e2)))) -> (~((op (e0) (e0)) = (e3))) -> (((op (e0) (e0)) = (e3))\/(((op (e0) (e1)) = (e3))\/(((op (e0) (e2)) = (e3))\/((op (e0) (e3)) = (e3))))) -> (~((e0) = (e1))) -> False). % 15.55/15.73 do 0 intro. intros zenon_Hf0 zenon_H20 zenon_H3c zenon_H1f6 zenon_H2ab zenon_Hd7 zenon_H1d8 zenon_H1d2 zenon_H1cf zenon_H1c3 zenon_H15f zenon_H10c zenon_H45 zenon_Hbe zenon_Hb7 zenon_Hb4 zenon_H2b4 zenon_H247 zenon_H105 zenon_H254 zenon_H146 zenon_H135 zenon_H90 zenon_H17d zenon_H25e zenon_H2b8 zenon_H1b4 zenon_H22e zenon_H228 zenon_Ha7 zenon_H7d zenon_H35 zenon_H80 zenon_H84 zenon_Hab zenon_Hc9 zenon_Hf1 zenon_H3b zenon_H36 zenon_H166 zenon_H175 zenon_H1e5 zenon_H10e zenon_H1a2 zenon_H6a zenon_H157 zenon_H1b3 zenon_H138 zenon_H1df zenon_H2be zenon_H10d zenon_H2d5 zenon_H87 zenon_H1d5 zenon_H11b zenon_H44 zenon_H109 zenon_H10f zenon_H1e3 zenon_H1d3 zenon_H104 zenon_Hce zenon_H1d0 zenon_H117 zenon_Ha3 zenon_H121 zenon_H106 zenon_H140 zenon_He6 zenon_Hde zenon_H30 zenon_H2af zenon_H59 zenon_H58 zenon_H9e. % 15.55/15.73 apply (zenon_or_s _ _ zenon_Hf0); [ zenon_intro zenon_H1f | zenon_intro zenon_Hf2 ]. % 15.55/15.73 exact (zenon_H20 zenon_H1f). % 15.55/15.73 apply (zenon_or_s _ _ zenon_Hf2); [ zenon_intro zenon_Had | zenon_intro zenon_Hf3 ]. % 15.55/15.73 apply (zenon_L1310_); trivial. % 15.55/15.73 apply (zenon_or_s _ _ zenon_Hf3); [ zenon_intro zenon_Hcf | zenon_intro zenon_Hdb ]. % 15.55/15.73 apply (zenon_or_s _ _ zenon_H44); [ zenon_intro zenon_H47 | zenon_intro zenon_H46 ]. % 15.55/15.73 exact (zenon_H45 zenon_H47). % 15.55/15.73 apply (zenon_or_s _ _ zenon_H46); [ zenon_intro zenon_H22 | zenon_intro zenon_H48 ]. % 15.55/15.73 apply (zenon_L1309_); trivial. % 15.55/15.73 apply (zenon_or_s _ _ zenon_H48); [ zenon_intro zenon_H29 | zenon_intro zenon_H37 ]. % 15.55/15.73 apply (zenon_L37_); trivial. % 15.55/15.73 apply (zenon_L1264_); trivial. % 15.55/15.73 apply (zenon_or_s _ _ zenon_Hf1); [ zenon_intro zenon_H47 | zenon_intro zenon_Hf4 ]. % 15.55/15.73 exact (zenon_H45 zenon_H47). % 15.55/15.73 apply (zenon_or_s _ _ zenon_Hf4); [ zenon_intro zenon_Hd8 | zenon_intro zenon_Hf5 ]. % 15.55/15.73 apply (zenon_L1307_); trivial. % 15.55/15.73 apply (zenon_or_s _ _ zenon_Hf5); [ zenon_intro zenon_Hae | zenon_intro zenon_Hee ]. % 15.55/15.73 apply (zenon_L1103_); trivial. % 15.55/15.73 apply (zenon_L71_); trivial. % 15.55/15.73 (* end of lemma zenon_L1311_ *) % 15.55/15.73 assert (zenon_L1312_ : (((op (e3) (e2)) = (e0))\/(((op (e3) (e2)) = (e1))\/(((op (e3) (e2)) = (e2))\/((op (e3) (e2)) = (e3))))) -> (~((op (e3) (e3)) = (e3))) -> (~((op (e3) (e3)) = (e2))) -> ((op (e1) (e1)) = (e2)) -> (~((op (e3) (e3)) = (e0))) -> (((op (e3) (e3)) = (e0))\/(((op (e3) (e3)) = (e1))\/(((op (e3) (e3)) = (e2))\/((op (e3) (e3)) = (e3))))) -> ((op (e1) (e2)) = (e1)) -> (~((op (e1) (e2)) = (op (e3) (e2)))) -> ((op (e2) (e2)) = (e2)) -> (~((op (e2) (op (e3) (e2))) = (op (e3) (e2)))) -> ((op (e0) (e2)) = (e3)) -> (~((op (e0) (e2)) = (op (e3) (e2)))) -> False). % 15.55/15.73 do 0 intro. intros zenon_H25e zenon_H3e zenon_H3d zenon_H6e zenon_H3c zenon_H3b zenon_H117 zenon_H17d zenon_H35 zenon_H2af zenon_H50 zenon_H140. % 15.55/15.73 apply (zenon_or_s _ _ zenon_H25e); [ zenon_intro zenon_H167 | zenon_intro zenon_H25f ]. % 15.55/15.73 apply (zenon_L498_); trivial. % 15.55/15.73 apply (zenon_or_s _ _ zenon_H25f); [ zenon_intro zenon_H119 | zenon_intro zenon_H260 ]. % 15.55/15.73 apply (zenon_L759_); trivial. % 15.55/15.73 apply (zenon_or_s _ _ zenon_H260); [ zenon_intro zenon_H1dd | zenon_intro zenon_H106 ]. % 15.55/15.73 apply (zenon_L1083_); trivial. % 15.55/15.73 apply (zenon_L533_); trivial. % 15.55/15.73 (* end of lemma zenon_L1312_ *) % 15.55/15.73 assert (zenon_L1313_ : (((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) (e2)) = (op (e3) (e2)))) -> ((op (e0) (e2)) = (e3)) -> (~((op (e2) (op (e3) (e2))) = (op (e3) (e2)))) -> ((op (e2) (e2)) = (e2)) -> (~((op (e1) (e2)) = (op (e3) (e2)))) -> ((op (e1) (e2)) = (e1)) -> (((op (e3) (e3)) = (e0))\/(((op (e3) (e3)) = (e1))\/(((op (e3) (e3)) = (e2))\/((op (e3) (e3)) = (e3))))) -> (~((op (e3) (e3)) = (e0))) -> (~((op (e3) (e3)) = (e2))) -> (~((op (e3) (e3)) = (e3))) -> (((op (e3) (e2)) = (e0))\/(((op (e3) (e2)) = (e1))\/(((op (e3) (e2)) = (e2))\/((op (e3) (e2)) = (e3))))) -> (~((op (e1) (e1)) = (e3))) -> False). % 15.55/15.73 do 0 intro. intros zenon_H1b3 zenon_H145 zenon_H1b4 zenon_H140 zenon_H50 zenon_H2af zenon_H35 zenon_H17d zenon_H117 zenon_H3b zenon_H3c zenon_H3d zenon_H3e zenon_H25e zenon_H182. % 15.55/15.73 apply (zenon_or_s _ _ zenon_H1b3); [ zenon_intro zenon_H149 | zenon_intro zenon_H1b5 ]. % 15.55/15.73 exact (zenon_H145 zenon_H149). % 15.55/15.73 apply (zenon_or_s _ _ zenon_H1b5); [ zenon_intro zenon_H21 | zenon_intro zenon_H1b6 ]. % 15.55/15.73 exact (zenon_H1b4 zenon_H21). % 15.55/15.73 apply (zenon_or_s _ _ zenon_H1b6); [ zenon_intro zenon_H6e | zenon_intro zenon_H96 ]. % 15.55/15.73 apply (zenon_L1312_); trivial. % 15.55/15.73 exact (zenon_H182 zenon_H96). % 15.55/15.73 (* end of lemma zenon_L1313_ *) % 15.55/15.73 assert (zenon_L1314_ : ((~((op (e3) (e3)) = (e2)))\/((op (e3) (e2)) = (e3))) -> (((op (e0) (e2)) = (e3))\/(((op (e1) (e2)) = (e3))\/(((op (e2) (e2)) = (e3))\/((op (e3) (e2)) = (e3))))) -> ((op (e3) (e1)) = (e3)) -> (~((op (e3) (e1)) = (op (e3) (e2)))) -> (~((op (e2) (e2)) = (e3))) -> (~((e1) = (e3))) -> (~((op (e1) (e1)) = (e0))) -> (~((op (e1) (e1)) = (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)) = (e2)) -> (~((op (e2) (op (e3) (e2))) = (op (e3) (e2)))) -> ((op (e1) (e2)) = (e1)) -> (~((op (e1) (e2)) = (op (e3) (e2)))) -> (~((op (e3) (e3)) = (e0))) -> (((op (e3) (e3)) = (e0))\/(((op (e3) (e3)) = (e1))\/(((op (e3) (e3)) = (e2))\/((op (e3) (e3)) = (e3))))) -> (~((op (e1) (e1)) = (e3))) -> (((op (e1) (e1)) = (e0))\/(((op (e1) (e1)) = (e1))\/(((op (e1) (e1)) = (e2))\/((op (e1) (e1)) = (e3))))) -> (~((op (e3) (op (e3) (e3))) = (op (e3) (e3)))) -> ((~((op (e3) (e3)) = (e3)))\/((op (e3) (e3)) = (e3))) -> False). % 15.55/15.73 do 0 intro. intros zenon_H10e zenon_H175 zenon_H10a zenon_H135 zenon_H30 zenon_Ha3 zenon_H145 zenon_H1b4 zenon_H25e zenon_H140 zenon_H35 zenon_H2af zenon_H117 zenon_H17d zenon_H3c zenon_H3b zenon_H182 zenon_H1b3 zenon_H2be zenon_H10d. % 15.55/15.73 apply (zenon_or_s _ _ zenon_H10e); [ zenon_intro zenon_H3d | zenon_intro zenon_H106 ]. % 15.55/15.73 apply (zenon_or_s _ _ zenon_H10d); [ zenon_intro zenon_H3e | zenon_intro zenon_H42 ]. % 15.55/15.73 apply (zenon_or_s _ _ zenon_H175); [ zenon_intro zenon_H50 | zenon_intro zenon_H176 ]. % 15.55/15.73 apply (zenon_L1313_); trivial. % 15.55/15.73 apply (zenon_or_s _ _ zenon_H176); [ zenon_intro zenon_H88 | zenon_intro zenon_H177 ]. % 15.55/15.73 apply (zenon_L196_); trivial. % 15.55/15.73 apply (zenon_or_s _ _ zenon_H177); [ zenon_intro zenon_H34 | zenon_intro zenon_H106 ]. % 15.55/15.73 exact (zenon_H30 zenon_H34). % 15.55/15.73 apply (zenon_L115_); trivial. % 15.55/15.73 apply (zenon_L1041_); trivial. % 15.55/15.73 apply (zenon_L115_); trivial. % 15.55/15.73 (* end of lemma zenon_L1314_ *) % 15.55/15.73 assert (zenon_L1315_ : (~((op (e1) (e1)) = (e3))) -> (~((op (e1) (e1)) = (e0))) -> ((~((op (e3) (e3)) = (e3)))\/((op (e3) (e3)) = (e3))) -> (~((op (e3) (op (e3) (e3))) = (op (e3) (e3)))) -> (~((op (e0) (e0)) = (e1))) -> (((op (e0) (e0)) = (e1))\/(((op (e1) (e0)) = (e1))\/(((op (e2) (e0)) = (e1))\/((op (e3) (e0)) = (e1))))) -> (~((op (e0) (op (e3) (e0))) = (op (e3) (e0)))) -> (((op (e3) (e3)) = (e0))\/(((op (e3) (e3)) = (e1))\/(((op (e3) (e3)) = (e2))\/((op (e3) (e3)) = (e3))))) -> (~((op (e0) (e3)) = (op (e3) (e3)))) -> (~((op (e3) (e3)) = (e0))) -> (~((op (e1) (e2)) = (op (e1) (e3)))) -> (~((op (e2) (e0)) = (op (e2) (e3)))) -> (((op (e0) (e3)) = (e1))\/(((op (e1) (e3)) = (e1))\/(((op (e2) (e3)) = (e1))\/((op (e3) (e3)) = (e1))))) -> ((op (e1) (e2)) = (e1)) -> (~((op (e1) (e0)) = (op (e1) (e2)))) -> (~((e0) = (e1))) -> ((op (e0) (e2)) = (e0)) -> (((op (e0) (e0)) = (e1))\/(((op (e0) (e1)) = (e1))\/(((op (e0) (e2)) = (e1))\/((op (e0) (e3)) = (e1))))) -> (((op (e0) (e0)) = (e0))\/(((op (e1) (e0)) = (e0))\/(((op (e2) (e0)) = (e0))\/((op (e3) (e0)) = (e0))))) -> (((op (e2) (e3)) = (e0))\/(((op (e2) (e3)) = (e1))\/(((op (e2) (e3)) = (e2))\/((op (e2) (e3)) = (e3))))) -> (((op (e2) (e0)) = (e3))\/(((op (e2) (e1)) = (e3))\/(((op (e2) (e2)) = (e3))\/((op (e2) (e3)) = (e3))))) -> (~((op (e2) (e2)) = (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)) = (e2)))\/((op (e1) (e2)) = (e1))) -> ((~((op (e2) (e2)) = (e1)))\/((op (e2) (e1)) = (e2))) -> ((~((op (e3) (e3)) = (e0)))\/((op (e3) (e0)) = (e3))) -> (~((op (e3) (e0)) = (op (e3) (e1)))) -> (~((op (e0) (e0)) = (e3))) -> (~((e1) = (e3))) -> (((op (e0) (e2)) = (e1))\/(((op (e1) (e2)) = (e1))\/(((op (e2) (e2)) = (e1))\/((op (e3) (e2)) = (e1))))) -> (((op (e1) (e2)) = (e0))\/(((op (e1) (e2)) = (e1))\/(((op (e1) (e2)) = (e2))\/((op (e1) (e2)) = (e3))))) -> (~((op (e0) (e2)) = (op (e1) (e2)))) -> (((op (e3) (e0)) = (e3))\/(((op (e3) (e1)) = (e3))\/(((op (e3) (e2)) = (e3))\/((op (e3) (e3)) = (e3))))) -> (((op (e3) (e0)) = (e2))\/(((op (e3) (e1)) = (e2))\/(((op (e3) (e2)) = (e2))\/((op (e3) (e3)) = (e2))))) -> (~((op (e0) (e1)) = (op (e3) (e1)))) -> (((op (e1) (e1)) = (e0))\/(((op (e1) (e1)) = (e1))\/(((op (e1) (e1)) = (e2))\/((op (e1) (e1)) = (e3))))) -> (~((op (e2) (e1)) = (op (e2) (e2)))) -> (~((e2) = (e3))) -> (((op (e0) (e1)) = (e2))\/(((op (e1) (e1)) = (e2))\/(((op (e2) (e1)) = (e2))\/((op (e3) (e1)) = (e2))))) -> ((~((op (e3) (e3)) = (e2)))\/((op (e3) (e2)) = (e3))) -> (~((op (e2) (e0)) = (op (e3) (e0)))) -> (((op (e0) (e2)) = (e3))\/(((op (e1) (e2)) = (e3))\/(((op (e2) (e2)) = (e3))\/((op (e3) (e2)) = (e3))))) -> (~((op (e0) (e2)) = (op (e0) (e3)))) -> (((op (e1) (e0)) = (e2))\/(((op (e1) (e1)) = (e2))\/(((op (e1) (e2)) = (e2))\/((op (e1) (e3)) = (e2))))) -> (~((op (e0) (e3)) = (op (e1) (e3)))) -> ((op (e2) (e2)) = (e2)) -> (~((op (e1) (e2)) = (op (e2) (e2)))) -> (~((e1) = (e2))) -> (((op (e0) (e1)) = (e1))\/(((op (e1) (e1)) = (e1))\/(((op (e2) (e1)) = (e1))\/((op (e3) (e1)) = (e1))))) -> (~((op (e1) (e0)) = (op (e3) (e0)))) -> (((op (e3) (e2)) = (e0))\/(((op (e3) (e2)) = (e1))\/(((op (e3) (e2)) = (e2))\/((op (e3) (e2)) = (e3))))) -> (~((op (e1) (e2)) = (op (e3) (e2)))) -> (((op (e1) (e0)) = (e3))\/(((op (e1) (e1)) = (e3))\/(((op (e1) (e2)) = (e3))\/((op (e1) (e3)) = (e3))))) -> (~((op (e2) (op (e3) (e2))) = (op (e3) (e2)))) -> (~((op (e3) (e1)) = (op (e3) (e2)))) -> (~((op (e0) (e2)) = (op (e3) (e2)))) -> (((op (e3) (e0)) = (e1))\/(((op (e3) (e1)) = (e1))\/(((op (e3) (e2)) = (e1))\/((op (e3) (e3)) = (e1))))) -> (((op (e0) (e3)) = (e0))\/(((op (e0) (e3)) = (e1))\/(((op (e0) (e3)) = (e2))\/((op (e0) (e3)) = (e3))))) -> (~((op (e3) (e0)) = (op (e3) (e2)))) -> (~((op (e1) (e0)) = (op (e2) (e0)))) -> (~((op (e1) (op (e3) (e1))) = (op (e3) (e1)))) -> (~((op (e0) (e3)) = (op (e2) (e3)))) -> (((op (e2) (e0)) = (e1))\/(((op (e2) (e1)) = (e1))\/(((op (e2) (e2)) = (e1))\/((op (e2) (e3)) = (e1))))) -> (((op (e0) (e0)) = (e3))\/(((op (e1) (e0)) = (e3))\/(((op (e2) (e0)) = (e3))\/((op (e3) (e0)) = (e3))))) -> ((~((op (e3) (e3)) = (e1)))\/((op (e3) (e1)) = (e3))) -> (~((op (e2) (e2)) = (op (e2) (e3)))) -> ((~((op (e2) (e2)) = (e3)))\/((op (e2) (e3)) = (e2))) -> (~((op (e1) (e0)) = (op (e1) (e3)))) -> ((~((op (e1) (e1)) = (e3)))\/((op (e1) (e3)) = (e1))) -> (~((op (e1) (e0)) = (op (e1) (e1)))) -> ((~((op (e1) (e1)) = (e1)))\/((op (e1) (e1)) = (e1))) -> (((op (e3) (e0)) = (e0))\/(((op (e3) (e1)) = (e0))\/(((op (e3) (e2)) = (e0))\/((op (e3) (e3)) = (e0))))) -> (~((op (e1) (e1)) = (e1))) -> (~((op (e0) (e0)) = (e0))) -> False). % 15.55/15.73 do 0 intro. intros zenon_H182 zenon_H145 zenon_H10d zenon_H2be zenon_H45 zenon_Hf1 zenon_H2b8 zenon_H3b zenon_H36 zenon_H3c zenon_H1d0 zenon_Hce zenon_H121 zenon_H117 zenon_H166 zenon_H9e zenon_Hab zenon_H44 zenon_Hf0 zenon_H2ab zenon_He6 zenon_H30 zenon_Hde zenon_H58 zenon_H1d3 zenon_H1e3 zenon_H10f zenon_H109 zenon_H59 zenon_Ha3 zenon_H11b zenon_H1d5 zenon_H87 zenon_H2d5 zenon_H1df zenon_H138 zenon_H1b3 zenon_H157 zenon_H6a zenon_H1a2 zenon_H10e zenon_H1e5 zenon_H175 zenon_Hc9 zenon_H84 zenon_H80 zenon_H35 zenon_H7d zenon_Ha7 zenon_H228 zenon_H22e zenon_H25e zenon_H17d zenon_H90 zenon_H2af zenon_H135 zenon_H140 zenon_H146 zenon_H254 zenon_H105 zenon_H247 zenon_H2b4 zenon_Hb4 zenon_Hb7 zenon_Hbe zenon_H10c zenon_H15f zenon_H1c3 zenon_H1cf zenon_H1d2 zenon_Hd7 zenon_H1d8 zenon_H1f6 zenon_H1b4 zenon_H20. % 15.55/15.73 apply (zenon_or_s _ _ zenon_H10c); [ zenon_intro zenon_H104 | zenon_intro zenon_H10a ]. % 15.55/15.73 apply (zenon_or_s _ _ zenon_H10e); [ zenon_intro zenon_H3d | zenon_intro zenon_H106 ]. % 15.55/15.73 apply (zenon_or_s _ _ zenon_H10d); [ zenon_intro zenon_H3e | zenon_intro zenon_H42 ]. % 15.55/15.73 apply (zenon_L1305_); trivial. % 15.55/15.73 apply (zenon_L1041_); trivial. % 15.55/15.73 apply (zenon_L1311_); trivial. % 15.55/15.73 apply (zenon_L1314_); trivial. % 15.55/15.73 (* end of lemma zenon_L1315_ *) % 15.55/15.73 assert (zenon_L1316_ : (((op (e0) (e2)) = (e1))\/(((op (e1) (e2)) = (e1))\/(((op (e2) (e2)) = (e1))\/((op (e3) (e2)) = (e1))))) -> (~((e0) = (e1))) -> (~((e1) = (e3))) -> ((op (e1) (e2)) = (e3)) -> (~((op (e2) (e2)) = (e1))) -> (((op (e3) (e0)) = (e0))\/(((op (e3) (e1)) = (e0))\/(((op (e3) (e2)) = (e0))\/((op (e3) (e3)) = (e0))))) -> ((op (e3) (e0)) = (e3)) -> (~((e0) = (e3))) -> ((op (e1) (e0)) = (e0)) -> (~((op (e1) (op (e3) (e1))) = (op (e3) (e1)))) -> ((op (e0) (e2)) = (e0)) -> (~((op (e0) (e2)) = (op (e3) (e2)))) -> ((op (e0) (e0)) = (e2)) -> False). % 15.55/15.73 do 0 intro. intros zenon_H11b zenon_H9e zenon_Ha3 zenon_H88 zenon_H52 zenon_H1f6 zenon_Hba zenon_H4b zenon_Had zenon_H2b4 zenon_Hab zenon_H140 zenon_H92. % 15.55/15.73 apply (zenon_or_s _ _ zenon_H11b); [ zenon_intro zenon_H29 | zenon_intro zenon_H11c ]. % 15.55/15.73 apply (zenon_L37_); trivial. % 15.55/15.73 apply (zenon_or_s _ _ zenon_H11c); [ zenon_intro zenon_H117 | zenon_intro zenon_H11d ]. % 15.55/15.73 apply (zenon_L196_); trivial. % 15.55/15.73 apply (zenon_or_s _ _ zenon_H11d); [ zenon_intro zenon_H2a | zenon_intro zenon_H119 ]. % 15.55/15.73 exact (zenon_H52 zenon_H2a). % 15.55/15.73 apply (zenon_L1240_); trivial. % 15.55/15.73 (* end of lemma zenon_L1316_ *) % 15.55/15.73 assert (zenon_L1317_ : (~((op (e0) (e0)) = (e0))) -> (~((op (e1) (e1)) = (e1))) -> (((op (e3) (e0)) = (e0))\/(((op (e3) (e1)) = (e0))\/(((op (e3) (e2)) = (e0))\/((op (e3) (e3)) = (e0))))) -> ((~((op (e1) (e1)) = (e1)))\/((op (e1) (e1)) = (e1))) -> (~((op (e1) (e0)) = (op (e1) (e1)))) -> ((~((op (e1) (e1)) = (e3)))\/((op (e1) (e3)) = (e1))) -> (~((op (e1) (e0)) = (op (e1) (e3)))) -> ((~((op (e2) (e2)) = (e3)))\/((op (e2) (e3)) = (e2))) -> (~((op (e2) (e2)) = (op (e2) (e3)))) -> ((~((op (e3) (e3)) = (e1)))\/((op (e3) (e1)) = (e3))) -> (((op (e0) (e0)) = (e3))\/(((op (e1) (e0)) = (e3))\/(((op (e2) (e0)) = (e3))\/((op (e3) (e0)) = (e3))))) -> (((op (e2) (e0)) = (e1))\/(((op (e2) (e1)) = (e1))\/(((op (e2) (e2)) = (e1))\/((op (e2) (e3)) = (e1))))) -> (~((op (e0) (e3)) = (op (e2) (e3)))) -> (~((op (e1) (op (e3) (e1))) = (op (e3) (e1)))) -> (~((op (e1) (e0)) = (op (e2) (e0)))) -> (~((op (e3) (e0)) = (op (e3) (e2)))) -> (((op (e0) (e3)) = (e0))\/(((op (e0) (e3)) = (e1))\/(((op (e0) (e3)) = (e2))\/((op (e0) (e3)) = (e3))))) -> (((op (e3) (e0)) = (e1))\/(((op (e3) (e1)) = (e1))\/(((op (e3) (e2)) = (e1))\/((op (e3) (e3)) = (e1))))) -> (~((op (e0) (e2)) = (op (e3) (e2)))) -> (~((op (e3) (e1)) = (op (e3) (e2)))) -> (~((op (e2) (op (e3) (e2))) = (op (e3) (e2)))) -> (((op (e1) (e0)) = (e3))\/(((op (e1) (e1)) = (e3))\/(((op (e1) (e2)) = (e3))\/((op (e1) (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 (e1) (e0)) = (op (e3) (e0)))) -> (((op (e0) (e1)) = (e1))\/(((op (e1) (e1)) = (e1))\/(((op (e2) (e1)) = (e1))\/((op (e3) (e1)) = (e1))))) -> (~((e1) = (e2))) -> (~((op (e1) (e2)) = (op (e2) (e2)))) -> ((op (e2) (e2)) = (e2)) -> (~((op (e0) (e3)) = (op (e1) (e3)))) -> (((op (e1) (e0)) = (e2))\/(((op (e1) (e1)) = (e2))\/(((op (e1) (e2)) = (e2))\/((op (e1) (e3)) = (e2))))) -> (~((op (e0) (e2)) = (op (e0) (e3)))) -> (((op (e0) (e2)) = (e3))\/(((op (e1) (e2)) = (e3))\/(((op (e2) (e2)) = (e3))\/((op (e3) (e2)) = (e3))))) -> (~((op (e2) (e0)) = (op (e3) (e0)))) -> ((~((op (e3) (e3)) = (e2)))\/((op (e3) (e2)) = (e3))) -> (((op (e0) (e1)) = (e2))\/(((op (e1) (e1)) = (e2))\/(((op (e2) (e1)) = (e2))\/((op (e3) (e1)) = (e2))))) -> (~((e2) = (e3))) -> (~((op (e2) (e1)) = (op (e2) (e2)))) -> (((op (e1) (e1)) = (e0))\/(((op (e1) (e1)) = (e1))\/(((op (e1) (e1)) = (e2))\/((op (e1) (e1)) = (e3))))) -> (~((op (e0) (e1)) = (op (e3) (e1)))) -> (((op (e3) (e0)) = (e2))\/(((op (e3) (e1)) = (e2))\/(((op (e3) (e2)) = (e2))\/((op (e3) (e3)) = (e2))))) -> (((op (e3) (e0)) = (e3))\/(((op (e3) (e1)) = (e3))\/(((op (e3) (e2)) = (e3))\/((op (e3) (e3)) = (e3))))) -> (~((op (e0) (e2)) = (op (e1) (e2)))) -> (((op (e1) (e2)) = (e0))\/(((op (e1) (e2)) = (e1))\/(((op (e1) (e2)) = (e2))\/((op (e1) (e2)) = (e3))))) -> (((op (e0) (e2)) = (e1))\/(((op (e1) (e2)) = (e1))\/(((op (e2) (e2)) = (e1))\/((op (e3) (e2)) = (e1))))) -> (~((e1) = (e3))) -> (~((op (e0) (e0)) = (e3))) -> (~((op (e3) (e0)) = (op (e3) (e1)))) -> ((~((op (e3) (e3)) = (e0)))\/((op (e3) (e0)) = (e3))) -> ((~((op (e2) (e2)) = (e1)))\/((op (e2) (e1)) = (e2))) -> ((~((op (e1) (e1)) = (e2)))\/((op (e1) (e2)) = (e1))) -> (((op (e0) (e0)) = (e3))\/(((op (e0) (e1)) = (e3))\/(((op (e0) (e2)) = (e3))\/((op (e0) (e3)) = (e3))))) -> (~((op (e0) (e1)) = (op (e2) (e1)))) -> (((op (e2) (e0)) = (e3))\/(((op (e2) (e1)) = (e3))\/(((op (e2) (e2)) = (e3))\/((op (e2) (e3)) = (e3))))) -> (((op (e2) (e3)) = (e0))\/(((op (e2) (e3)) = (e1))\/(((op (e2) (e3)) = (e2))\/((op (e2) (e3)) = (e3))))) -> (((op (e0) (e0)) = (e0))\/(((op (e1) (e0)) = (e0))\/(((op (e2) (e0)) = (e0))\/((op (e3) (e0)) = (e0))))) -> (((op (e0) (e0)) = (e1))\/(((op (e0) (e1)) = (e1))\/(((op (e0) (e2)) = (e1))\/((op (e0) (e3)) = (e1))))) -> ((op (e0) (e2)) = (e0)) -> (~((e0) = (e1))) -> (~((op (e1) (e0)) = (op (e1) (e2)))) -> ((op (e1) (e2)) = (e1)) -> (((op (e0) (e3)) = (e1))\/(((op (e1) (e3)) = (e1))\/(((op (e2) (e3)) = (e1))\/((op (e3) (e3)) = (e1))))) -> (~((op (e2) (e0)) = (op (e2) (e3)))) -> (~((op (e1) (e2)) = (op (e1) (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) (op (e3) (e0))) = (op (e3) (e0)))) -> (((op (e0) (e0)) = (e1))\/(((op (e1) (e0)) = (e1))\/(((op (e2) (e0)) = (e1))\/((op (e3) (e0)) = (e1))))) -> (~((op (e0) (e0)) = (e1))) -> (~((op (e3) (op (e3) (e3))) = (op (e3) (e3)))) -> ((~((op (e3) (e3)) = (e3)))\/((op (e3) (e3)) = (e3))) -> (~((op (e1) (e1)) = (e0))) -> False). % 15.55/15.73 do 0 intro. intros zenon_H20 zenon_H1b4 zenon_H1f6 zenon_H1d8 zenon_Hd7 zenon_H1d2 zenon_H1cf zenon_H1c3 zenon_H15f zenon_H10c zenon_Hbe zenon_Hb7 zenon_Hb4 zenon_H2b4 zenon_H247 zenon_H105 zenon_H254 zenon_H146 zenon_H140 zenon_H135 zenon_H2af zenon_H90 zenon_H17d zenon_H25e zenon_H22e zenon_H228 zenon_Ha7 zenon_H7d zenon_H35 zenon_H80 zenon_H84 zenon_Hc9 zenon_H175 zenon_H1e5 zenon_H10e zenon_H1a2 zenon_H6a zenon_H157 zenon_H1b3 zenon_H138 zenon_H1df zenon_H2d5 zenon_H87 zenon_H1d5 zenon_H11b zenon_Ha3 zenon_H59 zenon_H109 zenon_H10f zenon_H1e3 zenon_H1d3 zenon_H58 zenon_Hde zenon_He6 zenon_H2ab zenon_Hf0 zenon_H44 zenon_Hab zenon_H9e zenon_H166 zenon_H117 zenon_H121 zenon_Hce zenon_H1d0 zenon_H36 zenon_H3b zenon_H2b8 zenon_Hf1 zenon_H45 zenon_H2be zenon_H10d zenon_H145. % 15.55/15.73 apply (zenon_or_s _ _ zenon_H1d2); [ zenon_intro zenon_H182 | zenon_intro zenon_H11f ]. % 15.55/15.73 apply (zenon_or_s _ _ zenon_H1c3); [ zenon_intro zenon_H30 | zenon_intro zenon_H124 ]. % 15.55/15.73 apply (zenon_or_s _ _ zenon_H10f); [ zenon_intro zenon_H3c | zenon_intro zenon_Hba ]. % 15.55/15.73 apply (zenon_L1315_); trivial. % 15.55/15.73 apply (zenon_L1095_); trivial. % 15.55/15.73 apply (zenon_L137_); trivial. % 15.55/15.73 apply (zenon_L237_); trivial. % 15.55/15.73 (* end of lemma zenon_L1317_ *) % 15.55/15.73 assert (zenon_L1318_ : (~((op (e1) (e1)) = (e0))) -> ((~((op (e3) (e3)) = (e3)))\/((op (e3) (e3)) = (e3))) -> (~((op (e3) (op (e3) (e3))) = (op (e3) (e3)))) -> (~((op (e0) (e0)) = (e1))) -> (((op (e0) (e0)) = (e1))\/(((op (e1) (e0)) = (e1))\/(((op (e2) (e0)) = (e1))\/((op (e3) (e0)) = (e1))))) -> (~((op (e0) (op (e3) (e0))) = (op (e3) (e0)))) -> (((op (e3) (e3)) = (e0))\/(((op (e3) (e3)) = (e1))\/(((op (e3) (e3)) = (e2))\/((op (e3) (e3)) = (e3))))) -> (~((op (e0) (e3)) = (op (e3) (e3)))) -> (~((op (e1) (e2)) = (op (e1) (e3)))) -> (~((op (e2) (e0)) = (op (e2) (e3)))) -> (((op (e0) (e3)) = (e1))\/(((op (e1) (e3)) = (e1))\/(((op (e2) (e3)) = (e1))\/((op (e3) (e3)) = (e1))))) -> (~((op (e1) (e0)) = (op (e1) (e2)))) -> (~((e0) = (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 (e2) (e0)) = (e0))\/((op (e3) (e0)) = (e0))))) -> (((op (e2) (e3)) = (e0))\/(((op (e2) (e3)) = (e1))\/(((op (e2) (e3)) = (e2))\/((op (e2) (e3)) = (e3))))) -> (((op (e2) (e0)) = (e3))\/(((op (e2) (e1)) = (e3))\/(((op (e2) (e2)) = (e3))\/((op (e2) (e3)) = (e3))))) -> (~((op (e0) (e1)) = (op (e2) (e1)))) -> (((op (e0) (e0)) = (e3))\/(((op (e0) (e1)) = (e3))\/(((op (e0) (e2)) = (e3))\/((op (e0) (e3)) = (e3))))) -> ((~((op (e1) (e1)) = (e2)))\/((op (e1) (e2)) = (e1))) -> ((~((op (e2) (e2)) = (e1)))\/((op (e2) (e1)) = (e2))) -> ((~((op (e3) (e3)) = (e0)))\/((op (e3) (e0)) = (e3))) -> (~((op (e3) (e0)) = (op (e3) (e1)))) -> (~((op (e0) (e0)) = (e3))) -> (~((e1) = (e3))) -> (((op (e0) (e2)) = (e1))\/(((op (e1) (e2)) = (e1))\/(((op (e2) (e2)) = (e1))\/((op (e3) (e2)) = (e1))))) -> (((op (e3) (e0)) = (e3))\/(((op (e3) (e1)) = (e3))\/(((op (e3) (e2)) = (e3))\/((op (e3) (e3)) = (e3))))) -> (((op (e3) (e0)) = (e2))\/(((op (e3) (e1)) = (e2))\/(((op (e3) (e2)) = (e2))\/((op (e3) (e3)) = (e2))))) -> (~((op (e0) (e1)) = (op (e3) (e1)))) -> (((op (e1) (e1)) = (e0))\/(((op (e1) (e1)) = (e1))\/(((op (e1) (e1)) = (e2))\/((op (e1) (e1)) = (e3))))) -> (~((op (e2) (e1)) = (op (e2) (e2)))) -> (~((e2) = (e3))) -> (((op (e0) (e1)) = (e2))\/(((op (e1) (e1)) = (e2))\/(((op (e2) (e1)) = (e2))\/((op (e3) (e1)) = (e2))))) -> ((~((op (e3) (e3)) = (e2)))\/((op (e3) (e2)) = (e3))) -> (~((op (e2) (e0)) = (op (e3) (e0)))) -> (((op (e0) (e2)) = (e3))\/(((op (e1) (e2)) = (e3))\/(((op (e2) (e2)) = (e3))\/((op (e3) (e2)) = (e3))))) -> (~((op (e0) (e2)) = (op (e0) (e3)))) -> (((op (e1) (e0)) = (e2))\/(((op (e1) (e1)) = (e2))\/(((op (e1) (e2)) = (e2))\/((op (e1) (e3)) = (e2))))) -> (~((op (e0) (e3)) = (op (e1) (e3)))) -> (~((e1) = (e2))) -> (((op (e0) (e1)) = (e1))\/(((op (e1) (e1)) = (e1))\/(((op (e2) (e1)) = (e1))\/((op (e3) (e1)) = (e1))))) -> (~((op (e1) (e0)) = (op (e3) (e0)))) -> (((op (e3) (e2)) = (e0))\/(((op (e3) (e2)) = (e1))\/(((op (e3) (e2)) = (e2))\/((op (e3) (e2)) = (e3))))) -> (((op (e1) (e0)) = (e3))\/(((op (e1) (e1)) = (e3))\/(((op (e1) (e2)) = (e3))\/((op (e1) (e3)) = (e3))))) -> (~((op (e2) (op (e3) (e2))) = (op (e3) (e2)))) -> (~((op (e3) (e1)) = (op (e3) (e2)))) -> (~((op (e0) (e2)) = (op (e3) (e2)))) -> (((op (e3) (e0)) = (e1))\/(((op (e3) (e1)) = (e1))\/(((op (e3) (e2)) = (e1))\/((op (e3) (e3)) = (e1))))) -> (((op (e0) (e3)) = (e0))\/(((op (e0) (e3)) = (e1))\/(((op (e0) (e3)) = (e2))\/((op (e0) (e3)) = (e3))))) -> (~((op (e3) (e0)) = (op (e3) (e2)))) -> (~((op (e1) (e0)) = (op (e2) (e0)))) -> (~((op (e1) (op (e3) (e1))) = (op (e3) (e1)))) -> (~((op (e0) (e3)) = (op (e2) (e3)))) -> (((op (e2) (e0)) = (e1))\/(((op (e2) (e1)) = (e1))\/(((op (e2) (e2)) = (e1))\/((op (e2) (e3)) = (e1))))) -> (((op (e0) (e0)) = (e3))\/(((op (e1) (e0)) = (e3))\/(((op (e2) (e0)) = (e3))\/((op (e3) (e0)) = (e3))))) -> ((~((op (e3) (e3)) = (e1)))\/((op (e3) (e1)) = (e3))) -> (~((op (e2) (e2)) = (op (e2) (e3)))) -> ((~((op (e2) (e2)) = (e3)))\/((op (e2) (e3)) = (e2))) -> (~((op (e1) (e0)) = (op (e1) (e3)))) -> ((~((op (e1) (e1)) = (e3)))\/((op (e1) (e3)) = (e1))) -> (~((op (e1) (e0)) = (op (e1) (e1)))) -> ((~((op (e1) (e1)) = (e1)))\/((op (e1) (e1)) = (e1))) -> (((op (e3) (e0)) = (e0))\/(((op (e3) (e1)) = (e0))\/(((op (e3) (e2)) = (e0))\/((op (e3) (e3)) = (e0))))) -> (~((op (e1) (e1)) = (e1))) -> (~((op (e0) (e0)) = (e0))) -> (~((op (e2) (e2)) = (e1))) -> (((op (e1) (e2)) = (e0))\/(((op (e1) (e2)) = (e1))\/(((op (e1) (e2)) = (e2))\/((op (e1) (e2)) = (e3))))) -> ((op (e0) (e2)) = (e0)) -> (~((op (e1) (e2)) = (op (e3) (e2)))) -> (~((op (e1) (e2)) = (op (e2) (e2)))) -> ((op (e2) (e2)) = (e2)) -> (~((op (e0) (e2)) = (op (e1) (e2)))) -> ((op (e0) (e2)) = (e3)) -> False). % 15.55/15.73 do 0 intro. intros zenon_H145 zenon_H10d zenon_H2be zenon_H45 zenon_Hf1 zenon_H2b8 zenon_H3b zenon_H36 zenon_H1d0 zenon_Hce zenon_H121 zenon_H166 zenon_H9e zenon_H44 zenon_Hf0 zenon_H2ab zenon_He6 zenon_Hde zenon_H58 zenon_H1d3 zenon_H1e3 zenon_H10f zenon_H109 zenon_H59 zenon_Ha3 zenon_H11b zenon_H2d5 zenon_H1df zenon_H138 zenon_H1b3 zenon_H157 zenon_H6a zenon_H1a2 zenon_H10e zenon_H1e5 zenon_H175 zenon_Hc9 zenon_H84 zenon_H80 zenon_Ha7 zenon_H228 zenon_H22e zenon_H25e zenon_H90 zenon_H2af zenon_H135 zenon_H140 zenon_H146 zenon_H254 zenon_H105 zenon_H247 zenon_H2b4 zenon_Hb4 zenon_Hb7 zenon_Hbe zenon_H10c zenon_H15f zenon_H1c3 zenon_H1cf zenon_H1d2 zenon_Hd7 zenon_H1d8 zenon_H1f6 zenon_H1b4 zenon_H20 zenon_H52 zenon_H1d5 zenon_Hab zenon_H17d zenon_H7d zenon_H35 zenon_H87 zenon_H50. % 15.55/15.73 apply (zenon_or_s _ _ zenon_H11b); [ zenon_intro zenon_H29 | zenon_intro zenon_H11c ]. % 15.55/15.73 apply (zenon_L29_); trivial. % 15.55/15.73 apply (zenon_or_s _ _ zenon_H11c); [ zenon_intro zenon_H117 | zenon_intro zenon_H11d ]. % 15.55/15.73 apply (zenon_L1317_); trivial. % 15.55/15.73 apply (zenon_or_s _ _ zenon_H11d); [ zenon_intro zenon_H2a | zenon_intro zenon_H119 ]. % 15.55/15.73 exact (zenon_H52 zenon_H2a). % 15.55/15.73 apply (zenon_L760_); trivial. % 15.55/15.73 (* end of lemma zenon_L1318_ *) % 15.55/15.73 assert (zenon_L1319_ : (~((op (e0) (e2)) = (op (e1) (e2)))) -> ((op (e2) (e2)) = (e2)) -> (~((op (e1) (e2)) = (op (e2) (e2)))) -> (~((op (e1) (e2)) = (op (e3) (e2)))) -> ((op (e0) (e2)) = (e0)) -> (((op (e1) (e2)) = (e0))\/(((op (e1) (e2)) = (e1))\/(((op (e1) (e2)) = (e2))\/((op (e1) (e2)) = (e3))))) -> (~((op (e2) (e2)) = (e1))) -> (~((op (e0) (e0)) = (e0))) -> (~((op (e1) (e1)) = (e1))) -> (((op (e3) (e0)) = (e0))\/(((op (e3) (e1)) = (e0))\/(((op (e3) (e2)) = (e0))\/((op (e3) (e3)) = (e0))))) -> ((~((op (e1) (e1)) = (e1)))\/((op (e1) (e1)) = (e1))) -> (~((op (e1) (e0)) = (op (e1) (e1)))) -> ((~((op (e1) (e1)) = (e3)))\/((op (e1) (e3)) = (e1))) -> (~((op (e1) (e0)) = (op (e1) (e3)))) -> ((~((op (e2) (e2)) = (e3)))\/((op (e2) (e3)) = (e2))) -> (~((op (e2) (e2)) = (op (e2) (e3)))) -> ((~((op (e3) (e3)) = (e1)))\/((op (e3) (e1)) = (e3))) -> (((op (e0) (e0)) = (e3))\/(((op (e1) (e0)) = (e3))\/(((op (e2) (e0)) = (e3))\/((op (e3) (e0)) = (e3))))) -> (((op (e2) (e0)) = (e1))\/(((op (e2) (e1)) = (e1))\/(((op (e2) (e2)) = (e1))\/((op (e2) (e3)) = (e1))))) -> (~((op (e1) (op (e3) (e1))) = (op (e3) (e1)))) -> (~((op (e1) (e0)) = (op (e2) (e0)))) -> (~((op (e3) (e0)) = (op (e3) (e2)))) -> (((op (e0) (e3)) = (e0))\/(((op (e0) (e3)) = (e1))\/(((op (e0) (e3)) = (e2))\/((op (e0) (e3)) = (e3))))) -> (((op (e3) (e0)) = (e1))\/(((op (e3) (e1)) = (e1))\/(((op (e3) (e2)) = (e1))\/((op (e3) (e3)) = (e1))))) -> (~((op (e0) (e2)) = (op (e3) (e2)))) -> (~((op (e3) (e1)) = (op (e3) (e2)))) -> (~((op (e2) (op (e3) (e2))) = (op (e3) (e2)))) -> (((op (e1) (e0)) = (e3))\/(((op (e1) (e1)) = (e3))\/(((op (e1) (e2)) = (e3))\/((op (e1) (e3)) = (e3))))) -> (((op (e3) (e2)) = (e0))\/(((op (e3) (e2)) = (e1))\/(((op (e3) (e2)) = (e2))\/((op (e3) (e2)) = (e3))))) -> (~((op (e1) (e0)) = (op (e3) (e0)))) -> (((op (e0) (e1)) = (e1))\/(((op (e1) (e1)) = (e1))\/(((op (e2) (e1)) = (e1))\/((op (e3) (e1)) = (e1))))) -> (~((e1) = (e2))) -> (~((op (e0) (e3)) = (op (e1) (e3)))) -> (((op (e1) (e0)) = (e2))\/(((op (e1) (e1)) = (e2))\/(((op (e1) (e2)) = (e2))\/((op (e1) (e3)) = (e2))))) -> (~((op (e0) (e2)) = (op (e0) (e3)))) -> (((op (e0) (e2)) = (e3))\/(((op (e1) (e2)) = (e3))\/(((op (e2) (e2)) = (e3))\/((op (e3) (e2)) = (e3))))) -> (~((op (e2) (e0)) = (op (e3) (e0)))) -> ((~((op (e3) (e3)) = (e2)))\/((op (e3) (e2)) = (e3))) -> (((op (e0) (e1)) = (e2))\/(((op (e1) (e1)) = (e2))\/(((op (e2) (e1)) = (e2))\/((op (e3) (e1)) = (e2))))) -> (~((e2) = (e3))) -> (~((op (e2) (e1)) = (op (e2) (e2)))) -> (((op (e1) (e1)) = (e0))\/(((op (e1) (e1)) = (e1))\/(((op (e1) (e1)) = (e2))\/((op (e1) (e1)) = (e3))))) -> (~((op (e0) (e1)) = (op (e3) (e1)))) -> (((op (e3) (e0)) = (e2))\/(((op (e3) (e1)) = (e2))\/(((op (e3) (e2)) = (e2))\/((op (e3) (e3)) = (e2))))) -> (((op (e3) (e0)) = (e3))\/(((op (e3) (e1)) = (e3))\/(((op (e3) (e2)) = (e3))\/((op (e3) (e3)) = (e3))))) -> (((op (e0) (e2)) = (e1))\/(((op (e1) (e2)) = (e1))\/(((op (e2) (e2)) = (e1))\/((op (e3) (e2)) = (e1))))) -> (~((op (e0) (e0)) = (e3))) -> (~((op (e3) (e0)) = (op (e3) (e1)))) -> ((~((op (e3) (e3)) = (e0)))\/((op (e3) (e0)) = (e3))) -> ((~((op (e2) (e2)) = (e1)))\/((op (e2) (e1)) = (e2))) -> ((~((op (e1) (e1)) = (e2)))\/((op (e1) (e2)) = (e1))) -> (((op (e0) (e0)) = (e3))\/(((op (e0) (e1)) = (e3))\/(((op (e0) (e2)) = (e3))\/((op (e0) (e3)) = (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) (e0)) = (e0))\/(((op (e1) (e0)) = (e0))\/(((op (e2) (e0)) = (e0))\/((op (e3) (e0)) = (e0))))) -> (((op (e0) (e0)) = (e1))\/(((op (e0) (e1)) = (e1))\/(((op (e0) (e2)) = (e1))\/((op (e0) (e3)) = (e1))))) -> (~((e0) = (e1))) -> (~((op (e1) (e0)) = (op (e1) (e2)))) -> (((op (e0) (e3)) = (e1))\/(((op (e1) (e3)) = (e1))\/(((op (e2) (e3)) = (e1))\/((op (e3) (e3)) = (e1))))) -> (~((op (e2) (e0)) = (op (e2) (e3)))) -> (~((op (e1) (e2)) = (op (e1) (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) (op (e3) (e0))) = (op (e3) (e0)))) -> (((op (e0) (e0)) = (e1))\/(((op (e1) (e0)) = (e1))\/(((op (e2) (e0)) = (e1))\/((op (e3) (e0)) = (e1))))) -> (~((op (e0) (e0)) = (e1))) -> (~((op (e3) (op (e3) (e3))) = (op (e3) (e3)))) -> ((~((op (e3) (e3)) = (e3)))\/((op (e3) (e3)) = (e3))) -> (~((op (e1) (e1)) = (e0))) -> (((op (e2) (e0)) = (e3))\/(((op (e2) (e1)) = (e3))\/(((op (e2) (e2)) = (e3))\/((op (e2) (e3)) = (e3))))) -> (~((e1) = (e3))) -> ((op (e2) (e0)) = (e1)) -> (~((op (e2) (e1)) = (op (e3) (e1)))) -> ((op (e3) (e1)) = (e3)) -> (~((op (e2) (e2)) = (e3))) -> (~((op (e0) (e3)) = (op (e2) (e3)))) -> False). % 15.55/15.73 do 0 intro. intros zenon_H87 zenon_H35 zenon_H7d zenon_H17d zenon_Hab zenon_H1d5 zenon_H52 zenon_H20 zenon_H1b4 zenon_H1f6 zenon_H1d8 zenon_Hd7 zenon_H1d2 zenon_H1cf zenon_H1c3 zenon_H15f zenon_H10c zenon_Hbe zenon_Hb7 zenon_H2b4 zenon_H247 zenon_H105 zenon_H254 zenon_H146 zenon_H140 zenon_H135 zenon_H2af zenon_H90 zenon_H25e zenon_H22e zenon_H228 zenon_Ha7 zenon_H80 zenon_H84 zenon_Hc9 zenon_H175 zenon_H1e5 zenon_H10e zenon_H1a2 zenon_H6a zenon_H157 zenon_H1b3 zenon_H138 zenon_H1df zenon_H2d5 zenon_H11b zenon_H59 zenon_H109 zenon_H10f zenon_H1e3 zenon_H1d3 zenon_H58 zenon_Hde zenon_H2ab zenon_Hf0 zenon_H44 zenon_H9e zenon_H166 zenon_H121 zenon_Hce zenon_H1d0 zenon_H36 zenon_H3b zenon_H2b8 zenon_Hf1 zenon_H45 zenon_H2be zenon_H10d zenon_H145 zenon_He6 zenon_Ha3 zenon_Hae zenon_H13c zenon_H10a zenon_H30 zenon_Hb4. % 15.55/15.73 apply (zenon_or_s _ _ zenon_H58); [ zenon_intro zenon_H5b | zenon_intro zenon_H5a ]. % 15.55/15.73 exact (zenon_H59 zenon_H5b). % 15.55/15.73 apply (zenon_or_s _ _ zenon_H5a); [ zenon_intro zenon_H4a | zenon_intro zenon_H5c ]. % 15.55/15.73 apply (zenon_L120_); trivial. % 15.55/15.73 apply (zenon_or_s _ _ zenon_H5c); [ zenon_intro zenon_H50 | zenon_intro zenon_H53 ]. % 15.55/15.73 apply (zenon_L1318_); trivial. % 15.55/15.73 apply (zenon_L536_); trivial. % 15.55/15.73 (* end of lemma zenon_L1319_ *) % 15.55/15.73 assert (zenon_L1320_ : (((op (e0) (e0)) = (e1))\/(((op (e1) (e0)) = (e1))\/(((op (e2) (e0)) = (e1))\/((op (e3) (e0)) = (e1))))) -> (~((op (e0) (e0)) = (e1))) -> ((op (e1) (e3)) = (e1)) -> (~((op (e1) (e0)) = (op (e1) (e3)))) -> (~((op (e0) (e3)) = (op (e2) (e3)))) -> (~((op (e2) (e2)) = (e3))) -> (~((op (e2) (e1)) = (op (e3) (e1)))) -> (~((e1) = (e3))) -> (((op (e2) (e0)) = (e3))\/(((op (e2) (e1)) = (e3))\/(((op (e2) (e2)) = (e3))\/((op (e2) (e3)) = (e3))))) -> (~((op (e0) (e1)) = (op (e3) (e1)))) -> (~((op (e0) (e0)) = (e3))) -> (((op (e0) (e0)) = (e3))\/(((op (e0) (e1)) = (e3))\/(((op (e0) (e2)) = (e3))\/((op (e0) (e3)) = (e3))))) -> (((op (e3) (e0)) = (e2))\/(((op (e3) (e1)) = (e2))\/(((op (e3) (e2)) = (e2))\/((op (e3) (e3)) = (e2))))) -> ((op (e0) (e2)) = (e1)) -> (~((op (e0) (op (e3) (e0))) = (op (e3) (e0)))) -> ((op (e3) (e1)) = (e3)) -> (~((e2) = (e3))) -> ((op (e2) (e2)) = (e2)) -> (~((op (e2) (op (e3) (e2))) = (op (e3) (e2)))) -> (~((op (e3) (e3)) = (e2))) -> False). % 15.55/15.73 do 0 intro. intros zenon_Hf1 zenon_H45 zenon_H11f zenon_H1cf zenon_Hb4 zenon_H30 zenon_H13c zenon_Ha3 zenon_He6 zenon_H138 zenon_H59 zenon_H58 zenon_H1df zenon_H29 zenon_H2b8 zenon_H10a zenon_H6a zenon_H35 zenon_H2af zenon_H3d. % 15.55/15.73 apply (zenon_or_s _ _ zenon_Hf1); [ zenon_intro zenon_H47 | zenon_intro zenon_Hf4 ]. % 15.55/15.73 exact (zenon_H45 zenon_H47). % 15.55/15.73 apply (zenon_or_s _ _ zenon_Hf4); [ zenon_intro zenon_Hd8 | zenon_intro zenon_Hf5 ]. % 15.55/15.73 apply (zenon_L224_); trivial. % 15.55/15.73 apply (zenon_or_s _ _ zenon_Hf5); [ zenon_intro zenon_Hae | zenon_intro zenon_Hee ]. % 15.55/15.73 apply (zenon_L1097_); trivial. % 15.55/15.73 apply (zenon_L1098_); trivial. % 15.55/15.73 (* end of lemma zenon_L1320_ *) % 15.55/15.73 assert (zenon_L1321_ : (~((op (e0) (e2)) = (op (e1) (e2)))) -> (~((op (e1) (e2)) = (op (e2) (e2)))) -> (~((op (e1) (e2)) = (op (e3) (e2)))) -> ((op (e0) (e2)) = (e0)) -> (((op (e1) (e2)) = (e0))\/(((op (e1) (e2)) = (e1))\/(((op (e1) (e2)) = (e2))\/((op (e1) (e2)) = (e3))))) -> (~((op (e2) (e2)) = (e1))) -> (~((op (e0) (e0)) = (e0))) -> (~((op (e1) (e1)) = (e1))) -> (((op (e3) (e0)) = (e0))\/(((op (e3) (e1)) = (e0))\/(((op (e3) (e2)) = (e0))\/((op (e3) (e3)) = (e0))))) -> ((~((op (e1) (e1)) = (e1)))\/((op (e1) (e1)) = (e1))) -> (~((op (e1) (e0)) = (op (e1) (e1)))) -> ((~((op (e1) (e1)) = (e3)))\/((op (e1) (e3)) = (e1))) -> ((~((op (e2) (e2)) = (e3)))\/((op (e2) (e3)) = (e2))) -> (~((op (e2) (e2)) = (op (e2) (e3)))) -> ((~((op (e3) (e3)) = (e1)))\/((op (e3) (e1)) = (e3))) -> (((op (e0) (e0)) = (e3))\/(((op (e1) (e0)) = (e3))\/(((op (e2) (e0)) = (e3))\/((op (e3) (e0)) = (e3))))) -> (((op (e2) (e0)) = (e1))\/(((op (e2) (e1)) = (e1))\/(((op (e2) (e2)) = (e1))\/((op (e2) (e3)) = (e1))))) -> (~((op (e1) (op (e3) (e1))) = (op (e3) (e1)))) -> (~((op (e1) (e0)) = (op (e2) (e0)))) -> (~((op (e3) (e0)) = (op (e3) (e2)))) -> (((op (e0) (e3)) = (e0))\/(((op (e0) (e3)) = (e1))\/(((op (e0) (e3)) = (e2))\/((op (e0) (e3)) = (e3))))) -> (((op (e3) (e0)) = (e1))\/(((op (e3) (e1)) = (e1))\/(((op (e3) (e2)) = (e1))\/((op (e3) (e3)) = (e1))))) -> (~((op (e0) (e2)) = (op (e3) (e2)))) -> (~((op (e3) (e1)) = (op (e3) (e2)))) -> (((op (e1) (e0)) = (e3))\/(((op (e1) (e1)) = (e3))\/(((op (e1) (e2)) = (e3))\/((op (e1) (e3)) = (e3))))) -> (((op (e3) (e2)) = (e0))\/(((op (e3) (e2)) = (e1))\/(((op (e3) (e2)) = (e2))\/((op (e3) (e2)) = (e3))))) -> (~((op (e1) (e0)) = (op (e3) (e0)))) -> (((op (e0) (e1)) = (e1))\/(((op (e1) (e1)) = (e1))\/(((op (e2) (e1)) = (e1))\/((op (e3) (e1)) = (e1))))) -> (~((e1) = (e2))) -> (~((op (e0) (e3)) = (op (e1) (e3)))) -> (((op (e1) (e0)) = (e2))\/(((op (e1) (e1)) = (e2))\/(((op (e1) (e2)) = (e2))\/((op (e1) (e3)) = (e2))))) -> (~((op (e0) (e2)) = (op (e0) (e3)))) -> (((op (e0) (e2)) = (e3))\/(((op (e1) (e2)) = (e3))\/(((op (e2) (e2)) = (e3))\/((op (e3) (e2)) = (e3))))) -> (~((op (e2) (e0)) = (op (e3) (e0)))) -> ((~((op (e3) (e3)) = (e2)))\/((op (e3) (e2)) = (e3))) -> (((op (e0) (e1)) = (e2))\/(((op (e1) (e1)) = (e2))\/(((op (e2) (e1)) = (e2))\/((op (e3) (e1)) = (e2))))) -> (~((op (e2) (e1)) = (op (e2) (e2)))) -> (((op (e1) (e1)) = (e0))\/(((op (e1) (e1)) = (e1))\/(((op (e1) (e1)) = (e2))\/((op (e1) (e1)) = (e3))))) -> (((op (e3) (e0)) = (e3))\/(((op (e3) (e1)) = (e3))\/(((op (e3) (e2)) = (e3))\/((op (e3) (e3)) = (e3))))) -> (((op (e0) (e2)) = (e1))\/(((op (e1) (e2)) = (e1))\/(((op (e2) (e2)) = (e1))\/((op (e3) (e2)) = (e1))))) -> (~((op (e3) (e0)) = (op (e3) (e1)))) -> ((~((op (e3) (e3)) = (e0)))\/((op (e3) (e0)) = (e3))) -> ((~((op (e2) (e2)) = (e1)))\/((op (e2) (e1)) = (e2))) -> ((~((op (e1) (e1)) = (e2)))\/((op (e1) (e2)) = (e1))) -> (~((op (e0) (e1)) = (op (e2) (e1)))) -> (((op (e2) (e3)) = (e0))\/(((op (e2) (e3)) = (e1))\/(((op (e2) (e3)) = (e2))\/((op (e2) (e3)) = (e3))))) -> (((op (e0) (e0)) = (e0))\/(((op (e1) (e0)) = (e0))\/(((op (e2) (e0)) = (e0))\/((op (e3) (e0)) = (e0))))) -> (((op (e0) (e0)) = (e1))\/(((op (e0) (e1)) = (e1))\/(((op (e0) (e2)) = (e1))\/((op (e0) (e3)) = (e1))))) -> (~((e0) = (e1))) -> (~((op (e1) (e0)) = (op (e1) (e2)))) -> (((op (e0) (e3)) = (e1))\/(((op (e1) (e3)) = (e1))\/(((op (e2) (e3)) = (e1))\/((op (e3) (e3)) = (e1))))) -> (~((op (e2) (e0)) = (op (e2) (e3)))) -> (~((op (e1) (e2)) = (op (e1) (e3)))) -> (~((op (e3) (op (e3) (e3))) = (op (e3) (e3)))) -> ((~((op (e3) (e3)) = (e3)))\/((op (e3) (e3)) = (e3))) -> (~((op (e1) (e1)) = (e0))) -> (~((op (e2) (op (e3) (e2))) = (op (e3) (e2)))) -> ((op (e2) (e2)) = (e2)) -> (~((e2) = (e3))) -> ((op (e3) (e1)) = (e3)) -> (~((op (e0) (op (e3) (e0))) = (op (e3) (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))))) -> (~((op (e0) (e0)) = (e3))) -> (~((op (e0) (e1)) = (op (e3) (e1)))) -> (((op (e2) (e0)) = (e3))\/(((op (e2) (e1)) = (e3))\/(((op (e2) (e2)) = (e3))\/((op (e2) (e3)) = (e3))))) -> (~((e1) = (e3))) -> (~((op (e2) (e1)) = (op (e3) (e1)))) -> (~((op (e2) (e2)) = (e3))) -> (~((op (e0) (e3)) = (op (e2) (e3)))) -> (~((op (e1) (e0)) = (op (e1) (e3)))) -> ((op (e1) (e3)) = (e1)) -> (~((op (e0) (e0)) = (e1))) -> (((op (e0) (e0)) = (e1))\/(((op (e1) (e0)) = (e1))\/(((op (e2) (e0)) = (e1))\/((op (e3) (e0)) = (e1))))) -> (((op (e3) (e3)) = (e0))\/(((op (e3) (e3)) = (e1))\/(((op (e3) (e3)) = (e2))\/((op (e3) (e3)) = (e3))))) -> (~((op (e3) (e3)) = (e0))) -> (~((op (e0) (e3)) = (op (e3) (e3)))) -> (~((op (e3) (e3)) = (e2))) -> (~((op (e3) (e3)) = (e3))) -> False). % 15.55/15.73 do 0 intro. intros zenon_H87 zenon_H7d zenon_H17d zenon_Hab zenon_H1d5 zenon_H52 zenon_H20 zenon_H1b4 zenon_H1f6 zenon_H1d8 zenon_Hd7 zenon_H1d2 zenon_H1c3 zenon_H15f zenon_H10c zenon_Hbe zenon_Hb7 zenon_H2b4 zenon_H247 zenon_H105 zenon_H254 zenon_H146 zenon_H140 zenon_H135 zenon_H90 zenon_H25e zenon_H22e zenon_H228 zenon_Ha7 zenon_H80 zenon_H84 zenon_Hc9 zenon_H175 zenon_H1e5 zenon_H10e zenon_H1a2 zenon_H157 zenon_H1b3 zenon_H2d5 zenon_H11b zenon_H109 zenon_H10f zenon_H1e3 zenon_H1d3 zenon_Hde zenon_H2ab zenon_Hf0 zenon_H44 zenon_H9e zenon_H166 zenon_H121 zenon_Hce zenon_H1d0 zenon_H2be zenon_H10d zenon_H145 zenon_H2af zenon_H35 zenon_H6a zenon_H10a zenon_H2b8 zenon_H1df zenon_H58 zenon_H59 zenon_H138 zenon_He6 zenon_Ha3 zenon_H13c zenon_H30 zenon_Hb4 zenon_H1cf zenon_H11f zenon_H45 zenon_Hf1 zenon_H3b zenon_H3c zenon_H36 zenon_H3d zenon_H3e. % 15.55/15.73 apply (zenon_or_s _ _ zenon_H44); [ zenon_intro zenon_H47 | zenon_intro zenon_H46 ]. % 15.55/15.73 exact (zenon_H45 zenon_H47). % 15.55/15.73 apply (zenon_or_s _ _ zenon_H46); [ zenon_intro zenon_H22 | zenon_intro zenon_H48 ]. % 15.55/15.73 apply (zenon_or_s _ _ zenon_Hf1); [ zenon_intro zenon_H47 | zenon_intro zenon_Hf4 ]. % 15.55/15.73 exact (zenon_H45 zenon_H47). % 15.55/15.73 apply (zenon_or_s _ _ zenon_Hf4); [ zenon_intro zenon_Hd8 | zenon_intro zenon_Hf5 ]. % 15.55/15.73 apply (zenon_L224_); trivial. % 15.55/15.73 apply (zenon_or_s _ _ zenon_Hf5); [ zenon_intro zenon_Hae | zenon_intro zenon_Hee ]. % 15.55/15.73 apply (zenon_L1319_); trivial. % 15.55/15.73 apply (zenon_L1054_); trivial. % 15.55/15.73 apply (zenon_or_s _ _ zenon_H48); [ zenon_intro zenon_H29 | zenon_intro zenon_H37 ]. % 15.55/15.73 apply (zenon_L1320_); trivial. % 15.55/15.73 apply (zenon_L7_); trivial. % 15.55/15.73 (* end of lemma zenon_L1321_ *) % 15.55/15.73 assert (zenon_L1322_ : (~((op (e3) (e3)) = (e0))) -> (~((op (e0) (e2)) = (op (e3) (e2)))) -> ((op (e0) (e2)) = (e0)) -> (~((op (e1) (op (e3) (e1))) = (op (e3) (e1)))) -> ((op (e1) (e0)) = (e0)) -> (~((e0) = (e1))) -> (((op (e3) (e0)) = (e0))\/(((op (e3) (e1)) = (e0))\/(((op (e3) (e2)) = (e0))\/((op (e3) (e3)) = (e0))))) -> (((op (e0) (e0)) = (e3))\/(((op (e0) (e1)) = (e3))\/(((op (e0) (e2)) = (e3))\/((op (e0) (e3)) = (e3))))) -> (~((op (e0) (e0)) = (e3))) -> (~((op (e2) (op (e3) (e2))) = (op (e3) (e2)))) -> (~((op (e2) (e2)) = (e3))) -> (~((op (e0) (e1)) = (op (e2) (e1)))) -> (((op (e2) (e0)) = (e3))\/(((op (e2) (e1)) = (e3))\/(((op (e2) (e2)) = (e3))\/((op (e2) (e3)) = (e3))))) -> ((~((op (e1) (e1)) = (e2)))\/((op (e1) (e2)) = (e1))) -> ((~((op (e2) (e2)) = (e1)))\/((op (e2) (e1)) = (e2))) -> ((~((op (e3) (e3)) = (e0)))\/((op (e3) (e0)) = (e3))) -> (~((op (e3) (e0)) = (op (e3) (e1)))) -> (((op (e0) (e0)) = (e1))\/(((op (e0) (e1)) = (e1))\/(((op (e0) (e2)) = (e1))\/((op (e0) (e3)) = (e1))))) -> (((op (e0) (e2)) = (e1))\/(((op (e1) (e2)) = (e1))\/(((op (e2) (e2)) = (e1))\/((op (e3) (e2)) = (e1))))) -> (((op (e1) (e2)) = (e0))\/(((op (e1) (e2)) = (e1))\/(((op (e1) (e2)) = (e2))\/((op (e1) (e2)) = (e3))))) -> (~((op (e0) (e2)) = (op (e1) (e2)))) -> (((op (e3) (e0)) = (e3))\/(((op (e3) (e1)) = (e3))\/(((op (e3) (e2)) = (e3))\/((op (e3) (e3)) = (e3))))) -> ((~((op (e3) (e3)) = (e3)))\/((op (e3) (e3)) = (e3))) -> (~((op (e3) (op (e3) (e3))) = (op (e3) (e3)))) -> (((op (e3) (e0)) = (e2))\/(((op (e3) (e1)) = (e2))\/(((op (e3) (e2)) = (e2))\/((op (e3) (e3)) = (e2))))) -> (~((op (e0) (e1)) = (op (e3) (e1)))) -> (((op (e1) (e1)) = (e0))\/(((op (e1) (e1)) = (e1))\/(((op (e1) (e1)) = (e2))\/((op (e1) (e1)) = (e3))))) -> (~((op (e2) (e1)) = (op (e2) (e2)))) -> (~((e2) = (e3))) -> (((op (e0) (e1)) = (e2))\/(((op (e1) (e1)) = (e2))\/(((op (e2) (e1)) = (e2))\/((op (e3) (e1)) = (e2))))) -> ((~((op (e3) (e3)) = (e2)))\/((op (e3) (e2)) = (e3))) -> (~((op (e2) (e0)) = (op (e3) (e0)))) -> (((op (e0) (e2)) = (e3))\/(((op (e1) (e2)) = (e3))\/(((op (e2) (e2)) = (e3))\/((op (e3) (e2)) = (e3))))) -> (~((op (e1) (e0)) = (op (e1) (e2)))) -> (((op (e0) (e3)) = (e1))\/(((op (e1) (e3)) = (e1))\/(((op (e2) (e3)) = (e1))\/((op (e3) (e3)) = (e1))))) -> (~((op (e2) (e0)) = (op (e2) (e3)))) -> (~((op (e1) (e2)) = (op (e1) (e3)))) -> (~((op (e0) (e3)) = (op (e3) (e3)))) -> (((op (e3) (e3)) = (e0))\/(((op (e3) (e3)) = (e1))\/(((op (e3) (e3)) = (e2))\/((op (e3) (e3)) = (e3))))) -> (((op (e0) (e0)) = (e1))\/(((op (e1) (e0)) = (e1))\/(((op (e2) (e0)) = (e1))\/((op (e3) (e0)) = (e1))))) -> (~((op (e0) (e2)) = (op (e0) (e3)))) -> (((op (e1) (e0)) = (e2))\/(((op (e1) (e1)) = (e2))\/(((op (e1) (e2)) = (e2))\/((op (e1) (e3)) = (e2))))) -> (~((op (e0) (e3)) = (op (e1) (e3)))) -> ((op (e2) (e2)) = (e2)) -> (~((op (e1) (e2)) = (op (e2) (e2)))) -> (~((e1) = (e2))) -> (((op (e0) (e1)) = (e1))\/(((op (e1) (e1)) = (e1))\/(((op (e2) (e1)) = (e1))\/((op (e3) (e1)) = (e1))))) -> (~((op (e1) (e0)) = (op (e3) (e0)))) -> (~((op (e1) (e1)) = (e1))) -> (~((op (e0) (op (e3) (e0))) = (op (e3) (e0)))) -> (((op (e3) (e2)) = (e0))\/(((op (e3) (e2)) = (e1))\/(((op (e3) (e2)) = (e2))\/((op (e3) (e2)) = (e3))))) -> (~((op (e1) (e2)) = (op (e3) (e2)))) -> (((op (e1) (e0)) = (e3))\/(((op (e1) (e1)) = (e3))\/(((op (e1) (e2)) = (e3))\/((op (e1) (e3)) = (e3))))) -> (~((op (e3) (e1)) = (op (e3) (e2)))) -> (((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 (e3) (e0)) = (op (e3) (e2)))) -> (~((op (e1) (e0)) = (op (e2) (e0)))) -> (~((op (e0) (e3)) = (op (e2) (e3)))) -> (((op (e2) (e0)) = (e1))\/(((op (e2) (e1)) = (e1))\/(((op (e2) (e2)) = (e1))\/((op (e2) (e3)) = (e1))))) -> (((op (e0) (e0)) = (e3))\/(((op (e1) (e0)) = (e3))\/(((op (e2) (e0)) = (e3))\/((op (e3) (e0)) = (e3))))) -> (~((op (e0) (e0)) = (e1))) -> ((~((op (e3) (e3)) = (e1)))\/((op (e3) (e1)) = (e3))) -> (~((op (e2) (e2)) = (op (e2) (e3)))) -> ((~((op (e2) (e2)) = (e3)))\/((op (e2) (e3)) = (e2))) -> (~((op (e1) (e0)) = (op (e1) (e3)))) -> ((~((op (e1) (e1)) = (e3)))\/((op (e1) (e3)) = (e1))) -> (~((op (e1) (e0)) = (op (e1) (e1)))) -> ((~((op (e1) (e1)) = (e1)))\/((op (e1) (e1)) = (e1))) -> (~((op (e3) (e3)) = (e1))) -> (~((op (e2) (e2)) = (e1))) -> (~((e1) = (e3))) -> ((op (e3) (e2)) = (e3)) -> False). % 15.55/15.74 do 0 intro. intros zenon_H3c zenon_H140 zenon_Hab zenon_H2b4 zenon_Had zenon_H9e zenon_H1f6 zenon_H58 zenon_H59 zenon_H2af zenon_H30 zenon_Hde zenon_He6 zenon_H1d3 zenon_H1e3 zenon_H10f zenon_H109 zenon_H44 zenon_H11b zenon_H1d5 zenon_H87 zenon_H2d5 zenon_H10d zenon_H2be zenon_H1df zenon_H138 zenon_H1b3 zenon_H157 zenon_H6a zenon_H1a2 zenon_H10e zenon_H1e5 zenon_H175 zenon_H166 zenon_H121 zenon_Hce zenon_H1d0 zenon_H36 zenon_H3b zenon_Hf1 zenon_Hc9 zenon_H84 zenon_H80 zenon_H35 zenon_H7d zenon_Ha7 zenon_H228 zenon_H22e zenon_H1b4 zenon_H2b8 zenon_H25e zenon_H17d zenon_H90 zenon_H135 zenon_H146 zenon_H254 zenon_H105 zenon_H247 zenon_Hb4 zenon_Hb7 zenon_Hbe zenon_H45 zenon_H10c zenon_H15f zenon_H1c3 zenon_H1cf zenon_H1d2 zenon_Hd7 zenon_H1d8 zenon_H104 zenon_H52 zenon_Ha3 zenon_H106. % 15.55/15.74 apply (zenon_or_s _ _ zenon_H11b); [ zenon_intro zenon_H29 | zenon_intro zenon_H11c ]. % 15.55/15.74 apply (zenon_L37_); trivial. % 15.55/15.74 apply (zenon_or_s _ _ zenon_H11c); [ zenon_intro zenon_H117 | zenon_intro zenon_H11d ]. % 15.55/15.74 apply (zenon_L1310_); trivial. % 15.55/15.74 apply (zenon_or_s _ _ zenon_H11d); [ zenon_intro zenon_H2a | zenon_intro zenon_H119 ]. % 15.55/15.74 exact (zenon_H52 zenon_H2a). % 15.55/15.74 apply (zenon_L87_); trivial. % 15.55/15.74 (* end of lemma zenon_L1322_ *) % 15.55/15.74 assert (zenon_L1323_ : ((~((op (e3) (e3)) = (e1)))\/((op (e3) (e1)) = (e3))) -> (~((op (e3) (e0)) = (op (e3) (e1)))) -> ((~((op (e3) (e3)) = (e3)))\/((op (e3) (e3)) = (e3))) -> (~((op (e3) (op (e3) (e3))) = (op (e3) (e3)))) -> (~((op (e0) (e0)) = (e0))) -> (((op (e0) (e0)) = (e2))\/(((op (e0) (e1)) = (e2))\/(((op (e0) (e2)) = (e2))\/((op (e0) (e3)) = (e2))))) -> (((op (e1) (e1)) = (e0))\/(((op (e1) (e1)) = (e1))\/(((op (e1) (e1)) = (e2))\/((op (e1) (e1)) = (e3))))) -> (((op (e3) (e3)) = (e0))\/(((op (e3) (e3)) = (e1))\/(((op (e3) (e3)) = (e2))\/((op (e3) (e3)) = (e3))))) -> (~((op (e1) (e1)) = (e2))) -> (~((op (e1) (e1)) = (e1))) -> (~((op (e1) (e1)) = (e0))) -> (~((op (e1) (e2)) = (op (e2) (e2)))) -> (~((op (e0) (e3)) = (op (e1) (e3)))) -> (((op (e1) (e0)) = (e2))\/(((op (e1) (e1)) = (e2))\/(((op (e1) (e2)) = (e2))\/((op (e1) (e3)) = (e2))))) -> (~((op (e0) (e2)) = (op (e2) (e2)))) -> (~((op (e0) (e1)) = (op (e3) (e1)))) -> (~((e0) = (e1))) -> ((op (e0) (e2)) = (e0)) -> (((op (e3) (e0)) = (e1))\/(((op (e3) (e1)) = (e1))\/(((op (e3) (e2)) = (e1))\/((op (e3) (e3)) = (e1))))) -> (~((op (e1) (e2)) = (op (e3) (e2)))) -> (~((e2) = (e3))) -> (~((op (e1) (op (e3) (e1))) = (op (e3) (e1)))) -> (~((op (e2) (op (e3) (e2))) = (op (e3) (e2)))) -> ((op (e2) (e2)) = (e2)) -> (((op (e3) (e0)) = (e2))\/(((op (e3) (e1)) = (e2))\/(((op (e3) (e2)) = (e2))\/((op (e3) (e3)) = (e2))))) -> ((op (e3) (e0)) = (e3)) -> (~((e1) = (e3))) -> (~((op (e2) (e2)) = (e1))) -> (((op (e3) (e0)) = (e0))\/(((op (e3) (e1)) = (e0))\/(((op (e3) (e2)) = (e0))\/((op (e3) (e3)) = (e0))))) -> (~((op (e0) (e2)) = (op (e3) (e2)))) -> (~((e0) = (e3))) -> (((op (e0) (e2)) = (e1))\/(((op (e1) (e2)) = (e1))\/(((op (e2) (e2)) = (e1))\/((op (e3) (e2)) = (e1))))) -> (((op (e0) (e0)) = (e1))\/(((op (e1) (e0)) = (e1))\/(((op (e2) (e0)) = (e1))\/((op (e3) (e0)) = (e1))))) -> (~((op (e0) (e2)) = (op (e0) (e3)))) -> (((op (e0) (e1)) = (e2))\/(((op (e1) (e1)) = (e2))\/(((op (e2) (e1)) = (e2))\/((op (e3) (e1)) = (e2))))) -> (~((op (e1) (e0)) = (op (e2) (e0)))) -> (~((op (e0) (e3)) = (op (e2) (e3)))) -> (((op (e2) (e0)) = (e1))\/(((op (e2) (e1)) = (e1))\/(((op (e2) (e2)) = (e1))\/((op (e2) (e3)) = (e1))))) -> (~((op (e2) (e1)) = (op (e2) (e2)))) -> (~((e1) = (e2))) -> (~((op (e0) (op (e3) (e0))) = (op (e3) (e0)))) -> (((op (e0) (e3)) = (e0))\/(((op (e0) (e3)) = (e1))\/(((op (e0) (e3)) = (e2))\/((op (e0) (e3)) = (e3))))) -> (~((op (e0) (e0)) = (e1))) -> (((op (e0) (e0)) = (e0))\/(((op (e1) (e0)) = (e0))\/(((op (e2) (e0)) = (e0))\/((op (e3) (e0)) = (e0))))) -> (~((op (e3) (e0)) = (op (e3) (e2)))) -> ((~((op (e3) (e3)) = (e2)))\/((op (e3) (e2)) = (e3))) -> False). % 15.55/15.74 do 0 intro. intros zenon_H10c zenon_H109 zenon_H10d zenon_H2be zenon_H20 zenon_H8e zenon_H1b3 zenon_H3b zenon_Hd6 zenon_H1b4 zenon_H145 zenon_H7d zenon_H80 zenon_H84 zenon_H28 zenon_H138 zenon_H9e zenon_Hab zenon_H146 zenon_H17d zenon_H6a zenon_H2b4 zenon_H2af zenon_H35 zenon_H1df zenon_Hba zenon_Ha3 zenon_H52 zenon_H1f6 zenon_H140 zenon_H4b zenon_H11b zenon_Hf1 zenon_Hc9 zenon_H1a2 zenon_H247 zenon_Hb4 zenon_Hb7 zenon_H157 zenon_Ha7 zenon_H2b8 zenon_H254 zenon_H45 zenon_Hf0 zenon_H105 zenon_H10e. % 15.55/15.74 apply (zenon_or_s _ _ zenon_H10c); [ zenon_intro zenon_H104 | zenon_intro zenon_H10a ]. % 15.55/15.74 apply (zenon_or_s _ _ zenon_H10e); [ zenon_intro zenon_H3d | zenon_intro zenon_H106 ]. % 15.55/15.74 apply (zenon_or_s _ _ zenon_H10d); [ zenon_intro zenon_H3e | zenon_intro zenon_H42 ]. % 15.55/15.74 apply (zenon_or_s _ _ zenon_Hf0); [ zenon_intro zenon_H1f | zenon_intro zenon_Hf2 ]. % 15.55/15.74 exact (zenon_H20 zenon_H1f). % 15.55/15.74 apply (zenon_or_s _ _ zenon_Hf2); [ zenon_intro zenon_Had | zenon_intro zenon_Hf3 ]. % 15.55/15.74 apply (zenon_or_s _ _ zenon_H8e); [ zenon_intro zenon_H92 | zenon_intro zenon_H91 ]. % 15.55/15.74 apply (zenon_or_s _ _ zenon_H11b); [ zenon_intro zenon_H29 | zenon_intro zenon_H11c ]. % 15.55/15.74 apply (zenon_L37_); trivial. % 15.55/15.74 apply (zenon_or_s _ _ zenon_H11c); [ zenon_intro zenon_H117 | zenon_intro zenon_H11d ]. % 15.55/15.74 apply (zenon_L1094_); trivial. % 15.55/15.74 apply (zenon_or_s _ _ zenon_H11d); [ zenon_intro zenon_H2a | zenon_intro zenon_H119 ]. % 15.55/15.74 exact (zenon_H52 zenon_H2a). % 15.55/15.74 apply (zenon_L1240_); trivial. % 15.55/15.74 apply (zenon_or_s _ _ zenon_H91); [ zenon_intro zenon_H5d | zenon_intro zenon_H93 ]. % 15.55/15.74 apply (zenon_L1091_); trivial. % 15.55/15.74 apply (zenon_or_s _ _ zenon_H93); [ zenon_intro zenon_H63 | zenon_intro zenon_H81 ]. % 15.55/15.74 apply (zenon_L15_); trivial. % 15.55/15.74 apply (zenon_L522_); trivial. % 15.55/15.74 apply (zenon_or_s _ _ zenon_Hf3); [ zenon_intro zenon_Hcf | zenon_intro zenon_Hdb ]. % 15.55/15.74 apply (zenon_or_s _ _ zenon_Hf1); [ zenon_intro zenon_H47 | zenon_intro zenon_Hf4 ]. % 15.55/15.74 exact (zenon_H45 zenon_H47). % 15.55/15.74 apply (zenon_or_s _ _ zenon_Hf4); [ zenon_intro zenon_Hd8 | zenon_intro zenon_Hf5 ]. % 15.55/15.74 apply (zenon_L1247_); trivial. % 15.55/15.74 apply (zenon_or_s _ _ zenon_Hf5); [ zenon_intro zenon_Hae | zenon_intro zenon_Hee ]. % 15.55/15.74 apply (zenon_L269_); trivial. % 15.55/15.74 apply (zenon_L79_); trivial. % 15.55/15.74 apply (zenon_L62_); trivial. % 15.55/15.74 apply (zenon_L1041_); trivial. % 15.55/15.74 apply (zenon_L81_); trivial. % 15.55/15.74 apply (zenon_L82_); trivial. % 15.55/15.74 (* end of lemma zenon_L1323_ *) % 15.55/15.74 assert (zenon_L1324_ : ((~((op (e3) (e3)) = (e2)))\/((op (e3) (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)) = (e1))) -> (((op (e0) (e3)) = (e0))\/(((op (e0) (e3)) = (e1))\/(((op (e0) (e3)) = (e2))\/((op (e0) (e3)) = (e3))))) -> (~((e1) = (e2))) -> (~((op (e2) (e1)) = (op (e2) (e2)))) -> (((op (e2) (e0)) = (e1))\/(((op (e2) (e1)) = (e1))\/(((op (e2) (e2)) = (e1))\/((op (e2) (e3)) = (e1))))) -> (~((op (e0) (e3)) = (op (e2) (e3)))) -> (~((op (e1) (e0)) = (op (e2) (e0)))) -> (((op (e0) (e1)) = (e2))\/(((op (e1) (e1)) = (e2))\/(((op (e2) (e1)) = (e2))\/((op (e3) (e1)) = (e2))))) -> (~((op (e0) (e2)) = (op (e0) (e3)))) -> (((op (e0) (e0)) = (e1))\/(((op (e1) (e0)) = (e1))\/(((op (e2) (e0)) = (e1))\/((op (e3) (e0)) = (e1))))) -> (((op (e0) (e2)) = (e1))\/(((op (e1) (e2)) = (e1))\/(((op (e2) (e2)) = (e1))\/((op (e3) (e2)) = (e1))))) -> (~((e0) = (e3))) -> (~((op (e0) (e2)) = (op (e3) (e2)))) -> (((op (e3) (e0)) = (e0))\/(((op (e3) (e1)) = (e0))\/(((op (e3) (e2)) = (e0))\/((op (e3) (e3)) = (e0))))) -> (~((op (e2) (e2)) = (e1))) -> (~((e1) = (e3))) -> (((op (e3) (e0)) = (e2))\/(((op (e3) (e1)) = (e2))\/(((op (e3) (e2)) = (e2))\/((op (e3) (e3)) = (e2))))) -> ((op (e2) (e2)) = (e2)) -> (~((op (e2) (op (e3) (e2))) = (op (e3) (e2)))) -> (~((op (e1) (op (e3) (e1))) = (op (e3) (e1)))) -> (~((e2) = (e3))) -> (~((op (e1) (e2)) = (op (e3) (e2)))) -> (((op (e3) (e0)) = (e1))\/(((op (e3) (e1)) = (e1))\/(((op (e3) (e2)) = (e1))\/((op (e3) (e3)) = (e1))))) -> ((op (e0) (e2)) = (e0)) -> (~((e0) = (e1))) -> (~((op (e0) (e1)) = (op (e3) (e1)))) -> (~((op (e0) (e2)) = (op (e2) (e2)))) -> (((op (e1) (e0)) = (e2))\/(((op (e1) (e1)) = (e2))\/(((op (e1) (e2)) = (e2))\/((op (e1) (e3)) = (e2))))) -> (~((op (e0) (e3)) = (op (e1) (e3)))) -> (~((op (e1) (e2)) = (op (e2) (e2)))) -> (~((op (e1) (e1)) = (e0))) -> (~((op (e1) (e1)) = (e1))) -> (~((op (e1) (e1)) = (e2))) -> (((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 (e0) (e0)) = (e2))\/(((op (e0) (e1)) = (e2))\/(((op (e0) (e2)) = (e2))\/((op (e0) (e3)) = (e2))))) -> (~((op (e0) (e0)) = (e0))) -> (~((op (e3) (op (e3) (e3))) = (op (e3) (e3)))) -> ((~((op (e3) (e3)) = (e3)))\/((op (e3) (e3)) = (e3))) -> (~((op (e3) (e0)) = (op (e3) (e1)))) -> ((~((op (e3) (e3)) = (e1)))\/((op (e3) (e1)) = (e3))) -> (((op (e1) (e0)) = (e0))\/(((op (e1) (e1)) = (e0))\/(((op (e1) (e2)) = (e0))\/((op (e1) (e3)) = (e0))))) -> ((op (e3) (e2)) = (e3)) -> (~((op (e3) (e3)) = (e1))) -> ((~((op (e1) (e1)) = (e1)))\/((op (e1) (e1)) = (e1))) -> (~((op (e1) (e0)) = (op (e1) (e1)))) -> ((~((op (e1) (e1)) = (e3)))\/((op (e1) (e3)) = (e1))) -> (~((op (e1) (e0)) = (op (e1) (e3)))) -> ((~((op (e2) (e2)) = (e3)))\/((op (e2) (e3)) = (e2))) -> (~((op (e2) (e2)) = (op (e2) (e3)))) -> (((op (e0) (e0)) = (e3))\/(((op (e1) (e0)) = (e3))\/(((op (e2) (e0)) = (e3))\/((op (e3) (e0)) = (e3))))) -> (~((op (e3) (e1)) = (op (e3) (e2)))) -> (((op (e1) (e0)) = (e3))\/(((op (e1) (e1)) = (e3))\/(((op (e1) (e2)) = (e3))\/((op (e1) (e3)) = (e3))))) -> (((op (e3) (e2)) = (e0))\/(((op (e3) (e2)) = (e1))\/(((op (e3) (e2)) = (e2))\/((op (e3) (e2)) = (e3))))) -> (~((op (e1) (e0)) = (op (e3) (e0)))) -> (((op (e0) (e1)) = (e1))\/(((op (e1) (e1)) = (e1))\/(((op (e2) (e1)) = (e1))\/((op (e3) (e1)) = (e1))))) -> (~((op (e0) (e3)) = (op (e3) (e3)))) -> (~((op (e1) (e2)) = (op (e1) (e3)))) -> (~((op (e2) (e0)) = (op (e2) (e3)))) -> (((op (e0) (e3)) = (e1))\/(((op (e1) (e3)) = (e1))\/(((op (e2) (e3)) = (e1))\/((op (e3) (e3)) = (e1))))) -> (~((op (e1) (e0)) = (op (e1) (e2)))) -> (((op (e0) (e2)) = (e3))\/(((op (e1) (e2)) = (e3))\/(((op (e2) (e2)) = (e3))\/((op (e3) (e2)) = (e3))))) -> (~((op (e2) (e0)) = (op (e3) (e0)))) -> (((op (e3) (e0)) = (e3))\/(((op (e3) (e1)) = (e3))\/(((op (e3) (e2)) = (e3))\/((op (e3) (e3)) = (e3))))) -> (((op (e1) (e2)) = (e0))\/(((op (e1) (e2)) = (e1))\/(((op (e1) (e2)) = (e2))\/((op (e1) (e2)) = (e3))))) -> (((op (e0) (e0)) = (e1))\/(((op (e0) (e1)) = (e1))\/(((op (e0) (e2)) = (e1))\/((op (e0) (e3)) = (e1))))) -> ((~((op (e3) (e3)) = (e0)))\/((op (e3) (e0)) = (e3))) -> ((~((op (e2) (e2)) = (e1)))\/((op (e2) (e1)) = (e2))) -> ((~((op (e1) (e1)) = (e2)))\/((op (e1) (e2)) = (e1))) -> (((op (e2) (e0)) = (e3))\/(((op (e2) (e1)) = (e3))\/(((op (e2) (e2)) = (e3))\/((op (e2) (e3)) = (e3))))) -> (~((op (e0) (e1)) = (op (e2) (e1)))) -> (~((op (e2) (e2)) = (e3))) -> (~((op (e0) (e0)) = (e3))) -> (((op (e0) (e0)) = (e3))\/(((op (e0) (e1)) = (e3))\/(((op (e0) (e2)) = (e3))\/((op (e0) (e3)) = (e3))))) -> (~((op (e3) (e3)) = (e0))) -> (~((op (e0) (e2)) = (op (e1) (e2)))) -> (~((e0) = (e2))) -> (~((op (e0) (op (e3) (e0))) = (op (e3) (e0)))) -> ((op (e0) (e1)) = (e1)) -> False). % 15.55/15.74 do 0 intro. intros zenon_H10e zenon_H105 zenon_Hf0 zenon_H45 zenon_H254 zenon_Ha7 zenon_H157 zenon_Hb7 zenon_Hb4 zenon_H247 zenon_H1a2 zenon_Hc9 zenon_Hf1 zenon_H11b zenon_H4b zenon_H140 zenon_H1f6 zenon_H52 zenon_Ha3 zenon_H1df zenon_H35 zenon_H2af zenon_H2b4 zenon_H6a zenon_H17d zenon_H146 zenon_Hab zenon_H9e zenon_H138 zenon_H28 zenon_H84 zenon_H80 zenon_H7d zenon_H145 zenon_H1b4 zenon_Hd6 zenon_H3b zenon_H1b3 zenon_H8e zenon_H20 zenon_H2be zenon_H10d zenon_H109 zenon_H10c zenon_H163 zenon_H106 zenon_H104 zenon_H1d8 zenon_Hd7 zenon_H1d2 zenon_H1cf zenon_H1c3 zenon_H15f zenon_Hbe zenon_H135 zenon_H90 zenon_H25e zenon_H22e zenon_H228 zenon_H36 zenon_H1d0 zenon_Hce zenon_H121 zenon_H166 zenon_H175 zenon_H1e5 zenon_H2d5 zenon_H1d5 zenon_H44 zenon_H10f zenon_H1e3 zenon_H1d3 zenon_He6 zenon_Hde zenon_H30 zenon_H59 zenon_H58 zenon_H3c zenon_H87 zenon_H5e zenon_H2b8 zenon_H22. % 15.55/15.74 apply (zenon_or_s _ _ zenon_Hf1); [ zenon_intro zenon_H47 | zenon_intro zenon_Hf4 ]. % 15.55/15.74 exact (zenon_H45 zenon_H47). % 15.55/15.74 apply (zenon_or_s _ _ zenon_Hf4); [ zenon_intro zenon_Hd8 | zenon_intro zenon_Hf5 ]. % 15.55/15.74 apply (zenon_L1307_); trivial. % 15.55/15.74 apply (zenon_or_s _ _ zenon_Hf5); [ zenon_intro zenon_Hae | zenon_intro zenon_Hee ]. % 15.55/15.74 apply (zenon_or_s _ _ zenon_Hbe); [ zenon_intro zenon_H5b | zenon_intro zenon_Hbf ]. % 15.55/15.74 exact (zenon_H59 zenon_H5b). % 15.55/15.74 apply (zenon_or_s _ _ zenon_Hbf); [ zenon_intro zenon_H69 | zenon_intro zenon_Hc0 ]. % 15.55/15.74 apply (zenon_or_s _ _ zenon_H163); [ zenon_intro zenon_Had | zenon_intro zenon_H164 ]. % 15.55/15.74 apply (zenon_L1322_); trivial. % 15.55/15.74 apply (zenon_or_s _ _ zenon_H164); [ zenon_intro zenon_H149 | zenon_intro zenon_H165 ]. % 15.55/15.74 exact (zenon_H145 zenon_H149). % 15.55/15.74 apply (zenon_or_s _ _ zenon_H165); [ zenon_intro zenon_H15d | zenon_intro zenon_Hcc ]. % 15.55/15.74 apply (zenon_L136_); trivial. % 15.55/15.74 apply (zenon_L524_); trivial. % 15.55/15.74 apply (zenon_or_s _ _ zenon_Hc0); [ zenon_intro zenon_Haf | zenon_intro zenon_Hba ]. % 15.55/15.74 apply (zenon_L39_); trivial. % 15.55/15.74 apply (zenon_L1323_); trivial. % 15.55/15.74 apply (zenon_L1054_); trivial. % 15.55/15.74 (* end of lemma zenon_L1324_ *) % 15.55/15.74 assert (zenon_L1325_ : ((~((op (e1) (e1)) = (e3)))\/((op (e1) (e3)) = (e1))) -> (~((op (e1) (e0)) = (op (e1) (e3)))) -> ((~((op (e2) (e2)) = (e3)))\/((op (e2) (e3)) = (e2))) -> (~((op (e2) (e2)) = (op (e2) (e3)))) -> ((~((op (e3) (e3)) = (e1)))\/((op (e3) (e1)) = (e3))) -> (~((op (e0) (e0)) = (e1))) -> (((op (e0) (e0)) = (e3))\/(((op (e1) (e0)) = (e3))\/(((op (e2) (e0)) = (e3))\/((op (e3) (e0)) = (e3))))) -> (((op (e2) (e0)) = (e1))\/(((op (e2) (e1)) = (e1))\/(((op (e2) (e2)) = (e1))\/((op (e2) (e3)) = (e1))))) -> (~((op (e0) (e3)) = (op (e2) (e3)))) -> (~((op (e1) (op (e3) (e1))) = (op (e3) (e1)))) -> (~((op (e1) (e0)) = (op (e2) (e0)))) -> (~((op (e3) (e0)) = (op (e3) (e2)))) -> (((op (e0) (e3)) = (e0))\/(((op (e0) (e3)) = (e1))\/(((op (e0) (e3)) = (e2))\/((op (e0) (e3)) = (e3))))) -> (((op (e3) (e0)) = (e1))\/(((op (e3) (e1)) = (e1))\/(((op (e3) (e2)) = (e1))\/((op (e3) (e3)) = (e1))))) -> (~((op (e3) (e1)) = (op (e3) (e2)))) -> (((op (e1) (e0)) = (e3))\/(((op (e1) (e1)) = (e3))\/(((op (e1) (e2)) = (e3))\/((op (e1) (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 (e0) (op (e3) (e0))) = (op (e3) (e0)))) -> (~((op (e1) (e1)) = (e1))) -> (~((op (e1) (e0)) = (op (e3) (e0)))) -> (((op (e0) (e1)) = (e1))\/(((op (e1) (e1)) = (e1))\/(((op (e2) (e1)) = (e1))\/((op (e3) (e1)) = (e1))))) -> (~((e1) = (e2))) -> (~((op (e1) (e2)) = (op (e2) (e2)))) -> ((op (e2) (e2)) = (e2)) -> (~((op (e0) (e3)) = (op (e1) (e3)))) -> (((op (e1) (e0)) = (e2))\/(((op (e1) (e1)) = (e2))\/(((op (e1) (e2)) = (e2))\/((op (e1) (e3)) = (e2))))) -> ((op (e0) (e2)) = (e0)) -> (~((op (e0) (e2)) = (op (e0) (e3)))) -> (((op (e0) (e0)) = (e1))\/(((op (e1) (e0)) = (e1))\/(((op (e2) (e0)) = (e1))\/((op (e3) (e0)) = (e1))))) -> (((op (e3) (e3)) = (e0))\/(((op (e3) (e3)) = (e1))\/(((op (e3) (e3)) = (e2))\/((op (e3) (e3)) = (e3))))) -> (~((op (e0) (e3)) = (op (e3) (e3)))) -> (~((op (e1) (e2)) = (op (e1) (e3)))) -> (~((op (e2) (e0)) = (op (e2) (e3)))) -> (((op (e0) (e3)) = (e1))\/(((op (e1) (e3)) = (e1))\/(((op (e2) (e3)) = (e1))\/((op (e3) (e3)) = (e1))))) -> (~((op (e1) (e0)) = (op (e1) (e2)))) -> (((op (e0) (e2)) = (e3))\/(((op (e1) (e2)) = (e3))\/(((op (e2) (e2)) = (e3))\/((op (e3) (e2)) = (e3))))) -> (~((op (e2) (e0)) = (op (e3) (e0)))) -> ((~((op (e3) (e3)) = (e2)))\/((op (e3) (e2)) = (e3))) -> (((op (e0) (e1)) = (e2))\/(((op (e1) (e1)) = (e2))\/(((op (e2) (e1)) = (e2))\/((op (e3) (e1)) = (e2))))) -> (~((e2) = (e3))) -> (~((op (e2) (e1)) = (op (e2) (e2)))) -> (((op (e1) (e1)) = (e0))\/(((op (e1) (e1)) = (e1))\/(((op (e1) (e1)) = (e2))\/((op (e1) (e1)) = (e3))))) -> (~((op (e0) (e1)) = (op (e3) (e1)))) -> (((op (e3) (e0)) = (e2))\/(((op (e3) (e1)) = (e2))\/(((op (e3) (e2)) = (e2))\/((op (e3) (e3)) = (e2))))) -> (~((op (e3) (op (e3) (e3))) = (op (e3) (e3)))) -> ((~((op (e3) (e3)) = (e3)))\/((op (e3) (e3)) = (e3))) -> (((op (e3) (e0)) = (e3))\/(((op (e3) (e1)) = (e3))\/(((op (e3) (e2)) = (e3))\/((op (e3) (e3)) = (e3))))) -> (~((op (e0) (e2)) = (op (e1) (e2)))) -> (((op (e1) (e2)) = (e0))\/(((op (e1) (e2)) = (e1))\/(((op (e1) (e2)) = (e2))\/((op (e1) (e2)) = (e3))))) -> (((op (e0) (e2)) = (e1))\/(((op (e1) (e2)) = (e1))\/(((op (e2) (e2)) = (e1))\/((op (e3) (e2)) = (e1))))) -> (((op (e0) (e0)) = (e1))\/(((op (e0) (e1)) = (e1))\/(((op (e0) (e2)) = (e1))\/((op (e0) (e3)) = (e1))))) -> (~((op (e3) (e0)) = (op (e3) (e1)))) -> ((~((op (e3) (e3)) = (e0)))\/((op (e3) (e0)) = (e3))) -> ((~((op (e2) (e2)) = (e1)))\/((op (e2) (e1)) = (e2))) -> ((~((op (e1) (e1)) = (e2)))\/((op (e1) (e2)) = (e1))) -> (~((e1) = (e3))) -> ((op (e0) (e3)) = (e1)) -> ((op (e3) (e2)) = (e3)) -> (~((op (e0) (e2)) = (op (e3) (e2)))) -> (((op (e2) (e0)) = (e3))\/(((op (e2) (e1)) = (e3))\/(((op (e2) (e2)) = (e3))\/((op (e2) (e3)) = (e3))))) -> (~((op (e0) (e1)) = (op (e2) (e1)))) -> (~((op (e2) (e2)) = (e3))) -> (~((op (e2) (op (e3) (e2))) = (op (e3) (e2)))) -> (~((op (e0) (e0)) = (e3))) -> (((op (e0) (e0)) = (e3))\/(((op (e0) (e1)) = (e3))\/(((op (e0) (e2)) = (e3))\/((op (e0) (e3)) = (e3))))) -> ((op (e3) (e0)) = (e0)) -> (~((e0) = (e1))) -> False). % 15.55/15.74 do 0 intro. intros zenon_H1d2 zenon_H1cf zenon_H1c3 zenon_H15f zenon_H10c zenon_H45 zenon_Hbe zenon_Hb7 zenon_Hb4 zenon_H2b4 zenon_H247 zenon_H105 zenon_H254 zenon_H146 zenon_H135 zenon_H90 zenon_H17d zenon_H25e zenon_H2b8 zenon_H1b4 zenon_H22e zenon_H228 zenon_Ha7 zenon_H7d zenon_H35 zenon_H80 zenon_H84 zenon_Hab zenon_Hc9 zenon_Hf1 zenon_H3b zenon_H36 zenon_H1d0 zenon_Hce zenon_H121 zenon_H166 zenon_H175 zenon_H1e5 zenon_H10e zenon_H1a2 zenon_H6a zenon_H157 zenon_H1b3 zenon_H138 zenon_H1df zenon_H2be zenon_H10d zenon_H2d5 zenon_H87 zenon_H1d5 zenon_H11b zenon_H44 zenon_H109 zenon_H10f zenon_H1e3 zenon_H1d3 zenon_Ha3 zenon_H37 zenon_H106 zenon_H140 zenon_He6 zenon_Hde zenon_H30 zenon_H2af zenon_H59 zenon_H58 zenon_Hdb zenon_H9e. % 15.55/15.74 apply (zenon_or_s _ _ zenon_Hf1); [ zenon_intro zenon_H47 | zenon_intro zenon_Hf4 ]. % 15.55/15.74 exact (zenon_H45 zenon_H47). % 15.55/15.74 apply (zenon_or_s _ _ zenon_Hf4); [ zenon_intro zenon_Hd8 | zenon_intro zenon_Hf5 ]. % 15.55/15.74 apply (zenon_L1307_); trivial. % 15.55/15.74 apply (zenon_or_s _ _ zenon_Hf5); [ zenon_intro zenon_Hae | zenon_intro zenon_Hee ]. % 15.55/15.74 apply (zenon_L1110_); trivial. % 15.55/15.74 apply (zenon_L71_); trivial. % 15.55/15.74 (* end of lemma zenon_L1325_ *) % 15.55/15.74 assert (zenon_L1326_ : (((op (e2) (e3)) = (e0))\/(((op (e2) (e3)) = (e1))\/(((op (e2) (e3)) = (e2))\/((op (e2) (e3)) = (e3))))) -> (~((e0) = (e2))) -> (~((op (e3) (e3)) = (e0))) -> (~((op (e1) (e0)) = (op (e1) (e1)))) -> ((~((op (e1) (e1)) = (e1)))\/((op (e1) (e1)) = (e1))) -> (~((op (e3) (e3)) = (e1))) -> (((op (e1) (e0)) = (e0))\/(((op (e1) (e1)) = (e0))\/(((op (e1) (e2)) = (e0))\/((op (e1) (e3)) = (e0))))) -> (~((op (e0) (e0)) = (e0))) -> (((op (e0) (e0)) = (e2))\/(((op (e0) (e1)) = (e2))\/(((op (e0) (e2)) = (e2))\/((op (e0) (e3)) = (e2))))) -> (~((op (e1) (e1)) = (e2))) -> (~((op (e1) (e1)) = (e0))) -> (~((op (e0) (e2)) = (op (e2) (e2)))) -> (~((op (e2) (e2)) = (e1))) -> (((op (e3) (e0)) = (e0))\/(((op (e3) (e1)) = (e0))\/(((op (e3) (e2)) = (e0))\/((op (e3) (e3)) = (e0))))) -> (~((e0) = (e3))) -> (((op (e0) (e0)) = (e0))\/(((op (e1) (e0)) = (e0))\/(((op (e2) (e0)) = (e0))\/((op (e3) (e0)) = (e0))))) -> ((~((op (e1) (e1)) = (e3)))\/((op (e1) (e3)) = (e1))) -> (~((op (e1) (e0)) = (op (e1) (e3)))) -> ((~((op (e2) (e2)) = (e3)))\/((op (e2) (e3)) = (e2))) -> (~((op (e2) (e2)) = (op (e2) (e3)))) -> ((~((op (e3) (e3)) = (e1)))\/((op (e3) (e1)) = (e3))) -> (~((op (e0) (e0)) = (e1))) -> (((op (e0) (e0)) = (e3))\/(((op (e1) (e0)) = (e3))\/(((op (e2) (e0)) = (e3))\/((op (e3) (e0)) = (e3))))) -> (((op (e2) (e0)) = (e1))\/(((op (e2) (e1)) = (e1))\/(((op (e2) (e2)) = (e1))\/((op (e2) (e3)) = (e1))))) -> (~((op (e0) (e3)) = (op (e2) (e3)))) -> (~((op (e1) (op (e3) (e1))) = (op (e3) (e1)))) -> (~((op (e1) (e0)) = (op (e2) (e0)))) -> (~((op (e3) (e0)) = (op (e3) (e2)))) -> (((op (e0) (e3)) = (e0))\/(((op (e0) (e3)) = (e1))\/(((op (e0) (e3)) = (e2))\/((op (e0) (e3)) = (e3))))) -> (((op (e3) (e0)) = (e1))\/(((op (e3) (e1)) = (e1))\/(((op (e3) (e2)) = (e1))\/((op (e3) (e3)) = (e1))))) -> (~((op (e3) (e1)) = (op (e3) (e2)))) -> (((op (e1) (e0)) = (e3))\/(((op (e1) (e1)) = (e3))\/(((op (e1) (e2)) = (e3))\/((op (e1) (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 (e0) (op (e3) (e0))) = (op (e3) (e0)))) -> (~((op (e1) (e1)) = (e1))) -> (~((op (e1) (e0)) = (op (e3) (e0)))) -> (((op (e0) (e1)) = (e1))\/(((op (e1) (e1)) = (e1))\/(((op (e2) (e1)) = (e1))\/((op (e3) (e1)) = (e1))))) -> (~((e1) = (e2))) -> (~((op (e1) (e2)) = (op (e2) (e2)))) -> ((op (e2) (e2)) = (e2)) -> (~((op (e0) (e3)) = (op (e1) (e3)))) -> (((op (e1) (e0)) = (e2))\/(((op (e1) (e1)) = (e2))\/(((op (e1) (e2)) = (e2))\/((op (e1) (e3)) = (e2))))) -> ((op (e0) (e2)) = (e0)) -> (~((op (e0) (e2)) = (op (e0) (e3)))) -> (((op (e0) (e0)) = (e1))\/(((op (e1) (e0)) = (e1))\/(((op (e2) (e0)) = (e1))\/((op (e3) (e0)) = (e1))))) -> (((op (e3) (e3)) = (e0))\/(((op (e3) (e3)) = (e1))\/(((op (e3) (e3)) = (e2))\/((op (e3) (e3)) = (e3))))) -> (~((op (e0) (e3)) = (op (e3) (e3)))) -> (~((op (e1) (e2)) = (op (e1) (e3)))) -> (~((op (e2) (e0)) = (op (e2) (e3)))) -> (((op (e0) (e3)) = (e1))\/(((op (e1) (e3)) = (e1))\/(((op (e2) (e3)) = (e1))\/((op (e3) (e3)) = (e1))))) -> (~((op (e1) (e0)) = (op (e1) (e2)))) -> (((op (e0) (e2)) = (e3))\/(((op (e1) (e2)) = (e3))\/(((op (e2) (e2)) = (e3))\/((op (e3) (e2)) = (e3))))) -> (~((op (e2) (e0)) = (op (e3) (e0)))) -> ((~((op (e3) (e3)) = (e2)))\/((op (e3) (e2)) = (e3))) -> (((op (e0) (e1)) = (e2))\/(((op (e1) (e1)) = (e2))\/(((op (e2) (e1)) = (e2))\/((op (e3) (e1)) = (e2))))) -> (~((e2) = (e3))) -> (~((op (e2) (e1)) = (op (e2) (e2)))) -> (((op (e1) (e1)) = (e0))\/(((op (e1) (e1)) = (e1))\/(((op (e1) (e1)) = (e2))\/((op (e1) (e1)) = (e3))))) -> (~((op (e0) (e1)) = (op (e3) (e1)))) -> (((op (e3) (e0)) = (e2))\/(((op (e3) (e1)) = (e2))\/(((op (e3) (e2)) = (e2))\/((op (e3) (e3)) = (e2))))) -> (~((op (e3) (op (e3) (e3))) = (op (e3) (e3)))) -> ((~((op (e3) (e3)) = (e3)))\/((op (e3) (e3)) = (e3))) -> (((op (e3) (e0)) = (e3))\/(((op (e3) (e1)) = (e3))\/(((op (e3) (e2)) = (e3))\/((op (e3) (e3)) = (e3))))) -> (~((op (e0) (e2)) = (op (e1) (e2)))) -> (((op (e1) (e2)) = (e0))\/(((op (e1) (e2)) = (e1))\/(((op (e1) (e2)) = (e2))\/((op (e1) (e2)) = (e3))))) -> (((op (e0) (e2)) = (e1))\/(((op (e1) (e2)) = (e1))\/(((op (e2) (e2)) = (e1))\/((op (e3) (e2)) = (e1))))) -> (((op (e0) (e0)) = (e1))\/(((op (e0) (e1)) = (e1))\/(((op (e0) (e2)) = (e1))\/((op (e0) (e3)) = (e1))))) -> (~((op (e3) (e0)) = (op (e3) (e1)))) -> ((~((op (e3) (e3)) = (e0)))\/((op (e3) (e0)) = (e3))) -> ((~((op (e2) (e2)) = (e1)))\/((op (e2) (e1)) = (e2))) -> ((~((op (e1) (e1)) = (e2)))\/((op (e1) (e2)) = (e1))) -> (~((e1) = (e3))) -> ((op (e3) (e2)) = (e3)) -> (~((op (e0) (e2)) = (op (e3) (e2)))) -> (((op (e2) (e0)) = (e3))\/(((op (e2) (e1)) = (e3))\/(((op (e2) (e2)) = (e3))\/((op (e2) (e3)) = (e3))))) -> (~((op (e0) (e1)) = (op (e2) (e1)))) -> (~((op (e2) (e2)) = (e3))) -> (~((op (e2) (op (e3) (e2))) = (op (e3) (e2)))) -> (~((op (e0) (e0)) = (e3))) -> (((op (e0) (e0)) = (e3))\/(((op (e0) (e1)) = (e3))\/(((op (e0) (e2)) = (e3))\/((op (e0) (e3)) = (e3))))) -> (~((e0) = (e1))) -> False). % 15.55/15.74 do 0 intro. intros zenon_H2ab zenon_H5e zenon_H3c zenon_Hd7 zenon_H1d8 zenon_H104 zenon_H163 zenon_H20 zenon_H8e zenon_Hd6 zenon_H145 zenon_H28 zenon_H52 zenon_H1f6 zenon_H4b zenon_Hf0 zenon_H1d2 zenon_H1cf zenon_H1c3 zenon_H15f zenon_H10c zenon_H45 zenon_Hbe zenon_Hb7 zenon_Hb4 zenon_H2b4 zenon_H247 zenon_H105 zenon_H254 zenon_H146 zenon_H135 zenon_H90 zenon_H17d zenon_H25e zenon_H2b8 zenon_H1b4 zenon_H22e zenon_H228 zenon_Ha7 zenon_H7d zenon_H35 zenon_H80 zenon_H84 zenon_Hab zenon_Hc9 zenon_Hf1 zenon_H3b zenon_H36 zenon_H1d0 zenon_Hce zenon_H121 zenon_H166 zenon_H175 zenon_H1e5 zenon_H10e zenon_H1a2 zenon_H6a zenon_H157 zenon_H1b3 zenon_H138 zenon_H1df zenon_H2be zenon_H10d zenon_H2d5 zenon_H87 zenon_H1d5 zenon_H11b zenon_H44 zenon_H109 zenon_H10f zenon_H1e3 zenon_H1d3 zenon_Ha3 zenon_H106 zenon_H140 zenon_He6 zenon_Hde zenon_H30 zenon_H2af zenon_H59 zenon_H58 zenon_H9e. % 15.55/15.74 apply (zenon_or_s _ _ zenon_Hf0); [ zenon_intro zenon_H1f | zenon_intro zenon_Hf2 ]. % 15.55/15.74 exact (zenon_H20 zenon_H1f). % 15.55/15.74 apply (zenon_or_s _ _ zenon_Hf2); [ zenon_intro zenon_Had | zenon_intro zenon_Hf3 ]. % 15.55/15.74 apply (zenon_L1322_); trivial. % 15.55/15.74 apply (zenon_or_s _ _ zenon_Hf3); [ zenon_intro zenon_Hcf | zenon_intro zenon_Hdb ]. % 15.55/15.74 apply (zenon_or_s _ _ zenon_H44); [ zenon_intro zenon_H47 | zenon_intro zenon_H46 ]. % 15.55/15.74 exact (zenon_H45 zenon_H47). % 15.55/15.74 apply (zenon_or_s _ _ zenon_H46); [ zenon_intro zenon_H22 | zenon_intro zenon_H48 ]. % 15.55/15.74 apply (zenon_L1324_); trivial. % 15.55/15.74 apply (zenon_or_s _ _ zenon_H48); [ zenon_intro zenon_H29 | zenon_intro zenon_H37 ]. % 15.55/15.74 apply (zenon_L37_); trivial. % 15.55/15.74 apply (zenon_L1264_); trivial. % 15.55/15.74 apply (zenon_or_s _ _ zenon_H44); [ zenon_intro zenon_H47 | zenon_intro zenon_H46 ]. % 15.55/15.74 exact (zenon_H45 zenon_H47). % 15.55/15.74 apply (zenon_or_s _ _ zenon_H46); [ zenon_intro zenon_H22 | zenon_intro zenon_H48 ]. % 15.55/15.74 apply (zenon_L1324_); trivial. % 15.55/15.74 apply (zenon_or_s _ _ zenon_H48); [ zenon_intro zenon_H29 | zenon_intro zenon_H37 ]. % 15.55/15.74 apply (zenon_L37_); trivial. % 15.55/15.74 apply (zenon_L1325_); trivial. % 15.55/15.74 (* end of lemma zenon_L1326_ *) % 15.55/15.74 assert (zenon_L1327_ : (((op (e0) (e0)) = (e3))\/(((op (e0) (e1)) = (e3))\/(((op (e0) (e2)) = (e3))\/((op (e0) (e3)) = (e3))))) -> (~((op (e0) (e0)) = (e3))) -> (~((op (e2) (op (e3) (e2))) = (op (e3) (e2)))) -> (~((op (e2) (e2)) = (e3))) -> (~((op (e0) (e1)) = (op (e2) (e1)))) -> (((op (e2) (e0)) = (e3))\/(((op (e2) (e1)) = (e3))\/(((op (e2) (e2)) = (e3))\/((op (e2) (e3)) = (e3))))) -> (~((op (e0) (e2)) = (op (e3) (e2)))) -> (~((e1) = (e3))) -> ((~((op (e1) (e1)) = (e2)))\/((op (e1) (e2)) = (e1))) -> ((~((op (e2) (e2)) = (e1)))\/((op (e2) (e1)) = (e2))) -> ((~((op (e3) (e3)) = (e0)))\/((op (e3) (e0)) = (e3))) -> (~((op (e3) (e0)) = (op (e3) (e1)))) -> (((op (e0) (e0)) = (e1))\/(((op (e0) (e1)) = (e1))\/(((op (e0) (e2)) = (e1))\/((op (e0) (e3)) = (e1))))) -> (((op (e0) (e2)) = (e1))\/(((op (e1) (e2)) = (e1))\/(((op (e2) (e2)) = (e1))\/((op (e3) (e2)) = (e1))))) -> (((op (e1) (e2)) = (e0))\/(((op (e1) (e2)) = (e1))\/(((op (e1) (e2)) = (e2))\/((op (e1) (e2)) = (e3))))) -> (((op (e3) (e0)) = (e3))\/(((op (e3) (e1)) = (e3))\/(((op (e3) (e2)) = (e3))\/((op (e3) (e3)) = (e3))))) -> ((~((op (e3) (e3)) = (e3)))\/((op (e3) (e3)) = (e3))) -> (~((op (e3) (op (e3) (e3))) = (op (e3) (e3)))) -> (((op (e3) (e0)) = (e2))\/(((op (e3) (e1)) = (e2))\/(((op (e3) (e2)) = (e2))\/((op (e3) (e3)) = (e2))))) -> (~((op (e0) (e1)) = (op (e3) (e1)))) -> (((op (e1) (e1)) = (e0))\/(((op (e1) (e1)) = (e1))\/(((op (e1) (e1)) = (e2))\/((op (e1) (e1)) = (e3))))) -> (~((op (e2) (e1)) = (op (e2) (e2)))) -> (~((e2) = (e3))) -> (((op (e0) (e1)) = (e2))\/(((op (e1) (e1)) = (e2))\/(((op (e2) (e1)) = (e2))\/((op (e3) (e1)) = (e2))))) -> ((~((op (e3) (e3)) = (e2)))\/((op (e3) (e2)) = (e3))) -> (~((op (e2) (e0)) = (op (e3) (e0)))) -> (((op (e0) (e2)) = (e3))\/(((op (e1) (e2)) = (e3))\/(((op (e2) (e2)) = (e3))\/((op (e3) (e2)) = (e3))))) -> (~((op (e1) (e0)) = (op (e1) (e2)))) -> (((op (e0) (e3)) = (e1))\/(((op (e1) (e3)) = (e1))\/(((op (e2) (e3)) = (e1))\/((op (e3) (e3)) = (e1))))) -> (~((op (e2) (e0)) = (op (e2) (e3)))) -> (~((op (e1) (e2)) = (op (e1) (e3)))) -> (~((op (e0) (e3)) = (op (e3) (e3)))) -> (((op (e3) (e3)) = (e0))\/(((op (e3) (e3)) = (e1))\/(((op (e3) (e3)) = (e2))\/((op (e3) (e3)) = (e3))))) -> (((op (e0) (e0)) = (e1))\/(((op (e1) (e0)) = (e1))\/(((op (e2) (e0)) = (e1))\/((op (e3) (e0)) = (e1))))) -> (~((op (e0) (e2)) = (op (e0) (e3)))) -> (((op (e1) (e0)) = (e2))\/(((op (e1) (e1)) = (e2))\/(((op (e1) (e2)) = (e2))\/((op (e1) (e3)) = (e2))))) -> (~((op (e0) (e3)) = (op (e1) (e3)))) -> ((op (e2) (e2)) = (e2)) -> (~((op (e1) (e2)) = (op (e2) (e2)))) -> (~((e1) = (e2))) -> (((op (e0) (e1)) = (e1))\/(((op (e1) (e1)) = (e1))\/(((op (e2) (e1)) = (e1))\/((op (e3) (e1)) = (e1))))) -> (~((op (e1) (e0)) = (op (e3) (e0)))) -> (~((op (e1) (e1)) = (e1))) -> (~((op (e0) (op (e3) (e0))) = (op (e3) (e0)))) -> (((op (e3) (e2)) = (e0))\/(((op (e3) (e2)) = (e1))\/(((op (e3) (e2)) = (e2))\/((op (e3) (e2)) = (e3))))) -> (~((op (e1) (e2)) = (op (e3) (e2)))) -> (((op (e1) (e0)) = (e3))\/(((op (e1) (e1)) = (e3))\/(((op (e1) (e2)) = (e3))\/((op (e1) (e3)) = (e3))))) -> (~((op (e3) (e1)) = (op (e3) (e2)))) -> (((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 (e3) (e0)) = (op (e3) (e2)))) -> (~((op (e1) (e0)) = (op (e2) (e0)))) -> (~((op (e1) (op (e3) (e1))) = (op (e3) (e1)))) -> (~((op (e0) (e3)) = (op (e2) (e3)))) -> (((op (e2) (e0)) = (e1))\/(((op (e2) (e1)) = (e1))\/(((op (e2) (e2)) = (e1))\/((op (e2) (e3)) = (e1))))) -> (((op (e0) (e0)) = (e3))\/(((op (e1) (e0)) = (e3))\/(((op (e2) (e0)) = (e3))\/((op (e3) (e0)) = (e3))))) -> (~((op (e0) (e0)) = (e1))) -> ((~((op (e3) (e3)) = (e1)))\/((op (e3) (e1)) = (e3))) -> (~((op (e2) (e2)) = (op (e2) (e3)))) -> ((~((op (e2) (e2)) = (e3)))\/((op (e2) (e3)) = (e2))) -> (~((op (e1) (e0)) = (op (e1) (e3)))) -> ((~((op (e1) (e1)) = (e3)))\/((op (e1) (e3)) = (e1))) -> (((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))))) -> (~((op (e2) (e2)) = (e1))) -> (~((op (e0) (e2)) = (op (e2) (e2)))) -> (~((op (e1) (e1)) = (e2))) -> (((op (e0) (e0)) = (e2))\/(((op (e0) (e1)) = (e2))\/(((op (e0) (e2)) = (e2))\/((op (e0) (e3)) = (e2))))) -> (~((op (e0) (e0)) = (e0))) -> (((op (e1) (e0)) = (e0))\/(((op (e1) (e1)) = (e0))\/(((op (e1) (e2)) = (e0))\/((op (e1) (e3)) = (e0))))) -> (~((op (e3) (e3)) = (e1))) -> ((~((op (e1) (e1)) = (e1)))\/((op (e1) (e1)) = (e1))) -> (~((op (e1) (e0)) = (op (e1) (e1)))) -> (~((op (e3) (e3)) = (e0))) -> (~((e0) = (e2))) -> (((op (e2) (e3)) = (e0))\/(((op (e2) (e3)) = (e1))\/(((op (e2) (e3)) = (e2))\/((op (e2) (e3)) = (e3))))) -> ((op (e0) (e0)) = (e2)) -> (~((op (e3) (e3)) = (e2))) -> (~((op (e2) (e1)) = (op (e3) (e1)))) -> (~((op (e3) (e3)) = (e3))) -> ((op (e2) (e0)) = (e1)) -> (~((op (e1) (e1)) = (e0))) -> ((op (e0) (e2)) = (e0)) -> (~((op (e0) (e2)) = (op (e1) (e2)))) -> (~((e0) = (e1))) -> ((op (e1) (e3)) = (e1)) -> False). % 15.55/15.74 do 0 intro. intros zenon_H58 zenon_H59 zenon_H2af zenon_H30 zenon_Hde zenon_He6 zenon_H140 zenon_Ha3 zenon_H1d3 zenon_H1e3 zenon_H10f zenon_H109 zenon_H44 zenon_H11b zenon_H1d5 zenon_H2d5 zenon_H10d zenon_H2be zenon_H1df zenon_H138 zenon_H1b3 zenon_H157 zenon_H6a zenon_H1a2 zenon_H10e zenon_H1e5 zenon_H175 zenon_H166 zenon_H121 zenon_Hce zenon_H1d0 zenon_H36 zenon_H3b zenon_Hf1 zenon_Hc9 zenon_H84 zenon_H80 zenon_H35 zenon_H7d zenon_Ha7 zenon_H228 zenon_H22e zenon_H1b4 zenon_H2b8 zenon_H25e zenon_H17d zenon_H90 zenon_H135 zenon_H146 zenon_H254 zenon_H105 zenon_H247 zenon_H2b4 zenon_Hb4 zenon_Hb7 zenon_Hbe zenon_H45 zenon_H10c zenon_H15f zenon_H1c3 zenon_H1cf zenon_H1d2 zenon_Hf0 zenon_H4b zenon_H1f6 zenon_H52 zenon_H28 zenon_Hd6 zenon_H8e zenon_H20 zenon_H163 zenon_H104 zenon_H1d8 zenon_Hd7 zenon_H3c zenon_H5e zenon_H2ab zenon_H92 zenon_H3d zenon_H13c zenon_H3e zenon_Hae zenon_H145 zenon_Hab zenon_H87 zenon_H9e zenon_H11f. % 15.55/15.74 apply (zenon_or_s _ _ zenon_H163); [ zenon_intro zenon_Had | zenon_intro zenon_H164 ]. % 15.55/15.74 apply (zenon_or_s _ _ zenon_H11b); [ zenon_intro zenon_H29 | zenon_intro zenon_H11c ]. % 15.55/15.74 apply (zenon_L37_); trivial. % 15.55/15.74 apply (zenon_or_s _ _ zenon_H11c); [ zenon_intro zenon_H117 | zenon_intro zenon_H11d ]. % 15.55/15.74 apply (zenon_L763_); trivial. % 15.55/15.74 apply (zenon_or_s _ _ zenon_H11d); [ zenon_intro zenon_H2a | zenon_intro zenon_H119 ]. % 15.55/15.74 exact (zenon_H52 zenon_H2a). % 15.55/15.74 apply (zenon_or_s _ _ zenon_H175); [ zenon_intro zenon_H50 | zenon_intro zenon_H176 ]. % 15.55/15.74 apply (zenon_L760_); trivial. % 15.55/15.74 apply (zenon_or_s _ _ zenon_H176); [ zenon_intro zenon_H88 | zenon_intro zenon_H177 ]. % 15.55/15.74 apply (zenon_or_s _ _ zenon_H2d5); [ zenon_intro zenon_Hba | zenon_intro zenon_H2d6 ]. % 15.55/15.74 apply (zenon_L1316_); trivial. % 15.55/15.74 apply (zenon_or_s _ _ zenon_H2d6); [ zenon_intro zenon_H10a | zenon_intro zenon_H2d7 ]. % 15.55/15.74 apply (zenon_L1321_); trivial. % 15.55/15.74 apply (zenon_or_s _ _ zenon_H2d7); [ zenon_intro zenon_H106 | zenon_intro zenon_H42 ]. % 15.55/15.74 apply (zenon_L164_); trivial. % 15.55/15.74 exact (zenon_H3e zenon_H42). % 15.55/15.74 apply (zenon_or_s _ _ zenon_H177); [ zenon_intro zenon_H34 | zenon_intro zenon_H106 ]. % 15.55/15.74 exact (zenon_H30 zenon_H34). % 15.55/15.74 apply (zenon_L1326_); trivial. % 15.55/15.74 apply (zenon_or_s _ _ zenon_H164); [ zenon_intro zenon_H149 | zenon_intro zenon_H165 ]. % 15.55/15.74 exact (zenon_H145 zenon_H149). % 15.55/15.74 apply (zenon_or_s _ _ zenon_H165); [ zenon_intro zenon_H15d | zenon_intro zenon_Hcc ]. % 15.55/15.74 apply (zenon_L136_); trivial. % 15.55/15.74 apply (zenon_L208_); trivial. % 15.55/15.74 (* end of lemma zenon_L1327_ *) % 15.55/15.74 assert (zenon_L1328_ : (((op (e0) (e0)) = (e2))\/(((op (e1) (e0)) = (e2))\/(((op (e2) (e0)) = (e2))\/((op (e3) (e0)) = (e2))))) -> ((op (e1) (e3)) = (e1)) -> (~((e0) = (e1))) -> (~((op (e0) (e2)) = (op (e1) (e2)))) -> ((op (e2) (e0)) = (e1)) -> (~((op (e2) (e1)) = (op (e3) (e1)))) -> (((op (e2) (e3)) = (e0))\/(((op (e2) (e3)) = (e1))\/(((op (e2) (e3)) = (e2))\/((op (e2) (e3)) = (e3))))) -> (~((e0) = (e2))) -> (~((op (e1) (e0)) = (op (e1) (e1)))) -> ((~((op (e1) (e1)) = (e1)))\/((op (e1) (e1)) = (e1))) -> (((op (e1) (e0)) = (e0))\/(((op (e1) (e1)) = (e0))\/(((op (e1) (e2)) = (e0))\/((op (e1) (e3)) = (e0))))) -> (~((op (e0) (e0)) = (e0))) -> (((op (e0) (e0)) = (e2))\/(((op (e0) (e1)) = (e2))\/(((op (e0) (e2)) = (e2))\/((op (e0) (e3)) = (e2))))) -> (~((op (e0) (e2)) = (op (e2) (e2)))) -> (~((op (e2) (e2)) = (e1))) -> (~((e0) = (e3))) -> (((op (e0) (e0)) = (e0))\/(((op (e1) (e0)) = (e0))\/(((op (e2) (e0)) = (e0))\/((op (e3) (e0)) = (e0))))) -> ((~((op (e1) (e1)) = (e3)))\/((op (e1) (e3)) = (e1))) -> (~((op (e1) (e0)) = (op (e1) (e3)))) -> ((~((op (e2) (e2)) = (e3)))\/((op (e2) (e3)) = (e2))) -> (~((op (e2) (e2)) = (op (e2) (e3)))) -> ((~((op (e3) (e3)) = (e1)))\/((op (e3) (e1)) = (e3))) -> (~((op (e0) (e0)) = (e1))) -> (((op (e0) (e0)) = (e3))\/(((op (e1) (e0)) = (e3))\/(((op (e2) (e0)) = (e3))\/((op (e3) (e0)) = (e3))))) -> (((op (e2) (e0)) = (e1))\/(((op (e2) (e1)) = (e1))\/(((op (e2) (e2)) = (e1))\/((op (e2) (e3)) = (e1))))) -> (~((op (e0) (e3)) = (op (e2) (e3)))) -> (~((op (e1) (e0)) = (op (e2) (e0)))) -> (~((op (e3) (e0)) = (op (e3) (e2)))) -> (((op (e0) (e3)) = (e0))\/(((op (e0) (e3)) = (e1))\/(((op (e0) (e3)) = (e2))\/((op (e0) (e3)) = (e3))))) -> (((op (e3) (e0)) = (e1))\/(((op (e3) (e1)) = (e1))\/(((op (e3) (e2)) = (e1))\/((op (e3) (e3)) = (e1))))) -> (~((op (e3) (e1)) = (op (e3) (e2)))) -> (((op (e1) (e0)) = (e3))\/(((op (e1) (e1)) = (e3))\/(((op (e1) (e2)) = (e3))\/((op (e1) (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 (e1) (e0)) = (op (e3) (e0)))) -> (((op (e0) (e1)) = (e1))\/(((op (e1) (e1)) = (e1))\/(((op (e2) (e1)) = (e1))\/((op (e3) (e1)) = (e1))))) -> (~((e1) = (e2))) -> (~((op (e1) (e2)) = (op (e2) (e2)))) -> (~((op (e0) (e3)) = (op (e1) (e3)))) -> (((op (e1) (e0)) = (e2))\/(((op (e1) (e1)) = (e2))\/(((op (e1) (e2)) = (e2))\/((op (e1) (e3)) = (e2))))) -> (~((op (e0) (e2)) = (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 (e1) (e2)) = (op (e1) (e3)))) -> (~((op (e2) (e0)) = (op (e2) (e3)))) -> (((op (e0) (e3)) = (e1))\/(((op (e1) (e3)) = (e1))\/(((op (e2) (e3)) = (e1))\/((op (e3) (e3)) = (e1))))) -> (~((op (e1) (e0)) = (op (e1) (e2)))) -> (((op (e0) (e2)) = (e3))\/(((op (e1) (e2)) = (e3))\/(((op (e2) (e2)) = (e3))\/((op (e3) (e2)) = (e3))))) -> (~((op (e2) (e0)) = (op (e3) (e0)))) -> ((~((op (e3) (e3)) = (e2)))\/((op (e3) (e2)) = (e3))) -> (((op (e0) (e1)) = (e2))\/(((op (e1) (e1)) = (e2))\/(((op (e2) (e1)) = (e2))\/((op (e3) (e1)) = (e2))))) -> (~((e2) = (e3))) -> (~((op (e2) (e1)) = (op (e2) (e2)))) -> (~((op (e0) (e1)) = (op (e3) (e1)))) -> (((op (e3) (e0)) = (e2))\/(((op (e3) (e1)) = (e2))\/(((op (e3) (e2)) = (e2))\/((op (e3) (e3)) = (e2))))) -> (~((op (e3) (op (e3) (e3))) = (op (e3) (e3)))) -> ((~((op (e3) (e3)) = (e3)))\/((op (e3) (e3)) = (e3))) -> (((op (e3) (e0)) = (e3))\/(((op (e3) (e1)) = (e3))\/(((op (e3) (e2)) = (e3))\/((op (e3) (e3)) = (e3))))) -> (((op (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 (e0) (e0)) = (e1))\/(((op (e0) (e1)) = (e1))\/(((op (e0) (e2)) = (e1))\/((op (e0) (e3)) = (e1))))) -> (~((op (e3) (e0)) = (op (e3) (e1)))) -> ((~((op (e3) (e3)) = (e0)))\/((op (e3) (e0)) = (e3))) -> ((~((op (e2) (e2)) = (e1)))\/((op (e2) (e1)) = (e2))) -> ((~((op (e1) (e1)) = (e2)))\/((op (e1) (e2)) = (e1))) -> (~((e1) = (e3))) -> (((op (e2) (e0)) = (e3))\/(((op (e2) (e1)) = (e3))\/(((op (e2) (e2)) = (e3))\/((op (e2) (e3)) = (e3))))) -> (~((op (e0) (e1)) = (op (e2) (e1)))) -> (~((op (e2) (e2)) = (e3))) -> (~((op (e2) (op (e3) (e2))) = (op (e3) (e2)))) -> (~((op (e0) (e0)) = (e3))) -> (((op (e0) (e0)) = (e3))\/(((op (e0) (e1)) = (e3))\/(((op (e0) (e2)) = (e3))\/((op (e0) (e3)) = (e3))))) -> (~((op (e3) (e3)) = (e3))) -> (~((op (e3) (e3)) = (e2))) -> (~((op (e3) (e3)) = (e1))) -> (((op (e3) (e3)) = (e0))\/(((op (e3) (e3)) = (e1))\/(((op (e3) (e3)) = (e2))\/((op (e3) (e3)) = (e3))))) -> (~((op (e1) (e1)) = (e2))) -> (~((op (e1) (e1)) = (e1))) -> (~((op (e1) (e1)) = (e0))) -> (((op (e1) (e1)) = (e0))\/(((op (e1) (e1)) = (e1))\/(((op (e1) (e1)) = (e2))\/((op (e1) (e1)) = (e3))))) -> (~((op (e2) (e0)) = (op (e2) (e2)))) -> ((op (e2) (e2)) = (e2)) -> (((op (e3) (e0)) = (e0))\/(((op (e3) (e1)) = (e0))\/(((op (e3) (e2)) = (e0))\/((op (e3) (e3)) = (e0))))) -> (~((op (e0) (op (e3) (e0))) = (op (e3) (e0)))) -> ((op (e1) (e0)) = (e0)) -> (~((op (e1) (op (e3) (e1))) = (op (e3) (e1)))) -> ((op (e0) (e2)) = (e0)) -> (~((op (e0) (e2)) = (op (e3) (e2)))) -> (~((op (e3) (e3)) = (e0))) -> False). % 15.55/15.74 do 0 intro. intros zenon_Heb zenon_H11f zenon_H9e zenon_H87 zenon_Hae zenon_H13c zenon_H2ab zenon_H5e zenon_Hd7 zenon_H1d8 zenon_H163 zenon_H20 zenon_H8e zenon_H28 zenon_H52 zenon_H4b zenon_Hf0 zenon_H1d2 zenon_H1cf zenon_H1c3 zenon_H15f zenon_H10c zenon_H45 zenon_Hbe zenon_Hb7 zenon_Hb4 zenon_H247 zenon_H105 zenon_H254 zenon_H146 zenon_H135 zenon_H90 zenon_H17d zenon_H25e zenon_H22e zenon_H228 zenon_Ha7 zenon_H7d zenon_H80 zenon_H84 zenon_Hc9 zenon_Hf1 zenon_H36 zenon_H1d0 zenon_Hce zenon_H121 zenon_H166 zenon_H175 zenon_H1e5 zenon_H10e zenon_H1a2 zenon_H6a zenon_H157 zenon_H138 zenon_H1df zenon_H2be zenon_H10d zenon_H2d5 zenon_H1d5 zenon_H11b zenon_H44 zenon_H109 zenon_H10f zenon_H1e3 zenon_H1d3 zenon_Ha3 zenon_He6 zenon_Hde zenon_H30 zenon_H2af zenon_H59 zenon_H58 zenon_H3e zenon_H3d zenon_H104 zenon_H3b zenon_Hd6 zenon_H1b4 zenon_H145 zenon_H1b3 zenon_H17a zenon_H35 zenon_H1f6 zenon_H2b8 zenon_Had zenon_H2b4 zenon_Hab zenon_H140 zenon_H3c. % 15.55/15.74 apply (zenon_or_s _ _ zenon_Heb); [ zenon_intro zenon_H92 | zenon_intro zenon_Hec ]. % 15.55/15.74 apply (zenon_L1327_); trivial. % 15.55/15.74 apply (zenon_or_s _ _ zenon_Hec); [ zenon_intro zenon_H68 | zenon_intro zenon_Hed ]. % 15.55/15.74 apply (zenon_L357_); trivial. % 15.55/15.74 apply (zenon_or_s _ _ zenon_Hed); [ zenon_intro zenon_Hdd | zenon_intro zenon_He9 ]. % 15.55/15.74 apply (zenon_L161_); trivial. % 15.55/15.74 apply (zenon_L1137_); trivial. % 15.55/15.74 (* end of lemma zenon_L1328_ *) % 15.55/15.74 assert (zenon_L1329_ : (~((op (e0) (e2)) = (op (e3) (e2)))) -> ((op (e0) (e2)) = (e0)) -> (~((op (e1) (op (e3) (e1))) = (op (e3) (e1)))) -> (~((op (e0) (op (e3) (e0))) = (op (e3) (e0)))) -> (((op (e3) (e0)) = (e0))\/(((op (e3) (e1)) = (e0))\/(((op (e3) (e2)) = (e0))\/((op (e3) (e3)) = (e0))))) -> (~((op (e2) (e0)) = (op (e2) (e2)))) -> (~((op (e3) (e3)) = (e2))) -> (((op (e0) (e0)) = (e3))\/(((op (e0) (e1)) = (e3))\/(((op (e0) (e2)) = (e3))\/((op (e0) (e3)) = (e3))))) -> (~((op (e0) (e0)) = (e3))) -> (~((op (e2) (op (e3) (e2))) = (op (e3) (e2)))) -> (~((op (e2) (e2)) = (e3))) -> (~((op (e0) (e1)) = (op (e2) (e1)))) -> (((op (e2) (e0)) = (e3))\/(((op (e2) (e1)) = (e3))\/(((op (e2) (e2)) = (e3))\/((op (e2) (e3)) = (e3))))) -> (~((e1) = (e3))) -> ((~((op (e1) (e1)) = (e2)))\/((op (e1) (e2)) = (e1))) -> ((~((op (e2) (e2)) = (e1)))\/((op (e2) (e1)) = (e2))) -> ((~((op (e3) (e3)) = (e0)))\/((op (e3) (e0)) = (e3))) -> (~((op (e3) (e0)) = (op (e3) (e1)))) -> (((op (e0) (e0)) = (e1))\/(((op (e0) (e1)) = (e1))\/(((op (e0) (e2)) = (e1))\/((op (e0) (e3)) = (e1))))) -> (((op (e0) (e2)) = (e1))\/(((op (e1) (e2)) = (e1))\/(((op (e2) (e2)) = (e1))\/((op (e3) (e2)) = (e1))))) -> (((op (e1) (e2)) = (e0))\/(((op (e1) (e2)) = (e1))\/(((op (e1) (e2)) = (e2))\/((op (e1) (e2)) = (e3))))) -> (((op (e3) (e0)) = (e3))\/(((op (e3) (e1)) = (e3))\/(((op (e3) (e2)) = (e3))\/((op (e3) (e3)) = (e3))))) -> ((~((op (e3) (e3)) = (e3)))\/((op (e3) (e3)) = (e3))) -> (~((op (e3) (op (e3) (e3))) = (op (e3) (e3)))) -> (((op (e3) (e0)) = (e2))\/(((op (e3) (e1)) = (e2))\/(((op (e3) (e2)) = (e2))\/((op (e3) (e3)) = (e2))))) -> (~((op (e0) (e1)) = (op (e3) (e1)))) -> (~((op (e2) (e1)) = (op (e2) (e2)))) -> (((op (e0) (e1)) = (e2))\/(((op (e1) (e1)) = (e2))\/(((op (e2) (e1)) = (e2))\/((op (e3) (e1)) = (e2))))) -> ((~((op (e3) (e3)) = (e2)))\/((op (e3) (e2)) = (e3))) -> (~((op (e2) (e0)) = (op (e3) (e0)))) -> (((op (e0) (e2)) = (e3))\/(((op (e1) (e2)) = (e3))\/(((op (e2) (e2)) = (e3))\/((op (e3) (e2)) = (e3))))) -> (~((op (e1) (e0)) = (op (e1) (e2)))) -> (((op (e0) (e3)) = (e1))\/(((op (e1) (e3)) = (e1))\/(((op (e2) (e3)) = (e1))\/((op (e3) (e3)) = (e1))))) -> (~((op (e2) (e0)) = (op (e2) (e3)))) -> (~((op (e1) (e2)) = (op (e1) (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)) = (op (e0) (e3)))) -> (~((op (e0) (e3)) = (op (e1) (e3)))) -> (~((e1) = (e2))) -> (((op (e0) (e1)) = (e1))\/(((op (e1) (e1)) = (e1))\/(((op (e2) (e1)) = (e1))\/((op (e3) (e1)) = (e1))))) -> (~((op (e1) (e0)) = (op (e3) (e0)))) -> (((op (e3) (e2)) = (e0))\/(((op (e3) (e2)) = (e1))\/(((op (e3) (e2)) = (e2))\/((op (e3) (e2)) = (e3))))) -> (~((op (e1) (e2)) = (op (e3) (e2)))) -> (((op (e1) (e0)) = (e3))\/(((op (e1) (e1)) = (e3))\/(((op (e1) (e2)) = (e3))\/((op (e1) (e3)) = (e3))))) -> (~((op (e3) (e1)) = (op (e3) (e2)))) -> (((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 (e3) (e0)) = (op (e3) (e2)))) -> (~((op (e1) (e0)) = (op (e2) (e0)))) -> (~((op (e0) (e3)) = (op (e2) (e3)))) -> (((op (e2) (e0)) = (e1))\/(((op (e2) (e1)) = (e1))\/(((op (e2) (e2)) = (e1))\/((op (e2) (e3)) = (e1))))) -> (((op (e0) (e0)) = (e3))\/(((op (e1) (e0)) = (e3))\/(((op (e2) (e0)) = (e3))\/((op (e3) (e0)) = (e3))))) -> (~((op (e0) (e0)) = (e1))) -> ((~((op (e3) (e3)) = (e1)))\/((op (e3) (e1)) = (e3))) -> (~((op (e2) (e2)) = (op (e2) (e3)))) -> ((~((op (e2) (e2)) = (e3)))\/((op (e2) (e3)) = (e2))) -> (~((op (e1) (e0)) = (op (e1) (e3)))) -> ((~((op (e1) (e1)) = (e3)))\/((op (e1) (e3)) = (e1))) -> (((op (e0) (e0)) = (e0))\/(((op (e1) (e0)) = (e0))\/(((op (e2) (e0)) = (e0))\/((op (e3) (e0)) = (e0))))) -> (~((e0) = (e3))) -> (~((op (e2) (e2)) = (e1))) -> (~((op (e0) (e2)) = (op (e2) (e2)))) -> (((op (e0) (e0)) = (e2))\/(((op (e0) (e1)) = (e2))\/(((op (e0) (e2)) = (e2))\/((op (e0) (e3)) = (e2))))) -> (~((op (e0) (e0)) = (e0))) -> (((op (e1) (e0)) = (e0))\/(((op (e1) (e1)) = (e0))\/(((op (e1) (e2)) = (e0))\/((op (e1) (e3)) = (e0))))) -> ((~((op (e1) (e1)) = (e1)))\/((op (e1) (e1)) = (e1))) -> (~((op (e1) (e0)) = (op (e1) (e1)))) -> (((op (e2) (e3)) = (e0))\/(((op (e2) (e3)) = (e1))\/(((op (e2) (e3)) = (e2))\/((op (e2) (e3)) = (e3))))) -> (~((op (e2) (e1)) = (op (e3) (e1)))) -> ((op (e2) (e0)) = (e1)) -> (~((op (e0) (e2)) = (op (e1) (e2)))) -> (~((e0) = (e1))) -> (((op (e0) (e0)) = (e2))\/(((op (e1) (e0)) = (e2))\/(((op (e2) (e0)) = (e2))\/((op (e3) (e0)) = (e2))))) -> (~((op (e1) (e1)) = (e3))) -> (((op (e1) (e0)) = (e1))\/(((op (e1) (e1)) = (e1))\/(((op (e1) (e2)) = (e1))\/((op (e1) (e3)) = (e1))))) -> (~((op (e3) (e3)) = (e3))) -> (~((op (e3) (e3)) = (e1))) -> (~((op (e3) (e3)) = (e0))) -> (((op (e3) (e3)) = (e0))\/(((op (e3) (e3)) = (e1))\/(((op (e3) (e3)) = (e2))\/((op (e3) (e3)) = (e3))))) -> (~((op (e1) (e1)) = (e1))) -> (~((op (e1) (e1)) = (e0))) -> (((op (e1) (e1)) = (e0))\/(((op (e1) (e1)) = (e1))\/(((op (e1) (e1)) = (e2))\/((op (e1) (e1)) = (e3))))) -> (((op (e1) (e0)) = (e2))\/(((op (e1) (e1)) = (e2))\/(((op (e1) (e2)) = (e2))\/((op (e1) (e3)) = (e2))))) -> (~((e2) = (e3))) -> ((op (e1) (e0)) = (e3)) -> (~((op (e1) (e1)) = (e2))) -> (~((op (e1) (e2)) = (op (e2) (e2)))) -> ((op (e2) (e2)) = (e2)) -> (~((e0) = (e2))) -> False). % 15.55/15.74 do 0 intro. intros zenon_H140 zenon_Hab zenon_H2b4 zenon_H2b8 zenon_H1f6 zenon_H17a zenon_H3d zenon_H58 zenon_H59 zenon_H2af zenon_H30 zenon_Hde zenon_He6 zenon_Ha3 zenon_H1d3 zenon_H1e3 zenon_H10f zenon_H109 zenon_H44 zenon_H11b zenon_H1d5 zenon_H2d5 zenon_H10d zenon_H2be zenon_H1df zenon_H138 zenon_H157 zenon_H1a2 zenon_H10e zenon_H1e5 zenon_H175 zenon_H166 zenon_H121 zenon_Hce zenon_H1d0 zenon_H36 zenon_Hf1 zenon_Hc9 zenon_H80 zenon_Ha7 zenon_H228 zenon_H22e zenon_H25e zenon_H17d zenon_H90 zenon_H135 zenon_H146 zenon_H254 zenon_H105 zenon_H247 zenon_Hb4 zenon_Hb7 zenon_Hbe zenon_H45 zenon_H10c zenon_H15f zenon_H1c3 zenon_H1cf zenon_H1d2 zenon_Hf0 zenon_H4b zenon_H52 zenon_H28 zenon_H8e zenon_H20 zenon_H163 zenon_H1d8 zenon_Hd7 zenon_H2ab zenon_H13c zenon_Hae zenon_H87 zenon_H9e zenon_Heb zenon_H182 zenon_H1c5 zenon_H3e zenon_H104 zenon_H3c zenon_H3b zenon_H1b4 zenon_H145 zenon_H1b3 zenon_H84 zenon_H6a zenon_H69 zenon_Hd6 zenon_H7d zenon_H35 zenon_H5e. % 15.55/15.74 apply (zenon_or_s _ _ zenon_H163); [ zenon_intro zenon_Had | zenon_intro zenon_H164 ]. % 15.55/15.74 apply (zenon_or_s _ _ zenon_H1c5); [ zenon_intro zenon_Hd8 | zenon_intro zenon_H1c6 ]. % 15.55/15.74 apply (zenon_L163_); trivial. % 15.55/15.74 apply (zenon_or_s _ _ zenon_H1c6); [ zenon_intro zenon_H21 | zenon_intro zenon_H1c7 ]. % 15.55/15.74 exact (zenon_H1b4 zenon_H21). % 15.55/15.74 apply (zenon_or_s _ _ zenon_H1c7); [ zenon_intro zenon_H117 | zenon_intro zenon_H11f ]. % 15.55/15.74 apply (zenon_L1315_); trivial. % 15.55/15.74 apply (zenon_L1328_); trivial. % 15.55/15.74 apply (zenon_or_s _ _ zenon_H164); [ zenon_intro zenon_H149 | zenon_intro zenon_H165 ]. % 15.55/15.74 exact (zenon_H145 zenon_H149). % 15.55/15.74 apply (zenon_or_s _ _ zenon_H165); [ zenon_intro zenon_H15d | zenon_intro zenon_Hcc ]. % 15.55/15.74 apply (zenon_L490_); trivial. % 15.55/15.74 apply (zenon_L524_); trivial. % 15.55/15.74 (* end of lemma zenon_L1329_ *) % 15.55/15.74 assert (zenon_L1330_ : (~((e0) = (e2))) -> (~((op (e3) (e3)) = (e0))) -> (~((op (e3) (e3)) = (e1))) -> (~((op (e3) (e3)) = (e3))) -> (((op (e1) (e0)) = (e1))\/(((op (e1) (e1)) = (e1))\/(((op (e1) (e2)) = (e1))\/((op (e1) (e3)) = (e1))))) -> (~((op (e1) (e1)) = (e3))) -> (((op (e0) (e0)) = (e2))\/(((op (e1) (e0)) = (e2))\/(((op (e2) (e0)) = (e2))\/((op (e3) (e0)) = (e2))))) -> (~((op (e0) (e2)) = (op (e1) (e2)))) -> (~((op (e2) (e1)) = (op (e3) (e1)))) -> (((op (e2) (e3)) = (e0))\/(((op (e2) (e3)) = (e1))\/(((op (e2) (e3)) = (e2))\/((op (e2) (e3)) = (e3))))) -> (~((op (e1) (e0)) = (op (e1) (e1)))) -> ((~((op (e1) (e1)) = (e1)))\/((op (e1) (e1)) = (e1))) -> (((op (e1) (e0)) = (e0))\/(((op (e1) (e1)) = (e0))\/(((op (e1) (e2)) = (e0))\/((op (e1) (e3)) = (e0))))) -> ((~((op (e1) (e1)) = (e3)))\/((op (e1) (e3)) = (e1))) -> (~((op (e1) (e0)) = (op (e1) (e3)))) -> ((~((op (e2) (e2)) = (e3)))\/((op (e2) (e3)) = (e2))) -> (~((op (e2) (e2)) = (op (e2) (e3)))) -> (((op (e0) (e0)) = (e3))\/(((op (e1) (e0)) = (e3))\/(((op (e2) (e0)) = (e3))\/((op (e3) (e0)) = (e3))))) -> (~((op (e3) (e1)) = (op (e3) (e2)))) -> (((op (e1) (e0)) = (e3))\/(((op (e1) (e1)) = (e3))\/(((op (e1) (e2)) = (e3))\/((op (e1) (e3)) = (e3))))) -> (((op (e3) (e2)) = (e0))\/(((op (e3) (e2)) = (e1))\/(((op (e3) (e2)) = (e2))\/((op (e3) (e2)) = (e3))))) -> (~((op (e1) (e0)) = (op (e3) (e0)))) -> (((op (e0) (e1)) = (e1))\/(((op (e1) (e1)) = (e1))\/(((op (e2) (e1)) = (e1))\/((op (e3) (e1)) = (e1))))) -> (~((op (e0) (e3)) = (op (e3) (e3)))) -> (~((op (e1) (e2)) = (op (e1) (e3)))) -> (~((op (e2) (e0)) = (op (e2) (e3)))) -> (((op (e0) (e3)) = (e1))\/(((op (e1) (e3)) = (e1))\/(((op (e2) (e3)) = (e1))\/((op (e3) (e3)) = (e1))))) -> (~((op (e1) (e0)) = (op (e1) (e2)))) -> (((op (e0) (e2)) = (e3))\/(((op (e1) (e2)) = (e3))\/(((op (e2) (e2)) = (e3))\/((op (e3) (e2)) = (e3))))) -> (~((op (e2) (e0)) = (op (e3) (e0)))) -> (((op (e3) (e0)) = (e3))\/(((op (e3) (e1)) = (e3))\/(((op (e3) (e2)) = (e3))\/((op (e3) (e3)) = (e3))))) -> (((op (e1) (e2)) = (e0))\/(((op (e1) (e2)) = (e1))\/(((op (e1) (e2)) = (e2))\/((op (e1) (e2)) = (e3))))) -> (((op (e0) (e0)) = (e1))\/(((op (e0) (e1)) = (e1))\/(((op (e0) (e2)) = (e1))\/((op (e0) (e3)) = (e1))))) -> ((~((op (e3) (e3)) = (e0)))\/((op (e3) (e0)) = (e3))) -> ((~((op (e2) (e2)) = (e1)))\/((op (e2) (e1)) = (e2))) -> ((~((op (e1) (e1)) = (e2)))\/((op (e1) (e2)) = (e1))) -> (((op (e2) (e0)) = (e3))\/(((op (e2) (e1)) = (e3))\/(((op (e2) (e2)) = (e3))\/((op (e2) (e3)) = (e3))))) -> (~((op (e0) (e1)) = (op (e2) (e1)))) -> (~((op (e2) (e2)) = (e3))) -> (~((op (e0) (e0)) = (e3))) -> (((op (e0) (e0)) = (e3))\/(((op (e0) (e1)) = (e3))\/(((op (e0) (e2)) = (e3))\/((op (e0) (e3)) = (e3))))) -> (~((op (e3) (e3)) = (e2))) -> (~((op (e2) (e0)) = (op (e2) (e2)))) -> ((op (e2) (e0)) = (e1)) -> ((~((op (e3) (e3)) = (e1)))\/((op (e3) (e1)) = (e3))) -> (~((op (e3) (e0)) = (op (e3) (e1)))) -> ((~((op (e3) (e3)) = (e3)))\/((op (e3) (e3)) = (e3))) -> (~((op (e3) (op (e3) (e3))) = (op (e3) (e3)))) -> (~((op (e0) (e0)) = (e0))) -> (((op (e0) (e0)) = (e2))\/(((op (e0) (e1)) = (e2))\/(((op (e0) (e2)) = (e2))\/((op (e0) (e3)) = (e2))))) -> (((op (e1) (e1)) = (e0))\/(((op (e1) (e1)) = (e1))\/(((op (e1) (e1)) = (e2))\/((op (e1) (e1)) = (e3))))) -> (((op (e3) (e3)) = (e0))\/(((op (e3) (e3)) = (e1))\/(((op (e3) (e3)) = (e2))\/((op (e3) (e3)) = (e3))))) -> (~((op (e1) (e1)) = (e2))) -> (~((op (e1) (e1)) = (e1))) -> (~((op (e1) (e1)) = (e0))) -> (~((op (e1) (e2)) = (op (e2) (e2)))) -> (~((op (e0) (e3)) = (op (e1) (e3)))) -> (((op (e1) (e0)) = (e2))\/(((op (e1) (e1)) = (e2))\/(((op (e1) (e2)) = (e2))\/((op (e1) (e3)) = (e2))))) -> (~((op (e0) (e2)) = (op (e2) (e2)))) -> (~((op (e0) (e1)) = (op (e3) (e1)))) -> (~((e0) = (e1))) -> ((op (e0) (e2)) = (e0)) -> (((op (e3) (e0)) = (e1))\/(((op (e3) (e1)) = (e1))\/(((op (e3) (e2)) = (e1))\/((op (e3) (e3)) = (e1))))) -> (~((op (e1) (e2)) = (op (e3) (e2)))) -> (~((e2) = (e3))) -> (~((op (e1) (op (e3) (e1))) = (op (e3) (e1)))) -> (~((op (e2) (op (e3) (e2))) = (op (e3) (e2)))) -> ((op (e2) (e2)) = (e2)) -> (((op (e3) (e0)) = (e2))\/(((op (e3) (e1)) = (e2))\/(((op (e3) (e2)) = (e2))\/((op (e3) (e3)) = (e2))))) -> (~((e1) = (e3))) -> (~((op (e2) (e2)) = (e1))) -> (((op (e3) (e0)) = (e0))\/(((op (e3) (e1)) = (e0))\/(((op (e3) (e2)) = (e0))\/((op (e3) (e3)) = (e0))))) -> (~((op (e0) (e2)) = (op (e3) (e2)))) -> (~((e0) = (e3))) -> (((op (e0) (e2)) = (e1))\/(((op (e1) (e2)) = (e1))\/(((op (e2) (e2)) = (e1))\/((op (e3) (e2)) = (e1))))) -> (((op (e0) (e0)) = (e1))\/(((op (e1) (e0)) = (e1))\/(((op (e2) (e0)) = (e1))\/((op (e3) (e0)) = (e1))))) -> (~((op (e0) (e2)) = (op (e0) (e3)))) -> (((op (e0) (e1)) = (e2))\/(((op (e1) (e1)) = (e2))\/(((op (e2) (e1)) = (e2))\/((op (e3) (e1)) = (e2))))) -> (~((op (e1) (e0)) = (op (e2) (e0)))) -> (~((op (e0) (e3)) = (op (e2) (e3)))) -> (((op (e2) (e0)) = (e1))\/(((op (e2) (e1)) = (e1))\/(((op (e2) (e2)) = (e1))\/((op (e2) (e3)) = (e1))))) -> (~((op (e2) (e1)) = (op (e2) (e2)))) -> (~((e1) = (e2))) -> (~((op (e0) (op (e3) (e0))) = (op (e3) (e0)))) -> (((op (e0) (e3)) = (e0))\/(((op (e0) (e3)) = (e1))\/(((op (e0) (e3)) = (e2))\/((op (e0) (e3)) = (e3))))) -> (~((op (e0) (e0)) = (e1))) -> (((op (e0) (e0)) = (e0))\/(((op (e1) (e0)) = (e0))\/(((op (e2) (e0)) = (e0))\/((op (e3) (e0)) = (e0))))) -> (~((op (e3) (e0)) = (op (e3) (e2)))) -> ((~((op (e3) (e3)) = (e2)))\/((op (e3) (e2)) = (e3))) -> False). % 15.55/15.74 do 0 intro. intros zenon_H5e zenon_H3c zenon_H104 zenon_H3e zenon_H1c5 zenon_H182 zenon_Heb zenon_H87 zenon_H13c zenon_H2ab zenon_Hd7 zenon_H1d8 zenon_H163 zenon_H1d2 zenon_H1cf zenon_H1c3 zenon_H15f zenon_Hbe zenon_H135 zenon_H90 zenon_H25e zenon_H22e zenon_H228 zenon_H36 zenon_H1d0 zenon_Hce zenon_H121 zenon_H166 zenon_H175 zenon_H1e5 zenon_H2d5 zenon_H1d5 zenon_H44 zenon_H10f zenon_H1e3 zenon_H1d3 zenon_He6 zenon_Hde zenon_H30 zenon_H59 zenon_H58 zenon_H3d zenon_H17a zenon_Hae zenon_H10c zenon_H109 zenon_H10d zenon_H2be zenon_H20 zenon_H8e zenon_H1b3 zenon_H3b zenon_Hd6 zenon_H1b4 zenon_H145 zenon_H7d zenon_H80 zenon_H84 zenon_H28 zenon_H138 zenon_H9e zenon_Hab zenon_H146 zenon_H17d zenon_H6a zenon_H2b4 zenon_H2af zenon_H35 zenon_H1df zenon_Ha3 zenon_H52 zenon_H1f6 zenon_H140 zenon_H4b zenon_H11b zenon_Hf1 zenon_Hc9 zenon_H1a2 zenon_H247 zenon_Hb4 zenon_Hb7 zenon_H157 zenon_Ha7 zenon_H2b8 zenon_H254 zenon_H45 zenon_Hf0 zenon_H105 zenon_H10e. % 15.55/15.74 apply (zenon_or_s _ _ zenon_Hbe); [ zenon_intro zenon_H5b | zenon_intro zenon_Hbf ]. % 15.55/15.74 exact (zenon_H59 zenon_H5b). % 15.55/15.74 apply (zenon_or_s _ _ zenon_Hbf); [ zenon_intro zenon_H69 | zenon_intro zenon_Hc0 ]. % 15.55/15.74 apply (zenon_L1329_); trivial. % 15.55/15.74 apply (zenon_or_s _ _ zenon_Hc0); [ zenon_intro zenon_Haf | zenon_intro zenon_Hba ]. % 15.55/15.74 apply (zenon_L39_); trivial. % 15.55/15.74 apply (zenon_L1323_); trivial. % 15.55/15.74 (* end of lemma zenon_L1330_ *) % 15.55/15.74 assert (zenon_L1331_ : (~((op (e0) (op (e3) (e0))) = (op (e3) (e0)))) -> ((op (e2) (e0)) = (e0)) -> ((~((op (e1) (e1)) = (e2)))\/((op (e1) (e2)) = (e1))) -> ((~((op (e2) (e2)) = (e1)))\/((op (e2) (e1)) = (e2))) -> ((~((op (e3) (e3)) = (e0)))\/((op (e3) (e0)) = (e3))) -> (~((op (e3) (e0)) = (op (e3) (e1)))) -> (((op (e0) (e0)) = (e1))\/(((op (e0) (e1)) = (e1))\/(((op (e0) (e2)) = (e1))\/((op (e0) (e3)) = (e1))))) -> (~((op (e0) (e0)) = (e3))) -> (~((e1) = (e3))) -> (((op (e0) (e2)) = (e1))\/(((op (e1) (e2)) = (e1))\/(((op (e2) (e2)) = (e1))\/((op (e3) (e2)) = (e1))))) -> (((op (e1) (e2)) = (e0))\/(((op (e1) (e2)) = (e1))\/(((op (e1) (e2)) = (e2))\/((op (e1) (e2)) = (e3))))) -> (~((op (e0) (e2)) = (op (e1) (e2)))) -> (((op (e3) (e0)) = (e3))\/(((op (e3) (e1)) = (e3))\/(((op (e3) (e2)) = (e3))\/((op (e3) (e3)) = (e3))))) -> ((~((op (e3) (e3)) = (e3)))\/((op (e3) (e3)) = (e3))) -> (~((op (e3) (op (e3) (e3))) = (op (e3) (e3)))) -> (((op (e3) (e0)) = (e2))\/(((op (e3) (e1)) = (e2))\/(((op (e3) (e2)) = (e2))\/((op (e3) (e3)) = (e2))))) -> (~((op (e0) (e1)) = (op (e3) (e1)))) -> (((op (e1) (e1)) = (e0))\/(((op (e1) (e1)) = (e1))\/(((op (e1) (e1)) = (e2))\/((op (e1) (e1)) = (e3))))) -> (~((op (e2) (e1)) = (op (e2) (e2)))) -> (~((e2) = (e3))) -> (((op (e0) (e1)) = (e2))\/(((op (e1) (e1)) = (e2))\/(((op (e2) (e1)) = (e2))\/((op (e3) (e1)) = (e2))))) -> ((~((op (e3) (e3)) = (e2)))\/((op (e3) (e2)) = (e3))) -> (~((op (e2) (e0)) = (op (e3) (e0)))) -> (((op (e0) (e2)) = (e3))\/(((op (e1) (e2)) = (e3))\/(((op (e2) (e2)) = (e3))\/((op (e3) (e2)) = (e3))))) -> (~((op (e1) (e0)) = (op (e1) (e2)))) -> (((op (e0) (e3)) = (e1))\/(((op (e1) (e3)) = (e1))\/(((op (e2) (e3)) = (e1))\/((op (e3) (e3)) = (e1))))) -> (~((op (e2) (e0)) = (op (e2) (e3)))) -> (~((op (e1) (e2)) = (op (e1) (e3)))) -> (((op (e0) (e0)) = (e1))\/(((op (e1) (e0)) = (e1))\/(((op (e2) (e0)) = (e1))\/((op (e3) (e0)) = (e1))))) -> (~((op (e0) (e2)) = (op (e0) (e3)))) -> (((op (e1) (e0)) = (e2))\/(((op (e1) (e1)) = (e2))\/(((op (e1) (e2)) = (e2))\/((op (e1) (e3)) = (e2))))) -> (~((op (e0) (e3)) = (op (e1) (e3)))) -> ((op (e2) (e2)) = (e2)) -> (~((op (e1) (e2)) = (op (e2) (e2)))) -> (~((e1) = (e2))) -> (((op (e0) (e1)) = (e1))\/(((op (e1) (e1)) = (e1))\/(((op (e2) (e1)) = (e1))\/((op (e3) (e1)) = (e1))))) -> (~((op (e1) (e0)) = (op (e3) (e0)))) -> (~((op (e1) (e1)) = (e1))) -> (((op (e3) (e2)) = (e0))\/(((op (e3) (e2)) = (e1))\/(((op (e3) (e2)) = (e2))\/((op (e3) (e2)) = (e3))))) -> (~((op (e1) (e2)) = (op (e3) (e2)))) -> (((op (e1) (e0)) = (e3))\/(((op (e1) (e1)) = (e3))\/(((op (e1) (e2)) = (e3))\/((op (e1) (e3)) = (e3))))) -> (~((op (e2) (op (e3) (e2))) = (op (e3) (e2)))) -> (~((op (e3) (e1)) = (op (e3) (e2)))) -> (~((op (e0) (e2)) = (op (e3) (e2)))) -> (((op (e3) (e0)) = (e1))\/(((op (e3) (e1)) = (e1))\/(((op (e3) (e2)) = (e1))\/((op (e3) (e3)) = (e1))))) -> (((op (e0) (e3)) = (e0))\/(((op (e0) (e3)) = (e1))\/(((op (e0) (e3)) = (e2))\/((op (e0) (e3)) = (e3))))) -> (~((op (e3) (e0)) = (op (e3) (e2)))) -> (~((op (e1) (e0)) = (op (e2) (e0)))) -> (~((op (e1) (op (e3) (e1))) = (op (e3) (e1)))) -> (~((op (e0) (e3)) = (op (e2) (e3)))) -> (((op (e2) (e0)) = (e1))\/(((op (e2) (e1)) = (e1))\/(((op (e2) (e2)) = (e1))\/((op (e2) (e3)) = (e1))))) -> (((op (e0) (e0)) = (e3))\/(((op (e1) (e0)) = (e3))\/(((op (e2) (e0)) = (e3))\/((op (e3) (e0)) = (e3))))) -> (~((op (e0) (e0)) = (e1))) -> ((~((op (e3) (e3)) = (e1)))\/((op (e3) (e1)) = (e3))) -> (~((op (e2) (e2)) = (op (e2) (e3)))) -> ((~((op (e2) (e2)) = (e3)))\/((op (e2) (e3)) = (e2))) -> (~((op (e1) (e0)) = (op (e1) (e3)))) -> ((~((op (e1) (e1)) = (e3)))\/((op (e1) (e3)) = (e1))) -> (~((e0) = (e1))) -> ((op (e0) (e2)) = (e0)) -> (((op (e3) (e3)) = (e0))\/(((op (e3) (e3)) = (e1))\/(((op (e3) (e3)) = (e2))\/((op (e3) (e3)) = (e3))))) -> (~((op (e3) (e3)) = (e0))) -> (~((op (e0) (e3)) = (op (e3) (e3)))) -> (~((op (e3) (e3)) = (e2))) -> (~((op (e3) (e3)) = (e3))) -> False). % 15.55/15.74 do 0 intro. intros zenon_H2b8 zenon_Hcf zenon_H1d3 zenon_H1e3 zenon_H10f zenon_H109 zenon_H44 zenon_H59 zenon_Ha3 zenon_H11b zenon_H1d5 zenon_H87 zenon_H2d5 zenon_H10d zenon_H2be zenon_H1df zenon_H138 zenon_H1b3 zenon_H157 zenon_H6a zenon_H1a2 zenon_H10e zenon_H1e5 zenon_H175 zenon_H166 zenon_H121 zenon_Hce zenon_H1d0 zenon_Hf1 zenon_Hc9 zenon_H84 zenon_H80 zenon_H35 zenon_H7d zenon_Ha7 zenon_H228 zenon_H22e zenon_H1b4 zenon_H25e zenon_H17d zenon_H90 zenon_H2af zenon_H135 zenon_H140 zenon_H146 zenon_H254 zenon_H105 zenon_H247 zenon_H2b4 zenon_Hb4 zenon_Hb7 zenon_Hbe zenon_H45 zenon_H10c zenon_H15f zenon_H1c3 zenon_H1cf zenon_H1d2 zenon_H9e zenon_Hab zenon_H3b zenon_H3c zenon_H36 zenon_H3d zenon_H3e. % 15.55/15.74 apply (zenon_or_s _ _ zenon_H44); [ zenon_intro zenon_H47 | zenon_intro zenon_H46 ]. % 15.55/15.74 exact (zenon_H45 zenon_H47). % 15.55/15.74 apply (zenon_or_s _ _ zenon_H46); [ zenon_intro zenon_H22 | zenon_intro zenon_H48 ]. % 15.55/15.74 apply (zenon_or_s _ _ zenon_Hf1); [ zenon_intro zenon_H47 | zenon_intro zenon_Hf4 ]. % 15.55/15.74 exact (zenon_H45 zenon_H47). % 15.55/15.74 apply (zenon_or_s _ _ zenon_Hf4); [ zenon_intro zenon_Hd8 | zenon_intro zenon_Hf5 ]. % 15.55/15.74 apply (zenon_L1307_); trivial. % 15.55/15.74 apply (zenon_or_s _ _ zenon_Hf5); [ zenon_intro zenon_Hae | zenon_intro zenon_Hee ]. % 15.55/15.74 apply (zenon_L269_); trivial. % 15.55/15.74 apply (zenon_L1054_); trivial. % 15.55/15.74 apply (zenon_or_s _ _ zenon_H48); [ zenon_intro zenon_H29 | zenon_intro zenon_H37 ]. % 15.55/15.74 apply (zenon_L37_); trivial. % 15.55/15.74 apply (zenon_L7_); trivial. % 15.55/15.74 (* end of lemma zenon_L1331_ *) % 15.55/15.74 assert (zenon_L1332_ : ((~((op (e3) (e3)) = (e2)))\/((op (e3) (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)) = (e1))) -> (((op (e0) (e3)) = (e0))\/(((op (e0) (e3)) = (e1))\/(((op (e0) (e3)) = (e2))\/((op (e0) (e3)) = (e3))))) -> (~((op (e0) (op (e3) (e0))) = (op (e3) (e0)))) -> (~((e1) = (e2))) -> (~((op (e2) (e1)) = (op (e2) (e2)))) -> (((op (e2) (e0)) = (e1))\/(((op (e2) (e1)) = (e1))\/(((op (e2) (e2)) = (e1))\/((op (e2) (e3)) = (e1))))) -> (~((op (e0) (e3)) = (op (e2) (e3)))) -> (~((op (e1) (e0)) = (op (e2) (e0)))) -> (((op (e0) (e1)) = (e2))\/(((op (e1) (e1)) = (e2))\/(((op (e2) (e1)) = (e2))\/((op (e3) (e1)) = (e2))))) -> (~((op (e0) (e2)) = (op (e0) (e3)))) -> (((op (e0) (e0)) = (e1))\/(((op (e1) (e0)) = (e1))\/(((op (e2) (e0)) = (e1))\/((op (e3) (e0)) = (e1))))) -> (((op (e0) (e2)) = (e1))\/(((op (e1) (e2)) = (e1))\/(((op (e2) (e2)) = (e1))\/((op (e3) (e2)) = (e1))))) -> (~((e0) = (e3))) -> (~((op (e0) (e2)) = (op (e3) (e2)))) -> (((op (e3) (e0)) = (e0))\/(((op (e3) (e1)) = (e0))\/(((op (e3) (e2)) = (e0))\/((op (e3) (e3)) = (e0))))) -> (~((op (e2) (e2)) = (e1))) -> (~((e1) = (e3))) -> (((op (e3) (e0)) = (e2))\/(((op (e3) (e1)) = (e2))\/(((op (e3) (e2)) = (e2))\/((op (e3) (e3)) = (e2))))) -> ((op (e2) (e2)) = (e2)) -> (~((op (e2) (op (e3) (e2))) = (op (e3) (e2)))) -> (~((op (e1) (op (e3) (e1))) = (op (e3) (e1)))) -> (~((e2) = (e3))) -> (~((op (e1) (e2)) = (op (e3) (e2)))) -> (((op (e3) (e0)) = (e1))\/(((op (e3) (e1)) = (e1))\/(((op (e3) (e2)) = (e1))\/((op (e3) (e3)) = (e1))))) -> ((op (e0) (e2)) = (e0)) -> (~((op (e0) (e1)) = (op (e3) (e1)))) -> (~((op (e0) (e2)) = (op (e2) (e2)))) -> (((op (e1) (e0)) = (e2))\/(((op (e1) (e1)) = (e2))\/(((op (e1) (e2)) = (e2))\/((op (e1) (e3)) = (e2))))) -> (~((op (e0) (e3)) = (op (e1) (e3)))) -> (~((op (e1) (e2)) = (op (e2) (e2)))) -> (~((op (e1) (e1)) = (e0))) -> (~((op (e1) (e1)) = (e1))) -> (~((op (e1) (e1)) = (e2))) -> (((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 (e0) (e0)) = (e2))\/(((op (e0) (e1)) = (e2))\/(((op (e0) (e2)) = (e2))\/((op (e0) (e3)) = (e2))))) -> (~((op (e0) (e0)) = (e0))) -> (~((op (e3) (op (e3) (e3))) = (op (e3) (e3)))) -> ((~((op (e3) (e3)) = (e3)))\/((op (e3) (e3)) = (e3))) -> (~((op (e3) (e0)) = (op (e3) (e1)))) -> ((~((op (e3) (e3)) = (e1)))\/((op (e3) (e1)) = (e3))) -> (~((op (e2) (e0)) = (op (e2) (e2)))) -> (~((op (e3) (e3)) = (e2))) -> (((op (e0) (e0)) = (e3))\/(((op (e0) (e1)) = (e3))\/(((op (e0) (e2)) = (e3))\/((op (e0) (e3)) = (e3))))) -> (~((op (e0) (e0)) = (e3))) -> (~((op (e2) (e2)) = (e3))) -> (~((op (e0) (e1)) = (op (e2) (e1)))) -> (((op (e2) (e0)) = (e3))\/(((op (e2) (e1)) = (e3))\/(((op (e2) (e2)) = (e3))\/((op (e2) (e3)) = (e3))))) -> ((~((op (e1) (e1)) = (e2)))\/((op (e1) (e2)) = (e1))) -> ((~((op (e2) (e2)) = (e1)))\/((op (e2) (e1)) = (e2))) -> ((~((op (e3) (e3)) = (e0)))\/((op (e3) (e0)) = (e3))) -> (((op (e0) (e0)) = (e1))\/(((op (e0) (e1)) = (e1))\/(((op (e0) (e2)) = (e1))\/((op (e0) (e3)) = (e1))))) -> (((op (e1) (e2)) = (e0))\/(((op (e1) (e2)) = (e1))\/(((op (e1) (e2)) = (e2))\/((op (e1) (e2)) = (e3))))) -> (((op (e3) (e0)) = (e3))\/(((op (e3) (e1)) = (e3))\/(((op (e3) (e2)) = (e3))\/((op (e3) (e3)) = (e3))))) -> (~((op (e2) (e0)) = (op (e3) (e0)))) -> (((op (e0) (e2)) = (e3))\/(((op (e1) (e2)) = (e3))\/(((op (e2) (e2)) = (e3))\/((op (e3) (e2)) = (e3))))) -> (~((op (e1) (e0)) = (op (e1) (e2)))) -> (((op (e0) (e3)) = (e1))\/(((op (e1) (e3)) = (e1))\/(((op (e2) (e3)) = (e1))\/((op (e3) (e3)) = (e1))))) -> (~((op (e2) (e0)) = (op (e2) (e3)))) -> (~((op (e1) (e2)) = (op (e1) (e3)))) -> (~((op (e0) (e3)) = (op (e3) (e3)))) -> (((op (e0) (e1)) = (e1))\/(((op (e1) (e1)) = (e1))\/(((op (e2) (e1)) = (e1))\/((op (e3) (e1)) = (e1))))) -> (~((op (e1) (e0)) = (op (e3) (e0)))) -> (((op (e3) (e2)) = (e0))\/(((op (e3) (e2)) = (e1))\/(((op (e3) (e2)) = (e2))\/((op (e3) (e2)) = (e3))))) -> (((op (e1) (e0)) = (e3))\/(((op (e1) (e1)) = (e3))\/(((op (e1) (e2)) = (e3))\/((op (e1) (e3)) = (e3))))) -> (~((op (e3) (e1)) = (op (e3) (e2)))) -> (((op (e0) (e0)) = (e3))\/(((op (e1) (e0)) = (e3))\/(((op (e2) (e0)) = (e3))\/((op (e3) (e0)) = (e3))))) -> (~((op (e2) (e2)) = (op (e2) (e3)))) -> ((~((op (e2) (e2)) = (e3)))\/((op (e2) (e3)) = (e2))) -> (~((op (e1) (e0)) = (op (e1) (e3)))) -> ((~((op (e1) (e1)) = (e3)))\/((op (e1) (e3)) = (e1))) -> (((op (e1) (e0)) = (e0))\/(((op (e1) (e1)) = (e0))\/(((op (e1) (e2)) = (e0))\/((op (e1) (e3)) = (e0))))) -> ((~((op (e1) (e1)) = (e1)))\/((op (e1) (e1)) = (e1))) -> (~((op (e1) (e0)) = (op (e1) (e1)))) -> (((op (e2) (e3)) = (e0))\/(((op (e2) (e3)) = (e1))\/(((op (e2) (e3)) = (e2))\/((op (e2) (e3)) = (e3))))) -> (~((op (e2) (e1)) = (op (e3) (e1)))) -> (~((op (e0) (e2)) = (op (e1) (e2)))) -> (((op (e0) (e0)) = (e2))\/(((op (e1) (e0)) = (e2))\/(((op (e2) (e0)) = (e2))\/((op (e3) (e0)) = (e2))))) -> (~((op (e1) (e1)) = (e3))) -> (((op (e1) (e0)) = (e1))\/(((op (e1) (e1)) = (e1))\/(((op (e1) (e2)) = (e1))\/((op (e1) (e3)) = (e1))))) -> (~((op (e3) (e3)) = (e3))) -> (~((op (e3) (e3)) = (e1))) -> (~((op (e3) (e3)) = (e0))) -> (~((e0) = (e2))) -> (~((e0) = (e1))) -> False). % 15.55/15.75 do 0 intro. intros zenon_H10e zenon_H105 zenon_Hf0 zenon_H45 zenon_H254 zenon_H2b8 zenon_Ha7 zenon_H157 zenon_Hb7 zenon_Hb4 zenon_H247 zenon_H1a2 zenon_Hc9 zenon_Hf1 zenon_H11b zenon_H4b zenon_H140 zenon_H1f6 zenon_H52 zenon_Ha3 zenon_H1df zenon_H35 zenon_H2af zenon_H2b4 zenon_H6a zenon_H17d zenon_H146 zenon_Hab zenon_H138 zenon_H28 zenon_H84 zenon_H80 zenon_H7d zenon_H145 zenon_H1b4 zenon_Hd6 zenon_H3b zenon_H1b3 zenon_H8e zenon_H20 zenon_H2be zenon_H10d zenon_H109 zenon_H10c zenon_H17a zenon_H3d zenon_H58 zenon_H59 zenon_H30 zenon_Hde zenon_He6 zenon_H1d3 zenon_H1e3 zenon_H10f zenon_H44 zenon_H1d5 zenon_H2d5 zenon_H1e5 zenon_H175 zenon_H166 zenon_H121 zenon_Hce zenon_H1d0 zenon_H36 zenon_H228 zenon_H22e zenon_H25e zenon_H90 zenon_H135 zenon_Hbe zenon_H15f zenon_H1c3 zenon_H1cf zenon_H1d2 zenon_H163 zenon_H1d8 zenon_Hd7 zenon_H2ab zenon_H13c zenon_H87 zenon_Heb zenon_H182 zenon_H1c5 zenon_H3e zenon_H104 zenon_H3c zenon_H5e zenon_H9e. % 15.55/15.75 apply (zenon_or_s _ _ zenon_Hf0); [ zenon_intro zenon_H1f | zenon_intro zenon_Hf2 ]. % 15.55/15.75 exact (zenon_H20 zenon_H1f). % 15.55/15.75 apply (zenon_or_s _ _ zenon_Hf2); [ zenon_intro zenon_Had | zenon_intro zenon_Hf3 ]. % 15.55/15.75 apply (zenon_or_s _ _ zenon_H44); [ zenon_intro zenon_H47 | zenon_intro zenon_H46 ]. % 15.55/15.75 exact (zenon_H45 zenon_H47). % 15.55/15.75 apply (zenon_or_s _ _ zenon_H46); [ zenon_intro zenon_H22 | zenon_intro zenon_H48 ]. % 15.55/15.75 apply (zenon_or_s _ _ zenon_Hf1); [ zenon_intro zenon_H47 | zenon_intro zenon_Hf4 ]. % 15.55/15.75 exact (zenon_H45 zenon_H47). % 15.55/15.75 apply (zenon_or_s _ _ zenon_Hf4); [ zenon_intro zenon_Hd8 | zenon_intro zenon_Hf5 ]. % 15.55/15.75 apply (zenon_L1304_); trivial. % 15.55/15.75 apply (zenon_or_s _ _ zenon_Hf5); [ zenon_intro zenon_Hae | zenon_intro zenon_Hee ]. % 15.55/15.75 apply (zenon_L1330_); trivial. % 15.55/15.75 apply (zenon_L1277_); trivial. % 15.55/15.75 apply (zenon_or_s _ _ zenon_H48); [ zenon_intro zenon_H29 | zenon_intro zenon_H37 ]. % 15.55/15.75 apply (zenon_L37_); trivial. % 15.55/15.75 apply (zenon_L7_); trivial. % 15.55/15.75 apply (zenon_or_s _ _ zenon_Hf3); [ zenon_intro zenon_Hcf | zenon_intro zenon_Hdb ]. % 15.55/15.75 apply (zenon_L1331_); trivial. % 15.55/15.75 apply (zenon_or_s _ _ zenon_Hf1); [ zenon_intro zenon_H47 | zenon_intro zenon_Hf4 ]. % 15.55/15.75 exact (zenon_H45 zenon_H47). % 15.55/15.75 apply (zenon_or_s _ _ zenon_Hf4); [ zenon_intro zenon_Hd8 | zenon_intro zenon_Hf5 ]. % 15.55/15.75 apply (zenon_L1306_); trivial. % 15.55/15.75 apply (zenon_or_s _ _ zenon_Hf5); [ zenon_intro zenon_Hae | zenon_intro zenon_Hee ]. % 15.55/15.75 apply (zenon_L1330_); trivial. % 15.55/15.75 apply (zenon_L71_); trivial. % 15.55/15.75 (* end of lemma zenon_L1332_ *) % 15.55/15.75 assert (zenon_L1333_ : ((~((op (e3) (e3)) = (e3)))\/((op (e3) (e3)) = (e3))) -> (~((op (e3) (op (e3) (e3))) = (op (e3) (e3)))) -> (~((op (e0) (e0)) = (e2))) -> (((op (e0) (e0)) = (e0))\/(((op (e0) (e0)) = (e1))\/(((op (e0) (e0)) = (e2))\/((op (e0) (e0)) = (e3))))) -> (~((op (e3) (e3)) = (e0))) -> (~((op (e3) (e3)) = (e2))) -> (((op (e3) (e3)) = (e0))\/(((op (e3) (e3)) = (e1))\/(((op (e3) (e3)) = (e2))\/((op (e3) (e3)) = (e3))))) -> (~((op (e0) (e0)) = (e1))) -> (~((op (e0) (e0)) = (e0))) -> (~((op (e0) (e2)) = (op (e2) (e2)))) -> ((op (e2) (e2)) = (e2)) -> (~((e0) = (e2))) -> ((op (e0) (e3)) = (e0)) -> (((op (e0) (e0)) = (e2))\/(((op (e0) (e1)) = (e2))\/(((op (e0) (e2)) = (e2))\/((op (e0) (e3)) = (e2))))) -> False). % 15.55/15.75 do 0 intro. intros zenon_H10d zenon_H2be zenon_H8f zenon_H12a zenon_H3c zenon_H3d zenon_H3b zenon_H45 zenon_H20 zenon_H28 zenon_H35 zenon_H5e zenon_Hca zenon_H8e. % 15.55/15.75 apply (zenon_or_s _ _ zenon_H10d); [ zenon_intro zenon_H3e | zenon_intro zenon_H42 ]. % 15.55/15.75 apply (zenon_L182_); trivial. % 15.55/15.75 apply (zenon_L1041_); trivial. % 15.55/15.75 (* end of lemma zenon_L1333_ *) % 15.55/15.75 assert (zenon_L1334_ : (((op (e3) (e0)) = (e2))\/(((op (e3) (e1)) = (e2))\/(((op (e3) (e2)) = (e2))\/((op (e3) (e3)) = (e2))))) -> ((op (e3) (e0)) = (e0)) -> ((op (e0) (e2)) = (e0)) -> (~((op (e0) (op (e3) (e0))) = (op (e3) (e0)))) -> ((op (e0) (e1)) = (e2)) -> (~((op (e0) (e1)) = (op (e3) (e1)))) -> ((op (e2) (e2)) = (e2)) -> (~((op (e2) (op (e3) (e2))) = (op (e3) (e2)))) -> (~((op (e3) (e3)) = (e2))) -> False). % 15.55/15.75 do 0 intro. intros zenon_H1df zenon_Hdb zenon_Hab zenon_H2b8 zenon_H5d zenon_H138 zenon_H35 zenon_H2af zenon_H3d. % 15.55/15.75 apply (zenon_or_s _ _ zenon_H1df); [ zenon_intro zenon_He9 | zenon_intro zenon_H1e0 ]. % 15.55/15.75 apply (zenon_L1135_); trivial. % 15.55/15.75 apply (zenon_or_s _ _ zenon_H1e0); [ zenon_intro zenon_H16a | zenon_intro zenon_H1e1 ]. % 15.55/15.75 apply (zenon_L146_); trivial. % 15.55/15.75 apply (zenon_or_s _ _ zenon_H1e1); [ zenon_intro zenon_H1dd | zenon_intro zenon_H43 ]. % 15.55/15.75 apply (zenon_L1083_); trivial. % 15.55/15.75 exact (zenon_H3d zenon_H43). % 15.55/15.75 (* end of lemma zenon_L1334_ *) % 15.55/15.75 assert (zenon_L1335_ : (~((op (e2) (e0)) = (op (e2) (e2)))) -> (((op (e0) (e0)) = (e2))\/(((op (e1) (e0)) = (e2))\/(((op (e2) (e0)) = (e2))\/((op (e3) (e0)) = (e2))))) -> (~((op (e0) (e3)) = (op (e1) (e3)))) -> ((op (e2) (e2)) = (e2)) -> (~((op (e1) (e2)) = (op (e2) (e2)))) -> (~((op (e1) (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 (e3) (e3)) = (e0))\/(((op (e3) (e3)) = (e1))\/(((op (e3) (e3)) = (e2))\/((op (e3) (e3)) = (e3))))) -> (~((op (e3) (e3)) = (e1))) -> (~((op (e3) (e3)) = (e2))) -> (~((op (e3) (e3)) = (e3))) -> (((op (e1) (e0)) = (e2))\/(((op (e1) (e1)) = (e2))\/(((op (e1) (e2)) = (e2))\/((op (e1) (e3)) = (e2))))) -> (~((op (e0) (e2)) = (op (e2) (e2)))) -> (((op (e3) (e0)) = (e2))\/(((op (e3) (e1)) = (e2))\/(((op (e3) (e2)) = (e2))\/((op (e3) (e3)) = (e2))))) -> ((op (e0) (e2)) = (e0)) -> (~((op (e0) (op (e3) (e0))) = (op (e3) (e0)))) -> (~((op (e0) (e1)) = (op (e3) (e1)))) -> (~((op (e2) (op (e3) (e2))) = (op (e3) (e2)))) -> (((op (e0) (e0)) = (e3))\/(((op (e0) (e1)) = (e3))\/(((op (e0) (e2)) = (e3))\/((op (e0) (e3)) = (e3))))) -> (~((op (e0) (e0)) = (e3))) -> (~((op (e2) (e2)) = (e3))) -> (~((op (e0) (e1)) = (op (e2) (e1)))) -> (((op (e2) (e0)) = (e3))\/(((op (e2) (e1)) = (e3))\/(((op (e2) (e2)) = (e3))\/((op (e2) (e3)) = (e3))))) -> (~((op (e0) (e2)) = (op (e3) (e2)))) -> (~((e1) = (e3))) -> ((~((op (e1) (e1)) = (e2)))\/((op (e1) (e2)) = (e1))) -> ((~((op (e2) (e2)) = (e1)))\/((op (e2) (e1)) = (e2))) -> ((~((op (e3) (e3)) = (e0)))\/((op (e3) (e0)) = (e3))) -> (~((op (e3) (e0)) = (op (e3) (e1)))) -> (((op (e0) (e0)) = (e1))\/(((op (e0) (e1)) = (e1))\/(((op (e0) (e2)) = (e1))\/((op (e0) (e3)) = (e1))))) -> (((op (e0) (e2)) = (e1))\/(((op (e1) (e2)) = (e1))\/(((op (e2) (e2)) = (e1))\/((op (e3) (e2)) = (e1))))) -> (((op (e1) (e2)) = (e0))\/(((op (e1) (e2)) = (e1))\/(((op (e1) (e2)) = (e2))\/((op (e1) (e2)) = (e3))))) -> (((op (e3) (e0)) = (e3))\/(((op (e3) (e1)) = (e3))\/(((op (e3) (e2)) = (e3))\/((op (e3) (e3)) = (e3))))) -> ((~((op (e3) (e3)) = (e3)))\/((op (e3) (e3)) = (e3))) -> (~((op (e3) (op (e3) (e3))) = (op (e3) (e3)))) -> (~((op (e2) (e1)) = (op (e2) (e2)))) -> (~((e2) = (e3))) -> (((op (e0) (e1)) = (e2))\/(((op (e1) (e1)) = (e2))\/(((op (e2) (e1)) = (e2))\/((op (e3) (e1)) = (e2))))) -> ((~((op (e3) (e3)) = (e2)))\/((op (e3) (e2)) = (e3))) -> (~((op (e2) (e0)) = (op (e3) (e0)))) -> (((op (e0) (e2)) = (e3))\/(((op (e1) (e2)) = (e3))\/(((op (e2) (e2)) = (e3))\/((op (e3) (e2)) = (e3))))) -> (~((op (e1) (e0)) = (op (e1) (e2)))) -> (((op (e0) (e3)) = (e1))\/(((op (e1) (e3)) = (e1))\/(((op (e2) (e3)) = (e1))\/((op (e3) (e3)) = (e1))))) -> (~((op (e2) (e0)) = (op (e2) (e3)))) -> (~((op (e1) (e2)) = (op (e1) (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)) = (op (e0) (e3)))) -> (~((e1) = (e2))) -> (((op (e0) (e1)) = (e1))\/(((op (e1) (e1)) = (e1))\/(((op (e2) (e1)) = (e1))\/((op (e3) (e1)) = (e1))))) -> (~((op (e1) (e0)) = (op (e3) (e0)))) -> (((op (e3) (e2)) = (e0))\/(((op (e3) (e2)) = (e1))\/(((op (e3) (e2)) = (e2))\/((op (e3) (e2)) = (e3))))) -> (~((op (e1) (e2)) = (op (e3) (e2)))) -> (((op (e1) (e0)) = (e3))\/(((op (e1) (e1)) = (e3))\/(((op (e1) (e2)) = (e3))\/((op (e1) (e3)) = (e3))))) -> (~((op (e3) (e1)) = (op (e3) (e2)))) -> (((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 (e3) (e0)) = (op (e3) (e2)))) -> (~((op (e1) (e0)) = (op (e2) (e0)))) -> (~((op (e1) (op (e3) (e1))) = (op (e3) (e1)))) -> (~((op (e0) (e3)) = (op (e2) (e3)))) -> (((op (e2) (e0)) = (e1))\/(((op (e2) (e1)) = (e1))\/(((op (e2) (e2)) = (e1))\/((op (e2) (e3)) = (e1))))) -> (((op (e0) (e0)) = (e3))\/(((op (e1) (e0)) = (e3))\/(((op (e2) (e0)) = (e3))\/((op (e3) (e0)) = (e3))))) -> (~((op (e0) (e0)) = (e1))) -> ((~((op (e3) (e3)) = (e1)))\/((op (e3) (e1)) = (e3))) -> (~((op (e2) (e2)) = (op (e2) (e3)))) -> ((~((op (e2) (e2)) = (e3)))\/((op (e2) (e3)) = (e2))) -> (~((op (e1) (e0)) = (op (e1) (e3)))) -> ((~((op (e1) (e1)) = (e3)))\/((op (e1) (e3)) = (e1))) -> (((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))))) -> (~((op (e2) (e2)) = (e1))) -> (((op (e0) (e0)) = (e2))\/(((op (e0) (e1)) = (e2))\/(((op (e0) (e2)) = (e2))\/((op (e0) (e3)) = (e2))))) -> (~((op (e0) (e0)) = (e0))) -> (((op (e1) (e0)) = (e0))\/(((op (e1) (e1)) = (e0))\/(((op (e1) (e2)) = (e0))\/((op (e1) (e3)) = (e0))))) -> ((~((op (e1) (e1)) = (e1)))\/((op (e1) (e1)) = (e1))) -> (~((op (e1) (e0)) = (op (e1) (e1)))) -> (~((op (e3) (e3)) = (e0))) -> (~((e0) = (e2))) -> (((op (e2) (e3)) = (e0))\/(((op (e2) (e3)) = (e1))\/(((op (e2) (e3)) = (e2))\/((op (e2) (e3)) = (e3))))) -> (~((op (e2) (e1)) = (op (e3) (e1)))) -> (~((op (e0) (e2)) = (op (e1) (e2)))) -> ((op (e1) (e3)) = (e1)) -> (~((e0) = (e1))) -> False). % 15.55/15.75 do 0 intro. intros zenon_H17a zenon_Heb zenon_H80 zenon_H35 zenon_H7d zenon_Hd6 zenon_H1b3 zenon_H145 zenon_H1b4 zenon_H3b zenon_H104 zenon_H3d zenon_H3e zenon_H84 zenon_H28 zenon_H1df zenon_Hab zenon_H2b8 zenon_H138 zenon_H2af zenon_H58 zenon_H59 zenon_H30 zenon_Hde zenon_He6 zenon_H140 zenon_Ha3 zenon_H1d3 zenon_H1e3 zenon_H10f zenon_H109 zenon_H44 zenon_H11b zenon_H1d5 zenon_H2d5 zenon_H10d zenon_H2be zenon_H157 zenon_H6a zenon_H1a2 zenon_H10e zenon_H1e5 zenon_H175 zenon_H166 zenon_H121 zenon_Hce zenon_H1d0 zenon_H36 zenon_Hf1 zenon_Hc9 zenon_Ha7 zenon_H228 zenon_H22e zenon_H25e zenon_H17d zenon_H90 zenon_H135 zenon_H146 zenon_H254 zenon_H105 zenon_H247 zenon_H2b4 zenon_Hb4 zenon_Hb7 zenon_Hbe zenon_H45 zenon_H10c zenon_H15f zenon_H1c3 zenon_H1cf zenon_H1d2 zenon_Hf0 zenon_H4b zenon_H1f6 zenon_H52 zenon_H8e zenon_H20 zenon_H163 zenon_H1d8 zenon_Hd7 zenon_H3c zenon_H5e zenon_H2ab zenon_H13c zenon_H87 zenon_H11f zenon_H9e. % 15.55/15.75 apply (zenon_or_s _ _ zenon_Hf0); [ zenon_intro zenon_H1f | zenon_intro zenon_Hf2 ]. % 15.55/15.75 exact (zenon_H20 zenon_H1f). % 15.55/15.75 apply (zenon_or_s _ _ zenon_Hf2); [ zenon_intro zenon_Had | zenon_intro zenon_Hf3 ]. % 15.55/15.75 apply (zenon_or_s _ _ zenon_H44); [ zenon_intro zenon_H47 | zenon_intro zenon_H46 ]. % 15.55/15.75 exact (zenon_H45 zenon_H47). % 15.55/15.75 apply (zenon_or_s _ _ zenon_H46); [ zenon_intro zenon_H22 | zenon_intro zenon_H48 ]. % 15.55/15.75 apply (zenon_or_s _ _ zenon_Hf1); [ zenon_intro zenon_H47 | zenon_intro zenon_Hf4 ]. % 15.55/15.75 exact (zenon_H45 zenon_H47). % 15.55/15.75 apply (zenon_or_s _ _ zenon_Hf4); [ zenon_intro zenon_Hd8 | zenon_intro zenon_Hf5 ]. % 15.55/15.75 apply (zenon_L224_); trivial. % 15.55/15.75 apply (zenon_or_s _ _ zenon_Hf5); [ zenon_intro zenon_Hae | zenon_intro zenon_Hee ]. % 15.55/15.75 apply (zenon_L1328_); trivial. % 15.55/15.75 apply (zenon_L1054_); trivial. % 15.55/15.75 apply (zenon_or_s _ _ zenon_H48); [ zenon_intro zenon_H29 | zenon_intro zenon_H37 ]. % 15.55/15.75 apply (zenon_L37_); trivial. % 15.55/15.75 apply (zenon_L7_); trivial. % 15.55/15.75 apply (zenon_or_s _ _ zenon_Hf3); [ zenon_intro zenon_Hcf | zenon_intro zenon_Hdb ]. % 15.55/15.75 apply (zenon_L1331_); trivial. % 15.55/15.75 apply (zenon_or_s _ _ zenon_Hf1); [ zenon_intro zenon_H47 | zenon_intro zenon_Hf4 ]. % 15.55/15.75 exact (zenon_H45 zenon_H47). % 15.55/15.75 apply (zenon_or_s _ _ zenon_Hf4); [ zenon_intro zenon_Hd8 | zenon_intro zenon_Hf5 ]. % 15.55/15.75 apply (zenon_L224_); trivial. % 15.55/15.75 apply (zenon_or_s _ _ zenon_Hf5); [ zenon_intro zenon_Hae | zenon_intro zenon_Hee ]. % 15.55/15.75 apply (zenon_or_s _ _ zenon_H8e); [ zenon_intro zenon_H92 | zenon_intro zenon_H91 ]. % 15.55/15.75 apply (zenon_L1327_); trivial. % 15.55/15.75 apply (zenon_or_s _ _ zenon_H91); [ zenon_intro zenon_H5d | zenon_intro zenon_H93 ]. % 15.55/15.75 apply (zenon_L1334_); trivial. % 15.55/15.75 apply (zenon_or_s _ _ zenon_H93); [ zenon_intro zenon_H63 | zenon_intro zenon_H81 ]. % 15.55/15.75 apply (zenon_L15_); trivial. % 15.55/15.75 apply (zenon_L522_); trivial. % 15.55/15.75 apply (zenon_L71_); trivial. % 15.55/15.75 (* end of lemma zenon_L1335_ *) % 15.55/15.75 assert (zenon_L1336_ : ((~((op (e0) (e0)) = (e3)))\/((op (e0) (e3)) = (e0))) -> (~((op (e1) (e1)) = (op (e1) (e2)))) -> (~((op (e0) (e1)) = (op (e1) (e1)))) -> (~((op (e0) (e0)) = (e0))) -> (((op (e0) (e0)) = (e3))\/(((op (e1) (e0)) = (e3))\/(((op (e2) (e0)) = (e3))\/((op (e3) (e0)) = (e3))))) -> (((op (e2) (e0)) = (e1))\/(((op (e2) (e1)) = (e1))\/(((op (e2) (e2)) = (e1))\/((op (e2) (e3)) = (e1))))) -> (~((op (e0) (e3)) = (op (e2) (e3)))) -> (~((op (e1) (op (e3) (e1))) = (op (e3) (e1)))) -> (~((op (e1) (e0)) = (op (e2) (e0)))) -> (~((op (e3) (e0)) = (op (e3) (e2)))) -> (((op (e0) (e3)) = (e0))\/(((op (e0) (e3)) = (e1))\/(((op (e0) (e3)) = (e2))\/((op (e0) (e3)) = (e3))))) -> (((op (e3) (e0)) = (e1))\/(((op (e3) (e1)) = (e1))\/(((op (e3) (e2)) = (e1))\/((op (e3) (e3)) = (e1))))) -> (~((op (e0) (e2)) = (op (e3) (e2)))) -> (~((op (e3) (e1)) = (op (e3) (e2)))) -> (~((op (e2) (op (e3) (e2))) = (op (e3) (e2)))) -> (((op (e1) (e0)) = (e3))\/(((op (e1) (e1)) = (e3))\/(((op (e1) (e2)) = (e3))\/((op (e1) (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 (e0) (op (e3) (e0))) = (op (e3) (e0)))) -> (~((op (e1) (e0)) = (op (e3) (e0)))) -> (((op (e0) (e1)) = (e1))\/(((op (e1) (e1)) = (e1))\/(((op (e2) (e1)) = (e1))\/((op (e3) (e1)) = (e1))))) -> (~((e1) = (e2))) -> (~((op (e1) (e2)) = (op (e2) (e2)))) -> ((op (e2) (e2)) = (e2)) -> (~((op (e0) (e3)) = (op (e1) (e3)))) -> (((op (e1) (e0)) = (e2))\/(((op (e1) (e1)) = (e2))\/(((op (e1) (e2)) = (e2))\/((op (e1) (e3)) = (e2))))) -> ((op (e0) (e2)) = (e0)) -> (~((op (e0) (e2)) = (op (e0) (e3)))) -> (((op (e0) (e0)) = (e1))\/(((op (e1) (e0)) = (e1))\/(((op (e2) (e0)) = (e1))\/((op (e3) (e0)) = (e1))))) -> (((op (e3) (e3)) = (e0))\/(((op (e3) (e3)) = (e1))\/(((op (e3) (e3)) = (e2))\/((op (e3) (e3)) = (e3))))) -> (~((op (e0) (e3)) = (op (e3) (e3)))) -> (~((op (e1) (e2)) = (op (e1) (e3)))) -> (~((op (e2) (e0)) = (op (e2) (e3)))) -> (((op (e0) (e3)) = (e1))\/(((op (e1) (e3)) = (e1))\/(((op (e2) (e3)) = (e1))\/((op (e3) (e3)) = (e1))))) -> (~((op (e1) (e0)) = (op (e1) (e2)))) -> (((op (e0) (e2)) = (e3))\/(((op (e1) (e2)) = (e3))\/(((op (e2) (e2)) = (e3))\/((op (e3) (e2)) = (e3))))) -> (~((op (e2) (e0)) = (op (e3) (e0)))) -> ((~((op (e3) (e3)) = (e2)))\/((op (e3) (e2)) = (e3))) -> (((op (e0) (e1)) = (e2))\/(((op (e1) (e1)) = (e2))\/(((op (e2) (e1)) = (e2))\/((op (e3) (e1)) = (e2))))) -> (~((e2) = (e3))) -> (~((op (e2) (e1)) = (op (e2) (e2)))) -> (((op (e1) (e1)) = (e0))\/(((op (e1) (e1)) = (e1))\/(((op (e1) (e1)) = (e2))\/((op (e1) (e1)) = (e3))))) -> (~((op (e0) (e1)) = (op (e3) (e1)))) -> (((op (e3) (e0)) = (e2))\/(((op (e3) (e1)) = (e2))\/(((op (e3) (e2)) = (e2))\/((op (e3) (e3)) = (e2))))) -> (~((op (e3) (op (e3) (e3))) = (op (e3) (e3)))) -> ((~((op (e3) (e3)) = (e3)))\/((op (e3) (e3)) = (e3))) -> (((op (e3) (e0)) = (e3))\/(((op (e3) (e1)) = (e3))\/(((op (e3) (e2)) = (e3))\/((op (e3) (e3)) = (e3))))) -> (~((op (e0) (e2)) = (op (e1) (e2)))) -> (((op (e1) (e2)) = (e0))\/(((op (e1) (e2)) = (e1))\/(((op (e1) (e2)) = (e2))\/((op (e1) (e2)) = (e3))))) -> (((op (e0) (e2)) = (e1))\/(((op (e1) (e2)) = (e1))\/(((op (e2) (e2)) = (e1))\/((op (e3) (e2)) = (e1))))) -> (~((e1) = (e3))) -> (((op (e1) (e0)) = (e1))\/(((op (e1) (e1)) = (e1))\/(((op (e1) (e2)) = (e1))\/((op (e1) (e3)) = (e1))))) -> (~((op (e0) (e2)) = (op (e2) (e2)))) -> (((op (e0) (e0)) = (e2))\/(((op (e0) (e1)) = (e2))\/(((op (e0) (e2)) = (e2))\/((op (e0) (e3)) = (e2))))) -> (~((e0) = (e2))) -> (((op (e1) (e0)) = (e0))\/(((op (e1) (e1)) = (e0))\/(((op (e1) (e2)) = (e0))\/((op (e1) (e3)) = (e0))))) -> (~((e0) = (e3))) -> (~((op (e2) (e1)) = (op (e3) (e1)))) -> (~((op (e2) (e0)) = (op (e2) (e2)))) -> (((op (e0) (e0)) = (e2))\/(((op (e1) (e0)) = (e2))\/(((op (e2) (e0)) = (e2))\/((op (e3) (e0)) = (e2))))) -> (((op (e3) (e0)) = (e0))\/(((op (e3) (e1)) = (e0))\/(((op (e3) (e2)) = (e0))\/((op (e3) (e3)) = (e0))))) -> ((~((op (e1) (e1)) = (e1)))\/((op (e1) (e1)) = (e1))) -> (~((op (e1) (e0)) = (op (e1) (e1)))) -> ((~((op (e1) (e1)) = (e3)))\/((op (e1) (e3)) = (e1))) -> (~((op (e1) (e0)) = (op (e1) (e3)))) -> ((~((op (e2) (e2)) = (e3)))\/((op (e2) (e3)) = (e2))) -> (~((op (e2) (e2)) = (op (e2) (e3)))) -> ((~((op (e3) (e3)) = (e1)))\/((op (e3) (e1)) = (e3))) -> (~((op (e3) (e0)) = (op (e3) (e1)))) -> ((~((op (e3) (e3)) = (e0)))\/((op (e3) (e0)) = (e3))) -> ((~((op (e2) (e2)) = (e1)))\/((op (e2) (e1)) = (e2))) -> ((~((op (e1) (e1)) = (e2)))\/((op (e1) (e2)) = (e1))) -> (((op (e0) (e0)) = (e3))\/(((op (e0) (e1)) = (e3))\/(((op (e0) (e2)) = (e3))\/((op (e0) (e3)) = (e3))))) -> (~((op (e0) (e1)) = (op (e2) (e1)))) -> (((op (e2) (e0)) = (e3))\/(((op (e2) (e1)) = (e3))\/(((op (e2) (e2)) = (e3))\/((op (e2) (e3)) = (e3))))) -> (((op (e2) (e3)) = (e0))\/(((op (e2) (e3)) = (e1))\/(((op (e2) (e3)) = (e2))\/((op (e2) (e3)) = (e3))))) -> (((op (e0) (e0)) = (e0))\/(((op (e1) (e0)) = (e0))\/(((op (e2) (e0)) = (e0))\/((op (e3) (e0)) = (e0))))) -> (((op (e0) (e0)) = (e1))\/(((op (e0) (e1)) = (e1))\/(((op (e0) (e2)) = (e1))\/((op (e0) (e3)) = (e1))))) -> (~((e0) = (e1))) -> (~((op (e0) (e0)) = (e1))) -> ((~((op (e1) (e1)) = (e0)))\/((op (e1) (e0)) = (e1))) -> False). % 15.55/15.75 do 0 intro. intros zenon_H236 zenon_H116 zenon_H23 zenon_H20 zenon_Hbe zenon_Hb7 zenon_Hb4 zenon_H2b4 zenon_H247 zenon_H105 zenon_H254 zenon_H146 zenon_H140 zenon_H135 zenon_H2af zenon_H90 zenon_H17d zenon_H25e zenon_H2b8 zenon_H22e zenon_H228 zenon_Ha7 zenon_H7d zenon_H35 zenon_H80 zenon_H84 zenon_Hab zenon_Hc9 zenon_Hf1 zenon_H3b zenon_H36 zenon_H1d0 zenon_Hce zenon_H121 zenon_H166 zenon_H175 zenon_H1e5 zenon_H10e zenon_H1a2 zenon_H6a zenon_H157 zenon_H1b3 zenon_H138 zenon_H1df zenon_H2be zenon_H10d zenon_H2d5 zenon_H87 zenon_H1d5 zenon_H11b zenon_Ha3 zenon_H1c5 zenon_H28 zenon_H8e zenon_H5e zenon_H163 zenon_H4b zenon_H13c zenon_H17a zenon_Heb zenon_H1f6 zenon_H1d8 zenon_Hd7 zenon_H1d2 zenon_H1cf zenon_H1c3 zenon_H15f zenon_H10c zenon_H109 zenon_H10f zenon_H1e3 zenon_H1d3 zenon_H58 zenon_Hde zenon_He6 zenon_H2ab zenon_Hf0 zenon_H44 zenon_H9e zenon_H45 zenon_H1e4. % 15.55/15.75 apply (zenon_or_s _ _ zenon_H236); [ zenon_intro zenon_H59 | zenon_intro zenon_Hca ]. % 15.55/15.75 apply (zenon_or_s _ _ zenon_H1e4); [ zenon_intro zenon_H145 | zenon_intro zenon_Hd8 ]. % 15.55/15.75 apply (zenon_or_s _ _ zenon_H1d8); [ zenon_intro zenon_H1b4 | zenon_intro zenon_H21 ]. % 15.55/15.75 apply (zenon_or_s _ _ zenon_H1d3); [ zenon_intro zenon_Hd6 | zenon_intro zenon_H117 ]. % 15.55/15.75 apply (zenon_or_s _ _ zenon_H1d2); [ zenon_intro zenon_H182 | zenon_intro zenon_H11f ]. % 15.55/15.75 apply (zenon_or_s _ _ zenon_H1e3); [ zenon_intro zenon_H52 | zenon_intro zenon_H156 ]. % 15.55/15.75 apply (zenon_or_s _ _ zenon_H1c3); [ zenon_intro zenon_H30 | zenon_intro zenon_H124 ]. % 15.55/15.75 apply (zenon_or_s _ _ zenon_H10f); [ zenon_intro zenon_H3c | zenon_intro zenon_Hba ]. % 15.55/15.75 apply (zenon_or_s _ _ zenon_H10c); [ zenon_intro zenon_H104 | zenon_intro zenon_H10a ]. % 15.55/15.75 apply (zenon_or_s _ _ zenon_H10e); [ zenon_intro zenon_H3d | zenon_intro zenon_H106 ]. % 15.55/15.75 apply (zenon_or_s _ _ zenon_H10d); [ zenon_intro zenon_H3e | zenon_intro zenon_H42 ]. % 15.55/15.75 apply (zenon_L1332_); trivial. % 15.55/15.75 apply (zenon_L1041_); trivial. % 15.55/15.75 apply (zenon_L1326_); trivial. % 15.55/15.75 apply (zenon_L1302_); trivial. % 15.55/15.75 apply (zenon_L1323_); trivial. % 15.55/15.75 apply (zenon_L137_); trivial. % 15.55/15.75 apply (zenon_L134_); trivial. % 15.55/15.75 apply (zenon_or_s _ _ zenon_H1e3); [ zenon_intro zenon_H52 | zenon_intro zenon_H156 ]. % 15.55/15.75 apply (zenon_or_s _ _ zenon_H1c3); [ zenon_intro zenon_H30 | zenon_intro zenon_H124 ]. % 15.55/15.75 apply (zenon_or_s _ _ zenon_H10f); [ zenon_intro zenon_H3c | zenon_intro zenon_Hba ]. % 15.55/15.75 apply (zenon_or_s _ _ zenon_H10c); [ zenon_intro zenon_H104 | zenon_intro zenon_H10a ]. % 15.55/15.75 apply (zenon_or_s _ _ zenon_H10e); [ zenon_intro zenon_H3d | zenon_intro zenon_H106 ]. % 15.55/15.75 apply (zenon_or_s _ _ zenon_H10d); [ zenon_intro zenon_H3e | zenon_intro zenon_H42 ]. % 15.55/15.75 apply (zenon_L1335_); trivial. % 15.55/15.75 apply (zenon_L1041_); trivial. % 15.55/15.75 apply (zenon_L1326_); trivial. % 15.55/15.75 apply (zenon_or_s _ _ zenon_H10e); [ zenon_intro zenon_H3d | zenon_intro zenon_H106 ]. % 15.55/15.75 apply (zenon_or_s _ _ zenon_H10d); [ zenon_intro zenon_H3e | zenon_intro zenon_H42 ]. % 15.55/15.75 apply (zenon_L1321_); trivial. % 15.55/15.75 apply (zenon_L1041_); trivial. % 15.55/15.75 apply (zenon_L115_); trivial. % 15.55/15.75 apply (zenon_L1323_); trivial. % 15.55/15.75 apply (zenon_L137_); trivial. % 15.55/15.75 apply (zenon_L134_); trivial. % 15.55/15.75 apply (zenon_L1317_); trivial. % 15.55/15.75 apply (zenon_or_s _ _ zenon_H1d3); [ zenon_intro zenon_Hd6 | zenon_intro zenon_H117 ]. % 15.55/15.75 apply (zenon_or_s _ _ zenon_H1e3); [ zenon_intro zenon_H52 | zenon_intro zenon_H156 ]. % 15.55/15.75 apply (zenon_L1294_); trivial. % 15.55/15.75 apply (zenon_L134_); trivial. % 15.55/15.75 apply (zenon_L86_); trivial. % 15.55/15.75 apply (zenon_L1308_); trivial. % 15.55/15.75 apply (zenon_L53_); trivial. % 15.55/15.75 (* end of lemma zenon_L1336_ *) % 15.55/15.75 assert (zenon_L1337_ : (((op (e1) (e2)) = (e0))\/(((op (e1) (e2)) = (e1))\/(((op (e1) (e2)) = (e2))\/((op (e1) (e2)) = (e3))))) -> ((op (e3) (e2)) = (e0)) -> (~((op (e3) (e3)) = (e1))) -> (~((op (e2) (e0)) = (op (e2) (e3)))) -> ((op (e2) (e0)) = (e1)) -> (~((op (e1) (e2)) = (op (e1) (e3)))) -> ((op (e0) (e3)) = (e3)) -> (~((e1) = (e3))) -> (((op (e0) (e3)) = (e1))\/(((op (e1) (e3)) = (e1))\/(((op (e2) (e3)) = (e1))\/((op (e3) (e3)) = (e1))))) -> (~((op (e1) (e2)) = (op (e2) (e2)))) -> ((op (e2) (e2)) = (e2)) -> ((op (e3) (e2)) = (e3)) -> (~((op (e1) (e2)) = (op (e3) (e2)))) -> False). % 15.55/15.75 do 0 intro. intros zenon_H1d5 zenon_H167 zenon_H104 zenon_Hce zenon_Hae zenon_H1d0 zenon_H53 zenon_Ha3 zenon_H121 zenon_H7d zenon_H35 zenon_H106 zenon_H17d. % 15.55/15.75 apply (zenon_or_s _ _ zenon_H1d5); [ zenon_intro zenon_H15d | zenon_intro zenon_H1d6 ]. % 15.55/15.75 apply (zenon_L626_); trivial. % 15.55/15.75 apply (zenon_or_s _ _ zenon_H1d6); [ zenon_intro zenon_H117 | zenon_intro zenon_H1d7 ]. % 15.55/15.75 apply (zenon_L549_); trivial. % 15.55/15.75 apply (zenon_or_s _ _ zenon_H1d7); [ zenon_intro zenon_H7c | zenon_intro zenon_H88 ]. % 15.55/15.75 apply (zenon_L21_); trivial. % 15.55/15.75 apply (zenon_L164_); trivial. % 15.55/15.75 (* end of lemma zenon_L1337_ *) % 15.55/15.75 assert (zenon_L1338_ : (((op (e0) (e3)) = (e3))\/(((op (e1) (e3)) = (e3))\/(((op (e2) (e3)) = (e3))\/((op (e3) (e3)) = (e3))))) -> (~((op (e1) (e2)) = (op (e3) (e2)))) -> ((op (e2) (e2)) = (e2)) -> (~((op (e1) (e2)) = (op (e2) (e2)))) -> (((op (e0) (e3)) = (e1))\/(((op (e1) (e3)) = (e1))\/(((op (e2) (e3)) = (e1))\/((op (e3) (e3)) = (e1))))) -> (~((op (e1) (e2)) = (op (e1) (e3)))) -> ((op (e2) (e0)) = (e1)) -> (~((op (e2) (e0)) = (op (e2) (e3)))) -> (~((op (e3) (e3)) = (e1))) -> ((op (e3) (e2)) = (e0)) -> (((op (e1) (e2)) = (e0))\/(((op (e1) (e2)) = (e1))\/(((op (e1) (e2)) = (e2))\/((op (e1) (e2)) = (e3))))) -> (~((e1) = (e3))) -> ((op (e1) (e3)) = (e1)) -> ((op (e3) (e2)) = (e3)) -> (~((op (e2) (op (e3) (e2))) = (op (e3) (e2)))) -> (~((op (e3) (e3)) = (e3))) -> False). % 15.55/15.75 do 0 intro. intros zenon_H2d0 zenon_H17d zenon_H35 zenon_H7d zenon_H121 zenon_H1d0 zenon_Hae zenon_Hce zenon_H104 zenon_H167 zenon_H1d5 zenon_Ha3 zenon_H11f zenon_H106 zenon_H2af zenon_H3e. % 15.55/15.75 apply (zenon_or_s _ _ zenon_H2d0); [ zenon_intro zenon_H53 | zenon_intro zenon_H2d1 ]. % 15.55/15.75 apply (zenon_L1337_); trivial. % 15.55/15.75 apply (zenon_or_s _ _ zenon_H2d1); [ zenon_intro zenon_H8a | zenon_intro zenon_H2d2 ]. % 15.55/15.75 apply (zenon_L772_); trivial. % 15.55/15.75 apply (zenon_or_s _ _ zenon_H2d2); [ zenon_intro zenon_He2 | zenon_intro zenon_H42 ]. % 15.55/15.75 apply (zenon_L1065_); trivial. % 15.55/15.75 exact (zenon_H3e zenon_H42). % 15.55/15.75 (* end of lemma zenon_L1338_ *) % 15.55/15.75 assert (zenon_L1339_ : (((op (e0) (e2)) = (e0))\/(((op (e1) (e2)) = (e0))\/(((op (e2) (e2)) = (e0))\/((op (e3) (e2)) = (e0))))) -> ((~((op (e1) (e1)) = (e0)))\/((op (e1) (e0)) = (e1))) -> (~((op (e0) (e0)) = (e1))) -> (~((e0) = (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 (e2) (e0)) = (e0))\/((op (e3) (e0)) = (e0))))) -> (((op (e2) (e3)) = (e0))\/(((op (e2) (e3)) = (e1))\/(((op (e2) (e3)) = (e2))\/((op (e2) (e3)) = (e3))))) -> (((op (e2) (e0)) = (e3))\/(((op (e2) (e1)) = (e3))\/(((op (e2) (e2)) = (e3))\/((op (e2) (e3)) = (e3))))) -> (~((op (e0) (e1)) = (op (e2) (e1)))) -> (((op (e0) (e0)) = (e3))\/(((op (e0) (e1)) = (e3))\/(((op (e0) (e2)) = (e3))\/((op (e0) (e3)) = (e3))))) -> ((~((op (e1) (e1)) = (e2)))\/((op (e1) (e2)) = (e1))) -> ((~((op (e2) (e2)) = (e1)))\/((op (e2) (e1)) = (e2))) -> ((~((op (e3) (e3)) = (e0)))\/((op (e3) (e0)) = (e3))) -> (~((op (e3) (e0)) = (op (e3) (e1)))) -> ((~((op (e3) (e3)) = (e1)))\/((op (e3) (e1)) = (e3))) -> (~((op (e2) (e2)) = (op (e2) (e3)))) -> ((~((op (e2) (e2)) = (e3)))\/((op (e2) (e3)) = (e2))) -> (~((op (e1) (e0)) = (op (e1) (e3)))) -> ((~((op (e1) (e1)) = (e3)))\/((op (e1) (e3)) = (e1))) -> (~((op (e1) (e0)) = (op (e1) (e1)))) -> ((~((op (e1) (e1)) = (e1)))\/((op (e1) (e1)) = (e1))) -> (((op (e3) (e0)) = (e0))\/(((op (e3) (e1)) = (e0))\/(((op (e3) (e2)) = (e0))\/((op (e3) (e3)) = (e0))))) -> (((op (e0) (e0)) = (e2))\/(((op (e1) (e0)) = (e2))\/(((op (e2) (e0)) = (e2))\/((op (e3) (e0)) = (e2))))) -> (~((op (e2) (e0)) = (op (e2) (e2)))) -> (~((op (e2) (e1)) = (op (e3) (e1)))) -> (~((e0) = (e3))) -> (((op (e1) (e0)) = (e0))\/(((op (e1) (e1)) = (e0))\/(((op (e1) (e2)) = (e0))\/((op (e1) (e3)) = (e0))))) -> (~((e0) = (e2))) -> (((op (e0) (e0)) = (e2))\/(((op (e0) (e1)) = (e2))\/(((op (e0) (e2)) = (e2))\/((op (e0) (e3)) = (e2))))) -> (~((op (e0) (e2)) = (op (e2) (e2)))) -> (((op (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) (e2)) = (op (e1) (e2)))) -> (((op (e3) (e0)) = (e3))\/(((op (e3) (e1)) = (e3))\/(((op (e3) (e2)) = (e3))\/((op (e3) (e3)) = (e3))))) -> ((~((op (e3) (e3)) = (e3)))\/((op (e3) (e3)) = (e3))) -> (~((op (e3) (op (e3) (e3))) = (op (e3) (e3)))) -> (((op (e3) (e0)) = (e2))\/(((op (e3) (e1)) = (e2))\/(((op (e3) (e2)) = (e2))\/((op (e3) (e3)) = (e2))))) -> (~((op (e0) (e1)) = (op (e3) (e1)))) -> (((op (e1) (e1)) = (e0))\/(((op (e1) (e1)) = (e1))\/(((op (e1) (e1)) = (e2))\/((op (e1) (e1)) = (e3))))) -> (~((op (e2) (e1)) = (op (e2) (e2)))) -> (~((e2) = (e3))) -> (((op (e0) (e1)) = (e2))\/(((op (e1) (e1)) = (e2))\/(((op (e2) (e1)) = (e2))\/((op (e3) (e1)) = (e2))))) -> ((~((op (e3) (e3)) = (e2)))\/((op (e3) (e2)) = (e3))) -> (~((op (e2) (e0)) = (op (e3) (e0)))) -> (((op (e0) (e2)) = (e3))\/(((op (e1) (e2)) = (e3))\/(((op (e2) (e2)) = (e3))\/((op (e3) (e2)) = (e3))))) -> (~((op (e1) (e0)) = (op (e1) (e2)))) -> (~((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)) = (op (e0) (e3)))) -> (((op (e1) (e0)) = (e2))\/(((op (e1) (e1)) = (e2))\/(((op (e1) (e2)) = (e2))\/((op (e1) (e3)) = (e2))))) -> (~((op (e0) (e3)) = (op (e1) (e3)))) -> (~((e1) = (e2))) -> (((op (e0) (e1)) = (e1))\/(((op (e1) (e1)) = (e1))\/(((op (e2) (e1)) = (e1))\/((op (e3) (e1)) = (e1))))) -> (~((op (e1) (e0)) = (op (e3) (e0)))) -> (~((op (e0) (op (e3) (e0))) = (op (e3) (e0)))) -> (((op (e3) (e2)) = (e0))\/(((op (e3) (e2)) = (e1))\/(((op (e3) (e2)) = (e2))\/((op (e3) (e2)) = (e3))))) -> (((op (e1) (e0)) = (e3))\/(((op (e1) (e1)) = (e3))\/(((op (e1) (e2)) = (e3))\/((op (e1) (e3)) = (e3))))) -> (~((op (e3) (e1)) = (op (e3) (e2)))) -> (~((op (e0) (e2)) = (op (e3) (e2)))) -> (((op (e3) (e0)) = (e1))\/(((op (e3) (e1)) = (e1))\/(((op (e3) (e2)) = (e1))\/((op (e3) (e3)) = (e1))))) -> (((op (e0) (e3)) = (e0))\/(((op (e0) (e3)) = (e1))\/(((op (e0) (e3)) = (e2))\/((op (e0) (e3)) = (e3))))) -> (~((op (e3) (e0)) = (op (e3) (e2)))) -> (~((op (e1) (e0)) = (op (e2) (e0)))) -> (~((op (e1) (op (e3) (e1))) = (op (e3) (e1)))) -> (~((op (e0) (e3)) = (op (e2) (e3)))) -> (((op (e2) (e0)) = (e1))\/(((op (e2) (e1)) = (e1))\/(((op (e2) (e2)) = (e1))\/((op (e2) (e3)) = (e1))))) -> (((op (e0) (e0)) = (e3))\/(((op (e1) (e0)) = (e3))\/(((op (e2) (e0)) = (e3))\/((op (e3) (e0)) = (e3))))) -> (~((op (e0) (e0)) = (e0))) -> (~((op (e0) (e1)) = (op (e1) (e1)))) -> (~((op (e1) (e1)) = (op (e1) (e2)))) -> ((~((op (e0) (e0)) = (e3)))\/((op (e0) (e3)) = (e0))) -> ((op (e1) (e1)) = (e3)) -> (~((op (e3) (e3)) = (e0))) -> (((op (e3) (e3)) = (e0))\/(((op (e3) (e3)) = (e1))\/(((op (e3) (e3)) = (e2))\/((op (e3) (e3)) = (e3))))) -> (~((op (e2) (e2)) = (e0))) -> (((op (e0) (e3)) = (e3))\/(((op (e1) (e3)) = (e3))\/(((op (e2) (e3)) = (e3))\/((op (e3) (e3)) = (e3))))) -> (~((op (e1) (e2)) = (op (e3) (e2)))) -> ((op (e2) (e2)) = (e2)) -> (~((op (e1) (e2)) = (op (e2) (e2)))) -> (((op (e0) (e3)) = (e1))\/(((op (e1) (e3)) = (e1))\/(((op (e2) (e3)) = (e1))\/((op (e3) (e3)) = (e1))))) -> (~((op (e1) (e2)) = (op (e1) (e3)))) -> ((op (e2) (e0)) = (e1)) -> (~((op (e2) (e0)) = (op (e2) (e3)))) -> (~((op (e3) (e3)) = (e1))) -> (((op (e1) (e2)) = (e0))\/(((op (e1) (e2)) = (e1))\/(((op (e1) (e2)) = (e2))\/((op (e1) (e2)) = (e3))))) -> (~((e1) = (e3))) -> ((op (e1) (e3)) = (e1)) -> ((op (e3) (e2)) = (e3)) -> (~((op (e2) (op (e3) (e2))) = (op (e3) (e2)))) -> (~((op (e3) (e3)) = (e3))) -> False). % 15.55/15.75 do 0 intro. intros zenon_H16f zenon_H1e4 zenon_H45 zenon_H9e zenon_H44 zenon_Hf0 zenon_H2ab zenon_He6 zenon_Hde zenon_H58 zenon_H1d3 zenon_H1e3 zenon_H10f zenon_H109 zenon_H10c zenon_H15f zenon_H1c3 zenon_H1cf zenon_H1d2 zenon_Hd7 zenon_H1d8 zenon_H1f6 zenon_Heb zenon_H17a zenon_H13c zenon_H4b zenon_H163 zenon_H5e zenon_H8e zenon_H28 zenon_H1c5 zenon_H11b zenon_H87 zenon_H2d5 zenon_H10d zenon_H2be zenon_H1df zenon_H138 zenon_H1b3 zenon_H157 zenon_H6a zenon_H1a2 zenon_H10e zenon_H1e5 zenon_H175 zenon_H166 zenon_H36 zenon_Hf1 zenon_Hc9 zenon_H84 zenon_H80 zenon_Ha7 zenon_H228 zenon_H22e zenon_H2b8 zenon_H25e zenon_H90 zenon_H135 zenon_H140 zenon_H146 zenon_H254 zenon_H105 zenon_H247 zenon_H2b4 zenon_Hb4 zenon_Hb7 zenon_Hbe zenon_H20 zenon_H23 zenon_H116 zenon_H236 zenon_H96 zenon_H3c zenon_H3b zenon_H2e zenon_H2d0 zenon_H17d zenon_H35 zenon_H7d zenon_H121 zenon_H1d0 zenon_Hae zenon_Hce zenon_H104 zenon_H1d5 zenon_Ha3 zenon_H11f zenon_H106 zenon_H2af zenon_H3e. % 15.55/15.75 apply (zenon_or_s _ _ zenon_H16f); [ zenon_intro zenon_Hab | zenon_intro zenon_H170 ]. % 15.55/15.75 apply (zenon_L1336_); trivial. % 15.55/15.75 apply (zenon_or_s _ _ zenon_H170); [ zenon_intro zenon_H15d | zenon_intro zenon_H171 ]. % 15.55/15.75 apply (zenon_L489_); trivial. % 15.55/15.75 apply (zenon_or_s _ _ zenon_H171); [ zenon_intro zenon_H32 | zenon_intro zenon_H167 ]. % 15.55/15.75 exact (zenon_H2e zenon_H32). % 15.55/15.75 apply (zenon_L1338_); trivial. % 15.55/15.75 (* end of lemma zenon_L1339_ *) % 15.55/15.75 assert (zenon_L1340_ : (~((op (e0) (e0)) = (e2))) -> ((~((op (e1) (e1)) = (e0)))\/((op (e1) (e0)) = (e1))) -> (~((op (e0) (e0)) = (e1))) -> (~((e0) = (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 (e2) (e0)) = (e0))\/((op (e3) (e0)) = (e0))))) -> (((op (e2) (e3)) = (e0))\/(((op (e2) (e3)) = (e1))\/(((op (e2) (e3)) = (e2))\/((op (e2) (e3)) = (e3))))) -> (((op (e2) (e0)) = (e3))\/(((op (e2) (e1)) = (e3))\/(((op (e2) (e2)) = (e3))\/((op (e2) (e3)) = (e3))))) -> (~((op (e0) (e1)) = (op (e2) (e1)))) -> (((op (e0) (e0)) = (e3))\/(((op (e0) (e1)) = (e3))\/(((op (e0) (e2)) = (e3))\/((op (e0) (e3)) = (e3))))) -> ((~((op (e1) (e1)) = (e2)))\/((op (e1) (e2)) = (e1))) -> ((~((op (e2) (e2)) = (e1)))\/((op (e2) (e1)) = (e2))) -> ((~((op (e3) (e3)) = (e0)))\/((op (e3) (e0)) = (e3))) -> (~((op (e3) (e0)) = (op (e3) (e1)))) -> ((~((op (e3) (e3)) = (e1)))\/((op (e3) (e1)) = (e3))) -> (~((op (e2) (e2)) = (op (e2) (e3)))) -> ((~((op (e2) (e2)) = (e3)))\/((op (e2) (e3)) = (e2))) -> (~((op (e1) (e0)) = (op (e1) (e3)))) -> ((~((op (e1) (e1)) = (e3)))\/((op (e1) (e3)) = (e1))) -> (~((op (e1) (e0)) = (op (e1) (e1)))) -> ((~((op (e1) (e1)) = (e1)))\/((op (e1) (e1)) = (e1))) -> (((op (e0) (e0)) = (e2))\/(((op (e1) (e0)) = (e2))\/(((op (e2) (e0)) = (e2))\/((op (e3) (e0)) = (e2))))) -> (~((op (e2) (e1)) = (op (e3) (e1)))) -> (~((e0) = (e3))) -> (((op (e1) (e0)) = (e0))\/(((op (e1) (e1)) = (e0))\/(((op (e1) (e2)) = (e0))\/((op (e1) (e3)) = (e0))))) -> (~((e0) = (e2))) -> (((op (e0) (e0)) = (e2))\/(((op (e0) (e1)) = (e2))\/(((op (e0) (e2)) = (e2))\/((op (e0) (e3)) = (e2))))) -> (~((op (e0) (e2)) = (op (e2) (e2)))) -> (((op (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) (e2)) = (op (e1) (e2)))) -> (((op (e3) (e0)) = (e3))\/(((op (e3) (e1)) = (e3))\/(((op (e3) (e2)) = (e3))\/((op (e3) (e3)) = (e3))))) -> ((~((op (e3) (e3)) = (e3)))\/((op (e3) (e3)) = (e3))) -> (~((op (e3) (op (e3) (e3))) = (op (e3) (e3)))) -> (((op (e3) (e0)) = (e2))\/(((op (e3) (e1)) = (e2))\/(((op (e3) (e2)) = (e2))\/((op (e3) (e3)) = (e2))))) -> (~((op (e0) (e1)) = (op (e3) (e1)))) -> (~((op (e2) (e1)) = (op (e2) (e2)))) -> (~((e2) = (e3))) -> (((op (e0) (e1)) = (e2))\/(((op (e1) (e1)) = (e2))\/(((op (e2) (e1)) = (e2))\/((op (e3) (e1)) = (e2))))) -> ((~((op (e3) (e3)) = (e2)))\/((op (e3) (e2)) = (e3))) -> (~((op (e2) (e0)) = (op (e3) (e0)))) -> (((op (e0) (e2)) = (e3))\/(((op (e1) (e2)) = (e3))\/(((op (e2) (e2)) = (e3))\/((op (e3) (e2)) = (e3))))) -> (~((op (e1) (e0)) = (op (e1) (e2)))) -> (~((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)) = (op (e0) (e3)))) -> (((op (e1) (e0)) = (e2))\/(((op (e1) (e1)) = (e2))\/(((op (e1) (e2)) = (e2))\/((op (e1) (e3)) = (e2))))) -> (~((op (e0) (e3)) = (op (e1) (e3)))) -> (~((e1) = (e2))) -> (((op (e0) (e1)) = (e1))\/(((op (e1) (e1)) = (e1))\/(((op (e2) (e1)) = (e1))\/((op (e3) (e1)) = (e1))))) -> (~((op (e1) (e0)) = (op (e3) (e0)))) -> (((op (e3) (e2)) = (e0))\/(((op (e3) (e2)) = (e1))\/(((op (e3) (e2)) = (e2))\/((op (e3) (e2)) = (e3))))) -> (((op (e1) (e0)) = (e3))\/(((op (e1) (e1)) = (e3))\/(((op (e1) (e2)) = (e3))\/((op (e1) (e3)) = (e3))))) -> (~((op (e3) (e1)) = (op (e3) (e2)))) -> (((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 (e3) (e0)) = (op (e3) (e2)))) -> (~((op (e1) (e0)) = (op (e2) (e0)))) -> (~((op (e0) (e3)) = (op (e2) (e3)))) -> (((op (e2) (e0)) = (e1))\/(((op (e2) (e1)) = (e1))\/(((op (e2) (e2)) = (e1))\/((op (e2) (e3)) = (e1))))) -> (((op (e0) (e0)) = (e3))\/(((op (e1) (e0)) = (e3))\/(((op (e2) (e0)) = (e3))\/((op (e3) (e0)) = (e3))))) -> (~((op (e0) (e0)) = (e0))) -> (~((op (e0) (e1)) = (op (e1) (e1)))) -> (~((op (e1) (e1)) = (op (e1) (e2)))) -> ((~((op (e0) (e0)) = (e3)))\/((op (e0) (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 (e0) (e2)) = (op (e3) (e2)))) -> (~((op (e1) (op (e3) (e1))) = (op (e3) (e1)))) -> ((op (e1) (e0)) = (e0)) -> (~((op (e0) (op (e3) (e0))) = (op (e3) (e0)))) -> (((op (e3) (e0)) = (e0))\/(((op (e3) (e1)) = (e0))\/(((op (e3) (e2)) = (e0))\/((op (e3) (e3)) = (e0))))) -> (~((op (e3) (e3)) = (e0))) -> (((op (e3) (e3)) = (e0))\/(((op (e3) (e3)) = (e1))\/(((op (e3) (e3)) = (e2))\/((op (e3) (e3)) = (e3))))) -> (~((op (e1) (e1)) = (e2))) -> (~((op (e1) (e1)) = (e1))) -> (~((op (e1) (e1)) = (e0))) -> (((op (e1) (e1)) = (e0))\/(((op (e1) (e1)) = (e1))\/(((op (e1) (e1)) = (e2))\/((op (e1) (e1)) = (e3))))) -> (~((op (e2) (e2)) = (e0))) -> (((op (e0) (e3)) = (e3))\/(((op (e1) (e3)) = (e3))\/(((op (e2) (e3)) = (e3))\/((op (e3) (e3)) = (e3))))) -> (~((op (e1) (e2)) = (op (e3) (e2)))) -> ((op (e2) (e2)) = (e2)) -> (~((op (e1) (e2)) = (op (e2) (e2)))) -> (((op (e0) (e3)) = (e1))\/(((op (e1) (e3)) = (e1))\/(((op (e2) (e3)) = (e1))\/((op (e3) (e3)) = (e1))))) -> (~((op (e1) (e2)) = (op (e1) (e3)))) -> ((op (e2) (e0)) = (e1)) -> (~((op (e2) (e0)) = (op (e2) (e3)))) -> (~((op (e3) (e3)) = (e1))) -> (((op (e1) (e2)) = (e0))\/(((op (e1) (e2)) = (e1))\/(((op (e1) (e2)) = (e2))\/((op (e1) (e2)) = (e3))))) -> (~((e1) = (e3))) -> ((op (e1) (e3)) = (e1)) -> ((op (e3) (e2)) = (e3)) -> (~((op (e2) (op (e3) (e2))) = (op (e3) (e2)))) -> (~((op (e3) (e3)) = (e3))) -> False). % 15.55/15.75 do 0 intro. intros zenon_H8f zenon_H1e4 zenon_H45 zenon_H9e zenon_H44 zenon_Hf0 zenon_H2ab zenon_He6 zenon_Hde zenon_H58 zenon_H1d3 zenon_H1e3 zenon_H10f zenon_H109 zenon_H10c zenon_H15f zenon_H1c3 zenon_H1cf zenon_H1d2 zenon_Hd7 zenon_H1d8 zenon_Heb zenon_H13c zenon_H4b zenon_H163 zenon_H5e zenon_H8e zenon_H28 zenon_H1c5 zenon_H11b zenon_H87 zenon_H2d5 zenon_H10d zenon_H2be zenon_H1df zenon_H138 zenon_H157 zenon_H6a zenon_H1a2 zenon_H10e zenon_H1e5 zenon_H175 zenon_H166 zenon_H36 zenon_Hf1 zenon_Hc9 zenon_H84 zenon_H80 zenon_Ha7 zenon_H228 zenon_H22e zenon_H25e zenon_H90 zenon_H135 zenon_H146 zenon_H254 zenon_H105 zenon_H247 zenon_Hb4 zenon_Hb7 zenon_Hbe zenon_H20 zenon_H23 zenon_H116 zenon_H236 zenon_H17a zenon_H16f zenon_H140 zenon_H2b4 zenon_Had zenon_H2b8 zenon_H1f6 zenon_H3c zenon_H3b zenon_Hd6 zenon_H1b4 zenon_H145 zenon_H1b3 zenon_H2e zenon_H2d0 zenon_H17d zenon_H35 zenon_H7d zenon_H121 zenon_H1d0 zenon_Hae zenon_Hce zenon_H104 zenon_H1d5 zenon_Ha3 zenon_H11f zenon_H106 zenon_H2af zenon_H3e. % 15.55/15.75 apply (zenon_or_s _ _ zenon_Heb); [ zenon_intro zenon_H92 | zenon_intro zenon_Hec ]. % 15.55/15.75 exact (zenon_H8f zenon_H92). % 15.55/15.75 apply (zenon_or_s _ _ zenon_Hec); [ zenon_intro zenon_H68 | zenon_intro zenon_Hed ]. % 15.55/15.75 apply (zenon_or_s _ _ zenon_H90); [ zenon_intro zenon_H69 | zenon_intro zenon_H94 ]. % 15.55/15.75 apply (zenon_L17_); trivial. % 15.55/15.75 apply (zenon_or_s _ _ zenon_H94); [ zenon_intro zenon_H96 | zenon_intro zenon_H95 ]. % 15.55/15.75 apply (zenon_L1339_); trivial. % 15.55/15.75 apply (zenon_or_s _ _ zenon_H95); [ zenon_intro zenon_H88 | zenon_intro zenon_H8a ]. % 15.55/15.75 apply (zenon_L164_); trivial. % 15.55/15.75 apply (zenon_L772_); trivial. % 15.55/15.75 apply (zenon_or_s _ _ zenon_Hed); [ zenon_intro zenon_Hdd | zenon_intro zenon_He9 ]. % 15.55/15.75 apply (zenon_L161_); trivial. % 15.55/15.75 apply (zenon_or_s _ _ zenon_H16f); [ zenon_intro zenon_Hab | zenon_intro zenon_H170 ]. % 15.55/15.75 apply (zenon_L1137_); trivial. % 15.55/15.75 apply (zenon_or_s _ _ zenon_H170); [ zenon_intro zenon_H15d | zenon_intro zenon_H171 ]. % 15.55/15.75 apply (zenon_L490_); trivial. % 15.55/15.75 apply (zenon_or_s _ _ zenon_H171); [ zenon_intro zenon_H32 | zenon_intro zenon_H167 ]. % 15.55/15.75 exact (zenon_H2e zenon_H32). % 15.55/15.75 apply (zenon_L1338_); trivial. % 15.55/15.75 (* end of lemma zenon_L1340_ *) % 15.55/15.75 assert (zenon_L1341_ : (((op (e0) (e2)) = (e1))\/(((op (e1) (e2)) = (e1))\/(((op (e2) (e2)) = (e1))\/((op (e3) (e2)) = (e1))))) -> ((op (e3) (e0)) = (e1)) -> ((op (e3) (e0)) = (e2)) -> (~((op (e0) (op (e3) (e0))) = (op (e3) (e0)))) -> ((op (e1) (e3)) = (e1)) -> (~((op (e1) (e2)) = (op (e1) (e3)))) -> (~((op (e2) (e2)) = (e1))) -> (~((op (e2) (op (e3) (e2))) = (op (e3) (e2)))) -> ((op (e2) (e1)) = (e1)) -> False). % 15.55/15.75 do 0 intro. intros zenon_H11b zenon_Hee zenon_He9 zenon_H2b8 zenon_H11f zenon_H1d0 zenon_H52 zenon_H2af zenon_Hb2. % 15.55/15.75 apply (zenon_or_s _ _ zenon_H11b); [ zenon_intro zenon_H29 | zenon_intro zenon_H11c ]. % 15.55/15.75 apply (zenon_L1082_); trivial. % 15.55/15.75 apply (zenon_or_s _ _ zenon_H11c); [ zenon_intro zenon_H117 | zenon_intro zenon_H11d ]. % 15.55/15.75 apply (zenon_L237_); trivial. % 15.55/15.75 apply (zenon_or_s _ _ zenon_H11d); [ zenon_intro zenon_H2a | zenon_intro zenon_H119 ]. % 15.55/15.75 exact (zenon_H52 zenon_H2a). % 15.55/15.75 apply (zenon_L1024_); trivial. % 15.55/15.75 (* end of lemma zenon_L1341_ *) % 15.55/15.75 assert (zenon_L1342_ : (((op (e0) (e2)) = (e1))\/(((op (e1) (e2)) = (e1))\/(((op (e2) (e2)) = (e1))\/((op (e3) (e2)) = (e1))))) -> (~((op (e0) (e2)) = (op (e0) (e3)))) -> ((op (e0) (e3)) = (e1)) -> (((op (e0) (e0)) = (e2))\/(((op (e0) (e1)) = (e2))\/(((op (e0) (e2)) = (e2))\/((op (e0) (e3)) = (e2))))) -> ((op (e0) (e3)) = (e0)) -> (~((e0) = (e2))) -> ((op (e2) (e2)) = (e2)) -> (~((op (e0) (e2)) = (op (e2) (e2)))) -> (~((op (e1) (e1)) = (e0))) -> (~((op (e1) (e1)) = (e1))) -> (~((op (e0) (e1)) = (op (e1) (e1)))) -> (((op (e1) (e1)) = (e0))\/(((op (e1) (e1)) = (e1))\/(((op (e1) (e1)) = (e2))\/((op (e1) (e1)) = (e3))))) -> (~((op (e0) (e0)) = (e2))) -> (~((op (e1) (e2)) = (op (e1) (e3)))) -> ((~((op (e1) (e1)) = (e3)))\/((op (e1) (e3)) = (e1))) -> (~((op (e2) (e2)) = (e1))) -> (~((e1) = (e3))) -> ((op (e3) (e2)) = (e3)) -> False). % 15.55/15.75 do 0 intro. intros zenon_H11b zenon_Hc9 zenon_H37 zenon_H8e zenon_Hca zenon_H5e zenon_H35 zenon_H28 zenon_H145 zenon_H1b4 zenon_H23 zenon_H1b3 zenon_H8f zenon_H1d0 zenon_H1d2 zenon_H52 zenon_Ha3 zenon_H106. % 15.55/15.75 apply (zenon_or_s _ _ zenon_H11b); [ zenon_intro zenon_H29 | zenon_intro zenon_H11c ]. % 15.55/15.75 apply (zenon_L85_); trivial. % 15.55/15.75 apply (zenon_or_s _ _ zenon_H11c); [ zenon_intro zenon_H117 | zenon_intro zenon_H11d ]. % 15.55/15.75 apply (zenon_L438_); trivial. % 15.55/15.75 apply (zenon_or_s _ _ zenon_H11d); [ zenon_intro zenon_H2a | zenon_intro zenon_H119 ]. % 15.55/15.75 exact (zenon_H52 zenon_H2a). % 15.55/15.75 apply (zenon_L87_); trivial. % 15.55/15.75 (* end of lemma zenon_L1342_ *) % 15.55/15.75 assert (zenon_L1343_ : ((~((op (e3) (e3)) = (e3)))\/((op (e3) (e3)) = (e3))) -> (~((op (e3) (op (e3) (e3))) = (op (e3) (e3)))) -> (~((op (e0) (e0)) = (e2))) -> (~((e0) = (e2))) -> ((op (e0) (e1)) = (e0)) -> (~((op (e0) (e2)) = (op (e2) (e2)))) -> ((op (e2) (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)) = (e1))) -> (~((op (e3) (e3)) = (e0))) -> (((op (e0) (e0)) = (e2))\/(((op (e0) (e1)) = (e2))\/(((op (e0) (e2)) = (e2))\/((op (e0) (e3)) = (e2))))) -> False). % 15.55/15.75 do 0 intro. intros zenon_H10d zenon_H2be zenon_H8f zenon_H5e zenon_H49 zenon_H28 zenon_H35 zenon_H3b zenon_H36 zenon_H104 zenon_H3c zenon_H8e. % 15.55/15.75 apply (zenon_or_s _ _ zenon_H10d); [ zenon_intro zenon_H3e | zenon_intro zenon_H42 ]. % 15.55/15.75 apply (zenon_L131_); trivial. % 15.55/15.75 apply (zenon_L1041_); trivial. % 15.55/15.75 (* end of lemma zenon_L1343_ *) % 15.55/15.75 assert (zenon_L1344_ : ((~((op (e3) (e3)) = (e1)))\/((op (e3) (e1)) = (e3))) -> (~((op (e1) (e1)) = (e2))) -> (~((op (e2) (e1)) = (op (e2) (e2)))) -> (~((e2) = (e3))) -> (((op (e0) (e1)) = (e2))\/(((op (e1) (e1)) = (e2))\/(((op (e2) (e1)) = (e2))\/((op (e3) (e1)) = (e2))))) -> (((op (e0) (e0)) = (e2))\/(((op (e0) (e1)) = (e2))\/(((op (e0) (e2)) = (e2))\/((op (e0) (e3)) = (e2))))) -> (~((op (e3) (e3)) = (e0))) -> (~((op (e0) (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) (e2)) = (op (e2) (e2)))) -> ((op (e0) (e1)) = (e0)) -> (~((e0) = (e2))) -> (~((op (e0) (e0)) = (e2))) -> (~((op (e3) (op (e3) (e3))) = (op (e3) (e3)))) -> ((~((op (e3) (e3)) = (e3)))\/((op (e3) (e3)) = (e3))) -> False). % 15.55/15.75 do 0 intro. intros zenon_H10c zenon_Hd6 zenon_H157 zenon_H6a zenon_H1a2 zenon_H8e zenon_H3c zenon_H36 zenon_H3b zenon_H35 zenon_H28 zenon_H49 zenon_H5e zenon_H8f zenon_H2be zenon_H10d. % 15.55/15.75 apply (zenon_or_s _ _ zenon_H10c); [ zenon_intro zenon_H104 | zenon_intro zenon_H10a ]. % 15.55/15.75 apply (zenon_L1343_); trivial. % 15.55/15.75 apply (zenon_L349_); trivial. % 15.55/15.75 (* end of lemma zenon_L1344_ *) % 15.55/15.75 assert (zenon_L1345_ : ((~((op (e3) (e3)) = (e1)))\/((op (e3) (e1)) = (e3))) -> (~((op (e3) (e0)) = (op (e3) (e1)))) -> ((~((op (e3) (e3)) = (e3)))\/((op (e3) (e3)) = (e3))) -> (~((op (e3) (op (e3) (e3))) = (op (e3) (e3)))) -> (~((op (e0) (e0)) = (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 (e1) (e1)) = (e2))) -> (~((op (e1) (e1)) = (e1))) -> (~((op (e1) (e1)) = (e0))) -> (~((op (e2) (e0)) = (op (e2) (e2)))) -> ((op (e2) (e2)) = (e2)) -> (~((e2) = (e3))) -> ((op (e3) (e0)) = (e3)) -> (((op (e0) (e0)) = (e2))\/(((op (e1) (e0)) = (e2))\/(((op (e2) (e0)) = (e2))\/((op (e3) (e0)) = (e2))))) -> (~((op (e3) (e0)) = (op (e3) (e2)))) -> ((~((op (e3) (e3)) = (e2)))\/((op (e3) (e2)) = (e3))) -> False). % 15.55/15.75 do 0 intro. intros zenon_H10c zenon_H109 zenon_H10d zenon_H2be zenon_H8f zenon_H1b3 zenon_H3b zenon_Hd6 zenon_H1b4 zenon_H145 zenon_H17a zenon_H35 zenon_H6a zenon_Hba zenon_Heb zenon_H105 zenon_H10e. % 15.55/15.75 apply (zenon_or_s _ _ zenon_H10c); [ zenon_intro zenon_H104 | zenon_intro zenon_H10a ]. % 15.55/15.75 apply (zenon_or_s _ _ zenon_H10e); [ zenon_intro zenon_H3d | zenon_intro zenon_H106 ]. % 15.55/15.75 apply (zenon_or_s _ _ zenon_H10d); [ zenon_intro zenon_H3e | zenon_intro zenon_H42 ]. % 15.55/15.75 apply (zenon_L358_); trivial. % 15.55/15.75 apply (zenon_L1041_); trivial. % 15.55/15.75 apply (zenon_L81_); trivial. % 15.55/15.75 apply (zenon_L82_); trivial. % 15.55/15.75 (* end of lemma zenon_L1345_ *) % 15.55/15.75 assert (zenon_L1346_ : ((~((op (e1) (e1)) = (e2)))\/((op (e1) (e2)) = (e1))) -> ((~((op (e2) (e2)) = (e3)))\/((op (e2) (e3)) = (e2))) -> (~((op (e2) (e2)) = (op (e2) (e3)))) -> (~((op (e1) (e2)) = (op (e3) (e2)))) -> (~((op (e2) (op (e3) (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))))) -> (~((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 (e3) (e0)) = (e1))\/(((op (e3) (e1)) = (e1))\/(((op (e3) (e2)) = (e1))\/((op (e3) (e3)) = (e1))))) -> (~((op (e1) (op (e3) (e1))) = (op (e3) (e1)))) -> (((op (e3) (e0)) = (e2))\/(((op (e3) (e1)) = (e2))\/(((op (e3) (e2)) = (e2))\/((op (e3) (e3)) = (e2))))) -> (~((op (e1) (e2)) = (op (e1) (e3)))) -> ((~((op (e1) (e1)) = (e3)))\/((op (e1) (e3)) = (e1))) -> ((~((op (e3) (e3)) = (e1)))\/((op (e3) (e1)) = (e3))) -> (~((op (e2) (e1)) = (op (e2) (e2)))) -> (~((e2) = (e3))) -> (((op (e0) (e1)) = (e2))\/(((op (e1) (e1)) = (e2))\/(((op (e2) (e1)) = (e2))\/((op (e3) (e1)) = (e2))))) -> (((op (e0) (e0)) = (e2))\/(((op (e0) (e1)) = (e2))\/(((op (e0) (e2)) = (e2))\/((op (e0) (e3)) = (e2))))) -> (~((op (e0) (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) (e2)) = (op (e2) (e2)))) -> ((op (e0) (e1)) = (e0)) -> (~((e0) = (e2))) -> (~((op (e0) (e0)) = (e2))) -> (~((op (e3) (op (e3) (e3))) = (op (e3) (e3)))) -> ((~((op (e3) (e3)) = (e3)))\/((op (e3) (e3)) = (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)) = (e0))) -> (~((op (e2) (e0)) = (op (e2) (e2)))) -> (((op (e0) (e0)) = (e2))\/(((op (e1) (e0)) = (e2))\/(((op (e2) (e0)) = (e2))\/((op (e3) (e0)) = (e2))))) -> (~((op (e3) (e0)) = (op (e3) (e2)))) -> ((~((op (e3) (e3)) = (e2)))\/((op (e3) (e2)) = (e3))) -> ((~((op (e3) (e3)) = (e0)))\/((op (e3) (e0)) = (e3))) -> False). % 15.55/15.75 do 0 intro. intros zenon_H1d3 zenon_H1c3 zenon_H15f zenon_H17d zenon_H2af zenon_H140 zenon_H25e zenon_Ha3 zenon_H135 zenon_H175 zenon_H146 zenon_H2b4 zenon_H1df zenon_H1d0 zenon_H1d2 zenon_H10c zenon_H157 zenon_H6a zenon_H1a2 zenon_H8e zenon_H36 zenon_H3b zenon_H35 zenon_H28 zenon_H49 zenon_H5e zenon_H8f zenon_H2be zenon_H10d zenon_H109 zenon_H1b3 zenon_H1b4 zenon_H145 zenon_H17a zenon_Heb zenon_H105 zenon_H10e zenon_H10f. % 15.55/15.75 apply (zenon_or_s _ _ zenon_H1d3); [ zenon_intro zenon_Hd6 | zenon_intro zenon_H117 ]. % 15.55/15.75 apply (zenon_or_s _ _ zenon_H10f); [ zenon_intro zenon_H3c | zenon_intro zenon_Hba ]. % 15.55/15.75 apply (zenon_L1344_); trivial. % 15.55/15.75 apply (zenon_L1345_); trivial. % 15.55/15.75 apply (zenon_or_s _ _ zenon_H1d2); [ zenon_intro zenon_H182 | zenon_intro zenon_H11f ]. % 15.55/15.75 apply (zenon_or_s _ _ zenon_H1c3); [ zenon_intro zenon_H30 | zenon_intro zenon_H124 ]. % 15.55/15.75 apply (zenon_or_s _ _ zenon_H10f); [ zenon_intro zenon_H3c | zenon_intro zenon_Hba ]. % 15.55/15.75 apply (zenon_or_s _ _ zenon_H10c); [ zenon_intro zenon_H104 | zenon_intro zenon_H10a ]. % 15.55/15.75 apply (zenon_L1343_); trivial. % 15.55/15.75 apply (zenon_L1314_); trivial. % 15.55/15.75 apply (zenon_L1095_); trivial. % 15.55/15.75 apply (zenon_L137_); trivial. % 15.55/15.75 apply (zenon_L237_); trivial. % 15.55/15.75 (* end of lemma zenon_L1346_ *) % 15.55/15.75 assert (zenon_L1347_ : ((op (e3) (e2)) = (e3)) -> (~((op (e2) (e2)) = (e1))) -> ((op (e0) (e3)) = (e0)) -> (((op (e0) (e3)) = (e3))\/(((op (e1) (e3)) = (e3))\/(((op (e2) (e3)) = (e3))\/((op (e3) (e3)) = (e3))))) -> (((op (e0) (e0)) = (e0))\/(((op (e0) (e0)) = (e1))\/(((op (e0) (e0)) = (e2))\/((op (e0) (e0)) = (e3))))) -> ((op (e1) (e3)) = (e1)) -> (((op (e0) (e1)) = (e0))\/(((op (e1) (e1)) = (e0))\/(((op (e2) (e1)) = (e0))\/((op (e3) (e1)) = (e0))))) -> (~((op (e0) (e0)) = (e2))) -> (~((op (e2) (e0)) = (op (e2) (e1)))) -> (((op (e0) (e2)) = (e0))\/(((op (e1) (e2)) = (e0))\/(((op (e2) (e2)) = (e0))\/((op (e3) (e2)) = (e0))))) -> ((~((op (e1) (e1)) = (e0)))\/((op (e1) (e0)) = (e1))) -> (~((op (e0) (e0)) = (e1))) -> (~((e0) = (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 (e2) (e0)) = (e0))\/((op (e3) (e0)) = (e0))))) -> (((op (e2) (e3)) = (e0))\/(((op (e2) (e3)) = (e1))\/(((op (e2) (e3)) = (e2))\/((op (e2) (e3)) = (e3))))) -> (((op (e2) (e0)) = (e3))\/(((op (e2) (e1)) = (e3))\/(((op (e2) (e2)) = (e3))\/((op (e2) (e3)) = (e3))))) -> (~((op (e0) (e1)) = (op (e2) (e1)))) -> (((op (e0) (e0)) = (e3))\/(((op (e0) (e1)) = (e3))\/(((op (e0) (e2)) = (e3))\/((op (e0) (e3)) = (e3))))) -> ((~((op (e1) (e1)) = (e2)))\/((op (e1) (e2)) = (e1))) -> ((~((op (e2) (e2)) = (e1)))\/((op (e2) (e1)) = (e2))) -> ((~((op (e3) (e3)) = (e0)))\/((op (e3) (e0)) = (e3))) -> (~((op (e3) (e0)) = (op (e3) (e1)))) -> ((~((op (e3) (e3)) = (e1)))\/((op (e3) (e1)) = (e3))) -> (~((op (e2) (e2)) = (op (e2) (e3)))) -> ((~((op (e2) (e2)) = (e3)))\/((op (e2) (e3)) = (e2))) -> (~((op (e1) (e0)) = (op (e1) (e3)))) -> ((~((op (e1) (e1)) = (e3)))\/((op (e1) (e3)) = (e1))) -> (~((op (e1) (e0)) = (op (e1) (e1)))) -> ((~((op (e1) (e1)) = (e1)))\/((op (e1) (e1)) = (e1))) -> (((op (e3) (e0)) = (e0))\/(((op (e3) (e1)) = (e0))\/(((op (e3) (e2)) = (e0))\/((op (e3) (e3)) = (e0))))) -> (((op (e0) (e0)) = (e2))\/(((op (e1) (e0)) = (e2))\/(((op (e2) (e0)) = (e2))\/((op (e3) (e0)) = (e2))))) -> (~((op (e2) (e0)) = (op (e2) (e2)))) -> (~((op (e2) (e1)) = (op (e3) (e1)))) -> (~((e0) = (e3))) -> (((op (e1) (e0)) = (e0))\/(((op (e1) (e1)) = (e0))\/(((op (e1) (e2)) = (e0))\/((op (e1) (e3)) = (e0))))) -> (~((e0) = (e2))) -> (((op (e0) (e0)) = (e2))\/(((op (e0) (e1)) = (e2))\/(((op (e0) (e2)) = (e2))\/((op (e0) (e3)) = (e2))))) -> (~((op (e0) (e2)) = (op (e2) (e2)))) -> (((op (e1) (e0)) = (e1))\/(((op (e1) (e1)) = (e1))\/(((op (e1) (e2)) = (e1))\/((op (e1) (e3)) = (e1))))) -> (~((e1) = (e3))) -> (((op (e0) (e2)) = (e1))\/(((op (e1) (e2)) = (e1))\/(((op (e2) (e2)) = (e1))\/((op (e3) (e2)) = (e1))))) -> (((op (e1) (e2)) = (e0))\/(((op (e1) (e2)) = (e1))\/(((op (e1) (e2)) = (e2))\/((op (e1) (e2)) = (e3))))) -> (~((op (e0) (e2)) = (op (e1) (e2)))) -> (((op (e3) (e0)) = (e3))\/(((op (e3) (e1)) = (e3))\/(((op (e3) (e2)) = (e3))\/((op (e3) (e3)) = (e3))))) -> ((~((op (e3) (e3)) = (e3)))\/((op (e3) (e3)) = (e3))) -> (~((op (e3) (op (e3) (e3))) = (op (e3) (e3)))) -> (((op (e3) (e0)) = (e2))\/(((op (e3) (e1)) = (e2))\/(((op (e3) (e2)) = (e2))\/((op (e3) (e3)) = (e2))))) -> (~((op (e0) (e1)) = (op (e3) (e1)))) -> (~((op (e2) (e1)) = (op (e2) (e2)))) -> (~((e2) = (e3))) -> (((op (e0) (e1)) = (e2))\/(((op (e1) (e1)) = (e2))\/(((op (e2) (e1)) = (e2))\/((op (e3) (e1)) = (e2))))) -> ((~((op (e3) (e3)) = (e2)))\/((op (e3) (e2)) = (e3))) -> (~((op (e2) (e0)) = (op (e3) (e0)))) -> (((op (e0) (e2)) = (e3))\/(((op (e1) (e2)) = (e3))\/(((op (e2) (e2)) = (e3))\/((op (e3) (e2)) = (e3))))) -> (~((op (e1) (e0)) = (op (e1) (e2)))) -> (((op (e0) (e3)) = (e1))\/(((op (e1) (e3)) = (e1))\/(((op (e2) (e3)) = (e1))\/((op (e3) (e3)) = (e1))))) -> (~((op (e2) (e0)) = (op (e2) (e3)))) -> (~((op (e1) (e2)) = (op (e1) (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)) = (op (e0) (e3)))) -> (((op (e1) (e0)) = (e2))\/(((op (e1) (e1)) = (e2))\/(((op (e1) (e2)) = (e2))\/((op (e1) (e3)) = (e2))))) -> (~((op (e0) (e3)) = (op (e1) (e3)))) -> ((op (e2) (e2)) = (e2)) -> (~((op (e1) (e2)) = (op (e2) (e2)))) -> (~((e1) = (e2))) -> (((op (e0) (e1)) = (e1))\/(((op (e1) (e1)) = (e1))\/(((op (e2) (e1)) = (e1))\/((op (e3) (e1)) = (e1))))) -> (~((op (e1) (e0)) = (op (e3) (e0)))) -> (~((op (e0) (op (e3) (e0))) = (op (e3) (e0)))) -> (((op (e3) (e2)) = (e0))\/(((op (e3) (e2)) = (e1))\/(((op (e3) (e2)) = (e2))\/((op (e3) (e2)) = (e3))))) -> (~((op (e1) (e2)) = (op (e3) (e2)))) -> (((op (e1) (e0)) = (e3))\/(((op (e1) (e1)) = (e3))\/(((op (e1) (e2)) = (e3))\/((op (e1) (e3)) = (e3))))) -> (~((op (e2) (op (e3) (e2))) = (op (e3) (e2)))) -> (~((op (e3) (e1)) = (op (e3) (e2)))) -> (~((op (e0) (e2)) = (op (e3) (e2)))) -> (((op (e3) (e0)) = (e1))\/(((op (e3) (e1)) = (e1))\/(((op (e3) (e2)) = (e1))\/((op (e3) (e3)) = (e1))))) -> (((op (e0) (e3)) = (e0))\/(((op (e0) (e3)) = (e1))\/(((op (e0) (e3)) = (e2))\/((op (e0) (e3)) = (e3))))) -> (~((op (e1) (e0)) = (op (e2) (e0)))) -> (~((op (e1) (op (e3) (e1))) = (op (e3) (e1)))) -> (~((op (e0) (e3)) = (op (e2) (e3)))) -> (((op (e2) (e0)) = (e1))\/(((op (e2) (e1)) = (e1))\/(((op (e2) (e2)) = (e1))\/((op (e2) (e3)) = (e1))))) -> (((op (e0) (e0)) = (e3))\/(((op (e1) (e0)) = (e3))\/(((op (e2) (e0)) = (e3))\/((op (e3) (e0)) = (e3))))) -> (~((op (e0) (e0)) = (e0))) -> (~((op (e0) (e1)) = (op (e1) (e1)))) -> (~((op (e1) (e1)) = (op (e1) (e2)))) -> ((~((op (e0) (e0)) = (e3)))\/((op (e0) (e3)) = (e0))) -> (~((op (e3) (e3)) = (e3))) -> (~((op (e3) (e3)) = (e1))) -> (~((op (e3) (e3)) = (e0))) -> (((op (e3) (e3)) = (e0))\/(((op (e3) (e3)) = (e1))\/(((op (e3) (e3)) = (e2))\/((op (e3) (e3)) = (e3))))) -> (~((op (e1) (e1)) = (e2))) -> (~((op (e1) (e1)) = (e1))) -> (~((op (e1) (e1)) = (e0))) -> (((op (e1) (e1)) = (e0))\/(((op (e1) (e1)) = (e1))\/(((op (e1) (e1)) = (e2))\/((op (e1) (e1)) = (e3))))) -> (~((op (e2) (e2)) = (e0))) -> (~((op (e3) (e0)) = (op (e3) (e2)))) -> False). % 15.55/15.75 do 0 intro. intros zenon_H106 zenon_H52 zenon_Hca zenon_H2d0 zenon_H12a zenon_H11f zenon_H144 zenon_H8f zenon_H154 zenon_H16f zenon_H1e4 zenon_H45 zenon_H9e zenon_H44 zenon_Hf0 zenon_H2ab zenon_He6 zenon_Hde zenon_H58 zenon_H1d3 zenon_H1e3 zenon_H10f zenon_H109 zenon_H10c zenon_H15f zenon_H1c3 zenon_H1cf zenon_H1d2 zenon_Hd7 zenon_H1d8 zenon_H1f6 zenon_Heb zenon_H17a zenon_H13c zenon_H4b zenon_H163 zenon_H5e zenon_H8e zenon_H28 zenon_H1c5 zenon_Ha3 zenon_H11b zenon_H1d5 zenon_H87 zenon_H2d5 zenon_H10d zenon_H2be zenon_H1df zenon_H138 zenon_H157 zenon_H6a zenon_H1a2 zenon_H10e zenon_H1e5 zenon_H175 zenon_H166 zenon_H121 zenon_Hce zenon_H1d0 zenon_H36 zenon_Hf1 zenon_Hc9 zenon_H84 zenon_H80 zenon_H35 zenon_H7d zenon_Ha7 zenon_H228 zenon_H22e zenon_H2b8 zenon_H25e zenon_H17d zenon_H90 zenon_H2af zenon_H135 zenon_H140 zenon_H146 zenon_H254 zenon_H247 zenon_H2b4 zenon_Hb4 zenon_Hb7 zenon_Hbe zenon_H20 zenon_H23 zenon_H116 zenon_H236 zenon_H3e zenon_H104 zenon_H3c zenon_H3b zenon_Hd6 zenon_H1b4 zenon_H145 zenon_H1b3 zenon_H2e zenon_H105. % 15.55/15.75 apply (zenon_or_s _ _ zenon_Hf0); [ zenon_intro zenon_H1f | zenon_intro zenon_Hf2 ]. % 15.55/15.75 exact (zenon_H20 zenon_H1f). % 15.55/15.75 apply (zenon_or_s _ _ zenon_Hf2); [ zenon_intro zenon_Had | zenon_intro zenon_Hf3 ]. % 15.55/15.75 apply (zenon_or_s _ _ zenon_H44); [ zenon_intro zenon_H47 | zenon_intro zenon_H46 ]. % 15.55/15.75 exact (zenon_H45 zenon_H47). % 15.55/15.75 apply (zenon_or_s _ _ zenon_H46); [ zenon_intro zenon_H22 | zenon_intro zenon_H48 ]. % 15.55/15.75 apply (zenon_or_s _ _ zenon_Hf1); [ zenon_intro zenon_H47 | zenon_intro zenon_Hf4 ]. % 15.55/15.75 exact (zenon_H45 zenon_H47). % 15.55/15.75 apply (zenon_or_s _ _ zenon_Hf4); [ zenon_intro zenon_Hd8 | zenon_intro zenon_Hf5 ]. % 15.55/15.75 apply (zenon_L1255_); trivial. % 15.55/15.75 apply (zenon_or_s _ _ zenon_Hf5); [ zenon_intro zenon_Hae | zenon_intro zenon_Hee ]. % 15.55/15.75 apply (zenon_L1340_); trivial. % 15.55/15.75 apply (zenon_L1054_); trivial. % 15.55/15.75 apply (zenon_or_s _ _ zenon_H48); [ zenon_intro zenon_H29 | zenon_intro zenon_H37 ]. % 15.55/15.75 apply (zenon_or_s _ _ zenon_Hf1); [ zenon_intro zenon_H47 | zenon_intro zenon_Hf4 ]. % 15.55/15.75 exact (zenon_H45 zenon_H47). % 15.55/15.75 apply (zenon_or_s _ _ zenon_Hf4); [ zenon_intro zenon_Hd8 | zenon_intro zenon_Hf5 ]. % 15.55/15.75 apply (zenon_L224_); trivial. % 15.55/15.75 apply (zenon_or_s _ _ zenon_Hf5); [ zenon_intro zenon_Hae | zenon_intro zenon_Hee ]. % 15.55/15.75 apply (zenon_L1340_); trivial. % 15.55/15.75 apply (zenon_or_s _ _ zenon_H8e); [ zenon_intro zenon_H92 | zenon_intro zenon_H91 ]. % 15.55/15.75 exact (zenon_H8f zenon_H92). % 15.55/15.75 apply (zenon_or_s _ _ zenon_H91); [ zenon_intro zenon_H5d | zenon_intro zenon_H93 ]. % 15.55/15.75 apply (zenon_or_s _ _ zenon_H228); [ zenon_intro zenon_H22 | zenon_intro zenon_H229 ]. % 15.55/15.75 apply (zenon_L1054_); trivial. % 15.55/15.75 apply (zenon_or_s _ _ zenon_H229); [ zenon_intro zenon_H21 | zenon_intro zenon_H22a ]. % 15.55/15.75 exact (zenon_H1b4 zenon_H21). % 15.55/15.75 apply (zenon_or_s _ _ zenon_H22a); [ zenon_intro zenon_Hb2 | zenon_intro zenon_H13e ]. % 15.55/15.75 apply (zenon_or_s _ _ zenon_H1df); [ zenon_intro zenon_He9 | zenon_intro zenon_H1e0 ]. % 15.55/15.75 apply (zenon_L1341_); trivial. % 15.55/15.75 apply (zenon_or_s _ _ zenon_H1e0); [ zenon_intro zenon_H16a | zenon_intro zenon_H1e1 ]. % 15.55/15.75 apply (zenon_L146_); trivial. % 15.55/15.75 apply (zenon_or_s _ _ zenon_H1e1); [ zenon_intro zenon_H1dd | zenon_intro zenon_H43 ]. % 15.55/15.75 apply (zenon_L1083_); trivial. % 15.55/15.75 apply (zenon_L175_); trivial. % 15.55/15.75 apply (zenon_L145_); trivial. % 15.55/15.75 apply (zenon_or_s _ _ zenon_H93); [ zenon_intro zenon_H63 | zenon_intro zenon_H81 ]. % 15.55/15.75 apply (zenon_L15_); trivial. % 15.55/15.75 apply (zenon_L107_); trivial. % 15.55/15.75 apply (zenon_L1342_); trivial. % 15.55/15.75 apply (zenon_or_s _ _ zenon_Hf3); [ zenon_intro zenon_Hcf | zenon_intro zenon_Hdb ]. % 15.55/15.75 apply (zenon_or_s _ _ zenon_H163); [ zenon_intro zenon_Had | zenon_intro zenon_H164 ]. % 15.55/15.75 apply (zenon_or_s _ _ zenon_H144); [ zenon_intro zenon_H49 | zenon_intro zenon_H147 ]. % 15.55/15.75 apply (zenon_L1346_); trivial. % 15.55/15.75 apply (zenon_or_s _ _ zenon_H147); [ zenon_intro zenon_H149 | zenon_intro zenon_H148 ]. % 15.55/15.75 exact (zenon_H145 zenon_H149). % 15.55/15.75 apply (zenon_or_s _ _ zenon_H148); [ zenon_intro zenon_H14a | zenon_intro zenon_H142 ]. % 15.55/15.75 apply (zenon_L133_); trivial. % 15.55/15.75 apply (zenon_L1136_); trivial. % 15.55/15.75 apply (zenon_or_s _ _ zenon_H164); [ zenon_intro zenon_H149 | zenon_intro zenon_H165 ]. % 15.55/15.75 exact (zenon_H145 zenon_H149). % 15.55/15.75 apply (zenon_or_s _ _ zenon_H165); [ zenon_intro zenon_H15d | zenon_intro zenon_Hcc ]. % 15.55/15.75 apply (zenon_L490_); trivial. % 15.55/15.75 apply (zenon_L208_); trivial. % 15.55/15.75 apply (zenon_or_s _ _ zenon_H16f); [ zenon_intro zenon_Hab | zenon_intro zenon_H170 ]. % 15.55/15.75 apply (zenon_L1336_); trivial. % 15.55/15.75 apply (zenon_or_s _ _ zenon_H170); [ zenon_intro zenon_H15d | zenon_intro zenon_H171 ]. % 15.55/15.75 apply (zenon_L490_); trivial. % 15.55/15.75 apply (zenon_or_s _ _ zenon_H171); [ zenon_intro zenon_H32 | zenon_intro zenon_H167 ]. % 15.55/15.75 exact (zenon_H2e zenon_H32). % 15.55/15.75 apply (zenon_L156_); trivial. % 15.55/15.75 (* end of lemma zenon_L1347_ *) % 15.55/15.75 assert (zenon_L1348_ : ((~((op (e3) (e3)) = (e3)))\/((op (e3) (e3)) = (e3))) -> (~((op (e3) (op (e3) (e3))) = (op (e3) (e3)))) -> (~((op (e0) (e0)) = (e2))) -> (((op (e0) (e0)) = (e0))\/(((op (e0) (e0)) = (e1))\/(((op (e0) (e0)) = (e2))\/((op (e0) (e0)) = (e3))))) -> (~((op (e3) (e3)) = (e0))) -> (((op (e3) (e3)) = (e0))\/(((op (e3) (e3)) = (e1))\/(((op (e3) (e3)) = (e2))\/((op (e3) (e3)) = (e3))))) -> (~((op (e0) (e0)) = (e1))) -> (~((op (e0) (e0)) = (e0))) -> (~((op (e0) (e2)) = (op (e2) (e2)))) -> ((op (e2) (e2)) = (e2)) -> (~((e0) = (e2))) -> ((op (e0) (e3)) = (e0)) -> (((op (e0) (e0)) = (e2))\/(((op (e0) (e1)) = (e2))\/(((op (e0) (e2)) = (e2))\/((op (e0) (e3)) = (e2))))) -> (~((op (e2) (e2)) = (e1))) -> ((~((op (e1) (e1)) = (e2)))\/((op (e1) (e2)) = (e1))) -> (~((op (e1) (e0)) = (op (e1) (e2)))) -> ((~((op (e3) (e3)) = (e0)))\/((op (e3) (e0)) = (e3))) -> (~((op (e0) (e3)) = (op (e1) (e3)))) -> (~((op (e0) (e1)) = (op (e3) (e1)))) -> (~((op (e2) (op (e3) (e2))) = (op (e3) (e2)))) -> (((op (e3) (e0)) = (e2))\/(((op (e3) (e1)) = (e2))\/(((op (e3) (e2)) = (e2))\/((op (e3) (e3)) = (e2))))) -> (~((op (e3) (e0)) = (op (e3) (e2)))) -> (~((e1) = (e2))) -> (~((op (e2) (e0)) = (op (e2) (e2)))) -> (((op (e1) (e1)) = (e0))\/(((op (e1) (e1)) = (e1))\/(((op (e1) (e1)) = (e2))\/((op (e1) (e1)) = (e3))))) -> (~((op (e1) (e1)) = (e1))) -> (((op (e0) (e0)) = (e2))\/(((op (e1) (e0)) = (e2))\/(((op (e2) (e0)) = (e2))\/((op (e3) (e0)) = (e2))))) -> (((op (e1) (e0)) = (e2))\/(((op (e1) (e1)) = (e2))\/(((op (e1) (e2)) = (e2))\/((op (e1) (e3)) = (e2))))) -> (~((e1) = (e3))) -> (~((op (e1) (e2)) = (op (e3) (e2)))) -> (~((e2) = (e3))) -> (((op (e1) (e0)) = (e3))\/(((op (e1) (e1)) = (e3))\/(((op (e1) (e2)) = (e3))\/((op (e1) (e3)) = (e3))))) -> (~((op (e1) (e2)) = (op (e2) (e2)))) -> ((~((op (e3) (e3)) = (e2)))\/((op (e3) (e2)) = (e3))) -> (~((op (e1) (e0)) = (op (e1) (e3)))) -> ((~((op (e1) (e1)) = (e3)))\/((op (e1) (e3)) = (e1))) -> (~((op (e1) (e1)) = (e2))) -> (~((op (e1) (e1)) = (e0))) -> (((op (e0) (e2)) = (e0))\/(((op (e1) (e2)) = (e0))\/(((op (e2) (e2)) = (e0))\/((op (e3) (e2)) = (e0))))) -> ((op (e1) (e3)) = (e1)) -> (((op (e0) (e3)) = (e3))\/(((op (e1) (e3)) = (e3))\/(((op (e2) (e3)) = (e3))\/((op (e3) (e3)) = (e3))))) -> (~((op (e2) (e2)) = (e0))) -> ((~((op (e1) (e1)) = (e0)))\/((op (e1) (e0)) = (e1))) -> (~((e0) = (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 (e2) (e0)) = (e0))\/((op (e3) (e0)) = (e0))))) -> (((op (e2) (e3)) = (e0))\/(((op (e2) (e3)) = (e1))\/(((op (e2) (e3)) = (e2))\/((op (e2) (e3)) = (e3))))) -> (((op (e2) (e0)) = (e3))\/(((op (e2) (e1)) = (e3))\/(((op (e2) (e2)) = (e3))\/((op (e2) (e3)) = (e3))))) -> (~((op (e0) (e1)) = (op (e2) (e1)))) -> (((op (e0) (e0)) = (e3))\/(((op (e0) (e1)) = (e3))\/(((op (e0) (e2)) = (e3))\/((op (e0) (e3)) = (e3))))) -> ((~((op (e2) (e2)) = (e1)))\/((op (e2) (e1)) = (e2))) -> (~((op (e3) (e0)) = (op (e3) (e1)))) -> ((~((op (e3) (e3)) = (e1)))\/((op (e3) (e1)) = (e3))) -> (~((op (e2) (e2)) = (op (e2) (e3)))) -> ((~((op (e2) (e2)) = (e3)))\/((op (e2) (e3)) = (e2))) -> (~((op (e1) (e0)) = (op (e1) (e1)))) -> ((~((op (e1) (e1)) = (e1)))\/((op (e1) (e1)) = (e1))) -> (((op (e3) (e0)) = (e0))\/(((op (e3) (e1)) = (e0))\/(((op (e3) (e2)) = (e0))\/((op (e3) (e3)) = (e0))))) -> (~((op (e2) (e1)) = (op (e3) (e1)))) -> (~((e0) = (e3))) -> (((op (e1) (e0)) = (e0))\/(((op (e1) (e1)) = (e0))\/(((op (e1) (e2)) = (e0))\/((op (e1) (e3)) = (e0))))) -> (((op (e1) (e0)) = (e1))\/(((op (e1) (e1)) = (e1))\/(((op (e1) (e2)) = (e1))\/((op (e1) (e3)) = (e1))))) -> (((op (e0) (e2)) = (e1))\/(((op (e1) (e2)) = (e1))\/(((op (e2) (e2)) = (e1))\/((op (e3) (e2)) = (e1))))) -> (((op (e1) (e2)) = (e0))\/(((op (e1) (e2)) = (e1))\/(((op (e1) (e2)) = (e2))\/((op (e1) (e2)) = (e3))))) -> (~((op (e0) (e2)) = (op (e1) (e2)))) -> (((op (e3) (e0)) = (e3))\/(((op (e3) (e1)) = (e3))\/(((op (e3) (e2)) = (e3))\/((op (e3) (e3)) = (e3))))) -> (~((op (e2) (e1)) = (op (e2) (e2)))) -> (((op (e0) (e1)) = (e2))\/(((op (e1) (e1)) = (e2))\/(((op (e2) (e1)) = (e2))\/((op (e3) (e1)) = (e2))))) -> (~((op (e2) (e0)) = (op (e3) (e0)))) -> (((op (e0) (e2)) = (e3))\/(((op (e1) (e2)) = (e3))\/(((op (e2) (e2)) = (e3))\/((op (e3) (e2)) = (e3))))) -> (((op (e0) (e3)) = (e1))\/(((op (e1) (e3)) = (e1))\/(((op (e2) (e3)) = (e1))\/((op (e3) (e3)) = (e1))))) -> (~((op (e2) (e0)) = (op (e2) (e3)))) -> (~((op (e1) (e2)) = (op (e1) (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)) = (op (e0) (e3)))) -> (((op (e0) (e1)) = (e1))\/(((op (e1) (e1)) = (e1))\/(((op (e2) (e1)) = (e1))\/((op (e3) (e1)) = (e1))))) -> (~((op (e1) (e0)) = (op (e3) (e0)))) -> (~((op (e0) (op (e3) (e0))) = (op (e3) (e0)))) -> (((op (e3) (e2)) = (e0))\/(((op (e3) (e2)) = (e1))\/(((op (e3) (e2)) = (e2))\/((op (e3) (e2)) = (e3))))) -> (~((op (e3) (e1)) = (op (e3) (e2)))) -> (~((op (e0) (e2)) = (op (e3) (e2)))) -> (((op (e3) (e0)) = (e1))\/(((op (e3) (e1)) = (e1))\/(((op (e3) (e2)) = (e1))\/((op (e3) (e3)) = (e1))))) -> (((op (e0) (e3)) = (e0))\/(((op (e0) (e3)) = (e1))\/(((op (e0) (e3)) = (e2))\/((op (e0) (e3)) = (e3))))) -> (~((op (e1) (e0)) = (op (e2) (e0)))) -> (~((op (e1) (op (e3) (e1))) = (op (e3) (e1)))) -> (~((op (e0) (e3)) = (op (e2) (e3)))) -> (((op (e2) (e0)) = (e1))\/(((op (e2) (e1)) = (e1))\/(((op (e2) (e2)) = (e1))\/((op (e2) (e3)) = (e1))))) -> (((op (e0) (e0)) = (e3))\/(((op (e1) (e0)) = (e3))\/(((op (e2) (e0)) = (e3))\/((op (e3) (e0)) = (e3))))) -> (~((op (e0) (e1)) = (op (e1) (e1)))) -> (~((op (e1) (e1)) = (op (e1) (e2)))) -> ((~((op (e0) (e0)) = (e3)))\/((op (e0) (e3)) = (e0))) -> (~((op (e2) (e0)) = (op (e2) (e1)))) -> (((op (e0) (e1)) = (e0))\/(((op (e1) (e1)) = (e0))\/(((op (e2) (e1)) = (e0))\/((op (e3) (e1)) = (e0))))) -> False). % 15.55/15.75 do 0 intro. intros zenon_H10d zenon_H2be zenon_H8f zenon_H12a zenon_H3c zenon_H3b zenon_H45 zenon_H20 zenon_H28 zenon_H35 zenon_H5e zenon_Hca zenon_H8e zenon_H52 zenon_H1d3 zenon_H166 zenon_H10f zenon_H80 zenon_H138 zenon_H2af zenon_H1df zenon_H105 zenon_Ha7 zenon_H17a zenon_H1b3 zenon_H1b4 zenon_Heb zenon_H84 zenon_Ha3 zenon_H17d zenon_H6a zenon_H90 zenon_H7d zenon_H10e zenon_H1cf zenon_H1d2 zenon_Hd6 zenon_H145 zenon_H16f zenon_H11f zenon_H2d0 zenon_H2e zenon_H1e4 zenon_H9e zenon_H44 zenon_Hf0 zenon_H2ab zenon_He6 zenon_Hde zenon_H58 zenon_H1e3 zenon_H109 zenon_H10c zenon_H15f zenon_H1c3 zenon_Hd7 zenon_H1d8 zenon_H1f6 zenon_H13c zenon_H4b zenon_H163 zenon_H1c5 zenon_H11b zenon_H1d5 zenon_H87 zenon_H2d5 zenon_H157 zenon_H1a2 zenon_H1e5 zenon_H175 zenon_H121 zenon_Hce zenon_H1d0 zenon_H36 zenon_Hf1 zenon_Hc9 zenon_H228 zenon_H22e zenon_H2b8 zenon_H25e zenon_H135 zenon_H140 zenon_H146 zenon_H254 zenon_H247 zenon_H2b4 zenon_Hb4 zenon_Hb7 zenon_Hbe zenon_H23 zenon_H116 zenon_H236 zenon_H154 zenon_H144. % 15.65/15.76 apply (zenon_or_s _ _ zenon_H10c); [ zenon_intro zenon_H104 | zenon_intro zenon_H10a ]. % 15.65/15.76 apply (zenon_or_s _ _ zenon_H10e); [ zenon_intro zenon_H3d | zenon_intro zenon_H106 ]. % 15.65/15.76 apply (zenon_L1333_); trivial. % 15.65/15.76 apply (zenon_or_s _ _ zenon_H10d); [ zenon_intro zenon_H3e | zenon_intro zenon_H42 ]. % 15.65/15.76 apply (zenon_L1347_); trivial. % 15.65/15.76 apply (zenon_L1041_); trivial. % 15.65/15.76 apply (zenon_or_s _ _ zenon_H10e); [ zenon_intro zenon_H3d | zenon_intro zenon_H106 ]. % 15.65/15.76 apply (zenon_L1333_); trivial. % 15.65/15.76 apply (zenon_L115_); trivial. % 15.65/15.76 (* end of lemma zenon_L1348_ *) % 15.65/15.76 assert (zenon_L1349_ : ((~((op (e3) (e3)) = (e3)))\/((op (e3) (e3)) = (e3))) -> (~((op (e3) (op (e3) (e3))) = (op (e3) (e3)))) -> (((op (e0) (e0)) = (e0))\/(((op (e0) (e0)) = (e1))\/(((op (e0) (e0)) = (e2))\/((op (e0) (e0)) = (e3))))) -> (((op (e3) (e3)) = (e0))\/(((op (e3) (e3)) = (e1))\/(((op (e3) (e3)) = (e2))\/((op (e3) (e3)) = (e3))))) -> (~((op (e0) (e0)) = (e1))) -> (~((op (e0) (e0)) = (e0))) -> ((~((op (e1) (e1)) = (e2)))\/((op (e1) (e2)) = (e1))) -> (~((op (e1) (e0)) = (op (e1) (e2)))) -> ((~((op (e3) (e3)) = (e0)))\/((op (e3) (e0)) = (e3))) -> (~((op (e0) (e3)) = (op (e1) (e3)))) -> (~((op (e0) (e1)) = (op (e3) (e1)))) -> (~((op (e2) (op (e3) (e2))) = (op (e3) (e2)))) -> (((op (e3) (e0)) = (e2))\/(((op (e3) (e1)) = (e2))\/(((op (e3) (e2)) = (e2))\/((op (e3) (e3)) = (e2))))) -> (~((op (e3) (e0)) = (op (e3) (e2)))) -> (~((e1) = (e2))) -> (~((op (e2) (e0)) = (op (e2) (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))))) -> (~((e1) = (e3))) -> (~((op (e1) (e2)) = (op (e3) (e2)))) -> (~((e2) = (e3))) -> (((op (e1) (e0)) = (e3))\/(((op (e1) (e1)) = (e3))\/(((op (e1) (e2)) = (e3))\/((op (e1) (e3)) = (e3))))) -> (~((op (e1) (e2)) = (op (e2) (e2)))) -> ((~((op (e3) (e3)) = (e2)))\/((op (e3) (e2)) = (e3))) -> (~((op (e1) (e0)) = (op (e1) (e3)))) -> ((~((op (e1) (e1)) = (e3)))\/((op (e1) (e3)) = (e1))) -> (~((op (e1) (e1)) = (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))))) -> ((~((op (e1) (e1)) = (e0)))\/((op (e1) (e0)) = (e1))) -> (~((e0) = (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 (e2) (e0)) = (e0))\/((op (e3) (e0)) = (e0))))) -> (((op (e2) (e3)) = (e0))\/(((op (e2) (e3)) = (e1))\/(((op (e2) (e3)) = (e2))\/((op (e2) (e3)) = (e3))))) -> (((op (e2) (e0)) = (e3))\/(((op (e2) (e1)) = (e3))\/(((op (e2) (e2)) = (e3))\/((op (e2) (e3)) = (e3))))) -> (~((op (e0) (e1)) = (op (e2) (e1)))) -> (((op (e0) (e0)) = (e3))\/(((op (e0) (e1)) = (e3))\/(((op (e0) (e2)) = (e3))\/((op (e0) (e3)) = (e3))))) -> ((~((op (e2) (e2)) = (e1)))\/((op (e2) (e1)) = (e2))) -> (~((op (e3) (e0)) = (op (e3) (e1)))) -> ((~((op (e3) (e3)) = (e1)))\/((op (e3) (e1)) = (e3))) -> (~((op (e2) (e2)) = (op (e2) (e3)))) -> ((~((op (e2) (e2)) = (e3)))\/((op (e2) (e3)) = (e2))) -> (~((op (e1) (e0)) = (op (e1) (e1)))) -> ((~((op (e1) (e1)) = (e1)))\/((op (e1) (e1)) = (e1))) -> (((op (e3) (e0)) = (e0))\/(((op (e3) (e1)) = (e0))\/(((op (e3) (e2)) = (e0))\/((op (e3) (e3)) = (e0))))) -> (~((op (e2) (e1)) = (op (e3) (e1)))) -> (~((e0) = (e3))) -> (((op (e1) (e0)) = (e0))\/(((op (e1) (e1)) = (e0))\/(((op (e1) (e2)) = (e0))\/((op (e1) (e3)) = (e0))))) -> (((op (e1) (e0)) = (e1))\/(((op (e1) (e1)) = (e1))\/(((op (e1) (e2)) = (e1))\/((op (e1) (e3)) = (e1))))) -> (((op (e0) (e2)) = (e1))\/(((op (e1) (e2)) = (e1))\/(((op (e2) (e2)) = (e1))\/((op (e3) (e2)) = (e1))))) -> (((op (e1) (e2)) = (e0))\/(((op (e1) (e2)) = (e1))\/(((op (e1) (e2)) = (e2))\/((op (e1) (e2)) = (e3))))) -> (~((op (e0) (e2)) = (op (e1) (e2)))) -> (((op (e3) (e0)) = (e3))\/(((op (e3) (e1)) = (e3))\/(((op (e3) (e2)) = (e3))\/((op (e3) (e3)) = (e3))))) -> (~((op (e2) (e1)) = (op (e2) (e2)))) -> (((op (e0) (e1)) = (e2))\/(((op (e1) (e1)) = (e2))\/(((op (e2) (e1)) = (e2))\/((op (e3) (e1)) = (e2))))) -> (~((op (e2) (e0)) = (op (e3) (e0)))) -> (((op (e0) (e2)) = (e3))\/(((op (e1) (e2)) = (e3))\/(((op (e2) (e2)) = (e3))\/((op (e3) (e2)) = (e3))))) -> (((op (e0) (e3)) = (e1))\/(((op (e1) (e3)) = (e1))\/(((op (e2) (e3)) = (e1))\/((op (e3) (e3)) = (e1))))) -> (~((op (e2) (e0)) = (op (e2) (e3)))) -> (~((op (e1) (e2)) = (op (e1) (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)) = (op (e0) (e3)))) -> (((op (e0) (e1)) = (e1))\/(((op (e1) (e1)) = (e1))\/(((op (e2) (e1)) = (e1))\/((op (e3) (e1)) = (e1))))) -> (~((op (e1) (e0)) = (op (e3) (e0)))) -> (~((op (e0) (op (e3) (e0))) = (op (e3) (e0)))) -> (((op (e3) (e2)) = (e0))\/(((op (e3) (e2)) = (e1))\/(((op (e3) (e2)) = (e2))\/((op (e3) (e2)) = (e3))))) -> (~((op (e3) (e1)) = (op (e3) (e2)))) -> (~((op (e0) (e2)) = (op (e3) (e2)))) -> (((op (e3) (e0)) = (e1))\/(((op (e3) (e1)) = (e1))\/(((op (e3) (e2)) = (e1))\/((op (e3) (e3)) = (e1))))) -> (((op (e0) (e3)) = (e0))\/(((op (e0) (e3)) = (e1))\/(((op (e0) (e3)) = (e2))\/((op (e0) (e3)) = (e3))))) -> (~((op (e1) (e0)) = (op (e2) (e0)))) -> (~((op (e1) (op (e3) (e1))) = (op (e3) (e1)))) -> (~((op (e0) (e3)) = (op (e2) (e3)))) -> (((op (e2) (e0)) = (e1))\/(((op (e2) (e1)) = (e1))\/(((op (e2) (e2)) = (e1))\/((op (e2) (e3)) = (e1))))) -> (((op (e0) (e0)) = (e3))\/(((op (e1) (e0)) = (e3))\/(((op (e2) (e0)) = (e3))\/((op (e3) (e0)) = (e3))))) -> (~((op (e1) (e1)) = (op (e1) (e2)))) -> ((~((op (e0) (e0)) = (e3)))\/((op (e0) (e3)) = (e0))) -> (~((op (e2) (e0)) = (op (e2) (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 (e1) (e1)) = (e0))\/(((op (e1) (e1)) = (e1))\/(((op (e1) (e1)) = (e2))\/((op (e1) (e1)) = (e3))))) -> (~((op (e0) (e1)) = (op (e1) (e1)))) -> (~((op (e1) (e1)) = (e1))) -> (~((op (e1) (e1)) = (e0))) -> (~((op (e0) (e2)) = (op (e2) (e2)))) -> ((op (e2) (e2)) = (e2)) -> (~((e0) = (e2))) -> ((op (e0) (e3)) = (e0)) -> (((op (e0) (e0)) = (e2))\/(((op (e0) (e1)) = (e2))\/(((op (e0) (e2)) = (e2))\/((op (e0) (e3)) = (e2))))) -> False). % 15.65/15.76 do 0 intro. intros zenon_H10d zenon_H2be zenon_H12a zenon_H3b zenon_H45 zenon_H20 zenon_H1d3 zenon_H166 zenon_H10f zenon_H80 zenon_H138 zenon_H2af zenon_H1df zenon_H105 zenon_Ha7 zenon_H17a zenon_Heb zenon_H84 zenon_Ha3 zenon_H17d zenon_H6a zenon_H90 zenon_H7d zenon_H10e zenon_H1cf zenon_H1d2 zenon_Hd6 zenon_H16f zenon_H2d0 zenon_H1e4 zenon_H9e zenon_H44 zenon_Hf0 zenon_H2ab zenon_He6 zenon_Hde zenon_H58 zenon_H1e3 zenon_H109 zenon_H10c zenon_H15f zenon_H1c3 zenon_Hd7 zenon_H1d8 zenon_H1f6 zenon_H13c zenon_H4b zenon_H163 zenon_H1c5 zenon_H11b zenon_H1d5 zenon_H87 zenon_H2d5 zenon_H157 zenon_H1a2 zenon_H1e5 zenon_H175 zenon_H121 zenon_Hce zenon_H1d0 zenon_H36 zenon_Hf1 zenon_Hc9 zenon_H228 zenon_H22e zenon_H2b8 zenon_H25e zenon_H135 zenon_H140 zenon_H146 zenon_H254 zenon_H247 zenon_H2b4 zenon_Hb4 zenon_Hb7 zenon_Hbe zenon_H116 zenon_H236 zenon_H154 zenon_H144 zenon_H1d4 zenon_H8f zenon_H1b3 zenon_H23 zenon_H1b4 zenon_H145 zenon_H28 zenon_H35 zenon_H5e zenon_Hca zenon_H8e. % 15.65/15.76 apply (zenon_or_s _ _ zenon_H1d2); [ zenon_intro zenon_H182 | zenon_intro zenon_H11f ]. % 15.65/15.76 apply (zenon_L343_); trivial. % 15.65/15.76 apply (zenon_or_s _ _ zenon_H1d4); [ zenon_intro zenon_H2e | zenon_intro zenon_Hdd ]. % 15.65/15.76 apply (zenon_or_s _ _ zenon_H1e3); [ zenon_intro zenon_H52 | zenon_intro zenon_H156 ]. % 15.65/15.76 apply (zenon_or_s _ _ zenon_H10f); [ zenon_intro zenon_H3c | zenon_intro zenon_Hba ]. % 15.65/15.76 apply (zenon_L1348_); trivial. % 15.65/15.76 apply (zenon_L1345_); trivial. % 15.65/15.76 apply (zenon_L134_); trivial. % 15.65/15.76 apply (zenon_L161_); trivial. % 15.65/15.76 (* end of lemma zenon_L1349_ *) % 15.65/15.76 assert (zenon_L1350_ : ((~((op (e3) (e3)) = (e3)))\/((op (e3) (e3)) = (e3))) -> (~((op (e3) (op (e3) (e3))) = (op (e3) (e3)))) -> (~((op (e0) (e0)) = (e2))) -> (~((op (e0) (e0)) = (e3))) -> (~((e2) = (e3))) -> (((op (e1) (e0)) = (e3))\/(((op (e1) (e1)) = (e3))\/(((op (e1) (e2)) = (e3))\/((op (e1) (e3)) = (e3))))) -> (~((e1) = (e3))) -> (~((op (e1) (e1)) = (op (e2) (e1)))) -> ((op (e1) (e1)) = (e1)) -> (~((op (e2) (e2)) = (e1))) -> (((op (e0) (e2)) = (e1))\/(((op (e1) (e2)) = (e1))\/(((op (e2) (e2)) = (e1))\/((op (e3) (e2)) = (e1))))) -> (~((op (e1) (e1)) = (op (e1) (e2)))) -> (((op (e3) (e0)) = (e1))\/(((op (e3) (e1)) = (e1))\/(((op (e3) (e2)) = (e1))\/((op (e3) (e3)) = (e1))))) -> (~((op (e3) (e3)) = (e1))) -> (~((op (e0) (e2)) = (op (e3) (e2)))) -> (~((op (e1) (op (e3) (e1))) = (op (e3) (e1)))) -> (~((op (e0) (op (e3) (e0))) = (op (e3) (e0)))) -> (~((op (e0) (e1)) = (op (e3) (e1)))) -> (~((op (e2) (op (e3) (e2))) = (op (e3) (e2)))) -> ((op (e2) (e2)) = (e2)) -> (((op (e0) (e3)) = (e0))\/(((op (e0) (e3)) = (e1))\/(((op (e0) (e3)) = (e2))\/((op (e0) (e3)) = (e3))))) -> (~((op (e0) (e3)) = (op (e1) (e3)))) -> (~((op (e0) (e3)) = (op (e3) (e3)))) -> (~((op (e0) (e3)) = (op (e2) (e3)))) -> ((op (e0) (e1)) = (e0)) -> (~((op (e0) (e1)) = (op (e0) (e3)))) -> (((op (e3) (e0)) = (e2))\/(((op (e3) (e1)) = (e2))\/(((op (e3) (e2)) = (e2))\/((op (e3) (e3)) = (e2))))) -> (((op (e2) (e0)) = (e1))\/(((op (e2) (e1)) = (e1))\/(((op (e2) (e2)) = (e1))\/((op (e2) (e3)) = (e1))))) -> ((op (e3) (e2)) = (e3)) -> (~((op (e1) (e2)) = (op (e3) (e2)))) -> (~((op (e1) (e1)) = (e3))) -> ((~((op (e3) (e3)) = (e2)))\/((op (e3) (e2)) = (e3))) -> (~((op (e3) (e0)) = (op (e3) (e2)))) -> (((op (e0) (e0)) = (e2))\/(((op (e1) (e0)) = (e2))\/(((op (e2) (e0)) = (e2))\/((op (e3) (e0)) = (e2))))) -> (~((op (e2) (e0)) = (op (e2) (e2)))) -> (~((op (e1) (e1)) = (e2))) -> (~((op (e2) (e1)) = (op (e2) (e2)))) -> (((op (e3) (e0)) = (e0))\/(((op (e3) (e1)) = (e0))\/(((op (e3) (e2)) = (e0))\/((op (e3) (e3)) = (e0))))) -> (~((op (e1) (e2)) = (op (e2) (e2)))) -> (~((op (e0) (e2)) = (op (e1) (e2)))) -> (((op (e1) (e2)) = (e0))\/(((op (e1) (e2)) = (e1))\/(((op (e1) (e2)) = (e2))\/((op (e1) (e2)) = (e3))))) -> (~((e0) = (e3))) -> (((op (e0) (e2)) = (e0))\/(((op (e0) (e2)) = (e1))\/(((op (e0) (e2)) = (e2))\/((op (e0) (e2)) = (e3))))) -> (~((op (e0) (e2)) = (op (e2) (e2)))) -> (~((op (e0) (e1)) = (op (e0) (e2)))) -> (~((op (e2) (e2)) = (e3))) -> (((op (e0) (e2)) = (e3))\/(((op (e1) (e2)) = (e3))\/(((op (e2) (e2)) = (e3))\/((op (e3) (e2)) = (e3))))) -> (((op (e0) (e1)) = (e2))\/(((op (e1) (e1)) = (e2))\/(((op (e2) (e1)) = (e2))\/((op (e3) (e1)) = (e2))))) -> (~((op (e0) (e1)) = (op (e1) (e1)))) -> (((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)) = (e1))\/(((op (e0) (e2)) = (e1))\/((op (e0) (e3)) = (e1))))) -> (((op (e0) (e0)) = (e3))\/(((op (e1) (e0)) = (e3))\/(((op (e2) (e0)) = (e3))\/((op (e3) (e0)) = (e3))))) -> (((op (e3) (e3)) = (e0))\/(((op (e3) (e3)) = (e1))\/(((op (e3) (e3)) = (e2))\/((op (e3) (e3)) = (e3))))) -> (~((op (e3) (e3)) = (e0))) -> False). % 15.65/15.76 do 0 intro. intros zenon_H10d zenon_H2be zenon_H8f zenon_H59 zenon_H6a zenon_H90 zenon_Ha3 zenon_Hb1 zenon_H21 zenon_H52 zenon_H11b zenon_H116 zenon_H146 zenon_H104 zenon_H140 zenon_H2b4 zenon_H2b8 zenon_H138 zenon_H2af zenon_H35 zenon_H254 zenon_H80 zenon_H36 zenon_Hb4 zenon_H49 zenon_H1cd zenon_H1df zenon_Hb7 zenon_H106 zenon_H17d zenon_H182 zenon_H10e zenon_H105 zenon_Heb zenon_H17a zenon_Hd6 zenon_H157 zenon_H1f6 zenon_H7d zenon_H87 zenon_H1d5 zenon_H4b zenon_H251 zenon_H28 zenon_H23e zenon_H30 zenon_H175 zenon_H1a2 zenon_H23 zenon_H8e zenon_Ha7 zenon_H44 zenon_Hbe zenon_H3b zenon_H3c. % 15.65/15.76 apply (zenon_or_s _ _ zenon_H10d); [ zenon_intro zenon_H3e | zenon_intro zenon_H42 ]. % 15.65/15.76 apply (zenon_L1239_); trivial. % 15.65/15.76 apply (zenon_L1041_); trivial. % 15.65/15.76 (* end of lemma zenon_L1350_ *) % 15.65/15.76 assert (zenon_L1351_ : (((op (e3) (e0)) = (e3))\/(((op (e3) (e1)) = (e3))\/(((op (e3) (e2)) = (e3))\/((op (e3) (e3)) = (e3))))) -> ((op (e3) (e0)) = (e2)) -> (~((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 (e3) (e3)) = (e0))) -> (((op (e3) (e3)) = (e0))\/(((op (e3) (e3)) = (e1))\/(((op (e3) (e3)) = (e2))\/((op (e3) (e3)) = (e3))))) -> (((op (e0) (e0)) = (e3))\/(((op (e1) (e0)) = (e3))\/(((op (e2) (e0)) = (e3))\/((op (e3) (e0)) = (e3))))) -> (((op (e0) (e0)) = (e1))\/(((op (e0) (e1)) = (e1))\/(((op (e0) (e2)) = (e1))\/((op (e0) (e3)) = (e1))))) -> (~((e1) = (e2))) -> (((op (e0) (e0)) = (e2))\/(((op (e0) (e1)) = (e2))\/(((op (e0) (e2)) = (e2))\/((op (e0) (e3)) = (e2))))) -> (~((op (e0) (e1)) = (op (e1) (e1)))) -> (((op (e0) (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 (e2) (e2)) = (e3))) -> (~((op (e0) (e1)) = (op (e0) (e2)))) -> (~((op (e0) (e2)) = (op (e2) (e2)))) -> (((op (e0) (e2)) = (e0))\/(((op (e0) (e2)) = (e1))\/(((op (e0) (e2)) = (e2))\/((op (e0) (e2)) = (e3))))) -> (~((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 (e1) (e2)) = (op (e2) (e2)))) -> (((op (e3) (e0)) = (e0))\/(((op (e3) (e1)) = (e0))\/(((op (e3) (e2)) = (e0))\/((op (e3) (e3)) = (e0))))) -> (~((op (e2) (e1)) = (op (e2) (e2)))) -> (~((op (e1) (e1)) = (e2))) -> (~((op (e2) (e0)) = (op (e2) (e2)))) -> (((op (e0) (e0)) = (e2))\/(((op (e1) (e0)) = (e2))\/(((op (e2) (e0)) = (e2))\/((op (e3) (e0)) = (e2))))) -> (~((op (e3) (e0)) = (op (e3) (e2)))) -> ((~((op (e3) (e3)) = (e2)))\/((op (e3) (e2)) = (e3))) -> (~((op (e1) (e1)) = (e3))) -> (~((op (e1) (e2)) = (op (e3) (e2)))) -> (((op (e2) (e0)) = (e1))\/(((op (e2) (e1)) = (e1))\/(((op (e2) (e2)) = (e1))\/((op (e2) (e3)) = (e1))))) -> (((op (e3) (e0)) = (e2))\/(((op (e3) (e1)) = (e2))\/(((op (e3) (e2)) = (e2))\/((op (e3) (e3)) = (e2))))) -> (~((op (e0) (e1)) = (op (e0) (e3)))) -> ((op (e0) (e1)) = (e0)) -> (~((op (e0) (e3)) = (op (e2) (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 (e2) (e2)) = (e2)) -> (~((op (e2) (op (e3) (e2))) = (op (e3) (e2)))) -> (~((op (e0) (e1)) = (op (e3) (e1)))) -> (~((op (e0) (op (e3) (e0))) = (op (e3) (e0)))) -> (~((op (e1) (op (e3) (e1))) = (op (e3) (e1)))) -> (~((op (e0) (e2)) = (op (e3) (e2)))) -> (~((op (e3) (e3)) = (e1))) -> (((op (e3) (e0)) = (e1))\/(((op (e3) (e1)) = (e1))\/(((op (e3) (e2)) = (e1))\/((op (e3) (e3)) = (e1))))) -> (~((op (e1) (e1)) = (op (e1) (e2)))) -> (((op (e0) (e2)) = (e1))\/(((op (e1) (e2)) = (e1))\/(((op (e2) (e2)) = (e1))\/((op (e3) (e2)) = (e1))))) -> (~((op (e2) (e2)) = (e1))) -> ((op (e1) (e1)) = (e1)) -> (~((op (e1) (e1)) = (op (e2) (e1)))) -> (~((e1) = (e3))) -> (((op (e1) (e0)) = (e3))\/(((op (e1) (e1)) = (e3))\/(((op (e1) (e2)) = (e3))\/((op (e1) (e3)) = (e3))))) -> (~((e2) = (e3))) -> (~((op (e0) (e0)) = (e3))) -> (~((op (e0) (e0)) = (e2))) -> (~((op (e3) (op (e3) (e3))) = (op (e3) (e3)))) -> ((~((op (e3) (e3)) = (e3)))\/((op (e3) (e3)) = (e3))) -> (~((op (e3) (e3)) = (e3))) -> False). % 15.65/15.76 do 0 intro. intros zenon_H2d5 zenon_He9 zenon_H13c zenon_Hde zenon_H15a zenon_H3c zenon_H3b zenon_Hbe zenon_H44 zenon_Ha7 zenon_H8e zenon_H23 zenon_H1a2 zenon_H175 zenon_H30 zenon_H23e zenon_H28 zenon_H251 zenon_H4b zenon_H1d5 zenon_H87 zenon_H7d zenon_H1f6 zenon_H157 zenon_Hd6 zenon_H17a zenon_Heb zenon_H105 zenon_H10e zenon_H182 zenon_H17d zenon_Hb7 zenon_H1df zenon_H1cd zenon_H49 zenon_Hb4 zenon_H36 zenon_H80 zenon_H254 zenon_H35 zenon_H2af zenon_H138 zenon_H2b8 zenon_H2b4 zenon_H140 zenon_H104 zenon_H146 zenon_H116 zenon_H11b zenon_H52 zenon_H21 zenon_Hb1 zenon_Ha3 zenon_H90 zenon_H6a zenon_H59 zenon_H8f zenon_H2be zenon_H10d zenon_H3e. % 15.65/15.76 apply (zenon_or_s _ _ zenon_H2d5); [ zenon_intro zenon_Hba | zenon_intro zenon_H2d6 ]. % 15.65/15.76 apply (zenon_L220_); trivial. % 15.65/15.76 apply (zenon_or_s _ _ zenon_H2d6); [ zenon_intro zenon_H10a | zenon_intro zenon_H2d7 ]. % 15.65/15.76 apply (zenon_L181_); trivial. % 15.65/15.76 apply (zenon_or_s _ _ zenon_H2d7); [ zenon_intro zenon_H106 | zenon_intro zenon_H42 ]. % 15.65/15.76 apply (zenon_L1350_); trivial. % 15.65/15.76 exact (zenon_H3e zenon_H42). % 15.65/15.76 (* end of lemma zenon_L1351_ *) % 15.65/15.76 assert (zenon_L1352_ : ((~((op (e2) (e2)) = (e3)))\/((op (e2) (e3)) = (e2))) -> (~((op (e2) (e2)) = (op (e2) (e3)))) -> ((~((op (e3) (e3)) = (e1)))\/((op (e3) (e1)) = (e3))) -> (~((op (e0) (e0)) = (e2))) -> (~((e2) = (e3))) -> (((op (e2) (e1)) = (e0))\/(((op (e2) (e1)) = (e1))\/(((op (e2) (e1)) = (e2))\/((op (e2) (e1)) = (e3))))) -> (~((op (e2) (e1)) = (op (e3) (e1)))) -> ((op (e2) (e2)) = (e2)) -> (~((op (e2) (e1)) = (op (e2) (e2)))) -> ((op (e1) (e1)) = (e1)) -> (~((op (e1) (e1)) = (op (e2) (e1)))) -> ((op (e0) (e1)) = (e0)) -> (~((op (e0) (e1)) = (op (e2) (e1)))) -> ((~((op (e3) (e3)) = (e3)))\/((op (e3) (e3)) = (e3))) -> (~((op (e3) (op (e3) (e3))) = (op (e3) (e3)))) -> (~((op (e0) (e0)) = (e3))) -> (((op (e1) (e0)) = (e3))\/(((op (e1) (e1)) = (e3))\/(((op (e1) (e2)) = (e3))\/((op (e1) (e3)) = (e3))))) -> (~((e1) = (e3))) -> (~((op (e2) (e2)) = (e1))) -> (((op (e0) (e2)) = (e1))\/(((op (e1) (e2)) = (e1))\/(((op (e2) (e2)) = (e1))\/((op (e3) (e2)) = (e1))))) -> (~((op (e1) (e1)) = (op (e1) (e2)))) -> (((op (e3) (e0)) = (e1))\/(((op (e3) (e1)) = (e1))\/(((op (e3) (e2)) = (e1))\/((op (e3) (e3)) = (e1))))) -> (~((op (e0) (e2)) = (op (e3) (e2)))) -> (~((op (e1) (op (e3) (e1))) = (op (e3) (e1)))) -> (~((op (e0) (op (e3) (e0))) = (op (e3) (e0)))) -> (~((op (e0) (e1)) = (op (e3) (e1)))) -> (~((op (e2) (op (e3) (e2))) = (op (e3) (e2)))) -> (((op (e0) (e3)) = (e0))\/(((op (e0) (e3)) = (e1))\/(((op (e0) (e3)) = (e2))\/((op (e0) (e3)) = (e3))))) -> (~((op (e0) (e3)) = (op (e1) (e3)))) -> (~((op (e0) (e3)) = (op (e3) (e3)))) -> (~((op (e0) (e3)) = (op (e2) (e3)))) -> (~((op (e0) (e1)) = (op (e0) (e3)))) -> (((op (e3) (e0)) = (e2))\/(((op (e3) (e1)) = (e2))\/(((op (e3) (e2)) = (e2))\/((op (e3) (e3)) = (e2))))) -> (((op (e2) (e0)) = (e1))\/(((op (e2) (e1)) = (e1))\/(((op (e2) (e2)) = (e1))\/((op (e2) (e3)) = (e1))))) -> (~((op (e1) (e2)) = (op (e3) (e2)))) -> (~((op (e1) (e1)) = (e3))) -> ((~((op (e3) (e3)) = (e2)))\/((op (e3) (e2)) = (e3))) -> (~((op (e3) (e0)) = (op (e3) (e2)))) -> (((op (e0) (e0)) = (e2))\/(((op (e1) (e0)) = (e2))\/(((op (e2) (e0)) = (e2))\/((op (e3) (e0)) = (e2))))) -> (~((op (e2) (e0)) = (op (e2) (e2)))) -> (~((op (e1) (e1)) = (e2))) -> (((op (e3) (e0)) = (e0))\/(((op (e3) (e1)) = (e0))\/(((op (e3) (e2)) = (e0))\/((op (e3) (e3)) = (e0))))) -> (~((op (e1) (e2)) = (op (e2) (e2)))) -> (~((op (e0) (e2)) = (op (e1) (e2)))) -> (((op (e1) (e2)) = (e0))\/(((op (e1) (e2)) = (e1))\/(((op (e1) (e2)) = (e2))\/((op (e1) (e2)) = (e3))))) -> (~((e0) = (e3))) -> (((op (e0) (e2)) = (e0))\/(((op (e0) (e2)) = (e1))\/(((op (e0) (e2)) = (e2))\/((op (e0) (e2)) = (e3))))) -> (~((op (e0) (e2)) = (op (e2) (e2)))) -> (~((op (e0) (e1)) = (op (e0) (e2)))) -> (((op (e0) (e2)) = (e3))\/(((op (e1) (e2)) = (e3))\/(((op (e2) (e2)) = (e3))\/((op (e3) (e2)) = (e3))))) -> (((op (e0) (e1)) = (e2))\/(((op (e1) (e1)) = (e2))\/(((op (e2) (e1)) = (e2))\/((op (e3) (e1)) = (e2))))) -> (~((op (e0) (e1)) = (op (e1) (e1)))) -> (((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)) = (e1))\/(((op (e0) (e2)) = (e1))\/((op (e0) (e3)) = (e1))))) -> (((op (e0) (e0)) = (e3))\/(((op (e1) (e0)) = (e3))\/(((op (e2) (e0)) = (e3))\/((op (e3) (e0)) = (e3))))) -> (((op (e3) (e3)) = (e0))\/(((op (e3) (e3)) = (e1))\/(((op (e3) (e3)) = (e2))\/((op (e3) (e3)) = (e3))))) -> (((op (e3) (e0)) = (e3))\/(((op (e3) (e1)) = (e3))\/(((op (e3) (e2)) = (e3))\/((op (e3) (e3)) = (e3))))) -> (~((op (e3) (e0)) = (op (e3) (e1)))) -> ((~((op (e3) (e3)) = (e0)))\/((op (e3) (e0)) = (e3))) -> False). % 15.65/15.76 do 0 intro. intros zenon_H1c3 zenon_H15f zenon_H10c zenon_H8f zenon_H6a zenon_H15a zenon_H13c zenon_H35 zenon_H157 zenon_H21 zenon_Hb1 zenon_H49 zenon_Hde zenon_H10d zenon_H2be zenon_H59 zenon_H90 zenon_Ha3 zenon_H52 zenon_H11b zenon_H116 zenon_H146 zenon_H140 zenon_H2b4 zenon_H2b8 zenon_H138 zenon_H2af zenon_H254 zenon_H80 zenon_H36 zenon_Hb4 zenon_H1cd zenon_H1df zenon_Hb7 zenon_H17d zenon_H182 zenon_H10e zenon_H105 zenon_Heb zenon_H17a zenon_Hd6 zenon_H1f6 zenon_H7d zenon_H87 zenon_H1d5 zenon_H4b zenon_H251 zenon_H28 zenon_H23e zenon_H175 zenon_H1a2 zenon_H23 zenon_H8e zenon_Ha7 zenon_H44 zenon_Hbe zenon_H3b zenon_H2d5 zenon_H109 zenon_H10f. % 15.65/15.76 apply (zenon_or_s _ _ zenon_H1c3); [ zenon_intro zenon_H30 | zenon_intro zenon_H124 ]. % 15.65/15.76 apply (zenon_or_s _ _ zenon_H10f); [ zenon_intro zenon_H3c | zenon_intro zenon_Hba ]. % 15.65/15.76 apply (zenon_or_s _ _ zenon_H10c); [ zenon_intro zenon_H104 | zenon_intro zenon_H10a ]. % 15.65/15.76 apply (zenon_or_s _ _ zenon_H10e); [ zenon_intro zenon_H3d | zenon_intro zenon_H106 ]. % 15.65/15.76 apply (zenon_or_s _ _ zenon_H10d); [ zenon_intro zenon_H3e | zenon_intro zenon_H42 ]. % 15.65/15.76 apply (zenon_or_s _ _ zenon_H8e); [ zenon_intro zenon_H92 | zenon_intro zenon_H91 ]. % 15.65/15.76 exact (zenon_H8f zenon_H92). % 15.65/15.76 apply (zenon_or_s _ _ zenon_H91); [ zenon_intro zenon_H5d | zenon_intro zenon_H93 ]. % 15.65/15.76 apply (zenon_or_s _ _ zenon_H1df); [ zenon_intro zenon_He9 | zenon_intro zenon_H1e0 ]. % 15.65/15.76 apply (zenon_L1351_); trivial. % 15.65/15.76 apply (zenon_or_s _ _ zenon_H1e0); [ zenon_intro zenon_H16a | zenon_intro zenon_H1e1 ]. % 15.65/15.76 apply (zenon_L146_); trivial. % 15.65/15.76 apply (zenon_or_s _ _ zenon_H1e1); [ zenon_intro zenon_H1dd | zenon_intro zenon_H43 ]. % 15.65/15.76 apply (zenon_L1083_); trivial. % 15.65/15.76 exact (zenon_H3d zenon_H43). % 15.65/15.76 apply (zenon_or_s _ _ zenon_H93); [ zenon_intro zenon_H63 | zenon_intro zenon_H81 ]. % 15.65/15.76 apply (zenon_L15_); trivial. % 15.65/15.76 apply (zenon_L107_); trivial. % 15.65/15.76 apply (zenon_L1041_); trivial. % 15.65/15.76 apply (zenon_L1350_); trivial. % 15.65/15.76 apply (zenon_L181_); trivial. % 15.65/15.76 apply (zenon_or_s _ _ zenon_H10c); [ zenon_intro zenon_H104 | zenon_intro zenon_H10a ]. % 15.65/15.76 apply (zenon_L1238_); trivial. % 15.65/15.76 apply (zenon_L82_); trivial. % 15.65/15.76 apply (zenon_L137_); trivial. % 15.65/15.76 (* end of lemma zenon_L1352_ *) % 15.65/15.76 assert (zenon_L1353_ : ((~((op (e0) (e0)) = (e1)))\/((op (e0) (e1)) = (e0))) -> (~((op (e1) (e1)) = (op (e1) (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) (e1)) = (op (e0) (e3)))) -> (~((op (e1) (e1)) = (op (e2) (e1)))) -> (((op (e2) (e1)) = (e0))\/(((op (e2) (e1)) = (e1))\/(((op (e2) (e1)) = (e2))\/((op (e2) (e1)) = (e3))))) -> (((op (e3) (e1)) = (e0))\/(((op (e3) (e1)) = (e1))\/(((op (e3) (e1)) = (e2))\/((op (e3) (e1)) = (e3))))) -> (~((op (e0) (e0)) = (e0))) -> (((op (e0) (e0)) = (e2))\/(((op (e0) (e1)) = (e2))\/(((op (e0) (e2)) = (e2))\/((op (e0) (e3)) = (e2))))) -> (~((op (e0) (e3)) = (op (e3) (e3)))) -> (((op (e3) (e3)) = (e0))\/(((op (e3) (e3)) = (e1))\/(((op (e3) (e3)) = (e2))\/((op (e3) (e3)) = (e3))))) -> ((op (e2) (e2)) = (e2)) -> (~((op (e0) (e2)) = (op (e2) (e2)))) -> (~((e0) = (e2))) -> (~((e0) = (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 (e2) (e0)) = (e0))\/((op (e3) (e0)) = (e0))))) -> (((op (e2) (e3)) = (e0))\/(((op (e2) (e3)) = (e1))\/(((op (e2) (e3)) = (e2))\/((op (e2) (e3)) = (e3))))) -> (((op (e2) (e0)) = (e3))\/(((op (e2) (e1)) = (e3))\/(((op (e2) (e2)) = (e3))\/((op (e2) (e3)) = (e3))))) -> (~((op (e0) (e1)) = (op (e2) (e1)))) -> (((op (e0) (e0)) = (e3))\/(((op (e0) (e1)) = (e3))\/(((op (e0) (e2)) = (e3))\/((op (e0) (e3)) = (e3))))) -> ((~((op (e1) (e1)) = (e2)))\/((op (e1) (e2)) = (e1))) -> ((~((op (e2) (e2)) = (e1)))\/((op (e2) (e1)) = (e2))) -> ((~((op (e3) (e3)) = (e0)))\/((op (e3) (e0)) = (e3))) -> (~((op (e3) (e0)) = (op (e3) (e1)))) -> ((~((op (e3) (e3)) = (e1)))\/((op (e3) (e1)) = (e3))) -> (~((op (e2) (e2)) = (op (e2) (e3)))) -> ((~((op (e2) (e2)) = (e3)))\/((op (e2) (e3)) = (e2))) -> (~((op (e1) (e0)) = (op (e1) (e3)))) -> ((~((op (e1) (e1)) = (e3)))\/((op (e1) (e3)) = (e1))) -> (~((op (e1) (e0)) = (op (e1) (e1)))) -> ((~((op (e1) (e1)) = (e1)))\/((op (e1) (e1)) = (e1))) -> (((op (e3) (e0)) = (e0))\/(((op (e3) (e1)) = (e0))\/(((op (e3) (e2)) = (e0))\/((op (e3) (e3)) = (e0))))) -> (((op (e0) (e0)) = (e2))\/(((op (e1) (e0)) = (e2))\/(((op (e2) (e0)) = (e2))\/((op (e3) (e0)) = (e2))))) -> (~((op (e2) (e0)) = (op (e2) (e2)))) -> (~((op (e2) (e1)) = (op (e3) (e1)))) -> (~((e0) = (e3))) -> (((op (e1) (e0)) = (e0))\/(((op (e1) (e1)) = (e0))\/(((op (e1) (e2)) = (e0))\/((op (e1) (e3)) = (e0))))) -> (((op (e1) (e0)) = (e1))\/(((op (e1) (e1)) = (e1))\/(((op (e1) (e2)) = (e1))\/((op (e1) (e3)) = (e1))))) -> (~((e1) = (e3))) -> (((op (e0) (e2)) = (e1))\/(((op (e1) (e2)) = (e1))\/(((op (e2) (e2)) = (e1))\/((op (e3) (e2)) = (e1))))) -> (((op (e1) (e2)) = (e0))\/(((op (e1) (e2)) = (e1))\/(((op (e1) (e2)) = (e2))\/((op (e1) (e2)) = (e3))))) -> (~((op (e0) (e2)) = (op (e1) (e2)))) -> (((op (e3) (e0)) = (e3))\/(((op (e3) (e1)) = (e3))\/(((op (e3) (e2)) = (e3))\/((op (e3) (e3)) = (e3))))) -> ((~((op (e3) (e3)) = (e3)))\/((op (e3) (e3)) = (e3))) -> (~((op (e3) (op (e3) (e3))) = (op (e3) (e3)))) -> (((op (e3) (e0)) = (e2))\/(((op (e3) (e1)) = (e2))\/(((op (e3) (e2)) = (e2))\/((op (e3) (e3)) = (e2))))) -> (~((op (e0) (e1)) = (op (e3) (e1)))) -> (((op (e1) (e1)) = (e0))\/(((op (e1) (e1)) = (e1))\/(((op (e1) (e1)) = (e2))\/((op (e1) (e1)) = (e3))))) -> (~((op (e2) (e1)) = (op (e2) (e2)))) -> (~((e2) = (e3))) -> (((op (e0) (e1)) = (e2))\/(((op (e1) (e1)) = (e2))\/(((op (e2) (e1)) = (e2))\/((op (e3) (e1)) = (e2))))) -> ((~((op (e3) (e3)) = (e2)))\/((op (e3) (e2)) = (e3))) -> (~((op (e2) (e0)) = (op (e3) (e0)))) -> (((op (e0) (e2)) = (e3))\/(((op (e1) (e2)) = (e3))\/(((op (e2) (e2)) = (e3))\/((op (e3) (e2)) = (e3))))) -> (~((op (e1) (e0)) = (op (e1) (e2)))) -> (((op (e0) (e3)) = (e1))\/(((op (e1) (e3)) = (e1))\/(((op (e2) (e3)) = (e1))\/((op (e3) (e3)) = (e1))))) -> (~((op (e2) (e0)) = (op (e2) (e3)))) -> (~((op (e1) (e2)) = (op (e1) (e3)))) -> (((op (e0) (e0)) = (e1))\/(((op (e1) (e0)) = (e1))\/(((op (e2) (e0)) = (e1))\/((op (e3) (e0)) = (e1))))) -> (~((op (e0) (e2)) = (op (e0) (e3)))) -> (((op (e1) (e0)) = (e2))\/(((op (e1) (e1)) = (e2))\/(((op (e1) (e2)) = (e2))\/((op (e1) (e3)) = (e2))))) -> (~((op (e0) (e3)) = (op (e1) (e3)))) -> (~((op (e1) (e2)) = (op (e2) (e2)))) -> (~((e1) = (e2))) -> (((op (e0) (e1)) = (e1))\/(((op (e1) (e1)) = (e1))\/(((op (e2) (e1)) = (e1))\/((op (e3) (e1)) = (e1))))) -> (~((op (e1) (e0)) = (op (e3) (e0)))) -> (~((op (e0) (op (e3) (e0))) = (op (e3) (e0)))) -> (((op (e3) (e2)) = (e0))\/(((op (e3) (e2)) = (e1))\/(((op (e3) (e2)) = (e2))\/((op (e3) (e2)) = (e3))))) -> (~((op (e1) (e2)) = (op (e3) (e2)))) -> (((op (e1) (e0)) = (e3))\/(((op (e1) (e1)) = (e3))\/(((op (e1) (e2)) = (e3))\/((op (e1) (e3)) = (e3))))) -> (~((op (e2) (op (e3) (e2))) = (op (e3) (e2)))) -> (~((op (e3) (e1)) = (op (e3) (e2)))) -> (~((op (e0) (e2)) = (op (e3) (e2)))) -> (((op (e3) (e0)) = (e1))\/(((op (e3) (e1)) = (e1))\/(((op (e3) (e2)) = (e1))\/((op (e3) (e3)) = (e1))))) -> (((op (e0) (e3)) = (e0))\/(((op (e0) (e3)) = (e1))\/(((op (e0) (e3)) = (e2))\/((op (e0) (e3)) = (e3))))) -> (~((op (e3) (e0)) = (op (e3) (e2)))) -> (~((op (e1) (e0)) = (op (e2) (e0)))) -> (~((op (e1) (op (e3) (e1))) = (op (e3) (e1)))) -> (~((op (e0) (e3)) = (op (e2) (e3)))) -> (((op (e2) (e0)) = (e1))\/(((op (e2) (e1)) = (e1))\/(((op (e2) (e2)) = (e1))\/((op (e2) (e3)) = (e1))))) -> (((op (e0) (e0)) = (e3))\/(((op (e1) (e0)) = (e3))\/(((op (e2) (e0)) = (e3))\/((op (e3) (e0)) = (e3))))) -> (~((op (e0) (e1)) = (op (e1) (e1)))) -> (((op (e0) (e0)) = (e0))\/(((op (e0) (e1)) = (e0))\/(((op (e0) (e2)) = (e0))\/((op (e0) (e3)) = (e0))))) -> (((op (e0) (e0)) = (e0))\/(((op (e0) (e0)) = (e1))\/(((op (e0) (e0)) = (e2))\/((op (e0) (e0)) = (e3))))) -> (((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))))) -> ((~((op (e1) (e1)) = (e0)))\/((op (e1) (e0)) = (e1))) -> (~((op (e1) (e1)) = (op (e1) (e2)))) -> ((~((op (e0) (e0)) = (e3)))\/((op (e0) (e3)) = (e0))) -> (~((op (e2) (e0)) = (op (e2) (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) (e2)) = (e0))) -> False). % 15.65/15.76 do 0 intro. intros zenon_H24b zenon_H11e zenon_H23e zenon_H251 zenon_H1cd zenon_Hb1 zenon_H15a zenon_H16c zenon_H20 zenon_H8e zenon_H36 zenon_H3b zenon_H35 zenon_H28 zenon_H5e zenon_H9e zenon_H44 zenon_Hf0 zenon_H2ab zenon_He6 zenon_Hde zenon_H58 zenon_H1d3 zenon_H1e3 zenon_H10f zenon_H109 zenon_H10c zenon_H15f zenon_H1c3 zenon_H1cf zenon_H1d2 zenon_Hd7 zenon_H1d8 zenon_H1f6 zenon_Heb zenon_H17a zenon_H13c zenon_H4b zenon_H163 zenon_H1c5 zenon_Ha3 zenon_H11b zenon_H1d5 zenon_H87 zenon_H2d5 zenon_H10d zenon_H2be zenon_H1df zenon_H138 zenon_H1b3 zenon_H157 zenon_H6a zenon_H1a2 zenon_H10e zenon_H1e5 zenon_H175 zenon_H166 zenon_H121 zenon_Hce zenon_H1d0 zenon_Hf1 zenon_Hc9 zenon_H84 zenon_H80 zenon_H7d zenon_Ha7 zenon_H228 zenon_H22e zenon_H2b8 zenon_H25e zenon_H17d zenon_H90 zenon_H2af zenon_H135 zenon_H140 zenon_H146 zenon_H254 zenon_H105 zenon_H247 zenon_H2b4 zenon_Hb4 zenon_Hb7 zenon_Hbe zenon_H23 zenon_H110 zenon_H12a zenon_H16f zenon_H2d0 zenon_H1e4 zenon_H116 zenon_H236 zenon_H154 zenon_H144 zenon_H1d4 zenon_H24a. % 15.65/15.76 apply (zenon_or_s _ _ zenon_H24b); [ zenon_intro zenon_H45 | zenon_intro zenon_H49 ]. % 15.65/15.76 apply (zenon_or_s _ _ zenon_H24a); [ zenon_intro zenon_H8f | zenon_intro zenon_Hab ]. % 15.65/15.76 apply (zenon_or_s _ _ zenon_H236); [ zenon_intro zenon_H59 | zenon_intro zenon_Hca ]. % 15.65/15.76 apply (zenon_or_s _ _ zenon_H1e4); [ zenon_intro zenon_H145 | zenon_intro zenon_Hd8 ]. % 15.65/15.76 apply (zenon_or_s _ _ zenon_H1d8); [ zenon_intro zenon_H1b4 | zenon_intro zenon_H21 ]. % 15.65/15.76 apply (zenon_or_s _ _ zenon_H1d3); [ zenon_intro zenon_Hd6 | zenon_intro zenon_H117 ]. % 15.65/15.76 apply (zenon_or_s _ _ zenon_H1d2); [ zenon_intro zenon_H182 | zenon_intro zenon_H11f ]. % 15.65/15.76 apply (zenon_or_s _ _ zenon_H1e3); [ zenon_intro zenon_H52 | zenon_intro zenon_H156 ]. % 15.65/15.76 apply (zenon_or_s _ _ zenon_H1c3); [ zenon_intro zenon_H30 | zenon_intro zenon_H124 ]. % 15.65/15.76 apply (zenon_or_s _ _ zenon_H10f); [ zenon_intro zenon_H3c | zenon_intro zenon_Hba ]. % 15.65/15.76 apply (zenon_or_s _ _ zenon_H10c); [ zenon_intro zenon_H104 | zenon_intro zenon_H10a ]. % 15.65/15.76 apply (zenon_or_s _ _ zenon_H10e); [ zenon_intro zenon_H3d | zenon_intro zenon_H106 ]. % 15.65/15.76 apply (zenon_or_s _ _ zenon_H10d); [ zenon_intro zenon_H3e | zenon_intro zenon_H42 ]. % 15.65/15.76 apply (zenon_or_s _ _ zenon_H110); [ zenon_intro zenon_H1f | zenon_intro zenon_H111 ]. % 15.65/15.76 exact (zenon_H20 zenon_H1f). % 15.65/15.76 apply (zenon_or_s _ _ zenon_H111); [ zenon_intro zenon_H49 | zenon_intro zenon_H112 ]. % 15.65/15.76 apply (zenon_L131_); trivial. % 15.65/15.76 apply (zenon_or_s _ _ zenon_H112); [ zenon_intro zenon_Hab | zenon_intro zenon_Hca ]. % 15.65/15.76 apply (zenon_L1332_); trivial. % 15.65/15.76 apply (zenon_L343_); trivial. % 15.65/15.76 apply (zenon_L1041_); trivial. % 15.65/15.76 apply (zenon_or_s _ _ zenon_H10d); [ zenon_intro zenon_H3e | zenon_intro zenon_H42 ]. % 15.65/15.76 apply (zenon_or_s _ _ zenon_H110); [ zenon_intro zenon_H1f | zenon_intro zenon_H111 ]. % 15.65/15.76 exact (zenon_H20 zenon_H1f). % 15.65/15.76 apply (zenon_or_s _ _ zenon_H111); [ zenon_intro zenon_H49 | zenon_intro zenon_H112 ]. % 15.65/15.76 apply (zenon_L131_); trivial. % 15.65/15.76 apply (zenon_or_s _ _ zenon_H112); [ zenon_intro zenon_Hab | zenon_intro zenon_Hca ]. % 15.65/15.76 apply (zenon_L1326_); trivial. % 15.65/15.76 apply (zenon_L1349_); trivial. % 15.65/15.76 apply (zenon_L1041_); trivial. % 15.65/15.76 apply (zenon_L1302_); trivial. % 15.65/15.76 apply (zenon_L1345_); trivial. % 15.65/15.76 apply (zenon_L137_); trivial. % 15.65/15.76 apply (zenon_L134_); trivial. % 15.65/15.76 apply (zenon_or_s _ _ zenon_H1d4); [ zenon_intro zenon_H2e | zenon_intro zenon_Hdd ]. % 15.65/15.76 apply (zenon_or_s _ _ zenon_H1e3); [ zenon_intro zenon_H52 | zenon_intro zenon_H156 ]. % 15.65/15.76 apply (zenon_or_s _ _ zenon_H1c3); [ zenon_intro zenon_H30 | zenon_intro zenon_H124 ]. % 15.65/15.76 apply (zenon_or_s _ _ zenon_H10f); [ zenon_intro zenon_H3c | zenon_intro zenon_Hba ]. % 15.65/15.76 apply (zenon_or_s _ _ zenon_H10c); [ zenon_intro zenon_H104 | zenon_intro zenon_H10a ]. % 15.65/15.76 apply (zenon_or_s _ _ zenon_H10e); [ zenon_intro zenon_H3d | zenon_intro zenon_H106 ]. % 15.65/15.76 apply (zenon_or_s _ _ zenon_H10d); [ zenon_intro zenon_H3e | zenon_intro zenon_H42 ]. % 15.65/15.76 apply (zenon_or_s _ _ zenon_H110); [ zenon_intro zenon_H1f | zenon_intro zenon_H111 ]. % 15.65/15.76 exact (zenon_H20 zenon_H1f). % 15.65/15.76 apply (zenon_or_s _ _ zenon_H111); [ zenon_intro zenon_H49 | zenon_intro zenon_H112 ]. % 15.65/15.76 apply (zenon_L131_); trivial. % 15.65/15.76 apply (zenon_or_s _ _ zenon_H112); [ zenon_intro zenon_Hab | zenon_intro zenon_Hca ]. % 15.65/15.76 apply (zenon_L1335_); trivial. % 15.65/15.76 apply (zenon_L1348_); trivial. % 15.65/15.76 apply (zenon_L1041_); trivial. % 15.65/15.76 apply (zenon_or_s _ _ zenon_H10d); [ zenon_intro zenon_H3e | zenon_intro zenon_H42 ]. % 15.65/15.76 apply (zenon_or_s _ _ zenon_H110); [ zenon_intro zenon_H1f | zenon_intro zenon_H111 ]. % 15.65/15.76 exact (zenon_H20 zenon_H1f). % 15.65/15.76 apply (zenon_or_s _ _ zenon_H111); [ zenon_intro zenon_H49 | zenon_intro zenon_H112 ]. % 15.65/15.76 apply (zenon_L131_); trivial. % 15.65/15.76 apply (zenon_or_s _ _ zenon_H112); [ zenon_intro zenon_Hab | zenon_intro zenon_Hca ]. % 15.65/15.76 apply (zenon_L1326_); trivial. % 15.65/15.76 apply (zenon_L1347_); trivial. % 15.65/15.76 apply (zenon_L1041_); trivial. % 15.65/15.76 apply (zenon_or_s _ _ zenon_H10e); [ zenon_intro zenon_H3d | zenon_intro zenon_H106 ]. % 15.65/15.76 apply (zenon_or_s _ _ zenon_H10d); [ zenon_intro zenon_H3e | zenon_intro zenon_H42 ]. % 15.65/15.76 apply (zenon_or_s _ _ zenon_H110); [ zenon_intro zenon_H1f | zenon_intro zenon_H111 ]. % 15.65/15.76 exact (zenon_H20 zenon_H1f). % 15.65/15.76 apply (zenon_or_s _ _ zenon_H111); [ zenon_intro zenon_H49 | zenon_intro zenon_H112 ]. % 15.65/15.76 apply (zenon_L1344_); trivial. % 15.65/15.76 apply (zenon_or_s _ _ zenon_H112); [ zenon_intro zenon_Hab | zenon_intro zenon_Hca ]. % 15.65/15.76 apply (zenon_L1321_); trivial. % 15.65/15.76 apply (zenon_L182_); trivial. % 15.65/15.76 apply (zenon_L1041_); trivial. % 15.65/15.76 apply (zenon_L115_); trivial. % 15.65/15.76 apply (zenon_L1345_); trivial. % 15.65/15.76 apply (zenon_L137_); trivial. % 15.65/15.76 apply (zenon_L134_); trivial. % 15.65/15.76 apply (zenon_L161_); trivial. % 15.65/15.76 apply (zenon_or_s _ _ zenon_H1d2); [ zenon_intro zenon_H182 | zenon_intro zenon_H11f ]. % 15.65/15.76 apply (zenon_or_s _ _ zenon_H1c3); [ zenon_intro zenon_H30 | zenon_intro zenon_H124 ]. % 15.65/15.76 apply (zenon_or_s _ _ zenon_H10f); [ zenon_intro zenon_H3c | zenon_intro zenon_Hba ]. % 15.65/15.76 apply (zenon_or_s _ _ zenon_H10c); [ zenon_intro zenon_H104 | zenon_intro zenon_H10a ]. % 15.65/15.76 apply (zenon_or_s _ _ zenon_H10e); [ zenon_intro zenon_H3d | zenon_intro zenon_H106 ]. % 15.65/15.76 apply (zenon_or_s _ _ zenon_H10d); [ zenon_intro zenon_H3e | zenon_intro zenon_H42 ]. % 15.65/15.76 apply (zenon_or_s _ _ zenon_H110); [ zenon_intro zenon_H1f | zenon_intro zenon_H111 ]. % 15.65/15.76 exact (zenon_H20 zenon_H1f). % 15.65/15.76 apply (zenon_or_s _ _ zenon_H111); [ zenon_intro zenon_H49 | zenon_intro zenon_H112 ]. % 15.65/15.76 apply (zenon_L131_); trivial. % 15.65/15.76 apply (zenon_or_s _ _ zenon_H112); [ zenon_intro zenon_Hab | zenon_intro zenon_Hca ]. % 15.65/15.76 apply (zenon_L1305_); trivial. % 15.65/15.76 apply (zenon_L182_); trivial. % 15.65/15.76 apply (zenon_L1041_); trivial. % 15.65/15.76 apply (zenon_or_s _ _ zenon_H10d); [ zenon_intro zenon_H3e | zenon_intro zenon_H42 ]. % 15.65/15.76 apply (zenon_or_s _ _ zenon_H110); [ zenon_intro zenon_H1f | zenon_intro zenon_H111 ]. % 15.65/15.76 exact (zenon_H20 zenon_H1f). % 15.65/15.76 apply (zenon_or_s _ _ zenon_H111); [ zenon_intro zenon_H49 | zenon_intro zenon_H112 ]. % 15.65/15.76 apply (zenon_L131_); trivial. % 15.65/15.76 apply (zenon_or_s _ _ zenon_H112); [ zenon_intro zenon_Hab | zenon_intro zenon_Hca ]. % 15.65/15.76 apply (zenon_L1311_); trivial. % 15.65/15.76 apply (zenon_L343_); trivial. % 15.65/15.76 apply (zenon_L1041_); trivial. % 15.65/15.76 apply (zenon_L1314_); trivial. % 15.65/15.76 apply (zenon_L1095_); trivial. % 15.65/15.76 apply (zenon_L137_); trivial. % 15.65/15.76 apply (zenon_L237_); trivial. % 15.65/15.76 apply (zenon_or_s _ _ zenon_H1d3); [ zenon_intro zenon_Hd6 | zenon_intro zenon_H117 ]. % 15.65/15.76 apply (zenon_or_s _ _ zenon_H1d2); [ zenon_intro zenon_H182 | zenon_intro zenon_H11f ]. % 15.65/15.76 apply (zenon_L1296_); trivial. % 15.65/15.76 apply (zenon_L90_); trivial. % 15.65/15.76 apply (zenon_L86_); trivial. % 15.65/15.76 apply (zenon_L1256_); trivial. % 15.65/15.76 apply (zenon_or_s _ _ zenon_H1e4); [ zenon_intro zenon_H145 | zenon_intro zenon_Hd8 ]. % 15.65/15.76 apply (zenon_or_s _ _ zenon_H1d8); [ zenon_intro zenon_H1b4 | zenon_intro zenon_H21 ]. % 15.65/15.76 apply (zenon_or_s _ _ zenon_H1d3); [ zenon_intro zenon_Hd6 | zenon_intro zenon_H117 ]. % 15.65/15.76 apply (zenon_L1349_); trivial. % 15.65/15.76 apply (zenon_L438_); trivial. % 15.65/15.76 apply (zenon_or_s _ _ zenon_H1d3); [ zenon_intro zenon_Hd6 | zenon_intro zenon_H117 ]. % 15.65/15.76 apply (zenon_or_s _ _ zenon_H1d2); [ zenon_intro zenon_H182 | zenon_intro zenon_H11f ]. % 15.65/15.76 apply (zenon_or_s _ _ zenon_H1e3); [ zenon_intro zenon_H52 | zenon_intro zenon_H156 ]. % 15.65/15.76 apply (zenon_L1284_); trivial. % 15.65/15.76 apply (zenon_L134_); trivial. % 15.65/15.76 apply (zenon_L90_); trivial. % 15.65/15.76 apply (zenon_L86_); trivial. % 15.65/15.76 apply (zenon_L1256_); trivial. % 15.65/15.76 apply (zenon_L1336_); trivial. % 15.65/15.76 apply (zenon_or_s _ _ zenon_H24a); [ zenon_intro zenon_H8f | zenon_intro zenon_Hab ]. % 15.65/15.76 apply (zenon_or_s _ _ zenon_H236); [ zenon_intro zenon_H59 | zenon_intro zenon_Hca ]. % 15.65/15.76 apply (zenon_or_s _ _ zenon_H1e4); [ zenon_intro zenon_H145 | zenon_intro zenon_Hd8 ]. % 15.65/15.76 apply (zenon_or_s _ _ zenon_H1d8); [ zenon_intro zenon_H1b4 | zenon_intro zenon_H21 ]. % 15.65/15.76 apply (zenon_L1346_); trivial. % 15.65/15.76 apply (zenon_or_s _ _ zenon_H1d3); [ zenon_intro zenon_Hd6 | zenon_intro zenon_H117 ]. % 15.65/15.76 apply (zenon_or_s _ _ zenon_H1d2); [ zenon_intro zenon_H182 | zenon_intro zenon_H11f ]. % 15.65/15.76 apply (zenon_or_s _ _ zenon_H1e3); [ zenon_intro zenon_H52 | zenon_intro zenon_H156 ]. % 15.65/15.76 apply (zenon_L1352_); trivial. % 15.65/15.76 apply (zenon_L134_); trivial. % 15.65/15.76 apply (zenon_L90_); trivial. % 15.65/15.76 apply (zenon_L86_); trivial. % 15.65/15.76 apply (zenon_L484_); trivial. % 15.65/15.76 apply (zenon_L463_); trivial. % 15.65/15.76 apply (zenon_L485_); trivial. % 15.65/15.76 (* end of lemma zenon_L1353_ *) % 15.65/15.76 apply (zenon_and_s _ _ ax1). zenon_intro zenon_H12a. zenon_intro zenon_H2dd. % 15.65/15.76 apply (zenon_and_s _ _ zenon_H2dd). zenon_intro zenon_H1e9. zenon_intro zenon_H2de. % 15.65/15.76 apply (zenon_and_s _ _ zenon_H2de). zenon_intro zenon_H251. zenon_intro zenon_H2df. % 15.65/15.76 apply (zenon_and_s _ _ zenon_H2df). zenon_intro zenon_H254. zenon_intro zenon_H2e0. % 15.65/15.76 apply (zenon_and_s _ _ zenon_H2e0). zenon_intro zenon_H2e2. zenon_intro zenon_H2e1. % 15.65/15.76 apply (zenon_and_s _ _ zenon_H2e1). zenon_intro zenon_H1b3. zenon_intro zenon_H2e3. % 15.65/15.76 apply (zenon_and_s _ _ zenon_H2e3). zenon_intro zenon_H1d5. zenon_intro zenon_H2e4. % 15.65/15.76 apply (zenon_and_s _ _ zenon_H2e4). zenon_intro zenon_H25b. zenon_intro zenon_H2e5. % 15.65/15.76 apply (zenon_and_s _ _ zenon_H2e5). zenon_intro zenon_H281. zenon_intro zenon_H2e6. % 15.65/15.76 apply (zenon_and_s _ _ zenon_H2e6). zenon_intro zenon_H15a. zenon_intro zenon_H2e7. % 15.65/15.76 apply (zenon_and_s _ _ zenon_H2e7). zenon_intro zenon_H2d. zenon_intro zenon_H2e8. % 15.65/15.76 apply (zenon_and_s _ _ zenon_H2e8). zenon_intro zenon_H2ab. zenon_intro zenon_H2e9. % 15.65/15.76 apply (zenon_and_s _ _ zenon_H2e9). zenon_intro zenon_H2eb. zenon_intro zenon_H2ea. % 15.65/15.76 apply (zenon_and_s _ _ zenon_H2ea). zenon_intro zenon_H16c. zenon_intro zenon_H2ec. % 15.65/15.76 apply (zenon_and_s _ _ zenon_H2ec). zenon_intro zenon_H25e. zenon_intro zenon_H3b. % 15.65/15.76 apply (zenon_and_s _ _ ax2). zenon_intro zenon_H110. zenon_intro zenon_H2ed. % 15.65/15.76 apply (zenon_and_s _ _ zenon_H2ed). zenon_intro zenon_Hf0. zenon_intro zenon_H2ee. % 15.65/15.76 apply (zenon_and_s _ _ zenon_H2ee). zenon_intro zenon_H44. zenon_intro zenon_H2ef. % 15.65/15.76 apply (zenon_and_s _ _ zenon_H2ef). zenon_intro zenon_Hf1. zenon_intro zenon_H2f0. % 15.65/15.76 apply (zenon_and_s _ _ zenon_H2f0). zenon_intro zenon_H8e. zenon_intro zenon_H2f1. % 15.65/15.76 apply (zenon_and_s _ _ zenon_H2f1). zenon_intro zenon_Heb. zenon_intro zenon_H2f2. % 15.65/15.76 apply (zenon_and_s _ _ zenon_H2f2). zenon_intro zenon_H58. zenon_intro zenon_H2f3. % 15.65/15.76 apply (zenon_and_s _ _ zenon_H2f3). zenon_intro zenon_Hbe. zenon_intro zenon_H2f4. % 15.65/15.76 apply (zenon_and_s _ _ zenon_H2f4). zenon_intro zenon_H163. zenon_intro zenon_H2f5. % 15.65/15.76 apply (zenon_and_s _ _ zenon_H2f5). zenon_intro zenon_H144. zenon_intro zenon_H2f6. % 15.65/15.76 apply (zenon_and_s _ _ zenon_H2f6). zenon_intro zenon_H1c5. zenon_intro zenon_H2f7. % 15.65/15.76 apply (zenon_and_s _ _ zenon_H2f7). zenon_intro zenon_H228. zenon_intro zenon_H2f8. % 15.65/15.76 apply (zenon_and_s _ _ zenon_H2f8). zenon_intro zenon_H84. zenon_intro zenon_H2f9. % 15.65/15.76 apply (zenon_and_s _ _ zenon_H2f9). zenon_intro zenon_H1a2. zenon_intro zenon_H2fa. % 15.65/15.76 apply (zenon_and_s _ _ zenon_H2fa). zenon_intro zenon_H90. zenon_intro zenon_H2fb. % 15.65/15.76 apply (zenon_and_s _ _ zenon_H2fb). zenon_intro zenon_H199. zenon_intro zenon_H2fc. % 15.65/15.76 apply (zenon_and_s _ _ zenon_H2fc). zenon_intro zenon_H1f5. zenon_intro zenon_H2fd. % 15.65/15.76 apply (zenon_and_s _ _ zenon_H2fd). zenon_intro zenon_H16f. zenon_intro zenon_H2fe. % 15.65/15.76 apply (zenon_and_s _ _ zenon_H2fe). zenon_intro zenon_Hb7. zenon_intro zenon_H2ff. % 15.65/15.76 apply (zenon_and_s _ _ zenon_H2ff). zenon_intro zenon_H11b. zenon_intro zenon_H300. % 15.65/15.76 apply (zenon_and_s _ _ zenon_H300). zenon_intro zenon_H237. zenon_intro zenon_H301. % 15.65/15.76 apply (zenon_and_s _ _ zenon_H301). zenon_intro zenon_H27c. zenon_intro zenon_H302. % 15.65/15.76 apply (zenon_and_s _ _ zenon_H302). zenon_intro zenon_He6. zenon_intro zenon_H303. % 15.65/15.76 apply (zenon_and_s _ _ zenon_H303). zenon_intro zenon_H175. zenon_intro zenon_H304. % 15.65/15.76 apply (zenon_and_s _ _ zenon_H304). zenon_intro zenon_H1f6. zenon_intro zenon_H305. % 15.65/15.76 apply (zenon_and_s _ _ zenon_H305). zenon_intro zenon_Hd3. zenon_intro zenon_H306. % 15.65/15.76 apply (zenon_and_s _ _ zenon_H306). zenon_intro zenon_H146. zenon_intro zenon_H307. % 15.65/15.76 apply (zenon_and_s _ _ zenon_H307). zenon_intro zenon_H121. zenon_intro zenon_H308. % 15.65/15.76 apply (zenon_and_s _ _ zenon_H308). zenon_intro zenon_H1df. zenon_intro zenon_H309. % 15.65/15.76 apply (zenon_and_s _ _ zenon_H309). zenon_intro zenon_H160. zenon_intro zenon_H30a. % 15.65/15.76 apply (zenon_and_s _ _ zenon_H30a). zenon_intro zenon_H2d5. zenon_intro zenon_H2d0. % 15.65/15.76 apply (zenon_and_s _ _ ax3). zenon_intro zenon_H24c. zenon_intro zenon_H30b. % 15.65/15.76 apply (zenon_and_s _ _ zenon_H30b). zenon_intro zenon_H258. zenon_intro zenon_H30c. % 15.65/15.76 apply (zenon_and_s _ _ zenon_H30c). zenon_intro zenon_H30e. zenon_intro zenon_H30d. % 15.65/15.76 apply (zenon_and_s _ _ zenon_H30d). zenon_intro zenon_H247. zenon_intro zenon_H30f. % 15.65/15.76 apply (zenon_and_s _ _ zenon_H30f). zenon_intro zenon_H22e. zenon_intro zenon_H310. % 15.65/15.76 apply (zenon_and_s _ _ zenon_H310). zenon_intro zenon_H1e5. zenon_intro zenon_H311. % 15.65/15.76 apply (zenon_and_s _ _ zenon_H311). zenon_intro zenon_H23. zenon_intro zenon_H312. % 15.65/15.76 apply (zenon_and_s _ _ zenon_H312). zenon_intro zenon_Hde. zenon_intro zenon_H313. % 15.65/15.76 apply (zenon_and_s _ _ zenon_H313). zenon_intro zenon_H138. zenon_intro zenon_H314. % 15.65/15.76 apply (zenon_and_s _ _ zenon_H314). zenon_intro zenon_Hb1. zenon_intro zenon_H315. % 15.65/15.76 apply (zenon_and_s _ _ zenon_H315). zenon_intro zenon_H317. zenon_intro zenon_H316. % 15.65/15.76 apply (zenon_and_s _ _ zenon_H316). zenon_intro zenon_H13c. zenon_intro zenon_H318. % 15.65/15.76 apply (zenon_and_s _ _ zenon_H318). zenon_intro zenon_H87. zenon_intro zenon_H319. % 15.65/15.76 apply (zenon_and_s _ _ zenon_H319). zenon_intro zenon_H28. zenon_intro zenon_H31a. % 15.65/15.76 apply (zenon_and_s _ _ zenon_H31a). zenon_intro zenon_H140. zenon_intro zenon_H31b. % 15.65/15.76 apply (zenon_and_s _ _ zenon_H31b). zenon_intro zenon_H7d. zenon_intro zenon_H31c. % 15.65/15.76 apply (zenon_and_s _ _ zenon_H31c). zenon_intro zenon_H17d. zenon_intro zenon_H31d. % 15.65/15.76 apply (zenon_and_s _ _ zenon_H31d). zenon_intro zenon_H31f. zenon_intro zenon_H31e. % 15.65/15.76 apply (zenon_and_s _ _ zenon_H31e). zenon_intro zenon_H80. zenon_intro zenon_H320. % 15.65/15.76 apply (zenon_and_s _ _ zenon_H320). zenon_intro zenon_Hb4. zenon_intro zenon_H321. % 15.65/15.76 apply (zenon_and_s _ _ zenon_H321). zenon_intro zenon_H36. zenon_intro zenon_H322. % 15.65/15.76 apply (zenon_and_s _ _ zenon_H322). zenon_intro zenon_H244. zenon_intro zenon_H323. % 15.65/15.76 apply (zenon_and_s _ _ zenon_H323). zenon_intro zenon_H8b. zenon_intro zenon_H324. % 15.65/15.76 apply (zenon_and_s _ _ zenon_H324). zenon_intro zenon_He3. zenon_intro zenon_H325. % 15.65/15.76 apply (zenon_and_s _ _ zenon_H325). zenon_intro zenon_H25a. zenon_intro zenon_H326. % 15.65/15.76 apply (zenon_and_s _ _ zenon_H326). zenon_intro zenon_H250. zenon_intro zenon_H327. % 15.65/15.76 apply (zenon_and_s _ _ zenon_H327). zenon_intro zenon_H24f. zenon_intro zenon_H328. % 15.65/15.76 apply (zenon_and_s _ _ zenon_H328). zenon_intro zenon_H23e. zenon_intro zenon_H329. % 15.65/15.76 apply (zenon_and_s _ _ zenon_H329). zenon_intro zenon_H1cd. zenon_intro zenon_H32a. % 15.65/15.76 apply (zenon_and_s _ _ zenon_H32a). zenon_intro zenon_Hc9. zenon_intro zenon_H32b. % 15.65/15.76 apply (zenon_and_s _ _ zenon_H32b). zenon_intro zenon_Hd7. zenon_intro zenon_H32c. % 15.65/15.76 apply (zenon_and_s _ _ zenon_H32c). zenon_intro zenon_H166. zenon_intro zenon_H32d. % 15.65/15.76 apply (zenon_and_s _ _ zenon_H32d). zenon_intro zenon_H1cf. zenon_intro zenon_H32e. % 15.65/15.76 apply (zenon_and_s _ _ zenon_H32e). zenon_intro zenon_H116. zenon_intro zenon_H32f. % 15.65/15.76 apply (zenon_and_s _ _ zenon_H32f). zenon_intro zenon_H11e. zenon_intro zenon_H330. % 15.65/15.76 apply (zenon_and_s _ _ zenon_H330). zenon_intro zenon_H1d0. zenon_intro zenon_H331. % 15.65/15.76 apply (zenon_and_s _ _ zenon_H331). zenon_intro zenon_H154. zenon_intro zenon_H332. % 15.65/15.76 apply (zenon_and_s _ _ zenon_H332). zenon_intro zenon_H17a. zenon_intro zenon_H333. % 15.65/15.76 apply (zenon_and_s _ _ zenon_H333). zenon_intro zenon_Hce. zenon_intro zenon_H334. % 15.65/15.76 apply (zenon_and_s _ _ zenon_H334). zenon_intro zenon_H157. zenon_intro zenon_H335. % 15.65/15.76 apply (zenon_and_s _ _ zenon_H335). zenon_intro zenon_H1e2. zenon_intro zenon_H336. % 15.65/15.76 apply (zenon_and_s _ _ zenon_H336). zenon_intro zenon_H15f. zenon_intro zenon_H337. % 15.65/15.76 apply (zenon_and_s _ _ zenon_H337). zenon_intro zenon_H109. zenon_intro zenon_H338. % 15.65/15.76 apply (zenon_and_s _ _ zenon_H338). zenon_intro zenon_H105. zenon_intro zenon_H339. % 15.65/15.76 apply (zenon_and_s _ _ zenon_H339). zenon_intro zenon_Hbb. zenon_intro zenon_H33a. % 15.65/15.76 apply (zenon_and_s _ _ zenon_H33a). zenon_intro zenon_H135. zenon_intro zenon_H33b. % 15.65/15.76 apply (zenon_and_s _ _ zenon_H33b). zenon_intro zenon_H12d. zenon_intro zenon_H173. % 15.65/15.76 apply (zenon_and_s _ _ ax4). zenon_intro zenon_H9e. zenon_intro zenon_H33c. % 15.65/15.76 apply (zenon_and_s _ _ zenon_H33c). zenon_intro zenon_H5e. zenon_intro zenon_H33d. % 15.65/15.76 apply (zenon_and_s _ _ zenon_H33d). zenon_intro zenon_H4b. zenon_intro zenon_H33e. % 15.65/15.76 apply (zenon_and_s _ _ zenon_H33e). zenon_intro zenon_Ha7. zenon_intro zenon_H33f. % 15.65/15.76 apply (zenon_and_s _ _ zenon_H33f). zenon_intro zenon_Ha3. zenon_intro zenon_H6a. % 15.65/15.76 apply (zenon_and_s _ _ ax5). zenon_intro zenon_H341. zenon_intro zenon_H340. % 15.65/15.76 apply (zenon_and_s _ _ zenon_H340). zenon_intro zenon_H343. zenon_intro zenon_H342. % 15.65/15.76 apply (zenon_and_s _ _ zenon_H342). zenon_intro zenon_H249. zenon_intro zenon_H344. % 15.65/15.76 apply (zenon_and_s _ _ zenon_H344). zenon_intro zenon_H24b. zenon_intro zenon_H345. % 15.65/15.76 apply (zenon_and_s _ _ zenon_H345). zenon_intro zenon_H24a. zenon_intro zenon_H346. % 15.65/15.76 apply (zenon_and_s _ _ zenon_H346). zenon_intro zenon_H236. zenon_intro zenon_H347. % 15.65/15.76 apply (zenon_and_s _ _ zenon_H347). zenon_intro zenon_H1e4. zenon_intro zenon_H348. % 15.65/15.76 apply (zenon_and_s _ _ zenon_H348). zenon_intro zenon_H1d8. zenon_intro zenon_H349. % 15.65/15.76 apply (zenon_and_s _ _ zenon_H349). zenon_intro zenon_H1d3. zenon_intro zenon_H34a. % 15.65/15.76 apply (zenon_and_s _ _ zenon_H34a). zenon_intro zenon_H1d2. zenon_intro zenon_H34b. % 15.65/15.76 apply (zenon_and_s _ _ zenon_H34b). zenon_intro zenon_H1d4. zenon_intro zenon_H34c. % 15.65/15.76 apply (zenon_and_s _ _ zenon_H34c). zenon_intro zenon_H1e3. zenon_intro zenon_H34d. % 15.65/15.76 apply (zenon_and_s _ _ zenon_H34d). zenon_intro zenon_Haa. zenon_intro zenon_H34e. % 15.65/15.76 apply (zenon_and_s _ _ zenon_H34e). zenon_intro zenon_H1c3. zenon_intro zenon_H34f. % 15.65/15.76 apply (zenon_and_s _ _ zenon_H34f). zenon_intro zenon_H10f. zenon_intro zenon_H350. % 15.65/15.76 apply (zenon_and_s _ _ zenon_H350). zenon_intro zenon_H10c. zenon_intro zenon_H351. % 15.65/15.76 apply (zenon_and_s _ _ zenon_H351). zenon_intro zenon_H10e. zenon_intro zenon_H10d. % 15.65/15.76 apply (zenon_or_s _ _ zenon_H341); [ zenon_intro zenon_H353 | zenon_intro zenon_H352 ]. % 15.65/15.76 apply (zenon_and_s _ _ zenon_H353). zenon_intro zenon_H1e. zenon_intro zenon_H354. % 15.65/15.76 apply (zenon_and_s _ _ zenon_H354). zenon_intro zenon_H1ff. zenon_intro zenon_H355. % 15.65/15.76 apply (zenon_and_s _ _ zenon_H355). zenon_intro zenon_H20c. zenon_intro zenon_H192. % 15.65/15.76 apply (zenon_or_s _ _ zenon_H343); [ zenon_intro zenon_H1f | zenon_intro zenon_H356 ]. % 15.65/15.76 apply (zenon_L2_); trivial. % 15.65/15.76 apply (zenon_or_s _ _ zenon_H356); [ zenon_intro zenon_H21 | zenon_intro zenon_H357 ]. % 15.65/15.76 apply (zenon_or_s _ _ zenon_H249); [ zenon_intro zenon_H20 | zenon_intro zenon_H1f ]. % 15.65/15.76 apply (zenon_or_s _ _ zenon_H24b); [ zenon_intro zenon_H45 | zenon_intro zenon_H49 ]. % 15.65/15.76 apply (zenon_or_s _ _ zenon_H24a); [ zenon_intro zenon_H8f | zenon_intro zenon_Hab ]. % 15.65/15.76 apply (zenon_or_s _ _ zenon_H236); [ zenon_intro zenon_H59 | zenon_intro zenon_Hca ]. % 15.65/15.76 apply (zenon_or_s _ _ zenon_H1e4); [ zenon_intro zenon_H145 | zenon_intro zenon_Hd8 ]. % 15.65/15.76 apply (zenon_or_s _ _ zenon_H1d3); [ zenon_intro zenon_Hd6 | zenon_intro zenon_H117 ]. % 15.65/15.76 apply (zenon_or_s _ _ zenon_H1d2); [ zenon_intro zenon_H182 | zenon_intro zenon_H11f ]. % 15.65/15.76 apply (zenon_or_s _ _ zenon_H1d4); [ zenon_intro zenon_H2e | zenon_intro zenon_Hdd ]. % 15.65/15.76 apply (zenon_or_s _ _ zenon_H1e3); [ zenon_intro zenon_H52 | zenon_intro zenon_H156 ]. % 15.65/15.76 apply (zenon_or_s _ _ zenon_Haa); [ zenon_intro zenon_H2f | zenon_intro zenon_H35 ]. % 15.65/15.76 apply (zenon_or_s _ _ zenon_H1c3); [ zenon_intro zenon_H30 | zenon_intro zenon_H124 ]. % 15.65/15.76 apply (zenon_or_s _ _ zenon_H10f); [ zenon_intro zenon_H3c | zenon_intro zenon_Hba ]. % 15.65/15.76 apply (zenon_or_s _ _ zenon_H10e); [ zenon_intro zenon_H3d | zenon_intro zenon_H106 ]. % 15.65/15.76 apply (zenon_or_s _ _ zenon_H10d); [ zenon_intro zenon_H3e | zenon_intro zenon_H42 ]. % 15.65/15.76 apply (zenon_L8_); trivial. % 15.65/15.76 apply (zenon_L84_); trivial. % 15.65/15.76 apply (zenon_L89_); trivial. % 15.65/15.76 apply (zenon_L83_); trivial. % 15.65/15.76 apply (zenon_or_s _ _ zenon_H10f); [ zenon_intro zenon_H3c | zenon_intro zenon_Hba ]. % 15.65/15.76 apply (zenon_or_s _ _ zenon_H10c); [ zenon_intro zenon_H104 | zenon_intro zenon_H10a ]. % 15.65/15.76 apply (zenon_or_s _ _ zenon_H10e); [ zenon_intro zenon_H3d | zenon_intro zenon_H106 ]. % 15.65/15.76 apply (zenon_or_s _ _ zenon_H10d); [ zenon_intro zenon_H3e | zenon_intro zenon_H42 ]. % 15.65/15.76 apply (zenon_L95_); trivial. % 15.65/15.76 apply (zenon_L103_); trivial. % 15.65/15.76 apply (zenon_L118_); trivial. % 15.65/15.76 apply (zenon_L130_); trivial. % 15.65/15.76 apply (zenon_L83_); trivial. % 15.65/15.76 apply (zenon_L277_); trivial. % 15.65/15.76 apply (zenon_or_s _ _ zenon_Haa); [ zenon_intro zenon_H2f | zenon_intro zenon_H35 ]. % 15.65/15.76 apply (zenon_or_s _ _ zenon_H1c3); [ zenon_intro zenon_H30 | zenon_intro zenon_H124 ]. % 15.65/15.76 apply (zenon_or_s _ _ zenon_H10f); [ zenon_intro zenon_H3c | zenon_intro zenon_Hba ]. % 15.65/15.76 apply (zenon_or_s _ _ zenon_H10c); [ zenon_intro zenon_H104 | zenon_intro zenon_H10a ]. % 15.65/15.76 apply (zenon_or_s _ _ zenon_H10e); [ zenon_intro zenon_H3d | zenon_intro zenon_H106 ]. % 15.65/15.76 apply (zenon_or_s _ _ zenon_H10d); [ zenon_intro zenon_H3e | zenon_intro zenon_H42 ]. % 15.65/15.76 apply (zenon_L8_); trivial. % 15.65/15.76 apply (zenon_L288_); trivial. % 15.65/15.76 apply (zenon_or_s _ _ zenon_H110); [ zenon_intro zenon_H1f | zenon_intro zenon_H111 ]. % 15.65/15.76 exact (zenon_H20 zenon_H1f). % 15.65/15.76 apply (zenon_or_s _ _ zenon_H111); [ zenon_intro zenon_H49 | zenon_intro zenon_H112 ]. % 15.65/15.76 apply (zenon_L303_); trivial. % 15.65/15.76 apply (zenon_or_s _ _ zenon_H112); [ zenon_intro zenon_Hab | zenon_intro zenon_Hca ]. % 15.65/15.76 apply (zenon_L315_); trivial. % 15.65/15.76 apply (zenon_L324_); trivial. % 15.65/15.76 apply (zenon_L325_); trivial. % 15.65/15.76 apply (zenon_or_s _ _ zenon_H10c); [ zenon_intro zenon_H104 | zenon_intro zenon_H10a ]. % 15.65/15.76 apply (zenon_or_s _ _ zenon_H10e); [ zenon_intro zenon_H3d | zenon_intro zenon_H106 ]. % 15.65/15.76 apply (zenon_or_s _ _ zenon_H110); [ zenon_intro zenon_H1f | zenon_intro zenon_H111 ]. % 15.65/15.76 exact (zenon_H20 zenon_H1f). % 15.65/15.76 apply (zenon_or_s _ _ zenon_H111); [ zenon_intro zenon_H49 | zenon_intro zenon_H112 ]. % 15.65/15.76 apply (zenon_L190_); trivial. % 15.65/15.76 apply (zenon_or_s _ _ zenon_H112); [ zenon_intro zenon_Hab | zenon_intro zenon_Hca ]. % 15.65/15.76 apply (zenon_L327_); trivial. % 15.65/15.76 apply (zenon_L275_); trivial. % 15.65/15.76 apply (zenon_L81_); trivial. % 15.65/15.76 apply (zenon_L82_); trivial. % 15.65/15.76 apply (zenon_L256_); trivial. % 15.65/15.76 apply (zenon_L134_); trivial. % 15.65/15.76 apply (zenon_or_s _ _ zenon_H1e3); [ zenon_intro zenon_H52 | zenon_intro zenon_H156 ]. % 15.65/15.76 apply (zenon_or_s _ _ zenon_Haa); [ zenon_intro zenon_H2f | zenon_intro zenon_H35 ]. % 15.65/15.76 apply (zenon_or_s _ _ zenon_H1c3); [ zenon_intro zenon_H30 | zenon_intro zenon_H124 ]. % 15.65/15.76 apply (zenon_or_s _ _ zenon_H10f); [ zenon_intro zenon_H3c | zenon_intro zenon_Hba ]. % 15.65/15.76 apply (zenon_or_s _ _ zenon_H10c); [ zenon_intro zenon_H104 | zenon_intro zenon_H10a ]. % 15.65/15.76 apply (zenon_or_s _ _ zenon_H10e); [ zenon_intro zenon_H3d | zenon_intro zenon_H106 ]. % 15.65/15.76 apply (zenon_or_s _ _ zenon_H10d); [ zenon_intro zenon_H3e | zenon_intro zenon_H42 ]. % 15.65/15.76 apply (zenon_L329_); trivial. % 15.65/15.76 apply (zenon_L455_); trivial. % 15.65/15.76 apply (zenon_L458_); trivial. % 15.65/15.76 apply (zenon_or_s _ _ zenon_H10e); [ zenon_intro zenon_H3d | zenon_intro zenon_H106 ]. % 15.65/15.76 apply (zenon_or_s _ _ zenon_H10d); [ zenon_intro zenon_H3e | zenon_intro zenon_H42 ]. % 15.65/15.76 apply (zenon_L329_); trivial. % 15.65/15.76 apply (zenon_L102_); trivial. % 15.65/15.76 apply (zenon_L115_); trivial. % 15.65/15.76 apply (zenon_L310_); trivial. % 15.65/15.76 apply (zenon_L119_); trivial. % 15.65/15.76 apply (zenon_L161_); trivial. % 15.65/15.76 apply (zenon_L284_); trivial. % 15.65/15.76 apply (zenon_L90_); trivial. % 15.65/15.76 apply (zenon_L86_); trivial. % 15.65/15.76 apply (zenon_L61_); trivial. % 15.65/15.76 apply (zenon_or_s _ _ zenon_H1e4); [ zenon_intro zenon_H145 | zenon_intro zenon_Hd8 ]. % 15.65/15.76 apply (zenon_or_s _ _ zenon_H1d3); [ zenon_intro zenon_Hd6 | zenon_intro zenon_H117 ]. % 15.65/15.76 apply (zenon_or_s _ _ zenon_H1d2); [ zenon_intro zenon_H182 | zenon_intro zenon_H11f ]. % 15.65/15.76 apply (zenon_L324_); trivial. % 15.65/15.76 apply (zenon_L90_); trivial. % 15.65/15.76 apply (zenon_L86_); trivial. % 15.65/15.76 apply (zenon_L61_); trivial. % 15.65/15.76 apply (zenon_or_s _ _ zenon_H236); [ zenon_intro zenon_H59 | zenon_intro zenon_Hca ]. % 15.65/15.76 apply (zenon_L328_); trivial. % 15.65/15.76 apply (zenon_L53_); trivial. % 15.65/15.76 apply (zenon_or_s _ _ zenon_H24a); [ zenon_intro zenon_H8f | zenon_intro zenon_Hab ]. % 15.65/15.76 apply (zenon_or_s _ _ zenon_H236); [ zenon_intro zenon_H59 | zenon_intro zenon_Hca ]. % 15.65/15.76 apply (zenon_or_s _ _ zenon_H1e4); [ zenon_intro zenon_H145 | zenon_intro zenon_Hd8 ]. % 15.65/15.76 apply (zenon_or_s _ _ zenon_H1d3); [ zenon_intro zenon_Hd6 | zenon_intro zenon_H117 ]. % 15.65/15.76 apply (zenon_or_s _ _ zenon_H1d2); [ zenon_intro zenon_H182 | zenon_intro zenon_H11f ]. % 15.65/15.76 apply (zenon_or_s _ _ zenon_H1d4); [ zenon_intro zenon_H2e | zenon_intro zenon_Hdd ]. % 15.65/15.76 apply (zenon_or_s _ _ zenon_H1e3); [ zenon_intro zenon_H52 | zenon_intro zenon_H156 ]. % 15.65/15.76 apply (zenon_or_s _ _ zenon_Haa); [ zenon_intro zenon_H2f | zenon_intro zenon_H35 ]. % 15.65/15.76 apply (zenon_or_s _ _ zenon_H1c3); [ zenon_intro zenon_H30 | zenon_intro zenon_H124 ]. % 15.65/15.76 apply (zenon_or_s _ _ zenon_H10f); [ zenon_intro zenon_H3c | zenon_intro zenon_Hba ]. % 15.65/15.76 apply (zenon_or_s _ _ zenon_H10c); [ zenon_intro zenon_H104 | zenon_intro zenon_H10a ]. % 15.65/15.76 apply (zenon_or_s _ _ zenon_H10e); [ zenon_intro zenon_H3d | zenon_intro zenon_H106 ]. % 15.65/15.76 apply (zenon_or_s _ _ zenon_H10d); [ zenon_intro zenon_H3e | zenon_intro zenon_H42 ]. % 15.65/15.76 apply (zenon_or_s _ _ zenon_Hf0); [ zenon_intro zenon_H1f | zenon_intro zenon_Hf2 ]. % 15.65/15.76 exact (zenon_H20 zenon_H1f). % 15.65/15.76 apply (zenon_or_s _ _ zenon_Hf2); [ zenon_intro zenon_Had | zenon_intro zenon_Hf3 ]. % 15.65/15.76 apply (zenon_L289_); trivial. % 15.65/15.76 apply (zenon_or_s _ _ zenon_Hf3); [ zenon_intro zenon_Hcf | zenon_intro zenon_Hdb ]. % 15.65/15.76 apply (zenon_or_s _ _ zenon_H44); [ zenon_intro zenon_H47 | zenon_intro zenon_H46 ]. % 15.65/15.76 apply (zenon_or_s _ _ zenon_H8e); [ zenon_intro zenon_H92 | zenon_intro zenon_H91 ]. % 15.65/15.76 exact (zenon_H8f zenon_H92). % 15.65/15.76 apply (zenon_or_s _ _ zenon_H91); [ zenon_intro zenon_H5d | zenon_intro zenon_H93 ]. % 15.65/15.76 apply (zenon_L14_); trivial. % 15.65/15.76 apply (zenon_or_s _ _ zenon_H93); [ zenon_intro zenon_H63 | zenon_intro zenon_H81 ]. % 15.65/15.76 apply (zenon_or_s _ _ zenon_Heb); [ zenon_intro zenon_H92 | zenon_intro zenon_Hec ]. % 15.65/15.76 exact (zenon_H8f zenon_H92). % 15.65/15.76 apply (zenon_or_s _ _ zenon_Hec); [ zenon_intro zenon_H68 | zenon_intro zenon_Hed ]. % 15.65/15.76 apply (zenon_or_s _ _ zenon_H58); [ zenon_intro zenon_H5b | zenon_intro zenon_H5a ]. % 15.65/15.76 exact (zenon_H59 zenon_H5b). % 15.65/15.76 apply (zenon_or_s _ _ zenon_H5a); [ zenon_intro zenon_H4a | zenon_intro zenon_H5c ]. % 15.65/15.76 apply (zenon_L9_); trivial. % 15.65/15.76 apply (zenon_or_s _ _ zenon_H5c); [ zenon_intro zenon_H50 | zenon_intro zenon_H53 ]. % 15.65/15.76 apply (zenon_L31_); trivial. % 15.65/15.76 apply (zenon_or_s _ _ zenon_Hbe); [ zenon_intro zenon_H5b | zenon_intro zenon_Hbf ]. % 15.65/15.76 exact (zenon_H59 zenon_H5b). % 15.65/15.76 apply (zenon_or_s _ _ zenon_Hbf); [ zenon_intro zenon_H69 | zenon_intro zenon_Hc0 ]. % 15.65/15.76 apply (zenon_L17_); trivial. % 15.65/15.76 apply (zenon_or_s _ _ zenon_Hc0); [ zenon_intro zenon_Haf | zenon_intro zenon_Hba ]. % 15.65/15.76 apply (zenon_L462_); trivial. % 15.65/15.76 apply (zenon_L189_); trivial. % 15.65/15.76 apply (zenon_or_s _ _ zenon_Hed); [ zenon_intro zenon_Hdd | zenon_intro zenon_He9 ]. % 15.65/15.76 apply (zenon_L467_); trivial. % 15.65/15.76 apply (zenon_L469_); trivial. % 15.65/15.76 apply (zenon_L107_); trivial. % 15.65/15.76 apply (zenon_or_s _ _ zenon_H46); [ zenon_intro zenon_H22 | zenon_intro zenon_H48 ]. % 15.65/15.76 apply (zenon_L27_); trivial. % 15.65/15.76 apply (zenon_or_s _ _ zenon_H48); [ zenon_intro zenon_H29 | zenon_intro zenon_H37 ]. % 15.65/15.76 apply (zenon_L168_); trivial. % 15.65/15.76 apply (zenon_L7_); trivial. % 15.65/15.76 apply (zenon_L471_); trivial. % 15.65/15.76 apply (zenon_L13_); trivial. % 15.65/15.76 apply (zenon_L296_); trivial. % 15.65/15.76 apply (zenon_or_s _ _ zenon_H10e); [ zenon_intro zenon_H3d | zenon_intro zenon_H106 ]. % 15.65/15.76 apply (zenon_or_s _ _ zenon_Hf0); [ zenon_intro zenon_H1f | zenon_intro zenon_Hf2 ]. % 15.65/15.76 exact (zenon_H20 zenon_H1f). % 15.65/15.76 apply (zenon_or_s _ _ zenon_Hf2); [ zenon_intro zenon_Had | zenon_intro zenon_Hf3 ]. % 15.65/15.76 apply (zenon_L289_); trivial. % 15.65/15.76 apply (zenon_or_s _ _ zenon_Hf3); [ zenon_intro zenon_Hcf | zenon_intro zenon_Hdb ]. % 15.65/15.76 apply (zenon_or_s _ _ zenon_H44); [ zenon_intro zenon_H47 | zenon_intro zenon_H46 ]. % 15.65/15.76 apply (zenon_or_s _ _ zenon_H8e); [ zenon_intro zenon_H92 | zenon_intro zenon_H91 ]. % 15.65/15.76 exact (zenon_H8f zenon_H92). % 15.65/15.76 apply (zenon_or_s _ _ zenon_H91); [ zenon_intro zenon_H5d | zenon_intro zenon_H93 ]. % 15.65/15.76 apply (zenon_L14_); trivial. % 15.65/15.76 apply (zenon_or_s _ _ zenon_H93); [ zenon_intro zenon_H63 | zenon_intro zenon_H81 ]. % 15.65/15.76 apply (zenon_or_s _ _ zenon_Heb); [ zenon_intro zenon_H92 | zenon_intro zenon_Hec ]. % 15.65/15.76 exact (zenon_H8f zenon_H92). % 15.65/15.76 apply (zenon_or_s _ _ zenon_Hec); [ zenon_intro zenon_H68 | zenon_intro zenon_Hed ]. % 15.65/15.76 apply (zenon_L472_); trivial. % 15.65/15.76 apply (zenon_or_s _ _ zenon_Hed); [ zenon_intro zenon_Hdd | zenon_intro zenon_He9 ]. % 15.65/15.76 apply (zenon_L177_); trivial. % 15.65/15.76 apply (zenon_L469_); trivial. % 15.65/15.76 apply (zenon_L473_); trivial. % 15.65/15.76 apply (zenon_or_s _ _ zenon_H46); [ zenon_intro zenon_H22 | zenon_intro zenon_H48 ]. % 15.65/15.76 apply (zenon_L474_); trivial. % 15.65/15.76 apply (zenon_or_s _ _ zenon_H48); [ zenon_intro zenon_H29 | zenon_intro zenon_H37 ]. % 15.65/15.76 apply (zenon_L5_); trivial. % 15.65/15.76 apply (zenon_L34_); trivial. % 15.65/15.76 apply (zenon_or_s _ _ zenon_H8e); [ zenon_intro zenon_H92 | zenon_intro zenon_H91 ]. % 15.65/15.76 exact (zenon_H8f zenon_H92). % 15.65/15.76 apply (zenon_or_s _ _ zenon_H91); [ zenon_intro zenon_H5d | zenon_intro zenon_H93 ]. % 15.65/15.76 apply (zenon_L14_); trivial. % 15.65/15.76 apply (zenon_or_s _ _ zenon_H93); [ zenon_intro zenon_H63 | zenon_intro zenon_H81 ]. % 15.65/15.76 apply (zenon_or_s _ _ zenon_Heb); [ zenon_intro zenon_H92 | zenon_intro zenon_Hec ]. % 15.65/15.76 exact (zenon_H8f zenon_H92). % 15.65/15.76 apply (zenon_or_s _ _ zenon_Hec); [ zenon_intro zenon_H68 | zenon_intro zenon_Hed ]. % 15.65/15.76 apply (zenon_or_s _ _ zenon_H58); [ zenon_intro zenon_H5b | zenon_intro zenon_H5a ]. % 15.65/15.76 exact (zenon_H59 zenon_H5b). % 15.65/15.76 apply (zenon_or_s _ _ zenon_H5a); [ zenon_intro zenon_H4a | zenon_intro zenon_H5c ]. % 15.65/15.76 apply (zenon_L120_); trivial. % 15.65/15.76 apply (zenon_or_s _ _ zenon_H5c); [ zenon_intro zenon_H50 | zenon_intro zenon_H53 ]. % 15.65/15.76 apply (zenon_L31_); trivial. % 15.65/15.76 apply (zenon_or_s _ _ zenon_Hbe); [ zenon_intro zenon_H5b | zenon_intro zenon_Hbf ]. % 15.65/15.76 exact (zenon_H59 zenon_H5b). % 15.65/15.76 apply (zenon_or_s _ _ zenon_Hbf); [ zenon_intro zenon_H69 | zenon_intro zenon_Hc0 ]. % 15.65/15.76 apply (zenon_L17_); trivial. % 15.65/15.76 apply (zenon_or_s _ _ zenon_Hc0); [ zenon_intro zenon_Haf | zenon_intro zenon_Hba ]. % 15.65/15.76 apply (zenon_L462_); trivial. % 15.65/15.76 apply (zenon_L62_); trivial. % 15.65/15.76 apply (zenon_or_s _ _ zenon_Hed); [ zenon_intro zenon_Hdd | zenon_intro zenon_He9 ]. % 15.65/15.76 apply (zenon_L299_); trivial. % 15.65/15.76 apply (zenon_L69_); trivial. % 15.65/15.76 apply (zenon_L473_); trivial. % 15.65/15.76 apply (zenon_L115_); trivial. % 15.65/15.76 apply (zenon_L475_); trivial. % 15.65/15.76 apply (zenon_or_s _ _ zenon_H10f); [ zenon_intro zenon_H3c | zenon_intro zenon_Hba ]. % 15.65/15.76 apply (zenon_or_s _ _ zenon_H10c); [ zenon_intro zenon_H104 | zenon_intro zenon_H10a ]. % 15.65/15.76 apply (zenon_L476_); trivial. % 15.65/15.76 apply (zenon_or_s _ _ zenon_Hf0); [ zenon_intro zenon_H1f | zenon_intro zenon_Hf2 ]. % 15.65/15.76 exact (zenon_H20 zenon_H1f). % 15.65/15.76 apply (zenon_or_s _ _ zenon_Hf2); [ zenon_intro zenon_Had | zenon_intro zenon_Hf3 ]. % 15.65/15.76 apply (zenon_L289_); trivial. % 15.65/15.76 apply (zenon_or_s _ _ zenon_Hf3); [ zenon_intro zenon_Hcf | zenon_intro zenon_Hdb ]. % 15.65/15.76 apply (zenon_L477_); trivial. % 15.65/15.76 apply (zenon_L479_); trivial. % 15.65/15.76 apply (zenon_L475_); trivial. % 15.65/15.76 apply (zenon_L480_); trivial. % 15.65/15.76 apply (zenon_or_s _ _ zenon_Haa); [ zenon_intro zenon_H2f | zenon_intro zenon_H35 ]. % 15.65/15.76 apply (zenon_or_s _ _ zenon_H1c3); [ zenon_intro zenon_H30 | zenon_intro zenon_H124 ]. % 15.65/15.76 apply (zenon_or_s _ _ zenon_H10f); [ zenon_intro zenon_H3c | zenon_intro zenon_Hba ]. % 15.65/15.76 apply (zenon_or_s _ _ zenon_H10c); [ zenon_intro zenon_H104 | zenon_intro zenon_H10a ]. % 15.65/15.76 apply (zenon_or_s _ _ zenon_H10e); [ zenon_intro zenon_H3d | zenon_intro zenon_H106 ]. % 15.65/15.76 apply (zenon_or_s _ _ zenon_H10d); [ zenon_intro zenon_H3e | zenon_intro zenon_H42 ]. % 15.65/15.76 apply (zenon_or_s _ _ zenon_Hf0); [ zenon_intro zenon_H1f | zenon_intro zenon_Hf2 ]. % 15.65/15.76 exact (zenon_H20 zenon_H1f). % 15.65/15.76 apply (zenon_or_s _ _ zenon_Hf2); [ zenon_intro zenon_Had | zenon_intro zenon_Hf3 ]. % 15.65/15.76 apply (zenon_L289_); trivial. % 15.65/15.76 apply (zenon_or_s _ _ zenon_Hf3); [ zenon_intro zenon_Hcf | zenon_intro zenon_Hdb ]. % 15.65/15.76 apply (zenon_L292_); trivial. % 15.65/15.76 apply (zenon_L481_); trivial. % 15.65/15.76 apply (zenon_L278_); trivial. % 15.65/15.76 apply (zenon_L303_); trivial. % 15.65/15.76 apply (zenon_or_s _ _ zenon_H10e); [ zenon_intro zenon_H3d | zenon_intro zenon_H106 ]. % 15.65/15.76 apply (zenon_or_s _ _ zenon_Hf0); [ zenon_intro zenon_H1f | zenon_intro zenon_Hf2 ]. % 15.65/15.76 exact (zenon_H20 zenon_H1f). % 15.65/15.76 apply (zenon_or_s _ _ zenon_Hf2); [ zenon_intro zenon_Had | zenon_intro zenon_Hf3 ]. % 15.65/15.76 apply (zenon_L289_); trivial. % 15.65/15.76 apply (zenon_or_s _ _ zenon_Hf3); [ zenon_intro zenon_Hcf | zenon_intro zenon_Hdb ]. % 15.65/15.76 apply (zenon_or_s _ _ zenon_H58); [ zenon_intro zenon_H5b | zenon_intro zenon_H5a ]. % 15.65/15.76 exact (zenon_H59 zenon_H5b). % 15.65/15.76 apply (zenon_or_s _ _ zenon_H5a); [ zenon_intro zenon_H4a | zenon_intro zenon_H5c ]. % 15.65/15.76 apply (zenon_L9_); trivial. % 15.65/15.76 apply (zenon_or_s _ _ zenon_H5c); [ zenon_intro zenon_H50 | zenon_intro zenon_H53 ]. % 15.65/15.76 apply (zenon_or_s _ _ zenon_He6); [ zenon_intro zenon_Haf | zenon_intro zenon_He7 ]. % 15.65/15.76 apply (zenon_L57_); trivial. % 15.65/15.76 apply (zenon_or_s _ _ zenon_He7); [ zenon_intro zenon_Hdf | zenon_intro zenon_He8 ]. % 15.65/15.76 apply (zenon_L121_); trivial. % 15.65/15.76 apply (zenon_or_s _ _ zenon_He8); [ zenon_intro zenon_H34 | zenon_intro zenon_He2 ]. % 15.65/15.76 exact (zenon_H30 zenon_H34). % 15.65/15.76 cut (((op (e2) (e3)) = (e3)) = ((op (e2) (op (e0) (e2))) = (op (e0) (e2)))). % 15.65/15.76 intro zenon_D_pnotp. % 15.65/15.76 apply zenon_H20c. % 15.65/15.76 rewrite <- zenon_D_pnotp. % 15.65/15.76 exact zenon_He2. % 15.65/15.76 cut (((e3) = (op (e0) (e2)))); [idtac | apply NNPP; zenon_intro zenon_H246]. % 15.65/15.76 cut (((op (e2) (e3)) = (op (e2) (op (e0) (e2))))); [idtac | apply NNPP; zenon_intro zenon_H358]. % 15.65/15.76 congruence. % 15.65/15.76 elim (classic ((op (e2) (op (e0) (e2))) = (op (e2) (op (e0) (e2))))); [ zenon_intro zenon_H20f | zenon_intro zenon_H210 ]. % 15.65/15.76 cut (((op (e2) (op (e0) (e2))) = (op (e2) (op (e0) (e2)))) = ((op (e2) (e3)) = (op (e2) (op (e0) (e2))))). % 15.65/15.76 intro zenon_D_pnotp. % 15.65/15.76 apply zenon_H358. % 15.65/15.76 rewrite <- zenon_D_pnotp. % 15.65/15.76 exact zenon_H20f. % 15.65/15.76 cut (((op (e2) (op (e0) (e2))) = (op (e2) (op (e0) (e2))))); [idtac | apply NNPP; zenon_intro zenon_H210]. % 15.65/15.76 cut (((op (e2) (op (e0) (e2))) = (op (e2) (e3)))); [idtac | apply NNPP; zenon_intro zenon_H359]. % 15.65/15.76 congruence. % 15.65/15.76 cut (((op (e0) (e2)) = (e3))); [idtac | apply NNPP; zenon_intro zenon_Ha5]. % 15.65/15.76 cut (((e2) = (e2))); [idtac | apply NNPP; zenon_intro zenon_H60]. % 15.65/15.76 congruence. % 15.65/15.76 apply zenon_H60. apply refl_equal. % 15.65/15.76 exact (zenon_Ha5 zenon_H50). % 15.65/15.76 apply zenon_H210. apply refl_equal. % 15.65/15.76 apply zenon_H210. apply refl_equal. % 15.65/15.76 apply zenon_H246. apply sym_equal. exact zenon_H50. % 15.65/15.76 apply (zenon_L290_); trivial. % 15.65/15.76 apply (zenon_or_s _ _ zenon_H8e); [ zenon_intro zenon_H92 | zenon_intro zenon_H91 ]. % 15.65/15.76 exact (zenon_H8f zenon_H92). % 15.65/15.76 apply (zenon_or_s _ _ zenon_H91); [ zenon_intro zenon_H5d | zenon_intro zenon_H93 ]. % 15.65/15.76 apply (zenon_L14_); trivial. % 15.65/15.76 apply (zenon_or_s _ _ zenon_H93); [ zenon_intro zenon_H63 | zenon_intro zenon_H81 ]. % 15.65/15.76 apply (zenon_L470_); trivial. % 15.65/15.76 apply (zenon_or_s _ _ zenon_Heb); [ zenon_intro zenon_H92 | zenon_intro zenon_Hec ]. % 15.65/15.76 exact (zenon_H8f zenon_H92). % 15.65/15.76 apply (zenon_or_s _ _ zenon_Hec); [ zenon_intro zenon_H68 | zenon_intro zenon_Hed ]. % 15.65/15.76 apply (zenon_or_s _ _ zenon_Hbe); [ zenon_intro zenon_H5b | zenon_intro zenon_Hbf ]. % 15.65/15.76 exact (zenon_H59 zenon_H5b). % 15.65/15.76 apply (zenon_or_s _ _ zenon_Hbf); [ zenon_intro zenon_H69 | zenon_intro zenon_Hc0 ]. % 15.65/15.76 apply (zenon_L17_); trivial. % 15.65/15.76 apply (zenon_or_s _ _ zenon_Hc0); [ zenon_intro zenon_Haf | zenon_intro zenon_Hba ]. % 15.65/15.76 apply (zenon_or_s _ _ zenon_H1f5); [ zenon_intro zenon_Hcf | zenon_intro zenon_H1f9 ]. % 15.65/15.76 apply (zenon_L57_); trivial. % 15.65/15.76 apply (zenon_or_s _ _ zenon_H1f9); [ zenon_intro zenon_H14a | zenon_intro zenon_H1fa ]. % 15.65/15.76 apply (zenon_L352_); trivial. % 15.65/15.76 apply (zenon_or_s _ _ zenon_H1fa); [ zenon_intro zenon_H32 | zenon_intro zenon_Hd0 ]. % 15.65/15.76 exact (zenon_H2e zenon_H32). % 15.65/15.76 apply (zenon_or_s _ _ zenon_H1df); [ zenon_intro zenon_He9 | zenon_intro zenon_H1e0 ]. % 15.65/15.76 apply (zenon_L69_); trivial. % 15.65/15.76 apply (zenon_or_s _ _ zenon_H1e0); [ zenon_intro zenon_H16a | zenon_intro zenon_H1e1 ]. % 15.65/15.76 apply (zenon_L482_); trivial. % 15.65/15.76 apply (zenon_or_s _ _ zenon_H1e1); [ zenon_intro zenon_H1dd | zenon_intro zenon_H43 ]. % 15.65/15.76 apply (zenon_L483_); trivial. % 15.65/15.76 exact (zenon_H3d zenon_H43). % 15.65/15.76 apply (zenon_L62_); trivial. % 15.65/15.76 apply (zenon_or_s _ _ zenon_Hed); [ zenon_intro zenon_Hdd | zenon_intro zenon_He9 ]. % 15.65/15.76 apply (zenon_L298_); trivial. % 15.65/15.76 apply (zenon_L69_); trivial. % 15.65/15.76 apply (zenon_L115_); trivial. % 15.65/15.76 apply (zenon_L184_); trivial. % 15.65/15.76 apply (zenon_L256_); trivial. % 15.65/15.76 apply (zenon_L134_); trivial. % 15.65/15.76 apply (zenon_L302_); trivial. % 15.65/15.76 apply (zenon_L90_); trivial. % 15.65/15.76 apply (zenon_L86_); trivial. % 15.65/15.76 apply (zenon_L484_); trivial. % 15.65/15.76 apply (zenon_L463_); trivial. % 15.65/15.76 apply (zenon_L485_); trivial. % 15.65/15.76 apply (zenon_L2_); trivial. % 15.65/15.76 apply (zenon_or_s _ _ zenon_H357); [ zenon_intro zenon_H35 | zenon_intro zenon_H42 ]. % 15.65/15.76 apply (zenon_or_s _ _ zenon_H249); [ zenon_intro zenon_H20 | zenon_intro zenon_H1f ]. % 15.65/15.76 apply (zenon_or_s _ _ zenon_H24b); [ zenon_intro zenon_H45 | zenon_intro zenon_H49 ]. % 15.65/15.76 apply (zenon_or_s _ _ zenon_H24a); [ zenon_intro zenon_H8f | zenon_intro zenon_Hab ]. % 15.65/15.76 apply (zenon_or_s _ _ zenon_H236); [ zenon_intro zenon_H59 | zenon_intro zenon_Hca ]. % 15.65/15.76 apply (zenon_or_s _ _ zenon_H1e4); [ zenon_intro zenon_H145 | zenon_intro zenon_Hd8 ]. % 15.65/15.76 apply (zenon_or_s _ _ zenon_H1d8); [ zenon_intro zenon_H1b4 | zenon_intro zenon_H21 ]. % 15.65/15.76 apply (zenon_or_s _ _ zenon_H1d3); [ zenon_intro zenon_Hd6 | zenon_intro zenon_H117 ]. % 15.65/15.76 apply (zenon_or_s _ _ zenon_H1d2); [ zenon_intro zenon_H182 | zenon_intro zenon_H11f ]. % 15.65/15.76 apply (zenon_L360_); trivial. % 15.65/15.76 apply (zenon_or_s _ _ zenon_H10f); [ zenon_intro zenon_H3c | zenon_intro zenon_Hba ]. % 15.65/15.76 apply (zenon_or_s _ _ zenon_H10c); [ zenon_intro zenon_H104 | zenon_intro zenon_H10a ]. % 15.65/15.76 apply (zenon_or_s _ _ zenon_H10e); [ zenon_intro zenon_H3d | zenon_intro zenon_H106 ]. % 15.65/15.76 apply (zenon_L487_); trivial. % 15.65/15.76 apply (zenon_L492_); trivial. % 15.65/15.76 apply (zenon_L494_); trivial. % 15.65/15.76 apply (zenon_L359_); trivial. % 15.65/15.76 apply (zenon_or_s _ _ zenon_H1d2); [ zenon_intro zenon_H182 | zenon_intro zenon_H11f ]. % 15.65/15.76 apply (zenon_or_s _ _ zenon_H1d4); [ zenon_intro zenon_H2e | zenon_intro zenon_Hdd ]. % 15.65/15.76 apply (zenon_or_s _ _ zenon_H1c3); [ zenon_intro zenon_H30 | zenon_intro zenon_H124 ]. % 15.65/15.76 apply (zenon_or_s _ _ zenon_H10f); [ zenon_intro zenon_H3c | zenon_intro zenon_Hba ]. % 15.65/15.76 apply (zenon_L503_); trivial. % 15.65/15.76 apply (zenon_or_s _ _ zenon_H10c); [ zenon_intro zenon_H104 | zenon_intro zenon_H10a ]. % 15.65/15.76 apply (zenon_or_s _ _ zenon_H10e); [ zenon_intro zenon_H3d | zenon_intro zenon_H106 ]. % 15.65/15.76 apply (zenon_or_s _ _ zenon_H10d); [ zenon_intro zenon_H3e | zenon_intro zenon_H42 ]. % 15.65/15.76 apply (zenon_or_s _ _ zenon_H110); [ zenon_intro zenon_H1f | zenon_intro zenon_H111 ]. % 15.65/15.76 exact (zenon_H20 zenon_H1f). % 15.65/15.76 apply (zenon_or_s _ _ zenon_H111); [ zenon_intro zenon_H49 | zenon_intro zenon_H112 ]. % 15.65/15.76 apply (zenon_L506_); trivial. % 15.65/15.76 apply (zenon_or_s _ _ zenon_H112); [ zenon_intro zenon_Hab | zenon_intro zenon_Hca ]. % 15.65/15.76 apply (zenon_L507_); trivial. % 15.65/15.76 apply (zenon_L343_); trivial. % 15.65/15.76 apply (zenon_L43_); trivial. % 15.65/15.76 apply (zenon_L81_); trivial. % 15.65/15.76 apply (zenon_L82_); trivial. % 15.65/15.76 apply (zenon_L137_); trivial. % 15.65/15.76 apply (zenon_L161_); trivial. % 15.65/15.76 apply (zenon_L237_); trivial. % 15.65/15.76 apply (zenon_or_s _ _ zenon_H1d3); [ zenon_intro zenon_Hd6 | zenon_intro zenon_H117 ]. % 15.65/15.76 apply (zenon_or_s _ _ zenon_H1d2); [ zenon_intro zenon_H182 | zenon_intro zenon_H11f ]. % 15.65/15.76 apply (zenon_or_s _ _ zenon_H1d4); [ zenon_intro zenon_H2e | zenon_intro zenon_Hdd ]. % 15.65/15.76 apply (zenon_or_s _ _ zenon_H1e3); [ zenon_intro zenon_H52 | zenon_intro zenon_H156 ]. % 15.65/15.76 apply (zenon_L277_); trivial. % 15.65/15.76 apply (zenon_L134_); trivial. % 15.65/15.76 apply (zenon_L161_); trivial. % 15.65/15.76 apply (zenon_L90_); trivial. % 15.65/15.76 apply (zenon_L86_); trivial. % 15.65/15.76 apply (zenon_or_s _ _ zenon_H1d8); [ zenon_intro zenon_H1b4 | zenon_intro zenon_H21 ]. % 15.65/15.76 apply (zenon_or_s _ _ zenon_H1d3); [ zenon_intro zenon_Hd6 | zenon_intro zenon_H117 ]. % 15.65/15.76 apply (zenon_or_s _ _ zenon_H1d2); [ zenon_intro zenon_H182 | zenon_intro zenon_H11f ]. % 15.65/15.76 apply (zenon_or_s _ _ zenon_H1d4); [ zenon_intro zenon_H2e | zenon_intro zenon_Hdd ]. % 15.65/15.76 apply (zenon_or_s _ _ zenon_H1e3); [ zenon_intro zenon_H52 | zenon_intro zenon_H156 ]. % 15.65/15.76 apply (zenon_or_s _ _ zenon_H10f); [ zenon_intro zenon_H3c | zenon_intro zenon_Hba ]. % 15.65/15.76 apply (zenon_or_s _ _ zenon_H10e); [ zenon_intro zenon_H3d | zenon_intro zenon_H106 ]. % 15.65/15.76 apply (zenon_or_s _ _ zenon_H10d); [ zenon_intro zenon_H3e | zenon_intro zenon_H42 ]. % 15.65/15.76 apply (zenon_L508_); trivial. % 15.65/15.76 apply (zenon_L445_); trivial. % 15.65/15.76 apply (zenon_L167_); trivial. % 15.65/15.76 apply (zenon_L510_); trivial. % 15.65/15.76 apply (zenon_L134_); trivial. % 15.65/15.76 apply (zenon_L161_); trivial. % 15.65/15.76 apply (zenon_L224_); trivial. % 15.65/15.76 apply (zenon_L248_); trivial. % 15.65/15.76 apply (zenon_L61_); trivial. % 15.65/15.76 apply (zenon_or_s _ _ zenon_H1e4); [ zenon_intro zenon_H145 | zenon_intro zenon_Hd8 ]. % 15.65/15.76 apply (zenon_or_s _ _ zenon_H1d8); [ zenon_intro zenon_H1b4 | zenon_intro zenon_H21 ]. % 15.65/15.76 apply (zenon_or_s _ _ zenon_H1d3); [ zenon_intro zenon_Hd6 | zenon_intro zenon_H117 ]. % 15.65/15.76 apply (zenon_or_s _ _ zenon_H1d2); [ zenon_intro zenon_H182 | zenon_intro zenon_H11f ]. % 15.65/15.76 apply (zenon_L343_); trivial. % 15.65/15.76 apply (zenon_or_s _ _ zenon_H10f); [ zenon_intro zenon_H3c | zenon_intro zenon_Hba ]. % 15.65/15.76 apply (zenon_or_s _ _ zenon_H10c); [ zenon_intro zenon_H104 | zenon_intro zenon_H10a ]. % 15.65/15.76 apply (zenon_or_s _ _ zenon_H10e); [ zenon_intro zenon_H3d | zenon_intro zenon_H106 ]. % 15.65/15.76 apply (zenon_L424_); trivial. % 15.65/15.76 apply (zenon_L492_); trivial. % 15.65/15.76 apply (zenon_L494_); trivial. % 15.65/15.76 apply (zenon_L359_); trivial. % 15.65/15.76 apply (zenon_L438_); trivial. % 15.65/15.76 apply (zenon_or_s _ _ zenon_H1d3); [ zenon_intro zenon_Hd6 | zenon_intro zenon_H117 ]. % 15.65/15.76 apply (zenon_or_s _ _ zenon_H1d2); [ zenon_intro zenon_H182 | zenon_intro zenon_H11f ]. % 15.65/15.76 apply (zenon_or_s _ _ zenon_H1d4); [ zenon_intro zenon_H2e | zenon_intro zenon_Hdd ]. % 15.65/15.76 apply (zenon_or_s _ _ zenon_H1e3); [ zenon_intro zenon_H52 | zenon_intro zenon_H156 ]. % 15.65/15.76 apply (zenon_L317_); trivial. % 15.65/15.76 apply (zenon_L318_); trivial. % 15.65/15.76 apply (zenon_L161_); trivial. % 15.65/15.76 apply (zenon_L90_); trivial. % 15.65/15.76 apply (zenon_L86_); trivial. % 15.65/15.76 apply (zenon_or_s _ _ zenon_H1d8); [ zenon_intro zenon_H1b4 | zenon_intro zenon_H21 ]. % 15.65/15.76 apply (zenon_or_s _ _ zenon_H1d3); [ zenon_intro zenon_Hd6 | zenon_intro zenon_H117 ]. % 15.65/15.76 apply (zenon_or_s _ _ zenon_H1d2); [ zenon_intro zenon_H182 | zenon_intro zenon_H11f ]. % 15.65/15.76 apply (zenon_or_s _ _ zenon_H1d4); [ zenon_intro zenon_H2e | zenon_intro zenon_Hdd ]. % 15.65/15.76 apply (zenon_or_s _ _ zenon_H10f); [ zenon_intro zenon_H3c | zenon_intro zenon_Hba ]. % 15.65/15.76 apply (zenon_or_s _ _ zenon_H10e); [ zenon_intro zenon_H3d | zenon_intro zenon_H106 ]. % 15.65/15.76 apply (zenon_or_s _ _ zenon_H10d); [ zenon_intro zenon_H3e | zenon_intro zenon_H42 ]. % 15.65/15.76 apply (zenon_L511_); trivial. % 15.65/15.76 apply (zenon_L409_); trivial. % 15.65/15.76 apply (zenon_L167_); trivial. % 15.65/15.76 apply (zenon_L510_); trivial. % 15.65/15.76 apply (zenon_L161_); trivial. % 15.65/15.76 apply (zenon_L224_); trivial. % 15.65/15.76 apply (zenon_L248_); trivial. % 15.65/15.76 apply (zenon_L61_); trivial. % 15.65/15.76 apply (zenon_or_s _ _ zenon_H236); [ zenon_intro zenon_H59 | zenon_intro zenon_Hca ]. % 15.65/15.76 apply (zenon_or_s _ _ zenon_H1e4); [ zenon_intro zenon_H145 | zenon_intro zenon_Hd8 ]. % 15.65/15.76 apply (zenon_or_s _ _ zenon_H1d8); [ zenon_intro zenon_H1b4 | zenon_intro zenon_H21 ]. % 15.65/15.76 apply (zenon_or_s _ _ zenon_H1d3); [ zenon_intro zenon_Hd6 | zenon_intro zenon_H117 ]. % 15.65/15.76 apply (zenon_or_s _ _ zenon_H1d2); [ zenon_intro zenon_H182 | zenon_intro zenon_H11f ]. % 15.65/15.76 apply (zenon_or_s _ _ zenon_H1d4); [ zenon_intro zenon_H2e | zenon_intro zenon_Hdd ]. % 15.65/15.76 apply (zenon_or_s _ _ zenon_H1e3); [ zenon_intro zenon_H52 | zenon_intro zenon_H156 ]. % 15.65/15.76 apply (zenon_or_s _ _ zenon_H1c3); [ zenon_intro zenon_H30 | zenon_intro zenon_H124 ]. % 15.65/15.76 apply (zenon_or_s _ _ zenon_H10f); [ zenon_intro zenon_H3c | zenon_intro zenon_Hba ]. % 15.65/15.76 apply (zenon_or_s _ _ zenon_H10c); [ zenon_intro zenon_H104 | zenon_intro zenon_H10a ]. % 15.65/15.76 apply (zenon_or_s _ _ zenon_H10e); [ zenon_intro zenon_H3d | zenon_intro zenon_H106 ]. % 15.65/15.76 apply (zenon_or_s _ _ zenon_H10d); [ zenon_intro zenon_H3e | zenon_intro zenon_H42 ]. % 15.65/15.76 apply (zenon_or_s _ _ zenon_Hf0); [ zenon_intro zenon_H1f | zenon_intro zenon_Hf2 ]. % 15.65/15.76 exact (zenon_H20 zenon_H1f). % 15.65/15.76 apply (zenon_or_s _ _ zenon_Hf2); [ zenon_intro zenon_Had | zenon_intro zenon_Hf3 ]. % 15.65/15.76 apply (zenon_or_s _ _ zenon_H8e); [ zenon_intro zenon_H92 | zenon_intro zenon_H91 ]. % 15.65/15.76 apply (zenon_or_s _ _ zenon_H58); [ zenon_intro zenon_H5b | zenon_intro zenon_H5a ]. % 15.65/15.76 exact (zenon_H59 zenon_H5b). % 15.65/15.76 apply (zenon_or_s _ _ zenon_H5a); [ zenon_intro zenon_H4a | zenon_intro zenon_H5c ]. % 15.65/15.76 apply (zenon_L520_); trivial. % 15.65/15.76 apply (zenon_or_s _ _ zenon_H5c); [ zenon_intro zenon_H50 | zenon_intro zenon_H53 ]. % 15.65/15.76 apply (zenon_L48_); trivial. % 15.65/15.76 apply (zenon_or_s _ _ zenon_H1c5); [ zenon_intro zenon_Hd8 | zenon_intro zenon_H1c6 ]. % 15.65/15.76 apply (zenon_L509_); trivial. % 15.65/15.76 apply (zenon_or_s _ _ zenon_H1c6); [ zenon_intro zenon_H21 | zenon_intro zenon_H1c7 ]. % 15.65/15.76 exact (zenon_H1b4 zenon_H21). % 15.65/15.76 apply (zenon_or_s _ _ zenon_H1c7); [ zenon_intro zenon_H117 | zenon_intro zenon_H11f ]. % 15.65/15.76 apply (zenon_L521_); trivial. % 15.65/15.76 apply (zenon_L513_); trivial. % 15.65/15.76 apply (zenon_or_s _ _ zenon_H91); [ zenon_intro zenon_H5d | zenon_intro zenon_H93 ]. % 15.65/15.76 apply (zenon_L214_); trivial. % 15.65/15.76 apply (zenon_or_s _ _ zenon_H93); [ zenon_intro zenon_H63 | zenon_intro zenon_H81 ]. % 15.65/15.76 apply (zenon_L15_); trivial. % 15.65/15.76 apply (zenon_L522_); trivial. % 15.65/15.76 apply (zenon_or_s _ _ zenon_Hf3); [ zenon_intro zenon_Hcf | zenon_intro zenon_Hdb ]. % 15.65/15.76 apply (zenon_L312_); trivial. % 15.65/15.76 apply (zenon_L526_); trivial. % 15.65/15.76 apply (zenon_L232_); trivial. % 15.65/15.76 apply (zenon_or_s _ _ zenon_H10d); [ zenon_intro zenon_H3e | zenon_intro zenon_H42 ]. % 15.65/15.76 apply (zenon_or_s _ _ zenon_Hf0); [ zenon_intro zenon_H1f | zenon_intro zenon_Hf2 ]. % 15.65/15.76 exact (zenon_H20 zenon_H1f). % 15.65/15.76 apply (zenon_or_s _ _ zenon_Hf2); [ zenon_intro zenon_Had | zenon_intro zenon_Hf3 ]. % 15.65/15.76 apply (zenon_or_s _ _ zenon_H44); [ zenon_intro zenon_H47 | zenon_intro zenon_H46 ]. % 15.65/15.76 exact (zenon_H45 zenon_H47). % 15.65/15.76 apply (zenon_or_s _ _ zenon_H46); [ zenon_intro zenon_H22 | zenon_intro zenon_H48 ]. % 15.65/15.76 apply (zenon_L532_); trivial. % 15.65/15.76 apply (zenon_or_s _ _ zenon_H48); [ zenon_intro zenon_H29 | zenon_intro zenon_H37 ]. % 15.65/15.76 apply (zenon_L37_); trivial. % 15.65/15.76 apply (zenon_or_s _ _ zenon_H8e); [ zenon_intro zenon_H92 | zenon_intro zenon_H91 ]. % 15.65/15.76 apply (zenon_or_s _ _ zenon_H58); [ zenon_intro zenon_H5b | zenon_intro zenon_H5a ]. % 15.65/15.76 exact (zenon_H59 zenon_H5b). % 15.65/15.76 apply (zenon_or_s _ _ zenon_H5a); [ zenon_intro zenon_H4a | zenon_intro zenon_H5c ]. % 15.65/15.76 apply (zenon_L520_); trivial. % 15.65/15.76 apply (zenon_or_s _ _ zenon_H5c); [ zenon_intro zenon_H50 | zenon_intro zenon_H53 ]. % 15.65/15.76 apply (zenon_L533_); trivial. % 15.65/15.76 apply (zenon_L32_); trivial. % 15.65/15.76 apply (zenon_or_s _ _ zenon_H91); [ zenon_intro zenon_H5d | zenon_intro zenon_H93 ]. % 15.65/15.76 apply (zenon_L534_); trivial. % 15.65/15.76 apply (zenon_or_s _ _ zenon_H93); [ zenon_intro zenon_H63 | zenon_intro zenon_H81 ]. % 15.65/15.76 apply (zenon_L15_); trivial. % 15.65/15.76 apply (zenon_L33_); trivial. % 15.65/15.76 apply (zenon_or_s _ _ zenon_Hf3); [ zenon_intro zenon_Hcf | zenon_intro zenon_Hdb ]. % 15.65/15.76 apply (zenon_L312_); trivial. % 15.65/15.76 apply (zenon_L526_); trivial. % 15.65/15.76 apply (zenon_L153_); trivial. % 15.65/15.76 apply (zenon_L538_); trivial. % 15.65/15.76 apply (zenon_L547_); trivial. % 15.65/15.76 apply (zenon_L137_); trivial. % 15.65/15.76 apply (zenon_L134_); trivial. % 15.65/15.76 apply (zenon_L161_); trivial. % 15.65/15.76 apply (zenon_L519_); trivial. % 15.65/15.76 apply (zenon_or_s _ _ zenon_H1d2); [ zenon_intro zenon_H182 | zenon_intro zenon_H11f ]. % 15.65/15.76 apply (zenon_or_s _ _ zenon_H1d4); [ zenon_intro zenon_H2e | zenon_intro zenon_Hdd ]. % 15.65/15.76 apply (zenon_or_s _ _ zenon_H1c3); [ zenon_intro zenon_H30 | zenon_intro zenon_H124 ]. % 15.65/15.76 apply (zenon_or_s _ _ zenon_H10f); [ zenon_intro zenon_H3c | zenon_intro zenon_Hba ]. % 15.65/15.76 apply (zenon_or_s _ _ zenon_H10c); [ zenon_intro zenon_H104 | zenon_intro zenon_H10a ]. % 15.65/15.76 apply (zenon_or_s _ _ zenon_H10e); [ zenon_intro zenon_H3d | zenon_intro zenon_H106 ]. % 15.65/15.76 apply (zenon_or_s _ _ zenon_H10d); [ zenon_intro zenon_H3e | zenon_intro zenon_H42 ]. % 15.65/15.76 apply (zenon_or_s _ _ zenon_Hf0); [ zenon_intro zenon_H1f | zenon_intro zenon_Hf2 ]. % 15.65/15.76 exact (zenon_H20 zenon_H1f). % 15.65/15.76 apply (zenon_or_s _ _ zenon_Hf2); [ zenon_intro zenon_Had | zenon_intro zenon_Hf3 ]. % 15.65/15.76 apply (zenon_L548_); trivial. % 15.65/15.76 apply (zenon_or_s _ _ zenon_Hf3); [ zenon_intro zenon_Hcf | zenon_intro zenon_Hdb ]. % 15.65/15.76 apply (zenon_L312_); trivial. % 15.65/15.76 apply (zenon_or_s _ _ zenon_H44); [ zenon_intro zenon_H47 | zenon_intro zenon_H46 ]. % 15.65/15.76 exact (zenon_H45 zenon_H47). % 15.65/15.76 apply (zenon_or_s _ _ zenon_H46); [ zenon_intro zenon_H22 | zenon_intro zenon_H48 ]. % 15.65/15.76 apply (zenon_L550_); trivial. % 15.65/15.76 apply (zenon_or_s _ _ zenon_H48); [ zenon_intro zenon_H29 | zenon_intro zenon_H37 ]. % 15.65/15.76 apply (zenon_L37_); trivial. % 15.65/15.76 apply (zenon_L7_); trivial. % 15.65/15.76 apply (zenon_L239_); trivial. % 15.65/15.76 apply (zenon_or_s _ _ zenon_Hf0); [ zenon_intro zenon_H1f | zenon_intro zenon_Hf2 ]. % 15.65/15.76 exact (zenon_H20 zenon_H1f). % 15.65/15.76 apply (zenon_or_s _ _ zenon_Hf2); [ zenon_intro zenon_Had | zenon_intro zenon_Hf3 ]. % 15.65/15.76 apply (zenon_L548_); trivial. % 15.65/15.76 apply (zenon_or_s _ _ zenon_Hf3); [ zenon_intro zenon_Hcf | zenon_intro zenon_Hdb ]. % 15.65/15.76 apply (zenon_L312_); trivial. % 15.65/15.76 apply (zenon_or_s _ _ zenon_H44); [ zenon_intro zenon_H47 | zenon_intro zenon_H46 ]. % 15.65/15.76 exact (zenon_H45 zenon_H47). % 15.65/15.76 apply (zenon_or_s _ _ zenon_H46); [ zenon_intro zenon_H22 | zenon_intro zenon_H48 ]. % 15.65/15.76 apply (zenon_L550_); trivial. % 15.65/15.76 apply (zenon_or_s _ _ zenon_H48); [ zenon_intro zenon_H29 | zenon_intro zenon_H37 ]. % 15.65/15.76 apply (zenon_L552_); trivial. % 15.65/15.76 apply (zenon_L314_); trivial. % 15.65/15.76 apply (zenon_L502_); trivial. % 15.65/15.76 apply (zenon_L507_); trivial. % 15.65/15.76 apply (zenon_L137_); trivial. % 15.65/15.76 apply (zenon_L161_); trivial. % 15.65/15.76 apply (zenon_L237_); trivial. % 15.65/15.76 apply (zenon_L273_); trivial. % 15.65/15.76 apply (zenon_L553_); trivial. % 15.65/15.76 apply (zenon_L53_); trivial. % 15.65/15.76 apply (zenon_or_s _ _ zenon_H24a); [ zenon_intro zenon_H8f | zenon_intro zenon_Hab ]. % 15.65/15.76 apply (zenon_or_s _ _ zenon_H236); [ zenon_intro zenon_H59 | zenon_intro zenon_Hca ]. % 15.65/15.76 apply (zenon_or_s _ _ zenon_H1e4); [ zenon_intro zenon_H145 | zenon_intro zenon_Hd8 ]. % 15.65/15.76 apply (zenon_or_s _ _ zenon_H1d8); [ zenon_intro zenon_H1b4 | zenon_intro zenon_H21 ]. % 15.65/15.76 apply (zenon_L557_); trivial. % 15.65/15.76 apply (zenon_or_s _ _ zenon_H1d3); [ zenon_intro zenon_Hd6 | zenon_intro zenon_H117 ]. % 15.65/15.76 apply (zenon_or_s _ _ zenon_H1d2); [ zenon_intro zenon_H182 | zenon_intro zenon_H11f ]. % 15.65/15.76 apply (zenon_or_s _ _ zenon_H1d4); [ zenon_intro zenon_H2e | zenon_intro zenon_Hdd ]. % 15.65/15.76 apply (zenon_or_s _ _ zenon_H1e3); [ zenon_intro zenon_H52 | zenon_intro zenon_H156 ]. % 15.65/15.76 apply (zenon_L480_); trivial. % 15.65/15.76 apply (zenon_L134_); trivial. % 15.65/15.76 apply (zenon_L161_); trivial. % 15.65/15.76 apply (zenon_L90_); trivial. % 15.65/15.76 apply (zenon_L86_); trivial. % 15.65/15.76 apply (zenon_L484_); trivial. % 15.65/15.76 apply (zenon_L463_); trivial. % 15.65/15.76 apply (zenon_L485_); trivial. % 15.65/15.76 apply (zenon_L2_); trivial. % 15.65/15.76 apply (zenon_L558_); trivial. % 15.65/15.76 apply (zenon_or_s _ _ zenon_H352); [ zenon_intro zenon_H35b | zenon_intro zenon_H35a ]. % 15.65/15.76 apply (zenon_and_s _ _ zenon_H35b). zenon_intro zenon_H261. zenon_intro zenon_H35c. % 15.65/15.76 apply (zenon_and_s _ _ zenon_H35c). zenon_intro zenon_H27b. zenon_intro zenon_H35d. % 15.65/15.76 apply (zenon_and_s _ _ zenon_H35d). zenon_intro zenon_H277. zenon_intro zenon_H26e. % 15.65/15.76 apply (zenon_or_s _ _ zenon_H343); [ zenon_intro zenon_H1f | zenon_intro zenon_H356 ]. % 15.65/15.76 apply (zenon_or_s _ _ zenon_H24b); [ zenon_intro zenon_H45 | zenon_intro zenon_H49 ]. % 15.65/15.76 apply (zenon_or_s _ _ zenon_H24a); [ zenon_intro zenon_H8f | zenon_intro zenon_Hab ]. % 15.65/15.76 apply (zenon_or_s _ _ zenon_H236); [ zenon_intro zenon_H59 | zenon_intro zenon_Hca ]. % 15.65/15.76 apply (zenon_or_s _ _ zenon_H1e4); [ zenon_intro zenon_H145 | zenon_intro zenon_Hd8 ]. % 15.65/15.76 apply (zenon_or_s _ _ zenon_H1d8); [ zenon_intro zenon_H1b4 | zenon_intro zenon_H21 ]. % 15.65/15.76 apply (zenon_or_s _ _ zenon_H1d3); [ zenon_intro zenon_Hd6 | zenon_intro zenon_H117 ]. % 15.65/15.76 apply (zenon_or_s _ _ zenon_H1d2); [ zenon_intro zenon_H182 | zenon_intro zenon_H11f ]. % 15.65/15.76 apply (zenon_or_s _ _ zenon_H1d4); [ zenon_intro zenon_H2e | zenon_intro zenon_Hdd ]. % 15.65/15.76 apply (zenon_or_s _ _ zenon_H1e3); [ zenon_intro zenon_H52 | zenon_intro zenon_H156 ]. % 15.65/15.76 apply (zenon_or_s _ _ zenon_Haa); [ zenon_intro zenon_H2f | zenon_intro zenon_H35 ]. % 15.65/15.76 apply (zenon_or_s _ _ zenon_H1c3); [ zenon_intro zenon_H30 | zenon_intro zenon_H124 ]. % 15.65/15.76 apply (zenon_or_s _ _ zenon_H10f); [ zenon_intro zenon_H3c | zenon_intro zenon_Hba ]. % 15.65/15.76 apply (zenon_or_s _ _ zenon_H10c); [ zenon_intro zenon_H104 | zenon_intro zenon_H10a ]. % 15.65/15.76 apply (zenon_or_s _ _ zenon_H10e); [ zenon_intro zenon_H3d | zenon_intro zenon_H106 ]. % 15.65/15.76 apply (zenon_L637_); trivial. % 15.65/15.76 apply (zenon_or_s _ _ zenon_H10d); [ zenon_intro zenon_H3e | zenon_intro zenon_H42 ]. % 15.65/15.76 apply (zenon_or_s _ _ zenon_H44); [ zenon_intro zenon_H47 | zenon_intro zenon_H46 ]. % 15.65/15.76 exact (zenon_H45 zenon_H47). % 15.65/15.76 apply (zenon_or_s _ _ zenon_H46); [ zenon_intro zenon_H22 | zenon_intro zenon_H48 ]. % 15.65/15.76 apply (zenon_L664_); trivial. % 15.65/15.76 apply (zenon_or_s _ _ zenon_H48); [ zenon_intro zenon_H29 | zenon_intro zenon_H37 ]. % 15.65/15.76 apply (zenon_L665_); trivial. % 15.65/15.76 apply (zenon_or_s _ _ zenon_H8e); [ zenon_intro zenon_H92 | zenon_intro zenon_H91 ]. % 15.65/15.76 exact (zenon_H8f zenon_H92). % 15.65/15.76 apply (zenon_or_s _ _ zenon_H91); [ zenon_intro zenon_H5d | zenon_intro zenon_H93 ]. % 15.65/15.76 apply (zenon_L534_); trivial. % 15.65/15.76 apply (zenon_or_s _ _ zenon_H93); [ zenon_intro zenon_H63 | zenon_intro zenon_H81 ]. % 15.65/15.76 apply (zenon_L662_); trivial. % 15.65/15.76 apply (zenon_L33_); trivial. % 15.65/15.76 apply (zenon_L153_); trivial. % 15.65/15.76 apply (zenon_or_s _ _ zenon_H10e); [ zenon_intro zenon_H3d | zenon_intro zenon_H106 ]. % 15.65/15.76 apply (zenon_or_s _ _ zenon_H10d); [ zenon_intro zenon_H3e | zenon_intro zenon_H42 ]. % 15.65/15.76 apply (zenon_or_s _ _ zenon_H44); [ zenon_intro zenon_H47 | zenon_intro zenon_H46 ]. % 15.65/15.76 exact (zenon_H45 zenon_H47). % 15.65/15.76 apply (zenon_or_s _ _ zenon_H46); [ zenon_intro zenon_H22 | zenon_intro zenon_H48 ]. % 15.65/15.76 apply (zenon_L664_); trivial. % 15.65/15.76 apply (zenon_or_s _ _ zenon_H48); [ zenon_intro zenon_H29 | zenon_intro zenon_H37 ]. % 15.65/15.76 apply (zenon_L666_); trivial. % 15.65/15.76 apply (zenon_L7_); trivial. % 15.65/15.76 apply (zenon_L102_); trivial. % 15.65/15.76 apply (zenon_L115_); trivial. % 15.65/15.76 apply (zenon_or_s _ _ zenon_H10c); [ zenon_intro zenon_H104 | zenon_intro zenon_H10a ]. % 15.65/15.76 apply (zenon_or_s _ _ zenon_H10e); [ zenon_intro zenon_H3d | zenon_intro zenon_H106 ]. % 15.65/15.76 apply (zenon_or_s _ _ zenon_H10d); [ zenon_intro zenon_H3e | zenon_intro zenon_H42 ]. % 15.65/15.76 apply (zenon_or_s _ _ zenon_Hf1); [ zenon_intro zenon_H47 | zenon_intro zenon_Hf4 ]. % 15.65/15.76 exact (zenon_H45 zenon_H47). % 15.65/15.76 apply (zenon_or_s _ _ zenon_Hf4); [ zenon_intro zenon_Hd8 | zenon_intro zenon_Hf5 ]. % 15.65/15.76 apply (zenon_L671_); trivial. % 15.65/15.76 apply (zenon_or_s _ _ zenon_Hf5); [ zenon_intro zenon_Hae | zenon_intro zenon_Hee ]. % 15.65/15.76 apply (zenon_L78_); trivial. % 15.65/15.76 apply (zenon_L79_); trivial. % 15.65/15.76 apply (zenon_L43_); trivial. % 15.65/15.76 apply (zenon_L81_); trivial. % 15.65/15.76 apply (zenon_L82_); trivial. % 15.65/15.76 apply (zenon_or_s _ _ zenon_H10f); [ zenon_intro zenon_H3c | zenon_intro zenon_Hba ]. % 15.65/15.76 apply (zenon_or_s _ _ zenon_H10c); [ zenon_intro zenon_H104 | zenon_intro zenon_H10a ]. % 15.65/15.76 apply (zenon_or_s _ _ zenon_H10e); [ zenon_intro zenon_H3d | zenon_intro zenon_H106 ]. % 15.65/15.76 apply (zenon_L637_); trivial. % 15.65/15.76 apply (zenon_or_s _ _ zenon_H10d); [ zenon_intro zenon_H3e | zenon_intro zenon_H42 ]. % 15.65/15.76 apply (zenon_or_s _ _ zenon_H44); [ zenon_intro zenon_H47 | zenon_intro zenon_H46 ]. % 15.65/15.76 exact (zenon_H45 zenon_H47). % 15.65/15.76 apply (zenon_or_s _ _ zenon_H46); [ zenon_intro zenon_H22 | zenon_intro zenon_H48 ]. % 15.65/15.76 apply (zenon_or_s _ _ zenon_Hf1); [ zenon_intro zenon_H47 | zenon_intro zenon_Hf4 ]. % 15.65/15.76 exact (zenon_H45 zenon_H47). % 15.65/15.76 apply (zenon_or_s _ _ zenon_Hf4); [ zenon_intro zenon_Hd8 | zenon_intro zenon_Hf5 ]. % 15.65/15.76 apply (zenon_L675_); trivial. % 15.65/15.76 apply (zenon_or_s _ _ zenon_Hf5); [ zenon_intro zenon_Hae | zenon_intro zenon_Hee ]. % 15.65/15.76 apply (zenon_or_s _ _ zenon_H8e); [ zenon_intro zenon_H92 | zenon_intro zenon_H91 ]. % 15.65/15.76 exact (zenon_H8f zenon_H92). % 15.65/15.76 apply (zenon_or_s _ _ zenon_H91); [ zenon_intro zenon_H5d | zenon_intro zenon_H93 ]. % 15.65/15.76 apply (zenon_L214_); trivial. % 15.65/15.76 apply (zenon_or_s _ _ zenon_H93); [ zenon_intro zenon_H63 | zenon_intro zenon_H81 ]. % 15.65/15.76 apply (zenon_L676_); trivial. % 15.65/15.76 apply (zenon_L663_); trivial. % 15.65/15.76 apply (zenon_L678_); trivial. % 15.65/15.76 apply (zenon_or_s _ _ zenon_H48); [ zenon_intro zenon_H29 | zenon_intro zenon_H37 ]. % 15.65/15.76 apply (zenon_L665_); trivial. % 15.65/15.76 apply (zenon_or_s _ _ zenon_Hf1); [ zenon_intro zenon_H47 | zenon_intro zenon_Hf4 ]. % 15.65/15.76 exact (zenon_H45 zenon_H47). % 15.65/15.76 apply (zenon_or_s _ _ zenon_Hf4); [ zenon_intro zenon_Hd8 | zenon_intro zenon_Hf5 ]. % 15.65/15.76 apply (zenon_L674_); trivial. % 15.65/15.76 apply (zenon_or_s _ _ zenon_Hf5); [ zenon_intro zenon_Hae | zenon_intro zenon_Hee ]. % 15.65/15.76 apply (zenon_or_s _ _ zenon_H8e); [ zenon_intro zenon_H92 | zenon_intro zenon_H91 ]. % 15.65/15.76 exact (zenon_H8f zenon_H92). % 15.65/15.76 apply (zenon_or_s _ _ zenon_H91); [ zenon_intro zenon_H5d | zenon_intro zenon_H93 ]. % 15.65/15.76 apply (zenon_L214_); trivial. % 15.65/15.76 apply (zenon_or_s _ _ zenon_H93); [ zenon_intro zenon_H63 | zenon_intro zenon_H81 ]. % 15.65/15.76 apply (zenon_or_s _ _ zenon_Heb); [ zenon_intro zenon_H92 | zenon_intro zenon_Hec ]. % 15.65/15.76 exact (zenon_H8f zenon_H92). % 15.65/15.76 apply (zenon_or_s _ _ zenon_Hec); [ zenon_intro zenon_H68 | zenon_intro zenon_Hed ]. % 15.65/15.76 apply (zenon_L638_); trivial. % 15.65/15.76 apply (zenon_or_s _ _ zenon_Hed); [ zenon_intro zenon_Hdd | zenon_intro zenon_He9 ]. % 15.65/15.76 apply (zenon_L660_); trivial. % 15.65/15.76 apply (zenon_or_s _ _ zenon_Hbe); [ zenon_intro zenon_H5b | zenon_intro zenon_Hbf ]. % 15.65/15.76 exact (zenon_H59 zenon_H5b). % 15.65/15.76 apply (zenon_or_s _ _ zenon_Hbf); [ zenon_intro zenon_H69 | zenon_intro zenon_Hc0 ]. % 15.65/15.76 apply (zenon_L679_); trivial. % 15.65/15.76 apply (zenon_or_s _ _ zenon_Hc0); [ zenon_intro zenon_Haf | zenon_intro zenon_Hba ]. % 15.65/15.76 apply (zenon_L39_); trivial. % 15.65/15.76 apply (zenon_L220_); trivial. % 15.65/15.76 apply (zenon_L33_); trivial. % 15.65/15.76 apply (zenon_or_s _ _ zenon_H8e); [ zenon_intro zenon_H92 | zenon_intro zenon_H91 ]. % 15.65/15.76 exact (zenon_H8f zenon_H92). % 15.65/15.76 apply (zenon_or_s _ _ zenon_H91); [ zenon_intro zenon_H5d | zenon_intro zenon_H93 ]. % 15.65/15.76 apply (zenon_L534_); trivial. % 15.65/15.76 apply (zenon_or_s _ _ zenon_H93); [ zenon_intro zenon_H63 | zenon_intro zenon_H81 ]. % 15.65/15.76 apply (zenon_L677_); trivial. % 15.65/15.76 apply (zenon_L107_); trivial. % 15.65/15.76 apply (zenon_L153_); trivial. % 15.65/15.76 apply (zenon_L681_); trivial. % 15.65/15.76 apply (zenon_or_s _ _ zenon_H10c); [ zenon_intro zenon_H104 | zenon_intro zenon_H10a ]. % 15.65/15.76 apply (zenon_or_s _ _ zenon_H10e); [ zenon_intro zenon_H3d | zenon_intro zenon_H106 ]. % 15.65/15.76 apply (zenon_or_s _ _ zenon_H10d); [ zenon_intro zenon_H3e | zenon_intro zenon_H42 ]. % 15.65/15.76 apply (zenon_or_s _ _ zenon_Hf1); [ zenon_intro zenon_H47 | zenon_intro zenon_Hf4 ]. % 15.65/15.76 exact (zenon_H45 zenon_H47). % 15.65/15.76 apply (zenon_or_s _ _ zenon_Hf4); [ zenon_intro zenon_Hd8 | zenon_intro zenon_Hf5 ]. % 15.65/15.76 apply (zenon_L682_); trivial. % 15.65/15.76 apply (zenon_or_s _ _ zenon_Hf5); [ zenon_intro zenon_Hae | zenon_intro zenon_Hee ]. % 15.65/15.76 apply (zenon_L684_); trivial. % 15.65/15.76 apply (zenon_L79_); trivial. % 15.65/15.76 apply (zenon_L43_); trivial. % 15.65/15.76 apply (zenon_L81_); trivial. % 15.65/15.76 apply (zenon_L82_); trivial. % 15.65/15.76 apply (zenon_L685_); trivial. % 15.65/15.76 apply (zenon_or_s _ _ zenon_Haa); [ zenon_intro zenon_H2f | zenon_intro zenon_H35 ]. % 15.65/15.76 apply (zenon_or_s _ _ zenon_H1c3); [ zenon_intro zenon_H30 | zenon_intro zenon_H124 ]. % 15.65/15.76 apply (zenon_or_s _ _ zenon_H10f); [ zenon_intro zenon_H3c | zenon_intro zenon_Hba ]. % 15.65/15.76 apply (zenon_or_s _ _ zenon_H10c); [ zenon_intro zenon_H104 | zenon_intro zenon_H10a ]. % 15.65/15.76 apply (zenon_or_s _ _ zenon_H10e); [ zenon_intro zenon_H3d | zenon_intro zenon_H106 ]. % 15.65/15.76 apply (zenon_or_s _ _ zenon_H10d); [ zenon_intro zenon_H3e | zenon_intro zenon_H42 ]. % 15.65/15.76 apply (zenon_L686_); trivial. % 15.65/15.76 apply (zenon_L635_); trivial. % 15.65/15.76 apply (zenon_or_s _ _ zenon_H10d); [ zenon_intro zenon_H3e | zenon_intro zenon_H42 ]. % 15.65/15.76 apply (zenon_L686_); trivial. % 15.65/15.76 apply (zenon_L153_); trivial. % 15.65/15.76 apply (zenon_or_s _ _ zenon_H10e); [ zenon_intro zenon_H3d | zenon_intro zenon_H106 ]. % 15.65/15.76 apply (zenon_or_s _ _ zenon_H10d); [ zenon_intro zenon_H3e | zenon_intro zenon_H42 ]. % 15.65/15.76 apply (zenon_or_s _ _ zenon_H44); [ zenon_intro zenon_H47 | zenon_intro zenon_H46 ]. % 15.65/15.76 exact (zenon_H45 zenon_H47). % 15.65/15.76 apply (zenon_or_s _ _ zenon_H46); [ zenon_intro zenon_H22 | zenon_intro zenon_H48 ]. % 15.65/15.76 apply (zenon_or_s _ _ zenon_Hf1); [ zenon_intro zenon_H47 | zenon_intro zenon_Hf4 ]. % 15.65/15.76 exact (zenon_H45 zenon_H47). % 15.65/15.76 apply (zenon_or_s _ _ zenon_Hf4); [ zenon_intro zenon_Hd8 | zenon_intro zenon_Hf5 ]. % 15.65/15.76 apply (zenon_L644_); trivial. % 15.65/15.76 apply (zenon_or_s _ _ zenon_Hf5); [ zenon_intro zenon_Hae | zenon_intro zenon_Hee ]. % 15.65/15.76 apply (zenon_L427_); trivial. % 15.65/15.76 apply (zenon_L624_); trivial. % 15.65/15.76 apply (zenon_or_s _ _ zenon_H48); [ zenon_intro zenon_H29 | zenon_intro zenon_H37 ]. % 15.65/15.76 apply (zenon_L5_); trivial. % 15.65/15.76 apply (zenon_L7_); trivial. % 15.65/15.76 apply (zenon_L102_); trivial. % 15.65/15.76 apply (zenon_L115_); trivial. % 15.65/15.76 apply (zenon_L689_); trivial. % 15.65/15.76 apply (zenon_L256_); trivial. % 15.65/15.76 apply (zenon_L134_); trivial. % 15.65/15.76 apply (zenon_or_s _ _ zenon_H1e3); [ zenon_intro zenon_H52 | zenon_intro zenon_H156 ]. % 15.65/15.76 apply (zenon_L660_); trivial. % 15.65/15.76 apply (zenon_L284_); trivial. % 15.65/15.76 apply (zenon_or_s _ _ zenon_H1d4); [ zenon_intro zenon_H2e | zenon_intro zenon_Hdd ]. % 15.65/15.76 apply (zenon_or_s _ _ zenon_H1e3); [ zenon_intro zenon_H52 | zenon_intro zenon_H156 ]. % 15.65/15.76 apply (zenon_or_s _ _ zenon_Haa); [ zenon_intro zenon_H2f | zenon_intro zenon_H35 ]. % 15.65/15.76 apply (zenon_or_s _ _ zenon_H1c3); [ zenon_intro zenon_H30 | zenon_intro zenon_H124 ]. % 15.65/15.76 apply (zenon_L603_); trivial. % 15.65/15.76 apply (zenon_or_s _ _ zenon_H10f); [ zenon_intro zenon_H3c | zenon_intro zenon_Hba ]. % 15.65/15.76 apply (zenon_L604_); trivial. % 15.65/15.76 apply (zenon_or_s _ _ zenon_H10c); [ zenon_intro zenon_H104 | zenon_intro zenon_H10a ]. % 15.65/15.76 apply (zenon_or_s _ _ zenon_H10e); [ zenon_intro zenon_H3d | zenon_intro zenon_H106 ]. % 15.65/15.76 apply (zenon_or_s _ _ zenon_H10d); [ zenon_intro zenon_H3e | zenon_intro zenon_H42 ]. % 15.65/15.76 apply (zenon_or_s _ _ zenon_Hf1); [ zenon_intro zenon_H47 | zenon_intro zenon_Hf4 ]. % 15.65/15.76 exact (zenon_H45 zenon_H47). % 15.65/15.76 apply (zenon_or_s _ _ zenon_Hf4); [ zenon_intro zenon_Hd8 | zenon_intro zenon_Hf5 ]. % 15.65/15.76 apply (zenon_L224_); trivial. % 15.65/15.76 apply (zenon_or_s _ _ zenon_Hf5); [ zenon_intro zenon_Hae | zenon_intro zenon_Hee ]. % 15.65/15.76 apply (zenon_L684_); trivial. % 15.65/15.76 apply (zenon_L79_); trivial. % 15.65/15.76 apply (zenon_L43_); trivial. % 15.65/15.76 apply (zenon_L81_); trivial. % 15.65/15.76 apply (zenon_L82_); trivial. % 15.65/15.76 apply (zenon_L692_); trivial. % 15.65/15.76 apply (zenon_or_s _ _ zenon_Haa); [ zenon_intro zenon_H2f | zenon_intro zenon_H35 ]. % 15.65/15.76 apply (zenon_or_s _ _ zenon_H1c3); [ zenon_intro zenon_H30 | zenon_intro zenon_H124 ]. % 15.65/15.76 apply (zenon_or_s _ _ zenon_H10f); [ zenon_intro zenon_H3c | zenon_intro zenon_Hba ]. % 15.65/15.76 apply (zenon_or_s _ _ zenon_H10c); [ zenon_intro zenon_H104 | zenon_intro zenon_H10a ]. % 15.65/15.76 apply (zenon_or_s _ _ zenon_H10e); [ zenon_intro zenon_H3d | zenon_intro zenon_H106 ]. % 15.65/15.76 apply (zenon_L693_); trivial. % 15.65/15.76 apply (zenon_L691_); trivial. % 15.65/15.76 apply (zenon_or_s _ _ zenon_H10e); [ zenon_intro zenon_H3d | zenon_intro zenon_H106 ]. % 15.65/15.76 apply (zenon_L693_); trivial. % 15.65/15.76 apply (zenon_L115_); trivial. % 15.65/15.76 apply (zenon_L689_); trivial. % 15.65/15.76 apply (zenon_L256_); trivial. % 15.65/15.76 apply (zenon_L134_); trivial. % 15.65/15.76 apply (zenon_L695_); trivial. % 15.65/15.76 apply (zenon_or_s _ _ zenon_H1d2); [ zenon_intro zenon_H182 | zenon_intro zenon_H11f ]. % 15.65/15.76 apply (zenon_or_s _ _ zenon_H1d4); [ zenon_intro zenon_H2e | zenon_intro zenon_Hdd ]. % 15.65/15.76 apply (zenon_or_s _ _ zenon_H1e3); [ zenon_intro zenon_H52 | zenon_intro zenon_H156 ]. % 15.65/15.76 apply (zenon_or_s _ _ zenon_Haa); [ zenon_intro zenon_H2f | zenon_intro zenon_H35 ]. % 15.65/15.76 apply (zenon_or_s _ _ zenon_H1c3); [ zenon_intro zenon_H30 | zenon_intro zenon_H124 ]. % 15.65/15.76 apply (zenon_or_s _ _ zenon_H10f); [ zenon_intro zenon_H3c | zenon_intro zenon_Hba ]. % 15.65/15.76 apply (zenon_or_s _ _ zenon_H10c); [ zenon_intro zenon_H104 | zenon_intro zenon_H10a ]. % 15.65/15.76 apply (zenon_or_s _ _ zenon_H10e); [ zenon_intro zenon_H3d | zenon_intro zenon_H106 ]. % 15.65/15.76 apply (zenon_or_s _ _ zenon_H10d); [ zenon_intro zenon_H3e | zenon_intro zenon_H42 ]. % 15.65/15.76 apply (zenon_or_s _ _ zenon_H44); [ zenon_intro zenon_H47 | zenon_intro zenon_H46 ]. % 15.65/15.76 exact (zenon_H45 zenon_H47). % 15.65/15.76 apply (zenon_or_s _ _ zenon_H46); [ zenon_intro zenon_H22 | zenon_intro zenon_H48 ]. % 15.65/15.76 apply (zenon_or_s _ _ zenon_Hf1); [ zenon_intro zenon_H47 | zenon_intro zenon_Hf4 ]. % 15.65/15.76 exact (zenon_H45 zenon_H47). % 15.65/15.76 apply (zenon_or_s _ _ zenon_Hf4); [ zenon_intro zenon_Hd8 | zenon_intro zenon_Hf5 ]. % 15.65/15.76 apply (zenon_L644_); trivial. % 15.65/15.76 apply (zenon_or_s _ _ zenon_Hf5); [ zenon_intro zenon_Hae | zenon_intro zenon_Hee ]. % 15.65/15.76 apply (zenon_L578_); trivial. % 15.65/15.76 apply (zenon_L306_); trivial. % 15.65/15.76 apply (zenon_or_s _ _ zenon_H48); [ zenon_intro zenon_H29 | zenon_intro zenon_H37 ]. % 15.65/15.76 apply (zenon_L5_); trivial. % 15.65/15.76 apply (zenon_L7_); trivial. % 15.65/15.76 apply (zenon_L588_); trivial. % 15.65/15.76 apply (zenon_L590_); trivial. % 15.65/15.76 apply (zenon_L502_); trivial. % 15.65/15.76 apply (zenon_L437_); trivial. % 15.65/15.76 apply (zenon_or_s _ _ zenon_H10f); [ zenon_intro zenon_H3c | zenon_intro zenon_Hba ]. % 15.65/15.76 apply (zenon_or_s _ _ zenon_H10c); [ zenon_intro zenon_H104 | zenon_intro zenon_H10a ]. % 15.65/15.76 apply (zenon_or_s _ _ zenon_H10e); [ zenon_intro zenon_H3d | zenon_intro zenon_H106 ]. % 15.65/15.76 apply (zenon_or_s _ _ zenon_H10d); [ zenon_intro zenon_H3e | zenon_intro zenon_H42 ]. % 15.65/15.76 apply (zenon_or_s _ _ zenon_H44); [ zenon_intro zenon_H47 | zenon_intro zenon_H46 ]. % 15.65/15.76 exact (zenon_H45 zenon_H47). % 15.65/15.76 apply (zenon_or_s _ _ zenon_H46); [ zenon_intro zenon_H22 | zenon_intro zenon_H48 ]. % 15.65/15.76 apply (zenon_or_s _ _ zenon_Hf1); [ zenon_intro zenon_H47 | zenon_intro zenon_Hf4 ]. % 15.65/15.76 exact (zenon_H45 zenon_H47). % 15.65/15.76 apply (zenon_or_s _ _ zenon_Hf4); [ zenon_intro zenon_Hd8 | zenon_intro zenon_Hf5 ]. % 15.65/15.76 apply (zenon_L644_); trivial. % 15.65/15.76 apply (zenon_or_s _ _ zenon_Hf5); [ zenon_intro zenon_Hae | zenon_intro zenon_Hee ]. % 15.65/15.76 apply (zenon_L578_); trivial. % 15.65/15.76 apply (zenon_L678_); trivial. % 15.65/15.76 apply (zenon_or_s _ _ zenon_H48); [ zenon_intro zenon_H29 | zenon_intro zenon_H37 ]. % 15.65/15.76 apply (zenon_L665_); trivial. % 15.65/15.76 apply (zenon_L7_); trivial. % 15.65/15.76 apply (zenon_L593_); trivial. % 15.65/15.76 apply (zenon_L590_); trivial. % 15.65/15.76 apply (zenon_L681_); trivial. % 15.65/15.76 apply (zenon_L437_); trivial. % 15.65/15.76 apply (zenon_L739_); trivial. % 15.65/15.76 apply (zenon_L601_); trivial. % 15.65/15.76 apply (zenon_or_s _ _ zenon_H1e3); [ zenon_intro zenon_H52 | zenon_intro zenon_H156 ]. % 15.65/15.76 apply (zenon_or_s _ _ zenon_Haa); [ zenon_intro zenon_H2f | zenon_intro zenon_H35 ]. % 15.65/15.76 apply (zenon_or_s _ _ zenon_H1c3); [ zenon_intro zenon_H30 | zenon_intro zenon_H124 ]. % 15.65/15.76 apply (zenon_or_s _ _ zenon_H10f); [ zenon_intro zenon_H3c | zenon_intro zenon_Hba ]. % 15.65/15.76 apply (zenon_or_s _ _ zenon_H10c); [ zenon_intro zenon_H104 | zenon_intro zenon_H10a ]. % 15.65/15.76 apply (zenon_or_s _ _ zenon_H10e); [ zenon_intro zenon_H3d | zenon_intro zenon_H106 ]. % 15.65/15.76 apply (zenon_or_s _ _ zenon_H10d); [ zenon_intro zenon_H3e | zenon_intro zenon_H42 ]. % 15.65/15.76 apply (zenon_or_s _ _ zenon_H44); [ zenon_intro zenon_H47 | zenon_intro zenon_H46 ]. % 15.65/15.76 exact (zenon_H45 zenon_H47). % 15.65/15.76 apply (zenon_or_s _ _ zenon_H46); [ zenon_intro zenon_H22 | zenon_intro zenon_H48 ]. % 15.65/15.76 apply (zenon_or_s _ _ zenon_Hf1); [ zenon_intro zenon_H47 | zenon_intro zenon_Hf4 ]. % 15.65/15.76 exact (zenon_H45 zenon_H47). % 15.65/15.76 apply (zenon_or_s _ _ zenon_Hf4); [ zenon_intro zenon_Hd8 | zenon_intro zenon_Hf5 ]. % 15.65/15.76 apply (zenon_L644_); trivial. % 15.65/15.76 apply (zenon_or_s _ _ zenon_Hf5); [ zenon_intro zenon_Hae | zenon_intro zenon_Hee ]. % 15.65/15.76 apply (zenon_L304_); trivial. % 15.65/15.76 apply (zenon_L306_); trivial. % 15.65/15.76 apply (zenon_or_s _ _ zenon_H48); [ zenon_intro zenon_H29 | zenon_intro zenon_H37 ]. % 15.65/15.76 apply (zenon_L740_); trivial. % 15.65/15.76 apply (zenon_L7_); trivial. % 15.65/15.76 apply (zenon_L732_); trivial. % 15.65/15.76 apply (zenon_L458_); trivial. % 15.65/15.76 apply (zenon_or_s _ _ zenon_H10e); [ zenon_intro zenon_H3d | zenon_intro zenon_H106 ]. % 15.65/15.76 apply (zenon_or_s _ _ zenon_H10d); [ zenon_intro zenon_H3e | zenon_intro zenon_H42 ]. % 15.65/15.76 apply (zenon_or_s _ _ zenon_H44); [ zenon_intro zenon_H47 | zenon_intro zenon_H46 ]. % 15.65/15.76 exact (zenon_H45 zenon_H47). % 15.65/15.76 apply (zenon_or_s _ _ zenon_H46); [ zenon_intro zenon_H22 | zenon_intro zenon_H48 ]. % 15.65/15.76 apply (zenon_or_s _ _ zenon_Hf1); [ zenon_intro zenon_H47 | zenon_intro zenon_Hf4 ]. % 15.65/15.76 exact (zenon_H45 zenon_H47). % 15.65/15.76 apply (zenon_or_s _ _ zenon_Hf4); [ zenon_intro zenon_Hd8 | zenon_intro zenon_Hf5 ]. % 15.65/15.76 apply (zenon_L644_); trivial. % 15.65/15.76 apply (zenon_or_s _ _ zenon_Hf5); [ zenon_intro zenon_Hae | zenon_intro zenon_Hee ]. % 15.65/15.76 apply (zenon_L304_); trivial. % 15.65/15.76 apply (zenon_or_s _ _ zenon_H8e); [ zenon_intro zenon_H92 | zenon_intro zenon_H91 ]. % 15.65/15.76 exact (zenon_H8f zenon_H92). % 15.65/15.76 apply (zenon_or_s _ _ zenon_H91); [ zenon_intro zenon_H5d | zenon_intro zenon_H93 ]. % 15.65/15.76 apply (zenon_L214_); trivial. % 15.65/15.76 apply (zenon_or_s _ _ zenon_H93); [ zenon_intro zenon_H63 | zenon_intro zenon_H81 ]. % 15.65/15.76 apply (zenon_or_s _ _ zenon_H58); [ zenon_intro zenon_H5b | zenon_intro zenon_H5a ]. % 15.65/15.76 exact (zenon_H59 zenon_H5b). % 15.65/15.76 apply (zenon_or_s _ _ zenon_H5a); [ zenon_intro zenon_H4a | zenon_intro zenon_H5c ]. % 15.65/15.76 apply (zenon_L743_); trivial. % 15.65/15.76 apply (zenon_or_s _ _ zenon_H5c); [ zenon_intro zenon_H50 | zenon_intro zenon_H53 ]. % 15.65/15.76 apply (zenon_L31_); trivial. % 15.65/15.76 apply (zenon_L744_); trivial. % 15.65/15.76 apply (zenon_L580_); trivial. % 15.65/15.76 apply (zenon_or_s _ _ zenon_H48); [ zenon_intro zenon_H29 | zenon_intro zenon_H37 ]. % 15.65/15.76 apply (zenon_L646_); trivial. % 15.65/15.76 apply (zenon_L7_); trivial. % 15.65/15.76 apply (zenon_L102_); trivial. % 15.65/15.76 apply (zenon_L115_); trivial. % 15.65/15.76 apply (zenon_or_s _ _ zenon_Hf1); [ zenon_intro zenon_H47 | zenon_intro zenon_Hf4 ]. % 15.65/15.76 exact (zenon_H45 zenon_H47). % 15.65/15.76 apply (zenon_or_s _ _ zenon_Hf4); [ zenon_intro zenon_Hd8 | zenon_intro zenon_Hf5 ]. % 15.65/15.76 apply (zenon_L248_); trivial. % 15.65/15.76 apply (zenon_or_s _ _ zenon_Hf5); [ zenon_intro zenon_Hae | zenon_intro zenon_Hee ]. % 15.65/15.76 apply (zenon_L304_); trivial. % 15.65/15.76 apply (zenon_L79_); trivial. % 15.65/15.76 apply (zenon_L119_); trivial. % 15.65/15.76 apply (zenon_L745_); trivial. % 15.65/15.76 apply (zenon_L284_); trivial. % 15.65/15.76 apply (zenon_L237_); trivial. % 15.65/15.76 apply (zenon_L698_); trivial. % 15.65/15.76 apply (zenon_or_s _ _ zenon_H1d8); [ zenon_intro zenon_H1b4 | zenon_intro zenon_H21 ]. % 15.65/15.76 apply (zenon_or_s _ _ zenon_H1d3); [ zenon_intro zenon_Hd6 | zenon_intro zenon_H117 ]. % 15.65/15.76 apply (zenon_or_s _ _ zenon_H1d2); [ zenon_intro zenon_H182 | zenon_intro zenon_H11f ]. % 15.65/15.76 apply (zenon_or_s _ _ zenon_H1d4); [ zenon_intro zenon_H2e | zenon_intro zenon_Hdd ]. % 15.65/15.76 apply (zenon_or_s _ _ zenon_H1e3); [ zenon_intro zenon_H52 | zenon_intro zenon_H156 ]. % 15.65/15.76 apply (zenon_or_s _ _ zenon_Haa); [ zenon_intro zenon_H2f | zenon_intro zenon_H35 ]. % 15.65/15.76 apply (zenon_or_s _ _ zenon_H1c3); [ zenon_intro zenon_H30 | zenon_intro zenon_H124 ]. % 15.65/15.76 apply (zenon_or_s _ _ zenon_H10f); [ zenon_intro zenon_H3c | zenon_intro zenon_Hba ]. % 15.65/15.76 apply (zenon_or_s _ _ zenon_H10c); [ zenon_intro zenon_H104 | zenon_intro zenon_H10a ]. % 15.65/15.76 apply (zenon_or_s _ _ zenon_H10e); [ zenon_intro zenon_H3d | zenon_intro zenon_H106 ]. % 15.65/15.76 apply (zenon_or_s _ _ zenon_H10d); [ zenon_intro zenon_H3e | zenon_intro zenon_H42 ]. % 15.65/15.76 apply (zenon_L673_); trivial. % 15.65/15.76 apply (zenon_L574_); trivial. % 15.65/15.76 apply (zenon_L748_); trivial. % 15.65/15.76 apply (zenon_L750_); trivial. % 15.65/15.76 apply (zenon_or_s _ _ zenon_H10c); [ zenon_intro zenon_H104 | zenon_intro zenon_H10a ]. % 15.65/15.76 apply (zenon_or_s _ _ zenon_H10e); [ zenon_intro zenon_H3d | zenon_intro zenon_H106 ]. % 15.65/15.76 apply (zenon_L671_); trivial. % 15.65/15.76 apply (zenon_L81_); trivial. % 15.65/15.76 apply (zenon_L82_); trivial. % 15.65/15.76 apply (zenon_or_s _ _ zenon_H10f); [ zenon_intro zenon_H3c | zenon_intro zenon_Hba ]. % 15.65/15.76 apply (zenon_or_s _ _ zenon_H10c); [ zenon_intro zenon_H104 | zenon_intro zenon_H10a ]. % 15.65/15.76 apply (zenon_L675_); trivial. % 15.65/15.76 apply (zenon_L750_); trivial. % 15.65/15.76 apply (zenon_or_s _ _ zenon_H10c); [ zenon_intro zenon_H104 | zenon_intro zenon_H10a ]. % 15.65/15.76 apply (zenon_L682_); trivial. % 15.65/15.76 apply (zenon_L82_); trivial. % 15.65/15.76 apply (zenon_L751_); trivial. % 15.65/15.76 apply (zenon_or_s _ _ zenon_Haa); [ zenon_intro zenon_H2f | zenon_intro zenon_H35 ]. % 15.65/15.76 apply (zenon_or_s _ _ zenon_H1c3); [ zenon_intro zenon_H30 | zenon_intro zenon_H124 ]. % 15.65/15.76 apply (zenon_or_s _ _ zenon_H10f); [ zenon_intro zenon_H3c | zenon_intro zenon_Hba ]. % 15.65/15.76 apply (zenon_or_s _ _ zenon_H10e); [ zenon_intro zenon_H3d | zenon_intro zenon_H106 ]. % 15.65/15.76 apply (zenon_or_s _ _ zenon_H10d); [ zenon_intro zenon_H3e | zenon_intro zenon_H42 ]. % 15.65/15.76 apply (zenon_L407_); trivial. % 15.65/15.76 apply (zenon_L566_); trivial. % 15.65/15.76 apply (zenon_or_s _ _ zenon_H44); [ zenon_intro zenon_H47 | zenon_intro zenon_H46 ]. % 15.65/15.76 exact (zenon_H45 zenon_H47). % 15.65/15.76 apply (zenon_or_s _ _ zenon_H46); [ zenon_intro zenon_H22 | zenon_intro zenon_H48 ]. % 15.65/15.76 apply (zenon_L644_); trivial. % 15.65/15.76 apply (zenon_or_s _ _ zenon_H48); [ zenon_intro zenon_H29 | zenon_intro zenon_H37 ]. % 15.65/15.76 apply (zenon_L5_); trivial. % 15.65/15.76 apply (zenon_or_s _ _ zenon_H8e); [ zenon_intro zenon_H92 | zenon_intro zenon_H91 ]. % 15.65/15.76 exact (zenon_H8f zenon_H92). % 15.65/15.76 apply (zenon_or_s _ _ zenon_H91); [ zenon_intro zenon_H5d | zenon_intro zenon_H93 ]. % 15.65/15.76 apply (zenon_L534_); trivial. % 15.65/15.76 apply (zenon_or_s _ _ zenon_H93); [ zenon_intro zenon_H63 | zenon_intro zenon_H81 ]. % 15.65/15.76 apply (zenon_or_s _ _ zenon_Heb); [ zenon_intro zenon_H92 | zenon_intro zenon_Hec ]. % 15.65/15.76 exact (zenon_H8f zenon_H92). % 15.65/15.76 apply (zenon_or_s _ _ zenon_Hec); [ zenon_intro zenon_H68 | zenon_intro zenon_Hed ]. % 15.65/15.76 apply (zenon_L638_); trivial. % 15.65/15.76 apply (zenon_or_s _ _ zenon_Hed); [ zenon_intro zenon_Hdd | zenon_intro zenon_He9 ]. % 15.65/15.76 apply (zenon_L456_); trivial. % 15.65/15.76 apply (zenon_L746_); trivial. % 15.65/15.76 apply (zenon_L33_); trivial. % 15.65/15.76 apply (zenon_or_s _ _ zenon_H10e); [ zenon_intro zenon_H3d | zenon_intro zenon_H106 ]. % 15.65/15.76 apply (zenon_or_s _ _ zenon_H44); [ zenon_intro zenon_H47 | zenon_intro zenon_H46 ]. % 15.65/15.76 exact (zenon_H45 zenon_H47). % 15.65/15.76 apply (zenon_or_s _ _ zenon_H46); [ zenon_intro zenon_H22 | zenon_intro zenon_H48 ]. % 15.65/15.76 apply (zenon_L644_); trivial. % 15.65/15.76 apply (zenon_or_s _ _ zenon_H48); [ zenon_intro zenon_H29 | zenon_intro zenon_H37 ]. % 15.65/15.76 apply (zenon_L5_); trivial. % 15.65/15.76 apply (zenon_L688_); trivial. % 15.65/15.76 apply (zenon_L81_); trivial. % 15.65/15.76 apply (zenon_L256_); trivial. % 15.65/15.76 apply (zenon_L134_); trivial. % 15.65/15.76 apply (zenon_or_s _ _ zenon_H1e3); [ zenon_intro zenon_H52 | zenon_intro zenon_H156 ]. % 15.65/15.76 apply (zenon_or_s _ _ zenon_H1c3); [ zenon_intro zenon_H30 | zenon_intro zenon_H124 ]. % 15.65/15.76 apply (zenon_or_s _ _ zenon_H10f); [ zenon_intro zenon_H3c | zenon_intro zenon_Hba ]. % 15.65/15.76 apply (zenon_or_s _ _ zenon_H10c); [ zenon_intro zenon_H104 | zenon_intro zenon_H10a ]. % 15.65/15.76 apply (zenon_or_s _ _ zenon_H10e); [ zenon_intro zenon_H3d | zenon_intro zenon_H106 ]. % 15.65/15.76 apply (zenon_or_s _ _ zenon_H10d); [ zenon_intro zenon_H3e | zenon_intro zenon_H42 ]. % 15.65/15.76 apply (zenon_L672_); trivial. % 15.65/15.76 apply (zenon_L576_); trivial. % 15.65/15.76 apply (zenon_L456_); trivial. % 15.65/15.76 apply (zenon_or_s _ _ zenon_H10e); [ zenon_intro zenon_H3d | zenon_intro zenon_H106 ]. % 15.65/15.76 apply (zenon_or_s _ _ zenon_H10d); [ zenon_intro zenon_H3e | zenon_intro zenon_H42 ]. % 15.65/15.76 apply (zenon_or_s _ _ zenon_H44); [ zenon_intro zenon_H47 | zenon_intro zenon_H46 ]. % 15.65/15.76 exact (zenon_H45 zenon_H47). % 15.65/15.76 apply (zenon_or_s _ _ zenon_H46); [ zenon_intro zenon_H22 | zenon_intro zenon_H48 ]. % 15.65/15.76 apply (zenon_L644_); trivial. % 15.65/15.76 apply (zenon_or_s _ _ zenon_H48); [ zenon_intro zenon_H29 | zenon_intro zenon_H37 ]. % 15.65/15.76 apply (zenon_L749_); trivial. % 15.65/15.76 apply (zenon_L7_); trivial. % 15.65/15.76 apply (zenon_L102_); trivial. % 15.65/15.76 apply (zenon_L115_); trivial. % 15.65/15.76 apply (zenon_or_s _ _ zenon_H10c); [ zenon_intro zenon_H104 | zenon_intro zenon_H10a ]. % 15.65/15.76 apply (zenon_or_s _ _ zenon_H10e); [ zenon_intro zenon_H3d | zenon_intro zenon_H106 ]. % 15.65/15.76 apply (zenon_L659_); trivial. % 15.65/15.76 apply (zenon_L81_); trivial. % 15.65/15.76 apply (zenon_L82_); trivial. % 15.65/15.76 apply (zenon_L119_); trivial. % 15.65/15.76 apply (zenon_L284_); trivial. % 15.65/15.76 apply (zenon_L224_); trivial. % 15.65/15.76 apply (zenon_L248_); trivial. % 15.65/15.76 apply (zenon_L61_); trivial. % 15.65/15.76 apply (zenon_L562_); trivial. % 15.65/15.76 apply (zenon_L567_); trivial. % 15.65/15.76 apply (zenon_L610_); trivial. % 15.65/15.76 apply (zenon_or_s _ _ zenon_H356); [ zenon_intro zenon_H21 | zenon_intro zenon_H357 ]. % 15.65/15.76 apply (zenon_L698_); trivial. % 15.65/15.76 apply (zenon_or_s _ _ zenon_H357); [ zenon_intro zenon_H35 | zenon_intro zenon_H42 ]. % 15.65/15.76 apply (zenon_or_s _ _ zenon_H249); [ zenon_intro zenon_H20 | zenon_intro zenon_H1f ]. % 15.65/15.76 apply (zenon_or_s _ _ zenon_H24b); [ zenon_intro zenon_H45 | zenon_intro zenon_H49 ]. % 15.65/15.76 apply (zenon_or_s _ _ zenon_H24a); [ zenon_intro zenon_H8f | zenon_intro zenon_Hab ]. % 15.65/15.76 apply (zenon_or_s _ _ zenon_H236); [ zenon_intro zenon_H59 | zenon_intro zenon_Hca ]. % 15.65/15.76 apply (zenon_or_s _ _ zenon_H1e4); [ zenon_intro zenon_H145 | zenon_intro zenon_Hd8 ]. % 15.65/15.76 apply (zenon_or_s _ _ zenon_H1d8); [ zenon_intro zenon_H1b4 | zenon_intro zenon_H21 ]. % 15.65/15.76 apply (zenon_or_s _ _ zenon_H1d3); [ zenon_intro zenon_Hd6 | zenon_intro zenon_H117 ]. % 15.65/15.76 apply (zenon_or_s _ _ zenon_H1d2); [ zenon_intro zenon_H182 | zenon_intro zenon_H11f ]. % 15.65/15.76 apply (zenon_L360_); trivial. % 15.65/15.76 apply (zenon_or_s _ _ zenon_H1d4); [ zenon_intro zenon_H2e | zenon_intro zenon_Hdd ]. % 15.65/15.76 apply (zenon_or_s _ _ zenon_H1e3); [ zenon_intro zenon_H52 | zenon_intro zenon_H156 ]. % 15.65/15.76 apply (zenon_or_s _ _ zenon_H10f); [ zenon_intro zenon_H3c | zenon_intro zenon_Hba ]. % 15.65/15.76 apply (zenon_or_s _ _ zenon_H10c); [ zenon_intro zenon_H104 | zenon_intro zenon_H10a ]. % 15.65/15.76 apply (zenon_or_s _ _ zenon_H10e); [ zenon_intro zenon_H3d | zenon_intro zenon_H106 ]. % 15.65/15.76 apply (zenon_L487_); trivial. % 15.65/15.76 apply (zenon_or_s _ _ zenon_H10d); [ zenon_intro zenon_H3e | zenon_intro zenon_H42 ]. % 15.65/15.76 apply (zenon_or_s _ _ zenon_H110); [ zenon_intro zenon_H1f | zenon_intro zenon_H111 ]. % 15.65/15.76 exact (zenon_H20 zenon_H1f). % 15.65/15.76 apply (zenon_or_s _ _ zenon_H111); [ zenon_intro zenon_H49 | zenon_intro zenon_H112 ]. % 15.65/15.76 apply (zenon_L131_); trivial. % 15.65/15.76 apply (zenon_or_s _ _ zenon_H112); [ zenon_intro zenon_Hab | zenon_intro zenon_Hca ]. % 15.65/15.76 apply (zenon_L753_); trivial. % 15.65/15.76 apply (zenon_L774_); trivial. % 15.65/15.76 apply (zenon_L153_); trivial. % 15.65/15.76 apply (zenon_L554_); trivial. % 15.65/15.76 apply (zenon_L359_); trivial. % 15.65/15.76 apply (zenon_L134_); trivial. % 15.65/15.76 apply (zenon_L161_); trivial. % 15.65/15.76 apply (zenon_or_s _ _ zenon_H1d2); [ zenon_intro zenon_H182 | zenon_intro zenon_H11f ]. % 15.65/15.76 apply (zenon_or_s _ _ zenon_H1d4); [ zenon_intro zenon_H2e | zenon_intro zenon_Hdd ]. % 15.65/15.76 apply (zenon_or_s _ _ zenon_H1c3); [ zenon_intro zenon_H30 | zenon_intro zenon_H124 ]. % 15.65/15.76 apply (zenon_or_s _ _ zenon_H10f); [ zenon_intro zenon_H3c | zenon_intro zenon_Hba ]. % 15.65/15.76 apply (zenon_L503_); trivial. % 15.65/15.76 apply (zenon_or_s _ _ zenon_H10c); [ zenon_intro zenon_H104 | zenon_intro zenon_H10a ]. % 15.65/15.76 apply (zenon_or_s _ _ zenon_H10e); [ zenon_intro zenon_H3d | zenon_intro zenon_H106 ]. % 15.65/15.76 apply (zenon_or_s _ _ zenon_H110); [ zenon_intro zenon_H1f | zenon_intro zenon_H111 ]. % 15.65/15.76 exact (zenon_H20 zenon_H1f). % 15.65/15.76 apply (zenon_or_s _ _ zenon_H111); [ zenon_intro zenon_H49 | zenon_intro zenon_H112 ]. % 15.65/15.76 apply (zenon_L556_); trivial. % 15.65/15.76 apply (zenon_or_s _ _ zenon_H112); [ zenon_intro zenon_Hab | zenon_intro zenon_Hca ]. % 15.65/15.76 apply (zenon_L766_); trivial. % 15.65/15.76 apply (zenon_L438_); trivial. % 15.65/15.76 apply (zenon_L81_); trivial. % 15.65/15.76 apply (zenon_L82_); trivial. % 15.65/15.76 apply (zenon_L137_); trivial. % 15.65/15.76 apply (zenon_L161_); trivial. % 15.65/15.76 apply (zenon_L237_); trivial. % 15.65/15.76 apply (zenon_L698_); trivial. % 15.65/15.76 apply (zenon_L775_); trivial. % 15.65/15.76 apply (zenon_or_s _ _ zenon_H1e4); [ zenon_intro zenon_H145 | zenon_intro zenon_Hd8 ]. % 15.65/15.76 apply (zenon_or_s _ _ zenon_H1d8); [ zenon_intro zenon_H1b4 | zenon_intro zenon_H21 ]. % 15.65/15.76 apply (zenon_or_s _ _ zenon_H1d3); [ zenon_intro zenon_Hd6 | zenon_intro zenon_H117 ]. % 15.65/15.76 apply (zenon_or_s _ _ zenon_H1d2); [ zenon_intro zenon_H182 | zenon_intro zenon_H11f ]. % 15.65/15.76 apply (zenon_L343_); trivial. % 15.65/15.76 apply (zenon_or_s _ _ zenon_H1d4); [ zenon_intro zenon_H2e | zenon_intro zenon_Hdd ]. % 15.65/15.76 apply (zenon_or_s _ _ zenon_H10f); [ zenon_intro zenon_H3c | zenon_intro zenon_Hba ]. % 15.65/15.76 apply (zenon_or_s _ _ zenon_H10c); [ zenon_intro zenon_H104 | zenon_intro zenon_H10a ]. % 15.65/15.76 apply (zenon_or_s _ _ zenon_H10e); [ zenon_intro zenon_H3d | zenon_intro zenon_H106 ]. % 15.65/15.76 apply (zenon_L424_); trivial. % 15.65/15.76 apply (zenon_L774_); trivial. % 15.65/15.76 apply (zenon_L554_); trivial. % 15.65/15.76 apply (zenon_L359_); trivial. % 15.65/15.76 apply (zenon_L161_); trivial. % 15.65/15.76 apply (zenon_L438_); trivial. % 15.65/15.76 apply (zenon_L698_); trivial. % 15.65/15.76 apply (zenon_L775_); trivial. % 15.65/15.76 apply (zenon_L770_); trivial. % 15.65/15.76 apply (zenon_or_s _ _ zenon_H24a); [ zenon_intro zenon_H8f | zenon_intro zenon_Hab ]. % 15.65/15.76 apply (zenon_or_s _ _ zenon_H236); [ zenon_intro zenon_H59 | zenon_intro zenon_Hca ]. % 15.65/15.76 apply (zenon_or_s _ _ zenon_H1e4); [ zenon_intro zenon_H145 | zenon_intro zenon_Hd8 ]. % 15.65/15.76 apply (zenon_or_s _ _ zenon_H1d8); [ zenon_intro zenon_H1b4 | zenon_intro zenon_H21 ]. % 15.65/15.76 apply (zenon_L557_); trivial. % 15.65/15.76 apply (zenon_L698_); trivial. % 15.65/15.76 apply (zenon_L484_); trivial. % 15.65/15.76 apply (zenon_L463_); trivial. % 15.65/15.76 apply (zenon_L485_); trivial. % 15.65/15.76 apply (zenon_or_s _ _ zenon_H24b); [ zenon_intro zenon_H45 | zenon_intro zenon_H49 ]. % 15.65/15.76 apply (zenon_or_s _ _ zenon_H24a); [ zenon_intro zenon_H8f | zenon_intro zenon_Hab ]. % 15.65/15.76 apply (zenon_or_s _ _ zenon_H236); [ zenon_intro zenon_H59 | zenon_intro zenon_Hca ]. % 15.65/15.76 apply (zenon_or_s _ _ zenon_H1e4); [ zenon_intro zenon_H145 | zenon_intro zenon_Hd8 ]. % 15.65/15.76 apply (zenon_or_s _ _ zenon_H1d8); [ zenon_intro zenon_H1b4 | zenon_intro zenon_H21 ]. % 15.65/15.76 apply (zenon_or_s _ _ zenon_H1d3); [ zenon_intro zenon_Hd6 | zenon_intro zenon_H117 ]. % 15.65/15.76 apply (zenon_or_s _ _ zenon_H1d2); [ zenon_intro zenon_H182 | zenon_intro zenon_H11f ]. % 15.65/15.76 apply (zenon_or_s _ _ zenon_H1d4); [ zenon_intro zenon_H2e | zenon_intro zenon_Hdd ]. % 15.65/15.76 apply (zenon_or_s _ _ zenon_H1e3); [ zenon_intro zenon_H52 | zenon_intro zenon_H156 ]. % 15.65/15.76 apply (zenon_L685_); trivial. % 15.65/15.76 apply (zenon_L134_); trivial. % 15.65/15.76 apply (zenon_L161_); trivial. % 15.65/15.76 apply (zenon_or_s _ _ zenon_H1e3); [ zenon_intro zenon_H52 | zenon_intro zenon_H156 ]. % 15.65/15.76 apply (zenon_L692_); trivial. % 15.65/15.76 apply (zenon_L134_); trivial. % 15.65/15.76 apply (zenon_or_s _ _ zenon_H1d2); [ zenon_intro zenon_H182 | zenon_intro zenon_H11f ]. % 15.65/15.76 apply (zenon_L745_); trivial. % 15.65/15.76 apply (zenon_L237_); trivial. % 15.65/15.76 apply (zenon_L698_); trivial. % 15.65/15.76 apply (zenon_L736_); trivial. % 15.65/15.76 apply (zenon_L562_); trivial. % 15.65/15.76 apply (zenon_L567_); trivial. % 15.65/15.76 apply (zenon_L610_); trivial. % 15.65/15.76 apply (zenon_L733_); trivial. % 15.65/15.76 apply (zenon_or_s _ _ zenon_H35a); [ zenon_intro zenon_H35f | zenon_intro zenon_H35e ]. % 15.65/15.76 apply (zenon_and_s _ _ zenon_H35f). zenon_intro zenon_H295. zenon_intro zenon_H360. % 15.65/15.76 apply (zenon_and_s _ _ zenon_H360). zenon_intro zenon_H290. zenon_intro zenon_H361. % 15.65/15.76 apply (zenon_and_s _ _ zenon_H361). zenon_intro zenon_H294. zenon_intro zenon_H28a. % 15.65/15.76 apply (zenon_or_s _ _ zenon_H343); [ zenon_intro zenon_H1f | zenon_intro zenon_H356 ]. % 15.65/15.76 apply (zenon_or_s _ _ zenon_H24b); [ zenon_intro zenon_H45 | zenon_intro zenon_H49 ]. % 15.65/15.76 apply (zenon_or_s _ _ zenon_H24a); [ zenon_intro zenon_H8f | zenon_intro zenon_Hab ]. % 15.65/15.76 apply (zenon_or_s _ _ zenon_H236); [ zenon_intro zenon_H59 | zenon_intro zenon_Hca ]. % 15.65/15.76 apply (zenon_or_s _ _ zenon_H1e4); [ zenon_intro zenon_H145 | zenon_intro zenon_Hd8 ]. % 15.65/15.76 apply (zenon_or_s _ _ zenon_H1d8); [ zenon_intro zenon_H1b4 | zenon_intro zenon_H21 ]. % 15.65/15.76 apply (zenon_or_s _ _ zenon_H1d3); [ zenon_intro zenon_Hd6 | zenon_intro zenon_H117 ]. % 15.65/15.76 apply (zenon_or_s _ _ zenon_H1d2); [ zenon_intro zenon_H182 | zenon_intro zenon_H11f ]. % 15.65/15.76 apply (zenon_or_s _ _ zenon_H1d4); [ zenon_intro zenon_H2e | zenon_intro zenon_Hdd ]. % 15.65/15.76 apply (zenon_or_s _ _ zenon_H1e3); [ zenon_intro zenon_H52 | zenon_intro zenon_H156 ]. % 15.65/15.76 apply (zenon_or_s _ _ zenon_Haa); [ zenon_intro zenon_H2f | zenon_intro zenon_H35 ]. % 15.65/15.76 apply (zenon_or_s _ _ zenon_H1c3); [ zenon_intro zenon_H30 | zenon_intro zenon_H124 ]. % 15.65/15.76 apply (zenon_or_s _ _ zenon_H10f); [ zenon_intro zenon_H3c | zenon_intro zenon_Hba ]. % 15.65/15.76 apply (zenon_or_s _ _ zenon_H10c); [ zenon_intro zenon_H104 | zenon_intro zenon_H10a ]. % 15.65/15.76 apply (zenon_or_s _ _ zenon_H10e); [ zenon_intro zenon_H3d | zenon_intro zenon_H106 ]. % 15.65/15.76 apply (zenon_or_s _ _ zenon_H10d); [ zenon_intro zenon_H3e | zenon_intro zenon_H42 ]. % 15.65/15.76 apply (zenon_L560_); trivial. % 15.65/15.76 apply (zenon_L802_); trivial. % 15.65/15.76 apply (zenon_or_s _ _ zenon_H10d); [ zenon_intro zenon_H3e | zenon_intro zenon_H42 ]. % 15.65/15.76 apply (zenon_or_s _ _ zenon_H44); [ zenon_intro zenon_H47 | zenon_intro zenon_H46 ]. % 15.65/15.76 exact (zenon_H45 zenon_H47). % 15.65/15.76 apply (zenon_or_s _ _ zenon_H46); [ zenon_intro zenon_H22 | zenon_intro zenon_H48 ]. % 15.65/15.76 apply (zenon_or_s _ _ zenon_Hf1); [ zenon_intro zenon_H47 | zenon_intro zenon_Hf4 ]. % 15.65/15.76 exact (zenon_H45 zenon_H47). % 15.65/15.76 apply (zenon_or_s _ _ zenon_Hf4); [ zenon_intro zenon_Hd8 | zenon_intro zenon_Hf5 ]. % 15.65/15.76 apply (zenon_L815_); trivial. % 15.65/15.76 apply (zenon_or_s _ _ zenon_Hf5); [ zenon_intro zenon_Hae | zenon_intro zenon_Hee ]. % 15.65/15.76 apply (zenon_L816_); trivial. % 15.65/15.76 apply (zenon_L306_); trivial. % 15.65/15.76 apply (zenon_or_s _ _ zenon_H48); [ zenon_intro zenon_H29 | zenon_intro zenon_H37 ]. % 15.65/15.76 apply (zenon_L5_); trivial. % 15.65/15.76 apply (zenon_or_s _ _ zenon_Hf1); [ zenon_intro zenon_H47 | zenon_intro zenon_Hf4 ]. % 15.65/15.76 exact (zenon_H45 zenon_H47). % 15.65/15.76 apply (zenon_or_s _ _ zenon_Hf4); [ zenon_intro zenon_Hd8 | zenon_intro zenon_Hf5 ]. % 15.65/15.76 apply (zenon_L747_); trivial. % 15.65/15.76 apply (zenon_or_s _ _ zenon_Hf5); [ zenon_intro zenon_Hae | zenon_intro zenon_Hee ]. % 15.65/15.76 apply (zenon_or_s _ _ zenon_H8e); [ zenon_intro zenon_H92 | zenon_intro zenon_H91 ]. % 15.65/15.76 exact (zenon_H8f zenon_H92). % 15.65/15.76 apply (zenon_or_s _ _ zenon_H91); [ zenon_intro zenon_H5d | zenon_intro zenon_H93 ]. % 15.65/15.76 apply (zenon_L214_); trivial. % 15.65/15.76 apply (zenon_or_s _ _ zenon_H93); [ zenon_intro zenon_H63 | zenon_intro zenon_H81 ]. % 15.65/15.76 apply (zenon_or_s _ _ zenon_Heb); [ zenon_intro zenon_H92 | zenon_intro zenon_Hec ]. % 15.65/15.76 exact (zenon_H8f zenon_H92). % 15.65/15.76 apply (zenon_or_s _ _ zenon_Hec); [ zenon_intro zenon_H68 | zenon_intro zenon_Hed ]. % 15.65/15.76 apply (zenon_L528_); trivial. % 15.65/15.76 apply (zenon_or_s _ _ zenon_Hed); [ zenon_intro zenon_Hdd | zenon_intro zenon_He9 ]. % 15.65/15.76 apply (zenon_L821_); trivial. % 15.65/15.76 apply (zenon_L661_); trivial. % 15.65/15.76 apply (zenon_L33_); trivial. % 15.65/15.76 apply (zenon_L306_); trivial. % 15.65/15.76 apply (zenon_L820_); trivial. % 15.65/15.76 apply (zenon_L849_); trivial. % 15.65/15.76 apply (zenon_or_s _ _ zenon_H10c); [ zenon_intro zenon_H104 | zenon_intro zenon_H10a ]. % 15.65/15.76 apply (zenon_or_s _ _ zenon_H10e); [ zenon_intro zenon_H3d | zenon_intro zenon_H106 ]. % 15.65/15.76 apply (zenon_or_s _ _ zenon_H10d); [ zenon_intro zenon_H3e | zenon_intro zenon_H42 ]. % 15.65/15.76 apply (zenon_or_s _ _ zenon_Hf1); [ zenon_intro zenon_H47 | zenon_intro zenon_Hf4 ]. % 15.65/15.76 exact (zenon_H45 zenon_H47). % 15.65/15.76 apply (zenon_or_s _ _ zenon_Hf4); [ zenon_intro zenon_Hd8 | zenon_intro zenon_Hf5 ]. % 15.65/15.76 apply (zenon_L833_); trivial. % 15.65/15.76 apply (zenon_or_s _ _ zenon_Hf5); [ zenon_intro zenon_Hae | zenon_intro zenon_Hee ]. % 15.65/15.76 apply (zenon_L78_); trivial. % 15.65/15.76 apply (zenon_L79_); trivial. % 15.65/15.76 apply (zenon_L43_); trivial. % 15.65/15.76 apply (zenon_L81_); trivial. % 15.65/15.76 apply (zenon_L82_); trivial. % 15.65/15.76 apply (zenon_or_s _ _ zenon_H10f); [ zenon_intro zenon_H3c | zenon_intro zenon_Hba ]. % 15.65/15.76 apply (zenon_or_s _ _ zenon_H10c); [ zenon_intro zenon_H104 | zenon_intro zenon_H10a ]. % 15.65/15.76 apply (zenon_or_s _ _ zenon_H10e); [ zenon_intro zenon_H3d | zenon_intro zenon_H106 ]. % 15.65/15.76 apply (zenon_or_s _ _ zenon_H10d); [ zenon_intro zenon_H3e | zenon_intro zenon_H42 ]. % 15.65/15.76 apply (zenon_L854_); trivial. % 15.65/15.76 apply (zenon_L799_); trivial. % 15.65/15.76 apply (zenon_or_s _ _ zenon_H10d); [ zenon_intro zenon_H3e | zenon_intro zenon_H42 ]. % 15.65/15.76 apply (zenon_or_s _ _ zenon_H44); [ zenon_intro zenon_H47 | zenon_intro zenon_H46 ]. % 15.65/15.76 exact (zenon_H45 zenon_H47). % 15.65/15.76 apply (zenon_or_s _ _ zenon_H46); [ zenon_intro zenon_H22 | zenon_intro zenon_H48 ]. % 15.65/15.76 apply (zenon_or_s _ _ zenon_Hf1); [ zenon_intro zenon_H47 | zenon_intro zenon_Hf4 ]. % 15.65/15.76 exact (zenon_H45 zenon_H47). % 15.65/15.76 apply (zenon_or_s _ _ zenon_Hf4); [ zenon_intro zenon_Hd8 | zenon_intro zenon_Hf5 ]. % 15.65/15.76 apply (zenon_L837_); trivial. % 15.65/15.76 apply (zenon_or_s _ _ zenon_Hf5); [ zenon_intro zenon_Hae | zenon_intro zenon_Hee ]. % 15.65/15.76 apply (zenon_L816_); trivial. % 15.65/15.76 apply (zenon_or_s _ _ zenon_H8e); [ zenon_intro zenon_H92 | zenon_intro zenon_H91 ]. % 15.65/15.76 exact (zenon_H8f zenon_H92). % 15.65/15.76 apply (zenon_or_s _ _ zenon_H91); [ zenon_intro zenon_H5d | zenon_intro zenon_H93 ]. % 15.65/15.76 apply (zenon_L214_); trivial. % 15.65/15.76 apply (zenon_or_s _ _ zenon_H93); [ zenon_intro zenon_H63 | zenon_intro zenon_H81 ]. % 15.65/15.76 apply (zenon_L860_); trivial. % 15.65/15.76 apply (zenon_L663_); trivial. % 15.65/15.76 apply (zenon_or_s _ _ zenon_H48); [ zenon_intro zenon_H29 | zenon_intro zenon_H37 ]. % 15.65/15.76 apply (zenon_L665_); trivial. % 15.65/15.76 apply (zenon_or_s _ _ zenon_Hf1); [ zenon_intro zenon_H47 | zenon_intro zenon_Hf4 ]. % 15.65/15.76 exact (zenon_H45 zenon_H47). % 15.65/15.76 apply (zenon_or_s _ _ zenon_Hf4); [ zenon_intro zenon_Hd8 | zenon_intro zenon_Hf5 ]. % 15.65/15.76 apply (zenon_L842_); trivial. % 15.65/15.76 apply (zenon_or_s _ _ zenon_Hf5); [ zenon_intro zenon_Hae | zenon_intro zenon_Hee ]. % 15.65/15.76 apply (zenon_or_s _ _ zenon_H8e); [ zenon_intro zenon_H92 | zenon_intro zenon_H91 ]. % 15.65/15.76 exact (zenon_H8f zenon_H92). % 15.65/15.76 apply (zenon_or_s _ _ zenon_H91); [ zenon_intro zenon_H5d | zenon_intro zenon_H93 ]. % 15.65/15.76 apply (zenon_L214_); trivial. % 15.65/15.76 apply (zenon_or_s _ _ zenon_H93); [ zenon_intro zenon_H63 | zenon_intro zenon_H81 ]. % 15.65/15.76 apply (zenon_or_s _ _ zenon_Heb); [ zenon_intro zenon_H92 | zenon_intro zenon_Hec ]. % 15.65/15.76 exact (zenon_H8f zenon_H92). % 15.65/15.76 apply (zenon_or_s _ _ zenon_Hec); [ zenon_intro zenon_H68 | zenon_intro zenon_Hed ]. % 15.65/15.76 apply (zenon_L528_); trivial. % 15.65/15.76 apply (zenon_or_s _ _ zenon_Hed); [ zenon_intro zenon_Hdd | zenon_intro zenon_He9 ]. % 15.65/15.76 apply (zenon_L304_); trivial. % 15.65/15.76 apply (zenon_or_s _ _ zenon_H58); [ zenon_intro zenon_H5b | zenon_intro zenon_H5a ]. % 15.65/15.76 exact (zenon_H59 zenon_H5b). % 15.65/15.76 apply (zenon_or_s _ _ zenon_H5a); [ zenon_intro zenon_H4a | zenon_intro zenon_H5c ]. % 15.65/15.76 apply (zenon_or_s _ _ zenon_Hbe); [ zenon_intro zenon_H5b | zenon_intro zenon_Hbf ]. % 15.65/15.76 exact (zenon_H59 zenon_H5b). % 15.65/15.76 apply (zenon_or_s _ _ zenon_Hbf); [ zenon_intro zenon_H69 | zenon_intro zenon_Hc0 ]. % 15.65/15.76 apply (zenon_L679_); trivial. % 15.65/15.76 apply (zenon_or_s _ _ zenon_Hc0); [ zenon_intro zenon_Haf | zenon_intro zenon_Hba ]. % 15.65/15.76 apply (zenon_L859_); trivial. % 15.65/15.76 apply (zenon_L220_); trivial. % 15.65/15.76 apply (zenon_or_s _ _ zenon_H5c); [ zenon_intro zenon_H50 | zenon_intro zenon_H53 ]. % 15.65/15.76 apply (zenon_L533_); trivial. % 15.65/15.76 apply (zenon_L32_); trivial. % 15.65/15.76 apply (zenon_L107_); trivial. % 15.65/15.76 apply (zenon_or_s _ _ zenon_H8e); [ zenon_intro zenon_H92 | zenon_intro zenon_H91 ]. % 15.65/15.76 exact (zenon_H8f zenon_H92). % 15.65/15.76 apply (zenon_or_s _ _ zenon_H91); [ zenon_intro zenon_H5d | zenon_intro zenon_H93 ]. % 15.65/15.76 apply (zenon_L214_); trivial. % 15.65/15.76 apply (zenon_or_s _ _ zenon_H93); [ zenon_intro zenon_H63 | zenon_intro zenon_H81 ]. % 15.65/15.76 apply (zenon_L860_); trivial. % 15.65/15.76 apply (zenon_L33_); trivial. % 15.65/15.76 apply (zenon_L153_); trivial. % 15.65/15.76 apply (zenon_L849_); trivial. % 15.65/15.76 apply (zenon_L861_); trivial. % 15.65/15.76 apply (zenon_L794_); trivial. % 15.65/15.76 apply (zenon_or_s _ _ zenon_Haa); [ zenon_intro zenon_H2f | zenon_intro zenon_H35 ]. % 15.65/15.76 apply (zenon_or_s _ _ zenon_H1c3); [ zenon_intro zenon_H30 | zenon_intro zenon_H124 ]. % 15.65/15.76 apply (zenon_or_s _ _ zenon_H10f); [ zenon_intro zenon_H3c | zenon_intro zenon_Hba ]. % 15.65/15.76 apply (zenon_or_s _ _ zenon_H10c); [ zenon_intro zenon_H104 | zenon_intro zenon_H10a ]. % 15.65/15.76 apply (zenon_or_s _ _ zenon_H10e); [ zenon_intro zenon_H3d | zenon_intro zenon_H106 ]. % 15.65/15.76 apply (zenon_or_s _ _ zenon_H10d); [ zenon_intro zenon_H3e | zenon_intro zenon_H42 ]. % 15.65/15.76 apply (zenon_L560_); trivial. % 15.65/15.76 apply (zenon_L800_); trivial. % 15.65/15.76 apply (zenon_or_s _ _ zenon_H10d); [ zenon_intro zenon_H3e | zenon_intro zenon_H42 ]. % 15.65/15.76 apply (zenon_or_s _ _ zenon_H44); [ zenon_intro zenon_H47 | zenon_intro zenon_H46 ]. % 15.65/15.76 exact (zenon_H45 zenon_H47). % 15.65/15.76 apply (zenon_or_s _ _ zenon_H46); [ zenon_intro zenon_H22 | zenon_intro zenon_H48 ]. % 15.65/15.76 apply (zenon_L862_); trivial. % 15.65/15.76 apply (zenon_or_s _ _ zenon_H48); [ zenon_intro zenon_H29 | zenon_intro zenon_H37 ]. % 15.65/15.76 apply (zenon_L665_); trivial. % 15.65/15.76 apply (zenon_L864_); trivial. % 15.65/15.76 apply (zenon_L153_); trivial. % 15.65/15.76 apply (zenon_or_s _ _ zenon_H10e); [ zenon_intro zenon_H3d | zenon_intro zenon_H106 ]. % 15.65/15.76 apply (zenon_or_s _ _ zenon_H10d); [ zenon_intro zenon_H3e | zenon_intro zenon_H42 ]. % 15.65/15.76 apply (zenon_or_s _ _ zenon_H44); [ zenon_intro zenon_H47 | zenon_intro zenon_H46 ]. % 15.65/15.76 exact (zenon_H45 zenon_H47). % 15.65/15.76 apply (zenon_or_s _ _ zenon_H46); [ zenon_intro zenon_H22 | zenon_intro zenon_H48 ]. % 15.65/15.76 apply (zenon_L862_); trivial. % 15.65/15.76 apply (zenon_or_s _ _ zenon_H48); [ zenon_intro zenon_H29 | zenon_intro zenon_H37 ]. % 15.65/15.76 apply (zenon_L5_); trivial. % 15.65/15.76 apply (zenon_L7_); trivial. % 15.65/15.76 apply (zenon_L102_); trivial. % 15.65/15.76 apply (zenon_L115_); trivial. % 15.65/15.76 apply (zenon_L865_); trivial. % 15.65/15.76 apply (zenon_L256_); trivial. % 15.65/15.76 apply (zenon_L134_); trivial. % 15.65/15.76 apply (zenon_or_s _ _ zenon_H1e3); [ zenon_intro zenon_H52 | zenon_intro zenon_H156 ]. % 15.65/15.76 apply (zenon_or_s _ _ zenon_Haa); [ zenon_intro zenon_H2f | zenon_intro zenon_H35 ]. % 15.65/15.76 apply (zenon_or_s _ _ zenon_H1c3); [ zenon_intro zenon_H30 | zenon_intro zenon_H124 ]. % 15.65/15.76 apply (zenon_or_s _ _ zenon_H10f); [ zenon_intro zenon_H3c | zenon_intro zenon_Hba ]. % 15.65/15.76 apply (zenon_or_s _ _ zenon_H10c); [ zenon_intro zenon_H104 | zenon_intro zenon_H10a ]. % 15.65/15.76 apply (zenon_or_s _ _ zenon_H10e); [ zenon_intro zenon_H3d | zenon_intro zenon_H106 ]. % 15.65/15.76 apply (zenon_or_s _ _ zenon_H10d); [ zenon_intro zenon_H3e | zenon_intro zenon_H42 ]. % 15.65/15.76 apply (zenon_L560_); trivial. % 15.65/15.76 apply (zenon_L868_); trivial. % 15.65/15.76 apply (zenon_L821_); trivial. % 15.65/15.76 apply (zenon_or_s _ _ zenon_H10e); [ zenon_intro zenon_H3d | zenon_intro zenon_H106 ]. % 15.65/15.76 apply (zenon_or_s _ _ zenon_H10d); [ zenon_intro zenon_H3e | zenon_intro zenon_H42 ]. % 15.65/15.76 apply (zenon_or_s _ _ zenon_Hbe); [ zenon_intro zenon_H5b | zenon_intro zenon_Hbf ]. % 15.65/15.76 exact (zenon_H59 zenon_H5b). % 15.65/15.76 apply (zenon_or_s _ _ zenon_Hbf); [ zenon_intro zenon_H69 | zenon_intro zenon_Hc0 ]. % 15.65/15.76 apply (zenon_or_s _ _ zenon_H163); [ zenon_intro zenon_Had | zenon_intro zenon_H164 ]. % 15.65/15.76 apply (zenon_L559_); trivial. % 15.65/15.76 apply (zenon_or_s _ _ zenon_H164); [ zenon_intro zenon_H149 | zenon_intro zenon_H165 ]. % 15.65/15.76 exact (zenon_H145 zenon_H149). % 15.65/15.76 apply (zenon_or_s _ _ zenon_H165); [ zenon_intro zenon_H15d | zenon_intro zenon_Hcc ]. % 15.65/15.76 apply (zenon_L335_); trivial. % 15.65/15.76 apply (zenon_or_s _ _ zenon_H1c5); [ zenon_intro zenon_Hd8 | zenon_intro zenon_H1c6 ]. % 15.65/15.76 apply (zenon_L163_); trivial. % 15.65/15.76 apply (zenon_or_s _ _ zenon_H1c6); [ zenon_intro zenon_H21 | zenon_intro zenon_H1c7 ]. % 15.65/15.76 exact (zenon_H1b4 zenon_H21). % 15.65/15.76 apply (zenon_or_s _ _ zenon_H1c7); [ zenon_intro zenon_H117 | zenon_intro zenon_H11f ]. % 15.65/15.76 apply (zenon_L870_); trivial. % 15.65/15.76 apply (zenon_L208_); trivial. % 15.65/15.76 apply (zenon_or_s _ _ zenon_Hc0); [ zenon_intro zenon_Haf | zenon_intro zenon_Hba ]. % 15.65/15.76 apply (zenon_L64_); trivial. % 15.65/15.76 apply (zenon_L82_); trivial. % 15.65/15.76 apply (zenon_L102_); trivial. % 15.65/15.76 apply (zenon_L115_); trivial. % 15.65/15.76 apply (zenon_or_s _ _ zenon_H10c); [ zenon_intro zenon_H104 | zenon_intro zenon_H10a ]. % 15.65/15.76 apply (zenon_or_s _ _ zenon_H10e); [ zenon_intro zenon_H3d | zenon_intro zenon_H106 ]. % 15.65/15.76 apply (zenon_or_s _ _ zenon_H44); [ zenon_intro zenon_H47 | zenon_intro zenon_H46 ]. % 15.65/15.76 exact (zenon_H45 zenon_H47). % 15.65/15.76 apply (zenon_or_s _ _ zenon_H46); [ zenon_intro zenon_H22 | zenon_intro zenon_H48 ]. % 15.65/15.76 apply (zenon_L846_); trivial. % 15.65/15.76 apply (zenon_or_s _ _ zenon_H48); [ zenon_intro zenon_H29 | zenon_intro zenon_H37 ]. % 15.65/15.76 apply (zenon_or_s _ _ zenon_Hf1); [ zenon_intro zenon_H47 | zenon_intro zenon_Hf4 ]. % 15.65/15.76 exact (zenon_H45 zenon_H47). % 15.65/15.76 apply (zenon_or_s _ _ zenon_Hf4); [ zenon_intro zenon_Hd8 | zenon_intro zenon_Hf5 ]. % 15.65/15.76 apply (zenon_L809_); trivial. % 15.65/15.76 apply (zenon_or_s _ _ zenon_Hf5); [ zenon_intro zenon_Hae | zenon_intro zenon_Hee ]. % 15.65/15.76 apply (zenon_L304_); trivial. % 15.65/15.76 apply (zenon_L79_); trivial. % 15.65/15.76 apply (zenon_L871_); trivial. % 15.65/15.76 apply (zenon_L81_); trivial. % 15.65/15.76 apply (zenon_L82_); trivial. % 15.65/15.76 apply (zenon_L119_); trivial. % 15.65/15.76 apply (zenon_L161_); trivial. % 15.65/15.76 apply (zenon_L284_); trivial. % 15.65/15.76 apply (zenon_or_s _ _ zenon_H1d4); [ zenon_intro zenon_H2e | zenon_intro zenon_Hdd ]. % 15.65/15.76 apply (zenon_or_s _ _ zenon_H1e3); [ zenon_intro zenon_H52 | zenon_intro zenon_H156 ]. % 15.65/15.76 apply (zenon_or_s _ _ zenon_Haa); [ zenon_intro zenon_H2f | zenon_intro zenon_H35 ]. % 15.65/15.76 apply (zenon_or_s _ _ zenon_H1c3); [ zenon_intro zenon_H30 | zenon_intro zenon_H124 ]. % 15.65/15.76 apply (zenon_L603_); trivial. % 15.65/15.76 apply (zenon_or_s _ _ zenon_H10f); [ zenon_intro zenon_H3c | zenon_intro zenon_Hba ]. % 15.65/15.76 apply (zenon_L604_); trivial. % 15.65/15.76 apply (zenon_L861_); trivial. % 15.65/15.76 apply (zenon_L794_); trivial. % 15.65/15.76 apply (zenon_or_s _ _ zenon_Haa); [ zenon_intro zenon_H2f | zenon_intro zenon_H35 ]. % 15.65/15.76 apply (zenon_or_s _ _ zenon_H1c3); [ zenon_intro zenon_H30 | zenon_intro zenon_H124 ]. % 15.65/15.76 apply (zenon_or_s _ _ zenon_H10f); [ zenon_intro zenon_H3c | zenon_intro zenon_Hba ]. % 15.65/15.76 apply (zenon_or_s _ _ zenon_H10c); [ zenon_intro zenon_H104 | zenon_intro zenon_H10a ]. % 15.65/15.76 apply (zenon_or_s _ _ zenon_H10e); [ zenon_intro zenon_H3d | zenon_intro zenon_H106 ]. % 15.65/15.76 apply (zenon_or_s _ _ zenon_H10d); [ zenon_intro zenon_H3e | zenon_intro zenon_H42 ]. % 15.65/15.76 apply (zenon_L560_); trivial. % 15.65/15.76 apply (zenon_L797_); trivial. % 15.65/15.76 apply (zenon_or_s _ _ zenon_H10d); [ zenon_intro zenon_H3e | zenon_intro zenon_H42 ]. % 15.65/15.76 apply (zenon_or_s _ _ zenon_H44); [ zenon_intro zenon_H47 | zenon_intro zenon_H46 ]. % 15.65/15.76 exact (zenon_H45 zenon_H47). % 15.65/15.76 apply (zenon_or_s _ _ zenon_H46); [ zenon_intro zenon_H22 | zenon_intro zenon_H48 ]. % 15.65/15.76 apply (zenon_or_s _ _ zenon_Hf1); [ zenon_intro zenon_H47 | zenon_intro zenon_Hf4 ]. % 15.65/15.76 exact (zenon_H45 zenon_H47). % 15.65/15.76 apply (zenon_or_s _ _ zenon_Hf4); [ zenon_intro zenon_Hd8 | zenon_intro zenon_Hf5 ]. % 15.65/15.76 apply (zenon_L224_); trivial. % 15.65/15.76 apply (zenon_or_s _ _ zenon_Hf5); [ zenon_intro zenon_Hae | zenon_intro zenon_Hee ]. % 15.65/15.76 apply (zenon_L816_); trivial. % 15.65/15.76 apply (zenon_or_s _ _ zenon_H8e); [ zenon_intro zenon_H92 | zenon_intro zenon_H91 ]. % 15.65/15.76 exact (zenon_H8f zenon_H92). % 15.65/15.76 apply (zenon_or_s _ _ zenon_H91); [ zenon_intro zenon_H5d | zenon_intro zenon_H93 ]. % 15.65/15.76 apply (zenon_L251_); trivial. % 15.65/15.76 apply (zenon_or_s _ _ zenon_H93); [ zenon_intro zenon_H63 | zenon_intro zenon_H81 ]. % 15.65/15.76 apply (zenon_or_s _ _ zenon_Heb); [ zenon_intro zenon_H92 | zenon_intro zenon_Hec ]. % 15.65/15.76 exact (zenon_H8f zenon_H92). % 15.65/15.76 apply (zenon_or_s _ _ zenon_Hec); [ zenon_intro zenon_H68 | zenon_intro zenon_Hed ]. % 15.65/15.76 apply (zenon_L853_); trivial. % 15.65/15.76 apply (zenon_or_s _ _ zenon_Hed); [ zenon_intro zenon_Hdd | zenon_intro zenon_He9 ]. % 15.65/15.76 apply (zenon_L812_); trivial. % 15.65/15.76 apply (zenon_L122_); trivial. % 15.65/15.76 apply (zenon_L874_); trivial. % 15.65/15.76 apply (zenon_or_s _ _ zenon_H48); [ zenon_intro zenon_H29 | zenon_intro zenon_H37 ]. % 15.65/15.76 apply (zenon_L5_); trivial. % 15.65/15.76 apply (zenon_L864_); trivial. % 15.65/15.76 apply (zenon_L153_); trivial. % 15.65/15.76 apply (zenon_or_s _ _ zenon_H10e); [ zenon_intro zenon_H3d | zenon_intro zenon_H106 ]. % 15.65/15.76 apply (zenon_or_s _ _ zenon_H10d); [ zenon_intro zenon_H3e | zenon_intro zenon_H42 ]. % 15.65/15.76 apply (zenon_or_s _ _ zenon_H44); [ zenon_intro zenon_H47 | zenon_intro zenon_H46 ]. % 15.65/15.76 exact (zenon_H45 zenon_H47). % 15.65/15.76 apply (zenon_or_s _ _ zenon_H46); [ zenon_intro zenon_H22 | zenon_intro zenon_H48 ]. % 15.65/15.76 apply (zenon_or_s _ _ zenon_Hf1); [ zenon_intro zenon_H47 | zenon_intro zenon_Hf4 ]. % 15.65/15.76 exact (zenon_H45 zenon_H47). % 15.65/15.76 apply (zenon_or_s _ _ zenon_Hf4); [ zenon_intro zenon_Hd8 | zenon_intro zenon_Hf5 ]. % 15.65/15.76 apply (zenon_L224_); trivial. % 15.65/15.76 apply (zenon_or_s _ _ zenon_Hf5); [ zenon_intro zenon_Hae | zenon_intro zenon_Hee ]. % 15.65/15.76 apply (zenon_L816_); trivial. % 15.65/15.76 apply (zenon_or_s _ _ zenon_H8e); [ zenon_intro zenon_H92 | zenon_intro zenon_H91 ]. % 15.65/15.76 exact (zenon_H8f zenon_H92). % 15.65/15.76 apply (zenon_or_s _ _ zenon_H91); [ zenon_intro zenon_H5d | zenon_intro zenon_H93 ]. % 15.65/15.76 apply (zenon_L251_); trivial. % 15.65/15.76 apply (zenon_or_s _ _ zenon_H93); [ zenon_intro zenon_H63 | zenon_intro zenon_H81 ]. % 15.65/15.76 apply (zenon_L254_); trivial. % 15.65/15.76 apply (zenon_L874_); trivial. % 15.65/15.76 apply (zenon_or_s _ _ zenon_H48); [ zenon_intro zenon_H29 | zenon_intro zenon_H37 ]. % 15.65/15.76 apply (zenon_L5_); trivial. % 15.65/15.76 apply (zenon_L7_); trivial. % 15.65/15.76 apply (zenon_L102_); trivial. % 15.65/15.76 apply (zenon_L115_); trivial. % 15.65/15.76 apply (zenon_L865_); trivial. % 15.65/15.76 apply (zenon_L256_); trivial. % 15.65/15.76 apply (zenon_L134_); trivial. % 15.65/15.76 apply (zenon_L695_); trivial. % 15.65/15.76 apply (zenon_or_s _ _ zenon_H1d2); [ zenon_intro zenon_H182 | zenon_intro zenon_H11f ]. % 15.65/15.76 apply (zenon_or_s _ _ zenon_H1d4); [ zenon_intro zenon_H2e | zenon_intro zenon_Hdd ]. % 15.65/15.76 apply (zenon_or_s _ _ zenon_H1e3); [ zenon_intro zenon_H52 | zenon_intro zenon_H156 ]. % 15.65/15.76 apply (zenon_or_s _ _ zenon_Haa); [ zenon_intro zenon_H2f | zenon_intro zenon_H35 ]. % 15.65/15.76 apply (zenon_or_s _ _ zenon_H1c3); [ zenon_intro zenon_H30 | zenon_intro zenon_H124 ]. % 15.65/15.76 apply (zenon_or_s _ _ zenon_H10f); [ zenon_intro zenon_H3c | zenon_intro zenon_Hba ]. % 15.65/15.76 apply (zenon_or_s _ _ zenon_H10c); [ zenon_intro zenon_H104 | zenon_intro zenon_H10a ]. % 15.65/15.76 apply (zenon_or_s _ _ zenon_H10e); [ zenon_intro zenon_H3d | zenon_intro zenon_H106 ]. % 15.65/15.76 apply (zenon_or_s _ _ zenon_H10d); [ zenon_intro zenon_H3e | zenon_intro zenon_H42 ]. % 15.65/15.76 apply (zenon_or_s _ _ zenon_H44); [ zenon_intro zenon_H47 | zenon_intro zenon_H46 ]. % 15.65/15.76 exact (zenon_H45 zenon_H47). % 15.65/15.76 apply (zenon_or_s _ _ zenon_H46); [ zenon_intro zenon_H22 | zenon_intro zenon_H48 ]. % 15.65/15.76 apply (zenon_or_s _ _ zenon_Hf1); [ zenon_intro zenon_H47 | zenon_intro zenon_Hf4 ]. % 15.65/15.76 exact (zenon_H45 zenon_H47). % 15.65/15.76 apply (zenon_or_s _ _ zenon_Hf4); [ zenon_intro zenon_Hd8 | zenon_intro zenon_Hf5 ]. % 15.65/15.76 apply (zenon_L248_); trivial. % 15.65/15.76 apply (zenon_or_s _ _ zenon_Hf5); [ zenon_intro zenon_Hae | zenon_intro zenon_Hee ]. % 15.65/15.76 apply (zenon_L816_); trivial. % 15.65/15.76 apply (zenon_L306_); trivial. % 15.65/15.76 apply (zenon_or_s _ _ zenon_H48); [ zenon_intro zenon_H29 | zenon_intro zenon_H37 ]. % 15.65/15.76 apply (zenon_L665_); trivial. % 15.65/15.76 apply (zenon_L7_); trivial. % 15.65/15.76 apply (zenon_L791_); trivial. % 15.65/15.76 apply (zenon_L590_); trivial. % 15.65/15.76 apply (zenon_L849_); trivial. % 15.65/15.76 apply (zenon_L437_); trivial. % 15.65/15.76 apply (zenon_or_s _ _ zenon_H10f); [ zenon_intro zenon_H3c | zenon_intro zenon_Hba ]. % 15.65/15.76 apply (zenon_or_s _ _ zenon_H10c); [ zenon_intro zenon_H104 | zenon_intro zenon_H10a ]. % 15.65/15.76 apply (zenon_L855_); trivial. % 15.65/15.76 apply (zenon_or_s _ _ zenon_H10e); [ zenon_intro zenon_H3d | zenon_intro zenon_H106 ]. % 15.65/15.76 apply (zenon_or_s _ _ zenon_H10d); [ zenon_intro zenon_H3e | zenon_intro zenon_H42 ]. % 15.65/15.76 apply (zenon_or_s _ _ zenon_H44); [ zenon_intro zenon_H47 | zenon_intro zenon_H46 ]. % 15.65/15.76 exact (zenon_H45 zenon_H47). % 15.65/15.76 apply (zenon_or_s _ _ zenon_H46); [ zenon_intro zenon_H22 | zenon_intro zenon_H48 ]. % 15.65/15.76 apply (zenon_or_s _ _ zenon_Hf1); [ zenon_intro zenon_H47 | zenon_intro zenon_Hf4 ]. % 15.65/15.76 exact (zenon_H45 zenon_H47). % 15.65/15.76 apply (zenon_or_s _ _ zenon_Hf4); [ zenon_intro zenon_Hd8 | zenon_intro zenon_Hf5 ]. % 15.65/15.76 apply (zenon_L248_); trivial. % 15.65/15.76 apply (zenon_or_s _ _ zenon_Hf5); [ zenon_intro zenon_Hae | zenon_intro zenon_Hee ]. % 15.65/15.76 apply (zenon_L816_); trivial. % 15.65/15.76 apply (zenon_or_s _ _ zenon_H8e); [ zenon_intro zenon_H92 | zenon_intro zenon_H91 ]. % 15.65/15.76 exact (zenon_H8f zenon_H92). % 15.65/15.76 apply (zenon_or_s _ _ zenon_H91); [ zenon_intro zenon_H5d | zenon_intro zenon_H93 ]. % 15.65/15.76 apply (zenon_L852_); trivial. % 15.65/15.76 apply (zenon_or_s _ _ zenon_H93); [ zenon_intro zenon_H63 | zenon_intro zenon_H81 ]. % 15.65/15.76 apply (zenon_L848_); trivial. % 15.65/15.76 apply (zenon_L663_); trivial. % 15.65/15.76 apply (zenon_or_s _ _ zenon_H48); [ zenon_intro zenon_H29 | zenon_intro zenon_H37 ]. % 15.65/15.76 apply (zenon_L666_); trivial. % 15.65/15.76 apply (zenon_L7_); trivial. % 15.65/15.76 apply (zenon_L102_); trivial. % 15.65/15.76 apply (zenon_L115_); trivial. % 15.65/15.76 apply (zenon_L861_); trivial. % 15.65/15.76 apply (zenon_L794_); trivial. % 15.65/15.76 apply (zenon_L601_); trivial. % 15.65/15.76 apply (zenon_or_s _ _ zenon_H1e3); [ zenon_intro zenon_H52 | zenon_intro zenon_H156 ]. % 15.65/15.76 apply (zenon_or_s _ _ zenon_Haa); [ zenon_intro zenon_H2f | zenon_intro zenon_H35 ]. % 15.65/15.76 apply (zenon_or_s _ _ zenon_H1c3); [ zenon_intro zenon_H30 | zenon_intro zenon_H124 ]. % 15.65/15.76 apply (zenon_or_s _ _ zenon_H10f); [ zenon_intro zenon_H3c | zenon_intro zenon_Hba ]. % 15.65/15.76 apply (zenon_or_s _ _ zenon_H10c); [ zenon_intro zenon_H104 | zenon_intro zenon_H10a ]. % 15.65/15.76 apply (zenon_or_s _ _ zenon_H10e); [ zenon_intro zenon_H3d | zenon_intro zenon_H106 ]. % 15.65/15.76 apply (zenon_or_s _ _ zenon_H10d); [ zenon_intro zenon_H3e | zenon_intro zenon_H42 ]. % 15.65/15.76 apply (zenon_or_s _ _ zenon_H44); [ zenon_intro zenon_H47 | zenon_intro zenon_H46 ]. % 15.65/15.76 exact (zenon_H45 zenon_H47). % 15.65/15.76 apply (zenon_or_s _ _ zenon_H46); [ zenon_intro zenon_H22 | zenon_intro zenon_H48 ]. % 15.65/15.76 apply (zenon_L869_); trivial. % 15.65/15.76 apply (zenon_or_s _ _ zenon_H48); [ zenon_intro zenon_H29 | zenon_intro zenon_H37 ]. % 15.65/15.76 apply (zenon_L740_); trivial. % 15.65/15.76 apply (zenon_L7_); trivial. % 15.65/15.76 apply (zenon_L875_); trivial. % 15.65/15.76 apply (zenon_L821_); trivial. % 15.65/15.76 apply (zenon_or_s _ _ zenon_H10e); [ zenon_intro zenon_H3d | zenon_intro zenon_H106 ]. % 15.65/15.76 apply (zenon_or_s _ _ zenon_H10d); [ zenon_intro zenon_H3e | zenon_intro zenon_H42 ]. % 15.65/15.76 apply (zenon_L870_); trivial. % 15.65/15.76 apply (zenon_L102_); trivial. % 15.65/15.76 apply (zenon_L115_); trivial. % 15.65/15.76 apply (zenon_or_s _ _ zenon_H10c); [ zenon_intro zenon_H104 | zenon_intro zenon_H10a ]. % 15.65/15.76 apply (zenon_or_s _ _ zenon_H10e); [ zenon_intro zenon_H3d | zenon_intro zenon_H106 ]. % 15.65/15.76 apply (zenon_or_s _ _ zenon_H44); [ zenon_intro zenon_H47 | zenon_intro zenon_H46 ]. % 15.65/15.76 exact (zenon_H45 zenon_H47). % 15.65/15.76 apply (zenon_or_s _ _ zenon_H46); [ zenon_intro zenon_H22 | zenon_intro zenon_H48 ]. % 15.65/15.76 apply (zenon_L846_); trivial. % 15.65/15.76 apply (zenon_or_s _ _ zenon_H48); [ zenon_intro zenon_H29 | zenon_intro zenon_H37 ]. % 15.65/15.76 apply (zenon_L876_); trivial. % 15.65/15.76 apply (zenon_L871_); trivial. % 15.65/15.76 apply (zenon_L81_); trivial. % 15.65/15.76 apply (zenon_L82_); trivial. % 15.65/15.76 apply (zenon_L119_); trivial. % 15.65/15.76 apply (zenon_L161_); trivial. % 15.65/15.76 apply (zenon_L284_); trivial. % 15.65/15.76 apply (zenon_L237_); trivial. % 15.65/15.76 apply (zenon_L913_); trivial. % 15.65/15.76 apply (zenon_L845_); trivial. % 15.65/15.76 apply (zenon_L562_); trivial. % 15.65/15.76 apply (zenon_L567_); trivial. % 15.65/15.76 apply (zenon_L610_); trivial. % 15.65/15.76 apply (zenon_or_s _ _ zenon_H356); [ zenon_intro zenon_H21 | zenon_intro zenon_H357 ]. % 15.65/15.76 apply (zenon_or_s _ _ zenon_H249); [ zenon_intro zenon_H20 | zenon_intro zenon_H1f ]. % 15.65/15.76 apply (zenon_or_s _ _ zenon_H24b); [ zenon_intro zenon_H45 | zenon_intro zenon_H49 ]. % 15.65/15.76 apply (zenon_or_s _ _ zenon_H24a); [ zenon_intro zenon_H8f | zenon_intro zenon_Hab ]. % 15.65/15.76 apply (zenon_or_s _ _ zenon_H236); [ zenon_intro zenon_H59 | zenon_intro zenon_Hca ]. % 15.65/15.76 apply (zenon_or_s _ _ zenon_H1e4); [ zenon_intro zenon_H145 | zenon_intro zenon_Hd8 ]. % 15.65/15.76 apply (zenon_or_s _ _ zenon_H1d3); [ zenon_intro zenon_Hd6 | zenon_intro zenon_H117 ]. % 15.65/15.76 apply (zenon_or_s _ _ zenon_H1d2); [ zenon_intro zenon_H182 | zenon_intro zenon_H11f ]. % 15.65/15.76 apply (zenon_or_s _ _ zenon_H1d4); [ zenon_intro zenon_H2e | zenon_intro zenon_Hdd ]. % 15.65/15.76 apply (zenon_or_s _ _ zenon_H1e3); [ zenon_intro zenon_H52 | zenon_intro zenon_H156 ]. % 15.65/15.76 apply (zenon_or_s _ _ zenon_Haa); [ zenon_intro zenon_H2f | zenon_intro zenon_H35 ]. % 15.65/15.76 apply (zenon_or_s _ _ zenon_H1c3); [ zenon_intro zenon_H30 | zenon_intro zenon_H124 ]. % 15.65/15.76 apply (zenon_or_s _ _ zenon_H10f); [ zenon_intro zenon_H3c | zenon_intro zenon_Hba ]. % 15.65/15.76 apply (zenon_or_s _ _ zenon_H10e); [ zenon_intro zenon_H3d | zenon_intro zenon_H106 ]. % 15.65/15.76 apply (zenon_L919_); trivial. % 15.65/15.76 apply (zenon_L89_); trivial. % 15.65/15.76 apply (zenon_L83_); trivial. % 15.65/15.76 apply (zenon_or_s _ _ zenon_H10f); [ zenon_intro zenon_H3c | zenon_intro zenon_Hba ]. % 15.65/15.76 apply (zenon_or_s _ _ zenon_H10c); [ zenon_intro zenon_H104 | zenon_intro zenon_H10a ]. % 15.65/15.76 apply (zenon_or_s _ _ zenon_H10e); [ zenon_intro zenon_H3d | zenon_intro zenon_H106 ]. % 15.65/15.76 apply (zenon_or_s _ _ zenon_H10d); [ zenon_intro zenon_H3e | zenon_intro zenon_H42 ]. % 15.65/15.76 apply (zenon_L95_); trivial. % 15.65/15.76 apply (zenon_L976_); trivial. % 15.65/15.76 apply (zenon_L118_); trivial. % 15.65/15.76 apply (zenon_L130_); trivial. % 15.65/15.76 apply (zenon_L83_); trivial. % 15.65/15.76 apply (zenon_L794_); trivial. % 15.65/15.76 apply (zenon_or_s _ _ zenon_Haa); [ zenon_intro zenon_H2f | zenon_intro zenon_H35 ]. % 15.65/15.76 apply (zenon_or_s _ _ zenon_H1c3); [ zenon_intro zenon_H30 | zenon_intro zenon_H124 ]. % 15.65/15.76 apply (zenon_or_s _ _ zenon_H10f); [ zenon_intro zenon_H3c | zenon_intro zenon_Hba ]. % 15.65/15.76 apply (zenon_or_s _ _ zenon_H10c); [ zenon_intro zenon_H104 | zenon_intro zenon_H10a ]. % 15.65/15.76 apply (zenon_or_s _ _ zenon_H10e); [ zenon_intro zenon_H3d | zenon_intro zenon_H106 ]. % 15.65/15.76 apply (zenon_L977_); trivial. % 15.65/15.76 apply (zenon_or_s _ _ zenon_H10d); [ zenon_intro zenon_H3e | zenon_intro zenon_H42 ]. % 15.65/15.76 apply (zenon_or_s _ _ zenon_H110); [ zenon_intro zenon_H1f | zenon_intro zenon_H111 ]. % 15.65/15.76 exact (zenon_H20 zenon_H1f). % 15.65/15.76 apply (zenon_or_s _ _ zenon_H111); [ zenon_intro zenon_H49 | zenon_intro zenon_H112 ]. % 15.65/15.76 apply (zenon_L979_); trivial. % 15.65/15.76 apply (zenon_or_s _ _ zenon_H112); [ zenon_intro zenon_Hab | zenon_intro zenon_Hca ]. % 15.65/15.76 apply (zenon_L994_); trivial. % 15.65/15.76 apply (zenon_L287_); trivial. % 15.65/15.76 apply (zenon_L153_); trivial. % 15.65/15.76 apply (zenon_L986_); trivial. % 15.65/15.76 apply (zenon_or_s _ _ zenon_H10c); [ zenon_intro zenon_H104 | zenon_intro zenon_H10a ]. % 15.65/15.76 apply (zenon_or_s _ _ zenon_H10e); [ zenon_intro zenon_H3d | zenon_intro zenon_H106 ]. % 15.65/15.76 apply (zenon_or_s _ _ zenon_H10d); [ zenon_intro zenon_H3e | zenon_intro zenon_H42 ]. % 15.65/15.76 apply (zenon_or_s _ _ zenon_H110); [ zenon_intro zenon_H1f | zenon_intro zenon_H111 ]. % 15.65/15.76 exact (zenon_H20 zenon_H1f). % 15.65/15.76 apply (zenon_or_s _ _ zenon_H111); [ zenon_intro zenon_H49 | zenon_intro zenon_H112 ]. % 15.65/15.76 apply (zenon_L189_); trivial. % 15.65/15.76 apply (zenon_or_s _ _ zenon_H112); [ zenon_intro zenon_Hab | zenon_intro zenon_Hca ]. % 15.65/15.76 apply (zenon_L995_); trivial. % 15.65/15.76 apply (zenon_L74_); trivial. % 15.65/15.76 apply (zenon_L997_); trivial. % 15.65/15.76 apply (zenon_L81_); trivial. % 15.65/15.76 apply (zenon_L82_); trivial. % 15.65/15.76 apply (zenon_L256_); trivial. % 15.65/15.76 apply (zenon_L134_); trivial. % 15.65/15.76 apply (zenon_or_s _ _ zenon_H1e3); [ zenon_intro zenon_H52 | zenon_intro zenon_H156 ]. % 15.65/15.76 apply (zenon_or_s _ _ zenon_Haa); [ zenon_intro zenon_H2f | zenon_intro zenon_H35 ]. % 15.65/15.76 apply (zenon_or_s _ _ zenon_H1c3); [ zenon_intro zenon_H30 | zenon_intro zenon_H124 ]. % 15.65/15.76 apply (zenon_or_s _ _ zenon_H10f); [ zenon_intro zenon_H3c | zenon_intro zenon_Hba ]. % 15.65/15.76 apply (zenon_or_s _ _ zenon_H10c); [ zenon_intro zenon_H104 | zenon_intro zenon_H10a ]. % 15.65/15.76 apply (zenon_L907_); trivial. % 15.65/15.76 apply (zenon_or_s _ _ zenon_H10e); [ zenon_intro zenon_H3d | zenon_intro zenon_H106 ]. % 15.65/15.76 apply (zenon_or_s _ _ zenon_H10d); [ zenon_intro zenon_H3e | zenon_intro zenon_H42 ]. % 15.65/15.76 apply (zenon_or_s _ _ zenon_H110); [ zenon_intro zenon_H1f | zenon_intro zenon_H111 ]. % 15.65/15.76 exact (zenon_H20 zenon_H1f). % 15.65/15.76 apply (zenon_or_s _ _ zenon_H111); [ zenon_intro zenon_H49 | zenon_intro zenon_H112 ]. % 15.65/15.76 apply (zenon_L990_); trivial. % 15.65/15.76 apply (zenon_or_s _ _ zenon_H112); [ zenon_intro zenon_Hab | zenon_intro zenon_Hca ]. % 15.65/15.76 apply (zenon_L998_); trivial. % 15.65/15.76 apply (zenon_L114_); trivial. % 15.65/15.76 apply (zenon_L999_); trivial. % 15.65/15.76 apply (zenon_L115_); trivial. % 15.65/15.76 apply (zenon_L310_); trivial. % 15.65/15.76 apply (zenon_L119_); trivial. % 15.65/15.76 apply (zenon_L161_); trivial. % 15.65/15.76 apply (zenon_L284_); trivial. % 15.65/15.76 apply (zenon_L90_); trivial. % 15.65/15.76 apply (zenon_L86_); trivial. % 15.65/15.76 apply (zenon_L61_); trivial. % 15.65/15.76 apply (zenon_or_s _ _ zenon_H1d4); [ zenon_intro zenon_H2e | zenon_intro zenon_Hdd ]. % 15.65/15.76 apply (zenon_or_s _ _ zenon_H1e3); [ zenon_intro zenon_H52 | zenon_intro zenon_H156 ]. % 15.65/15.76 apply (zenon_or_s _ _ zenon_Haa); [ zenon_intro zenon_H2f | zenon_intro zenon_H35 ]. % 15.65/15.76 apply (zenon_L316_); trivial. % 15.65/15.76 apply (zenon_L794_); trivial. % 15.65/15.76 apply (zenon_L318_); trivial. % 15.65/15.76 apply (zenon_or_s _ _ zenon_H1e3); [ zenon_intro zenon_H52 | zenon_intro zenon_H156 ]. % 15.65/15.76 apply (zenon_or_s _ _ zenon_Haa); [ zenon_intro zenon_H2f | zenon_intro zenon_H35 ]. % 15.65/15.76 apply (zenon_or_s _ _ zenon_H1c3); [ zenon_intro zenon_H30 | zenon_intro zenon_H124 ]. % 15.65/15.76 apply (zenon_or_s _ _ zenon_H10f); [ zenon_intro zenon_H3c | zenon_intro zenon_Hba ]. % 15.65/15.76 apply (zenon_or_s _ _ zenon_H10c); [ zenon_intro zenon_H104 | zenon_intro zenon_H10a ]. % 15.65/15.76 apply (zenon_or_s _ _ zenon_H10d); [ zenon_intro zenon_H3e | zenon_intro zenon_H42 ]. % 15.65/15.76 apply (zenon_L307_); trivial. % 15.65/15.76 apply (zenon_L1002_); trivial. % 15.65/15.76 apply (zenon_L116_); trivial. % 15.65/15.76 apply (zenon_L310_); trivial. % 15.65/15.76 apply (zenon_L119_); trivial. % 15.65/15.76 apply (zenon_L161_); trivial. % 15.65/15.76 apply (zenon_L284_); trivial. % 15.65/15.76 apply (zenon_or_s _ _ zenon_H236); [ zenon_intro zenon_H59 | zenon_intro zenon_Hca ]. % 15.65/15.76 apply (zenon_L998_); trivial. % 15.65/15.76 apply (zenon_L53_); trivial. % 15.65/15.76 apply (zenon_L991_); trivial. % 15.65/15.76 apply (zenon_or_s _ _ zenon_H24b); [ zenon_intro zenon_H45 | zenon_intro zenon_H49 ]. % 15.65/15.76 apply (zenon_or_s _ _ zenon_H24a); [ zenon_intro zenon_H8f | zenon_intro zenon_Hab ]. % 15.65/15.76 apply (zenon_or_s _ _ zenon_H236); [ zenon_intro zenon_H59 | zenon_intro zenon_Hca ]. % 15.65/15.76 apply (zenon_or_s _ _ zenon_H1e4); [ zenon_intro zenon_H145 | zenon_intro zenon_Hd8 ]. % 15.65/15.76 apply (zenon_L913_); trivial. % 15.65/15.76 apply (zenon_L61_); trivial. % 15.65/15.76 apply (zenon_L562_); trivial. % 15.65/15.76 apply (zenon_L567_); trivial. % 15.65/15.76 apply (zenon_L610_); trivial. % 15.65/15.76 apply (zenon_or_s _ _ zenon_H357); [ zenon_intro zenon_H35 | zenon_intro zenon_H42 ]. % 15.65/15.76 apply (zenon_L794_); trivial. % 15.65/15.76 apply (zenon_or_s _ _ zenon_H249); [ zenon_intro zenon_H20 | zenon_intro zenon_H1f ]. % 15.65/15.76 apply (zenon_or_s _ _ zenon_H24b); [ zenon_intro zenon_H45 | zenon_intro zenon_H49 ]. % 15.65/15.76 apply (zenon_or_s _ _ zenon_H24a); [ zenon_intro zenon_H8f | zenon_intro zenon_Hab ]. % 15.65/15.76 apply (zenon_or_s _ _ zenon_H236); [ zenon_intro zenon_H59 | zenon_intro zenon_Hca ]. % 15.65/15.76 apply (zenon_or_s _ _ zenon_H1e4); [ zenon_intro zenon_H145 | zenon_intro zenon_Hd8 ]. % 15.65/15.76 apply (zenon_L976_); trivial. % 15.65/15.76 apply (zenon_L943_); trivial. % 15.65/15.76 apply (zenon_or_s _ _ zenon_H1e4); [ zenon_intro zenon_H145 | zenon_intro zenon_Hd8 ]. % 15.65/15.76 apply (zenon_or_s _ _ zenon_H1d8); [ zenon_intro zenon_H1b4 | zenon_intro zenon_H21 ]. % 15.65/15.76 apply (zenon_or_s _ _ zenon_H1d2); [ zenon_intro zenon_H182 | zenon_intro zenon_H11f ]. % 15.65/15.76 apply (zenon_or_s _ _ zenon_H1d4); [ zenon_intro zenon_H2e | zenon_intro zenon_Hdd ]. % 15.65/15.76 apply (zenon_or_s _ _ zenon_H1e3); [ zenon_intro zenon_H52 | zenon_intro zenon_H156 ]. % 15.65/15.76 apply (zenon_L968_); trivial. % 15.65/15.76 apply (zenon_L1003_); trivial. % 15.65/15.76 apply (zenon_L1004_); trivial. % 15.65/15.76 apply (zenon_or_s _ _ zenon_H1d4); [ zenon_intro zenon_H2e | zenon_intro zenon_Hdd ]. % 15.65/15.76 apply (zenon_or_s _ _ zenon_H1e3); [ zenon_intro zenon_H52 | zenon_intro zenon_H156 ]. % 15.65/15.76 apply (zenon_or_s _ _ zenon_Haa); [ zenon_intro zenon_H2f | zenon_intro zenon_H35 ]. % 15.65/15.76 apply (zenon_or_s _ _ zenon_H1c3); [ zenon_intro zenon_H30 | zenon_intro zenon_H124 ]. % 15.65/15.76 apply (zenon_L969_); trivial. % 15.65/15.76 apply (zenon_or_s _ _ zenon_H10f); [ zenon_intro zenon_H3c | zenon_intro zenon_Hba ]. % 15.65/15.76 apply (zenon_or_s _ _ zenon_H10c); [ zenon_intro zenon_H104 | zenon_intro zenon_H10a ]. % 15.65/15.76 apply (zenon_or_s _ _ zenon_H10e); [ zenon_intro zenon_H3d | zenon_intro zenon_H106 ]. % 15.65/15.76 apply (zenon_L971_); trivial. % 15.65/15.76 apply (zenon_L153_); trivial. % 15.65/15.76 apply (zenon_L102_); trivial. % 15.65/15.76 apply (zenon_L43_); trivial. % 15.65/15.76 apply (zenon_L794_); trivial. % 15.65/15.76 apply (zenon_L1003_); trivial. % 15.65/15.76 apply (zenon_or_s _ _ zenon_H1e3); [ zenon_intro zenon_H52 | zenon_intro zenon_H156 ]. % 15.65/15.76 apply (zenon_or_s _ _ zenon_Haa); [ zenon_intro zenon_H2f | zenon_intro zenon_H35 ]. % 15.65/15.76 apply (zenon_or_s _ _ zenon_H1c3); [ zenon_intro zenon_H30 | zenon_intro zenon_H124 ]. % 15.65/15.76 apply (zenon_L1002_); trivial. % 15.65/15.76 apply (zenon_L119_); trivial. % 15.65/15.76 apply (zenon_L161_); trivial. % 15.65/15.76 apply (zenon_L284_); trivial. % 15.65/15.76 apply (zenon_or_s _ _ zenon_H1d4); [ zenon_intro zenon_H2e | zenon_intro zenon_Hdd ]. % 15.65/15.76 apply (zenon_or_s _ _ zenon_H1e3); [ zenon_intro zenon_H52 | zenon_intro zenon_H156 ]. % 15.65/15.76 apply (zenon_L917_); trivial. % 15.65/15.76 apply (zenon_L1003_); trivial. % 15.65/15.76 apply (zenon_L1005_); trivial. % 15.65/15.76 apply (zenon_L1018_); trivial. % 15.65/15.76 apply (zenon_L960_); trivial. % 15.65/15.76 apply (zenon_L1019_); trivial. % 15.65/15.76 apply (zenon_or_s _ _ zenon_H24b); [ zenon_intro zenon_H45 | zenon_intro zenon_H49 ]. % 15.65/15.76 apply (zenon_or_s _ _ zenon_H24a); [ zenon_intro zenon_H8f | zenon_intro zenon_Hab ]. % 15.65/15.76 apply (zenon_or_s _ _ zenon_H236); [ zenon_intro zenon_H59 | zenon_intro zenon_Hca ]. % 15.65/15.76 apply (zenon_or_s _ _ zenon_H1e4); [ zenon_intro zenon_H145 | zenon_intro zenon_Hd8 ]. % 15.65/15.76 apply (zenon_or_s _ _ zenon_H1d8); [ zenon_intro zenon_H1b4 | zenon_intro zenon_H21 ]. % 15.65/15.76 apply (zenon_or_s _ _ zenon_H1d3); [ zenon_intro zenon_Hd6 | zenon_intro zenon_H117 ]. % 15.65/15.76 apply (zenon_or_s _ _ zenon_H1d2); [ zenon_intro zenon_H182 | zenon_intro zenon_H11f ]. % 15.65/15.76 apply (zenon_or_s _ _ zenon_H1d4); [ zenon_intro zenon_H2e | zenon_intro zenon_Hdd ]. % 15.65/15.76 apply (zenon_L802_); trivial. % 15.65/15.76 apply (zenon_or_s _ _ zenon_H1e3); [ zenon_intro zenon_H52 | zenon_intro zenon_H156 ]. % 15.65/15.76 apply (zenon_or_s _ _ zenon_Haa); [ zenon_intro zenon_H2f | zenon_intro zenon_H35 ]. % 15.65/15.76 apply (zenon_L875_); trivial. % 15.65/15.76 apply (zenon_L161_); trivial. % 15.65/15.76 apply (zenon_L284_); trivial. % 15.65/15.76 apply (zenon_or_s _ _ zenon_H1d4); [ zenon_intro zenon_H2e | zenon_intro zenon_Hdd ]. % 15.65/15.76 apply (zenon_L798_); trivial. % 15.65/15.76 apply (zenon_L695_); trivial. % 15.65/15.76 apply (zenon_or_s _ _ zenon_H1d2); [ zenon_intro zenon_H182 | zenon_intro zenon_H11f ]. % 15.65/15.76 apply (zenon_or_s _ _ zenon_H1d4); [ zenon_intro zenon_H2e | zenon_intro zenon_Hdd ]. % 15.65/15.76 apply (zenon_or_s _ _ zenon_H1e3); [ zenon_intro zenon_H52 | zenon_intro zenon_H156 ]. % 15.65/15.76 apply (zenon_L795_); trivial. % 15.65/15.76 apply (zenon_L601_); trivial. % 15.65/15.76 apply (zenon_L974_); trivial. % 15.65/15.76 apply (zenon_L237_); trivial. % 15.65/15.76 apply (zenon_or_s _ _ zenon_H1d3); [ zenon_intro zenon_Hd6 | zenon_intro zenon_H117 ]. % 15.65/15.76 apply (zenon_or_s _ _ zenon_H1d2); [ zenon_intro zenon_H182 | zenon_intro zenon_H11f ]. % 15.65/15.76 apply (zenon_or_s _ _ zenon_H1d4); [ zenon_intro zenon_H2e | zenon_intro zenon_Hdd ]. % 15.65/15.76 apply (zenon_or_s _ _ zenon_H1e3); [ zenon_intro zenon_H52 | zenon_intro zenon_H156 ]. % 15.65/15.76 apply (zenon_or_s _ _ zenon_Haa); [ zenon_intro zenon_H2f | zenon_intro zenon_H35 ]. % 15.65/15.76 apply (zenon_or_s _ _ zenon_H1c3); [ zenon_intro zenon_H30 | zenon_intro zenon_H124 ]. % 15.65/15.76 apply (zenon_or_s _ _ zenon_H10c); [ zenon_intro zenon_H104 | zenon_intro zenon_H10a ]. % 15.65/15.76 apply (zenon_or_s _ _ zenon_H10e); [ zenon_intro zenon_H3d | zenon_intro zenon_H106 ]. % 15.65/15.76 apply (zenon_L886_); trivial. % 15.65/15.76 apply (zenon_L820_); trivial. % 15.65/15.76 apply (zenon_L1021_); trivial. % 15.65/15.76 apply (zenon_or_s _ _ zenon_H10f); [ zenon_intro zenon_H3c | zenon_intro zenon_Hba ]. % 15.65/15.76 apply (zenon_or_s _ _ zenon_H10c); [ zenon_intro zenon_H104 | zenon_intro zenon_H10a ]. % 15.65/15.76 apply (zenon_L894_); trivial. % 15.65/15.76 apply (zenon_L102_); trivial. % 15.65/15.76 apply (zenon_L43_); trivial. % 15.65/15.76 apply (zenon_L794_); trivial. % 15.65/15.76 apply (zenon_L1022_); trivial. % 15.65/15.76 apply (zenon_L959_); trivial. % 15.65/15.76 apply (zenon_L90_); trivial. % 15.65/15.76 apply (zenon_L86_); trivial. % 15.65/15.76 apply (zenon_L879_); trivial. % 15.65/15.76 apply (zenon_L562_); trivial. % 15.65/15.76 apply (zenon_L567_); trivial. % 15.65/15.76 apply (zenon_L610_); trivial. % 15.65/15.76 apply (zenon_and_s _ _ zenon_H35e). zenon_intro zenon_H2b8. zenon_intro zenon_H362. % 15.65/15.76 apply (zenon_and_s _ _ zenon_H362). zenon_intro zenon_H2b4. zenon_intro zenon_H363. % 15.65/15.76 apply (zenon_and_s _ _ zenon_H363). zenon_intro zenon_H2af. zenon_intro zenon_H2be. % 15.65/15.76 apply (zenon_or_s _ _ zenon_H343); [ zenon_intro zenon_H1f | zenon_intro zenon_H356 ]. % 15.65/15.76 apply (zenon_or_s _ _ zenon_H24b); [ zenon_intro zenon_H45 | zenon_intro zenon_H49 ]. % 15.65/15.76 apply (zenon_or_s _ _ zenon_H24a); [ zenon_intro zenon_H8f | zenon_intro zenon_Hab ]. % 15.65/15.77 apply (zenon_or_s _ _ zenon_H236); [ zenon_intro zenon_H59 | zenon_intro zenon_Hca ]. % 15.65/15.77 apply (zenon_or_s _ _ zenon_H1e4); [ zenon_intro zenon_H145 | zenon_intro zenon_Hd8 ]. % 15.65/15.77 apply (zenon_or_s _ _ zenon_H1d8); [ zenon_intro zenon_H1b4 | zenon_intro zenon_H21 ]. % 15.65/15.77 apply (zenon_or_s _ _ zenon_H1d3); [ zenon_intro zenon_Hd6 | zenon_intro zenon_H117 ]. % 15.65/15.77 apply (zenon_or_s _ _ zenon_H1d2); [ zenon_intro zenon_H182 | zenon_intro zenon_H11f ]. % 15.65/15.77 apply (zenon_or_s _ _ zenon_H1d4); [ zenon_intro zenon_H2e | zenon_intro zenon_Hdd ]. % 15.65/15.77 apply (zenon_or_s _ _ zenon_H1e3); [ zenon_intro zenon_H52 | zenon_intro zenon_H156 ]. % 15.65/15.77 apply (zenon_or_s _ _ zenon_H10f); [ zenon_intro zenon_H3c | zenon_intro zenon_Hba ]. % 15.65/15.77 apply (zenon_L1147_); trivial. % 15.65/15.77 apply (zenon_L1145_); trivial. % 15.65/15.77 apply (zenon_or_s _ _ zenon_H1c3); [ zenon_intro zenon_H30 | zenon_intro zenon_H124 ]. % 15.65/15.77 apply (zenon_or_s _ _ zenon_H10f); [ zenon_intro zenon_H3c | zenon_intro zenon_Hba ]. % 15.65/15.77 apply (zenon_or_s _ _ zenon_H10c); [ zenon_intro zenon_H104 | zenon_intro zenon_H10a ]. % 15.65/15.77 apply (zenon_or_s _ _ zenon_H10e); [ zenon_intro zenon_H3d | zenon_intro zenon_H106 ]. % 15.65/15.77 apply (zenon_L1116_); trivial. % 15.65/15.77 apply (zenon_or_s _ _ zenon_H10d); [ zenon_intro zenon_H3e | zenon_intro zenon_H42 ]. % 15.65/15.77 apply (zenon_or_s _ _ zenon_H44); [ zenon_intro zenon_H47 | zenon_intro zenon_H46 ]. % 15.65/15.77 exact (zenon_H45 zenon_H47). % 15.65/15.77 apply (zenon_or_s _ _ zenon_H46); [ zenon_intro zenon_H22 | zenon_intro zenon_H48 ]. % 15.65/15.77 apply (zenon_or_s _ _ zenon_Hf1); [ zenon_intro zenon_H47 | zenon_intro zenon_Hf4 ]. % 15.65/15.77 exact (zenon_H45 zenon_H47). % 15.65/15.77 apply (zenon_or_s _ _ zenon_Hf4); [ zenon_intro zenon_Hd8 | zenon_intro zenon_Hf5 ]. % 15.65/15.77 apply (zenon_L1051_); trivial. % 15.65/15.77 apply (zenon_or_s _ _ zenon_Hf5); [ zenon_intro zenon_Hae | zenon_intro zenon_Hee ]. % 15.65/15.77 apply (zenon_or_s _ _ zenon_H8e); [ zenon_intro zenon_H92 | zenon_intro zenon_H91 ]. % 15.65/15.77 exact (zenon_H8f zenon_H92). % 15.65/15.77 apply (zenon_or_s _ _ zenon_H91); [ zenon_intro zenon_H5d | zenon_intro zenon_H93 ]. % 15.65/15.77 apply (zenon_L214_); trivial. % 15.65/15.77 apply (zenon_or_s _ _ zenon_H93); [ zenon_intro zenon_H63 | zenon_intro zenon_H81 ]. % 15.65/15.77 apply (zenon_or_s _ _ zenon_Heb); [ zenon_intro zenon_H92 | zenon_intro zenon_Hec ]. % 15.65/15.77 exact (zenon_H8f zenon_H92). % 15.65/15.77 apply (zenon_or_s _ _ zenon_Hec); [ zenon_intro zenon_H68 | zenon_intro zenon_Hed ]. % 15.65/15.77 apply (zenon_L1148_); trivial. % 15.65/15.77 apply (zenon_or_s _ _ zenon_Hed); [ zenon_intro zenon_Hdd | zenon_intro zenon_He9 ]. % 15.65/15.77 apply (zenon_L304_); trivial. % 15.65/15.77 apply (zenon_L1106_); trivial. % 15.65/15.77 apply (zenon_L107_); trivial. % 15.65/15.77 apply (zenon_L1054_); trivial. % 15.65/15.77 apply (zenon_or_s _ _ zenon_H48); [ zenon_intro zenon_H29 | zenon_intro zenon_H37 ]. % 15.65/15.77 apply (zenon_L665_); trivial. % 15.65/15.77 apply (zenon_L1151_); trivial. % 15.65/15.77 apply (zenon_L1041_); trivial. % 15.65/15.77 apply (zenon_L1059_); trivial. % 15.65/15.77 apply (zenon_L1145_); trivial. % 15.65/15.77 apply (zenon_L256_); trivial. % 15.65/15.77 apply (zenon_or_s _ _ zenon_H1e3); [ zenon_intro zenon_H52 | zenon_intro zenon_H156 ]. % 15.65/15.77 apply (zenon_or_s _ _ zenon_Haa); [ zenon_intro zenon_H2f | zenon_intro zenon_H35 ]. % 15.65/15.77 apply (zenon_or_s _ _ zenon_H1c3); [ zenon_intro zenon_H30 | zenon_intro zenon_H124 ]. % 15.65/15.77 apply (zenon_or_s _ _ zenon_H10f); [ zenon_intro zenon_H3c | zenon_intro zenon_Hba ]. % 15.65/15.77 apply (zenon_or_s _ _ zenon_H10c); [ zenon_intro zenon_H104 | zenon_intro zenon_H10a ]. % 15.65/15.77 apply (zenon_or_s _ _ zenon_H10e); [ zenon_intro zenon_H3d | zenon_intro zenon_H106 ]. % 15.65/15.77 apply (zenon_L1116_); trivial. % 15.65/15.77 apply (zenon_L1152_); trivial. % 15.65/15.77 apply (zenon_or_s _ _ zenon_H10e); [ zenon_intro zenon_H3d | zenon_intro zenon_H106 ]. % 15.65/15.77 apply (zenon_or_s _ _ zenon_H10d); [ zenon_intro zenon_H3e | zenon_intro zenon_H42 ]. % 15.65/15.77 apply (zenon_or_s _ _ zenon_H44); [ zenon_intro zenon_H47 | zenon_intro zenon_H46 ]. % 15.65/15.77 exact (zenon_H45 zenon_H47). % 15.65/15.77 apply (zenon_or_s _ _ zenon_H46); [ zenon_intro zenon_H22 | zenon_intro zenon_H48 ]. % 15.65/15.77 apply (zenon_or_s _ _ zenon_Hf1); [ zenon_intro zenon_H47 | zenon_intro zenon_Hf4 ]. % 15.65/15.77 exact (zenon_H45 zenon_H47). % 15.65/15.77 apply (zenon_or_s _ _ zenon_Hf4); [ zenon_intro zenon_Hd8 | zenon_intro zenon_Hf5 ]. % 15.65/15.77 apply (zenon_L1052_); trivial. % 15.65/15.77 apply (zenon_or_s _ _ zenon_Hf5); [ zenon_intro zenon_Hae | zenon_intro zenon_Hee ]. % 15.65/15.77 apply (zenon_L304_); trivial. % 15.65/15.77 apply (zenon_L1054_); trivial. % 15.65/15.77 apply (zenon_or_s _ _ zenon_H48); [ zenon_intro zenon_H29 | zenon_intro zenon_H37 ]. % 15.65/15.77 apply (zenon_L1112_); trivial. % 15.65/15.77 apply (zenon_L7_); trivial. % 15.65/15.77 apply (zenon_L1041_); trivial. % 15.65/15.77 apply (zenon_L115_); trivial. % 15.65/15.77 apply (zenon_L1113_); trivial. % 15.65/15.77 apply (zenon_L119_); trivial. % 15.65/15.77 apply (zenon_L1157_); trivial. % 15.65/15.77 apply (zenon_L284_); trivial. % 15.65/15.77 apply (zenon_L1146_); trivial. % 15.65/15.77 apply (zenon_L1115_); trivial. % 15.65/15.77 apply (zenon_L1205_); trivial. % 15.65/15.77 apply (zenon_L1063_); trivial. % 15.65/15.77 apply (zenon_L562_); trivial. % 15.65/15.77 apply (zenon_L567_); trivial. % 15.65/15.77 apply (zenon_L610_); trivial. % 15.65/15.77 apply (zenon_or_s _ _ zenon_H356); [ zenon_intro zenon_H21 | zenon_intro zenon_H357 ]. % 15.65/15.77 apply (zenon_or_s _ _ zenon_H249); [ zenon_intro zenon_H20 | zenon_intro zenon_H1f ]. % 15.65/15.77 apply (zenon_or_s _ _ zenon_H24b); [ zenon_intro zenon_H45 | zenon_intro zenon_H49 ]. % 15.65/15.77 apply (zenon_or_s _ _ zenon_H24a); [ zenon_intro zenon_H8f | zenon_intro zenon_Hab ]. % 15.65/15.77 apply (zenon_or_s _ _ zenon_H236); [ zenon_intro zenon_H59 | zenon_intro zenon_Hca ]. % 15.65/15.77 apply (zenon_or_s _ _ zenon_H1e4); [ zenon_intro zenon_H145 | zenon_intro zenon_Hd8 ]. % 15.65/15.77 apply (zenon_or_s _ _ zenon_H1d3); [ zenon_intro zenon_Hd6 | zenon_intro zenon_H117 ]. % 15.65/15.77 apply (zenon_or_s _ _ zenon_H1d2); [ zenon_intro zenon_H182 | zenon_intro zenon_H11f ]. % 15.65/15.77 apply (zenon_or_s _ _ zenon_H1d4); [ zenon_intro zenon_H2e | zenon_intro zenon_Hdd ]. % 15.65/15.77 apply (zenon_or_s _ _ zenon_H1e3); [ zenon_intro zenon_H52 | zenon_intro zenon_H156 ]. % 15.65/15.77 apply (zenon_or_s _ _ zenon_Haa); [ zenon_intro zenon_H2f | zenon_intro zenon_H35 ]. % 15.65/15.77 apply (zenon_or_s _ _ zenon_H1c3); [ zenon_intro zenon_H30 | zenon_intro zenon_H124 ]. % 15.65/15.77 apply (zenon_or_s _ _ zenon_H10f); [ zenon_intro zenon_H3c | zenon_intro zenon_Hba ]. % 15.65/15.77 apply (zenon_or_s _ _ zenon_H10c); [ zenon_intro zenon_H104 | zenon_intro zenon_H10a ]. % 15.65/15.77 apply (zenon_or_s _ _ zenon_H10e); [ zenon_intro zenon_H3d | zenon_intro zenon_H106 ]. % 15.65/15.77 apply (zenon_L1209_); trivial. % 15.65/15.77 apply (zenon_L1213_); trivial. % 15.65/15.77 apply (zenon_L1225_); trivial. % 15.65/15.77 apply (zenon_L1226_); trivial. % 15.65/15.77 apply (zenon_or_s _ _ zenon_H10f); [ zenon_intro zenon_H3c | zenon_intro zenon_Hba ]. % 15.65/15.77 apply (zenon_or_s _ _ zenon_H10c); [ zenon_intro zenon_H104 | zenon_intro zenon_H10a ]. % 15.65/15.77 apply (zenon_or_s _ _ zenon_H10e); [ zenon_intro zenon_H3d | zenon_intro zenon_H106 ]. % 15.65/15.77 apply (zenon_L1209_); trivial. % 15.65/15.77 apply (zenon_L1165_); trivial. % 15.65/15.77 apply (zenon_L1225_); trivial. % 15.65/15.77 apply (zenon_L1226_); trivial. % 15.65/15.77 apply (zenon_L1266_); trivial. % 15.65/15.77 apply (zenon_or_s _ _ zenon_H1c3); [ zenon_intro zenon_H30 | zenon_intro zenon_H124 ]. % 15.65/15.77 apply (zenon_or_s _ _ zenon_H10f); [ zenon_intro zenon_H3c | zenon_intro zenon_Hba ]. % 15.65/15.77 apply (zenon_or_s _ _ zenon_H10c); [ zenon_intro zenon_H104 | zenon_intro zenon_H10a ]. % 15.65/15.77 apply (zenon_or_s _ _ zenon_H10e); [ zenon_intro zenon_H3d | zenon_intro zenon_H106 ]. % 15.65/15.77 apply (zenon_or_s _ _ zenon_H10d); [ zenon_intro zenon_H3e | zenon_intro zenon_H42 ]. % 15.65/15.77 apply (zenon_or_s _ _ zenon_H110); [ zenon_intro zenon_H1f | zenon_intro zenon_H111 ]. % 15.65/15.77 exact (zenon_H20 zenon_H1f). % 15.65/15.77 apply (zenon_or_s _ _ zenon_H111); [ zenon_intro zenon_H49 | zenon_intro zenon_H112 ]. % 15.65/15.77 apply (zenon_L1267_); trivial. % 15.65/15.77 apply (zenon_or_s _ _ zenon_H112); [ zenon_intro zenon_Hab | zenon_intro zenon_Hca ]. % 15.65/15.77 apply (zenon_L132_); trivial. % 15.65/15.77 apply (zenon_L114_); trivial. % 15.65/15.77 apply (zenon_L1041_); trivial. % 15.65/15.77 apply (zenon_or_s _ _ zenon_H10d); [ zenon_intro zenon_H3e | zenon_intro zenon_H42 ]. % 15.65/15.77 apply (zenon_or_s _ _ zenon_H110); [ zenon_intro zenon_H1f | zenon_intro zenon_H111 ]. % 15.65/15.77 exact (zenon_H20 zenon_H1f). % 15.65/15.77 apply (zenon_or_s _ _ zenon_H111); [ zenon_intro zenon_H49 | zenon_intro zenon_H112 ]. % 15.65/15.77 apply (zenon_L1276_); trivial. % 15.65/15.77 apply (zenon_or_s _ _ zenon_H112); [ zenon_intro zenon_Hab | zenon_intro zenon_Hca ]. % 15.65/15.77 apply (zenon_L1279_); trivial. % 15.65/15.77 apply (zenon_L1290_); trivial. % 15.65/15.77 apply (zenon_L1041_); trivial. % 15.65/15.77 apply (zenon_L1225_); trivial. % 15.65/15.77 apply (zenon_L1202_); trivial. % 15.65/15.77 apply (zenon_L256_); trivial. % 15.65/15.77 apply (zenon_or_s _ _ zenon_H1e3); [ zenon_intro zenon_H52 | zenon_intro zenon_H156 ]. % 15.65/15.77 apply (zenon_or_s _ _ zenon_Haa); [ zenon_intro zenon_H2f | zenon_intro zenon_H35 ]. % 15.65/15.77 apply (zenon_or_s _ _ zenon_H1c3); [ zenon_intro zenon_H30 | zenon_intro zenon_H124 ]. % 15.65/15.77 apply (zenon_or_s _ _ zenon_H10f); [ zenon_intro zenon_H3c | zenon_intro zenon_Hba ]. % 15.65/15.77 apply (zenon_or_s _ _ zenon_H10c); [ zenon_intro zenon_H104 | zenon_intro zenon_H10a ]. % 15.65/15.77 apply (zenon_L1171_); trivial. % 15.65/15.77 apply (zenon_or_s _ _ zenon_H10e); [ zenon_intro zenon_H3d | zenon_intro zenon_H106 ]. % 15.65/15.77 apply (zenon_or_s _ _ zenon_H10d); [ zenon_intro zenon_H3e | zenon_intro zenon_H42 ]. % 15.65/15.77 apply (zenon_or_s _ _ zenon_H110); [ zenon_intro zenon_H1f | zenon_intro zenon_H111 ]. % 15.65/15.77 exact (zenon_H20 zenon_H1f). % 15.65/15.77 apply (zenon_or_s _ _ zenon_H111); [ zenon_intro zenon_H49 | zenon_intro zenon_H112 ]. % 15.65/15.77 apply (zenon_L1272_); trivial. % 15.65/15.77 apply (zenon_or_s _ _ zenon_H112); [ zenon_intro zenon_Hab | zenon_intro zenon_Hca ]. % 15.65/15.77 apply (zenon_L1295_); trivial. % 15.65/15.77 apply (zenon_L114_); trivial. % 15.65/15.77 apply (zenon_L1041_); trivial. % 15.65/15.77 apply (zenon_L115_); trivial. % 15.65/15.77 apply (zenon_L310_); trivial. % 15.65/15.77 apply (zenon_L119_); trivial. % 15.65/15.77 apply (zenon_L1296_); trivial. % 15.65/15.77 apply (zenon_L284_); trivial. % 15.65/15.77 apply (zenon_L90_); trivial. % 15.65/15.77 apply (zenon_L86_); trivial. % 15.65/15.77 apply (zenon_L61_); trivial. % 15.65/15.77 apply (zenon_or_s _ _ zenon_H1e4); [ zenon_intro zenon_H145 | zenon_intro zenon_Hd8 ]. % 15.65/15.77 apply (zenon_or_s _ _ zenon_H1d3); [ zenon_intro zenon_Hd6 | zenon_intro zenon_H117 ]. % 15.65/15.77 apply (zenon_or_s _ _ zenon_H1d2); [ zenon_intro zenon_H182 | zenon_intro zenon_H11f ]. % 15.65/15.77 apply (zenon_or_s _ _ zenon_H1d4); [ zenon_intro zenon_H2e | zenon_intro zenon_Hdd ]. % 15.65/15.77 apply (zenon_or_s _ _ zenon_H1e3); [ zenon_intro zenon_H52 | zenon_intro zenon_H156 ]. % 15.65/15.77 apply (zenon_or_s _ _ zenon_Haa); [ zenon_intro zenon_H2f | zenon_intro zenon_H35 ]. % 15.65/15.77 apply (zenon_or_s _ _ zenon_H1c3); [ zenon_intro zenon_H30 | zenon_intro zenon_H124 ]. % 15.65/15.77 apply (zenon_or_s _ _ zenon_H10f); [ zenon_intro zenon_H3c | zenon_intro zenon_Hba ]. % 15.65/15.77 apply (zenon_or_s _ _ zenon_H10c); [ zenon_intro zenon_H104 | zenon_intro zenon_H10a ]. % 15.65/15.77 apply (zenon_or_s _ _ zenon_H10e); [ zenon_intro zenon_H3d | zenon_intro zenon_H106 ]. % 15.65/15.77 apply (zenon_L1282_); trivial. % 15.65/15.77 apply (zenon_L1213_); trivial. % 15.65/15.77 apply (zenon_L1283_); trivial. % 15.65/15.77 apply (zenon_L1226_); trivial. % 15.65/15.77 apply (zenon_or_s _ _ zenon_H10f); [ zenon_intro zenon_H3c | zenon_intro zenon_Hba ]. % 15.65/15.77 apply (zenon_or_s _ _ zenon_H10c); [ zenon_intro zenon_H104 | zenon_intro zenon_H10a ]. % 15.65/15.77 apply (zenon_or_s _ _ zenon_H10e); [ zenon_intro zenon_H3d | zenon_intro zenon_H106 ]. % 15.65/15.77 apply (zenon_L1282_); trivial. % 15.65/15.77 apply (zenon_or_s _ _ zenon_Hf0); [ zenon_intro zenon_H1f | zenon_intro zenon_Hf2 ]. % 15.65/15.77 exact (zenon_H20 zenon_H1f). % 15.65/15.77 apply (zenon_or_s _ _ zenon_Hf2); [ zenon_intro zenon_Had | zenon_intro zenon_Hf3 ]. % 15.65/15.77 apply (zenon_L1211_); trivial. % 15.65/15.77 apply (zenon_or_s _ _ zenon_Hf3); [ zenon_intro zenon_Hcf | zenon_intro zenon_Hdb ]. % 15.65/15.77 apply (zenon_L477_); trivial. % 15.65/15.77 apply (zenon_L1257_); trivial. % 15.65/15.77 apply (zenon_L1283_); trivial. % 15.65/15.77 apply (zenon_L1226_); trivial. % 15.65/15.77 apply (zenon_L1284_); trivial. % 15.65/15.77 apply (zenon_or_s _ _ zenon_H10f); [ zenon_intro zenon_H3c | zenon_intro zenon_Hba ]. % 15.65/15.77 apply (zenon_or_s _ _ zenon_H10c); [ zenon_intro zenon_H104 | zenon_intro zenon_H10a ]. % 15.65/15.77 apply (zenon_or_s _ _ zenon_H10e); [ zenon_intro zenon_H3d | zenon_intro zenon_H106 ]. % 15.65/15.77 apply (zenon_L1282_); trivial. % 15.65/15.77 apply (zenon_L1290_); trivial. % 15.65/15.77 apply (zenon_L1283_); trivial. % 15.65/15.77 apply (zenon_L1202_); trivial. % 15.65/15.77 apply (zenon_L1285_); trivial. % 15.65/15.77 apply (zenon_L90_); trivial. % 15.65/15.77 apply (zenon_L86_); trivial. % 15.65/15.77 apply (zenon_L61_); trivial. % 15.65/15.77 apply (zenon_or_s _ _ zenon_H236); [ zenon_intro zenon_H59 | zenon_intro zenon_Hca ]. % 15.65/15.77 apply (zenon_or_s _ _ zenon_H1e4); [ zenon_intro zenon_H145 | zenon_intro zenon_Hd8 ]. % 15.65/15.77 apply (zenon_or_s _ _ zenon_H1d3); [ zenon_intro zenon_Hd6 | zenon_intro zenon_H117 ]. % 15.65/15.77 apply (zenon_or_s _ _ zenon_H1d4); [ zenon_intro zenon_H2e | zenon_intro zenon_Hdd ]. % 15.65/15.77 apply (zenon_or_s _ _ zenon_H1e3); [ zenon_intro zenon_H52 | zenon_intro zenon_H156 ]. % 15.65/15.77 apply (zenon_or_s _ _ zenon_Haa); [ zenon_intro zenon_H2f | zenon_intro zenon_H35 ]. % 15.65/15.77 apply (zenon_or_s _ _ zenon_H10f); [ zenon_intro zenon_H3c | zenon_intro zenon_Hba ]. % 15.65/15.77 apply (zenon_or_s _ _ zenon_H10e); [ zenon_intro zenon_H3d | zenon_intro zenon_H106 ]. % 15.65/15.77 apply (zenon_L1291_); trivial. % 15.65/15.77 apply (zenon_L109_); trivial. % 15.65/15.77 apply (zenon_or_s _ _ zenon_H10c); [ zenon_intro zenon_H104 | zenon_intro zenon_H10a ]. % 15.65/15.77 apply (zenon_or_s _ _ zenon_Hf0); [ zenon_intro zenon_H1f | zenon_intro zenon_Hf2 ]. % 15.65/15.77 exact (zenon_H20 zenon_H1f). % 15.65/15.77 apply (zenon_or_s _ _ zenon_Hf2); [ zenon_intro zenon_Had | zenon_intro zenon_Hf3 ]. % 15.65/15.77 apply (zenon_or_s _ _ zenon_Hf1); [ zenon_intro zenon_H47 | zenon_intro zenon_Hf4 ]. % 15.65/15.77 exact (zenon_H45 zenon_H47). % 15.65/15.77 apply (zenon_or_s _ _ zenon_Hf4); [ zenon_intro zenon_Hd8 | zenon_intro zenon_Hf5 ]. % 15.65/15.77 apply (zenon_L61_); trivial. % 15.65/15.77 apply (zenon_or_s _ _ zenon_Hf5); [ zenon_intro zenon_Hae | zenon_intro zenon_Hee ]. % 15.65/15.77 apply (zenon_or_s _ _ zenon_Heb); [ zenon_intro zenon_H92 | zenon_intro zenon_Hec ]. % 15.65/15.77 apply (zenon_L1241_); trivial. % 15.65/15.77 apply (zenon_or_s _ _ zenon_Hec); [ zenon_intro zenon_H68 | zenon_intro zenon_Hed ]. % 15.65/15.77 apply (zenon_or_s _ _ zenon_H1f6); [ zenon_intro zenon_Hdb | zenon_intro zenon_H1f7 ]. % 15.65/15.77 apply (zenon_L63_); trivial. % 15.65/15.77 apply (zenon_or_s _ _ zenon_H1f7); [ zenon_intro zenon_H142 | zenon_intro zenon_H1f8 ]. % 15.65/15.77 apply (zenon_L1136_); trivial. % 15.65/15.77 apply (zenon_or_s _ _ zenon_H1f8); [ zenon_intro zenon_H167 | zenon_intro zenon_H40 ]. % 15.65/15.77 apply (zenon_L267_); trivial. % 15.65/15.77 apply (zenon_L683_); trivial. % 15.65/15.77 apply (zenon_or_s _ _ zenon_Hed); [ zenon_intro zenon_Hdd | zenon_intro zenon_He9 ]. % 15.65/15.77 apply (zenon_L1297_); trivial. % 15.65/15.77 apply (zenon_L220_); trivial. % 15.65/15.77 apply (zenon_L79_); trivial. % 15.65/15.77 apply (zenon_or_s _ _ zenon_Hf3); [ zenon_intro zenon_Hcf | zenon_intro zenon_Hdb ]. % 15.65/15.77 apply (zenon_L270_); trivial. % 15.65/15.77 apply (zenon_L62_); trivial. % 15.65/15.77 apply (zenon_L82_); trivial. % 15.65/15.77 apply (zenon_L1294_); trivial. % 15.65/15.77 apply (zenon_or_s _ _ zenon_H1c3); [ zenon_intro zenon_H30 | zenon_intro zenon_H124 ]. % 15.65/15.77 apply (zenon_or_s _ _ zenon_H10f); [ zenon_intro zenon_H3c | zenon_intro zenon_Hba ]. % 15.65/15.77 apply (zenon_or_s _ _ zenon_H10c); [ zenon_intro zenon_H104 | zenon_intro zenon_H10a ]. % 15.65/15.77 apply (zenon_or_s _ _ zenon_H10e); [ zenon_intro zenon_H3d | zenon_intro zenon_H106 ]. % 15.65/15.77 apply (zenon_L1291_); trivial. % 15.65/15.77 apply (zenon_or_s _ _ zenon_H10d); [ zenon_intro zenon_H3e | zenon_intro zenon_H42 ]. % 15.65/15.77 apply (zenon_L1279_); trivial. % 15.65/15.77 apply (zenon_L1041_); trivial. % 15.65/15.77 apply (zenon_L1292_); trivial. % 15.65/15.77 apply (zenon_L1202_); trivial. % 15.65/15.77 apply (zenon_L256_); trivial. % 15.65/15.77 apply (zenon_L1297_); trivial. % 15.65/15.77 apply (zenon_L86_); trivial. % 15.65/15.77 apply (zenon_L61_); trivial. % 15.65/15.77 apply (zenon_L53_); trivial. % 15.65/15.77 apply (zenon_L1289_); trivial. % 15.65/15.77 apply (zenon_or_s _ _ zenon_H24b); [ zenon_intro zenon_H45 | zenon_intro zenon_H49 ]. % 15.65/15.77 apply (zenon_or_s _ _ zenon_H24a); [ zenon_intro zenon_H8f | zenon_intro zenon_Hab ]. % 15.65/15.77 apply (zenon_or_s _ _ zenon_H236); [ zenon_intro zenon_H59 | zenon_intro zenon_Hca ]. % 15.65/15.77 apply (zenon_or_s _ _ zenon_H1e4); [ zenon_intro zenon_H145 | zenon_intro zenon_Hd8 ]. % 15.65/15.77 apply (zenon_L1205_); trivial. % 15.65/15.77 apply (zenon_L61_); trivial. % 15.65/15.77 apply (zenon_L562_); trivial. % 15.65/15.77 apply (zenon_L567_); trivial. % 15.65/15.77 apply (zenon_L610_); trivial. % 15.65/15.77 apply (zenon_or_s _ _ zenon_H357); [ zenon_intro zenon_H35 | zenon_intro zenon_H42 ]. % 15.65/15.77 apply (zenon_or_s _ _ zenon_H249); [ zenon_intro zenon_H20 | zenon_intro zenon_H1f ]. % 15.65/15.77 apply (zenon_L1353_); trivial. % 15.65/15.77 apply (zenon_or_s _ _ zenon_H24b); [ zenon_intro zenon_H45 | zenon_intro zenon_H49 ]. % 15.65/15.77 apply (zenon_or_s _ _ zenon_H24a); [ zenon_intro zenon_H8f | zenon_intro zenon_Hab ]. % 15.65/15.77 apply (zenon_or_s _ _ zenon_H236); [ zenon_intro zenon_H59 | zenon_intro zenon_Hca ]. % 15.65/15.77 apply (zenon_or_s _ _ zenon_H1e4); [ zenon_intro zenon_H145 | zenon_intro zenon_Hd8 ]. % 15.65/15.77 apply (zenon_or_s _ _ zenon_H1d8); [ zenon_intro zenon_H1b4 | zenon_intro zenon_H21 ]. % 15.65/15.77 apply (zenon_or_s _ _ zenon_H1d3); [ zenon_intro zenon_Hd6 | zenon_intro zenon_H117 ]. % 15.65/15.77 apply (zenon_or_s _ _ zenon_H1d2); [ zenon_intro zenon_H182 | zenon_intro zenon_H11f ]. % 15.65/15.77 apply (zenon_L1157_); trivial. % 15.65/15.77 apply (zenon_or_s _ _ zenon_H1e3); [ zenon_intro zenon_H52 | zenon_intro zenon_H156 ]. % 15.65/15.77 apply (zenon_L1133_); trivial. % 15.65/15.77 apply (zenon_L134_); trivial. % 15.65/15.77 apply (zenon_or_s _ _ zenon_H1d2); [ zenon_intro zenon_H182 | zenon_intro zenon_H11f ]. % 15.65/15.77 apply (zenon_L1101_); trivial. % 15.65/15.77 apply (zenon_L237_); trivial. % 15.65/15.77 apply (zenon_or_s _ _ zenon_H1d3); [ zenon_intro zenon_Hd6 | zenon_intro zenon_H117 ]. % 15.65/15.77 apply (zenon_or_s _ _ zenon_H1d2); [ zenon_intro zenon_H182 | zenon_intro zenon_H11f ]. % 15.65/15.77 apply (zenon_or_s _ _ zenon_H1e3); [ zenon_intro zenon_H52 | zenon_intro zenon_H156 ]. % 15.65/15.77 apply (zenon_L1184_); trivial. % 15.65/15.77 apply (zenon_L134_); trivial. % 15.65/15.77 apply (zenon_L90_); trivial. % 15.65/15.77 apply (zenon_L86_); trivial. % 15.65/15.77 apply (zenon_L1176_); trivial. % 15.65/15.77 apply (zenon_L562_); trivial. % 15.65/15.77 apply (zenon_L567_); trivial. % 15.65/15.77 apply (zenon_L610_); trivial. % 15.65/15.77 apply (zenon_L1041_); trivial. % 15.65/15.77 Qed. % 15.65/15.77 % SZS output end Proof % 15.65/15.77 (* END-PROOF *) % 15.65/15.77 nodes searched: 404989 % 15.65/15.77 max branch formulas: 340 % 15.65/15.77 proof nodes created: 16835 % 15.65/15.77 formulas created: 113561 % 15.65/15.77 %------------------------------------------------------------------------------